id	sid	tid	token	lemma	pos
fumecheng-10953	1	1	10953	10953	NUM
fumecheng-10953	1	2	facta	facta	PROPN
fumecheng-10953	1	3	universitatis	universitatis	PROPN
fumecheng-10953	1	4	series	series	NOUN
fumecheng-10953	1	5	:	:	PUNCT
fumecheng-10953	1	6	mechanical	mechanical	ADJ
fumecheng-10953	1	7	engineering	engineering	NOUN
fumecheng-10953	1	8	vol	vol	NOUN
fumecheng-10953	1	9	.	.	PROPN
fumecheng-10953	1	10	20	20	NUM
fumecheng-10953	1	11	,	,	PUNCT
fumecheng-10953	1	12	no	no	DET
fumecheng-10953	1	13	3	3	NUM
fumecheng-10953	1	14	,	,	PUNCT
fumecheng-10953	1	15	2022	2022	NUM
fumecheng-10953	1	16	,	,	PUNCT
fumecheng-10953	1	17	pp	pp	ADJ
fumecheng-10953	1	18	.	.	PUNCT
fumecheng-10953	2	1	539	539	NUM
fumecheng-10953	2	2	552	552	NUM
fumecheng-10953	2	3	https://doi.org/10.22190/fume220703035f	https://doi.org/10.22190/fume220703035f	PROPN
fumecheng-10953	2	4	©	©	PROPN
fumecheng-10953	2	5	2022	2022	NUM
fumecheng-10953	2	6	by	by	ADP
fumecheng-10953	2	7	university	university	PROPN
fumecheng-10953	2	8	of	of	ADP
fumecheng-10953	2	9	niš	niš	PROPN
fumecheng-10953	2	10	,	,	PUNCT
fumecheng-10953	2	11	serbia	serbia	PROPN
fumecheng-10953	2	12	|	|	ADV
fumecheng-10953	2	13	creative	creative	ADJ
fumecheng-10953	2	14	commons	common	NOUN
fumecheng-10953	2	15	license	license	NOUN
fumecheng-10953	2	16	:	:	PUNCT
fumecheng-10953	2	17	cc	cc	VERB
fumecheng-10953	2	18	by	by	ADP
fumecheng-10953	2	19	-	-	PUNCT
fumecheng-10953	2	20	nc	nc	VERB
fumecheng-10953	2	21	-	-	PUNCT
fumecheng-10953	2	22	nd	nd	ADV
fumecheng-10953	2	23	original	original	ADJ
fumecheng-10953	2	24	scientific	scientific	ADJ
fumecheng-10953	2	25	paper	paper	ADJ
fumecheng-10953	2	26	dynamic	dynamic	ADJ
fumecheng-10953	2	27	characteristics	characteristic	NOUN
fumecheng-10953	2	28	of	of	ADP
fumecheng-10953	2	29	mixture	mixture	NOUN
fumecheng-10953	2	30	unified	unify	VERB
fumecheng-10953	2	31	gradient	gradient	ADJ
fumecheng-10953	2	32	elastic	elastic	ADJ
fumecheng-10953	2	33	nanobeams	nanobeam	NOUN
fumecheng-10953	2	34	seyed	seyed	PROPN
fumecheng-10953	2	35	ali	ali	PROPN
fumecheng-10953	2	36	faghidian1	faghidian1	PROPN
fumecheng-10953	2	37	,	,	PUNCT
fumecheng-10953	2	38	abdelouahed	abdelouahe	VERB
fumecheng-10953	2	39	tounsi2,3	tounsi2,3	PROPN
fumecheng-10953	2	40	1department	1department	NUM
fumecheng-10953	2	41	of	of	ADP
fumecheng-10953	2	42	mechanical	mechanical	ADJ
fumecheng-10953	2	43	engineering	engineering	NOUN
fumecheng-10953	2	44	,	,	PUNCT
fumecheng-10953	2	45	science	science	NOUN
fumecheng-10953	2	46	and	and	CCONJ
fumecheng-10953	2	47	research	research	NOUN
fumecheng-10953	2	48	branch	branch	NOUN
fumecheng-10953	2	49	,	,	PUNCT
fumecheng-10953	2	50	islamic	islamic	PROPN
fumecheng-10953	2	51	azad	azad	PROPN
fumecheng-10953	2	52	university	university	PROPN
fumecheng-10953	2	53	,	,	PUNCT
fumecheng-10953	2	54	tehran	tehran	PROPN
fumecheng-10953	2	55	,	,	PUNCT
fumecheng-10953	2	56	iran	iran	PROPN
fumecheng-10953	2	57	2yfl	2yfl	NUM
fumecheng-10953	2	58	(	(	PUNCT
fumecheng-10953	2	59	yonsei	yonsei	PROPN
fumecheng-10953	2	60	frontier	frontier	NOUN
fumecheng-10953	2	61	lab	lab	NOUN
fumecheng-10953	2	62	)	)	PUNCT
fumecheng-10953	2	63	,	,	PUNCT
fumecheng-10953	2	64	yonsei	yonsei	PROPN
fumecheng-10953	2	65	university	university	PROPN
fumecheng-10953	2	66	,	,	PUNCT
fumecheng-10953	2	67	seoul	seoul	PROPN
fumecheng-10953	2	68	,	,	PUNCT
fumecheng-10953	2	69	south	south	PROPN
fumecheng-10953	2	70	korea	korea	PROPN
fumecheng-10953	2	71	3material	3material	NUM
fumecheng-10953	2	72	and	and	CCONJ
fumecheng-10953	2	73	hydrology	hydrology	NOUN
fumecheng-10953	2	74	laboratory	laboratory	NOUN
fumecheng-10953	2	75	,	,	PUNCT
fumecheng-10953	2	76	university	university	NOUN
fumecheng-10953	2	77	of	of	ADP
fumecheng-10953	2	78	sidi	sidi	PROPN
fumecheng-10953	2	79	bel	bel	PROPN
fumecheng-10953	2	80	abbes	abbes	PROPN
fumecheng-10953	2	81	,	,	PUNCT
fumecheng-10953	2	82	faculty	faculty	NOUN
fumecheng-10953	2	83	of	of	ADP
fumecheng-10953	2	84	technology	technology	NOUN
fumecheng-10953	2	85	,	,	PUNCT
fumecheng-10953	2	86	civil	civil	ADJ
fumecheng-10953	2	87	engineering	engineering	NOUN
fumecheng-10953	2	88	department	department	PROPN
fumecheng-10953	2	89	,	,	PUNCT
fumecheng-10953	2	90	algeria	algeria	PROPN
fumecheng-10953	2	91	abstract	abstract	NOUN
fumecheng-10953	2	92	.	.	PUNCT
fumecheng-10953	3	1	the	the	DET
fumecheng-10953	3	2	mixture	mixture	NOUN
fumecheng-10953	3	3	unified	unify	VERB
fumecheng-10953	3	4	gradient	gradient	NOUN
fumecheng-10953	3	5	theory	theory	NOUN
fumecheng-10953	3	6	of	of	ADP
fumecheng-10953	3	7	elasticity	elasticity	NOUN
fumecheng-10953	3	8	is	be	AUX
fumecheng-10953	3	9	invoked	invoke	VERB
fumecheng-10953	3	10	for	for	ADP
fumecheng-10953	3	11	the	the	DET
fumecheng-10953	3	12	rigorous	rigorous	ADJ
fumecheng-10953	3	13	analysis	analysis	NOUN
fumecheng-10953	3	14	of	of	ADP
fumecheng-10953	3	15	the	the	DET
fumecheng-10953	3	16	dynamic	dynamic	ADJ
fumecheng-10953	3	17	characteristics	characteristic	NOUN
fumecheng-10953	3	18	of	of	ADP
fumecheng-10953	3	19	elastic	elastic	ADJ
fumecheng-10953	3	20	nanobeams	nanobeam	NOUN
fumecheng-10953	3	21	.	.	PUNCT
fumecheng-10953	4	1	a	a	DET
fumecheng-10953	4	2	consistent	consistent	ADJ
fumecheng-10953	4	3	variational	variational	ADJ
fumecheng-10953	4	4	framework	framework	NOUN
fumecheng-10953	4	5	is	be	AUX
fumecheng-10953	4	6	established	establish	VERB
fumecheng-10953	4	7	and	and	CCONJ
fumecheng-10953	4	8	the	the	DET
fumecheng-10953	4	9	boundary	boundary	ADJ
fumecheng-10953	4	10	-	-	PUNCT
fumecheng-10953	4	11	value	value	NOUN
fumecheng-10953	4	12	problem	problem	NOUN
fumecheng-10953	4	13	of	of	ADP
fumecheng-10953	4	14	dynamic	dynamic	ADJ
fumecheng-10953	4	15	equilibrium	equilibrium	NOUN
fumecheng-10953	4	16	enriched	enrich	VERB
fumecheng-10953	4	17	with	with	ADP
fumecheng-10953	4	18	proper	proper	ADJ
fumecheng-10953	4	19	form	form	NOUN
fumecheng-10953	4	20	of	of	ADP
fumecheng-10953	4	21	the	the	DET
fumecheng-10953	4	22	extra	extra	ADJ
fumecheng-10953	4	23	non	non	ADJ
fumecheng-10953	4	24	-	-	ADJ
fumecheng-10953	4	25	standard	standard	ADJ
fumecheng-10953	4	26	boundary	boundary	ADJ
fumecheng-10953	4	27	conditions	condition	NOUN
fumecheng-10953	4	28	is	be	AUX
fumecheng-10953	4	29	detected	detect	VERB
fumecheng-10953	4	30	.	.	PUNCT
fumecheng-10953	5	1	as	as	ADP
fumecheng-10953	5	2	a	a	DET
fumecheng-10953	5	3	well	well	ADV
fumecheng-10953	5	4	-	-	PUNCT
fumecheng-10953	5	5	established	establish	VERB
fumecheng-10953	5	6	privilege	privilege	NOUN
fumecheng-10953	5	7	of	of	ADP
fumecheng-10953	5	8	the	the	DET
fumecheng-10953	5	9	stationary	stationary	ADJ
fumecheng-10953	5	10	variational	variational	ADJ
fumecheng-10953	5	11	theorems	theorem	NOUN
fumecheng-10953	5	12	,	,	PUNCT
fumecheng-10953	5	13	the	the	DET
fumecheng-10953	5	14	constitutive	constitutive	ADJ
fumecheng-10953	5	15	laws	law	NOUN
fumecheng-10953	5	16	of	of	ADP
fumecheng-10953	5	17	the	the	DET
fumecheng-10953	5	18	resultant	resultant	NOUN
fumecheng-10953	5	19	fields	field	NOUN
fumecheng-10953	5	20	cast	cast	VERB
fumecheng-10953	5	21	as	as	ADP
fumecheng-10953	5	22	differential	differential	ADJ
fumecheng-10953	5	23	relations	relation	NOUN
fumecheng-10953	5	24	.	.	PUNCT
fumecheng-10953	6	1	the	the	DET
fumecheng-10953	6	2	wave	wave	NOUN
fumecheng-10953	6	3	dispersion	dispersion	NOUN
fumecheng-10953	6	4	response	response	NOUN
fumecheng-10953	6	5	of	of	ADP
fumecheng-10953	6	6	elastic	elastic	ADJ
fumecheng-10953	6	7	nano	nano	NOUN
fumecheng-10953	6	8	-	-	PUNCT
fumecheng-10953	6	9	sized	sized	ADJ
fumecheng-10953	6	10	beams	beam	NOUN
fumecheng-10953	6	11	is	be	AUX
fumecheng-10953	6	12	analytically	analytically	ADV
fumecheng-10953	6	13	addressed	address	VERB
fumecheng-10953	6	14	and	and	CCONJ
fumecheng-10953	6	15	the	the	DET
fumecheng-10953	6	16	closed	closed	ADJ
fumecheng-10953	6	17	form	form	NOUN
fumecheng-10953	6	18	solution	solution	NOUN
fumecheng-10953	6	19	of	of	ADP
fumecheng-10953	6	20	the	the	DET
fumecheng-10953	6	21	phase	phase	NOUN
fumecheng-10953	6	22	velocity	velocity	NOUN
fumecheng-10953	6	23	is	be	AUX
fumecheng-10953	6	24	determined	determine	VERB
fumecheng-10953	6	25	.	.	PUNCT
fumecheng-10953	7	1	the	the	DET
fumecheng-10953	7	2	free	free	ADJ
fumecheng-10953	7	3	vibrations	vibration	NOUN
fumecheng-10953	7	4	of	of	ADP
fumecheng-10953	7	5	the	the	DET
fumecheng-10953	7	6	mixture	mixture	NOUN
fumecheng-10953	7	7	unified	unify	VERB
fumecheng-10953	7	8	gradient	gradient	ADJ
fumecheng-10953	7	9	elastic	elastic	ADJ
fumecheng-10953	7	10	beam	beam	NOUN
fumecheng-10953	7	11	is	be	AUX
fumecheng-10953	7	12	,	,	PUNCT
fumecheng-10953	7	13	furthermore	furthermore	ADV
fumecheng-10953	7	14	,	,	PUNCT
fumecheng-10953	7	15	analytically	analytically	ADV
fumecheng-10953	7	16	studied	study	VERB
fumecheng-10953	7	17	.	.	PUNCT
fumecheng-10953	8	1	the	the	DET
fumecheng-10953	8	2	dynamic	dynamic	ADJ
fumecheng-10953	8	3	characteristics	characteristic	NOUN
fumecheng-10953	8	4	of	of	ADP
fumecheng-10953	8	5	elastic	elastic	ADJ
fumecheng-10953	8	6	nanobeams	nanobeam	NOUN
fumecheng-10953	8	7	is	be	AUX
fumecheng-10953	8	8	numerically	numerically	ADV
fumecheng-10953	8	9	evaluated	evaluate	VERB
fumecheng-10953	8	10	,	,	PUNCT
fumecheng-10953	8	11	graphically	graphically	ADV
fumecheng-10953	8	12	illustrated	illustrate	VERB
fumecheng-10953	8	13	,	,	PUNCT
fumecheng-10953	8	14	and	and	CCONJ
fumecheng-10953	8	15	commented	comment	VERB
fumecheng-10953	8	16	upon	upon	SCONJ
fumecheng-10953	8	17	.	.	PUNCT
fumecheng-10953	9	1	the	the	DET
fumecheng-10953	9	2	efficacy	efficacy	NOUN
fumecheng-10953	9	3	of	of	ADP
fumecheng-10953	9	4	the	the	DET
fumecheng-10953	9	5	established	establish	VERB
fumecheng-10953	9	6	augmented	augment	VERB
fumecheng-10953	9	7	elasticity	elasticity	NOUN
fumecheng-10953	9	8	theory	theory	NOUN
fumecheng-10953	9	9	in	in	ADP
fumecheng-10953	9	10	realizing	realize	VERB
fumecheng-10953	9	11	the	the	DET
fumecheng-10953	9	12	softening	soften	VERB
fumecheng-10953	9	13	and	and	CCONJ
fumecheng-10953	9	14	stiffening	stiffen	VERB
fumecheng-10953	9	15	responses	response	NOUN
fumecheng-10953	9	16	of	of	ADP
fumecheng-10953	9	17	nano	nano	NOUN
fumecheng-10953	9	18	-	-	PUNCT
fumecheng-10953	9	19	sized	sized	ADJ
fumecheng-10953	9	20	beams	beam	NOUN
fumecheng-10953	9	21	is	be	AUX
fumecheng-10953	9	22	evinced	evince	VERB
fumecheng-10953	9	23	.	.	PUNCT
fumecheng-10953	10	1	new	new	ADJ
fumecheng-10953	10	2	numerical	numerical	ADJ
fumecheng-10953	10	3	benchmark	benchmark	NOUN
fumecheng-10953	10	4	is	be	AUX
fumecheng-10953	10	5	detected	detect	VERB
fumecheng-10953	10	6	for	for	ADP
fumecheng-10953	10	7	dynamic	dynamic	ADJ
fumecheng-10953	10	8	analysis	analysis	NOUN
fumecheng-10953	10	9	of	of	ADP
fumecheng-10953	10	10	elastic	elastic	ADJ
fumecheng-10953	10	11	nanobeams	nanobeam	NOUN
fumecheng-10953	10	12	.	.	PUNCT
fumecheng-10953	11	1	the	the	DET
fumecheng-10953	11	2	established	establish	VERB
fumecheng-10953	11	3	mixture	mixture	NOUN
fumecheng-10953	11	4	unified	unify	VERB
fumecheng-10953	11	5	gradient	gradient	NOUN
fumecheng-10953	11	6	elasticity	elasticity	NOUN
fumecheng-10953	11	7	model	model	NOUN
fumecheng-10953	11	8	provides	provide	VERB
fumecheng-10953	11	9	a	a	DET
fumecheng-10953	11	10	practical	practical	ADJ
fumecheng-10953	11	11	approach	approach	NOUN
fumecheng-10953	11	12	to	to	PART
fumecheng-10953	11	13	tackle	tackle	VERB
fumecheng-10953	11	14	dynamics	dynamic	NOUN
fumecheng-10953	11	15	of	of	ADP
fumecheng-10953	11	16	nano	nano	NOUN
fumecheng-10953	11	17	-	-	PUNCT
fumecheng-10953	11	18	structures	structure	NOUN
fumecheng-10953	11	19	in	in	ADP
fumecheng-10953	11	20	pioneering	pioneer	VERB
fumecheng-10953	11	21	mems	mem	NOUN
fumecheng-10953	11	22	/	/	SYM
fumecheng-10953	11	23	nems	nem	NOUN
fumecheng-10953	11	24	.	.	PUNCT
fumecheng-10953	12	1	key	key	ADJ
fumecheng-10953	12	2	words	word	NOUN
fumecheng-10953	12	3	:	:	PUNCT
fumecheng-10953	12	4	stationary	stationary	ADJ
fumecheng-10953	12	5	variational	variational	ADJ
fumecheng-10953	12	6	principle	principle	NOUN
fumecheng-10953	12	7	,	,	PUNCT
fumecheng-10953	12	8	nanobeam	nanobeam	ADJ
fumecheng-10953	12	9	,	,	PUNCT
fumecheng-10953	12	10	free	free	ADJ
fumecheng-10953	12	11	vibrations	vibration	NOUN
fumecheng-10953	12	12	,	,	PUNCT
fumecheng-10953	12	13	wave	wave	NOUN
fumecheng-10953	12	14	dispersion	dispersion	NOUN
fumecheng-10953	12	15	,	,	PUNCT
fumecheng-10953	12	16	stress	stress	NOUN
fumecheng-10953	12	17	gradient	gradient	NOUN
fumecheng-10953	12	18	elasticity	elasticity	NOUN
fumecheng-10953	12	19	,	,	PUNCT
fumecheng-10953	12	20	strain	strain	NOUN
fumecheng-10953	12	21	gradient	gradient	NOUN
fumecheng-10953	12	22	theory	theory	NOUN
fumecheng-10953	12	23	received	receive	VERB
fumecheng-10953	12	24	:	:	PUNCT
fumecheng-10953	12	25	july	july	PROPN
fumecheng-10953	12	26	03	03	NUM
fumecheng-10953	12	27	,	,	PUNCT
fumecheng-10953	12	28	2022	2022	NUM
fumecheng-10953	12	29	/	/	SYM
fumecheng-10953	12	30	accepted	accept	VERB
fumecheng-10953	12	31	august	august	PROPN
fumecheng-10953	12	32	25	25	NUM
fumecheng-10953	12	33	,	,	PUNCT
fumecheng-10953	12	34	2022	2022	NUM
fumecheng-10953	12	35	corresponding	correspond	VERB
fumecheng-10953	12	36	author	author	NOUN
fumecheng-10953	12	37	:	:	PUNCT
fumecheng-10953	12	38	seyed	seyed	PROPN
fumecheng-10953	12	39	ali	ali	PROPN
fumecheng-10953	12	40	faghidian	faghidian	PROPN
fumecheng-10953	12	41	department	department	PROPN
fumecheng-10953	12	42	of	of	ADP
fumecheng-10953	12	43	mechanical	mechanical	ADJ
fumecheng-10953	12	44	engineering	engineering	NOUN
fumecheng-10953	12	45	,	,	PUNCT
fumecheng-10953	12	46	science	science	NOUN
fumecheng-10953	12	47	and	and	CCONJ
fumecheng-10953	12	48	research	research	NOUN
fumecheng-10953	12	49	branch	branch	NOUN
fumecheng-10953	12	50	,	,	PUNCT
fumecheng-10953	12	51	islamic	islamic	PROPN
fumecheng-10953	12	52	azad	azad	PROPN
fumecheng-10953	12	53	university	university	PROPN
fumecheng-10953	12	54	,	,	PUNCT
fumecheng-10953	12	55	tehran	tehran	PROPN
fumecheng-10953	12	56	,	,	PUNCT
fumecheng-10953	12	57	iran	iran	PROPN
fumecheng-10953	12	58	e	e	NOUN
fumecheng-10953	12	59	-	-	NOUN
fumecheng-10953	12	60	mail	mail	NOUN
fumecheng-10953	12	61	:	:	PUNCT
fumecheng-10953	12	62	faghidian@gmail.com	faghidian@gmail.com	NOUN
fumecheng-10953	12	63	;	;	PUNCT
fumecheng-10953	12	64	faghidian@srbiau.ac.ir	faghidian@srbiau.ac.ir	PROPN
fumecheng-10953	12	65	540	540	NUM
fumecheng-10953	12	66	s.	s.	PROPN
fumecheng-10953	12	67	a.	a.	PROPN
fumecheng-10953	12	68	faghidian	faghidian	PROPN
fumecheng-10953	12	69	,	,	PUNCT
fumecheng-10953	12	70	a.	a.	NOUN
fumecheng-10953	12	71	tounsi	tounsi	NOUN
fumecheng-10953	12	72	1	1	NUM
fumecheng-10953	12	73	.	.	PUNCT
fumecheng-10953	13	1	introduction	introduction	NOUN
fumecheng-10953	13	2	micro-/nano	micro-/nano	NOUN
fumecheng-10953	13	3	-	-	NOUN
fumecheng-10953	13	4	sensors	sensor	NOUN
fumecheng-10953	13	5	are	be	AUX
fumecheng-10953	13	6	one	one	NUM
fumecheng-10953	13	7	of	of	ADP
fumecheng-10953	13	8	the	the	DET
fumecheng-10953	13	9	representative	representative	ADJ
fumecheng-10953	13	10	elements	element	NOUN
fumecheng-10953	13	11	of	of	ADP
fumecheng-10953	13	12	micro-/nanoelectromechanical	micro-/nanoelectromechanical	ADJ
fumecheng-10953	13	13	systems	system	NOUN
fumecheng-10953	13	14	(	(	PUNCT
fumecheng-10953	13	15	mems	mem	NOUN
fumecheng-10953	13	16	/	/	SYM
fumecheng-10953	13	17	nems	nem	NOUN
fumecheng-10953	13	18	)	)	PUNCT
fumecheng-10953	13	19	that	that	PRON
fumecheng-10953	13	20	found	find	VERB
fumecheng-10953	13	21	a	a	DET
fumecheng-10953	13	22	variety	variety	NOUN
fumecheng-10953	13	23	of	of	ADP
fumecheng-10953	13	24	applications	application	NOUN
fumecheng-10953	13	25	in	in	ADP
fumecheng-10953	13	26	pioneering	pioneer	VERB
fumecheng-10953	13	27	engineering	engineering	NOUN
fumecheng-10953	13	28	systems	system	NOUN
fumecheng-10953	13	29	[	[	X
fumecheng-10953	13	30	1	1	NUM
fumecheng-10953	13	31	,	,	PUNCT
fumecheng-10953	13	32	2	2	NUM
fumecheng-10953	13	33	]	]	PUNCT
fumecheng-10953	13	34	.	.	PUNCT
fumecheng-10953	14	1	structural	structural	ADJ
fumecheng-10953	14	2	analysis	analysis	NOUN
fumecheng-10953	14	3	of	of	ADP
fumecheng-10953	14	4	vibrating	vibrate	VERB
fumecheng-10953	14	5	modules	module	NOUN
fumecheng-10953	14	6	of	of	ADP
fumecheng-10953	14	7	mems	mem	NOUN
fumecheng-10953	14	8	/	/	SYM
fumecheng-10953	14	9	nems	nem	NOUN
fumecheng-10953	14	10	is	be	AUX
fumecheng-10953	14	11	a	a	DET
fumecheng-10953	14	12	challenging	challenging	ADJ
fumecheng-10953	14	13	issue	issue	NOUN
fumecheng-10953	14	14	that	that	PRON
fumecheng-10953	14	15	stimulated	stimulate	VERB
fumecheng-10953	14	16	a	a	DET
fumecheng-10953	14	17	great	great	ADJ
fumecheng-10953	14	18	deal	deal	NOUN
fumecheng-10953	14	19	of	of	ADP
fumecheng-10953	14	20	interest	interest	NOUN
fumecheng-10953	14	21	[	[	X
fumecheng-10953	14	22	3	3	NUM
fumecheng-10953	14	23	-	-	SYM
fumecheng-10953	14	24	15	15	NUM
fumecheng-10953	14	25	]	]	PUNCT
fumecheng-10953	14	26	.	.	PUNCT
fumecheng-10953	15	1	in	in	ADP
fumecheng-10953	15	2	view	view	NOUN
fumecheng-10953	15	3	of	of	ADP
fumecheng-10953	15	4	inadequacy	inadequacy	NOUN
fumecheng-10953	15	5	of	of	ADP
fumecheng-10953	15	6	the	the	DET
fumecheng-10953	15	7	classical	classical	ADJ
fumecheng-10953	15	8	elasticity	elasticity	NOUN
fumecheng-10953	15	9	theory	theory	NOUN
fumecheng-10953	15	10	in	in	ADP
fumecheng-10953	15	11	appropriate	appropriate	ADJ
fumecheng-10953	15	12	prediction	prediction	NOUN
fumecheng-10953	15	13	of	of	ADP
fumecheng-10953	15	14	the	the	DET
fumecheng-10953	15	15	peculiar	peculiar	ADJ
fumecheng-10953	15	16	behavior	behavior	NOUN
fumecheng-10953	15	17	of	of	ADP
fumecheng-10953	15	18	nano	nano	NOUN
fumecheng-10953	15	19	-	-	PUNCT
fumecheng-10953	15	20	scale	scale	NOUN
fumecheng-10953	15	21	structures	structure	NOUN
fumecheng-10953	15	22	,	,	PUNCT
fumecheng-10953	15	23	several	several	ADJ
fumecheng-10953	15	24	augmented	augment	VERB
fumecheng-10953	15	25	elasticity	elasticity	NOUN
fumecheng-10953	15	26	theories	theory	NOUN
fumecheng-10953	15	27	are	be	AUX
fumecheng-10953	15	28	introduced	introduce	VERB
fumecheng-10953	15	29	in	in	ADP
fumecheng-10953	15	30	literature	literature	NOUN
fumecheng-10953	15	31	.	.	PUNCT
fumecheng-10953	16	1	the	the	DET
fumecheng-10953	16	2	constitutive	constitutive	ADJ
fumecheng-10953	16	3	model	model	NOUN
fumecheng-10953	16	4	associated	associate	VERB
fumecheng-10953	16	5	with	with	ADP
fumecheng-10953	16	6	the	the	DET
fumecheng-10953	16	7	augmented	augment	VERB
fumecheng-10953	16	8	elasticity	elasticity	NOUN
fumecheng-10953	16	9	theory	theory	NOUN
fumecheng-10953	16	10	is	be	AUX
fumecheng-10953	16	11	,	,	PUNCT
fumecheng-10953	16	12	accordingly	accordingly	ADV
fumecheng-10953	16	13	,	,	PUNCT
fumecheng-10953	16	14	enriched	enrich	VERB
fumecheng-10953	16	15	via	via	ADP
fumecheng-10953	16	16	incorporation	incorporation	NOUN
fumecheng-10953	16	17	of	of	ADP
fumecheng-10953	16	18	the	the	DET
fumecheng-10953	16	19	gradient	gradient	ADJ
fumecheng-10953	16	20	effects	effect	NOUN
fumecheng-10953	16	21	or	or	CCONJ
fumecheng-10953	16	22	of	of	ADP
fumecheng-10953	16	23	the	the	DET
fumecheng-10953	16	24	nonlocality	nonlocality	NOUN
fumecheng-10953	16	25	.	.	PUNCT
fumecheng-10953	17	1	within	within	ADP
fumecheng-10953	17	2	the	the	DET
fumecheng-10953	17	3	framework	framework	NOUN
fumecheng-10953	17	4	of	of	ADP
fumecheng-10953	17	5	the	the	DET
fumecheng-10953	17	6	strain	strain	NOUN
fumecheng-10953	17	7	gradient	gradient	NOUN
fumecheng-10953	17	8	theory	theory	NOUN
fumecheng-10953	17	9	,	,	PUNCT
fumecheng-10953	17	10	the	the	DET
fumecheng-10953	17	11	material	material	NOUN
fumecheng-10953	17	12	response	response	NOUN
fumecheng-10953	17	13	is	be	AUX
fumecheng-10953	17	14	assumed	assume	VERB
fumecheng-10953	17	15	to	to	PART
fumecheng-10953	17	16	be	be	AUX
fumecheng-10953	17	17	a	a	DET
fumecheng-10953	17	18	function	function	NOUN
fumecheng-10953	17	19	of	of	ADP
fumecheng-10953	17	20	the	the	DET
fumecheng-10953	17	21	classical	classical	ADJ
fumecheng-10953	17	22	kinematics	kinematic	NOUN
fumecheng-10953	17	23	along	along	ADP
fumecheng-10953	17	24	with	with	ADP
fumecheng-10953	17	25	the	the	DET
fumecheng-10953	17	26	gradients	gradient	NOUN
fumecheng-10953	17	27	of	of	ADP
fumecheng-10953	17	28	various	various	ADJ
fumecheng-10953	17	29	order	order	NOUN
fumecheng-10953	18	1	[	[	X
fumecheng-10953	18	2	16	16	NUM
fumecheng-10953	18	3	]	]	PUNCT
fumecheng-10953	18	4	.	.	PUNCT
fumecheng-10953	19	1	the	the	DET
fumecheng-10953	19	2	strain	strain	NOUN
fumecheng-10953	19	3	gradient	gradient	NOUN
fumecheng-10953	19	4	theory	theory	NOUN
fumecheng-10953	19	5	can	can	AUX
fumecheng-10953	19	6	efficiently	efficiently	ADV
fumecheng-10953	19	7	predict	predict	VERB
fumecheng-10953	19	8	the	the	DET
fumecheng-10953	19	9	smaller	small	ADJ
fumecheng-10953	19	10	-	-	PUNCT
fumecheng-10953	19	11	is	be	AUX
fumecheng-10953	19	12	-	-	PUNCT
fumecheng-10953	19	13	stiffer	stiff	ADJ
fumecheng-10953	19	14	phenomenon	phenomenon	NOUN
fumecheng-10953	19	15	at	at	ADP
fumecheng-10953	19	16	the	the	DET
fumecheng-10953	19	17	ultra	ultra	ADJ
fumecheng-10953	19	18	-	-	ADJ
fumecheng-10953	19	19	small	small	ADJ
fumecheng-10953	19	20	scale	scale	NOUN
fumecheng-10953	19	21	[	[	X
fumecheng-10953	19	22	17	17	NUM
fumecheng-10953	19	23	-	-	SYM
fumecheng-10953	19	24	21	21	NUM
fumecheng-10953	19	25	]	]	PUNCT
fumecheng-10953	19	26	.	.	PUNCT
fumecheng-10953	20	1	alternatively	alternatively	ADV
fumecheng-10953	20	2	,	,	PUNCT
fumecheng-10953	20	3	the	the	DET
fumecheng-10953	20	4	material	material	NOUN
fumecheng-10953	20	5	response	response	NOUN
fumecheng-10953	20	6	can	can	AUX
fumecheng-10953	20	7	be	be	AUX
fumecheng-10953	20	8	considered	consider	VERB
fumecheng-10953	20	9	to	to	PART
fumecheng-10953	20	10	depend	depend	VERB
fumecheng-10953	20	11	on	on	ADP
fumecheng-10953	20	12	the	the	DET
fumecheng-10953	20	13	classical	classical	ADJ
fumecheng-10953	20	14	kinetic	kinetic	NOUN
fumecheng-10953	20	15	variables	variable	NOUN
fumecheng-10953	20	16	together	together	ADV
fumecheng-10953	20	17	with	with	ADP
fumecheng-10953	20	18	the	the	DET
fumecheng-10953	20	19	gradients	gradient	NOUN
fumecheng-10953	20	20	of	of	ADP
fumecheng-10953	20	21	various	various	ADJ
fumecheng-10953	20	22	order	order	NOUN
fumecheng-10953	20	23	which	which	PRON
fumecheng-10953	20	24	yields	yield	VERB
fumecheng-10953	20	25	the	the	DET
fumecheng-10953	20	26	stress	stress	NOUN
fumecheng-10953	20	27	gradient	gradient	NOUN
fumecheng-10953	20	28	theory	theory	NOUN
fumecheng-10953	20	29	[	[	X
fumecheng-10953	20	30	22	22	NUM
fumecheng-10953	20	31	,	,	PUNCT
fumecheng-10953	20	32	23	23	NUM
fumecheng-10953	20	33	]	]	PUNCT
fumecheng-10953	20	34	.	.	PUNCT
fumecheng-10953	21	1	the	the	DET
fumecheng-10953	21	2	long	long	ADJ
fumecheng-10953	21	3	-	-	PUNCT
fumecheng-10953	21	4	range	range	NOUN
fumecheng-10953	21	5	interactions	interaction	NOUN
fumecheng-10953	21	6	can	can	AUX
fumecheng-10953	21	7	be	be	AUX
fumecheng-10953	21	8	modeled	model	VERB
fumecheng-10953	21	9	within	within	ADP
fumecheng-10953	21	10	the	the	DET
fumecheng-10953	21	11	context	context	NOUN
fumecheng-10953	21	12	of	of	ADP
fumecheng-10953	21	13	the	the	DET
fumecheng-10953	21	14	nonlocal	nonlocal	ADJ
fumecheng-10953	21	15	elasticity	elasticity	NOUN
fumecheng-10953	21	16	theory	theory	NOUN
fumecheng-10953	21	17	wherein	wherein	SCONJ
fumecheng-10953	21	18	the	the	DET
fumecheng-10953	21	19	constitutive	constitutive	ADJ
fumecheng-10953	21	20	model	model	NOUN
fumecheng-10953	21	21	is	be	AUX
fumecheng-10953	21	22	modified	modify	VERB
fumecheng-10953	21	23	employing	employ	VERB
fumecheng-10953	21	24	the	the	DET
fumecheng-10953	21	25	nonlocal	nonlocal	ADJ
fumecheng-10953	21	26	kernel	kernel	NOUN
fumecheng-10953	21	27	function	function	NOUN
fumecheng-10953	21	28	[	[	X
fumecheng-10953	21	29	24	24	NUM
fumecheng-10953	21	30	]	]	PUNCT
fumecheng-10953	21	31	.	.	PUNCT
fumecheng-10953	22	1	the	the	DET
fumecheng-10953	22	2	smaller	small	ADJ
fumecheng-10953	22	3	-	-	PUNCT
fumecheng-10953	22	4	is	be	AUX
fumecheng-10953	22	5	-	-	PUNCT
fumecheng-10953	22	6	softer	soft	ADJ
fumecheng-10953	22	7	phenomenon	phenomenon	NOUN
fumecheng-10953	22	8	is	be	AUX
fumecheng-10953	22	9	,	,	PUNCT
fumecheng-10953	22	10	therefore	therefore	ADV
fumecheng-10953	22	11	,	,	PUNCT
fumecheng-10953	22	12	realized	realize	VERB
fumecheng-10953	22	13	via	via	ADP
fumecheng-10953	22	14	implementation	implementation	NOUN
fumecheng-10953	22	15	of	of	ADP
fumecheng-10953	22	16	the	the	DET
fumecheng-10953	22	17	nonlocal	nonlocal	ADJ
fumecheng-10953	22	18	elasticity	elasticity	NOUN
fumecheng-10953	22	19	model	model	NOUN
fumecheng-10953	22	20	.	.	PUNCT
fumecheng-10953	23	1	as	as	SCONJ
fumecheng-10953	23	2	the	the	DET
fumecheng-10953	23	3	nonlocality	nonlocality	NOUN
fumecheng-10953	23	4	concept	concept	NOUN
fumecheng-10953	23	5	is	be	AUX
fumecheng-10953	23	6	a	a	DET
fumecheng-10953	23	7	topic	topic	NOUN
fumecheng-10953	23	8	of	of	ADP
fumecheng-10953	23	9	major	major	ADJ
fumecheng-10953	23	10	interest	interest	NOUN
fumecheng-10953	23	11	in	in	ADP
fumecheng-10953	23	12	the	the	DET
fumecheng-10953	23	13	size	size	NOUN
fumecheng-10953	23	14	-	-	PUNCT
fumecheng-10953	23	15	dependent	dependent	ADJ
fumecheng-10953	23	16	mechanics	mechanic	NOUN
fumecheng-10953	23	17	[	[	X
fumecheng-10953	23	18	25	25	NUM
fumecheng-10953	23	19	-	-	SYM
fumecheng-10953	23	20	35	35	NUM
fumecheng-10953	23	21	]	]	PUNCT
fumecheng-10953	23	22	,	,	PUNCT
fumecheng-10953	23	23	severe	severe	ADJ
fumecheng-10953	23	24	concern	concern	NOUN
fumecheng-10953	23	25	exists	exist	VERB
fumecheng-10953	23	26	in	in	ADP
fumecheng-10953	23	27	its	its	PRON
fumecheng-10953	23	28	application	application	NOUN
fumecheng-10953	23	29	to	to	ADP
fumecheng-10953	23	30	nano	nano	NOUN
fumecheng-10953	23	31	-	-	PUNCT
fumecheng-10953	23	32	scale	scale	NOUN
fumecheng-10953	23	33	continua	continuum	NOUN
fumecheng-10953	23	34	with	with	ADP
fumecheng-10953	23	35	finite	finite	ADJ
fumecheng-10953	23	36	domain	domain	NOUN
fumecheng-10953	23	37	[	[	X
fumecheng-10953	23	38	36	36	NUM
fumecheng-10953	23	39	]	]	PUNCT
fumecheng-10953	23	40	.	.	PUNCT
fumecheng-10953	24	1	either	either	CCONJ
fumecheng-10953	24	2	the	the	DET
fumecheng-10953	24	3	strain	strain	NOUN
fumecheng-10953	24	4	gradient	gradient	NOUN
fumecheng-10953	24	5	theory	theory	NOUN
fumecheng-10953	24	6	of	of	ADP
fumecheng-10953	24	7	elasticity	elasticity	NOUN
fumecheng-10953	24	8	or	or	CCONJ
fumecheng-10953	24	9	the	the	DET
fumecheng-10953	24	10	nonlocal	nonlocal	ADJ
fumecheng-10953	24	11	elasticity	elasticity	NOUN
fumecheng-10953	24	12	model	model	NOUN
fumecheng-10953	24	13	can	can	AUX
fumecheng-10953	24	14	solely	solely	ADV
fumecheng-10953	24	15	predict	predict	VERB
fumecheng-10953	24	16	the	the	DET
fumecheng-10953	24	17	stiffening	stiffening	NOUN
fumecheng-10953	24	18	or	or	CCONJ
fumecheng-10953	24	19	the	the	DET
fumecheng-10953	24	20	softening	soften	VERB
fumecheng-10953	24	21	material	material	NOUN
fumecheng-10953	24	22	behavior	behavior	NOUN
fumecheng-10953	24	23	,	,	PUNCT
fumecheng-10953	24	24	and	and	CCONJ
fumecheng-10953	24	25	therefore	therefore	ADV
fumecheng-10953	24	26	,	,	PUNCT
fumecheng-10953	24	27	they	they	PRON
fumecheng-10953	24	28	can	can	AUX
fumecheng-10953	24	29	not	not	PART
fumecheng-10953	24	30	cover	cover	VERB
fumecheng-10953	24	31	the	the	DET
fumecheng-10953	24	32	wide	wide	ADJ
fumecheng-10953	24	33	spectrum	spectrum	NOUN
fumecheng-10953	24	34	of	of	ADP
fumecheng-10953	24	35	material	material	NOUN
fumecheng-10953	24	36	characteristics	characteristic	NOUN
fumecheng-10953	24	37	at	at	ADP
fumecheng-10953	24	38	the	the	DET
fumecheng-10953	24	39	ultra	ultra	ADJ
fumecheng-10953	24	40	-	-	ADJ
fumecheng-10953	24	41	small	small	ADJ
fumecheng-10953	24	42	scale	scale	NOUN
fumecheng-10953	24	43	.	.	PUNCT
fumecheng-10953	25	1	to	to	PART
fumecheng-10953	25	2	overcome	overcome	VERB
fumecheng-10953	25	3	this	this	DET
fumecheng-10953	25	4	deficiency	deficiency	NOUN
fumecheng-10953	25	5	,	,	PUNCT
fumecheng-10953	25	6	dissimilar	dissimilar	ADJ
fumecheng-10953	25	7	size	size	NOUN
fumecheng-10953	25	8	-	-	PUNCT
fumecheng-10953	25	9	dependent	dependent	ADJ
fumecheng-10953	25	10	elasticity	elasticity	NOUN
fumecheng-10953	25	11	models	model	NOUN
fumecheng-10953	25	12	are	be	AUX
fumecheng-10953	25	13	integrated	integrate	VERB
fumecheng-10953	25	14	to	to	PART
fumecheng-10953	25	15	introduce	introduce	VERB
fumecheng-10953	25	16	novel	novel	ADJ
fumecheng-10953	25	17	augmented	augment	VERB
fumecheng-10953	25	18	theories	theory	NOUN
fumecheng-10953	25	19	,	,	PUNCT
fumecheng-10953	25	20	such	such	ADJ
fumecheng-10953	25	21	as	as	ADP
fumecheng-10953	25	22	the	the	DET
fumecheng-10953	25	23	nonlocal	nonlocal	ADJ
fumecheng-10953	25	24	strain	strain	NOUN
fumecheng-10953	25	25	gradient	gradient	NOUN
fumecheng-10953	25	26	model	model	NOUN
fumecheng-10953	25	27	[	[	X
fumecheng-10953	25	28	37	37	NUM
fumecheng-10953	25	29	,	,	PUNCT
fumecheng-10953	25	30	38	38	NUM
fumecheng-10953	25	31	]	]	PUNCT
fumecheng-10953	25	32	,	,	PUNCT
fumecheng-10953	25	33	the	the	DET
fumecheng-10953	25	34	nonlocal	nonlocal	ADJ
fumecheng-10953	25	35	modified	modify	VERB
fumecheng-10953	25	36	gradient	gradient	NOUN
fumecheng-10953	25	37	theory	theory	NOUN
fumecheng-10953	25	38	[	[	X
fumecheng-10953	25	39	39	39	NUM
fumecheng-10953	25	40	,	,	PUNCT
fumecheng-10953	25	41	40	40	NUM
fumecheng-10953	25	42	]	]	PUNCT
fumecheng-10953	25	43	,	,	PUNCT
fumecheng-10953	25	44	the	the	DET
fumecheng-10953	25	45	higher	high	ADJ
fumecheng-10953	25	46	-	-	PUNCT
fumecheng-10953	25	47	order	order	NOUN
fumecheng-10953	25	48	nonlocal	nonlocal	ADJ
fumecheng-10953	25	49	gradient	gradient	NOUN
fumecheng-10953	25	50	theory	theory	NOUN
fumecheng-10953	25	51	[	[	X
fumecheng-10953	25	52	4143	4143	NOUN
fumecheng-10953	25	53	]	]	PUNCT
fumecheng-10953	25	54	,	,	PUNCT
fumecheng-10953	25	55	the	the	DET
fumecheng-10953	25	56	nonlocal	nonlocal	ADJ
fumecheng-10953	25	57	surface	surface	NOUN
fumecheng-10953	25	58	elasticity	elasticity	NOUN
fumecheng-10953	26	1	[	[	X
fumecheng-10953	26	2	44	44	NUM
fumecheng-10953	26	3	-	-	SYM
fumecheng-10953	26	4	46	46	NUM
fumecheng-10953	26	5	]	]	PUNCT
fumecheng-10953	26	6	,	,	PUNCT
fumecheng-10953	26	7	and	and	CCONJ
fumecheng-10953	26	8	the	the	DET
fumecheng-10953	26	9	mixture	mixture	NOUN
fumecheng-10953	26	10	stress	stress	NOUN
fumecheng-10953	26	11	gradient	gradient	NOUN
fumecheng-10953	26	12	theory	theory	NOUN
fumecheng-10953	26	13	[	[	X
fumecheng-10953	26	14	47	47	NUM
fumecheng-10953	26	15	]	]	PUNCT
fumecheng-10953	26	16	.	.	PUNCT
fumecheng-10953	27	1	utilization	utilization	NOUN
fumecheng-10953	27	2	of	of	ADP
fumecheng-10953	27	3	the	the	DET
fumecheng-10953	27	4	integrated	integrate	VERB
fumecheng-10953	27	5	size	size	NOUN
fumecheng-10953	27	6	-	-	PUNCT
fumecheng-10953	27	7	dependent	dependent	ADJ
fumecheng-10953	27	8	elasticity	elasticity	NOUN
fumecheng-10953	27	9	models	model	NOUN
fumecheng-10953	27	10	for	for	ADP
fumecheng-10953	27	11	nanoscopic	nanoscopic	ADJ
fumecheng-10953	27	12	study	study	NOUN
fumecheng-10953	27	13	of	of	ADP
fumecheng-10953	27	14	the	the	DET
fumecheng-10953	27	15	field	field	NOUN
fumecheng-10953	27	16	quantities	quantity	NOUN
fumecheng-10953	27	17	,	,	PUNCT
fumecheng-10953	27	18	accordingly	accordingly	ADV
fumecheng-10953	27	19	,	,	PUNCT
fumecheng-10953	27	20	received	receive	VERB
fumecheng-10953	27	21	increasing	increase	VERB
fumecheng-10953	27	22	interest	interest	NOUN
fumecheng-10953	27	23	in	in	ADP
fumecheng-10953	27	24	recent	recent	ADJ
fumecheng-10953	27	25	literature	literature	NOUN
fumecheng-10953	27	26	[	[	X
fumecheng-10953	27	27	48	48	NUM
fumecheng-10953	27	28	-	-	SYM
fumecheng-10953	27	29	51	51	NUM
fumecheng-10953	27	30	]	]	PUNCT
fumecheng-10953	27	31	.	.	PUNCT
fumecheng-10953	28	1	the	the	DET
fumecheng-10953	28	2	present	present	ADJ
fumecheng-10953	28	3	study	study	NOUN
fumecheng-10953	28	4	provides	provide	VERB
fumecheng-10953	28	5	significant	significant	ADJ
fumecheng-10953	28	6	insight	insight	NOUN
fumecheng-10953	28	7	and	and	CCONJ
fumecheng-10953	28	8	critical	critical	ADJ
fumecheng-10953	28	9	analysis	analysis	NOUN
fumecheng-10953	28	10	of	of	ADP
fumecheng-10953	28	11	the	the	DET
fumecheng-10953	28	12	dynamic	dynamic	ADJ
fumecheng-10953	28	13	characteristics	characteristic	NOUN
fumecheng-10953	28	14	of	of	ADP
fumecheng-10953	28	15	nano	nano	NOUN
fumecheng-10953	28	16	-	-	PUNCT
fumecheng-10953	28	17	scaled	scale	VERB
fumecheng-10953	28	18	structures	structure	NOUN
fumecheng-10953	28	19	and	and	CCONJ
fumecheng-10953	28	20	offers	offer	VERB
fumecheng-10953	28	21	necessary	necessary	ADJ
fumecheng-10953	28	22	guidance	guidance	NOUN
fumecheng-10953	28	23	for	for	ADP
fumecheng-10953	28	24	the	the	DET
fumecheng-10953	28	25	reliable	reliable	ADJ
fumecheng-10953	28	26	assessment	assessment	NOUN
fumecheng-10953	28	27	of	of	ADP
fumecheng-10953	28	28	the	the	DET
fumecheng-10953	28	29	dynamic	dynamic	ADJ
fumecheng-10953	28	30	response	response	NOUN
fumecheng-10953	28	31	of	of	ADP
fumecheng-10953	28	32	nano	nano	NOUN
fumecheng-10953	28	33	-	-	PUNCT
fumecheng-10953	28	34	components	component	NOUN
fumecheng-10953	28	35	in	in	ADP
fumecheng-10953	28	36	advanced	advanced	ADJ
fumecheng-10953	28	37	mems	mem	NOUN
fumecheng-10953	28	38	/	/	SYM
fumecheng-10953	28	39	nems	nem	NOUN
fumecheng-10953	28	40	.	.	PUNCT
fumecheng-10953	29	1	the	the	DET
fumecheng-10953	29	2	mixture	mixture	NOUN
fumecheng-10953	29	3	unified	unify	VERB
fumecheng-10953	29	4	gradient	gradient	NOUN
fumecheng-10953	29	5	theory	theory	NOUN
fumecheng-10953	29	6	of	of	ADP
fumecheng-10953	29	7	elasticity	elasticity	NOUN
fumecheng-10953	29	8	,	,	PUNCT
fumecheng-10953	29	9	as	as	ADP
fumecheng-10953	29	10	a	a	DET
fumecheng-10953	29	11	proficient	proficient	ADJ
fumecheng-10953	29	12	alternative	alternative	NOUN
fumecheng-10953	29	13	to	to	ADP
fumecheng-10953	29	14	the	the	DET
fumecheng-10953	29	15	two	two	NUM
fumecheng-10953	29	16	-	-	PUNCT
fumecheng-10953	29	17	phase	phase	NOUN
fumecheng-10953	29	18	local	local	ADJ
fumecheng-10953	29	19	/	/	SYM
fumecheng-10953	29	20	nonlocal	nonlocal	ADJ
fumecheng-10953	29	21	gradient	gradient	NOUN
fumecheng-10953	29	22	theory	theory	NOUN
fumecheng-10953	29	23	,	,	PUNCT
fumecheng-10953	29	24	is	be	AUX
fumecheng-10953	29	25	invoked	invoke	VERB
fumecheng-10953	29	26	to	to	PART
fumecheng-10953	29	27	properly	properly	ADV
fumecheng-10953	29	28	realize	realize	VERB
fumecheng-10953	29	29	the	the	DET
fumecheng-10953	29	30	size	size	NOUN
fumecheng-10953	29	31	-	-	PUNCT
fumecheng-10953	29	32	effects	effect	NOUN
fumecheng-10953	29	33	.	.	PUNCT
fumecheng-10953	30	1	both	both	CCONJ
fumecheng-10953	30	2	the	the	DET
fumecheng-10953	30	3	softening	softening	NOUN
fumecheng-10953	30	4	and	and	CCONJ
fumecheng-10953	30	5	the	the	DET
fumecheng-10953	30	6	stiffening	stiffen	VERB
fumecheng-10953	30	7	material	material	NOUN
fumecheng-10953	30	8	behaviors	behavior	NOUN
fumecheng-10953	30	9	can	can	AUX
fumecheng-10953	30	10	be	be	AUX
fumecheng-10953	30	11	effectively	effectively	ADV
fumecheng-10953	30	12	captured	capture	VERB
fumecheng-10953	30	13	in	in	ADP
fumecheng-10953	30	14	view	view	NOUN
fumecheng-10953	30	15	of	of	ADP
fumecheng-10953	30	16	consistent	consistent	ADJ
fumecheng-10953	30	17	unification	unification	NOUN
fumecheng-10953	30	18	of	of	ADP
fumecheng-10953	30	19	the	the	DET
fumecheng-10953	30	20	stress	stress	NOUN
fumecheng-10953	30	21	gradient	gradient	NOUN
fumecheng-10953	30	22	,	,	PUNCT
fumecheng-10953	30	23	the	the	DET
fumecheng-10953	30	24	strain	strain	NOUN
fumecheng-10953	30	25	gradient	gradient	NOUN
fumecheng-10953	30	26	,	,	PUNCT
fumecheng-10953	30	27	and	and	CCONJ
fumecheng-10953	30	28	the	the	DET
fumecheng-10953	30	29	classical	classical	ADJ
fumecheng-10953	30	30	elasticity	elasticity	NOUN
fumecheng-10953	30	31	theory	theory	NOUN
fumecheng-10953	30	32	.	.	PUNCT
fumecheng-10953	31	1	the	the	DET
fumecheng-10953	31	2	wave	wave	NOUN
fumecheng-10953	31	3	dispersion	dispersion	NOUN
fumecheng-10953	31	4	response	response	NOUN
fumecheng-10953	31	5	of	of	ADP
fumecheng-10953	31	6	the	the	DET
fumecheng-10953	31	7	flexural	flexural	ADJ
fumecheng-10953	31	8	waves	wave	NOUN
fumecheng-10953	31	9	along	along	ADP
fumecheng-10953	31	10	with	with	ADP
fumecheng-10953	31	11	the	the	DET
fumecheng-10953	31	12	free	free	ADJ
fumecheng-10953	31	13	vibrations	vibration	NOUN
fumecheng-10953	31	14	of	of	ADP
fumecheng-10953	31	15	nano	nano	NOUN
fumecheng-10953	31	16	-	-	PUNCT
fumecheng-10953	31	17	sized	sized	ADJ
fumecheng-10953	31	18	elastic	elastic	ADJ
fumecheng-10953	31	19	beams	beam	NOUN
fumecheng-10953	31	20	is	be	AUX
fumecheng-10953	31	21	rigorously	rigorously	ADV
fumecheng-10953	31	22	examined	examine	VERB
fumecheng-10953	31	23	.	.	PUNCT
fumecheng-10953	32	1	the	the	DET
fumecheng-10953	32	2	dynamic	dynamic	ADJ
fumecheng-10953	32	3	characteristics	characteristic	NOUN
fumecheng-10953	32	4	of	of	ADP
fumecheng-10953	32	5	mixture	mixture	NOUN
fumecheng-10953	32	6	unified	unify	VERB
fumecheng-10953	32	7	gradient	gradient	ADJ
fumecheng-10953	32	8	elastic	elastic	ADJ
fumecheng-10953	32	9	nanobeams	nanobeam	NOUN
fumecheng-10953	32	10	are	be	AUX
fumecheng-10953	32	11	analytically	analytically	ADV
fumecheng-10953	32	12	addressed	address	VERB
fumecheng-10953	32	13	and	and	CCONJ
fumecheng-10953	32	14	numerically	numerically	ADV
fumecheng-10953	32	15	demonstrated	demonstrate	VERB
fumecheng-10953	32	16	.	.	PUNCT
fumecheng-10953	33	1	the	the	DET
fumecheng-10953	33	2	paper	paper	NOUN
fumecheng-10953	33	3	proceeds	proceed	NOUN
fumecheng-10953	33	4	as	as	SCONJ
fumecheng-10953	33	5	follows	follow	VERB
fumecheng-10953	33	6	;	;	PUNCT
fumecheng-10953	33	7	a	a	DET
fumecheng-10953	33	8	stationary	stationary	ADJ
fumecheng-10953	33	9	variational	variational	ADJ
fumecheng-10953	33	10	framework	framework	NOUN
fumecheng-10953	33	11	is	be	AUX
fumecheng-10953	33	12	conceived	conceive	VERB
fumecheng-10953	33	13	in	in	ADP
fumecheng-10953	33	14	section	section	NOUN
fumecheng-10953	33	15	2	2	NUM
fumecheng-10953	33	16	to	to	PART
fumecheng-10953	33	17	suitably	suitably	ADV
fumecheng-10953	33	18	integrate	integrate	VERB
fumecheng-10953	33	19	all	all	DET
fumecheng-10953	33	20	the	the	DET
fumecheng-10953	33	21	governing	govern	VERB
fumecheng-10953	33	22	equations	equation	NOUN
fumecheng-10953	33	23	into	into	ADP
fumecheng-10953	33	24	a	a	DET
fumecheng-10953	33	25	single	single	ADJ
fumecheng-10953	33	26	functional	functional	NOUN
fumecheng-10953	33	27	.	.	PUNCT
fumecheng-10953	34	1	the	the	DET
fumecheng-10953	34	2	corresponding	corresponding	ADJ
fumecheng-10953	34	3	boundary	boundary	ADJ
fumecheng-10953	34	4	-	-	PUNCT
fumecheng-10953	34	5	value	value	NOUN
fumecheng-10953	34	6	problem	problem	NOUN
fumecheng-10953	34	7	of	of	ADP
fumecheng-10953	34	8	dynamic	dynamic	ADJ
fumecheng-10953	34	9	equilibrium	equilibrium	NOUN
fumecheng-10953	34	10	is	be	AUX
fumecheng-10953	34	11	determined	determine	VERB
fumecheng-10953	34	12	and	and	CCONJ
fumecheng-10953	34	13	equipped	equip	VERB
fumecheng-10953	34	14	with	with	ADP
fumecheng-10953	34	15	suitable	suitable	ADJ
fumecheng-10953	34	16	extra	extra	ADJ
fumecheng-10953	34	17	non	non	ADJ
fumecheng-10953	34	18	-	-	ADJ
fumecheng-10953	34	19	standard	standard	ADJ
fumecheng-10953	34	20	boundary	boundary	ADJ
fumecheng-10953	34	21	conditions	condition	NOUN
fumecheng-10953	34	22	.	.	PUNCT
fumecheng-10953	35	1	nanoscopic	nanoscopic	ADJ
fumecheng-10953	35	2	analysis	analysis	NOUN
fumecheng-10953	35	3	of	of	ADP
fumecheng-10953	35	4	the	the	DET
fumecheng-10953	35	5	flexural	flexural	ADJ
fumecheng-10953	35	6	wave	wave	NOUN
fumecheng-10953	35	7	dispersion	dispersion	NOUN
fumecheng-10953	35	8	is	be	AUX
fumecheng-10953	35	9	performed	perform	VERB
fumecheng-10953	35	10	in	in	ADP
fumecheng-10953	35	11	section	section	NOUN
