id	sid	tid	token	lemma	pos
fumecheng-12619	1	1	12619	12619	NUM
fumecheng-12619	1	2	facta	facta	PROPN
fumecheng-12619	1	3	universitatis	universitatis	PROPN
fumecheng-12619	1	4	series	series	NOUN
fumecheng-12619	1	5	:	:	PUNCT
fumecheng-12619	1	6	mechanical	mechanical	ADJ
fumecheng-12619	1	7	engineering	engineering	NOUN
fumecheng-12619	1	8	vol	vol	NOUN
fumecheng-12619	1	9	.	.	PROPN
fumecheng-12619	1	10	23	23	NUM
fumecheng-12619	1	11	,	,	PUNCT
fumecheng-12619	1	12	no	no	DET
fumecheng-12619	1	13	2	2	NUM
fumecheng-12619	1	14	,	,	PUNCT
fumecheng-12619	1	15	2025	2025	NUM
fumecheng-12619	1	16	,	,	PUNCT
fumecheng-12619	1	17	pp	pp	ADJ
fumecheng-12619	1	18	.	.	PUNCT
fumecheng-12619	2	1	311	311	NUM
fumecheng-12619	2	2	334	334	NUM
fumecheng-12619	2	3	https://doi.org/10.22190/fume240903011k	https://doi.org/10.22190/fume240903011k	ADP
fumecheng-12619	2	4	©	©	PROPN
fumecheng-12619	2	5	2025	2025	NUM
fumecheng-12619	2	6	by	by	ADP
fumecheng-12619	2	7	university	university	PROPN
fumecheng-12619	2	8	of	of	ADP
fumecheng-12619	2	9	niš	niš	PROPN
fumecheng-12619	2	10	,	,	PUNCT
fumecheng-12619	2	11	serbia	serbia	PROPN
fumecheng-12619	2	12	|	|	ADV
fumecheng-12619	2	13	creative	creative	ADJ
fumecheng-12619	2	14	commons	common	NOUN
fumecheng-12619	2	15	license	license	NOUN
fumecheng-12619	2	16	:	:	PUNCT
fumecheng-12619	2	17	cc	cc	VERB
fumecheng-12619	2	18	by	by	ADP
fumecheng-12619	2	19	-	-	PUNCT
fumecheng-12619	2	20	nc	nc	VERB
fumecheng-12619	2	21	-	-	PUNCT
fumecheng-12619	2	22	nd	nd	ADV
fumecheng-12619	2	23	original	original	ADJ
fumecheng-12619	2	24	scientific	scientific	ADJ
fumecheng-12619	2	25	paper	paper	ADJ
fumecheng-12619	2	26	comparison	comparison	NOUN
fumecheng-12619	2	27	of	of	ADP
fumecheng-12619	2	28	nonclassical	nonclassical	ADJ
fumecheng-12619	2	29	controllers	controller	NOUN
fumecheng-12619	2	30	on	on	ADP
fumecheng-12619	2	31	nonlinear	nonlinear	ADJ
fumecheng-12619	2	32	vibrations	vibration	NOUN
fumecheng-12619	2	33	analysis	analysis	NOUN
fumecheng-12619	2	34	of	of	ADP
fumecheng-12619	2	35	piezoelectric	piezoelectric	ADJ
fumecheng-12619	2	36	nanoresonator	nanoresonator	NOUN
fumecheng-12619	2	37	sayyid	sayyid	PROPN
fumecheng-12619	2	38	h.	h.	PROPN
fumecheng-12619	2	39	hashemi	hashemi	PROPN
fumecheng-12619	2	40	kachapi1	kachapi1	PROPN
fumecheng-12619	2	41	,	,	PUNCT
fumecheng-12619	3	1	sayyideh	sayyideh	PROPN
fumecheng-12619	3	2	gh	gh	PROPN
fumecheng-12619	3	3	.	.	PROPN
fumecheng-12619	3	4	hashemi	hashemi	PROPN
fumecheng-12619	3	5	kachapi2	kachapi2	PROPN
fumecheng-12619	4	1	1department	1department	NUM
fumecheng-12619	4	2	of	of	ADP
fumecheng-12619	4	3	mechanical	mechanical	ADJ
fumecheng-12619	4	4	engineering	engineering	NOUN
fumecheng-12619	4	5	,	,	PUNCT
fumecheng-12619	4	6	faculty	faculty	NOUN
fumecheng-12619	4	7	of	of	ADP
fumecheng-12619	4	8	engineering	engineering	NOUN
fumecheng-12619	4	9	and	and	CCONJ
fumecheng-12619	4	10	technology	technology	NOUN
fumecheng-12619	4	11	,	,	PUNCT
fumecheng-12619	4	12	university	university	NOUN
fumecheng-12619	4	13	of	of	ADP
fumecheng-12619	4	14	mazandaran	mazandaran	PROPN
fumecheng-12619	4	15	,	,	PUNCT
fumecheng-12619	4	16	babolsar	babolsar	PROPN
fumecheng-12619	4	17	,	,	PUNCT
fumecheng-12619	4	18	iran	iran	PROPN
fumecheng-12619	4	19	2department	2department	NUM
fumecheng-12619	4	20	of	of	ADP
fumecheng-12619	4	21	physics	physics	PROPN
fumecheng-12619	4	22	,	,	PUNCT
fumecheng-12619	4	23	university	university	NOUN
fumecheng-12619	4	24	of	of	ADP
fumecheng-12619	4	25	kashan	kashan	PROPN
fumecheng-12619	4	26	,	,	PUNCT
fumecheng-12619	4	27	kashan	kashan	PROPN
fumecheng-12619	4	28	,	,	PUNCT
fumecheng-12619	4	29	iran	iran	PROPN
fumecheng-12619	4	30	orcid	orcid	NOUN
fumecheng-12619	4	31	ids	ids	PROPN
fumecheng-12619	4	32	:	:	PUNCT
fumecheng-12619	4	33	sayyid	sayyid	PROPN
fumecheng-12619	4	34	h.	h.	PROPN
fumecheng-12619	4	35	hashemi	hashemi	PROPN
fumecheng-12619	4	36	kachapi	kachapi	PROPN
fumecheng-12619	4	37	https://orcid.org/0000-0002-5384-9724	https://orcid.org/0000-0002-5384-9724	PROPN
fumecheng-12619	4	38	sayyideh	sayyideh	PROPN
fumecheng-12619	4	39	gh	gh	PROPN
fumecheng-12619	4	40	.	.	PROPN
fumecheng-12619	4	41	hashemi	hashemi	PROPN
fumecheng-12619	4	42	kachapi	kachapi	VERB
fumecheng-12619	4	43	https://orcid.org/0009-0004-8518-4386	https://orcid.org/0009-0004-8518-4386	PRON
fumecheng-12619	4	44	abstract	abstract	NOUN
fumecheng-12619	4	45	.	.	PUNCT
fumecheng-12619	5	1	this	this	DET
fumecheng-12619	5	2	study	study	NOUN
fumecheng-12619	5	3	explores	explore	VERB
fumecheng-12619	5	4	the	the	DET
fumecheng-12619	5	5	influence	influence	NOUN
fumecheng-12619	5	6	of	of	ADP
fumecheng-12619	5	7	advanced	advanced	ADJ
fumecheng-12619	5	8	continuum	continuum	ADJ
fumecheng-12619	5	9	mechanics	mechanic	NOUN
fumecheng-12619	5	10	frameworks	framework	NOUN
fumecheng-12619	5	11	,	,	PUNCT
fumecheng-12619	5	12	specifically	specifically	ADV
fumecheng-12619	5	13	strain	strain	VERB
fumecheng-12619	5	14	gradient	gradient	ADJ
fumecheng-12619	5	15	theory	theory	NOUN
fumecheng-12619	5	16	(	(	PUNCT
fumecheng-12619	5	17	sgt	sgt	PROPN
fumecheng-12619	5	18	)	)	PUNCT
fumecheng-12619	5	19	,	,	PUNCT
fumecheng-12619	5	20	nonlocal	nonlocal	ADJ
fumecheng-12619	5	21	theory	theory	NOUN
fumecheng-12619	5	22	(	(	PUNCT
fumecheng-12619	5	23	nlt	nlt	PROPN
fumecheng-12619	5	24	)	)	PUNCT
fumecheng-12619	5	25	,	,	PUNCT
fumecheng-12619	5	26	and	and	CCONJ
fumecheng-12619	5	27	gurtin	gurtin	PROPN
fumecheng-12619	5	28	-	-	PUNCT
fumecheng-12619	5	29	murdoch	murdoch	PROPN
fumecheng-12619	5	30	surface	surface	NOUN
fumecheng-12619	5	31	/	/	SYM
fumecheng-12619	5	32	interface	interface	NOUN
fumecheng-12619	5	33	theory	theory	NOUN
fumecheng-12619	5	34	(	(	PUNCT
fumecheng-12619	5	35	gmsit	gmsit	NOUN
fumecheng-12619	5	36	)	)	PUNCT
fumecheng-12619	5	37	,	,	PUNCT
fumecheng-12619	5	38	on	on	ADP
fumecheng-12619	5	39	the	the	DET
fumecheng-12619	5	40	nonlinear	nonlinear	ADJ
fumecheng-12619	5	41	vibrational	vibrational	ADJ
fumecheng-12619	5	42	characteristics	characteristic	NOUN
fumecheng-12619	5	43	of	of	ADP
fumecheng-12619	5	44	a	a	DET
fumecheng-12619	5	45	piezoelectric	piezoelectric	ADJ
fumecheng-12619	5	46	nanoresonator	nanoresonator	NOUN
fumecheng-12619	5	47	(	(	PUNCT
fumecheng-12619	5	48	penr	penr	PROPN
fumecheng-12619	5	49	)	)	PUNCT
fumecheng-12619	5	50	.	.	PUNCT
fumecheng-12619	6	1	these	these	DET
fumecheng-12619	6	2	findings	finding	NOUN
fumecheng-12619	6	3	are	be	AUX
fumecheng-12619	6	4	then	then	ADV
fumecheng-12619	6	5	juxtaposed	juxtapose	VERB
fumecheng-12619	6	6	with	with	ADP
fumecheng-12619	6	7	those	those	PRON
fumecheng-12619	6	8	derived	derive	VERB
fumecheng-12619	6	9	from	from	ADP
fumecheng-12619	6	10	conventional	conventional	ADJ
fumecheng-12619	6	11	continuum	continuum	ADJ
fumecheng-12619	6	12	mechanics	mechanic	NOUN
fumecheng-12619	6	13	.	.	PUNCT
fumecheng-12619	7	1	the	the	DET
fumecheng-12619	7	2	penr	penr	PROPN
fumecheng-12619	7	3	is	be	AUX
fumecheng-12619	7	4	driven	drive	VERB
fumecheng-12619	7	5	by	by	ADP
fumecheng-12619	7	6	a	a	DET
fumecheng-12619	7	7	nonlinear	nonlinear	ADJ
fumecheng-12619	7	8	electrostatic	electrostatic	ADJ
fumecheng-12619	7	9	force	force	NOUN
fumecheng-12619	7	10	,	,	PUNCT
fumecheng-12619	7	11	incorporating	incorporate	VERB
fumecheng-12619	7	12	both	both	CCONJ
fumecheng-12619	7	13	static	static	ADJ
fumecheng-12619	7	14	and	and	CCONJ
fumecheng-12619	7	15	dynamic	dynamic	ADJ
fumecheng-12619	7	16	voltage	voltage	NOUN
fumecheng-12619	7	17	components	component	NOUN
fumecheng-12619	7	18	,	,	PUNCT
fumecheng-12619	7	19	and	and	CCONJ
fumecheng-12619	7	20	is	be	AUX
fumecheng-12619	7	21	situated	situate	VERB
fumecheng-12619	7	22	within	within	ADP
fumecheng-12619	7	23	a	a	DET
fumecheng-12619	7	24	viscoelastic	viscoelastic	ADJ
fumecheng-12619	7	25	foundation	foundation	NOUN
fumecheng-12619	7	26	of	of	ADP
fumecheng-12619	7	27	the	the	DET
fumecheng-12619	7	28	pasternak	pasternak	PROPN
fumecheng-12619	7	29	type	type	NOUN
fumecheng-12619	7	30	.	.	PUNCT
fumecheng-12619	8	1	to	to	PART
fumecheng-12619	8	2	dissect	dissect	VERB
fumecheng-12619	8	3	the	the	DET
fumecheng-12619	8	4	nonlinear	nonlinear	ADJ
fumecheng-12619	8	5	frequency	frequency	NOUN
fumecheng-12619	8	6	response	response	NOUN
fumecheng-12619	8	7	and	and	CCONJ
fumecheng-12619	8	8	stability	stability	NOUN
fumecheng-12619	8	9	of	of	ADP
fumecheng-12619	8	10	the	the	DET
fumecheng-12619	8	11	penr	penr	NOUN
fumecheng-12619	8	12	,	,	PUNCT
fumecheng-12619	8	13	a	a	DET
fumecheng-12619	8	14	methodology	methodology	NOUN
fumecheng-12619	8	15	combining	combine	VERB
fumecheng-12619	8	16	hamilton	hamilton	PROPN
fumecheng-12619	8	17	’s	’s	PART
fumecheng-12619	8	18	principle	principle	PROPN
fumecheng-12619	8	19	,	,	PUNCT
fumecheng-12619	8	20	galerkin	galerkin	PROPN
fumecheng-12619	8	21	’s	’s	PART
fumecheng-12619	8	22	method	method	NOUN
fumecheng-12619	8	23	,	,	PUNCT
fumecheng-12619	8	24	complex	complex	ADJ
fumecheng-12619	8	25	averaging	averaging	NOUN
fumecheng-12619	8	26	techniques	technique	NOUN
fumecheng-12619	8	27	,	,	PUNCT
fumecheng-12619	8	28	and	and	CCONJ
fumecheng-12619	8	29	arc	arc	NOUN
fumecheng-12619	8	30	-	-	PUNCT
fumecheng-12619	8	31	length	length	NOUN
fumecheng-12619	8	32	continuation	continuation	NOUN
fumecheng-12619	8	33	is	be	AUX
fumecheng-12619	8	34	utilized	utilize	VERB
fumecheng-12619	8	35	.	.	PUNCT
fumecheng-12619	9	1	the	the	DET
fumecheng-12619	9	2	analysis	analysis	NOUN
fumecheng-12619	9	3	reveals	reveal	VERB
fumecheng-12619	9	4	that	that	SCONJ
fumecheng-12619	9	5	disregarding	disregard	VERB
fumecheng-12619	9	6	nanoscale	nanoscale	NOUN
fumecheng-12619	9	7	and	and	CCONJ
fumecheng-12619	9	8	interfacial	interfacial	ADJ
fumecheng-12619	9	9	effects	effect	NOUN
fumecheng-12619	9	10	results	result	NOUN
fumecheng-12619	9	11	in	in	ADP
fumecheng-12619	9	12	significant	significant	ADJ
fumecheng-12619	9	13	deviations	deviation	NOUN
fumecheng-12619	9	14	from	from	ADP
fumecheng-12619	9	15	the	the	DET
fumecheng-12619	9	16	actual	actual	ADJ
fumecheng-12619	9	17	vibrational	vibrational	ADJ
fumecheng-12619	9	18	response	response	NOUN
fumecheng-12619	9	19	of	of	ADP
fumecheng-12619	9	20	the	the	DET
fumecheng-12619	9	21	penr	penr	NOUN
fumecheng-12619	9	22	.	.	PUNCT
fumecheng-12619	10	1	notably	notably	ADV
fumecheng-12619	10	2	,	,	PUNCT
fumecheng-12619	10	3	under	under	ADP
fumecheng-12619	10	4	diverse	diverse	ADJ
fumecheng-12619	10	5	boundary	boundary	ADJ
fumecheng-12619	10	6	constraints	constraint	NOUN
fumecheng-12619	10	7	,	,	PUNCT
fumecheng-12619	10	8	the	the	DET
fumecheng-12619	10	9	material	material	NOUN
fumecheng-12619	10	10	length	length	NOUN
fumecheng-12619	10	11	scale	scale	NOUN
fumecheng-12619	10	12	parameter	parameter	NOUN
fumecheng-12619	10	13	(	(	PUNCT
fumecheng-12619	10	14	associated	associate	VERB
fumecheng-12619	10	15	with	with	ADP
fumecheng-12619	10	16	sgt	sgt	PROPN
fumecheng-12619	10	17	)	)	PUNCT
fumecheng-12619	10	18	induces	induce	VERB
fumecheng-12619	10	19	a	a	DET
fumecheng-12619	10	20	reduction	reduction	NOUN
fumecheng-12619	10	21	in	in	ADP
fumecheng-12619	10	22	the	the	DET
fumecheng-12619	10	23	penr	penr	NOUN
fumecheng-12619	10	24	's	's	PART
fumecheng-12619	10	25	rigidity	rigidity	NOUN
fumecheng-12619	10	26	,	,	PUNCT
fumecheng-12619	10	27	whereas	whereas	SCONJ
fumecheng-12619	10	28	the	the	DET
fumecheng-12619	10	29	nonlocal	nonlocal	ADJ
fumecheng-12619	10	30	scale	scale	NOUN
fumecheng-12619	10	31	parameter	parameter	NOUN
fumecheng-12619	10	32	(	(	PUNCT
fumecheng-12619	10	33	associated	associate	VERB
fumecheng-12619	10	34	with	with	ADP
fumecheng-12619	10	35	nlt	nlt	PROPN
fumecheng-12619	10	36	)	)	PUNCT
fumecheng-12619	10	37	yields	yield	VERB
fumecheng-12619	10	38	the	the	DET
fumecheng-12619	10	39	opposite	opposite	ADJ
fumecheng-12619	10	40	effect	effect	NOUN
fumecheng-12619	10	41	,	,	PUNCT
fumecheng-12619	10	42	enhancing	enhance	VERB
fumecheng-12619	10	43	stiffness	stiffness	NOUN
fumecheng-12619	10	44	.	.	PUNCT
fumecheng-12619	11	1	moreover	moreover	ADV
fumecheng-12619	11	2	,	,	PUNCT
fumecheng-12619	11	3	the	the	DET
fumecheng-12619	11	4	oscillation	oscillation	NOUN
fumecheng-12619	11	5	amplitude	amplitude	NOUN
fumecheng-12619	11	6	and	and	CCONJ
fumecheng-12619	11	7	the	the	DET
fumecheng-12619	11	8	extent	extent	NOUN
fumecheng-12619	11	9	of	of	ADP
fumecheng-12619	11	10	instability	instability	NOUN
fumecheng-12619	11	11	predicted	predict	VERB
fumecheng-12619	11	12	by	by	ADP
fumecheng-12619	11	13	the	the	DET
fumecheng-12619	11	14	advanced	advanced	ADJ
fumecheng-12619	11	15	theories	theory	NOUN
fumecheng-12619	11	16	(	(	PUNCT
fumecheng-12619	11	17	nlt	nlt	PROPN
fumecheng-12619	11	18	and	and	CCONJ
fumecheng-12619	11	19	sgt	sgt	PROPN
fumecheng-12619	11	20	)	)	PUNCT
fumecheng-12619	11	21	surpass	surpass	VERB
fumecheng-12619	11	22	those	those	PRON
fumecheng-12619	11	23	obtained	obtain	VERB
fumecheng-12619	11	24	via	via	ADP
fumecheng-12619	11	25	classical	classical	ADJ
fumecheng-12619	11	26	analysis	analysis	NOUN
fumecheng-12619	11	27	.	.	PUNCT
fumecheng-12619	12	1	fluctuations	fluctuation	NOUN
fumecheng-12619	12	2	in	in	ADP
fumecheng-12619	12	3	the	the	DET
fumecheng-12619	12	4	surface	surface	NOUN
fumecheng-12619	12	5	/	/	SYM
fumecheng-12619	12	6	interface	interface	NOUN
fumecheng-12619	12	7	parameters	parameter	NOUN
fumecheng-12619	12	8	are	be	AUX
fumecheng-12619	12	9	demonstrated	demonstrate	VERB
fumecheng-12619	12	10	to	to	PART
fumecheng-12619	12	11	exert	exert	VERB
fumecheng-12619	12	12	a	a	DET
fumecheng-12619	12	13	considerable	considerable	ADJ
fumecheng-12619	12	14	influence	influence	NOUN
fumecheng-12619	12	15	on	on	ADP
fumecheng-12619	12	16	the	the	DET
fumecheng-12619	12	17	penr	penr	NOUN
fumecheng-12619	12	18	's	's	PART
fumecheng-12619	12	19	normalized	normalize	VERB
fumecheng-12619	12	20	natural	natural	ADJ
fumecheng-12619	12	21	frequency	frequency	NOUN
fumecheng-12619	12	22	,	,	PUNCT
fumecheng-12619	12	23	resonance	resonance	NOUN
fumecheng-12619	12	24	frequency	frequency	NOUN
fumecheng-12619	12	25	,	,	PUNCT
fumecheng-12619	12	26	resonance	resonance	NOUN
fumecheng-12619	12	27	amplitude	amplitude	NOUN
fumecheng-12619	12	28	,	,	PUNCT
fumecheng-12619	12	29	nonlinear	nonlinear	ADJ
fumecheng-12619	12	30	dynamics	dynamic	NOUN
fumecheng-12619	12	31	,	,	PUNCT
fumecheng-12619	12	32	and	and	CCONJ
fumecheng-12619	12	33	system	system	NOUN
fumecheng-12619	12	34	stability	stability	NOUN
fumecheng-12619	12	35	,	,	PUNCT
fumecheng-12619	12	36	manifesting	manifest	VERB
fumecheng-12619	12	37	as	as	ADP
fumecheng-12619	12	38	either	either	PRON
fumecheng-12619	12	39	augmentations	augmentation	NOUN
fumecheng-12619	12	40	or	or	CCONJ
fumecheng-12619	12	41	diminutions	diminution	NOUN
fumecheng-12619	12	42	contingent	contingent	NOUN
fumecheng-12619	12	43	upon	upon	SCONJ
fumecheng-12619	12	44	the	the	DET
fumecheng-12619	12	45	specific	specific	ADJ
fumecheng-12619	12	46	parameter	parameter	NOUN
fumecheng-12619	12	47	under	under	ADP
fumecheng-12619	12	48	consideration	consideration	NOUN
fumecheng-12619	12	49	.	.	PUNCT
fumecheng-12619	13	1	key	key	ADJ
fumecheng-12619	13	2	words	word	NOUN
fumecheng-12619	13	3	:	:	PUNCT
fumecheng-12619	13	4	piezoelectric	piezoelectric	NOUN
fumecheng-12619	13	5	nanoresonator	nanoresonator	NOUN
fumecheng-12619	13	6	,	,	PUNCT
fumecheng-12619	13	7	nonlocal	nonlocal	ADJ
fumecheng-12619	13	8	strain	strain	NOUN
fumecheng-12619	13	9	gradient	gradient	NOUN
fumecheng-12619	13	10	theory	theory	NOUN
fumecheng-12619	13	11	,	,	PUNCT
fumecheng-12619	13	12	gurtin	gurtin	PROPN
fumecheng-12619	13	13	–	–	PUNCT
fumecheng-12619	13	14	murdoch	murdoch	PROPN
fumecheng-12619	13	15	surface	surface	NOUN
fumecheng-12619	13	16	/	/	SYM
fumecheng-12619	13	17	interface	interface	NOUN
fumecheng-12619	13	18	,	,	PUNCT
fumecheng-12619	13	19	nonlinear	nonlinear	ADJ
fumecheng-12619	13	20	frequency	frequency	NOUN
fumecheng-12619	13	21	response	response	NOUN
fumecheng-12619	13	22	,	,	PUNCT
fumecheng-12619	13	23	complex	complex	ADJ
fumecheng-12619	13	24	averaging	averaging	NOUN
fumecheng-12619	13	25	received	receive	VERB
fumecheng-12619	13	26	:	:	PUNCT
fumecheng-12619	13	27	september	september	PROPN
fumecheng-12619	13	28	03	03	NUM
fumecheng-12619	13	29	,	,	PUNCT
fumecheng-12619	13	30	2024	2024	NUM
fumecheng-12619	13	31	/	/	SYM
fumecheng-12619	13	32	accepted	accept	VERB
fumecheng-12619	13	33	march	march	PROPN
fumecheng-12619	13	34	10	10	NUM
fumecheng-12619	13	35	,	,	PUNCT
fumecheng-12619	13	36	2025	2025	NUM
fumecheng-12619	13	37	corresponding	correspond	VERB
fumecheng-12619	13	38	author	author	NOUN
fumecheng-12619	13	39	:	:	PUNCT
fumecheng-12619	13	40	sayyid	sayyid	PROPN
fumecheng-12619	13	41	h.	h.	PROPN
fumecheng-12619	13	42	hashemi	hashemi	PROPN
fumecheng-12619	13	43	kachapi	kachapi	PROPN
fumecheng-12619	13	44	department	department	PROPN
fumecheng-12619	13	45	of	of	ADP
fumecheng-12619	13	46	mechanical	mechanical	ADJ
fumecheng-12619	13	47	engineering	engineering	NOUN
fumecheng-12619	13	48	,	,	PUNCT
fumecheng-12619	13	49	faculty	faculty	NOUN
fumecheng-12619	13	50	of	of	ADP
fumecheng-12619	13	51	engineering	engineering	NOUN
fumecheng-12619	13	52	and	and	CCONJ
fumecheng-12619	13	53	technology	technology	NOUN
fumecheng-12619	13	54	,	,	PUNCT
fumecheng-12619	13	55	university	university	NOUN
fumecheng-12619	13	56	of	of	ADP
fumecheng-12619	13	57	mazandaran	mazandaran	PROPN
fumecheng-12619	13	58	,	,	PUNCT
fumecheng-12619	13	59	babolsar	babolsar	PROPN
fumecheng-12619	13	60	,	,	PUNCT
fumecheng-12619	13	61	iran	iran	PROPN
fumecheng-12619	13	62	e	e	NOUN
fumecheng-12619	13	63	-	-	NOUN
fumecheng-12619	13	64	mail	mail	NOUN
fumecheng-12619	13	65	:	:	PUNCT
fumecheng-12619	14	1	shhashemi.kachapi@umz.ac.ir	shhashemi.kachapi@umz.ac.ir	ADV
fumecheng-12619	14	2	,	,	PUNCT
fumecheng-12619	14	3	sha.hashemi.kachapi@gmail.com	sha.hashemi.kachapi@gmail.com	PROPN
fumecheng-12619	14	4	mailto:shhashemi.kachapi@umz.ac.ir	mailto:shhashemi.kachapi@umz.ac.ir	PROPN
fumecheng-12619	14	5	mailto:sha.hashemi.kachapi@gmail.com	mailto:sha.hashemi.kachapi@gmail.com	PROPN
fumecheng-12619	14	6	312	312	NUM
fumecheng-12619	14	7	s.h	s.h	PROPN
fumecheng-12619	14	8	.	.	PROPN
fumecheng-12619	14	9	hashemi	hashemi	PROPN
fumecheng-12619	14	10	kachapi	kachapi	PROPN
fumecheng-12619	14	11	,	,	PUNCT
fumecheng-12619	14	12	s.	s.	PROPN
fumecheng-12619	14	13	gh	gh	PROPN
fumecheng-12619	14	14	.	.	PROPN
fumecheng-12619	15	1	hashemi	hashemi	PROPN
fumecheng-12619	15	2	kachapi	kachapi	PROPN
fumecheng-12619	15	3	1	1	NUM
fumecheng-12619	15	4	.	.	X
fumecheng-12619	15	5	introduction	introduction	NOUN
fumecheng-12619	15	6	the	the	DET
fumecheng-12619	15	7	relentless	relentless	ADJ
fumecheng-12619	15	8	march	march	NOUN
fumecheng-12619	15	9	of	of	ADP
fumecheng-12619	15	10	technological	technological	ADJ
fumecheng-12619	15	11	innovation	innovation	NOUN
fumecheng-12619	15	12	has	have	AUX
fumecheng-12619	15	13	spurred	spur	VERB
fumecheng-12619	15	14	the	the	DET
fumecheng-12619	15	15	proliferation	proliferation	NOUN
fumecheng-12619	15	16	of	of	ADP
fumecheng-12619	15	17	intelligent	intelligent	ADJ
fumecheng-12619	15	18	materials	material	NOUN
fumecheng-12619	15	19	and	and	CCONJ
fumecheng-12619	15	20	adaptable	adaptable	ADJ
fumecheng-12619	15	21	structural	structural	ADJ
fumecheng-12619	15	22	systems	system	NOUN
fumecheng-12619	16	1	[	[	X
fumecheng-12619	16	2	1	1	NUM
fumecheng-12619	16	3	,	,	PUNCT
fumecheng-12619	16	4	2	2	NUM
fumecheng-12619	16	5	]	]	PUNCT
fumecheng-12619	16	6	.	.	PUNCT
fumecheng-12619	17	1	within	within	ADP
fumecheng-12619	17	2	this	this	DET
fumecheng-12619	17	3	domain	domain	NOUN
fumecheng-12619	17	4	,	,	PUNCT
fumecheng-12619	17	5	piezoelectric	piezoelectric	NOUN
fumecheng-12619	17	6	nanostructures	nanostructure	NOUN
fumecheng-12619	17	7	,	,	PUNCT
fumecheng-12619	17	8	endowed	endow	VERB
fumecheng-12619	17	9	with	with	ADP
fumecheng-12619	17	10	exceptional	exceptional	ADJ
fumecheng-12619	17	11	attributes	attribute	NOUN
fumecheng-12619	17	12	,	,	PUNCT
fumecheng-12619	17	13	have	have	AUX
fumecheng-12619	17	14	garnered	garner	VERB
fumecheng-12619	17	15	substantial	substantial	ADJ
fumecheng-12619	17	16	interest	interest	NOUN
fumecheng-12619	17	17	,	,	PUNCT
fumecheng-12619	17	18	promising	promise	VERB
fumecheng-12619	17	19	transformative	transformative	ADJ
fumecheng-12619	17	20	applications	application	NOUN
fumecheng-12619	17	21	across	across	ADP
fumecheng-12619	17	22	diverse	diverse	ADJ
fumecheng-12619	17	23	sectors	sector	NOUN
fumecheng-12619	17	24	[	[	X
fumecheng-12619	17	25	3	3	NUM
fumecheng-12619	17	26	,	,	PUNCT
fumecheng-12619	17	27	4	4	NUM
fumecheng-12619	17	28	]	]	PUNCT
fumecheng-12619	17	29	.	.	PUNCT
fumecheng-12619	18	1	notably	notably	ADV
fumecheng-12619	18	2	,	,	PUNCT
fumecheng-12619	18	3	piezoelectric	piezoelectric	ADJ
fumecheng-12619	18	4	shell	shell	NOUN
fumecheng-12619	18	5	architectures	architecture	NOUN
fumecheng-12619	18	6	are	be	AUX
fumecheng-12619	18	7	extensively	extensively	ADV
fumecheng-12619	18	8	deployed	deploy	VERB
fumecheng-12619	18	9	in	in	ADP
fumecheng-12619	18	10	sensing	sense	VERB
fumecheng-12619	18	11	and	and	CCONJ
fumecheng-12619	18	12	actuation	actuation	NOUN
fumecheng-12619	18	13	technologies	technology	NOUN
fumecheng-12619	18	14	[	[	X
fumecheng-12619	18	15	5	5	NUM
fumecheng-12619	18	16	,	,	PUNCT
fumecheng-12619	18	17	6	6	NUM
fumecheng-12619	18	18	]	]	PUNCT
fumecheng-12619	18	19	.	.	PUNCT
fumecheng-12619	19	1	precise	precise	ADJ
fumecheng-12619	19	2	dynamic	dynamic	ADJ
fumecheng-12619	19	3	analysis	analysis	NOUN
fumecheng-12619	19	4	and	and	CCONJ
fumecheng-12619	19	5	mathematical	mathematical	ADJ
fumecheng-12619	19	6	modeling	modeling	NOUN
fumecheng-12619	19	7	of	of	ADP
fumecheng-12619	19	8	these	these	DET
fumecheng-12619	19	9	nanoscale	nanoscale	NOUN
fumecheng-12619	19	10	systems	system	NOUN
fumecheng-12619	19	11	necessitate	necessitate	ADJ
fumecheng-12619	19	12	the	the	DET
fumecheng-12619	19	13	incorporation	incorporation	NOUN
fumecheng-12619	19	14	of	of	ADP
fumecheng-12619	19	15	scale	scale	NOUN
fumecheng-12619	19	16	-	-	PUNCT
fumecheng-12619	19	17	dependent	dependent	ADJ
fumecheng-12619	19	18	parameters	parameter	NOUN
fumecheng-12619	19	19	.	.	PUNCT
fumecheng-12619	20	1	consequently	consequently	ADV
fumecheng-12619	20	2	,	,	PUNCT
fumecheng-12619	20	3	advanced	advanced	ADJ
fumecheng-12619	20	4	continuum	continuum	ADJ
fumecheng-12619	20	5	theories	theory	NOUN
fumecheng-12619	20	6	,	,	PUNCT
fumecheng-12619	20	7	encompassing	encompass	VERB
fumecheng-12619	20	8	nonlocal	nonlocal	ADJ
fumecheng-12619	20	9	[	[	X
fumecheng-12619	20	10	7	7	NUM
fumecheng-12619	20	11	]	]	PUNCT
fumecheng-12619	20	12	,	,	PUNCT
fumecheng-12619	20	13	strain	strain	VERB
fumecheng-12619	20	14	gradient	gradient	NOUN
fumecheng-12619	20	15	[	[	X
fumecheng-12619	20	16	8	8	NUM
fumecheng-12619	20	17	]	]	PUNCT
fumecheng-12619	20	18	,	,	PUNCT
fumecheng-12619	20	19	and	and	CCONJ
fumecheng-12619	20	20	gurtin	gurtin	NOUN
fumecheng-12619	20	21	-	-	PUNCT
fumecheng-12619	20	22	murdoch	murdoch	PROPN
fumecheng-12619	20	23	surface	surface	PROPN
fumecheng-12619	20	24	/	/	SYM
fumecheng-12619	20	25	interface	interface	NOUN
fumecheng-12619	20	26	[	[	X
fumecheng-12619	20	27	9	9	NUM
fumecheng-12619	20	28	]	]	PUNCT
fumecheng-12619	20	29	frameworks	framework	NOUN
fumecheng-12619	20	30	,	,	PUNCT
fumecheng-12619	20	31	are	be	AUX
fumecheng-12619	20	32	employed	employ	VERB
fumecheng-12619	20	33	to	to	PART
fumecheng-12619	20	34	probe	probe	VERB
fumecheng-12619	20	35	their	their	PRON
fumecheng-12619	20	36	nonlinear	nonlinear	ADJ
fumecheng-12619	20	37	vibrational	vibrational	ADJ
fumecheng-12619	20	38	and	and	CCONJ
fumecheng-12619	20	39	dynamic	dynamic	ADJ
fumecheng-12619	20	40	behaviors	behavior	NOUN
fumecheng-12619	20	41	.	.	PUNCT
fumecheng-12619	21	1	drawing	draw	VERB
fumecheng-12619	21	2	upon	upon	SCONJ
fumecheng-12619	21	3	nonlocal	nonlocal	ADJ
fumecheng-12619	21	4	elasticity	elasticity	NOUN
fumecheng-12619	21	5	principles	principle	NOUN
fumecheng-12619	21	6	,	,	PUNCT
fumecheng-12619	21	7	feng	feng	PROPN
fumecheng-12619	21	8	et	et	PROPN
fumecheng-12619	21	9	al	al	PROPN
fumecheng-12619	21	10	.	.	PROPN
fumecheng-12619	21	11	explored	explore	VERB
fumecheng-12619	21	12	the	the	DET
fumecheng-12619	21	13	axial	axial	ADJ
fumecheng-12619	21	14	vibrational	vibrational	ADJ
fumecheng-12619	21	15	characteristics	characteristic	NOUN
fumecheng-12619	21	16	of	of	ADP
fumecheng-12619	21	17	single	single	ADJ
fumecheng-12619	21	18	-	-	PUNCT
fumecheng-12619	21	19	walled	wall	VERB
fumecheng-12619	21	20	carbon	carbon	NOUN
fumecheng-12619	21	21	nanotube	nanotube	NOUN
fumecheng-12619	21	22	-	-	PUNCT
fumecheng-12619	21	23	based	base	VERB
fumecheng-12619	21	24	mass	mass	NOUN
fumecheng-12619	21	25	sensors	sensor	NOUN
fumecheng-12619	21	26	[	[	X
fumecheng-12619	21	27	10	10	NUM
fumecheng-12619	21	28	]	]	PUNCT
fumecheng-12619	21	29	.	.	PUNCT
fumecheng-12619	22	1	soltani	soltani	PROPN
fumecheng-12619	22	2	et	et	PROPN
fumecheng-12619	22	3	al	al	PROPN
fumecheng-12619	22	4	.	.	PUNCT
fumecheng-12619	23	1	[	[	X
fumecheng-12619	23	2	11	11	NUM
fumecheng-12619	23	3	]	]	X
fumecheng-12619	23	4	leveraged	leveraged	ADJ
fumecheng-12619	23	5	nonlocal	nonlocal	ADJ
fumecheng-12619	23	6	elasticity	elasticity	NOUN
fumecheng-12619	23	7	to	to	PART
fumecheng-12619	23	8	analyze	analyze	VERB
fumecheng-12619	23	9	the	the	DET
fumecheng-12619	23	10	lateral	lateral	ADJ
fumecheng-12619	23	11	-	-	PUNCT
fumecheng-12619	23	12	torsional	torsional	ADJ
fumecheng-12619	23	13	buckling	buckle	VERB
fumecheng-12619	23	14	behavior	behavior	NOUN
fumecheng-12619	23	15	of	of	ADP
fumecheng-12619	23	16	axially	axially	ADV
fumecheng-12619	23	17	functionally	functionally	ADV
fumecheng-12619	23	18	graded	grade	VERB
fumecheng-12619	23	19	nonlocal	nonlocal	ADJ
fumecheng-12619	23	20	beams	beam	NOUN
fumecheng-12619	23	21	.	.	PUNCT
fumecheng-12619	24	1	furthermore	furthermore	ADV
fumecheng-12619	24	2	,	,	PUNCT
fumecheng-12619	24	3	arefi	arefi	PROPN
fumecheng-12619	24	4	demonstrated	demonstrate	VERB
fumecheng-12619	24	5	that	that	SCONJ
fumecheng-12619	24	6	an	an	DET
fumecheng-12619	24	7	increase	increase	NOUN
fumecheng-12619	24	8	in	in	ADP
fumecheng-12619	24	9	the	the	DET
fumecheng-12619	24	10	nonlocal	nonlocal	ADJ
fumecheng-12619	24	11	parameter	parameter	NOUN
fumecheng-12619	24	12	amplifies	amplify	VERB
fumecheng-12619	24	13	rotations	rotation	NOUN
fumecheng-12619	24	14	,	,	PUNCT
fumecheng-12619	24	15	in	in	ADP
fumecheng-12619	24	16	-	-	PUNCT
fumecheng-12619	24	17	plane	plane	NOUN
fumecheng-12619	24	18	displacements	displacement	NOUN
fumecheng-12619	24	19	,	,	PUNCT
fumecheng-12619	24	20	and	and	CCONJ
fumecheng-12619	24	21	transverse	transverse	NOUN
fumecheng-12619	24	22	deflections	deflection	NOUN
fumecheng-12619	24	23	within	within	ADP
fumecheng-12619	24	24	a	a	DET
fumecheng-12619	24	25	piezoelectric	piezoelectric	ADJ
fumecheng-12619	24	26	nanoshell	nanoshell	NOUN
fumecheng-12619	24	27	exhibiting	exhibit	VERB
fumecheng-12619	24	28	double	double	ADJ
fumecheng-12619	24	29	curvature	curvature	NOUN
fumecheng-12619	24	30	[	[	X
fumecheng-12619	24	31	12	12	NUM
fumecheng-12619	24	32	]	]	PUNCT
fumecheng-12619	24	33	.	.	PUNCT
fumecheng-12619	25	1	employing	employ	VERB
fumecheng-12619	25	2	nonlocal	nonlocal	ADJ
fumecheng-12619	25	3	strain	strain	NOUN
fumecheng-12619	25	4	gradient	gradient	NOUN
fumecheng-12619	25	5	theory	theory	NOUN
fumecheng-12619	25	6	,	,	PUNCT
fumecheng-12619	25	7	boyina	boyina	PROPN
fumecheng-12619	25	8	et	et	PROPN
fumecheng-12619	25	9	al	al	PROPN
fumecheng-12619	25	10	.	.	PUNCT
fumecheng-12619	26	1	[	[	X
fumecheng-12619	26	2	13	13	NUM
fumecheng-12619	26	3	]	]	PUNCT
fumecheng-12619	26	4	investigated	investigate	VERB
fumecheng-12619	26	5	wave	wave	NOUN
fumecheng-12619	26	6	propagation	propagation	NOUN
fumecheng-12619	26	7	in	in	ADP
fumecheng-12619	26	8	viscoelastic	viscoelastic	ADJ
fumecheng-12619	26	9	timoshenko	timoshenko	NOUN
fumecheng-12619	26	10	nanobeams	nanobeam	NOUN
fumecheng-12619	26	11	under	under	ADP
fumecheng-12619	26	12	the	the	DET
fumecheng-12619	26	13	influence	influence	NOUN
fumecheng-12619	26	14	of	of	ADP
fumecheng-12619	26	15	surface	surface	NOUN
fumecheng-12619	26	16	and	and	CCONJ
fumecheng-12619	26	17	magnetic	magnetic	ADJ
fumecheng-12619	26	18	field	field	NOUN
fumecheng-12619	26	19	effects	effect	NOUN
fumecheng-12619	26	20	.	.	PUNCT
fumecheng-12619	27	1	similarly	similarly	ADV
fumecheng-12619	27	2	,	,	PUNCT
fumecheng-12619	27	3	liang	liang	PROPN
fumecheng-12619	27	4	et	et	PROPN
fumecheng-12619	27	5	al	al	PROPN
fumecheng-12619	27	6	.	.	PROPN
fumecheng-12619	27	7	explored	explore	VERB
fumecheng-12619	27	8	wave	wave	NOUN
fumecheng-12619	27	9	dispersion	dispersion	NOUN
fumecheng-12619	27	10	characteristics	characteristic	NOUN
fumecheng-12619	27	11	in	in	ADP
fumecheng-12619	27	12	lipid	lipid	ADJ
fumecheng-12619	27	13	tubules	tubule	NOUN
fumecheng-12619	27	14	,	,	PUNCT
fumecheng-12619	27	15	modeling	model	VERB
fumecheng-12619	27	16	them	they	PRON
fumecheng-12619	27	17	as	as	ADP
fumecheng-12619	27	18	shells	shell	NOUN
fumecheng-12619	27	19	,	,	PUNCT
fumecheng-12619	27	20	within	within	ADP
fumecheng-12619	27	21	the	the	DET
fumecheng-12619	27	22	framework	framework	NOUN
fumecheng-12619	27	23	of	of	ADP
fumecheng-12619	27	24	nonlocal	nonlocal	ADJ
fumecheng-12619	27	25	strain	strain	NOUN
fumecheng-12619	27	26	gradient	gradient	NOUN
fumecheng-12619	27	27	theory	theory	NOUN
fumecheng-12619	27	28	[	[	X
fumecheng-12619	27	29	14	14	NUM
fumecheng-12619	27	30	]	]	PUNCT
fumecheng-12619	27	31	.	.	PUNCT
fumecheng-12619	28	1	nonlinear	nonlinear	ADJ
fumecheng-12619	28	2	vibration	vibration	NOUN
fumecheng-12619	28	3	responses	response	NOUN
fumecheng-12619	28	4	of	of	ADP
fumecheng-12619	28	5	piezoelectric	piezoelectric	ADJ
fumecheng-12619	28	6	nanosensors	nanosensor	NOUN
fumecheng-12619	28	7	and	and	CCONJ
fumecheng-12619	28	8	nanoresonators	nanoresonator	NOUN
fumecheng-12619	28	9	have	have	AUX
fumecheng-12619	28	10	been	be	AUX
fumecheng-12619	28	11	addressed	address	VERB
fumecheng-12619	28	12	by	by	ADP
fumecheng-12619	28	13	hashemi	hashemi	NOUN
fumecheng-12619	28	14	kachapi	kachapi	PROPN
fumecheng-12619	28	15	et	et	PROPN
fumecheng-12619	28	16	al	al	PROPN
fumecheng-12619	28	17	.	.	PUNCT
fumecheng-12619	29	1	[	[	X
fumecheng-12619	29	2	15	15	NUM
fumecheng-12619	29	3	,	,	PUNCT
fumecheng-12619	29	4	16	16	NUM
fumecheng-12619	29	5	]	]	PUNCT
fumecheng-12619	29	6	considering	consider	VERB
fumecheng-12619	29	7	nonlocal	nonlocal	ADJ
fumecheng-12619	29	8	and	and	CCONJ
fumecheng-12619	29	9	surface	surface	NOUN
fumecheng-12619	29	10	/	/	SYM
fumecheng-12619	29	11	interface	interface	NOUN
fumecheng-12619	29	12	effects	effect	NOUN
fumecheng-12619	29	13	.	.	PUNCT
fumecheng-12619	30	1	adopting	adopt	VERB
fumecheng-12619	30	2	the	the	DET
fumecheng-12619	30	3	gurtin	gurtin	NOUN
fumecheng-12619	30	4	-	-	PUNCT
fumecheng-12619	30	5	murdoch	murdoch	PROPN
fumecheng-12619	30	6	approach	approach	NOUN
fumecheng-12619	30	7	to	to	ADP
fumecheng-12619	30	8	surface	surface	NOUN
fumecheng-12619	30	9	elasticity	elasticity	NOUN
fumecheng-12619	30	10	,	,	PUNCT
fumecheng-12619	30	11	fang	fang	X
fumecheng-12619	30	12	et	et	PROPN
fumecheng-12619	30	13	al	al	PROPN
fumecheng-12619	30	14	.	.	PUNCT
fumecheng-12619	31	1	[	[	X
fumecheng-12619	31	2	17	17	NUM
fumecheng-12619	31	3	,	,	PUNCT
fumecheng-12619	31	4	18	18	NUM
fumecheng-12619	31	5	]	]	PUNCT
fumecheng-12619	31	6	investigated	investigate	VERB
fumecheng-12619	31	7	the	the	DET
fumecheng-12619	31	8	nonlinear	nonlinear	ADJ
fumecheng-12619	31	9	buckling	buckling	NOUN
fumecheng-12619	31	10	,	,	PUNCT
fumecheng-12619	31	11	post	post	ADJ
fumecheng-12619	31	12	-	-	ADJ
fumecheng-12619	31	13	buckling	buckling	ADJ
fumecheng-12619	31	14	,	,	PUNCT
fumecheng-12619	31	15	and	and	CCONJ
fumecheng-12619	31	16	vibration	vibration	NOUN
fumecheng-12619	31	17	characteristics	characteristic	NOUN
fumecheng-12619	31	18	of	of	ADP
fumecheng-12619	31	19	piezoelectric	piezoelectric	ADJ
fumecheng-12619	31	20	nanostructures	nanostructure	NOUN
fumecheng-12619	31	21	.	.	PUNCT
fumecheng-12619	32	1	hashemi	hashemi	PROPN
fumecheng-12619	32	2	kachapi	kachapi	PROPN
fumecheng-12619	32	3	et	et	PROPN
fumecheng-12619	32	4	al	al	PROPN
fumecheng-12619	32	5	.	.	PUNCT
fumecheng-12619	33	1	[	[	X
fumecheng-12619	33	2	19	19	NUM
fumecheng-12619	33	3	,	,	PUNCT
fumecheng-12619	33	4	20	20	NUM
fumecheng-12619	33	5	]	]	PUNCT
fumecheng-12619	33	6	employed	employ	VERB
fumecheng-12619	33	7	surface	surface	NOUN
fumecheng-12619	33	8	/	/	SYM
fumecheng-12619	33	9	interface	interface	NOUN
fumecheng-12619	33	10	and	and	CCONJ
fumecheng-12619	33	11	nonlocal	nonlocal	ADJ
fumecheng-12619	33	12	strain	strain	NOUN
fumecheng-12619	33	13	gradient	gradient	NOUN
fumecheng-12619	33	14	effects	effect	NOUN
fumecheng-12619	33	15	to	to	PART
fumecheng-12619	33	16	investigate	investigate	VERB
fumecheng-12619	33	17	the	the	DET
fumecheng-12619	33	18	effects	effect	NOUN
fumecheng-12619	33	19	of	of	ADP
fumecheng-12619	33	20	the	the	DET
fumecheng-12619	33	21	small	small	ADJ
fumecheng-12619	33	22	scale	scale	NOUN
fumecheng-12619	33	23	on	on	ADP
fumecheng-12619	33	24	the	the	DET
fumecheng-12619	33	25	natural	natural	ADJ
fumecheng-12619	33	26	frequencies	frequency	NOUN
fumecheng-12619	33	27	,	,	PUNCT
fumecheng-12619	33	28	nonlinear	nonlinear	ADJ
fumecheng-12619	33	29	vibration	vibration	NOUN
fumecheng-12619	33	30	,	,	PUNCT
fumecheng-12619	33	31	and	and	CCONJ
fumecheng-12619	33	32	stability	stability	NOUN
fumecheng-12619	33	33	analysis	analysis	NOUN
fumecheng-12619	33	34	of	of	ADP
fumecheng-12619	33	35	piezoelectric	piezoelectric	ADJ
fumecheng-12619	33	36	nanostructures	nanostructure	NOUN
fumecheng-12619	33	37	subjected	subject	VERB
fumecheng-12619	33	38	to	to	ADP
fumecheng-12619	33	39	electrostatic	electrostatic	ADJ
fumecheng-12619	33	40	and	and	CCONJ
fumecheng-12619	33	41	harmonic	harmonic	ADJ
fumecheng-12619	33	42	excitations	excitation	NOUN
fumecheng-12619	33	43	.	.	PUNCT
fumecheng-12619	34	1	it	it	PRON
fumecheng-12619	34	2	is	be	AUX
fumecheng-12619	34	3	noteworthy	noteworthy	ADJ
fumecheng-12619	34	4	that	that	SCONJ
fumecheng-12619	34	5	,	,	PUNCT
fumecheng-12619	34	6	beyond	beyond	ADP
fumecheng-12619	34	7	the	the	DET
fumecheng-12619	34	8	work	work	NOUN
fumecheng-12619	34	9	of	of	ADP
fumecheng-12619	34	10	hashemi	hashemi	PROPN
fumecheng-12619	34	11	kachapi	kachapi	PROPN
fumecheng-12619	34	12	et	et	PROPN
fumecheng-12619	34	13	al	al	PROPN
fumecheng-12619	34	14	.	.	PUNCT
fumecheng-12619	35	1	[	[	X
fumecheng-12619	35	2	20	20	NUM
fumecheng-12619	35	3	]	]	PUNCT
fumecheng-12619	35	4	,	,	PUNCT
fumecheng-12619	35	5	studies	study	NOUN
fumecheng-12619	35	6	that	that	PRON
fumecheng-12619	35	7	consider	consider	VERB
fumecheng-12619	35	8	simultaneously	simultaneously	ADV
fumecheng-12619	35	9	both	both	CCONJ
fumecheng-12619	35	10	surface	surface	NOUN
fumecheng-12619	35	11	and	and	CCONJ
fumecheng-12619	35	12	small	small	ADJ
fumecheng-12619	35	13	-	-	PUNCT
fumecheng-12619	35	14	scale	scale	NOUN
fumecheng-12619	35	15	effects	effect	NOUN
fumecheng-12619	35	16	in	in	ADP
fumecheng-12619	35	17	piezoelectric	piezoelectric	ADJ
fumecheng-12619	35	18	materials	material	NOUN
fumecheng-12619	35	19	remain	remain	VERB
fumecheng-12619	35	20	scarce	scarce	ADJ
fumecheng-12619	35	21	.	.	PUNCT
fumecheng-12619	36	1	farrokhian	farrokhian	NOUN
fumecheng-12619	36	2	et	et	PROPN
fumecheng-12619	36	3	al	al	PROPN
fumecheng-12619	36	4	.	.	PUNCT
fumecheng-12619	37	1	[	[	X
fumecheng-12619	37	2	21	21	NUM
fumecheng-12619	37	3	]	]	PUNCT
fumecheng-12619	37	4	investigated	investigate	VERB
fumecheng-12619	37	5	the	the	DET
fumecheng-12619	37	6	vibration	vibration	NOUN
fumecheng-12619	37	7	and	and	CCONJ
fumecheng-12619	37	8	damping	damp	VERB
fumecheng-12619	37	9	behavior	behavior	NOUN
fumecheng-12619	37	10	of	of	ADP
fumecheng-12619	37	11	smart	smart	ADJ
fumecheng-12619	37	12	sandwich	sandwich	NOUN
fumecheng-12619	37	13	nanotubes	nanotube	NOUN
fumecheng-12619	37	14	using	use	VERB
fumecheng-12619	37	15	nonlocal	nonlocal	ADJ
fumecheng-12619	37	16	and	and	CCONJ
fumecheng-12619	37	17	surface	surface	NOUN
fumecheng-12619	37	18	piezoelasticity	piezoelasticity	NOUN
fumecheng-12619	37	19	theories	theory	NOUN
fumecheng-12619	37	20	.	.	PUNCT
fumecheng-12619	38	1	additionally	additionally	ADV
fumecheng-12619	38	2	,	,	PUNCT
fumecheng-12619	38	3	ghorbani	ghorbani	NOUN
fumecheng-12619	38	4	et	et	PROPN
fumecheng-12619	38	5	al	al	PROPN
fumecheng-12619	38	6	.	.	PUNCT
fumecheng-12619	39	1	[	[	X
fumecheng-12619	39	2	22	22	NUM
fumecheng-12619	39	3	]	]	PUNCT
fumecheng-12619	39	4	revealed	reveal	VERB
fumecheng-12619	39	5	that	that	SCONJ
fumecheng-12619	39	6	the	the	DET
fumecheng-12619	39	7	material	material	NOUN
fumecheng-12619	39	8	length	length	NOUN
fumecheng-12619	39	9	scale	scale	NOUN
fumecheng-12619	39	10	(	(	PUNCT
fumecheng-12619	39	11	mls	mls	PROPN
fumecheng-12619	39	12	)	)	PUNCT
fumecheng-12619	39	13	parameter	parameter	NOUN
fumecheng-12619	39	14	augments	augment	VERB
fumecheng-12619	39	15	natural	natural	ADJ
fumecheng-12619	39	16	frequency	frequency	NOUN
fumecheng-12619	39	17	,	,	PUNCT
fumecheng-12619	39	18	while	while	SCONJ
fumecheng-12619	39	19	the	the	DET
fumecheng-12619	39	20	nonlocal	nonlocal	ADJ
fumecheng-12619	39	21	(	(	PUNCT
fumecheng-12619	39	22	nl	nl	NOUN
fumecheng-12619	39	23	)	)	PUNCT
fumecheng-12619	39	24	parameter	parameter	NOUN
fumecheng-12619	39	25	diminishes	diminish	VERB
fumecheng-12619	39	26	it	it	PRON
fumecheng-12619	39	27	.	.	PUNCT
fumecheng-12619	40	1	lovisi	lovisi	VERB
fumecheng-12619	41	1	[	[	X
fumecheng-12619	41	2	23	23	NUM
fumecheng-12619	41	3	]	]	PUNCT
fumecheng-12619	41	4	explored	explore	VERB
fumecheng-12619	41	5	the	the	DET
fumecheng-12619	41	6	bending	bend	VERB
fumecheng-12619	41	7	response	response	NOUN
fumecheng-12619	41	8	of	of	ADP
fumecheng-12619	41	9	functionally	functionally	ADV
fumecheng-12619	41	10	graded	grade	VERB
fumecheng-12619	41	11	cracked	crack	VERB
fumecheng-12619	41	12	nanobeams	nanobeam	NOUN
fumecheng-12619	41	13	,	,	PUNCT
fumecheng-12619	41	14	incorporating	incorporate	VERB
fumecheng-12619	41	15	surface	surface	NOUN
fumecheng-12619	41	16	and	and	CCONJ
fumecheng-12619	41	17	nonlocal	nonlocal	ADJ
fumecheng-12619	41	18	effects	effect	NOUN
fumecheng-12619	41	19	.	.	PUNCT
fumecheng-12619	42	1	sun	sun	PROPN
fumecheng-12619	42	2	et	et	PROPN
fumecheng-12619	42	3	al	al	PROPN
fumecheng-12619	42	4	.	.	PUNCT
fumecheng-12619	43	1	[	[	X
fumecheng-12619	43	2	24	24	NUM
fumecheng-12619	43	3	]	]	PUNCT
fumecheng-12619	43	4	employed	employ	VERB
fumecheng-12619	43	5	nonlocal	nonlocal	ADJ
fumecheng-12619	43	6	and	and	CCONJ
fumecheng-12619	43	7	surface	surface	NOUN
fumecheng-12619	43	8	effects	effect	NOUN
fumecheng-12619	43	9	to	to	PART
fumecheng-12619	43	10	analyze	analyze	VERB
fumecheng-12619	43	11	the	the	DET
fumecheng-12619	43	12	buckling	buckling	NOUN
fumecheng-12619	43	13	of	of	ADP
fumecheng-12619	43	14	piezoelectric	piezoelectric	NOUN
fumecheng-12619	43	15	nanoshells	nanoshell	NOUN
fumecheng-12619	43	16	under	under	ADP
fumecheng-12619	43	17	external	external	ADJ
fumecheng-12619	43	18	voltages	voltage	NOUN
fumecheng-12619	43	19	and	and	CCONJ
fumecheng-12619	43	20	compressive	compressive	ADJ
fumecheng-12619	43	21	loads	load	NOUN
fumecheng-12619	43	22	.	.	PUNCT
fumecheng-12619	44	1	it	it	PRON
fumecheng-12619	44	2	is	be	AUX
fumecheng-12619	44	3	worth	worth	ADJ
fumecheng-12619	44	4	noting	note	VERB
fumecheng-12619	44	5	that	that	SCONJ
fumecheng-12619	44	6	in	in	ADP
fumecheng-12619	44	7	other	other	ADJ
fumecheng-12619	44	8	works	work	NOUN
fumecheng-12619	44	9	by	by	ADP
fumecheng-12619	44	10	hashemi	hashemi	NOUN
fumecheng-12619	44	11	kachapi	kachapi	PROPN
fumecheng-12619	44	12	et	et	PROPN
fumecheng-12619	44	13	al	al	PROPN
fumecheng-12619	44	14	.	.	PUNCT
fumecheng-12619	45	1	[	[	X
fumecheng-12619	45	2	25	25	NUM
fumecheng-12619	45	3	,	,	PUNCT
fumecheng-12619	45	4	26	26	NUM
fumecheng-12619	45	5	]	]	PUNCT
fumecheng-12619	45	6	,	,	PUNCT
fumecheng-12619	45	7	nonlinear	nonlinear	ADJ
fumecheng-12619	45	8	vibration	vibration	NOUN
fumecheng-12619	45	9	and	and	CCONJ
fumecheng-12619	45	10	stability	stability	NOUN
fumecheng-12619	45	11	analyses	analysis	NOUN
fumecheng-12619	45	12	considering	consider	VERB
fumecheng-12619	45	13	nonclassical	nonclassical	ADJ
fumecheng-12619	45	14	effects	effect	NOUN
fumecheng-12619	45	15	were	be	AUX
fumecheng-12619	45	16	investigated	investigate	VERB
fumecheng-12619	45	17	for	for	ADP
fumecheng-12619	45	18	double	double	ADJ
fumecheng-12619	45	19	-	-	PUNCT
fumecheng-12619	45	20	walled	wall	VERB
fumecheng-12619	45	21	cases	case	NOUN
fumecheng-12619	45	22	of	of	ADP
fumecheng-12619	45	23	piezoelectric	piezoelectric	NOUN
fumecheng-12619	45	24	nanostructures	nanostructure	NOUN
fumecheng-12619	45	25	.	.	PUNCT
fumecheng-12619	46	1	while	while	SCONJ
fumecheng-12619	46	2	prior	prior	ADJ
fumecheng-12619	46	3	research	research	NOUN
fumecheng-12619	46	4	has	have	AUX
fumecheng-12619	46	5	extensively	extensively	ADV
fumecheng-12619	46	6	explored	explore	VERB
fumecheng-12619	46	7	the	the	DET
fumecheng-12619	46	8	vibrational	vibrational	ADJ
fumecheng-12619	46	9	and	and	CCONJ
fumecheng-12619	46	10	stability	stability	NOUN
fumecheng-12619	46	11	characteristics	characteristic	NOUN
fumecheng-12619	46	12	of	of	ADP
fumecheng-12619	46	13	piezoelectric	piezoelectric	NOUN
fumecheng-12619	46	14	nanostructures	nanostructure	NOUN
fumecheng-12619	46	15	,	,	PUNCT
fumecheng-12619	46	16	a	a	DET
fumecheng-12619	46	17	notable	notable	ADJ
fumecheng-12619	46	18	gap	gap	NOUN
fumecheng-12619	46	19	persists	persist	VERB
fumecheng-12619	46	20	in	in	ADP
fumecheng-12619	46	21	studies	study	NOUN
fumecheng-12619	46	22	that	that	PRON
fumecheng-12619	46	23	concurrently	concurrently	ADV
fumecheng-12619	46	24	incorporate	incorporate	VERB
fumecheng-12619	46	25	strain	strain	NOUN
fumecheng-12619	46	26	gradient	gradient	NOUN
fumecheng-12619	46	27	,	,	PUNCT
fumecheng-12619	46	28	gurtin	gurtin	NOUN
fumecheng-12619	46	29	-	-	PUNCT
fumecheng-12619	46	30	murdoch	murdoch	PROPN
fumecheng-12619	46	31	surface	surface	NOUN
fumecheng-12619	46	32	/	/	SYM
fumecheng-12619	46	33	interface	interface	NOUN
fumecheng-12619	46	34	,	,	PUNCT
fumecheng-12619	46	35	and	and	CCONJ
fumecheng-12619	46	36	nonlocal	nonlocal	ADJ
fumecheng-12619	46	37	effects	effect	NOUN
fumecheng-12619	46	38	.	.	PUNCT
fumecheng-12619	47	1	the	the	DET
fumecheng-12619	47	2	present	present	ADJ
fumecheng-12619	47	3	investigation	investigation	NOUN
fumecheng-12619	47	4	extends	extend	VERB
fumecheng-12619	47	5	the	the	DET
fumecheng-12619	47	6	research	research	NOUN
fumecheng-12619	47	7	trajectory	trajectory	NOUN
fumecheng-12619	47	8	initiated	initiate	VERB
