id	sid	tid	token	lemma	pos
fumecheng-7253	1	1	facta	facta	PROPN
fumecheng-7253	1	2	universitatis	universitatis	PROPN
fumecheng-7253	1	3	series	series	NOUN
fumecheng-7253	1	4	:	:	PUNCT
fumecheng-7253	1	5	mechanical	mechanical	ADJ
fumecheng-7253	1	6	engineering	engineering	NOUN
fumecheng-7253	1	7	vol	vol	NOUN
fumecheng-7253	1	8	.	.	PROPN
fumecheng-7253	2	1	19	19	NUM
fumecheng-7253	2	2	,	,	PUNCT
fumecheng-7253	2	3	no	no	DET
fumecheng-7253	2	4	4	4	NUM
fumecheng-7253	2	5	,	,	PUNCT
fumecheng-7253	2	6	2021	2021	NUM
fumecheng-7253	2	7	,	,	PUNCT
fumecheng-7253	2	8	pp	pp	ADV
fumecheng-7253	2	9	.	.	PUNCT
fumecheng-7253	3	1	633	633	NUM
fumecheng-7253	3	2	656	656	NUM
fumecheng-7253	3	3	https://doi.org/10.22190/fume201222024a	https://doi.org/10.22190/fume201222024a	VERB
fumecheng-7253	3	4	©	©	PROPN
fumecheng-7253	3	5	2021	2021	NUM
fumecheng-7253	3	6	by	by	ADP
fumecheng-7253	3	7	university	university	PROPN
fumecheng-7253	3	8	of	of	ADP
fumecheng-7253	3	9	niš	niš	PROPN
fumecheng-7253	3	10	,	,	PUNCT
fumecheng-7253	3	11	serbia	serbia	PROPN
fumecheng-7253	3	12	|	|	ADV
fumecheng-7253	3	13	creative	creative	ADJ
fumecheng-7253	3	14	commons	common	NOUN
fumecheng-7253	3	15	license	license	NOUN
fumecheng-7253	3	16	:	:	PUNCT
fumecheng-7253	3	17	cc	cc	VERB
fumecheng-7253	3	18	by	by	ADP
fumecheng-7253	3	19	-	-	PUNCT
fumecheng-7253	3	20	nc	nc	VERB
fumecheng-7253	3	21	-	-	PUNCT
fumecheng-7253	3	22	nd	nd	ADV
fumecheng-7253	3	23	original	original	ADJ
fumecheng-7253	3	24	scientific	scientific	ADJ
fumecheng-7253	3	25	paper	paper	ADJ
fumecheng-7253	3	26	temperature	temperature	NOUN
fumecheng-7253	3	27	-	-	PUNCT
fumecheng-7253	3	28	dependent	dependent	ADJ
fumecheng-7253	3	29	physical	physical	ADJ
fumecheng-7253	3	30	characteristics	characteristic	NOUN
fumecheng-7253	3	31	of	of	ADP
fumecheng-7253	3	32	the	the	DET
fumecheng-7253	3	33	rotating	rotate	VERB
fumecheng-7253	3	34	nonlocal	nonlocal	ADJ
fumecheng-7253	3	35	nanobeams	nanobeam	NOUN
fumecheng-7253	3	36	subject	subject	ADJ
fumecheng-7253	3	37	to	to	ADP
fumecheng-7253	3	38	a	a	DET
fumecheng-7253	3	39	varying	vary	VERB
fumecheng-7253	3	40	heat	heat	NOUN
fumecheng-7253	3	41	source	source	NOUN
fumecheng-7253	3	42	and	and	CCONJ
fumecheng-7253	3	43	a	a	DET
fumecheng-7253	3	44	dynamic	dynamic	ADJ
fumecheng-7253	3	45	load	load	NOUN
fumecheng-7253	3	46	ahmed	ahmed	PROPN
fumecheng-7253	3	47	e.	e.	PROPN
fumecheng-7253	3	48	abouelregal1,2	abouelregal1,2	PROPN
fumecheng-7253	3	49	,	,	PUNCT
fumecheng-7253	3	50	hamid	hamid	PROPN
fumecheng-7253	3	51	mohammad	mohammad	PROPN
fumecheng-7253	3	52	-	-	PUNCT
fumecheng-7253	3	53	sedighi3,4	sedighi3,4	PROPN
fumecheng-7253	3	54	,	,	PUNCT
fumecheng-7253	3	55	seyed	seyed	PROPN
fumecheng-7253	3	56	ali	ali	PROPN
fumecheng-7253	3	57	faghidian5	faghidian5	PROPN
fumecheng-7253	3	58	,	,	PUNCT
fumecheng-7253	3	59	ali	ali	PROPN
fumecheng-7253	3	60	heidari	heidari	PROPN
fumecheng-7253	3	61	shirazi3	shirazi3	PROPN
fumecheng-7253	4	1	1department	1department	NUM
fumecheng-7253	4	2	of	of	ADP
fumecheng-7253	4	3	mathematics	mathematic	NOUN
fumecheng-7253	4	4	,	,	PUNCT
fumecheng-7253	4	5	college	college	NOUN
fumecheng-7253	4	6	of	of	ADP
fumecheng-7253	4	7	science	science	NOUN
fumecheng-7253	4	8	and	and	CCONJ
fumecheng-7253	4	9	arts	art	NOUN
fumecheng-7253	4	10	,	,	PUNCT
fumecheng-7253	4	11	jouf	jouf	PROPN
fumecheng-7253	4	12	university	university	PROPN
fumecheng-7253	4	13	,	,	PUNCT
fumecheng-7253	4	14	al	al	PROPN
fumecheng-7253	4	15	-	-	PUNCT
fumecheng-7253	4	16	qurayyat	qurayyat	PROPN
fumecheng-7253	4	17	,	,	PUNCT
fumecheng-7253	4	18	saudi	saudi	PROPN
fumecheng-7253	4	19	arabia	arabia	PROPN
fumecheng-7253	4	20	2department	2department	NUM
fumecheng-7253	4	21	of	of	ADP
fumecheng-7253	4	22	mathematics	mathematic	NOUN
fumecheng-7253	4	23	,	,	PUNCT
fumecheng-7253	4	24	faculty	faculty	NOUN
fumecheng-7253	4	25	of	of	ADP
fumecheng-7253	4	26	science	science	NOUN
fumecheng-7253	4	27	,	,	PUNCT
fumecheng-7253	4	28	mansoura	mansoura	PROPN
fumecheng-7253	4	29	university	university	NOUN
fumecheng-7253	4	30	,	,	PUNCT
fumecheng-7253	4	31	mansoura	mansoura	PROPN
fumecheng-7253	4	32	,	,	PUNCT
fumecheng-7253	4	33	egypt	egypt	PROPN
fumecheng-7253	4	34	3mechanical	3mechanical	NUM
fumecheng-7253	4	35	engineering	engineering	NOUN
fumecheng-7253	4	36	department	department	NOUN
fumecheng-7253	4	37	,	,	PUNCT
fumecheng-7253	4	38	faculty	faculty	NOUN
fumecheng-7253	4	39	of	of	ADP
fumecheng-7253	4	40	engineering	engineering	NOUN
fumecheng-7253	4	41	,	,	PUNCT
fumecheng-7253	4	42	shahid	shahid	PROPN
fumecheng-7253	4	43	chamran	chamran	PROPN
fumecheng-7253	4	44	university	university	PROPN
fumecheng-7253	4	45	of	of	ADP
fumecheng-7253	4	46	ahvaz	ahvaz	PROPN
fumecheng-7253	4	47	,	,	PUNCT
fumecheng-7253	4	48	ahvaz	ahvaz	PROPN
fumecheng-7253	4	49	,	,	PUNCT
fumecheng-7253	4	50	iran	iran	PROPN
fumecheng-7253	4	51	4drilling	4drilling	NUM
fumecheng-7253	4	52	center	center	NOUN
fumecheng-7253	4	53	of	of	ADP
fumecheng-7253	4	54	excellence	excellence	NOUN
fumecheng-7253	4	55	and	and	CCONJ
fumecheng-7253	4	56	research	research	NOUN
fumecheng-7253	4	57	center	center	NOUN
fumecheng-7253	4	58	,	,	PUNCT
fumecheng-7253	4	59	shahid	shahid	PROPN
fumecheng-7253	4	60	chamran	chamran	PROPN
fumecheng-7253	4	61	university	university	PROPN
fumecheng-7253	4	62	of	of	ADP
fumecheng-7253	4	63	ahvaz	ahvaz	PROPN
fumecheng-7253	4	64	,	,	PUNCT
fumecheng-7253	4	65	ahvaz	ahvaz	PROPN
fumecheng-7253	4	66	,	,	PUNCT
fumecheng-7253	4	67	iran	iran	PROPN
fumecheng-7253	4	68	5department	5department	NUM
fumecheng-7253	4	69	of	of	ADP
fumecheng-7253	4	70	mechanical	mechanical	ADJ
fumecheng-7253	4	71	engineering	engineering	NOUN
fumecheng-7253	4	72	,	,	PUNCT
fumecheng-7253	4	73	science	science	NOUN
fumecheng-7253	4	74	and	and	CCONJ
fumecheng-7253	4	75	research	research	NOUN
fumecheng-7253	4	76	branch	branch	NOUN
fumecheng-7253	4	77	,	,	PUNCT
fumecheng-7253	4	78	islamic	islamic	PROPN
fumecheng-7253	4	79	azad	azad	PROPN
fumecheng-7253	4	80	university	university	PROPN
fumecheng-7253	4	81	,	,	PUNCT
fumecheng-7253	4	82	tehran	tehran	PROPN
fumecheng-7253	4	83	,	,	PUNCT
fumecheng-7253	4	84	iran	iran	PROPN
fumecheng-7253	4	85	abstract	abstract	ADJ
fumecheng-7253	4	86	.	.	PUNCT
fumecheng-7253	5	1	in	in	ADP
fumecheng-7253	5	2	this	this	DET
fumecheng-7253	5	3	article	article	NOUN
fumecheng-7253	5	4	,	,	PUNCT
fumecheng-7253	5	5	the	the	DET
fumecheng-7253	5	6	influence	influence	NOUN
fumecheng-7253	5	7	of	of	ADP
fumecheng-7253	5	8	thermal	thermal	ADJ
fumecheng-7253	5	9	conductivity	conductivity	NOUN
fumecheng-7253	5	10	on	on	ADP
fumecheng-7253	5	11	the	the	DET
fumecheng-7253	5	12	dynamics	dynamic	NOUN
fumecheng-7253	5	13	of	of	ADP
fumecheng-7253	5	14	a	a	DET
fumecheng-7253	5	15	rotating	rotate	VERB
fumecheng-7253	5	16	nanobeam	nanobeam	NOUN
fumecheng-7253	5	17	is	be	AUX
fumecheng-7253	5	18	established	establish	VERB
fumecheng-7253	5	19	in	in	ADP
fumecheng-7253	5	20	the	the	DET
fumecheng-7253	5	21	context	context	NOUN
fumecheng-7253	5	22	of	of	ADP
fumecheng-7253	5	23	nonlocal	nonlocal	ADJ
fumecheng-7253	5	24	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	5	25	theory	theory	NOUN
fumecheng-7253	5	26	.	.	PUNCT
fumecheng-7253	6	1	to	to	ADP
fumecheng-7253	6	2	this	this	DET
fumecheng-7253	6	3	end	end	NOUN
fumecheng-7253	6	4	,	,	PUNCT
fumecheng-7253	6	5	the	the	DET
fumecheng-7253	6	6	governing	govern	VERB
fumecheng-7253	6	7	equations	equation	NOUN
fumecheng-7253	6	8	are	be	AUX
fumecheng-7253	6	9	derived	derive	VERB
fumecheng-7253	6	10	using	use	VERB
fumecheng-7253	6	11	generalized	generalized	ADJ
fumecheng-7253	6	12	heat	heat	NOUN
fumecheng-7253	6	13	conduction	conduction	NOUN
fumecheng-7253	6	14	including	include	VERB
fumecheng-7253	6	15	phase	phase	NOUN
fumecheng-7253	6	16	lags	lag	VERB
fumecheng-7253	6	17	on	on	ADP
fumecheng-7253	6	18	the	the	DET
fumecheng-7253	6	19	basis	basis	NOUN
fumecheng-7253	6	20	of	of	ADP
fumecheng-7253	6	21	the	the	DET
fumecheng-7253	6	22	euler	euler	PROPN
fumecheng-7253	6	23	–	–	PUNCT
fumecheng-7253	6	24	bernoulli	bernoulli	PROPN
fumecheng-7253	6	25	beam	beam	NOUN
fumecheng-7253	6	26	theory	theory	NOUN
fumecheng-7253	6	27	.	.	PUNCT
fumecheng-7253	7	1	the	the	DET
fumecheng-7253	7	2	thermal	thermal	ADJ
fumecheng-7253	7	3	conductivity	conductivity	NOUN
fumecheng-7253	7	4	of	of	ADP
fumecheng-7253	7	5	the	the	DET
fumecheng-7253	7	6	proposed	propose	VERB
fumecheng-7253	7	7	model	model	NOUN
fumecheng-7253	7	8	linearly	linearly	ADV
fumecheng-7253	7	9	changes	change	VERB
fumecheng-7253	7	10	with	with	ADP
fumecheng-7253	7	11	temperature	temperature	NOUN
fumecheng-7253	7	12	and	and	CCONJ
fumecheng-7253	7	13	the	the	DET
fumecheng-7253	7	14	considered	consider	VERB
fumecheng-7253	7	15	nanobeam	nanobeam	NOUN
fumecheng-7253	7	16	is	be	AUX
fumecheng-7253	7	17	excited	excite	VERB
fumecheng-7253	7	18	with	with	ADP
fumecheng-7253	7	19	a	a	DET
fumecheng-7253	7	20	variable	variable	ADJ
fumecheng-7253	7	21	harmonic	harmonic	ADJ
fumecheng-7253	7	22	heat	heat	NOUN
fumecheng-7253	7	23	source	source	NOUN
fumecheng-7253	7	24	and	and	CCONJ
fumecheng-7253	7	25	exposed	expose	VERB
fumecheng-7253	7	26	to	to	ADP
fumecheng-7253	7	27	a	a	DET
fumecheng-7253	7	28	time	time	NOUN
fumecheng-7253	7	29	-	-	PUNCT
fumecheng-7253	7	30	dependent	dependent	ADJ
fumecheng-7253	7	31	load	load	NOUN
fumecheng-7253	7	32	with	with	ADP
fumecheng-7253	7	33	exponential	exponential	ADJ
fumecheng-7253	7	34	decay	decay	NOUN
fumecheng-7253	7	35	.	.	PUNCT
fumecheng-7253	8	1	the	the	DET
fumecheng-7253	8	2	analytic	analytic	ADJ
fumecheng-7253	8	3	solutions	solution	NOUN
fumecheng-7253	8	4	for	for	ADP
fumecheng-7253	8	5	bending	bend	VERB
fumecheng-7253	8	6	moment	moment	NOUN
fumecheng-7253	8	7	,	,	PUNCT
fumecheng-7253	8	8	deflection	deflection	NOUN
fumecheng-7253	8	9	and	and	CCONJ
fumecheng-7253	8	10	temperature	temperature	NOUN
fumecheng-7253	8	11	of	of	ADP
fumecheng-7253	8	12	rotating	rotate	VERB
fumecheng-7253	8	13	nonlocal	nonlocal	ADJ
fumecheng-7253	8	14	nanobeams	nanobeam	NOUN
fumecheng-7253	8	15	are	be	AUX
fumecheng-7253	8	16	achieved	achieve	VERB
fumecheng-7253	8	17	by	by	ADP
fumecheng-7253	8	18	means	mean	NOUN
fumecheng-7253	8	19	of	of	ADP
fumecheng-7253	8	20	the	the	DET
fumecheng-7253	8	21	laplace	laplace	NOUN
fumecheng-7253	8	22	transform	transform	NOUN
fumecheng-7253	8	23	procedure	procedure	NOUN
fumecheng-7253	8	24	.	.	PUNCT
fumecheng-7253	9	1	a	a	DET
fumecheng-7253	9	2	qualitative	qualitative	ADJ
fumecheng-7253	9	3	study	study	NOUN
fumecheng-7253	9	4	is	be	AUX
fumecheng-7253	9	5	conducted	conduct	VERB
fumecheng-7253	9	6	to	to	PART
fumecheng-7253	9	7	justify	justify	VERB
fumecheng-7253	9	8	the	the	DET
fumecheng-7253	9	9	soundness	soundness	NOUN
fumecheng-7253	9	10	of	of	ADP
fumecheng-7253	9	11	the	the	DET
fumecheng-7253	9	12	present	present	ADJ
fumecheng-7253	9	13	analysis	analysis	NOUN
fumecheng-7253	9	14	while	while	SCONJ
fumecheng-7253	9	15	the	the	DET
fumecheng-7253	9	16	impact	impact	NOUN
fumecheng-7253	9	17	of	of	ADP
fumecheng-7253	9	18	nonlocal	nonlocal	ADJ
fumecheng-7253	9	19	parameter	parameter	NOUN
fumecheng-7253	9	20	and	and	CCONJ
fumecheng-7253	9	21	varying	vary	VERB
fumecheng-7253	9	22	heat	heat	NOUN
fumecheng-7253	9	23	source	source	NOUN
fumecheng-7253	9	24	are	be	AUX
fumecheng-7253	9	25	discussed	discuss	VERB
fumecheng-7253	9	26	in	in	ADP
fumecheng-7253	9	27	detail	detail	NOUN
fumecheng-7253	9	28	.	.	PUNCT
fumecheng-7253	10	1	it	it	PRON
fumecheng-7253	10	2	also	also	ADV
fumecheng-7253	10	3	shows	show	VERB
fumecheng-7253	10	4	the	the	DET
fumecheng-7253	10	5	way	way	NOUN
fumecheng-7253	10	6	in	in	ADP
fumecheng-7253	10	7	which	which	PRON
fumecheng-7253	10	8	the	the	DET
fumecheng-7253	10	9	variations	variation	NOUN
fumecheng-7253	10	10	of	of	ADP
fumecheng-7253	10	11	physical	physical	ADJ
fumecheng-7253	10	12	properties	property	NOUN
fumecheng-7253	10	13	due	due	ADJ
fumecheng-7253	10	14	to	to	ADP
fumecheng-7253	10	15	temperature	temperature	NOUN
fumecheng-7253	10	16	changes	change	NOUN
fumecheng-7253	10	17	affect	affect	VERB
fumecheng-7253	10	18	the	the	DET
fumecheng-7253	10	19	static	static	ADJ
fumecheng-7253	10	20	and	and	CCONJ
fumecheng-7253	10	21	dynamic	dynamic	ADJ
fumecheng-7253	10	22	behavior	behavior	NOUN
fumecheng-7253	10	23	of	of	ADP
fumecheng-7253	10	24	rotating	rotate	VERB
fumecheng-7253	10	25	nanobeams	nanobeam	NOUN
fumecheng-7253	10	26	.	.	PUNCT
fumecheng-7253	11	1	it	it	PRON
fumecheng-7253	11	2	is	be	AUX
fumecheng-7253	11	3	found	find	VERB
fumecheng-7253	11	4	that	that	SCONJ
fumecheng-7253	11	5	the	the	DET
fumecheng-7253	11	6	physical	physical	ADJ
fumecheng-7253	11	7	fields	field	NOUN
fumecheng-7253	11	8	strongly	strongly	ADV
fumecheng-7253	11	9	depend	depend	VERB
fumecheng-7253	11	10	on	on	ADP
fumecheng-7253	11	11	the	the	DET
fumecheng-7253	11	12	nonlocal	nonlocal	ADJ
fumecheng-7253	11	13	parameter	parameter	NOUN
fumecheng-7253	11	14	,	,	PUNCT
fumecheng-7253	11	15	the	the	DET
fumecheng-7253	11	16	change	change	NOUN
fumecheng-7253	11	17	of	of	ADP
fumecheng-7253	11	18	the	the	DET
fumecheng-7253	11	19	thermal	thermal	ADJ
fumecheng-7253	11	20	conductivity	conductivity	NOUN
fumecheng-7253	11	21	,	,	PUNCT
fumecheng-7253	11	22	rotation	rotation	NOUN
fumecheng-7253	11	23	speed	speed	NOUN
fumecheng-7253	11	24	and	and	CCONJ
fumecheng-7253	11	25	the	the	DET
fumecheng-7253	11	26	mechanical	mechanical	ADJ
fumecheng-7253	11	27	loads	load	NOUN
fumecheng-7253	11	28	and	and	CCONJ
fumecheng-7253	11	29	,	,	PUNCT
fumecheng-7253	11	30	therefore	therefore	ADV
fumecheng-7253	11	31	,	,	PUNCT
fumecheng-7253	11	32	it	it	PRON
fumecheng-7253	11	33	is	be	AUX
fumecheng-7253	11	34	not	not	PART
fumecheng-7253	11	35	possible	possible	ADJ
fumecheng-7253	11	36	to	to	PART
fumecheng-7253	11	37	neglect	neglect	VERB
fumecheng-7253	11	38	their	their	PRON
fumecheng-7253	11	39	effects	effect	NOUN
fumecheng-7253	11	40	on	on	ADP
fumecheng-7253	11	41	the	the	DET
fumecheng-7253	11	42	manufacturing	manufacturing	NOUN
fumecheng-7253	11	43	process	process	NOUN
fumecheng-7253	11	44	of	of	ADP
fumecheng-7253	11	45	precise	precise	ADJ
fumecheng-7253	11	46	/	/	SYM
fumecheng-7253	11	47	intelligent	intelligent	ADJ
fumecheng-7253	11	48	machines	machine	NOUN
fumecheng-7253	11	49	and	and	CCONJ
fumecheng-7253	11	50	devices	device	NOUN
fumecheng-7253	11	51	.	.	PUNCT
fumecheng-7253	12	1	key	key	ADJ
fumecheng-7253	12	2	words	word	NOUN
fumecheng-7253	12	3	:	:	PUNCT
fumecheng-7253	12	4	nonlocal	nonlocal	ADJ
fumecheng-7253	12	5	elasticity	elasticity	NOUN
fumecheng-7253	12	6	,	,	PUNCT
fumecheng-7253	12	7	rotating	rotate	VERB
fumecheng-7253	12	8	nanobeam	nanobeam	NOUN
fumecheng-7253	12	9	,	,	PUNCT
fumecheng-7253	12	10	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	12	11	,	,	PUNCT
fumecheng-7253	12	12	variable	variable	ADJ
fumecheng-7253	12	13	thermal	thermal	ADJ
fumecheng-7253	12	14	conductivity	conductivity	NOUN
fumecheng-7253	12	15	,	,	PUNCT
fumecheng-7253	12	16	varying	vary	VERB
fumecheng-7253	12	17	load	load	NOUN
fumecheng-7253	12	18	received	receive	VERB
fumecheng-7253	12	19	december	december	PROPN
fumecheng-7253	12	20	22	22	NUM
fumecheng-7253	12	21	,	,	PUNCT
fumecheng-7253	12	22	2020	2020	NUM
fumecheng-7253	12	23	/	/	SYM
fumecheng-7253	12	24	accepted	accept	VERB
fumecheng-7253	12	25	february	february	PROPN
fumecheng-7253	12	26	28	28	NUM
fumecheng-7253	12	27	,	,	PUNCT
fumecheng-7253	12	28	2021	2021	NUM
fumecheng-7253	12	29	corresponding	correspond	VERB
fumecheng-7253	12	30	author	author	NOUN
fumecheng-7253	12	31	:	:	PUNCT
fumecheng-7253	12	32	hamid	hamid	PROPN
fumecheng-7253	12	33	mohammad	mohammad	PROPN
fumecheng-7253	12	34	-	-	PUNCT
fumecheng-7253	12	35	sedighi	sedighi	PROPN
fumecheng-7253	12	36	mechanical	mechanical	PROPN
fumecheng-7253	12	37	engineering	engineering	PROPN
fumecheng-7253	12	38	department	department	PROPN
fumecheng-7253	12	39	,	,	PUNCT
fumecheng-7253	12	40	faculty	faculty	NOUN
fumecheng-7253	12	41	of	of	ADP
fumecheng-7253	12	42	engineering	engineering	NOUN
fumecheng-7253	12	43	,	,	PUNCT
fumecheng-7253	12	44	shahidchamranuniversity	shahidchamranuniversity	NOUN
fumecheng-7253	12	45	of	of	ADP
fumecheng-7253	12	46	ahvaz	ahvaz	NOUN
fumecheng-7253	12	47	,	,	PUNCT
fumecheng-7253	12	48	ahvaz	ahvaz	PROPN
fumecheng-7253	12	49	,	,	PUNCT
fumecheng-7253	12	50	iran	iran	PROPN
fumecheng-7253	12	51	e	e	X
fumecheng-7253	12	52	-	-	PUNCT
fumecheng-7253	12	53	mails	mail	NOUN
fumecheng-7253	12	54	:	:	PUNCT
fumecheng-7253	12	55	h.msedighi@scu.ac.ir	h.msedighi@scu.ac.ir	NUM
fumecheng-7253	12	56	;	;	PUNCT
fumecheng-7253	12	57	hmsedighi@gmail.com	hmsedighi@gmail.com	PROPN
fumecheng-7253	12	58	mailto:h.msedighi@scu.ac.ir	mailto:h.msedighi@scu.ac.ir	NOUN
fumecheng-7253	12	59	634	634	NUM
fumecheng-7253	12	60	a.	a.	NOUN
fumecheng-7253	12	61	e.	e.	PROPN
fumecheng-7253	12	62	abouelregal	abouelregal	PROPN
fumecheng-7253	12	63	,	,	PUNCT
fumecheng-7253	12	64	h.	h.	PROPN
fumecheng-7253	12	65	m.	m.	PROPN
fumecheng-7253	12	66	sedighi	sedighi	PROPN
fumecheng-7253	12	67	,	,	PUNCT
fumecheng-7253	12	68	s.	s.	PROPN
fumecheng-7253	12	69	a.	a.	PROPN
fumecheng-7253	12	70	faghidian	faghidian	PROPN
fumecheng-7253	12	71	,	,	PUNCT
fumecheng-7253	12	72	a.	a.	PROPN
fumecheng-7253	12	73	h.	h.	PROPN
fumecheng-7253	12	74	shirazi	shirazi	PROPN
fumecheng-7253	12	75	1	1	NUM
fumecheng-7253	12	76	.	.	PUNCT
fumecheng-7253	13	1	introduction	introduction	NOUN
fumecheng-7253	13	2	thermomechanical	thermomechanical	ADJ
fumecheng-7253	13	3	effects	effect	NOUN
fumecheng-7253	13	4	resulting	result	VERB
fumecheng-7253	13	5	from	from	ADP
fumecheng-7253	13	6	the	the	DET
fumecheng-7253	13	7	interaction	interaction	NOUN
fumecheng-7253	13	8	of	of	ADP
fumecheng-7253	13	9	temperature	temperature	NOUN
fumecheng-7253	13	10	and	and	CCONJ
fumecheng-7253	13	11	deformation	deformation	NOUN
fumecheng-7253	13	12	fields	field	NOUN
fumecheng-7253	13	13	are	be	AUX
fumecheng-7253	13	14	of	of	ADP
fumecheng-7253	13	15	particular	particular	ADJ
fumecheng-7253	13	16	significance	significance	NOUN
fumecheng-7253	13	17	in	in	ADP
fumecheng-7253	13	18	various	various	ADJ
fumecheng-7253	13	19	modern	modern	ADJ
fumecheng-7253	13	20	designs	design	NOUN
fumecheng-7253	13	21	such	such	ADJ
fumecheng-7253	13	22	as	as	ADP
fumecheng-7253	13	23	high	high	ADJ
fumecheng-7253	13	24	-	-	PUNCT
fumecheng-7253	13	25	speed	speed	NOUN
fumecheng-7253	13	26	aircrafts	aircraft	NOUN
fumecheng-7253	13	27	,	,	PUNCT
fumecheng-7253	13	28	jets	jet	NOUN
fumecheng-7253	13	29	,	,	PUNCT
fumecheng-7253	13	30	gas	gas	NOUN
fumecheng-7253	13	31	and	and	CCONJ
fumecheng-7253	13	32	steam	steam	NOUN
fumecheng-7253	13	33	turbines	turbine	NOUN
fumecheng-7253	13	34	,	,	PUNCT
fumecheng-7253	13	35	nuclear	nuclear	ADJ
fumecheng-7253	13	36	reactors	reactor	NOUN
fumecheng-7253	13	37	and	and	CCONJ
fumecheng-7253	13	38	missiles	missile	NOUN
fumecheng-7253	13	39	.	.	PUNCT
fumecheng-7253	14	1	both	both	DET
fumecheng-7253	14	2	theoretical	theoretical	ADJ
fumecheng-7253	14	3	and	and	CCONJ
fumecheng-7253	14	4	practical	practical	ADJ
fumecheng-7253	14	5	concerns	concern	NOUN
fumecheng-7253	14	6	,	,	PUNCT
fumecheng-7253	14	7	including	include	VERB
fumecheng-7253	14	8	a	a	DET
fumecheng-7253	14	9	rapid	rapid	ADJ
fumecheng-7253	14	10	supply	supply	NOUN
fumecheng-7253	14	11	of	of	ADP
fumecheng-7253	14	12	thermal	thermal	ADJ
fumecheng-7253	14	13	energy	energy	NOUN
fumecheng-7253	14	14	,	,	PUNCT
fumecheng-7253	14	15	have	have	AUX
fumecheng-7253	14	16	been	be	AUX
fumecheng-7253	14	17	gaining	gain	VERB
fumecheng-7253	14	18	increasing	increase	VERB
fumecheng-7253	14	19	attention	attention	NOUN
fumecheng-7253	14	20	.	.	PUNCT
fumecheng-7253	15	1	the	the	DET
fumecheng-7253	15	2	conventional	conventional	ADJ
fumecheng-7253	15	3	heat	heat	NOUN
fumecheng-7253	15	4	conduction	conduction	NOUN
fumecheng-7253	15	5	theory	theory	NOUN
fumecheng-7253	15	6	,	,	PUNCT
fumecheng-7253	15	7	on	on	ADP
fumecheng-7253	15	8	the	the	DET
fumecheng-7253	15	9	basis	basis	NOUN
fumecheng-7253	15	10	of	of	ADP
fumecheng-7253	15	11	the	the	DET
fumecheng-7253	15	12	fourier	fourier	NOUN
fumecheng-7253	15	13	’s	’s	PART
fumecheng-7253	15	14	law	law	NOUN
fumecheng-7253	15	15	,	,	PUNCT
fumecheng-7253	15	16	takes	take	VERB
fumecheng-7253	15	17	an	an	DET
fumecheng-7253	15	18	instant	instant	ADJ
fumecheng-7253	15	19	reaction	reaction	NOUN
fumecheng-7253	15	20	to	to	ADP
fumecheng-7253	15	21	the	the	DET
fumecheng-7253	15	22	temperature	temperature	NOUN
fumecheng-7253	15	23	gradient	gradient	NOUN
fumecheng-7253	15	24	and	and	CCONJ
fumecheng-7253	15	25	gives	give	VERB
fumecheng-7253	15	26	a	a	DET
fumecheng-7253	15	27	distinctive	distinctive	ADJ
fumecheng-7253	15	28	parabolic	parabolic	ADJ
fumecheng-7253	15	29	equation	equation	NOUN
fumecheng-7253	15	30	for	for	ADP
fumecheng-7253	15	31	temperature	temperature	NOUN
fumecheng-7253	15	32	change	change	NOUN
fumecheng-7253	15	33	.	.	PUNCT
fumecheng-7253	16	1	to	to	PART
fumecheng-7253	16	2	solve	solve	VERB
fumecheng-7253	16	3	the	the	DET
fumecheng-7253	16	4	infinite	infinite	ADJ
fumecheng-7253	16	5	speed	speed	NOUN
fumecheng-7253	16	6	thermal	thermal	ADJ
fumecheng-7253	16	7	propagation	propagation	NOUN
fumecheng-7253	16	8	phenomena	phenomenon	NOUN
fumecheng-7253	16	9	predicted	predict	VERB
fumecheng-7253	16	10	by	by	ADP
fumecheng-7253	16	11	the	the	DET
fumecheng-7253	16	12	classical	classical	ADJ
fumecheng-7253	16	13	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	16	14	theory	theory	NOUN
fumecheng-7253	16	15	,	,	PUNCT
fumecheng-7253	16	16	modified	modify	VERB
fumecheng-7253	16	17	generalized	generalized	ADJ
fumecheng-7253	16	18	theories	theory	NOUN
fumecheng-7253	16	19	of	of	ADP
fumecheng-7253	16	20	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	16	21	have	have	AUX
fumecheng-7253	16	22	been	be	AUX
fumecheng-7253	16	23	established	establish	VERB
fumecheng-7253	16	24	.	.	PUNCT
fumecheng-7253	17	1	lord	lord	PROPN
fumecheng-7253	17	2	and	and	CCONJ
fumecheng-7253	17	3	shulman	shulman	PROPN
fumecheng-7253	17	4	[	[	X
fumecheng-7253	17	5	1	1	NUM
fumecheng-7253	17	6	]	]	PUNCT
fumecheng-7253	17	7	suggested	suggest	VERB
fumecheng-7253	17	8	one	one	NUM
fumecheng-7253	17	9	of	of	ADP
fumecheng-7253	17	10	the	the	DET
fumecheng-7253	17	11	modified	modify	VERB
fumecheng-7253	17	12	generalized	generalized	ADJ
fumecheng-7253	17	13	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	17	14	theories	theory	NOUN
fumecheng-7253	17	15	containing	contain	VERB
fumecheng-7253	17	16	a	a	DET
fumecheng-7253	17	17	relaxation	relaxation	NOUN
fumecheng-7253	17	18	time	time	NOUN
fumecheng-7253	17	19	by	by	ADP
fumecheng-7253	17	20	introducing	introduce	VERB
fumecheng-7253	17	21	a	a	DET
fumecheng-7253	17	22	novel	novel	ADJ
fumecheng-7253	17	23	rule	rule	NOUN
fumecheng-7253	17	24	for	for	ADP
fumecheng-7253	17	25	thermal	thermal	ADJ
fumecheng-7253	17	26	conductivity	conductivity	NOUN
fumecheng-7253	17	27	to	to	PART
fumecheng-7253	17	28	modify	modify	VERB
fumecheng-7253	17	29	the	the	DET
fumecheng-7253	17	30	classic	classic	ADJ
fumecheng-7253	17	31	fourier	fourier	NOUN
fumecheng-7253	17	32	law	law	NOUN
fumecheng-7253	17	33	.	.	PUNCT
fumecheng-7253	18	1	the	the	DET
fumecheng-7253	18	2	refined	refined	ADJ
fumecheng-7253	18	3	law	law	NOUN
fumecheng-7253	18	4	includes	include	VERB
fumecheng-7253	18	5	the	the	DET
fumecheng-7253	18	6	heat	heat	NOUN
fumecheng-7253	18	7	flux	flux	NOUN
fumecheng-7253	18	8	and	and	CCONJ
fumecheng-7253	18	9	its	its	PRON
fumecheng-7253	18	10	partial	partial	ADJ
fumecheng-7253	18	11	derivative	derivative	NOUN
fumecheng-7253	18	12	with	with	ADP
fumecheng-7253	18	13	respect	respect	NOUN
fumecheng-7253	18	14	to	to	ADP
fumecheng-7253	18	15	time	time	NOUN
fumecheng-7253	18	16	.	.	PUNCT
fumecheng-7253	19	1	among	among	ADP
fumecheng-7253	19	2	the	the	DET
fumecheng-7253	19	3	models	model	NOUN
fumecheng-7253	19	4	that	that	PRON
fumecheng-7253	19	5	have	have	AUX
fumecheng-7253	19	6	gained	gain	VERB
fumecheng-7253	19	7	great	great	ADJ
fumecheng-7253	19	8	popularity	popularity	NOUN
fumecheng-7253	19	9	in	in	ADP
fumecheng-7253	19	10	recent	recent	ADJ
fumecheng-7253	19	11	years	year	NOUN
fumecheng-7253	19	12	,	,	PUNCT
fumecheng-7253	19	13	the	the	DET
fumecheng-7253	19	14	model	model	NOUN
fumecheng-7253	19	15	presented	present	VERB
fumecheng-7253	19	16	by	by	ADP
fumecheng-7253	19	17	tzou	tzou	NOUN
fumecheng-7253	20	1	[	[	X
fumecheng-7253	20	2	2	2	NUM
fumecheng-7253	20	3	-	-	SYM
fumecheng-7253	20	4	4	4	NUM
fumecheng-7253	20	5	]	]	PUNCT
fumecheng-7253	20	6	is	be	AUX
fumecheng-7253	20	7	of	of	ADP
fumecheng-7253	20	8	great	great	ADJ
fumecheng-7253	20	9	interest	interest	NOUN
fumecheng-7253	20	10	to	to	ADP
fumecheng-7253	20	11	the	the	DET
fumecheng-7253	20	12	researchers	researcher	NOUN
fumecheng-7253	20	13	in	in	ADP
fumecheng-7253	20	14	the	the	DET
fumecheng-7253	20	15	field	field	NOUN
fumecheng-7253	20	16	.	.	PUNCT
fumecheng-7253	21	1	in	in	ADP
fumecheng-7253	21	2	this	this	DET
fumecheng-7253	21	3	model	model	NOUN
fumecheng-7253	21	4	,	,	PUNCT
fumecheng-7253	21	5	tzou	tzou	NOUN
fumecheng-7253	21	6	introduced	introduce	VERB
fumecheng-7253	21	7	thermal	thermal	ADJ
fumecheng-7253	21	8	heat	heat	NOUN
fumecheng-7253	21	9	conduction	conduction	NOUN
fumecheng-7253	21	10	model	model	NOUN
fumecheng-7253	21	11	with	with	ADP
fumecheng-7253	21	12	dual	dual	ADJ
fumecheng-7253	21	13	-	-	PUNCT
fumecheng-7253	21	14	phase	phase	NOUN
fumecheng-7253	21	15	lag	lag	NOUN
fumecheng-7253	21	16	(	(	PUNCT
fumecheng-7253	21	17	dpl	dpl	NOUN
fumecheng-7253	21	18	)	)	PUNCT
fumecheng-7253	21	19	to	to	PART
fumecheng-7253	21	20	include	include	VERB
fumecheng-7253	21	21	the	the	DET
fumecheng-7253	21	22	effects	effect	NOUN
fumecheng-7253	21	23	of	of	ADP
fumecheng-7253	21	24	microscopic	microscopic	ADJ
fumecheng-7253	21	25	reactions	reaction	NOUN
fumecheng-7253	21	26	in	in	ADP
fumecheng-7253	21	27	the	the	DET
fumecheng-7253	21	28	rapid	rapid	ADJ
fumecheng-7253	21	29	transit	transit	NOUN
fumecheng-7253	21	30	of	of	ADP
fumecheng-7253	21	31	heat	heat	NOUN
fumecheng-7253	21	32	transfer	transfer	NOUN
fumecheng-7253	21	33	mechanism	mechanism	NOUN
fumecheng-7253	21	34	into	into	ADP
fumecheng-7253	21	35	a	a	DET
fumecheng-7253	21	36	microscopic	microscopic	ADJ
fumecheng-7253	21	37	formula	formula	NOUN
fumecheng-7253	21	38	.	.	PUNCT
fumecheng-7253	22	1	in	in	ADP
fumecheng-7253	22	2	the	the	DET
fumecheng-7253	22	3	constitutive	constitutive	ADJ
fumecheng-7253	22	4	relationship	relationship	NOUN
fumecheng-7253	22	5	between	between	ADP
fumecheng-7253	22	6	the	the	DET
fumecheng-7253	22	7	temperature	temperature	NOUN
fumecheng-7253	22	8	gradient	gradient	NOUN
fumecheng-7253	22	9	and	and	CCONJ
fumecheng-7253	22	10	heat	heat	NOUN
fumecheng-7253	22	11	flux	flux	NOUN
fumecheng-7253	22	12	,	,	PUNCT
fumecheng-7253	22	13	two	two	NUM
fumecheng-7253	22	14	different	different	ADJ
fumecheng-7253	22	15	phase	phase	NOUN
fumecheng-7253	22	16	-	-	PUNCT
fumecheng-7253	22	17	lags	lag	NOUN
fumecheng-7253	22	18	have	have	AUX
fumecheng-7253	22	19	been	be	AUX
fumecheng-7253	22	20	introduced	introduce	VERB
fumecheng-7253	22	21	.	.	PUNCT
fumecheng-7253	23	1	many	many	ADJ
fumecheng-7253	23	2	efforts	effort	NOUN
fumecheng-7253	23	3	were	be	AUX
fumecheng-7253	23	4	made	make	VERB
fumecheng-7253	23	5	to	to	PART
fumecheng-7253	23	6	overcome	overcome	VERB
fumecheng-7253	23	7	the	the	DET
fumecheng-7253	23	8	problem	problem	NOUN
fumecheng-7253	23	9	of	of	ADP
fumecheng-7253	23	10	unlimited	unlimited	ADJ
fumecheng-7253	23	11	speeds	speed	NOUN
fumecheng-7253	23	12	of	of	ADP
fumecheng-7253	23	13	heat	heat	NOUN
fumecheng-7253	23	14	waves	wave	NOUN
fumecheng-7253	23	15	predicted	predict	VERB
fumecheng-7253	23	16	by	by	ADP
fumecheng-7253	23	17	the	the	DET
fumecheng-7253	23	18	classical	classical	ADJ
fumecheng-7253	23	19	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	23	20	theory	theory	NOUN
fumecheng-7253	23	21	[	[	X
fumecheng-7253	23	22	5	5	NUM
fumecheng-7253	23	23	-	-	SYM
fumecheng-7253	23	24	8	8	NUM
fumecheng-7253	23	25	]	]	PUNCT
fumecheng-7253	23	26	.	.	PUNCT
fumecheng-7253	24	1	at	at	ADP
fumecheng-7253	24	2	high	high	ADJ
fumecheng-7253	24	3	operating	operating	NOUN
fumecheng-7253	24	4	temperatures	temperature	NOUN
fumecheng-7253	24	5	,	,	PUNCT
fumecheng-7253	24	6	thermal	thermal	ADJ
fumecheng-7253	24	7	conductivity	conductivity	NOUN
fumecheng-7253	24	8	becomes	become	VERB
fumecheng-7253	24	9	more	more	ADV
fumecheng-7253	24	10	significant	significant	ADJ
fumecheng-7253	24	11	in	in	ADP
fumecheng-7253	24	12	popular	popular	ADJ
fumecheng-7253	24	13	areas	area	NOUN
fumecheng-7253	24	14	such	such	ADJ
fumecheng-7253	24	15	as	as	ADP
fumecheng-7253	24	16	materials	material	NOUN
fumecheng-7253	24	17	science	science	NOUN
fumecheng-7253	24	18	,	,	PUNCT
fumecheng-7253	24	19	electronics	electronics	NOUN
fumecheng-7253	24	20	and	and	CCONJ
fumecheng-7253	24	21	building	building	NOUN
fumecheng-7253	24	22	insulation	insulation	NOUN
fumecheng-7253	24	23	.	.	PUNCT
fumecheng-7253	25	1	temperature	temperature	NOUN
fumecheng-7253	25	2	has	have	VERB
fumecheng-7253	25	3	a	a	DET
fumecheng-7253	25	4	distinctive	distinctive	ADJ
fumecheng-7253	25	5	impact	impact	NOUN
fumecheng-7253	25	6	on	on	ADP
fumecheng-7253	25	7	thermal	thermal	ADJ
fumecheng-7253	25	8	conductivity	conductivity	NOUN
fumecheng-7253	25	9	of	of	ADP
fumecheng-7253	25	10	metals	metal	NOUN
fumecheng-7253	25	11	and	and	CCONJ
fumecheng-7253	25	12	non	non	ADJ
fumecheng-7253	25	13	-	-	ADJ
fumecheng-7253	25	14	metal	metal	ADJ
fumecheng-7253	25	15	materials	material	NOUN
fumecheng-7253	25	16	.	.	PUNCT
fumecheng-7253	26	1	thermal	thermal	ADJ
fumecheng-7253	26	2	conductivity	conductivity	NOUN
fumecheng-7253	26	3	in	in	ADP
fumecheng-7253	26	4	physics	physics	NOUN
fumecheng-7253	26	5	is	be	AUX
fumecheng-7253	26	6	defined	define	VERB
fumecheng-7253	26	7	as	as	ADP
fumecheng-7253	26	8	the	the	DET
fumecheng-7253	26	9	capacity	capacity	NOUN
fumecheng-7253	26	10	of	of	ADP
fumecheng-7253	26	11	materials	material	NOUN
fumecheng-7253	26	12	for	for	ADP
fumecheng-7253	26	13	heat	heat	NOUN
fumecheng-7253	26	14	transfer	transfer	NOUN
fumecheng-7253	26	15	.	.	PUNCT
fumecheng-7253	27	1	this	this	PRON
fumecheng-7253	27	2	specifically	specifically	ADV
fumecheng-7253	27	3	occurs	occur	VERB
fumecheng-7253	27	4	in	in	ADP
fumecheng-7253	27	5	the	the	DET
fumecheng-7253	27	6	fourier	fourier	NOUN
fumecheng-7253	27	7	's	's	PART
fumecheng-7253	27	8	heat	heat	NOUN
fumecheng-7253	27	9	conduction	conduction	NOUN
fumecheng-7253	27	10	theory	theory	NOUN
fumecheng-7253	27	11	.	.	PUNCT
fumecheng-7253	28	1	it	it	PRON
fumecheng-7253	28	2	was	be	AUX
fumecheng-7253	28	3	demonstrated	demonstrate	VERB
fumecheng-7253	28	4	through	through	ADP
fumecheng-7253	28	5	practical	practical	ADJ
fumecheng-7253	28	6	experiments	experiment	NOUN
fumecheng-7253	28	7	that	that	SCONJ
fumecheng-7253	28	8	as	as	ADP
fumecheng-7253	28	9	temperature	temperature	NOUN
fumecheng-7253	28	10	rises	rise	NOUN
fumecheng-7253	28	11	,	,	PUNCT
fumecheng-7253	28	12	thermal	thermal	ADJ
fumecheng-7253	28	13	conductivity	conductivity	NOUN
fumecheng-7253	28	14	of	of	ADP
fumecheng-7253	28	15	pure	pure	ADJ
fumecheng-7253	28	16	metals	metal	NOUN
fumecheng-7253	28	17	decreases	decrease	NOUN
fumecheng-7253	28	18	.	.	PUNCT
fumecheng-7253	29	1	in	in	ADP
fumecheng-7253	29	2	alloys	alloy	NOUN
fumecheng-7253	29	3	,	,	PUNCT
fumecheng-7253	29	4	any	any	DET
fumecheng-7253	29	5	rise	rise	NOUN
fumecheng-7253	29	6	in	in	ADP
fumecheng-7253	29	7	temperature	temperature	NOUN
fumecheng-7253	29	8	results	result	NOUN
fumecheng-7253	29	9	in	in	ADP
fumecheng-7253	29	10	increasing	increase	VERB
fumecheng-7253	29	11	thermal	thermal	ADJ
fumecheng-7253	29	12	conductivity	conductivity	NOUN
fumecheng-7253	29	13	,	,	PUNCT
fumecheng-7253	29	14	and	and	CCONJ
fumecheng-7253	29	15	generally	generally	ADV
fumecheng-7253	29	16	,	,	PUNCT
fumecheng-7253	29	17	the	the	DET
fumecheng-7253	29	18	variation	variation	NOUN
fumecheng-7253	29	19	of	of	ADP
fumecheng-7253	29	20	electrical	electrical	ADJ
fumecheng-7253	29	21	conductivity	conductivity	NOUN
fumecheng-7253	29	22	is	be	AUX
fumecheng-7253	29	23	smaller	small	ADJ
fumecheng-7253	29	24	than	than	ADP
fumecheng-7253	29	25	that	that	PRON
fumecheng-7253	29	26	for	for	ADP
fumecheng-7253	29	27	temperature	temperature	NOUN
fumecheng-7253	29	28	[	[	X
fumecheng-7253	29	29	9	9	NUM
fumecheng-7253	29	30	]	]	PUNCT
fumecheng-7253	29	31	.	.	PUNCT
fumecheng-7253	30	1	the	the	DET
fumecheng-7253	30	2	rapid	rapid	ADJ
fumecheng-7253	30	3	development	development	NOUN
fumecheng-7253	30	4	in	in	ADP
fumecheng-7253	30	5	micro	micro	ADJ
fumecheng-7253	30	6	-	-	ADJ
fumecheng-7253	30	7	electromechanical	electromechanical	ADJ
fumecheng-7253	30	8	systems	system	NOUN
fumecheng-7253	30	9	(	(	PUNCT
fumecheng-7253	30	10	mems	mem	NOUN
fumecheng-7253	30	11	)	)	PUNCT
fumecheng-7253	30	12	led	lead	VERB
fumecheng-7253	30	13	to	to	ADP
fumecheng-7253	30	14	more	more	ADV
fumecheng-7253	30	15	complex	complex	ADJ
fumecheng-7253	30	16	sensors	sensor	NOUN
fumecheng-7253	30	17	and	and	CCONJ
fumecheng-7253	30	18	electronic	electronic	ADJ
fumecheng-7253	30	19	devices	device	NOUN
fumecheng-7253	30	20	.	.	PUNCT
fumecheng-7253	31	1	in	in	ADP
fumecheng-7253	31	2	order	order	NOUN
fumecheng-7253	31	3	to	to	PART
fumecheng-7253	31	4	satisfy	satisfy	VERB
fumecheng-7253	31	5	the	the	DET
fumecheng-7253	31	6	industrial	industrial	ADJ
fumecheng-7253	31	7	requirements	requirement	NOUN
fumecheng-7253	31	8	,	,	PUNCT
fumecheng-7253	31	9	new	new	ADJ
fumecheng-7253	31	10	technologies	technology	NOUN
fumecheng-7253	31	11	have	have	AUX
fumecheng-7253	31	12	been	be	AUX
fumecheng-7253	31	13	exploited	exploit	VERB
fumecheng-7253	31	14	to	to	PART
fumecheng-7253	31	15	design	design	VERB
fumecheng-7253	31	16	high	high	ADJ
fumecheng-7253	31	17	-	-	PUNCT
fumecheng-7253	31	18	tech	tech	NOUN
fumecheng-7253	31	19	mems	mem	NOUN
fumecheng-7253	31	20	products	product	NOUN
fumecheng-7253	31	21	.	.	PUNCT
fumecheng-7253	32	1	mems	mem	NOUN
fumecheng-7253	32	2	structures	structure	NOUN
fumecheng-7253	32	3	include	include	VERB
fumecheng-7253	32	4	mechanical	mechanical	ADJ
fumecheng-7253	32	5	components	component	NOUN
fumecheng-7253	32	6	,	,	PUNCT
fumecheng-7253	32	7	e.g.	e.g.	ADV
fumecheng-7253	32	8	small	small	ADJ
fumecheng-7253	32	9	cantilevers	cantilever	NOUN
fumecheng-7253	32	10	,	,	PUNCT
fumecheng-7253	32	11	extensions	extension	NOUN
fumecheng-7253	32	12	and	and	CCONJ
fumecheng-7253	32	13	films	film	NOUN
fumecheng-7253	32	14	that	that	PRON
fumecheng-7253	32	15	have	have	AUX
fumecheng-7253	32	16	been	be	AUX
fumecheng-7253	32	17	frequently	frequently	ADV
fumecheng-7253	32	18	filled	fill	VERB
fumecheng-7253	32	19	with	with	ADP
fumecheng-7253	32	20	a	a	DET
fumecheng-7253	32	21	variety	variety	NOUN
fumecheng-7253	32	22	of	of	ADP
fumecheng-7253	32	23	geometrical	geometrical	ADJ
fumecheng-7253	32	24	measurements	measurement	NOUN
fumecheng-7253	32	25	and	and	CCONJ
fumecheng-7253	32	26	arrangements	arrangement	NOUN
fumecheng-7253	32	27	[	[	X
fumecheng-7253	32	28	10	10	NUM
fumecheng-7253	32	29	]	]	PUNCT
fumecheng-7253	32	30	.	.	PUNCT
fumecheng-7253	33	1	the	the	DET
fumecheng-7253	33	2	influences	influence	NOUN
fumecheng-7253	33	3	of	of	ADP
fumecheng-7253	33	4	small	small	ADJ
fumecheng-7253	33	5	-	-	PUNCT
fumecheng-7253	33	6	scale	scale	NOUN
fumecheng-7253	33	7	interactions	interaction	NOUN
fumecheng-7253	33	8	between	between	ADP
fumecheng-7253	33	9	the	the	DET
fumecheng-7253	33	10	neighboring	neighboring	NOUN
fumecheng-7253	33	11	material	material	NOUN
fumecheng-7253	33	12	particles	particle	NOUN
fumecheng-7253	33	13	or	or	CCONJ
fumecheng-7253	33	14	constituents	constituent	NOUN
fumecheng-7253	33	15	must	must	AUX
fumecheng-7253	33	16	be	be	AUX
fumecheng-7253	33	17	taken	take	VERB
fumecheng-7253	33	18	into	into	ADP
fumecheng-7253	33	19	account	account	NOUN
fumecheng-7253	33	20	for	for	ADP
fumecheng-7253	33	21	these	these	DET
fumecheng-7253	33	22	micro	micro	ADJ
fumecheng-7253	33	23	/	/	SYM
fumecheng-7253	33	24	nano	nano	NOUN
fumecheng-7253	33	25	-	-	PUNCT
fumecheng-7253	33	26	structures	structure	NOUN
fumecheng-7253	33	27	.	.	PUNCT
fumecheng-7253	34	1	this	this	DET
fumecheng-7253	34	2	effect	effect	NOUN
fumecheng-7253	34	3	can	can	AUX