fumecheng-10953	35	12	3	3	NUM
fumecheng-10953	35	13	wherein	wherein	SCONJ
fumecheng-10953	35	14	the	the	DET
fumecheng-10953	35	15	analytical	analytical	ADJ
fumecheng-10953	35	16	solution	solution	NOUN
fumecheng-10953	35	17	of	of	ADP
fumecheng-10953	35	18	the	the	DET
fumecheng-10953	35	19	phase	phase	NOUN
fumecheng-10953	35	20	velocity	velocity	NOUN
fumecheng-10953	35	21	is	be	AUX
fumecheng-10953	35	22	derived	derive	VERB
fumecheng-10953	35	23	.	.	PUNCT
fumecheng-10953	36	1	section	section	NOUN
fumecheng-10953	36	2	3	3	NUM
fumecheng-10953	36	3	is	be	AUX
fumecheng-10953	36	4	,	,	PUNCT
fumecheng-10953	36	5	furthermore	furthermore	ADV
fumecheng-10953	36	6	,	,	PUNCT
fumecheng-10953	36	7	enriched	enrich	VERB
fumecheng-10953	36	8	with	with	ADP
fumecheng-10953	36	9	numerical	numerical	ADJ
fumecheng-10953	36	10	illustrations	illustration	NOUN
fumecheng-10953	36	11	of	of	ADP
fumecheng-10953	36	12	the	the	DET
fumecheng-10953	36	13	wave	wave	NOUN
fumecheng-10953	36	14	dispersion	dispersion	NOUN
fumecheng-10953	36	15	features	feature	VERB
fumecheng-10953	36	16	in	in	ADP
fumecheng-10953	36	17	an	an	DET
fumecheng-10953	36	18	elastic	elastic	ADJ
fumecheng-10953	36	19	nanobeam	nanobeam	NOUN
fumecheng-10953	36	20	.	.	PUNCT
fumecheng-10953	37	1	the	the	DET
fumecheng-10953	37	2	free	free	ADJ
fumecheng-10953	37	3	vibrations	vibration	NOUN
fumecheng-10953	37	4	of	of	ADP
fumecheng-10953	37	5	dynamic	dynamic	ADJ
fumecheng-10953	37	6	characteristics	characteristic	NOUN
fumecheng-10953	37	7	of	of	ADP
fumecheng-10953	37	8	mixture	mixture	NOUN
fumecheng-10953	37	9	unified	unify	VERB
fumecheng-10953	37	10	gradient	gradient	ADJ
fumecheng-10953	37	11	elastic	elastic	ADJ
fumecheng-10953	37	12	nanobeams	nanobeam	NOUN
fumecheng-10953	37	13	541	541	NUM
fumecheng-10953	37	14	nano	nano	NOUN
fumecheng-10953	37	15	-	-	PUNCT
fumecheng-10953	37	16	sized	sized	ADJ
fumecheng-10953	37	17	beams	beam	NOUN
fumecheng-10953	37	18	,	,	PUNCT
fumecheng-10953	37	19	associated	associate	VERB
fumecheng-10953	37	20	with	with	ADP
fumecheng-10953	37	21	the	the	DET
fumecheng-10953	37	22	framework	framework	NOUN
fumecheng-10953	37	23	of	of	ADP
fumecheng-10953	37	24	the	the	DET
fumecheng-10953	37	25	mixture	mixture	NOUN
fumecheng-10953	37	26	unified	unify	VERB
fumecheng-10953	37	27	gradient	gradient	NOUN
fumecheng-10953	37	28	theory	theory	NOUN
fumecheng-10953	37	29	of	of	ADP
fumecheng-10953	37	30	elasticity	elasticity	NOUN
fumecheng-10953	37	31	,	,	PUNCT
fumecheng-10953	37	32	is	be	AUX
fumecheng-10953	37	33	addressed	address	VERB
fumecheng-10953	37	34	in	in	ADP
fumecheng-10953	37	35	section	section	NOUN
fumecheng-10953	37	36	4	4	NUM
fumecheng-10953	37	37	.	.	PUNCT
fumecheng-10953	37	38	fundamental	fundamental	ADJ
fumecheng-10953	37	39	frequencies	frequency	NOUN
fumecheng-10953	37	40	of	of	ADP
fumecheng-10953	37	41	elastic	elastic	ADJ
fumecheng-10953	37	42	nano	nano	NOUN
fumecheng-10953	37	43	-	-	PUNCT
fumecheng-10953	37	44	scaled	scale	VERB
fumecheng-10953	37	45	beams	beam	NOUN
fumecheng-10953	37	46	are	be	AUX
fumecheng-10953	37	47	analytically	analytically	ADV
fumecheng-10953	37	48	determined	determine	VERB
fumecheng-10953	37	49	,	,	PUNCT
fumecheng-10953	37	50	numerically	numerically	ADV
fumecheng-10953	37	51	illustrated	illustrate	VERB
fumecheng-10953	37	52	and	and	CCONJ
fumecheng-10953	37	53	commented	comment	VERB
fumecheng-10953	37	54	upon	upon	SCONJ
fumecheng-10953	37	55	.	.	PUNCT
fumecheng-10953	38	1	section	section	NOUN
fumecheng-10953	38	2	5	5	NUM
fumecheng-10953	38	3	summarizes	summarize	NOUN
fumecheng-10953	38	4	the	the	DET
fumecheng-10953	38	5	paper	paper	NOUN
fumecheng-10953	38	6	and	and	CCONJ
fumecheng-10953	38	7	draws	draw	VERB
fumecheng-10953	38	8	the	the	DET
fumecheng-10953	38	9	conclusion	conclusion	NOUN
fumecheng-10953	38	10	.	.	PUNCT
fumecheng-10953	39	1	2	2	X
fumecheng-10953	39	2	.	.	X
fumecheng-10953	39	3	mixture	mixture	NOUN
fumecheng-10953	39	4	unified	unify	VERB
fumecheng-10953	39	5	gradient	gradient	ADJ
fumecheng-10953	39	6	elastic	elastic	ADJ
fumecheng-10953	39	7	beams	beam	NOUN
fumecheng-10953	39	8	to	to	PART
fumecheng-10953	39	9	establish	establish	VERB
fumecheng-10953	39	10	the	the	DET
fumecheng-10953	39	11	elasticity	elasticity	NOUN
fumecheng-10953	39	12	framework	framework	NOUN
fumecheng-10953	39	13	of	of	ADP
fumecheng-10953	39	14	the	the	DET
fumecheng-10953	39	15	mixture	mixture	NOUN
fumecheng-10953	39	16	unified	unify	VERB
fumecheng-10953	39	17	gradient	gradient	NOUN
fumecheng-10953	39	18	theory	theory	NOUN
fumecheng-10953	39	19	,	,	PUNCT
fumecheng-10953	39	20	an	an	DET
fumecheng-10953	39	21	elastic	elastic	ADJ
fumecheng-10953	39	22	homogenous	homogenous	ADJ
fumecheng-10953	39	23	beam	beam	NOUN
fumecheng-10953	39	24	of	of	ADP
fumecheng-10953	39	25	symmetric	symmetric	ADJ
fumecheng-10953	39	26	cross	cross	NOUN
fumecheng-10953	39	27	-	-	NOUN
fumecheng-10953	39	28	section	section	NOUN
fumecheng-10953	39	29	is	be	AUX
fumecheng-10953	39	30	considered	consider	VERB
fumecheng-10953	39	31	.	.	PUNCT
fumecheng-10953	40	1	in	in	ADP
fumecheng-10953	40	2	the	the	DET
fumecheng-10953	40	3	undeformed	undeformed	ADJ
fumecheng-10953	40	4	state	state	NOUN
fumecheng-10953	40	5	,	,	PUNCT
fumecheng-10953	40	6	the	the	DET
fumecheng-10953	40	7	beam	beam	NOUN
fumecheng-10953	40	8	is	be	AUX
fumecheng-10953	40	9	referred	refer	VERB
fumecheng-10953	40	10	to	to	ADP
fumecheng-10953	40	11	orthogonal	orthogonal	ADJ
fumecheng-10953	40	12	cartesian	cartesian	ADJ
fumecheng-10953	40	13	co	co	NOUN
fumecheng-10953	40	14	-	-	NOUN
fumecheng-10953	40	15	ordinates	ordinate	NOUN
fumecheng-10953	40	16	(	(	PUNCT
fumecheng-10953	40	17	x	x	X
fumecheng-10953	40	18	,	,	PUNCT
fumecheng-10953	40	19	y	y	PROPN
fumecheng-10953	40	20	,	,	PUNCT
fumecheng-10953	40	21	z	z	NOUN
fumecheng-10953	40	22	)	)	PUNCT
fumecheng-10953	40	23	with	with	ADP
fumecheng-10953	40	24	the	the	DET
fumecheng-10953	40	25	x	x	PUNCT
fumecheng-10953	40	26	axis	axis	NOUN
fumecheng-10953	40	27	coinciding	coincide	VERB
fumecheng-10953	40	28	with	with	ADP
fumecheng-10953	40	29	the	the	DET
fumecheng-10953	40	30	beam	beam	NOUN
fumecheng-10953	40	31	longitudinal	longitudinal	ADJ
fumecheng-10953	40	32	axis	axis	NOUN
fumecheng-10953	40	33	and	and	CCONJ
fumecheng-10953	40	34	the	the	DET
fumecheng-10953	40	35	y	y	PROPN
fumecheng-10953	40	36	and	and	CCONJ
fumecheng-10953	40	37	z	z	PROPN
fumecheng-10953	40	38	axes	axis	NOUN
fumecheng-10953	40	39	,	,	PUNCT
fumecheng-10953	40	40	respectively	respectively	ADV
fumecheng-10953	40	41	,	,	PUNCT
fumecheng-10953	40	42	coinciding	coincide	VERB
fumecheng-10953	40	43	with	with	ADP
fumecheng-10953	40	44	the	the	DET
fumecheng-10953	40	45	width	width	NOUN
fumecheng-10953	40	46	and	and	CCONJ
fumecheng-10953	40	47	the	the	DET
fumecheng-10953	40	48	thickness	thickness	NOUN
fumecheng-10953	40	49	directions	direction	NOUN
fumecheng-10953	40	50	.	.	PUNCT
fumecheng-10953	41	1	the	the	DET
fumecheng-10953	41	2	beam	beam	NOUN
fumecheng-10953	41	3	is	be	AUX
fumecheng-10953	41	4	constrained	constrain	VERB
fumecheng-10953	41	5	at	at	ADP
fumecheng-10953	41	6	the	the	DET
fumecheng-10953	41	7	ends	end	NOUN
fumecheng-10953	41	8	x=0	x=0	PROPN
fumecheng-10953	41	9	and	and	CCONJ
fumecheng-10953	41	10	x	x	PUNCT
fumecheng-10953	41	11	=	=	NOUN
fumecheng-10953	41	12	l	l	X
fumecheng-10953	41	13	impeding	impede	VERB
fumecheng-10953	41	14	any	any	DET
fumecheng-10953	41	15	rigid	rigid	ADJ
fumecheng-10953	41	16	-	-	PUNCT
fumecheng-10953	41	17	body	body	NOUN
fumecheng-10953	41	18	motion	motion	NOUN
fumecheng-10953	41	19	.	.	PUNCT
fumecheng-10953	42	1	the	the	DET
fumecheng-10953	42	2	beam	beam	NOUN
fumecheng-10953	42	3	is	be	AUX
fumecheng-10953	42	4	subjected	subject	VERB
fumecheng-10953	42	5	to	to	ADP
fumecheng-10953	42	6	a	a	DET
fumecheng-10953	42	7	generalized	generalize	VERB
fumecheng-10953	42	8	transversal	transversal	NOUN
fumecheng-10953	42	9	load	load	NOUN
fumecheng-10953	42	10	per	per	ADP
fumecheng-10953	42	11	unit	unit	NOUN
fumecheng-10953	42	12	length	length	NOUN
fumecheng-10953	42	13	f	f	PROPN
fumecheng-10953	42	14	where	where	SCONJ
fumecheng-10953	42	15	the	the	DET
fumecheng-10953	42	16	inertia	inertia	NOUN
fumecheng-10953	42	17	force	force	NOUN
fumecheng-10953	42	18	is	be	AUX
fumecheng-10953	42	19	assumed	assume	VERB
fumecheng-10953	42	20	to	to	PART
fumecheng-10953	42	21	be	be	AUX
fumecheng-10953	42	22	incorporated	incorporate	VERB
fumecheng-10953	42	23	as	as	ADP
fumecheng-10953	42	24	the	the	DET
fumecheng-10953	42	25	body	body	NOUN
fumecheng-10953	42	26	force	force	NOUN
fumecheng-10953	42	27	.	.	PUNCT
fumecheng-10953	43	1	the	the	DET
fumecheng-10953	43	2	shear	shear	NOUN
fumecheng-10953	43	3	and	and	CCONJ
fumecheng-10953	43	4	warping	warping	NOUN
fumecheng-10953	43	5	effects	effect	NOUN
fumecheng-10953	43	6	are	be	AUX
fumecheng-10953	43	7	overlooked	overlook	VERB
fumecheng-10953	43	8	,	,	PUNCT
fumecheng-10953	43	9	and	and	CCONJ
fumecheng-10953	43	10	accordingly	accordingly	ADV
fumecheng-10953	43	11	,	,	PUNCT
fumecheng-10953	43	12	the	the	DET
fumecheng-10953	43	13	kinematics	kinematic	NOUN
fumecheng-10953	43	14	of	of	ADP
fumecheng-10953	43	15	the	the	DET
fumecheng-10953	43	16	beam	beam	NOUN
fumecheng-10953	43	17	in	in	ADP
fumecheng-10953	43	18	accordance	accordance	NOUN
fumecheng-10953	43	19	with	with	ADP
fumecheng-10953	43	20	the	the	DET
fumecheng-10953	43	21	classical	classical	ADJ
fumecheng-10953	43	22	beam	beam	NOUN
fumecheng-10953	43	23	theory	theory	NOUN
fumecheng-10953	43	24	is	be	AUX
fumecheng-10953	43	25	taken	take	VERB
fumecheng-10953	43	26	in	in	ADP
fumecheng-10953	43	27	the	the	DET
fumecheng-10953	43	28	form	form	NOUN
fumecheng-10953	43	29	1	1	NUM
fumecheng-10953	43	30	2	2	NUM
fumecheng-10953	43	31	3	3	NUM
fumecheng-10953	43	32	(	(	PUNCT
fumecheng-10953	43	33	,	,	PUNCT
fumecheng-10953	43	34	)	)	PUNCT
fumecheng-10953	43	35	,	,	PUNCT
fumecheng-10953	43	36	0	0	NUM
fumecheng-10953	43	37	,	,	PUNCT
fumecheng-10953	43	38	(	(	PUNCT
fumecheng-10953	43	39	,	,	PUNCT
fumecheng-10953	43	40	)	)	PUNCT
fumecheng-10953	44	1	xu	xu	PROPN
fumecheng-10953	45	1	z	z	PROPN
fumecheng-10953	45	2	w	w	PROPN
fumecheng-10953	45	3	x	x	PUNCT
fumecheng-10953	45	4	t	t	PROPN
fumecheng-10953	45	5	u	u	X
fumecheng-10953	45	6	u	u	PROPN
fumecheng-10953	45	7	w	w	PROPN
fumecheng-10953	45	8	x	x	X
fumecheng-10953	45	9	t=	t=	NOUN
fumecheng-10953	45	10	−	−	PROPN
fumecheng-10953	45	11			NOUN
fumecheng-10953	45	12	=	=	SYM
fumecheng-10953	45	13	=	=	SYM
fumecheng-10953	45	14	(	(	PUNCT
fumecheng-10953	45	15	1	1	NUM
fumecheng-10953	45	16	)	)	PUNCT
fumecheng-10953	45	17	where	where	SCONJ
fumecheng-10953	45	18	1	1	NUM
fumecheng-10953	45	19	2	2	NUM
fumecheng-10953	45	20	3	3	NUM
fumecheng-10953	45	21	,	,	PUNCT
fumecheng-10953	45	22	,	,	PUNCT
fumecheng-10953	45	23	u	u	NOUN
fumecheng-10953	45	24	u	u	NOUN
fumecheng-10953	45	25	u	u	NOUN
fumecheng-10953	45	26	denote	denote	VERB
fumecheng-10953	45	27	the	the	DET
fumecheng-10953	45	28	components	component	NOUN
fumecheng-10953	45	29	of	of	ADP
fumecheng-10953	45	30	the	the	DET
fumecheng-10953	45	31	displacement	displacement	ADJ
fumecheng-10953	45	32	field	field	NOUN
fumecheng-10953	45	33	at	at	ADP
fumecheng-10953	45	34	a	a	DET
fumecheng-10953	45	35	generic	generic	ADJ
fumecheng-10953	45	36	point	point	NOUN
fumecheng-10953	45	37	of	of	ADP
fumecheng-10953	45	38	the	the	DET
fumecheng-10953	45	39	beam	beam	NOUN
fumecheng-10953	45	40	along	along	ADP
fumecheng-10953	45	41	with	with	ADP
fumecheng-10953	45	42	w	w	NOUN
fumecheng-10953	45	43	designating	designate	VERB
fumecheng-10953	45	44	the	the	DET
fumecheng-10953	45	45	transverse	transverse	ADJ
fumecheng-10953	45	46	displacement	displacement	NOUN
fumecheng-10953	45	47	of	of	ADP
fumecheng-10953	45	48	the	the	DET
fumecheng-10953	45	49	beam	beam	NOUN
fumecheng-10953	45	50	centroid	centroid	NOUN
fumecheng-10953	45	51	at	at	ADP
fumecheng-10953	45	52	time	time	NOUN
fumecheng-10953	45	53	t.	t.	PROPN
fumecheng-10953	45	54	the	the	DET
fumecheng-10953	45	55	strain	strain	ADJ
fumecheng-10953	45	56	state	state	NOUN
fumecheng-10953	45	57	of	of	ADP
fumecheng-10953	45	58	the	the	DET
fumecheng-10953	45	59	beam	beam	NOUN
fumecheng-10953	45	60	,	,	PUNCT
fumecheng-10953	45	61	consequent	consequent	ADJ
fumecheng-10953	45	62	to	to	ADP
fumecheng-10953	45	63	the	the	DET
fumecheng-10953	45	64	assumed	assumed	ADJ
fumecheng-10953	45	65	kinematics	kinematic	NOUN
fumecheng-10953	45	66	,	,	PUNCT
fumecheng-10953	45	67	can	can	AUX
fumecheng-10953	45	68	be	be	AUX
fumecheng-10953	45	69	written	write	VERB
fumecheng-10953	45	70	as	as	ADP
fumecheng-10953	45	71	(	(	PUNCT
fumecheng-10953	45	72	,	,	PUNCT
fumecheng-10953	45	73	)	)	PUNCT
fumecheng-10953	45	74	(	(	PUNCT
fumecheng-10953	45	75	,	,	PUNCT
fumecheng-10953	45	76	)	)	PUNCT
fumecheng-10953	45	77	xxz	xxz	NOUN
fumecheng-10953	46	1	w	w	NOUN
fumecheng-10953	46	2	x	x	SYM
fumecheng-10953	46	3	t	t	PROPN
fumecheng-10953	46	4	z	z	NOUN
fumecheng-10953	46	5	x	x	SYM
fumecheng-10953	46	6	t	t	PRON
fumecheng-10953	46	7	=	=	PROPN
fumecheng-10953	46	8	−	−	PROPN
fumecheng-10953	46	9			NOUN
fumecheng-10953	46	10	=	=	SYM
fumecheng-10953	46	11	−	−	PROPN
fumecheng-10953	46	12	(	(	PUNCT
fumecheng-10953	46	13	2	2	NUM
fumecheng-10953	46	14	)	)	PUNCT
fumecheng-10953	46	15	with	with	ADP
fumecheng-10953	46	16	xxw	xxw	NOUN
fumecheng-10953	46	17	=	=	SYM
fumecheng-10953	46	18			NOUN
fumecheng-10953	46	19	denoting	denote	VERB
fumecheng-10953	46	20	the	the	DET
fumecheng-10953	46	21	curvature	curvature	NOUN
fumecheng-10953	46	22	of	of	ADP
fumecheng-10953	46	23	the	the	DET
fumecheng-10953	46	24	beam	beam	NOUN
fumecheng-10953	46	25	centroidal	centroidal	PROPN
fumecheng-10953	46	26	axis	axis	NOUN
fumecheng-10953	46	27	.	.	PUNCT
fumecheng-10953	47	1	the	the	DET
fumecheng-10953	47	2	variational	variational	ADJ
fumecheng-10953	47	3	functionala	functionala	NOUN
fumecheng-10953	47	4	consistent	consistent	ADJ
fumecheng-10953	47	5	with	with	ADP
fumecheng-10953	47	6	the	the	DET
fumecheng-10953	47	7	mixture	mixture	NOUN
fumecheng-10953	47	8	unified	unify	VERB
fumecheng-10953	47	9	gradient	gradient	NOUN
fumecheng-10953	47	10	theory	theory	NOUN
fumecheng-10953	47	11	of	of	ADP
fumecheng-10953	47	12	elasticity	elasticity	NOUN
fumecheng-10953	47	13	is	be	AUX
fumecheng-10953	47	14	introduced	introduce	VERB
fumecheng-10953	47	15	as	as	ADP
fumecheng-10953	47	16	2	2	NUM
fumecheng-10953	47	17	2	2	NUM
fumecheng-10953	47	18	2	2	NUM
fumecheng-10953	47	19	0	0	NUM
fumecheng-10953	47	20	0	0	NUM
fumecheng-10953	47	21	0	0	NUM
fumecheng-10953	47	22	0	0	NUM
fumecheng-10953	47	23	2	2	NUM
fumecheng-10953	47	24	1	1	NUM
fumecheng-10953	47	25	12	12	NUM
fumecheng-10953	47	26	2	2	NUM
fumecheng-10953	47	27	2	2	NUM
fumecheng-10953	47	28	2	2	NUM
fumecheng-10953	47	29	12	12	NUM
fumecheng-10953	47	30	2	2	NUM
fumecheng-10953	47	31	1	1	NUM
fumecheng-10953	47	32	(	(	PUNCT
fumecheng-10953	47	33	,	,	PUNCT
fumecheng-10953	47	34	)	)	PUNCT
fumecheng-10953	47	35	(	(	PUNCT
fumecheng-10953	47	36	,	,	PUNCT
fumecheng-10953	47	37	)	)	PUNCT
fumecheng-10953	47	38	(	(	PUNCT
fumecheng-10953	47	39	(	(	PUNCT
fumecheng-10953	47	40	,	,	PUNCT
fumecheng-10953	47	41	)	)	PUNCT
fumecheng-10953	47	42	)	)	PUNCT
fumecheng-10953	48	1	(	(	PUNCT
fumecheng-10953	48	2	(	(	PUNCT
fumecheng-10953	48	3	,	,	PUNCT
fumecheng-10953	48	4	)	)	PUNCT
fumecheng-10953	48	5	)	)	PUNCT
fumecheng-10953	48	6	2	2	NUM
fumecheng-10953	48	7	2	2	NUM
fumecheng-10953	48	8	1	1	NUM
fumecheng-10953	48	9	(	(	PUNCT
fumecheng-10953	48	10	,	,	PUNCT
fumecheng-10953	48	11	)	)	PUNCT
fumecheng-10953	48	12	(	(	PUNCT
fumecheng-10953	48	13	,	,	PUNCT
fumecheng-10953	48	14	)	)	PUNCT
fumecheng-10953	48	15	(	(	PUNCT
fumecheng-10953	48	16	(	(	PUNCT
fumecheng-10953	48	17	,	,	PUNCT
fumecheng-10953	48	18	)	)	PUNCT
fumecheng-10953	48	19	)	)	PUNCT
fumecheng-10953	48	20	2	2	NUM
fumecheng-10953	48	21	(	(	PUNCT
fumecheng-10953	48	22	)	)	PUNCT
fumecheng-10953	48	23	(	(	PUNCT
fumecheng-10953	48	24	(	(	PUNCT
fumecheng-10953	48	25	,	,	PUNCT
fumecheng-10953	48	26	)	)	PUNCT
fumecheng-10953	48	27	)	)	PUNCT
fumecheng-10953	48	28	(	(	PUNCT
fumecheng-10953	48	29	,	,	PUNCT
fumecheng-10953	48	30	)	)	PUNCT
fumecheng-10953	48	31	(	(	PUNCT
fumecheng-10953	48	32	,	,	PUNCT
fumecheng-10953	48	33	)	)	PUNCT
fumecheng-10953	48	34	2	2	NUM
fumecheng-10953	48	35	(	(	PUNCT
fumecheng-10953	48	36	)	)	PUNCT
fumecheng-10953	49	1	l	l	NOUN
fumecheng-10953	49	2	c	c	NOUN
fumecheng-10953	49	3	xx	xx	NUM
fumecheng-10953	49	4	x	x	PUNCT
fumecheng-10953	49	5	e	e	NOUN
fumecheng-10953	49	6	e	e	X
fumecheng-10953	49	7	xxx	xxx	X
fumecheng-10953	50	1	e	e	X
fumecheng-10953	50	2	c	c	NOUN
fumecheng-10953	50	3	s	s	PART
fumecheng-10953	50	4	c	c	NOUN
fumecheng-10953	50	5	x	x	PUNCT
fumecheng-10953	50	6	e	e	X
fumecheng-10953	50	7	c	c	NOUN
fumecheng-10953	50	8	s	s	PART
fumecheng-10953	50	9	m	m	VERB
fumecheng-10953	50	10	x	x	X
fumecheng-10953	50	11	t	t	PROPN
fumecheng-10953	50	12	w	w	PROPN
fumecheng-10953	50	13	x	x	PROPN
fumecheng-10953	50	14	t	t	PROPN
fumecheng-10953	50	15	m	m	NOUN
fumecheng-10953	50	16	x	x	PROPN
fumecheng-10953	50	17	t	t	NOUN
fumecheng-10953	50	18	m	m	NOUN
fumecheng-10953	50	19	x	x	X
fumecheng-10953	51	1	t	t	NOUN
fumecheng-10953	51	2	i	i	PRON
fumecheng-10953	52	1	i	i	PRON
fumecheng-10953	52	2	m	m	VERB
fumecheng-10953	52	3	x	x	X
fumecheng-10953	52	4	t	t	PROPN
fumecheng-10953	52	5	w	w	PROPN
fumecheng-10953	52	6	x	x	PROPN
fumecheng-10953	52	7	t	t	PROPN
fumecheng-10953	52	8	m	m	NOUN
fumecheng-10953	52	9	x	x	NOUN
fumecheng-10953	53	1	t	t	NOUN
fumecheng-10953	53	2	i	i	PRON
fumecheng-10953	53	3	m	m	VERB
fumecheng-10953	53	4	x	x	X
fumecheng-10953	54	1	t	t	NOUN
fumecheng-10953	54	2	f	f	X
fumecheng-10953	54	3	x	x	X
fumecheng-10953	55	1	t	t	PROPN
fumecheng-10953	55	2	w	w	NOUN
fumecheng-10953	55	3	x	x	PROPN
fumecheng-10953	55	4	t	t	PROPN
fumecheng-10953	55	5	dx	dx	PROPN
fumecheng-10953	55	6	i	i	PRON
fumecheng-10953	55	7			NOUN
fumecheng-10953	55	8	=	=	SYM
fumecheng-10953	55	9			PROPN
fumecheng-10953	55	10	+	+	X
fumecheng-10953	56	1	+	+	CCONJ
fumecheng-10953	56	2			ADJ
fumecheng-10953	56	3			PROPN
fumecheng-10953	56	4	+	+	NUM
fumecheng-10953	56	5			ADJ
fumecheng-10953	56	6	+	+	CCONJ
fumecheng-10953	56	7			NOUN
fumecheng-10953	57	1	+	+	CCONJ
fumecheng-10953	57	2			NOUN
fumecheng-10953	57	3	+	+	CCONJ
fumecheng-10953	57	4			PROPN
fumecheng-10953	57	5	+	+	CCONJ
fumecheng-10953	57	6			PROPN
fumecheng-10953	57	7			NOUN
fumecheng-10953	58	1	+	+	NUM
fumecheng-10953	58	2			NOUN
fumecheng-10953	58	3	a	a	ADJ
fumecheng-10953	58	4	(	(	PUNCT
fumecheng-10953	58	5	3	3	NUM
fumecheng-10953	58	6	)	)	PUNCT
fumecheng-10953	58	7	where	where	SCONJ
fumecheng-10953	58	8	the	the	DET
fumecheng-10953	58	9	flexural	flexural	ADJ
fumecheng-10953	58	10	stiffness	stiffness	NOUN
fumecheng-10953	58	11	ie	ie	X
fumecheng-10953	58	12	is	be	AUX
fumecheng-10953	58	13	defined	define	VERB
fumecheng-10953	58	14	by	by	ADP
fumecheng-10953	58	15	the	the	DET
fumecheng-10953	58	16	second	second	ADJ
fumecheng-10953	58	17	moment	moment	NOUN
fumecheng-10953	58	18	of	of	ADP
fumecheng-10953	58	19	the	the	DET
fumecheng-10953	58	20	elastic	elastic	ADJ
fumecheng-10953	58	21	area	area	NOUN
fumecheng-10953	58	22	,	,	PUNCT
fumecheng-10953	58	23	weighted	weight	VERB
fumecheng-10953	58	24	with	with	ADP
fumecheng-10953	58	25	the	the	DET
fumecheng-10953	58	26	scalar	scalar	ADJ
fumecheng-10953	58	27	field	field	NOUN
fumecheng-10953	58	28	of	of	ADP
fumecheng-10953	58	29	the	the	DET
fumecheng-10953	58	30	elastic	elastic	ADJ
fumecheng-10953	58	31	modulus	modulus	NOUN
fumecheng-10953	58	32	e	e	NOUN
fumecheng-10953	58	33	,	,	PUNCT
fumecheng-10953	58	34	about	about	ADP
fumecheng-10953	58	35	the	the	DET
fumecheng-10953	58	36	flexural	flexural	ADJ
fumecheng-10953	58	37	axis	axis	NOUN
fumecheng-10953	58	38	.	.	PUNCT
fumecheng-10953	59	1	the	the	DET
fumecheng-10953	59	2	resultant	resultant	NOUN
fumecheng-10953	59	3	moments	moment	NOUN
fumecheng-10953	59	4	m0	m0	PROPN
fumecheng-10953	59	5	and	and	CCONJ
fumecheng-10953	59	6	m1	m1	PROPN
fumecheng-10953	59	7	are	be	AUX
fumecheng-10953	59	8	,	,	PUNCT
fumecheng-10953	59	9	correspondingly	correspondingly	ADV
fumecheng-10953	59	10	,	,	PUNCT
fumecheng-10953	59	11	defined	define	VERB
fumecheng-10953	59	12	as	as	ADP
fumecheng-10953	59	13	the	the	DET
fumecheng-10953	59	14	dual	dual	ADJ
fumecheng-10953	59	15	fields	field	NOUN
fumecheng-10953	59	16	of	of	ADP
fumecheng-10953	59	17	the	the	DET
fumecheng-10953	59	18	curvature	curvature	NOUN
fumecheng-10953	59	19			NOUN
fumecheng-10953	59	20	and	and	CCONJ
fumecheng-10953	59	21	of	of	ADP
fumecheng-10953	59	22	its	its	PRON
fumecheng-10953	59	23	first	first	ADJ
fumecheng-10953	59	24	-	-	PUNCT
fumecheng-10953	59	25	order	order	NOUN
fumecheng-10953	59	26	derivative	derivative	NOUN
fumecheng-10953	59	27	along	along	ADP
fumecheng-10953	59	28	the	the	DET
fumecheng-10953	59	29	beam	beam	NOUN
fumecheng-10953	59	30	axis	axis	NOUN
fumecheng-10953	59	31	x.	x.	PROPN
fumecheng-10953	59	32	as	as	SCONJ
fumecheng-10953	59	33	the	the	DET
fumecheng-10953	59	34	mixture	mixture	NOUN
fumecheng-10953	59	35	parameter	parameter	NOUN
fumecheng-10953	59	36	is	be	AUX
fumecheng-10953	59	37	denoted	denote	VERB
fumecheng-10953	59	38	by	by	NOUN
fumecheng-10953	59	39	,	,	PUNCT
fumecheng-10953	59	40	the	the	DET
fumecheng-10953	59	41	stress	stress	NOUN
fumecheng-10953	59	42	gradient	gradient	NOUN
fumecheng-10953	59	43	characteristic	characteristic	ADJ
fumecheng-10953	59	44	length	length	NOUN
fumecheng-10953	59	45	c	c	PROPN
fumecheng-10953	59	46	and	and	CCONJ
fumecheng-10953	59	47	the	the	DET
fumecheng-10953	59	48	strain	strain	NOUN
fumecheng-10953	59	49	gradient	gradient	ADJ
fumecheng-10953	59	50	length	length	NOUN
fumecheng-10953	59	51	-	-	PUNCT
fumecheng-10953	59	52	scale	scale	NOUN
fumecheng-10953	59	53	parameter	parameter	NOUN
fumecheng-10953	59	54	s	s	PRON
fumecheng-10953	59	55	are	be	AUX
fumecheng-10953	59	56	introduced	introduce	VERB
fumecheng-10953	59	57	to	to	PART
fumecheng-10953	59	58	address	address	VERB
fumecheng-10953	59	59	the	the	DET
fumecheng-10953	59	60	significance	significance	NOUN
fumecheng-10953	59	61	of	of	ADP
fumecheng-10953	59	62	the	the	DET
fumecheng-10953	59	63	corresponding	corresponding	ADJ
fumecheng-10953	59	64	gradient	gradient	PROPN
fumecheng-10953	59	65	elasticity	elasticity	NOUN
fumecheng-10953	59	66	theory	theory	NOUN
fumecheng-10953	59	67	.	.	PUNCT
fumecheng-10953	60	1	within	within	ADP
fumecheng-10953	60	2	the	the	DET
fumecheng-10953	60	3	context	context	NOUN
fumecheng-10953	60	4	of	of	ADP
fumecheng-10953	60	5	the	the	DET
fumecheng-10953	60	6	stationary	stationary	ADJ
fumecheng-10953	60	7	variational	variational	ADJ
fumecheng-10953	60	8	formulation	formulation	NOUN
fumecheng-10953	60	9	,	,	PUNCT
fumecheng-10953	60	10	the	the	DET
fumecheng-10953	60	11	kinetic	kinetic	ADJ
fumecheng-10953	60	12	field	field	NOUN
fumecheng-10953	60	13	variables	variable	NOUN
fumecheng-10953	60	14	are	be	AUX
fumecheng-10953	60	15	also	also	ADV
fumecheng-10953	60	16	treated	treat	VERB
fumecheng-10953	60	17	as	as	ADP
fumecheng-10953	60	18	independent	independent	ADJ
fumecheng-10953	60	19	variables	variable	NOUN
fumecheng-10953	60	20	along	along	ADP
fumecheng-10953	60	21	with	with	ADP
fumecheng-10953	60	22	the	the	DET
fumecheng-10953	60	23	kinematic	kinematic	ADJ
fumecheng-10953	60	24	field	field	NOUN
fumecheng-10953	60	25	variables	variable	NOUN
fumecheng-10953	60	26	;	;	PUNCT
fumecheng-10953	60	27	all	all	DET
fumecheng-10953	60	28	the	the	DET
fumecheng-10953	60	29	field	field	NOUN
fumecheng-10953	60	30	variables	variable	NOUN
fumecheng-10953	60	31	are	be	AUX
fumecheng-10953	60	32	,	,	PUNCT
fumecheng-10953	60	33	therefore	therefore	ADV
fumecheng-10953	60	34	,	,	PUNCT
fumecheng-10953	60	35	considered	consider	VERB
fumecheng-10953	60	36	to	to	PART
fumecheng-10953	60	37	be	be	AUX
fumecheng-10953	60	38	subject	subject	ADJ
fumecheng-10953	60	39	to	to	ADP
fumecheng-10953	60	40	variation	variation	NOUN
fumecheng-10953	60	41	[	[	X
fumecheng-10953	60	42	52	52	NUM
fumecheng-10953	60	43	]	]	PUNCT
fumecheng-10953	60	44	.	.	PUNCT
fumecheng-10953	61	1	assuming	assume	VERB
fumecheng-10953	61	2	the	the	DET
fumecheng-10953	61	3	542	542	NUM
fumecheng-10953	61	4	s.	s.	PROPN
fumecheng-10953	61	5	a.	a.	PROPN
fumecheng-10953	61	6	faghidian	faghidian	PROPN
fumecheng-10953	61	7	,	,	PUNCT
fumecheng-10953	61	8	a.	a.	NOUN
fumecheng-10953	61	9	tounsi	tounsi	NOUN
fumecheng-10953	61	10	virtual	virtual	ADJ
fumecheng-10953	61	11	kinetic	kinetic	ADJ
fumecheng-10953	61	12	test	test	NOUN
fumecheng-10953	61	13	fields	field	NOUN
fumecheng-10953	61	14	to	to	PART
fumecheng-10953	61	15	have	have	VERB
fumecheng-10953	61	16	compact	compact	ADJ
fumecheng-10953	61	17	support	support	NOUN
fumecheng-10953	61	18	on	on	ADP
fumecheng-10953	61	19	the	the	DET
fumecheng-10953	61	20	domain	domain	NOUN
fumecheng-10953	61	21	,	,	PUNCT
fumecheng-10953	61	22	the	the	DET
fumecheng-10953	61	23	first	first	ADJ
fumecheng-10953	61	24	variation	variation	NOUN
fumecheng-10953	61	25	of	of	ADP
fumecheng-10953	61	26	the	the	DET
fumecheng-10953	61	27	functionala	functionala	NOUN
fumecheng-10953	61	28	,	,	PUNCT
fumecheng-10953	61	29	following	follow	VERB
fumecheng-10953	61	30	the	the	DET
fumecheng-10953	61	31	integration	integration	NOUN
fumecheng-10953	61	32	by	by	ADP
fumecheng-10953	61	33	parts	part	NOUN
fumecheng-10953	61	34	,	,	PUNCT
fumecheng-10953	61	35	reads	read	NOUN
fumecheng-10953	61	36	(	(	PUNCT
fumecheng-10953	61	37	)	)	PUNCT
fumecheng-10953	61	38	(	(	PUNCT
fumecheng-10953	61	39	(	(	PUNCT
fumecheng-10953	61	40	)	)	PUNCT
fumecheng-10953	61	41	(	(	PUNCT
fumecheng-10953	61	42	)	)	PUNCT
fumecheng-10953	61	43	(	(	PUNCT
fumecheng-10953	61	44	)	)	PUNCT
fumecheng-10953	61	45	0	0	NUM
fumecheng-10953	62	1	1	1	NUM
fumecheng-10953	62	2	0	0	NUM
fumecheng-10953	62	3	2	2	NUM
fumecheng-10953	62	4	0	0	NUM
fumecheng-10953	62	5	0	0	NUM
fumecheng-10953	62	6	0	0	NUM
fumecheng-10953	62	7	2	2	NUM
fumecheng-10953	62	8	1	1	NUM
fumecheng-10953	62	9	1	1	NUM
fumecheng-10953	62	10	12	12	NUM
fumecheng-10953	62	11	2	2	NUM
fumecheng-10953	62	12	0	0	NUM
fumecheng-10953	62	13	1	1	NUM
fumecheng-10953	62	14	00	00	NUM
fumecheng-10953	62	15	(	(	PUNCT
fumecheng-10953	62	16	,	,	PUNCT
fumecheng-10953	62	17	)	)	PUNCT
fumecheng-10953	62	18	(	(	PUNCT
fumecheng-10953	62	19	,	,	PUNCT
fumecheng-10953	62	20	)	)	PUNCT
fumecheng-10953	62	21	(	(	PUNCT
fumecheng-10953	62	22	,	,	PUNCT
fumecheng-10953	62	23	)	)	PUNCT
fumecheng-10953	62	24	(	(	PUNCT
fumecheng-10953	62	25	,	,	PUNCT
fumecheng-10953	62	26	)	)	PUNCT
fumecheng-10953	62	27	1	1	NUM
fumecheng-10953	62	28	(	(	PUNCT
fumecheng-10953	62	29	,	,	PUNCT
fumecheng-10953	62	30	)	)	PUNCT
fumecheng-10953	62	31	(	(	PUNCT
fumecheng-10953	62	32	,	,	PUNCT
fumecheng-10953	62	33	)	)	PUNCT
fumecheng-10953	62	34	(	(	PUNCT
fumecheng-10953	62	35	,	,	PUNCT
fumecheng-10953	62	36	)	)	PUNCT
fumecheng-10953	62	37	(	(	PUNCT
fumecheng-10953	62	38	,	,	PUNCT
fumecheng-10953	62	39	)	)	PUNCT
fumecheng-10953	62	40	1	1	NUM
fumecheng-10953	62	41	(	(	PUNCT
fumecheng-10953	62	42	,	,	PUNCT
fumecheng-10953	62	43	)	)	PUNCT
fumecheng-10953	62	44	(	(	PUNCT
fumecheng-10953	62	45	,	,	PUNCT
fumecheng-10953	62	46	)	)	PUNCT
fumecheng-10953	62	47	(	(	PUNCT
fumecheng-10953	62	48	,	,	PUNCT
fumecheng-10953	62	49	)	)	PUNCT
fumecheng-10953	62	50	(	(	PUNCT
fumecheng-10953	62	51	,	,	PUNCT
fumecheng-10953	62	52	)	)	PUNCT
fumecheng-10953	62	53	(	(	PUNCT
fumecheng-10953	62	54	)	)	PUNCT
fumecheng-10953	62	55	(	(	PUNCT
fumecheng-10953	62	56	,	,	PUNCT
fumecheng-10953	62	57	)	)	PUNCT
fumecheng-10953	62	58	(	(	PUNCT
fumecheng-10953	62	59	,	,	PUNCT
fumecheng-10953	62	60	)	)	PUNCT
fumecheng-10953	63	1	(	(	PUNCT
fumecheng-10953	63	2	l	l	NOUN
fumecheng-10953	63	3	xx	xx	NUM
fumecheng-10953	64	1	xxx	xxx	NOUN
fumecheng-10953	65	1	xx	xx	NUM
fumecheng-10953	66	1	c	c	NOUN
fumecheng-10953	66	2	xx	xx	NUM
fumecheng-10953	66	3	e	e	X
fumecheng-10953	66	4	xxx	xxx	NOUN
fumecheng-10953	66	5	c	c	NOUN
fumecheng-10953	66	6	xx	xx	NUM
fumecheng-10953	67	1	e	e	X
fumecheng-10953	67	2	c	c	NOUN
fumecheng-10953	67	3	s	s	PART
fumecheng-10953	67	4	x	x	X
fumecheng-10953	67	5	l	l	NOUN
fumecheng-10953	67	6	x	x	PUNCT
fumecheng-10953	67	7	xx	xx	NUM
fumecheng-10953	67	8	x	x	SYM
fumecheng-10953	67	9	m	m	VERB
fumecheng-10953	67	10	x	x	X
fumecheng-10953	67	11	t	t	NOUN
fumecheng-10953	67	12	m	m	NOUN
fumecheng-10953	67	13	x	x	X
fumecheng-10953	68	1	t	t	NOUN
fumecheng-10953	68	2	f	f	X
fumecheng-10953	68	3	x	x	X
fumecheng-10953	69	1	t	t	PROPN
fumecheng-10953	69	2	w	w	PROPN
fumecheng-10953	69	3	x	x	PROPN
fumecheng-10953	69	4	t	t	PROPN
fumecheng-10953	69	5	m	m	NOUN
fumecheng-10953	69	6	x	x	X
fumecheng-10953	69	7	t	t	PROPN
fumecheng-10953	69	8	w	w	PROPN
fumecheng-10953	69	9	x	x	PROPN
fumecheng-10953	69	10	t	t	PROPN
fumecheng-10953	69	11	m	m	NOUN
fumecheng-10953	69	12	x	x	PROPN
fumecheng-10953	69	13	t	t	NOUN
fumecheng-10953	69	14	m	m	NOUN
fumecheng-10953	69	15	x	x	X
fumecheng-10953	70	1	t	t	NOUN
fumecheng-10953	70	2	i	i	PRON
fumecheng-10953	70	3	m	m	VERB
fumecheng-10953	70	4	x	x	X
fumecheng-10953	70	5	t	t	PROPN
fumecheng-10953	70	6	w	w	PROPN
fumecheng-10953	70	7	x	x	PROPN
fumecheng-10953	70	8	t	t	PROPN
fumecheng-10953	70	9	m	m	NOUN
fumecheng-10953	70	10	x	x	PROPN
fumecheng-10953	71	1	t	t	NOUN
fumecheng-10953	71	2	m	m	NOUN
fumecheng-10953	71	3	x	x	PROPN
fumecheng-10953	71	4	t	t	NOUN
fumecheng-10953	71	5	dx	dx	PROPN
fumecheng-10953	72	1	i	i	PRON
fumecheng-10953	72	2	m	m	VERB
fumecheng-10953	72	3	x	x	VERB
fumecheng-10953	72	4	t	t	NOUN
fumecheng-10953	72	5	m	m	NOUN
fumecheng-10953	72	6	x	x	PROPN
fumecheng-10953	72	7	t	t	PROPN
fumecheng-10953	72	8	w	w	NOUN
fumecheng-10953	72	9	m	m	VERB
fumecheng-10953	72	10	x	x	PUNCT
fumecheng-10953	73	1			NUM
fumecheng-10953	73	2			NUM
fumecheng-10953	73	3			NUM
fumecheng-10953	73	4			NUM
fumecheng-10953	73	5			NUM
fumecheng-10953	73	6	=	=	SYM
fumecheng-10953	73	7	=	=	SYM
fumecheng-10953	73	8	=	=	SYM
fumecheng-10953	73	9			PROPN
fumecheng-10953	73	10	−	−	ADP
fumecheng-10953	73	11			PROPN
fumecheng-10953	73	12	+	+	NUM
fumecheng-10953	73	13			NOUN
fumecheng-10953	73	14			NOUN
fumecheng-10953	73	15	+	+	CCONJ
fumecheng-10953	73	16			ADJ
fumecheng-10953	73	17	+	+	CCONJ
fumecheng-10953	73	18	−	−	PROPN
fumecheng-10953	73	19			VERB
fumecheng-10953	73	20			PRON
fumecheng-10953	73	21			PROPN
fumecheng-10953	73	22			NOUN
fumecheng-10953	73	23			PROPN
fumecheng-10953	73	24			PROPN
fumecheng-10953	73	25	+	+	CCONJ
fumecheng-10953	73	26			ADJ
fumecheng-10953	73	27	+	+	CCONJ
fumecheng-10953	73	28	−	−	PROPN
fumecheng-10953	73	29			ADJ
fumecheng-10953	73	30			X
fumecheng-10953	74	1			PROPN
fumecheng-10953	75	1	+	+	PROPN
fumecheng-10953	75	2			PROPN
fumecheng-10953	75	3			PROPN
fumecheng-10953	75	4	−	−	ADP
fumecheng-10953	75	5			ADJ
fumecheng-10953	75	6	−	−	ADP
fumecheng-10953	75	7			PROPN
fumecheng-10953	75	8	+	+	CCONJ
fumecheng-10953	76	1	a	a	PROPN
fumecheng-10953	76	2	(	(	PUNCT
fumecheng-10953	76	3	)	)	PUNCT
fumecheng-10953	76	4	1	1	NUM
fumecheng-10953	76	5	0	0	NUM
fumecheng-10953	76	6	1	1	NUM
fumecheng-10953	76	7	0	0	NUM
fumecheng-10953	76	8	,	,	PUNCT
fumecheng-10953	76	9	)	)	PUNCT
fumecheng-10953	76	10	(	(	PUNCT
fumecheng-10953	76	11	,	,	PUNCT
fumecheng-10953	76	12	)	)	PUNCT
fumecheng-10953	76	13	(	(	PUNCT
fumecheng-10953	76	14	,	,	PUNCT
fumecheng-10953	76	15	)	)	PUNCT
fumecheng-10953	76	16	x	x	X
fumecheng-10953	77	1	l	l	NOUN
fumecheng-10953	77	2	x	x	PUNCT
fumecheng-10953	78	1	x	x	PUNCT
fumecheng-10953	78	2	x	x	PUNCT
fumecheng-10953	78	3	x	x	PUNCT
fumecheng-10953	78	4	l	l	NOUN
fumecheng-10953	79	1	xx	xx	NUM
fumecheng-10953	79	2	x	x	SYM
fumecheng-10953	80	1	t	t	NOUN
fumecheng-10953	80	2	m	m	NOUN
fumecheng-10953	80	3	x	x	PROPN
fumecheng-10953	80	4	t	t	PROPN
fumecheng-10953	80	5	w	w	NOUN
fumecheng-10953	80	6	m	m	PROPN
fumecheng-10953	80	7	x	x	X
fumecheng-10953	80	8	t	t	NOUN
fumecheng-10953	80	9	w	w	NOUN
fumecheng-10953	80	10			NUM
fumecheng-10953	80	11			NUM
fumecheng-10953	80	12	=	=	SYM
fumecheng-10953	80	13	=	=	SYM
fumecheng-10953	80	14	=	=	PUNCT
fumecheng-10953	80	15	=	=	SYM
fumecheng-10953	80	16	−	−	ADP
fumecheng-10953	80	17			ADJ
fumecheng-10953	80	18			PROPN
fumecheng-10953	80	19	+	+	CCONJ
fumecheng-10953	80	20			ADJ
fumecheng-10953	80	21	(	(	PUNCT
fumecheng-10953	80	22	4	4	NUM
fumecheng-10953	80	23	)	)	PUNCT
fumecheng-10953	80	24	where	where	SCONJ
fumecheng-10953	80	25	the	the	DET
fumecheng-10953	80	26	extra	extra	ADJ
fumecheng-10953	80	27	gradient	gradient	NOUN
fumecheng-10953	80	28	-	-	PUNCT
fumecheng-10953	80	29	induced	induce	VERB
fumecheng-10953	80	30	boundary	boundary	ADJ
fumecheng-10953	80	31	terms	term	NOUN
fumecheng-10953	80	32	are	be	AUX
fumecheng-10953	80	33	released	release	VERB
fumecheng-10953	80	34	in	in	ADP
fumecheng-10953	80	35	consideration	consideration	NOUN
fumecheng-10953	80	36	of	of	ADP
fumecheng-10953	80	37	the	the	DET
fumecheng-10953	80	38	virtual	virtual	ADJ
fumecheng-10953	80	39	kinetic	kinetic	ADJ
fumecheng-10953	80	40	test	test	NOUN
fumecheng-10953	80	41	fields	field	NOUN
fumecheng-10953	80	42	having	have	VERB
fumecheng-10953	80	43	compact	compact	ADJ
fumecheng-10953	80	44	support	support	NOUN
fumecheng-10953	80	45	on	on	ADP
fumecheng-10953	80	46	the	the	DET
fumecheng-10953	80	47	domain	domain	NOUN
fumecheng-10953	80	48	[	[	X
fumecheng-10953	80	49	53	53	NUM
fumecheng-10953	80	50	]	]	PUNCT
fumecheng-10953	80	51	.	.	PUNCT
fumecheng-10953	81	1	prescribing	prescribe	VERB
fumecheng-10953	81	2	the	the	DET
fumecheng-10953	81	3	stationarity	stationarity	NOUN
fumecheng-10953	81	4	of	of	ADP
fumecheng-10953	81	5	the	the	DET
fumecheng-10953	81	6	functional	functional	ADJ
fumecheng-10953	81	7	0	0	X
fumecheng-10953	82	1	=	=	SYM
fumecheng-10953	82	2	a	a	PRON
fumecheng-10953	82	3	,	,	PUNCT
fumecheng-10953	82	4	the	the	DET
fumecheng-10953	82	5	differential	differential	ADJ
fumecheng-10953	82	6	and	and	CCONJ
fumecheng-10953	82	7	boundary	boundary	ADJ
fumecheng-10953	82	8	conditions	condition	NOUN
fumecheng-10953	82	9	of	of	ADP
fumecheng-10953	82	10	dynamic	dynamic	ADJ
fumecheng-10953	82	11	equilibrium	equilibrium	NOUN
fumecheng-10953	82	12	for	for	ADP
fumecheng-10953	82	13	the	the	DET
fumecheng-10953	82	14	elastic	elastic	ADJ
fumecheng-10953	82	15	nano	nano	NOUN
fumecheng-10953	82	16	-	-	PUNCT
fumecheng-10953	82	17	sized	sized	ADJ
fumecheng-10953	82	18	beam	beam	NOUN
fumecheng-10953	82	19	consistent	consistent	ADJ
fumecheng-10953	82	20	with	with	ADP
fumecheng-10953	82	21	the	the	DET
fumecheng-10953	82	22	mixture	mixture	NOUN
fumecheng-10953	82	23	unified	unify	VERB
fumecheng-10953	82	24	gradient	gradient	NOUN
fumecheng-10953	82	25	theory	theory	NOUN
fumecheng-10953	82	26	cast	cast	VERB
fumecheng-10953	82	27	in	in	ADP
fumecheng-10953	82	28	the	the	DET
fumecheng-10953	82	29	form	form	NOUN
fumecheng-10953	82	30	(	(	PUNCT
fumecheng-10953	82	31	)	)	PUNCT
fumecheng-10953	82	32	(	(	PUNCT
fumecheng-10953	82	33	)	)	PUNCT
fumecheng-10953	82	34	0	0	NUM
fumecheng-10953	83	1	1	1	NUM
fumecheng-10953	83	2	0	0	NUM
fumecheng-10953	83	3	1	1	NUM
fumecheng-10953	83	4	0	0	NUM
fumecheng-10953	83	5	0	0	NUM
fumecheng-10953	83	6	1	1	NUM
fumecheng-10953	83	7	0	0	NUM
fumecheng-10953	83	8	1	1	NUM
fumecheng-10953	83	9	0	0	NUM
fumecheng-10953	83	10	(	(	PUNCT
fumecheng-10953	83	11	,	,	PUNCT
fumecheng-10953	83	12	)	)	PUNCT
fumecheng-10953	83	13	(	(	PUNCT
fumecheng-10953	83	14	,	,	PUNCT
fumecheng-10953	83	15	)	)	PUNCT
fumecheng-10953	83	16	(	(	PUNCT
fumecheng-10953	83	17	)	)	PUNCT
fumecheng-10953	83	18	(	(	PUNCT
fumecheng-10953	83	19	,	,	PUNCT
fumecheng-10953	83	20	)	)	PUNCT
fumecheng-10953	83	21	(	(	PUNCT
fumecheng-10953	83	22	,	,	PUNCT
fumecheng-10953	83	23	)	)	PUNCT
fumecheng-10953	83	24	(	(	PUNCT
fumecheng-10953	83	25	,	,	PUNCT
fumecheng-10953	83	26	)	)	PUNCT
fumecheng-10953	83	27	(	(	PUNCT
fumecheng-10953	83	28	,	,	PUNCT
fumecheng-10953	83	29	)	)	PUNCT
fumecheng-10953	83	30	0	0	NUM
fumecheng-10953	84	1	(	(	PUNCT
fumecheng-10953	84	2	,	,	PUNCT
fumecheng-10953	84	3	)	)	PUNCT
fumecheng-10953	84	4	(	(	PUNCT
fumecheng-10953	84	5	,	,	PUNCT
fumecheng-10953	84	6	)	)	PUNCT
fumecheng-10953	84	7	0	0	NUM
fumecheng-10953	85	1	(	(	PUNCT
fumecheng-10953	85	2	,	,	PUNCT
fumecheng-10953	85	3	)	)	PUNCT
fumecheng-10953	85	4	0	0	NUM
fumecheng-10953	86	1	xx	xx	NUM
fumecheng-10953	86	2	xxx	xxx	NOUN
fumecheng-10953	87	1	tt	tt	PROPN
fumecheng-10953	87	2	xxtt	xxtt	NOUN
fumecheng-10953	87	3	x	x	X
fumecheng-10953	87	4	l	l	PUNCT
fumecheng-10953	87	5	x	x	PUNCT
fumecheng-10953	88	1	xx	xx	NUM
fumecheng-10953	88	2	x	x	SYM
fumecheng-10953	88	3	x	x	X
fumecheng-10953	88	4	l	l	NOUN
fumecheng-10953	88	5	x	x	PUNCT
fumecheng-10953	88	6	x	x	PUNCT
fumecheng-10953	88	7	x	x	PUNCT
fumecheng-10953	88	8	x	x	PUNCT
fumecheng-10953	88	9	l	l	NOUN
fumecheng-10953	88	10	x	x	PUNCT
fumecheng-10953	88	11	m	m	VERB
fumecheng-10953	88	12	x	x	X
fumecheng-10953	88	13	t	t	NOUN
fumecheng-10953	88	14	m	m	NOUN
fumecheng-10953	88	15	x	x	X
fumecheng-10953	88	16	t	t	NOUN
fumecheng-10953	88	17	f	f	X
fumecheng-10953	88	18	x	x	X
fumecheng-10953	88	19	a	a	DET
fumecheng-10953	88	20	w	w	NOUN
fumecheng-10953	88	21	x	x	SYM
fumecheng-10953	88	22	t	t	NOUN
fumecheng-10953	88	23	i	i	PRON
fumecheng-10953	88	24	w	w	PROPN
fumecheng-10953	88	25	x	x	X
fumecheng-10953	88	26	t	t	NOUN
fumecheng-10953	88	27	m	m	NOUN
fumecheng-10953	88	28	x	x	PROPN
fumecheng-10953	89	1	t	t	NOUN
fumecheng-10953	89	2	m	m	NOUN
fumecheng-10953	89	3	x	x	PROPN
fumecheng-10953	89	4	t	t	PROPN
fumecheng-10953	89	5	w	w	NOUN
fumecheng-10953	89	6	m	m	PROPN
fumecheng-10953	89	7	x	x	X
fumecheng-10953	89	8	t	t	NOUN
fumecheng-10953	89	9	m	m	NOUN
fumecheng-10953	89	10	x	x	PROPN
fumecheng-10953	89	11	t	t	PROPN
fumecheng-10953	89	12	w	w	NOUN
fumecheng-10953	89	13	m	m	PROPN
fumecheng-10953	89	14	x	x	PROPN
fumecheng-10953	89	15	t	t	NOUN
fumecheng-10953	89	16			NOUN
fumecheng-10953	89	17			ADP
fumecheng-10953	89	18			NUM
fumecheng-10953	89	19			NUM
fumecheng-10953	89	20	=	=	SYM
fumecheng-10953	89	21	=	=	SYM
fumecheng-10953	89	22	=	=	PUNCT
fumecheng-10953	89	23	=	=	PUNCT
fumecheng-10953	89	24	=	=	SYM
fumecheng-10953	89	25	=	=	SYM
fumecheng-10953	89	26			ADJ
fumecheng-10953	89	27	−	−	X
fumecheng-10953	89	28	+	+	SYM
fumecheng-10953	89	29	=	=	NOUN
fumecheng-10953	89	30			ADJ
fumecheng-10953	90	1	−	−	ADP
fumecheng-10953	90	2			ADJ
fumecheng-10953	90	3			ADJ
fumecheng-10953	90	4	−	−	NOUN
fumecheng-10953	90	5	=	=	SYM
fumecheng-10953	90	6	−	−	PROPN
fumecheng-10953	90	7			NOUN
fumecheng-10953	90	8	=	=	SYM
fumecheng-10953	90	9	=	=	SYM
fumecheng-10953	90	10	(	(	PUNCT
fumecheng-10953	90	11	5	5	NUM
fumecheng-10953	90	12	)	)	PUNCT
fumecheng-10953	90	13	where	where	SCONJ
fumecheng-10953	90	14	the	the	DET
fumecheng-10953	90	15	curvature	curvature	NOUN
fumecheng-10953	90	16	field	field	NOUN
fumecheng-10953	90	17	is	be	AUX
fumecheng-10953	90	18	considered	consider	VERB
fumecheng-10953	90	19	to	to	PART
fumecheng-10953	90	20	have	have	VERB
fumecheng-10953	90	21	arbitrary	arbitrary	ADJ
fumecheng-10953	90	22	variations	variation	NOUN
fumecheng-10953	90	23	at	at	ADP
fumecheng-10953	90	24	the	the	DET
fumecheng-10953	90	25	beam	beam	NOUN
fumecheng-10953	90	26	ends	end	VERB
fumecheng-10953	90	27	.	.	PUNCT
fumecheng-10953	91	1	noteworthily	noteworthily	ADV
fumecheng-10953	91	2	,	,	PUNCT
fumecheng-10953	91	3	the	the	DET
fumecheng-10953	91	4	dynamic	dynamic	ADJ
fumecheng-10953	91	5	form	form	NOUN
fumecheng-10953	91	6	of	of	ADP
fumecheng-10953	91	7	the	the	DET
fumecheng-10953	91	8	differential	differential	ADJ
fumecheng-10953	91	9	condition	condition	NOUN
fumecheng-10953	91	10	of	of	ADP
fumecheng-10953	91	11	equilibrium	equilibrium	NOUN
fumecheng-10953	91	12	is	be	AUX
fumecheng-10953	91	13	developed	develop	VERB
fumecheng-10953	91	14	by	by	ADP
fumecheng-10953	91	15	application	application	NOUN
fumecheng-10953	91	16	of	of	ADP
fumecheng-10953	91	17	the	the	DET
fumecheng-10953	91	18	d’alembert	d’alembert	NOUN