fumecheng-12619	47	9	by	by	ADP
fumecheng-12619	47	10	hashemi	hashemi	NOUN
fumecheng-12619	47	11	kachapi	kachapi	PROPN
fumecheng-12619	47	12	et	et	PROPN
fumecheng-12619	47	13	al	al	PROPN
fumecheng-12619	48	1	[	[	X
fumecheng-12619	48	2	20	20	NUM
fumecheng-12619	48	3	]	]	PUNCT
fumecheng-12619	48	4	.	.	PUNCT
fumecheng-12619	49	1	however	however	ADV
fumecheng-12619	49	2	,	,	PUNCT
fumecheng-12619	49	3	it	it	PRON
fumecheng-12619	49	4	distinguishes	distinguish	VERB
fumecheng-12619	49	5	itself	itself	PRON
fumecheng-12619	49	6	through	through	ADP
fumecheng-12619	49	7	a	a	DET
fumecheng-12619	49	8	distinct	distinct	ADJ
fumecheng-12619	49	9	subject	subject	NOUN
fumecheng-12619	49	10	matter	matter	NOUN
fumecheng-12619	49	11	,	,	PUNCT
fumecheng-12619	49	12	particularly	particularly	ADV
fumecheng-12619	49	13	regarding	regard	VERB
fumecheng-12619	49	14	the	the	DET
fumecheng-12619	49	15	excitation	excitation	NOUN
fumecheng-12619	49	16	forces	force	NOUN
fumecheng-12619	49	17	and	and	CCONJ
fumecheng-12619	49	18	resulting	result	VERB
fumecheng-12619	49	19	findings	finding	NOUN
fumecheng-12619	49	20	,	,	PUNCT
fumecheng-12619	49	21	which	which	PRON
fumecheng-12619	49	22	are	be	AUX
fumecheng-12619	49	23	entirely	entirely	ADV
fumecheng-12619	49	24	independent	independent	ADJ
fumecheng-12619	49	25	of	of	ADP
fumecheng-12619	49	26	our	our	PRON
fumecheng-12619	49	27	previous	previous	ADJ
fumecheng-12619	49	28	comparison	comparison	NOUN
fumecheng-12619	49	29	of	of	ADP
fumecheng-12619	49	30	nonclassical	nonclassical	ADJ
fumecheng-12619	49	31	controllers	controller	NOUN
fumecheng-12619	49	32	on	on	ADP
fumecheng-12619	49	33	nonlinear	nonlinear	ADJ
fumecheng-12619	49	34	vibrations	vibration	NOUN
fumecheng-12619	49	35	analysis	analysis	NOUN
fumecheng-12619	49	36	of	of	ADP
fumecheng-12619	49	37	piezoelectric	piezoelectric	NOUN
fumecheng-12619	49	38	...	...	PUNCT
fumecheng-12619	49	39	313	313	NUM
fumecheng-12619	49	40	work	work	NOUN
fumecheng-12619	49	41	.	.	PUNCT
fumecheng-12619	50	1	unlike	unlike	ADP
fumecheng-12619	50	2	the	the	DET
fumecheng-12619	50	3	earlier	early	ADJ
fumecheng-12619	50	4	study	study	NOUN
fumecheng-12619	50	5	,	,	PUNCT
fumecheng-12619	50	6	this	this	DET
fumecheng-12619	50	7	analysis	analysis	NOUN
fumecheng-12619	50	8	examines	examine	VERB
fumecheng-12619	50	9	a	a	DET
fumecheng-12619	50	10	nanostructure	nanostructure	NOUN
fumecheng-12619	50	11	subjected	subject	VERB
fumecheng-12619	50	12	to	to	ADP
fumecheng-12619	50	13	a	a	DET
fumecheng-12619	50	14	complex	complex	ADJ
fumecheng-12619	50	15	nonlinear	nonlinear	ADJ
fumecheng-12619	50	16	electrostatic	electrostatic	ADJ
fumecheng-12619	50	17	excitation	excitation	NOUN
fumecheng-12619	50	18	,	,	PUNCT
fumecheng-12619	50	19	encompassing	encompass	VERB
fumecheng-12619	50	20	both	both	CCONJ
fumecheng-12619	50	21	direct	direct	ADJ
fumecheng-12619	50	22	(	(	PUNCT
fumecheng-12619	50	23	dc	dc	PROPN
fumecheng-12619	50	24	)	)	PUNCT
fumecheng-12619	50	25	and	and	CCONJ
fumecheng-12619	50	26	alternating	alternate	VERB
fumecheng-12619	50	27	(	(	PUNCT
fumecheng-12619	50	28	ac	ac	PROPN
fumecheng-12619	50	29	)	)	PUNCT
fumecheng-12619	50	30	voltage	voltage	NOUN
fumecheng-12619	50	31	components	component	NOUN
fumecheng-12619	50	32	,	,	PUNCT
fumecheng-12619	50	33	while	while	SCONJ
fumecheng-12619	50	34	also	also	ADV
fumecheng-12619	50	35	considering	consider	VERB
fumecheng-12619	50	36	the	the	DET
fumecheng-12619	50	37	influence	influence	NOUN
fumecheng-12619	50	38	of	of	ADP
fumecheng-12619	50	39	a	a	DET
fumecheng-12619	50	40	visco	visco	ADJ
fumecheng-12619	50	41	-	-	PUNCT
fumecheng-12619	50	42	pasternak	pasternak	ADJ
fumecheng-12619	50	43	medium	medium	NOUN
fumecheng-12619	50	44	.	.	PUNCT
fumecheng-12619	51	1	the	the	DET
fumecheng-12619	51	2	primary	primary	ADJ
fumecheng-12619	51	3	objective	objective	NOUN
fumecheng-12619	51	4	of	of	ADP
fumecheng-12619	51	5	this	this	DET
fumecheng-12619	51	6	study	study	NOUN
fumecheng-12619	51	7	is	be	AUX
fumecheng-12619	51	8	to	to	PART
fumecheng-12619	51	9	elucidate	elucidate	VERB
fumecheng-12619	51	10	the	the	DET
fumecheng-12619	51	11	impact	impact	NOUN
fumecheng-12619	51	12	of	of	ADP
fumecheng-12619	51	13	these	these	DET
fumecheng-12619	51	14	combined	combine	VERB
fumecheng-12619	51	15	effects	effect	NOUN
fumecheng-12619	51	16	on	on	ADP
fumecheng-12619	51	17	the	the	DET
fumecheng-12619	51	18	nonlinear	nonlinear	ADJ
fumecheng-12619	51	19	vibration	vibration	NOUN
fumecheng-12619	51	20	and	and	CCONJ
fumecheng-12619	51	21	stability	stability	NOUN
fumecheng-12619	51	22	behavior	behavior	NOUN
fumecheng-12619	51	23	of	of	ADP
fumecheng-12619	51	24	a	a	DET
fumecheng-12619	51	25	piezoelectric	piezoelectric	ADJ
fumecheng-12619	51	26	nanoresonator	nanoresonator	NOUN
fumecheng-12619	51	27	,	,	PUNCT
fumecheng-12619	51	28	in	in	ADP
fumecheng-12619	51	29	comparison	comparison	NOUN
fumecheng-12619	51	30	to	to	ADP
fumecheng-12619	51	31	predictions	prediction	NOUN
fumecheng-12619	51	32	derived	derive	VERB
fumecheng-12619	51	33	from	from	ADP
fumecheng-12619	51	34	classical	classical	ADJ
fumecheng-12619	51	35	continuum	continuum	ADJ
fumecheng-12619	51	36	theory	theory	NOUN
fumecheng-12619	51	37	.	.	PUNCT
fumecheng-12619	52	1	to	to	PART
fumecheng-12619	52	2	achieve	achieve	VERB
fumecheng-12619	52	3	this	this	PRON
fumecheng-12619	52	4	,	,	PUNCT
fumecheng-12619	52	5	a	a	DET
fumecheng-12619	52	6	comprehensive	comprehensive	ADJ
fumecheng-12619	52	7	analytical	analytical	ADJ
fumecheng-12619	52	8	framework	framework	NOUN
fumecheng-12619	52	9	is	be	AUX
fumecheng-12619	52	10	employed	employ	VERB
fumecheng-12619	52	11	,	,	PUNCT
fumecheng-12619	52	12	integrating	integrate	VERB
fumecheng-12619	52	13	hamilton	hamilton	PROPN
fumecheng-12619	52	14	’s	’s	PART
fumecheng-12619	52	15	principle	principle	NOUN
fumecheng-12619	52	16	,	,	PUNCT
fumecheng-12619	52	17	the	the	DET
fumecheng-12619	52	18	galerkin	galerkin	ADJ
fumecheng-12619	52	19	method	method	NOUN
fumecheng-12619	52	20	,	,	PUNCT
fumecheng-12619	52	21	and	and	CCONJ
fumecheng-12619	52	22	a	a	DET
fumecheng-12619	52	23	hybrid	hybrid	ADJ
fumecheng-12619	52	24	complex	complex	ADJ
fumecheng-12619	52	25	averaging	averaging	NOUN
fumecheng-12619	52	26	technique	technique	NOUN
fumecheng-12619	52	27	coupled	couple	VERB
fumecheng-12619	52	28	with	with	ADP
fumecheng-12619	52	29	arc	arc	NOUN
fumecheng-12619	52	30	-	-	PUNCT
fumecheng-12619	52	31	length	length	NOUN
fumecheng-12619	52	32	continuation	continuation	NOUN
fumecheng-12619	52	33	.	.	PUNCT
fumecheng-12619	53	1	this	this	DET
fumecheng-12619	53	2	methodology	methodology	NOUN
fumecheng-12619	53	3	facilitates	facilitate	VERB
fumecheng-12619	53	4	a	a	DET
fumecheng-12619	53	5	direct	direct	ADJ
fumecheng-12619	53	6	comparison	comparison	NOUN
fumecheng-12619	53	7	of	of	ADP
fumecheng-12619	53	8	three	three	NUM
fumecheng-12619	53	9	nonclassical	nonclassical	ADJ
fumecheng-12619	53	10	theoriesstrain	theoriesstrain	NOUN
fumecheng-12619	53	11	gradient	gradient	NOUN
fumecheng-12619	53	12	theory	theory	NOUN
fumecheng-12619	53	13	(	(	PUNCT
fumecheng-12619	53	14	sgt	sgt	PROPN
fumecheng-12619	53	15	)	)	PUNCT
fumecheng-12619	53	16	,	,	PUNCT
fumecheng-12619	53	17	nonlocal	nonlocal	ADJ
fumecheng-12619	53	18	theory	theory	NOUN
fumecheng-12619	53	19	(	(	PUNCT
fumecheng-12619	53	20	nlt	nlt	PROPN
fumecheng-12619	53	21	)	)	PUNCT
fumecheng-12619	53	22	,	,	PUNCT
fumecheng-12619	53	23	and	and	CCONJ
fumecheng-12619	53	24	gurtin	gurtin	PROPN
fumecheng-12619	53	25	-	-	PUNCT
fumecheng-12619	53	26	murdoch	murdoch	PROPN
fumecheng-12619	53	27	surface	surface	NOUN
fumecheng-12619	53	28	/	/	SYM
fumecheng-12619	53	29	interface	interface	NOUN
fumecheng-12619	53	30	theory	theory	NOUN
fumecheng-12619	53	31	(	(	PUNCT
fumecheng-12619	53	32	gmsit)with	gmsit)with	ADP
fumecheng-12619	53	33	classical	classical	ADJ
fumecheng-12619	53	34	continuum	continuum	ADJ
fumecheng-12619	53	35	theory	theory	NOUN
fumecheng-12619	53	36	(	(	PUNCT
fumecheng-12619	53	37	ct	ct	PROPN
fumecheng-12619	53	38	)	)	PUNCT
fumecheng-12619	53	39	.	.	PUNCT
fumecheng-12619	54	1	consequently	consequently	ADV
fumecheng-12619	54	2	,	,	PUNCT
fumecheng-12619	54	3	the	the	DET
fumecheng-12619	54	4	study	study	NOUN
fumecheng-12619	54	5	investigates	investigate	VERB
fumecheng-12619	54	6	the	the	DET
fumecheng-12619	54	7	influence	influence	NOUN
fumecheng-12619	54	8	of	of	ADP
fumecheng-12619	54	9	nanoscale	nanoscale	NOUN
fumecheng-12619	54	10	and	and	CCONJ
fumecheng-12619	54	11	surface	surface	NOUN
fumecheng-12619	54	12	/	/	SYM
fumecheng-12619	54	13	interface	interface	NOUN
fumecheng-12619	54	14	effects	effect	NOUN
fumecheng-12619	54	15	,	,	PUNCT
fumecheng-12619	54	16	the	the	DET
fumecheng-12619	54	17	elastic	elastic	ADJ
fumecheng-12619	54	18	medium	medium	NOUN
fumecheng-12619	54	19	,	,	PUNCT
fumecheng-12619	54	20	electrostatic	electrostatic	ADJ
fumecheng-12619	54	21	and	and	CCONJ
fumecheng-12619	54	22	piezoelectric	piezoelectric	ADJ
fumecheng-12619	54	23	voltages	voltage	NOUN
fumecheng-12619	54	24	,	,	PUNCT
fumecheng-12619	54	25	and	and	CCONJ
fumecheng-12619	54	26	other	other	ADJ
fumecheng-12619	54	27	relevant	relevant	ADJ
fumecheng-12619	54	28	parameters	parameter	NOUN
fumecheng-12619	54	29	on	on	ADP
fumecheng-12619	54	30	the	the	DET
fumecheng-12619	54	31	dimensionless	dimensionless	ADJ
fumecheng-12619	54	32	natural	natural	ADJ
fumecheng-12619	54	33	frequency	frequency	NOUN
fumecheng-12619	54	34	(	(	PUNCT
fumecheng-12619	54	35	dnf	dnf	PROPN
fumecheng-12619	54	36	)	)	PUNCT
fumecheng-12619	54	37	,	,	PUNCT
fumecheng-12619	54	38	pull	pull	NOUN
fumecheng-12619	54	39	-	-	PUNCT
fumecheng-12619	54	40	in	in	ADP
fumecheng-12619	54	41	voltage	voltage	NOUN
fumecheng-12619	54	42	,	,	PUNCT
fumecheng-12619	54	43	nonlinear	nonlinear	ADJ
fumecheng-12619	54	44	frequency	frequency	NOUN
fumecheng-12619	54	45	response	response	NOUN
fumecheng-12619	54	46	,	,	PUNCT
fumecheng-12619	54	47	and	and	CCONJ
fumecheng-12619	54	48	stability	stability	NOUN
fumecheng-12619	54	49	of	of	ADP
fumecheng-12619	54	50	the	the	DET
fumecheng-12619	54	51	piezoelectric	piezoelectric	NOUN
fumecheng-12619	54	52	nanoresonator	nanoresonator	NOUN
fumecheng-12619	54	53	.	.	PUNCT
fumecheng-12619	55	1	2	2	X
fumecheng-12619	55	2	.	.	X
fumecheng-12619	55	3	mathematical	mathematical	ADJ
fumecheng-12619	55	4	formulation	formulation	NOUN
fumecheng-12619	55	5	fig	fig	NOUN
fumecheng-12619	55	6	.	.	PUNCT
fumecheng-12619	56	1	1	1	NUM
fumecheng-12619	56	2	depicts	depict	VERB
fumecheng-12619	56	3	the	the	DET
fumecheng-12619	56	4	configuration	configuration	NOUN
fumecheng-12619	56	5	of	of	ADP
fumecheng-12619	56	6	a	a	DET
fumecheng-12619	56	7	cylindrical	cylindrical	ADJ
fumecheng-12619	56	8	nanoshell	nanoshell	NOUN
fumecheng-12619	56	9	-	-	PUNCT
fumecheng-12619	56	10	based	base	VERB
fumecheng-12619	56	11	piezoelectric	piezoelectric	NOUN
fumecheng-12619	56	12	nanoresonator	nanoresonator	NOUN
fumecheng-12619	56	13	subjected	subject	VERB
fumecheng-12619	56	14	to	to	ADP
fumecheng-12619	56	15	a	a	DET
fumecheng-12619	56	16	visco	visco	ADJ
fumecheng-12619	56	17	-	-	ADJ
fumecheng-12619	56	18	pasternak	pasternak	ADJ
fumecheng-12619	56	19	medium	medium	ADJ
fumecheng-12619	56	20	and	and	CCONJ
fumecheng-12619	56	21	nonlinear	nonlinear	ADJ
fumecheng-12619	56	22	electrostatic	electrostatic	ADJ
fumecheng-12619	56	23	excitation	excitation	NOUN
fumecheng-12619	56	24	.	.	PUNCT
fumecheng-12619	57	1	fig	fig	NOUN
fumecheng-12619	57	2	.	.	PUNCT
fumecheng-12619	58	1	1	1	NUM
fumecheng-12619	58	2	a	a	DET
fumecheng-12619	58	3	piezoelectric	piezoelectric	NOUN
fumecheng-12619	58	4	nanoresonator	nanoresonator	NOUN
fumecheng-12619	58	5	subjected	subject	VERB
fumecheng-12619	58	6	to	to	ADP
fumecheng-12619	58	7	nonlinear	nonlinear	ADJ
fumecheng-12619	58	8	electrostatic	electrostatic	ADJ
fumecheng-12619	58	9	excitation	excitation	NOUN
fumecheng-12619	58	10	the	the	DET
fumecheng-12619	58	11	nanoresonator	nanoresonator	NOUN
fumecheng-12619	58	12	is	be	AUX
fumecheng-12619	58	13	actuated	actuate	VERB
fumecheng-12619	58	14	by	by	ADP
fumecheng-12619	58	15	a	a	DET
fumecheng-12619	58	16	superimposed	superimpose	VERB
fumecheng-12619	58	17	electrostatic	electrostatic	ADJ
fumecheng-12619	58	18	field	field	NOUN
fumecheng-12619	58	19	,	,	PUNCT
fumecheng-12619	58	20	consisting	consist	VERB
fumecheng-12619	58	21	of	of	ADP
fumecheng-12619	58	22	an	an	DET
fumecheng-12619	58	23	alternating	alternate	VERB
fumecheng-12619	58	24	voltage	voltage	NOUN
fumecheng-12619	58	25	component	component	NOUN
fumecheng-12619	58	26	,	,	PUNCT
fumecheng-12619	58	27	𝑉𝐴𝐶	𝑉𝐴𝐶	PROPN
fumecheng-12619	58	28	,	,	PUNCT
fumecheng-12619	58	29	and	and	CCONJ
fumecheng-12619	58	30	a	a	DET
fumecheng-12619	58	31	direct	direct	ADJ
fumecheng-12619	58	32	voltage	voltage	NOUN
fumecheng-12619	58	33	component	component	NOUN
fumecheng-12619	58	34	,	,	PUNCT
fumecheng-12619	58	35	𝑉𝐷𝐶.	𝑉𝐷𝐶.	ADP
fumecheng-12619	58	36	the	the	DET
fumecheng-12619	58	37	geometric	geometric	ADJ
fumecheng-12619	58	38	configuration	configuration	NOUN
fumecheng-12619	58	39	of	of	ADP
fumecheng-12619	58	40	the	the	DET
fumecheng-12619	58	41	piezoelectric	piezoelectric	ADJ
fumecheng-12619	58	42	nanoresonator	nanoresonator	NOUN
fumecheng-12619	58	43	is	be	AUX
fumecheng-12619	58	44	defined	define	VERB
fumecheng-12619	58	45	by	by	ADP
fumecheng-12619	58	46	the	the	DET
fumecheng-12619	58	47	following	follow	VERB
fumecheng-12619	58	48	parameters	parameter	NOUN
fumecheng-12619	58	49	:	:	PUNCT
fumecheng-12619	58	50	mid	mid	ADJ
fumecheng-12619	58	51	-	-	ADJ
fumecheng-12619	58	52	surface	surface	ADJ
fumecheng-12619	58	53	radius	radius	NOUN
fumecheng-12619	58	54	,	,	PUNCT
fumecheng-12619	58	55	𝑅	𝑅	NOUN
fumecheng-12619	58	56	;	;	PUNCT
fumecheng-12619	58	57	axial	axial	ADJ
fumecheng-12619	58	58	length	length	NOUN
fumecheng-12619	58	59	,	,	PUNCT
fumecheng-12619	58	60	𝐿	𝐿	NOUN
fumecheng-12619	58	61	;	;	PUNCT
fumecheng-12619	58	62	piezoelectric	piezoelectric	NOUN
fumecheng-12619	58	63	material	material	NOUN
fumecheng-12619	58	64	layer	layer	NOUN
fumecheng-12619	58	65	thickness	thickness	NOUN
fumecheng-12619	58	66	,	,	PUNCT
fumecheng-12619	58	67	2ℎ𝑝	2ℎ𝑝	NOUN
fumecheng-12619	58	68	;	;	PUNCT
fumecheng-12619	58	69	and	and	CCONJ
fumecheng-12619	58	70	cylindrical	cylindrical	ADJ
fumecheng-12619	58	71	shell	shell	NOUN
fumecheng-12619	58	72	thickness	thickness	NOUN
fumecheng-12619	58	73	,	,	PUNCT
fumecheng-12619	58	74	2ℎ𝑁.	2ℎ𝑁.	NUM
fumecheng-12619	58	75	a	a	DET
fumecheng-12619	58	76	cartesian	cartesian	ADJ
fumecheng-12619	58	77	coordinate	coordinate	NOUN
fumecheng-12619	58	78	system	system	NOUN
fumecheng-12619	58	79	is	be	AUX
fumecheng-12619	58	80	established	establish	VERB
fumecheng-12619	58	81	with	with	ADP
fumecheng-12619	58	82	its	its	PRON
fumecheng-12619	58	83	origin	origin	NOUN
fumecheng-12619	58	84	positioned	position	VERB
fumecheng-12619	58	85	at	at	ADP
fumecheng-12619	58	86	the	the	DET
fumecheng-12619	58	87	mid	mid	NOUN
fumecheng-12619	58	88	-	-	NOUN
fumecheng-12619	58	89	surface	surface	NOUN
fumecheng-12619	58	90	of	of	ADP
fumecheng-12619	58	91	the	the	DET
fumecheng-12619	58	92	nanoshell	nanoshell	NOUN
fumecheng-12619	58	93	,	,	PUNCT
fumecheng-12619	58	94	where	where	SCONJ
fumecheng-12619	58	95	𝑥	𝑥	NOUN
fumecheng-12619	58	96	,	,	PUNCT
fumecheng-12619	58	97	𝜃	𝜃	NOUN
fumecheng-12619	58	98	,	,	PUNCT
fumecheng-12619	58	99	and	and	CCONJ
fumecheng-12619	58	100	𝑧	𝑧	PRON
fumecheng-12619	58	101	denote	denote	VERB
fumecheng-12619	58	102	the	the	DET
fumecheng-12619	58	103	coordinates	coordinate	NOUN
fumecheng-12619	58	104	in	in	ADP
fumecheng-12619	58	105	the	the	DET
fumecheng-12619	58	106	axial	axial	ADJ
fumecheng-12619	58	107	,	,	PUNCT
fumecheng-12619	58	108	circumferential	circumferential	ADJ
fumecheng-12619	58	109	,	,	PUNCT
fumecheng-12619	58	110	and	and	CCONJ
fumecheng-12619	58	111	radial	radial	ADJ
fumecheng-12619	58	112	directions	direction	NOUN
fumecheng-12619	58	113	,	,	PUNCT
fumecheng-12619	58	114	respectively	respectively	ADV
fumecheng-12619	58	115	.	.	PUNCT
fumecheng-12619	59	1	the	the	DET
fumecheng-12619	59	2	supporting	support	VERB
fumecheng-12619	59	3	medium	medium	NOUN
fumecheng-12619	59	4	is	be	AUX
fumecheng-12619	59	5	characterized	characterize	VERB
fumecheng-12619	59	6	by	by	ADP
fumecheng-12619	59	7	a	a	DET
fumecheng-12619	59	8	visco	visco	ADJ
fumecheng-12619	59	9	-	-	PUNCT
fumecheng-12619	59	10	pasternak	pasternak	PROPN
fumecheng-12619	59	11	foundation	foundation	NOUN
fumecheng-12619	59	12	,	,	PUNCT
fumecheng-12619	59	13	with	with	ADP
fumecheng-12619	59	14	𝐾𝑤	𝐾𝑤	PROPN
fumecheng-12619	59	15	representing	represent	VERB
fumecheng-12619	59	16	the	the	DET
fumecheng-12619	59	17	winkler	winkler	PROPN
fumecheng-12619	59	18	foundation	foundation	PROPN
fumecheng-12619	59	19	314	314	NUM
fumecheng-12619	59	20	s.h	s.h	PROPN
fumecheng-12619	59	21	.	.	PROPN
fumecheng-12619	59	22	hashemi	hashemi	PROPN
fumecheng-12619	59	23	kachapi	kachapi	PROPN
fumecheng-12619	59	24	,	,	PUNCT
fumecheng-12619	59	25	s.	s.	PROPN
fumecheng-12619	59	26	gh	gh	PROPN
fumecheng-12619	59	27	.	.	PROPN
fumecheng-12619	60	1	hashemi	hashemi	PROPN
fumecheng-12619	60	2	kachapi	kachapi	PROPN
fumecheng-12619	60	3	stiffness	stiffness	ADJ
fumecheng-12619	60	4	coefficient	coefficient	NOUN
fumecheng-12619	60	5	,	,	PUNCT
fumecheng-12619	60	6	𝐾𝑝	𝐾𝑝	ADV
fumecheng-12619	60	7	denoting	denote	VERB
fumecheng-12619	60	8	the	the	DET
fumecheng-12619	60	9	shear	shear	NOUN
fumecheng-12619	60	10	layer	layer	NOUN
fumecheng-12619	60	11	stiffness	stiffness	NOUN
fumecheng-12619	60	12	of	of	ADP
fumecheng-12619	60	13	the	the	DET
fumecheng-12619	60	14	pasternak	pasternak	PROPN
fumecheng-12619	60	15	foundation	foundation	PROPN
fumecheng-12619	60	16	,	,	PUNCT
fumecheng-12619	60	17	and	and	CCONJ
fumecheng-12619	60	18	𝐶𝑤	𝐶𝑤	PROPN
fumecheng-12619	60	19	signifying	signify	VERB
fumecheng-12619	60	20	the	the	DET
fumecheng-12619	60	21	damping	damp	VERB
fumecheng-12619	60	22	coefficient	coefficient	NOUN
fumecheng-12619	60	23	of	of	ADP
fumecheng-12619	60	24	the	the	DET
fumecheng-12619	60	25	viscous	viscous	ADJ
fumecheng-12619	60	26	medium	medium	NOUN
fumecheng-12619	60	27	for	for	ADP
fumecheng-12619	60	28	transverse	transverse	NOUN
fumecheng-12619	60	29	motion	motion	NOUN
fumecheng-12619	60	30	.	.	PUNCT
fumecheng-12619	61	1	additional	additional	ADJ
fumecheng-12619	61	2	physical	physical	ADJ
fumecheng-12619	61	3	and	and	CCONJ
fumecheng-12619	61	4	geometric	geometric	ADJ
fumecheng-12619	61	5	properties	property	NOUN
fumecheng-12619	61	6	of	of	ADP
fumecheng-12619	61	7	the	the	DET
fumecheng-12619	61	8	nanostructure	nanostructure	NOUN
fumecheng-12619	61	9	are	be	AUX
fumecheng-12619	61	10	detailed	detail	VERB
fumecheng-12619	61	11	in	in	ADP
fumecheng-12619	61	12	hashemi	hashemi	X
fumecheng-12619	61	13	kachapi	kachapi	PROPN
fumecheng-12619	61	14	et	et	PROPN
fumecheng-12619	61	15	al	al	PROPN
fumecheng-12619	61	16	.	.	PUNCT
fumecheng-12619	62	1	[	[	X
fumecheng-12619	62	2	19	19	NUM
fumecheng-12619	62	3	]	]	PUNCT
fumecheng-12619	62	4	.	.	PUNCT
fumecheng-12619	63	1	2.1	2.1	NUM
fumecheng-12619	63	2	.	.	PUNCT
fumecheng-12619	64	1	governing	govern	VERB
fumecheng-12619	64	2	equations	equation	NOUN
fumecheng-12619	64	3	this	this	DET
fumecheng-12619	64	4	section	section	NOUN
fumecheng-12619	64	5	delineates	delineate	VERB
fumecheng-12619	64	6	the	the	DET
fumecheng-12619	64	7	derivation	derivation	NOUN
fumecheng-12619	64	8	of	of	ADP
fumecheng-12619	64	9	the	the	DET
fumecheng-12619	64	10	governing	govern	VERB
fumecheng-12619	64	11	equations	equation	NOUN
fumecheng-12619	64	12	of	of	ADP
fumecheng-12619	64	13	motion	motion	NOUN
fumecheng-12619	64	14	and	and	CCONJ
fumecheng-12619	64	15	associated	associate	VERB
fumecheng-12619	64	16	boundary	boundary	ADJ
fumecheng-12619	64	17	conditions	condition	NOUN
fumecheng-12619	64	18	for	for	ADP
fumecheng-12619	64	19	the	the	DET
fumecheng-12619	64	20	piezoelectric	piezoelectric	ADJ
fumecheng-12619	64	21	shell	shell	NOUN
fumecheng-12619	64	22	,	,	PUNCT
fumecheng-12619	64	23	utilizing	utilize	VERB
fumecheng-12619	64	24	hamilton	hamilton	PROPN
fumecheng-12619	64	25	's	's	PART
fumecheng-12619	64	26	principle	principle	NOUN
fumecheng-12619	64	27	:	:	PUNCT
fumecheng-12619	64	28	∫	∫	PROPN
fumecheng-12619	64	29	(	(	PUNCT
fumecheng-12619	64	30	𝛿𝑇	𝛿𝑇	ADJ
fumecheng-12619	64	31	−	−	NOUN
fumecheng-12619	64	32	𝛿𝜋	𝛿𝜋	ADP
fumecheng-12619	64	33	+	+	ADV
fumecheng-12619	64	34	𝛿𝑤𝑣𝑓	𝛿𝑤𝑣𝑓	VERB
fumecheng-12619	64	35	+	+	CCONJ
fumecheng-12619	64	36	𝛿𝑤𝑒)𝑑𝑡	𝛿𝑤𝑒)𝑑𝑡	NOUN
fumecheng-12619	64	37	=	=	SYM
fumecheng-12619	64	38	0	0	NUM
fumecheng-12619	64	39	,	,	PUNCT
fumecheng-12619	64	40	𝑡	𝑡	X
fumecheng-12619	64	41	0	0	NUM
fumecheng-12619	64	42	(	(	PUNCT
fumecheng-12619	64	43	1	1	NUM
fumecheng-12619	64	44	)	)	PUNCT
fumecheng-12619	64	45	in	in	ADP
fumecheng-12619	64	46	this	this	DET
fumecheng-12619	64	47	expression	expression	NOUN
fumecheng-12619	64	48	,	,	PUNCT
fumecheng-12619	64	49	𝛿𝑇	𝛿𝑇	ADJ
fumecheng-12619	64	50	,	,	PUNCT
fumecheng-12619	64	51	𝛿𝜋	𝛿𝜋	NOUN
fumecheng-12619	64	52	,	,	PUNCT
fumecheng-12619	64	53	𝛿𝑤𝑣𝑓	𝛿𝑤𝑣𝑓	VERB
fumecheng-12619	64	54	and	and	CCONJ
fumecheng-12619	64	55	𝛿𝑤𝑒	𝛿𝑤𝑒	NOUN
fumecheng-12619	64	56	represent	represent	VERB
fumecheng-12619	64	57	the	the	DET
fumecheng-12619	64	58	first	first	ADJ
fumecheng-12619	64	59	variations	variation	NOUN
fumecheng-12619	64	60	of	of	ADP
fumecheng-12619	64	61	strain	strain	ADJ
fumecheng-12619	64	62	energy	energy	NOUN
fumecheng-12619	64	63	,	,	PUNCT
fumecheng-12619	64	64	kinetic	kinetic	ADJ
fumecheng-12619	64	65	energy	energy	NOUN
fumecheng-12619	64	66	,	,	PUNCT
fumecheng-12619	64	67	work	work	NOUN
fumecheng-12619	64	68	done	do	VERB
fumecheng-12619	64	69	by	by	ADP
fumecheng-12619	64	70	the	the	DET
fumecheng-12619	64	71	viscoelastic	viscoelastic	PROPN
fumecheng-12619	64	72	foundation	foundation	PROPN
fumecheng-12619	64	73	,	,	PUNCT
fumecheng-12619	64	74	and	and	CCONJ
fumecheng-12619	64	75	work	work	NOUN
fumecheng-12619	64	76	done	do	VERB
fumecheng-12619	64	77	by	by	ADP
fumecheng-12619	64	78	the	the	DET
fumecheng-12619	64	79	nonlinear	nonlinear	ADJ
fumecheng-12619	64	80	electrostatic	electrostatic	ADJ
fumecheng-12619	64	81	excitation	excitation	NOUN
fumecheng-12619	64	82	,	,	PUNCT
fumecheng-12619	64	83	respectively	respectively	ADV
fumecheng-12619	64	84	.	.	PUNCT
fumecheng-12619	65	1	it	it	PRON
fumecheng-12619	65	2	is	be	AUX
fumecheng-12619	65	3	crucial	crucial	ADJ
fumecheng-12619	65	4	to	to	PART
fumecheng-12619	65	5	note	note	VERB
fumecheng-12619	65	6	that	that	SCONJ
fumecheng-12619	65	7	all	all	DET
fumecheng-12619	65	8	constitutive	constitutive	ADJ
fumecheng-12619	65	9	relations	relation	NOUN
fumecheng-12619	65	10	,	,	PUNCT
fumecheng-12619	65	11	coefficients	coefficient	NOUN
fumecheng-12619	65	12	,	,	PUNCT
fumecheng-12619	65	13	and	and	CCONJ
fumecheng-12619	65	14	expressions	expression	NOUN
fumecheng-12619	65	15	related	relate	VERB
fumecheng-12619	65	16	to	to	ADP
fumecheng-12619	65	17	nonlocal	nonlocal	ADJ
fumecheng-12619	65	18	strain	strain	NOUN
fumecheng-12619	65	19	gradient	gradient	NOUN
fumecheng-12619	65	20	theory	theory	NOUN
fumecheng-12619	65	21	,	,	PUNCT
fumecheng-12619	65	22	surface	surface	NOUN
fumecheng-12619	65	23	/	/	SYM
fumecheng-12619	65	24	interface	interface	NOUN
fumecheng-12619	65	25	theory	theory	NOUN
fumecheng-12619	65	26	,	,	PUNCT
fumecheng-12619	65	27	nonlocal	nonlocal	ADJ
fumecheng-12619	65	28	strain	strain	NOUN
fumecheng-12619	65	29	gradient	gradient	ADJ
fumecheng-12619	65	30	surface	surface	NOUN
fumecheng-12619	65	31	/	/	SYM
fumecheng-12619	65	32	interface	interface	NOUN
fumecheng-12619	65	33	theory	theory	NOUN
fumecheng-12619	65	34	,	,	PUNCT
fumecheng-12619	65	35	nanoscale	nanoscale	NOUN
fumecheng-12619	65	36	stress	stress	NOUN
fumecheng-12619	65	37	-	-	PUNCT
fumecheng-12619	65	38	strain	strain	NOUN
fumecheng-12619	65	39	relationships	relationship	NOUN
fumecheng-12619	65	40	,	,	PUNCT
fumecheng-12619	65	41	and	and	CCONJ
fumecheng-12619	65	42	the	the	DET
fumecheng-12619	65	43	physical	physical	ADJ
fumecheng-12619	65	44	and	and	CCONJ
fumecheng-12619	65	45	geometric	geometric	ADJ
fumecheng-12619	65	46	properties	property	NOUN
fumecheng-12619	65	47	employed	employ	VERB
fumecheng-12619	65	48	herein	herein	NOUN
fumecheng-12619	65	49	are	be	AUX
fumecheng-12619	65	50	comprehensively	comprehensively	ADV
fumecheng-12619	65	51	detailed	detailed	ADJ
fumecheng-12619	65	52	in	in	ADP
fumecheng-12619	65	53	hashemi	hashemi	X
fumecheng-12619	65	54	kachapi	kachapi	PROPN
fumecheng-12619	65	55	et	et	PROPN
fumecheng-12619	65	56	al	al	PROPN
fumecheng-12619	66	1	[	[	X
fumecheng-12619	66	2	20	20	NUM
fumecheng-12619	66	3	]	]	PUNCT
fumecheng-12619	66	4	.	.	PUNCT
fumecheng-12619	67	1	the	the	DET
fumecheng-12619	67	2	first	first	ADJ
fumecheng-12619	67	3	variation	variation	NOUN
fumecheng-12619	67	4	of	of	ADP
fumecheng-12619	67	5	strain	strain	NOUN
fumecheng-12619	67	6	energy	energy	NOUN
fumecheng-12619	67	7	,	,	PUNCT
fumecheng-12619	67	8	𝛿𝜋	𝛿𝜋	ADP
fumecheng-12619	67	9	,	,	PUNCT
fumecheng-12619	67	10	is	be	AUX
fumecheng-12619	67	11	expressed	express	VERB
fumecheng-12619	67	12	as	as	ADP
fumecheng-12619	67	13	:	:	PUNCT
fumecheng-12619	67	14	𝛿𝜋	𝛿𝜋	ADP
fumecheng-12619	67	15	=	=	PUNCT
fumecheng-12619	68	1	∫	∫	PROPN
fumecheng-12619	68	2	∫	∫	PROPN
fumecheng-12619	68	3	{	{	PUNCT
fumecheng-12619	68	4	𝑁𝑥𝑥	𝑁𝑥𝑥	NOUN
fumecheng-12619	68	5	(	(	PUNCT
fumecheng-12619	68	6	𝜕𝛿𝑢	𝜕𝛿𝑢	X
fumecheng-12619	68	7	𝜕𝑥	𝜕𝑥	X
fumecheng-12619	68	8	+	+	CCONJ
fumecheng-12619	68	9	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-12619	68	10	𝜕𝑥	𝜕𝑥	X
fumecheng-12619	68	11	𝜕𝛿𝑤	𝜕𝛿𝑤	NOUN
fumecheng-12619	68	12	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-12619	68	13	)	)	PUNCT
fumecheng-12619	69	1	−𝑀𝑥𝑥	−𝑀𝑥𝑥	NOUN
fumecheng-12619	69	2	(	(	PUNCT
fumecheng-12619	69	3	𝜕2𝛿𝑤	𝜕2𝛿𝑤	PROPN
fumecheng-12619	69	4	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-12619	69	5	)	)	PUNCT
fumecheng-12619	70	1	+	+	CCONJ
fumecheng-12619	70	2	𝑁𝜃𝜃	𝑁𝜃𝜃	NUM
fumecheng-12619	70	3	(	(	PUNCT
fumecheng-12619	70	4	1	1	NUM
fumecheng-12619	70	5	𝑅	𝑅	PROPN
fumecheng-12619	70	6	(	(	PUNCT
fumecheng-12619	70	7	𝜕𝛿𝑣	𝜕𝛿𝑣	PUNCT
fumecheng-12619	70	8	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	70	9	+	+	CCONJ
fumecheng-12619	70	10	𝛿𝑤	𝛿𝑤	X
fumecheng-12619	70	11	)	)	PUNCT
fumecheng-12619	70	12	+	+	CCONJ
fumecheng-12619	70	13	1	1	NUM
fumecheng-12619	70	14	𝑅2	𝑅2	NOUN
fumecheng-12619	70	15	𝜕𝑤	𝜕𝑤	VERB
fumecheng-12619	70	16	𝜕𝜃	𝜕𝜃	ADJ
fumecheng-12619	70	17	𝜕𝛿𝑤	𝜕𝛿𝑤	NOUN
fumecheng-12619	70	18	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	70	19	)	)	PUNCT
fumecheng-12619	71	1	−𝑀𝜃𝜃	−𝑀𝜃𝜃	CCONJ
fumecheng-12619	71	2	(	(	PUNCT
fumecheng-12619	71	3	1	1	NUM
fumecheng-12619	71	4	𝑅2	𝑅2	NOUN
fumecheng-12619	71	5	𝜕2𝛿𝑤	𝜕2𝛿𝑤	PROPN
fumecheng-12619	71	6	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	71	7	)	)	PUNCT
fumecheng-12619	72	1	+	+	CCONJ
fumecheng-12619	72	2	𝑁𝑥𝜃	𝑁𝑥𝜃	PROPN
fumecheng-12619	72	3	(	(	PUNCT
fumecheng-12619	72	4	1	1	NUM
fumecheng-12619	72	5	𝑅	𝑅	PROPN
fumecheng-12619	72	6	𝜕𝛿𝑢	𝜕𝛿𝑢	ADJ
fumecheng-12619	72	7	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	72	8	+	+	CCONJ
fumecheng-12619	72	9	𝜕𝛿𝑣	𝜕𝛿𝑣	PUNCT
fumecheng-12619	72	10	𝜕𝑥	𝜕𝑥	X
fumecheng-12619	72	11	+	+	CCONJ
fumecheng-12619	72	12	1	1	NUM
fumecheng-12619	72	13	𝑅	𝑅	PROPN
fumecheng-12619	72	14	𝜕𝛿𝑤	𝜕𝛿𝑤	NOUN
fumecheng-12619	72	15	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-12619	72	16	𝜕𝑤	𝜕𝑤	VERB
fumecheng-12619	72	17	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	72	18	+	+	CCONJ
fumecheng-12619	72	19	1	1	NUM
fumecheng-12619	72	20	𝑅	𝑅	NOUN
fumecheng-12619	72	21	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-12619	72	22	𝜕𝑥	𝜕𝑥	X
fumecheng-12619	72	23	𝜕𝛿𝑤	𝜕𝛿𝑤	NOUN
fumecheng-12619	72	24	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	72	25	)	)	PUNCT
fumecheng-12619	73	1	−𝑀𝑥𝜃	−𝑀𝑥𝜃	NOUN
fumecheng-12619	73	2	(	(	PUNCT
fumecheng-12619	73	3	2	2	NUM
fumecheng-12619	73	4	𝑅	𝑅	PROPN
fumecheng-12619	73	5	𝜕2𝛿𝑤	𝜕2𝛿𝑤	PROPN
fumecheng-12619	73	6	𝜕𝑥𝜕𝜃	𝜕𝑥𝜕𝜃	PROPN
fumecheng-12619	73	7	)	)	PUNCT
fumecheng-12619	73	8	}	}	PUNCT
fumecheng-12619	73	9	2𝜋	2𝜋	NOUN
fumecheng-12619	73	10	0	0	X
fumecheng-12619	74	1	𝐿	𝐿	PROPN
fumecheng-12619	74	2	0	0	X
fumecheng-12619	74	3	𝑅𝑑𝜃𝑑𝑥	𝑅𝑑𝜃𝑑𝑥	PROPN
fumecheng-12619	74	4	(	(	PUNCT
fumecheng-12619	74	5	2	2	NUM
fumecheng-12619	74	6	)	)	PUNCT
fumecheng-12619	74	7	the	the	DET
fumecheng-12619	74	8	first	first	ADJ
fumecheng-12619	74	9	variation	variation	NOUN
fumecheng-12619	74	10	of	of	ADP
fumecheng-12619	74	11	kinetic	kinetic	ADJ
fumecheng-12619	74	12	energy	energy	NOUN
fumecheng-12619	74	13	can	can	AUX
fumecheng-12619	74	14	then	then	ADV
fumecheng-12619	74	15	be	be	AUX
fumecheng-12619	74	16	expressed	express	VERB
fumecheng-12619	74	17	as	as	ADP
fumecheng-12619	74	18	:	:	PUNCT
fumecheng-12619	74	19	in	in	ADP
fumecheng-12619	74	20	eq	eq	ADP
fumecheng-12619	74	21	.	.	PUNCT
fumecheng-12619	75	1	(	(	PUNCT
fumecheng-12619	75	2	2	2	NUM
fumecheng-12619	75	3	)	)	PUNCT
fumecheng-12619	75	4	,	,	PUNCT
fumecheng-12619	75	5	the	the	DET
fumecheng-12619	75	6	force	force	NOUN
fumecheng-12619	75	7	resultants	resultant	NOUN
fumecheng-12619	75	8	,	,	PUNCT
fumecheng-12619	75	9	𝑁	𝑁	PROPN
fumecheng-12619	75	10	,	,	PUNCT
fumecheng-12619	75	11	and	and	CCONJ
fumecheng-12619	75	12	moment	moment	NOUN
fumecheng-12619	75	13	resultants	resultant	NOUN
fumecheng-12619	75	14	,	,	PUNCT
fumecheng-12619	75	15	𝑀	𝑀	PROPN
fumecheng-12619	75	16	,	,	PUNCT
fumecheng-12619	75	17	are	be	AUX
fumecheng-12619	75	18	defined	define	VERB
fumecheng-12619	75	19	as	as	SCONJ
fumecheng-12619	75	20	specified	specify	VERB
fumecheng-12619	75	21	in	in	ADP
fumecheng-12619	75	22	hashemi	hashemi	X
fumecheng-12619	75	23	kachapi	kachapi	PROPN
fumecheng-12619	75	24	et	et	PROPN
fumecheng-12619	75	25	al	al	PROPN
fumecheng-12619	75	26	.	.	PUNCT
fumecheng-12619	76	1	[	[	X
fumecheng-12619	76	2	19	19	NUM
fumecheng-12619	76	3	]	]	PUNCT
fumecheng-12619	76	4	.	.	PUNCT
fumecheng-12619	77	1	the	the	DET
fumecheng-12619	77	2	first	first	ADJ
fumecheng-12619	77	3	variation	variation	NOUN
fumecheng-12619	77	4	of	of	ADP
fumecheng-12619	77	5	kinetic	kinetic	ADJ
fumecheng-12619	77	6	energy	energy	NOUN
fumecheng-12619	77	7	is	be	AUX
fumecheng-12619	77	8	given	give	VERB
fumecheng-12619	77	9	by	by	ADP
fumecheng-12619	77	10	:	:	PUNCT
fumecheng-12619	77	11	𝛿	𝛿	ADJ
fumecheng-12619	77	12	∫	∫	PROPN
fumecheng-12619	77	13	𝑇𝑑𝑡	𝑇𝑑𝑡	PROPN
fumecheng-12619	77	14	𝑡2	𝑡2	NOUN
fumecheng-12619	77	15	𝑡1	𝑡1	NOUN
fumecheng-12619	77	16	=	=	PUNCT
fumecheng-12619	77	17	−∫	−∫	NOUN
fumecheng-12619	77	18	∬{𝐼	∬{𝐼	X
fumecheng-12619	77	19	(	(	PUNCT
fumecheng-12619	77	20	(	(	PUNCT
fumecheng-12619	77	21	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	77	22	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-12619	77	23	)	)	PUNCT
fumecheng-12619	77	24	𝛿𝑢	𝛿𝑢	PROPN
fumecheng-12619	77	25	+	+	CCONJ
fumecheng-12619	77	26	(	(	PUNCT
fumecheng-12619	77	27	𝜕2𝑣	𝜕2𝑣	PROPN
fumecheng-12619	77	28	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-12619	77	29	)	)	PUNCT
fumecheng-12619	78	1	𝛿𝑣	𝛿𝑣	PROPN
fumecheng-12619	79	1	+	+	CCONJ
fumecheng-12619	79	2	(	(	PUNCT
fumecheng-12619	79	3	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-12619	79	4	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-12619	79	5	)	)	PUNCT
fumecheng-12619	79	6	𝛿𝑤)}𝑅𝑑𝜃𝑑𝑥𝑑𝑡	𝛿𝑤)}𝑅𝑑𝜃𝑑𝑥𝑑𝑡	ADJ
fumecheng-12619	79	7	𝑡2	𝑡2	PROPN
fumecheng-12619	79	8	𝑡1	𝑡1	NOUN
fumecheng-12619	79	9	(	(	PUNCT
fumecheng-12619	79	10	3	3	NUM
fumecheng-12619	79	11	)	)	PUNCT
fumecheng-12619	79	12	where	where	SCONJ
fumecheng-12619	79	13	𝐼	𝐼	PROPN
fumecheng-12619	79	14	=	=	PUNCT
fumecheng-12619	79	15	∫	∫	PROPN
fumecheng-12619	80	1	𝜌𝑁	𝜌𝑁	PROPN
fumecheng-12619	80	2	ℎ𝑁	ℎ𝑁	PROPN
fumecheng-12619	80	3	−ℎ𝑁	−ℎ𝑁	PROPN
fumecheng-12619	80	4	𝑑𝑧	𝑑𝑧	PROPN
fumecheng-12619	80	5	+	+	CCONJ
fumecheng-12619	80	6	∫	∫	PROPN
fumecheng-12619	80	7	𝜌𝑝	𝜌𝑝	NOUN
fumecheng-12619	80	8	−ℎ𝑁	−ℎ𝑁	NOUN
fumecheng-12619	80	9	−ℎ𝑁−ℎ𝑝	−ℎ𝑁−ℎ𝑝	PROPN
fumecheng-12619	80	10	𝑑𝑧	𝑑𝑧	PROPN
fumecheng-12619	80	11	+	+	CCONJ
fumecheng-12619	80	12	∫	∫	PROPN
fumecheng-12619	80	13	𝜌𝑝	𝜌𝑝	NOUN
fumecheng-12619	80	14	ℎ𝑁+ℎ𝑝	ℎ𝑁+ℎ𝑝	PROPN
fumecheng-12619	80	15	ℎ𝑁	ℎ𝑁	PROPN
fumecheng-12619	80	16	𝑑𝑧	𝑑𝑧	PROPN
fumecheng-12619	80	17	+	+	CCONJ
fumecheng-12619	80	18	𝜌𝑆,𝐼	𝜌𝑆,𝐼	NOUN
fumecheng-12619	80	19	=	=	SYM
fumecheng-12619	80	20	2	2	NUM
fumecheng-12619	80	21	(	(	PUNCT
fumecheng-12619	80	22	𝜌𝑁ℎ𝑁	𝜌𝑁ℎ𝑁	X
fumecheng-12619	80	23	+	+	CCONJ
fumecheng-12619	80	24	𝜌𝑝ℎ𝑝	𝜌𝑝ℎ𝑝	VERB
fumecheng-12619	80	25	+	+	SYM
fumecheng-12619	80	26	𝜌𝑆	𝜌𝑆	PROPN
fumecheng-12619	80	27	+	+	CCONJ
fumecheng-12619	80	28	𝜌𝐼	𝜌𝐼	PROPN
fumecheng-12619	80	29	)	)	PUNCT
fumecheng-12619	80	30	(	(	PUNCT
fumecheng-12619	80	31	4	4	X
fumecheng-12619	80	32	)	)	PUNCT
fumecheng-12619	80	33	the	the	DET
fumecheng-12619	80	34	first	first	ADJ
fumecheng-12619	80	35	variations	variation	NOUN
fumecheng-12619	80	36	of	of	ADP
fumecheng-12619	80	37	the	the	DET
fumecheng-12619	80	38	work	work	NOUN
fumecheng-12619	80	39	done	do	VERB
fumecheng-12619	80	40	by	by	ADP
fumecheng-12619	80	41	the	the	DET
fumecheng-12619	80	42	viscoelastic	viscoelastic	PROPN
fumecheng-12619	80	43	foundation	foundation	PROPN
fumecheng-12619	80	44	and	and	CCONJ
fumecheng-12619	80	45	the	the	DET
fumecheng-12619	80	46	nonlinear	nonlinear	ADJ
fumecheng-12619	80	47	electrostatic	electrostatic	ADJ
fumecheng-12619	80	48	excitation	excitation	NOUN
fumecheng-12619	80	49	,	,	PUNCT
fumecheng-12619	80	50	are	be	AUX
fumecheng-12619	80	51	expressed	express	VERB
fumecheng-12619	80	52	as	as	ADP
fumecheng-12619	80	53	[	[	X
fumecheng-12619	80	54	19	19	NUM
fumecheng-12619	80	55	,	,	PUNCT
fumecheng-12619	80	56	20	20	NUM
fumecheng-12619	80	57	,	,	PUNCT
fumecheng-12619	80	58	27	27	NUM
fumecheng-12619	80	59	]	]	PUNCT
fumecheng-12619	80	60	:	:	PUNCT
fumecheng-12619	81	1	𝛿𝑊𝑣𝑓	𝛿𝑊𝑣𝑓	PROPN
fumecheng-12619	81	2	=	=	PUNCT
fumecheng-12619	81	3	−∫	−∫	NOUN
fumecheng-12619	81	4	∫	∫	PROPN
fumecheng-12619	81	5	∫	∫	PROPN
fumecheng-12619	81	6	(	(	PUNCT
fumecheng-12619	81	7	𝐾𝑤𝑤	𝐾𝑤𝑤	PROPN
fumecheng-12619	81	8	−	−	PROPN
fumecheng-12619	81	9	𝐾𝑝𝛻	𝐾𝑝𝛻	PROPN
fumecheng-12619	81	10	2𝑤	2𝑤	NUM
fumecheng-12619	82	1	+	+	CCONJ
fumecheng-12619	82	2	𝐶𝑤	𝐶𝑤	NOUN
fumecheng-12619	82	3	𝜕𝑤	𝜕𝑤	VERB
fumecheng-12619	82	4	𝜕𝑡	𝜕𝑡	NOUN
fumecheng-12619	82	5	)	)	PUNCT
fumecheng-12619	82	6	𝛿𝑤	𝛿𝑤	ADP
fumecheng-12619	82	7	𝑤	𝑤	ADP
fumecheng-12619	82	8	0	0	NUM
fumecheng-12619	82	9	2𝜋	2𝜋	NOUN
fumecheng-12619	82	10	0	0	PUNCT
fumecheng-12619	83	1	𝐿	𝐿	PROPN
fumecheng-12619	83	2	0	0	NUM
fumecheng-12619	83	3	𝑅𝑑𝜃𝑑𝑥	𝑅𝑑𝜃𝑑𝑥	PROPN
fumecheng-12619	83	4	,	,	PUNCT
fumecheng-12619	83	5	(	(	PUNCT
fumecheng-12619	83	6	5	5	X
fumecheng-12619	83	7	)	)	PUNCT
fumecheng-12619	83	8	𝛿𝑊𝑒	𝛿𝑊𝑒	NOUN
fumecheng-12619	83	9	=	=	SYM
fumecheng-12619	83	10	∫	∫	PROPN
fumecheng-12619	83	11	∫	∫	PROPN
fumecheng-12619	83	12	∫	∫	PROPN
fumecheng-12619	83	13	𝜋𝛶(𝑉𝐷𝐶+𝑉𝐴𝐶	𝜋𝛶(𝑉𝐷𝐶+𝑉𝐴𝐶	PROPN
fumecheng-12619	83	14	cos(𝜔𝑡	cos(𝜔𝑡	PROPN
fumecheng-12619	83	15	)	)	PUNCT
fumecheng-12619	83	16	)	)	PUNCT
fumecheng-12619	83	17	2	2	NUM
fumecheng-12619	83	18	(	(	PUNCT
fumecheng-12619	83	19	√(𝑏−𝑤)(2𝑅+𝑏−𝑤	√(𝑏−𝑤)(2𝑅+𝑏−𝑤	X
fumecheng-12619	83	20	)	)	PUNCT
fumecheng-12619	84	1	[	[	X
fumecheng-12619	84	2	cosh−1	cosh−1	NOUN
fumecheng-12619	84	3	(	(	PUNCT
fumecheng-12619	84	4	1	1	NUM
fumecheng-12619	84	5	+	+	NUM
fumecheng-12619	84	6	𝑏−𝑤	𝑏−𝑤	NOUN
fumecheng-12619	84	7	𝑅	𝑅	PROPN
fumecheng-12619	84	8	)	)	PUNCT
fumecheng-12619	84	9	]	]	PUNCT
fumecheng-12619	84	10	2	2	X
fumecheng-12619	84	11	)	)	PUNCT
fumecheng-12619	84	12	𝛿𝑤	𝛿𝑤	NOUN
fumecheng-12619	84	13	𝑤	𝑤	ADP
fumecheng-12619	84	14	0	0	NUM
fumecheng-12619	84	15	2𝜋	2𝜋	NOUN
fumecheng-12619	84	16	0	0	PUNCT
fumecheng-12619	85	1	𝐿	𝐿	NOUN
fumecheng-12619	85	2	0	0	X
fumecheng-12619	85	3	𝑅𝑑𝜃𝑑𝑥	𝑅𝑑𝜃𝑑𝑥	PROPN
fumecheng-12619	85	4	(	(	PUNCT
fumecheng-12619	85	5	6	6	NUM
fumecheng-12619	85	6	)	)	PUNCT
fumecheng-12619	85	7	comparison	comparison	NOUN
fumecheng-12619	85	8	of	of	ADP
fumecheng-12619	85	9	nonclassical	nonclassical	ADJ
fumecheng-12619	85	10	controllers	controller	NOUN
fumecheng-12619	85	11	on	on	ADP
fumecheng-12619	85	12	nonlinear	nonlinear	ADJ
fumecheng-12619	85	13	vibrations	vibration	NOUN
fumecheng-12619	85	14	analysis	analysis	NOUN
fumecheng-12619	85	15	of	of	ADP
fumecheng-12619	85	16	piezoelectric	piezoelectric	NOUN
fumecheng-12619	85	17	...	...	PUNCT
fumecheng-12619	85	18	315	315	NUM
fumecheng-12619	85	19	the	the	DET
fumecheng-12619	85	20	explicit	explicit	ADJ
fumecheng-12619	85	21	definitions	definition	NOUN
fumecheng-12619	85	22	of	of	ADP
fumecheng-12619	85	23	all	all	DET
fumecheng-12619	85	24	coefficients	coefficient	NOUN
fumecheng-12619	85	25	and	and	CCONJ
fumecheng-12619	85	26	expressions	expression	NOUN
fumecheng-12619	85	27	presented	present	VERB
fumecheng-12619	85	28	in	in	ADP
fumecheng-12619	85	29	eqs	eqs	PROPN
fumecheng-12619	85	30	.	.	PUNCT
fumecheng-12619	85	31	(	(	PUNCT
fumecheng-12619	85	32	5	5	NUM
fumecheng-12619	85	33	)	)	PUNCT
fumecheng-12619	85	34	and	and	CCONJ
fumecheng-12619	85	35	(	(	PUNCT
fumecheng-12619	85	36	6	6	NUM
fumecheng-12619	85	37	)	)	PUNCT
fumecheng-12619	85	38	are	be	AUX
fumecheng-12619	85	39	provided	provide	VERB
fumecheng-12619	85	40	in	in	ADP
fumecheng-12619	85	41	hashemi	hashemi	X
fumecheng-12619	85	42	kachapi	kachapi	PROPN
fumecheng-12619	85	43	et	et	PROPN
fumecheng-12619	85	44	al	al	PROPN
fumecheng-12619	85	45	.	.	PUNCT
fumecheng-12619	86	1	[	[	X
fumecheng-12619	86	2	19	19	NUM
fumecheng-12619	86	3	,	,	PUNCT
fumecheng-12619	86	4	20	20	NUM
fumecheng-12619	86	5	]	]	PUNCT
fumecheng-12619	86	6	.	.	PUNCT
fumecheng-12619	87	1	substituting	substitute	VERB
fumecheng-12619	87	2	eqs	eqs	PROPN
fumecheng-12619	87	3	.	.	PUNCT
fumecheng-12619	88	1	(	(	PUNCT
fumecheng-12619	88	2	2	2	NUM
fumecheng-12619	88	3	-	-	SYM
fumecheng-12619	88	4	6	6	NUM
fumecheng-12619	88	5	)	)	PUNCT
fumecheng-12619	88	6	into	into	ADP
fumecheng-12619	88	7	eq	eq	NOUN
fumecheng-12619	88	8	.	.	PUNCT
fumecheng-12619	89	1	(	(	PUNCT
fumecheng-12619	89	2	1	1	X
fumecheng-12619	89	3	)	)	PUNCT
fumecheng-12619	89	4	results	result	NOUN
fumecheng-12619	89	5	in	in	ADP
fumecheng-12619	89	6	the	the	DET
fumecheng-12619	89	7	derivation	derivation	NOUN
fumecheng-12619	89	8	of	of	ADP
fumecheng-12619	89	9	the	the	DET
fumecheng-12619	89	10	governing	govern	VERB
fumecheng-12619	89	11	equations	equation	NOUN
fumecheng-12619	89	12	of	of	ADP
fumecheng-12619	89	13	motion	motion	NOUN
fumecheng-12619	89	14	and	and	CCONJ
fumecheng-12619	89	15	associated	associate	VERB
fumecheng-12619	89	16	boundary	boundary	ADJ
fumecheng-12619	89	17	conditions	condition	NOUN
fumecheng-12619	89	18	for	for	ADP
fumecheng-12619	89	19	the	the	DET
fumecheng-12619	89	20	piezoelectric	piezoelectric	ADJ
fumecheng-12619	89	21	nanoresonator	nanoresonator	NOUN
fumecheng-12619	89	22	(	(	PUNCT
fumecheng-12619	89	23	penr	penr	PROPN
fumecheng-12619	89	24	)	)	PUNCT
fumecheng-12619	89	25	,	,	PUNCT
fumecheng-12619	89	26	as	as	SCONJ
fumecheng-12619	89	27	comprehensively	comprehensively	ADV
fumecheng-12619	89	28	documented	document	VERB
fumecheng-12619	89	29	in	in	ADP
fumecheng-12619	89	30	hashemi	hashemi	PROPN
fumecheng-12619	89	31	kachapi	kachapi	PROPN
fumecheng-12619	89	32	et	et	PROPN
fumecheng-12619	89	33	al	al	PROPN
fumecheng-12619	89	34	.	.	PUNCT
fumecheng-12619	90	1	[	[	X
fumecheng-12619	90	2	19	19	NUM
fumecheng-12619	90	3	,	,	PUNCT
fumecheng-12619	90	4	20	20	NUM
fumecheng-12619	90	5	]	]	PUNCT
fumecheng-12619	90	6	.	.	PUNCT
fumecheng-12619	91	1	by	by	ADP
fumecheng-12619	91	2	employing	employ	VERB
fumecheng-12619	91	3	the	the	DET
fumecheng-12619	91	4	dimensionless	dimensionless	NOUN
fumecheng-12619	91	5	parameters	parameter	NOUN
fumecheng-12619	91	6	defined	define	VERB
fumecheng-12619	91	7	in	in	ADP
fumecheng-12619	91	8	hashemi	hashemi	X
fumecheng-12619	91	9	kachapi	kachapi	PROPN
fumecheng-12619	91	10	et	et	PROPN
fumecheng-12619	91	11	al	al	PROPN
fumecheng-12619	91	12	.	.	PUNCT
fumecheng-12619	92	1	[	[	X
fumecheng-12619	92	2	19	19	NUM
fumecheng-12619	92	3	]	]	PUNCT
fumecheng-12619	92	4	,	,	PUNCT
fumecheng-12619	92	5	and	and	CCONJ
fumecheng-12619	92	6	subsequently	subsequently	ADV
fumecheng-12619	92	7	incorporating	incorporate	VERB
fumecheng-12619	92	8	nonlocal	nonlocal	ADJ
fumecheng-12619	92	9	and	and	CCONJ
fumecheng-12619	92	10	material	material	NOUN
fumecheng-12619	92	11	length	length	NOUN
fumecheng-12619	92	12	scale	scale	NOUN
fumecheng-12619	92	13	effects	effect	NOUN
fumecheng-12619	92	14	,	,	PUNCT
fumecheng-12619	92	15	along	along	ADP
fumecheng-12619	92	16	with	with	ADP
fumecheng-12619	92	17	nonlocal	nonlocal	ADJ
fumecheng-12619	92	18	strain	strain	NOUN
fumecheng-12619	92	19	gradient	gradient	ADJ
fumecheng-12619	92	20	surface	surface	NOUN
fumecheng-12619	92	21	/	/	SYM
fumecheng-12619	92	22	interface	interface	NOUN
fumecheng-12619	92	23	effects	effect	NOUN
fumecheng-12619	92	24	(	(	PUNCT
fumecheng-12619	92	25	as	as	SCONJ
fumecheng-12619	92	26	detailed	detailed	ADJ
fumecheng-12619	92	27	in	in	ADP
fumecheng-12619	92	28	hashemi	hashemi	X
fumecheng-12619	92	29	kachapi	kachapi	PROPN
fumecheng-12619	92	30	et	et	PROPN
fumecheng-12619	92	31	al	al	PROPN
fumecheng-12619	93	1	[	[	X
fumecheng-12619	93	2	20	20	NUM
fumecheng-12619	93	3	]	]	NUM
fumecheng-12619	93	4	)	)	PUNCT
fumecheng-12619	93	5	,	,	PUNCT
fumecheng-12619	93	6	the	the	DET
fumecheng-12619	93	7	dimensionless	dimensionless	NOUN
fumecheng-12619	93	8	governing	govern	VERB
fumecheng-12619	93	9	equations	equation	NOUN
fumecheng-12619	93	10	are	be	AUX
fumecheng-12619	93	11	obtained	obtain	VERB
fumecheng-12619	93	12	.	.	PUNCT
fumecheng-12619	94	1	(	(	PUNCT
fumecheng-12619	94	2	1	1	NUM
fumecheng-12619	94	3	−	−	PRON
fumecheng-12619	94	4	�	�	NOUN
fumecheng-12619	94	5	̅	̅	NOUN
fumecheng-12619	94	6	�	�	PROPN
fumecheng-12619	94	7	�	�	PROPN
fumecheng-12619	94	8	̅	̅	NOUN
fumecheng-12619	94	9	�	�	NOUN
fumecheng-12619	94	10	2	2	NUM
fumecheng-12619	94	11	)	)	PUNCT
fumecheng-12619	94	12	(	(	PUNCT
fumecheng-12619	94	13	𝛼1𝑢	𝛼1𝑢	NOUN
fumecheng-12619	94	14	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	94	15	𝜕𝜉2	𝜕𝜉2	PROPN
fumecheng-12619	94	16	+	+	CCONJ
fumecheng-12619	94	17	𝛼2𝑢	𝛼2𝑢	NOUN
fumecheng-12619	94	18	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	94	19	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	94	20	+	+	CCONJ
fumecheng-12619	94	21	𝛼3𝑢	𝛼3𝑢	NOUN
fumecheng-12619	94	22	𝜕2	𝜕2	NOUN
fumecheng-12619	94	23	�	�	NOUN
fumecheng-12619	94	24	̅	̅	NOUN
fumecheng-12619	94	25	�	�	NOUN
fumecheng-12619	94	26	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	94	27	+	+	SYM
fumecheng-12619	94	28	𝛼4𝑢	𝛼4𝑢	PROPN
fumecheng-12619	94	29	𝜕	𝜕	NOUN
fumecheng-12619	94	30	�	�	NOUN
fumecheng-12619	94	31	̅	̅	NOUN
fumecheng-12619	94	32	�	�	NOUN
fumecheng-12619	94	33	𝜕𝜉	𝜕𝜉	VERB
fumecheng-12619	94	34	+	+	NOUN
fumecheng-12619	94	35	𝛼5𝑢	𝛼5𝑢	PROPN