fumecheng-7253	34	4	be	be	AUX
fumecheng-7253	34	5	observed	observe	VERB
fumecheng-7253	34	6	in	in	ADP
fumecheng-7253	34	7	miniaturized	miniaturize	VERB
fumecheng-7253	34	8	sub	sub	ADJ
fumecheng-7253	34	9	-	-	ADJ
fumecheng-7253	34	10	micron	micron	ADJ
fumecheng-7253	34	11	systems	system	NOUN
fumecheng-7253	34	12	like	like	ADP
fumecheng-7253	34	13	nano	nano	NOUN
fumecheng-7253	34	14	-	-	PUNCT
fumecheng-7253	34	15	actuators	actuator	NOUN
fumecheng-7253	34	16	and	and	CCONJ
fumecheng-7253	34	17	nano	nano	NOUN
fumecheng-7253	34	18	-	-	NOUN
fumecheng-7253	34	19	sensors	sensor	NOUN
fumecheng-7253	34	20	,	,	PUNCT
fumecheng-7253	34	21	microscopes	microscope	NOUN
fumecheng-7253	34	22	and	and	CCONJ
fumecheng-7253	34	23	micro	micro	NOUN
fumecheng-7253	34	24	/	/	SYM
fumecheng-7253	34	25	nano	nano	NOUN
fumecheng-7253	34	26	-	-	PUNCT
fumecheng-7253	34	27	electronic	electronic	ADJ
fumecheng-7253	34	28	systems	system	NOUN
fumecheng-7253	34	29	.	.	PUNCT
fumecheng-7253	35	1	it	it	PRON
fumecheng-7253	35	2	is	be	AUX
fumecheng-7253	35	3	important	important	ADJ
fumecheng-7253	35	4	for	for	SCONJ
fumecheng-7253	35	5	designers	designer	NOUN
fumecheng-7253	35	6	and	and	CCONJ
fumecheng-7253	35	7	engineers	engineer	NOUN
fumecheng-7253	35	8	to	to	PART
fumecheng-7253	35	9	discover	discover	VERB
fumecheng-7253	35	10	the	the	DET
fumecheng-7253	35	11	accurate	accurate	ADJ
fumecheng-7253	35	12	thermomechanical	thermomechanical	ADJ
fumecheng-7253	35	13	features	feature	NOUN
fumecheng-7253	35	14	of	of	ADP
fumecheng-7253	35	15	ultra	ultra	ADJ
fumecheng-7253	35	16	-	-	ADJ
fumecheng-7253	35	17	high	high	ADJ
fumecheng-7253	35	18	sensitive	sensitive	ADJ
fumecheng-7253	35	19	devices	device	NOUN
fumecheng-7253	35	20	in	in	ADP
fumecheng-7253	35	21	order	order	NOUN
fumecheng-7253	35	22	to	to	PART
fumecheng-7253	35	23	attain	attain	VERB
fumecheng-7253	35	24	the	the	DET
fumecheng-7253	35	25	true	true	ADJ
fumecheng-7253	35	26	aim	aim	NOUN
fumecheng-7253	35	27	of	of	ADP
fumecheng-7253	35	28	providing	provide	VERB
fumecheng-7253	35	29	for	for	ADP
fumecheng-7253	35	30	the	the	DET
fumecheng-7253	35	31	measure	measure	NOUN
fumecheng-7253	35	32	of	of	ADP
fumecheng-7253	35	33	diversion	diversion	NOUN
fumecheng-7253	35	34	from	from	ADP
fumecheng-7253	35	35	associated	associated	ADJ
fumecheng-7253	35	36	loads	load	NOUN
fumecheng-7253	35	37	in	in	ADP
fumecheng-7253	35	38	order	order	NOUN
fumecheng-7253	35	39	to	to	PART
fumecheng-7253	35	40	forestall	forestall	VERB
fumecheng-7253	35	41	cracks	crack	NOUN
fumecheng-7253	35	42	,	,	PUNCT
fumecheng-7253	35	43	improve	improve	VERB
fumecheng-7253	35	44	the	the	DET
fumecheng-7253	35	45	execution	execution	NOUN
fumecheng-7253	35	46	and	and	CCONJ
fumecheng-7253	35	47	produce	produce	VERB
fumecheng-7253	35	48	the	the	DET
fumecheng-7253	35	49	suitable	suitable	ADJ
fumecheng-7253	35	50	lifetime	lifetime	NOUN
fumecheng-7253	35	51	for	for	ADP
fumecheng-7253	35	52	mems	mem	NOUN
fumecheng-7253	35	53	devices	device	NOUN
fumecheng-7253	35	54	[	[	X
fumecheng-7253	35	55	11	11	NUM
fumecheng-7253	35	56	]	]	PUNCT
fumecheng-7253	35	57	.	.	PUNCT
fumecheng-7253	36	1	from	from	ADP
fumecheng-7253	36	2	the	the	DET
fumecheng-7253	36	3	discussion	discussion	NOUN
fumecheng-7253	36	4	above	above	ADV
fumecheng-7253	36	5	,	,	PUNCT
fumecheng-7253	36	6	the	the	DET
fumecheng-7253	36	7	principle	principle	NOUN
fumecheng-7253	36	8	of	of	ADP
fumecheng-7253	36	9	vibration	vibration	NOUN
fumecheng-7253	36	10	is	be	AUX
fumecheng-7253	36	11	well	well	ADV
fumecheng-7253	36	12	-	-	PUNCT
fumecheng-7253	36	13	known	know	VERB
fumecheng-7253	36	14	and	and	CCONJ
fumecheng-7253	36	15	well	well	ADV
fumecheng-7253	36	16	-	-	PUNCT
fumecheng-7253	36	17	studied	study	VERB
fumecheng-7253	36	18	in	in	ADP
fumecheng-7253	36	19	dual	dual	ADJ
fumecheng-7253	36	20	beam	beam	NOUN
fumecheng-7253	36	21	systems	system	NOUN
fumecheng-7253	36	22	.	.	PUNCT
fumecheng-7253	37	1	nevertheless	nevertheless	ADV
fumecheng-7253	37	2	,	,	PUNCT
fumecheng-7253	37	3	the	the	DET
fumecheng-7253	37	4	scale	scale	NOUN
fumecheng-7253	37	5	-	-	PUNCT
fumecheng-7253	37	6	dependent	dependent	ADJ
fumecheng-7253	37	7	vibration	vibration	NOUN
fumecheng-7253	37	8	of	of	ADP
fumecheng-7253	37	9	beam	beam	NOUN
fumecheng-7253	37	10	systems	system	NOUN
fumecheng-7253	37	11	makes	make	VERB
fumecheng-7253	37	12	few	few	ADJ
fumecheng-7253	37	13	contributions	contribution	NOUN
fumecheng-7253	37	14	.	.	PUNCT
fumecheng-7253	38	1	the	the	DET
fumecheng-7253	38	2	structures	structure	NOUN
fumecheng-7253	38	3	of	of	ADP
fumecheng-7253	38	4	scale	scale	NOUN
fumecheng-7253	38	5	-	-	PUNCT
fumecheng-7253	38	6	dependent	dependent	ADJ
fumecheng-7253	38	7	nanobeams	nanobeam	NOUN
fumecheng-7253	38	8	are	be	AUX
fumecheng-7253	38	9	constructed	construct	VERB
fumecheng-7253	38	10	from	from	ADP
fumecheng-7253	38	11	nano	nano	NOUN
fumecheng-7253	38	12	-	-	PUNCT
fumecheng-7253	38	13	materials	material	NOUN
fumecheng-7253	38	14	with	with	ADP
fumecheng-7253	38	15	special	special	ADJ
fumecheng-7253	38	16	properties	property	NOUN
fumecheng-7253	38	17	because	because	SCONJ
fumecheng-7253	38	18	of	of	ADP
fumecheng-7253	38	19	their	their	PRON
fumecheng-7253	38	20	dimensions	dimension	NOUN
fumecheng-7253	38	21	at	at	ADP
fumecheng-7253	38	22	the	the	DET
fumecheng-7253	38	23	nanoscale	nanoscale	NOUN
fumecheng-7253	38	24	.	.	PUNCT
fumecheng-7253	39	1	temperature	temperature	NOUN
fumecheng-7253	39	2	-	-	PUNCT
fumecheng-7253	39	3	dependent	dependent	ADJ
fumecheng-7253	39	4	physical	physical	ADJ
fumecheng-7253	39	5	characteristics	characteristic	NOUN
fumecheng-7253	39	6	of	of	ADP
fumecheng-7253	39	7	rotating	rotate	VERB
fumecheng-7253	39	8	nonlocal	nonlocal	ADJ
fumecheng-7253	39	9	nanobeams	nanobeam	NOUN
fumecheng-7253	39	10	subject	subject	ADJ
fumecheng-7253	39	11	to	to	ADP
fumecheng-7253	39	12	...	...	PUNCT
fumecheng-7253	39	13	635	635	NUM
fumecheng-7253	39	14	nanoparticles	nanoparticle	NOUN
fumecheng-7253	39	15	,	,	PUNCT
fumecheng-7253	39	16	nanowires	nanowire	NOUN
fumecheng-7253	39	17	and	and	CCONJ
fumecheng-7253	39	18	nanotubes	nanotube	NOUN
fumecheng-7253	39	19	are	be	AUX
fumecheng-7253	39	20	common	common	ADJ
fumecheng-7253	39	21	examples	example	NOUN
fumecheng-7253	39	22	of	of	ADP
fumecheng-7253	39	23	the	the	DET
fumecheng-7253	39	24	materials	material	NOUN
fumecheng-7253	39	25	with	with	ADP
fumecheng-7253	39	26	attractive	attractive	ADJ
fumecheng-7253	39	27	features	feature	NOUN
fumecheng-7253	39	28	in	in	ADP
fumecheng-7253	39	29	sub	sub	ADJ
fumecheng-7253	39	30	-	-	ADJ
fumecheng-7253	39	31	micron	micron	ADJ
fumecheng-7253	39	32	scales	scale	NOUN
fumecheng-7253	39	33	[	[	X
fumecheng-7253	39	34	12	12	NUM
fumecheng-7253	39	35	]	]	PUNCT
fumecheng-7253	39	36	.	.	PUNCT
fumecheng-7253	40	1	nanomaterials	nanomaterial	NOUN
fumecheng-7253	40	2	are	be	AUX
fumecheng-7253	40	3	the	the	DET
fumecheng-7253	40	4	base	base	ADJ
fumecheng-7253	40	5	choices	choice	NOUN
fumecheng-7253	40	6	of	of	ADP
fumecheng-7253	40	7	technological	technological	ADJ
fumecheng-7253	40	8	products	product	NOUN
fumecheng-7253	40	9	for	for	ADP
fumecheng-7253	40	10	the	the	DET
fumecheng-7253	40	11	next	next	ADJ
fumecheng-7253	40	12	century	century	NOUN
fumecheng-7253	40	13	and	and	CCONJ
fumecheng-7253	40	14	have	have	AUX
fumecheng-7253	40	15	intensified	intensify	VERB
fumecheng-7253	40	16	the	the	DET
fumecheng-7253	40	17	interest	interest	NOUN
fumecheng-7253	40	18	of	of	ADP
fumecheng-7253	40	19	the	the	DET
fumecheng-7253	40	20	scientific	scientific	ADJ
fumecheng-7253	40	21	community	community	NOUN
fumecheng-7253	40	22	in	in	ADP
fumecheng-7253	40	23	advanced	advanced	ADJ
fumecheng-7253	40	24	physics	physics	NOUN
fumecheng-7253	40	25	,	,	PUNCT
fumecheng-7253	40	26	chemistry	chemistry	NOUN
fumecheng-7253	40	27	,	,	PUNCT
fumecheng-7253	40	28	biomedicine	biomedicine	NOUN
fumecheng-7253	40	29	and	and	CCONJ
fumecheng-7253	40	30	different	different	ADJ
fumecheng-7253	40	31	branches	branch	NOUN
fumecheng-7253	40	32	of	of	ADP
fumecheng-7253	40	33	technological	technological	ADJ
fumecheng-7253	40	34	sciences	science	NOUN
fumecheng-7253	40	35	.	.	PUNCT
fumecheng-7253	41	1	from	from	ADP
fumecheng-7253	41	2	mechanical	mechanical	ADJ
fumecheng-7253	41	3	point	point	NOUN
fumecheng-7253	41	4	of	of	ADP
fumecheng-7253	41	5	view	view	NOUN
fumecheng-7253	41	6	,	,	PUNCT
fumecheng-7253	41	7	due	due	ADP
fumecheng-7253	41	8	to	to	ADP
fumecheng-7253	41	9	their	their	PRON
fumecheng-7253	41	10	sub	sub	ADJ
fumecheng-7253	41	11	-	-	ADJ
fumecheng-7253	41	12	micron	micron	ADJ
fumecheng-7253	41	13	dimensions	dimension	NOUN
fumecheng-7253	41	14	,	,	PUNCT
fumecheng-7253	41	15	the	the	DET
fumecheng-7253	41	16	impact	impact	NOUN
fumecheng-7253	41	17	of	of	ADP
fumecheng-7253	41	18	small	small	ADJ
fumecheng-7253	41	19	-	-	PUNCT
fumecheng-7253	41	20	scale	scale	NOUN
fumecheng-7253	41	21	exhibits	exhibit	VERB
fumecheng-7253	41	22	significant	significant	ADJ
fumecheng-7253	41	23	features	feature	NOUN
fumecheng-7253	41	24	resulting	result	VERB
fumecheng-7253	41	25	from	from	ADP
fumecheng-7253	41	26	the	the	DET
fumecheng-7253	41	27	measurements	measurement	NOUN
fumecheng-7253	41	28	of	of	ADP
fumecheng-7253	41	29	atomic	atomic	ADJ
fumecheng-7253	41	30	fission	fission	NOUN
fumecheng-7253	41	31	.	.	PUNCT
fumecheng-7253	42	1	the	the	DET
fumecheng-7253	42	2	strength	strength	NOUN
fumecheng-7253	42	3	of	of	ADP
fumecheng-7253	42	4	the	the	DET
fumecheng-7253	42	5	mechanical	mechanical	ADJ
fumecheng-7253	42	6	piezomagnetic	piezomagnetic	ADJ
fumecheng-7253	42	7	nanosized	nanosized	ADJ
fumecheng-7253	42	8	sensors	sensor	NOUN
fumecheng-7253	42	9	was	be	AUX
fumecheng-7253	42	10	studied	study	VERB
fumecheng-7253	42	11	in	in	ADP
fumecheng-7253	42	12	post	post	ADJ
fumecheng-7253	42	13	-	-	ADJ
fumecheng-7253	42	14	buckling	buckling	ADJ
fumecheng-7253	42	15	state	state	NOUN
fumecheng-7253	42	16	by	by	ADP
fumecheng-7253	42	17	malikanet	malikanet	PROPN
fumecheng-7253	42	18	al	al	PROPN
fumecheng-7253	42	19	.	.	PUNCT
fumecheng-7253	43	1	[	[	X
fumecheng-7253	43	2	13	13	NUM
fumecheng-7253	43	3	]	]	PUNCT
fumecheng-7253	43	4	.	.	PUNCT
fumecheng-7253	44	1	a	a	DET
fumecheng-7253	44	2	powerful	powerful	ADJ
fumecheng-7253	44	3	flexomagnetic	flexomagnetic	ADJ
fumecheng-7253	44	4	characteristic	characteristic	NOUN
fumecheng-7253	44	5	is	be	AUX
fumecheng-7253	44	6	also	also	ADV
fumecheng-7253	44	7	considered	consider	VERB
fumecheng-7253	44	8	in	in	ADP
fumecheng-7253	44	9	this	this	DET
fumecheng-7253	44	10	research	research	NOUN
fumecheng-7253	44	11	.	.	PUNCT
fumecheng-7253	45	1	furthermore	furthermore	ADV
fumecheng-7253	45	2	,	,	PUNCT
fumecheng-7253	45	3	as	as	ADP
fumecheng-7253	45	4	a	a	DET
fumecheng-7253	45	5	result	result	NOUN
fumecheng-7253	45	6	of	of	ADP
fumecheng-7253	45	7	the	the	DET
fumecheng-7253	45	8	flexomagnetic	flexomagnetic	ADJ
fumecheng-7253	45	9	effects	effect	NOUN
fumecheng-7253	45	10	,	,	PUNCT
fumecheng-7253	45	11	the	the	DET
fumecheng-7253	45	12	stability	stability	NOUN
fumecheng-7253	45	13	of	of	ADP
fumecheng-7253	45	14	the	the	DET
fumecheng-7253	45	15	euler	euler	NOUN
fumecheng-7253	45	16	-	-	PUNCT
fumecheng-7253	45	17	bernoulli	bernoulli	PROPN
fumecheng-7253	45	18	porous	porous	ADJ
fumecheng-7253	45	19	nanobeam	nanobeam	NOUN
fumecheng-7253	45	20	was	be	AUX
fumecheng-7253	45	21	thoroughly	thoroughly	ADV
fumecheng-7253	45	22	investigated	investigate	VERB
fumecheng-7253	45	23	by	by	ADP
fumecheng-7253	45	24	malikan	malikan	PROPN
fumecheng-7253	45	25	et	et	PROPN
fumecheng-7253	45	26	al	al	PROPN
fumecheng-7253	45	27	.	.	PUNCT
fumecheng-7253	46	1	[	[	X
fumecheng-7253	46	2	14	14	NUM
fumecheng-7253	46	3	]	]	PUNCT
fumecheng-7253	46	4	.	.	PUNCT
fumecheng-7253	47	1	the	the	DET
fumecheng-7253	47	2	magnetization	magnetization	NOUN
fumecheng-7253	47	3	with	with	ADP
fumecheng-7253	47	4	strain	strain	ADJ
fumecheng-7253	47	5	gradients	gradient	NOUN
fumecheng-7253	47	6	is	be	AUX
fumecheng-7253	47	7	related	relate	VERB
fumecheng-7253	47	8	to	to	ADP
fumecheng-7253	47	9	the	the	DET
fumecheng-7253	47	10	flexomagnetics	flexomagnetic	NOUN
fumecheng-7253	47	11	.	.	PUNCT
fumecheng-7253	48	1	malikan	malikan	PROPN
fumecheng-7253	48	2	et	et	PROPN
fumecheng-7253	48	3	al	al	PROPN
fumecheng-7253	48	4	.	.	PUNCT
fumecheng-7253	49	1	[	[	X
fumecheng-7253	49	2	15	15	NUM
fumecheng-7253	49	3	]	]	PUNCT
fumecheng-7253	49	4	created	create	VERB
fumecheng-7253	49	5	an	an	DET
fumecheng-7253	49	6	euler	euler	VERB
fumecheng-7253	49	7	-	-	PUNCT
fumecheng-7253	49	8	bernoulli	bernoulli	PROPN
fumecheng-7253	49	9	beam	beam	NOUN
fumecheng-7253	49	10	model	model	NOUN
fumecheng-7253	49	11	incorporating	incorporate	VERB
fumecheng-7253	49	12	the	the	DET
fumecheng-7253	49	13	combination	combination	NOUN
fumecheng-7253	49	14	of	of	ADP
fumecheng-7253	49	15	piezomagnetic	piezomagnetic	ADJ
fumecheng-7253	49	16	-	-	PUNCT
fumecheng-7253	49	17	flexomagnetic	flexomagnetic	ADJ
fumecheng-7253	49	18	properties	property	NOUN
fumecheng-7253	49	19	and	and	CCONJ
fumecheng-7253	49	20	small	small	ADJ
fumecheng-7253	49	21	-	-	PUNCT
fumecheng-7253	49	22	scale	scale	NOUN
fumecheng-7253	49	23	effects	effect	NOUN
fumecheng-7253	49	24	.	.	PUNCT
fumecheng-7253	50	1	flexoelectricity	flexoelectricity	NOUN
fumecheng-7253	50	2	was	be	AUX
fumecheng-7253	50	3	also	also	ADV
fumecheng-7253	50	4	studied	study	VERB
fumecheng-7253	50	5	for	for	ADP
fumecheng-7253	50	6	a	a	DET
fumecheng-7253	50	7	piezoelectric	piezoelectric	ADJ
fumecheng-7253	50	8	nanobeam	nanobeam	NOUN
fumecheng-7253	50	9	by	by	ADP
fumecheng-7253	50	10	considering	consider	VERB
fumecheng-7253	50	11	the	the	DET
fumecheng-7253	50	12	internal	internal	ADJ
fumecheng-7253	50	13	viscoelasticity	viscoelasticity	NOUN
fumecheng-7253	50	14	[	[	X
fumecheng-7253	50	15	16	16	NUM
fumecheng-7253	50	16	]	]	PUNCT
fumecheng-7253	50	17	.	.	PUNCT
fumecheng-7253	51	1	as	as	SCONJ
fumecheng-7253	51	2	mentioned	mention	VERB
fumecheng-7253	51	3	earlier	early	ADV
fumecheng-7253	51	4	,	,	PUNCT
fumecheng-7253	51	5	the	the	DET
fumecheng-7253	51	6	size	size	NOUN
fumecheng-7253	51	7	effect	effect	NOUN
fumecheng-7253	51	8	has	have	VERB
fumecheng-7253	51	9	a	a	DET
fumecheng-7253	51	10	great	great	ADJ
fumecheng-7253	51	11	contribution	contribution	NOUN
fumecheng-7253	51	12	in	in	ADP
fumecheng-7253	51	13	the	the	DET
fumecheng-7253	51	14	static	static	ADJ
fumecheng-7253	51	15	and	and	CCONJ
fumecheng-7253	51	16	dynamic	dynamic	ADJ
fumecheng-7253	51	17	behavior	behavior	NOUN
fumecheng-7253	51	18	of	of	ADP
fumecheng-7253	51	19	micro	micro	PROPN
fumecheng-7253	51	20	and	and	CCONJ
fumecheng-7253	51	21	nanoscale	nanoscale	NOUN
fumecheng-7253	51	22	structures	structure	NOUN
fumecheng-7253	51	23	and	and	CCONJ
fumecheng-7253	51	24	should	should	AUX
fumecheng-7253	51	25	not	not	PART
fumecheng-7253	51	26	be	be	AUX
fumecheng-7253	51	27	neglected	neglect	VERB
fumecheng-7253	51	28	,	,	PUNCT
fumecheng-7253	51	29	that	that	ADV
fumecheng-7253	51	30	is	is	ADV
fumecheng-7253	51	31	,	,	PUNCT
fumecheng-7253	51	32	the	the	DET
fumecheng-7253	51	33	classical	classical	ADJ
fumecheng-7253	51	34	continuum	continuum	ADJ
fumecheng-7253	51	35	mechanics	mechanic	NOUN
fumecheng-7253	51	36	at	at	ADP
fumecheng-7253	51	37	nanoscale	nanoscale	NOUN
fumecheng-7253	51	38	does	do	AUX
fumecheng-7253	51	39	not	not	PART
fumecheng-7253	51	40	make	make	VERB
fumecheng-7253	51	41	any	any	DET
fumecheng-7253	51	42	sense	sense	NOUN
fumecheng-7253	51	43	and	and	CCONJ
fumecheng-7253	51	44	must	must	AUX
fumecheng-7253	51	45	be	be	AUX
fumecheng-7253	51	46	modified	modify	VERB
fumecheng-7253	51	47	accordingly	accordingly	ADV
fumecheng-7253	51	48	.	.	PUNCT
fumecheng-7253	52	1	nanomaterials	nanomaterial	NOUN
fumecheng-7253	52	2	are	be	AUX
fumecheng-7253	52	3	used	use	VERB
fumecheng-7253	52	4	in	in	ADP
fumecheng-7253	52	5	complex	complex	ADJ
fumecheng-7253	52	6	nanoelectromechanical	nanoelectromechanical	ADJ
fumecheng-7253	52	7	systems	system	NOUN
fumecheng-7253	52	8	(	(	PUNCT
fumecheng-7253	52	9	nems	nem	NOUN
fumecheng-7253	52	10	)	)	PUNCT
fumecheng-7253	52	11	as	as	ADV
fumecheng-7253	52	12	well	well	ADV
fumecheng-7253	52	13	as	as	ADP
fumecheng-7253	52	14	nanocomposites	nanocomposite	NOUN
fumecheng-7253	52	15	due	due	ADP
fumecheng-7253	52	16	to	to	ADP
fumecheng-7253	52	17	their	their	PRON
fumecheng-7253	52	18	attractive	attractive	ADJ
fumecheng-7253	52	19	properties	property	NOUN
fumecheng-7253	52	20	.	.	PUNCT
fumecheng-7253	53	1	nanoscale	nanoscale	NOUN
fumecheng-7253	53	2	devices	device	NOUN
fumecheng-7253	53	3	are	be	AUX
fumecheng-7253	53	4	referred	refer	VERB
fumecheng-7253	53	5	to	to	ADP
fumecheng-7253	53	6	the	the	DET
fumecheng-7253	53	7	structures	structure	NOUN
fumecheng-7253	53	8	and	and	CCONJ
fumecheng-7253	53	9	systems	system	NOUN
fumecheng-7253	53	10	constructed	construct	VERB
fumecheng-7253	53	11	from	from	ADP
fumecheng-7253	53	12	nanosize	nanosize	NOUN
fumecheng-7253	53	13	materials	material	NOUN
fumecheng-7253	53	14	.	.	PUNCT
fumecheng-7253	54	1	the	the	DET
fumecheng-7253	54	2	smallscale	smallscale	ADJ
fumecheng-7253	54	3	impact	impact	NOUN
fumecheng-7253	54	4	in	in	ADP
fumecheng-7253	54	5	the	the	DET
fumecheng-7253	54	6	nonlocal	nonlocal	ADJ
fumecheng-7253	54	7	elasticity	elasticity	NOUN
fumecheng-7253	54	8	is	be	AUX
fumecheng-7253	54	9	defined	define	VERB
fumecheng-7253	54	10	by	by	ADP
fumecheng-7253	54	11	the	the	DET
fumecheng-7253	54	12	assumption	assumption	NOUN
fumecheng-7253	54	13	that	that	SCONJ
fumecheng-7253	54	14	stress	stress	NOUN
fumecheng-7253	54	15	vector	vector	NOUN
fumecheng-7253	54	16	is	be	AUX
fumecheng-7253	54	17	related	relate	VERB
fumecheng-7253	54	18	to	to	ADP
fumecheng-7253	54	19	the	the	DET
fumecheng-7253	54	20	entire	entire	ADJ
fumecheng-7253	54	21	strain	strain	NOUN
fumecheng-7253	54	22	field	field	NOUN
fumecheng-7253	54	23	of	of	ADP
fumecheng-7253	54	24	the	the	DET
fumecheng-7253	54	25	whole	whole	ADJ
fumecheng-7253	54	26	body	body	NOUN
fumecheng-7253	54	27	(	(	PUNCT
fumecheng-7253	54	28	eringen	eringen	X
fumecheng-7253	54	29	,	,	PUNCT
fumecheng-7253	54	30	[	[	X
fumecheng-7253	54	31	17	17	NUM
fumecheng-7253	54	32	]	]	NUM
fumecheng-7253	54	33	)	)	PUNCT
fumecheng-7253	54	34	.	.	PUNCT
fumecheng-7253	55	1	it	it	PRON
fumecheng-7253	55	2	is	be	AUX
fumecheng-7253	55	3	distinct	distinct	ADJ
fumecheng-7253	55	4	from	from	ADP
fumecheng-7253	55	5	the	the	DET
fumecheng-7253	55	6	classical	classical	ADJ
fumecheng-7253	55	7	theory	theory	NOUN
fumecheng-7253	55	8	of	of	ADP
fumecheng-7253	55	9	elasticity	elasticity	NOUN
fumecheng-7253	55	10	.	.	PUNCT
fumecheng-7253	56	1	nonlocal	nonlocal	ADJ
fumecheng-7253	56	2	theory	theory	NOUN
fumecheng-7253	56	3	takes	take	VERB
fumecheng-7253	56	4	into	into	ADP
fumecheng-7253	56	5	account	account	NOUN
fumecheng-7253	56	6	interatomic	interatomic	ADJ
fumecheng-7253	56	7	interactions	interaction	NOUN
fumecheng-7253	56	8	over	over	ADP
fumecheng-7253	56	9	a	a	DET
fumecheng-7253	56	10	long	long	ADJ
fumecheng-7253	56	11	time	time	NOUN
fumecheng-7253	56	12	and	and	CCONJ
fumecheng-7253	56	13	its	its	PRON
fumecheng-7253	56	14	findings	finding	NOUN
fumecheng-7253	56	15	depend	depend	VERB
fumecheng-7253	56	16	on	on	ADP
fumecheng-7253	56	17	the	the	DET
fumecheng-7253	56	18	dimensions	dimension	NOUN
fumecheng-7253	56	19	of	of	ADP
fumecheng-7253	56	20	the	the	DET
fumecheng-7253	56	21	body	body	NOUN
fumecheng-7253	56	22	.	.	PUNCT
fumecheng-7253	57	1	the	the	DET
fumecheng-7253	57	2	nonlocal	nonlocal	ADJ
fumecheng-7253	57	3	theory	theory	NOUN
fumecheng-7253	57	4	includes	include	VERB
fumecheng-7253	57	5	the	the	DET
fumecheng-7253	57	6	knowledge	knowledge	NOUN
fumecheng-7253	57	7	about	about	ADP
fumecheng-7253	57	8	the	the	DET
fumecheng-7253	57	9	long	long	ADJ
fumecheng-7253	57	10	-	-	PUNCT
fumecheng-7253	57	11	range	range	NOUN
fumecheng-7253	57	12	forces	force	NOUN
fumecheng-7253	57	13	between	between	ADP
fumecheng-7253	57	14	points	point	NOUN
fumecheng-7253	57	15	along	along	ADP
fumecheng-7253	57	16	these	these	DET
fumecheng-7253	57	17	lines	line	NOUN
fumecheng-7253	57	18	and	and	CCONJ
fumecheng-7253	57	19	the	the	DET
fumecheng-7253	57	20	internal	internal	ADJ
fumecheng-7253	57	21	length	length	NOUN
fumecheng-7253	57	22	scale	scale	NOUN
fumecheng-7253	57	23	is	be	AUX
fumecheng-7253	57	24	essentially	essentially	ADV
fumecheng-7253	57	25	used	use	VERB
fumecheng-7253	57	26	as	as	ADP
fumecheng-7253	57	27	a	a	DET
fumecheng-7253	57	28	material	material	NOUN
fumecheng-7253	57	29	parameter	parameter	NOUN
fumecheng-7253	57	30	to	to	PART
fumecheng-7253	57	31	detect	detect	VERB
fumecheng-7253	57	32	the	the	DET
fumecheng-7253	57	33	small	small	ADJ
fumecheng-7253	57	34	scale	scale	NOUN
fumecheng-7253	57	35	effects	effect	NOUN
fumecheng-7253	57	36	.	.	PUNCT
fumecheng-7253	58	1	any	any	DET
fumecheng-7253	58	2	inconveniences	inconvenience	NOUN
fumecheng-7253	58	3	of	of	ADP
fumecheng-7253	58	4	classical	classical	ADJ
fumecheng-7253	58	5	continuum	continuum	ADJ
fumecheng-7253	58	6	theory	theory	NOUN
fumecheng-7253	58	7	can	can	AUX
fumecheng-7253	58	8	be	be	AUX
fumecheng-7253	58	9	easily	easily	ADV
fumecheng-7253	58	10	avoided	avoid	VERB
fumecheng-7253	58	11	and	and	CCONJ
fumecheng-7253	58	12	then	then	ADV
fumecheng-7253	58	13	on	on	ADP
fumecheng-7253	58	14	local	local	ADJ
fumecheng-7253	58	15	elasticity	elasticity	NOUN
fumecheng-7253	58	16	theory	theory	NOUN
fumecheng-7253	58	17	may	may	AUX
fumecheng-7253	58	18	appropriately	appropriately	ADV
fumecheng-7253	58	19	describe	describe	VERB
fumecheng-7253	58	20	the	the	DET
fumecheng-7253	58	21	size	size	NOUN
fumecheng-7253	58	22	-	-	PUNCT
fumecheng-7253	58	23	dependent	dependent	ADJ
fumecheng-7253	58	24	phenomena	phenomenon	NOUN
fumecheng-7253	58	25	.	.	PUNCT
fumecheng-7253	59	1	the	the	DET
fumecheng-7253	59	2	use	use	NOUN
fumecheng-7253	59	3	of	of	ADP
fumecheng-7253	59	4	the	the	DET
fumecheng-7253	59	5	conventional	conventional	ADJ
fumecheng-7253	59	6	theory	theory	NOUN
fumecheng-7253	59	7	in	in	ADP
fumecheng-7253	59	8	studying	study	VERB
fumecheng-7253	59	9	the	the	DET
fumecheng-7253	59	10	behavior	behavior	NOUN
fumecheng-7253	59	11	of	of	ADP
fumecheng-7253	59	12	nanostructures	nanostructure	NOUN
fumecheng-7253	59	13	is	be	AUX
fumecheng-7253	59	14	inappropriate	inappropriate	ADJ
fumecheng-7253	59	15	in	in	ADP
fumecheng-7253	59	16	many	many	ADJ
fumecheng-7253	59	17	cases	case	NOUN
fumecheng-7253	59	18	because	because	SCONJ
fumecheng-7253	59	19	the	the	DET
fumecheng-7253	59	20	classical	classical	ADJ
fumecheng-7253	59	21	theories	theory	NOUN
fumecheng-7253	59	22	are	be	AUX
fumecheng-7253	59	23	not	not	PART
fumecheng-7253	59	24	responsible	responsible	ADJ
fumecheng-7253	59	25	for	for	ADP
fumecheng-7253	59	26	small	small	ADJ
fumecheng-7253	59	27	-	-	PUNCT
fumecheng-7253	59	28	scale	scale	NOUN
fumecheng-7253	59	29	effects	effect	NOUN
fumecheng-7253	59	30	.	.	PUNCT
fumecheng-7253	60	1	recent	recent	ADJ
fumecheng-7253	60	2	nanotechnological	nanotechnological	ADJ
fumecheng-7253	60	3	considerations	consideration	NOUN
fumecheng-7253	60	4	have	have	AUX
fumecheng-7253	60	5	led	lead	VERB
fumecheng-7253	60	6	to	to	ADP
fumecheng-7253	60	7	the	the	DET
fumecheng-7253	60	8	application	application	NOUN
fumecheng-7253	60	9	of	of	ADP
fumecheng-7253	60	10	nonlocal	nonlocal	ADJ
fumecheng-7253	60	11	elasticity	elasticity	NOUN
fumecheng-7253	60	12	in	in	ADP
fumecheng-7253	60	13	submicron	submicron	NOUN
fumecheng-7253	60	14	scales	scale	NOUN
fumecheng-7253	60	15	and	and	CCONJ
fumecheng-7253	60	16	the	the	DET
fumecheng-7253	60	17	literature	literature	NOUN
fumecheng-7253	60	18	indicates	indicate	VERB
fumecheng-7253	60	19	that	that	SCONJ
fumecheng-7253	60	20	the	the	DET
fumecheng-7253	60	21	nonlocal	nonlocal	ADJ
fumecheng-7253	60	22	theory	theory	NOUN
fumecheng-7253	60	23	of	of	ADP
fumecheng-7253	60	24	elasticity	elasticity	NOUN
fumecheng-7253	60	25	is	be	AUX
fumecheng-7253	60	26	typically	typically	ADV
fumecheng-7253	60	27	used	use	VERB
fumecheng-7253	60	28	progressively	progressively	ADV
fumecheng-7253	60	29	to	to	PART
fumecheng-7253	60	30	analyze	analyze	VERB
fumecheng-7253	60	31	the	the	DET
fumecheng-7253	60	32	nanostructures	nanostructure	NOUN
fumecheng-7253	60	33	in	in	ADP
fumecheng-7253	60	34	a	a	DET
fumecheng-7253	60	35	consistent	consistent	ADJ
fumecheng-7253	60	36	and	and	CCONJ
fumecheng-7253	60	37	fair	fair	ADJ
fumecheng-7253	60	38	manner	manner	NOUN
fumecheng-7253	60	39	.	.	PUNCT
fumecheng-7253	61	1	the	the	DET
fumecheng-7253	61	2	fundamental	fundamental	ADJ
fumecheng-7253	61	3	contrast	contrast	NOUN
fumecheng-7253	61	4	of	of	ADP
fumecheng-7253	61	5	the	the	DET
fumecheng-7253	61	6	conventional	conventional	ADJ
fumecheng-7253	61	7	local	local	ADJ
fumecheng-7253	61	8	elasticity	elasticity	NOUN
fumecheng-7253	61	9	theory	theory	NOUN
fumecheng-7253	61	10	to	to	ADP
fumecheng-7253	61	11	those	those	PRON
fumecheng-7253	61	12	proposed	propose	VERB
fumecheng-7253	61	13	by	by	ADP
fumecheng-7253	61	14	eringen	eringen	PROPN
fumecheng-7253	61	15	called	call	VERB
fumecheng-7253	61	16	nonlocal	nonlocal	ADJ
fumecheng-7253	61	17	one	one	NUM
fumecheng-7253	61	18	[	[	X
fumecheng-7253	61	19	17–19	17–19	NUM
fumecheng-7253	61	20	]	]	PUNCT
fumecheng-7253	61	21	substantially	substantially	ADV
fumecheng-7253	61	22	depends	depend	VERB
fumecheng-7253	61	23	on	on	ADP
fumecheng-7253	61	24	the	the	DET
fumecheng-7253	61	25	definition	definition	NOUN
fumecheng-7253	61	26	of	of	ADP
fumecheng-7253	61	27	the	the	DET
fumecheng-7253	61	28	stress	stress	NOUN
fumecheng-7253	61	29	vector	vector	NOUN
fumecheng-7253	61	30	.	.	PUNCT
fumecheng-7253	62	1	the	the	DET
fumecheng-7253	62	2	nonlocal	nonlocal	ADJ
fumecheng-7253	62	3	theory	theory	NOUN
fumecheng-7253	62	4	of	of	ADP
fumecheng-7253	62	5	elasticity	elasticity	NOUN
fumecheng-7253	62	6	,	,	PUNCT
fumecheng-7253	62	7	however	however	ADV
fumecheng-7253	62	8	,	,	PUNCT
fumecheng-7253	62	9	has	have	AUX
fumecheng-7253	62	10	been	be	AUX
fumecheng-7253	62	11	applied	apply	VERB
fumecheng-7253	62	12	in	in	ADP
fumecheng-7253	62	13	various	various	ADJ
fumecheng-7253	62	14	fields	field	NOUN
fumecheng-7253	62	15	including	include	VERB
fumecheng-7253	62	16	elastic	elastic	ADJ
fumecheng-7253	62	17	wave	wave	NOUN
fumecheng-7253	62	18	dispersion	dispersion	NOUN
fumecheng-7253	62	19	,	,	PUNCT
fumecheng-7253	62	20	mechanical	mechanical	ADJ
fumecheng-7253	62	21	decomposition	decomposition	NOUN
fumecheng-7253	62	22	,	,	PUNCT
fumecheng-7253	62	23	etc	etc	X
fumecheng-7253	62	24	.	.	X
fumecheng-7253	63	1	the	the	DET
fumecheng-7253	63	2	eringen	eringen	PROPN
fumecheng-7253	63	3	nonlocal	nonlocal	ADJ
fumecheng-7253	63	4	elasticity	elasticity	NOUN
fumecheng-7253	63	5	theory	theory	NOUN
fumecheng-7253	63	6	(	(	PUNCT
fumecheng-7253	63	7	enet	enet	PROPN
fumecheng-7253	63	8	)	)	PUNCT
fumecheng-7253	63	9	has	have	AUX
fumecheng-7253	63	10	been	be	AUX
fumecheng-7253	63	11	applied	apply	VERB
fumecheng-7253	63	12	in	in	ADP
fumecheng-7253	63	13	many	many	ADJ
fumecheng-7253	63	14	theoretical	theoretical	ADJ
fumecheng-7253	63	15	investigations	investigation	NOUN
fumecheng-7253	63	16	on	on	ADP
fumecheng-7253	63	17	the	the	DET
fumecheng-7253	63	18	free	free	ADJ
fumecheng-7253	63	19	vibrations	vibration	NOUN
fumecheng-7253	63	20	of	of	ADP
fumecheng-7253	63	21	nanoparticles	nanoparticle	NOUN
fumecheng-7253	63	22	and	and	CCONJ
fumecheng-7253	63	23	nanobeams	nanobeam	NOUN
fumecheng-7253	63	24	taking	take	VERB
fumecheng-7253	63	25	into	into	ADP
fumecheng-7253	63	26	account	account	NOUN
fumecheng-7253	63	27	the	the	DET
fumecheng-7253	63	28	assumptions	assumption	NOUN
fumecheng-7253	63	29	of	of	ADP
fumecheng-7253	63	30	euler	euler	NOUN
fumecheng-7253	63	31	-	-	PUNCT
fumecheng-7253	63	32	bernoulli	bernoulli	PROPN
fumecheng-7253	63	33	(	(	PUNCT
fumecheng-7253	63	34	ebt	ebt	PROPN
fumecheng-7253	63	35	)	)	PUNCT
fumecheng-7253	63	36	and	and	CCONJ
fumecheng-7253	63	37	timoshenko	timoshenko	NOUN
fumecheng-7253	63	38	beams	beam	NOUN
fumecheng-7253	63	39	(	(	PUNCT
fumecheng-7253	63	40	tbt	tbt	PROPN
fumecheng-7253	63	41	)	)	PUNCT
fumecheng-7253	63	42	models	model	NOUN
fumecheng-7253	63	43	[	[	X
fumecheng-7253	63	44	20	20	NUM
fumecheng-7253	63	45	-	-	SYM
fumecheng-7253	63	46	27	27	NUM
fumecheng-7253	63	47	]	]	PUNCT
fumecheng-7253	63	48	.	.	PUNCT
fumecheng-7253	64	1	another	another	DET
fumecheng-7253	64	2	area	area	NOUN
fumecheng-7253	64	3	of	of	ADP
fumecheng-7253	64	4	research	research	NOUN
fumecheng-7253	64	5	which	which	PRON
fumecheng-7253	64	6	is	be	AUX
fumecheng-7253	64	7	emerging	emerge	VERB
fumecheng-7253	64	8	due	due	ADP
fumecheng-7253	64	9	to	to	ADP
fumecheng-7253	64	10	its	its	PRON
fumecheng-7253	64	11	current	current	NOUN
fumecheng-7253	64	12	as	as	ADV
fumecheng-7253	64	13	well	well	ADV
fumecheng-7253	64	14	as	as	ADP
fumecheng-7253	64	15	future	future	ADJ
fumecheng-7253	64	16	applications	application	NOUN
fumecheng-7253	64	17	is	be	AUX
fumecheng-7253	64	18	therefore	therefore	ADV
fumecheng-7253	64	19	theoretical	theoretical	ADJ
fumecheng-7253	64	20	studies	study	NOUN
fumecheng-7253	64	21	on	on	ADP
fumecheng-7253	64	22	the	the	DET
fumecheng-7253	64	23	nanoscale	nanoscale	NOUN
fumecheng-7253	64	24	behavior	behavior	NOUN
fumecheng-7253	64	25	of	of	ADP
fumecheng-7253	64	26	rotating	rotate	VERB
fumecheng-7253	64	27	micro	micro	NOUN
fumecheng-7253	64	28	/	/	NOUN
fumecheng-7253	64	29	nanobeams	nanobeam	NOUN
fumecheng-7253	64	30	in	in	ADP
fumecheng-7253	64	31	different	different	ADJ
fumecheng-7253	64	32	environment	environment	NOUN
fumecheng-7253	64	33	.	.	PUNCT
fumecheng-7253	65	1	rotating	rotate	VERB
fumecheng-7253	65	2	nanostructures	nanostructure	NOUN
fumecheng-7253	65	3	include	include	VERB
fumecheng-7253	65	4	different	different	ADJ
fumecheng-7253	65	5	fields	field	NOUN
fumecheng-7253	65	6	like	like	ADP
fumecheng-7253	65	7	nano	nano	NOUN
fumecheng-7253	65	8	-	-	PUNCT
fumecheng-7253	65	9	turbines	turbine	NOUN
fumecheng-7253	65	10	,	,	PUNCT
fumecheng-7253	65	11	nano	nano	NOUN
fumecheng-7253	65	12	gears	gear	NOUN
fumecheng-7253	65	13	and	and	CCONJ
fumecheng-7253	65	14	motors	motor	NOUN
fumecheng-7253	65	15	and	and	CCONJ
fumecheng-7253	65	16	miniaturized	miniaturize	VERB
fumecheng-7253	65	17	bearings	bearing	NOUN
fumecheng-7253	65	18	.	.	PUNCT
fumecheng-7253	66	1	taking	take	VERB
fumecheng-7253	66	2	into	into	ADP
fumecheng-7253	66	3	account	account	NOUN
fumecheng-7253	66	4	a	a	DET
fumecheng-7253	66	5	great	great	ADJ
fumecheng-7253	66	6	deal	deal	NOUN
fumecheng-7253	66	7	of	of	ADP
fumecheng-7253	66	8	studies	study	NOUN
fumecheng-7253	66	9	on	on	ADP
fumecheng-7253	66	10	the	the	DET
fumecheng-7253	66	11	sustainability	sustainability	NOUN
fumecheng-7253	66	12	of	of	ADP
fumecheng-7253	66	13	rotating	rotate	VERB
fumecheng-7253	66	14	nanoscale	nanoscale	NOUN
fumecheng-7253	66	15	structures	structure	NOUN
fumecheng-7253	66	16	,	,	PUNCT
fumecheng-7253	66	17	this	this	DET
fumecheng-7253	66	18	idea	idea	NOUN
fumecheng-7253	66	19	is	be	AUX
fumecheng-7253	66	20	expected	expect	VERB
fumecheng-7253	66	21	to	to	PART
fumecheng-7253	66	22	draw	draw	VERB
fumecheng-7253	66	23	significant	significant	ADJ
fumecheng-7253	66	24	attention	attention	NOUN
fumecheng-7253	66	25	in	in	ADP
fumecheng-7253	66	26	the	the	DET
fumecheng-7253	66	27	future	future	NOUN
fumecheng-7253	66	28	;	;	PUNCT
fumecheng-7253	66	29	existing	exist	VERB
fumecheng-7253	66	30	samples	sample	NOUN
fumecheng-7253	66	31	636	636	NUM
fumecheng-7253	66	32	a.	a.	NOUN
fumecheng-7253	66	33	e.	e.	PROPN
fumecheng-7253	66	34	abouelregal	abouelregal	PROPN
fumecheng-7253	66	35	,	,	PUNCT
fumecheng-7253	66	36	h.	h.	PROPN
fumecheng-7253	66	37	m.	m.	PROPN
fumecheng-7253	66	38	sedighi	sedighi	PROPN
fumecheng-7253	66	39	,	,	PUNCT
fumecheng-7253	66	40	s.	s.	PROPN
fumecheng-7253	66	41	a.	a.	PROPN
fumecheng-7253	66	42	faghidian	faghidian	PROPN
fumecheng-7253	66	43	,	,	PUNCT
fumecheng-7253	66	44	a.	a.	PROPN
fumecheng-7253	66	45	h.	h.	PROPN
fumecheng-7253	66	46	shirazi	shirazi	PROPN
fumecheng-7253	66	47	include	include	VERB
fumecheng-7253	66	48	the	the	DET
fumecheng-7253	66	49	analysis	analysis	NOUN
fumecheng-7253	66	50	of	of	ADP
fumecheng-7253	66	51	molecular	molecular	ADJ
fumecheng-7253	66	52	carbon	carbon	NOUN
fumecheng-7253	66	53	nanotubes	nanotube	NOUN
fumecheng-7253	66	54	and	and	CCONJ
fumecheng-7253	66	55	gears	gear	NOUN
fumecheng-7253	66	56	,	,	PUNCT
fumecheng-7253	66	57	nano	nano	NOUN
fumecheng-7253	66	58	-	-	PUNCT
fumecheng-7253	66	59	motors	motor	NOUN
fumecheng-7253	66	60	and	and	CCONJ
fumecheng-7253	66	61	nano	nano	NOUN
fumecheng-7253	66	62	-	-	PUNCT
fumecheng-7253	66	63	shafts	shafts	ADJ
fumecheng-7253	66	64	[	[	X
fumecheng-7253	66	65	28	28	NUM
fumecheng-7253	66	66	,	,	PUNCT
fumecheng-7253	66	67	29	29	NUM
fumecheng-7253	66	68	]	]	PUNCT
fumecheng-7253	66	69	.	.	PUNCT
fumecheng-7253	67	1	the	the	DET
fumecheng-7253	67	2	dynamics	dynamic	NOUN
fumecheng-7253	67	3	of	of	ADP
fumecheng-7253	67	4	rotating	rotate	VERB
fumecheng-7253	67	5	nanotubes	nanotube	NOUN
fumecheng-7253	67	6	and	and	CCONJ
fumecheng-7253	67	7	gears	gear	NOUN
fumecheng-7253	67	8	were	be	AUX
fumecheng-7253	67	9	investigated	investigate	VERB
fumecheng-7253	67	10	by	by	ADP
fumecheng-7253	67	11	srivastava	srivastava	PROPN
fumecheng-7253	67	12	[	[	X
fumecheng-7253	67	13	30	30	NUM
fumecheng-7253	67	14	]	]	PUNCT
fumecheng-7253	67	15	under	under	ADP
fumecheng-7253	67	16	a	a	DET
fumecheng-7253	67	17	single	single	ADJ
fumecheng-7253	67	18	imposed	impose	VERB
fumecheng-7253	67	19	laser	laser	NOUN
fumecheng-7253	67	20	beam	beam	NOUN
fumecheng-7253	67	21	.	.	PUNCT
fumecheng-7253	68	1	the	the	DET
fumecheng-7253	68	2	mathematical	mathematical	ADJ
fumecheng-7253	68	3	modeling	modeling	NOUN
fumecheng-7253	68	4	for	for	ADP
fumecheng-7253	68	5	rotating	rotate	VERB
fumecheng-7253	68	6	nanomotor	nanomotor	NOUN
fumecheng-7253	68	7	was	be	AUX
fumecheng-7253	68	8	carried	carry	VERB
fumecheng-7253	68	9	out	out	ADP
fumecheng-7253	68	10	by	by	ADP
fumecheng-7253	68	11	lohrasebi	lohrasebi	NOUN
fumecheng-7253	68	12	and	and	CCONJ
fumecheng-7253	68	13	rafii	rafii	ADJ
fumecheng-7253	68	14	-	-	PUNCT
fumecheng-7253	68	15	tabar	tabar	NOUN
fumecheng-7253	68	16	[	[	X
fumecheng-7253	68	17	31	31	NUM
fumecheng-7253	68	18	]	]	PUNCT
fumecheng-7253	68	19	.	.	PUNCT
fumecheng-7253	69	1	nanoelectromechanical	nanoelectromechanical	ADJ
fumecheng-7253	69	2	(	(	PUNCT
fumecheng-7253	69	3	nems	nem	NOUN
fumecheng-7253	69	4	)	)	PUNCT
fumecheng-7253	69	5	devices	device	NOUN
fumecheng-7253	69	6	emerge	emerge	VERB
fumecheng-7253	69	7	as	as	ADP
fumecheng-7253	69	8	the	the	DET
fumecheng-7253	69	9	next	next	ADJ
fumecheng-7253	69	10	generation	generation	NOUN
fumecheng-7253	69	11	of	of	ADP
fumecheng-7253	69	12	advanced	advanced	ADJ
fumecheng-7253	69	13	technology	technology	NOUN
fumecheng-7253	69	14	,	,	PUNCT
fumecheng-7253	69	15	which	which	PRON
fumecheng-7253	69	16	is	be	AUX
fumecheng-7253	69	17	capable	capable	ADJ
fumecheng-7253	69	18	of	of	ADP
fumecheng-7253	69	19	making	make	VERB
fumecheng-7253	69	20	a	a	DET
fumecheng-7253	69	21	significant	significant	ADJ
fumecheng-7253	69	22	evolution	evolution	NOUN
fumecheng-7253	69	23	in	in	ADP
fumecheng-7253	69	24	people	people	NOUN
fumecheng-7253	69	25	's	's	PART
fumecheng-7253	69	26	lives	life	NOUN
fumecheng-7253	69	27	.	.	PUNCT
fumecheng-7253	70	1	considering	consider	VERB
fumecheng-7253	70	2	that	that	SCONJ
fumecheng-7253	70	3	rotating	rotate	VERB
fumecheng-7253	70	4	motors	motor	NOUN
fumecheng-7253	70	5	and	and	CCONJ
fumecheng-7253	70	6	other	other	ADJ
fumecheng-7253	70	7	devices	device	NOUN
fumecheng-7253	70	8	are	be	AUX
fumecheng-7253	70	9	particularly	particularly	ADV
fumecheng-7253	70	10	of	of	ADP
fumecheng-7253	70	11	interest	interest	NOUN
fumecheng-7253	70	12	in	in	ADP
fumecheng-7253	70	13	advanced	advanced	ADJ
fumecheng-7253	70	14	technology	technology	NOUN
fumecheng-7253	70	15	,	,	PUNCT
fumecheng-7253	70	16	nanobeams	nanobeam	NOUN
fumecheng-7253	70	17	under	under	ADP
fumecheng-7253	70	18	rotation	rotation	NOUN
fumecheng-7253	70	19	are	be	AUX
fumecheng-7253	70	20	analyzed	analyze	VERB
fumecheng-7253	70	21	in	in	ADP
fumecheng-7253	70	22	the	the	DET
fumecheng-7253	70	23	present	present	ADJ
fumecheng-7253	70	24	research	research	NOUN
fumecheng-7253	70	25	to	to	PART
fumecheng-7253	70	26	determine	determine	VERB