fumecheng-10953	91	19	principle	principle	NOUN
fumecheng-10953	91	20	.	.	PUNCT
fumecheng-10953	92	1	the	the	DET
fumecheng-10953	92	2	cross	cross	ADJ
fumecheng-10953	92	3	-	-	ADJ
fumecheng-10953	92	4	sectional	sectional	ADJ
fumecheng-10953	92	5	mass	mass	NOUN
fumecheng-10953	92	6	a	a	NOUN
fumecheng-10953	92	7	is	be	AUX
fumecheng-10953	92	8	defined	define	VERB
fumecheng-10953	92	9	by	by	ADP
fumecheng-10953	92	10	the	the	DET
fumecheng-10953	92	11	cross	cross	ADJ
fumecheng-10953	92	12	-	-	ADJ
fumecheng-10953	92	13	sectional	sectional	ADJ
fumecheng-10953	92	14	area	area	NOUN
fumecheng-10953	92	15	weighted	weight	VERB
fumecheng-10953	92	16	with	with	ADP
fumecheng-10953	92	17	the	the	DET
fumecheng-10953	92	18	scalar	scalar	ADJ
fumecheng-10953	92	19	field	field	NOUN
fumecheng-10953	92	20	of	of	ADP
fumecheng-10953	92	21	the	the	DET
fumecheng-10953	92	22	material	material	NOUN
fumecheng-10953	92	23	density	density	NOUN
fumecheng-10953	92	24	.	.	ADP
fumecheng-10953	92	25	likewise	likewise	ADV
fumecheng-10953	92	26	,	,	PUNCT
fumecheng-10953	92	27	the	the	DET
fumecheng-10953	92	28	rotatory	rotatory	ADJ
fumecheng-10953	92	29	inertia	inertia	NOUN
fumecheng-10953	92	30	i	i	PRON
fumecheng-10953	92	31	is	be	AUX
fumecheng-10953	92	32	introduced	introduce	VERB
fumecheng-10953	92	33	as	as	ADP
fumecheng-10953	92	34	the	the	DET
fumecheng-10953	92	35	second	second	ADJ
fumecheng-10953	92	36	moment	moment	NOUN
fumecheng-10953	92	37	of	of	ADP
fumecheng-10953	92	38	area	area	NOUN
fumecheng-10953	92	39	,	,	PUNCT
fumecheng-10953	92	40	weighted	weight	VERB
fumecheng-10953	92	41	with	with	ADP
fumecheng-10953	92	42	the	the	DET
fumecheng-10953	92	43	scalar	scalar	ADJ
fumecheng-10953	92	44	field	field	NOUN
fumecheng-10953	92	45	of	of	ADP
fumecheng-10953	92	46	the	the	DET
fumecheng-10953	92	47	material	material	NOUN
fumecheng-10953	92	48	density	density	NOUN
fumecheng-10953	92	49			NOUN
fumecheng-10953	92	50	,	,	PUNCT
fumecheng-10953	92	51	about	about	ADP
fumecheng-10953	92	52	the	the	DET
fumecheng-10953	92	53	flexural	flexural	ADJ
fumecheng-10953	92	54	axis	axis	NOUN
fumecheng-10953	92	55	.	.	PUNCT
fumecheng-10953	93	1	to	to	PART
fumecheng-10953	93	2	further	far	ADV
fumecheng-10953	93	3	simplify	simplify	VERB
fumecheng-10953	93	4	the	the	DET
fumecheng-10953	93	5	boundary	boundary	ADJ
fumecheng-10953	93	6	-	-	PUNCT
fumecheng-10953	93	7	value	value	NOUN
fumecheng-10953	93	8	problem	problem	NOUN
fumecheng-10953	93	9	of	of	ADP
fumecheng-10953	93	10	dynamic	dynamic	ADJ
fumecheng-10953	93	11	equilibrium	equilibrium	NOUN
fumecheng-10953	93	12	,	,	PUNCT
fumecheng-10953	93	13	the	the	DET
fumecheng-10953	93	14	concept	concept	NOUN
fumecheng-10953	93	15	of	of	ADP
fumecheng-10953	93	16	the	the	DET
fumecheng-10953	93	17	total	total	ADJ
fumecheng-10953	93	18	flexural	flexural	ADJ
fumecheng-10953	93	19	moment	moment	NOUN
fumecheng-10953	93	20	is	be	AUX
fumecheng-10953	93	21	utilized	utilize	VERB
fumecheng-10953	93	22	within	within	ADP
fumecheng-10953	93	23	the	the	DET
fumecheng-10953	93	24	framework	framework	NOUN
fumecheng-10953	93	25	of	of	ADP
fumecheng-10953	93	26	the	the	DET
fumecheng-10953	93	27	gradient	gradient	PROPN
fumecheng-10953	93	28	elasticity	elasticity	NOUN
fumecheng-10953	93	29	theory	theory	NOUN
fumecheng-10953	93	30	,	,	PUNCT
fumecheng-10953	93	31	and	and	CCONJ
fumecheng-10953	93	32	is	be	AUX
fumecheng-10953	93	33	introduced	introduce	VERB
fumecheng-10953	93	34	as	as	ADP
fumecheng-10953	93	35	0	0	NUM
fumecheng-10953	93	36	1	1	NUM
fumecheng-10953	93	37	(	(	PUNCT
fumecheng-10953	93	38	,	,	PUNCT
fumecheng-10953	93	39	)	)	PUNCT
fumecheng-10953	93	40	(	(	PUNCT
fumecheng-10953	93	41	,	,	PUNCT
fumecheng-10953	93	42	)	)	PUNCT
fumecheng-10953	93	43	(	(	PUNCT
fumecheng-10953	93	44	,	,	PUNCT
fumecheng-10953	93	45	)	)	PUNCT
fumecheng-10953	93	46	xm	xm	PROPN
fumecheng-10953	94	1	x	x	PUNCT
fumecheng-10953	95	1	t	t	PROPN
fumecheng-10953	95	2	m	m	NOUN
fumecheng-10953	95	3	x	x	PROPN
fumecheng-10953	95	4	t	t	NOUN
fumecheng-10953	95	5	m	m	VERB
fumecheng-10953	95	6	x	x	X
fumecheng-10953	95	7	t=	t=	PRON
fumecheng-10953	95	8	−	−	NOUN
fumecheng-10953	95	9	(	(	PUNCT
fumecheng-10953	95	10	6	6	NUM
fumecheng-10953	95	11	)	)	PUNCT
fumecheng-10953	95	12	the	the	DET
fumecheng-10953	95	13	boundary	boundary	ADJ
fumecheng-10953	95	14	-	-	PUNCT
fumecheng-10953	95	15	value	value	NOUN
fumecheng-10953	95	16	problem	problem	NOUN
fumecheng-10953	95	17	of	of	ADP
fumecheng-10953	95	18	the	the	DET
fumecheng-10953	95	19	dynamic	dynamic	ADJ
fumecheng-10953	95	20	equilibrium	equilibrium	NOUN
fumecheng-10953	95	21	of	of	ADP
fumecheng-10953	95	22	the	the	DET
fumecheng-10953	95	23	mixture	mixture	NOUN
fumecheng-10953	95	24	unified	unify	VERB
fumecheng-10953	95	25	gradient	gradient	ADJ
fumecheng-10953	95	26	elastic	elastic	ADJ
fumecheng-10953	95	27	beam	beam	NOUN
fumecheng-10953	95	28	is	be	AUX
fumecheng-10953	95	29	,	,	PUNCT
fumecheng-10953	95	30	therefore	therefore	ADV
fumecheng-10953	95	31	,	,	PUNCT
fumecheng-10953	95	32	modified	modify	VERB
fumecheng-10953	95	33	as	as	ADP
fumecheng-10953	95	34	(	(	PUNCT
fumecheng-10953	95	35	)	)	PUNCT
fumecheng-10953	95	36	0	0	NUM
fumecheng-10953	96	1	0	0	NUM
fumecheng-10953	96	2	1	1	NUM
fumecheng-10953	96	3	0	0	NUM
fumecheng-10953	96	4	(	(	PUNCT
fumecheng-10953	96	5	,	,	PUNCT
fumecheng-10953	96	6	)	)	PUNCT
fumecheng-10953	96	7	(	(	PUNCT
fumecheng-10953	96	8	,	,	PUNCT
fumecheng-10953	96	9	)	)	PUNCT
fumecheng-10953	96	10	(	(	PUNCT
fumecheng-10953	96	11	,	,	PUNCT
fumecheng-10953	96	12	)	)	PUNCT
fumecheng-10953	96	13	(	(	PUNCT
fumecheng-10953	96	14	,	,	PUNCT
fumecheng-10953	96	15	)	)	PUNCT
fumecheng-10953	96	16	(	(	PUNCT
fumecheng-10953	96	17	,	,	PUNCT
fumecheng-10953	96	18	)	)	PUNCT
fumecheng-10953	96	19	0	0	NUM
fumecheng-10953	97	1	(	(	PUNCT
fumecheng-10953	97	2	,	,	PUNCT
fumecheng-10953	97	3	)	)	PUNCT
fumecheng-10953	97	4	0	0	NUM
fumecheng-10953	98	1	xx	xx	NUM
fumecheng-10953	98	2	tt	tt	PROPN
fumecheng-10953	98	3	xxtt	xxtt	NOUN
fumecheng-10953	98	4	x	x	X
fumecheng-10953	98	5	l	l	NOUN
fumecheng-10953	98	6	x	x	PUNCT
fumecheng-10953	98	7	l	l	NOUN
fumecheng-10953	98	8	x	x	PUNCT
fumecheng-10953	99	1	xx	xx	NUM
fumecheng-10953	99	2	x	x	SYM
fumecheng-10953	99	3	x	x	PUNCT
fumecheng-10953	99	4	l	l	NOUN
fumecheng-10953	99	5	x	x	PUNCT
fumecheng-10953	99	6	m	m	VERB
fumecheng-10953	99	7	x	x	X
fumecheng-10953	99	8	t	t	NOUN
fumecheng-10953	99	9	f	f	X
fumecheng-10953	99	10	x	x	X
fumecheng-10953	99	11	a	a	DET
fumecheng-10953	99	12	w	w	NOUN
fumecheng-10953	99	13	x	x	SYM
fumecheng-10953	99	14	t	t	NOUN
fumecheng-10953	99	15	i	i	PRON
fumecheng-10953	99	16	w	w	PROPN
fumecheng-10953	99	17	x	x	X
fumecheng-10953	99	18	t	t	NOUN
fumecheng-10953	99	19	m	m	NOUN
fumecheng-10953	99	20	x	x	PROPN
fumecheng-10953	99	21	t	t	PROPN
fumecheng-10953	99	22	w	w	NOUN
fumecheng-10953	99	23	m	m	PROPN
fumecheng-10953	99	24	x	x	X
fumecheng-10953	99	25	t	t	PROPN
fumecheng-10953	99	26	w	w	NOUN
fumecheng-10953	99	27	m	m	PROPN
fumecheng-10953	99	28	x	x	PROPN
fumecheng-10953	99	29	t	t	NOUN
fumecheng-10953	99	30			NOUN
fumecheng-10953	99	31			ADP
fumecheng-10953	99	32			NUM
fumecheng-10953	99	33			NUM
fumecheng-10953	99	34	=	=	SYM
fumecheng-10953	99	35	=	=	SYM
fumecheng-10953	99	36	=	=	PUNCT
fumecheng-10953	99	37	=	=	PUNCT
fumecheng-10953	99	38	=	=	SYM
fumecheng-10953	99	39	=	=	SYM
fumecheng-10953	99	40			NOUN
fumecheng-10953	99	41	+	+	SYM
fumecheng-10953	99	42	=	=	NOUN
fumecheng-10953	99	43			ADJ
fumecheng-10953	99	44	−	−	ADP
fumecheng-10953	99	45			ADJ
fumecheng-10953	99	46			ADJ
fumecheng-10953	99	47	=	=	SYM
fumecheng-10953	99	48			PROPN
fumecheng-10953	99	49	=	=	SYM
fumecheng-10953	99	50	=	=	SYM
fumecheng-10953	99	51	(	(	PUNCT
fumecheng-10953	99	52	7	7	X
fumecheng-10953	99	53	)	)	PUNCT
fumecheng-10953	99	54	dynamic	dynamic	ADJ
fumecheng-10953	99	55	characteristics	characteristic	NOUN
fumecheng-10953	99	56	of	of	ADP
fumecheng-10953	99	57	mixture	mixture	NOUN
fumecheng-10953	99	58	unified	unify	VERB
fumecheng-10953	99	59	gradient	gradient	ADJ
fumecheng-10953	99	60	elastic	elastic	ADJ
fumecheng-10953	99	61	nanobeams	nanobeam	NOUN
fumecheng-10953	99	62	543	543	NUM
fumecheng-10953	99	63	as	as	ADP
fumecheng-10953	99	64	a	a	DET
fumecheng-10953	99	65	distinguished	distinguished	ADJ
fumecheng-10953	99	66	privilege	privilege	NOUN
fumecheng-10953	99	67	of	of	ADP
fumecheng-10953	99	68	implementing	implement	VERB
fumecheng-10953	99	69	the	the	DET
fumecheng-10953	99	70	stationary	stationary	ADJ
fumecheng-10953	99	71	variational	variational	ADJ
fumecheng-10953	99	72	principle	principle	NOUN
fumecheng-10953	99	73	,	,	PUNCT
fumecheng-10953	99	74	the	the	DET
fumecheng-10953	99	75	constitutive	constitutive	ADJ
fumecheng-10953	99	76	model	model	NOUN
fumecheng-10953	99	77	of	of	ADP
fumecheng-10953	99	78	the	the	DET
fumecheng-10953	99	79	associated	associated	ADJ
fumecheng-10953	99	80	elasticity	elasticity	NOUN
fumecheng-10953	99	81	theory	theory	NOUN
fumecheng-10953	99	82	is	be	AUX
fumecheng-10953	99	83	,	,	PUNCT
fumecheng-10953	99	84	furthermore	furthermore	ADV
fumecheng-10953	99	85	,	,	PUNCT
fumecheng-10953	99	86	detected	detect	VERB
fumecheng-10953	99	87	.	.	PUNCT
fumecheng-10953	100	1	the	the	DET
fumecheng-10953	100	2	constitutive	constitutive	ADJ
fumecheng-10953	100	3	laws	law	NOUN
fumecheng-10953	100	4	of	of	ADP
fumecheng-10953	100	5	the	the	DET
fumecheng-10953	100	6	resultant	resultant	NOUN
fumecheng-10953	100	7	fields	field	NOUN
fumecheng-10953	100	8	consistent	consistent	ADJ
fumecheng-10953	100	9	with	with	ADP
fumecheng-10953	100	10	the	the	DET
fumecheng-10953	100	11	framework	framework	NOUN
fumecheng-10953	100	12	of	of	ADP
fumecheng-10953	100	13	the	the	DET
fumecheng-10953	100	14	mixture	mixture	NOUN
fumecheng-10953	100	15	unified	unify	VERB
fumecheng-10953	100	16	gradient	gradient	NOUN
fumecheng-10953	100	17	theory	theory	NOUN
fumecheng-10953	100	18	,	,	PUNCT
fumecheng-10953	100	19	accordingly	accordingly	ADV
fumecheng-10953	100	20	,	,	PUNCT
fumecheng-10953	100	21	are	be	AUX
fumecheng-10953	100	22	cast	cast	VERB
fumecheng-10953	100	23	as	as	ADP
fumecheng-10953	100	24	the	the	DET
fumecheng-10953	100	25	subsequent	subsequent	ADJ
fumecheng-10953	100	26	ordinary	ordinary	ADJ
fumecheng-10953	100	27	differential	differential	ADJ
fumecheng-10953	100	28	relations	relation	NOUN
fumecheng-10953	100	29	(	(	PUNCT
fumecheng-10953	100	30	)	)	PUNCT
fumecheng-10953	100	31	2	2	NUM
fumecheng-10953	100	32	0	0	NUM
fumecheng-10953	100	33	0	0	NUM
fumecheng-10953	100	34	2	2	NUM
fumecheng-10953	100	35	2	2	NUM
fumecheng-10953	100	36	2	2	NUM
fumecheng-10953	100	37	1	1	NUM
fumecheng-10953	100	38	1	1	NUM
fumecheng-10953	100	39	2	2	NUM
fumecheng-10953	100	40	2	2	NUM
fumecheng-10953	100	41	2	2	NUM
fumecheng-10953	100	42	(	(	PUNCT
fumecheng-10953	100	43	,	,	PUNCT
fumecheng-10953	100	44	)	)	PUNCT
fumecheng-10953	100	45	(	(	PUNCT
fumecheng-10953	100	46	,	,	PUNCT
fumecheng-10953	100	47	)	)	PUNCT
fumecheng-10953	100	48	(	(	PUNCT
fumecheng-10953	100	49	,	,	PUNCT
fumecheng-10953	100	50	)	)	PUNCT
fumecheng-10953	100	51	(	(	PUNCT
fumecheng-10953	100	52	,	,	PUNCT
fumecheng-10953	100	53	)	)	PUNCT
fumecheng-10953	100	54	(	(	PUNCT
fumecheng-10953	100	55	,	,	PUNCT
fumecheng-10953	100	56	)	)	PUNCT
fumecheng-10953	100	57	(	(	PUNCT
fumecheng-10953	100	58	)	)	PUNCT
fumecheng-10953	100	59	(	(	PUNCT
fumecheng-10953	100	60	,	,	PUNCT
fumecheng-10953	100	61	)	)	PUNCT
fumecheng-10953	100	62	(	(	PUNCT
fumecheng-10953	100	63	,	,	PUNCT
fumecheng-10953	100	64	)	)	PUNCT
fumecheng-10953	100	65	(	(	PUNCT
fumecheng-10953	100	66	,	,	PUNCT
fumecheng-10953	100	67	)	)	PUNCT
fumecheng-10953	100	68	(	(	PUNCT
fumecheng-10953	100	69	,	,	PUNCT
fumecheng-10953	100	70	)	)	PUNCT
fumecheng-10953	100	71	(	(	PUNCT
fumecheng-10953	100	72	)	)	PUNCT
fumecheng-10953	100	73	(	(	PUNCT
fumecheng-10953	100	74	,	,	PUNCT
fumecheng-10953	100	75	)	)	PUNCT
fumecheng-10953	100	76	c	c	NOUN
fumecheng-10953	101	1	xx	xx	NUM
fumecheng-10953	102	1	e	e	NOUN
fumecheng-10953	102	2	xx	xx	NUM
fumecheng-10953	102	3	c	c	NOUN
fumecheng-10953	102	4	xx	xx	NUM
fumecheng-10953	103	1	e	e	X
fumecheng-10953	103	2	c	c	NOUN
fumecheng-10953	103	3	s	s	X
fumecheng-10953	103	4	xxx	xxx	NOUN
fumecheng-10953	104	1	c	c	NOUN
fumecheng-10953	104	2	xx	xx	NUM
fumecheng-10953	105	1	e	e	X
fumecheng-10953	105	2	xx	xx	NUM
fumecheng-10953	106	1	c	c	NOUN
fumecheng-10953	106	2	s	s	X
fumecheng-10953	106	3	xxxx	xxxx	NOUN
fumecheng-10953	106	4	m	m	ADJ
fumecheng-10953	106	5	x	x	X
fumecheng-10953	106	6	t	t	NOUN
fumecheng-10953	106	7	m	m	NOUN
fumecheng-10953	106	8	x	x	X
fumecheng-10953	107	1	t	t	NOUN
fumecheng-10953	107	2	i	i	PRON
fumecheng-10953	107	3	w	w	PROPN
fumecheng-10953	107	4	x	x	X
fumecheng-10953	107	5	t	t	NOUN
fumecheng-10953	107	6	m	m	NOUN
fumecheng-10953	107	7	x	x	PROPN
fumecheng-10953	108	1	t	t	NOUN
fumecheng-10953	108	2	m	m	NOUN
fumecheng-10953	108	3	x	x	X
fumecheng-10953	109	1	t	t	NOUN
fumecheng-10953	109	2	i	i	PRON
fumecheng-10953	109	3	w	w	PROPN
fumecheng-10953	109	4	x	x	X
fumecheng-10953	109	5	t	t	NOUN
fumecheng-10953	109	6	m	m	NOUN
fumecheng-10953	109	7	x	x	PROPN
fumecheng-10953	110	1	t	t	NOUN
fumecheng-10953	110	2	m	m	NOUN
fumecheng-10953	110	3	x	x	X
fumecheng-10953	110	4	t	t	NOUN
fumecheng-10953	110	5	i	i	PRON
fumecheng-10953	110	6	w	w	PROPN
fumecheng-10953	110	7	x	x	X
fumecheng-10953	110	8	t	t	PROPN
fumecheng-10953	110	9	w	w	PROPN
fumecheng-10953	110	10	x	x	PROPN
fumecheng-10953	110	11	t	t	PROPN
fumecheng-10953	110	12	−	−	PROPN
fumecheng-10953	110	13			PROPN
fumecheng-10953	110	14	=	=	SYM
fumecheng-10953	110	15	−	−	PROPN
fumecheng-10953	110	16			PROPN
fumecheng-10953	110	17	−	−	ADP
fumecheng-10953	110	18			PROPN
fumecheng-10953	110	19	=	=	SYM
fumecheng-10953	110	20	−	−	NOUN
fumecheng-10953	110	21			NOUN
fumecheng-10953	110	22	+	+	CCONJ
fumecheng-10953	110	23			ADJ
fumecheng-10953	110	24	−	−	ADP
fumecheng-10953	110	25			PROPN
fumecheng-10953	110	26	=	=	SYM
fumecheng-10953	111	1	−	−	PROPN
fumecheng-10953	111	2			ADJ
fumecheng-10953	111	3	−	−	PROPN
fumecheng-10953	111	4			NOUN
fumecheng-10953	111	5	+	+	CCONJ
fumecheng-10953	111	6			ADJ
fumecheng-10953	111	7	(	(	PUNCT
fumecheng-10953	111	8	8)	8)	NUM
fumecheng-10953	111	9	where	where	SCONJ
fumecheng-10953	111	10	the	the	DET
fumecheng-10953	111	11	constitutive	constitutive	ADJ
fumecheng-10953	111	12	laws	law	NOUN
fumecheng-10953	111	13	of	of	ADP
fumecheng-10953	111	14	the	the	DET
fumecheng-10953	111	15	flexural	flexural	ADJ
fumecheng-10953	111	16	resultants	resultant	NOUN
fumecheng-10953	111	17	m0	m0	PROPN
fumecheng-10953	111	18	,	,	PUNCT
fumecheng-10953	111	19	m1	m1	PROPN
fumecheng-10953	111	20	are	be	AUX
fumecheng-10953	111	21	directly	directly	ADV
fumecheng-10953	111	22	determined	determine	VERB
fumecheng-10953	111	23	in	in	ADP
fumecheng-10953	111	24	view	view	NOUN
fumecheng-10953	111	25	of	of	ADP
fumecheng-10953	111	26	the	the	DET
fumecheng-10953	111	27	stationarity	stationarity	NOUN
fumecheng-10953	111	28	of	of	ADP
fumecheng-10953	111	29	the	the	DET
fumecheng-10953	111	30	functional	functional	ADJ
fumecheng-10953	111	31	0	0	X
fumecheng-10953	112	1	=	=	SYM
fumecheng-10953	112	2	a	a	PRON
fumecheng-10953	112	3	,	,	PUNCT
fumecheng-10953	112	4	and	and	CCONJ
fumecheng-10953	112	5	the	the	DET
fumecheng-10953	112	6	constitutive	constitutive	ADJ
fumecheng-10953	112	7	relation	relation	NOUN
fumecheng-10953	112	8	of	of	ADP
fumecheng-10953	112	9	the	the	DET
fumecheng-10953	112	10	flexural	flexural	ADJ
fumecheng-10953	112	11	moment	moment	NOUN
fumecheng-10953	112	12	m	m	NOUN
fumecheng-10953	112	13	is	be	AUX
fumecheng-10953	112	14	detected	detect	VERB
fumecheng-10953	112	15	utilizing	utilize	VERB
fumecheng-10953	112	16	its	its	PRON
fumecheng-10953	112	17	definition	definition	NOUN
fumecheng-10953	112	18	as	as	ADP
fumecheng-10953	112	19	eq	eq	ADP
fumecheng-10953	112	20	.	.	PUNCT
fumecheng-10953	113	1	(	(	PUNCT
fumecheng-10953	113	2	6	6	NUM
fumecheng-10953	113	3	)	)	PUNCT
fumecheng-10953	113	4	.	.	PUNCT
fumecheng-10953	114	1	the	the	DET
fumecheng-10953	114	2	noticeable	noticeable	ADJ
fumecheng-10953	114	3	advantage	advantage	NOUN
fumecheng-10953	114	4	of	of	ADP
fumecheng-10953	114	5	the	the	DET
fumecheng-10953	114	6	established	establish	VERB
fumecheng-10953	114	7	stationary	stationary	ADJ
fumecheng-10953	114	8	variational	variational	ADJ
fumecheng-10953	114	9	framework	framework	NOUN
fumecheng-10953	114	10	is	be	AUX
fumecheng-10953	114	11	to	to	PART
fumecheng-10953	114	12	integrate	integrate	VERB
fumecheng-10953	114	13	all	all	DET
fumecheng-10953	114	14	the	the	DET
fumecheng-10953	114	15	governing	govern	VERB
fumecheng-10953	114	16	equations	equation	NOUN
fumecheng-10953	114	17	,	,	PUNCT
fumecheng-10953	114	18	i.e.	i.e.	X
fumecheng-10953	114	19	the	the	DET
fumecheng-10953	114	20	differential	differential	ADJ
fumecheng-10953	114	21	condition	condition	NOUN
fumecheng-10953	114	22	of	of	ADP
fumecheng-10953	114	23	dynamic	dynamic	ADJ
fumecheng-10953	114	24	equilibrium	equilibrium	NOUN
fumecheng-10953	114	25	,	,	PUNCT
fumecheng-10953	114	26	the	the	DET
fumecheng-10953	114	27	classical	classical	ADJ
fumecheng-10953	114	28	and	and	CCONJ
fumecheng-10953	114	29	the	the	DET
fumecheng-10953	114	30	extra	extra	ADJ
fumecheng-10953	114	31	non	non	ADJ
fumecheng-10953	114	32	-	-	ADJ
fumecheng-10953	114	33	standard	standard	ADJ
fumecheng-10953	114	34	boundary	boundary	ADJ
fumecheng-10953	114	35	conditions	condition	NOUN
fumecheng-10953	114	36	along	along	ADP
fumecheng-10953	114	37	with	with	ADP
fumecheng-10953	114	38	the	the	DET
fumecheng-10953	114	39	constitutive	constitutive	ADJ
fumecheng-10953	114	40	differential	differential	ADJ
fumecheng-10953	114	41	relations	relation	NOUN
fumecheng-10953	114	42	of	of	ADP
fumecheng-10953	114	43	the	the	DET
fumecheng-10953	114	44	resultant	resultant	NOUN
fumecheng-10953	114	45	fields	field	NOUN
fumecheng-10953	114	46	,	,	PUNCT
fumecheng-10953	114	47	into	into	ADP
fumecheng-10953	114	48	the	the	DET
fumecheng-10953	114	49	functionala	functionala	NOUN
fumecheng-10953	114	50	.	.	PUNCT
fumecheng-10953	115	1	the	the	DET
fumecheng-10953	115	2	constitutive	constitutive	ADJ
fumecheng-10953	115	3	laws	law	NOUN
fumecheng-10953	115	4	of	of	ADP
fumecheng-10953	115	5	the	the	DET
fumecheng-10953	115	6	resultant	resultant	NOUN
fumecheng-10953	115	7	fields	field	NOUN
fumecheng-10953	115	8	are	be	AUX
fumecheng-10953	115	9	of	of	ADP
fumecheng-10953	115	10	higher	high	ADJ
fumecheng-10953	115	11	-	-	PUNCT
fumecheng-10953	115	12	order	order	NOUN
fumecheng-10953	115	13	compared	compare	VERB
fumecheng-10953	115	14	with	with	ADP
fumecheng-10953	115	15	the	the	DET
fumecheng-10953	115	16	classical	classical	ADJ
fumecheng-10953	115	17	elasticity	elasticity	NOUN
fumecheng-10953	115	18	model	model	NOUN
fumecheng-10953	115	19	,	,	PUNCT
fumecheng-10953	115	20	and	and	CCONJ
fumecheng-10953	115	21	therefore	therefore	ADV
fumecheng-10953	115	22	,	,	PUNCT
fumecheng-10953	115	23	to	to	PART
fumecheng-10953	115	24	close	close	VERB
fumecheng-10953	115	25	the	the	DET
fumecheng-10953	115	26	associated	associated	ADJ
fumecheng-10953	115	27	boundary	boundary	ADJ
fumecheng-10953	115	28	-	-	PUNCT
fumecheng-10953	115	29	value	value	NOUN
fumecheng-10953	115	30	problem	problem	NOUN
fumecheng-10953	115	31	of	of	ADP
fumecheng-10953	115	32	dynamic	dynamic	ADJ
fumecheng-10953	115	33	equilibrium	equilibrium	NOUN
fumecheng-10953	115	34	on	on	ADP
fumecheng-10953	115	35	finite	finite	ADJ
fumecheng-10953	115	36	domains	domain	NOUN
fumecheng-10953	115	37	,	,	PUNCT
fumecheng-10953	115	38	extra	extra	ADJ
fumecheng-10953	115	39	non	non	ADJ
fumecheng-10953	115	40	-	-	ADJ
fumecheng-10953	115	41	standard	standard	ADJ
fumecheng-10953	115	42	boundary	boundary	ADJ
fumecheng-10953	115	43	conditions	condition	NOUN
fumecheng-10953	115	44	should	should	AUX
fumecheng-10953	115	45	be	be	AUX
fumecheng-10953	115	46	imposed	impose	VERB
fumecheng-10953	115	47	.	.	PUNCT
fumecheng-10953	116	1	realizing	realize	VERB
fumecheng-10953	116	2	the	the	DET
fumecheng-10953	116	3	proper	proper	ADJ
fumecheng-10953	116	4	mathematical	mathematical	ADJ
fumecheng-10953	116	5	form	form	NOUN
fumecheng-10953	116	6	of	of	ADP
fumecheng-10953	116	7	the	the	DET
fumecheng-10953	116	8	non	non	ADJ
fumecheng-10953	116	9	-	-	ADJ
fumecheng-10953	116	10	standard	standard	ADJ
fumecheng-10953	116	11	flexural	flexural	ADJ
fumecheng-10953	116	12	resultants	resultant	NOUN
fumecheng-10953	116	13	is	be	AUX
fumecheng-10953	116	14	of	of	ADP
fumecheng-10953	116	15	supreme	supreme	ADJ
fumecheng-10953	116	16	importance	importance	NOUN
fumecheng-10953	116	17	[	[	X
fumecheng-10953	116	18	54	54	NUM
fumecheng-10953	116	19	]	]	PUNCT
fumecheng-10953	116	20	;	;	PUNCT
fumecheng-10953	116	21	otherwise	otherwise	ADV
fumecheng-10953	116	22	,	,	PUNCT
fumecheng-10953	116	23	it	it	PRON
fumecheng-10953	116	24	yields	yield	VERB
fumecheng-10953	116	25	superfluous	superfluous	ADJ
fumecheng-10953	116	26	inference	inference	NOUN
fumecheng-10953	116	27	vis	vis	X
fumecheng-10953	116	28	-	-	X
fumecheng-10953	116	29	à	à	X
fumecheng-10953	116	30	-	-	PUNCT
fumecheng-10953	116	31	vis	vis	X
fumecheng-10953	116	32	the	the	DET
fumecheng-10953	116	33	size	size	NOUN
fumecheng-10953	116	34	-	-	PUNCT
fumecheng-10953	116	35	dependent	dependent	ADJ
fumecheng-10953	116	36	response	response	NOUN
fumecheng-10953	116	37	of	of	ADP
fumecheng-10953	116	38	ultra	ultra	ADJ
fumecheng-10953	116	39	-	-	ADJ
fumecheng-10953	116	40	small	small	ADJ
fumecheng-10953	116	41	structures	structure	NOUN
fumecheng-10953	116	42	[	[	X
fumecheng-10953	116	43	21	21	NUM
fumecheng-10953	116	44	,	,	PUNCT
fumecheng-10953	116	45	55	55	NUM
fumecheng-10953	116	46	]	]	PUNCT
fumecheng-10953	116	47	.	.	PUNCT
fumecheng-10953	117	1	the	the	DET
fumecheng-10953	117	2	explicit	explicit	ADJ
fumecheng-10953	117	3	constitutive	constitutive	ADJ
fumecheng-10953	117	4	relation	relation	NOUN
fumecheng-10953	117	5	of	of	ADP
fumecheng-10953	117	6	the	the	DET
fumecheng-10953	117	7	resultant	resultant	NOUN
fumecheng-10953	117	8	moment	moment	NOUN
fumecheng-10953	117	9	m1	m1	PROPN
fumecheng-10953	117	10	associated	associate	VERB
fumecheng-10953	117	11	with	with	ADP
fumecheng-10953	117	12	the	the	DET
fumecheng-10953	117	13	mixture	mixture	NOUN
fumecheng-10953	117	14	unified	unify	VERB
fumecheng-10953	117	15	gradient	gradient	NOUN
fumecheng-10953	117	16	theory	theory	NOUN
fumecheng-10953	117	17	,	,	PUNCT
fumecheng-10953	117	18	subsequent	subsequent	ADJ
fumecheng-10953	117	19	to	to	ADP
fumecheng-10953	117	20	some	some	DET
fumecheng-10953	117	21	straightforward	straightforward	ADJ
fumecheng-10953	117	22	mathematics	mathematic	NOUN
fumecheng-10953	117	23	,	,	PUNCT
fumecheng-10953	117	24	can	can	AUX
fumecheng-10953	117	25	be	be	AUX
fumecheng-10953	117	26	cast	cast	VERB
fumecheng-10953	117	27	in	in	ADP
fumecheng-10953	117	28	the	the	DET
fumecheng-10953	117	29	form	form	NOUN
fumecheng-10953	117	30	(	(	PUNCT
fumecheng-10953	117	31	)	)	PUNCT
fumecheng-10953	117	32	2	2	NUM
fumecheng-10953	117	33	2	2	NUM
fumecheng-10953	117	34	4	4	NUM
fumecheng-10953	117	35	1	1	NUM
fumecheng-10953	117	36	2	2	NUM
fumecheng-10953	117	37	2	2	NUM
fumecheng-10953	117	38	2	2	NUM
fumecheng-10953	117	39	2	2	NUM
fumecheng-10953	117	40	2	2	NUM
fumecheng-10953	117	41	2	2	NUM
fumecheng-10953	117	42	2	2	NUM
fumecheng-10953	117	43	2	2	NUM
fumecheng-10953	117	44	2	2	NUM
fumecheng-10953	117	45	2	2	NUM
fumecheng-10953	117	46	(	(	PUNCT
fumecheng-10953	117	47	)	)	PUNCT
fumecheng-10953	117	48	(	(	PUNCT
fumecheng-10953	117	49	,	,	PUNCT
fumecheng-10953	117	50	)	)	PUNCT
fumecheng-10953	117	51	(	(	PUNCT
fumecheng-10953	117	52	)	)	PUNCT
fumecheng-10953	117	53	(	(	PUNCT
fumecheng-10953	117	54	,	,	PUNCT
fumecheng-10953	117	55	)	)	PUNCT
fumecheng-10953	117	56	(	(	PUNCT
fumecheng-10953	117	57	,	,	PUNCT
fumecheng-10953	117	58	)	)	PUNCT
fumecheng-10953	118	1	(	(	PUNCT
fumecheng-10953	118	2	1	1	X
fumecheng-10953	118	3	)	)	PUNCT
fumecheng-10953	118	4	(	(	PUNCT
fumecheng-10953	118	5	)	)	PUNCT
fumecheng-10953	118	6	(	(	PUNCT
fumecheng-10953	118	7	)	)	PUNCT
fumecheng-10953	118	8	(	(	PUNCT
fumecheng-10953	118	9	,	,	PUNCT
fumecheng-10953	118	10	)	)	PUNCT
fumecheng-10953	118	11	(	(	PUNCT
fumecheng-10953	118	12	,	,	PUNCT
fumecheng-10953	118	13	)	)	PUNCT
fumecheng-10953	118	14	(	(	PUNCT
fumecheng-10953	118	15	1	1	X
fumecheng-10953	118	16	)	)	PUNCT
fumecheng-10953	118	17	c	c	PROPN
fumecheng-10953	118	18	s	s	NOUN
fumecheng-10953	118	19	c	c	NOUN
fumecheng-10953	118	20	x	x	X
fumecheng-10953	118	21	xtt	xtt	NOUN
fumecheng-10953	118	22	xxxtt	xxxtt	NOUN
fumecheng-10953	119	1	c	c	NOUN
fumecheng-10953	119	2	s	s	ADP
fumecheng-10953	119	3	c	c	NOUN
fumecheng-10953	119	4	s	s	X
fumecheng-10953	119	5	c	c	NOUN
fumecheng-10953	119	6	e	e	X
fumecheng-10953	119	7	c	c	NOUN
fumecheng-10953	119	8	s	s	PART
fumecheng-10953	119	9	xxx	xxx	PROPN
fumecheng-10953	119	10	e	e	PROPN
fumecheng-10953	119	11	xxxxx	xxxxx	PROPN
fumecheng-10953	119	12	c	c	PROPN
fumecheng-10953	119	13	s	s	PROPN
fumecheng-10953	119	14	m	m	VERB
fumecheng-10953	119	15	x	x	X
fumecheng-10953	119	16	t	t	NOUN
fumecheng-10953	119	17	q	q	NOUN
fumecheng-10953	119	18	x	x	X
fumecheng-10953	119	19	a	a	DET
fumecheng-10953	119	20	w	w	NOUN
fumecheng-10953	119	21	x	x	SYM
fumecheng-10953	119	22	t	t	NOUN
fumecheng-10953	119	23	i	i	PRON
fumecheng-10953	119	24	w	w	PROPN
fumecheng-10953	119	25	x	x	X
fumecheng-10953	119	26	t	t	NOUN
fumecheng-10953	119	27	i	i	PRON
fumecheng-10953	119	28	w	w	PROPN
fumecheng-10953	119	29	x	x	X
fumecheng-10953	120	1	t	t	NOUN
fumecheng-10953	120	2	i	i	PRON
fumecheng-10953	120	3	w	w	PROPN
fumecheng-10953	120	4	x	x	PROPN
fumecheng-10953	120	5	t	t	PROPN
fumecheng-10953	120	6			NOUN
fumecheng-10953	120	7			ADP
fumecheng-10953	120	8			VERB
fumecheng-10953	121	1	+	+	X
fumecheng-10953	121	2	=	=	SYM
fumecheng-10953	121	3	−	−	PROPN
fumecheng-10953	121	4			PROPN
fumecheng-10953	121	5	−	−	PROPN
fumecheng-10953	121	6			PROPN
fumecheng-10953	121	7	+	+	ADP
fumecheng-10953	121	8			ADJ
fumecheng-10953	121	9	−	−	PROPN
fumecheng-10953	121	10	−	−	PROPN
fumecheng-10953	121	11			NOUN
fumecheng-10953	121	12	+	+	CCONJ
fumecheng-10953	121	13	−	−	NOUN
fumecheng-10953	121	14			NOUN
fumecheng-10953	121	15	+	+	CCONJ
fumecheng-10953	121	16			ADJ
fumecheng-10953	121	17	+	+	CCONJ
fumecheng-10953	121	18			PROPN
fumecheng-10953	121	19	−	−	PROPN
fumecheng-10953	121	20	−	−	PROPN
fumecheng-10953	121	21	(	(	PUNCT
fumecheng-10953	121	22	9	9	X
fumecheng-10953	121	23	)	)	PUNCT
fumecheng-10953	121	24	several	several	ADJ
fumecheng-10953	121	25	types	type	NOUN
fumecheng-10953	121	26	of	of	ADP
fumecheng-10953	121	27	the	the	DET
fumecheng-10953	121	28	gradient	gradient	NOUN
fumecheng-10953	121	29	elasticity	elasticity	NOUN
fumecheng-10953	121	30	theory	theory	NOUN
fumecheng-10953	121	31	are	be	AUX
fumecheng-10953	121	32	,	,	PUNCT
fumecheng-10953	121	33	noticeably	noticeably	ADV
fumecheng-10953	121	34	,	,	PUNCT
fumecheng-10953	121	35	retrieved	retrieve	VERB
fumecheng-10953	121	36	as	as	ADP
fumecheng-10953	121	37	special	special	ADJ
fumecheng-10953	121	38	cases	case	NOUN
fumecheng-10953	121	39	of	of	ADP
fumecheng-10953	121	40	the	the	DET
fumecheng-10953	121	41	established	establish	VERB
fumecheng-10953	121	42	mixture	mixture	NOUN
fumecheng-10953	121	43	unified	unify	VERB
fumecheng-10953	121	44	gradient	gradient	NOUN
fumecheng-10953	121	45	theory	theory	NOUN
fumecheng-10953	121	46	under	under	ADP
fumecheng-10953	121	47	ad	ad	X
fumecheng-10953	121	48	hoc	hoc	X
fumecheng-10953	121	49	assumptions	assumption	NOUN
fumecheng-10953	121	50	on	on	ADP
fumecheng-10953	121	51	the	the	DET
fumecheng-10953	121	52	gradient	gradient	ADJ
fumecheng-10953	121	53	characteristic	characteristic	ADJ
fumecheng-10953	121	54	lengths	length	NOUN
fumecheng-10953	121	55	.	.	PUNCT
fumecheng-10953	122	1	the	the	DET
fumecheng-10953	122	2	classical	classical	ADJ
fumecheng-10953	122	3	elasticity	elasticity	NOUN
fumecheng-10953	122	4	model	model	NOUN
fumecheng-10953	122	5	is	be	AUX
fumecheng-10953	122	6	obtained	obtain	VERB
fumecheng-10953	122	7	via	via	ADP
fumecheng-10953	122	8	either	either	CCONJ
fumecheng-10953	122	9	setting	set	VERB
fumecheng-10953	122	10	the	the	DET
fumecheng-10953	122	11	gradient	gradient	ADJ
fumecheng-10953	122	12	characteristic	characteristic	ADJ
fumecheng-10953	122	13	lengths	length	NOUN
fumecheng-10953	122	14	to	to	ADP
fumecheng-10953	122	15	zero	zero	NUM
fumecheng-10953	122	16	or	or	CCONJ
fumecheng-10953	122	17	via	via	ADP
fumecheng-10953	122	18	letting	let	VERB
fumecheng-10953	122	19	the	the	DET
fumecheng-10953	122	20	mixture	mixture	NOUN
fumecheng-10953	122	21	parameter	parameter	NOUN
fumecheng-10953	122	22	approach	approach	NOUN
fumecheng-10953	122	23	unity	unity	NOUN
fumecheng-10953	122	24	in	in	ADP
fumecheng-10953	122	25	the	the	DET
fumecheng-10953	122	26	absence	absence	NOUN
fumecheng-10953	122	27	of	of	ADP
fumecheng-10953	122	28	the	the	DET
fumecheng-10953	122	29	strain	strain	NOUN
fumecheng-10953	122	30	gradient	gradient	ADJ
fumecheng-10953	122	31	length	length	NOUN
fumecheng-10953	122	32	-	-	PUNCT
fumecheng-10953	122	33	scale	scale	NOUN
fumecheng-10953	122	34	parameter	parameter	NOUN
fumecheng-10953	122	35	.	.	PUNCT
fumecheng-10953	123	1	as	as	SCONJ
fumecheng-10953	123	2	the	the	DET
fumecheng-10953	123	3	vanishing	vanishing	NOUN
fumecheng-10953	123	4	of	of	ADP
fumecheng-10953	123	5	the	the	DET
fumecheng-10953	123	6	mixture	mixture	NOUN
fumecheng-10953	123	7	parameter	parameter	NOUN
fumecheng-10953	123	8	yields	yield	VERB
fumecheng-10953	123	9	the	the	DET
fumecheng-10953	123	10	unified	unified	ADJ
fumecheng-10953	123	11	gradient	gradient	NOUN
fumecheng-10953	123	12	elasticity	elasticity	NOUN
fumecheng-10953	123	13	theory	theory	NOUN
fumecheng-10953	123	14	,	,	PUNCT
fumecheng-10953	123	15	the	the	DET
fumecheng-10953	123	16	strain	strain	NOUN
fumecheng-10953	123	17	gradient	gradient	NOUN
fumecheng-10953	123	18	and	and	CCONJ
fumecheng-10953	123	19	the	the	DET
fumecheng-10953	123	20	stress	stress	NOUN
fumecheng-10953	123	21	gradient	gradient	NOUN
fumecheng-10953	123	22	theory	theory	NOUN
fumecheng-10953	123	23	can	can	AUX
fumecheng-10953	123	24	be	be	AUX
fumecheng-10953	123	25	,	,	PUNCT
fumecheng-10953	123	26	likewise	likewise	ADV
fumecheng-10953	123	27	,	,	PUNCT
fumecheng-10953	123	28	retrieved	retrieve	VERB
fumecheng-10953	123	29	via	via	ADP
fumecheng-10953	123	30	setting	set	VERB
fumecheng-10953	123	31	the	the	DET
fumecheng-10953	123	32	pertinent	pertinent	ADJ
fumecheng-10953	123	33	gradient	gradient	ADJ
fumecheng-10953	123	34	lengthscale	lengthscale	NOUN
fumecheng-10953	123	35	parameter	parameter	NOUN
fumecheng-10953	123	36	to	to	ADP
fumecheng-10953	123	37	zero	zero	NUM
fumecheng-10953	123	38	.	.	PUNCT
fumecheng-10953	124	1	moreover	moreover	ADV
fumecheng-10953	124	2	,	,	PUNCT
fumecheng-10953	124	3	the	the	DET
fumecheng-10953	124	4	mixture	mixture	NOUN
fumecheng-10953	124	5	stress	stress	NOUN
fumecheng-10953	124	6	gradient	gradient	NOUN
fumecheng-10953	124	7	theory	theory	NOUN
fumecheng-10953	124	8	can	can	AUX
fumecheng-10953	124	9	be	be	AUX
fumecheng-10953	124	10	recovered	recover	VERB
fumecheng-10953	124	11	via	via	ADP
fumecheng-10953	124	12	vanishing	vanish	VERB
fumecheng-10953	124	13	the	the	DET
fumecheng-10953	124	14	strain	strain	NOUN
fumecheng-10953	124	15	gradient	gradient	ADJ
fumecheng-10953	124	16	length	length	NOUN
fumecheng-10953	124	17	-	-	PUNCT
fumecheng-10953	124	18	scale	scale	NOUN
fumecheng-10953	124	19	parameter	parameter	NOUN
fumecheng-10953	124	20	.	.	PUNCT
fumecheng-10953	125	1	the	the	DET
fumecheng-10953	125	2	peculiar	peculiar	ADJ
fumecheng-10953	125	3	size	size	NOUN
fumecheng-10953	125	4	-	-	PUNCT
fumecheng-10953	125	5	dependent	dependent	ADJ
fumecheng-10953	125	6	dynamic	dynamic	ADJ
fumecheng-10953	125	7	behavior	behavior	NOUN
fumecheng-10953	125	8	of	of	ADP
fumecheng-10953	125	9	nano	nano	NOUN
fumecheng-10953	125	10	-	-	PUNCT
fumecheng-10953	125	11	scale	scale	NOUN
fumecheng-10953	125	12	beams	beam	NOUN
fumecheng-10953	125	13	can	can	AUX
fumecheng-10953	125	14	be	be	AUX
fumecheng-10953	125	15	competently	competently	ADV
fumecheng-10953	125	16	captured	capture	VERB
fumecheng-10953	125	17	within	within	ADP
fumecheng-10953	125	18	the	the	DET
fumecheng-10953	125	19	framework	framework	NOUN
fumecheng-10953	125	20	of	of	ADP
fumecheng-10953	125	21	the	the	DET
fumecheng-10953	125	22	mixture	mixture	NOUN
fumecheng-10953	125	23	unified	unify	VERB
fumecheng-10953	125	24	gradient	gradient	NOUN
fumecheng-10953	125	25	theory	theory	NOUN
fumecheng-10953	125	26	as	as	ADP
fumecheng-10953	125	27	evinced	evince	VERB
fumecheng-10953	125	28	via	via	ADP
fumecheng-10953	125	29	rigorous	rigorous	ADJ
fumecheng-10953	125	30	examination	examination	NOUN
fumecheng-10953	125	31	of	of	ADP
fumecheng-10953	125	32	the	the	DET
fumecheng-10953	125	33	wave	wave	NOUN
fumecheng-10953	125	34	dispersion	dispersion	NOUN
fumecheng-10953	125	35	and	and	CCONJ
fumecheng-10953	125	36	the	the	DET
fumecheng-10953	125	37	free	free	ADJ
fumecheng-10953	125	38	vibrations	vibration	NOUN
fumecheng-10953	125	39	of	of	ADP
fumecheng-10953	125	40	elastic	elastic	ADJ
fumecheng-10953	125	41	inflected	inflect	VERB
fumecheng-10953	125	42	nanobeams	nanobeam	NOUN
fumecheng-10953	125	43	.	.	PUNCT
fumecheng-10953	126	1	544	544	NUM
fumecheng-10953	126	2	s.	s.	PROPN
fumecheng-10953	126	3	a.	a.	PROPN
fumecheng-10953	126	4	faghidian	faghidian	PROPN
fumecheng-10953	126	5	,	,	PUNCT
fumecheng-10953	126	6	a.	a.	NOUN
fumecheng-10953	126	7	tounsi	tounsi	NOUN
fumecheng-10953	126	8	3	3	NUM
fumecheng-10953	126	9	.	.	PUNCT
fumecheng-10953	126	10	wave	wave	NOUN
fumecheng-10953	126	11	dispersion	dispersion	NOUN
fumecheng-10953	126	12	characteristics	characteristic	VERB
fumecheng-10953	126	13	the	the	DET
fumecheng-10953	126	14	size	size	NOUN
fumecheng-10953	126	15	-	-	PUNCT
fumecheng-10953	126	16	dependent	dependent	ADJ
fumecheng-10953	126	17	physical	physical	ADJ
fumecheng-10953	126	18	characteristics	characteristic	NOUN
fumecheng-10953	126	19	of	of	ADP
fumecheng-10953	126	20	nano	nano	NOUN
fumecheng-10953	126	21	-	-	PUNCT
fumecheng-10953	126	22	structures	structure	NOUN
fumecheng-10953	126	23	can	can	AUX
fumecheng-10953	126	24	be	be	AUX
fumecheng-10953	126	25	effectively	effectively	ADV
fumecheng-10953	126	26	realized	realize	VERB
fumecheng-10953	126	27	by	by	ADP
fumecheng-10953	126	28	the	the	DET
fumecheng-10953	126	29	analysis	analysis	NOUN
fumecheng-10953	126	30	of	of	ADP
fumecheng-10953	126	31	the	the	DET
fumecheng-10953	126	32	wave	wave	NOUN
fumecheng-10953	126	33	dispersion	dispersion	NOUN
fumecheng-10953	126	34	.	.	PUNCT
fumecheng-10953	127	1	examination	examination	NOUN
fumecheng-10953	127	2	of	of	ADP
fumecheng-10953	127	3	dispersive	dispersive	ADJ
fumecheng-10953	127	4	waves	wave	NOUN
fumecheng-10953	127	5	can	can	AUX
fumecheng-10953	127	6	be	be	AUX
fumecheng-10953	127	7	,	,	PUNCT
fumecheng-10953	127	8	furthermore	furthermore	ADV
fumecheng-10953	127	9	,	,	PUNCT
fumecheng-10953	127	10	exploited	exploit	VERB
fumecheng-10953	127	11	for	for	ADP
fumecheng-10953	127	12	inverse	inverse	ADJ
fumecheng-10953	127	13	determination	determination	NOUN
fumecheng-10953	127	14	of	of	ADP
fumecheng-10953	127	15	the	the	DET
fumecheng-10953	127	16	gradient	gradient	ADJ
fumecheng-10953	127	17	characteristic	characteristic	ADJ
fumecheng-10953	127	18	parameters	parameter	NOUN
fumecheng-10953	127	19	applying	apply	VERB
fumecheng-10953	127	20	the	the	DET
fumecheng-10953	127	21	inverse	inverse	NOUN
fumecheng-10953	127	22	theory	theory	NOUN
fumecheng-10953	127	23	approach	approach	NOUN
fumecheng-10953	127	24	[	[	X
fumecheng-10953	127	25	56	56	NUM
fumecheng-10953	127	26	,	,	PUNCT
fumecheng-10953	127	27	57	57	NUM
fumecheng-10953	127	28	]	]	PUNCT
fumecheng-10953	127	29	.	.	PUNCT
fumecheng-10953	128	1	to	to	PART
fumecheng-10953	128	2	examine	examine	VERB
fumecheng-10953	128	3	the	the	DET
fumecheng-10953	128	4	flexural	flexural	ADJ
fumecheng-10953	128	5	waves	wave	NOUN
fumecheng-10953	128	6	dispersing	disperse	VERB
fumecheng-10953	128	7	in	in	ADP
fumecheng-10953	128	8	the	the	DET
fumecheng-10953	128	9	elastic	elastic	ADJ
fumecheng-10953	128	10	nanobeam	nanobeam	NOUN
fumecheng-10953	128	11	,	,	PUNCT
fumecheng-10953	128	12	the	the	DET
fumecheng-10953	128	13	differential	differential	ADJ
fumecheng-10953	128	14	condition	condition	NOUN
fumecheng-10953	128	15	of	of	ADP
fumecheng-10953	128	16	dynamic	dynamic	ADJ
fumecheng-10953	128	17	equilibrium	equilibrium	NOUN
fumecheng-10953	128	18	should	should	AUX
fumecheng-10953	128	19	be	be	AUX
fumecheng-10953	128	20	expressed	express	VERB
fumecheng-10953	128	21	in	in	ADP
fumecheng-10953	128	22	terms	term	NOUN
fumecheng-10953	128	23	of	of	ADP
fumecheng-10953	128	24	the	the	DET
fumecheng-10953	128	25	transverse	transverse	ADJ
fumecheng-10953	128	26	displacement	displacement	NOUN
fumecheng-10953	128	27	of	of	ADP
fumecheng-10953	128	28	the	the	DET
fumecheng-10953	128	29	beam	beam	NOUN
fumecheng-10953	128	30	.	.	PUNCT
fumecheng-10953	129	1	the	the	DET
fumecheng-10953	129	2	total	total	ADJ
fumecheng-10953	129	3	flexural	flexural	ADJ
fumecheng-10953	129	4	moment	moment	NOUN
fumecheng-10953	129	5	is	be	AUX
fumecheng-10953	129	6	,	,	PUNCT
fumecheng-10953	129	7	accordingly	accordingly	ADV
fumecheng-10953	129	8	,	,	PUNCT
fumecheng-10953	129	9	obtained	obtain	VERB
fumecheng-10953	129	10	by	by	ADP
fumecheng-10953	129	11	imposing	impose	VERB
fumecheng-10953	129	12	the	the	DET
fumecheng-10953	129	13	dynamic	dynamic	ADJ
fumecheng-10953	129	14	equilibrium	equilibrium	NOUN
fumecheng-10953	129	15	condition	condition	NOUN
fumecheng-10953	129	16	eq	eq	ADP
fumecheng-10953	129	17	.	.	PUNCT
fumecheng-10953	130	1	(	(	PUNCT
fumecheng-10953	130	2	7)1	7)1	NUM
fumecheng-10953	130	3	to	to	ADP
fumecheng-10953	130	4	the	the	DET
fumecheng-10953	130	5	constitutive	constitutive	ADJ
fumecheng-10953	130	6	law	law	NOUN
fumecheng-10953	130	7	of	of	ADP
fumecheng-10953	130	8	the	the	DET
fumecheng-10953	130	9	flexural	flexural	ADJ
fumecheng-10953	130	10	moment	moment	NOUN
fumecheng-10953	130	11	eq	eq	ADJ
fumecheng-10953	130	12	.	.	PUNCT
fumecheng-10953	131	1	(	(	PUNCT
fumecheng-10953	131	2	8)3	8)3	NOUN
fumecheng-10953	131	3	,	,	PUNCT
fumecheng-10953	131	4	namely	namely	ADV
fumecheng-10953	131	5	,	,	PUNCT
fumecheng-10953	131	6	2	2	NUM
fumecheng-10953	131	7	2	2	NUM
fumecheng-10953	131	8	2	2	NUM
fumecheng-10953	131	9	2	2	NUM
fumecheng-10953	131	10	(	(	PUNCT
fumecheng-10953	131	11	,	,	PUNCT
fumecheng-10953	131	12	)	)	PUNCT
fumecheng-10953	131	13	(	(	PUNCT
fumecheng-10953	131	14	,	,	PUNCT
fumecheng-10953	131	15	)	)	PUNCT
fumecheng-10953	131	16	(	(	PUNCT
fumecheng-10953	131	17	,	,	PUNCT
fumecheng-10953	131	18	)	)	PUNCT
fumecheng-10953	131	19	(	(	PUNCT
fumecheng-10953	131	20	,	,	PUNCT
fumecheng-10953	131	21	)	)	PUNCT
fumecheng-10953	131	22	(	(	PUNCT
fumecheng-10953	131	23	)	)	PUNCT
fumecheng-10953	131	24	(	(	PUNCT
fumecheng-10953	131	25	,	,	PUNCT
fumecheng-10953	131	26	)	)	PUNCT
fumecheng-10953	131	27	c	c	PROPN
fumecheng-10953	131	28	tt	tt	PROPN
fumecheng-10953	131	29	c	c	PROPN
fumecheng-10953	131	30	xxtt	xxtt	PROPN
fumecheng-10953	131	31	e	e	NOUN
fumecheng-10953	132	1	xx	xx	NUM
fumecheng-10953	132	2	c	c	NOUN
fumecheng-10953	132	3	s	s	NOUN
fumecheng-10953	132	4	e	e	NOUN
fumecheng-10953	132	5	xxxx	xxxx	NOUN
fumecheng-10953	132	6	m	m	VERB
fumecheng-10953	132	7	x	x	SYM
fumecheng-10953	132	8	t	t	PROPN
fumecheng-10953	132	9	a	a	PRON
fumecheng-10953	132	10	w	w	NOUN
fumecheng-10953	132	11	x	x	SYM
fumecheng-10953	132	12	t	t	NOUN
fumecheng-10953	132	13	i	i	PRON
fumecheng-10953	132	14	w	w	PROPN
fumecheng-10953	132	15	x	x	X
fumecheng-10953	132	16	t	t	NOUN
fumecheng-10953	132	17	i	i	PRON
fumecheng-10953	132	18	w	w	PROPN
fumecheng-10953	133	1	x	x	X
fumecheng-10953	133	2	t	t	NOUN
fumecheng-10953	133	3	i	i	PRON
fumecheng-10953	133	4	w	w	PROPN
