id	sid	tid	token	lemma	pos
fumecheng-11587	1	1	11587	11587	NUM
fumecheng-11587	1	2	facta	facta	PROPN
fumecheng-11587	1	3	universitatis	universitatis	PROPN
fumecheng-11587	1	4	series	series	NOUN
fumecheng-11587	1	5	:	:	PUNCT
fumecheng-11587	1	6	mechanical	mechanical	ADJ
fumecheng-11587	1	7	engineering	engineering	NOUN
fumecheng-11587	1	8	vol	vol	NOUN
fumecheng-11587	1	9	.	.	PROPN
fumecheng-11587	1	10	23	23	NUM
fumecheng-11587	1	11	,	,	PUNCT
fumecheng-11587	1	12	no	no	DET
fumecheng-11587	1	13	4	4	NUM
fumecheng-11587	1	14	,	,	PUNCT
fumecheng-11587	1	15	2025	2025	NUM
fumecheng-11587	1	16	,	,	PUNCT
fumecheng-11587	1	17	pp	pp	ADV
fumecheng-11587	1	18	.	.	PUNCT
fumecheng-11587	2	1	709	709	NUM
fumecheng-11587	2	2	733	733	NUM
fumecheng-11587	3	1	https://doi.org/10.22190/fume230419022n	https://doi.org/10.22190/fume230419022n	ADV
fumecheng-11587	3	2	©	©	PROPN
fumecheng-11587	3	3	2025	2025	NUM
fumecheng-11587	3	4	by	by	ADP
fumecheng-11587	3	5	university	university	PROPN
fumecheng-11587	3	6	of	of	ADP
fumecheng-11587	3	7	niš	niš	PROPN
fumecheng-11587	3	8	,	,	PUNCT
fumecheng-11587	3	9	serbia	serbia	PROPN
fumecheng-11587	3	10	|	|	ADV
fumecheng-11587	3	11	creative	creative	ADJ
fumecheng-11587	3	12	commons	common	NOUN
fumecheng-11587	3	13	license	license	NOUN
fumecheng-11587	3	14	:	:	PUNCT
fumecheng-11587	3	15	cc	cc	VERB
fumecheng-11587	3	16	by	by	ADP
fumecheng-11587	3	17	-	-	PUNCT
fumecheng-11587	3	18	nc	nc	VERB
fumecheng-11587	3	19	-	-	PUNCT
fumecheng-11587	3	20	nd	nd	ADV
fumecheng-11587	3	21	original	original	ADJ
fumecheng-11587	3	22	scientific	scientific	ADJ
fumecheng-11587	3	23	paper	paper	ADJ
fumecheng-11587	3	24	vibration	vibration	NOUN
fumecheng-11587	3	25	and	and	CCONJ
fumecheng-11587	3	26	stability	stability	NOUN
fumecheng-11587	3	27	of	of	ADP
fumecheng-11587	3	28	a	a	DET
fumecheng-11587	3	29	nonlinear	nonlinear	ADJ
fumecheng-11587	3	30	nonlocal	nonlocal	ADJ
fumecheng-11587	3	31	strain	strain	NOUN
fumecheng-11587	3	32	-	-	PUNCT
fumecheng-11587	3	33	gradient	gradient	NOUN
fumecheng-11587	3	34	fg	fg	PROPN
fumecheng-11587	3	35	beam	beam	NOUN
fumecheng-11587	3	36	on	on	ADP
fumecheng-11587	3	37	a	a	DET
fumecheng-11587	3	38	visco	visco	ADJ
fumecheng-11587	3	39	-	-	PUNCT
fumecheng-11587	3	40	pasternak	pasternak	PROPN
fumecheng-11587	3	41	foundation	foundation	PROPN
fumecheng-11587	3	42	nikola	nikola	PROPN
fumecheng-11587	3	43	nešić1	nešić1	PROPN
fumecheng-11587	3	44	,	,	PUNCT
fumecheng-11587	3	45	milan	milan	PROPN
fumecheng-11587	3	46	cajić2	cajić2	PROPN
fumecheng-11587	3	47	,	,	PUNCT
fumecheng-11587	3	48	danilo	danilo	PROPN
fumecheng-11587	3	49	karličić2	karličić2	PROPN
fumecheng-11587	3	50	,	,	PUNCT
fumecheng-11587	3	51	mihailo	mihailo	ADJ
fumecheng-11587	3	52	lazarević3	lazarević3	PROPN
fumecheng-11587	3	53	,	,	PUNCT
fumecheng-11587	3	54	sondipon	sondipon	ADJ
fumecheng-11587	3	55	adhikari4	adhikari4	NOUN
fumecheng-11587	3	56	1faculty	1faculty	NUM
fumecheng-11587	3	57	of	of	ADP
fumecheng-11587	3	58	technical	technical	ADJ
fumecheng-11587	3	59	sciences	science	NOUN
fumecheng-11587	3	60	,	,	PUNCT
fumecheng-11587	3	61	university	university	PROPN
fumecheng-11587	3	62	of	of	ADP
fumecheng-11587	3	63	priština	priština	PROPN
fumecheng-11587	3	64	,	,	PUNCT
fumecheng-11587	3	65	kosovska	kosovska	PROPN
fumecheng-11587	3	66	mitrovica	mitrovica	PROPN
fumecheng-11587	3	67	,	,	PUNCT
fumecheng-11587	3	68	serbia	serbia	PROPN
fumecheng-11587	3	69	2mathematical	2mathematical	NUM
fumecheng-11587	3	70	institute	institute	NOUN
fumecheng-11587	3	71	of	of	ADP
fumecheng-11587	3	72	the	the	DET
fumecheng-11587	3	73	serbian	serbian	PROPN
fumecheng-11587	3	74	academy	academy	PROPN
fumecheng-11587	3	75	of	of	ADP
fumecheng-11587	3	76	sciences	sciences	PROPN
fumecheng-11587	3	77	and	and	CCONJ
fumecheng-11587	3	78	arts	art	NOUN
fumecheng-11587	3	79	,	,	PUNCT
fumecheng-11587	3	80	belgrade	belgrade	PROPN
fumecheng-11587	3	81	,	,	PUNCT
fumecheng-11587	3	82	serbia	serbia	PROPN
fumecheng-11587	3	83	3faculty	3faculty	NUM
fumecheng-11587	3	84	of	of	ADP
fumecheng-11587	3	85	mechanical	mechanical	ADJ
fumecheng-11587	3	86	engineering	engineering	NOUN
fumecheng-11587	3	87	,	,	PUNCT
fumecheng-11587	3	88	university	university	PROPN
fumecheng-11587	3	89	of	of	ADP
fumecheng-11587	3	90	belgrade	belgrade	PROPN
fumecheng-11587	3	91	,	,	PUNCT
fumecheng-11587	3	92	serbia	serbia	PROPN
fumecheng-11587	3	93	4james	4james	PROPN
fumecheng-11587	3	94	watt	watt	NOUN
fumecheng-11587	3	95	school	school	NOUN
fumecheng-11587	3	96	of	of	ADP
fumecheng-11587	3	97	engineering	engineering	NOUN
fumecheng-11587	3	98	,	,	PUNCT
fumecheng-11587	3	99	university	university	NOUN
fumecheng-11587	3	100	of	of	ADP
fumecheng-11587	3	101	glasgow	glasgow	PROPN
fumecheng-11587	3	102	,	,	PUNCT
fumecheng-11587	3	103	united	united	ADJ
fumecheng-11587	3	104	kingdom	kingdom	PROPN
fumecheng-11587	3	105	orcid	orcid	PROPN
fumecheng-11587	3	106	ids	ids	PROPN
fumecheng-11587	3	107	:	:	PUNCT
fumecheng-11587	3	108	nikola	nikola	PROPN
fumecheng-11587	3	109	nešić	nešić	PROPN
fumecheng-11587	3	110	https://orcid.org/0000-0001-6237-4735	https://orcid.org/0000-0001-6237-4735	PROPN
fumecheng-11587	3	111	milan	milan	PROPN
fumecheng-11587	3	112	cajić	cajić	PROPN
fumecheng-11587	3	113	https://orcid.org/0000-0001-5513-0417	https://orcid.org/0000-0001-5513-0417	PROPN
fumecheng-11587	3	114	danilo	danilo	PROPN
fumecheng-11587	3	115	karličić	karličić	PROPN
fumecheng-11587	3	116	https://orcid.org/0000-0002-7547-9293	https://orcid.org/0000-0002-7547-9293	PROPN
fumecheng-11587	3	117	mihailo	mihailo	ADV
fumecheng-11587	3	118	lazarević	lazarević	PROPN
fumecheng-11587	3	119	https://orcid.org/0000-0002-3326-6636	https://orcid.org/0000-0002-3326-6636	PROPN
fumecheng-11587	3	120	sondipon	sondipon	ADV
fumecheng-11587	3	121	adhikari	adhikari	PROPN
fumecheng-11587	3	122	https://orcid.org/0000-0003-4181-3457	https://orcid.org/0000-0003-4181-3457	PROPN
fumecheng-11587	3	123	abstract	abstract	ADJ
fumecheng-11587	3	124	.	.	PUNCT
fumecheng-11587	4	1	this	this	DET
fumecheng-11587	4	2	study	study	NOUN
fumecheng-11587	4	3	investigates	investigate	VERB
fumecheng-11587	4	4	the	the	DET
fumecheng-11587	4	5	stability	stability	NOUN
fumecheng-11587	4	6	of	of	ADP
fumecheng-11587	4	7	periodic	periodic	ADJ
fumecheng-11587	4	8	solutions	solution	NOUN
fumecheng-11587	4	9	of	of	ADP
fumecheng-11587	4	10	a	a	DET
fumecheng-11587	4	11	nonlinear	nonlinear	ADJ
fumecheng-11587	4	12	nonlocal	nonlocal	ADJ
fumecheng-11587	4	13	strain	strain	NOUN
fumecheng-11587	4	14	gradient	gradient	NOUN
fumecheng-11587	4	15	functionally	functionally	ADV
fumecheng-11587	4	16	graded	grade	VERB
fumecheng-11587	4	17	euler	euler	NOUN
fumecheng-11587	4	18	–	–	PUNCT
fumecheng-11587	4	19	bernoulli	bernoulli	PROPN
fumecheng-11587	4	20	beam	beam	PROPN
fumecheng-11587	4	21	model	model	NOUN
fumecheng-11587	4	22	resting	rest	VERB
fumecheng-11587	4	23	on	on	ADP
fumecheng-11587	4	24	a	a	DET
fumecheng-11587	4	25	visco	visco	ADJ
fumecheng-11587	4	26	-	-	PUNCT
fumecheng-11587	4	27	pasternak	pasternak	PROPN
fumecheng-11587	4	28	foundation	foundation	NOUN
fumecheng-11587	4	29	and	and	CCONJ
fumecheng-11587	4	30	subjected	subject	VERB
fumecheng-11587	4	31	to	to	ADP
fumecheng-11587	4	32	external	external	ADJ
fumecheng-11587	4	33	harmonic	harmonic	ADJ
fumecheng-11587	4	34	excitation	excitation	NOUN
fumecheng-11587	4	35	.	.	PUNCT
fumecheng-11587	5	1	the	the	DET
fumecheng-11587	5	2	nonlinearity	nonlinearity	NOUN
fumecheng-11587	5	3	of	of	ADP
fumecheng-11587	5	4	the	the	DET
fumecheng-11587	5	5	beam	beam	NOUN
fumecheng-11587	5	6	arises	arise	VERB
fumecheng-11587	5	7	from	from	ADP
fumecheng-11587	5	8	the	the	DET
fumecheng-11587	5	9	von	von	PROPN
fumecheng-11587	5	10	kármán	kármán	PROPN
fumecheng-11587	5	11	strain	strain	NOUN
fumecheng-11587	5	12	-	-	PUNCT
fumecheng-11587	5	13	displacement	displacement	NOUN
fumecheng-11587	5	14	relation	relation	NOUN
fumecheng-11587	5	15	.	.	PUNCT
fumecheng-11587	6	1	nonlocal	nonlocal	ADJ
fumecheng-11587	6	2	stress	stress	NOUN
fumecheng-11587	6	3	gradient	gradient	NOUN
fumecheng-11587	6	4	theory	theory	NOUN
fumecheng-11587	6	5	combined	combine	VERB
fumecheng-11587	6	6	with	with	ADP
fumecheng-11587	6	7	the	the	DET
fumecheng-11587	6	8	strain	strain	NOUN
fumecheng-11587	6	9	gradient	gradient	NOUN
fumecheng-11587	6	10	theory	theory	NOUN
fumecheng-11587	6	11	is	be	AUX
fumecheng-11587	6	12	used	use	VERB
fumecheng-11587	6	13	to	to	PART
fumecheng-11587	6	14	describe	describe	VERB
fumecheng-11587	6	15	the	the	DET
fumecheng-11587	6	16	stress	stress	NOUN
fumecheng-11587	6	17	-	-	PUNCT
fumecheng-11587	6	18	strain	strain	NOUN
fumecheng-11587	6	19	relation	relation	NOUN
fumecheng-11587	6	20	.	.	PUNCT
fumecheng-11587	7	1	variations	variation	NOUN
fumecheng-11587	7	2	of	of	ADP
fumecheng-11587	7	3	material	material	NOUN
fumecheng-11587	7	4	properties	property	NOUN
fumecheng-11587	7	5	across	across	ADP
fumecheng-11587	7	6	the	the	DET
fumecheng-11587	7	7	thickness	thickness	NOUN
fumecheng-11587	7	8	direction	direction	NOUN
fumecheng-11587	7	9	are	be	AUX
fumecheng-11587	7	10	defined	define	VERB
fumecheng-11587	7	11	by	by	ADP
fumecheng-11587	7	12	the	the	DET
fumecheng-11587	7	13	power	power	NOUN
fumecheng-11587	7	14	-	-	PUNCT
fumecheng-11587	7	15	law	law	NOUN
fumecheng-11587	7	16	model	model	NOUN
fumecheng-11587	7	17	.	.	PUNCT
fumecheng-11587	8	1	the	the	DET
fumecheng-11587	8	2	governing	govern	VERB
fumecheng-11587	8	3	differential	differential	ADJ
fumecheng-11587	8	4	equation	equation	NOUN
fumecheng-11587	8	5	of	of	ADP
fumecheng-11587	8	6	motion	motion	NOUN
fumecheng-11587	8	7	is	be	AUX
fumecheng-11587	8	8	derived	derive	VERB
fumecheng-11587	8	9	by	by	ADP
fumecheng-11587	8	10	using	use	VERB
fumecheng-11587	8	11	hamilton	hamilton	PROPN
fumecheng-11587	8	12	's	's	PART
fumecheng-11587	8	13	principle	principle	NOUN
fumecheng-11587	8	14	and	and	CCONJ
fumecheng-11587	8	15	discretized	discretize	VERB
fumecheng-11587	8	16	by	by	ADP
fumecheng-11587	8	17	the	the	DET
fumecheng-11587	8	18	galerkin	galerkin	PROPN
fumecheng-11587	8	19	approximation	approximation	NOUN
fumecheng-11587	8	20	.	.	PUNCT
fumecheng-11587	9	1	the	the	DET
fumecheng-11587	9	2	methodology	methodology	NOUN
fumecheng-11587	9	3	for	for	ADP
fumecheng-11587	9	4	obtaining	obtain	VERB
fumecheng-11587	9	5	the	the	DET
fumecheng-11587	9	6	steady	steady	ADJ
fumecheng-11587	9	7	-	-	PUNCT
fumecheng-11587	9	8	state	state	NOUN
fumecheng-11587	9	9	amplitude	amplitude	NOUN
fumecheng-11587	9	10	-	-	PUNCT
fumecheng-11587	9	11	frequency	frequency	NOUN
fumecheng-11587	9	12	responses	response	NOUN
fumecheng-11587	9	13	via	via	ADP
fumecheng-11587	9	14	the	the	DET
fumecheng-11587	9	15	incremental	incremental	ADJ
fumecheng-11587	9	16	harmonic	harmonic	ADJ
fumecheng-11587	9	17	balance	balance	NOUN
fumecheng-11587	9	18	method	method	NOUN
fumecheng-11587	9	19	and	and	CCONJ
fumecheng-11587	9	20	continuation	continuation	NOUN
fumecheng-11587	9	21	technique	technique	NOUN
fumecheng-11587	9	22	is	be	AUX
fumecheng-11587	9	23	presented	present	VERB
fumecheng-11587	9	24	.	.	PUNCT
fumecheng-11587	10	1	the	the	DET
fumecheng-11587	10	2	obtained	obtain	VERB
fumecheng-11587	10	3	periodic	periodic	ADJ
fumecheng-11587	10	4	solutions	solution	NOUN
fumecheng-11587	10	5	are	be	AUX
fumecheng-11587	10	6	verified	verify	VERB
fumecheng-11587	10	7	against	against	ADP
fumecheng-11587	10	8	the	the	DET
fumecheng-11587	10	9	numerical	numerical	ADJ
fumecheng-11587	10	10	integration	integration	NOUN
fumecheng-11587	10	11	method	method	NOUN
fumecheng-11587	10	12	and	and	CCONJ
fumecheng-11587	10	13	stability	stability	NOUN
fumecheng-11587	10	14	analysis	analysis	NOUN
fumecheng-11587	10	15	is	be	AUX
fumecheng-11587	10	16	performed	perform	VERB
fumecheng-11587	10	17	by	by	ADP
fumecheng-11587	10	18	utilizing	utilize	VERB
fumecheng-11587	10	19	the	the	DET
fumecheng-11587	10	20	floquet	floquet	NOUN
fumecheng-11587	10	21	theory	theory	NOUN
fumecheng-11587	10	22	.	.	PUNCT
fumecheng-11587	11	1	key	key	ADJ
fumecheng-11587	11	2	words	word	NOUN
fumecheng-11587	11	3	:	:	PUNCT
fumecheng-11587	11	4	nonlocal	nonlocal	ADJ
fumecheng-11587	11	5	strain	strain	NOUN
fumecheng-11587	11	6	gradient	gradient	NOUN
fumecheng-11587	11	7	theory	theory	NOUN
fumecheng-11587	11	8	,	,	PUNCT
fumecheng-11587	11	9	functionally	functionally	ADV
fumecheng-11587	11	10	graded	grade	VERB
fumecheng-11587	11	11	beams	beam	NOUN
fumecheng-11587	11	12	,	,	PUNCT
fumecheng-11587	11	13	pasternak	pasternak	ADJ
fumecheng-11587	11	14	layer	layer	NOUN
fumecheng-11587	11	15	,	,	PUNCT
fumecheng-11587	11	16	duffing	duffe	VERB
fumecheng-11587	11	17	oscillator	oscillator	NOUN
fumecheng-11587	11	18	,	,	PUNCT
fumecheng-11587	11	19	incremental	incremental	ADJ
fumecheng-11587	11	20	harmonic	harmonic	ADJ
fumecheng-11587	11	21	balance	balance	NOUN
fumecheng-11587	11	22	method	method	NOUN
fumecheng-11587	11	23	,	,	PUNCT
fumecheng-11587	11	24	floquet	floquet	PROPN
fumecheng-11587	11	25	multipliers	multiplier	NOUN
fumecheng-11587	11	26	received	receive	VERB
fumecheng-11587	11	27	:	:	PUNCT
fumecheng-11587	11	28	april	april	PROPN
fumecheng-11587	11	29	19	19	NUM
fumecheng-11587	11	30	,	,	PUNCT
fumecheng-11587	11	31	2023	2023	NUM
fumecheng-11587	11	32	/	/	PUNCT
fumecheng-11587	11	33	accepted	accept	VERB
fumecheng-11587	11	34	july	july	PROPN
fumecheng-11587	11	35	29	29	NUM
fumecheng-11587	11	36	,	,	PUNCT
fumecheng-11587	11	37	2023	2023	NUM
fumecheng-11587	11	38	corresponding	correspond	VERB
fumecheng-11587	11	39	author	author	NOUN
fumecheng-11587	11	40	:	:	PUNCT
fumecheng-11587	11	41	nikola	nikola	PROPN
fumecheng-11587	11	42	nešić	nešić	ADJ
fumecheng-11587	11	43	faculty	faculty	NOUN
fumecheng-11587	11	44	of	of	ADP
fumecheng-11587	11	45	technical	technical	ADJ
fumecheng-11587	11	46	sciences	sciences	PROPN
fumecheng-11587	11	47	,	,	PUNCT
fumecheng-11587	11	48	university	university	PROPN
fumecheng-11587	11	49	of	of	ADP
fumecheng-11587	11	50	priština	priština	PROPN
fumecheng-11587	11	51	,	,	PUNCT
fumecheng-11587	11	52	38220	38220	NUM
fumecheng-11587	11	53	kosovska	kosovska	PROPN
fumecheng-11587	11	54	mitrovica	mitrovica	PROPN
fumecheng-11587	11	55	,	,	PUNCT
fumecheng-11587	11	56	kneza	kneza	PROPN
fumecheng-11587	11	57	miloša	miloša	NOUN
fumecheng-11587	11	58	7	7	NUM
fumecheng-11587	11	59	,	,	PUNCT
fumecheng-11587	11	60	serbia	serbia	NOUN
fumecheng-11587	11	61	e	e	NOUN
fumecheng-11587	11	62	-	-	NOUN
fumecheng-11587	11	63	mail	mail	NOUN
fumecheng-11587	11	64	:	:	PUNCT
fumecheng-11587	11	65	nikola.nesic@pr.ac.rs	nikola.nesic@pr.ac.rs	PROPN
fumecheng-11587	11	66	710	710	NUM
fumecheng-11587	11	67	n.	n.	NOUN
fumecheng-11587	11	68	nešić	nešić	PROPN
fumecheng-11587	11	69	,	,	PUNCT
fumecheng-11587	11	70	m.	m.	NOUN
fumecheng-11587	11	71	cajić	cajić	NOUN
fumecheng-11587	11	72	,	,	PUNCT
fumecheng-11587	11	73	d.	d.	PROPN
fumecheng-11587	11	74	karličić	karličić	PROPN
fumecheng-11587	11	75	,	,	PUNCT
fumecheng-11587	11	76	m.	m.	NOUN
fumecheng-11587	11	77	lazarević	lazarević	PROPN
fumecheng-11587	11	78	,	,	PUNCT
fumecheng-11587	11	79	s.	s.	PROPN
fumecheng-11587	11	80	adhikari	adhikari	PROPN
fumecheng-11587	11	81	1	1	NUM
fumecheng-11587	11	82	.	.	PUNCT
fumecheng-11587	12	1	introduction	introduction	NOUN
fumecheng-11587	12	2	traditional	traditional	ADJ
fumecheng-11587	12	3	composites	composite	NOUN
fumecheng-11587	12	4	are	be	AUX
fumecheng-11587	12	5	homogeneous	homogeneous	ADJ
fumecheng-11587	12	6	mixtures	mixture	NOUN
fumecheng-11587	12	7	of	of	ADP
fumecheng-11587	12	8	two	two	NUM
fumecheng-11587	12	9	or	or	CCONJ
fumecheng-11587	12	10	more	more	ADJ
fumecheng-11587	12	11	materials	material	NOUN
fumecheng-11587	12	12	,	,	PUNCT
fumecheng-11587	12	13	where	where	SCONJ
fumecheng-11587	12	14	compromise	compromise	NOUN
fumecheng-11587	12	15	is	be	AUX
fumecheng-11587	12	16	made	make	VERB
fumecheng-11587	12	17	between	between	ADP
fumecheng-11587	12	18	the	the	DET
fumecheng-11587	12	19	desirable	desirable	ADJ
fumecheng-11587	12	20	properties	property	NOUN
fumecheng-11587	12	21	of	of	ADP
fumecheng-11587	12	22	the	the	DET
fumecheng-11587	12	23	component	component	NOUN
fumecheng-11587	12	24	materials	material	NOUN
fumecheng-11587	12	25	.	.	PUNCT
fumecheng-11587	13	1	on	on	ADP
fumecheng-11587	13	2	the	the	DET
fumecheng-11587	13	3	contrary	contrary	NOUN
fumecheng-11587	13	4	,	,	PUNCT
fumecheng-11587	13	5	a	a	DET
fumecheng-11587	13	6	functionally	functionally	ADV
fumecheng-11587	13	7	graded	grade	VERB
fumecheng-11587	13	8	material	material	NOUN
fumecheng-11587	13	9	(	(	PUNCT
fumecheng-11587	13	10	fgm	fgm	PROPN
fumecheng-11587	13	11	)	)	PUNCT
fumecheng-11587	13	12	is	be	AUX
fumecheng-11587	13	13	a	a	DET
fumecheng-11587	13	14	two	two	NUM
fumecheng-11587	13	15	-	-	PUNCT
fumecheng-11587	13	16	component	component	NOUN
fumecheng-11587	13	17	composite	composite	NOUN
fumecheng-11587	13	18	characterized	characterize	VERB
fumecheng-11587	13	19	by	by	ADP
fumecheng-11587	13	20	a	a	DET
fumecheng-11587	13	21	compositional	compositional	ADJ
fumecheng-11587	13	22	gradient	gradient	NOUN
fumecheng-11587	13	23	from	from	ADP
fumecheng-11587	13	24	one	one	NUM
fumecheng-11587	13	25	component	component	NOUN
fumecheng-11587	13	26	to	to	ADP
fumecheng-11587	13	27	the	the	DET
fumecheng-11587	13	28	other	other	ADJ
fumecheng-11587	13	29	and	and	CCONJ
fumecheng-11587	13	30	because	because	SCONJ
fumecheng-11587	13	31	significant	significant	ADJ
fumecheng-11587	13	32	proportions	proportion	NOUN
fumecheng-11587	13	33	of	of	ADP
fumecheng-11587	13	34	fgm	fgm	PROPN
fumecheng-11587	13	35	contain	contain	VERB
fumecheng-11587	13	36	pure	pure	ADJ
fumecheng-11587	13	37	forms	form	NOUN
fumecheng-11587	13	38	of	of	ADP
fumecheng-11587	13	39	each	each	DET
fumecheng-11587	13	40	component	component	NOUN
fumecheng-11587	13	41	,	,	PUNCT
fumecheng-11587	13	42	the	the	DET
fumecheng-11587	13	43	need	need	NOUN
fumecheng-11587	13	44	for	for	ADP
fumecheng-11587	13	45	compromise	compromise	NOUN
fumecheng-11587	13	46	is	be	AUX
fumecheng-11587	13	47	eliminated	eliminate	VERB
fumecheng-11587	13	48	.	.	PUNCT
fumecheng-11587	14	1	in	in	ADP
fumecheng-11587	14	2	such	such	DET
fumecheng-11587	14	3	a	a	DET
fumecheng-11587	14	4	case	case	NOUN
fumecheng-11587	14	5	,	,	PUNCT
fumecheng-11587	14	6	the	the	DET
fumecheng-11587	14	7	properties	property	NOUN
fumecheng-11587	14	8	of	of	ADP
fumecheng-11587	14	9	both	both	DET
fumecheng-11587	14	10	components	component	NOUN
fumecheng-11587	14	11	can	can	AUX
fumecheng-11587	14	12	be	be	AUX
fumecheng-11587	14	13	fully	fully	ADV
fumecheng-11587	14	14	utilized	utilize	VERB
fumecheng-11587	14	15	[	[	PUNCT
fumecheng-11587	14	16	1	1	NUM
fumecheng-11587	14	17	,	,	PUNCT
fumecheng-11587	14	18	2	2	NUM
fumecheng-11587	14	19	]	]	PUNCT
fumecheng-11587	14	20	.	.	PUNCT
fumecheng-11587	15	1	although	although	SCONJ
fumecheng-11587	15	2	a	a	DET
fumecheng-11587	15	3	significant	significant	ADJ
fumecheng-11587	15	4	amount	amount	NOUN
fumecheng-11587	15	5	of	of	ADP
fumecheng-11587	15	6	work	work	NOUN
fumecheng-11587	15	7	is	be	AUX
fumecheng-11587	15	8	done	do	VERB
fumecheng-11587	15	9	in	in	ADP
fumecheng-11587	15	10	the	the	DET
fumecheng-11587	15	11	field	field	NOUN
fumecheng-11587	15	12	of	of	ADP
fumecheng-11587	15	13	fg	fg	PROPN
fumecheng-11587	15	14	structures	structure	NOUN
fumecheng-11587	15	15	,	,	PUNCT
fumecheng-11587	15	16	there	there	PRON
fumecheng-11587	15	17	is	be	VERB
fumecheng-11587	15	18	still	still	ADV
fumecheng-11587	15	19	a	a	DET
fumecheng-11587	15	20	lot	lot	NOUN
fumecheng-11587	15	21	of	of	ADP
fumecheng-11587	15	22	space	space	NOUN
fumecheng-11587	15	23	and	and	CCONJ
fumecheng-11587	15	24	need	need	NOUN
fumecheng-11587	15	25	for	for	ADP
fumecheng-11587	15	26	the	the	DET
fumecheng-11587	15	27	investigation	investigation	NOUN
fumecheng-11587	15	28	of	of	ADP
fumecheng-11587	15	29	mems	mem	NOUN
fumecheng-11587	15	30	/	/	SYM
fumecheng-11587	15	31	nems	nem	NOUN
fumecheng-11587	15	32	systems	system	NOUN
fumecheng-11587	15	33	composed	compose	VERB
fumecheng-11587	15	34	of	of	ADP
fumecheng-11587	15	35	fgms	fgms	PROPN
fumecheng-11587	15	36	.	.	PUNCT
fumecheng-11587	16	1	nanobeams	nanobeam	NOUN
fumecheng-11587	16	2	and	and	CCONJ
fumecheng-11587	16	3	nanoplates	nanoplate	NOUN
fumecheng-11587	16	4	are	be	AUX
fumecheng-11587	16	5	used	use	VERB
fumecheng-11587	16	6	in	in	ADP
fumecheng-11587	16	7	different	different	ADJ
fumecheng-11587	16	8	mems	mem	NOUN
fumecheng-11587	16	9	/	/	SYM
fumecheng-11587	16	10	nems	nem	NOUN
fumecheng-11587	16	11	devices	device	NOUN
fumecheng-11587	16	12	[	[	X
fumecheng-11587	16	13	3	3	NUM
fumecheng-11587	16	14	,	,	PUNCT
fumecheng-11587	16	15	4	4	NUM
fumecheng-11587	16	16	]	]	PUNCT
fumecheng-11587	16	17	,	,	PUNCT
fumecheng-11587	16	18	such	such	ADJ
fumecheng-11587	16	19	as	as	ADP
fumecheng-11587	16	20	microactuators	microactuator	NOUN
fumecheng-11587	16	21	[	[	X
fumecheng-11587	16	22	5	5	NUM
fumecheng-11587	16	23	]	]	PUNCT
fumecheng-11587	16	24	,	,	PUNCT
fumecheng-11587	16	25	microswitches	microswitche	VERB
fumecheng-11587	16	26	[	[	X
fumecheng-11587	16	27	6	6	NUM
fumecheng-11587	16	28	]	]	PUNCT
fumecheng-11587	16	29	,	,	PUNCT
fumecheng-11587	16	30	micro	micro	ADJ
fumecheng-11587	16	31	sensors	sensor	NOUN
fumecheng-11587	16	32	[	[	X
fumecheng-11587	16	33	7	7	NUM
fumecheng-11587	16	34	,	,	PUNCT
fumecheng-11587	16	35	8	8	NUM
fumecheng-11587	16	36	]	]	PUNCT
fumecheng-11587	16	37	,	,	PUNCT
fumecheng-11587	16	38	nanoscale	nanoscale	NOUN
fumecheng-11587	16	39	resonators	resonator	NOUN
fumecheng-11587	16	40	[	[	X
fumecheng-11587	16	41	9	9	NUM
fumecheng-11587	16	42	]	]	PUNCT
fumecheng-11587	16	43	,	,	PUNCT
fumecheng-11587	16	44	energy	energy	NOUN
fumecheng-11587	16	45	harvesting	harvesting	NOUN
fumecheng-11587	16	46	nanodevices	nanodevice	NOUN
fumecheng-11587	16	47	[	[	X
fumecheng-11587	16	48	10	10	NUM
fumecheng-11587	16	49	]	]	PUNCT
fumecheng-11587	16	50	,	,	PUNCT
fumecheng-11587	16	51	etc	etc	X
fumecheng-11587	16	52	.	.	X
fumecheng-11587	17	1	besides	besides	SCONJ
fumecheng-11587	17	2	that	that	PRON
fumecheng-11587	17	3	,	,	PUNCT
fumecheng-11587	17	4	carbon	carbon	NOUN
fumecheng-11587	17	5	nanotubes	nanotube	NOUN
fumecheng-11587	17	6	are	be	AUX
fumecheng-11587	17	7	used	use	VERB
fumecheng-11587	17	8	as	as	ADP
fumecheng-11587	17	9	an	an	DET
fumecheng-11587	17	10	addition	addition	NOUN
fumecheng-11587	17	11	in	in	ADP
fumecheng-11587	17	12	some	some	DET
fumecheng-11587	17	13	mixtures	mixture	NOUN
fumecheng-11587	17	14	to	to	PART
fumecheng-11587	17	15	increase	increase	VERB
fumecheng-11587	17	16	the	the	DET
fumecheng-11587	17	17	dynamic	dynamic	ADJ
fumecheng-11587	17	18	stability	stability	NOUN
fumecheng-11587	17	19	of	of	ADP
fumecheng-11587	17	20	the	the	DET
fumecheng-11587	17	21	material	material	NOUN
fumecheng-11587	17	22	[	[	X
fumecheng-11587	17	23	11	11	NUM
fumecheng-11587	17	24	]	]	PUNCT
fumecheng-11587	17	25	.	.	PUNCT
fumecheng-11587	18	1	the	the	DET
fumecheng-11587	18	2	dynamics	dynamic	NOUN
fumecheng-11587	18	3	of	of	ADP
fumecheng-11587	18	4	such	such	ADJ
fumecheng-11587	18	5	systems	system	NOUN
fumecheng-11587	18	6	can	can	AUX
fumecheng-11587	18	7	be	be	AUX
fumecheng-11587	18	8	studied	study	VERB
fumecheng-11587	18	9	through	through	ADP
fumecheng-11587	18	10	experiments	experiment	NOUN
fumecheng-11587	18	11	[	[	X
fumecheng-11587	18	12	12	12	NUM
fumecheng-11587	18	13	,	,	PUNCT
fumecheng-11587	18	14	13	13	NUM
fumecheng-11587	18	15	]	]	PUNCT
fumecheng-11587	18	16	,	,	PUNCT
fumecheng-11587	18	17	molecular	molecular	ADJ
fumecheng-11587	18	18	dynamics	dynamic	NOUN
fumecheng-11587	18	19	simulations	simulation	NOUN
fumecheng-11587	18	20	[	[	X
fumecheng-11587	18	21	14	14	NUM
fumecheng-11587	18	22	]	]	PUNCT
fumecheng-11587	18	23	,	,	PUNCT
fumecheng-11587	18	24	and	and	CCONJ
fumecheng-11587	18	25	continuum	continuum	ADJ
fumecheng-11587	18	26	mechanics	mechanic	NOUN
fumecheng-11587	19	1	[	[	X
fumecheng-11587	19	2	15	15	NUM
fumecheng-11587	19	3	,	,	PUNCT
fumecheng-11587	19	4	16	16	NUM
fumecheng-11587	19	5	,	,	PUNCT
fumecheng-11587	19	6	17	17	NUM
fumecheng-11587	19	7	]	]	PUNCT
fumecheng-11587	19	8	.	.	PUNCT
fumecheng-11587	20	1	the	the	DET
fumecheng-11587	20	2	most	most	ADV
fumecheng-11587	20	3	vastly	vastly	ADV
fumecheng-11587	20	4	used	use	VERB
fumecheng-11587	20	5	continuum	continuum	ADJ
fumecheng-11587	20	6	theories	theory	NOUN
fumecheng-11587	20	7	for	for	ADP
fumecheng-11587	20	8	studying	study	VERB
fumecheng-11587	20	9	nanostructures	nanostructure	NOUN
fumecheng-11587	20	10	are	be	AUX
fumecheng-11587	20	11	:	:	PUNCT
fumecheng-11587	20	12	nonlocal	nonlocal	ADJ
fumecheng-11587	20	13	elasticity	elasticity	NOUN
fumecheng-11587	20	14	theory	theory	NOUN
fumecheng-11587	20	15	[	[	X
fumecheng-11587	20	16	17	17	NUM
fumecheng-11587	20	17	,	,	PUNCT
fumecheng-11587	20	18	18	18	NUM
fumecheng-11587	20	19	]	]	PUNCT
fumecheng-11587	20	20	,	,	PUNCT
fumecheng-11587	20	21	strain	strain	VERB
fumecheng-11587	20	22	gradient	gradient	ADJ
fumecheng-11587	20	23	theory	theory	NOUN
fumecheng-11587	20	24	[	[	X
fumecheng-11587	20	25	13	13	NUM
fumecheng-11587	20	26	,	,	PUNCT
fumecheng-11587	20	27	19	19	NUM
fumecheng-11587	20	28	]	]	PUNCT
fumecheng-11587	20	29	,	,	PUNCT
fumecheng-11587	20	30	modified	modify	VERB
fumecheng-11587	20	31	couple	couple	NOUN
fumecheng-11587	20	32	stress	stress	NOUN
fumecheng-11587	20	33	theory	theory	NOUN
fumecheng-11587	20	34	(	(	PUNCT
fumecheng-11587	20	35	or	or	CCONJ
fumecheng-11587	20	36	modified	modify	VERB
fumecheng-11587	20	37	strain	strain	NOUN
fumecheng-11587	20	38	gradient	gradient	NOUN
fumecheng-11587	20	39	theory	theory	NOUN
fumecheng-11587	20	40	)	)	PUNCT
fumecheng-11587	21	1	[	[	X
fumecheng-11587	21	2	20	20	NUM
fumecheng-11587	21	3	]	]	PUNCT
fumecheng-11587	21	4	,	,	PUNCT
fumecheng-11587	21	5	the	the	DET
fumecheng-11587	21	6	surface	surface	NOUN
fumecheng-11587	21	7	elasticity	elasticity	NOUN
fumecheng-11587	21	8	theory	theory	NOUN
fumecheng-11587	21	9	[	[	X
fumecheng-11587	21	10	21	21	NUM
fumecheng-11587	21	11	]	]	PUNCT
fumecheng-11587	21	12	,	,	PUNCT
fumecheng-11587	21	13	and	and	CCONJ
fumecheng-11587	21	14	the	the	DET
fumecheng-11587	21	15	nonlocal	nonlocal	ADJ
fumecheng-11587	21	16	strain	strain	NOUN
fumecheng-11587	21	17	gradient	gradient	NOUN
fumecheng-11587	21	18	theory	theory	NOUN
fumecheng-11587	21	19	(	(	PUNCT
fumecheng-11587	21	20	nlsgt	nlsgt	NOUN
fumecheng-11587	21	21	)	)	PUNCT
fumecheng-11587	22	1	[	[	X
fumecheng-11587	22	2	22	22	NUM
fumecheng-11587	22	3	]	]	PUNCT
fumecheng-11587	22	4	,	,	PUNCT
fumecheng-11587	22	5	which	which	PRON
fumecheng-11587	22	6	includes	include	VERB
fumecheng-11587	22	7	both	both	CCONJ
fumecheng-11587	22	8	nonlocal	nonlocal	ADJ
fumecheng-11587	22	9	and	and	CCONJ
fumecheng-11587	22	10	length	length	NOUN
fumecheng-11587	22	11	scale	scale	NOUN
fumecheng-11587	22	12	effects	effect	NOUN
fumecheng-11587	22	13	into	into	ADP
fumecheng-11587	22	14	consideration	consideration	NOUN
fumecheng-11587	22	15	.	.	PUNCT
fumecheng-11587	23	1	an	an	DET
fumecheng-11587	23	2	overview	overview	NOUN
fumecheng-11587	23	3	of	of	ADP
fumecheng-11587	23	4	available	available	ADJ
fumecheng-11587	23	5	theories	theory	NOUN
fumecheng-11587	23	6	and	and	CCONJ
fumecheng-11587	23	7	methodologies	methodology	NOUN
fumecheng-11587	23	8	for	for	ADP
fumecheng-11587	23	9	the	the	DET
fumecheng-11587	23	10	analysis	analysis	NOUN
fumecheng-11587	23	11	of	of	ADP
fumecheng-11587	23	12	nano	nano	NOUN
fumecheng-11587	23	13	-	-	PUNCT
fumecheng-11587	23	14	isotropic	isotropic	NOUN
fumecheng-11587	23	15	,	,	PUNCT
fumecheng-11587	23	16	nano	nano	NOUN
fumecheng-11587	23	17	-	-	PUNCT
fumecheng-11587	23	18	functionally	functionally	ADV
fumecheng-11587	23	19	graded	grade	VERB
fumecheng-11587	23	20	,	,	PUNCT
fumecheng-11587	23	21	and	and	CCONJ
fumecheng-11587	23	22	cnt	cnt	PROPN
fumecheng-11587	23	23	reinforced	reinforce	VERB
fumecheng-11587	23	24	nanocomposite	nanocomposite	NOUN
fumecheng-11587	23	25	structures	structure	NOUN
fumecheng-11587	23	26	is	be	AUX
fumecheng-11587	23	27	given	give	VERB
fumecheng-11587	23	28	by	by	ADP
fumecheng-11587	23	29	garg	garg	PROPN
fumecheng-11587	23	30	et	et	PROPN
fumecheng-11587	23	31	al	al	PROPN
fumecheng-11587	23	32	.	.	PUNCT
fumecheng-11587	24	1	[	[	X
fumecheng-11587	24	2	23	23	NUM
fumecheng-11587	24	3	]	]	PUNCT
fumecheng-11587	24	4	.	.	PUNCT
fumecheng-11587	25	1	nonlinearity	nonlinearity	NOUN
fumecheng-11587	25	2	can	can	AUX
fumecheng-11587	25	3	be	be	AUX
fumecheng-11587	25	4	introduced	introduce	VERB
fumecheng-11587	25	5	in	in	ADP
fumecheng-11587	25	6	beam	beam	NOUN
fumecheng-11587	25	7	vibration	vibration	NOUN
fumecheng-11587	25	8	problems	problem	NOUN
fumecheng-11587	25	9	through	through	ADP
fumecheng-11587	25	10	geometric	geometric	ADJ
fumecheng-11587	25	11	imperfections	imperfection	NOUN
fumecheng-11587	25	12	in	in	ADP
fumecheng-11587	25	13	beam	beam	NOUN
fumecheng-11587	25	14	material	material	NOUN
fumecheng-11587	25	15	[	[	X
fumecheng-11587	25	16	24	24	NUM
fumecheng-11587	25	17	]	]	PUNCT
fumecheng-11587	25	18	and	and	CCONJ
fumecheng-11587	25	19	foundation	foundation	NOUN
fumecheng-11587	26	1	[	[	X
fumecheng-11587	26	2	25	25	NUM
fumecheng-11587	26	3	]	]	PUNCT
fumecheng-11587	26	4	.	.	PUNCT
fumecheng-11587	27	1	geometric	geometric	ADJ
fumecheng-11587	27	2	material	material	NOUN
fumecheng-11587	27	3	nonlinearity	nonlinearity	NOUN
fumecheng-11587	27	4	is	be	AUX
fumecheng-11587	27	5	usually	usually	ADV
fumecheng-11587	27	6	introduced	introduce	VERB
fumecheng-11587	27	7	with	with	ADP
fumecheng-11587	27	8	von	von	PROPN
fumecheng-11587	27	9	kármán	kármán	PROPN
fumecheng-11587	27	10	strain	strain	NOUN
fumecheng-11587	27	11	-	-	PUNCT
fumecheng-11587	27	12	displacement	displacement	NOUN
fumecheng-11587	27	13	relation	relation	NOUN
fumecheng-11587	27	14	[	[	X
fumecheng-11587	27	15	24	24	NUM
fumecheng-11587	27	16	,	,	PUNCT
fumecheng-11587	27	17	26	26	NUM
fumecheng-11587	27	18	,	,	PUNCT
fumecheng-11587	27	19	27	27	NUM
fumecheng-11587	27	20	]	]	PUNCT
fumecheng-11587	27	21	.	.	PUNCT
fumecheng-11587	28	1	simsek	simsek	NOUN
fumecheng-11587	29	1	[	[	X
fumecheng-11587	29	2	26	26	NUM
fumecheng-11587	29	3	]	]	PUNCT
fumecheng-11587	29	4	examined	examine	VERB
fumecheng-11587	29	5	the	the	DET
fumecheng-11587	29	6	nonlinear	nonlinear	ADJ
fumecheng-11587	29	7	vibration	vibration	NOUN
fumecheng-11587	29	8	behavior	behavior	NOUN
fumecheng-11587	29	9	of	of	ADP
fumecheng-11587	29	10	an	an	DET
fumecheng-11587	29	11	nlsgt	nlsgt	NOUN
fumecheng-11587	29	12	euler	euler	NOUN
fumecheng-11587	29	13	-	-	PUNCT
fumecheng-11587	29	14	bernoulli	bernoulli	PROPN
fumecheng-11587	29	15	fg	fg	PROPN
fumecheng-11587	29	16	beam	beam	PROPN
fumecheng-11587	29	17	with	with	ADP
fumecheng-11587	29	18	von	von	PROPN
fumecheng-11587	29	19	kármán	kármán	PROPN
fumecheng-11587	29	20	’s	’s	PART
fumecheng-11587	29	21	geometric	geometric	ADJ
fumecheng-11587	29	22	nonlinearity	nonlinearity	NOUN
fumecheng-11587	29	23	.	.	PUNCT
fumecheng-11587	30	1	liu	liu	PROPN
fumecheng-11587	30	2	et	et	PROPN
fumecheng-11587	30	3	al	al	PROPN
fumecheng-11587	30	4	.	.	PUNCT
fumecheng-11587	31	1	[	[	X
fumecheng-11587	31	2	24	24	NUM
fumecheng-11587	31	3	]	]	PUNCT
fumecheng-11587	31	4	studied	study	VERB
fumecheng-11587	31	5	the	the	DET
fumecheng-11587	31	6	nonlinear	nonlinear	ADJ
fumecheng-11587	31	7	vibration	vibration	NOUN
fumecheng-11587	31	8	of	of	ADP
fumecheng-11587	31	9	fg	fg	PROPN
fumecheng-11587	31	10	sandwich	sandwich	NOUN
fumecheng-11587	31	11	nlsgt	nlsgt	NOUN
fumecheng-11587	31	12	beams	beam	NOUN
fumecheng-11587	31	13	in	in	ADP
fumecheng-11587	31	14	the	the	DET
fumecheng-11587	31	15	presence	presence	NOUN
fumecheng-11587	31	16	of	of	ADP
fumecheng-11587	31	17	initial	initial	ADJ
fumecheng-11587	31	18	geometric	geometric	ADJ
fumecheng-11587	31	19	imperfection	imperfection	NOUN
fumecheng-11587	31	20	induced	induce	VERB
fumecheng-11587	31	21	by	by	ADP
fumecheng-11587	31	22	the	the	DET
fumecheng-11587	31	23	von	von	PROPN
fumecheng-11587	31	24	kármán	kármán	PROPN
fumecheng-11587	31	25	theory	theory	NOUN
fumecheng-11587	31	26	and	and	CCONJ
fumecheng-11587	31	27	a	a	DET
fumecheng-11587	31	28	cosine	cosine	NOUN
fumecheng-11587	31	29	function	function	NOUN
fumecheng-11587	31	30	.	.	PUNCT
fumecheng-11587	32	1	they	they	PRON
fumecheng-11587	32	2	solved	solve	VERB
fumecheng-11587	32	3	a	a	DET
fumecheng-11587	32	4	nonlinear	nonlinear	ADJ
fumecheng-11587	32	5	differential	differential	ADJ
fumecheng-11587	32	6	equation	equation	NOUN
fumecheng-11587	32	7	and	and	CCONJ
fumecheng-11587	32	8	obtained	obtain	VERB
fumecheng-11587	32	9	nonlinear	nonlinear	ADJ
fumecheng-11587	32	10	frequency	frequency	NOUN
fumecheng-11587	32	11	relation	relation	NOUN
fumecheng-11587	32	12	by	by	ADP
fumecheng-11587	32	13	using	use	VERB
fumecheng-11587	32	14	he	he	PRON
fumecheng-11587	32	15	’s	’s	PART
fumecheng-11587	32	16	variational	variational	ADJ
fumecheng-11587	32	17	principle	principle	NOUN
fumecheng-11587	32	18	.	.	PUNCT
fumecheng-11587	33	1	a	a	DET
fumecheng-11587	33	2	nonlocal	nonlocal	ADJ
fumecheng-11587	33	3	theory	theory	NOUN
fumecheng-11587	33	4	proposed	propose	VERB
fumecheng-11587	33	5	by	by	ADP
fumecheng-11587	33	6	eringen	eringen	PROPN
fumecheng-11587	33	7	can	can	AUX
fumecheng-11587	33	8	be	be	AUX
fumecheng-11587	33	9	utilized	utilize	VERB
fumecheng-11587	33	10	in	in	ADP
fumecheng-11587	33	11	differential	differential	ADJ
fumecheng-11587	33	12	and	and	CCONJ
fumecheng-11587	33	13	integral	integral	ADJ
fumecheng-11587	33	14	forms	form	NOUN
fumecheng-11587	33	15	.	.	PUNCT
fumecheng-11587	34	1	the	the	DET
fumecheng-11587	34	2	integral	integral	ADJ
fumecheng-11587	34	3	form	form	NOUN
fumecheng-11587	34	4	is	be	AUX
fumecheng-11587	34	5	more	more	ADV
fumecheng-11587	34	6	general	general	ADJ
fumecheng-11587	34	7	and	and	CCONJ
fumecheng-11587	34	8	accurate	accurate	ADJ
fumecheng-11587	34	9	but	but	CCONJ
fumecheng-11587	34	10	complex	complex	ADJ
fumecheng-11587	34	11	to	to	PART
fumecheng-11587	34	12	apply	apply	VERB
fumecheng-11587	34	13	when	when	SCONJ
fumecheng-11587	34	14	solving	solve	VERB
fumecheng-11587	34	15	advanced	advanced	ADJ
fumecheng-11587	34	16	problems	problem	NOUN
fumecheng-11587	34	17	.	.	PUNCT
fumecheng-11587	35	1	the	the	DET
fumecheng-11587	35	2	differential	differential	ADJ
fumecheng-11587	35	3	form	form	NOUN
fumecheng-11587	35	4	is	be	AUX
fumecheng-11587	35	5	straighter	straighter	ADV
fumecheng-11587	35	6	forward	forward	ADV
fumecheng-11587	35	7	in	in	ADP
fumecheng-11587	35	8	the	the	DET
fumecheng-11587	35	9	application	application	NOUN
fumecheng-11587	35	10	.	.	PUNCT
fumecheng-11587	36	1	for	for	ADP
fumecheng-11587	36	2	most	most	ADJ
fumecheng-11587	36	3	cases	case	NOUN
fumecheng-11587	36	4	of	of	ADP
fumecheng-11587	36	5	boundary	boundary	ADJ
fumecheng-11587	36	6	conditions	condition	NOUN
fumecheng-11587	36	7	,	,	PUNCT
fumecheng-11587	36	8	it	it	PRON
fumecheng-11587	36	9	is	be	AUX
fumecheng-11587	36	10	scientifically	scientifically	ADV
fumecheng-11587	36	11	proven	prove	VERB
fumecheng-11587	36	12	that	that	SCONJ
fumecheng-11587	36	13	the	the	DET
fumecheng-11587	36	14	differential	differential	ADJ
fumecheng-11587	36	15	form	form	NOUN
fumecheng-11587	36	16	is	be	AUX
fumecheng-11587	36	17	equal	equal	ADJ
fumecheng-11587	36	18	to	to	ADP
fumecheng-11587	36	19	the	the	DET
fumecheng-11587	36	20	integral	integral	ADJ
fumecheng-11587	36	21	form	form	NOUN
fumecheng-11587	36	22	.	.	PUNCT
fumecheng-11587	37	1	however	however	ADV
fumecheng-11587	37	2	,	,	PUNCT
fumecheng-11587	37	3	cantilever	cantilever	NOUN
fumecheng-11587	37	4	beams	beam	NOUN
fumecheng-11587	37	5	give	give	VERB
fumecheng-11587	37	6	contradictory	contradictory	ADJ
fumecheng-11587	37	7	results	result	NOUN
fumecheng-11587	37	8	when	when	SCONJ
fumecheng-11587	37	9	employing	employ	VERB
fumecheng-11587	37	10	integral	integral	ADJ
fumecheng-11587	37	11	and	and	CCONJ
fumecheng-11587	37	12	differential	differential	ADJ
fumecheng-11587	37	13	forms	form	NOUN
fumecheng-11587	37	14	.	.	PUNCT
fumecheng-11587	38	1	barreta	barreta	NOUN
fumecheng-11587	38	2	and	and	CCONJ
fumecheng-11587	38	3	marotti	marotti	PROPN
fumecheng-11587	38	4	de	de	X
fumecheng-11587	38	5	sciarra	sciarra	NOUN
fumecheng-11587	38	6	[	[	X
fumecheng-11587	38	7	28	28	NUM
fumecheng-11587	38	8	]	]	PUNCT
fumecheng-11587	38	9	suggested	suggest	VERB
fumecheng-11587	38	10	a	a	DET
fumecheng-11587	38	11	methodology	methodology	NOUN
fumecheng-11587	38	12	to	to	PART
fumecheng-11587	38	13	bridge	bridge	VERB
fumecheng-11587	38	14	two	two	NUM
fumecheng-11587	38	15	forms	form	NOUN
fumecheng-11587	38	16	by	by	ADP
fumecheng-11587	38	17	replacing	replace	VERB
fumecheng-11587	38	18	the	the	DET
fumecheng-11587	38	19	integral	integral	ADJ
fumecheng-11587	38	20	form	form	NOUN
fumecheng-11587	38	21	with	with	ADP
fumecheng-11587	38	22	differential	differential	NOUN
fumecheng-11587	38	23	with	with	ADP
fumecheng-11587	38	24	additional	additional	ADJ
fumecheng-11587	38	25	constitutive	constitutive	ADJ
fumecheng-11587	38	26	boundary	boundary	ADJ
fumecheng-11587	38	27	conditions	condition	NOUN
fumecheng-11587	38	28	which	which	PRON
fumecheng-11587	38	29	is	be	AUX
fumecheng-11587	38	30	applied	apply	VERB
fumecheng-11587	38	31	to	to	ADP
fumecheng-11587	38	32	several	several	ADJ
fumecheng-11587	38	33	simple	simple	ADJ
fumecheng-11587	38	34	problems	problem	NOUN
fumecheng-11587	38	35	[	[	X
fumecheng-11587	38	36	29	29	NUM
fumecheng-11587	38	37	,	,	PUNCT
fumecheng-11587	38	38	30	30	NUM
fumecheng-11587	38	39	,	,	PUNCT
fumecheng-11587	38	40	31	31	NUM
fumecheng-11587	38	41	]	]	PUNCT
fumecheng-11587	38	42	.	.	PUNCT
fumecheng-11587	39	1	still	still	ADV
fumecheng-11587	39	2	,	,	PUNCT
fumecheng-11587	39	3	the	the	DET
fumecheng-11587	39	4	equation	equation	NOUN
fumecheng-11587	39	5	of	of	ADP
fumecheng-11587	39	6	motion	motion	NOUN
fumecheng-11587	39	7	,	,	PUNCT
fumecheng-11587	39	8	for	for	ADP
fumecheng-11587	39	9	a	a	DET
fumecheng-11587	39	10	problem	problem	NOUN
fumecheng-11587	39	11	similar	similar	ADJ
fumecheng-11587	39	12	in	in	ADP
fumecheng-11587	39	13	complexity	complexity	NOUN
fumecheng-11587	39	14	to	to	ADP
fumecheng-11587	39	15	ours	ours	PRON
fumecheng-11587	39	16	,	,	PUNCT
fumecheng-11587	39	17	is	be	AUX
fumecheng-11587	39	18	exclusively	exclusively	ADV
fumecheng-11587	39	19	derived	derive	VERB
fumecheng-11587	39	20	in	in	ADP
fumecheng-11587	39	21	differential	differential	ADJ
fumecheng-11587	39	22	form	form	NOUN
fumecheng-11587	39	23	as	as	SCONJ
fumecheng-11587	39	24	can	can	AUX
fumecheng-11587	39	25	be	be	AUX
fumecheng-11587	39	26	found	find	VERB
fumecheng-11587	39	27	in	in	ADP
fumecheng-11587	39	28	recently	recently	ADV
fumecheng-11587	39	29	published	publish	VERB
fumecheng-11587	39	30	papers	paper	NOUN
fumecheng-11587	39	31	[	[	X
fumecheng-11587	39	32	24	24	NUM
fumecheng-11587	39	33	,	,	PUNCT
fumecheng-11587	39	34	26	26	NUM
fumecheng-11587	39	35	,	,	PUNCT
fumecheng-11587	39	36	32	32	NUM
fumecheng-11587	39	37	,	,	PUNCT
fumecheng-11587	39	38	33	33	NUM
fumecheng-11587	39	39	,	,	PUNCT
fumecheng-11587	39	40	34	34	NUM
fumecheng-11587	39	41	]	]	PUNCT
fumecheng-11587	39	42	.	.	PUNCT
fumecheng-11587	40	1	therefore	therefore	ADV
fumecheng-11587	40	2	,	,	PUNCT
fumecheng-11587	40	3	we	we	PRON
fumecheng-11587	40	4	will	will	AUX
fumecheng-11587	40	5	utilize	utilize	VERB
fumecheng-11587	40	6	differential	differential	ADJ
fumecheng-11587	40	7	approach	approach	NOUN
fumecheng-11587	40	8	,	,	PUNCT
fumecheng-11587	40	9	but	but	CCONJ
fumecheng-11587	40	10	limit	limit	VERB
fumecheng-11587	40	11	our	our	PRON
fumecheng-11587	40	12	research	research	NOUN
fumecheng-11587	40	13	on	on	ADP
fumecheng-11587	40	14	pinned	pin	VERB
fumecheng-11587	40	15	-	-	PUNCT
fumecheng-11587	40	16	pinned	pin	VERB
fumecheng-11587	40	17	,	,	PUNCT
fumecheng-11587	40	18	clampedpinned	clampedpinne	VERB
fumecheng-11587	40	19	and	and	CCONJ
fumecheng-11587	40	20	clamped	clamp	VERB
fumecheng-11587	40	21	-	-	PUNCT
fumecheng-11587	40	22	clamped	clamp	VERB
fumecheng-11587	40	23	boundary	boundary	ADJ
fumecheng-11587	40	24	conditions	condition	NOUN
fumecheng-11587	40	25	,	,	PUNCT
fumecheng-11587	40	26	since	since	SCONJ
fumecheng-11587	40	27	clamped	clamp	VERB
fumecheng-11587	40	28	-	-	PUNCT
fumecheng-11587	40	29	free	free	ADJ
fumecheng-11587	40	30	boundary	boundary	ADJ
fumecheng-11587	40	31	conditions	condition	NOUN
fumecheng-11587	40	32	produce	produce	VERB
fumecheng-11587	40	33	contradictory	contradictory	ADJ
fumecheng-11587	40	34	results	result	NOUN
fumecheng-11587	40	35	.	.	PUNCT
fumecheng-11587	41	1	in	in	ADP
fumecheng-11587	41	2	recent	recent	ADJ
fumecheng-11587	41	3	times	time	NOUN
fumecheng-11587	41	4	,	,	PUNCT
fumecheng-11587	41	5	stress	stress	NOUN
fumecheng-11587	41	6	-	-	PUNCT
fumecheng-11587	41	7	driven	drive	VERB
fumecheng-11587	41	8	,	,	PUNCT
fumecheng-11587	41	9	strain	strain	NOUN
fumecheng-11587	41	10	-	-	PUNCT
fumecheng-11587	41	11	driven	drive	VERB
fumecheng-11587	41	12	,	,	PUNCT
fumecheng-11587	41	13	and	and	CCONJ
fumecheng-11587	41	14	foundation	foundation	NOUN
fumecheng-11587	41	15	-	-	PUNCT
fumecheng-11587	41	16	driven	drive	VERB
fumecheng-11587	41	17	vibrations	vibration	NOUN
fumecheng-11587	41	18	have	have	AUX
fumecheng-11587	41	19	become	become	VERB
fumecheng-11587	41	20	in	in	ADP
fumecheng-11587	41	21	research	research	NOUN
fumecheng-11587	41	22	focus	focus	NOUN
fumecheng-11587	41	23	.	.	PUNCT
fumecheng-11587	42	1	penna	penna	PROPN
fumecheng-11587	42	2	et	et	PROPN
fumecheng-11587	42	3	al	al	PROPN
fumecheng-11587	42	4	.	.	PUNCT
fumecheng-11587	43	1	[	[	X
fumecheng-11587	43	2	35	35	NUM
fumecheng-11587	43	3	]	]	PUNCT
fumecheng-11587	43	4	investigated	investigate	VERB
fumecheng-11587	43	5	nonlinear	nonlinear	ADJ
fumecheng-11587	43	6	free	free	ADJ
fumecheng-11587	43	7	vibrations	vibration	NOUN
fumecheng-11587	43	8	of	of	ADP
fumecheng-11587	43	9	geometrically	geometrically	ADV
fumecheng-11587	43	10	imperfect	imperfect	ADJ
fumecheng-11587	43	11	fg	fg	ADP
fumecheng-11587	43	12	nano	nano	NOUN
fumecheng-11587	43	13	-	-	PUNCT
fumecheng-11587	43	14	beams	beam	NOUN
fumecheng-11587	43	15	based	base	VERB
fumecheng-11587	43	16	on	on	ADP
fumecheng-11587	43	17	stress	stress	NOUN
fumecheng-11587	43	18	-	-	PUNCT
fumecheng-11587	43	19	driven	drive	VERB
fumecheng-11587	43	20	nonlocal	nonlocal	ADJ
fumecheng-11587	43	21	elasticity	elasticity	NOUN
fumecheng-11587	43	22	.	.	PUNCT
fumecheng-11587	44	1	penna	penna	PROPN
fumecheng-11587	44	2	and	and	CCONJ
fumecheng-11587	44	3	feo	feo	X
fumecheng-11587	44	4	[	[	X
fumecheng-11587	44	5	36	36	NUM
fumecheng-11587	44	6	]	]	PUNCT
fumecheng-11587	44	7	studied	study	VERB
fumecheng-11587	44	8	nonlinear	nonlinear	ADJ
fumecheng-11587	44	9	free	free	ADJ
fumecheng-11587	44	10	vibrations	vibration	NOUN
fumecheng-11587	44	11	of	of	ADP
fumecheng-11587	44	12	functionally	functionally	ADV
fumecheng-11587	44	13	graded	grade	VERB
fumecheng-11587	44	14	porous	porous	ADJ
fumecheng-11587	44	15	bernoulli	bernoulli	NOUN
fumecheng-11587	44	16	–	–	PUNCT
fumecheng-11587	44	17	vibration	vibration	NOUN
fumecheng-11587	44	18	and	and	CCONJ
fumecheng-11587	44	19	stability	stability	NOUN
fumecheng-11587	44	20	of	of	ADP
fumecheng-11587	44	21	a	a	DET
fumecheng-11587	44	22	nonlinear	nonlinear	ADJ
fumecheng-11587	44	23	nonlocal	nonlocal	ADJ
fumecheng-11587	44	24	strain	strain	NOUN
fumecheng-11587	44	25	-	-	PUNCT
fumecheng-11587	44	26	gradient	gradient	NOUN
fumecheng-11587	44	27	fg	fg	PROPN
fumecheng-11587	44	28	beam	beam	NOUN
fumecheng-11587	44	29	on	on	ADP
fumecheng-11587	44	30	a	a	DET
fumecheng-11587	44	31	visco	visco	ADJ
fumecheng-11587	44	32	-	-	PUNCT
fumecheng-11587	44	33	pasternak	pasternak	NOUN
fumecheng-11587	44	34	...	...	PUNCT
fumecheng-11587	44	35	711	711	NUM
fumecheng-11587	44	36	euler	euler	NOUN
fumecheng-11587	44	37	nano	nano	NOUN
fumecheng-11587	44	38	-	-	PUNCT
fumecheng-11587	44	39	beams	beam	NOUN
fumecheng-11587	44	40	resting	rest	VERB
fumecheng-11587	44	41	on	on	ADP
fumecheng-11587	44	42	a	a	DET
fumecheng-11587	44	43	winkler	winkler	NOUN
fumecheng-11587	44	44	elastic	elastic	ADJ
fumecheng-11587	44	45	foundation	foundation	NOUN
fumecheng-11587	44	46	through	through	ADP
fumecheng-11587	44	47	a	a	DET
fumecheng-11587	44	48	stress	stress	NOUN
fumecheng-11587	44	49	-	-	PUNCT
fumecheng-11587	44	50	driven	drive	VERB
fumecheng-11587	44	51	nonlocal	nonlocal	ADJ
fumecheng-11587	44	52	elasticity	elasticity	NOUN
fumecheng-11587	44	53	model	model	NOUN
fumecheng-11587	44	54	.	.	PUNCT
fumecheng-11587	45	1	vaccaro	vaccaro	PROPN
fumecheng-11587	45	2	et	et	PROPN
fumecheng-11587	45	3	al	al	PROPN
fumecheng-11587	45	4	.	.	PUNCT
fumecheng-11587	46	1	[	[	X
fumecheng-11587	46	2	37	37	NUM
fumecheng-11587	46	3	]	]	PUNCT
fumecheng-11587	46	4	studied	study	VERB
fumecheng-11587	46	5	the	the	DET
fumecheng-11587	46	6	size	size	NOUN
fumecheng-11587	46	7	-	-	PUNCT
fumecheng-11587	46	8	dependent	dependent	ADJ
fumecheng-11587	46	9	behavior	behavior	NOUN
fumecheng-11587	46	10	of	of	ADP
fumecheng-11587	46	11	nonlocal	nonlocal	ADJ
fumecheng-11587	46	12	elastic	elastic	ADJ
fumecheng-11587	46	13	beams	beam	NOUN
fumecheng-11587	46	14	by	by	ADP
fumecheng-11587	46	15	adopting	adopt	VERB
fumecheng-11587	46	16	the	the	DET
fumecheng-11587	46	17	stress	stress	NOUN
fumecheng-11587	46	18	-	-	PUNCT
fumecheng-11587	46	19	driven	drive	VERB
fumecheng-11587	46	20	elasticity	elasticity	NOUN
fumecheng-11587	46	21	theory	theory	NOUN
fumecheng-11587	46	22	where	where	SCONJ
fumecheng-11587	46	23	the	the	DET
fumecheng-11587	46	24	kinematics	kinematic	NOUN
fumecheng-11587	46	25	of	of	ADP
fumecheng-11587	46	26	beams	beam	NOUN
fumecheng-11587	46	27	is	be	AUX
fumecheng-11587	46	28	modeled	model	VERB
fumecheng-11587	46	29	by	by	ADP
fumecheng-11587	46	30	the	the	DET
fumecheng-11587	46	31	reddy	reddy	PROPN
fumecheng-11587	46	32	variational	variational	ADJ
fumecheng-11587	46	33	third	third	ADJ
fumecheng-11587	46	34	-	-	PUNCT
fumecheng-11587	46	35	order	order	NOUN
fumecheng-11587	46	36	beam	beam	NOUN
fumecheng-11587	46	37	theory	theory	NOUN
fumecheng-11587	46	38	.	.	PUNCT
fumecheng-11587	47	1	ansari	ansari	PROPN
fumecheng-11587	47	2	et	et	PROPN
fumecheng-11587	47	3	al	al	PROPN
fumecheng-11587	47	4	.	.	PUNCT
fumecheng-11587	48	1	[	[	X
fumecheng-11587	48	2	38	38	NUM
fumecheng-11587	48	3	]	]	PUNCT
fumecheng-11587	48	4	used	use	VERB
fumecheng-11587	48	5	straindriven	straindriven	VERB
fumecheng-11587	48	6	nonlocal	nonlocal	ADJ
fumecheng-11587	48	7	formulations	formulation	NOUN
fumecheng-11587	48	8	of	of	ADP
fumecheng-11587	48	9	eringen	eringen	PROPN
fumecheng-11587	48	10	’s	’s	PART
fumecheng-11587	48	11	theory	theory	NOUN
fumecheng-11587	48	12	in	in	ADP
fumecheng-11587	48	13	both	both	CCONJ
fumecheng-11587	48	14	differential	differential	ADJ
fumecheng-11587	48	15	and	and	CCONJ
fumecheng-11587	48	16	integral	integral	ADJ
fumecheng-11587	48	17	forms	form	NOUN
fumecheng-11587	48	18	for	for	ADP
fumecheng-11587	48	19	a	a	DET
fumecheng-11587	48	20	numerical	numerical	ADJ
fumecheng-11587	48	21	study	study	NOUN
fumecheng-11587	48	22	of	of	ADP
fumecheng-11587	48	23	free	free	ADJ
fumecheng-11587	48	24	vibration	vibration	NOUN
fumecheng-11587	48	25	behavior	behavior	NOUN
fumecheng-11587	48	26	of	of	ADP
fumecheng-11587	48	27	piezoelectric	piezoelectric	ADJ
fumecheng-11587	48	28	bernoulli	bernoulli	PROPN
fumecheng-11587	48	29	–	–	PUNCT
fumecheng-11587	48	30	euler	euler	NOUN
fumecheng-11587	48	31	nanoscale	nanoscale	NOUN
fumecheng-11587	48	32	beams	beam	NOUN
fumecheng-11587	48	33	considering	consider	VERB
fumecheng-11587	48	34	flexoelectric	flexoelectric	ADJ
fumecheng-11587	48	35	and	and	CCONJ
fumecheng-11587	48	36	nonlocal	nonlocal	ADJ
fumecheng-11587	48	37	effects	effect	NOUN
fumecheng-11587	48	38	.	.	PUNCT
fumecheng-11587	49	1	comparative	comparative	ADJ
fumecheng-11587	49	2	studies	study	NOUN
fumecheng-11587	49	3	between	between	ADP
fumecheng-11587	49	4	stressdriven	stressdriven	ADJ
fumecheng-11587	49	5	and	and	CCONJ
fumecheng-11587	49	6	strain	strain	NOUN
fumecheng-11587	49	7	-	-	PUNCT
fumecheng-11587	49	8	driven	drive	VERB
fumecheng-11587	49	9	nonlocal	nonlocal	ADJ
fumecheng-11587	49	10	elasticity	elasticity	NOUN
fumecheng-11587	49	11	theory	theory	NOUN
fumecheng-11587	49	12	have	have	AUX
fumecheng-11587	49	13	been	be	AUX
fumecheng-11587	49	14	made	make	VERB
fumecheng-11587	49	15	by	by	ADP
fumecheng-11587	49	16	several	several	ADJ
fumecheng-11587	49	17	authors	author	NOUN
fumecheng-11587	49	18	[	[	X
fumecheng-11587	49	19	39	39	NUM
fumecheng-11587	49	20	,	,	PUNCT
fumecheng-11587	49	21	40	40	NUM
fumecheng-11587	49	22	,	,	PUNCT
fumecheng-11587	49	23	41	41	NUM
fumecheng-11587	49	24	]	]	PUNCT
fumecheng-11587	49	25	.	.	PUNCT
fumecheng-11587	50	1	elasto	elasto	PROPN
fumecheng-11587	50	2	-	-	PUNCT
fumecheng-11587	50	3	statical	statical	ADJ
fumecheng-11587	50	4	displacement	displacement	NOUN
fumecheng-11587	50	5	-	-	PUNCT
fumecheng-11587	50	6	driven	drive	VERB
fumecheng-11587	50	7	nonlocal	nonlocal	ADJ
fumecheng-11587	50	8	problems	problem	NOUN
fumecheng-11587	50	9	are	be	AUX
fumecheng-11587	50	10	studied	study	VERB
fumecheng-11587	50	11	by	by	ADP
fumecheng-11587	50	12	vaccaro	vaccaro	NOUN
fumecheng-11587	51	1	[	[	X
fumecheng-11587	51	2	42	42	NUM
fumecheng-11587	51	3	]	]	PUNCT
fumecheng-11587	51	4	,	,	PUNCT
fumecheng-11587	51	5	patnaik	patnaik	PROPN
fumecheng-11587	52	1	[	[	X
fumecheng-11587	52	2	43	43	NUM
fumecheng-11587	52	3	]	]	PUNCT
fumecheng-11587	52	4	and	and	CCONJ
fumecheng-11587	52	5	pinnola	pinnola	PROPN
fumecheng-11587	53	1	[	[	X
fumecheng-11587	53	2	44	44	NUM
fumecheng-11587	53	3	]	]	PUNCT
fumecheng-11587	53	4	.	.	PUNCT
fumecheng-11587	54	1	moreover	moreover	ADV
fumecheng-11587	54	2	,	,	PUNCT
fumecheng-11587	54	3	pinnola	pinnola	PROPN
fumecheng-11587	54	4	et	et	PROPN
fumecheng-11587	54	5	al	al	PROPN
fumecheng-11587	54	6	.	.	PUNCT
fumecheng-11587	55	1	[	[	X
fumecheng-11587	55	2	44	44	NUM
fumecheng-11587	55	3	]	]	PUNCT
fumecheng-11587	55	4	have	have	AUX
fumecheng-11587	55	5	studied	study	VERB
fumecheng-11587	55	6	the	the	DET
fumecheng-11587	55	7	elastostatic	elastostatic	ADJ
fumecheng-11587	55	8	problems	problem	NOUN
fumecheng-11587	55	9	of	of	ADP
fumecheng-11587	55	10	classical	classical	ADJ
fumecheng-11587	55	11	euler	euler	NOUN
fumecheng-11587	55	12	-	-	PUNCT
fumecheng-11587	55	13	bernoulli	bernoulli	PROPN
fumecheng-11587	55	14	beam	beam	NOUN
fumecheng-11587	55	15	on	on	ADP
fumecheng-11587	55	16	a	a	DET
fumecheng-11587	55	17	reaction	reaction	NOUN
fumecheng-11587	55	18	-	-	PUNCT
fumecheng-11587	55	19	driven	drive	VERB
fumecheng-11587	55	20	nonlocal	nonlocal	ADJ
fumecheng-11587	55	21	foundation	foundation	NOUN
fumecheng-11587	55	22	.	.	PUNCT
fumecheng-11587	56	1	they	they	PRON
fumecheng-11587	56	2	proposed	propose	VERB
fumecheng-11587	56	3	an	an	DET
fumecheng-11587	56	4	integral	integral	ADJ
fumecheng-11587	56	5	elasticity	elasticity	NOUN
fumecheng-11587	56	6	mixture	mixture	NOUN
fumecheng-11587	56	7	considering	consider	VERB
fumecheng-11587	56	8	a	a	DET
fumecheng-11587	56	9	convex	convex	ADJ
fumecheng-11587	56	10	combination	combination	NOUN
fumecheng-11587	56	11	of	of	ADP
fumecheng-11587	56	12	winkler	winkler	NOUN
fumecheng-11587	56	13	(	(	PUNCT
fumecheng-11587	56	14	local	local	ADJ
fumecheng-11587	56	15	)	)	PUNCT
fumecheng-11587	56	16	and	and	CCONJ
fumecheng-11587	56	17	wieghardt	wieghardt	ADJ
fumecheng-11587	56	18	(	(	PUNCT
fumecheng-11587	56	19	nonlocal	nonlocal	ADJ
fumecheng-11587	56	20	)	)	PUNCT
fumecheng-11587	56	21	laws	law	NOUN
fumecheng-11587	56	22	and	and	CCONJ
fumecheng-11587	56	23	applied	apply	VERB
fumecheng-11587	56	24	the	the	DET
fumecheng-11587	56	25	proposed	propose	VERB
fumecheng-11587	56	26	methodology	methodology	NOUN
fumecheng-11587	56	27	to	to	PART
fumecheng-11587	56	28	find	find	VERB
fumecheng-11587	56	29	analytical	analytical	ADJ
fumecheng-11587	56	30	solutions	solution	NOUN
fumecheng-11587	56	31	to	to	ADP
fumecheng-11587	56	32	simple	simple	ADJ
fumecheng-11587	56	33	elasto	elasto	NOUN
fumecheng-11587	56	34	-	-	PUNCT
fumecheng-11587	56	35	static	static	ADJ
fumecheng-11587	56	36	problems	problem	NOUN
fumecheng-11587	56	37	in	in	ADP
fumecheng-11587	56	38	structural	structural	ADJ
fumecheng-11587	56	39	mechanics	mechanic	NOUN
fumecheng-11587	56	40	.	.	PUNCT
fumecheng-11587	57	1	the	the	DET
fumecheng-11587	57	2	dynamic	dynamic	ADJ
fumecheng-11587	57	3	behaviour	behaviour	NOUN
fumecheng-11587	57	4	of	of	ADP
fumecheng-11587	57	5	nlsgt	nlsgt	NOUN
fumecheng-11587	57	6	structures	structure	NOUN
fumecheng-11587	57	7	composed	compose	VERB
fumecheng-11587	57	8	of	of	ADP
fumecheng-11587	57	9	fgm	fgm	PROPN
fumecheng-11587	57	10	was	be	AUX
fumecheng-11587	57	11	studied	study	VERB
fumecheng-11587	57	12	by	by	ADP
fumecheng-11587	57	13	many	many	ADJ
fumecheng-11587	57	14	authors	author	NOUN
fumecheng-11587	57	15	.	.	PUNCT
fumecheng-11587	58	1	the	the	DET
fumecheng-11587	58	2	most	most	ADV
fumecheng-11587	58	3	common	common	ADJ
fumecheng-11587	58	4	approach	approach	NOUN
fumecheng-11587	58	5	in	in	ADP
fumecheng-11587	58	6	their	their	PRON
fumecheng-11587	58	7	analysis	analysis	NOUN
fumecheng-11587	58	8	includes	include	VERB
fumecheng-11587	58	9	applying	apply	VERB
fumecheng-11587	58	10	different	different	ADJ
fumecheng-11587	58	11	perturbation	perturbation	NOUN
fumecheng-11587	58	12	methods	method	NOUN
fumecheng-11587	58	13	.	.	PUNCT
fumecheng-11587	59	1	for	for	ADP
fumecheng-11587	59	2	example	example	NOUN
fumecheng-11587	59	3	,	,	PUNCT
fumecheng-11587	59	4	gao	gao	PROPN
fumecheng-11587	59	5	et	et	PROPN
fumecheng-11587	59	6	al	al	PROPN
fumecheng-11587	59	7	.	.	PUNCT
fumecheng-11587	60	1	[	[	X
fumecheng-11587	60	2	45	45	NUM
fumecheng-11587	60	3	]	]	PUNCT
fumecheng-11587	60	4	studied	study	VERB
fumecheng-11587	60	5	the	the	DET
fumecheng-11587	60	6	nonlinear	nonlinear	ADJ
fumecheng-11587	60	7	free	free	ADJ
fumecheng-11587	60	8	vibration	vibration	NOUN
fumecheng-11587	60	9	of	of	ADP
fumecheng-11587	60	10	fg	fg	PROPN
fumecheng-11587	60	11	circular	circular	ADJ
fumecheng-11587	60	12	nanotubes	nanotube	NOUN
fumecheng-11587	60	13	using	use	VERB
fumecheng-11587	60	14	nlsgt	nlsgt	NOUN
fumecheng-11587	60	15	and	and	CCONJ
fumecheng-11587	60	16	two	two	NUM
fumecheng-11587	60	17	steps	step	NOUN
fumecheng-11587	60	18	perturbation	perturbation	NOUN
fumecheng-11587	60	19	method	method	NOUN
fumecheng-11587	60	20	.	.	PUNCT
fumecheng-11587	61	1	by	by	ADP
fumecheng-11587	61	2	using	use	VERB
fumecheng-11587	61	3	the	the	DET
fumecheng-11587	61	4	same	same	ADJ
fumecheng-11587	61	5	methodology	methodology	NOUN
fumecheng-11587	61	6	,	,	PUNCT
fumecheng-11587	61	7	they	they	PRON
fumecheng-11587	61	8	also	also	ADV
fumecheng-11587	61	9	studied	study	VERB
fumecheng-11587	61	10	the	the	DET
fumecheng-11587	61	11	vibration	vibration	NOUN
fumecheng-11587	61	12	of	of	ADP
fumecheng-11587	61	13	nano	nano	NOUN
fumecheng-11587	61	14	arches	arch	NOUN
fumecheng-11587	61	15	[	[	X
fumecheng-11587	61	16	46	46	NUM
fumecheng-11587	61	17	]	]	PUNCT
fumecheng-11587	61	18	,	,	PUNCT
fumecheng-11587	61	19	and	and	CCONJ
fumecheng-11587	61	20	fg	fg	PROPN
fumecheng-11587	61	21	nanobeams	nanobeam	NOUN
fumecheng-11587	61	22	with	with	ADP
fumecheng-11587	61	23	several	several	ADJ
fumecheng-11587	61	24	different	different	ADJ
fumecheng-11587	61	25	functionally	functionally	ADV
fumecheng-11587	61	26	graded	grade	VERB
fumecheng-11587	61	27	distributions	distribution	NOUN
fumecheng-11587	61	28	[	[	X
fumecheng-11587	61	29	47	47	NUM
fumecheng-11587	61	30	]	]	PUNCT
fumecheng-11587	61	31	.	.	PUNCT
fumecheng-11587	62	1	el	el	PROPN
fumecheng-11587	62	2	-	-	PUNCT
fumecheng-11587	62	3	borgi	borgi	NOUN
fumecheng-11587	62	4	et	et	PROPN
fumecheng-11587	62	5	al	al	PROPN
fumecheng-11587	62	6	.	.	PUNCT
fumecheng-11587	63	1	[	[	X
fumecheng-11587	63	2	15	15	NUM
fumecheng-11587	63	3	]	]	PUNCT
fumecheng-11587	63	4	investigated	investigate	VERB
fumecheng-11587	63	5	the	the	DET
fumecheng-11587	63	6	free	free	ADJ
fumecheng-11587	63	7	and	and	CCONJ
fumecheng-11587	63	8	forced	force	VERB
fumecheng-11587	63	9	vibration	vibration	NOUN
fumecheng-11587	63	10	response	response	NOUN
fumecheng-11587	63	11	of	of	ADP
fumecheng-11587	63	12	a	a	DET
fumecheng-11587	63	13	simply	simply	ADV
fumecheng-11587	63	14	supported	support	VERB
fumecheng-11587	63	15	fg	fg	PROPN
fumecheng-11587	63	16	beam	beam	PROPN
fumecheng-11587	63	17	resting	rest	VERB
fumecheng-11587	63	18	on	on	ADP
fumecheng-11587	63	19	the	the	DET
fumecheng-11587	63	20	nonlinear	nonlinear	ADJ
fumecheng-11587	63	21	elastic	elastic	ADJ
fumecheng-11587	63	22	foundation	foundation	NOUN
fumecheng-11587	63	23	using	use	VERB
fumecheng-11587	63	24	the	the	DET
fumecheng-11587	63	25	perturbation	perturbation	NOUN
fumecheng-11587	63	26	multiple	multiple	NOUN
fumecheng-11587	63	27	scales	scale	VERB
fumecheng-11587	63	28	method	method	NOUN
fumecheng-11587	63	29	to	to	PART
fumecheng-11587	63	30	obtain	obtain	VERB
fumecheng-11587	63	31	the	the	DET
fumecheng-11587	63	32	amplitude	amplitude	NOUN
fumecheng-11587	63	33	-	-	PUNCT
fumecheng-11587	63	34	frequency	frequency	NOUN
fumecheng-11587	63	35	curves	curve	NOUN
fumecheng-11587	63	36	of	of	ADP
fumecheng-11587	63	37	the	the	DET
fumecheng-11587	63	38	system	system	NOUN
fumecheng-11587	63	39	.	.	PUNCT
fumecheng-11587	64	1	wang	wang	PROPN
fumecheng-11587	64	2	and	and	CCONJ
fumecheng-11587	64	3	shen	shen	VERB
fumecheng-11587	65	1	[	[	X
fumecheng-11587	65	2	48	48	NUM
fumecheng-11587	65	3	]	]	PUNCT
fumecheng-11587	65	4	studied	study	VERB
fumecheng-11587	65	5	the	the	DET
fumecheng-11587	65	6	lateral	lateral	ADJ
fumecheng-11587	65	7	nonlinear	nonlinear	ADJ
fumecheng-11587	65	8	vibration	vibration	NOUN
fumecheng-11587	65	9	of	of	ADP
fumecheng-11587	65	10	an	an	DET
fumecheng-11587	65	11	axially	axially	ADV
fumecheng-11587	65	12	moving	move	VERB
fumecheng-11587	65	13	simply	simply	ADV
fumecheng-11587	65	14	supported	support	VERB
fumecheng-11587	65	15	viscoelastic	viscoelastic	ADJ
fumecheng-11587	65	16	nlsgt	nlsgt	NOUN
fumecheng-11587	65	17	beam	beam	NOUN
fumecheng-11587	65	18	.	.	PUNCT
fumecheng-11587	66	1	for	for	ADP
fumecheng-11587	66	2	obtaining	obtain	VERB
fumecheng-11587	66	3	the	the	DET
fumecheng-11587	66	4	steady	steady	ADJ
fumecheng-11587	66	5	-	-	PUNCT
fumecheng-11587	66	6	state	state	NOUN
fumecheng-11587	66	7	amplitude	amplitude	NOUN
fumecheng-11587	66	8	-	-	PUNCT
fumecheng-11587	66	9	frequency	frequency	NOUN
fumecheng-11587	66	10	responses	response	NOUN
fumecheng-11587	66	11	in	in	ADP
fumecheng-11587	66	12	the	the	DET
fumecheng-11587	66	13	subharmonic	subharmonic	ADJ
fumecheng-11587	66	14	parametric	parametric	ADJ
fumecheng-11587	66	15	resonance	resonance	NOUN
fumecheng-11587	66	16	regime	regime	VERB
fumecheng-11587	66	17	a	a	DET
fumecheng-11587	66	18	direct	direct	ADJ
fumecheng-11587	66	19	multiple	multiple	ADJ
fumecheng-11587	66	20	scales	scale	NOUN
fumecheng-11587	66	21	method	method	NOUN
fumecheng-11587	66	22	is	be	AUX
fumecheng-11587	66	23	used	use	VERB
fumecheng-11587	66	24	.	.	PUNCT
fumecheng-11587	67	1	jafarsadeghi	jafarsadeghi	PROPN
fumecheng-11587	67	2	-	-	PUNCT
fumecheng-11587	67	3	pournaki	pournaki	PROPN
fumecheng-11587	67	4	et	et	PROPN
fumecheng-11587	67	5	al	al	PROPN
fumecheng-11587	67	6	.	.	PUNCT
fumecheng-11587	68	1	[	[	X
fumecheng-11587	68	2	49	49	NUM
fumecheng-11587	68	3	]	]	PUNCT
fumecheng-11587	68	4	investigated	investigate	VERB
fumecheng-11587	68	5	the	the	DET
fumecheng-11587	68	6	heat	heat	NOUN
fumecheng-11587	68	7	-	-	PUNCT
fumecheng-11587	68	8	induced	induce	VERB
fumecheng-11587	68	9	nonlinear	nonlinear	ADJ
fumecheng-11587	68	10	vibration	vibration	NOUN
fumecheng-11587	68	11	of	of	ADP
fumecheng-11587	68	12	fg	fg	PROPN
fumecheng-11587	68	13	capacitive	capacitive	ADJ
fumecheng-11587	68	14	nanobeam	nanobeam	NOUN
fumecheng-11587	68	15	based	base	VERB
fumecheng-11587	68	16	on	on	ADP
fumecheng-11587	68	17	nlsgt	nlsgt	NOUN
fumecheng-11587	68	18	.	.	PUNCT
fumecheng-11587	69	1	they	they	PRON
fumecheng-11587	69	2	used	use	VERB
fumecheng-11587	69	3	averaging	average	VERB
fumecheng-11587	69	4	perturbation	perturbation	NOUN
fumecheng-11587	69	5	method	method	NOUN
fumecheng-11587	69	6	to	to	PART
fumecheng-11587	69	7	obtain	obtain	VERB
fumecheng-11587	69	8	the	the	DET
fumecheng-11587	69	9	governing	govern	VERB
fumecheng-11587	69	10	equations	equation	NOUN
fumecheng-11587	69	11	and	and	CCONJ
fumecheng-11587	69	12	study	study	VERB
fumecheng-11587	69	13	the	the	DET
fumecheng-11587	69	14	steady	steady	ADJ
fumecheng-11587	69	15	-	-	PUNCT
fumecheng-11587	69	16	state	state	NOUN
fumecheng-11587	69	17	responses	response	NOUN
fumecheng-11587	69	18	.	.	PUNCT
fumecheng-11587	70	1	li	li	PROPN
fumecheng-11587	70	2	et	et	PROPN
fumecheng-11587	70	3	al	al	PROPN
fumecheng-11587	70	4	.	.	PUNCT
fumecheng-11587	71	1	[	[	X
fumecheng-11587	71	2	50	50	NUM
fumecheng-11587	71	3	]	]	PUNCT
fumecheng-11587	71	4	studied	study	VERB
fumecheng-11587	71	5	analytically	analytically	ADV
fumecheng-11587	71	6	the	the	DET
fumecheng-11587	71	7	longitudinal	longitudinal	ADJ
fumecheng-11587	71	8	vibration	vibration	NOUN
fumecheng-11587	71	9	of	of	ADP
fumecheng-11587	71	10	nlsgt	nlsgt	NOUN
fumecheng-11587	71	11	rods	rod	NOUN
fumecheng-11587	71	12	and	and	CCONJ
fumecheng-11587	71	13	discovered	discover	VERB
fumecheng-11587	71	14	that	that	SCONJ
fumecheng-11587	71	15	the	the	DET
fumecheng-11587	71	16	nlsgt	nlsgt	NOUN
fumecheng-11587	71	17	rod	rod	NOUN
fumecheng-11587	71	18	model	model	NOUN
fumecheng-11587	71	19	shows	show	VERB
fumecheng-11587	71	20	a	a	DET
fumecheng-11587	71	21	stiffness	stiffness	NOUN
fumecheng-11587	71	22	-	-	PUNCT
fumecheng-11587	71	23	softening	soften	VERB
fumecheng-11587	71	24	effect	effect	NOUN
fumecheng-11587	71	25	when	when	SCONJ
fumecheng-11587	71	26	the	the	DET
fumecheng-11587	71	27	nonlocal	nonlocal	ADJ
fumecheng-11587	71	28	parameter	parameter	NOUN
fumecheng-11587	71	29	is	be	AUX
fumecheng-11587	71	30	larger	large	ADJ
fumecheng-11587	71	31	than	than	ADP
fumecheng-11587	71	32	the	the	DET
fumecheng-11587	71	33	length	length	NOUN
fumecheng-11587	71	34	scale	scale	NOUN
fumecheng-11587	71	35	parameter	parameter	NOUN
fumecheng-11587	71	36	and	and	CCONJ
fumecheng-11587	71	37	a	a	DET
fumecheng-11587	71	38	stiffness	stiffness	NOUN
fumecheng-11587	71	39	-	-	PUNCT
fumecheng-11587	71	40	hardening	harden	VERB
fumecheng-11587	71	41	effect	effect	NOUN
fumecheng-11587	71	42	in	in	ADP
fumecheng-11587	71	43	the	the	DET
fumecheng-11587	71	44	opposite	opposite	ADJ
fumecheng-11587	71	45	case	case	NOUN
fumecheng-11587	71	46	.	.	PUNCT
fumecheng-11587	72	1	however	however	ADV
fumecheng-11587	72	2	,	,	PUNCT
fumecheng-11587	72	3	the	the	DET
fumecheng-11587	72	4	main	main	ADJ
fumecheng-11587	72	5	disadvantage	disadvantage	NOUN
fumecheng-11587	72	6	of	of	ADP
fumecheng-11587	72	7	perturbation	perturbation	NOUN
fumecheng-11587	72	8	methods	method	NOUN
fumecheng-11587	72	9	is	be	AUX
fumecheng-11587	72	10	that	that	SCONJ
fumecheng-11587	72	11	they	they	PRON
fumecheng-11587	72	12	can	can	AUX
fumecheng-11587	72	13	only	only	ADV
fumecheng-11587	72	14	treat	treat	VERB
fumecheng-11587	72	15	systems	system	NOUN
fumecheng-11587	72	16	with	with	ADP
fumecheng-11587	72	17	small	small	ADJ
fumecheng-11587	72	18	nonlinearity	nonlinearity	NOUN
fumecheng-11587	72	19	.	.	PUNCT
fumecheng-11587	73	1	nanostructures	nanostructure	NOUN
fumecheng-11587	73	2	modeled	model	VERB
fumecheng-11587	73	3	by	by	ADP
fumecheng-11587	73	4	nonlocal	nonlocal	ADJ
fumecheng-11587	73	5	stress	stress	NOUN
fumecheng-11587	73	6	and	and	CCONJ
fumecheng-11587	73	7	strain	strain	NOUN
fumecheng-11587	73	8	gradient	gradient	NOUN
fumecheng-11587	73	9	theory	theory	NOUN
fumecheng-11587	73	10	are	be	AUX
fumecheng-11587	73	11	also	also	ADV
fumecheng-11587	73	12	studied	study	VERB
fumecheng-11587	73	13	by	by	ADP
fumecheng-11587	73	14	other	other	ADJ
fumecheng-11587	73	15	methods	method	NOUN
fumecheng-11587	73	16	,	,	PUNCT
fumecheng-11587	73	17	for	for	ADP
fumecheng-11587	73	18	example	example	NOUN
fumecheng-11587	73	19	,	,	PUNCT
fumecheng-11587	73	20	the	the	DET
fumecheng-11587	73	21	differential	differential	ADJ
fumecheng-11587	73	22	quadrature	quadrature	NOUN
fumecheng-11587	73	23	method	method	NOUN
fumecheng-11587	73	24	.	.	PUNCT
fumecheng-11587	74	1	li	li	PROPN
fumecheng-11587	75	1	[	[	X
fumecheng-11587	75	2	51	51	NUM
fumecheng-11587	75	3	]	]	PUNCT
fumecheng-11587	75	4	used	use	VERB
fumecheng-11587	75	5	the	the	DET
fumecheng-11587	75	6	generalized	generalize	VERB
fumecheng-11587	75	7	differential	differential	ADJ
fumecheng-11587	75	8	quadrature	quadrature	NOUN
fumecheng-11587	75	9	method	method	NOUN
fumecheng-11587	75	10	to	to	PART
fumecheng-11587	75	11	investigate	investigate	VERB