fumecheng-7253	70	27	their	their	PRON
fumecheng-7253	70	28	vibrational	vibrational	ADJ
fumecheng-7253	70	29	characteristics	characteristic	NOUN
fumecheng-7253	70	30	.	.	PUNCT
fumecheng-7253	71	1	the	the	DET
fumecheng-7253	71	2	analysis	analysis	NOUN
fumecheng-7253	71	3	of	of	ADP
fumecheng-7253	71	4	vibrational	vibrational	ADJ
fumecheng-7253	71	5	behavior	behavior	NOUN
fumecheng-7253	71	6	of	of	ADP
fumecheng-7253	71	7	rotating	rotate	VERB
fumecheng-7253	71	8	beam	beam	NOUN
fumecheng-7253	71	9	-	-	PUNCT
fumecheng-7253	71	10	like	like	ADJ
fumecheng-7253	71	11	structures	structure	NOUN
fumecheng-7253	71	12	in	in	ADP
fumecheng-7253	71	13	the	the	DET
fumecheng-7253	71	14	framework	framework	NOUN
fumecheng-7253	71	15	of	of	ADP
fumecheng-7253	71	16	classical	classical	ADJ
fumecheng-7253	71	17	theory	theory	NOUN
fumecheng-7253	71	18	,	,	PUNCT
fumecheng-7253	71	19	thanks	thank	NOUN
fumecheng-7253	71	20	to	to	ADP
fumecheng-7253	71	21	their	their	PRON
fumecheng-7253	71	22	significance	significance	NOUN
fumecheng-7253	71	23	in	in	ADP
fumecheng-7253	71	24	practical	practical	ADJ
fumecheng-7253	71	25	applications	application	NOUN
fumecheng-7253	71	26	,	,	PUNCT
fumecheng-7253	71	27	has	have	AUX
fumecheng-7253	71	28	been	be	AUX
fumecheng-7253	71	29	an	an	DET
fumecheng-7253	71	30	interesting	interesting	ADJ
fumecheng-7253	71	31	and	and	CCONJ
fumecheng-7253	71	32	challenging	challenging	ADJ
fumecheng-7253	71	33	question	question	NOUN
fumecheng-7253	71	34	in	in	ADP
fumecheng-7253	71	35	recent	recent	ADJ
fumecheng-7253	71	36	decades	decade	NOUN
fumecheng-7253	71	37	.	.	PUNCT
fumecheng-7253	72	1	some	some	PRON
fumecheng-7253	72	2	of	of	ADP
fumecheng-7253	72	3	these	these	DET
fumecheng-7253	72	4	fundamental	fundamental	ADJ
fumecheng-7253	72	5	studies	study	NOUN
fumecheng-7253	72	6	are	be	AUX
fumecheng-7253	72	7	conducted	conduct	VERB
fumecheng-7253	72	8	on	on	ADP
fumecheng-7253	72	9	homogenous	homogenous	ADJ
fumecheng-7253	72	10	rotating	rotate	VERB
fumecheng-7253	72	11	beam	beam	NOUN
fumecheng-7253	72	12	structures	structure	NOUN
fumecheng-7253	72	13	[	[	X
fumecheng-7253	72	14	32–40	32–40	NUM
fumecheng-7253	72	15	]	]	PUNCT
fumecheng-7253	72	16	.	.	PUNCT
fumecheng-7253	73	1	research	research	NOUN
fumecheng-7253	73	2	of	of	ADP
fumecheng-7253	73	3	different	different	ADJ
fumecheng-7253	73	4	features	feature	NOUN
fumecheng-7253	73	5	of	of	ADP
fumecheng-7253	73	6	nanoscale	nanoscale	NOUN
fumecheng-7253	73	7	beams	beam	NOUN
fumecheng-7253	73	8	is	be	AUX
fumecheng-7253	73	9	an	an	DET
fumecheng-7253	73	10	attractive	attractive	ADJ
fumecheng-7253	73	11	subject	subject	NOUN
fumecheng-7253	73	12	in	in	ADP
fumecheng-7253	73	13	nanotechnology	nanotechnology	NOUN
fumecheng-7253	73	14	as	as	SCONJ
fumecheng-7253	73	15	it	it	PRON
fumecheng-7253	73	16	encompasses	encompass	VERB
fumecheng-7253	73	17	the	the	DET
fumecheng-7253	73	18	electronic	electronic	ADJ
fumecheng-7253	73	19	and	and	CCONJ
fumecheng-7253	73	20	optical	optical	ADJ
fumecheng-7253	73	21	characteristics	characteristic	NOUN
fumecheng-7253	73	22	of	of	ADP
fumecheng-7253	73	23	nano	nano	NOUN
fumecheng-7253	73	24	-	-	PUNCT
fumecheng-7253	73	25	devices	device	NOUN
fumecheng-7253	73	26	.	.	PUNCT
fumecheng-7253	74	1	the	the	DET
fumecheng-7253	74	2	main	main	ADJ
fumecheng-7253	74	3	objective	objective	NOUN
fumecheng-7253	74	4	of	of	ADP
fumecheng-7253	74	5	this	this	DET
fumecheng-7253	74	6	article	article	NOUN
fumecheng-7253	74	7	is	be	AUX
fumecheng-7253	74	8	to	to	PART
fumecheng-7253	74	9	discover	discover	VERB
fumecheng-7253	74	10	the	the	DET
fumecheng-7253	74	11	vibrational	vibrational	ADJ
fumecheng-7253	74	12	behavior	behavior	NOUN
fumecheng-7253	74	13	of	of	ADP
fumecheng-7253	74	14	rotating	rotate	VERB
fumecheng-7253	74	15	isotropic	isotropic	NOUN
fumecheng-7253	74	16	nanobeams	nanobeam	NOUN
fumecheng-7253	74	17	in	in	ADP
fumecheng-7253	74	18	a	a	DET
fumecheng-7253	74	19	mathematical	mathematical	ADJ
fumecheng-7253	74	20	framework	framework	NOUN
fumecheng-7253	74	21	using	use	VERB
fumecheng-7253	74	22	the	the	DET
fumecheng-7253	74	23	eringen	eringen	NOUN
fumecheng-7253	74	24	's	's	PART
fumecheng-7253	74	25	nonlocal	nonlocal	ADJ
fumecheng-7253	74	26	theory	theory	NOUN
fumecheng-7253	74	27	of	of	ADP
fumecheng-7253	74	28	elasticity	elasticity	NOUN
fumecheng-7253	74	29	.	.	PUNCT
fumecheng-7253	75	1	since	since	SCONJ
fumecheng-7253	75	2	the	the	DET
fumecheng-7253	75	3	rotating	rotate	VERB
fumecheng-7253	75	4	devices	device	NOUN
fumecheng-7253	75	5	such	such	ADJ
fumecheng-7253	75	6	as	as	ADP
fumecheng-7253	75	7	rotary	rotary	ADJ
fumecheng-7253	75	8	engines	engine	NOUN
fumecheng-7253	75	9	are	be	AUX
fumecheng-7253	75	10	of	of	ADP
fumecheng-7253	75	11	particular	particular	ADJ
fumecheng-7253	75	12	importance	importance	NOUN
fumecheng-7253	75	13	to	to	ADP
fumecheng-7253	75	14	such	such	ADJ
fumecheng-7253	75	15	modern	modern	ADJ
fumecheng-7253	75	16	technologies	technology	NOUN
fumecheng-7253	75	17	,	,	PUNCT
fumecheng-7253	75	18	the	the	DET
fumecheng-7253	75	19	vibration	vibration	NOUN
fumecheng-7253	75	20	characteristics	characteristic	NOUN
fumecheng-7253	75	21	of	of	ADP
fumecheng-7253	75	22	rotating	rotate	VERB
fumecheng-7253	75	23	nanobeams	nanobeam	NOUN
fumecheng-7253	75	24	are	be	AUX
fumecheng-7253	75	25	investigated	investigate	VERB
fumecheng-7253	75	26	in	in	ADP
fumecheng-7253	75	27	the	the	DET
fumecheng-7253	75	28	current	current	ADJ
fumecheng-7253	75	29	research	research	NOUN
fumecheng-7253	75	30	work	work	NOUN
fumecheng-7253	75	31	.	.	PUNCT
fumecheng-7253	76	1	the	the	DET
fumecheng-7253	76	2	considered	consider	VERB
fumecheng-7253	76	3	model	model	NOUN
fumecheng-7253	76	4	is	be	AUX
fumecheng-7253	76	5	on	on	ADP
fumecheng-7253	76	6	the	the	DET
fumecheng-7253	76	7	basis	basis	NOUN
fumecheng-7253	76	8	of	of	ADP
fumecheng-7253	76	9	the	the	DET
fumecheng-7253	76	10	euler	euler	PROPN
fumecheng-7253	76	11	-	-	PUNCT
fumecheng-7253	76	12	bernoulli	bernoulli	PROPN
fumecheng-7253	76	13	theory	theory	NOUN
fumecheng-7253	76	14	,	,	PUNCT
fumecheng-7253	76	15	generalized	generalize	VERB
fumecheng-7253	76	16	dual	dual	ADJ
fumecheng-7253	76	17	phase	phase	NOUN
fumecheng-7253	76	18	-	-	PUNCT
fumecheng-7253	76	19	lag	lag	NOUN
fumecheng-7253	76	20	heat	heat	NOUN
fumecheng-7253	76	21	conduction	conduction	NOUN
fumecheng-7253	76	22	and	and	CCONJ
fumecheng-7253	76	23	includes	include	VERB
fumecheng-7253	76	24	the	the	DET
fumecheng-7253	76	25	coriolis	corioli	NOUN
fumecheng-7253	76	26	and	and	CCONJ
fumecheng-7253	76	27	spin	spin	NOUN
fumecheng-7253	76	28	-	-	PUNCT
fumecheng-7253	76	29	smoothing	smooth	VERB
fumecheng-7253	76	30	phenomena	phenomenon	NOUN
fumecheng-7253	76	31	.	.	PUNCT
fumecheng-7253	77	1	for	for	ADP
fumecheng-7253	77	2	the	the	DET
fumecheng-7253	77	3	first	first	ADJ
fumecheng-7253	77	4	time	time	NOUN
fumecheng-7253	77	5	ever	ever	ADV
fumecheng-7253	77	6	,	,	PUNCT
fumecheng-7253	77	7	the	the	DET
fumecheng-7253	77	8	features	feature	NOUN
fumecheng-7253	77	9	of	of	ADP
fumecheng-7253	77	10	the	the	DET
fumecheng-7253	77	11	mentioned	mention	VERB
fumecheng-7253	77	12	advanced	advanced	ADJ
fumecheng-7253	77	13	nano	nano	NOUN
fumecheng-7253	77	14	-	-	PUNCT
fumecheng-7253	77	15	rotating	rotate	VERB
fumecheng-7253	77	16	mechanism	mechanism	NOUN
fumecheng-7253	77	17	are	be	AUX
fumecheng-7253	77	18	reported	report	VERB
fumecheng-7253	77	19	.	.	PUNCT
fumecheng-7253	78	1	this	this	DET
fumecheng-7253	78	2	study	study	NOUN
fumecheng-7253	78	3	would	would	AUX
fumecheng-7253	78	4	contribute	contribute	VERB
fumecheng-7253	78	5	to	to	ADP
fumecheng-7253	78	6	a	a	DET
fumecheng-7253	78	7	thorough	thorough	ADJ
fumecheng-7253	78	8	understanding	understanding	NOUN
fumecheng-7253	78	9	of	of	ADP
fumecheng-7253	78	10	the	the	DET
fumecheng-7253	78	11	dynamics	dynamic	NOUN
fumecheng-7253	78	12	of	of	ADP
fumecheng-7253	78	13	rotating	rotate	VERB
fumecheng-7253	78	14	nanobeams	nanobeam	NOUN
fumecheng-7253	78	15	.	.	PUNCT
fumecheng-7253	79	1	different	different	ADJ
fumecheng-7253	79	2	aspects	aspect	NOUN
fumecheng-7253	79	3	of	of	ADP
fumecheng-7253	79	4	the	the	DET
fumecheng-7253	79	5	studied	studied	ADJ
fumecheng-7253	79	6	model	model	NOUN
fumecheng-7253	79	7	including	include	VERB
fumecheng-7253	79	8	thermomechanical	thermomechanical	ADJ
fumecheng-7253	79	9	vibration	vibration	NOUN
fumecheng-7253	79	10	,	,	PUNCT
fumecheng-7253	79	11	point	point	NOUN
fumecheng-7253	79	12	load	load	NOUN
fumecheng-7253	79	13	and	and	CCONJ
fumecheng-7253	79	14	nonlocal	nonlocal	ADJ
fumecheng-7253	79	15	effects	effect	NOUN
fumecheng-7253	79	16	are	be	AUX
fumecheng-7253	79	17	taken	take	VERB
fumecheng-7253	79	18	into	into	ADP
fumecheng-7253	79	19	account	account	NOUN
fumecheng-7253	79	20	.	.	PUNCT
fumecheng-7253	80	1	moreover	moreover	ADV
fumecheng-7253	80	2	,	,	PUNCT
fumecheng-7253	80	3	numerical	numerical	ADJ
fumecheng-7253	80	4	examples	example	NOUN
fumecheng-7253	80	5	are	be	AUX
fumecheng-7253	80	6	presented	present	VERB
fumecheng-7253	80	7	to	to	PART
fumecheng-7253	80	8	indicate	indicate	VERB
fumecheng-7253	80	9	the	the	DET
fumecheng-7253	80	10	impact	impact	NOUN
fumecheng-7253	80	11	of	of	ADP
fumecheng-7253	80	12	several	several	ADJ
fumecheng-7253	80	13	parameters	parameter	NOUN
fumecheng-7253	80	14	on	on	ADP
fumecheng-7253	80	15	the	the	DET
fumecheng-7253	80	16	deflection	deflection	NOUN
fumecheng-7253	80	17	,	,	PUNCT
fumecheng-7253	80	18	temperature	temperature	NOUN
fumecheng-7253	80	19	change	change	NOUN
fumecheng-7253	80	20	and	and	CCONJ
fumecheng-7253	80	21	bending	bend	VERB
fumecheng-7253	80	22	moment	moment	NOUN
fumecheng-7253	80	23	of	of	ADP
fumecheng-7253	80	24	rotating	rotate	VERB
fumecheng-7253	80	25	nanobeams	nanobeam	NOUN
fumecheng-7253	80	26	.	.	PUNCT
fumecheng-7253	81	1	this	this	DET
fumecheng-7253	81	2	study	study	NOUN
fumecheng-7253	81	3	will	will	AUX
fumecheng-7253	81	4	recognize	recognize	VERB
fumecheng-7253	81	5	various	various	ADJ
fumecheng-7253	81	6	requirements	requirement	NOUN
fumecheng-7253	81	7	for	for	ADP
fumecheng-7253	81	8	design	design	NOUN
fumecheng-7253	81	9	and	and	CCONJ
fumecheng-7253	81	10	production	production	NOUN
fumecheng-7253	81	11	of	of	ADP
fumecheng-7253	81	12	environmentally	environmentally	ADV
fumecheng-7253	81	13	sensitive	sensitive	ADJ
fumecheng-7253	81	14	resonator	resonator	NOUN
fumecheng-7253	81	15	machines	machine	NOUN
fumecheng-7253	81	16	.	.	PUNCT
fumecheng-7253	82	1	2	2	X
fumecheng-7253	82	2	.	.	NOUN
fumecheng-7253	82	3	nonlocal	nonlocal	ADJ
fumecheng-7253	82	4	model	model	NOUN
fumecheng-7253	82	5	of	of	ADP
fumecheng-7253	82	6	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	82	7	eringen	eringen	NOUN
fumecheng-7253	82	8	[	[	X
fumecheng-7253	82	9	17	17	NUM
fumecheng-7253	82	10	]	]	PUNCT
fumecheng-7253	82	11	theoretically	theoretically	ADV
fumecheng-7253	82	12	introduced	introduce	VERB
fumecheng-7253	82	13	a	a	DET
fumecheng-7253	82	14	fundamental	fundamental	ADJ
fumecheng-7253	82	15	continuum	continuum	ADJ
fumecheng-7253	82	16	mechanics	mechanic	NOUN
fumecheng-7253	82	17	in	in	ADP
fumecheng-7253	82	18	the	the	DET
fumecheng-7253	82	19	context	context	NOUN
fumecheng-7253	82	20	of	of	ADP
fumecheng-7253	82	21	nonlocal	nonlocal	ADJ
fumecheng-7253	82	22	theory	theory	NOUN
fumecheng-7253	82	23	of	of	ADP
fumecheng-7253	82	24	elasticity	elasticity	NOUN
fumecheng-7253	82	25	to	to	PART
fumecheng-7253	82	26	explore	explore	VERB
fumecheng-7253	82	27	the	the	DET
fumecheng-7253	82	28	structural	structural	ADJ
fumecheng-7253	82	29	issues	issue	NOUN
fumecheng-7253	82	30	at	at	ADP
fumecheng-7253	82	31	micro	micro	ADJ
fumecheng-7253	82	32	-	-	NOUN
fumecheng-7253	82	33	scale	scale	ADJ
fumecheng-7253	82	34	dimensions	dimension	NOUN
fumecheng-7253	82	35	.	.	PUNCT
fumecheng-7253	83	1	for	for	ADP
fumecheng-7253	83	2	nano	nano	NOUN
fumecheng-7253	83	3	-	-	PUNCT
fumecheng-7253	83	4	scale	scale	NOUN
fumecheng-7253	83	5	beams	beam	NOUN
fumecheng-7253	83	6	,	,	PUNCT
fumecheng-7253	83	7	the	the	DET
fumecheng-7253	83	8	general	general	ADJ
fumecheng-7253	83	9	governing	govern	VERB
fumecheng-7253	83	10	equations	equation	NOUN
fumecheng-7253	83	11	of	of	ADP
fumecheng-7253	83	12	nonlocal	nonlocal	ADJ
fumecheng-7253	83	13	constituent	constituent	NOUN
fumecheng-7253	83	14	relations	relation	NOUN
fumecheng-7253	83	15	can	can	AUX
fumecheng-7253	83	16	be	be	AUX
fumecheng-7253	83	17	described	describe	VERB
fumecheng-7253	83	18	as	as	ADP
fumecheng-7253	83	19	follows	follow	VERB
fumecheng-7253	83	20	[	[	X
fumecheng-7253	83	21	18	18	NUM
fumecheng-7253	83	22	]	]	X
fumecheng-7253	84	1	[	[	X
fumecheng-7253	84	2	1	1	NUM
fumecheng-7253	84	3	−	−	PROPN
fumecheng-7253	84	4	(	(	PUNCT
fumecheng-7253	84	5	𝑒0𝑎)2∇2]𝜏𝑘𝑙	𝑒0𝑎)2∇2]𝜏𝑘𝑙	PROPN
fumecheng-7253	84	6	=	=	SYM
fumecheng-7253	84	7	𝜎𝑘𝑙	𝜎𝑘𝑙	NOUN
fumecheng-7253	84	8	,	,	PUNCT
fumecheng-7253	84	9	(	(	PUNCT
fumecheng-7253	84	10	1	1	X
fumecheng-7253	84	11	)	)	PUNCT
fumecheng-7253	84	12	where	where	SCONJ
fumecheng-7253	84	13	𝑒0	𝑒0	VERB
fumecheng-7253	84	14	denotes	denote	VERB
fumecheng-7253	84	15	a	a	DET
fumecheng-7253	84	16	correlation	correlation	NOUN
fumecheng-7253	84	17	coefficient	coefficient	NOUN
fumecheng-7253	84	18	depending	depend	VERB
fumecheng-7253	84	19	on	on	ADP
fumecheng-7253	84	20	the	the	DET
fumecheng-7253	84	21	type	type	NOUN
fumecheng-7253	84	22	of	of	ADP
fumecheng-7253	84	23	material	material	NOUN
fumecheng-7253	84	24	,	,	PUNCT
fumecheng-7253	84	25	𝑎	𝑎	X
fumecheng-7253	84	26	stands	stand	NOUN
fumecheng-7253	84	27	for	for	ADP
fumecheng-7253	84	28	the	the	DET
fumecheng-7253	84	29	internal	internal	ADJ
fumecheng-7253	84	30	length	length	NOUN
fumecheng-7253	84	31	scale	scale	NOUN
fumecheng-7253	84	32	,	,	PUNCT
fumecheng-7253	84	33	∇2	∇2	PROPN
fumecheng-7253	84	34	refers	refer	VERB
fumecheng-7253	84	35	to	to	ADP
fumecheng-7253	84	36	the	the	DET
fumecheng-7253	84	37	laplacian	laplacian	NOUN
fumecheng-7253	84	38	operator,𝜏𝑘𝑙symbolizes	operator,𝜏𝑘𝑙symbolizes	ADP
fumecheng-7253	84	39	the	the	DET
fumecheng-7253	84	40	nonlocal	nonlocal	ADJ
fumecheng-7253	84	41	stress	stress	NOUN
fumecheng-7253	84	42	tensor	tensor	NOUN
fumecheng-7253	84	43	and	and	CCONJ
fumecheng-7253	84	44	𝜎𝑘𝑙	𝜎𝑘𝑙	NOUN
fumecheng-7253	84	45	represents	represent	VERB
fumecheng-7253	84	46	the	the	DET
fumecheng-7253	84	47	classic	classic	ADJ
fumecheng-7253	84	48	stress	stress	NOUN
fumecheng-7253	84	49	tensor	tensor	NOUN
fumecheng-7253	84	50	.	.	PUNCT
fumecheng-7253	85	1	the	the	DET
fumecheng-7253	85	2	classical	classical	ADJ
fumecheng-7253	85	3	elasticity	elasticity	NOUN
fumecheng-7253	85	4	equation	equation	NOUN
fumecheng-7253	85	5	is	be	AUX
fumecheng-7253	85	6	accessible	accessible	ADJ
fumecheng-7253	85	7	if	if	SCONJ
fumecheng-7253	85	8	parameter	parameter	NOUN
fumecheng-7253	85	9	𝑎	𝑎	NOUN
fumecheng-7253	85	10	takes	take	NOUN
fumecheng-7253	85	11	zero	zero	NUM
fumecheng-7253	85	12	value	value	NOUN
fumecheng-7253	85	13	(	(	PUNCT
fumecheng-7253	85	14	𝑒0𝑎	𝑒0𝑎	PROPN
fumecheng-7253	85	15	=	=	SYM
fumecheng-7253	85	16	0	0	NUM
fumecheng-7253	85	17	)	)	PUNCT
fumecheng-7253	85	18	.	.	PUNCT
fumecheng-7253	86	1	the	the	DET
fumecheng-7253	86	2	constitutive	constitutive	ADJ
fumecheng-7253	86	3	equation	equation	NOUN
fumecheng-7253	86	4	is	be	AUX
fumecheng-7253	86	5	expressed	express	VERB
fumecheng-7253	86	6	as	as	ADP
fumecheng-7253	86	7	𝜎𝑖𝑗	𝜎𝑖𝑗	PROPN
fumecheng-7253	86	8	=	=	SYM
fumecheng-7253	86	9	2𝜇𝑒𝑖𝑗	2𝜇𝑒𝑖𝑗	NUM
fumecheng-7253	86	10	+	+	CCONJ
fumecheng-7253	87	1	[	[	X
fumecheng-7253	87	2	𝜆𝑒𝑘𝑘	𝜆𝑒𝑘𝑘	NOUN
fumecheng-7253	87	3	−	−	NOUN
fumecheng-7253	87	4	𝛾(𝑇	𝛾(𝑇	VERB
fumecheng-7253	87	5	−	−	PROPN
fumecheng-7253	87	6	𝑇0)]𝛿𝑖𝑗	𝑇0)]𝛿𝑖𝑗	NOUN
fumecheng-7253	87	7	,	,	PUNCT
fumecheng-7253	87	8	(	(	PUNCT
fumecheng-7253	87	9	2	2	NUM
fumecheng-7253	87	10	)	)	PUNCT
fumecheng-7253	87	11	in	in	ADP
fumecheng-7253	87	12	which	which	PRON
fumecheng-7253	87	13	𝜇	𝜇	ADP
fumecheng-7253	87	14	and	and	CCONJ
fumecheng-7253	87	15	𝜆	𝜆	PRON
fumecheng-7253	87	16	represent	represent	VERB
fumecheng-7253	87	17	the	the	DET
fumecheng-7253	87	18	lame	lame	ADJ
fumecheng-7253	87	19	coefficients	coefficient	NOUN
fumecheng-7253	87	20	and	and	CCONJ
fumecheng-7253	87	21	𝛿𝑖𝑗	𝛿𝑖𝑗	NOUN
fumecheng-7253	87	22	refers	refer	VERB
fumecheng-7253	87	23	to	to	ADP
fumecheng-7253	87	24	kronecker	kronecker	NOUN
fumecheng-7253	87	25	’s	’s	PART
fumecheng-7253	87	26	delta	delta	NOUN
fumecheng-7253	87	27	operator	operator	NOUN
fumecheng-7253	87	28	.	.	PUNCT
fumecheng-7253	88	1	moreover	moreover	ADV
fumecheng-7253	88	2	,	,	PUNCT
fumecheng-7253	88	3	𝜃	𝜃	X
fumecheng-7253	88	4	=	=	SYM
fumecheng-7253	88	5	𝑇	𝑇	PROPN
fumecheng-7253	88	6	−	−	PROPN
fumecheng-7253	88	7	𝑇0	𝑇0	NOUN
fumecheng-7253	88	8	stands	stand	VERB
fumecheng-7253	88	9	for	for	ADP
fumecheng-7253	88	10	a	a	DET
fumecheng-7253	88	11	temperature	temperature	NOUN
fumecheng-7253	88	12	change	change	NOUN
fumecheng-7253	88	13	with	with	ADP
fumecheng-7253	88	14	respect	respect	NOUN
fumecheng-7253	88	15	to	to	PART
fumecheng-7253	88	16	reference	reference	VERB
fumecheng-7253	88	17	temperature	temperature	NOUN
fumecheng-7253	88	18	temperature	temperature	NOUN
fumecheng-7253	88	19	-	-	PUNCT
fumecheng-7253	88	20	dependent	dependent	ADJ
fumecheng-7253	88	21	physical	physical	ADJ
fumecheng-7253	88	22	characteristics	characteristic	NOUN
fumecheng-7253	88	23	of	of	ADP
fumecheng-7253	88	24	rotating	rotate	VERB
fumecheng-7253	88	25	nonlocal	nonlocal	ADJ
fumecheng-7253	88	26	nanobeams	nanobeam	NOUN
fumecheng-7253	88	27	subject	subject	ADJ
fumecheng-7253	88	28	to	to	ADP
fumecheng-7253	88	29	...	...	PUNCT
fumecheng-7253	88	30	637	637	NUM
fumecheng-7253	88	31	𝑇0	𝑇0	NOUN
fumecheng-7253	88	32	,	,	PUNCT
fumecheng-7253	88	33	𝑒	𝑒	PROPN
fumecheng-7253	88	34	=	=	VERB
fumecheng-7253	88	35	div	div	X
fumecheng-7253	88	36	�	�	PROPN
fumecheng-7253	88	37	⃗	⃗	NOUN
fumecheng-7253	88	38	�	�	PROPN
fumecheng-7253	88	39	is	be	AUX
fumecheng-7253	88	40	the	the	DET
fumecheng-7253	88	41	volumetric	volumetric	ADJ
fumecheng-7253	88	42	strain	strain	NOUN
fumecheng-7253	88	43	and	and	CCONJ
fumecheng-7253	88	44	�	�	NOUN
fumecheng-7253	88	45	⃗	⃗	NOUN
fumecheng-7253	88	46	�	�	PROPN
fumecheng-7253	88	47	denotes	denote	VERB
fumecheng-7253	88	48	the	the	DET
fumecheng-7253	88	49	displacement	displacement	NOUN
fumecheng-7253	88	50	vector	vector	NOUN
fumecheng-7253	88	51	.	.	PUNCT
fumecheng-7253	89	1	lame	lame	PROPN
fumecheng-7253	89	2	’s	’s	PART
fumecheng-7253	89	3	constants	constant	NOUN
fumecheng-7253	89	4	and	and	CCONJ
fumecheng-7253	89	5	shear	shear	NOUN
fumecheng-7253	89	6	modulus	modulus	NOUN
fumecheng-7253	89	7	are	be	AUX
fumecheng-7253	89	8	defined	define	VERB
fumecheng-7253	89	9	by	by	ADP
fumecheng-7253	89	10	:	:	PUNCT
fumecheng-7253	89	11	𝜆	𝜆	X
fumecheng-7253	89	12	=	=	PUNCT
fumecheng-7253	89	13	𝐸𝜈	𝐸𝜈	ADJ
fumecheng-7253	89	14	(	(	PUNCT
fumecheng-7253	89	15	1+𝜈)(1−2𝜈	1+𝜈)(1−2𝜈	NUM
fumecheng-7253	89	16	)	)	PUNCT
fumecheng-7253	89	17	,	,	PUNCT
fumecheng-7253	89	18	𝜇	𝜇	X
fumecheng-7253	89	19	=	=	X
fumecheng-7253	89	20	𝐸	𝐸	PROPN
fumecheng-7253	89	21	2(1+𝜈	2(1+𝜈	NUM
fumecheng-7253	89	22	)	)	PUNCT
fumecheng-7253	89	23	.	.	PUNCT
fumecheng-7253	90	1	(	(	PUNCT
fumecheng-7253	90	2	3	3	X
fumecheng-7253	90	3	)	)	PUNCT
fumecheng-7253	90	4	the	the	DET
fumecheng-7253	90	5	modified	modify	VERB
fumecheng-7253	90	6	heat	heat	NOUN
fumecheng-7253	90	7	conduction	conduction	NOUN
fumecheng-7253	90	8	equation	equation	NOUN
fumecheng-7253	90	9	that	that	PRON
fumecheng-7253	90	10	includes	include	VERB
fumecheng-7253	90	11	two	two	NUM
fumecheng-7253	90	12	phase	phase	NOUN
fumecheng-7253	90	13	lags	lag	NOUN
fumecheng-7253	90	14	is	be	AUX
fumecheng-7253	90	15	described	describe	VERB
fumecheng-7253	90	16	as	as	SCONJ
fumecheng-7253	90	17	follows	follow	VERB
fumecheng-7253	90	18	[	[	X
fumecheng-7253	90	19	2	2	NUM
fumecheng-7253	90	20	-	-	SYM
fumecheng-7253	90	21	4	4	NUM
fumecheng-7253	90	22	]	]	PUNCT
fumecheng-7253	90	23	:	:	PUNCT
fumecheng-7253	90	24	(	(	PUNCT
fumecheng-7253	90	25	1	1	X
fumecheng-7253	90	26	+	+	NUM
fumecheng-7253	90	27	𝜏𝜃	𝜏𝜃	ADP
fumecheng-7253	90	28	𝜕	𝜕	PROPN
fumecheng-7253	90	29	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	90	30	)	)	PUNCT
fumecheng-7253	90	31	(	(	PUNCT
fumecheng-7253	90	32	𝐾𝜃,𝑖),𝑖	𝐾𝜃,𝑖),𝑖	PUNCT
fumecheng-7253	91	1	=	=	SYM
fumecheng-7253	91	2	(	(	PUNCT
fumecheng-7253	91	3	1	1	NUM
fumecheng-7253	91	4	+	+	NUM
fumecheng-7253	91	5	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	91	6	𝜕	𝜕	PROPN
fumecheng-7253	91	7	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	91	8	+	+	CCONJ
fumecheng-7253	91	9	1	1	NUM
fumecheng-7253	91	10	2	2	NUM
fumecheng-7253	91	11	𝜏𝑞	𝜏𝑞	ADP
fumecheng-7253	91	12	2	2	NUM
fumecheng-7253	91	13	𝜕2	𝜕2	NOUN
fumecheng-7253	91	14	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	91	15	)	)	PUNCT
fumecheng-7253	91	16	(	(	PUNCT
fumecheng-7253	91	17	𝜌𝐶𝐸	𝜌𝐶𝐸	NOUN
fumecheng-7253	91	18	𝜕𝜃	𝜕𝜃	ADV
fumecheng-7253	91	19	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	91	20	+	+	PROPN
fumecheng-7253	91	21	𝛾𝑇0	𝛾𝑇0	PROPN
fumecheng-7253	91	22	𝜕𝑒	𝜕𝑒	NOUN
fumecheng-7253	91	23	𝜕𝑡	𝜕𝑡	NOUN
fumecheng-7253	91	24	−	−	PROPN
fumecheng-7253	91	25	𝜌𝑄	𝜌𝑄	NOUN
fumecheng-7253	91	26	)	)	PUNCT
fumecheng-7253	91	27	,	,	PUNCT
fumecheng-7253	91	28	(	(	PUNCT
fumecheng-7253	91	29	4	4	X
fumecheng-7253	91	30	)	)	PUNCT
fumecheng-7253	91	31	where	where	SCONJ
fumecheng-7253	91	32	𝑄	𝑄	PRON
fumecheng-7253	91	33	represents	represent	VERB
fumecheng-7253	91	34	the	the	DET
fumecheng-7253	91	35	heat	heat	NOUN
fumecheng-7253	91	36	source	source	NOUN
fumecheng-7253	91	37	,	,	PUNCT
fumecheng-7253	91	38	𝛾	𝛾	PROPN
fumecheng-7253	91	39	=	=	PUNCT
fumecheng-7253	91	40	𝐸𝛼𝑇/(1	𝐸𝛼𝑇/(1	ADJ
fumecheng-7253	91	41	−	−	PROPN
fumecheng-7253	91	42	2𝜈	2𝜈	NUM
fumecheng-7253	91	43	)	)	PUNCT
fumecheng-7253	91	44	,	,	PUNCT
fumecheng-7253	91	45	in	in	ADP
fumecheng-7253	91	46	which	which	PRON
fumecheng-7253	91	47	𝛼𝑇	𝛼𝑇	NOUN
fumecheng-7253	91	48	is	be	AUX
fumecheng-7253	91	49	the	the	DET
fumecheng-7253	91	50	thermal	thermal	ADJ
fumecheng-7253	91	51	expansion	expansion	NOUN
fumecheng-7253	91	52	constant	constant	ADJ
fumecheng-7253	91	53	,	,	PUNCT
fumecheng-7253	91	54	𝐸	𝐸	PROPN
fumecheng-7253	91	55	denotes	denote	VERB
fumecheng-7253	91	56	the	the	DET
fumecheng-7253	91	57	module	module	NOUN
fumecheng-7253	91	58	of	of	ADP
fumecheng-7253	91	59	elasticity	elasticity	NOUN
fumecheng-7253	91	60	,	,	PUNCT
fumecheng-7253	91	61	𝐾	𝐾	PROPN
fumecheng-7253	91	62	implies	imply	VERB
fumecheng-7253	91	63	the	the	DET
fumecheng-7253	91	64	thermal	thermal	ADJ
fumecheng-7253	91	65	conductivity	conductivity	NOUN
fumecheng-7253	91	66	,	,	PUNCT
fumecheng-7253	91	67	𝐶𝐸	𝐶𝐸	PROPN
fumecheng-7253	91	68	refers	refer	VERB
fumecheng-7253	91	69	to	to	ADP
fumecheng-7253	91	70	the	the	DET
fumecheng-7253	91	71	specific	specific	ADJ
fumecheng-7253	91	72	heat	heat	NOUN
fumecheng-7253	91	73	and	and	CCONJ
fumecheng-7253	91	74	𝜌	𝜌	PRON
fumecheng-7253	91	75	symbolizes	symbolize	VERB
fumecheng-7253	91	76	the	the	DET
fumecheng-7253	91	77	density	density	NOUN
fumecheng-7253	91	78	of	of	ADP
fumecheng-7253	91	79	material	material	NOUN
fumecheng-7253	91	80	.	.	PUNCT
fumecheng-7253	92	1	the	the	DET
fumecheng-7253	92	2	theory	theory	NOUN
fumecheng-7253	92	3	of	of	ADP
fumecheng-7253	92	4	classical	classical	ADJ
fumecheng-7253	92	5	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	92	6	,	,	PUNCT
fumecheng-7253	92	7	i.e.	i.e.	X
fumecheng-7253	92	8	the	the	DET
fumecheng-7253	92	9	lord	lord	PROPN
fumecheng-7253	92	10	and	and	CCONJ
fumecheng-7253	92	11	shulman	shulman	PROPN
fumecheng-7253	92	12	model	model	PROPN
fumecheng-7253	93	1	[	[	X
fumecheng-7253	93	2	1	1	NUM
fumecheng-7253	93	3	]	]	PUNCT
fumecheng-7253	93	4	,	,	PUNCT
fumecheng-7253	93	5	and	and	CCONJ
fumecheng-7253	93	6	dual	dual	ADJ
fumecheng-7253	93	7	-	-	PUNCT
fumecheng-7253	93	8	phase	phase	NOUN
fumecheng-7253	93	9	-	-	PUNCT
fumecheng-7253	93	10	delay	delay	NOUN
fumecheng-7253	93	11	model	model	NOUN
fumecheng-7253	93	12	[	[	X
fumecheng-7253	93	13	2	2	NUM
fumecheng-7253	93	14	-	-	SYM
fumecheng-7253	93	15	4	4	NUM
fumecheng-7253	93	16	]	]	PUNCT
fumecheng-7253	93	17	can	can	AUX
fumecheng-7253	93	18	be	be	AUX
fumecheng-7253	93	19	derived	derive	VERB
fumecheng-7253	93	20	from	from	ADP
fumecheng-7253	93	21	eq	eq	ADP
fumecheng-7253	93	22	.	.	PUNCT
fumecheng-7253	94	1	(	(	PUNCT
fumecheng-7253	94	2	3	3	X
fumecheng-7253	94	3	)	)	PUNCT
fumecheng-7253	94	4	for	for	ADP
fumecheng-7253	94	5	the	the	DET
fumecheng-7253	94	6	selection	selection	NOUN
fumecheng-7253	94	7	of	of	ADP
fumecheng-7253	94	8	different	different	ADJ
fumecheng-7253	94	9	phase	phase	NOUN
fumecheng-7253	94	10	lag	lag	NOUN
fumecheng-7253	94	11	parameters	parameter	NOUN
fumecheng-7253	94	12	𝜏𝜃	𝜏𝜃	X
fumecheng-7253	94	13	and	and	CCONJ
fumecheng-7253	94	14	𝜏𝑞.	𝜏𝑞.	ADJ
fumecheng-7253	94	15	•	•	NUM
fumecheng-7253	94	16	by	by	ADP
fumecheng-7253	94	17	putting	put	VERB
fumecheng-7253	94	18	𝜏𝜃	𝜏𝜃	X
fumecheng-7253	94	19	=	=	NOUN
fumecheng-7253	94	20	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	94	21	=	=	NOUN
fumecheng-7253	94	22	0	0	NUM
fumecheng-7253	94	23	in	in	ADP
fumecheng-7253	94	24	eq	eq	ADP
fumecheng-7253	94	25	.	.	PUNCT
fumecheng-7253	95	1	(	(	PUNCT
fumecheng-7253	95	2	3	3	NUM
fumecheng-7253	95	3	)	)	PUNCT
fumecheng-7253	95	4	,	,	PUNCT
fumecheng-7253	95	5	we	we	PRON
fumecheng-7253	95	6	get	get	VERB
fumecheng-7253	95	7	the	the	DET
fumecheng-7253	95	8	nonlocal	nonlocal	ADJ
fumecheng-7253	95	9	theory	theory	NOUN
fumecheng-7253	95	10	of	of	ADP
fumecheng-7253	95	11	coupled	couple	VERB
fumecheng-7253	95	12	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	95	13	(	(	PUNCT
fumecheng-7253	95	14	cte	cte	NOUN
fumecheng-7253	95	15	)	)	PUNCT
fumecheng-7253	95	16	.	.	PUNCT
fumecheng-7253	96	1	•	•	NUM
fumecheng-7253	96	2	the	the	DET
fumecheng-7253	96	3	generalized	generalized	ADJ
fumecheng-7253	96	4	theory	theory	NOUN
fumecheng-7253	96	5	of	of	ADP
fumecheng-7253	96	6	nonlocal	nonlocal	ADJ
fumecheng-7253	96	7	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	96	8	(	(	PUNCT
fumecheng-7253	96	9	ls	ls	PROPN
fumecheng-7253	96	10	theory	theory	NOUN
fumecheng-7253	96	11	)	)	PUNCT
fumecheng-7253	96	12	can	can	AUX
fumecheng-7253	96	13	be	be	AUX
fumecheng-7253	96	14	obtained	obtain	VERB
fumecheng-7253	96	15	by	by	ADP
fumecheng-7253	96	16	putting	put	VERB
fumecheng-7253	96	17	𝜏𝜃	𝜏𝜃	NOUN
fumecheng-7253	96	18	=	=	SYM
fumecheng-7253	96	19	0	0	NUM
fumecheng-7253	96	20	and	and	CCONJ
fumecheng-7253	96	21	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	96	22	=	=	NOUN
fumecheng-7253	96	23	𝜏0	𝜏0	PROPN
fumecheng-7253	96	24	(	(	PUNCT
fumecheng-7253	96	25	𝜏0refers	𝜏0refer	NOUN
fumecheng-7253	96	26	to	to	ADP
fumecheng-7253	96	27	the	the	DET
fumecheng-7253	96	28	relaxation	relaxation	NOUN
fumecheng-7253	96	29	time	time	NOUN
fumecheng-7253	96	30	)	)	PUNCT
fumecheng-7253	96	31	.	.	PUNCT
fumecheng-7253	97	1	•	•	NOUN
fumecheng-7253	97	2	the	the	DET
fumecheng-7253	97	3	nonlocal	nonlocal	ADJ
fumecheng-7253	97	4	dual	dual	ADJ
fumecheng-7253	97	5	-	-	PUNCT
fumecheng-7253	97	6	phase	phase	NOUN
fumecheng-7253	97	7	-	-	PUNCT
fumecheng-7253	97	8	lag	lag	NOUN
fumecheng-7253	97	9	model	model	NOUN
fumecheng-7253	97	10	(	(	PUNCT
fumecheng-7253	97	11	dpl	dpl	NOUN
fumecheng-7253	97	12	)	)	PUNCT
fumecheng-7253	97	13	is	be	AUX
fumecheng-7253	97	14	accessible	accessible	ADJ
fumecheng-7253	97	15	when	when	SCONJ
fumecheng-7253	97	16	𝜏𝜃	𝜏𝜃	ADP
fumecheng-7253	97	17	falls	fall	VERB
fumecheng-7253	97	18	within	within	ADP
fumecheng-7253	97	19	the	the	DET
fumecheng-7253	97	20	interval	interval	NOUN
fumecheng-7253	97	21	[	[	X
fumecheng-7253	97	22	0	0	NUM
fumecheng-7253	97	23	,	,	PUNCT
fumecheng-7253	97	24	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	97	25	]	]	PUNCT
fumecheng-7253	97	26	.	.	PUNCT
fumecheng-7253	98	1	it	it	PRON
fumecheng-7253	98	2	is	be	AUX
fumecheng-7253	98	3	worth	worth	ADJ
fumecheng-7253	98	4	mentioning	mention	VERB
fumecheng-7253	98	5	that	that	SCONJ
fumecheng-7253	98	6	if	if	SCONJ
fumecheng-7253	98	7	one	one	NUM
fumecheng-7253	98	8	of	of	ADP
fumecheng-7253	98	9	the	the	DET
fumecheng-7253	98	10	thermo	thermo	NOUN
fumecheng-7253	98	11	-	-	PUNCT
fumecheng-7253	98	12	physical	physical	ADJ
fumecheng-7253	98	13	characteristics	characteristic	NOUN
fumecheng-7253	98	14	(	(	PUNCT
fumecheng-7253	98	15	𝐾,𝐶𝐸and	𝐾,𝐶𝐸and	NOUN
fumecheng-7253	98	16	𝜌	𝜌	X
fumecheng-7253	98	17	)	)	PUNCT
fumecheng-7253	98	18	depends	depend	VERB
fumecheng-7253	98	19	on	on	ADP
fumecheng-7253	98	20	temperature	temperature	NOUN
fumecheng-7253	98	21	,	,	PUNCT
fumecheng-7253	98	22	eq	eq	NOUN
fumecheng-7253	98	23	.	.	PUNCT
fumecheng-7253	99	1	(	(	PUNCT
fumecheng-7253	99	2	3	3	X
fumecheng-7253	99	3	)	)	PUNCT
fumecheng-7253	99	4	is	be	AUX
fumecheng-7253	99	5	converted	convert	VERB
fumecheng-7253	99	6	to	to	ADP
fumecheng-7253	99	7	a	a	DET
fumecheng-7253	99	8	nonlinear	nonlinear	ADJ
fumecheng-7253	99	9	partial	partial	ADJ
fumecheng-7253	99	10	differential	differential	NOUN
fumecheng-7253	99	11	equation	equation	NOUN
fumecheng-7253	99	12	.	.	PUNCT
fumecheng-7253	100	1	3	3	X
fumecheng-7253	100	2	.	.	X
fumecheng-7253	100	3	problem	problem	NOUN
fumecheng-7253	100	4	formulation	formulation	NOUN
fumecheng-7253	100	5	fig	fig	NOUN
fumecheng-7253	100	6	.	.	PUNCT
fumecheng-7253	101	1	1	1	NUM
fumecheng-7253	101	2	displays	display	VERB
fumecheng-7253	101	3	the	the	DET
fumecheng-7253	101	4	configuration	configuration	NOUN
fumecheng-7253	101	5	of	of	ADP
fumecheng-7253	101	6	a	a	DET
fumecheng-7253	101	7	thermoelastic	thermoelastic	ADJ
fumecheng-7253	101	8	rotating	rotate	VERB
fumecheng-7253	101	9	nanoscale	nanoscale	NOUN
fumecheng-7253	101	10	beam	beam	NOUN
fumecheng-7253	101	11	.	.	PUNCT
fumecheng-7253	102	1	the	the	DET
fumecheng-7253	102	2	considered	consider	VERB
fumecheng-7253	102	3	nanobeam	nanobeam	NOUN
fumecheng-7253	102	4	has	have	VERB
fumecheng-7253	102	5	thickness	thickness	NOUN
fumecheng-7253	102	6	ℎ	ℎ	NOUN
fumecheng-7253	102	7	,	,	PUNCT
fumecheng-7253	102	8	width	width	ADJ
fumecheng-7253	102	9	𝑏	𝑏	NOUN
fumecheng-7253	102	10	and	and	CCONJ
fumecheng-7253	102	11	length	length	NOUN
fumecheng-7253	102	12	𝐿.	𝐿.	VERB
fumecheng-7253	102	13	the	the	DET
fumecheng-7253	102	14	𝑥-axis	𝑥-axis	NOUN
fumecheng-7253	102	15	lies	lie	VERB
fumecheng-7253	102	16	in	in	ADP
fumecheng-7253	102	17	the	the	DET
fumecheng-7253	102	18	axial	axial	ADJ
fumecheng-7253	102	19	direction	direction	NOUN
fumecheng-7253	102	20	of	of	ADP
fumecheng-7253	102	21	nanobeam	nanobeam	NOUN
fumecheng-7253	102	22	and	and	CCONJ
fumecheng-7253	102	23	its	its	PRON
fumecheng-7253	102	24	width	width	NOUN
fumecheng-7253	102	25	and	and	CCONJ
fumecheng-7253	102	26	thickness	thickness	NOUN
fumecheng-7253	102	27	are	be	AUX
fumecheng-7253	102	28	in	in	ADP
fumecheng-7253	102	29	𝑦	𝑦	NOUN
fumecheng-7253	102	30	and	and	CCONJ
fumecheng-7253	102	31	𝑧	𝑧	DET
fumecheng-7253	102	32	directions	direction	NOUN
fumecheng-7253	102	33	,	,	PUNCT
fumecheng-7253	102	34	respectively	respectively	ADV
fumecheng-7253	102	35	.	.	PUNCT
fumecheng-7253	103	1	initially	initially	ADV
fumecheng-7253	103	2	,	,	PUNCT
fumecheng-7253	103	3	it	it	PRON
fumecheng-7253	103	4	is	be	AUX
fumecheng-7253	103	5	supposed	suppose	VERB
fumecheng-7253	103	6	that	that	SCONJ
fumecheng-7253	103	7	the	the	DET
fumecheng-7253	103	8	nanobeam	nanobeam	NOUN
fumecheng-7253	103	9	is	be	AUX
fumecheng-7253	103	10	stress	stress	NOUN
fumecheng-7253	103	11	free	free	ADJ
fumecheng-7253	103	12	and	and	CCONJ
fumecheng-7253	103	13	the	the	DET
fumecheng-7253	103	14	temperature	temperature	NOUN
fumecheng-7253	103	15	is	be	AUX
fumecheng-7253	103	16	tentatively	tentatively	ADV
fumecheng-7253	103	17	at	at	ADP
fumecheng-7253	103	18	𝑇0.the	𝑇0.the	DET
fumecheng-7253	103	19	displacement	displacement	ADJ
fumecheng-7253	103	20	components	component	NOUN
fumecheng-7253	103	21	can	can	AUX
fumecheng-7253	103	22	be	be	AUX
fumecheng-7253	103	23	described	describe	VERB
fumecheng-7253	103	24	as	as	SCONJ
fumecheng-7253	103	25	follows	follow	VERB
fumecheng-7253	103	26	:	:	PUNCT
fumecheng-7253	103	27	𝑢	𝑢	X
fumecheng-7253	103	28	=	=	PUNCT
fumecheng-7253	103	29	−𝑧	−𝑧	PROPN
fumecheng-7253	103	30	𝜕𝑤	𝜕𝑤	VERB
fumecheng-7253	103	31	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-7253	103	32	,	,	PUNCT
fumecheng-7253	103	33	𝑣	𝑣	X
fumecheng-7253	103	34	=	=	SYM
fumecheng-7253	103	35	0	0	NUM
fumecheng-7253	103	36	,	,	PUNCT
fumecheng-7253	103	37	𝑤	𝑤	ADP
fumecheng-7253	103	38	=	=	SYM
fumecheng-7253	103	39	𝑤(𝑥	𝑤(𝑥	NOUN
fumecheng-7253	103	40	,	,	PUNCT
fumecheng-7253	103	41	𝑡	𝑡	NOUN
fumecheng-7253	103	42	)	)	PUNCT
fumecheng-7253	103	43	,	,	PUNCT
fumecheng-7253	103	44	(	(	PUNCT
fumecheng-7253	103	45	5	5	X
fumecheng-7253	103	46	)	)	PUNCT
fumecheng-7253	103	47	where	where	SCONJ
fumecheng-7253	103	48	𝑤	𝑤	AUX
fumecheng-7253	103	49	denotes	denote	VERB
fumecheng-7253	103	50	the	the	DET
fumecheng-7253	103	51	transverse	transverse	NOUN
fumecheng-7253	103	52	deflection	deflection	NOUN
fumecheng-7253	103	53	.	.	PUNCT
fumecheng-7253	104	1	638	638	NUM
fumecheng-7253	104	2	a.	a.	NOUN
fumecheng-7253	104	3	e.	e.	PROPN
fumecheng-7253	104	4	abouelregal	abouelregal	PROPN
fumecheng-7253	104	5	,	,	PUNCT
fumecheng-7253	104	6	h.	h.	PROPN
fumecheng-7253	104	7	m.	m.	PROPN
fumecheng-7253	104	8	sedighi	sedighi	PROPN
fumecheng-7253	104	9	,	,	PUNCT
fumecheng-7253	104	10	s.	s.	PROPN
fumecheng-7253	104	11	a.	a.	PROPN
fumecheng-7253	104	12	faghidian	faghidian	PROPN
fumecheng-7253	104	13	,	,	PUNCT
fumecheng-7253	104	14	a.	a.	PROPN
fumecheng-7253	104	15	h.	h.	PROPN
fumecheng-7253	104	16	shirazi	shirazi	PROPN
fumecheng-7253	104	17	fig	fig	PROPN
fumecheng-7253	104	18	.	.	PUNCT
fumecheng-7253	105	1	1	1	NUM
fumecheng-7253	105	2	schematic	schematic	ADJ
fumecheng-7253	105	3	configuration	configuration	NOUN
fumecheng-7253	105	4	of	of	ADP
fumecheng-7253	105	5	rotating	rotate	VERB
fumecheng-7253	105	6	nanobeam	nanobeam	NOUN
fumecheng-7253	105	7	eq	eq	ADP
fumecheng-7253	105	8	.	.	PUNCT
fumecheng-7253	106	1	(	(	PUNCT
fumecheng-7253	106	2	5	5	X
fumecheng-7253	106	3	)	)	PUNCT
fumecheng-7253	106	4	can	can	AUX
fumecheng-7253	106	5	be	be	AUX
fumecheng-7253	106	6	used	use	VERB
fumecheng-7253	106	7	to	to	PART
fumecheng-7253	106	8	simplify	simplify	VERB
fumecheng-7253	106	9	the	the	DET
fumecheng-7253	106	10	one	one	NUM
fumecheng-7253	106	11	dimension	dimension	NOUN
fumecheng-7253	106	12	constitutive	constitutive	ADJ
fumecheng-7253	106	13	relationship	relationship	NOUN
fumecheng-7253	106	14	(	(	PUNCT
fumecheng-7253	106	15	1	1	NUM
fumecheng-7253	106	16	)	)	PUNCT
fumecheng-7253	106	17	as	as	ADP
fumecheng-7253	106	18	𝜎𝑥	𝜎𝑥	ADP
fumecheng-7253	106	19	−	−	NOUN
fumecheng-7253	106	20	𝜉	𝜉	NOUN
fumecheng-7253	106	21	𝜕2𝜎𝑥	𝜕2𝜎𝑥	PROPN
fumecheng-7253	106	22	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	107	1	=	=	PUNCT
fumecheng-7253	107	2	−𝐸	−𝐸	NOUN
fumecheng-7253	107	3	(	(	PUNCT
fumecheng-7253	107	4	𝑧	𝑧	PROPN
fumecheng-7253	107	5	𝜕2𝑤	𝜕2𝑤	PROPN
fumecheng-7253	107	6	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	107	7	+	+	CCONJ
fumecheng-7253	107	8	𝛼𝑇𝜃	𝛼𝑇𝜃	NOUN
fumecheng-7253	107	9	)	)	PUNCT
fumecheng-7253	107	10	,	,	PUNCT
fumecheng-7253	107	11	(	(	PUNCT
fumecheng-7253	107	12	6	6	NUM
fumecheng-7253	107	13	)	)	PUNCT
fumecheng-7253	107	14	in	in	ADP
fumecheng-7253	107	15	which	which	PRON
fumecheng-7253	107	16	𝜎𝑥	𝜎𝑥	NOUN
fumecheng-7253	107	17	indicates	indicate	VERB
fumecheng-7253	107	18	the	the	DET
fumecheng-7253	107	19	nonlocal	nonlocal	ADJ
fumecheng-7253	107	20	axial	axial	ADJ
fumecheng-7253	107	21	thermal	thermal	ADJ
fumecheng-7253	107	22	stress	stress	NOUN
fumecheng-7253	107	23	,	,	PUNCT
fumecheng-7253	107	24	𝛼𝑇	𝛼𝑇	NOUN
fumecheng-7253	107	25	=	=	SYM
fumecheng-7253	107	26	𝛼𝑡/(1	𝛼𝑡/(1	NUM
fumecheng-7253	108	1	−	−	PROPN
fumecheng-7253	108	2	2𝜈	2𝜈	NUM
fumecheng-7253	108	3	)	)	PUNCT
fumecheng-7253	108	4	and	and	CCONJ
fumecheng-7253	108	5	𝜉	𝜉	X
fumecheng-7253	108	6	=	=	SYM
fumecheng-7253	108	7	(	(	PUNCT
fumecheng-7253	108	8	𝑒0𝑎)2	𝑒0𝑎)2	PROPN
fumecheng-7253	108	9	.	.	PUNCT
fumecheng-7253	109	1	bending	bend	VERB
fumecheng-7253	109	2	moment	moment	NOUN
fumecheng-7253	109	3	m	m	VERB
fumecheng-7253	109	4	may	may	AUX
fumecheng-7253	109	5	be	be	AUX
fumecheng-7253	109	6	calculated	calculate	VERB
fumecheng-7253	109	7	by	by	ADP
fumecheng-7253	109	8	the	the	DET
fumecheng-7253	109	9	following	follow	VERB