fumecheng-10953	133	5	x	x	X
fumecheng-10953	133	6	t	t	NOUN
fumecheng-10953	133	7			NOUN
fumecheng-10953	133	8	=	=	ADV
fumecheng-10953	133	9			ADJ
fumecheng-10953	133	10	−	−	ADP
fumecheng-10953	133	11			PROPN
fumecheng-10953	133	12	−	−	PROPN
fumecheng-10953	133	13			PROPN
fumecheng-10953	133	14	+	+	CCONJ
fumecheng-10953	134	1			NOUN
fumecheng-10953	134	2	+	+	X
fumecheng-10953	134	3			ADJ
fumecheng-10953	134	4	(	(	PUNCT
fumecheng-10953	134	5	10	10	NUM
fumecheng-10953	134	6	)	)	PUNCT
fumecheng-10953	134	7	where	where	SCONJ
fumecheng-10953	134	8	the	the	DET
fumecheng-10953	134	9	transverse	transverse	NOUN
fumecheng-10953	134	10	body	body	NOUN
fumecheng-10953	134	11	force	force	NOUN
fumecheng-10953	134	12	is	be	AUX
fumecheng-10953	134	13	overlooked	overlook	VERB
fumecheng-10953	134	14	in	in	ADP
fumecheng-10953	134	15	the	the	DET
fumecheng-10953	134	16	dynamic	dynamic	ADJ
fumecheng-10953	134	17	analysis	analysis	NOUN
fumecheng-10953	134	18	of	of	ADP
fumecheng-10953	134	19	nano	nano	NOUN
fumecheng-10953	134	20	-	-	PUNCT
fumecheng-10953	134	21	sized	sized	ADJ
fumecheng-10953	134	22	beams	beam	NOUN
fumecheng-10953	134	23	.	.	PUNCT
fumecheng-10953	135	1	the	the	DET
fumecheng-10953	135	2	governing	govern	VERB
fumecheng-10953	135	3	equation	equation	NOUN
fumecheng-10953	135	4	on	on	ADP
fumecheng-10953	135	5	the	the	DET
fumecheng-10953	135	6	dynamic	dynamic	ADJ
fumecheng-10953	135	7	response	response	NOUN
fumecheng-10953	135	8	of	of	ADP
fumecheng-10953	135	9	the	the	DET
fumecheng-10953	135	10	mixture	mixture	NOUN
fumecheng-10953	135	11	unified	unify	VERB
fumecheng-10953	135	12	gradient	gradient	ADJ
fumecheng-10953	135	13	elastic	elastic	ADJ
fumecheng-10953	135	14	beam	beam	NOUN
fumecheng-10953	135	15	is	be	AUX
fumecheng-10953	135	16	achieved	achieve	VERB
fumecheng-10953	135	17	via	via	ADP
fumecheng-10953	135	18	utilizing	utilize	VERB
fumecheng-10953	135	19	the	the	DET
fumecheng-10953	135	20	detected	detect	VERB
fumecheng-10953	135	21	result	result	NOUN
fumecheng-10953	135	22	for	for	ADP
fumecheng-10953	135	23	the	the	DET
fumecheng-10953	135	24	flexural	flexural	ADJ
fumecheng-10953	135	25	moment	moment	NOUN
fumecheng-10953	135	26	in	in	ADP
fumecheng-10953	135	27	the	the	DET
fumecheng-10953	135	28	differential	differential	ADJ
fumecheng-10953	135	29	condition	condition	NOUN
fumecheng-10953	135	30	of	of	ADP
fumecheng-10953	135	31	dynamic	dynamic	ADJ
fumecheng-10953	135	32	equilibrium	equilibrium	NOUN
fumecheng-10953	135	33	as	as	ADP
fumecheng-10953	135	34	2	2	NUM
fumecheng-10953	135	35	2	2	NUM
fumecheng-10953	135	36	2	2	NUM
fumecheng-10953	135	37	2	2	NUM
fumecheng-10953	135	38	(	(	PUNCT
fumecheng-10953	135	39	,	,	PUNCT
fumecheng-10953	135	40	)	)	PUNCT
fumecheng-10953	135	41	(	(	PUNCT
fumecheng-10953	135	42	,	,	PUNCT
fumecheng-10953	135	43	)	)	PUNCT
fumecheng-10953	135	44	(	(	PUNCT
fumecheng-10953	135	45	)	)	PUNCT
fumecheng-10953	135	46	(	(	PUNCT
fumecheng-10953	135	47	,	,	PUNCT
fumecheng-10953	135	48	)	)	PUNCT
fumecheng-10953	135	49	(	(	PUNCT
fumecheng-10953	135	50	,	,	PUNCT
fumecheng-10953	135	51	)	)	PUNCT
fumecheng-10953	135	52	(	(	PUNCT
fumecheng-10953	135	53	)	)	PUNCT
fumecheng-10953	135	54	(	(	PUNCT
fumecheng-10953	135	55	,	,	PUNCT
fumecheng-10953	135	56	)	)	PUNCT
fumecheng-10953	135	57	0	0	PUNCT
fumecheng-10953	136	1	c	c	NOUN
fumecheng-10953	136	2	xxxxtt	xxxxtt	NOUN
fumecheng-10953	136	3	e	e	NOUN
fumecheng-10953	136	4	xxxx	xxxx	NOUN
fumecheng-10953	136	5	c	c	PROPN
fumecheng-10953	136	6	s	s	PROPN
fumecheng-10953	136	7	e	e	X
fumecheng-10953	136	8	xxxxxx	xxxxxx	PROPN
fumecheng-10953	136	9	tt	tt	PROPN
fumecheng-10953	136	10	c	c	PROPN
fumecheng-10953	136	11	xxtt	xxtt	PROPN
fumecheng-10953	137	1	i	i	PRON
fumecheng-10953	137	2	w	w	PROPN
fumecheng-10953	137	3	x	x	X
fumecheng-10953	137	4	t	t	NOUN
fumecheng-10953	137	5	i	i	PRON
fumecheng-10953	137	6	w	w	PROPN
fumecheng-10953	137	7	x	x	X
fumecheng-10953	137	8	t	t	NOUN
fumecheng-10953	137	9	i	i	PRON
fumecheng-10953	137	10	w	w	VERB
fumecheng-10953	137	11	x	x	X
fumecheng-10953	137	12	t	t	PROPN
fumecheng-10953	137	13	a	a	DET
fumecheng-10953	137	14	w	w	NOUN
fumecheng-10953	137	15	x	x	SYM
fumecheng-10953	137	16	t	t	NOUN
fumecheng-10953	138	1	i	i	PRON
fumecheng-10953	138	2	a	a	DET
fumecheng-10953	138	3	w	w	NOUN
fumecheng-10953	138	4	x	x	SYM
fumecheng-10953	138	5	t	t	NOUN
fumecheng-10953	138	6			NOUN
fumecheng-10953	138	7			ADP
fumecheng-10953	138	8			X
fumecheng-10953	138	9			ADP
fumecheng-10953	138	10			PROPN
fumecheng-10953	138	11	+	+	CCONJ
fumecheng-10953	138	12			ADJ
fumecheng-10953	138	13	−	−	PROPN
fumecheng-10953	138	14			NOUN
fumecheng-10953	139	1	+	+	CCONJ
fumecheng-10953	139	2			ADJ
fumecheng-10953	139	3	+	+	CCONJ
fumecheng-10953	139	4			ADJ
fumecheng-10953	139	5	−	−	NOUN
fumecheng-10953	140	1	+	+	NUM
fumecheng-10953	140	2			ADJ
fumecheng-10953	140	3	=	=	SYM
fumecheng-10953	140	4	(	(	PUNCT
fumecheng-10953	140	5	11	11	NUM
fumecheng-10953	140	6	)	)	PUNCT
fumecheng-10953	140	7	for	for	ADP
fumecheng-10953	140	8	the	the	DET
fumecheng-10953	140	9	harmonic	harmonic	ADJ
fumecheng-10953	140	10	wave	wave	NOUN
fumecheng-10953	140	11	dispersion	dispersion	NOUN
fumecheng-10953	140	12	in	in	ADP
fumecheng-10953	140	13	infinitely	infinitely	ADV
fumecheng-10953	140	14	extended	extend	VERB
fumecheng-10953	140	15	homogeneous	homogeneous	ADJ
fumecheng-10953	140	16	structures	structure	NOUN
fumecheng-10953	140	17	,	,	PUNCT
fumecheng-10953	140	18	vanishing	vanish	VERB
fumecheng-10953	140	19	the	the	DET
fumecheng-10953	140	20	boundary	boundary	ADJ
fumecheng-10953	140	21	conditions	condition	NOUN
fumecheng-10953	140	22	is	be	AUX
fumecheng-10953	140	23	tacitly	tacitly	ADV
fumecheng-10953	140	24	fulfilled	fulfil	VERB
fumecheng-10953	140	25	;	;	PUNCT
fumecheng-10953	140	26	the	the	DET
fumecheng-10953	140	27	corresponding	corresponding	ADJ
fumecheng-10953	140	28	solution	solution	NOUN
fumecheng-10953	140	29	of	of	ADP
fumecheng-10953	140	30	the	the	DET
fumecheng-10953	140	31	wave	wave	NOUN
fumecheng-10953	140	32	response	response	NOUN
fumecheng-10953	140	33	,	,	PUNCT
fumecheng-10953	140	34	thus	thus	ADV
fumecheng-10953	140	35	,	,	PUNCT
fumecheng-10953	140	36	takes	take	VERB
fumecheng-10953	140	37	the	the	DET
fumecheng-10953	140	38	form	form	NOUN
fumecheng-10953	140	39	(	(	PUNCT
fumecheng-10953	140	40	,	,	PUNCT
fumecheng-10953	140	41	)	)	PUNCT
fumecheng-10953	140	42	exp	exp	NOUN
fumecheng-10953	140	43	(	(	PUNCT
fumecheng-10953	140	44	(	(	PUNCT
fumecheng-10953	140	45	)	)	PUNCT
fumecheng-10953	140	46	)	)	PUNCT
fumecheng-10953	141	1	w	w	X
fumecheng-10953	141	2	x	x	SYM
fumecheng-10953	141	3	t	t	PROPN
fumecheng-10953	141	4	w	w	NOUN
fumecheng-10953	141	5	i	i	NOUN
fumecheng-10953	141	6	x	x	PROPN
fumecheng-10953	142	1	vt=	vt=	NOUN
fumecheng-10953	142	2	−	−	PROPN
fumecheng-10953	142	3	(	(	PUNCT
fumecheng-10953	142	4	12	12	NUM
fumecheng-10953	142	5	)	)	PUNCT
fumecheng-10953	142	6	with	with	ADP
fumecheng-10953	142	7	i	i	PRON
fumecheng-10953	142	8	being	be	AUX
fumecheng-10953	142	9	the	the	DET
fumecheng-10953	142	10	unit	unit	NOUN
fumecheng-10953	142	11	imaginary	imaginary	ADJ
fumecheng-10953	142	12	number	number	NOUN
fumecheng-10953	142	13	,	,	PUNCT
fumecheng-10953	142	14			ADJ
fumecheng-10953	142	15	and	and	CCONJ
fumecheng-10953	142	16	v	v	NOUN
fumecheng-10953	142	17	,	,	PUNCT
fumecheng-10953	142	18	respectively	respectively	ADV
fumecheng-10953	142	19	,	,	PUNCT
fumecheng-10953	142	20	denote	denote	VERB
fumecheng-10953	142	21	the	the	DET
fumecheng-10953	142	22	wave	wave	NOUN
fumecheng-10953	142	23	number	number	NOUN
fumecheng-10953	142	24	and	and	CCONJ
fumecheng-10953	142	25	the	the	DET
fumecheng-10953	142	26	phase	phase	NOUN
fumecheng-10953	142	27	velocity	velocity	NOUN
fumecheng-10953	142	28	along	along	ADP
fumecheng-10953	142	29	with	with	ADP
fumecheng-10953	142	30	w	w	NOUN
fumecheng-10953	142	31	standing	stand	VERB
fumecheng-10953	142	32	for	for	ADP
fumecheng-10953	142	33	the	the	DET
fumecheng-10953	142	34	wave	wave	NOUN
fumecheng-10953	142	35	amplitude	amplitude	NOUN
fumecheng-10953	142	36	.	.	PUNCT
fumecheng-10953	143	1	by	by	ADP
fumecheng-10953	143	2	substituting	substitute	VERB
fumecheng-10953	143	3	the	the	DET
fumecheng-10953	143	4	displacement	displacement	ADJ
fumecheng-10953	143	5	solution	solution	NOUN
fumecheng-10953	143	6	eq	eq	ADP
fumecheng-10953	143	7	.	.	PUNCT
fumecheng-10953	144	1	(	(	PUNCT
fumecheng-10953	144	2	12	12	NUM
fumecheng-10953	144	3	)	)	PUNCT
fumecheng-10953	144	4	into	into	ADP
fumecheng-10953	144	5	the	the	DET
fumecheng-10953	144	6	governing	govern	VERB
fumecheng-10953	144	7	equation	equation	NOUN
fumecheng-10953	144	8	on	on	ADP
fumecheng-10953	144	9	the	the	DET
fumecheng-10953	144	10	dynamics	dynamic	NOUN
fumecheng-10953	144	11	of	of	ADP
fumecheng-10953	144	12	the	the	DET
fumecheng-10953	144	13	elastic	elastic	ADJ
fumecheng-10953	144	14	nanobeam	nanobeam	NOUN
fumecheng-10953	144	15	eq	eq	ADP
fumecheng-10953	144	16	.	.	PUNCT
fumecheng-10953	145	1	(	(	PUNCT
fumecheng-10953	145	2	11	11	NUM
fumecheng-10953	145	3	)	)	PUNCT
fumecheng-10953	145	4	,	,	PUNCT
fumecheng-10953	145	5	based	base	VERB
fumecheng-10953	145	6	on	on	ADP
fumecheng-10953	145	7	the	the	DET
fumecheng-10953	145	8	mixture	mixture	NOUN
fumecheng-10953	145	9	unified	unify	VERB
fumecheng-10953	145	10	gradient	gradient	NOUN
fumecheng-10953	145	11	theory	theory	NOUN
fumecheng-10953	145	12	,	,	PUNCT
fumecheng-10953	145	13	the	the	DET
fumecheng-10953	145	14	subsequent	subsequent	ADJ
fumecheng-10953	145	15	phase	phase	NOUN
fumecheng-10953	145	16	velocity	velocity	NOUN
fumecheng-10953	145	17	is	be	AUX
fumecheng-10953	145	18	obtained	obtain	VERB
fumecheng-10953	145	19	2	2	NUM
fumecheng-10953	145	20	2	2	NUM
fumecheng-10953	145	21	2	2	NUM
fumecheng-10953	145	22	2	2	NUM
fumecheng-10953	145	23	2	2	NUM
fumecheng-10953	145	24	2	2	NUM
fumecheng-10953	145	25	(	(	PUNCT
fumecheng-10953	145	26	)	)	PUNCT
fumecheng-10953	145	27	1	1	NUM
fumecheng-10953	145	28	e	e	NOUN
fumecheng-10953	145	29	e	e	X
fumecheng-10953	145	30	c	c	NOUN
fumecheng-10953	145	31	s	s	X
fumecheng-10953	145	32	c	c	NOUN
fumecheng-10953	146	1	i	i	PRON
fumecheng-10953	146	2	i	i	PRON
fumecheng-10953	146	3	v	v	VERB
fumecheng-10953	146	4	a	a	DET
fumecheng-10953	146	5	i	i	NOUN
fumecheng-10953	146	6			ADP
fumecheng-10953	146	7			ADJ
fumecheng-10953	146	8			ADJ
fumecheng-10953	146	9			ADJ
fumecheng-10953	146	10			ADJ
fumecheng-10953	146	11	+	+	X
fumecheng-10953	146	12			NOUN
fumecheng-10953	146	13	+	+	NOUN
fumecheng-10953	147	1	=	=	PUNCT
fumecheng-10953	148	1	+	+	CCONJ
fumecheng-10953	148	2	+	+	CCONJ
fumecheng-10953	148	3	(	(	PUNCT
fumecheng-10953	148	4	13	13	NUM
fumecheng-10953	148	5	)	)	PUNCT
fumecheng-10953	148	6	noteworthily	noteworthily	ADV
fumecheng-10953	148	7	,	,	PUNCT
fumecheng-10953	148	8	the	the	DET
fumecheng-10953	148	9	wave	wave	NOUN
fumecheng-10953	148	10	dispersion	dispersion	NOUN
fumecheng-10953	148	11	response	response	NOUN
fumecheng-10953	148	12	of	of	ADP
fumecheng-10953	148	13	the	the	DET
fumecheng-10953	148	14	nano	nano	NOUN
fumecheng-10953	148	15	-	-	PUNCT
fumecheng-10953	148	16	sized	sized	ADJ
fumecheng-10953	148	17	beam	beam	NOUN
fumecheng-10953	148	18	consistent	consistent	ADJ
fumecheng-10953	148	19	with	with	ADP
fumecheng-10953	148	20	the	the	DET
fumecheng-10953	148	21	unified	unified	ADJ
fumecheng-10953	148	22	gradient	gradient	NOUN
fumecheng-10953	148	23	theory	theory	NOUN
fumecheng-10953	148	24	is	be	AUX
fumecheng-10953	148	25	recovered	recover	VERB
fumecheng-10953	148	26	in	in	ADP
fumecheng-10953	148	27	the	the	DET
fumecheng-10953	148	28	absence	absence	NOUN
fumecheng-10953	148	29	of	of	ADP
fumecheng-10953	148	30	the	the	DET
fumecheng-10953	148	31	mixture	mixture	NOUN
fumecheng-10953	148	32	parameter	parameter	NOUN
fumecheng-10953	148	33	[	[	X
fumecheng-10953	148	34	40	40	NUM
fumecheng-10953	148	35	,	,	PUNCT
fumecheng-10953	148	36	43	43	NUM
fumecheng-10953	148	37	]	]	PUNCT
fumecheng-10953	148	38	.	.	PUNCT
fumecheng-10953	149	1	the	the	DET
fumecheng-10953	149	2	size	size	NOUN
fumecheng-10953	149	3	-	-	PUNCT
fumecheng-10953	149	4	effects	effect	NOUN
fumecheng-10953	149	5	of	of	ADP
fumecheng-10953	149	6	the	the	DET
fumecheng-10953	149	7	gradient	gradient	ADJ
fumecheng-10953	149	8	length	length	NOUN
fumecheng-10953	149	9	-	-	PUNCT
fumecheng-10953	149	10	scale	scale	NOUN
fumecheng-10953	149	11	parameters	parameter	NOUN
fumecheng-10953	149	12	on	on	ADP
fumecheng-10953	149	13	the	the	DET
fumecheng-10953	149	14	dispersive	dispersive	ADJ
fumecheng-10953	149	15	characteristics	characteristic	NOUN
fumecheng-10953	149	16	of	of	ADP
fumecheng-10953	149	17	waves	wave	NOUN
fumecheng-10953	149	18	are	be	AUX
fumecheng-10953	149	19	graphically	graphically	ADV
fumecheng-10953	149	20	illustrated	illustrate	VERB
fumecheng-10953	149	21	and	and	CCONJ
fumecheng-10953	149	22	thoroughly	thoroughly	ADV
fumecheng-10953	149	23	discussed	discuss	VERB
fumecheng-10953	149	24	here	here	ADV
fumecheng-10953	149	25	.	.	PUNCT
fumecheng-10953	150	1	for	for	ADP
fumecheng-10953	150	2	the	the	DET
fumecheng-10953	150	3	sake	sake	NOUN
fumecheng-10953	150	4	of	of	ADP
fumecheng-10953	150	5	consistency	consistency	NOUN
fumecheng-10953	150	6	,	,	PUNCT
fumecheng-10953	150	7	the	the	DET
fumecheng-10953	150	8	non	non	ADJ
fumecheng-10953	150	9	-	-	ADJ
fumecheng-10953	150	10	dimensional	dimensional	ADJ
fumecheng-10953	150	11	form	form	NOUN
fumecheng-10953	150	12	of	of	ADP
fumecheng-10953	150	13	the	the	DET
fumecheng-10953	150	14	gyration	gyration	NOUN
fumecheng-10953	150	15	radius	radius	NOUN
fumecheng-10953	150	16	,	,	PUNCT
fumecheng-10953	150	17	stress	stress	NOUN
fumecheng-10953	150	18	gradient	gradient	ADJ
fumecheng-10953	150	19	characteristic	characteristic	ADJ
fumecheng-10953	150	20	parameter	parameter	NOUN
fumecheng-10953	150	21			PROPN
fumecheng-10953	150	22	,	,	PUNCT
fumecheng-10953	150	23	strain	strain	VERB
fumecheng-10953	150	24	gradient	gradient	ADJ
fumecheng-10953	150	25	characteristic	characteristic	ADJ
fumecheng-10953	150	26	parameters	parameter	NOUN
fumecheng-10953	150	27			NUM
fumecheng-10953	150	28	,	,	PUNCT
fumecheng-10953	150	29	wave	wave	NOUN
fumecheng-10953	150	30	number	number	NOUN
fumecheng-10953	150	31			ADJ
fumecheng-10953	150	32	,	,	PUNCT
fumecheng-10953	150	33	and	and	CCONJ
fumecheng-10953	150	34	phase	phase	NOUN
fumecheng-10953	150	35	velocity	velocity	NOUN
fumecheng-10953	150	36	v	v	NOUN
fumecheng-10953	150	37	are	be	AUX
fumecheng-10953	150	38	defined	define	VERB
fumecheng-10953	150	39	as	as	ADP
fumecheng-10953	150	40	1	1	NUM
fumecheng-10953	150	41	,	,	PUNCT
fumecheng-10953	150	42	,	,	PUNCT
fumecheng-10953	150	43	,	,	PUNCT
fumecheng-10953	150	44	,	,	PUNCT
fumecheng-10953	150	45	c	c	PROPN
fumecheng-10953	150	46	s	s	X
fumecheng-10953	150	47	e	e	NOUN
fumecheng-10953	150	48	i	i	PRON
fumecheng-10953	150	49	a	a	PROPN
fumecheng-10953	150	50	l	l	NOUN
fumecheng-10953	150	51	v	v	NOUN
fumecheng-10953	151	1	vl	vl	PROPN
fumecheng-10953	151	2	l	l	PROPN
fumecheng-10953	152	1	a	a	X
fumecheng-10953	152	2	l	l	NOUN
fumecheng-10953	152	3	l	l	NOUN
fumecheng-10953	153	1	i	i	PRON
fumecheng-10953	153	2			X
fumecheng-10953	153	3			X
fumecheng-10953	153	4			X
fumecheng-10953	153	5			NOUN
fumecheng-10953	153	6			PROPN
fumecheng-10953	153	7			CCONJ
fumecheng-10953	153	8			X
fumecheng-10953	153	9	=	=	X
fumecheng-10953	153	10	=	=	SYM
fumecheng-10953	153	11	=	=	SYM
fumecheng-10953	153	12	=	=	SYM
fumecheng-10953	153	13	=	=	SYM
fumecheng-10953	153	14	(	(	PUNCT
fumecheng-10953	153	15	14	14	NUM
fumecheng-10953	153	16	)	)	PUNCT
fumecheng-10953	153	17	dynamic	dynamic	ADJ
fumecheng-10953	153	18	characteristics	characteristic	NOUN
fumecheng-10953	153	19	of	of	ADP
fumecheng-10953	153	20	mixture	mixture	NOUN
fumecheng-10953	153	21	unified	unify	VERB
fumecheng-10953	153	22	gradient	gradient	ADJ
fumecheng-10953	153	23	elastic	elastic	ADJ
fumecheng-10953	153	24	nanobeams	nanobeam	NOUN
fumecheng-10953	153	25	545	545	NUM
fumecheng-10953	153	26	3d	3d	NUM
fumecheng-10953	153	27	variation	variation	NOUN
fumecheng-10953	153	28	of	of	ADP
fumecheng-10953	153	29	the	the	DET
fumecheng-10953	153	30	non	non	ADJ
fumecheng-10953	153	31	-	-	ADJ
fumecheng-10953	153	32	dimensional	dimensional	ADJ
fumecheng-10953	153	33	phase	phase	NOUN
fumecheng-10953	153	34	velocity	velocity	NOUN
fumecheng-10953	153	35	in	in	ADP
fumecheng-10953	153	36	terms	term	NOUN
fumecheng-10953	153	37	of	of	ADP
fumecheng-10953	153	38	the	the	DET
fumecheng-10953	153	39	stress	stress	NOUN
fumecheng-10953	153	40	gradient	gradient	NOUN
fumecheng-10953	153	41	characteristic	characteristic	ADJ
fumecheng-10953	153	42	parameter	parameter	NOUN
fumecheng-10953	153	43			NOUN
fumecheng-10953	153	44	and	and	CCONJ
fumecheng-10953	153	45	the	the	DET
fumecheng-10953	153	46	strain	strain	NOUN
fumecheng-10953	153	47	gradient	gradient	ADJ
fumecheng-10953	153	48	characteristic	characteristic	ADJ
fumecheng-10953	153	49	parameters	parameter	NOUN
fumecheng-10953	153	50			NUM
fumecheng-10953	153	51	is	be	AUX
fumecheng-10953	153	52	,	,	PUNCT
fumecheng-10953	153	53	respectively	respectively	ADV
fumecheng-10953	153	54	,	,	PUNCT
fumecheng-10953	153	55	demonstrated	demonstrate	VERB
fumecheng-10953	153	56	in	in	ADP
fumecheng-10953	153	57	figs	fig	NOUN
fumecheng-10953	153	58	.	.	PUNCT
fumecheng-10953	154	1	1	1	NUM
fumecheng-10953	154	2	and	and	CCONJ
fumecheng-10953	154	3	2	2	NUM
fumecheng-10953	154	4	where	where	SCONJ
fumecheng-10953	154	5	the	the	DET
fumecheng-10953	154	6	logarithmic	logarithmic	ADJ
fumecheng-10953	154	7	scaling	scaling	NOUN
fumecheng-10953	154	8	of	of	ADP
fumecheng-10953	154	9	the	the	DET
fumecheng-10953	154	10	non	non	ADJ
fumecheng-10953	154	11	-	-	ADJ
fumecheng-10953	154	12	dimensional	dimensional	ADJ
fumecheng-10953	154	13	wave	wave	NOUN
fumecheng-10953	154	14	number	number	NOUN
fumecheng-10953	154	15			VERB
fumecheng-10953	154	16	is	be	AUX
fumecheng-10953	154	17	utilized	utilize	VERB
fumecheng-10953	154	18	[	[	PUNCT
fumecheng-10953	154	19	58	58	NUM
fumecheng-10953	154	20	]	]	PUNCT
fumecheng-10953	154	21	.	.	PUNCT
fumecheng-10953	155	1	as	as	SCONJ
fumecheng-10953	155	2	the	the	DET
fumecheng-10953	155	3	stress	stress	NOUN
fumecheng-10953	155	4	gradient	gradient	NOUN
fumecheng-10953	155	5	characteristic	characteristic	ADJ
fumecheng-10953	155	6	parameter	parameter	NOUN
fumecheng-10953	155	7	is	be	AUX
fumecheng-10953	155	8	assumed	assume	VERB
fumecheng-10953	155	9	to	to	PART
fumecheng-10953	155	10	range	range	VERB
fumecheng-10953	155	11	in	in	ADP
fumecheng-10953	155	12	the	the	DET
fumecheng-10953	155	13	interval	interval	NOUN
fumecheng-10953	155	14	[	[	X
fumecheng-10953	155	15	0,1	0,1	X
fumecheng-10953	155	16	]	]	PUNCT
fumecheng-10953	155	17	in	in	ADP
fumecheng-10953	155	18	fig	fig	NOUN
fumecheng-10953	155	19	.	.	PUNCT
fumecheng-10953	156	1	1	1	NUM
fumecheng-10953	156	2	,	,	PUNCT
fumecheng-10953	156	3	two	two	NUM
fumecheng-10953	156	4	values	value	NOUN
fumecheng-10953	156	5	of	of	ADP
fumecheng-10953	156	6	the	the	DET
fumecheng-10953	156	7	mixture	mixture	NOUN
fumecheng-10953	156	8	parameter	parameter	NOUN
fumecheng-10953	156	9			NOUN
fumecheng-10953	156	10	=	=	PUNCT
fumecheng-10953	157	1	0,1/2	0,1/2	PROPN
fumecheng-10953	157	2	are	be	AUX
fumecheng-10953	157	3	prescribed	prescribe	VERB
fumecheng-10953	157	4	for	for	ADP
fumecheng-10953	157	5	a	a	DET
fumecheng-10953	157	6	fixed	fix	VERB
fumecheng-10953	157	7	strain	strain	NOUN
fumecheng-10953	157	8	gradient	gradient	ADJ
fumecheng-10953	157	9	characteristic	characteristic	ADJ
fumecheng-10953	157	10	parameter	parameter	NOUN
fumecheng-10953	157	11			NUM
fumecheng-10953	157	12	=	=	SYM
fumecheng-10953	157	13	1/3	1/3	NUM
fumecheng-10953	157	14	.	.	PUNCT
fumecheng-10953	158	1	likewise	likewise	ADV
fumecheng-10953	158	2	in	in	ADP
fumecheng-10953	158	3	fig	fig	NOUN
fumecheng-10953	158	4	.	.	PUNCT
fumecheng-10953	159	1	2	2	NUM
fumecheng-10953	159	2	,	,	PUNCT
fumecheng-10953	159	3	the	the	DET
fumecheng-10953	159	4	strain	strain	NOUN
fumecheng-10953	159	5	gradient	gradient	ADJ
fumecheng-10953	159	6	characteristic	characteristic	ADJ
fumecheng-10953	159	7	parameter	parameter	NOUN
fumecheng-10953	159	8	is	be	AUX
fumecheng-10953	159	9	ranging	range	VERB
fumecheng-10953	159	10	in	in	ADP
fumecheng-10953	159	11	the	the	DET
fumecheng-10953	159	12	interval	interval	NOUN
fumecheng-10953	159	13	[	[	X
fumecheng-10953	159	14	0,1	0,1	X
fumecheng-10953	159	15	]	]	PUNCT
fumecheng-10953	159	16	while	while	SCONJ
fumecheng-10953	159	17	two	two	NUM
fumecheng-10953	159	18	values	value	NOUN
fumecheng-10953	159	19	of	of	ADP
fumecheng-10953	159	20	the	the	DET
fumecheng-10953	159	21	mixture	mixture	NOUN
fumecheng-10953	159	22	parameter	parameter	NOUN
fumecheng-10953	159	23			NOUN
fumecheng-10953	159	24	=	=	PUNCT
fumecheng-10953	159	25	0,1/2	0,1/2	NUM
fumecheng-10953	159	26	are	be	AUX
fumecheng-10953	159	27	applied	apply	VERB
fumecheng-10953	159	28	for	for	ADP
fumecheng-10953	159	29	a	a	DET
fumecheng-10953	159	30	prescribed	prescribed	ADJ
fumecheng-10953	159	31	value	value	NOUN
fumecheng-10953	159	32	of	of	ADP
fumecheng-10953	159	33	the	the	DET
fumecheng-10953	159	34	stress	stress	NOUN
fumecheng-10953	159	35	gradient	gradient	NOUN
fumecheng-10953	159	36	characteristic	characteristic	ADJ
fumecheng-10953	159	37	parameter	parameter	NOUN
fumecheng-10953	160	1			NOUN
fumecheng-10953	160	2	=	=	SYM
fumecheng-10953	160	3	1/3	1/3	NUM
fumecheng-10953	160	4	.	.	PUNCT
fumecheng-10953	161	1	in	in	ADP
fumecheng-10953	161	2	all	all	DET
fumecheng-10953	161	3	the	the	DET
fumecheng-10953	161	4	numerical	numerical	ADJ
fumecheng-10953	161	5	illustrations	illustration	NOUN
fumecheng-10953	161	6	of	of	ADP
fumecheng-10953	161	7	the	the	DET
fumecheng-10953	161	8	wave	wave	NOUN
fumecheng-10953	161	9	dispersion	dispersion	NOUN
fumecheng-10953	161	10	,	,	PUNCT
fumecheng-10953	161	11	the	the	DET
fumecheng-10953	161	12	(	(	PUNCT
fumecheng-10953	161	13	logarithm	logarithm	NOUN
fumecheng-10953	161	14	of	of	ADP
fumecheng-10953	161	15	)	)	PUNCT
fumecheng-10953	161	16	non	non	ADJ
fumecheng-10953	161	17	-	-	ADJ
fumecheng-10953	161	18	dimensional	dimensional	ADJ
fumecheng-10953	161	19	wave	wave	NOUN
fumecheng-10953	161	20	number	number	NOUN
fumecheng-10953	161	21			X
fumecheng-10953	161	22	is	be	AUX
fumecheng-10953	161	23	ranging	range	VERB
fumecheng-10953	161	24	in	in	ADP
fumecheng-10953	161	25	the	the	DET
fumecheng-10953	161	26	interval	interval	NOUN
fumecheng-10953	161	27	[	[	X
fumecheng-10953	161	28	10−1,10	10−1,10	NUM
fumecheng-10953	161	29	+	+	NOUN
fumecheng-10953	161	30	1	1	NUM
fumecheng-10953	161	31	]	]	PUNCT
fumecheng-10953	161	32	.	.	PUNCT
fumecheng-10953	162	1	the	the	DET
fumecheng-10953	162	2	non	non	ADJ
fumecheng-10953	162	3	-	-	ADJ
fumecheng-10953	162	4	dimensional	dimensional	ADJ
fumecheng-10953	162	5	gyration	gyration	NOUN
fumecheng-10953	162	6	radius	radius	NOUN
fumecheng-10953	162	7	is	be	AUX
fumecheng-10953	162	8	,	,	PUNCT
fumecheng-10953	162	9	moreover	moreover	ADV
fumecheng-10953	162	10	,	,	PUNCT
fumecheng-10953	162	11	prescribed	prescribe	VERB
fumecheng-10953	162	12	as	as	ADP
fumecheng-10953	162	13	1/	1/	NUM
fumecheng-10953	162	14	20	20	NUM
fumecheng-10953	162	15	=	=	SYM
fumecheng-10953	162	16	.	.	PUNCT
fumecheng-10953	163	1	as	as	SCONJ
fumecheng-10953	163	2	deducible	deducible	ADJ
fumecheng-10953	163	3	from	from	ADP
fumecheng-10953	163	4	the	the	DET
fumecheng-10953	163	5	numerical	numerical	ADJ
fumecheng-10953	163	6	illustration	illustration	NOUN
fumecheng-10953	163	7	in	in	ADP
fumecheng-10953	163	8	fig	fig	NOUN
fumecheng-10953	163	9	.	.	PUNCT
fumecheng-10953	164	1	1	1	NUM
fumecheng-10953	164	2	,	,	PUNCT
fumecheng-10953	164	3	a	a	DET
fumecheng-10953	164	4	larger	large	ADJ
fumecheng-10953	164	5	value	value	NOUN
fumecheng-10953	164	6	of	of	ADP
fumecheng-10953	164	7	the	the	DET
fumecheng-10953	164	8	stress	stress	NOUN
fumecheng-10953	164	9	gradient	gradient	NOUN
fumecheng-10953	164	10	parameter	parameter	PROPN
fumecheng-10953	164	11	involves	involve	VERB
fumecheng-10953	164	12	a	a	DET
fumecheng-10953	164	13	smaller	small	ADJ
fumecheng-10953	164	14	value	value	NOUN
fumecheng-10953	164	15	of	of	ADP
fumecheng-10953	164	16	the	the	DET
fumecheng-10953	164	17	phase	phase	NOUN
fumecheng-10953	164	18	velocity	velocity	NOUN
fumecheng-10953	164	19	.	.	PUNCT
fumecheng-10953	165	1	the	the	DET
fumecheng-10953	165	2	phase	phase	NOUN
fumecheng-10953	165	3	velocity	velocity	NOUN
fumecheng-10953	165	4	of	of	ADP
fumecheng-10953	165	5	dispersive	dispersive	ADJ
fumecheng-10953	165	6	waves	wave	NOUN
fumecheng-10953	165	7	,	,	PUNCT
fumecheng-10953	165	8	therefore	therefore	ADV
fumecheng-10953	165	9	,	,	PUNCT
fumecheng-10953	165	10	reveals	reveal	VERB
fumecheng-10953	165	11	a	a	DET
fumecheng-10953	165	12	softening	soften	VERB
fumecheng-10953	165	13	response	response	NOUN
fumecheng-10953	165	14	in	in	ADP
fumecheng-10953	165	15	terms	term	NOUN
fumecheng-10953	165	16	of	of	ADP
fumecheng-10953	165	17	the	the	DET
fumecheng-10953	165	18	stress	stress	NOUN
fumecheng-10953	165	19	gradient	gradient	NOUN
fumecheng-10953	165	20	characteristic	characteristic	ADJ
fumecheng-10953	165	21	parameter	parameter	NOUN
fumecheng-10953	165	22	.	.	X
fumecheng-10953	165	23	contrarily	contrarily	ADV
fumecheng-10953	165	24	as	as	SCONJ
fumecheng-10953	165	25	demonstrated	demonstrate	VERB
fumecheng-10953	165	26	in	in	ADP
fumecheng-10953	165	27	fig	fig	NOUN
fumecheng-10953	165	28	.	.	PUNCT
fumecheng-10953	166	1	2	2	NUM
fumecheng-10953	166	2	,	,	PUNCT
fumecheng-10953	166	3	the	the	DET
fumecheng-10953	166	4	phase	phase	NOUN
fumecheng-10953	166	5	velocity	velocity	NOUN
fumecheng-10953	166	6	associated	associate	VERB
fumecheng-10953	166	7	with	with	ADP
fumecheng-10953	166	8	waves	wave	NOUN
fumecheng-10953	166	9	disperse	disperse	VERB
fumecheng-10953	166	10	in	in	ADP
fumecheng-10953	166	11	the	the	DET
fumecheng-10953	166	12	mixture	mixture	NOUN
fumecheng-10953	166	13	unified	unify	VERB
fumecheng-10953	166	14	gradient	gradient	ADJ
fumecheng-10953	166	15	elastic	elastic	ADJ
fumecheng-10953	166	16	beam	beam	NOUN
fumecheng-10953	166	17	increases	increase	NOUN
fumecheng-10953	166	18	by	by	ADP
fumecheng-10953	166	19	increasing	increase	VERB
fumecheng-10953	166	20	the	the	DET
fumecheng-10953	166	21	strain	strain	NOUN
fumecheng-10953	166	22	gradient	gradient	NOUN
fumecheng-10953	166	23	parameter	parameter	NOUN
fumecheng-10953	166	24			NUM
fumecheng-10953	166	25	,	,	PUNCT
fumecheng-10953	166	26	and	and	CCONJ
fumecheng-10953	166	27	accordingly	accordingly	ADV
fumecheng-10953	166	28	,	,	PUNCT
fumecheng-10953	166	29	a	a	DET
fumecheng-10953	166	30	stiffening	stiffen	VERB
fumecheng-10953	166	31	behavior	behavior	NOUN
fumecheng-10953	166	32	in	in	ADP
fumecheng-10953	166	33	terms	term	NOUN
fumecheng-10953	166	34	of	of	ADP
fumecheng-10953	166	35	the	the	DET
fumecheng-10953	166	36	strain	strain	NOUN
fumecheng-10953	166	37	gradient	gradient	ADJ
fumecheng-10953	166	38	characteristic	characteristic	ADJ
fumecheng-10953	166	39	parameter	parameter	NOUN
fumecheng-10953	166	40			NUM
fumecheng-10953	166	41	is	be	AUX
fumecheng-10953	166	42	observed	observe	VERB
fumecheng-10953	166	43	.	.	PUNCT
fumecheng-10953	167	1	the	the	DET
fumecheng-10953	167	2	effect	effect	NOUN
fumecheng-10953	167	3	of	of	ADP
fumecheng-10953	167	4	the	the	DET
fumecheng-10953	167	5	stress	stress	NOUN
fumecheng-10953	167	6	gradient	gradient	NOUN
fumecheng-10953	167	7	theory	theory	NOUN
fumecheng-10953	167	8	in	in	ADP
fumecheng-10953	167	9	the	the	DET
fumecheng-10953	167	10	mixture	mixture	NOUN
fumecheng-10953	167	11	unified	unify	VERB
fumecheng-10953	167	12	gradient	gradient	NOUN
fumecheng-10953	167	13	elasticity	elasticity	NOUN
fumecheng-10953	167	14	is	be	AUX
fumecheng-10953	167	15	continuously	continuously	ADV
fumecheng-10953	167	16	reinstated	reinstate	VERB
fumecheng-10953	167	17	with	with	ADP
fumecheng-10953	167	18	the	the	DET
fumecheng-10953	167	19	classical	classical	ADJ
fumecheng-10953	167	20	elasticity	elasticity	NOUN
fumecheng-10953	167	21	theory	theory	NOUN
fumecheng-10953	167	22	as	as	SCONJ
fumecheng-10953	167	23	the	the	DET
fumecheng-10953	167	24	mixture	mixture	NOUN
fumecheng-10953	167	25	parameter	parameter	NOUN
fumecheng-10953	167	26			NOUN
fumecheng-10953	167	27	varies	vary	VERB
fumecheng-10953	167	28	from	from	ADP
fumecheng-10953	167	29	0	0	NUM
fumecheng-10953	167	30	to	to	ADP
fumecheng-10953	167	31	1	1	NUM
fumecheng-10953	167	32	.	.	PUNCT
fumecheng-10953	168	1	a	a	DET
fumecheng-10953	168	2	stiffening	stiffen	VERB
fumecheng-10953	168	3	behavior	behavior	NOUN
fumecheng-10953	168	4	in	in	ADP
fumecheng-10953	168	5	terms	term	NOUN
fumecheng-10953	168	6	of	of	ADP
fumecheng-10953	168	7	the	the	DET
fumecheng-10953	168	8	mixture	mixture	NOUN
fumecheng-10953	168	9	parameter	parameter	NOUN
fumecheng-10953	168	10			NOUN
fumecheng-10953	168	11	is	be	AUX
fumecheng-10953	168	12	,	,	PUNCT
fumecheng-10953	168	13	thus	thus	ADV
fumecheng-10953	168	14	,	,	PUNCT
fumecheng-10953	168	15	realized	realize	VERB
fumecheng-10953	168	16	as	as	SCONJ
fumecheng-10953	168	17	the	the	DET
fumecheng-10953	168	18	phase	phase	NOUN
fumecheng-10953	168	19	velocity	velocity	NOUN
fumecheng-10953	168	20	of	of	ADP
fumecheng-10953	168	21	dispersive	dispersive	ADJ
fumecheng-10953	168	22	waves	wave	NOUN
fumecheng-10953	168	23	increases	increase	VERB
fumecheng-10953	168	24	with	with	ADP
fumecheng-10953	168	25	increasing	increase	VERB
fumecheng-10953	168	26	the	the	DET
fumecheng-10953	168	27	mixture	mixture	NOUN
fumecheng-10953	168	28	parameter	parameter	NOUN
fumecheng-10953	168	29	.	.	PROPN
fumecheng-10953	169	1	the	the	DET
fumecheng-10953	169	2	phase	phase	NOUN
fumecheng-10953	169	3	velocity	velocity	NOUN
fumecheng-10953	169	4	detected	detect	VERB
fumecheng-10953	169	5	within	within	ADP
fumecheng-10953	169	6	the	the	DET
fumecheng-10953	169	7	framework	framework	NOUN
fumecheng-10953	169	8	of	of	ADP
fumecheng-10953	169	9	the	the	DET
fumecheng-10953	169	10	mixture	mixture	NOUN
fumecheng-10953	169	11	unified	unify	VERB
fumecheng-10953	169	12	gradient	gradient	NOUN
fumecheng-10953	169	13	elasticity	elasticity	NOUN
fumecheng-10953	169	14	is	be	AUX
fumecheng-10953	169	15	observed	observe	VERB
fumecheng-10953	169	16	to	to	PART
fumecheng-10953	169	17	remain	remain	VERB
fumecheng-10953	169	18	unaffected	unaffected	ADJ
fumecheng-10953	169	19	for	for	ADP
fumecheng-10953	169	20	low	low	ADJ
fumecheng-10953	169	21	wave	wave	NOUN
fumecheng-10953	169	22	numbers	number	NOUN
fumecheng-10953	169	23	.	.	PUNCT
fumecheng-10953	170	1	this	this	DET
fumecheng-10953	170	2	phenomenon	phenomenon	NOUN
fumecheng-10953	170	3	is	be	AUX
fumecheng-10953	170	4	in	in	ADP
fumecheng-10953	170	5	complete	complete	ADJ
fumecheng-10953	170	6	agreement	agreement	NOUN
fumecheng-10953	170	7	with	with	ADP
fumecheng-10953	170	8	the	the	DET
fumecheng-10953	170	9	fact	fact	NOUN
fumecheng-10953	170	10	that	that	SCONJ
fumecheng-10953	170	11	the	the	DET
fumecheng-10953	170	12	dispersive	dispersive	ADJ
fumecheng-10953	170	13	behavior	behavior	NOUN
fumecheng-10953	170	14	of	of	ADP
fumecheng-10953	170	15	flexural	flexural	ADJ
fumecheng-10953	170	16	waves	wave	NOUN
fumecheng-10953	170	17	is	be	AUX
fumecheng-10953	170	18	insensitive	insensitive	ADJ
fumecheng-10953	170	19	to	to	ADP
fumecheng-10953	170	20	the	the	DET
fumecheng-10953	170	21	physical	physical	ADJ
fumecheng-10953	170	22	characteristics	characteristic	NOUN
fumecheng-10953	170	23	for	for	ADP
fumecheng-10953	170	24	large	large	ADJ
fumecheng-10953	170	25	wavelengths	wavelength	NOUN
fumecheng-10953	170	26	.	.	PUNCT
fumecheng-10953	171	1	accordingly	accordingly	ADV
fumecheng-10953	171	2	,	,	PUNCT
fumecheng-10953	171	3	effects	effect	NOUN
fumecheng-10953	171	4	of	of	ADP
fumecheng-10953	171	5	the	the	DET
fumecheng-10953	171	6	gradient	gradient	ADJ
fumecheng-10953	171	7	characteristic	characteristic	ADJ
fumecheng-10953	171	8	parameters	parameter	NOUN
fumecheng-10953	171	9	on	on	ADP
fumecheng-10953	171	10	the	the	DET
fumecheng-10953	171	11	wave	wave	NOUN
fumecheng-10953	171	12	dispersion	dispersion	NOUN
fumecheng-10953	171	13	response	response	NOUN
fumecheng-10953	171	14	are	be	AUX
fumecheng-10953	171	15	significantly	significantly	ADV
fumecheng-10953	171	16	enhanced	enhance	VERB
fumecheng-10953	171	17	at	at	ADP
fumecheng-10953	171	18	higher	high	ADJ
fumecheng-10953	171	19	wave	wave	NOUN
fumecheng-10953	171	20	numbers	number	NOUN
fumecheng-10953	171	21	.	.	PUNCT
fumecheng-10953	172	1	the	the	DET
fumecheng-10953	172	2	classical	classical	ADJ
fumecheng-10953	172	3	dispersion	dispersion	NOUN
fumecheng-10953	172	4	relation	relation	NOUN
fumecheng-10953	172	5	of	of	ADP
fumecheng-10953	172	6	the	the	DET
fumecheng-10953	172	7	phase	phase	NOUN
fumecheng-10953	172	8	velocity	velocity	NOUN
fumecheng-10953	172	9	is	be	AUX
fumecheng-10953	172	10	,	,	PUNCT
fumecheng-10953	172	11	also	also	ADV
fumecheng-10953	172	12	,	,	PUNCT
fumecheng-10953	172	13	recovered	recover	VERB
fumecheng-10953	172	14	as	as	SCONJ
fumecheng-10953	172	15	the	the	DET
fumecheng-10953	172	16	gradient	gradient	ADJ
fumecheng-10953	172	17	characteristic	characteristic	ADJ
fumecheng-10953	172	18	parameters	parameter	NOUN
fumecheng-10953	172	19	tend	tend	VERB
fumecheng-10953	172	20	to	to	ADP
fumecheng-10953	172	21	zero	zero	NUM
fumecheng-10953	172	22	,	,	PUNCT
fumecheng-10953	172	23	or	or	CCONJ
fumecheng-10953	172	24	alternatively	alternatively	ADV
fumecheng-10953	172	25	,	,	PUNCT
fumecheng-10953	172	26	as	as	SCONJ
fumecheng-10953	172	27	the	the	DET
fumecheng-10953	172	28	mixture	mixture	NOUN
fumecheng-10953	172	29	parameter	parameter	NOUN
fumecheng-10953	172	30	approaches	approach	VERB
fumecheng-10953	172	31	unity	unity	NOUN
fumecheng-10953	172	32	in	in	ADP
fumecheng-10953	172	33	the	the	DET
fumecheng-10953	172	34	absence	absence	NOUN
fumecheng-10953	172	35	of	of	ADP
fumecheng-10953	172	36	the	the	DET
fumecheng-10953	172	37	strain	strain	NOUN
fumecheng-10953	172	38	gradient	gradient	ADJ
fumecheng-10953	172	39	characteristic	characteristic	ADJ
fumecheng-10953	172	40	parameter	parameter	NOUN
fumecheng-10953	172	41	.	.	PUNCT
fumecheng-10953	173	1	fig	fig	NOUN
fumecheng-10953	173	2	.	.	PUNCT
fumecheng-10953	174	1	1	1	NUM
fumecheng-10953	174	2	wave	wave	NOUN
fumecheng-10953	174	3	dispersion	dispersion	NOUN
fumecheng-10953	174	4	response	response	NOUN
fumecheng-10953	174	5	by	by	ADP
fumecheng-10953	174	6	the	the	DET
fumecheng-10953	174	7	mixture	mixture	NOUN
fumecheng-10953	174	8	unified	unify	VERB
fumecheng-10953	174	9	gradient	gradient	NOUN
fumecheng-10953	174	10	theory	theory	NOUN
fumecheng-10953	174	11	:	:	PUNCT
fumecheng-10953	174	12	v	v	X
fumecheng-10953	174	13	vs.	vs.	X
fumecheng-10953	174	14			NOUN
fumecheng-10953	174	15	for	for	ADP
fumecheng-10953	174	16			NUM
fumecheng-10953	174	17	=	=	SYM
fumecheng-10953	174	18	1/3	1/3	NUM
fumecheng-10953	174	19	and	and	CCONJ
fumecheng-10953	174	20			NOUN
fumecheng-10953	174	21	=	=	PUNCT
fumecheng-10953	175	1	0,1/2	0,1/2	PROPN
fumecheng-10953	175	2	546	546	NUM
fumecheng-10953	175	3	s.	s.	PROPN
fumecheng-10953	175	4	a.	a.	PROPN
fumecheng-10953	175	5	faghidian	faghidian	PROPN
fumecheng-10953	175	6	,	,	PUNCT
fumecheng-10953	175	7	a.	a.	NOUN
fumecheng-10953	175	8	tounsi	tounsi	NOUN
fumecheng-10953	175	9	fig	fig	NOUN
fumecheng-10953	175	10	.	.	PUNCT
fumecheng-10953	176	1	2	2	NUM
fumecheng-10953	176	2	wave	wave	NOUN
fumecheng-10953	176	3	dispersion	dispersion	NOUN
fumecheng-10953	176	4	response	response	NOUN
fumecheng-10953	176	5	by	by	ADP
fumecheng-10953	176	6	the	the	DET
fumecheng-10953	176	7	mixture	mixture	NOUN
fumecheng-10953	176	8	unified	unify	VERB
fumecheng-10953	176	9	gradient	gradient	NOUN
fumecheng-10953	176	10	theory	theory	NOUN
fumecheng-10953	176	11	:	:	PUNCT
fumecheng-10953	176	12	v	v	NOUN
fumecheng-10953	176	13	vs.	vs.	X
fumecheng-10953	176	14			PUNCT
fumecheng-10953	176	15	for	for	ADP
fumecheng-10953	176	16			NOUN
fumecheng-10953	177	1	=	=	SYM
fumecheng-10953	177	2	1/3	1/3	NUM
fumecheng-10953	177	3	and	and	CCONJ
fumecheng-10953	177	4			NOUN
fumecheng-10953	177	5	=	=	PUNCT
fumecheng-10953	177	6	0,1/2	0,1/2	NUM
fumecheng-10953	177	7	4	4	NUM
fumecheng-10953	177	8	.	.	PUNCT
fumecheng-10953	177	9	free	free	ADJ
fumecheng-10953	177	10	vibrations	vibration	NOUN
fumecheng-10953	177	11	characteristics	characteristic	NOUN
fumecheng-10953	177	12	the	the	DET
fumecheng-10953	177	13	differential	differential	ADJ
fumecheng-10953	177	14	condition	condition	NOUN
fumecheng-10953	177	15	of	of	ADP
fumecheng-10953	177	16	dynamic	dynamic	ADJ
fumecheng-10953	177	17	equilibrium	equilibrium	NOUN
fumecheng-10953	177	18	governing	govern	VERB
fumecheng-10953	177	19	the	the	DET
fumecheng-10953	177	20	free	free	ADJ
fumecheng-10953	177	21	vibrations	vibration	NOUN
fumecheng-10953	177	22	of	of	ADP
fumecheng-10953	177	23	a	a	DET
fumecheng-10953	177	24	mixture	mixture	NOUN
fumecheng-10953	177	25	unified	unify	VERB
fumecheng-10953	177	26	gradient	gradient	ADJ
fumecheng-10953	177	27	elastic	elastic	ADJ
fumecheng-10953	177	28	beam	beam	NOUN
fumecheng-10953	177	29	is	be	AUX
fumecheng-10953	177	30	the	the	DET
fumecheng-10953	177	31	same	same	ADJ
fumecheng-10953	177	32	as	as	ADP
fumecheng-10953	177	33	differential	differential	ADJ
fumecheng-10953	177	34	equation	equation	NOUN
fumecheng-10953	177	35	addressed	address	VERB
fumecheng-10953	177	36	in	in	ADP
fumecheng-10953	177	37	eq	eq	ADP
fumecheng-10953	177	38	.	.	PUNCT
fumecheng-10953	178	1	(	(	PUNCT
fumecheng-10953	178	2	11	11	NUM
fumecheng-10953	178	3	)	)	PUNCT
fumecheng-10953	178	4	and	and	CCONJ
fumecheng-10953	178	5	can	can	AUX
fumecheng-10953	178	6	be	be	AUX
fumecheng-10953	178	7	detected	detect	VERB
fumecheng-10953	178	8	employing	employ	VERB
fumecheng-10953	178	9	literally	literally	ADV
fumecheng-10953	178	10	the	the	DET
fumecheng-10953	178	11	same	same	ADJ
fumecheng-10953	178	12	approach	approach	NOUN
fumecheng-10953	178	13	.	.	PUNCT
fumecheng-10953	179	1	nevertheless	nevertheless	ADV
fumecheng-10953	179	2	,	,	PUNCT
fumecheng-10953	179	3	the	the	DET
fumecheng-10953	179	4	boundary	boundary	ADJ
fumecheng-10953	179	5	-	-	PUNCT
fumecheng-10953	179	6	value	value	NOUN
fumecheng-10953	179	7	problem	problem	NOUN
fumecheng-10953	179	8	of	of	ADP
fumecheng-10953	179	9	free	free	ADJ
fumecheng-10953	179	10	vibrations	vibration	NOUN
fumecheng-10953	179	11	of	of	ADP
fumecheng-10953	179	12	elastic	elastic	ADJ
fumecheng-10953	179	13	nanobeams	nanobeam	NOUN
fumecheng-10953	179	14	is	be	AUX
fumecheng-10953	179	15	defined	define	VERB
fumecheng-10953	179	16	on	on	ADP
fumecheng-10953	179	17	bounded	bounded	ADJ
fumecheng-10953	179	18	structural	structural	ADJ
fumecheng-10953	179	19	domains	domain	NOUN
fumecheng-10953	179	20	,	,	PUNCT
fumecheng-10953	179	21	and	and	CCONJ
fumecheng-10953	179	22	accordingly	accordingly	ADV
fumecheng-10953	179	23	,	,	PUNCT
fumecheng-10953	179	24	the	the	DET
fumecheng-10953	179	25	governing	govern	VERB
fumecheng-10953	179	26	differential	differential	ADJ
fumecheng-10953	179	27	equation	equation	NOUN
fumecheng-10953	179	28	of	of	ADP
fumecheng-10953	179	29	dynamic	dynamic	ADJ
fumecheng-10953	179	30	equilibrium	equilibrium	NOUN
fumecheng-10953	179	31	is	be	AUX
fumecheng-10953	179	32	subject	subject	ADJ
fumecheng-10953	179	33	to	to	ADP
fumecheng-10953	179	34	the	the	DET
fumecheng-10953	179	35	classical	classical	NOUN
fumecheng-10953	179	36	and	and	CCONJ
fumecheng-10953	179	37	the	the	DET
fumecheng-10953	179	38	extra	extra	ADJ
fumecheng-10953	179	39	non	non	ADJ
fumecheng-10953	179	40	-	-	ADJ
fumecheng-10953	179	41	standard	standard	ADJ
fumecheng-10953	179	42	boundary	boundary	ADJ
fumecheng-10953	179	43	conditions	condition	NOUN
fumecheng-10953	179	44	as	as	SCONJ
fumecheng-10953	179	45	expressed	express	VERB
fumecheng-10953	179	46	by	by	ADP
fumecheng-10953	179	47	eq	eq	PROPN
fumecheng-10953	179	48	.	.	PUNCT
fumecheng-10953	180	1	(	(	PUNCT