fumecheng-11587	75	12	the	the	DET
fumecheng-11587	75	13	vibration	vibration	NOUN
fumecheng-11587	75	14	of	of	ADP
fumecheng-11587	75	15	axially	axially	ADV
fumecheng-11587	75	16	fg	fg	NOUN
fumecheng-11587	75	17	beams	beam	NOUN
fumecheng-11587	75	18	based	base	VERB
fumecheng-11587	75	19	on	on	ADP
fumecheng-11587	75	20	nlsgt	nlsgt	NOUN
fumecheng-11587	75	21	and	and	CCONJ
fumecheng-11587	75	22	euler	euler	NOUN
fumecheng-11587	75	23	-	-	PUNCT
fumecheng-11587	75	24	bernoulli	bernoulli	PROPN
fumecheng-11587	75	25	beam	beam	NOUN
fumecheng-11587	75	26	theory	theory	NOUN
fumecheng-11587	75	27	.	.	PUNCT
fumecheng-11587	76	1	however	however	ADV
fumecheng-11587	76	2	,	,	PUNCT
fumecheng-11587	76	3	in	in	ADP
fumecheng-11587	76	4	the	the	DET
fumecheng-11587	76	5	recent	recent	ADJ
fumecheng-11587	76	6	time	time	NOUN
fumecheng-11587	76	7	,	,	PUNCT
fumecheng-11587	76	8	the	the	DET
fumecheng-11587	76	9	ihb	ihb	PRON
fumecheng-11587	76	10	method	method	NOUN
fumecheng-11587	76	11	becomes	become	VERB
fumecheng-11587	76	12	popular	popular	ADJ
fumecheng-11587	76	13	in	in	ADP
fumecheng-11587	76	14	the	the	DET
fumecheng-11587	76	15	investigation	investigation	NOUN
fumecheng-11587	76	16	of	of	ADP
fumecheng-11587	76	17	nonlinear	nonlinear	ADJ
fumecheng-11587	76	18	dynamical	dynamical	ADJ
fumecheng-11587	76	19	systems	system	NOUN
fumecheng-11587	76	20	with	with	ADP
fumecheng-11587	76	21	harmonically	harmonically	ADV
fumecheng-11587	76	22	varied	varied	ADJ
fumecheng-11587	76	23	excitation	excitation	NOUN
fumecheng-11587	76	24	.	.	PUNCT
fumecheng-11587	77	1	in	in	ADP
fumecheng-11587	77	2	an	an	DET
fumecheng-11587	77	3	interesting	interesting	ADJ
fumecheng-11587	77	4	work	work	NOUN
fumecheng-11587	77	5	of	of	ADP
fumecheng-11587	77	6	bhattiprolu	bhattiprolu	PROPN
fumecheng-11587	77	7	et	et	PROPN
fumecheng-11587	77	8	al	al	PROPN
fumecheng-11587	77	9	.	.	PUNCT
fumecheng-11587	78	1	[	[	X
fumecheng-11587	78	2	52	52	NUM
fumecheng-11587	78	3	]	]	PUNCT
fumecheng-11587	78	4	,	,	PUNCT
fumecheng-11587	78	5	they	they	PRON
fumecheng-11587	78	6	found	find	VERB
fumecheng-11587	78	7	periodic	periodic	ADJ
fumecheng-11587	78	8	solutions	solution	NOUN
fumecheng-11587	78	9	of	of	ADP
fumecheng-11587	78	10	a	a	DET
fumecheng-11587	78	11	nonlinear	nonlinear	ADJ
fumecheng-11587	78	12	euler	euler	NOUN
fumecheng-11587	78	13	-	-	PUNCT
fumecheng-11587	78	14	bernoulli	bernoulli	PROPN
fumecheng-11587	78	15	beam	beam	NOUN
fumecheng-11587	78	16	resting	rest	VERB
fumecheng-11587	78	17	on	on	ADP
fumecheng-11587	78	18	viscoelastic	viscoelastic	PROPN
fumecheng-11587	78	19	uniand	uniand	NOUN
fumecheng-11587	78	20	bilateral	bilateral	ADJ
fumecheng-11587	78	21	foundations	foundation	NOUN
fumecheng-11587	78	22	by	by	ADP
fumecheng-11587	78	23	using	use	VERB
fumecheng-11587	78	24	the	the	DET
fumecheng-11587	78	25	incremental	incremental	ADJ
fumecheng-11587	78	26	harmonic	harmonic	ADJ
fumecheng-11587	78	27	balance	balance	NOUN
fumecheng-11587	78	28	method	method	NOUN
fumecheng-11587	78	29	(	(	PUNCT
fumecheng-11587	78	30	ihbm	ihbm	PROPN
fumecheng-11587	78	31	)	)	PUNCT
fumecheng-11587	78	32	.	.	PUNCT
fumecheng-11587	79	1	however	however	ADV
fumecheng-11587	79	2	,	,	PUNCT
fumecheng-11587	79	3	they	they	PRON
fumecheng-11587	79	4	investigated	investigate	VERB
fumecheng-11587	79	5	vibration	vibration	NOUN
fumecheng-11587	79	6	of	of	ADP
fumecheng-11587	79	7	a	a	DET
fumecheng-11587	79	8	linear	linear	ADJ
fumecheng-11587	79	9	beam	beam	NOUN
fumecheng-11587	79	10	on	on	ADP
fumecheng-11587	79	11	a	a	DET
fumecheng-11587	79	12	nonlinear	nonlinear	ADJ
fumecheng-11587	79	13	foundation	foundation	NOUN
fumecheng-11587	79	14	subjected	subject	VERB
fumecheng-11587	79	15	to	to	ADP
fumecheng-11587	79	16	multiple	multiple	ADJ
fumecheng-11587	79	17	concentrated	concentrated	ADJ
fumecheng-11587	79	18	forces	force	NOUN
fumecheng-11587	79	19	and	and	CCONJ
fumecheng-11587	79	20	only	only	ADV
fumecheng-11587	79	21	pinned	pin	VERB
fumecheng-11587	79	22	-	-	PUNCT
fumecheng-11587	79	23	pinned	pin	VERB
fumecheng-11587	79	24	boundary	boundary	ADJ
fumecheng-11587	79	25	conditions	condition	NOUN
fumecheng-11587	79	26	.	.	PUNCT
fumecheng-11587	80	1	our	our	PRON
fumecheng-11587	80	2	considered	consider	VERB
fumecheng-11587	80	3	beam	beam	NOUN
fumecheng-11587	80	4	is	be	AUX
fumecheng-11587	80	5	nonlinear	nonlinear	ADJ
fumecheng-11587	80	6	with	with	ADP
fumecheng-11587	80	7	three	three	NUM
fumecheng-11587	80	8	different	different	ADJ
fumecheng-11587	80	9	boundary	boundary	ADJ
fumecheng-11587	80	10	conditions	condition	NOUN
fumecheng-11587	80	11	.	.	PUNCT
fumecheng-11587	81	1	the	the	DET
fumecheng-11587	81	2	advantage	advantage	NOUN
fumecheng-11587	81	3	of	of	ADP
fumecheng-11587	81	4	ihb	ihb	NOUN
fumecheng-11587	81	5	over	over	ADP
fumecheng-11587	81	6	other	other	ADJ
fumecheng-11587	81	7	methods	method	NOUN
fumecheng-11587	81	8	is	be	AUX
fumecheng-11587	81	9	in	in	ADP
fumecheng-11587	81	10	its	its	PRON
fumecheng-11587	81	11	accuracy	accuracy	NOUN
fumecheng-11587	81	12	,	,	PUNCT
fumecheng-11587	81	13	the	the	DET
fumecheng-11587	81	14	possibility	possibility	NOUN
fumecheng-11587	81	15	to	to	PART
fumecheng-11587	81	16	treat	treat	VERB
fumecheng-11587	81	17	small	small	ADJ
fumecheng-11587	81	18	and	and	CCONJ
fumecheng-11587	81	19	huge	huge	ADJ
fumecheng-11587	81	20	nonlinearities	nonlinearitie	NOUN
fumecheng-11587	81	21	,	,	PUNCT
fumecheng-11587	81	22	and	and	CCONJ
fumecheng-11587	81	23	relatively	relatively	ADV
fumecheng-11587	81	24	simply	simply	ADV
fumecheng-11587	81	25	implementation	implementation	NOUN
fumecheng-11587	81	26	.	.	PUNCT
fumecheng-11587	82	1	perturbation	perturbation	NOUN
fumecheng-11587	82	2	methods	method	NOUN
fumecheng-11587	82	3	can	can	AUX
fumecheng-11587	82	4	solve	solve	VERB
fumecheng-11587	82	5	differential	differential	ADJ
fumecheng-11587	82	6	equations	equation	NOUN
fumecheng-11587	82	7	with	with	ADP
fumecheng-11587	82	8	small	small	ADJ
fumecheng-11587	82	9	nonlinear	nonlinear	ADJ
fumecheng-11587	82	10	terms	term	NOUN
fumecheng-11587	82	11	and	and	CCONJ
fumecheng-11587	82	12	rather	rather	ADV
fumecheng-11587	82	13	simple	simple	ADJ
fumecheng-11587	82	14	problems	problem	NOUN
fumecheng-11587	82	15	.	.	PUNCT
fumecheng-11587	83	1	therefore	therefore	ADV
fumecheng-11587	83	2	,	,	PUNCT
fumecheng-11587	83	3	ihb	ihb	ADV
fumecheng-11587	83	4	is	be	AUX
fumecheng-11587	83	5	used	use	VERB
fumecheng-11587	83	6	in	in	ADP
fumecheng-11587	83	7	our	our	PRON
fumecheng-11587	83	8	work	work	NOUN
fumecheng-11587	83	9	to	to	PART
fumecheng-11587	83	10	find	find	VERB
fumecheng-11587	83	11	periodic	periodic	ADJ
fumecheng-11587	83	12	solutions	solution	NOUN
fumecheng-11587	83	13	when	when	SCONJ
fumecheng-11587	83	14	strong	strong	ADJ
fumecheng-11587	83	15	nonlinearity	nonlinearity	NOUN
fumecheng-11587	83	16	is	be	AUX
fumecheng-11587	83	17	present	present	ADJ
fumecheng-11587	83	18	in	in	ADP
fumecheng-11587	83	19	the	the	DET
fumecheng-11587	83	20	system	system	NOUN
fumecheng-11587	83	21	.	.	PUNCT
fumecheng-11587	84	1	712	712	NUM
fumecheng-11587	84	2	n.	n.	NOUN
fumecheng-11587	84	3	nešić	nešić	PROPN
fumecheng-11587	84	4	,	,	PUNCT
fumecheng-11587	84	5	m.	m.	NOUN
fumecheng-11587	84	6	cajić	cajić	NOUN
fumecheng-11587	84	7	,	,	PUNCT
fumecheng-11587	84	8	d.	d.	PROPN
fumecheng-11587	84	9	karličić	karličić	PROPN
fumecheng-11587	84	10	,	,	PUNCT
fumecheng-11587	84	11	m.	m.	NOUN
fumecheng-11587	84	12	lazarević	lazarević	PROPN
fumecheng-11587	84	13	,	,	PUNCT
fumecheng-11587	84	14	s.	s.	PROPN
fumecheng-11587	84	15	adhikari	adhikari	PROPN
fumecheng-11587	84	16	stability	stability	NOUN
fumecheng-11587	84	17	of	of	ADP
fumecheng-11587	84	18	fg	fg	PROPN
fumecheng-11587	84	19	nanobeams	nanobeam	NOUN
fumecheng-11587	84	20	has	have	AUX
fumecheng-11587	84	21	been	be	AUX
fumecheng-11587	84	22	investigated	investigate	VERB
fumecheng-11587	84	23	in	in	ADP
fumecheng-11587	84	24	the	the	DET
fumecheng-11587	84	25	literature	literature	NOUN
fumecheng-11587	84	26	by	by	ADP
fumecheng-11587	84	27	using	use	VERB
fumecheng-11587	84	28	several	several	ADJ
fumecheng-11587	84	29	different	different	ADJ
fumecheng-11587	84	30	criteria	criterion	NOUN
fumecheng-11587	84	31	and	and	CCONJ
fumecheng-11587	84	32	methods	method	NOUN
fumecheng-11587	84	33	.	.	PUNCT
fumecheng-11587	85	1	wang	wang	PROPN
fumecheng-11587	85	2	and	and	CCONJ
fumecheng-11587	85	3	shen	shen	VERB
fumecheng-11587	86	1	[	[	X
fumecheng-11587	86	2	48	48	NUM
fumecheng-11587	86	3	]	]	PUNCT
fumecheng-11587	86	4	employed	employ	VERB
fumecheng-11587	86	5	the	the	DET
fumecheng-11587	86	6	routh	routh	PROPN
fumecheng-11587	86	7	–	–	PUNCT
fumecheng-11587	86	8	hurwitz	hurwitz	PROPN
fumecheng-11587	86	9	criterion	criterion	NOUN
fumecheng-11587	86	10	to	to	PART
fumecheng-11587	86	11	determine	determine	VERB
fumecheng-11587	86	12	the	the	DET
fumecheng-11587	86	13	stability	stability	NOUN
fumecheng-11587	86	14	of	of	ADP
fumecheng-11587	86	15	the	the	DET
fumecheng-11587	86	16	(	(	PUNCT
fumecheng-11587	86	17	non-	non-	SYM
fumecheng-11587	86	18	)	)	PUNCT
fumecheng-11587	86	19	zero	zero	NUM
fumecheng-11587	86	20	equilibrium	equilibrium	NOUN
fumecheng-11587	86	21	solution	solution	NOUN
fumecheng-11587	86	22	of	of	ADP
fumecheng-11587	86	23	nonlinear	nonlinear	ADJ
fumecheng-11587	86	24	laterally	laterally	ADV
fumecheng-11587	86	25	vibrating	vibrate	VERB
fumecheng-11587	86	26	axially	axially	ADV
fumecheng-11587	86	27	moving	move	VERB
fumecheng-11587	86	28	simply	simply	ADV
fumecheng-11587	86	29	supported	support	VERB
fumecheng-11587	86	30	viscoelastic	viscoelastic	ADJ
fumecheng-11587	86	31	nlsgt	nlsgt	NOUN
fumecheng-11587	86	32	beam	beam	NOUN
fumecheng-11587	86	33	.	.	PUNCT
fumecheng-11587	87	1	jafarsadeghipournaki	jafarsadeghipournaki	PROPN
fumecheng-11587	87	2	et	et	PROPN
fumecheng-11587	87	3	al	al	PROPN
fumecheng-11587	87	4	.	.	PUNCT
fumecheng-11587	88	1	[	[	X
fumecheng-11587	88	2	49	49	NUM
fumecheng-11587	88	3	]	]	PUNCT
fumecheng-11587	88	4	used	use	VERB
fumecheng-11587	88	5	a	a	DET
fumecheng-11587	88	6	shooting	shooting	NOUN
fumecheng-11587	88	7	technique	technique	NOUN
fumecheng-11587	88	8	in	in	ADP
fumecheng-11587	88	9	conjunction	conjunction	NOUN
fumecheng-11587	88	10	with	with	ADP
fumecheng-11587	88	11	the	the	DET
fumecheng-11587	88	12	floquet	floquet	NOUN
fumecheng-11587	88	13	theory	theory	NOUN
fumecheng-11587	88	14	for	for	ADP
fumecheng-11587	88	15	capturing	capture	VERB
fumecheng-11587	88	16	the	the	DET
fumecheng-11587	88	17	periodic	periodic	ADJ
fumecheng-11587	88	18	motions	motion	NOUN
fumecheng-11587	88	19	and	and	CCONJ
fumecheng-11587	88	20	examining	examine	VERB
fumecheng-11587	88	21	their	their	PRON
fumecheng-11587	88	22	stability	stability	NOUN
fumecheng-11587	88	23	of	of	ADP
fumecheng-11587	88	24	heat	heat	NOUN
fumecheng-11587	88	25	-	-	PUNCT
fumecheng-11587	88	26	induced	induce	VERB
fumecheng-11587	88	27	nonlinear	nonlinear	ADJ
fumecheng-11587	88	28	vibration	vibration	NOUN
fumecheng-11587	88	29	of	of	ADP
fumecheng-11587	88	30	fg	fg	PROPN
fumecheng-11587	88	31	nlsgt	nlsgt	NOUN
fumecheng-11587	88	32	capacitive	capacitive	ADJ
fumecheng-11587	88	33	nanobeam	nanobeam	NOUN
fumecheng-11587	88	34	.	.	PUNCT
fumecheng-11587	89	1	jalaei	jalaei	NOUN
fumecheng-11587	89	2	et	et	PROPN
fumecheng-11587	89	3	al	al	PROPN
fumecheng-11587	89	4	.	.	PUNCT
fumecheng-11587	90	1	[	[	X
fumecheng-11587	90	2	53	53	NUM
fumecheng-11587	90	3	]	]	PUNCT
fumecheng-11587	90	4	investigated	investigate	VERB
fumecheng-11587	90	5	the	the	DET
fumecheng-11587	90	6	dynamic	dynamic	ADJ
fumecheng-11587	90	7	stability	stability	NOUN
fumecheng-11587	90	8	of	of	ADP
fumecheng-11587	90	9	a	a	DET
fumecheng-11587	90	10	temperature	temperature	NOUN
fumecheng-11587	90	11	-	-	PUNCT
fumecheng-11587	90	12	dependent	dependent	ADJ
fumecheng-11587	90	13	timoshenko	timoshenko	NOUN
fumecheng-11587	90	14	fg	fg	ADP
fumecheng-11587	90	15	nanobeam	nanobeam	NOUN
fumecheng-11587	90	16	under	under	ADP
fumecheng-11587	90	17	the	the	DET
fumecheng-11587	90	18	axial	axial	ADJ
fumecheng-11587	90	19	excitation	excitation	NOUN
fumecheng-11587	90	20	load	load	NOUN
fumecheng-11587	90	21	and	and	CCONJ
fumecheng-11587	90	22	magnetic	magnetic	ADJ
fumecheng-11587	90	23	field	field	NOUN
fumecheng-11587	90	24	in	in	ADP
fumecheng-11587	90	25	a	a	DET
fumecheng-11587	90	26	thermal	thermal	ADJ
fumecheng-11587	90	27	environment	environment	NOUN
fumecheng-11587	90	28	by	by	ADP
fumecheng-11587	90	29	using	use	VERB
fumecheng-11587	90	30	navier	navier	NOUN
fumecheng-11587	90	31	's	's	PART
fumecheng-11587	90	32	and	and	CCONJ
fumecheng-11587	90	33	bolotin	bolotin	PROPN
fumecheng-11587	90	34	's	's	PART
fumecheng-11587	90	35	method	method	NOUN
fumecheng-11587	90	36	.	.	PUNCT
fumecheng-11587	91	1	in	in	ADP
fumecheng-11587	91	2	this	this	DET
fumecheng-11587	91	3	paper	paper	NOUN
fumecheng-11587	91	4	,	,	PUNCT
fumecheng-11587	91	5	we	we	PRON
fumecheng-11587	91	6	used	use	VERB
fumecheng-11587	91	7	floquet	floquet	NOUN
fumecheng-11587	91	8	theory	theory	NOUN
fumecheng-11587	91	9	to	to	PART
fumecheng-11587	91	10	determine	determine	VERB
fumecheng-11587	91	11	the	the	DET
fumecheng-11587	91	12	stability	stability	NOUN
fumecheng-11587	91	13	of	of	ADP
fumecheng-11587	91	14	our	our	PRON
fumecheng-11587	91	15	model	model	NOUN
fumecheng-11587	91	16	because	because	SCONJ
fumecheng-11587	91	17	it	it	PRON
fumecheng-11587	91	18	is	be	AUX
fumecheng-11587	91	19	suitable	suitable	ADJ
fumecheng-11587	91	20	to	to	PART
fumecheng-11587	91	21	be	be	AUX
fumecheng-11587	91	22	implemented	implement	VERB
fumecheng-11587	91	23	coupled	couple	VERB
fumecheng-11587	91	24	with	with	ADP
fumecheng-11587	91	25	the	the	DET
fumecheng-11587	91	26	ihb	ihb	NOUN
fumecheng-11587	91	27	method	method	NOUN
fumecheng-11587	91	28	.	.	PUNCT
fumecheng-11587	92	1	nešić	nešić	PROPN
fumecheng-11587	92	2	et	et	PROPN
fumecheng-11587	92	3	al	al	PROPN
fumecheng-11587	92	4	.	.	PUNCT
fumecheng-11587	93	1	[	[	X
fumecheng-11587	93	2	27	27	NUM
fumecheng-11587	93	3	]	]	PUNCT
fumecheng-11587	93	4	studied	study	VERB
fumecheng-11587	93	5	the	the	DET
fumecheng-11587	93	6	vibration	vibration	NOUN
fumecheng-11587	93	7	of	of	ADP
fumecheng-11587	93	8	a	a	DET
fumecheng-11587	93	9	nonlocal	nonlocal	ADJ
fumecheng-11587	93	10	nonlinear	nonlinear	NOUN
fumecheng-11587	93	11	fg	fg	PROPN
fumecheng-11587	93	12	beam	beam	NOUN
fumecheng-11587	93	13	on	on	ADP
fumecheng-11587	93	14	the	the	DET
fumecheng-11587	93	15	fractional	fractional	ADJ
fumecheng-11587	93	16	visco	visco	ADJ
fumecheng-11587	93	17	-	-	PUNCT
fumecheng-11587	93	18	pasternak	pasternak	PROPN
fumecheng-11587	93	19	foundation	foundation	NOUN
fumecheng-11587	93	20	based	base	VERB
fumecheng-11587	93	21	on	on	ADP
fumecheng-11587	93	22	the	the	DET
fumecheng-11587	93	23	amplitude	amplitude	NOUN
fumecheng-11587	93	24	-	-	PUNCT
fumecheng-11587	93	25	frequency	frequency	NOUN
fumecheng-11587	93	26	response	response	NOUN
fumecheng-11587	93	27	analysis	analysis	NOUN
fumecheng-11587	93	28	and	and	CCONJ
fumecheng-11587	93	29	utilizing	utilize	VERB
fumecheng-11587	93	30	the	the	DET
fumecheng-11587	93	31	ihb	ihb	NOUN
fumecheng-11587	93	32	,	,	PUNCT
fumecheng-11587	93	33	perturbation	perturbation	NOUN
fumecheng-11587	93	34	multiple	multiple	ADJ
fumecheng-11587	93	35	scales	scale	NOUN
fumecheng-11587	93	36	,	,	PUNCT
fumecheng-11587	93	37	and	and	CCONJ
fumecheng-11587	93	38	newmark	newmark	NOUN
fumecheng-11587	93	39	methods	method	NOUN
fumecheng-11587	93	40	to	to	PART
fumecheng-11587	93	41	find	find	VERB
fumecheng-11587	93	42	and	and	CCONJ
fumecheng-11587	93	43	confirm	confirm	VERB
fumecheng-11587	93	44	the	the	DET
fumecheng-11587	93	45	periodic	periodic	ADJ
fumecheng-11587	93	46	solution	solution	NOUN
fumecheng-11587	93	47	.	.	PUNCT
fumecheng-11587	94	1	in	in	ADP
fumecheng-11587	94	2	the	the	DET
fumecheng-11587	94	3	current	current	ADJ
fumecheng-11587	94	4	paper	paper	NOUN
fumecheng-11587	94	5	,	,	PUNCT
fumecheng-11587	94	6	the	the	DET
fumecheng-11587	94	7	stability	stability	NOUN
fumecheng-11587	94	8	of	of	ADP
fumecheng-11587	94	9	periodic	periodic	ADJ
fumecheng-11587	94	10	solutions	solution	NOUN
fumecheng-11587	94	11	is	be	AUX
fumecheng-11587	94	12	investigated	investigate	VERB
fumecheng-11587	94	13	for	for	ADP
fumecheng-11587	94	14	the	the	DET
fumecheng-11587	94	15	amplitude	amplitude	NOUN
fumecheng-11587	94	16	-	-	PUNCT
fumecheng-11587	94	17	frequency	frequency	NOUN
fumecheng-11587	94	18	responses	response	NOUN
fumecheng-11587	94	19	of	of	ADP
fumecheng-11587	94	20	a	a	DET
fumecheng-11587	94	21	nonlinear	nonlinear	ADJ
fumecheng-11587	94	22	nonlocal	nonlocal	ADJ
fumecheng-11587	94	23	strain	strain	NOUN
fumecheng-11587	94	24	gradient	gradient	NOUN
fumecheng-11587	94	25	functionally	functionally	ADV
fumecheng-11587	94	26	graded	grade	VERB
fumecheng-11587	94	27	euler	euler	NOUN
fumecheng-11587	94	28	–	–	PUNCT
fumecheng-11587	94	29	bernoulli	bernoulli	PROPN
fumecheng-11587	94	30	beam	beam	PROPN
fumecheng-11587	94	31	model	model	NOUN
fumecheng-11587	94	32	resting	rest	VERB
fumecheng-11587	94	33	on	on	ADP
fumecheng-11587	94	34	a	a	DET
fumecheng-11587	94	35	visco	visco	ADJ
fumecheng-11587	94	36	-	-	PUNCT
fumecheng-11587	94	37	pasternak	pasternak	PROPN
fumecheng-11587	94	38	foundation	foundation	NOUN
fumecheng-11587	94	39	and	and	CCONJ
fumecheng-11587	94	40	subjected	subject	VERB
fumecheng-11587	94	41	to	to	ADP
fumecheng-11587	94	42	external	external	ADJ
fumecheng-11587	94	43	harmonic	harmonic	ADJ
fumecheng-11587	94	44	excitation	excitation	NOUN
fumecheng-11587	94	45	.	.	PUNCT
fumecheng-11587	95	1	therefore	therefore	ADV
fumecheng-11587	95	2	,	,	PUNCT
fumecheng-11587	95	3	this	this	DET
fumecheng-11587	95	4	study	study	NOUN
fumecheng-11587	95	5	can	can	AUX
fumecheng-11587	95	6	be	be	AUX
fumecheng-11587	95	7	considered	consider	VERB
fumecheng-11587	95	8	as	as	ADP
fumecheng-11587	95	9	a	a	DET
fumecheng-11587	95	10	special	special	ADJ
fumecheng-11587	95	11	case	case	NOUN
fumecheng-11587	95	12	and	and	CCONJ
fumecheng-11587	95	13	natural	natural	ADJ
fumecheng-11587	95	14	extension	extension	NOUN
fumecheng-11587	95	15	of	of	ADP
fumecheng-11587	95	16	the	the	DET
fumecheng-11587	95	17	work	work	NOUN
fumecheng-11587	95	18	done	do	VERB
fumecheng-11587	95	19	by	by	ADP
fumecheng-11587	95	20	nešić	nešić	PROPN
fumecheng-11587	95	21	et	et	PROPN
fumecheng-11587	95	22	al	al	PROPN
fumecheng-11587	95	23	.	.	PUNCT
fumecheng-11587	96	1	in	in	ADP
fumecheng-11587	96	2	[	[	X
fumecheng-11587	96	3	27	27	NUM
fumecheng-11587	96	4	]	]	PUNCT
fumecheng-11587	96	5	since	since	SCONJ
fumecheng-11587	96	6	a	a	DET
fumecheng-11587	96	7	special	special	ADJ
fumecheng-11587	96	8	case	case	NOUN
fumecheng-11587	96	9	of	of	ADP
fumecheng-11587	96	10	the	the	DET
fumecheng-11587	96	11	visco	visco	ADJ
fumecheng-11587	96	12	-	-	PUNCT
fumecheng-11587	96	13	pasternak	pasternak	PROPN
fumecheng-11587	96	14	foundation	foundation	NOUN
fumecheng-11587	96	15	model	model	NOUN
fumecheng-11587	96	16	without	without	ADP
fumecheng-11587	96	17	fractional	fractional	ADJ
fumecheng-11587	96	18	derivatives	derivative	NOUN
fumecheng-11587	96	19	is	be	AUX
fumecheng-11587	96	20	adopted	adopt	VERB
fumecheng-11587	96	21	and	and	CCONJ
fumecheng-11587	96	22	stability	stability	NOUN
fumecheng-11587	96	23	of	of	ADP
fumecheng-11587	96	24	periodic	periodic	ADJ
fumecheng-11587	96	25	solutions	solution	NOUN
fumecheng-11587	96	26	analysis	analysis	NOUN
fumecheng-11587	96	27	is	be	AUX
fumecheng-11587	96	28	performed	perform	VERB
fumecheng-11587	96	29	.	.	PUNCT
fumecheng-11587	97	1	nonlinear	nonlinear	PROPN
fumecheng-11587	97	2	von	von	PROPN
fumecheng-11587	97	3	kármán	kármán	PROPN
fumecheng-11587	97	4	strain	strain	PROPN
fumecheng-11587	97	5	-	-	PUNCT
fumecheng-11587	97	6	displacement	displacement	NOUN
fumecheng-11587	97	7	relation	relation	NOUN
fumecheng-11587	97	8	is	be	AUX
fumecheng-11587	97	9	used	use	VERB
fumecheng-11587	97	10	together	together	ADV
fumecheng-11587	97	11	with	with	ADP
fumecheng-11587	97	12	the	the	DET
fumecheng-11587	97	13	nonlocal	nonlocal	ADJ
fumecheng-11587	97	14	stress	stress	NOUN
fumecheng-11587	97	15	and	and	CCONJ
fumecheng-11587	97	16	strain	strain	VERB
fumecheng-11587	97	17	gradient	gradient	ADJ
fumecheng-11587	97	18	theories	theory	NOUN
fumecheng-11587	97	19	.	.	PUNCT
fumecheng-11587	98	1	variations	variation	NOUN
fumecheng-11587	98	2	of	of	ADP
fumecheng-11587	98	3	material	material	NOUN
fumecheng-11587	98	4	properties	property	NOUN
fumecheng-11587	98	5	across	across	ADP
fumecheng-11587	98	6	the	the	DET
fumecheng-11587	98	7	thickness	thickness	NOUN
fumecheng-11587	98	8	direction	direction	NOUN
fumecheng-11587	98	9	are	be	AUX
fumecheng-11587	98	10	defined	define	VERB
fumecheng-11587	98	11	by	by	ADP
fumecheng-11587	98	12	the	the	DET
fumecheng-11587	98	13	power	power	NOUN
fumecheng-11587	98	14	-	-	PUNCT
fumecheng-11587	98	15	law	law	NOUN
fumecheng-11587	98	16	model	model	NOUN
fumecheng-11587	98	17	.	.	PUNCT
fumecheng-11587	99	1	the	the	DET
fumecheng-11587	99	2	governing	govern	VERB
fumecheng-11587	99	3	differential	differential	ADJ
fumecheng-11587	99	4	equation	equation	NOUN
fumecheng-11587	99	5	of	of	ADP
fumecheng-11587	99	6	motion	motion	NOUN
fumecheng-11587	99	7	is	be	AUX
fumecheng-11587	99	8	derived	derive	VERB
fumecheng-11587	99	9	by	by	ADP
fumecheng-11587	99	10	using	use	VERB
fumecheng-11587	99	11	hamilton	hamilton	PROPN
fumecheng-11587	99	12	's	's	PART
fumecheng-11587	99	13	principle	principle	NOUN
fumecheng-11587	99	14	and	and	CCONJ
fumecheng-11587	99	15	then	then	ADV
fumecheng-11587	99	16	discretized	discretize	VERB
fumecheng-11587	99	17	by	by	ADP
fumecheng-11587	99	18	the	the	DET
fumecheng-11587	99	19	galerkin	galerkin	PROPN
fumecheng-11587	99	20	approximation	approximation	NOUN
fumecheng-11587	99	21	.	.	PUNCT
fumecheng-11587	100	1	the	the	DET
fumecheng-11587	100	2	incremental	incremental	ADJ
fumecheng-11587	100	3	harmonic	harmonic	ADJ
fumecheng-11587	100	4	balance	balance	NOUN
fumecheng-11587	100	5	method	method	NOUN
fumecheng-11587	100	6	and	and	CCONJ
fumecheng-11587	100	7	continuation	continuation	NOUN
fumecheng-11587	100	8	technique	technique	NOUN
fumecheng-11587	100	9	are	be	AUX
fumecheng-11587	100	10	employed	employ	VERB
fumecheng-11587	100	11	to	to	PART
fumecheng-11587	100	12	obtain	obtain	VERB
fumecheng-11587	100	13	the	the	DET
fumecheng-11587	100	14	amplitude	amplitude	NOUN
fumecheng-11587	100	15	-	-	PUNCT
fumecheng-11587	100	16	frequency	frequency	NOUN
fumecheng-11587	100	17	responses	response	NOUN
fumecheng-11587	100	18	and	and	CCONJ
fumecheng-11587	100	19	some	some	DET
fumecheng-11587	100	20	periodic	periodic	ADJ
fumecheng-11587	100	21	solutions	solution	NOUN
fumecheng-11587	100	22	are	be	AUX
fumecheng-11587	100	23	verified	verify	VERB
fumecheng-11587	100	24	against	against	ADP
fumecheng-11587	100	25	the	the	DET
fumecheng-11587	100	26	numerical	numerical	ADJ
fumecheng-11587	100	27	integration	integration	NOUN
fumecheng-11587	100	28	runge	runge	NOUN
fumecheng-11587	100	29	-	-	PUNCT
fumecheng-11587	100	30	kutta	kutta	NOUN
fumecheng-11587	100	31	method	method	NOUN
fumecheng-11587	100	32	.	.	PUNCT
fumecheng-11587	101	1	for	for	ADP
fumecheng-11587	101	2	each	each	DET
fumecheng-11587	101	3	periodic	periodic	ADJ
fumecheng-11587	101	4	solution	solution	NOUN
fumecheng-11587	101	5	,	,	PUNCT
fumecheng-11587	101	6	a	a	DET
fumecheng-11587	101	7	stability	stability	NOUN
fumecheng-11587	101	8	check	check	NOUN
fumecheng-11587	101	9	is	be	AUX
fumecheng-11587	101	10	performed	perform	VERB
fumecheng-11587	101	11	by	by	ADP
fumecheng-11587	101	12	utilizing	utilize	VERB
fumecheng-11587	101	13	floquet	floquet	NOUN
fumecheng-11587	101	14	theory	theory	NOUN
fumecheng-11587	101	15	.	.	PUNCT
fumecheng-11587	102	1	the	the	DET
fumecheng-11587	102	2	novelty	novelty	NOUN
fumecheng-11587	102	3	in	in	ADP
fumecheng-11587	102	4	presented	present	VERB
fumecheng-11587	102	5	paper	paper	NOUN
fumecheng-11587	102	6	includes	include	VERB
fumecheng-11587	102	7	introduction	introduction	NOUN
fumecheng-11587	102	8	of	of	ADP
fumecheng-11587	102	9	the	the	DET
fumecheng-11587	102	10	model	model	NOUN
fumecheng-11587	102	11	of	of	ADP
fumecheng-11587	102	12	nonlocal	nonlocal	ADJ
fumecheng-11587	102	13	nonlinear	nonlinear	NOUN
fumecheng-11587	102	14	fg	fg	PROPN
fumecheng-11587	102	15	beam	beam	PROPN
fumecheng-11587	102	16	vibrating	vibrate	VERB
fumecheng-11587	102	17	on	on	ADP
fumecheng-11587	102	18	the	the	DET
fumecheng-11587	102	19	visco	visco	ADJ
fumecheng-11587	102	20	-	-	PUNCT
fumecheng-11587	102	21	pasternak	pasternak	PROPN
fumecheng-11587	102	22	foundation	foundation	PROPN
fumecheng-11587	102	23	.	.	PUNCT
fumecheng-11587	103	1	nonlinearity	nonlinearity	NOUN
fumecheng-11587	103	2	is	be	AUX
fumecheng-11587	103	3	introduced	introduce	VERB
fumecheng-11587	103	4	via	via	ADP
fumecheng-11587	103	5	von	von	PROPN
fumecheng-11587	103	6	karman	karman	PROPN
fumecheng-11587	103	7	strain	strain	PROPN
fumecheng-11587	103	8	-	-	PUNCT
fumecheng-11587	103	9	displacement	displacement	NOUN
fumecheng-11587	103	10	relation	relation	NOUN
fumecheng-11587	103	11	and	and	CCONJ
fumecheng-11587	103	12	nonlocality	nonlocality	NOUN
fumecheng-11587	103	13	through	through	ADP
fumecheng-11587	103	14	strain	strain	NOUN
fumecheng-11587	103	15	gradient	gradient	NOUN
fumecheng-11587	103	16	and	and	CCONJ
fumecheng-11587	103	17	stress	stress	NOUN
fumecheng-11587	103	18	gradient	gradient	ADJ
fumecheng-11587	103	19	constitutive	constitutive	ADJ
fumecheng-11587	103	20	relations	relation	NOUN
fumecheng-11587	103	21	.	.	PUNCT
fumecheng-11587	104	1	the	the	DET
fumecheng-11587	104	2	proposed	propose	VERB
fumecheng-11587	104	3	visco	visco	ADJ
fumecheng-11587	104	4	-	-	PUNCT
fumecheng-11587	104	5	pasternak	pasternak	PROPN
fumecheng-11587	104	6	foundation	foundation	NOUN
fumecheng-11587	104	7	is	be	AUX
fumecheng-11587	104	8	defined	define	VERB
fumecheng-11587	104	9	with	with	ADP
fumecheng-11587	104	10	four	four	NUM
fumecheng-11587	104	11	parameters	parameter	NOUN
fumecheng-11587	104	12	enabling	enable	VERB
fumecheng-11587	104	13	modeling	modeling	NOUN
fumecheng-11587	104	14	of	of	ADP
fumecheng-11587	104	15	vast	vast	ADJ
fumecheng-11587	104	16	range	range	NOUN
fumecheng-11587	104	17	of	of	ADP
fumecheng-11587	104	18	practical	practical	ADJ
fumecheng-11587	104	19	foundations	foundation	NOUN
fumecheng-11587	104	20	.	.	PUNCT
fumecheng-11587	105	1	originality	originality	NOUN
fumecheng-11587	105	2	is	be	AUX
fumecheng-11587	105	3	obtaining	obtain	VERB
fumecheng-11587	105	4	periodic	periodic	ADJ
fumecheng-11587	105	5	solutions	solution	NOUN
fumecheng-11587	105	6	for	for	ADP
fumecheng-11587	105	7	such	such	DET
fumecheng-11587	105	8	a	a	DET
fumecheng-11587	105	9	system	system	NOUN
fumecheng-11587	105	10	by	by	ADP
fumecheng-11587	105	11	using	use	VERB
fumecheng-11587	105	12	ihb	ihb	DET
fumecheng-11587	105	13	method	method	NOUN
fumecheng-11587	105	14	and	and	CCONJ
fumecheng-11587	105	15	continuation	continuation	NOUN
fumecheng-11587	105	16	technique	technique	NOUN
fumecheng-11587	105	17	and	and	CCONJ
fumecheng-11587	105	18	analyzing	analyze	VERB
fumecheng-11587	105	19	amplitude	amplitude	NOUN
fumecheng-11587	105	20	-	-	PUNCT
fumecheng-11587	105	21	frequency	frequency	NOUN
fumecheng-11587	105	22	response	response	NOUN
fumecheng-11587	105	23	curves	curve	NOUN
fumecheng-11587	105	24	for	for	ADP
fumecheng-11587	105	25	different	different	ADJ
fumecheng-11587	105	26	parameters	parameter	NOUN
fumecheng-11587	105	27	.	.	PUNCT
fumecheng-11587	106	1	additional	additional	ADJ
fumecheng-11587	106	2	novelty	novelty	NOUN
fumecheng-11587	106	3	is	be	AUX
fumecheng-11587	106	4	utilizing	utilize	VERB
fumecheng-11587	106	5	floquet	floquet	NOUN
fumecheng-11587	106	6	theory	theory	NOUN
fumecheng-11587	106	7	to	to	PART
fumecheng-11587	106	8	determine	determine	VERB
fumecheng-11587	106	9	stability	stability	NOUN
fumecheng-11587	106	10	of	of	ADP
fumecheng-11587	106	11	periodic	periodic	ADJ
fumecheng-11587	106	12	solutions	solution	NOUN
fumecheng-11587	106	13	for	for	ADP
fumecheng-11587	106	14	different	different	ADJ
fumecheng-11587	106	15	excitation	excitation	NOUN
fumecheng-11587	106	16	frequencies	frequency	NOUN
fumecheng-11587	106	17	of	of	ADP
fumecheng-11587	106	18	such	such	ADJ
fumecheng-11587	106	19	vibrating	vibrate	VERB
fumecheng-11587	106	20	system	system	NOUN
fumecheng-11587	106	21	and	and	CCONJ
fumecheng-11587	106	22	usage	usage	NOUN
fumecheng-11587	106	23	of	of	ADP
fumecheng-11587	106	24	basins	basin	NOUN
fumecheng-11587	106	25	of	of	ADP
fumecheng-11587	106	26	attraction	attraction	NOUN
fumecheng-11587	106	27	to	to	PART
fumecheng-11587	106	28	determine	determine	VERB
fumecheng-11587	106	29	stability	stability	NOUN
fumecheng-11587	106	30	of	of	ADP
fumecheng-11587	106	31	the	the	DET
fumecheng-11587	106	32	solution	solution	NOUN
fumecheng-11587	106	33	based	base	VERB
fumecheng-11587	106	34	on	on	ADP
fumecheng-11587	106	35	initial	initial	ADJ
fumecheng-11587	106	36	conditions	condition	NOUN
fumecheng-11587	106	37	.	.	PUNCT
fumecheng-11587	107	1	technical	technical	ADJ
fumecheng-11587	107	2	interest	interest	NOUN
fumecheng-11587	107	3	in	in	ADP
fumecheng-11587	107	4	considering	consider	VERB
fumecheng-11587	107	5	such	such	ADJ
fumecheng-11587	107	6	structural	structural	ADJ
fumecheng-11587	107	7	schemes	scheme	NOUN
fumecheng-11587	107	8	includes	include	VERB
fumecheng-11587	107	9	the	the	DET
fumecheng-11587	107	10	development	development	NOUN
fumecheng-11587	107	11	of	of	ADP
fumecheng-11587	107	12	mems	mem	NOUN
fumecheng-11587	107	13	/	/	SYM
fumecheng-11587	107	14	nems	nem	NOUN
fumecheng-11587	107	15	devices	device	NOUN
fumecheng-11587	107	16	composed	compose	VERB
fumecheng-11587	107	17	of	of	ADP
fumecheng-11587	107	18	small	small	ADJ
fumecheng-11587	107	19	beams	beam	NOUN
fumecheng-11587	107	20	that	that	PRON
fumecheng-11587	107	21	can	can	AUX
fumecheng-11587	107	22	vibrate	vibrate	VERB
fumecheng-11587	107	23	on	on	ADP
fumecheng-11587	107	24	a	a	DET
fumecheng-11587	107	25	broad	broad	ADJ
fumecheng-11587	107	26	type	type	NOUN
fumecheng-11587	107	27	of	of	ADP
fumecheng-11587	107	28	elastic	elastic	ADJ
fumecheng-11587	107	29	supports	support	NOUN
fumecheng-11587	107	30	.	.	PUNCT
fumecheng-11587	108	1	in	in	ADP
fumecheng-11587	108	2	the	the	DET
fumecheng-11587	108	3	practical	practical	ADJ
fumecheng-11587	108	4	implementation	implementation	NOUN
fumecheng-11587	108	5	,	,	PUNCT
fumecheng-11587	108	6	specific	specific	ADJ
fumecheng-11587	108	7	end	end	NOUN
fumecheng-11587	108	8	supports	support	NOUN
fumecheng-11587	108	9	might	might	AUX
fumecheng-11587	108	10	be	be	AUX
fumecheng-11587	108	11	preferable	preferable	ADJ
fumecheng-11587	108	12	.	.	PUNCT
fumecheng-11587	109	1	therefore	therefore	ADV
fumecheng-11587	109	2	,	,	PUNCT
fumecheng-11587	109	3	three	three	NUM
fumecheng-11587	109	4	different	different	ADJ
fumecheng-11587	109	5	boundary	boundary	ADJ
fumecheng-11587	109	6	conditions	condition	NOUN
fumecheng-11587	109	7	are	be	AUX
fumecheng-11587	109	8	considered	consider	VERB
fumecheng-11587	109	9	to	to	PART
fumecheng-11587	109	10	demonstrate	demonstrate	VERB
fumecheng-11587	109	11	their	their	PRON
fumecheng-11587	109	12	influence	influence	NOUN
fumecheng-11587	109	13	on	on	ADP
fumecheng-11587	109	14	vibration	vibration	NOUN
fumecheng-11587	109	15	behavior	behavior	NOUN
fumecheng-11587	109	16	.	.	PUNCT
fumecheng-11587	110	1	vibration	vibration	NOUN
fumecheng-11587	110	2	and	and	CCONJ
fumecheng-11587	110	3	stability	stability	NOUN
fumecheng-11587	110	4	of	of	ADP
fumecheng-11587	110	5	a	a	DET
fumecheng-11587	110	6	nonlinear	nonlinear	ADJ
fumecheng-11587	110	7	nonlocal	nonlocal	ADJ
fumecheng-11587	110	8	strain	strain	NOUN
fumecheng-11587	110	9	-	-	PUNCT
fumecheng-11587	110	10	gradient	gradient	NOUN
fumecheng-11587	110	11	fg	fg	PROPN
fumecheng-11587	110	12	beam	beam	NOUN
fumecheng-11587	110	13	on	on	ADP
fumecheng-11587	110	14	a	a	DET
fumecheng-11587	110	15	visco	visco	ADJ
fumecheng-11587	110	16	-	-	PUNCT
fumecheng-11587	110	17	pasternak	pasternak	NOUN
fumecheng-11587	110	18	...	...	PUNCT
fumecheng-11587	110	19	713	713	NUM
fumecheng-11587	110	20	2	2	NUM
fumecheng-11587	110	21	.	.	PUNCT
fumecheng-11587	110	22	governing	govern	VERB
fumecheng-11587	110	23	equation	equation	NOUN
fumecheng-11587	110	24	of	of	ADP
fumecheng-11587	110	25	fg	fg	PROPN
fumecheng-11587	110	26	beam	beam	PROPN
fumecheng-11587	110	27	on	on	ADP
fumecheng-11587	110	28	a	a	DET
fumecheng-11587	110	29	visco	visco	ADJ
fumecheng-11587	110	30	-	-	PUNCT
fumecheng-11587	110	31	pasternak	pasternak	PROPN
fumecheng-11587	110	32	foundation	foundation	NOUN
fumecheng-11587	110	33	let	let	VERB
fumecheng-11587	110	34	us	we	PRON
fumecheng-11587	110	35	consider	consider	VERB
fumecheng-11587	110	36	a	a	DET
fumecheng-11587	110	37	mechanical	mechanical	ADJ
fumecheng-11587	110	38	model	model	NOUN
fumecheng-11587	110	39	of	of	ADP
fumecheng-11587	110	40	a	a	DET
fumecheng-11587	110	41	beam	beam	NOUN
fumecheng-11587	110	42	as	as	SCONJ
fumecheng-11587	110	43	given	give	VERB
fumecheng-11587	110	44	in	in	ADP
fumecheng-11587	110	45	fig	fig	NOUN
fumecheng-11587	110	46	.	.	PUNCT
fumecheng-11587	111	1	1	1	X
fumecheng-11587	111	2	.	.	X
fumecheng-11587	111	3	relations	relation	NOUN
fumecheng-11587	111	4	for	for	ADP
fumecheng-11587	111	5	young	young	ADJ
fumecheng-11587	111	6	's	's	PART
fumecheng-11587	111	7	modulus	modulus	NOUN
fumecheng-11587	111	8	and	and	CCONJ
fumecheng-11587	111	9	density	density	NOUN
fumecheng-11587	111	10	of	of	ADP
fumecheng-11587	111	11	fg	fg	PROPN
fumecheng-11587	111	12	beam	beam	PROPN
fumecheng-11587	111	13	,	,	PUNCT
fumecheng-11587	111	14	as	as	ADV
fumecheng-11587	111	15	well	well	ADV
fumecheng-11587	111	16	as	as	ADP
fumecheng-11587	111	17	relations	relation	NOUN
fumecheng-11587	111	18	for	for	ADP
fumecheng-11587	111	19	the	the	DET
fumecheng-11587	111	20	nonlocal	nonlocal	ADJ
fumecheng-11587	111	21	strain	strain	NOUN
fumecheng-11587	111	22	gradient	gradient	NOUN
fumecheng-11587	111	23	theory	theory	NOUN
fumecheng-11587	111	24	can	can	AUX
fumecheng-11587	111	25	be	be	AUX
fumecheng-11587	111	26	found	find	VERB
fumecheng-11587	111	27	in	in	ADP
fumecheng-11587	111	28	the	the	DET
fumecheng-11587	111	29	appendix	appendix	NOUN
fumecheng-11587	111	30	of	of	ADP
fumecheng-11587	111	31	the	the	DET
fumecheng-11587	111	32	paper	paper	NOUN
fumecheng-11587	111	33	[	[	X
fumecheng-11587	111	34	27	27	NUM
fumecheng-11587	111	35	]	]	PUNCT
fumecheng-11587	111	36	.	.	PUNCT
fumecheng-11587	112	1	fig	fig	NOUN
fumecheng-11587	112	2	.	.	PUNCT
fumecheng-11587	113	1	1	1	NUM
fumecheng-11587	113	2	model	model	NOUN
fumecheng-11587	113	3	of	of	ADP
fumecheng-11587	113	4	the	the	DET
fumecheng-11587	113	5	simply	simply	ADV
fumecheng-11587	113	6	-	-	PUNCT
fumecheng-11587	113	7	supported	support	VERB
fumecheng-11587	113	8	nonlinear	nonlinear	ADJ
fumecheng-11587	113	9	nonlocal	nonlocal	ADJ
fumecheng-11587	113	10	strain	strain	NOUN
fumecheng-11587	113	11	gradient	gradient	NOUN
fumecheng-11587	113	12	fg	fg	PROPN
fumecheng-11587	113	13	beam	beam	PROPN
fumecheng-11587	113	14	resting	rest	VERB
fumecheng-11587	113	15	on	on	ADP
fumecheng-11587	113	16	a	a	DET
fumecheng-11587	113	17	visco	visco	ADJ
fumecheng-11587	113	18	-	-	PUNCT
fumecheng-11587	113	19	pasternak	pasternak	PROPN
fumecheng-11587	113	20	foundation	foundation	NOUN
fumecheng-11587	113	21	and	and	CCONJ
fumecheng-11587	113	22	excited	excite	VERB
fumecheng-11587	113	23	by	by	ADP
fumecheng-11587	113	24	traverse	traverse	NOUN
fumecheng-11587	113	25	load	load	NOUN
fumecheng-11587	113	26	the	the	DET
fumecheng-11587	113	27	displacement	displacement	ADJ
fumecheng-11587	113	28	field	field	NOUN
fumecheng-11587	113	29	of	of	ADP
fumecheng-11587	113	30	the	the	DET
fumecheng-11587	113	31	euler	euler	PROPN
fumecheng-11587	113	32	-	-	PUNCT
fumecheng-11587	113	33	bernoulli	bernoulli	PROPN
fumecheng-11587	113	34	beam	beam	NOUN
fumecheng-11587	113	35	is	be	AUX
fumecheng-11587	113	36	given	give	VERB
fumecheng-11587	113	37	as	as	ADP
fumecheng-11587	113	38	:	:	PUNCT
fumecheng-11587	113	39	𝑢𝑥(𝑥	𝑢𝑥(𝑥	NUM
fumecheng-11587	113	40	,	,	PUNCT
fumecheng-11587	113	41	𝑧	𝑧	X
fumecheng-11587	113	42	,	,	PUNCT
fumecheng-11587	113	43	𝑡	𝑡	NOUN
fumecheng-11587	113	44	)	)	PUNCT
fumecheng-11587	113	45	=	=	SYM
fumecheng-11587	113	46	𝑢(𝑥	𝑢(𝑥	PROPN
fumecheng-11587	113	47	,	,	PUNCT
fumecheng-11587	113	48	𝑡	𝑡	NOUN
fumecheng-11587	113	49	)	)	PUNCT
fumecheng-11587	113	50	−	−	ADP
fumecheng-11587	113	51	𝑧	𝑧	DET
fumecheng-11587	113	52	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-11587	113	53	𝜕𝑥	𝜕𝑥	X
fumecheng-11587	113	54	,	,	PUNCT
fumecheng-11587	113	55	𝑢𝑦(𝑥	𝑢𝑦(𝑥	NOUN
fumecheng-11587	113	56	,	,	PUNCT
fumecheng-11587	113	57	𝑧	𝑧	NOUN
fumecheng-11587	113	58	,	,	PUNCT
fumecheng-11587	113	59	𝑡	𝑡	NOUN
fumecheng-11587	113	60	)	)	PUNCT
fumecheng-11587	113	61	=	=	SYM
fumecheng-11587	113	62	0	0	NUM
fumecheng-11587	113	63	,	,	PUNCT
fumecheng-11587	113	64	𝑢𝑧(𝑥	𝑢𝑧(𝑥	NUM
fumecheng-11587	113	65	,	,	PUNCT
fumecheng-11587	113	66	𝑧	𝑧	NOUN
fumecheng-11587	113	67	,	,	PUNCT
fumecheng-11587	113	68	𝑡	𝑡	NOUN
fumecheng-11587	113	69	)	)	PUNCT
fumecheng-11587	113	70	=	=	SYM
fumecheng-11587	113	71	𝑤(𝑥	𝑤(𝑥	NOUN
fumecheng-11587	113	72	,	,	PUNCT
fumecheng-11587	113	73	𝑡	𝑡	NOUN
fumecheng-11587	113	74	)	)	PUNCT
fumecheng-11587	113	75	,	,	PUNCT
fumecheng-11587	113	76	(	(	PUNCT
fumecheng-11587	113	77	1	1	X
fumecheng-11587	113	78	)	)	PUNCT
fumecheng-11587	113	79	where	where	SCONJ
fumecheng-11587	113	80	ux	ux	PROPN
fumecheng-11587	113	81	,	,	PUNCT
fumecheng-11587	113	82	uy	uy	PROPN
fumecheng-11587	113	83	,	,	PUNCT
fumecheng-11587	113	84	and	and	CCONJ
fumecheng-11587	113	85	uz	uz	PROPN
fumecheng-11587	113	86	denote	denote	VERB
fumecheng-11587	113	87	the	the	DET
fumecheng-11587	113	88	displacements	displacement	NOUN
fumecheng-11587	113	89	along	along	ADP
fumecheng-11587	113	90	with	with	ADP
fumecheng-11587	113	91	the	the	DET
fumecheng-11587	113	92	length	length	NOUN
fumecheng-11587	113	93	,	,	PUNCT
fumecheng-11587	113	94	width	width	ADJ
fumecheng-11587	113	95	,	,	PUNCT
fumecheng-11587	113	96	and	and	CCONJ
fumecheng-11587	113	97	thickness	thickness	NOUN
fumecheng-11587	113	98	directions	direction	NOUN
fumecheng-11587	113	99	,	,	PUNCT
fumecheng-11587	113	100	described	describe	VERB
fumecheng-11587	113	101	by	by	ADP
fumecheng-11587	113	102	x	x	PROPN
fumecheng-11587	113	103	,	,	PUNCT
fumecheng-11587	113	104	y	y	PROPN
fumecheng-11587	113	105	and	and	CCONJ
fumecheng-11587	113	106	z	z	PROPN
fumecheng-11587	113	107	coordinates	coordinate	NOUN
fumecheng-11587	113	108	,	,	PUNCT
fumecheng-11587	113	109	respectively	respectively	ADV
fumecheng-11587	113	110	.	.	PUNCT
fumecheng-11587	114	1	functions	function	NOUN
fumecheng-11587	114	2	u	u	PROPN
fumecheng-11587	114	3	and	and	CCONJ
fumecheng-11587	114	4	w	w	NOUN
fumecheng-11587	114	5	are	be	AUX
fumecheng-11587	114	6	the	the	DET
fumecheng-11587	114	7	axial	axial	ADJ
fumecheng-11587	114	8	and	and	CCONJ
fumecheng-11587	114	9	transverse	transverse	NOUN
fumecheng-11587	114	10	displacements	displacement	NOUN
fumecheng-11587	114	11	of	of	ADP
fumecheng-11587	114	12	the	the	DET
fumecheng-11587	114	13	physical	physical	ADJ
fumecheng-11587	114	14	middle	middle	ADJ
fumecheng-11587	114	15	surface	surface	NOUN
fumecheng-11587	114	16	,	,	PUNCT
fumecheng-11587	114	17	respectively	respectively	ADV
fumecheng-11587	114	18	.	.	PUNCT
fumecheng-11587	115	1	the	the	DET
fumecheng-11587	115	2	only	only	ADJ
fumecheng-11587	115	3	nonzero	nonzero	ADJ
fumecheng-11587	115	4	strain	strain	NOUN
fumecheng-11587	115	5	component	component	NOUN
fumecheng-11587	115	6	of	of	ADP
fumecheng-11587	115	7	the	the	DET
fumecheng-11587	115	8	euler	euler	NOUN
fumecheng-11587	115	9	-	-	PUNCT
fumecheng-11587	115	10	bernoulli	bernoulli	PROPN
fumecheng-11587	115	11	beam	beam	NOUN
fumecheng-11587	115	12	is	be	AUX
fumecheng-11587	115	13	described	describe	VERB
fumecheng-11587	115	14	in	in	ADP
fumecheng-11587	115	15	terms	term	NOUN
fumecheng-11587	115	16	of	of	ADP
fumecheng-11587	115	17	displacements	displacement	NOUN
fumecheng-11587	115	18	with	with	ADP
fumecheng-11587	115	19	von	von	PROPN
fumecheng-11587	115	20	kármán	kármán	PROPN
fumecheng-11587	115	21	's	's	PART
fumecheng-11587	115	22	nonlinearity	nonlinearity	NOUN
fumecheng-11587	115	23	as	as	ADP
fumecheng-11587	115	24	𝜀𝑥𝑥	𝜀𝑥𝑥	NOUN
fumecheng-11587	115	25	=	=	SYM
fumecheng-11587	115	26	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-11587	115	27	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-11587	115	28	+	+	CCONJ
fumecheng-11587	115	29	1	1	NUM
fumecheng-11587	115	30	2	2	NUM
fumecheng-11587	115	31	(	(	PUNCT
fumecheng-11587	115	32	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-11587	115	33	𝜕𝑥	𝜕𝑥	X
fumecheng-11587	115	34	)	)	PUNCT
fumecheng-11587	115	35	2	2	NUM
fumecheng-11587	115	36	−	−	NOUN
fumecheng-11587	115	37	𝑧	𝑧	PROPN
fumecheng-11587	115	38	𝜕2𝑤	𝜕2𝑤	PROPN
fumecheng-11587	115	39	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-11587	115	40	.	.	PUNCT
fumecheng-11587	116	1	(	(	PUNCT
fumecheng-11587	116	2	2	2	X
fumecheng-11587	116	3	)	)	PUNCT
fumecheng-11587	116	4	following	follow	VERB
fumecheng-11587	116	5	stress	stress	NOUN
fumecheng-11587	116	6	resultants	resultant	NOUN
fumecheng-11587	116	7	are	be	AUX
fumecheng-11587	116	8	considered	consider	VERB
fumecheng-11587	116	9	in	in	ADP
fumecheng-11587	116	10	further	further	ADJ
fumecheng-11587	116	11	study	study	NOUN
fumecheng-11587	116	12	:	:	PUNCT
fumecheng-11587	116	13	𝑁𝑥𝑥	𝑁𝑥𝑥	NOUN
fumecheng-11587	116	14	=	=	SYM
fumecheng-11587	116	15	∫	∫	PROPN
fumecheng-11587	116	16	𝑡𝑥𝑥𝑑𝐴	𝑡𝑥𝑥𝑑𝐴	PROPN
fumecheng-11587	116	17	𝐴	𝐴	PROPN
fumecheng-11587	116	18	,	,	PUNCT
fumecheng-11587	116	19	𝑁𝑥𝑥	𝑁𝑥𝑥	PROPN
fumecheng-11587	116	20	(	(	PUNCT
fumecheng-11587	116	21	0	0	NUM
fumecheng-11587	116	22	)	)	PUNCT
fumecheng-11587	117	1	=	=	SYM
fumecheng-11587	117	2	∫	∫	PROPN
fumecheng-11587	118	1	𝜎𝑥𝑥𝑑𝐴	𝜎𝑥𝑥𝑑𝐴	PROPN
fumecheng-11587	118	2	,	,	PUNCT
fumecheng-11587	118	3	𝐴	𝐴	PROPN
fumecheng-11587	118	4	𝑁𝑥𝑥	𝑁𝑥𝑥	PROPN
fumecheng-11587	118	5	(	(	PUNCT
fumecheng-11587	118	6	1	1	NUM
fumecheng-11587	118	7	)	)	PUNCT
fumecheng-11587	118	8	=	=	SYM
fumecheng-11587	119	1	∫	∫	PROPN
fumecheng-11587	119	2	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
fumecheng-11587	119	3	(	(	PUNCT
fumecheng-11587	119	4	1	1	X
fumecheng-11587	119	5	)	)	PUNCT
fumecheng-11587	119	6	𝑑𝐴	𝑑𝐴	NOUN
fumecheng-11587	119	7	,	,	PUNCT
fumecheng-11587	119	8	𝐴	𝐴	PROPN
fumecheng-11587	119	9	𝑀	𝑀	PROPN
fumecheng-11587	119	10	=	=	SYM
fumecheng-11587	119	11	∫	∫	PROPN
fumecheng-11587	119	12	𝑧𝑡𝑥𝑥𝑑𝐴	𝑧𝑡𝑥𝑥𝑑𝐴	PROPN
fumecheng-11587	119	13	𝐴	𝐴	PROPN
fumecheng-11587	119	14	,	,	PUNCT
fumecheng-11587	119	15	𝑀(0	𝑀(0	X
fumecheng-11587	119	16	)	)	PUNCT
fumecheng-11587	119	17	=	=	SYM
fumecheng-11587	120	1	∫	∫	PROPN
fumecheng-11587	120	2	𝑧𝜎𝑥𝑥𝑑𝐴	𝑧𝜎𝑥𝑥𝑑𝐴	PROPN
fumecheng-11587	120	3	𝐴	𝐴	PROPN
fumecheng-11587	120	4	,	,	PUNCT
fumecheng-11587	120	5	𝑀(1	𝑀(1	NOUN
fumecheng-11587	120	6	)	)	PUNCT
fumecheng-11587	120	7	=	=	SYM
fumecheng-11587	121	1	∫	∫	PROPN
fumecheng-11587	121	2	𝑧𝜎𝑥𝑥	𝑧𝜎𝑥𝑥	PROPN
fumecheng-11587	121	3	(	(	PUNCT
fumecheng-11587	121	4	1	1	X
fumecheng-11587	121	5	)	)	PUNCT
fumecheng-11587	121	6	𝑑𝐴.	𝑑𝐴.	PROPN
fumecheng-11587	121	7	𝐴	𝐴	NOUN
fumecheng-11587	121	8	(	(	PUNCT
fumecheng-11587	121	9	3	3	NUM
fumecheng-11587	121	10	)	)	PUNCT
fumecheng-11587	121	11	where	where	SCONJ
fumecheng-11587	121	12	nxx	nxx	PROPN
fumecheng-11587	121	13	,	,	PUNCT
fumecheng-11587	121	14	n(0	n(0	PROPN
fumecheng-11587	121	15	)	)	PUNCT
fumecheng-11587	121	16	xx	xx	NUM
fumecheng-11587	121	17	and	and	CCONJ
fumecheng-11587	121	18	n(1	n(1	NOUN
fumecheng-11587	121	19	)	)	PUNCT
fumecheng-11587	121	20	xx	xx	NUM
fumecheng-11587	121	21	are	be	AUX
fumecheng-11587	121	22	axial	axial	ADJ
fumecheng-11587	121	23	forces	force	NOUN
fumecheng-11587	121	24	due	due	ADJ
fumecheng-11587	121	25	to	to	ADP
fumecheng-11587	121	26	total	total	ADJ
fumecheng-11587	121	27	stress	stress	NOUN
fumecheng-11587	121	28	txx	txx	NOUN
fumecheng-11587	121	29	,	,	PUNCT
fumecheng-11587	121	30	nonlocal	nonlocal	ADJ
fumecheng-11587	121	31	stress	stress	NOUN
fumecheng-11587	121	32	σxx	σxx	NOUN
fumecheng-11587	121	33	and	and	CCONJ
fumecheng-11587	121	34	high	high	ADJ
fumecheng-11587	121	35	-	-	PUNCT
fumecheng-11587	121	36	order	order	NOUN
fumecheng-11587	121	37	nonlocal	nonlocal	ADJ
fumecheng-11587	121	38	stress	stress	NOUN
fumecheng-11587	121	39	σ(1	σ(1	PROPN
fumecheng-11587	121	40	)	)	PUNCT
fumecheng-11587	121	41	xx	xx	PROPN
fumecheng-11587	121	42	,	,	PUNCT
fumecheng-11587	121	43	respectively	respectively	ADV
fumecheng-11587	121	44	.	.	PUNCT
fumecheng-11587	122	1	all	all	DET
fumecheng-11587	122	2	stresses	stress	NOUN
fumecheng-11587	122	3	are	be	AUX
fumecheng-11587	122	4	in	in	ADP
fumecheng-11587	122	5	axial	axial	ADJ
fumecheng-11587	122	6	direction	direction	NOUN
fumecheng-11587	122	7	.	.	PUNCT
fumecheng-11587	123	1	m	m	PROPN
fumecheng-11587	123	2	,	,	PUNCT
fumecheng-11587	123	3	m(0	m(0	PROPN
fumecheng-11587	123	4	)	)	PUNCT
fumecheng-11587	123	5	and	and	CCONJ
fumecheng-11587	123	6	m(1	m(1	NOUN
fumecheng-11587	123	7	)	)	PUNCT
fumecheng-11587	123	8	are	be	AUX
fumecheng-11587	123	9	bending	bend	VERB
fumecheng-11587	123	10	moments	moment	NOUN
fumecheng-11587	123	11	resulting	result	VERB
fumecheng-11587	123	12	from	from	ADP
fumecheng-11587	123	13	the	the	DET
fumecheng-11587	123	14	following	follow	VERB
fumecheng-11587	123	15	stresses	stress	NOUN
fumecheng-11587	123	16	in	in	ADP
fumecheng-11587	123	17	axial	axial	ADJ
fumecheng-11587	123	18	direction	direction	NOUN
fumecheng-11587	123	19	:	:	PUNCT
fumecheng-11587	123	20	total	total	ADJ
fumecheng-11587	123	21	,	,	PUNCT
fumecheng-11587	123	22	nonlocal	nonlocal	ADJ
fumecheng-11587	123	23	and	and	CCONJ
fumecheng-11587	123	24	high	high	ADJ
fumecheng-11587	123	25	-	-	PUNCT
fumecheng-11587	123	26	order	order	NOUN
fumecheng-11587	123	27	nonlocal	nonlocal	ADJ
fumecheng-11587	123	28	,	,	PUNCT
fumecheng-11587	123	29	respectively	respectively	ADV
fumecheng-11587	123	30	.	.	PUNCT
fumecheng-11587	124	1	additionally	additionally	ADV
fumecheng-11587	124	2	,	,	PUNCT
fumecheng-11587	124	3	the	the	DET
fumecheng-11587	124	4	extensional	extensional	ADJ
fumecheng-11587	124	5	axx	axx	PROPN
fumecheng-11587	124	6	and	and	CCONJ
fumecheng-11587	124	7	the	the	DET
fumecheng-11587	124	8	bending	bend	VERB
fumecheng-11587	124	9	coefficient	coefficient	NOUN
fumecheng-11587	124	10	dxx	dxx	PROPN
fumecheng-11587	124	11	are	be	AUX
fumecheng-11587	124	12	defined	define	VERB
fumecheng-11587	124	13	in	in	ADP
fumecheng-11587	124	14	the	the	DET
fumecheng-11587	124	15	following	follow	VERB
fumecheng-11587	124	16	form	form	NOUN
fumecheng-11587	124	17	:	:	PUNCT
fumecheng-11587	124	18	{	{	PUNCT
fumecheng-11587	124	19	𝐴𝑥𝑥	𝐴𝑥𝑥	PROPN
fumecheng-11587	124	20	,	,	PUNCT
fumecheng-11587	124	21	𝐷𝑥𝑥	𝐷𝑥𝑥	PROPN
fumecheng-11587	124	22	}	}	PUNCT
fumecheng-11587	124	23	=	=	SYM
fumecheng-11587	125	1	𝑏	𝑏	PROPN
fumecheng-11587	125	2	∫	∫	PROPN
fumecheng-11587	125	3	{	{	PUNCT
fumecheng-11587	125	4	1	1	NUM
fumecheng-11587	125	5	,	,	PUNCT
fumecheng-11587	125	6	𝑧2	𝑧2	NOUN
fumecheng-11587	125	7	}	}	PUNCT
fumecheng-11587	125	8	𝐻/2−𝑐	𝐻/2−𝑐	PROPN
fumecheng-11587	125	9	−𝐻/2−𝑐	−𝐻/2−𝑐	PROPN
fumecheng-11587	125	10	𝐸(𝑧)𝑑𝑧	𝐸(𝑧)𝑑𝑧	PROPN
fumecheng-11587	125	11	,	,	PUNCT
fumecheng-11587	125	12	(	(	PUNCT
fumecheng-11587	125	13	4	4	X
fumecheng-11587	125	14	)	)	PUNCT
fumecheng-11587	125	15	where	where	SCONJ
fumecheng-11587	125	16	h	h	NOUN
fumecheng-11587	125	17	represents	represent	VERB
fumecheng-11587	125	18	the	the	DET
fumecheng-11587	125	19	beam	beam	NOUN
fumecheng-11587	125	20	height	height	NOUN
fumecheng-11587	125	21	and	and	CCONJ
fumecheng-11587	125	22	c	c	NOUN
fumecheng-11587	125	23	is	be	AUX
fumecheng-11587	125	24	the	the	DET
fumecheng-11587	125	25	distance	distance	NOUN
fumecheng-11587	125	26	between	between	ADP
fumecheng-11587	125	27	physical	physical	ADJ
fumecheng-11587	125	28	and	and	CCONJ
fumecheng-11587	125	29	geometrical	geometrical	ADJ
fumecheng-11587	125	30	middle	middle	ADJ
fumecheng-11587	125	31	surfaces	surface	NOUN
fumecheng-11587	125	32	of	of	ADP
fumecheng-11587	125	33	the	the	DET
fumecheng-11587	125	34	beam	beam	NOUN
fumecheng-11587	125	35	.	.	PUNCT
fumecheng-11587	126	1	note	note	VERB
fumecheng-11587	126	2	that	that	SCONJ
fumecheng-11587	126	3	for	for	ADP
fumecheng-11587	126	4	homogeneous	homogeneous	ADJ
fumecheng-11587	126	5	beam	beam	NOUN
fumecheng-11587	126	6	axx	axx	PROPN
fumecheng-11587	126	7	=	=	SYM
fumecheng-11587	126	8	ea	ea	PROPN
fumecheng-11587	126	9	and	and	CCONJ
fumecheng-11587	126	10	dxx	dxx	PROPN
fumecheng-11587	126	11	=	=	SYM
fumecheng-11587	126	12	ei	ei	PROPN
fumecheng-11587	126	13	,	,	PUNCT
fumecheng-11587	126	14	with	with	ADP
fumecheng-11587	126	15	714	714	NUM
fumecheng-11587	126	16	n.	n.	NOUN
fumecheng-11587	126	17	nešić	nešić	PROPN
fumecheng-11587	126	18	,	,	PUNCT
fumecheng-11587	126	19	m.	m.	NOUN
fumecheng-11587	126	20	cajić	cajić	NOUN
fumecheng-11587	126	21	,	,	PUNCT
fumecheng-11587	126	22	d.	d.	PROPN
fumecheng-11587	126	23	karličić	karličić	PROPN
fumecheng-11587	126	24	,	,	PUNCT
fumecheng-11587	126	25	m.	m.	NOUN
fumecheng-11587	126	26	lazarević	lazarević	PROPN
fumecheng-11587	126	27	,	,	PUNCT
fumecheng-11587	126	28	s.	s.	PROPN
fumecheng-11587	126	29	adhikari	adhikari	PROPN
fumecheng-11587	126	30	e	e	PROPN
fumecheng-11587	126	31	denoting	denote	VERB
fumecheng-11587	126	32	young	young	PROPN
fumecheng-11587	126	33	’s	’s	PART
fumecheng-11587	126	34	modulus	modulus	NOUN
fumecheng-11587	126	35	,	,	PUNCT
fumecheng-11587	126	36	a	a	DET
fumecheng-11587	126	37	cross	cross	ADJ
fumecheng-11587	126	38	sectional	sectional	ADJ
fumecheng-11587	126	39	area	area	NOUN
fumecheng-11587	126	40	and	and	CCONJ
fumecheng-11587	126	41	i	i	PRON
fumecheng-11587	126	42	second	second	ADJ
fumecheng-11587	126	43	moment	moment	NOUN
fumecheng-11587	126	44	of	of	ADP
fumecheng-11587	126	45	area	area	NOUN
fumecheng-11587	126	46	.	.	PUNCT
fumecheng-11587	127	1	reaction	reaction	NOUN
fumecheng-11587	127	2	force	force	NOUN
fumecheng-11587	127	3	of	of	ADP
fumecheng-11587	127	4	the	the	DET
fumecheng-11587	127	5	visco	visco	ADJ
fumecheng-11587	127	6	-	-	PUNCT
fumecheng-11587	127	7	pasternak	pasternak	PROPN
fumecheng-11587	127	8	foundation	foundation	NOUN
fumecheng-11587	127	9	acting	act	VERB
fumecheng-11587	127	10	on	on	ADP
fumecheng-11587	127	11	the	the	DET
fumecheng-11587	127	12	beam	beam	NOUN
fumecheng-11587	127	13	is	be	AUX
fumecheng-11587	127	14	defined	define	VERB
fumecheng-11587	127	15	as	as	ADP
fumecheng-11587	127	16	[	[	X
fumecheng-11587	127	17	27	27	NUM
fumecheng-11587	127	18	]	]	SYM
fumecheng-11587	127	19	:	:	PUNCT
fumecheng-11587	128	1	𝐹𝑚	𝐹𝑚	NUM
fumecheng-11587	128	2	=	=	SYM
fumecheng-11587	128	3	(	(	PUNCT
fumecheng-11587	128	4	𝑘𝑤	𝑘𝑤	ADP
fumecheng-11587	128	5	+	+	CCONJ
fumecheng-11587	128	6	𝐾𝑤	𝐾𝑤	PROPN
fumecheng-11587	128	7	𝜕	𝜕	PROPN
fumecheng-11587	128	8	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-11587	128	9	)	)	PUNCT
fumecheng-11587	128	10	𝑤	𝑤	ADP
fumecheng-11587	128	11	−	−	PROPN
fumecheng-11587	128	12	(	(	PUNCT
fumecheng-11587	128	13	𝑘𝑔	𝑘𝑔	VERB
fumecheng-11587	128	14	+	+	CCONJ
fumecheng-11587	128	15	𝐾𝑔	𝐾𝑔	PROPN
fumecheng-11587	128	16	𝜕	𝜕	PROPN
fumecheng-11587	128	17	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-11587	128	18	)	)	PUNCT
fumecheng-11587	129	1	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-11587	129	2	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-11587	129	3	,	,	PUNCT
fumecheng-11587	129	4	(	(	PUNCT
fumecheng-11587	129	5	5	5	NUM
fumecheng-11587	129	6	)	)	PUNCT
fumecheng-11587	129	7	with	with	ADP
fumecheng-11587	129	8	the	the	DET
fumecheng-11587	129	9	elastic	elastic	ADJ
fumecheng-11587	129	10	pasternak	pasternak	NOUN
fumecheng-11587	129	11	parameters	parameter	NOUN
fumecheng-11587	129	12	kw	kw	VERB
fumecheng-11587	129	13	,	,	PUNCT
fumecheng-11587	129	14	kg	kg	INTJ
fumecheng-11587	129	15	and	and	CCONJ
fumecheng-11587	129	16	viscose	viscose	VERB
fumecheng-11587	129	17	constants	constant	NOUN
fumecheng-11587	129	18	kw	kw	VERB
fumecheng-11587	129	19	,	,	PUNCT
fumecheng-11587	129	20	kg	kg	PRON
fumecheng-11587	129	21	shown	show	VERB
fumecheng-11587	129	22	in	in	ADP
fumecheng-11587	129	23	fig	fig	NOUN
fumecheng-11587	129	24	.	.	PUNCT
fumecheng-11587	130	1	1	1	X
fumecheng-11587	130	2	.	.	X
fumecheng-11587	130	3	note	note	VERB
fumecheng-11587	130	4	that	that	SCONJ
fumecheng-11587	130	5	the	the	DET
fumecheng-11587	130	6	time	time	NOUN
fumecheng-11587	130	7	derivative	derivative	ADJ
fumecheng-11587	130	8	in	in	ADP
fumecheng-11587	130	9	eq	eq	ADP
fumecheng-11587	130	10	.	.	PUNCT
fumecheng-11587	131	1	(	(	PUNCT
fumecheng-11587	131	2	5	5	X
fumecheng-11587	131	3	)	)	PUNCT
fumecheng-11587	131	4	is	be	AUX
fumecheng-11587	131	5	in	in	ADP
fumecheng-11587	131	6	the	the	DET
fumecheng-11587	131	7	paper	paper	NOUN
fumecheng-11587	131	8	[	[	X
fumecheng-11587	131	9	27	27	NUM
fumecheng-11587	131	10	]	]	PUNCT
fumecheng-11587	131	11	replaced	replace	VERB
fumecheng-11587	131	12	with	with	ADP
fumecheng-11587	131	13	a	a	DET
fumecheng-11587	131	14	more	more	ADV
fumecheng-11587	131	15	general	general	ADJ
fumecheng-11587	131	16	fractional	fractional	ADJ
fumecheng-11587	131	17	derivative	derivative	NOUN
fumecheng-11587	131	18	,	,	PUNCT
fumecheng-11587	131	19	being	be	AUX
fumecheng-11587	131	20	a	a	DET
fumecheng-11587	131	21	real	real	ADJ
fumecheng-11587	131	22	number	number	NOUN
fumecheng-11587	131	23	,	,	PUNCT
fumecheng-11587	131	24	with	with	ADP
fumecheng-11587	131	25	values	value	NOUN
fumecheng-11587	131	26	between	between	ADP
fumecheng-11587	131	27	0	0	NUM
fumecheng-11587	131	28	and	and	CCONJ
fumecheng-11587	131	29	1	1	NUM
fumecheng-11587	131	30	that	that	PRON
fumecheng-11587	131	31	have	have	VERB
fumecheng-11587	131	32	a	a	DET
fumecheng-11587	131	33	physical	physical	ADJ
fumecheng-11587	131	34	meaning	meaning	NOUN
fumecheng-11587	131	35	.	.	PUNCT
fumecheng-11587	132	1	foundations	foundation	NOUN
fumecheng-11587	132	2	described	describe	VERB
fumecheng-11587	132	3	with	with	ADP
fumecheng-11587	132	4	fractional	fractional	ADJ
fumecheng-11587	132	5	derivatives	derivative	NOUN
fumecheng-11587	132	6	as	as	ADP
fumecheng-11587	132	7	in	in	ADP
fumecheng-11587	132	8	[	[	X
fumecheng-11587	132	9	27	27	NUM
fumecheng-11587	132	10	]	]	PUNCT
fumecheng-11587	132	11	are	be	AUX
fumecheng-11587	132	12	more	more	ADV
fumecheng-11587	132	13	general	general	ADJ
fumecheng-11587	132	14	and	and	CCONJ
fumecheng-11587	132	15	therefore	therefore	ADV
fumecheng-11587	132	16	can	can	AUX
fumecheng-11587	132	17	describe	describe	VERB
fumecheng-11587	132	18	a	a	DET
fumecheng-11587	132	19	broader	broad	ADJ
fumecheng-11587	132	20	range	range	NOUN
fumecheng-11587	132	21	of	of	ADP
fumecheng-11587	132	22	real	real	ADJ
fumecheng-11587	132	23	value	value	NOUN
fumecheng-11587	132	24	applications	application	NOUN
fumecheng-11587	132	25	.	.	PUNCT
fumecheng-11587	133	1	however	however	ADV
fumecheng-11587	133	2	,	,	PUNCT
fumecheng-11587	133	3	a	a	DET
fumecheng-11587	133	4	disadvantage	disadvantage	NOUN
fumecheng-11587	133	5	of	of	ADP
fumecheng-11587	133	6	the	the	DET
fumecheng-11587	133	7	fractional	fractional	ADJ
fumecheng-11587	133	8	derivative	derivative	ADJ
fumecheng-11587	133	9	model	model	NOUN
fumecheng-11587	133	10	is	be	AUX
fumecheng-11587	133	11	that	that	SCONJ
fumecheng-11587	133	12	a	a	DET
fumecheng-11587	133	13	stability	stability	NOUN
fumecheng-11587	133	14	analysis	analysis	NOUN
fumecheng-11587	133	15	of	of	ADP
fumecheng-11587	133	16	fractional	fractional	ADJ
fumecheng-11587	133	17	differential	differential	ADJ
fumecheng-11587	133	18	equations	equation	NOUN
fumecheng-11587	133	19	can	can	AUX
fumecheng-11587	133	20	not	not	PART
fumecheng-11587	133	21	be	be	AUX
fumecheng-11587	133	22	done	do	VERB
fumecheng-11587	133	23	with	with	ADP
fumecheng-11587	133	24	straightforward	straightforward	ADJ
fumecheng-11587	133	25	methods	method	NOUN
fumecheng-11587	133	26	presented	present	VERB
fumecheng-11587	133	27	in	in	ADP
fumecheng-11587	133	28	this	this	DET
fumecheng-11587	133	29	paper	paper	NOUN
fumecheng-11587	133	30	.	.	PUNCT
fumecheng-11587	134	1	after	after	ADP
fumecheng-11587	134	2	following	follow	VERB
fumecheng-11587	134	3	of	of	ADP
fumecheng-11587	134	4	the	the	DET
fumecheng-11587	134	5	procedure	procedure	NOUN
fumecheng-11587	134	6	presented	present	VERB
fumecheng-11587	134	7	in	in	ADP
fumecheng-11587	134	8	[	[	X
fumecheng-11587	134	9	27	27	NUM
fumecheng-11587	134	10	]	]	PUNCT
fumecheng-11587	134	11	,	,	PUNCT
fumecheng-11587	134	12	we	we	PRON
fumecheng-11587	134	13	obtain	obtain	VERB
fumecheng-11587	134	14	expressions	expression	NOUN
fumecheng-11587	134	15	for	for	ADP
fumecheng-11587	134	16	variations	variation	NOUN
fumecheng-11587	134	17	of	of	ADP
fumecheng-11587	134	18	strain	strain	NOUN
fumecheng-11587	134	19	,	,	PUNCT
fumecheng-11587	134	20	kinetic	kinetic	ADJ
fumecheng-11587	134	21	and	and	CCONJ
fumecheng-11587	134	22	external	external	ADJ
fumecheng-11587	134	23	energy	energy	NOUN
fumecheng-11587	134	24	.	.	PUNCT
fumecheng-11587	135	1	after	after	ADP
fumecheng-11587	135	2	applying	apply	VERB
fumecheng-11587	135	3	hamilton	hamilton	PROPN
fumecheng-11587	135	4	's	's	PART
fumecheng-11587	135	5	principle	principle	NOUN
fumecheng-11587	135	6	as	as	SCONJ
fumecheng-11587	135	7	given	give	VERB
fumecheng-11587	135	8	in	in	ADP
fumecheng-11587	135	9	[	[	X
fumecheng-11587	135	10	27	27	NUM
fumecheng-11587	135	11	]	]	PUNCT
fumecheng-11587	135	12	,	,	PUNCT
fumecheng-11587	135	13	two	two	NUM
fumecheng-11587	135	14	equations	equation	NOUN
fumecheng-11587	135	15	of	of	ADP
fumecheng-11587	135	16	motion	motion	NOUN
fumecheng-11587	135	17	are	be	AUX
fumecheng-11587	135	18	obtained	obtain	VERB
fumecheng-11587	135	19	.	.	PUNCT
fumecheng-11587	136	1	we	we	PRON
fumecheng-11587	136	2	assume	assume	VERB
fumecheng-11587	136	3	fast	fast	ADJ
fumecheng-11587	136	4	dynamics	dynamic	NOUN
fumecheng-11587	136	5	,	,	PUNCT
fumecheng-11587	136	6	which	which	PRON
fumecheng-11587	136	7	means	mean	VERB
fumecheng-11587	136	8	that	that	SCONJ
fumecheng-11587	136	9	acceleration	acceleration	NOUN
fumecheng-11587	136	10	in	in	ADP
fumecheng-11587	136	11	an	an	DET
fumecheng-11587	136	12	axial	axial	ADJ
fumecheng-11587	136	13	direction	direction	NOUN
fumecheng-11587	136	14	is	be	AUX
fumecheng-11587	136	15	negligible	negligible	ADJ
fumecheng-11587	136	16	.	.	PUNCT
fumecheng-11587	137	1	finally	finally	ADV
fumecheng-11587	137	2	,	,	PUNCT
fumecheng-11587	137	3	this	this	PRON
fumecheng-11587	137	4	leads	lead	VERB
fumecheng-11587	137	5	us	we	PRON
fumecheng-11587	137	6	to	to	ADP
fumecheng-11587	137	7	the	the	DET
fumecheng-11587	137	8	following	follow	VERB
fumecheng-11587	137	9	equation	equation	NOUN
fumecheng-11587	137	10	of	of	ADP
fumecheng-11587	137	11	motion	motion	NOUN
fumecheng-11587	137	12	of	of	ADP
fumecheng-11587	137	13	a	a	DET
fumecheng-11587	137	14	nonlinear	nonlinear	NOUN
fumecheng-11587	137	15	fg	fg	PROPN
fumecheng-11587	137	16	beam	beam	PROPN
fumecheng-11587	137	17	resting	rest	VERB
fumecheng-11587	137	18	on	on	ADP
fumecheng-11587	137	19	the	the	DET
fumecheng-11587	137	20	visco	visco	ADJ
fumecheng-11587	137	21	-	-	PUNCT
fumecheng-11587	137	22	pasternak	pasternak	PROPN
fumecheng-11587	137	23	foundation	foundation	NOUN
fumecheng-11587	137	24	:	:	PUNCT
fumecheng-11587	137	25	(	(	PUNCT
fumecheng-11587	137	26	1	1	NUM
fumecheng-11587	137	27	−	−	PROPN
fumecheng-11587	137	28	𝜇2	𝜇2	NOUN
fumecheng-11587	137	29	𝜕2	𝜕2	PUNCT
fumecheng-11587	137	30	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-11587	137	31	)	)	PUNCT
fumecheng-11587	138	1	[	[	X
fumecheng-11587	138	2	−	−	X
fumecheng-11587	138	3	𝐴𝑥𝑥	𝐴𝑥𝑥	ADJ
fumecheng-11587	138	4	2𝐿	2𝐿	ADJ
fumecheng-11587	138	5	∫	∫	NOUN
fumecheng-11587	138	6	(	(	PUNCT
fumecheng-11587	138	7	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-11587	138	8	𝜕𝑥	𝜕𝑥	X
fumecheng-11587	138	9	)	)	PUNCT
fumecheng-11587	138	10	2	2	NUM
fumecheng-11587	138	11	𝑑𝑥	𝑑𝑥	VERB
fumecheng-11587	138	12	𝜕2𝑤	𝜕2𝑤	NOUN
fumecheng-11587	138	13	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-11587	138	14	𝐿	𝐿	PROPN
fumecheng-11587	138	15	0	0	NUM
fumecheng-11587	138	16	−	−	PROPN
fumecheng-11587	138	17	𝑚2	𝑚2	NOUN
fumecheng-11587	138	18	𝜕4𝑤	𝜕4𝑤	NOUN
fumecheng-11587	138	19	𝜕𝑥2𝜕𝑡2	𝜕𝑥2𝜕𝑡2	NOUN
fumecheng-11587	138	20	+	+	CCONJ
fumecheng-11587	139	1	𝜕2𝑤	𝜕2𝑤	CCONJ
fumecheng-11587	139	2	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-11587	139	3	+	+	CCONJ
fumecheng-11587	139	4	𝑏𝑘𝑤𝑤	𝑏𝑘𝑤𝑤	NOUN
fumecheng-11587	139	5	+	+	CCONJ
fumecheng-11587	139	6	𝑏𝐾𝑤	𝑏𝐾𝑤	NOUN
fumecheng-11587	139	7	𝜕𝑤	𝜕𝑤	VERB
fumecheng-11587	139	8	𝜕𝑡	𝜕𝑡	ADJ
fumecheng-11587	139	9	−𝑏𝑘𝑔	−𝑏𝑘𝑔	NOUN
fumecheng-11587	139	10	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-11587	139	11	𝜕𝑥2	𝜕𝑥2	VERB
fumecheng-11587	139	12	−	−	NOUN
fumecheng-11587	139	13	𝑏𝐾𝑔	𝑏𝐾𝑔	NOUN
fumecheng-11587	139	14	𝜕3𝑤	𝜕3𝑤	ADJ
fumecheng-11587	139	15	𝜕𝑡𝜕𝑥2	𝜕𝑡𝜕𝑥2	NOUN
fumecheng-11587	139	16	+	+	CCONJ
fumecheng-11587	139	17	𝑄	𝑄	PROPN
fumecheng-11587	139	18	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	139	19	𝛺1	𝛺1	VERB
fumecheng-11587	139	20	𝑡	𝑡	X
fumecheng-11587	139	21	]	]	X
fumecheng-11587	140	1	+	+	CCONJ
fumecheng-11587	140	2	𝐷𝑥𝑥	𝐷𝑥𝑥	PROPN
fumecheng-11587	140	3	(	(	PUNCT
fumecheng-11587	140	4	1	1	NUM
fumecheng-11587	140	5	−	−	PROPN
fumecheng-11587	140	6	𝑙2	𝑙2	PROPN
fumecheng-11587	140	7	𝜕2	𝜕2	PUNCT
fumecheng-11587	140	8	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-11587	140	9	)	)	PUNCT
fumecheng-11587	140	10	𝜕4𝑤	𝜕4𝑤	ADP
fumecheng-11587	140	11	𝜕𝑥4	𝜕𝑥4	ADJ
fumecheng-11587	140	12	=	=	SYM
fumecheng-11587	140	13	0	0	NUM
fumecheng-11587	140	14	,	,	PUNCT
fumecheng-11587	140	15	(	(	PUNCT
fumecheng-11587	140	16	6	6	NUM
fumecheng-11587	140	17	)	)	PUNCT
fumecheng-11587	140	18	where	where	SCONJ
fumecheng-11587	140	19	b	b	NOUN
fumecheng-11587	140	20	is	be	AUX
fumecheng-11587	140	21	the	the	DET
fumecheng-11587	140	22	beam	beam	NOUN
fumecheng-11587	140	23	width	width	NOUN
fumecheng-11587	140	24	,	,	PUNCT
fumecheng-11587	140	25	μ	μ	PROPN
fumecheng-11587	140	26	and	and	CCONJ
fumecheng-11587	140	27	l	l	NOUN
fumecheng-11587	140	28	are	be	AUX
fumecheng-11587	140	29	small	small	ADJ
fumecheng-11587	140	30	parameters	parameter	NOUN
fumecheng-11587	140	31	in	in	ADP
fumecheng-11587	140	32	nonlocal	nonlocal	ADJ
fumecheng-11587	140	33	and	and	CCONJ
fumecheng-11587	140	34	strain	strain	VERB
fumecheng-11587	140	35	gradient	gradient	NOUN
fumecheng-11587	140	36	theory	theory	NOUN
fumecheng-11587	140	37	,	,	PUNCT
fumecheng-11587	140	38	m2	m2	PROPN
fumecheng-11587	140	39	is	be	AUX
fumecheng-11587	140	40	the	the	DET
fumecheng-11587	140	41	second	second	ADJ
fumecheng-11587	140	42	moment	moment	NOUN
fumecheng-11587	140	43	of	of	ADP
fumecheng-11587	140	44	inertia	inertia	NOUN
fumecheng-11587	140	45	,	,	PUNCT
fumecheng-11587	140	46	q	q	NOUN
fumecheng-11587	140	47	and	and	CCONJ
fumecheng-11587	140	48	ω1	ω1	PROPN
fumecheng-11587	140	49	are	be	AUX
fumecheng-11587	140	50	the	the	DET
fumecheng-11587	140	51	external	external	ADJ
fumecheng-11587	140	52	force	force	NOUN
fumecheng-11587	140	53	magnitude	magnitude	NOUN
fumecheng-11587	140	54	and	and	CCONJ
fumecheng-11587	140	55	frequency	frequency	NOUN
fumecheng-11587	140	56	,	,	PUNCT
fumecheng-11587	140	57	respectively	respectively	ADV
fumecheng-11587	140	58	.	.	PUNCT
fumecheng-11587	141	1	eq	eq	X
fumecheng-11587	141	2	.	.	PUNCT
fumecheng-11587	142	1	(	(	PUNCT
fumecheng-11587	142	2	6	6	NUM
fumecheng-11587	142	3	)	)	PUNCT
fumecheng-11587	142	4	is	be	AUX
fumecheng-11587	142	5	non	non	ADJ
fumecheng-11587	142	6	-	-	ADJ
fumecheng-11587	142	7	dimensional	dimensional	ADJ
fumecheng-11587	142	8	with	with	ADP
fumecheng-11587	142	9	the	the	DET
fumecheng-11587	142	10	following	follow	VERB
fumecheng-11587	142	11	relations	relation	NOUN
fumecheng-11587	142	12	:	:	PUNCT
fumecheng-11587	142	13	𝑋	𝑋	NOUN
fumecheng-11587	142	14	=	=	SYM
fumecheng-11587	142	15	𝑥	𝑥	PROPN
fumecheng-11587	142	16	𝐿	𝐿	PROPN
fumecheng-11587	142	17	,	,	PUNCT
fumecheng-11587	142	18	𝑊	𝑊	PROPN
fumecheng-11587	142	19	=	=	PUNCT
fumecheng-11587	142	20	𝑤	𝑤	PART
fumecheng-11587	142	21	𝑘𝑥	𝑘𝑥	PRON
fumecheng-11587	142	22	,	,	PUNCT
fumecheng-11587	142	23	𝛴	𝛴	PROPN
fumecheng-11587	142	24	=	=	SYM
fumecheng-11587	142	25	𝑙	𝑙	PROPN
fumecheng-11587	142	26	𝐿	𝐿	PROPN
fumecheng-11587	142	27	,	,	PUNCT
fumecheng-11587	142	28	𝜆	𝜆	PROPN
fumecheng-11587	142	29	=	=	PUNCT
fumecheng-11587	142	30	𝜇	𝜇	ADP
fumecheng-11587	142	31	𝐿	𝐿	PROPN
fumecheng-11587	142	32	,	,	PUNCT
fumecheng-11587	142	33	𝜁	𝜁	PROPN
fumecheng-11587	142	34	=	=	SYM
fumecheng-11587	142	35	𝑏	𝑏	PROPN
fumecheng-11587	142	36	𝐿	𝐿	PROPN