fumecheng-7253	109	10	integration	integration	NOUN
fumecheng-7253	109	11	formula	formula	NOUN
fumecheng-7253	109	12	:	:	PUNCT
fumecheng-7253	109	13	𝑀(𝑥	𝑀(𝑥	NUM
fumecheng-7253	109	14	,	,	PUNCT
fumecheng-7253	109	15	𝑡	𝑡	NOUN
fumecheng-7253	109	16	)	)	PUNCT
fumecheng-7253	109	17	=	=	SYM
fumecheng-7253	109	18	∫	∫	PROPN
fumecheng-7253	109	19	𝑧𝜎𝑥d𝑧	𝑧𝜎𝑥d𝑧	NOUN
fumecheng-7253	109	20	ℎ/2	ℎ/2	VERB
fumecheng-7253	109	21	−ℎ/2	−ℎ/2	NOUN
fumecheng-7253	109	22	.	.	PUNCT
fumecheng-7253	110	1	(	(	PUNCT
fumecheng-7253	110	2	7	7	X
fumecheng-7253	110	3	)	)	PUNCT
fumecheng-7253	110	4	thereby	thereby	ADV
fumecheng-7253	110	5	,	,	PUNCT
fumecheng-7253	110	6	the	the	DET
fumecheng-7253	110	7	following	follow	VERB
fumecheng-7253	110	8	partial	partial	ADJ
fumecheng-7253	110	9	differential	differential	NOUN
fumecheng-7253	110	10	equation	equation	NOUN
fumecheng-7253	110	11	is	be	AUX
fumecheng-7253	110	12	satisfied	satisfied	ADJ
fumecheng-7253	110	13	by	by	ADP
fumecheng-7253	110	14	the	the	DET
fumecheng-7253	110	15	bending	bend	VERB
fumecheng-7253	110	16	moment	moment	NOUN
fumecheng-7253	110	17	after	after	ADP
fumecheng-7253	110	18	substituting	substitute	VERB
fumecheng-7253	110	19	eq	eq	ADP
fumecheng-7253	110	20	.	.	PUNCT
fumecheng-7253	111	1	(	(	PUNCT
fumecheng-7253	111	2	6	6	NUM
fumecheng-7253	111	3	)	)	PUNCT
fumecheng-7253	111	4	into	into	ADP
fumecheng-7253	111	5	eq	eq	NOUN
fumecheng-7253	111	6	.	.	PUNCT
fumecheng-7253	112	1	(	(	PUNCT
fumecheng-7253	112	2	7	7	X
fumecheng-7253	112	3	)	)	PUNCT
fumecheng-7253	112	4	𝑀(𝑥	𝑀(𝑥	NOUN
fumecheng-7253	112	5	,	,	PUNCT
fumecheng-7253	112	6	𝑡	𝑡	NOUN
fumecheng-7253	112	7	)	)	PUNCT
fumecheng-7253	112	8	−	−	ADP
fumecheng-7253	112	9	𝜉	𝜉	ADP
fumecheng-7253	112	10	𝜕2𝑀	𝜕2𝑀	NOUN
fumecheng-7253	112	11	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	112	12	=	=	PUNCT
fumecheng-7253	113	1	−𝐸𝐼	−𝐸𝐼	ADJ
fumecheng-7253	113	2	(	(	PUNCT
fumecheng-7253	113	3	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	113	4	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	113	5	+	+	CCONJ
fumecheng-7253	113	6	𝛼𝑇𝑀𝑇	𝛼𝑇𝑀𝑇	NUM
fumecheng-7253	113	7	)	)	PUNCT
fumecheng-7253	113	8	,	,	PUNCT
fumecheng-7253	113	9	(	(	PUNCT
fumecheng-7253	113	10	8)	8)	NUM
fumecheng-7253	113	11	where	where	SCONJ
fumecheng-7253	113	12	𝐸𝐼	𝐸𝐼	PROPN
fumecheng-7253	113	13	and	and	CCONJ
fumecheng-7253	113	14	𝐼	𝐼	PROPN
fumecheng-7253	113	15	=	=	PROPN
fumecheng-7253	113	16	𝑏ℎ3/12	𝑏ℎ3/12	PROPN
fumecheng-7253	113	17	represent	represent	VERB
fumecheng-7253	113	18	the	the	DET
fumecheng-7253	113	19	bending	bend	VERB
fumecheng-7253	113	20	rigidity	rigidity	NOUN
fumecheng-7253	113	21	of	of	ADP
fumecheng-7253	113	22	nanobeam	nanobeam	NOUN
fumecheng-7253	113	23	and	and	CCONJ
fumecheng-7253	113	24	cross	cross	ADJ
fumecheng-7253	113	25	-	-	ADJ
fumecheng-7253	113	26	sectional	sectional	ADJ
fumecheng-7253	113	27	moment	moment	NOUN
fumecheng-7253	113	28	of	of	ADP
fumecheng-7253	113	29	inertia	inertia	NOUN
fumecheng-7253	113	30	,	,	PUNCT
fumecheng-7253	113	31	respectively	respectively	ADV
fumecheng-7253	113	32	.	.	PUNCT
fumecheng-7253	114	1	in	in	ADP
fumecheng-7253	114	2	eq	eq	ADP
fumecheng-7253	114	3	.	.	PUNCT
fumecheng-7253	114	4	(	(	PUNCT
fumecheng-7253	114	5	8)	8)	NUM
fumecheng-7253	114	6	,	,	PUNCT
fumecheng-7253	114	7	𝑀𝑇	𝑀𝑇	PROPN
fumecheng-7253	114	8	indicates	indicate	VERB
fumecheng-7253	114	9	the	the	DET
fumecheng-7253	114	10	thermal	thermal	ADJ
fumecheng-7253	114	11	moment	moment	NOUN
fumecheng-7253	114	12	of	of	ADP
fumecheng-7253	114	13	nanobeam	nanobeam	NOUN
fumecheng-7253	114	14	and	and	CCONJ
fumecheng-7253	114	15	can	can	AUX
fumecheng-7253	114	16	be	be	AUX
fumecheng-7253	114	17	written	write	VERB
fumecheng-7253	114	18	by	by	ADP
fumecheng-7253	114	19	:	:	PUNCT
fumecheng-7253	114	20	𝑀𝑇	𝑀𝑇	PROPN
fumecheng-7253	114	21	=	=	NOUN
fumecheng-7253	114	22	12	12	NUM
fumecheng-7253	114	23	ℎ3	ℎ3	PROPN
fumecheng-7253	114	24	∫	∫	PROPN
fumecheng-7253	114	25	𝜃(𝑥	𝜃(𝑥	PROPN
fumecheng-7253	114	26	,	,	PUNCT
fumecheng-7253	114	27	𝑧	𝑧	PROPN
fumecheng-7253	114	28	,	,	PUNCT
fumecheng-7253	114	29	𝑡)𝑧d𝑧	𝑡)𝑧d𝑧	NOUN
fumecheng-7253	114	30	ℎ/2	ℎ/2	X
fumecheng-7253	114	31	−ℎ/2	−ℎ/2	NOUN
fumecheng-7253	114	32	.	.	PUNCT
fumecheng-7253	115	1	(	(	PUNCT
fumecheng-7253	115	2	9	9	X
fumecheng-7253	115	3	)	)	PUNCT
fumecheng-7253	115	4	it	it	PRON
fumecheng-7253	115	5	is	be	AUX
fumecheng-7253	115	6	assumed	assume	VERB
fumecheng-7253	115	7	that	that	SCONJ
fumecheng-7253	115	8	the	the	DET
fumecheng-7253	115	9	nanoscale	nanoscale	NOUN
fumecheng-7253	115	10	beam	beam	NOUN
fumecheng-7253	115	11	is	be	AUX
fumecheng-7253	115	12	distributed	distribute	VERB
fumecheng-7253	115	13	by	by	ADP
fumecheng-7253	115	14	a	a	DET
fumecheng-7253	115	15	transversely	transversely	NOUN
fumecheng-7253	115	16	varying	vary	VERB
fumecheng-7253	115	17	force	force	NOUN
fumecheng-7253	115	18	𝑞(𝑥	𝑞(𝑥	PROPN
fumecheng-7253	115	19	,	,	PUNCT
fumecheng-7253	115	20	𝑡	𝑡	PROPN
fumecheng-7253	115	21	)	)	PUNCT
fumecheng-7253	115	22	and	and	CCONJ
fumecheng-7253	115	23	,	,	PUNCT
fumecheng-7253	115	24	therefore	therefore	ADV
fumecheng-7253	115	25	,	,	PUNCT
fumecheng-7253	115	26	the	the	DET
fumecheng-7253	115	27	transversal	transversal	ADJ
fumecheng-7253	115	28	equation	equation	NOUN
fumecheng-7253	115	29	of	of	ADP
fumecheng-7253	115	30	motion	motion	NOUN
fumecheng-7253	115	31	can	can	AUX
fumecheng-7253	115	32	be	be	AUX
fumecheng-7253	115	33	written	write	VERB
fumecheng-7253	115	34	as	as	ADP
fumecheng-7253	115	35	[	[	X
fumecheng-7253	115	36	37	37	NUM
fumecheng-7253	115	37	]	]	PUNCT
fumecheng-7253	115	38	𝜕2𝑀	𝜕2𝑀	NOUN
fumecheng-7253	115	39	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-7253	115	40	=	=	SYM
fumecheng-7253	115	41	−𝑞(𝑥	−𝑞(𝑥	PROPN
fumecheng-7253	115	42	,	,	PUNCT
fumecheng-7253	115	43	𝑡	𝑡	X
fumecheng-7253	115	44	)	)	PUNCT
fumecheng-7253	115	45	+	+	CCONJ
fumecheng-7253	115	46	𝜌𝑏ℎ	𝜌𝑏ℎ	VERB
fumecheng-7253	115	47	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	115	48	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	115	49	,	,	PUNCT
fumecheng-7253	115	50	(	(	PUNCT
fumecheng-7253	115	51	10	10	NUM
fumecheng-7253	115	52	)	)	PUNCT
fumecheng-7253	115	53	it	it	PRON
fumecheng-7253	115	54	is	be	AUX
fumecheng-7253	115	55	supposed	suppose	VERB
fumecheng-7253	115	56	that	that	SCONJ
fumecheng-7253	115	57	the	the	DET
fumecheng-7253	115	58	nanobeam	nanobeam	NOUN
fumecheng-7253	115	59	rotates	rotate	VERB
fumecheng-7253	115	60	with	with	ADP
fumecheng-7253	115	61	angular	angular	ADJ
fumecheng-7253	115	62	velocity	velocity	NOUN
fumecheng-7253	115	63	ω	ω	PROPN
fumecheng-7253	115	64	(	(	PUNCT
fumecheng-7253	115	65	about	about	ADP
fumecheng-7253	115	66	the	the	DET
fumecheng-7253	115	67	axis	axis	NOUN
fumecheng-7253	115	68	which	which	PRON
fumecheng-7253	115	69	is	be	AUX
fumecheng-7253	115	70	parallel	parallel	ADJ
fumecheng-7253	115	71	to	to	ADP
fumecheng-7253	115	72	𝑧	𝑧	DET
fumecheng-7253	115	73	axis	axis	NOUN
fumecheng-7253	115	74	)	)	PUNCT
fumecheng-7253	115	75	centered	center	VERB
fumecheng-7253	115	76	at	at	ADP
fumecheng-7253	115	77	a	a	DET
fumecheng-7253	115	78	small	small	ADJ
fumecheng-7253	115	79	distance	distance	NOUN
fumecheng-7253	115	80	𝑟	𝑟	NOUN
fumecheng-7253	115	81	from	from	ADP
fumecheng-7253	115	82	the	the	DET
fumecheng-7253	115	83	left	left	ADJ
fumecheng-7253	115	84	edge	edge	NOUN
fumecheng-7253	115	85	of	of	ADP
fumecheng-7253	115	86	the	the	DET
fumecheng-7253	115	87	nanobeam	nanobeam	NOUN
fumecheng-7253	115	88	.	.	PUNCT
fumecheng-7253	116	1	centrifugal	centrifugal	ADJ
fumecheng-7253	116	2	tension	tension	NOUN
fumecheng-7253	116	3	force	force	NOUN
fumecheng-7253	116	4	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	116	5	)	)	PUNCT
fumecheng-7253	116	6	is	be	AUX
fumecheng-7253	116	7	introduced	introduce	VERB
fumecheng-7253	116	8	as	as	ADP
fumecheng-7253	116	9	a	a	DET
fumecheng-7253	116	10	result	result	NOUN
fumecheng-7253	116	11	of	of	ADP
fumecheng-7253	116	12	rotation	rotation	NOUN
fumecheng-7253	116	13	.	.	PUNCT
fumecheng-7253	117	1	in	in	ADP
fumecheng-7253	117	2	this	this	DET
fumecheng-7253	117	3	case	case	NOUN
fumecheng-7253	117	4	,	,	PUNCT
fumecheng-7253	117	5	the	the	DET
fumecheng-7253	117	6	equation	equation	NOUN
fumecheng-7253	117	7	of	of	ADP
fumecheng-7253	117	8	motion	motion	NOUN
fumecheng-7253	117	9	(	(	PUNCT
fumecheng-7253	117	10	10	10	NUM
fumecheng-7253	117	11	)	)	PUNCT
fumecheng-7253	117	12	is	be	AUX
fumecheng-7253	117	13	given	give	VERB
fumecheng-7253	117	14	as	as	ADP
fumecheng-7253	117	15	[	[	X
fumecheng-7253	117	16	41	41	NUM
fumecheng-7253	117	17	]	]	PUNCT
fumecheng-7253	117	18	temperature	temperature	NOUN
fumecheng-7253	117	19	-	-	PUNCT
fumecheng-7253	117	20	dependent	dependent	ADJ
fumecheng-7253	117	21	physical	physical	ADJ
fumecheng-7253	117	22	characteristics	characteristic	NOUN
fumecheng-7253	117	23	of	of	ADP
fumecheng-7253	117	24	rotating	rotate	VERB
fumecheng-7253	117	25	nonlocal	nonlocal	ADJ
fumecheng-7253	117	26	nanobeams	nanobeam	NOUN
fumecheng-7253	117	27	subject	subject	ADJ
fumecheng-7253	117	28	to	to	ADP
fumecheng-7253	117	29	...	...	PUNCT
fumecheng-7253	117	30	639	639	NUM
fumecheng-7253	117	31	𝜕2𝑀	𝜕2𝑀	NOUN
fumecheng-7253	117	32	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	117	33	+	+	CCONJ
fumecheng-7253	117	34	𝜕	𝜕	PROPN
fumecheng-7253	117	35	𝜕𝑥	𝜕𝑥	X
fumecheng-7253	117	36	(	(	PUNCT
fumecheng-7253	117	37	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	117	38	)	)	PUNCT
fumecheng-7253	117	39	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-7253	117	40	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-7253	117	41	)	)	PUNCT
fumecheng-7253	118	1	+	+	CCONJ
fumecheng-7253	118	2	𝑞(𝑥	𝑞(𝑥	PROPN
fumecheng-7253	118	3	,	,	PUNCT
fumecheng-7253	118	4	𝑡	𝑡	X
fumecheng-7253	118	5	)	)	PUNCT
fumecheng-7253	118	6	=	=	PUNCT
fumecheng-7253	118	7	𝜌𝑏ℎ	𝜌𝑏ℎ	ADP
fumecheng-7253	118	8	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	118	9	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	118	10	(	(	PUNCT
fumecheng-7253	118	11	11	11	NUM
fumecheng-7253	118	12	)	)	PUNCT
fumecheng-7253	118	13	centrifugal	centrifugal	ADJ
fumecheng-7253	118	14	force	force	NOUN
fumecheng-7253	118	15	𝑅	𝑅	PROPN
fumecheng-7253	118	16	vanishes	vanish	VERB
fumecheng-7253	118	17	when	when	SCONJ
fumecheng-7253	118	18	angular	angular	ADJ
fumecheng-7253	118	19	velocity	velocity	NOUN
fumecheng-7253	118	20	ω	ω	PROPN
fumecheng-7253	118	21	is	be	AUX
fumecheng-7253	118	22	equal	equal	ADJ
fumecheng-7253	118	23	to	to	ADP
fumecheng-7253	118	24	zero	zero	NUM
fumecheng-7253	118	25	and	and	CCONJ
fumecheng-7253	118	26	the	the	DET
fumecheng-7253	118	27	nanobeam	nanobeam	NOUN
fumecheng-7253	118	28	is	be	AUX
fumecheng-7253	118	29	in	in	ADP
fumecheng-7253	118	30	stationary	stationary	ADJ
fumecheng-7253	118	31	state	state	NOUN
fumecheng-7253	118	32	.	.	PUNCT
fumecheng-7253	119	1	the	the	DET
fumecheng-7253	119	2	centrifugal	centrifugal	ADJ
fumecheng-7253	119	3	stiffening	stiffening	NOUN
fumecheng-7253	119	4	effect	effect	NOUN
fumecheng-7253	119	5	can	can	AUX
fumecheng-7253	119	6	be	be	AUX
fumecheng-7253	119	7	modeled	model	VERB
fumecheng-7253	119	8	by	by	ADP
fumecheng-7253	119	9	including	include	VERB
fumecheng-7253	119	10	axial	axial	ADJ
fumecheng-7253	119	11	-	-	PUNCT
fumecheng-7253	119	12	type	type	NOUN
fumecheng-7253	119	13	load	load	NOUN
fumecheng-7253	119	14	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	119	15	)	)	PUNCT
fumecheng-7253	119	16	which	which	PRON
fumecheng-7253	119	17	can	can	AUX
fumecheng-7253	119	18	be	be	AUX
fumecheng-7253	119	19	described	describe	VERB
fumecheng-7253	119	20	as	as	ADP
fumecheng-7253	119	21	[	[	X
fumecheng-7253	119	22	41	41	NUM
fumecheng-7253	119	23	,	,	PUNCT
fumecheng-7253	119	24	42	42	NUM
fumecheng-7253	119	25	]	]	PUNCT
fumecheng-7253	119	26	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	119	27	)	)	PUNCT
fumecheng-7253	119	28	=	=	SYM
fumecheng-7253	119	29	∫	∫	NOUN
fumecheng-7253	120	1	𝜌𝐴ω2(𝑟	𝜌𝐴ω2(𝑟	ADJ
fumecheng-7253	120	2	+	+	CCONJ
fumecheng-7253	120	3	𝑥)𝑑𝑥	𝑥)𝑑𝑥	PROPN
fumecheng-7253	120	4	𝐿	𝐿	PROPN
fumecheng-7253	120	5	𝑥	𝑥	PROPN
fumecheng-7253	120	6	(	(	PUNCT
fumecheng-7253	120	7	12	12	NUM
fumecheng-7253	120	8	)	)	PUNCT
fumecheng-7253	120	9	in	in	ADP
fumecheng-7253	120	10	which	which	PRON
fumecheng-7253	120	11	x	x	PRON
fumecheng-7253	120	12	represents	represent	VERB
fumecheng-7253	120	13	the	the	DET
fumecheng-7253	120	14	distance	distance	NOUN
fumecheng-7253	120	15	from	from	ADP
fumecheng-7253	120	16	the	the	DET
fumecheng-7253	120	17	origin	origin	NOUN
fumecheng-7253	120	18	(	(	PUNCT
fumecheng-7253	120	19	see	see	VERB
fumecheng-7253	120	20	fig	fig	NOUN
fumecheng-7253	120	21	.	.	PUNCT
fumecheng-7253	121	1	1	1	NUM
fumecheng-7253	121	2	)	)	PUNCT
fumecheng-7253	121	3	.	.	PUNCT
fumecheng-7253	122	1	parameter	parameter	PROPN
fumecheng-7253	122	2	𝑟	𝑟	PRON
fumecheng-7253	122	3	refers	refer	VERB
fumecheng-7253	122	4	to	to	ADP
fumecheng-7253	122	5	the	the	DET
fumecheng-7253	122	6	distance	distance	NOUN
fumecheng-7253	122	7	from	from	ADP
fumecheng-7253	122	8	the	the	DET
fumecheng-7253	122	9	rotation	rotation	NOUN
fumecheng-7253	122	10	axis	axis	NOUN
fumecheng-7253	122	11	to	to	ADP
fumecheng-7253	122	12	the	the	DET
fumecheng-7253	122	13	left	left	ADJ
fumecheng-7253	122	14	edge	edge	NOUN
fumecheng-7253	122	15	of	of	ADP
fumecheng-7253	122	16	the	the	DET
fumecheng-7253	122	17	nanobeam	nanobeam	NOUN
fumecheng-7253	122	18	(	(	PUNCT
fumecheng-7253	122	19	a	a	DET
fumecheng-7253	122	20	hub	hub	NOUN
fumecheng-7253	122	21	radius	radius	NOUN
fumecheng-7253	122	22	in	in	ADP
fumecheng-7253	122	23	fig	fig	NOUN
fumecheng-7253	122	24	.	.	PUNCT
fumecheng-7253	123	1	1	1	NUM
fumecheng-7253	123	2	)	)	PUNCT
fumecheng-7253	123	3	.	.	PUNCT
fumecheng-7253	124	1	after	after	ADP
fumecheng-7253	124	2	some	some	DET
fumecheng-7253	124	3	computations	computation	NOUN
fumecheng-7253	124	4	,	,	PUNCT
fumecheng-7253	124	5	eq	eq	NOUN
fumecheng-7253	124	6	.	.	PUNCT
fumecheng-7253	125	1	(	(	PUNCT
fumecheng-7253	125	2	12	12	NUM
fumecheng-7253	125	3	)	)	PUNCT
fumecheng-7253	125	4	can	can	AUX
fumecheng-7253	125	5	be	be	AUX
fumecheng-7253	125	6	simplified	simplify	VERB
fumecheng-7253	125	7	as	as	ADP
fumecheng-7253	125	8	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	125	9	)	)	PUNCT
fumecheng-7253	125	10	=	=	PUNCT
fumecheng-7253	126	1	𝜌𝐴ω2	𝜌𝐴ω2	X
fumecheng-7253	126	2	2	2	NUM
fumecheng-7253	126	3	[	[	X
fumecheng-7253	126	4	(	(	PUNCT
fumecheng-7253	126	5	𝐿	𝐿	NOUN
fumecheng-7253	126	6	+	+	NOUN
fumecheng-7253	126	7	𝑟)2	𝑟)2	NOUN
fumecheng-7253	126	8	−	−	NOUN
fumecheng-7253	126	9	(	(	PUNCT
fumecheng-7253	126	10	𝐿	𝐿	PROPN
fumecheng-7253	126	11	+	+	CCONJ
fumecheng-7253	126	12	𝑥)2	𝑥)2	PROPN
fumecheng-7253	126	13	]	]	X
fumecheng-7253	126	14	=	=	SYM
fumecheng-7253	127	1	𝜌𝐴ω2	𝜌𝐴ω2	X
fumecheng-7253	127	2	2	2	NUM
fumecheng-7253	127	3	[	[	X
fumecheng-7253	127	4	(	(	PUNCT
fumecheng-7253	127	5	𝑟	𝑟	NOUN
fumecheng-7253	127	6	−	−	NOUN
fumecheng-7253	127	7	𝑥)(2𝐿	𝑥)(2𝐿	X
fumecheng-7253	127	8	+	+	NOUN
fumecheng-7253	127	9	𝑟	𝑟	NOUN
fumecheng-7253	127	10	+	+	CCONJ
fumecheng-7253	127	11	𝑥	𝑥	NOUN
fumecheng-7253	127	12	)	)	PUNCT
fumecheng-7253	127	13	]	]	PUNCT
fumecheng-7253	127	14	(	(	PUNCT
fumecheng-7253	127	15	13	13	NUM
fumecheng-7253	127	16	)	)	PUNCT
fumecheng-7253	127	17	for	for	ADP
fumecheng-7253	127	18	calculating	calculate	VERB
fumecheng-7253	127	19	bending	bend	VERB
fumecheng-7253	127	20	moment	moment	NOUN
fumecheng-7253	127	21	𝑀(𝑥	𝑀(𝑥	ADP
fumecheng-7253	127	22	,	,	PUNCT
fumecheng-7253	127	23	𝑡	𝑡	NOUN
fumecheng-7253	127	24	)	)	PUNCT
fumecheng-7253	127	25	,	,	PUNCT
fumecheng-7253	127	26	eqs	eqs	X
fumecheng-7253	127	27	.	.	PUNCT
fumecheng-7253	128	1	(	(	PUNCT
fumecheng-7253	128	2	11	11	NUM
fumecheng-7253	128	3	)	)	PUNCT
fumecheng-7253	128	4	and	and	CCONJ
fumecheng-7253	128	5	(	(	PUNCT
fumecheng-7253	128	6	13	13	NUM
fumecheng-7253	128	7	)	)	PUNCT
fumecheng-7253	128	8	can	can	AUX
fumecheng-7253	128	9	be	be	AUX
fumecheng-7253	128	10	utilized	utilize	VERB
fumecheng-7253	128	11	𝑀(𝑥	𝑀(𝑥	NOUN
fumecheng-7253	128	12	,	,	PUNCT
fumecheng-7253	128	13	𝑡	𝑡	NOUN
fumecheng-7253	128	14	)	)	PUNCT
fumecheng-7253	128	15	=	=	SYM
fumecheng-7253	128	16	𝜉	𝜉	NOUN
fumecheng-7253	128	17	(	(	PUNCT
fumecheng-7253	128	18	𝜌𝐴	𝜌𝐴	ADJ
fumecheng-7253	128	19	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	128	20	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	128	21	−	−	ADP
fumecheng-7253	128	22	𝑞(𝑥	𝑞(𝑥	PROPN
fumecheng-7253	128	23	,	,	PUNCT
fumecheng-7253	128	24	𝑡	𝑡	PROPN
fumecheng-7253	128	25	)	)	PUNCT
fumecheng-7253	128	26	−	−	PROPN
fumecheng-7253	128	27	𝜕	𝜕	PROPN
fumecheng-7253	128	28	𝜕𝑥	𝜕𝑥	X
fumecheng-7253	128	29	(	(	PUNCT
fumecheng-7253	128	30	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	128	31	)	)	PUNCT
fumecheng-7253	128	32	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-7253	128	33	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-7253	128	34	)	)	PUNCT
fumecheng-7253	128	35	)	)	PUNCT
fumecheng-7253	129	1	−	−	PROPN
fumecheng-7253	129	2	𝐸𝐼	𝐸𝐼	PROPN
fumecheng-7253	129	3	(	(	PUNCT
fumecheng-7253	129	4	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	129	5	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-7253	129	6	+	+	CCONJ
fumecheng-7253	129	7	𝛼𝑇𝑀𝑇	𝛼𝑇𝑀𝑇	NUM
fumecheng-7253	129	8	)	)	PUNCT
fumecheng-7253	129	9	(	(	PUNCT
fumecheng-7253	129	10	14	14	NUM
fumecheng-7253	129	11	)	)	PUNCT
fumecheng-7253	129	12	if	if	SCONJ
fumecheng-7253	129	13	moment	moment	NOUN
fumecheng-7253	129	14	𝑀	𝑀	PROPN
fumecheng-7253	129	15	is	be	AUX
fumecheng-7253	129	16	omitted	omit	VERB
fumecheng-7253	129	17	in	in	ADP
fumecheng-7253	129	18	eqs	eqs	PROPN
fumecheng-7253	129	19	.	.	PUNCT
fumecheng-7253	130	1	(	(	PUNCT
fumecheng-7253	130	2	11	11	NUM
fumecheng-7253	130	3	)	)	PUNCT
fumecheng-7253	130	4	and	and	CCONJ
fumecheng-7253	130	5	(	(	PUNCT
fumecheng-7253	130	6	14	14	NUM
fumecheng-7253	130	7	)	)	PUNCT
fumecheng-7253	130	8	,	,	PUNCT
fumecheng-7253	130	9	the	the	DET
fumecheng-7253	130	10	governing	govern	VERB
fumecheng-7253	130	11	equation	equation	NOUN
fumecheng-7253	130	12	can	can	AUX
fumecheng-7253	130	13	be	be	AUX
fumecheng-7253	130	14	expressed	express	VERB
fumecheng-7253	130	15	as	as	ADP
fumecheng-7253	130	16	[	[	PUNCT
fumecheng-7253	130	17	𝜕4	𝜕4	NOUN
fumecheng-7253	130	18	𝜕𝑥4	𝜕𝑥4	PROPN
fumecheng-7253	130	19	+	+	NUM
fumecheng-7253	130	20	𝜌𝐴	𝜌𝐴	ADJ
fumecheng-7253	130	21	𝐸𝐼	𝐸𝐼	PROPN
fumecheng-7253	130	22	𝜕2	𝜕2	NOUN
fumecheng-7253	130	23	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	130	24	(	(	PUNCT
fumecheng-7253	130	25	1	1	NUM
fumecheng-7253	130	26	−	−	NOUN
fumecheng-7253	130	27	𝜉	𝜉	NOUN
fumecheng-7253	130	28	𝜕2	𝜕2	NOUN
fumecheng-7253	130	29	𝜕𝑥2)]𝑤	𝜕𝑥2)]𝑤	NOUN
fumecheng-7253	130	30	−	−	PROPN
fumecheng-7253	130	31	1	1	NUM
fumecheng-7253	130	32	𝐸𝐼	𝐸𝐼	PROPN
fumecheng-7253	130	33	(	(	PUNCT
fumecheng-7253	130	34	1	1	NUM
fumecheng-7253	130	35	−	−	NOUN
fumecheng-7253	130	36	𝜉	𝜉	NOUN
fumecheng-7253	130	37	𝜕2	𝜕2	NOUN
fumecheng-7253	130	38	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	130	39	)	)	PUNCT
fumecheng-7253	131	1	[	[	X
fumecheng-7253	131	2	𝑞	𝑞	X
fumecheng-7253	131	3	+	+	PUNCT
fumecheng-7253	131	4	𝜕	𝜕	PROPN
fumecheng-7253	131	5	𝜕𝑥	𝜕𝑥	X
fumecheng-7253	131	6	(	(	PUNCT
fumecheng-7253	131	7	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	131	8	)	)	PUNCT
fumecheng-7253	131	9	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-7253	131	10	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-7253	131	11	)	)	PUNCT
fumecheng-7253	131	12	]	]	PUNCT
fumecheng-7253	132	1	+	+	PUNCT
fumecheng-7253	132	2	𝛼𝑇	𝛼𝑇	NOUN
fumecheng-7253	132	3	𝜕2𝑀𝑇	𝜕2𝑀𝑇	PROPN
fumecheng-7253	132	4	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	132	5	=	=	SYM
fumecheng-7253	132	6	0	0	PUNCT
fumecheng-7253	132	7	(	(	PUNCT
fumecheng-7253	132	8	15	15	NUM
fumecheng-7253	132	9	)	)	PUNCT
fumecheng-7253	132	10	in	in	ADP
fumecheng-7253	132	11	the	the	DET
fumecheng-7253	132	12	absence	absence	NOUN
fumecheng-7253	132	13	of	of	ADP
fumecheng-7253	132	14	heat	heat	NOUN
fumecheng-7253	132	15	source	source	NOUN
fumecheng-7253	132	16	(	(	PUNCT
fumecheng-7253	132	17	𝑄	𝑄	NOUN
fumecheng-7253	132	18	=	=	SYM
fumecheng-7253	132	19	0	0	NUM
fumecheng-7253	132	20	)	)	PUNCT
fumecheng-7253	132	21	,	,	PUNCT
fumecheng-7253	132	22	the	the	DET
fumecheng-7253	132	23	modified	modify	VERB
fumecheng-7253	132	24	heat	heat	NOUN
fumecheng-7253	132	25	conduction	conduction	NOUN
fumecheng-7253	132	26	relation	relation	NOUN
fumecheng-7253	132	27	(	(	PUNCT
fumecheng-7253	132	28	4	4	X
fumecheng-7253	132	29	)	)	PUNCT
fumecheng-7253	132	30	can	can	AUX
fumecheng-7253	132	31	be	be	AUX
fumecheng-7253	132	32	defined	define	VERB
fumecheng-7253	132	33	as	as	ADP
fumecheng-7253	132	34	(	(	PUNCT
fumecheng-7253	132	35	1	1	NUM
fumecheng-7253	132	36	+	+	CCONJ
fumecheng-7253	132	37	𝜏𝜃	𝜏𝜃	ADP
fumecheng-7253	132	38	𝜕	𝜕	PROPN
fumecheng-7253	132	39	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	132	40	)	)	PUNCT
fumecheng-7253	132	41	∇.	∇.	PROPN
fumecheng-7253	132	42	(	(	PUNCT
fumecheng-7253	132	43	𝐾𝑥∇𝜃	𝐾𝑥∇𝜃	PROPN
fumecheng-7253	132	44	)	)	PUNCT
fumecheng-7253	132	45	=	=	PUNCT
fumecheng-7253	132	46	(	(	PUNCT
fumecheng-7253	132	47	1	1	NUM
fumecheng-7253	132	48	+	+	NUM
fumecheng-7253	132	49	𝜏𝑞	𝜏𝑞	PROPN
fumecheng-7253	132	50	𝜕	𝜕	PROPN
fumecheng-7253	132	51	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	132	52	+	+	NOUN
fumecheng-7253	132	53	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	132	54	2	2	NUM
fumecheng-7253	132	55	2	2	NUM
fumecheng-7253	132	56	𝜕2	𝜕2	NOUN
fumecheng-7253	132	57	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	132	58	)	)	PUNCT
fumecheng-7253	132	59	𝜕	𝜕	PROPN
fumecheng-7253	132	60	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	132	61	(	(	PUNCT
fumecheng-7253	132	62	𝜌𝐶𝐸𝜃	𝜌𝐶𝐸𝜃	PROPN
fumecheng-7253	132	63	−	−	PROPN
fumecheng-7253	132	64	𝛾𝑇0𝑧	𝛾𝑇0𝑧	PROPN
fumecheng-7253	132	65	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	132	66	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-7253	132	67	)	)	PUNCT
fumecheng-7253	132	68	(	(	PUNCT
fumecheng-7253	132	69	16	16	NUM
fumecheng-7253	132	70	)	)	PUNCT
fumecheng-7253	132	71	4	4	NUM
fumecheng-7253	132	72	.	.	PUNCT
fumecheng-7253	132	73	thermal	thermal	ADJ
fumecheng-7253	132	74	properties	property	NOUN
fumecheng-7253	132	75	of	of	ADP
fumecheng-7253	132	76	materials	material	NOUN
fumecheng-7253	132	77	the	the	DET
fumecheng-7253	132	78	identification	identification	NOUN
fumecheng-7253	132	79	of	of	ADP
fumecheng-7253	132	80	nonlinear	nonlinear	ADJ
fumecheng-7253	132	81	problems	problem	NOUN
fumecheng-7253	132	82	will	will	AUX
fumecheng-7253	132	83	be	be	AUX
fumecheng-7253	132	84	carried	carry	VERB
fumecheng-7253	132	85	out	out	ADP
fumecheng-7253	132	86	if	if	SCONJ
fumecheng-7253	132	87	the	the	DET
fumecheng-7253	132	88	material	material	NOUN
fumecheng-7253	132	89	properties	property	NOUN
fumecheng-7253	132	90	are	be	AUX
fumecheng-7253	132	91	temperature	temperature	NOUN
fumecheng-7253	132	92	-	-	PUNCT
fumecheng-7253	132	93	dependent	dependent	ADJ
fumecheng-7253	132	94	which	which	PRON
fumecheng-7253	132	95	means	mean	VERB
fumecheng-7253	132	96	specific	specific	ADJ
fumecheng-7253	132	97	heat	heat	NOUN
fumecheng-7253	132	98	𝐶𝐸	𝐶𝐸	NOUN
fumecheng-7253	132	99	and	and	CCONJ
fumecheng-7253	132	100	thermal	thermal	ADJ
fumecheng-7253	132	101	conductivity	conductivity	NOUN
fumecheng-7253	132	102	𝐾	𝐾	PROPN
fumecheng-7253	132	103	depend	depend	VERB
fumecheng-7253	132	104	upon	upon	SCONJ
fumecheng-7253	132	105	the	the	DET
fumecheng-7253	132	106	temperature	temperature	NOUN
fumecheng-7253	132	107	distribution	distribution	NOUN
fumecheng-7253	132	108	[	[	X
fumecheng-7253	132	109	28	28	NUM
fumecheng-7253	132	110	]	]	PUNCT
fumecheng-7253	132	111	.	.	PUNCT
fumecheng-7253	133	1	in	in	ADP
fumecheng-7253	133	2	the	the	DET
fumecheng-7253	133	3	current	current	ADJ
fumecheng-7253	133	4	work	work	NOUN
fumecheng-7253	133	5	,	,	PUNCT
fumecheng-7253	133	6	it	it	PRON
fumecheng-7253	133	7	is	be	AUX
fumecheng-7253	133	8	assumed	assume	VERB
fumecheng-7253	133	9	that	that	SCONJ
fumecheng-7253	133	10	other	other	ADJ
fumecheng-7253	133	11	physical	physical	ADJ
fumecheng-7253	133	12	parameters	parameter	NOUN
fumecheng-7253	133	13	are	be	AUX
fumecheng-7253	133	14	constant	constant	ADJ
fumecheng-7253	133	15	and	and	CCONJ
fumecheng-7253	133	16	not	not	PART
fumecheng-7253	133	17	dependent	dependent	ADJ
fumecheng-7253	133	18	on	on	ADP
fumecheng-7253	133	19	the	the	DET
fumecheng-7253	133	20	temperature	temperature	NOUN
fumecheng-7253	133	21	changes	change	NOUN
fumecheng-7253	133	22	[	[	X
fumecheng-7253	133	23	43	43	NUM
fumecheng-7253	133	24	]	]	PUNCT
fumecheng-7253	133	25	.	.	PUNCT
fumecheng-7253	134	1	the	the	DET
fumecheng-7253	134	2	material	material	NOUN
fumecheng-7253	134	3	's	's	PART
fumecheng-7253	134	4	thermal	thermal	ADJ
fumecheng-7253	134	5	conductivity	conductivity	NOUN
fumecheng-7253	134	6	𝐾	𝐾	PROPN
fumecheng-7253	134	7	is	be	AUX
fumecheng-7253	134	8	supposed	suppose	VERB
fumecheng-7253	134	9	to	to	PART
fumecheng-7253	134	10	be	be	AUX
fumecheng-7253	134	11	defined	define	VERB
fumecheng-7253	134	12	by	by	ADP
fumecheng-7253	134	13	a	a	DET
fumecheng-7253	134	14	linear	linear	ADJ
fumecheng-7253	134	15	function	function	NOUN
fumecheng-7253	134	16	of	of	ADP
fumecheng-7253	134	17	temperature	temperature	NOUN
fumecheng-7253	134	18	change	change	NOUN
fumecheng-7253	134	19	[	[	X
fumecheng-7253	134	20	44	44	NUM
fumecheng-7253	134	21	]	]	PUNCT
fumecheng-7253	134	22	as	as	SCONJ
fumecheng-7253	134	23	follows	follow	VERB
fumecheng-7253	134	24	:	:	PUNCT
fumecheng-7253	134	25	𝐾𝑥	𝐾𝑥	PROPN
fumecheng-7253	134	26	=	=	PUNCT
fumecheng-7253	134	27	𝐾𝑥(𝜃	𝐾𝑥(𝜃	PROPN
fumecheng-7253	134	28	)	)	PUNCT
fumecheng-7253	134	29	=	=	PUNCT
fumecheng-7253	134	30	𝐾0(1	𝐾0(1	VERB
fumecheng-7253	134	31	+	+	CCONJ
fumecheng-7253	135	1	𝐾1𝜃	𝐾1𝜃	PROPN
fumecheng-7253	135	2	)	)	PUNCT
fumecheng-7253	135	3	,	,	PUNCT
fumecheng-7253	135	4	(	(	PUNCT
fumecheng-7253	135	5	17	17	NUM
fumecheng-7253	135	6	)	)	PUNCT
fumecheng-7253	135	7	in	in	ADP
fumecheng-7253	135	8	which	which	PRON
fumecheng-7253	135	9	parameter	parameter	NOUN
fumecheng-7253	135	10	𝐾0	𝐾0	PROPN
fumecheng-7253	135	11	denotes	denote	VERB
fumecheng-7253	135	12	the	the	DET
fumecheng-7253	135	13	thermal	thermal	ADJ
fumecheng-7253	135	14	conductivity	conductivity	NOUN
fumecheng-7253	135	15	at	at	ADP
fumecheng-7253	135	16	reference	reference	NOUN
fumecheng-7253	135	17	temperature	temperature	NOUN
fumecheng-7253	135	18	t0	t0	PROPN
fumecheng-7253	135	19	and	and	CCONJ
fumecheng-7253	135	20	𝐾1	𝐾1	PROPN
fumecheng-7253	135	21	denotes	denote	NOUN
fumecheng-7253	135	22	a	a	DET
fumecheng-7253	135	23	factor	factor	NOUN
fumecheng-7253	135	24	that	that	PRON
fumecheng-7253	135	25	characterizes	characterize	VERB
fumecheng-7253	135	26	thermal	thermal	ADJ
fumecheng-7253	135	27	conductivity	conductivity	NOUN
fumecheng-7253	135	28	variability	variability	NOUN
fumecheng-7253	135	29	.	.	PUNCT
fumecheng-7253	136	1	by	by	ADP
fumecheng-7253	136	2	substituting	substitute	VERB
fumecheng-7253	136	3	eq	eq	PROPN
fumecheng-7253	136	4	.	.	PUNCT
fumecheng-7253	137	1	(	(	PUNCT
fumecheng-7253	137	2	17	17	NUM
fumecheng-7253	137	3	)	)	PUNCT
fumecheng-7253	137	4	into	into	ADP
fumecheng-7253	137	5	eq	eq	NOUN
fumecheng-7253	137	6	.	.	PUNCT
fumecheng-7253	138	1	(	(	PUNCT
fumecheng-7253	138	2	16	16	NUM
fumecheng-7253	138	3	)	)	PUNCT
fumecheng-7253	138	4	,	,	PUNCT
fumecheng-7253	138	5	the	the	DET
fumecheng-7253	138	6	partial	partial	ADJ
fumecheng-7253	138	7	nonlinear	nonlinear	ADJ
fumecheng-7253	138	8	differential	differential	ADJ
fumecheng-7253	138	9	equation	equation	NOUN
fumecheng-7253	138	10	is	be	AUX
fumecheng-7253	138	11	obtained	obtain	VERB
fumecheng-7253	138	12	in	in	ADP
fumecheng-7253	138	13	the	the	DET
fumecheng-7253	138	14	form	form	NOUN
fumecheng-7253	138	15	640	640	NUM
fumecheng-7253	138	16	a.	a.	NOUN
fumecheng-7253	138	17	e.	e.	PROPN
fumecheng-7253	138	18	abouelregal	abouelregal	PROPN
fumecheng-7253	138	19	,	,	PUNCT
fumecheng-7253	138	20	h.	h.	PROPN
fumecheng-7253	138	21	m.	m.	PROPN
fumecheng-7253	138	22	sedighi	sedighi	PROPN
fumecheng-7253	138	23	,	,	PUNCT
fumecheng-7253	138	24	s.	s.	PROPN
fumecheng-7253	138	25	a.	a.	PROPN
fumecheng-7253	138	26	faghidian	faghidian	PROPN
fumecheng-7253	138	27	,	,	PUNCT
fumecheng-7253	138	28	a.	a.	PROPN
fumecheng-7253	138	29	h.	h.	PROPN
fumecheng-7253	138	30	shirazi	shirazi	PROPN
fumecheng-7253	138	31	𝐾0	𝐾0	PROPN
fumecheng-7253	138	32	(	(	PUNCT
fumecheng-7253	138	33	1	1	NUM
fumecheng-7253	138	34	+	+	CCONJ
fumecheng-7253	138	35	𝜏𝜃	𝜏𝜃	ADP
fumecheng-7253	138	36	𝜕	𝜕	PROPN
fumecheng-7253	138	37	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	138	38	)	)	PUNCT
fumecheng-7253	138	39	∇.	∇.	NOUN
fumecheng-7253	138	40	(	(	PUNCT
fumecheng-7253	138	41	(	(	PUNCT
fumecheng-7253	138	42	1	1	NUM
fumecheng-7253	138	43	+	+	NUM
fumecheng-7253	138	44	𝐾1𝜃)∇𝜃	𝐾1𝜃)∇𝜃	PUNCT
fumecheng-7253	138	45	)	)	PUNCT
fumecheng-7253	139	1	=	=	SYM
fumecheng-7253	139	2	(	(	PUNCT
fumecheng-7253	139	3	1	1	NUM
fumecheng-7253	139	4	+	+	NUM
fumecheng-7253	139	5	𝜏𝑞	𝜏𝑞	PROPN
fumecheng-7253	139	6	𝜕	𝜕	PROPN
fumecheng-7253	139	7	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	139	8	+	+	NOUN
fumecheng-7253	139	9	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	139	10	2	2	NUM
fumecheng-7253	139	11	2	2	NUM
fumecheng-7253	139	12	𝜕2	𝜕2	NOUN
fumecheng-7253	139	13	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	139	14	)	)	PUNCT
fumecheng-7253	139	15	𝜕	𝜕	PROPN
fumecheng-7253	139	16	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	139	17	(	(	PUNCT
fumecheng-7253	139	18	𝜌𝐶𝐸𝜃	𝜌𝐶𝐸𝜃	PROPN
fumecheng-7253	139	19	−	−	PROPN
fumecheng-7253	139	20	𝛾𝑇0𝑧	𝛾𝑇0𝑧	PROPN
fumecheng-7253	139	21	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	139	22	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-7253	139	23	)	)	PUNCT
fumecheng-7253	139	24	(	(	PUNCT
fumecheng-7253	139	25	18	18	NUM
fumecheng-7253	139	26	)	)	PUNCT
fumecheng-7253	139	27	the	the	DET
fumecheng-7253	139	28	previous	previous	ADJ
fumecheng-7253	139	29	equation	equation	NOUN
fumecheng-7253	139	30	can	can	AUX
fumecheng-7253	139	31	be	be	AUX
fumecheng-7253	139	32	converted	convert	VERB
fumecheng-7253	139	33	to	to	ADP
fumecheng-7253	139	34	a	a	DET
fumecheng-7253	139	35	linear	linear	ADJ
fumecheng-7253	139	36	equation	equation	NOUN
fumecheng-7253	139	37	by	by	ADP
fumecheng-7253	139	38	defining	define	VERB
fumecheng-7253	139	39	the	the	DET
fumecheng-7253	139	40	mapping	mapping	NOUN
fumecheng-7253	139	41	[	[	X
fumecheng-7253	139	42	43	43	NUM
fumecheng-7253	139	43	]	]	PUNCT
fumecheng-7253	139	44	𝐾0𝜓	𝐾0𝜓	PROPN
fumecheng-7253	140	1	=	=	PUNCT
fumecheng-7253	141	1	∫	∫	PROPN
fumecheng-7253	141	2	𝐾𝑥(𝜃)d𝜃	𝐾𝑥(𝜃)d𝜃	PROPN
fumecheng-7253	142	1	𝜃	𝜃	PROPN
fumecheng-7253	142	2	0	0	NUM
fumecheng-7253	142	3	,	,	PUNCT
fumecheng-7253	142	4	(	(	PUNCT
fumecheng-7253	142	5	19	19	NUM
fumecheng-7253	142	6	)	)	PUNCT
fumecheng-7253	142	7	after	after	ADP
fumecheng-7253	142	8	inserting	insert	VERB
fumecheng-7253	142	9	eq	eq	ADP
fumecheng-7253	142	10	.	.	PUNCT
fumecheng-7253	142	11	(	(	PUNCT
fumecheng-7253	142	12	17	17	NUM
fumecheng-7253	142	13	)	)	PUNCT
fumecheng-7253	142	14	into	into	ADP
fumecheng-7253	142	15	eq	eq	NOUN
fumecheng-7253	142	16	.	.	PUNCT
fumecheng-7253	143	1	(	(	PUNCT
fumecheng-7253	143	2	19	19	NUM
fumecheng-7253	143	3	)	)	PUNCT
fumecheng-7253	143	4	and	and	CCONJ
fumecheng-7253	143	5	computing	compute	VERB
fumecheng-7253	143	6	the	the	DET
fumecheng-7253	143	7	integration	integration	NOUN
fumecheng-7253	143	8	,	,	PUNCT
fumecheng-7253	143	9	we	we	PRON
fumecheng-7253	143	10	have	have	VERB
fumecheng-7253	143	11	[	[	X
fumecheng-7253	143	12	43	43	NUM
fumecheng-7253	143	13	]	]	X
fumecheng-7253	143	14	𝜓	𝜓	NOUN
fumecheng-7253	143	15	=	=	PUNCT
fumecheng-7253	143	16	𝜃(1	𝜃(1	PUNCT
fumecheng-7253	144	1	+	+	CCONJ
fumecheng-7253	144	2	1	1	NUM
fumecheng-7253	144	3	2	2	NUM
fumecheng-7253	144	4	𝐾1𝜃	𝐾1𝜃	PROPN
fumecheng-7253	144	5	)	)	PUNCT
fumecheng-7253	144	6	.	.	PUNCT
fumecheng-7253	145	1	(	(	PUNCT
fumecheng-7253	145	2	20	20	NUM
fumecheng-7253	145	3	)	)	PUNCT
fumecheng-7253	145	4	through	through	ADP
fumecheng-7253	145	5	differentiating	differentiate	VERB
fumecheng-7253	145	6	relation	relation	NOUN
fumecheng-7253	145	7	eq	eq	ADP
fumecheng-7253	145	8	.	.	PUNCT
fumecheng-7253	146	1	(	(	PUNCT
fumecheng-7253	146	2	20	20	NUM
fumecheng-7253	146	3	)	)	PUNCT
fumecheng-7253	146	4	with	with	ADP
fumecheng-7253	146	5	regard	regard	NOUN
fumecheng-7253	146	6	to	to	ADP
fumecheng-7253	146	7	distance	distance	NOUN
fumecheng-7253	146	8	variable	variable	NOUN
fumecheng-7253	146	9	and	and	CCONJ
fumecheng-7253	146	10	also	also	ADV
fumecheng-7253	146	11	with	with	ADP
fumecheng-7253	146	12	respect	respect	NOUN
fumecheng-7253	146	13	to	to	ADP
fumecheng-7253	146	14	time	time	NOUN
fumecheng-7253	146	15	variable	variable	PROPN
fumecheng-7253	146	16	t	t	PROPN
fumecheng-7253	146	17	,	,	PUNCT
fumecheng-7253	146	18	the	the	DET
fumecheng-7253	146	19	following	follow	VERB
fumecheng-7253	146	20	relationships	relationship	NOUN
fumecheng-7253	146	21	are	be	AUX
fumecheng-7253	146	22	deduced	deduce	VERB
fumecheng-7253	146	23	∇𝜓	∇𝜓	PROPN
fumecheng-7253	146	24	=	=	SYM
fumecheng-7253	146	25	𝐾𝑟(𝜃	𝐾𝑟(𝜃	NOUN
fumecheng-7253	146	26	)	)	PUNCT
fumecheng-7253	146	27	𝐾0	𝐾0	PROPN
fumecheng-7253	146	28	∇𝜃	∇𝜃	PROPN
fumecheng-7253	146	29	,	,	PUNCT
fumecheng-7253	146	30	(	(	PUNCT
fumecheng-7253	146	31	21	21	NUM
fumecheng-7253	146	32	)	)	PUNCT
fumecheng-7253	146	33	𝜕𝜓	𝜕𝜓	NOUN
fumecheng-7253	146	34	𝜕𝑡	𝜕𝑡	NOUN
fumecheng-7253	146	35	=	=	SYM
fumecheng-7253	146	36	𝐾𝑟(𝜃	𝐾𝑟(𝜃	NOUN
fumecheng-7253	146	37	)	)	PUNCT
fumecheng-7253	146	38	𝐾0	𝐾0	PROPN
fumecheng-7253	146	39	𝜕𝜃	𝜕𝜃	NOUN
fumecheng-7253	146	40	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	146	41	.	.	PUNCT
fumecheng-7253	147	1	(	(	PUNCT
fumecheng-7253	147	2	22	22	NUM
fumecheng-7253	147	3	)	)	PUNCT
fumecheng-7253	147	4	by	by	ADP
fumecheng-7253	147	5	employing	employ	VERB
fumecheng-7253	147	6	eqs	eqs	PROPN
fumecheng-7253	147	7	.	.	PUNCT
fumecheng-7253	148	1	(	(	PUNCT
fumecheng-7253	148	2	21	21	NUM
fumecheng-7253	148	3	)	)	PUNCT
fumecheng-7253	148	4	and	and	CCONJ
fumecheng-7253	148	5	(	(	PUNCT
fumecheng-7253	148	6	22	22	NUM
fumecheng-7253	148	7	)	)	PUNCT
fumecheng-7253	148	8	,	,	PUNCT
fumecheng-7253	148	9	therefore	therefore	ADV
fumecheng-7253	148	10	,	,	PUNCT
fumecheng-7253	148	11	the	the	DET
fumecheng-7253	148	12	heat	heat	NOUN
fumecheng-7253	148	13	conduction	conduction	NOUN
fumecheng-7253	148	14	equation	equation	NOUN
fumecheng-7253	148	15	(	(	PUNCT
fumecheng-7253	148	16	18	18	NUM
fumecheng-7253	148	17	)	)	PUNCT
fumecheng-7253	148	18	is	be	AUX
fumecheng-7253	148	19	simplified	simplify	VERB
fumecheng-7253	148	20	to	to	PART
fumecheng-7253	148	21	(	(	PUNCT
fumecheng-7253	148	22	1	1	NUM
fumecheng-7253	148	23	+	+	CCONJ
fumecheng-7253	148	24	𝜏𝜃	𝜏𝜃	ADP
fumecheng-7253	148	25	𝜕	𝜕	PROPN
fumecheng-7253	148	26	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	148	27	)	)	PUNCT
fumecheng-7253	148	28	(	(	PUNCT
fumecheng-7253	148	29	𝜕2	𝜕2	NUM
fumecheng-7253	148	30	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	148	31	+	+	CCONJ
fumecheng-7253	148	32	𝜕2	𝜕2	NOUN
fumecheng-7253	148	33	𝜕𝑧2)𝜓	𝜕𝑧2)𝜓	X
fumecheng-7253	148	34	=	=	PUNCT
fumecheng-7253	148	35	(	(	PUNCT
fumecheng-7253	148	36	1	1	NUM
fumecheng-7253	148	37	+	+	NUM
fumecheng-7253	148	38	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	148	39	𝜕	𝜕	PROPN
fumecheng-7253	148	40	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	148	41	+	+	CCONJ
fumecheng-7253	148	42	1	1	NUM
fumecheng-7253	148	43	2	2	NUM
fumecheng-7253	148	44	𝜏𝑞	𝜏𝑞	ADP
fumecheng-7253	148	45	2	2	NUM
fumecheng-7253	148	46	𝜕2	𝜕2	NOUN
fumecheng-7253	148	47	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	148	48	)	)	PUNCT
fumecheng-7253	148	49	𝜕	𝜕	PROPN
fumecheng-7253	148	50	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	148	51	(	(	PUNCT
fumecheng-7253	148	52	𝜂𝜓	𝜂𝜓	ADP
fumecheng-7253	148	53	−	−	PROPN
fumecheng-7253	148	54	𝛾𝑇0	𝛾𝑇0	PROPN
fumecheng-7253	148	55	𝐾	𝐾	PROPN
fumecheng-7253	148	56	𝑧	𝑧	PROPN
fumecheng-7253	148	57	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	148	58	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-7253	148	59	)	)	PUNCT
fumecheng-7253	148	60	.	.	PUNCT
fumecheng-7253	149	1	(	(	PUNCT