fumecheng-10953	180	2	7)2	7)2	PROPN
fumecheng-10953	180	3	-	-	SYM
fumecheng-10953	180	4	3	3	NUM
fumecheng-10953	180	5	.	.	PUNCT
fumecheng-10953	181	1	the	the	DET
fumecheng-10953	181	2	standard	standard	ADJ
fumecheng-10953	181	3	procedure	procedure	NOUN
fumecheng-10953	181	4	of	of	ADP
fumecheng-10953	181	5	separating	separate	VERB
fumecheng-10953	181	6	spatial	spatial	ADJ
fumecheng-10953	181	7	and	and	CCONJ
fumecheng-10953	181	8	time	time	NOUN
fumecheng-10953	181	9	variables	variable	NOUN
fumecheng-10953	181	10	is	be	AUX
fumecheng-10953	181	11	employed	employ	VERB
fumecheng-10953	181	12	to	to	PART
fumecheng-10953	181	13	analyze	analyze	VERB
fumecheng-10953	181	14	the	the	DET
fumecheng-10953	181	15	free	free	ADJ
fumecheng-10953	181	16	vibrations	vibration	NOUN
fumecheng-10953	181	17	of	of	ADP
fumecheng-10953	181	18	elastic	elastic	ADJ
fumecheng-10953	181	19	nanobeams	nanobeam	NOUN
fumecheng-10953	181	20	,	,	PUNCT
fumecheng-10953	181	21	namely	namely	ADV
fumecheng-10953	181	22	,	,	PUNCT
fumecheng-10953	181	23	(	(	PUNCT
fumecheng-10953	181	24	,	,	PUNCT
fumecheng-10953	181	25	)	)	PUNCT
fumecheng-10953	181	26	(	(	PUNCT
fumecheng-10953	181	27	)	)	PUNCT
fumecheng-10953	181	28	exp	exp	NOUN
fumecheng-10953	181	29	(	(	PUNCT
fumecheng-10953	181	30	)	)	PUNCT
fumecheng-10953	181	31	w	w	NOUN
fumecheng-10953	181	32	x	x	SYM
fumecheng-10953	181	33	t	t	NOUN
fumecheng-10953	181	34	x	x	PUNCT
fumecheng-10953	181	35	i	i	PRON
fumecheng-10953	181	36	t=	t=	VERB
fumecheng-10953	181	37	(	(	PUNCT
fumecheng-10953	181	38	15	15	NUM
fumecheng-10953	181	39	)	)	PUNCT
fumecheng-10953	181	40	with	with	ADP
fumecheng-10953	181	41	and	and	NOUN
fumecheng-10953	181	42	,	,	PUNCT
fumecheng-10953	181	43	respectively	respectively	ADV
fumecheng-10953	181	44	,	,	PUNCT
fumecheng-10953	181	45	denoting	denote	VERB
fumecheng-10953	181	46	the	the	DET
fumecheng-10953	181	47	spatial	spatial	ADJ
fumecheng-10953	181	48	mode	mode	NOUN
fumecheng-10953	181	49	shape	shape	NOUN
fumecheng-10953	181	50	and	and	CCONJ
fumecheng-10953	181	51	the	the	DET
fumecheng-10953	181	52	natural	natural	ADJ
fumecheng-10953	181	53	frequency	frequency	NOUN
fumecheng-10953	181	54	of	of	ADP
fumecheng-10953	181	55	free	free	ADJ
fumecheng-10953	181	56	vibrations	vibration	NOUN
fumecheng-10953	181	57	.	.	PUNCT
fumecheng-10953	182	1	prescribing	prescribe	VERB
fumecheng-10953	182	2	the	the	DET
fumecheng-10953	182	3	separation	separation	NOUN
fumecheng-10953	182	4	of	of	ADP
fumecheng-10953	182	5	variables	variable	NOUN
fumecheng-10953	182	6	eq	eq	ADP
fumecheng-10953	182	7	.	.	PUNCT
fumecheng-10953	183	1	(	(	PUNCT
fumecheng-10953	183	2	15	15	NUM
fumecheng-10953	183	3	)	)	PUNCT
fumecheng-10953	183	4	to	to	ADP
fumecheng-10953	183	5	the	the	DET
fumecheng-10953	183	6	differential	differential	ADJ
fumecheng-10953	183	7	condition	condition	NOUN
fumecheng-10953	183	8	of	of	ADP
fumecheng-10953	183	9	dynamic	dynamic	ADJ
fumecheng-10953	183	10	equilibrium	equilibrium	NOUN
fumecheng-10953	183	11	eq	eq	ADP
fumecheng-10953	183	12	.	.	PUNCT
fumecheng-10953	184	1	(	(	PUNCT
fumecheng-10953	184	2	11	11	NUM
fumecheng-10953	184	3	)	)	PUNCT
fumecheng-10953	184	4	,	,	PUNCT
fumecheng-10953	184	5	the	the	DET
fumecheng-10953	184	6	governing	govern	VERB
fumecheng-10953	184	7	equation	equation	NOUN
fumecheng-10953	184	8	on	on	ADP
fumecheng-10953	184	9	the	the	DET
fumecheng-10953	184	10	spatial	spatial	ADJ
fumecheng-10953	184	11	mode	mode	NOUN
fumecheng-10953	184	12	shape	shape	NOUN
fumecheng-10953	184	13	is	be	AUX
fumecheng-10953	184	14	detected	detect	VERB
fumecheng-10953	184	15	as	as	ADP
fumecheng-10953	184	16	2	2	NUM
fumecheng-10953	184	17	2	2	NUM
fumecheng-10953	184	18	2	2	NUM
fumecheng-10953	184	19	2	2	NUM
fumecheng-10953	184	20	2	2	NUM
fumecheng-10953	184	21	2	2	NUM
fumecheng-10953	184	22	2	2	NUM
fumecheng-10953	184	23	2	2	NUM
fumecheng-10953	184	24	(	(	PUNCT
fumecheng-10953	184	25	)	)	PUNCT
fumecheng-10953	184	26	(	(	PUNCT
fumecheng-10953	184	27	)	)	PUNCT
fumecheng-10953	184	28	(	(	PUNCT
fumecheng-10953	184	29	)	)	PUNCT
fumecheng-10953	184	30	(	(	PUNCT
fumecheng-10953	184	31	)	)	PUNCT
fumecheng-10953	184	32	(	(	PUNCT
fumecheng-10953	184	33	)	)	PUNCT
fumecheng-10953	184	34	(	(	PUNCT
fumecheng-10953	184	35	)	)	PUNCT
fumecheng-10953	184	36	(	(	PUNCT
fumecheng-10953	184	37	)	)	PUNCT
fumecheng-10953	184	38	0	0	PUNCT
fumecheng-10953	185	1	e	e	X
fumecheng-10953	185	2	c	c	PROPN
fumecheng-10953	185	3	s	s	X
fumecheng-10953	185	4	xxxxxx	xxxxxx	PROPN
fumecheng-10953	185	5	e	e	PROPN
fumecheng-10953	185	6	c	c	PROPN
fumecheng-10953	185	7	xxxx	xxxx	PROPN
fumecheng-10953	186	1	c	c	NOUN
fumecheng-10953	186	2	xx	xx	INTJ
fumecheng-10953	187	1	i	i	INTJ
fumecheng-10953	187	2	x	x	VERB
fumecheng-10953	188	1	i	i	PRON
fumecheng-10953	188	2	i	i	VERB
fumecheng-10953	188	3	x	x	VERB
fumecheng-10953	188	4	a	a	PRON
fumecheng-10953	188	5	i	i	NOUN
fumecheng-10953	188	6	x	x	SYM
fumecheng-10953	188	7	a	a	PRON
fumecheng-10953	188	8	x	x	X
fumecheng-10953	188	9			ADP
fumecheng-10953	188	10			ADP
fumecheng-10953	188	11			X
fumecheng-10953	188	12			ADP
fumecheng-10953	188	13			X
fumecheng-10953	188	14			X
fumecheng-10953	188	15			X
fumecheng-10953	188	16			X
fumecheng-10953	188	17	−	−	NOUN
fumecheng-10953	188	18			NOUN
fumecheng-10953	188	19	+	+	CCONJ
fumecheng-10953	188	20			ADJ
fumecheng-10953	188	21	+	+	CCONJ
fumecheng-10953	188	22	−	−	PROPN
fumecheng-10953	188	23			ADJ
fumecheng-10953	188	24	+	+	SYM
fumecheng-10953	188	25	+	+	NUM
fumecheng-10953	188	26			ADJ
fumecheng-10953	188	27	−	−	PROPN
fumecheng-10953	188	28	=	=	SYM
fumecheng-10953	188	29	(	(	PUNCT
fumecheng-10953	188	30	16	16	NUM
fumecheng-10953	188	31	)	)	PUNCT
fumecheng-10953	188	32	the	the	DET
fumecheng-10953	188	33	analytical	analytical	ADJ
fumecheng-10953	188	34	solution	solution	NOUN
fumecheng-10953	188	35	of	of	ADP
fumecheng-10953	188	36	the	the	DET
fumecheng-10953	188	37	preceding	precede	VERB
fumecheng-10953	188	38	differential	differential	ADJ
fumecheng-10953	188	39	equation	equation	NOUN
fumecheng-10953	188	40	for	for	ADP
fumecheng-10953	188	41	the	the	DET
fumecheng-10953	188	42	spatial	spatial	ADJ
fumecheng-10953	188	43	mode	mode	NOUN
fumecheng-10953	188	44	shape	shape	NOUN
fumecheng-10953	188	45	can	can	AUX
fumecheng-10953	188	46	be	be	AUX
fumecheng-10953	188	47	cast	cast	VERB
fumecheng-10953	188	48	in	in	ADP
fumecheng-10953	188	49	the	the	DET
fumecheng-10953	188	50	form	form	NOUN
fumecheng-10953	188	51	1	1	NUM
fumecheng-10953	188	52	1	1	NUM
fumecheng-10953	188	53	2	2	NUM
fumecheng-10953	188	54	2	2	NUM
fumecheng-10953	188	55	3	3	NUM
fumecheng-10953	188	56	3	3	NUM
fumecheng-10953	188	57	4	4	NUM
fumecheng-10953	188	58	4	4	NUM
fumecheng-10953	188	59	5	5	NUM
fumecheng-10953	188	60	5	5	NUM
fumecheng-10953	188	61	6	6	NUM
fumecheng-10953	188	62	6	6	NUM
fumecheng-10953	188	63	(	(	PUNCT
fumecheng-10953	188	64	)	)	PUNCT
fumecheng-10953	188	65	exp	exp	NOUN
fumecheng-10953	188	66	(	(	PUNCT
fumecheng-10953	188	67	)	)	PUNCT
fumecheng-10953	188	68	exp	exp	NOUN
fumecheng-10953	188	69	(	(	PUNCT
fumecheng-10953	188	70	)	)	PUNCT
fumecheng-10953	188	71	exp	exp	NOUN
fumecheng-10953	188	72	(	(	PUNCT
fumecheng-10953	188	73	)	)	PUNCT
fumecheng-10953	188	74	exp	exp	NOUN
fumecheng-10953	188	75	(	(	PUNCT
fumecheng-10953	188	76	)	)	PUNCT
fumecheng-10953	188	77	exp	exp	NOUN
fumecheng-10953	188	78	(	(	PUNCT
fumecheng-10953	188	79	)	)	PUNCT
fumecheng-10953	188	80	exp	exp	NOUN
fumecheng-10953	188	81	(	(	PUNCT
fumecheng-10953	188	82	)	)	PUNCT
fumecheng-10953	188	83	x	x	PUNCT
fumecheng-10953	188	84	x	x	PUNCT
fumecheng-10953	188	85	x	x	PUNCT
fumecheng-10953	188	86	x	x	PUNCT
fumecheng-10953	188	87	x	x	PUNCT
fumecheng-10953	188	88	x	x	PUNCT
fumecheng-10953	188	89	x	x	SYM
fumecheng-10953	188	90	=	=	PUNCT
fumecheng-10953	188	91			PUNCT
fumecheng-10953	188	92	+	+	NOUN
fumecheng-10953	188	93			PUNCT
fumecheng-10953	188	94	+	+	NUM
fumecheng-10953	188	95			PUNCT
fumecheng-10953	188	96	+	+	NUM
fumecheng-10953	188	97			PUNCT
fumecheng-10953	188	98	+	+	NUM
fumecheng-10953	188	99			PUNCT
fumecheng-10953	188	100	+	+	NUM
fumecheng-10953	188	101			PUNCT
fumecheng-10953	188	102	(	(	PUNCT
fumecheng-10953	188	103	17	17	NUM
fumecheng-10953	188	104	)	)	PUNCT
fumecheng-10953	188	105	where	where	SCONJ
fumecheng-10953	188	106	unknown	unknown	ADJ
fumecheng-10953	188	107	integration	integration	NOUN
fumecheng-10953	188	108	constants	constant	VERB
fumecheng-10953	188	109	j	j	PROPN
fumecheng-10953	188	110	(	(	PUNCT
fumecheng-10953	188	111	j=1	j=1	PROPN
fumecheng-10953	188	112	..	..	PROPN
fumecheng-10953	188	113	6	6	NUM
fumecheng-10953	188	114	)	)	PUNCT
fumecheng-10953	188	115	yet	yet	ADV
fumecheng-10953	188	116	required	require	VERB
fumecheng-10953	188	117	to	to	PART
fumecheng-10953	188	118	be	be	AUX
fumecheng-10953	188	119	determined	determine	VERB
fumecheng-10953	188	120	via	via	ADP
fumecheng-10953	188	121	imposing	impose	VERB
fumecheng-10953	188	122	the	the	DET
fumecheng-10953	188	123	classical	classical	NOUN
fumecheng-10953	188	124	and	and	CCONJ
fumecheng-10953	188	125	the	the	DET
fumecheng-10953	188	126	extra	extra	ADJ
fumecheng-10953	188	127	non	non	ADJ
fumecheng-10953	188	128	-	-	ADJ
fumecheng-10953	188	129	standard	standard	ADJ
fumecheng-10953	188	130	boundary	boundary	ADJ
fumecheng-10953	188	131	conditions	condition	NOUN
fumecheng-10953	188	132	along	along	ADP
fumecheng-10953	188	133	with	with	ADP
fumecheng-10953	188	134	j(j=1	j(j=1	NOUN
fumecheng-10953	188	135	..	..	PROPN
fumecheng-10953	188	136	6	6	NUM
fumecheng-10953	188	137	)	)	PUNCT
fumecheng-10953	188	138	denoting	denote	VERB
fumecheng-10953	188	139	the	the	DET
fumecheng-10953	188	140	roots	root	NOUN
fumecheng-10953	188	141	of	of	ADP
fumecheng-10953	188	142	the	the	DET
fumecheng-10953	188	143	characteristic	characteristic	ADJ
fumecheng-10953	188	144	equation	equation	NOUN
fumecheng-10953	188	145	associated	associate	VERB
fumecheng-10953	188	146	with	with	ADP
fumecheng-10953	188	147	the	the	DET
fumecheng-10953	188	148	differential	differential	ADJ
fumecheng-10953	188	149	equation	equation	NOUN
fumecheng-10953	188	150	eq	eq	ADJ
fumecheng-10953	188	151	.	.	PUNCT
fumecheng-10953	189	1	(	(	PUNCT
fumecheng-10953	189	2	16	16	NUM
fumecheng-10953	189	3	)	)	PUNCT
fumecheng-10953	189	4	.	.	PUNCT
fumecheng-10953	190	1	imposing	impose	VERB
fumecheng-10953	190	2	the	the	DET
fumecheng-10953	190	3	classical	classical	NOUN
fumecheng-10953	190	4	and	and	CCONJ
fumecheng-10953	190	5	the	the	DET
fumecheng-10953	190	6	extra	extra	ADJ
fumecheng-10953	190	7	non	non	ADJ
fumecheng-10953	190	8	-	-	ADJ
fumecheng-10953	190	9	standard	standard	ADJ
fumecheng-10953	190	10	boundary	boundary	ADJ
fumecheng-10953	190	11	conditions	condition	NOUN
fumecheng-10953	190	12	to	to	ADP
fumecheng-10953	190	13	the	the	DET
fumecheng-10953	190	14	analytical	analytical	ADJ
fumecheng-10953	190	15	dynamic	dynamic	ADJ
fumecheng-10953	190	16	characteristics	characteristic	NOUN
fumecheng-10953	190	17	of	of	ADP
fumecheng-10953	190	18	mixture	mixture	NOUN
fumecheng-10953	190	19	unified	unify	VERB
fumecheng-10953	190	20	gradient	gradient	ADJ
fumecheng-10953	190	21	elastic	elastic	ADJ
fumecheng-10953	190	22	nanobeams	nanobeam	NOUN
fumecheng-10953	190	23	547	547	NUM
fumecheng-10953	190	24	solution	solution	NOUN
fumecheng-10953	190	25	addressed	address	VERB
fumecheng-10953	190	26	for	for	ADP
fumecheng-10953	190	27	the	the	DET
fumecheng-10953	190	28	spatial	spatial	ADJ
fumecheng-10953	190	29	mode	mode	NOUN
fumecheng-10953	190	30	shape	shape	NOUN
fumecheng-10953	190	31	yields	yield	VERB
fumecheng-10953	190	32	a	a	DET
fumecheng-10953	190	33	homogeneous	homogeneous	ADJ
fumecheng-10953	190	34	sixth	sixth	ADJ
fumecheng-10953	190	35	-	-	PUNCT
fumecheng-10953	190	36	order	order	NOUN
fumecheng-10953	190	37	algebraic	algebraic	ADJ
fumecheng-10953	190	38	system	system	NOUN
fumecheng-10953	190	39	in	in	ADP
fumecheng-10953	190	40	terms	term	NOUN
fumecheng-10953	190	41	of	of	ADP
fumecheng-10953	190	42	the	the	DET
fumecheng-10953	190	43	unknown	unknown	ADJ
fumecheng-10953	190	44	integration	integration	NOUN
fumecheng-10953	190	45	constants	constant	VERB
fumecheng-10953	190	46	j	j	PROPN
fumecheng-10953	190	47	(	(	PUNCT
fumecheng-10953	190	48	j=1	j=1	PROPN
fumecheng-10953	190	49	..	..	PROPN
fumecheng-10953	190	50	6	6	NUM
fumecheng-10953	190	51	)	)	PUNCT
fumecheng-10953	190	52	.	.	PUNCT
fumecheng-10953	191	1	the	the	DET
fumecheng-10953	191	2	resulted	resulted	ADJ
fumecheng-10953	191	3	system	system	NOUN
fumecheng-10953	191	4	of	of	ADP
fumecheng-10953	191	5	algebraic	algebraic	ADJ
fumecheng-10953	191	6	equations	equation	NOUN
fumecheng-10953	191	7	should	should	AUX
fumecheng-10953	191	8	be	be	AUX
fumecheng-10953	191	9	singular	singular	ADJ
fumecheng-10953	191	10	to	to	PART
fumecheng-10953	191	11	have	have	VERB
fumecheng-10953	191	12	the	the	DET
fumecheng-10953	191	13	non	non	ADJ
fumecheng-10953	191	14	-	-	ADJ
fumecheng-10953	191	15	trivial	trivial	ADJ
fumecheng-10953	191	16	solution	solution	NOUN
fumecheng-10953	191	17	,	,	PUNCT
fumecheng-10953	191	18	and	and	CCONJ
fumecheng-10953	191	19	as	as	ADP
fumecheng-10953	191	20	a	a	DET
fumecheng-10953	191	21	result	result	NOUN
fumecheng-10953	191	22	,	,	PUNCT
fumecheng-10953	191	23	the	the	DET
fumecheng-10953	191	24	determinant	determinant	NOUN
fumecheng-10953	191	25	of	of	ADP
fumecheng-10953	191	26	the	the	DET
fumecheng-10953	191	27	coefficients	coefficient	NOUN
fumecheng-10953	191	28	of	of	ADP
fumecheng-10953	191	29	the	the	DET
fumecheng-10953	191	30	homogeneous	homogeneous	ADJ
fumecheng-10953	191	31	sixth	sixth	ADJ
fumecheng-10953	191	32	-	-	PUNCT
fumecheng-10953	191	33	order	order	NOUN
fumecheng-10953	191	34	algebraic	algebraic	ADJ
fumecheng-10953	191	35	system	system	NOUN
fumecheng-10953	191	36	should	should	AUX
fumecheng-10953	191	37	vanish	vanish	VERB
fumecheng-10953	191	38	.	.	PUNCT
fumecheng-10953	192	1	the	the	DET
fumecheng-10953	192	2	analytical	analytical	ADJ
fumecheng-10953	192	3	solution	solution	NOUN
fumecheng-10953	192	4	approach	approach	NOUN
fumecheng-10953	192	5	yields	yield	VERB
fumecheng-10953	192	6	a	a	DET
fumecheng-10953	192	7	strongly	strongly	ADV
fumecheng-10953	192	8	nonlinear	nonlinear	ADJ
fumecheng-10953	192	9	characteristic	characteristic	ADJ
fumecheng-10953	192	10	equation	equation	NOUN
fumecheng-10953	192	11	in	in	ADP
fumecheng-10953	192	12	terms	term	NOUN
fumecheng-10953	192	13	of	of	ADP
fumecheng-10953	192	14	the	the	DET
fumecheng-10953	192	15	fundamental	fundamental	ADJ
fumecheng-10953	192	16	frequency	frequency	NOUN
fumecheng-10953	192	17	which	which	PRON
fumecheng-10953	192	18	requires	require	VERB
fumecheng-10953	192	19	to	to	PART
fumecheng-10953	192	20	be	be	AUX
fumecheng-10953	192	21	numerically	numerically	ADV
fumecheng-10953	192	22	solved	solve	VERB
fumecheng-10953	192	23	.	.	PUNCT
fumecheng-10953	193	1	the	the	DET
fumecheng-10953	193	2	influence	influence	NOUN
fumecheng-10953	193	3	of	of	ADP
fumecheng-10953	193	4	the	the	DET
fumecheng-10953	193	5	gradient	gradient	ADJ
fumecheng-10953	193	6	characteristic	characteristic	ADJ
fumecheng-10953	193	7	parameters	parameter	NOUN
fumecheng-10953	193	8	along	along	ADP
fumecheng-10953	193	9	with	with	ADP
fumecheng-10953	193	10	the	the	DET
fumecheng-10953	193	11	mixture	mixture	NOUN
fumecheng-10953	193	12	parameter	parameter	NOUN
fumecheng-10953	193	13	on	on	ADP
fumecheng-10953	193	14	the	the	DET
fumecheng-10953	193	15	fundamental	fundamental	ADJ
fumecheng-10953	193	16	frequency	frequency	NOUN
fumecheng-10953	193	17	of	of	ADP
fumecheng-10953	193	18	mixture	mixture	NOUN
fumecheng-10953	193	19	unified	unify	VERB
fumecheng-10953	193	20	gradient	gradient	ADJ
fumecheng-10953	193	21	elastic	elastic	ADJ
fumecheng-10953	193	22	beams	beam	NOUN
fumecheng-10953	193	23	is	be	AUX
fumecheng-10953	193	24	demonstrated	demonstrate	VERB
fumecheng-10953	193	25	in	in	ADP
fumecheng-10953	193	26	figs	fig	NOUN
fumecheng-10953	193	27	.	.	PUNCT
fumecheng-10953	194	1	3	3	NUM
fumecheng-10953	194	2	and	and	CCONJ
fumecheng-10953	194	3	4	4	NUM
fumecheng-10953	194	4	for	for	ADP
fumecheng-10953	194	5	elastic	elastic	ADJ
fumecheng-10953	194	6	nanobeams	nanobeam	NOUN
fumecheng-10953	194	7	with	with	ADP
fumecheng-10953	194	8	kinematic	kinematic	ADJ
fumecheng-10953	194	9	constraints	constraint	NOUN
fumecheng-10953	194	10	of	of	ADP
fumecheng-10953	194	11	interest	interest	NOUN
fumecheng-10953	194	12	in	in	ADP
fumecheng-10953	194	13	nano	nano	NOUN
fumecheng-10953	194	14	-	-	NOUN
fumecheng-10953	194	15	mechanics	mechanic	NOUN
fumecheng-10953	194	16	,	,	PUNCT
fumecheng-10953	194	17	viz	viz	NOUN
fumecheng-10953	194	18	.	.	PUNCT
fumecheng-10953	194	19	fully	fully	ADV
fumecheng-10953	194	20	-	-	PUNCT
fumecheng-10953	194	21	fixed	fix	VERB
fumecheng-10953	194	22	and	and	CCONJ
fumecheng-10953	194	23	cantilever	cantilever	NOUN
fumecheng-10953	194	24	beams	beam	NOUN
fumecheng-10953	194	25	.	.	PUNCT
fumecheng-10953	195	1	the	the	DET
fumecheng-10953	195	2	detected	detect	VERB
fumecheng-10953	195	3	fundamental	fundamental	ADJ
fumecheng-10953	195	4	frequencies	frequency	NOUN
fumecheng-10953	195	5	are	be	AUX
fumecheng-10953	195	6	,	,	PUNCT
fumecheng-10953	195	7	additionally	additionally	ADV
fumecheng-10953	195	8	,	,	PUNCT
fumecheng-10953	195	9	normalized	normalize	VERB
fumecheng-10953	195	10	utilizing	utilize	VERB
fumecheng-10953	195	11	the	the	DET
fumecheng-10953	195	12	corresponding	corresponding	ADJ
fumecheng-10953	195	13	classical	classical	ADJ
fumecheng-10953	195	14	natural	natural	ADJ
fumecheng-10953	195	15	frequencies	frequency	NOUN
fumecheng-10953	195	16	0	0	PRON
fumecheng-10953	195	17	.	.	PUNCT
fumecheng-10953	196	1	the	the	DET
fumecheng-10953	196	2	strain	strain	NOUN
fumecheng-10953	196	3	gradient	gradient	NOUN
fumecheng-10953	196	4	and	and	CCONJ
fumecheng-10953	196	5	the	the	DET
fumecheng-10953	196	6	stress	stress	NOUN
fumecheng-10953	196	7	gradient	gradient	ADJ
fumecheng-10953	196	8	characteristic	characteristic	ADJ
fumecheng-10953	196	9	parameters	parameter	NOUN
fumecheng-10953	196	10	are	be	AUX
fumecheng-10953	196	11	,	,	PUNCT
fumecheng-10953	196	12	respectively	respectively	ADV
fumecheng-10953	196	13	,	,	PUNCT
fumecheng-10953	196	14	ranging	range	VERB
fumecheng-10953	196	15	in	in	ADP
fumecheng-10953	196	16	the	the	DET
fumecheng-10953	196	17	intervals	interval	NOUN
fumecheng-10953	196	18	[	[	X
fumecheng-10953	196	19	0.1,1	0.1,1	X
fumecheng-10953	196	20	]	]	PUNCT
fumecheng-10953	196	21	and	and	CCONJ
fumecheng-10953	196	22	[	[	X
fumecheng-10953	196	23	0,1	0,1	NUM
fumecheng-10953	196	24	]	]	PUNCT
fumecheng-10953	196	25	,	,	PUNCT
fumecheng-10953	196	26	as	as	ADP
fumecheng-10953	196	27	two	two	NUM
fumecheng-10953	196	28	values	value	NOUN
fumecheng-10953	196	29	of	of	ADP
fumecheng-10953	196	30	the	the	DET
fumecheng-10953	196	31	mixture	mixture	NOUN
fumecheng-10953	196	32	parameter	parameter	NOUN
fumecheng-10953	196	33			NOUN
fumecheng-10953	196	34	=	=	PUNCT
fumecheng-10953	197	1	0,1/2	0,1/2	PROPN
fumecheng-10953	197	2	are	be	AUX
fumecheng-10953	197	3	implemented	implement	VERB
fumecheng-10953	197	4	.	.	PUNCT
fumecheng-10953	198	1	the	the	DET
fumecheng-10953	198	2	non	non	ADJ
fumecheng-10953	198	3	-	-	ADJ
fumecheng-10953	198	4	dimensional	dimensional	ADJ
fumecheng-10953	198	5	gyration	gyration	ADJ
fumecheng-10953	198	6	radius	radius	NOUN
fumecheng-10953	198	7	of	of	ADP
fumecheng-10953	198	8	the	the	DET
fumecheng-10953	198	9	elastic	elastic	ADJ
fumecheng-10953	198	10	nanobeam	nanobeam	NOUN
fumecheng-10953	198	11	is	be	AUX
fumecheng-10953	198	12	,	,	PUNCT
fumecheng-10953	198	13	also	also	ADV
fumecheng-10953	198	14	,	,	PUNCT
fumecheng-10953	198	15	set	set	VERB
fumecheng-10953	198	16	as	as	ADP
fumecheng-10953	198	17	1/	1/	NUM
fumecheng-10953	198	18	20	20	NUM
fumecheng-10953	198	19	=	=	SYM
fumecheng-10953	198	20	.	.	PUNCT
fumecheng-10953	199	1	furthermore	furthermore	ADV
fumecheng-10953	199	2	,	,	PUNCT
fumecheng-10953	199	3	the	the	DET
fumecheng-10953	199	4	non	non	ADJ
fumecheng-10953	199	5	-	-	ADJ
fumecheng-10953	199	6	dimensional	dimensional	ADJ
fumecheng-10953	199	7	fundamental	fundamental	ADJ
fumecheng-10953	199	8	frequency	frequency	PROPN
fumecheng-10953	199	9	is	be	AUX
fumecheng-10953	199	10	defined	define	VERB
fumecheng-10953	199	11	for	for	ADP
fumecheng-10953	199	12	the	the	DET
fumecheng-10953	199	13	sake	sake	NOUN
fumecheng-10953	199	14	of	of	ADP
fumecheng-10953	199	15	consistency	consistency	NOUN
fumecheng-10953	199	16	of	of	ADP
fumecheng-10953	199	17	the	the	DET
fumecheng-10953	199	18	illustrations	illustration	NOUN
fumecheng-10953	199	19	as	as	ADP
fumecheng-10953	199	20	2	2	NUM
fumecheng-10953	199	21	e	e	NOUN
fumecheng-10953	199	22	a	a	DET
fumecheng-10953	199	23	l	l	X
fumecheng-10953	199	24	i	i	PRON
fumecheng-10953	199	25			VERB
fumecheng-10953	199	26			X
fumecheng-10953	199	27	=	=	PROPN
fumecheng-10953	199	28	(	(	PUNCT
fumecheng-10953	199	29	18	18	NUM
fumecheng-10953	199	30	)	)	PUNCT
fumecheng-10953	199	31	fig	fig	NOUN
fumecheng-10953	199	32	.	.	PUNCT
fumecheng-10953	200	1	3	3	NUM
fumecheng-10953	200	2	normalized	normalize	VERB
fumecheng-10953	200	3	fundamental	fundamental	ADJ
fumecheng-10953	200	4	frequency	frequency	NOUN
fumecheng-10953	200	5	of	of	ADP
fumecheng-10953	200	6	mixture	mixture	NOUN
fumecheng-10953	200	7	unified	unify	VERB
fumecheng-10953	200	8	gradient	gradient	ADJ
fumecheng-10953	200	9	elastic	elastic	ADJ
fumecheng-10953	200	10	beams	beam	NOUN
fumecheng-10953	200	11	with	with	ADP
fumecheng-10953	200	12	fully	fully	ADV
fumecheng-10953	200	13	-	-	PUNCT
fumecheng-10953	200	14	fixed	fix	VERB
fumecheng-10953	200	15	ends	end	NOUN
fumecheng-10953	200	16	548	548	NUM
fumecheng-10953	200	17	s.	s.	PROPN
fumecheng-10953	200	18	a.	a.	PROPN
fumecheng-10953	200	19	faghidian	faghidian	PROPN
fumecheng-10953	200	20	,	,	PUNCT
fumecheng-10953	200	21	a.	a.	NOUN
fumecheng-10953	200	22	tounsi	tounsi	PROPN
fumecheng-10953	200	23	fig	fig	NOUN
fumecheng-10953	200	24	.	.	PUNCT
fumecheng-10953	201	1	4	4	NUM
fumecheng-10953	201	2	normalized	normalize	VERB
fumecheng-10953	201	3	fundamental	fundamental	ADJ
fumecheng-10953	201	4	frequency	frequency	NOUN
fumecheng-10953	201	5	of	of	ADP
fumecheng-10953	201	6	mixture	mixture	NOUN
fumecheng-10953	201	7	unified	unify	VERB
fumecheng-10953	201	8	gradient	gradient	ADJ
fumecheng-10953	201	9	elastic	elastic	ADJ
fumecheng-10953	201	10	beams	beam	NOUN
fumecheng-10953	201	11	with	with	ADP
fumecheng-10953	201	12	cantilever	cantilever	NOUN
fumecheng-10953	201	13	ends	end	NOUN
fumecheng-10953	201	14	as	as	SCONJ
fumecheng-10953	201	15	noticeably	noticeably	ADV
fumecheng-10953	201	16	observed	observe	VERB
fumecheng-10953	201	17	from	from	ADP
fumecheng-10953	201	18	the	the	DET
fumecheng-10953	201	19	numerical	numerical	ADJ
fumecheng-10953	201	20	illustrations	illustration	NOUN
fumecheng-10953	201	21	in	in	ADP
fumecheng-10953	201	22	figs	fig	NOUN
fumecheng-10953	201	23	.	.	PUNCT
fumecheng-10953	202	1	3	3	NUM
fumecheng-10953	202	2	and	and	CCONJ
fumecheng-10953	202	3	4	4	NUM
fumecheng-10953	202	4	,	,	PUNCT
fumecheng-10953	202	5	the	the	DET
fumecheng-10953	202	6	stress	stress	NOUN
fumecheng-10953	202	7	gradient	gradient	NOUN
fumecheng-10953	202	8	characteristic	characteristic	ADJ
fumecheng-10953	202	9	parameter	parameter	NOUN
fumecheng-10953	202	10			PROPN
fumecheng-10953	202	11	has	have	VERB
fumecheng-10953	202	12	the	the	DET
fumecheng-10953	202	13	effect	effect	NOUN
fumecheng-10953	202	14	of	of	ADP
fumecheng-10953	202	15	decreasing	decrease	VERB
fumecheng-10953	202	16	the	the	DET
fumecheng-10953	202	17	fundamental	fundamental	ADJ
fumecheng-10953	202	18	frequency	frequency	NOUN
fumecheng-10953	202	19	,	,	PUNCT
fumecheng-10953	202	20	viz	viz	PROPN
fumecheng-10953	202	21	.	.	PUNCT
fumecheng-10953	203	1	a	a	DET
fumecheng-10953	203	2	larger	large	ADJ
fumecheng-10953	203	3			NOUN
fumecheng-10953	203	4	involves	involve	VERB
fumecheng-10953	203	5	a	a	DET
fumecheng-10953	203	6	smaller	small	ADJ
fumecheng-10953	203	7	natural	natural	ADJ
fumecheng-10953	203	8	frequency	frequency	NOUN
fumecheng-10953	203	9	for	for	ADP
fumecheng-10953	203	10	given	give	VERB
fumecheng-10953	203	11	values	value	NOUN
fumecheng-10953	203	12	of	of	ADP
fumecheng-10953	203	13	the	the	DET
fumecheng-10953	203	14	characteristic	characteristic	ADJ
fumecheng-10953	203	15	parameters	parameter	NOUN
fumecheng-10953	203	16	,.	,.	PROPN
fumecheng-10953	203	17	the	the	DET
fumecheng-10953	203	18	fundamental	fundamental	ADJ
fumecheng-10953	203	19	frequency	frequency	NOUN
fumecheng-10953	203	20	of	of	ADP
fumecheng-10953	203	21	elastic	elastic	ADJ
fumecheng-10953	203	22	nanobeams	nanobeam	NOUN
fumecheng-10953	203	23	within	within	ADP
fumecheng-10953	203	24	the	the	DET
fumecheng-10953	203	25	framework	framework	NOUN
fumecheng-10953	203	26	of	of	ADP
fumecheng-10953	203	27	the	the	DET
fumecheng-10953	203	28	mixture	mixture	NOUN
fumecheng-10953	203	29	unified	unify	VERB
fumecheng-10953	203	30	gradient	gradient	NOUN
fumecheng-10953	203	31	theory	theory	NOUN
fumecheng-10953	203	32	,	,	PUNCT
fumecheng-10953	203	33	therefore	therefore	ADV
fumecheng-10953	203	34	,	,	PUNCT
fumecheng-10953	203	35	reveals	reveal	VERB
fumecheng-10953	203	36	a	a	DET
fumecheng-10953	203	37	softening	soften	VERB
fumecheng-10953	203	38	response	response	NOUN
fumecheng-10953	203	39	in	in	ADP
fumecheng-10953	203	40	terms	term	NOUN
fumecheng-10953	203	41	of	of	ADP
fumecheng-10953	203	42	the	the	DET
fumecheng-10953	203	43	stress	stress	NOUN
fumecheng-10953	203	44	gradient	gradient	ADJ
fumecheng-10953	203	45	characteristic	characteristic	ADJ
fumecheng-10953	203	46	parameter	parameter	NOUN
fumecheng-10953	203	47	.	.	PUNCT
fumecheng-10953	204	1	on	on	ADP
fumecheng-10953	204	2	the	the	DET
fumecheng-10953	204	3	contrary	contrary	NOUN
fumecheng-10953	204	4	,	,	PUNCT
fumecheng-10953	204	5	the	the	DET
fumecheng-10953	204	6	fundamental	fundamental	ADJ
fumecheng-10953	204	7	frequency	frequency	NOUN
fumecheng-10953	204	8	of	of	ADP
fumecheng-10953	204	9	free	free	ADJ
fumecheng-10953	204	10	vibrations	vibration	NOUN
fumecheng-10953	204	11	of	of	ADP
fumecheng-10953	204	12	a	a	DET
fumecheng-10953	204	13	mixture	mixture	NOUN
fumecheng-10953	204	14	unified	unify	VERB
fumecheng-10953	204	15	gradient	gradient	ADJ
fumecheng-10953	204	16	elastic	elastic	ADJ
fumecheng-10953	204	17	beam	beam	NOUN
fumecheng-10953	204	18	increases	increase	NOUN
fumecheng-10953	204	19	by	by	ADP
fumecheng-10953	204	20	increasing	increase	VERB
fumecheng-10953	204	21	either	either	CCONJ
fumecheng-10953	204	22	the	the	DET
fumecheng-10953	204	23	strain	strain	ADJ
fumecheng-10953	204	24	gradient	gradient	ADJ
fumecheng-10953	204	25	characteristic	characteristic	ADJ
fumecheng-10953	204	26	parameter	parameter	NOUN
fumecheng-10953	204	27			NUM
fumecheng-10953	204	28	or	or	CCONJ
fumecheng-10953	204	29	the	the	DET
fumecheng-10953	204	30	mixture	mixture	NOUN
fumecheng-10953	204	31	parameter	parameter	NOUN
fumecheng-10953	204	32	.	.	PROPN
fumecheng-10953	205	1	a	a	DET
fumecheng-10953	205	2	stiffening	stiffen	VERB
fumecheng-10953	205	3	response	response	NOUN
fumecheng-10953	205	4	in	in	ADP
fumecheng-10953	205	5	terms	term	NOUN
fumecheng-10953	205	6	of	of	ADP
fumecheng-10953	205	7	the	the	DET
fumecheng-10953	205	8	characteristic	characteristic	ADJ
fumecheng-10953	205	9	parameters	parameter	NOUN
fumecheng-10953	205	10	,	,	NOUN
fumecheng-10953	205	11	is	be	AUX
fumecheng-10953	205	12	,	,	PUNCT
fumecheng-10953	205	13	thus	thus	ADV
fumecheng-10953	205	14	,	,	PUNCT
fumecheng-10953	205	15	confirmed	confirm	VERB
fumecheng-10953	205	16	for	for	ADP
fumecheng-10953	205	17	a	a	DET
fumecheng-10953	205	18	given	give	VERB
fumecheng-10953	205	19	value	value	NOUN
fumecheng-10953	205	20	of	of	ADP
fumecheng-10953	205	21	.	.	ADJ
fumecheng-10953	205	22	table	table	NOUN
fumecheng-10953	205	23	1	1	NUM
fumecheng-10953	205	24	normalized	normalize	VERB
fumecheng-10953	205	25	fundamental	fundamental	ADJ
fumecheng-10953	205	26	frequencies	frequency	NOUN
fumecheng-10953	205	27	of	of	ADP
fumecheng-10953	205	28	fully	fully	ADV
fumecheng-10953	205	29	-	-	PUNCT
fumecheng-10953	205	30	fixed	fix	VERB
fumecheng-10953	205	31	nanobeams	nanobeam	NOUN
fumecheng-10953	205	32	:	:	PUNCT
fumecheng-10953	205	33	mixture	mixture	NOUN
fumecheng-10953	205	34	unified	unify	VERB
fumecheng-10953	205	35	gradient	gradient	NOUN
fumecheng-10953	205	36	theory	theory	NOUN
fumecheng-10953	205	37	(	(	PUNCT
fumecheng-10953	205	38			NOUN
fumecheng-10953	205	39	=	=	SYM
fumecheng-10953	205	40	0	0	NUM
fumecheng-10953	205	41	)	)	PUNCT
fumecheng-10953	205	42	0/	0/	NOUN
fumecheng-10953	206	1			X
fumecheng-10953	206	2			NOUN
fumecheng-10953	206	3	0.1	0.1	X
fumecheng-10953	207	1	=	=	SYM
fumecheng-10953	207	2	0.3	0.3	NUM
fumecheng-10953	208	1	=	=	SYM
fumecheng-10953	208	2	0.5	0.5	NUM
fumecheng-10953	208	3	=	=	SYM
fumecheng-10953	208	4	0.7	0.7	X
fumecheng-10953	208	5	=	=	SYM
fumecheng-10953	208	6	1	1	NUM
fumecheng-10953	208	7	=	=	SYM
fumecheng-10953	208	8	0	0	NUM
fumecheng-10953	208	9	+	+	NUM
fumecheng-10953	208	10	1.19212	1.19212	NUM
fumecheng-10953	208	11	2.16205	2.16205	NUM
fumecheng-10953	208	12	3.34212	3.34212	NUM
fumecheng-10953	208	13	4.57294	4.57294	NUM
fumecheng-10953	208	14	6.45084	6.45084	NUM
fumecheng-10953	208	15	0.2	0.2	NUM
fumecheng-10953	209	1	0.72725	0.72725	NUM
fumecheng-10953	209	2	1.33248	1.33248	NUM
fumecheng-10953	209	3	2.06215	2.06215	NUM
fumecheng-10953	209	4	2.82252	2.82252	NUM
fumecheng-10953	209	5	3.98232	3.98232	NUM
fumecheng-10953	209	6	0.4	0.4	NUM
fumecheng-10953	209	7	0.42807	0.42807	NUM
fumecheng-10953	209	8	0.78774	0.78774	NUM
fumecheng-10953	209	9	1.21969	1.21969	NUM
fumecheng-10953	209	10	1.66966	1.66966	NUM
fumecheng-10953	209	11	2.35591	2.35591	NUM
fumecheng-10953	209	12	0.6	0.6	NUM
fumecheng-10953	209	13	0.29615	0.29615	NUM
fumecheng-10953	209	14	0.54564	0.54564	NUM
fumecheng-10953	209	15	0.84496	0.84496	NUM
fumecheng-10953	209	16	1.15673	1.15673	NUM
fumecheng-10953	209	17	1.63220	1.63220	NUM
fumecheng-10953	209	18	0.8	0.8	NUM
fumecheng-10953	209	19	0.22516	0.22516	NUM
fumecheng-10953	209	20	0.41505	0.41505	NUM
fumecheng-10953	209	21	0.64276	0.64276	NUM
fumecheng-10953	209	22	0.87994	0.87994	NUM
fumecheng-10953	209	23	1.24164	1.24164	NUM
fumecheng-10953	209	24	1.0	1.0	NUM
fumecheng-10953	209	25	0.18129	0.18129	NUM
fumecheng-10953	209	26	0.33426	0.33426	NUM
fumecheng-10953	209	27	0.51767	0.51767	NUM
fumecheng-10953	209	28	0.70869	0.70869	NUM
fumecheng-10953	209	29	1.00098	1.00098	NUM
fumecheng-10953	209	30	table	table	NOUN
fumecheng-10953	209	31	2	2	NUM
fumecheng-10953	209	32	normalized	normalize	VERB
fumecheng-10953	209	33	fundamental	fundamental	ADJ
fumecheng-10953	209	34	frequencies	frequency	NOUN
fumecheng-10953	209	35	of	of	ADP
fumecheng-10953	209	36	fully	fully	ADV
fumecheng-10953	209	37	-	-	PUNCT
fumecheng-10953	209	38	fixed	fix	VERB
fumecheng-10953	209	39	nanobeams	nanobeam	NOUN
fumecheng-10953	209	40	:	:	PUNCT
fumecheng-10953	209	41	mixture	mixture	NOUN
fumecheng-10953	209	42	unified	unify	VERB
fumecheng-10953	209	43	gradient	gradient	NOUN
fumecheng-10953	209	44	theory	theory	NOUN
fumecheng-10953	209	45	(	(	PUNCT
fumecheng-10953	209	46			NOUN
fumecheng-10953	209	47	=	=	SYM
fumecheng-10953	209	48	1/2	1/2	NUM
fumecheng-10953	209	49	)	)	PUNCT
fumecheng-10953	209	50	0/	0/	NOUN
fumecheng-10953	210	1			X
fumecheng-10953	210	2			NOUN
fumecheng-10953	210	3	0.1	0.1	X
fumecheng-10953	211	1	=	=	SYM
fumecheng-10953	211	2	0.3	0.3	NUM
fumecheng-10953	212	1	=	=	SYM
fumecheng-10953	212	2	0.5	0.5	NUM
fumecheng-10953	212	3	=	=	SYM
fumecheng-10953	212	4	0.7	0.7	X
fumecheng-10953	212	5	=	=	SYM
fumecheng-10953	212	6	1	1	NUM
fumecheng-10953	212	7	=	=	SYM
fumecheng-10953	212	8	0	0	NUM
fumecheng-10953	212	9	+	+	NUM
fumecheng-10953	212	10	1.19212	1.19212	NUM
fumecheng-10953	212	11	2.16205	2.16205	NUM
fumecheng-10953	212	12	3.34212	3.34212	NUM
fumecheng-10953	212	13	4.57294	4.57294	NUM
fumecheng-10953	212	14	6.45084	6.45084	NUM
fumecheng-10953	212	15	0.2	0.2	NUM
fumecheng-10953	212	16	0.91885	0.91885	NUM
fumecheng-10953	212	17	1.44405	1.44405	NUM
fumecheng-10953	212	18	2.13588	2.13588	NUM
fumecheng-10953	212	19	2.87683	2.87683	NUM
fumecheng-10953	212	20	4.02099	4.02099	NUM
fumecheng-10953	212	21	0.4	0.4	NUM
fumecheng-10953	212	22	0.78774	0.78774	NUM
fumecheng-10953	212	23	1.02674	1.02674	NUM
fumecheng-10953	212	24	1.38602	1.38602	NUM
fumecheng-10953	212	25	1.79475	1.79475	NUM
fumecheng-10953	212	26	2.44615	2.44615	NUM
fumecheng-10953	212	27	0.6	0.6	NUM
fumecheng-10953	212	28	0.74694	0.74694	NUM
fumecheng-10953	212	29	0.87520	0.87520	NUM
fumecheng-10953	212	30	1.08721	1.08721	NUM
fumecheng-10953	212	31	1.34389	1.34389	NUM
fumecheng-10953	212	32	1.76976	1.76976	NUM
fumecheng-10953	212	33	0.8	0.8	NUM
fumecheng-10953	212	34	0.73043	0.73043	NUM
fumecheng-10953	212	35	0.80865	0.80865	NUM
fumecheng-10953	212	36	0.94587	0.94587	NUM
fumecheng-10953	212	37	1.12062	1.12062	NUM
fumecheng-10953	212	38	1.42238	1.42238	NUM
fumecheng-10953	212	39	1.0	1.0	NUM
fumecheng-10953	212	40	0.72233	0.72233	NUM
fumecheng-10953	212	41	0.77449	0.77449	NUM
fumecheng-10953	212	42	0.86948	0.86948	NUM
fumecheng-10953	212	43	0.99511	0.99511	NUM
fumecheng-10953	212	44	1.21983	1.21983	NUM
fumecheng-10953	212	45	dynamic	dynamic	ADJ
fumecheng-10953	212	46	characteristics	characteristic	NOUN
fumecheng-10953	212	47	of	of	ADP
fumecheng-10953	212	48	mixture	mixture	NOUN
fumecheng-10953	212	49	unified	unify	VERB
fumecheng-10953	212	50	gradient	gradient	ADJ
fumecheng-10953	212	51	elastic	elastic	ADJ
fumecheng-10953	212	52	nanobeams	nanobeam	NOUN
fumecheng-10953	212	53	549	549	NUM
fumecheng-10953	212	54	as	as	SCONJ
fumecheng-10953	212	55	expected	expect	VERB
fumecheng-10953	213	1	,	,	PUNCT
fumecheng-10953	213	2	the	the	DET
fumecheng-10953	213	3	mixture	mixture	NOUN
fumecheng-10953	213	4	unified	unify	VERB
fumecheng-10953	213	5	gradient	gradient	NOUN
fumecheng-10953	213	6	theory	theory	NOUN
fumecheng-10953	213	7	of	of	ADP
fumecheng-10953	213	8	elasticity	elasticity	NOUN
fumecheng-10953	213	9	reveals	reveal	VERB
fumecheng-10953	213	10	a	a	DET
fumecheng-10953	213	11	stiffening	stiffen	VERB
fumecheng-10953	213	12	response	response	NOUN
fumecheng-10953	213	13	in	in	ADP
fumecheng-10953	213	14	terms	term	NOUN
fumecheng-10953	213	15	of	of	ADP
fumecheng-10953	213	16	the	the	DET
fumecheng-10953	213	17	number	number	NOUN
fumecheng-10953	213	18	of	of	ADP
fumecheng-10953	213	19	kinematic	kinematic	ADJ
fumecheng-10953	213	20	boundary	boundary	ADJ
fumecheng-10953	213	21	constraints	constraint	NOUN
fumecheng-10953	213	22	.	.	PUNCT
fumecheng-10953	214	1	in	in	ADP
fumecheng-10953	214	2	the	the	DET
fumecheng-10953	214	3	numerical	numerical	ADJ
fumecheng-10953	214	4	illustrations	illustration	NOUN
fumecheng-10953	214	5	of	of	ADP
fumecheng-10953	214	6	free	free	ADJ
fumecheng-10953	214	7	vibrations	vibration	NOUN
fumecheng-10953	214	8	of	of	ADP
fumecheng-10953	214	9	elastic	elastic	ADJ
fumecheng-10953	214	10	nanobeams	nanobeam	NOUN
fumecheng-10953	214	11	within	within	ADP
fumecheng-10953	214	12	the	the	DET
fumecheng-10953	214	13	context	context	NOUN
fumecheng-10953	214	14	of	of	ADP
fumecheng-10953	214	15	the	the	DET
fumecheng-10953	214	16	mixture	mixture	NOUN
fumecheng-10953	214	17	unified	unify	VERB
fumecheng-10953	214	18	gradient	gradient	NOUN
fumecheng-10953	214	19	theory	theory	NOUN
fumecheng-10953	214	20	,	,	PUNCT
fumecheng-10953	214	21	the	the	DET
fumecheng-10953	214	22	influence	influence	NOUN
fumecheng-10953	214	23	of	of	ADP
fumecheng-10953	214	24	the	the	DET
fumecheng-10953	214	25	gradient	gradient	ADJ
fumecheng-10953	214	26	characteristic	characteristic	ADJ
fumecheng-10953	214	27	parameters	parameter	NOUN
fumecheng-10953	214	28	is	be	AUX
fumecheng-10953	214	29	more	more	ADV
fumecheng-10953	214	30	noticeable	noticeable	ADJ
fumecheng-10953	214	31	in	in	ADP
fumecheng-10953	214	32	elastic	elastic	ADJ
fumecheng-10953	214	33	nanobeams	nanobeam	NOUN
fumecheng-10953	214	34	with	with	ADP
fumecheng-10953	214	35	fully	fully	ADV
fumecheng-10953	214	36	-	-	PUNCT
fumecheng-10953	214	37	fixed	fix	VERB
fumecheng-10953	214	38	ends	end	NOUN
fumecheng-10953	214	39	.	.	PUNCT
fumecheng-10953	215	1	the	the	DET
fumecheng-10953	215	2	fundamental	fundamental	ADJ
fumecheng-10953	215	3	frequency	frequency	NOUN
fumecheng-10953	215	4	of	of	ADP
fumecheng-10953	215	5	the	the	DET
fumecheng-10953	215	6	classical	classical	ADJ
fumecheng-10953	215	7	elastic	elastic	ADJ
fumecheng-10953	215	8	beam	beam	NOUN
fumecheng-10953	215	9	is	be	AUX
fumecheng-10953	215	10	,	,	PUNCT
fumecheng-10953	215	11	also	also	ADV
fumecheng-10953	215	12	,	,	PUNCT
fumecheng-10953	215	13	retrieved	retrieve	VERB
fumecheng-10953	215	14	as	as	ADP
fumecheng-10953	215	15	either	either	CCONJ
fumecheng-10953	215	16	the	the	DET
fumecheng-10953	215	17	gradient	gradient	ADJ
fumecheng-10953	215	18	characteristic	characteristic	ADJ
fumecheng-10953	215	19	parameters	parameter	NOUN
fumecheng-10953	215	20	tend	tend	VERB
fumecheng-10953	215	21	to	to	ADP
fumecheng-10953	215	22	zero	zero	NUM
fumecheng-10953	215	23	or	or	CCONJ
fumecheng-10953	215	24	as	as	SCONJ
fumecheng-10953	215	25	the	the	DET
fumecheng-10953	215	26	mixture	mixture	NOUN
fumecheng-10953	215	27	parameter	parameter	NOUN
fumecheng-10953	215	28	approaches	approach	VERB
fumecheng-10953	215	29	unity	unity	NOUN
fumecheng-10953	215	30	in	in	ADP
fumecheng-10953	215	31	the	the	DET
fumecheng-10953	215	32	absence	absence	NOUN
fumecheng-10953	215	33	of	of	ADP
fumecheng-10953	215	34	the	the	DET
fumecheng-10953	215	35	strain	strain	NOUN
fumecheng-10953	215	36	gradient	gradient	ADJ
fumecheng-10953	215	37	characteristic	characteristic	ADJ
fumecheng-10953	215	38	parameter	parameter	NOUN
fumecheng-10953	215	39	.	.	PUNCT
fumecheng-10953	216	1	numerical	numerical	ADJ
fumecheng-10953	216	2	values	value	NOUN
fumecheng-10953	216	3	of	of	ADP
fumecheng-10953	216	4	normalized	normalize	VERB
fumecheng-10953	216	5	fundamental	fundamental	ADJ
fumecheng-10953	216	6	frequencies	frequency	NOUN
fumecheng-10953	216	7	of	of	ADP
fumecheng-10953	216	8	fully	fully	ADV
fumecheng-10953	216	9	-	-	PUNCT
fumecheng-10953	216	10	fixed	fix	VERB
fumecheng-10953	216	11	and	and	CCONJ
fumecheng-10953	216	12	cantilever	cantilever	NOUN
fumecheng-10953	216	13	nano	nano	NOUN
fumecheng-10953	216	14	-	-	PUNCT
fumecheng-10953	216	15	sized	sized	ADJ
fumecheng-10953	216	16	beams	beam	NOUN
fumecheng-10953	216	17	determined	determine	VERB
fumecheng-10953	216	18	within	within	ADP
fumecheng-10953	216	19	the	the	DET
fumecheng-10953	216	20	context	context	NOUN
fumecheng-10953	216	21	of	of	ADP
fumecheng-10953	216	22	the	the	DET
fumecheng-10953	216	23	mixture	mixture	NOUN
fumecheng-10953	216	24	unified	unify	VERB
fumecheng-10953	216	25	gradient	gradient	NOUN
fumecheng-10953	216	26	theory	theory	NOUN
fumecheng-10953	216	27	are	be	AUX
fumecheng-10953	216	28	collected	collect	VERB
fumecheng-10953	216	29	in	in	ADP
fumecheng-10953	216	30	tables	table	NOUN
fumecheng-10953	216	31	1	1	NUM
fumecheng-10953	216	32	through	through	ADP
fumecheng-10953	216	33	4	4	NUM
fumecheng-10953	216	34	,	,	PUNCT
fumecheng-10953	216	35	correspondingly	correspondingly	ADV
fumecheng-10953	216	36	,	,	PUNCT
fumecheng-10953	216	37	for	for	ADP
fumecheng-10953	216	38	the	the	DET
fumecheng-10953	216	39	mixture	mixture	NOUN
fumecheng-10953	216	40	parameter	parameter	NOUN
fumecheng-10953	216	41			NOUN
fumecheng-10953	217	1	=	=	PUNCT
fumecheng-10953	217	2	0	0	NUM
fumecheng-10953	217	3	and	and	CCONJ
fumecheng-10953	217	4			NOUN
fumecheng-10953	217	5	=	=	SYM
fumecheng-10953	217	6	1/2	1/2	NUM
fumecheng-10953	217	7	.	.	PUNCT
fumecheng-10953	217	8	table	table	NOUN
fumecheng-10953	217	9	3	3	NUM
fumecheng-10953	217	10	normalized	normalize	VERB
fumecheng-10953	217	11	fundamental	fundamental	ADJ
fumecheng-10953	217	12	frequencies	frequency	NOUN