fumecheng-12619	94	36	𝜕	𝜕	PROPN
fumecheng-12619	94	37	�	�	PROPN
fumecheng-12619	94	38	̅	̅	NOUN
fumecheng-12619	94	39	�	�	NOUN
fumecheng-12619	95	1	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	95	2	𝜕2	𝜕2	NOUN
fumecheng-12619	95	3	�	�	NOUN
fumecheng-12619	95	4	̅	̅	NOUN
fumecheng-12619	95	5	�	�	NOUN
fumecheng-12619	95	6	𝜕𝜉2	𝜕𝜉2	PROPN
fumecheng-12619	95	7	+	+	CCONJ
fumecheng-12619	95	8	𝛼6𝑢	𝛼6𝑢	PROPN
fumecheng-12619	95	9	𝜕	𝜕	PROPN
fumecheng-12619	95	10	�	�	PROPN
fumecheng-12619	95	11	̅	̅	NOUN
fumecheng-12619	95	12	�	�	NOUN
fumecheng-12619	95	13	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	95	14	𝜕2	𝜕2	NOUN
fumecheng-12619	95	15	�	�	NOUN
fumecheng-12619	95	16	̅	̅	NOUN
fumecheng-12619	95	17	�	�	NOUN
fumecheng-12619	95	18	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	95	19	+	+	CCONJ
fumecheng-12619	95	20	𝛼7𝑢	𝛼7𝑢	NUM
fumecheng-12619	95	21	𝜕2	𝜕2	NOUN
fumecheng-12619	95	22	�	�	NOUN
fumecheng-12619	95	23	̅	̅	NOUN
fumecheng-12619	95	24	�	�	PROPN
fumecheng-12619	95	25	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	95	26	𝜕	𝜕	PROPN
fumecheng-12619	95	27	�	�	NOUN
fumecheng-12619	95	28	̅	̅	NOUN
fumecheng-12619	95	29	�	�	NOUN
fumecheng-12619	95	30	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	95	31	)	)	PUNCT
fumecheng-12619	96	1	=	=	PUNCT
fumecheng-12619	96	2	(	(	PUNCT
fumecheng-12619	96	3	1	1	NUM
fumecheng-12619	96	4	−	−	PRON
fumecheng-12619	96	5	�	�	NOUN
fumecheng-12619	96	6	̅	̅	NOUN
fumecheng-12619	96	7	�	�	PROPN
fumecheng-12619	96	8	�	�	PROPN
fumecheng-12619	96	9	̅	̅	NOUN
fumecheng-12619	96	10	�	�	NOUN
fumecheng-12619	96	11	2	2	NUM
fumecheng-12619	96	12	)	)	PUNCT
fumecheng-12619	96	13	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	96	14	𝜕𝜏2	𝜕𝜏2	PROPN
fumecheng-12619	96	15	,	,	PUNCT
fumecheng-12619	96	16	(	(	PUNCT
fumecheng-12619	96	17	7	7	NUM
fumecheng-12619	96	18	)	)	PUNCT
fumecheng-12619	96	19	(	(	PUNCT
fumecheng-12619	96	20	1	1	NUM
fumecheng-12619	96	21	−	−	PRON
fumecheng-12619	96	22	�	�	NOUN
fumecheng-12619	96	23	̅	̅	NOUN
fumecheng-12619	96	24	�	�	PROPN
fumecheng-12619	96	25	�	�	PROPN
fumecheng-12619	96	26	̅	̅	NOUN
fumecheng-12619	96	27	�	�	NOUN
fumecheng-12619	96	28	2	2	NUM
fumecheng-12619	96	29	)	)	PUNCT
fumecheng-12619	96	30	(	(	PUNCT
fumecheng-12619	96	31	𝛼1𝑣	𝛼1𝑣	PROPN
fumecheng-12619	96	32	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	96	33	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	96	34	+	+	CCONJ
fumecheng-12619	96	35	𝛼2𝑣	𝛼2𝑣	NUM
fumecheng-12619	96	36	𝜕2	𝜕2	NOUN
fumecheng-12619	96	37	�	�	NOUN
fumecheng-12619	96	38	̅	̅	NOUN
fumecheng-12619	96	39	�	�	NOUN
fumecheng-12619	96	40	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	96	41	+	+	CCONJ
fumecheng-12619	96	42	𝛼3𝑣	𝛼3𝑣	PROPN
fumecheng-12619	96	43	𝜕2	𝜕2	NOUN
fumecheng-12619	96	44	�	�	NOUN
fumecheng-12619	96	45	̅	̅	NOUN
fumecheng-12619	96	46	�	�	NOUN
fumecheng-12619	96	47	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	96	48	+	+	CCONJ
fumecheng-12619	96	49	𝛼4𝑣	𝛼4𝑣	PROPN
fumecheng-12619	96	50	𝜕	𝜕	PROPN
fumecheng-12619	96	51	�	�	PROPN
fumecheng-12619	96	52	̅	̅	NOUN
fumecheng-12619	96	53	�	�	NOUN
fumecheng-12619	96	54	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	96	55	𝜕2	𝜕2	NOUN
fumecheng-12619	96	56	�	�	NOUN
fumecheng-12619	96	57	̅	̅	NOUN
fumecheng-12619	96	58	�	�	NOUN
fumecheng-12619	96	59	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	NOUN
fumecheng-12619	96	60	+	+	NOUN
fumecheng-12619	96	61	𝛼5𝑣	𝛼5𝑣	NOUN
fumecheng-12619	96	62	𝜕2	𝜕2	NOUN
fumecheng-12619	96	63	�	�	NOUN
fumecheng-12619	96	64	̅	̅	NOUN
fumecheng-12619	96	65	�	�	PROPN
fumecheng-12619	96	66	𝜕𝜉2	𝜕𝜉2	PROPN
fumecheng-12619	96	67	𝜕	𝜕	PROPN
fumecheng-12619	96	68	�	�	PROPN
fumecheng-12619	96	69	̅	̅	NOUN
fumecheng-12619	96	70	�	�	NOUN
fumecheng-12619	96	71	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	96	72	+	+	CCONJ
fumecheng-12619	96	73	𝛼6𝑣	𝛼6𝑣	PROPN
fumecheng-12619	96	74	𝜕	𝜕	NOUN
fumecheng-12619	96	75	�	�	NOUN
fumecheng-12619	96	76	̅	̅	NOUN
fumecheng-12619	96	77	�	�	NOUN
fumecheng-12619	96	78	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	96	79	+	+	CCONJ
fumecheng-12619	96	80	𝛼7𝑣	𝛼7𝑣	PROPN
fumecheng-12619	96	81	𝜕	𝜕	PROPN
fumecheng-12619	96	82	�	�	NOUN
fumecheng-12619	96	83	̅	̅	NOUN
fumecheng-12619	96	84	�	�	NOUN
fumecheng-12619	96	85	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	96	86	𝜕2	𝜕2	NOUN
fumecheng-12619	96	87	�	�	NOUN
fumecheng-12619	96	88	̅	̅	NOUN
fumecheng-12619	96	89	�	�	NOUN
fumecheng-12619	96	90	𝜕𝜃2	𝜕𝜃2	ADJ
fumecheng-12619	96	91	)	)	PUNCT
fumecheng-12619	97	1	=	=	SYM
fumecheng-12619	97	2	(	(	PUNCT
fumecheng-12619	97	3	1	1	NUM
fumecheng-12619	97	4	−	−	PRON
fumecheng-12619	97	5	�	�	NOUN
fumecheng-12619	97	6	̅	̅	NOUN
fumecheng-12619	97	7	�	�	PROPN
fumecheng-12619	97	8	�	�	PROPN
fumecheng-12619	97	9	̅	̅	NOUN
fumecheng-12619	97	10	�	�	NOUN
fumecheng-12619	97	11	2	2	NUM
fumecheng-12619	97	12	)	)	PUNCT
fumecheng-12619	97	13	𝜕2	𝜕2	NOUN
fumecheng-12619	97	14	�	�	NOUN
fumecheng-12619	97	15	̅	̅	NOUN
fumecheng-12619	97	16	�	�	PROPN
fumecheng-12619	97	17	𝜕𝜏2	𝜕𝜏2	PROPN
fumecheng-12619	97	18	,	,	PUNCT
fumecheng-12619	97	19	(	(	PUNCT
fumecheng-12619	97	20	8)	8)	NUM
fumecheng-12619	97	21	(	(	PUNCT
fumecheng-12619	97	22	1	1	NUM
fumecheng-12619	97	23	−	−	PRON
fumecheng-12619	97	24	�	�	NOUN
fumecheng-12619	97	25	̅	̅	NOUN
fumecheng-12619	97	26	�	�	PROPN
fumecheng-12619	97	27	�	�	PROPN
fumecheng-12619	97	28	̅	̅	NOUN
fumecheng-12619	97	29	�	�	NOUN
fumecheng-12619	97	30	2	2	NUM
fumecheng-12619	97	31	)	)	PUNCT
fumecheng-12619	97	32	(	(	PUNCT
fumecheng-12619	97	33	𝛼1𝑤	𝛼1𝑤	ADP
fumecheng-12619	97	34	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-12619	97	35	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	97	36	+	+	NUM
fumecheng-12619	97	37	𝛼2𝑤	𝛼2𝑤	NOUN
fumecheng-12619	97	38	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-12619	97	39	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	97	40	𝜕2	𝜕2	NOUN
fumecheng-12619	97	41	�	�	NOUN
fumecheng-12619	97	42	̅	̅	NOUN
fumecheng-12619	97	43	�	�	NOUN
fumecheng-12619	97	44	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	97	45	+	+	CCONJ
fumecheng-12619	98	1	𝛼3𝑤	𝛼3𝑤	ADP
fumecheng-12619	98	2	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-12619	98	3	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	98	4	𝜕2	𝜕2	NOUN
fumecheng-12619	98	5	�	�	NOUN
fumecheng-12619	98	6	̅	̅	NOUN
fumecheng-12619	98	7	�	�	NOUN
fumecheng-12619	98	8	𝜕𝜃2	𝜕𝜃2	X
fumecheng-12619	98	9	+	+	CCONJ
fumecheng-12619	98	10	𝛼4𝑤	𝛼4𝑤	PROPN
fumecheng-12619	98	11	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	98	12	𝜕𝜉2	𝜕𝜉2	PROPN
fumecheng-12619	98	13	𝜕	𝜕	PROPN
fumecheng-12619	98	14	�	�	PROPN
fumecheng-12619	98	15	̅	̅	NOUN
fumecheng-12619	98	16	�	�	NOUN
fumecheng-12619	98	17	𝜕𝜉	𝜕𝜉	VERB
fumecheng-12619	98	18	+	+	CCONJ
fumecheng-12619	98	19	𝛼5𝑤	𝛼5𝑤	NUM
fumecheng-12619	98	20	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	98	21	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	98	22	𝜕	𝜕	NOUN
fumecheng-12619	98	23	�	�	NOUN
fumecheng-12619	98	24	̅	̅	NOUN
fumecheng-12619	98	25	�	�	NOUN
fumecheng-12619	98	26	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	98	27	+	+	PROPN
fumecheng-12619	98	28	𝛼6𝑤	𝛼6𝑤	NOUN
fumecheng-12619	98	29	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	98	30	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	98	31	𝜕	𝜕	NOUN
fumecheng-12619	98	32	�	�	NOUN
fumecheng-12619	98	33	̅	̅	NOUN
fumecheng-12619	98	34	�	�	NOUN
fumecheng-12619	98	35	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	98	36	+	+	CCONJ
fumecheng-12619	99	1	𝛼7𝑤	𝛼7𝑤	NUM
fumecheng-12619	99	2	𝜕𝑢	𝜕𝑢	ADJ
fumecheng-12619	99	3	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	99	4	𝜕2	𝜕2	NOUN
fumecheng-12619	99	5	�	�	NOUN
fumecheng-12619	99	6	̅	̅	NOUN
fumecheng-12619	99	7	�	�	NOUN
fumecheng-12619	99	8	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	99	9	+	+	NUM
fumecheng-12619	99	10	𝛼8𝑤	𝛼8𝑤	NUM
fumecheng-12619	99	11	𝜕2𝑢	𝜕2𝑢	PROPN
fumecheng-12619	99	12	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	99	13	𝜕	𝜕	NOUN
fumecheng-12619	99	14	�	�	NOUN
fumecheng-12619	99	15	̅	̅	NOUN
fumecheng-12619	99	16	�	�	NOUN
fumecheng-12619	99	17	𝜕𝜉	𝜕𝜉	VERB
fumecheng-12619	99	18	+	+	CCONJ
fumecheng-12619	99	19	𝛼9𝑤	𝛼9𝑤	NUM
fumecheng-12619	99	20	𝜕	𝜕	NOUN
fumecheng-12619	99	21	�	�	NOUN
fumecheng-12619	99	22	̅	̅	NOUN
fumecheng-12619	99	23	�	�	NOUN
fumecheng-12619	99	24	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	99	25	𝜕2	𝜕2	NOUN
fumecheng-12619	99	26	�	�	NOUN
fumecheng-12619	99	27	̅	̅	NOUN
fumecheng-12619	99	28	�	�	NOUN
fumecheng-12619	99	29	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	99	30	+	+	PROPN
fumecheng-12619	99	31	𝛼10𝑤	𝛼10𝑤	PROPN
fumecheng-12619	99	32	𝜕2	𝜕2	NOUN
fumecheng-12619	99	33	�	�	NOUN
fumecheng-12619	99	34	̅	̅	NOUN
fumecheng-12619	100	1	�	�	PROPN
fumecheng-12619	100	2	𝜕𝜉2	𝜕𝜉2	PROPN
fumecheng-12619	100	3	𝜕	𝜕	PROPN
fumecheng-12619	100	4	�	�	PROPN
fumecheng-12619	100	5	̅	̅	NOUN
fumecheng-12619	100	6	�	�	NOUN
fumecheng-12619	100	7	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	100	8	+	+	CCONJ
fumecheng-12619	100	9	𝛼11𝑤	𝛼11𝑤	PROPN
fumecheng-12619	100	10	𝜕2	𝜕2	NOUN
fumecheng-12619	100	11	�	�	NOUN
fumecheng-12619	100	12	̅	̅	NOUN
fumecheng-12619	100	13	�	�	PROPN
fumecheng-12619	100	14	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	100	15	𝜕	𝜕	PROPN
fumecheng-12619	100	16	�	�	NOUN
fumecheng-12619	100	17	̅	̅	NOUN
fumecheng-12619	100	18	�	�	NOUN
fumecheng-12619	100	19	𝜕𝜉	𝜕𝜉	VERB
fumecheng-12619	100	20	+	+	NUM
fumecheng-12619	100	21	𝛼12𝑤	𝛼12𝑤	NUM
fumecheng-12619	100	22	𝜕	𝜕	PROPN
fumecheng-12619	100	23	�	�	NOUN
fumecheng-12619	100	24	̅	̅	NOUN
fumecheng-12619	100	25	�	�	NOUN
fumecheng-12619	100	26	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	100	27	+	+	CCONJ
fumecheng-12619	101	1	𝛼13𝑤	𝛼13𝑤	NUM
fumecheng-12619	101	2	𝜕	𝜕	NOUN
fumecheng-12619	101	3	�	�	NOUN
fumecheng-12619	101	4	̅	̅	NOUN
fumecheng-12619	101	5	�	�	NOUN
fumecheng-12619	101	6	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	101	7	𝜕2	𝜕2	NOUN
fumecheng-12619	101	8	�	�	NOUN
fumecheng-12619	101	9	̅	̅	NOUN
fumecheng-12619	101	10	�	�	NOUN
fumecheng-12619	101	11	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	101	12	+	+	ADV
fumecheng-12619	101	13	𝛼14𝑤	𝛼14𝑤	VERB
fumecheng-12619	101	14	𝜕	𝜕	PROPN
fumecheng-12619	101	15	�	�	NOUN
fumecheng-12619	101	16	̅	̅	NOUN
fumecheng-12619	101	17	�	�	NOUN
fumecheng-12619	101	18	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	101	19	𝜕2	𝜕2	NOUN
fumecheng-12619	101	20	�	�	NOUN
fumecheng-12619	101	21	̅	̅	NOUN
fumecheng-12619	101	22	�	�	NOUN
fumecheng-12619	101	23	𝜕𝜃2	𝜕𝜃2	ADJ
fumecheng-12619	101	24	+	+	X
fumecheng-12619	101	25	𝛼15𝑤	𝛼15𝑤	NUM
fumecheng-12619	101	26	𝜕2	𝜕2	NOUN
fumecheng-12619	101	27	�	�	NOUN
fumecheng-12619	101	28	̅	̅	NOUN
fumecheng-12619	101	29	�	�	PROPN
fumecheng-12619	101	30	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	101	31	𝜕	𝜕	NOUN
fumecheng-12619	101	32	�	�	NOUN
fumecheng-12619	101	33	̅	̅	NOUN
fumecheng-12619	101	34	�	�	NOUN
fumecheng-12619	101	35	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	101	36	+	+	CCONJ
fumecheng-12619	101	37	𝛼16𝑤	𝛼16𝑤	NOUN
fumecheng-12619	101	38	�	�	NOUN
fumecheng-12619	101	39	̅	̅	NOUN
fumecheng-12619	101	40	�	�	PROPN
fumecheng-12619	101	41	+	+	CCONJ
fumecheng-12619	101	42	𝛼17𝑤	𝛼17𝑤	PROPN
fumecheng-12619	101	43	�	�	NOUN
fumecheng-12619	101	44	̅	̅	NOUN
fumecheng-12619	101	45	�	�	PROPN
fumecheng-12619	101	46	𝜕2	𝜕2	SYM
fumecheng-12619	101	47	�	�	NOUN
fumecheng-12619	101	48	̅	̅	NOUN
fumecheng-12619	101	49	�	�	NOUN
fumecheng-12619	101	50	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	101	51	+	+	CCONJ
fumecheng-12619	101	52	𝛼18𝑤	𝛼18𝑤	PROPN
fumecheng-12619	101	53	�	�	PROPN
fumecheng-12619	101	54	̅	̅	ADJ
fumecheng-12619	101	55	�	�	PROPN
fumecheng-12619	101	56	𝜕2	𝜕2	SYM
fumecheng-12619	101	57	�	�	NOUN
fumecheng-12619	101	58	̅	̅	NOUN
fumecheng-12619	101	59	�	�	NOUN
fumecheng-12619	101	60	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	101	61	+	+	PROPN
fumecheng-12619	101	62	𝛼19𝑤	𝛼19𝑤	NUM
fumecheng-12619	101	63	𝜕2	𝜕2	NOUN
fumecheng-12619	101	64	�	�	NOUN
fumecheng-12619	101	65	̅	̅	NOUN
fumecheng-12619	101	66	�	�	NOUN
fumecheng-12619	101	67	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	101	68	+	+	CCONJ
fumecheng-12619	101	69	𝛼20𝑤	𝛼20𝑤	PROPN
fumecheng-12619	101	70	𝜕	𝜕	PROPN
fumecheng-12619	101	71	�	�	PROPN
fumecheng-12619	101	72	̅	̅	NOUN
fumecheng-12619	101	73	�	�	NOUN
fumecheng-12619	101	74	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	101	75	𝜕2	𝜕2	NOUN
fumecheng-12619	101	76	�	�	NOUN
fumecheng-12619	101	77	̅	̅	NOUN
fumecheng-12619	101	78	�	�	PROPN
fumecheng-12619	101	79	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	101	80	𝜕	𝜕	PROPN
fumecheng-12619	101	81	�	�	NOUN
fumecheng-12619	101	82	̅	̅	NOUN
fumecheng-12619	101	83	�	�	NOUN
fumecheng-12619	101	84	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	101	85	+	+	CCONJ
fumecheng-12619	101	86	𝛼21𝑤	𝛼21𝑤	NUM
fumecheng-12619	101	87	𝜕2	𝜕2	NOUN
fumecheng-12619	101	88	�	�	NOUN
fumecheng-12619	101	89	̅	̅	NOUN
fumecheng-12619	101	90	�	�	NOUN
fumecheng-12619	101	91	𝜕𝜉2	𝜕𝜉2	PROPN
fumecheng-12619	101	92	(	(	PUNCT
fumecheng-12619	101	93	𝜕	𝜕	NOUN
fumecheng-12619	101	94	�	�	NOUN
fumecheng-12619	101	95	̅	̅	NOUN
fumecheng-12619	101	96	�	�	NOUN
fumecheng-12619	101	97	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	101	98	)	)	PUNCT
fumecheng-12619	101	99	2	2	NUM
fumecheng-12619	102	1	+	+	CCONJ
fumecheng-12619	102	2	𝛼22𝑤	𝛼22𝑤	PROPN
fumecheng-12619	102	3	𝜕2	𝜕2	NOUN
fumecheng-12619	102	4	�	�	NOUN
fumecheng-12619	102	5	̅	̅	NOUN
fumecheng-12619	102	6	�	�	NOUN
fumecheng-12619	102	7	𝜕𝜉2	𝜕𝜉2	PROPN
fumecheng-12619	102	8	(	(	PUNCT
fumecheng-12619	102	9	𝜕	𝜕	NOUN
fumecheng-12619	102	10	�	�	NOUN
fumecheng-12619	102	11	̅	̅	NOUN
fumecheng-12619	102	12	�	�	NOUN
fumecheng-12619	102	13	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	102	14	)	)	PUNCT
fumecheng-12619	102	15	2	2	NUM
fumecheng-12619	103	1	+	+	PROPN
fumecheng-12619	103	2	𝛼23𝑤	𝛼23𝑤	PROPN
fumecheng-12619	103	3	𝜕4	𝜕4	PROPN
fumecheng-12619	103	4	�	�	PROPN
fumecheng-12619	103	5	̅	̅	NOUN
fumecheng-12619	103	6	�	�	PROPN
fumecheng-12619	103	7	𝜕𝜉4	𝜕𝜉4	PROPN
fumecheng-12619	103	8	+	+	CCONJ
fumecheng-12619	103	9	𝛼24𝑤	𝛼24𝑤	PROPN
fumecheng-12619	103	10	(	(	PUNCT
fumecheng-12619	103	11	𝜕	𝜕	NOUN
fumecheng-12619	103	12	�	�	NOUN
fumecheng-12619	103	13	̅	̅	NOUN
fumecheng-12619	103	14	�	�	NOUN
fumecheng-12619	103	15	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	103	16	)	)	PUNCT
fumecheng-12619	103	17	2	2	NUM
fumecheng-12619	104	1	+	+	CCONJ
fumecheng-12619	104	2	𝛼25𝑤	𝛼25𝑤	NUM
fumecheng-12619	104	3	𝜕4	𝜕4	PROPN
fumecheng-12619	104	4	�	�	NOUN
fumecheng-12619	104	5	̅	̅	NOUN
fumecheng-12619	104	6	�	�	NOUN
fumecheng-12619	104	7	𝜕𝜉2𝜕𝜃2	𝜕𝜉2𝜕𝜃2	PROPN
fumecheng-12619	104	8	+	+	PROPN
fumecheng-12619	104	9	𝛼26𝑤	𝛼26𝑤	NOUN
fumecheng-12619	104	10	(	(	PUNCT
fumecheng-12619	104	11	𝜕	𝜕	NOUN
fumecheng-12619	104	12	�	�	NOUN
fumecheng-12619	104	13	̅	̅	NOUN
fumecheng-12619	104	14	�	�	NOUN
fumecheng-12619	104	15	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	104	16	)	)	PUNCT
fumecheng-12619	104	17	2	2	NUM
fumecheng-12619	104	18	𝜕2	𝜕2	NOUN
fumecheng-12619	104	19	�	�	NOUN
fumecheng-12619	104	20	̅	̅	NOUN
fumecheng-12619	104	21	�	�	NOUN
fumecheng-12619	104	22	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	104	23	+	+	PROPN
fumecheng-12619	104	24	𝛼27𝑤	𝛼27𝑤	PROPN
fumecheng-12619	104	25	𝜕2	𝜕2	SYM
fumecheng-12619	104	26	�	�	NOUN
fumecheng-12619	104	27	̅	̅	NOUN
fumecheng-12619	104	28	�	�	NOUN
fumecheng-12619	104	29	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	104	30	+	+	PROPN
fumecheng-12619	104	31	𝛼28𝑤	𝛼28𝑤	ADJ
fumecheng-12619	104	32	𝜕4	𝜕4	PROPN
fumecheng-12619	104	33	�	�	NOUN
fumecheng-12619	104	34	̅	̅	NOUN
fumecheng-12619	104	35	�	�	NOUN
fumecheng-12619	104	36	𝜕𝜃4	𝜕𝜃4	ADJ
fumecheng-12619	104	37	+	+	CCONJ
fumecheng-12619	104	38	𝛼29𝑤	𝛼29𝑤	NUM
fumecheng-12619	104	39	𝜕2	𝜕2	NOUN
fumecheng-12619	104	40	�	�	NOUN
fumecheng-12619	104	41	̅	̅	NOUN
fumecheng-12619	104	42	�	�	PROPN
fumecheng-12619	104	43	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	104	44	(	(	PUNCT
fumecheng-12619	104	45	𝜕	𝜕	NOUN
fumecheng-12619	104	46	�	�	NOUN
fumecheng-12619	104	47	̅	̅	NOUN
fumecheng-12619	104	48	�	�	NOUN
fumecheng-12619	104	49	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	104	50	)	)	PUNCT
fumecheng-12619	104	51	2	2	NUM
fumecheng-12619	105	1	+	+	CCONJ
fumecheng-12619	105	2	𝛼30𝑤	𝛼30𝑤	PROPN
fumecheng-12619	105	3	(	(	PUNCT
fumecheng-12619	105	4	𝜕	𝜕	NOUN
fumecheng-12619	105	5	�	�	NOUN
fumecheng-12619	105	6	̅	̅	NOUN
fumecheng-12619	105	7	�	�	NOUN
fumecheng-12619	105	8	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	105	9	)	)	PUNCT
fumecheng-12619	105	10	2	2	NUM
fumecheng-12619	106	1	+	+	ADJ
fumecheng-12619	106	2	𝛼31𝑤	𝛼31𝑤	NUM
fumecheng-12619	106	3	𝜕4	𝜕4	PROPN
fumecheng-12619	106	4	�	�	NOUN
fumecheng-12619	106	5	̅	̅	NOUN
fumecheng-12619	106	6	�	�	NOUN
fumecheng-12619	106	7	𝜕𝜉2𝜕𝜏2	𝜕𝜉2𝜕𝜏2	PROPN
fumecheng-12619	106	8	+	+	NUM
fumecheng-12619	106	9	𝛼32𝑤	𝛼32𝑤	PROPN
fumecheng-12619	106	10	𝜕4	𝜕4	PROPN
fumecheng-12619	106	11	�	�	NOUN
fumecheng-12619	106	12	̅	̅	NOUN
fumecheng-12619	106	13	�	�	PROPN
fumecheng-12619	106	14	𝜕𝜃2𝜕𝜏2	𝜕𝜃2𝜕𝜏2	PROPN
fumecheng-12619	106	15	+	+	CCONJ
fumecheng-12619	106	16	𝛼33𝑤	𝛼33𝑤	NOUN
fumecheng-12619	106	17	)	)	PUNCT
fumecheng-12619	106	18	(	(	PUNCT
fumecheng-12619	106	19	9	9	X
fumecheng-12619	106	20	)	)	PUNCT
fumecheng-12619	106	21	=	=	PUNCT
fumecheng-12619	106	22	(	(	PUNCT
fumecheng-12619	106	23	1	1	NUM
fumecheng-12619	106	24	−	−	PRON
fumecheng-12619	106	25	�	�	NOUN
fumecheng-12619	106	26	̅	̅	NOUN
fumecheng-12619	106	27	�	�	PROPN
fumecheng-12619	106	28	�	�	PROPN
fumecheng-12619	106	29	̅	̅	NOUN
fumecheng-12619	106	30	�	�	NOUN
fumecheng-12619	106	31	2	2	NUM
fumecheng-12619	106	32	)	)	PUNCT
fumecheng-12619	106	33	(	(	PUNCT
fumecheng-12619	106	34	𝜕2	𝜕2	NOUN
fumecheng-12619	106	35	�	�	NOUN
fumecheng-12619	106	36	̅	̅	NOUN
fumecheng-12619	106	37	�	�	PROPN
fumecheng-12619	106	38	𝜕𝜏2	𝜕𝜏2	PROPN
fumecheng-12619	106	39	+	+	CCONJ
fumecheng-12619	106	40	𝐶	𝐶	PROPN
fumecheng-12619	106	41	�	�	PROPN
fumecheng-12619	106	42	̅	̅	NOUN
fumecheng-12619	106	43	�	�	PROPN
fumecheng-12619	106	44	𝜕	𝜕	PROPN
fumecheng-12619	106	45	�	�	PROPN
fumecheng-12619	106	46	̅	̅	NOUN
fumecheng-12619	106	47	�	�	NOUN
fumecheng-12619	106	48	𝜕𝜏	𝜕𝜏	NOUN
fumecheng-12619	106	49	+	+	CCONJ
fumecheng-12619	106	50	𝐾𝑤	𝐾𝑤	PROPN
fumecheng-12619	106	51	�	�	PROPN
fumecheng-12619	106	52	̅	̅	NOUN
fumecheng-12619	106	53	�	�	NOUN
fumecheng-12619	106	54	−	−	ADP
fumecheng-12619	106	55	𝐾𝑝	𝐾𝑝	PROPN
fumecheng-12619	106	56	�	�	NOUN
fumecheng-12619	106	57	̅	̅	NOUN
fumecheng-12619	106	58	�	�	PROPN
fumecheng-12619	106	59	2	2	NUM
fumecheng-12619	106	60	�	�	PROPN
fumecheng-12619	106	61	̅	̅	NOUN
fumecheng-12619	106	62	�	�	PROPN
fumecheng-12619	106	63	−	−	PROPN
fumecheng-12619	106	64	�	�	PROPN
fumecheng-12619	106	65	̅	̅	NOUN
fumecheng-12619	106	66	�	�	NOUN
fumecheng-12619	106	67	𝑒(	𝑒(	NUM
fumecheng-12619	106	68	�	�	NOUN
fumecheng-12619	106	69	̅	̅	NOUN
fumecheng-12619	106	70	�	�	NOUN
fumecheng-12619	106	71	𝐷𝐶	𝐷𝐶	PROPN
fumecheng-12619	106	72	+	+	CCONJ
fumecheng-12619	106	73	�	�	NOUN
fumecheng-12619	106	74	̅	̅	NOUN
fumecheng-12619	106	75	�	�	NOUN
fumecheng-12619	106	76	𝐴𝐶	𝐴𝐶	PROPN
fumecheng-12619	106	77	𝑐𝑜𝑠(	𝑐𝑜𝑠(	PROPN
fumecheng-12619	106	78	�	�	PROPN
fumecheng-12619	106	79	̅	̅	NOUN
fumecheng-12619	106	80	�	�	NOUN
fumecheng-12619	106	81	𝜏	𝜏	NOUN
fumecheng-12619	106	82	)	)	PUNCT
fumecheng-12619	106	83	)	)	PUNCT
fumecheng-12619	106	84	2	2	NUM
fumecheng-12619	106	85	√(𝑚1	√(𝑚1	ADP
fumecheng-12619	106	86	�	�	NOUN
fumecheng-12619	106	87	̅	̅	NOUN
fumecheng-12619	106	88	�	�	PROPN
fumecheng-12619	106	89	−	−	PROPN
fumecheng-12619	106	90	�	�	NOUN
fumecheng-12619	106	91	̅	̅	NOUN
fumecheng-12619	106	92	�	�	SYM
fumecheng-12619	106	93	)(2𝑚4	)(2𝑚4	NOUN
fumecheng-12619	106	94	�	�	NOUN
fumecheng-12619	106	95	̅	̅	NOUN
fumecheng-12619	106	96	�	�	PROPN
fumecheng-12619	106	97	+	+	CCONJ
fumecheng-12619	106	98	𝑚1	𝑚1	PROPN
fumecheng-12619	106	99	�	�	PROPN
fumecheng-12619	106	100	̅	̅	NOUN
fumecheng-12619	106	101	�	�	PROPN
fumecheng-12619	106	102	−	−	PROPN
fumecheng-12619	106	103	�	�	PROPN
fumecheng-12619	106	104	̅	̅	NOUN
fumecheng-12619	106	105	�	�	NOUN
fumecheng-12619	106	106	)	)	PUNCT
fumecheng-12619	106	107	×	×	NOUN
fumecheng-12619	107	1	[	[	X
fumecheng-12619	107	2	𝑐𝑜𝑠ℎ−1	𝑐𝑜𝑠ℎ−1	X
fumecheng-12619	107	3	(	(	PUNCT
fumecheng-12619	107	4	1	1	NUM
fumecheng-12619	107	5	+	+	NUM
fumecheng-12619	107	6	𝑚1	𝑚1	NOUN
fumecheng-12619	107	7	�	�	PROPN
fumecheng-12619	107	8	̅	̅	NOUN
fumecheng-12619	107	9	�	�	PROPN
fumecheng-12619	107	10	−	−	PROPN
fumecheng-12619	107	11	�	�	NOUN
fumecheng-12619	107	12	̅	̅	NOUN
fumecheng-12619	107	13	�	�	PROPN
fumecheng-12619	107	14	𝑚4	𝑚4	PROPN
fumecheng-12619	107	15	�	�	PROPN
fumecheng-12619	107	16	̅	̅	NOUN
fumecheng-12619	107	17	�	�	NOUN
fumecheng-12619	107	18	)	)	PUNCT
fumecheng-12619	107	19	]	]	PUNCT
fumecheng-12619	107	20	2	2	X
fumecheng-12619	107	21	)	)	PUNCT
fumecheng-12619	107	22	,	,	PUNCT
fumecheng-12619	107	23	where	where	SCONJ
fumecheng-12619	107	24	�	�	NOUN
fumecheng-12619	107	25	̅	̅	NOUN
fumecheng-12619	107	26	�	�	NOUN
fumecheng-12619	107	27	2	2	NUM
fumecheng-12619	107	28	=	=	SYM
fumecheng-12619	107	29	𝜕2	𝜕2	NOUN
fumecheng-12619	107	30	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	107	31	+	+	NOUN
fumecheng-12619	107	32	𝑚0	𝑚0	NOUN
fumecheng-12619	107	33	2	2	NUM
fumecheng-12619	107	34	𝜕2	𝜕2	NOUN
fumecheng-12619	107	35	𝜕𝜃2	𝜕𝜃2	ADJ
fumecheng-12619	107	36	and	and	CCONJ
fumecheng-12619	107	37	the	the	DET
fumecheng-12619	107	38	coefficients	coefficient	NOUN
fumecheng-12619	107	39	of	of	ADP
fumecheng-12619	107	40	𝛼𝑖𝑢(𝑖	𝛼𝑖𝑢(𝑖	PROPN
fumecheng-12619	107	41	=	=	SYM
fumecheng-12619	107	42	1	1	NUM
fumecheng-12619	107	43	.	.	NUM
fumecheng-12619	107	44	.7	.7	PROPN
fumecheng-12619	107	45	)	)	PUNCT
fumecheng-12619	107	46	,	,	PUNCT
fumecheng-12619	107	47	𝛼𝑗𝑣(𝑗	𝛼𝑗𝑣(𝑗	PROPN
fumecheng-12619	107	48	=	=	SYM
fumecheng-12619	107	49	1	1	NUM
fumecheng-12619	107	50	.	.	NUM
fumecheng-12619	107	51	.7	.7	NUM
fumecheng-12619	107	52	)	)	PUNCT
fumecheng-12619	107	53	and	and	CCONJ
fumecheng-12619	107	54	𝛼𝑘𝑤(𝑘	𝛼𝑘𝑤(𝑘	NOUN
fumecheng-12619	107	55	=	=	SYM
fumecheng-12619	107	56	1	1	NUM
fumecheng-12619	107	57	.	.	NOUN
fumecheng-12619	107	58	.33	.33	NUM
fumecheng-12619	107	59	)	)	PUNCT
fumecheng-12619	107	60	are	be	AUX
fumecheng-12619	107	61	defined	define	VERB
fumecheng-12619	107	62	in	in	ADP
fumecheng-12619	107	63	hashemi	hashemi	PROPN
fumecheng-12619	107	64	kachapi	kachapi	PROPN
fumecheng-12619	107	65	et	et	PROPN
fumecheng-12619	107	66	al	al	PROPN
fumecheng-12619	108	1	[	[	X
fumecheng-12619	108	2	20	20	NUM
fumecheng-12619	108	3	]	]	PUNCT
fumecheng-12619	108	4	.	.	PUNCT
fumecheng-12619	109	1	the	the	DET
fumecheng-12619	109	2	corresponding	corresponding	ADJ
fumecheng-12619	109	3	boundary	boundary	ADJ
fumecheng-12619	109	4	conditions	condition	NOUN
fumecheng-12619	109	5	,	,	PUNCT
fumecheng-12619	109	6	expressed	express	VERB
fumecheng-12619	109	7	in	in	ADP
fumecheng-12619	109	8	dimensionless	dimensionless	NOUN
fumecheng-12619	109	9	form	form	NOUN
fumecheng-12619	109	10	,	,	PUNCT
fumecheng-12619	109	11	are	be	AUX
fumecheng-12619	109	12	given	give	VERB
fumecheng-12619	109	13	by	by	ADP
fumecheng-12619	109	14	:	:	PUNCT
fumecheng-12619	109	15	316	316	NUM
fumecheng-12619	109	16	s.h	s.h	PROPN
fumecheng-12619	109	17	.	.	PROPN
fumecheng-12619	109	18	hashemi	hashemi	PROPN
fumecheng-12619	109	19	kachapi	kachapi	PROPN
fumecheng-12619	109	20	,	,	PUNCT
fumecheng-12619	109	21	s.	s.	PROPN
fumecheng-12619	109	22	gh	gh	PROPN
fumecheng-12619	109	23	.	.	PROPN
fumecheng-12619	110	1	hashemi	hashemi	PROPN
fumecheng-12619	110	2	kachapi	kachapi	PROPN
fumecheng-12619	110	3	�	�	PROPN
fumecheng-12619	110	4	̅	̅	NOUN
fumecheng-12619	110	5	�	�	NOUN
fumecheng-12619	110	6	=	=	SYM
fumecheng-12619	110	7	0	0	NUM
fumecheng-12619	110	8	:	:	PUNCT
fumecheng-12619	110	9	(	(	PUNCT
fumecheng-12619	110	10	𝛼1𝑢	𝛼1𝑢	NOUN
fumecheng-12619	110	11	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	110	12	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-12619	110	13	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	110	14	+	+	CCONJ
fumecheng-12619	110	15	𝛼2𝑢	𝛼2𝑢	PROPN
fumecheng-12619	110	16	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	110	17	𝜕	𝜕	PROPN
fumecheng-12619	110	18	�	�	PROPN
fumecheng-12619	110	19	̅	̅	NOUN
fumecheng-12619	110	20	�	�	NOUN
fumecheng-12619	110	21	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	110	22	+	+	CCONJ
fumecheng-12619	110	23	𝛼3𝑢	𝛼3𝑢	PROPN
fumecheng-12619	110	24	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	110	25	�	�	PROPN
fumecheng-12619	110	26	̅	̅	NOUN
fumecheng-12619	110	27	�	�	NOUN
fumecheng-12619	110	28	+	+	NOUN
fumecheng-12619	110	29	𝛼4𝑢	𝛼4𝑢	PROPN
fumecheng-12619	110	30	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	110	31	(	(	PUNCT
fumecheng-12619	110	32	𝜕	𝜕	NOUN
fumecheng-12619	110	33	�	�	NOUN
fumecheng-12619	110	34	̅	̅	NOUN
fumecheng-12619	110	35	�	�	NOUN
fumecheng-12619	110	36	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	110	37	)	)	PUNCT
fumecheng-12619	110	38	2	2	NUM
fumecheng-12619	111	1	+	+	CCONJ
fumecheng-12619	111	2	𝛼5𝑢	𝛼5𝑢	NUM
fumecheng-12619	111	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	111	4	(	(	PUNCT
fumecheng-12619	111	5	𝜕	𝜕	NOUN
fumecheng-12619	111	6	�	�	NOUN
fumecheng-12619	111	7	̅	̅	NOUN
fumecheng-12619	111	8	�	�	NOUN
fumecheng-12619	111	9	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	111	10	)	)	PUNCT
fumecheng-12619	111	11	2	2	NUM
fumecheng-12619	112	1	+	+	NOUN
fumecheng-12619	112	2	𝛼6𝑢	𝛼6𝑢	NUM
fumecheng-12619	112	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	112	4	)	)	PUNCT
fumecheng-12619	112	5	𝛿	𝛿	PROPN
fumecheng-12619	112	6	�	�	PROPN
fumecheng-12619	112	7	̅	̅	NOUN
fumecheng-12619	112	8	�	�	NOUN
fumecheng-12619	112	9	𝜉|	𝜉|	ADJ
fumecheng-12619	112	10	|	|	NOUN
fumecheng-12619	112	11	0	0	NUM
fumecheng-12619	112	12	1	1	NUM
fumecheng-12619	112	13	+	+	CCONJ
fumecheng-12619	112	14	(	(	PUNCT
fumecheng-12619	112	15	𝛼7𝑢	𝛼7𝑢	NUM
fumecheng-12619	112	16	𝑏𝑐	𝑏𝑐	PRON
fumecheng-12619	112	17	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-12619	112	18	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	113	1	+	+	CCONJ
fumecheng-12619	113	2	𝛼8𝑢	𝛼8𝑢	PROPN
fumecheng-12619	113	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	113	4	𝜕	𝜕	NOUN
fumecheng-12619	113	5	�	�	PROPN
fumecheng-12619	113	6	̅	̅	NOUN
fumecheng-12619	113	7	�	�	NOUN
fumecheng-12619	113	8	𝜕𝜉	𝜕𝜉	VERB
fumecheng-12619	113	9	+	+	NOUN
fumecheng-12619	113	10	𝛼9𝑢	𝛼9𝑢	NUM
fumecheng-12619	113	11	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	113	12	𝜕	𝜕	PROPN
fumecheng-12619	113	13	�	�	PROPN
fumecheng-12619	113	14	̅	̅	NOUN
fumecheng-12619	113	15	�	�	PROPN
fumecheng-12619	113	16	𝜕𝜉	𝜕𝜉	PROPN
fumecheng-12619	113	17	𝜕	𝜕	NOUN
fumecheng-12619	113	18	�	�	NOUN
fumecheng-12619	113	19	̅	̅	NOUN
fumecheng-12619	113	20	�	�	NOUN
fumecheng-12619	113	21	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	113	22	)	)	PUNCT
fumecheng-12619	113	23	𝛿	𝛿	PRON
fumecheng-12619	113	24	�	�	PROPN
fumecheng-12619	113	25	̅	̅	NOUN
fumecheng-12619	113	26	�	�	NOUN
fumecheng-12619	113	27	𝜃|	𝜃|	NOUN
fumecheng-12619	113	28	0	0	NUM
fumecheng-12619	113	29	2𝜋	2𝜋	NOUN
fumecheng-12619	113	30	=	=	SYM
fumecheng-12619	113	31	0	0	NUM
fumecheng-12619	113	32	,	,	PUNCT
fumecheng-12619	113	33	(	(	PUNCT
fumecheng-12619	113	34	10	10	NUM
fumecheng-12619	113	35	)	)	PUNCT
fumecheng-12619	113	36	𝛿	𝛿	DET
fumecheng-12619	113	37	�	�	PROPN
fumecheng-12619	113	38	̅	̅	NOUN
fumecheng-12619	113	39	�	�	NOUN
fumecheng-12619	113	40	=	=	SYM
fumecheng-12619	113	41	0	0	NUM
fumecheng-12619	113	42	:	:	PUNCT
fumecheng-12619	113	43	(	(	PUNCT
fumecheng-12619	113	44	𝛼1𝑣	𝛼1𝑣	X
fumecheng-12619	113	45	𝑏𝑐	𝑏𝑐	ADP
fumecheng-12619	113	46	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-12619	113	47	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	113	48	+	+	CCONJ
fumecheng-12619	113	49	𝛼2𝑣	𝛼2𝑣	NUM
fumecheng-12619	113	50	𝑏𝑐	𝑏𝑐	ADP
fumecheng-12619	113	51	𝜕	𝜕	NOUN
fumecheng-12619	113	52	�	�	PROPN
fumecheng-12619	113	53	̅	̅	NOUN
fumecheng-12619	113	54	�	�	NOUN
fumecheng-12619	113	55	𝜕𝜉	𝜕𝜉	VERB
fumecheng-12619	113	56	+	+	ADJ
fumecheng-12619	113	57	𝛼3𝑣	𝛼3𝑣	PROPN
fumecheng-12619	113	58	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	113	59	𝜕	𝜕	PROPN
fumecheng-12619	113	60	�	�	PROPN
fumecheng-12619	113	61	̅	̅	NOUN
fumecheng-12619	113	62	�	�	PROPN
fumecheng-12619	113	63	𝜕𝜉	𝜕𝜉	PROPN
fumecheng-12619	113	64	𝜕	𝜕	NOUN
fumecheng-12619	113	65	�	�	NOUN
fumecheng-12619	113	66	̅	̅	NOUN
fumecheng-12619	113	67	�	�	NOUN
fumecheng-12619	113	68	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	113	69	)	)	PUNCT
fumecheng-12619	113	70	𝛿	𝛿	PRON
fumecheng-12619	113	71	�	�	PROPN
fumecheng-12619	113	72	̅	̅	NOUN
fumecheng-12619	113	73	�	�	NOUN
fumecheng-12619	113	74	𝜉|	𝜉|	PROPN
fumecheng-12619	113	75	0	0	NUM
fumecheng-12619	113	76	1	1	NUM
fumecheng-12619	114	1	+	+	CCONJ
fumecheng-12619	114	2	(	(	PUNCT
fumecheng-12619	114	3	𝛼4𝑣	𝛼4𝑣	X
fumecheng-12619	114	4	𝑏𝑐	𝑏𝑐	ADP
fumecheng-12619	114	5	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-12619	114	6	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	114	7	+	+	CCONJ
fumecheng-12619	114	8	𝛼5𝑣	𝛼5𝑣	NOUN
fumecheng-12619	114	9	𝑏𝑐	𝑏𝑐	ADP
fumecheng-12619	114	10	𝜕	𝜕	NOUN
fumecheng-12619	114	11	�	�	PROPN
fumecheng-12619	114	12	̅	̅	NOUN
fumecheng-12619	114	13	�	�	NOUN
fumecheng-12619	114	14	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	114	15	+	+	CCONJ
fumecheng-12619	114	16	𝛼6𝑣	𝛼6𝑣	PROPN
fumecheng-12619	114	17	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	114	18	�	�	PROPN
fumecheng-12619	114	19	̅	̅	NOUN
fumecheng-12619	114	20	�	�	NOUN
fumecheng-12619	114	21	+	+	NOUN
fumecheng-12619	114	22	𝛼7𝑣	𝛼7𝑣	PROPN
fumecheng-12619	114	23	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	114	24	(	(	PUNCT
fumecheng-12619	114	25	𝜕	𝜕	NOUN
fumecheng-12619	114	26	�	�	NOUN
fumecheng-12619	114	27	̅	̅	NOUN
fumecheng-12619	114	28	�	�	NOUN
fumecheng-12619	114	29	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	114	30	)	)	PUNCT
fumecheng-12619	114	31	2	2	NUM
fumecheng-12619	115	1	+	+	CCONJ
fumecheng-12619	115	2	𝛼8𝑣	𝛼8𝑣	NUM
fumecheng-12619	115	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	115	4	(	(	PUNCT
fumecheng-12619	115	5	𝜕	𝜕	NOUN
fumecheng-12619	115	6	�	�	NOUN
fumecheng-12619	115	7	̅	̅	NOUN
fumecheng-12619	115	8	�	�	NOUN
fumecheng-12619	115	9	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	115	10	)	)	PUNCT
fumecheng-12619	115	11	2	2	NUM
fumecheng-12619	116	1	+	+	NOUN
fumecheng-12619	116	2	𝛼9𝑣	𝛼9𝑣	NOUN
fumecheng-12619	116	3	𝑏𝑐	𝑏𝑐	ADJ
fumecheng-12619	116	4	)	)	PUNCT
fumecheng-12619	116	5	𝛿	𝛿	PRON
fumecheng-12619	116	6	�	�	PROPN
fumecheng-12619	116	7	̅	̅	NOUN
fumecheng-12619	116	8	�	�	NOUN
fumecheng-12619	116	9	𝜃|	𝜃|	NOUN
fumecheng-12619	116	10	|	|	NOUN
fumecheng-12619	116	11	0	0	NUM
fumecheng-12619	116	12	2𝜋	2𝜋	NOUN
fumecheng-12619	116	13	=	=	SYM
fumecheng-12619	116	14	0	0	NUM
fumecheng-12619	116	15	,	,	PUNCT
fumecheng-12619	116	16	(	(	PUNCT
fumecheng-12619	116	17	11	11	NUM
fumecheng-12619	116	18	)	)	PUNCT
fumecheng-12619	116	19	𝛿	𝛿	DET
fumecheng-12619	116	20	�	�	PROPN
fumecheng-12619	116	21	̅	̅	NOUN
fumecheng-12619	116	22	�	�	NOUN
fumecheng-12619	116	23	=	=	SYM
fumecheng-12619	116	24	0	0	NUM
fumecheng-12619	116	25	:	:	PUNCT
fumecheng-12619	116	26	(	(	PUNCT
fumecheng-12619	116	27	+	+	ADP
fumecheng-12619	116	28	𝛼1𝑤	𝛼1𝑤	PROPN
fumecheng-12619	116	29	𝑏𝑐	𝑏𝑐	ADP
fumecheng-12619	116	30	𝜕𝑢	𝜕𝑢	NOUN
fumecheng-12619	116	31	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	116	32	𝜕	𝜕	NOUN
fumecheng-12619	116	33	�	�	NOUN
fumecheng-12619	116	34	̅	̅	NOUN
fumecheng-12619	116	35	�	�	NOUN
fumecheng-12619	116	36	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	116	37	+	+	CCONJ
fumecheng-12619	116	38	𝛼2𝑤	𝛼2𝑤	AUX
fumecheng-12619	116	39	𝑏𝑐	𝑏𝑐	ADP
fumecheng-12619	116	40	𝜕𝑢	𝜕𝑢	ADJ
fumecheng-12619	116	41	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	116	42	𝜕	𝜕	NOUN
fumecheng-12619	116	43	�	�	NOUN
fumecheng-12619	116	44	̅	̅	NOUN
fumecheng-12619	116	45	�	�	NOUN
fumecheng-12619	116	46	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	116	47	+	+	CCONJ
fumecheng-12619	116	48	𝛼3𝑤	𝛼3𝑤	PROPN
fumecheng-12619	116	49	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	116	50	𝜕	𝜕	PROPN
fumecheng-12619	116	51	�	�	PROPN
fumecheng-12619	116	52	̅	̅	NOUN
fumecheng-12619	116	53	�	�	PROPN
fumecheng-12619	116	54	𝜕𝜉	𝜕𝜉	PROPN
fumecheng-12619	116	55	𝜕	𝜕	NOUN
fumecheng-12619	116	56	�	�	NOUN
fumecheng-12619	116	57	̅	̅	NOUN
fumecheng-12619	116	58	�	�	NOUN
fumecheng-12619	116	59	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	116	60	+	+	CCONJ
fumecheng-12619	116	61	𝛼4𝑤	𝛼4𝑤	PROPN
fumecheng-12619	116	62	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	116	63	𝜕	𝜕	PROPN
fumecheng-12619	116	64	�	�	PROPN
fumecheng-12619	116	65	̅	̅	NOUN
fumecheng-12619	116	66	�	�	PROPN
fumecheng-12619	116	67	𝜕𝜃	𝜕𝜃	PROPN
fumecheng-12619	116	68	𝜕	𝜕	PROPN
fumecheng-12619	116	69	�	�	NOUN
fumecheng-12619	116	70	̅	̅	NOUN
fumecheng-12619	116	71	�	�	NOUN
fumecheng-12619	116	72	𝜕𝜉	𝜕𝜉	VERB
fumecheng-12619	117	1	+	+	NOUN
fumecheng-12619	117	2	𝛼5𝑤	𝛼5𝑤	PROPN
fumecheng-12619	117	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	117	4	�	�	PROPN
fumecheng-12619	117	5	̅	̅	NOUN
fumecheng-12619	117	6	�	�	PROPN
fumecheng-12619	117	7	𝜕	𝜕	PROPN
fumecheng-12619	117	8	�	�	PROPN
fumecheng-12619	117	9	̅	̅	NOUN
fumecheng-12619	117	10	�	�	NOUN
fumecheng-12619	117	11	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	117	12	+	+	NUM
fumecheng-12619	117	13	𝛼6𝑤	𝛼6𝑤	NUM
fumecheng-12619	117	14	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	117	15	𝜕	𝜕	PROPN
fumecheng-12619	117	16	�	�	PROPN
fumecheng-12619	117	17	̅	̅	NOUN
fumecheng-12619	117	18	�	�	NOUN
fumecheng-12619	117	19	𝜕𝜉	𝜕𝜉	VERB
fumecheng-12619	117	20	+	+	CCONJ
fumecheng-12619	117	21	𝛼7𝑤	𝛼7𝑤	PROPN
fumecheng-12619	117	22	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	117	23	𝜕3	𝜕3	NOUN
fumecheng-12619	117	24	�	�	NOUN
fumecheng-12619	117	25	̅	̅	NOUN
fumecheng-12619	117	26	�	�	NOUN
fumecheng-12619	117	27	𝜕𝜉3	𝜕𝜉3	NOUN
fumecheng-12619	117	28	+	+	CCONJ
fumecheng-12619	117	29	𝛼8𝑤	𝛼8𝑤	NUM
fumecheng-12619	117	30	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	117	31	𝜕3	𝜕3	NOUN
fumecheng-12619	117	32	�	�	NOUN
fumecheng-12619	117	33	̅	̅	NOUN
fumecheng-12619	117	34	�	�	NOUN
fumecheng-12619	117	35	𝜕𝜉𝜕𝜃2	𝜕𝜉𝜕𝜃2	NOUN
fumecheng-12619	117	36	+	+	PROPN
fumecheng-12619	117	37	𝛼9𝑤	𝛼9𝑤	PROPN
fumecheng-12619	117	38	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	117	39	𝜕	𝜕	PROPN
fumecheng-12619	117	40	�	�	PROPN
fumecheng-12619	117	41	̅	̅	NOUN
fumecheng-12619	117	42	�	�	NOUN
fumecheng-12619	117	43	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	117	44	(	(	PUNCT
fumecheng-12619	117	45	𝜕	𝜕	NOUN
fumecheng-12619	117	46	�	�	NOUN
fumecheng-12619	117	47	̅	̅	NOUN
fumecheng-12619	117	48	�	�	NOUN
fumecheng-12619	117	49	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	117	50	)	)	PUNCT
fumecheng-12619	117	51	2	2	NUM
fumecheng-12619	118	1	+	+	CCONJ
fumecheng-12619	118	2	𝛼10𝑤	𝛼10𝑤	NUM
fumecheng-12619	118	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	118	4	𝜕	𝜕	PROPN
fumecheng-12619	118	5	�	�	PROPN
fumecheng-12619	118	6	̅	̅	NOUN
fumecheng-12619	118	7	�	�	NOUN
fumecheng-12619	118	8	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	118	9	(	(	PUNCT
fumecheng-12619	118	10	𝜕	𝜕	NOUN
fumecheng-12619	118	11	�	�	NOUN
fumecheng-12619	118	12	̅	̅	NOUN
fumecheng-12619	118	13	�	�	NOUN
fumecheng-12619	118	14	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	118	15	)	)	PUNCT
fumecheng-12619	118	16	2	2	NUM
fumecheng-12619	119	1	+	+	NUM
fumecheng-12619	119	2	𝛼11𝑤	𝛼11𝑤	NUM
fumecheng-12619	119	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	119	4	𝜕3	𝜕3	NOUN
fumecheng-12619	119	5	�	�	NOUN
fumecheng-12619	119	6	̅	̅	NOUN
fumecheng-12619	119	7	�	�	PROPN
fumecheng-12619	119	8	𝜕𝜉𝜕𝜏2	𝜕𝜉𝜕𝜏2	PROPN
fumecheng-12619	119	9	)	)	PUNCT
fumecheng-12619	119	10	𝛿	𝛿	PRON
fumecheng-12619	119	11	�	�	PROPN
fumecheng-12619	119	12	̅	̅	NOUN
fumecheng-12619	119	13	�	�	NOUN
fumecheng-12619	119	14	𝜉	𝜉	NOUN
fumecheng-12619	119	15	|	|	ADV
fumecheng-12619	119	16	|	|	ADV
fumecheng-12619	119	17	0	0	NUM
fumecheng-12619	119	18	1	1	NUM
fumecheng-12619	119	19	=	=	SYM
fumecheng-12619	119	20	0	0	NUM
fumecheng-12619	119	21	,	,	PUNCT
fumecheng-12619	119	22	(	(	PUNCT
fumecheng-12619	119	23	12	12	NUM
fumecheng-12619	119	24	)	)	PUNCT
fumecheng-12619	119	25	𝜕	𝜕	NOUN
fumecheng-12619	119	26	�	�	NOUN
fumecheng-12619	119	27	̅	̅	NOUN
fumecheng-12619	119	28	�	�	NOUN
fumecheng-12619	119	29	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	119	30	=	=	SYM
fumecheng-12619	119	31	0	0	NUM
fumecheng-12619	119	32	:	:	PUNCT
fumecheng-12619	119	33	(	(	PUNCT
fumecheng-12619	119	34	𝛼23𝑤	𝛼23𝑤	PROPN
fumecheng-12619	119	35	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	119	36	𝜕2	𝜕2	NOUN
fumecheng-12619	119	37	�	�	NOUN
fumecheng-12619	119	38	̅	̅	NOUN
fumecheng-12619	119	39	�	�	NOUN
fumecheng-12619	119	40	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	119	41	+	+	CCONJ
fumecheng-12619	119	42	𝛼24𝑤	𝛼24𝑤	NUM
fumecheng-12619	119	43	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	119	44	𝜕2	𝜕2	NOUN
fumecheng-12619	119	45	�	�	NOUN
fumecheng-12619	119	46	̅	̅	NOUN
fumecheng-12619	119	47	�	�	NOUN
fumecheng-12619	119	48	𝜕𝜃2	𝜕𝜃2	ADJ
fumecheng-12619	119	49	+	+	PROPN
fumecheng-12619	119	50	𝛼25𝑤	𝛼25𝑤	PROPN
fumecheng-12619	119	51	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	120	1	+	+	NUM
fumecheng-12619	120	2	𝛼26𝑤	𝛼26𝑤	PROPN
fumecheng-12619	120	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	120	4	𝜕2	𝜕2	NOUN
fumecheng-12619	120	5	�	�	NOUN
fumecheng-12619	120	6	̅	̅	NOUN
fumecheng-12619	120	7	�	�	NOUN
fumecheng-12619	120	8	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	120	9	+	+	PROPN
fumecheng-12619	120	10	𝛼27𝑤	𝛼27𝑤	PROPN
fumecheng-12619	120	11	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	120	12	𝜕2	𝜕2	NOUN
fumecheng-12619	120	13	�	�	NOUN
fumecheng-12619	120	14	̅	̅	NOUN
fumecheng-12619	120	15	�	�	NOUN
fumecheng-12619	120	16	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	120	17	+	+	PROPN
fumecheng-12619	120	18	𝛼28𝑤	𝛼28𝑤	NUM
fumecheng-12619	120	19	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	120	20	𝜕2	𝜕2	NOUN
fumecheng-12619	120	21	�	�	NOUN
fumecheng-12619	120	22	̅	̅	NOUN
fumecheng-12619	120	23	�	�	PROPN
fumecheng-12619	120	24	𝜕𝜏2	𝜕𝜏2	PROPN
fumecheng-12619	120	25	)	)	PUNCT
fumecheng-12619	121	1	𝛿	𝛿	PROPN
fumecheng-12619	121	2	(	(	PUNCT
fumecheng-12619	121	3	𝜕	𝜕	NOUN
fumecheng-12619	121	4	�	�	NOUN
fumecheng-12619	121	5	̅	̅	NOUN
fumecheng-12619	121	6	�	�	NOUN
fumecheng-12619	121	7	𝜉	𝜉	NOUN
fumecheng-12619	121	8	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	121	9	)	)	PUNCT
fumecheng-12619	122	1	|	|	ADV
fumecheng-12619	122	2	|	|	ADV
fumecheng-12619	122	3	0	0	NUM
fumecheng-12619	122	4	1	1	NUM
fumecheng-12619	123	1	+	+	CCONJ
fumecheng-12619	124	1	(	(	PUNCT
fumecheng-12619	124	2	𝛼29𝑤	𝛼29𝑤	NUM
fumecheng-12619	124	3	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	124	4	𝜕2	𝜕2	NOUN
fumecheng-12619	124	5	�	�	NOUN
fumecheng-12619	124	6	̅	̅	NOUN
fumecheng-12619	124	7	�	�	NOUN
fumecheng-12619	124	8	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	124	9	)	)	PUNCT
fumecheng-12619	124	10	𝛿	𝛿	PROPN
fumecheng-12619	124	11	(	(	PUNCT
fumecheng-12619	124	12	𝜕	𝜕	NOUN
fumecheng-12619	124	13	�	�	NOUN
fumecheng-12619	124	14	̅	̅	NOUN
fumecheng-12619	124	15	�	�	NOUN
fumecheng-12619	124	16	𝜃	𝜃	NOUN
fumecheng-12619	124	17	𝜕𝜉	𝜕𝜉	NOUN
fumecheng-12619	124	18	)	)	PUNCT
fumecheng-12619	125	1	|	|	ADV
fumecheng-12619	125	2	0	0	NUM
fumecheng-12619	125	3	2𝜋	2𝜋	NUM
fumecheng-12619	125	4	=	=	SYM
fumecheng-12619	125	5	0	0	NUM
fumecheng-12619	125	6	,	,	PUNCT
fumecheng-12619	125	7	(	(	PUNCT
fumecheng-12619	125	8	13	13	NUM
fumecheng-12619	125	9	)	)	PUNCT
fumecheng-12619	125	10	𝜕	𝜕	NOUN
fumecheng-12619	125	11	�	�	NOUN
fumecheng-12619	125	12	̅	̅	NOUN
fumecheng-12619	125	13	�	�	NOUN
fumecheng-12619	125	14	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	125	15	=	=	SYM
fumecheng-12619	125	16	0	0	NUM
fumecheng-12619	125	17	:	:	PUNCT
fumecheng-12619	125	18	(	(	PUNCT
fumecheng-12619	125	19	𝛼30𝑤	𝛼30𝑤	PROPN
fumecheng-12619	125	20	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	125	21	𝜕2	𝜕2	NOUN
fumecheng-12619	125	22	�	�	NOUN
fumecheng-12619	125	23	̅	̅	NOUN
fumecheng-12619	125	24	�	�	NOUN
fumecheng-12619	125	25	𝜕𝜉𝜕𝜃	𝜕𝜉𝜕𝜃	PROPN
fumecheng-12619	125	26	)	)	PUNCT
fumecheng-12619	125	27	𝛿	𝛿	PROPN
fumecheng-12619	125	28	(	(	PUNCT
fumecheng-12619	125	29	𝜕	𝜕	NOUN
fumecheng-12619	125	30	�	�	NOUN
fumecheng-12619	125	31	̅	̅	NOUN
fumecheng-12619	125	32	�	�	NOUN
fumecheng-12619	125	33	𝜉	𝜉	X
fumecheng-12619	125	34	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	125	35	)	)	PUNCT
fumecheng-12619	126	1	|	|	ADV
fumecheng-12619	126	2	0	0	NUM
fumecheng-12619	126	3	1	1	NUM
fumecheng-12619	126	4	+	+	CCONJ
fumecheng-12619	126	5	(	(	PUNCT
fumecheng-12619	126	6	𝛼31𝑤	𝛼31𝑤	NUM
fumecheng-12619	126	7	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	126	8	𝜕2	𝜕2	NOUN
fumecheng-12619	126	9	�	�	NOUN
fumecheng-12619	126	10	̅	̅	NOUN
fumecheng-12619	126	11	�	�	NOUN
fumecheng-12619	126	12	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	126	13	+	+	CCONJ
fumecheng-12619	126	14	𝛼32𝑤	𝛼32𝑤	PROPN
fumecheng-12619	126	15	𝑏𝑐	𝑏𝑐	ADP
fumecheng-12619	126	16	𝜕2	𝜕2	NOUN
fumecheng-12619	126	17	�	�	NOUN
fumecheng-12619	126	18	̅	̅	NOUN
fumecheng-12619	126	19	�	�	NOUN
fumecheng-12619	126	20	𝜕𝜃2	𝜕𝜃2	ADJ
fumecheng-12619	126	21	+	+	NOUN
fumecheng-12619	126	22	𝛼33𝑤	𝛼33𝑤	NOUN
fumecheng-12619	126	23	𝑏𝑐	𝑏𝑐	NOUN
fumecheng-12619	126	24	+	+	NUM
fumecheng-12619	126	25	𝛼34𝑤	𝛼34𝑤	NUM
fumecheng-12619	126	26	𝑏𝑐	𝑏𝑐	NUM
fumecheng-12619	126	27	𝜕2	𝜕2	NOUN
fumecheng-12619	126	28	�	�	NOUN
fumecheng-12619	126	29	̅	̅	NOUN
fumecheng-12619	126	30	�	�	NOUN
fumecheng-12619	126	31	𝜕𝜉2	𝜕𝜉2	NOUN
fumecheng-12619	126	32	+	+	PROPN
fumecheng-12619	126	33	𝛼35𝑤	𝛼35𝑤	ADJ
fumecheng-12619	126	34	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	126	35	𝜕2	𝜕2	NOUN
fumecheng-12619	126	36	�	�	NOUN
fumecheng-12619	126	37	̅	̅	NOUN
fumecheng-12619	126	38	�	�	NOUN
fumecheng-12619	126	39	𝜕𝜃2	𝜕𝜃2	PROPN
fumecheng-12619	126	40	+	+	CCONJ
fumecheng-12619	126	41	𝛼36𝑤	𝛼36𝑤	NUM
fumecheng-12619	126	42	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	126	43	𝜕2	𝜕2	NOUN
fumecheng-12619	126	44	�	�	NOUN
fumecheng-12619	126	45	̅	̅	NOUN
fumecheng-12619	126	46	�	�	PROPN
fumecheng-12619	126	47	𝜕𝜏2	𝜕𝜏2	PROPN
fumecheng-12619	126	48	)	)	PUNCT
fumecheng-12619	127	1	𝛿	𝛿	PROPN
fumecheng-12619	127	2	(	(	PUNCT
fumecheng-12619	127	3	𝜕	𝜕	NOUN