fumecheng-7253	149	2	23	23	NUM
fumecheng-7253	149	3	)	)	PUNCT
fumecheng-7253	149	4	in	in	ADP
fumecheng-7253	149	5	which	which	PRON
fumecheng-7253	149	6	1/𝜂	1/𝜂	PROPN
fumecheng-7253	149	7	=	=	PUNCT
fumecheng-7253	149	8	𝐾/𝜌𝐶𝐸stands	𝐾/𝜌𝐶𝐸stands	PROPN
fumecheng-7253	149	9	for	for	ADP
fumecheng-7253	149	10	thermal	thermal	ADJ
fumecheng-7253	149	11	diffusivity	diffusivity	NOUN
fumecheng-7253	149	12	.	.	PUNCT
fumecheng-7253	150	1	5	5	X
fumecheng-7253	150	2	.	.	X
fumecheng-7253	150	3	sinusoidal	sinusoidal	ADJ
fumecheng-7253	150	4	solution	solution	NOUN
fumecheng-7253	150	5	in	in	ADP
fumecheng-7253	150	6	order	order	NOUN
fumecheng-7253	150	7	to	to	PART
fumecheng-7253	150	8	calculate	calculate	VERB
fumecheng-7253	150	9	the	the	DET
fumecheng-7253	150	10	solution	solution	NOUN
fumecheng-7253	150	11	of	of	ADP
fumecheng-7253	150	12	the	the	DET
fumecheng-7253	150	13	problem	problem	NOUN
fumecheng-7253	150	14	,	,	PUNCT
fumecheng-7253	150	15	we	we	PRON
fumecheng-7253	150	16	take	take	VERB
fumecheng-7253	150	17	the	the	DET
fumecheng-7253	150	18	temperature	temperature	NOUN
fumecheng-7253	150	19	change	change	NOUN
fumecheng-7253	150	20	response	response	NOUN
fumecheng-7253	150	21	as	as	ADP
fumecheng-7253	150	22	a	a	DET
fumecheng-7253	150	23	sinusoidal	sinusoidal	ADJ
fumecheng-7253	150	24	solution	solution	NOUN
fumecheng-7253	150	25	{	{	PUNCT
fumecheng-7253	150	26	𝜓	𝜓	NOUN
fumecheng-7253	150	27	,	,	PUNCT
fumecheng-7253	150	28	𝜃}(𝑥	𝜃}(𝑥	PROPN
fumecheng-7253	150	29	,	,	PUNCT
fumecheng-7253	150	30	𝑧	𝑧	PROPN
fumecheng-7253	150	31	,	,	PUNCT
fumecheng-7253	150	32	𝑡	𝑡	NOUN
fumecheng-7253	150	33	)	)	PUNCT
fumecheng-7253	150	34	=	=	SYM
fumecheng-7253	150	35	{	{	PUNCT
fumecheng-7253	150	36	ψ	ψ	NOUN
fumecheng-7253	150	37	,	,	PUNCT
fumecheng-7253	150	38	θ}(𝑥	θ}(𝑥	PROPN
fumecheng-7253	150	39	,	,	PUNCT
fumecheng-7253	150	40	𝑡	𝑡	NOUN
fumecheng-7253	150	41	)	)	PUNCT
fumecheng-7253	150	42	sin	sin	NOUN
fumecheng-7253	150	43	(	(	PUNCT
fumecheng-7253	150	44	𝜋	𝜋	NOUN
fumecheng-7253	150	45	ℎ	ℎ	X
fumecheng-7253	150	46	𝑧	𝑧	PART
fumecheng-7253	150	47	)	)	PUNCT
fumecheng-7253	150	48	.	.	PUNCT
fumecheng-7253	151	1	(	(	PUNCT
fumecheng-7253	151	2	24	24	NUM
fumecheng-7253	151	3	)	)	PUNCT
fumecheng-7253	151	4	substituting	substitute	VERB
fumecheng-7253	151	5	eq	eq	PROPN
fumecheng-7253	151	6	.	.	PUNCT
fumecheng-7253	152	1	(	(	PUNCT
fumecheng-7253	152	2	24	24	NUM
fumecheng-7253	152	3	)	)	PUNCT
fumecheng-7253	152	4	into	into	ADP
fumecheng-7253	152	5	eqs	eqs	PROPN
fumecheng-7253	152	6	.	.	PUNCT
fumecheng-7253	153	1	(	(	PUNCT
fumecheng-7253	153	2	14	14	NUM
fumecheng-7253	153	3	)	)	PUNCT
fumecheng-7253	153	4	,	,	PUNCT
fumecheng-7253	153	5	(	(	PUNCT
fumecheng-7253	153	6	15	15	NUM
fumecheng-7253	153	7	)	)	PUNCT
fumecheng-7253	153	8	and	and	CCONJ
fumecheng-7253	153	9	(	(	PUNCT
fumecheng-7253	153	10	23	23	NUM
fumecheng-7253	153	11	)	)	PUNCT
fumecheng-7253	153	12	,	,	PUNCT
fumecheng-7253	153	13	which	which	PRON
fumecheng-7253	153	14	leads	lead	VERB
fumecheng-7253	153	15	to	to	ADP
fumecheng-7253	153	16	[	[	PUNCT
fumecheng-7253	153	17	𝜕4	𝜕4	X
fumecheng-7253	153	18	𝜕𝑥4	𝜕𝑥4	PROPN
fumecheng-7253	153	19	+	+	NUM
fumecheng-7253	153	20	𝜌𝐴	𝜌𝐴	ADJ
fumecheng-7253	153	21	𝐸𝐼	𝐸𝐼	PROPN
fumecheng-7253	153	22	𝜕2	𝜕2	NOUN
fumecheng-7253	153	23	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	153	24	(	(	PUNCT
fumecheng-7253	154	1	1	1	NUM
fumecheng-7253	154	2	−	−	NOUN
fumecheng-7253	154	3	𝜉	𝜉	NOUN
fumecheng-7253	154	4	𝜕2	𝜕2	NOUN
fumecheng-7253	154	5	𝜕𝑥2)]𝑤	𝜕𝑥2)]𝑤	NOUN
fumecheng-7253	154	6	−	−	PROPN
fumecheng-7253	154	7	1	1	NUM
fumecheng-7253	154	8	𝐸𝐼	𝐸𝐼	PROPN
fumecheng-7253	154	9	(	(	PUNCT
fumecheng-7253	154	10	1	1	NUM
fumecheng-7253	154	11	−	−	NOUN
fumecheng-7253	154	12	𝜉	𝜉	NOUN
fumecheng-7253	154	13	𝜕2	𝜕2	ADP
fumecheng-7253	154	14	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	154	15	)	)	PUNCT
fumecheng-7253	155	1	𝑞	𝑞	PROPN
fumecheng-7253	155	2	+	+	PROPN
fumecheng-7253	155	3	24𝛼𝑇	24𝛼𝑇	NUM
fumecheng-7253	155	4	𝜋2ℎ	𝜋2ℎ	ADJ
fumecheng-7253	155	5	𝜕2ψ	𝜕2ψ	NUM
fumecheng-7253	155	6	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	155	7	=	=	SYM
fumecheng-7253	155	8	0	0	NUM
fumecheng-7253	155	9	,	,	PUNCT
fumecheng-7253	155	10	(	(	PUNCT
fumecheng-7253	155	11	25	25	NUM
fumecheng-7253	155	12	)	)	PUNCT
fumecheng-7253	155	13	𝑀(𝑥	𝑀(𝑥	NOUN
fumecheng-7253	155	14	,	,	PUNCT
fumecheng-7253	155	15	𝑡	𝑡	NOUN
fumecheng-7253	155	16	)	)	PUNCT
fumecheng-7253	155	17	=	=	SYM
fumecheng-7253	155	18	𝜉	𝜉	NOUN
fumecheng-7253	155	19	(	(	PUNCT
fumecheng-7253	155	20	𝜌𝐴	𝜌𝐴	ADJ
fumecheng-7253	155	21	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	155	22	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	155	23	−	−	ADP
fumecheng-7253	155	24	𝑞	𝑞	SYM
fumecheng-7253	155	25	)	)	PUNCT
fumecheng-7253	155	26	−	−	PROPN
fumecheng-7253	155	27	𝐸𝐼	𝐸𝐼	PROPN
fumecheng-7253	155	28	(	(	PUNCT
fumecheng-7253	155	29	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	155	30	𝜕𝑥2	𝜕𝑥2	VERB
fumecheng-7253	155	31	+	+	CCONJ
fumecheng-7253	155	32	24𝑇0𝛼𝑇	24𝑇0𝛼𝑇	NUM
fumecheng-7253	155	33	𝜋2ℎ	𝜋2ℎ	ADJ
fumecheng-7253	155	34	θ	θ	NOUN
fumecheng-7253	155	35	)	)	PUNCT
fumecheng-7253	155	36	,	,	PUNCT
fumecheng-7253	155	37	(	(	PUNCT
fumecheng-7253	155	38	26	26	NUM
fumecheng-7253	155	39	)	)	PUNCT
fumecheng-7253	155	40	(	(	PUNCT
fumecheng-7253	155	41	1	1	NUM
fumecheng-7253	155	42	+	+	CCONJ
fumecheng-7253	155	43	𝜏𝜃	𝜏𝜃	ADP
fumecheng-7253	155	44	𝜕	𝜕	PROPN
fumecheng-7253	155	45	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	155	46	)	)	PUNCT
fumecheng-7253	155	47	(	(	PUNCT
fumecheng-7253	155	48	𝜕2	𝜕2	NUM
fumecheng-7253	155	49	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	155	50	−	−	PROPN
fumecheng-7253	155	51	𝜋2	𝜋2	PROPN
fumecheng-7253	155	52	ℎ2)ψ	ℎ2)ψ	ADJ
fumecheng-7253	155	53	=	=	PUNCT
fumecheng-7253	155	54	(	(	PUNCT
fumecheng-7253	155	55	1	1	NUM
fumecheng-7253	155	56	+	+	NUM
fumecheng-7253	155	57	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	155	58	𝜕	𝜕	PROPN
fumecheng-7253	155	59	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	155	60	+	+	CCONJ
fumecheng-7253	155	61	1	1	NUM
fumecheng-7253	155	62	2	2	NUM
fumecheng-7253	155	63	𝜏𝑞	𝜏𝑞	ADP
fumecheng-7253	155	64	2	2	NUM
fumecheng-7253	155	65	𝜕2	𝜕2	NOUN
fumecheng-7253	155	66	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	155	67	)	)	PUNCT
fumecheng-7253	155	68	𝜕	𝜕	PROPN
fumecheng-7253	155	69	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	155	70	(	(	PUNCT
fumecheng-7253	155	71	𝜂ψ	𝜂ψ	ADP
fumecheng-7253	155	72	−	−	PROPN
fumecheng-7253	155	73	𝛾𝑇0𝜋2ℎ	𝛾𝑇0𝜋2ℎ	NOUN
fumecheng-7253	155	74	24𝐾	24𝐾	NUM
fumecheng-7253	155	75	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	155	76	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-7253	155	77	)	)	PUNCT
fumecheng-7253	155	78	.	.	PUNCT
fumecheng-7253	156	1	(	(	PUNCT
fumecheng-7253	156	2	27	27	NUM
fumecheng-7253	156	3	)	)	PUNCT
fumecheng-7253	156	4	some	some	DET
fumecheng-7253	156	5	nondimensional	nondimensional	ADJ
fumecheng-7253	156	6	variables	variable	NOUN
fumecheng-7253	156	7	are	be	AUX
fumecheng-7253	156	8	provided	provide	VERB
fumecheng-7253	156	9	below	below	ADP
fumecheng-7253	156	10	for	for	ADP
fumecheng-7253	156	11	the	the	DET
fumecheng-7253	156	12	sake	sake	NOUN
fumecheng-7253	156	13	of	of	ADP
fumecheng-7253	156	14	generality	generality	NOUN
fumecheng-7253	156	15	{	{	PUNCT
fumecheng-7253	156	16	𝑢′	𝑢′	NUM
fumecheng-7253	156	17	,	,	PUNCT
fumecheng-7253	156	18	𝑥′	𝑥′	NUM
fumecheng-7253	156	19	,	,	PUNCT
fumecheng-7253	156	20	𝐿′	𝐿′	NOUN
fumecheng-7253	156	21	,	,	PUNCT
fumecheng-7253	156	22	𝑤′	𝑤′	NUM
fumecheng-7253	156	23	,	,	PUNCT
fumecheng-7253	156	24	𝑧′	𝑧′	NUM
fumecheng-7253	156	25	,	,	PUNCT
fumecheng-7253	156	26	ℎ′	ℎ′	NOUN
fumecheng-7253	156	27	,	,	PUNCT
fumecheng-7253	156	28	𝑏′	𝑏′	PROPN
fumecheng-7253	156	29	}	}	PUNCT
fumecheng-7253	156	30	=	=	SYM
fumecheng-7253	156	31	𝜂𝑐{𝑢	𝜂𝑐{𝑢	PROPN
fumecheng-7253	156	32	,	,	PUNCT
fumecheng-7253	156	33	𝑥	𝑥	PROPN
fumecheng-7253	156	34	,	,	PUNCT
fumecheng-7253	156	35	𝐿	𝐿	PROPN
fumecheng-7253	156	36	,	,	PUNCT
fumecheng-7253	156	37	𝑤	𝑤	PROPN
fumecheng-7253	156	38	,	,	PUNCT
fumecheng-7253	156	39	𝑧	𝑧	PROPN
fumecheng-7253	156	40	,	,	PUNCT
fumecheng-7253	156	41	ℎ	ℎ	PROPN
fumecheng-7253	156	42	,	,	PUNCT
fumecheng-7253	156	43	𝑏	𝑏	NOUN
fumecheng-7253	156	44	}	}	PUNCT
fumecheng-7253	156	45	,	,	PUNCT
fumecheng-7253	156	46	{	{	PUNCT
fumecheng-7253	156	47	𝑡′	𝑡′	NUM
fumecheng-7253	156	48	,	,	PUNCT
fumecheng-7253	156	49	𝜏𝑞	𝜏𝑞	DET
fumecheng-7253	156	50	′	′	NUM
fumecheng-7253	156	51	,	,	PUNCT
fumecheng-7253	156	52	𝜏𝜃	𝜏𝜃	CCONJ
fumecheng-7253	156	53	′	′	NOUN
fumecheng-7253	156	54	}	}	PUNCT
fumecheng-7253	156	55	=	=	SYM
fumecheng-7253	156	56	𝜂𝑐2{𝑡	𝜂𝑐2{𝑡	PROPN
fumecheng-7253	156	57	,	,	PUNCT
fumecheng-7253	156	58	𝜏𝑞	𝜏𝑞	INTJ
fumecheng-7253	156	59	,	,	PUNCT
fumecheng-7253	156	60	𝜏𝜃	𝜏𝜃	ADP
fumecheng-7253	156	61	}	}	PUNCT
fumecheng-7253	156	62	,	,	PUNCT
fumecheng-7253	156	63	𝜉′	𝜉′	PROPN
fumecheng-7253	156	64	=	=	SYM
fumecheng-7253	156	65	𝜂2𝑐2𝜉	𝜂2𝑐2𝜉	NUM
fumecheng-7253	156	66	,	,	PUNCT
fumecheng-7253	156	67	{	{	PUNCT
fumecheng-7253	156	68	θ′	θ′	NOUN
fumecheng-7253	156	69	,	,	PUNCT
fumecheng-7253	156	70	ψ′	ψ′	NUM
fumecheng-7253	156	71	}	}	PUNCT
fumecheng-7253	156	72	=	=	SYM
fumecheng-7253	156	73	1	1	NUM
fumecheng-7253	156	74	𝑇0	𝑇0	X
fumecheng-7253	156	75	{	{	PUNCT
fumecheng-7253	156	76	θ	θ	NOUN
fumecheng-7253	156	77	,	,	PUNCT
fumecheng-7253	156	78	ψ	ψ	NOUN
fumecheng-7253	156	79	}	}	PUNCT
fumecheng-7253	156	80	,	,	PUNCT
fumecheng-7253	156	81	𝑀′	𝑀′	NOUN
fumecheng-7253	156	82	=	=	SYM
fumecheng-7253	156	83	1	1	NUM
fumecheng-7253	156	84	𝜂𝑐𝐸𝐼	𝜂𝑐𝐸𝐼	NOUN
fumecheng-7253	156	85	𝑀	𝑀	PROPN
fumecheng-7253	156	86	,	,	PUNCT
fumecheng-7253	156	87	𝑞′	𝑞′	NOUN
fumecheng-7253	156	88	=	=	SYM
fumecheng-7253	156	89	𝐴	𝐴	PROPN
fumecheng-7253	156	90	𝐸𝐼	𝐸𝐼	PROPN
fumecheng-7253	156	91	𝑞	𝑞	PROPN
fumecheng-7253	156	92	,	,	PUNCT
fumecheng-7253	156	93	𝑐2	𝑐2	NOUN
fumecheng-7253	156	94	=	=	SYM
fumecheng-7253	156	95	𝐸	𝐸	PROPN
fumecheng-7253	156	96	𝜌	𝜌	X
fumecheng-7253	156	97	.	.	PUNCT
fumecheng-7253	157	1	(	(	PUNCT
fumecheng-7253	157	2	28	28	NUM
fumecheng-7253	157	3	)	)	PUNCT
fumecheng-7253	157	4	after	after	ADP
fumecheng-7253	157	5	introducing	introduce	VERB
fumecheng-7253	157	6	dimensionless	dimensionless	NOUN
fumecheng-7253	157	7	parameters	parameter	NOUN
fumecheng-7253	157	8	in	in	ADP
fumecheng-7253	157	9	eqs	eqs	PROPN
fumecheng-7253	157	10	.	.	PUNCT
fumecheng-7253	158	1	(	(	PUNCT
fumecheng-7253	158	2	25	25	NUM
fumecheng-7253	158	3	)	)	PUNCT
fumecheng-7253	158	4	to	to	ADP
fumecheng-7253	158	5	(	(	PUNCT
fumecheng-7253	158	6	27	27	NUM
fumecheng-7253	158	7	)	)	PUNCT
fumecheng-7253	158	8	,	,	PUNCT
fumecheng-7253	158	9	one	one	PRON
fumecheng-7253	158	10	can	can	AUX
fumecheng-7253	158	11	obtain	obtain	VERB
fumecheng-7253	158	12	[	[	PUNCT
fumecheng-7253	158	13	𝜕4	𝜕4	NOUN
fumecheng-7253	158	14	𝜕𝑥4	𝜕𝑥4	PROPN
fumecheng-7253	158	15	+	+	NUM
fumecheng-7253	158	16	12	12	NUM
fumecheng-7253	158	17	ℎ2	ℎ2	NOUN
fumecheng-7253	158	18	𝜕2	𝜕2	NOUN
fumecheng-7253	158	19	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	158	20	(	(	PUNCT
fumecheng-7253	158	21	1	1	NUM
fumecheng-7253	158	22	−	−	NOUN
fumecheng-7253	158	23	𝜉	𝜉	NOUN
fumecheng-7253	158	24	𝜕2	𝜕2	NOUN
fumecheng-7253	159	1	𝜕𝑥2)]𝑤	𝜕𝑥2)]𝑤	NOUN
fumecheng-7253	159	2	−	−	PROPN
fumecheng-7253	159	3	(	(	PUNCT
fumecheng-7253	159	4	1	1	NUM
fumecheng-7253	159	5	−	−	NOUN
fumecheng-7253	159	6	𝜉	𝜉	NOUN
fumecheng-7253	159	7	𝜕2	𝜕2	NOUN
fumecheng-7253	159	8	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	159	9	)	)	PUNCT
fumecheng-7253	160	1	[	[	X
fumecheng-7253	160	2	𝑞	𝑞	X
fumecheng-7253	160	3	+	+	PUNCT
fumecheng-7253	160	4	𝜕	𝜕	PROPN
fumecheng-7253	160	5	𝜕𝑥	𝜕𝑥	X
fumecheng-7253	160	6	(	(	PUNCT
fumecheng-7253	160	7	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	160	8	)	)	PUNCT
fumecheng-7253	160	9	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-7253	160	10	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-7253	160	11	)	)	PUNCT
fumecheng-7253	160	12	]	]	PUNCT
fumecheng-7253	161	1	+	+	PUNCT
fumecheng-7253	161	2	24𝑇0𝛼𝑇	24𝑇0𝛼𝑇	NUM
fumecheng-7253	161	3	𝜋2ℎ	𝜋2ℎ	ADJ
fumecheng-7253	161	4	𝜕2θ	𝜕2θ	NUM
fumecheng-7253	161	5	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	161	6	=	=	SYM
fumecheng-7253	161	7	0	0	NUM
fumecheng-7253	161	8	(	(	PUNCT
fumecheng-7253	161	9	29	29	NUM
fumecheng-7253	161	10	)	)	PUNCT
fumecheng-7253	161	11	temperature	temperature	NOUN
fumecheng-7253	161	12	-	-	PUNCT
fumecheng-7253	161	13	dependent	dependent	ADJ
fumecheng-7253	161	14	physical	physical	ADJ
fumecheng-7253	161	15	characteristics	characteristic	NOUN
fumecheng-7253	161	16	of	of	ADP
fumecheng-7253	161	17	rotating	rotate	VERB
fumecheng-7253	161	18	nonlocal	nonlocal	ADJ
fumecheng-7253	161	19	nanobeams	nanobeam	NOUN
fumecheng-7253	161	20	subject	subject	ADJ
fumecheng-7253	161	21	to	to	ADP
fumecheng-7253	161	22	...	...	PUNCT
fumecheng-7253	161	23	641	641	NUM
fumecheng-7253	161	24	(	(	PUNCT
fumecheng-7253	161	25	1	1	NUM
fumecheng-7253	161	26	+	+	CCONJ
fumecheng-7253	161	27	𝜏𝜃	𝜏𝜃	ADP
fumecheng-7253	161	28	𝜕	𝜕	PROPN
fumecheng-7253	161	29	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	161	30	)	)	PUNCT
fumecheng-7253	161	31	(	(	PUNCT
fumecheng-7253	161	32	𝜕2	𝜕2	NUM
fumecheng-7253	161	33	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	161	34	−	−	PROPN
fumecheng-7253	161	35	𝜋2	𝜋2	PROPN
fumecheng-7253	161	36	ℎ2)ψ	ℎ2)ψ	ADJ
fumecheng-7253	161	37	=	=	PUNCT
fumecheng-7253	161	38	(	(	PUNCT
fumecheng-7253	161	39	1	1	NUM
fumecheng-7253	161	40	+	+	NUM
fumecheng-7253	161	41	𝜏𝑞	𝜏𝑞	PROPN
fumecheng-7253	161	42	𝜕	𝜕	PROPN
fumecheng-7253	161	43	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	161	44	+	+	NOUN
fumecheng-7253	161	45	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	161	46	2	2	NUM
fumecheng-7253	161	47	2	2	NUM
fumecheng-7253	161	48	𝜕2	𝜕2	NOUN
fumecheng-7253	161	49	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	161	50	)	)	PUNCT
fumecheng-7253	161	51	𝜕	𝜕	PROPN
fumecheng-7253	161	52	𝜕𝑡	𝜕𝑡	PROPN
fumecheng-7253	161	53	(	(	PUNCT
fumecheng-7253	161	54	ψ	ψ	X
fumecheng-7253	161	55	−	−	PROPN
fumecheng-7253	161	56	𝛾𝜋2ℎ	𝛾𝜋2ℎ	ADJ
fumecheng-7253	161	57	24𝐾𝜂	24𝐾𝜂	NUM
fumecheng-7253	161	58	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	161	59	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-7253	161	60	)	)	PUNCT
fumecheng-7253	161	61	(	(	PUNCT
fumecheng-7253	161	62	30	30	NUM
fumecheng-7253	161	63	)	)	PUNCT
fumecheng-7253	161	64	𝑀(𝑥	𝑀(𝑥	NOUN
fumecheng-7253	161	65	,	,	PUNCT
fumecheng-7253	161	66	𝑡	𝑡	NOUN
fumecheng-7253	161	67	)	)	PUNCT
fumecheng-7253	161	68	=	=	NOUN
fumecheng-7253	161	69	12𝜉	12𝜉	NOUN
fumecheng-7253	161	70	ℎ2	ℎ2	NOUN
fumecheng-7253	161	71	𝜕2𝑤	𝜕2𝑤	CCONJ
fumecheng-7253	161	72	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	161	73	−	−	NOUN
fumecheng-7253	161	74	𝜉	𝜉	X
fumecheng-7253	162	1	[	[	X
fumecheng-7253	162	2	𝑞	𝑞	X
fumecheng-7253	162	3	+	+	NUM
fumecheng-7253	162	4	𝜕	𝜕	PROPN
fumecheng-7253	162	5	𝜕𝑥	𝜕𝑥	X
fumecheng-7253	162	6	(	(	PUNCT
fumecheng-7253	162	7	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	162	8	)	)	PUNCT
fumecheng-7253	162	9	𝜕𝑤	𝜕𝑤	NOUN
fumecheng-7253	162	10	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-7253	162	11	)	)	PUNCT
fumecheng-7253	162	12	]	]	PUNCT
fumecheng-7253	163	1	−	−	PUNCT
fumecheng-7253	163	2	𝜕2𝑤	𝜕2𝑤	CCONJ
fumecheng-7253	163	3	𝜕𝑥2	𝜕𝑥2	VERB
fumecheng-7253	163	4	−	−	PROPN
fumecheng-7253	163	5	24𝑇0𝛼𝑇	24𝑇0𝛼𝑇	NUM
fumecheng-7253	163	6	𝜋2ℎ	𝜋2ℎ	PROPN
fumecheng-7253	163	7	θ	θ	PROPN
fumecheng-7253	163	8	(	(	PUNCT
fumecheng-7253	163	9	31	31	NUM
fumecheng-7253	163	10	)	)	PUNCT
fumecheng-7253	163	11	in	in	ADP
fumecheng-7253	163	12	eqs	eqs	PROPN
fumecheng-7253	163	13	.	.	PUNCT
fumecheng-7253	163	14	(	(	PUNCT
fumecheng-7253	163	15	29)-(31	29)-(31	NUM
fumecheng-7253	163	16	)	)	PUNCT
fumecheng-7253	163	17	,	,	PUNCT
fumecheng-7253	163	18	the	the	DET
fumecheng-7253	163	19	primes	prime	NOUN
fumecheng-7253	163	20	are	be	AUX
fumecheng-7253	163	21	omitted	omit	VERB
fumecheng-7253	163	22	for	for	ADP
fumecheng-7253	163	23	the	the	DET
fumecheng-7253	163	24	sake	sake	NOUN
fumecheng-7253	163	25	of	of	ADP
fumecheng-7253	163	26	simplicity	simplicity	NOUN
fumecheng-7253	163	27	.	.	PUNCT
fumecheng-7253	164	1	a	a	DET
fumecheng-7253	164	2	specific	specific	ADJ
fumecheng-7253	164	3	type	type	NOUN
fumecheng-7253	164	4	of	of	ADP
fumecheng-7253	164	5	external	external	ADJ
fumecheng-7253	164	6	transverse	transverse	NOUN
fumecheng-7253	164	7	load	load	NOUN
fumecheng-7253	164	8	is	be	AUX
fumecheng-7253	164	9	now	now	ADV
fumecheng-7253	164	10	taken	take	VERB
fumecheng-7253	164	11	into	into	ADP
fumecheng-7253	164	12	account	account	NOUN
fumecheng-7253	164	13	.	.	PUNCT
fumecheng-7253	165	1	it	it	PRON
fumecheng-7253	165	2	is	be	AUX
fumecheng-7253	165	3	considered	consider	VERB
fumecheng-7253	165	4	that	that	SCONJ
fumecheng-7253	165	5	the	the	DET
fumecheng-7253	165	6	vertical	vertical	ADJ
fumecheng-7253	165	7	load	load	NOUN
fumecheng-7253	165	8	decays	decay	VERB
fumecheng-7253	165	9	exponentially	exponentially	ADV
fumecheng-7253	165	10	with	with	ADP
fumecheng-7253	165	11	time	time	NOUN
fumecheng-7253	165	12	,	,	PUNCT
fumecheng-7253	165	13	acting	act	VERB
fumecheng-7253	165	14	towards	towards	ADP
fumecheng-7253	165	15	the	the	DET
fumecheng-7253	165	16	thickness	thickness	NOUN
fumecheng-7253	165	17	of	of	ADP
fumecheng-7253	165	18	the	the	DET
fumecheng-7253	165	19	beam	beam	NOUN
fumecheng-7253	165	20	[	[	X
fumecheng-7253	165	21	45	45	NUM
fumecheng-7253	165	22	]	]	PUNCT
fumecheng-7253	165	23	as	as	SCONJ
fumecheng-7253	165	24	follows	follow	VERB
fumecheng-7253	165	25	𝑞(𝑥	𝑞(𝑥	PROPN
fumecheng-7253	165	26	,	,	PUNCT
fumecheng-7253	165	27	𝑡	𝑡	X
fumecheng-7253	165	28	)	)	PUNCT
fumecheng-7253	165	29	=	=	SYM
fumecheng-7253	165	30	−𝑞0(1	−𝑞0(1	NUM
fumecheng-7253	165	31	−	−	PROPN
fumecheng-7253	165	32	𝛿e−𝛽𝑡	𝛿e−𝛽𝑡	NOUN
fumecheng-7253	165	33	)	)	PUNCT
fumecheng-7253	165	34	(	(	PUNCT
fumecheng-7253	165	35	32	32	NUM
fumecheng-7253	165	36	)	)	PUNCT
fumecheng-7253	165	37	where	where	SCONJ
fumecheng-7253	165	38	𝑞0	𝑞0	NOUN
fumecheng-7253	165	39	is	be	AUX
fumecheng-7253	165	40	the	the	DET
fumecheng-7253	165	41	magnitude	magnitude	NOUN
fumecheng-7253	165	42	of	of	ADP
fumecheng-7253	165	43	the	the	DET
fumecheng-7253	165	44	dimensionless	dimensionless	NOUN
fumecheng-7253	165	45	point	point	NOUN
fumecheng-7253	165	46	load	load	NOUN
fumecheng-7253	165	47	and	and	CCONJ
fumecheng-7253	165	48	𝛽	𝛽	NOUN
fumecheng-7253	165	49	is	be	AUX
fumecheng-7253	165	50	the	the	DET
fumecheng-7253	165	51	dimensionless	dimensionless	NOUN
fumecheng-7253	165	52	decaying	decay	VERB
fumecheng-7253	165	53	parameter	parameter	NOUN
fumecheng-7253	165	54	of	of	ADP
fumecheng-7253	165	55	the	the	DET
fumecheng-7253	165	56	external	external	ADJ
fumecheng-7253	165	57	force	force	NOUN
fumecheng-7253	165	58	,	,	PUNCT
fumecheng-7253	165	59	respectively	respectively	ADV
fumecheng-7253	165	60	(	(	PUNCT
fumecheng-7253	165	61	𝛿	𝛿	NOUN
fumecheng-7253	165	62	=	=	SYM
fumecheng-7253	165	63	0	0	NUM
fumecheng-7253	165	64	can	can	AUX
fumecheng-7253	165	65	be	be	AUX
fumecheng-7253	165	66	used	use	VERB
fumecheng-7253	165	67	in	in	ADP
fumecheng-7253	165	68	the	the	DET
fumecheng-7253	165	69	case	case	NOUN
fumecheng-7253	165	70	of	of	ADP
fumecheng-7253	165	71	uniform	uniform	ADJ
fumecheng-7253	165	72	distributed	distribute	VERB
fumecheng-7253	165	73	force	force	NOUN
fumecheng-7253	165	74	)	)	PUNCT
fumecheng-7253	165	75	.	.	PUNCT
fumecheng-7253	166	1	it	it	PRON
fumecheng-7253	166	2	is	be	AUX
fumecheng-7253	166	3	also	also	ADV
fumecheng-7253	166	4	assumed	assume	VERB
fumecheng-7253	166	5	that	that	SCONJ
fumecheng-7253	166	6	the	the	DET
fumecheng-7253	166	7	system	system	NOUN
fumecheng-7253	166	8	works	work	VERB
fumecheng-7253	166	9	at	at	ADP
fumecheng-7253	166	10	constant	constant	ADJ
fumecheng-7253	166	11	rotating	rotating	NOUN
fumecheng-7253	166	12	speed	speed	NOUN
fumecheng-7253	166	13	and	and	CCONJ
fumecheng-7253	166	14	centrifugal	centrifugal	ADJ
fumecheng-7253	166	15	tension	tension	NOUN
fumecheng-7253	166	16	load	load	NOUN
fumecheng-7253	166	17	𝑅(𝑥	𝑅(𝑥	NOUN
fumecheng-7253	166	18	)	)	PUNCT
fumecheng-7253	166	19	is	be	AUX
fumecheng-7253	166	20	considered	consider	VERB
fumecheng-7253	166	21	to	to	PART
fumecheng-7253	166	22	have	have	VERB
fumecheng-7253	166	23	its	its	PRON
fumecheng-7253	166	24	maximum	maximum	ADJ
fumecheng-7253	166	25	value	value	NOUN
fumecheng-7253	166	26	(	(	PUNCT
fumecheng-7253	166	27	at𝑥	at𝑥	NOUN
fumecheng-7253	166	28	=	=	SYM
fumecheng-7253	166	29	0	0	NUM
fumecheng-7253	166	30	)	)	PUNCT
fumecheng-7253	166	31	which	which	PRON
fumecheng-7253	166	32	takes	take	VERB
fumecheng-7253	166	33	the	the	DET
fumecheng-7253	166	34	following	follow	VERB
fumecheng-7253	166	35	form	form	NOUN
fumecheng-7253	166	36	[	[	X
fumecheng-7253	166	37	41	41	NUM
fumecheng-7253	166	38	]	]	X
fumecheng-7253	166	39	𝑅𝑚𝑎𝑥	𝑅𝑚𝑎𝑥	PROPN
fumecheng-7253	166	40	=	=	PUNCT
fumecheng-7253	166	41	∫	∫	NOUN
fumecheng-7253	166	42	𝜌𝐴ω2(𝑟	𝜌𝐴ω2(𝑟	NOUN
fumecheng-7253	167	1	+	+	CCONJ
fumecheng-7253	167	2	𝑥)𝑑𝑥	𝑥)𝑑𝑥	PROPN
fumecheng-7253	167	3	=	=	SYM
fumecheng-7253	167	4	1	1	NUM
fumecheng-7253	167	5	2	2	NUM
fumecheng-7253	167	6	𝜌𝐴ω2𝐿(2𝑟	𝜌𝐴ω2𝐿(2𝑟	ADJ
fumecheng-7253	167	7	+	+	CCONJ
fumecheng-7253	167	8	𝐿	𝐿	PROPN
fumecheng-7253	167	9	)	)	PUNCT
fumecheng-7253	167	10	𝐿	𝐿	NOUN
fumecheng-7253	167	11	0	0	NUM
fumecheng-7253	167	12	(	(	PUNCT
fumecheng-7253	167	13	33	33	NUM
fumecheng-7253	167	14	)	)	PUNCT
fumecheng-7253	167	15	thereby	thereby	ADV
fumecheng-7253	167	16	,	,	PUNCT
fumecheng-7253	167	17	the	the	DET
fumecheng-7253	167	18	equation	equation	NOUN
fumecheng-7253	167	19	of	of	ADP
fumecheng-7253	167	20	motion	motion	NOUN
fumecheng-7253	167	21	(	(	PUNCT
fumecheng-7253	167	22	29	29	NUM
fumecheng-7253	167	23	)	)	PUNCT
fumecheng-7253	167	24	can	can	AUX
fumecheng-7253	167	25	be	be	AUX
fumecheng-7253	167	26	described	describe	VERB
fumecheng-7253	167	27	as	as	ADP
fumecheng-7253	167	28	[	[	PUNCT
fumecheng-7253	167	29	𝜕4	𝜕4	NOUN
fumecheng-7253	167	30	𝜕𝑥4	𝜕𝑥4	PROPN
fumecheng-7253	167	31	+	+	NUM
fumecheng-7253	167	32	12	12	NUM
fumecheng-7253	167	33	ℎ2	ℎ2	NOUN
fumecheng-7253	167	34	𝜕2	𝜕2	NOUN
fumecheng-7253	167	35	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	167	36	(	(	PUNCT
fumecheng-7253	167	37	1	1	NUM
fumecheng-7253	167	38	−	−	NOUN
fumecheng-7253	167	39	𝜉	𝜉	NOUN
fumecheng-7253	167	40	𝜕2	𝜕2	NOUN
fumecheng-7253	167	41	𝜕𝑥2)]𝑤	𝜕𝑥2)]𝑤	NOUN
fumecheng-7253	167	42	−	−	PROPN
fumecheng-7253	168	1	(	(	PUNCT
fumecheng-7253	168	2	1	1	NUM
fumecheng-7253	168	3	−	−	NOUN
fumecheng-7253	168	4	𝜉	𝜉	NOUN
fumecheng-7253	168	5	𝜕2	𝜕2	NOUN
fumecheng-7253	168	6	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	168	7	)	)	PUNCT
fumecheng-7253	169	1	[	[	X
fumecheng-7253	169	2	𝑞	𝑞	X
fumecheng-7253	169	3	+	+	NOUN
fumecheng-7253	169	4	6𝐿ω2(2𝑟+𝐿	6𝐿ω2(2𝑟+𝐿	NUM
fumecheng-7253	169	5	)	)	PUNCT
fumecheng-7253	169	6	ℎ2	ℎ2	NOUN
fumecheng-7253	169	7	𝜕2𝑤	𝜕2𝑤	NUM
fumecheng-7253	169	8	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	169	9	]	]	PUNCT
fumecheng-7253	170	1	+	+	CCONJ
fumecheng-7253	170	2	24𝑇0𝛼𝑇	24𝑇0𝛼𝑇	NUM
fumecheng-7253	170	3	𝜋2ℎ	𝜋2ℎ	ADJ
fumecheng-7253	170	4	𝜕2θ	𝜕2θ	NUM
fumecheng-7253	170	5	𝜕𝑥2	𝜕𝑥2	NOUN
fumecheng-7253	170	6	=	=	SYM
fumecheng-7253	170	7	0	0	NUM
fumecheng-7253	170	8	(	(	PUNCT
fumecheng-7253	170	9	34	34	NUM
fumecheng-7253	170	10	)	)	PUNCT
fumecheng-7253	170	11	the	the	DET
fumecheng-7253	170	12	bending	bend	VERB
fumecheng-7253	170	13	moment	moment	NOUN
fumecheng-7253	170	14	in	in	ADP
fumecheng-7253	170	15	eq	eq	ADP
fumecheng-7253	170	16	.	.	PUNCT
fumecheng-7253	171	1	(	(	PUNCT
fumecheng-7253	171	2	31	31	NUM
fumecheng-7253	171	3	)	)	PUNCT
fumecheng-7253	171	4	may	may	AUX
fumecheng-7253	171	5	also	also	ADV
fumecheng-7253	171	6	be	be	AUX
fumecheng-7253	171	7	defined	define	VERB
fumecheng-7253	171	8	as	as	ADP
fumecheng-7253	171	9	𝑀(𝑥	𝑀(𝑥	NOUN
fumecheng-7253	171	10	,	,	PUNCT
fumecheng-7253	171	11	𝑡	𝑡	NOUN
fumecheng-7253	171	12	)	)	PUNCT
fumecheng-7253	171	13	=	=	NOUN
fumecheng-7253	171	14	12𝜉	12𝜉	NOUN
fumecheng-7253	171	15	ℎ2	ℎ2	NOUN
fumecheng-7253	171	16	𝜕2𝑤	𝜕2𝑤	CCONJ
fumecheng-7253	171	17	𝜕𝑡2	𝜕𝑡2	NOUN
fumecheng-7253	171	18	−	−	NOUN
fumecheng-7253	171	19	𝜉	𝜉	X
fumecheng-7253	171	20	[	[	X
fumecheng-7253	171	21	𝑞	𝑞	X
fumecheng-7253	171	22	+	+	NOUN
fumecheng-7253	171	23	6𝐿ω2(2𝑟+𝐿	6𝐿ω2(2𝑟+𝐿	NUM
fumecheng-7253	171	24	)	)	PUNCT
fumecheng-7253	171	25	ℎ2	ℎ2	NOUN
fumecheng-7253	171	26	𝜕2𝑤	𝜕2𝑤	ADP
fumecheng-7253	171	27	𝜕𝑥2	𝜕𝑥2	PROPN
fumecheng-7253	171	28	]	]	PUNCT
fumecheng-7253	172	1	−	−	PROPN
fumecheng-7253	173	1	𝜕2𝑤	𝜕2𝑤	CCONJ
fumecheng-7253	173	2	𝜕𝑥2	𝜕𝑥2	VERB
fumecheng-7253	173	3	−	−	PROPN
fumecheng-7253	173	4	24𝑇0𝛼𝑇	24𝑇0𝛼𝑇	NUM
fumecheng-7253	173	5	𝜋2ℎ	𝜋2ℎ	PROPN
fumecheng-7253	173	6	θ	θ	PROPN
fumecheng-7253	173	7	(	(	PUNCT
fumecheng-7253	173	8	35	35	NUM
fumecheng-7253	173	9	)	)	PUNCT
fumecheng-7253	173	10	the	the	DET
fumecheng-7253	173	11	initial	initial	ADJ
fumecheng-7253	173	12	conditions	condition	NOUN
fumecheng-7253	173	13	are	be	AUX
fumecheng-7253	173	14	supposed	suppose	VERB
fumecheng-7253	173	15	to	to	PART
fumecheng-7253	173	16	be	be	AUX
fumecheng-7253	173	17	ψ(𝑥	ψ(𝑥	NOUN
fumecheng-7253	173	18	,	,	PUNCT
fumecheng-7253	173	19	0	0	NUM
fumecheng-7253	173	20	)	)	PUNCT
fumecheng-7253	173	21	=	=	SYM
fumecheng-7253	173	22	𝜕ψ(𝑥,0	𝜕ψ(𝑥,0	NOUN
fumecheng-7253	173	23	)	)	PUNCT
fumecheng-7253	173	24	𝜕𝑡	𝜕𝑡	NOUN
fumecheng-7253	174	1	=	=	NOUN
fumecheng-7253	174	2	0	0	NUM
fumecheng-7253	174	3	,	,	PUNCT
fumecheng-7253	174	4	𝑤(𝑥	𝑤(𝑥	NOUN
fumecheng-7253	174	5	,	,	PUNCT
fumecheng-7253	174	6	0	0	NUM
fumecheng-7253	174	7	)	)	PUNCT
fumecheng-7253	174	8	=	=	SYM
fumecheng-7253	174	9	𝜕𝑤(𝑥,0	𝜕𝑤(𝑥,0	NOUN
fumecheng-7253	174	10	)	)	PUNCT
fumecheng-7253	174	11	𝜕𝑡	𝜕𝑡	NOUN
fumecheng-7253	174	12	=	=	NOUN
fumecheng-7253	174	13	0	0	PROPN
fumecheng-7253	174	14	.	.	PUNCT
fumecheng-7253	175	1	(	(	PUNCT
fumecheng-7253	175	2	36	36	NUM
fumecheng-7253	175	3	)	)	PUNCT
fumecheng-7253	175	4	the	the	DET
fumecheng-7253	175	5	nanobeam	nanobeam	ADJ
fumecheng-7253	175	6	subjects	subject	NOUN
fumecheng-7253	175	7	to	to	ADP
fumecheng-7253	175	8	the	the	DET
fumecheng-7253	175	9	following	follow	VERB
fumecheng-7253	175	10	boundary	boundary	ADJ
fumecheng-7253	175	11	conditions	condition	NOUN
fumecheng-7253	175	12	:	:	PUNCT
fumecheng-7253	175	13	▪	▪	NOUN
fumecheng-7253	175	14	doubly	doubly	ADV
fumecheng-7253	175	15	-	-	PUNCT
fumecheng-7253	175	16	clamped	clamp	VERB
fumecheng-7253	175	17	ends	end	NOUN
fumecheng-7253	175	18	with	with	ADP
fumecheng-7253	175	19	the	the	DET
fumecheng-7253	175	20	following	follow	VERB
fumecheng-7253	175	21	conditions	condition	NOUN
fumecheng-7253	175	22	𝑤(𝑥	𝑤(𝑥	NOUN
fumecheng-7253	175	23	,	,	PUNCT
fumecheng-7253	175	24	𝑡)|𝑥=0,𝐿	𝑡)|𝑥=0,𝐿	NOUN
fumecheng-7253	175	25	=	=	SYM
fumecheng-7253	175	26	0	0	NUM
fumecheng-7253	175	27	,	,	PUNCT
fumecheng-7253	175	28	𝜕𝑤(𝑥,𝑡	𝜕𝑤(𝑥,𝑡	NOUN
fumecheng-7253	175	29	)	)	PUNCT
fumecheng-7253	175	30	𝜕𝑥	𝜕𝑥	X
fumecheng-7253	176	1	|	|	ADV
fumecheng-7253	176	2	𝑥=0,𝐿	𝑥=0,𝐿	VERB
fumecheng-7253	176	3	=	=	NOUN
fumecheng-7253	176	4	0	0	NUM
fumecheng-7253	176	5	.	.	PUNCT
fumecheng-7253	176	6	(	(	PUNCT
fumecheng-7253	176	7	37	37	NUM
fumecheng-7253	176	8	)	)	PUNCT
fumecheng-7253	176	9	▪	▪	NOUN
fumecheng-7253	176	10	the	the	DET
fumecheng-7253	176	11	nanobeam	nanobeam	NOUN
fumecheng-7253	176	12	is	be	AUX
fumecheng-7253	176	13	harmonically	harmonically	ADV
fumecheng-7253	176	14	heated	heated	ADJ
fumecheng-7253	176	15	as	as	ADP
fumecheng-7253	176	16	θ(0	θ(0	PROPN
fumecheng-7253	176	17	,	,	PUNCT
fumecheng-7253	176	18	𝑡	𝑡	NOUN
fumecheng-7253	176	19	)	)	PUNCT
fumecheng-7253	176	20	=	=	SYM
fumecheng-7253	176	21	θ0	θ0	NOUN
fumecheng-7253	176	22	cos(𝜔𝑡	cos(𝜔𝑡	NUM
fumecheng-7253	176	23	)	)	PUNCT
fumecheng-7253	176	24	,	,	PUNCT
fumecheng-7253	176	25	𝜔	𝜔	X
fumecheng-7253	176	26	>	>	X
fumecheng-7253	176	27	0	0	NUM
fumecheng-7253	176	28	,	,	PUNCT
fumecheng-7253	176	29	(	(	PUNCT
fumecheng-7253	176	30	38	38	NUM
fumecheng-7253	176	31	)	)	PUNCT
fumecheng-7253	176	32	in	in	ADP
fumecheng-7253	176	33	which	which	PRON
fumecheng-7253	176	34	θ0	θ0	PROPN
fumecheng-7253	176	35	is	be	AUX
fumecheng-7253	176	36	its	its	PRON
fumecheng-7253	176	37	amplitude	amplitude	NOUN
fumecheng-7253	176	38	and	and	CCONJ
fumecheng-7253	176	39	𝜔	𝜔	AUX
fumecheng-7253	176	40	denotes	denote	NOUN
fumecheng-7253	176	41	the	the	DET
fumecheng-7253	176	42	thermal	thermal	ADJ
fumecheng-7253	176	43	angular	angular	ADJ
fumecheng-7253	176	44	frequency	frequency	NOUN
fumecheng-7253	176	45	.	.	PUNCT
fumecheng-7253	177	1	in	in	ADP
fumecheng-7253	177	2	the	the	DET
fumecheng-7253	177	3	case	case	NOUN
fumecheng-7253	177	4	of	of	ADP
fumecheng-7253	177	5	𝜔	𝜔	NOUN
fumecheng-7253	177	6	=	=	SYM
fumecheng-7253	177	7	0	0	NUM
fumecheng-7253	177	8	,	,	PUNCT
fumecheng-7253	177	9	the	the	DET
fumecheng-7253	177	10	above	above	ADJ
fumecheng-7253	177	11	condition	condition	NOUN
fumecheng-7253	177	12	is	be	AUX
fumecheng-7253	177	13	utilized	utilize	VERB
fumecheng-7253	177	14	for	for	ADP
fumecheng-7253	177	15	thermal	thermal	ADJ
fumecheng-7253	177	16	shock	shock	NOUN
fumecheng-7253	177	17	loading	loading	NOUN
fumecheng-7253	177	18	.	.	PUNCT
fumecheng-7253	178	1	using	use	VERB
fumecheng-7253	178	2	eq	eq	X
fumecheng-7253	178	3	.	.	PUNCT
fumecheng-7253	179	1	(	(	PUNCT
fumecheng-7253	179	2	15	15	NUM
fumecheng-7253	179	3	)	)	PUNCT
fumecheng-7253	179	4	and	and	CCONJ
fumecheng-7253	179	5	eq	eq	NOUN
fumecheng-7253	179	6	.	.	PUNCT
fumecheng-7253	180	1	(	(	PUNCT
fumecheng-7253	180	2	20	20	NUM
fumecheng-7253	180	3	)	)	PUNCT
fumecheng-7253	180	4	yields	yield	NOUN
fumecheng-7253	180	5	ψ(0	ψ(0	PROPN
fumecheng-7253	180	6	,	,	PUNCT
fumecheng-7253	180	7	𝑡	𝑡	X
fumecheng-7253	180	8	)	)	PUNCT
fumecheng-7253	180	9	=	=	SYM
fumecheng-7253	180	10	θ0	θ0	NOUN
fumecheng-7253	180	11	cos(𝜔𝑡	cos(𝜔𝑡	X
fumecheng-7253	180	12	)	)	PUNCT
fumecheng-7253	181	1	+	+	CCONJ
fumecheng-7253	181	2	1	1	NUM
fumecheng-7253	181	3	2	2	NUM
fumecheng-7253	181	4	𝐾1[θ0	𝐾1[θ0	NOUN
fumecheng-7253	181	5	cos(𝜔𝑡)]2	cos(𝜔𝑡)]2	NOUN
fumecheng-7253	181	6	.	.	PUNCT
fumecheng-7253	182	1	(	(	PUNCT
fumecheng-7253	182	2	39	39	NUM
fumecheng-7253	182	3	)	)	PUNCT
fumecheng-7253	182	4	▪	▪	NOUN
fumecheng-7253	182	5	the	the	DET
fumecheng-7253	182	6	surface	surface	NOUN
fumecheng-7253	182	7	𝑥	𝑥	NOUN
fumecheng-7253	182	8	=	=	SYM
fumecheng-7253	182	9	𝐿	𝐿	PROPN
fumecheng-7253	182	10	is	be	AUX
fumecheng-7253	182	11	assumed	assume	VERB
fumecheng-7253	182	12	to	to	PART
fumecheng-7253	182	13	be	be	AUX
fumecheng-7253	182	14	thermally	thermally	ADV
fumecheng-7253	182	15	isolated	isolate	VERB
fumecheng-7253	182	16	𝜕ψ(𝐿,𝑡	𝜕ψ(𝐿,𝑡	NOUN
fumecheng-7253	182	17	)	)	PUNCT
fumecheng-7253	182	18	𝜕𝑥	𝜕𝑥	NOUN
fumecheng-7253	182	19	=	=	SYM
fumecheng-7253	183	1	0	0	X
fumecheng-7253	183	2	.	.	PUNCT
fumecheng-7253	184	1	(	(	PUNCT
fumecheng-7253	184	2	40	40	NUM
fumecheng-7253	184	3	)	)	PUNCT
fumecheng-7253	184	4	642	642	NUM
fumecheng-7253	184	5	a.	a.	PROPN
fumecheng-7253	184	6	e.	e.	PROPN
fumecheng-7253	184	7	abouelregal	abouelregal	PROPN
fumecheng-7253	184	8	,	,	PUNCT
fumecheng-7253	184	9	h.	h.	PROPN
fumecheng-7253	184	10	m.	m.	PROPN
fumecheng-7253	184	11	sedighi	sedighi	PROPN
fumecheng-7253	184	12	,	,	PUNCT
fumecheng-7253	184	13	s.	s.	PROPN
fumecheng-7253	184	14	a.	a.	PROPN
fumecheng-7253	184	15	faghidian	faghidian	PROPN
fumecheng-7253	184	16	,	,	PUNCT
fumecheng-7253	184	17	a.	a.	PROPN
fumecheng-7253	184	18	h.	h.	PROPN
fumecheng-7253	184	19	shirazi	shirazi	PROPN
fumecheng-7253	184	20	6	6	NUM
fumecheng-7253	184	21	.	.	PUNCT
fumecheng-7253	185	1	laplace	laplace	NOUN
fumecheng-7253	185	2	transform	transform	VERB
fumecheng-7253	185	3	strategy	strategy	NOUN
fumecheng-7253	185	4	using	use	VERB
fumecheng-7253	185	5	laplace	laplace	NOUN
fumecheng-7253	185	6	technique	technique	NOUN
fumecheng-7253	185	7	,	,	PUNCT
fumecheng-7253	185	8	eqs	eqs	X
fumecheng-7253	185	9	.	.	PUNCT
fumecheng-7253	186	1	(	(	PUNCT
fumecheng-7253	186	2	30	30	NUM
fumecheng-7253	186	3	)	)	PUNCT
fumecheng-7253	186	4	,	,	PUNCT
fumecheng-7253	186	5	(	(	PUNCT
fumecheng-7253	186	6	34	34	NUM
fumecheng-7253	186	7	)	)	PUNCT
fumecheng-7253	186	8	and	and	CCONJ
fumecheng-7253	186	9	(	(	PUNCT
fumecheng-7253	186	10	35	35	NUM
fumecheng-7253	186	11	)	)	PUNCT
fumecheng-7253	186	12	are	be	AUX
fumecheng-7253	186	13	converted	convert	VERB
fumecheng-7253	186	14	to	to	ADP
fumecheng-7253	186	15	the	the	DET
fumecheng-7253	186	16	following	follow	VERB
fumecheng-7253	186	17	equations	equation	NOUN
fumecheng-7253	186	18	[	[	X
fumecheng-7253	186	19	(	(	PUNCT
fumecheng-7253	186	20	1	1	NUM
fumecheng-7253	186	21	+	+	NUM
fumecheng-7253	186	22	6𝜉𝐿ω2(2𝑟+𝐿	6𝜉𝐿ω2(2𝑟+𝐿	NUM
fumecheng-7253	186	23	)	)	PUNCT
fumecheng-7253	186	24	ℎ2	ℎ2	ADJ
fumecheng-7253	186	25	)	)	PUNCT
fumecheng-7253	186	26	d4	d4	PROPN
fumecheng-7253	186	27	d𝑥4	d𝑥4	NOUN
fumecheng-7253	186	28	−	−	PROPN
fumecheng-7253	186	29	(	(	PUNCT
fumecheng-7253	186	30	12𝜉𝑠2	12𝜉𝑠2	ADJ
fumecheng-7253	186	31	ℎ2	ℎ2	NOUN
fumecheng-7253	186	32	+	+	CCONJ
fumecheng-7253	187	1	6𝐿ω2(2𝑟+𝐿	6𝐿ω2(2𝑟+𝐿	NUM
fumecheng-7253	187	2	)	)	PUNCT
fumecheng-7253	187	3	ℎ2	ℎ2	NOUN
fumecheng-7253	187	4	)	)	PUNCT
fumecheng-7253	187	5	d2	d2	PROPN
fumecheng-7253	187	6	d𝑥2	d𝑥2	PROPN
fumecheng-7253	188	1	+	+	CCONJ
fumecheng-7253	188	2	12𝑠2	12𝑠2	NUM
fumecheng-7253	188	3	ℎ2	ℎ2	NOUN
fumecheng-7253	188	4	]	]	PUNCT
fumecheng-7253	188	5	�	�	SYM
fumecheng-7253	188	6	̅	̅	NOUN
fumecheng-7253	188	7	�	�	NOUN
fumecheng-7253	188	8	=	=	SYM
fumecheng-7253	188	9	−	−	PROPN
fumecheng-7253	188	10	24𝑇0𝛼𝑇	24𝑇0𝛼𝑇	NUM
fumecheng-7253	188	11	𝜋2ℎ	𝜋2ℎ	ADJ
fumecheng-7253	188	12	d2θ̅	d2θ̅	PROPN
fumecheng-7253	188	13	d𝑥2	d𝑥2	PROPN
fumecheng-7253	188	14	−	−	PROPN
fumecheng-7253	188	15	�	�	NOUN
fumecheng-7253	188	16	̅	̅	NOUN
fumecheng-7253	188	17	�	�	NOUN
fumecheng-7253	188	18	(𝑠	(𝑠	NOUN
fumecheng-7253	188	19	)	)	PUNCT
fumecheng-7253	188	20	(	(	PUNCT
fumecheng-7253	188	21	41	41	NUM
fumecheng-7253	188	22	)	)	PUNCT
fumecheng-7253	188	23	(	(	PUNCT
fumecheng-7253	188	24	1	1	NUM
fumecheng-7253	188	25	+	+	NUM
fumecheng-7253	188	26	𝜏𝜃𝑠	𝜏𝜃𝑠	PROPN
fumecheng-7253	188	27	)	)	PUNCT
fumecheng-7253	188	28	(	(	PUNCT
fumecheng-7253	188	29	d2	d2	PROPN
fumecheng-7253	188	30	d𝑥2	d𝑥2	PROPN
fumecheng-7253	188	31	−	−	PROPN
fumecheng-7253	188	32	𝜋2	𝜋2	PROPN
fumecheng-7253	188	33	ℎ2	ℎ2	PROPN
fumecheng-7253	188	34	)	)	PUNCT
fumecheng-7253	188	35	ψ̅	ψ̅	NOUN
fumecheng-7253	188	36	=	=	SYM
fumecheng-7253	188	37	𝑠(1	𝑠(1	PROPN
fumecheng-7253	188	38	+	+	CCONJ
fumecheng-7253	188	39	𝜏𝑞s	𝜏𝑞s	NOUN
fumecheng-7253	188	40	+	+	CCONJ
fumecheng-7253	188	41	𝑠2𝜏𝑞	𝑠2𝜏𝑞	ADJ
fumecheng-7253	188	42	2/2	2/2	NUM
fumecheng-7253	188	43	)	)	PUNCT
fumecheng-7253	188	44	(	(	PUNCT
fumecheng-7253	188	45	ψ̅	ψ̅	PROPN
fumecheng-7253	188	46	−	−	PROPN
fumecheng-7253	188	47	𝛾𝜋2ℎ	𝛾𝜋2ℎ	PROPN
fumecheng-7253	188	48	24𝐾𝜂	24𝐾𝜂	NUM
fumecheng-7253	188	49	d2	d2	PROPN
fumecheng-7253	188	50	�	�	PROPN
fumecheng-7253	188	51	̅	̅	NOUN
fumecheng-7253	188	52	�	�	PROPN
fumecheng-7253	188	53	d𝑥2	d𝑥2	PROPN
fumecheng-7253	188	54	)	)	PUNCT
fumecheng-7253	188	55	(	(	PUNCT
fumecheng-7253	188	56	42	42	X
fumecheng-7253	188	57	)	)	PUNCT
fumecheng-7253	188	58	�	�	PROPN
fumecheng-7253	188	59	̅	̅	NOUN
fumecheng-7253	188	60	�	�	NOUN
fumecheng-7253	189	1	(𝑥	(𝑥	NOUN
fumecheng-7253	189	2	,	,	PUNCT
fumecheng-7253	189	3	𝑠	𝑠	NOUN
fumecheng-7253	189	4	)	)	PUNCT
fumecheng-7253	190	1	=	=	SYM
fumecheng-7253	190	2	12𝜉𝑠2	12𝜉𝑠2	ADJ
fumecheng-7253	190	3	ℎ2	ℎ2	ADJ
fumecheng-7253	190	4	�	�	NOUN
fumecheng-7253	190	5	̅	̅	NOUN
fumecheng-7253	190	6	�	�	NOUN
fumecheng-7253	190	7	−	−	PROPN
fumecheng-7253	190	8	(	(	PUNCT
fumecheng-7253	190	9	1	1	NUM
fumecheng-7253	190	10	+	+	NUM
fumecheng-7253	190	11	6𝜉𝐿ω2(2𝑟+𝐿	6𝜉𝐿ω2(2𝑟+𝐿	NUM
fumecheng-7253	190	12	)	)	PUNCT
fumecheng-7253	190	13	ℎ2	ℎ2	ADJ
fumecheng-7253	190	14	)	)	PUNCT
fumecheng-7253	190	15	d2	d2	PROPN
fumecheng-7253	190	16	�	�	PROPN
fumecheng-7253	190	17	̅	̅	NOUN
fumecheng-7253	190	18	�	�	PROPN
fumecheng-7253	190	19	d𝑥2	d𝑥2	PROPN
fumecheng-7253	190	20	−	−	PROPN
fumecheng-7253	190	21	24𝑇0𝛼𝑇	24𝑇0𝛼𝑇	NUM
fumecheng-7253	190	22	𝜋2ℎ	𝜋2ℎ	ADJ
fumecheng-7253	190	23	θ̅	θ̅	NOUN
fumecheng-7253	190	24	−	−	NOUN
fumecheng-7253	190	25	𝜉	𝜉	X
fumecheng-7253	190	26	�	�	NOUN
fumecheng-7253	190	27	̅	̅	NOUN
fumecheng-7253	190	28	�	�	NOUN
fumecheng-7253	190	29	(𝑠	(𝑠	NOUN
fumecheng-7253	190	30	)	)	PUNCT
fumecheng-7253	190	31	(	(	PUNCT