fumecheng-11587	142	37	,	,	PUNCT
fumecheng-11587	142	38	𝜏	𝜏	X
fumecheng-11587	142	39	=	=	PUNCT
fumecheng-11587	142	40	𝑡	𝑡	PROPN
fumecheng-11587	142	41	𝑘𝑥	𝑘𝑥	NOUN
fumecheng-11587	142	42	𝐿2	𝐿2	ADV
fumecheng-11587	142	43	√	√	PROPN
fumecheng-11587	143	1	𝐴𝑥𝑥	𝐴𝑥𝑥	ADJ
fumecheng-11587	143	2	𝑚0	𝑚0	NOUN
fumecheng-11587	143	3	,	,	PUNCT
fumecheng-11587	143	4	𝛺	𝛺	PROPN
fumecheng-11587	143	5	=	=	PUNCT
fumecheng-11587	143	6	𝛺1	𝛺1	PROPN
fumecheng-11587	143	7	𝐿2	𝐿2	PROPN
fumecheng-11587	143	8	𝑘𝑥	𝑘𝑥	PROPN
fumecheng-11587	144	1	√	√	NUM
fumecheng-11587	144	2	𝑚0	𝑚0	NOUN
fumecheng-11587	145	1	𝐴𝑥𝑥	𝐴𝑥𝑥	PROPN
fumecheng-11587	145	2	,	,	PUNCT
fumecheng-11587	145	3	𝐹	𝐹	PROPN
fumecheng-11587	145	4	=	=	SYM
fumecheng-11587	145	5	𝑄𝐿4	𝑄𝐿4	PROPN
fumecheng-11587	145	6	𝐴𝑥𝑥𝑘𝑥	𝐴𝑥𝑥𝑘𝑥	PROPN
fumecheng-11587	145	7	3	3	NUM
fumecheng-11587	145	8	,	,	PUNCT
fumecheng-11587	145	9	𝑦	𝑦	NOUN
fumecheng-11587	145	10	=	=	SYM
fumecheng-11587	145	11	𝑚2	𝑚2	PROPN
fumecheng-11587	145	12	𝑚0𝐿2	𝑚0𝐿2	PRON
fumecheng-11587	145	13	,	,	PUNCT
fumecheng-11587	145	14	𝑘𝑥	𝑘𝑥	NOUN
fumecheng-11587	145	15	=	=	PUNCT
fumecheng-11587	145	16	√	√	PROPN
fumecheng-11587	146	1	𝐷𝑥𝑥	𝐷𝑥𝑥	PROPN
fumecheng-11587	146	2	𝐴𝑥𝑥	𝐴𝑥𝑥	PROPN
fumecheng-11587	146	3	,	,	PUNCT
fumecheng-11587	146	4	𝑘1	𝑘1	NOUN
fumecheng-11587	146	5	=	=	PUNCT
fumecheng-11587	146	6	𝜁𝑘𝑤𝐿5	𝜁𝑘𝑤𝐿5	X
fumecheng-11587	146	7	𝐴𝑥𝑥𝑘𝑥	𝐴𝑥𝑥𝑘𝑥	PROPN
fumecheng-11587	146	8	2	2	NUM
fumecheng-11587	146	9	,	,	PUNCT
fumecheng-11587	146	10	𝐾1	𝐾1	PROPN
fumecheng-11587	146	11	=	=	SYM
fumecheng-11587	146	12	𝜁𝐾𝑤𝐿3	𝜁𝐾𝑤𝐿3	PROPN
fumecheng-11587	147	1	𝑘𝑥√𝐴𝑥𝑥𝑚0	𝑘𝑥√𝐴𝑥𝑥𝑚0	PROPN
fumecheng-11587	147	2	,	,	PUNCT
fumecheng-11587	147	3	𝑘2	𝑘2	PROPN
fumecheng-11587	147	4	=	=	PUNCT
fumecheng-11587	147	5	𝜁𝑘𝑔𝐿3	𝜁𝑘𝑔𝐿3	X
fumecheng-11587	147	6	𝐴𝑥𝑥𝑘𝑥	𝐴𝑥𝑥𝑘𝑥	PROPN
fumecheng-11587	147	7	2	2	NUM
fumecheng-11587	147	8	,	,	PUNCT
fumecheng-11587	147	9	𝐾2	𝐾2	NOUN
fumecheng-11587	147	10	=	=	SYM
fumecheng-11587	147	11	𝜁𝐾𝑔𝐿	𝜁𝐾𝑔𝐿	NOUN
fumecheng-11587	147	12	𝑘𝑥√𝐴𝑥𝑥𝑚0	𝑘𝑥√𝐴𝑥𝑥𝑚0	PROPN
fumecheng-11587	147	13	.	.	PUNCT
fumecheng-11587	148	1	(	(	PUNCT
fumecheng-11587	148	2	7	7	X
fumecheng-11587	148	3	)	)	PUNCT
fumecheng-11587	148	4	note	note	NOUN
fumecheng-11587	148	5	that	that	SCONJ
fumecheng-11587	148	6	radius	radius	NOUN
fumecheng-11587	148	7	of	of	ADP
fumecheng-11587	148	8	gyration	gyration	ADJ
fumecheng-11587	148	9	kx	kx	PROPN
fumecheng-11587	148	10	,	,	PUNCT
fumecheng-11587	148	11	appearing	appear	VERB
fumecheng-11587	148	12	in	in	ADP
fumecheng-11587	148	13	eq	eq	ADP
fumecheng-11587	148	14	.	.	PUNCT
fumecheng-11587	149	1	(	(	PUNCT
fumecheng-11587	149	2	7	7	NUM
fumecheng-11587	149	3	)	)	PUNCT
fumecheng-11587	149	4	,	,	PUNCT
fumecheng-11587	149	5	for	for	ADP
fumecheng-11587	149	6	the	the	DET
fumecheng-11587	149	7	homogenous	homogenous	ADJ
fumecheng-11587	149	8	beam	beam	NOUN
fumecheng-11587	149	9	is	be	AUX
fumecheng-11587	149	10	kx	kx	PROPN
fumecheng-11587	149	11	=	=	PUNCT
fumecheng-11587	149	12	(	(	PUNCT
fumecheng-11587	149	13	ix	ix	PROPN
fumecheng-11587	149	14	/a)1/2	/a)1/2	PROPN
fumecheng-11587	149	15	.	.	PUNCT
fumecheng-11587	150	1	non	non	ADJ
fumecheng-11587	150	2	-	-	ADJ
fumecheng-11587	150	3	dimensional	dimensional	ADJ
fumecheng-11587	150	4	form	form	NOUN
fumecheng-11587	150	5	of	of	ADP
fumecheng-11587	150	6	equation	equation	NOUN
fumecheng-11587	150	7	of	of	ADP
fumecheng-11587	150	8	motion	motion	NOUN
fumecheng-11587	150	9	eq	eq	ADP
fumecheng-11587	150	10	.	.	PUNCT
fumecheng-11587	151	1	(	(	PUNCT
fumecheng-11587	151	2	6	6	NUM
fumecheng-11587	151	3	)	)	PUNCT
fumecheng-11587	151	4	,	,	PUNCT
fumecheng-11587	151	5	obtained	obtain	VERB
fumecheng-11587	151	6	by	by	ADP
fumecheng-11587	151	7	substituting	substitute	VERB
fumecheng-11587	151	8	eq	eq	PROPN
fumecheng-11587	151	9	.	.	PUNCT
fumecheng-11587	152	1	(	(	PUNCT
fumecheng-11587	152	2	7	7	NUM
fumecheng-11587	152	3	)	)	PUNCT
fumecheng-11587	152	4	in	in	ADP
fumecheng-11587	152	5	eq	eq	ADP
fumecheng-11587	152	6	.	.	PUNCT
fumecheng-11587	153	1	(	(	PUNCT
fumecheng-11587	153	2	6	6	NUM
fumecheng-11587	153	3	)	)	PUNCT
fumecheng-11587	153	4	is	be	AUX
fumecheng-11587	153	5	(	(	PUNCT
fumecheng-11587	153	6	1	1	NUM
fumecheng-11587	153	7	−	−	NUM
fumecheng-11587	153	8	𝜆2	𝜆2	NOUN
fumecheng-11587	153	9	𝜕2	𝜕2	NOUN
fumecheng-11587	153	10	𝜕𝑋	𝜕𝑋	X
fumecheng-11587	153	11	2	2	NUM
fumecheng-11587	153	12	)	)	PUNCT
fumecheng-11587	154	1	[	[	X
fumecheng-11587	154	2	−	−	NOUN
fumecheng-11587	154	3	1	1	NUM
fumecheng-11587	154	4	2	2	NUM
fumecheng-11587	154	5	∫	∫	NOUN
fumecheng-11587	154	6	(	(	PUNCT
fumecheng-11587	154	7	𝜕𝑊	𝜕𝑊	NOUN
fumecheng-11587	154	8	𝜕𝑋	𝜕𝑋	NOUN
fumecheng-11587	154	9	)	)	PUNCT
fumecheng-11587	154	10	2	2	NUM
fumecheng-11587	154	11	𝑑𝑋	𝑑𝑋	PROPN
fumecheng-11587	154	12	𝜕2𝑊	𝜕2𝑊	ADJ
fumecheng-11587	154	13	𝜕𝑋	𝜕𝑋	PUNCT
fumecheng-11587	154	14	2	2	NUM
fumecheng-11587	154	15	1	1	NUM
fumecheng-11587	154	16	0	0	NUM
fumecheng-11587	154	17	−	−	NOUN
fumecheng-11587	154	18	𝑦	𝑦	NOUN
fumecheng-11587	154	19	𝜕4𝑊	𝜕4𝑊	NOUN
fumecheng-11587	154	20	𝜕𝑋	𝜕𝑋	PROPN
fumecheng-11587	154	21	2	2	NUM
fumecheng-11587	154	22	𝜕𝜏2	𝜕𝜏2	NOUN
fumecheng-11587	154	23	+	+	CCONJ
fumecheng-11587	154	24	𝜕2𝑊	𝜕2𝑊	ADJ
fumecheng-11587	154	25	𝜕𝜏2	𝜕𝜏2	NOUN
fumecheng-11587	154	26	+	+	CCONJ
fumecheng-11587	154	27	𝑘1𝑊	𝑘1𝑊	NOUN
fumecheng-11587	154	28	+	+	CCONJ
fumecheng-11587	154	29	𝐾1	𝐾1	PROPN
fumecheng-11587	154	30	𝜕𝑊	𝜕𝑊	NUM
fumecheng-11587	154	31	𝜕𝜏	𝜕𝜏	NOUN
fumecheng-11587	154	32	−𝑘2	−𝑘2	ADP
fumecheng-11587	154	33	𝜕2𝑊	𝜕2𝑊	ADJ
fumecheng-11587	154	34	𝜕𝑋	𝜕𝑋	PROPN
fumecheng-11587	154	35	2	2	NUM
fumecheng-11587	154	36	−	−	NOUN
fumecheng-11587	154	37	𝐾2	𝐾2	ADJ
fumecheng-11587	154	38	𝜕3𝑋	𝜕3𝑋	NOUN
fumecheng-11587	154	39	𝜕𝜏𝜕𝑋	𝜕𝜏𝜕𝑋	PROPN
fumecheng-11587	154	40	2	2	NUM
fumecheng-11587	155	1	+	+	NUM
fumecheng-11587	155	2	𝐹	𝐹	PROPN
fumecheng-11587	155	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	155	4	𝛺	𝛺	PROPN
fumecheng-11587	155	5	𝜏	𝜏	NOUN
fumecheng-11587	155	6	]	]	X
fumecheng-11587	155	7	+	+	CCONJ
fumecheng-11587	155	8	(	(	PUNCT
fumecheng-11587	155	9	1	1	NUM
fumecheng-11587	155	10	−	−	PROPN
fumecheng-11587	155	11	𝛴2	𝛴2	NOUN
fumecheng-11587	155	12	𝜕2	𝜕2	NOUN
fumecheng-11587	155	13	𝜕𝑋	𝜕𝑋	X
fumecheng-11587	155	14	2	2	NUM
fumecheng-11587	155	15	)	)	PUNCT
fumecheng-11587	155	16	𝜕4𝑊	𝜕4𝑊	NOUN
fumecheng-11587	155	17	𝜕𝑋	𝜕𝑋	NOUN
fumecheng-11587	155	18	4	4	NUM
fumecheng-11587	155	19	=	=	SYM
fumecheng-11587	155	20	0	0	NUM
fumecheng-11587	155	21	.	.	PUNCT
fumecheng-11587	156	1	(	(	PUNCT
fumecheng-11587	156	2	8)	8)	NUM
fumecheng-11587	156	3	the	the	DET
fumecheng-11587	156	4	solution	solution	NOUN
fumecheng-11587	156	5	of	of	ADP
fumecheng-11587	156	6	eq	eq	PROPN
fumecheng-11587	156	7	.	.	PUNCT
fumecheng-11587	157	1	(	(	PUNCT
fumecheng-11587	157	2	8)	8)	NUM
fumecheng-11587	157	3	could	could	AUX
fumecheng-11587	157	4	be	be	AUX
fumecheng-11587	157	5	assumed	assume	VERB
fumecheng-11587	157	6	as	as	ADP
fumecheng-11587	157	7	a	a	DET
fumecheng-11587	157	8	sum	sum	NOUN
fumecheng-11587	157	9	of	of	ADP
fumecheng-11587	157	10	products	product	NOUN
fumecheng-11587	157	11	of	of	ADP
fumecheng-11587	157	12	amplitude	amplitude	NOUN
fumecheng-11587	157	13	and	and	CCONJ
fumecheng-11587	157	14	time	time	NOUN
fumecheng-11587	157	15	functions	function	NOUN
fumecheng-11587	157	16	for	for	ADP
fumecheng-11587	157	17	each	each	DET
fumecheng-11587	157	18	mode	mode	NOUN
fumecheng-11587	157	19	.	.	PUNCT
fumecheng-11587	158	1	nayfeh	nayfeh	PROPN
fumecheng-11587	158	2	and	and	CCONJ
fumecheng-11587	158	3	lacarbonara	lacarbonara	ADJ
fumecheng-11587	159	1	[	[	X
fumecheng-11587	159	2	54	54	NUM
fumecheng-11587	159	3	]	]	PUNCT
fumecheng-11587	159	4	have	have	AUX
fumecheng-11587	159	5	shown	show	VERB
fumecheng-11587	159	6	in	in	ADP
fumecheng-11587	159	7	their	their	PRON
fumecheng-11587	159	8	study	study	NOUN
fumecheng-11587	159	9	that	that	SCONJ
fumecheng-11587	159	10	in	in	ADP
fumecheng-11587	159	11	certain	certain	ADJ
fumecheng-11587	159	12	cases	case	NOUN
fumecheng-11587	159	13	one	one	NUM
fumecheng-11587	159	14	-	-	PUNCT
fumecheng-11587	159	15	mode	mode	NOUN
fumecheng-11587	159	16	galerkin	galerkin	ADJ
fumecheng-11587	159	17	approximation	approximation	NOUN
fumecheng-11587	159	18	fails	fail	VERB
fumecheng-11587	159	19	to	to	PART
fumecheng-11587	159	20	predict	predict	VERB
fumecheng-11587	159	21	the	the	DET
fumecheng-11587	159	22	dynamic	dynamic	ADJ
fumecheng-11587	159	23	behavior	behavior	NOUN
fumecheng-11587	159	24	of	of	ADP
fumecheng-11587	159	25	hinged	hinge	VERB
fumecheng-11587	159	26	-	-	PUNCT
fumecheng-11587	159	27	hinged	hinge	VERB
fumecheng-11587	159	28	beams	beam	NOUN
fumecheng-11587	159	29	,	,	PUNCT
fumecheng-11587	159	30	especially	especially	ADV
fumecheng-11587	159	31	when	when	SCONJ
fumecheng-11587	159	32	quadratic	quadratic	ADJ
fumecheng-11587	159	33	type	type	NOUN
fumecheng-11587	159	34	nonlinearity	nonlinearity	NOUN
fumecheng-11587	159	35	is	be	AUX
fumecheng-11587	159	36	involved	involve	VERB
fumecheng-11587	159	37	and	and	CCONJ
fumecheng-11587	159	38	even	even	ADV
fumecheng-11587	159	39	modes	mode	NOUN
fumecheng-11587	159	40	are	be	AUX
fumecheng-11587	159	41	observed	observe	VERB
fumecheng-11587	159	42	in	in	ADP
fumecheng-11587	159	43	certain	certain	ADJ
fumecheng-11587	159	44	subharmonic	subharmonic	ADJ
fumecheng-11587	159	45	or	or	CCONJ
fumecheng-11587	159	46	superharmonic	superharmonic	ADJ
fumecheng-11587	159	47	resonance	resonance	NOUN
fumecheng-11587	159	48	conditions	condition	NOUN
fumecheng-11587	159	49	.	.	PUNCT
fumecheng-11587	160	1	since	since	SCONJ
fumecheng-11587	160	2	we	we	PRON
fumecheng-11587	160	3	have	have	VERB
fumecheng-11587	160	4	only	only	ADV
fumecheng-11587	160	5	a	a	DET
fumecheng-11587	160	6	cubic	cubic	ADJ
fumecheng-11587	160	7	nonlinear	nonlinear	ADJ
fumecheng-11587	160	8	term	term	NOUN
fumecheng-11587	160	9	,	,	PUNCT
fumecheng-11587	160	10	we	we	PRON
fumecheng-11587	160	11	will	will	AUX
fumecheng-11587	160	12	use	use	VERB
fumecheng-11587	160	13	only	only	ADV
fumecheng-11587	160	14	a	a	DET
fumecheng-11587	160	15	single	single	ADJ
fumecheng-11587	160	16	mode	mode	NOUN
fumecheng-11587	160	17	discretization	discretization	NOUN
fumecheng-11587	160	18	which	which	DET
fumecheng-11587	160	19	vibration	vibration	NOUN
fumecheng-11587	160	20	and	and	CCONJ
fumecheng-11587	160	21	stability	stability	NOUN
fumecheng-11587	160	22	of	of	ADP
fumecheng-11587	160	23	a	a	DET
fumecheng-11587	160	24	nonlinear	nonlinear	ADJ
fumecheng-11587	160	25	nonlocal	nonlocal	ADJ
fumecheng-11587	160	26	strain	strain	NOUN
fumecheng-11587	160	27	-	-	PUNCT
fumecheng-11587	160	28	gradient	gradient	NOUN
fumecheng-11587	160	29	fg	fg	PROPN
fumecheng-11587	160	30	beam	beam	NOUN
fumecheng-11587	160	31	on	on	ADP
fumecheng-11587	160	32	a	a	DET
fumecheng-11587	160	33	visco	visco	ADJ
fumecheng-11587	160	34	-	-	PUNCT
fumecheng-11587	160	35	pasternak	pasternak	NOUN
fumecheng-11587	160	36	...	...	PUNCT
fumecheng-11587	160	37	715	715	NUM
fumecheng-11587	160	38	is	be	AUX
fumecheng-11587	160	39	the	the	DET
fumecheng-11587	160	40	most	most	ADV
fumecheng-11587	160	41	commonly	commonly	ADV
fumecheng-11587	160	42	used	use	VERB
fumecheng-11587	160	43	method	method	NOUN
fumecheng-11587	160	44	in	in	ADP
fumecheng-11587	160	45	the	the	DET
fumecheng-11587	160	46	investigation	investigation	NOUN
fumecheng-11587	160	47	of	of	ADP
fumecheng-11587	160	48	nonlinear	nonlinear	ADJ
fumecheng-11587	160	49	structural	structural	ADJ
fumecheng-11587	160	50	vibration	vibration	NOUN
fumecheng-11587	160	51	problems	problem	NOUN
fumecheng-11587	160	52	[	[	X
fumecheng-11587	160	53	15	15	NUM
fumecheng-11587	160	54	,	,	PUNCT
fumecheng-11587	160	55	22	22	NUM
fumecheng-11587	160	56	,	,	PUNCT
fumecheng-11587	160	57	26	26	NUM
fumecheng-11587	160	58	,	,	PUNCT
fumecheng-11587	160	59	55	55	NUM
fumecheng-11587	160	60	,	,	PUNCT
fumecheng-11587	160	61	56	56	NUM
fumecheng-11587	160	62	]	]	PUNCT
fumecheng-11587	160	63	.	.	PUNCT
fumecheng-11587	161	1	the	the	DET
fumecheng-11587	161	2	solution	solution	NOUN
fumecheng-11587	161	3	of	of	ADP
fumecheng-11587	161	4	eq	eq	PROPN
fumecheng-11587	161	5	.	.	PUNCT
fumecheng-11587	162	1	(	(	PUNCT
fumecheng-11587	162	2	8)	8)	NUM
fumecheng-11587	162	3	is	be	AUX
fumecheng-11587	162	4	assumed	assume	VERB
fumecheng-11587	162	5	as	as	ADP
fumecheng-11587	162	6	𝑊(𝑋	𝑊(𝑋	PROPN
fumecheng-11587	162	7	,	,	PUNCT
fumecheng-11587	162	8	𝜏	𝜏	NOUN
fumecheng-11587	162	9	)	)	PUNCT
fumecheng-11587	162	10	=	=	SYM
fumecheng-11587	162	11	𝜑𝑛(𝑋)𝑞(𝜏	𝜑𝑛(𝑋)𝑞(𝜏	NOUN
fumecheng-11587	162	12	)	)	PUNCT
fumecheng-11587	162	13	,	,	PUNCT
fumecheng-11587	162	14	(	(	PUNCT
fumecheng-11587	162	15	9	9	X
fumecheng-11587	162	16	)	)	PUNCT
fumecheng-11587	162	17	where	where	SCONJ
fumecheng-11587	162	18	φn	φn	NOUN
fumecheng-11587	162	19	is	be	AUX
fumecheng-11587	162	20	the	the	DET
fumecheng-11587	162	21	amplitude	amplitude	NOUN
fumecheng-11587	162	22	function	function	NOUN
fumecheng-11587	162	23	,	,	PUNCT
fumecheng-11587	162	24	q	q	PROPN
fumecheng-11587	162	25	is	be	AUX
fumecheng-11587	162	26	the	the	DET
fumecheng-11587	162	27	time	time	NOUN
fumecheng-11587	162	28	function	function	NOUN
fumecheng-11587	162	29	and	and	CCONJ
fumecheng-11587	162	30	n	n	CCONJ
fumecheng-11587	162	31	=	=	SYM
fumecheng-11587	162	32	1	1	NUM
fumecheng-11587	162	33	,	,	PUNCT
fumecheng-11587	162	34	2	2	NUM
fumecheng-11587	162	35	,	,	PUNCT
fumecheng-11587	162	36	...	...	PUNCT
fumecheng-11587	162	37	is	be	AUX
fumecheng-11587	162	38	the	the	DET
fumecheng-11587	162	39	mode	mode	NOUN
fumecheng-11587	162	40	number	number	NOUN
fumecheng-11587	162	41	.	.	PUNCT
fumecheng-11587	163	1	amplitude	amplitude	NOUN
fumecheng-11587	163	2	function	function	NOUN
fumecheng-11587	163	3	φn	φn	NOUN
fumecheng-11587	163	4	,	,	PUNCT
fumecheng-11587	163	5	also	also	ADV
fumecheng-11587	163	6	known	know	VERB
fumecheng-11587	163	7	as	as	ADP
fumecheng-11587	163	8	eigenfunction	eigenfunction	NOUN
fumecheng-11587	163	9	,	,	PUNCT
fumecheng-11587	163	10	can	can	AUX
fumecheng-11587	163	11	be	be	AUX
fumecheng-11587	163	12	defined	define	VERB
fumecheng-11587	163	13	as	as	ADP
fumecheng-11587	163	14	the	the	DET
fumecheng-11587	163	15	form	form	NOUN
fumecheng-11587	163	16	of	of	ADP
fumecheng-11587	163	17	trigonometric	trigonometric	ADJ
fumecheng-11587	163	18	functions	function	NOUN
fumecheng-11587	163	19	and	and	CCONJ
fumecheng-11587	163	20	should	should	AUX
fumecheng-11587	163	21	satisfy	satisfy	VERB
fumecheng-11587	163	22	the	the	DET
fumecheng-11587	163	23	boundary	boundary	ADJ
fumecheng-11587	163	24	conditions	condition	NOUN
fumecheng-11587	163	25	.	.	PUNCT
fumecheng-11587	164	1	in	in	ADP
fumecheng-11587	164	2	the	the	DET
fumecheng-11587	164	3	present	present	ADJ
fumecheng-11587	164	4	paper	paper	NOUN
fumecheng-11587	164	5	,	,	PUNCT
fumecheng-11587	164	6	three	three	NUM
fumecheng-11587	164	7	different	different	ADJ
fumecheng-11587	164	8	boundary	boundary	ADJ
fumecheng-11587	164	9	conditions	condition	NOUN
fumecheng-11587	164	10	are	be	AUX
fumecheng-11587	164	11	taken	take	VERB
fumecheng-11587	164	12	into	into	ADP
fumecheng-11587	164	13	account	account	NOUN
fumecheng-11587	164	14	:	:	PUNCT
fumecheng-11587	164	15	pinned	pin	VERB
fumecheng-11587	164	16	-	-	PUNCT
fumecheng-11587	164	17	pinned	pin	VERB
fumecheng-11587	164	18	(	(	PUNCT
fumecheng-11587	164	19	p	p	NOUN
fumecheng-11587	164	20	-	-	PUNCT
fumecheng-11587	164	21	p	p	NOUN
fumecheng-11587	164	22	)	)	PUNCT
fumecheng-11587	164	23	,	,	PUNCT
fumecheng-11587	164	24	clampedpinned	clampedpinne	VERB
fumecheng-11587	164	25	(	(	PUNCT
fumecheng-11587	164	26	c	c	NOUN
fumecheng-11587	164	27	-	-	PUNCT
fumecheng-11587	164	28	p	p	X
fumecheng-11587	164	29	)	)	PUNCT
fumecheng-11587	164	30	and	and	CCONJ
fumecheng-11587	164	31	clamped	clamp	VERB
fumecheng-11587	164	32	-	-	PUNCT
fumecheng-11587	164	33	clamped	clamp	VERB
fumecheng-11587	164	34	(	(	PUNCT
fumecheng-11587	164	35	c	c	NOUN
fumecheng-11587	164	36	-	-	PUNCT
fumecheng-11587	164	37	c	c	NOUN
fumecheng-11587	164	38	)	)	PUNCT
fumecheng-11587	164	39	,	,	PUNCT
fumecheng-11587	164	40	and	and	CCONJ
fumecheng-11587	164	41	the	the	DET
fumecheng-11587	164	42	amplitude	amplitude	NOUN
fumecheng-11587	164	43	function	function	NOUN
fumecheng-11587	164	44	for	for	ADP
fumecheng-11587	164	45	each	each	DET
fumecheng-11587	164	46	case	case	NOUN
fumecheng-11587	164	47	is	be	AUX
fumecheng-11587	164	48	given	give	VERB
fumecheng-11587	164	49	in	in	ADP
fumecheng-11587	164	50	eq	eq	ADP
fumecheng-11587	164	51	.	.	PUNCT
fumecheng-11587	165	1	(	(	PUNCT
fumecheng-11587	165	2	10	10	NUM
fumecheng-11587	165	3	)	)	PUNCT
fumecheng-11587	165	4	,	,	PUNCT
fumecheng-11587	165	5	respectively	respectively	ADV
fumecheng-11587	165	6	[	[	X
fumecheng-11587	165	7	34	34	NUM
fumecheng-11587	165	8	]	]	PUNCT
fumecheng-11587	165	9	,	,	PUNCT
fumecheng-11587	165	10	as	as	ADP
fumecheng-11587	165	11	𝜑𝑛(𝑋	𝜑𝑛(𝑋	NOUN
fumecheng-11587	165	12	)	)	PUNCT
fumecheng-11587	165	13	=	=	PUNCT
fumecheng-11587	166	1	|	|	ADV
fumecheng-11587	166	2	|	|	ADV
fumecheng-11587	166	3	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
fumecheng-11587	166	4	𝛾𝑛	𝛾𝑛	INTJ
fumecheng-11587	166	5	𝑋	𝑋	PROPN
fumecheng-11587	166	6	,	,	PUNCT
fumecheng-11587	166	7	𝛾𝑛	𝛾𝑛	NOUN
fumecheng-11587	166	8	=	=	SYM
fumecheng-11587	166	9	𝑛𝜋	𝑛𝜋	PROPN
fumecheng-11587	166	10	,	,	PUNCT
fumecheng-11587	166	11	(	(	PUNCT
fumecheng-11587	166	12	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
fumecheng-11587	166	13	𝛾𝑛	𝛾𝑛	ADP
fumecheng-11587	166	14	𝑋	𝑋	PROPN
fumecheng-11587	166	15	−	−	PROPN
fumecheng-11587	166	16	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
fumecheng-11587	166	17	𝛾𝑛	𝛾𝑛	ADP
fumecheng-11587	166	18	𝑋	𝑋	PROPN
fumecheng-11587	166	19	)	)	PUNCT
fumecheng-11587	166	20	−	−	PROPN
fumecheng-11587	166	21	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
fumecheng-11587	166	22	𝛾𝑛+𝑠𝑖𝑛ℎ	𝛾𝑛+𝑠𝑖𝑛ℎ	PROPN
fumecheng-11587	166	23	𝛾𝑛	𝛾𝑛	INTJ
fumecheng-11587	167	1	𝑐𝑜𝑠	𝑐𝑜𝑠	PROPN
fumecheng-11587	167	2	𝛾𝑛+𝑐𝑜𝑠ℎ	𝛾𝑛+𝑐𝑜𝑠ℎ	PROPN
fumecheng-11587	167	3	𝛾𝑛	𝛾𝑛	PROPN
fumecheng-11587	168	1	(	(	PUNCT
fumecheng-11587	168	2	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	168	3	𝛾𝑛	𝛾𝑛	VERB
fumecheng-11587	168	4	𝑋	𝑋	PROPN
fumecheng-11587	168	5	−	−	PROPN
fumecheng-11587	168	6	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
fumecheng-11587	168	7	𝛾𝑛	𝛾𝑛	X
fumecheng-11587	168	8	𝑋	𝑋	PROPN
fumecheng-11587	168	9	)	)	PUNCT
fumecheng-11587	168	10	,	,	PUNCT
fumecheng-11587	168	11	𝑡𝑎𝑛	𝑡𝑎𝑛	NOUN
fumecheng-11587	168	12	𝛾𝑛	𝛾𝑛	NOUN
fumecheng-11587	168	13	=	=	VERB
fumecheng-11587	168	14	𝑡𝑎𝑛ℎ	𝑡𝑎𝑛ℎ	NOUN
fumecheng-11587	168	15	𝛾𝑛	𝛾𝑛	INTJ
fumecheng-11587	168	16	,	,	PUNCT
fumecheng-11587	168	17	(	(	PUNCT
fumecheng-11587	168	18	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
fumecheng-11587	168	19	𝛾𝑛	𝛾𝑛	ADP
fumecheng-11587	168	20	𝑋	𝑋	PROPN
fumecheng-11587	168	21	−	−	PROPN
fumecheng-11587	168	22	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
fumecheng-11587	168	23	𝛾𝑛	𝛾𝑛	ADP
fumecheng-11587	168	24	𝑋	𝑋	PROPN
fumecheng-11587	168	25	)	)	PUNCT
fumecheng-11587	168	26	−	−	PROPN
fumecheng-11587	168	27	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
fumecheng-11587	168	28	𝛾𝑛−𝑠𝑖𝑛ℎ	𝛾𝑛−𝑠𝑖𝑛ℎ	ADP
fumecheng-11587	168	29	𝛾𝑛	𝛾𝑛	INTJ
fumecheng-11587	169	1	𝑐𝑜𝑠	𝑐𝑜𝑠	PROPN
fumecheng-11587	169	2	𝛾𝑛−𝑐𝑜𝑠ℎ	𝛾𝑛−𝑐𝑜𝑠ℎ	PROPN
fumecheng-11587	169	3	𝛾𝑛	𝛾𝑛	INTJ
fumecheng-11587	170	1	(	(	PUNCT
fumecheng-11587	170	2	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	170	3	𝛾𝑛	𝛾𝑛	VERB
fumecheng-11587	171	1	𝑋	𝑋	PROPN
fumecheng-11587	171	2	−	−	PROPN
fumecheng-11587	171	3	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
fumecheng-11587	171	4	𝛾𝑛	𝛾𝑛	X
fumecheng-11587	171	5	𝑋	𝑋	PROPN
fumecheng-11587	171	6	)	)	PUNCT
fumecheng-11587	171	7	,	,	PUNCT
fumecheng-11587	171	8	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	171	9	𝛾𝑛	𝛾𝑛	INTJ
fumecheng-11587	171	10	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	PROPN
fumecheng-11587	171	11	𝛾𝑛	𝛾𝑛	PROPN
fumecheng-11587	172	1	=	=	SYM
fumecheng-11587	172	2	−1	−1	NOUN
fumecheng-11587	172	3	.	.	PUNCT
fumecheng-11587	173	1	(	(	PUNCT
fumecheng-11587	173	2	10	10	NUM
fumecheng-11587	173	3	)	)	PUNCT
fumecheng-11587	173	4	coefficients	coefficient	NOUN
fumecheng-11587	173	5	s0	s0	PROPN
fumecheng-11587	173	6	s5	s5	PROPN
fumecheng-11587	173	7	are	be	AUX
fumecheng-11587	173	8	calculated	calculate	VERB
fumecheng-11587	173	9	as	as	ADP
fumecheng-11587	173	10	{	{	PUNCT
fumecheng-11587	173	11	𝑠0	𝑠0	NOUN
fumecheng-11587	173	12	,	,	PUNCT
fumecheng-11587	173	13	𝑠1	𝑠1	PROPN
fumecheng-11587	173	14	,	,	PUNCT
fumecheng-11587	173	15	𝑠2	𝑠2	PROPN
fumecheng-11587	173	16	,	,	PUNCT
fumecheng-11587	173	17	𝑠3	𝑠3	NOUN
fumecheng-11587	173	18	,	,	PUNCT
fumecheng-11587	173	19	𝑠4	𝑠4	PROPN
fumecheng-11587	173	20	,	,	PUNCT
fumecheng-11587	173	21	𝑠5	𝑠5	PROPN
fumecheng-11587	173	22	}	}	PUNCT
fumecheng-11587	173	23	=	=	SYM
fumecheng-11587	173	24	∫	∫	PROPN
fumecheng-11587	173	25	{	{	PUNCT
fumecheng-11587	173	26	𝜑	𝜑	PROPN
fumecheng-11587	173	27	,	,	PUNCT
fumecheng-11587	173	28	𝜑2	𝜑2	ADJ
fumecheng-11587	173	29	,	,	PUNCT
fumecheng-11587	173	30	𝜑″𝜑	𝜑″𝜑	NOUN
fumecheng-11587	173	31	,	,	PUNCT
fumecheng-11587	173	32	𝜑𝐼𝑉𝜑	𝜑𝐼𝑉𝜑	PROPN
fumecheng-11587	173	33	,	,	PUNCT
fumecheng-11587	173	34	𝜑𝑉𝐼𝜑	𝜑𝑉𝐼𝜑	NOUN
fumecheng-11587	173	35	,	,	PUNCT
fumecheng-11587	173	36	𝜑′2}𝑑𝑋.	𝜑′2}𝑑𝑋.	X
fumecheng-11587	173	37	1	1	NUM
fumecheng-11587	173	38	0	0	NUM
fumecheng-11587	173	39	(	(	PUNCT
fumecheng-11587	173	40	11	11	NUM
fumecheng-11587	173	41	)	)	PUNCT
fumecheng-11587	173	42	we	we	PRON
fumecheng-11587	173	43	replace	replace	VERB
fumecheng-11587	173	44	eq	eq	ADP
fumecheng-11587	173	45	.	.	PUNCT
fumecheng-11587	174	1	(	(	PUNCT
fumecheng-11587	174	2	9	9	NUM
fumecheng-11587	174	3	)	)	PUNCT
fumecheng-11587	174	4	into	into	ADP
fumecheng-11587	174	5	eq	eq	NOUN
fumecheng-11587	174	6	.	.	PUNCT
fumecheng-11587	175	1	(	(	PUNCT
fumecheng-11587	175	2	8)	8)	NUM
fumecheng-11587	175	3	,	,	PUNCT
fumecheng-11587	175	4	and	and	CCONJ
fumecheng-11587	175	5	use	use	VERB
fumecheng-11587	175	6	eq	eq	ADJ
fumecheng-11587	175	7	.	.	PUNCT
fumecheng-11587	176	1	(	(	PUNCT
fumecheng-11587	176	2	11	11	NUM
fumecheng-11587	176	3	)	)	PUNCT
fumecheng-11587	176	4	to	to	PART
fumecheng-11587	176	5	obtain	obtain	VERB
fumecheng-11587	176	6	nonlinear	nonlinear	ADJ
fumecheng-11587	176	7	differential	differential	ADJ
fumecheng-11587	176	8	equation	equation	NOUN
fumecheng-11587	176	9	as	as	ADP
fumecheng-11587	176	10	�	�	PROPN
fumecheng-11587	176	11	̈	̈	X
fumecheng-11587	176	12	�	�	PROPN
fumecheng-11587	176	13	+	+	CCONJ
fumecheng-11587	176	14	𝛾	𝛾	PROPN
fumecheng-11587	176	15	�	�	PROPN
fumecheng-11587	176	16	̇	̇	VERB
fumecheng-11587	176	17	�	�	PROPN
fumecheng-11587	176	18	+	+	CCONJ
fumecheng-11587	176	19	𝜔0	𝜔0	NOUN
fumecheng-11587	176	20	2𝑞	2𝑞	NOUN
fumecheng-11587	176	21	+	+	CCONJ
fumecheng-11587	176	22	𝜃𝑞3	𝜃𝑞3	NOUN
fumecheng-11587	176	23	=	=	SYM
fumecheng-11587	176	24	𝑓	𝑓	DET
fumecheng-11587	176	25	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	176	26	𝛺	𝛺	ADJ
fumecheng-11587	176	27	𝜏	𝜏	NOUN
fumecheng-11587	176	28	,	,	PUNCT
fumecheng-11587	176	29	(	(	PUNCT
fumecheng-11587	176	30	12	12	NUM
fumecheng-11587	176	31	)	)	PUNCT
fumecheng-11587	176	32	with	with	ADP
fumecheng-11587	176	33	the	the	DET
fumecheng-11587	176	34	following	follow	VERB
fumecheng-11587	176	35	coefficients	coefficient	NOUN
fumecheng-11587	176	36	𝛾	𝛾	PROPN
fumecheng-11587	176	37	=	=	SYM
fumecheng-11587	176	38	𝐾1𝑠1−𝐾2𝑠2−𝜆2𝐾1𝑠2+𝜆2𝐾2𝑠3	𝐾1𝑠1−𝐾2𝑠2−𝜆2𝐾1𝑠2+𝜆2𝐾2𝑠3	NOUN
fumecheng-11587	176	39	𝑠1−𝑦𝑠2−𝜆2𝑠2+𝑦𝜆2𝑠3	𝑠1−𝑦𝑠2−𝜆2𝑠2+𝑦𝜆2𝑠3	NUM
fumecheng-11587	176	40	,	,	PUNCT
fumecheng-11587	176	41	𝜔0	𝜔0	NOUN
fumecheng-11587	176	42	2	2	NUM
fumecheng-11587	176	43	=	=	SYM
fumecheng-11587	176	44	𝑘1𝑠1−𝑘2𝑠2−𝜆2𝑘1𝑠2+𝜆2𝑘2𝑠3+𝑠3−𝛴2𝑠4	𝑘1𝑠1−𝑘2𝑠2−𝜆2𝑘1𝑠2+𝜆2𝑘2𝑠3+𝑠3−𝛴2𝑠4	NUM
fumecheng-11587	176	45	𝑠1−𝑦𝑠2−𝜆2𝑠2+𝑦𝜆2𝑠3	𝑠1−𝑦𝑠2−𝜆2𝑠2+𝑦𝜆2𝑠3	NUM
fumecheng-11587	176	46	,	,	PUNCT
fumecheng-11587	176	47	𝜃	𝜃	PROPN
fumecheng-11587	176	48	=	=	SYM
fumecheng-11587	176	49	−	−	PROPN
fumecheng-11587	176	50	1	1	NUM
fumecheng-11587	176	51	2	2	NUM
fumecheng-11587	176	52	𝑠5𝑠2	𝑠5𝑠2	NOUN
fumecheng-11587	176	53	+	+	NUM
fumecheng-11587	176	54	1	1	NUM
fumecheng-11587	176	55	2	2	NUM
fumecheng-11587	176	56	𝑠5𝑠3𝜆2	𝑠5𝑠3𝜆2	NOUN
fumecheng-11587	176	57	𝑠1−𝑦𝑠2−𝜆2𝑠2+𝑦𝜆2𝑠3	𝑠1−𝑦𝑠2−𝜆2𝑠2+𝑦𝜆2𝑠3	NUM
fumecheng-11587	176	58	,	,	PUNCT
fumecheng-11587	176	59	𝑓	𝑓	PROPN
fumecheng-11587	176	60	=	=	PUNCT
fumecheng-11587	176	61	−𝑠0𝐹	−𝑠0𝐹	PROPN
fumecheng-11587	176	62	𝑠1−𝑦𝑠2−𝜆2𝑠2+𝑦𝜆2𝑠3	𝑠1−𝑦𝑠2−𝜆2𝑠2+𝑦𝜆2𝑠3	NUM
fumecheng-11587	176	63	.	.	PUNCT
fumecheng-11587	177	1	(	(	PUNCT
fumecheng-11587	177	2	13	13	NUM
fumecheng-11587	177	3	)	)	PUNCT
fumecheng-11587	177	4	3	3	NUM
fumecheng-11587	177	5	.	.	PUNCT
fumecheng-11587	178	1	nonlinear	nonlinear	ADJ
fumecheng-11587	178	2	periodic	periodic	ADJ
fumecheng-11587	178	3	response	response	NOUN
fumecheng-11587	178	4	for	for	ADP
fumecheng-11587	178	5	obtaining	obtain	VERB
fumecheng-11587	178	6	the	the	DET
fumecheng-11587	178	7	amplitude	amplitude	NOUN
fumecheng-11587	178	8	-	-	PUNCT
fumecheng-11587	178	9	frequency	frequency	NOUN
fumecheng-11587	178	10	response	response	NOUN
fumecheng-11587	178	11	of	of	ADP
fumecheng-11587	178	12	a	a	DET
fumecheng-11587	178	13	nonlinear	nonlinear	ADJ
fumecheng-11587	178	14	problem	problem	NOUN
fumecheng-11587	178	15	described	describe	VERB
fumecheng-11587	178	16	by	by	ADP
fumecheng-11587	178	17	eq	eq	PROPN
fumecheng-11587	178	18	.	.	PUNCT
fumecheng-11587	179	1	(	(	PUNCT
fumecheng-11587	179	2	12	12	NUM
fumecheng-11587	179	3	)	)	PUNCT
fumecheng-11587	179	4	,	,	PUNCT
fumecheng-11587	179	5	the	the	DET
fumecheng-11587	179	6	ihb	ihb	NOUN
fumecheng-11587	179	7	method	method	NOUN
fumecheng-11587	179	8	and	and	CCONJ
fumecheng-11587	179	9	continuation	continuation	NOUN
fumecheng-11587	179	10	technique	technique	NOUN
fumecheng-11587	179	11	will	will	AUX
fumecheng-11587	179	12	be	be	AUX
fumecheng-11587	179	13	used	use	VERB
fumecheng-11587	179	14	.	.	PUNCT
fumecheng-11587	180	1	ihb	ihb	PRON
fumecheng-11587	180	2	is	be	AUX
fumecheng-11587	180	3	a	a	DET
fumecheng-11587	180	4	vastly	vastly	ADV
fumecheng-11587	180	5	used	use	VERB
fumecheng-11587	180	6	procedure	procedure	NOUN
fumecheng-11587	180	7	for	for	ADP
fumecheng-11587	180	8	solving	solve	VERB
fumecheng-11587	180	9	the	the	DET
fumecheng-11587	180	10	nonlinear	nonlinear	ADJ
fumecheng-11587	180	11	differential	differential	ADJ
fumecheng-11587	180	12	equations	equation	NOUN
fumecheng-11587	180	13	of	of	ADP
fumecheng-11587	180	14	duffing	duffing	NOUN
fumecheng-11587	180	15	and	and	CCONJ
fumecheng-11587	180	16	mathieu	mathieu	PROPN
fumecheng-11587	180	17	-	-	PUNCT
fumecheng-11587	180	18	duffing	duffing	NOUN
fumecheng-11587	180	19	type	type	NOUN
fumecheng-11587	180	20	[	[	X
fumecheng-11587	180	21	27	27	NUM
fumecheng-11587	180	22	,	,	PUNCT
fumecheng-11587	180	23	57	57	NUM
fumecheng-11587	180	24	]	]	PUNCT
fumecheng-11587	180	25	.	.	PUNCT
fumecheng-11587	181	1	the	the	DET
fumecheng-11587	181	2	continuation	continuation	NOUN
fumecheng-11587	181	3	technique	technique	NOUN
fumecheng-11587	181	4	serves	serve	VERB
fumecheng-11587	181	5	as	as	ADP
fumecheng-11587	181	6	a	a	DET
fumecheng-11587	181	7	supporting	support	VERB
fumecheng-11587	181	8	methodology	methodology	NOUN
fumecheng-11587	181	9	for	for	ADP
fumecheng-11587	181	10	obtaining	obtain	VERB
fumecheng-11587	181	11	the	the	DET
fumecheng-11587	181	12	periodic	periodic	ADJ
fumecheng-11587	181	13	solutions	solution	NOUN
fumecheng-11587	181	14	in	in	ADP
fumecheng-11587	181	15	points	point	NOUN
fumecheng-11587	181	16	close	close	ADV
fumecheng-11587	181	17	to	to	PART
fumecheng-11587	181	18	resonant	resonant	VERB
fumecheng-11587	181	19	states	state	NOUN
fumecheng-11587	181	20	.	.	PUNCT
fumecheng-11587	182	1	3.1	3.1	NUM
fumecheng-11587	182	2	.	.	PUNCT
fumecheng-11587	183	1	the	the	DET
fumecheng-11587	183	2	incremental	incremental	ADJ
fumecheng-11587	183	3	harmonic	harmonic	ADJ
fumecheng-11587	183	4	balance	balance	NOUN
fumecheng-11587	183	5	method	method	NOUN
fumecheng-11587	183	6	to	to	PART
fumecheng-11587	183	7	apply	apply	VERB
fumecheng-11587	183	8	the	the	DET
fumecheng-11587	183	9	ihb	ihb	NOUN
fumecheng-11587	183	10	method	method	NOUN
fumecheng-11587	183	11	,	,	PUNCT
fumecheng-11587	183	12	we	we	PRON
fumecheng-11587	183	13	introduce	introduce	VERB
fumecheng-11587	183	14	a	a	DET
fumecheng-11587	183	15	new	new	ADJ
fumecheng-11587	183	16	time	time	NOUN
fumecheng-11587	183	17	scale	scale	NOUN
fumecheng-11587	183	18	τ	τ	X
fumecheng-11587	183	19	̅	̅	NOUN
fumecheng-11587	183	20	=	=	SYM
fumecheng-11587	183	21	ωτ	ωτ	NOUN
fumecheng-11587	183	22	into	into	ADP
fumecheng-11587	183	23	eq	eq	PROPN
fumecheng-11587	183	24	.	.	PUNCT
fumecheng-11587	184	1	(	(	PUNCT
fumecheng-11587	184	2	12	12	NUM
fumecheng-11587	184	3	)	)	PUNCT
fumecheng-11587	184	4	to	to	PART
fumecheng-11587	184	5	obtain	obtain	VERB
fumecheng-11587	184	6	the	the	DET
fumecheng-11587	184	7	system	system	NOUN
fumecheng-11587	184	8	of	of	ADP
fumecheng-11587	184	9	nonlinear	nonlinear	ADJ
fumecheng-11587	184	10	ordinary	ordinary	ADJ
fumecheng-11587	184	11	differential	differential	ADJ
fumecheng-11587	184	12	equations	equation	NOUN
fumecheng-11587	184	13	in	in	ADP
fumecheng-11587	184	14	the	the	DET
fumecheng-11587	184	15	following	follow	VERB
fumecheng-11587	184	16	form	form	NOUN
fumecheng-11587	184	17	𝛺2	𝛺2	VERB
fumecheng-11587	184	18	𝑑2𝑞	𝑑2𝑞	PROPN
fumecheng-11587	184	19	𝑑𝜏	𝑑𝜏	PROPN
fumecheng-11587	184	20	2	2	NUM
fumecheng-11587	184	21	+	+	CCONJ
fumecheng-11587	184	22	𝛾𝛺	𝛾𝛺	ADJ
fumecheng-11587	184	23	𝑑𝑞	𝑑𝑞	X
fumecheng-11587	184	24	𝑑𝜏	𝑑𝜏	NOUN
fumecheng-11587	184	25	+	+	CCONJ
fumecheng-11587	184	26	𝜔0	𝜔0	NOUN
fumecheng-11587	184	27	2𝑞	2𝑞	NOUN
fumecheng-11587	184	28	+	+	CCONJ
fumecheng-11587	184	29	𝜃𝑞3	𝜃𝑞3	NOUN
fumecheng-11587	184	30	=	=	SYM
fumecheng-11587	184	31	𝑓	𝑓	DET
fumecheng-11587	184	32	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	184	33	𝜏.	𝜏.	NOUN
fumecheng-11587	184	34	(	(	PUNCT
fumecheng-11587	184	35	14	14	NUM
fumecheng-11587	184	36	)	)	PUNCT
fumecheng-11587	184	37	716	716	NUM
fumecheng-11587	184	38	n.	n.	NOUN
fumecheng-11587	184	39	nešić	nešić	PROPN
fumecheng-11587	184	40	,	,	PUNCT
fumecheng-11587	184	41	m.	m.	NOUN
fumecheng-11587	184	42	cajić	cajić	NOUN
fumecheng-11587	184	43	,	,	PUNCT
fumecheng-11587	184	44	d.	d.	PROPN
fumecheng-11587	184	45	karličić	karličić	PROPN
fumecheng-11587	184	46	,	,	PUNCT
fumecheng-11587	184	47	m.	m.	NOUN
fumecheng-11587	184	48	lazarević	lazarević	PROPN
fumecheng-11587	184	49	,	,	PUNCT
fumecheng-11587	184	50	s.	s.	PROPN
fumecheng-11587	184	51	adhikari	adhikari	PROPN
fumecheng-11587	184	52	for	for	ADP
fumecheng-11587	184	53	arbitrarily	arbitrarily	ADV
fumecheng-11587	184	54	chosen	choose	VERB
fumecheng-11587	184	55	initial	initial	ADJ
fumecheng-11587	184	56	values	value	NOUN
fumecheng-11587	184	57	of	of	ADP
fumecheng-11587	184	58	q0	q0	NOUN
fumecheng-11587	184	59	and	and	CCONJ
fumecheng-11587	184	60	ω0	ω0	ADV
fumecheng-11587	184	61	for	for	ADP
fumecheng-11587	184	62	the	the	DET
fumecheng-11587	184	63	steady	steady	ADJ
fumecheng-11587	184	64	-	-	PUNCT
fumecheng-11587	184	65	state	state	NOUN
fumecheng-11587	184	66	modal	modal	ADJ
fumecheng-11587	184	67	amplitude	amplitude	NOUN
fumecheng-11587	184	68	,	,	PUNCT
fumecheng-11587	184	69	a	a	DET
fumecheng-11587	184	70	neighboring	neighbor	VERB
fumecheng-11587	184	71	state	state	NOUN
fumecheng-11587	184	72	of	of	ADP
fumecheng-11587	184	73	motion	motion	NOUN
fumecheng-11587	184	74	is	be	AUX
fumecheng-11587	184	75	incrementally	incrementally	ADV
fumecheng-11587	184	76	changed	change	VERB
fumecheng-11587	184	77	to	to	ADP
fumecheng-11587	184	78	the	the	DET
fumecheng-11587	184	79	current	current	ADJ
fumecheng-11587	184	80	state	state	NOUN
fumecheng-11587	184	81	and	and	CCONJ
fumecheng-11587	184	82	it	it	PRON
fumecheng-11587	184	83	can	can	AUX
fumecheng-11587	184	84	be	be	AUX
fumecheng-11587	184	85	expressed	express	VERB
fumecheng-11587	184	86	in	in	ADP
fumecheng-11587	184	87	the	the	DET
fumecheng-11587	184	88	following	follow	VERB
fumecheng-11587	184	89	form	form	NOUN
fumecheng-11587	184	90	𝑞	𝑞	X
fumecheng-11587	184	91	=	=	NOUN
fumecheng-11587	184	92	𝑞0	𝑞0	PROPN
fumecheng-11587	184	93	+	+	X
fumecheng-11587	185	1	𝛥𝑞	𝛥𝑞	ADJ
fumecheng-11587	185	2	,	,	PUNCT
fumecheng-11587	185	3	𝛺	𝛺	PROPN
fumecheng-11587	185	4	=	=	SYM
fumecheng-11587	185	5	𝛺0	𝛺0	PROPN
fumecheng-11587	185	6	+	+	NUM
fumecheng-11587	185	7	𝛥𝛺.	𝛥𝛺.	X
fumecheng-11587	185	8	(	(	PUNCT
fumecheng-11587	185	9	15	15	NUM
fumecheng-11587	185	10	)	)	PUNCT
fumecheng-11587	185	11	substituting	substitute	VERB
fumecheng-11587	185	12	eq	eq	PROPN
fumecheng-11587	185	13	.	.	PUNCT
fumecheng-11587	186	1	(	(	PUNCT
fumecheng-11587	186	2	15	15	NUM
fumecheng-11587	186	3	)	)	PUNCT
fumecheng-11587	186	4	into	into	ADP
fumecheng-11587	186	5	eq	eq	NOUN
fumecheng-11587	186	6	.	.	PUNCT
fumecheng-11587	187	1	(	(	PUNCT
fumecheng-11587	187	2	14	14	NUM
fumecheng-11587	187	3	)	)	PUNCT
fumecheng-11587	187	4	and	and	CCONJ
fumecheng-11587	187	5	neglecting	neglect	VERB
fumecheng-11587	187	6	higher	high	ADJ
fumecheng-11587	187	7	-	-	PUNCT
fumecheng-11587	187	8	order	order	NOUN
fumecheng-11587	187	9	terms	term	NOUN
fumecheng-11587	187	10	,	,	PUNCT
fumecheng-11587	187	11	we	we	PRON
fumecheng-11587	187	12	obtain	obtain	VERB
fumecheng-11587	187	13	a	a	DET
fumecheng-11587	187	14	linearized	linearize	VERB
fumecheng-11587	187	15	incremental	incremental	ADJ
fumecheng-11587	187	16	relation	relation	NOUN
fumecheng-11587	187	17	given	give	VERB
fumecheng-11587	187	18	as	as	ADP
fumecheng-11587	187	19	𝛺0	𝛺0	PROPN
fumecheng-11587	187	20	2𝛥𝑞″	2𝛥𝑞″	PROPN
fumecheng-11587	187	21	+	+	CCONJ
fumecheng-11587	187	22	𝛾𝛺0𝛥𝑞′	𝛾𝛺0𝛥𝑞′	AUX
fumecheng-11587	187	23	+	+	CCONJ
fumecheng-11587	187	24	𝜔0	𝜔0	NOUN
fumecheng-11587	187	25	2𝛥𝑞	2𝛥𝑞	NUM
fumecheng-11587	187	26	+	+	CCONJ
fumecheng-11587	187	27	3𝜃𝑞0	3𝜃𝑞0	NUM
fumecheng-11587	187	28	2𝛥𝑞	2𝛥𝑞	NUM
fumecheng-11587	187	29	=	=	SYM
fumecheng-11587	187	30	𝑟	𝑟	NOUN
fumecheng-11587	187	31	−	−	PROPN
fumecheng-11587	187	32	2𝛺0𝑞0	2𝛺0𝑞0	NUM
fumecheng-11587	187	33	″	″	PROPN
fumecheng-11587	187	34	𝛥𝛺	𝛥𝛺	PROPN
fumecheng-11587	187	35	+	+	CCONJ
fumecheng-11587	187	36	𝑓	𝑓	PRON
fumecheng-11587	187	37	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	187	38	𝜏	𝜏	NOUN
fumecheng-11587	187	39	,	,	PUNCT
fumecheng-11587	187	40	(	(	PUNCT
fumecheng-11587	187	41	16	16	NUM
fumecheng-11587	187	42	)	)	PUNCT
fumecheng-11587	187	43	where	where	SCONJ
fumecheng-11587	187	44	r	r	NOUN
fumecheng-11587	187	45	is	be	AUX
fumecheng-11587	187	46	the	the	DET
fumecheng-11587	187	47	residual	residual	ADJ
fumecheng-11587	187	48	term	term	NOUN
fumecheng-11587	187	49	given	give	VERB
fumecheng-11587	187	50	as	as	ADP
fumecheng-11587	187	51	𝑟	𝑟	NOUN
fumecheng-11587	187	52	=	=	SYM
fumecheng-11587	187	53	−(𝛺0	−(𝛺0	NOUN
fumecheng-11587	187	54	2𝑞0	2𝑞0	NUM
fumecheng-11587	187	55	″	″	PROPN
fumecheng-11587	187	56	+	+	NUM
fumecheng-11587	187	57	𝛾𝛺0𝑞0	𝛾𝛺0𝑞0	NUM
fumecheng-11587	187	58	′	′	NUM
fumecheng-11587	188	1	+	+	CCONJ
fumecheng-11587	188	2	𝜔0	𝜔0	NOUN
fumecheng-11587	188	3	2𝑞0	2𝑞0	NUM
fumecheng-11587	188	4	+	+	NUM
fumecheng-11587	188	5	𝜃𝑞0	𝜃𝑞0	NOUN
fumecheng-11587	188	6	3	3	NUM
fumecheng-11587	188	7	)	)	PUNCT
fumecheng-11587	188	8	.	.	PUNCT
fumecheng-11587	189	1	(	(	PUNCT
fumecheng-11587	189	2	17	17	NUM
fumecheng-11587	189	3	)	)	PUNCT
fumecheng-11587	189	4	to	to	PART
fumecheng-11587	189	5	obtain	obtain	VERB
fumecheng-11587	189	6	the	the	DET
fumecheng-11587	189	7	periodic	periodic	ADJ
fumecheng-11587	189	8	solutions	solution	NOUN
fumecheng-11587	189	9	of	of	ADP
fumecheng-11587	189	10	the	the	DET
fumecheng-11587	189	11	differential	differential	ADJ
fumecheng-11587	189	12	equation	equation	NOUN
fumecheng-11587	189	13	,	,	PUNCT
fumecheng-11587	189	14	q0	q0	PROPN
fumecheng-11587	189	15	and	and	CCONJ
fumecheng-11587	189	16	δq	δq	PROPN
fumecheng-11587	189	17	are	be	AUX
fumecheng-11587	189	18	expanded	expand	VERB
fumecheng-11587	189	19	into	into	ADP
fumecheng-11587	189	20	finite	finite	ADJ
fumecheng-11587	189	21	fourier	fourier	PROPN
fumecheng-11587	189	22	series	series	NOUN
fumecheng-11587	189	23	of	of	ADP
fumecheng-11587	189	24	n	n	PROPN
fumecheng-11587	189	25	terms	term	NOUN
fumecheng-11587	189	26	as	as	ADP
fumecheng-11587	189	27	𝑞0	𝑞0	NOUN
fumecheng-11587	189	28	=	=	SYM
fumecheng-11587	189	29	𝑎0	𝑎0	PROPN
fumecheng-11587	189	30	+	+	NOUN
fumecheng-11587	189	31	∑	∑	PUNCT
fumecheng-11587	190	1	[	[	X
fumecheng-11587	190	2	𝑎𝑛	𝑎𝑛	PRON
fumecheng-11587	190	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	190	4	𝑛	𝑛	PRON
fumecheng-11587	190	5	𝜏	𝜏	X
fumecheng-11587	190	6	+	+	PROPN
fumecheng-11587	190	7	𝑏𝑛	𝑏𝑛	ADP
fumecheng-11587	190	8	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
fumecheng-11587	190	9	𝑛	𝑛	ADP
fumecheng-11587	190	10	𝜏]𝑁	𝜏]𝑁	ADJ
fumecheng-11587	190	11	𝑛=1	𝑛=1	NOUN
fumecheng-11587	190	12	=	=	SYM
fumecheng-11587	190	13	𝑪𝑨𝟎	𝑪𝑨𝟎	PROPN
fumecheng-11587	190	14	,	,	PUNCT
fumecheng-11587	190	15	(	(	PUNCT
fumecheng-11587	190	16	18	18	NUM
fumecheng-11587	190	17	)	)	PUNCT
fumecheng-11587	190	18	𝛥𝑞	𝛥𝑞	PROPN
fumecheng-11587	190	19	=	=	PUNCT
fumecheng-11587	190	20	𝛥𝑎0	𝛥𝑎0	NOUN
fumecheng-11587	191	1	+	+	CCONJ
fumecheng-11587	191	2	∑	∑	PUNCT
fumecheng-11587	192	1	[	[	X
fumecheng-11587	192	2	𝛥𝑎𝑛	𝛥𝑎𝑛	NOUN
fumecheng-11587	192	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	192	4	𝑛	𝑛	PRON
fumecheng-11587	192	5	𝜏	𝜏	NOUN
fumecheng-11587	192	6	+	+	CCONJ
fumecheng-11587	192	7	𝛥𝑏𝑛	𝛥𝑏𝑛	ADJ
fumecheng-11587	192	8	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
fumecheng-11587	192	9	𝑛	𝑛	ADP
fumecheng-11587	192	10	𝜏]𝑁	𝜏]𝑁	ADJ
fumecheng-11587	192	11	𝑛=1	𝑛=1	NOUN
fumecheng-11587	192	12	=	=	SYM
fumecheng-11587	192	13	𝑪𝜟𝑨	𝑪𝜟𝑨	PROPN
fumecheng-11587	192	14	,	,	PUNCT
fumecheng-11587	192	15	(	(	PUNCT
fumecheng-11587	192	16	19	19	NUM
fumecheng-11587	192	17	)	)	PUNCT
fumecheng-11587	192	18	where	where	SCONJ
fumecheng-11587	192	19	the	the	DET
fumecheng-11587	192	20	vector	vector	NOUN
fumecheng-11587	192	21	c	c	NOUN
fumecheng-11587	192	22	,	,	PUNCT
fumecheng-11587	192	23	and	and	CCONJ
fumecheng-11587	192	24	vectors	vector	NOUN
fumecheng-11587	192	25	a0	a0	NOUN
fumecheng-11587	192	26	and	and	CCONJ
fumecheng-11587	192	27	δa	δa	NOUN
fumecheng-11587	192	28	with	with	ADP
fumecheng-11587	192	29	unknown	unknown	ADJ
fumecheng-11587	192	30	constants	constant	NOUN
fumecheng-11587	192	31	are	be	AUX
fumecheng-11587	192	32	given	give	VERB
fumecheng-11587	192	33	as	as	ADP
fumecheng-11587	192	34	:	:	PUNCT
fumecheng-11587	192	35	𝑪	𝑪	X
fumecheng-11587	192	36	=	=	PUNCT
fumecheng-11587	193	1	[	[	X
fumecheng-11587	193	2	1	1	NUM
fumecheng-11587	193	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	193	4	𝜏	𝜏	X
fumecheng-11587	193	5	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	193	6	2	2	NUM
fumecheng-11587	193	7	𝜏	𝜏	NOUN
fumecheng-11587	193	8	…	…	PUNCT
fumecheng-11587	193	9	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	194	1	𝑁	𝑁	PROPN
fumecheng-11587	194	2	𝜏	𝜏	X
fumecheng-11587	194	3	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
fumecheng-11587	194	4	𝜏	𝜏	DET
fumecheng-11587	194	5	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
fumecheng-11587	194	6	2	2	NUM
fumecheng-11587	194	7	𝜏	𝜏	NOUN
fumecheng-11587	194	8	…	…	PUNCT
fumecheng-11587	194	9	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
fumecheng-11587	194	10	𝑁	𝑁	PROPN
fumecheng-11587	194	11	𝜏	𝜏	NOUN
fumecheng-11587	194	12	]	]	PUNCT
fumecheng-11587	194	13	,	,	PUNCT
fumecheng-11587	194	14	(	(	PUNCT
fumecheng-11587	194	15	20	20	NUM
fumecheng-11587	194	16	)	)	PUNCT
fumecheng-11587	194	17	𝑨𝟎	𝑨𝟎	NOUN
fumecheng-11587	195	1	=	=	PUNCT
fumecheng-11587	196	1	[	[	X
fumecheng-11587	196	2	𝑎0	𝑎0	ADV
fumecheng-11587	196	3	𝑎1	𝑎1	VERB
fumecheng-11587	196	4	𝑎2	𝑎2	NOUN
fumecheng-11587	196	5	…	…	PUNCT
fumecheng-11587	196	6	𝑎𝑁	𝑎𝑁	ADJ
fumecheng-11587	196	7	𝑏1	𝑏1	ADJ
fumecheng-11587	196	8	𝑏2	𝑏2	NOUN
fumecheng-11587	196	9	…	…	PUNCT
fumecheng-11587	196	10	𝑏𝑁]𝑇	𝑏𝑁]𝑇	PROPN
fumecheng-11587	196	11	,	,	PUNCT
fumecheng-11587	196	12	(	(	PUNCT
fumecheng-11587	196	13	21	21	NUM
fumecheng-11587	196	14	)	)	PUNCT
fumecheng-11587	196	15	𝜟𝑨	𝜟𝑨	NOUN
fumecheng-11587	196	16	=	=	PUNCT
fumecheng-11587	197	1	[	[	X
fumecheng-11587	197	2	𝛥𝑎0	𝛥𝑎0	NOUN
fumecheng-11587	197	3	𝛥𝑎1	𝛥𝑎1	PROPN
fumecheng-11587	197	4	𝛥𝑎2	𝛥𝑎2	NOUN
fumecheng-11587	197	5	…	…	PUNCT
fumecheng-11587	197	6	𝛥𝑎𝑁	𝛥𝑎𝑁	PROPN
fumecheng-11587	197	7	𝛥𝑏1	𝛥𝑏1	NOUN
fumecheng-11587	197	8	𝛥𝑏2	𝛥𝑏2	NOUN
fumecheng-11587	197	9	…	…	PUNCT
fumecheng-11587	197	10	𝛥𝑏𝑁]𝑇	𝛥𝑏𝑁]𝑇	X
fumecheng-11587	197	11	.	.	PUNCT
fumecheng-11587	198	1	(	(	PUNCT
fumecheng-11587	198	2	22	22	NUM
fumecheng-11587	198	3	)	)	PUNCT
fumecheng-11587	198	4	substituting	substitute	VERB
fumecheng-11587	198	5	eqs.(18)-(22	eqs.(18)-(22	NOUN
fumecheng-11587	198	6	)	)	PUNCT
fumecheng-11587	198	7	into	into	ADP
fumecheng-11587	198	8	eq	eq	NOUN
fumecheng-11587	198	9	.	.	PUNCT
fumecheng-11587	199	1	(	(	PUNCT
fumecheng-11587	199	2	16	16	NUM
fumecheng-11587	199	3	)	)	PUNCT
fumecheng-11587	199	4	and	and	CCONJ
fumecheng-11587	199	5	applying	apply	VERB
fumecheng-11587	199	6	the	the	DET
fumecheng-11587	199	7	galerkin	galerkin	ADJ
fumecheng-11587	199	8	procedure	procedure	NOUN
fumecheng-11587	199	9	leads	lead	VERB
fumecheng-11587	199	10	to	to	ADP
fumecheng-11587	199	11	the	the	DET
fumecheng-11587	199	12	system	system	NOUN
fumecheng-11587	199	13	of	of	ADP
fumecheng-11587	199	14	linearized	linearize	VERB
fumecheng-11587	199	15	algebraic	algebraic	ADJ
fumecheng-11587	199	16	equations	equation	NOUN
fumecheng-11587	199	17	in	in	ADP
fumecheng-11587	199	18	terms	term	NOUN
fumecheng-11587	199	19	of	of	ADP
fumecheng-11587	199	20	δa	δa	NOUN
fumecheng-11587	199	21	given	give	VERB
fumecheng-11587	199	22	as	as	ADP
fumecheng-11587	199	23	𝑲𝜟𝑨	𝑲𝜟𝑨	PROPN
fumecheng-11587	199	24	+	+	CCONJ
fumecheng-11587	199	25	𝑽𝛥𝛺	𝑽𝛥𝛺	NOUN
fumecheng-11587	199	26	=	=	SYM
fumecheng-11587	199	27	𝑹	𝑹	NOUN
fumecheng-11587	199	28	,	,	PUNCT
fumecheng-11587	199	29	(	(	PUNCT
fumecheng-11587	199	30	23	23	NUM
fumecheng-11587	199	31	)	)	PUNCT
fumecheng-11587	199	32	where	where	SCONJ
fumecheng-11587	199	33	,	,	PUNCT
fumecheng-11587	199	34	elements	element	NOUN
fumecheng-11587	199	35	of	of	ADP
fumecheng-11587	199	36	the	the	DET
fumecheng-11587	199	37	jacobi	jacobi	PROPN
fumecheng-11587	199	38	matrix	matrix	NOUN
fumecheng-11587	199	39	k	k	NOUN
fumecheng-11587	199	40	of	of	ADP
fumecheng-11587	199	41	size	size	NOUN
fumecheng-11587	199	42	[	[	X
fumecheng-11587	199	43	2n+1	2n+1	PROPN
fumecheng-11587	199	44	,	,	PUNCT
fumecheng-11587	199	45	2n+1	2n+1	PROPN
fumecheng-11587	199	46	]	]	PUNCT
fumecheng-11587	199	47	,	,	PUNCT
fumecheng-11587	199	48	the	the	DET
fumecheng-11587	199	49	corrective	corrective	ADJ
fumecheng-11587	199	50	vector	vector	NOUN
fumecheng-11587	199	51	r	r	NOUN
fumecheng-11587	199	52	,	,	PUNCT
fumecheng-11587	199	53	and	and	CCONJ
fumecheng-11587	199	54	vector	vector	NOUN
fumecheng-11587	199	55	v	v	NOUN
fumecheng-11587	199	56	,	,	PUNCT
fumecheng-11587	199	57	both	both	DET
fumecheng-11587	199	58	of	of	ADP
fumecheng-11587	199	59	size	size	NOUN
fumecheng-11587	199	60	[	[	X
fumecheng-11587	199	61	2n+1	2n+1	PROPN
fumecheng-11587	199	62	,	,	PUNCT
fumecheng-11587	199	63	1	1	NUM
fumecheng-11587	199	64	]	]	PUNCT
fumecheng-11587	199	65	,	,	PUNCT
fumecheng-11587	199	66	are	be	AUX
fumecheng-11587	199	67	defined	define	VERB
fumecheng-11587	199	68	as	as	ADP
fumecheng-11587	199	69	:	:	PUNCT
fumecheng-11587	199	70	𝑲	𝑲	NOUN
fumecheng-11587	199	71	=	=	SYM
fumecheng-11587	199	72	1	1	NUM
fumecheng-11587	199	73	2𝜋	2𝜋	NUM
fumecheng-11587	199	74	∫	∫	NOUN
fumecheng-11587	200	1	[	[	X
fumecheng-11587	200	2	𝛺0	𝛺0	PROPN
fumecheng-11587	200	3	2𝑪𝑇𝑪″	2𝑪𝑇𝑪″	PROPN
fumecheng-11587	201	1	+	+	CCONJ
fumecheng-11587	201	2	𝛾𝛺0𝑪𝑇𝑪′	𝛾𝛺0𝑪𝑇𝑪′	NOUN
fumecheng-11587	201	3	+	+	NUM
fumecheng-11587	201	4	𝜔0	𝜔0	NOUN
fumecheng-11587	201	5	2𝑪𝑇𝑪	2𝑪𝑇𝑪	NOUN
fumecheng-11587	201	6	+	+	CCONJ
fumecheng-11587	201	7	3𝜃𝑞0	3𝜃𝑞0	NUM
fumecheng-11587	201	8	2𝑪𝑇𝑪	2𝑪𝑇𝑪	NOUN
fumecheng-11587	201	9	]	]	PUNCT
fumecheng-11587	201	10	2𝜋	2𝜋	NOUN
fumecheng-11587	201	11	0	0	NUM
fumecheng-11587	201	12	𝑑𝜏	𝑑𝜏	PROPN
fumecheng-11587	201	13	,	,	PUNCT
fumecheng-11587	201	14	(	(	PUNCT
fumecheng-11587	201	15	24	24	NUM
fumecheng-11587	201	16	)	)	PUNCT
fumecheng-11587	201	17	𝑹	𝑹	NOUN
fumecheng-11587	201	18	=	=	PUNCT
fumecheng-11587	201	19	−	−	PROPN
fumecheng-11587	201	20	1	1	NUM
fumecheng-11587	201	21	2𝜋	2𝜋	NUM
fumecheng-11587	201	22	∫	∫	NOUN
fumecheng-11587	202	1	[	[	X
fumecheng-11587	202	2	(	(	PUNCT
fumecheng-11587	202	3	𝛺0	𝛺0	PROPN
fumecheng-11587	202	4	2𝑪𝑇𝑪″	2𝑪𝑇𝑪″	PROPN
fumecheng-11587	203	1	+	+	CCONJ
fumecheng-11587	203	2	𝛾𝛺0𝑪𝑇𝑪′	𝛾𝛺0𝑪𝑇𝑪′	NOUN
fumecheng-11587	203	3	+	+	NUM
fumecheng-11587	203	4	𝜔0	𝜔0	NOUN
fumecheng-11587	203	5	2𝑪𝑇𝑪	2𝑪𝑇𝑪	NOUN
fumecheng-11587	203	6	+	+	CCONJ
fumecheng-11587	203	7	𝜃𝑞0	𝜃𝑞0	X
fumecheng-11587	203	8	2𝑪𝑇𝑪)𝑨𝟎	2𝑪𝑇𝑪)𝑨𝟎	NUM
fumecheng-11587	203	9	+	+	CCONJ
fumecheng-11587	203	10	𝑪𝑇𝑓	𝑪𝑇𝑓	NOUN
fumecheng-11587	203	11	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
fumecheng-11587	203	12	𝜏	𝜏	X
fumecheng-11587	203	13	]	]	X
fumecheng-11587	203	14	2𝜋	2𝜋	NOUN
fumecheng-11587	203	15	0	0	NUM
fumecheng-11587	203	16	𝑑𝜏	𝑑𝜏	PROPN
fumecheng-11587	203	17	,	,	PUNCT
fumecheng-11587	203	18	(	(	PUNCT
fumecheng-11587	203	19	25	25	NUM
fumecheng-11587	203	20	)	)	PUNCT
fumecheng-11587	203	21	𝑽	𝑽	NOUN
fumecheng-11587	203	22	=	=	SYM
fumecheng-11587	203	23	1	1	NUM
fumecheng-11587	203	24	2𝜋	2𝜋	NUM
fumecheng-11587	203	25	∫	∫	NOUN
fumecheng-11587	204	1	[	[	X
fumecheng-11587	204	2	2𝛺𝑪𝑇𝑪″	2𝛺𝑪𝑇𝑪″	NUM
fumecheng-11587	204	3	]	]	X
fumecheng-11587	204	4	2𝜋	2𝜋	NOUN
fumecheng-11587	204	5	0	0	PUNCT
fumecheng-11587	205	1	𝑑𝜏𝑨𝟎	𝑑𝜏𝑨𝟎	PROPN
fumecheng-11587	205	2	,	,	PUNCT
fumecheng-11587	205	3	(	(	PUNCT
fumecheng-11587	205	4	26	26	NUM
fumecheng-11587	205	5	)	)	PUNCT
fumecheng-11587	205	6	with	with	ADP
fumecheng-11587	205	7	(	(	PUNCT
fumecheng-11587	205	8	)	)	PUNCT
fumecheng-11587	205	9	'	'	PUNCT
fumecheng-11587	205	10	denoting	denote	VERB
fumecheng-11587	205	11	the	the	DET
fumecheng-11587	205	12	derivative	derivative	NOUN
fumecheng-11587	205	13	with	with	ADP
fumecheng-11587	205	14	respect	respect	NOUN
fumecheng-11587	205	15	to	to	ADP
fumecheng-11587	205	16	non	non	ADJ
fumecheng-11587	205	17	-	-	ADJ
fumecheng-11587	205	18	dimensional	dimensional	ADJ
fumecheng-11587	205	19	time	time	NOUN
fumecheng-11587	205	20	τ̅.	τ̅.	NOUN
fumecheng-11587	205	21	if	if	SCONJ
fumecheng-11587	205	22	we	we	PRON
fumecheng-11587	205	23	want	want	VERB
fumecheng-11587	205	24	to	to	PART
fumecheng-11587	205	25	get	get	VERB
fumecheng-11587	205	26	the	the	DET
fumecheng-11587	205	27	solution	solution	NOUN
fumecheng-11587	205	28	at	at	ADP
fumecheng-11587	205	29	a	a	DET
fumecheng-11587	205	30	given	give	VERB
fumecheng-11587	205	31	single	single	ADJ
fumecheng-11587	205	32	frequency	frequency	NOUN
fumecheng-11587	205	33	,	,	PUNCT
fumecheng-11587	205	34	we	we	PRON
fumecheng-11587	205	35	should	should	AUX
fumecheng-11587	205	36	set	set	VERB
fumecheng-11587	205	37	δω	δω	NOUN
fumecheng-11587	205	38	to	to	ADP
fumecheng-11587	205	39	zero	zero	NUM
fumecheng-11587	205	40	in	in	ADP
fumecheng-11587	205	41	eq	eq	ADP
fumecheng-11587	205	42	.	.	PUNCT
fumecheng-11587	206	1	(	(	PUNCT
fumecheng-11587	206	2	23	23	NUM
fumecheng-11587	206	3	)	)	PUNCT
fumecheng-11587	206	4	.	.	PUNCT
fumecheng-11587	207	1	otherwise	otherwise	ADV
fumecheng-11587	207	2	,	,	PUNCT
fumecheng-11587	207	3	we	we	PRON
fumecheng-11587	207	4	solve	solve	VERB
fumecheng-11587	207	5	eq	eq	ADP
fumecheng-11587	207	6	.	.	PUNCT
fumecheng-11587	208	1	(	(	PUNCT
fumecheng-11587	208	2	23	23	NUM
fumecheng-11587	208	3	)	)	PUNCT
fumecheng-11587	208	4	for	for	ADP
fumecheng-11587	208	5	both	both	CCONJ
fumecheng-11587	208	6	δa	δa	NOUN
fumecheng-11587	208	7	and	and	CCONJ
fumecheng-11587	208	8	δω	δω	PROPN
fumecheng-11587	208	9	,	,	PUNCT
fumecheng-11587	208	10	by	by	ADP
fumecheng-11587	208	11	inserting	insert	VERB
fumecheng-11587	208	12	δω	δω	NOUN
fumecheng-11587	208	13	in	in	ADP
fumecheng-11587	208	14	the	the	DET
fumecheng-11587	208	15	first	first	ADJ
fumecheng-11587	208	16	entry	entry	NOUN
fumecheng-11587	208	17	of	of	ADP
fumecheng-11587	208	18	the	the	DET
fumecheng-11587	208	19	vector	vector	NOUN
fumecheng-11587	208	20	δa	δa	ADV
fumecheng-11587	208	21	and	and	CCONJ
fumecheng-11587	208	22	transforming	transform	VERB
fumecheng-11587	208	23	the	the	DET
fumecheng-11587	208	24	system	system	NOUN
fumecheng-11587	208	25	of	of	ADP
fumecheng-11587	208	26	equations	equation	NOUN
fumecheng-11587	208	27	.	.	PUNCT
fumecheng-11587	209	1	we	we	PRON
fumecheng-11587	209	2	initialize	initialize	VERB
fumecheng-11587	209	3	the	the	DET
fumecheng-11587	209	4	solution	solution	NOUN
fumecheng-11587	209	5	process	process	NOUN
fumecheng-11587	209	6	by	by	ADP
fumecheng-11587	209	7	entering	enter	VERB
fumecheng-11587	209	8	guessed	guess	VERB
fumecheng-11587	209	9	values	value	NOUN
fumecheng-11587	209	10	of	of	ADP
fumecheng-11587	209	11	a	a	PRON
fumecheng-11587	209	12	,	,	PUNCT
fumecheng-11587	209	13	and	and	CCONJ
fumecheng-11587	209	14	calculating	calculate	VERB
fumecheng-11587	209	15	δa	δa	ADV
fumecheng-11587	209	16	by	by	ADP
fumecheng-11587	209	17	using	use	VERB
fumecheng-11587	209	18	the	the	DET
fumecheng-11587	209	19	eq	eq	NOUN
fumecheng-11587	209	20	.	.	PUNCT
fumecheng-11587	210	1	(	(	PUNCT
fumecheng-11587	210	2	23	23	NUM
fumecheng-11587	210	3	)	)	PUNCT
fumecheng-11587	210	4	.	.	PUNCT
fumecheng-11587	211	1	the	the	DET
fumecheng-11587	211	2	solution	solution	NOUN
fumecheng-11587	211	3	δa	δa	ADV
fumecheng-11587	211	4	is	be	AUX
fumecheng-11587	211	5	then	then	ADV
fumecheng-11587	211	6	added	add	VERB
fumecheng-11587	211	7	to	to	ADP
fumecheng-11587	211	8	the	the	DET
fumecheng-11587	211	9	current	current	ADJ
fumecheng-11587	211	10	estimated	estimate	VERB
fumecheng-11587	211	11	value	value	NOUN
fumecheng-11587	211	12	of	of	ADP
fumecheng-11587	211	13	a	a	PRON
fumecheng-11587	211	14	to	to	PART
fumecheng-11587	211	15	determine	determine	VERB
fumecheng-11587	211	16	the	the	DET
fumecheng-11587	211	17	new	new	ADJ
fumecheng-11587	211	18	vector	vector	NOUN
fumecheng-11587	211	19	a	a	PROPN
fumecheng-11587	211	20	,	,	PUNCT
fumecheng-11587	211	21	i.e	i.e	PROPN
fumecheng-11587	211	22	,	,	PUNCT
fumecheng-11587	211	23	𝑨𝒌+𝟏	𝑨𝒌+𝟏	X
fumecheng-11587	211	24	=	=	PUNCT
fumecheng-11587	212	1	𝑨𝒌	𝑨𝒌	PROPN
fumecheng-11587	212	2	+	+	CCONJ
fumecheng-11587	212	3	𝜟𝑨.	𝜟𝑨.	ADP
fumecheng-11587	212	4	(	(	PUNCT
fumecheng-11587	212	5	27	27	NUM
fumecheng-11587	212	6	)	)	PUNCT
fumecheng-11587	212	7	we	we	PRON
fumecheng-11587	212	8	repeat	repeat	VERB
fumecheng-11587	212	9	this	this	DET
fumecheng-11587	212	10	process	process	NOUN
fumecheng-11587	212	11	until	until	SCONJ
fumecheng-11587	212	12	the	the	DET
fumecheng-11587	212	13	value	value	NOUN
fumecheng-11587	212	14	of	of	ADP
fumecheng-11587	212	15	the	the	DET
fumecheng-11587	212	16	residuum	residuum	NOUN
fumecheng-11587	212	17	norm	norm	NOUN
fumecheng-11587	212	18	|r|	|r|	NOUN
fumecheng-11587	212	19	is	be	AUX
fumecheng-11587	212	20	within	within	ADP
fumecheng-11587	212	21	the	the	DET
fumecheng-11587	212	22	preset	preset	ADJ
fumecheng-11587	212	23	tolerance	tolerance	NOUN
fumecheng-11587	212	24	(	(	PUNCT
fumecheng-11587	212	25	in	in	ADP
fumecheng-11587	212	26	our	our	PRON
fumecheng-11587	212	27	case	case	NOUN
fumecheng-11587	212	28	less	less	ADJ
fumecheng-11587	212	29	than	than	ADP
fumecheng-11587	212	30	10	10	NUM
fumecheng-11587	212	31	-	-	SYM
fumecheng-11587	212	32	10	10	NUM
fumecheng-11587	212	33	)	)	PUNCT
fumecheng-11587	212	34	.	.	PUNCT
fumecheng-11587	213	1	vibration	vibration	NOUN
fumecheng-11587	213	2	and	and	CCONJ
fumecheng-11587	213	3	stability	stability	NOUN
fumecheng-11587	213	4	of	of	ADP
fumecheng-11587	213	5	a	a	DET
fumecheng-11587	213	6	nonlinear	nonlinear	ADJ
fumecheng-11587	213	7	nonlocal	nonlocal	ADJ
fumecheng-11587	213	8	strain	strain	NOUN
fumecheng-11587	213	9	-	-	PUNCT
fumecheng-11587	213	10	gradient	gradient	NOUN
fumecheng-11587	213	11	fg	fg	PROPN
fumecheng-11587	213	12	beam	beam	NOUN
fumecheng-11587	213	13	on	on	ADP
fumecheng-11587	213	14	a	a	DET
fumecheng-11587	213	15	visco	visco	ADJ
fumecheng-11587	213	16	-	-	PUNCT
fumecheng-11587	213	17	pasternak	pasternak	NOUN
fumecheng-11587	213	18	...	...	PUNCT
fumecheng-11587	213	19	717	717	NUM
fumecheng-11587	213	20	3.1.1	3.1.1	NUM
fumecheng-11587	213	21	.	.	PUNCT
fumecheng-11587	214	1	the	the	DET
fumecheng-11587	214	2	continuation	continuation	NOUN
fumecheng-11587	214	3	method	method	VERB
fumecheng-11587	214	4	the	the	DET
fumecheng-11587	214	5	main	main	ADJ
fumecheng-11587	214	6	benefit	benefit	NOUN
fumecheng-11587	214	7	of	of	ADP
fumecheng-11587	214	8	using	use	VERB
fumecheng-11587	214	9	the	the	DET
fumecheng-11587	214	10	continuation	continuation	NOUN
fumecheng-11587	214	11	method	method	NOUN
fumecheng-11587	214	12	is	be	AUX
fumecheng-11587	214	13	the	the	DET
fumecheng-11587	214	14	possibility	possibility	NOUN
fumecheng-11587	214	15	to	to	PART
fumecheng-11587	214	16	compute	compute	VERB
fumecheng-11587	214	17	periodic	periodic	ADJ
fumecheng-11587	214	18	solutions	solution	NOUN
fumecheng-11587	214	19	at	at	ADP
fumecheng-11587	214	20	each	each	DET
fumecheng-11587	214	21	point	point	NOUN
fumecheng-11587	214	22	.	.	PUNCT
fumecheng-11587	215	1	the	the	DET
fumecheng-11587	215	2	requirement	requirement	NOUN
fumecheng-11587	215	3	for	for	ADP
fumecheng-11587	215	4	starting	start	VERB
fumecheng-11587	215	5	the	the	DET
fumecheng-11587	215	6	continuation	continuation	NOUN
fumecheng-11587	215	7	process	process	NOUN
fumecheng-11587	215	8	is	be	AUX
fumecheng-11587	215	9	the	the	DET
fumecheng-11587	215	10	determination	determination	NOUN
fumecheng-11587	215	11	of	of	ADP
fumecheng-11587	215	12	the	the	DET
fumecheng-11587	215	13	periodic	periodic	ADJ
fumecheng-11587	215	14	solutions	solution	NOUN
fumecheng-11587	215	15	in	in	ADP
fumecheng-11587	215	16	two	two	NUM
fumecheng-11587	215	17	successive	successive	ADJ
fumecheng-11587	215	18	points	point	NOUN
fumecheng-11587	215	19	by	by	ADP
fumecheng-11587	215	20	using	use	VERB
fumecheng-11587	215	21	the	the	DET
fumecheng-11587	215	22	ihb	ihb	NOUN
fumecheng-11587	215	23	method	method	NOUN
fumecheng-11587	215	24	.	.	PUNCT
fumecheng-11587	216	1	it	it	PRON
fumecheng-11587	216	2	is	be	AUX
fumecheng-11587	216	3	usual	usual	ADJ
fumecheng-11587	216	4	that	that	SCONJ
fumecheng-11587	216	5	these	these	DET
fumecheng-11587	216	6	initial	initial	ADJ
fumecheng-11587	216	7	points	point	NOUN
fumecheng-11587	216	8	are	be	AUX
fumecheng-11587	216	9	taken	take	VERB
fumecheng-11587	216	10	far	far	ADV
fumecheng-11587	216	11	from	from	ADP
fumecheng-11587	216	12	the	the	DET
fumecheng-11587	216	13	resonant	resonant	ADJ
fumecheng-11587	216	14	state	state	NOUN
fumecheng-11587	216	15	since	since	SCONJ
fumecheng-11587	216	16	response	response	NOUN
fumecheng-11587	216	17	amplitudes	amplitude	NOUN
fumecheng-11587	216	18	at	at	ADP
fumecheng-11587	216	19	both	both	DET
fumecheng-11587	216	20	points	point	NOUN
fumecheng-11587	216	21	have	have	VERB
fumecheng-11587	216	22	similar	similar	ADJ
fumecheng-11587	216	23	values	value	NOUN
fumecheng-11587	216	24	,	,	PUNCT
fumecheng-11587	216	25	which	which	PRON
fumecheng-11587	216	26	are	be	AUX
fumecheng-11587	216	27	also	also	ADV
fumecheng-11587	216	28	small	small	ADJ
fumecheng-11587	216	29	.	.	PUNCT
fumecheng-11587	217	1	subsequently	subsequently	ADV
fumecheng-11587	217	2	,	,	PUNCT
fumecheng-11587	217	3	the	the	DET
fumecheng-11587	217	4	predictor	predictor	NOUN
fumecheng-11587	217	5	-	-	PUNCT
fumecheng-11587	217	6	corrector	corrector	NOUN
fumecheng-11587	217	7	method	method	NOUN
fumecheng-11587	217	8	can	can	AUX
fumecheng-11587	217	9	be	be	AUX
fumecheng-11587	217	10	used	use	VERB
fumecheng-11587	217	11	to	to	PART
fumecheng-11587	217	12	make	make	VERB
fumecheng-11587	217	13	point	point	NOUN
fumecheng-11587	217	14	-	-	PUNCT
fumecheng-11587	217	15	to	to	ADP
fumecheng-11587	217	16	-	-	PUNCT
fumecheng-11587	217	17	point	point	NOUN
fumecheng-11587	217	18	computations	computation	NOUN
fumecheng-11587	217	19	and	and	CCONJ
fumecheng-11587	217	20	obtain	obtain	VERB
fumecheng-11587	217	21	corresponding	correspond	VERB
fumecheng-11587	217	22	branches	branch	NOUN
fumecheng-11587	217	23	of	of	ADP
fumecheng-11587	217	24	the	the	DET
fumecheng-11587	217	25	amplitude	amplitude	NOUN
fumecheng-11587	217	26	-	-	PUNCT
fumecheng-11587	217	27	frequency	frequency	NOUN
fumecheng-11587	217	28	responses	response	NOUN
fumecheng-11587	217	29	.	.	PUNCT
fumecheng-11587	218	1	we	we	PRON
fumecheng-11587	218	2	introduce	introduce	VERB
fumecheng-11587	218	3	new	new	ADJ
fumecheng-11587	218	4	vectors	vector	NOUN
fumecheng-11587	218	5	x	x	PUNCT
fumecheng-11587	219	1	=	=	PUNCT
fumecheng-11587	220	1	[	[	X
fumecheng-11587	220	2	a	a	X
fumecheng-11587	220	3	,	,	PUNCT
fumecheng-11587	220	4	ω]t	ω]t	NOUN
fumecheng-11587	220	5	and	and	CCONJ
fumecheng-11587	220	6	δx	δx	X
fumecheng-11587	221	1	=	=	X
fumecheng-11587	221	2	[	[	X
fumecheng-11587	221	3	δa	δa	NOUN
fumecheng-11587	221	4	,	,	PUNCT
fumecheng-11587	221	5	δω]t	δω]t	PROPN
fumecheng-11587	221	6	,	,	PUNCT
fumecheng-11587	221	7	a	a	DET
fumecheng-11587	221	8	function	function	NOUN
fumecheng-11587	221	9	of	of	ADP
fumecheng-11587	221	10	vector	vector	NOUN
fumecheng-11587	221	11	g(x	g(x	NOUN
fumecheng-11587	221	12	)	)	PUNCT
fumecheng-11587	221	13	=	=	SYM
fumecheng-11587	221	14	xtx	xtx	PROPN
fumecheng-11587	221	15	,	,	PUNCT
fumecheng-11587	221	16	and	and	CCONJ
fumecheng-11587	221	17	an	an	DET
fumecheng-11587	221	18	arc	arc	NOUN
fumecheng-11587	221	19	-	-	PUNCT
fumecheng-11587	221	20	length	length	NOUN
fumecheng-11587	221	21	parameter	parameter	PROPN
fumecheng-11587	221	22	η	η	PROPN
fumecheng-11587	221	23	to	to	PART
fumecheng-11587	221	24	follow	follow	VERB
fumecheng-11587	221	25	direction	direction	NOUN
fumecheng-11587	221	26	of	of	ADP
fumecheng-11587	221	27	the	the	DET
fumecheng-11587	221	28	path	path	NOUN
fumecheng-11587	221	29	.	.	PUNCT
fumecheng-11587	222	1	an	an	DET
fumecheng-11587	222	2	augmented	augment	VERB
fumecheng-11587	222	3	equation	equation	NOUN
fumecheng-11587	222	4	is	be	AUX
fumecheng-11587	222	5	given	give	VERB
fumecheng-11587	222	6	as	as	ADP
fumecheng-11587	222	7	𝑔(𝑿	𝑔(𝑿	NOUN
fumecheng-11587	222	8	)	)	PUNCT
fumecheng-11587	222	9	−	−	ADP
fumecheng-11587	222	10	𝜂	𝜂	NOUN
fumecheng-11587	222	11	=	=	SYM
fumecheng-11587	222	12	0	0	PROPN
fumecheng-11587	222	13	.	.	PUNCT
fumecheng-11587	223	1	(	(	PUNCT
fumecheng-11587	223	2	28	28	NUM
fumecheng-11587	223	3	)	)	PUNCT
fumecheng-11587	223	4	when	when	SCONJ
fumecheng-11587	223	5	two	two	NUM
fumecheng-11587	223	6	previous	previous	ADJ
fumecheng-11587	223	7	points	point	NOUN
fumecheng-11587	223	8	xk-1	xk-1	PUNCT
fumecheng-11587	223	9	and	and	CCONJ
fumecheng-11587	223	10	xk-2	xk-2	PROPN
fumecheng-11587	223	11	of	of	ADP
fumecheng-11587	223	12	the	the	DET
fumecheng-11587	223	13	response	response	NOUN
fumecheng-11587	223	14	curve	curve	NOUN
fumecheng-11587	223	15	are	be	AUX
fumecheng-11587	223	16	known	know	VERB
fumecheng-11587	223	17	,	,	PUNCT
fumecheng-11587	223	18	the	the	DET
fumecheng-11587	223	19	slope	slope	NOUN
fumecheng-11587	223	20	for	for	ADP
fumecheng-11587	223	21	computation	computation	NOUN
fumecheng-11587	223	22	of	of	ADP
fumecheng-11587	223	23	the	the	DET
fumecheng-11587	223	24	next	next	ADJ
fumecheng-11587	223	25	point	point	NOUN
fumecheng-11587	223	26	can	can	AUX
fumecheng-11587	223	27	be	be	AUX
fumecheng-11587	223	28	determined	determine	VERB
fumecheng-11587	223	29	as	as	ADP
fumecheng-11587	223	30	𝑿′	𝑿′	PROPN
fumecheng-11587	223	31	=	=	SYM
fumecheng-11587	223	32	𝑿𝒌−𝟏−𝑿𝒌−𝟐	𝑿𝒌−𝟏−𝑿𝒌−𝟐	PROPN
fumecheng-11587	223	33	‖𝑿𝒌−𝟏−𝑿𝒌−𝟐‖	‖𝑿𝒌−𝟏−𝑿𝒌−𝟐‖	NOUN
fumecheng-11587	223	34	.	.	PUNCT
fumecheng-11587	224	1	(	(	PUNCT
fumecheng-11587	224	2	29	29	NUM
fumecheng-11587	224	3	)	)	PUNCT
fumecheng-11587	224	4	the	the	DET
fumecheng-11587	224	5	first	first	ADJ
fumecheng-11587	224	6	prediction	prediction	NOUN
fumecheng-11587	224	7	of	of	ADP
fumecheng-11587	224	8	the	the	DET
fumecheng-11587	224	9	next	next	ADJ
fumecheng-11587	224	10	point	point	NOUN
fumecheng-11587	224	11	is	be	AUX
fumecheng-11587	224	12	obtained	obtain	VERB
fumecheng-11587	224	13	by	by	ADP
fumecheng-11587	224	14	𝑿𝒖	𝑿𝒖	PROPN
fumecheng-11587	224	15	=	=	PUNCT
fumecheng-11587	224	16	𝑿𝒌−𝟏	𝑿𝒌−𝟏	PROPN
fumecheng-11587	224	17	+	+	CCONJ
fumecheng-11587	224	18	𝛥𝜂𝑿′.	𝛥𝜂𝑿′.	NUM
fumecheng-11587	224	19	(	(	PUNCT
fumecheng-11587	224	20	30	30	NUM
fumecheng-11587	224	21	)	)	PUNCT
fumecheng-11587	224	22	after	after	ADP
fumecheng-11587	224	23	extending	extend	VERB
fumecheng-11587	224	24	eq	eq	ADP
fumecheng-11587	224	25	.	.	PUNCT
fumecheng-11587	225	1	(	(	PUNCT
fumecheng-11587	225	2	23	23	NUM
fumecheng-11587	225	3	)	)	PUNCT
fumecheng-11587	225	4	with	with	ADP
fumecheng-11587	225	5	eq	eq	NOUN
fumecheng-11587	225	6	.	.	PUNCT
fumecheng-11587	226	1	(	(	PUNCT
fumecheng-11587	226	2	28	28	NUM
fumecheng-11587	226	3	)	)	PUNCT
fumecheng-11587	226	4	we	we	PRON
fumecheng-11587	226	5	have	have	VERB
fumecheng-11587	226	6	[	[	PUNCT
fumecheng-11587	226	7	𝑲	𝑲	DET
fumecheng-11587	226	8	𝑽	𝑽	PROPN
fumecheng-11587	226	9	𝜕𝑔	𝜕𝑔	VERB
fumecheng-11587	226	10	𝜕𝑨	𝜕𝑨	NOUN
fumecheng-11587	226	11	𝜕𝑔	𝜕𝑔	NOUN
fumecheng-11587	226	12	𝜕𝛺	𝜕𝛺	PROPN
fumecheng-11587	226	13	]	]	PUNCT
fumecheng-11587	226	14	[	[	PUNCT
fumecheng-11587	226	15	𝜟𝑨	𝜟𝑨	PROPN
fumecheng-11587	226	16	𝛥𝛺	𝛥𝛺	PROPN
fumecheng-11587	226	17	]	]	X
fumecheng-11587	226	18	=	=	PUNCT
fumecheng-11587	227	1	[	[	PUNCT
fumecheng-11587	227	2	𝑹	𝑹	NOUN
fumecheng-11587	227	3	𝛥𝜂	𝛥𝜂	PROPN
fumecheng-11587	227	4	−	−	NOUN
fumecheng-11587	227	5	𝑔	𝑔	X
fumecheng-11587	227	6	]	]	PUNCT
fumecheng-11587	227	7	.	.	PUNCT
fumecheng-11587	228	1	(	(	PUNCT
fumecheng-11587	228	2	31	31	NUM
fumecheng-11587	228	3	)	)	PUNCT
fumecheng-11587	228	4	more	more	ADJ
fumecheng-11587	228	5	information	information	NOUN
fumecheng-11587	228	6	about	about	ADP
fumecheng-11587	228	7	the	the	DET
fumecheng-11587	228	8	continuation	continuation	NOUN
fumecheng-11587	228	9	method	method	NOUN
fumecheng-11587	228	10	one	one	PRON
fumecheng-11587	228	11	can	can	AUX
fumecheng-11587	228	12	find	find	VERB
fumecheng-11587	228	13	in	in	ADP
fumecheng-11587	228	14	[	[	X
fumecheng-11587	228	15	52	52	NUM
fumecheng-11587	228	16	,	,	PUNCT
fumecheng-11587	228	17	58	58	NUM
fumecheng-11587	228	18	,	,	PUNCT
fumecheng-11587	228	19	59	59	NUM
fumecheng-11587	228	20	]	]	PUNCT
fumecheng-11587	228	21	.	.	PUNCT
fumecheng-11587	229	1	4	4	X
fumecheng-11587	229	2	.	.	X
fumecheng-11587	229	3	stability	stability	NOUN
fumecheng-11587	229	4	analysis	analysis	NOUN
fumecheng-11587	229	5	when	when	SCONJ
fumecheng-11587	229	6	the	the	DET
fumecheng-11587	229	7	periodic	periodic	ADJ
fumecheng-11587	229	8	solution	solution	NOUN
fumecheng-11587	229	9	is	be	AUX
fumecheng-11587	229	10	obtained	obtain	VERB
fumecheng-11587	229	11	in	in	ADP
fumecheng-11587	229	12	the	the	DET
fumecheng-11587	229	13	form	form	NOUN
fumecheng-11587	229	14	of	of	ADP
fumecheng-11587	229	15	fourier	fourier	ADJ
fumecheng-11587	229	16	series	series	NOUN
fumecheng-11587	229	17	as	as	ADP
fumecheng-11587	229	18	in	in	ADP
fumecheng-11587	229	19	eq	eq	ADP
fumecheng-11587	229	20	.	.	PUNCT
fumecheng-11587	230	1	(	(	PUNCT
fumecheng-11587	230	2	18	18	NUM
fumecheng-11587	230	3	)	)	PUNCT
fumecheng-11587	230	4	for	for	ADP
fumecheng-11587	230	5	a	a	DET
fumecheng-11587	230	6	chosen	choose	VERB
fumecheng-11587	230	7	value	value	NOUN
fumecheng-11587	230	8	of	of	ADP
fumecheng-11587	230	9	ω	ω	PROPN
fumecheng-11587	230	10	,	,	PUNCT
fumecheng-11587	230	11	we	we	PRON
fumecheng-11587	230	12	can	can	AUX
fumecheng-11587	230	13	investigate	investigate	VERB
fumecheng-11587	230	14	the	the	DET
fumecheng-11587	230	15	local	local	ADJ
fumecheng-11587	230	16	stability	stability	NOUN
fumecheng-11587	230	17	of	of	ADP
fumecheng-11587	230	18	such	such	ADJ
fumecheng-11587	230	19	periodic	periodic	ADJ
fumecheng-11587	230	20	solution	solution	NOUN
fumecheng-11587	230	21	by	by	ADP
fumecheng-11587	230	22	using	use	VERB
fumecheng-11587	230	23	the	the	DET
fumecheng-11587	230	24	floquet	floquet	NOUN
fumecheng-11587	230	25	theory	theory	NOUN
fumecheng-11587	230	26	[	[	X
fumecheng-11587	230	27	60	60	NUM
fumecheng-11587	230	28	,	,	PUNCT
fumecheng-11587	230	29	61	61	NUM
fumecheng-11587	230	30	]	]	PUNCT
fumecheng-11587	230	31	.	.	PUNCT
fumecheng-11587	231	1	based	base	VERB
fumecheng-11587	231	2	on	on	ADP
fumecheng-11587	231	3	this	this	DET
fumecheng-11587	231	4	theory	theory	NOUN
fumecheng-11587	231	5	,	,	PUNCT
fumecheng-11587	231	6	we	we	PRON
fumecheng-11587	231	7	applied	apply	VERB
fumecheng-11587	231	8	the	the	DET
fumecheng-11587	231	9	methodology	methodology	NOUN
fumecheng-11587	231	10	given	give	VERB
fumecheng-11587	231	11	by	by	ADP
fumecheng-11587	231	12	hsu	hsu	PROPN
fumecheng-11587	232	1	[	[	X
fumecheng-11587	232	2	62	62	NUM
fumecheng-11587	232	3	]	]	PUNCT