fumecheng-12619	127	4	�	�	PROPN
fumecheng-12619	127	5	̅	̅	NOUN
fumecheng-12619	127	6	�	�	NOUN
fumecheng-12619	127	7	𝜃	𝜃	NOUN
fumecheng-12619	127	8	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-12619	127	9	)	)	PUNCT
fumecheng-12619	128	1	|	|	ADV
fumecheng-12619	128	2	|	|	ADV
fumecheng-12619	128	3	0	0	NUM
fumecheng-12619	128	4	2𝜋	2𝜋	NUM
fumecheng-12619	128	5	=	=	SYM
fumecheng-12619	128	6	0	0	X
fumecheng-12619	128	7	.	.	PUNCT
fumecheng-12619	129	1	(	(	PUNCT
fumecheng-12619	129	2	14	14	NUM
fumecheng-12619	129	3	)	)	PUNCT
fumecheng-12619	129	4	the	the	DET
fumecheng-12619	129	5	coefficients	coefficient	NOUN
fumecheng-12619	129	6	of	of	ADP
fumecheng-12619	129	7	𝛼𝑙𝑢	𝛼𝑙𝑢	NOUN
fumecheng-12619	129	8	𝑏𝑐(𝑙	𝑏𝑐(𝑙	PUNCT
fumecheng-12619	130	1	=	=	SYM
fumecheng-12619	130	2	1	1	X
fumecheng-12619	130	3	.	.	NUM
fumecheng-12619	130	4	.9	.9	NUM
fumecheng-12619	130	5	)	)	PUNCT
fumecheng-12619	130	6	,	,	PUNCT
fumecheng-12619	130	7	𝛼𝑚𝑣	𝛼𝑚𝑣	PROPN
fumecheng-12619	130	8	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	130	9	(	(	PUNCT
fumecheng-12619	130	10	𝑚	𝑚	X
fumecheng-12619	130	11	=	=	SYM
fumecheng-12619	130	12	1	1	NUM
fumecheng-12619	130	13	.	.	NUM
fumecheng-12619	130	14	.9	.9	NUM
fumecheng-12619	130	15	)	)	PUNCT
fumecheng-12619	130	16	and	and	CCONJ
fumecheng-12619	130	17	𝛼𝑛𝑤	𝛼𝑛𝑤	NOUN
fumecheng-12619	131	1	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	131	2	(	(	PUNCT
fumecheng-12619	131	3	𝑛	𝑛	NOUN
fumecheng-12619	131	4	=	=	SYM
fumecheng-12619	131	5	1	1	NUM
fumecheng-12619	131	6	.	.	NOUN
fumecheng-12619	131	7	.36	.36	NUM
fumecheng-12619	131	8	)	)	PUNCT
fumecheng-12619	131	9	are	be	AUX
fumecheng-12619	131	10	defined	define	VERB
fumecheng-12619	131	11	in	in	ADP
fumecheng-12619	131	12	hashemi	hashemi	PROPN
fumecheng-12619	131	13	kachapi	kachapi	PROPN
fumecheng-12619	131	14	et	et	PROPN
fumecheng-12619	131	15	al	al	PROPN
fumecheng-12619	132	1	[	[	X
fumecheng-12619	132	2	20	20	NUM
fumecheng-12619	132	3	]	]	PUNCT
fumecheng-12619	132	4	.	.	PUNCT
fumecheng-12619	133	1	utilizing	utilize	VERB
fumecheng-12619	133	2	the	the	DET
fumecheng-12619	133	3	lsqcurvefit	lsqcurvefit	NOUN
fumecheng-12619	133	4	function	function	NOUN
fumecheng-12619	133	5	within	within	ADP
fumecheng-12619	133	6	the	the	DET
fumecheng-12619	133	7	matlab	matlab	PROPN
fumecheng-12619	133	8	toolbox	toolbox	NOUN
fumecheng-12619	133	9	,	,	PUNCT
fumecheng-12619	133	10	a	a	DET
fumecheng-12619	133	11	nonlinear	nonlinear	ADJ
fumecheng-12619	133	12	leastsquares	leastsquare	NOUN
fumecheng-12619	133	13	curve	curve	NOUN
fumecheng-12619	133	14	-	-	PUNCT
fumecheng-12619	133	15	fitting	fit	VERB
fumecheng-12619	133	16	technique	technique	NOUN
fumecheng-12619	133	17	,	,	PUNCT
fumecheng-12619	133	18	the	the	DET
fumecheng-12619	133	19	electrostatic	electrostatic	ADJ
fumecheng-12619	133	20	force	force	NOUN
fumecheng-12619	133	21	in	in	ADP
fumecheng-12619	133	22	eq	eq	ADP
fumecheng-12619	133	23	.	.	PUNCT
fumecheng-12619	134	1	(	(	PUNCT
fumecheng-12619	134	2	6	6	NUM
fumecheng-12619	134	3	)	)	PUNCT
fumecheng-12619	134	4	is	be	AUX
fumecheng-12619	134	5	approximated	approximate	VERB
fumecheng-12619	134	6	as	as	ADP
fumecheng-12619	134	7	a	a	DET
fumecheng-12619	134	8	polynomial	polynomial	NOUN
fumecheng-12619	134	9	.	.	PUNCT
fumecheng-12619	135	1	consequently	consequently	ADV
fumecheng-12619	135	2	,	,	PUNCT
fumecheng-12619	135	3	the	the	DET
fumecheng-12619	135	4	dimensionless	dimensionless	NOUN
fumecheng-12619	135	5	work	work	NOUN
fumecheng-12619	135	6	performed	perform	VERB
fumecheng-12619	135	7	by	by	ADP
fumecheng-12619	135	8	the	the	DET
fumecheng-12619	135	9	electrostatic	electrostatic	ADJ
fumecheng-12619	135	10	force	force	NOUN
fumecheng-12619	135	11	can	can	AUX
fumecheng-12619	135	12	be	be	AUX
fumecheng-12619	135	13	represented	represent	VERB
fumecheng-12619	135	14	as	as	ADP
fumecheng-12619	135	15	:	:	PUNCT
fumecheng-12619	135	16	𝛿𝑊𝑒	𝛿𝑊𝑒	NOUN
fumecheng-12619	135	17	=	=	PUNCT
fumecheng-12619	135	18	∫	∫	PROPN
fumecheng-12619	135	19	∫	∫	PROPN
fumecheng-12619	135	20	{	{	PUNCT
fumecheng-12619	135	21	∫	∫	PROPN
fumecheng-12619	135	22	(	(	PUNCT
fumecheng-12619	135	23	�	�	PROPN
fumecheng-12619	135	24	̅	̅	NOUN
fumecheng-12619	135	25	�	�	NOUN
fumecheng-12619	135	26	𝑒(	𝑒(	NUM
fumecheng-12619	135	27	�	�	NOUN
fumecheng-12619	135	28	̅	̅	NOUN
fumecheng-12619	135	29	�	�	NOUN
fumecheng-12619	135	30	𝐷𝐶	𝐷𝐶	PROPN
fumecheng-12619	135	31	+	+	CCONJ
fumecheng-12619	135	32	�	�	NOUN
fumecheng-12619	135	33	̅	̅	NOUN
fumecheng-12619	135	34	�	�	NOUN
fumecheng-12619	135	35	𝐴𝐶	𝐴𝐶	PROPN
fumecheng-12619	135	36	cos(ω𝜏	cos(ω𝜏	NOUN
fumecheng-12619	135	37	)	)	PUNCT
fumecheng-12619	135	38	)	)	PUNCT
fumecheng-12619	135	39	2	2	NUM
fumecheng-12619	135	40	×	×	NOUN
fumecheng-12619	135	41	(	(	PUNCT
fumecheng-12619	135	42	𝐶1̅	𝐶1̅	ADV
fumecheng-12619	135	43	+	+	ADJ
fumecheng-12619	135	44	𝐶2̅	𝐶2̅	NUM
fumecheng-12619	135	45	�	�	NOUN
fumecheng-12619	135	46	̅	̅	NOUN
fumecheng-12619	135	47	�	�	NOUN
fumecheng-12619	135	48	+	+	SYM
fumecheng-12619	135	49	𝐶3̅	𝐶3̅	NOUN
fumecheng-12619	135	50	�	�	NOUN
fumecheng-12619	135	51	̅	̅	NOUN
fumecheng-12619	135	52	�	�	NOUN
fumecheng-12619	135	53	2	2	NUM
fumecheng-12619	135	54	+	+	NOUN
fumecheng-12619	135	55	⋯+	⋯+	NOUN
fumecheng-12619	135	56	𝐶	𝐶	PROPN
fumecheng-12619	135	57	�	�	PROPN
fumecheng-12619	135	58	̅	̅	NOUN
fumecheng-12619	135	59	�	�	NOUN
fumecheng-12619	135	60	�	�	NOUN
fumecheng-12619	135	61	̅	̅	NOUN
fumecheng-12619	135	62	�	�	PROPN
fumecheng-12619	135	63	𝑛−1	𝑛−1	NUM
fumecheng-12619	135	64	)	)	PUNCT
fumecheng-12619	135	65	)	)	PUNCT
fumecheng-12619	135	66	�	�	PROPN
fumecheng-12619	135	67	̅	̅	NOUN
fumecheng-12619	135	68	�	�	PROPN
fumecheng-12619	135	69	0	0	NUM
fumecheng-12619	135	70	𝛿	𝛿	PROPN
fumecheng-12619	135	71	�	�	PROPN
fumecheng-12619	135	72	̅	̅	NOUN
fumecheng-12619	135	73	�	�	NOUN
fumecheng-12619	135	74	}	}	PUNCT
fumecheng-12619	135	75	2𝜋	2𝜋	NOUN
fumecheng-12619	135	76	0	0	X
fumecheng-12619	135	77	𝐿	𝐿	PROPN
fumecheng-12619	135	78	0	0	NUM
fumecheng-12619	135	79	𝛿𝜃𝛿𝜉	𝛿𝜃𝛿𝜉	NOUN
fumecheng-12619	135	80	(	(	PUNCT
fumecheng-12619	135	81	15	15	NUM
fumecheng-12619	135	82	)	)	PUNCT
fumecheng-12619	135	83	which	which	PRON
fumecheng-12619	135	84	𝐶1̅	𝐶1̅	ADV
fumecheng-12619	135	85	−	−	PROPN
fumecheng-12619	135	86	𝐶	𝐶	PROPN
fumecheng-12619	135	87	�	�	PROPN
fumecheng-12619	135	88	̅	̅	NOUN
fumecheng-12619	135	89	�	�	NOUN
fumecheng-12619	135	90	are	be	AUX
fumecheng-12619	135	91	constant	constant	ADJ
fumecheng-12619	135	92	.	.	PUNCT
fumecheng-12619	136	1	2.2	2.2	NUM
fumecheng-12619	136	2	.	.	PUNCT
fumecheng-12619	136	3	solution	solution	NOUN
fumecheng-12619	136	4	procedure	procedure	NOUN
fumecheng-12619	136	5	to	to	PART
fumecheng-12619	136	6	transform	transform	VERB
fumecheng-12619	136	7	the	the	DET
fumecheng-12619	136	8	governing	govern	VERB
fumecheng-12619	136	9	partial	partial	ADJ
fumecheng-12619	136	10	differential	differential	ADJ
fumecheng-12619	136	11	equations	equation	NOUN
fumecheng-12619	136	12	into	into	ADP
fumecheng-12619	136	13	a	a	DET
fumecheng-12619	136	14	set	set	NOUN
fumecheng-12619	136	15	of	of	ADP
fumecheng-12619	136	16	ordinary	ordinary	ADJ
fumecheng-12619	136	17	differential	differential	ADJ
fumecheng-12619	136	18	equations	equation	NOUN
fumecheng-12619	136	19	,	,	PUNCT
fumecheng-12619	136	20	the	the	DET
fumecheng-12619	136	21	galerkin	galerkin	ADJ
fumecheng-12619	136	22	method	method	NOUN
fumecheng-12619	136	23	is	be	AUX
fumecheng-12619	136	24	employed	employ	VERB
fumecheng-12619	136	25	.	.	PUNCT
fumecheng-12619	137	1	the	the	DET
fumecheng-12619	137	2	displacement	displacement	ADJ
fumecheng-12619	137	3	field	field	NOUN
fumecheng-12619	137	4	is	be	AUX
fumecheng-12619	137	5	approximated	approximate	VERB
fumecheng-12619	137	6	using	use	VERB
fumecheng-12619	137	7	a	a	DET
fumecheng-12619	137	8	series	series	NOUN
fumecheng-12619	137	9	expansion	expansion	NOUN
fumecheng-12619	137	10	of	of	ADP
fumecheng-12619	137	11	generalized	generalized	ADJ
fumecheng-12619	137	12	coordinates	coordinate	NOUN
fumecheng-12619	137	13	and	and	CCONJ
fumecheng-12619	137	14	mode	mode	NOUN
fumecheng-12619	137	15	functions	function	NOUN
fumecheng-12619	137	16	,	,	PUNCT
fumecheng-12619	137	17	as	as	SCONJ
fumecheng-12619	137	18	follows	follow	VERB
fumecheng-12619	137	19	[	[	X
fumecheng-12619	137	20	28	28	NUM
fumecheng-12619	137	21	]	]	X
fumecheng-12619	137	22	:	:	PUNCT
fumecheng-12619	137	23	comparison	comparison	NOUN
fumecheng-12619	137	24	of	of	ADP
fumecheng-12619	137	25	nonclassical	nonclassical	ADJ
fumecheng-12619	137	26	controllers	controller	NOUN
fumecheng-12619	137	27	on	on	ADP
fumecheng-12619	137	28	nonlinear	nonlinear	ADJ
fumecheng-12619	137	29	vibrations	vibration	NOUN
fumecheng-12619	137	30	analysis	analysis	NOUN
fumecheng-12619	137	31	of	of	ADP
fumecheng-12619	137	32	piezoelectric	piezoelectric	NOUN
fumecheng-12619	137	33	...	...	PUNCT
fumecheng-12619	137	34	317	317	NUM
fumecheng-12619	137	35	[	[	PUNCT
fumecheng-12619	137	36	𝑢(𝑥	𝑢(𝑥	PROPN
fumecheng-12619	137	37	,	,	PUNCT
fumecheng-12619	137	38	𝜃	𝜃	NOUN
fumecheng-12619	137	39	,	,	PUNCT
fumecheng-12619	137	40	𝑡	𝑡	NOUN
fumecheng-12619	137	41	)	)	PUNCT
fumecheng-12619	137	42	𝑣(𝑥	𝑣(𝑥	PROPN
fumecheng-12619	137	43	,	,	PUNCT
fumecheng-12619	137	44	𝜃	𝜃	NOUN
fumecheng-12619	137	45	,	,	PUNCT
fumecheng-12619	137	46	𝑡	𝑡	NOUN
fumecheng-12619	137	47	)	)	PUNCT
fumecheng-12619	137	48	𝑤(𝑥	𝑤(𝑥	NOUN
fumecheng-12619	137	49	,	,	PUNCT
fumecheng-12619	137	50	𝜃	𝜃	NOUN
fumecheng-12619	137	51	,	,	PUNCT
fumecheng-12619	137	52	𝑡	𝑡	NOUN
fumecheng-12619	137	53	)	)	PUNCT
fumecheng-12619	137	54	]	]	PUNCT
fumecheng-12619	138	1	=	=	PUNCT
fumecheng-12619	138	2	∑	∑	PUNCT
fumecheng-12619	138	3	∑	∑	PUNCT
fumecheng-12619	138	4	[	[	PUNCT
fumecheng-12619	138	5	[	[	PUNCT
fumecheng-12619	138	6	𝑢𝑚,𝑗,𝑐(𝜏	𝑢𝑚,𝑗,𝑐(𝜏	NUM
fumecheng-12619	138	7	)	)	PUNCT
fumecheng-12619	138	8	cos(𝑗𝜃	cos(𝑗𝜃	NOUN
fumecheng-12619	138	9	)	)	PUNCT
fumecheng-12619	138	10	+	+	ADJ
fumecheng-12619	138	11	𝑢𝑚,𝑗,𝑠(𝜏	𝑢𝑚,𝑗,𝑠(𝜏	ADJ
fumecheng-12619	138	12	)	)	PUNCT
fumecheng-12619	138	13	sin(𝑗𝜃	sin(𝑗𝜃	NOUN
fumecheng-12619	138	14	)	)	PUNCT
fumecheng-12619	138	15	]	]	PUNCT
fumecheng-12619	139	1	𝜒𝑚𝑗(𝜉	𝜒𝑚𝑗(𝜉	X
fumecheng-12619	139	2	)	)	PUNCT
fumecheng-12619	139	3	[	[	PUNCT
fumecheng-12619	139	4	𝑣𝑚,𝑗,𝑐(𝜏	𝑣𝑚,𝑗,𝑐(𝜏	NUM
fumecheng-12619	139	5	)	)	PUNCT
fumecheng-12619	139	6	sin(𝑗𝜃	sin(𝑗𝜃	NOUN
fumecheng-12619	139	7	)	)	PUNCT
fumecheng-12619	139	8	+	+	ADJ
fumecheng-12619	139	9	𝑣𝑚,𝑗,𝑠(𝜏	𝑣𝑚,𝑗,𝑠(𝜏	ADJ
fumecheng-12619	139	10	)	)	PUNCT
fumecheng-12619	139	11	cos(𝑗𝜃	cos(𝑗𝜃	NOUN
fumecheng-12619	139	12	)	)	PUNCT
fumecheng-12619	139	13	]	]	PUNCT
fumecheng-12619	140	1	𝜙𝑚𝑗(𝜉	𝜙𝑚𝑗(𝜉	X
fumecheng-12619	140	2	)	)	PUNCT
fumecheng-12619	140	3	[	[	PUNCT
fumecheng-12619	140	4	𝑤𝑚,𝑗,𝑐(𝜏	𝑤𝑚,𝑗,𝑐(𝜏	NOUN
fumecheng-12619	140	5	)	)	PUNCT
fumecheng-12619	140	6	cos(𝑗𝜃	cos(𝑗𝜃	NOUN
fumecheng-12619	140	7	)	)	PUNCT
fumecheng-12619	140	8	+	+	NOUN
fumecheng-12619	140	9	𝑤𝑚,𝑗,𝑠(𝜏	𝑤𝑚,𝑗,𝑠(𝜏	ADJ
fumecheng-12619	140	10	)	)	PUNCT
fumecheng-12619	140	11	sin(𝑗𝜃	sin(𝑗𝜃	NOUN
fumecheng-12619	140	12	)	)	PUNCT
fumecheng-12619	140	13	]	]	PUNCT
fumecheng-12619	141	1	𝛽𝑚𝑗(𝜉	𝛽𝑚𝑗(𝜉	PROPN
fumecheng-12619	141	2	)	)	PUNCT
fumecheng-12619	141	3	]	]	PUNCT
fumecheng-12619	142	1	𝑁	𝑁	PROPN
fumecheng-12619	142	2	𝑗=1	𝑗=1	PROPN
fumecheng-12619	142	3	𝑀1	𝑀1	ADV
fumecheng-12619	142	4	𝑚=1	𝑚=1	PUNCT
fumecheng-12619	143	1	+	+	CCONJ
fumecheng-12619	143	2	∑	∑	PROPN
fumecheng-12619	143	3	[	[	PUNCT
fumecheng-12619	143	4	𝑢𝑚,0(𝜏)𝜒𝑚0(𝜉	𝑢𝑚,0(𝜏)𝜒𝑚0(𝜉	ADJ
fumecheng-12619	143	5	)	)	PUNCT
fumecheng-12619	143	6	𝑣𝑚,0(𝜏)𝜙𝑚0(𝜉	𝑣𝑚,0(𝜏)𝜙𝑚0(𝜉	NOUN
fumecheng-12619	143	7	)	)	PUNCT
fumecheng-12619	143	8	𝑤𝑚,0(𝜏)𝛽𝑚0(𝜉	𝑤𝑚,0(𝜏)𝛽𝑚0(𝜉	NUM
fumecheng-12619	143	9	)	)	PUNCT
fumecheng-12619	143	10	]	]	PUNCT
fumecheng-12619	143	11	𝑀2	𝑀2	PROPN
fumecheng-12619	143	12	𝑚=1	𝑚=1	X
fumecheng-12619	143	13	=	=	SYM
fumecheng-12619	143	14	∑	∑	PUNCT
fumecheng-12619	143	15	[	[	PUNCT
fumecheng-12619	143	16	𝑢𝑖(𝜏)𝜒𝑖(𝜉)𝜗𝑖(𝜃	𝑢𝑖(𝜏)𝜒𝑖(𝜉)𝜗𝑖(𝜃	PROPN
fumecheng-12619	143	17	)	)	PUNCT
fumecheng-12619	143	18	𝑣𝑟(𝜏)𝜙𝑟(𝜉)𝛼𝑟(𝜃	𝑣𝑟(𝜏)𝜙𝑟(𝜉)𝛼𝑟(𝜃	ADJ
fumecheng-12619	143	19	)	)	PUNCT
fumecheng-12619	143	20	𝑤𝑠(𝜏)𝛽𝑠(𝜉)𝜓𝑠(𝜃	𝑤𝑠(𝜏)𝛽𝑠(𝜉)𝜓𝑠(𝜃	NOUN
fumecheng-12619	143	21	)	)	PUNCT
fumecheng-12619	143	22	]	]	PUNCT
fumecheng-12619	143	23	𝑀2+𝑀1×𝑁	𝑀2+𝑀1×𝑁	NOUN
fumecheng-12619	143	24	(	(	PUNCT
fumecheng-12619	143	25	𝑖,𝑟,𝑠)=1	𝑖,𝑟,𝑠)=1	PROPN
fumecheng-12619	143	26	(	(	PUNCT
fumecheng-12619	143	27	16	16	NUM
fumecheng-12619	143	28	)	)	PUNCT
fumecheng-12619	143	29	in	in	ADP
fumecheng-12619	143	30	the	the	DET
fumecheng-12619	143	31	galerkin	galerkin	ADJ
fumecheng-12619	143	32	method	method	NOUN
fumecheng-12619	143	33	,	,	PUNCT
fumecheng-12619	143	34	the	the	DET
fumecheng-12619	143	35	trial	trial	NOUN
fumecheng-12619	143	36	functions	function	NOUN
fumecheng-12619	143	37	,	,	PUNCT
fumecheng-12619	143	38	𝜒𝑖(𝜉	𝜒𝑖(𝜉	NUM
fumecheng-12619	143	39	)	)	PUNCT
fumecheng-12619	143	40	,	,	PUNCT
fumecheng-12619	143	41	𝜙𝑟(𝜉	𝜙𝑟(𝜉	NUM
fumecheng-12619	143	42	)	)	PUNCT
fumecheng-12619	143	43	and	and	CCONJ
fumecheng-12619	143	44	𝛽𝑠(𝜉	𝛽𝑠(𝜉	NUM
fumecheng-12619	143	45	)	)	PUNCT
fumecheng-12619	143	46	,	,	PUNCT
fumecheng-12619	143	47	must	must	AUX
fumecheng-12619	143	48	satisfy	satisfy	VERB
fumecheng-12619	143	49	all	all	DET
fumecheng-12619	143	50	geometric	geometric	ADJ
fumecheng-12619	143	51	and	and	CCONJ
fumecheng-12619	143	52	natural	natural	ADJ
fumecheng-12619	143	53	boundary	boundary	ADJ
fumecheng-12619	143	54	conditions	condition	NOUN
fumecheng-12619	143	55	.	.	PUNCT
fumecheng-12619	144	1	substituting	substitute	VERB
fumecheng-12619	144	2	eq	eq	ADP
fumecheng-12619	144	3	.	.	PUNCT
fumecheng-12619	145	1	(	(	PUNCT
fumecheng-12619	145	2	16	16	NUM
fumecheng-12619	145	3	)	)	PUNCT
fumecheng-12619	145	4	into	into	ADP
fumecheng-12619	145	5	eqs	eqs	PROPN
fumecheng-12619	145	6	.	.	PUNCT
fumecheng-12619	146	1	(	(	PUNCT
fumecheng-12619	146	2	7	7	NUM
fumecheng-12619	146	3	-	-	SYM
fumecheng-12619	146	4	14	14	NUM
fumecheng-12619	146	5	)	)	PUNCT
fumecheng-12619	146	6	and	and	CCONJ
fumecheng-12619	146	7	applying	apply	VERB
fumecheng-12619	146	8	the	the	DET
fumecheng-12619	146	9	galerkin	galerkin	ADJ
fumecheng-12619	146	10	procedure	procedure	NOUN
fumecheng-12619	146	11	yields	yield	VERB
fumecheng-12619	146	12	the	the	DET
fumecheng-12619	146	13	reduced	reduce	VERB
fumecheng-12619	146	14	-	-	PUNCT
fumecheng-12619	146	15	order	order	NOUN
fumecheng-12619	146	16	equation	equation	NOUN
fumecheng-12619	146	17	of	of	ADP
fumecheng-12619	146	18	motion	motion	NOUN
fumecheng-12619	146	19	:	:	PUNCT
fumecheng-12619	147	1	[	[	X
fumecheng-12619	147	2	(	(	PUNCT
fumecheng-12619	147	3	𝐾)𝑢	𝐾)𝑢	X
fumecheng-12619	147	4	𝑢	𝑢	X
fumecheng-12619	147	5	+	+	X
fumecheng-12619	147	6	(	(	PUNCT
fumecheng-12619	147	7	𝐾𝑏𝑐)𝑢	𝐾𝑏𝑐)𝑢	PROPN
fumecheng-12619	147	8	𝑢]{	𝑢]{	NOUN
fumecheng-12619	147	9	�	�	PROPN
fumecheng-12619	147	10	̅	̅	NOUN
fumecheng-12619	147	11	�	�	NOUN
fumecheng-12619	147	12	}	}	PUNCT
fumecheng-12619	147	13	+	+	CCONJ
fumecheng-12619	148	1	[	[	X
fumecheng-12619	148	2	(	(	PUNCT
fumecheng-12619	148	3	𝐾)𝑢	𝐾)𝑢	NOUN
fumecheng-12619	148	4	𝑣	𝑣	X
fumecheng-12619	148	5	+	+	CCONJ
fumecheng-12619	148	6	(	(	PUNCT
fumecheng-12619	148	7	𝐾𝑏𝑐)𝑢	𝐾𝑏𝑐)𝑢	NOUN
fumecheng-12619	148	8	𝑣	𝑣	X
fumecheng-12619	148	9	]	]	X
fumecheng-12619	148	10	{	{	PUNCT
fumecheng-12619	148	11	�	�	NOUN
fumecheng-12619	148	12	̅	̅	NOUN
fumecheng-12619	148	13	�	�	NOUN
fumecheng-12619	148	14	}	}	PUNCT
fumecheng-12619	148	15	+	+	CCONJ
fumecheng-12619	149	1	[	[	X
fumecheng-12619	149	2	(	(	PUNCT
fumecheng-12619	149	3	𝐾)𝑢	𝐾)𝑢	PRON
fumecheng-12619	149	4	𝑤	𝑤	SYM
fumecheng-12619	149	5	+	+	CCONJ
fumecheng-12619	149	6	(	(	PUNCT
fumecheng-12619	149	7	𝐾𝑏𝑐)𝑢	𝐾𝑏𝑐)𝑢	PROPN
fumecheng-12619	149	8	𝑤]{	𝑤]{	NOUN
fumecheng-12619	149	9	�	�	PROPN
fumecheng-12619	149	10	̅	̅	NOUN
fumecheng-12619	149	11	�	�	NOUN
fumecheng-12619	149	12	}	}	PUNCT
fumecheng-12619	149	13	+	+	CCONJ
fumecheng-12619	149	14	[	[	X
fumecheng-12619	149	15	(	(	PUNCT
fumecheng-12619	149	16	𝑁𝐿)𝑢	𝑁𝐿)𝑢	X
fumecheng-12619	149	17	𝑤	𝑤	PART
fumecheng-12619	149	18	+	+	CCONJ
fumecheng-12619	149	19	(	(	PUNCT
fumecheng-12619	149	20	𝑁𝐿𝑏𝑐)𝑢	𝑁𝐿𝑏𝑐)𝑢	NOUN
fumecheng-12619	149	21	𝑤]{	𝑤]{	PRON
fumecheng-12619	149	22	�	�	NOUN
fumecheng-12619	149	23	̅	̅	NOUN
fumecheng-12619	149	24	�	�	NOUN
fumecheng-12619	149	25	2	2	NUM
fumecheng-12619	149	26	}	}	PUNCT
fumecheng-12619	149	27	=	=	SYM
fumecheng-12619	150	1	[	[	X
fumecheng-12619	150	2	(	(	PUNCT
fumecheng-12619	150	3	𝑀)𝑢	𝑀)𝑢	ADJ
fumecheng-12619	150	4	𝑢]{	𝑢]{	NOUN
fumecheng-12619	150	5	�	�	PROPN
fumecheng-12619	150	6	̈̅	̈̅	PROPN
fumecheng-12619	150	7	�	�	PROPN
fumecheng-12619	150	8	}	}	PUNCT
fumecheng-12619	150	9	+	+	NOUN
fumecheng-12619	150	10	�	�	NOUN
fumecheng-12619	150	11	̅	̅	NOUN
fumecheng-12619	150	12	�	�	NOUN
fumecheng-12619	150	13	𝑢𝑝	𝑢𝑝	NOUN
fumecheng-12619	150	14	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	150	15	,	,	PUNCT
fumecheng-12619	150	16	(	(	PUNCT
fumecheng-12619	150	17	17	17	NUM
fumecheng-12619	150	18	)	)	PUNCT
fumecheng-12619	151	1	[	[	X
fumecheng-12619	151	2	(	(	PUNCT
fumecheng-12619	151	3	𝐾)𝑣	𝐾)𝑣	ADJ
fumecheng-12619	151	4	𝑢	𝑢	X
fumecheng-12619	151	5	+	+	X
fumecheng-12619	151	6	(	(	PUNCT
fumecheng-12619	151	7	𝐾𝑏𝑐)𝑣	𝐾𝑏𝑐)𝑣	ADJ
fumecheng-12619	151	8	𝑢]{	𝑢]{	NOUN
fumecheng-12619	151	9	�	�	PROPN
fumecheng-12619	151	10	̅	̅	NOUN
fumecheng-12619	151	11	�	�	NOUN
fumecheng-12619	151	12	}	}	PUNCT
fumecheng-12619	151	13	+	+	CCONJ
fumecheng-12619	151	14	[	[	X
fumecheng-12619	151	15	(	(	PUNCT
fumecheng-12619	151	16	𝐾)𝑣	𝐾)𝑣	ADJ
fumecheng-12619	151	17	𝑣	𝑣	X
fumecheng-12619	151	18	+	+	CCONJ
fumecheng-12619	151	19	(	(	PUNCT
fumecheng-12619	151	20	𝐾𝑏𝑐)𝑣	𝐾𝑏𝑐)𝑣	ADJ
fumecheng-12619	151	21	𝑣]{𝑣	𝑣]{𝑣	NOUN
fumecheng-12619	151	22	}	}	PUNCT
fumecheng-12619	151	23	+	+	CCONJ
fumecheng-12619	152	1	[	[	X
fumecheng-12619	152	2	(	(	PUNCT
fumecheng-12619	152	3	𝐾)𝑣	𝐾)𝑣	X
fumecheng-12619	152	4	𝑤	𝑤	PART
fumecheng-12619	152	5	+	+	CCONJ
fumecheng-12619	152	6	(	(	PUNCT
fumecheng-12619	152	7	𝐾𝑏𝑐)𝑣	𝐾𝑏𝑐)𝑣	ADJ
fumecheng-12619	152	8	𝑤]{	𝑤]{	NOUN
fumecheng-12619	152	9	�	�	PROPN
fumecheng-12619	152	10	̅	̅	NOUN
fumecheng-12619	152	11	�	�	NOUN
fumecheng-12619	152	12	}	}	PUNCT
fumecheng-12619	152	13	+	+	CCONJ
fumecheng-12619	152	14	[	[	X
fumecheng-12619	152	15	(	(	PUNCT
fumecheng-12619	152	16	𝑁𝐿)𝑣	𝑁𝐿)𝑣	NOUN
fumecheng-12619	152	17	𝑤	𝑤	PART
fumecheng-12619	152	18	+	+	CCONJ
fumecheng-12619	152	19	(	(	PUNCT
fumecheng-12619	152	20	𝑁𝐿𝑏𝑐)𝑣	𝑁𝐿𝑏𝑐)𝑣	VERB
fumecheng-12619	152	21	𝑤]{	𝑤]{	NOUN
fumecheng-12619	152	22	�	�	PROPN
fumecheng-12619	152	23	̅	̅	NOUN
fumecheng-12619	152	24	�	�	NOUN
fumecheng-12619	152	25	2	2	NUM
fumecheng-12619	152	26	}	}	PUNCT
fumecheng-12619	152	27	=	=	SYM
fumecheng-12619	153	1	[	[	X
fumecheng-12619	153	2	(	(	PUNCT
fumecheng-12619	153	3	𝑀)𝑣	𝑀)𝑣	ADJ
fumecheng-12619	153	4	𝑣]{	𝑣]{	NOUN
fumecheng-12619	153	5	�	�	PROPN
fumecheng-12619	153	6	̈̅	̈̅	NOUN
fumecheng-12619	153	7	�	�	PROPN
fumecheng-12619	153	8	}	}	PUNCT
fumecheng-12619	153	9	+	+	NOUN
fumecheng-12619	153	10	�	�	NOUN
fumecheng-12619	153	11	̅	̅	NOUN
fumecheng-12619	153	12	�	�	NOUN
fumecheng-12619	153	13	𝑣𝑝	𝑣𝑝	PRON
fumecheng-12619	153	14	𝑏𝑐	𝑏𝑐	PROPN
fumecheng-12619	153	15	,	,	PUNCT
fumecheng-12619	153	16	(	(	PUNCT
fumecheng-12619	153	17	18	18	NUM
fumecheng-12619	153	18	)	)	PUNCT
fumecheng-12619	153	19	[	[	X
fumecheng-12619	153	20	(	(	PUNCT
fumecheng-12619	153	21	𝐾)𝑤	𝐾)𝑤	NOUN
fumecheng-12619	153	22	𝑢	𝑢	X
fumecheng-12619	153	23	]	]	X
fumecheng-12619	153	24	{	{	PUNCT
fumecheng-12619	153	25	�	�	NOUN
fumecheng-12619	153	26	̅	̅	NOUN
fumecheng-12619	153	27	�	�	NOUN
fumecheng-12619	153	28	}	}	PUNCT
fumecheng-12619	153	29	+	+	CCONJ
fumecheng-12619	153	30	[	[	X
fumecheng-12619	153	31	(	(	PUNCT
fumecheng-12619	153	32	𝐾)𝑤	𝐾)𝑤	ADJ
fumecheng-12619	153	33	𝑣	𝑣	X
fumecheng-12619	153	34	]	]	X
fumecheng-12619	153	35	{	{	PUNCT
fumecheng-12619	153	36	�	�	NOUN
fumecheng-12619	153	37	̅	̅	NOUN
fumecheng-12619	153	38	�	�	NOUN
fumecheng-12619	153	39	}	}	PUNCT
fumecheng-12619	153	40	+	+	CCONJ
fumecheng-12619	153	41	[	[	X
fumecheng-12619	153	42	(	(	PUNCT
fumecheng-12619	153	43	𝐾)𝑤	𝐾)𝑤	NOUN
fumecheng-12619	153	44	𝑤	𝑤	PART
fumecheng-12619	153	45	+	+	X
fumecheng-12619	153	46	(	(	PUNCT
fumecheng-12619	153	47	𝐾𝑏𝑐)𝑤	𝐾𝑏𝑐)𝑤	X
fumecheng-12619	153	48	𝑤	𝑤	PART
fumecheng-12619	153	49	−	−	PROPN
fumecheng-12619	153	50	(	(	PUNCT
fumecheng-12619	153	51	𝐾𝑣𝑝)𝑤	𝐾𝑣𝑝)𝑤	NOUN
fumecheng-12619	153	52	𝑤	𝑤	X
fumecheng-12619	153	53	−	−	PROPN
fumecheng-12619	153	54	(	(	PUNCT
fumecheng-12619	153	55	𝐾𝑒2)𝑤	𝐾𝑒2)𝑤	NOUN
fumecheng-12619	153	56	𝑤	𝑤	PROPN
fumecheng-12619	153	57	]	]	X
fumecheng-12619	153	58	{	{	PUNCT
fumecheng-12619	153	59	�	�	NOUN
fumecheng-12619	153	60	̅	̅	NOUN
fumecheng-12619	153	61	�	�	NOUN
fumecheng-12619	153	62	}	}	PUNCT
fumecheng-12619	153	63	+	+	CCONJ
fumecheng-12619	154	1	[	[	X
fumecheng-12619	154	2	(	(	PUNCT
fumecheng-12619	154	3	𝑁𝐿)𝑤	𝑁𝐿)𝑤	NOUN
fumecheng-12619	154	4	𝑢	𝑢	X
fumecheng-12619	154	5	+	+	X
fumecheng-12619	154	6	(	(	PUNCT
fumecheng-12619	154	7	𝑁𝐿𝑏𝑐)𝑤	𝑁𝐿𝑏𝑐)𝑤	INTJ
fumecheng-12619	154	8	𝑢	𝑢	X
fumecheng-12619	154	9	]	]	X
fumecheng-12619	154	10	{	{	PUNCT
fumecheng-12619	154	11	�	�	NOUN
fumecheng-12619	154	12	̅	̅	NOUN
fumecheng-12619	154	13	�	�	NOUN
fumecheng-12619	154	14	�	�	NOUN
fumecheng-12619	154	15	̅	̅	NOUN
fumecheng-12619	154	16	�	�	NOUN
fumecheng-12619	154	17	}	}	PUNCT
fumecheng-12619	154	18	+	+	CCONJ
fumecheng-12619	154	19	[	[	X
fumecheng-12619	154	20	(	(	PUNCT
fumecheng-12619	154	21	𝑁𝐿)𝑤	𝑁𝐿)𝑤	NOUN
fumecheng-12619	154	22	𝑣	𝑣	X
fumecheng-12619	154	23	+	+	X
fumecheng-12619	154	24	(	(	PUNCT
fumecheng-12619	154	25	𝑁𝐿𝑏𝑐)𝑤	𝑁𝐿𝑏𝑐)𝑤	INTJ
fumecheng-12619	154	26	𝑣	𝑣	X
fumecheng-12619	154	27	]	]	X
fumecheng-12619	154	28	{	{	PUNCT
fumecheng-12619	154	29	�	�	NOUN
fumecheng-12619	154	30	̅	̅	NOUN
fumecheng-12619	154	31	�	�	NOUN
fumecheng-12619	154	32	�	�	NOUN
fumecheng-12619	154	33	̅	̅	NOUN
fumecheng-12619	154	34	�	�	NOUN
fumecheng-12619	154	35	}	}	PUNCT
fumecheng-12619	154	36	+	+	CCONJ
fumecheng-12619	154	37	[	[	X
fumecheng-12619	154	38	(	(	PUNCT
fumecheng-12619	154	39	𝑁𝐿)𝑤2	𝑁𝐿)𝑤2	PROPN
fumecheng-12619	154	40	𝑤	𝑤	ADP
fumecheng-12619	154	41	+	+	CCONJ
fumecheng-12619	154	42	(	(	PUNCT
fumecheng-12619	154	43	𝑁𝐿𝑏𝑐)𝑤2	𝑁𝐿𝑏𝑐)𝑤2	X
fumecheng-12619	154	44	𝑤	𝑤	PART
fumecheng-12619	154	45	−	−	PROPN
fumecheng-12619	154	46	(	(	PUNCT
fumecheng-12619	154	47	𝑁𝐿2𝑒)𝑤2	𝑁𝐿2𝑒)𝑤2	NOUN
fumecheng-12619	154	48	𝑤	𝑤	X
fumecheng-12619	154	49	]	]	X
fumecheng-12619	154	50	{	{	PUNCT
fumecheng-12619	154	51	�	�	NOUN
fumecheng-12619	154	52	̅	̅	NOUN
fumecheng-12619	154	53	�	�	NOUN
fumecheng-12619	154	54	2	2	NUM
fumecheng-12619	154	55	}	}	PUNCT
fumecheng-12619	154	56	+	+	PROPN
fumecheng-12619	154	57	[	[	X
fumecheng-12619	154	58	(	(	PUNCT
fumecheng-12619	154	59	𝑁𝐿)𝑤3	𝑁𝐿)𝑤3	PROPN
fumecheng-12619	154	60	𝑤	𝑤	ADP
fumecheng-12619	154	61	+	+	CCONJ
fumecheng-12619	154	62	(	(	PUNCT
fumecheng-12619	154	63	𝑁𝐿𝑏𝑐)𝑤3	𝑁𝐿𝑏𝑐)𝑤3	NUM
fumecheng-12619	154	64	𝑤	𝑤	PART
fumecheng-12619	154	65	−	−	PROPN
fumecheng-12619	154	66	(	(	PUNCT
fumecheng-12619	154	67	𝑁𝐿3𝑒)𝑤3	𝑁𝐿3𝑒)𝑤3	VERB
fumecheng-12619	154	68	𝑤	𝑤	X
fumecheng-12619	154	69	]	]	X
fumecheng-12619	154	70	{	{	PUNCT
fumecheng-12619	154	71	�	�	NOUN
fumecheng-12619	154	72	̅	̅	NOUN
fumecheng-12619	154	73	�	�	NOUN
fumecheng-12619	154	74	3	3	NUM
fumecheng-12619	154	75	}	}	PUNCT
fumecheng-12619	154	76	=	=	SYM
fumecheng-12619	154	77	(	(	PUNCT
fumecheng-12619	154	78	[	[	X
fumecheng-12619	154	79	(	(	PUNCT
fumecheng-12619	154	80	𝑀)𝑤	𝑀)𝑤	PART
fumecheng-12619	154	81	𝑤	𝑤	ADP
fumecheng-12619	154	82	+	+	CCONJ
fumecheng-12619	154	83	(	(	PUNCT
fumecheng-12619	154	84	𝑀𝑏𝑐)𝑤	𝑀𝑏𝑐)𝑤	CCONJ
fumecheng-12619	154	85	𝑤]){	𝑤]){	SYM
fumecheng-12619	154	86	�	�	NOUN
fumecheng-12619	154	87	̈̅	̈̅	NOUN
fumecheng-12619	154	88	�	�	NOUN
fumecheng-12619	154	89	}	}	PUNCT
fumecheng-12619	154	90	+	+	CCONJ
fumecheng-12619	154	91	(	(	PUNCT
fumecheng-12619	154	92	[	[	X
fumecheng-12619	154	93	(	(	PUNCT
fumecheng-12619	154	94	𝐶)𝑤	𝐶)𝑤	X
fumecheng-12619	154	95	𝑤	𝑤	ADP
fumecheng-12619	154	96	]	]	PUNCT
fumecheng-12619	154	97	+	+	CCONJ
fumecheng-12619	154	98	[	[	X
fumecheng-12619	154	99	(	(	PUNCT
fumecheng-12619	154	100	𝐶𝑏𝑐)𝑤	𝐶𝑏𝑐)𝑤	SYM
fumecheng-12619	154	101	𝑤]){	𝑤]){	NOUN
fumecheng-12619	154	102	�	�	PROPN
fumecheng-12619	154	103	̇̅	̇̅	NOUN
fumecheng-12619	154	104	�	�	NOUN
fumecheng-12619	154	105	}	}	PUNCT
fumecheng-12619	154	106	)	)	PUNCT
fumecheng-12619	155	1	+	+	CCONJ
fumecheng-12619	155	2	�	�	NOUN
fumecheng-12619	155	3	̅	̅	NOUN
fumecheng-12619	155	4	�	�	NOUN
fumecheng-12619	155	5	𝑤𝑝	𝑤𝑝	ADJ
fumecheng-12619	155	6	+	+	NUM
fumecheng-12619	155	7	�	�	NOUN
fumecheng-12619	155	8	̅	̅	NOUN
fumecheng-12619	155	9	�	�	NOUN
fumecheng-12619	155	10	𝑤𝑝	𝑤𝑝	NOUN
fumecheng-12619	155	11	𝑏𝑐	𝑏𝑐	ADP
fumecheng-12619	155	12	−	−	PROPN
fumecheng-12619	155	13	�	�	NOUN
fumecheng-12619	155	14	̅	̅	NOUN
fumecheng-12619	155	15	�	�	NOUN
fumecheng-12619	155	16	𝑤𝑒	𝑤𝑒	PROPN
fumecheng-12619	155	17	−	−	PROPN
fumecheng-12619	155	18	�	�	PROPN
fumecheng-12619	155	19	̅	̅	NOUN
fumecheng-12619	155	20	�	�	NOUN
fumecheng-12619	155	21	𝑒	𝑒	PART
fumecheng-12619	155	22	{	{	PUNCT
fumecheng-12619	155	23	(	(	PUNCT
fumecheng-12619	155	24	(	(	PUNCT
fumecheng-12619	155	25	�	�	NOUN
fumecheng-12619	155	26	̅	̅	NOUN
fumecheng-12619	155	27	�	�	PROPN
fumecheng-12619	155	28	𝐴𝐶cos	𝐴𝐶cos	PROPN
fumecheng-12619	155	29	�	�	PROPN
fumecheng-12619	155	30	̅	̅	NOUN
fumecheng-12619	155	31	�	�	NOUN
fumecheng-12619	155	32	𝜏	𝜏	NOUN
fumecheng-12619	155	33	)	)	PUNCT
fumecheng-12619	155	34	2	2	NUM
fumecheng-12619	155	35	+	+	SYM
fumecheng-12619	155	36	2	2	NUM
fumecheng-12619	155	37	�	�	NOUN
fumecheng-12619	155	38	̅	̅	NOUN
fumecheng-12619	155	39	�	�	PROPN
fumecheng-12619	155	40	𝐴𝐶	𝐴𝐶	PROPN
fumecheng-12619	155	41	�	�	PROPN
fumecheng-12619	155	42	̅	̅	NOUN
fumecheng-12619	155	43	�	�	PROPN
fumecheng-12619	155	44	𝐷𝐶cos	𝐷𝐶cos	PROPN
fumecheng-12619	155	45	�	�	PROPN
fumecheng-12619	155	46	̅	̅	NOUN
fumecheng-12619	155	47	�	�	NOUN
fumecheng-12619	155	48	𝜏	𝜏	NOUN
fumecheng-12619	155	49	)	)	PUNCT
fumecheng-12619	155	50	×	×	NOUN
fumecheng-12619	155	51	(	(	PUNCT
fumecheng-12619	155	52	𝐶4̅(𝑁𝐿𝑒)𝑤3	𝐶4̅(𝑁𝐿𝑒)𝑤3	NOUN
fumecheng-12619	155	53	𝑤	𝑤	ADP
fumecheng-12619	155	54	+	+	NUM
fumecheng-12619	155	55	𝐶3̅(𝑁𝐿𝑒)𝑤2	𝐶3̅(𝑁𝐿𝑒)𝑤2	NOUN
fumecheng-12619	155	56	𝑤	𝑤	NOUN
fumecheng-12619	155	57	+	+	NUM
fumecheng-12619	155	58	𝐶2̅(𝐾𝑒)𝑤	𝐶2̅(𝐾𝑒)𝑤	NOUN
fumecheng-12619	155	59	𝑤	𝑤	ADP
fumecheng-12619	155	60	+	+	CCONJ
fumecheng-12619	155	61	𝐶1̅	𝐶1̅	ADV
fumecheng-12619	155	62	�	�	NOUN
fumecheng-12619	155	63	̅	̅	NOUN
fumecheng-12619	155	64	�	�	NOUN
fumecheng-12619	155	65	1	1	NUM
fumecheng-12619	155	66	)	)	PUNCT
fumecheng-12619	155	67	}	}	PUNCT
fumecheng-12619	155	68	(	(	PUNCT
fumecheng-12619	155	69	19	19	NUM
fumecheng-12619	155	70	)	)	PUNCT
fumecheng-12619	155	71	where	where	SCONJ
fumecheng-12619	155	72	all	all	DET
fumecheng-12619	155	73	coefficients	coefficient	NOUN
fumecheng-12619	155	74	and	and	CCONJ
fumecheng-12619	155	75	phrases	phrase	NOUN
fumecheng-12619	155	76	of	of	ADP
fumecheng-12619	155	77	eqs	eqs	PROPN
fumecheng-12619	155	78	.	.	PUNCT
fumecheng-12619	156	1	(	(	PUNCT
fumecheng-12619	156	2	17	17	NUM
fumecheng-12619	156	3	-	-	SYM
fumecheng-12619	156	4	19	19	NUM
fumecheng-12619	156	5	)	)	PUNCT
fumecheng-12619	156	6	are	be	AUX
fumecheng-12619	156	7	defined	define	VERB
fumecheng-12619	156	8	by	by	ADP
fumecheng-12619	156	9	hashemi	hashemi	NOUN
fumecheng-12619	156	10	kachapi	kachapi	PROPN
fumecheng-12619	157	1	[	[	X
fumecheng-12619	157	2	20	20	NUM
fumecheng-12619	157	3	]	]	PUNCT
fumecheng-12619	157	4	and	and	CCONJ
fumecheng-12619	157	5	only	only	ADJ
fumecheng-12619	157	6	coefficients	coefficient	NOUN
fumecheng-12619	157	7	of	of	ADP
fumecheng-12619	157	8	visco	visco	ADJ
fumecheng-12619	157	9	-	-	ADJ
fumecheng-12619	157	10	pasternak	pasternak	PROPN
fumecheng-12619	157	11	medium	medium	NOUN
fumecheng-12619	157	12	,	,	PUNCT
fumecheng-12619	157	13	(	(	PUNCT
fumecheng-12619	157	14	𝐾𝑣𝑝)𝑤	𝐾𝑣𝑝)𝑤	NOUN
fumecheng-12619	157	15	𝑤	𝑤	X
fumecheng-12619	157	16	,	,	PUNCT
fumecheng-12619	157	17	are	be	AUX
fumecheng-12619	157	18	presented	present	VERB
fumecheng-12619	157	19	in	in	ADP
fumecheng-12619	157	20	following	follow	VERB
fumecheng-12619	157	21	eq	eq	ADP
fumecheng-12619	157	22	.	.	PUNCT
fumecheng-12619	158	1	(	(	PUNCT
fumecheng-12619	158	2	20	20	NUM
fumecheng-12619	158	3	)	)	PUNCT
fumecheng-12619	158	4	of	of	ADP
fumecheng-12619	158	5	current	current	ADJ
fumecheng-12619	158	6	work	work	NOUN
fumecheng-12619	158	7	:	:	PUNCT
fumecheng-12619	158	8	(	(	PUNCT
fumecheng-12619	158	9	𝐾𝑣𝑝)𝑤	𝐾𝑣𝑝)𝑤	X
fumecheng-12619	158	10	𝑤	𝑤	X
fumecheng-12619	158	11	=	=	PUNCT
fumecheng-12619	158	12	∬	∬	NOUN
fumecheng-12619	158	13	(	(	PUNCT
fumecheng-12619	158	14	�	�	NOUN
fumecheng-12619	158	15	̅	̅	NOUN
fumecheng-12619	158	16	�	�	NOUN
fumecheng-12619	158	17	𝑤	𝑤	SYM
fumecheng-12619	158	18	(	(	PUNCT
fumecheng-12619	158	19	𝛽𝑟𝛽𝑜𝜓𝑠𝜓𝑝	𝛽𝑟𝛽𝑜𝜓𝑠𝜓𝑝	ADJ
fumecheng-12619	158	20	−	−	PROPN
fumecheng-12619	158	21	�	�	PROPN
fumecheng-12619	158	22	̅	̅	NOUN
fumecheng-12619	158	23	�	�	NOUN
fumecheng-12619	158	24	(𝛽𝑟𝛽𝑜	(𝛽𝑟𝛽𝑜	PUNCT
fumecheng-12619	158	25	′′𝜓𝑠𝜓𝑝	′′𝜓𝑠𝜓𝑝	NOUN
fumecheng-12619	158	26	+	+	ADJ
fumecheng-12619	158	27	𝑚0	𝑚0	NOUN
fumecheng-12619	158	28	2𝛽𝑟𝛽𝑜𝜓𝑠𝜓𝑝	2𝛽𝑟𝛽𝑜𝜓𝑠𝜓𝑝	NUM
fumecheng-12619	158	29	′′	′′	PROPN
fumecheng-12619	158	30	)	)	PUNCT
fumecheng-12619	158	31	)	)	PUNCT
fumecheng-12619	159	1	−	−	ADP
fumecheng-12619	159	2	�	�	NOUN
fumecheng-12619	159	3	̅	̅	NOUN
fumecheng-12619	159	4	�	�	NOUN
fumecheng-12619	159	5	𝑝(𝛽𝑟𝛽0	𝑝(𝛽𝑟𝛽0	NOUN
fumecheng-12619	159	6	′′𝜓𝑠𝜓𝑝	′′𝜓𝑠𝜓𝑝	PROPN
fumecheng-12619	160	1	+	+	ADJ
fumecheng-12619	160	2	𝑚0	𝑚0	NOUN
fumecheng-12619	160	3	2𝛽𝑟𝛽𝑜𝜓𝑠𝜓𝑝	2𝛽𝑟𝛽𝑜𝜓𝑠𝜓𝑝	NUM
fumecheng-12619	160	4	′′	′′	PROPN
fumecheng-12619	160	5	)	)	PUNCT
fumecheng-12619	160	6	+	+	NOUN
fumecheng-12619	160	7	�	�	NOUN
fumecheng-12619	160	8	̅	̅	NOUN
fumecheng-12619	160	9	�	�	PROPN
fumecheng-12619	160	10	𝑝	𝑝	NOUN
fumecheng-12619	160	11	�	�	NOUN
fumecheng-12619	160	12	̅	̅	NOUN
fumecheng-12619	160	13	�	�	PROPN
fumecheng-12619	160	14	(	(	PUNCT
fumecheng-12619	160	15	𝛽𝑟𝛽0	𝛽𝑟𝛽0	PROPN
fumecheng-12619	160	16	′′′′𝜓𝑠𝜓𝑝	′′′′𝜓𝑠𝜓𝑝	VERB
fumecheng-12619	160	17	+	+	PROPN
fumecheng-12619	160	18	2𝑚0	2𝑚0	NUM
fumecheng-12619	160	19	2𝛽𝑟𝛽0	2𝛽𝑟𝛽0	NUM
fumecheng-12619	160	20	′′𝜓𝑠𝜓𝑝	′′𝜓𝑠𝜓𝑝	NOUN
fumecheng-12619	160	21	′′	′′	PROPN
fumecheng-12619	160	22	+	+	ADP
fumecheng-12619	160	23	𝑚0	𝑚0	NOUN
fumecheng-12619	160	24	4𝛽𝑟𝛽𝑜𝜓𝑠𝜓𝑝	4𝛽𝑟𝛽𝑜𝜓𝑠𝜓𝑝	PROPN
fumecheng-12619	160	25	′′′′	′′′′	PROPN
fumecheng-12619	160	26	)	)	PUNCT
fumecheng-12619	160	27	)	)	PUNCT
fumecheng-12619	160	28	𝑑𝜉	𝑑𝜉	ADP
fumecheng-12619	160	29	𝑑𝜃	𝑑𝜃	PROPN
fumecheng-12619	160	30	,	,	PUNCT
fumecheng-12619	160	31	(	(	PUNCT
fumecheng-12619	160	32	20	20	NUM
fumecheng-12619	160	33	)	)	PUNCT
fumecheng-12619	160	34	to	to	PART
fumecheng-12619	160	35	solve	solve	VERB
fumecheng-12619	160	36	the	the	DET
fumecheng-12619	160	37	nonlinear	nonlinear	ADJ
fumecheng-12619	160	38	equations	equation	NOUN
fumecheng-12619	160	39	of	of	ADP
fumecheng-12619	160	40	the	the	DET
fumecheng-12619	160	41	system	system	NOUN
fumecheng-12619	160	42	(	(	PUNCT
fumecheng-12619	160	43	eqs	eqs	X
fumecheng-12619	160	44	.	.	PROPN
fumecheng-12619	160	45	17	17	NUM
fumecheng-12619	160	46	-	-	SYM
fumecheng-12619	160	47	19	19	NUM
fumecheng-12619	160	48	)	)	PUNCT
fumecheng-12619	160	49	,	,	PUNCT
fumecheng-12619	160	50	the	the	DET
fumecheng-12619	160	51	complex	complex	ADJ
fumecheng-12619	160	52	averaging	averaging	NOUN
fumecheng-12619	160	53	method	method	NOUN
fumecheng-12619	160	54	combined	combine	VERB
fumecheng-12619	160	55	with	with	ADP
fumecheng-12619	160	56	arc	arc	NOUN
fumecheng-12619	160	57	-	-	PUNCT
fumecheng-12619	160	58	length	length	NOUN
fumecheng-12619	160	59	continuation	continuation	NOUN
fumecheng-12619	160	60	is	be	AUX
fumecheng-12619	160	61	employed	employ	VERB
fumecheng-12619	160	62	[	[	X
fumecheng-12619	160	63	19	19	NUM
fumecheng-12619	160	64	,	,	PUNCT
fumecheng-12619	160	65	20	20	NUM
fumecheng-12619	160	66	,	,	PUNCT
fumecheng-12619	160	67	29	29	NUM
fumecheng-12619	160	68	]	]	PUNCT
fumecheng-12619	160	69	.	.	PUNCT
fumecheng-12619	161	1	318	318	NUM
fumecheng-12619	161	2	s.h	s.h	PROPN
fumecheng-12619	161	3	.	.	PROPN
fumecheng-12619	161	4	hashemi	hashemi	PROPN
fumecheng-12619	161	5	kachapi	kachapi	PROPN
fumecheng-12619	161	6	,	,	PUNCT
fumecheng-12619	161	7	s.	s.	PROPN
fumecheng-12619	161	8	gh	gh	PROPN
fumecheng-12619	161	9	.	.	PROPN
fumecheng-12619	162	1	hashemi	hashemi	PROPN
fumecheng-12619	162	2	kachapi	kachapi	PROPN
fumecheng-12619	162	3	3	3	X
fumecheng-12619	162	4	.	.	NOUN
fumecheng-12619	162	5	results	result	NOUN
fumecheng-12619	162	6	and	and	CCONJ
fumecheng-12619	162	7	discussions	discussion	NOUN
fumecheng-12619	162	8	validation	validation	NOUN
fumecheng-12619	162	9	studies	study	NOUN
fumecheng-12619	162	10	for	for	ADP
fumecheng-12619	162	11	piezoelectric	piezoelectric	ADJ
fumecheng-12619	162	12	nanostructures	nanostructure	NOUN
fumecheng-12619	162	13	are	be	AUX
fumecheng-12619	162	14	documented	document	VERB
fumecheng-12619	162	15	in	in	ADP
fumecheng-12619	162	16	hashemi	hashemi	PROPN
fumecheng-12619	162	17	kachapi	kachapi	PROPN
fumecheng-12619	162	18	et	et	PROPN
fumecheng-12619	162	19	al	al	PROPN
fumecheng-12619	162	20	.	.	PUNCT
fumecheng-12619	163	1	[	[	X
fumecheng-12619	163	2	19	19	NUM
fumecheng-12619	163	3	,	,	PUNCT
fumecheng-12619	163	4	20	20	NUM
fumecheng-12619	163	5	]	]	PUNCT
fumecheng-12619	163	6	.	.	PUNCT
fumecheng-12619	164	1	this	this	DET
fumecheng-12619	164	2	section	section	NOUN
fumecheng-12619	164	3	examines	examine	VERB
fumecheng-12619	164	4	the	the	DET
fumecheng-12619	164	5	influence	influence	NOUN
fumecheng-12619	164	6	of	of	ADP
fumecheng-12619	164	7	diverse	diverse	ADJ
fumecheng-12619	164	8	material	material	NOUN
fumecheng-12619	164	9	and	and	CCONJ
fumecheng-12619	164	10	geometric	geometric	ADJ
fumecheng-12619	164	11	parameters	parameter	NOUN
fumecheng-12619	164	12	,	,	PUNCT
fumecheng-12619	164	13	both	both	CCONJ
fumecheng-12619	164	14	with	with	ADP
fumecheng-12619	164	15	and	and	CCONJ
fumecheng-12619	164	16	without	without	ADP
fumecheng-12619	164	17	the	the	DET
fumecheng-12619	164	18	inclusion	inclusion	NOUN
fumecheng-12619	164	19	of	of	ADP
fumecheng-12619	164	20	nonlocal	nonlocal	ADJ
fumecheng-12619	164	21	,	,	PUNCT
fumecheng-12619	164	22	strain	strain	NOUN
fumecheng-12619	164	23	gradient	gradient	NOUN
fumecheng-12619	164	24	,	,	PUNCT
fumecheng-12619	164	25	and	and	CCONJ
fumecheng-12619	164	26	surface	surface	NOUN
fumecheng-12619	164	27	/	/	SYM
fumecheng-12619	164	28	interface	interface	NOUN
fumecheng-12619	164	29	effects	effect	NOUN
fumecheng-12619	164	30	,	,	PUNCT
fumecheng-12619	164	31	on	on	ADP
fumecheng-12619	164	32	the	the	DET
fumecheng-12619	164	33	dimensionless	dimensionless	ADJ
fumecheng-12619	164	34	natural	natural	ADJ
fumecheng-12619	164	35	frequency	frequency	NOUN
fumecheng-12619	164	36	,	,	PUNCT
fumecheng-12619	164	37	stability	stability	NOUN
fumecheng-12619	164	38	characteristics	characteristic	NOUN
fumecheng-12619	164	39	,	,	PUNCT
fumecheng-12619	164	40	and	and	CCONJ
fumecheng-12619	164	41	frequency	frequency	NOUN
fumecheng-12619	164	42	response	response	NOUN
fumecheng-12619	164	43	.	.	PUNCT
fumecheng-12619	165	1	analyses	analysis	NOUN
fumecheng-12619	165	2	are	be	AUX
fumecheng-12619	165	3	performed	perform	VERB
fumecheng-12619	165	4	for	for	ADP
fumecheng-12619	165	5	clamped	clamp	VERB
fumecheng-12619	165	6	-	-	PUNCT
fumecheng-12619	165	7	clamped	clamp	VERB
fumecheng-12619	165	8	(	(	PUNCT
fumecheng-12619	165	9	cc	cc	NOUN
fumecheng-12619	165	10	)	)	PUNCT
fumecheng-12619	165	11	,	,	PUNCT
fumecheng-12619	165	12	simply	simply	ADV
fumecheng-12619	165	13	supported	support	VERB
fumecheng-12619	165	14	-	-	PUNCT
fumecheng-12619	165	15	simply	simply	ADV
fumecheng-12619	165	16	supported	support	VERB
fumecheng-12619	165	17	(	(	PUNCT
fumecheng-12619	165	18	ss	ss	NOUN
fumecheng-12619	165	19	)	)	PUNCT
fumecheng-12619	165	20	,	,	PUNCT
fumecheng-12619	165	21	clamped	clamp	VERB
fumecheng-12619	165	22	-	-	PUNCT
fumecheng-12619	165	23	simply	simply	ADV
fumecheng-12619	165	24	supported	support	VERB
fumecheng-12619	165	25	(	(	PUNCT
fumecheng-12619	165	26	cs	cs	ADJ
fumecheng-12619	165	27	)	)	PUNCT
fumecheng-12619	165	28	,	,	PUNCT
fumecheng-12619	165	29	and	and	CCONJ
fumecheng-12619	165	30	clamped	clamp	VERB
fumecheng-12619	165	31	-	-	PUNCT
fumecheng-12619	165	32	free	free	ADJ
fumecheng-12619	165	33	(	(	PUNCT
fumecheng-12619	165	34	cf	cf	NOUN
fumecheng-12619	165	35	)	)	PUNCT
fumecheng-12619	165	36	boundary	boundary	ADJ
fumecheng-12619	165	37	conditions	condition	NOUN
fumecheng-12619	165	38	.	.	PUNCT
fumecheng-12619	166	1	the	the	DET
fumecheng-12619	166	2	surface	surface	NOUN
fumecheng-12619	166	3	and	and	CCONJ
fumecheng-12619	166	4	bulk	bulk	ADJ
fumecheng-12619	166	5	material	material	NOUN
fumecheng-12619	166	6	properties	property	NOUN
fumecheng-12619	166	7	of	of	ADP
fumecheng-12619	166	8	the	the	DET
fumecheng-12619	166	9	aluminum	aluminum	NOUN
fumecheng-12619	166	10	(	(	PUNCT
fumecheng-12619	166	11	al	al	PROPN
fumecheng-12619	166	12	)	)	PUNCT
fumecheng-12619	166	13	nanoshell	nanoshell	NOUN
fumecheng-12619	166	14	and	and	CCONJ
fumecheng-12619	166	15	pzt	pzt	ADJ
fumecheng-12619	166	16	piezoelectric	piezoelectric	NOUN
fumecheng-12619	166	17	layer	layer	NOUN
fumecheng-12619	166	18	are	be	AUX
fumecheng-12619	166	19	tabulated	tabulate	VERB
fumecheng-12619	166	20	in	in	ADP
fumecheng-12619	166	21	tables	table	NOUN
fumecheng-12619	166	22	1	1	NUM
fumecheng-12619	166	23	and	and	CCONJ
fumecheng-12619	166	24	2	2	NUM
fumecheng-12619	166	25	,	,	PUNCT
fumecheng-12619	166	26	respectively	respectively	ADV
fumecheng-12619	166	27	[	[	X
fumecheng-12619	166	28	19	19	NUM
fumecheng-12619	166	29	,	,	PUNCT
fumecheng-12619	166	30	20	20	NUM
fumecheng-12619	166	31	]	]	PUNCT
fumecheng-12619	166	32	.	.	PUNCT
fumecheng-12619	167	1	table	table	NOUN
fumecheng-12619	167	2	1	1	NUM
fumecheng-12619	167	3	surface	surface	NOUN
fumecheng-12619	167	4	and	and	CCONJ
fumecheng-12619	167	5	bulk	bulk	ADJ
fumecheng-12619	167	6	properties	property	NOUN
fumecheng-12619	167	7	of	of	ADP
fumecheng-12619	167	8	al	al	PROPN
fumecheng-12619	167	9	𝑬𝑵[𝑮𝑷𝒂	𝑬𝑵[𝑮𝑷𝒂	PROPN
fumecheng-12619	167	10	]	]	PUNCT
fumecheng-12619	168	1	𝝊𝑵	𝝊𝑵	NOUN
fumecheng-12619	168	2	𝝆𝑵[𝒌𝒈	𝝆𝑵[𝒌𝒈	NOUN
fumecheng-12619	169	1	𝒎𝟑⁄	𝒎𝟑⁄	PROPN
fumecheng-12619	169	2	]	]	PUNCT
fumecheng-12619	169	3	𝝀𝑰[𝑵	𝝀𝑰[𝑵	PROPN
fumecheng-12619	169	4	𝒎⁄	𝒎⁄	PROPN
fumecheng-12619	169	5	]	]	PUNCT
fumecheng-12619	169	6	𝝁𝑰[𝑵	𝝁𝑰[𝑵	PROPN
fumecheng-12619	170	1	𝒎⁄	𝒎⁄	PROPN
fumecheng-12619	170	2	]	]	PUNCT
fumecheng-12619	170	3	𝝉𝟎	𝝉𝟎	PROPN
fumecheng-12619	170	4	𝑰	𝑰	PROPN
fumecheng-12619	170	5	[	[	X
fumecheng-12619	170	6	𝑵	𝑵	PROPN
fumecheng-12619	170	7	𝒎⁄	𝒎⁄	PROPN
fumecheng-12619	170	8	]	]	PUNCT
fumecheng-12619	171	1	𝝆𝑰[𝒌𝒈	𝝆𝑰[𝒌𝒈	PROPN
fumecheng-12619	171	2	𝒎𝟐⁄	𝒎𝟐⁄	PROPN
fumecheng-12619	171	3	]	]	PUNCT
fumecheng-12619	171	4	𝟕𝟎	𝟕𝟎	NUM
fumecheng-12619	171	5	0.33	0.33	NUM
fumecheng-12619	171	6	2700	2700	NUM
fumecheng-12619	171	7	3.786	3.786	NUM
fumecheng-12619	171	8	1.95	1.95	NUM
fumecheng-12619	171	9	0.9108	0.9108	NUM
fumecheng-12619	171	10	5.46	5.46	NUM
fumecheng-12619	171	11	×	×	NOUN
fumecheng-12619	171	12	10−7	10−7	NUM
fumecheng-12619	171	13	table	table	NOUN
fumecheng-12619	171	14	2	2	NUM
fumecheng-12619	171	15	surface	surface	NOUN
fumecheng-12619	171	16	and	and	CCONJ
fumecheng-12619	171	17	bulk	bulk	ADJ
fumecheng-12619	171	18	properties	property	NOUN
fumecheng-12619	171	19	of	of	ADP
fumecheng-12619	171	20	pzt-4	pzt-4	NOUN
fumecheng-12619	171	21	𝑪𝟏𝟏𝒑[𝑮𝑷𝒂	𝑪𝟏𝟏𝒑[𝑮𝑷𝒂	ADV
fumecheng-12619	171	22	]	]	X
fumecheng-12619	171	23	𝑪𝟐𝟐𝒑[𝑮𝑷𝒂	𝑪𝟐𝟐𝒑[𝑮𝑷𝒂	X
fumecheng-12619	171	24	]	]	PUNCT
fumecheng-12619	171	25	𝑪𝟏𝟐𝒑[𝑮𝑷𝒂	𝑪𝟏𝟐𝒑[𝑮𝑷𝒂	NOUN
fumecheng-12619	171	26	]	]	X
fumecheng-12619	171	27	𝑪𝟐𝟏𝒑[𝑮𝑷𝒂	𝑪𝟐𝟏𝒑[𝑮𝑷𝒂	NOUN
fumecheng-12619	171	28	]	]	X
fumecheng-12619	171	29	𝑪𝟔𝟔𝒑[𝑮𝑷𝒂	𝑪𝟔𝟔𝒑[𝑮𝑷𝒂	NOUN
fumecheng-12619	171	30	]	]	PUNCT
fumecheng-12619	171	31	𝑬𝒑[𝑮𝑷𝒂	𝑬𝒑[𝑮𝑷𝒂	NOUN
fumecheng-12619	171	32	]	]	X
fumecheng-12619	171	33	𝟏𝟑𝟗	𝟏𝟑𝟗	NUM
fumecheng-12619	171	34	139	139	NUM
fumecheng-12619	171	35	77.8	77.8	NUM
fumecheng-12619	171	36	77.8	77.8	NUM
fumecheng-12619	171	37	30.5	30.5	NUM
fumecheng-12619	171	38	95	95	NUM
fumecheng-12619	171	39	𝝊𝒑	𝝊𝒑	NOUN
fumecheng-12619	171	40	𝜌𝑝[𝑘𝑔	𝜌𝑝[𝑘𝑔	PROPN
fumecheng-12619	171	41	𝑚	𝑚	X
fumecheng-12619	171	42	−3	−3	NOUN
fumecheng-12619	171	43	]	]	PUNCT
fumecheng-12619	171	44	𝜂33𝑝[10	𝜂33𝑝[10	CCONJ
fumecheng-12619	172	1	−8	−8	X
fumecheng-12619	172	2	𝐹	𝐹	PROPN
fumecheng-12619	173	1	𝑚⁄	𝑚⁄	X
fumecheng-12619	173	2	]	]	PUNCT
fumecheng-12619	173	3	𝜆𝑆[𝑁	𝜆𝑆[𝑁	PROPN
fumecheng-12619	173	4	𝑚⁄	𝑚⁄	X
fumecheng-12619	173	5	]	]	PUNCT
fumecheng-12619	173	6	𝜇𝑆[𝑁	𝜇𝑆[𝑁	PROPN
fumecheng-12619	173	7	𝑚⁄	𝑚⁄	X
fumecheng-12619	173	8	]	]	PUNCT
fumecheng-12619	173	9	𝜏0	𝜏0	PROPN
fumecheng-12619	173	10	𝑆[𝑁	𝑆[𝑁	NOUN
fumecheng-12619	173	11	𝑚⁄	𝑚⁄	ADP
fumecheng-12619	173	12	]	]	PUNCT
fumecheng-12619	173	13	𝟎.	𝟎.	X
fumecheng-12619	173	14	𝟑	𝟑	NUM
fumecheng-12619	173	15	7500	7500	NUM
fumecheng-12619	173	16	8.91	8.91	NUM
fumecheng-12619	173	17	4.488	4.488	NUM
fumecheng-12619	173	18	2.774	2.774	NUM
fumecheng-12619	173	19	0.6048	0.6048	NUM
fumecheng-12619	173	20	𝒆𝟑𝟏𝒑[𝑪	𝒆𝟑𝟏𝒑[𝑪	NOUN
fumecheng-12619	173	21	𝒎𝟐⁄	𝒎𝟐⁄	PROPN
fumecheng-12619	173	22	]	]	PUNCT
fumecheng-12619	174	1	𝑒32𝑝[𝐶	𝑒32𝑝[𝐶	PROPN
fumecheng-12619	174	2	𝑚2⁄	𝑚2⁄	NUM
fumecheng-12619	174	3	]	]	PUNCT
fumecheng-12619	174	4	𝑒31𝑝	𝑒31𝑝	NOUN
fumecheng-12619	175	1	𝑆	𝑆	PROPN
fumecheng-12619	175	2	[	[	X
fumecheng-12619	175	3	𝐶	𝐶	PROPN
fumecheng-12619	175	4	𝑚⁄	𝑚⁄	X
fumecheng-12619	175	5	]	]	PUNCT
fumecheng-12619	175	6	𝑒32𝑝	𝑒32𝑝	ADP
fumecheng-12619	175	7	𝑆	𝑆	PROPN
fumecheng-12619	175	8	[	[	SYM
fumecheng-12619	175	9	𝐶	𝐶	PROPN
fumecheng-12619	175	10	𝑚⁄	𝑚⁄	PRON
fumecheng-12619	175	11	]	]	PUNCT
fumecheng-12619	175	12	𝜌𝑆[𝑘𝑔	𝜌𝑆[𝑘𝑔	PROPN
fumecheng-12619	176	1	𝑚2⁄	𝑚2⁄	X
fumecheng-12619	176	2	]	]	PUNCT
fumecheng-12619	177	1	−𝟓.𝟐	−𝟓.𝟐	PROPN
fumecheng-12619	178	1	−5.2	−5.2	NOUN
fumecheng-12619	178	2	−3	−3	PROPN
fumecheng-12619	179	1	×	×	NOUN
fumecheng-12619	179	2	10−8	10−8	NUM
fumecheng-12619	179	3	−3	−3	ADJ
fumecheng-12619	179	4	×	×	NOUN
fumecheng-12619	179	5	10−8	10−8	NUM
fumecheng-12619	179	6	5.61	5.61	NUM
fumecheng-12619	179	7	×	×	NOUN
fumecheng-12619	179	8	10−6	10−6	NUM
fumecheng-12619	179	9	the	the	DET
fumecheng-12619	179	10	remaining	remain	VERB
fumecheng-12619	179	11	physical	physical	ADJ
fumecheng-12619	179	12	and	and	CCONJ
fumecheng-12619	179	13	geometrical	geometrical	ADJ
fumecheng-12619	179	14	parameters	parameter	NOUN
fumecheng-12619	179	15	of	of	ADP
fumecheng-12619	179	16	the	the	DET
fumecheng-12619	179	17	penr	penr	PROPN
fumecheng-12619	179	18	used	use	VERB
fumecheng-12619	179	19	in	in	ADP
fumecheng-12619	179	20	the	the	DET
fumecheng-12619	179	21	following	following	ADJ
fumecheng-12619	179	22	results	result	NOUN
fumecheng-12619	179	23	are	be	AUX
fumecheng-12619	179	24	listed	list	VERB
fumecheng-12619	179	25	in	in	ADP
fumecheng-12619	179	26	table	table	NOUN