fumecheng-7253	190	32	43	43	NUM
fumecheng-7253	190	33	)	)	PUNCT
fumecheng-7253	190	34	where	where	SCONJ
fumecheng-7253	190	35	�	�	NOUN
fumecheng-7253	190	36	̅	̅	NOUN
fumecheng-7253	190	37	�	�	NOUN
fumecheng-7253	190	38	(𝑠	(𝑠	NOUN
fumecheng-7253	190	39	)	)	PUNCT
fumecheng-7253	190	40	=	=	SYM
fumecheng-7253	190	41	𝑞0	𝑞0	NOUN
fumecheng-7253	190	42	(	(	PUNCT
fumecheng-7253	190	43	1	1	NUM
fumecheng-7253	190	44	𝑠	𝑠	NUM
fumecheng-7253	190	45	−	−	NOUN
fumecheng-7253	190	46	𝛿	𝛿	PROPN
fumecheng-7253	190	47	𝛽+𝑠	𝛽+𝑠	PROPN
fumecheng-7253	190	48	)	)	PUNCT
fumecheng-7253	190	49	.	.	PUNCT
fumecheng-7253	191	1	the	the	DET
fumecheng-7253	191	2	following	follow	VERB
fumecheng-7253	191	3	differential	differential	ADJ
fumecheng-7253	191	4	equation	equation	NOUN
fumecheng-7253	191	5	can	can	AUX
fumecheng-7253	191	6	be	be	AUX
fumecheng-7253	191	7	obtained	obtain	VERB
fumecheng-7253	191	8	once	once	ADV
fumecheng-7253	191	9	function	function	NOUN
fumecheng-7253	191	10	θ	θ	PROPN
fumecheng-7253	191	11	̅is	̅is	PUNCT
fumecheng-7253	191	12	extracted	extract	VERB
fumecheng-7253	191	13	from	from	ADP
fumecheng-7253	191	14	eqs	eqs	PROPN
fumecheng-7253	191	15	.	.	PUNCT
fumecheng-7253	192	1	(	(	PUNCT
fumecheng-7253	192	2	41	41	NUM
fumecheng-7253	192	3	)	)	PUNCT
fumecheng-7253	192	4	and	and	CCONJ
fumecheng-7253	192	5	(	(	PUNCT
fumecheng-7253	192	6	42	42	NUM
fumecheng-7253	192	7	)	)	PUNCT
fumecheng-7253	192	8	[	[	PUNCT
fumecheng-7253	192	9	d6	d6	NOUN
fumecheng-7253	192	10	d𝑥6	d𝑥6	NOUN
fumecheng-7253	192	11	−	−	PROPN
fumecheng-7253	192	12	𝐴	𝐴	PROPN
fumecheng-7253	192	13	d4	d4	VERB
fumecheng-7253	192	14	d𝑥4	d𝑥4	NOUN
fumecheng-7253	192	15	+	+	CCONJ
fumecheng-7253	192	16	𝐵	𝐵	PROPN
fumecheng-7253	192	17	d2	d2	PROPN
fumecheng-7253	192	18	d𝑥2	d𝑥2	PROPN
fumecheng-7253	193	1	−	−	PROPN
fumecheng-7253	193	2	𝐶	𝐶	PROPN
fumecheng-7253	193	3	]	]	PUNCT
fumecheng-7253	193	4	�	�	PROPN
fumecheng-7253	193	5	̅	̅	NOUN
fumecheng-7253	193	6	�	�	NOUN
fumecheng-7253	193	7	=	=	SYM
fumecheng-7253	193	8	𝐴5	𝐴5	PROPN
fumecheng-7253	193	9	�	�	PROPN
fumecheng-7253	193	10	̅	̅	NOUN
fumecheng-7253	193	11	�	�	NOUN
fumecheng-7253	193	12	(𝑠)/𝐴1	(𝑠)/𝐴1	NUM
fumecheng-7253	193	13	(	(	PUNCT
fumecheng-7253	193	14	44	44	NUM
fumecheng-7253	193	15	)	)	PUNCT
fumecheng-7253	193	16	where	where	SCONJ
fumecheng-7253	193	17	𝐴	𝐴	NOUN
fumecheng-7253	193	18	=	=	PUNCT
fumecheng-7253	193	19	1	1	NUM
fumecheng-7253	193	20	𝐴1	𝐴1	NOUN
fumecheng-7253	193	21	(	(	PUNCT
fumecheng-7253	193	22	𝐴5𝐴1	𝐴5𝐴1	NOUN
fumecheng-7253	193	23	+	+	CCONJ
fumecheng-7253	193	24	𝐴2	𝐴2	PROPN
fumecheng-7253	193	25	+	+	CCONJ
fumecheng-7253	193	26	𝐴4𝐴6	𝐴4𝐴6	PROPN
fumecheng-7253	193	27	)	)	PUNCT
fumecheng-7253	193	28	,	,	PUNCT
fumecheng-7253	193	29	𝐵	𝐵	NOUN
fumecheng-7253	193	30	=	=	SYM
fumecheng-7253	193	31	1	1	NUM
fumecheng-7253	193	32	𝐴1	𝐴1	NOUN
fumecheng-7253	193	33	(	(	PUNCT
fumecheng-7253	193	34	𝐴5𝐴2	𝐴5𝐴2	PROPN
fumecheng-7253	193	35	+	+	CCONJ
fumecheng-7253	193	36	𝐴3	𝐴3	PROPN
fumecheng-7253	193	37	)	)	PUNCT
fumecheng-7253	193	38	,	,	PUNCT
fumecheng-7253	193	39	𝐶	𝐶	PROPN
fumecheng-7253	193	40	=	=	PUNCT
fumecheng-7253	194	1	𝐴5𝐴3	𝐴5𝐴3	INTJ
fumecheng-7253	194	2	𝐴1	𝐴1	PROPN
fumecheng-7253	194	3	,	,	PUNCT
fumecheng-7253	194	4	𝐴1	𝐴1	PROPN
fumecheng-7253	194	5	=	=	PUNCT
fumecheng-7253	194	6	(	(	PUNCT
fumecheng-7253	194	7	1	1	NUM
fumecheng-7253	194	8	+	+	NUM
fumecheng-7253	194	9	6𝜉𝐿ω2(2𝑟+𝐿	6𝜉𝐿ω2(2𝑟+𝐿	NUM
fumecheng-7253	194	10	)	)	PUNCT
fumecheng-7253	194	11	ℎ2	ℎ2	NOUN
fumecheng-7253	194	12	)	)	PUNCT
fumecheng-7253	194	13	,	,	PUNCT
fumecheng-7253	194	14	𝐴2	𝐴2	PROPN
fumecheng-7253	194	15	=	=	PUNCT
fumecheng-7253	194	16	(	(	PUNCT
fumecheng-7253	194	17	12𝜉𝑠2	12𝜉𝑠2	ADJ
fumecheng-7253	194	18	ℎ2	ℎ2	NOUN
fumecheng-7253	194	19	+	+	CCONJ
fumecheng-7253	194	20	6𝐿ω2(2𝑟+𝐿	6𝐿ω2(2𝑟+𝐿	NUM
fumecheng-7253	194	21	)	)	PUNCT
fumecheng-7253	194	22	ℎ2	ℎ2	NOUN
fumecheng-7253	194	23	)	)	PUNCT
fumecheng-7253	194	24	,	,	PUNCT
fumecheng-7253	194	25	𝐴4	𝐴4	NOUN
fumecheng-7253	194	26	=	=	SYM
fumecheng-7253	194	27	24𝑇0𝛼𝑇	24𝑇0𝛼𝑇	NUM
fumecheng-7253	194	28	𝜋2ℎ	𝜋2ℎ	NOUN
fumecheng-7253	194	29	,	,	PUNCT
fumecheng-7253	194	30	𝐴3	𝐴3	PROPN
fumecheng-7253	194	31	=	=	PUNCT
fumecheng-7253	195	1	12𝑠2	12𝑠2	NUM
fumecheng-7253	195	2	ℎ2	ℎ2	NOUN
fumecheng-7253	195	3	,	,	PUNCT
fumecheng-7253	195	4	𝐴5	𝐴5	NOUN
fumecheng-7253	195	5	=	=	PUNCT
fumecheng-7253	195	6	𝜋2	𝜋2	PROPN
fumecheng-7253	195	7	ℎ2	ℎ2	NOUN
fumecheng-7253	195	8	+	+	CCONJ
fumecheng-7253	195	9	𝑠(1+𝜏𝑞s+𝑠2𝜏𝑞	𝑠(1+𝜏𝑞s+𝑠2𝜏𝑞	ADJ
fumecheng-7253	195	10	2/2	2/2	NUM
fumecheng-7253	195	11	)	)	PUNCT
fumecheng-7253	195	12	1+𝜏𝜃𝑠	1+𝜏𝜃𝑠	NUM
fumecheng-7253	195	13	,	,	PUNCT
fumecheng-7253	195	14	𝐴6	𝐴6	PROPN
fumecheng-7253	195	15	=	=	SYM
fumecheng-7253	195	16	𝑠(1+𝜏𝑞s+𝑠2𝜏𝑞	𝑠(1+𝜏𝑞s+𝑠2𝜏𝑞	PROPN
fumecheng-7253	195	17	2/2	2/2	NUM
fumecheng-7253	195	18	)	)	PUNCT
fumecheng-7253	195	19	1+𝜏𝜃𝑠	1+𝜏𝜃𝑠	NOUN
fumecheng-7253	195	20	(	(	PUNCT
fumecheng-7253	195	21	𝛾𝜋2ℎ	𝛾𝜋2ℎ	PROPN
fumecheng-7253	195	22	24𝐾𝜂	24𝐾𝜂	NUM
fumecheng-7253	195	23	)	)	PUNCT
fumecheng-7253	195	24	.	.	PUNCT
fumecheng-7253	196	1	(	(	PUNCT
fumecheng-7253	196	2	45	45	NUM
fumecheng-7253	196	3	)	)	PUNCT
fumecheng-7253	196	4	then	then	ADV
fumecheng-7253	196	5	the	the	DET
fumecheng-7253	196	6	general	general	ADJ
fumecheng-7253	196	7	solution	solution	NOUN
fumecheng-7253	196	8	for	for	ADP
fumecheng-7253	196	9	𝑤	𝑤	ADP
fumecheng-7253	196	10	̅̅	̅̅	PROPN
fumecheng-7253	196	11	̅can	̅can	ADJ
fumecheng-7253	196	12	be	be	AUX
fumecheng-7253	196	13	achieved	achieve	VERB
fumecheng-7253	196	14	by	by	ADP
fumecheng-7253	196	15	solving	solve	VERB
fumecheng-7253	196	16	the	the	DET
fumecheng-7253	196	17	differential	differential	NOUN
fumecheng-7253	196	18	eq	eq	ADP
fumecheng-7253	196	19	.	.	PUNCT
fumecheng-7253	197	1	(	(	PUNCT
fumecheng-7253	197	2	44	44	NUM
fumecheng-7253	197	3	)	)	PUNCT
fumecheng-7253	197	4	as	as	SCONJ
fumecheng-7253	197	5	follows	follow	VERB
fumecheng-7253	197	6	�	�	PROPN
fumecheng-7253	197	7	̅	̅	NOUN
fumecheng-7253	197	8	�	�	NOUN
fumecheng-7253	198	1	(𝑥	(𝑥	NOUN
fumecheng-7253	198	2	,	,	PUNCT
fumecheng-7253	198	3	𝑠	𝑠	NOUN
fumecheng-7253	198	4	)	)	PUNCT
fumecheng-7253	199	1	=	=	PUNCT
fumecheng-7253	199	2	∑	∑	PUNCT
fumecheng-7253	199	3	(	(	PUNCT
fumecheng-7253	199	4	𝐶𝑗e	𝐶𝑗e	PROPN
fumecheng-7253	199	5	−𝑚𝑗𝑥	−𝑚𝑗𝑥	PROPN
fumecheng-7253	199	6	+	+	CCONJ
fumecheng-7253	199	7	𝐶𝑗+3e	𝐶𝑗+3e	PROPN
fumecheng-7253	199	8	𝑚𝑗𝑥	𝑚𝑗𝑥	PROPN
fumecheng-7253	199	9	)	)	PUNCT
fumecheng-7253	199	10	−	−	ADP
fumecheng-7253	199	11	𝐴5	𝐴5	PROPN
fumecheng-7253	199	12	�	�	PROPN
fumecheng-7253	199	13	̅	̅	NOUN
fumecheng-7253	199	14	�	�	NOUN
fumecheng-7253	199	15	(𝑠	(𝑠	NOUN
fumecheng-7253	199	16	)	)	PUNCT
fumecheng-7253	199	17	𝐶𝐴1	𝐶𝐴1	PROPN
fumecheng-7253	199	18	3	3	NUM
fumecheng-7253	199	19	𝑗=1	𝑗=1	PROPN
fumecheng-7253	199	20	(	(	PUNCT
fumecheng-7253	199	21	46	46	NUM
fumecheng-7253	199	22	)	)	PUNCT
fumecheng-7253	199	23	from	from	ADP
fumecheng-7253	199	24	the	the	DET
fumecheng-7253	199	25	given	give	VERB
fumecheng-7253	199	26	boundary	boundary	ADJ
fumecheng-7253	199	27	conditions	condition	NOUN
fumecheng-7253	199	28	,	,	PUNCT
fumecheng-7253	199	29	undetermined	undetermined	ADJ
fumecheng-7253	199	30	parameters	parameter	NOUN
fumecheng-7253	199	31	𝐶𝑗	𝐶𝑗	NOUN
fumecheng-7253	199	32	,	,	PUNCT
fumecheng-7253	199	33	(	(	PUNCT
fumecheng-7253	199	34	𝑗	𝑗	NOUN
fumecheng-7253	199	35	=	=	SYM
fumecheng-7253	199	36	1,2	1,2	NUM
fumecheng-7253	199	37	.	.	PUNCT
fumecheng-7253	199	38	.	.	PUNCT
fumecheng-7253	200	1	,	,	PUNCT
fumecheng-7253	200	2	6	6	NUM
fumecheng-7253	200	3	)	)	PUNCT
fumecheng-7253	200	4	,	,	PUNCT
fumecheng-7253	200	5	can	can	AUX
fumecheng-7253	200	6	be	be	AUX
fumecheng-7253	200	7	calculated	calculate	VERB
fumecheng-7253	200	8	.	.	PUNCT
fumecheng-7253	201	1	parameters	parameter	NOUN
fumecheng-7253	201	2	𝑚1	𝑚1	VERB
fumecheng-7253	201	3	2	2	NUM
fumecheng-7253	201	4	,	,	PUNCT
fumecheng-7253	201	5	𝑚2	𝑚2	NOUN
fumecheng-7253	201	6	2	2	NUM
fumecheng-7253	201	7	and	and	CCONJ
fumecheng-7253	201	8	𝑚3	𝑚3	NOUN
fumecheng-7253	201	9	2	2	NUM
fumecheng-7253	201	10	also	also	ADV
fumecheng-7253	201	11	satisfy	satisfy	VERB
fumecheng-7253	201	12	the	the	DET
fumecheng-7253	201	13	following	follow	VERB
fumecheng-7253	201	14	equation	equation	NOUN
fumecheng-7253	201	15	𝑚6	𝑚6	NUM
fumecheng-7253	201	16	−	−	PROPN
fumecheng-7253	201	17	𝐴𝑚4	𝐴𝑚4	NOUN
fumecheng-7253	201	18	+	+	NUM
fumecheng-7253	201	19	𝐵𝑚2	𝐵𝑚2	NOUN
fumecheng-7253	201	20	−	−	PROPN
fumecheng-7253	201	21	𝐶	𝐶	PROPN
fumecheng-7253	201	22	=	=	SYM
fumecheng-7253	201	23	0	0	PROPN
fumecheng-7253	202	1	(	(	PUNCT
fumecheng-7253	202	2	47	47	NUM
fumecheng-7253	202	3	)	)	PUNCT
fumecheng-7253	202	4	eq	eq	NOUN
fumecheng-7253	202	5	.	.	PUNCT
fumecheng-7253	203	1	(	(	PUNCT
fumecheng-7253	203	2	46	46	NUM
fumecheng-7253	203	3	)	)	PUNCT
fumecheng-7253	203	4	is	be	AUX
fumecheng-7253	203	5	incorporated	incorporate	VERB
fumecheng-7253	203	6	into	into	ADP
fumecheng-7253	203	7	eq	eq	NOUN
fumecheng-7253	203	8	.	.	PUNCT
fumecheng-7253	204	1	(	(	PUNCT
fumecheng-7253	204	2	41	41	NUM
fumecheng-7253	204	3	)	)	PUNCT
fumecheng-7253	204	4	and	and	CCONJ
fumecheng-7253	204	5	yields	yield	NOUN
fumecheng-7253	204	6	ψ̅(𝑥	ψ̅(𝑥	VERB
fumecheng-7253	204	7	,	,	PUNCT
fumecheng-7253	204	8	𝑠	𝑠	X
fumecheng-7253	204	9	)	)	PUNCT
fumecheng-7253	204	10	=	=	SYM
fumecheng-7253	205	1	−	−	PROPN
fumecheng-7253	205	2	1	1	NUM
fumecheng-7253	205	3	𝐴4𝐴5	𝐴4𝐴5	PROPN
fumecheng-7253	205	4	[	[	X
fumecheng-7253	205	5	𝐴1	𝐴1	PROPN
fumecheng-7253	205	6	d4	d4	PROPN
fumecheng-7253	205	7	�	�	PROPN
fumecheng-7253	205	8	̅	̅	NOUN
fumecheng-7253	205	9	�	�	PROPN
fumecheng-7253	205	10	d𝑥4	d𝑥4	NOUN
fumecheng-7253	205	11	−	−	PROPN
fumecheng-7253	205	12	(	(	PUNCT
fumecheng-7253	205	13	𝐴2	𝐴2	PROPN
fumecheng-7253	205	14	+	+	CCONJ
fumecheng-7253	205	15	𝐴4𝐴6	𝐴4𝐴6	PROPN
fumecheng-7253	205	16	)	)	PUNCT
fumecheng-7253	205	17	d2	d2	PROPN
fumecheng-7253	205	18	�	�	PROPN
fumecheng-7253	205	19	̅	̅	NOUN
fumecheng-7253	205	20	�	�	PROPN
fumecheng-7253	205	21	d𝑥2	d𝑥2	PROPN
fumecheng-7253	205	22	+	+	CCONJ
fumecheng-7253	205	23	𝐴3	𝐴3	PROPN
fumecheng-7253	205	24	�	�	PROPN
fumecheng-7253	205	25	̅	̅	NOUN
fumecheng-7253	205	26	�	�	PROPN
fumecheng-7253	205	27	+	+	CCONJ
fumecheng-7253	205	28	�	�	NOUN
fumecheng-7253	205	29	̅	̅	NOUN
fumecheng-7253	205	30	�	�	NOUN
fumecheng-7253	205	31	(𝑠	(𝑠	NOUN
fumecheng-7253	205	32	)	)	PUNCT
fumecheng-7253	205	33	]	]	PUNCT
fumecheng-7253	205	34	(	(	PUNCT
fumecheng-7253	205	35	48	48	NUM
fumecheng-7253	205	36	)	)	PUNCT
fumecheng-7253	205	37	with	with	ADP
fumecheng-7253	205	38	the	the	DET
fumecheng-7253	205	39	help	help	NOUN
fumecheng-7253	205	40	of	of	ADP
fumecheng-7253	205	41	eq	eq	PROPN
fumecheng-7253	205	42	.	.	PUNCT
fumecheng-7253	206	1	(	(	PUNCT
fumecheng-7253	206	2	46	46	NUM
fumecheng-7253	206	3	)	)	PUNCT
fumecheng-7253	206	4	,	,	PUNCT
fumecheng-7253	206	5	the	the	DET
fumecheng-7253	206	6	solution	solution	NOUN
fumecheng-7253	206	7	of	of	ADP
fumecheng-7253	206	8	eq	eq	PROPN
fumecheng-7253	206	9	.	.	PUNCT
fumecheng-7253	207	1	(	(	PUNCT
fumecheng-7253	207	2	48	48	NUM
fumecheng-7253	207	3	)	)	PUNCT
fumecheng-7253	207	4	can	can	AUX
fumecheng-7253	207	5	be	be	AUX
fumecheng-7253	207	6	simplified	simplify	VERB
fumecheng-7253	207	7	as	as	ADP
fumecheng-7253	207	8	ψ̅(𝑥	ψ̅(𝑥	PROPN
fumecheng-7253	207	9	,	,	PUNCT
fumecheng-7253	207	10	𝑠	𝑠	PROPN
fumecheng-7253	207	11	)	)	PUNCT
fumecheng-7253	207	12	=	=	SYM
fumecheng-7253	207	13	∑	∑	PUNCT
fumecheng-7253	207	14	𝐻𝑗(𝐶𝑗e	𝐻𝑗(𝐶𝑗e	PROPN
fumecheng-7253	207	15	−𝑚𝑗𝑥	−𝑚𝑗𝑥	PROPN
fumecheng-7253	207	16	+	+	CCONJ
fumecheng-7253	208	1	𝐶𝑗+3e	𝐶𝑗+3e	PROPN
fumecheng-7253	208	2	𝑚𝑗𝑥)3	𝑚𝑗𝑥)3	PROPN
fumecheng-7253	208	3	𝑗	𝑗	PROPN
fumecheng-7253	208	4	=	=	ADJ
fumecheng-7253	208	5	1	1	NUM
fumecheng-7253	208	6	−	−	PROPN
fumecheng-7253	208	7	𝐻4	𝐻4	NOUN
fumecheng-7253	208	8	,	,	PUNCT
fumecheng-7253	208	9	(	(	PUNCT
fumecheng-7253	208	10	49	49	NUM
fumecheng-7253	208	11	)	)	PUNCT
fumecheng-7253	209	1	where	where	SCONJ
fumecheng-7253	209	2	𝐻𝑗	𝐻𝑗	PROPN
fumecheng-7253	209	3	=	=	SYM
fumecheng-7253	209	4	−	−	PROPN
fumecheng-7253	209	5	1	1	NUM
fumecheng-7253	209	6	𝐴4𝐴5	𝐴4𝐴5	PROPN
fumecheng-7253	210	1	[	[	X
fumecheng-7253	210	2	𝐴1𝑚𝑗	𝐴1𝑚𝑗	VERB
fumecheng-7253	210	3	4	4	NUM
fumecheng-7253	210	4	−	−	NOUN
fumecheng-7253	210	5	(	(	PUNCT
fumecheng-7253	210	6	𝐴2	𝐴2	PROPN
fumecheng-7253	210	7	+	+	SYM
fumecheng-7253	210	8	𝐴4𝐴6)𝑚𝑗	𝐴4𝐴6)𝑚𝑗	PROPN
fumecheng-7253	210	9	2	2	NUM
fumecheng-7253	210	10	+	+	SYM
fumecheng-7253	210	11	𝐴3	𝐴3	PROPN
fumecheng-7253	210	12	]	]	X
fumecheng-7253	210	13	,	,	PUNCT
fumecheng-7253	210	14	𝐻4	𝐻4	PROPN
fumecheng-7253	210	15	=	=	SYM
fumecheng-7253	210	16	�	�	PROPN
fumecheng-7253	210	17	̅	̅	NOUN
fumecheng-7253	210	18	�	�	NOUN
fumecheng-7253	210	19	(𝑠)(𝐴4−𝐶	(𝑠)(𝐴4−𝐶	NOUN
fumecheng-7253	210	20	)	)	PUNCT
fumecheng-7253	210	21	𝐶𝐴4𝐴5	𝐶𝐴4𝐴5	NOUN
fumecheng-7253	210	22	(	(	PUNCT
fumecheng-7253	210	23	50	50	NUM
fumecheng-7253	210	24	)	)	PUNCT
fumecheng-7253	210	25	bending	bend	VERB
fumecheng-7253	210	26	moment	moment	NOUN
fumecheng-7253	210	27	�	�	NOUN
fumecheng-7253	210	28	̅	̅	NOUN
fumecheng-7253	210	29	�	�	NOUN
fumecheng-7253	210	30	is	be	AUX
fumecheng-7253	210	31	determined	determine	VERB
fumecheng-7253	210	32	from	from	ADP
fumecheng-7253	210	33	(	(	PUNCT
fumecheng-7253	210	34	43	43	NUM
fumecheng-7253	210	35	)	)	PUNCT
fumecheng-7253	210	36	using	use	VERB
fumecheng-7253	210	37	the	the	DET
fumecheng-7253	210	38	solutions	solution	NOUN
fumecheng-7253	210	39	(	(	PUNCT
fumecheng-7253	210	40	46	46	NUM
fumecheng-7253	210	41	)	)	PUNCT
fumecheng-7253	210	42	and	and	CCONJ
fumecheng-7253	210	43	(	(	PUNCT
fumecheng-7253	210	44	49	49	NUM
fumecheng-7253	210	45	)	)	PUNCT
fumecheng-7253	210	46	�	�	NOUN
fumecheng-7253	210	47	̅	̅	NOUN
fumecheng-7253	210	48	�	�	NOUN
fumecheng-7253	210	49	(𝑥	(𝑥	NOUN
fumecheng-7253	210	50	,	,	PUNCT
fumecheng-7253	210	51	𝑠	𝑠	NOUN
fumecheng-7253	210	52	)	)	PUNCT
fumecheng-7253	210	53	=	=	SYM
fumecheng-7253	211	1	∑	∑	PUNCT
fumecheng-7253	211	2	𝐿𝑗(𝐶𝑗e	𝐿𝑗(𝐶𝑗e	NOUN
fumecheng-7253	211	3	−𝑚𝑗𝑥	−𝑚𝑗𝑥	NOUN
fumecheng-7253	211	4	+	+	CCONJ
fumecheng-7253	211	5	𝐶𝑗+3e	𝐶𝑗+3e	PROPN
fumecheng-7253	211	6	𝑚𝑗𝑥)3	𝑚𝑗𝑥)3	PROPN
fumecheng-7253	211	7	𝑗=1	𝑗=1	PROPN
fumecheng-7253	211	8	+	+	NUM
fumecheng-7253	211	9	𝐿4	𝐿4	PROPN
fumecheng-7253	211	10	(	(	PUNCT
fumecheng-7253	211	11	51	51	NUM
fumecheng-7253	211	12	)	)	PUNCT
fumecheng-7253	211	13	temperature	temperature	NOUN
fumecheng-7253	211	14	-	-	PUNCT
fumecheng-7253	211	15	dependent	dependent	ADJ
fumecheng-7253	211	16	physical	physical	ADJ
fumecheng-7253	211	17	characteristics	characteristic	NOUN
fumecheng-7253	211	18	of	of	ADP
fumecheng-7253	211	19	rotating	rotate	VERB
fumecheng-7253	211	20	nonlocal	nonlocal	ADJ
fumecheng-7253	211	21	nanobeams	nanobeam	NOUN
fumecheng-7253	211	22	subject	subject	ADJ
fumecheng-7253	211	23	to	to	ADP
fumecheng-7253	211	24	...	...	PUNCT
fumecheng-7253	211	25	643	643	NUM
fumecheng-7253	211	26	where	where	SCONJ
fumecheng-7253	211	27	𝐿𝑗	𝐿𝑗	PROPN
fumecheng-7253	211	28	=	=	SYM
fumecheng-7253	211	29	−(𝐴1𝑚𝑗	−(𝐴1𝑚𝑗	PROPN
fumecheng-7253	211	30	2	2	NUM
fumecheng-7253	211	31	+	+	CCONJ
fumecheng-7253	211	32	𝐴4𝐻𝑗	𝐴4𝐻𝑗	ADJ
fumecheng-7253	211	33	−	−	PROPN
fumecheng-7253	211	34	𝐴0	𝐴0	PROPN
fumecheng-7253	211	35	)	)	PUNCT
fumecheng-7253	211	36	,	,	PUNCT
fumecheng-7253	211	37	𝐿4	𝐿4	PROPN
fumecheng-7253	211	38	=	=	SYM
fumecheng-7253	211	39	�	�	PROPN
fumecheng-7253	211	40	̅	̅	NOUN
fumecheng-7253	211	41	�	�	NOUN
fumecheng-7253	211	42	(𝑠	(𝑠	NOUN
fumecheng-7253	211	43	)	)	PUNCT
fumecheng-7253	211	44	(	(	PUNCT
fumecheng-7253	211	45	𝐴4𝐻4	𝐴4𝐻4	PROPN
fumecheng-7253	211	46	−	−	PROPN
fumecheng-7253	211	47	𝐴0𝐴5	𝐴0𝐴5	PROPN
fumecheng-7253	211	48	𝐶𝐴1	𝐶𝐴1	VERB
fumecheng-7253	211	49	−	−	PROPN
fumecheng-7253	211	50	𝜉	𝜉	NOUN
fumecheng-7253	211	51	)	)	PUNCT
fumecheng-7253	211	52	,	,	PUNCT
fumecheng-7253	211	53	𝐴0	𝐴0	PROPN
fumecheng-7253	211	54	=	=	SYM
fumecheng-7253	211	55	12𝜉𝑠2	12𝜉𝑠2	ADJ
fumecheng-7253	211	56	ℎ2	ℎ2	NOUN
fumecheng-7253	211	57	(	(	PUNCT
fumecheng-7253	211	58	52	52	NUM
fumecheng-7253	211	59	)	)	PUNCT
fumecheng-7253	211	60	axial	axial	ADJ
fumecheng-7253	211	61	displacement	displacement	NOUN
fumecheng-7253	211	62	�	�	NOUN
fumecheng-7253	211	63	̅	̅	NOUN
fumecheng-7253	211	64	�	�	NOUN
fumecheng-7253	211	65	can	can	AUX
fumecheng-7253	211	66	be	be	AUX
fumecheng-7253	211	67	calculated	calculate	VERB
fumecheng-7253	211	68	by	by	ADP
fumecheng-7253	211	69	using	use	VERB
fumecheng-7253	211	70	eq	eq	ADP
fumecheng-7253	211	71	.	.	PUNCT
fumecheng-7253	212	1	(	(	PUNCT
fumecheng-7253	212	2	46	46	NUM
fumecheng-7253	212	3	)	)	PUNCT
fumecheng-7253	212	4	�	�	NOUN
fumecheng-7253	212	5	̅	̅	NOUN
fumecheng-7253	212	6	�	�	NOUN
fumecheng-7253	212	7	=	=	PUNCT
fumecheng-7253	212	8	−𝑧	−𝑧	PROPN
fumecheng-7253	212	9	d	d	PROPN
fumecheng-7253	212	10	�	�	PROPN
fumecheng-7253	212	11	̅	̅	NOUN
fumecheng-7253	212	12	�	�	NOUN
fumecheng-7253	212	13	d𝑥	d𝑥	NOUN
fumecheng-7253	212	14	=	=	SYM
fumecheng-7253	212	15	𝑧∑	𝑧∑	PROPN
fumecheng-7253	212	16	𝑚𝑗(𝐶𝑗e	𝑚𝑗(𝐶𝑗e	NOUN
fumecheng-7253	212	17	−𝑚𝑗𝑥	−𝑚𝑗𝑥	PRON
fumecheng-7253	212	18	−	−	PROPN
fumecheng-7253	212	19	𝐶𝑗+3e	𝐶𝑗+3e	PROPN
fumecheng-7253	212	20	𝑚𝑗𝑥)3	𝑚𝑗𝑥)3	PROPN
fumecheng-7253	212	21	𝑗=1	𝑗=1	PROPN
fumecheng-7253	212	22	.	.	PUNCT
fumecheng-7253	213	1	(	(	PUNCT
fumecheng-7253	213	2	53	53	NUM
fumecheng-7253	213	3	)	)	PUNCT
fumecheng-7253	213	4	boundary	boundary	ADJ
fumecheng-7253	213	5	conditions	condition	NOUN
fumecheng-7253	213	6	(	(	PUNCT
fumecheng-7253	213	7	37)-(40	37)-(40	NUM
fumecheng-7253	213	8	)	)	PUNCT
fumecheng-7253	213	9	are	be	AUX
fumecheng-7253	213	10	reduced	reduce	VERB
fumecheng-7253	213	11	in	in	ADP
fumecheng-7253	213	12	the	the	DET
fumecheng-7253	213	13	laplace	laplace	NOUN
fumecheng-7253	213	14	transform	transform	NOUN
fumecheng-7253	213	15	field	field	NOUN
fumecheng-7253	213	16	to	to	ADP
fumecheng-7253	213	17	�	�	NOUN
fumecheng-7253	213	18	̅	̅	NOUN
fumecheng-7253	213	19	�	�	NOUN
fumecheng-7253	213	20	(𝑥	(𝑥	NOUN
fumecheng-7253	213	21	,	,	PUNCT
fumecheng-7253	213	22	𝑠)|𝑥=0,𝐿	𝑠)|𝑥=0,𝐿	PROPN
fumecheng-7253	213	23	=	=	SYM
fumecheng-7253	213	24	0	0	NUM
fumecheng-7253	213	25	,	,	PUNCT
fumecheng-7253	213	26	d2	d2	PROPN
fumecheng-7253	213	27	�	�	PROPN
fumecheng-7253	213	28	̅	̅	NOUN
fumecheng-7253	213	29	�	�	NOUN
fumecheng-7253	213	30	(𝑥,𝑠	(𝑥,𝑠	NOUN
fumecheng-7253	213	31	)	)	PUNCT
fumecheng-7253	213	32	d𝑥2	d𝑥2	PROPN
fumecheng-7253	214	1	|	|	ADV
fumecheng-7253	214	2	𝑥=0,𝐿	𝑥=0,𝐿	VERB
fumecheng-7253	214	3	=	=	SYM
fumecheng-7253	214	4	0	0	NUM
fumecheng-7253	214	5	,	,	PUNCT
fumecheng-7253	214	6	(	(	PUNCT
fumecheng-7253	214	7	54	54	NUM
fumecheng-7253	214	8	)	)	PUNCT
fumecheng-7253	214	9	ψ̅(𝑥	ψ̅(𝑥	ADP
fumecheng-7253	214	10	,	,	PUNCT
fumecheng-7253	214	11	𝑠)|𝑥=0	𝑠)|𝑥=0	PROPN
fumecheng-7253	214	12	=	=	SYM
fumecheng-7253	214	13	θ0	θ0	PROPN
fumecheng-7253	214	14	[	[	PUNCT
fumecheng-7253	214	15	𝑠	𝑠	PROPN
fumecheng-7253	214	16	𝑠2+𝜔2	𝑠2+𝜔2	PROPN
fumecheng-7253	214	17	+	+	PROPN
fumecheng-7253	214	18	𝐾1(𝑠2	𝐾1(𝑠2	PROPN
fumecheng-7253	214	19	+	+	NOUN
fumecheng-7253	214	20	2𝜔2	2𝜔2	NUM
fumecheng-7253	214	21	)	)	PUNCT
fumecheng-7253	214	22	2𝑠(𝑠2	2𝑠(𝑠2	NUM
fumecheng-7253	214	23	+	+	NOUN
fumecheng-7253	214	24	4𝜔2	4𝜔2	NUM
fumecheng-7253	214	25	)	)	PUNCT
fumecheng-7253	214	26	]	]	PUNCT
fumecheng-7253	215	1	=	=	PUNCT
fumecheng-7253	215	2	�	�	SYM
fumecheng-7253	215	3	̅	̅	NOUN
fumecheng-7253	215	4	�	�	NOUN
fumecheng-7253	215	5	(𝑠	(𝑠	NOUN
fumecheng-7253	215	6	)	)	PUNCT
fumecheng-7253	215	7	,	,	PUNCT
fumecheng-7253	215	8	(	(	PUNCT
fumecheng-7253	215	9	55	55	X
fumecheng-7253	215	10	)	)	PUNCT
fumecheng-7253	215	11	dθ̅	dθ̅	VERB
fumecheng-7253	215	12	d𝑥	d𝑥	NOUN
fumecheng-7253	215	13	|	|	ADV
fumecheng-7253	215	14	𝑥=𝐿	𝑥=𝐿	ADV
fumecheng-7253	215	15	=	=	NOUN
fumecheng-7253	215	16	0	0	NUM
fumecheng-7253	215	17	.	.	PUNCT
fumecheng-7253	216	1	(	(	PUNCT
fumecheng-7253	216	2	56	56	NUM
fumecheng-7253	216	3	)	)	PUNCT
fumecheng-7253	216	4	by	by	ADP
fumecheng-7253	216	5	applying	apply	VERB
fumecheng-7253	216	6	these	these	DET
fumecheng-7253	216	7	conditions	condition	NOUN
fumecheng-7253	216	8	in	in	ADP
fumecheng-7253	216	9	eqs	eqs	PROPN
fumecheng-7253	216	10	.	.	PUNCT
fumecheng-7253	217	1	(	(	PUNCT
fumecheng-7253	217	2	46	46	NUM
fumecheng-7253	217	3	)	)	PUNCT
fumecheng-7253	217	4	and	and	CCONJ
fumecheng-7253	217	5	(	(	PUNCT
fumecheng-7253	217	6	49	49	NUM
fumecheng-7253	217	7	)	)	PUNCT
fumecheng-7253	217	8	,	,	PUNCT
fumecheng-7253	217	9	the	the	DET
fumecheng-7253	217	10	following	follow	VERB
fumecheng-7253	217	11	system	system	NOUN
fumecheng-7253	217	12	of	of	ADP
fumecheng-7253	217	13	equations	equation	NOUN
fumecheng-7253	217	14	are	be	AUX
fumecheng-7253	217	15	obtained	obtain	VERB
fumecheng-7253	217	16	∑	∑	PUNCT
fumecheng-7253	217	17	(	(	PUNCT
fumecheng-7253	217	18	𝐶𝑗	𝐶𝑗	NOUN
fumecheng-7253	217	19	+	+	NOUN
fumecheng-7253	217	20	𝐶𝑗+3	𝐶𝑗+3	NOUN
fumecheng-7253	217	21	)	)	PUNCT
fumecheng-7253	217	22	=	=	SYM
fumecheng-7253	217	23	𝐴5	𝐴5	PROPN
fumecheng-7253	217	24	�	�	PROPN
fumecheng-7253	217	25	̅	̅	NOUN
fumecheng-7253	217	26	�	�	NOUN
fumecheng-7253	217	27	(𝑠	(𝑠	NOUN
fumecheng-7253	217	28	)	)	PUNCT
fumecheng-7253	217	29	𝐶𝐴1	𝐶𝐴1	PROPN
fumecheng-7253	217	30	3	3	NUM
fumecheng-7253	217	31	𝑗=1	𝑗=1	NOUN
fumecheng-7253	217	32	(	(	PUNCT
fumecheng-7253	217	33	57	57	NUM
fumecheng-7253	217	34	)	)	PUNCT
fumecheng-7253	217	35	∑	∑	PUNCT
fumecheng-7253	218	1	(	(	PUNCT
fumecheng-7253	218	2	𝐶𝑗e	𝐶𝑗e	PROPN
fumecheng-7253	218	3	−𝑚𝑗𝐿	−𝑚𝑗𝐿	PROPN
fumecheng-7253	218	4	+	+	CCONJ
fumecheng-7253	218	5	𝐶𝑗+3e	𝐶𝑗+3e	PROPN
fumecheng-7253	218	6	𝑚𝑗𝐿	𝑚𝑗𝐿	PROPN
fumecheng-7253	218	7	)	)	PUNCT
fumecheng-7253	219	1	=	=	PUNCT
fumecheng-7253	219	2	𝐴5	𝐴5	PROPN
fumecheng-7253	219	3	�	�	PROPN
fumecheng-7253	219	4	̅	̅	NOUN
fumecheng-7253	219	5	�	�	NOUN
fumecheng-7253	219	6	(𝑠	(𝑠	NOUN
fumecheng-7253	219	7	)	)	PUNCT
fumecheng-7253	219	8	𝐶𝐴1	𝐶𝐴1	PROPN
fumecheng-7253	219	9	3	3	NUM
fumecheng-7253	219	10	𝑗=1	𝑗=1	PROPN
fumecheng-7253	219	11	(	(	PUNCT
fumecheng-7253	219	12	58	58	NUM
fumecheng-7253	219	13	)	)	PUNCT
fumecheng-7253	219	14	∑	∑	ADV
fumecheng-7253	219	15	𝑚𝑗	𝑚𝑗	PROPN
fumecheng-7253	219	16	2(𝐶𝑗	2(𝐶𝑗	NUM
fumecheng-7253	219	17	+	+	NUM
fumecheng-7253	219	18	𝐶𝑗+3	𝐶𝑗+3	NOUN
fumecheng-7253	219	19	)	)	PUNCT
fumecheng-7253	220	1	=	=	SYM
fumecheng-7253	220	2	𝐴5	𝐴5	PROPN
fumecheng-7253	220	3	�	�	PROPN
fumecheng-7253	220	4	̅	̅	NOUN
fumecheng-7253	220	5	�	�	NOUN
fumecheng-7253	220	6	(𝑠	(𝑠	NOUN
fumecheng-7253	220	7	)	)	PUNCT
fumecheng-7253	220	8	𝐶𝐴1	𝐶𝐴1	PROPN
fumecheng-7253	220	9	3	3	NUM
fumecheng-7253	220	10	𝑗=1	𝑗=1	PROPN
fumecheng-7253	220	11	(	(	PUNCT
fumecheng-7253	220	12	59	59	NUM
fumecheng-7253	220	13	)	)	PUNCT
fumecheng-7253	220	14	∑	∑	ADV
fumecheng-7253	220	15	𝑚𝑗	𝑚𝑗	PROPN
fumecheng-7253	220	16	2(𝐶𝑗𝑒	2(𝐶𝑗𝑒	NUM
fumecheng-7253	220	17	−𝑚𝑗𝐿	−𝑚𝑗𝐿	X
fumecheng-7253	221	1	+	+	CCONJ
fumecheng-7253	221	2	𝐶𝑗+3𝑒	𝐶𝑗+3𝑒	PROPN
fumecheng-7253	221	3	𝑚𝑗𝐿	𝑚𝑗𝐿	PROPN
fumecheng-7253	221	4	)	)	PUNCT
fumecheng-7253	222	1	=	=	PUNCT
fumecheng-7253	222	2	𝐴5	𝐴5	PROPN
fumecheng-7253	222	3	�	�	PROPN
fumecheng-7253	222	4	̅	̅	NOUN
fumecheng-7253	222	5	�	�	NOUN
fumecheng-7253	222	6	(𝑠	(𝑠	NOUN
fumecheng-7253	222	7	)	)	PUNCT
fumecheng-7253	222	8	𝐶𝐴1	𝐶𝐴1	PROPN
fumecheng-7253	222	9	3	3	NUM
fumecheng-7253	222	10	𝑗=1	𝑗=1	PROPN
fumecheng-7253	222	11	(	(	PUNCT
fumecheng-7253	222	12	60	60	NUM
fumecheng-7253	222	13	)	)	PUNCT
fumecheng-7253	222	14	∑	∑	PUNCT
fumecheng-7253	222	15	𝐻𝑗(𝐶𝑗	𝐻𝑗(𝐶𝑗	PROPN
fumecheng-7253	222	16	+	+	NUM
fumecheng-7253	222	17	𝐶𝑗+3	𝐶𝑗+3	NOUN
fumecheng-7253	222	18	)	)	PUNCT
fumecheng-7253	222	19	3	3	NUM
fumecheng-7253	222	20	𝑗=1	𝑗=1	NOUN
fumecheng-7253	222	21	=	=	SYM
fumecheng-7253	222	22	𝐻4	𝐻4	PROPN
fumecheng-7253	222	23	+	+	CCONJ
fumecheng-7253	222	24	�	�	PROPN
fumecheng-7253	222	25	̅	̅	NOUN
fumecheng-7253	222	26	�	�	NOUN
fumecheng-7253	222	27	(𝑠	(𝑠	NOUN
fumecheng-7253	222	28	)	)	PUNCT
fumecheng-7253	222	29	,	,	PUNCT
fumecheng-7253	222	30	(	(	PUNCT
fumecheng-7253	222	31	61	61	NUM
fumecheng-7253	222	32	)	)	PUNCT
fumecheng-7253	222	33	∑	∑	PUNCT
fumecheng-7253	222	34	𝑚𝑗𝐻𝑗(𝐶𝑗𝑒	𝑚𝑗𝐻𝑗(𝐶𝑗𝑒	PROPN
fumecheng-7253	222	35	−𝑚𝑗𝐿	−𝑚𝑗𝐿	X
fumecheng-7253	222	36	−	−	PROPN
fumecheng-7253	222	37	𝐶𝑗+3𝑒	𝐶𝑗+3𝑒	PROPN
fumecheng-7253	222	38	𝑚𝑗𝐿)3	𝑚𝑗𝐿)3	PROPN
fumecheng-7253	222	39	𝑗=1	𝑗=1	PROPN
fumecheng-7253	222	40	=	=	SYM
fumecheng-7253	222	41	0	0	NUM
fumecheng-7253	222	42	,	,	PUNCT
fumecheng-7253	222	43	(	(	PUNCT
fumecheng-7253	222	44	62	62	NUM
fumecheng-7253	222	45	)	)	PUNCT
fumecheng-7253	222	46	parameters	parameter	NOUN
fumecheng-7253	222	47	𝐶𝑗	𝐶𝑗	NOUN
fumecheng-7253	222	48	,	,	PUNCT
fumecheng-7253	222	49	(	(	PUNCT
fumecheng-7253	222	50	𝑗	𝑗	NOUN
fumecheng-7253	222	51	=	=	SYM
fumecheng-7253	222	52	1,2	1,2	NUM
fumecheng-7253	222	53	.	.	PUNCT
fumecheng-7253	222	54	.	.	PUNCT
fumecheng-7253	223	1	,	,	PUNCT
fumecheng-7253	223	2	6	6	NUM
fumecheng-7253	223	3	)	)	PUNCT
fumecheng-7253	223	4	are	be	AUX
fumecheng-7253	223	5	unknown	unknown	ADJ
fumecheng-7253	223	6	and	and	CCONJ
fumecheng-7253	223	7	have	have	VERB
fumecheng-7253	223	8	to	to	PART
fumecheng-7253	223	9	be	be	AUX
fumecheng-7253	223	10	determined	determine	VERB
fumecheng-7253	223	11	and	and	CCONJ
fumecheng-7253	223	12	,	,	PUNCT
fumecheng-7253	223	13	thereby	thereby	ADV
fumecheng-7253	223	14	,	,	PUNCT
fumecheng-7253	223	15	the	the	DET
fumecheng-7253	223	16	analytical	analytical	ADJ
fumecheng-7253	223	17	solutions	solution	NOUN
fumecheng-7253	223	18	for	for	ADP
fumecheng-7253	223	19	the	the	DET
fumecheng-7253	223	20	physical	physical	ADJ
fumecheng-7253	223	21	parameters	parameter	NOUN
fumecheng-7253	223	22	in	in	ADP
fumecheng-7253	223	23	the	the	DET
fumecheng-7253	223	24	laplace	laplace	NOUN
fumecheng-7253	223	25	domain	domain	NOUN
fumecheng-7253	223	26	can	can	AUX
fumecheng-7253	223	27	be	be	AUX
fumecheng-7253	223	28	achieved	achieve	VERB
fumecheng-7253	223	29	.	.	PUNCT
fumecheng-7253	224	1	it	it	PRON
fumecheng-7253	224	2	is	be	AUX
fumecheng-7253	224	3	difficult	difficult	ADJ
fumecheng-7253	224	4	to	to	PART
fumecheng-7253	224	5	take	take	VERB
fumecheng-7253	224	6	the	the	DET
fumecheng-7253	224	7	laplace	laplace	NOUN
fumecheng-7253	224	8	inversion	inversion	NOUN
fumecheng-7253	224	9	of	of	ADP
fumecheng-7253	224	10	the	the	DET
fumecheng-7253	224	11	complicated	complicate	VERB
fumecheng-7253	224	12	transformed	transform	VERB
fumecheng-7253	224	13	field	field	NOUN
fumecheng-7253	224	14	variables	variable	VERB
fumecheng-7253	224	15	expressions	expression	NOUN
fumecheng-7253	224	16	.	.	PUNCT
fumecheng-7253	225	1	within	within	ADP
fumecheng-7253	225	2	the	the	DET
fumecheng-7253	225	3	next	next	ADJ
fumecheng-7253	225	4	section	section	NOUN
fumecheng-7253	225	5	,	,	PUNCT
fumecheng-7253	225	6	the	the	DET
fumecheng-7253	225	7	results	result	NOUN
fumecheng-7253	225	8	are	be	AUX
fumecheng-7253	225	9	evaluated	evaluate	VERB
fumecheng-7253	225	10	numerically	numerically	ADV
fumecheng-7253	225	11	using	use	VERB
fumecheng-7253	225	12	the	the	DET
fumecheng-7253	225	13	expansion	expansion	NOUN
fumecheng-7253	225	14	technique	technique	NOUN
fumecheng-7253	225	15	of	of	ADP
fumecheng-7253	225	16	the	the	DET
fumecheng-7253	225	17	fourier	fourier	NOUN
fumecheng-7253	225	18	series	series	NOUN
fumecheng-7253	225	19	.	.	PUNCT
fumecheng-7253	226	1	temperature	temperature	NOUN
fumecheng-7253	226	2	�	�	PROPN
fumecheng-7253	226	3	̅	̅	NOUN
fumecheng-7253	226	4	�	�	NOUN
fumecheng-7253	226	5	can	can	AUX
fumecheng-7253	226	6	be	be	AUX
fumecheng-7253	226	7	obtained	obtain	VERB
fumecheng-7253	226	8	by	by	ADP
fumecheng-7253	226	9	solving	solve	VERB
fumecheng-7253	226	10	eq	eq	ADJ
fumecheng-7253	226	11	.	.	PUNCT
fumecheng-7253	227	1	(	(	PUNCT
fumecheng-7253	227	2	20	20	NUM
fumecheng-7253	227	3	)	)	PUNCT
fumecheng-7253	227	4	after	after	ADP
fumecheng-7253	227	5	applying	apply	VERB
fumecheng-7253	227	6	the	the	DET
fumecheng-7253	227	7	laplace	laplace	NOUN
fumecheng-7253	227	8	transform	transform	NOUN
fumecheng-7253	227	9	as	as	ADP
fumecheng-7253	227	10	�	�	NOUN
fumecheng-7253	227	11	̅	̅	NOUN
fumecheng-7253	227	12	�	�	NOUN
fumecheng-7253	227	13	(𝑥	(𝑥	NOUN
fumecheng-7253	227	14	,	,	PUNCT
fumecheng-7253	227	15	𝑠	𝑠	NOUN
fumecheng-7253	227	16	)	)	PUNCT
fumecheng-7253	227	17	=	=	VERB
fumecheng-7253	227	18	sin	sin	NOUN
fumecheng-7253	227	19	(	(	PUNCT
fumecheng-7253	227	20	𝜋	𝜋	NOUN
fumecheng-7253	227	21	ℎ	ℎ	X
fumecheng-7253	227	22	𝑧	𝑧	PART
fumecheng-7253	227	23	)	)	PUNCT
fumecheng-7253	227	24	[	[	PUNCT
fumecheng-7253	227	25	−1+√1	−1+√1	X
fumecheng-7253	227	26	+	+	SYM
fumecheng-7253	227	27	2𝐾1	2𝐾1	NUM
fumecheng-7253	227	28	�	�	NOUN
fumecheng-7253	227	29	̅	̅	NOUN
fumecheng-7253	227	30	�	�	NOUN
fumecheng-7253	227	31	𝐾1	𝐾1	PROPN
fumecheng-7253	227	32	]	]	PUNCT
fumecheng-7253	227	33	(	(	PUNCT
fumecheng-7253	227	34	63	63	NUM
fumecheng-7253	227	35	)	)	PUNCT
fumecheng-7253	227	36	7	7	NUM
fumecheng-7253	227	37	.	.	PUNCT
fumecheng-7253	227	38	laplace	laplace	NOUN
fumecheng-7253	227	39	transform	transform	VERB
fumecheng-7253	227	40	inversion	inversion	NOUN
fumecheng-7253	227	41	with	with	ADP
fumecheng-7253	227	42	the	the	DET
fumecheng-7253	227	43	aim	aim	NOUN
fumecheng-7253	227	44	of	of	ADP
fumecheng-7253	227	45	solutions	solution	NOUN
fumecheng-7253	227	46	in	in	ADP
fumecheng-7253	227	47	the	the	DET
fumecheng-7253	227	48	physical	physical	ADJ
fumecheng-7253	227	49	domain	domain	NOUN
fumecheng-7253	227	50	,	,	PUNCT
fumecheng-7253	227	51	at	at	ADP
fumecheng-7253	227	52	last	last	ADJ
fumecheng-7253	227	53	,	,	PUNCT
fumecheng-7253	227	54	we	we	PRON
fumecheng-7253	227	55	invert	invert	VERB
fumecheng-7253	227	56	the	the	DET
fumecheng-7253	227	57	transformation	transformation	NOUN
fumecheng-7253	227	58	of	of	ADP
fumecheng-7253	227	59	laplace	laplace	NOUN
fumecheng-7253	227	60	to	to	ADP
fumecheng-7253	227	61	the	the	DET
fumecheng-7253	227	62	functions	function	NOUN
fumecheng-7253	227	63	that	that	PRON
fumecheng-7253	227	64	govern	govern	VERB
fumecheng-7253	227	65	the	the	DET
fumecheng-7253	227	66	motion	motion	NOUN
fumecheng-7253	227	67	of	of	ADP
fumecheng-7253	227	68	the	the	DET
fumecheng-7253	227	69	system	system	NOUN
fumecheng-7253	227	70	.	.	PUNCT
fumecheng-7253	228	1	we	we	PRON
fumecheng-7253	228	2	now	now	ADV
fumecheng-7253	228	3	follow	follow	VERB
fumecheng-7253	228	4	a	a	DET
fumecheng-7253	228	5	numerical	numerical	ADJ
fumecheng-7253	228	6	overlay	overlay	NOUN
fumecheng-7253	228	7	strategy	strategy	NOUN
fumecheng-7253	228	8	based	base	VERB
fumecheng-7253	228	9	on	on	ADP
fumecheng-7253	228	10	an	an	DET
fumecheng-7253	228	11	extension	extension	NOUN
fumecheng-7253	228	12	of	of	ADP
fumecheng-7253	228	13	the	the	DET
fumecheng-7253	228	14	fourier	fourier	ADJ
fumecheng-7253	228	15	series	series	NOUN
fumecheng-7253	228	16	[	[	X
fumecheng-7253	228	17	46	46	NUM
fumecheng-7253	228	18	]	]	PUNCT
fumecheng-7253	228	19	.	.	PUNCT
fumecheng-7253	229	1	any	any	DET
fumecheng-7253	229	2	functions	function	NOUN
fumecheng-7253	229	3	in	in	ADP
fumecheng-7253	229	4	644	644	NUM
fumecheng-7253	229	5	a.	a.	NOUN
fumecheng-7253	229	6	e.	e.	PROPN
fumecheng-7253	229	7	abouelregal	abouelregal	PROPN
fumecheng-7253	229	8	,	,	PUNCT
fumecheng-7253	229	9	h.	h.	PROPN
fumecheng-7253	229	10	m.	m.	PROPN
fumecheng-7253	229	11	sedighi	sedighi	PROPN
fumecheng-7253	229	12	,	,	PUNCT
fumecheng-7253	229	13	s.	s.	PROPN
fumecheng-7253	229	14	a.	a.	PROPN
fumecheng-7253	229	15	faghidian	faghidian	PROPN
fumecheng-7253	229	16	,	,	PUNCT
fumecheng-7253	229	17	a.	a.	PROPN
fumecheng-7253	229	18	h.	h.	PROPN
fumecheng-7253	229	19	shirazi	shirazi	PROPN
fumecheng-7253	229	20	the	the	DET
fumecheng-7253	229	21	laplace	laplace	NOUN
fumecheng-7253	229	22	domain	domain	NOUN
fumecheng-7253	229	23	,	,	PUNCT
fumecheng-7253	229	24	i.e.	i.e.	X
fumecheng-7253	229	25	�	�	SYM
fumecheng-7253	229	26	̅	̅	NOUN
fumecheng-7253	229	27	�	�	PROPN
fumecheng-7253	229	28	(	(	PUNCT
fumecheng-7253	229	29	𝑥	𝑥	PROPN
fumecheng-7253	229	30	,	,	PUNCT
fumecheng-7253	229	31	𝑠	𝑠	PROPN
fumecheng-7253	229	32	)	)	PUNCT
fumecheng-7253	229	33	,	,	PUNCT
fumecheng-7253	229	34	is	be	AUX
fumecheng-7253	229	35	transferred	transfer	VERB
fumecheng-7253	229	36	to	to	ADP
fumecheng-7253	229	37	the	the	DET
fumecheng-7253	229	38	time	time	NOUN
fumecheng-7253	229	39	domain	domain	NOUN
fumecheng-7253	229	40	,	,	PUNCT
fumecheng-7253	229	41	i.e.	i.e.	X
fumecheng-7253	229	42	𝑔(𝑥	𝑔(𝑥	PROPN
fumecheng-7253	229	43	,	,	PUNCT
fumecheng-7253	229	44	𝑡	𝑡	NOUN
fumecheng-7253	229	45	)	)	PUNCT
fumecheng-7253	229	46	,	,	PUNCT
fumecheng-7253	229	47	by	by	ADP
fumecheng-7253	229	48	using	use	VERB
fumecheng-7253	229	49	the	the	DET
fumecheng-7253	229	50	following	follow	VERB
fumecheng-7253	229	51	procedure	procedure	NOUN
fumecheng-7253	229	52	:	:	PUNCT
fumecheng-7253	229	53	𝑔(𝑥	𝑔(𝑥	NOUN
fumecheng-7253	229	54	,	,	PUNCT
fumecheng-7253	229	55	𝑡	𝑡	X
fumecheng-7253	229	56	)	)	PUNCT
fumecheng-7253	229	57	=	=	PUNCT
fumecheng-7253	229	58	e𝑐𝑡	e𝑐𝑡	NOUN
fumecheng-7253	229	59	𝑡	𝑡	SYM
fumecheng-7253	229	60	{	{	PUNCT
fumecheng-7253	229	61	1	1	NUM
fumecheng-7253	229	62	2	2	NUM
fumecheng-7253	229	63	�	�	NOUN
fumecheng-7253	229	64	̅	̅	NOUN
fumecheng-7253	229	65	�	�	NOUN
fumecheng-7253	229	66	(𝑥	(𝑥	NOUN
fumecheng-7253	229	67	,	,	PUNCT
fumecheng-7253	229	68	𝑐	𝑐	NOUN
fumecheng-7253	229	69	)	)	PUNCT
fumecheng-7253	229	70	+	+	X
fumecheng-7253	229	71	re	re	VERB
fumecheng-7253	229	72	[	[	NOUN
fumecheng-7253	229	73	∑	∑	INTJ
fumecheng-7253	229	74	(	(	PUNCT
fumecheng-7253	229	75	−1)𝑛𝑁	−1)𝑛𝑁	NOUN
fumecheng-7253	229	76	𝑛=1	𝑛=1	NOUN
fumecheng-7253	229	77	�	�	PROPN
fumecheng-7253	229	78	̅	̅	NOUN
fumecheng-7253	229	79	�	�	PROPN
fumecheng-7253	229	80	(	(	PUNCT
fumecheng-7253	229	81	𝑥	𝑥	PROPN
fumecheng-7253	229	82	,	,	PUNCT
fumecheng-7253	229	83	𝑐	𝑐	PROPN
fumecheng-7253	229	84	+	+	NUM
fumecheng-7253	229	85	i𝑛𝜋	i𝑛𝜋	NUM
fumecheng-7253	229	86	𝑡	𝑡	PROPN
fumecheng-7253	229	87	)	)	PUNCT
fumecheng-7253	229	88	]	]	PUNCT
fumecheng-7253	229	89	}	}	PUNCT
fumecheng-7253	229	90	,	,	PUNCT
fumecheng-7253	229	91	(	(	PUNCT
fumecheng-7253	229	92	64	64	NUM
fumecheng-7253	229	93	)	)	PUNCT
fumecheng-7253	229	94	where	where	SCONJ
fumecheng-7253	229	95	𝑁	𝑁	PROPN
fumecheng-7253	229	96	represents	represent	VERB
fumecheng-7253	229	97	a	a	DET
fumecheng-7253	229	98	large	large	ADJ
fumecheng-7253	229	99	value	value	NOUN
fumecheng-7253	229	100	denoting	denote	VERB
fumecheng-7253	229	101	the	the	DET
fumecheng-7253	229	102	number	number	NOUN
fumecheng-7253	229	103	of	of	ADP
fumecheng-7253	229	104	truncated	truncated	ADJ
fumecheng-7253	229	105	terms	term	NOUN
fumecheng-7253	229	106	in	in	ADP
fumecheng-7253	229	107	the	the	DET
fumecheng-7253	229	108	original	original	ADJ
fumecheng-7253	229	109	fourier	fourier	NOUN
fumecheng-7253	229	110	series	series	NOUN
fumecheng-7253	229	111	and	and	CCONJ
fumecheng-7253	229	112	can	can	AUX
fumecheng-7253	229	113	be	be	AUX
fumecheng-7253	229	114	selected	select	VERB
fumecheng-7253	229	115	to	to	PART
fumecheng-7253	229	116	satisfy	satisfy	VERB
fumecheng-7253	229	117	e𝑐𝑡re	e𝑐𝑡re	NOUN
fumecheng-7253	229	118	{	{	PUNCT
fumecheng-7253	229	119	(	(	PUNCT
fumecheng-7253	229	120	−1)𝑛	−1)𝑛	X
fumecheng-7253	229	121	�	�	NOUN
fumecheng-7253	229	122	̅	̅	NOUN
fumecheng-7253	229	123	�	�	PROPN
fumecheng-7253	229	124	(	(	PUNCT
fumecheng-7253	229	125	𝑥	𝑥	PROPN
fumecheng-7253	229	126	,	,	PUNCT
fumecheng-7253	229	127	𝑐	𝑐	PROPN
fumecheng-7253	229	128	+	+	NUM
fumecheng-7253	229	129	i𝑛𝜋	i𝑛𝜋	NUM
fumecheng-7253	229	130	𝑡	𝑡	NOUN
fumecheng-7253	229	131	)	)	PUNCT
fumecheng-7253	229	132	}	}	PUNCT
fumecheng-7253	229	133	≤	≤	NUM
fumecheng-7253	229	134	휀1	휀1	NOUN
fumecheng-7253	229	135	,	,	PUNCT
fumecheng-7253	229	136	(	(	PUNCT
fumecheng-7253	229	137	65	65	NUM
fumecheng-7253	229	138	)	)	PUNCT
fumecheng-7253	229	139	in	in	ADP
fumecheng-7253	229	140	which	which	PRON
fumecheng-7253	229	141	휀1	휀1	NOUN
fumecheng-7253	229	142	is	be	AUX
fumecheng-7253	229	143	a	a	DET
fumecheng-7253	229	144	small	small	ADJ
fumecheng-7253	229	145	positive	positive	ADJ
fumecheng-7253	229	146	integer	integer	NOUN
fumecheng-7253	229	147	corresponds	correspond	VERB
fumecheng-7253	229	148	to	to	PART
fumecheng-7253	229	149	achieve	achieve	VERB
fumecheng-7253	229	150	the	the	DET
fumecheng-7253	229	151	desired	desire	VERB
fumecheng-7253	229	152	accuracy	accuracy	NOUN
fumecheng-7253	229	153	.	.	PUNCT
fumecheng-7253	230	1	various	various	ADJ
fumecheng-7253	230	2	numerical	numerical	ADJ
fumecheng-7253	230	3	studies	study	NOUN
fumecheng-7253	230	4	demonstrated	demonstrate	VERB
fumecheng-7253	230	5	that	that	SCONJ
fumecheng-7253	230	6	parameter	parameter	PROPN