fumecheng-11587	232	4	for	for	ADP
fumecheng-11587	232	5	the	the	DET
fumecheng-11587	232	6	approximation	approximation	NOUN
fumecheng-11587	232	7	of	of	ADP
fumecheng-11587	232	8	the	the	DET
fumecheng-11587	232	9	transition	transition	NOUN
fumecheng-11587	232	10	matrix	matrix	NOUN
fumecheng-11587	232	11	during	during	ADP
fumecheng-11587	232	12	one	one	NUM
fumecheng-11587	232	13	period	period	NOUN
fumecheng-11587	232	14	.	.	PUNCT
fumecheng-11587	233	1	let	let	VERB
fumecheng-11587	233	2	us	we	PRON
fumecheng-11587	233	3	consider	consider	VERB
fumecheng-11587	233	4	that	that	SCONJ
fumecheng-11587	233	5	the	the	DET
fumecheng-11587	233	6	solution	solution	NOUN
fumecheng-11587	233	7	of	of	ADP
fumecheng-11587	233	8	eq	eq	PROPN
fumecheng-11587	233	9	.	.	PUNCT
fumecheng-11587	234	1	(	(	PUNCT
fumecheng-11587	234	2	14	14	NUM
fumecheng-11587	234	3	)	)	PUNCT
fumecheng-11587	234	4	is	be	AUX
fumecheng-11587	234	5	given	give	VERB
fumecheng-11587	234	6	as	as	ADP
fumecheng-11587	234	7	𝑞(𝜏	𝑞(𝜏	NOUN
fumecheng-11587	234	8	)	)	PUNCT
fumecheng-11587	234	9	=	=	SYM
fumecheng-11587	234	10	𝑞0(𝜏	𝑞0(𝜏	PROPN
fumecheng-11587	234	11	)	)	PUNCT
fumecheng-11587	234	12	+	+	CCONJ
fumecheng-11587	235	1	𝛥𝑞	𝛥𝑞	PROPN
fumecheng-11587	235	2	(	(	PUNCT
fumecheng-11587	235	3	32	32	NUM
fumecheng-11587	235	4	)	)	PUNCT
fumecheng-11587	235	5	where	where	SCONJ
fumecheng-11587	235	6	δq	δq	ADP
fumecheng-11587	235	7	denotes	denote	VERB
fumecheng-11587	235	8	a	a	DET
fumecheng-11587	235	9	small	small	ADJ
fumecheng-11587	235	10	perturbation	perturbation	NOUN
fumecheng-11587	235	11	in	in	ADP
fumecheng-11587	235	12	the	the	DET
fumecheng-11587	235	13	proximity	proximity	NOUN
fumecheng-11587	235	14	of	of	ADP
fumecheng-11587	235	15	previously	previously	ADV
fumecheng-11587	235	16	determined	determine	VERB
fumecheng-11587	235	17	periodic	periodic	ADJ
fumecheng-11587	235	18	solution	solution	NOUN
fumecheng-11587	235	19	q0	q0	NOUN
fumecheng-11587	235	20	.	.	PUNCT
fumecheng-11587	236	1	by	by	ADP
fumecheng-11587	236	2	substituting	substitute	VERB
fumecheng-11587	236	3	eq	eq	PROPN
fumecheng-11587	236	4	.	.	PUNCT
fumecheng-11587	237	1	(	(	PUNCT
fumecheng-11587	237	2	32	32	NUM
fumecheng-11587	237	3	)	)	PUNCT
fumecheng-11587	237	4	into	into	ADP
fumecheng-11587	237	5	eq	eq	NOUN
fumecheng-11587	237	6	.	.	PUNCT
fumecheng-11587	238	1	(	(	PUNCT
fumecheng-11587	238	2	14	14	NUM
fumecheng-11587	238	3	)	)	PUNCT
fumecheng-11587	238	4	,	,	PUNCT
fumecheng-11587	238	5	and	and	CCONJ
fumecheng-11587	238	6	after	after	ADP
fumecheng-11587	238	7	linearization	linearization	NOUN
fumecheng-11587	238	8	,	,	PUNCT
fumecheng-11587	238	9	one	one	PRON
fumecheng-11587	238	10	can	can	AUX
fumecheng-11587	238	11	obtain	obtain	VERB
fumecheng-11587	238	12	the	the	DET
fumecheng-11587	238	13	linear	linear	ADJ
fumecheng-11587	238	14	differential	differential	ADJ
fumecheng-11587	238	15	equation	equation	NOUN
fumecheng-11587	238	16	with	with	ADP
fumecheng-11587	238	17	time	time	NOUN
fumecheng-11587	238	18	-	-	PUNCT
fumecheng-11587	238	19	periodic	periodic	ADJ
fumecheng-11587	238	20	coefficients	coefficient	NOUN
fumecheng-11587	238	21	given	give	VERB
fumecheng-11587	238	22	as	as	ADP
fumecheng-11587	238	23	:	:	PUNCT
fumecheng-11587	238	24	𝛺2𝛥𝑞″	𝛺2𝛥𝑞″	NOUN
fumecheng-11587	238	25	+	+	PRON
fumecheng-11587	238	26	𝛾𝛺𝛥𝑞′	𝛾𝛺𝛥𝑞′	PART
fumecheng-11587	239	1	+	+	NUM
fumecheng-11587	239	2	𝜔0	𝜔0	NOUN
fumecheng-11587	239	3	2𝛥𝑞	2𝛥𝑞	NUM
fumecheng-11587	239	4	+	+	NOUN
fumecheng-11587	239	5	3𝜃𝑞0	3𝜃𝑞0	NUM
fumecheng-11587	239	6	2𝛥𝑞	2𝛥𝑞	NUM
fumecheng-11587	239	7	=	=	SYM
fumecheng-11587	239	8	0	0	NUM
fumecheng-11587	239	9	,	,	PUNCT
fumecheng-11587	239	10	(	(	PUNCT
fumecheng-11587	239	11	33	33	NUM
fumecheng-11587	239	12	)	)	PUNCT
fumecheng-11587	239	13	to	to	PART
fumecheng-11587	239	14	determine	determine	VERB
fumecheng-11587	239	15	the	the	DET
fumecheng-11587	239	16	stability	stability	NOUN
fumecheng-11587	239	17	of	of	ADP
fumecheng-11587	239	18	the	the	DET
fumecheng-11587	239	19	obtained	obtain	VERB
fumecheng-11587	239	20	periodic	periodic	ADJ
fumecheng-11587	239	21	solutions	solution	NOUN
fumecheng-11587	239	22	using	use	VERB
fumecheng-11587	239	23	the	the	DET
fumecheng-11587	239	24	floquet	floquet	NOUN
fumecheng-11587	239	25	theory	theory	NOUN
fumecheng-11587	239	26	,	,	PUNCT
fumecheng-11587	239	27	the	the	DET
fumecheng-11587	239	28	transformation	transformation	NOUN
fumecheng-11587	239	29	of	of	ADP
fumecheng-11587	239	30	eq	eq	PROPN
fumecheng-11587	239	31	.	.	PUNCT
fumecheng-11587	240	1	(	(	PUNCT
fumecheng-11587	240	2	33	33	NUM
fumecheng-11587	240	3	)	)	PUNCT
fumecheng-11587	240	4	into	into	ADP
fumecheng-11587	240	5	the	the	DET
fumecheng-11587	240	6	state	state	NOUN
fumecheng-11587	240	7	-	-	PUNCT
fumecheng-11587	240	8	space	space	NOUN
fumecheng-11587	240	9	form	form	NOUN
fumecheng-11587	240	10	should	should	AUX
fumecheng-11587	240	11	be	be	AUX
fumecheng-11587	240	12	performed	perform	VERB
fumecheng-11587	240	13	as	as	ADP
fumecheng-11587	240	14	𝑑𝒀	𝑑𝒀	ADJ
fumecheng-11587	240	15	𝑑𝜏	𝑑𝜏	NOUN
fumecheng-11587	240	16	=	=	SYM
fumecheng-11587	240	17	𝑷(𝜏)𝒀	𝑷(𝜏)𝒀	X
fumecheng-11587	240	18	(	(	PUNCT
fumecheng-11587	240	19	34	34	NUM
fumecheng-11587	240	20	)	)	PUNCT
fumecheng-11587	240	21	where	where	SCONJ
fumecheng-11587	240	22	y	y	PROPN
fumecheng-11587	240	23	(	(	PUNCT
fumecheng-11587	240	24	τ	τ	PROPN
fumecheng-11587	240	25	)	)	PUNCT
fumecheng-11587	241	1	=	=	PUNCT
fumecheng-11587	242	1	[	[	X
fumecheng-11587	242	2	δq	δq	X
fumecheng-11587	242	3	,	,	PUNCT
fumecheng-11587	242	4	δq']t	δq']t	PROPN
fumecheng-11587	242	5	and	and	CCONJ
fumecheng-11587	242	6	p	p	PROPN
fumecheng-11587	242	7	(	(	PUNCT
fumecheng-11587	242	8	τ	τ	PROPN
fumecheng-11587	242	9	)	)	PUNCT
fumecheng-11587	242	10	denotes	denote	VERB
fumecheng-11587	242	11	the	the	DET
fumecheng-11587	242	12	periodic	periodic	ADJ
fumecheng-11587	242	13	matrix	matrix	NOUN
fumecheng-11587	242	14	with	with	ADP
fumecheng-11587	242	15	the	the	DET
fumecheng-11587	242	16	period	period	NOUN
fumecheng-11587	242	17	t	t	NOUN
fumecheng-11587	242	18	=	=	PUNCT
fumecheng-11587	242	19	2π	2π	NOUN
fumecheng-11587	242	20	.	.	PUNCT
fumecheng-11587	243	1	718	718	NUM
fumecheng-11587	243	2	n.	n.	PROPN
fumecheng-11587	243	3	nešić	nešić	PROPN
fumecheng-11587	243	4	,	,	PUNCT
fumecheng-11587	243	5	m.	m.	NOUN
fumecheng-11587	243	6	cajić	cajić	NOUN
fumecheng-11587	243	7	,	,	PUNCT
fumecheng-11587	243	8	d.	d.	PROPN
fumecheng-11587	243	9	karličić	karličić	PROPN
fumecheng-11587	243	10	,	,	PUNCT
fumecheng-11587	243	11	m.	m.	NOUN
fumecheng-11587	243	12	lazarević	lazarević	PROPN
fumecheng-11587	243	13	,	,	PUNCT
fumecheng-11587	243	14	s.	s.	PROPN
fumecheng-11587	243	15	adhikari	adhikari	PROPN
fumecheng-11587	244	1	the	the	DET
fumecheng-11587	244	2	stability	stability	NOUN
fumecheng-11587	244	3	criteria	criterion	NOUN
fumecheng-11587	244	4	based	base	VERB
fumecheng-11587	244	5	on	on	ADP
fumecheng-11587	244	6	the	the	DET
fumecheng-11587	244	7	floquet	floquet	NOUN
fumecheng-11587	244	8	theory	theory	NOUN
fumecheng-11587	244	9	is	be	AUX
fumecheng-11587	244	10	used	use	VERB
fumecheng-11587	244	11	for	for	ADP
fumecheng-11587	244	12	the	the	DET
fumecheng-11587	244	13	determination	determination	NOUN
fumecheng-11587	244	14	of	of	ADP
fumecheng-11587	244	15	the	the	DET
fumecheng-11587	244	16	local	local	ADJ
fumecheng-11587	244	17	stability	stability	NOUN
fumecheng-11587	244	18	of	of	ADP
fumecheng-11587	244	19	periodic	periodic	ADJ
fumecheng-11587	244	20	solutions	solution	NOUN
fumecheng-11587	244	21	and	and	CCONJ
fumecheng-11587	244	22	it	it	PRON
fumecheng-11587	244	23	is	be	AUX
fumecheng-11587	244	24	related	relate	VERB
fumecheng-11587	244	25	to	to	ADP
fumecheng-11587	244	26	the	the	DET
fumecheng-11587	244	27	determination	determination	NOUN
fumecheng-11587	244	28	of	of	ADP
fumecheng-11587	244	29	the	the	DET
fumecheng-11587	244	30	floquet	floquet	NOUN
fumecheng-11587	244	31	multipliers	multiplier	NOUN
fumecheng-11587	244	32	as	as	SCONJ
fumecheng-11587	244	33	hsu	hsu	PROPN
fumecheng-11587	244	34	gave	give	VERB
fumecheng-11587	244	35	in	in	ADP
fumecheng-11587	244	36	[	[	X
fumecheng-11587	244	37	62	62	NUM
fumecheng-11587	244	38	]	]	PUNCT
fumecheng-11587	244	39	.	.	PUNCT
fumecheng-11587	245	1	the	the	DET
fumecheng-11587	245	2	floquet	floquet	PROPN
fumecheng-11587	245	3	multipliers	multiplier	NOUN
fumecheng-11587	245	4	are	be	AUX
fumecheng-11587	245	5	represented	represent	VERB
fumecheng-11587	245	6	by	by	ADP
fumecheng-11587	245	7	the	the	DET
fumecheng-11587	245	8	eigenvalues	eigenvalue	NOUN
fumecheng-11587	245	9	of	of	ADP
fumecheng-11587	245	10	the	the	DET
fumecheng-11587	245	11	monodromy	monodromy	NOUN
fumecheng-11587	245	12	matrix	matrix	NOUN
fumecheng-11587	245	13	.	.	PUNCT
fumecheng-11587	246	1	by	by	ADP
fumecheng-11587	246	2	solving	solve	VERB
fumecheng-11587	246	3	the	the	DET
fumecheng-11587	246	4	corresponding	corresponding	ADJ
fumecheng-11587	246	5	eigenvalue	eigenvalue	PROPN
fumecheng-11587	246	6	problem	problem	NOUN
fumecheng-11587	246	7	,	,	PUNCT
fumecheng-11587	246	8	for	for	ADP
fumecheng-11587	246	9	the	the	DET
fumecheng-11587	246	10	case	case	NOUN
fumecheng-11587	246	11	when	when	SCONJ
fumecheng-11587	246	12	all	all	DET
fumecheng-11587	246	13	floquet	floquet	NOUN
fumecheng-11587	246	14	multipliers	multiplier	NOUN
fumecheng-11587	246	15	are	be	AUX
fumecheng-11587	246	16	located	locate	VERB
fumecheng-11587	246	17	inside	inside	ADP
fumecheng-11587	246	18	the	the	DET
fumecheng-11587	246	19	unit	unit	NOUN
fumecheng-11587	246	20	circle	circle	NOUN
fumecheng-11587	246	21	centered	center	VERB
fumecheng-11587	246	22	at	at	ADP
fumecheng-11587	246	23	the	the	DET
fumecheng-11587	246	24	origin	origin	NOUN
fumecheng-11587	246	25	of	of	ADP
fumecheng-11587	246	26	the	the	DET
fumecheng-11587	246	27	complex	complex	ADJ
fumecheng-11587	246	28	plane	plane	NOUN
fumecheng-11587	246	29	,	,	PUNCT
fumecheng-11587	246	30	the	the	DET
fumecheng-11587	246	31	determined	determined	ADJ
fumecheng-11587	246	32	periodic	periodic	ADJ
fumecheng-11587	246	33	solutions	solution	NOUN
fumecheng-11587	246	34	are	be	AUX
fumecheng-11587	246	35	stable	stable	ADJ
fumecheng-11587	246	36	or	or	CCONJ
fumecheng-11587	246	37	asymptotically	asymptotically	ADV
fumecheng-11587	246	38	stable	stable	ADJ
fumecheng-11587	246	39	.	.	PUNCT
fumecheng-11587	247	1	otherwise	otherwise	ADV
fumecheng-11587	247	2	,	,	PUNCT
fumecheng-11587	247	3	when	when	SCONJ
fumecheng-11587	247	4	the	the	DET
fumecheng-11587	247	5	values	value	NOUN
fumecheng-11587	247	6	of	of	ADP
fumecheng-11587	247	7	floquet	floquet	NOUN
fumecheng-11587	247	8	multipliers	multiplier	NOUN
fumecheng-11587	247	9	are	be	AUX
fumecheng-11587	247	10	outside	outside	ADP
fumecheng-11587	247	11	the	the	DET
fumecheng-11587	247	12	unit	unit	NOUN
fumecheng-11587	247	13	circle	circle	NOUN
fumecheng-11587	247	14	,	,	PUNCT
fumecheng-11587	247	15	the	the	DET
fumecheng-11587	247	16	periodic	periodic	ADJ
fumecheng-11587	247	17	solutions	solution	NOUN
fumecheng-11587	247	18	are	be	AUX
fumecheng-11587	247	19	unstable	unstable	ADJ
fumecheng-11587	247	20	[	[	X
fumecheng-11587	247	21	60	60	NUM
fumecheng-11587	247	22	]	]	PUNCT
fumecheng-11587	247	23	.	.	PUNCT
fumecheng-11587	248	1	depending	depend	VERB
fumecheng-11587	248	2	on	on	ADP
fumecheng-11587	248	3	where	where	SCONJ
fumecheng-11587	248	4	the	the	DET
fumecheng-11587	248	5	floquet	floquet	NOUN
fumecheng-11587	248	6	multipliers	multiplier	NOUN
fumecheng-11587	248	7	or	or	CCONJ
fumecheng-11587	248	8	a	a	DET
fumecheng-11587	248	9	pair	pair	NOUN
fumecheng-11587	248	10	of	of	ADP
fumecheng-11587	248	11	complex	complex	ADJ
fumecheng-11587	248	12	conjugate	conjugate	ADJ
fumecheng-11587	248	13	multipliers	multiplier	NOUN
fumecheng-11587	248	14	cross	cross	VERB
fumecheng-11587	248	15	the	the	DET
fumecheng-11587	248	16	complex	complex	ADJ
fumecheng-11587	248	17	plane	plane	NOUN
fumecheng-11587	248	18	unit	unit	NOUN
fumecheng-11587	248	19	circle	circle	NOUN
fumecheng-11587	248	20	,	,	PUNCT
fumecheng-11587	248	21	different	different	ADJ
fumecheng-11587	248	22	bifurcation	bifurcation	NOUN
fumecheng-11587	248	23	points	point	NOUN
fumecheng-11587	248	24	can	can	AUX
fumecheng-11587	248	25	be	be	AUX
fumecheng-11587	248	26	detected	detect	VERB
fumecheng-11587	248	27	.	.	PUNCT
fumecheng-11587	249	1	introduction	introduction	NOUN
fumecheng-11587	249	2	of	of	ADP
fumecheng-11587	249	3	the	the	DET
fumecheng-11587	249	4	hsu	hsu	PROPN
fumecheng-11587	249	5	procedures	procedure	NOUN
fumecheng-11587	249	6	for	for	ADP
fumecheng-11587	249	7	the	the	DET
fumecheng-11587	249	8	numerical	numerical	ADJ
fumecheng-11587	249	9	approximation	approximation	NOUN
fumecheng-11587	249	10	of	of	ADP
fumecheng-11587	249	11	the	the	DET
fumecheng-11587	249	12	transition	transition	NOUN
fumecheng-11587	249	13	matrix	matrix	NOUN
fumecheng-11587	249	14	during	during	ADP
fumecheng-11587	249	15	one	one	NUM
fumecheng-11587	249	16	period	period	NOUN
fumecheng-11587	249	17	leads	lead	VERB
fumecheng-11587	249	18	to	to	ADP
fumecheng-11587	249	19	the	the	DET
fumecheng-11587	249	20	numerical	numerical	ADJ
fumecheng-11587	249	21	determination	determination	NOUN
fumecheng-11587	249	22	of	of	ADP
fumecheng-11587	249	23	floquet	floquet	NOUN
fumecheng-11587	249	24	multipliers	multiplier	NOUN
fumecheng-11587	249	25	as	as	ADP
fumecheng-11587	249	26	a	a	DET
fumecheng-11587	249	27	solution	solution	NOUN
fumecheng-11587	249	28	of	of	ADP
fumecheng-11587	249	29	the	the	DET
fumecheng-11587	249	30	corresponding	corresponding	ADJ
fumecheng-11587	249	31	eigenvalue	eigenvalue	PROPN
fumecheng-11587	249	32	problem	problem	NOUN
fumecheng-11587	249	33	as	as	SCONJ
fumecheng-11587	249	34	shen	shen	PROPN
fumecheng-11587	249	35	et	et	PROPN
fumecheng-11587	249	36	al	al	PROPN
fumecheng-11587	249	37	.	.	PROPN
fumecheng-11587	249	38	stated	state	VERB
fumecheng-11587	249	39	in	in	ADP
fumecheng-11587	249	40	[	[	X
fumecheng-11587	249	41	60	60	NUM
fumecheng-11587	249	42	]	]	PUNCT
fumecheng-11587	249	43	.	.	PUNCT
fumecheng-11587	250	1	it	it	PRON
fumecheng-11587	250	2	is	be	AUX
fumecheng-11587	250	3	assumed	assume	VERB
fumecheng-11587	250	4	that	that	SCONJ
fumecheng-11587	250	5	the	the	DET
fumecheng-11587	250	6	period	period	NOUN
fumecheng-11587	250	7	t	t	NOUN
fumecheng-11587	250	8	=	=	NOUN
fumecheng-11587	250	9	2π	2π	NOUN
fumecheng-11587	250	10	of	of	ADP
fumecheng-11587	250	11	the	the	DET
fumecheng-11587	250	12	periodic	periodic	ADJ
fumecheng-11587	250	13	solution	solution	NOUN
fumecheng-11587	250	14	q0	q0	PROPN
fumecheng-11587	250	15	(	(	PUNCT
fumecheng-11587	250	16	τ	τ	X
fumecheng-11587	250	17	)	)	PUNCT
fumecheng-11587	250	18	is	be	AUX
fumecheng-11587	250	19	divided	divide	VERB
fumecheng-11587	250	20	into	into	ADP
fumecheng-11587	250	21	nk	nk	PROPN
fumecheng-11587	250	22	sub	sub	NOUN
fumecheng-11587	250	23	-	-	NOUN
fumecheng-11587	250	24	intervals	interval	NOUN
fumecheng-11587	250	25	,	,	PUNCT
fumecheng-11587	250	26	where	where	SCONJ
fumecheng-11587	250	27	the	the	DET
fumecheng-11587	250	28	k	k	NOUN
fumecheng-11587	250	29	-	-	PUNCT
fumecheng-11587	250	30	th	th	VERB
fumecheng-11587	250	31	interval	interval	NOUN
fumecheng-11587	250	32	is	be	AUX
fumecheng-11587	250	33	equal	equal	ADJ
fumecheng-11587	250	34	to	to	ADP
fumecheng-11587	250	35	δk	δk	ADJ
fumecheng-11587	250	36	=	=	NOUN
fumecheng-11587	250	37	τk	τk	ADP
fumecheng-11587	250	38	τk-1	τk-1	X
fumecheng-11587	250	39	for	for	ADP
fumecheng-11587	250	40	τk	τk	NOUN
fumecheng-11587	250	41	=	=	PUNCT
fumecheng-11587	250	42	kt	kt	PROPN
fumecheng-11587	250	43	/	/	SYM
fumecheng-11587	250	44	n.	n.	PROPN
fumecheng-11587	250	45	furthermore	furthermore	ADV
fumecheng-11587	250	46	,	,	PUNCT
fumecheng-11587	250	47	p	p	X
fumecheng-11587	250	48	(	(	PUNCT
fumecheng-11587	250	49	τ	τ	X
fumecheng-11587	250	50	)	)	PUNCT
fumecheng-11587	250	51	is	be	AUX
fumecheng-11587	250	52	the	the	DET
fumecheng-11587	250	53	continuous	continuous	ADJ
fumecheng-11587	250	54	periodic	periodic	ADJ
fumecheng-11587	250	55	matrix	matrix	NOUN
fumecheng-11587	250	56	with	with	ADP
fumecheng-11587	250	57	respect	respect	NOUN
fumecheng-11587	250	58	to	to	ADP
fumecheng-11587	250	59	τ	τ	PROPN
fumecheng-11587	250	60	and	and	CCONJ
fumecheng-11587	250	61	period	period	NOUN
fumecheng-11587	250	62	t	t	PROPN
fumecheng-11587	250	63	,	,	PUNCT
fumecheng-11587	250	64	wherein	wherein	SCONJ
fumecheng-11587	250	65	the	the	DET
fumecheng-11587	250	66	k	k	NOUN
fumecheng-11587	250	67	-	-	PUNCT
fumecheng-11587	250	68	th	th	VERB
fumecheng-11587	250	69	interval	interval	NOUN
fumecheng-11587	250	70	it	it	PRON
fumecheng-11587	250	71	can	can	AUX
fumecheng-11587	250	72	be	be	AUX
fumecheng-11587	250	73	replaced	replace	VERB
fumecheng-11587	250	74	by	by	ADP
fumecheng-11587	250	75	the	the	DET
fumecheng-11587	250	76	constant	constant	ADJ
fumecheng-11587	250	77	matrix	matrix	NOUN
fumecheng-11587	250	78	provided	provide	VERB
fumecheng-11587	250	79	in	in	ADP
fumecheng-11587	250	80	the	the	DET
fumecheng-11587	250	81	case	case	NOUN
fumecheng-11587	250	82	when	when	SCONJ
fumecheng-11587	250	83	nk	nk	PROPN
fumecheng-11587	250	84	is	be	AUX
fumecheng-11587	250	85	chosen	choose	VERB
fumecheng-11587	250	86	to	to	PART
fumecheng-11587	250	87	be	be	AUX
fumecheng-11587	250	88	sufficiently	sufficiently	ADV
fumecheng-11587	250	89	large	large	ADJ
fumecheng-11587	250	90	:	:	PUNCT
fumecheng-11587	251	1	𝑷𝒌	𝑷𝒌	ADP
fumecheng-11587	251	2	=	=	SYM
fumecheng-11587	251	3	1	1	NUM
fumecheng-11587	251	4	𝛥𝑘	𝛥𝑘	PROPN
fumecheng-11587	251	5	∫	∫	PROPN
fumecheng-11587	251	6	𝑷(𝜏)𝑑𝜏.	𝑷(𝜏)𝑑𝜏.	NUM
fumecheng-11587	251	7	𝜏𝑘	𝜏𝑘	ADP
fumecheng-11587	251	8	𝜏𝑘−1	𝜏𝑘−1	PROPN
fumecheng-11587	251	9	(	(	PUNCT
fumecheng-11587	251	10	35	35	NUM
fumecheng-11587	251	11	)	)	PUNCT
fumecheng-11587	251	12	the	the	DET
fumecheng-11587	251	13	monodromy	monodromy	NOUN
fumecheng-11587	251	14	(	(	PUNCT
fumecheng-11587	251	15	transition	transition	NOUN
fumecheng-11587	251	16	)	)	PUNCT
fumecheng-11587	251	17	matrix	matrix	NOUN
fumecheng-11587	251	18	can	can	AUX
fumecheng-11587	251	19	be	be	AUX
fumecheng-11587	251	20	written	write	VERB
fumecheng-11587	251	21	in	in	ADP
fumecheng-11587	251	22	the	the	DET
fumecheng-11587	251	23	following	follow	VERB
fumecheng-11587	251	24	form	form	NOUN
fumecheng-11587	251	25	𝑀=	𝑀=	PROPN
fumecheng-11587	251	26	∏	∏	PROPN
fumecheng-11587	251	27	𝑒𝑷𝒊𝛥𝑖	𝑒𝑷𝒊𝛥𝑖	VERB
fumecheng-11587	251	28	𝑁𝑘	𝑁𝑘	PROPN
fumecheng-11587	251	29	𝑖=1	𝑖=1	PROPN
fumecheng-11587	251	30	≈	≈	PROPN
fumecheng-11587	251	31	∏	∏	PROPN
fumecheng-11587	251	32	(	(	PUNCT
fumecheng-11587	251	33	𝑰	𝑰	PROPN
fumecheng-11587	251	34	+	+	NOUN
fumecheng-11587	251	35	∑	∑	PROPN
fumecheng-11587	251	36	(	(	PUNCT
fumecheng-11587	251	37	𝑷𝒊𝛥𝑖)𝑗	𝑷𝒊𝛥𝑖)𝑗	NOUN
fumecheng-11587	251	38	𝑗	𝑗	INTJ
fumecheng-11587	251	39	!	!	PUNCT
fumecheng-11587	252	1	𝑁𝑗	𝑁𝑗	PROPN
fumecheng-11587	252	2	𝑗=1	𝑗=1	PROPN
fumecheng-11587	252	3	)	)	PUNCT
fumecheng-11587	253	1	𝑁𝑘	𝑁𝑘	PROPN
fumecheng-11587	253	2	𝑖=1	𝑖=1	PROPN
fumecheng-11587	253	3	,	,	PUNCT
fumecheng-11587	253	4	(	(	PUNCT
fumecheng-11587	253	5	36	36	NUM
fumecheng-11587	253	6	)	)	PUNCT
fumecheng-11587	253	7	where	where	SCONJ
fumecheng-11587	253	8	nj	nj	PROPN
fumecheng-11587	253	9	denotes	denote	VERB
fumecheng-11587	253	10	the	the	DET
fumecheng-11587	253	11	number	number	NOUN
fumecheng-11587	253	12	of	of	ADP
fumecheng-11587	253	13	terms	term	NOUN
fumecheng-11587	253	14	in	in	ADP
fumecheng-11587	253	15	taylor	taylor	PROPN
fumecheng-11587	253	16	series	series	PROPN
fumecheng-11587	253	17	,	,	PUNCT
fumecheng-11587	253	18	for	for	ADP
fumecheng-11587	253	19	the	the	DET
fumecheng-11587	253	20	approximation	approximation	NOUN
fumecheng-11587	253	21	of	of	ADP
fumecheng-11587	253	22	matrix	matrix	NOUN
fumecheng-11587	253	23	exponent	exponent	NOUN
fumecheng-11587	253	24	of	of	ADP
fumecheng-11587	253	25	the	the	DET
fumecheng-11587	253	26	constant	constant	ADJ
fumecheng-11587	253	27	matrix	matrix	NOUN
fumecheng-11587	253	28	pk	pk	NOUN
fumecheng-11587	253	29	.	.	PROPN
fumecheng-11587	253	30	from	from	ADP
fumecheng-11587	253	31	the	the	DET
fumecheng-11587	253	32	monodromy	monodromy	NOUN
fumecheng-11587	253	33	matrix	matrix	NOUN
fumecheng-11587	253	34	m	m	NOUN
fumecheng-11587	253	35	,	,	PUNCT
fumecheng-11587	253	36	given	give	VERB
fumecheng-11587	253	37	in	in	ADP
fumecheng-11587	253	38	eq	eq	ADP
fumecheng-11587	253	39	.	.	PUNCT
fumecheng-11587	254	1	(	(	PUNCT
fumecheng-11587	254	2	36	36	NUM
fumecheng-11587	254	3	)	)	PUNCT
fumecheng-11587	254	4	,	,	PUNCT
fumecheng-11587	254	5	one	one	PRON
fumecheng-11587	254	6	can	can	AUX
fumecheng-11587	254	7	obtain	obtain	VERB
fumecheng-11587	254	8	floquet	floquet	NOUN
fumecheng-11587	254	9	multipliers	multiplier	NOUN
fumecheng-11587	254	10	as	as	ADP
fumecheng-11587	254	11	its	its	PRON
fumecheng-11587	254	12	eigenvalues	eigenvalues	PROPN
fumecheng-11587	254	13	σ	σ	NOUN
fumecheng-11587	254	14	from	from	ADP
fumecheng-11587	254	15	relation	relation	NOUN
fumecheng-11587	254	16	:	:	PUNCT
fumecheng-11587	254	17	𝑑𝑒𝑡(𝑴	𝑑𝑒𝑡(𝑴	X
fumecheng-11587	254	18	−	−	PROPN
fumecheng-11587	254	19	𝜎𝑰	𝜎𝑰	NOUN
fumecheng-11587	254	20	)	)	PUNCT
fumecheng-11587	254	21	=	=	PUNCT
fumecheng-11587	255	1	𝟎.	𝟎.	X
fumecheng-11587	255	2	(	(	PUNCT
fumecheng-11587	255	3	37	37	NUM
fumecheng-11587	255	4	)	)	PUNCT
fumecheng-11587	255	5	for	for	ADP
fumecheng-11587	255	6	eq	eq	PROPN
fumecheng-11587	255	7	.	.	PUNCT
fumecheng-11587	256	1	(	(	PUNCT
fumecheng-11587	256	2	14	14	NUM
fumecheng-11587	256	3	)	)	PUNCT
fumecheng-11587	256	4	,	,	PUNCT
fumecheng-11587	256	5	the	the	DET
fumecheng-11587	256	6	periodic	periodic	ADJ
fumecheng-11587	256	7	matrix	matrix	NOUN
fumecheng-11587	256	8	p	p	NOUN
fumecheng-11587	256	9	(	(	PUNCT
fumecheng-11587	256	10	τ	τ	X
fumecheng-11587	256	11	)	)	PUNCT
fumecheng-11587	256	12	can	can	AUX
fumecheng-11587	256	13	be	be	AUX
fumecheng-11587	256	14	obtained	obtain	VERB
fumecheng-11587	256	15	in	in	ADP
fumecheng-11587	256	16	the	the	DET
fumecheng-11587	256	17	following	follow	VERB
fumecheng-11587	256	18	form	form	NOUN
fumecheng-11587	256	19	𝑷(𝜏	𝑷(𝜏	NUM
fumecheng-11587	256	20	)	)	PUNCT
fumecheng-11587	257	1	=	=	PUNCT
fumecheng-11587	257	2	[	[	PUNCT
fumecheng-11587	257	3	0	0	NUM
fumecheng-11587	257	4	1	1	NUM
fumecheng-11587	257	5	−	−	NOUN
fumecheng-11587	257	6	𝜔0	𝜔0	NOUN
fumecheng-11587	257	7	2	2	NUM
fumecheng-11587	257	8	+	+	NOUN
fumecheng-11587	257	9	3𝜃𝑞0	3𝜃𝑞0	NUM
fumecheng-11587	257	10	2	2	NUM
fumecheng-11587	257	11	𝛺2	𝛺2	ADP
fumecheng-11587	257	12	−	−	NOUN
fumecheng-11587	257	13	𝛾	𝛾	ADP
fumecheng-11587	257	14	𝛺	𝛺	PROPN
fumecheng-11587	257	15	]	]	PUNCT
fumecheng-11587	257	16	.	.	PUNCT
fumecheng-11587	258	1	(	(	PUNCT
fumecheng-11587	258	2	38	38	NUM
fumecheng-11587	258	3	)	)	PUNCT
fumecheng-11587	258	4	in	in	ADP
fumecheng-11587	258	5	this	this	DET
fumecheng-11587	258	6	study	study	NOUN
fumecheng-11587	258	7	,	,	PUNCT
fumecheng-11587	258	8	for	for	ADP
fumecheng-11587	258	9	approximation	approximation	NOUN
fumecheng-11587	258	10	of	of	ADP
fumecheng-11587	258	11	the	the	DET
fumecheng-11587	258	12	monodromy	monodromy	NOUN
fumecheng-11587	258	13	matrix	matrix	NOUN
fumecheng-11587	258	14	the	the	DET
fumecheng-11587	258	15	values	value	NOUN
fumecheng-11587	258	16	nk	nk	PROPN
fumecheng-11587	259	1	=	=	SYM
fumecheng-11587	259	2	5000	5000	NUM
fumecheng-11587	259	3	and	and	CCONJ
fumecheng-11587	259	4	nj	nj	NUM
fumecheng-11587	259	5	=	=	SYM
fumecheng-11587	259	6	5	5	NUM
fumecheng-11587	259	7	are	be	AUX
fumecheng-11587	259	8	adopted	adopt	VERB
fumecheng-11587	259	9	as	as	ADP
fumecheng-11587	259	10	the	the	DET
fumecheng-11587	259	11	optimal	optimal	ADJ
fumecheng-11587	259	12	values	value	NOUN
fumecheng-11587	259	13	compromising	compromise	VERB
fumecheng-11587	259	14	computational	computational	ADJ
fumecheng-11587	259	15	cost	cost	NOUN
fumecheng-11587	259	16	and	and	CCONJ
fumecheng-11587	259	17	precision	precision	NOUN
fumecheng-11587	259	18	.	.	PUNCT
fumecheng-11587	260	1	larger	large	ADJ
fumecheng-11587	260	2	values	value	NOUN
fumecheng-11587	260	3	for	for	ADP
fumecheng-11587	260	4	nk	nk	PROPN
fumecheng-11587	260	5	and	and	CCONJ
fumecheng-11587	260	6	nj	nj	PROPN
fumecheng-11587	260	7	would	would	AUX
fumecheng-11587	260	8	n’t	not	PART
fumecheng-11587	260	9	offer	offer	VERB
fumecheng-11587	260	10	some	some	DET
fumecheng-11587	260	11	benefit	benefit	NOUN
fumecheng-11587	260	12	in	in	ADP
fumecheng-11587	260	13	determination	determination	NOUN
fumecheng-11587	260	14	whether	whether	SCONJ
fumecheng-11587	260	15	point	point	NOUN
fumecheng-11587	260	16	is	be	AUX
fumecheng-11587	260	17	stable	stable	ADJ
fumecheng-11587	260	18	or	or	CCONJ
fumecheng-11587	260	19	unstable	unstable	ADJ
fumecheng-11587	260	20	in	in	ADP
fumecheng-11587	260	21	this	this	DET
fumecheng-11587	260	22	particular	particular	ADJ
fumecheng-11587	260	23	numerical	numerical	ADJ
fumecheng-11587	260	24	example	example	NOUN
fumecheng-11587	260	25	,	,	PUNCT
fumecheng-11587	260	26	but	but	CCONJ
fumecheng-11587	260	27	would	would	AUX
fumecheng-11587	260	28	increase	increase	VERB
fumecheng-11587	260	29	computation	computation	NOUN
fumecheng-11587	260	30	time	time	NOUN
fumecheng-11587	260	31	significantly	significantly	ADV
fumecheng-11587	260	32	.	.	PUNCT
fumecheng-11587	261	1	5	5	X
fumecheng-11587	261	2	.	.	X
fumecheng-11587	261	3	numerical	numerical	ADJ
fumecheng-11587	261	4	results	result	NOUN
fumecheng-11587	261	5	here	here	ADV
fumecheng-11587	261	6	,	,	PUNCT
fumecheng-11587	261	7	the	the	DET
fumecheng-11587	261	8	stability	stability	NOUN
fumecheng-11587	261	9	of	of	ADP
fumecheng-11587	261	10	the	the	DET
fumecheng-11587	261	11	obtained	obtain	VERB
fumecheng-11587	261	12	periodic	periodic	ADJ
fumecheng-11587	261	13	solutions	solution	NOUN
fumecheng-11587	261	14	of	of	ADP
fumecheng-11587	261	15	the	the	DET
fumecheng-11587	261	16	forced	force	VERB
fumecheng-11587	261	17	duffing	duffing	NOUN
fumecheng-11587	261	18	differential	differential	ADJ
fumecheng-11587	261	19	equation	equation	NOUN
fumecheng-11587	261	20	eq	eq	ADJ
fumecheng-11587	261	21	.	.	PUNCT
fumecheng-11587	262	1	(	(	PUNCT
fumecheng-11587	262	2	12	12	NUM
fumecheng-11587	262	3	)	)	PUNCT
fumecheng-11587	262	4	is	be	AUX
fumecheng-11587	262	5	checked	check	VERB
fumecheng-11587	262	6	by	by	ADP
fumecheng-11587	262	7	using	use	VERB
fumecheng-11587	262	8	the	the	DET
fumecheng-11587	262	9	methodology	methodology	NOUN
fumecheng-11587	262	10	given	give	VERB
fumecheng-11587	262	11	in	in	ADP
fumecheng-11587	262	12	the	the	DET
fumecheng-11587	262	13	previous	previous	ADJ
fumecheng-11587	262	14	section	section	NOUN
fumecheng-11587	262	15	.	.	PUNCT
fumecheng-11587	263	1	the	the	DET
fumecheng-11587	263	2	ihb	ihb	NOUN
fumecheng-11587	263	3	and	and	CCONJ
fumecheng-11587	263	4	continuation	continuation	NOUN
fumecheng-11587	263	5	method	method	NOUN
fumecheng-11587	263	6	are	be	AUX
fumecheng-11587	263	7	numerically	numerically	ADV
fumecheng-11587	263	8	applied	apply	VERB
fumecheng-11587	263	9	to	to	PART
fumecheng-11587	263	10	trace	trace	VERB
fumecheng-11587	263	11	the	the	DET
fumecheng-11587	263	12	periodic	periodic	ADJ
fumecheng-11587	263	13	solutions	solution	NOUN
fumecheng-11587	263	14	branches	branch	NOUN
fumecheng-11587	263	15	of	of	ADP
fumecheng-11587	263	16	a	a	DET
fumecheng-11587	263	17	nonlinear	nonlinear	ADJ
fumecheng-11587	263	18	model	model	NOUN
fumecheng-11587	263	19	of	of	ADP
fumecheng-11587	263	20	a	a	DET
fumecheng-11587	263	21	nonlocal	nonlocal	ADJ
fumecheng-11587	263	22	strain	strain	NOUN
fumecheng-11587	263	23	-	-	PUNCT
fumecheng-11587	263	24	gradient	gradient	NOUN
fumecheng-11587	263	25	beam	beam	NOUN
fumecheng-11587	263	26	resting	rest	VERB
fumecheng-11587	263	27	on	on	ADP
fumecheng-11587	263	28	a	a	DET
fumecheng-11587	263	29	visco	visco	ADJ
fumecheng-11587	263	30	-	-	PUNCT
fumecheng-11587	263	31	pasternak	pasternak	ADJ
fumecheng-11587	263	32	foundation	foundation	NOUN
fumecheng-11587	263	33	with	with	ADP
fumecheng-11587	263	34	direct	direct	ADJ
fumecheng-11587	263	35	transverse	transverse	NOUN
fumecheng-11587	263	36	harmonic	harmonic	ADJ
fumecheng-11587	263	37	excitation	excitation	NOUN
fumecheng-11587	263	38	.	.	PUNCT
fumecheng-11587	264	1	moreover	moreover	ADV
fumecheng-11587	264	2	,	,	PUNCT
fumecheng-11587	264	3	the	the	DET
fumecheng-11587	264	4	floquet	floquet	NOUN
fumecheng-11587	264	5	theory	theory	NOUN
fumecheng-11587	264	6	is	be	AUX
fumecheng-11587	264	7	applied	apply	VERB
fumecheng-11587	264	8	to	to	PART
fumecheng-11587	264	9	check	check	VERB
fumecheng-11587	264	10	the	the	DET
fumecheng-11587	264	11	stability	stability	NOUN
fumecheng-11587	264	12	of	of	ADP
fumecheng-11587	264	13	periodic	periodic	ADJ
fumecheng-11587	264	14	solutions	solution	NOUN
fumecheng-11587	264	15	for	for	ADP
fumecheng-11587	264	16	given	give	VERB
fumecheng-11587	264	17	amplitude	amplitude	NOUN
fumecheng-11587	264	18	-	-	PUNCT
fumecheng-11587	264	19	frequency	frequency	NOUN
fumecheng-11587	264	20	curves	curve	NOUN
fumecheng-11587	264	21	.	.	PUNCT
fumecheng-11587	265	1	in	in	ADP
fumecheng-11587	265	2	the	the	DET
fumecheng-11587	265	3	first	first	ADJ
fumecheng-11587	265	4	part	part	NOUN
fumecheng-11587	265	5	of	of	ADP
fumecheng-11587	265	6	the	the	DET
fumecheng-11587	265	7	numerical	numerical	ADJ
fumecheng-11587	265	8	study	study	NOUN
fumecheng-11587	265	9	,	,	PUNCT
fumecheng-11587	265	10	we	we	PRON
fumecheng-11587	265	11	validate	validate	VERB
fumecheng-11587	265	12	our	our	PRON
fumecheng-11587	265	13	model	model	NOUN
fumecheng-11587	265	14	by	by	ADP
fumecheng-11587	265	15	comparing	compare	VERB
fumecheng-11587	265	16	the	the	DET
fumecheng-11587	265	17	beam	beam	NOUN
fumecheng-11587	265	18	's	's	PART
fumecheng-11587	265	19	natural	natural	ADJ
fumecheng-11587	265	20	frequencies	frequency	NOUN
fumecheng-11587	265	21	in	in	ADP
fumecheng-11587	265	22	two	two	NUM
fumecheng-11587	265	23	vibration	vibration	NOUN
fumecheng-11587	265	24	and	and	CCONJ
fumecheng-11587	265	25	stability	stability	NOUN
fumecheng-11587	265	26	of	of	ADP
fumecheng-11587	265	27	a	a	DET
fumecheng-11587	265	28	nonlinear	nonlinear	ADJ
fumecheng-11587	265	29	nonlocal	nonlocal	ADJ
fumecheng-11587	265	30	strain	strain	NOUN
fumecheng-11587	265	31	-	-	PUNCT
fumecheng-11587	265	32	gradient	gradient	NOUN
fumecheng-11587	265	33	fg	fg	PROPN
fumecheng-11587	265	34	beam	beam	NOUN
fumecheng-11587	265	35	on	on	ADP
fumecheng-11587	265	36	a	a	DET
fumecheng-11587	265	37	visco	visco	ADJ
fumecheng-11587	265	38	-	-	PUNCT
fumecheng-11587	265	39	pasternak	pasternak	NOUN
fumecheng-11587	265	40	...	...	PUNCT
fumecheng-11587	265	41	719	719	NUM
fumecheng-11587	265	42	simplified	simplified	ADJ
fumecheng-11587	265	43	cases	case	NOUN
fumecheng-11587	265	44	with	with	ADP
fumecheng-11587	265	45	the	the	DET
fumecheng-11587	265	46	results	result	NOUN
fumecheng-11587	265	47	available	available	ADJ
fumecheng-11587	265	48	in	in	ADP
fumecheng-11587	265	49	the	the	DET
fumecheng-11587	265	50	literature	literature	NOUN
fumecheng-11587	265	51	(	(	PUNCT
fumecheng-11587	265	52	tables	table	NOUN
fumecheng-11587	265	53	1	1	NUM
fumecheng-11587	265	54	and	and	CCONJ
fumecheng-11587	265	55	2	2	NUM
fumecheng-11587	265	56	)	)	PUNCT
fumecheng-11587	265	57	.	.	PUNCT
fumecheng-11587	266	1	then	then	ADV
fumecheng-11587	266	2	,	,	PUNCT
fumecheng-11587	266	3	the	the	DET
fumecheng-11587	266	4	validity	validity	NOUN
fumecheng-11587	266	5	of	of	ADP
fumecheng-11587	266	6	the	the	DET
fumecheng-11587	266	7	results	result	NOUN
fumecheng-11587	266	8	from	from	ADP
fumecheng-11587	266	9	the	the	DET
fumecheng-11587	266	10	ihb	ihb	PRON
fumecheng-11587	266	11	method	method	NOUN
fumecheng-11587	266	12	is	be	AUX
fumecheng-11587	266	13	examined	examine	VERB
fumecheng-11587	266	14	,	,	PUNCT
fumecheng-11587	266	15	which	which	PRON
fumecheng-11587	266	16	is	be	AUX
fumecheng-11587	266	17	then	then	ADV
fumecheng-11587	266	18	followed	follow	VERB
fumecheng-11587	266	19	by	by	ADP
fumecheng-11587	266	20	the	the	DET
fumecheng-11587	266	21	parametric	parametric	ADJ
fumecheng-11587	266	22	and	and	CCONJ
fumecheng-11587	266	23	stability	stability	NOUN
fumecheng-11587	266	24	study	study	NOUN
fumecheng-11587	266	25	in	in	ADP
fumecheng-11587	266	26	the	the	DET
fumecheng-11587	266	27	frequency	frequency	NOUN
fumecheng-11587	266	28	domain	domain	NOUN
fumecheng-11587	266	29	.	.	PUNCT
fumecheng-11587	267	1	the	the	DET
fumecheng-11587	267	2	parameters	parameter	NOUN
fumecheng-11587	267	3	used	use	VERB
fumecheng-11587	267	4	in	in	ADP
fumecheng-11587	267	5	simulations	simulation	NOUN
fumecheng-11587	267	6	are	be	AUX
fumecheng-11587	267	7	adopted	adopt	VERB
fumecheng-11587	267	8	from	from	ADP
fumecheng-11587	267	9	the	the	DET
fumecheng-11587	267	10	paper	paper	NOUN
fumecheng-11587	267	11	[	[	X
fumecheng-11587	267	12	33	33	NUM
fumecheng-11587	267	13	]	]	PUNCT
fumecheng-11587	267	14	and	and	CCONJ
fumecheng-11587	267	15	extended	extend	VERB
fumecheng-11587	267	16	with	with	ADP
fumecheng-11587	267	17	the	the	DET
fumecheng-11587	267	18	parameters	parameter	NOUN
fumecheng-11587	267	19	for	for	ADP
fumecheng-11587	267	20	the	the	DET
fumecheng-11587	267	21	pasternak	pasternak	PROPN
fumecheng-11587	267	22	layer	layer	NOUN
fumecheng-11587	267	23	,	,	PUNCT
fumecheng-11587	267	24	fg	fg	PROPN
fumecheng-11587	267	25	material	material	NOUN
fumecheng-11587	267	26	,	,	PUNCT
fumecheng-11587	267	27	and	and	CCONJ
fumecheng-11587	267	28	excitation	excitation	NOUN
fumecheng-11587	267	29	force	force	NOUN
fumecheng-11587	267	30	as	as	SCONJ
fumecheng-11587	267	31	given	give	VERB
fumecheng-11587	267	32	in	in	ADP
fumecheng-11587	267	33	table	table	NOUN
fumecheng-11587	267	34	3	3	NUM
fumecheng-11587	267	35	,	,	PUNCT
fumecheng-11587	267	36	unless	unless	SCONJ
fumecheng-11587	267	37	other	other	ADJ
fumecheng-11587	267	38	specified	specify	VERB
fumecheng-11587	267	39	.	.	PUNCT
fumecheng-11587	268	1	the	the	DET
fumecheng-11587	268	2	number	number	NOUN
fumecheng-11587	268	3	of	of	ADP
fumecheng-11587	268	4	adopted	adopt	VERB
fumecheng-11587	268	5	harmonics	harmonic	NOUN
fumecheng-11587	268	6	in	in	ADP
fumecheng-11587	268	7	the	the	DET
fumecheng-11587	268	8	fourier	fourier	NOUN
fumecheng-11587	268	9	series	series	NOUN
fumecheng-11587	268	10	is	be	AUX
fumecheng-11587	268	11	n	n	NOUN
fumecheng-11587	268	12	=	=	SYM
fumecheng-11587	268	13	6	6	NUM
fumecheng-11587	268	14	.	.	PUNCT
fumecheng-11587	269	1	the	the	DET
fumecheng-11587	269	2	amplitudes	amplitude	NOUN
fumecheng-11587	269	3	corresponding	correspond	VERB
fumecheng-11587	269	4	to	to	ADP
fumecheng-11587	269	5	particular	particular	ADJ
fumecheng-11587	269	6	fourier	fourier	NOUN
fumecheng-11587	269	7	coefficients	coefficient	NOUN
fumecheng-11587	269	8	(	(	PUNCT
fumecheng-11587	269	9	eq	eq	NOUN
fumecheng-11587	269	10	.	.	PUNCT
fumecheng-11587	269	11	(	(	PUNCT
fumecheng-11587	269	12	21	21	NUM
fumecheng-11587	269	13	)	)	PUNCT
fumecheng-11587	269	14	)	)	PUNCT
fumecheng-11587	269	15	and	and	CCONJ
fumecheng-11587	269	16	harmonics	harmonic	NOUN
fumecheng-11587	269	17	(	(	PUNCT
fumecheng-11587	269	18	eq	eq	NOUN
fumecheng-11587	269	19	.	.	PUNCT
fumecheng-11587	269	20	(	(	PUNCT
fumecheng-11587	269	21	20	20	NUM
fumecheng-11587	269	22	)	)	PUNCT
fumecheng-11587	269	23	)	)	PUNCT
fumecheng-11587	269	24	are	be	AUX
fumecheng-11587	269	25	computed	compute	VERB
fumecheng-11587	269	26	as	as	ADP
fumecheng-11587	269	27	𝐴0	𝐴0	PROPN
fumecheng-11587	269	28	=	=	PUNCT
fumecheng-11587	269	29	𝑎0	𝑎0	PROPN
fumecheng-11587	269	30	,	,	PUNCT
fumecheng-11587	269	31	𝐴𝑖	𝐴𝑖	PROPN
fumecheng-11587	269	32	=	=	SYM
fumecheng-11587	269	33	√𝑎𝑖	√𝑎𝑖	PROPN
fumecheng-11587	269	34	2	2	NUM
fumecheng-11587	269	35	+	+	CCONJ
fumecheng-11587	269	36	𝑏𝑖	𝑏𝑖	PROPN
fumecheng-11587	269	37	2	2	NUM
fumecheng-11587	269	38	,	,	PUNCT
fumecheng-11587	269	39	(	(	PUNCT
fumecheng-11587	269	40	𝑖	𝑖	SYM
fumecheng-11587	269	41	=	=	SYM
fumecheng-11587	269	42	1,2	1,2	NUM
fumecheng-11587	269	43	,	,	PUNCT
fumecheng-11587	269	44	.	.	PUNCT
fumecheng-11587	269	45	.	.	PUNCT
fumecheng-11587	270	1	.	.	PUNCT
fumecheng-11587	271	1	,	,	PUNCT
fumecheng-11587	271	2	𝑁	𝑁	PROPN
fumecheng-11587	271	3	)	)	PUNCT
fumecheng-11587	271	4	.	.	PUNCT
fumecheng-11587	272	1	(	(	PUNCT
fumecheng-11587	272	2	39	39	NUM
fumecheng-11587	272	3	)	)	PUNCT
fumecheng-11587	272	4	table	table	NOUN
fumecheng-11587	272	5	1	1	NUM
fumecheng-11587	272	6	the	the	DET
fumecheng-11587	272	7	first	first	ADJ
fumecheng-11587	272	8	five	five	NUM
fumecheng-11587	272	9	non	non	ADJ
fumecheng-11587	272	10	-	-	ADJ
fumecheng-11587	272	11	dimensional	dimensional	ADJ
fumecheng-11587	272	12	fundamental	fundamental	ADJ
fumecheng-11587	272	13	natural	natural	ADJ
fumecheng-11587	272	14	frequencies	frequency	NOUN
fumecheng-11587	272	15	of	of	ADP
fumecheng-11587	272	16	a	a	DET
fumecheng-11587	272	17	local	local	ADJ
fumecheng-11587	272	18	eulerbernoulli	eulerbernoulli	NOUN
fumecheng-11587	272	19	beam	beam	NOUN
fumecheng-11587	272	20	resting	rest	VERB
fumecheng-11587	272	21	on	on	ADP
fumecheng-11587	272	22	winkler	winkler	NOUN
fumecheng-11587	272	23	-	-	PUNCT
fumecheng-11587	272	24	pasternak	pasternak	PROPN
fumecheng-11587	272	25	foundation	foundation	NOUN
fumecheng-11587	272	26	for	for	ADP
fumecheng-11587	272	27	the	the	DET
fumecheng-11587	272	28	simply	simply	ADV
fumecheng-11587	272	29	-	-	PUNCT
fumecheng-11587	272	30	supported	support	VERB
fumecheng-11587	272	31	boundary	boundary	ADJ
fumecheng-11587	272	32	conditions	condition	NOUN
fumecheng-11587	272	33	(	(	PUNCT
fumecheng-11587	272	34	k1	k1	NOUN
fumecheng-11587	272	35	=	=	SYM
fumecheng-11587	272	36	25	25	NUM
fumecheng-11587	272	37	,	,	PUNCT
fumecheng-11587	272	38	k2	k2	NOUN
fumecheng-11587	272	39	=	=	SYM
fumecheng-11587	272	40	25	25	NUM
fumecheng-11587	272	41	)	)	PUNCT
fumecheng-11587	272	42	present	present	ADJ
fumecheng-11587	272	43	ref.[63	ref.[63	NOUN
fumecheng-11587	272	44	]	]	PUNCT
fumecheng-11587	272	45	ref.[64	ref.[64	NOUN
fumecheng-11587	272	46	]	]	PUNCT
fumecheng-11587	272	47	ref.[65	ref.[65	NOUN
fumecheng-11587	272	48	]	]	X
fumecheng-11587	272	49	ref.[66	ref.[66	NOUN
fumecheng-11587	272	50	]	]	X
fumecheng-11587	272	51	19.2133	19.2133	NUM
fumecheng-11587	272	52	19.2133	19.2133	NUM
fumecheng-11587	272	53	19.2133	19.2133	NUM
fumecheng-11587	272	54	19.21	19.21	NUM
fumecheng-11587	272	55	19.2178	19.2178	NUM
fumecheng-11587	272	56	50.7002	50.7002	NUM
fumecheng-11587	272	57	50.7002	50.7002	NUM
fumecheng-11587	272	58	50.7002	50.7002	NUM
fumecheng-11587	272	59	50.7	50.7	NUM
fumecheng-11587	272	60	50.7804	50.7804	NUM
fumecheng-11587	272	61	100.6767	100.6767	NUM
fumecheng-11587	272	62	100.677	100.677	NUM
fumecheng-11587	272	63	100.6767	100.6767	NUM
fumecheng-11587	272	64	100.7	100.7	NUM
fumecheng-11587	272	65	170.0281	170.0281	NUM
fumecheng-11587	272	66	170.028	170.028	NUM
fumecheng-11587	272	67	170.0281	170.0281	NUM
fumecheng-11587	272	68	170.1	170.1	NUM
fumecheng-11587	272	69	258.9868	258.9868	NUM
fumecheng-11587	272	70	258.987	258.987	NUM
fumecheng-11587	272	71	258.9868	258.9868	NUM
fumecheng-11587	272	72	259.1	259.1	NUM
fumecheng-11587	272	73	table	table	NOUN
fumecheng-11587	272	74	2	2	NUM
fumecheng-11587	272	75	comparison	comparison	NOUN
fumecheng-11587	272	76	of	of	ADP
fumecheng-11587	272	77	non	non	ADJ
fumecheng-11587	272	78	-	-	ADJ
fumecheng-11587	272	79	dimensional	dimensional	ADJ
fumecheng-11587	272	80	fundamental	fundamental	ADJ
fumecheng-11587	272	81	natural	natural	ADJ
fumecheng-11587	272	82	frequencies	frequency	NOUN
fumecheng-11587	272	83	of	of	ADP
fumecheng-11587	272	84	simplysupported	simplysupporte	VERB
fumecheng-11587	272	85	nonlocal	nonlocal	ADJ
fumecheng-11587	272	86	euler	euler	NOUN
fumecheng-11587	272	87	-	-	PUNCT
fumecheng-11587	272	88	bernoulli	bernoulli	NOUN
fumecheng-11587	272	89	beam	beam	NOUN
fumecheng-11587	272	90	with	with	ADP
fumecheng-11587	272	91	different	different	ADJ
fumecheng-11587	272	92	nonlocal	nonlocal	ADJ
fumecheng-11587	272	93	parameters	parameter	NOUN
fumecheng-11587	272	94	μ	μ	NOUN
fumecheng-11587	272	95	(	(	PUNCT
fumecheng-11587	272	96	l	l	NOUN
fumecheng-11587	272	97	=	=	SYM
fumecheng-11587	272	98	10	10	NUM
fumecheng-11587	272	99	,	,	PUNCT
fumecheng-11587	272	100	h	h	NOUN
fumecheng-11587	272	101	=	=	SYM
fumecheng-11587	272	102	1	1	NUM
fumecheng-11587	272	103	,	,	PUNCT
fumecheng-11587	272	104	ρ	ρ	PROPN
fumecheng-11587	272	105	=	=	SYM
fumecheng-11587	272	106	1	1	NUM
fumecheng-11587	272	107	,	,	PUNCT
fumecheng-11587	272	108	e	e	X
fumecheng-11587	272	109	=	=	SYM
fumecheng-11587	272	110	30∙106	30∙106	NUM
fumecheng-11587	272	111	,	,	PUNCT
fumecheng-11587	272	112	ν	ν	X
fumecheng-11587	272	113	=	=	SYM
fumecheng-11587	272	114	0.3	0.3	NUM
fumecheng-11587	272	115	)	)	PUNCT
fumecheng-11587	272	116	μ	μ	PROPN
fumecheng-11587	272	117	present	present	ADJ
fumecheng-11587	272	118	ref.[17	ref.[17	VERB
fumecheng-11587	272	119	]	]	PUNCT
fumecheng-11587	272	120	ref.[67	ref.[67	X
fumecheng-11587	272	121	]	]	PUNCT
fumecheng-11587	272	122	ref.[68	ref.[68	X
fumecheng-11587	272	123	]	]	PUNCT
fumecheng-11587	272	124	0	0	NUM
fumecheng-11587	273	1	9.8293	9.8293	NUM
fumecheng-11587	273	2	9.8696	9.8696	NUM
fumecheng-11587	273	3	9.8298	9.8298	NUM
fumecheng-11587	273	4	9.8696	9.8696	NUM
fumecheng-11587	273	5	1	1	NUM
fumecheng-11587	273	6	9.3774	9.3774	NUM
fumecheng-11587	273	7	9.4159	9.4159	NUM
fumecheng-11587	273	8	8.3814	8.3814	NUM
fumecheng-11587	273	9	9.4159	9.4159	NUM
fumecheng-11587	273	10	2	2	NUM
fumecheng-11587	273	11	8.9826	8.9826	NUM
fumecheng-11587	273	12	9.0195	9.0195	NUM
fumecheng-11587	273	13	8.9892	8.9892	NUM
fumecheng-11587	273	14	9.0195	9.0195	NUM
fumecheng-11587	273	15	3	3	NUM
fumecheng-11587	273	16	8.6338	8.6338	NUM
fumecheng-11587	273	17	8.6693	8.6693	NUM
fumecheng-11587	273	18	8.6424	8.6424	NUM
fumecheng-11587	273	19	8.6693	8.6693	NUM
fumecheng-11587	273	20	4	4	NUM
fumecheng-11587	273	21	8.3228	8.3228	NUM
fumecheng-11587	273	22	8.3569	8.3569	NUM
fumecheng-11587	273	23	8.3329	8.3329	NUM
fumecheng-11587	273	24	8.3569	8.3569	NUM
fumecheng-11587	273	25	table	table	NOUN
fumecheng-11587	273	26	3	3	NUM
fumecheng-11587	273	27	parameter	parameter	NOUN
fumecheng-11587	273	28	values	value	NOUN
fumecheng-11587	273	29	of	of	ADP
fumecheng-11587	273	30	the	the	DET
fumecheng-11587	273	31	presented	present	VERB
fumecheng-11587	273	32	mechanical	mechanical	ADJ
fumecheng-11587	273	33	model	model	NOUN
fumecheng-11587	273	34	parameter	parameter	NOUN
fumecheng-11587	273	35	symbol	symbol	PROPN
fumecheng-11587	273	36	value	value	NOUN
fumecheng-11587	273	37	unit	unit	NOUN
fumecheng-11587	273	38	young	young	PROPN
fumecheng-11587	273	39	's	's	PART
fumecheng-11587	273	40	modulus	modulus	NOUN
fumecheng-11587	273	41	at	at	ADP
fumecheng-11587	273	42	top	top	ADJ
fumecheng-11587	273	43	et	et	PROPN
fumecheng-11587	273	44	390	390	NUM
fumecheng-11587	273	45	gpa	gpa	PROPN
fumecheng-11587	273	46	young	young	PROPN
fumecheng-11587	273	47	's	's	PART
fumecheng-11587	273	48	modulus	modulus	NOUN
fumecheng-11587	273	49	at	at	ADP
fumecheng-11587	273	50	bottom	bottom	PROPN
fumecheng-11587	273	51	eb	eb	PROPN
fumecheng-11587	273	52	210	210	NUM
fumecheng-11587	273	53	gpa	gpa	PROPN
fumecheng-11587	273	54	density	density	NOUN
fumecheng-11587	273	55	at	at	ADP
fumecheng-11587	273	56	top	top	NOUN
fumecheng-11587	273	57	ρt	ρt	ADP
fumecheng-11587	273	58	3960	3960	NUM
fumecheng-11587	273	59	kg	kg	NOUN
fumecheng-11587	273	60	/	/	SYM
fumecheng-11587	273	61	m3	m3	PROPN
fumecheng-11587	273	62	density	density	NOUN
fumecheng-11587	273	63	at	at	ADP
fumecheng-11587	273	64	bottom	bottom	NOUN
fumecheng-11587	273	65	ρb	ρb	NUM
fumecheng-11587	273	66	7800	7800	NUM
fumecheng-11587	273	67	kg	kg	PROPN
fumecheng-11587	273	68	/	/	SYM
fumecheng-11587	273	69	m3	m3	PROPN
fumecheng-11587	273	70	power	power	NOUN
fumecheng-11587	273	71	-	-	PUNCT
fumecheng-11587	273	72	law	law	NOUN
fumecheng-11587	273	73	index	index	NOUN
fumecheng-11587	273	74	k	k	PROPN
fumecheng-11587	273	75	1	1	NUM
fumecheng-11587	273	76	height	height	NOUN
fumecheng-11587	273	77	of	of	ADP
fumecheng-11587	273	78	the	the	DET
fumecheng-11587	273	79	beam	beam	NOUN
fumecheng-11587	273	80	h	h	NOUN
fumecheng-11587	273	81	100	100	NUM
fumecheng-11587	273	82	nm	nm	ADJ
fumecheng-11587	273	83	width	width	NOUN
fumecheng-11587	273	84	of	of	ADP
fumecheng-11587	273	85	the	the	DET
fumecheng-11587	273	86	beam	beam	NOUN
fumecheng-11587	273	87	b	b	PROPN
fumecheng-11587	273	88	1	1	NUM
fumecheng-11587	273	89	μm	μm	NOUN
fumecheng-11587	273	90	length	length	NOUN
fumecheng-11587	273	91	of	of	ADP
fumecheng-11587	273	92	the	the	DET
fumecheng-11587	273	93	beam	beam	NOUN
fumecheng-11587	273	94	l	l	NOUN
fumecheng-11587	273	95	10	10	NUM
fumecheng-11587	273	96	μm	μm	NUM
fumecheng-11587	273	97	nonlocal	nonlocal	ADJ
fumecheng-11587	273	98	parameter	parameter	NOUN
fumecheng-11587	273	99	μ	μ	PROPN
fumecheng-11587	273	100	10	10	NUM
fumecheng-11587	273	101	nm	nm	NOUN
fumecheng-11587	273	102	length	length	NOUN
fumecheng-11587	273	103	scale	scale	NOUN
fumecheng-11587	273	104	parameter	parameter	NOUN
fumecheng-11587	273	105	l	l	PROPN
fumecheng-11587	273	106	100	100	NUM
fumecheng-11587	273	107	nm	nm	ADJ
fumecheng-11587	273	108	winkler	winkler	PROPN
fumecheng-11587	273	109	coeff	coeff	PROPN
fumecheng-11587	273	110	.	.	PUNCT
fumecheng-11587	274	1	of	of	ADP
fumecheng-11587	274	2	viscoelastic	viscoelastic	ADJ
fumecheng-11587	274	3	layer	layer	NOUN
fumecheng-11587	274	4	kw	kw	PROPN
fumecheng-11587	274	5	1e-8	1e-8	NUM
fumecheng-11587	274	6	m-1	m-1	PROPN
fumecheng-11587	274	7	winkler	winkler	PROPN
fumecheng-11587	274	8	coeff	coeff	PROPN
fumecheng-11587	274	9	.	.	PROPN
fumecheng-11587	275	1	of	of	ADP
fumecheng-11587	275	2	viscoelastic	viscoelastic	ADJ
fumecheng-11587	275	3	layer	layer	NOUN
fumecheng-11587	275	4	kw	kw	VERB
fumecheng-11587	275	5	1e-8	1e-8	NUM
fumecheng-11587	275	6	nsα	nsα	NOUN
fumecheng-11587	275	7	/	/	SYM
fumecheng-11587	275	8	m3	m3	PROPN
fumecheng-11587	275	9	pasternak	pasternak	PROPN
fumecheng-11587	275	10	coeff	coeff	PROPN
fumecheng-11587	275	11	.	.	PUNCT
fumecheng-11587	276	1	of	of	ADP
fumecheng-11587	276	2	viscoelastic	viscoelastic	ADJ
fumecheng-11587	276	3	layer	layer	NOUN
fumecheng-11587	276	4	kg	kg	X
fumecheng-11587	276	5	1e-8	1e-8	NUM
fumecheng-11587	276	6	m	m	PROPN
fumecheng-11587	276	7	pasternak	pasternak	PROPN
fumecheng-11587	276	8	coeff	coeff	PROPN
fumecheng-11587	276	9	.	.	PUNCT
fumecheng-11587	277	1	of	of	ADP
fumecheng-11587	277	2	viscoelastic	viscoelastic	ADJ
fumecheng-11587	277	3	layer	layer	NOUN
fumecheng-11587	277	4	kg	kg	VERB
fumecheng-11587	277	5	1e-8	1e-8	NUM
fumecheng-11587	277	6	nsα	nsα	NOUN
fumecheng-11587	277	7	/	/	SYM
fumecheng-11587	277	8	m	m	NOUN
fumecheng-11587	277	9	amplitude	amplitude	NOUN
fumecheng-11587	277	10	of	of	ADP
fumecheng-11587	277	11	excitation	excitation	NOUN
fumecheng-11587	277	12	force	force	NOUN
fumecheng-11587	277	13	q	q	PROPN
fumecheng-11587	277	14	0.002	0.002	NUM
fumecheng-11587	277	15	n	n	DET
fumecheng-11587	277	16	720	720	NUM
fumecheng-11587	277	17	n.	n.	NOUN
fumecheng-11587	277	18	nešić	nešić	PROPN
fumecheng-11587	277	19	,	,	PUNCT
fumecheng-11587	277	20	m.	m.	NOUN
fumecheng-11587	277	21	cajić	cajić	NOUN
fumecheng-11587	277	22	,	,	PUNCT
fumecheng-11587	277	23	d.	d.	PROPN
fumecheng-11587	277	24	karličić	karličić	PROPN
fumecheng-11587	277	25	,	,	PUNCT
fumecheng-11587	277	26	m.	m.	NOUN
fumecheng-11587	277	27	lazarević	lazarević	PROPN
fumecheng-11587	277	28	,	,	PUNCT
fumecheng-11587	277	29	s.	s.	PROPN
fumecheng-11587	277	30	adhikari	adhikari	PROPN
fumecheng-11587	277	31	5.1	5.1	NUM
fumecheng-11587	277	32	.	.	PUNCT
fumecheng-11587	278	1	verification	verification	NOUN
fumecheng-11587	278	2	table	table	NOUN
fumecheng-11587	278	3	1	1	NUM
fumecheng-11587	278	4	compares	compare	VERB
fumecheng-11587	278	5	the	the	DET
fumecheng-11587	278	6	first	first	ADJ
fumecheng-11587	278	7	five	five	NUM
fumecheng-11587	278	8	non	non	ADJ
fumecheng-11587	278	9	-	-	ADJ
fumecheng-11587	278	10	dimensional	dimensional	ADJ
fumecheng-11587	278	11	fundamental	fundamental	ADJ
fumecheng-11587	278	12	natural	natural	ADJ
fumecheng-11587	278	13	frequencies	frequency	NOUN
fumecheng-11587	278	14	of	of	ADP
fumecheng-11587	278	15	a	a	DET
fumecheng-11587	278	16	local	local	ADJ
fumecheng-11587	278	17	euler	euler	NOUN
fumecheng-11587	278	18	-	-	PUNCT
fumecheng-11587	278	19	bernoulli	bernoulli	PROPN
fumecheng-11587	278	20	beam	beam	NOUN
fumecheng-11587	278	21	resting	rest	VERB
fumecheng-11587	278	22	on	on	ADP
fumecheng-11587	278	23	winkler	winkler	NOUN
fumecheng-11587	278	24	-	-	PUNCT
fumecheng-11587	278	25	pasternak	pasternak	PROPN
fumecheng-11587	278	26	foundation	foundation	NOUN
fumecheng-11587	278	27	for	for	ADP
fumecheng-11587	278	28	the	the	DET
fumecheng-11587	278	29	simply	simply	ADV
fumecheng-11587	278	30	supported	support	VERB
fumecheng-11587	278	31	boundary	boundary	ADJ
fumecheng-11587	278	32	conditions	condition	NOUN
fumecheng-11587	278	33	with	with	ADP
fumecheng-11587	278	34	foundation	foundation	NOUN
fumecheng-11587	278	35	parameters	parameter	NOUN
fumecheng-11587	278	36	k1	k1	PROPN
fumecheng-11587	278	37	=	=	SYM
fumecheng-11587	278	38	25	25	NUM
fumecheng-11587	278	39	,	,	PUNCT
fumecheng-11587	278	40	k2	k2	NOUN
fumecheng-11587	278	41	=	=	SYM
fumecheng-11587	278	42	25	25	NUM
fumecheng-11587	278	43	,	,	PUNCT
fumecheng-11587	278	44	taking	take	VERB
fumecheng-11587	278	45	the	the	DET
fumecheng-11587	278	46	values	value	NOUN
fumecheng-11587	278	47	obtained	obtain	VERB
fumecheng-11587	278	48	in	in	ADP
fumecheng-11587	278	49	[	[	PROPN
fumecheng-11587	278	50	63	63	NUM
fumecheng-11587	278	51	,	,	PUNCT
fumecheng-11587	278	52	64	64	NUM
fumecheng-11587	278	53	,	,	PUNCT
fumecheng-11587	278	54	65	65	NUM
fumecheng-11587	278	55	,	,	PUNCT
fumecheng-11587	278	56	66	66	NUM
fumecheng-11587	278	57	]	]	PUNCT
fumecheng-11587	278	58	,	,	PUNCT
fumecheng-11587	278	59	where	where	SCONJ
fumecheng-11587	278	60	fine	fine	ADJ
fumecheng-11587	278	61	agreement	agreement	NOUN
fumecheng-11587	278	62	is	be	AUX
fumecheng-11587	278	63	achieved	achieve	VERB
fumecheng-11587	278	64	.	.	PUNCT
fumecheng-11587	279	1	besides	besides	SCONJ
fumecheng-11587	279	2	that	that	PRON
fumecheng-11587	279	3	,	,	PUNCT
fumecheng-11587	279	4	we	we	PRON
fumecheng-11587	279	5	made	make	VERB
fumecheng-11587	279	6	a	a	DET
fumecheng-11587	279	7	comparison	comparison	NOUN
fumecheng-11587	279	8	of	of	ADP
fumecheng-11587	279	9	non	non	ADJ
fumecheng-11587	279	10	-	-	ADJ
fumecheng-11587	279	11	dimensional	dimensional	ADJ
fumecheng-11587	279	12	fundamental	fundamental	ADJ
fumecheng-11587	279	13	natural	natural	ADJ
fumecheng-11587	279	14	frequencies	frequency	NOUN
fumecheng-11587	279	15	of	of	ADP
fumecheng-11587	279	16	simply	simply	ADV
fumecheng-11587	279	17	supported	support	VERB
fumecheng-11587	279	18	nonlocal	nonlocal	ADJ
fumecheng-11587	279	19	euler	euler	NOUN
fumecheng-11587	279	20	-	-	PUNCT
fumecheng-11587	279	21	bernoulli	bernoulli	NOUN
fumecheng-11587	279	22	beam	beam	NOUN
fumecheng-11587	279	23	with	with	ADP
fumecheng-11587	279	24	different	different	ADJ
fumecheng-11587	279	25	values	value	NOUN
fumecheng-11587	279	26	of	of	ADP
fumecheng-11587	279	27	nonlocal	nonlocal	ADJ
fumecheng-11587	279	28	stress	stress	NOUN
fumecheng-11587	279	29	-	-	PUNCT
fumecheng-11587	279	30	gradient	gradient	NOUN
fumecheng-11587	279	31	parameter	parameter	NOUN
fumecheng-11587	279	32	μ	μ	PROPN
fumecheng-11587	279	33	with	with	ADP
fumecheng-11587	279	34	data	datum	NOUN
fumecheng-11587	279	35	available	available	ADJ
fumecheng-11587	279	36	in	in	ADP
fumecheng-11587	279	37	the	the	DET
fumecheng-11587	279	38	literature	literature	NOUN
fumecheng-11587	279	39	[	[	X
fumecheng-11587	279	40	17	17	NUM
fumecheng-11587	279	41	,	,	PUNCT
fumecheng-11587	279	42	67	67	NUM
fumecheng-11587	279	43	,	,	PUNCT
fumecheng-11587	279	44	68	68	NUM
fumecheng-11587	279	45	]	]	PUNCT
fumecheng-11587	279	46	.	.	PUNCT
fumecheng-11587	280	1	these	these	DET
fumecheng-11587	280	2	results	result	NOUN
fumecheng-11587	280	3	are	be	AUX
fumecheng-11587	280	4	also	also	ADV
fumecheng-11587	280	5	in	in	ADP
fumecheng-11587	280	6	good	good	ADJ
fumecheng-11587	280	7	agreement	agreement	NOUN
fumecheng-11587	280	8	(	(	PUNCT
fumecheng-11587	280	9	table	table	NOUN
fumecheng-11587	280	10	2	2	NUM
fumecheng-11587	280	11	)	)	PUNCT
fumecheng-11587	280	12	.	.	PUNCT
fumecheng-11587	281	1	to	to	PART
fumecheng-11587	281	2	demonstrate	demonstrate	VERB
fumecheng-11587	281	3	the	the	DET
fumecheng-11587	281	4	reliability	reliability	NOUN
fumecheng-11587	281	5	and	and	CCONJ
fumecheng-11587	281	6	accuracy	accuracy	NOUN
fumecheng-11587	281	7	of	of	ADP
fumecheng-11587	281	8	the	the	DET
fumecheng-11587	281	9	presented	present	VERB
fumecheng-11587	281	10	methodology	methodology	NOUN
fumecheng-11587	281	11	for	for	ADP
fumecheng-11587	281	12	the	the	DET
fumecheng-11587	281	13	determination	determination	NOUN
fumecheng-11587	281	14	of	of	ADP
fumecheng-11587	281	15	the	the	DET
fumecheng-11587	281	16	amplitude	amplitude	NOUN
fumecheng-11587	281	17	-	-	PUNCT
fumecheng-11587	281	18	frequency	frequency	NOUN
fumecheng-11587	281	19	responses	response	NOUN
fumecheng-11587	281	20	and	and	CCONJ
fumecheng-11587	281	21	corresponding	correspond	VERB
fumecheng-11587	281	22	periodic	periodic	ADJ
fumecheng-11587	281	23	solutions	solution	NOUN
fumecheng-11587	281	24	,	,	PUNCT
fumecheng-11587	281	25	the	the	DET
fumecheng-11587	281	26	obtained	obtain	VERB
fumecheng-11587	281	27	results	result	NOUN
fumecheng-11587	281	28	from	from	ADP
fumecheng-11587	281	29	the	the	DET
fumecheng-11587	281	30	ihb	ihb	NOUN
fumecheng-11587	281	31	are	be	AUX
fumecheng-11587	281	32	verified	verify	VERB
fumecheng-11587	281	33	with	with	ADP
fumecheng-11587	281	34	the	the	DET
fumecheng-11587	281	35	direct	direct	ADJ
fumecheng-11587	281	36	numerical	numerical	ADJ
fumecheng-11587	281	37	integration	integration	NOUN
fumecheng-11587	281	38	by	by	ADP
fumecheng-11587	281	39	using	use	VERB
fumecheng-11587	281	40	the	the	DET
fumecheng-11587	281	41	runge	runge	NOUN
fumecheng-11587	281	42	-	-	PUNCT
fumecheng-11587	281	43	kutta	kutta	NOUN
fumecheng-11587	281	44	method	method	NOUN
fumecheng-11587	281	45	.	.	PUNCT
fumecheng-11587	282	1	choosing	choose	VERB
fumecheng-11587	282	2	the	the	DET
fumecheng-11587	282	3	desired	desire	VERB
fumecheng-11587	282	4	ihb	ihb	ADP
fumecheng-11587	282	5	periodic	periodic	ADJ
fumecheng-11587	282	6	solutions	solution	NOUN
fumecheng-11587	282	7	at	at	ADP
fumecheng-11587	282	8	the	the	DET
fumecheng-11587	282	9	corresponding	corresponding	ADJ
fumecheng-11587	282	10	excitation	excitation	NOUN
fumecheng-11587	282	11	frequency	frequency	NOUN
fumecheng-11587	282	12	(	(	PUNCT
fumecheng-11587	282	13	magenta	magenta	NOUN
fumecheng-11587	282	14	and	and	CCONJ
fumecheng-11587	282	15	cyan	cyan	NOUN
fumecheng-11587	282	16	stars	star	NOUN
fumecheng-11587	282	17	)	)	PUNCT
fumecheng-11587	282	18	from	from	ADP
fumecheng-11587	282	19	fig	fig	NOUN
fumecheng-11587	282	20	.	.	PUNCT
fumecheng-11587	283	1	2	2	NUM
fumecheng-11587	283	2	(	(	PUNCT
fumecheng-11587	283	3	a	a	DET
fumecheng-11587	283	4	,	,	PUNCT
fumecheng-11587	283	5	b	b	NOUN
fumecheng-11587	283	6	)	)	PUNCT
fumecheng-11587	283	7	and	and	CCONJ
fumecheng-11587	283	8	extracting	extract	VERB
fumecheng-11587	283	9	the	the	DET
fumecheng-11587	283	10	initial	initial	ADJ
fumecheng-11587	283	11	conditions	condition	NOUN
fumecheng-11587	283	12	for	for	ADP
fumecheng-11587	283	13	the	the	DET
fumecheng-11587	283	14	use	use	NOUN
fumecheng-11587	283	15	in	in	ADP
fumecheng-11587	283	16	the	the	DET
fumecheng-11587	283	17	runge	runge	NOUN
fumecheng-11587	283	18	-	-	PUNCT
fumecheng-11587	283	19	kutta	kutta	NOUN
fumecheng-11587	283	20	method	method	NOUN
fumecheng-11587	283	21	,	,	PUNCT
fumecheng-11587	283	22	two	two	NUM
fumecheng-11587	283	23	solutions	solution	NOUN
fumecheng-11587	283	24	are	be	AUX
fumecheng-11587	283	25	compared	compare	VERB
fumecheng-11587	283	26	in	in	ADP
fumecheng-11587	283	27	fig	fig	NOUN
fumecheng-11587	283	28	.	.	PUNCT
fumecheng-11587	284	1	3	3	NUM
fumecheng-11587	284	2	where	where	SCONJ
fumecheng-11587	284	3	excellent	excellent	ADJ
fumecheng-11587	284	4	matching	matching	NOUN
fumecheng-11587	284	5	of	of	ADP
fumecheng-11587	284	6	the	the	DET
fumecheng-11587	284	7	results	result	NOUN
fumecheng-11587	284	8	from	from	ADP
fumecheng-11587	284	9	two	two	NUM
fumecheng-11587	284	10	different	different	ADJ
fumecheng-11587	284	11	methods	method	NOUN
fumecheng-11587	284	12	ihb	ihb	NOUN
fumecheng-11587	284	13	and	and	CCONJ
fumecheng-11587	284	14	runge	runge	NOUN
fumecheng-11587	284	15	-	-	PUNCT
fumecheng-11587	284	16	kutta	kutta	NOUN
fumecheng-11587	284	17	can	can	AUX
fumecheng-11587	284	18	be	be	AUX
fumecheng-11587	284	19	observed	observe	VERB
fumecheng-11587	284	20	for	for	ADP
fumecheng-11587	284	21	both	both	DET
fumecheng-11587	284	22	excitation	excitation	NOUN
fumecheng-11587	284	23	frequency	frequency	NOUN
fumecheng-11587	284	24	examples	example	NOUN
fumecheng-11587	284	25	.	.	PUNCT
fumecheng-11587	285	1	periodic	periodic	ADJ
fumecheng-11587	285	2	solutions	solution	NOUN
fumecheng-11587	285	3	in	in	ADP
fumecheng-11587	285	4	fig	fig	NOUN
fumecheng-11587	285	5	.	.	PUNCT
fumecheng-11587	286	1	3	3	NUM
fumecheng-11587	286	2	are	be	AUX
fumecheng-11587	286	3	depicted	depict	VERB
fumecheng-11587	286	4	in	in	ADP
fumecheng-11587	286	5	the	the	DET
fumecheng-11587	286	6	phase	phase	NOUN
fumecheng-11587	286	7	plane	plane	NOUN
fumecheng-11587	286	8	where	where	SCONJ
fumecheng-11587	286	9	the	the	DET
fumecheng-11587	286	10	velocity	velocity	NOUN
fumecheng-11587	286	11	is	be	AUX
fumecheng-11587	286	12	given	give	VERB
fumecheng-11587	286	13	on	on	ADP
fumecheng-11587	286	14	the	the	DET
fumecheng-11587	286	15	ordinate	ordinate	NOUN
fumecheng-11587	286	16	axis	axis	ADJ
fumecheng-11587	286	17	,	,	PUNCT
fumecheng-11587	286	18	while	while	SCONJ
fumecheng-11587	286	19	the	the	DET
fumecheng-11587	286	20	displacement	displacement	NOUN
fumecheng-11587	286	21	is	be	AUX
fumecheng-11587	286	22	given	give	VERB
fumecheng-11587	286	23	on	on	ADP
fumecheng-11587	286	24	the	the	DET
fumecheng-11587	286	25	abscissa	abscissa	NOUN
fumecheng-11587	286	26	.	.	PUNCT
fumecheng-11587	287	1	5.2	5.2	NUM
fumecheng-11587	287	2	.	.	PUNCT
fumecheng-11587	288	1	numerical	numerical	ADJ
fumecheng-11587	288	2	results	result	NOUN
fumecheng-11587	288	3	of	of	ADP
fumecheng-11587	288	4	stability	stability	NOUN
fumecheng-11587	288	5	analysis	analysis	NOUN
fumecheng-11587	288	6	in	in	ADP
fumecheng-11587	288	7	this	this	DET
fumecheng-11587	288	8	section	section	NOUN
fumecheng-11587	288	9	,	,	PUNCT
fumecheng-11587	288	10	we	we	PRON
fumecheng-11587	288	11	investigate	investigate	VERB
fumecheng-11587	288	12	how	how	SCONJ
fumecheng-11587	288	13	excitation	excitation	NOUN
fumecheng-11587	288	14	force	force	NOUN
fumecheng-11587	288	15	,	,	PUNCT
fumecheng-11587	288	16	parameters	parameter	NOUN
fumecheng-11587	288	17	of	of	ADP
fumecheng-11587	288	18	the	the	DET
fumecheng-11587	288	19	functionally	functionally	ADV
fumecheng-11587	288	20	graded	grade	VERB
fumecheng-11587	288	21	material	material	NOUN
fumecheng-11587	288	22	,	,	PUNCT
fumecheng-11587	288	23	and	and	CCONJ
fumecheng-11587	288	24	foundation	foundation	NOUN
fumecheng-11587	288	25	are	be	AUX
fumecheng-11587	288	26	affecting	affect	VERB
fumecheng-11587	288	27	the	the	DET
fumecheng-11587	288	28	frequency	frequency	NOUN
fumecheng-11587	288	29	response	response	NOUN
fumecheng-11587	288	30	curves	curve	NOUN
fumecheng-11587	288	31	in	in	ADP
fumecheng-11587	288	32	terms	term	NOUN
fumecheng-11587	288	33	of	of	ADP
fumecheng-11587	288	34	the	the	DET
fumecheng-11587	288	35	first	first	ADJ
fumecheng-11587	288	36	and	and	CCONJ
fumecheng-11587	288	37	third	third	ADJ
fumecheng-11587	288	38	amplitudes	amplitude	NOUN
fumecheng-11587	288	39	.	.	PUNCT
fumecheng-11587	289	1	for	for	ADP
fumecheng-11587	289	2	pinned	pin	VERB
fumecheng-11587	289	3	-	-	PUNCT
fumecheng-11587	289	4	pinned	pin	VERB
fumecheng-11587	289	5	boundary	boundary	ADJ
fumecheng-11587	289	6	conditions	condition	NOUN
fumecheng-11587	289	7	,	,	PUNCT
fumecheng-11587	289	8	fig	fig	NOUN
fumecheng-11587	289	9	.	.	NOUN
fumecheng-11587	290	1	2	2	NUM
fumecheng-11587	290	2	(	(	PUNCT
fumecheng-11587	290	3	a	a	DET
fumecheng-11587	290	4	,	,	PUNCT
fumecheng-11587	290	5	b	b	NOUN
fumecheng-11587	290	6	)	)	PUNCT
fumecheng-11587	290	7	shows	show	VERB
fumecheng-11587	290	8	the	the	DET
fumecheng-11587	290	9	frequency	frequency	NOUN
fumecheng-11587	290	10	response	response	NOUN
fumecheng-11587	290	11	curves	curve	NOUN
fumecheng-11587	290	12	for	for	ADP
fumecheng-11587	290	13	the	the	DET
fumecheng-11587	290	14	amplitudes	amplitude	NOUN
fumecheng-11587	290	15	a1	a1	NOUN
fumecheng-11587	290	16	and	and	CCONJ
fumecheng-11587	290	17	a3	a3	NOUN
fumecheng-11587	290	18	,	,	PUNCT
fumecheng-11587	290	19	respectively	respectively	ADV
fumecheng-11587	290	20	,	,	PUNCT
fumecheng-11587	290	21	which	which	PRON
fumecheng-11587	290	22	are	be	AUX
fumecheng-11587	290	23	then	then	ADV
fumecheng-11587	290	24	given	give	VERB
fumecheng-11587	290	25	on	on	ADP
fumecheng-11587	290	26	the	the	DET
fumecheng-11587	290	27	ordinate	ordinate	NOUN
fumecheng-11587	290	28	axis	axis	NOUN
fumecheng-11587	290	29	while	while	SCONJ
fumecheng-11587	290	30	the	the	DET
fumecheng-11587	290	31	excitation	excitation	NOUN
fumecheng-11587	290	32	frequency	frequency	NOUN
fumecheng-11587	290	33	ω	ω	PROPN
fumecheng-11587	290	34	is	be	AUX
fumecheng-11587	290	35	on	on	ADP
fumecheng-11587	290	36	the	the	DET
fumecheng-11587	290	37	abscissa	abscissa	NOUN
fumecheng-11587	290	38	.	.	PUNCT
fumecheng-11587	291	1	here	here	ADV
fumecheng-11587	291	2	,	,	PUNCT
fumecheng-11587	291	3	one	one	PRON
fumecheng-11587	291	4	can	can	AUX
fumecheng-11587	291	5	observe	observe	VERB
fumecheng-11587	291	6	that	that	SCONJ
fumecheng-11587	291	7	the	the	DET
fumecheng-11587	291	8	maximum	maximum	ADJ
fumecheng-11587	291	9	amplitude	amplitude	NOUN
fumecheng-11587	291	10	experiences	experience	VERB
fumecheng-11587	291	11	a	a	DET
fumecheng-11587	291	12	rise	rise	NOUN
fumecheng-11587	291	13	at	at	ADP
fumecheng-11587	291	14	two	two	NUM
fumecheng-11587	291	15	resonance	resonance	NOUN
fumecheng-11587	291	16	frequencies	frequency	NOUN
fumecheng-11587	291	17	.	.	PUNCT
fumecheng-11587	292	1	two	two	NUM
fumecheng-11587	292	2	such	such	ADJ
fumecheng-11587	292	3	regions	region	NOUN
fumecheng-11587	292	4	can	can	AUX
fumecheng-11587	292	5	be	be	AUX
fumecheng-11587	292	6	noticed	notice	VERB
fumecheng-11587	292	7	at	at	ADP
fumecheng-11587	292	8	frequencies	frequency	NOUN
fumecheng-11587	292	9	around	around	ADP
fumecheng-11587	292	10	ω	ω	NUM
fumecheng-11587	292	11	=	=	SYM
fumecheng-11587	292	12	4	4	NUM
fumecheng-11587	292	13	and	and	CCONJ
fumecheng-11587	292	14	ω	ω	NUM
fumecheng-11587	292	15	=	=	SYM
fumecheng-11587	292	16	16	16	NUM
fumecheng-11587	292	17	-	-	SYM
fumecheng-11587	292	18	27	27	NUM
fumecheng-11587	292	19	,	,	PUNCT
fumecheng-11587	292	20	depending	depend	VERB
fumecheng-11587	292	21	on	on	ADP
fumecheng-11587	292	22	q.	q.	NOUN
fumecheng-11587	292	23	in	in	ADP
fumecheng-11587	292	24	the	the	DET
fumecheng-11587	292	25	case	case	NOUN
fumecheng-11587	292	26	of	of	ADP
fumecheng-11587	292	27	the	the	DET
fumecheng-11587	292	28	first	first	ADJ
fumecheng-11587	292	29	dominant	dominant	ADJ
fumecheng-11587	292	30	amplitude	amplitude	NOUN
fumecheng-11587	292	31	a1	a1	NOUN
fumecheng-11587	292	32	,	,	PUNCT
fumecheng-11587	292	33	this	this	DET
fumecheng-11587	292	34	change	change	NOUN
fumecheng-11587	292	35	is	be	AUX
fumecheng-11587	292	36	weak	weak	ADJ
fumecheng-11587	292	37	in	in	ADP
fumecheng-11587	292	38	the	the	DET
fumecheng-11587	292	39	first	first	ADJ
fumecheng-11587	292	40	resonance	resonance	NOUN
fumecheng-11587	292	41	region	region	NOUN
fumecheng-11587	292	42	while	while	SCONJ
fumecheng-11587	292	43	it	it	PRON
fumecheng-11587	292	44	is	be	AUX
fumecheng-11587	292	45	very	very	ADV
fumecheng-11587	292	46	high	high	ADJ
fumecheng-11587	292	47	for	for	ADP
fumecheng-11587	292	48	the	the	DET
fumecheng-11587	292	49	second	second	ADJ
fumecheng-11587	292	50	region	region	NOUN
fumecheng-11587	292	51	,	,	PUNCT
fumecheng-11587	292	52	where	where	SCONJ
fumecheng-11587	292	53	the	the	DET
fumecheng-11587	292	54	system	system	NOUN
fumecheng-11587	292	55	experiences	experience	VERB
fumecheng-11587	292	56	the	the	DET
fumecheng-11587	292	57	hardening	harden	VERB
fumecheng-11587	292	58	stiffness	stiffness	ADJ
fumecheng-11587	292	59	nonlinearity	nonlinearity	NOUN
fumecheng-11587	292	60	.	.	PUNCT
fumecheng-11587	293	1	here	here	ADV
fumecheng-11587	293	2	,	,	PUNCT
fumecheng-11587	293	3	one	one	PRON
fumecheng-11587	293	4	can	can	AUX
fumecheng-11587	293	5	observe	observe	VERB
fumecheng-11587	293	6	jump	jump	NOUN
fumecheng-11587	293	7	-	-	PUNCT