fumecheng-10953	217	13	of	of	ADP
fumecheng-10953	217	14	cantilever	cantilever	NOUN
fumecheng-10953	217	15	nanobeams	nanobeam	NOUN
fumecheng-10953	217	16	:	:	PUNCT
fumecheng-10953	217	17	mixture	mixture	NOUN
fumecheng-10953	217	18	unified	unify	VERB
fumecheng-10953	217	19	gradient	gradient	NOUN
fumecheng-10953	217	20	theory	theory	NOUN
fumecheng-10953	217	21	(	(	PUNCT
fumecheng-10953	217	22			NOUN
fumecheng-10953	217	23	=	=	SYM
fumecheng-10953	217	24	0	0	NUM
fumecheng-10953	217	25	)	)	PUNCT
fumecheng-10953	217	26	0/	0/	NOUN
fumecheng-10953	218	1			X
fumecheng-10953	218	2			NOUN
fumecheng-10953	218	3	0.1	0.1	X
fumecheng-10953	219	1	=	=	SYM
fumecheng-10953	219	2	0.3	0.3	NUM
fumecheng-10953	220	1	=	=	SYM
fumecheng-10953	220	2	0.5	0.5	NUM
fumecheng-10953	220	3	=	=	SYM
fumecheng-10953	220	4	0.7	0.7	X
fumecheng-10953	220	5	=	=	SYM
fumecheng-10953	220	6	1	1	NUM
fumecheng-10953	220	7	=	=	SYM
fumecheng-10953	220	8	0	0	PUNCT
fumecheng-10953	220	9	+	+	NUM
fumecheng-10953	220	10	1.01961	1.01961	NUM
fumecheng-10953	220	11	1.10882	1.10882	NUM
fumecheng-10953	220	12	1.17691	1.17691	NUM
fumecheng-10953	220	13	1.21442	1.21442	NUM
fumecheng-10953	220	14	1.24183	1.24183	NUM
fumecheng-10953	220	15	0.2	0.2	NUM
fumecheng-10953	220	16	0.94703	0.94703	NUM
fumecheng-10953	220	17	1.05644	1.05644	NUM
fumecheng-10953	220	18	1.14256	1.14256	NUM
fumecheng-10953	220	19	1.19185	1.19185	NUM
fumecheng-10953	220	20	1.22880	1.22880	NUM
fumecheng-10953	220	21	0.4	0.4	NUM
fumecheng-10953	220	22	0.79510	0.79510	NUM
fumecheng-10953	220	23	0.93391	0.93391	NUM
fumecheng-10953	220	24	1.05452	1.05452	NUM
fumecheng-10953	220	25	1.13066	1.13066	NUM
fumecheng-10953	220	26	1.19190	1.19190	NUM
fumecheng-10953	220	27	0.6	0.6	NUM
fumecheng-10953	220	28	0.64946	0.64946	NUM
fumecheng-10953	220	29	0.79839	0.79839	NUM
fumecheng-10953	220	30	0.94334	0.94334	NUM
fumecheng-10953	220	31	1.04607	1.04607	NUM
fumecheng-10953	220	32	1.13681	1.13681	NUM
fumecheng-10953	220	33	0.8	0.8	NUM
fumecheng-10953	220	34	0.53583	0.53583	NUM
fumecheng-10953	220	35	0.67976	0.67976	NUM
fumecheng-10953	220	36	0.83312	0.83312	NUM
fumecheng-10953	220	37	0.95355	0.95355	NUM
fumecheng-10953	220	38	1.06970	1.06970	NUM
fumecheng-10953	220	39	1.0	1.0	NUM
fumecheng-10953	220	40	0.45096	0.45096	NUM
fumecheng-10953	220	41	0.58396	0.58396	NUM
fumecheng-10953	220	42	0.73510	0.73510	NUM
fumecheng-10953	220	43	0.86370	0.86370	NUM
fumecheng-10953	220	44	1.00036	1.00036	NUM
fumecheng-10953	220	45	table	table	NOUN
fumecheng-10953	220	46	4	4	NUM
fumecheng-10953	220	47	normalized	normalize	VERB
fumecheng-10953	220	48	fundamental	fundamental	ADJ
fumecheng-10953	220	49	frequencies	frequency	NOUN
fumecheng-10953	220	50	of	of	ADP
fumecheng-10953	220	51	cantilever	cantilever	NOUN
fumecheng-10953	220	52	nanobeams	nanobeam	NOUN
fumecheng-10953	220	53	:	:	PUNCT
fumecheng-10953	220	54	mixture	mixture	NOUN
fumecheng-10953	220	55	unified	unify	VERB
fumecheng-10953	220	56	gradient	gradient	NOUN
fumecheng-10953	220	57	theory	theory	NOUN
fumecheng-10953	220	58	(	(	PUNCT
fumecheng-10953	220	59			NOUN
fumecheng-10953	220	60	=	=	SYM
fumecheng-10953	220	61	1/2	1/2	NUM
fumecheng-10953	220	62	)	)	PUNCT
fumecheng-10953	220	63	0/	0/	NOUN
fumecheng-10953	221	1			X
fumecheng-10953	221	2			NOUN
fumecheng-10953	221	3	0.1	0.1	X
fumecheng-10953	222	1	=	=	SYM
fumecheng-10953	222	2	0.3	0.3	NUM
fumecheng-10953	223	1	=	=	SYM
fumecheng-10953	223	2	0.5	0.5	NUM
fumecheng-10953	223	3	=	=	SYM
fumecheng-10953	223	4	0.7	0.7	X
fumecheng-10953	223	5	=	=	SYM
fumecheng-10953	223	6	1	1	NUM
fumecheng-10953	223	7	=	=	SYM
fumecheng-10953	223	8	0	0	PUNCT
fumecheng-10953	223	9	+	+	NUM
fumecheng-10953	223	10	1.01961	1.01961	NUM
fumecheng-10953	223	11	1.10882	1.10882	NUM
fumecheng-10953	223	12	1.17691	1.17691	NUM
fumecheng-10953	223	13	1.21442	1.21442	NUM
fumecheng-10953	223	14	1.24183	1.24183	NUM
fumecheng-10953	223	15	0.2	0.2	NUM
fumecheng-10953	223	16	0.98474	0.98474	NUM
fumecheng-10953	223	17	1.07291	1.07291	NUM
fumecheng-10953	223	18	1.14878	1.14878	NUM
fumecheng-10953	223	19	1.19436	1.19436	NUM
fumecheng-10953	223	20	1.22960	1.22960	NUM
fumecheng-10953	223	21	0.4	0.4	NUM
fumecheng-10953	223	22	0.93391	0.93391	NUM
fumecheng-10953	223	23	1.00737	1.00737	NUM
fumecheng-10953	223	24	1.08749	1.08749	NUM
fumecheng-10953	223	25	1.14557	1.14557	NUM
fumecheng-10953	223	26	1.19711	1.19711	NUM
fumecheng-10953	223	27	0.6	0.6	NUM
fumecheng-10953	223	28	0.90107	0.90107	NUM
fumecheng-10953	223	29	0.95534	0.95534	NUM
fumecheng-10953	223	30	1.02689	1.02689	NUM
fumecheng-10953	223	31	1.08913	1.08913	NUM
fumecheng-10953	223	32	1.15380	1.15380	NUM
fumecheng-10953	223	33	0.8	0.8	NUM
fumecheng-10953	223	34	0.88244	0.88244	NUM
fumecheng-10953	223	35	0.92161	0.92161	NUM
fumecheng-10953	223	36	0.98013	0.98013	NUM
fumecheng-10953	223	37	1.03862	1.03862	NUM
fumecheng-10953	223	38	1.10865	1.10865	NUM
fumecheng-10953	223	39	1.0	1.0	NUM
fumecheng-10953	223	40	0.87161	0.87161	NUM
fumecheng-10953	223	41	0.90034	0.90034	NUM
fumecheng-10953	223	42	0.94687	0.94687	NUM
fumecheng-10953	223	43	0.99821	0.99821	NUM
fumecheng-10953	223	44	1.06713	1.06713	NUM
fumecheng-10953	223	45	5	5	NUM
fumecheng-10953	223	46	.	.	PUNCT
fumecheng-10953	223	47	closing	closing	NOUN
fumecheng-10953	223	48	remarks	remark	NOUN
fumecheng-10953	223	49	a	a	DET
fumecheng-10953	223	50	stationary	stationary	ADJ
fumecheng-10953	223	51	variational	variational	ADJ
fumecheng-10953	223	52	framework	framework	NOUN
fumecheng-10953	223	53	is	be	AUX
fumecheng-10953	223	54	conceived	conceive	VERB
fumecheng-10953	223	55	to	to	PART
fumecheng-10953	223	56	study	study	VERB
fumecheng-10953	223	57	the	the	DET
fumecheng-10953	223	58	dynamic	dynamic	ADJ
fumecheng-10953	223	59	characteristics	characteristic	NOUN
fumecheng-10953	223	60	of	of	ADP
fumecheng-10953	223	61	elastic	elastic	ADJ
fumecheng-10953	223	62	nanobeams	nanobeam	NOUN
fumecheng-10953	223	63	within	within	ADP
fumecheng-10953	223	64	the	the	DET
fumecheng-10953	223	65	context	context	NOUN
fumecheng-10953	223	66	of	of	ADP
fumecheng-10953	223	67	the	the	DET
fumecheng-10953	223	68	mixture	mixture	NOUN
fumecheng-10953	223	69	unified	unify	VERB
fumecheng-10953	223	70	gradient	gradient	NOUN
fumecheng-10953	223	71	theory	theory	NOUN
fumecheng-10953	223	72	of	of	ADP
fumecheng-10953	223	73	elasticity	elasticity	NOUN
fumecheng-10953	223	74	.	.	PUNCT
fumecheng-10953	224	1	in	in	ADP
fumecheng-10953	224	2	view	view	NOUN
fumecheng-10953	224	3	of	of	ADP
fumecheng-10953	224	4	consistent	consistent	ADJ
fumecheng-10953	224	5	integration	integration	NOUN
fumecheng-10953	224	6	of	of	ADP
fumecheng-10953	224	7	the	the	DET
fumecheng-10953	224	8	stress	stress	NOUN
fumecheng-10953	224	9	gradient	gradient	NOUN
fumecheng-10953	224	10	theory	theory	NOUN
fumecheng-10953	224	11	,	,	PUNCT
fumecheng-10953	224	12	the	the	DET
fumecheng-10953	224	13	strain	strain	NOUN
fumecheng-10953	224	14	gradient	gradient	NOUN
fumecheng-10953	224	15	model	model	NOUN
fumecheng-10953	224	16	,	,	PUNCT
fumecheng-10953	224	17	and	and	CCONJ
fumecheng-10953	224	18	the	the	DET
fumecheng-10953	224	19	classical	classical	ADJ
fumecheng-10953	224	20	elasticity	elasticity	NOUN
fumecheng-10953	224	21	theory	theory	NOUN
fumecheng-10953	224	22	,	,	PUNCT
fumecheng-10953	224	23	the	the	DET
fumecheng-10953	224	24	peculiar	peculiar	ADJ
fumecheng-10953	224	25	size	size	NOUN
fumecheng-10953	224	26	-	-	PUNCT
fumecheng-10953	224	27	dependent	dependent	ADJ
fumecheng-10953	224	28	response	response	NOUN
fumecheng-10953	224	29	of	of	ADP
fumecheng-10953	224	30	the	the	DET
fumecheng-10953	224	31	elastic	elastic	ADJ
fumecheng-10953	224	32	nano	nano	NOUN
fumecheng-10953	224	33	-	-	PUNCT
fumecheng-10953	224	34	sized	sized	ADJ
fumecheng-10953	224	35	beams	beam	NOUN
fumecheng-10953	224	36	is	be	AUX
fumecheng-10953	224	37	efficiently	efficiently	ADV
fumecheng-10953	224	38	captured	capture	VERB
fumecheng-10953	224	39	.	.	PUNCT
fumecheng-10953	225	1	the	the	DET
fumecheng-10953	225	2	differential	differential	ADJ
fumecheng-10953	225	3	condition	condition	NOUN
fumecheng-10953	225	4	of	of	ADP
fumecheng-10953	225	5	dynamic	dynamic	ADJ
fumecheng-10953	225	6	equilibrium	equilibrium	NOUN
fumecheng-10953	225	7	,	,	PUNCT
fumecheng-10953	225	8	the	the	DET
fumecheng-10953	225	9	classical	classical	ADJ
fumecheng-10953	225	10	and	and	CCONJ
fumecheng-10953	225	11	the	the	DET
fumecheng-10953	225	12	extra	extra	ADJ
fumecheng-10953	225	13	non	non	ADJ
fumecheng-10953	225	14	-	-	ADJ
fumecheng-10953	225	15	standard	standard	ADJ
fumecheng-10953	225	16	boundary	boundary	ADJ
fumecheng-10953	225	17	conditions	condition	NOUN
fumecheng-10953	225	18	,	,	PUNCT
fumecheng-10953	225	19	and	and	CCONJ
fumecheng-10953	225	20	the	the	DET
fumecheng-10953	225	21	constitutive	constitutive	ADJ
fumecheng-10953	225	22	differential	differential	ADJ
fumecheng-10953	225	23	model	model	NOUN
fumecheng-10953	225	24	of	of	ADP
fumecheng-10953	225	25	the	the	DET
fumecheng-10953	225	26	elastic	elastic	ADJ
fumecheng-10953	225	27	nanobeams	nanobeam	NOUN
fumecheng-10953	225	28	are	be	AUX
fumecheng-10953	225	29	all	all	PRON
fumecheng-10953	225	30	incorporated	incorporate	VERB
fumecheng-10953	225	31	to	to	ADP
fumecheng-10953	225	32	the	the	DET
fumecheng-10953	225	33	introduced	introduce	VERB
fumecheng-10953	225	34	functional	functional	ADJ
fumecheng-10953	225	35	.	.	PUNCT
fumecheng-10953	226	1	to	to	PART
fumecheng-10953	226	2	close	close	VERB
fumecheng-10953	226	3	the	the	DET
fumecheng-10953	226	4	boundaryvalue	boundaryvalue	NOUN
fumecheng-10953	226	5	problem	problem	NOUN
fumecheng-10953	226	6	associated	associate	VERB
fumecheng-10953	226	7	with	with	ADP
fumecheng-10953	226	8	dynamics	dynamic	NOUN
fumecheng-10953	226	9	of	of	ADP
fumecheng-10953	226	10	elastic	elastic	ADJ
fumecheng-10953	226	11	nanobeams	nanobeam	NOUN
fumecheng-10953	226	12	,	,	PUNCT
fumecheng-10953	226	13	the	the	DET
fumecheng-10953	226	14	appropriate	appropriate	ADJ
fumecheng-10953	226	15	mathematical	mathematical	ADJ
fumecheng-10953	226	16	550	550	NUM
fumecheng-10953	226	17	s.	s.	PROPN
fumecheng-10953	226	18	a.	a.	PROPN
fumecheng-10953	226	19	faghidian	faghidian	PROPN
fumecheng-10953	226	20	,	,	PUNCT
fumecheng-10953	226	21	a.	a.	NOUN
fumecheng-10953	226	22	tounsi	tounsi	NOUN
fumecheng-10953	226	23	form	form	NOUN
fumecheng-10953	226	24	of	of	ADP
fumecheng-10953	226	25	the	the	DET
fumecheng-10953	226	26	extra	extra	ADJ
fumecheng-10953	226	27	non	non	ADJ
fumecheng-10953	226	28	-	-	ADJ
fumecheng-10953	226	29	standard	standard	ADJ
fumecheng-10953	226	30	boundary	boundary	ADJ
fumecheng-10953	226	31	conditions	condition	NOUN
fumecheng-10953	226	32	is	be	AUX
fumecheng-10953	226	33	determined	determine	VERB
fumecheng-10953	226	34	and	and	CCONJ
fumecheng-10953	226	35	prescribed	prescribe	VERB
fumecheng-10953	226	36	.	.	PUNCT
fumecheng-10953	227	1	various	various	ADJ
fumecheng-10953	227	2	augmented	augment	VERB
fumecheng-10953	227	3	elasticity	elasticity	NOUN
fumecheng-10953	227	4	theories	theory	NOUN
fumecheng-10953	227	5	of	of	ADP
fumecheng-10953	227	6	gradient	gradient	ADJ
fumecheng-10953	227	7	type	type	NOUN
fumecheng-10953	227	8	are	be	AUX
fumecheng-10953	227	9	retrieved	retrieve	VERB
fumecheng-10953	227	10	as	as	ADP
fumecheng-10953	227	11	special	special	ADJ
fumecheng-10953	227	12	cases	case	NOUN
fumecheng-10953	227	13	of	of	ADP
fumecheng-10953	227	14	the	the	DET
fumecheng-10953	227	15	introduced	introduce	VERB
fumecheng-10953	227	16	mixture	mixture	NOUN
fumecheng-10953	227	17	unified	unify	VERB
fumecheng-10953	227	18	gradient	gradient	NOUN
fumecheng-10953	227	19	theory	theory	NOUN
fumecheng-10953	227	20	via	via	ADP
fumecheng-10953	227	21	appropriate	appropriate	ADJ
fumecheng-10953	227	22	assumptions	assumption	NOUN
fumecheng-10953	227	23	on	on	ADP
fumecheng-10953	227	24	the	the	DET
fumecheng-10953	227	25	gradient	gradient	ADJ
fumecheng-10953	227	26	characteristic	characteristic	ADJ
fumecheng-10953	227	27	lengths	length	NOUN
fumecheng-10953	227	28	.	.	PUNCT
fumecheng-10953	228	1	the	the	DET
fumecheng-10953	228	2	classical	classical	ADJ
fumecheng-10953	228	3	elasticity	elasticity	NOUN
fumecheng-10953	228	4	model	model	NOUN
fumecheng-10953	228	5	is	be	AUX
fumecheng-10953	228	6	demonstrated	demonstrate	VERB
fumecheng-10953	228	7	to	to	PART
fumecheng-10953	228	8	be	be	AUX
fumecheng-10953	228	9	recovered	recover	VERB
fumecheng-10953	228	10	via	via	ADP
fumecheng-10953	228	11	either	either	CCONJ
fumecheng-10953	228	12	vanishing	vanish	VERB
fumecheng-10953	228	13	the	the	DET
fumecheng-10953	228	14	gradient	gradient	ADJ
fumecheng-10953	228	15	characteristic	characteristic	ADJ
fumecheng-10953	228	16	lengths	length	NOUN
fumecheng-10953	228	17	or	or	CCONJ
fumecheng-10953	228	18	by	by	ADP
fumecheng-10953	228	19	approaching	approach	VERB
fumecheng-10953	228	20	the	the	DET
fumecheng-10953	228	21	mixture	mixture	NOUN
fumecheng-10953	228	22	parameter	parameter	NOUN
fumecheng-10953	228	23	to	to	ADP
fumecheng-10953	228	24	unity	unity	NOUN
fumecheng-10953	228	25	in	in	ADP
fumecheng-10953	228	26	the	the	DET
fumecheng-10953	228	27	absence	absence	NOUN
fumecheng-10953	228	28	of	of	ADP
fumecheng-10953	228	29	the	the	DET
fumecheng-10953	228	30	strain	strain	NOUN
fumecheng-10953	228	31	gradient	gradient	ADJ
fumecheng-10953	228	32	length	length	NOUN
fumecheng-10953	228	33	-	-	PUNCT
fumecheng-10953	228	34	scale	scale	NOUN
fumecheng-10953	228	35	parameter	parameter	NOUN
fumecheng-10953	228	36	.	.	PUNCT
fumecheng-10953	229	1	the	the	DET
fumecheng-10953	229	2	wave	wave	NOUN
fumecheng-10953	229	3	dispersion	dispersion	NOUN
fumecheng-10953	229	4	response	response	NOUN
fumecheng-10953	229	5	of	of	ADP
fumecheng-10953	229	6	nano	nano	NOUN
fumecheng-10953	229	7	-	-	PUNCT
fumecheng-10953	229	8	sized	sized	ADJ
fumecheng-10953	229	9	beams	beam	NOUN
fumecheng-10953	229	10	is	be	AUX
fumecheng-10953	229	11	rigorously	rigorously	ADV
fumecheng-10953	229	12	examined	examine	VERB
fumecheng-10953	229	13	and	and	CCONJ
fumecheng-10953	229	14	the	the	DET
fumecheng-10953	229	15	analytical	analytical	ADJ
fumecheng-10953	229	16	solution	solution	NOUN
fumecheng-10953	229	17	of	of	ADP
fumecheng-10953	229	18	the	the	DET
fumecheng-10953	229	19	phase	phase	NOUN
fumecheng-10953	229	20	velocity	velocity	NOUN
fumecheng-10953	229	21	of	of	ADP
fumecheng-10953	229	22	dispersive	dispersive	ADJ
fumecheng-10953	229	23	waves	wave	NOUN
fumecheng-10953	229	24	is	be	AUX
fumecheng-10953	229	25	addressed	address	VERB
fumecheng-10953	229	26	.	.	PUNCT
fumecheng-10953	230	1	the	the	DET
fumecheng-10953	230	2	dispersive	dispersive	ADJ
fumecheng-10953	230	3	response	response	NOUN
fumecheng-10953	230	4	of	of	ADP
fumecheng-10953	230	5	waves	wave	NOUN
fumecheng-10953	230	6	within	within	ADP
fumecheng-10953	230	7	the	the	DET
fumecheng-10953	230	8	context	context	NOUN
fumecheng-10953	230	9	of	of	ADP
fumecheng-10953	230	10	the	the	DET
fumecheng-10953	230	11	mixture	mixture	NOUN
fumecheng-10953	230	12	unified	unify	VERB
fumecheng-10953	230	13	gradient	gradient	NOUN
fumecheng-10953	230	14	theory	theory	NOUN
fumecheng-10953	230	15	is	be	AUX
fumecheng-10953	230	16	graphically	graphically	ADV
fumecheng-10953	230	17	demonstrated	demonstrate	VERB
fumecheng-10953	230	18	and	and	CCONJ
fumecheng-10953	230	19	thoroughly	thoroughly	ADV
fumecheng-10953	230	20	discussed	discuss	VERB
fumecheng-10953	230	21	.	.	PUNCT
fumecheng-10953	231	1	the	the	DET
fumecheng-10953	231	2	free	free	ADJ
fumecheng-10953	231	3	vibrations	vibration	NOUN
fumecheng-10953	231	4	of	of	ADP
fumecheng-10953	231	5	nano	nano	NOUN
fumecheng-10953	231	6	-	-	PUNCT
fumecheng-10953	231	7	sized	sized	ADJ
fumecheng-10953	231	8	beams	beam	NOUN
fumecheng-10953	231	9	consistent	consistent	ADJ
fumecheng-10953	231	10	with	with	ADP
fumecheng-10953	231	11	the	the	DET
fumecheng-10953	231	12	mixture	mixture	NOUN
fumecheng-10953	231	13	unified	unify	VERB
fumecheng-10953	231	14	gradient	gradient	NOUN
fumecheng-10953	231	15	theory	theory	NOUN
fumecheng-10953	231	16	of	of	ADP
fumecheng-10953	231	17	elasticity	elasticity	NOUN
fumecheng-10953	231	18	is	be	AUX
fumecheng-10953	231	19	analytically	analytically	ADV
fumecheng-10953	231	20	examined	examine	VERB
fumecheng-10953	231	21	.	.	PUNCT
fumecheng-10953	232	1	numerical	numerical	ADJ
fumecheng-10953	232	2	vales	vale	NOUN
fumecheng-10953	232	3	of	of	ADP
fumecheng-10953	232	4	the	the	DET
fumecheng-10953	232	5	fundamental	fundamental	ADJ
fumecheng-10953	232	6	frequency	frequency	NOUN
fumecheng-10953	232	7	of	of	ADP
fumecheng-10953	232	8	mixture	mixture	NOUN
fumecheng-10953	232	9	unified	unify	VERB
fumecheng-10953	232	10	gradient	gradient	ADJ
fumecheng-10953	232	11	elastic	elastic	ADJ
fumecheng-10953	232	12	beams	beam	NOUN
fumecheng-10953	232	13	with	with	ADP
fumecheng-10953	232	14	kinematic	kinematic	ADJ
fumecheng-10953	232	15	constraints	constraint	NOUN
fumecheng-10953	232	16	of	of	ADP
fumecheng-10953	232	17	interest	interest	NOUN
fumecheng-10953	232	18	in	in	ADP
fumecheng-10953	232	19	nano	nano	NOUN
fumecheng-10953	232	20	-	-	NOUN
fumecheng-10953	232	21	mechanics	mechanic	NOUN
fumecheng-10953	232	22	,	,	PUNCT
fumecheng-10953	232	23	nanobeams	nanobeam	NOUN
fumecheng-10953	232	24	with	with	ADP
fumecheng-10953	232	25	fully	fully	ADV
fumecheng-10953	232	26	-	-	PUNCT
fumecheng-10953	232	27	fixed	fix	VERB
fumecheng-10953	232	28	and	and	CCONJ
fumecheng-10953	232	29	cantilever	cantilever	NOUN
fumecheng-10953	232	30	ends	end	VERB
fumecheng-10953	232	31	,	,	PUNCT
fumecheng-10953	232	32	are	be	AUX
fumecheng-10953	232	33	detected	detect	VERB
fumecheng-10953	232	34	,	,	PUNCT
fumecheng-10953	232	35	graphically	graphically	ADV
fumecheng-10953	232	36	illustrated	illustrate	VERB
fumecheng-10953	232	37	,	,	PUNCT
fumecheng-10953	232	38	and	and	CCONJ
fumecheng-10953	232	39	comprehensively	comprehensively	ADV
fumecheng-10953	232	40	commented	comment	VERB
fumecheng-10953	232	41	up	up	ADP
fumecheng-10953	232	42	on	on	ADP
fumecheng-10953	232	43	.	.	PUNCT
fumecheng-10953	233	1	the	the	DET
fumecheng-10953	233	2	expected	expect	VERB
fumecheng-10953	233	3	peculiar	peculiar	ADJ
fumecheng-10953	233	4	size	size	NOUN
fumecheng-10953	233	5	-	-	PUNCT
fumecheng-10953	233	6	dependent	dependent	ADJ
fumecheng-10953	233	7	behaviors	behavior	NOUN
fumecheng-10953	233	8	of	of	ADP
fumecheng-10953	233	9	elastic	elastic	ADJ
fumecheng-10953	233	10	nanobeams	nanobeam	NOUN
fumecheng-10953	233	11	,	,	PUNCT
fumecheng-10953	233	12	viz	viz	PROPN
fumecheng-10953	233	13	.	.	PUNCT
fumecheng-10953	234	1	the	the	DET
fumecheng-10953	234	2	stiffening	stiffen	VERB
fumecheng-10953	234	3	behavior	behavior	NOUN
fumecheng-10953	234	4	in	in	ADP
fumecheng-10953	234	5	terms	term	NOUN
fumecheng-10953	234	6	of	of	ADP
fumecheng-10953	234	7	the	the	DET
fumecheng-10953	234	8	strain	strain	NOUN
fumecheng-10953	234	9	gradient	gradient	ADJ
fumecheng-10953	234	10	characteristic	characteristic	ADJ
fumecheng-10953	234	11	parameter	parameter	NOUN
fumecheng-10953	234	12	and	and	CCONJ
fumecheng-10953	234	13	the	the	DET
fumecheng-10953	234	14	mixture	mixture	NOUN
fumecheng-10953	234	15	parameter	parameter	NOUN
fumecheng-10953	234	16	along	along	ADP
fumecheng-10953	234	17	with	with	ADP
fumecheng-10953	234	18	the	the	DET
fumecheng-10953	234	19	softening	soften	VERB
fumecheng-10953	234	20	response	response	NOUN
fumecheng-10953	234	21	in	in	ADP
fumecheng-10953	234	22	terms	term	NOUN
fumecheng-10953	234	23	of	of	ADP
fumecheng-10953	234	24	the	the	DET
fumecheng-10953	234	25	stress	stress	NOUN
fumecheng-10953	234	26	gradient	gradient	ADJ
fumecheng-10953	234	27	characteristic	characteristic	ADJ
fumecheng-10953	234	28	parameter	parameter	NOUN
fumecheng-10953	234	29	,	,	PUNCT
fumecheng-10953	234	30	are	be	AUX
fumecheng-10953	234	31	effectually	effectually	ADV
fumecheng-10953	234	32	confirmed	confirm	VERB
fumecheng-10953	234	33	.	.	PUNCT
fumecheng-10953	235	1	a	a	DET
fumecheng-10953	235	2	meticulous	meticulous	ADJ
fumecheng-10953	235	3	analysis	analysis	NOUN
fumecheng-10953	235	4	of	of	ADP
fumecheng-10953	235	5	the	the	DET
fumecheng-10953	235	6	dynamic	dynamic	ADJ
fumecheng-10953	235	7	characteristics	characteristic	NOUN
fumecheng-10953	235	8	of	of	ADP
fumecheng-10953	235	9	nano	nano	NOUN
fumecheng-10953	235	10	-	-	PUNCT
fumecheng-10953	235	11	scaled	scale	VERB
fumecheng-10953	235	12	elastic	elastic	ADJ
fumecheng-10953	235	13	beams	beam	NOUN
fumecheng-10953	235	14	is	be	AUX
fumecheng-10953	235	15	performed	perform	VERB
fumecheng-10953	235	16	presenting	present	VERB
fumecheng-10953	235	17	the	the	DET
fumecheng-10953	235	18	essential	essential	ADJ
fumecheng-10953	235	19	guide	guide	NOUN
fumecheng-10953	235	20	for	for	ADP
fumecheng-10953	235	21	the	the	DET
fumecheng-10953	235	22	practical	practical	ADJ
fumecheng-10953	235	23	assessment	assessment	NOUN
fumecheng-10953	235	24	of	of	ADP
fumecheng-10953	235	25	dynamics	dynamic	NOUN
fumecheng-10953	235	26	of	of	ADP
fumecheng-10953	235	27	beam	beam	NOUN
fumecheng-10953	235	28	-	-	PUNCT
fumecheng-10953	235	29	type	type	NOUN
fumecheng-10953	235	30	nano	nano	NOUN
fumecheng-10953	235	31	-	-	PUNCT
fumecheng-10953	235	32	components	component	NOUN
fumecheng-10953	235	33	of	of	ADP
fumecheng-10953	235	34	groundbreaking	groundbreake	VERB
fumecheng-10953	235	35	mems	mem	NOUN
fumecheng-10953	235	36	/	/	SYM
fumecheng-10953	235	37	nems	nem	NOUN
fumecheng-10953	235	38	.	.	PUNCT
fumecheng-10953	236	1	references	reference	NOUN
fumecheng-10953	236	2	1	1	NUM
fumecheng-10953	236	3	.	.	PUNCT
fumecheng-10953	237	1	dilena	dilena	PROPN
fumecheng-10953	237	2	,	,	PUNCT
fumecheng-10953	237	3	m.	m.	NOUN
fumecheng-10953	237	4	,	,	PUNCT
fumecheng-10953	237	5	fedele	fedele	PROPN
fumecheng-10953	237	6	dell’oste	dell’oste	NOUN
fumecheng-10953	237	7	,	,	PUNCT
fumecheng-10953	237	8	m.	m.	NOUN
fumecheng-10953	237	9	,	,	PUNCT
fumecheng-10953	237	10	fernández	fernández	PROPN
fumecheng-10953	237	11	-	-	PUNCT
fumecheng-10953	237	12	sáez	sáez	PROPN
fumecheng-10953	237	13	,	,	PUNCT
fumecheng-10953	237	14	j.	j.	PROPN
fumecheng-10953	237	15	,	,	PUNCT
fumecheng-10953	237	16	morassi	morassi	ADJ
fumecheng-10953	237	17	,	,	PUNCT
fumecheng-10953	237	18	a.	a.	PROPN
fumecheng-10953	237	19	,	,	PUNCT
fumecheng-10953	237	20	zaera	zaera	PROPN
fumecheng-10953	237	21	,	,	PUNCT
fumecheng-10953	237	22	r.	r.	PROPN
fumecheng-10953	237	23	,	,	PUNCT
fumecheng-10953	237	24	2020	2020	NUM
fumecheng-10953	237	25	,	,	PUNCT
fumecheng-10953	237	26	hearing	hear	VERB
fumecheng-10953	237	27	distributed	distribute	VERB
fumecheng-10953	237	28	mass	mass	NOUN
fumecheng-10953	237	29	in	in	ADP
fumecheng-10953	237	30	nanobeam	nanobeam	ADJ
fumecheng-10953	237	31	resonators	resonator	NOUN
fumecheng-10953	237	32	,	,	PUNCT
fumecheng-10953	237	33	international	international	ADJ
fumecheng-10953	237	34	journal	journal	NOUN
fumecheng-10953	237	35	of	of	ADP
fumecheng-10953	237	36	solids	solid	NOUN
fumecheng-10953	237	37	and	and	CCONJ
fumecheng-10953	237	38	structures	structure	NOUN
fumecheng-10953	237	39	,	,	PUNCT
fumecheng-10953	237	40	193–194	193–194	NUM
fumecheng-10953	237	41	,	,	PUNCT
fumecheng-10953	237	42	pp	pp	ADJ
fumecheng-10953	237	43	.	.	PUNCT
fumecheng-10953	238	1	568	568	NUM
fumecheng-10953	238	2	-	-	SYM
fumecheng-10953	238	3	592	592	NUM
fumecheng-10953	238	4	.	.	NOUN
fumecheng-10953	239	1	2	2	X
fumecheng-10953	239	2	.	.	X
fumecheng-10953	239	3	dilena	dilena	PROPN
fumecheng-10953	239	4	,	,	PUNCT
fumecheng-10953	239	5	m.	m.	NOUN
fumecheng-10953	239	6	,	,	PUNCT
fumecheng-10953	239	7	fedele	fedele	PROPN
fumecheng-10953	239	8	dell’oste	dell’oste	NOUN
fumecheng-10953	239	9	,	,	PUNCT
fumecheng-10953	239	10	m.	m.	NOUN
fumecheng-10953	239	11	,	,	PUNCT
fumecheng-10953	239	12	morassi	morassi	ADJ
fumecheng-10953	239	13	,	,	PUNCT
fumecheng-10953	239	14	a.	a.	NOUN
fumecheng-10953	239	15	,	,	PUNCT
fumecheng-10953	239	16	zaera	zaera	PROPN
fumecheng-10953	239	17	,	,	PUNCT
fumecheng-10953	239	18	r.	r.	PROPN
fumecheng-10953	239	19	,	,	PUNCT
fumecheng-10953	239	20	2021	2021	NUM
fumecheng-10953	239	21	,	,	PUNCT
fumecheng-10953	239	22	the	the	DET
fumecheng-10953	239	23	role	role	NOUN
fumecheng-10953	239	24	of	of	ADP
fumecheng-10953	239	25	boundary	boundary	ADJ
fumecheng-10953	239	26	conditions	condition	NOUN
fumecheng-10953	239	27	in	in	ADP
fumecheng-10953	239	28	resonatorbased	resonatorbase	VERB
fumecheng-10953	239	29	mass	mass	NOUN
fumecheng-10953	239	30	identification	identification	NOUN
fumecheng-10953	239	31	in	in	ADP
fumecheng-10953	239	32	nanorods	nanorod	NOUN
fumecheng-10953	239	33	,	,	PUNCT
fumecheng-10953	239	34	mechanics	mechanic	NOUN
fumecheng-10953	239	35	of	of	ADP
fumecheng-10953	239	36	advanced	advanced	ADJ
fumecheng-10953	239	37	materials	material	NOUN
fumecheng-10953	239	38	and	and	CCONJ
fumecheng-10953	239	39	structures	structure	NOUN
fumecheng-10953	239	40	.	.	PUNCT
fumecheng-10953	240	1	3	3	X
fumecheng-10953	240	2	.	.	X
fumecheng-10953	240	3	jena	jena	PROPN
fumecheng-10953	240	4	,	,	PUNCT
fumecheng-10953	240	5	s.k	s.k	PROPN
fumecheng-10953	240	6	.	.	PROPN
fumecheng-10953	240	7	,	,	PUNCT
fumecheng-10953	240	8	chakraverty	chakraverty	PROPN
fumecheng-10953	240	9	,	,	PUNCT
fumecheng-10953	240	10	s.	s.	PROPN
fumecheng-10953	240	11	,	,	PUNCT
fumecheng-10953	240	12	malikan	malikan	PROPN
fumecheng-10953	240	13	,	,	PUNCT
fumecheng-10953	240	14	m.	m.	NOUN
fumecheng-10953	240	15	,	,	PUNCT
fumecheng-10953	240	16	mohammad	mohammad	PROPN
fumecheng-10953	240	17	-	-	PUNCT
fumecheng-10953	240	18	sedighi	sedighi	PROPN
fumecheng-10953	240	19	,	,	PUNCT
fumecheng-10953	240	20	h.	h.	PROPN
fumecheng-10953	240	21	,	,	PUNCT
fumecheng-10953	240	22	2020	2020	NUM
fumecheng-10953	240	23	,	,	PUNCT
fumecheng-10953	240	24	hygro	hygro	NOUN
fumecheng-10953	240	25	-	-	PUNCT
fumecheng-10953	240	26	magnetic	magnetic	ADJ
fumecheng-10953	240	27	vibration	vibration	NOUN
fumecheng-10953	240	28	of	of	ADP
fumecheng-10953	240	29	the	the	DET
fumecheng-10953	240	30	single	single	ADJ
fumecheng-10953	240	31	-	-	PUNCT
fumecheng-10953	240	32	walled	wall	VERB
fumecheng-10953	240	33	carbon	carbon	NOUN
fumecheng-10953	240	34	nanotube	nanotube	NOUN
fumecheng-10953	240	35	with	with	ADP
fumecheng-10953	240	36	nonlinear	nonlinear	ADJ
fumecheng-10953	240	37	temperature	temperature	NOUN
fumecheng-10953	240	38	distribution	distribution	NOUN
fumecheng-10953	240	39	based	base	VERB
fumecheng-10953	240	40	on	on	ADP
fumecheng-10953	240	41	a	a	DET
fumecheng-10953	240	42	modified	modify	VERB
fumecheng-10953	240	43	beam	beam	NOUN
fumecheng-10953	240	44	theory	theory	NOUN
fumecheng-10953	240	45	and	and	CCONJ
fumecheng-10953	240	46	nonlocal	nonlocal	ADJ
fumecheng-10953	240	47	strain	strain	NOUN
fumecheng-10953	240	48	gradient	gradient	NOUN
fumecheng-10953	240	49	model	model	NOUN
fumecheng-10953	240	50	,	,	PUNCT
fumecheng-10953	240	51	international	international	ADJ
fumecheng-10953	240	52	journal	journal	NOUN
fumecheng-10953	240	53	of	of	ADP
fumecheng-10953	240	54	applied	apply	VERB
fumecheng-10953	240	55	mechanics	mechanic	NOUN
fumecheng-10953	240	56	,	,	PUNCT
fumecheng-10953	240	57	12	12	NUM
fumecheng-10953	240	58	,	,	PUNCT
fumecheng-10953	240	59	2050054	2050054	NUM
fumecheng-10953	240	60	.	.	PUNCT
fumecheng-10953	241	1	4	4	NUM
fumecheng-10953	241	2	.	.	X
fumecheng-10953	241	3	sedighi	sedighi	PROPN
fumecheng-10953	241	4	,	,	PUNCT
fumecheng-10953	241	5	h.m	h.m	PROPN
fumecheng-10953	241	6	.	.	PROPN
fumecheng-10953	241	7	,	,	PUNCT
fumecheng-10953	241	8	malikan	malikan	PROPN
fumecheng-10953	241	9	,	,	PUNCT
fumecheng-10953	241	10	m.	m.	NOUN
fumecheng-10953	241	11	,	,	PUNCT
fumecheng-10953	241	12	valipour	valipour	ADJ
fumecheng-10953	241	13	,	,	PUNCT
fumecheng-10953	241	14	a.	a.	NOUN
fumecheng-10953	241	15	,	,	PUNCT
fumecheng-10953	241	16	żur	żur	PROPN
fumecheng-10953	241	17	,	,	PUNCT
fumecheng-10953	241	18	k.k	k.k	PROPN
fumecheng-10953	241	19	.	.	PROPN
fumecheng-10953	241	20	,	,	PUNCT
fumecheng-10953	241	21	2020	2020	NUM
fumecheng-10953	241	22	,	,	PUNCT
fumecheng-10953	241	23	nonlocal	nonlocal	ADJ
fumecheng-10953	241	24	vibration	vibration	NOUN
fumecheng-10953	241	25	of	of	ADP
fumecheng-10953	241	26	carbon	carbon	NOUN
fumecheng-10953	241	27	/	/	SYM
fumecheng-10953	241	28	boron	boron	NOUN
fumecheng-10953	241	29	-	-	PUNCT
fumecheng-10953	241	30	nitride	nitride	NOUN
fumecheng-10953	241	31	nanohetero	nanohetero	NOUN
fumecheng-10953	241	32	-	-	PUNCT
fumecheng-10953	241	33	structure	structure	NOUN
fumecheng-10953	241	34	in	in	ADP
fumecheng-10953	241	35	thermal	thermal	ADJ
fumecheng-10953	241	36	and	and	CCONJ
fumecheng-10953	241	37	magnetic	magnetic	ADJ
fumecheng-10953	241	38	fields	field	NOUN
fumecheng-10953	241	39	by	by	ADP
fumecheng-10953	241	40	means	mean	NOUN
fumecheng-10953	241	41	of	of	ADP
fumecheng-10953	241	42	nonlinear	nonlinear	ADJ
fumecheng-10953	241	43	finite	finite	PROPN
fumecheng-10953	241	44	element	element	NOUN
fumecheng-10953	241	45	method	method	NOUN
fumecheng-10953	241	46	,	,	PUNCT
fumecheng-10953	241	47	journal	journal	NOUN
fumecheng-10953	241	48	of	of	ADP
fumecheng-10953	241	49	computational	computational	ADJ
fumecheng-10953	241	50	design	design	NOUN
fumecheng-10953	241	51	and	and	CCONJ
fumecheng-10953	241	52	engineering,7	engineering,7	NOUN
fumecheng-10953	241	53	,	,	PUNCT
fumecheng-10953	241	54	pp	pp	ADV
fumecheng-10953	241	55	.	.	PUNCT
fumecheng-10953	242	1	591	591	NUM
fumecheng-10953	242	2	-	-	SYM
fumecheng-10953	242	3	602	602	NUM
fumecheng-10953	242	4	.	.	PUNCT
fumecheng-10953	243	1	5	5	X
fumecheng-10953	243	2	.	.	X
fumecheng-10953	243	3	ghandourah	ghandourah	PROPN
fumecheng-10953	243	4	,	,	PUNCT
fumecheng-10953	243	5	e.e	e.e	PROPN
fumecheng-10953	243	6	.	.	PROPN
fumecheng-10953	243	7	,	,	PUNCT
fumecheng-10953	243	8	ahmed	ahmed	PROPN
fumecheng-10953	243	9	,	,	PUNCT
fumecheng-10953	243	10	h.m	h.m	PROPN
fumecheng-10953	243	11	.	.	PROPN
fumecheng-10953	243	12	,	,	PUNCT
fumecheng-10953	243	13	eltaher	eltaher	PROPN
fumecheng-10953	243	14	,	,	PUNCT
fumecheng-10953	243	15	m.a	m.a	PROPN
fumecheng-10953	243	16	.	.	PROPN
fumecheng-10953	243	17	,	,	PUNCT
fumecheng-10953	243	18	attia	attia	PROPN
fumecheng-10953	243	19	,	,	PUNCT
fumecheng-10953	243	20	m.a	m.a	PROPN
fumecheng-10953	243	21	.	.	PROPN
fumecheng-10953	243	22	,	,	PUNCT
fumecheng-10953	243	23	abdraboh	abdraboh	PROPN
fumecheng-10953	243	24	,	,	PUNCT
fumecheng-10953	243	25	a.m.	a.m.	ADV
fumecheng-10953	243	26	,	,	PUNCT
fumecheng-10953	243	27	2021	2021	NUM
fumecheng-10953	243	28	,	,	PUNCT
fumecheng-10953	243	29	free	free	ADJ
fumecheng-10953	243	30	vibration	vibration	NOUN
fumecheng-10953	243	31	of	of	ADP
fumecheng-10953	243	32	porous	porous	ADJ
fumecheng-10953	243	33	fg	fg	PROPN
fumecheng-10953	243	34	nonlocal	nonlocal	ADJ
fumecheng-10953	243	35	modified	modify	VERB
fumecheng-10953	243	36	couple	couple	NOUN
fumecheng-10953	243	37	nanobeams	nanobeam	NOUN
fumecheng-10953	243	38	via	via	ADP
fumecheng-10953	243	39	a	a	DET
fumecheng-10953	243	40	modified	modify	VERB
fumecheng-10953	243	41	porosity	porosity	NOUN
fumecheng-10953	243	42	model	model	NOUN
fumecheng-10953	243	43	,	,	PUNCT
fumecheng-10953	243	44	advances	advance	NOUN
fumecheng-10953	243	45	in	in	ADP
fumecheng-10953	243	46	nano	nano	NOUN
fumecheng-10953	243	47	research	research	NOUN
fumecheng-10953	243	48	,	,	PUNCT
fumecheng-10953	243	49	11	11	NUM
fumecheng-10953	243	50	,	,	PUNCT
fumecheng-10953	243	51	pp	pp	ADJ
fumecheng-10953	243	52	.	.	PUNCT
fumecheng-10953	244	1	405	405	NUM
fumecheng-10953	244	2	-	-	SYM
fumecheng-10953	244	3	422	422	NUM
fumecheng-10953	244	4	.	.	NOUN
fumecheng-10953	245	1	6	6	NUM
fumecheng-10953	245	2	.	.	X
fumecheng-10953	245	3	noroozi	noroozi	PROPN
fumecheng-10953	245	4	,	,	PUNCT
fumecheng-10953	245	5	m.	m.	NOUN
fumecheng-10953	245	6	,	,	PUNCT
fumecheng-10953	245	7	ghadiri	ghadiri	NOUN
fumecheng-10953	245	8	,	,	PUNCT
fumecheng-10953	245	9	m.	m.	NOUN
fumecheng-10953	245	10	,	,	PUNCT
fumecheng-10953	245	11	2021	2021	NUM
fumecheng-10953	245	12	,	,	PUNCT
fumecheng-10953	245	13	nonlinear	nonlinear	ADJ
fumecheng-10953	245	14	vibration	vibration	NOUN
fumecheng-10953	245	15	and	and	CCONJ
fumecheng-10953	245	16	stability	stability	NOUN
fumecheng-10953	245	17	analysis	analysis	NOUN
fumecheng-10953	245	18	of	of	ADP
fumecheng-10953	245	19	a	a	DET
fumecheng-10953	245	20	size	size	NOUN
fumecheng-10953	245	21	-	-	PUNCT
fumecheng-10953	245	22	dependent	dependent	ADJ
fumecheng-10953	245	23	viscoelastic	viscoelastic	NOUN
fumecheng-10953	245	24	cantilever	cantilever	NOUN
fumecheng-10953	245	25	nanobeam	nanobeam	NOUN
fumecheng-10953	245	26	with	with	ADP
fumecheng-10953	245	27	axial	axial	ADJ
fumecheng-10953	245	28	excitation	excitation	NOUN
fumecheng-10953	245	29	,	,	PUNCT
fumecheng-10953	245	30	proceedings	proceeding	NOUN
fumecheng-10953	245	31	of	of	ADP
fumecheng-10953	245	32	the	the	DET
fumecheng-10953	245	33	institution	institution	NOUN
fumecheng-10953	245	34	of	of	ADP
fumecheng-10953	245	35	mechanical	mechanical	ADJ
fumecheng-10953	245	36	engineers	engineer	NOUN
fumecheng-10953	245	37	,	,	PUNCT
fumecheng-10953	245	38	part	part	NOUN
fumecheng-10953	245	39	c	c	NOUN
fumecheng-10953	245	40	:	:	PUNCT
fumecheng-10953	245	41	journal	journal	NOUN
fumecheng-10953	245	42	of	of	ADP
fumecheng-10953	245	43	mechanical	mechanical	ADJ
fumecheng-10953	245	44	engineering	engineering	NOUN
fumecheng-10953	245	45	science	science	NOUN
fumecheng-10953	245	46	,	,	PUNCT
fumecheng-10953	245	47	235	235	NUM
fumecheng-10953	245	48	,	,	PUNCT
fumecheng-10953	245	49	pp	pp	ADJ
fumecheng-10953	245	50	.	.	PUNCT
fumecheng-10953	246	1	3624	3624	NUM
fumecheng-10953	246	2	-	-	SYM
fumecheng-10953	246	3	3640	3640	NUM
fumecheng-10953	246	4	.	.	PUNCT
fumecheng-10953	247	1	7	7	X
fumecheng-10953	247	2	.	.	X
fumecheng-10953	247	3	singhal	singhal	PROPN
fumecheng-10953	247	4	,	,	PUNCT
fumecheng-10953	247	5	a.	a.	PROPN
fumecheng-10953	247	6	,	,	PUNCT
fumecheng-10953	247	7	mohammad	mohammad	PROPN
fumecheng-10953	247	8	sedighi	sedighi	PROPN
fumecheng-10953	247	9	,	,	PUNCT
fumecheng-10953	247	10	h.	h.	PROPN
fumecheng-10953	247	11	,	,	PUNCT
fumecheng-10953	247	12	ebrahimi	ebrahimi	PROPN
fumecheng-10953	247	13	,	,	PUNCT
fumecheng-10953	247	14	f.	f.	PROPN
fumecheng-10953	247	15	,	,	PUNCT
fumecheng-10953	247	16	kuznetsova	kuznetsova	PROPN
fumecheng-10953	247	17	,	,	PUNCT
fumecheng-10953	247	18	i.	i.	PROPN
fumecheng-10953	247	19	,	,	PUNCT
fumecheng-10953	247	20	2021	2021	NUM
fumecheng-10953	247	21	,	,	PUNCT
fumecheng-10953	247	22	comparative	comparative	ADJ
fumecheng-10953	247	23	study	study	NOUN
fumecheng-10953	247	24	of	of	ADP
fumecheng-10953	247	25	the	the	DET
fumecheng-10953	247	26	flexoelectricity	flexoelectricity	NOUN
fumecheng-10953	247	27	effect	effect	NOUN
fumecheng-10953	247	28	with	with	ADP
fumecheng-10953	247	29	a	a	DET
fumecheng-10953	247	30	highly	highly	ADV
fumecheng-10953	247	31	/	/	SYM
fumecheng-10953	247	32	weakly	weakly	ADJ
fumecheng-10953	247	33	interface	interface	NOUN
fumecheng-10953	247	34	in	in	ADP
fumecheng-10953	247	35	distinct	distinct	ADJ
fumecheng-10953	247	36	piezoelectric	piezoelectric	NOUN
fumecheng-10953	247	37	materials	material	NOUN
fumecheng-10953	247	38	(	(	PUNCT
fumecheng-10953	247	39	pzt-2	pzt-2	NUM
fumecheng-10953	247	40	,	,	PUNCT
fumecheng-10953	247	41	pzt-4	pzt-4	NOUN
fumecheng-10953	247	42	,	,	PUNCT
fumecheng-10953	247	43	pzt-5h	pzt-5h	PROPN
fumecheng-10953	247	44	,	,	PUNCT
fumecheng-10953	247	45	linbo3	linbo3	ADJ
fumecheng-10953	247	46	,	,	PUNCT
fumecheng-10953	247	47	batio3	batio3	NOUN
fumecheng-10953	247	48	)	)	PUNCT
fumecheng-10953	247	49	,	,	PUNCT
fumecheng-10953	247	50	waves	wave	NOUN
fumecheng-10953	247	51	in	in	ADP
fumecheng-10953	247	52	random	random	ADJ
fumecheng-10953	247	53	and	and	CCONJ
fumecheng-10953	247	54	complex	complex	ADJ
fumecheng-10953	247	55	media	medium	NOUN
fumecheng-10953	247	56	,	,	PUNCT
fumecheng-10953	247	57	31	31	NUM
fumecheng-10953	247	58	,	,	PUNCT
fumecheng-10953	247	59	pp	pp	ADJ
fumecheng-10953	247	60	.	.	PUNCT
fumecheng-10953	247	61	1780	1780	NUM
fumecheng-10953	247	62	-	-	SYM
fumecheng-10953	247	63	1798	1798	NUM
fumecheng-10953	247	64	.	.	PUNCT
fumecheng-10953	248	1	8	8	X
fumecheng-10953	248	2	.	.	X
fumecheng-10953	249	1	abouelregal	abouelregal	ADJ
fumecheng-10953	249	2	,	,	PUNCT
fumecheng-10953	249	3	a.e	a.e	PROPN
fumecheng-10953	249	4	.	.	PROPN
fumecheng-10953	249	5	,	,	PUNCT
fumecheng-10953	249	6	mohammad	mohammad	PROPN
fumecheng-10953	249	7	sedighi	sedighi	PROPN
fumecheng-10953	249	8	,	,	PUNCT
fumecheng-10953	249	9	h.	h.	PROPN
fumecheng-10953	249	10	,	,	PUNCT
fumecheng-10953	249	11	2021	2021	NUM
fumecheng-10953	249	12	,	,	PUNCT
fumecheng-10953	249	13	a	a	DET
fumecheng-10953	249	14	new	new	ADJ
fumecheng-10953	249	15	insight	insight	NOUN
fumecheng-10953	249	16	into	into	ADP
fumecheng-10953	249	17	the	the	DET
fumecheng-10953	249	18	interaction	interaction	NOUN
fumecheng-10953	249	19	of	of	ADP
fumecheng-10953	249	20	thermoelasticity	thermoelasticity	NOUN
fumecheng-10953	249	21	with	with	ADP
fumecheng-10953	249	22	mass	mass	ADJ
fumecheng-10953	249	23	diffusion	diffusion	NOUN
fumecheng-10953	249	24	for	for	ADP
fumecheng-10953	249	25	a	a	DET
fumecheng-10953	249	26	half	half	ADJ
fumecheng-10953	249	27	-	-	PUNCT
fumecheng-10953	249	28	space	space	NOUN
fumecheng-10953	249	29	in	in	ADP
fumecheng-10953	249	30	the	the	DET
fumecheng-10953	249	31	context	context	NOUN
fumecheng-10953	249	32	of	of	ADP
fumecheng-10953	249	33	moore	moore	PROPN
fumecheng-10953	249	34	–	–	PUNCT
fumecheng-10953	249	35	gibson	gibson	PROPN
fumecheng-10953	249	36	–	–	PUNCT
fumecheng-10953	249	37	thompson	thompson	NOUN
fumecheng-10953	249	38	thermodiffusion	thermodiffusion	NOUN
fumecheng-10953	249	39	theory	theory	NOUN
fumecheng-10953	249	40	,	,	PUNCT
fumecheng-10953	249	41	applied	apply	VERB
fumecheng-10953	249	42	physics	physics	PROPN
fumecheng-10953	249	43	a	a	NOUN
fumecheng-10953	249	44	,	,	PUNCT
fumecheng-10953	249	45	127	127	NUM
fumecheng-10953	249	46	,	,	PUNCT
fumecheng-10953	249	47	582	582	NUM
fumecheng-10953	249	48	.	.	NOUN
fumecheng-10953	249	49	9	9	NUM
fumecheng-10953	249	50	.	.	NOUN
fumecheng-10953	249	51	jalaei	jalaei	NOUN
fumecheng-10953	249	52	,	,	PUNCT
fumecheng-10953	249	53	m.h	m.h	PROPN
fumecheng-10953	249	54	.	.	PROPN
fumecheng-10953	249	55	,	,	PUNCT
fumecheng-10953	249	56	thai	thai	PROPN
fumecheng-10953	249	57	,	,	PUNCT
fumecheng-10953	249	58	h.t	h.t	PROPN
fumecheng-10953	249	59	.	.	PROPN
fumecheng-10953	249	60	,	,	PUNCT
fumecheng-10953	249	61	civalek	civalek	PROPN
fumecheng-10953	249	62	ö.	ö.	PROPN
fumecheng-10953	249	63	,	,	PUNCT
fumecheng-10953	249	64	2022	2022	NUM
fumecheng-10953	249	65	,	,	PUNCT
fumecheng-10953	249	66	on	on	ADP
fumecheng-10953	249	67	viscoelastic	viscoelastic	ADJ
fumecheng-10953	249	68	transient	transient	ADJ
fumecheng-10953	249	69	response	response	NOUN
fumecheng-10953	249	70	of	of	ADP
fumecheng-10953	249	71	magnetically	magnetically	ADV
fumecheng-10953	249	72	imperfect	imperfect	ADJ
fumecheng-10953	249	73	functionally	functionally	ADV
fumecheng-10953	249	74	graded	grade	VERB
fumecheng-10953	249	75	nanobeams	nanobeam	NOUN
fumecheng-10953	249	76	,	,	PUNCT
fumecheng-10953	249	77	international	international	ADJ
fumecheng-10953	249	78	journal	journal	NOUN
fumecheng-10953	249	79	of	of	ADP
fumecheng-10953	249	80	engineering	engineering	NOUN
fumecheng-10953	249	81	science	science	NOUN
fumecheng-10953	249	82	172	172	NUM
fumecheng-10953	249	83	,	,	PUNCT
fumecheng-10953	249	84	103629	103629	NUM
fumecheng-10953	249	85	.	.	PUNCT
fumecheng-10953	250	1	10	10	NUM
fumecheng-10953	250	2	.	.	PUNCT
fumecheng-10953	251	1	mohammad	mohammad	PROPN
fumecheng-10953	251	2	sedighi	sedighi	PROPN
fumecheng-10953	251	3	,	,	PUNCT
fumecheng-10953	251	4	h.	h.	PROPN
fumecheng-10953	251	5	,	,	PUNCT
fumecheng-10953	251	6	2020	2020	NUM
fumecheng-10953	251	7	,	,	PUNCT
fumecheng-10953	251	8	divergence	divergence	NOUN