fumecheng-7253	230	7	𝑐	𝑐	PROPN
fumecheng-7253	230	8	can	can	AUX
fumecheng-7253	230	9	be	be	AUX
fumecheng-7253	230	10	determined	determine	VERB
fumecheng-7253	230	11	as	as	ADP
fumecheng-7253	230	12	𝑐𝑡	𝑐𝑡	ADP
fumecheng-7253	230	13	≈	≈	PROPN
fumecheng-7253	230	14	4.7	4.7	NUM
fumecheng-7253	230	15	for	for	ADP
fumecheng-7253	230	16	appropriate	appropriate	ADJ
fumecheng-7253	230	17	convergence	convergence	NOUN
fumecheng-7253	230	18	[	[	X
fumecheng-7253	230	19	47	47	NUM
fumecheng-7253	230	20	]	]	PUNCT
fumecheng-7253	230	21	.	.	PUNCT
fumecheng-7253	231	1	8	8	X
fumecheng-7253	231	2	.	.	X
fumecheng-7253	231	3	results	result	NOUN
fumecheng-7253	231	4	and	and	CCONJ
fumecheng-7253	231	5	discussion	discussion	NOUN
fumecheng-7253	231	6	throughout	throughout	ADP
fumecheng-7253	231	7	this	this	DET
fumecheng-7253	231	8	section	section	NOUN
fumecheng-7253	231	9	,	,	PUNCT
fumecheng-7253	231	10	some	some	DET
fumecheng-7253	231	11	discussions	discussion	NOUN
fumecheng-7253	231	12	and	and	CCONJ
fumecheng-7253	231	13	numerical	numerical	ADJ
fumecheng-7253	231	14	results	result	NOUN
fumecheng-7253	231	15	are	be	AUX
fumecheng-7253	231	16	provided	provide	VERB
fumecheng-7253	231	17	to	to	PART
fumecheng-7253	231	18	illustrate	illustrate	VERB
fumecheng-7253	231	19	the	the	DET
fumecheng-7253	231	20	general	general	ADJ
fumecheng-7253	231	21	response	response	NOUN
fumecheng-7253	231	22	of	of	ADP
fumecheng-7253	231	23	the	the	DET
fumecheng-7253	231	24	problem	problem	NOUN
fumecheng-7253	231	25	.	.	PUNCT
fumecheng-7253	232	1	moreover	moreover	ADV
fumecheng-7253	232	2	,	,	PUNCT
fumecheng-7253	232	3	the	the	DET
fumecheng-7253	232	4	numerical	numerical	ADJ
fumecheng-7253	232	5	examples	example	NOUN
fumecheng-7253	232	6	are	be	AUX
fumecheng-7253	232	7	presented	present	VERB
fumecheng-7253	232	8	to	to	PART
fumecheng-7253	232	9	explore	explore	VERB
fumecheng-7253	232	10	the	the	DET
fumecheng-7253	232	11	impacts	impact	NOUN
fumecheng-7253	232	12	of	of	ADP
fumecheng-7253	232	13	the	the	DET
fumecheng-7253	232	14	physical	physical	ADJ
fumecheng-7253	232	15	fields	field	NOUN
fumecheng-7253	232	16	analyzed	analyze	VERB
fumecheng-7253	232	17	with	with	ADP
fumecheng-7253	232	18	three	three	NUM
fumecheng-7253	232	19	appropriate	appropriate	ADJ
fumecheng-7253	232	20	parameters	parameter	NOUN
fumecheng-7253	232	21	.	.	PUNCT
fumecheng-7253	233	1	specific	specific	ADJ
fumecheng-7253	233	2	physical	physical	ADJ
fumecheng-7253	233	3	parameters	parameter	NOUN
fumecheng-7253	233	4	are	be	AUX
fumecheng-7253	233	5	taken	take	VERB
fumecheng-7253	233	6	into	into	ADP
fumecheng-7253	233	7	consideration	consideration	NOUN
fumecheng-7253	233	8	from	from	ADP
fumecheng-7253	233	9	the	the	DET
fumecheng-7253	233	10	published	publish	VERB
fumecheng-7253	233	11	works	work	NOUN
fumecheng-7253	233	12	in	in	ADP
fumecheng-7253	233	13	the	the	DET
fumecheng-7253	233	14	literature	literature	NOUN
fumecheng-7253	233	15	for	for	ADP
fumecheng-7253	233	16	computational	computational	ADJ
fumecheng-7253	233	17	purposes	purpose	NOUN
fumecheng-7253	233	18	.	.	PUNCT
fumecheng-7253	234	1	in	in	ADP
fumecheng-7253	234	2	our	our	PRON
fumecheng-7253	234	3	analysis	analysis	NOUN
fumecheng-7253	234	4	,	,	PUNCT
fumecheng-7253	234	5	the	the	DET
fumecheng-7253	234	6	following	follow	VERB
fumecheng-7253	234	7	properties	property	NOUN
fumecheng-7253	234	8	are	be	AUX
fumecheng-7253	234	9	utilized	utilize	VERB
fumecheng-7253	234	10	for	for	ADP
fumecheng-7253	234	11	silicon	silicon	NOUN
fumecheng-7253	234	12	-	-	PUNCT
fumecheng-7253	234	13	based	base	VERB
fumecheng-7253	234	14	material	material	NOUN
fumecheng-7253	234	15	:	:	PUNCT
fumecheng-7253	234	16	𝐸	𝐸	PROPN
fumecheng-7253	234	17	=	=	SYM
fumecheng-7253	234	18	169	169	NUM
fumecheng-7253	234	19	gpa	gpa	PROPN
fumecheng-7253	234	20	,	,	PUNCT
fumecheng-7253	234	21	𝜌	𝜌	X
fumecheng-7253	234	22	=	=	SYM
fumecheng-7253	234	23	2330	2330	NUM
fumecheng-7253	234	24	(	(	PUNCT
fumecheng-7253	234	25	kg	kg	PROPN
fumecheng-7253	234	26	m3	m3	PROPN
fumecheng-7253	234	27	)	)	PUNCT
fumecheng-7253	234	28	,	,	PUNCT
fumecheng-7253	234	29	𝐶𝐸	𝐶𝐸	PROPN
fumecheng-7253	234	30	=	=	SYM
fumecheng-7253	234	31	713	713	NUM
fumecheng-7253	234	32	(	(	PUNCT
fumecheng-7253	234	33	j	j	PROPN
fumecheng-7253	234	34	kg	kg	X
fumecheng-7253	234	35	k	k	PROPN
fumecheng-7253	234	36	)	)	PUNCT
fumecheng-7253	234	37	,	,	PUNCT
fumecheng-7253	235	1	𝛼𝑇	𝛼𝑇	NOUN
fumecheng-7253	235	2	=	=	SYM
fumecheng-7253	235	3	2.59	2.59	NUM
fumecheng-7253	235	4	×	×	NOUN
fumecheng-7253	235	5	10−9	10−9	NUM
fumecheng-7253	235	6	(	(	PUNCT
fumecheng-7253	235	7	1	1	NUM
fumecheng-7253	235	8	k	k	NOUN
fumecheng-7253	235	9	)	)	PUNCT
fumecheng-7253	235	10	,	,	PUNCT
fumecheng-7253	235	11	𝜈	𝜈	X
fumecheng-7253	235	12	=	=	SYM
fumecheng-7253	235	13	0.22	0.22	NUM
fumecheng-7253	235	14	,	,	PUNCT
fumecheng-7253	235	15	𝑇0	𝑇0	NOUN
fumecheng-7253	235	16	=	=	SYM
fumecheng-7253	235	17	293	293	NUM
fumecheng-7253	235	18	𝐾	𝐾	NOUN
fumecheng-7253	235	19	,	,	PUNCT
fumecheng-7253	235	20	𝐾	𝐾	PROPN
fumecheng-7253	235	21	=	=	SYM
fumecheng-7253	235	22	156	156	NUM
fumecheng-7253	235	23	(	(	PUNCT
fumecheng-7253	235	24	w	w	PROPN
fumecheng-7253	235	25	mk	mk	PROPN
fumecheng-7253	235	26	)	)	PUNCT
fumecheng-7253	235	27	.	.	PUNCT
fumecheng-7253	236	1	we	we	PRON
fumecheng-7253	236	2	consider	consider	VERB
fumecheng-7253	236	3	a	a	DET
fumecheng-7253	236	4	nanobeam	nanobeam	NOUN
fumecheng-7253	236	5	with	with	ADP
fumecheng-7253	236	6	dimensionless	dimensionless	NOUN
fumecheng-7253	236	7	parameters	parameter	NOUN
fumecheng-7253	236	8	as	as	SCONJ
fumecheng-7253	236	9	given	give	VERB
fumecheng-7253	236	10	in	in	ADP
fumecheng-7253	236	11	eq	eq	ADP
fumecheng-7253	236	12	.	.	PUNCT
fumecheng-7253	237	1	(	(	PUNCT
fumecheng-7253	237	2	24	24	NUM
fumecheng-7253	237	3	)	)	PUNCT
fumecheng-7253	237	4	.	.	PUNCT
fumecheng-7253	238	1	the	the	DET
fumecheng-7253	238	2	following	follow	VERB
fumecheng-7253	238	3	values	value	NOUN
fumecheng-7253	238	4	are	be	AUX
fumecheng-7253	238	5	set	set	VERB
fumecheng-7253	238	6	in	in	ADP
fumecheng-7253	238	7	our	our	PRON
fumecheng-7253	238	8	calculations	calculation	NOUN
fumecheng-7253	238	9	,	,	PUNCT
fumecheng-7253	238	10	i.e.	i.e.	X
fumecheng-7253	238	11	,	,	PUNCT
fumecheng-7253	238	12	𝐿/ℎ	𝐿/ℎ	PROPN
fumecheng-7253	238	13	=	=	PUNCT
fumecheng-7253	238	14	10and	10and	NOUN
fumecheng-7253	238	15	𝑏/ℎ	𝑏/ℎ	NOUN
fumecheng-7253	238	16	=	=	NOUN
fumecheng-7253	238	17	0.5	0.5	NUM
fumecheng-7253	238	18	.	.	PUNCT
fumecheng-7253	239	1	the	the	DET
fumecheng-7253	239	2	dimensionless	dimensionless	NOUN
fumecheng-7253	239	3	length	length	NOUN
fumecheng-7253	239	4	is	be	AUX
fumecheng-7253	239	5	taken	take	VERB
fumecheng-7253	239	6	as	as	ADP
fumecheng-7253	239	7	𝐿	𝐿	PROPN
fumecheng-7253	239	8	=	=	PROPN
fumecheng-7253	239	9	1	1	NUM
fumecheng-7253	239	10	and	and	CCONJ
fumecheng-7253	239	11	it	it	PRON
fumecheng-7253	239	12	is	be	AUX
fumecheng-7253	239	13	assumed	assume	VERB
fumecheng-7253	239	14	that	that	SCONJ
fumecheng-7253	239	15	𝑡	𝑡	PROPN
fumecheng-7253	239	16	=	=	NOUN
fumecheng-7253	239	17	0.1	0.1	NUM
fumecheng-7253	239	18	.	.	PUNCT
fumecheng-7253	240	1	as	as	SCONJ
fumecheng-7253	240	2	mentioned	mention	VERB
fumecheng-7253	240	3	before	before	ADV
fumecheng-7253	240	4	,	,	PUNCT
fumecheng-7253	240	5	a	a	DET
fumecheng-7253	240	6	linear	linear	ADJ
fumecheng-7253	240	7	function	function	NOUN
fumecheng-7253	240	8	of	of	ADP
fumecheng-7253	240	9	temperature	temperature	NOUN
fumecheng-7253	240	10	change	change	NOUN
fumecheng-7253	240	11	𝜃	𝜃	NOUN
fumecheng-7253	240	12	is	be	AUX
fumecheng-7253	240	13	considered	consider	VERB
fumecheng-7253	240	14	for	for	ADP
fumecheng-7253	240	15	the	the	DET
fumecheng-7253	240	16	thermal	thermal	ADJ
fumecheng-7253	240	17	conductivity	conductivity	NOUN
fumecheng-7253	240	18	of	of	ADP
fumecheng-7253	240	19	the	the	DET
fumecheng-7253	240	20	material	material	NOUN
fumecheng-7253	240	21	(	(	PUNCT
fumecheng-7253	240	22	see	see	VERB
fumecheng-7253	240	23	eq	eq	ADP
fumecheng-7253	240	24	.	.	PUNCT
fumecheng-7253	241	1	(	(	PUNCT
fumecheng-7253	241	2	13	13	NUM
fumecheng-7253	241	3	)	)	PUNCT
fumecheng-7253	241	4	)	)	PUNCT
fumecheng-7253	241	5	.	.	PUNCT
fumecheng-7253	242	1	figs	fig	NOUN
fumecheng-7253	242	2	.	.	PUNCT
fumecheng-7253	243	1	2	2	NUM
fumecheng-7253	243	2	-	-	SYM
fumecheng-7253	243	3	5	5	NUM
fumecheng-7253	243	4	show	show	VERB
fumecheng-7253	243	5	the	the	DET
fumecheng-7253	243	6	variations	variation	NOUN
fumecheng-7253	243	7	of	of	ADP
fumecheng-7253	243	8	nondimensional	nondimensional	ADJ
fumecheng-7253	243	9	displacement	displacement	NOUN
fumecheng-7253	243	10	,	,	PUNCT
fumecheng-7253	243	11	bending	bend	VERB
fumecheng-7253	243	12	moment	moment	NOUN
fumecheng-7253	243	13	and	and	CCONJ
fumecheng-7253	243	14	temperature	temperature	NOUN
fumecheng-7253	243	15	gradient	gradient	NOUN
fumecheng-7253	243	16	for	for	ADP
fumecheng-7253	243	17	different	different	ADJ
fumecheng-7253	243	18	values	value	NOUN
fumecheng-7253	243	19	of	of	ADP
fumecheng-7253	243	20	𝐾1	𝐾1	NOUN
fumecheng-7253	243	21	-	-	PUNCT
fumecheng-7253	243	22	parameter	parameter	NOUN
fumecheng-7253	243	23	to	to	PART
fumecheng-7253	243	24	illustrate	illustrate	VERB
fumecheng-7253	243	25	the	the	DET
fumecheng-7253	243	26	thermal	thermal	ADJ
fumecheng-7253	243	27	properties	property	NOUN
fumecheng-7253	243	28	of	of	ADP
fumecheng-7253	243	29	the	the	DET
fumecheng-7253	243	30	nanobeam	nanobeam	NOUN
fumecheng-7253	243	31	that	that	PRON
fumecheng-7253	243	32	vary	vary	VERB
fumecheng-7253	243	33	in	in	ADP
fumecheng-7253	243	34	terms	term	NOUN
fumecheng-7253	243	35	of	of	ADP
fumecheng-7253	243	36	temperature	temperature	NOUN
fumecheng-7253	243	37	variable	variable	NOUN
fumecheng-7253	243	38	𝜃.	𝜃.	VERB
fumecheng-7253	243	39	two	two	NUM
fumecheng-7253	243	40	different	different	ADJ
fumecheng-7253	243	41	thermal	thermal	ADJ
fumecheng-7253	243	42	conduction	conduction	NOUN
fumecheng-7253	243	43	parameters	parameter	NOUN
fumecheng-7253	243	44	will	will	AUX
fumecheng-7253	243	45	be	be	AUX
fumecheng-7253	243	46	considered	consider	VERB
fumecheng-7253	243	47	.	.	PUNCT
fumecheng-7253	244	1	when	when	SCONJ
fumecheng-7253	244	2	the	the	DET
fumecheng-7253	244	3	thermal	thermal	ADJ
fumecheng-7253	244	4	conductivity	conductivity	NOUN
fumecheng-7253	244	5	depends	depend	VERB
fumecheng-7253	244	6	on	on	ADP
fumecheng-7253	244	7	temperature	temperature	NOUN
fumecheng-7253	244	8	,	,	PUNCT
fumecheng-7253	244	9	values	value	VERB
fumecheng-7253	244	10	𝐾1	𝐾1	NOUN
fumecheng-7253	244	11	=	=	SYM
fumecheng-7253	244	12	−1	−1	NOUN
fumecheng-7253	244	13	and	and	CCONJ
fumecheng-7253	244	14	𝐾1	𝐾1	NOUN
fumecheng-7253	244	15	=	=	SYM
fumecheng-7253	244	16	−0.5	−0.5	NOUN
fumecheng-7253	244	17	are	be	AUX
fumecheng-7253	244	18	taken	take	VERB
fumecheng-7253	244	19	into	into	ADP
fumecheng-7253	244	20	account	account	NOUN
fumecheng-7253	244	21	.	.	PUNCT
fumecheng-7253	245	1	if	if	SCONJ
fumecheng-7253	245	2	the	the	DET
fumecheng-7253	245	3	thermal	thermal	ADJ
fumecheng-7253	245	4	conductivity	conductivity	NOUN
fumecheng-7253	245	5	remains	remain	VERB
fumecheng-7253	245	6	constant	constant	ADJ
fumecheng-7253	245	7	,	,	PUNCT
fumecheng-7253	245	8	then	then	ADV
fumecheng-7253	245	9	𝐾1	𝐾1	PROPN
fumecheng-7253	245	10	is	be	AUX
fumecheng-7253	245	11	equal	equal	ADJ
fumecheng-7253	245	12	to	to	ADP
fumecheng-7253	245	13	zero	zero	NUM
fumecheng-7253	245	14	.	.	PUNCT
fumecheng-7253	246	1	it	it	PRON
fumecheng-7253	246	2	is	be	AUX
fumecheng-7253	246	3	assumed	assume	VERB
fumecheng-7253	246	4	that	that	SCONJ
fumecheng-7253	246	5	the	the	DET
fumecheng-7253	246	6	other	other	ADJ
fumecheng-7253	246	7	parameters	parameter	NOUN
fumecheng-7253	246	8	are	be	AUX
fumecheng-7253	246	9	fixed	fix	VERB
fumecheng-7253	246	10	and	and	CCONJ
fumecheng-7253	246	11	take	take	VERB
fumecheng-7253	246	12	the	the	DET
fumecheng-7253	246	13	values	value	NOUN
fumecheng-7253	246	14	𝜉	𝜉	X
fumecheng-7253	246	15	=	=	NOUN
fumecheng-7253	246	16	0.01	0.01	NUM
fumecheng-7253	246	17	,	,	PUNCT
fumecheng-7253	246	18	𝜔	𝜔	PRON
fumecheng-7253	246	19	=	=	SYM
fumecheng-7253	246	20	5	5	NUM
fumecheng-7253	246	21	,	,	PUNCT
fumecheng-7253	246	22	ω	ω	X
fumecheng-7253	246	23	=	=	SYM
fumecheng-7253	246	24	0.3	0.3	NUM
fumecheng-7253	246	25	,	,	PUNCT
fumecheng-7253	246	26	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	246	27	=	=	NUM
fumecheng-7253	246	28	0.02	0.02	NUM
fumecheng-7253	246	29	and	and	CCONJ
fumecheng-7253	246	30	𝜏𝜃	𝜏𝜃	X
fumecheng-7253	246	31	=	=	NOUN
fumecheng-7253	246	32	0.01	0.01	NUM
fumecheng-7253	246	33	.	.	PUNCT
fumecheng-7253	247	1	from	from	ADP
fumecheng-7253	247	2	the	the	DET
fumecheng-7253	247	3	illustrative	illustrative	ADJ
fumecheng-7253	247	4	results	result	NOUN
fumecheng-7253	247	5	,	,	PUNCT
fumecheng-7253	247	6	it	it	PRON
fumecheng-7253	247	7	is	be	AUX
fumecheng-7253	247	8	observed	observe	VERB
fumecheng-7253	247	9	that	that	SCONJ
fumecheng-7253	247	10	any	any	DET
fumecheng-7253	247	11	change	change	NOUN
fumecheng-7253	247	12	in	in	ADP
fumecheng-7253	247	13	parameter	parameter	PROPN
fumecheng-7253	247	14	𝐾1	𝐾1	PROPN
fumecheng-7253	247	15	has	have	VERB
fumecheng-7253	247	16	a	a	DET
fumecheng-7253	247	17	remarkable	remarkable	ADJ
fumecheng-7253	247	18	influence	influence	NOUN
fumecheng-7253	247	19	on	on	ADP
fumecheng-7253	247	20	all	all	DET
fumecheng-7253	247	21	studied	study	VERB
fumecheng-7253	247	22	fields	field	NOUN
fumecheng-7253	247	23	that	that	PRON
fumecheng-7253	247	24	proves	prove	VERB
fumecheng-7253	247	25	that	that	SCONJ
fumecheng-7253	247	26	the	the	DET
fumecheng-7253	247	27	consideration	consideration	NOUN
fumecheng-7253	247	28	of	of	ADP
fumecheng-7253	247	29	variable	variable	ADJ
fumecheng-7253	247	30	thermal	thermal	ADJ
fumecheng-7253	247	31	conductivity	conductivity	NOUN
fumecheng-7253	247	32	is	be	AUX
fumecheng-7253	247	33	essential	essential	ADJ
fumecheng-7253	247	34	for	for	ADP
fumecheng-7253	247	35	this	this	DET
fumecheng-7253	247	36	kind	kind	NOUN
fumecheng-7253	247	37	of	of	ADP
fumecheng-7253	247	38	analysis	analysis	NOUN
fumecheng-7253	247	39	.	.	PUNCT
fumecheng-7253	248	1	it	it	PRON
fumecheng-7253	248	2	is	be	AUX
fumecheng-7253	248	3	also	also	ADV
fumecheng-7253	248	4	noted	note	VERB
fumecheng-7253	248	5	that	that	SCONJ
fumecheng-7253	248	6	the	the	DET
fumecheng-7253	248	7	behavior	behavior	NOUN
fumecheng-7253	248	8	of	of	ADP
fumecheng-7253	248	9	nanostructures	nanostructure	NOUN
fumecheng-7253	248	10	are	be	AUX
fumecheng-7253	248	11	dependent	dependent	ADJ
fumecheng-7253	248	12	on	on	ADP
fumecheng-7253	248	13	temperature	temperature	NOUN
fumecheng-7253	248	14	changes	change	NOUN
fumecheng-7253	248	15	and	and	CCONJ
fumecheng-7253	248	16	with	with	ADP
fumecheng-7253	248	17	the	the	DET
fumecheng-7253	248	18	increase	increase	NOUN
fumecheng-7253	248	19	in	in	ADP
fumecheng-7253	248	20	the	the	DET
fumecheng-7253	248	21	external	external	ADJ
fumecheng-7253	248	22	temperatures	temperature	NOUN
fumecheng-7253	248	23	,	,	PUNCT
fumecheng-7253	248	24	the	the	DET
fumecheng-7253	248	25	results	result	NOUN
fumecheng-7253	248	26	of	of	ADP
fumecheng-7253	248	27	small	small	ADJ
fumecheng-7253	248	28	-	-	PUNCT
fumecheng-7253	248	29	scale	scale	NOUN
fumecheng-7253	248	30	nonlocal	nonlocal	ADJ
fumecheng-7253	248	31	theories	theory	NOUN
fumecheng-7253	248	32	also	also	ADV
fumecheng-7253	248	33	increase	increase	VERB
fumecheng-7253	248	34	.	.	PUNCT
fumecheng-7253	249	1	the	the	DET
fumecheng-7253	249	2	variation	variation	NOUN
fumecheng-7253	249	3	of	of	ADP
fumecheng-7253	249	4	deflection	deflection	NOUN
fumecheng-7253	249	5	𝑤	𝑤	ADP
fumecheng-7253	249	6	versus	versus	ADP
fumecheng-7253	249	7	distance	distance	NOUN
fumecheng-7253	249	8	x	x	PUNCT
fumecheng-7253	249	9	for	for	ADP
fumecheng-7253	249	10	different	different	ADJ
fumecheng-7253	249	11	values	value	NOUN
fumecheng-7253	249	12	of	of	ADP
fumecheng-7253	249	13	thermal	thermal	ADJ
fumecheng-7253	249	14	conductivity	conductivity	NOUN
fumecheng-7253	249	15	parameter	parameter	NOUN
fumecheng-7253	249	16	𝐾1	𝐾1	PROPN
fumecheng-7253	249	17	is	be	AUX
fumecheng-7253	249	18	shown	show	VERB
fumecheng-7253	249	19	in	in	ADP
fumecheng-7253	249	20	fig	fig	NOUN
fumecheng-7253	249	21	.	.	PUNCT
fumecheng-7253	250	1	2	2	NUM
fumecheng-7253	250	2	.	.	X
fumecheng-7253	250	3	as	as	SCONJ
fumecheng-7253	250	4	can	can	AUX
fumecheng-7253	250	5	be	be	AUX
fumecheng-7253	250	6	seen	see	VERB
fumecheng-7253	250	7	,	,	PUNCT
fumecheng-7253	250	8	increasing	increase	VERB
fumecheng-7253	250	9	the	the	DET
fumecheng-7253	250	10	values	value	NOUN
fumecheng-7253	250	11	of	of	ADP
fumecheng-7253	250	12	parameter	parameter	PROPN
fumecheng-7253	250	13	𝐾1	𝐾1	PROPN
fumecheng-7253	250	14	results	result	VERB
fumecheng-7253	250	15	temperature	temperature	NOUN
fumecheng-7253	250	16	-	-	PUNCT
fumecheng-7253	250	17	dependent	dependent	ADJ
fumecheng-7253	250	18	physical	physical	ADJ
fumecheng-7253	250	19	characteristics	characteristic	NOUN
fumecheng-7253	250	20	of	of	ADP
fumecheng-7253	250	21	rotating	rotate	VERB
fumecheng-7253	250	22	nonlocal	nonlocal	ADJ
fumecheng-7253	250	23	nanobeams	nanobeam	NOUN
fumecheng-7253	250	24	subject	subject	ADJ
fumecheng-7253	250	25	to	to	ADP
fumecheng-7253	250	26	...	...	PUNCT
fumecheng-7253	250	27	645	645	NUM
fumecheng-7253	250	28	in	in	ADP
fumecheng-7253	250	29	decreasing	decrease	VERB
fumecheng-7253	250	30	lateral	lateral	ADJ
fumecheng-7253	250	31	vibration	vibration	NOUN
fumecheng-7253	250	32	𝑤.	𝑤.	NOUN
fumecheng-7253	250	33	fig	fig	NOUN
fumecheng-7253	250	34	.	.	PUNCT
fumecheng-7253	251	1	2	2	NUM
fumecheng-7253	251	2	illustrates	illustrate	VERB
fumecheng-7253	251	3	that	that	SCONJ
fumecheng-7253	251	4	the	the	DET
fumecheng-7253	251	5	deflection	deflection	NOUN
fumecheng-7253	251	6	distribution	distribution	NOUN
fumecheng-7253	251	7	𝑤	𝑤	NOUN
fumecheng-7253	251	8	has	have	VERB
fumecheng-7253	251	9	zero	zero	NUM
fumecheng-7253	251	10	values	value	NOUN
fumecheng-7253	251	11	at	at	ADP
fumecheng-7253	251	12	both	both	DET
fumecheng-7253	251	13	ends	end	NOUN
fumecheng-7253	251	14	(	(	PUNCT
fumecheng-7253	251	15	i.e.	i.e.	X
fumecheng-7253	251	16	disappears	disappear	VERB
fumecheng-7253	251	17	)	)	PUNCT
fumecheng-7253	251	18	and	and	CCONJ
fumecheng-7253	251	19	meets	meet	VERB
fumecheng-7253	251	20	the	the	DET
fumecheng-7253	251	21	limit	limit	NOUN
fumecheng-7253	251	22	conditions	condition	NOUN
fumecheng-7253	251	23	of	of	ADP
fumecheng-7253	251	24	the	the	DET
fumecheng-7253	251	25	rotating	rotate	VERB
fumecheng-7253	251	26	nanobeam	nanobeam	NOUN
fumecheng-7253	251	27	at	at	ADP
fumecheng-7253	251	28	𝑥	𝑥	NOUN
fumecheng-7253	251	29	=	=	SYM
fumecheng-7253	251	30	0	0	NUM
fumecheng-7253	251	31	and	and	CCONJ
fumecheng-7253	251	32	𝑥	𝑥	NOUN
fumecheng-7253	251	33	=	=	SYM
fumecheng-7253	251	34	𝐿.	𝐿.	VERB
fumecheng-7253	251	35	temperature	temperature	NOUN
fumecheng-7253	251	36	𝜃	𝜃	NOUN
fumecheng-7253	251	37	is	be	AUX
fumecheng-7253	251	38	also	also	ADV
fumecheng-7253	251	39	depicted	depict	VERB
fumecheng-7253	251	40	in	in	ADP
fumecheng-7253	251	41	terms	term	NOUN
fumecheng-7253	251	42	of	of	ADP
fumecheng-7253	251	43	parameter	parameter	PROPN
fumecheng-7253	251	44	𝐾1	𝐾1	PROPN
fumecheng-7253	251	45	in	in	ADP
fumecheng-7253	251	46	fig	fig	NOUN
fumecheng-7253	251	47	.	.	PUNCT
fumecheng-7253	252	1	3	3	X
fumecheng-7253	252	2	.	.	X
fumecheng-7253	252	3	temperature	temperature	NOUN
fumecheng-7253	252	4	𝜃	𝜃	NOUN
fumecheng-7253	252	5	will	will	AUX
fumecheng-7253	252	6	decrease	decrease	VERB
fumecheng-7253	252	7	while	while	SCONJ
fumecheng-7253	252	8	distance	distance	NOUN
fumecheng-7253	252	9	x	x	PRON
fumecheng-7253	252	10	becomes	become	VERB
fumecheng-7253	252	11	larger	large	ADJ
fumecheng-7253	252	12	to	to	PART
fumecheng-7253	252	13	drive	drive	VERB
fumecheng-7253	252	14	towards	towards	ADP
fumecheng-7253	252	15	wave	wave	NOUN
fumecheng-7253	252	16	propagation	propagation	NOUN
fumecheng-7253	252	17	,	,	PUNCT
fumecheng-7253	252	18	as	as	SCONJ
fumecheng-7253	252	19	shown	show	VERB
fumecheng-7253	252	20	in	in	ADP
fumecheng-7253	252	21	fig	fig	NOUN
fumecheng-7253	252	22	.	.	PUNCT
fumecheng-7253	253	1	3	3	X
fumecheng-7253	253	2	.	.	X
fumecheng-7253	253	3	from	from	ADP
fumecheng-7253	253	4	theoretical	theoretical	ADJ
fumecheng-7253	253	5	experiments	experiment	NOUN
fumecheng-7253	253	6	,	,	PUNCT
fumecheng-7253	253	7	it	it	PRON
fumecheng-7253	253	8	is	be	AUX
fumecheng-7253	253	9	found	find	VERB
fumecheng-7253	253	10	that	that	SCONJ
fumecheng-7253	253	11	the	the	DET
fumecheng-7253	253	12	thermal	thermal	ADJ
fumecheng-7253	253	13	conductivity	conductivity	NOUN
fumecheng-7253	253	14	of	of	ADP
fumecheng-7253	253	15	pure	pure	ADJ
fumecheng-7253	253	16	metals	metal	NOUN
fumecheng-7253	253	17	decreases	decrease	NOUN
fumecheng-7253	253	18	as	as	ADP
fumecheng-7253	253	19	the	the	DET
fumecheng-7253	253	20	temperature	temperature	NOUN
fumecheng-7253	253	21	increases	increase	NOUN
fumecheng-7253	253	22	.	.	PUNCT
fumecheng-7253	254	1	however	however	ADV
fumecheng-7253	254	2	,	,	PUNCT
fumecheng-7253	254	3	the	the	DET
fumecheng-7253	254	4	thermal	thermal	ADJ
fumecheng-7253	254	5	conductivity	conductivity	NOUN
fumecheng-7253	254	6	drops	drop	VERB
fumecheng-7253	254	7	dramatically	dramatically	ADV
fumecheng-7253	254	8	as	as	SCONJ
fumecheng-7253	254	9	the	the	DET
fumecheng-7253	254	10	temperatures	temperature	NOUN
fumecheng-7253	254	11	exceed	exceed	VERB
fumecheng-7253	254	12	absolute	absolute	ADJ
fumecheng-7253	254	13	zero	zero	NUM
fumecheng-7253	254	14	[	[	X
fumecheng-7253	254	15	48	48	NUM
fumecheng-7253	254	16	]	]	PUNCT
fumecheng-7253	254	17	.	.	PUNCT
fumecheng-7253	255	1	fig	fig	NOUN
fumecheng-7253	255	2	.	.	PUNCT
fumecheng-7253	256	1	3	3	NUM
fumecheng-7253	256	2	indicates	indicate	VERB
fumecheng-7253	256	3	that	that	SCONJ
fumecheng-7253	256	4	any	any	DET
fumecheng-7253	256	5	reduction	reduction	NOUN
fumecheng-7253	256	6	in	in	ADP
fumecheng-7253	256	7	parameter	parameter	PROPN
fumecheng-7253	256	8	𝐾1	𝐾1	PROPN
fumecheng-7253	256	9	results	result	NOUN
fumecheng-7253	256	10	in	in	ADP
fumecheng-7253	256	11	increasing	increase	VERB
fumecheng-7253	256	12	temperature	temperature	NOUN
fumecheng-7253	256	13	values	value	NOUN
fumecheng-7253	256	14	𝜃.	𝜃.	ADP
fumecheng-7253	256	15	this	this	DET
fumecheng-7253	256	16	phenomenon	phenomenon	NOUN
fumecheng-7253	256	17	is	be	AUX
fumecheng-7253	256	18	verified	verify	VERB
fumecheng-7253	256	19	by	by	ADP
fumecheng-7253	256	20	the	the	DET
fumecheng-7253	256	21	experimental	experimental	ADJ
fumecheng-7253	256	22	results	result	NOUN
fumecheng-7253	256	23	reported	report	VERB
fumecheng-7253	256	24	by	by	ADP
fumecheng-7253	256	25	abo‐dahab	abo‐dahab	X
fumecheng-7253	256	26	et	et	PROPN
fumecheng-7253	256	27	al	al	PROPN
fumecheng-7253	256	28	.	.	PUNCT
fumecheng-7253	257	1	[	[	X
fumecheng-7253	257	2	49	49	NUM
fumecheng-7253	257	3	]	]	PUNCT
fumecheng-7253	257	4	.	.	PUNCT
fumecheng-7253	258	1	fig	fig	NOUN
fumecheng-7253	258	2	.	.	PUNCT
fumecheng-7253	259	1	2	2	NUM
fumecheng-7253	259	2	deflection	deflection	NOUN
fumecheng-7253	259	3	𝑤	𝑤	ADP
fumecheng-7253	259	4	under	under	ADP
fumecheng-7253	259	5	the	the	DET
fumecheng-7253	259	6	influence	influence	NOUN
fumecheng-7253	259	7	of	of	ADP
fumecheng-7253	259	8	variable	variable	ADJ
fumecheng-7253	259	9	thermal	thermal	ADJ
fumecheng-7253	259	10	properties	property	NOUN
fumecheng-7253	259	11	fig	fig	NOUN
fumecheng-7253	259	12	.	.	PUNCT
fumecheng-7253	260	1	3	3	NUM
fumecheng-7253	260	2	temperature	temperature	NOUN
fumecheng-7253	260	3	𝜃	𝜃	NOUN
fumecheng-7253	260	4	under	under	ADP
fumecheng-7253	260	5	the	the	DET
fumecheng-7253	260	6	influence	influence	NOUN
fumecheng-7253	260	7	of	of	ADP
fumecheng-7253	260	8	variable	variable	ADJ
fumecheng-7253	260	9	thermal	thermal	ADJ
fumecheng-7253	260	10	properties	property	NOUN
fumecheng-7253	260	11	fig	fig	NOUN
fumecheng-7253	260	12	.	.	PUNCT
fumecheng-7253	261	1	4	4	NUM
fumecheng-7253	261	2	demonstrates	demonstrate	VERB
fumecheng-7253	261	3	that	that	SCONJ
fumecheng-7253	261	4	the	the	DET
fumecheng-7253	261	5	values	value	NOUN
fumecheng-7253	261	6	of	of	ADP
fumecheng-7253	261	7	displacement	displacement	ADJ
fumecheng-7253	261	8	decrease	decrease	NOUN
fumecheng-7253	261	9	from	from	ADP
fumecheng-7253	261	10	0	0	NUM
fumecheng-7253	261	11	to	to	ADP
fumecheng-7253	261	12	0.3	0.3	NUM
fumecheng-7253	261	13	and	and	CCONJ
fumecheng-7253	261	14	consequently	consequently	ADV
fumecheng-7253	261	15	in	in	ADP
fumecheng-7253	261	16	the	the	DET
fumecheng-7253	261	17	range	range	NOUN
fumecheng-7253	261	18	0.3	0.3	NUM
fumecheng-7253	261	19	to	to	PART
fumecheng-7253	261	20	0.8	0.8	NUM
fumecheng-7253	261	21	shift	shift	VERB
fumecheng-7253	261	22	upward	upward	ADV
fumecheng-7253	261	23	to	to	ADP
fumecheng-7253	261	24	the	the	DET
fumecheng-7253	261	25	highest	high	ADJ
fumecheng-7253	261	26	amplifications	amplification	NOUN
fumecheng-7253	261	27	.	.	PUNCT
fumecheng-7253	262	1	in	in	ADP
fumecheng-7253	262	2	addition	addition	NOUN
fumecheng-7253	262	3	,	,	PUNCT
fumecheng-7253	262	4	the	the	DET
fumecheng-7253	262	5	646	646	NUM
fumecheng-7253	262	6	a.	a.	NOUN
fumecheng-7253	262	7	e.	e.	PROPN
fumecheng-7253	262	8	abouelregal	abouelregal	PROPN
fumecheng-7253	262	9	,	,	PUNCT
fumecheng-7253	262	10	h.	h.	PROPN
fumecheng-7253	262	11	m.	m.	PROPN
fumecheng-7253	262	12	sedighi	sedighi	PROPN
fumecheng-7253	262	13	,	,	PUNCT
fumecheng-7253	262	14	s.	s.	PROPN
fumecheng-7253	262	15	a.	a.	PROPN
fumecheng-7253	262	16	faghidian	faghidian	PROPN
fumecheng-7253	262	17	,	,	PUNCT
fumecheng-7253	262	18	a.	a.	PROPN
fumecheng-7253	262	19	h.	h.	PROPN
fumecheng-7253	262	20	shirazi	shirazi	PROPN
fumecheng-7253	262	21	values	value	NOUN
fumecheng-7253	262	22	of	of	ADP
fumecheng-7253	262	23	𝑢	𝑢	PRON
fumecheng-7253	262	24	vary	vary	VERB
fumecheng-7253	262	25	linearly	linearly	ADV
fumecheng-7253	262	26	in	in	ADP
fumecheng-7253	262	27	the	the	DET
fumecheng-7253	262	28	last	last	ADJ
fumecheng-7253	262	29	interval	interval	NOUN
fumecheng-7253	262	30	0.8	0.8	NUM
fumecheng-7253	262	31	≤	≤	NUM
fumecheng-7253	262	32	𝑥	𝑥	DET
fumecheng-7253	262	33	≤	≤	NUM
fumecheng-7253	262	34	1	1	NUM
fumecheng-7253	262	35	of	of	ADP
fumecheng-7253	262	36	wave	wave	NOUN
fumecheng-7253	262	37	propagation	propagation	NOUN
fumecheng-7253	262	38	.	.	PUNCT
fumecheng-7253	263	1	it	it	PRON
fumecheng-7253	263	2	should	should	AUX
fumecheng-7253	263	3	be	be	AUX
fumecheng-7253	263	4	noted	note	VERB
fumecheng-7253	263	5	that	that	SCONJ
fumecheng-7253	263	6	the	the	DET
fumecheng-7253	263	7	displacement	displacement	ADJ
fumecheng-7253	263	8	distribution	distribution	NOUN
fumecheng-7253	263	9	is	be	AUX
fumecheng-7253	263	10	highly	highly	ADV
fumecheng-7253	263	11	influenced	influence	VERB
fumecheng-7253	263	12	by	by	ADP
fumecheng-7253	263	13	the	the	DET
fumecheng-7253	263	14	variation	variation	NOUN
fumecheng-7253	263	15	of	of	ADP
fumecheng-7253	263	16	parameter	parameter	PROPN
fumecheng-7253	263	17	𝐾1	𝐾1	PROPN
fumecheng-7253	263	18	.	.	PUNCT
fumecheng-7253	264	1	according	accord	VERB
fumecheng-7253	264	2	to	to	ADP
fumecheng-7253	264	3	fig	fig	NOUN
fumecheng-7253	264	4	.	.	PUNCT
fumecheng-7253	265	1	5	5	NUM
fumecheng-7253	265	2	,	,	PUNCT
fumecheng-7253	265	3	the	the	DET
fumecheng-7253	265	4	effect	effect	NOUN
fumecheng-7253	265	5	of	of	ADP
fumecheng-7253	265	6	parameter	parameter	NOUN
fumecheng-7253	265	7	𝐾1is	𝐾1i	NOUN
fumecheng-7253	265	8	revealed	reveal	VERB
fumecheng-7253	265	9	as	as	ADP
fumecheng-7253	265	10	increasing	increase	VERB
fumecheng-7253	265	11	the	the	DET
fumecheng-7253	265	12	distribution	distribution	NOUN
fumecheng-7253	265	13	of	of	ADP
fumecheng-7253	265	14	bending	bend	VERB
fumecheng-7253	265	15	moment	moment	NOUN
fumecheng-7253	265	16	𝑀	𝑀	PROPN
fumecheng-7253	265	17	which	which	PRON
fumecheng-7253	265	18	implies	imply	VERB
fumecheng-7253	265	19	that	that	SCONJ
fumecheng-7253	265	20	the	the	DET
fumecheng-7253	265	21	impact	impact	NOUN
fumecheng-7253	265	22	of	of	ADP
fumecheng-7253	265	23	thermal	thermal	ADJ
fumecheng-7253	265	24	conductivity	conductivity	NOUN
fumecheng-7253	265	25	variation	variation	NOUN
fumecheng-7253	265	26	can	can	AUX
fumecheng-7253	265	27	not	not	PART
fumecheng-7253	265	28	be	be	AUX
fumecheng-7253	265	29	disregarded	disregard	VERB
fumecheng-7253	265	30	[	[	X
fumecheng-7253	265	31	48	48	NUM
fumecheng-7253	265	32	]	]	PUNCT
fumecheng-7253	265	33	.	.	PUNCT
fumecheng-7253	266	1	the	the	DET
fumecheng-7253	266	2	mechanical	mechanical	ADJ
fumecheng-7253	266	3	characteristics	characteristic	NOUN
fumecheng-7253	266	4	of	of	ADP
fumecheng-7253	266	5	the	the	DET
fumecheng-7253	266	6	nanobeam	nanobeam	NOUN
fumecheng-7253	266	7	emphasize	emphasize	VERB
fumecheng-7253	266	8	that	that	SCONJ
fumecheng-7253	266	9	the	the	DET
fumecheng-7253	266	10	wave	wave	NOUN
fumecheng-7253	266	11	propagates	propagate	VERB
fumecheng-7253	266	12	in	in	ADP
fumecheng-7253	266	13	the	the	DET
fumecheng-7253	266	14	medium	medium	NOUN
fumecheng-7253	266	15	with	with	ADP
fumecheng-7253	266	16	finite	finite	ADJ
fumecheng-7253	266	17	speed	speed	NOUN
fumecheng-7253	266	18	[	[	X
fumecheng-7253	266	19	49	49	NUM
fumecheng-7253	266	20	]	]	PUNCT
fumecheng-7253	266	21	.	.	PUNCT
fumecheng-7253	267	1	fig	fig	NOUN
fumecheng-7253	267	2	.	.	PUNCT
fumecheng-7253	268	1	4	4	NUM
fumecheng-7253	268	2	displacement	displacement	ADJ
fumecheng-7253	268	3	𝑢	𝑢	NOUN
fumecheng-7253	268	4	under	under	ADP
fumecheng-7253	268	5	the	the	DET
fumecheng-7253	268	6	influence	influence	NOUN
fumecheng-7253	268	7	of	of	ADP
fumecheng-7253	268	8	variable	variable	ADJ
fumecheng-7253	268	9	thermal	thermal	ADJ
fumecheng-7253	268	10	properties	property	NOUN
fumecheng-7253	268	11	fig	fig	NOUN
fumecheng-7253	268	12	.	.	PUNCT
fumecheng-7253	269	1	5	5	NUM
fumecheng-7253	269	2	bending	bend	VERB
fumecheng-7253	269	3	moment	moment	NOUN
fumecheng-7253	269	4	𝑀	𝑀	PROPN
fumecheng-7253	270	1	under	under	ADP
fumecheng-7253	270	2	the	the	DET
fumecheng-7253	270	3	influence	influence	NOUN
fumecheng-7253	270	4	of	of	ADP
fumecheng-7253	270	5	variable	variable	ADJ
fumecheng-7253	270	6	thermal	thermal	ADJ
fumecheng-7253	270	7	properties	property	NOUN
fumecheng-7253	270	8	in	in	ADP
fumecheng-7253	270	9	the	the	DET
fumecheng-7253	270	10	second	second	ADJ
fumecheng-7253	270	11	case	case	NOUN
fumecheng-7253	270	12	,	,	PUNCT
fumecheng-7253	270	13	the	the	DET
fumecheng-7253	270	14	influence	influence	NOUN
fumecheng-7253	270	15	of	of	ADP
fumecheng-7253	270	16	angular	angular	ADJ
fumecheng-7253	270	17	rotation	rotation	NOUN
fumecheng-7253	270	18	velocity	velocity	NOUN
fumecheng-7253	270	19	ω	ω	PROPN
fumecheng-7253	270	20	on	on	ADP
fumecheng-7253	270	21	the	the	DET
fumecheng-7253	270	22	dimensionless	dimensionless	NOUN
fumecheng-7253	270	23	field	field	NOUN
fumecheng-7253	270	24	quantities	quantity	NOUN
fumecheng-7253	270	25	is	be	AUX
fumecheng-7253	270	26	illustrated	illustrate	VERB
fumecheng-7253	270	27	.	.	PUNCT
fumecheng-7253	271	1	it	it	PRON
fumecheng-7253	271	2	is	be	AUX
fumecheng-7253	271	3	supposed	suppose	VERB
fumecheng-7253	271	4	that	that	SCONJ
fumecheng-7253	271	5	our	our	PRON
fumecheng-7253	271	6	findings	finding	NOUN
fumecheng-7253	271	7	are	be	AUX
fumecheng-7253	271	8	consistent	consistent	ADJ
fumecheng-7253	271	9	with	with	ADP
fumecheng-7253	271	10	both	both	PRON
fumecheng-7253	271	11	nonlocal	nonlocal	ADJ
fumecheng-7253	271	12	parameter	parameter	NOUN
fumecheng-7253	271	13	𝜉	𝜉	PROPN
fumecheng-7253	271	14	,	,	PUNCT
fumecheng-7253	271	15	the	the	DET
fumecheng-7253	271	16	angular	angular	ADJ
fumecheng-7253	271	17	excitation	excitation	NOUN
fumecheng-7253	271	18	of	of	ADP
fumecheng-7253	271	19	thermal	thermal	ADJ
fumecheng-7253	271	20	load	load	NOUN
fumecheng-7253	271	21	𝜔	𝜔	ADP
fumecheng-7253	271	22	,	,	PUNCT
fumecheng-7253	271	23	and	and	CCONJ
fumecheng-7253	271	24	phase	phase	NOUN
fumecheng-7253	271	25	lags	lag	VERB
fumecheng-7253	271	26	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	271	27	and	and	CCONJ
fumecheng-7253	271	28	𝜏𝜃.	𝜏𝜃.	VERB
fumecheng-7253	271	29	our	our	PRON
fumecheng-7253	271	30	calculations	calculation	NOUN
fumecheng-7253	271	31	are	be	AUX
fumecheng-7253	271	32	performed	perform	VERB
fumecheng-7253	271	33	using	use	VERB
fumecheng-7253	271	34	fixed	fix	VERB
fumecheng-7253	271	35	values	value	NOUN
fumecheng-7253	271	36	for	for	ADP
fumecheng-7253	271	37	system	system	NOUN
fumecheng-7253	271	38	parameters	parameter	NOUN
fumecheng-7253	271	39	as	as	ADP
fumecheng-7253	271	40	𝜉	𝜉	X
fumecheng-7253	271	41	=	=	NOUN
fumecheng-7253	271	42	0.1	0.1	NUM
fumecheng-7253	271	43	,	,	PUNCT
fumecheng-7253	271	44	𝜔	𝜔	PRON
fumecheng-7253	271	45	=	=	SYM
fumecheng-7253	271	46	5	5	NUM
fumecheng-7253	271	47	,	,	PUNCT
fumecheng-7253	271	48	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	271	49	=	=	NUM
fumecheng-7253	271	50	0.02	0.02	NUM
fumecheng-7253	271	51	and	and	CCONJ
fumecheng-7253	271	52	𝜏𝜃	𝜏𝜃	X
fumecheng-7253	271	53	=	=	NOUN
fumecheng-7253	271	54	0.01	0.01	NUM
fumecheng-7253	271	55	.	.	PUNCT
fumecheng-7253	272	1	temperature	temperature	NOUN
fumecheng-7253	272	2	-	-	PUNCT
fumecheng-7253	272	3	dependent	dependent	ADJ
fumecheng-7253	272	4	physical	physical	ADJ
fumecheng-7253	272	5	characteristics	characteristic	NOUN
fumecheng-7253	272	6	of	of	ADP
fumecheng-7253	272	7	rotating	rotate	VERB
fumecheng-7253	272	8	nonlocal	nonlocal	ADJ
fumecheng-7253	272	9	nanobeams	nanobeam	NOUN
fumecheng-7253	272	10	subject	subject	ADJ
fumecheng-7253	272	11	to	to	ADP
fumecheng-7253	272	12	...	...	PUNCT
fumecheng-7253	272	13	647	647	NUM
fumecheng-7253	272	14	the	the	DET
fumecheng-7253	272	15	variations	variation	NOUN
fumecheng-7253	272	16	of	of	ADP
fumecheng-7253	272	17	the	the	DET
fumecheng-7253	272	18	fields	field	NOUN
fumecheng-7253	272	19	studied	study	VERB
fumecheng-7253	272	20	for	for	ADP
fumecheng-7253	272	21	three	three	NUM
fumecheng-7253	272	22	assigned	assign	VERB
fumecheng-7253	272	23	values	value	NOUN
fumecheng-7253	272	24	of	of	ADP
fumecheng-7253	272	25	rotational	rotational	ADJ
fumecheng-7253	272	26	speed	speed	NOUN
fumecheng-7253	272	27	(	(	PUNCT
fumecheng-7253	272	28	ω	ω	NOUN
fumecheng-7253	272	29	=	=	SYM
fumecheng-7253	272	30	0	0	NUM
fumecheng-7253	272	31	,	,	PUNCT
fumecheng-7253	272	32	0.1	0.1	NUM
fumecheng-7253	272	33	,	,	PUNCT
fumecheng-7253	272	34	0.3	0.3	NUM
fumecheng-7253	272	35	)	)	PUNCT
fumecheng-7253	272	36	are	be	AUX
fumecheng-7253	272	37	shown	show	VERB
fumecheng-7253	272	38	in	in	ADP
fumecheng-7253	272	39	figs	fig	NOUN
fumecheng-7253	272	40	.	.	PUNCT
fumecheng-7253	273	1	6	6	NUM
fumecheng-7253	273	2	-	-	SYM
fumecheng-7253	273	3	9	9	NUM
fumecheng-7253	273	4	.	.	PUNCT
fumecheng-7253	274	1	in	in	ADP
fumecheng-7253	274	2	the	the	DET
fumecheng-7253	274	3	case	case	NOUN
fumecheng-7253	274	4	of	of	ADP
fumecheng-7253	274	5	stationary	stationary	ADJ
fumecheng-7253	274	6	nanobeam	nanobeam	NOUN
fumecheng-7253	274	7	,	,	PUNCT
fumecheng-7253	274	8	the	the	DET
fumecheng-7253	274	9	rotational	rotational	ADJ
fumecheng-7253	274	10	speed	speed	NOUN
fumecheng-7253	274	11	is	be	AUX
fumecheng-7253	274	12	set	set	VERB
fumecheng-7253	274	13	to	to	PART
fumecheng-7253	274	14	be	be	AUX
fumecheng-7253	274	15	zero	zero	NUM
fumecheng-7253	274	16	(	(	PUNCT
fumecheng-7253	274	17	ω	ω	NOUN
fumecheng-7253	274	18	=	=	NOUN
fumecheng-7253	274	19	0	0	NUM
fumecheng-7253	274	20	)	)	PUNCT
fumecheng-7253	274	21	,	,	PUNCT
fumecheng-7253	274	22	as	as	ADP
fumecheng-7253	274	23	a	a	DET
fumecheng-7253	274	24	special	special	ADJ
fumecheng-7253	274	25	case	case	NOUN
fumecheng-7253	274	26	in	in	ADP
fumecheng-7253	274	27	our	our	PRON
fumecheng-7253	274	28	simulations	simulation	NOUN
fumecheng-7253	274	29	.	.	PUNCT
fumecheng-7253	275	1	the	the	DET
fumecheng-7253	275	2	variation	variation	NOUN
fumecheng-7253	275	3	of	of	ADP
fumecheng-7253	275	4	angular	angular	ADJ
fumecheng-7253	275	5	speed	speed	NOUN
fumecheng-7253	275	6	ω	ω	NOUN
fumecheng-7253	275	7	which	which	PRON
fumecheng-7253	275	8	cases	case	VERB
fumecheng-7253	275	9	the	the	DET
fumecheng-7253	275	10	variation	variation	NOUN
fumecheng-7253	275	11	in	in	ADP
fumecheng-7253	275	12	deflection	deflection	NOUN
fumecheng-7253	275	13	w	w	PROPN
fumecheng-7253	275	14	,	,	PUNCT
fumecheng-7253	275	15	is	be	AUX
fumecheng-7253	275	16	depicted	depict	VERB
fumecheng-7253	275	17	in	in	ADP