fumecheng-11587	293	8	down	down	NOUN
fumecheng-11587	293	9	and	and	CCONJ
fumecheng-11587	293	10	jump	jump	VERB
fumecheng-11587	293	11	-	-	PUNCT
fumecheng-11587	293	12	up	up	ADP
fumecheng-11587	293	13	behavior	behavior	NOUN
fumecheng-11587	293	14	as	as	ADV
fumecheng-11587	293	15	well	well	ADV
fumecheng-11587	293	16	as	as	ADP
fumecheng-11587	293	17	coexisting	coexist	VERB
fumecheng-11587	293	18	periodic	periodic	ADJ
fumecheng-11587	293	19	solutions	solution	NOUN
fumecheng-11587	293	20	,	,	PUNCT
fumecheng-11587	293	21	which	which	PRON
fumecheng-11587	293	22	is	be	AUX
fumecheng-11587	293	23	the	the	DET
fumecheng-11587	293	24	characteristic	characteristic	NOUN
fumecheng-11587	293	25	of	of	ADP
fumecheng-11587	293	26	this	this	DET
fumecheng-11587	293	27	nonlinear	nonlinear	ADJ
fumecheng-11587	293	28	phenomenon	phenomenon	NOUN
fumecheng-11587	293	29	[	[	X
fumecheng-11587	293	30	69	69	NUM
fumecheng-11587	293	31	]	]	PUNCT
fumecheng-11587	293	32	.	.	PUNCT
fumecheng-11587	294	1	on	on	ADP
fumecheng-11587	294	2	the	the	DET
fumecheng-11587	294	3	other	other	ADJ
fumecheng-11587	294	4	side	side	NOUN
fumecheng-11587	294	5	,	,	PUNCT
fumecheng-11587	294	6	despite	despite	SCONJ
fumecheng-11587	294	7	the	the	DET
fumecheng-11587	294	8	much	much	ADV
fumecheng-11587	294	9	lower	low	ADJ
fumecheng-11587	294	10	values	value	NOUN
fumecheng-11587	294	11	than	than	ADP
fumecheng-11587	294	12	a1	a1	NOUN
fumecheng-11587	294	13	,	,	PUNCT
fumecheng-11587	294	14	the	the	DET
fumecheng-11587	294	15	amplitudes	amplitude	NOUN
fumecheng-11587	294	16	a3	a3	NOUN
fumecheng-11587	294	17	show	show	VERB
fumecheng-11587	294	18	an	an	DET
fumecheng-11587	294	19	increase	increase	NOUN
fumecheng-11587	294	20	in	in	ADP
fumecheng-11587	294	21	the	the	DET
fumecheng-11587	294	22	first	first	ADJ
fumecheng-11587	294	23	resonance	resonance	NOUN
fumecheng-11587	294	24	region	region	NOUN
fumecheng-11587	294	25	that	that	PRON
fumecheng-11587	294	26	is	be	AUX
fumecheng-11587	294	27	more	more	ADV
fumecheng-11587	294	28	pronounced	pronounced	ADJ
fumecheng-11587	294	29	compared	compare	VERB
fumecheng-11587	294	30	to	to	ADP
fumecheng-11587	294	31	those	those	PRON
fumecheng-11587	294	32	occurring	occur	VERB
fumecheng-11587	294	33	within	within	ADP
fumecheng-11587	294	34	the	the	DET
fumecheng-11587	294	35	second	second	ADJ
fumecheng-11587	294	36	region	region	NOUN
fumecheng-11587	294	37	but	but	CCONJ
fumecheng-11587	294	38	displaying	display	VERB
fumecheng-11587	294	39	only	only	ADV
fumecheng-11587	294	40	the	the	DET
fumecheng-11587	294	41	linear	linear	ADJ
fumecheng-11587	294	42	-	-	PUNCT
fumecheng-11587	294	43	like	like	ADJ
fumecheng-11587	294	44	behavior	behavior	NOUN
fumecheng-11587	294	45	.	.	PUNCT
fumecheng-11587	295	1	however	however	ADV
fumecheng-11587	295	2	,	,	PUNCT
fumecheng-11587	295	3	in	in	ADP
fumecheng-11587	295	4	the	the	DET
fumecheng-11587	295	5	second	second	ADJ
fumecheng-11587	295	6	resonance	resonance	NOUN
fumecheng-11587	295	7	region	region	NOUN
fumecheng-11587	295	8	,	,	PUNCT
fumecheng-11587	295	9	a	a	DET
fumecheng-11587	295	10	strong	strong	ADJ
fumecheng-11587	295	11	nonlinear	nonlinear	ADJ
fumecheng-11587	295	12	hardening	harden	VERB
fumecheng-11587	295	13	stiffness	stiffness	ADJ
fumecheng-11587	295	14	behavior	behavior	NOUN
fumecheng-11587	295	15	occurs	occur	VERB
fumecheng-11587	295	16	even	even	ADV
fumecheng-11587	295	17	for	for	ADP
fumecheng-11587	295	18	very	very	ADV
fumecheng-11587	295	19	low	low	ADJ
fumecheng-11587	295	20	values	value	NOUN
fumecheng-11587	295	21	of	of	ADP
fumecheng-11587	295	22	the	the	DET
fumecheng-11587	295	23	amplitude	amplitude	NOUN
fumecheng-11587	295	24	.	.	PUNCT
fumecheng-11587	296	1	an	an	DET
fumecheng-11587	296	2	increase	increase	NOUN
fumecheng-11587	296	3	of	of	ADP
fumecheng-11587	296	4	the	the	DET
fumecheng-11587	296	5	excitation	excitation	NOUN
fumecheng-11587	296	6	force	force	NOUN
fumecheng-11587	296	7	amplitude	amplitude	NOUN
fumecheng-11587	296	8	q	q	NOUN
fumecheng-11587	296	9	increases	increase	VERB
fumecheng-11587	296	10	the	the	DET
fumecheng-11587	296	11	amplitude	amplitude	NOUN
fumecheng-11587	296	12	values	value	NOUN
fumecheng-11587	296	13	and	and	CCONJ
fumecheng-11587	296	14	resonant	resonant	ADJ
fumecheng-11587	296	15	picks	pick	NOUN
fumecheng-11587	296	16	.	.	PUNCT
fumecheng-11587	297	1	moreover	moreover	ADV
fumecheng-11587	297	2	,	,	PUNCT
fumecheng-11587	297	3	a	a	DET
fumecheng-11587	297	4	forward	forward	ADJ
fumecheng-11587	297	5	frequency	frequency	NOUN
fumecheng-11587	297	6	sweeping	sweeping	ADJ
fumecheng-11587	297	7	due	due	ADP
fumecheng-11587	297	8	to	to	ADP
fumecheng-11587	297	9	an	an	DET
fumecheng-11587	297	10	increase	increase	NOUN
fumecheng-11587	297	11	of	of	ADP
fumecheng-11587	297	12	the	the	DET
fumecheng-11587	297	13	excitation	excitation	NOUN
fumecheng-11587	297	14	frequency	frequency	NOUN
fumecheng-11587	297	15	ω	ω	PROPN
fumecheng-11587	297	16	,	,	PUNCT
fumecheng-11587	297	17	starting	start	VERB
fumecheng-11587	297	18	from	from	ADP
fumecheng-11587	297	19	small	small	ADJ
fumecheng-11587	297	20	values	value	NOUN
fumecheng-11587	297	21	,	,	PUNCT
fumecheng-11587	297	22	shows	show	VERB
fumecheng-11587	297	23	changes	change	NOUN
fumecheng-11587	297	24	of	of	ADP
fumecheng-11587	297	25	response	response	NOUN
fumecheng-11587	297	26	amplitudes	amplitude	NOUN
fumecheng-11587	297	27	up	up	ADP
fumecheng-11587	297	28	to	to	ADP
fumecheng-11587	297	29	the	the	DET
fumecheng-11587	297	30	point	point	NOUN
fumecheng-11587	297	31	when	when	SCONJ
fumecheng-11587	297	32	the	the	DET
fumecheng-11587	297	33	periodic	periodic	ADJ
fumecheng-11587	297	34	response	response	NOUN
fumecheng-11587	297	35	loses	lose	VERB
fumecheng-11587	297	36	its	its	PRON
fumecheng-11587	297	37	stability	stability	NOUN
fumecheng-11587	297	38	.	.	PUNCT
fumecheng-11587	298	1	this	this	DET
fumecheng-11587	298	2	critical	critical	ADJ
fumecheng-11587	298	3	point	point	NOUN
fumecheng-11587	298	4	known	know	VERB
fumecheng-11587	298	5	as	as	ADP
fumecheng-11587	298	6	fold	fold	ADJ
fumecheng-11587	298	7	point	point	NOUN
fumecheng-11587	298	8	is	be	AUX
fumecheng-11587	298	9	given	give	VERB
fumecheng-11587	298	10	as	as	ADP
fumecheng-11587	298	11	upper	upper	ADJ
fumecheng-11587	298	12	brown	brown	ADJ
fumecheng-11587	298	13	dot	dot	NOUN
fumecheng-11587	298	14	in	in	ADP
fumecheng-11587	298	15	fig	fig	NOUN
fumecheng-11587	298	16	.	.	PUNCT
fumecheng-11587	299	1	2	2	X
fumecheng-11587	299	2	.	.	X
fumecheng-11587	299	3	it	it	PRON
fumecheng-11587	299	4	can	can	AUX
fumecheng-11587	299	5	be	be	AUX
fumecheng-11587	299	6	observed	observe	VERB
fumecheng-11587	299	7	that	that	SCONJ
fumecheng-11587	299	8	further	far	ADV
fumecheng-11587	299	9	forward	forward	ADV
fumecheng-11587	299	10	frequency	frequency	NOUN
fumecheng-11587	299	11	sweeping	sweeping	ADJ
fumecheng-11587	299	12	produces	produce	VERB
fumecheng-11587	299	13	another	another	DET
fumecheng-11587	299	14	branch	branch	NOUN
fumecheng-11587	299	15	of	of	ADP
fumecheng-11587	299	16	stable	stable	ADJ
fumecheng-11587	299	17	periodic	periodic	ADJ
fumecheng-11587	299	18	solutions	solution	NOUN
fumecheng-11587	299	19	,	,	PUNCT
fumecheng-11587	299	20	which	which	PRON
fumecheng-11587	299	21	is	be	AUX
fumecheng-11587	299	22	also	also	ADV
fumecheng-11587	299	23	known	know	VERB
fumecheng-11587	299	24	as	as	ADP
fumecheng-11587	299	25	the	the	DET
fumecheng-11587	299	26	lower	low	ADJ
fumecheng-11587	299	27	branch	branch	NOUN
fumecheng-11587	299	28	of	of	ADP
fumecheng-11587	299	29	periodic	periodic	ADJ
fumecheng-11587	299	30	solutions	solution	NOUN
fumecheng-11587	299	31	.	.	PUNCT
fumecheng-11587	300	1	vibration	vibration	NOUN
fumecheng-11587	300	2	and	and	CCONJ
fumecheng-11587	300	3	stability	stability	NOUN
fumecheng-11587	300	4	of	of	ADP
fumecheng-11587	300	5	a	a	DET
fumecheng-11587	300	6	nonlinear	nonlinear	ADJ
fumecheng-11587	300	7	nonlocal	nonlocal	ADJ
fumecheng-11587	300	8	strain	strain	NOUN
fumecheng-11587	300	9	-	-	PUNCT
fumecheng-11587	300	10	gradient	gradient	NOUN
fumecheng-11587	300	11	fg	fg	PROPN
fumecheng-11587	300	12	beam	beam	NOUN
fumecheng-11587	300	13	on	on	ADP
fumecheng-11587	300	14	a	a	DET
fumecheng-11587	300	15	visco	visco	ADJ
fumecheng-11587	300	16	-	-	PUNCT
fumecheng-11587	300	17	pasternak	pasternak	NOUN
fumecheng-11587	300	18	...	...	PUNCT
fumecheng-11587	300	19	721	721	NUM
fumecheng-11587	301	1	it	it	PRON
fumecheng-11587	301	2	can	can	AUX
fumecheng-11587	301	3	be	be	AUX
fumecheng-11587	301	4	noticed	notice	VERB
fumecheng-11587	301	5	in	in	ADP
fumecheng-11587	301	6	fig	fig	NOUN
fumecheng-11587	301	7	.	.	PUNCT
fumecheng-11587	302	1	2	2	NUM
fumecheng-11587	302	2	that	that	PRON
fumecheng-11587	302	3	the	the	DET
fumecheng-11587	302	4	upper	upper	ADJ
fumecheng-11587	302	5	branch	branch	NOUN
fumecheng-11587	302	6	of	of	ADP
fumecheng-11587	302	7	the	the	DET
fumecheng-11587	302	8	amplitude	amplitude	NOUN
fumecheng-11587	302	9	grows	grow	VERB
fumecheng-11587	302	10	until	until	ADP
fumecheng-11587	302	11	the	the	DET
fumecheng-11587	302	12	critical	critical	ADJ
fumecheng-11587	302	13	moment	moment	NOUN
fumecheng-11587	302	14	(	(	PUNCT
fumecheng-11587	302	15	response	response	NOUN
fumecheng-11587	302	16	peak	peak	PROPN
fumecheng-11587	302	17	)	)	PUNCT
fumecheng-11587	302	18	which	which	PRON
fumecheng-11587	302	19	represents	represent	VERB
fumecheng-11587	302	20	the	the	DET
fumecheng-11587	302	21	maximal	maximal	ADJ
fumecheng-11587	302	22	value	value	NOUN
fumecheng-11587	302	23	of	of	ADP
fumecheng-11587	302	24	the	the	DET
fumecheng-11587	302	25	response	response	NOUN
fumecheng-11587	302	26	amplitude	amplitude	NOUN
fumecheng-11587	302	27	.	.	PUNCT
fumecheng-11587	303	1	fig	fig	NOUN
fumecheng-11587	303	2	.	.	PUNCT
fumecheng-11587	304	1	2	2	NUM
fumecheng-11587	304	2	the	the	DET
fumecheng-11587	304	3	amplitude	amplitude	NOUN
fumecheng-11587	304	4	-	-	PUNCT
fumecheng-11587	304	5	frequency	frequency	NOUN
fumecheng-11587	304	6	response	response	NOUN
fumecheng-11587	304	7	curves	curve	NOUN
fumecheng-11587	304	8	of	of	ADP
fumecheng-11587	304	9	the	the	DET
fumecheng-11587	304	10	nlsgt	nlsgt	NOUN
fumecheng-11587	304	11	beam	beam	NOUN
fumecheng-11587	304	12	on	on	ADP
fumecheng-11587	304	13	visco	visco	ADJ
fumecheng-11587	304	14	-	-	PUNCT
fumecheng-11587	304	15	pasternak	pasternak	PROPN
fumecheng-11587	304	16	foundation	foundation	NOUN
fumecheng-11587	304	17	for	for	ADP
fumecheng-11587	304	18	pinned	pin	VERB
fumecheng-11587	304	19	-	-	PUNCT
fumecheng-11587	304	20	pinned	pin	VERB
fumecheng-11587	304	21	(	(	PUNCT
fumecheng-11587	304	22	a	a	DET
fumecheng-11587	304	23	,	,	PUNCT
fumecheng-11587	304	24	b	b	NOUN
fumecheng-11587	304	25	)	)	PUNCT
fumecheng-11587	304	26	,	,	PUNCT
fumecheng-11587	304	27	clamped	clamp	VERB
fumecheng-11587	304	28	-	-	PUNCT
fumecheng-11587	304	29	pinned	pin	VERB
fumecheng-11587	304	30	(	(	PUNCT
fumecheng-11587	304	31	c	c	X
fumecheng-11587	304	32	,	,	PUNCT
fumecheng-11587	304	33	d	d	NOUN
fumecheng-11587	304	34	)	)	PUNCT
fumecheng-11587	304	35	and	and	CCONJ
fumecheng-11587	304	36	clamped	clamp	VERB
fumecheng-11587	304	37	-	-	PUNCT
fumecheng-11587	304	38	clamped	clamp	VERB
fumecheng-11587	304	39	(	(	PUNCT
fumecheng-11587	304	40	e	e	NOUN
fumecheng-11587	304	41	,	,	PUNCT
fumecheng-11587	304	42	f	f	X
fumecheng-11587	304	43	)	)	PUNCT
fumecheng-11587	304	44	boundary	boundary	ADJ
fumecheng-11587	304	45	conditions	condition	NOUN
fumecheng-11587	304	46	.	.	PUNCT
fumecheng-11587	305	1	amplitudes	amplitude	NOUN
fumecheng-11587	305	2	a1	a1	NOUN
fumecheng-11587	305	3	and	and	CCONJ
fumecheng-11587	305	4	a3	a3	NOUN
fumecheng-11587	305	5	are	be	AUX
fumecheng-11587	305	6	plotted	plot	VERB
fumecheng-11587	305	7	for	for	ADP
fumecheng-11587	305	8	different	different	ADJ
fumecheng-11587	305	9	values	value	NOUN
fumecheng-11587	305	10	of	of	ADP
fumecheng-11587	305	11	external	external	ADJ
fumecheng-11587	305	12	load	load	NOUN
fumecheng-11587	305	13	parameter	parameter	PROPN
fumecheng-11587	305	14	q.	q.	PROPN
fumecheng-11587	305	15	the	the	DET
fumecheng-11587	305	16	unstable	unstable	ADJ
fumecheng-11587	305	17	periodic	periodic	ADJ
fumecheng-11587	305	18	solutions	solution	NOUN
fumecheng-11587	305	19	are	be	AUX
fumecheng-11587	305	20	represented	represent	VERB
fumecheng-11587	305	21	by	by	ADP
fumecheng-11587	305	22	the	the	DET
fumecheng-11587	305	23	tick	tick	NOUN
fumecheng-11587	305	24	solid	solid	ADJ
fumecheng-11587	305	25	lines	line	NOUN
fumecheng-11587	305	26	.	.	PUNCT
fumecheng-11587	306	1	722	722	NUM
fumecheng-11587	306	2	n.	n.	NOUN
fumecheng-11587	306	3	nešić	nešić	PROPN
fumecheng-11587	306	4	,	,	PUNCT
fumecheng-11587	306	5	m.	m.	NOUN
fumecheng-11587	306	6	cajić	cajić	NOUN
fumecheng-11587	306	7	,	,	PUNCT
fumecheng-11587	306	8	d.	d.	PROPN
fumecheng-11587	306	9	karličić	karličić	PROPN
fumecheng-11587	306	10	,	,	PUNCT
fumecheng-11587	306	11	m.	m.	NOUN
fumecheng-11587	306	12	lazarević	lazarević	PROPN
fumecheng-11587	306	13	,	,	PUNCT
fumecheng-11587	306	14	s.	s.	PROPN
fumecheng-11587	306	15	adhikari	adhikari	PROPN
fumecheng-11587	306	16	at	at	ADP
fumecheng-11587	306	17	this	this	DET
fumecheng-11587	306	18	peak	peak	NOUN
fumecheng-11587	306	19	point	point	NOUN
fumecheng-11587	306	20	,	,	PUNCT
fumecheng-11587	306	21	periodic	periodic	ADJ
fumecheng-11587	306	22	solutions	solution	NOUN
fumecheng-11587	306	23	lose	lose	VERB
fumecheng-11587	306	24	their	their	PRON
fumecheng-11587	306	25	stability	stability	NOUN
fumecheng-11587	306	26	leading	lead	VERB
fumecheng-11587	306	27	to	to	ADP
fumecheng-11587	306	28	the	the	DET
fumecheng-11587	306	29	jump	jump	VERB
fumecheng-11587	306	30	-	-	PUNCT
fumecheng-11587	306	31	down	down	ADP
fumecheng-11587	306	32	phenomena	phenomenon	NOUN
fumecheng-11587	306	33	of	of	ADP
fumecheng-11587	306	34	the	the	DET
fumecheng-11587	306	35	response	response	NOUN
fumecheng-11587	306	36	amplitude	amplitude	NOUN
fumecheng-11587	306	37	i.e.	i.e.	X
fumecheng-11587	306	38	a	a	DET
fumecheng-11587	306	39	sudden	sudden	ADJ
fumecheng-11587	306	40	jump	jump	NOUN
fumecheng-11587	306	41	of	of	ADP
fumecheng-11587	306	42	the	the	DET
fumecheng-11587	306	43	response	response	NOUN
fumecheng-11587	306	44	amplitude	amplitude	NOUN
fumecheng-11587	306	45	to	to	ADP
fumecheng-11587	306	46	some	some	DET
fumecheng-11587	306	47	lower	low	ADJ
fumecheng-11587	306	48	values	value	NOUN
fumecheng-11587	306	49	.	.	PUNCT
fumecheng-11587	307	1	further	far	ADV
fumecheng-11587	307	2	forward	forward	ADV
fumecheng-11587	307	3	frequency	frequency	NOUN
fumecheng-11587	307	4	sweeping	sweep	VERB
fumecheng-11587	307	5	produces	produce	VERB
fumecheng-11587	307	6	stable	stable	ADJ
fumecheng-11587	307	7	periodic	periodic	ADJ
fumecheng-11587	307	8	solutions	solution	NOUN
fumecheng-11587	307	9	.	.	PUNCT
fumecheng-11587	308	1	on	on	ADP
fumecheng-11587	308	2	the	the	DET
fumecheng-11587	308	3	contrary	contrary	NOUN
fumecheng-11587	308	4	,	,	PUNCT
fumecheng-11587	308	5	the	the	DET
fumecheng-11587	308	6	backward	backward	ADJ
fumecheng-11587	308	7	frequency	frequency	NOUN
fumecheng-11587	308	8	sweeping	sweeping	ADJ
fumecheng-11587	308	9	process	process	NOUN
fumecheng-11587	308	10	starts	start	VERB
fumecheng-11587	308	11	from	from	ADP
fumecheng-11587	308	12	values	value	NOUN
fumecheng-11587	308	13	higher	high	ADJ
fumecheng-11587	308	14	than	than	ADP
fumecheng-11587	308	15	the	the	DET
fumecheng-11587	308	16	resonant	resonant	ADJ
fumecheng-11587	308	17	frequency	frequency	NOUN
fumecheng-11587	308	18	.	.	PUNCT
fumecheng-11587	309	1	by	by	ADP
fumecheng-11587	309	2	moving	move	VERB
fumecheng-11587	309	3	backward	backward	ADV
fumecheng-11587	309	4	,	,	PUNCT
fumecheng-11587	309	5	response	response	NOUN
fumecheng-11587	309	6	amplitude	amplitude	NOUN
fumecheng-11587	309	7	increases	increase	VERB
fumecheng-11587	309	8	slowly	slowly	ADV
fumecheng-11587	309	9	until	until	SCONJ
fumecheng-11587	309	10	the	the	DET
fumecheng-11587	309	11	critical	critical	ADJ
fumecheng-11587	309	12	point	point	NOUN
fumecheng-11587	309	13	(	(	PUNCT
fumecheng-11587	309	14	another	another	DET
fumecheng-11587	309	15	fold	fold	ADJ
fumecheng-11587	309	16	point	point	NOUN
fumecheng-11587	309	17	)	)	PUNCT
fumecheng-11587	309	18	where	where	SCONJ
fumecheng-11587	309	19	the	the	DET
fumecheng-11587	309	20	periodic	periodic	ADJ
fumecheng-11587	309	21	solution	solution	NOUN
fumecheng-11587	309	22	loses	lose	VERB
fumecheng-11587	309	23	its	its	PRON
fumecheng-11587	309	24	stability	stability	NOUN
fumecheng-11587	309	25	and	and	CCONJ
fumecheng-11587	309	26	the	the	DET
fumecheng-11587	309	27	jump	jump	NOUN
fumecheng-11587	309	28	-	-	PUNCT
fumecheng-11587	309	29	up	up	ADP
fumecheng-11587	309	30	phenomena	phenomenon	NOUN
fumecheng-11587	309	31	occur	occur	VERB
fumecheng-11587	309	32	.	.	PUNCT
fumecheng-11587	310	1	if	if	SCONJ
fumecheng-11587	310	2	we	we	PRON
fumecheng-11587	310	3	further	far	ADV
fumecheng-11587	310	4	decrease	decrease	VERB
fumecheng-11587	310	5	the	the	DET
fumecheng-11587	310	6	excitation	excitation	NOUN
fumecheng-11587	310	7	frequency	frequency	NOUN
fumecheng-11587	310	8	another	another	DET
fumecheng-11587	310	9	stable	stable	ADJ
fumecheng-11587	310	10	(	(	PUNCT
fumecheng-11587	310	11	upper	upper	ADJ
fumecheng-11587	310	12	)	)	PUNCT
fumecheng-11587	310	13	branch	branch	NOUN
fumecheng-11587	310	14	of	of	ADP
fumecheng-11587	310	15	periodic	periodic	ADJ
fumecheng-11587	310	16	solutions	solution	NOUN
fumecheng-11587	310	17	occurs	occur	VERB
fumecheng-11587	310	18	.	.	PUNCT
fumecheng-11587	311	1	the	the	DET
fumecheng-11587	311	2	branches	branch	NOUN
fumecheng-11587	311	3	of	of	ADP
fumecheng-11587	311	4	unstable	unstable	ADJ
fumecheng-11587	311	5	periodic	periodic	ADJ
fumecheng-11587	311	6	solutions	solution	NOUN
fumecheng-11587	311	7	displayed	display	VERB
fumecheng-11587	311	8	as	as	ADP
fumecheng-11587	311	9	thick	thick	ADJ
fumecheng-11587	311	10	solid	solid	ADJ
fumecheng-11587	311	11	lines	line	NOUN
fumecheng-11587	311	12	can	can	AUX
fumecheng-11587	311	13	be	be	AUX
fumecheng-11587	311	14	detected	detect	VERB
fumecheng-11587	311	15	in	in	ADP
fumecheng-11587	311	16	between	between	ADP
fumecheng-11587	311	17	the	the	DET
fumecheng-11587	311	18	two	two	NUM
fumecheng-11587	311	19	different	different	ADJ
fumecheng-11587	311	20	fold	fold	ADJ
fumecheng-11587	311	21	points	point	NOUN
fumecheng-11587	311	22	of	of	ADP
fumecheng-11587	311	23	the	the	DET
fumecheng-11587	311	24	same	same	ADJ
fumecheng-11587	311	25	curve	curve	NOUN
fumecheng-11587	311	26	by	by	ADP
fumecheng-11587	311	27	applying	apply	VERB
fumecheng-11587	311	28	the	the	DET
fumecheng-11587	311	29	path	path	NOUN
fumecheng-11587	311	30	following	follow	VERB
fumecheng-11587	311	31	method	method	NOUN
fumecheng-11587	311	32	in	in	ADP
fumecheng-11587	311	33	combination	combination	NOUN
fumecheng-11587	311	34	with	with	ADP
fumecheng-11587	311	35	the	the	DET
fumecheng-11587	311	36	floquet	floquet	NOUN
fumecheng-11587	311	37	theory	theory	NOUN
fumecheng-11587	311	38	.	.	PUNCT
fumecheng-11587	312	1	similar	similar	ADJ
fumecheng-11587	312	2	observations	observation	NOUN
fumecheng-11587	312	3	can	can	AUX
fumecheng-11587	312	4	be	be	AUX
fumecheng-11587	312	5	made	make	VERB
fumecheng-11587	312	6	for	for	ADP
fumecheng-11587	312	7	the	the	DET
fumecheng-11587	312	8	fig	fig	NOUN
fumecheng-11587	312	9	.	.	PUNCT
fumecheng-11587	313	1	2	2	NUM
fumecheng-11587	313	2	(	(	PUNCT
fumecheng-11587	313	3	c	c	NOUN
fumecheng-11587	313	4	,	,	PUNCT
fumecheng-11587	313	5	f	f	NOUN
fumecheng-11587	313	6	)	)	PUNCT
fumecheng-11587	313	7	,	,	PUNCT
fumecheng-11587	313	8	for	for	ADP
fumecheng-11587	313	9	clamped	clamp	VERB
fumecheng-11587	313	10	-	-	PUNCT
fumecheng-11587	313	11	pinned	pin	VERB
fumecheng-11587	313	12	and	and	CCONJ
fumecheng-11587	313	13	clamped	clamp	VERB
fumecheng-11587	313	14	-	-	PUNCT
fumecheng-11587	313	15	clamped	clamp	VERB
fumecheng-11587	313	16	boundary	boundary	ADJ
fumecheng-11587	313	17	conditions	condition	NOUN
fumecheng-11587	313	18	.	.	PUNCT
fumecheng-11587	314	1	fig	fig	NOUN
fumecheng-11587	314	2	.	.	PUNCT
fumecheng-11587	315	1	3	3	NUM
fumecheng-11587	315	2	periodic	periodic	ADJ
fumecheng-11587	315	3	response	response	NOUN
fumecheng-11587	315	4	obtained	obtain	VERB
fumecheng-11587	315	5	by	by	ADP
fumecheng-11587	315	6	ihb	ihb	NOUN
fumecheng-11587	315	7	and	and	CCONJ
fumecheng-11587	315	8	rk	rk	NOUN
fumecheng-11587	315	9	method	method	VERB
fumecheng-11587	315	10	for	for	ADP
fumecheng-11587	315	11	two	two	NUM
fumecheng-11587	315	12	points	point	NOUN
fumecheng-11587	315	13	fig	fig	NOUN
fumecheng-11587	315	14	.	.	PUNCT
fumecheng-11587	316	1	4	4	NUM
fumecheng-11587	316	2	shows	show	VERB
fumecheng-11587	316	3	the	the	DET
fumecheng-11587	316	4	amplitude	amplitude	NOUN
fumecheng-11587	316	5	-	-	PUNCT
fumecheng-11587	316	6	frequency	frequency	NOUN
fumecheng-11587	316	7	responses	response	NOUN
fumecheng-11587	316	8	for	for	ADP
fumecheng-11587	316	9	four	four	NUM
fumecheng-11587	316	10	different	different	ADJ
fumecheng-11587	316	11	values	value	NOUN
fumecheng-11587	316	12	of	of	ADP
fumecheng-11587	316	13	the	the	DET
fumecheng-11587	316	14	functional	functional	ADJ
fumecheng-11587	316	15	graded	grade	VERB
fumecheng-11587	316	16	material	material	NOUN
fumecheng-11587	316	17	parameter	parameter	PROPN
fumecheng-11587	316	18	k.	k.	PROPN
fumecheng-11587	316	19	for	for	ADP
fumecheng-11587	316	20	pinned	pin	VERB
fumecheng-11587	316	21	-	-	PUNCT
fumecheng-11587	316	22	pinned	pin	VERB
fumecheng-11587	316	23	boundary	boundary	ADJ
fumecheng-11587	316	24	conditions	condition	NOUN
fumecheng-11587	316	25	,	,	PUNCT
fumecheng-11587	316	26	the	the	DET
fumecheng-11587	316	27	first	first	ADJ
fumecheng-11587	316	28	(	(	PUNCT
fumecheng-11587	316	29	fig	fig	NOUN
fumecheng-11587	316	30	.	.	PUNCT
fumecheng-11587	317	1	4	4	NUM
fumecheng-11587	317	2	(	(	PUNCT
fumecheng-11587	317	3	a	a	NOUN
fumecheng-11587	317	4	)	)	PUNCT
fumecheng-11587	317	5	)	)	PUNCT
fumecheng-11587	318	1	and	and	CCONJ
fumecheng-11587	318	2	the	the	DET
fumecheng-11587	318	3	third	third	ADJ
fumecheng-11587	318	4	(	(	PUNCT
fumecheng-11587	318	5	fig	fig	NOUN
fumecheng-11587	318	6	.	.	PUNCT
fumecheng-11587	319	1	4	4	NUM
fumecheng-11587	319	2	(	(	PUNCT
fumecheng-11587	319	3	b	b	NOUN
fumecheng-11587	319	4	)	)	PUNCT
fumecheng-11587	319	5	)	)	PUNCT
fumecheng-11587	319	6	amplitude	amplitude	NOUN
fumecheng-11587	319	7	are	be	AUX
fumecheng-11587	319	8	traced	trace	VERB
fumecheng-11587	319	9	,	,	PUNCT
fumecheng-11587	319	10	displaying	display	VERB
fumecheng-11587	319	11	both	both	CCONJ
fumecheng-11587	319	12	stable	stable	ADJ
fumecheng-11587	319	13	and	and	CCONJ
fumecheng-11587	319	14	unstable	unstable	ADJ
fumecheng-11587	319	15	branches	branch	NOUN
fumecheng-11587	319	16	of	of	ADP
fumecheng-11587	319	17	the	the	DET
fumecheng-11587	319	18	response	response	NOUN
fumecheng-11587	319	19	.	.	PUNCT
fumecheng-11587	320	1	the	the	DET
fumecheng-11587	320	2	linear	linear	ADJ
fumecheng-11587	320	3	growth	growth	NOUN
fumecheng-11587	320	4	of	of	ADP
fumecheng-11587	320	5	response	response	NOUN
fumecheng-11587	320	6	amplitude	amplitude	NOUN
fumecheng-11587	320	7	a1	a1	NOUN
fumecheng-11587	320	8	(	(	PUNCT
fumecheng-11587	320	9	or	or	CCONJ
fumecheng-11587	320	10	a3	a3	NOUN
fumecheng-11587	320	11	)	)	PUNCT
fumecheng-11587	320	12	appears	appear	VERB
fumecheng-11587	320	13	for	for	ADP
fumecheng-11587	320	14	an	an	DET
fumecheng-11587	320	15	increase	increase	NOUN
fumecheng-11587	320	16	of	of	ADP
fumecheng-11587	320	17	the	the	DET
fumecheng-11587	320	18	excitation	excitation	NOUN
fumecheng-11587	320	19	frequency	frequency	NOUN
fumecheng-11587	320	20	from	from	ADP
fumecheng-11587	320	21	some	some	DET
fumecheng-11587	320	22	small	small	ADJ
fumecheng-11587	320	23	values	value	NOUN
fumecheng-11587	320	24	until	until	ADP
fumecheng-11587	320	25	the	the	DET
fumecheng-11587	320	26	fold	fold	ADJ
fumecheng-11587	320	27	point	point	NOUN
fumecheng-11587	320	28	when	when	SCONJ
fumecheng-11587	320	29	the	the	DET
fumecheng-11587	320	30	periodic	periodic	ADJ
fumecheng-11587	320	31	response	response	NOUN
fumecheng-11587	320	32	loses	lose	VERB
fumecheng-11587	320	33	its	its	PRON
fumecheng-11587	320	34	stability	stability	NOUN
fumecheng-11587	320	35	.	.	PUNCT
fumecheng-11587	321	1	same	same	ADJ
fumecheng-11587	321	2	as	as	ADP
fumecheng-11587	321	3	in	in	ADP
fumecheng-11587	321	4	the	the	DET
fumecheng-11587	321	5	previous	previous	ADJ
fumecheng-11587	321	6	case	case	NOUN
fumecheng-11587	321	7	,	,	PUNCT
fumecheng-11587	321	8	further	far	ADV
fumecheng-11587	321	9	forward	forward	ADV
fumecheng-11587	321	10	frequency	frequency	NOUN
fumecheng-11587	321	11	sweeping	sweeping	ADJ
fumecheng-11587	321	12	produces	produce	VERB
fumecheng-11587	321	13	a	a	DET
fumecheng-11587	321	14	lower	low	ADJ
fumecheng-11587	321	15	branch	branch	NOUN
fumecheng-11587	321	16	of	of	ADP
fumecheng-11587	321	17	stable	stable	ADJ
fumecheng-11587	321	18	periodic	periodic	ADJ
fumecheng-11587	321	19	solutions	solution	NOUN
fumecheng-11587	321	20	.	.	PUNCT
fumecheng-11587	322	1	therefore	therefore	ADV
fumecheng-11587	322	2	,	,	PUNCT
fumecheng-11587	322	3	the	the	DET
fumecheng-11587	322	4	upper	upper	ADJ
fumecheng-11587	322	5	branch	branch	NOUN
fumecheng-11587	322	6	of	of	ADP
fumecheng-11587	322	7	the	the	DET
fumecheng-11587	322	8	amplitude	amplitude	NOUN
fumecheng-11587	322	9	grows	grow	VERB
fumecheng-11587	322	10	until	until	ADP
fumecheng-11587	322	11	the	the	DET
fumecheng-11587	322	12	critical	critical	ADJ
fumecheng-11587	322	13	moment	moment	NOUN
fumecheng-11587	322	14	(	(	PUNCT
fumecheng-11587	322	15	response	response	NOUN
fumecheng-11587	322	16	peak	peak	PROPN
fumecheng-11587	322	17	)	)	PUNCT
fumecheng-11587	322	18	which	which	PRON
fumecheng-11587	322	19	represents	represent	VERB
fumecheng-11587	322	20	the	the	DET
fumecheng-11587	322	21	maximal	maximal	ADJ
fumecheng-11587	322	22	value	value	NOUN
fumecheng-11587	322	23	of	of	ADP
fumecheng-11587	322	24	the	the	DET
fumecheng-11587	322	25	response	response	NOUN
fumecheng-11587	322	26	amplitude	amplitude	NOUN
fumecheng-11587	322	27	.	.	PUNCT
fumecheng-11587	323	1	at	at	ADP
fumecheng-11587	323	2	this	this	DET
fumecheng-11587	323	3	peak	peak	NOUN
fumecheng-11587	323	4	point	point	NOUN
fumecheng-11587	323	5	,	,	PUNCT
fumecheng-11587	323	6	periodic	periodic	ADJ
fumecheng-11587	323	7	solutions	solution	NOUN
fumecheng-11587	323	8	lose	lose	VERB
fumecheng-11587	323	9	their	their	PRON
fumecheng-11587	323	10	stability	stability	NOUN
fumecheng-11587	323	11	leading	lead	VERB
fumecheng-11587	323	12	to	to	ADP
fumecheng-11587	323	13	the	the	DET
fumecheng-11587	323	14	jump	jump	VERB
fumecheng-11587	323	15	-	-	PUNCT
fumecheng-11587	323	16	down	down	ADP
fumecheng-11587	323	17	phenomena	phenomenon	NOUN
fumecheng-11587	323	18	of	of	ADP
fumecheng-11587	323	19	the	the	DET
fumecheng-11587	323	20	response	response	NOUN
fumecheng-11587	323	21	amplitude	amplitude	NOUN
fumecheng-11587	323	22	.	.	PUNCT
fumecheng-11587	324	1	again	again	ADV
fumecheng-11587	324	2	,	,	PUNCT
fumecheng-11587	324	3	the	the	DET
fumecheng-11587	324	4	backward	backward	ADJ
fumecheng-11587	324	5	frequency	frequency	NOUN
fumecheng-11587	324	6	sweeping	sweeping	ADJ
fumecheng-11587	324	7	process	process	NOUN
fumecheng-11587	324	8	starting	start	VERB
fumecheng-11587	324	9	from	from	ADP
fumecheng-11587	324	10	the	the	DET
fumecheng-11587	324	11	values	value	NOUN
fumecheng-11587	324	12	higher	high	ADJ
fumecheng-11587	324	13	than	than	ADP
fumecheng-11587	324	14	the	the	DET
fumecheng-11587	324	15	resonant	resonant	ADJ
fumecheng-11587	324	16	frequency	frequency	NOUN
fumecheng-11587	324	17	displays	display	VERB
fumecheng-11587	324	18	a	a	DET
fumecheng-11587	324	19	slow	slow	ADJ
fumecheng-11587	324	20	increase	increase	NOUN
fumecheng-11587	324	21	until	until	SCONJ
fumecheng-11587	324	22	critical	critical	ADJ
fumecheng-11587	324	23	point	point	NOUN
fumecheng-11587	324	24	where	where	SCONJ
fumecheng-11587	324	25	the	the	DET
fumecheng-11587	324	26	periodic	periodic	ADJ
fumecheng-11587	324	27	solution	solution	NOUN
fumecheng-11587	324	28	loses	lose	VERB
fumecheng-11587	324	29	its	its	PRON
fumecheng-11587	324	30	stability	stability	NOUN
fumecheng-11587	324	31	and	and	CCONJ
fumecheng-11587	324	32	the	the	DET
fumecheng-11587	324	33	jump	jump	NOUN
fumecheng-11587	324	34	-	-	PUNCT
fumecheng-11587	324	35	up	up	ADP
fumecheng-11587	324	36	phenomenon	phenomenon	NOUN
fumecheng-11587	324	37	occurs	occur	VERB
fumecheng-11587	324	38	.	.	PUNCT
fumecheng-11587	325	1	a	a	DET
fumecheng-11587	325	2	further	further	ADJ
fumecheng-11587	325	3	decrease	decrease	NOUN
fumecheng-11587	325	4	of	of	ADP
fumecheng-11587	325	5	the	the	DET
fumecheng-11587	325	6	excitation	excitation	NOUN
fumecheng-11587	325	7	frequency	frequency	NOUN
fumecheng-11587	325	8	gives	give	VERB
fumecheng-11587	325	9	the	the	DET
fumecheng-11587	325	10	stable	stable	ADJ
fumecheng-11587	325	11	(	(	PUNCT
fumecheng-11587	325	12	upper	upper	ADJ
fumecheng-11587	325	13	)	)	PUNCT
fumecheng-11587	325	14	branch	branch	NOUN
fumecheng-11587	325	15	of	of	ADP
fumecheng-11587	325	16	the	the	DET
fumecheng-11587	325	17	periodic	periodic	ADJ
fumecheng-11587	325	18	responses	response	NOUN
fumecheng-11587	325	19	.	.	PUNCT
fumecheng-11587	326	1	the	the	DET
fumecheng-11587	326	2	branches	branch	NOUN
fumecheng-11587	326	3	of	of	ADP
fumecheng-11587	326	4	unstable	unstable	ADJ
fumecheng-11587	326	5	periodic	periodic	ADJ
fumecheng-11587	326	6	solutions	solution	NOUN
fumecheng-11587	326	7	can	can	AUX
fumecheng-11587	326	8	be	be	AUX
fumecheng-11587	326	9	detected	detect	VERB
fumecheng-11587	326	10	between	between	ADP
fumecheng-11587	326	11	two	two	NUM
fumecheng-11587	326	12	instability	instability	NOUN
fumecheng-11587	326	13	points	point	NOUN
fumecheng-11587	326	14	(	(	PUNCT
fumecheng-11587	326	15	lower	low	ADJ
fumecheng-11587	326	16	and	and	CCONJ
fumecheng-11587	326	17	upper	upper	ADJ
fumecheng-11587	326	18	brown	brown	ADJ
fumecheng-11587	326	19	points	point	NOUN
fumecheng-11587	326	20	in	in	ADP
fumecheng-11587	326	21	fig	fig	NOUN
fumecheng-11587	326	22	.	.	PUNCT
fumecheng-11587	327	1	4	4	NUM
fumecheng-11587	327	2	)	)	PUNCT
fumecheng-11587	327	3	and	and	CCONJ
fumecheng-11587	327	4	they	they	PRON
fumecheng-11587	327	5	are	be	AUX
fumecheng-11587	327	6	represented	represent	VERB
fumecheng-11587	327	7	by	by	ADP
fumecheng-11587	327	8	the	the	DET
fumecheng-11587	327	9	thicker	thick	ADJ
fumecheng-11587	327	10	solid	solid	ADJ
fumecheng-11587	327	11	lines	line	NOUN
fumecheng-11587	327	12	.	.	PUNCT
fumecheng-11587	328	1	in	in	ADP
fumecheng-11587	328	2	these	these	DET
fumecheng-11587	328	3	unstable	unstable	ADJ
fumecheng-11587	328	4	points	point	NOUN
fumecheng-11587	328	5	,	,	PUNCT
fumecheng-11587	328	6	floquet	floquet	PROPN
fumecheng-11587	328	7	multipliers	multiplier	NOUN
fumecheng-11587	328	8	exit	exit	VERB
fumecheng-11587	328	9	the	the	DET
fumecheng-11587	328	10	unit	unit	NOUN
fumecheng-11587	328	11	circle	circle	NOUN
fumecheng-11587	328	12	of	of	ADP
fumecheng-11587	328	13	the	the	DET
fumecheng-11587	328	14	complex	complex	ADJ
fumecheng-11587	328	15	plane	plane	NOUN
fumecheng-11587	328	16	as	as	SCONJ
fumecheng-11587	328	17	displayed	display	VERB
fumecheng-11587	328	18	on	on	ADP
fumecheng-11587	328	19	the	the	DET
fumecheng-11587	328	20	fig	fig	NOUN
fumecheng-11587	328	21	.	.	PUNCT
fumecheng-11587	329	1	7	7	X
fumecheng-11587	329	2	.	.	X
fumecheng-11587	329	3	similar	similar	ADJ
fumecheng-11587	329	4	observations	observation	NOUN
fumecheng-11587	329	5	can	can	AUX
fumecheng-11587	329	6	be	be	AUX
fumecheng-11587	329	7	made	make	VERB
fumecheng-11587	329	8	for	for	ADP
fumecheng-11587	329	9	clampedpinned	clampedpinne	VERB
fumecheng-11587	329	10	and	and	CCONJ
fumecheng-11587	329	11	clamped	clamp	VERB
fumecheng-11587	329	12	-	-	PUNCT
fumecheng-11587	329	13	clamped	clamp	VERB
fumecheng-11587	329	14	boundary	boundary	ADJ
fumecheng-11587	329	15	conditions	condition	NOUN
fumecheng-11587	329	16	(	(	PUNCT
fumecheng-11587	329	17	fig	fig	NOUN
fumecheng-11587	329	18	.	.	PUNCT
fumecheng-11587	330	1	4	4	NUM
fumecheng-11587	330	2	(	(	PUNCT
fumecheng-11587	330	3	c	c	NOUN
fumecheng-11587	330	4	,	,	PUNCT
fumecheng-11587	330	5	f	f	NOUN
fumecheng-11587	330	6	)	)	PUNCT
fumecheng-11587	330	7	)	)	PUNCT
fumecheng-11587	330	8	.	.	PUNCT
fumecheng-11587	331	1	vibration	vibration	NOUN
fumecheng-11587	331	2	and	and	CCONJ
fumecheng-11587	331	3	stability	stability	NOUN
fumecheng-11587	331	4	of	of	ADP
fumecheng-11587	331	5	a	a	DET
fumecheng-11587	331	6	nonlinear	nonlinear	ADJ
fumecheng-11587	331	7	nonlocal	nonlocal	ADJ
fumecheng-11587	331	8	strain	strain	NOUN
fumecheng-11587	331	9	-	-	PUNCT
fumecheng-11587	331	10	gradient	gradient	NOUN
fumecheng-11587	331	11	fg	fg	PROPN
fumecheng-11587	331	12	beam	beam	NOUN
fumecheng-11587	331	13	on	on	ADP
fumecheng-11587	331	14	a	a	DET
fumecheng-11587	331	15	visco	visco	ADJ
fumecheng-11587	331	16	-	-	PUNCT
fumecheng-11587	331	17	pasternak	pasternak	NOUN
fumecheng-11587	331	18	...	...	PUNCT
fumecheng-11587	331	19	723	723	NUM
fumecheng-11587	331	20	fig	fig	NOUN
fumecheng-11587	331	21	.	.	PUNCT
fumecheng-11587	331	22	4	4	NUM
fumecheng-11587	331	23	the	the	DET
fumecheng-11587	331	24	amplitude	amplitude	NOUN
fumecheng-11587	331	25	-	-	PUNCT
fumecheng-11587	331	26	frequency	frequency	NOUN
fumecheng-11587	331	27	response	response	NOUN
fumecheng-11587	331	28	curves	curve	NOUN
fumecheng-11587	331	29	of	of	ADP
fumecheng-11587	331	30	the	the	DET
fumecheng-11587	331	31	nonlinear	nonlinear	ADJ
fumecheng-11587	331	32	nlsgt	nlsgt	NOUN
fumecheng-11587	331	33	fg	fg	PROPN
fumecheng-11587	331	34	beam	beam	VERB
fumecheng-11587	331	35	on	on	ADP
fumecheng-11587	331	36	viscopasternak	viscopasternak	NOUN
fumecheng-11587	331	37	foundation	foundation	NOUN
fumecheng-11587	331	38	for	for	ADP
fumecheng-11587	331	39	pinned	pin	VERB
fumecheng-11587	331	40	-	-	PUNCT
fumecheng-11587	331	41	pinned	pin	VERB
fumecheng-11587	331	42	(	(	PUNCT
fumecheng-11587	331	43	a	a	DET
fumecheng-11587	331	44	,	,	PUNCT
fumecheng-11587	331	45	b	b	NOUN
fumecheng-11587	331	46	)	)	PUNCT
fumecheng-11587	331	47	,	,	PUNCT
fumecheng-11587	331	48	clamped	clamp	VERB
fumecheng-11587	331	49	-	-	PUNCT
fumecheng-11587	331	50	pinned	pin	VERB
fumecheng-11587	331	51	(	(	PUNCT
fumecheng-11587	331	52	c	c	X
fumecheng-11587	331	53	,	,	PUNCT
fumecheng-11587	331	54	d	d	NOUN
fumecheng-11587	331	55	)	)	PUNCT
fumecheng-11587	331	56	and	and	CCONJ
fumecheng-11587	331	57	clampedclamped	clampedclampe	VERB
fumecheng-11587	331	58	(	(	PUNCT
fumecheng-11587	331	59	e	e	NOUN
fumecheng-11587	331	60	,	,	PUNCT
fumecheng-11587	331	61	f	f	X
fumecheng-11587	331	62	)	)	PUNCT
fumecheng-11587	331	63	boundary	boundary	ADJ
fumecheng-11587	331	64	conditions	condition	NOUN
fumecheng-11587	331	65	.	.	PUNCT
fumecheng-11587	332	1	amplitudes	amplitude	NOUN
fumecheng-11587	332	2	a1	a1	NOUN
fumecheng-11587	332	3	and	and	CCONJ
fumecheng-11587	332	4	a3	a3	NOUN
fumecheng-11587	332	5	are	be	AUX
fumecheng-11587	332	6	plotted	plot	VERB
fumecheng-11587	332	7	for	for	ADP
fumecheng-11587	332	8	different	different	ADJ
fumecheng-11587	332	9	values	value	NOUN
fumecheng-11587	332	10	of	of	ADP
fumecheng-11587	332	11	parameter	parameter	PROPN
fumecheng-11587	332	12	k.	k.	PROPN
fumecheng-11587	333	1	the	the	DET
fumecheng-11587	333	2	unstable	unstable	ADJ
fumecheng-11587	333	3	periodic	periodic	ADJ
fumecheng-11587	333	4	solutions	solution	NOUN
fumecheng-11587	333	5	are	be	AUX
fumecheng-11587	333	6	represented	represent	VERB
fumecheng-11587	333	7	by	by	ADP
fumecheng-11587	333	8	the	the	DET
fumecheng-11587	333	9	tick	tick	NOUN
fumecheng-11587	333	10	solid	solid	ADJ
fumecheng-11587	333	11	lines	line	NOUN
fumecheng-11587	333	12	.	.	PUNCT
fumecheng-11587	334	1	724	724	NUM
fumecheng-11587	334	2	n.	n.	NOUN
fumecheng-11587	334	3	nešić	nešić	PROPN
fumecheng-11587	334	4	,	,	PUNCT
fumecheng-11587	334	5	m.	m.	NOUN
fumecheng-11587	334	6	cajić	cajić	NOUN
fumecheng-11587	334	7	,	,	PUNCT
fumecheng-11587	334	8	d.	d.	PROPN
fumecheng-11587	334	9	karličić	karličić	PROPN
fumecheng-11587	334	10	,	,	PUNCT
fumecheng-11587	334	11	m.	m.	NOUN
fumecheng-11587	334	12	lazarević	lazarević	PROPN
fumecheng-11587	334	13	,	,	PUNCT
fumecheng-11587	334	14	s.	s.	PROPN
fumecheng-11587	334	15	adhikari	adhikari	PROPN
fumecheng-11587	334	16	fig	fig	PROPN
fumecheng-11587	334	17	.	.	PUNCT
fumecheng-11587	335	1	5	5	NUM
fumecheng-11587	335	2	the	the	DET
fumecheng-11587	335	3	amplitude	amplitude	NOUN
fumecheng-11587	335	4	-	-	PUNCT
fumecheng-11587	335	5	frequency	frequency	NOUN
fumecheng-11587	335	6	response	response	NOUN
fumecheng-11587	335	7	curves	curve	NOUN
fumecheng-11587	335	8	of	of	ADP
fumecheng-11587	335	9	the	the	DET
fumecheng-11587	335	10	nonlinear	nonlinear	ADJ
fumecheng-11587	335	11	nlsgt	nlsgt	NOUN
fumecheng-11587	335	12	fg	fg	PROPN
fumecheng-11587	335	13	beam	beam	VERB
fumecheng-11587	335	14	on	on	ADP
fumecheng-11587	335	15	viscopasternak	viscopasternak	NOUN
fumecheng-11587	335	16	foundation	foundation	NOUN
fumecheng-11587	335	17	for	for	ADP
fumecheng-11587	335	18	pinned	pin	VERB
fumecheng-11587	335	19	-	-	PUNCT
fumecheng-11587	335	20	pinned	pin	VERB
fumecheng-11587	335	21	(	(	PUNCT
fumecheng-11587	335	22	a	a	DET
fumecheng-11587	335	23	,	,	PUNCT
fumecheng-11587	335	24	b	b	NOUN
fumecheng-11587	335	25	)	)	PUNCT
fumecheng-11587	335	26	,	,	PUNCT
fumecheng-11587	335	27	clamped	clamp	VERB
fumecheng-11587	335	28	-	-	PUNCT
fumecheng-11587	335	29	pinned	pin	VERB
fumecheng-11587	335	30	(	(	PUNCT
fumecheng-11587	335	31	c	c	X
fumecheng-11587	335	32	,	,	PUNCT
fumecheng-11587	335	33	d	d	NOUN
fumecheng-11587	335	34	)	)	PUNCT
fumecheng-11587	335	35	and	and	CCONJ
fumecheng-11587	335	36	clampedclamped	clampedclampe	VERB
fumecheng-11587	335	37	(	(	PUNCT
fumecheng-11587	335	38	e	e	NOUN
fumecheng-11587	335	39	,	,	PUNCT
fumecheng-11587	335	40	f	f	X
fumecheng-11587	335	41	)	)	PUNCT
fumecheng-11587	335	42	boundary	boundary	ADJ
fumecheng-11587	335	43	conditions	condition	NOUN
fumecheng-11587	335	44	.	.	PUNCT
fumecheng-11587	336	1	amplitudes	amplitude	NOUN
fumecheng-11587	336	2	a1	a1	NOUN
fumecheng-11587	336	3	and	and	CCONJ
fumecheng-11587	336	4	a3	a3	NOUN
fumecheng-11587	336	5	are	be	AUX
fumecheng-11587	336	6	plotted	plot	VERB
fumecheng-11587	336	7	for	for	ADP
fumecheng-11587	336	8	different	different	ADJ
fumecheng-11587	336	9	values	value	NOUN
fumecheng-11587	336	10	of	of	ADP
fumecheng-11587	336	11	parameter	parameter	PROPN
fumecheng-11587	336	12	kg	kg	PROPN
fumecheng-11587	336	13	.	.	PUNCT
fumecheng-11587	337	1	the	the	DET
fumecheng-11587	337	2	unstable	unstable	ADJ
fumecheng-11587	337	3	periodic	periodic	ADJ
fumecheng-11587	337	4	solutions	solution	NOUN
fumecheng-11587	337	5	are	be	AUX
fumecheng-11587	337	6	represented	represent	VERB
fumecheng-11587	337	7	by	by	ADP
fumecheng-11587	337	8	the	the	DET
fumecheng-11587	337	9	tick	tick	NOUN
fumecheng-11587	337	10	solid	solid	ADJ
fumecheng-11587	337	11	lines	line	NOUN
fumecheng-11587	337	12	.	.	PUNCT
fumecheng-11587	338	1	vibration	vibration	NOUN
fumecheng-11587	338	2	and	and	CCONJ
fumecheng-11587	338	3	stability	stability	NOUN
fumecheng-11587	338	4	of	of	ADP
fumecheng-11587	338	5	a	a	DET
fumecheng-11587	338	6	nonlinear	nonlinear	ADJ
fumecheng-11587	338	7	nonlocal	nonlocal	ADJ
fumecheng-11587	338	8	strain	strain	NOUN
fumecheng-11587	338	9	-	-	PUNCT
fumecheng-11587	338	10	gradient	gradient	NOUN
fumecheng-11587	338	11	fg	fg	PROPN
fumecheng-11587	338	12	beam	beam	NOUN
fumecheng-11587	338	13	on	on	ADP
fumecheng-11587	338	14	a	a	DET
fumecheng-11587	338	15	visco	visco	ADJ
fumecheng-11587	338	16	-	-	PUNCT
fumecheng-11587	338	17	pasternak	pasternak	NOUN
fumecheng-11587	338	18	...	...	PUNCT
fumecheng-11587	338	19	725	725	NUM
fumecheng-11587	338	20	further	further	ADJ
fumecheng-11587	338	21	,	,	PUNCT
fumecheng-11587	338	22	fig	fig	NOUN
fumecheng-11587	338	23	.	.	PUNCT
fumecheng-11587	339	1	5	5	NUM
fumecheng-11587	339	2	shows	show	VERB
fumecheng-11587	339	3	amplitude	amplitude	NOUN
fumecheng-11587	339	4	-	-	PUNCT
fumecheng-11587	339	5	frequency	frequency	NOUN
fumecheng-11587	339	6	response	response	NOUN
fumecheng-11587	339	7	curves	curve	NOUN
fumecheng-11587	339	8	for	for	ADP
fumecheng-11587	339	9	changes	change	NOUN
fumecheng-11587	339	10	of	of	ADP
fumecheng-11587	339	11	the	the	DET
fumecheng-11587	339	12	parameter	parameter	NOUN
fumecheng-11587	339	13	kg	kg	PROPN
fumecheng-11587	339	14	of	of	ADP
fumecheng-11587	339	15	the	the	DET
fumecheng-11587	339	16	visco	visco	ADJ
fumecheng-11587	339	17	-	-	PUNCT
fumecheng-11587	339	18	pasternak	pasternak	PROPN
fumecheng-11587	339	19	foundation	foundation	NOUN
fumecheng-11587	339	20	.	.	PUNCT
fumecheng-11587	340	1	one	one	PRON
fumecheng-11587	340	2	can	can	AUX
fumecheng-11587	340	3	observe	observe	VERB
fumecheng-11587	340	4	that	that	SCONJ
fumecheng-11587	340	5	the	the	DET
fumecheng-11587	340	6	change	change	NOUN
fumecheng-11587	340	7	of	of	ADP
fumecheng-11587	340	8	this	this	DET
fumecheng-11587	340	9	parameter	parameter	NOUN
fumecheng-11587	340	10	yields	yield	VERB
fumecheng-11587	340	11	similar	similar	ADJ
fumecheng-11587	340	12	shapes	shape	NOUN
fumecheng-11587	340	13	of	of	ADP
fumecheng-11587	340	14	amplitude	amplitude	NOUN
fumecheng-11587	340	15	-	-	PUNCT
fumecheng-11587	340	16	frequency	frequency	NOUN
fumecheng-11587	340	17	response	response	NOUN
fumecheng-11587	340	18	curves	curve	NOUN
fumecheng-11587	340	19	exhibiting	exhibit	VERB
fumecheng-11587	340	20	the	the	DET
fumecheng-11587	340	21	nonlinear	nonlinear	ADJ
fumecheng-11587	340	22	hardening	harden	VERB
fumecheng-11587	340	23	stiffness	stiffness	ADJ
fumecheng-11587	340	24	behavior	behavior	NOUN
fumecheng-11587	340	25	.	.	PUNCT
fumecheng-11587	341	1	moreover	moreover	ADV
fumecheng-11587	341	2	,	,	PUNCT
fumecheng-11587	341	3	an	an	DET
fumecheng-11587	341	4	increase	increase	NOUN
fumecheng-11587	341	5	of	of	ADP
fumecheng-11587	341	6	parameter	parameter	NOUN
fumecheng-11587	341	7	kg	kg	PROPN
fumecheng-11587	341	8	,	,	PUNCT
fumecheng-11587	341	9	related	relate	VERB
fumecheng-11587	341	10	to	to	ADP
fumecheng-11587	341	11	viscous	viscous	ADJ
fumecheng-11587	341	12	properties	property	NOUN
fumecheng-11587	341	13	of	of	ADP
fumecheng-11587	341	14	the	the	DET
fumecheng-11587	341	15	foundation	foundation	NOUN
fumecheng-11587	341	16	,	,	PUNCT
fumecheng-11587	341	17	results	result	VERB
fumecheng-11587	341	18	in	in	ADP
fumecheng-11587	341	19	a	a	DET
fumecheng-11587	341	20	decrease	decrease	NOUN
fumecheng-11587	341	21	of	of	ADP
fumecheng-11587	341	22	pick	pick	VERB
fumecheng-11587	341	23	amplitude	amplitude	NOUN
fumecheng-11587	341	24	values	value	NOUN
fumecheng-11587	341	25	.	.	PUNCT
fumecheng-11587	342	1	consequently	consequently	ADV
fumecheng-11587	342	2	,	,	PUNCT
fumecheng-11587	342	3	this	this	DET
fumecheng-11587	342	4	yields	yield	NOUN
fumecheng-11587	342	5	shortened	shorten	VERB
fumecheng-11587	342	6	unstable	unstable	ADJ
fumecheng-11587	342	7	branches	branch	NOUN
fumecheng-11587	342	8	(	(	PUNCT
fumecheng-11587	342	9	thick	thick	ADJ
fumecheng-11587	342	10	bold	bold	ADJ
fumecheng-11587	342	11	lines	line	NOUN
fumecheng-11587	342	12	)	)	PUNCT
fumecheng-11587	342	13	of	of	ADP
fumecheng-11587	342	14	the	the	DET
fumecheng-11587	342	15	periodic	periodic	ADJ
fumecheng-11587	342	16	solutions	solution	NOUN
fumecheng-11587	342	17	located	locate	VERB
fumecheng-11587	342	18	in	in	ADP
fumecheng-11587	342	19	between	between	ADP
fumecheng-11587	342	20	the	the	DET
fumecheng-11587	342	21	corresponding	corresponding	ADJ
fumecheng-11587	342	22	fold	fold	ADJ
fumecheng-11587	342	23	points	point	NOUN
fumecheng-11587	342	24	(	(	PUNCT
fumecheng-11587	342	25	fig	fig	NOUN
fumecheng-11587	342	26	.	.	PUNCT
fumecheng-11587	342	27	5	5	NUM
fumecheng-11587	342	28	)	)	PUNCT
fumecheng-11587	342	29	.	.	PUNCT
fumecheng-11587	343	1	this	this	DET
fumecheng-11587	343	2	behavior	behavior	NOUN
fumecheng-11587	343	3	can	can	AUX
fumecheng-11587	343	4	be	be	AUX
fumecheng-11587	343	5	observed	observe	VERB
fumecheng-11587	343	6	for	for	ADP
fumecheng-11587	343	7	both	both	PRON
fumecheng-11587	343	8	amplitudes	amplitude	NOUN
fumecheng-11587	343	9	a1	a1	NOUN
fumecheng-11587	343	10	and	and	CCONJ
fumecheng-11587	343	11	a3	a3	NOUN
fumecheng-11587	343	12	.	.	PUNCT
fumecheng-11587	344	1	for	for	ADP
fumecheng-11587	344	2	clamped	clamp	VERB
fumecheng-11587	344	3	-	-	PUNCT
fumecheng-11587	344	4	pinned	pin	VERB
fumecheng-11587	344	5	and	and	CCONJ
fumecheng-11587	344	6	clamped	clamp	VERB
fumecheng-11587	344	7	-	-	PUNCT
fumecheng-11587	344	8	clamped	clamp	VERB
fumecheng-11587	344	9	boundary	boundary	ADJ
fumecheng-11587	344	10	conditions	condition	NOUN
fumecheng-11587	344	11	,	,	PUNCT
fumecheng-11587	344	12	an	an	DET
fumecheng-11587	344	13	increase	increase	NOUN
fumecheng-11587	344	14	of	of	ADP
fumecheng-11587	344	15	parameter	parameter	NOUN
fumecheng-11587	344	16	kg	kg	PROPN
fumecheng-11587	344	17	can	can	AUX
fumecheng-11587	344	18	even	even	ADV
fumecheng-11587	344	19	stabilize	stabilize	VERB
fumecheng-11587	344	20	the	the	DET
fumecheng-11587	344	21	system	system	NOUN
fumecheng-11587	344	22	by	by	ADP
fumecheng-11587	344	23	making	make	VERB
fumecheng-11587	344	24	an	an	DET
fumecheng-11587	344	25	unstable	unstable	ADJ
fumecheng-11587	344	26	region	region	NOUN
fumecheng-11587	344	27	(	(	PUNCT
fumecheng-11587	344	28	bold	bold	ADJ
fumecheng-11587	344	29	line	line	NOUN
fumecheng-11587	344	30	)	)	PUNCT
fumecheng-11587	344	31	disappear	disappear	VERB
fumecheng-11587	344	32	.	.	PUNCT
fumecheng-11587	345	1	a	a	DET
fumecheng-11587	345	2	more	more	ADV
fumecheng-11587	345	3	detailed	detailed	ADJ
fumecheng-11587	345	4	parametric	parametric	ADJ
fumecheng-11587	345	5	study	study	NOUN
fumecheng-11587	345	6	of	of	ADP
fumecheng-11587	345	7	amplitude	amplitude	NOUN
fumecheng-11587	345	8	-	-	PUNCT
fumecheng-11587	345	9	frequency	frequency	NOUN
fumecheng-11587	345	10	responses	response	NOUN
fumecheng-11587	345	11	of	of	ADP
fumecheng-11587	345	12	the	the	DET
fumecheng-11587	345	13	similar	similar	ADJ
fumecheng-11587	345	14	system	system	NOUN
fumecheng-11587	345	15	with	with	ADP
fumecheng-11587	345	16	nonlocal	nonlocal	ADJ
fumecheng-11587	345	17	strain	strain	NOUN
fumecheng-11587	345	18	gradient	gradient	NOUN
fumecheng-11587	345	19	functionally	functionally	ADV
fumecheng-11587	345	20	graded	grade	VERB
fumecheng-11587	345	21	beam	beam	NOUN
fumecheng-11587	345	22	on	on	ADP
fumecheng-11587	345	23	the	the	DET
fumecheng-11587	345	24	fractional	fractional	ADJ
fumecheng-11587	345	25	visco	visco	ADJ
fumecheng-11587	345	26	-	-	PUNCT
fumecheng-11587	345	27	pasternak	pasternak	PROPN
fumecheng-11587	345	28	foundation	foundation	NOUN
fumecheng-11587	345	29	can	can	AUX
fumecheng-11587	345	30	be	be	AUX
fumecheng-11587	345	31	found	find	VERB
fumecheng-11587	345	32	in	in	ADP
fumecheng-11587	345	33	the	the	DET
fumecheng-11587	345	34	paper	paper	NOUN
fumecheng-11587	345	35	by	by	ADP
fumecheng-11587	345	36	nešić	nešić	PROPN
fumecheng-11587	345	37	et	et	PROPN
fumecheng-11587	345	38	al	al	PROPN
fumecheng-11587	345	39	.	.	PUNCT
fumecheng-11587	346	1	[	[	X
fumecheng-11587	346	2	27	27	NUM
fumecheng-11587	346	3	]	]	PUNCT
fumecheng-11587	346	4	.	.	PUNCT
fumecheng-11587	347	1	to	to	PART
fumecheng-11587	347	2	study	study	VERB
fumecheng-11587	347	3	the	the	DET
fumecheng-11587	347	4	influence	influence	NOUN
fumecheng-11587	347	5	of	of	ADP
fumecheng-11587	347	6	the	the	DET
fumecheng-11587	347	7	type	type	NOUN
fumecheng-11587	347	8	of	of	ADP
fumecheng-11587	347	9	boundary	boundary	ADJ
fumecheng-11587	347	10	conditions	condition	NOUN
fumecheng-11587	347	11	on	on	ADP
fumecheng-11587	347	12	the	the	DET
fumecheng-11587	347	13	amplitude	amplitude	NOUN
fumecheng-11587	347	14	-	-	PUNCT
fumecheng-11587	347	15	frequency	frequency	NOUN
fumecheng-11587	347	16	response	response	NOUN
fumecheng-11587	347	17	curve	curve	NOUN
fumecheng-11587	347	18	three	three	NUM
fumecheng-11587	347	19	different	different	ADJ
fumecheng-11587	347	20	cases	case	NOUN
fumecheng-11587	347	21	(	(	PUNCT
fumecheng-11587	347	22	pinned	pin	VERB
fumecheng-11587	347	23	-	-	PUNCT
fumecheng-11587	347	24	pinned	pin	VERB
fumecheng-11587	347	25	,	,	PUNCT
fumecheng-11587	347	26	clamped	clamp	VERB
fumecheng-11587	347	27	-	-	PUNCT
fumecheng-11587	347	28	pinned	pin	VERB
fumecheng-11587	347	29	,	,	PUNCT
fumecheng-11587	347	30	and	and	CCONJ
fumecheng-11587	347	31	clampedclamped	clampedclampe	VERB
fumecheng-11587	347	32	boundary	boundary	ADJ
fumecheng-11587	347	33	conditions	condition	NOUN
fumecheng-11587	347	34	)	)	PUNCT
fumecheng-11587	347	35	are	be	AUX
fumecheng-11587	347	36	plotted	plot	VERB
fumecheng-11587	347	37	in	in	ADP
fumecheng-11587	347	38	fig	fig	NOUN
fumecheng-11587	347	39	.	.	PUNCT
fumecheng-11587	348	1	6	6	NUM
fumecheng-11587	348	2	.	.	X
fumecheng-11587	348	3	it	it	PRON
fumecheng-11587	348	4	can	can	AUX
fumecheng-11587	348	5	be	be	AUX
fumecheng-11587	348	6	observed	observe	VERB
fumecheng-11587	348	7	that	that	SCONJ
fumecheng-11587	348	8	reducing	reduce	VERB
fumecheng-11587	348	9	degrees	degree	NOUN
fumecheng-11587	348	10	of	of	ADP
fumecheng-11587	348	11	freedom	freedom	NOUN
fumecheng-11587	348	12	in	in	ADP
fumecheng-11587	348	13	supports	support	NOUN
fumecheng-11587	348	14	decrease	decrease	VERB
fumecheng-11587	348	15	maximal	maximal	ADJ
fumecheng-11587	348	16	amplitude	amplitude	NOUN
fumecheng-11587	348	17	and	and	CCONJ
fumecheng-11587	348	18	shifts	shift	NOUN
fumecheng-11587	348	19	resonant	resonant	VERB
fumecheng-11587	348	20	frequency	frequency	NOUN
fumecheng-11587	348	21	to	to	ADP
fumecheng-11587	348	22	the	the	DET
fumecheng-11587	348	23	right	right	NOUN
fumecheng-11587	348	24	,	,	PUNCT
fumecheng-11587	348	25	which	which	PRON
fumecheng-11587	348	26	is	be	AUX
fumecheng-11587	348	27	expected	expect	VERB
fumecheng-11587	348	28	behavior	behavior	NOUN
fumecheng-11587	348	29	.	.	PUNCT
fumecheng-11587	349	1	fig	fig	NOUN
fumecheng-11587	349	2	.	.	PUNCT
fumecheng-11587	350	1	6	6	NUM
fumecheng-11587	350	2	different	different	ADJ
fumecheng-11587	350	3	boundary	boundary	ADJ
fumecheng-11587	350	4	conditions	condition	NOUN
fumecheng-11587	350	5	in	in	ADP
fumecheng-11587	350	6	all	all	DET
fumecheng-11587	350	7	previous	previous	ADJ
fumecheng-11587	350	8	examples	example	NOUN
fumecheng-11587	350	9	,	,	PUNCT
fumecheng-11587	350	10	the	the	DET
fumecheng-11587	350	11	unstable	unstable	ADJ
fumecheng-11587	350	12	periodic	periodic	ADJ
fumecheng-11587	350	13	solutions	solution	NOUN
fumecheng-11587	350	14	are	be	AUX
fumecheng-11587	350	15	detected	detect	VERB
fumecheng-11587	350	16	by	by	ADP
fumecheng-11587	350	17	the	the	DET
fumecheng-11587	350	18	calculation	calculation	NOUN
fumecheng-11587	350	19	of	of	ADP
fumecheng-11587	350	20	floquet	floquet	NOUN
fumecheng-11587	350	21	multipliers	multiplier	NOUN
fumecheng-11587	350	22	,	,	PUNCT
fumecheng-11587	350	23	where	where	SCONJ
fumecheng-11587	350	24	at	at	ADV
fumecheng-11587	350	25	least	least	ADV
fumecheng-11587	350	26	one	one	NUM
fumecheng-11587	350	27	of	of	ADP
fumecheng-11587	350	28	them	they	PRON
fumecheng-11587	350	29	crosses	cross	VERB
fumecheng-11587	350	30	the	the	DET
fumecheng-11587	350	31	unit	unit	NOUN
fumecheng-11587	350	32	circle	circle	NOUN
fumecheng-11587	350	33	in	in	ADP
fumecheng-11587	350	34	the	the	DET
fumecheng-11587	350	35	complex	complex	ADJ
fumecheng-11587	350	36	plane	plane	NOUN
fumecheng-11587	350	37	in	in	ADP
fumecheng-11587	350	38	the	the	DET
fumecheng-11587	350	39	+1	+1	ADJ
fumecheng-11587	350	40	direction	direction	NOUN
fumecheng-11587	350	41	.	.	PUNCT
fumecheng-11587	351	1	fig	fig	NOUN
fumecheng-11587	351	2	.	.	PUNCT
fumecheng-11587	352	1	7	7	NUM
fumecheng-11587	352	2	displays	display	VERB
fumecheng-11587	352	3	a	a	DET
fumecheng-11587	352	4	unit	unit	NOUN
fumecheng-11587	352	5	circle	circle	NOUN
fumecheng-11587	352	6	in	in	ADP
fumecheng-11587	352	7	the	the	DET
fumecheng-11587	352	8	complex	complex	ADJ
fumecheng-11587	352	9	plane	plane	NOUN
fumecheng-11587	352	10	and	and	CCONJ
fumecheng-11587	352	11	floquet	floquet	NOUN
fumecheng-11587	352	12	multipliers	multiplier	NOUN
fumecheng-11587	352	13	for	for	ADP
fumecheng-11587	352	14	the	the	DET
fumecheng-11587	352	15	case	case	NOUN
fumecheng-11587	352	16	of	of	ADP
fumecheng-11587	352	17	parameters	parameter	NOUN
fumecheng-11587	352	18	adopted	adopt	VERB
fumecheng-11587	352	19	from	from	ADP
fumecheng-11587	352	20	table	table	NOUN
fumecheng-11587	352	21	3	3	NUM
fumecheng-11587	352	22	.	.	PUNCT
fumecheng-11587	353	1	it	it	PRON
fumecheng-11587	353	2	can	can	AUX
fumecheng-11587	353	3	be	be	AUX
fumecheng-11587	353	4	observed	observe	VERB
fumecheng-11587	353	5	that	that	SCONJ
fumecheng-11587	353	6	floquet	floquet	NOUN
fumecheng-11587	353	7	multiplies	multiplie	NOUN
fumecheng-11587	353	8	are	be	AUX
fumecheng-11587	353	9	crossing	cross	VERB
fumecheng-11587	353	10	the	the	DET
fumecheng-11587	353	11	unit	unit	NOUN
fumecheng-11587	353	12	circle	circle	NOUN
fumecheng-11587	353	13	in	in	ADP
fumecheng-11587	353	14	the	the	DET
fumecheng-11587	353	15	complex	complex	ADJ
fumecheng-11587	353	16	plane	plane	NOUN
fumecheng-11587	353	17	in	in	ADP
fumecheng-11587	353	18	the	the	DET
fumecheng-11587	353	19	+1	+1	ADJ
fumecheng-11587	353	20	direction	direction	NOUN
fumecheng-11587	353	21	for	for	ADP
fumecheng-11587	353	22	the	the	DET
fumecheng-11587	353	23	unstable	unstable	ADJ
fumecheng-11587	353	24	periodic	periodic	ADJ
fumecheng-11587	353	25	solutions	solution	NOUN
fumecheng-11587	353	26	located	locate	VERB
fumecheng-11587	353	27	between	between	ADP
fumecheng-11587	353	28	the	the	DET
fumecheng-11587	353	29	two	two	NUM
fumecheng-11587	353	30	different	different	ADJ
fumecheng-11587	353	31	fold	fold	ADJ
fumecheng-11587	353	32	points	point	NOUN
fumecheng-11587	353	33	of	of	ADP
fumecheng-11587	353	34	the	the	DET
fumecheng-11587	353	35	amplitudefrequency	amplitudefrequency	NOUN
fumecheng-11587	353	36	response	response	NOUN
fumecheng-11587	353	37	curve	curve	NOUN
fumecheng-11587	353	38	.	.	PUNCT
fumecheng-11587	354	1	it	it	PRON
fumecheng-11587	354	2	is	be	AUX
fumecheng-11587	354	3	well	well	ADV
fumecheng-11587	354	4	known	know	VERB
fumecheng-11587	354	5	that	that	SCONJ
fumecheng-11587	354	6	different	different	ADJ
fumecheng-11587	354	7	bifurcation	bifurcation	NOUN
fumecheng-11587	354	8	points	point	NOUN
fumecheng-11587	354	9	can	can	AUX
fumecheng-11587	354	10	be	be	AUX
fumecheng-11587	354	11	detected	detect	VERB
fumecheng-11587	354	12	depending	depend	VERB
fumecheng-11587	354	13	on	on	ADP
fumecheng-11587	354	14	where	where	SCONJ
fumecheng-11587	354	15	the	the	DET
fumecheng-11587	354	16	floquet	floquet	NOUN
fumecheng-11587	354	17	multipliers	multiplier	NOUN
fumecheng-11587	354	18	are	be	AUX
fumecheng-11587	354	19	crossing	cross	VERB
fumecheng-11587	354	20	the	the	DET
fumecheng-11587	354	21	unit	unit	NOUN
fumecheng-11587	354	22	circle	circle	NOUN
fumecheng-11587	354	23	.	.	PUNCT
fumecheng-11587	355	1	therefore	therefore	ADV
fumecheng-11587	355	2	,	,	PUNCT
fumecheng-11587	355	3	when	when	SCONJ
fumecheng-11587	355	4	floquet	floquet	PROPN
fumecheng-11587	355	5	multipliers	multiplier	NOUN
fumecheng-11587	355	6	are	be	AUX
fumecheng-11587	355	7	crossing	cross	VERB
fumecheng-11587	355	8	the	the	DET
fumecheng-11587	355	9	unit	unit	NOUN
fumecheng-11587	355	10	circle	circle	NOUN
fumecheng-11587	355	11	in	in	ADP
fumecheng-11587	355	12	the	the	DET
fumecheng-11587	355	13	+1	+1	ADJ
fumecheng-11587	355	14	direction	direction	NOUN
fumecheng-11587	355	15	,	,	PUNCT
fumecheng-11587	355	16	one	one	PRON
fumecheng-11587	355	17	can	can	AUX
fumecheng-11587	355	18	expect	expect	VERB
fumecheng-11587	355	19	that	that	SCONJ
fumecheng-11587	355	20	a	a	DET
fumecheng-11587	355	21	saddle	saddle	NOUN
fumecheng-11587	355	22	-	-	PUNCT
fumecheng-11587	355	23	node	node	NOUN
fumecheng-11587	355	24	bifurcation	bifurcation	NOUN
fumecheng-11587	355	25	point	point	NOUN
fumecheng-11587	355	26	occurs	occur	VERB
fumecheng-11587	355	27	in	in	ADP
fumecheng-11587	355	28	that	that	DET
fumecheng-11587	355	29	case	case	NOUN
fumecheng-11587	355	30	.	.	PUNCT
fumecheng-11587	356	1	we	we	PRON
fumecheng-11587	356	2	also	also	ADV
fumecheng-11587	356	3	observe	observe	VERB
fumecheng-11587	356	4	that	that	DET
fumecheng-11587	356	5	number	number	NOUN
fumecheng-11587	356	6	of	of	ADP
fumecheng-11587	356	7	floquet	floquet	NOUN
fumecheng-11587	356	8	multipliers	multiplier	NOUN
fumecheng-11587	356	9	crossing	cross	VERB
fumecheng-11587	356	10	the	the	DET
fumecheng-11587	356	11	unit	unit	NOUN
fumecheng-11587	356	12	circle	circle	NOUN
fumecheng-11587	356	13	is	be	AUX
fumecheng-11587	356	14	the	the	DET
fumecheng-11587	356	15	highest	high	ADJ
fumecheng-11587	356	16	in	in	ADP
fumecheng-11587	356	17	the	the	DET
fumecheng-11587	356	18	case	case	NOUN
fumecheng-11587	356	19	of	of	ADP
fumecheng-11587	356	20	the	the	DET
fumecheng-11587	356	21	simple	simple	ADJ
fumecheng-11587	356	22	supports	support	NOUN
fumecheng-11587	356	23	and	and	CCONJ
fumecheng-11587	356	24	that	that	SCONJ
fumecheng-11587	356	25	the	the	DET
fumecheng-11587	356	26	ones	one	NOUN
fumecheng-11587	356	27	that	that	PRON
fumecheng-11587	356	28	are	be	AUX
fumecheng-11587	356	29	crossing	cross	VERB
fumecheng-11587	356	30	the	the	DET
fumecheng-11587	356	31	unit	unit	NOUN
fumecheng-11587	356	32	circle	circle	NOUN
fumecheng-11587	356	33	are	be	AUX
fumecheng-11587	356	34	the	the	DET
fumecheng-11587	356	35	most	most	ADV
fumecheng-11587	356	36	distant	distant	ADJ
fumecheng-11587	356	37	to	to	ADP
fumecheng-11587	356	38	it	it	PRON
fumecheng-11587	356	39	compared	compare	VERB
fumecheng-11587	356	40	to	to	ADP
fumecheng-11587	356	41	other	other	ADJ
fumecheng-11587	356	42	726	726	NUM
fumecheng-11587	356	43	n.	n.	NOUN
fumecheng-11587	356	44	nešić	nešić	PROPN
fumecheng-11587	356	45	,	,	PUNCT
fumecheng-11587	356	46	m.	m.	NOUN
fumecheng-11587	356	47	cajić	cajić	NOUN
fumecheng-11587	356	48	,	,	PUNCT
fumecheng-11587	356	49	d.	d.	PROPN
fumecheng-11587	356	50	karličić	karličić	PROPN
fumecheng-11587	356	51	,	,	PUNCT
fumecheng-11587	356	52	m.	m.	NOUN
fumecheng-11587	356	53	lazarević	lazarević	PROPN
fumecheng-11587	356	54	,	,	PUNCT
fumecheng-11587	356	55	s.	s.	PROPN
fumecheng-11587	356	56	adhikari	adhikari	PROPN
fumecheng-11587	356	57	boundary	boundary	ADJ
fumecheng-11587	356	58	conditions	condition	NOUN
fumecheng-11587	356	59	.	.	PUNCT
fumecheng-11587	357	1	on	on	ADP
fumecheng-11587	357	2	the	the	DET
fumecheng-11587	357	3	other	other	ADJ
fumecheng-11587	357	4	hand	hand	NOUN
fumecheng-11587	357	5	,	,	PUNCT
fumecheng-11587	357	6	in	in	ADP
fumecheng-11587	357	7	the	the	DET
fumecheng-11587	357	8	case	case	NOUN
fumecheng-11587	357	9	of	of	ADP
fumecheng-11587	357	10	clamped	clamp	VERB
fumecheng-11587	357	11	-	-	PUNCT
fumecheng-11587	357	12	clamped	clamp	VERB
fumecheng-11587	357	13	supports	support	NOUN
fumecheng-11587	357	14	,	,	PUNCT
fumecheng-11587	357	15	the	the	DET
fumecheng-11587	357	16	number	number	NOUN
fumecheng-11587	357	17	of	of	ADP
fumecheng-11587	357	18	floquet	floquet	NOUN
fumecheng-11587	357	19	multipliers	multiplier	NOUN
fumecheng-11587	357	20	crossing	cross	VERB
fumecheng-11587	357	21	the	the	DET
fumecheng-11587	357	22	unit	unit	NOUN
fumecheng-11587	357	23	circle	circle	NOUN
fumecheng-11587	357	24	and	and	CCONJ
fumecheng-11587	357	25	their	their	PRON
fumecheng-11587	357	26	distance	distance	NOUN
fumecheng-11587	357	27	to	to	ADP
fumecheng-11587	357	28	it	it	PRON
fumecheng-11587	357	29	is	be	AUX
fumecheng-11587	357	30	minimal	minimal	ADJ
fumecheng-11587	357	31	.	.	PUNCT
fumecheng-11587	358	1	consequently	consequently	ADV
fumecheng-11587	358	2	to	to	ADP
fumecheng-11587	358	3	this	this	DET
fumecheng-11587	358	4	behavior	behavior	NOUN
fumecheng-11587	358	5	,	,	PUNCT
fumecheng-11587	358	6	clamped	clamp	VERB
fumecheng-11587	358	7	-	-	PUNCT
fumecheng-11587	358	8	clamped	clamp	VERB
fumecheng-11587	358	9	boundary	boundary	ADJ
fumecheng-11587	358	10	conditions	condition	NOUN
fumecheng-11587	358	11	contribute	contribute	VERB
fumecheng-11587	358	12	to	to	ADP
fumecheng-11587	358	13	the	the	DET
fumecheng-11587	358	14	most	most	ADV
fumecheng-11587	358	15	and	and	CCONJ
fumecheng-11587	358	16	pinned	pin	VERB
fumecheng-11587	358	17	-	-	PUNCT
fumecheng-11587	358	18	pinned	pin	VERB
fumecheng-11587	358	19	boundary	boundary	ADJ
fumecheng-11587	358	20	conditions	condition	NOUN
fumecheng-11587	358	21	to	to	ADP
fumecheng-11587	358	22	the	the	DET
fumecheng-11587	358	23	least	least	ADJ
fumecheng-11587	358	24	stable	stable	ADJ
fumecheng-11587	358	25	system	system	NOUN
fumecheng-11587	358	26	.	.	PUNCT
fumecheng-11587	359	1	therefore	therefore	ADV
fumecheng-11587	359	2	the	the	DET
fumecheng-11587	359	3	influence	influence	NOUN
fumecheng-11587	359	4	of	of	ADP
fumecheng-11587	359	5	the	the	DET
fumecheng-11587	359	6	boundary	boundary	ADJ
fumecheng-11587	359	7	conditions	condition	NOUN
fumecheng-11587	359	8	on	on	ADP
fumecheng-11587	359	9	stability	stability	NOUN
fumecheng-11587	359	10	can	can	AUX
fumecheng-11587	359	11	not	not	PART
fumecheng-11587	359	12	be	be	AUX
fumecheng-11587	359	13	neglected	neglect	VERB
fumecheng-11587	359	14	.	.	PUNCT
fumecheng-11587	360	1	fig	fig	NOUN
fumecheng-11587	360	2	.	.	PUNCT
fumecheng-11587	361	1	7	7	NUM
fumecheng-11587	361	2	floquet	floquet	PROPN
fumecheng-11587	361	3	multipliers	multiplier	NOUN
fumecheng-11587	361	4	crossing	crossing	NOUN
fumecheng-11587	361	5	unit	unit	NOUN
fumecheng-11587	361	6	circle	circle	NOUN
fumecheng-11587	361	7	(	(	PUNCT
fumecheng-11587	361	8	vertical	vertical	ADJ
fumecheng-11587	361	9	axis	axis	NOUN
fumecheng-11587	361	10	is	be	AUX
fumecheng-11587	361	11	imaginary	imaginary	ADJ
fumecheng-11587	361	12	,	,	PUNCT
fumecheng-11587	361	13	horizontal	horizontal	ADJ
fumecheng-11587	361	14	real	real	NOUN
fumecheng-11587	361	15	):	):	PUNCT
fumecheng-11587	361	16	a	a	X
fumecheng-11587	361	17	)	)	PUNCT
fumecheng-11587	361	18	simply	simply	ADV
fumecheng-11587	361	19	-	-	PUNCT
fumecheng-11587	361	20	supported	support	VERB
fumecheng-11587	361	21	,	,	PUNCT
fumecheng-11587	361	22	b	b	NOUN
fumecheng-11587	361	23	)	)	PUNCT
fumecheng-11587	361	24	clamped	clamp	VERB
fumecheng-11587	361	25	-	-	PUNCT
fumecheng-11587	361	26	pinned	pin	VERB
fumecheng-11587	361	27	and	and	CCONJ
fumecheng-11587	361	28	c	c	NOUN
fumecheng-11587	361	29	)	)	PUNCT
fumecheng-11587	361	30	clamped	clamp	VERB
fumecheng-11587	361	31	-	-	PUNCT
fumecheng-11587	361	32	clamped	clamp	VERB
fumecheng-11587	361	33	boundary	boundary	ADJ
fumecheng-11587	361	34	conditions	condition	NOUN
fumecheng-11587	361	35	fig	fig	NOUN
fumecheng-11587	361	36	.	.	PUNCT
fumecheng-11587	361	37	8	8	NUM
fumecheng-11587	361	38	shows	show	VERB
fumecheng-11587	361	39	a	a	DET
fumecheng-11587	361	40	pair	pair	NOUN
fumecheng-11587	361	41	of	of	ADP
fumecheng-11587	361	42	floquet	floquet	NOUN
fumecheng-11587	361	43	multipliers	multiplier	NOUN
fumecheng-11587	361	44	for	for	ADP
fumecheng-11587	361	45	points	point	NOUN
fumecheng-11587	361	46	with	with	ADP
fumecheng-11587	361	47	different	different	ADJ
fumecheng-11587	361	48	excitation	excitation	NOUN
fumecheng-11587	361	49	frequency	frequency	NOUN
fumecheng-11587	361	50	ω	ω	NOUN
fumecheng-11587	361	51	.	.	PUNCT
fumecheng-11587	362	1	we	we	PRON
fumecheng-11587	362	2	can	can	AUX
fumecheng-11587	362	3	observe	observe	VERB
fumecheng-11587	362	4	in	in	ADP
fumecheng-11587	362	5	fig	fig	NOUN
fumecheng-11587	362	6	.	.	PUNCT
fumecheng-11587	363	1	8	8	NUM
fumecheng-11587	363	2	(	(	PUNCT
fumecheng-11587	363	3	a	a	DET
fumecheng-11587	363	4	,	,	PUNCT
fumecheng-11587	363	5	b	b	NOUN
fumecheng-11587	363	6	)	)	PUNCT
fumecheng-11587	363	7	that	that	SCONJ
fumecheng-11587	363	8	between	between	ADP
fumecheng-11587	363	9	approximately	approximately	ADV
fumecheng-11587	363	10	ω	ω	NOUN
fumecheng-11587	363	11	=	=	SYM
fumecheng-11587	363	12	14.5	14.5	NUM
fumecheng-11587	363	13	and	and	CCONJ
fumecheng-11587	363	14	ω	ω	NUM
fumecheng-11587	363	15	=	=	SYM
fumecheng-11587	364	1	23	23	NUM
fumecheng-11587	364	2	at	at	ADV
fumecheng-11587	364	3	least	least	ADJ
fumecheng-11587	364	4	one	one	NUM
fumecheng-11587	364	5	of	of	ADP
fumecheng-11587	364	6	two	two	NUM
fumecheng-11587	364	7	floquet	floquet	NOUN
fumecheng-11587	364	8	multipliers	multiplier	NOUN
fumecheng-11587	364	9	has	have	VERB
fumecheng-11587	364	10	modulus	modulus	NOUN
fumecheng-11587	364	11	greater	great	ADJ
fumecheng-11587	364	12	than	than	ADP
fumecheng-11587	364	13	one	one	NUM
fumecheng-11587	364	14	,	,	PUNCT
fumecheng-11587	364	15	meaning	mean	VERB
fumecheng-11587	364	16	that	that	SCONJ
fumecheng-11587	364	17	this	this	DET
fumecheng-11587	364	18	region	region	NOUN
fumecheng-11587	364	19	is	be	AUX
fumecheng-11587	364	20	unstable	unstable	ADJ
fumecheng-11587	364	21	.	.	PUNCT