fumecheng-12619	179	27	3	3	NUM
fumecheng-12619	179	28	[	[	X
fumecheng-12619	179	29	19	19	NUM
fumecheng-12619	179	30	,	,	PUNCT
fumecheng-12619	179	31	20	20	NUM
fumecheng-12619	179	32	,	,	PUNCT
fumecheng-12619	179	33	22	22	NUM
fumecheng-12619	179	34	]	]	PUNCT
fumecheng-12619	179	35	.	.	PUNCT
fumecheng-12619	180	1	table	table	NOUN
fumecheng-12619	180	2	3	3	NUM
fumecheng-12619	180	3	the	the	DET
fumecheng-12619	180	4	material	material	NOUN
fumecheng-12619	180	5	and	and	CCONJ
fumecheng-12619	180	6	geometrical	geometrical	ADJ
fumecheng-12619	180	7	parameters	parameter	NOUN
fumecheng-12619	180	8	𝑹[𝒎	𝑹[𝒎	VERB
fumecheng-12619	180	9	]	]	X
fumecheng-12619	180	10	𝑳	𝑳	NOUN
fumecheng-12619	180	11	𝑹⁄	𝑹⁄	PROPN
fumecheng-12619	180	12	𝒉𝑵	𝒉𝑵	SYM
fumecheng-12619	180	13	𝑹⁄	𝑹⁄	PROPN
fumecheng-12619	180	14	𝒉𝒑	𝒉𝒑	NOUN
fumecheng-12619	180	15	𝑹⁄	𝑹⁄	PROPN
fumecheng-12619	180	16	𝒃	𝒃	ADP
fumecheng-12619	180	17	𝑹⁄	𝑹⁄	PROPN
fumecheng-12619	180	18	𝑪𝒘[𝑵.	𝑪𝒘[𝑵.	PROPN
fumecheng-12619	180	19	𝑺/𝒎	𝑺/𝒎	PROPN
fumecheng-12619	180	20	]	]	X
fumecheng-12619	180	21	𝟏	𝟏	NUM
fumecheng-12619	180	22	×	×	NOUN
fumecheng-12619	180	23	𝟏𝟎−𝟗	𝟏𝟎−𝟗	PROPN
fumecheng-12619	180	24	10	10	NUM
fumecheng-12619	180	25	0.01	0.01	NUM
fumecheng-12619	180	26	0.005	0.005	NUM
fumecheng-12619	180	27	0.1	0.1	NUM
fumecheng-12619	180	28	1	1	NUM
fumecheng-12619	180	29	×	×	NOUN
fumecheng-12619	180	30	10−3	10−3	NUM
fumecheng-12619	180	31	𝑲𝒘[𝑵	𝑲𝒘[𝑵	PUNCT
fumecheng-12619	180	32	𝒎𝟑⁄	𝒎𝟑⁄	PROPN
fumecheng-12619	180	33	]	]	PUNCT
fumecheng-12619	180	34	𝐾𝑝[𝑁	𝐾𝑝[𝑁	PUNCT
fumecheng-12619	180	35	𝑚⁄	𝑚⁄	X
fumecheng-12619	180	36	]	]	PUNCT
fumecheng-12619	180	37	𝑉𝑝[𝑉	𝑉𝑝[𝑉	X
fumecheng-12619	180	38	]	]	PUNCT
fumecheng-12619	180	39	𝑉0	𝑉0	PROPN
fumecheng-12619	180	40	𝑉𝐷𝐶[𝑉	𝑉𝐷𝐶[𝑉	PROPN
fumecheng-12619	180	41	]	]	PUNCT
fumecheng-12619	180	42	𝑉𝐴𝐶[𝑉	𝑉𝐴𝐶[𝑉	PROPN
fumecheng-12619	180	43	]	]	X
fumecheng-12619	180	44	𝟗	𝟗	NUM
fumecheng-12619	180	45	×	×	NOUN
fumecheng-12619	180	46	𝟏𝟎𝟏𝟕	𝟏𝟎𝟏𝟕	NUM
fumecheng-12619	180	47	2.07	2.07	NUM
fumecheng-12619	180	48	1	1	NUM
fumecheng-12619	180	49	×	×	NOUN
fumecheng-12619	180	50	10−5	10−5	NUM
fumecheng-12619	180	51	1	1	NUM
fumecheng-12619	180	52	1.5	1.5	NUM
fumecheng-12619	180	53	0.5	0.5	NUM
fumecheng-12619	180	54	𝝁[𝒎𝟐	𝝁[𝒎𝟐	NOUN
fumecheng-12619	180	55	]	]	PUNCT
fumecheng-12619	180	56	𝜂[𝑚2	𝜂[𝑚2	NOUN
fumecheng-12619	180	57	]	]	PUNCT
fumecheng-12619	180	58	(	(	PUNCT
fumecheng-12619	180	59	𝟏	𝟏	NUM
fumecheng-12619	180	60	×	×	NOUN
fumecheng-12619	180	61	𝟏𝟎−𝟏𝟎	𝟏𝟎−𝟏𝟎	PROPN
fumecheng-12619	180	62	)	)	PUNCT
fumecheng-12619	180	63	𝟐	𝟐	NUM
fumecheng-12619	180	64	(	(	PUNCT
fumecheng-12619	180	65	1	1	NUM
fumecheng-12619	180	66	×	×	NOUN
fumecheng-12619	180	67	10−11)2	10−11)2	NUM
fumecheng-12619	180	68	3.1	3.1	NUM
fumecheng-12619	180	69	.	.	PUNCT
fumecheng-12619	181	1	nonlinear	nonlinear	ADJ
fumecheng-12619	181	2	frequency	frequency	NOUN
fumecheng-12619	181	3	response	response	NOUN
fumecheng-12619	181	4	and	and	CCONJ
fumecheng-12619	181	5	stability	stability	NOUN
fumecheng-12619	181	6	analysis	analysis	NOUN
fumecheng-12619	181	7	this	this	DET
fumecheng-12619	181	8	section	section	NOUN
fumecheng-12619	181	9	compares	compare	VERB
fumecheng-12619	181	10	the	the	DET
fumecheng-12619	181	11	predictions	prediction	NOUN
fumecheng-12619	181	12	of	of	ADP
fumecheng-12619	181	13	three	three	NUM
fumecheng-12619	181	14	nonclassical	nonclassical	ADJ
fumecheng-12619	181	15	continuum	continuum	ADJ
fumecheng-12619	181	16	theories	theory	NOUN
fumecheng-12619	181	17	-	-	PUNCT
fumecheng-12619	181	18	nonlocal	nonlocal	ADJ
fumecheng-12619	181	19	theory	theory	NOUN
fumecheng-12619	181	20	(	(	PUNCT
fumecheng-12619	181	21	nlt	nlt	PROPN
fumecheng-12619	181	22	)	)	PUNCT
fumecheng-12619	181	23	,	,	PUNCT
fumecheng-12619	181	24	strain	strain	NOUN
fumecheng-12619	181	25	gradient	gradient	NOUN
fumecheng-12619	181	26	theory	theory	NOUN
fumecheng-12619	181	27	(	(	PUNCT
fumecheng-12619	181	28	sgt	sgt	PROPN
fumecheng-12619	181	29	)	)	PUNCT
fumecheng-12619	181	30	,	,	PUNCT
fumecheng-12619	181	31	and	and	CCONJ
fumecheng-12619	181	32	gurtin	gurtin	PROPN
fumecheng-12619	181	33	-	-	PUNCT
fumecheng-12619	181	34	murdoch	murdoch	PROPN
fumecheng-12619	181	35	surface	surface	NOUN
fumecheng-12619	181	36	/	/	SYM
fumecheng-12619	181	37	interface	interface	NOUN
fumecheng-12619	181	38	theory	theory	NOUN
fumecheng-12619	181	39	(	(	PUNCT
fumecheng-12619	181	40	gmsit)with	gmsit)with	ADP
fumecheng-12619	181	41	those	those	PRON
fumecheng-12619	181	42	of	of	ADP
fumecheng-12619	181	43	classical	classical	ADJ
fumecheng-12619	181	44	continuum	continuum	ADJ
fumecheng-12619	181	45	theory	theory	NOUN
fumecheng-12619	181	46	(	(	PUNCT
fumecheng-12619	181	47	ct	ct	PROPN
fumecheng-12619	181	48	)	)	PUNCT
fumecheng-12619	181	49	.	.	PUNCT
fumecheng-12619	182	1	the	the	DET
fumecheng-12619	182	2	analysis	analysis	NOUN
fumecheng-12619	182	3	investigates	investigate	VERB
fumecheng-12619	182	4	the	the	DET
fumecheng-12619	182	5	impact	impact	NOUN
fumecheng-12619	182	6	of	of	ADP
fumecheng-12619	182	7	various	various	ADJ
fumecheng-12619	182	8	geometric	geometric	ADJ
fumecheng-12619	182	9	and	and	CCONJ
fumecheng-12619	182	10	material	material	NOUN
fumecheng-12619	182	11	parameters	parameter	NOUN
fumecheng-12619	182	12	,	,	PUNCT
fumecheng-12619	182	13	incorporating	incorporate	VERB
fumecheng-12619	182	14	and	and	CCONJ
fumecheng-12619	182	15	excluding	exclude	VERB
fumecheng-12619	182	16	strain	strain	NOUN
fumecheng-12619	182	17	gradient	gradient	ADJ
fumecheng-12619	182	18	,	,	PUNCT
fumecheng-12619	182	19	nonlocal	nonlocal	ADJ
fumecheng-12619	182	20	,	,	PUNCT
fumecheng-12619	182	21	and	and	CCONJ
fumecheng-12619	182	22	surface	surface	NOUN
fumecheng-12619	182	23	/	/	SYM
fumecheng-12619	182	24	interface	interface	NOUN
fumecheng-12619	182	25	effects	effect	NOUN
fumecheng-12619	182	26	,	,	PUNCT
fumecheng-12619	182	27	on	on	ADP
fumecheng-12619	182	28	the	the	DET
fumecheng-12619	182	29	dimensionless	dimensionless	ADJ
fumecheng-12619	182	30	natural	natural	ADJ
fumecheng-12619	182	31	frequency	frequency	NOUN
fumecheng-12619	182	32	(	(	PUNCT
fumecheng-12619	182	33	dnf	dnf	PROPN
fumecheng-12619	182	34	)	)	PUNCT
fumecheng-12619	182	35	,	,	PUNCT
fumecheng-12619	182	36	stability	stability	NOUN
fumecheng-12619	182	37	,	,	PUNCT
fumecheng-12619	182	38	and	and	CCONJ
fumecheng-12619	182	39	nonlinear	nonlinear	ADJ
fumecheng-12619	182	40	frequency	frequency	NOUN
fumecheng-12619	182	41	response	response	NOUN
fumecheng-12619	182	42	of	of	ADP
fumecheng-12619	182	43	the	the	DET
fumecheng-12619	182	44	piezoelectric	piezoelectric	ADJ
fumecheng-12619	182	45	nanoresonator	nanoresonator	NOUN
fumecheng-12619	182	46	(	(	PUNCT
fumecheng-12619	182	47	penr	penr	PROPN
fumecheng-12619	182	48	)	)	PUNCT
fumecheng-12619	182	49	.	.	PUNCT
fumecheng-12619	183	1	arc	arc	NOUN
fumecheng-12619	183	2	-	-	PUNCT
fumecheng-12619	183	3	length	length	NOUN
fumecheng-12619	183	4	continuation	continuation	NOUN
fumecheng-12619	183	5	is	be	AUX
fumecheng-12619	183	6	employed	employ	VERB
fumecheng-12619	183	7	as	as	ADP
fumecheng-12619	183	8	the	the	DET
fumecheng-12619	183	9	numerical	numerical	ADJ
fumecheng-12619	183	10	solution	solution	NOUN
fumecheng-12619	183	11	method	method	NOUN
fumecheng-12619	183	12	,	,	PUNCT
fumecheng-12619	183	13	utilizing	utilize	VERB
fumecheng-12619	183	14	the	the	DET
fumecheng-12619	183	15	penr	penr	ADJ
fumecheng-12619	183	16	specifications	specification	NOUN
fumecheng-12619	183	17	provided	provide	VERB
fumecheng-12619	183	18	in	in	ADP
fumecheng-12619	183	19	tables	table	NOUN
fumecheng-12619	183	20	1	1	NUM
fumecheng-12619	183	21	-	-	SYM
fumecheng-12619	183	22	3	3	NUM
fumecheng-12619	183	23	.	.	PUNCT
fumecheng-12619	184	1	specifically	specifically	ADV
fumecheng-12619	184	2	,	,	PUNCT
fumecheng-12619	184	3	the	the	DET
fumecheng-12619	184	4	nlt	nlt	PROPN
fumecheng-12619	184	5	analysis	analysis	NOUN
fumecheng-12619	184	6	considers	consider	VERB
fumecheng-12619	184	7	the	the	DET
fumecheng-12619	184	8	nonlocal	nonlocal	ADJ
fumecheng-12619	184	9	parameter	parameter	NOUN
fumecheng-12619	184	10	,	,	PUNCT
fumecheng-12619	184	11	�	�	PROPN
fumecheng-12619	184	12	̅	̅	NOUN
fumecheng-12619	184	13	�	�	NOUN
fumecheng-12619	184	14	;	;	PUNCT
fumecheng-12619	184	15	the	the	DET
fumecheng-12619	184	16	sgt	sgt	PROPN
fumecheng-12619	184	17	analysis	analysis	NOUN
fumecheng-12619	184	18	considers	consider	VERB
fumecheng-12619	184	19	the	the	DET
fumecheng-12619	184	20	material	material	NOUN
fumecheng-12619	184	21	length	length	NOUN
fumecheng-12619	184	22	scale	scale	NOUN
fumecheng-12619	184	23	parameters	parameter	NOUN
fumecheng-12619	184	24	,	,	PUNCT
fumecheng-12619	184	25	the	the	DET
fumecheng-12619	184	26	comparison	comparison	NOUN
fumecheng-12619	184	27	of	of	ADP
fumecheng-12619	184	28	nonclassical	nonclassical	ADJ
fumecheng-12619	184	29	controllers	controller	NOUN
fumecheng-12619	184	30	on	on	ADP
fumecheng-12619	184	31	nonlinear	nonlinear	ADJ
fumecheng-12619	184	32	vibrations	vibration	NOUN
fumecheng-12619	184	33	analysis	analysis	NOUN
fumecheng-12619	184	34	of	of	ADP
fumecheng-12619	184	35	piezoelectric	piezoelectric	NOUN
fumecheng-12619	184	36	...	...	PUNCT
fumecheng-12619	184	37	319	319	NUM
fumecheng-12619	184	38	�	�	NOUN
fumecheng-12619	184	39	̅	̅	NOUN
fumecheng-12619	184	40	�	�	PROPN
fumecheng-12619	184	41	and	and	CCONJ
fumecheng-12619	184	42	�	�	PROPN
fumecheng-12619	184	43	̅	̅	NOUN
fumecheng-12619	184	44	�	�	NOUN
fumecheng-12619	184	45	parameters	parameter	NOUN
fumecheng-12619	184	46	;	;	PUNCT
fumecheng-12619	184	47	and	and	CCONJ
fumecheng-12619	184	48	the	the	DET
fumecheng-12619	184	49	gmsit	gmsit	NOUN
fumecheng-12619	184	50	analysis	analysis	NOUN
fumecheng-12619	184	51	incorporates	incorporate	VERB
fumecheng-12619	184	52	surface	surface	NOUN
fumecheng-12619	184	53	/	/	SYM
fumecheng-12619	184	54	interface	interface	NOUN
fumecheng-12619	184	55	(	(	PUNCT
fumecheng-12619	184	56	s	s	NOUN
fumecheng-12619	184	57	/	/	SYM
fumecheng-12619	184	58	i	i	NOUN
fumecheng-12619	184	59	)	)	PUNCT
fumecheng-12619	184	60	effects	effect	NOUN
fumecheng-12619	184	61	.	.	PUNCT
fumecheng-12619	185	1	recognizing	recognize	VERB
fumecheng-12619	185	2	the	the	DET
fumecheng-12619	185	3	substantial	substantial	ADJ
fumecheng-12619	185	4	influence	influence	NOUN
fumecheng-12619	185	5	of	of	ADP
fumecheng-12619	185	6	surface	surface	NOUN
fumecheng-12619	185	7	/	/	SYM
fumecheng-12619	185	8	interface	interface	NOUN
fumecheng-12619	185	9	densities	density	NOUN
fumecheng-12619	185	10	on	on	ADP
fumecheng-12619	185	11	nanostructure	nanostructure	ADJ
fumecheng-12619	185	12	vibration	vibration	NOUN
fumecheng-12619	185	13	,	,	PUNCT
fumecheng-12619	185	14	two	two	NUM
fumecheng-12619	185	15	distinct	distinct	ADJ
fumecheng-12619	185	16	surface	surface	NOUN
fumecheng-12619	185	17	density	density	NOUN
fumecheng-12619	185	18	cases	case	NOUN
fumecheng-12619	185	19	,	,	PUNCT
fumecheng-12619	185	20	as	as	SCONJ
fumecheng-12619	185	21	defined	define	VERB
fumecheng-12619	185	22	in	in	ADP
fumecheng-12619	185	23	table	table	NOUN
fumecheng-12619	185	24	4	4	NUM
fumecheng-12619	185	25	,	,	PUNCT
fumecheng-12619	185	26	are	be	AUX
fumecheng-12619	185	27	presented	present	VERB
fumecheng-12619	185	28	.	.	PUNCT
fumecheng-12619	186	1	table	table	NOUN
fumecheng-12619	186	2	4	4	NUM
fumecheng-12619	186	3	two	two	NUM
fumecheng-12619	186	4	case	case	NOUN
fumecheng-12619	186	5	of	of	ADP
fumecheng-12619	186	6	surface	surface	NOUN
fumecheng-12619	186	7	density	density	NOUN
fumecheng-12619	186	8	case	case	NOUN
fumecheng-12619	186	9	1	1	NUM
fumecheng-12619	186	10	case	case	NOUN
fumecheng-12619	186	11	2	2	NUM
fumecheng-12619	186	12	𝝆𝑰[𝒌𝒈	𝝆𝑰[𝒌𝒈	NOUN
fumecheng-12619	186	13	𝒎𝟐⁄	𝒎𝟐⁄	PROPN
fumecheng-12619	186	14	]	]	PUNCT
fumecheng-12619	186	15	𝜌𝑆[𝑘𝑔	𝜌𝑆[𝑘𝑔	PROPN
fumecheng-12619	187	1	𝑚2⁄	𝑚2⁄	X
fumecheng-12619	187	2	]	]	PUNCT
fumecheng-12619	187	3	𝜌𝐼[𝑘𝑔	𝜌𝐼[𝑘𝑔	PROPN
fumecheng-12619	188	1	𝑚2⁄	𝑚2⁄	X
fumecheng-12619	188	2	]	]	PUNCT
fumecheng-12619	188	3	𝜌𝑆[𝑘𝑔	𝜌𝑆[𝑘𝑔	PROPN
fumecheng-12619	189	1	𝑚2⁄	𝑚2⁄	X
fumecheng-12619	189	2	]	]	PUNCT
fumecheng-12619	189	3	𝟓.	𝟓.	X
fumecheng-12619	189	4	𝟒𝟔	𝟒𝟔	NUM
fumecheng-12619	189	5	×	×	NOUN
fumecheng-12619	189	6	𝟏𝟎−𝟕	𝟏𝟎−𝟕	PROPN
fumecheng-12619	189	7	5.61	5.61	NUM
fumecheng-12619	189	8	×	×	NOUN
fumecheng-12619	189	9	10−6	10−6	NUM
fumecheng-12619	189	10	5.46	5.46	NUM
fumecheng-12619	189	11	×	×	NOUN
fumecheng-12619	189	12	10−8	10−8	NUM
fumecheng-12619	189	13	5.61	5.61	NUM
fumecheng-12619	189	14	×	×	NOUN
fumecheng-12619	189	15	10−7	10−7	NUM
fumecheng-12619	189	16	figs	fig	NOUN
fumecheng-12619	189	17	.	.	PUNCT
fumecheng-12619	190	1	2	2	NUM
fumecheng-12619	190	2	and	and	CCONJ
fumecheng-12619	190	3	3	3	NUM
fumecheng-12619	190	4	illustrate	illustrate	VERB
fumecheng-12619	190	5	the	the	DET
fumecheng-12619	190	6	dimensionless	dimensionless	ADJ
fumecheng-12619	190	7	natural	natural	ADJ
fumecheng-12619	190	8	frequencies	frequency	NOUN
fumecheng-12619	190	9	of	of	ADP
fumecheng-12619	190	10	the	the	DET
fumecheng-12619	190	11	piezoelectric	piezoelectric	ADJ
fumecheng-12619	190	12	nanoresonator	nanoresonator	NOUN
fumecheng-12619	190	13	(	(	PUNCT
fumecheng-12619	190	14	penr	penr	PROPN
fumecheng-12619	190	15	)	)	PUNCT
fumecheng-12619	190	16	as	as	ADP
fumecheng-12619	190	17	a	a	DET
fumecheng-12619	190	18	function	function	NOUN
fumecheng-12619	190	19	of	of	ADP
fumecheng-12619	190	20	the	the	DET
fumecheng-12619	190	21	dimensionless	dimensionless	ADJ
fumecheng-12619	190	22	nonlocal	nonlocal	ADJ
fumecheng-12619	190	23	scale	scale	NOUN
fumecheng-12619	190	24	parameter	parameter	NOUN
fumecheng-12619	190	25	�	�	PROPN
fumecheng-12619	190	26	̅	̅	NOUN
fumecheng-12619	190	27	�	�	PROPN
fumecheng-12619	190	28	and	and	CCONJ
fumecheng-12619	190	29	the	the	DET
fumecheng-12619	190	30	dimensionless	dimensionless	NOUN
fumecheng-12619	190	31	material	material	NOUN
fumecheng-12619	190	32	length	length	NOUN
fumecheng-12619	190	33	scale	scale	NOUN
fumecheng-12619	190	34	parameter	parameter	PROPN
fumecheng-12619	190	35	�	�	PROPN
fumecheng-12619	190	36	̅	̅	NOUN
fumecheng-12619	190	37	�	�	PROPN
fumecheng-12619	190	38	,	,	PUNCT
fumecheng-12619	190	39	respectively	respectively	ADV
fumecheng-12619	190	40	,	,	PUNCT
fumecheng-12619	190	41	both	both	CCONJ
fumecheng-12619	190	42	with	with	ADP
fumecheng-12619	190	43	and	and	CCONJ
fumecheng-12619	190	44	without	without	ADP
fumecheng-12619	190	45	surface	surface	NOUN
fumecheng-12619	190	46	/	/	SYM
fumecheng-12619	190	47	interface	interface	NOUN
fumecheng-12619	190	48	effects	effect	NOUN
fumecheng-12619	190	49	.	.	PUNCT
fumecheng-12619	191	1	as	as	SCONJ
fumecheng-12619	191	2	depicted	depict	VERB
fumecheng-12619	191	3	in	in	ADP
fumecheng-12619	191	4	fig	fig	NOUN
fumecheng-12619	191	5	.	.	PUNCT
fumecheng-12619	192	1	2	2	NUM
fumecheng-12619	192	2	,	,	PUNCT
fumecheng-12619	192	3	surface	surface	NOUN
fumecheng-12619	192	4	/	/	SYM
fumecheng-12619	192	5	interface	interface	NOUN
fumecheng-12619	192	6	densities	density	NOUN
fumecheng-12619	192	7	corresponding	correspond	VERB
fumecheng-12619	192	8	to	to	PART
fumecheng-12619	192	9	case	case	NOUN
fumecheng-12619	192	10	1	1	NUM
fumecheng-12619	192	11	result	result	NOUN
fumecheng-12619	192	12	in	in	ADP
fumecheng-12619	192	13	a	a	DET
fumecheng-12619	192	14	reduction	reduction	NOUN
fumecheng-12619	192	15	of	of	ADP
fumecheng-12619	192	16	penr	penr	ADJ
fumecheng-12619	192	17	stiffness	stiffness	NOUN
fumecheng-12619	192	18	,	,	PUNCT
fumecheng-12619	192	19	leading	lead	VERB
fumecheng-12619	192	20	to	to	ADP
fumecheng-12619	192	21	a	a	DET
fumecheng-12619	192	22	lower	low	ADJ
fumecheng-12619	192	23	dimensionless	dimensionless	ADJ
fumecheng-12619	192	24	natural	natural	ADJ
fumecheng-12619	192	25	frequency	frequency	NOUN
fumecheng-12619	192	26	compared	compare	VERB
fumecheng-12619	192	27	to	to	ADP
fumecheng-12619	192	28	the	the	DET
fumecheng-12619	192	29	absence	absence	NOUN
fumecheng-12619	192	30	of	of	ADP
fumecheng-12619	192	31	surface	surface	NOUN
fumecheng-12619	192	32	/	/	SYM
fumecheng-12619	192	33	interface	interface	NOUN
fumecheng-12619	192	34	effects	effect	NOUN
fumecheng-12619	192	35	.	.	PUNCT
fumecheng-12619	193	1	conversely	conversely	ADV
fumecheng-12619	193	2	,	,	PUNCT
fumecheng-12619	193	3	surface	surface	NOUN
fumecheng-12619	193	4	/	/	SYM
fumecheng-12619	193	5	interface	interface	NOUN
fumecheng-12619	193	6	densities	density	NOUN
fumecheng-12619	193	7	associated	associate	VERB
fumecheng-12619	193	8	with	with	ADP
fumecheng-12619	193	9	case	case	NOUN
fumecheng-12619	193	10	2	2	NUM
fumecheng-12619	193	11	induce	induce	VERB
fumecheng-12619	193	12	an	an	DET
fumecheng-12619	193	13	increase	increase	NOUN
fumecheng-12619	193	14	in	in	ADP
fumecheng-12619	193	15	penr	penr	ADJ
fumecheng-12619	193	16	stiffness	stiffness	NOUN
fumecheng-12619	193	17	,	,	PUNCT
fumecheng-12619	193	18	consequently	consequently	ADV
fumecheng-12619	193	19	yielding	yield	VERB
fumecheng-12619	193	20	a	a	DET
fumecheng-12619	193	21	higher	high	ADJ
fumecheng-12619	193	22	dimensionless	dimensionless	ADJ
fumecheng-12619	193	23	natural	natural	ADJ
fumecheng-12619	193	24	frequency	frequency	NOUN
fumecheng-12619	193	25	.	.	PUNCT
fumecheng-12619	194	1	fig	fig	NOUN
fumecheng-12619	194	2	.	.	PUNCT
fumecheng-12619	195	1	2	2	NUM
fumecheng-12619	195	2	natural	natural	ADJ
fumecheng-12619	195	3	frequency	frequency	NOUN
fumecheng-12619	195	4	vs.	vs.	ADP
fumecheng-12619	195	5	dimensionless	dimensionless	NOUN
fumecheng-12619	195	6	nonlocal	nonlocal	ADJ
fumecheng-12619	195	7	scale	scale	NOUN
fumecheng-12619	195	8	parameter	parameter	NOUN
fumecheng-12619	195	9	�	�	PROPN
fumecheng-12619	195	10	̅	̅	NOUN
fumecheng-12619	195	11	�	�	NOUN
fumecheng-12619	195	12	with	with	ADP
fumecheng-12619	195	13	�	�	NOUN
fumecheng-12619	195	14	̅	̅	NOUN
fumecheng-12619	195	15	�	�	NOUN
fumecheng-12619	195	16	=	=	NOUN
fumecheng-12619	195	17	0.01	0.01	NUM
fumecheng-12619	195	18	:	:	PUNCT
fumecheng-12619	195	19	influence	influence	NOUN
fumecheng-12619	195	20	of	of	ADP
fumecheng-12619	195	21	surface	surface	NOUN
fumecheng-12619	195	22	/	/	SYM
fumecheng-12619	195	23	interface	interface	NOUN
fumecheng-12619	195	24	effects	effect	NOUN
fumecheng-12619	195	25	for	for	ADP
fumecheng-12619	195	26	different	different	ADJ
fumecheng-12619	195	27	boundary	boundary	ADJ
fumecheng-12619	195	28	conditions	condition	NOUN
fumecheng-12619	195	29	in	in	ADP
fumecheng-12619	195	30	all	all	DET
fumecheng-12619	195	31	cases	case	NOUN
fumecheng-12619	195	32	,	,	PUNCT
fumecheng-12619	195	33	the	the	DET
fumecheng-12619	195	34	dimensionless	dimensionless	ADJ
fumecheng-12619	195	35	natural	natural	ADJ
fumecheng-12619	195	36	frequency	frequency	NOUN
fumecheng-12619	195	37	(	(	PUNCT
fumecheng-12619	195	38	dnf	dnf	X
fumecheng-12619	195	39	)	)	PUNCT
fumecheng-12619	195	40	decreases	decrease	VERB
fumecheng-12619	195	41	with	with	ADP
fumecheng-12619	195	42	increasing	increase	VERB
fumecheng-12619	195	43	nonlocal	nonlocal	ADJ
fumecheng-12619	195	44	scale	scale	NOUN
fumecheng-12619	195	45	parameter	parameter	NOUN
fumecheng-12619	195	46	�	�	PROPN
fumecheng-12619	195	47	̅	̅	NOUN
fumecheng-12619	195	48	�	�	NOUN
fumecheng-12619	195	49	with	with	ADP
fumecheng-12619	195	50	�	�	NOUN
fumecheng-12619	195	51	̅	̅	NOUN
fumecheng-12619	195	52	�	�	NOUN
fumecheng-12619	195	53	=	=	SYM
fumecheng-12619	195	54	0.01	0.01	NUM
fumecheng-12619	195	55	,	,	PUNCT
fumecheng-12619	195	56	attributable	attributable	ADJ
fumecheng-12619	195	57	to	to	ADP
fumecheng-12619	195	58	the	the	DET
fumecheng-12619	195	59	reduced	reduced	ADJ
fumecheng-12619	195	60	stiffness	stiffness	NOUN
fumecheng-12619	195	61	of	of	ADP
fumecheng-12619	195	62	the	the	DET
fumecheng-12619	195	63	porous	porous	ADJ
fumecheng-12619	195	64	elastic	elastic	ADJ
fumecheng-12619	195	65	nanorod	nanorod	NOUN
fumecheng-12619	195	66	(	(	PUNCT
fumecheng-12619	195	67	penr	penr	PROPN
fumecheng-12619	195	68	)	)	PUNCT
fumecheng-12619	195	69	.	.	PUNCT
fumecheng-12619	196	1	as	as	SCONJ
fumecheng-12619	196	2	shown	show	VERB
fumecheng-12619	196	3	in	in	ADP
fumecheng-12619	196	4	fig	fig	NOUN
fumecheng-12619	196	5	.	.	PUNCT
fumecheng-12619	197	1	3	3	NUM
fumecheng-12619	197	2	,	,	PUNCT
fumecheng-12619	197	3	the	the	DET
fumecheng-12619	197	4	dnf	dnf	PROPN
fumecheng-12619	197	5	increases	increase	VERB
fumecheng-12619	197	6	with	with	ADP
fumecheng-12619	197	7	the	the	DET
fumecheng-12619	197	8	dimensionless	dimensionless	NOUN
fumecheng-12619	197	9	material	material	NOUN
fumecheng-12619	197	10	length	length	NOUN
fumecheng-12619	197	11	scale	scale	NOUN
fumecheng-12619	197	12	parameter	parameter	PROPN
fumecheng-12619	197	13	�	�	PROPN
fumecheng-12619	197	14	̅	̅	NOUN
fumecheng-12619	197	15	�	�	NOUN
fumecheng-12619	197	16	with	with	ADP
fumecheng-12619	197	17	�	�	NOUN
fumecheng-12619	197	18	̅	̅	NOUN
fumecheng-12619	197	19	�	�	NOUN
fumecheng-12619	197	20	=	=	SYM
fumecheng-12619	197	21	0.1	0.1	NUM
fumecheng-12619	197	22	across	across	ADP
fumecheng-12619	197	23	all	all	DET
fumecheng-12619	197	24	scenarios	scenario	NOUN
fumecheng-12619	197	25	,	,	PUNCT
fumecheng-12619	197	26	owing	owe	VERB
fumecheng-12619	197	27	to	to	ADP
fumecheng-12619	197	28	the	the	DET
fumecheng-12619	197	29	enhanced	enhanced	ADJ
fumecheng-12619	197	30	penr	penr	ADJ
fumecheng-12619	197	31	stiffness	stiffness	NOUN
fumecheng-12619	197	32	.	.	PUNCT
fumecheng-12619	198	1	these	these	DET
fumecheng-12619	198	2	results	result	NOUN
fumecheng-12619	198	3	align	align	VERB
fumecheng-12619	198	4	with	with	ADP
fumecheng-12619	198	5	the	the	DET
fumecheng-12619	198	6	previously	previously	ADV
fumecheng-12619	198	7	discussed	discuss	VERB
fumecheng-12619	198	8	effects	effect	NOUN
fumecheng-12619	198	9	of	of	ADP
fumecheng-12619	198	10	surface	surface	NOUN
fumecheng-12619	198	11	/	/	SYM
fumecheng-12619	198	12	interface	interface	NOUN
fumecheng-12619	198	13	320	320	NUM
fumecheng-12619	198	14	s.h	s.h	NOUN
fumecheng-12619	198	15	.	.	PROPN
fumecheng-12619	198	16	hashemi	hashemi	PROPN
fumecheng-12619	198	17	kachapi	kachapi	PROPN
fumecheng-12619	198	18	,	,	PUNCT
fumecheng-12619	198	19	s.	s.	PROPN
fumecheng-12619	198	20	gh	gh	PROPN
fumecheng-12619	198	21	.	.	PROPN
fumecheng-12619	199	1	hashemi	hashemi	PROPN
fumecheng-12619	199	2	kachapi	kachapi	PROPN
fumecheng-12619	199	3	densities	density	NOUN
fumecheng-12619	199	4	.	.	PUNCT
fumecheng-12619	200	1	the	the	DET
fumecheng-12619	200	2	trends	trend	NOUN
fumecheng-12619	200	3	in	in	ADP
fumecheng-12619	200	4	figs	fig	NOUN
fumecheng-12619	200	5	.	.	PUNCT
fumecheng-12619	201	1	2	2	NUM
fumecheng-12619	201	2	and	and	CCONJ
fumecheng-12619	201	3	3	3	NUM
fumecheng-12619	201	4	demonstrate	demonstrate	VERB
fumecheng-12619	201	5	that	that	SCONJ
fumecheng-12619	201	6	the	the	DET
fumecheng-12619	201	7	nonlocal	nonlocal	ADJ
fumecheng-12619	201	8	scale	scale	NOUN
fumecheng-12619	201	9	parameter	parameter	NOUN
fumecheng-12619	201	10	�	�	PROPN
fumecheng-12619	201	11	̅	̅	NOUN
fumecheng-12619	201	12	�	�	PROPN
fumecheng-12619	201	13	and	and	CCONJ
fumecheng-12619	201	14	material	material	NOUN
fumecheng-12619	201	15	length	length	NOUN
fumecheng-12619	201	16	scale	scale	NOUN
fumecheng-12619	201	17	parameter	parameter	PROPN
fumecheng-12619	201	18	�	�	PROPN
fumecheng-12619	201	19	̅	̅	NOUN
fumecheng-12619	201	20	�	�	NOUN
fumecheng-12619	201	21	inversely	inversely	ADV
fumecheng-12619	201	22	influence	influence	VERB
fumecheng-12619	201	23	penr	penr	ADJ
fumecheng-12619	201	24	stiffness	stiffness	NOUN
fumecheng-12619	201	25	:	:	PUNCT
fumecheng-12619	201	26	�	�	NOUN
fumecheng-12619	201	27	̅	̅	NOUN
fumecheng-12619	201	28	�	�	NOUN
fumecheng-12619	201	29	reduces	reduce	VERB
fumecheng-12619	201	30	stiffness	stiffness	NOUN
fumecheng-12619	201	31	,	,	PUNCT
fumecheng-12619	201	32	thereby	thereby	ADV
fumecheng-12619	201	33	lowering	lower	VERB
fumecheng-12619	201	34	the	the	DET
fumecheng-12619	201	35	dnf	dnf	PROPN
fumecheng-12619	201	36	,	,	PUNCT
fumecheng-12619	201	37	while	while	SCONJ
fumecheng-12619	201	38	�	�	NOUN
fumecheng-12619	201	39	̅	̅	NOUN
fumecheng-12619	201	40	�	�	NOUN
fumecheng-12619	201	41	enhances	enhance	VERB
fumecheng-12619	201	42	stiffness	stiffness	NOUN
fumecheng-12619	201	43	,	,	PUNCT
fumecheng-12619	201	44	increasing	increase	VERB
fumecheng-12619	201	45	the	the	DET
fumecheng-12619	201	46	dnf	dnf	PROPN
fumecheng-12619	201	47	.	.	PUNCT
fumecheng-12619	202	1	additionally	additionally	ADV
fumecheng-12619	202	2	,	,	PUNCT
fumecheng-12619	202	3	the	the	DET
fumecheng-12619	202	4	dimensionless	dimensionless	ADJ
fumecheng-12619	202	5	natural	natural	ADJ
fumecheng-12619	202	6	frequency	frequency	NOUN
fumecheng-12619	202	7	associated	associate	VERB
fumecheng-12619	202	8	with	with	ADP
fumecheng-12619	202	9	the	the	DET
fumecheng-12619	202	10	cc	cc	PROPN
fumecheng-12619	202	11	boundary	boundary	ADJ
fumecheng-12619	202	12	condition	condition	NOUN
fumecheng-12619	202	13	consistently	consistently	ADV
fumecheng-12619	202	14	exceeds	exceed	VERB
fumecheng-12619	202	15	those	those	PRON
fumecheng-12619	202	16	of	of	ADP
fumecheng-12619	202	17	cs	cs	PROPN
fumecheng-12619	202	18	,	,	PUNCT
fumecheng-12619	202	19	ss	ss	NOUN
fumecheng-12619	202	20	,	,	PUNCT
fumecheng-12619	202	21	and	and	CCONJ
fumecheng-12619	202	22	cf	cf	NOUN
fumecheng-12619	202	23	configurations	configuration	NOUN
fumecheng-12619	202	24	.	.	PUNCT
fumecheng-12619	203	1	this	this	DET
fumecheng-12619	203	2	disparity	disparity	NOUN
fumecheng-12619	203	3	arises	arise	VERB
fumecheng-12619	203	4	from	from	ADP
fumecheng-12619	203	5	the	the	DET
fumecheng-12619	203	6	greater	great	ADJ
fumecheng-12619	203	7	structural	structural	ADJ
fumecheng-12619	203	8	rigidity	rigidity	NOUN
fumecheng-12619	203	9	inherent	inherent	ADJ
fumecheng-12619	203	10	to	to	ADP
fumecheng-12619	203	11	the	the	DET
fumecheng-12619	203	12	cc	cc	PROPN
fumecheng-12619	203	13	boundary	boundary	ADJ
fumecheng-12619	203	14	condition	condition	NOUN
fumecheng-12619	203	15	compared	compare	VERB
fumecheng-12619	203	16	to	to	ADP
fumecheng-12619	203	17	others	other	NOUN
fumecheng-12619	203	18	.	.	PUNCT
fumecheng-12619	204	1	fig	fig	NOUN
fumecheng-12619	204	2	.	.	PUNCT
fumecheng-12619	205	1	3	3	NUM
fumecheng-12619	205	2	natural	natural	ADJ
fumecheng-12619	205	3	frequency	frequency	NOUN
fumecheng-12619	205	4	vs.	vs.	ADP
fumecheng-12619	205	5	dimensionless	dimensionless	NOUN
fumecheng-12619	205	6	material	material	NOUN
fumecheng-12619	205	7	length	length	NOUN
fumecheng-12619	205	8	scale	scale	NOUN
fumecheng-12619	205	9	parameter	parameter	PROPN
fumecheng-12619	205	10	�	�	PROPN
fumecheng-12619	205	11	̅	̅	NOUN
fumecheng-12619	205	12	�	�	NOUN
fumecheng-12619	205	13	with	with	ADP
fumecheng-12619	205	14	�	�	NOUN
fumecheng-12619	205	15	̅	̅	NOUN
fumecheng-12619	205	16	�	�	NOUN
fumecheng-12619	205	17	=	=	SYM
fumecheng-12619	205	18	0.1	0.1	NUM
fumecheng-12619	205	19	:	:	PUNCT
fumecheng-12619	205	20	influence	influence	NOUN
fumecheng-12619	205	21	of	of	ADP
fumecheng-12619	205	22	surface	surface	NOUN
fumecheng-12619	205	23	/	/	SYM
fumecheng-12619	205	24	interface	interface	NOUN
fumecheng-12619	205	25	effects	effect	NOUN
fumecheng-12619	205	26	for	for	ADP
fumecheng-12619	205	27	different	different	ADJ
fumecheng-12619	205	28	boundary	boundary	ADJ
fumecheng-12619	205	29	conditions	condition	NOUN
fumecheng-12619	205	30	fig	fig	NOUN
fumecheng-12619	205	31	.	.	PUNCT
fumecheng-12619	206	1	4	4	NUM
fumecheng-12619	206	2	illustrates	illustrate	VERB
fumecheng-12619	206	3	the	the	DET
fumecheng-12619	206	4	influence	influence	NOUN
fumecheng-12619	206	5	of	of	ADP
fumecheng-12619	206	6	the	the	DET
fumecheng-12619	206	7	length	length	NOUN
fumecheng-12619	206	8	to	to	PART
fumecheng-12619	206	9	radius	radius	NOUN
fumecheng-12619	206	10	ratio	ratio	NOUN
fumecheng-12619	206	11	(	(	PUNCT
fumecheng-12619	206	12	𝑳	𝑳	NOUN
fumecheng-12619	206	13	𝑹⁄	𝑹⁄	NOUN
fumecheng-12619	206	14	)	)	PUNCT
fumecheng-12619	206	15	on	on	ADP
fumecheng-12619	206	16	the	the	DET
fumecheng-12619	206	17	dimensionless	dimensionless	ADJ
fumecheng-12619	206	18	natural	natural	ADJ
fumecheng-12619	206	19	frequency	frequency	NOUN
fumecheng-12619	206	20	(	(	PUNCT
fumecheng-12619	206	21	dnf	dnf	PROPN
fumecheng-12619	206	22	)	)	PUNCT
fumecheng-12619	206	23	as	as	ADP
fumecheng-12619	206	24	a	a	DET
fumecheng-12619	206	25	function	function	NOUN
fumecheng-12619	206	26	of	of	ADP
fumecheng-12619	206	27	the	the	DET
fumecheng-12619	206	28	dimensionless	dimensionless	ADJ
fumecheng-12619	206	29	nonlocal	nonlocal	ADJ
fumecheng-12619	206	30	scale	scale	NOUN
fumecheng-12619	206	31	parameter	parameter	NOUN
fumecheng-12619	206	32	(	(	PUNCT
fumecheng-12619	206	33	�	�	NOUN
fumecheng-12619	206	34	̅	̅	NOUN
fumecheng-12619	206	35	�	�	NOUN
fumecheng-12619	206	36	)	)	PUNCT
fumecheng-12619	206	37	for	for	ADP
fumecheng-12619	206	38	ss	ss	PROPN
fumecheng-12619	206	39	penr	penr	PROPN
fumecheng-12619	206	40	.	.	PUNCT
fumecheng-12619	207	1	the	the	DET
fumecheng-12619	207	2	results	result	NOUN
fumecheng-12619	207	3	incorporate	incorporate	VERB
fumecheng-12619	207	4	all	all	DET
fumecheng-12619	207	5	surface	surface	NOUN
fumecheng-12619	207	6	/	/	SYM
fumecheng-12619	207	7	interface	interface	NOUN
fumecheng-12619	207	8	effects	effect	NOUN
fumecheng-12619	207	9	,	,	PUNCT
fumecheng-12619	207	10	with	with	ADP
fumecheng-12619	207	11	�	�	NOUN
fumecheng-12619	207	12	̅	̅	NOUN
fumecheng-12619	207	13	�	�	NOUN
fumecheng-12619	207	14	=	=	SYM
fumecheng-12619	208	1	𝟎.	𝟎.	X
fumecheng-12619	208	2	𝟎𝟏.	𝟎𝟏.	NOUN
fumecheng-12619	208	3	as	as	ADP
fumecheng-12619	208	4	evident	evident	ADJ
fumecheng-12619	208	5	from	from	ADP
fumecheng-12619	208	6	fig	fig	NOUN
fumecheng-12619	208	7	.	.	PUNCT
fumecheng-12619	209	1	4	4	NUM
fumecheng-12619	209	2	,	,	PUNCT
fumecheng-12619	209	3	the	the	DET
fumecheng-12619	209	4	dimensionless	dimensionless	ADJ
fumecheng-12619	209	5	natural	natural	ADJ
fumecheng-12619	209	6	frequency	frequency	NOUN
fumecheng-12619	209	7	(	(	PUNCT
fumecheng-12619	209	8	dnf	dnf	X
fumecheng-12619	209	9	)	)	PUNCT
fumecheng-12619	209	10	decreases	decrease	VERB
fumecheng-12619	209	11	with	with	ADP
fumecheng-12619	209	12	increasing	increase	VERB
fumecheng-12619	209	13	values	value	NOUN
fumecheng-12619	209	14	of	of	ADP
fumecheng-12619	209	15	both	both	CCONJ
fumecheng-12619	209	16	the	the	DET
fumecheng-12619	209	17	length	length	NOUN
fumecheng-12619	209	18	to	to	PART
fumecheng-12619	209	19	radius	radius	NOUN
fumecheng-12619	209	20	ratio	ratio	NOUN
fumecheng-12619	209	21	(	(	PUNCT
fumecheng-12619	209	22	𝑳/𝑹	𝑳/𝑹	ADJ
fumecheng-12619	209	23	)	)	PUNCT
fumecheng-12619	209	24	and	and	CCONJ
fumecheng-12619	209	25	the	the	DET
fumecheng-12619	209	26	nonlocal	nonlocal	ADJ
fumecheng-12619	209	27	scale	scale	NOUN
fumecheng-12619	209	28	parameter	parameter	NOUN
fumecheng-12619	209	29	(	(	PUNCT
fumecheng-12619	209	30	�	�	NOUN
fumecheng-12619	209	31	̅	̅	NOUN
fumecheng-12619	209	32	�	�	NOUN
fumecheng-12619	209	33	)	)	PUNCT
fumecheng-12619	209	34	.	.	PUNCT
fumecheng-12619	210	1	this	this	DET
fumecheng-12619	210	2	trend	trend	NOUN
fumecheng-12619	210	3	is	be	AUX
fumecheng-12619	210	4	attributed	attribute	VERB
fumecheng-12619	210	5	to	to	ADP
fumecheng-12619	210	6	the	the	DET
fumecheng-12619	210	7	reduction	reduction	NOUN
fumecheng-12619	210	8	in	in	ADP
fumecheng-12619	210	9	stiffness	stiffness	NOUN
fumecheng-12619	210	10	of	of	ADP
fumecheng-12619	210	11	the	the	DET
fumecheng-12619	210	12	penr	penr	PROPN
fumecheng-12619	210	13	.	.	PUNCT
fumecheng-12619	211	1	fig	fig	NOUN
fumecheng-12619	211	2	.	.	PUNCT
fumecheng-12619	212	1	5	5	NUM
fumecheng-12619	212	2	depicts	depict	VERB
fumecheng-12619	212	3	the	the	DET
fumecheng-12619	212	4	variation	variation	NOUN
fumecheng-12619	212	5	of	of	ADP
fumecheng-12619	212	6	the	the	DET
fumecheng-12619	212	7	dnf	dnf	PROPN
fumecheng-12619	212	8	as	as	ADP
fumecheng-12619	212	9	a	a	DET
fumecheng-12619	212	10	function	function	NOUN
fumecheng-12619	212	11	of	of	ADP
fumecheng-12619	212	12	the	the	DET
fumecheng-12619	212	13	dimensionless	dimensionless	NOUN
fumecheng-12619	212	14	material	material	NOUN
fumecheng-12619	212	15	length	length	NOUN
fumecheng-12619	212	16	scale	scale	NOUN
fumecheng-12619	212	17	parameter	parameter	NOUN
fumecheng-12619	212	18	(	(	PUNCT
fumecheng-12619	212	19	�	�	NOUN
fumecheng-12619	212	20	̅	̅	NOUN
fumecheng-12619	212	21	�	�	NOUN
fumecheng-12619	212	22	)	)	PUNCT
fumecheng-12619	212	23	for	for	ADP
fumecheng-12619	212	24	ss	ss	PROPN
fumecheng-12619	212	25	penr	penr	PROPN
fumecheng-12619	212	26	under	under	ADP
fumecheng-12619	212	27	different	different	ADJ
fumecheng-12619	212	28	𝑳/𝑹	𝑳/𝑹	VERB
fumecheng-12619	212	29	ratios	ratio	NOUN
fumecheng-12619	212	30	.	.	PUNCT
fumecheng-12619	213	1	the	the	DET
fumecheng-12619	213	2	analysis	analysis	NOUN
fumecheng-12619	213	3	incorporates	incorporate	VERB
fumecheng-12619	213	4	all	all	DET
fumecheng-12619	213	5	surface	surface	NOUN
fumecheng-12619	213	6	/	/	SYM
fumecheng-12619	213	7	interface	interface	NOUN
fumecheng-12619	213	8	effects	effect	NOUN
fumecheng-12619	213	9	,	,	PUNCT
fumecheng-12619	213	10	with	with	ADP
fumecheng-12619	213	11	�	�	NOUN
fumecheng-12619	213	12	̅	̅	NOUN
fumecheng-12619	213	13	�	�	NOUN
fumecheng-12619	213	14	=	=	SYM
fumecheng-12619	213	15	𝟎.	𝟎.	NOUN
fumecheng-12619	213	16	𝟏.	𝟏.	PUNCT
fumecheng-12619	213	17	as	as	SCONJ
fumecheng-12619	213	18	shown	show	VERB
fumecheng-12619	213	19	in	in	ADP
fumecheng-12619	213	20	the	the	DET
fumecheng-12619	213	21	figure	figure	NOUN
fumecheng-12619	213	22	,	,	PUNCT
fumecheng-12619	213	23	the	the	DET
fumecheng-12619	213	24	dimensionless	dimensionless	ADJ
fumecheng-12619	213	25	natural	natural	ADJ
fumecheng-12619	213	26	frequency	frequency	NOUN
fumecheng-12619	213	27	increases	increase	NOUN
fumecheng-12619	213	28	with	with	ADP
fumecheng-12619	213	29	the	the	DET
fumecheng-12619	213	30	nonlocal	nonlocal	ADJ
fumecheng-12619	213	31	parameter	parameter	NOUN
fumecheng-12619	213	32	but	but	CCONJ
fumecheng-12619	213	33	decreases	decrease	VERB
fumecheng-12619	213	34	with	with	ADP
fumecheng-12619	213	35	the	the	DET
fumecheng-12619	213	36	𝑳/𝑹	𝑳/𝑹	ADJ
fumecheng-12619	213	37	ratio	ratio	NOUN
fumecheng-12619	213	38	.	.	PUNCT
fumecheng-12619	214	1	comparison	comparison	NOUN
fumecheng-12619	214	2	of	of	ADP
fumecheng-12619	214	3	nonclassical	nonclassical	ADJ
fumecheng-12619	214	4	controllers	controller	NOUN
fumecheng-12619	214	5	on	on	ADP
fumecheng-12619	214	6	nonlinear	nonlinear	ADJ
fumecheng-12619	214	7	vibrations	vibration	NOUN
fumecheng-12619	214	8	analysis	analysis	NOUN
fumecheng-12619	214	9	of	of	ADP
fumecheng-12619	214	10	piezoelectric	piezoelectric	NOUN
fumecheng-12619	214	11	...	...	PUNCT
fumecheng-12619	214	12	321	321	NUM
fumecheng-12619	214	13	fig	fig	NOUN
fumecheng-12619	214	14	.	.	PUNCT
fumecheng-12619	215	1	4	4	NUM
fumecheng-12619	215	2	natural	natural	ADJ
fumecheng-12619	215	3	frequency	frequency	NOUN
fumecheng-12619	215	4	vs.	vs.	ADP
fumecheng-12619	215	5	dimensionless	dimensionless	NOUN
fumecheng-12619	215	6	nonlocal	nonlocal	ADJ
fumecheng-12619	215	7	scale	scale	NOUN
fumecheng-12619	215	8	parameter	parameter	NOUN
fumecheng-12619	215	9	�	�	PROPN
fumecheng-12619	215	10	̅	̅	NOUN
fumecheng-12619	215	11	�	�	NOUN
fumecheng-12619	215	12	:	:	PUNCT
fumecheng-12619	215	13	influence	influence	NOUN
fumecheng-12619	215	14	of	of	ADP
fumecheng-12619	215	15	𝐿	𝐿	PROPN
fumecheng-12619	215	16	𝑅⁄	𝑅⁄	PROPN
fumecheng-12619	215	17	ratio	ratio	NOUN
fumecheng-12619	215	18	with	with	ADP
fumecheng-12619	215	19	all	all	DET
fumecheng-12619	215	20	surface	surface	NOUN
fumecheng-12619	215	21	/	/	SYM
fumecheng-12619	215	22	interface	interface	NOUN
fumecheng-12619	215	23	effects	effect	NOUN
fumecheng-12619	215	24	and	and	CCONJ
fumecheng-12619	215	25	�	�	NOUN
fumecheng-12619	215	26	̅	̅	NOUN
fumecheng-12619	215	27	�	�	NOUN
fumecheng-12619	215	28	=	=	SYM
fumecheng-12619	215	29	0.01	0.01	NUM
fumecheng-12619	215	30	fig	fig	NOUN
fumecheng-12619	215	31	.	.	PUNCT
fumecheng-12619	216	1	5	5	NUM
fumecheng-12619	216	2	natural	natural	ADJ
fumecheng-12619	216	3	frequency	frequency	NOUN
fumecheng-12619	216	4	vs.	vs.	ADP
fumecheng-12619	216	5	dimensionless	dimensionless	NOUN
fumecheng-12619	216	6	material	material	NOUN
fumecheng-12619	216	7	length	length	NOUN
fumecheng-12619	216	8	scale	scale	NOUN
fumecheng-12619	216	9	parameter	parameter	PROPN
fumecheng-12619	216	10	�	�	PROPN
fumecheng-12619	216	11	̅	̅	NOUN
fumecheng-12619	216	12	�	�	NOUN
fumecheng-12619	216	13	:	:	PUNCT
fumecheng-12619	216	14	influence	influence	NOUN
fumecheng-12619	216	15	of	of	ADP
fumecheng-12619	216	16	𝐿	𝐿	PROPN
fumecheng-12619	216	17	𝑅⁄	𝑅⁄	PROPN
fumecheng-12619	216	18	ratio	ratio	NOUN
fumecheng-12619	216	19	with	with	ADP
fumecheng-12619	216	20	all	all	DET
fumecheng-12619	216	21	surface/	surface/	NUM
fumecheng-12619	216	22	interface	interface	NOUN
fumecheng-12619	216	23	effects	effect	NOUN
fumecheng-12619	216	24	and	and	CCONJ
fumecheng-12619	216	25	μ̅	μ̅	NOUN
fumecheng-12619	216	26	=	=	SYM
fumecheng-12619	216	27	0.1	0.1	NUM
fumecheng-12619	216	28	fig	fig	NOUN
fumecheng-12619	216	29	.	.	PUNCT
fumecheng-12619	217	1	6	6	NUM
fumecheng-12619	217	2	compares	compare	VERB
fumecheng-12619	217	3	the	the	DET
fumecheng-12619	217	4	dimensionless	dimensionless	ADJ
fumecheng-12619	217	5	natural	natural	ADJ
fumecheng-12619	217	6	frequency	frequency	NOUN
fumecheng-12619	217	7	predicted	predict	VERB
fumecheng-12619	217	8	by	by	ADP
fumecheng-12619	217	9	three	three	NUM
fumecheng-12619	217	10	nonclassical	nonclassical	ADJ
fumecheng-12619	217	11	theories	theory	NOUN
fumecheng-12619	217	12	,	,	PUNCT
fumecheng-12619	217	13	nlt	nlt	PROPN
fumecheng-12619	217	14	,	,	PUNCT
fumecheng-12619	217	15	sgt	sgt	PROPN
fumecheng-12619	217	16	,	,	PUNCT
fumecheng-12619	217	17	and	and	CCONJ
fumecheng-12619	217	18	gmsit	gmsit	NOUN
fumecheng-12619	217	19	,	,	PUNCT
fumecheng-12619	217	20	against	against	ADP
fumecheng-12619	217	21	the	the	DET
fumecheng-12619	217	22	classical	classical	ADJ
fumecheng-12619	217	23	theory	theory	NOUN
fumecheng-12619	217	24	ct	ct	NUM
fumecheng-12619	217	25	for	for	ADP
fumecheng-12619	217	26	ss	ss	PROPN
fumecheng-12619	217	27	penr	penr	PROPN
fumecheng-12619	217	28	under	under	ADP
fumecheng-12619	217	29	varying	vary	VERB
fumecheng-12619	217	30	piezoelectric	piezoelectric	ADJ
fumecheng-12619	217	31	thickness	thickness	NOUN
fumecheng-12619	217	32	to	to	PART
fumecheng-12619	217	33	radius	radius	NOUN
fumecheng-12619	217	34	ratios	ratio	NOUN
fumecheng-12619	217	35	(	(	PUNCT
fumecheng-12619	217	36	𝒉𝒑	𝒉𝒑	PROPN
fumecheng-12619	217	37	𝑹⁄	𝑹⁄	PROPN
fumecheng-12619	217	38	)	)	PUNCT
fumecheng-12619	217	39	.	.	PUNCT
fumecheng-12619	218	1	as	as	ADP
fumecheng-12619	218	2	evident	evident	ADJ
fumecheng-12619	218	3	from	from	ADP
fumecheng-12619	218	4	the	the	DET
fumecheng-12619	218	5	figure	figure	NOUN
fumecheng-12619	218	6	,	,	PUNCT
fumecheng-12619	218	7	the	the	DET
fumecheng-12619	218	8	322	322	NUM
fumecheng-12619	218	9	s.h	s.h	PROPN
fumecheng-12619	218	10	.	.	PROPN
fumecheng-12619	218	11	hashemi	hashemi	PROPN
fumecheng-12619	218	12	kachapi	kachapi	PROPN
fumecheng-12619	218	13	,	,	PUNCT
fumecheng-12619	218	14	s.	s.	PROPN
fumecheng-12619	218	15	gh	gh	PROPN
fumecheng-12619	218	16	.	.	PROPN
fumecheng-12619	219	1	hashemi	hashemi	PROPN
fumecheng-12619	219	2	kachapi	kachapi	PROPN
fumecheng-12619	219	3	gmsit	gmsit	PROPN
fumecheng-12619	219	4	(	(	PUNCT
fumecheng-12619	219	5	case	case	NOUN
fumecheng-12619	219	6	2	2	NUM
fumecheng-12619	219	7	)	)	PUNCT
fumecheng-12619	219	8	yields	yield	VERB
fumecheng-12619	219	9	the	the	DET
fumecheng-12619	219	10	highest	high	ADJ
fumecheng-12619	219	11	dnf	dnf	PROPN
fumecheng-12619	219	12	,	,	PUNCT
fumecheng-12619	219	13	indicating	indicate	VERB
fumecheng-12619	219	14	greater	great	ADJ
fumecheng-12619	219	15	structural	structural	ADJ
fumecheng-12619	219	16	rigidity	rigidity	NOUN
fumecheng-12619	219	17	in	in	ADP
fumecheng-12619	219	18	this	this	DET
fumecheng-12619	219	19	configuration	configuration	NOUN
fumecheng-12619	219	20	compared	compare	VERB
fumecheng-12619	219	21	to	to	ADP
fumecheng-12619	219	22	other	other	ADJ
fumecheng-12619	219	23	cases	case	NOUN
fumecheng-12619	219	24	.	.	PUNCT
fumecheng-12619	220	1	the	the	DET
fumecheng-12619	220	2	lowest	low	ADJ
fumecheng-12619	220	3	natural	natural	ADJ
fumecheng-12619	220	4	frequency	frequency	NOUN
fumecheng-12619	220	5	is	be	AUX
fumecheng-12619	220	6	observed	observe	VERB
fumecheng-12619	220	7	when	when	SCONJ
fumecheng-12619	220	8	gmsit	gmsit	NOUN
fumecheng-12619	220	9	(	(	PUNCT
fumecheng-12619	220	10	case	case	NOUN
fumecheng-12619	220	11	1	1	NUM
fumecheng-12619	220	12	)	)	PUNCT
fumecheng-12619	220	13	is	be	AUX
fumecheng-12619	220	14	considered	consider	VERB
fumecheng-12619	220	15	in	in	ADP
fumecheng-12619	220	16	combination	combination	NOUN
fumecheng-12619	220	17	with	with	ADP
fumecheng-12619	220	18	sgt	sgt	PROPN
fumecheng-12619	220	19	,	,	PUNCT
fumecheng-12619	220	20	i.e.	i.e.	X
fumecheng-12619	220	21	gmsit+sgt	gmsit+sgt	NOUN
fumecheng-12619	220	22	(	(	PUNCT
fumecheng-12619	220	23	�	�	NOUN
fumecheng-12619	220	24	̅	̅	NOUN
fumecheng-12619	220	25	�	�	NOUN
fumecheng-12619	220	26	=	=	SYM
fumecheng-12619	220	27	𝟎.	𝟎.	NOUN
fumecheng-12619	220	28	𝟏	𝟏	NUM
fumecheng-12619	220	29	,	,	PUNCT
fumecheng-12619	220	30	�	�	NOUN
fumecheng-12619	220	31	̅	̅	NOUN
fumecheng-12619	220	32	�	�	NOUN
fumecheng-12619	220	33	=	=	SYM
fumecheng-12619	220	34	𝟎.	𝟎.	X
fumecheng-12619	220	35	𝟎𝟏	𝟎𝟏	NUM
fumecheng-12619	220	36	)	)	PUNCT
fumecheng-12619	220	37	,	,	PUNCT
fumecheng-12619	220	38	indicating	indicate	VERB
fumecheng-12619	220	39	that	that	SCONJ
fumecheng-12619	220	40	this	this	DET
fumecheng-12619	220	41	combination	combination	NOUN
fumecheng-12619	220	42	results	result	VERB
fumecheng-12619	220	43	in	in	ADP
fumecheng-12619	220	44	the	the	DET
fumecheng-12619	220	45	lowest	low	ADJ
fumecheng-12619	220	46	system	system	NOUN
fumecheng-12619	220	47	stiffness	stiffness	NOUN
fumecheng-12619	220	48	.	.	PUNCT
fumecheng-12619	221	1	additionally	additionally	ADV
fumecheng-12619	221	2	,	,	PUNCT
fumecheng-12619	221	3	the	the	DET
fumecheng-12619	221	4	natural	natural	ADJ
fumecheng-12619	221	5	frequency	frequency	NOUN
fumecheng-12619	221	6	predicted	predict	VERB
fumecheng-12619	221	7	by	by	ADP
fumecheng-12619	221	8	classical	classical	ADJ
fumecheng-12619	221	9	theory	theory	NOUN
fumecheng-12619	221	10	is	be	AUX
fumecheng-12619	221	11	higher	high	ADJ
fumecheng-12619	221	12	than	than	ADP
fumecheng-12619	221	13	those	those	PRON
fumecheng-12619	221	14	predicted	predict	VERB
fumecheng-12619	221	15	by	by	ADP
fumecheng-12619	221	16	nlt	nlt	PROPN
fumecheng-12619	221	17	and	and	CCONJ
fumecheng-12619	221	18	sgt	sgt	PROPN
fumecheng-12619	221	19	,	,	PUNCT
fumecheng-12619	221	20	demonstrating	demonstrate	VERB
fumecheng-12619	221	21	a	a	DET
fumecheng-12619	221	22	reduction	reduction	NOUN