fumecheng-10953	251	9	and	and	CCONJ
fumecheng-10953	251	10	flutter	flutter	NOUN
fumecheng-10953	251	11	instability	instability	NOUN
fumecheng-10953	251	12	of	of	ADP
fumecheng-10953	251	13	magneto	magneto	NOUN
fumecheng-10953	251	14	-	-	PUNCT
fumecheng-10953	251	15	thermo	thermo	NOUN
fumecheng-10953	251	16	-	-	PUNCT
fumecheng-10953	251	17	elastic	elastic	ADJ
fumecheng-10953	251	18	c	c	NOUN
fumecheng-10953	251	19	-	-	PUNCT
fumecheng-10953	251	20	bn	bn	NOUN
fumecheng-10953	251	21	heteronanotubes	heteronanotube	NOUN
fumecheng-10953	251	22	conveying	convey	VERB
fumecheng-10953	251	23	fluid	fluid	NOUN
fumecheng-10953	251	24	,	,	PUNCT
fumecheng-10953	251	25	acta	acta	PROPN
fumecheng-10953	251	26	mechanica	mechanica	PROPN
fumecheng-10953	251	27	sinica	sinica	PROPN
fumecheng-10953	251	28	,	,	PUNCT
fumecheng-10953	251	29	36	36	NUM
fumecheng-10953	251	30	,	,	PUNCT
fumecheng-10953	251	31	pp	pp	ADJ
fumecheng-10953	251	32	.	.	PUNCT
fumecheng-10953	252	1	381	381	NUM
fumecheng-10953	252	2	-	-	SYM
fumecheng-10953	252	3	396	396	NUM
fumecheng-10953	252	4	.	.	PUNCT
fumecheng-10953	253	1	11	11	NUM
fumecheng-10953	253	2	.	.	X
fumecheng-10953	253	3	fang	fang	PROPN
fumecheng-10953	253	4	,	,	PUNCT
fumecheng-10953	253	5	j.	j.	PROPN
fumecheng-10953	253	6	,	,	PUNCT
fumecheng-10953	253	7	yin	yin	PROPN
fumecheng-10953	253	8	,	,	PUNCT
fumecheng-10953	253	9	b.	b.	PROPN
fumecheng-10953	253	10	,	,	PUNCT
fumecheng-10953	253	11	zhang	zhang	PROPN
fumecheng-10953	253	12	,	,	PUNCT
fumecheng-10953	253	13	x.	x.	PROPN
fumecheng-10953	253	14	,	,	PUNCT
fumecheng-10953	253	15	yang	yang	PROPN
fumecheng-10953	253	16	,	,	PUNCT
fumecheng-10953	253	17	b.	b.	PROPN
fumecheng-10953	253	18	,	,	PUNCT
fumecheng-10953	253	19	2022	2022	NUM
fumecheng-10953	253	20	,	,	PUNCT
fumecheng-10953	253	21	size	size	NOUN
fumecheng-10953	253	22	-	-	PUNCT
fumecheng-10953	253	23	dependent	dependent	ADJ
fumecheng-10953	253	24	vibration	vibration	NOUN
fumecheng-10953	253	25	of	of	ADP
fumecheng-10953	253	26	functionally	functionally	ADV
fumecheng-10953	253	27	graded	grade	VERB
fumecheng-10953	253	28	rotating	rotate	VERB
fumecheng-10953	253	29	nanobeams	nanobeam	NOUN
fumecheng-10953	253	30	with	with	ADP
fumecheng-10953	253	31	different	different	ADJ
fumecheng-10953	253	32	boundary	boundary	ADJ
fumecheng-10953	253	33	conditions	condition	NOUN
fumecheng-10953	253	34	based	base	VERB
fumecheng-10953	253	35	on	on	ADP
fumecheng-10953	253	36	nonlocal	nonlocal	ADJ
fumecheng-10953	253	37	elasticity	elasticity	NOUN
fumecheng-10953	253	38	theory	theory	NOUN
fumecheng-10953	253	39	,	,	PUNCT
fumecheng-10953	253	40	proceedings	proceeding	NOUN
fumecheng-10953	253	41	of	of	ADP
fumecheng-10953	253	42	the	the	DET
fumecheng-10953	253	43	institution	institution	NOUN
fumecheng-10953	253	44	of	of	ADP
fumecheng-10953	253	45	mechanical	mechanical	ADJ
fumecheng-10953	253	46	engineers	engineer	NOUN
fumecheng-10953	253	47	,	,	PUNCT
fumecheng-10953	253	48	part	part	NOUN
fumecheng-10953	253	49	c	c	NOUN
fumecheng-10953	253	50	:	:	PUNCT
fumecheng-10953	253	51	journal	journal	NOUN
fumecheng-10953	253	52	of	of	ADP
fumecheng-10953	253	53	mechanical	mechanical	ADJ
fumecheng-10953	253	54	engineering	engineering	NOUN
fumecheng-10953	253	55	science	science	NOUN
fumecheng-10953	253	56	,	,	PUNCT
fumecheng-10953	253	57	236	236	NUM
fumecheng-10953	253	58	,	,	PUNCT
fumecheng-10953	253	59	pp	pp	ADJ
fumecheng-10953	253	60	.	.	PUNCT
fumecheng-10953	254	1	2756	2756	NUM
fumecheng-10953	254	2	-	-	SYM
fumecheng-10953	254	3	2774	2774	NUM
fumecheng-10953	254	4	.	.	PUNCT
fumecheng-10953	255	1	dynamic	dynamic	ADJ
fumecheng-10953	255	2	characteristics	characteristic	NOUN
fumecheng-10953	255	3	of	of	ADP
fumecheng-10953	255	4	mixture	mixture	NOUN
fumecheng-10953	255	5	unified	unify	VERB
fumecheng-10953	255	6	gradient	gradient	ADJ
fumecheng-10953	255	7	elastic	elastic	ADJ
fumecheng-10953	255	8	nanobeams	nanobeam	NOUN
fumecheng-10953	255	9	551	551	NUM
fumecheng-10953	255	10	12	12	NUM
fumecheng-10953	255	11	.	.	PUNCT
fumecheng-10953	256	1	faghidian	faghidian	ADJ
fumecheng-10953	256	2	,	,	PUNCT
fumecheng-10953	256	3	s.a	s.a	PROPN
fumecheng-10953	256	4	.	.	PROPN
fumecheng-10953	256	5	,	,	PUNCT
fumecheng-10953	256	6	żur	żur	PROPN
fumecheng-10953	256	7	,	,	PUNCT
fumecheng-10953	256	8	k.k	k.k	PROPN
fumecheng-10953	256	9	.	.	PROPN
fumecheng-10953	256	10	,	,	PUNCT
fumecheng-10953	256	11	reddy	reddy	PROPN
fumecheng-10953	256	12	,	,	PUNCT
fumecheng-10953	256	13	j.n	j.n	PROPN
fumecheng-10953	256	14	.	.	PROPN
fumecheng-10953	256	15	,	,	PUNCT
fumecheng-10953	256	16	ferreira	ferreira	PROPN
fumecheng-10953	256	17	,	,	PUNCT
fumecheng-10953	256	18	a.j.m	a.j.m	NOUN
fumecheng-10953	256	19	.	.	PUNCT
fumecheng-10953	256	20	,	,	PUNCT
fumecheng-10953	256	21	2022	2022	NUM
fumecheng-10953	256	22	,	,	PUNCT
fumecheng-10953	256	23	on	on	ADP
fumecheng-10953	256	24	the	the	DET
fumecheng-10953	256	25	wave	wave	NOUN
fumecheng-10953	256	26	dispersion	dispersion	NOUN
fumecheng-10953	256	27	in	in	ADP
fumecheng-10953	256	28	functionally	functionally	ADV
fumecheng-10953	256	29	graded	grade	VERB
fumecheng-10953	256	30	porous	porous	ADJ
fumecheng-10953	256	31	timoshenko	timoshenko	NOUN
fumecheng-10953	256	32	-	-	PUNCT
fumecheng-10953	256	33	ehrenfest	ehrenfest	NOUN
fumecheng-10953	256	34	nanobeams	nanobeam	NOUN
fumecheng-10953	256	35	based	base	VERB
fumecheng-10953	256	36	on	on	ADP
fumecheng-10953	256	37	the	the	DET
fumecheng-10953	256	38	higher	high	ADJ
fumecheng-10953	256	39	-	-	PUNCT
fumecheng-10953	256	40	order	order	NOUN
fumecheng-10953	256	41	nonlocal	nonlocal	ADJ
fumecheng-10953	256	42	gradient	gradient	NOUN
fumecheng-10953	256	43	elasticity	elasticity	NOUN
fumecheng-10953	256	44	,	,	PUNCT
fumecheng-10953	256	45	composite	composite	ADJ
fumecheng-10953	256	46	structures	structure	NOUN
fumecheng-10953	256	47	,	,	PUNCT
fumecheng-10953	256	48	279	279	NUM
fumecheng-10953	256	49	,	,	PUNCT
fumecheng-10953	256	50	114819	114819	NUM
fumecheng-10953	256	51	.	.	PUNCT
fumecheng-10953	257	1	13	13	NUM
fumecheng-10953	257	2	.	.	PUNCT
fumecheng-10953	257	3	attia	attia	PROPN
fumecheng-10953	257	4	,	,	PUNCT
fumecheng-10953	257	5	a.	a.	NOUN
fumecheng-10953	257	6	,	,	PUNCT
fumecheng-10953	257	7	berrabah	berrabah	NOUN
fumecheng-10953	257	8	,	,	PUNCT
fumecheng-10953	257	9	a.t	a.t	PROPN
fumecheng-10953	257	10	.	.	PROPN
fumecheng-10953	257	11	,	,	PUNCT
fumecheng-10953	257	12	bousahla	bousahla	PROPN
fumecheng-10953	257	13	,	,	PUNCT
fumecheng-10953	257	14	a.a	a.a	PROPN
fumecheng-10953	257	15	.	.	PROPN
fumecheng-10953	257	16	,	,	PUNCT
fumecheng-10953	257	17	bourada	bourada	PROPN
fumecheng-10953	257	18	,	,	PUNCT
fumecheng-10953	257	19	f.	f.	PROPN
fumecheng-10953	257	20	,	,	PUNCT
fumecheng-10953	257	21	tounsi	tounsi	PROPN
fumecheng-10953	257	22	,	,	PUNCT
fumecheng-10953	257	23	a.	a.	NOUN
fumecheng-10953	257	24	,	,	PUNCT
fumecheng-10953	257	25	mahmoud	mahmoud	PROPN
fumecheng-10953	257	26	,	,	PUNCT
fumecheng-10953	257	27	s.r	s.r	PROPN
fumecheng-10953	257	28	.	.	PROPN
fumecheng-10953	257	29	,	,	PUNCT
fumecheng-10953	257	30	2021	2021	NUM
fumecheng-10953	257	31	,	,	PUNCT
fumecheng-10953	257	32	free	free	ADJ
fumecheng-10953	257	33	vibration	vibration	NOUN
fumecheng-10953	257	34	analysis	analysis	NOUN
fumecheng-10953	257	35	of	of	ADP
fumecheng-10953	257	36	fg	fg	PROPN
fumecheng-10953	257	37	plates	plate	NOUN
fumecheng-10953	257	38	under	under	ADP
fumecheng-10953	257	39	thermal	thermal	ADJ
fumecheng-10953	257	40	environment	environment	NOUN
fumecheng-10953	257	41	via	via	ADP
fumecheng-10953	257	42	a	a	DET
fumecheng-10953	257	43	simple	simple	ADJ
fumecheng-10953	257	44	4	4	NUM
fumecheng-10953	257	45	-	-	ADJ
fumecheng-10953	257	46	unknown	unknown	ADJ
fumecheng-10953	257	47	hsdt	hsdt	NOUN
fumecheng-10953	257	48	,	,	PUNCT
fumecheng-10953	257	49	steel	steel	NOUN
fumecheng-10953	257	50	and	and	CCONJ
fumecheng-10953	257	51	composite	composite	ADJ
fumecheng-10953	257	52	structures	structure	NOUN
fumecheng-10953	257	53	,	,	PUNCT
fumecheng-10953	257	54	41	41	NUM
fumecheng-10953	257	55	,	,	PUNCT
fumecheng-10953	257	56	pp	pp	ADJ
fumecheng-10953	257	57	.	.	PUNCT
fumecheng-10953	258	1	899	899	NUM
fumecheng-10953	258	2	-	-	SYM
fumecheng-10953	258	3	910	910	NUM
fumecheng-10953	258	4	.	.	PUNCT
fumecheng-10953	259	1	14	14	NUM
fumecheng-10953	259	2	.	.	PUNCT
fumecheng-10953	259	3	hellal	hellal	PROPN
fumecheng-10953	259	4	,	,	PUNCT
fumecheng-10953	259	5	h.	h.	PROPN
fumecheng-10953	259	6	,	,	PUNCT
fumecheng-10953	259	7	bourada	bourada	PROPN
fumecheng-10953	259	8	,	,	PUNCT
fumecheng-10953	259	9	m.	m.	NOUN
fumecheng-10953	259	10	,	,	PUNCT
fumecheng-10953	259	11	hebali	hebali	PROPN
fumecheng-10953	259	12	,	,	PUNCT
fumecheng-10953	259	13	h.	h.	PROPN
fumecheng-10953	259	14	,	,	PUNCT
fumecheng-10953	259	15	bourada	bourada	PROPN
fumecheng-10953	259	16	,	,	PUNCT
fumecheng-10953	259	17	f.	f.	PROPN
fumecheng-10953	259	18	,	,	PUNCT
fumecheng-10953	259	19	tounsi	tounsi	NOUN
fumecheng-10953	259	20	,	,	PUNCT
fumecheng-10953	259	21	a.	a.	NOUN
fumecheng-10953	259	22	,	,	PUNCT
fumecheng-10953	259	23	bousahla	bousahla	NOUN
fumecheng-10953	259	24	,	,	PUNCT
fumecheng-10953	259	25	a.a	a.a	PROPN
fumecheng-10953	259	26	.	.	PROPN
fumecheng-10953	259	27	,	,	PUNCT
fumecheng-10953	259	28	mahmoud	mahmoud	PROPN
fumecheng-10953	259	29	,	,	PUNCT
fumecheng-10953	259	30	s.r	s.r	PROPN
fumecheng-10953	259	31	.	.	PROPN
fumecheng-10953	259	32	,	,	PUNCT
fumecheng-10953	259	33	2021	2021	NUM
fumecheng-10953	259	34	,	,	PUNCT
fumecheng-10953	259	35	dynamic	dynamic	ADJ
fumecheng-10953	259	36	and	and	CCONJ
fumecheng-10953	259	37	stability	stability	NOUN
fumecheng-10953	259	38	analysis	analysis	NOUN
fumecheng-10953	259	39	of	of	ADP
fumecheng-10953	259	40	functionally	functionally	ADV
fumecheng-10953	259	41	graded	grade	VERB
fumecheng-10953	259	42	material	material	NOUN
fumecheng-10953	259	43	sandwich	sandwich	NOUN
fumecheng-10953	259	44	plates	plate	NOUN
fumecheng-10953	259	45	in	in	ADP
fumecheng-10953	259	46	hygro	hygro	PROPN
fumecheng-10953	259	47	-	-	PUNCT
fumecheng-10953	259	48	thermal	thermal	ADJ
fumecheng-10953	259	49	environment	environment	NOUN
fumecheng-10953	259	50	using	use	VERB
fumecheng-10953	259	51	a	a	DET
fumecheng-10953	259	52	simple	simple	ADJ
fumecheng-10953	259	53	higher	high	ADJ
fumecheng-10953	259	54	shear	shear	NOUN
fumecheng-10953	259	55	deformation	deformation	NOUN
fumecheng-10953	259	56	theory	theory	NOUN
fumecheng-10953	259	57	,	,	PUNCT
fumecheng-10953	259	58	journal	journal	NOUN
fumecheng-10953	259	59	of	of	ADP
fumecheng-10953	259	60	sandwich	sandwich	NOUN
fumecheng-10953	259	61	structures	structure	NOUN
fumecheng-10953	259	62	&	&	CCONJ
fumecheng-10953	259	63	materials	material	NOUN
fumecheng-10953	259	64	,	,	PUNCT
fumecheng-10953	259	65	23	23	NUM
fumecheng-10953	259	66	,	,	PUNCT
fumecheng-10953	259	67	pp	pp	ADJ
fumecheng-10953	259	68	.	.	PUNCT
fumecheng-10953	260	1	814	814	NUM
fumecheng-10953	260	2	-	-	SYM
fumecheng-10953	260	3	851	851	NUM
fumecheng-10953	260	4	.	.	PUNCT
fumecheng-10953	261	1	15	15	NUM
fumecheng-10953	261	2	.	.	PUNCT
fumecheng-10953	262	1	liu	liu	PROPN
fumecheng-10953	262	2	,	,	PUNCT
fumecheng-10953	262	3	g.	g.	PROPN
fumecheng-10953	262	4	,	,	PUNCT
fumecheng-10953	262	5	wu	wu	PROPN
fumecheng-10953	262	6	,	,	PUNCT
fumecheng-10953	262	7	s.	s.	PROPN
fumecheng-10953	262	8	,	,	PUNCT
fumecheng-10953	262	9	shahsavari	shahsavari	NOUN
fumecheng-10953	262	10	,	,	PUNCT
fumecheng-10953	262	11	d.	d.	PROPN
fumecheng-10953	262	12	,	,	PUNCT
fumecheng-10953	262	13	karami	karami	PROPN
fumecheng-10953	262	14	,	,	PUNCT
fumecheng-10953	262	15	b.	b.	PROPN
fumecheng-10953	262	16	,	,	PUNCT
fumecheng-10953	262	17	tounsi	tounsi	PROPN
fumecheng-10953	262	18	,	,	PUNCT
fumecheng-10953	262	19	a.	a.	NOUN
fumecheng-10953	262	20	,	,	PUNCT
fumecheng-10953	262	21	2022	2022	NUM
fumecheng-10953	262	22	,	,	PUNCT
fumecheng-10953	262	23	dynamics	dynamic	NOUN
fumecheng-10953	262	24	of	of	ADP
fumecheng-10953	262	25	imperfect	imperfect	ADJ
fumecheng-10953	262	26	inhomogeneous	inhomogeneous	ADJ
fumecheng-10953	262	27	nanoplate	nanoplate	NOUN
fumecheng-10953	262	28	with	with	ADP
fumecheng-10953	262	29	exponentially	exponentially	ADV
fumecheng-10953	262	30	-	-	PUNCT
fumecheng-10953	262	31	varying	vary	VERB
fumecheng-10953	262	32	properties	property	NOUN
fumecheng-10953	262	33	resting	rest	VERB
fumecheng-10953	262	34	on	on	ADP
fumecheng-10953	262	35	viscoelastic	viscoelastic	ADJ
fumecheng-10953	262	36	foundation	foundation	PROPN
fumecheng-10953	262	37	,	,	PUNCT
fumecheng-10953	262	38	european	european	PROPN
fumecheng-10953	262	39	journal	journal	PROPN
fumecheng-10953	262	40	of	of	ADP
fumecheng-10953	262	41	mechanics	mechanic	NOUN
fumecheng-10953	262	42	a	a	DET
fumecheng-10953	262	43	/	/	SYM
fumecheng-10953	262	44	solids	solid	NOUN
fumecheng-10953	262	45	,	,	PUNCT
fumecheng-10953	262	46	95	95	NUM
fumecheng-10953	262	47	,	,	PUNCT
fumecheng-10953	262	48	104649	104649	NUM
fumecheng-10953	262	49	.	.	PUNCT
fumecheng-10953	263	1	16	16	NUM
fumecheng-10953	263	2	.	.	PUNCT
fumecheng-10953	264	1	mindlin	mindlin	PROPN
fumecheng-10953	264	2	,	,	PUNCT
fumecheng-10953	264	3	r.d	r.d	PROPN
fumecheng-10953	264	4	.	.	PROPN
fumecheng-10953	264	5	,	,	PUNCT
fumecheng-10953	264	6	1965	1965	NUM
fumecheng-10953	264	7	,	,	PUNCT
fumecheng-10953	264	8	second	second	ADJ
fumecheng-10953	264	9	gradient	gradient	NOUN
fumecheng-10953	264	10	of	of	ADP
fumecheng-10953	264	11	strain	strain	NOUN
fumecheng-10953	264	12	and	and	CCONJ
fumecheng-10953	264	13	surface	surface	NOUN
fumecheng-10953	264	14	-	-	PUNCT
fumecheng-10953	264	15	tension	tension	NOUN
fumecheng-10953	264	16	in	in	ADP
fumecheng-10953	264	17	linear	linear	PROPN
fumecheng-10953	264	18	elasticity	elasticity	NOUN
fumecheng-10953	264	19	,	,	PUNCT
fumecheng-10953	264	20	international	international	ADJ
fumecheng-10953	264	21	journal	journal	NOUN
fumecheng-10953	264	22	of	of	ADP
fumecheng-10953	264	23	solids	solid	NOUN
fumecheng-10953	264	24	and	and	CCONJ
fumecheng-10953	264	25	structures	structure	NOUN
fumecheng-10953	264	26	,	,	PUNCT
fumecheng-10953	264	27	1	1	NUM
fumecheng-10953	264	28	,	,	PUNCT
fumecheng-10953	264	29	pp	pp	ADJ
fumecheng-10953	264	30	.	.	PUNCT
fumecheng-10953	265	1	417–438	417–438	NUM
fumecheng-10953	265	2	.	.	NOUN
fumecheng-10953	265	3	17	17	NUM
fumecheng-10953	265	4	.	.	PUNCT
fumecheng-10953	266	1	banerjee	banerjee	PROPN
fumecheng-10953	266	2	,	,	PUNCT
fumecheng-10953	266	3	j.r	j.r	PROPN
fumecheng-10953	266	4	.	.	PROPN
fumecheng-10953	266	5	,	,	PUNCT
fumecheng-10953	266	6	papkov	papkov	PROPN
fumecheng-10953	266	7	,	,	PUNCT
fumecheng-10953	266	8	s.o	s.o	PROPN
fumecheng-10953	266	9	.	.	PROPN
fumecheng-10953	266	10	,	,	PUNCT
fumecheng-10953	266	11	vo	vo	PROPN
fumecheng-10953	266	12	,	,	PUNCT
fumecheng-10953	266	13	t.p	t.p	PROPN
fumecheng-10953	266	14	.	.	PROPN
fumecheng-10953	266	15	,	,	PUNCT
fumecheng-10953	266	16	elishakoff	elishakoff	NOUN
fumecheng-10953	266	17	,	,	PUNCT
fumecheng-10953	266	18	i.	i.	NOUN
fumecheng-10953	266	19	,	,	PUNCT
fumecheng-10953	266	20	2021	2021	NUM
fumecheng-10953	266	21	,	,	PUNCT
fumecheng-10953	266	22	dynamic	dynamic	ADJ
fumecheng-10953	266	23	stiffness	stiffness	NOUN
fumecheng-10953	266	24	formulation	formulation	NOUN
fumecheng-10953	266	25	for	for	ADP
fumecheng-10953	266	26	a	a	DET
fumecheng-10953	266	27	micro	micro	ADJ
fumecheng-10953	266	28	beam	beam	NOUN
fumecheng-10953	266	29	using	use	VERB
fumecheng-10953	266	30	timoshenko	timoshenko	NOUN
fumecheng-10953	266	31	–	–	PUNCT
fumecheng-10953	266	32	ehrenfest	ehrenf	ADJ
fumecheng-10953	266	33	and	and	CCONJ
fumecheng-10953	266	34	modified	modify	VERB
fumecheng-10953	266	35	couple	couple	NOUN
fumecheng-10953	266	36	stress	stress	NOUN
fumecheng-10953	266	37	theories	theory	NOUN
fumecheng-10953	266	38	with	with	ADP
fumecheng-10953	266	39	applications	application	NOUN
fumecheng-10953	266	40	,	,	PUNCT
fumecheng-10953	266	41	journal	journal	NOUN
fumecheng-10953	266	42	of	of	ADP
fumecheng-10953	266	43	vibration	vibration	NOUN
fumecheng-10953	266	44	and	and	CCONJ
fumecheng-10953	266	45	control	control	NOUN
fumecheng-10953	266	46	.	.	PUNCT
fumecheng-10953	267	1	18	18	NUM
fumecheng-10953	267	2	.	.	X
fumecheng-10953	267	3	ramezani	ramezani	PROPN
fumecheng-10953	267	4	,	,	PUNCT
fumecheng-10953	267	5	m.	m.	NOUN
fumecheng-10953	267	6	,	,	PUNCT
fumecheng-10953	267	7	rezaiee	rezaiee	NOUN
fumecheng-10953	267	8	-	-	PUNCT
fumecheng-10953	267	9	pajand	pajand	NOUN
fumecheng-10953	267	10	,	,	PUNCT
fumecheng-10953	267	11	m.	m.	NOUN
fumecheng-10953	267	12	,	,	PUNCT
fumecheng-10953	267	13	tornabene	tornabene	NOUN
fumecheng-10953	267	14	,	,	PUNCT
fumecheng-10953	267	15	f.	f.	PROPN
fumecheng-10953	267	16	,	,	PUNCT
fumecheng-10953	267	17	2022	2022	NUM
fumecheng-10953	267	18	,	,	PUNCT
fumecheng-10953	267	19	linear	linear	ADJ
fumecheng-10953	267	20	and	and	CCONJ
fumecheng-10953	267	21	nonlinear	nonlinear	ADJ
fumecheng-10953	267	22	mechanical	mechanical	ADJ
fumecheng-10953	267	23	responses	response	NOUN
fumecheng-10953	267	24	of	of	ADP
fumecheng-10953	267	25	fggplrc	fggplrc	NOUN
fumecheng-10953	267	26	plates	plate	NOUN
fumecheng-10953	267	27	using	use	VERB
fumecheng-10953	267	28	a	a	DET
fumecheng-10953	267	29	novel	novel	ADJ
fumecheng-10953	267	30	strain	strain	NOUN
fumecheng-10953	267	31	-	-	PUNCT
fumecheng-10953	267	32	based	base	VERB
fumecheng-10953	267	33	formulation	formulation	NOUN
fumecheng-10953	267	34	of	of	ADP
fumecheng-10953	267	35	modified	modify	VERB
fumecheng-10953	267	36	fsdt	fsdt	NOUN
fumecheng-10953	267	37	theory	theory	NOUN
fumecheng-10953	267	38	,	,	PUNCT
fumecheng-10953	267	39	international	international	ADJ
fumecheng-10953	267	40	journal	journal	NOUN
fumecheng-10953	267	41	of	of	ADP
fumecheng-10953	267	42	nonlinear	nonlinear	ADJ
fumecheng-10953	267	43	mechanics	mechanic	NOUN
fumecheng-10953	267	44	,	,	PUNCT
fumecheng-10953	267	45	140	140	NUM
fumecheng-10953	267	46	,	,	PUNCT
fumecheng-10953	267	47	103923	103923	NUM
fumecheng-10953	267	48	.	.	PUNCT
fumecheng-10953	268	1	19	19	NUM
fumecheng-10953	268	2	.	.	PUNCT
fumecheng-10953	268	3	jena	jena	PROPN
fumecheng-10953	268	4	,	,	PUNCT
fumecheng-10953	268	5	s.k	s.k	PROPN
fumecheng-10953	268	6	.	.	PROPN
fumecheng-10953	268	7	,	,	PUNCT
fumecheng-10953	268	8	chakraverty	chakraverty	PROPN
fumecheng-10953	268	9	,	,	PUNCT
fumecheng-10953	268	10	s.	s.	PROPN
fumecheng-10953	268	11	,	,	PUNCT
fumecheng-10953	268	12	mahesh	mahesh	PROPN
fumecheng-10953	268	13	,	,	PUNCT
fumecheng-10953	268	14	v.	v.	PROPN
fumecheng-10953	268	15	,	,	PUNCT
fumecheng-10953	268	16	harursampath	harursampath	PROPN
fumecheng-10953	268	17	,	,	PUNCT
fumecheng-10953	268	18	d.	d.	PROPN
fumecheng-10953	268	19	,	,	PUNCT
fumecheng-10953	268	20	2022	2022	NUM
fumecheng-10953	268	21	,	,	PUNCT
fumecheng-10953	268	22	application	application	NOUN
fumecheng-10953	268	23	of	of	ADP
fumecheng-10953	268	24	haar	haar	PROPN
fumecheng-10953	268	25	wavelet	wavelet	NOUN
fumecheng-10953	268	26	discretization	discretization	NOUN
fumecheng-10953	268	27	and	and	CCONJ
fumecheng-10953	268	28	differential	differential	ADJ
fumecheng-10953	268	29	quadrature	quadrature	NOUN
fumecheng-10953	268	30	methods	method	NOUN
fumecheng-10953	268	31	for	for	ADP
fumecheng-10953	268	32	free	free	ADJ
fumecheng-10953	268	33	vibration	vibration	NOUN
fumecheng-10953	268	34	of	of	ADP
fumecheng-10953	268	35	functionally	functionally	ADV
fumecheng-10953	268	36	graded	grade	VERB
fumecheng-10953	268	37	micro	micro	NOUN
fumecheng-10953	268	38	-	-	NOUN
fumecheng-10953	268	39	beam	beam	ADJ
fumecheng-10953	268	40	with	with	ADP
fumecheng-10953	268	41	porosity	porosity	NOUN
fumecheng-10953	268	42	using	use	VERB
fumecheng-10953	268	43	modified	modify	VERB
fumecheng-10953	268	44	couple	couple	NOUN
fumecheng-10953	268	45	stress	stress	NOUN
fumecheng-10953	268	46	theory	theory	NOUN
fumecheng-10953	268	47	,	,	PUNCT
fumecheng-10953	268	48	engineering	engineer	VERB
fumecheng-10953	268	49	analysis	analysis	NOUN
fumecheng-10953	268	50	with	with	ADP
fumecheng-10953	268	51	boundary	boundary	ADJ
fumecheng-10953	268	52	elements	element	NOUN
fumecheng-10953	268	53	,	,	PUNCT
fumecheng-10953	268	54	140	140	NUM
fumecheng-10953	268	55	,	,	PUNCT
fumecheng-10953	268	56	pp	pp	ADJ
fumecheng-10953	268	57	.	.	PUNCT
fumecheng-10953	269	1	167	167	NUM
fumecheng-10953	269	2	-	-	SYM
fumecheng-10953	269	3	185	185	NUM
fumecheng-10953	269	4	.	.	PUNCT
fumecheng-10953	270	1	20	20	NUM
fumecheng-10953	270	2	.	.	PUNCT
fumecheng-10953	271	1	jiang	jiang	PROPN
fumecheng-10953	271	2	,	,	PUNCT
fumecheng-10953	271	3	y.	y.	PROPN
fumecheng-10953	271	4	,	,	PUNCT
fumecheng-10953	271	5	li	li	PROPN
fumecheng-10953	271	6	,	,	PUNCT
fumecheng-10953	271	7	l.	l.	PROPN
fumecheng-10953	271	8	,	,	PUNCT
fumecheng-10953	271	9	hu	hu	PROPN
fumecheng-10953	271	10	,	,	PUNCT
fumecheng-10953	271	11	y.	y.	NOUN
fumecheng-10953	271	12	,	,	PUNCT
fumecheng-10953	271	13	2022	2022	NUM
fumecheng-10953	271	14	,	,	PUNCT
fumecheng-10953	271	15	strain	strain	VERB
fumecheng-10953	271	16	gradient	gradient	ADJ
fumecheng-10953	271	17	elasticity	elasticity	NOUN
fumecheng-10953	271	18	theory	theory	NOUN
fumecheng-10953	271	19	of	of	ADP
fumecheng-10953	271	20	polymer	polymer	NOUN
fumecheng-10953	271	21	networks	network	NOUN
fumecheng-10953	271	22	,	,	PUNCT
fumecheng-10953	271	23	acta	acta	PROPN
fumecheng-10953	271	24	mechanica	mechanica	PROPN
fumecheng-10953	271	25	.	.	PROPN
fumecheng-10953	272	1	21	21	NUM
fumecheng-10953	272	2	.	.	PUNCT
fumecheng-10953	273	1	barretta	barretta	PROPN
fumecheng-10953	273	2	,	,	PUNCT
fumecheng-10953	273	3	r.	r.	PROPN
fumecheng-10953	273	4	,	,	PUNCT
fumecheng-10953	273	5	faghidian	faghidian	PROPN
fumecheng-10953	273	6	,	,	PUNCT
fumecheng-10953	273	7	s.a	s.a	PROPN
fumecheng-10953	273	8	.	.	PROPN
fumecheng-10953	273	9	,	,	PUNCT
fumecheng-10953	273	10	marotti	marotti	PROPN
fumecheng-10953	273	11	de	de	X
fumecheng-10953	273	12	sciarra	sciarra	PROPN
fumecheng-10953	273	13	,	,	PUNCT
fumecheng-10953	273	14	f.	f.	PROPN
fumecheng-10953	273	15	,	,	PUNCT
fumecheng-10953	273	16	2019	2019	NUM
fumecheng-10953	273	17	,	,	PUNCT
fumecheng-10953	273	18	aifantis	aifantis	PROPN
fumecheng-10953	273	19	versus	versus	ADP
fumecheng-10953	273	20	lam	lam	PROPN
fumecheng-10953	273	21	strain	strain	VERB
fumecheng-10953	273	22	gradient	gradient	NOUN
fumecheng-10953	273	23	models	model	NOUN
fumecheng-10953	273	24	of	of	ADP
fumecheng-10953	273	25	bishop	bishop	NOUN
fumecheng-10953	273	26	elastic	elastic	ADJ
fumecheng-10953	273	27	rods	rod	NOUN
fumecheng-10953	273	28	,	,	PUNCT
fumecheng-10953	273	29	acta	acta	PROPN
fumecheng-10953	273	30	mechanica	mechanica	PROPN
fumecheng-10953	273	31	,	,	PUNCT
fumecheng-10953	273	32	230	230	NUM
fumecheng-10953	273	33	,	,	PUNCT
fumecheng-10953	273	34	pp	pp	ADJ
fumecheng-10953	273	35	.	.	PUNCT
fumecheng-10953	274	1	2799–2812	2799–2812	NUM
fumecheng-10953	274	2	.	.	PUNCT
fumecheng-10953	275	1	22	22	NUM
fumecheng-10953	275	2	.	.	PUNCT
fumecheng-10953	276	1	forest	forest	NOUN
fumecheng-10953	276	2	,	,	PUNCT
fumecheng-10953	276	3	s.	s.	PROPN
fumecheng-10953	276	4	,	,	PUNCT
fumecheng-10953	276	5	sab	sab	PROPN
fumecheng-10953	276	6	,	,	PUNCT
fumecheng-10953	276	7	k.	k.	PROPN
fumecheng-10953	276	8	,	,	PUNCT
fumecheng-10953	276	9	2012	2012	NUM
fumecheng-10953	276	10	,	,	PUNCT
fumecheng-10953	276	11	stress	stress	NOUN
fumecheng-10953	276	12	gradient	gradient	ADJ
fumecheng-10953	276	13	continuum	continuum	ADJ
fumecheng-10953	276	14	theory	theory	NOUN
fumecheng-10953	276	15	,	,	PUNCT
fumecheng-10953	276	16	mechanics	mechanic	NOUN
fumecheng-10953	276	17	research	research	NOUN
fumecheng-10953	276	18	communications	communication	NOUN
fumecheng-10953	276	19	,	,	PUNCT
fumecheng-10953	276	20	40	40	NUM
fumecheng-10953	276	21	,	,	PUNCT
fumecheng-10953	276	22	pp	pp	ADJ
fumecheng-10953	276	23	.	.	PUNCT
fumecheng-10953	277	1	16	16	NUM
fumecheng-10953	277	2	-	-	SYM
fumecheng-10953	277	3	25	25	NUM
fumecheng-10953	277	4	.	.	PUNCT
fumecheng-10953	278	1	23	23	NUM
fumecheng-10953	278	2	.	.	PUNCT
fumecheng-10953	279	1	polizzotto	polizzotto	PROPN
fumecheng-10953	279	2	,	,	PUNCT
fumecheng-10953	279	3	c.	c.	NOUN
fumecheng-10953	279	4	,	,	PUNCT
fumecheng-10953	279	5	2014	2014	NUM
fumecheng-10953	279	6	,	,	PUNCT
fumecheng-10953	279	7	stress	stress	NOUN
fumecheng-10953	279	8	gradient	gradient	NOUN
fumecheng-10953	279	9	versus	versus	ADP
fumecheng-10953	279	10	strain	strain	NOUN
fumecheng-10953	279	11	gradient	gradient	ADJ
fumecheng-10953	279	12	constitutive	constitutive	ADJ
fumecheng-10953	279	13	models	model	NOUN
fumecheng-10953	279	14	within	within	ADP
fumecheng-10953	279	15	elasticity	elasticity	NOUN
fumecheng-10953	279	16	,	,	PUNCT
fumecheng-10953	279	17	international	international	ADJ
fumecheng-10953	279	18	journal	journal	NOUN
fumecheng-10953	279	19	of	of	ADP
fumecheng-10953	279	20	solids	solid	NOUN
fumecheng-10953	279	21	and	and	CCONJ
fumecheng-10953	279	22	structures	structure	NOUN
fumecheng-10953	279	23	,	,	PUNCT
fumecheng-10953	279	24	51	51	NUM
fumecheng-10953	279	25	,	,	PUNCT
fumecheng-10953	279	26	pp	pp	ADJ
fumecheng-10953	279	27	.	.	PUNCT
fumecheng-10953	280	1	1809	1809	NUM
fumecheng-10953	280	2	-	-	SYM
fumecheng-10953	280	3	1818	1818	NUM
fumecheng-10953	280	4	.	.	PUNCT
fumecheng-10953	281	1	24	24	NUM
fumecheng-10953	281	2	.	.	PUNCT
fumecheng-10953	282	1	eringen	eringen	PROPN
fumecheng-10953	282	2	,	,	PUNCT
fumecheng-10953	282	3	a.c	a.c	PROPN
fumecheng-10953	282	4	.	.	PROPN
fumecheng-10953	282	5	,	,	PUNCT
fumecheng-10953	282	6	2002	2002	NUM
fumecheng-10953	282	7	,	,	PUNCT
fumecheng-10953	282	8	nonlocal	nonlocal	ADJ
fumecheng-10953	282	9	continuum	continuum	ADJ
fumecheng-10953	282	10	field	field	NOUN
fumecheng-10953	282	11	theories	theory	NOUN
fumecheng-10953	282	12	,	,	PUNCT
fumecheng-10953	282	13	springer	springer	NOUN
fumecheng-10953	282	14	,	,	PUNCT
fumecheng-10953	282	15	new	new	PROPN
fumecheng-10953	282	16	york	york	PROPN
fumecheng-10953	282	17	.	.	PUNCT
fumecheng-10953	283	1	25	25	NUM
fumecheng-10953	283	2	.	.	X
fumecheng-10953	284	1	abouelregal	abouelregal	ADJ
fumecheng-10953	284	2	,	,	PUNCT
fumecheng-10953	284	3	a.e	a.e	PROPN
fumecheng-10953	284	4	.	.	PROPN
fumecheng-10953	284	5	,	,	PUNCT
fumecheng-10953	284	6	mohammad	mohammad	PROPN
fumecheng-10953	284	7	-	-	PUNCT
fumecheng-10953	284	8	sedighi	sedighi	PROPN
fumecheng-10953	284	9	,	,	PUNCT
fumecheng-10953	284	10	h.	h.	PROPN
fumecheng-10953	284	11	,	,	PUNCT
fumecheng-10953	284	12	faghidian	faghidian	PROPN
fumecheng-10953	284	13	,	,	PUNCT
fumecheng-10953	284	14	s.a	s.a	PROPN
fumecheng-10953	284	15	.	.	PROPN
fumecheng-10953	284	16	,	,	PUNCT
fumecheng-10953	284	17	shirazi	shirazi	PROPN
fumecheng-10953	284	18	,	,	PUNCT
fumecheng-10953	284	19	a.h	a.h	PROPN
fumecheng-10953	284	20	.	.	PROPN
fumecheng-10953	284	21	,	,	PUNCT
fumecheng-10953	284	22	2021	2021	NUM
fumecheng-10953	284	23	,	,	PUNCT
fumecheng-10953	284	24	temperature	temperature	NOUN
fumecheng-10953	284	25	-	-	PUNCT
fumecheng-10953	284	26	dependent	dependent	ADJ
fumecheng-10953	284	27	physical	physical	ADJ
fumecheng-10953	284	28	characteristics	characteristic	NOUN
fumecheng-10953	284	29	of	of	ADP
fumecheng-10953	284	30	the	the	DET
fumecheng-10953	284	31	rotating	rotate	VERB
fumecheng-10953	284	32	nonlocal	nonlocal	ADJ
fumecheng-10953	284	33	nanobeams	nanobeam	NOUN
fumecheng-10953	284	34	subject	subject	ADJ
fumecheng-10953	284	35	to	to	ADP
fumecheng-10953	284	36	a	a	DET
fumecheng-10953	284	37	varying	vary	VERB
fumecheng-10953	284	38	heat	heat	NOUN
fumecheng-10953	284	39	source	source	NOUN
fumecheng-10953	284	40	and	and	CCONJ
fumecheng-10953	284	41	a	a	DET
fumecheng-10953	284	42	dynamic	dynamic	ADJ
fumecheng-10953	284	43	load	load	NOUN
fumecheng-10953	284	44	,	,	PUNCT
fumecheng-10953	284	45	facta	facta	PROPN
fumecheng-10953	284	46	universitatis	universitatis	PROPN
fumecheng-10953	284	47	,	,	PUNCT
fumecheng-10953	284	48	series	series	NOUN
fumecheng-10953	284	49	:	:	PUNCT
fumecheng-10953	284	50	mechanical	mechanical	ADJ
fumecheng-10953	284	51	engineering	engineering	NOUN
fumecheng-10953	284	52	,	,	PUNCT
fumecheng-10953	284	53	19	19	NUM
fumecheng-10953	284	54	,	,	PUNCT
fumecheng-10953	284	55	pp	pp	ADJ
fumecheng-10953	284	56	.	.	PUNCT
fumecheng-10953	285	1	633	633	NUM
fumecheng-10953	285	2	-	-	SYM
fumecheng-10953	285	3	56	56	NUM
fumecheng-10953	285	4	.	.	NOUN
fumecheng-10953	286	1	26	26	NUM
fumecheng-10953	286	2	.	.	PUNCT
fumecheng-10953	287	1	pisano	pisano	PROPN
fumecheng-10953	287	2	,	,	PUNCT
fumecheng-10953	287	3	a.a	a.a	PROPN
fumecheng-10953	287	4	.	.	PROPN
fumecheng-10953	287	5	,	,	PUNCT
fumecheng-10953	287	6	fuschi	fuschi	PROPN
fumecheng-10953	287	7	,	,	PUNCT
fumecheng-10953	287	8	p.	p.	NOUN
fumecheng-10953	287	9	,	,	PUNCT
fumecheng-10953	287	10	polizzotto	polizzotto	PROPN
fumecheng-10953	287	11	,	,	PUNCT
fumecheng-10953	287	12	c.	c.	NOUN
fumecheng-10953	287	13	,	,	PUNCT
fumecheng-10953	287	14	2021	2021	NUM
fumecheng-10953	287	15	,	,	PUNCT
fumecheng-10953	287	16	integral	integral	ADJ
fumecheng-10953	287	17	and	and	CCONJ
fumecheng-10953	287	18	differential	differential	ADJ
fumecheng-10953	287	19	approaches	approach	NOUN
fumecheng-10953	287	20	to	to	ADP
fumecheng-10953	287	21	eringen	eringen	PROPN
fumecheng-10953	287	22	’s	’s	PART
fumecheng-10953	287	23	nonlocal	nonlocal	ADJ
fumecheng-10953	287	24	elasticity	elasticity	NOUN
fumecheng-10953	287	25	models	model	NOUN
fumecheng-10953	287	26	accounting	account	VERB
fumecheng-10953	287	27	for	for	ADP
fumecheng-10953	287	28	boundary	boundary	ADJ
fumecheng-10953	287	29	effects	effect	NOUN
fumecheng-10953	287	30	with	with	ADP
fumecheng-10953	287	31	applications	application	NOUN
fumecheng-10953	287	32	to	to	ADP
fumecheng-10953	287	33	beams	beam	NOUN
fumecheng-10953	287	34	in	in	ADP
fumecheng-10953	287	35	bending	bend	VERB
fumecheng-10953	287	36	,	,	PUNCT
fumecheng-10953	287	37	zamm	zamm	PROPN
fumecheng-10953	287	38	journal	journal	PROPN
fumecheng-10953	287	39	of	of	ADP
fumecheng-10953	287	40	applied	apply	VERB
fumecheng-10953	287	41	mathematics	mathematic	NOUN
fumecheng-10953	287	42	and	and	CCONJ
fumecheng-10953	287	43	mechanics	mechanic	NOUN
fumecheng-10953	287	44	,	,	PUNCT
fumecheng-10953	287	45	101	101	NUM
fumecheng-10953	287	46	,	,	PUNCT
fumecheng-10953	287	47	202000152	202000152	NUM
fumecheng-10953	287	48	.	.	PUNCT
fumecheng-10953	288	1	27	27	NUM
fumecheng-10953	288	2	.	.	X
fumecheng-10953	288	3	pisano	pisano	PROPN
fumecheng-10953	288	4	,	,	PUNCT
fumecheng-10953	288	5	a.a	a.a	PROPN
fumecheng-10953	288	6	.	.	PROPN
fumecheng-10953	288	7	,	,	PUNCT
fumecheng-10953	288	8	fuschi	fuschi	PROPN
fumecheng-10953	288	9	,	,	PUNCT
fumecheng-10953	288	10	p.	p.	NOUN
fumecheng-10953	288	11	,	,	PUNCT
fumecheng-10953	288	12	polizzotto	polizzotto	PROPN
fumecheng-10953	288	13	,	,	PUNCT
fumecheng-10953	288	14	c.	c.	NOUN
fumecheng-10953	288	15	,	,	PUNCT
fumecheng-10953	288	16	2020	2020	NUM
fumecheng-10953	288	17	,	,	PUNCT
fumecheng-10953	288	18	a	a	DET
fumecheng-10953	288	19	strain	strain	NOUN
fumecheng-10953	288	20	-	-	PUNCT
fumecheng-10953	288	21	difference	difference	NOUN
fumecheng-10953	288	22	based	base	VERB
fumecheng-10953	288	23	nonlocal	nonlocal	ADJ
fumecheng-10953	288	24	elasticity	elasticity	NOUN
fumecheng-10953	288	25	theory	theory	NOUN
fumecheng-10953	288	26	for	for	ADP
fumecheng-10953	288	27	smallscale	smallscale	ADJ
fumecheng-10953	288	28	shear	shear	NOUN
fumecheng-10953	288	29	deformable	deformable	ADJ
fumecheng-10953	288	30	beams	beam	NOUN
fumecheng-10953	288	31	with	with	ADP
fumecheng-10953	288	32	parametric	parametric	ADJ
fumecheng-10953	288	33	warping	warping	NOUN
fumecheng-10953	288	34	,	,	PUNCT
fumecheng-10953	288	35	international	international	ADJ
fumecheng-10953	288	36	journal	journal	NOUN
fumecheng-10953	288	37	for	for	ADP
fumecheng-10953	288	38	multiscale	multiscale	ADJ
fumecheng-10953	288	39	computational	computational	ADJ
fumecheng-10953	288	40	engineering	engineering	NOUN
fumecheng-10953	288	41	,	,	PUNCT
fumecheng-10953	288	42	18	18	NUM
fumecheng-10953	288	43	,	,	PUNCT
fumecheng-10953	288	44	pp	pp	ADJ
fumecheng-10953	288	45	.	.	PUNCT
fumecheng-10953	289	1	83–102	83–102	NUM
fumecheng-10953	289	2	.	.	NOUN
fumecheng-10953	289	3	28	28	NUM
fumecheng-10953	289	4	.	.	PUNCT
fumecheng-10953	290	1	akgöz	akgöz	PROPN
fumecheng-10953	290	2	,	,	PUNCT
fumecheng-10953	290	3	b.	b.	PROPN
fumecheng-10953	290	4	,	,	PUNCT
fumecheng-10953	290	5	civalek	civalek	NOUN
fumecheng-10953	290	6	,	,	PUNCT
fumecheng-10953	290	7	ö.	ö.	NOUN
fumecheng-10953	290	8	,	,	PUNCT
fumecheng-10953	290	9	2017	2017	NUM
fumecheng-10953	290	10	,	,	PUNCT
fumecheng-10953	290	11	a	a	DET
fumecheng-10953	290	12	size	size	NOUN
fumecheng-10953	290	13	-	-	PUNCT
fumecheng-10953	290	14	dependent	dependent	ADJ
fumecheng-10953	290	15	beam	beam	NOUN
fumecheng-10953	290	16	model	model	NOUN
fumecheng-10953	290	17	for	for	ADP
fumecheng-10953	290	18	stability	stability	NOUN
fumecheng-10953	290	19	of	of	ADP
fumecheng-10953	290	20	axially	axially	ADV
fumecheng-10953	290	21	loaded	load	VERB
fumecheng-10953	290	22	carbon	carbon	NOUN
fumecheng-10953	290	23	nanotubes	nanotube	NOUN
fumecheng-10953	290	24	surrounded	surround	VERB
fumecheng-10953	290	25	by	by	ADP
fumecheng-10953	290	26	pasternak	pasternak	PROPN
fumecheng-10953	290	27	elastic	elastic	PROPN
fumecheng-10953	290	28	foundation	foundation	NOUN
fumecheng-10953	290	29	,	,	PUNCT
fumecheng-10953	290	30	composite	composite	ADJ
fumecheng-10953	290	31	structures	structure	NOUN
fumecheng-10953	290	32	,	,	PUNCT
fumecheng-10953	290	33	176	176	NUM
fumecheng-10953	290	34	,	,	PUNCT
fumecheng-10953	290	35	pp	pp	ADJ
fumecheng-10953	290	36	.	.	PUNCT
fumecheng-10953	291	1	1028	1028	NUM
fumecheng-10953	291	2	-	-	SYM
fumecheng-10953	291	3	1038	1038	NUM
fumecheng-10953	291	4	.	.	PUNCT
fumecheng-10953	292	1	29	29	NUM
fumecheng-10953	292	2	.	.	X
fumecheng-10953	292	3	elishakoff	elishakoff	PROPN
fumecheng-10953	292	4	,	,	PUNCT
fumecheng-10953	292	5	i.	i.	PROPN
fumecheng-10953	292	6	,	,	PUNCT
fumecheng-10953	292	7	ajenjo	ajenjo	VERB
fumecheng-10953	292	8	,	,	PUNCT
fumecheng-10953	292	9	a.	a.	NOUN
fumecheng-10953	292	10	,	,	PUNCT
fumecheng-10953	292	11	livshits	livshit	NOUN
fumecheng-10953	292	12	,	,	PUNCT
fumecheng-10953	292	13	d.	d.	PROPN
fumecheng-10953	292	14	,	,	PUNCT
fumecheng-10953	292	15	2020	2020	NUM
fumecheng-10953	292	16	,	,	PUNCT
fumecheng-10953	292	17	generalization	generalization	NOUN
fumecheng-10953	292	18	of	of	ADP
fumecheng-10953	292	19	eringen	eringen	PROPN
fumecheng-10953	292	20	's	's	PART
fumecheng-10953	292	21	result	result	NOUN
fumecheng-10953	292	22	for	for	ADP
fumecheng-10953	292	23	random	random	ADJ
fumecheng-10953	292	24	response	response	NOUN
fumecheng-10953	292	25	of	of	ADP
fumecheng-10953	292	26	a	a	DET
fumecheng-10953	292	27	beam	beam	NOUN
fumecheng-10953	292	28	on	on	ADP
fumecheng-10953	292	29	elastic	elastic	ADJ
fumecheng-10953	292	30	foundation	foundation	NOUN
fumecheng-10953	292	31	,	,	PUNCT
fumecheng-10953	292	32	european	european	PROPN
fumecheng-10953	292	33	journal	journal	PROPN
fumecheng-10953	292	34	of	of	ADP
fumecheng-10953	292	35	mechanics	mechanic	NOUN
fumecheng-10953	292	36	a	a	DET
fumecheng-10953	292	37	/	/	SYM
fumecheng-10953	292	38	solids	solid	NOUN
fumecheng-10953	292	39	,	,	PUNCT
fumecheng-10953	292	40	81	81	NUM
fumecheng-10953	292	41	,	,	PUNCT
fumecheng-10953	292	42	103931	103931	NUM
fumecheng-10953	292	43	.	.	PUNCT
fumecheng-10953	293	1	30	30	NUM
fumecheng-10953	293	2	.	.	X
fumecheng-10953	294	1	civalek	civalek	PROPN
fumecheng-10953	294	2	,	,	PUNCT
fumecheng-10953	294	3	ö.	ö.	PROPN
fumecheng-10953	294	4	,	,	PUNCT
fumecheng-10953	294	5	uzun	uzun	PROPN
fumecheng-10953	294	6	,	,	PUNCT
fumecheng-10953	294	7	b.	b.	PROPN
fumecheng-10953	294	8	,	,	PUNCT
fumecheng-10953	294	9	yaylı	yaylı	NOUN
fumecheng-10953	294	10	,	,	PUNCT
fumecheng-10953	294	11	m.ö	m.ö	PROPN
fumecheng-10953	294	12	.	.	PROPN
fumecheng-10953	294	13	,	,	PUNCT
fumecheng-10953	294	14	akgöz	akgöz	PROPN
fumecheng-10953	294	15	,	,	PUNCT
fumecheng-10953	294	16	b.	b.	PROPN
fumecheng-10953	294	17	,	,	PUNCT
fumecheng-10953	294	18	2020	2020	NUM
fumecheng-10953	294	19	,	,	PUNCT
fumecheng-10953	294	20	size	size	NOUN
fumecheng-10953	294	21	-	-	PUNCT
fumecheng-10953	294	22	dependent	dependent	ADJ
fumecheng-10953	294	23	transverse	transverse	NOUN
fumecheng-10953	294	24	and	and	CCONJ
fumecheng-10953	294	25	longitudinal	longitudinal	ADJ
fumecheng-10953	294	26	vibrations	vibration	NOUN
fumecheng-10953	294	27	of	of	ADP
fumecheng-10953	294	28	embedded	embed	VERB
fumecheng-10953	294	29	carbon	carbon	NOUN
fumecheng-10953	294	30	and	and	CCONJ
fumecheng-10953	294	31	silica	silica	NOUN
fumecheng-10953	294	32	carbide	carbide	NOUN
fumecheng-10953	294	33	nanotubes	nanotube	NOUN
fumecheng-10953	294	34	by	by	ADP
fumecheng-10953	294	35	nonlocal	nonlocal	ADJ
fumecheng-10953	294	36	finite	finite	PROPN
fumecheng-10953	294	37	element	element	NOUN
fumecheng-10953	294	38	method	method	NOUN
fumecheng-10953	294	39	,	,	PUNCT
fumecheng-10953	294	40	european	european	PROPN
fumecheng-10953	294	41	physical	physical	PROPN
fumecheng-10953	294	42	journal	journal	PROPN
fumecheng-10953	294	43	plus	plus	CCONJ
fumecheng-10953	294	44	,	,	PUNCT
fumecheng-10953	294	45	135	135	NUM
fumecheng-10953	294	46	,	,	PUNCT
fumecheng-10953	294	47	381	381	NUM
fumecheng-10953	294	48	.	.	NOUN
fumecheng-10953	294	49	31	31	NUM
fumecheng-10953	294	50	.	.	PUNCT
fumecheng-10953	295	1	hache	hache	PROPN
fumecheng-10953	295	2	,	,	PUNCT
fumecheng-10953	295	3	f.	f.	PROPN
fumecheng-10953	295	4	,	,	PUNCT
fumecheng-10953	295	5	challamel	challamel	ADJ
fumecheng-10953	295	6	,	,	PUNCT
fumecheng-10953	295	7	n.	n.	NOUN
fumecheng-10953	295	8	,	,	PUNCT
fumecheng-10953	295	9	elishakoff	elishakoff	NOUN
fumecheng-10953	295	10	,	,	PUNCT
fumecheng-10953	295	11	i.	i.	NOUN
fumecheng-10953	295	12	,	,	PUNCT
fumecheng-10953	295	13	2019	2019	NUM
fumecheng-10953	295	14	,	,	PUNCT
fumecheng-10953	295	15	asymptotic	asymptotic	ADJ
fumecheng-10953	295	16	derivation	derivation	NOUN
fumecheng-10953	295	17	of	of	ADP
fumecheng-10953	295	18	nonlocal	nonlocal	ADJ
fumecheng-10953	295	19	plate	plate	NOUN
fumecheng-10953	295	20	models	model	NOUN
fumecheng-10953	295	21	from	from	ADP
fumecheng-10953	295	22	threedimensional	threedimensional	ADJ
fumecheng-10953	295	23	stress	stress	NOUN
fumecheng-10953	295	24	gradient	gradient	NOUN
fumecheng-10953	295	25	elasticity	elasticity	NOUN
fumecheng-10953	295	26	,	,	PUNCT
fumecheng-10953	295	27	continuum	continuum	ADJ
fumecheng-10953	295	28	mechanics	mechanic	NOUN
fumecheng-10953	295	29	and	and	CCONJ
fumecheng-10953	295	30	thermodynamics	thermodynamic	NOUN
fumecheng-10953	295	31	,	,	PUNCT
fumecheng-10953	295	32	31	31	NUM
fumecheng-10953	295	33	,	,	PUNCT
fumecheng-10953	295	34	pp	pp	ADJ
fumecheng-10953	295	35	.	.	PUNCT
fumecheng-10953	296	1	47–70	47–70	NUM
fumecheng-10953	296	2	.	.	PUNCT
fumecheng-10953	297	1	32	32	NUM
fumecheng-10953	297	2	.	.	PUNCT
fumecheng-10953	298	1	bendaida	bendaida	PROPN
fumecheng-10953	298	2	,	,	PUNCT
fumecheng-10953	298	3	m.	m.	NOUN
fumecheng-10953	298	4	,	,	PUNCT
fumecheng-10953	298	5	bousahla	bousahla	NOUN
fumecheng-10953	298	6	,	,	PUNCT
fumecheng-10953	298	7	a.a	a.a	PROPN
fumecheng-10953	298	8	.	.	PROPN
fumecheng-10953	298	9	,	,	PUNCT
fumecheng-10953	298	10	mouffoki	mouffoki	PROPN
fumecheng-10953	298	11	,	,	PUNCT
fumecheng-10953	298	12	a.	a.	NOUN
fumecheng-10953	298	13	,	,	PUNCT
fumecheng-10953	298	14	heireche	heireche	PROPN
fumecheng-10953	298	15	,	,	PUNCT
fumecheng-10953	298	16	h.	h.	PROPN
fumecheng-10953	298	17	,	,	PUNCT
fumecheng-10953	298	18	bourada	bourada	PROPN
fumecheng-10953	298	19	,	,	PUNCT
fumecheng-10953	298	20	f.	f.	PROPN
fumecheng-10953	298	21	,	,	PUNCT
fumecheng-10953	298	22	tounsi	tounsi	PROPN
fumecheng-10953	298	23	,	,	PUNCT
fumecheng-10953	298	24	a.	a.	NOUN
fumecheng-10953	298	25	,	,	PUNCT
fumecheng-10953	298	26	benachour	benachour	NOUN