fumecheng-11587	365	1	the	the	DET
fumecheng-11587	365	2	stability	stability	NOUN
fumecheng-11587	365	3	border	border	NOUN
fumecheng-11587	365	4	is	be	AUX
fumecheng-11587	365	5	reached	reach	VERB
fumecheng-11587	365	6	when	when	SCONJ
fumecheng-11587	365	7	floquet	floquet	PROPN
fumecheng-11587	365	8	multipliers	multiplier	NOUN
fumecheng-11587	365	9	modulus	modulus	NOUN
fumecheng-11587	365	10	(	(	PUNCT
fumecheng-11587	365	11	fmm	fmm	PROPN
fumecheng-11587	365	12	)	)	PUNCT
fumecheng-11587	365	13	is	be	AUX
fumecheng-11587	365	14	equal	equal	ADJ
fumecheng-11587	365	15	to	to	ADP
fumecheng-11587	365	16	one	one	NUM
fumecheng-11587	365	17	.	.	PUNCT
fumecheng-11587	366	1	the	the	DET
fumecheng-11587	366	2	degree	degree	NOUN
fumecheng-11587	366	3	of	of	ADP
fumecheng-11587	366	4	instability	instability	NOUN
fumecheng-11587	366	5	is	be	AUX
fumecheng-11587	366	6	defined	define	VERB
fumecheng-11587	366	7	by	by	ADP
fumecheng-11587	366	8	the	the	DET
fumecheng-11587	366	9	distance	distance	NOUN
fumecheng-11587	366	10	of	of	ADP
fumecheng-11587	366	11	a	a	DET
fumecheng-11587	366	12	point	point	NOUN
fumecheng-11587	366	13	in	in	ADP
fumecheng-11587	366	14	the	the	DET
fumecheng-11587	366	15	instability	instability	NOUN
fumecheng-11587	366	16	region	region	NOUN
fumecheng-11587	366	17	from	from	ADP
fumecheng-11587	366	18	the	the	DET
fumecheng-11587	366	19	unit	unit	NOUN
fumecheng-11587	366	20	circle	circle	NOUN
fumecheng-11587	366	21	(	(	PUNCT
fumecheng-11587	366	22	fig	fig	NOUN
fumecheng-11587	366	23	.	.	PUNCT
fumecheng-11587	367	1	7	7	NUM
fumecheng-11587	367	2	)	)	PUNCT
fumecheng-11587	367	3	which	which	PRON
fumecheng-11587	367	4	is	be	AUX
fumecheng-11587	367	5	equivalent	equivalent	ADJ
fumecheng-11587	367	6	to	to	ADP
fumecheng-11587	367	7	the	the	DET
fumecheng-11587	367	8	distance	distance	NOUN
fumecheng-11587	367	9	of	of	ADP
fumecheng-11587	367	10	slowly	slowly	ADV
fumecheng-11587	367	11	growing	grow	VERB
fumecheng-11587	367	12	curve	curve	NOUN
fumecheng-11587	367	13	(	(	PUNCT
fumecheng-11587	367	14	with	with	ADP
fumecheng-11587	367	15	small	small	ADJ
fumecheng-11587	367	16	slope	slope	NOUN
fumecheng-11587	367	17	)	)	PUNCT
fumecheng-11587	367	18	on	on	ADP
fumecheng-11587	367	19	fig	fig	NOUN
fumecheng-11587	367	20	.	.	PUNCT
fumecheng-11587	368	1	8	8	NUM
fumecheng-11587	368	2	.	.	X
fumecheng-11587	369	1	for	for	ADP
fumecheng-11587	369	2	example	example	NOUN
fumecheng-11587	369	3	,	,	PUNCT
fumecheng-11587	369	4	for	for	ADP
fumecheng-11587	369	5	the	the	DET
fumecheng-11587	369	6	case	case	NOUN
fumecheng-11587	369	7	of	of	ADP
fumecheng-11587	369	8	simply	simply	ADV
fumecheng-11587	369	9	-	-	PUNCT
fumecheng-11587	369	10	supported	support	VERB
fumecheng-11587	369	11	beam	beam	NOUN
fumecheng-11587	369	12	and	and	CCONJ
fumecheng-11587	369	13	ω	ω	NUM
fumecheng-11587	369	14	=	=	SYM
fumecheng-11587	369	15	16	16	NUM
fumecheng-11587	369	16	instability	instability	NOUN
fumecheng-11587	369	17	is	be	AUX
fumecheng-11587	369	18	higher	high	ADJ
fumecheng-11587	369	19	than	than	ADP
fumecheng-11587	369	20	in	in	ADP
fumecheng-11587	369	21	the	the	DET
fumecheng-11587	369	22	case	case	NOUN
fumecheng-11587	369	23	ω	ω	X
fumecheng-11587	369	24	=	=	SYM
fumecheng-11587	369	25	22	22	NUM
fumecheng-11587	369	26	(	(	PUNCT
fumecheng-11587	369	27	fig	fig	NOUN
fumecheng-11587	369	28	.	.	NOUN
fumecheng-11587	369	29	8	8	NUM
fumecheng-11587	369	30	(	(	PUNCT
fumecheng-11587	369	31	a	a	DET
fumecheng-11587	369	32	,	,	PUNCT
fumecheng-11587	369	33	b	b	NOUN
fumecheng-11587	369	34	)	)	PUNCT
fumecheng-11587	369	35	)	)	PUNCT
fumecheng-11587	369	36	.	.	PUNCT
fumecheng-11587	370	1	we	we	PRON
fumecheng-11587	370	2	can	can	AUX
fumecheng-11587	370	3	also	also	ADV
fumecheng-11587	370	4	observe	observe	VERB
fumecheng-11587	370	5	from	from	ADP
fumecheng-11587	370	6	fig	fig	NOUN
fumecheng-11587	370	7	.	.	PUNCT
fumecheng-11587	371	1	8	8	NUM
fumecheng-11587	371	2	that	that	PRON
fumecheng-11587	371	3	with	with	ADP
fumecheng-11587	371	4	an	an	DET
fumecheng-11587	371	5	increase	increase	NOUN
fumecheng-11587	371	6	of	of	ADP
fumecheng-11587	371	7	the	the	DET
fumecheng-11587	371	8	system	system	NOUN
fumecheng-11587	371	9	's	's	PART
fumecheng-11587	371	10	stiffness	stiffness	NOUN
fumecheng-11587	371	11	by	by	ADP
fumecheng-11587	371	12	reducing	reduce	VERB
fumecheng-11587	371	13	degrees	degree	NOUN
fumecheng-11587	371	14	of	of	ADP
fumecheng-11587	371	15	freedom	freedom	NOUN
fumecheng-11587	371	16	in	in	ADP
fumecheng-11587	371	17	boundary	boundary	ADJ
fumecheng-11587	371	18	conditions	condition	NOUN
fumecheng-11587	371	19	,	,	PUNCT
fumecheng-11587	371	20	the	the	DET
fumecheng-11587	371	21	main	main	ADJ
fumecheng-11587	371	22	instability	instability	NOUN
fumecheng-11587	371	23	region	region	NOUN
fumecheng-11587	371	24	is	be	AUX
fumecheng-11587	371	25	decreased	decrease	VERB
fumecheng-11587	371	26	and	and	CCONJ
fumecheng-11587	371	27	shifted	shift	VERB
fumecheng-11587	371	28	to	to	ADP
fumecheng-11587	371	29	the	the	DET
fumecheng-11587	371	30	right	right	NOUN
fumecheng-11587	371	31	towards	towards	ADP
fumecheng-11587	371	32	higher	high	ADJ
fumecheng-11587	371	33	excitation	excitation	NOUN
fumecheng-11587	371	34	frequencies	frequency	NOUN
fumecheng-11587	371	35	.	.	PUNCT
fumecheng-11587	372	1	the	the	DET
fumecheng-11587	372	2	stability	stability	NOUN
fumecheng-11587	372	3	of	of	ADP
fumecheng-11587	372	4	the	the	DET
fumecheng-11587	372	5	solution	solution	NOUN
fumecheng-11587	372	6	for	for	ADP
fumecheng-11587	372	7	higher	high	ADJ
fumecheng-11587	372	8	excitation	excitation	NOUN
fumecheng-11587	372	9	frequencies	frequency	NOUN
fumecheng-11587	372	10	can	can	AUX
fumecheng-11587	372	11	be	be	AUX
fumecheng-11587	372	12	achieved	achieve	VERB
fumecheng-11587	372	13	by	by	ADP
fumecheng-11587	372	14	introducing	introduce	VERB
fumecheng-11587	372	15	the	the	DET
fumecheng-11587	372	16	pinned	pin	VERB
fumecheng-11587	372	17	-	-	PUNCT
fumecheng-11587	372	18	pinned	pin	VERB
fumecheng-11587	372	19	boundary	boundary	ADJ
fumecheng-11587	372	20	conditions	condition	NOUN
fumecheng-11587	372	21	.	.	PUNCT
fumecheng-11587	373	1	on	on	ADP
fumecheng-11587	373	2	the	the	DET
fumecheng-11587	373	3	contrary	contrary	NOUN
fumecheng-11587	373	4	,	,	PUNCT
fumecheng-11587	373	5	stability	stability	NOUN
fumecheng-11587	373	6	on	on	ADP
fumecheng-11587	373	7	lower	low	ADJ
fumecheng-11587	373	8	excitation	excitation	NOUN
fumecheng-11587	373	9	frequencies	frequency	NOUN
fumecheng-11587	373	10	can	can	AUX
fumecheng-11587	373	11	be	be	AUX
fumecheng-11587	373	12	reached	reach	VERB
fumecheng-11587	373	13	with	with	ADP
fumecheng-11587	373	14	clamped	clamp	VERB
fumecheng-11587	373	15	-	-	PUNCT
fumecheng-11587	373	16	clamped	clamp	VERB
fumecheng-11587	373	17	(	(	PUNCT
fumecheng-11587	373	18	a	a	NOUN
fumecheng-11587	373	19	)	)	PUNCT
fumecheng-11587	373	20	(	(	PUNCT
fumecheng-11587	373	21	b	b	X
fumecheng-11587	373	22	)	)	PUNCT
fumecheng-11587	373	23	(	(	PUNCT
fumecheng-11587	373	24	c	c	NOUN
fumecheng-11587	373	25	)	)	PUNCT
fumecheng-11587	373	26	vibration	vibration	NOUN
fumecheng-11587	373	27	and	and	CCONJ
fumecheng-11587	373	28	stability	stability	NOUN
fumecheng-11587	373	29	of	of	ADP
fumecheng-11587	373	30	a	a	DET
fumecheng-11587	373	31	nonlinear	nonlinear	ADJ
fumecheng-11587	373	32	nonlocal	nonlocal	ADJ
fumecheng-11587	373	33	strain	strain	NOUN
fumecheng-11587	373	34	-	-	PUNCT
fumecheng-11587	373	35	gradient	gradient	NOUN
fumecheng-11587	373	36	fg	fg	PROPN
fumecheng-11587	373	37	beam	beam	NOUN
fumecheng-11587	373	38	on	on	ADP
fumecheng-11587	373	39	a	a	DET
fumecheng-11587	373	40	visco	visco	ADJ
fumecheng-11587	373	41	-	-	PUNCT
fumecheng-11587	373	42	pasternak	pasternak	NOUN
fumecheng-11587	373	43	...	...	PUNCT
fumecheng-11587	373	44	727	727	NUM
fumecheng-11587	373	45	boundary	boundary	ADJ
fumecheng-11587	373	46	conditions	condition	NOUN
fumecheng-11587	373	47	.	.	PUNCT
fumecheng-11587	374	1	an	an	DET
fumecheng-11587	374	2	unstable	unstable	ADJ
fumecheng-11587	374	3	region	region	NOUN
fumecheng-11587	374	4	with	with	ADP
fumecheng-11587	374	5	clamped	clamp	VERB
fumecheng-11587	374	6	-	-	PUNCT
fumecheng-11587	374	7	free	free	ADJ
fumecheng-11587	374	8	boundary	boundary	ADJ
fumecheng-11587	374	9	conditions	condition	NOUN
fumecheng-11587	374	10	is	be	AUX
fumecheng-11587	374	11	between	between	ADP
fumecheng-11587	374	12	unstable	unstable	ADJ
fumecheng-11587	374	13	regions	region	NOUN
fumecheng-11587	374	14	for	for	ADP
fumecheng-11587	374	15	another	another	DET
fumecheng-11587	374	16	two	two	NUM
fumecheng-11587	374	17	pairs	pair	NOUN
fumecheng-11587	374	18	of	of	ADP
fumecheng-11587	374	19	boundary	boundary	ADJ
fumecheng-11587	374	20	conditions	condition	NOUN
fumecheng-11587	374	21	.	.	PUNCT
fumecheng-11587	375	1	this	this	DET
fumecheng-11587	375	2	result	result	NOUN
fumecheng-11587	375	3	can	can	AUX
fumecheng-11587	375	4	be	be	AUX
fumecheng-11587	375	5	utilized	utilize	VERB
fumecheng-11587	375	6	for	for	ADP
fumecheng-11587	375	7	the	the	DET
fumecheng-11587	375	8	practical	practical	ADJ
fumecheng-11587	375	9	realization	realization	NOUN
fumecheng-11587	375	10	of	of	ADP
fumecheng-11587	375	11	such	such	DET
fumecheng-11587	375	12	a	a	DET
fumecheng-11587	375	13	system	system	NOUN
fumecheng-11587	375	14	.	.	PUNCT
fumecheng-11587	376	1	depending	depend	VERB
fumecheng-11587	376	2	on	on	ADP
fumecheng-11587	376	3	the	the	DET
fumecheng-11587	376	4	excitation	excitation	NOUN
fumecheng-11587	376	5	frequency	frequency	NOUN
fumecheng-11587	376	6	and	and	CCONJ
fumecheng-11587	376	7	operation	operation	NOUN
fumecheng-11587	376	8	range	range	NOUN
fumecheng-11587	376	9	of	of	ADP
fumecheng-11587	376	10	the	the	DET
fumecheng-11587	376	11	system	system	NOUN
fumecheng-11587	376	12	,	,	PUNCT
fumecheng-11587	376	13	boundary	boundary	ADJ
fumecheng-11587	376	14	conditions	condition	NOUN
fumecheng-11587	376	15	can	can	AUX
fumecheng-11587	376	16	be	be	AUX
fumecheng-11587	376	17	selected	select	VERB
fumecheng-11587	376	18	and	and	CCONJ
fumecheng-11587	376	19	physically	physically	ADV
fumecheng-11587	376	20	established	establish	VERB
fumecheng-11587	376	21	so	so	SCONJ
fumecheng-11587	376	22	that	that	SCONJ
fumecheng-11587	376	23	unstable	unstable	ADJ
fumecheng-11587	376	24	solutions	solution	NOUN
fumecheng-11587	376	25	for	for	ADP
fumecheng-11587	376	26	amplitudes	amplitude	NOUN
fumecheng-11587	376	27	are	be	AUX
fumecheng-11587	376	28	avoided	avoid	VERB
fumecheng-11587	376	29	,	,	PUNCT
fumecheng-11587	376	30	which	which	PRON
fumecheng-11587	376	31	can	can	AUX
fumecheng-11587	376	32	prolong	prolong	VERB
fumecheng-11587	376	33	the	the	DET
fumecheng-11587	376	34	duration	duration	NOUN
fumecheng-11587	376	35	of	of	ADP
fumecheng-11587	376	36	the	the	DET
fumecheng-11587	376	37	system	system	NOUN
fumecheng-11587	376	38	.	.	PUNCT
fumecheng-11587	377	1	fig	fig	NOUN
fumecheng-11587	377	2	.	.	PUNCT
fumecheng-11587	378	1	8	8	NUM
fumecheng-11587	378	2	floquet	floquet	NOUN
fumecheng-11587	378	3	multipliers	multiplier	NOUN
fumecheng-11587	378	4	modulus	modulus	NOUN
fumecheng-11587	378	5	(	(	PUNCT
fumecheng-11587	378	6	fmm	fmm	PROPN
fumecheng-11587	378	7	)	)	PUNCT
fumecheng-11587	378	8	of	of	ADP
fumecheng-11587	378	9	the	the	DET
fumecheng-11587	378	10	first	first	ADJ
fumecheng-11587	378	11	(	(	PUNCT
fumecheng-11587	378	12	fmm1	fmm1	NOUN
fumecheng-11587	378	13	)	)	PUNCT
fumecheng-11587	378	14	and	and	CCONJ
fumecheng-11587	378	15	second	second	ADJ
fumecheng-11587	378	16	(	(	PUNCT
fumecheng-11587	378	17	fmm2	fmm2	ADJ
fumecheng-11587	378	18	)	)	PUNCT
fumecheng-11587	378	19	floquet	floquet	VERB
fumecheng-11587	378	20	multiplier	multipli	ADJ
fumecheng-11587	378	21	versus	versus	ADP
fumecheng-11587	378	22	excitation	excitation	NOUN
fumecheng-11587	378	23	frequency	frequency	NOUN
fumecheng-11587	378	24	ω	ω	PROPN
fumecheng-11587	378	25	moreover	moreover	ADV
fumecheng-11587	378	26	,	,	PUNCT
fumecheng-11587	378	27	in	in	ADP
fumecheng-11587	378	28	the	the	DET
fumecheng-11587	378	29	amplitude	amplitude	NOUN
fumecheng-11587	378	30	-	-	PUNCT
fumecheng-11587	378	31	frequency	frequency	NOUN
fumecheng-11587	378	32	responses	response	NOUN
fumecheng-11587	378	33	,	,	PUNCT
fumecheng-11587	378	34	one	one	PRON
fumecheng-11587	378	35	can	can	AUX
fumecheng-11587	378	36	notice	notice	VERB
fumecheng-11587	378	37	that	that	SCONJ
fumecheng-11587	378	38	the	the	DET
fumecheng-11587	378	39	coexisting	coexist	VERB
fumecheng-11587	378	40	periodic	periodic	ADJ
fumecheng-11587	378	41	solutions	solution	NOUN
fumecheng-11587	378	42	exist	exist	VERB
fumecheng-11587	378	43	for	for	ADP
fumecheng-11587	378	44	certain	certain	ADJ
fumecheng-11587	378	45	frequency	frequency	NOUN
fumecheng-11587	378	46	ranges	range	NOUN
fumecheng-11587	378	47	.	.	PUNCT
fumecheng-11587	379	1	knowing	know	VERB
fumecheng-11587	379	2	that	that	SCONJ
fumecheng-11587	379	3	the	the	DET
fumecheng-11587	379	4	amplitudes	amplitude	NOUN
fumecheng-11587	379	5	of	of	ADP
fumecheng-11587	379	6	these	these	DET
fumecheng-11587	379	7	periodic	periodic	ADJ
fumecheng-11587	379	8	solutions	solution	NOUN
fumecheng-11587	379	9	are	be	AUX
fumecheng-11587	379	10	dependent	dependent	ADJ
fumecheng-11587	379	11	on	on	ADP
fumecheng-11587	379	12	initial	initial	ADJ
fumecheng-11587	379	13	conditions	condition	NOUN
fumecheng-11587	379	14	and	and	CCONJ
fumecheng-11587	379	15	starting	start	VERB
fumecheng-11587	379	16	positions	position	NOUN
fumecheng-11587	379	17	in	in	ADP
fumecheng-11587	379	18	excitation	excitation	NOUN
fumecheng-11587	379	19	frequency	frequency	NOUN
fumecheng-11587	379	20	sweeping	sweeping	ADJ
fumecheng-11587	379	21	,	,	PUNCT
fumecheng-11587	379	22	there	there	PRON
fumecheng-11587	379	23	are	be	VERB
fumecheng-11587	379	24	two	two	NUM
fumecheng-11587	379	25	sets	set	NOUN
fumecheng-11587	379	26	of	of	ADP
fumecheng-11587	379	27	initial	initial	ADJ
fumecheng-11587	379	28	conditions	condition	NOUN
fumecheng-11587	379	29	for	for	ADP
fumecheng-11587	379	30	which	which	PRON
fumecheng-11587	379	31	the	the	DET
fumecheng-11587	379	32	response	response	NOUN
fumecheng-11587	379	33	amplitude	amplitude	NOUN
fumecheng-11587	379	34	will	will	AUX
fumecheng-11587	379	35	converge	converge	VERB
fumecheng-11587	379	36	towards	towards	ADP
fumecheng-11587	379	37	the	the	DET
fumecheng-11587	379	38	lower	low	ADJ
fumecheng-11587	379	39	or	or	CCONJ
fumecheng-11587	379	40	upper	upper	ADJ
fumecheng-11587	379	41	branch	branch	NOUN
fumecheng-11587	379	42	of	of	ADP
fumecheng-11587	379	43	the	the	DET
fumecheng-11587	379	44	periodic	periodic	ADJ
fumecheng-11587	379	45	solutions	solution	NOUN
fumecheng-11587	379	46	forming	form	VERB
fumecheng-11587	379	47	the	the	DET
fumecheng-11587	379	48	basin	basin	NOUN
fumecheng-11587	379	49	of	of	ADP
fumecheng-11587	379	50	attraction	attraction	NOUN
fumecheng-11587	379	51	as	as	SCONJ
fumecheng-11587	379	52	given	give	VERB
fumecheng-11587	379	53	in	in	ADP
fumecheng-11587	379	54	fig	fig	NOUN
fumecheng-11587	379	55	.	.	PUNCT
fumecheng-11587	380	1	9	9	NUM
fumecheng-11587	380	2	and	and	CCONJ
fumecheng-11587	380	3	fig	fig	NOUN
fumecheng-11587	380	4	.	.	PUNCT
fumecheng-11587	381	1	10	10	NUM
fumecheng-11587	381	2	.	.	PUNCT
fumecheng-11587	382	1	therefore	therefore	ADV
fumecheng-11587	382	2	,	,	PUNCT
fumecheng-11587	382	3	the	the	DET
fumecheng-11587	382	4	system	system	NOUN
fumecheng-11587	382	5	will	will	AUX
fumecheng-11587	382	6	possess	possess	VERB
fumecheng-11587	382	7	two	two	NUM
fumecheng-11587	382	8	attractors	attractor	NOUN
fumecheng-11587	382	9	for	for	ADP
fumecheng-11587	382	10	the	the	DET
fumecheng-11587	382	11	given	give	VERB
fumecheng-11587	382	12	excitation	excitation	NOUN
fumecheng-11587	382	13	frequency	frequency	NOUN
fumecheng-11587	382	14	and	and	CCONJ
fumecheng-11587	382	15	system	system	NOUN
fumecheng-11587	382	16	parameters	parameter	NOUN
fumecheng-11587	382	17	.	.	PUNCT
fumecheng-11587	383	1	these	these	DET
fumecheng-11587	383	2	two	two	NUM
fumecheng-11587	383	3	attractors	attractor	NOUN
fumecheng-11587	383	4	are	be	AUX
fumecheng-11587	383	5	highlighted	highlight	VERB
fumecheng-11587	383	6	in	in	ADP
fumecheng-11587	383	7	two	two	NUM
fumecheng-11587	383	8	different	different	ADJ
fumecheng-11587	383	9	colors	color	NOUN
fumecheng-11587	383	10	for	for	ADP
fumecheng-11587	383	11	two	two	NUM
fumecheng-11587	383	12	sets	set	NOUN
fumecheng-11587	383	13	of	of	ADP
fumecheng-11587	383	14	initial	initial	ADJ
fumecheng-11587	383	15	conditions	condition	NOUN
fumecheng-11587	383	16	.	.	PUNCT
fumecheng-11587	384	1	for	for	ADP
fumecheng-11587	384	2	the	the	DET
fumecheng-11587	384	3	presented	present	VERB
fumecheng-11587	384	4	nonlinear	nonlinear	ADJ
fumecheng-11587	384	5	system	system	NOUN
fumecheng-11587	384	6	,	,	PUNCT
fumecheng-11587	384	7	the	the	DET
fumecheng-11587	384	8	basin	basin	NOUN
fumecheng-11587	384	9	of	of	ADP
fumecheng-11587	384	10	attraction	attraction	NOUN
fumecheng-11587	384	11	is	be	AUX
fumecheng-11587	384	12	given	give	VERB
fumecheng-11587	384	13	in	in	ADP
fumecheng-11587	384	14	fig	fig	NOUN
fumecheng-11587	384	15	.	.	PUNCT
fumecheng-11587	385	1	9	9	NUM
fumecheng-11587	385	2	and	and	CCONJ
fumecheng-11587	385	3	fig	fig	NOUN
fumecheng-11587	385	4	.	.	PUNCT
fumecheng-11587	386	1	10	10	NUM
fumecheng-11587	387	1	and	and	CCONJ
fumecheng-11587	387	2	for	for	ADP
fumecheng-11587	387	3	the	the	DET
fumecheng-11587	387	4	excitation	excitation	NOUN
fumecheng-11587	387	5	frequency	frequency	NOUN
fumecheng-11587	387	6	ω	ω	NOUN
fumecheng-11587	387	7	=	=	SYM
fumecheng-11587	388	1	20	20	NUM
fumecheng-11587	388	2	and	and	CCONJ
fumecheng-11587	388	3	ω	ω	NUM
fumecheng-11587	389	1	=	=	SYM
fumecheng-11587	389	2	25	25	NUM
fumecheng-11587	389	3	and	and	CCONJ
fumecheng-11587	389	4	coexisting	coexist	VERB
fumecheng-11587	389	5	periodic	periodic	ADJ
fumecheng-11587	389	6	solutions	solution	NOUN
fumecheng-11587	389	7	from	from	ADP
fumecheng-11587	389	8	the	the	DET
fumecheng-11587	389	9	728	728	NUM
fumecheng-11587	389	10	n.	n.	NOUN
fumecheng-11587	389	11	nešić	nešić	PROPN
fumecheng-11587	389	12	,	,	PUNCT
fumecheng-11587	389	13	m.	m.	NOUN
fumecheng-11587	389	14	cajić	cajić	NOUN
fumecheng-11587	389	15	,	,	PUNCT
fumecheng-11587	389	16	d.	d.	PROPN
fumecheng-11587	389	17	karličić	karličić	PROPN
fumecheng-11587	389	18	,	,	PUNCT
fumecheng-11587	389	19	m.	m.	NOUN
fumecheng-11587	389	20	lazarević	lazarević	PROPN
fumecheng-11587	389	21	,	,	PUNCT
fumecheng-11587	389	22	s.	s.	PROPN
fumecheng-11587	389	23	adhikari	adhikari	PROPN
fumecheng-11587	389	24	amplitude	amplitude	NOUN
fumecheng-11587	389	25	-	-	PUNCT
fumecheng-11587	389	26	frequency	frequency	NOUN
fumecheng-11587	389	27	response	response	NOUN
fumecheng-11587	389	28	curve	curve	NOUN
fumecheng-11587	389	29	given	give	VERB
fumecheng-11587	389	30	in	in	ADP
fumecheng-11587	389	31	fig	fig	NOUN
fumecheng-11587	389	32	.	.	PUNCT
fumecheng-11587	390	1	2	2	NUM
fumecheng-11587	390	2	and	and	CCONJ
fumecheng-11587	390	3	varying	vary	VERB
fumecheng-11587	390	4	initial	initial	ADJ
fumecheng-11587	390	5	conditions	condition	NOUN
fumecheng-11587	390	6	.	.	PUNCT
fumecheng-11587	391	1	one	one	PRON
fumecheng-11587	391	2	can	can	AUX
fumecheng-11587	391	3	observe	observe	VERB
fumecheng-11587	391	4	that	that	SCONJ
fumecheng-11587	391	5	the	the	DET
fumecheng-11587	391	6	basin	basin	NOUN
fumecheng-11587	391	7	of	of	ADP
fumecheng-11587	391	8	attraction	attraction	NOUN
fumecheng-11587	391	9	is	be	AUX
fumecheng-11587	391	10	displaying	display	VERB
fumecheng-11587	391	11	two	two	NUM
fumecheng-11587	391	12	colors	color	NOUN
fumecheng-11587	391	13	with	with	ADP
fumecheng-11587	391	14	two	two	NUM
fumecheng-11587	391	15	coexisting	coexist	VERB
fumecheng-11587	391	16	periodic	periodic	ADJ
fumecheng-11587	391	17	solutions	solution	NOUN
fumecheng-11587	391	18	in	in	ADP
fumecheng-11587	391	19	fig	fig	NOUN
fumecheng-11587	391	20	.	.	PUNCT
fumecheng-11587	392	1	9	9	NUM
fumecheng-11587	392	2	and	and	CCONJ
fumecheng-11587	392	3	fig	fig	NOUN
fumecheng-11587	392	4	.	.	PUNCT
fumecheng-11587	393	1	10	10	NUM
fumecheng-11587	393	2	.	.	PUNCT
fumecheng-11587	394	1	here	here	ADV
fumecheng-11587	394	2	,	,	PUNCT
fumecheng-11587	394	3	the	the	DET
fumecheng-11587	394	4	case	case	NOUN
fumecheng-11587	394	5	with	with	ADP
fumecheng-11587	394	6	the	the	DET
fumecheng-11587	394	7	initial	initial	ADJ
fumecheng-11587	394	8	condition	condition	NOUN
fumecheng-11587	394	9	highlighted	highlight	VERB
fumecheng-11587	394	10	in	in	ADP
fumecheng-11587	394	11	red	red	ADJ
fumecheng-11587	394	12	color	color	NOUN
fumecheng-11587	394	13	converges	converge	NOUN
fumecheng-11587	394	14	to	to	ADP
fumecheng-11587	394	15	the	the	DET
fumecheng-11587	394	16	upper	upper	ADJ
fumecheng-11587	394	17	stable	stable	ADJ
fumecheng-11587	394	18	branch	branch	NOUN
fumecheng-11587	394	19	while	while	SCONJ
fumecheng-11587	394	20	the	the	DET
fumecheng-11587	394	21	case	case	NOUN
fumecheng-11587	394	22	with	with	ADP
fumecheng-11587	394	23	the	the	DET
fumecheng-11587	394	24	initial	initial	ADJ
fumecheng-11587	394	25	conditions	condition	NOUN
fumecheng-11587	394	26	highlighted	highlight	VERB
fumecheng-11587	394	27	in	in	ADP
fumecheng-11587	394	28	blue	blue	ADJ
fumecheng-11587	394	29	converges	converge	NOUN
fumecheng-11587	394	30	to	to	ADP
fumecheng-11587	394	31	the	the	DET
fumecheng-11587	394	32	lower	low	ADJ
fumecheng-11587	394	33	stable	stable	ADJ
fumecheng-11587	394	34	branch	branch	NOUN
fumecheng-11587	394	35	.	.	PUNCT
fumecheng-11587	395	1	since	since	SCONJ
fumecheng-11587	395	2	excitation	excitation	NOUN
fumecheng-11587	395	3	frequency	frequency	NOUN
fumecheng-11587	395	4	is	be	AUX
fumecheng-11587	395	5	close	close	ADJ
fumecheng-11587	395	6	to	to	ADP
fumecheng-11587	395	7	the	the	DET
fumecheng-11587	395	8	bifurcation	bifurcation	NOUN
fumecheng-11587	395	9	point	point	NOUN
fumecheng-11587	395	10	,	,	PUNCT
fumecheng-11587	395	11	the	the	DET
fumecheng-11587	395	12	solution	solution	NOUN
fumecheng-11587	395	13	converges	converge	VERB
fumecheng-11587	395	14	to	to	ADP
fumecheng-11587	395	15	both	both	CCONJ
fumecheng-11587	395	16	upper	upper	ADJ
fumecheng-11587	395	17	and	and	CCONJ
fumecheng-11587	395	18	lower	low	ADJ
fumecheng-11587	395	19	stable	stable	ADJ
fumecheng-11587	395	20	branches	branch	NOUN
fumecheng-11587	395	21	of	of	ADP
fumecheng-11587	395	22	periodic	periodic	ADJ
fumecheng-11587	395	23	solutions	solution	NOUN
fumecheng-11587	395	24	.	.	PUNCT
fumecheng-11587	396	1	in	in	ADP
fumecheng-11587	396	2	the	the	DET
fumecheng-11587	396	3	special	special	ADJ
fumecheng-11587	396	4	case	case	NOUN
fumecheng-11587	396	5	of	of	ADP
fumecheng-11587	396	6	simple	simple	ADJ
fumecheng-11587	396	7	-	-	PUNCT
fumecheng-11587	396	8	supported	support	VERB
fumecheng-11587	396	9	beam	beam	NOUN
fumecheng-11587	396	10	,	,	PUNCT
fumecheng-11587	396	11	the	the	DET
fumecheng-11587	396	12	set	set	NOUN
fumecheng-11587	396	13	of	of	ADP
fumecheng-11587	396	14	initial	initial	ADJ
fumecheng-11587	396	15	conditions	condition	NOUN
fumecheng-11587	396	16	that	that	PRON
fumecheng-11587	396	17	converges	converge	VERB
fumecheng-11587	396	18	to	to	ADP
fumecheng-11587	396	19	the	the	DET
fumecheng-11587	396	20	upper	upper	ADJ
fumecheng-11587	396	21	stable	stable	ADJ
fumecheng-11587	396	22	branch	branch	NOUN
fumecheng-11587	396	23	of	of	ADP
fumecheng-11587	396	24	periodic	periodic	ADJ
fumecheng-11587	396	25	solutions	solution	NOUN
fumecheng-11587	396	26	is	be	AUX
fumecheng-11587	396	27	dominating	dominate	VERB
fumecheng-11587	396	28	over	over	ADP
fumecheng-11587	396	29	the	the	DET
fumecheng-11587	396	30	set	set	NOUN
fumecheng-11587	396	31	of	of	ADP
fumecheng-11587	396	32	initial	initial	ADJ
fumecheng-11587	396	33	conditions	condition	NOUN
fumecheng-11587	396	34	that	that	PRON
fumecheng-11587	396	35	converges	converge	VERB
fumecheng-11587	396	36	to	to	ADP
fumecheng-11587	396	37	the	the	DET
fumecheng-11587	396	38	lower	low	ADJ
fumecheng-11587	396	39	branch	branch	NOUN
fumecheng-11587	396	40	of	of	ADP
fumecheng-11587	396	41	solutions	solution	NOUN
fumecheng-11587	396	42	.	.	PUNCT
fumecheng-11587	397	1	fig	fig	NOUN
fumecheng-11587	397	2	.	.	PUNCT
fumecheng-11587	398	1	9	9	NUM
fumecheng-11587	398	2	basin	basin	NOUN
fumecheng-11587	398	3	of	of	ADP
fumecheng-11587	398	4	attraction	attraction	NOUN
fumecheng-11587	398	5	for	for	ADP
fumecheng-11587	398	6	ω	ω	NOUN
fumecheng-11587	398	7	=	=	SYM
fumecheng-11587	398	8	20	20	NUM
fumecheng-11587	398	9	fig	fig	NOUN
fumecheng-11587	398	10	.	.	PUNCT
fumecheng-11587	399	1	10	10	NUM
fumecheng-11587	399	2	basin	basin	NOUN
fumecheng-11587	399	3	of	of	ADP
fumecheng-11587	399	4	attraction	attraction	NOUN
fumecheng-11587	399	5	for	for	ADP
fumecheng-11587	399	6	ω	ω	NOUN
fumecheng-11587	399	7	=	=	SYM
fumecheng-11587	399	8	25	25	NUM
fumecheng-11587	399	9	for	for	ADP
fumecheng-11587	399	10	clamped	clamp	VERB
fumecheng-11587	399	11	-	-	PUNCT
fumecheng-11587	399	12	clamped	clamp	VERB
fumecheng-11587	399	13	boundary	boundary	ADJ
fumecheng-11587	399	14	conditions	condition	NOUN
fumecheng-11587	399	15	to	to	PART
fumecheng-11587	399	16	summarize	summarize	VERB
fumecheng-11587	399	17	,	,	PUNCT
fumecheng-11587	399	18	in	in	ADP
fumecheng-11587	399	19	this	this	DET
fumecheng-11587	399	20	chapter	chapter	NOUN
fumecheng-11587	399	21	,	,	PUNCT
fumecheng-11587	399	22	after	after	ADP
fumecheng-11587	399	23	a	a	DET
fumecheng-11587	399	24	short	short	ADJ
fumecheng-11587	399	25	verification	verification	NOUN
fumecheng-11587	399	26	of	of	ADP
fumecheng-11587	399	27	eigenfrequencies	eigenfrequencie	NOUN
fumecheng-11587	399	28	for	for	ADP
fumecheng-11587	399	29	simplified	simplified	ADJ
fumecheng-11587	399	30	model	model	NOUN
fumecheng-11587	399	31	with	with	ADP
fumecheng-11587	399	32	the	the	DET
fumecheng-11587	399	33	results	result	NOUN
fumecheng-11587	399	34	available	available	ADJ
fumecheng-11587	399	35	in	in	ADP
fumecheng-11587	399	36	the	the	DET
fumecheng-11587	399	37	literature	literature	NOUN
fumecheng-11587	399	38	,	,	PUNCT
fumecheng-11587	399	39	stability	stability	NOUN
fumecheng-11587	399	40	analysis	analysis	NOUN
fumecheng-11587	399	41	is	be	AUX
fumecheng-11587	399	42	performed	perform	VERB
fumecheng-11587	399	43	.	.	PUNCT
fumecheng-11587	400	1	for	for	ADP
fumecheng-11587	400	2	different	different	ADJ
fumecheng-11587	400	3	values	value	NOUN
fumecheng-11587	400	4	of	of	ADP
fumecheng-11587	400	5	excitation	excitation	NOUN
fumecheng-11587	400	6	frequency	frequency	NOUN
fumecheng-11587	400	7	acting	act	VERB
fumecheng-11587	400	8	in	in	ADP
fumecheng-11587	400	9	transversal	transversal	ADJ
fumecheng-11587	400	10	direction	direction	NOUN
fumecheng-11587	400	11	,	,	PUNCT
fumecheng-11587	400	12	the	the	DET
fumecheng-11587	400	13	first	first	ADJ
fumecheng-11587	400	14	(	(	PUNCT
fumecheng-11587	400	15	a1	a1	NOUN
fumecheng-11587	400	16	)	)	PUNCT
fumecheng-11587	400	17	and	and	CCONJ
fumecheng-11587	400	18	the	the	DET
fumecheng-11587	400	19	third	third	ADJ
fumecheng-11587	400	20	(	(	PUNCT
fumecheng-11587	400	21	a3	a3	NOUN
fumecheng-11587	400	22	)	)	PUNCT
fumecheng-11587	400	23	harmonic	harmonic	NOUN
fumecheng-11587	400	24	of	of	ADP
fumecheng-11587	400	25	the	the	DET
fumecheng-11587	400	26	amplitudes	amplitude	NOUN
fumecheng-11587	400	27	for	for	ADP
fumecheng-11587	400	28	displacement	displacement	NOUN
fumecheng-11587	400	29	of	of	ADP
fumecheng-11587	400	30	the	the	DET
fumecheng-11587	400	31	beam	beam	NOUN
fumecheng-11587	400	32	in	in	ADP
fumecheng-11587	400	33	transversal	transversal	ADJ
fumecheng-11587	400	34	direction	direction	NOUN
fumecheng-11587	400	35	are	be	AUX
fumecheng-11587	400	36	obtained	obtain	VERB
fumecheng-11587	400	37	and	and	CCONJ
fumecheng-11587	400	38	given	give	VERB
fumecheng-11587	400	39	in	in	ADP
fumecheng-11587	400	40	the	the	DET
fumecheng-11587	400	41	figs	fig	NOUN
fumecheng-11587	400	42	.	.	PUNCT
fumecheng-11587	401	1	2	2	NUM
fumecheng-11587	401	2	,	,	PUNCT
fumecheng-11587	401	3	4	4	NUM
fumecheng-11587	401	4	,	,	PUNCT
fumecheng-11587	401	5	5	5	NUM
fumecheng-11587	401	6	.	.	PUNCT
fumecheng-11587	402	1	these	these	DET
fumecheng-11587	402	2	figures	figure	NOUN
fumecheng-11587	402	3	,	,	PUNCT
fumecheng-11587	402	4	for	for	ADP
fumecheng-11587	402	5	given	give	VERB
fumecheng-11587	402	6	frequency	frequency	NOUN
fumecheng-11587	402	7	,	,	PUNCT
fumecheng-11587	402	8	give	give	VERB
fumecheng-11587	402	9	us	we	PRON
fumecheng-11587	402	10	information	information	NOUN
fumecheng-11587	402	11	about	about	ADP
fumecheng-11587	402	12	the	the	DET
fumecheng-11587	402	13	number	number	NOUN
fumecheng-11587	402	14	of	of	ADP
fumecheng-11587	402	15	solutions	solution	NOUN
fumecheng-11587	402	16	(	(	PUNCT
fumecheng-11587	402	17	1	1	NUM
fumecheng-11587	402	18	,	,	PUNCT
fumecheng-11587	402	19	2	2	NUM
fumecheng-11587	402	20	or	or	CCONJ
fumecheng-11587	402	21	3	3	NUM
fumecheng-11587	402	22	)	)	PUNCT
fumecheng-11587	402	23	for	for	ADP
fumecheng-11587	402	24	each	each	PRON
fumecheng-11587	402	25	of	of	ADP
fumecheng-11587	402	26	the	the	DET
fumecheng-11587	402	27	amplitudes	amplitude	NOUN
fumecheng-11587	402	28	vibration	vibration	NOUN
fumecheng-11587	402	29	and	and	CCONJ
fumecheng-11587	402	30	stability	stability	NOUN
fumecheng-11587	402	31	of	of	ADP
fumecheng-11587	402	32	a	a	DET
fumecheng-11587	402	33	nonlinear	nonlinear	ADJ
fumecheng-11587	402	34	nonlocal	nonlocal	ADJ
fumecheng-11587	402	35	strain	strain	NOUN
fumecheng-11587	402	36	-	-	PUNCT
fumecheng-11587	402	37	gradient	gradient	NOUN
fumecheng-11587	402	38	fg	fg	PROPN
fumecheng-11587	402	39	beam	beam	NOUN
fumecheng-11587	402	40	on	on	ADP
fumecheng-11587	402	41	a	a	DET
fumecheng-11587	402	42	visco	visco	ADJ
fumecheng-11587	402	43	-	-	PUNCT
fumecheng-11587	402	44	pasternak	pasternak	NOUN
fumecheng-11587	402	45	...	...	PUNCT
fumecheng-11587	402	46	729	729	NUM
fumecheng-11587	402	47	(	(	PUNCT
fumecheng-11587	402	48	a1	a1	NOUN
fumecheng-11587	402	49	and	and	CCONJ
fumecheng-11587	402	50	a3	a3	NOUN
fumecheng-11587	402	51	)	)	PUNCT
fumecheng-11587	402	52	and	and	CCONJ
fumecheng-11587	402	53	whether	whether	SCONJ
fumecheng-11587	402	54	the	the	DET
fumecheng-11587	402	55	solution	solution	NOUN
fumecheng-11587	402	56	is	be	AUX
fumecheng-11587	402	57	stable	stable	ADJ
fumecheng-11587	402	58	or	or	CCONJ
fumecheng-11587	402	59	not	not	PART
fumecheng-11587	402	60	.	.	PUNCT
fumecheng-11587	403	1	all	all	DET
fumecheng-11587	403	2	this	this	PRON
fumecheng-11587	403	3	is	be	AUX
fumecheng-11587	403	4	to	to	PART
fumecheng-11587	403	5	predict	predict	VERB
fumecheng-11587	403	6	the	the	DET
fumecheng-11587	403	7	vibration	vibration	NOUN
fumecheng-11587	403	8	behavior	behavior	NOUN
fumecheng-11587	403	9	of	of	ADP
fumecheng-11587	403	10	the	the	DET
fumecheng-11587	403	11	beam	beam	NOUN
fumecheng-11587	403	12	at	at	ADP
fumecheng-11587	403	13	certain	certain	ADJ
fumecheng-11587	403	14	frequency	frequency	NOUN
fumecheng-11587	403	15	and	and	CCONJ
fumecheng-11587	403	16	set	set	NOUN
fumecheng-11587	403	17	of	of	ADP
fumecheng-11587	403	18	the	the	DET
fumecheng-11587	403	19	parameters	parameter	NOUN
fumecheng-11587	403	20	.	.	PUNCT
fumecheng-11587	404	1	selected	select	VERB
fumecheng-11587	404	2	solution	solution	NOUN
fumecheng-11587	404	3	for	for	ADP
fumecheng-11587	404	4	amplitude	amplitude	NOUN
fumecheng-11587	404	5	is	be	AUX
fumecheng-11587	404	6	stable	stable	ADJ
fumecheng-11587	404	7	if	if	SCONJ
fumecheng-11587	404	8	a	a	DET
fumecheng-11587	404	9	pair	pair	NOUN
fumecheng-11587	404	10	of	of	ADP
fumecheng-11587	404	11	floquet	floquet	NOUN
fumecheng-11587	404	12	multipliers	multiplier	NOUN
fumecheng-11587	404	13	is	be	AUX
fumecheng-11587	404	14	in	in	ADP
fumecheng-11587	404	15	the	the	DET
fumecheng-11587	404	16	unit	unit	NOUN
fumecheng-11587	404	17	circle	circle	NOUN
fumecheng-11587	404	18	of	of	ADP
fumecheng-11587	404	19	the	the	DET
fumecheng-11587	404	20	complex	complex	ADJ
fumecheng-11587	404	21	plane	plane	NOUN
fumecheng-11587	404	22	as	as	SCONJ
fumecheng-11587	404	23	presented	present	VERB
fumecheng-11587	404	24	on	on	ADP
fumecheng-11587	404	25	the	the	DET
fumecheng-11587	404	26	fig	fig	NOUN
fumecheng-11587	404	27	.	.	PUNCT
fumecheng-11587	405	1	7	7	X
fumecheng-11587	405	2	.	.	NUM
fumecheng-11587	405	3	floquet	floquet	PROPN
fumecheng-11587	405	4	theory	theory	NOUN
fumecheng-11587	405	5	is	be	AUX
fumecheng-11587	405	6	basically	basically	ADV
fumecheng-11587	405	7	a	a	DET
fumecheng-11587	405	8	tool	tool	NOUN
fumecheng-11587	405	9	for	for	ADP
fumecheng-11587	405	10	proving	prove	VERB
fumecheng-11587	405	11	stability	stability	NOUN
fumecheng-11587	405	12	.	.	PUNCT
fumecheng-11587	406	1	in	in	ADP
fumecheng-11587	406	2	figs	fig	NOUN
fumecheng-11587	406	3	7	7	NUM
fumecheng-11587	406	4	-	-	SYM
fumecheng-11587	406	5	8	8	NUM
fumecheng-11587	406	6	are	be	AUX
fumecheng-11587	406	7	graphically	graphically	ADV
fumecheng-11587	406	8	given	give	VERB
fumecheng-11587	406	9	values	value	NOUN
fumecheng-11587	406	10	of	of	ADP
fumecheng-11587	406	11	floquet	floquet	NOUN
fumecheng-11587	406	12	multipliers	multiplier	NOUN
fumecheng-11587	406	13	for	for	ADP
fumecheng-11587	406	14	different	different	ADJ
fumecheng-11587	406	15	values	value	NOUN
fumecheng-11587	406	16	of	of	ADP
fumecheng-11587	406	17	excitation	excitation	NOUN
fumecheng-11587	406	18	frequency	frequency	NOUN
fumecheng-11587	406	19	from	from	ADP
fumecheng-11587	406	20	the	the	DET
fumecheng-11587	406	21	range	range	NOUN
fumecheng-11587	406	22	ω	ω	X
fumecheng-11587	406	23	=	=	SYM
fumecheng-11587	406	24	0	0	NUM
fumecheng-11587	406	25	–	–	PUNCT
fumecheng-11587	406	26	30	30	NUM
fumecheng-11587	406	27	,	,	PUNCT
fumecheng-11587	406	28	enabling	enable	VERB
fumecheng-11587	406	29	reader	reader	NOUN
fumecheng-11587	406	30	to	to	PART
fumecheng-11587	406	31	determine	determine	VERB
fumecheng-11587	406	32	how	how	SCONJ
fumecheng-11587	406	33	far	far	ADV
fumecheng-11587	406	34	from	from	ADP
fumecheng-11587	406	35	stability	stability	NOUN
fumecheng-11587	406	36	border	border	NOUN
fumecheng-11587	406	37	are	be	AUX
fumecheng-11587	406	38	solutions	solution	NOUN
fumecheng-11587	406	39	at	at	ADP
fumecheng-11587	406	40	particular	particular	ADJ
fumecheng-11587	406	41	excitation	excitation	NOUN
fumecheng-11587	406	42	frequency	frequency	NOUN
fumecheng-11587	406	43	.	.	PUNCT
fumecheng-11587	407	1	finally	finally	ADV
fumecheng-11587	407	2	,	,	PUNCT
fumecheng-11587	407	3	for	for	ADP
fumecheng-11587	407	4	specific	specific	ADJ
fumecheng-11587	407	5	frequency	frequency	NOUN
fumecheng-11587	407	6	,	,	PUNCT
fumecheng-11587	407	7	which	which	PRON
fumecheng-11587	407	8	is	be	AUX
fumecheng-11587	407	9	in	in	ADP
fumecheng-11587	407	10	the	the	DET
fumecheng-11587	407	11	range	range	NOUN
fumecheng-11587	407	12	of	of	ADP
fumecheng-11587	407	13	multiple	multiple	ADJ
fumecheng-11587	407	14	amplitude	amplitude	NOUN
fumecheng-11587	407	15	solutions	solution	NOUN
fumecheng-11587	407	16	,	,	PUNCT
fumecheng-11587	407	17	basins	basin	NOUN
fumecheng-11587	407	18	of	of	ADP
fumecheng-11587	407	19	attractions	attraction	NOUN
fumecheng-11587	407	20	are	be	AUX
fumecheng-11587	407	21	given	give	VERB
fumecheng-11587	407	22	in	in	ADP
fumecheng-11587	407	23	figs	fig	NOUN
fumecheng-11587	407	24	.	.	PUNCT
fumecheng-11587	408	1	9	9	NUM
fumecheng-11587	408	2	-	-	SYM
fumecheng-11587	408	3	10	10	NUM
fumecheng-11587	408	4	,	,	PUNCT
fumecheng-11587	408	5	describing	describe	VERB
fumecheng-11587	408	6	whether	whether	SCONJ
fumecheng-11587	408	7	amplitude	amplitude	NOUN
fumecheng-11587	408	8	will	will	AUX
fumecheng-11587	408	9	be	be	AUX
fumecheng-11587	408	10	greater	great	ADJ
fumecheng-11587	408	11	or	or	CCONJ
fumecheng-11587	408	12	smaller	small	ADJ
fumecheng-11587	408	13	,	,	PUNCT
fumecheng-11587	408	14	depending	depend	VERB
fumecheng-11587	408	15	on	on	ADP
fumecheng-11587	408	16	initial	initial	ADJ
fumecheng-11587	408	17	conditions	condition	NOUN
fumecheng-11587	408	18	.	.	PUNCT
fumecheng-11587	409	1	6	6	X
fumecheng-11587	409	2	.	.	X
fumecheng-11587	409	3	conclusions	conclusion	NOUN
fumecheng-11587	409	4	in	in	ADP
fumecheng-11587	409	5	this	this	DET
fumecheng-11587	409	6	work	work	NOUN
fumecheng-11587	409	7	,	,	PUNCT
fumecheng-11587	409	8	a	a	DET
fumecheng-11587	409	9	stability	stability	NOUN
fumecheng-11587	409	10	analysis	analysis	NOUN
fumecheng-11587	409	11	of	of	ADP
fumecheng-11587	409	12	a	a	DET
fumecheng-11587	409	13	nonlinear	nonlinear	ADJ
fumecheng-11587	409	14	nonlocal	nonlocal	ADJ
fumecheng-11587	409	15	strain	strain	NOUN
fumecheng-11587	409	16	-	-	PUNCT
fumecheng-11587	409	17	gradient	gradient	NOUN
fumecheng-11587	409	18	beam	beam	NOUN
fumecheng-11587	409	19	resting	rest	VERB
fumecheng-11587	409	20	on	on	ADP
fumecheng-11587	409	21	the	the	DET
fumecheng-11587	409	22	visco	visco	ADJ
fumecheng-11587	409	23	-	-	PUNCT
fumecheng-11587	409	24	pasternak	pasternak	PROPN
fumecheng-11587	409	25	foundation	foundation	NOUN
fumecheng-11587	409	26	is	be	AUX
fumecheng-11587	409	27	performed	perform	VERB
fumecheng-11587	409	28	.	.	PUNCT
fumecheng-11587	410	1	the	the	DET
fumecheng-11587	410	2	governing	govern	VERB
fumecheng-11587	410	3	equation	equation	NOUN
fumecheng-11587	410	4	of	of	ADP
fumecheng-11587	410	5	the	the	DET
fumecheng-11587	410	6	system	system	NOUN
fumecheng-11587	410	7	is	be	AUX
fumecheng-11587	410	8	derived	derive	VERB
fumecheng-11587	410	9	by	by	ADP
fumecheng-11587	410	10	using	use	VERB
fumecheng-11587	410	11	hamilton	hamilton	PROPN
fumecheng-11587	410	12	's	's	PART
fumecheng-11587	410	13	principle	principle	NOUN
fumecheng-11587	410	14	and	and	CCONJ
fumecheng-11587	410	15	then	then	ADV
fumecheng-11587	410	16	discretized	discretize	VERB
fumecheng-11587	410	17	by	by	ADP
fumecheng-11587	410	18	using	use	VERB
fumecheng-11587	410	19	the	the	DET
fumecheng-11587	410	20	galerkin	galerkin	ADJ
fumecheng-11587	410	21	approximation	approximation	NOUN
fumecheng-11587	410	22	method	method	NOUN
fumecheng-11587	410	23	.	.	PUNCT
fumecheng-11587	411	1	the	the	DET
fumecheng-11587	411	2	periodic	periodic	ADJ
fumecheng-11587	411	3	solutions	solution	NOUN
fumecheng-11587	411	4	of	of	ADP
fumecheng-11587	411	5	the	the	DET
fumecheng-11587	411	6	strongly	strongly	ADV
fumecheng-11587	411	7	nonlinear	nonlinear	ADJ
fumecheng-11587	411	8	differential	differential	ADJ
fumecheng-11587	411	9	equation	equation	NOUN
fumecheng-11587	411	10	are	be	AUX
fumecheng-11587	411	11	then	then	ADV
fumecheng-11587	411	12	sought	seek	VERB
fumecheng-11587	411	13	by	by	ADP
fumecheng-11587	411	14	using	use	VERB
fumecheng-11587	411	15	the	the	DET
fumecheng-11587	411	16	incremental	incremental	ADJ
fumecheng-11587	411	17	harmonic	harmonic	ADJ
fumecheng-11587	411	18	balance	balance	NOUN
fumecheng-11587	411	19	method	method	NOUN
fumecheng-11587	411	20	in	in	ADP
fumecheng-11587	411	21	combination	combination	NOUN
fumecheng-11587	411	22	with	with	ADP
fumecheng-11587	411	23	the	the	DET
fumecheng-11587	411	24	continuation	continuation	NOUN
fumecheng-11587	411	25	technique	technique	NOUN
fumecheng-11587	411	26	.	.	PUNCT
fumecheng-11587	412	1	the	the	DET
fumecheng-11587	412	2	results	result	NOUN
fumecheng-11587	412	3	obtained	obtain	VERB
fumecheng-11587	412	4	by	by	ADP
fumecheng-11587	412	5	the	the	DET
fumecheng-11587	412	6	proposed	propose	VERB
fumecheng-11587	412	7	approach	approach	NOUN
fumecheng-11587	412	8	are	be	AUX
fumecheng-11587	412	9	verified	verify	VERB
fumecheng-11587	412	10	with	with	ADP
fumecheng-11587	412	11	the	the	DET
fumecheng-11587	412	12	direct	direct	ADJ
fumecheng-11587	412	13	numerical	numerical	ADJ
fumecheng-11587	412	14	integration	integration	NOUN
fumecheng-11587	412	15	technique	technique	NOUN
fumecheng-11587	412	16	(	(	PUNCT
fumecheng-11587	412	17	runge	runge	NOUN
fumecheng-11587	412	18	-	-	PUNCT
fumecheng-11587	412	19	kutta	kutta	NOUN
fumecheng-11587	412	20	method	method	NOUN
fumecheng-11587	412	21	)	)	PUNCT
fumecheng-11587	412	22	and	and	CCONJ
fumecheng-11587	412	23	good	good	ADJ
fumecheng-11587	412	24	agreement	agreement	NOUN
fumecheng-11587	412	25	is	be	AUX
fumecheng-11587	412	26	confirmed	confirm	VERB
fumecheng-11587	412	27	.	.	PUNCT
fumecheng-11587	413	1	a	a	DET
fumecheng-11587	413	2	parametric	parametric	ADJ
fumecheng-11587	413	3	study	study	NOUN
fumecheng-11587	413	4	is	be	AUX
fumecheng-11587	413	5	performed	perform	VERB
fumecheng-11587	413	6	through	through	ADP
fumecheng-11587	413	7	the	the	DET
fumecheng-11587	413	8	amplitude	amplitude	NOUN
fumecheng-11587	413	9	-	-	PUNCT
fumecheng-11587	413	10	frequency	frequency	NOUN
fumecheng-11587	413	11	responses	response	NOUN
fumecheng-11587	413	12	and	and	CCONJ
fumecheng-11587	413	13	the	the	DET
fumecheng-11587	413	14	stability	stability	NOUN
fumecheng-11587	413	15	of	of	ADP
fumecheng-11587	413	16	each	each	DET
fumecheng-11587	413	17	periodic	periodic	ADJ
fumecheng-11587	413	18	solution	solution	NOUN
fumecheng-11587	413	19	is	be	AUX
fumecheng-11587	413	20	examined	examine	VERB
fumecheng-11587	413	21	by	by	ADP
fumecheng-11587	413	22	using	use	VERB
fumecheng-11587	413	23	the	the	DET
fumecheng-11587	413	24	floquet	floquet	NOUN
fumecheng-11587	413	25	stability	stability	NOUN
fumecheng-11587	413	26	theory	theory	NOUN
fumecheng-11587	413	27	and	and	CCONJ
fumecheng-11587	413	28	hsu	hsu	PROPN
fumecheng-11587	413	29	procedures	procedure	NOUN
fumecheng-11587	413	30	.	.	PUNCT
fumecheng-11587	414	1	the	the	DET
fumecheng-11587	414	2	main	main	ADJ
fumecheng-11587	414	3	contributions	contribution	NOUN
fumecheng-11587	414	4	of	of	ADP
fumecheng-11587	414	5	this	this	DET
fumecheng-11587	414	6	work	work	NOUN
fumecheng-11587	414	7	can	can	AUX
fumecheng-11587	414	8	be	be	AUX
fumecheng-11587	414	9	summarized	summarize	VERB
fumecheng-11587	414	10	as	as	SCONJ
fumecheng-11587	414	11	follows	follow	VERB
fumecheng-11587	414	12	:	:	PUNCT
fumecheng-11587	414	13	▪	▪	X
fumecheng-11587	414	14	the	the	DET
fumecheng-11587	414	15	parametric	parametric	ADJ
fumecheng-11587	414	16	study	study	NOUN
fumecheng-11587	414	17	is	be	AUX
fumecheng-11587	414	18	performed	perform	VERB
fumecheng-11587	414	19	and	and	CCONJ
fumecheng-11587	414	20	stability	stability	NOUN
fumecheng-11587	414	21	of	of	ADP
fumecheng-11587	414	22	obtained	obtain	VERB
fumecheng-11587	414	23	periodic	periodic	ADJ
fumecheng-11587	414	24	solutions	solution	NOUN
fumecheng-11587	414	25	of	of	ADP
fumecheng-11587	414	26	a	a	DET
fumecheng-11587	414	27	nonlocal	nonlocal	ADJ
fumecheng-11587	414	28	strain	strain	NOUN
fumecheng-11587	414	29	-	-	PUNCT
fumecheng-11587	414	30	gradient	gradient	NOUN
fumecheng-11587	414	31	functionally	functionally	ADV
fumecheng-11587	414	32	graded	grade	VERB
fumecheng-11587	414	33	beam	beam	NOUN
fumecheng-11587	414	34	on	on	ADP
fumecheng-11587	414	35	the	the	DET
fumecheng-11587	414	36	visco	visco	ADJ
fumecheng-11587	414	37	-	-	PUNCT
fumecheng-11587	414	38	pasternak	pasternak	PROPN
fumecheng-11587	414	39	foundation	foundation	NOUN
fumecheng-11587	414	40	is	be	AUX
fumecheng-11587	414	41	investigated	investigate	VERB
fumecheng-11587	414	42	.	.	PUNCT
fumecheng-11587	415	1	it	it	PRON
fumecheng-11587	415	2	is	be	AUX
fumecheng-11587	415	3	demonstrated	demonstrate	VERB
fumecheng-11587	415	4	that	that	SCONJ
fumecheng-11587	415	5	the	the	DET
fumecheng-11587	415	6	hardening	harden	VERB
fumecheng-11587	415	7	stiffness	stiffness	ADJ
fumecheng-11587	415	8	nonlinearity	nonlinearity	NOUN
fumecheng-11587	415	9	becomes	become	VERB
fumecheng-11587	415	10	more	more	ADV
fumecheng-11587	415	11	apparent	apparent	ADJ
fumecheng-11587	415	12	for	for	ADP
fumecheng-11587	415	13	an	an	DET
fumecheng-11587	415	14	increase	increase	NOUN
fumecheng-11587	415	15	of	of	ADP
fumecheng-11587	415	16	the	the	DET
fumecheng-11587	415	17	excitation	excitation	NOUN
fumecheng-11587	415	18	amplitude	amplitude	NOUN
fumecheng-11587	415	19	and	and	CCONJ
fumecheng-11587	415	20	for	for	ADP
fumecheng-11587	415	21	lower	low	ADJ
fumecheng-11587	415	22	values	value	NOUN
fumecheng-11587	415	23	of	of	ADP
fumecheng-11587	415	24	the	the	DET
fumecheng-11587	415	25	parameter	parameter	NOUN
fumecheng-11587	415	26	of	of	ADP
fumecheng-11587	415	27	functionally	functionally	ADV
fumecheng-11587	415	28	graded	grade	VERB
fumecheng-11587	415	29	material	material	NOUN
fumecheng-11587	415	30	,	,	PUNCT
fumecheng-11587	415	31	which	which	PRON
fumecheng-11587	415	32	consequently	consequently	ADV
fumecheng-11587	415	33	leads	lead	VERB
fumecheng-11587	415	34	to	to	ADP
fumecheng-11587	415	35	an	an	DET
fumecheng-11587	415	36	increase	increase	NOUN
fumecheng-11587	415	37	of	of	ADP
fumecheng-11587	415	38	the	the	DET
fumecheng-11587	415	39	unstable	unstable	ADJ
fumecheng-11587	415	40	branches	branch	NOUN
fumecheng-11587	415	41	of	of	ADP
fumecheng-11587	415	42	periodic	periodic	ADJ
fumecheng-11587	415	43	solutions	solution	NOUN
fumecheng-11587	415	44	.	.	PUNCT
fumecheng-11587	416	1	opposite	opposite	ADJ
fumecheng-11587	416	2	to	to	ADP
fumecheng-11587	416	3	this	this	PRON
fumecheng-11587	416	4	,	,	PUNCT
fumecheng-11587	416	5	an	an	DET
fumecheng-11587	416	6	increase	increase	NOUN
fumecheng-11587	416	7	of	of	ADP
fumecheng-11587	416	8	the	the	DET
fumecheng-11587	416	9	parameter	parameter	NOUN
fumecheng-11587	416	10	related	relate	VERB
fumecheng-11587	416	11	to	to	ADP
fumecheng-11587	416	12	viscous	viscous	ADJ
fumecheng-11587	416	13	properties	property	NOUN
fumecheng-11587	416	14	of	of	ADP
fumecheng-11587	416	15	the	the	DET
fumecheng-11587	416	16	foundation	foundation	NOUN
fumecheng-11587	416	17	yields	yield	VERB
fumecheng-11587	416	18	lower	low	ADJ
fumecheng-11587	416	19	picks	pick	NOUN
fumecheng-11587	416	20	in	in	ADP
fumecheng-11587	416	21	the	the	DET
fumecheng-11587	416	22	amplitude	amplitude	NOUN
fumecheng-11587	416	23	-	-	PUNCT
fumecheng-11587	416	24	frequency	frequency	NOUN
fumecheng-11587	416	25	response	response	NOUN
fumecheng-11587	416	26	and	and	CCONJ
fumecheng-11587	416	27	smaller	small	ADJ
fumecheng-11587	416	28	unstable	unstable	ADJ
fumecheng-11587	416	29	branches	branch	NOUN
fumecheng-11587	416	30	,	,	PUNCT
fumecheng-11587	416	31	therefore	therefore	ADV
fumecheng-11587	416	32	increasing	increase	VERB
fumecheng-11587	416	33	the	the	DET
fumecheng-11587	416	34	stability	stability	NOUN
fumecheng-11587	416	35	of	of	ADP
fumecheng-11587	416	36	the	the	DET
fumecheng-11587	416	37	system	system	NOUN
fumecheng-11587	416	38	.	.	PUNCT
fumecheng-11587	417	1	▪	▪	ADJ
fumecheng-11587	417	2	investigation	investigation	NOUN
fumecheng-11587	417	3	of	of	ADP
fumecheng-11587	417	4	the	the	DET
fumecheng-11587	417	5	floquet	floquet	NOUN
fumecheng-11587	417	6	multipliers	multiplier	NOUN
fumecheng-11587	417	7	and	and	CCONJ
fumecheng-11587	417	8	their	their	PRON
fumecheng-11587	417	9	behavior	behavior	NOUN
fumecheng-11587	417	10	in	in	ADP
fumecheng-11587	417	11	the	the	DET
fumecheng-11587	417	12	complex	complex	ADJ
fumecheng-11587	417	13	plane	plane	NOUN
fumecheng-11587	417	14	revealed	reveal	VERB
fumecheng-11587	417	15	the	the	DET
fumecheng-11587	417	16	nature	nature	NOUN
fumecheng-11587	417	17	of	of	ADP
fumecheng-11587	417	18	bifurcation	bifurcation	NOUN
fumecheng-11587	417	19	points	point	NOUN
fumecheng-11587	417	20	where	where	SCONJ
fumecheng-11587	417	21	unstable	unstable	ADJ
fumecheng-11587	417	22	solution	solution	NOUN
fumecheng-11587	417	23	appears	appear	VERB
fumecheng-11587	417	24	.	.	PUNCT
fumecheng-11587	418	1	moreover	moreover	ADV
fumecheng-11587	418	2	,	,	PUNCT
fumecheng-11587	418	3	the	the	DET
fumecheng-11587	418	4	exiting	exiting	NOUN
fumecheng-11587	418	5	of	of	ADP
fumecheng-11587	418	6	floquet	floquet	PROPN
fumecheng-11587	418	7	multipliers	multiplier	NOUN
fumecheng-11587	418	8	out	out	ADP
fumecheng-11587	418	9	of	of	ADP
fumecheng-11587	418	10	the	the	DET
fumecheng-11587	418	11	unit	unit	NOUN
fumecheng-11587	418	12	circle	circle	NOUN
fumecheng-11587	418	13	in	in	ADP
fumecheng-11587	418	14	the	the	DET
fumecheng-11587	418	15	+1	+1	ADJ
fumecheng-11587	418	16	direction	direction	NOUN
fumecheng-11587	418	17	demonstrated	demonstrate	VERB
fumecheng-11587	418	18	the	the	DET
fumecheng-11587	418	19	existence	existence	NOUN
fumecheng-11587	418	20	of	of	ADP
fumecheng-11587	418	21	saddle	saddle	NOUN
fumecheng-11587	418	22	-	-	PUNCT
fumecheng-11587	418	23	node	node	NOUN
fumecheng-11587	418	24	bifurcation	bifurcation	NOUN
fumecheng-11587	418	25	points	point	NOUN
fumecheng-11587	418	26	.	.	PUNCT
fumecheng-11587	419	1	▪	▪	ADJ
fumecheng-11587	419	2	modulus	modulus	NOUN
fumecheng-11587	419	3	of	of	ADP
fumecheng-11587	419	4	floquet	floquet	NOUN
fumecheng-11587	419	5	multipliers	multiplier	NOUN
fumecheng-11587	419	6	is	be	AUX
fumecheng-11587	419	7	compared	compare	VERB
fumecheng-11587	419	8	for	for	ADP
fumecheng-11587	419	9	different	different	ADJ
fumecheng-11587	419	10	values	value	NOUN
fumecheng-11587	419	11	of	of	ADP
fumecheng-11587	419	12	excitation	excitation	NOUN
fumecheng-11587	419	13	frequencies	frequency	NOUN
fumecheng-11587	419	14	and	and	CCONJ
fumecheng-11587	419	15	shown	show	VERB
fumecheng-11587	419	16	that	that	SCONJ
fumecheng-11587	419	17	in	in	ADP
fumecheng-11587	419	18	an	an	DET
fumecheng-11587	419	19	unstable	unstable	ADJ
fumecheng-11587	419	20	region	region	NOUN
fumecheng-11587	419	21	,	,	PUNCT
fumecheng-11587	419	22	instability	instability	NOUN
fumecheng-11587	419	23	degree	degree	NOUN
fumecheng-11587	419	24	is	be	AUX
fumecheng-11587	419	25	higher	high	ADJ
fumecheng-11587	419	26	for	for	ADP
fumecheng-11587	419	27	lower	low	ADJ
fumecheng-11587	419	28	excitation	excitation	NOUN
fumecheng-11587	419	29	frequencies	frequency	NOUN
fumecheng-11587	419	30	.	.	PUNCT
fumecheng-11587	420	1	▪	▪	X
fumecheng-11587	420	2	to	to	PART
fumecheng-11587	420	3	obtain	obtain	VERB
fumecheng-11587	420	4	stable	stable	ADJ
fumecheng-11587	420	5	solutions	solution	NOUN
fumecheng-11587	420	6	on	on	ADP
fumecheng-11587	420	7	higher	high	ADJ
fumecheng-11587	420	8	excitation	excitation	NOUN
fumecheng-11587	420	9	frequencies	frequency	NOUN
fumecheng-11587	420	10	,	,	PUNCT
fumecheng-11587	420	11	pinned	pin	VERB
fumecheng-11587	420	12	-	-	PUNCT
fumecheng-11587	420	13	pinned	pin	VERB
fumecheng-11587	420	14	boundary	boundary	ADJ
fumecheng-11587	420	15	conditions	condition	NOUN
fumecheng-11587	420	16	should	should	AUX
fumecheng-11587	420	17	be	be	AUX
fumecheng-11587	420	18	applied	apply	VERB
fumecheng-11587	420	19	.	.	PUNCT
fumecheng-11587	421	1	on	on	ADP
fumecheng-11587	421	2	the	the	DET
fumecheng-11587	421	3	contrary	contrary	NOUN
fumecheng-11587	421	4	,	,	PUNCT
fumecheng-11587	421	5	stability	stability	NOUN
fumecheng-11587	421	6	on	on	ADP
fumecheng-11587	421	7	lower	low	ADJ
fumecheng-11587	421	8	excitation	excitation	NOUN
fumecheng-11587	421	9	frequencies	frequency	NOUN
fumecheng-11587	421	10	can	can	AUX
fumecheng-11587	421	11	be	be	AUX
fumecheng-11587	421	12	reached	reach	VERB
fumecheng-11587	421	13	with	with	ADP
fumecheng-11587	421	14	clamped	clamp	VERB
fumecheng-11587	421	15	-	-	PUNCT
fumecheng-11587	421	16	clamped	clamp	VERB
fumecheng-11587	421	17	boundary	boundary	ADJ
fumecheng-11587	421	18	conditions	condition	NOUN
fumecheng-11587	421	19	.	.	PUNCT
fumecheng-11587	422	1	an	an	DET
fumecheng-11587	422	2	unstable	unstable	ADJ
fumecheng-11587	422	3	region	region	NOUN
fumecheng-11587	422	4	with	with	ADP
fumecheng-11587	422	5	clamped	clamp	VERB
fumecheng-11587	422	6	-	-	PUNCT
fumecheng-11587	422	7	free	free	ADJ
fumecheng-11587	422	8	boundary	boundary	ADJ
fumecheng-11587	422	9	conditions	condition	NOUN
fumecheng-11587	422	10	is	be	AUX
fumecheng-11587	422	11	between	between	ADP
fumecheng-11587	422	12	unstable	unstable	ADJ
fumecheng-11587	422	13	regions	region	NOUN
fumecheng-11587	422	14	for	for	ADP
fumecheng-11587	422	15	another	another	DET
fumecheng-11587	422	16	two	two	NUM
fumecheng-11587	422	17	pairs	pair	NOUN
fumecheng-11587	422	18	of	of	ADP
fumecheng-11587	422	19	boundary	boundary	ADJ
fumecheng-11587	422	20	conditions	condition	NOUN
fumecheng-11587	422	21	.	.	PUNCT
fumecheng-11587	423	1	▪	▪	NOUN
fumecheng-11587	423	2	the	the	DET
fumecheng-11587	423	3	occurrence	occurrence	NOUN
fumecheng-11587	423	4	of	of	ADP
fumecheng-11587	423	5	coexisting	coexist	VERB
fumecheng-11587	423	6	periodic	periodic	ADJ
fumecheng-11587	423	7	solutions	solution	NOUN
fumecheng-11587	423	8	and	and	CCONJ
fumecheng-11587	423	9	hardening	harden	VERB
fumecheng-11587	423	10	stiffness	stiffness	ADJ
fumecheng-11587	423	11	effect	effect	NOUN
fumecheng-11587	423	12	in	in	ADP
fumecheng-11587	423	13	the	the	DET
fumecheng-11587	423	14	strongly	strongly	ADV
fumecheng-11587	423	15	nonlinear	nonlinear	ADJ
fumecheng-11587	423	16	functionally	functionally	ADV
fumecheng-11587	423	17	graded	grade	VERB
fumecheng-11587	423	18	beam	beam	NOUN
fumecheng-11587	423	19	system	system	NOUN
fumecheng-11587	423	20	is	be	AUX
fumecheng-11587	423	21	confirmed	confirm	VERB
fumecheng-11587	423	22	as	as	ADV
fumecheng-11587	423	23	well	well	ADV
fumecheng-11587	423	24	as	as	ADP
fumecheng-11587	423	25	their	their	PRON
fumecheng-11587	423	26	dependence	dependence	NOUN
fumecheng-11587	423	27	on	on	ADP
fumecheng-11587	423	28	the	the	DET
fumecheng-11587	423	29	initial	initial	ADJ
fumecheng-11587	423	30	conditions	condition	NOUN
fumecheng-11587	423	31	and	and	CCONJ
fumecheng-11587	423	32	starting	start	VERB
fumecheng-11587	423	33	positions	position	NOUN
fumecheng-11587	423	34	of	of	ADP
fumecheng-11587	423	35	the	the	DET
fumecheng-11587	423	36	excitation	excitation	NOUN
fumecheng-11587	423	37	frequency	frequency	NOUN
fumecheng-11587	423	38	sweeping	sweeping	ADJ
fumecheng-11587	423	39	.	.	PUNCT
fumecheng-11587	424	1	therefore	therefore	ADV
fumecheng-11587	424	2	,	,	PUNCT
fumecheng-11587	424	3	the	the	DET
fumecheng-11587	424	4	basin	basin	NOUN
fumecheng-11587	424	5	of	of	ADP
fumecheng-11587	424	6	attraction	attraction	NOUN
fumecheng-11587	424	7	is	be	AUX
fumecheng-11587	424	8	obtained	obtain	VERB
fumecheng-11587	424	9	for	for	ADP
fumecheng-11587	424	10	such	such	DET
fumecheng-11587	424	11	a	a	DET
fumecheng-11587	424	12	system	system	NOUN
fumecheng-11587	424	13	to	to	PART
fumecheng-11587	424	14	examine	examine	VERB
fumecheng-11587	424	15	which	which	PRON
fumecheng-11587	424	16	of	of	ADP
fumecheng-11587	424	17	the	the	DET
fumecheng-11587	424	18	stable	stable	ADJ
fumecheng-11587	424	19	periodic	periodic	ADJ
fumecheng-11587	424	20	solutions	solution	NOUN
fumecheng-11587	424	21	will	will	AUX
fumecheng-11587	424	22	prevail	prevail	VERB
fumecheng-11587	424	23	for	for	ADP
fumecheng-11587	424	24	different	different	ADJ
fumecheng-11587	424	25	sets	set	NOUN
fumecheng-11587	424	26	of	of	ADP
fumecheng-11587	424	27	initial	initial	ADJ
fumecheng-11587	424	28	conditions	condition	NOUN
fumecheng-11587	424	29	.	.	PUNCT
fumecheng-11587	425	1	730	730	NUM
fumecheng-11587	425	2	n.	n.	NOUN
fumecheng-11587	425	3	nešić	nešić	PROPN
fumecheng-11587	425	4	,	,	PUNCT
fumecheng-11587	425	5	m.	m.	NOUN
fumecheng-11587	425	6	cajić	cajić	NOUN
fumecheng-11587	425	7	,	,	PUNCT
fumecheng-11587	425	8	d.	d.	PROPN
fumecheng-11587	425	9	karličić	karličić	PROPN
fumecheng-11587	425	10	,	,	PUNCT
fumecheng-11587	425	11	m.	m.	NOUN
fumecheng-11587	425	12	lazarević	lazarević	PROPN
fumecheng-11587	425	13	,	,	PUNCT
fumecheng-11587	425	14	s.	s.	PROPN
fumecheng-11587	425	15	adhikari	adhikari	PROPN
fumecheng-11587	426	1	the	the	DET
fumecheng-11587	426	2	paper	paper	NOUN
fumecheng-11587	426	3	illustrates	illustrate	VERB
fumecheng-11587	426	4	how	how	SCONJ
fumecheng-11587	426	5	the	the	DET
fumecheng-11587	426	6	incremental	incremental	ADJ
fumecheng-11587	426	7	harmonic	harmonic	ADJ
fumecheng-11587	426	8	balance	balance	NOUN
fumecheng-11587	426	9	method	method	NOUN
fumecheng-11587	426	10	in	in	ADP
fumecheng-11587	426	11	combination	combination	NOUN
fumecheng-11587	426	12	with	with	ADP
fumecheng-11587	426	13	the	the	DET
fumecheng-11587	426	14	continuation	continuation	NOUN
fumecheng-11587	426	15	technique	technique	NOUN
fumecheng-11587	426	16	and	and	CCONJ
fumecheng-11587	426	17	floquet	floquet	PROPN
fumecheng-11587	426	18	theory	theory	NOUN
fumecheng-11587	426	19	can	can	AUX
fumecheng-11587	426	20	be	be	AUX
fumecheng-11587	426	21	efficiently	efficiently	ADV
fumecheng-11587	426	22	utilized	utilize	VERB
fumecheng-11587	426	23	to	to	PART
fumecheng-11587	426	24	study	study	VERB
fumecheng-11587	426	25	the	the	DET
fumecheng-11587	426	26	stability	stability	NOUN
fumecheng-11587	426	27	of	of	ADP
fumecheng-11587	426	28	strongly	strongly	ADV
fumecheng-11587	426	29	nonlinear	nonlinear	ADJ
fumecheng-11587	426	30	structural	structural	ADJ
fumecheng-11587	426	31	vibration	vibration	NOUN
fumecheng-11587	426	32	systems	system	NOUN
fumecheng-11587	426	33	with	with	ADP
fumecheng-11587	426	34	different	different	ADJ
fumecheng-11587	426	35	sizes	size	NOUN
fumecheng-11587	426	36	,	,	PUNCT
fumecheng-11587	426	37	boundary	boundary	ADJ
fumecheng-11587	426	38	conditions	condition	NOUN
fumecheng-11587	426	39	,	,	PUNCT
fumecheng-11587	426	40	and	and	CCONJ
fumecheng-11587	426	41	foundation	foundation	NOUN
fumecheng-11587	426	42	effects	effect	NOUN
fumecheng-11587	426	43	included	include	VERB
fumecheng-11587	426	44	.	.	PUNCT
fumecheng-11587	427	1	the	the	DET
fumecheng-11587	427	2	future	future	ADJ
fumecheng-11587	427	3	perspectives	perspective	NOUN
fumecheng-11587	427	4	of	of	ADP
fumecheng-11587	427	5	the	the	DET
fumecheng-11587	427	6	proposed	propose	VERB
fumecheng-11587	427	7	research	research	NOUN
fumecheng-11587	427	8	and	and	CCONJ
fumecheng-11587	427	9	the	the	DET
fumecheng-11587	427	10	developed	develop	VERB
fumecheng-11587	427	11	model	model	NOUN
fumecheng-11587	427	12	is	be	AUX
fumecheng-11587	427	13	application	application	NOUN
fumecheng-11587	427	14	of	of	ADP
fumecheng-11587	427	15	the	the	DET
fumecheng-11587	427	16	model	model	NOUN
fumecheng-11587	427	17	and	and	CCONJ
fumecheng-11587	427	18	methodology	methodology	NOUN
fumecheng-11587	427	19	presented	present	VERB
fumecheng-11587	427	20	in	in	ADP
fumecheng-11587	427	21	this	this	DET
fumecheng-11587	427	22	paper	paper	NOUN
fumecheng-11587	427	23	in	in	ADP
fumecheng-11587	427	24	the	the	DET
fumecheng-11587	427	25	development	development	NOUN
fumecheng-11587	427	26	of	of	ADP
fumecheng-11587	427	27	mems	mem	NOUN
fumecheng-11587	427	28	devices	device	NOUN
fumecheng-11587	427	29	,	,	PUNCT
fumecheng-11587	427	30	since	since	SCONJ
fumecheng-11587	427	31	the	the	DET
fumecheng-11587	427	32	presented	present	VERB
fumecheng-11587	427	33	model	model	NOUN
fumecheng-11587	427	34	describes	describe	VERB
fumecheng-11587	427	35	oscillating	oscillate	VERB
fumecheng-11587	427	36	nonlocal	nonlocal	ADJ
fumecheng-11587	427	37	beam	beam	NOUN
fumecheng-11587	427	38	,	,	PUNCT
fumecheng-11587	427	39	and	and	CCONJ
fumecheng-11587	427	40	nonlocal	nonlocal	ADJ
fumecheng-11587	427	41	theory	theory	NOUN
fumecheng-11587	427	42	is	be	AUX
fumecheng-11587	427	43	used	use	VERB
fumecheng-11587	427	44	in	in	ADP
fumecheng-11587	427	45	small	small	ADJ
fumecheng-11587	427	46	scale	scale	NOUN
fumecheng-11587	427	47	systems	system	NOUN
fumecheng-11587	427	48	.	.	PUNCT
fumecheng-11587	428	1	additionally	additionally	ADV
fumecheng-11587	428	2	,	,	PUNCT
fumecheng-11587	428	3	when	when	SCONJ
fumecheng-11587	428	4	neglecting	neglect	VERB
fumecheng-11587	428	5	two	two	NUM
fumecheng-11587	428	6	nonlocal	nonlocal	ADJ
fumecheng-11587	428	7	parameters	parameter	NOUN
fumecheng-11587	428	8	,	,	PUNCT
fumecheng-11587	428	9	presented	present	VERB
fumecheng-11587	428	10	model	model	NOUN
fumecheng-11587	428	11	of	of	ADP
fumecheng-11587	428	12	beam	beam	NOUN
fumecheng-11587	428	13	oscillating	oscillating	NOUN
fumecheng-11587	428	14	on	on	ADP
fumecheng-11587	428	15	viscopasternak	viscopasternak	NOUN
fumecheng-11587	428	16	foundation	foundation	NOUN
fumecheng-11587	428	17	with	with	ADP
fumecheng-11587	428	18	four	four	NUM
fumecheng-11587	428	19	adjustable	adjustable	ADJ
fumecheng-11587	428	20	parameters	parameter	NOUN
fumecheng-11587	428	21	can	can	AUX
fumecheng-11587	428	22	be	be	AUX
fumecheng-11587	428	23	used	use	VERB
fumecheng-11587	428	24	to	to	PART
fumecheng-11587	428	25	describe	describe	VERB
fumecheng-11587	428	26	wide	wide	ADJ
fumecheng-11587	428	27	range	range	NOUN
fumecheng-11587	428	28	of	of	ADP
fumecheng-11587	428	29	foundations	foundation	NOUN
fumecheng-11587	428	30	used	use	VERB
fumecheng-11587	428	31	in	in	ADP
fumecheng-11587	428	32	civil	civil	ADJ
fumecheng-11587	428	33	and	and	CCONJ
fumecheng-11587	428	34	mechanical	mechanical	ADJ
fumecheng-11587	428	35	engineering	engineering	NOUN
fumecheng-11587	428	36	and	and	CCONJ
fumecheng-11587	428	37	oscillatory	oscillatory	ADJ
fumecheng-11587	428	38	behavior	behavior	NOUN
fumecheng-11587	428	39	of	of	ADP
fumecheng-11587	428	40	the	the	DET
fumecheng-11587	428	41	nonlinear	nonlinear	ADJ
fumecheng-11587	428	42	beam	beam	NOUN
fumecheng-11587	428	43	resting	rest	VERB
fumecheng-11587	428	44	on	on	ADP
fumecheng-11587	428	45	it	it	PRON
fumecheng-11587	428	46	.	.	PUNCT
fumecheng-11587	429	1	acknowledgement	acknowledgement	NOUN
fumecheng-11587	429	2	:	:	PUNCT
fumecheng-11587	430	1	authors	author	NOUN
fumecheng-11587	430	2	n.	n.	PROPN
fumecheng-11587	430	3	nešić	nešić	PROPN
fumecheng-11587	430	4	,	,	PUNCT
fumecheng-11587	430	5	d.	d.	PROPN
fumecheng-11587	430	6	karličić	karličić	PROPN
fumecheng-11587	430	7	and	and	CCONJ
fumecheng-11587	430	8	m.	m.	NOUN
fumecheng-11587	430	9	lazarević	lazarević	PROPN
fumecheng-11587	430	10	acknowledge	acknowledge	VERB
fumecheng-11587	430	11	the	the	DET
fumecheng-11587	430	12	support	support	NOUN
fumecheng-11587	430	13	by	by	ADP
fumecheng-11587	430	14	the	the	DET
fumecheng-11587	430	15	serbian	serbian	PROPN
fumecheng-11587	430	16	ministry	ministry	PROPN
fumecheng-11587	430	17	of	of	ADP
fumecheng-11587	430	18	education	education	PROPN
fumecheng-11587	430	19	,	,	PUNCT
fumecheng-11587	430	20	science	science	NOUN
fumecheng-11587	430	21	,	,	PUNCT
fumecheng-11587	430	22	and	and	CCONJ
fumecheng-11587	430	23	technological	technological	ADJ
fumecheng-11587	430	24	development	development	NOUN
fumecheng-11587	430	25	through	through	ADP
fumecheng-11587	430	26	the	the	DET
fumecheng-11587	430	27	faculty	faculty	NOUN
fumecheng-11587	430	28	of	of	ADP
fumecheng-11587	430	29	technical	technical	ADJ
fumecheng-11587	430	30	sciences	sciences	PROPN
fumecheng-11587	430	31	,	,	PUNCT
fumecheng-11587	430	32	university	university	NOUN
fumecheng-11587	430	33	of	of	ADP
fumecheng-11587	430	34	priština	priština	PROPN
fumecheng-11587	430	35	in	in	ADP
fumecheng-11587	430	36	kosovska	kosovska	PROPN
fumecheng-11587	430	37	mitrovica	mitrovica	PROPN
fumecheng-11587	430	38	,	,	PUNCT
fumecheng-11587	430	39	the	the	DET
fumecheng-11587	430	40	mathematical	mathematical	ADJ
fumecheng-11587	430	41	institute	institute	NOUN
fumecheng-11587	430	42	of	of	ADP
fumecheng-11587	430	43	the	the	DET
fumecheng-11587	430	44	serbian	serbian	PROPN
fumecheng-11587	430	45	academy	academy	PROPN
fumecheng-11587	430	46	of	of	ADP
fumecheng-11587	430	47	sciences	sciences	PROPN
fumecheng-11587	430	48	and	and	CCONJ
fumecheng-11587	430	49	art	art	NOUN
fumecheng-11587	430	50	and	and	CCONJ
fumecheng-11587	430	51	faculty	faculty	NOUN
fumecheng-11587	430	52	of	of	ADP
fumecheng-11587	430	53	mechanical	mechanical	ADJ
fumecheng-11587	430	54	engineering	engineering	NOUN
fumecheng-11587	430	55	,	,	PUNCT
fumecheng-11587	430	56	univerisity	univerisity	NOUN
fumecheng-11587	430	57	of	of	ADP
fumecheng-11587	430	58	belgrade	belgrade	PROPN
fumecheng-11587	430	59	(	(	PUNCT
fumecheng-11587	430	60	grant	grant	VERB
fumecheng-11587	430	61	no	no	INTJ
fumecheng-11587	430	62	.	.	PUNCT
fumecheng-11587	431	1	451	451	NUM
fumecheng-11587	431	2	-	-	SYM
fumecheng-11587	431	3	03	03	NUM
fumecheng-11587	431	4	-	-	PUNCT
fumecheng-11587	431	5	68/2022	68/2022	NOUN
fumecheng-11587	431	6	-	-	PUNCT
fumecheng-11587	431	7	14/200105	14/200105	NUM
fumecheng-11587	431	8	)	)	PUNCT
fumecheng-11587	431	9	.	.	PUNCT
fumecheng-11587	432	1	authors	author	NOUN
fumecheng-11587	432	2	m.	m.	VERB
fumecheng-11587	432	3	cajić	cajić	NOUN
fumecheng-11587	432	4	and	and	CCONJ
fumecheng-11587	432	5	s.	s.	PROPN
fumecheng-11587	432	6	adhikari	adhikari	PROPN
fumecheng-11587	432	7	acknowledge	acknowledge	VERB
fumecheng-11587	432	8	funding	fund	VERB
fumecheng-11587	432	9	from	from	ADP
fumecheng-11587	432	10	european	european	PROPN
fumecheng-11587	432	11	union	union	PROPN
fumecheng-11587	432	12	’s	’s	PART
fumecheng-11587	432	13	horizon	horizon	NOUN
fumecheng-11587	432	14	2020	2020	NUM
fumecheng-11587	432	15	research	research	NOUN
fumecheng-11587	432	16	and	and	CCONJ
fumecheng-11587	432	17	innovation	innovation	NOUN
fumecheng-11587	432	18	program	program	NOUN
fumecheng-11587	432	19	under	under	ADP
fumecheng-11587	432	20	the	the	DET
fumecheng-11587	432	21	marie	marie	PROPN