fumecheng-12619	221	23	in	in	ADP
fumecheng-12619	221	24	system	system	NOUN
fumecheng-12619	221	25	rigidity	rigidity	NOUN
fumecheng-12619	221	26	when	when	SCONJ
fumecheng-12619	221	27	these	these	DET
fumecheng-12619	221	28	nonclassical	nonclassical	ADJ
fumecheng-12619	221	29	theories	theory	NOUN
fumecheng-12619	221	30	are	be	AUX
fumecheng-12619	221	31	considered	consider	VERB
fumecheng-12619	221	32	.	.	PUNCT
fumecheng-12619	222	1	nonlocal	nonlocal	ADJ
fumecheng-12619	222	2	theory	theory	NOUN
fumecheng-12619	222	3	predicts	predict	VERB
fumecheng-12619	222	4	a	a	DET
fumecheng-12619	222	5	higher	high	ADJ
fumecheng-12619	222	6	natural	natural	ADJ
fumecheng-12619	222	7	frequency	frequency	NOUN
fumecheng-12619	222	8	than	than	SCONJ
fumecheng-12619	222	9	strain	strain	VERB
fumecheng-12619	222	10	gradient	gradient	ADJ
fumecheng-12619	222	11	theory	theory	NOUN
fumecheng-12619	222	12	due	due	ADP
fumecheng-12619	222	13	to	to	ADP
fumecheng-12619	222	14	its	its	PRON
fumecheng-12619	222	15	greater	great	ADJ
fumecheng-12619	222	16	rigidity	rigidity	NOUN
fumecheng-12619	222	17	.	.	PUNCT
fumecheng-12619	223	1	surface	surface	NOUN
fumecheng-12619	223	2	/	/	SYM
fumecheng-12619	223	3	interface	interface	NOUN
fumecheng-12619	223	4	effects	effect	NOUN
fumecheng-12619	223	5	,	,	PUNCT
fumecheng-12619	223	6	depending	depend	VERB
fumecheng-12619	223	7	on	on	ADP
fumecheng-12619	223	8	the	the	DET
fumecheng-12619	223	9	surface	surface	NOUN
fumecheng-12619	223	10	/	/	SYM
fumecheng-12619	223	11	interface	interface	NOUN
fumecheng-12619	223	12	densities	density	NOUN
fumecheng-12619	223	13	,	,	PUNCT
fumecheng-12619	223	14	can	can	AUX
fumecheng-12619	223	15	result	result	VERB
fumecheng-12619	223	16	in	in	ADP
fumecheng-12619	223	17	natural	natural	ADJ
fumecheng-12619	223	18	frequencies	frequency	NOUN
fumecheng-12619	223	19	higher	high	ADJ
fumecheng-12619	223	20	or	or	CCONJ
fumecheng-12619	223	21	lower	low	ADJ
fumecheng-12619	223	22	than	than	ADP
fumecheng-12619	223	23	those	those	PRON
fumecheng-12619	223	24	predicted	predict	VERB
fumecheng-12619	223	25	by	by	ADP
fumecheng-12619	223	26	classical	classical	ADJ
fumecheng-12619	223	27	theory	theory	NOUN
fumecheng-12619	223	28	.	.	PUNCT
fumecheng-12619	224	1	however	however	ADV
fumecheng-12619	224	2	,	,	PUNCT
fumecheng-12619	224	3	the	the	DET
fumecheng-12619	224	4	combined	combined	ADJ
fumecheng-12619	224	5	application	application	NOUN
fumecheng-12619	224	6	of	of	ADP
fumecheng-12619	224	7	nlt	nlt	PROPN
fumecheng-12619	224	8	and	and	CCONJ
fumecheng-12619	224	9	sgt	sgt	PROPN
fumecheng-12619	224	10	consistently	consistently	ADV
fumecheng-12619	224	11	yields	yield	VERB
fumecheng-12619	224	12	a	a	DET
fumecheng-12619	224	13	lower	low	ADJ
fumecheng-12619	224	14	natural	natural	ADJ
fumecheng-12619	224	15	frequency	frequency	NOUN
fumecheng-12619	224	16	than	than	ADP
fumecheng-12619	224	17	classical	classical	ADJ
fumecheng-12619	224	18	theory	theory	NOUN
fumecheng-12619	224	19	.	.	PUNCT
fumecheng-12619	225	1	furthermore	furthermore	ADV
fumecheng-12619	225	2	,	,	PUNCT
fumecheng-12619	225	3	the	the	DET
fumecheng-12619	225	4	𝒉𝒑	𝒉𝒑	PROPN
fumecheng-12619	225	5	𝑹⁄	𝑹⁄	PROPN
fumecheng-12619	225	6	ratio	ratio	NOUN
fumecheng-12619	225	7	significantly	significantly	ADV
fumecheng-12619	225	8	influences	influence	VERB
fumecheng-12619	225	9	the	the	DET
fumecheng-12619	225	10	dimensionless	dimensionless	ADJ
fumecheng-12619	225	11	natural	natural	ADJ
fumecheng-12619	225	12	frequency	frequency	NOUN
fumecheng-12619	225	13	(	(	PUNCT
fumecheng-12619	225	14	dnf	dnf	PROPN
fumecheng-12619	225	15	)	)	PUNCT
fumecheng-12619	225	16	.	.	PUNCT
fumecheng-12619	226	1	an	an	DET
fumecheng-12619	226	2	increase	increase	NOUN
fumecheng-12619	226	3	in	in	ADP
fumecheng-12619	226	4	this	this	DET
fumecheng-12619	226	5	ratio	ratio	NOUN
fumecheng-12619	226	6	leads	lead	VERB
fumecheng-12619	226	7	to	to	ADP
fumecheng-12619	226	8	a	a	DET
fumecheng-12619	226	9	decrease	decrease	NOUN
fumecheng-12619	226	10	in	in	ADP
fumecheng-12619	226	11	penr	penr	ADJ
fumecheng-12619	226	12	stiffness	stiffness	NOUN
fumecheng-12619	226	13	and	and	CCONJ
fumecheng-12619	226	14	,	,	PUNCT
fumecheng-12619	226	15	consequently	consequently	ADV
fumecheng-12619	226	16	,	,	PUNCT
fumecheng-12619	226	17	a	a	DET
fumecheng-12619	226	18	decrease	decrease	NOUN
fumecheng-12619	226	19	in	in	ADP
fumecheng-12619	226	20	the	the	DET
fumecheng-12619	226	21	natural	natural	ADJ
fumecheng-12619	226	22	frequency	frequency	NOUN
fumecheng-12619	226	23	.	.	PUNCT
fumecheng-12619	227	1	fig	fig	NOUN
fumecheng-12619	227	2	.	.	PUNCT
fumecheng-12619	228	1	6	6	NUM
fumecheng-12619	228	2	dimensionless	dimensionless	NOUN
fumecheng-12619	228	3	natural	natural	ADJ
fumecheng-12619	228	4	frequency	frequency	NOUN
fumecheng-12619	228	5	vs.	vs.	ADP
fumecheng-12619	228	6	piezoelectric	piezoelectric	NOUN
fumecheng-12619	228	7	thickness	thickness	NOUN
fumecheng-12619	228	8	to	to	PART
fumecheng-12619	228	9	radius	radius	VERB
fumecheng-12619	228	10	ratio	ratio	NOUN
fumecheng-12619	228	11	ℎ𝑝	ℎ𝑝	DET
fumecheng-12619	228	12	𝑅⁄	𝑅⁄	PROPN
fumecheng-12619	228	13	:	:	PUNCT
fumecheng-12619	228	14	a	a	DET
fumecheng-12619	228	15	comparison	comparison	NOUN
fumecheng-12619	228	16	of	of	ADP
fumecheng-12619	228	17	non	non	ADJ
fumecheng-12619	228	18	-	-	ADJ
fumecheng-12619	228	19	classical	classical	ADJ
fumecheng-12619	228	20	and	and	CCONJ
fumecheng-12619	228	21	classical	classical	ADJ
fumecheng-12619	228	22	theories	theory	NOUN
fumecheng-12619	228	23	fig	fig	NOUN
fumecheng-12619	228	24	.	.	PUNCT
fumecheng-12619	229	1	7	7	NUM
fumecheng-12619	229	2	compares	compare	VERB
fumecheng-12619	229	3	the	the	DET
fumecheng-12619	229	4	dimensionless	dimensionless	ADJ
fumecheng-12619	229	5	natural	natural	ADJ
fumecheng-12619	229	6	frequency	frequency	NOUN
fumecheng-12619	229	7	predicted	predict	VERB
fumecheng-12619	229	8	by	by	ADP
fumecheng-12619	229	9	three	three	NUM
fumecheng-12619	229	10	nonclassical	nonclassical	ADJ
fumecheng-12619	229	11	theories	theory	NOUN
fumecheng-12619	229	12	,	,	PUNCT
fumecheng-12619	229	13	nlt	nlt	PROPN
fumecheng-12619	229	14	,	,	PUNCT
fumecheng-12619	229	15	sgt	sgt	PROPN
fumecheng-12619	229	16	,	,	PUNCT
fumecheng-12619	229	17	and	and	CCONJ
fumecheng-12619	229	18	gmsit	gmsit	NOUN
fumecheng-12619	229	19	,	,	PUNCT
fumecheng-12619	229	20	with	with	ADP
fumecheng-12619	229	21	classical	classical	ADJ
fumecheng-12619	229	22	theory	theory	NOUN
fumecheng-12619	229	23	(	(	PUNCT
fumecheng-12619	229	24	ct	ct	NOUN
fumecheng-12619	229	25	)	)	PUNCT
fumecheng-12619	229	26	at	at	ADP
fumecheng-12619	229	27	various	various	ADJ
fumecheng-12619	229	28	piezoelectric	piezoelectric	NOUN
fumecheng-12619	229	29	actuation	actuation	NOUN
fumecheng-12619	229	30	voltages	voltage	NOUN
fumecheng-12619	229	31	(	(	PUNCT
fumecheng-12619	229	32	�	�	NOUN
fumecheng-12619	229	33	̅	̅	NOUN
fumecheng-12619	229	34	�	�	NOUN
fumecheng-12619	229	35	𝒑	𝒑	NOUN
fumecheng-12619	229	36	)	)	PUNCT
fumecheng-12619	229	37	for	for	ADP
fumecheng-12619	229	38	ss	ss	PROPN
fumecheng-12619	229	39	penr	penr	PROPN
fumecheng-12619	229	40	.	.	PUNCT
fumecheng-12619	230	1	it	it	PRON
fumecheng-12619	230	2	reiterates	reiterate	VERB
fumecheng-12619	230	3	the	the	DET
fumecheng-12619	230	4	effects	effect	NOUN
fumecheng-12619	230	5	of	of	ADP
fumecheng-12619	230	6	the	the	DET
fumecheng-12619	230	7	various	various	ADJ
fumecheng-12619	230	8	theories	theory	NOUN
fumecheng-12619	230	9	on	on	ADP
fumecheng-12619	230	10	natural	natural	ADJ
fumecheng-12619	230	11	frequencies	frequency	NOUN
fumecheng-12619	230	12	,	,	PUNCT
fumecheng-12619	230	13	confirming	confirm	VERB
fumecheng-12619	230	14	the	the	DET
fumecheng-12619	230	15	previous	previous	ADJ
fumecheng-12619	230	16	findings	finding	NOUN
fumecheng-12619	230	17	.	.	PUNCT
fumecheng-12619	231	1	the	the	DET
fumecheng-12619	231	2	impact	impact	NOUN
fumecheng-12619	231	3	of	of	ADP
fumecheng-12619	231	4	piezoelectric	piezoelectric	ADJ
fumecheng-12619	231	5	voltage	voltage	NOUN
fumecheng-12619	231	6	on	on	ADP
fumecheng-12619	231	7	the	the	DET
fumecheng-12619	231	8	natural	natural	ADJ
fumecheng-12619	231	9	frequency	frequency	NOUN
fumecheng-12619	231	10	varies	vary	VERB
fumecheng-12619	231	11	across	across	ADP
fumecheng-12619	231	12	the	the	DET
fumecheng-12619	231	13	different	different	ADJ
fumecheng-12619	231	14	theories	theory	NOUN
fumecheng-12619	231	15	.	.	PUNCT
fumecheng-12619	232	1	gmsit	gmsit	NOUN
fumecheng-12619	232	2	cases	case	NOUN
fumecheng-12619	232	3	1	1	NUM
fumecheng-12619	232	4	and	and	CCONJ
fumecheng-12619	232	5	2	2	NUM
fumecheng-12619	232	6	,	,	PUNCT
fumecheng-12619	232	7	as	as	ADV
fumecheng-12619	232	8	well	well	ADV
fumecheng-12619	232	9	as	as	ADP
fumecheng-12619	232	10	the	the	DET
fumecheng-12619	232	11	combined	combined	ADJ
fumecheng-12619	232	12	gmsit+sgt	gmsit+sgt	NOUN
fumecheng-12619	232	13	,	,	PUNCT
fumecheng-12619	232	14	exhibit	exhibit	VERB
fumecheng-12619	232	15	the	the	DET
fumecheng-12619	232	16	most	most	ADV
fumecheng-12619	232	17	significant	significant	ADJ
fumecheng-12619	232	18	changes	change	NOUN
fumecheng-12619	232	19	,	,	PUNCT
fumecheng-12619	232	20	particularly	particularly	ADV
fumecheng-12619	232	21	at	at	ADP
fumecheng-12619	232	22	low	low	ADJ
fumecheng-12619	232	23	surface	surface	NOUN
fumecheng-12619	232	24	density	density	NOUN
fumecheng-12619	232	25	.	.	PUNCT
fumecheng-12619	233	1	in	in	ADP
fumecheng-12619	233	2	these	these	DET
fumecheng-12619	233	3	instances	instance	NOUN
fumecheng-12619	233	4	,	,	PUNCT
fumecheng-12619	233	5	increasing	increase	VERB
fumecheng-12619	233	6	voltage	voltage	NOUN
fumecheng-12619	233	7	leads	lead	VERB
fumecheng-12619	233	8	to	to	ADP
fumecheng-12619	233	9	increased	increase	VERB
fumecheng-12619	233	10	system	system	NOUN
fumecheng-12619	233	11	rigidity	rigidity	NOUN
fumecheng-12619	233	12	and	and	CCONJ
fumecheng-12619	233	13	,	,	PUNCT
fumecheng-12619	233	14	consequently	consequently	ADV
fumecheng-12619	233	15	,	,	PUNCT
fumecheng-12619	233	16	an	an	DET
fumecheng-12619	233	17	initial	initial	ADJ
fumecheng-12619	233	18	rise	rise	NOUN
fumecheng-12619	233	19	in	in	ADP
fumecheng-12619	233	20	frequency	frequency	NOUN
fumecheng-12619	233	21	,	,	PUNCT
fumecheng-12619	233	22	followed	follow	VERB
fumecheng-12619	233	23	by	by	ADP
fumecheng-12619	233	24	a	a	DET
fumecheng-12619	233	25	plateau	plateau	NOUN
fumecheng-12619	233	26	with	with	ADP
fumecheng-12619	233	27	a	a	DET
fumecheng-12619	233	28	slight	slight	ADJ
fumecheng-12619	233	29	slope	slope	NOUN
fumecheng-12619	233	30	.	.	PUNCT
fumecheng-12619	234	1	in	in	ADP
fumecheng-12619	234	2	contrast	contrast	NOUN
fumecheng-12619	234	3	,	,	PUNCT
fumecheng-12619	234	4	other	other	ADJ
fumecheng-12619	234	5	theories	theory	NOUN
fumecheng-12619	234	6	show	show	VERB
fumecheng-12619	234	7	minimal	minimal	ADJ
fumecheng-12619	234	8	sensitivity	sensitivity	NOUN
fumecheng-12619	234	9	of	of	ADP
fumecheng-12619	234	10	the	the	DET
fumecheng-12619	234	11	penr	penr	NOUN
fumecheng-12619	234	12	's	's	PART
fumecheng-12619	234	13	natural	natural	ADJ
fumecheng-12619	234	14	frequency	frequency	NOUN
fumecheng-12619	234	15	to	to	ADP
fumecheng-12619	234	16	piezoelectric	piezoelectric	ADJ
fumecheng-12619	234	17	voltage	voltage	NOUN
fumecheng-12619	234	18	variations	variation	NOUN
fumecheng-12619	234	19	.	.	PUNCT
fumecheng-12619	235	1	comparison	comparison	NOUN
fumecheng-12619	235	2	of	of	ADP
fumecheng-12619	235	3	nonclassical	nonclassical	ADJ
fumecheng-12619	235	4	controllers	controller	NOUN
fumecheng-12619	235	5	on	on	ADP
fumecheng-12619	235	6	nonlinear	nonlinear	ADJ
fumecheng-12619	235	7	vibrations	vibration	NOUN
fumecheng-12619	235	8	analysis	analysis	NOUN
fumecheng-12619	235	9	of	of	ADP
fumecheng-12619	235	10	piezoelectric	piezoelectric	NOUN
fumecheng-12619	235	11	...	...	PUNCT
fumecheng-12619	235	12	323	323	NUM
fumecheng-12619	235	13	fig	fig	NOUN
fumecheng-12619	235	14	.	.	PUNCT
fumecheng-12619	236	1	7	7	NUM
fumecheng-12619	236	2	dimensionless	dimensionless	NOUN
fumecheng-12619	236	3	natural	natural	ADJ
fumecheng-12619	236	4	frequency	frequency	NOUN
fumecheng-12619	236	5	vs.	vs.	ADP
fumecheng-12619	236	6	piezoelectric	piezoelectric	NOUN
fumecheng-12619	236	7	voltage	voltage	NOUN
fumecheng-12619	236	8	v̅p	v̅p	PROPN
fumecheng-12619	236	9	:	:	PUNCT
fumecheng-12619	236	10	comparison	comparison	NOUN
fumecheng-12619	236	11	of	of	ADP
fumecheng-12619	236	12	nonclassical	nonclassical	ADJ
fumecheng-12619	236	13	and	and	CCONJ
fumecheng-12619	236	14	classical	classical	ADJ
fumecheng-12619	236	15	theories	theory	NOUN
fumecheng-12619	236	16	fig	fig	NOUN
fumecheng-12619	236	17	.	.	PUNCT
fumecheng-12619	237	1	8	8	NUM
fumecheng-12619	237	2	presents	present	VERB
fumecheng-12619	237	3	a	a	DET
fumecheng-12619	237	4	comparison	comparison	NOUN
fumecheng-12619	237	5	of	of	ADP
fumecheng-12619	237	6	the	the	DET
fumecheng-12619	237	7	dimensionless	dimensionless	ADJ
fumecheng-12619	237	8	natural	natural	ADJ
fumecheng-12619	237	9	frequency	frequency	NOUN
fumecheng-12619	237	10	predicted	predict	VERB
fumecheng-12619	237	11	by	by	ADP
fumecheng-12619	237	12	nlt	nlt	PROPN
fumecheng-12619	237	13	,	,	PUNCT
fumecheng-12619	237	14	sgt	sgt	PROPN
fumecheng-12619	237	15	,	,	PUNCT
fumecheng-12619	237	16	gmsit	gmsit	NOUN
fumecheng-12619	237	17	,	,	PUNCT
fumecheng-12619	237	18	and	and	CCONJ
fumecheng-12619	237	19	ct	ct	NOUN
fumecheng-12619	237	20	as	as	ADP
fumecheng-12619	237	21	a	a	DET
fumecheng-12619	237	22	function	function	NOUN
fumecheng-12619	237	23	of	of	ADP
fumecheng-12619	237	24	direct	direct	ADJ
fumecheng-12619	237	25	pull	pull	NOUN
fumecheng-12619	237	26	-	-	PUNCT
fumecheng-12619	237	27	in	in	ADP
fumecheng-12619	237	28	voltage	voltage	NOUN
fumecheng-12619	237	29	(	(	PUNCT
fumecheng-12619	237	30	dc	dc	PROPN
fumecheng-12619	237	31	)	)	PUNCT
fumecheng-12619	237	32	for	for	ADP
fumecheng-12619	237	33	an	an	DET
fumecheng-12619	237	34	ss	ss	NOUN
fumecheng-12619	237	35	nanoshell	nanoshell	NOUN
fumecheng-12619	237	36	.	.	PUNCT
fumecheng-12619	238	1	the	the	DET
fumecheng-12619	238	2	inclusion	inclusion	NOUN
fumecheng-12619	238	3	of	of	ADP
fumecheng-12619	238	4	surface	surface	NOUN
fumecheng-12619	238	5	/	/	SYM
fumecheng-12619	238	6	interface	interface	NOUN
fumecheng-12619	238	7	effects	effect	NOUN
fumecheng-12619	238	8	is	be	AUX
fumecheng-12619	238	9	known	know	VERB
fumecheng-12619	238	10	to	to	PART
fumecheng-12619	238	11	enhance	enhance	VERB
fumecheng-12619	238	12	system	system	NOUN
fumecheng-12619	238	13	rigidity	rigidity	NOUN
fumecheng-12619	238	14	,	,	PUNCT
fumecheng-12619	238	15	thereby	thereby	ADV
fumecheng-12619	238	16	necessitating	necessitate	VERB
fumecheng-12619	238	17	a	a	DET
fumecheng-12619	238	18	greater	great	ADJ
fumecheng-12619	238	19	dc	dc	PROPN
fumecheng-12619	238	20	voltage	voltage	NOUN
fumecheng-12619	238	21	to	to	PART
fumecheng-12619	238	22	achieve	achieve	VERB
fumecheng-12619	238	23	pull	pull	NOUN
fumecheng-12619	238	24	-	-	PUNCT
fumecheng-12619	238	25	in	in	NOUN
fumecheng-12619	238	26	.	.	PUNCT
fumecheng-12619	239	1	in	in	ADP
fumecheng-12619	239	2	contrast	contrast	NOUN
fumecheng-12619	239	3	,	,	PUNCT
fumecheng-12619	239	4	the	the	DET
fumecheng-12619	239	5	reduced	reduced	ADJ
fumecheng-12619	239	6	stiffness	stiffness	NOUN
fumecheng-12619	239	7	associated	associate	VERB
fumecheng-12619	239	8	with	with	ADP
fumecheng-12619	239	9	nlt	nlt	PROPN
fumecheng-12619	239	10	,	,	PUNCT
fumecheng-12619	239	11	sgt	sgt	PROPN
fumecheng-12619	239	12	,	,	PUNCT
fumecheng-12619	239	13	and	and	CCONJ
fumecheng-12619	239	14	ct	ct	PRON
fumecheng-12619	239	15	leads	lead	VERB
fumecheng-12619	239	16	to	to	ADP
fumecheng-12619	239	17	a	a	DET
fumecheng-12619	239	18	lower	low	ADJ
fumecheng-12619	239	19	pull	pull	NOUN
fumecheng-12619	239	20	-	-	PUNCT
fumecheng-12619	239	21	in	in	ADP
fumecheng-12619	239	22	voltage	voltage	NOUN
fumecheng-12619	239	23	,	,	PUNCT
fumecheng-12619	239	24	with	with	ADP
fumecheng-12619	239	25	these	these	DET
fumecheng-12619	239	26	theories	theory	NOUN
fumecheng-12619	239	27	predicting	predict	VERB
fumecheng-12619	239	28	pull	pull	NOUN
fumecheng-12619	239	29	-	-	PUNCT
fumecheng-12619	239	30	in	in	NOUN
fumecheng-12619	239	31	at	at	ADP
fumecheng-12619	239	32	roughly	roughly	ADV
fumecheng-12619	239	33	the	the	DET
fumecheng-12619	239	34	same	same	ADJ
fumecheng-12619	239	35	voltage	voltage	NOUN
fumecheng-12619	239	36	level	level	NOUN
fumecheng-12619	239	37	.	.	PUNCT
fumecheng-12619	240	1	fig	fig	NOUN
fumecheng-12619	240	2	.	.	PUNCT
fumecheng-12619	241	1	8	8	NUM
fumecheng-12619	241	2	dimensionless	dimensionless	NOUN
fumecheng-12619	241	3	natural	natural	ADJ
fumecheng-12619	241	4	frequency	frequency	NOUN
fumecheng-12619	241	5	vs.	vs.	ADP
fumecheng-12619	241	6	direct	direct	ADJ
fumecheng-12619	241	7	pull	pull	NOUN
fumecheng-12619	241	8	-	-	PUNCT
fumecheng-12619	241	9	in	in	ADP
fumecheng-12619	241	10	voltage	voltage	NOUN
fumecheng-12619	241	11	(	(	PUNCT
fumecheng-12619	241	12	dc	dc	PROPN
fumecheng-12619	241	13	)	)	PUNCT
fumecheng-12619	241	14	of	of	ADP
fumecheng-12619	241	15	ss	ss	PROPN
fumecheng-12619	241	16	penr	penr	PROPN
fumecheng-12619	241	17	:	:	PUNCT
fumecheng-12619	241	18	a	a	DET
fumecheng-12619	241	19	comparison	comparison	NOUN
fumecheng-12619	241	20	of	of	ADP
fumecheng-12619	241	21	non	non	ADJ
fumecheng-12619	241	22	-	-	ADJ
fumecheng-12619	241	23	classical	classical	ADJ
fumecheng-12619	241	24	and	and	CCONJ
fumecheng-12619	241	25	classical	classical	ADJ
fumecheng-12619	241	26	theories	theory	NOUN
fumecheng-12619	241	27	324	324	NUM
fumecheng-12619	241	28	s.h	s.h	PROPN
fumecheng-12619	241	29	.	.	PROPN
fumecheng-12619	241	30	hashemi	hashemi	PROPN
fumecheng-12619	241	31	kachapi	kachapi	PROPN
fumecheng-12619	241	32	,	,	PUNCT
fumecheng-12619	241	33	s.	s.	PROPN
fumecheng-12619	241	34	gh	gh	PROPN
fumecheng-12619	241	35	.	.	PROPN
fumecheng-12619	242	1	hashemi	hashemi	PROPN
fumecheng-12619	242	2	kachapi	kachapi	VERB
fumecheng-12619	242	3	the	the	DET
fumecheng-12619	242	4	nonlinear	nonlinear	ADJ
fumecheng-12619	242	5	frequency	frequency	NOUN
fumecheng-12619	242	6	response	response	NOUN
fumecheng-12619	242	7	of	of	ADP
fumecheng-12619	242	8	ss	ss	NOUN
fumecheng-12619	242	9	and	and	CCONJ
fumecheng-12619	242	10	cc	cc	NOUN
fumecheng-12619	242	11	penrs	penrs	NOUN
fumecheng-12619	242	12	,	,	PUNCT
fumecheng-12619	242	13	as	as	SCONJ
fumecheng-12619	242	14	obtained	obtain	VERB
fumecheng-12619	242	15	from	from	ADP
fumecheng-12619	242	16	nlt	nlt	PROPN
fumecheng-12619	242	17	,	,	PUNCT
fumecheng-12619	242	18	sgt	sgt	PROPN
fumecheng-12619	242	19	,	,	PUNCT
fumecheng-12619	242	20	gmsit	gmsit	NOUN
fumecheng-12619	242	21	,	,	PUNCT
fumecheng-12619	242	22	and	and	CCONJ
fumecheng-12619	242	23	ct	ct	PROPN
fumecheng-12619	242	24	,	,	PUNCT
fumecheng-12619	242	25	is	be	AUX
fumecheng-12619	242	26	compared	compare	VERB
fumecheng-12619	242	27	in	in	ADP
fumecheng-12619	242	28	figs	fig	NOUN
fumecheng-12619	242	29	.	.	PUNCT
fumecheng-12619	243	1	9	9	NUM
fumecheng-12619	243	2	and	and	CCONJ
fumecheng-12619	243	3	10	10	NUM
fumecheng-12619	243	4	,	,	PUNCT
fumecheng-12619	243	5	respectively	respectively	ADV
fumecheng-12619	243	6	,	,	PUNCT
fumecheng-12619	243	7	for	for	ADP
fumecheng-12619	243	8	�	�	NOUN
fumecheng-12619	243	9	̅	̅	NOUN
fumecheng-12619	243	10	�	�	NOUN
fumecheng-12619	243	11	𝐷𝐶	𝐷𝐶	NOUN
fumecheng-12619	243	12	=	=	SYM
fumecheng-12619	243	13	1.7	1.7	NUM
fumecheng-12619	243	14	and	and	CCONJ
fumecheng-12619	243	15	�	�	NOUN
fumecheng-12619	243	16	̅	̅	NOUN
fumecheng-12619	243	17	�	�	NOUN
fumecheng-12619	243	18	𝐴𝐶	𝐴𝐶	NOUN
fumecheng-12619	243	19	=	=	SYM
fumecheng-12619	243	20	0.5	0.5	NUM
fumecheng-12619	243	21	.	.	PUNCT
fumecheng-12619	244	1	as	as	SCONJ
fumecheng-12619	244	2	depicted	depict	VERB
fumecheng-12619	244	3	in	in	ADP
fumecheng-12619	244	4	fig	fig	NOUN
fumecheng-12619	244	5	.	.	PUNCT
fumecheng-12619	245	1	9	9	NUM
fumecheng-12619	245	2	,	,	PUNCT
fumecheng-12619	245	3	the	the	DET
fumecheng-12619	245	4	frequency	frequency	NOUN
fumecheng-12619	245	5	analysis	analysis	NOUN
fumecheng-12619	245	6	indicates	indicate	VERB
fumecheng-12619	245	7	that	that	SCONJ
fumecheng-12619	245	8	the	the	DET
fumecheng-12619	245	9	incorporation	incorporation	NOUN
fumecheng-12619	245	10	of	of	ADP
fumecheng-12619	245	11	surface	surface	NOUN
fumecheng-12619	245	12	/	/	SYM
fumecheng-12619	245	13	interface	interface	NOUN
fumecheng-12619	245	14	effects	effect	NOUN
fumecheng-12619	245	15	in	in	ADP
fumecheng-12619	245	16	gmsit	gmsit	NOUN
fumecheng-12619	245	17	case	case	NOUN
fumecheng-12619	245	18	2	2	NUM
fumecheng-12619	245	19	(	(	PUNCT
fumecheng-12619	245	20	case	case	NOUN
fumecheng-12619	245	21	1	1	NUM
fumecheng-12619	245	22	)	)	PUNCT
fumecheng-12619	245	23	leads	lead	VERB
fumecheng-12619	245	24	to	to	ADP
fumecheng-12619	245	25	a	a	DET
fumecheng-12619	245	26	hardening	hardening	NOUN
fumecheng-12619	245	27	(	(	PUNCT
fumecheng-12619	245	28	softening	soften	VERB
fumecheng-12619	245	29	)	)	PUNCT
fumecheng-12619	245	30	of	of	ADP
fumecheng-12619	245	31	the	the	DET
fumecheng-12619	245	32	ss	ss	PROPN
fumecheng-12619	245	33	penr	penr	PROPN
fumecheng-12619	245	34	.	.	PUNCT
fumecheng-12619	246	1	this	this	PRON
fumecheng-12619	246	2	,	,	PUNCT
fumecheng-12619	246	3	in	in	ADP
fumecheng-12619	246	4	turn	turn	NOUN
fumecheng-12619	246	5	,	,	PUNCT
fumecheng-12619	246	6	results	result	VERB
fumecheng-12619	246	7	in	in	ADP
fumecheng-12619	246	8	an	an	DET
fumecheng-12619	246	9	increase	increase	NOUN
fumecheng-12619	246	10	(	(	PUNCT
fumecheng-12619	246	11	decrease	decrease	NOUN
fumecheng-12619	246	12	)	)	PUNCT
fumecheng-12619	246	13	in	in	ADP
fumecheng-12619	246	14	the	the	DET
fumecheng-12619	246	15	resonant	resonant	ADJ
fumecheng-12619	246	16	frequency	frequency	NOUN
fumecheng-12619	246	17	and	and	CCONJ
fumecheng-12619	246	18	a	a	DET
fumecheng-12619	246	19	corresponding	corresponding	ADJ
fumecheng-12619	246	20	decrease	decrease	NOUN
fumecheng-12619	246	21	in	in	ADP
fumecheng-12619	246	22	the	the	DET
fumecheng-12619	246	23	resonance	resonance	NOUN
fumecheng-12619	246	24	amplitude	amplitude	NOUN
fumecheng-12619	246	25	.	.	PUNCT
fumecheng-12619	247	1	fig	fig	NOUN
fumecheng-12619	247	2	.	.	PUNCT
fumecheng-12619	248	1	9	9	NUM
fumecheng-12619	248	2	nonlinear	nonlinear	ADJ
fumecheng-12619	248	3	vibration	vibration	NOUN
fumecheng-12619	248	4	and	and	CCONJ
fumecheng-12619	248	5	stability	stability	NOUN
fumecheng-12619	248	6	analysis	analysis	NOUN
fumecheng-12619	248	7	of	of	ADP
fumecheng-12619	248	8	ss	ss	PRON
fumecheng-12619	248	9	penr	penr	NOUN
fumecheng-12619	248	10	:	:	PUNCT
fumecheng-12619	248	11	comparison	comparison	NOUN
fumecheng-12619	248	12	of	of	ADP
fumecheng-12619	248	13	non	non	ADJ
fumecheng-12619	248	14	-	-	ADJ
fumecheng-12619	248	15	classical	classical	ADJ
fumecheng-12619	248	16	and	and	CCONJ
fumecheng-12619	248	17	classical	classical	ADJ
fumecheng-12619	248	18	theories	theory	NOUN
fumecheng-12619	248	19	the	the	DET
fumecheng-12619	248	20	gmsit	gmsit	NOUN
fumecheng-12619	248	21	model	model	NOUN
fumecheng-12619	248	22	does	do	AUX
fumecheng-12619	248	23	not	not	PART
fumecheng-12619	248	24	predict	predict	VERB
fumecheng-12619	248	25	instability	instability	NOUN
fumecheng-12619	248	26	under	under	ADP
fumecheng-12619	248	27	the	the	DET
fumecheng-12619	248	28	applied	apply	VERB
fumecheng-12619	248	29	voltage	voltage	NOUN
fumecheng-12619	248	30	conditions	condition	NOUN
fumecheng-12619	248	31	.	.	PUNCT
fumecheng-12619	249	1	conversely	conversely	ADV
fumecheng-12619	249	2	,	,	PUNCT
fumecheng-12619	249	3	ct	ct	PROPN
fumecheng-12619	249	4	,	,	PUNCT
fumecheng-12619	249	5	nlt	nlt	PROPN
fumecheng-12619	249	6	,	,	PUNCT
fumecheng-12619	249	7	and	and	CCONJ
fumecheng-12619	249	8	sgt	sgt	PROPN
fumecheng-12619	249	9	exhibit	exhibit	NOUN
fumecheng-12619	249	10	instability	instability	NOUN
fumecheng-12619	249	11	,	,	PUNCT
fumecheng-12619	249	12	manifested	manifest	VERB
fumecheng-12619	249	13	as	as	ADP
fumecheng-12619	249	14	saddle	saddle	NOUN
fumecheng-12619	249	15	-	-	PUNCT
fumecheng-12619	249	16	node	node	NOUN
fumecheng-12619	249	17	bifurcations	bifurcation	NOUN
fumecheng-12619	249	18	and	and	CCONJ
fumecheng-12619	249	19	nonlinear	nonlinear	ADJ
fumecheng-12619	249	20	hardening	harden	VERB
fumecheng-12619	249	21	behavior	behavior	NOUN
fumecheng-12619	249	22	.	.	PUNCT
fumecheng-12619	250	1	the	the	DET
fumecheng-12619	250	2	nonclassical	nonclassical	ADJ
fumecheng-12619	250	3	theories	theory	NOUN
fumecheng-12619	250	4	,	,	PUNCT
fumecheng-12619	250	5	nlt	nlt	PROPN
fumecheng-12619	250	6	and	and	CCONJ
fumecheng-12619	250	7	sgt	sgt	PROPN
fumecheng-12619	250	8	,	,	PUNCT
fumecheng-12619	250	9	predict	predict	VERB
fumecheng-12619	250	10	a	a	DET
fumecheng-12619	250	11	larger	large	ADJ
fumecheng-12619	250	12	oscillation	oscillation	NOUN
fumecheng-12619	250	13	amplitude	amplitude	NOUN
fumecheng-12619	250	14	and	and	CCONJ
fumecheng-12619	250	15	a	a	DET
fumecheng-12619	250	16	wider	wide	ADJ
fumecheng-12619	250	17	instability	instability	NOUN
fumecheng-12619	250	18	range	range	NOUN
fumecheng-12619	250	19	than	than	ADP
fumecheng-12619	250	20	the	the	DET
fumecheng-12619	250	21	classical	classical	ADJ
fumecheng-12619	250	22	theory	theory	NOUN
fumecheng-12619	250	23	(	(	PUNCT
fumecheng-12619	250	24	ct	ct	PROPN
fumecheng-12619	250	25	)	)	PUNCT
fumecheng-12619	250	26	.	.	PUNCT
fumecheng-12619	251	1	moreover	moreover	ADV
fumecheng-12619	251	2	,	,	PUNCT
fumecheng-12619	251	3	an	an	DET
fumecheng-12619	251	4	increase	increase	NOUN
fumecheng-12619	251	5	in	in	ADP
fumecheng-12619	251	6	𝜏̅	𝜏̅	PROPN
fumecheng-12619	251	7	and	and	CCONJ
fumecheng-12619	251	8	�	�	PROPN
fumecheng-12619	251	9	̅	̅	NOUN
fumecheng-12619	251	10	�	�	NOUN
fumecheng-12619	251	11	results	result	NOUN
fumecheng-12619	251	12	in	in	ADP
fumecheng-12619	251	13	an	an	DET
fumecheng-12619	251	14	amplified	amplify	VERB
fumecheng-12619	251	15	oscillation	oscillation	NOUN
fumecheng-12619	251	16	amplitude	amplitude	NOUN
fumecheng-12619	251	17	and	and	CCONJ
fumecheng-12619	251	18	an	an	DET
fumecheng-12619	251	19	expanded	expand	VERB
fumecheng-12619	251	20	instability	instability	NOUN
fumecheng-12619	251	21	range	range	NOUN
fumecheng-12619	251	22	,	,	PUNCT
fumecheng-12619	251	23	accompanied	accompany	VERB
fumecheng-12619	251	24	by	by	ADP
fumecheng-12619	251	25	a	a	DET
fumecheng-12619	251	26	reduction	reduction	NOUN
fumecheng-12619	251	27	in	in	ADP
fumecheng-12619	251	28	resonance	resonance	NOUN
fumecheng-12619	251	29	frequency	frequency	NOUN
fumecheng-12619	251	30	.	.	PUNCT
fumecheng-12619	252	1	as	as	SCONJ
fumecheng-12619	252	2	depicted	depict	VERB
fumecheng-12619	252	3	in	in	ADP
fumecheng-12619	252	4	fig	fig	NOUN
fumecheng-12619	252	5	.	.	PUNCT
fumecheng-12619	253	1	10	10	NUM
fumecheng-12619	253	2	,	,	PUNCT
fumecheng-12619	253	3	an	an	DET
fumecheng-12619	253	4	increase	increase	NOUN
fumecheng-12619	253	5	in	in	ADP
fumecheng-12619	253	6	the	the	DET
fumecheng-12619	253	7	dimensionless	dimensionless	ADJ
fumecheng-12619	253	8	nonlocal	nonlocal	ADJ
fumecheng-12619	253	9	parameter	parameter	NOUN
fumecheng-12619	253	10	results	result	NOUN
fumecheng-12619	253	11	in	in	ADP
fumecheng-12619	253	12	a	a	DET
fumecheng-12619	253	13	decrease	decrease	NOUN
fumecheng-12619	253	14	in	in	ADP
fumecheng-12619	253	15	the	the	DET
fumecheng-12619	253	16	resonance	resonance	NOUN
fumecheng-12619	253	17	amplitude	amplitude	NOUN
fumecheng-12619	253	18	.	.	PUNCT
fumecheng-12619	254	1	this	this	PRON
fumecheng-12619	254	2	suggests	suggest	VERB
fumecheng-12619	254	3	that	that	SCONJ
fumecheng-12619	254	4	small	small	ADJ
fumecheng-12619	254	5	-	-	PUNCT
fumecheng-12619	254	6	scale	scale	NOUN
fumecheng-12619	254	7	effects	effect	NOUN
fumecheng-12619	254	8	,	,	PUNCT
fumecheng-12619	254	9	as	as	SCONJ
fumecheng-12619	254	10	captured	capture	VERB
fumecheng-12619	254	11	by	by	ADP
fumecheng-12619	254	12	the	the	DET
fumecheng-12619	254	13	nonlocal	nonlocal	ADJ
fumecheng-12619	254	14	model	model	NOUN
fumecheng-12619	254	15	,	,	PUNCT
fumecheng-12619	254	16	enhance	enhance	VERB
fumecheng-12619	254	17	the	the	DET
fumecheng-12619	254	18	flexibility	flexibility	NOUN
fumecheng-12619	254	19	of	of	ADP
fumecheng-12619	254	20	the	the	DET
fumecheng-12619	254	21	cc	cc	PROPN
fumecheng-12619	254	22	penr	penr	PROPN
fumecheng-12619	254	23	.	.	PUNCT
fumecheng-12619	255	1	generally	generally	ADV
fumecheng-12619	255	2	,	,	PUNCT
fumecheng-12619	255	3	the	the	DET
fumecheng-12619	255	4	cc	cc	PROPN
fumecheng-12619	255	5	boundary	boundary	ADJ
fumecheng-12619	255	6	condition	condition	NOUN
fumecheng-12619	255	7	yields	yield	NOUN
fumecheng-12619	255	8	result	result	VERB
fumecheng-12619	255	9	comparable	comparable	ADJ
fumecheng-12619	255	10	to	to	ADP
fumecheng-12619	255	11	those	those	PRON
fumecheng-12619	255	12	of	of	ADP
fumecheng-12619	255	13	the	the	DET
fumecheng-12619	255	14	ss	ss	PROPN
fumecheng-12619	255	15	boundary	boundary	ADJ
fumecheng-12619	255	16	condition	condition	NOUN
fumecheng-12619	255	17	.	.	PUNCT
fumecheng-12619	256	1	however	however	ADV
fumecheng-12619	256	2	,	,	PUNCT
fumecheng-12619	256	3	a	a	DET
fumecheng-12619	256	4	notable	notable	ADJ
fumecheng-12619	256	5	exception	exception	NOUN
fumecheng-12619	256	6	is	be	AUX
fumecheng-12619	256	7	observed	observe	VERB
fumecheng-12619	256	8	in	in	ADP
fumecheng-12619	256	9	the	the	DET
fumecheng-12619	256	10	sgt	sgt	PROPN
fumecheng-12619	256	11	model	model	NOUN
fumecheng-12619	256	12	,	,	PUNCT
fumecheng-12619	256	13	where	where	SCONJ
fumecheng-12619	256	14	an	an	DET
fumecheng-12619	256	15	increase	increase	NOUN
fumecheng-12619	256	16	in	in	ADP
fumecheng-12619	256	17	𝜏̅	𝜏̅	PROPN
fumecheng-12619	256	18	and	and	CCONJ
fumecheng-12619	256	19	�	�	PROPN
fumecheng-12619	256	20	̅	̅	NOUN
fumecheng-12619	256	21	�	�	NOUN
fumecheng-12619	256	22	induces	induce	VERB
fumecheng-12619	256	23	comparison	comparison	NOUN
fumecheng-12619	256	24	of	of	ADP
fumecheng-12619	256	25	nonclassical	nonclassical	ADJ
fumecheng-12619	256	26	controllers	controller	NOUN
fumecheng-12619	256	27	on	on	ADP
fumecheng-12619	256	28	nonlinear	nonlinear	ADJ
fumecheng-12619	256	29	vibrations	vibration	NOUN
fumecheng-12619	256	30	analysis	analysis	NOUN
fumecheng-12619	256	31	of	of	ADP
fumecheng-12619	256	32	piezoelectric	piezoelectric	NOUN
fumecheng-12619	256	33	...	...	PUNCT
fumecheng-12619	256	34	325	325	NUM
fumecheng-12619	256	35	nonlinear	nonlinear	ADJ
fumecheng-12619	256	36	softening	soften	VERB
fumecheng-12619	256	37	instability	instability	NOUN
fumecheng-12619	256	38	in	in	ADP
fumecheng-12619	256	39	the	the	DET
fumecheng-12619	256	40	cc	cc	PROPN
fumecheng-12619	256	41	boundary	boundary	ADJ
fumecheng-12619	256	42	condition	condition	NOUN
fumecheng-12619	256	43	,	,	PUNCT
fumecheng-12619	256	44	while	while	SCONJ
fumecheng-12619	256	45	the	the	DET
fumecheng-12619	256	46	ss	ss	PROPN
fumecheng-12619	256	47	boundary	boundary	ADJ
fumecheng-12619	256	48	condition	condition	NOUN
fumecheng-12619	256	49	exhibits	exhibit	VERB
fumecheng-12619	256	50	nonlinear	nonlinear	ADJ
fumecheng-12619	256	51	hardening	harden	VERB
fumecheng-12619	256	52	instability	instability	NOUN
fumecheng-12619	256	53	.	.	PUNCT
fumecheng-12619	257	1	fig	fig	NOUN
fumecheng-12619	257	2	.	.	PUNCT
fumecheng-12619	258	1	10	10	NUM
fumecheng-12619	258	2	nonlinear	nonlinear	ADJ
fumecheng-12619	258	3	vibration	vibration	NOUN
fumecheng-12619	258	4	and	and	CCONJ
fumecheng-12619	258	5	stability	stability	NOUN
fumecheng-12619	258	6	analysis	analysis	NOUN
fumecheng-12619	258	7	of	of	ADP
fumecheng-12619	258	8	cc	cc	ADP
fumecheng-12619	258	9	penr	penr	PROPN
fumecheng-12619	258	10	:	:	PUNCT
fumecheng-12619	258	11	comparison	comparison	NOUN
fumecheng-12619	258	12	of	of	ADP
fumecheng-12619	258	13	nonclassical	nonclassical	ADJ
fumecheng-12619	258	14	and	and	CCONJ
fumecheng-12619	258	15	classical	classical	ADJ
fumecheng-12619	258	16	theories	theory	NOUN
fumecheng-12619	258	17	the	the	DET
fumecheng-12619	258	18	frequency	frequency	NOUN
fumecheng-12619	258	19	response	response	NOUN
fumecheng-12619	258	20	and	and	CCONJ
fumecheng-12619	258	21	stability	stability	NOUN
fumecheng-12619	258	22	characteristics	characteristic	NOUN
fumecheng-12619	258	23	of	of	ADP
fumecheng-12619	258	24	the	the	DET
fumecheng-12619	258	25	penr	penr	NOUN
fumecheng-12619	258	26	,	,	PUNCT
fumecheng-12619	258	27	subjected	subject	VERB
fumecheng-12619	258	28	to	to	ADP
fumecheng-12619	258	29	different	different	ADJ
fumecheng-12619	258	30	direct	direct	ADJ
fumecheng-12619	258	31	(	(	PUNCT
fumecheng-12619	258	32	�	�	NOUN
fumecheng-12619	258	33	̅	̅	NOUN
fumecheng-12619	258	34	�	�	NOUN
fumecheng-12619	258	35	𝐷𝐶	𝐷𝐶	NOUN
fumecheng-12619	258	36	)	)	PUNCT
fumecheng-12619	258	37	and	and	CCONJ
fumecheng-12619	258	38	alternating	alternate	VERB
fumecheng-12619	258	39	(	(	PUNCT
fumecheng-12619	258	40	�	�	NOUN
fumecheng-12619	258	41	̅	̅	NOUN
fumecheng-12619	258	42	�	�	PROPN
fumecheng-12619	258	43	𝐴𝐶	𝐴𝐶	PROPN
fumecheng-12619	258	44	)	)	PUNCT
fumecheng-12619	258	45	voltages	voltage	NOUN
fumecheng-12619	258	46	,	,	PUNCT
fumecheng-12619	258	47	are	be	AUX
fumecheng-12619	258	48	illustrated	illustrate	VERB
fumecheng-12619	258	49	in	in	ADP
fumecheng-12619	258	50	figs	fig	NOUN
fumecheng-12619	258	51	.	.	PUNCT
fumecheng-12619	259	1	11	11	NUM
fumecheng-12619	259	2	-	-	SYM
fumecheng-12619	259	3	16	16	NUM
fumecheng-12619	259	4	.	.	PUNCT
fumecheng-12619	260	1	these	these	DET
fumecheng-12619	260	2	figures	figure	NOUN
fumecheng-12619	260	3	compare	compare	VERB
fumecheng-12619	260	4	the	the	DET
fumecheng-12619	260	5	predictions	prediction	NOUN
fumecheng-12619	260	6	of	of	ADP
fumecheng-12619	260	7	ct	ct	PROPN
fumecheng-12619	260	8	,	,	PUNCT
fumecheng-12619	260	9	nlt	nlt	PROPN
fumecheng-12619	260	10	,	,	PUNCT
fumecheng-12619	260	11	sgt	sgt	PROPN
fumecheng-12619	260	12	,	,	PUNCT
fumecheng-12619	260	13	gmsit	gmsit	NOUN
fumecheng-12619	260	14	,	,	PUNCT
fumecheng-12619	260	15	and	and	CCONJ
fumecheng-12619	260	16	the	the	DET
fumecheng-12619	260	17	combined	combined	ADJ
fumecheng-12619	260	18	theories	theory	NOUN
fumecheng-12619	260	19	gmsit+nlt	gmsit+nlt	NOUN
fumecheng-12619	260	20	and	and	CCONJ
fumecheng-12619	260	21	gmsit+sgt	gmsit+sgt	NOUN
fumecheng-12619	260	22	for	for	ADP
fumecheng-12619	260	23	ss	ss	PROPN
fumecheng-12619	260	24	boundary	boundary	ADJ
fumecheng-12619	260	25	conditions	condition	NOUN
fumecheng-12619	260	26	.	.	PUNCT
fumecheng-12619	261	1	326	326	NUM
fumecheng-12619	261	2	s.h	s.h	PROPN
fumecheng-12619	261	3	.	.	PROPN
fumecheng-12619	261	4	hashemi	hashemi	PROPN
fumecheng-12619	261	5	kachapi	kachapi	PROPN
fumecheng-12619	261	6	,	,	PUNCT
fumecheng-12619	261	7	s.	s.	PROPN
fumecheng-12619	261	8	gh	gh	PROPN
fumecheng-12619	261	9	.	.	PROPN
fumecheng-12619	262	1	hashemi	hashemi	PROPN
fumecheng-12619	262	2	kachapi	kachapi	PROPN
fumecheng-12619	262	3	fig	fig	PROPN
fumecheng-12619	262	4	.	.	PUNCT
fumecheng-12619	263	1	11	11	NUM
fumecheng-12619	263	2	frequency	frequency	NOUN
fumecheng-12619	263	3	response	response	NOUN
fumecheng-12619	263	4	and	and	CCONJ
fumecheng-12619	263	5	stability	stability	NOUN
fumecheng-12619	263	6	analysis	analysis	NOUN
fumecheng-12619	263	7	of	of	ADP
fumecheng-12619	263	8	ss	ss	DET
fumecheng-12619	263	9	penr	penr	PROPN
fumecheng-12619	263	10	(	(	PUNCT
fumecheng-12619	263	11	ct	ct	NOUN
fumecheng-12619	263	12	)	)	PUNCT
fumecheng-12619	263	13	under	under	ADP
fumecheng-12619	263	14	varying	vary	VERB
fumecheng-12619	263	15	dc	dc	PROPN
fumecheng-12619	263	16	and	and	CCONJ
fumecheng-12619	263	17	ac	ac	PROPN
fumecheng-12619	263	18	voltages	voltage	NOUN
fumecheng-12619	263	19	fig	fig	PROPN
fumecheng-12619	263	20	.	.	PUNCT
fumecheng-12619	264	1	12	12	NUM
fumecheng-12619	264	2	frequency	frequency	NOUN
fumecheng-12619	264	3	response	response	NOUN
fumecheng-12619	264	4	and	and	CCONJ
fumecheng-12619	264	5	stability	stability	NOUN
fumecheng-12619	264	6	analysis	analysis	NOUN
fumecheng-12619	264	7	of	of	ADP
fumecheng-12619	264	8	ss	ss	DET
fumecheng-12619	264	9	penr	penr	PROPN
fumecheng-12619	264	10	(	(	PUNCT
fumecheng-12619	264	11	nlt	nlt	PROPN
fumecheng-12619	264	12	)	)	PUNCT
fumecheng-12619	264	13	under	under	ADP
fumecheng-12619	264	14	varying	vary	VERB
fumecheng-12619	264	15	dc	dc	PROPN
fumecheng-12619	264	16	and	and	CCONJ
fumecheng-12619	264	17	ac	ac	PROPN
fumecheng-12619	264	18	voltages	voltage	NOUN
fumecheng-12619	264	19	comparison	comparison	NOUN
fumecheng-12619	264	20	of	of	ADP
fumecheng-12619	264	21	nonclassical	nonclassical	ADJ
fumecheng-12619	264	22	controllers	controller	NOUN
fumecheng-12619	264	23	on	on	ADP
fumecheng-12619	264	24	nonlinear	nonlinear	ADJ
fumecheng-12619	264	25	vibrations	vibration	NOUN
fumecheng-12619	264	26	analysis	analysis	NOUN
fumecheng-12619	264	27	of	of	ADP
fumecheng-12619	264	28	piezoelectric	piezoelectric	NOUN
fumecheng-12619	264	29	...	...	PUNCT
fumecheng-12619	264	30	327	327	NUM
fumecheng-12619	264	31	fig	fig	NOUN
fumecheng-12619	264	32	.	.	PUNCT
fumecheng-12619	265	1	13	13	NUM
fumecheng-12619	265	2	frequency	frequency	NOUN
fumecheng-12619	265	3	response	response	NOUN
fumecheng-12619	265	4	and	and	CCONJ
fumecheng-12619	265	5	stability	stability	NOUN
fumecheng-12619	265	6	analysis	analysis	NOUN
fumecheng-12619	265	7	of	of	ADP
fumecheng-12619	265	8	ss	ss	DET
fumecheng-12619	265	9	penr	penr	PROPN
fumecheng-12619	265	10	(	(	PUNCT
fumecheng-12619	265	11	sgt	sgt	PROPN
fumecheng-12619	265	12	)	)	PUNCT
fumecheng-12619	265	13	under	under	ADP
fumecheng-12619	265	14	varying	vary	VERB
fumecheng-12619	265	15	dc	dc	PROPN
fumecheng-12619	265	16	and	and	CCONJ
fumecheng-12619	265	17	ac	ac	PROPN
fumecheng-12619	265	18	voltages	voltage	NOUN
fumecheng-12619	265	19	fig	fig	PROPN
fumecheng-12619	265	20	.	.	PUNCT
fumecheng-12619	266	1	14	14	NUM
fumecheng-12619	266	2	frequency	frequency	NOUN
fumecheng-12619	266	3	response	response	NOUN
fumecheng-12619	266	4	and	and	CCONJ
fumecheng-12619	266	5	stability	stability	NOUN
fumecheng-12619	266	6	analysis	analysis	NOUN
fumecheng-12619	266	7	of	of	ADP
fumecheng-12619	266	8	ss	ss	DET
fumecheng-12619	266	9	penr	penr	PROPN
fumecheng-12619	266	10	(	(	PUNCT
fumecheng-12619	266	11	gmsit	gmsit	NOUN
fumecheng-12619	266	12	)	)	PUNCT
fumecheng-12619	266	13	under	under	ADP
fumecheng-12619	266	14	varying	vary	VERB
fumecheng-12619	266	15	dc	dc	PROPN
fumecheng-12619	266	16	and	and	CCONJ
fumecheng-12619	266	17	ac	ac	PROPN
fumecheng-12619	266	18	voltages	voltage	VERB
fumecheng-12619	266	19	328	328	NUM
fumecheng-12619	266	20	s.h	s.h	PROPN
fumecheng-12619	266	21	.	.	PROPN
fumecheng-12619	266	22	hashemi	hashemi	PROPN
fumecheng-12619	266	23	kachapi	kachapi	PROPN
fumecheng-12619	266	24	,	,	PUNCT
fumecheng-12619	266	25	s.	s.	PROPN
fumecheng-12619	266	26	gh	gh	PROPN
fumecheng-12619	266	27	.	.	PROPN
fumecheng-12619	267	1	hashemi	hashemi	PROPN
fumecheng-12619	267	2	kachapi	kachapi	PROPN
fumecheng-12619	267	3	fig	fig	PROPN
fumecheng-12619	267	4	.	.	PUNCT
fumecheng-12619	268	1	15	15	NUM
fumecheng-12619	268	2	frequency	frequency	NOUN
fumecheng-12619	268	3	response	response	NOUN
fumecheng-12619	268	4	and	and	CCONJ
fumecheng-12619	268	5	stability	stability	NOUN
fumecheng-12619	268	6	analysis	analysis	NOUN
fumecheng-12619	268	7	of	of	ADP
fumecheng-12619	268	8	ss	ss	DET
fumecheng-12619	268	9	penr	penr	PROPN
fumecheng-12619	268	10	(	(	PUNCT
fumecheng-12619	268	11	gmsit+nlt	gmsit+nlt	PROPN
fumecheng-12619	268	12	)	)	PUNCT
fumecheng-12619	268	13	under	under	ADP
fumecheng-12619	268	14	varying	vary	VERB
fumecheng-12619	268	15	dc	dc	PROPN
fumecheng-12619	268	16	and	and	CCONJ
fumecheng-12619	268	17	ac	ac	PROPN
fumecheng-12619	268	18	voltages	voltage	NOUN
fumecheng-12619	268	19	fig	fig	PROPN
fumecheng-12619	268	20	.	.	PUNCT
fumecheng-12619	269	1	16	16	NUM
fumecheng-12619	269	2	frequency	frequency	NOUN
fumecheng-12619	269	3	response	response	NOUN
fumecheng-12619	269	4	and	and	CCONJ
fumecheng-12619	269	5	stability	stability	NOUN
fumecheng-12619	269	6	analysis	analysis	NOUN
fumecheng-12619	269	7	of	of	ADP
fumecheng-12619	269	8	ss	ss	PRON
fumecheng-12619	269	9	penr	penr	PROPN
fumecheng-12619	269	10	(	(	PUNCT
fumecheng-12619	269	11	gmsit+sgt	gmsit+sgt	NOUN
fumecheng-12619	269	12	)	)	PUNCT
fumecheng-12619	269	13	under	under	ADP
fumecheng-12619	269	14	varying	vary	VERB
fumecheng-12619	269	15	dc	dc	PROPN
fumecheng-12619	269	16	and	and	CCONJ
fumecheng-12619	269	17	ac	ac	PROPN
fumecheng-12619	269	18	voltages	voltage	NOUN
fumecheng-12619	269	19	comparison	comparison	NOUN
fumecheng-12619	269	20	of	of	ADP
fumecheng-12619	269	21	nonclassical	nonclassical	ADJ
fumecheng-12619	269	22	controllers	controller	NOUN
fumecheng-12619	269	23	on	on	ADP
fumecheng-12619	269	24	nonlinear	nonlinear	ADJ
fumecheng-12619	269	25	vibrations	vibration	NOUN
fumecheng-12619	269	26	analysis	analysis	NOUN
fumecheng-12619	269	27	of	of	ADP
fumecheng-12619	269	28	piezoelectric	piezoelectric	NOUN
fumecheng-12619	269	29	...	...	PUNCT
fumecheng-12619	269	30	329	329	NUM
fumecheng-12619	269	31	it	it	PRON
fumecheng-12619	269	32	can	can	AUX
fumecheng-12619	269	33	be	be	AUX
fumecheng-12619	269	34	concluded	conclude	VERB
fumecheng-12619	269	35	from	from	ADP
fumecheng-12619	269	36	figs	fig	NOUN
fumecheng-12619	269	37	.	.	PUNCT
fumecheng-12619	270	1	11	11	NUM
fumecheng-12619	270	2	-	-	SYM
fumecheng-12619	270	3	16	16	NUM
fumecheng-12619	270	4	that	that	SCONJ
fumecheng-12619	270	5	the	the	DET
fumecheng-12619	270	6	lowest	low	ADJ
fumecheng-12619	270	7	resonance	resonance	NOUN
fumecheng-12619	270	8	frequency	frequency	NOUN
fumecheng-12619	270	9	for	for	ADP
fumecheng-12619	270	10	the	the	DET
fumecheng-12619	270	11	unstable	unstable	ADJ
fumecheng-12619	270	12	amplitude	amplitude	NOUN
fumecheng-12619	270	13	is	be	AUX
fumecheng-12619	270	14	related	relate	VERB
fumecheng-12619	270	15	to	to	ADP
fumecheng-12619	270	16	fig	fig	NOUN
fumecheng-12619	270	17	.	.	PUNCT
fumecheng-12619	271	1	12	12	NUM
fumecheng-12619	271	2	for	for	ADP
fumecheng-12619	271	3	the	the	DET
fumecheng-12619	271	4	nlt	nlt	PROPN
fumecheng-12619	271	5	theory	theory	NOUN
fumecheng-12619	271	6	(	(	PUNCT
fumecheng-12619	271	7	of	of	ADP
fumecheng-12619	271	8	course	course	NOUN
fumecheng-12619	271	9	,	,	PUNCT
fumecheng-12619	271	10	in	in	ADP
fumecheng-12619	271	11	the	the	DET
fumecheng-12619	271	12	absence	absence	NOUN
fumecheng-12619	271	13	of	of	ADP
fumecheng-12619	271	14	gmsit	gmsit	PROPN
fumecheng-12619	271	15	case1	case1	PROPN
fumecheng-12619	271	16	,	,	PUNCT
fumecheng-12619	271	17	which	which	PRON
fumecheng-12619	271	18	has	have	VERB
fumecheng-12619	271	19	the	the	DET
fumecheng-12619	271	20	lowest	low	ADJ
fumecheng-12619	271	21	resonance	resonance	NOUN
fumecheng-12619	271	22	frequency	frequency	NOUN
fumecheng-12619	271	23	for	for	ADP
fumecheng-12619	271	24	the	the	DET
fumecheng-12619	271	25	unstable	unstable	ADJ