fumecheng-10953	298	27	,	,	PUNCT
fumecheng-10953	298	28	a.	a.	NOUN
fumecheng-10953	298	29	,	,	PUNCT
fumecheng-10953	298	30	tounsi	tounsi	NOUN
fumecheng-10953	298	31	,	,	PUNCT
fumecheng-10953	298	32	a.	a.	NOUN
fumecheng-10953	298	33	,	,	PUNCT
fumecheng-10953	298	34	hussain	hussain	PROPN
fumecheng-10953	298	35	,	,	PUNCT
fumecheng-10953	298	36	m.	m.	NOUN
fumecheng-10953	298	37	,	,	PUNCT
fumecheng-10953	298	38	2022	2022	NUM
fumecheng-10953	298	39	,	,	PUNCT
fumecheng-10953	298	40	dynamic	dynamic	ADJ
fumecheng-10953	298	41	properties	property	NOUN
fumecheng-10953	298	42	of	of	ADP
fumecheng-10953	298	43	nonlocal	nonlocal	ADJ
fumecheng-10953	298	44	temperature	temperature	NOUN
fumecheng-10953	298	45	-	-	PUNCT
fumecheng-10953	298	46	dependent	dependent	ADJ
fumecheng-10953	298	47	fg	fg	PROPN
fumecheng-10953	298	48	nanobeams	nanobeam	NOUN
fumecheng-10953	298	49	under	under	ADP
fumecheng-10953	298	50	various	various	ADJ
fumecheng-10953	298	51	thermal	thermal	ADJ
fumecheng-10953	298	52	environments	environment	NOUN
fumecheng-10953	298	53	,	,	PUNCT
fumecheng-10953	298	54	transport	transport	NOUN
fumecheng-10953	298	55	in	in	ADP
fumecheng-10953	298	56	porous	porous	ADJ
fumecheng-10953	298	57	media	medium	NOUN
fumecheng-10953	298	58	,	,	PUNCT
fumecheng-10953	298	59	142	142	NUM
fumecheng-10953	298	60	,	,	PUNCT
fumecheng-10953	298	61	pp	pp	ADJ
fumecheng-10953	298	62	.	.	PUNCT
fumecheng-10953	299	1	187–208	187–208	NUM
fumecheng-10953	299	2	.	.	NOUN
fumecheng-10953	300	1	33	33	NUM
fumecheng-10953	300	2	.	.	PUNCT
fumecheng-10953	300	3	vinh	vinh	PROPN
fumecheng-10953	300	4	,	,	PUNCT
fumecheng-10953	300	5	p.-v	p.-v	PROPN
fumecheng-10953	300	6	.	.	PROPN
fumecheng-10953	300	7	,	,	PUNCT
fumecheng-10953	300	8	tounsi	tounsi	NOUN
fumecheng-10953	300	9	,	,	PUNCT
fumecheng-10953	300	10	a.	a.	NOUN
fumecheng-10953	300	11	,	,	PUNCT
fumecheng-10953	300	12	2021	2021	NUM
fumecheng-10953	300	13	,	,	PUNCT
fumecheng-10953	300	14	the	the	DET
fumecheng-10953	300	15	role	role	NOUN
fumecheng-10953	300	16	of	of	ADP
fumecheng-10953	300	17	spatial	spatial	ADJ
fumecheng-10953	300	18	variation	variation	NOUN
fumecheng-10953	300	19	of	of	ADP
fumecheng-10953	300	20	the	the	DET
fumecheng-10953	300	21	nonlocal	nonlocal	ADJ
fumecheng-10953	300	22	parameter	parameter	NOUN
fumecheng-10953	300	23	on	on	ADP
fumecheng-10953	300	24	the	the	DET
fumecheng-10953	300	25	free	free	ADJ
fumecheng-10953	300	26	vibration	vibration	NOUN
fumecheng-10953	300	27	of	of	ADP
fumecheng-10953	300	28	functionally	functionally	ADV
fumecheng-10953	300	29	graded	grade	VERB
fumecheng-10953	300	30	sandwich	sandwich	NOUN
fumecheng-10953	300	31	nanoplates	nanoplate	NOUN
fumecheng-10953	300	32	,	,	PUNCT
fumecheng-10953	300	33	engineering	engineer	VERB
fumecheng-10953	300	34	with	with	ADP
fumecheng-10953	300	35	computers	computer	NOUN
fumecheng-10953	300	36	.	.	PUNCT
fumecheng-10953	301	1	34	34	NUM
fumecheng-10953	301	2	.	.	PUNCT
fumecheng-10953	302	1	abouelregal	abouelregal	PROPN
fumecheng-10953	302	2	,	,	PUNCT
fumecheng-10953	302	3	a.e	a.e	PROPN
fumecheng-10953	302	4	.	.	PROPN
fumecheng-10953	302	5	,	,	PUNCT
fumecheng-10953	302	6	ersoy	ersoy	PROPN
fumecheng-10953	302	7	,	,	PUNCT
fumecheng-10953	302	8	h.	h.	PROPN
fumecheng-10953	302	9	,	,	PUNCT
fumecheng-10953	302	10	civalek	civalek	PROPN
fumecheng-10953	302	11	,	,	PUNCT
fumecheng-10953	302	12	ö.	ö.	NOUN
fumecheng-10953	302	13	,	,	PUNCT
fumecheng-10953	302	14	2021	2021	NUM
fumecheng-10953	302	15	,	,	PUNCT
fumecheng-10953	302	16	solution	solution	NOUN
fumecheng-10953	302	17	of	of	ADP
fumecheng-10953	302	18	moore	moore	PROPN
fumecheng-10953	302	19	–	–	PUNCT
fumecheng-10953	302	20	gibson	gibson	PROPN
fumecheng-10953	302	21	–	–	PUNCT
fumecheng-10953	302	22	thompson	thompson	NOUN
fumecheng-10953	302	23	equation	equation	NOUN
fumecheng-10953	302	24	of	of	ADP
fumecheng-10953	302	25	an	an	DET
fumecheng-10953	302	26	unbounded	unbounded	ADJ
fumecheng-10953	302	27	medium	medium	NOUN
fumecheng-10953	302	28	with	with	ADP
fumecheng-10953	302	29	a	a	DET
fumecheng-10953	302	30	cylindrical	cylindrical	ADJ
fumecheng-10953	302	31	hole	hole	NOUN
fumecheng-10953	302	32	,	,	PUNCT
fumecheng-10953	302	33	mathematics	mathematic	NOUN
fumecheng-10953	302	34	,	,	PUNCT
fumecheng-10953	302	35	9	9	NUM
fumecheng-10953	302	36	,	,	PUNCT
fumecheng-10953	302	37	1536	1536	NUM
fumecheng-10953	302	38	.	.	PUNCT
fumecheng-10953	303	1	35	35	NUM
fumecheng-10953	303	2	.	.	PUNCT
fumecheng-10953	304	1	khorasani	khorasani	PROPN
fumecheng-10953	304	2	,	,	PUNCT
fumecheng-10953	304	3	m.	m.	NOUN
fumecheng-10953	304	4	,	,	PUNCT
fumecheng-10953	304	5	elahi	elahi	PROPN
fumecheng-10953	304	6	,	,	PUNCT
fumecheng-10953	304	7	h.	h.	PROPN
fumecheng-10953	304	8	,	,	PUNCT
fumecheng-10953	304	9	eugeni	eugeni	NOUN
fumecheng-10953	304	10	,	,	PUNCT
fumecheng-10953	304	11	m.	m.	NOUN
fumecheng-10953	304	12	,	,	PUNCT
fumecheng-10953	304	13	lampani	lampani	PROPN
fumecheng-10953	304	14	,	,	PUNCT
fumecheng-10953	304	15	l.	l.	PROPN
fumecheng-10953	304	16	,	,	PUNCT
fumecheng-10953	304	17	civalek	civalek	NOUN
fumecheng-10953	304	18	,	,	PUNCT
fumecheng-10953	304	19	ö.	ö.	NOUN
fumecheng-10953	304	20	,	,	PUNCT
fumecheng-10953	304	21	2022	2022	NUM
fumecheng-10953	304	22	,	,	PUNCT
fumecheng-10953	304	23	vibration	vibration	NOUN
fumecheng-10953	304	24	of	of	ADP
fumecheng-10953	304	25	fg	fg	PROPN
fumecheng-10953	304	26	porous	porous	ADJ
fumecheng-10953	304	27	threelayered	threelayere	VERB
fumecheng-10953	304	28	beams	beam	NOUN
fumecheng-10953	304	29	equipped	equip	VERB
fumecheng-10953	304	30	by	by	ADP
fumecheng-10953	304	31	agglomerated	agglomerate	VERB
fumecheng-10953	304	32	nanocomposite	nanocomposite	PROPN
fumecheng-10953	304	33	patches	patch	NOUN
fumecheng-10953	304	34	resting	rest	VERB
fumecheng-10953	304	35	on	on	ADP
fumecheng-10953	304	36	vlasov	vlasov	NOUN
fumecheng-10953	304	37	's	's	PART
fumecheng-10953	304	38	foundation	foundation	NOUN
fumecheng-10953	304	39	,	,	PUNCT
fumecheng-10953	304	40	transport	transport	NOUN
fumecheng-10953	304	41	in	in	ADP
fumecheng-10953	304	42	porous	porous	ADJ
fumecheng-10953	304	43	media	medium	NOUN
fumecheng-10953	304	44	,	,	PUNCT
fumecheng-10953	304	45	142	142	NUM
fumecheng-10953	304	46	,	,	PUNCT
fumecheng-10953	304	47	pp	pp	ADJ
fumecheng-10953	304	48	.	.	PUNCT
fumecheng-10953	305	1	157	157	NUM
fumecheng-10953	305	2	-	-	SYM
fumecheng-10953	305	3	186	186	NUM
fumecheng-10953	305	4	.	.	PUNCT
fumecheng-10953	306	1	552	552	NUM
fumecheng-10953	306	2	s.	s.	PROPN
fumecheng-10953	306	3	a.	a.	PROPN
fumecheng-10953	306	4	faghidian	faghidian	PROPN
fumecheng-10953	306	5	,	,	PUNCT
fumecheng-10953	306	6	a.	a.	NOUN
fumecheng-10953	306	7	tounsi	tounsi	NOUN
fumecheng-10953	306	8	36	36	NUM
fumecheng-10953	306	9	.	.	PUNCT
fumecheng-10953	307	1	romano	romano	NOUN
fumecheng-10953	307	2	,	,	PUNCT
fumecheng-10953	307	3	g.	g.	PROPN
fumecheng-10953	307	4	,	,	PUNCT
fumecheng-10953	307	5	diaco	diaco	PROPN
fumecheng-10953	307	6	,	,	PUNCT
fumecheng-10953	307	7	m.	m.	NOUN
fumecheng-10953	307	8	,	,	PUNCT
fumecheng-10953	307	9	2021	2021	NUM
fumecheng-10953	307	10	,	,	PUNCT
fumecheng-10953	307	11	on	on	ADP
fumecheng-10953	307	12	formulation	formulation	NOUN
fumecheng-10953	307	13	of	of	ADP
fumecheng-10953	307	14	nonlocal	nonlocal	ADJ
fumecheng-10953	307	15	elasticity	elasticity	NOUN
fumecheng-10953	307	16	problems	problem	NOUN
fumecheng-10953	307	17	,	,	PUNCT
fumecheng-10953	307	18	meccanica	meccanica	PROPN
fumecheng-10953	307	19	,	,	PUNCT
fumecheng-10953	307	20	56	56	NUM
fumecheng-10953	307	21	,	,	PUNCT
fumecheng-10953	307	22	pp	pp	ADJ
fumecheng-10953	307	23	.	.	PUNCT
fumecheng-10953	308	1	1303	1303	NUM
fumecheng-10953	308	2	-	-	SYM
fumecheng-10953	308	3	1328	1328	NUM
fumecheng-10953	308	4	.	.	PUNCT
fumecheng-10953	309	1	37	37	NUM
fumecheng-10953	309	2	.	.	PUNCT
fumecheng-10953	310	1	aifantis	aifantis	PROPN
fumecheng-10953	310	2	,	,	PUNCT
fumecheng-10953	310	3	a.c	a.c	PROPN
fumecheng-10953	310	4	.	.	PROPN
fumecheng-10953	310	5	,	,	PUNCT
fumecheng-10953	310	6	2011	2011	NUM
fumecheng-10953	310	7	,	,	PUNCT
fumecheng-10953	310	8	on	on	ADP
fumecheng-10953	310	9	the	the	DET
fumecheng-10953	310	10	gradient	gradient	NOUN
fumecheng-10953	310	11	approach	approach	NOUN
fumecheng-10953	310	12	–	–	PUNCT
fumecheng-10953	310	13	relation	relation	NOUN
fumecheng-10953	310	14	to	to	ADP
fumecheng-10953	310	15	eringen	eringen	PROPN
fumecheng-10953	310	16	’s	’s	PART
fumecheng-10953	310	17	nonlocal	nonlocal	ADJ
fumecheng-10953	310	18	theory	theory	NOUN
fumecheng-10953	310	19	,	,	PUNCT
fumecheng-10953	310	20	international	international	ADJ
fumecheng-10953	310	21	journal	journal	NOUN
fumecheng-10953	310	22	of	of	ADP
fumecheng-10953	310	23	engineering	engineering	NOUN
fumecheng-10953	310	24	science	science	NOUN
fumecheng-10953	310	25	,	,	PUNCT
fumecheng-10953	310	26	49	49	NUM
fumecheng-10953	310	27	,	,	PUNCT
fumecheng-10953	310	28	pp	pp	ADJ
fumecheng-10953	310	29	.	.	PUNCT
fumecheng-10953	311	1	1367–1377	1367–1377	NUM
fumecheng-10953	311	2	.	.	PROPN
fumecheng-10953	312	1	38	38	NUM
fumecheng-10953	312	2	.	.	PUNCT
fumecheng-10953	313	1	polizzotto	polizzotto	PROPN
fumecheng-10953	313	2	,	,	PUNCT
fumecheng-10953	313	3	c.	c.	NOUN
fumecheng-10953	313	4	,	,	PUNCT
fumecheng-10953	313	5	2015	2015	NUM
fumecheng-10953	313	6	,	,	PUNCT
fumecheng-10953	313	7	a	a	DET
fumecheng-10953	313	8	unifying	unifying	ADJ
fumecheng-10953	313	9	variational	variational	ADJ
fumecheng-10953	313	10	framework	framework	NOUN
fumecheng-10953	313	11	for	for	ADP
fumecheng-10953	313	12	stress	stress	NOUN
fumecheng-10953	313	13	gradient	gradient	NOUN
fumecheng-10953	313	14	and	and	CCONJ
fumecheng-10953	313	15	strain	strain	VERB
fumecheng-10953	313	16	gradient	gradient	ADJ
fumecheng-10953	313	17	elasticity	elasticity	NOUN
fumecheng-10953	313	18	theories	theory	NOUN
fumecheng-10953	313	19	,	,	PUNCT
fumecheng-10953	313	20	european	european	ADJ
fumecheng-10953	313	21	journal	journal	PROPN
fumecheng-10953	313	22	of	of	ADP
fumecheng-10953	313	23	mechanics	mechanic	NOUN
fumecheng-10953	313	24	a	a	DET
fumecheng-10953	313	25	/	/	SYM
fumecheng-10953	313	26	solids	solid	NOUN
fumecheng-10953	313	27	,	,	PUNCT
fumecheng-10953	313	28	49	49	NUM
fumecheng-10953	313	29	,	,	PUNCT
fumecheng-10953	313	30	pp	pp	ADJ
fumecheng-10953	313	31	.	.	PUNCT
fumecheng-10953	314	1	430	430	NUM
fumecheng-10953	314	2	-	-	SYM
fumecheng-10953	314	3	440	440	NUM
fumecheng-10953	314	4	.	.	PUNCT
fumecheng-10953	315	1	39	39	NUM
fumecheng-10953	315	2	.	.	PUNCT
fumecheng-10953	316	1	faghidian	faghidian	PROPN
fumecheng-10953	316	2	,	,	PUNCT
fumecheng-10953	316	3	s.a	s.a	PROPN
fumecheng-10953	316	4	.	.	PROPN
fumecheng-10953	316	5	,	,	PUNCT
fumecheng-10953	316	6	2021	2021	NUM
fumecheng-10953	316	7	,	,	PUNCT
fumecheng-10953	316	8	flexure	flexure	VERB
fumecheng-10953	316	9	mechanics	mechanic	NOUN
fumecheng-10953	316	10	of	of	ADP
fumecheng-10953	316	11	nonlocal	nonlocal	ADJ
fumecheng-10953	316	12	modified	modify	VERB
fumecheng-10953	316	13	gradient	gradient	NOUN
fumecheng-10953	316	14	nanobeams	nanobeam	NOUN
fumecheng-10953	316	15	,	,	PUNCT
fumecheng-10953	316	16	journal	journal	NOUN
fumecheng-10953	316	17	of	of	ADP
fumecheng-10953	316	18	computational	computational	ADJ
fumecheng-10953	316	19	design	design	NOUN
fumecheng-10953	316	20	and	and	CCONJ
fumecheng-10953	316	21	engineering	engineering	NOUN
fumecheng-10953	316	22	,	,	PUNCT
fumecheng-10953	316	23	8	8	NUM
fumecheng-10953	316	24	,	,	PUNCT
fumecheng-10953	316	25	pp	pp	ADJ
fumecheng-10953	316	26	.	.	PUNCT
fumecheng-10953	317	1	949–959	949–959	NUM
fumecheng-10953	317	2	.	.	NOUN
fumecheng-10953	318	1	40	40	NUM
fumecheng-10953	318	2	.	.	PUNCT
fumecheng-10953	319	1	faghidian	faghidian	PROPN
fumecheng-10953	319	2	,	,	PUNCT
fumecheng-10953	319	3	s.a	s.a	PROPN
fumecheng-10953	319	4	.	.	PROPN
fumecheng-10953	319	5	,	,	PUNCT
fumecheng-10953	319	6	2021	2021	NUM
fumecheng-10953	319	7	,	,	PUNCT
fumecheng-10953	319	8	contribution	contribution	NOUN
fumecheng-10953	319	9	of	of	ADP
fumecheng-10953	319	10	nonlocal	nonlocal	ADJ
fumecheng-10953	319	11	integral	integral	ADJ
fumecheng-10953	319	12	elasticity	elasticity	NOUN
fumecheng-10953	319	13	to	to	ADP
fumecheng-10953	319	14	modified	modified	ADJ
fumecheng-10953	319	15	strain	strain	NOUN
fumecheng-10953	319	16	gradient	gradient	NOUN
fumecheng-10953	319	17	theory	theory	NOUN
fumecheng-10953	319	18	,	,	PUNCT
fumecheng-10953	319	19	european	european	PROPN
fumecheng-10953	319	20	physical	physical	PROPN
fumecheng-10953	319	21	journal	journal	PROPN
fumecheng-10953	319	22	plus	plus	CCONJ
fumecheng-10953	319	23	,	,	PUNCT
fumecheng-10953	319	24	136	136	NUM
fumecheng-10953	319	25	,	,	PUNCT
fumecheng-10953	319	26	559	559	NUM
fumecheng-10953	319	27	.	.	NOUN
fumecheng-10953	319	28	41	41	NUM
fumecheng-10953	319	29	.	.	PUNCT
fumecheng-10953	320	1	faghidian	faghidian	PROPN
fumecheng-10953	320	2	,	,	PUNCT
fumecheng-10953	320	3	s.a	s.a	PROPN
fumecheng-10953	320	4	.	.	PROPN
fumecheng-10953	320	5	,	,	PUNCT
fumecheng-10953	320	6	żur	żur	PROPN
fumecheng-10953	320	7	,	,	PUNCT
fumecheng-10953	320	8	k.k	k.k	PROPN
fumecheng-10953	320	9	.	.	PROPN
fumecheng-10953	320	10	,	,	PUNCT
fumecheng-10953	320	11	reddy	reddy	PROPN
fumecheng-10953	320	12	,	,	PUNCT
fumecheng-10953	320	13	j.n	j.n	PROPN
fumecheng-10953	320	14	.	.	PROPN
fumecheng-10953	320	15	,	,	PUNCT
fumecheng-10953	320	16	2022	2022	NUM
fumecheng-10953	320	17	,	,	PUNCT
fumecheng-10953	320	18	a	a	DET
fumecheng-10953	320	19	mixed	mixed	ADJ
fumecheng-10953	320	20	variational	variational	ADJ
fumecheng-10953	320	21	framework	framework	NOUN
fumecheng-10953	320	22	for	for	ADP
fumecheng-10953	320	23	higher	high	ADJ
fumecheng-10953	320	24	-	-	PUNCT
fumecheng-10953	320	25	order	order	NOUN
fumecheng-10953	320	26	unified	unified	ADJ
fumecheng-10953	320	27	gradient	gradient	NOUN
fumecheng-10953	320	28	elasticity	elasticity	NOUN
fumecheng-10953	320	29	,	,	PUNCT
fumecheng-10953	320	30	international	international	ADJ
fumecheng-10953	320	31	journal	journal	NOUN
fumecheng-10953	320	32	of	of	ADP
fumecheng-10953	320	33	engineering	engineering	NOUN
fumecheng-10953	320	34	science	science	NOUN
fumecheng-10953	320	35	,	,	PUNCT
fumecheng-10953	320	36	170	170	NUM
fumecheng-10953	320	37	,	,	PUNCT
fumecheng-10953	320	38	103603	103603	NUM
fumecheng-10953	320	39	.	.	PUNCT
fumecheng-10953	321	1	42	42	NUM
fumecheng-10953	321	2	.	.	PUNCT
fumecheng-10953	322	1	faghidian	faghidian	PROPN
fumecheng-10953	322	2	,	,	PUNCT
fumecheng-10953	322	3	s.a	s.a	PROPN
fumecheng-10953	322	4	.	.	PROPN
fumecheng-10953	322	5	,	,	PUNCT
fumecheng-10953	322	6	2020	2020	NUM
fumecheng-10953	322	7	,	,	PUNCT
fumecheng-10953	322	8	two‐phase	two‐phase	DET
fumecheng-10953	322	9	local	local	ADJ
fumecheng-10953	322	10	/	/	SYM
fumecheng-10953	322	11	nonlocal	nonlocal	ADJ
fumecheng-10953	322	12	gradient	gradient	ADJ
fumecheng-10953	322	13	mechanics	mechanic	NOUN
fumecheng-10953	322	14	of	of	ADP
fumecheng-10953	322	15	elastic	elastic	ADJ
fumecheng-10953	322	16	torsion	torsion	NOUN
fumecheng-10953	322	17	,	,	PUNCT
fumecheng-10953	322	18	mathematical	mathematical	ADJ
fumecheng-10953	322	19	methods	method	NOUN
fumecheng-10953	322	20	in	in	ADP
fumecheng-10953	322	21	the	the	DET
fumecheng-10953	322	22	applied	apply	VERB
fumecheng-10953	322	23	sciences	science	NOUN
fumecheng-10953	322	24	.	.	PUNCT
fumecheng-10953	323	1	43	43	NUM
fumecheng-10953	323	2	.	.	PUNCT
fumecheng-10953	324	1	faghidian	faghidian	PROPN
fumecheng-10953	324	2	,	,	PUNCT
fumecheng-10953	324	3	s.a	s.a	PROPN
fumecheng-10953	324	4	.	.	PROPN
fumecheng-10953	324	5	,	,	PUNCT
fumecheng-10953	324	6	higher	high	ADJ
fumecheng-10953	324	7	-	-	PUNCT
fumecheng-10953	324	8	order	order	NOUN
fumecheng-10953	324	9	mixture	mixture	NOUN
fumecheng-10953	324	10	nonlocal	nonlocal	ADJ
fumecheng-10953	324	11	gradient	gradient	NOUN
fumecheng-10953	324	12	theory	theory	NOUN
fumecheng-10953	324	13	of	of	ADP
fumecheng-10953	324	14	wave	wave	NOUN
fumecheng-10953	324	15	propagation	propagation	NOUN
fumecheng-10953	324	16	,	,	PUNCT
fumecheng-10953	324	17	mathematical	mathematical	ADJ
fumecheng-10953	324	18	methods	method	NOUN
fumecheng-10953	324	19	in	in	ADP
fumecheng-10953	324	20	the	the	DET
fumecheng-10953	324	21	applied	apply	VERB
fumecheng-10953	324	22	sciences	science	NOUN
fumecheng-10953	324	23	.	.	PUNCT
fumecheng-10953	325	1	44	44	NUM
fumecheng-10953	325	2	.	.	PUNCT
fumecheng-10953	326	1	li	li	PROPN
fumecheng-10953	326	2	,	,	PUNCT
fumecheng-10953	326	3	l.	l.	PROPN
fumecheng-10953	326	4	,	,	PUNCT
fumecheng-10953	326	5	lin	lin	PROPN
fumecheng-10953	326	6	,	,	PUNCT
fumecheng-10953	326	7	r.	r.	PROPN
fumecheng-10953	326	8	,	,	PUNCT
fumecheng-10953	326	9	ng	ng	PROPN
fumecheng-10953	326	10	,	,	PUNCT
fumecheng-10953	326	11	t.y	t.y	PROPN
fumecheng-10953	326	12	.	.	PROPN
fumecheng-10953	326	13	,	,	PUNCT
fumecheng-10953	326	14	2020	2020	NUM
fumecheng-10953	326	15	,	,	PUNCT
fumecheng-10953	326	16	contribution	contribution	NOUN
fumecheng-10953	326	17	of	of	ADP
fumecheng-10953	326	18	nonlocality	nonlocality	NOUN
fumecheng-10953	326	19	to	to	ADP
fumecheng-10953	326	20	surface	surface	NOUN
fumecheng-10953	326	21	elasticity	elasticity	NOUN
fumecheng-10953	326	22	,	,	PUNCT
fumecheng-10953	326	23	international	international	ADJ
fumecheng-10953	326	24	journal	journal	NOUN
fumecheng-10953	326	25	of	of	ADP
fumecheng-10953	326	26	engineering	engineering	NOUN
fumecheng-10953	326	27	science	science	NOUN
fumecheng-10953	326	28	,	,	PUNCT
fumecheng-10953	326	29	152	152	NUM
fumecheng-10953	326	30	,	,	PUNCT
fumecheng-10953	326	31	103311	103311	NUM
fumecheng-10953	326	32	.	.	PUNCT
fumecheng-10953	327	1	45	45	NUM
fumecheng-10953	327	2	.	.	PUNCT
fumecheng-10953	327	3	jiang	jiang	PROPN
fumecheng-10953	327	4	,	,	PUNCT
fumecheng-10953	327	5	y.	y.	PROPN
fumecheng-10953	327	6	,	,	PUNCT
fumecheng-10953	327	7	li	li	PROPN
fumecheng-10953	327	8	,	,	PUNCT
fumecheng-10953	327	9	l.	l.	PROPN
fumecheng-10953	327	10	,	,	PUNCT
fumecheng-10953	327	11	hu	hu	PROPN
fumecheng-10953	327	12	,	,	PUNCT
fumecheng-10953	327	13	y.	y.	NOUN
fumecheng-10953	327	14	,	,	PUNCT
fumecheng-10953	327	15	2022	2022	NUM
fumecheng-10953	327	16	,	,	PUNCT
fumecheng-10953	327	17	a	a	DET
fumecheng-10953	327	18	nonlocal	nonlocal	ADJ
fumecheng-10953	327	19	surface	surface	NOUN
fumecheng-10953	327	20	theory	theory	NOUN
fumecheng-10953	327	21	for	for	ADP
fumecheng-10953	327	22	surface	surface	NOUN
fumecheng-10953	327	23	–	–	PUNCT
fumecheng-10953	327	24	bulk	bulk	ADJ
fumecheng-10953	327	25	interactions	interaction	NOUN
fumecheng-10953	327	26	and	and	CCONJ
fumecheng-10953	327	27	its	its	PRON
fumecheng-10953	327	28	application	application	NOUN
fumecheng-10953	327	29	to	to	ADP
fumecheng-10953	327	30	mechanics	mechanic	NOUN
fumecheng-10953	327	31	of	of	ADP
fumecheng-10953	327	32	nanobeams	nanobeam	NOUN
fumecheng-10953	327	33	,	,	PUNCT
fumecheng-10953	327	34	international	international	ADJ
fumecheng-10953	327	35	journal	journal	NOUN
fumecheng-10953	327	36	of	of	ADP
fumecheng-10953	327	37	engineering	engineering	NOUN
fumecheng-10953	327	38	science	science	NOUN
fumecheng-10953	327	39	,	,	PUNCT
fumecheng-10953	327	40	172	172	NUM
fumecheng-10953	327	41	,	,	PUNCT
fumecheng-10953	327	42	103624	103624	NUM
fumecheng-10953	327	43	.	.	PUNCT
fumecheng-10953	328	1	46	46	NUM
fumecheng-10953	328	2	.	.	PUNCT
fumecheng-10953	329	1	zhu	zhu	PROPN
fumecheng-10953	329	2	,	,	PUNCT
fumecheng-10953	329	3	x.w	x.w	PROPN
fumecheng-10953	329	4	.	.	PROPN
fumecheng-10953	329	5	,	,	PUNCT
fumecheng-10953	329	6	li	li	PROPN
fumecheng-10953	329	7	,	,	PUNCT
fumecheng-10953	329	8	l.	l.	PROPN
fumecheng-10953	329	9	,	,	PUNCT
fumecheng-10953	329	10	2021	2021	NUM
fumecheng-10953	329	11	,	,	PUNCT
fumecheng-10953	329	12	three	three	NUM
fumecheng-10953	329	13	-	-	PUNCT
fumecheng-10953	329	14	dimensionally	dimensionally	ADV
fumecheng-10953	329	15	nonlocal	nonlocal	ADJ
fumecheng-10953	329	16	tensile	tensile	NOUN
fumecheng-10953	329	17	nanobars	nanobar	NOUN
fumecheng-10953	329	18	incorporating	incorporate	VERB
fumecheng-10953	329	19	surface	surface	NOUN
fumecheng-10953	329	20	effect	effect	NOUN
fumecheng-10953	329	21	:	:	PUNCT
fumecheng-10953	329	22	a	a	DET
fumecheng-10953	329	23	selfconsistent	selfconsistent	NOUN
fumecheng-10953	329	24	variational	variational	ADJ
fumecheng-10953	329	25	and	and	CCONJ
fumecheng-10953	329	26	well	well	ADV
fumecheng-10953	329	27	-	-	PUNCT
fumecheng-10953	329	28	posed	pose	VERB
fumecheng-10953	329	29	model	model	NOUN
fumecheng-10953	329	30	,	,	PUNCT
fumecheng-10953	329	31	science	science	PROPN
fumecheng-10953	329	32	china	china	PROPN
fumecheng-10953	329	33	technological	technological	ADJ
fumecheng-10953	329	34	sciences	science	NOUN
fumecheng-10953	329	35	,	,	PUNCT
fumecheng-10953	329	36	64	64	NUM
fumecheng-10953	329	37	,	,	PUNCT
fumecheng-10953	329	38	pp	pp	ADJ
fumecheng-10953	329	39	.	.	PUNCT
fumecheng-10953	330	1	2495	2495	NUM
fumecheng-10953	330	2	-	-	SYM
fumecheng-10953	330	3	2508	2508	NUM
fumecheng-10953	330	4	.	.	PUNCT
fumecheng-10953	331	1	47	47	NUM
fumecheng-10953	331	2	.	.	PUNCT
fumecheng-10953	332	1	faghidian	faghidian	PROPN
fumecheng-10953	332	2	,	,	PUNCT
fumecheng-10953	332	3	s.a	s.a	PROPN
fumecheng-10953	332	4	.	.	PROPN
fumecheng-10953	332	5	,	,	PUNCT
fumecheng-10953	332	6	żur	żur	PROPN
fumecheng-10953	332	7	,	,	PUNCT
fumecheng-10953	332	8	k.k	k.k	PROPN
fumecheng-10953	332	9	.	.	PROPN
fumecheng-10953	332	10	,	,	PUNCT
fumecheng-10953	332	11	pan	pan	PROPN
fumecheng-10953	332	12	,	,	PUNCT
fumecheng-10953	332	13	e.	e.	PROPN
fumecheng-10953	332	14	,	,	PUNCT
fumecheng-10953	332	15	kim	kim	PROPN
fumecheng-10953	332	16	,	,	PUNCT
fumecheng-10953	332	17	j.	j.	PROPN
fumecheng-10953	332	18	,	,	PUNCT
fumecheng-10953	332	19	2022	2022	NUM
fumecheng-10953	332	20	,	,	PUNCT
fumecheng-10953	332	21	on	on	ADP
fumecheng-10953	332	22	the	the	DET
fumecheng-10953	332	23	analytical	analytical	ADJ
fumecheng-10953	332	24	and	and	CCONJ
fumecheng-10953	332	25	meshless	meshless	ADJ
fumecheng-10953	332	26	numerical	numerical	ADJ
fumecheng-10953	332	27	approaches	approach	NOUN
fumecheng-10953	332	28	to	to	ADP
fumecheng-10953	332	29	mixture	mixture	NOUN
fumecheng-10953	332	30	stress	stress	NOUN
fumecheng-10953	332	31	gradient	gradient	NOUN
fumecheng-10953	332	32	functionally	functionally	ADV
fumecheng-10953	332	33	graded	grade	VERB
fumecheng-10953	332	34	nano	nano	NOUN
fumecheng-10953	332	35	-	-	PUNCT
fumecheng-10953	332	36	bar	bar	NOUN
fumecheng-10953	332	37	in	in	ADP
fumecheng-10953	332	38	tension	tension	NOUN
fumecheng-10953	332	39	,	,	PUNCT
fumecheng-10953	332	40	engineering	engineer	VERB
fumecheng-10953	332	41	analysis	analysis	NOUN
fumecheng-10953	332	42	with	with	ADP
fumecheng-10953	332	43	boundary	boundary	ADJ
fumecheng-10953	332	44	element	element	NOUN
fumecheng-10953	332	45	,	,	PUNCT
fumecheng-10953	332	46	134	134	NUM
fumecheng-10953	332	47	,	,	PUNCT
fumecheng-10953	332	48	pp	pp	ADJ
fumecheng-10953	332	49	.	.	PUNCT
fumecheng-10953	333	1	571	571	NUM
fumecheng-10953	333	2	-	-	SYM
fumecheng-10953	333	3	580	580	NUM
fumecheng-10953	333	4	.	.	PUNCT
fumecheng-10953	334	1	48	48	NUM
fumecheng-10953	334	2	.	.	PUNCT
fumecheng-10953	335	1	jena	jena	PROPN
fumecheng-10953	335	2	,	,	PUNCT
fumecheng-10953	335	3	s.k	s.k	PROPN
fumecheng-10953	335	4	.	.	PROPN
fumecheng-10953	335	5	,	,	PUNCT
fumecheng-10953	335	6	chakraverty	chakraverty	PROPN
fumecheng-10953	335	7	,	,	PUNCT
fumecheng-10953	335	8	s.	s.	PROPN
fumecheng-10953	335	9	,	,	PUNCT
fumecheng-10953	335	10	mahesh	mahesh	PROPN
fumecheng-10953	335	11	,	,	PUNCT
fumecheng-10953	335	12	v.	v.	PROPN
fumecheng-10953	335	13	,	,	PUNCT
fumecheng-10953	335	14	harursampath	harursampath	PROPN
fumecheng-10953	335	15	,	,	PUNCT
fumecheng-10953	335	16	d.	d.	PROPN
fumecheng-10953	335	17	,	,	PUNCT
fumecheng-10953	335	18	2022	2022	NUM
fumecheng-10953	335	19	,	,	PUNCT
fumecheng-10953	335	20	wavelet	wavelet	NOUN
fumecheng-10953	335	21	-	-	PUNCT
fumecheng-10953	335	22	based	base	VERB
fumecheng-10953	335	23	techniques	technique	NOUN
fumecheng-10953	335	24	for	for	ADP
fumecheng-10953	335	25	hygromagneto	hygromagneto	NOUN
fumecheng-10953	335	26	-	-	PUNCT
fumecheng-10953	335	27	thermo	thermo	NOUN
fumecheng-10953	335	28	vibration	vibration	NOUN
fumecheng-10953	335	29	of	of	ADP
fumecheng-10953	335	30	nonlocal	nonlocal	ADJ
fumecheng-10953	335	31	strain	strain	NOUN
fumecheng-10953	335	32	gradient	gradient	ADJ
fumecheng-10953	335	33	nanobeam	nanobeam	NOUN
fumecheng-10953	335	34	resting	rest	VERB
fumecheng-10953	335	35	on	on	ADP
fumecheng-10953	335	36	winkler	winkler	NOUN
fumecheng-10953	335	37	-	-	PUNCT
fumecheng-10953	335	38	pasternak	pasternak	PROPN
fumecheng-10953	335	39	elastic	elastic	ADJ
fumecheng-10953	335	40	foundation	foundation	NOUN
fumecheng-10953	335	41	,	,	PUNCT
fumecheng-10953	335	42	engineering	engineer	VERB
fumecheng-10953	335	43	analysis	analysis	NOUN
fumecheng-10953	335	44	with	with	ADP
fumecheng-10953	335	45	boundary	boundary	ADJ
fumecheng-10953	335	46	elements	element	NOUN
fumecheng-10953	335	47	,	,	PUNCT
fumecheng-10953	335	48	140	140	NUM
fumecheng-10953	335	49	,	,	PUNCT
fumecheng-10953	335	50	pp	pp	ADJ
fumecheng-10953	335	51	.	.	PUNCT
fumecheng-10953	336	1	494	494	NUM
fumecheng-10953	336	2	-	-	SYM
fumecheng-10953	336	3	506	506	NUM
fumecheng-10953	336	4	.	.	PUNCT
fumecheng-10953	336	5	49	49	NUM
fumecheng-10953	336	6	.	.	PUNCT
fumecheng-10953	337	1	jena	jena	PROPN
fumecheng-10953	337	2	,	,	PUNCT
fumecheng-10953	337	3	s.k	s.k	PROPN
fumecheng-10953	337	4	.	.	PROPN
fumecheng-10953	337	5	,	,	PUNCT
fumecheng-10953	337	6	chakraverty	chakraverty	PROPN
fumecheng-10953	337	7	,	,	PUNCT
fumecheng-10953	337	8	s.	s.	PROPN
fumecheng-10953	337	9	,	,	PUNCT
fumecheng-10953	337	10	malikan	malikan	PROPN
fumecheng-10953	337	11	,	,	PUNCT
fumecheng-10953	337	12	m.	m.	NOUN
fumecheng-10953	337	13	,	,	PUNCT
fumecheng-10953	337	14	2020	2020	NUM
fumecheng-10953	337	15	,	,	PUNCT
fumecheng-10953	337	16	stability	stability	NOUN
fumecheng-10953	337	17	analysis	analysis	NOUN
fumecheng-10953	337	18	of	of	ADP
fumecheng-10953	337	19	nanobeams	nanobeam	NOUN
fumecheng-10953	337	20	in	in	ADP
fumecheng-10953	337	21	hygrothermal	hygrothermal	ADJ
fumecheng-10953	337	22	environment	environment	NOUN
fumecheng-10953	337	23	based	base	VERB
fumecheng-10953	337	24	on	on	ADP
fumecheng-10953	337	25	a	a	DET
fumecheng-10953	337	26	nonlocal	nonlocal	ADJ
fumecheng-10953	337	27	strain	strain	NOUN
fumecheng-10953	337	28	gradient	gradient	ADJ
fumecheng-10953	337	29	timoshenko	timoshenko	NOUN
fumecheng-10953	337	30	beam	beam	NOUN
fumecheng-10953	337	31	model	model	NOUN
fumecheng-10953	337	32	under	under	ADP
fumecheng-10953	337	33	nonlinear	nonlinear	ADJ
fumecheng-10953	337	34	thermal	thermal	ADJ
fumecheng-10953	337	35	field	field	NOUN
fumecheng-10953	337	36	,	,	PUNCT
fumecheng-10953	337	37	journal	journal	NOUN
fumecheng-10953	337	38	of	of	ADP
fumecheng-10953	337	39	computational	computational	ADJ
fumecheng-10953	337	40	design	design	NOUN
fumecheng-10953	337	41	and	and	CCONJ
fumecheng-10953	337	42	engineering	engineering	NOUN
fumecheng-10953	337	43	,	,	PUNCT
fumecheng-10953	337	44	7	7	NUM
fumecheng-10953	337	45	,	,	PUNCT
fumecheng-10953	337	46	pp	pp	ADJ
fumecheng-10953	337	47	.	.	PUNCT
fumecheng-10953	338	1	685–699	685–699	NUM
fumecheng-10953	338	2	.	.	PUNCT
fumecheng-10953	339	1	50	50	NUM
fumecheng-10953	339	2	.	.	PUNCT
fumecheng-10953	340	1	monaco	monaco	PROPN
fumecheng-10953	340	2	,	,	PUNCT
fumecheng-10953	340	3	g.t	g.t	PROPN
fumecheng-10953	340	4	.	.	PROPN
fumecheng-10953	340	5	,	,	PUNCT
fumecheng-10953	340	6	fantuzzi	fantuzzi	PROPN
fumecheng-10953	340	7	,	,	PUNCT
fumecheng-10953	340	8	n.	n.	NOUN
fumecheng-10953	340	9	,	,	PUNCT
fumecheng-10953	340	10	fabbrocino	fabbrocino	PROPN
fumecheng-10953	340	11	,	,	PUNCT
fumecheng-10953	340	12	f.	f.	PROPN
fumecheng-10953	340	13	,	,	PUNCT
fumecheng-10953	340	14	luciano	luciano	PROPN
fumecheng-10953	340	15	,	,	PUNCT
fumecheng-10953	340	16	r.	r.	PROPN
fumecheng-10953	340	17	,	,	PUNCT
fumecheng-10953	340	18	2021	2021	NUM
fumecheng-10953	340	19	,	,	PUNCT
fumecheng-10953	340	20	hygro	hygro	NOUN
fumecheng-10953	340	21	-	-	PUNCT
fumecheng-10953	340	22	thermal	thermal	ADJ
fumecheng-10953	340	23	vibrations	vibration	NOUN
fumecheng-10953	340	24	and	and	CCONJ
fumecheng-10953	340	25	buckling	buckling	NOUN
fumecheng-10953	340	26	of	of	ADP
fumecheng-10953	340	27	laminated	laminated	ADJ
fumecheng-10953	340	28	nanoplates	nanoplate	NOUN
fumecheng-10953	340	29	via	via	ADP
fumecheng-10953	340	30	nonlocal	nonlocal	ADJ
fumecheng-10953	340	31	strain	strain	NOUN
fumecheng-10953	340	32	gradient	gradient	NOUN
fumecheng-10953	340	33	theory	theory	NOUN
fumecheng-10953	340	34	,	,	PUNCT
fumecheng-10953	340	35	composite	composite	ADJ
fumecheng-10953	340	36	structures	structure	NOUN
fumecheng-10953	340	37	,	,	PUNCT
fumecheng-10953	340	38	262	262	NUM
fumecheng-10953	340	39	,	,	PUNCT
fumecheng-10953	340	40	113337	113337	NUM
fumecheng-10953	340	41	.	.	PUNCT
fumecheng-10953	341	1	51	51	NUM
fumecheng-10953	341	2	.	.	PUNCT
fumecheng-10953	342	1	monaco	monaco	PROPN
fumecheng-10953	342	2	,	,	PUNCT
fumecheng-10953	342	3	g.t	g.t	PROPN
fumecheng-10953	342	4	.	.	PROPN
fumecheng-10953	342	5	,	,	PUNCT
fumecheng-10953	342	6	fantuzzi	fantuzzi	PROPN
fumecheng-10953	342	7	,	,	PUNCT
fumecheng-10953	342	8	n.	n.	NOUN
fumecheng-10953	342	9	,	,	PUNCT
fumecheng-10953	342	10	fabbrocino	fabbrocino	PROPN
fumecheng-10953	342	11	,	,	PUNCT
fumecheng-10953	342	12	f.	f.	PROPN
fumecheng-10953	342	13	,	,	PUNCT
fumecheng-10953	342	14	luciano	luciano	PROPN
fumecheng-10953	342	15	,	,	PUNCT
fumecheng-10953	342	16	r.	r.	PROPN
fumecheng-10953	342	17	,	,	PUNCT
fumecheng-10953	342	18	2021	2021	NUM
fumecheng-10953	342	19	,	,	PUNCT
fumecheng-10953	342	20	trigonometric	trigonometric	ADJ
fumecheng-10953	342	21	solution	solution	NOUN
fumecheng-10953	342	22	for	for	ADP
fumecheng-10953	342	23	the	the	DET
fumecheng-10953	342	24	bending	bend	VERB
fumecheng-10953	342	25	analysis	analysis	NOUN
fumecheng-10953	342	26	of	of	ADP
fumecheng-10953	342	27	magneto	magneto	NOUN
fumecheng-10953	342	28	-	-	PUNCT
fumecheng-10953	342	29	electro	electro	ADJ
fumecheng-10953	342	30	-	-	PUNCT
fumecheng-10953	342	31	elastic	elastic	ADJ
fumecheng-10953	342	32	strain	strain	NOUN
fumecheng-10953	342	33	gradient	gradient	ADJ
fumecheng-10953	342	34	nonlocal	nonlocal	ADJ
fumecheng-10953	342	35	nanoplates	nanoplate	NOUN
fumecheng-10953	342	36	in	in	ADP
fumecheng-10953	342	37	hygro	hygro	PROPN
fumecheng-10953	342	38	-	-	PUNCT
fumecheng-10953	342	39	thermal	thermal	ADJ
fumecheng-10953	342	40	environment	environment	NOUN
fumecheng-10953	342	41	,	,	PUNCT
fumecheng-10953	342	42	mathematics	mathematic	NOUN
fumecheng-10953	342	43	,	,	PUNCT
fumecheng-10953	342	44	9	9	NUM
fumecheng-10953	342	45	,	,	PUNCT
fumecheng-10953	342	46	567	567	NUM
fumecheng-10953	342	47	.	.	NOUN
fumecheng-10953	342	48	52	52	NUM
fumecheng-10953	342	49	.	.	PUNCT
fumecheng-10953	343	1	reddy	reddy	PROPN
fumecheng-10953	343	2	,	,	PUNCT
fumecheng-10953	343	3	j.n	j.n	PROPN
fumecheng-10953	343	4	.	.	PROPN
fumecheng-10953	343	5	,	,	PUNCT
fumecheng-10953	343	6	2017	2017	NUM
fumecheng-10953	343	7	,	,	PUNCT
fumecheng-10953	343	8	energy	energy	NOUN
fumecheng-10953	343	9	principles	principle	NOUN
fumecheng-10953	343	10	and	and	CCONJ
fumecheng-10953	343	11	variational	variational	ADJ
fumecheng-10953	343	12	methods	method	NOUN
fumecheng-10953	343	13	in	in	ADP
fumecheng-10953	343	14	applied	applied	ADJ
fumecheng-10953	343	15	mechanics	mechanic	NOUN
fumecheng-10953	343	16	,	,	PUNCT
fumecheng-10953	343	17	3rd	3rd	ADJ
fumecheng-10953	343	18	ed	ed	NOUN
fumecheng-10953	343	19	.	.	PROPN
fumecheng-10953	343	20	,	,	PUNCT
fumecheng-10953	343	21	wiley	wiley	PROPN
fumecheng-10953	343	22	.	.	PUNCT
fumecheng-10953	344	1	53	53	NUM
fumecheng-10953	344	2	.	.	PUNCT
fumecheng-10953	344	3	yosida	yosida	PROPN
fumecheng-10953	344	4	,	,	PUNCT
fumecheng-10953	344	5	k.	k.	PROPN
fumecheng-10953	344	6	,	,	PUNCT
fumecheng-10953	344	7	1980	1980	NUM
fumecheng-10953	344	8	,	,	PUNCT
fumecheng-10953	344	9	functional	functional	ADJ
fumecheng-10953	344	10	analysis	analysis	NOUN
fumecheng-10953	344	11	,	,	PUNCT
fumecheng-10953	344	12	6th	6th	ADJ
fumecheng-10953	344	13	ed	ed	NOUN
fumecheng-10953	344	14	.	.	PROPN
fumecheng-10953	344	15	,	,	PUNCT
fumecheng-10953	344	16	springer	springer	NOUN
fumecheng-10953	344	17	,	,	PUNCT
fumecheng-10953	344	18	new	new	PROPN
fumecheng-10953	344	19	york	york	PROPN
fumecheng-10953	344	20	.	.	PUNCT
fumecheng-10953	345	1	54	54	NUM
fumecheng-10953	345	2	.	.	X
fumecheng-10953	346	1	żur	żur	PROPN
fumecheng-10953	346	2	,	,	PUNCT
fumecheng-10953	346	3	k.k	k.k	PROPN
fumecheng-10953	346	4	.	.	PROPN
fumecheng-10953	346	5	,	,	PUNCT
fumecheng-10953	346	6	faghidian	faghidian	PROPN
fumecheng-10953	346	7	,	,	PUNCT
fumecheng-10953	346	8	s.a	s.a	PROPN
fumecheng-10953	346	9	.	.	PROPN
fumecheng-10953	346	10	,	,	PUNCT
fumecheng-10953	346	11	2021	2021	NUM
fumecheng-10953	346	12	,	,	PUNCT
fumecheng-10953	346	13	analytical	analytical	ADJ
fumecheng-10953	346	14	and	and	CCONJ
fumecheng-10953	346	15	meshless	meshless	ADJ
fumecheng-10953	346	16	numerical	numerical	ADJ
fumecheng-10953	346	17	approaches	approach	NOUN
fumecheng-10953	346	18	to	to	ADP
fumecheng-10953	346	19	unified	unified	ADJ
fumecheng-10953	346	20	gradient	gradient	NOUN
fumecheng-10953	346	21	elasticity	elasticity	NOUN
fumecheng-10953	346	22	theory	theory	NOUN
fumecheng-10953	346	23	,	,	PUNCT
fumecheng-10953	346	24	engineering	engineer	VERB
fumecheng-10953	346	25	analysis	analysis	NOUN
fumecheng-10953	346	26	with	with	ADP
fumecheng-10953	346	27	boundary	boundary	ADJ
fumecheng-10953	346	28	elements	element	NOUN
fumecheng-10953	346	29	,	,	PUNCT
fumecheng-10953	346	30	130	130	NUM
fumecheng-10953	346	31	,	,	PUNCT
fumecheng-10953	346	32	pp	pp	ADJ
fumecheng-10953	346	33	.	.	PUNCT
fumecheng-10953	347	1	238	238	NUM
fumecheng-10953	347	2	-	-	SYM
fumecheng-10953	347	3	248	248	NUM
fumecheng-10953	347	4	.	.	PUNCT
fumecheng-10953	348	1	55	55	NUM
fumecheng-10953	348	2	.	.	PUNCT
fumecheng-10953	349	1	barretta	barretta	NOUN
fumecheng-10953	349	2	,	,	PUNCT
fumecheng-10953	349	3	r.	r.	PROPN
fumecheng-10953	349	4	,	,	PUNCT
fumecheng-10953	349	5	faghidian	faghidian	PROPN
fumecheng-10953	349	6	,	,	PUNCT
fumecheng-10953	349	7	s.a	s.a	PROPN
fumecheng-10953	349	8	.	.	PROPN
fumecheng-10953	349	9	,	,	PUNCT
fumecheng-10953	349	10	marotti	marotti	PROPN
fumecheng-10953	349	11	de	de	X
fumecheng-10953	349	12	sciarra	sciarra	PROPN
fumecheng-10953	349	13	,	,	PUNCT
fumecheng-10953	349	14	f.	f.	PROPN
fumecheng-10953	349	15	,	,	PUNCT
fumecheng-10953	349	16	penna	penna	PROPN
fumecheng-10953	349	17	,	,	PUNCT
fumecheng-10953	349	18	r.	r.	PROPN
fumecheng-10953	349	19	,	,	PUNCT
fumecheng-10953	349	20	pinnola	pinnola	PROPN
fumecheng-10953	349	21	,	,	PUNCT
fumecheng-10953	349	22	f.p	f.p	PROPN
fumecheng-10953	349	23	.	.	PROPN
fumecheng-10953	349	24	,	,	PUNCT
fumecheng-10953	349	25	2020	2020	NUM
fumecheng-10953	349	26	,	,	PUNCT
fumecheng-10953	349	27	on	on	ADP
fumecheng-10953	349	28	torsion	torsion	NOUN
fumecheng-10953	349	29	of	of	ADP
fumecheng-10953	349	30	nonlocal	nonlocal	ADJ
fumecheng-10953	349	31	lam	lam	PROPN
fumecheng-10953	349	32	strain	strain	NOUN
fumecheng-10953	349	33	gradient	gradient	NOUN
fumecheng-10953	349	34	fg	fg	PROPN
fumecheng-10953	349	35	elastic	elastic	ADJ
fumecheng-10953	349	36	beams	beam	NOUN
fumecheng-10953	349	37	,	,	PUNCT
fumecheng-10953	349	38	composite	composite	ADJ
fumecheng-10953	349	39	structures	structure	NOUN
fumecheng-10953	349	40	,	,	PUNCT
fumecheng-10953	349	41	233	233	NUM
fumecheng-10953	349	42	,	,	PUNCT
fumecheng-10953	349	43	111550	111550	NUM
fumecheng-10953	349	44	.	.	PUNCT
fumecheng-10953	350	1	56	56	NUM
fumecheng-10953	350	2	.	.	PUNCT
fumecheng-10953	351	1	faghidian	faghidian	PROPN
fumecheng-10953	351	2	,	,	PUNCT
fumecheng-10953	351	3	s.a	s.a	PROPN
fumecheng-10953	351	4	.	.	PROPN
fumecheng-10953	351	5	,	,	PUNCT
fumecheng-10953	351	6	2017	2017	NUM
fumecheng-10953	351	7	,	,	PUNCT
fumecheng-10953	351	8	analytical	analytical	ADJ
fumecheng-10953	351	9	inverse	inverse	NOUN
fumecheng-10953	351	10	solution	solution	NOUN
fumecheng-10953	351	11	of	of	ADP
fumecheng-10953	351	12	eigenstrains	eigenstrain	NOUN
fumecheng-10953	351	13	and	and	CCONJ
fumecheng-10953	351	14	residual	residual	ADJ
fumecheng-10953	351	15	fields	field	NOUN
fumecheng-10953	351	16	in	in	ADP
fumecheng-10953	351	17	autofrettaged	autofrettage	VERB
fumecheng-10953	351	18	thickwalled	thickwalle	VERB
fumecheng-10953	351	19	tubes	tube	NOUN
fumecheng-10953	351	20	,	,	PUNCT
fumecheng-10953	351	21	asme	asme	PROPN
fumecheng-10953	351	22	journal	journal	PROPN
fumecheng-10953	351	23	of	of	ADP
fumecheng-10953	351	24	pressure	pressure	NOUN
fumecheng-10953	351	25	vessel	vessel	NOUN
fumecheng-10953	351	26	technology	technology	NOUN
fumecheng-10953	351	27	,	,	PUNCT
fumecheng-10953	351	28	139	139	NUM
fumecheng-10953	351	29	,	,	PUNCT
fumecheng-10953	351	30	031205	031205	NUM
fumecheng-10953	351	31	.	.	PUNCT
fumecheng-10953	352	1	57	57	NUM
fumecheng-10953	352	2	.	.	PUNCT
fumecheng-10953	353	1	faghidian	faghidian	PROPN
fumecheng-10953	353	2	,	,	PUNCT
fumecheng-10953	353	3	s.a	s.a	PROPN
fumecheng-10953	353	4	.	.	PROPN
fumecheng-10953	353	5	,	,	PUNCT
fumecheng-10953	353	6	2017	2017	NUM
fumecheng-10953	353	7	,	,	PUNCT
fumecheng-10953	353	8	analytical	analytical	ADJ
fumecheng-10953	353	9	approach	approach	NOUN
fumecheng-10953	353	10	for	for	ADP
fumecheng-10953	353	11	inverse	inverse	ADJ
fumecheng-10953	353	12	reconstruction	reconstruction	NOUN
fumecheng-10953	353	13	of	of	ADP
fumecheng-10953	353	14	eigenstrains	eigenstrain	NOUN
fumecheng-10953	353	15	and	and	CCONJ
fumecheng-10953	353	16	residual	residual	ADJ
fumecheng-10953	353	17	stresses	stress	NOUN
fumecheng-10953	353	18	in	in	ADP
fumecheng-10953	353	19	autofrettaged	autofrettage	VERB
fumecheng-10953	353	20	spherical	spherical	ADJ
fumecheng-10953	353	21	pressure	pressure	NOUN
fumecheng-10953	353	22	vessels	vessel	NOUN
fumecheng-10953	353	23	,	,	PUNCT
fumecheng-10953	353	24	asme	asme	PROPN
fumecheng-10953	353	25	journal	journal	PROPN
fumecheng-10953	353	26	of	of	ADP
fumecheng-10953	353	27	pressure	pressure	NOUN
fumecheng-10953	353	28	vessel	vessel	NOUN
fumecheng-10953	353	29	technology	technology	NOUN
fumecheng-10953	353	30	,	,	PUNCT
fumecheng-10953	353	31	139	139	NUM
fumecheng-10953	353	32	,	,	PUNCT
fumecheng-10953	353	33	041202	041202	NUM
fumecheng-10953	353	34	.	.	PUNCT
fumecheng-10953	354	1	58	58	NUM
fumecheng-10953	354	2	.	.	PUNCT
fumecheng-10953	355	1	caprio	caprio	PROPN
fumecheng-10953	355	2	,	,	PUNCT
fumecheng-10953	355	3	m.a	m.a	PROPN
fumecheng-10953	355	4	.	.	PROPN
fumecheng-10953	355	5	,	,	PUNCT
fumecheng-10953	355	6	2005	2005	NUM
fumecheng-10953	355	7	,	,	PUNCT
fumecheng-10953	355	8	levelscheme	levelscheme	NOUN
fumecheng-10953	355	9	:	:	PUNCT
fumecheng-10953	355	10	a	a	DET
fumecheng-10953	355	11	level	level	NOUN
fumecheng-10953	355	12	scheme	scheme	NOUN
fumecheng-10953	355	13	drawing	drawing	NOUN
fumecheng-10953	355	14	and	and	CCONJ
fumecheng-10953	355	15	scientific	scientific	ADJ
fumecheng-10953	355	16	figure	figure	NOUN
fumecheng-10953	355	17	preparation	preparation	NOUN
fumecheng-10953	355	18	system	system	NOUN
fumecheng-10953	355	19	for	for	ADP
fumecheng-10953	355	20	mathematica	mathematica	PROPN
fumecheng-10953	355	21	,	,	PUNCT
fumecheng-10953	355	22	computer	computer	NOUN
fumecheng-10953	355	23	physics	physics	NOUN
fumecheng-10953	355	24	communications	communication	NOUN
fumecheng-10953	355	25	,	,	PUNCT
fumecheng-10953	355	26	171	171	NUM
fumecheng-10953	355	27	,	,	PUNCT
fumecheng-10953	355	28	pp	pp	ADJ
fumecheng-10953	355	29	.	.	PUNCT
fumecheng-10953	356	1	107	107	NUM
fumecheng-10953	356	2	-	-	SYM
fumecheng-10953	356	3	118	118	NUM
fumecheng-10953	356	4	.	.	PUNCT