fumecheng-11587	432	22	skłodowska	skłodowska	PROPN
fumecheng-11587	432	23	-	-	PUNCT
fumecheng-11587	432	24	curie	curie	PROPN
fumecheng-11587	432	25	grant	grant	NOUN
fumecheng-11587	432	26	agreement	agreement	NOUN
fumecheng-11587	432	27	no	no	INTJ
fumecheng-11587	432	28	.	.	NOUN
fumecheng-11587	432	29	896942	896942	NUM
fumecheng-11587	432	30	(	(	PUNCT
fumecheng-11587	432	31	metasink	metasink	PROPN
fumecheng-11587	432	32	)	)	PUNCT
fumecheng-11587	432	33	.	.	PUNCT
fumecheng-11587	433	1	references	reference	NOUN
fumecheng-11587	433	2	1	1	NUM
fumecheng-11587	433	3	.	.	X
fumecheng-11587	434	1	ghayesh	ghayesh	PROPN
fumecheng-11587	434	2	,	,	PUNCT
fumecheng-11587	434	3	m.h	m.h	PROPN
fumecheng-11587	434	4	.	.	PROPN
fumecheng-11587	434	5	,	,	PUNCT
fumecheng-11587	434	6	farajpour	farajpour	ADJ
fumecheng-11587	434	7	,	,	PUNCT
fumecheng-11587	434	8	a.	a.	NOUN
fumecheng-11587	434	9	,	,	PUNCT
fumecheng-11587	434	10	2019	2019	NUM
fumecheng-11587	434	11	,	,	PUNCT
fumecheng-11587	434	12	a	a	DET
fumecheng-11587	434	13	review	review	NOUN
fumecheng-11587	434	14	on	on	ADP
fumecheng-11587	434	15	the	the	DET
fumecheng-11587	434	16	mechanics	mechanic	NOUN
fumecheng-11587	434	17	of	of	ADP
fumecheng-11587	434	18	functionally	functionally	ADV
fumecheng-11587	434	19	graded	grade	VERB
fumecheng-11587	434	20	nanoscale	nanoscale	NOUN
fumecheng-11587	434	21	and	and	CCONJ
fumecheng-11587	434	22	microscale	microscale	ADJ
fumecheng-11587	434	23	structures	structure	NOUN
fumecheng-11587	434	24	,	,	PUNCT
fumecheng-11587	434	25	international	international	ADJ
fumecheng-11587	434	26	journal	journal	NOUN
fumecheng-11587	434	27	of	of	ADP
fumecheng-11587	434	28	engineering	engineering	NOUN
fumecheng-11587	434	29	science	science	NOUN
fumecheng-11587	434	30	,	,	PUNCT
fumecheng-11587	434	31	137	137	NUM
fumecheng-11587	434	32	,	,	PUNCT
fumecheng-11587	434	33	pp	pp	ADJ
fumecheng-11587	434	34	.	.	PUNCT
fumecheng-11587	435	1	8	8	NUM
fumecheng-11587	435	2	-	-	SYM
fumecheng-11587	435	3	36	36	NUM
fumecheng-11587	435	4	.	.	PUNCT
fumecheng-11587	436	1	2	2	NUM
fumecheng-11587	436	2	.	.	X
fumecheng-11587	436	3	mahamood	mahamood	PROPN
fumecheng-11587	436	4	,	,	PUNCT
fumecheng-11587	436	5	r.m	r.m	PROPN
fumecheng-11587	436	6	.	.	PROPN
fumecheng-11587	436	7	,	,	PUNCT
fumecheng-11587	436	8	akinlabi	akinlabi	PROPN
fumecheng-11587	436	9	,	,	PUNCT
fumecheng-11587	436	10	e.t	e.t	PROPN
fumecheng-11587	436	11	.	.	PROPN
fumecheng-11587	436	12	,	,	PUNCT
fumecheng-11587	436	13	shukla	shukla	NOUN
fumecheng-11587	436	14	,	,	PUNCT
fumecheng-11587	436	15	m.	m.	NOUN
fumecheng-11587	436	16	,	,	PUNCT
fumecheng-11587	436	17	pityana	pityana	PROPN
fumecheng-11587	436	18	,	,	PUNCT
fumecheng-11587	436	19	s.l	s.l	PROPN
fumecheng-11587	436	20	.	.	PROPN
fumecheng-11587	436	21	,	,	PUNCT
fumecheng-11587	436	22	2012	2012	NUM
fumecheng-11587	436	23	,	,	PUNCT
fumecheng-11587	436	24	functionally	functionally	ADV
fumecheng-11587	436	25	graded	grade	VERB
fumecheng-11587	436	26	material	material	NOUN
fumecheng-11587	436	27	:	:	PUNCT
fumecheng-11587	436	28	an	an	DET
fumecheng-11587	436	29	overview	overview	NOUN
fumecheng-11587	436	30	,	,	PUNCT
fumecheng-11587	436	31	proceedings	proceeding	NOUN
fumecheng-11587	436	32	of	of	ADP
fumecheng-11587	436	33	the	the	DET
fumecheng-11587	436	34	world	world	NOUN
fumecheng-11587	436	35	congress	congress	PROPN
fumecheng-11587	436	36	on	on	ADP
fumecheng-11587	436	37	engineering	engineering	NOUN
fumecheng-11587	436	38	,	,	PUNCT
fumecheng-11587	436	39	vol	vol	NOUN
fumecheng-11587	436	40	.	.	PROPN
fumecheng-11587	437	1	3	3	X
fumecheng-11587	437	2	.	.	X
fumecheng-11587	437	3	london	london	PROPN
fumecheng-11587	437	4	,	,	PUNCT
fumecheng-11587	437	5	uk	uk	PROPN
fumecheng-11587	437	6	:	:	PUNCT
fumecheng-11587	437	7	international	international	ADJ
fumecheng-11587	437	8	association	association	NOUN
fumecheng-11587	437	9	of	of	ADP
fumecheng-11587	437	10	engineers	engineer	NOUN
fumecheng-11587	437	11	(	(	PUNCT
fumecheng-11587	437	12	iaeng	iaeng	NOUN
fumecheng-11587	437	13	)	)	PUNCT
fumecheng-11587	437	14	.	.	PUNCT
fumecheng-11587	438	1	3	3	X
fumecheng-11587	438	2	.	.	X
fumecheng-11587	438	3	peddieson	peddieson	NOUN
fumecheng-11587	438	4	,	,	PUNCT
fumecheng-11587	438	5	j.	j.	PROPN
fumecheng-11587	438	6	,	,	PUNCT
fumecheng-11587	438	7	buchanan	buchanan	PROPN
fumecheng-11587	438	8	,	,	PUNCT
fumecheng-11587	438	9	g.r	g.r	PROPN
fumecheng-11587	438	10	.	.	PROPN
fumecheng-11587	438	11	,	,	PUNCT
fumecheng-11587	438	12	mcnitt	mcnitt	PROPN
fumecheng-11587	438	13	,	,	PUNCT
fumecheng-11587	438	14	r.p	r.p	PROPN
fumecheng-11587	438	15	.	.	PROPN
fumecheng-11587	438	16	,	,	PUNCT
fumecheng-11587	438	17	2003	2003	NUM
fumecheng-11587	438	18	,	,	PUNCT
fumecheng-11587	438	19	application	application	NOUN
fumecheng-11587	438	20	of	of	ADP
fumecheng-11587	438	21	nonlocal	nonlocal	ADJ
fumecheng-11587	438	22	continuum	continuum	ADJ
fumecheng-11587	438	23	models	model	NOUN
fumecheng-11587	438	24	to	to	ADP
fumecheng-11587	438	25	nanotechnology	nanotechnology	NOUN
fumecheng-11587	438	26	,	,	PUNCT
fumecheng-11587	438	27	international	international	ADJ
fumecheng-11587	438	28	journal	journal	NOUN
fumecheng-11587	438	29	of	of	ADP
fumecheng-11587	438	30	engineering	engineering	NOUN
fumecheng-11587	438	31	science	science	NOUN
fumecheng-11587	438	32	,	,	PUNCT
fumecheng-11587	438	33	41(3	41(3	NOUN
fumecheng-11587	438	34	-	-	PUNCT
fumecheng-11587	438	35	5	5	NUM
fumecheng-11587	438	36	)	)	PUNCT
fumecheng-11587	438	37	,	,	PUNCT
fumecheng-11587	438	38	pp	pp	ADJ
fumecheng-11587	438	39	.	.	PUNCT
fumecheng-11587	439	1	305	305	NUM
fumecheng-11587	439	2	-	-	SYM
fumecheng-11587	439	3	312	312	NUM
fumecheng-11587	439	4	.	.	NOUN
fumecheng-11587	439	5	4	4	NUM
fumecheng-11587	439	6	.	.	X
fumecheng-11587	439	7	li	li	PROPN
fumecheng-11587	439	8	,	,	PUNCT
fumecheng-11587	439	9	x.	x.	PROPN
fumecheng-11587	439	10	,	,	PUNCT
fumecheng-11587	439	11	bhushan	bhushan	PROPN
fumecheng-11587	439	12	,	,	PUNCT
fumecheng-11587	439	13	b.	b.	PROPN
fumecheng-11587	439	14	,	,	PUNCT
fumecheng-11587	439	15	takashima	takashima	PROPN
fumecheng-11587	439	16	,	,	PUNCT
fumecheng-11587	439	17	k.	k.	PROPN
fumecheng-11587	439	18	,	,	PUNCT
fumecheng-11587	439	19	baek	baek	PROPN
fumecheng-11587	439	20	,	,	PUNCT
fumecheng-11587	439	21	c.w	c.w	PROPN
fumecheng-11587	439	22	.	.	PROPN
fumecheng-11587	439	23	,	,	PUNCT
fumecheng-11587	439	24	kim	kim	PROPN
fumecheng-11587	439	25	,	,	PUNCT
fumecheng-11587	439	26	y.k	y.k	PROPN
fumecheng-11587	439	27	.	.	PROPN
fumecheng-11587	439	28	,	,	PUNCT
fumecheng-11587	439	29	2003	2003	NUM
fumecheng-11587	439	30	,	,	PUNCT
fumecheng-11587	439	31	mechanical	mechanical	ADJ
fumecheng-11587	439	32	characterization	characterization	NOUN
fumecheng-11587	439	33	of	of	ADP
fumecheng-11587	439	34	micro	micro	ADJ
fumecheng-11587	439	35	/	/	PROPN
fumecheng-11587	439	36	nanoscale	nanoscale	NOUN
fumecheng-11587	439	37	structures	structure	NOUN
fumecheng-11587	439	38	for	for	ADP
fumecheng-11587	439	39	mems	mem	NOUN
fumecheng-11587	439	40	/	/	SYM
fumecheng-11587	439	41	nems	nem	NOUN
fumecheng-11587	439	42	applications	application	NOUN
fumecheng-11587	439	43	using	use	VERB
fumecheng-11587	439	44	nanoindentation	nanoindentation	NOUN
fumecheng-11587	439	45	techniques	technique	NOUN
fumecheng-11587	439	46	,	,	PUNCT
fumecheng-11587	439	47	ultramicroscopy	ultramicroscopy	NOUN
fumecheng-11587	439	48	,	,	PUNCT
fumecheng-11587	439	49	97(1	97(1	NOUN
fumecheng-11587	439	50	-	-	PUNCT
fumecheng-11587	439	51	4	4	NUM
fumecheng-11587	439	52	)	)	PUNCT
fumecheng-11587	439	53	,	,	PUNCT
fumecheng-11587	439	54	pp	pp	ADP
fumecheng-11587	439	55	.	.	PUNCT
fumecheng-11587	440	1	481	481	NUM
fumecheng-11587	440	2	-	-	SYM
fumecheng-11587	440	3	494	494	NUM
fumecheng-11587	440	4	.	.	NOUN
fumecheng-11587	440	5	5	5	NUM
fumecheng-11587	440	6	.	.	X
fumecheng-11587	440	7	najar	najar	PROPN
fumecheng-11587	440	8	,	,	PUNCT
fumecheng-11587	440	9	f.	f.	PROPN
fumecheng-11587	440	10	,	,	PUNCT
fumecheng-11587	440	11	nayfeh	nayfeh	PROPN
fumecheng-11587	440	12	,	,	PUNCT
fumecheng-11587	440	13	a.h	a.h	PROPN
fumecheng-11587	440	14	.	.	PROPN
fumecheng-11587	440	15	,	,	PUNCT
fumecheng-11587	440	16	abdel	abdel	PROPN
fumecheng-11587	440	17	-	-	PUNCT
fumecheng-11587	440	18	rahman	rahman	PROPN
fumecheng-11587	440	19	,	,	PUNCT
fumecheng-11587	440	20	e.m	e.m	PROPN
fumecheng-11587	440	21	.	.	PROPN
fumecheng-11587	440	22	,	,	PUNCT
fumecheng-11587	440	23	choura	choura	NOUN
fumecheng-11587	440	24	,	,	PUNCT
fumecheng-11587	440	25	s.	s.	PROPN
fumecheng-11587	440	26	,	,	PUNCT
fumecheng-11587	440	27	el	el	PROPN
fumecheng-11587	440	28	-	-	PUNCT
fumecheng-11587	440	29	borgi	borgi	NOUN
fumecheng-11587	440	30	,	,	PUNCT
fumecheng-11587	440	31	s.	s.	PROPN
fumecheng-11587	440	32	,	,	PUNCT
fumecheng-11587	440	33	2010	2010	NUM
fumecheng-11587	440	34	,	,	PUNCT
fumecheng-11587	440	35	dynamics	dynamic	NOUN
fumecheng-11587	440	36	and	and	CCONJ
fumecheng-11587	440	37	global	global	ADJ
fumecheng-11587	440	38	stability	stability	NOUN
fumecheng-11587	440	39	of	of	ADP
fumecheng-11587	440	40	beam	beam	NOUN
fumecheng-11587	440	41	-	-	PUNCT
fumecheng-11587	440	42	based	base	VERB
fumecheng-11587	440	43	electrostatic	electrostatic	ADJ
fumecheng-11587	440	44	microactuators	microactuator	NOUN
fumecheng-11587	440	45	,	,	PUNCT
fumecheng-11587	440	46	journal	journal	NOUN
fumecheng-11587	440	47	of	of	ADP
fumecheng-11587	440	48	vibration	vibration	NOUN
fumecheng-11587	440	49	and	and	CCONJ
fumecheng-11587	440	50	control	control	NOUN
fumecheng-11587	440	51	,	,	PUNCT
fumecheng-11587	440	52	16(5	16(5	NUM
fumecheng-11587	440	53	)	)	PUNCT
fumecheng-11587	440	54	,	,	PUNCT
fumecheng-11587	440	55	pp	pp	PROPN
fumecheng-11587	440	56	.	.	PUNCT
fumecheng-11587	441	1	721	721	NUM
fumecheng-11587	441	2	-	-	SYM
fumecheng-11587	441	3	748	748	NUM
fumecheng-11587	441	4	.	.	NOUN
fumecheng-11587	442	1	6	6	NUM
fumecheng-11587	442	2	.	.	X
fumecheng-11587	443	1	zavracky	zavracky	ADJ
fumecheng-11587	443	2	,	,	PUNCT
fumecheng-11587	443	3	p.m.	p.m.	NOUN
fumecheng-11587	443	4	,	,	PUNCT
fumecheng-11587	443	5	mcgruer	mcgruer	PROPN
fumecheng-11587	443	6	,	,	PUNCT
fumecheng-11587	443	7	n.e	n.e	PROPN
fumecheng-11587	443	8	.	.	PROPN
fumecheng-11587	443	9	,	,	PUNCT
fumecheng-11587	443	10	morrison	morrison	PROPN
fumecheng-11587	443	11	,	,	PUNCT
fumecheng-11587	443	12	r.h	r.h	PROPN
fumecheng-11587	443	13	.	.	PROPN
fumecheng-11587	443	14	,	,	PUNCT
fumecheng-11587	443	15	potter	potter	PROPN
fumecheng-11587	443	16	,	,	PUNCT
fumecheng-11587	443	17	d.	d.	PROPN
fumecheng-11587	443	18	,	,	PUNCT
fumecheng-11587	443	19	1999	1999	NUM
fumecheng-11587	443	20	,	,	PUNCT
fumecheng-11587	443	21	microswitches	microswitche	NOUN
fumecheng-11587	443	22	and	and	CCONJ
fumecheng-11587	443	23	microrelays	microrelay	NOUN
fumecheng-11587	443	24	with	with	ADP
fumecheng-11587	443	25	a	a	DET
fumecheng-11587	443	26	view	view	NOUN
fumecheng-11587	443	27	toward	toward	ADP
fumecheng-11587	443	28	microwave	microwave	NOUN
fumecheng-11587	443	29	applications	application	NOUN
fumecheng-11587	443	30	,	,	PUNCT
fumecheng-11587	443	31	international	international	ADJ
fumecheng-11587	443	32	journal	journal	NOUN
fumecheng-11587	443	33	of	of	ADP
fumecheng-11587	443	34	rf	rf	NOUN
fumecheng-11587	443	35	and	and	CCONJ
fumecheng-11587	443	36	microwave	microwave	NOUN
fumecheng-11587	443	37	computer‐aided	computer‐aide	VERB
fumecheng-11587	443	38	engineering	engineering	NOUN
fumecheng-11587	443	39	,	,	PUNCT
fumecheng-11587	443	40	9(4	9(4	NUM
fumecheng-11587	443	41	)	)	PUNCT
fumecheng-11587	443	42	,	,	PUNCT
fumecheng-11587	443	43	pp	pp	PROPN
fumecheng-11587	443	44	.	.	PUNCT
fumecheng-11587	444	1	338	338	NUM
fumecheng-11587	444	2	-	-	SYM
fumecheng-11587	444	3	347	347	NUM
fumecheng-11587	444	4	.	.	PUNCT
fumecheng-11587	445	1	7	7	X
fumecheng-11587	445	2	.	.	X
fumecheng-11587	445	3	moser	moser	PROPN
fumecheng-11587	445	4	,	,	PUNCT
fumecheng-11587	445	5	y.	y.	PROPN
fumecheng-11587	445	6	,	,	PUNCT
fumecheng-11587	445	7	gijs	gijs	NOUN
fumecheng-11587	445	8	,	,	PUNCT
fumecheng-11587	445	9	m.a	m.a	PROPN
fumecheng-11587	445	10	.	.	PROPN
fumecheng-11587	445	11	,	,	PUNCT
fumecheng-11587	445	12	2007	2007	NUM
fumecheng-11587	445	13	,	,	PUNCT
fumecheng-11587	445	14	miniaturized	miniaturize	VERB
fumecheng-11587	445	15	flexible	flexible	ADJ
fumecheng-11587	445	16	temperature	temperature	NOUN
fumecheng-11587	445	17	sensor	sensor	NOUN
fumecheng-11587	445	18	,	,	PUNCT
fumecheng-11587	445	19	journal	journal	NOUN
fumecheng-11587	445	20	of	of	ADP
fumecheng-11587	445	21	microelectromechanical	microelectromechanical	ADJ
fumecheng-11587	445	22	systems	system	NOUN
fumecheng-11587	445	23	,	,	PUNCT
fumecheng-11587	445	24	16(6	16(6	NUM
fumecheng-11587	445	25	)	)	PUNCT
fumecheng-11587	445	26	,	,	PUNCT
fumecheng-11587	445	27	pp	pp	PROPN
fumecheng-11587	445	28	.	.	PUNCT
fumecheng-11587	446	1	1349	1349	NUM
fumecheng-11587	446	2	-	-	SYM
fumecheng-11587	446	3	1354	1354	NUM
fumecheng-11587	446	4	.	.	PUNCT
fumecheng-11587	447	1	8	8	NUM
fumecheng-11587	447	2	.	.	PUNCT
fumecheng-11587	447	3	ceballes	ceballe	NOUN
fumecheng-11587	447	4	,	,	PUNCT
fumecheng-11587	447	5	s.	s.	PROPN
fumecheng-11587	447	6	,	,	PUNCT
fumecheng-11587	447	7	abdelkefi	abdelkefi	PROPN
fumecheng-11587	447	8	,	,	PUNCT
fumecheng-11587	447	9	a.	a.	NOUN
fumecheng-11587	447	10	,	,	PUNCT
fumecheng-11587	447	11	2021	2021	NUM
fumecheng-11587	447	12	,	,	PUNCT
fumecheng-11587	447	13	uncertainty	uncertainty	NOUN
fumecheng-11587	447	14	analysis	analysis	NOUN
fumecheng-11587	447	15	and	and	CCONJ
fumecheng-11587	447	16	stochastic	stochastic	ADJ
fumecheng-11587	447	17	characterization	characterization	NOUN
fumecheng-11587	447	18	of	of	ADP
fumecheng-11587	447	19	carbon	carbon	NOUN
fumecheng-11587	447	20	nanotube	nanotube	NOUN
fumecheng-11587	447	21	-	-	PUNCT
fumecheng-11587	447	22	based	base	VERB
fumecheng-11587	447	23	mass	mass	NOUN
fumecheng-11587	447	24	sensor	sensor	NOUN
fumecheng-11587	447	25	with	with	ADP
fumecheng-11587	447	26	multiple	multiple	ADJ
fumecheng-11587	447	27	deposited	deposit	VERB
fumecheng-11587	447	28	nanoparticles	nanoparticle	NOUN
fumecheng-11587	447	29	,	,	PUNCT
fumecheng-11587	447	30	sensors	sensor	NOUN
fumecheng-11587	447	31	and	and	CCONJ
fumecheng-11587	447	32	actuators	actuator	NOUN
fumecheng-11587	447	33	a	a	DET
fumecheng-11587	447	34	:	:	PUNCT
fumecheng-11587	447	35	physical	physical	ADJ
fumecheng-11587	447	36	,	,	PUNCT
fumecheng-11587	447	37	332(2	332(2	NUM
fumecheng-11587	447	38	)	)	PUNCT
fumecheng-11587	447	39	,	,	PUNCT
fumecheng-11587	447	40	113182	113182	NUM
fumecheng-11587	447	41	.	.	PUNCT
fumecheng-11587	448	1	9	9	X
fumecheng-11587	448	2	.	.	X
fumecheng-11587	449	1	he	he	PRON
fumecheng-11587	449	2	,	,	PUNCT
fumecheng-11587	449	3	x.q	x.q	PROPN
fumecheng-11587	449	4	.	.	PROPN
fumecheng-11587	449	5	,	,	PUNCT
fumecheng-11587	449	6	kitipornchai	kitipornchai	PROPN
fumecheng-11587	449	7	,	,	PUNCT
fumecheng-11587	449	8	s.	s.	PROPN
fumecheng-11587	449	9	,	,	PUNCT
fumecheng-11587	449	10	liew	liew	PROPN
fumecheng-11587	449	11	,	,	PUNCT
fumecheng-11587	449	12	k.m	k.m	PROPN
fumecheng-11587	449	13	.	.	PROPN
fumecheng-11587	449	14	,	,	PUNCT
fumecheng-11587	449	15	2005	2005	NUM
fumecheng-11587	449	16	,	,	PUNCT
fumecheng-11587	449	17	resonance	resonance	NOUN
fumecheng-11587	449	18	analysis	analysis	NOUN
fumecheng-11587	449	19	of	of	ADP
fumecheng-11587	449	20	multi	multi	ADJ
fumecheng-11587	449	21	-	-	ADJ
fumecheng-11587	449	22	layered	layered	ADJ
fumecheng-11587	449	23	graphene	graphene	NOUN
fumecheng-11587	449	24	sheets	sheet	NOUN
fumecheng-11587	449	25	used	use	VERB
fumecheng-11587	449	26	as	as	ADP
fumecheng-11587	449	27	nanoscale	nanoscale	NOUN
fumecheng-11587	449	28	resonators	resonator	NOUN
fumecheng-11587	449	29	,	,	PUNCT
fumecheng-11587	449	30	nanotechnology	nanotechnology	NOUN
fumecheng-11587	449	31	,	,	PUNCT
fumecheng-11587	449	32	16(10	16(10	NOUN
fumecheng-11587	449	33	)	)	PUNCT
fumecheng-11587	449	34	,	,	PUNCT
fumecheng-11587	449	35	2086	2086	NUM
fumecheng-11587	449	36	.	.	PUNCT
fumecheng-11587	450	1	10	10	NUM
fumecheng-11587	450	2	.	.	X
fumecheng-11587	451	1	wang	wang	PROPN
fumecheng-11587	451	2	,	,	PUNCT
fumecheng-11587	451	3	z.l	z.l	PROPN
fumecheng-11587	451	4	.	.	PROPN
fumecheng-11587	451	5	,	,	PUNCT
fumecheng-11587	451	6	wu	wu	PROPN
fumecheng-11587	451	7	,	,	PUNCT
fumecheng-11587	451	8	w.	w.	PROPN
fumecheng-11587	451	9	,	,	PUNCT
fumecheng-11587	451	10	2012	2012	NUM
fumecheng-11587	451	11	,	,	PUNCT
fumecheng-11587	451	12	nanotechnology‐enabled	nanotechnology‐enable	VERB
fumecheng-11587	451	13	energy	energy	NOUN
fumecheng-11587	451	14	harvesting	harvesting	NOUN
fumecheng-11587	451	15	for	for	ADP
fumecheng-11587	451	16	self‐powered	self‐powere	VERB
fumecheng-11587	451	17	micro‐	micro‐	PROPN
fumecheng-11587	451	18	/nanosystems	/nanosystems	PROPN
fumecheng-11587	451	19	,	,	PUNCT
fumecheng-11587	451	20	angewandte	angewandte	PROPN
fumecheng-11587	451	21	chemie	chemie	PROPN
fumecheng-11587	451	22	international	international	PROPN
fumecheng-11587	451	23	edition	edition	PROPN
fumecheng-11587	451	24	,	,	PUNCT
fumecheng-11587	451	25	51(47	51(47	NUM
fumecheng-11587	451	26	)	)	PUNCT
fumecheng-11587	451	27	,	,	PUNCT
fumecheng-11587	451	28	pp	pp	PROPN
fumecheng-11587	451	29	.	.	PUNCT
fumecheng-11587	451	30	11700	11700	NUM
fumecheng-11587	451	31	-	-	SYM
fumecheng-11587	451	32	11721	11721	NUM
fumecheng-11587	451	33	.	.	PUNCT
fumecheng-11587	452	1	11	11	NUM
fumecheng-11587	452	2	.	.	PUNCT
fumecheng-11587	453	1	khan	khan	PROPN
fumecheng-11587	453	2	,	,	PUNCT
fumecheng-11587	453	3	a.a	a.a	PROPN
fumecheng-11587	453	4	.	.	PROPN
fumecheng-11587	453	5	,	,	PUNCT
fumecheng-11587	453	6	khan	khan	PROPN
fumecheng-11587	453	7	,	,	PUNCT
fumecheng-11587	453	8	i.u	i.u	PROPN
fumecheng-11587	453	9	.	.	PROPN
fumecheng-11587	453	10	,	,	PUNCT
fumecheng-11587	453	11	noman	noman	PROPN
fumecheng-11587	453	12	,	,	PUNCT
fumecheng-11587	453	13	m.	m.	NOUN
fumecheng-11587	453	14	,	,	PUNCT
fumecheng-11587	453	15	khan	khan	PROPN
fumecheng-11587	453	16	,	,	PUNCT
fumecheng-11587	453	17	u.a	u.a	PROPN
fumecheng-11587	453	18	.	.	PROPN
fumecheng-11587	453	19	and	and	CCONJ
fumecheng-11587	453	20	bilal	bilal	PROPN
fumecheng-11587	453	21	,	,	PUNCT
fumecheng-11587	453	22	m.	m.	NOUN
fumecheng-11587	453	23	,	,	PUNCT
fumecheng-11587	453	24	2022	2022	NUM
fumecheng-11587	453	25	,	,	PUNCT
fumecheng-11587	453	26	performance	performance	NOUN
fumecheng-11587	453	27	evaluation	evaluation	NOUN
fumecheng-11587	453	28	of	of	ADP
fumecheng-11587	453	29	flexible	flexible	ADJ
fumecheng-11587	453	30	pavement	pavement	NOUN
fumecheng-11587	453	31	using	use	VERB
fumecheng-11587	453	32	carbon	carbon	NOUN
fumecheng-11587	453	33	nanotubes	nanotube	NOUN
fumecheng-11587	453	34	and	and	CCONJ
fumecheng-11587	453	35	plastic	plastic	ADJ
fumecheng-11587	453	36	waste	waste	NOUN
fumecheng-11587	453	37	as	as	ADP
fumecheng-11587	453	38	admixtures	admixture	NOUN
fumecheng-11587	453	39	,	,	PUNCT
fumecheng-11587	453	40	tehnički	tehnički	PROPN
fumecheng-11587	453	41	vjesnik	vjesnik	PROPN
fumecheng-11587	453	42	,	,	PUNCT
fumecheng-11587	453	43	29(1	29(1	NUM
fumecheng-11587	453	44	)	)	PUNCT
fumecheng-11587	453	45	,	,	PUNCT
fumecheng-11587	453	46	pp	pp	ADP
fumecheng-11587	453	47	.	.	PUNCT
fumecheng-11587	454	1	9	9	NUM
fumecheng-11587	454	2	-	-	SYM
fumecheng-11587	454	3	14	14	NUM
fumecheng-11587	454	4	.	.	PUNCT
fumecheng-11587	455	1	12	12	NUM
fumecheng-11587	455	2	.	.	PUNCT
fumecheng-11587	456	1	moory	moory	NOUN
fumecheng-11587	456	2	-	-	PUNCT
fumecheng-11587	456	3	shirbani	shirbani	PROPN
fumecheng-11587	456	4	,	,	PUNCT
fumecheng-11587	456	5	m.	m.	NOUN
fumecheng-11587	456	6	,	,	PUNCT
fumecheng-11587	456	7	sedighi	sedighi	PROPN
fumecheng-11587	456	8	,	,	PUNCT
fumecheng-11587	456	9	h.m	h.m	PROPN
fumecheng-11587	456	10	.	.	PROPN
fumecheng-11587	456	11	,	,	PUNCT
fumecheng-11587	456	12	ouakad	ouakad	VERB
fumecheng-11587	456	13	,	,	PUNCT
fumecheng-11587	456	14	h.m	h.m	PROPN
fumecheng-11587	456	15	.	.	PROPN
fumecheng-11587	456	16	,	,	PUNCT
fumecheng-11587	456	17	najar	najar	PROPN
fumecheng-11587	456	18	,	,	PUNCT
fumecheng-11587	456	19	f.	f.	PROPN
fumecheng-11587	456	20	,	,	PUNCT
fumecheng-11587	456	21	2018	2018	NUM
fumecheng-11587	456	22	,	,	PUNCT
fumecheng-11587	456	23	experimental	experimental	ADJ
fumecheng-11587	456	24	and	and	CCONJ
fumecheng-11587	456	25	mathematical	mathematical	ADJ
fumecheng-11587	456	26	analysis	analysis	NOUN
fumecheng-11587	456	27	of	of	ADP
fumecheng-11587	456	28	a	a	DET
fumecheng-11587	456	29	piezoelectrically	piezoelectrically	ADV
fumecheng-11587	456	30	actuated	actuate	VERB
fumecheng-11587	456	31	multilayered	multilayere	VERB
fumecheng-11587	456	32	imperfect	imperfect	ADJ
fumecheng-11587	456	33	microbeam	microbeam	NOUN
fumecheng-11587	456	34	subjected	subject	VERB
fumecheng-11587	456	35	to	to	ADP
fumecheng-11587	456	36	applied	apply	VERB
fumecheng-11587	456	37	electric	electric	ADJ
fumecheng-11587	456	38	potential	potential	ADJ
fumecheng-11587	456	39	,	,	PUNCT
fumecheng-11587	456	40	composite	composite	ADJ
fumecheng-11587	456	41	structures	structure	NOUN
fumecheng-11587	456	42	,	,	PUNCT
fumecheng-11587	456	43	184	184	NUM
fumecheng-11587	456	44	,	,	PUNCT
fumecheng-11587	456	45	pp	pp	ADJ
fumecheng-11587	456	46	.	.	PUNCT
fumecheng-11587	457	1	950	950	NUM
fumecheng-11587	457	2	-	-	SYM
fumecheng-11587	457	3	960	960	NUM
fumecheng-11587	457	4	.	.	NOUN
fumecheng-11587	458	1	13	13	NUM
fumecheng-11587	458	2	.	.	PUNCT
fumecheng-11587	459	1	lam	lam	PROPN
fumecheng-11587	459	2	,	,	PUNCT
fumecheng-11587	459	3	d.c	d.c	PROPN
fumecheng-11587	459	4	.	.	PROPN
fumecheng-11587	459	5	,	,	PUNCT
fumecheng-11587	459	6	yang	yang	PROPN
fumecheng-11587	459	7	,	,	PUNCT
fumecheng-11587	459	8	f.	f.	PROPN
fumecheng-11587	459	9	,	,	PUNCT
fumecheng-11587	459	10	chong	chong	PROPN
fumecheng-11587	459	11	,	,	PUNCT
fumecheng-11587	459	12	a.c.m	a.c.m	PROPN
fumecheng-11587	459	13	.	.	PROPN
fumecheng-11587	459	14	,	,	PUNCT
fumecheng-11587	459	15	wang	wang	PROPN
fumecheng-11587	459	16	,	,	PUNCT
fumecheng-11587	459	17	j.	j.	PROPN
fumecheng-11587	459	18	,	,	PUNCT
fumecheng-11587	459	19	tong	tong	PROPN
fumecheng-11587	459	20	,	,	PUNCT
fumecheng-11587	459	21	p.	p.	PROPN
fumecheng-11587	459	22	,	,	PUNCT
fumecheng-11587	459	23	2003	2003	NUM
fumecheng-11587	459	24	,	,	PUNCT
fumecheng-11587	459	25	experiments	experiment	NOUN
fumecheng-11587	459	26	and	and	CCONJ
fumecheng-11587	459	27	theory	theory	NOUN
fumecheng-11587	459	28	in	in	ADP
fumecheng-11587	459	29	strain	strain	NOUN
fumecheng-11587	459	30	gradient	gradient	ADJ
fumecheng-11587	459	31	elasticity	elasticity	NOUN
fumecheng-11587	459	32	,	,	PUNCT
fumecheng-11587	459	33	journal	journal	NOUN
fumecheng-11587	459	34	of	of	ADP
fumecheng-11587	459	35	the	the	DET
fumecheng-11587	459	36	mechanics	mechanic	NOUN
fumecheng-11587	459	37	and	and	CCONJ
fumecheng-11587	459	38	physics	physic	NOUN
fumecheng-11587	459	39	of	of	ADP
fumecheng-11587	459	40	solids	solid	NOUN
fumecheng-11587	459	41	,	,	PUNCT
fumecheng-11587	459	42	51(8	51(8	NUM
fumecheng-11587	459	43	)	)	PUNCT
fumecheng-11587	459	44	,	,	PUNCT
fumecheng-11587	459	45	pp	pp	ADP
fumecheng-11587	459	46	.	.	PUNCT
fumecheng-11587	460	1	1477	1477	NUM
fumecheng-11587	460	2	-	-	SYM
fumecheng-11587	460	3	1508	1508	NUM
fumecheng-11587	460	4	.	.	PUNCT
fumecheng-11587	461	1	vibration	vibration	NOUN
fumecheng-11587	461	2	and	and	CCONJ
fumecheng-11587	461	3	stability	stability	NOUN
fumecheng-11587	461	4	of	of	ADP
fumecheng-11587	461	5	a	a	DET
fumecheng-11587	461	6	nonlinear	nonlinear	ADJ
fumecheng-11587	461	7	nonlocal	nonlocal	ADJ
fumecheng-11587	461	8	strain	strain	NOUN
fumecheng-11587	461	9	-	-	PUNCT
fumecheng-11587	461	10	gradient	gradient	NOUN
fumecheng-11587	461	11	fg	fg	PROPN
fumecheng-11587	461	12	beam	beam	NOUN
fumecheng-11587	461	13	on	on	ADP
fumecheng-11587	461	14	a	a	DET
fumecheng-11587	461	15	visco	visco	ADJ
fumecheng-11587	461	16	-	-	PUNCT
fumecheng-11587	461	17	pasternak	pasternak	NOUN
fumecheng-11587	461	18	...	...	PUNCT
fumecheng-11587	461	19	731	731	NUM
fumecheng-11587	461	20	14	14	NUM
fumecheng-11587	461	21	.	.	PUNCT
fumecheng-11587	462	1	mehralian	mehralian	PROPN
fumecheng-11587	462	2	,	,	PUNCT
fumecheng-11587	462	3	f.	f.	PROPN
fumecheng-11587	462	4	,	,	PUNCT
fumecheng-11587	462	5	beni	beni	PROPN
fumecheng-11587	462	6	,	,	PUNCT
fumecheng-11587	462	7	y.t	y.t	PROPN
fumecheng-11587	462	8	.	.	PROPN
fumecheng-11587	462	9	,	,	PUNCT
fumecheng-11587	462	10	zeverdejani	zeverdejani	NOUN
fumecheng-11587	462	11	,	,	PUNCT
fumecheng-11587	462	12	m.k	m.k	PROPN
fumecheng-11587	462	13	.	.	PROPN
fumecheng-11587	462	14	,	,	PUNCT
fumecheng-11587	462	15	2017	2017	NUM
fumecheng-11587	462	16	,	,	PUNCT
fumecheng-11587	462	17	calibration	calibration	NOUN
fumecheng-11587	462	18	of	of	ADP
fumecheng-11587	462	19	nonlocal	nonlocal	ADJ
fumecheng-11587	462	20	strain	strain	NOUN
fumecheng-11587	462	21	gradient	gradient	ADJ
fumecheng-11587	462	22	shell	shell	NOUN
fumecheng-11587	462	23	model	model	NOUN
fumecheng-11587	462	24	for	for	ADP
fumecheng-11587	462	25	buckling	buckle	VERB
fumecheng-11587	462	26	analysis	analysis	NOUN
fumecheng-11587	462	27	of	of	ADP
fumecheng-11587	462	28	nanotubes	nanotube	NOUN
fumecheng-11587	462	29	using	use	VERB
fumecheng-11587	462	30	molecular	molecular	ADJ
fumecheng-11587	462	31	dynamics	dynamic	NOUN
fumecheng-11587	462	32	simulations	simulation	NOUN
fumecheng-11587	462	33	,	,	PUNCT
fumecheng-11587	462	34	physica	physica	NOUN
fumecheng-11587	462	35	b	b	PROPN
fumecheng-11587	462	36	:	:	PUNCT
fumecheng-11587	462	37	condensed	condense	VERB
fumecheng-11587	462	38	matter	matter	NOUN
fumecheng-11587	462	39	,	,	PUNCT
fumecheng-11587	462	40	521	521	NUM
fumecheng-11587	462	41	,	,	PUNCT
fumecheng-11587	462	42	pp	pp	ADJ
fumecheng-11587	462	43	.	.	PUNCT
fumecheng-11587	463	1	102	102	NUM
fumecheng-11587	463	2	-	-	SYM
fumecheng-11587	463	3	111	111	NUM
fumecheng-11587	463	4	.	.	PUNCT
fumecheng-11587	463	5	15	15	NUM
fumecheng-11587	463	6	.	.	PUNCT
fumecheng-11587	464	1	el	el	NOUN
fumecheng-11587	464	2	-	-	PUNCT
fumecheng-11587	464	3	borgi	borgi	NOUN
fumecheng-11587	464	4	,	,	PUNCT
fumecheng-11587	464	5	s.	s.	PROPN
fumecheng-11587	464	6	,	,	PUNCT
fumecheng-11587	464	7	fernandes	fernandes	PROPN
fumecheng-11587	464	8	,	,	PUNCT
fumecheng-11587	464	9	r.	r.	PROPN
fumecheng-11587	464	10	,	,	PUNCT
fumecheng-11587	464	11	reddy	reddy	PROPN
fumecheng-11587	464	12	,	,	PUNCT
fumecheng-11587	464	13	j.n	j.n	PROPN
fumecheng-11587	464	14	.	.	PROPN
fumecheng-11587	464	15	,	,	PUNCT
fumecheng-11587	464	16	2015	2015	NUM
fumecheng-11587	464	17	,	,	PUNCT
fumecheng-11587	464	18	non	non	ADJ
fumecheng-11587	464	19	-	-	ADJ
fumecheng-11587	464	20	local	local	ADJ
fumecheng-11587	464	21	free	free	ADJ
fumecheng-11587	464	22	and	and	CCONJ
fumecheng-11587	464	23	forced	forced	ADJ
fumecheng-11587	464	24	vibrations	vibration	NOUN
fumecheng-11587	464	25	of	of	ADP
fumecheng-11587	464	26	graded	grade	VERB
fumecheng-11587	464	27	nanobeams	nanobeam	NOUN
fumecheng-11587	464	28	resting	rest	VERB
fumecheng-11587	464	29	on	on	ADP
fumecheng-11587	464	30	a	a	DET
fumecheng-11587	464	31	non	non	ADJ
fumecheng-11587	464	32	-	-	ADJ
fumecheng-11587	464	33	linear	linear	ADJ
fumecheng-11587	464	34	elastic	elastic	ADJ
fumecheng-11587	464	35	foundation	foundation	NOUN
fumecheng-11587	464	36	,	,	PUNCT
fumecheng-11587	464	37	international	international	ADJ
fumecheng-11587	464	38	journal	journal	NOUN
fumecheng-11587	464	39	of	of	ADP
fumecheng-11587	464	40	non	non	ADJ
fumecheng-11587	464	41	-	-	ADJ
fumecheng-11587	464	42	linear	linear	ADJ
fumecheng-11587	464	43	mechanics	mechanic	NOUN
fumecheng-11587	464	44	,	,	PUNCT
fumecheng-11587	464	45	77	77	NUM
fumecheng-11587	464	46	,	,	PUNCT
fumecheng-11587	464	47	pp	pp	ADJ
fumecheng-11587	464	48	.	.	PUNCT
fumecheng-11587	465	1	348	348	NUM
fumecheng-11587	465	2	-	-	SYM
fumecheng-11587	465	3	363	363	NUM
fumecheng-11587	465	4	.	.	PUNCT
fumecheng-11587	466	1	16	16	NUM
fumecheng-11587	466	2	.	.	PUNCT
fumecheng-11587	467	1	fan	fan	PROPN
fumecheng-11587	467	2	,	,	PUNCT
fumecheng-11587	467	3	y.	y.	PROPN
fumecheng-11587	467	4	,	,	PUNCT
fumecheng-11587	467	5	xiang	xiang	PROPN
fumecheng-11587	467	6	,	,	PUNCT
fumecheng-11587	467	7	y.	y.	PROPN
fumecheng-11587	467	8	,	,	PUNCT
fumecheng-11587	467	9	shen	shen	PROPN
fumecheng-11587	467	10	,	,	PUNCT
fumecheng-11587	467	11	h.s	h.s	PROPN
fumecheng-11587	467	12	.	.	PROPN
fumecheng-11587	467	13	,	,	PUNCT
fumecheng-11587	467	14	2020	2020	NUM
fumecheng-11587	467	15	,	,	PUNCT
fumecheng-11587	467	16	nonlinear	nonlinear	ADJ
fumecheng-11587	467	17	dynamics	dynamic	NOUN
fumecheng-11587	467	18	of	of	ADP
fumecheng-11587	467	19	temperature	temperature	NOUN
fumecheng-11587	467	20	-	-	PUNCT
fumecheng-11587	467	21	dependent	dependent	ADJ
fumecheng-11587	467	22	fg	fg	ADJ
fumecheng-11587	467	23	-	-	PUNCT
fumecheng-11587	467	24	grc	grc	NOUN
fumecheng-11587	467	25	laminated	laminate	VERB
fumecheng-11587	467	26	beams	beam	NOUN
fumecheng-11587	467	27	resting	rest	VERB
fumecheng-11587	467	28	on	on	ADP
fumecheng-11587	467	29	visco	visco	ADJ
fumecheng-11587	467	30	-	-	ADJ
fumecheng-11587	467	31	pasternak	pasternak	ADJ
fumecheng-11587	467	32	foundations	foundation	NOUN
fumecheng-11587	467	33	,	,	PUNCT
fumecheng-11587	467	34	international	international	ADJ
fumecheng-11587	467	35	journal	journal	NOUN
fumecheng-11587	467	36	of	of	ADP
fumecheng-11587	467	37	structural	structural	ADJ
fumecheng-11587	467	38	stability	stability	NOUN
fumecheng-11587	467	39	and	and	CCONJ
fumecheng-11587	467	40	dynamics	dynamic	NOUN
fumecheng-11587	467	41	,	,	PUNCT
fumecheng-11587	467	42	20(01	20(01	NOUN
fumecheng-11587	467	43	)	)	PUNCT
fumecheng-11587	467	44	,	,	PUNCT
fumecheng-11587	467	45	2050012	2050012	NUM
fumecheng-11587	467	46	.	.	PUNCT
fumecheng-11587	468	1	17	17	NUM
fumecheng-11587	468	2	.	.	X
fumecheng-11587	469	1	reddy	reddy	PROPN
fumecheng-11587	469	2	,	,	PUNCT
fumecheng-11587	469	3	j.	j.	PROPN
fumecheng-11587	469	4	,	,	PUNCT
fumecheng-11587	469	5	2007	2007	NUM
fumecheng-11587	469	6	,	,	PUNCT
fumecheng-11587	469	7	nonlocal	nonlocal	ADJ
fumecheng-11587	469	8	theories	theory	NOUN
fumecheng-11587	469	9	for	for	ADP
fumecheng-11587	469	10	bending	bend	VERB
fumecheng-11587	469	11	,	,	PUNCT
fumecheng-11587	469	12	buckling	buckling	NOUN
fumecheng-11587	469	13	and	and	CCONJ
fumecheng-11587	469	14	vibration	vibration	NOUN
fumecheng-11587	469	15	of	of	ADP
fumecheng-11587	469	16	beams	beam	NOUN
fumecheng-11587	469	17	,	,	PUNCT
fumecheng-11587	469	18	international	international	ADJ
fumecheng-11587	469	19	journal	journal	NOUN
fumecheng-11587	469	20	of	of	ADP
fumecheng-11587	469	21	engineering	engineering	NOUN
fumecheng-11587	469	22	science	science	NOUN
fumecheng-11587	469	23	,	,	PUNCT
fumecheng-11587	469	24	45(2	45(2	NOUN
fumecheng-11587	469	25	-	-	NOUN
fumecheng-11587	469	26	8)	8)	NUM
fumecheng-11587	469	27	,	,	PUNCT
fumecheng-11587	469	28	pp	pp	ADJ
fumecheng-11587	469	29	.	.	PUNCT
fumecheng-11587	470	1	288	288	NUM
fumecheng-11587	470	2	-	-	SYM
fumecheng-11587	470	3	307	307	NUM
fumecheng-11587	470	4	.	.	PUNCT
fumecheng-11587	471	1	18	18	NUM
fumecheng-11587	471	2	.	.	PUNCT
fumecheng-11587	472	1	pradhan	pradhan	PROPN
fumecheng-11587	472	2	,	,	PUNCT
fumecheng-11587	472	3	s.c	s.c	PROPN
fumecheng-11587	472	4	.	.	PROPN
fumecheng-11587	472	5	,	,	PUNCT
fumecheng-11587	472	6	phadikar	phadikar	PROPN
fumecheng-11587	472	7	,	,	PUNCT
fumecheng-11587	472	8	j.k	j.k	PROPN
fumecheng-11587	472	9	.	.	PROPN
fumecheng-11587	472	10	,	,	PUNCT
fumecheng-11587	472	11	2009	2009	NUM
fumecheng-11587	472	12	,	,	PUNCT
fumecheng-11587	472	13	nonlocal	nonlocal	ADJ
fumecheng-11587	472	14	elasticity	elasticity	NOUN
fumecheng-11587	472	15	theory	theory	NOUN
fumecheng-11587	472	16	for	for	ADP
fumecheng-11587	472	17	vibration	vibration	NOUN
fumecheng-11587	472	18	of	of	ADP
fumecheng-11587	472	19	nanoplates	nanoplate	NOUN
fumecheng-11587	472	20	,	,	PUNCT
fumecheng-11587	472	21	journal	journal	NOUN
fumecheng-11587	472	22	of	of	ADP
fumecheng-11587	472	23	sound	sound	NOUN
fumecheng-11587	472	24	and	and	CCONJ
fumecheng-11587	472	25	vibration	vibration	NOUN
fumecheng-11587	472	26	,	,	PUNCT
fumecheng-11587	472	27	325(1	325(1	NUM
fumecheng-11587	472	28	-	-	SYM
fumecheng-11587	472	29	2	2	NUM
fumecheng-11587	472	30	)	)	PUNCT
fumecheng-11587	472	31	,	,	PUNCT
fumecheng-11587	472	32	pp	pp	ADJ
fumecheng-11587	472	33	.	.	PUNCT
fumecheng-11587	473	1	206	206	NUM
fumecheng-11587	473	2	-	-	SYM
fumecheng-11587	473	3	223	223	NUM
fumecheng-11587	473	4	.	.	PUNCT
fumecheng-11587	474	1	19	19	NUM
fumecheng-11587	474	2	.	.	PUNCT
fumecheng-11587	474	3	limkatanyu	limkatanyu	PROPN
fumecheng-11587	474	4	,	,	PUNCT
fumecheng-11587	474	5	s.	s.	PROPN
fumecheng-11587	474	6	,	,	PUNCT
fumecheng-11587	474	7	sae	sae	PROPN
fumecheng-11587	474	8	-	-	PROPN
fumecheng-11587	474	9	long	long	ADV
fumecheng-11587	474	10	,	,	PUNCT
fumecheng-11587	474	11	w.	w.	PROPN
fumecheng-11587	474	12	,	,	PUNCT
fumecheng-11587	474	13	rungamornrat	rungamornrat	PROPN
fumecheng-11587	474	14	,	,	PUNCT
fumecheng-11587	474	15	j.	j.	PROPN
fumecheng-11587	474	16	,	,	PUNCT
fumecheng-11587	474	17	buachart	buachart	NOUN
fumecheng-11587	474	18	,	,	PUNCT
fumecheng-11587	474	19	c.	c.	NOUN
fumecheng-11587	474	20	,	,	PUNCT
fumecheng-11587	474	21	sukontasukkul	sukontasukkul	NOUN
fumecheng-11587	474	22	,	,	PUNCT
fumecheng-11587	474	23	p.	p.	NOUN
fumecheng-11587	474	24	,	,	PUNCT
fumecheng-11587	474	25	keawsawasvong	keawsawasvong	PROPN
fumecheng-11587	474	26	,	,	PUNCT
fumecheng-11587	474	27	s.	s.	PROPN
fumecheng-11587	474	28	and	and	CCONJ
fumecheng-11587	474	29	chindaprasirt	chindaprasirt	PROPN
fumecheng-11587	474	30	,	,	PUNCT
fumecheng-11587	474	31	p.	p.	NOUN
fumecheng-11587	474	32	,	,	PUNCT
fumecheng-11587	474	33	2022	2022	NUM
fumecheng-11587	474	34	.	.	PUNCT
fumecheng-11587	475	1	bending	bend	VERB
fumecheng-11587	475	2	,	,	PUNCT
fumecheng-11587	475	3	buckling	buckle	VERB
fumecheng-11587	475	4	and	and	CCONJ
fumecheng-11587	475	5	free	free	ADJ
fumecheng-11587	475	6	vibration	vibration	NOUN
fumecheng-11587	475	7	analyses	analysis	NOUN
fumecheng-11587	475	8	of	of	ADP
fumecheng-11587	475	9	nanobeam	nanobeam	ADJ
fumecheng-11587	475	10	-	-	PUNCT
fumecheng-11587	475	11	substrate	substrate	NOUN
fumecheng-11587	475	12	medium	medium	ADJ
fumecheng-11587	475	13	systems	system	NOUN
fumecheng-11587	475	14	,	,	PUNCT
fumecheng-11587	475	15	facta	facta	PROPN
fumecheng-11587	475	16	universitatis	universitatis	PROPN
fumecheng-11587	475	17	,	,	PUNCT
fumecheng-11587	475	18	series	series	NOUN
fumecheng-11587	475	19	:	:	PUNCT
fumecheng-11587	475	20	mechanical	mechanical	ADJ
fumecheng-11587	475	21	engineering	engineering	NOUN
fumecheng-11587	475	22	,	,	PUNCT
fumecheng-11587	475	23	20(3	20(3	NOUN
fumecheng-11587	475	24	)	)	PUNCT
fumecheng-11587	475	25	,	,	PUNCT
fumecheng-11587	475	26	pp	pp	ADP
fumecheng-11587	475	27	.	.	PUNCT
fumecheng-11587	476	1	561	561	NUM
fumecheng-11587	476	2	-	-	SYM
fumecheng-11587	476	3	587	587	NUM
fumecheng-11587	476	4	.	.	PUNCT
fumecheng-11587	477	1	20	20	NUM
fumecheng-11587	477	2	.	.	X
fumecheng-11587	478	1	yang	yang	PROPN
fumecheng-11587	478	2	,	,	PUNCT
fumecheng-11587	478	3	f.a.c.m	f.a.c.m	PROPN
fumecheng-11587	478	4	.	.	PROPN
fumecheng-11587	478	5	,	,	PUNCT
fumecheng-11587	478	6	chong	chong	PROPN
fumecheng-11587	478	7	,	,	PUNCT
fumecheng-11587	478	8	a.c.m	a.c.m	PROPN
fumecheng-11587	478	9	.	.	PROPN
fumecheng-11587	478	10	,	,	PUNCT
fumecheng-11587	478	11	lam	lam	PROPN
fumecheng-11587	478	12	,	,	PUNCT
fumecheng-11587	478	13	d.c.c	d.c.c	PROPN
fumecheng-11587	478	14	.	.	PROPN
fumecheng-11587	478	15	,	,	PUNCT
fumecheng-11587	478	16	tong	tong	PROPN
fumecheng-11587	478	17	,	,	PUNCT
fumecheng-11587	478	18	p.	p.	PROPN
fumecheng-11587	478	19	,	,	PUNCT
fumecheng-11587	478	20	2002	2002	NUM
fumecheng-11587	478	21	,	,	PUNCT
fumecheng-11587	478	22	couple	couple	NOUN
fumecheng-11587	478	23	stress	stress	NOUN
fumecheng-11587	478	24	based	base	VERB
fumecheng-11587	478	25	strain	strain	NOUN
fumecheng-11587	478	26	gradient	gradient	NOUN
fumecheng-11587	478	27	theory	theory	NOUN
fumecheng-11587	478	28	for	for	ADP
fumecheng-11587	478	29	elasticity	elasticity	NOUN
fumecheng-11587	478	30	,	,	PUNCT
fumecheng-11587	478	31	international	international	ADJ
fumecheng-11587	478	32	journal	journal	NOUN
fumecheng-11587	478	33	of	of	ADP
fumecheng-11587	478	34	solids	solid	NOUN
fumecheng-11587	478	35	and	and	CCONJ
fumecheng-11587	478	36	structures	structure	NOUN
fumecheng-11587	478	37	,	,	PUNCT
fumecheng-11587	478	38	39(10	39(10	NUM
fumecheng-11587	478	39	)	)	PUNCT
fumecheng-11587	478	40	,	,	PUNCT
fumecheng-11587	478	41	pp	pp	ADJ
fumecheng-11587	478	42	.	.	PUNCT
fumecheng-11587	479	1	2731	2731	NUM
fumecheng-11587	479	2	-	-	SYM
fumecheng-11587	479	3	2743	2743	NUM
fumecheng-11587	479	4	.	.	PUNCT
fumecheng-11587	480	1	21	21	NUM
fumecheng-11587	480	2	.	.	PUNCT
fumecheng-11587	481	1	wang	wang	PROPN
fumecheng-11587	481	2	,	,	PUNCT
fumecheng-11587	481	3	g.f	g.f	PROPN
fumecheng-11587	481	4	.	.	PROPN
fumecheng-11587	481	5	,	,	PUNCT
fumecheng-11587	481	6	feng	feng	PROPN
fumecheng-11587	481	7	,	,	PUNCT
fumecheng-11587	481	8	x.q	x.q	PROPN
fumecheng-11587	481	9	.	.	PROPN
fumecheng-11587	481	10	,	,	PUNCT
fumecheng-11587	481	11	2007	2007	NUM
fumecheng-11587	481	12	,	,	PUNCT
fumecheng-11587	481	13	effects	effect	NOUN
fumecheng-11587	481	14	of	of	ADP
fumecheng-11587	481	15	surface	surface	NOUN
fumecheng-11587	481	16	elasticity	elasticity	NOUN
fumecheng-11587	481	17	and	and	CCONJ
fumecheng-11587	481	18	residual	residual	ADJ
fumecheng-11587	481	19	surface	surface	NOUN
fumecheng-11587	481	20	tension	tension	NOUN
fumecheng-11587	481	21	on	on	ADP
fumecheng-11587	481	22	the	the	DET
fumecheng-11587	481	23	natural	natural	ADJ
fumecheng-11587	481	24	frequency	frequency	NOUN
fumecheng-11587	481	25	of	of	ADP
fumecheng-11587	481	26	microbeams	microbeam	NOUN
fumecheng-11587	481	27	,	,	PUNCT
fumecheng-11587	481	28	applied	apply	VERB
fumecheng-11587	481	29	physics	physics	NOUN
fumecheng-11587	481	30	letters	letter	NOUN
fumecheng-11587	481	31	,	,	PUNCT
fumecheng-11587	481	32	90(23	90(23	NOUN
fumecheng-11587	481	33	)	)	PUNCT
fumecheng-11587	481	34	,	,	PUNCT
fumecheng-11587	481	35	231904	231904	NUM
fumecheng-11587	481	36	.	.	PUNCT
fumecheng-11587	482	1	22	22	NUM
fumecheng-11587	482	2	.	.	PUNCT
fumecheng-11587	483	1	lim	lim	PROPN
fumecheng-11587	483	2	,	,	PUNCT
fumecheng-11587	483	3	c.w	c.w	PROPN
fumecheng-11587	483	4	.	.	PROPN
fumecheng-11587	483	5	,	,	PUNCT
fumecheng-11587	483	6	zhang	zhang	PROPN
fumecheng-11587	483	7	,	,	PUNCT
fumecheng-11587	483	8	g.	g.	PROPN
fumecheng-11587	483	9	,	,	PUNCT
fumecheng-11587	483	10	reddy	reddy	PROPN
fumecheng-11587	483	11	,	,	PUNCT
fumecheng-11587	483	12	j.	j.	PROPN
fumecheng-11587	483	13	,	,	PUNCT
fumecheng-11587	483	14	2015	2015	NUM
fumecheng-11587	483	15	,	,	PUNCT
fumecheng-11587	483	16	a	a	DET
fumecheng-11587	483	17	higher	high	ADJ
fumecheng-11587	483	18	-	-	PUNCT
fumecheng-11587	483	19	order	order	NOUN
fumecheng-11587	483	20	nonlocal	nonlocal	ADJ
fumecheng-11587	483	21	elasticity	elasticity	NOUN
fumecheng-11587	483	22	and	and	CCONJ
fumecheng-11587	483	23	strain	strain	VERB
fumecheng-11587	483	24	gradient	gradient	NOUN
fumecheng-11587	483	25	theory	theory	NOUN
fumecheng-11587	483	26	and	and	CCONJ
fumecheng-11587	483	27	its	its	PRON
fumecheng-11587	483	28	applications	application	NOUN
fumecheng-11587	483	29	in	in	ADP
fumecheng-11587	483	30	wave	wave	NOUN
fumecheng-11587	483	31	propagation	propagation	NOUN
fumecheng-11587	483	32	,	,	PUNCT
fumecheng-11587	483	33	journal	journal	NOUN
fumecheng-11587	483	34	of	of	ADP
fumecheng-11587	483	35	the	the	DET
fumecheng-11587	483	36	mechanics	mechanic	NOUN
fumecheng-11587	483	37	and	and	CCONJ
fumecheng-11587	483	38	physics	physic	NOUN
fumecheng-11587	483	39	of	of	ADP
fumecheng-11587	483	40	solids	solid	NOUN
fumecheng-11587	483	41	,	,	PUNCT
fumecheng-11587	483	42	78	78	NUM
fumecheng-11587	483	43	,	,	PUNCT
fumecheng-11587	483	44	pp	pp	ADJ
fumecheng-11587	483	45	.	.	PUNCT
fumecheng-11587	484	1	298	298	NUM
fumecheng-11587	484	2	-	-	SYM
fumecheng-11587	484	3	313	313	NUM
fumecheng-11587	484	4	.	.	PUNCT
fumecheng-11587	485	1	23	23	NUM
fumecheng-11587	485	2	.	.	PUNCT
fumecheng-11587	486	1	garg	garg	NOUN
fumecheng-11587	486	2	,	,	PUNCT
fumecheng-11587	486	3	a.	a.	NOUN
fumecheng-11587	486	4	,	,	PUNCT
fumecheng-11587	486	5	chalak	chalak	PROPN
fumecheng-11587	486	6	,	,	PUNCT
fumecheng-11587	486	7	h.d	h.d	PROPN
fumecheng-11587	486	8	.	.	PROPN
fumecheng-11587	486	9	,	,	PUNCT
fumecheng-11587	486	10	zenkour	zenkour	NOUN
fumecheng-11587	486	11	,	,	PUNCT
fumecheng-11587	486	12	a.m.	a.m.	ADV
fumecheng-11587	486	13	,	,	PUNCT
fumecheng-11587	486	14	belarbi	belarbi	NOUN
fumecheng-11587	486	15	,	,	PUNCT
fumecheng-11587	486	16	m.o	m.o	PROPN
fumecheng-11587	486	17	.	.	PROPN
fumecheng-11587	486	18	,	,	PUNCT
fumecheng-11587	486	19	houari	houari	PROPN
fumecheng-11587	486	20	,	,	PUNCT
fumecheng-11587	486	21	m.s.a	m.s.a	NOUN
fumecheng-11587	486	22	.	.	PROPN
fumecheng-11587	486	23	,	,	PUNCT
fumecheng-11587	486	24	2022	2022	NUM
fumecheng-11587	486	25	,	,	PUNCT
fumecheng-11587	486	26	a	a	DET
fumecheng-11587	486	27	review	review	NOUN
fumecheng-11587	486	28	of	of	ADP
fumecheng-11587	486	29	available	available	ADJ
fumecheng-11587	486	30	theories	theory	NOUN
fumecheng-11587	486	31	and	and	CCONJ
fumecheng-11587	486	32	methodologies	methodology	NOUN
fumecheng-11587	486	33	for	for	ADP
fumecheng-11587	486	34	the	the	DET
fumecheng-11587	486	35	analysis	analysis	NOUN
fumecheng-11587	486	36	of	of	ADP
fumecheng-11587	486	37	nano	nano	NOUN
fumecheng-11587	486	38	isotropic	isotropic	NOUN
fumecheng-11587	486	39	,	,	PUNCT
fumecheng-11587	486	40	nano	nano	NOUN
fumecheng-11587	486	41	functionally	functionally	ADV
fumecheng-11587	486	42	graded	grade	VERB
fumecheng-11587	486	43	,	,	PUNCT
fumecheng-11587	486	44	and	and	CCONJ
fumecheng-11587	486	45	cnt	cnt	PROPN
fumecheng-11587	486	46	reinforced	reinforce	VERB
fumecheng-11587	486	47	nanocomposite	nanocomposite	NOUN
fumecheng-11587	486	48	structures	structure	NOUN
fumecheng-11587	486	49	,	,	PUNCT
fumecheng-11587	486	50	archives	archive	NOUN
fumecheng-11587	486	51	of	of	ADP
fumecheng-11587	486	52	computational	computational	ADJ
fumecheng-11587	486	53	methods	method	NOUN
fumecheng-11587	486	54	in	in	ADP
fumecheng-11587	486	55	engineering	engineering	NOUN
fumecheng-11587	486	56	,	,	PUNCT
fumecheng-11587	486	57	29	29	NUM
fumecheng-11587	486	58	,	,	PUNCT
fumecheng-11587	486	59	pp	pp	ADJ
fumecheng-11587	486	60	.	.	PUNCT
fumecheng-11587	487	1	2237–2270	2237–2270	NUM
fumecheng-11587	487	2	.	.	NOUN
fumecheng-11587	488	1	24	24	NUM
fumecheng-11587	488	2	.	.	PUNCT
fumecheng-11587	489	1	liu	liu	PROPN
fumecheng-11587	489	2	,	,	PUNCT
fumecheng-11587	489	3	h.	h.	PROPN
fumecheng-11587	489	4	,	,	PUNCT
fumecheng-11587	489	5	lv	lv	PROPN
fumecheng-11587	489	6	,	,	PUNCT
fumecheng-11587	489	7	z.	z.	PROPN
fumecheng-11587	489	8	,	,	PUNCT
fumecheng-11587	489	9	wu	wu	PROPN
fumecheng-11587	489	10	,	,	PUNCT
fumecheng-11587	489	11	h.	h.	PROPN
fumecheng-11587	489	12	,	,	PUNCT
fumecheng-11587	489	13	2019	2019	NUM
fumecheng-11587	489	14	,	,	PUNCT
fumecheng-11587	489	15	nonlinear	nonlinear	ADJ
fumecheng-11587	489	16	free	free	ADJ
fumecheng-11587	489	17	vibration	vibration	NOUN
fumecheng-11587	489	18	of	of	ADP
fumecheng-11587	489	19	geometrically	geometrically	ADV
fumecheng-11587	489	20	imperfect	imperfect	ADJ
fumecheng-11587	489	21	functionally	functionally	ADV
fumecheng-11587	489	22	graded	grade	VERB
fumecheng-11587	489	23	sandwich	sandwich	NOUN
fumecheng-11587	489	24	nanobeams	nanobeam	NOUN
fumecheng-11587	489	25	based	base	VERB
fumecheng-11587	489	26	on	on	ADP
fumecheng-11587	489	27	nonlocal	nonlocal	ADJ
fumecheng-11587	489	28	strain	strain	NOUN
fumecheng-11587	489	29	gradient	gradient	NOUN
fumecheng-11587	489	30	theory	theory	NOUN
fumecheng-11587	489	31	,	,	PUNCT
fumecheng-11587	489	32	composite	composite	ADJ
fumecheng-11587	489	33	structures	structure	NOUN
fumecheng-11587	489	34	,	,	PUNCT
fumecheng-11587	489	35	214	214	NUM
fumecheng-11587	489	36	,	,	PUNCT
fumecheng-11587	489	37	pp	pp	ADJ
fumecheng-11587	489	38	.	.	PUNCT
fumecheng-11587	490	1	47	47	NUM
fumecheng-11587	490	2	-	-	SYM
fumecheng-11587	490	3	61	61	NUM
fumecheng-11587	490	4	.	.	PUNCT
fumecheng-11587	491	1	25	25	NUM
fumecheng-11587	491	2	.	.	PUNCT
fumecheng-11587	492	1	fallah	fallah	PROPN
fumecheng-11587	492	2	,	,	PUNCT
fumecheng-11587	492	3	a.	a.	NOUN
fumecheng-11587	492	4	,	,	PUNCT
fumecheng-11587	492	5	aghdam	aghdam	NOUN
fumecheng-11587	492	6	,	,	PUNCT
fumecheng-11587	492	7	m.m	m.m	PROPN
fumecheng-11587	492	8	.	.	PROPN
fumecheng-11587	492	9	,	,	PUNCT
fumecheng-11587	492	10	2011	2011	NUM
fumecheng-11587	492	11	,	,	PUNCT
fumecheng-11587	492	12	nonlinear	nonlinear	ADJ
fumecheng-11587	492	13	free	free	ADJ
fumecheng-11587	492	14	vibration	vibration	NOUN
fumecheng-11587	492	15	and	and	CCONJ
fumecheng-11587	492	16	post	post	ADJ
fumecheng-11587	492	17	-	-	ADJ
fumecheng-11587	492	18	buckling	buckling	ADJ
fumecheng-11587	492	19	analysis	analysis	NOUN
fumecheng-11587	492	20	of	of	ADP
fumecheng-11587	492	21	functionally	functionally	ADV
fumecheng-11587	492	22	graded	grade	VERB
fumecheng-11587	492	23	beams	beam	NOUN
fumecheng-11587	492	24	on	on	ADP
fumecheng-11587	492	25	nonlinear	nonlinear	ADJ
fumecheng-11587	492	26	elastic	elastic	ADJ
fumecheng-11587	492	27	foundation	foundation	NOUN
fumecheng-11587	492	28	,	,	PUNCT
fumecheng-11587	492	29	european	european	PROPN
fumecheng-11587	492	30	journal	journal	PROPN
fumecheng-11587	492	31	of	of	ADP
fumecheng-11587	492	32	mechanics	mechanic	NOUN
fumecheng-11587	492	33	-	-	PUNCT
fumecheng-11587	492	34	a	a	DET
fumecheng-11587	492	35	/	/	SYM
fumecheng-11587	492	36	solids	solid	NOUN
fumecheng-11587	492	37	,	,	PUNCT
fumecheng-11587	492	38	30(4	30(4	NUM
fumecheng-11587	492	39	)	)	PUNCT
fumecheng-11587	492	40	,	,	PUNCT
fumecheng-11587	492	41	pp	pp	PROPN
fumecheng-11587	492	42	.	.	PUNCT
fumecheng-11587	493	1	571	571	NUM
fumecheng-11587	493	2	-	-	SYM
fumecheng-11587	493	3	583	583	NUM
fumecheng-11587	493	4	.	.	PUNCT
fumecheng-11587	494	1	26	26	NUM
fumecheng-11587	494	2	.	.	PUNCT
fumecheng-11587	495	1	şimşek	şimşek	NOUN
fumecheng-11587	495	2	,	,	PUNCT
fumecheng-11587	495	3	m.	m.	NOUN
fumecheng-11587	495	4	,	,	PUNCT
fumecheng-11587	495	5	2016	2016	NUM
fumecheng-11587	495	6	,	,	PUNCT
fumecheng-11587	495	7	nonlinear	nonlinear	ADJ
fumecheng-11587	495	8	free	free	ADJ
fumecheng-11587	495	9	vibration	vibration	NOUN
fumecheng-11587	495	10	of	of	ADP
fumecheng-11587	495	11	a	a	DET
fumecheng-11587	495	12	functionally	functionally	ADV
fumecheng-11587	495	13	graded	grade	VERB
fumecheng-11587	495	14	nanobeam	nanobeam	NOUN
fumecheng-11587	495	15	using	use	VERB
fumecheng-11587	495	16	nonlocal	nonlocal	ADJ
fumecheng-11587	495	17	strain	strain	NOUN
fumecheng-11587	495	18	gradient	gradient	NOUN
fumecheng-11587	495	19	theory	theory	NOUN
fumecheng-11587	495	20	and	and	CCONJ
fumecheng-11587	495	21	a	a	DET
fumecheng-11587	495	22	novel	novel	ADJ
fumecheng-11587	495	23	hamiltonian	hamiltonian	ADJ
fumecheng-11587	495	24	approach	approach	NOUN
fumecheng-11587	495	25	,	,	PUNCT
fumecheng-11587	495	26	international	international	ADJ
fumecheng-11587	495	27	journal	journal	NOUN
fumecheng-11587	495	28	of	of	ADP
fumecheng-11587	495	29	engineering	engineering	NOUN
fumecheng-11587	495	30	science	science	NOUN
fumecheng-11587	495	31	,	,	PUNCT
fumecheng-11587	495	32	105	105	NUM
fumecheng-11587	495	33	,	,	PUNCT
fumecheng-11587	495	34	pp	pp	ADJ
fumecheng-11587	495	35	.	.	PUNCT
fumecheng-11587	496	1	12	12	NUM
fumecheng-11587	496	2	-	-	SYM
fumecheng-11587	496	3	27	27	NUM
fumecheng-11587	496	4	.	.	PUNCT
fumecheng-11587	497	1	27	27	NUM
fumecheng-11587	497	2	.	.	PUNCT
fumecheng-11587	498	1	nešić	nešić	PROPN
fumecheng-11587	498	2	,	,	PUNCT
fumecheng-11587	498	3	n.	n.	NOUN
fumecheng-11587	498	4	,	,	PUNCT
fumecheng-11587	498	5	cajić	cajić	NOUN
fumecheng-11587	498	6	,	,	PUNCT
fumecheng-11587	498	7	m.	m.	NOUN
fumecheng-11587	498	8	,	,	PUNCT
fumecheng-11587	498	9	karličić	karličić	PROPN
fumecheng-11587	498	10	,	,	PUNCT
fumecheng-11587	498	11	d.	d.	PROPN
fumecheng-11587	498	12	,	,	PUNCT
fumecheng-11587	498	13	obradović	obradović	PROPN
fumecheng-11587	498	14	,	,	PUNCT
fumecheng-11587	498	15	a.	a.	NOUN
fumecheng-11587	498	16	,	,	PUNCT
fumecheng-11587	498	17	simonović	simonović	PROPN
fumecheng-11587	498	18	,	,	PUNCT
fumecheng-11587	498	19	j.	j.	PROPN
fumecheng-11587	498	20	,	,	PUNCT
fumecheng-11587	498	21	2022	2022	NUM
fumecheng-11587	498	22	,	,	PUNCT
fumecheng-11587	498	23	nonlinear	nonlinear	ADJ
fumecheng-11587	498	24	vibration	vibration	NOUN
fumecheng-11587	498	25	of	of	ADP
fumecheng-11587	498	26	a	a	DET
fumecheng-11587	498	27	nonlocal	nonlocal	ADJ
fumecheng-11587	498	28	functionally	functionally	ADV
fumecheng-11587	498	29	graded	grade	VERB
fumecheng-11587	498	30	beam	beam	NOUN
fumecheng-11587	498	31	on	on	ADP
fumecheng-11587	498	32	fractional	fractional	ADJ
fumecheng-11587	498	33	visco	visco	PROPN
fumecheng-11587	498	34	-	-	PUNCT
fumecheng-11587	498	35	pasternak	pasternak	PROPN
fumecheng-11587	498	36	foundation	foundation	PROPN
fumecheng-11587	498	37	,	,	PUNCT
fumecheng-11587	498	38	nonlinear	nonlinear	ADJ
fumecheng-11587	498	39	dynamics	dynamic	NOUN
fumecheng-11587	498	40	,	,	PUNCT
fumecheng-11587	498	41	107(3	107(3	NUM
fumecheng-11587	498	42	)	)	PUNCT
fumecheng-11587	498	43	,	,	PUNCT
fumecheng-11587	498	44	pp	pp	PROPN
fumecheng-11587	498	45	.	.	PUNCT
fumecheng-11587	499	1	2003	2003	NUM
fumecheng-11587	499	2	-	-	SYM
fumecheng-11587	499	3	2026	2026	NUM
fumecheng-11587	499	4	.	.	PUNCT
fumecheng-11587	500	1	28	28	NUM
fumecheng-11587	500	2	.	.	PUNCT
fumecheng-11587	501	1	barretta	barretta	NOUN
fumecheng-11587	501	2	,	,	PUNCT
fumecheng-11587	501	3	r.	r.	PROPN
fumecheng-11587	501	4	,	,	PUNCT
fumecheng-11587	501	5	de	de	X
fumecheng-11587	501	6	sciarra	sciarra	PROPN
fumecheng-11587	501	7	,	,	PUNCT
fumecheng-11587	501	8	f.m	f.m	PROPN
fumecheng-11587	501	9	.	.	PROPN
fumecheng-11587	501	10	,	,	PUNCT
fumecheng-11587	501	11	2018	2018	NUM
fumecheng-11587	501	12	,	,	PUNCT
fumecheng-11587	501	13	constitutive	constitutive	ADJ
fumecheng-11587	501	14	boundary	boundary	ADJ
fumecheng-11587	501	15	conditions	condition	NOUN
fumecheng-11587	501	16	for	for	ADP
fumecheng-11587	501	17	nonlocal	nonlocal	ADJ
fumecheng-11587	501	18	strain	strain	NOUN
fumecheng-11587	501	19	gradient	gradient	ADJ
fumecheng-11587	501	20	elastic	elastic	ADJ
fumecheng-11587	501	21	nanobeams	nanobeam	NOUN
fumecheng-11587	501	22	,	,	PUNCT
fumecheng-11587	501	23	international	international	ADJ
fumecheng-11587	501	24	journal	journal	NOUN
fumecheng-11587	501	25	of	of	ADP
fumecheng-11587	501	26	engineering	engineering	NOUN
fumecheng-11587	501	27	science	science	NOUN
fumecheng-11587	501	28	,	,	PUNCT
fumecheng-11587	501	29	130	130	NUM
fumecheng-11587	501	30	,	,	PUNCT
fumecheng-11587	501	31	pp	pp	ADJ
fumecheng-11587	501	32	.	.	PUNCT
fumecheng-11587	502	1	187	187	NUM
fumecheng-11587	502	2	-	-	SYM
fumecheng-11587	502	3	198	198	NUM
fumecheng-11587	502	4	.	.	PUNCT
fumecheng-11587	503	1	29	29	NUM
fumecheng-11587	503	2	.	.	PUNCT
fumecheng-11587	504	1	apuzzo	apuzzo	PROPN
fumecheng-11587	504	2	,	,	PUNCT
fumecheng-11587	504	3	a.	a.	NOUN
fumecheng-11587	504	4	,	,	PUNCT
fumecheng-11587	504	5	barretta	barretta	PROPN
fumecheng-11587	504	6	,	,	PUNCT
fumecheng-11587	504	7	r.	r.	PROPN
fumecheng-11587	504	8	,	,	PUNCT
fumecheng-11587	504	9	faghidian	faghidian	PROPN
fumecheng-11587	504	10	,	,	PUNCT
fumecheng-11587	504	11	s.a	s.a	PROPN
fumecheng-11587	504	12	.	.	PROPN
fumecheng-11587	504	13	,	,	PUNCT
fumecheng-11587	504	14	luciano	luciano	PROPN
fumecheng-11587	504	15	,	,	PUNCT
fumecheng-11587	504	16	r.	r.	PROPN
fumecheng-11587	504	17	,	,	PUNCT
fumecheng-11587	504	18	de	de	X
fumecheng-11587	504	19	sciarra	sciarra	PROPN
fumecheng-11587	504	20	,	,	PUNCT
fumecheng-11587	504	21	f.m	f.m	PROPN
fumecheng-11587	504	22	.	.	PROPN
fumecheng-11587	504	23	,	,	PUNCT
fumecheng-11587	504	24	2019	2019	NUM
fumecheng-11587	504	25	,	,	PUNCT
fumecheng-11587	504	26	nonlocal	nonlocal	ADJ
fumecheng-11587	504	27	strain	strain	NOUN
fumecheng-11587	504	28	gradient	gradient	ADJ
fumecheng-11587	504	29	exact	exact	ADJ
fumecheng-11587	504	30	solutions	solution	NOUN
fumecheng-11587	504	31	for	for	ADP
fumecheng-11587	504	32	functionally	functionally	ADV
fumecheng-11587	504	33	graded	grade	VERB
fumecheng-11587	504	34	inflected	inflect	VERB
fumecheng-11587	504	35	nano	nano	NOUN
fumecheng-11587	504	36	-	-	PUNCT
fumecheng-11587	504	37	beams	beam	NOUN
fumecheng-11587	504	38	,	,	PUNCT
fumecheng-11587	504	39	composites	composite	VERB
fumecheng-11587	504	40	part	part	NOUN
fumecheng-11587	504	41	b	b	NOUN
fumecheng-11587	504	42	:	:	PUNCT
fumecheng-11587	504	43	engineering	engineering	NOUN
fumecheng-11587	504	44	,	,	PUNCT
fumecheng-11587	504	45	164	164	NUM
fumecheng-11587	504	46	,	,	PUNCT
fumecheng-11587	504	47	pp	pp	ADJ
fumecheng-11587	504	48	.	.	PUNCT
fumecheng-11587	505	1	667	667	NUM
fumecheng-11587	505	2	-	-	SYM
fumecheng-11587	505	3	674	674	NUM
fumecheng-11587	505	4	.	.	PUNCT
fumecheng-11587	506	1	30	30	NUM
fumecheng-11587	506	2	.	.	PUNCT
fumecheng-11587	507	1	barretta	barretta	NOUN
fumecheng-11587	507	2	,	,	PUNCT
fumecheng-11587	507	3	r.	r.	PROPN
fumecheng-11587	507	4	,	,	PUNCT
fumecheng-11587	507	5	faghidian	faghidian	PROPN
fumecheng-11587	507	6	,	,	PUNCT
fumecheng-11587	507	7	s.a	s.a	PROPN
fumecheng-11587	507	8	.	.	PROPN
fumecheng-11587	507	9	,	,	PUNCT
fumecheng-11587	507	10	luciano	luciano	PROPN
fumecheng-11587	507	11	,	,	PUNCT
fumecheng-11587	507	12	r.	r.	PROPN
fumecheng-11587	507	13	,	,	PUNCT
fumecheng-11587	507	14	medaglia	medaglia	PROPN
fumecheng-11587	507	15	,	,	PUNCT
fumecheng-11587	507	16	c.m	c.m	PROPN
fumecheng-11587	507	17	.	.	PROPN
fumecheng-11587	507	18	,	,	PUNCT
fumecheng-11587	507	19	penna	penna	PROPN
fumecheng-11587	507	20	,	,	PUNCT
fumecheng-11587	507	21	r.	r.	PROPN
fumecheng-11587	507	22	,	,	PUNCT
fumecheng-11587	507	23	2018	2018	NUM
fumecheng-11587	507	24	,	,	PUNCT
fumecheng-11587	507	25	free	free	ADJ
fumecheng-11587	507	26	vibrations	vibration	NOUN
fumecheng-11587	507	27	of	of	ADP
fumecheng-11587	507	28	fg	fg	PROPN
fumecheng-11587	507	29	elastic	elastic	ADJ
fumecheng-11587	507	30	timoshenko	timoshenko	NOUN
fumecheng-11587	507	31	nano	nano	NOUN
fumecheng-11587	507	32	-	-	PUNCT
fumecheng-11587	507	33	beams	beam	NOUN
fumecheng-11587	507	34	by	by	ADP
fumecheng-11587	507	35	strain	strain	NOUN
fumecheng-11587	507	36	gradient	gradient	NOUN
fumecheng-11587	507	37	and	and	CCONJ
fumecheng-11587	507	38	stress	stress	NOUN
fumecheng-11587	507	39	-	-	PUNCT
fumecheng-11587	507	40	driven	drive	VERB
fumecheng-11587	507	41	nonlocal	nonlocal	ADJ
fumecheng-11587	507	42	models	model	NOUN
fumecheng-11587	507	43	,	,	PUNCT
fumecheng-11587	507	44	composites	composite	VERB
fumecheng-11587	507	45	part	part	NOUN
fumecheng-11587	507	46	b	b	NOUN
fumecheng-11587	507	47	:	:	PUNCT
fumecheng-11587	507	48	engineering	engineering	NOUN
fumecheng-11587	507	49	,	,	PUNCT
fumecheng-11587	507	50	154	154	NUM
fumecheng-11587	507	51	,	,	PUNCT
fumecheng-11587	507	52	pp	pp	ADJ
fumecheng-11587	507	53	.	.	PUNCT
fumecheng-11587	508	1	20	20	NUM
fumecheng-11587	508	2	-	-	SYM
fumecheng-11587	508	3	32	32	NUM
fumecheng-11587	508	4	.	.	PUNCT
fumecheng-11587	509	1	31	31	NUM
fumecheng-11587	509	2	.	.	PUNCT
fumecheng-11587	510	1	pinnola	pinnola	PROPN
fumecheng-11587	510	2	,	,	PUNCT
fumecheng-11587	510	3	f.p	f.p	PROPN
fumecheng-11587	510	4	.	.	PROPN
fumecheng-11587	510	5	,	,	PUNCT
fumecheng-11587	510	6	faghidian	faghidian	PROPN
fumecheng-11587	510	7	,	,	PUNCT
fumecheng-11587	510	8	s.a	s.a	PROPN
fumecheng-11587	510	9	.	.	PROPN
fumecheng-11587	510	10	,	,	PUNCT
fumecheng-11587	510	11	barretta	barretta	PROPN
fumecheng-11587	510	12	,	,	PUNCT
fumecheng-11587	510	13	r.	r.	PROPN
fumecheng-11587	510	14	,	,	PUNCT
fumecheng-11587	510	15	de	de	X
fumecheng-11587	510	16	sciarra	sciarra	PROPN
fumecheng-11587	510	17	,	,	PUNCT
fumecheng-11587	510	18	f.m	f.m	PROPN
fumecheng-11587	510	19	.	.	PROPN
fumecheng-11587	510	20	,	,	PUNCT
fumecheng-11587	510	21	2020	2020	NUM
fumecheng-11587	510	22	,	,	PUNCT
fumecheng-11587	510	23	variationally	variationally	ADV
fumecheng-11587	510	24	consistent	consistent	ADJ
fumecheng-11587	510	25	dynamics	dynamic	NOUN
fumecheng-11587	510	26	of	of	ADP
fumecheng-11587	510	27	nonlocal	nonlocal	ADJ
fumecheng-11587	510	28	gradient	gradient	ADJ
fumecheng-11587	510	29	elastic	elastic	ADJ
fumecheng-11587	510	30	beams	beam	NOUN
fumecheng-11587	510	31	,	,	PUNCT
fumecheng-11587	510	32	international	international	ADJ
fumecheng-11587	510	33	journal	journal	NOUN
fumecheng-11587	510	34	of	of	ADP
fumecheng-11587	510	35	engineering	engineering	NOUN
fumecheng-11587	510	36	science	science	NOUN
fumecheng-11587	510	37	,	,	PUNCT
fumecheng-11587	510	38	149	149	NUM
fumecheng-11587	510	39	,	,	PUNCT
fumecheng-11587	510	40	103220	103220	NUM
fumecheng-11587	510	41	.	.	PUNCT
fumecheng-11587	511	1	32	32	NUM
fumecheng-11587	511	2	.	.	PUNCT
fumecheng-11587	511	3	sahmani	sahmani	PROPN
fumecheng-11587	511	4	,	,	PUNCT
fumecheng-11587	511	5	s.	s.	PROPN
fumecheng-11587	511	6	,	,	PUNCT
fumecheng-11587	511	7	safaei	safaei	PROPN
fumecheng-11587	511	8	,	,	PUNCT
fumecheng-11587	511	9	b.	b.	PROPN
fumecheng-11587	511	10	,	,	PUNCT
fumecheng-11587	511	11	2020	2020	NUM
fumecheng-11587	511	12	,	,	PUNCT
fumecheng-11587	511	13	influence	influence	NOUN
fumecheng-11587	511	14	of	of	ADP
fumecheng-11587	511	15	homogenization	homogenization	NOUN
fumecheng-11587	511	16	models	model	NOUN
fumecheng-11587	511	17	on	on	ADP
fumecheng-11587	511	18	size	size	NOUN
fumecheng-11587	511	19	-	-	PUNCT
fumecheng-11587	511	20	dependent	dependent	ADJ
fumecheng-11587	511	21	nonlinear	nonlinear	ADJ
fumecheng-11587	511	22	bending	bending	NOUN
fumecheng-11587	511	23	and	and	CCONJ
fumecheng-11587	511	24	postbuckling	postbuckling	NOUN
fumecheng-11587	511	25	of	of	ADP
fumecheng-11587	511	26	bi	bi	ADJ
fumecheng-11587	511	27	-	-	ADJ
fumecheng-11587	511	28	directional	directional	ADJ
fumecheng-11587	511	29	functionally	functionally	ADV
fumecheng-11587	511	30	graded	grade	VERB
fumecheng-11587	511	31	micro	micro	NOUN
fumecheng-11587	511	32	/	/	SYM
fumecheng-11587	511	33	nano	nano	NOUN
fumecheng-11587	511	34	-	-	PUNCT
fumecheng-11587	511	35	beams	beam	NOUN
fumecheng-11587	511	36	,	,	PUNCT
fumecheng-11587	511	37	applied	apply	VERB
fumecheng-11587	511	38	mathematical	mathematical	ADJ
fumecheng-11587	511	39	modelling	modelling	NOUN
fumecheng-11587	511	40	,	,	PUNCT
fumecheng-11587	511	41	82	82	NUM
fumecheng-11587	511	42	,	,	PUNCT
fumecheng-11587	511	43	pp	pp	ADJ
fumecheng-11587	511	44	.	.	PUNCT
fumecheng-11587	512	1	336	336	NUM
fumecheng-11587	512	2	-	-	NUM
fumecheng-11587	512	3	358	358	NUM
fumecheng-11587	512	4	.	.	PUNCT
fumecheng-11587	513	1	33	33	NUM
fumecheng-11587	513	2	.	.	PUNCT
fumecheng-11587	514	1	li	li	PROPN
fumecheng-11587	514	2	,	,	PUNCT
fumecheng-11587	514	3	l.	l.	PROPN
fumecheng-11587	514	4	,	,	PUNCT
fumecheng-11587	514	5	hu	hu	PROPN
fumecheng-11587	514	6	,	,	PUNCT
fumecheng-11587	514	7	y.	y.	PROPN
fumecheng-11587	514	8	,	,	PUNCT
fumecheng-11587	514	9	2016	2016	NUM
fumecheng-11587	514	10	,	,	PUNCT
fumecheng-11587	514	11	nonlinear	nonlinear	ADJ
fumecheng-11587	514	12	bending	bending	NOUN
fumecheng-11587	514	13	and	and	CCONJ
fumecheng-11587	514	14	free	free	ADJ
fumecheng-11587	514	15	vibration	vibration	NOUN
fumecheng-11587	514	16	analyses	analysis	NOUN
fumecheng-11587	514	17	of	of	ADP
fumecheng-11587	514	18	nonlocal	nonlocal	ADJ
fumecheng-11587	514	19	strain	strain	NOUN
fumecheng-11587	514	20	gradient	gradient	NOUN
fumecheng-11587	514	21	beams	beam	NOUN
fumecheng-11587	514	22	made	make	VERB
fumecheng-11587	514	23	of	of	ADP
fumecheng-11587	514	24	functionally	functionally	ADV
fumecheng-11587	514	25	graded	grade	VERB
fumecheng-11587	514	26	material	material	NOUN
fumecheng-11587	514	27	,	,	PUNCT
fumecheng-11587	514	28	international	international	ADJ
fumecheng-11587	514	29	journal	journal	NOUN
fumecheng-11587	514	30	of	of	ADP
fumecheng-11587	514	31	engineering	engineering	NOUN
fumecheng-11587	514	32	science	science	NOUN
fumecheng-11587	514	33	,	,	PUNCT
fumecheng-11587	514	34	107	107	NUM
fumecheng-11587	514	35	,	,	PUNCT
fumecheng-11587	514	36	pp	pp	ADJ
fumecheng-11587	514	37	.	.	PUNCT
fumecheng-11587	515	1	77	77	NUM
fumecheng-11587	515	2	-	-	SYM
fumecheng-11587	515	3	97	97	NUM
fumecheng-11587	515	4	.	.	PUNCT
fumecheng-11587	516	1	34	34	NUM
fumecheng-11587	516	2	.	.	PUNCT
fumecheng-11587	517	1	liu	liu	PROPN
fumecheng-11587	517	2	,	,	PUNCT
fumecheng-11587	517	3	h.	h.	PROPN
fumecheng-11587	517	4	,	,	PUNCT
fumecheng-11587	517	5	wu	wu	PROPN
fumecheng-11587	517	6	,	,	PUNCT
fumecheng-11587	517	7	h.	h.	PROPN
fumecheng-11587	517	8	,	,	PUNCT
fumecheng-11587	517	9	lyu	lyu	PROPN
fumecheng-11587	517	10	,	,	PUNCT
fumecheng-11587	517	11	z.	z.	PROPN
fumecheng-11587	517	12	,	,	PUNCT
fumecheng-11587	517	13	2020	2020	NUM
fumecheng-11587	517	14	,	,	PUNCT
fumecheng-11587	517	15	nonlinear	nonlinear	ADJ
fumecheng-11587	517	16	resonance	resonance	NOUN
fumecheng-11587	517	17	of	of	ADP
fumecheng-11587	517	18	fg	fg	PROPN
fumecheng-11587	517	19	multilayer	multilayer	PROPN
fumecheng-11587	517	20	beam	beam	NOUN
fumecheng-11587	517	21	-	-	PUNCT
fumecheng-11587	517	22	type	type	NOUN
fumecheng-11587	517	23	nanocomposites	nanocomposite	NOUN
fumecheng-11587	517	24	:	:	PUNCT
fumecheng-11587	517	25	effects	effect	NOUN
fumecheng-11587	517	26	of	of	ADP
fumecheng-11587	517	27	graphene	graphene	ADJ
fumecheng-11587	517	28	nanoplatelet	nanoplatelet	NOUN
fumecheng-11587	517	29	-	-	PUNCT
fumecheng-11587	517	30	reinforcement	reinforcement	NOUN
fumecheng-11587	517	31	and	and	CCONJ
fumecheng-11587	517	32	geometric	geometric	ADJ
fumecheng-11587	517	33	imperfection	imperfection	NOUN
fumecheng-11587	517	34	,	,	PUNCT
fumecheng-11587	517	35	aerospace	aerospace	NOUN
fumecheng-11587	517	36	science	science	NOUN
fumecheng-11587	517	37	and	and	CCONJ
fumecheng-11587	517	38	technology	technology	NOUN
fumecheng-11587	517	39	,	,	PUNCT
fumecheng-11587	517	40	98	98	NUM
fumecheng-11587	517	41	,	,	PUNCT
fumecheng-11587	517	42	105702	105702	NUM
fumecheng-11587	517	43	.	.	PUNCT
fumecheng-11587	518	1	35	35	NUM
fumecheng-11587	518	2	.	.	PUNCT
fumecheng-11587	519	1	penna	penna	PROPN
fumecheng-11587	519	2	,	,	PUNCT
fumecheng-11587	519	3	r.	r.	PROPN
fumecheng-11587	519	4	,	,	PUNCT
fumecheng-11587	519	5	feo	feo	PROPN
fumecheng-11587	519	6	,	,	PUNCT
fumecheng-11587	519	7	l.	l.	PROPN
fumecheng-11587	519	8	,	,	PUNCT
fumecheng-11587	519	9	fortunato	fortunato	PROPN
fumecheng-11587	519	10	,	,	PUNCT
fumecheng-11587	519	11	a.	a.	PROPN
fumecheng-11587	519	12	,	,	PUNCT
fumecheng-11587	519	13	luciano	luciano	PROPN
fumecheng-11587	519	14	,	,	PUNCT
fumecheng-11587	519	15	r.	r.	PROPN
fumecheng-11587	519	16	,	,	PUNCT
fumecheng-11587	519	17	2021	2021	NUM
fumecheng-11587	519	18	,	,	PUNCT
fumecheng-11587	519	19	nonlinear	nonlinear	ADJ
fumecheng-11587	519	20	free	free	ADJ
fumecheng-11587	519	21	vibrations	vibration	NOUN
fumecheng-11587	519	22	analysis	analysis	NOUN
fumecheng-11587	519	23	of	of	ADP
fumecheng-11587	519	24	geometrically	geometrically	ADV
fumecheng-11587	519	25	imperfect	imperfect	ADJ
fumecheng-11587	519	26	fg	fg	ADP
fumecheng-11587	519	27	nano	nano	NOUN
fumecheng-11587	519	28	-	-	PUNCT
fumecheng-11587	519	29	beams	beam	NOUN
fumecheng-11587	519	30	based	base	VERB
fumecheng-11587	519	31	on	on	ADP
fumecheng-11587	519	32	stress	stress	NOUN
fumecheng-11587	519	33	-	-	PUNCT
fumecheng-11587	519	34	driven	drive	VERB
fumecheng-11587	519	35	nonlocal	nonlocal	ADJ
fumecheng-11587	519	36	elasticity	elasticity	NOUN
fumecheng-11587	519	37	with	with	ADP
fumecheng-11587	519	38	initial	initial	ADJ
fumecheng-11587	519	39	pretension	pretension	NOUN
fumecheng-11587	519	40	force	force	NOUN
fumecheng-11587	519	41	,	,	PUNCT
fumecheng-11587	519	42	composite	composite	ADJ
fumecheng-11587	519	43	structures	structure	NOUN
fumecheng-11587	519	44	,	,	PUNCT
fumecheng-11587	519	45	255	255	NUM
fumecheng-11587	519	46	,	,	PUNCT
fumecheng-11587	519	47	112856	112856	NUM
fumecheng-11587	519	48	.	.	PUNCT
fumecheng-11587	520	1	36	36	NUM
fumecheng-11587	520	2	.	.	PUNCT
fumecheng-11587	521	1	penna	penna	PROPN
fumecheng-11587	521	2	,	,	PUNCT
fumecheng-11587	521	3	r.	r.	PROPN
fumecheng-11587	521	4	,	,	PUNCT
fumecheng-11587	521	5	feo	feo	PROPN
fumecheng-11587	521	6	,	,	PUNCT
fumecheng-11587	521	7	l.	l.	PROPN
fumecheng-11587	521	8	,	,	PUNCT
fumecheng-11587	521	9	2020	2020	NUM
fumecheng-11587	521	10	,	,	PUNCT