fumecheng-12619	271	26	amplitude	amplitude	NOUN
fumecheng-12619	271	27	)	)	PUNCT
fumecheng-12619	272	1	and	and	CCONJ
fumecheng-12619	272	2	the	the	DET
fumecheng-12619	272	3	maximum	maximum	ADJ
fumecheng-12619	272	4	value	value	NOUN
fumecheng-12619	272	5	is	be	AUX
fumecheng-12619	272	6	related	relate	VERB
fumecheng-12619	272	7	to	to	ADP
fumecheng-12619	272	8	fig	fig	NOUN
fumecheng-12619	272	9	.	.	PUNCT
fumecheng-12619	273	1	14	14	NUM
fumecheng-12619	273	2	for	for	ADP
fumecheng-12619	273	3	the	the	DET
fumecheng-12619	273	4	gmsit	gmsit	NOUN
fumecheng-12619	273	5	(	(	PUNCT
fumecheng-12619	273	6	case2	case2	PROPN
fumecheng-12619	273	7	)	)	PUNCT
fumecheng-12619	273	8	.	.	PUNCT
fumecheng-12619	274	1	as	as	SCONJ
fumecheng-12619	274	2	already	already	ADV
fumecheng-12619	274	3	mentioned	mention	VERB
fumecheng-12619	274	4	,	,	PUNCT
fumecheng-12619	274	5	the	the	DET
fumecheng-12619	274	6	three	three	NUM
fumecheng-12619	274	7	theories	theory	NOUN
fumecheng-12619	274	8	of	of	ADP
fumecheng-12619	274	9	ct	ct	PROPN
fumecheng-12619	274	10	,	,	PUNCT
fumecheng-12619	274	11	nlt	nlt	PROPN
fumecheng-12619	274	12	,	,	PUNCT
fumecheng-12619	274	13	and	and	CCONJ
fumecheng-12619	274	14	sgt	sgt	PROPN
fumecheng-12619	274	15	(	(	PUNCT
fumecheng-12619	274	16	respectively	respectively	ADV
fumecheng-12619	274	17	for	for	ADP
fumecheng-12619	274	18	figs	fig	NOUN
fumecheng-12619	274	19	.	.	PUNCT
fumecheng-12619	275	1	11	11	NUM
fumecheng-12619	275	2	-	-	SYM
fumecheng-12619	275	3	13	13	NUM
fumecheng-12619	275	4	)	)	PUNCT
fumecheng-12619	275	5	,	,	PUNCT
fumecheng-12619	275	6	due	due	ADP
fumecheng-12619	275	7	to	to	ADP
fumecheng-12619	275	8	the	the	DET
fumecheng-12619	275	9	softening	softening	NOUN
fumecheng-12619	275	10	of	of	ADP
fumecheng-12619	275	11	the	the	DET
fumecheng-12619	275	12	system	system	NOUN
fumecheng-12619	275	13	in	in	ADP
fumecheng-12619	275	14	these	these	DET
fumecheng-12619	275	15	cases	case	NOUN
fumecheng-12619	275	16	reach	reach	VERB
fumecheng-12619	275	17	the	the	DET
fumecheng-12619	275	18	unstable	unstable	ADJ
fumecheng-12619	275	19	amplitude	amplitude	NOUN
fumecheng-12619	275	20	at	at	ADP
fumecheng-12619	275	21	lower	low	ADJ
fumecheng-12619	275	22	voltages	voltage	NOUN
fumecheng-12619	275	23	from	from	ADP
fumecheng-12619	275	24	dc	dc	PROPN
fumecheng-12619	275	25	and	and	CCONJ
fumecheng-12619	275	26	ac	ac	PROPN
fumecheng-12619	275	27	and	and	CCONJ
fumecheng-12619	275	28	in	in	ADP
fumecheng-12619	275	29	order	order	NOUN
fumecheng-12619	275	30	to	to	PART
fumecheng-12619	275	31	reach	reach	VERB
fumecheng-12619	275	32	the	the	DET
fumecheng-12619	275	33	unstable	unstable	ADJ
fumecheng-12619	275	34	amplitude	amplitude	NOUN
fumecheng-12619	275	35	in	in	ADP
fumecheng-12619	275	36	the	the	DET
fumecheng-12619	275	37	gmsit	gmsit	NOUN
fumecheng-12619	275	38	theory	theory	NOUN
fumecheng-12619	275	39	,	,	PUNCT
fumecheng-12619	275	40	more	more	ADJ
fumecheng-12619	275	41	voltages	voltage	NOUN
fumecheng-12619	275	42	of	of	ADP
fumecheng-12619	275	43	dc	dc	PROPN
fumecheng-12619	275	44	and	and	CCONJ
fumecheng-12619	275	45	ac	ac	PROPN
fumecheng-12619	275	46	are	be	AUX
fumecheng-12619	275	47	needed	need	VERB
fumecheng-12619	275	48	.	.	PUNCT
fumecheng-12619	276	1	for	for	ADP
fumecheng-12619	276	2	example	example	NOUN
fumecheng-12619	276	3	,	,	PUNCT
fumecheng-12619	276	4	according	accord	VERB
fumecheng-12619	276	5	to	to	ADP
fumecheng-12619	276	6	the	the	DET
fumecheng-12619	276	7	data	datum	NOUN
fumecheng-12619	276	8	in	in	ADP
fumecheng-12619	276	9	this	this	DET
fumecheng-12619	276	10	work	work	NOUN
fumecheng-12619	276	11	,	,	PUNCT
fumecheng-12619	276	12	ct	ct	PROPN
fumecheng-12619	276	13	,	,	PUNCT
fumecheng-12619	276	14	nlt	nlt	PROPN
fumecheng-12619	276	15	and	and	CCONJ
fumecheng-12619	276	16	sgt	sgt	PROPN
fumecheng-12619	276	17	theories	theory	NOUN
fumecheng-12619	276	18	in	in	ADP
fumecheng-12619	276	19	�	�	NOUN
fumecheng-12619	276	20	̅	̅	NOUN
fumecheng-12619	276	21	�	�	NOUN
fumecheng-12619	276	22	𝑨𝑪	𝑨𝑪	NOUN
fumecheng-12619	276	23	=	=	SYM
fumecheng-12619	276	24	𝟎.	𝟎.	X
fumecheng-12619	276	25	𝟓	𝟓	NUM
fumecheng-12619	276	26	and	and	CCONJ
fumecheng-12619	276	27	�	�	NOUN
fumecheng-12619	276	28	̅	̅	NOUN
fumecheng-12619	276	29	�	�	NOUN
fumecheng-12619	276	30	𝑫𝑪	𝑫𝑪	NOUN
fumecheng-12619	276	31	=	=	SYM
fumecheng-12619	277	1	𝟏.	𝟏.	X
fumecheng-12619	277	2	𝟒𝟓	𝟒𝟓	NUM
fumecheng-12619	277	3	reach	reach	VERB
fumecheng-12619	277	4	unstable	unstable	ADJ
fumecheng-12619	277	5	amplitude	amplitude	NOUN
fumecheng-12619	277	6	,	,	PUNCT
fumecheng-12619	277	7	while	while	SCONJ
fumecheng-12619	277	8	gmsit	gmsit	NOUN
fumecheng-12619	277	9	theory	theory	NOUN
fumecheng-12619	277	10	and	and	CCONJ
fumecheng-12619	277	11	the	the	DET
fumecheng-12619	277	12	simultaneous	simultaneous	ADJ
fumecheng-12619	277	13	use	use	NOUN
fumecheng-12619	277	14	of	of	ADP
fumecheng-12619	277	15	this	this	DET
fumecheng-12619	277	16	theory	theory	NOUN
fumecheng-12619	277	17	with	with	ADP
fumecheng-12619	277	18	two	two	NUM
fumecheng-12619	277	19	non	non	ADJ
fumecheng-12619	277	20	-	-	ADJ
fumecheng-12619	277	21	classical	classical	ADJ
fumecheng-12619	277	22	theories	theory	NOUN
fumecheng-12619	277	23	,	,	PUNCT
fumecheng-12619	277	24	gmsit	gmsit	VERB
fumecheng-12619	277	25	+	+	CCONJ
fumecheng-12619	277	26	nlt	nlt	PROPN
fumecheng-12619	277	27	(	(	PUNCT
fumecheng-12619	277	28	fig	fig	NOUN
fumecheng-12619	277	29	.	.	PUNCT
fumecheng-12619	277	30	15	15	NUM
fumecheng-12619	277	31	)	)	PUNCT
fumecheng-12619	277	32	and	and	CCONJ
fumecheng-12619	277	33	gmsit	gmsit	VERB
fumecheng-12619	277	34	+	+	CCONJ
fumecheng-12619	278	1	sgt	sgt	PROPN
fumecheng-12619	278	2	(	(	PUNCT
fumecheng-12619	278	3	fig	fig	NOUN
fumecheng-12619	278	4	.	.	PUNCT
fumecheng-12619	278	5	16	16	NUM
fumecheng-12619	278	6	)	)	PUNCT
fumecheng-12619	278	7	,	,	PUNCT
fumecheng-12619	278	8	are	be	AUX
fumecheng-12619	278	9	required	require	VERB
fumecheng-12619	278	10	to	to	PART
fumecheng-12619	278	11	reach	reach	VERB
fumecheng-12619	278	12	the	the	DET
fumecheng-12619	278	13	unstable	unstable	ADJ
fumecheng-12619	278	14	amplitude	amplitude	NOUN
fumecheng-12619	278	15	to	to	ADP
fumecheng-12619	278	16	�	�	NOUN
fumecheng-12619	278	17	̅	̅	NOUN
fumecheng-12619	278	18	�	�	NOUN
fumecheng-12619	278	19	𝑨𝑪	𝑨𝑪	NOUN
fumecheng-12619	278	20	=	=	SYM
fumecheng-12619	278	21	𝟐	𝟐	NUM
fumecheng-12619	278	22	and	and	CCONJ
fumecheng-12619	278	23	�	�	NOUN
fumecheng-12619	278	24	̅	̅	NOUN
fumecheng-12619	278	25	�	�	NOUN
fumecheng-12619	278	26	𝑫𝑪	𝑫𝑪	NOUN
fumecheng-12619	278	27	=	=	SYM
fumecheng-12619	278	28	𝟒	𝟒	NUM
fumecheng-12619	278	29	voltages	voltage	NOUN
fumecheng-12619	278	30	.	.	PUNCT
fumecheng-12619	279	1	furthermore	furthermore	ADV
fumecheng-12619	279	2	,	,	PUNCT
fumecheng-12619	279	3	the	the	DET
fumecheng-12619	279	4	results	result	NOUN
fumecheng-12619	279	5	show	show	VERB
fumecheng-12619	279	6	that	that	SCONJ
fumecheng-12619	279	7	in	in	ADP
fumecheng-12619	279	8	all	all	DET
fumecheng-12619	279	9	cases	case	NOUN
fumecheng-12619	279	10	,	,	PUNCT
fumecheng-12619	279	11	with	with	ADP
fumecheng-12619	279	12	increasing	increase	VERB
fumecheng-12619	279	13	of	of	ADP
fumecheng-12619	279	14	ac	ac	PROPN
fumecheng-12619	279	15	and	and	CCONJ
fumecheng-12619	279	16	dc	dc	PROPN
fumecheng-12619	279	17	voltages	voltage	NOUN
fumecheng-12619	279	18	,	,	PUNCT
fumecheng-12619	279	19	the	the	DET
fumecheng-12619	279	20	frequency	frequency	NOUN
fumecheng-12619	279	21	amplitude	amplitude	NOUN
fumecheng-12619	279	22	is	be	AUX
fumecheng-12619	279	23	increased	increase	VERB
fumecheng-12619	279	24	and	and	CCONJ
fumecheng-12619	279	25	the	the	DET
fumecheng-12619	279	26	nanostructure	nanostructure	NOUN
fumecheng-12619	279	27	shows	show	VERB
fumecheng-12619	279	28	nonlinear	nonlinear	ADJ
fumecheng-12619	279	29	hardening	harden	VERB
fumecheng-12619	279	30	behavior	behavior	NOUN
fumecheng-12619	279	31	with	with	ADP
fumecheng-12619	279	32	saddle	saddle	NOUN
fumecheng-12619	279	33	-	-	PUNCT
fumecheng-12619	279	34	node	node	NOUN
fumecheng-12619	279	35	bifurcations	bifurcation	NOUN
fumecheng-12619	279	36	.	.	PUNCT
fumecheng-12619	280	1	also	also	ADV
fumecheng-12619	280	2	,	,	PUNCT
fumecheng-12619	280	3	figs	fig	NOUN
fumecheng-12619	280	4	.	.	PUNCT
fumecheng-12619	281	1	17	17	NUM
fumecheng-12619	281	2	-	-	SYM
fumecheng-12619	281	3	22	22	NUM
fumecheng-12619	281	4	present	present	ADJ
fumecheng-12619	281	5	frequency	frequency	NOUN
fumecheng-12619	281	6	response	response	NOUN
fumecheng-12619	281	7	and	and	CCONJ
fumecheng-12619	281	8	stability	stability	NOUN
fumecheng-12619	281	9	analysis	analysis	NOUN
fumecheng-12619	281	10	penr	penr	ADJ
fumecheng-12619	281	11	for	for	ADP
fumecheng-12619	281	12	different	different	ADJ
fumecheng-12619	281	13	values	value	NOUN
fumecheng-12619	281	14	of	of	ADP
fumecheng-12619	281	15	direct	direct	ADJ
fumecheng-12619	281	16	(	(	PUNCT
fumecheng-12619	281	17	�	�	NOUN
fumecheng-12619	281	18	̅	̅	NOUN
fumecheng-12619	281	19	�	�	NOUN
fumecheng-12619	281	20	𝑫𝑪	𝑫𝑪	NOUN
fumecheng-12619	281	21	)	)	PUNCT
fumecheng-12619	281	22	and	and	CCONJ
fumecheng-12619	281	23	alternating	alternate	VERB
fumecheng-12619	281	24	(	(	PUNCT
fumecheng-12619	281	25	�	�	NOUN
fumecheng-12619	281	26	̅	̅	NOUN
fumecheng-12619	281	27	�	�	NOUN
fumecheng-12619	281	28	𝑨𝑪	𝑨𝑪	NOUN
fumecheng-12619	281	29	)	)	PUNCT
fumecheng-12619	281	30	voltages	voltage	NOUN
fumecheng-12619	281	31	based	base	VERB
fumecheng-12619	281	32	on	on	ADP
fumecheng-12619	281	33	different	different	ADJ
fumecheng-12619	281	34	theories	theory	NOUN
fumecheng-12619	281	35	of	of	ADP
fumecheng-12619	281	36	ct	ct	PROPN
fumecheng-12619	281	37	,	,	PUNCT
fumecheng-12619	281	38	nlt	nlt	PROPN
fumecheng-12619	281	39	,	,	PUNCT
fumecheng-12619	281	40	sgt	sgt	PROPN
fumecheng-12619	281	41	,	,	PUNCT
fumecheng-12619	281	42	gmsit	gmsit	NOUN
fumecheng-12619	281	43	,	,	PUNCT
fumecheng-12619	281	44	gmsit	gmsit	NOUN
fumecheng-12619	281	45	combined	combine	VERB
fumecheng-12619	281	46	with	with	ADP
fumecheng-12619	281	47	nlt	nlt	PROPN
fumecheng-12619	281	48	and	and	CCONJ
fumecheng-12619	281	49	sgt	sgt	PROPN
fumecheng-12619	281	50	for	for	ADP
fumecheng-12619	281	51	cc	cc	PROPN
fumecheng-12619	281	52	boundary	boundary	ADJ
fumecheng-12619	281	53	conditions	condition	NOUN
fumecheng-12619	281	54	.	.	PUNCT
fumecheng-12619	282	1	the	the	DET
fumecheng-12619	282	2	results	result	NOUN
fumecheng-12619	282	3	of	of	ADP
fumecheng-12619	282	4	figs	fig	NOUN
fumecheng-12619	282	5	.	.	PUNCT
fumecheng-12619	283	1	17	17	NUM
fumecheng-12619	283	2	-	-	SYM
fumecheng-12619	283	3	22	22	NUM
fumecheng-12619	283	4	for	for	ADP
fumecheng-12619	283	5	cc	cc	PROPN
fumecheng-12619	283	6	penr	penr	PROPN
fumecheng-12619	283	7	approximately	approximately	ADV
fumecheng-12619	283	8	are	be	AUX
fumecheng-12619	283	9	similar	similar	ADJ
fumecheng-12619	283	10	to	to	ADP
fumecheng-12619	283	11	figs	fig	NOUN
fumecheng-12619	283	12	.	.	PUNCT
fumecheng-12619	284	1	11	11	NUM
fumecheng-12619	284	2	-	-	SYM
fumecheng-12619	284	3	16	16	NUM
fumecheng-12619	284	4	for	for	ADP
fumecheng-12619	284	5	ss	ss	PROPN
fumecheng-12619	284	6	penr	penr	PROPN
fumecheng-12619	284	7	.	.	PUNCT
fumecheng-12619	285	1	it	it	PRON
fumecheng-12619	285	2	is	be	AUX
fumecheng-12619	285	3	clear	clear	ADJ
fumecheng-12619	285	4	from	from	ADP
fumecheng-12619	285	5	figs	fig	NOUN
fumecheng-12619	285	6	.	.	PUNCT
fumecheng-12619	286	1	11	11	NUM
fumecheng-12619	286	2	-	-	SYM
fumecheng-12619	286	3	22	22	NUM
fumecheng-12619	286	4	that	that	PRON
fumecheng-12619	286	5	boundary	boundary	ADJ
fumecheng-12619	286	6	condition	condition	NOUN
fumecheng-12619	286	7	ss	ss	NOUN
fumecheng-12619	286	8	than	than	ADP
fumecheng-12619	286	9	condition	condition	NOUN
fumecheng-12619	286	10	cc	cc	NOUN
fumecheng-12619	286	11	,	,	PUNCT
fumecheng-12619	286	12	in	in	ADP
fumecheng-12619	286	13	some	some	DET
fumecheng-12619	286	14	approaches	approach	NOUN
fumecheng-12619	286	15	and	and	CCONJ
fumecheng-12619	286	16	under	under	ADP
fumecheng-12619	286	17	equal	equal	ADJ
fumecheng-12619	286	18	loading	loading	NOUN
fumecheng-12619	286	19	conditions	condition	NOUN
fumecheng-12619	286	20	,	,	PUNCT
fumecheng-12619	286	21	earlier	early	ADV
fumecheng-12619	286	22	reaches	reach	VERB
fumecheng-12619	286	23	the	the	DET
fumecheng-12619	286	24	instability	instability	NOUN
fumecheng-12619	286	25	region	region	NOUN
fumecheng-12619	286	26	.	.	PUNCT
fumecheng-12619	287	1	fig	fig	NOUN
fumecheng-12619	287	2	.	.	PUNCT
fumecheng-12619	288	1	17	17	NUM
fumecheng-12619	288	2	frequency	frequency	NOUN
fumecheng-12619	288	3	response	response	NOUN
fumecheng-12619	288	4	and	and	CCONJ
fumecheng-12619	288	5	stability	stability	NOUN
fumecheng-12619	288	6	analysis	analysis	NOUN
fumecheng-12619	288	7	of	of	ADP
fumecheng-12619	288	8	cc	cc	ADP
fumecheng-12619	288	9	penr	penr	PROPN
fumecheng-12619	288	10	(	(	PUNCT
fumecheng-12619	288	11	ct	ct	PROPN
fumecheng-12619	288	12	)	)	PUNCT
fumecheng-12619	288	13	under	under	ADP
fumecheng-12619	288	14	varying	vary	VERB
fumecheng-12619	288	15	dc	dc	PROPN
fumecheng-12619	288	16	and	and	CCONJ
fumecheng-12619	288	17	ac	ac	PROPN
fumecheng-12619	288	18	voltages	voltage	NOUN
fumecheng-12619	288	19	330	330	NUM
fumecheng-12619	288	20	s.h	s.h	PROPN
fumecheng-12619	288	21	.	.	PROPN
fumecheng-12619	288	22	hashemi	hashemi	PROPN
fumecheng-12619	288	23	kachapi	kachapi	PROPN
fumecheng-12619	288	24	,	,	PUNCT
fumecheng-12619	288	25	s.	s.	PROPN
fumecheng-12619	288	26	gh	gh	PROPN
fumecheng-12619	288	27	.	.	PROPN
fumecheng-12619	289	1	hashemi	hashemi	PROPN
fumecheng-12619	289	2	kachapi	kachapi	PROPN
fumecheng-12619	289	3	fig	fig	PROPN
fumecheng-12619	289	4	.	.	PUNCT
fumecheng-12619	290	1	18	18	NUM
fumecheng-12619	290	2	frequency	frequency	NOUN
fumecheng-12619	290	3	response	response	NOUN
fumecheng-12619	290	4	and	and	CCONJ
fumecheng-12619	290	5	stability	stability	NOUN
fumecheng-12619	290	6	analysis	analysis	NOUN
fumecheng-12619	290	7	of	of	ADP
fumecheng-12619	290	8	cc	cc	ADP
fumecheng-12619	290	9	penr	penr	PROPN
fumecheng-12619	290	10	(	(	PUNCT
fumecheng-12619	290	11	nlt	nlt	PROPN
fumecheng-12619	290	12	)	)	PUNCT
fumecheng-12619	290	13	under	under	ADP
fumecheng-12619	290	14	varying	vary	VERB
fumecheng-12619	290	15	dc	dc	PROPN
fumecheng-12619	290	16	and	and	CCONJ
fumecheng-12619	290	17	ac	ac	PROPN
fumecheng-12619	290	18	voltages	voltage	NOUN
fumecheng-12619	290	19	fig	fig	PROPN
fumecheng-12619	290	20	.	.	PUNCT
fumecheng-12619	291	1	19	19	NUM
fumecheng-12619	291	2	frequency	frequency	NOUN
fumecheng-12619	291	3	response	response	NOUN
fumecheng-12619	291	4	and	and	CCONJ
fumecheng-12619	291	5	stability	stability	NOUN
fumecheng-12619	291	6	analysis	analysis	NOUN
fumecheng-12619	291	7	of	of	ADP
fumecheng-12619	291	8	cc	cc	ADP
fumecheng-12619	291	9	penr	penr	PROPN
fumecheng-12619	291	10	(	(	PUNCT
fumecheng-12619	291	11	sgt	sgt	PROPN
fumecheng-12619	291	12	)	)	PUNCT
fumecheng-12619	291	13	under	under	ADP
fumecheng-12619	291	14	varying	vary	VERB
fumecheng-12619	291	15	dc	dc	PROPN
fumecheng-12619	291	16	and	and	CCONJ
fumecheng-12619	291	17	ac	ac	PROPN
fumecheng-12619	291	18	voltages	voltage	NOUN
fumecheng-12619	291	19	comparison	comparison	NOUN
fumecheng-12619	291	20	of	of	ADP
fumecheng-12619	291	21	nonclassical	nonclassical	ADJ
fumecheng-12619	291	22	controllers	controller	NOUN
fumecheng-12619	291	23	on	on	ADP
fumecheng-12619	291	24	nonlinear	nonlinear	ADJ
fumecheng-12619	291	25	vibrations	vibration	NOUN
fumecheng-12619	291	26	analysis	analysis	NOUN
fumecheng-12619	291	27	of	of	ADP
fumecheng-12619	291	28	piezoelectric	piezoelectric	NOUN
fumecheng-12619	291	29	...	...	PUNCT
fumecheng-12619	291	30	331	331	NUM
fumecheng-12619	291	31	fig	fig	NOUN
fumecheng-12619	291	32	.	.	PUNCT
fumecheng-12619	292	1	20	20	NUM
fumecheng-12619	292	2	frequency	frequency	NOUN
fumecheng-12619	292	3	response	response	NOUN
fumecheng-12619	292	4	and	and	CCONJ
fumecheng-12619	292	5	stability	stability	NOUN
fumecheng-12619	292	6	analysis	analysis	NOUN
fumecheng-12619	292	7	of	of	ADP
fumecheng-12619	292	8	cc	cc	ADP
fumecheng-12619	292	9	penr	penr	PROPN
fumecheng-12619	292	10	(	(	PUNCT
fumecheng-12619	292	11	gmsit	gmsit	NOUN
fumecheng-12619	292	12	)	)	PUNCT
fumecheng-12619	292	13	under	under	ADP
fumecheng-12619	292	14	varying	vary	VERB
fumecheng-12619	292	15	dc	dc	PROPN
fumecheng-12619	292	16	and	and	CCONJ
fumecheng-12619	292	17	ac	ac	PROPN
fumecheng-12619	292	18	voltages	voltage	NOUN
fumecheng-12619	292	19	fig	fig	PROPN
fumecheng-12619	292	20	.	.	PUNCT
fumecheng-12619	293	1	21	21	NUM
fumecheng-12619	293	2	frequency	frequency	NOUN
fumecheng-12619	293	3	response	response	NOUN
fumecheng-12619	293	4	and	and	CCONJ
fumecheng-12619	293	5	stability	stability	NOUN
fumecheng-12619	293	6	analysis	analysis	NOUN
fumecheng-12619	293	7	of	of	ADP
fumecheng-12619	293	8	cc	cc	ADP
fumecheng-12619	293	9	penr	penr	PROPN
fumecheng-12619	293	10	(	(	PUNCT
fumecheng-12619	293	11	gmsit+nlt	gmsit+nlt	PROPN
fumecheng-12619	293	12	)	)	PUNCT
fumecheng-12619	293	13	under	under	ADP
fumecheng-12619	293	14	varying	vary	VERB
fumecheng-12619	293	15	dc	dc	PROPN
fumecheng-12619	293	16	and	and	CCONJ
fumecheng-12619	293	17	ac	ac	PROPN
fumecheng-12619	293	18	voltages	voltage	VERB
fumecheng-12619	293	19	332	332	NUM
fumecheng-12619	293	20	s.h	s.h	PROPN
fumecheng-12619	293	21	.	.	PROPN
fumecheng-12619	293	22	hashemi	hashemi	PROPN
fumecheng-12619	293	23	kachapi	kachapi	PROPN
fumecheng-12619	293	24	,	,	PUNCT
fumecheng-12619	293	25	s.	s.	PROPN
fumecheng-12619	293	26	gh	gh	PROPN
fumecheng-12619	293	27	.	.	PROPN
fumecheng-12619	294	1	hashemi	hashemi	PROPN
fumecheng-12619	294	2	kachapi	kachapi	PROPN
fumecheng-12619	294	3	fig	fig	PROPN
fumecheng-12619	294	4	.	.	PUNCT
fumecheng-12619	295	1	22	22	NUM
fumecheng-12619	295	2	frequency	frequency	NOUN
fumecheng-12619	295	3	response	response	NOUN
fumecheng-12619	295	4	and	and	CCONJ
fumecheng-12619	295	5	stability	stability	NOUN
fumecheng-12619	295	6	analysis	analysis	NOUN
fumecheng-12619	295	7	of	of	ADP
fumecheng-12619	295	8	cc	cc	ADP
fumecheng-12619	295	9	penr	penr	PROPN
fumecheng-12619	295	10	(	(	PUNCT
fumecheng-12619	295	11	gmsit+	gmsit+	X
fumecheng-12619	295	12	sgt	sgt	PROPN
fumecheng-12619	295	13	)	)	PUNCT
fumecheng-12619	295	14	under	under	ADP
fumecheng-12619	295	15	varying	vary	VERB
fumecheng-12619	295	16	dc	dc	PROPN
fumecheng-12619	295	17	and	and	CCONJ
fumecheng-12619	295	18	ac	ac	PROPN
fumecheng-12619	295	19	voltages	voltage	NOUN
fumecheng-12619	295	20	4	4	NUM
fumecheng-12619	295	21	.	.	PUNCT
fumecheng-12619	295	22	conclusion	conclusion	NOUN
fumecheng-12619	295	23	this	this	DET
fumecheng-12619	295	24	study	study	NOUN
fumecheng-12619	295	25	investigates	investigate	VERB
fumecheng-12619	295	26	the	the	DET
fumecheng-12619	295	27	influence	influence	NOUN
fumecheng-12619	295	28	of	of	ADP
fumecheng-12619	295	29	surface	surface	NOUN
fumecheng-12619	295	30	/	/	SYM
fumecheng-12619	295	31	interface	interface	NOUN
fumecheng-12619	295	32	parameters	parameter	NOUN
fumecheng-12619	295	33	,	,	PUNCT
fumecheng-12619	295	34	specifically	specifically	ADV
fumecheng-12619	295	35	,	,	PUNCT
fumecheng-12619	295	36	lamé	lamé	NOUN
fumecheng-12619	295	37	's	's	PART
fumecheng-12619	295	38	constants	constant	NOUN
fumecheng-12619	295	39	(	(	PUNCT
fumecheng-12619	295	40	𝜆𝐼,𝑆	𝜆𝐼,𝑆	NOUN
fumecheng-12619	295	41	,	,	PUNCT
fumecheng-12619	295	42	𝜇𝐼,𝑆	𝜇𝐼,𝑆	NOUN
fumecheng-12619	295	43	)	)	PUNCT
fumecheng-12619	295	44	,	,	PUNCT
fumecheng-12619	295	45	residual	residual	ADJ
fumecheng-12619	295	46	stress	stress	NOUN
fumecheng-12619	295	47	(	(	PUNCT
fumecheng-12619	295	48	𝜏0	𝜏0	PROPN
fumecheng-12619	295	49	𝐼,𝑆	𝐼,𝑆	NOUN
fumecheng-12619	295	50	)	)	PUNCT
fumecheng-12619	295	51	,	,	PUNCT
fumecheng-12619	295	52	piezoelectric	piezoelectric	NOUN
fumecheng-12619	295	53	constants	constant	NOUN
fumecheng-12619	295	54	(	(	PUNCT
fumecheng-12619	295	55	𝑒31𝑝	𝑒31𝑝	NOUN
fumecheng-12619	295	56	𝑠𝑘	𝑠𝑘	NOUN
fumecheng-12619	295	57	,	,	PUNCT
fumecheng-12619	295	58	𝑒32𝑝	𝑒32𝑝	ADP
fumecheng-12619	295	59	𝑠𝑘	𝑠𝑘	NOUN
fumecheng-12619	295	60	)	)	PUNCT
fumecheng-12619	295	61	,	,	PUNCT
fumecheng-12619	295	62	and	and	CCONJ
fumecheng-12619	295	63	mass	mass	ADJ
fumecheng-12619	295	64	density	density	NOUN
fumecheng-12619	295	65	(	(	PUNCT
fumecheng-12619	295	66	𝜌𝐼,𝑆	𝜌𝐼,𝑆	NOUN
fumecheng-12619	295	67	)	)	PUNCT
fumecheng-12619	295	68	on	on	ADP
fumecheng-12619	295	69	the	the	DET
fumecheng-12619	295	70	pull	pull	NOUN
fumecheng-12619	295	71	-	-	PUNCT
fumecheng-12619	295	72	in	in	ADP
fumecheng-12619	295	73	instability	instability	NOUN
fumecheng-12619	295	74	,	,	PUNCT
fumecheng-12619	295	75	dimensionless	dimensionless	ADJ
fumecheng-12619	295	76	natural	natural	ADJ
fumecheng-12619	295	77	frequency	frequency	NOUN
fumecheng-12619	295	78	,	,	PUNCT
fumecheng-12619	295	79	and	and	CCONJ
fumecheng-12619	295	80	nonlinear	nonlinear	ADJ
fumecheng-12619	295	81	dynamic	dynamic	ADJ
fumecheng-12619	295	82	response	response	NOUN
fumecheng-12619	295	83	of	of	ADP
fumecheng-12619	295	84	a	a	DET
fumecheng-12619	295	85	piezoelectric	piezoelectric	ADJ
fumecheng-12619	295	86	nanosensor	nanosensor	NOUN
fumecheng-12619	295	87	.	.	PUNCT
fumecheng-12619	296	1	the	the	DET
fumecheng-12619	296	2	nanosensor	nanosensor	NOUN
fumecheng-12619	296	3	is	be	AUX
fumecheng-12619	296	4	subjected	subject	VERB
fumecheng-12619	296	5	to	to	ADP
fumecheng-12619	296	6	two	two	NUM
fumecheng-12619	296	7	piezoelectric	piezoelectric	ADJ
fumecheng-12619	296	8	layers	layer	NOUN
fumecheng-12619	296	9	,	,	PUNCT
fumecheng-12619	296	10	a	a	DET
fumecheng-12619	296	11	nonlinear	nonlinear	ADJ
fumecheng-12619	296	12	electrostatic	electrostatic	ADJ
fumecheng-12619	296	13	force	force	NOUN
fumecheng-12619	296	14	,	,	PUNCT
fumecheng-12619	296	15	harmonic	harmonic	ADJ
fumecheng-12619	296	16	excitations	excitation	NOUN
fumecheng-12619	296	17	,	,	PUNCT
fumecheng-12619	296	18	and	and	CCONJ
fumecheng-12619	296	19	structural	structural	ADJ
fumecheng-12619	296	20	damping	damping	NOUN
fumecheng-12619	296	21	.	.	PUNCT
fumecheng-12619	297	1	to	to	PART
fumecheng-12619	297	2	achieve	achieve	VERB
fumecheng-12619	297	3	this	this	PRON
fumecheng-12619	297	4	,	,	PUNCT
fumecheng-12619	297	5	hamilton	hamilton	PROPN
fumecheng-12619	297	6	's	's	PART
fumecheng-12619	297	7	principle	principle	NOUN
fumecheng-12619	297	8	,	,	PUNCT
fumecheng-12619	297	9	assumed	assume	VERB
fumecheng-12619	297	10	mode	mode	NOUN
fumecheng-12619	297	11	and	and	CCONJ
fumecheng-12619	297	12	lagrange	lagrange	PROPN
fumecheng-12619	297	13	-	-	PUNCT
fumecheng-12619	297	14	euler	euler	NOUN
fumecheng-12619	297	15	theories	theory	NOUN
fumecheng-12619	297	16	,	,	PUNCT
fumecheng-12619	297	17	along	along	ADP
fumecheng-12619	297	18	with	with	ADP
fumecheng-12619	297	19	arclength	arclength	NOUN
fumecheng-12619	297	20	continuation	continuation	NOUN
fumecheng-12619	297	21	and	and	CCONJ
fumecheng-12619	297	22	complex	complex	ADJ
fumecheng-12619	297	23	averaging	averaging	NOUN
fumecheng-12619	297	24	methods	method	NOUN
fumecheng-12619	297	25	,	,	PUNCT
fumecheng-12619	297	26	are	be	AUX
fumecheng-12619	297	27	employed	employ	VERB
fumecheng-12619	297	28	.	.	PUNCT
fumecheng-12619	298	1	the	the	DET
fumecheng-12619	298	2	following	follow	VERB
fumecheng-12619	298	3	conclusions	conclusion	NOUN
fumecheng-12619	298	4	are	be	AUX
fumecheng-12619	298	5	drawn	draw	VERB
fumecheng-12619	298	6	from	from	ADP
fumecheng-12619	298	7	this	this	DET
fumecheng-12619	298	8	investigation	investigation	NOUN
fumecheng-12619	298	9	:	:	PUNCT
fumecheng-12619	298	10	▪	▪	X
fumecheng-12619	298	11	under	under	ADP
fumecheng-12619	298	12	conditions	condition	NOUN
fumecheng-12619	298	13	of	of	ADP
fumecheng-12619	298	14	lower	low	ADJ
fumecheng-12619	298	15	surface	surface	NOUN
fumecheng-12619	298	16	/	/	SYM
fumecheng-12619	298	17	interface	interface	NOUN
fumecheng-12619	298	18	densities	density	NOUN
fumecheng-12619	298	19	,	,	PUNCT
fumecheng-12619	298	20	an	an	DET
fumecheng-12619	298	21	augmentation	augmentation	NOUN
fumecheng-12619	298	22	of	of	ADP
fumecheng-12619	298	23	stiffness	stiffness	NOUN
fumecheng-12619	298	24	is	be	AUX
fumecheng-12619	298	25	observed	observe	VERB
fumecheng-12619	298	26	,	,	PUNCT
fumecheng-12619	298	27	resulting	result	VERB
fumecheng-12619	298	28	in	in	ADP
fumecheng-12619	298	29	an	an	DET
fumecheng-12619	298	30	elevated	elevated	ADJ
fumecheng-12619	298	31	natural	natural	ADJ
fumecheng-12619	298	32	frequency	frequency	NOUN
fumecheng-12619	298	33	compared	compare	VERB
fumecheng-12619	298	34	to	to	ADP
fumecheng-12619	298	35	scenarios	scenario	NOUN
fumecheng-12619	298	36	lacking	lack	VERB
fumecheng-12619	298	37	surface	surface	NOUN
fumecheng-12619	298	38	/	/	SYM
fumecheng-12619	298	39	interface	interface	NOUN
fumecheng-12619	298	40	effects	effect	NOUN
fumecheng-12619	298	41	.	.	PUNCT
fumecheng-12619	299	1	conversely	conversely	ADV
fumecheng-12619	299	2	,	,	PUNCT
fumecheng-12619	299	3	higher	high	ADJ
fumecheng-12619	299	4	surface	surface	NOUN
fumecheng-12619	299	5	/	/	SYM
fumecheng-12619	299	6	interface	interface	NOUN
fumecheng-12619	299	7	densities	density	NOUN
fumecheng-12619	299	8	lead	lead	VERB
fumecheng-12619	299	9	to	to	ADP
fumecheng-12619	299	10	a	a	DET
fumecheng-12619	299	11	reduction	reduction	NOUN
fumecheng-12619	299	12	in	in	ADP
fumecheng-12619	299	13	stiffness	stiffness	NOUN
fumecheng-12619	299	14	and	and	CCONJ
fumecheng-12619	299	15	a	a	DET
fumecheng-12619	299	16	corresponding	corresponding	ADJ
fumecheng-12619	299	17	decrease	decrease	NOUN
fumecheng-12619	299	18	in	in	ADP
fumecheng-12619	299	19	natural	natural	ADJ
fumecheng-12619	299	20	frequency	frequency	NOUN
fumecheng-12619	299	21	.	.	PUNCT
fumecheng-12619	300	1	▪	▪	X
fumecheng-12619	300	2	cf	cf	NOUN
fumecheng-12619	300	3	(	(	PUNCT
fumecheng-12619	300	4	cc	cc	NOUN
fumecheng-12619	300	5	)	)	PUNCT
fumecheng-12619	300	6	boundary	boundary	ADJ
fumecheng-12619	300	7	condition	condition	NOUN
fumecheng-12619	300	8	with	with	ADP
fumecheng-12619	300	9	s	s	PROPN
fumecheng-12619	300	10	/	/	SYM
fumecheng-12619	300	11	i	i	NOUN
fumecheng-12619	300	12	case	case	NOUN
fumecheng-12619	300	13	1	1	NUM
fumecheng-12619	300	14	has	have	VERB
fumecheng-12619	300	15	the	the	DET
fumecheng-12619	300	16	lowest	low	ADJ
fumecheng-12619	300	17	(	(	PUNCT
fumecheng-12619	300	18	highest	high	ADJ
fumecheng-12619	300	19	)	)	PUNCT
fumecheng-12619	300	20	natural	natural	ADJ
fumecheng-12619	300	21	frequency	frequency	NOUN
fumecheng-12619	300	22	:	:	PUNCT
fumecheng-12619	300	23	this	this	PRON
fumecheng-12619	300	24	indicates	indicate	VERB
fumecheng-12619	300	25	that	that	SCONJ
fumecheng-12619	300	26	when	when	SCONJ
fumecheng-12619	300	27	one	one	NUM
fumecheng-12619	300	28	end	end	NOUN
fumecheng-12619	300	29	of	of	ADP
fumecheng-12619	300	30	the	the	DET
fumecheng-12619	300	31	nanoresonator	nanoresonator	NOUN
fumecheng-12619	300	32	is	be	AUX
fumecheng-12619	300	33	clamped	clamp	VERB
fumecheng-12619	300	34	and	and	CCONJ
fumecheng-12619	300	35	the	the	DET
fumecheng-12619	300	36	other	other	ADJ
fumecheng-12619	300	37	is	be	AUX
fumecheng-12619	300	38	free	free	ADJ
fumecheng-12619	300	39	,	,	PUNCT
fumecheng-12619	300	40	and	and	CCONJ
fumecheng-12619	300	41	the	the	DET
fumecheng-12619	300	42	surface	surface	NOUN
fumecheng-12619	300	43	/	/	SYM
fumecheng-12619	300	44	interface	interface	NOUN
fumecheng-12619	300	45	properties	property	NOUN
fumecheng-12619	300	46	correspond	correspond	VERB
fumecheng-12619	300	47	to	to	PART
fumecheng-12619	300	48	case	case	NOUN
fumecheng-12619	300	49	1	1	NUM
fumecheng-12619	300	50	,	,	PUNCT
fumecheng-12619	300	51	the	the	DET
fumecheng-12619	300	52	nanoresonator	nanoresonator	NOUN
fumecheng-12619	300	53	will	will	AUX
fumecheng-12619	300	54	vibrate	vibrate	VERB
fumecheng-12619	300	55	at	at	ADP
fumecheng-12619	300	56	its	its	PRON
fumecheng-12619	300	57	slowest	slow	ADJ
fumecheng-12619	300	58	natural	natural	ADJ
fumecheng-12619	300	59	frequency	frequency	NOUN
fumecheng-12619	300	60	.	.	PUNCT
fumecheng-12619	301	1	▪	▪	NOUN
fumecheng-12619	301	2	an	an	DET
fumecheng-12619	301	3	increase	increase	NOUN
fumecheng-12619	301	4	in	in	ADP
fumecheng-12619	301	5	surface	surface	NOUN
fumecheng-12619	301	6	/	/	SYM
fumecheng-12619	301	7	interface	interface	NOUN
fumecheng-12619	301	8	lamé	lamé	NOUN
fumecheng-12619	301	9	's	's	PART
fumecheng-12619	301	10	constants	constant	NOUN
fumecheng-12619	301	11	𝜆𝐼,𝑆	𝜆𝐼,𝑆	PROPN
fumecheng-12619	301	12	and	and	CCONJ
fumecheng-12619	301	13	𝜇𝐼,𝑆	𝜇𝐼,𝑆	NOUN
fumecheng-12619	301	14	,	,	PUNCT
fumecheng-12619	301	15	surface	surface	NOUN
fumecheng-12619	301	16	/	/	SYM
fumecheng-12619	301	17	interface	interface	NOUN
fumecheng-12619	301	18	residual	residual	ADJ
fumecheng-12619	301	19	stress	stress	NOUN
fumecheng-12619	301	20	𝜏0	𝜏0	NOUN
fumecheng-12619	301	21	𝐼,𝑆	𝐼,𝑆	NOUN
fumecheng-12619	301	22	,	,	PUNCT
fumecheng-12619	301	23	and	and	CCONJ
fumecheng-12619	301	24	the	the	DET
fumecheng-12619	301	25	magnitude	magnitude	NOUN
fumecheng-12619	301	26	of	of	ADP
fumecheng-12619	301	27	negative	negative	ADJ
fumecheng-12619	301	28	surface	surface	NOUN
fumecheng-12619	301	29	piezoelectricity	piezoelectricity	NOUN
fumecheng-12619	301	30	constants	constant	NOUN
fumecheng-12619	301	31	𝑒31𝑝	𝑒31𝑝	NOUN
fumecheng-12619	301	32	𝑠𝑘	𝑠𝑘	NOUN
fumecheng-12619	301	33	and	and	CCONJ
fumecheng-12619	301	34	𝑒32𝑝	𝑒32𝑝	ADP
fumecheng-12619	301	35	𝑠𝑘	𝑠𝑘	NOUN
fumecheng-12619	301	36	,	,	PUNCT
fumecheng-12619	301	37	results	result	NOUN
fumecheng-12619	301	38	in	in	ADP
fumecheng-12619	301	39	an	an	DET
fumecheng-12619	301	40	augmentation	augmentation	NOUN
fumecheng-12619	301	41	of	of	ADP
fumecheng-12619	301	42	the	the	DET
fumecheng-12619	301	43	piezoelectric	piezoelectric	ADJ
fumecheng-12619	301	44	nanosensor	nanosensor	NOUN
fumecheng-12619	301	45	(	(	PUNCT
fumecheng-12619	301	46	pens	pen	NOUN
fumecheng-12619	301	47	)	)	PUNCT
fumecheng-12619	301	48	comparison	comparison	NOUN
fumecheng-12619	301	49	of	of	ADP
fumecheng-12619	301	50	nonclassical	nonclassical	ADJ
fumecheng-12619	301	51	controllers	controller	NOUN
fumecheng-12619	301	52	on	on	ADP
fumecheng-12619	301	53	nonlinear	nonlinear	ADJ
fumecheng-12619	301	54	vibrations	vibration	NOUN
fumecheng-12619	301	55	analysis	analysis	NOUN
fumecheng-12619	301	56	of	of	ADP
fumecheng-12619	301	57	piezoelectric	piezoelectric	NOUN
fumecheng-12619	301	58	...	...	PUNCT
fumecheng-12619	301	59	333	333	NUM
fumecheng-12619	301	60	stiffness	stiffness	NOUN
fumecheng-12619	301	61	.	.	PUNCT
fumecheng-12619	302	1	consequently	consequently	ADV
fumecheng-12619	302	2	,	,	PUNCT
fumecheng-12619	302	3	this	this	DET
fumecheng-12619	302	4	stiffness	stiffness	NOUN
fumecheng-12619	302	5	increase	increase	NOUN
fumecheng-12619	302	6	leads	lead	VERB
fumecheng-12619	302	7	to	to	ADP
fumecheng-12619	302	8	a	a	DET
fumecheng-12619	302	9	higher	high	ADJ
fumecheng-12619	302	10	pull	pull	NOUN
fumecheng-12619	302	11	-	-	PUNCT
fumecheng-12619	302	12	in	in	ADP
fumecheng-12619	302	13	voltage	voltage	NOUN
fumecheng-12619	302	14	in	in	ADP
fumecheng-12619	302	15	both	both	CCONJ
fumecheng-12619	302	16	the	the	DET
fumecheng-12619	302	17	dimensionless	dimensionless	ADJ
fumecheng-12619	302	18	natural	natural	ADJ
fumecheng-12619	302	19	frequency	frequency	NOUN
fumecheng-12619	302	20	(	(	PUNCT
fumecheng-12619	302	21	dnf	dnf	X
fumecheng-12619	302	22	)	)	PUNCT
fumecheng-12619	302	23	and	and	CCONJ
fumecheng-12619	302	24	nonlinear	nonlinear	ADJ
fumecheng-12619	302	25	dynamic	dynamic	ADJ
fumecheng-12619	302	26	response	response	NOUN
fumecheng-12619	302	27	(	(	PUNCT
fumecheng-12619	302	28	ndr	ndr	PROPN
fumecheng-12619	302	29	)	)	PUNCT
fumecheng-12619	302	30	analyses	analysis	NOUN
fumecheng-12619	302	31	.	.	PUNCT
fumecheng-12619	303	1	▪	▪	NOUN
fumecheng-12619	303	2	an	an	DET
fumecheng-12619	303	3	increase	increase	NOUN
fumecheng-12619	303	4	in	in	ADP
fumecheng-12619	303	5	surface	surface	NOUN
fumecheng-12619	303	6	/	/	SYM
fumecheng-12619	303	7	interface	interface	NOUN
fumecheng-12619	303	8	mass	mass	NOUN
fumecheng-12619	303	9	density	density	NOUN
fumecheng-12619	303	10	𝜌𝐼,𝑆	𝜌𝐼,𝑆	NOUN
fumecheng-12619	303	11	leads	lead	VERB
fumecheng-12619	303	12	to	to	ADP
fumecheng-12619	303	13	a	a	DET
fumecheng-12619	303	14	reduction	reduction	NOUN
fumecheng-12619	303	15	in	in	ADP
fumecheng-12619	303	16	the	the	DET
fumecheng-12619	303	17	piezoelectric	piezoelectric	ADJ
fumecheng-12619	303	18	nanosensor	nanosensor	NOUN
fumecheng-12619	303	19	(	(	PUNCT
fumecheng-12619	303	20	pens	pen	NOUN
fumecheng-12619	303	21	)	)	PUNCT
fumecheng-12619	303	22	stiffness	stiffness	NOUN
fumecheng-12619	303	23	,	,	PUNCT
fumecheng-12619	303	24	resulting	result	VERB
fumecheng-12619	303	25	in	in	ADP
fumecheng-12619	303	26	a	a	DET
fumecheng-12619	303	27	significant	significant	ADJ
fumecheng-12619	303	28	decrease	decrease	NOUN
fumecheng-12619	303	29	in	in	ADP
fumecheng-12619	303	30	the	the	DET
fumecheng-12619	303	31	dimensionless	dimensionless	ADJ
fumecheng-12619	303	32	natural	natural	ADJ
fumecheng-12619	303	33	frequency	frequency	NOUN
fumecheng-12619	303	34	(	(	PUNCT
fumecheng-12619	303	35	dnf	dnf	PROPN
fumecheng-12619	303	36	)	)	PUNCT
fumecheng-12619	303	37	.	.	PUNCT
fumecheng-12619	304	1	however	however	ADV
fumecheng-12619	304	2	,	,	PUNCT
fumecheng-12619	304	3	this	this	DET
fumecheng-12619	304	4	increase	increase	NOUN
fumecheng-12619	304	5	in	in	ADP
fumecheng-12619	304	6	mass	mass	ADJ
fumecheng-12619	304	7	density	density	NOUN
fumecheng-12619	304	8	does	do	AUX
fumecheng-12619	304	9	not	not	PART
fumecheng-12619	304	10	significantly	significantly	ADV
fumecheng-12619	304	11	impact	impact	VERB
fumecheng-12619	304	12	the	the	DET
fumecheng-12619	304	13	pull	pull	NOUN
fumecheng-12619	304	14	-	-	PUNCT
fumecheng-12619	304	15	in	in	ADP
fumecheng-12619	304	16	voltage	voltage	NOUN
fumecheng-12619	304	17	or	or	CCONJ
fumecheng-12619	304	18	the	the	DET
fumecheng-12619	304	19	nonlinear	nonlinear	ADJ
fumecheng-12619	304	20	dynamic	dynamic	ADJ
fumecheng-12619	304	21	response	response	NOUN
fumecheng-12619	304	22	(	(	PUNCT
fumecheng-12619	304	23	ndr	ndr	PROPN
fumecheng-12619	304	24	)	)	PUNCT
fumecheng-12619	304	25	.	.	PUNCT
fumecheng-12619	304	26	▪	▪	NOUN
fumecheng-12619	304	27	in	in	ADP
fumecheng-12619	304	28	the	the	DET
fumecheng-12619	304	29	dimensionless	dimensionless	ADJ
fumecheng-12619	304	30	natural	natural	ADJ
fumecheng-12619	304	31	frequency	frequency	NOUN
fumecheng-12619	304	32	(	(	PUNCT
fumecheng-12619	304	33	dnf	dnf	ADJ
fumecheng-12619	304	34	)	)	PUNCT
fumecheng-12619	304	35	analysis	analysis	NOUN
fumecheng-12619	304	36	,	,	PUNCT
fumecheng-12619	304	37	when	when	SCONJ
fumecheng-12619	304	38	surface	surface	NOUN
fumecheng-12619	304	39	/	/	SYM
fumecheng-12619	304	40	interface	interface	NOUN
fumecheng-12619	304	41	density	density	NOUN
fumecheng-12619	304	42	𝜌𝐼,𝑆	𝜌𝐼,𝑆	PROPN
fumecheng-12619	304	43	and	and	CCONJ
fumecheng-12619	304	44	surface	surface	NOUN
fumecheng-12619	304	45	piezoelectric	piezoelectric	NOUN
fumecheng-12619	304	46	constants	constant	NOUN
fumecheng-12619	304	47	(	(	PUNCT
fumecheng-12619	304	48	𝑒31𝑝	𝑒31𝑝	NOUN
fumecheng-12619	304	49	𝑠𝑘	𝑠𝑘	NOUN
fumecheng-12619	304	50	,	,	PUNCT
fumecheng-12619	304	51	𝑒32𝑝	𝑒32𝑝	ADP
fumecheng-12619	304	52	𝑠𝑘	𝑠𝑘	NOUN
fumecheng-12619	304	53	)	)	PUNCT
fumecheng-12619	304	54	are	be	AUX
fumecheng-12619	304	55	disregarded	disregard	VERB
fumecheng-12619	304	56	,	,	PUNCT
fumecheng-12619	304	57	the	the	DET
fumecheng-12619	304	58	simply	simply	ADV
fumecheng-12619	304	59	supported	support	VERB
fumecheng-12619	304	60	(	(	PUNCT
fumecheng-12619	304	61	ss	ss	NOUN
fumecheng-12619	304	62	)	)	PUNCT
fumecheng-12619	304	63	piezoelectric	piezoelectric	NOUN
fumecheng-12619	304	64	nanosensor	nanosensor	NOUN
fumecheng-12619	304	65	(	(	PUNCT
fumecheng-12619	304	66	pens	pen	NOUN
fumecheng-12619	304	67	)	)	PUNCT
fumecheng-12619	304	68	exhibits	exhibit	VERB
fumecheng-12619	304	69	the	the	DET
fumecheng-12619	304	70	maximum	maximum	ADJ
fumecheng-12619	304	71	pull	pull	VERB
fumecheng-12619	304	72	-	-	PUNCT
fumecheng-12619	304	73	in	in	ADP
fumecheng-12619	304	74	voltage	voltage	NOUN
fumecheng-12619	304	75	across	across	ADP
fumecheng-12619	304	76	all	all	DET
fumecheng-12619	304	77	surface	surface	NOUN
fumecheng-12619	304	78	/	/	SYM
fumecheng-12619	304	79	interface	interface	NOUN
fumecheng-12619	304	80	(	(	PUNCT
fumecheng-12619	304	81	s	s	NOUN
fumecheng-12619	304	82	/	/	SYM
fumecheng-12619	304	83	i	i	NOUN
fumecheng-12619	304	84	)	)	PUNCT
fumecheng-12619	304	85	configurations	configuration	NOUN
fumecheng-12619	304	86	.	.	PUNCT
fumecheng-12619	305	1	however	however	ADV
fumecheng-12619	305	2	,	,	PUNCT
fumecheng-12619	305	3	in	in	ADP
fumecheng-12619	305	4	the	the	DET
fumecheng-12619	305	5	nonlinear	nonlinear	ADJ
fumecheng-12619	305	6	dynamic	dynamic	ADJ
fumecheng-12619	305	7	response	response	NOUN
fumecheng-12619	305	8	(	(	PUNCT
fumecheng-12619	305	9	ndr	ndr	PROPN
fumecheng-12619	305	10	)	)	PUNCT
fumecheng-12619	305	11	analysis	analysis	NOUN
fumecheng-12619	305	12	of	of	ADP
fumecheng-12619	305	13	the	the	DET
fumecheng-12619	305	14	ss	ss	NOUN
fumecheng-12619	305	15	pens	pen	NOUN
fumecheng-12619	305	16	,	,	PUNCT
fumecheng-12619	305	17	the	the	DET
fumecheng-12619	305	18	maximum	maximum	ADJ
fumecheng-12619	305	19	pull	pull	VERB
fumecheng-12619	305	20	-	-	PUNCT
fumecheng-12619	305	21	in	in	ADP
fumecheng-12619	305	22	voltage	voltage	NOUN
fumecheng-12619	305	23	is	be	AUX
fumecheng-12619	305	24	observed	observe	VERB
fumecheng-12619	305	25	in	in	ADP
fumecheng-12619	305	26	the	the	DET
fumecheng-12619	305	27	absence	absence	NOUN
fumecheng-12619	305	28	of	of	ADP
fumecheng-12619	305	29	all	all	DET
fumecheng-12619	305	30	surface	surface	NOUN
fumecheng-12619	305	31	/	/	SYM
fumecheng-12619	305	32	interface	interface	NOUN
fumecheng-12619	305	33	effects	effect	NOUN
fumecheng-12619	305	34	.	.	PUNCT
fumecheng-12619	306	1	▪	▪	NOUN
fumecheng-12619	306	2	in	in	ADP
fumecheng-12619	306	3	the	the	DET
fumecheng-12619	306	4	nonlinear	nonlinear	ADJ
fumecheng-12619	306	5	dynamic	dynamic	ADJ
fumecheng-12619	306	6	response	response	NOUN
fumecheng-12619	306	7	(	(	PUNCT
fumecheng-12619	306	8	ndr	ndr	PROPN
fumecheng-12619	306	9	)	)	PUNCT
fumecheng-12619	306	10	analysis	analysis	NOUN
fumecheng-12619	306	11	,	,	PUNCT
fumecheng-12619	306	12	variations	variation	NOUN
fumecheng-12619	306	13	in	in	ADP
fumecheng-12619	306	14	surface	surface	NOUN
fumecheng-12619	306	15	/	/	SYM
fumecheng-12619	306	16	interface	interface	NOUN
fumecheng-12619	306	17	parameters	parameter	NOUN
fumecheng-12619	306	18	lead	lead	VERB
fumecheng-12619	306	19	to	to	ADP
fumecheng-12619	306	20	the	the	DET
fumecheng-12619	306	21	system	system	NOUN
fumecheng-12619	306	22	exhibiting	exhibit	VERB
fumecheng-12619	306	23	either	either	CCONJ
fumecheng-12619	306	24	stable	stable	ADJ
fumecheng-12619	306	25	or	or	CCONJ
fumecheng-12619	306	26	unstable	unstable	ADJ
fumecheng-12619	306	27	equilibrium	equilibrium	NOUN
fumecheng-12619	306	28	points	point	NOUN
fumecheng-12619	306	29	,	,	PUNCT
fumecheng-12619	306	30	with	with	ADP
fumecheng-12619	306	31	transitions	transition	NOUN
fumecheng-12619	306	32	occurring	occur	VERB
fumecheng-12619	306	33	through	through	ADP
fumecheng-12619	306	34	saddle	saddle	NOUN
fumecheng-12619	306	35	-	-	PUNCT
fumecheng-12619	306	36	node	node	NOUN
fumecheng-12619	306	37	bifurcations	bifurcation	NOUN
fumecheng-12619	306	38	.	.	PUNCT
fumecheng-12619	307	1	references	reference	NOUN
fumecheng-12619	307	2	1	1	NUM
fumecheng-12619	307	3	.	.	PUNCT
fumecheng-12619	307	4	marinković	marinković	ADJ
fumecheng-12619	307	5	,	,	PUNCT
fumecheng-12619	307	6	d.	d.	PROPN
fumecheng-12619	307	7	,	,	PUNCT
fumecheng-12619	307	8	köppe	köppe	PROPN
fumecheng-12619	307	9	,	,	PUNCT
fumecheng-12619	307	10	h.	h.	PROPN
fumecheng-12619	307	11	,	,	PUNCT
fumecheng-12619	307	12	gabbert	gabbert	PROPN
fumecheng-12619	307	13	,	,	PUNCT
fumecheng-12619	307	14	u.	u.	PROPN
fumecheng-12619	307	15	,	,	PUNCT
fumecheng-12619	307	16	2008	2008	NUM
fumecheng-12619	307	17	,	,	PUNCT
fumecheng-12619	307	18	degenerated	degenerate	VERB
fumecheng-12619	307	19	shell	shell	ADJ
fumecheng-12619	307	20	element	element	NOUN
fumecheng-12619	307	21	for	for	ADP
fumecheng-12619	307	22	geometrically	geometrically	ADV
fumecheng-12619	307	23	nonlinear	nonlinear	ADJ
fumecheng-12619	307	24	analysis	analysis	NOUN
fumecheng-12619	307	25	of	of	ADP
fumecheng-12619	307	26	thin	thin	ADJ
fumecheng-12619	307	27	-	-	PUNCT
fumecheng-12619	307	28	walled	walled	ADJ
fumecheng-12619	307	29	piezoelectric	piezoelectric	ADJ
fumecheng-12619	307	30	active	active	ADJ
fumecheng-12619	307	31	structures	structure	NOUN
fumecheng-12619	307	32	,	,	PUNCT
fumecheng-12619	307	33	smart	smart	ADJ
fumecheng-12619	307	34	materials	material	NOUN
fumecheng-12619	307	35	and	and	CCONJ
fumecheng-12619	307	36	structures	structure	NOUN
fumecheng-12619	307	37	,	,	PUNCT
fumecheng-12619	307	38	17(1	17(1	NUM
fumecheng-12619	307	39	)	)	PUNCT
fumecheng-12619	307	40	,	,	PUNCT
fumecheng-12619	307	41	015030	015030	NUM
fumecheng-12619	307	42	.	.	PUNCT
fumecheng-12619	308	1	2	2	X
fumecheng-12619	308	2	.	.	X
fumecheng-12619	308	3	nestorović	nestorović	NOUN
fumecheng-12619	308	4	,	,	PUNCT
fumecheng-12619	308	5	t.	t.	PROPN
fumecheng-12619	308	6	,	,	PUNCT
fumecheng-12619	308	7	marinković	marinković	PROPN
fumecheng-12619	308	8	,	,	PUNCT
fumecheng-12619	308	9	d.	d.	PROPN
fumecheng-12619	308	10	,	,	PUNCT
fumecheng-12619	308	11	shabadi	shabadi	NOUN
fumecheng-12619	308	12	,	,	PUNCT
fumecheng-12619	308	13	s.	s.	PROPN
fumecheng-12619	308	14	,	,	PUNCT
fumecheng-12619	308	15	trajkov	trajkov	PROPN
fumecheng-12619	308	16	,	,	PUNCT
fumecheng-12619	308	17	m.	m.	NOUN
fumecheng-12619	308	18	,	,	PUNCT
fumecheng-12619	308	19	2014	2014	NUM
fumecheng-12619	308	20	,	,	PUNCT
fumecheng-12619	308	21	user	user	NOUN
fumecheng-12619	308	22	defined	define	VERB
fumecheng-12619	308	23	finite	finite	ADJ
fumecheng-12619	308	24	element	element	NOUN
fumecheng-12619	308	25	for	for	ADP
fumecheng-12619	308	26	modeling	modeling	NOUN
fumecheng-12619	308	27	and	and	CCONJ
fumecheng-12619	308	28	analysis	analysis	NOUN
fumecheng-12619	308	29	of	of	ADP
fumecheng-12619	308	30	active	active	ADJ
fumecheng-12619	308	31	piezoelectric	piezoelectric	ADJ
fumecheng-12619	308	32	shell	shell	NOUN
fumecheng-12619	308	33	structures	structure	NOUN
fumecheng-12619	308	34	,	,	PUNCT
fumecheng-12619	308	35	meccanica	meccanica	PROPN
fumecheng-12619	308	36	,	,	PUNCT
fumecheng-12619	308	37	49(8	49(8	PROPN
fumecheng-12619	308	38	)	)	PUNCT
fumecheng-12619	308	39	,	,	PUNCT
fumecheng-12619	308	40	pp	pp	ADP
fumecheng-12619	308	41	.	.	PUNCT
fumecheng-12619	309	1	1763	1763	NUM
fumecheng-12619	309	2	-	-	SYM
fumecheng-12619	309	3	1774	1774	NUM
fumecheng-12619	309	4	.	.	PUNCT
fumecheng-12619	310	1	3	3	X
fumecheng-12619	310	2	.	.	X
fumecheng-12619	311	1	chen	chen	PROPN