fumecheng-11587	521	11	nonlinear	nonlinear	ADJ
fumecheng-11587	521	12	dynamic	dynamic	ADJ
fumecheng-11587	521	13	behavior	behavior	NOUN
fumecheng-11587	521	14	of	of	ADP
fumecheng-11587	521	15	porous	porous	ADJ
fumecheng-11587	521	16	and	and	CCONJ
fumecheng-11587	521	17	imperfect	imperfect	ADJ
fumecheng-11587	521	18	bernoulli	bernoulli	NOUN
fumecheng-11587	521	19	-	-	PUNCT
fumecheng-11587	521	20	euler	euler	NOUN
fumecheng-11587	521	21	functionally	functionally	ADV
fumecheng-11587	521	22	graded	grade	VERB
fumecheng-11587	521	23	nanobeams	nanobeam	NOUN
fumecheng-11587	521	24	resting	rest	VERB
fumecheng-11587	521	25	on	on	ADP
fumecheng-11587	521	26	winkler	winkler	PROPN
fumecheng-11587	521	27	elastic	elastic	PROPN
fumecheng-11587	521	28	foundation	foundation	NOUN
fumecheng-11587	521	29	,	,	PUNCT
fumecheng-11587	521	30	technologies	technology	NOUN
fumecheng-11587	521	31	,	,	PUNCT
fumecheng-11587	521	32	8(4	8(4	NUM
fumecheng-11587	521	33	)	)	PUNCT
fumecheng-11587	521	34	,	,	PUNCT
fumecheng-11587	521	35	56	56	NUM
fumecheng-11587	521	36	.	.	NOUN
fumecheng-11587	521	37	37	37	NUM
fumecheng-11587	521	38	.	.	X
fumecheng-11587	522	1	vaccaro	vaccaro	PROPN
fumecheng-11587	522	2	,	,	PUNCT
fumecheng-11587	522	3	m.s	m.s	PROPN
fumecheng-11587	522	4	.	.	PROPN
fumecheng-11587	522	5	,	,	PUNCT
fumecheng-11587	522	6	barretta	barretta	PROPN
fumecheng-11587	522	7	,	,	PUNCT
fumecheng-11587	522	8	r.	r.	PROPN
fumecheng-11587	522	9	,	,	PUNCT
fumecheng-11587	522	10	marotti	marotti	PROPN
fumecheng-11587	522	11	de	de	X
fumecheng-11587	522	12	sciarra	sciarra	PROPN
fumecheng-11587	522	13	,	,	PUNCT
fumecheng-11587	522	14	f.	f.	PROPN
fumecheng-11587	522	15	,	,	PUNCT
fumecheng-11587	522	16	reddy	reddy	PROPN
fumecheng-11587	522	17	,	,	PUNCT
fumecheng-11587	522	18	j.n	j.n	PROPN
fumecheng-11587	522	19	.	.	PROPN
fumecheng-11587	522	20	,	,	PUNCT
fumecheng-11587	522	21	2022	2022	NUM
fumecheng-11587	522	22	,	,	PUNCT
fumecheng-11587	522	23	nonlocal	nonlocal	ADJ
fumecheng-11587	522	24	integral	integral	ADJ
fumecheng-11587	522	25	elasticity	elasticity	NOUN
fumecheng-11587	522	26	for	for	ADP
fumecheng-11587	522	27	third	third	ADJ
fumecheng-11587	522	28	-	-	PUNCT
fumecheng-11587	522	29	order	order	NOUN
fumecheng-11587	522	30	small	small	ADJ
fumecheng-11587	522	31	-	-	PUNCT
fumecheng-11587	522	32	scale	scale	NOUN
fumecheng-11587	522	33	beams	beam	NOUN
fumecheng-11587	522	34	,	,	PUNCT
fumecheng-11587	522	35	acta	acta	PROPN
fumecheng-11587	522	36	mechanica	mechanica	PROPN
fumecheng-11587	522	37	,	,	PUNCT
fumecheng-11587	522	38	233(6	233(6	NUM
fumecheng-11587	522	39	)	)	PUNCT
fumecheng-11587	522	40	.	.	PUNCT
fumecheng-11587	523	1	pp	pp	ADV
fumecheng-11587	523	2	.	.	PUNCT
fumecheng-11587	524	1	2393–2403	2393–2403	NOUN
fumecheng-11587	524	2	.	.	PUNCT
fumecheng-11587	525	1	38	38	NUM
fumecheng-11587	525	2	.	.	PUNCT
fumecheng-11587	526	1	ansari	ansari	PROPN
fumecheng-11587	526	2	,	,	PUNCT
fumecheng-11587	526	3	r.	r.	PROPN
fumecheng-11587	526	4	,	,	PUNCT
fumecheng-11587	526	5	faraji	faraji	NOUN
fumecheng-11587	526	6	oskouie	oskouie	NOUN
fumecheng-11587	526	7	,	,	PUNCT
fumecheng-11587	526	8	m.	m.	NOUN
fumecheng-11587	526	9	,	,	PUNCT
fumecheng-11587	526	10	nesarhosseini	nesarhosseini	PROPN
fumecheng-11587	526	11	,	,	PUNCT
fumecheng-11587	526	12	s.	s.	PROPN
fumecheng-11587	526	13	,	,	PUNCT
fumecheng-11587	526	14	rouhi	rouhi	NOUN
fumecheng-11587	526	15	,	,	PUNCT
fumecheng-11587	526	16	h.	h.	NOUN
fumecheng-11587	526	17	,	,	PUNCT
fumecheng-11587	526	18	2022	2022	NUM
fumecheng-11587	526	19	,	,	PUNCT
fumecheng-11587	526	20	vibrations	vibration	NOUN
fumecheng-11587	526	21	of	of	ADP
fumecheng-11587	526	22	piezoelectric	piezoelectric	NOUN
fumecheng-11587	526	23	nanobeams	nanobeam	NOUN
fumecheng-11587	526	24	considering	consider	VERB
fumecheng-11587	526	25	flexoelectricity	flexoelectricity	NOUN
fumecheng-11587	526	26	influence	influence	NOUN
fumecheng-11587	526	27	:	:	PUNCT
fumecheng-11587	526	28	a	a	DET
fumecheng-11587	526	29	numerical	numerical	ADJ
fumecheng-11587	526	30	approach	approach	NOUN
fumecheng-11587	526	31	based	base	VERB
fumecheng-11587	526	32	on	on	ADP
fumecheng-11587	526	33	strain	strain	NOUN
fumecheng-11587	526	34	-	-	PUNCT
fumecheng-11587	526	35	driven	drive	VERB
fumecheng-11587	526	36	nonlocal	nonlocal	ADJ
fumecheng-11587	526	37	differential	differential	ADJ
fumecheng-11587	526	38	/	/	SYM
fumecheng-11587	526	39	integral	integral	ADJ
fumecheng-11587	526	40	models	model	NOUN
fumecheng-11587	526	41	,	,	PUNCT
fumecheng-11587	526	42	journal	journal	NOUN
fumecheng-11587	526	43	of	of	ADP
fumecheng-11587	526	44	the	the	DET
fumecheng-11587	526	45	brazilian	brazilian	ADJ
fumecheng-11587	526	46	society	society	NOUN
fumecheng-11587	526	47	of	of	ADP
fumecheng-11587	526	48	mechanical	mechanical	ADJ
fumecheng-11587	526	49	sciences	science	NOUN
fumecheng-11587	526	50	and	and	CCONJ
fumecheng-11587	526	51	engineering	engineering	NOUN
fumecheng-11587	526	52	,	,	PUNCT
fumecheng-11587	526	53	44(2	44(2	NOUN
fumecheng-11587	526	54	)	)	PUNCT
fumecheng-11587	526	55	,	,	PUNCT
fumecheng-11587	526	56	57	57	NUM
fumecheng-11587	526	57	.	.	X
fumecheng-11587	526	58	732	732	NUM
fumecheng-11587	526	59	n.	n.	NOUN
fumecheng-11587	526	60	nešić	nešić	PROPN
fumecheng-11587	526	61	,	,	PUNCT
fumecheng-11587	526	62	m.	m.	NOUN
fumecheng-11587	526	63	cajić	cajić	NOUN
fumecheng-11587	526	64	,	,	PUNCT
fumecheng-11587	526	65	d.	d.	PROPN
fumecheng-11587	526	66	karličić	karličić	PROPN
fumecheng-11587	526	67	,	,	PUNCT
fumecheng-11587	526	68	m.	m.	NOUN
fumecheng-11587	526	69	lazarević	lazarević	PROPN
fumecheng-11587	526	70	,	,	PUNCT
fumecheng-11587	526	71	s.	s.	PROPN
fumecheng-11587	526	72	adhikari	adhikari	PROPN
fumecheng-11587	526	73	39	39	NUM
fumecheng-11587	526	74	.	.	PUNCT
fumecheng-11587	527	1	romano	romano	NOUN
fumecheng-11587	527	2	,	,	PUNCT
fumecheng-11587	527	3	g.	g.	PROPN
fumecheng-11587	527	4	,	,	PUNCT
fumecheng-11587	527	5	barretta	barretta	PROPN
fumecheng-11587	527	6	,	,	PUNCT
fumecheng-11587	527	7	r.	r.	PROPN
fumecheng-11587	527	8	,	,	PUNCT
fumecheng-11587	527	9	2017	2017	NUM
fumecheng-11587	527	10	,	,	PUNCT
fumecheng-11587	527	11	stress	stress	NOUN
fumecheng-11587	527	12	-	-	PUNCT
fumecheng-11587	527	13	driven	drive	VERB
fumecheng-11587	527	14	versus	versus	ADP
fumecheng-11587	527	15	strain	strain	NOUN
fumecheng-11587	527	16	-	-	PUNCT
fumecheng-11587	527	17	driven	drive	VERB
fumecheng-11587	527	18	nonlocal	nonlocal	ADJ
fumecheng-11587	527	19	integral	integral	ADJ
fumecheng-11587	527	20	model	model	NOUN
fumecheng-11587	527	21	for	for	ADP
fumecheng-11587	527	22	elastic	elastic	ADJ
fumecheng-11587	527	23	nanobeams	nanobeam	NOUN
fumecheng-11587	527	24	,	,	PUNCT
fumecheng-11587	527	25	composites	composite	VERB
fumecheng-11587	527	26	part	part	NOUN
fumecheng-11587	527	27	b	b	NOUN
fumecheng-11587	527	28	:	:	PUNCT
fumecheng-11587	527	29	engineering	engineering	NOUN
fumecheng-11587	527	30	,	,	PUNCT
fumecheng-11587	527	31	114	114	NUM
fumecheng-11587	527	32	,	,	PUNCT
fumecheng-11587	527	33	pp	pp	ADJ
fumecheng-11587	527	34	.	.	PUNCT
fumecheng-11587	528	1	184	184	NUM
fumecheng-11587	528	2	-	-	SYM
fumecheng-11587	528	3	188	188	NUM
fumecheng-11587	528	4	.	.	PUNCT
fumecheng-11587	529	1	40	40	NUM
fumecheng-11587	529	2	.	.	PUNCT
fumecheng-11587	530	1	faraji	faraji	PROPN
fumecheng-11587	530	2	oskouie	oskouie	PROPN
fumecheng-11587	530	3	,	,	PUNCT
fumecheng-11587	530	4	m.	m.	NOUN
fumecheng-11587	530	5	,	,	PUNCT
fumecheng-11587	530	6	ansari	ansari	PROPN
fumecheng-11587	530	7	,	,	PUNCT
fumecheng-11587	530	8	r.	r.	PROPN
fumecheng-11587	530	9	,	,	PUNCT
fumecheng-11587	530	10	rouhi	rouhi	NOUN
fumecheng-11587	530	11	,	,	PUNCT
fumecheng-11587	530	12	h.	h.	NOUN
fumecheng-11587	530	13	,	,	PUNCT
fumecheng-11587	530	14	2018	2018	NUM
fumecheng-11587	530	15	,	,	PUNCT
fumecheng-11587	530	16	bending	bend	VERB
fumecheng-11587	530	17	of	of	ADP
fumecheng-11587	530	18	euler	euler	NOUN
fumecheng-11587	530	19	–	–	PUNCT
fumecheng-11587	530	20	bernoulli	bernoulli	NOUN
fumecheng-11587	530	21	nanobeams	nanobeam	NOUN
fumecheng-11587	530	22	based	base	VERB
fumecheng-11587	530	23	on	on	ADP
fumecheng-11587	530	24	the	the	DET
fumecheng-11587	530	25	strain	strain	NOUN
fumecheng-11587	530	26	-	-	PUNCT
fumecheng-11587	530	27	driven	drive	VERB
fumecheng-11587	530	28	and	and	CCONJ
fumecheng-11587	530	29	stress	stress	NOUN
fumecheng-11587	530	30	-	-	PUNCT
fumecheng-11587	530	31	driven	drive	VERB
fumecheng-11587	530	32	nonlocal	nonlocal	ADJ
fumecheng-11587	530	33	integral	integral	ADJ
fumecheng-11587	530	34	models	model	NOUN
fumecheng-11587	530	35	:	:	PUNCT
fumecheng-11587	530	36	a	a	DET
fumecheng-11587	530	37	numerical	numerical	ADJ
fumecheng-11587	530	38	approach	approach	NOUN
fumecheng-11587	530	39	,	,	PUNCT
fumecheng-11587	530	40	acta	acta	PROPN
fumecheng-11587	530	41	mechanica	mechanica	PROPN
fumecheng-11587	530	42	sinica	sinica	PROPN
fumecheng-11587	530	43	,	,	PUNCT
fumecheng-11587	530	44	34(5	34(5	PROPN
fumecheng-11587	530	45	)	)	PUNCT
fumecheng-11587	530	46	,	,	PUNCT
fumecheng-11587	530	47	pp	pp	PROPN
fumecheng-11587	530	48	.	.	PUNCT
fumecheng-11587	531	1	871	871	NUM
fumecheng-11587	531	2	-	-	SYM
fumecheng-11587	531	3	882	882	NUM
fumecheng-11587	531	4	.	.	PUNCT
fumecheng-11587	532	1	41	41	NUM
fumecheng-11587	532	2	.	.	PUNCT
fumecheng-11587	533	1	faraji	faraji	PROPN
fumecheng-11587	533	2	oskouie	oskouie	PROPN
fumecheng-11587	533	3	,	,	PUNCT
fumecheng-11587	533	4	m.	m.	NOUN
fumecheng-11587	533	5	,	,	PUNCT
fumecheng-11587	533	6	ansari	ansari	PROPN
fumecheng-11587	533	7	,	,	PUNCT
fumecheng-11587	533	8	r.	r.	PROPN
fumecheng-11587	533	9	,	,	PUNCT
fumecheng-11587	533	10	rouhi	rouhi	NOUN
fumecheng-11587	533	11	,	,	PUNCT
fumecheng-11587	533	12	h.	h.	NOUN
fumecheng-11587	533	13	,	,	PUNCT
fumecheng-11587	533	14	2018	2018	NUM
fumecheng-11587	533	15	,	,	PUNCT
fumecheng-11587	533	16	a	a	DET
fumecheng-11587	533	17	numerical	numerical	ADJ
fumecheng-11587	533	18	study	study	NOUN
fumecheng-11587	533	19	on	on	ADP
fumecheng-11587	533	20	the	the	DET
fumecheng-11587	533	21	buckling	buckling	NOUN
fumecheng-11587	533	22	and	and	CCONJ
fumecheng-11587	533	23	vibration	vibration	NOUN
fumecheng-11587	533	24	of	of	ADP
fumecheng-11587	533	25	nanobeams	nanobeam	NOUN
fumecheng-11587	533	26	based	base	VERB
fumecheng-11587	533	27	on	on	ADP
fumecheng-11587	533	28	the	the	DET
fumecheng-11587	533	29	strain	strain	NOUN
fumecheng-11587	533	30	and	and	CCONJ
fumecheng-11587	533	31	stress	stress	NOUN
fumecheng-11587	533	32	-	-	PUNCT
fumecheng-11587	533	33	driven	drive	VERB
fumecheng-11587	533	34	nonlocal	nonlocal	ADJ
fumecheng-11587	533	35	integral	integral	ADJ
fumecheng-11587	533	36	models	model	NOUN
fumecheng-11587	533	37	,	,	PUNCT
fumecheng-11587	533	38	international	international	ADJ
fumecheng-11587	533	39	journal	journal	NOUN
fumecheng-11587	533	40	of	of	ADP
fumecheng-11587	533	41	computational	computational	ADJ
fumecheng-11587	533	42	materials	material	NOUN
fumecheng-11587	533	43	science	science	NOUN
fumecheng-11587	533	44	and	and	CCONJ
fumecheng-11587	533	45	engineering	engineering	NOUN
fumecheng-11587	533	46	,	,	PUNCT
fumecheng-11587	533	47	7(03	7(03	NUM
fumecheng-11587	533	48	)	)	PUNCT
fumecheng-11587	533	49	,	,	PUNCT
fumecheng-11587	533	50	1850016	1850016	NUM
fumecheng-11587	533	51	.	.	PUNCT
fumecheng-11587	534	1	42	42	NUM
fumecheng-11587	534	2	.	.	PUNCT
fumecheng-11587	534	3	vaccaro	vaccaro	PROPN
fumecheng-11587	534	4	,	,	PUNCT
fumecheng-11587	534	5	m.s	m.s	PROPN
fumecheng-11587	534	6	.	.	PROPN
fumecheng-11587	534	7	,	,	PUNCT
fumecheng-11587	534	8	pinnola	pinnola	PROPN
fumecheng-11587	534	9	,	,	PUNCT
fumecheng-11587	534	10	f.p	f.p	PROPN
fumecheng-11587	534	11	.	.	PROPN
fumecheng-11587	534	12	,	,	PUNCT
fumecheng-11587	534	13	marotti	marotti	PROPN
fumecheng-11587	534	14	de	de	X
fumecheng-11587	534	15	sciarra	sciarra	PROPN
fumecheng-11587	534	16	,	,	PUNCT
fumecheng-11587	534	17	f.	f.	PROPN
fumecheng-11587	534	18	,	,	PUNCT
fumecheng-11587	534	19	barretta	barretta	PROPN
fumecheng-11587	534	20	,	,	PUNCT
fumecheng-11587	534	21	r.	r.	PROPN
fumecheng-11587	534	22	,	,	PUNCT
fumecheng-11587	534	23	2021	2021	NUM
fumecheng-11587	534	24	,	,	PUNCT
fumecheng-11587	534	25	elastostatics	elastostatic	NOUN
fumecheng-11587	534	26	of	of	ADP
fumecheng-11587	534	27	bernoulli	bernoulli	PROPN
fumecheng-11587	534	28	–	–	PUNCT
fumecheng-11587	534	29	euler	euler	NOUN
fumecheng-11587	534	30	beams	beam	NOUN
fumecheng-11587	534	31	resting	rest	VERB
fumecheng-11587	534	32	on	on	ADP
fumecheng-11587	534	33	displacement	displacement	NOUN
fumecheng-11587	534	34	-	-	PUNCT
fumecheng-11587	534	35	driven	drive	VERB
fumecheng-11587	534	36	nonlocal	nonlocal	ADJ
fumecheng-11587	534	37	foundation	foundation	NOUN
fumecheng-11587	534	38	,	,	PUNCT
fumecheng-11587	534	39	nanomaterials	nanomaterial	NOUN
fumecheng-11587	534	40	,	,	PUNCT
fumecheng-11587	534	41	11(3	11(3	NUM
fumecheng-11587	534	42	)	)	PUNCT
fumecheng-11587	534	43	,	,	PUNCT
fumecheng-11587	534	44	573	573	NUM
fumecheng-11587	534	45	.	.	NOUN
fumecheng-11587	534	46	43	43	NUM
fumecheng-11587	534	47	.	.	PUNCT
fumecheng-11587	535	1	patnaik	patnaik	PROPN
fumecheng-11587	535	2	,	,	PUNCT
fumecheng-11587	535	3	s.	s.	PROPN
fumecheng-11587	535	4	,	,	PUNCT
fumecheng-11587	535	5	sidhardh	sidhardh	PROPN
fumecheng-11587	535	6	,	,	PUNCT
fumecheng-11587	535	7	s.	s.	PROPN
fumecheng-11587	535	8	,	,	PUNCT
fumecheng-11587	535	9	semperlotti	semperlotti	PROPN
fumecheng-11587	535	10	,	,	PUNCT
fumecheng-11587	535	11	f.	f.	PROPN
fumecheng-11587	535	12	,	,	PUNCT
fumecheng-11587	535	13	2022	2022	NUM
fumecheng-11587	535	14	,	,	PUNCT
fumecheng-11587	535	15	displacement	displacement	NOUN
fumecheng-11587	535	16	-	-	PUNCT
fumecheng-11587	535	17	driven	drive	VERB
fumecheng-11587	535	18	approach	approach	NOUN
fumecheng-11587	535	19	to	to	ADP
fumecheng-11587	535	20	nonlocal	nonlocal	ADJ
fumecheng-11587	535	21	elasticity	elasticity	NOUN
fumecheng-11587	535	22	,	,	PUNCT
fumecheng-11587	535	23	european	european	PROPN
fumecheng-11587	535	24	journal	journal	PROPN
fumecheng-11587	535	25	of	of	ADP
fumecheng-11587	535	26	mechanics	mechanic	NOUN
fumecheng-11587	535	27	-	-	PUNCT
fumecheng-11587	535	28	a	a	DET
fumecheng-11587	535	29	/	/	SYM
fumecheng-11587	535	30	solids	solid	NOUN
fumecheng-11587	535	31	,	,	PUNCT
fumecheng-11587	535	32	92	92	NUM
fumecheng-11587	535	33	,	,	PUNCT
fumecheng-11587	535	34	104434	104434	NUM
fumecheng-11587	535	35	.	.	PUNCT
fumecheng-11587	536	1	44	44	NUM
fumecheng-11587	536	2	.	.	PUNCT
fumecheng-11587	537	1	pinnola	pinnola	PROPN
fumecheng-11587	537	2	,	,	PUNCT
fumecheng-11587	537	3	f.p	f.p	PROPN
fumecheng-11587	537	4	.	.	PROPN
fumecheng-11587	537	5	,	,	PUNCT
fumecheng-11587	537	6	vaccaro	vaccaro	PROPN
fumecheng-11587	537	7	,	,	PUNCT
fumecheng-11587	537	8	m.s	m.s	PROPN
fumecheng-11587	537	9	.	.	PROPN
fumecheng-11587	537	10	,	,	PUNCT
fumecheng-11587	537	11	barretta	barretta	PROPN
fumecheng-11587	537	12	,	,	PUNCT
fumecheng-11587	537	13	r.	r.	PROPN
fumecheng-11587	537	14	,	,	PUNCT
fumecheng-11587	537	15	marotti	marotti	PROPN
fumecheng-11587	537	16	de	de	X
fumecheng-11587	537	17	sciarra	sciarra	PROPN
fumecheng-11587	537	18	,	,	PUNCT
fumecheng-11587	537	19	f.	f.	PROPN
fumecheng-11587	537	20	,	,	PUNCT
fumecheng-11587	537	21	ruta	ruta	PROPN
fumecheng-11587	537	22	,	,	PUNCT
fumecheng-11587	537	23	g.	g.	PROPN
fumecheng-11587	537	24	,	,	PUNCT
fumecheng-11587	537	25	2023	2023	NUM
fumecheng-11587	537	26	,	,	PUNCT
fumecheng-11587	537	27	elasticity	elasticity	NOUN
fumecheng-11587	537	28	problems	problem	NOUN
fumecheng-11587	537	29	of	of	ADP
fumecheng-11587	537	30	beams	beam	NOUN
fumecheng-11587	537	31	on	on	ADP
fumecheng-11587	537	32	reaction	reaction	NOUN
fumecheng-11587	537	33	-	-	PUNCT
fumecheng-11587	537	34	driven	drive	VERB
fumecheng-11587	537	35	nonlocal	nonlocal	ADJ
fumecheng-11587	537	36	foundation	foundation	NOUN
fumecheng-11587	537	37	,	,	PUNCT
fumecheng-11587	537	38	archive	archive	NOUN
fumecheng-11587	537	39	of	of	ADP
fumecheng-11587	537	40	applied	apply	VERB
fumecheng-11587	537	41	mechanics	mechanic	NOUN
fumecheng-11587	537	42	,	,	PUNCT
fumecheng-11587	537	43	93	93	NUM
fumecheng-11587	537	44	,	,	PUNCT
fumecheng-11587	537	45	pp	pp	ADJ
fumecheng-11587	537	46	.	.	PUNCT
fumecheng-11587	538	1	41–71	41–71	NOUN
fumecheng-11587	538	2	.	.	PUNCT
fumecheng-11587	539	1	45	45	NUM
fumecheng-11587	539	2	.	.	PUNCT
fumecheng-11587	540	1	gao	gao	PROPN
fumecheng-11587	540	2	,	,	PUNCT
fumecheng-11587	540	3	y.	y.	PROPN
fumecheng-11587	540	4	,	,	PUNCT
fumecheng-11587	540	5	xiao	xiao	PROPN
fumecheng-11587	540	6	,	,	PUNCT
fumecheng-11587	540	7	w.	w.	PROPN
fumecheng-11587	540	8	,	,	PUNCT
fumecheng-11587	540	9	zhu	zhu	PROPN
fumecheng-11587	540	10	,	,	PUNCT
fumecheng-11587	540	11	h.	h.	PROPN
fumecheng-11587	540	12	,	,	PUNCT
fumecheng-11587	540	13	2019	2019	NUM
fumecheng-11587	540	14	,	,	PUNCT
fumecheng-11587	540	15	nonlinear	nonlinear	ADJ
fumecheng-11587	540	16	vibration	vibration	NOUN
fumecheng-11587	540	17	of	of	ADP
fumecheng-11587	540	18	functionally	functionally	ADV
fumecheng-11587	540	19	graded	grade	VERB
fumecheng-11587	540	20	nano	nano	NOUN
fumecheng-11587	540	21	-	-	NOUN
fumecheng-11587	540	22	tubes	tube	NOUN
fumecheng-11587	540	23	using	use	VERB
fumecheng-11587	540	24	nonlocal	nonlocal	ADJ
fumecheng-11587	540	25	strain	strain	NOUN
fumecheng-11587	540	26	gradient	gradient	NOUN
fumecheng-11587	540	27	theory	theory	NOUN
fumecheng-11587	540	28	and	and	CCONJ
fumecheng-11587	540	29	a	a	DET
fumecheng-11587	540	30	two	two	NUM
fumecheng-11587	540	31	-	-	PUNCT
fumecheng-11587	540	32	steps	step	NOUN
fumecheng-11587	540	33	perturbation	perturbation	NOUN
fumecheng-11587	540	34	method	method	NOUN
fumecheng-11587	540	35	,	,	PUNCT
fumecheng-11587	540	36	structural	structural	ADJ
fumecheng-11587	540	37	engineering	engineering	NOUN
fumecheng-11587	540	38	and	and	CCONJ
fumecheng-11587	540	39	mechanics	mechanic	NOUN
fumecheng-11587	540	40	,	,	PUNCT
fumecheng-11587	540	41	69(2	69(2	NOUN
fumecheng-11587	540	42	)	)	PUNCT
fumecheng-11587	540	43	,	,	PUNCT
fumecheng-11587	540	44	pp	pp	PROPN
fumecheng-11587	540	45	.	.	PUNCT
fumecheng-11587	541	1	205	205	NUM
fumecheng-11587	541	2	-	-	SYM
fumecheng-11587	541	3	219	219	NUM
fumecheng-11587	541	4	.	.	PUNCT
fumecheng-11587	542	1	46	46	NUM
fumecheng-11587	542	2	.	.	PUNCT
fumecheng-11587	543	1	gao	gao	PROPN
fumecheng-11587	543	2	,	,	PUNCT
fumecheng-11587	543	3	y.	y.	PROPN
fumecheng-11587	543	4	,	,	PUNCT
fumecheng-11587	543	5	xiao	xiao	PROPN
fumecheng-11587	543	6	,	,	PUNCT
fumecheng-11587	543	7	w.s	w.s	PROPN
fumecheng-11587	543	8	.	.	PROPN
fumecheng-11587	543	9	,	,	PUNCT
fumecheng-11587	543	10	zhu	zhu	PROPN
fumecheng-11587	543	11	,	,	PUNCT
fumecheng-11587	543	12	h.	h.	PROPN
fumecheng-11587	543	13	,	,	PUNCT
fumecheng-11587	543	14	2020	2020	NUM
fumecheng-11587	543	15	,	,	PUNCT
fumecheng-11587	543	16	snap	snap	NOUN
fumecheng-11587	543	17	-	-	PUNCT
fumecheng-11587	543	18	buckling	buckling	NOUN
fumecheng-11587	543	19	of	of	ADP
fumecheng-11587	543	20	functionally	functionally	ADV
fumecheng-11587	543	21	graded	grade	VERB
fumecheng-11587	543	22	multilayer	multilayer	ADJ
fumecheng-11587	543	23	graphene	graphene	NOUN
fumecheng-11587	543	24	plateletreinforced	plateletreinforce	VERB
fumecheng-11587	543	25	composite	composite	ADJ
fumecheng-11587	543	26	curved	curve	VERB
fumecheng-11587	543	27	nanobeams	nanobeam	NOUN
fumecheng-11587	543	28	with	with	ADP
fumecheng-11587	543	29	geometrical	geometrical	ADJ
fumecheng-11587	543	30	imperfections	imperfection	NOUN
fumecheng-11587	543	31	,	,	PUNCT
fumecheng-11587	543	32	european	european	ADJ
fumecheng-11587	543	33	journal	journal	PROPN
fumecheng-11587	543	34	of	of	ADP
fumecheng-11587	543	35	mechanicsa	mechanicsa	PROPN
fumecheng-11587	543	36	/	/	SYM
fumecheng-11587	543	37	solids	solid	NOUN
fumecheng-11587	543	38	,	,	PUNCT
fumecheng-11587	543	39	82	82	NUM
fumecheng-11587	543	40	,	,	PUNCT
fumecheng-11587	543	41	103993	103993	NUM
fumecheng-11587	543	42	.	.	PUNCT
fumecheng-11587	544	1	47	47	NUM
fumecheng-11587	544	2	.	.	PUNCT
fumecheng-11587	545	1	gao	gao	PROPN
fumecheng-11587	545	2	,	,	PUNCT
fumecheng-11587	545	3	y.	y.	PROPN
fumecheng-11587	545	4	,	,	PUNCT
fumecheng-11587	545	5	xiao	xiao	PROPN
fumecheng-11587	545	6	,	,	PUNCT
fumecheng-11587	545	7	w.s	w.s	PROPN
fumecheng-11587	545	8	.	.	PROPN
fumecheng-11587	545	9	,	,	PUNCT
fumecheng-11587	545	10	zhu	zhu	PROPN
fumecheng-11587	545	11	,	,	PUNCT
fumecheng-11587	545	12	h.	h.	PROPN
fumecheng-11587	545	13	,	,	PUNCT
fumecheng-11587	545	14	2019	2019	NUM
fumecheng-11587	545	15	,	,	PUNCT
fumecheng-11587	545	16	nonlinear	nonlinear	ADJ
fumecheng-11587	545	17	vibration	vibration	NOUN
fumecheng-11587	545	18	analysis	analysis	NOUN
fumecheng-11587	545	19	of	of	ADP
fumecheng-11587	545	20	different	different	ADJ
fumecheng-11587	545	21	types	type	NOUN
fumecheng-11587	545	22	of	of	ADP
fumecheng-11587	545	23	functionally	functionally	ADV
fumecheng-11587	545	24	graded	grade	VERB
fumecheng-11587	545	25	beams	beam	NOUN
fumecheng-11587	545	26	using	use	VERB
fumecheng-11587	545	27	nonlocal	nonlocal	ADJ
fumecheng-11587	545	28	strain	strain	NOUN
fumecheng-11587	545	29	gradient	gradient	NOUN
fumecheng-11587	545	30	theory	theory	NOUN
fumecheng-11587	545	31	and	and	CCONJ
fumecheng-11587	545	32	a	a	DET
fumecheng-11587	545	33	two	two	NUM
fumecheng-11587	545	34	-	-	PUNCT
fumecheng-11587	545	35	step	step	NOUN
fumecheng-11587	545	36	perturbation	perturbation	NOUN
fumecheng-11587	545	37	method	method	NOUN
fumecheng-11587	545	38	,	,	PUNCT
fumecheng-11587	545	39	the	the	DET
fumecheng-11587	545	40	european	european	PROPN
fumecheng-11587	545	41	physical	physical	PROPN
fumecheng-11587	545	42	journal	journal	PROPN
fumecheng-11587	545	43	plus	plus	CCONJ
fumecheng-11587	545	44	,	,	PUNCT
fumecheng-11587	545	45	134(1	134(1	NUM
fumecheng-11587	545	46	)	)	PUNCT
fumecheng-11587	545	47	,	,	PUNCT
fumecheng-11587	545	48	23	23	NUM
fumecheng-11587	545	49	.	.	X
fumecheng-11587	545	50	48	48	NUM
fumecheng-11587	545	51	.	.	PUNCT
fumecheng-11587	546	1	wang	wang	PROPN
fumecheng-11587	546	2	,	,	PUNCT
fumecheng-11587	546	3	j.	j.	PROPN
fumecheng-11587	546	4	,	,	PUNCT
fumecheng-11587	546	5	shen	shen	PROPN
fumecheng-11587	546	6	,	,	PUNCT
fumecheng-11587	546	7	h.	h.	PROPN
fumecheng-11587	546	8	,	,	PUNCT
fumecheng-11587	546	9	2019	2019	NUM
fumecheng-11587	546	10	,	,	PUNCT
fumecheng-11587	546	11	nonlinear	nonlinear	ADJ
fumecheng-11587	546	12	vibrations	vibration	NOUN
fumecheng-11587	546	13	of	of	ADP
fumecheng-11587	546	14	axially	axially	ADV
fumecheng-11587	546	15	moving	move	VERB
fumecheng-11587	546	16	simply	simply	ADV
fumecheng-11587	546	17	supported	support	VERB
fumecheng-11587	546	18	viscoelastic	viscoelastic	NOUN
fumecheng-11587	546	19	nanobeams	nanobeam	NOUN
fumecheng-11587	546	20	based	base	VERB
fumecheng-11587	546	21	on	on	ADP
fumecheng-11587	546	22	nonlocal	nonlocal	ADJ
fumecheng-11587	546	23	strain	strain	NOUN
fumecheng-11587	546	24	gradient	gradient	NOUN
fumecheng-11587	546	25	theory	theory	NOUN
fumecheng-11587	546	26	.	.	PUNCT
fumecheng-11587	547	1	journal	journal	PROPN
fumecheng-11587	547	2	of	of	ADP
fumecheng-11587	547	3	physics	physics	PROPN
fumecheng-11587	547	4	:	:	PUNCT
fumecheng-11587	547	5	condensed	condense	VERB
fumecheng-11587	547	6	matter	matter	NOUN
fumecheng-11587	547	7	,	,	PUNCT
fumecheng-11587	547	8	31(48	31(48	NUM
fumecheng-11587	547	9	)	)	PUNCT
fumecheng-11587	547	10	,	,	PUNCT
fumecheng-11587	547	11	485403	485403	NUM
fumecheng-11587	547	12	.	.	PUNCT
fumecheng-11587	548	1	49	49	NUM
fumecheng-11587	548	2	.	.	PUNCT
fumecheng-11587	549	1	jafarsadeghi	jafarsadeghi	PROPN
fumecheng-11587	549	2	-	-	PUNCT
fumecheng-11587	549	3	pournaki	pournaki	PROPN
fumecheng-11587	549	4	,	,	PUNCT
fumecheng-11587	549	5	i.	i.	NOUN
fumecheng-11587	549	6	,	,	PUNCT
fumecheng-11587	549	7	azizi	azizi	PROPN
fumecheng-11587	549	8	,	,	PUNCT
fumecheng-11587	549	9	s.	s.	PROPN
fumecheng-11587	549	10	,	,	PUNCT
fumecheng-11587	549	11	zamanzadeh	zamanzadeh	PROPN
fumecheng-11587	549	12	,	,	PUNCT
fumecheng-11587	549	13	m.	m.	NOUN
fumecheng-11587	549	14	,	,	PUNCT
fumecheng-11587	549	15	madinei	madinei	NOUN
fumecheng-11587	549	16	,	,	PUNCT
fumecheng-11587	549	17	h.	h.	PROPN
fumecheng-11587	549	18	,	,	PUNCT
fumecheng-11587	549	19	shabani	shabani	PROPN
fumecheng-11587	549	20	,	,	PUNCT
fumecheng-11587	549	21	r.	r.	PROPN
fumecheng-11587	549	22	,	,	PUNCT
fumecheng-11587	549	23	rezazadeh	rezazadeh	PROPN
fumecheng-11587	549	24	,	,	PUNCT
fumecheng-11587	549	25	g.	g.	PROPN
fumecheng-11587	549	26	,	,	PUNCT
fumecheng-11587	549	27	2020	2020	NUM
fumecheng-11587	549	28	,	,	PUNCT
fumecheng-11587	549	29	sizedependent	sizedependent	NOUN
fumecheng-11587	549	30	dynamics	dynamic	NOUN
fumecheng-11587	549	31	of	of	ADP
fumecheng-11587	549	32	a	a	DET
fumecheng-11587	549	33	fg	fg	PROPN
fumecheng-11587	549	34	nanobeam	nanobeam	NOUN
fumecheng-11587	549	35	near	near	ADP
fumecheng-11587	549	36	nonlinear	nonlinear	ADJ
fumecheng-11587	549	37	resonances	resonance	NOUN
fumecheng-11587	549	38	induced	induce	VERB
fumecheng-11587	549	39	by	by	ADP
fumecheng-11587	549	40	heat	heat	NOUN
fumecheng-11587	549	41	,	,	PUNCT
fumecheng-11587	549	42	applied	apply	VERB
fumecheng-11587	549	43	mathematical	mathematical	ADJ
fumecheng-11587	549	44	modelling	modelling	NOUN
fumecheng-11587	549	45	,	,	PUNCT
fumecheng-11587	549	46	86	86	NUM
fumecheng-11587	549	47	,	,	PUNCT
fumecheng-11587	549	48	pp	pp	ADJ
fumecheng-11587	549	49	.	.	PUNCT
fumecheng-11587	550	1	349	349	NUM
fumecheng-11587	550	2	-	-	SYM
fumecheng-11587	550	3	367	367	NUM
fumecheng-11587	550	4	.	.	PUNCT
fumecheng-11587	551	1	50	50	NUM
fumecheng-11587	551	2	.	.	PUNCT
fumecheng-11587	552	1	li	li	PROPN
fumecheng-11587	552	2	,	,	PUNCT
fumecheng-11587	552	3	l.	l.	PROPN
fumecheng-11587	552	4	,	,	PUNCT
fumecheng-11587	552	5	hu	hu	PROPN
fumecheng-11587	552	6	,	,	PUNCT
fumecheng-11587	552	7	y.	y.	PROPN
fumecheng-11587	552	8	,	,	PUNCT
fumecheng-11587	552	9	li	li	PROPN
fumecheng-11587	552	10	,	,	PUNCT
fumecheng-11587	552	11	x.	x.	NOUN
fumecheng-11587	552	12	,	,	PUNCT
fumecheng-11587	552	13	2016	2016	NUM
fumecheng-11587	552	14	,	,	PUNCT
fumecheng-11587	552	15	longitudinal	longitudinal	ADJ
fumecheng-11587	552	16	vibration	vibration	NOUN
fumecheng-11587	552	17	of	of	ADP
fumecheng-11587	552	18	size	size	NOUN
fumecheng-11587	552	19	-	-	PUNCT
fumecheng-11587	552	20	dependent	dependent	ADJ
fumecheng-11587	552	21	rods	rod	NOUN
fumecheng-11587	552	22	via	via	ADP
fumecheng-11587	552	23	nonlocal	nonlocal	ADJ
fumecheng-11587	552	24	strain	strain	NOUN
fumecheng-11587	552	25	gradient	gradient	NOUN
fumecheng-11587	552	26	theory	theory	NOUN
fumecheng-11587	552	27	,	,	PUNCT
fumecheng-11587	552	28	international	international	ADJ
fumecheng-11587	552	29	journal	journal	NOUN
fumecheng-11587	552	30	of	of	ADP
fumecheng-11587	552	31	mechanical	mechanical	ADJ
fumecheng-11587	552	32	sciences	science	NOUN
fumecheng-11587	552	33	,	,	PUNCT
fumecheng-11587	552	34	115	115	NUM
fumecheng-11587	552	35	-	-	SYM
fumecheng-11587	552	36	116	116	NUM
fumecheng-11587	552	37	,	,	PUNCT
fumecheng-11587	552	38	pp	pp	ADJ
fumecheng-11587	552	39	.	.	PUNCT
fumecheng-11587	553	1	135	135	NUM
fumecheng-11587	553	2	-	-	SYM
fumecheng-11587	553	3	144	144	NUM
fumecheng-11587	553	4	.	.	PUNCT
fumecheng-11587	554	1	51	51	NUM
fumecheng-11587	554	2	.	.	PUNCT
fumecheng-11587	555	1	li	li	PROPN
fumecheng-11587	555	2	,	,	PUNCT
fumecheng-11587	555	3	x.	x.	PROPN
fumecheng-11587	555	4	,	,	PUNCT
fumecheng-11587	555	5	li	li	PROPN
fumecheng-11587	555	6	,	,	PUNCT
fumecheng-11587	555	7	l.	l.	PROPN
fumecheng-11587	555	8	,	,	PUNCT
fumecheng-11587	555	9	hu	hu	PROPN
fumecheng-11587	555	10	,	,	PUNCT
fumecheng-11587	555	11	y.	y.	NOUN
fumecheng-11587	555	12	,	,	PUNCT
fumecheng-11587	555	13	ding	ding	PROPN
fumecheng-11587	555	14	,	,	PUNCT
fumecheng-11587	555	15	z.	z.	PROPN
fumecheng-11587	555	16	,	,	PUNCT
fumecheng-11587	555	17	deng	deng	PROPN
fumecheng-11587	555	18	,	,	PUNCT
fumecheng-11587	555	19	w.	w.	PROPN
fumecheng-11587	555	20	,	,	PUNCT
fumecheng-11587	555	21	2017	2017	NUM
fumecheng-11587	555	22	.	.	PUNCT
fumecheng-11587	556	1	bending	bend	VERB
fumecheng-11587	556	2	,	,	PUNCT
fumecheng-11587	556	3	buckling	buckling	NOUN
fumecheng-11587	556	4	and	and	CCONJ
fumecheng-11587	556	5	vibration	vibration	NOUN
fumecheng-11587	556	6	of	of	ADP
fumecheng-11587	556	7	axially	axially	ADV
fumecheng-11587	556	8	functionally	functionally	ADV
fumecheng-11587	556	9	graded	grade	VERB
fumecheng-11587	556	10	beams	beam	NOUN
fumecheng-11587	556	11	based	base	VERB
fumecheng-11587	556	12	on	on	ADP
fumecheng-11587	556	13	nonlocal	nonlocal	ADJ
fumecheng-11587	556	14	strain	strain	NOUN
fumecheng-11587	556	15	gradient	gradient	NOUN
fumecheng-11587	556	16	theory	theory	NOUN
fumecheng-11587	556	17	,	,	PUNCT
fumecheng-11587	556	18	composite	composite	ADJ
fumecheng-11587	556	19	structures	structure	NOUN
fumecheng-11587	556	20	,	,	PUNCT
fumecheng-11587	556	21	165	165	NUM
fumecheng-11587	556	22	,	,	PUNCT
fumecheng-11587	556	23	pp	pp	ADJ
fumecheng-11587	556	24	.	.	PUNCT
fumecheng-11587	557	1	250	250	NUM
fumecheng-11587	557	2	-	-	SYM
fumecheng-11587	557	3	265	265	NUM
fumecheng-11587	557	4	.	.	PUNCT
fumecheng-11587	558	1	52	52	NUM
fumecheng-11587	558	2	.	.	PUNCT
fumecheng-11587	559	1	bhattiprolu	bhattiprolu	NOUN
fumecheng-11587	559	2	,	,	PUNCT
fumecheng-11587	559	3	u.	u.	PROPN
fumecheng-11587	559	4	,	,	PUNCT
fumecheng-11587	559	5	bajaj	bajaj	PROPN
fumecheng-11587	559	6	,	,	PUNCT
fumecheng-11587	559	7	a.k	a.k	PROPN
fumecheng-11587	559	8	.	.	PROPN
fumecheng-11587	559	9	,	,	PUNCT
fumecheng-11587	559	10	davies	davy	NOUN
fumecheng-11587	559	11	,	,	PUNCT
fumecheng-11587	559	12	p.	p.	NOUN
fumecheng-11587	559	13	,	,	PUNCT
fumecheng-11587	559	14	2016	2016	NUM
fumecheng-11587	559	15	,	,	PUNCT
fumecheng-11587	559	16	periodic	periodic	ADJ
fumecheng-11587	559	17	response	response	NOUN
fumecheng-11587	559	18	predictions	prediction	NOUN
fumecheng-11587	559	19	of	of	ADP
fumecheng-11587	559	20	beams	beam	NOUN
fumecheng-11587	559	21	on	on	ADP
fumecheng-11587	559	22	nonlinear	nonlinear	ADJ
fumecheng-11587	559	23	and	and	CCONJ
fumecheng-11587	559	24	viscoelastic	viscoelastic	ADJ
fumecheng-11587	559	25	unilateral	unilateral	ADJ
fumecheng-11587	559	26	foundations	foundation	NOUN
fumecheng-11587	559	27	using	use	VERB
fumecheng-11587	559	28	incremental	incremental	ADJ
fumecheng-11587	559	29	harmonic	harmonic	ADJ
fumecheng-11587	559	30	balance	balance	NOUN
fumecheng-11587	559	31	method	method	NOUN
fumecheng-11587	559	32	,	,	PUNCT
fumecheng-11587	559	33	international	international	ADJ
fumecheng-11587	559	34	journal	journal	NOUN
fumecheng-11587	559	35	of	of	ADP
fumecheng-11587	559	36	solids	solid	NOUN
fumecheng-11587	559	37	and	and	CCONJ
fumecheng-11587	559	38	structures	structure	NOUN
fumecheng-11587	559	39	,	,	PUNCT
fumecheng-11587	559	40	99	99	NUM
fumecheng-11587	559	41	,	,	PUNCT
fumecheng-11587	559	42	pp	pp	ADJ
fumecheng-11587	559	43	.	.	PUNCT
fumecheng-11587	560	1	28	28	NUM
fumecheng-11587	560	2	-	-	SYM
fumecheng-11587	560	3	39	39	NUM
fumecheng-11587	560	4	.	.	PUNCT
fumecheng-11587	561	1	53	53	NUM
fumecheng-11587	561	2	.	.	PUNCT
fumecheng-11587	561	3	jalaei	jalaei	NOUN
fumecheng-11587	561	4	,	,	PUNCT
fumecheng-11587	561	5	m.h	m.h	PROPN
fumecheng-11587	561	6	.	.	PROPN
fumecheng-11587	561	7	,	,	PUNCT
fumecheng-11587	561	8	arani	arani	PROPN
fumecheng-11587	561	9	,	,	PUNCT
fumecheng-11587	561	10	a.g	a.g	PROPN
fumecheng-11587	561	11	.	.	PROPN
fumecheng-11587	561	12	,	,	PUNCT
fumecheng-11587	561	13	nguyen	nguyen	PROPN
fumecheng-11587	561	14	-	-	PUNCT
fumecheng-11587	561	15	xuan	xuan	PROPN
fumecheng-11587	561	16	,	,	PUNCT
fumecheng-11587	561	17	h.	h.	PROPN
fumecheng-11587	561	18	,	,	PUNCT
fumecheng-11587	561	19	2019	2019	NUM
fumecheng-11587	561	20	,	,	PUNCT
fumecheng-11587	561	21	investigation	investigation	NOUN
fumecheng-11587	561	22	of	of	ADP
fumecheng-11587	561	23	thermal	thermal	ADJ
fumecheng-11587	561	24	and	and	CCONJ
fumecheng-11587	561	25	magnetic	magnetic	ADJ
fumecheng-11587	561	26	field	field	NOUN
fumecheng-11587	561	27	effects	effect	NOUN
fumecheng-11587	561	28	on	on	ADP
fumecheng-11587	561	29	the	the	DET
fumecheng-11587	561	30	dynamic	dynamic	ADJ
fumecheng-11587	561	31	instability	instability	NOUN
fumecheng-11587	561	32	of	of	ADP
fumecheng-11587	561	33	fg	fg	PROPN
fumecheng-11587	561	34	timoshenko	timoshenko	NOUN
fumecheng-11587	561	35	nanobeam	nanobeam	NOUN
fumecheng-11587	561	36	employing	employ	VERB
fumecheng-11587	561	37	nonlocal	nonlocal	ADJ
fumecheng-11587	561	38	strain	strain	NOUN
fumecheng-11587	561	39	gradient	gradient	NOUN
fumecheng-11587	561	40	theory	theory	NOUN
fumecheng-11587	561	41	,	,	PUNCT
fumecheng-11587	561	42	international	international	ADJ
fumecheng-11587	561	43	journal	journal	NOUN
fumecheng-11587	561	44	of	of	ADP
fumecheng-11587	561	45	mechanical	mechanical	ADJ
fumecheng-11587	561	46	sciences	science	NOUN
fumecheng-11587	561	47	,	,	PUNCT
fumecheng-11587	561	48	161	161	NUM
fumecheng-11587	561	49	-	-	SYM
fumecheng-11587	561	50	162	162	NUM
fumecheng-11587	561	51	,	,	PUNCT
fumecheng-11587	561	52	105043	105043	NUM
fumecheng-11587	561	53	.	.	PUNCT
fumecheng-11587	562	1	54	54	NUM
fumecheng-11587	562	2	.	.	PUNCT
fumecheng-11587	563	1	nayfeh	nayfeh	PROPN
fumecheng-11587	563	2	,	,	PUNCT
fumecheng-11587	563	3	a.h	a.h	PROPN
fumecheng-11587	563	4	.	.	PROPN
fumecheng-11587	563	5	,	,	PUNCT
fumecheng-11587	563	6	lacarbonara	lacarbonara	PROPN
fumecheng-11587	563	7	,	,	PUNCT
fumecheng-11587	563	8	w.	w.	NOUN
fumecheng-11587	563	9	,	,	PUNCT
fumecheng-11587	563	10	1997	1997	NUM
fumecheng-11587	563	11	,	,	PUNCT
fumecheng-11587	563	12	on	on	ADP
fumecheng-11587	563	13	the	the	DET
fumecheng-11587	563	14	discretization	discretization	NOUN
fumecheng-11587	563	15	of	of	ADP
fumecheng-11587	563	16	distributed	distribute	VERB
fumecheng-11587	563	17	-	-	PUNCT
fumecheng-11587	563	18	parameter	parameter	NOUN
fumecheng-11587	563	19	systems	system	NOUN
fumecheng-11587	563	20	with	with	ADP
fumecheng-11587	563	21	quadratic	quadratic	ADJ
fumecheng-11587	563	22	and	and	CCONJ
fumecheng-11587	563	23	cubic	cubic	ADJ
fumecheng-11587	563	24	nonlinearities	nonlinearitie	NOUN
fumecheng-11587	563	25	,	,	PUNCT
fumecheng-11587	563	26	nonlinear	nonlinear	ADJ
fumecheng-11587	563	27	dynamics	dynamic	NOUN
fumecheng-11587	563	28	,	,	PUNCT
fumecheng-11587	563	29	13(3	13(3	NUM
fumecheng-11587	563	30	)	)	PUNCT
fumecheng-11587	563	31	,	,	PUNCT
fumecheng-11587	563	32	pp	pp	ADP
fumecheng-11587	563	33	.	.	PUNCT
fumecheng-11587	564	1	203	203	NUM
fumecheng-11587	564	2	-	-	SYM
fumecheng-11587	564	3	220	220	NUM
fumecheng-11587	564	4	.	.	PUNCT
fumecheng-11587	565	1	55	55	NUM
fumecheng-11587	565	2	.	.	PUNCT
fumecheng-11587	566	1	hashemian	hashemian	ADJ
fumecheng-11587	566	2	,	,	PUNCT
fumecheng-11587	566	3	m.	m.	NOUN
fumecheng-11587	566	4	,	,	PUNCT
fumecheng-11587	566	5	falsafioon	falsafioon	NOUN
fumecheng-11587	566	6	,	,	PUNCT
fumecheng-11587	566	7	m.	m.	NOUN
fumecheng-11587	566	8	,	,	PUNCT
fumecheng-11587	566	9	pirmoradian	pirmoradian	NOUN
fumecheng-11587	566	10	,	,	PUNCT
fumecheng-11587	566	11	m.	m.	NOUN
fumecheng-11587	566	12	,	,	PUNCT
fumecheng-11587	566	13	toghraie	toghraie	PROPN
fumecheng-11587	566	14	,	,	PUNCT
fumecheng-11587	566	15	d.	d.	PROPN
fumecheng-11587	566	16	,	,	PUNCT
fumecheng-11587	566	17	2020	2020	NUM
fumecheng-11587	566	18	,	,	PUNCT
fumecheng-11587	566	19	nonlocal	nonlocal	ADJ
fumecheng-11587	566	20	dynamic	dynamic	ADJ
fumecheng-11587	566	21	stability	stability	NOUN
fumecheng-11587	566	22	analysis	analysis	NOUN
fumecheng-11587	566	23	of	of	ADP
fumecheng-11587	566	24	a	a	DET
fumecheng-11587	566	25	timoshenko	timoshenko	ADJ
fumecheng-11587	566	26	nanobeam	nanobeam	NOUN
fumecheng-11587	566	27	subjected	subject	VERB
fumecheng-11587	566	28	to	to	ADP
fumecheng-11587	566	29	a	a	DET
fumecheng-11587	566	30	sequence	sequence	NOUN
fumecheng-11587	566	31	of	of	ADP
fumecheng-11587	566	32	moving	move	VERB
fumecheng-11587	566	33	nanoparticles	nanoparticle	NOUN
fumecheng-11587	566	34	considering	consider	VERB
fumecheng-11587	566	35	surface	surface	NOUN
fumecheng-11587	566	36	effects	effect	NOUN
fumecheng-11587	566	37	,	,	PUNCT
fumecheng-11587	566	38	mechanics	mechanic	NOUN
fumecheng-11587	566	39	of	of	ADP
fumecheng-11587	566	40	materials	material	NOUN
fumecheng-11587	566	41	,	,	PUNCT
fumecheng-11587	566	42	148	148	NUM
fumecheng-11587	566	43	,	,	PUNCT
fumecheng-11587	566	44	103452	103452	NUM
fumecheng-11587	566	45	.	.	PUNCT
fumecheng-11587	567	1	56	56	NUM
fumecheng-11587	567	2	.	.	X
fumecheng-11587	567	3	trabelssi	trabelssi	NOUN
fumecheng-11587	567	4	,	,	PUNCT
fumecheng-11587	567	5	m.	m.	NOUN
fumecheng-11587	567	6	,	,	PUNCT
fumecheng-11587	567	7	el	el	PROPN
fumecheng-11587	567	8	-	-	PUNCT
fumecheng-11587	567	9	borgi	borgi	NOUN
fumecheng-11587	567	10	,	,	PUNCT
fumecheng-11587	567	11	s.	s.	PROPN
fumecheng-11587	567	12	,	,	PUNCT
fumecheng-11587	567	13	friswell	friswell	ADJ
fumecheng-11587	567	14	,	,	PUNCT
fumecheng-11587	567	15	m.i	m.i	PROPN
fumecheng-11587	567	16	.	.	PROPN
fumecheng-11587	567	17	,	,	PUNCT
fumecheng-11587	567	18	2020	2020	NUM
fumecheng-11587	567	19	,	,	PUNCT
fumecheng-11587	567	20	a	a	DET
fumecheng-11587	567	21	high	high	ADJ
fumecheng-11587	567	22	-	-	PUNCT
fumecheng-11587	567	23	order	order	NOUN
fumecheng-11587	567	24	fem	fem	NOUN
fumecheng-11587	567	25	formulation	formulation	NOUN
fumecheng-11587	567	26	for	for	ADP
fumecheng-11587	567	27	free	free	ADJ
fumecheng-11587	567	28	and	and	CCONJ
fumecheng-11587	567	29	forced	force	VERB
fumecheng-11587	567	30	vibration	vibration	NOUN
fumecheng-11587	567	31	analysis	analysis	NOUN
fumecheng-11587	567	32	of	of	ADP
fumecheng-11587	567	33	a	a	DET
fumecheng-11587	567	34	nonlocal	nonlocal	ADJ
fumecheng-11587	567	35	nonlinear	nonlinear	NOUN
fumecheng-11587	567	36	graded	grade	VERB
fumecheng-11587	567	37	timoshenko	timoshenko	ADJ
fumecheng-11587	567	38	nanobeam	nanobeam	NOUN
fumecheng-11587	567	39	based	base	VERB
fumecheng-11587	567	40	on	on	ADP
fumecheng-11587	567	41	the	the	DET
fumecheng-11587	567	42	weak	weak	ADJ
fumecheng-11587	567	43	form	form	NOUN
fumecheng-11587	567	44	quadrature	quadrature	NOUN
fumecheng-11587	567	45	element	element	NOUN
fumecheng-11587	567	46	method	method	NOUN
fumecheng-11587	567	47	,	,	PUNCT
fumecheng-11587	567	48	archive	archive	NOUN
fumecheng-11587	567	49	of	of	ADP
fumecheng-11587	567	50	applied	apply	VERB
fumecheng-11587	567	51	mechanics	mechanic	NOUN
fumecheng-11587	567	52	,	,	PUNCT
fumecheng-11587	567	53	90(10	90(10	NUM
fumecheng-11587	567	54	)	)	PUNCT
fumecheng-11587	567	55	,	,	PUNCT
fumecheng-11587	568	1	pp	pp	ADP
fumecheng-11587	568	2	.	.	PUNCT
fumecheng-11587	569	1	2133	2133	NUM
fumecheng-11587	569	2	-	-	SYM
fumecheng-11587	569	3	2156	2156	NUM
fumecheng-11587	569	4	.	.	PUNCT
fumecheng-11587	570	1	57	57	NUM
fumecheng-11587	570	2	.	.	PUNCT
fumecheng-11587	570	3	nešić	nešić	PROPN
fumecheng-11587	570	4	,	,	PUNCT
fumecheng-11587	570	5	n.	n.	NOUN
fumecheng-11587	570	6	,	,	PUNCT
fumecheng-11587	570	7	cajić	cajić	NOUN
fumecheng-11587	570	8	,	,	PUNCT
fumecheng-11587	570	9	m.	m.	NOUN
fumecheng-11587	570	10	,	,	PUNCT
fumecheng-11587	570	11	karličić	karličić	PROPN
fumecheng-11587	570	12	,	,	PUNCT
fumecheng-11587	570	13	d.	d.	PROPN
fumecheng-11587	570	14	,	,	PUNCT
fumecheng-11587	570	15	janevski	janevski	PROPN
fumecheng-11587	570	16	,	,	PUNCT
fumecheng-11587	570	17	g.	g.	PROPN
fumecheng-11587	570	18	,	,	PUNCT
fumecheng-11587	570	19	2021	2021	NUM
fumecheng-11587	570	20	,	,	PUNCT
fumecheng-11587	570	21	nonlinear	nonlinear	ADJ
fumecheng-11587	570	22	superharmonic	superharmonic	ADJ
fumecheng-11587	570	23	resonance	resonance	NOUN
fumecheng-11587	570	24	analysis	analysis	NOUN
fumecheng-11587	570	25	of	of	ADP
fumecheng-11587	570	26	a	a	DET
fumecheng-11587	570	27	nonlocal	nonlocal	ADJ
fumecheng-11587	570	28	beam	beam	NOUN
fumecheng-11587	570	29	on	on	ADP
fumecheng-11587	570	30	a	a	DET
fumecheng-11587	570	31	fractional	fractional	ADJ
fumecheng-11587	570	32	visco	visco	ADJ
fumecheng-11587	570	33	-	-	PUNCT
fumecheng-11587	570	34	pasternak	pasternak	PROPN
fumecheng-11587	570	35	foundation	foundation	NOUN
fumecheng-11587	570	36	,	,	PUNCT
fumecheng-11587	570	37	proceedings	proceeding	NOUN
fumecheng-11587	570	38	of	of	ADP
fumecheng-11587	570	39	the	the	DET
fumecheng-11587	570	40	institution	institution	NOUN
fumecheng-11587	570	41	of	of	ADP
fumecheng-11587	570	42	mechanical	mechanical	ADJ
fumecheng-11587	570	43	engineers	engineer	NOUN
fumecheng-11587	570	44	,	,	PUNCT
fumecheng-11587	570	45	part	part	NOUN
fumecheng-11587	570	46	c	c	NOUN
fumecheng-11587	570	47	:	:	PUNCT
fumecheng-11587	570	48	journal	journal	NOUN
fumecheng-11587	570	49	of	of	ADP
fumecheng-11587	570	50	mechanical	mechanical	ADJ
fumecheng-11587	570	51	engineering	engineering	NOUN
fumecheng-11587	570	52	science	science	NOUN
fumecheng-11587	570	53	,	,	PUNCT
fumecheng-11587	570	54	235(20	235(20	NUM
fumecheng-11587	570	55	)	)	PUNCT
fumecheng-11587	570	56	,	,	PUNCT
fumecheng-11587	570	57	pp	pp	PROPN
fumecheng-11587	570	58	.	.	PUNCT
fumecheng-11587	571	1	4594	4594	NUM
fumecheng-11587	571	2	-	-	SYM
fumecheng-11587	571	3	4611	4611	NUM
fumecheng-11587	571	4	.	.	PUNCT
fumecheng-11587	572	1	58	58	NUM
fumecheng-11587	572	2	.	.	PUNCT
fumecheng-11587	572	3	engelnkemper	engelnkemper	PROPN
fumecheng-11587	572	4	,	,	PUNCT
fumecheng-11587	572	5	s.	s.	PROPN
fumecheng-11587	572	6	,	,	PUNCT
fumecheng-11587	572	7	gurevich	gurevich	PROPN
fumecheng-11587	572	8	,	,	PUNCT
fumecheng-11587	572	9	s.v	s.v	PROPN
fumecheng-11587	572	10	.	.	PROPN
fumecheng-11587	572	11	,	,	PUNCT
fumecheng-11587	572	12	uecker	uecker	PROPN
fumecheng-11587	572	13	,	,	PUNCT
fumecheng-11587	572	14	h.	h.	PROPN
fumecheng-11587	572	15	,	,	PUNCT
fumecheng-11587	572	16	wetzel	wetzel	PROPN
fumecheng-11587	572	17	,	,	PUNCT
fumecheng-11587	572	18	d.	d.	PROPN
fumecheng-11587	572	19	,	,	PUNCT
fumecheng-11587	572	20	thiele	thiele	PROPN
fumecheng-11587	572	21	,	,	PUNCT
fumecheng-11587	572	22	u.	u.	PROPN
fumecheng-11587	572	23	,	,	PUNCT
fumecheng-11587	572	24	2019	2019	NUM
fumecheng-11587	572	25	,	,	PUNCT
fumecheng-11587	572	26	continuation	continuation	NOUN
fumecheng-11587	572	27	for	for	ADP
fumecheng-11587	572	28	thin	thin	ADJ
fumecheng-11587	572	29	film	film	NOUN
fumecheng-11587	572	30	hydrodynamics	hydrodynamic	NOUN
fumecheng-11587	572	31	and	and	CCONJ
fumecheng-11587	572	32	related	relate	VERB
fumecheng-11587	572	33	scalar	scalar	ADJ
fumecheng-11587	572	34	problems	problem	NOUN
fumecheng-11587	572	35	,	,	PUNCT
fumecheng-11587	572	36	computational	computational	ADJ
fumecheng-11587	572	37	modelling	modelling	NOUN
fumecheng-11587	572	38	of	of	ADP
fumecheng-11587	572	39	bifurcations	bifurcation	NOUN
fumecheng-11587	572	40	and	and	CCONJ
fumecheng-11587	572	41	instabilities	instability	NOUN
fumecheng-11587	572	42	in	in	ADP
fumecheng-11587	572	43	fluid	fluid	ADJ
fumecheng-11587	572	44	dynamics	dynamic	NOUN
fumecheng-11587	572	45	,	,	PUNCT
fumecheng-11587	572	46	computational	computational	ADJ
fumecheng-11587	572	47	methods	method	NOUN
fumecheng-11587	572	48	in	in	ADP
fumecheng-11587	572	49	applied	applied	ADJ
fumecheng-11587	572	50	sciences	science	NOUN
fumecheng-11587	572	51	,	,	PUNCT
fumecheng-11587	572	52	50	50	NUM
fumecheng-11587	572	53	,	,	PUNCT
fumecheng-11587	572	54	pp	pp	ADJ
fumecheng-11587	572	55	.	.	PUNCT
fumecheng-11587	573	1	459	459	NUM
fumecheng-11587	573	2	-	-	SYM
fumecheng-11587	573	3	501	501	NUM
fumecheng-11587	573	4	59	59	NUM
fumecheng-11587	573	5	.	.	PUNCT
fumecheng-11587	574	1	wang	wang	PROPN
fumecheng-11587	574	2	,	,	PUNCT
fumecheng-11587	574	3	s.	s.	PROPN
fumecheng-11587	574	4	,	,	PUNCT
fumecheng-11587	574	5	hua	hua	PROPN
fumecheng-11587	574	6	,	,	PUNCT
fumecheng-11587	574	7	l.	l.	PROPN
fumecheng-11587	574	8	,	,	PUNCT
fumecheng-11587	574	9	yang	yang	PROPN
fumecheng-11587	574	10	,	,	PUNCT
fumecheng-11587	574	11	c.	c.	PROPN
fumecheng-11587	574	12	,	,	PUNCT
fumecheng-11587	574	13	han	han	PROPN
fumecheng-11587	574	14	,	,	PUNCT
fumecheng-11587	574	15	x	x	PROPN
fumecheng-11587	574	16	..	..	PROPN
fumecheng-11587	574	17	su	su	PROPN
fumecheng-11587	574	18	,	,	PUNCT
fumecheng-11587	574	19	z.	z.	PROPN
fumecheng-11587	574	20	,	,	PUNCT
fumecheng-11587	574	21	2019	2019	NUM
fumecheng-11587	574	22	,	,	PUNCT
fumecheng-11587	574	23	applications	application	NOUN
fumecheng-11587	574	24	of	of	ADP
fumecheng-11587	574	25	incremental	incremental	ADJ
fumecheng-11587	574	26	harmonic	harmonic	ADJ
fumecheng-11587	574	27	balance	balance	NOUN
fumecheng-11587	574	28	method	method	NOUN
fumecheng-11587	574	29	combined	combine	VERB
fumecheng-11587	574	30	with	with	ADP
fumecheng-11587	574	31	equivalent	equivalent	ADJ
fumecheng-11587	574	32	piecewise	piecewise	NOUN
fumecheng-11587	574	33	linearization	linearization	NOUN
fumecheng-11587	574	34	on	on	ADP
fumecheng-11587	574	35	vibrations	vibration	NOUN
fumecheng-11587	574	36	of	of	ADP
fumecheng-11587	574	37	nonlinear	nonlinear	ADJ
fumecheng-11587	574	38	stiffness	stiffness	NOUN
fumecheng-11587	574	39	systems	system	NOUN
fumecheng-11587	574	40	,	,	PUNCT
fumecheng-11587	574	41	journal	journal	NOUN
fumecheng-11587	574	42	of	of	ADP
fumecheng-11587	574	43	sound	sound	NOUN
fumecheng-11587	574	44	and	and	CCONJ
fumecheng-11587	574	45	vibration	vibration	NOUN
fumecheng-11587	574	46	,	,	PUNCT
fumecheng-11587	574	47	441	441	NUM
fumecheng-11587	574	48	,	,	PUNCT
fumecheng-11587	574	49	pp	pp	ADJ
fumecheng-11587	574	50	.	.	PUNCT
fumecheng-11587	574	51	111	111	NUM
fumecheng-11587	574	52	-	-	SYM
fumecheng-11587	574	53	125	125	NUM
fumecheng-11587	574	54	.	.	PUNCT
fumecheng-11587	574	55	60	60	NUM
fumecheng-11587	574	56	.	.	PUNCT
fumecheng-11587	575	1	shen	shen	PROPN
fumecheng-11587	575	2	,	,	PUNCT
fumecheng-11587	575	3	j.h	j.h	PROPN
fumecheng-11587	575	4	.	.	PROPN
fumecheng-11587	575	5	,	,	PUNCT
fumecheng-11587	575	6	lin	lin	PROPN
fumecheng-11587	575	7	,	,	PUNCT
fumecheng-11587	575	8	k.c	k.c	PROPN
fumecheng-11587	575	9	.	.	PROPN
fumecheng-11587	575	10	,	,	PUNCT
fumecheng-11587	575	11	chen	chen	PROPN
fumecheng-11587	575	12	,	,	PUNCT
fumecheng-11587	575	13	s.h	s.h	PROPN
fumecheng-11587	575	14	.	.	PROPN
fumecheng-11587	575	15	,	,	PUNCT
fumecheng-11587	575	16	sze	sze	PROPN
fumecheng-11587	575	17	,	,	PUNCT
fumecheng-11587	575	18	k.y	k.y	PROPN
fumecheng-11587	575	19	.	.	PROPN
fumecheng-11587	575	20	,	,	PUNCT
fumecheng-11587	575	21	2008	2008	NUM
fumecheng-11587	575	22	,	,	PUNCT
fumecheng-11587	575	23	bifurcation	bifurcation	NOUN
fumecheng-11587	575	24	and	and	CCONJ
fumecheng-11587	575	25	route	route	NOUN
fumecheng-11587	575	26	-	-	PUNCT
fumecheng-11587	575	27	to	to	ADP
fumecheng-11587	575	28	-	-	PUNCT
fumecheng-11587	575	29	chaos	chaos	NOUN
fumecheng-11587	575	30	analyses	analysis	NOUN
fumecheng-11587	575	31	for	for	ADP
fumecheng-11587	575	32	mathieu	mathieu	PROPN
fumecheng-11587	575	33	–	–	PUNCT
fumecheng-11587	575	34	duffing	duffe	VERB
fumecheng-11587	575	35	oscillator	oscillator	NOUN
fumecheng-11587	575	36	by	by	ADP
fumecheng-11587	575	37	the	the	DET
fumecheng-11587	575	38	incremental	incremental	ADJ
fumecheng-11587	575	39	harmonic	harmonic	ADJ
fumecheng-11587	575	40	balance	balance	NOUN
fumecheng-11587	575	41	method	method	NOUN
fumecheng-11587	575	42	,	,	PUNCT
fumecheng-11587	575	43	nonlinear	nonlinear	ADJ
fumecheng-11587	575	44	dynamics	dynamic	NOUN
fumecheng-11587	575	45	,	,	PUNCT
fumecheng-11587	575	46	52(4	52(4	NUM
fumecheng-11587	575	47	)	)	PUNCT
fumecheng-11587	575	48	,	,	PUNCT
fumecheng-11587	575	49	pp	pp	ADP
fumecheng-11587	575	50	.	.	PUNCT
fumecheng-11587	576	1	403	403	NUM
fumecheng-11587	576	2	-	-	SYM
fumecheng-11587	576	3	414	414	NUM
fumecheng-11587	576	4	.	.	NOUN
fumecheng-11587	577	1	61	61	NUM
fumecheng-11587	577	2	.	.	PUNCT
fumecheng-11587	578	1	huang	huang	PROPN
fumecheng-11587	578	2	,	,	PUNCT
fumecheng-11587	578	3	j.l	j.l	PROPN
fumecheng-11587	578	4	.	.	PROPN
fumecheng-11587	578	5	,	,	PUNCT
fumecheng-11587	578	6	su	su	PROPN
fumecheng-11587	578	7	,	,	PUNCT
fumecheng-11587	578	8	r.k.l	r.k.l	PROPN
fumecheng-11587	578	9	.	.	PROPN
fumecheng-11587	578	10	,	,	PUNCT
fumecheng-11587	578	11	lee	lee	PROPN
fumecheng-11587	578	12	,	,	PUNCT
fumecheng-11587	578	13	y.y	y.y	PROPN
fumecheng-11587	578	14	.	.	PROPN
fumecheng-11587	578	15	,	,	PUNCT
fumecheng-11587	578	16	chen	chen	PROPN
fumecheng-11587	578	17	,	,	PUNCT
fumecheng-11587	578	18	s.h	s.h	PROPN
fumecheng-11587	578	19	.	.	PROPN
fumecheng-11587	578	20	,	,	PUNCT
fumecheng-11587	578	21	2011	2011	NUM
fumecheng-11587	578	22	,	,	PUNCT
fumecheng-11587	578	23	nonlinear	nonlinear	ADJ
fumecheng-11587	578	24	vibration	vibration	NOUN
fumecheng-11587	578	25	of	of	ADP
fumecheng-11587	578	26	a	a	DET
fumecheng-11587	578	27	curved	curved	ADJ
fumecheng-11587	578	28	beam	beam	NOUN
fumecheng-11587	578	29	under	under	ADP
fumecheng-11587	578	30	uniform	uniform	ADJ
fumecheng-11587	578	31	base	base	NOUN
fumecheng-11587	578	32	harmonic	harmonic	ADJ
fumecheng-11587	578	33	excitation	excitation	NOUN
fumecheng-11587	578	34	with	with	ADP
fumecheng-11587	578	35	quadratic	quadratic	ADJ
fumecheng-11587	578	36	and	and	CCONJ
fumecheng-11587	578	37	cubic	cubic	ADJ
fumecheng-11587	578	38	nonlinearities	nonlinearitie	NOUN
fumecheng-11587	578	39	,	,	PUNCT
fumecheng-11587	578	40	journal	journal	NOUN
fumecheng-11587	578	41	of	of	ADP
fumecheng-11587	578	42	sound	sound	NOUN
fumecheng-11587	578	43	and	and	CCONJ
fumecheng-11587	578	44	vibration	vibration	NOUN
fumecheng-11587	578	45	,	,	PUNCT
fumecheng-11587	578	46	330(21	330(21	NUM
fumecheng-11587	578	47	)	)	PUNCT
fumecheng-11587	578	48	,	,	PUNCT
fumecheng-11587	578	49	pp	pp	ADP
fumecheng-11587	578	50	.	.	PUNCT
fumecheng-11587	579	1	5151	5151	NUM
fumecheng-11587	579	2	-	-	SYM
fumecheng-11587	579	3	5164	5164	NUM
fumecheng-11587	579	4	.	.	PUNCT
fumecheng-11587	580	1	vibration	vibration	NOUN
fumecheng-11587	580	2	and	and	CCONJ
fumecheng-11587	580	3	stability	stability	NOUN
fumecheng-11587	580	4	of	of	ADP
fumecheng-11587	580	5	a	a	DET
fumecheng-11587	580	6	nonlinear	nonlinear	ADJ
fumecheng-11587	580	7	nonlocal	nonlocal	ADJ
fumecheng-11587	580	8	strain	strain	NOUN
fumecheng-11587	580	9	-	-	PUNCT
fumecheng-11587	580	10	gradient	gradient	NOUN
fumecheng-11587	580	11	fg	fg	PROPN
fumecheng-11587	580	12	beam	beam	NOUN
fumecheng-11587	580	13	on	on	ADP
fumecheng-11587	580	14	a	a	DET
fumecheng-11587	580	15	visco	visco	ADJ
fumecheng-11587	580	16	-	-	PUNCT
fumecheng-11587	580	17	pasternak	pasternak	NOUN
fumecheng-11587	580	18	...	...	PUNCT
fumecheng-11587	580	19	733	733	NUM
fumecheng-11587	580	20	62	62	NUM
fumecheng-11587	580	21	.	.	PUNCT
fumecheng-11587	581	1	hsu	hsu	PROPN
fumecheng-11587	581	2	,	,	PUNCT
fumecheng-11587	581	3	c.s	c.s	PROPN
fumecheng-11587	581	4	.	.	PROPN
fumecheng-11587	581	5	,	,	PUNCT
fumecheng-11587	581	6	1974	1974	NUM
fumecheng-11587	581	7	,	,	PUNCT
fumecheng-11587	581	8	on	on	ADP
fumecheng-11587	581	9	approximating	approximate	VERB
fumecheng-11587	581	10	a	a	DET
fumecheng-11587	581	11	general	general	ADJ
fumecheng-11587	581	12	linear	linear	ADJ
fumecheng-11587	581	13	periodic	periodic	ADJ
fumecheng-11587	581	14	system	system	NOUN
fumecheng-11587	581	15	,	,	PUNCT
fumecheng-11587	581	16	journal	journal	NOUN
fumecheng-11587	581	17	of	of	ADP
fumecheng-11587	581	18	mathematical	mathematical	ADJ
fumecheng-11587	581	19	analysis	analysis	NOUN
fumecheng-11587	581	20	and	and	CCONJ
fumecheng-11587	581	21	applications	application	NOUN
fumecheng-11587	581	22	,	,	PUNCT
fumecheng-11587	581	23	45(1	45(1	NOUN
fumecheng-11587	581	24	)	)	PUNCT
fumecheng-11587	581	25	,	,	PUNCT
fumecheng-11587	581	26	pp	pp	PROPN
fumecheng-11587	581	27	.	.	PUNCT
fumecheng-11587	582	1	234	234	NUM
fumecheng-11587	582	2	-	-	SYM
fumecheng-11587	582	3	251	251	NUM
fumecheng-11587	582	4	.	.	PUNCT
fumecheng-11587	583	1	63	63	NUM
fumecheng-11587	583	2	.	.	PUNCT
fumecheng-11587	583	3	togun	togun	PROPN
fumecheng-11587	583	4	,	,	PUNCT
fumecheng-11587	583	5	n.	n.	NOUN
fumecheng-11587	583	6	,	,	PUNCT
fumecheng-11587	583	7	bağdatlı	bağdatlı	NOUN
fumecheng-11587	583	8	,	,	PUNCT
fumecheng-11587	583	9	s.m	s.m	PROPN
fumecheng-11587	583	10	.	.	PROPN
fumecheng-11587	583	11	,	,	PUNCT
fumecheng-11587	583	12	2016	2016	NUM
fumecheng-11587	583	13	,	,	PUNCT
fumecheng-11587	583	14	nonlinear	nonlinear	ADJ
fumecheng-11587	583	15	vibration	vibration	NOUN
fumecheng-11587	583	16	of	of	ADP
fumecheng-11587	583	17	a	a	DET
fumecheng-11587	583	18	nanobeam	nanobeam	NOUN
fumecheng-11587	583	19	on	on	ADP
fumecheng-11587	583	20	a	a	DET
fumecheng-11587	583	21	pasternak	pasternak	PROPN
fumecheng-11587	583	22	elastic	elastic	ADJ
fumecheng-11587	583	23	foundation	foundation	NOUN
fumecheng-11587	583	24	based	base	VERB
fumecheng-11587	583	25	on	on	ADP
fumecheng-11587	583	26	non	non	ADJ
fumecheng-11587	583	27	-	-	ADJ
fumecheng-11587	583	28	local	local	ADJ
fumecheng-11587	583	29	euler	euler	NOUN
fumecheng-11587	583	30	-	-	PUNCT
fumecheng-11587	583	31	bernoulli	bernoulli	PROPN
fumecheng-11587	583	32	beam	beam	NOUN
fumecheng-11587	583	33	theory	theory	NOUN
fumecheng-11587	583	34	,	,	PUNCT
fumecheng-11587	583	35	mathematical	mathematical	ADJ
fumecheng-11587	583	36	and	and	CCONJ
fumecheng-11587	583	37	computational	computational	ADJ
fumecheng-11587	583	38	applications	application	NOUN
fumecheng-11587	583	39	,	,	PUNCT
fumecheng-11587	583	40	21(1	21(1	NUM
fumecheng-11587	583	41	)	)	PUNCT
fumecheng-11587	583	42	,	,	PUNCT
fumecheng-11587	583	43	3	3	NUM
fumecheng-11587	583	44	.	.	NOUN
fumecheng-11587	583	45	64	64	NUM
fumecheng-11587	583	46	.	.	PUNCT
fumecheng-11587	584	1	eyebe	eyebe	NOUN
fumecheng-11587	584	2	,	,	PUNCT
fumecheng-11587	584	3	g.j	g.j	PROPN
fumecheng-11587	584	4	.	.	PROPN
fumecheng-11587	584	5	,	,	PUNCT
fumecheng-11587	584	6	betchewe	betchewe	PROPN
fumecheng-11587	584	7	,	,	PUNCT
fumecheng-11587	584	8	g.	g.	PROPN
fumecheng-11587	584	9	,	,	PUNCT
fumecheng-11587	584	10	mohamadou	mohamadou	NOUN
fumecheng-11587	584	11	,	,	PUNCT
fumecheng-11587	584	12	a.	a.	NOUN
fumecheng-11587	584	13	,	,	PUNCT
fumecheng-11587	584	14	kofane	kofane	PROPN
fumecheng-11587	584	15	,	,	PUNCT
fumecheng-11587	584	16	t.c	t.c	PROPN
fumecheng-11587	584	17	.	.	PROPN
fumecheng-11587	584	18	,	,	PUNCT
fumecheng-11587	584	19	2018	2018	NUM
fumecheng-11587	584	20	,	,	PUNCT
fumecheng-11587	584	21	nonlinear	nonlinear	ADJ
fumecheng-11587	584	22	vibration	vibration	NOUN
fumecheng-11587	584	23	of	of	ADP
fumecheng-11587	584	24	a	a	DET
fumecheng-11587	584	25	nonlocal	nonlocal	ADJ
fumecheng-11587	584	26	nanobeam	nanobeam	NOUN
fumecheng-11587	584	27	resting	rest	VERB
fumecheng-11587	584	28	on	on	ADP
fumecheng-11587	584	29	fractional	fractional	ADJ
fumecheng-11587	584	30	-	-	PUNCT
fumecheng-11587	584	31	order	order	NOUN
fumecheng-11587	584	32	viscoelastic	viscoelastic	ADJ
fumecheng-11587	584	33	pasternak	pasternak	PROPN
fumecheng-11587	584	34	foundations	foundation	NOUN
fumecheng-11587	584	35	,	,	PUNCT
fumecheng-11587	584	36	fractal	fractal	ADJ
fumecheng-11587	584	37	and	and	CCONJ
fumecheng-11587	584	38	fractional	fractional	ADJ
fumecheng-11587	584	39	,	,	PUNCT
fumecheng-11587	584	40	2(3	2(3	NUM
fumecheng-11587	584	41	)	)	PUNCT
fumecheng-11587	584	42	,	,	PUNCT
fumecheng-11587	584	43	21	21	NUM
fumecheng-11587	584	44	.	.	PUNCT
fumecheng-11587	584	45	65	65	NUM
fumecheng-11587	584	46	.	.	PUNCT
fumecheng-11587	585	1	yokoyama	yokoyama	PROPN
fumecheng-11587	585	2	,	,	PUNCT
fumecheng-11587	585	3	t.	t.	PROPN
fumecheng-11587	585	4	,	,	PUNCT
fumecheng-11587	585	5	1987	1987	NUM
fumecheng-11587	585	6	,	,	PUNCT
fumecheng-11587	585	7	vibrations	vibration	NOUN
fumecheng-11587	585	8	and	and	CCONJ
fumecheng-11587	585	9	transient	transient	ADJ
fumecheng-11587	585	10	responses	response	NOUN
fumecheng-11587	585	11	of	of	ADP
fumecheng-11587	585	12	timoshenko	timoshenko	ADJ
fumecheng-11587	585	13	beams	beam	NOUN
fumecheng-11587	585	14	resting	rest	VERB
fumecheng-11587	585	15	on	on	ADP
fumecheng-11587	585	16	elastic	elastic	ADJ
fumecheng-11587	585	17	foundations	foundation	NOUN
fumecheng-11587	585	18	,	,	PUNCT
fumecheng-11587	585	19	ingenieur	ingenieur	PROPN
fumecheng-11587	585	20	-	-	PUNCT
fumecheng-11587	585	21	archiv	archiv	PROPN
fumecheng-11587	585	22	,	,	PUNCT
fumecheng-11587	585	23	57(2	57(2	NUM
fumecheng-11587	585	24	)	)	PUNCT
fumecheng-11587	585	25	,	,	PUNCT
fumecheng-11587	585	26	pp	pp	PROPN
fumecheng-11587	585	27	.	.	PUNCT
fumecheng-11587	586	1	81	81	NUM
fumecheng-11587	586	2	-	-	SYM
fumecheng-11587	586	3	90	90	NUM
fumecheng-11587	586	4	.	.	PUNCT
fumecheng-11587	587	1	66	66	NUM
fumecheng-11587	587	2	.	.	PUNCT
fumecheng-11587	588	1	mustapha	mustapha	PROPN
fumecheng-11587	588	2	,	,	PUNCT
fumecheng-11587	588	3	k.b	k.b	PROPN
fumecheng-11587	588	4	.	.	PROPN
fumecheng-11587	588	5	,	,	PUNCT
fumecheng-11587	588	6	zhong	zhong	PROPN
fumecheng-11587	588	7	,	,	PUNCT
fumecheng-11587	588	8	z.w	z.w	PROPN
fumecheng-11587	588	9	.	.	PROPN
fumecheng-11587	588	10	,	,	PUNCT
fumecheng-11587	588	11	2010	2010	NUM
fumecheng-11587	588	12	,	,	PUNCT
fumecheng-11587	588	13	free	free	ADJ
fumecheng-11587	588	14	transverse	transverse	NOUN
fumecheng-11587	588	15	vibration	vibration	NOUN
fumecheng-11587	588	16	of	of	ADP
fumecheng-11587	588	17	an	an	DET
fumecheng-11587	588	18	axially	axially	ADV
fumecheng-11587	588	19	loaded	load	VERB
fumecheng-11587	588	20	non	non	ADJ
fumecheng-11587	588	21	-	-	ADJ
fumecheng-11587	588	22	prismatic	prismatic	ADJ
fumecheng-11587	588	23	single	single	ADJ
fumecheng-11587	588	24	-	-	PUNCT
fumecheng-11587	588	25	walled	wall	VERB
fumecheng-11587	588	26	carbon	carbon	NOUN
fumecheng-11587	588	27	nanotube	nanotube	NOUN
fumecheng-11587	588	28	embedded	embed	VERB
fumecheng-11587	588	29	in	in	ADP
fumecheng-11587	588	30	a	a	DET
fumecheng-11587	588	31	two	two	NUM
fumecheng-11587	588	32	-	-	PUNCT
fumecheng-11587	588	33	parameter	parameter	NOUN
fumecheng-11587	588	34	elastic	elastic	ADJ
fumecheng-11587	588	35	medium	medium	NOUN
fumecheng-11587	588	36	,	,	PUNCT
fumecheng-11587	588	37	computational	computational	ADJ
fumecheng-11587	588	38	materials	material	NOUN
fumecheng-11587	588	39	science	science	NOUN
fumecheng-11587	588	40	,	,	PUNCT
fumecheng-11587	588	41	50(2	50(2	NUM
fumecheng-11587	588	42	)	)	PUNCT
fumecheng-11587	588	43	,	,	PUNCT
fumecheng-11587	588	44	pp	pp	ADJ
fumecheng-11587	588	45	.	.	PUNCT
fumecheng-11587	589	1	742	742	NUM
fumecheng-11587	589	2	-	-	SYM
fumecheng-11587	589	3	751	751	NUM
fumecheng-11587	589	4	.	.	PUNCT
fumecheng-11587	590	1	67	67	NUM
fumecheng-11587	590	2	.	.	PUNCT
fumecheng-11587	591	1	ansari	ansari	PROPN
fumecheng-11587	591	2	,	,	PUNCT
fumecheng-11587	591	3	r.	r.	PROPN
fumecheng-11587	591	4	,	,	PUNCT
fumecheng-11587	591	5	gholami	gholami	PROPN
fumecheng-11587	591	6	,	,	PUNCT
fumecheng-11587	591	7	r.	r.	PROPN
fumecheng-11587	591	8	,	,	PUNCT
fumecheng-11587	591	9	hosseini	hosseini	PROPN
fumecheng-11587	591	10	,	,	PUNCT
fumecheng-11587	591	11	k.	k.	PROPN
fumecheng-11587	591	12	,	,	PUNCT
fumecheng-11587	591	13	sahmani	sahmani	NOUN
fumecheng-11587	591	14	,	,	PUNCT
fumecheng-11587	591	15	s.	s.	PROPN
fumecheng-11587	591	16	,	,	PUNCT
fumecheng-11587	591	17	2011	2011	NUM
fumecheng-11587	591	18	,	,	PUNCT
fumecheng-11587	591	19	a	a	DET
fumecheng-11587	591	20	sixth	sixth	ADJ
fumecheng-11587	591	21	-	-	PUNCT
fumecheng-11587	591	22	order	order	NOUN
fumecheng-11587	591	23	compact	compact	ADJ
fumecheng-11587	591	24	finite	finite	ADJ
fumecheng-11587	591	25	difference	difference	NOUN
fumecheng-11587	591	26	method	method	NOUN
fumecheng-11587	591	27	for	for	ADP
fumecheng-11587	591	28	vibrational	vibrational	ADJ
fumecheng-11587	591	29	analysis	analysis	NOUN
fumecheng-11587	591	30	of	of	ADP
fumecheng-11587	591	31	nanobeams	nanobeam	NOUN
fumecheng-11587	591	32	embedded	embed	VERB
fumecheng-11587	591	33	in	in	ADP
fumecheng-11587	591	34	an	an	DET
fumecheng-11587	591	35	elastic	elastic	ADJ
fumecheng-11587	591	36	medium	medium	NOUN
fumecheng-11587	591	37	based	base	VERB
fumecheng-11587	591	38	on	on	ADP
fumecheng-11587	591	39	nonlocal	nonlocal	ADJ
fumecheng-11587	591	40	beam	beam	NOUN
fumecheng-11587	591	41	theory	theory	NOUN
fumecheng-11587	591	42	,	,	PUNCT
fumecheng-11587	591	43	mathematical	mathematical	ADJ
fumecheng-11587	591	44	and	and	CCONJ
fumecheng-11587	591	45	computer	computer	NOUN
fumecheng-11587	591	46	modelling	modelling	NOUN
fumecheng-11587	591	47	,	,	PUNCT
fumecheng-11587	591	48	54(11	54(11	NUM
fumecheng-11587	591	49	-	-	SYM
fumecheng-11587	591	50	12	12	NUM
fumecheng-11587	591	51	)	)	PUNCT
fumecheng-11587	591	52	,	,	PUNCT
fumecheng-11587	591	53	pp	pp	ADJ
fumecheng-11587	591	54	.	.	PUNCT
fumecheng-11587	592	1	2577	2577	NUM
fumecheng-11587	592	2	-	-	SYM
fumecheng-11587	592	3	2586	2586	NUM
fumecheng-11587	592	4	.	.	PUNCT
fumecheng-11587	593	1	68	68	NUM
fumecheng-11587	593	2	.	.	PUNCT
fumecheng-11587	594	1	zhao	zhao	PROPN
fumecheng-11587	594	2	,	,	PUNCT
fumecheng-11587	594	3	x.	x.	PROPN
fumecheng-11587	594	4	,	,	PUNCT
fumecheng-11587	594	5	wang	wang	PROPN
fumecheng-11587	594	6	,	,	PUNCT
fumecheng-11587	594	7	c.f	c.f	PROPN
fumecheng-11587	594	8	.	.	PROPN
fumecheng-11587	594	9	,	,	PUNCT
fumecheng-11587	594	10	zhu	zhu	PROPN
fumecheng-11587	594	11	,	,	PUNCT
fumecheng-11587	594	12	w.d	w.d	PROPN
fumecheng-11587	594	13	.	.	PROPN
fumecheng-11587	594	14	,	,	PUNCT
fumecheng-11587	594	15	li	li	PROPN
fumecheng-11587	594	16	,	,	PUNCT
fumecheng-11587	594	17	y.h	y.h	PROPN
fumecheng-11587	594	18	.	.	PROPN
fumecheng-11587	594	19	,	,	PUNCT
fumecheng-11587	594	20	wan	wan	PROPN
fumecheng-11587	594	21	,	,	PUNCT
fumecheng-11587	594	22	x.s	x.s	PROPN
fumecheng-11587	594	23	.	.	PROPN
fumecheng-11587	594	24	,	,	PUNCT
fumecheng-11587	594	25	2021	2021	NUM
fumecheng-11587	594	26	,	,	PUNCT
fumecheng-11587	594	27	coupled	couple	VERB
fumecheng-11587	594	28	thermoelastic	thermoelastic	ADJ
fumecheng-11587	594	29	nonlocal	nonlocal	ADJ
fumecheng-11587	594	30	forced	force	VERB
fumecheng-11587	594	31	vibration	vibration	NOUN
fumecheng-11587	594	32	of	of	ADP
fumecheng-11587	594	33	an	an	DET
fumecheng-11587	594	34	axially	axially	ADV
fumecheng-11587	594	35	moving	move	VERB
fumecheng-11587	594	36	micro	micro	ADJ
fumecheng-11587	594	37	/	/	SYM
fumecheng-11587	594	38	nano	nano	NOUN
fumecheng-11587	594	39	-	-	PUNCT
fumecheng-11587	594	40	beam	beam	NOUN
fumecheng-11587	594	41	,	,	PUNCT
fumecheng-11587	594	42	international	international	ADJ
fumecheng-11587	594	43	journal	journal	NOUN
fumecheng-11587	594	44	of	of	ADP
fumecheng-11587	594	45	mechanical	mechanical	ADJ
fumecheng-11587	594	46	sciences	science	NOUN
fumecheng-11587	594	47	,	,	PUNCT
fumecheng-11587	594	48	206	206	NUM
fumecheng-11587	594	49	,	,	PUNCT
fumecheng-11587	594	50	106600	106600	NUM
fumecheng-11587	594	51	.	.	PUNCT
fumecheng-11587	595	1	69	69	NUM
fumecheng-11587	595	2	.	.	PUNCT
fumecheng-11587	596	1	brennan	brennan	PROPN
fumecheng-11587	596	2	,	,	PUNCT
fumecheng-11587	596	3	m.j	m.j	PROPN
fumecheng-11587	596	4	.	.	PROPN
fumecheng-11587	596	5	,	,	PUNCT
fumecheng-11587	596	6	kovacic	kovacic	PROPN
fumecheng-11587	596	7	,	,	PUNCT
fumecheng-11587	596	8	i.	i.	PROPN
fumecheng-11587	596	9	,	,	PUNCT
fumecheng-11587	596	10	carrella	carrella	NOUN
fumecheng-11587	596	11	,	,	PUNCT
fumecheng-11587	596	12	a.	a.	NOUN
fumecheng-11587	596	13	,	,	PUNCT
fumecheng-11587	596	14	waters	water	NOUN
fumecheng-11587	596	15	,	,	PUNCT
fumecheng-11587	596	16	t.p	t.p	PROPN
fumecheng-11587	596	17	.	.	PROPN
fumecheng-11587	596	18	,	,	PUNCT
fumecheng-11587	596	19	2008	2008	NUM
fumecheng-11587	596	20	,	,	PUNCT
fumecheng-11587	596	21	on	on	ADP
fumecheng-11587	596	22	the	the	DET
fumecheng-11587	596	23	jump	jump	NOUN
fumecheng-11587	596	24	-	-	PUNCT
fumecheng-11587	596	25	up	up	NOUN
fumecheng-11587	596	26	and	and	CCONJ
fumecheng-11587	596	27	jump	jump	VERB
fumecheng-11587	596	28	-	-	PUNCT
fumecheng-11587	596	29	down	down	ADP
fumecheng-11587	596	30	frequencies	frequency	NOUN
fumecheng-11587	596	31	of	of	ADP
fumecheng-11587	596	32	the	the	DET
fumecheng-11587	596	33	duffing	duffing	NOUN
fumecheng-11587	596	34	oscillator	oscillator	NOUN
fumecheng-11587	596	35	,	,	PUNCT
fumecheng-11587	596	36	journal	journal	NOUN
fumecheng-11587	596	37	of	of	ADP
fumecheng-11587	596	38	sound	sound	NOUN
fumecheng-11587	596	39	and	and	CCONJ
fumecheng-11587	596	40	vibration	vibration	NOUN
fumecheng-11587	596	41	,	,	PUNCT
fumecheng-11587	596	42	318(4	318(4	NUM
fumecheng-11587	596	43	-	-	SYM
fumecheng-11587	596	44	5	5	NUM
fumecheng-11587	596	45	)	)	PUNCT
fumecheng-11587	596	46	,	,	PUNCT
fumecheng-11587	596	47	pp	pp	PROPN
fumecheng-11587	596	48	.	.	PUNCT
fumecheng-11587	596	49	1250	1250	NUM
fumecheng-11587	596	50	-	-	SYM
fumecheng-11587	596	51	1261	1261	NUM
fumecheng-11587	596	52	.	.	PUNCT