fumecheng-12619	311	2	,	,	PUNCT
fumecheng-12619	311	3	q.	q.	PROPN
fumecheng-12619	311	4	,	,	PUNCT
fumecheng-12619	311	5	chatzigeorgiou	chatzigeorgiou	NOUN
fumecheng-12619	311	6	,	,	PUNCT
fumecheng-12619	311	7	g.	g.	PROPN
fumecheng-12619	311	8	,	,	PUNCT
fumecheng-12619	311	9	meraghni	meraghni	PROPN
fumecheng-12619	311	10	.	.	PUNCT
fumecheng-12619	312	1	f.	f.	PROPN
fumecheng-12619	312	2	,	,	PUNCT
fumecheng-12619	312	3	javili	javili	PROPN
fumecheng-12619	312	4	.	.	PUNCT
fumecheng-12619	313	1	a.	a.	PROPN
fumecheng-12619	313	2	,	,	PUNCT
fumecheng-12619	313	3	2022	2022	NUM
fumecheng-12619	313	4	,	,	PUNCT
fumecheng-12619	313	5	homogenization	homogenization	NOUN
fumecheng-12619	313	6	of	of	ADP
fumecheng-12619	313	7	size	size	NOUN
fumecheng-12619	313	8	-	-	PUNCT
fumecheng-12619	313	9	dependent	dependent	ADJ
fumecheng-12619	313	10	multiphysics	multiphysic	NOUN
fumecheng-12619	313	11	behavior	behavior	NOUN
fumecheng-12619	313	12	of	of	ADP
fumecheng-12619	313	13	nanostructured	nanostructure	VERB
fumecheng-12619	313	14	piezoelectric	piezoelectric	ADJ
fumecheng-12619	313	15	composites	composite	NOUN
fumecheng-12619	313	16	with	with	ADP
fumecheng-12619	313	17	energetic	energetic	ADJ
fumecheng-12619	313	18	surfaces	surface	NOUN
fumecheng-12619	313	19	,	,	PUNCT
fumecheng-12619	313	20	european	european	ADJ
fumecheng-12619	313	21	journal	journal	PROPN
fumecheng-12619	313	22	of	of	ADP
fumecheng-12619	313	23	mechanics	mechanic	NOUN
fumecheng-12619	313	24	a	a	DET
fumecheng-12619	313	25	/	/	SYM
fumecheng-12619	313	26	solids	solid	NOUN
fumecheng-12619	313	27	,	,	PUNCT
fumecheng-12619	313	28	96	96	NUM
fumecheng-12619	313	29	,	,	PUNCT
fumecheng-12619	313	30	104731	104731	NUM
fumecheng-12619	313	31	.	.	PUNCT
fumecheng-12619	314	1	4	4	X
fumecheng-12619	314	2	.	.	X
fumecheng-12619	314	3	madunuri	madunuri	PROPN
fumecheng-12619	314	4	,	,	PUNCT
fumecheng-12619	314	5	c.	c.	PROPN
fumecheng-12619	314	6	s.	s.	PROPN
fumecheng-12619	314	7	,	,	PUNCT
fumecheng-12619	314	8	veena	veena	PROPN
fumecheng-12619	314	9	,	,	PUNCT
fumecheng-12619	314	10	e.	e.	PROPN
fumecheng-12619	314	11	,	,	PUNCT
fumecheng-12619	314	12	nagasamudram	nagasamudram	PROPN
fumecheng-12619	314	13	,	,	PUNCT
fumecheng-12619	314	14	s.	s.	PROPN
fumecheng-12619	314	15	k.	k.	PROPN
fumecheng-12619	314	16	,	,	PUNCT
fumecheng-12619	314	17	kadiyala	kadiyala	PROPN
fumecheng-12619	314	18	,	,	PUNCT
fumecheng-12619	314	19	c.	c.	PROPN
fumecheng-12619	314	20	b.	b.	PROPN
fumecheng-12619	314	21	n.	n.	PROPN
fumecheng-12619	314	22	,	,	PUNCT
fumecheng-12619	314	23	mallikarjuna	mallikarjuna	PROPN
fumecheng-12619	314	24	,	,	PUNCT
fumecheng-12619	314	25	a.	a.	PROPN
fumecheng-12619	314	26	,	,	PUNCT
fumecheng-12619	314	27	basha	basha	PROPN
fumecheng-12619	314	28	,	,	PUNCT
fumecheng-12619	314	29	b.	b.	PROPN
fumecheng-12619	314	30	,	,	PUNCT
fumecheng-12619	314	31	2022	2022	NUM
fumecheng-12619	314	32	,	,	PUNCT
fumecheng-12619	314	33	a	a	DET
fumecheng-12619	314	34	review	review	NOUN
fumecheng-12619	314	35	on	on	ADP
fumecheng-12619	314	36	piezoelectric	piezoelectric	ADJ
fumecheng-12619	314	37	materials	material	NOUN
fumecheng-12619	314	38	and	and	CCONJ
fumecheng-12619	314	39	their	their	PRON
fumecheng-12619	314	40	applications	application	NOUN
fumecheng-12619	314	41	,	,	PUNCT
fumecheng-12619	314	42	crystal	crystal	NOUN
fumecheng-12619	314	43	research	research	NOUN
fumecheng-12619	314	44	and	and	CCONJ
fumecheng-12619	314	45	technology	technology	NOUN
fumecheng-12619	314	46	,	,	PUNCT
fumecheng-12619	314	47	58(2	58(2	NUM
fumecheng-12619	314	48	)	)	PUNCT
fumecheng-12619	314	49	,	,	PUNCT
fumecheng-12619	314	50	2200130	2200130	NUM
fumecheng-12619	314	51	.	.	PUNCT
fumecheng-12619	315	1	5	5	NUM
fumecheng-12619	315	2	.	.	X
fumecheng-12619	315	3	milić	milić	NOUN
fumecheng-12619	315	4	,	,	PUNCT
fumecheng-12619	315	5	p.	p.	NOUN
fumecheng-12619	315	6	,	,	PUNCT
fumecheng-12619	315	7	marinković	marinković	PROPN
fumecheng-12619	315	8	,	,	PUNCT
fumecheng-12619	315	9	d.	d.	PROPN
fumecheng-12619	315	10	,	,	PUNCT
fumecheng-12619	315	11	klinge	klinge	PROPN
fumecheng-12619	315	12	,	,	PUNCT
fumecheng-12619	315	13	s.	s.	PROPN
fumecheng-12619	315	14	,	,	PUNCT
fumecheng-12619	315	15	ćojbašić	ćojbašić	PROPN
fumecheng-12619	315	16	,	,	PUNCT
fumecheng-12619	315	17	ž	ž	PROPN
fumecheng-12619	315	18	.	.	PROPN
fumecheng-12619	315	19	,	,	PUNCT
fumecheng-12619	315	20	2023	2023	NUM
fumecheng-12619	315	21	,	,	PUNCT
fumecheng-12619	315	22	reissner	reissner	NOUN
fumecheng-12619	315	23	-	-	PUNCT
fumecheng-12619	315	24	mindlin	mindlin	NOUN
fumecheng-12619	315	25	based	base	VERB
fumecheng-12619	315	26	isogeometric	isogeometric	ADJ
fumecheng-12619	315	27	finite	finite	PROPN
fumecheng-12619	315	28	element	element	NOUN
fumecheng-12619	315	29	formulation	formulation	NOUN
fumecheng-12619	315	30	for	for	ADP
fumecheng-12619	315	31	piezoelectric	piezoelectric	ADJ
fumecheng-12619	315	32	active	active	ADJ
fumecheng-12619	315	33	laminated	laminated	ADJ
fumecheng-12619	315	34	shells	shell	NOUN
fumecheng-12619	315	35	,	,	PUNCT
fumecheng-12619	315	36	tehnicki	tehnicki	NOUN
fumecheng-12619	315	37	vjesnik	vjesnik	PROPN
fumecheng-12619	315	38	,	,	PUNCT
fumecheng-12619	315	39	30(2	30(2	NUM
fumecheng-12619	315	40	)	)	PUNCT
fumecheng-12619	315	41	,	,	PUNCT
fumecheng-12619	315	42	pp	pp	PROPN
fumecheng-12619	315	43	.	.	PUNCT
fumecheng-12619	316	1	416	416	NUM
fumecheng-12619	316	2	-	-	SYM
fumecheng-12619	316	3	425	425	NUM
fumecheng-12619	316	4	.	.	NOUN
fumecheng-12619	317	1	6	6	NUM
fumecheng-12619	317	2	.	.	X
fumecheng-12619	317	3	rama	rama	PROPN
fumecheng-12619	317	4	,	,	PUNCT
fumecheng-12619	317	5	g.	g.	PROPN
fumecheng-12619	317	6	,	,	PUNCT
fumecheng-12619	317	7	marinković	marinković	PROPN
fumecheng-12619	317	8	,	,	PUNCT
fumecheng-12619	317	9	d.	d.	PROPN
fumecheng-12619	317	10	,	,	PUNCT
fumecheng-12619	317	11	zehn	zehn	PROPN
fumecheng-12619	317	12	,	,	PUNCT
fumecheng-12619	317	13	m.	m.	NOUN
fumecheng-12619	317	14	,	,	PUNCT
fumecheng-12619	317	15	2018	2018	NUM
fumecheng-12619	317	16	,	,	PUNCT
fumecheng-12619	317	17	efficient	efficient	ADJ
fumecheng-12619	317	18	three	three	NUM
fumecheng-12619	317	19	-	-	PUNCT
fumecheng-12619	317	20	node	node	ADJ
fumecheng-12619	317	21	finite	finite	PROPN
fumecheng-12619	317	22	shell	shell	NOUN
fumecheng-12619	317	23	element	element	NOUN
fumecheng-12619	317	24	for	for	ADP
fumecheng-12619	317	25	linear	linear	PROPN
fumecheng-12619	317	26	and	and	CCONJ
fumecheng-12619	317	27	geometrically	geometrically	ADV
fumecheng-12619	317	28	nonlinear	nonlinear	ADJ
fumecheng-12619	317	29	analyses	analysis	NOUN
fumecheng-12619	317	30	of	of	ADP
fumecheng-12619	317	31	piezoelectric	piezoelectric	ADJ
fumecheng-12619	317	32	laminated	laminate	VERB
fumecheng-12619	317	33	structures	structure	NOUN
fumecheng-12619	317	34	,	,	PUNCT
fumecheng-12619	317	35	journal	journal	NOUN
fumecheng-12619	317	36	of	of	ADP
fumecheng-12619	317	37	intelligent	intelligent	ADJ
fumecheng-12619	317	38	material	material	NOUN
fumecheng-12619	317	39	systems	system	NOUN
fumecheng-12619	317	40	and	and	CCONJ
fumecheng-12619	317	41	structures	structure	NOUN
fumecheng-12619	317	42	,	,	PUNCT
fumecheng-12619	317	43	29(3	29(3	NUM
fumecheng-12619	317	44	)	)	PUNCT
fumecheng-12619	317	45	,	,	PUNCT
fumecheng-12619	317	46	pp	pp	ADJ
fumecheng-12619	317	47	.	.	PUNCT
fumecheng-12619	318	1	345	345	NUM
fumecheng-12619	318	2	-	-	SYM
fumecheng-12619	318	3	357	357	NUM
fumecheng-12619	318	4	.	.	PUNCT
fumecheng-12619	319	1	7	7	NUM
fumecheng-12619	319	2	.	.	X
fumecheng-12619	319	3	eringen	eringen	PROPN
fumecheng-12619	319	4	,	,	PUNCT
fumecheng-12619	319	5	a.c	a.c	PROPN
fumecheng-12619	319	6	.	.	PROPN
fumecheng-12619	319	7	,	,	PUNCT
fumecheng-12619	319	8	2002	2002	NUM
fumecheng-12619	319	9	,	,	PUNCT
fumecheng-12619	319	10	nonlocal	nonlocal	ADJ
fumecheng-12619	319	11	continuum	continuum	ADJ
fumecheng-12619	319	12	field	field	NOUN
fumecheng-12619	319	13	theories	theory	NOUN
fumecheng-12619	319	14	,	,	PUNCT
fumecheng-12619	319	15	springer	springer	NOUN
fumecheng-12619	319	16	,	,	PUNCT
fumecheng-12619	319	17	new	new	PROPN
fumecheng-12619	319	18	york	york	PROPN
fumecheng-12619	319	19	,	,	PUNCT
fumecheng-12619	319	20	ny	ny	PROPN
fumecheng-12619	319	21	,	,	PUNCT
fumecheng-12619	319	22	usa	usa	PROPN
fumecheng-12619	319	23	.	.	PROPN
fumecheng-12619	319	24	8	8	NUM
fumecheng-12619	319	25	.	.	PUNCT
fumecheng-12619	320	1	lim	lim	PROPN
fumecheng-12619	320	2	,	,	PUNCT
fumecheng-12619	320	3	c.	c.	PROPN
fumecheng-12619	320	4	w.	w.	PROPN
fumecheng-12619	320	5	,	,	PUNCT
fumecheng-12619	320	6	zhang	zhang	PROPN
fumecheng-12619	320	7	,	,	PUNCT
fumecheng-12619	320	8	g.	g.	PROPN
fumecheng-12619	320	9	,	,	PUNCT
fumecheng-12619	320	10	reddy	reddy	PROPN
fumecheng-12619	320	11	,	,	PUNCT
fumecheng-12619	320	12	j.	j.	PROPN
fumecheng-12619	320	13	n.	n.	PROPN
fumecheng-12619	320	14	,	,	PUNCT
fumecheng-12619	320	15	2015	2015	NUM
fumecheng-12619	320	16	,	,	PUNCT
fumecheng-12619	320	17	a	a	DET
fumecheng-12619	320	18	higher	high	ADJ
fumecheng-12619	320	19	-	-	PUNCT
fumecheng-12619	320	20	order	order	NOUN
fumecheng-12619	320	21	nonlocal	nonlocal	ADJ
fumecheng-12619	320	22	elasticity	elasticity	NOUN
fumecheng-12619	320	23	and	and	CCONJ
fumecheng-12619	320	24	strain	strain	VERB
fumecheng-12619	320	25	gradient	gradient	NOUN
fumecheng-12619	320	26	theory	theory	NOUN
fumecheng-12619	320	27	and	and	CCONJ
fumecheng-12619	320	28	its	its	PRON
fumecheng-12619	320	29	applications	application	NOUN
fumecheng-12619	320	30	in	in	ADP
fumecheng-12619	320	31	wave	wave	NOUN
fumecheng-12619	320	32	propagation	propagation	NOUN
fumecheng-12619	320	33	,	,	PUNCT
fumecheng-12619	320	34	journal	journal	NOUN
fumecheng-12619	320	35	of	of	ADP
fumecheng-12619	320	36	the	the	DET
fumecheng-12619	320	37	mechanics	mechanic	NOUN
fumecheng-12619	320	38	and	and	CCONJ
fumecheng-12619	320	39	physics	physic	NOUN
fumecheng-12619	320	40	of	of	ADP
fumecheng-12619	320	41	solids	solid	NOUN
fumecheng-12619	320	42	,	,	PUNCT
fumecheng-12619	320	43	78	78	NUM
fumecheng-12619	320	44	,	,	PUNCT
fumecheng-12619	320	45	pp	pp	ADJ
fumecheng-12619	320	46	.	.	PUNCT
fumecheng-12619	321	1	298	298	NUM
fumecheng-12619	321	2	-	-	SYM
fumecheng-12619	321	3	313	313	NUM
fumecheng-12619	321	4	.	.	NOUN
fumecheng-12619	322	1	9	9	NUM
fumecheng-12619	322	2	.	.	X
fumecheng-12619	323	1	gurtin	gurtin	PROPN
fumecheng-12619	323	2	,	,	PUNCT
fumecheng-12619	323	3	m.e	m.e	PROPN
fumecheng-12619	323	4	.	.	PROPN
fumecheng-12619	323	5	,	,	PUNCT
fumecheng-12619	323	6	murdoch	murdoch	PROPN
fumecheng-12619	323	7	,	,	PUNCT
fumecheng-12619	323	8	a.i	a.i	PROPN
fumecheng-12619	323	9	.	.	PROPN
fumecheng-12619	323	10	,	,	PUNCT
fumecheng-12619	323	11	1978	1978	NUM
fumecheng-12619	323	12	,	,	PUNCT
fumecheng-12619	323	13	surface	surface	NOUN
fumecheng-12619	323	14	stress	stress	NOUN
fumecheng-12619	323	15	in	in	ADP
fumecheng-12619	323	16	solids	solid	NOUN
fumecheng-12619	323	17	,	,	PUNCT
fumecheng-12619	323	18	international	international	ADJ
fumecheng-12619	323	19	journal	journal	NOUN
fumecheng-12619	323	20	of	of	ADP
fumecheng-12619	323	21	solids	solid	NOUN
fumecheng-12619	323	22	and	and	CCONJ
fumecheng-12619	323	23	structures	structure	NOUN
fumecheng-12619	323	24	,	,	PUNCT
fumecheng-12619	323	25	14(6	14(6	NOUN
fumecheng-12619	323	26	)	)	PUNCT
fumecheng-12619	323	27	,	,	PUNCT
fumecheng-12619	323	28	pp	pp	ADP
fumecheng-12619	323	29	.	.	PUNCT
fumecheng-12619	324	1	431	431	NUM
fumecheng-12619	324	2	-	-	SYM
fumecheng-12619	324	3	40	40	NUM
fumecheng-12619	324	4	.	.	PUNCT
fumecheng-12619	325	1	10	10	NUM
fumecheng-12619	325	2	.	.	PUNCT
fumecheng-12619	326	1	feng	feng	PROPN
fumecheng-12619	326	2	,	,	PUNCT
fumecheng-12619	326	3	j.	j.	PROPN
fumecheng-12619	326	4	,	,	PUNCT
fumecheng-12619	326	5	yu	yu	PROPN
fumecheng-12619	326	6	,	,	PUNCT
fumecheng-12619	326	7	h.	h.	PROPN
fumecheng-12619	326	8	,	,	PUNCT
fumecheng-12619	326	9	ma	ma	PROPN
fumecheng-12619	326	10	,	,	PUNCT
fumecheng-12619	326	11	s.	s.	PROPN
fumecheng-12619	326	12	,	,	PUNCT
fumecheng-12619	326	13	hao	hao	PROPN
fumecheng-12619	326	14	,	,	PUNCT
fumecheng-12619	326	15	s.	s.	PROPN
fumecheng-12619	326	16	,	,	PUNCT
fumecheng-12619	326	17	wu	wu	PROPN
fumecheng-12619	326	18	,	,	PUNCT
fumecheng-12619	326	19	r.	r.	PROPN
fumecheng-12619	326	20	,	,	PUNCT
fumecheng-12619	326	21	2022	2022	NUM
fumecheng-12619	326	22	,	,	PUNCT
fumecheng-12619	326	23	axial	axial	ADJ
fumecheng-12619	326	24	vibration	vibration	NOUN
fumecheng-12619	326	25	characteristics	characteristic	NOUN
fumecheng-12619	326	26	of	of	ADP
fumecheng-12619	326	27	carbon	carbon	NOUN
fumecheng-12619	326	28	nanotube	nanotube	NOUN
fumecheng-12619	326	29	-	-	PUNCT
fumecheng-12619	326	30	based	base	VERB
fumecheng-12619	326	31	mass	mass	NOUN
fumecheng-12619	326	32	sensors	sensor	NOUN
fumecheng-12619	326	33	containing	contain	VERB
fumecheng-12619	326	34	nanoparticles	nanoparticle	NOUN
fumecheng-12619	326	35	using	use	VERB
fumecheng-12619	326	36	nonlocal	nonlocal	ADJ
fumecheng-12619	326	37	elasticity	elasticity	NOUN
fumecheng-12619	326	38	theory	theory	NOUN
fumecheng-12619	326	39	,	,	PUNCT
fumecheng-12619	326	40	physica	physica	PROPN
fumecheng-12619	326	41	b	b	PROPN
fumecheng-12619	326	42	:	:	PUNCT
fumecheng-12619	326	43	condensed	condensed	ADJ
fumecheng-12619	326	44	matter	matter	NOUN
fumecheng-12619	326	45	,	,	PUNCT
fumecheng-12619	326	46	634,413804	634,413804	NUM
fumecheng-12619	326	47	.	.	PUNCT
fumecheng-12619	327	1	11	11	NUM
fumecheng-12619	327	2	.	.	X
fumecheng-12619	327	3	soltani	soltani	PROPN
fumecheng-12619	327	4	,	,	PUNCT
fumecheng-12619	327	5	m.	m.	NOUN
fumecheng-12619	327	6	,	,	PUNCT
fumecheng-12619	327	7	atoufi	atoufi	NOUN
fumecheng-12619	327	8	,	,	PUNCT
fumecheng-12619	327	9	f.	f.	PROPN
fumecheng-12619	327	10	,	,	PUNCT
fumecheng-12619	327	11	mohri	mohri	PROPN
fumecheng-12619	327	12	,	,	PUNCT
fumecheng-12619	327	13	f.	f.	PROPN
fumecheng-12619	327	14	,	,	PUNCT
fumecheng-12619	327	15	dimitri	dimitri	PROPN
fumecheng-12619	327	16	,	,	PUNCT
fumecheng-12619	327	17	r.	r.	PROPN
fumecheng-12619	327	18	,	,	PUNCT
fumecheng-12619	327	19	tornabene	tornabene	NOUN
fumecheng-12619	327	20	,	,	PUNCT
fumecheng-12619	327	21	f.	f.	PROPN
fumecheng-12619	327	22	,	,	PUNCT
fumecheng-12619	327	23	2021	2021	NUM
fumecheng-12619	327	24	,	,	PUNCT
fumecheng-12619	327	25	nonlocal	nonlocal	ADJ
fumecheng-12619	327	26	elasticity	elasticity	NOUN
fumecheng-12619	327	27	theory	theory	NOUN
fumecheng-12619	327	28	for	for	ADP
fumecheng-12619	327	29	lateral	lateral	ADJ
fumecheng-12619	327	30	stability	stability	NOUN
fumecheng-12619	327	31	analysis	analysis	NOUN
fumecheng-12619	327	32	of	of	ADP
fumecheng-12619	327	33	tapered	tapered	ADJ
fumecheng-12619	327	34	thin	thin	ADJ
fumecheng-12619	327	35	-	-	PUNCT
fumecheng-12619	327	36	walled	walled	ADJ
fumecheng-12619	327	37	nanobeams	nanobeam	NOUN
fumecheng-12619	327	38	with	with	ADP
fumecheng-12619	327	39	axially	axially	ADV
fumecheng-12619	327	40	varying	vary	VERB
fumecheng-12619	327	41	materials	material	NOUN
fumecheng-12619	327	42	,	,	PUNCT
fumecheng-12619	327	43	thin	thin	ADJ
fumecheng-12619	327	44	-	-	PUNCT
fumecheng-12619	327	45	walled	walled	ADJ
fumecheng-12619	327	46	structures	structure	NOUN
fumecheng-12619	327	47	,	,	PUNCT
fumecheng-12619	327	48	159	159	NUM
fumecheng-12619	327	49	,	,	PUNCT
fumecheng-12619	327	50	107268	107268	NUM
fumecheng-12619	327	51	.	.	PUNCT
fumecheng-12619	328	1	12	12	NUM
fumecheng-12619	328	2	.	.	X
fumecheng-12619	329	1	arefi	arefi	PROPN
fumecheng-12619	329	2	,	,	PUNCT
fumecheng-12619	329	3	m.	m.	NOUN
fumecheng-12619	329	4	,	,	PUNCT
fumecheng-12619	329	5	2018	2018	NUM
fumecheng-12619	329	6	,	,	PUNCT
fumecheng-12619	329	7	analysis	analysis	NOUN
fumecheng-12619	329	8	of	of	ADP
fumecheng-12619	329	9	a	a	DET
fumecheng-12619	329	10	doubly	doubly	ADV
fumecheng-12619	329	11	curved	curved	ADJ
fumecheng-12619	329	12	piezoelectric	piezoelectric	NOUN
fumecheng-12619	329	13	nano	nano	NOUN
fumecheng-12619	329	14	shell	shell	NOUN
fumecheng-12619	329	15	:	:	PUNCT
fumecheng-12619	329	16	nonlocal	nonlocal	ADJ
fumecheng-12619	329	17	electro	electro	ADJ
fumecheng-12619	329	18	-	-	PUNCT
fumecheng-12619	329	19	elastic	elastic	ADJ
fumecheng-12619	329	20	bending	bending	NOUN
fumecheng-12619	329	21	solution	solution	NOUN
fumecheng-12619	329	22	,	,	PUNCT
fumecheng-12619	329	23	european	european	PROPN
fumecheng-12619	329	24	journal	journal	PROPN
fumecheng-12619	329	25	of	of	ADP
fumecheng-12619	329	26	mechanics	mechanic	NOUN
fumecheng-12619	329	27	a	a	DET
fumecheng-12619	329	28	/	/	SYM
fumecheng-12619	329	29	solids	solid	NOUN
fumecheng-12619	329	30	,	,	PUNCT
fumecheng-12619	329	31	70	70	NUM
fumecheng-12619	329	32	,	,	PUNCT
fumecheng-12619	329	33	pp	pp	ADJ
fumecheng-12619	329	34	.	.	PUNCT
fumecheng-12619	330	1	226	226	NUM
fumecheng-12619	330	2	-	-	SYM
fumecheng-12619	330	3	237	237	NUM
fumecheng-12619	330	4	.	.	PUNCT
fumecheng-12619	331	1	13	13	NUM
fumecheng-12619	331	2	.	.	X
fumecheng-12619	331	3	boyina	boyina	PROPN
fumecheng-12619	331	4	,	,	PUNCT
fumecheng-12619	331	5	k.	k.	PROPN
fumecheng-12619	331	6	,	,	PUNCT
fumecheng-12619	331	7	piska	piska	PROPN
fumecheng-12619	331	8	,	,	PUNCT
fumecheng-12619	331	9	r.	r.	PROPN
fumecheng-12619	331	10	,	,	PUNCT
fumecheng-12619	331	11	2023	2023	NUM
fumecheng-12619	331	12	,	,	PUNCT
fumecheng-12619	331	13	wave	wave	NOUN
fumecheng-12619	331	14	propagation	propagation	NOUN
fumecheng-12619	331	15	analysis	analysis	NOUN
fumecheng-12619	331	16	in	in	ADP
fumecheng-12619	331	17	viscoelastic	viscoelastic	ADJ
fumecheng-12619	331	18	timoshenko	timoshenko	NOUN
fumecheng-12619	331	19	nanobeams	nanobeam	NOUN
fumecheng-12619	331	20	under	under	ADP
fumecheng-12619	331	21	surface	surface	NOUN
fumecheng-12619	331	22	and	and	CCONJ
fumecheng-12619	331	23	magnetic	magnetic	ADJ
fumecheng-12619	331	24	field	field	NOUN
fumecheng-12619	331	25	effects	effect	NOUN
fumecheng-12619	331	26	based	base	VERB
fumecheng-12619	331	27	on	on	ADP
fumecheng-12619	331	28	nonlocal	nonlocal	ADJ
fumecheng-12619	331	29	strain	strain	NOUN
fumecheng-12619	331	30	gradient	gradient	NOUN
fumecheng-12619	331	31	theory	theory	NOUN
fumecheng-12619	331	32	,	,	PUNCT
fumecheng-12619	331	33	applied	apply	VERB
fumecheng-12619	331	34	mathematics	mathematic	NOUN
fumecheng-12619	331	35	and	and	CCONJ
fumecheng-12619	331	36	computation	computation	NOUN
fumecheng-12619	331	37	,	,	PUNCT
fumecheng-12619	331	38	439	439	NUM
fumecheng-12619	331	39	,	,	PUNCT
fumecheng-12619	331	40	127580	127580	NUM
fumecheng-12619	331	41	.	.	PUNCT
fumecheng-12619	332	1	https://www.sciencedirect.com/journal/european-journal-of-mechanics-a-solids	https://www.sciencedirect.com/journal/european-journal-of-mechanics-a-solid	NOUN
fumecheng-12619	332	2	https://www.sciencedirect.com/journal/european-journal-of-mechanics-a-solids	https://www.sciencedirect.com/journal/european-journal-of-mechanics-a-solids	PRON
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fumecheng-12619	332	4	https://onlinelibrary.wiley.com/authored-by/veena/eshwarappa	https://onlinelibrary.wiley.com/authored-by/veena/eshwarappa	PROPN
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fumecheng-12619	332	10	https://onlinelibrary.wiley.com/authored-by/basha/dudekula+baba	https://onlinelibrary.wiley.com/authored-by/basha/dudekula+baba	PROPN
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fumecheng-12619	332	12	https://www.sciencedirect.com/journal/journal-of-the-mechanics-and-physics-of-solids	https://www.sciencedirect.com/journal/journal-of-the-mechanics-and-physics-of-solid	NOUN
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fumecheng-12619	333	2	https://journals.sagepub.com/doi/full/10.1177/1045389x16672569	https://journals.sagepub.com/doi/full/10.1177/1045389x16672569	PROPN
fumecheng-12619	334	1	https://journals.sagepub.com/doi/full/10.1177/1045389x16672569	https://journals.sagepub.com/doi/full/10.1177/1045389x16672569	PROPN
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fumecheng-12619	334	10	dragan	dragan	NOUN
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fumecheng-12619	334	12	downloads/,%2011(28).%20https:/doi.org/10.1177/1045389x16672569	downloads/,%2011(28).%20https:/doi.org/10.1177/1045389x16672569	PROPN
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fumecheng-12619	337	2	.	.	X
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fumecheng-12619	338	4	.	.	PUNCT
fumecheng-12619	339	1	16	16	NUM
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fumecheng-12619	344	13	mohamadi	mohamadi	NOUN
fumecheng-12619	344	14	daniali	daniali	PROPN
fumecheng-12619	344	15	,	,	PUNCT
fumecheng-12619	344	16	h.	h.	PROPN
fumecheng-12619	344	17	,	,	PUNCT
fumecheng-12619	344	18	fathi	fathi	PROPN
fumecheng-12619	344	19	,	,	PUNCT
fumecheng-12619	344	20	a.	a.	PROPN
fumecheng-12619	344	21	,	,	PUNCT
fumecheng-12619	344	22	2019	2019	NUM
fumecheng-12619	344	23	,	,	PUNCT
fumecheng-12619	344	24	pull	pull	NOUN
fumecheng-12619	344	25	-	-	PUNCT
fumecheng-12619	344	26	in	in	ADP
fumecheng-12619	344	27	instability	instability	NOUN
fumecheng-12619	344	28	and	and	CCONJ
fumecheng-12619	344	29	nonlinear	nonlinear	ADJ
fumecheng-12619	344	30	vibration	vibration	NOUN
fumecheng-12619	344	31	analysis	analysis	NOUN
fumecheng-12619	344	32	of	of	ADP
fumecheng-12619	344	33	electrostatically	electrostatically	ADJ
fumecheng-12619	344	34	piezoelectric	piezoelectric	ADJ
fumecheng-12619	344	35	nanoresonator	nanoresonator	NOUN
fumecheng-12619	344	36	with	with	ADP
fumecheng-12619	344	37	surface	surface	NOUN
fumecheng-12619	344	38	/	/	SYM
fumecheng-12619	344	39	interface	interface	NOUN
fumecheng-12619	344	40	effects	effect	NOUN
fumecheng-12619	344	41	,	,	PUNCT
fumecheng-12619	344	42	thin	thin	ADJ
fumecheng-12619	344	43	-	-	PUNCT
fumecheng-12619	344	44	walled	walled	ADJ
fumecheng-12619	344	45	structures	structure	NOUN
fumecheng-12619	344	46	,	,	PUNCT
fumecheng-12619	344	47	143	143	NUM
fumecheng-12619	344	48	,	,	PUNCT
fumecheng-12619	344	49	106210	106210	NUM
fumecheng-12619	344	50	.	.	PUNCT
fumecheng-12619	345	1	20	20	NUM
fumecheng-12619	345	2	.	.	X
fumecheng-12619	346	1	hashemi	hashemi	PROPN
fumecheng-12619	346	2	kachapi	kachapi	PROPN
fumecheng-12619	346	3	,	,	PUNCT
fumecheng-12619	346	4	s.h	s.h	PROPN
fumecheng-12619	346	5	.	.	PROPN
fumecheng-12619	346	6	,	,	PUNCT
fumecheng-12619	346	7	dardel	dardel	PROPN
fumecheng-12619	346	8	,	,	PUNCT
fumecheng-12619	346	9	m.	m.	NOUN
fumecheng-12619	346	10	,	,	PUNCT
fumecheng-12619	346	11	mohamadi	mohamadi	NOUN
fumecheng-12619	346	12	daniali	daniali	PROPN
fumecheng-12619	346	13	,	,	PUNCT
fumecheng-12619	346	14	h.	h.	PROPN
fumecheng-12619	346	15	,	,	PUNCT
fumecheng-12619	346	16	fathi	fathi	PROPN
fumecheng-12619	346	17	,	,	PUNCT
fumecheng-12619	346	18	a.	a.	NOUN
fumecheng-12619	346	19	,	,	PUNCT
fumecheng-12619	346	20	2019	2019	NUM
fumecheng-12619	346	21	,	,	PUNCT
fumecheng-12619	346	22	nonlinear	nonlinear	ADJ
fumecheng-12619	346	23	dynamics	dynamic	NOUN
fumecheng-12619	346	24	and	and	CCONJ
fumecheng-12619	346	25	stability	stability	NOUN
fumecheng-12619	346	26	analysis	analysis	NOUN
fumecheng-12619	346	27	of	of	ADP
fumecheng-12619	346	28	piezo	piezo	ADJ
fumecheng-12619	346	29	-	-	ADJ
fumecheng-12619	346	30	visco	visco	ADJ
fumecheng-12619	346	31	medium	medium	ADJ
fumecheng-12619	346	32	nanoshell	nanoshell	NOUN
fumecheng-12619	346	33	resonator	resonator	NOUN
fumecheng-12619	346	34	with	with	ADP
fumecheng-12619	346	35	electrostatic	electrostatic	ADJ
fumecheng-12619	346	36	and	and	CCONJ
fumecheng-12619	346	37	harmonic	harmonic	ADJ
fumecheng-12619	346	38	actuation	actuation	NOUN
fumecheng-12619	346	39	,	,	PUNCT
fumecheng-12619	346	40	applied	apply	VERB
fumecheng-12619	346	41	mathematical	mathematical	ADJ
fumecheng-12619	346	42	modelling	modelling	NOUN
fumecheng-12619	346	43	,	,	PUNCT
fumecheng-12619	346	44	75	75	NUM
fumecheng-12619	346	45	,	,	PUNCT
fumecheng-12619	346	46	pp	pp	ADJ
fumecheng-12619	346	47	.	.	PUNCT
fumecheng-12619	347	1	279	279	NUM
fumecheng-12619	347	2	-	-	SYM
fumecheng-12619	347	3	309	309	NUM
fumecheng-12619	347	4	.	.	PUNCT
fumecheng-12619	348	1	21	21	NUM
fumecheng-12619	348	2	.	.	PUNCT
fumecheng-12619	349	1	farrokhian	farrokhian	PROPN
fumecheng-12619	349	2	,	,	PUNCT
fumecheng-12619	349	3	a.	a.	PROPN
fumecheng-12619	349	4	,	,	PUNCT
fumecheng-12619	349	5	salmani	salmani	NOUN
fumecheng-12619	349	6	-	-	PUNCT
fumecheng-12619	349	7	tehrani	tehrani	ADJ
fumecheng-12619	349	8	,	,	PUNCT
fumecheng-12619	349	9	m.	m.	NOUN
fumecheng-12619	349	10	,	,	PUNCT
fumecheng-12619	349	11	2022	2022	NUM
fumecheng-12619	349	12	,	,	PUNCT
fumecheng-12619	349	13	vibration	vibration	NOUN
fumecheng-12619	349	14	and	and	CCONJ
fumecheng-12619	349	15	damping	damp	VERB
fumecheng-12619	349	16	analysis	analysis	NOUN
fumecheng-12619	349	17	of	of	ADP
fumecheng-12619	349	18	smart	smart	ADJ
fumecheng-12619	349	19	sandwich	sandwich	NOUN
fumecheng-12619	349	20	nanotubes	nanotube	NOUN
fumecheng-12619	349	21	using	use	VERB
fumecheng-12619	349	22	surface	surface	NOUN
fumecheng-12619	349	23	-	-	PUNCT
fumecheng-12619	349	24	viscopiezo	viscopiezo	NOUN
fumecheng-12619	349	25	-	-	PUNCT
fumecheng-12619	349	26	elasticity	elasticity	NOUN
fumecheng-12619	349	27	theory	theory	NOUN
fumecheng-12619	349	28	for	for	ADP
fumecheng-12619	349	29	various	various	ADJ
fumecheng-12619	349	30	boundary	boundary	ADJ
fumecheng-12619	349	31	conditions	condition	NOUN
fumecheng-12619	349	32	,	,	PUNCT
fumecheng-12619	349	33	engineering	engineer	VERB
fumecheng-12619	349	34	analysis	analysis	NOUN
fumecheng-12619	349	35	with	with	ADP
fumecheng-12619	349	36	boundary	boundary	ADJ
fumecheng-12619	349	37	elements	element	NOUN
fumecheng-12619	349	38	,	,	PUNCT
fumecheng-12619	349	39	135	135	NUM
fumecheng-12619	349	40	,	,	PUNCT
fumecheng-12619	349	41	pp	pp	ADJ
fumecheng-12619	349	42	.	.	PUNCT
fumecheng-12619	350	1	337	337	NUM
fumecheng-12619	350	2	-	-	SYM
fumecheng-12619	350	3	358	358	NUM
fumecheng-12619	350	4	.	.	PUNCT
fumecheng-12619	351	1	22	22	NUM
fumecheng-12619	351	2	.	.	PUNCT
fumecheng-12619	352	1	ghorbani	ghorbani	NOUN
fumecheng-12619	352	2	,	,	PUNCT
fumecheng-12619	352	3	k.	k.	PROPN
fumecheng-12619	352	4	,	,	PUNCT
fumecheng-12619	352	5	mohammad	mohammad	PROPN
fumecheng-12619	352	6	,	,	PUNCT
fumecheng-12619	352	7	k.	k.	PROPN
fumecheng-12619	352	8	,	,	PUNCT
fumecheng-12619	352	9	rajabpour	rajabpour	PROPN
fumecheng-12619	352	10	,	,	PUNCT
fumecheng-12619	352	11	i.	i.	NOUN
fumecheng-12619	352	12	,	,	PUNCT
fumecheng-12619	352	13	ghadiri	ghadiri	NOUN
fumecheng-12619	352	14	,	,	PUNCT
fumecheng-12619	352	15	m.	m.	NOUN
fumecheng-12619	352	16	,	,	PUNCT
fumecheng-12619	352	17	2019	2019	NUM
fumecheng-12619	352	18	,	,	PUNCT
fumecheng-12619	352	19	surface	surface	NOUN
fumecheng-12619	352	20	and	and	CCONJ
fumecheng-12619	352	21	size	size	NOUN
fumecheng-12619	352	22	-	-	PUNCT
fumecheng-12619	352	23	dependent	dependent	ADJ
fumecheng-12619	352	24	effects	effect	NOUN
fumecheng-12619	352	25	on	on	ADP
fumecheng-12619	352	26	the	the	DET
fumecheng-12619	352	27	free	free	ADJ
fumecheng-12619	352	28	vibration	vibration	NOUN
fumecheng-12619	352	29	analysis	analysis	NOUN
fumecheng-12619	352	30	of	of	ADP
fumecheng-12619	352	31	cylindrical	cylindrical	ADJ
fumecheng-12619	352	32	shell	shell	NOUN
fumecheng-12619	352	33	based	base	VERB
fumecheng-12619	352	34	on	on	ADP
fumecheng-12619	352	35	gurtin	gurtin	NOUN
fumecheng-12619	352	36	-	-	PUNCT
fumecheng-12619	352	37	murdoch	murdoch	PROPN
fumecheng-12619	352	38	and	and	CCONJ
fumecheng-12619	352	39	nonlocal	nonlocal	ADJ
fumecheng-12619	352	40	strain	strain	NOUN
fumecheng-12619	352	41	gradient	gradient	NOUN
fumecheng-12619	352	42	theories	theory	NOUN
fumecheng-12619	352	43	,	,	PUNCT
fumecheng-12619	352	44	journal	journal	NOUN
fumecheng-12619	352	45	of	of	ADP
fumecheng-12619	352	46	physics	physics	NOUN
fumecheng-12619	352	47	and	and	CCONJ
fumecheng-12619	352	48	chemistry	chemistry	NOUN
fumecheng-12619	352	49	of	of	ADP
fumecheng-12619	352	50	solids	solid	NOUN
fumecheng-12619	352	51	,	,	PUNCT
fumecheng-12619	352	52	129	129	NUM
fumecheng-12619	352	53	,	,	PUNCT
fumecheng-12619	352	54	pp	pp	ADJ
fumecheng-12619	352	55	.	.	PUNCT
fumecheng-12619	353	1	140	140	NUM
fumecheng-12619	353	2	-	-	SYM
fumecheng-12619	353	3	150	150	NUM
fumecheng-12619	353	4	.	.	PUNCT
fumecheng-12619	354	1	23	23	NUM
fumecheng-12619	354	2	.	.	PUNCT
fumecheng-12619	355	1	lovisi	lovisi	PROPN
fumecheng-12619	355	2	,	,	PUNCT
fumecheng-12619	355	3	g.	g.	PROPN
fumecheng-12619	355	4	,	,	PUNCT
fumecheng-12619	355	5	2023	2023	NUM
fumecheng-12619	355	6	,	,	PUNCT
fumecheng-12619	355	7	application	application	NOUN
fumecheng-12619	355	8	of	of	ADP
fumecheng-12619	355	9	the	the	DET
fumecheng-12619	355	10	surface	surface	NOUN
fumecheng-12619	355	11	stress	stress	NOUN
fumecheng-12619	355	12	-	-	PUNCT
fumecheng-12619	355	13	driven	drive	VERB
fumecheng-12619	355	14	nonlocal	nonlocal	ADJ
fumecheng-12619	355	15	theory	theory	NOUN
fumecheng-12619	355	16	of	of	ADP
fumecheng-12619	355	17	elasticity	elasticity	NOUN
fumecheng-12619	355	18	for	for	ADP
fumecheng-12619	355	19	the	the	DET
fumecheng-12619	355	20	study	study	NOUN
fumecheng-12619	355	21	of	of	ADP
fumecheng-12619	355	22	the	the	DET
fumecheng-12619	355	23	bending	bend	VERB
fumecheng-12619	355	24	response	response	NOUN
fumecheng-12619	355	25	of	of	ADP
fumecheng-12619	355	26	fg	fg	PROPN
fumecheng-12619	355	27	cracked	crack	VERB
fumecheng-12619	355	28	nanobeams	nanobeam	NOUN
fumecheng-12619	355	29	,	,	PUNCT
fumecheng-12619	355	30	composite	composite	ADJ
fumecheng-12619	355	31	structures	structure	NOUN
fumecheng-12619	355	32	,	,	PUNCT
fumecheng-12619	355	33	324	324	NUM
fumecheng-12619	355	34	,	,	PUNCT
fumecheng-12619	355	35	pp	pp	ADJ
fumecheng-12619	355	36	.	.	PUNCT
fumecheng-12619	356	1	327	327	NUM
fumecheng-12619	356	2	-	-	SYM
fumecheng-12619	356	3	343	343	NUM
fumecheng-12619	356	4	.	.	PUNCT
fumecheng-12619	357	1	24	24	NUM
fumecheng-12619	357	2	.	.	PUNCT
fumecheng-12619	357	3	sun	sun	PROPN
fumecheng-12619	357	4	,	,	PUNCT
fumecheng-12619	357	5	j.	j.	PROPN
fumecheng-12619	357	6	,	,	PUNCT
fumecheng-12619	357	7	wang	wang	PROPN
fumecheng-12619	357	8	,	,	PUNCT
fumecheng-12619	357	9	z.	z.	PROPN
fumecheng-12619	357	10	,	,	PUNCT
fumecheng-12619	357	11	zhou	zhou	PROPN
fumecheng-12619	357	12	,	,	PUNCT
fumecheng-12619	357	13	z.	z.	PROPN
fumecheng-12619	357	14	,	,	PUNCT
fumecheng-12619	357	15	xu	xu	PROPN
fumecheng-12619	357	16	,	,	PUNCT
fumecheng-12619	357	17	x.g	x.g	PROPN
fumecheng-12619	357	18	,	,	PUNCT
fumecheng-12619	357	19	lim	lim	PROPN
fumecheng-12619	357	20	,	,	PUNCT
fumecheng-12619	357	21	c.w	c.w	PROPN
fumecheng-12619	357	22	.	.	PROPN
fumecheng-12619	357	23	,	,	PUNCT
fumecheng-12619	357	24	2018	2018	NUM
fumecheng-12619	357	25	,	,	PUNCT
fumecheng-12619	357	26	surface	surface	NOUN
fumecheng-12619	357	27	effects	effect	NOUN
fumecheng-12619	357	28	on	on	ADP
fumecheng-12619	357	29	the	the	DET
fumecheng-12619	357	30	buckling	buckle	VERB
fumecheng-12619	357	31	behaviors	behavior	NOUN
fumecheng-12619	357	32	of	of	ADP
fumecheng-12619	357	33	piezoelectric	piezoelectric	ADJ
fumecheng-12619	357	34	cylindrical	cylindrical	ADJ
fumecheng-12619	357	35	nanoshells	nanoshell	NOUN
fumecheng-12619	357	36	using	use	VERB
fumecheng-12619	357	37	nonlocal	nonlocal	ADJ
fumecheng-12619	357	38	continuum	continuum	ADJ
fumecheng-12619	357	39	model	model	NOUN
fumecheng-12619	357	40	,	,	PUNCT
fumecheng-12619	357	41	applied	apply	VERB
fumecheng-12619	357	42	mathematical	mathematical	ADJ
fumecheng-12619	357	43	modelling	modelling	NOUN
fumecheng-12619	357	44	,	,	PUNCT
fumecheng-12619	357	45	59	59	NUM
fumecheng-12619	357	46	,	,	PUNCT
fumecheng-12619	357	47	pp	pp	ADJ
fumecheng-12619	357	48	.	.	PUNCT
fumecheng-12619	358	1	341	341	NUM
fumecheng-12619	358	2	-	-	SYM
fumecheng-12619	358	3	356	356	NUM
fumecheng-12619	358	4	.	.	PUNCT
fumecheng-12619	359	1	25	25	NUM
fumecheng-12619	359	2	.	.	X
fumecheng-12619	360	1	hashemi	hashemi	PROPN
fumecheng-12619	360	2	kachapi	kachapi	PROPN
fumecheng-12619	360	3	,	,	PUNCT
fumecheng-12619	360	4	s.h	s.h	PROPN
fumecheng-12619	360	5	.	.	PROPN
fumecheng-12619	360	6	,	,	PUNCT
fumecheng-12619	360	7	2020	2020	NUM
fumecheng-12619	360	8	,	,	PUNCT
fumecheng-12619	360	9	nonlinear	nonlinear	ADJ
fumecheng-12619	360	10	and	and	CCONJ
fumecheng-12619	360	11	nonclassical	nonclassical	ADJ
fumecheng-12619	360	12	vibration	vibration	NOUN
fumecheng-12619	360	13	analysis	analysis	NOUN
fumecheng-12619	360	14	of	of	ADP
fumecheng-12619	360	15	double	double	ADJ
fumecheng-12619	360	16	walled	wall	VERB
fumecheng-12619	360	17	piezoelectric	piezoelectric	NOUN
fumecheng-12619	360	18	nano	nano	NOUN
fumecheng-12619	360	19	-	-	PUNCT
fumecheng-12619	360	20	structure	structure	NOUN
fumecheng-12619	360	21	,	,	PUNCT
fumecheng-12619	360	22	advances	advance	NOUN
fumecheng-12619	360	23	in	in	ADP
fumecheng-12619	360	24	nano	nano	NOUN
fumecheng-12619	360	25	research	research	NOUN
fumecheng-12619	360	26	,	,	PUNCT
fumecheng-12619	360	27	9(4	9(4	NUM
fumecheng-12619	360	28	)	)	PUNCT
fumecheng-12619	360	29	,	,	PUNCT
fumecheng-12619	360	30	pp	pp	PROPN
fumecheng-12619	360	31	.	.	PUNCT
fumecheng-12619	361	1	277	277	NUM
fumecheng-12619	361	2	-	-	SYM
fumecheng-12619	361	3	294	294	NUM
fumecheng-12619	361	4	.	.	PUNCT
fumecheng-12619	362	1	26	26	NUM
fumecheng-12619	362	2	.	.	X
fumecheng-12619	363	1	hashemi	hashemi	PROPN
fumecheng-12619	363	2	kachapi	kachapi	PROPN
fumecheng-12619	363	3	,	,	PUNCT
fumecheng-12619	363	4	s.h	s.h	PROPN
fumecheng-12619	363	5	.	.	PROPN
fumecheng-12619	363	6	,	,	PUNCT
fumecheng-12619	363	7	dardel	dardel	PROPN
fumecheng-12619	363	8	,	,	PUNCT
fumecheng-12619	363	9	m.	m.	NOUN
fumecheng-12619	363	10	,	,	PUNCT
fumecheng-12619	363	11	mohamadi	mohamadi	NOUN
fumecheng-12619	363	12	daniali	daniali	PROPN
fumecheng-12619	363	13	,	,	PUNCT
fumecheng-12619	363	14	h.	h.	PROPN
fumecheng-12619	363	15	,	,	PUNCT
fumecheng-12619	363	16	fathi	fathi	PROPN
fumecheng-12619	363	17	,	,	PUNCT
fumecheng-12619	363	18	a.	a.	PROPN
fumecheng-12619	363	19	,	,	PUNCT
fumecheng-12619	363	20	2020	2020	NUM
fumecheng-12619	363	21	,	,	PUNCT
fumecheng-12619	363	22	nonlinear	nonlinear	ADJ
fumecheng-12619	363	23	vibration	vibration	NOUN
fumecheng-12619	363	24	and	and	CCONJ
fumecheng-12619	363	25	stability	stability	NOUN
fumecheng-12619	363	26	analysis	analysis	NOUN
fumecheng-12619	363	27	of	of	ADP
fumecheng-12619	363	28	double	double	ADJ
fumecheng-12619	363	29	-	-	PUNCT
fumecheng-12619	363	30	walled	wall	VERB
fumecheng-12619	363	31	piezoelectric	piezoelectric	NOUN
fumecheng-12619	363	32	nanoresonator	nanoresonator	NOUN
fumecheng-12619	363	33	with	with	ADP
fumecheng-12619	363	34	nonlinear	nonlinear	ADJ
fumecheng-12619	363	35	van	van	PROPN
fumecheng-12619	363	36	der	der	ADJ
fumecheng-12619	363	37	waals	waal	NOUN
fumecheng-12619	363	38	and	and	CCONJ
fumecheng-12619	363	39	electrostatic	electrostatic	ADJ
fumecheng-12619	363	40	excitation	excitation	NOUN
fumecheng-12619	363	41	,	,	PUNCT
fumecheng-12619	363	42	journal	journal	NOUN
fumecheng-12619	363	43	of	of	ADP
fumecheng-12619	363	44	vibration	vibration	NOUN
fumecheng-12619	363	45	and	and	CCONJ
fumecheng-12619	363	46	control	control	NOUN
fumecheng-12619	363	47	,	,	PUNCT
fumecheng-12619	363	48	9	9	NUM
fumecheng-12619	363	49	-	-	SYM
fumecheng-12619	363	50	10(26	10(26	NUM
fumecheng-12619	363	51	)	)	PUNCT
fumecheng-12619	363	52	,	,	PUNCT
fumecheng-12619	363	53	pp	pp	ADJ
fumecheng-12619	363	54	.	.	PUNCT
fumecheng-12619	364	1	680	680	NUM
fumecheng-12619	364	2	-	-	SYM
fumecheng-12619	364	3	700	700	NUM
fumecheng-12619	364	4	.	.	PUNCT
fumecheng-12619	365	1	27	27	NUM
fumecheng-12619	365	2	.	.	PUNCT
fumecheng-12619	365	3	farokhi	farokhi	PROPN
fumecheng-12619	365	4	,	,	PUNCT
fumecheng-12619	365	5	h.	h.	PROPN
fumecheng-12619	365	6	,	,	PUNCT
fumecheng-12619	365	7	païdoussis	païdoussis	PRON
fumecheng-12619	365	8	,	,	PUNCT
fumecheng-12619	365	9	m.p	m.p	PROPN
fumecheng-12619	365	10	.	.	PROPN
fumecheng-12619	365	11	,	,	PUNCT
fumecheng-12619	365	12	misra	misra	PROPN
fumecheng-12619	365	13	,	,	PUNCT
fumecheng-12619	365	14	a.	a.	NOUN
fumecheng-12619	365	15	,	,	PUNCT
fumecheng-12619	365	16	2016	2016	NUM
fumecheng-12619	365	17	,	,	PUNCT
fumecheng-12619	365	18	a	a	DET
fumecheng-12619	365	19	new	new	ADJ
fumecheng-12619	365	20	nonlinear	nonlinear	ADJ
fumecheng-12619	365	21	model	model	NOUN
fumecheng-12619	365	22	for	for	ADP
fumecheng-12619	365	23	analyzing	analyze	VERB
fumecheng-12619	365	24	the	the	DET
fumecheng-12619	365	25	behaviour	behaviour	NOUN
fumecheng-12619	365	26	of	of	ADP
fumecheng-12619	365	27	carbon	carbon	NOUN
fumecheng-12619	365	28	nanotube	nanotube	NOUN
fumecheng-12619	365	29	-	-	PUNCT
fumecheng-12619	365	30	based	base	VERB
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fumecheng-12619	365	32	,	,	PUNCT
fumecheng-12619	365	33	journal	journal	NOUN
fumecheng-12619	365	34	of	of	ADP
fumecheng-12619	365	35	sound	sound	NOUN
fumecheng-12619	365	36	and	and	CCONJ
fumecheng-12619	365	37	vibration	vibration	NOUN
fumecheng-12619	365	38	,	,	PUNCT
fumecheng-12619	365	39	378	378	NUM
fumecheng-12619	365	40	,	,	PUNCT
fumecheng-12619	365	41	pp	pp	ADJ
fumecheng-12619	365	42	.	.	PUNCT
fumecheng-12619	366	1	56	56	NUM
fumecheng-12619	366	2	-	-	SYM
fumecheng-12619	366	3	75	75	NUM
fumecheng-12619	366	4	.	.	PUNCT
fumecheng-12619	367	1	28	28	NUM
fumecheng-12619	367	2	.	.	PUNCT
fumecheng-12619	368	1	amabili	amabili	NOUN
fumecheng-12619	368	2	,	,	PUNCT
fumecheng-12619	368	3	m.	m.	NOUN
fumecheng-12619	368	4	,	,	PUNCT
fumecheng-12619	368	5	2008	2008	NUM
fumecheng-12619	368	6	,	,	PUNCT
fumecheng-12619	368	7	nonlinear	nonlinear	ADJ
fumecheng-12619	368	8	vibrations	vibration	NOUN
fumecheng-12619	368	9	and	and	CCONJ
fumecheng-12619	368	10	stability	stability	NOUN
fumecheng-12619	368	11	of	of	ADP
fumecheng-12619	368	12	shells	shell	NOUN
fumecheng-12619	368	13	and	and	CCONJ
fumecheng-12619	368	14	plates	plate	NOUN
fumecheng-12619	368	15	,	,	PUNCT
fumecheng-12619	368	16	cambridge	cambridge	PROPN
fumecheng-12619	368	17	university	university	PROPN
fumecheng-12619	368	18	press	press	NOUN
fumecheng-12619	368	19	,	,	PUNCT
fumecheng-12619	368	20	new	new	PROPN
fumecheng-12619	368	21	york	york	PROPN
fumecheng-12619	368	22	.	.	PUNCT
fumecheng-12619	369	1	29	29	NUM
fumecheng-12619	369	2	.	.	X
fumecheng-12619	370	1	manevitch	manevitch	NOUN
fumecheng-12619	370	2	,	,	PUNCT
fumecheng-12619	370	3	a.i	a.i	PROPN
fumecheng-12619	370	4	.	.	PROPN
fumecheng-12619	370	5	,	,	PUNCT
fumecheng-12619	370	6	manevitch	manevitch	PROPN
fumecheng-12619	370	7	,	,	PUNCT
fumecheng-12619	370	8	l.i	l.i	PROPN
fumecheng-12619	370	9	.	.	PROPN
fumecheng-12619	370	10	,	,	PUNCT
fumecheng-12619	370	11	2005	2005	NUM
fumecheng-12619	370	12	,	,	PUNCT
fumecheng-12619	370	13	the	the	DET
fumecheng-12619	370	14	mechanics	mechanic	NOUN
fumecheng-12619	370	15	of	of	ADP
fumecheng-12619	370	16	nonlinear	nonlinear	ADJ
fumecheng-12619	370	17	systems	system	NOUN
fumecheng-12619	370	18	with	with	ADP
fumecheng-12619	370	19	internal	internal	ADJ
fumecheng-12619	370	20	resonance	resonance	NOUN
fumecheng-12619	370	21	,	,	PUNCT
fumecheng-12619	370	22	imperial	imperial	ADJ
fumecheng-12619	370	23	college	college	NOUN
fumecheng-12619	370	24	press	press	PROPN
fumecheng-12619	370	25	,	,	PUNCT
fumecheng-12619	370	26	london	london	PROPN
fumecheng-12619	370	27	.	.	PUNCT
fumecheng-12619	371	1	https://www.sciencedirect.com/journal/results-in-physics	https://www.sciencedirect.com/journal/results-in-physic	NOUN
fumecheng-12619	371	2	https://www.sciencedirect.com/science/article/pii/s0921452617307718	https://www.sciencedirect.com/science/article/pii/s0921452617307718	PROPN
fumecheng-12619	371	3	#	#	NUM
fumecheng-12619	371	4	!	!	PUNCT
fumecheng-12619	372	1	http://iopscience.iop.org/journal/2053-1591	http://iopscience.iop.org/journal/2053-1591	PROPN
fumecheng-12619	373	1	https://www.sciencedirect.com/science/journal/0307904x	https://www.sciencedirect.com/science/journal/0307904x	PROPN
fumecheng-12619	373	2	file:///c:/users	file:///c:/user	NOUN
fumecheng-12619	373	3	/	/	SYM
fumecheng-12619	373	4	dragan	dragan	NOUN
fumecheng-12619	373	5	/	/	SYM
fumecheng-12619	373	6	downloads/75,279	downloads/75,279	NOUN
fumecheng-12619	373	7	-	-	PUNCT
fumecheng-12619	373	8	309.%20https:/doi.org/10.1016	309.%20https:/doi.org/10.1016	NUM
fumecheng-12619	373	9	/	/	SYM
fumecheng-12619	373	10	j.apm.2019.05.035	j.apm.2019.05.035	PROPN
fumecheng-12619	373	11	https://www.sciencedirect.com/journal/engineering-analysis-with-boundary-elements	https://www.sciencedirect.com/journal/engineering-analysis-with-boundary-elements	PROPN
fumecheng-12619	373	12	https://www.sciencedirect.com/journal/engineering-analysis-with-boundary-elements	https://www.sciencedirect.com/journal/engineering-analysis-with-boundary-elements	PROPN
fumecheng-12619	373	13	https://www.sciencedirect.com/science/article/abs/pii/s0022369718323217	https://www.sciencedirect.com/science/article/abs/pii/s0022369718323217	ADJ
fumecheng-12619	373	14	#	#	NOUN
fumecheng-12619	373	15	!	!	PUNCT
fumecheng-12619	374	1	https://www.sciencedirect.com/science/article/abs/pii/s0022369718323217	https://www.sciencedirect.com/science/article/abs/pii/s0022369718323217	ADJ
fumecheng-12619	374	2	#	#	NOUN
fumecheng-12619	374	3	!	!	PUNCT
fumecheng-12619	375	1	https://www.sciencedirect.com/science/article/abs/pii/s0022369718323217	https://www.sciencedirect.com/science/article/abs/pii/s0022369718323217	ADJ
fumecheng-12619	375	2	#	#	NOUN
fumecheng-12619	375	3	!	!	PUNCT
fumecheng-12619	376	1	https://www.sciencedirect.com/science/journal/00223697/129/supp/c	https://www.sciencedirect.com/science/journal/00223697/129/supp/c	NOUN
fumecheng-12619	376	2	https://www.sciencedirect.com/science/article/abs/pii/s0022369717306765	https://www.sciencedirect.com/science/article/abs/pii/s0022369717306765	PROPN
fumecheng-12619	376	3	#	#	NOUN
fumecheng-12619	376	4	!	!	PUNCT
fumecheng-12619	377	1	https://www.sciencedirect.com/journal/composite-structures	https://www.sciencedirect.com/journal/composite-structure	NOUN
fumecheng-12619	377	2	https://www.sciencedirect.com/science/journal/0307904x	https://www.sciencedirect.com/science/journal/0307904x	PROPN
fumecheng-12619	377	3	https://www.sciencedirect.com/science/journal/0307904x/59/supp/c	https://www.sciencedirect.com/science/journal/0307904x/59/supp/c	X
fumecheng-12619	377	4	https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=2ahukewjuvfurgzrpahwyqhuihysmaeoqfjabegqiebac&url=https%3a%2f%2fonlinelibrary.wiley.com%2fjournal%2f15214001&usg=aovvaw2dqpwnctfmikcxbs1xlo57	https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=2ahukewjuvfurgzrpahwyqhuihysmaeoqfjabegqiebac&url=https%3a%2f%2fonlinelibrary.wiley.com%2fjournal%2f15214001&usg=aovvaw2dqpwnctfmikcxbs1xlo57	NOUN