fumecheng-7253	275	18	fig	fig	NOUN
fumecheng-7253	275	19	.	.	PUNCT
fumecheng-7253	276	1	6	6	NUM
fumecheng-7253	276	2	.	.	X
fumecheng-7253	276	3	as	as	SCONJ
fumecheng-7253	276	4	indicated	indicate	VERB
fumecheng-7253	276	5	,	,	PUNCT
fumecheng-7253	276	6	this	this	DET
fumecheng-7253	276	7	parameter	parameter	NOUN
fumecheng-7253	276	8	is	be	AUX
fumecheng-7253	276	9	found	find	VERB
fumecheng-7253	276	10	to	to	PART
fumecheng-7253	276	11	have	have	VERB
fumecheng-7253	276	12	a	a	DET
fumecheng-7253	276	13	substantial	substantial	ADJ
fumecheng-7253	276	14	effect	effect	NOUN
fumecheng-7253	276	15	on	on	ADP
fumecheng-7253	276	16	the	the	DET
fumecheng-7253	276	17	distribution	distribution	NOUN
fumecheng-7253	276	18	of	of	ADP
fumecheng-7253	276	19	deflection	deflection	NOUN
fumecheng-7253	276	20	𝑤	𝑤	VERB
fumecheng-7253	276	21	by	by	ADP
fumecheng-7253	276	22	comparing	compare	VERB
fumecheng-7253	276	23	the	the	DET
fumecheng-7253	276	24	results	result	NOUN
fumecheng-7253	276	25	of	of	ADP
fumecheng-7253	276	26	stationary	stationary	ADJ
fumecheng-7253	276	27	beam	beam	NOUN
fumecheng-7253	276	28	with	with	ADP
fumecheng-7253	276	29	rotating	rotate	VERB
fumecheng-7253	276	30	one	one	NUM
fumecheng-7253	276	31	.	.	PUNCT
fumecheng-7253	277	1	when	when	SCONJ
fumecheng-7253	277	2	angular	angular	ADJ
fumecheng-7253	277	3	velocity	velocity	NOUN
fumecheng-7253	277	4	ω	ω	PROPN
fumecheng-7253	277	5	becomes	become	VERB
fumecheng-7253	277	6	larger	large	ADJ
fumecheng-7253	277	7	,	,	PUNCT
fumecheng-7253	277	8	deflection	deflection	NOUN
fumecheng-7253	277	9	𝑤	𝑤	ADP
fumecheng-7253	277	10	takes	take	VERB
fumecheng-7253	277	11	smaller	small	ADJ
fumecheng-7253	277	12	values	value	NOUN
fumecheng-7253	277	13	.	.	PUNCT
fumecheng-7253	278	1	the	the	DET
fumecheng-7253	278	2	obtained	obtain	VERB
fumecheng-7253	278	3	results	result	NOUN
fumecheng-7253	278	4	are	be	AUX
fumecheng-7253	278	5	consistent	consistent	ADJ
fumecheng-7253	278	6	with	with	ADP
fumecheng-7253	278	7	those	those	PRON
fumecheng-7253	278	8	reported	report	VERB
fumecheng-7253	278	9	by	by	ADP
fumecheng-7253	278	10	ebrahimi	ebrahimi	PROPN
fumecheng-7253	278	11	et	et	PROPN
fumecheng-7253	278	12	al	al	PROPN
fumecheng-7253	278	13	.	.	PUNCT
fumecheng-7253	279	1	[	[	X
fumecheng-7253	279	2	50	50	NUM
fumecheng-7253	279	3	]	]	PUNCT
fumecheng-7253	279	4	.	.	PUNCT
fumecheng-7253	280	1	the	the	DET
fumecheng-7253	280	2	variation	variation	NOUN
fumecheng-7253	280	3	in	in	ADP
fumecheng-7253	280	4	temperature	temperature	NOUN
fumecheng-7253	280	5	𝜃	𝜃	NOUN
fumecheng-7253	280	6	with	with	ADP
fumecheng-7253	280	7	respect	respect	NOUN
fumecheng-7253	280	8	to	to	ADP
fumecheng-7253	280	9	distance	distance	NOUN
fumecheng-7253	280	10	𝑥	𝑥	NOUN
fumecheng-7253	280	11	is	be	AUX
fumecheng-7253	280	12	verified	verify	VERB
fumecheng-7253	280	13	by	by	ADP
fumecheng-7253	280	14	assuming	assume	VERB
fumecheng-7253	280	15	different	different	ADJ
fumecheng-7253	280	16	values	value	NOUN
fumecheng-7253	280	17	for	for	ADP
fumecheng-7253	280	18	rotational	rotational	ADJ
fumecheng-7253	280	19	speed	speed	NOUN
fumecheng-7253	280	20	ω	ω	NOUN
fumecheng-7253	280	21	,	,	PUNCT
fumecheng-7253	280	22	as	as	SCONJ
fumecheng-7253	280	23	demonstrated	demonstrate	VERB
fumecheng-7253	280	24	in	in	ADP
fumecheng-7253	280	25	fig	fig	NOUN
fumecheng-7253	280	26	,	,	PUNCT
fumecheng-7253	280	27	7	7	NUM
fumecheng-7253	280	28	.	.	PUNCT
fumecheng-7253	280	29	fig	fig	NOUN
fumecheng-7253	280	30	.	.	PUNCT
fumecheng-7253	281	1	6	6	NUM
fumecheng-7253	281	2	deflection	deflection	NOUN
fumecheng-7253	281	3	𝑤	𝑤	ADP
fumecheng-7253	281	4	vs	vs	ADP
fumecheng-7253	281	5	angular	angular	ADJ
fumecheng-7253	281	6	velocity	velocity	NOUN
fumecheng-7253	281	7	ω	ω	NUM
fumecheng-7253	281	8	fig	fig	NOUN
fumecheng-7253	281	9	.	.	PUNCT
fumecheng-7253	282	1	7	7	NUM
fumecheng-7253	282	2	temperature	temperature	NOUN
fumecheng-7253	282	3	𝜃	𝜃	NOUN
fumecheng-7253	282	4	vs	vs	ADP
fumecheng-7253	282	5	angular	angular	ADJ
fumecheng-7253	282	6	velocity	velocity	NOUN
fumecheng-7253	282	7	ω	ω	PROPN
fumecheng-7253	282	8	clearly	clearly	ADV
fumecheng-7253	282	9	,	,	PUNCT
fumecheng-7253	282	10	the	the	DET
fumecheng-7253	282	11	temperature	temperature	NOUN
fumecheng-7253	282	12	shifts	shift	NOUN
fumecheng-7253	282	13	upward	upward	ADV
fumecheng-7253	282	14	as	as	ADP
fumecheng-7253	282	15	angular	angular	ADJ
fumecheng-7253	282	16	velocity	velocity	NOUN
fumecheng-7253	282	17	ω	ω	NOUN
fumecheng-7253	282	18	increases	increase	NOUN
fumecheng-7253	282	19	which	which	PRON
fumecheng-7253	282	20	is	be	AUX
fumecheng-7253	282	21	also	also	ADV
fumecheng-7253	282	22	consistent	consistent	ADJ
fumecheng-7253	282	23	with	with	ADP
fumecheng-7253	282	24	the	the	DET
fumecheng-7253	282	25	observations	observation	NOUN
fumecheng-7253	282	26	of	of	ADP
fumecheng-7253	282	27	ebrahimi	ebrahimi	PROPN
fumecheng-7253	282	28	and	and	CCONJ
fumecheng-7253	282	29	shafie	shafie	NOUN
fumecheng-7253	282	30	[	[	X
fumecheng-7253	282	31	50	50	NUM
fumecheng-7253	282	32	,	,	PUNCT
fumecheng-7253	282	33	51	51	NUM
fumecheng-7253	282	34	]	]	PUNCT
fumecheng-7253	282	35	.	.	PUNCT
fumecheng-7253	283	1	648	648	NUM
fumecheng-7253	283	2	a.	a.	PROPN
fumecheng-7253	283	3	e.	e.	PROPN
fumecheng-7253	283	4	abouelregal	abouelregal	PROPN
fumecheng-7253	283	5	,	,	PUNCT
fumecheng-7253	283	6	h.	h.	PROPN
fumecheng-7253	283	7	m.	m.	PROPN
fumecheng-7253	283	8	sedighi	sedighi	PROPN
fumecheng-7253	283	9	,	,	PUNCT
fumecheng-7253	283	10	s.	s.	PROPN
fumecheng-7253	283	11	a.	a.	PROPN
fumecheng-7253	283	12	faghidian	faghidian	PROPN
fumecheng-7253	283	13	,	,	PUNCT
fumecheng-7253	283	14	a.	a.	PROPN
fumecheng-7253	283	15	h.	h.	PROPN
fumecheng-7253	283	16	shirazi	shirazi	PROPN
fumecheng-7253	283	17	fig	fig	PROPN
fumecheng-7253	283	18	.	.	PUNCT
fumecheng-7253	283	19	8	8	NUM
fumecheng-7253	283	20	presents	present	VERB
fumecheng-7253	283	21	a	a	DET
fumecheng-7253	283	22	survey	survey	NOUN
fumecheng-7253	283	23	of	of	ADP
fumecheng-7253	283	24	the	the	DET
fumecheng-7253	283	25	impact	impact	NOUN
fumecheng-7253	283	26	of	of	ADP
fumecheng-7253	283	27	angular	angular	ADJ
fumecheng-7253	283	28	speed	speed	NOUN
fumecheng-7253	283	29	ω	ω	NOUN
fumecheng-7253	283	30	on	on	ADP
fumecheng-7253	283	31	the	the	DET
fumecheng-7253	283	32	variation	variation	NOUN
fumecheng-7253	283	33	of	of	ADP
fumecheng-7253	283	34	displacement	displacement	ADJ
fumecheng-7253	283	35	𝑢.	𝑢.	NOUN
fumecheng-7253	283	36	it	it	PRON
fumecheng-7253	283	37	is	be	AUX
fumecheng-7253	283	38	inferred	infer	VERB
fumecheng-7253	283	39	that	that	SCONJ
fumecheng-7253	283	40	the	the	DET
fumecheng-7253	283	41	curves	curve	NOUN
fumecheng-7253	283	42	that	that	PRON
fumecheng-7253	283	43	reflect	reflect	VERB
fumecheng-7253	283	44	the	the	DET
fumecheng-7253	283	45	displacement	displacement	ADJ
fumecheng-7253	283	46	field	field	NOUN
fumecheng-7253	283	47	are	be	AUX
fumecheng-7253	283	48	influenced	influence	VERB
fumecheng-7253	283	49	by	by	ADP
fumecheng-7253	283	50	the	the	DET
fumecheng-7253	283	51	rotation	rotation	NOUN
fumecheng-7253	283	52	.	.	PUNCT
fumecheng-7253	284	1	this	this	DET
fumecheng-7253	284	2	figure	figure	NOUN
fumecheng-7253	284	3	shows	show	VERB
fumecheng-7253	284	4	that	that	SCONJ
fumecheng-7253	284	5	at	at	ADP
fumecheng-7253	284	6	certain	certain	ADJ
fumecheng-7253	284	7	ranges	range	NOUN
fumecheng-7253	284	8	,	,	PUNCT
fumecheng-7253	284	9	by	by	ADP
fumecheng-7253	284	10	increasing	increase	VERB
fumecheng-7253	284	11	the	the	DET
fumecheng-7253	284	12	rotation	rotation	NOUN
fumecheng-7253	284	13	speed	speed	NOUN
fumecheng-7253	284	14	,	,	PUNCT
fumecheng-7253	284	15	the	the	DET
fumecheng-7253	284	16	distribution	distribution	NOUN
fumecheng-7253	284	17	of	of	ADP
fumecheng-7253	284	18	displacement	displacement	NOUN
fumecheng-7253	284	19	𝑢	𝑢	PRON
fumecheng-7253	284	20	sharply	sharply	ADV
fumecheng-7253	284	21	decreases	decrease	VERB
fumecheng-7253	284	22	at	at	ADP
fumecheng-7253	284	23	first	first	ADV
fumecheng-7253	284	24	and	and	CCONJ
fumecheng-7253	284	25	then	then	ADV
fumecheng-7253	284	26	slightly	slightly	ADV
fumecheng-7253	284	27	increases	increase	NOUN
fumecheng-7253	284	28	.	.	PUNCT
fumecheng-7253	285	1	fig	fig	NOUN
fumecheng-7253	285	2	.	.	PUNCT
fumecheng-7253	286	1	9	9	NUM
fumecheng-7253	286	2	shows	show	VERB
fumecheng-7253	286	3	the	the	DET
fumecheng-7253	286	4	influence	influence	NOUN
fumecheng-7253	286	5	of	of	ADP
fumecheng-7253	286	6	the	the	DET
fumecheng-7253	286	7	variation	variation	NOUN
fumecheng-7253	286	8	of	of	ADP
fumecheng-7253	286	9	angular	angular	ADJ
fumecheng-7253	286	10	velocity	velocity	NOUN
fumecheng-7253	286	11	ω	ω	NOUN
fumecheng-7253	286	12	on	on	ADP
fumecheng-7253	286	13	the	the	DET
fumecheng-7253	286	14	distribution	distribution	NOUN
fumecheng-7253	286	15	of	of	ADP
fumecheng-7253	286	16	bending	bend	VERB
fumecheng-7253	286	17	moment	moment	NOUN
fumecheng-7253	286	18	𝑀for	𝑀for	ADP
fumecheng-7253	286	19	rotating	rotating	NOUN
fumecheng-7253	286	20	nanobeams	nanobeam	NOUN
fumecheng-7253	286	21	.	.	PUNCT
fumecheng-7253	287	1	it	it	PRON
fumecheng-7253	287	2	is	be	AUX
fumecheng-7253	287	3	observed	observe	VERB
fumecheng-7253	287	4	from	from	ADP
fumecheng-7253	287	5	the	the	DET
fumecheng-7253	287	6	figure	figure	NOUN
fumecheng-7253	287	7	that	that	SCONJ
fumecheng-7253	287	8	the	the	DET
fumecheng-7253	287	9	rotation	rotation	NOUN
fumecheng-7253	287	10	of	of	ADP
fumecheng-7253	287	11	the	the	DET
fumecheng-7253	287	12	nanobeam	nanobeam	NOUN
fumecheng-7253	287	13	has	have	AUX
fumecheng-7253	287	14	a	a	DET
fumecheng-7253	287	15	great	great	ADJ
fumecheng-7253	287	16	effect	effect	NOUN
fumecheng-7253	287	17	on	on	ADP
fumecheng-7253	287	18	the	the	DET
fumecheng-7253	287	19	values	value	NOUN
fumecheng-7253	287	20	of	of	ADP
fumecheng-7253	287	21	bending	bend	VERB
fumecheng-7253	287	22	moment	moment	NOUN
fumecheng-7253	287	23	and	and	CCONJ
fumecheng-7253	287	24	the	the	DET
fumecheng-7253	287	25	amplitude	amplitude	NOUN
fumecheng-7253	287	26	of	of	ADP
fumecheng-7253	287	27	the	the	DET
fumecheng-7253	287	28	moment	moment	NOUN
fumecheng-7253	287	29	becomes	become	VERB
fumecheng-7253	287	30	larger	large	ADJ
fumecheng-7253	287	31	by	by	ADP
fumecheng-7253	287	32	increasing	increase	VERB
fumecheng-7253	287	33	angular	angular	ADJ
fumecheng-7253	287	34	velocity	velocity	NOUN
fumecheng-7253	287	35	ω	ω	PROPN
fumecheng-7253	287	36	.	.	PUNCT
fumecheng-7253	288	1	fig	fig	NOUN
fumecheng-7253	288	2	.	.	PUNCT
fumecheng-7253	289	1	8	8	NUM
fumecheng-7253	289	2	displacement	displacement	NOUN
fumecheng-7253	289	3	𝑢	𝑢	NOUN
fumecheng-7253	289	4	vs	vs	ADP
fumecheng-7253	289	5	angular	angular	ADJ
fumecheng-7253	289	6	velocity	velocity	NOUN
fumecheng-7253	289	7	ω	ω	NUM
fumecheng-7253	289	8	fig	fig	NOUN
fumecheng-7253	289	9	.	.	PUNCT
fumecheng-7253	290	1	9	9	NUM
fumecheng-7253	290	2	bending	bend	VERB
fumecheng-7253	290	3	moment	moment	NOUN
fumecheng-7253	290	4	𝑀	𝑀	PROPN
fumecheng-7253	290	5	vs	vs	ADP
fumecheng-7253	290	6	angular	angular	ADJ
fumecheng-7253	290	7	velocity	velocity	NOUN
fumecheng-7253	290	8	ω	ω	NUM
fumecheng-7253	290	9	one	one	NUM
fumecheng-7253	290	10	of	of	ADP
fumecheng-7253	290	11	the	the	DET
fumecheng-7253	290	12	objectives	objective	NOUN
fumecheng-7253	290	13	of	of	ADP
fumecheng-7253	290	14	this	this	DET
fumecheng-7253	290	15	study	study	NOUN
fumecheng-7253	290	16	is	be	AUX
fumecheng-7253	290	17	to	to	PART
fumecheng-7253	290	18	explore	explore	VERB
fumecheng-7253	290	19	the	the	DET
fumecheng-7253	290	20	mechanical	mechanical	ADJ
fumecheng-7253	290	21	features	feature	NOUN
fumecheng-7253	290	22	of	of	ADP
fumecheng-7253	290	23	certain	certain	ADJ
fumecheng-7253	290	24	nano	nano	NOUN
fumecheng-7253	290	25	-	-	PUNCT
fumecheng-7253	290	26	devices	device	NOUN
fumecheng-7253	290	27	such	such	ADJ
fumecheng-7253	290	28	as	as	ADP
fumecheng-7253	290	29	nano	nano	NOUN
fumecheng-7253	290	30	-	-	PUNCT
fumecheng-7253	290	31	turbine	turbine	NOUN
fumecheng-7253	290	32	blades	blade	NOUN
fumecheng-7253	290	33	[	[	X
fumecheng-7253	290	34	52	52	NUM
fumecheng-7253	290	35	]	]	PUNCT
fumecheng-7253	290	36	in	in	ADP
fumecheng-7253	290	37	the	the	DET
fumecheng-7253	290	38	presence	presence	NOUN
fumecheng-7253	290	39	of	of	ADP
fumecheng-7253	290	40	temperature	temperature	NOUN
fumecheng-7253	290	41	field	field	NOUN
fumecheng-7253	290	42	and	and	CCONJ
fumecheng-7253	290	43	angular	angular	ADJ
fumecheng-7253	290	44	velocity	velocity	NOUN
fumecheng-7253	290	45	which	which	PRON
fumecheng-7253	290	46	may	may	AUX
fumecheng-7253	290	47	provide	provide	VERB
fumecheng-7253	290	48	valuable	valuable	ADJ
fumecheng-7253	290	49	insights	insight	NOUN
fumecheng-7253	290	50	for	for	ADP
fumecheng-7253	290	51	designers	designer	NOUN
fumecheng-7253	290	52	and	and	CCONJ
fumecheng-7253	290	53	engineers	engineer	NOUN
fumecheng-7253	290	54	.	.	PUNCT
fumecheng-7253	291	1	from	from	ADP
fumecheng-7253	291	2	the	the	DET
fumecheng-7253	291	3	previous	previous	ADJ
fumecheng-7253	291	4	observations	observation	NOUN
fumecheng-7253	291	5	,	,	PUNCT
fumecheng-7253	291	6	one	one	PRON
fumecheng-7253	291	7	can	can	AUX
fumecheng-7253	291	8	also	also	ADV
fumecheng-7253	291	9	deduce	deduce	VERB
fumecheng-7253	291	10	the	the	DET
fumecheng-7253	291	11	major	major	ADJ
fumecheng-7253	291	12	impact	impact	NOUN
fumecheng-7253	291	13	of	of	ADP
fumecheng-7253	291	14	rotation	rotation	NOUN
fumecheng-7253	291	15	on	on	ADP
fumecheng-7253	291	16	the	the	DET
fumecheng-7253	291	17	temperature	temperature	NOUN
fumecheng-7253	291	18	-	-	PUNCT
fumecheng-7253	291	19	dependent	dependent	ADJ
fumecheng-7253	291	20	physical	physical	ADJ
fumecheng-7253	291	21	characteristics	characteristic	NOUN
fumecheng-7253	291	22	of	of	ADP
fumecheng-7253	291	23	rotating	rotate	VERB
fumecheng-7253	291	24	nonlocal	nonlocal	ADJ
fumecheng-7253	291	25	nanobeams	nanobeam	NOUN
fumecheng-7253	291	26	subject	subject	ADJ
fumecheng-7253	291	27	to	to	ADP
fumecheng-7253	291	28	...	...	PUNCT
fumecheng-7253	291	29	649	649	NUM
fumecheng-7253	291	30	distribution	distribution	NOUN
fumecheng-7253	291	31	of	of	ADP
fumecheng-7253	291	32	physical	physical	ADJ
fumecheng-7253	291	33	properties	property	NOUN
fumecheng-7253	291	34	of	of	ADP
fumecheng-7253	291	35	such	such	ADJ
fumecheng-7253	291	36	devices	device	NOUN
fumecheng-7253	291	37	.	.	PUNCT
fumecheng-7253	292	1	it	it	PRON
fumecheng-7253	292	2	should	should	AUX
fumecheng-7253	292	3	be	be	AUX
fumecheng-7253	292	4	emphasized	emphasize	VERB
fumecheng-7253	292	5	that	that	SCONJ
fumecheng-7253	292	6	the	the	DET
fumecheng-7253	292	7	findings	finding	NOUN
fumecheng-7253	292	8	are	be	AUX
fumecheng-7253	292	9	in	in	ADP
fumecheng-7253	292	10	line	line	NOUN
fumecheng-7253	292	11	with	with	ADP
fumecheng-7253	292	12	the	the	DET
fumecheng-7253	292	13	earlier	early	ADJ
fumecheng-7253	292	14	results	result	NOUN
fumecheng-7253	292	15	in	in	ADP
fumecheng-7253	292	16	refs	ref	NOUN
fumecheng-7253	292	17	.	.	PUNCT
fumecheng-7253	293	1	[	[	X
fumecheng-7253	293	2	53	53	NUM
fumecheng-7253	293	3	-	-	SYM
fumecheng-7253	293	4	55	55	NUM
fumecheng-7253	293	5	]	]	PUNCT
fumecheng-7253	293	6	.	.	PUNCT
fumecheng-7253	294	1	when	when	SCONJ
fumecheng-7253	294	2	the	the	DET
fumecheng-7253	294	3	values	value	NOUN
fumecheng-7253	294	4	of	of	ADP
fumecheng-7253	294	5	parameters	parameter	NOUN
fumecheng-7253	294	6	(	(	PUNCT
fumecheng-7253	294	7	𝜔,𝐾1	𝜔,𝐾1	PROPN
fumecheng-7253	294	8	,	,	PUNCT
fumecheng-7253	294	9	ω	ω	NOUN
fumecheng-7253	294	10	,	,	PUNCT
fumecheng-7253	294	11	𝜏𝑞	𝜏𝑞	NOUN
fumecheng-7253	294	12	,	,	PUNCT
fumecheng-7253	294	13	𝜏𝜃	𝜏𝜃	CCONJ
fumecheng-7253	294	14	)	)	PUNCT
fumecheng-7253	294	15	are	be	AUX
fumecheng-7253	294	16	fixed	fix	VERB
fumecheng-7253	294	17	,	,	PUNCT
fumecheng-7253	294	18	the	the	DET
fumecheng-7253	294	19	effect	effect	NOUN
fumecheng-7253	294	20	of	of	ADP
fumecheng-7253	294	21	the	the	DET
fumecheng-7253	294	22	nonlocal	nonlocal	ADJ
fumecheng-7253	294	23	parameter	parameter	NOUN
fumecheng-7253	294	24	𝜉	𝜉	NOUN
fumecheng-7253	294	25	on	on	ADP
fumecheng-7253	294	26	the	the	DET
fumecheng-7253	294	27	non	non	ADJ
fumecheng-7253	294	28	-	-	ADJ
fumecheng-7253	294	29	dimensionalfield	dimensionalfield	ADJ
fumecheng-7253	294	30	variables	variable	NOUN
fumecheng-7253	294	31	can	can	AUX
fumecheng-7253	294	32	be	be	AUX
fumecheng-7253	294	33	examined	examine	VERB
fumecheng-7253	294	34	.	.	PUNCT
fumecheng-7253	295	1	through	through	ADP
fumecheng-7253	295	2	figs	fig	NOUN
fumecheng-7253	295	3	.	.	PUNCT
fumecheng-7253	295	4	1013	1013	NUM
fumecheng-7253	295	5	,	,	PUNCT
fumecheng-7253	295	6	along	along	ADP
fumecheng-7253	295	7	the	the	DET
fumecheng-7253	295	8	axial	axial	ADJ
fumecheng-7253	295	9	direction	direction	NOUN
fumecheng-7253	295	10	,	,	PUNCT
fumecheng-7253	295	11	the	the	DET
fumecheng-7253	295	12	thermoelastic	thermoelastic	ADJ
fumecheng-7253	295	13	behavior	behavior	NOUN
fumecheng-7253	295	14	of	of	ADP
fumecheng-7253	295	15	rotating	rotate	VERB
fumecheng-7253	295	16	nanobeam	nanobeam	NOUN
fumecheng-7253	295	17	is	be	AUX
fumecheng-7253	295	18	shown	show	VERB
fumecheng-7253	295	19	by	by	ADP
fumecheng-7253	295	20	plotting	plot	VERB
fumecheng-7253	295	21	the	the	DET
fumecheng-7253	295	22	variations	variation	NOUN
fumecheng-7253	295	23	of	of	ADP
fumecheng-7253	295	24	displacement	displacement	ADJ
fumecheng-7253	295	25	u	u	NOUN
fumecheng-7253	295	26	,	,	PUNCT
fumecheng-7253	295	27	bending	bend	VERB
fumecheng-7253	295	28	moment	moment	NOUN
fumecheng-7253	295	29	m	m	NOUN
fumecheng-7253	295	30	,	,	PUNCT
fumecheng-7253	295	31	deflection	deflection	NOUN
fumecheng-7253	295	32	w	w	NOUN
fumecheng-7253	295	33	and	and	CCONJ
fumecheng-7253	295	34	temperature	temperature	NOUN
fumecheng-7253	295	35	𝜃.	𝜃.	ADV
fumecheng-7253	295	36	the	the	DET
fumecheng-7253	295	37	values	value	NOUN
fumecheng-7253	295	38	of	of	ADP
fumecheng-7253	295	39	nonlocal	nonlocal	ADJ
fumecheng-7253	295	40	parameter	parameter	NOUN
fumecheng-7253	295	41	are	be	AUX
fumecheng-7253	295	42	considered	consider	VERB
fumecheng-7253	295	43	to	to	PART
fumecheng-7253	295	44	be	be	AUX
fumecheng-7253	295	45	𝜉	𝜉	X
fumecheng-7253	295	46	=	=	SYM
fumecheng-7253	295	47	0	0	PUNCT
fumecheng-7253	296	1	(	(	PUNCT
fumecheng-7253	296	2	classical	classical	ADJ
fumecheng-7253	296	3	theory	theory	NOUN
fumecheng-7253	296	4	)	)	PUNCT
fumecheng-7253	296	5	,	,	PUNCT
fumecheng-7253	296	6	𝜉	𝜉	X
fumecheng-7253	296	7	=	=	NOUN
fumecheng-7253	296	8	0.01	0.01	NUM
fumecheng-7253	296	9	and	and	CCONJ
fumecheng-7253	296	10	𝜉	𝜉	X
fumecheng-7253	296	11	=	=	NOUN
fumecheng-7253	296	12	0.03	0.03	NUM
fumecheng-7253	296	13	for	for	ADP
fumecheng-7253	296	14	comparison	comparison	NOUN
fumecheng-7253	296	15	.	.	PUNCT
fumecheng-7253	297	1	the	the	DET
fumecheng-7253	297	2	figures	figure	NOUN
fumecheng-7253	297	3	exhibit	exhibit	VERB
fumecheng-7253	297	4	that	that	SCONJ
fumecheng-7253	297	5	the	the	DET
fumecheng-7253	297	6	nonlocality	nonlocality	NOUN
fumecheng-7253	297	7	of	of	ADP
fumecheng-7253	297	8	the	the	DET
fumecheng-7253	297	9	nanobeam	nanobeam	NOUN
fumecheng-7253	297	10	has	have	VERB
fumecheng-7253	297	11	distinct	distinct	ADJ
fumecheng-7253	297	12	influences	influence	NOUN
fumecheng-7253	297	13	on	on	ADP
fumecheng-7253	297	14	all	all	DET
fumecheng-7253	297	15	fields	field	NOUN
fumecheng-7253	297	16	studied	study	VERB
fumecheng-7253	297	17	and	and	CCONJ
fumecheng-7253	297	18	illustrates	illustrate	VERB
fumecheng-7253	297	19	the	the	DET
fumecheng-7253	297	20	difference	difference	NOUN
fumecheng-7253	297	21	between	between	ADP
fumecheng-7253	297	22	classical	classical	ADJ
fumecheng-7253	297	23	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	297	24	theories	theory	NOUN
fumecheng-7253	297	25	and	and	CCONJ
fumecheng-7253	297	26	nonlocal	nonlocal	ADJ
fumecheng-7253	297	27	ones	one	NOUN
fumecheng-7253	297	28	.	.	PUNCT
fumecheng-7253	298	1	for	for	ADP
fumecheng-7253	298	2	various	various	ADJ
fumecheng-7253	298	3	three	three	NUM
fumecheng-7253	298	4	assigned	assign	VERB
fumecheng-7253	298	5	values	value	NOUN
fumecheng-7253	298	6	of	of	ADP
fumecheng-7253	298	7	nonlocal	nonlocal	ADJ
fumecheng-7253	298	8	scaling	scaling	NOUN
fumecheng-7253	298	9	parameter	parameter	NOUN
fumecheng-7253	298	10	𝜉	𝜉	PROPN
fumecheng-7253	298	11	,	,	PUNCT
fumecheng-7253	298	12	fig	fig	NOUN
fumecheng-7253	298	13	.	.	PUNCT
fumecheng-7253	299	1	10	10	NUM
fumecheng-7253	299	2	shows	show	VERB
fumecheng-7253	299	3	different	different	ADJ
fumecheng-7253	299	4	curves	curve	NOUN
fumecheng-7253	299	5	for	for	ADP
fumecheng-7253	299	6	the	the	DET
fumecheng-7253	299	7	deflection	deflection	NOUN
fumecheng-7253	299	8	of	of	ADP
fumecheng-7253	299	9	non	non	ADJ
fumecheng-7253	299	10	-	-	ADJ
fumecheng-7253	299	11	rotating	rotating	ADJ
fumecheng-7253	299	12	nanobeam	nanobeam	NOUN
fumecheng-7253	299	13	.	.	PUNCT
fumecheng-7253	300	1	it	it	PRON
fumecheng-7253	300	2	can	can	AUX
fumecheng-7253	300	3	be	be	AUX
fumecheng-7253	300	4	seen	see	VERB
fumecheng-7253	300	5	that	that	SCONJ
fumecheng-7253	300	6	with	with	ADP
fumecheng-7253	300	7	an	an	DET
fumecheng-7253	300	8	increase	increase	NOUN
fumecheng-7253	300	9	in	in	ADP
fumecheng-7253	300	10	the	the	DET
fumecheng-7253	300	11	nonlocal	nonlocal	ADJ
fumecheng-7253	300	12	parameter	parameter	NOUN
fumecheng-7253	300	13	,	,	PUNCT
fumecheng-7253	300	14	the	the	DET
fumecheng-7253	300	15	deflection	deflection	NOUN
fumecheng-7253	300	16	becomes	become	VERB
fumecheng-7253	300	17	very	very	ADV
fumecheng-7253	300	18	small	small	ADJ
fumecheng-7253	300	19	and	and	CCONJ
fumecheng-7253	300	20	the	the	DET
fumecheng-7253	300	21	dispersed	disperse	VERB
fumecheng-7253	300	22	nature	nature	NOUN
fumecheng-7253	300	23	turns	turn	VERB
fumecheng-7253	300	24	into	into	ADP
fumecheng-7253	300	25	a	a	DET
fumecheng-7253	300	26	non	non	ADJ
fumecheng-7253	300	27	-	-	ADJ
fumecheng-7253	300	28	dispersed	disperse	VERB
fumecheng-7253	300	29	form	form	NOUN
fumecheng-7253	300	30	.	.	PUNCT
fumecheng-7253	301	1	the	the	DET
fumecheng-7253	301	2	temperature	temperature	NOUN
fumecheng-7253	301	3	distributions	distribution	NOUN
fumecheng-7253	301	4	are	be	AUX
fumecheng-7253	301	5	also	also	ADV
fumecheng-7253	301	6	shown	show	VERB
fumecheng-7253	301	7	for	for	ADP
fumecheng-7253	301	8	various	various	ADJ
fumecheng-7253	301	9	nonlocal	nonlocal	ADJ
fumecheng-7253	301	10	scaling	scaling	NOUN
fumecheng-7253	301	11	parameter	parameter	NOUN
fumecheng-7253	301	12	versus	versus	ADP
fumecheng-7253	301	13	axial	axial	ADJ
fumecheng-7253	301	14	direction	direction	NOUN
fumecheng-7253	301	15	x	x	NOUN
fumecheng-7253	301	16	,	,	PUNCT
fumecheng-7253	301	17	in	in	ADP
fumecheng-7253	301	18	fig	fig	NOUN
fumecheng-7253	301	19	.	.	PUNCT
fumecheng-7253	302	1	11	11	NUM
fumecheng-7253	302	2	.	.	PUNCT
fumecheng-7253	303	1	it	it	PRON
fumecheng-7253	303	2	is	be	AUX
fumecheng-7253	303	3	concluded	conclude	VERB
fumecheng-7253	303	4	that	that	SCONJ
fumecheng-7253	303	5	the	the	DET
fumecheng-7253	303	6	temperature	temperature	NOUN
fumecheng-7253	303	7	convergence	convergence	NOUN
fumecheng-7253	303	8	can	can	AUX
fumecheng-7253	303	9	be	be	AUX
fumecheng-7253	303	10	achieved	achieve	VERB
fumecheng-7253	303	11	by	by	ADP
fumecheng-7253	303	12	increasing	increase	VERB
fumecheng-7253	303	13	the	the	DET
fumecheng-7253	303	14	nonlocal	nonlocal	ADJ
fumecheng-7253	303	15	scaling	scaling	NOUN
fumecheng-7253	303	16	parameter	parameter	NOUN
fumecheng-7253	303	17	.	.	PUNCT
fumecheng-7253	304	1	fig	fig	NOUN
fumecheng-7253	304	2	.	.	PUNCT
fumecheng-7253	305	1	12	12	NUM
fumecheng-7253	305	2	demonstrates	demonstrate	VERB
fumecheng-7253	305	3	that	that	SCONJ
fumecheng-7253	305	4	the	the	DET
fumecheng-7253	305	5	displacement	displacement	ADJ
fumecheng-7253	305	6	amplitude	amplitude	NOUN
fumecheng-7253	305	7	increases	increase	VERB
fumecheng-7253	305	8	with	with	ADP
fumecheng-7253	305	9	the	the	DET
fumecheng-7253	305	10	nonlocal	nonlocal	ADJ
fumecheng-7253	305	11	parameter	parameter	NOUN
fumecheng-7253	305	12	due	due	ADP
fumecheng-7253	305	13	to	to	ADP
fumecheng-7253	305	14	the	the	DET
fumecheng-7253	305	15	inclusion	inclusion	NOUN
fumecheng-7253	305	16	of	of	ADP
fumecheng-7253	305	17	nonlocality	nonlocality	NOUN
fumecheng-7253	305	18	in	in	ADP
fumecheng-7253	305	19	the	the	DET
fumecheng-7253	305	20	thermoelastic	thermoelastic	ADJ
fumecheng-7253	305	21	model	model	NOUN
fumecheng-7253	305	22	.	.	PUNCT
fumecheng-7253	306	1	the	the	DET
fumecheng-7253	306	2	influence	influence	NOUN
fumecheng-7253	306	3	of	of	ADP
fumecheng-7253	306	4	the	the	DET
fumecheng-7253	306	5	nonlocal	nonlocal	ADJ
fumecheng-7253	306	6	parameter	parameter	NOUN
fumecheng-7253	306	7	𝜉	𝜉	NOUN
fumecheng-7253	306	8	on	on	ADP
fumecheng-7253	306	9	the	the	DET
fumecheng-7253	306	10	variation	variation	NOUN
fumecheng-7253	306	11	of	of	ADP
fumecheng-7253	306	12	bending	bend	VERB
fumecheng-7253	306	13	moment	moment	NOUN
fumecheng-7253	306	14	is	be	AUX
fumecheng-7253	306	15	presented	present	VERB
fumecheng-7253	306	16	in	in	ADP
fumecheng-7253	306	17	fig	fig	NOUN
fumecheng-7253	306	18	.	.	PUNCT
fumecheng-7253	307	1	13	13	NUM
fumecheng-7253	307	2	.	.	PUNCT
fumecheng-7253	308	1	one	one	PRON
fumecheng-7253	308	2	observes	observe	VERB
fumecheng-7253	308	3	that	that	SCONJ
fumecheng-7253	308	4	as	as	ADP
fumecheng-7253	308	5	the	the	DET
fumecheng-7253	308	6	nonlocal	nonlocal	ADJ
fumecheng-7253	308	7	scale	scale	NOUN
fumecheng-7253	308	8	parameter	parameter	NOUN
fumecheng-7253	308	9	increases	increase	NOUN
fumecheng-7253	308	10	,	,	PUNCT
fumecheng-7253	308	11	the	the	DET
fumecheng-7253	308	12	bending	bend	VERB
fumecheng-7253	308	13	moment	moment	NOUN
fumecheng-7253	308	14	tends	tend	VERB
fumecheng-7253	308	15	to	to	PART
fumecheng-7253	308	16	decrease	decrease	VERB
fumecheng-7253	308	17	substantially	substantially	ADV
fumecheng-7253	308	18	.	.	PUNCT
fumecheng-7253	309	1	it	it	PRON
fumecheng-7253	309	2	is	be	AUX
fumecheng-7253	309	3	worth	worth	ADJ
fumecheng-7253	309	4	mentioning	mention	VERB
fumecheng-7253	309	5	that	that	SCONJ
fumecheng-7253	309	6	our	our	PRON
fumecheng-7253	309	7	findings	finding	NOUN
fumecheng-7253	309	8	and	and	CCONJ
fumecheng-7253	309	9	conclusions	conclusion	NOUN
fumecheng-7253	309	10	are	be	AUX
fumecheng-7253	309	11	in	in	ADP
fumecheng-7253	309	12	agreement	agreement	NOUN
fumecheng-7253	309	13	with	with	ADP
fumecheng-7253	309	14	those	those	PRON
fumecheng-7253	309	15	reported	report	VERB
fumecheng-7253	309	16	in	in	ADP
fumecheng-7253	309	17	the	the	DET
fumecheng-7253	309	18	literature	literature	NOUN
fumecheng-7253	309	19	[	[	X
fumecheng-7253	309	20	56	56	NUM
fumecheng-7253	309	21	]	]	PUNCT
fumecheng-7253	309	22	.	.	PUNCT
fumecheng-7253	310	1	the	the	DET
fumecheng-7253	310	2	results	result	NOUN
fumecheng-7253	310	3	typically	typically	ADV
fumecheng-7253	310	4	confirm	confirm	VERB
fumecheng-7253	310	5	that	that	SCONJ
fumecheng-7253	310	6	one	one	PRON
fumecheng-7253	310	7	should	should	AUX
fumecheng-7253	310	8	expect	expect	VERB
fumecheng-7253	310	9	significant	significant	ADJ
fumecheng-7253	310	10	diversity	diversity	NOUN
fumecheng-7253	310	11	in	in	ADP
fumecheng-7253	310	12	the	the	DET
fumecheng-7253	310	13	results	result	NOUN
fumecheng-7253	310	14	by	by	ADP
fumecheng-7253	310	15	considering	consider	VERB
fumecheng-7253	310	16	the	the	DET
fumecheng-7253	310	17	nonlocality	nonlocality	NOUN
fumecheng-7253	310	18	of	of	ADP
fumecheng-7253	310	19	nanobeam	nanobeam	NOUN
fumecheng-7253	310	20	rather	rather	ADV
fumecheng-7253	310	21	than	than	ADP
fumecheng-7253	310	22	classical	classical	ADJ
fumecheng-7253	310	23	one	one	NUM
fumecheng-7253	310	24	.	.	PUNCT
fumecheng-7253	311	1	the	the	DET
fumecheng-7253	311	2	distinction	distinction	NOUN
fumecheng-7253	311	3	between	between	ADP
fumecheng-7253	311	4	classical	classical	ADJ
fumecheng-7253	311	5	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	311	6	models	model	NOUN
fumecheng-7253	311	7	and	and	CCONJ
fumecheng-7253	311	8	nonlocal	nonlocal	ADJ
fumecheng-7253	311	9	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	311	10	theories	theory	NOUN
fumecheng-7253	311	11	in	in	ADP
fumecheng-7253	311	12	thermal	thermal	ADJ
fumecheng-7253	311	13	fields	field	NOUN
fumecheng-7253	311	14	is	be	AUX
fumecheng-7253	311	15	justified	justify	VERB
fumecheng-7253	311	16	[	[	X
fumecheng-7253	311	17	57	57	NUM
fumecheng-7253	311	18	]	]	PUNCT
fumecheng-7253	311	19	.	.	PUNCT
fumecheng-7253	312	1	in	in	ADP
fumecheng-7253	312	2	the	the	DET
fumecheng-7253	312	3	nanoscale	nanoscale	NOUN
fumecheng-7253	312	4	systems	system	NOUN
fumecheng-7253	312	5	and	and	CCONJ
fumecheng-7253	312	6	devices	device	NOUN
fumecheng-7253	312	7	,	,	PUNCT
fumecheng-7253	312	8	the	the	DET
fumecheng-7253	312	9	impact	impact	NOUN
fumecheng-7253	312	10	of	of	ADP
fumecheng-7253	312	11	this	this	DET
fumecheng-7253	312	12	parameter	parameter	NOUN
fumecheng-7253	312	13	should	should	AUX
fumecheng-7253	312	14	also	also	ADV
fumecheng-7253	312	15	be	be	AUX
fumecheng-7253	312	16	taken	take	VERB
fumecheng-7253	312	17	into	into	ADP
fumecheng-7253	312	18	account	account	NOUN
fumecheng-7253	312	19	.	.	PUNCT
fumecheng-7253	313	1	fig	fig	NOUN
fumecheng-7253	313	2	.	.	PUNCT
fumecheng-7253	314	1	10	10	NUM
fumecheng-7253	314	2	deflection	deflection	NOUN
fumecheng-7253	314	3	𝑤	𝑤	ADP
fumecheng-7253	314	4	distribution	distribution	NOUN
fumecheng-7253	314	5	vs	vs	ADP
fumecheng-7253	314	6	nonlocal	nonlocal	ADJ
fumecheng-7253	314	7	parameter	parameter	NOUN
fumecheng-7253	314	8	𝜉	𝜉	ADP
fumecheng-7253	314	9	650	650	NUM
fumecheng-7253	314	10	a.	a.	NOUN
fumecheng-7253	314	11	e.	e.	PROPN
fumecheng-7253	314	12	abouelregal	abouelregal	PROPN
fumecheng-7253	314	13	,	,	PUNCT
fumecheng-7253	314	14	h.	h.	PROPN
fumecheng-7253	314	15	m.	m.	PROPN
fumecheng-7253	314	16	sedighi	sedighi	PROPN
fumecheng-7253	314	17	,	,	PUNCT
fumecheng-7253	314	18	s.	s.	PROPN
fumecheng-7253	314	19	a.	a.	PROPN
fumecheng-7253	314	20	faghidian	faghidian	PROPN
fumecheng-7253	314	21	,	,	PUNCT
fumecheng-7253	314	22	a.	a.	PROPN
fumecheng-7253	314	23	h.	h.	PROPN
fumecheng-7253	314	24	shirazi	shirazi	PROPN
fumecheng-7253	314	25	fig	fig	PROPN
fumecheng-7253	314	26	.	.	PUNCT
fumecheng-7253	315	1	11	11	NUM
fumecheng-7253	315	2	temperature	temperature	NOUN
fumecheng-7253	315	3	𝜃	𝜃	PRON
fumecheng-7253	315	4	distribution	distribution	NOUN
fumecheng-7253	315	5	vs	vs	ADP
fumecheng-7253	315	6	nonlocal	nonlocal	ADJ
fumecheng-7253	315	7	parameter	parameter	NOUN
fumecheng-7253	315	8	𝜉	𝜉	PROPN
fumecheng-7253	315	9	fig	fig	NOUN
fumecheng-7253	315	10	.	.	PUNCT
fumecheng-7253	316	1	12	12	NUM
fumecheng-7253	316	2	displacement	displacement	NOUN
fumecheng-7253	316	3	𝑢	𝑢	PRON
fumecheng-7253	316	4	distribution	distribution	NOUN
fumecheng-7253	316	5	vs	vs	ADP
fumecheng-7253	316	6	nonlocal	nonlocal	ADJ
fumecheng-7253	316	7	parameter	parameter	NOUN
fumecheng-7253	316	8	𝜉	𝜉	PROPN
fumecheng-7253	316	9	fig	fig	NOUN
fumecheng-7253	316	10	.	.	PUNCT
fumecheng-7253	317	1	13	13	NUM
fumecheng-7253	317	2	bending	bend	VERB
fumecheng-7253	317	3	moment	moment	NOUN
fumecheng-7253	317	4	𝑀	𝑀	PROPN
fumecheng-7253	317	5	distribution	distribution	NOUN
fumecheng-7253	317	6	vs	vs	ADP
fumecheng-7253	317	7	nonlocal	nonlocal	ADJ
fumecheng-7253	317	8	parameter	parameter	NOUN
fumecheng-7253	317	9	𝜉	𝜉	ADP
fumecheng-7253	317	10	temperature	temperature	NOUN
fumecheng-7253	317	11	-	-	PUNCT
fumecheng-7253	317	12	dependent	dependent	ADJ
fumecheng-7253	317	13	physical	physical	ADJ
fumecheng-7253	317	14	characteristics	characteristic	NOUN
fumecheng-7253	317	15	of	of	ADP
fumecheng-7253	317	16	rotating	rotate	VERB
fumecheng-7253	317	17	nonlocal	nonlocal	ADJ
fumecheng-7253	317	18	nanobeams	nanobeam	NOUN
fumecheng-7253	317	19	subject	subject	ADJ
fumecheng-7253	317	20	to	to	ADP
fumecheng-7253	317	21	...	...	PUNCT
fumecheng-7253	317	22	651	651	NUM
fumecheng-7253	317	23	as	as	ADP
fumecheng-7253	317	24	the	the	DET
fumecheng-7253	317	25	last	last	ADJ
fumecheng-7253	317	26	effort	effort	NOUN
fumecheng-7253	317	27	in	in	ADP
fumecheng-7253	317	28	this	this	DET
fumecheng-7253	317	29	research	research	NOUN
fumecheng-7253	317	30	,	,	PUNCT
fumecheng-7253	317	31	the	the	DET
fumecheng-7253	317	32	variations	variation	NOUN
fumecheng-7253	317	33	of	of	ADP
fumecheng-7253	317	34	different	different	ADJ
fumecheng-7253	317	35	fields	field	NOUN
fumecheng-7253	317	36	variables	variable	NOUN
fumecheng-7253	317	37	in	in	ADP
fumecheng-7253	317	38	terms	term	NOUN
fumecheng-7253	317	39	of	of	ADP
fumecheng-7253	317	40	the	the	DET
fumecheng-7253	317	41	point	point	NOUN
fumecheng-7253	317	42	load	load	NOUN
fumecheng-7253	317	43	𝑞0	𝑞0	NOUN
fumecheng-7253	317	44	are	be	AUX
fumecheng-7253	317	45	plotted	plot	VERB
fumecheng-7253	317	46	in	in	ADP
fumecheng-7253	317	47	figs	fig	NOUN
fumecheng-7253	317	48	.	.	PUNCT
fumecheng-7253	318	1	14	14	NUM
fumecheng-7253	318	2	-	-	SYM
fumecheng-7253	318	3	17	17	NUM
fumecheng-7253	318	4	.	.	PUNCT
fumecheng-7253	319	1	there	there	PRON
fumecheng-7253	319	2	are	be	VERB
fumecheng-7253	319	3	three	three	NUM
fumecheng-7253	319	4	different	different	ADJ
fumecheng-7253	319	5	non	non	ADJ
fumecheng-7253	319	6	-	-	ADJ
fumecheng-7253	319	7	dimensional	dimensional	ADJ
fumecheng-7253	319	8	values	value	NOUN
fumecheng-7253	319	9	for	for	ADP
fumecheng-7253	319	10	point	point	NOUN
fumecheng-7253	319	11	load	load	NOUN
fumecheng-7253	319	12	𝑞0	𝑞0	NOUN
fumecheng-7253	319	13	which	which	PRON
fumecheng-7253	319	14	are	be	AUX
fumecheng-7253	319	15	taken	take	VERB
fumecheng-7253	319	16	into	into	ADP
fumecheng-7253	319	17	account	account	NOUN
fumecheng-7253	319	18	for	for	ADP
fumecheng-7253	319	19	the	the	DET
fumecheng-7253	319	20	sake	sake	NOUN
fumecheng-7253	319	21	of	of	ADP
fumecheng-7253	319	22	comparison	comparison	NOUN
fumecheng-7253	319	23	.	.	PUNCT
fumecheng-7253	320	1	the	the	DET
fumecheng-7253	320	2	plotted	plot	VERB
fumecheng-7253	320	3	curves	curve	NOUN
fumecheng-7253	320	4	show	show	VERB
fumecheng-7253	320	5	the	the	DET
fumecheng-7253	320	6	distinct	distinct	ADJ
fumecheng-7253	320	7	effect	effect	NOUN
fumecheng-7253	320	8	of	of	ADP
fumecheng-7253	320	9	the	the	DET
fumecheng-7253	320	10	point	point	NOUN
fumecheng-7253	320	11	load	load	NOUN
fumecheng-7253	320	12	on	on	ADP
fumecheng-7253	320	13	the	the	DET
fumecheng-7253	320	14	results	result	NOUN
fumecheng-7253	320	15	.	.	PUNCT
fumecheng-7253	321	1	in	in	ADP
fumecheng-7253	321	2	the	the	DET
fumecheng-7253	321	3	case	case	NOUN
fumecheng-7253	321	4	of	of	ADP
fumecheng-7253	321	5	uniform	uniform	ADJ
fumecheng-7253	321	6	distributed	distribute	VERB
fumecheng-7253	321	7	load	load	NOUN
fumecheng-7253	321	8	,	,	PUNCT
fumecheng-7253	321	9	it	it	PRON
fumecheng-7253	321	10	is	be	AUX
fumecheng-7253	321	11	assumed	assume	VERB
fumecheng-7253	321	12	that	that	SCONJ
fumecheng-7253	321	13	𝛿	𝛿	ADJ
fumecheng-7253	321	14	=	=	NOUN
fumecheng-7253	321	15	0	0	NUM
fumecheng-7253	321	16	,	,	PUNCT
fumecheng-7253	321	17	and	and	CCONJ
fumecheng-7253	321	18	for	for	ADP
fumecheng-7253	321	19	the	the	DET
fumecheng-7253	321	20	point	point	NOUN
fumecheng-7253	321	21	load	load	NOUN
fumecheng-7253	321	22	with	with	ADP
fumecheng-7253	321	23	exponential	exponential	ADJ
fumecheng-7253	321	24	decay	decay	NOUN
fumecheng-7253	321	25	in	in	ADP
fumecheng-7253	321	26	time	time	NOUN
fumecheng-7253	321	27	,	,	PUNCT
fumecheng-7253	321	28	it	it	PRON
fumecheng-7253	321	29	is	be	AUX
fumecheng-7253	321	30	considered	consider	VERB
fumecheng-7253	321	31	that	that	SCONJ
fumecheng-7253	321	32	𝛿	𝛿	ADJ
fumecheng-7253	321	33	=	=	ADJ
fumecheng-7253	321	34	1	1	NUM
fumecheng-7253	321	35	.	.	PUNCT
fumecheng-7253	322	1	clearly	clearly	ADV
fumecheng-7253	322	2	,	,	PUNCT
fumecheng-7253	322	3	the	the	DET
fumecheng-7253	322	4	difference	difference	NOUN
fumecheng-7253	322	5	between	between	ADP
fumecheng-7253	322	6	the	the	DET
fumecheng-7253	322	7	outcomes	outcome	NOUN
fumecheng-7253	322	8	becomes	become	VERB
fumecheng-7253	322	9	more	more	ADV
fumecheng-7253	322	10	significant	significant	ADJ
fumecheng-7253	322	11	with	with	ADP
fumecheng-7253	322	12	increasing	increase	VERB
fumecheng-7253	322	13	amplitude	amplitude	NOUN
fumecheng-7253	322	14	of	of	ADP
fumecheng-7253	322	15	point	point	NOUN
fumecheng-7253	322	16	load	load	NOUN
fumecheng-7253	322	17	𝑞0	𝑞0	NOUN
fumecheng-7253	322	18	.	.	PUNCT
fumecheng-7253	323	1	figs	fig	NOUN
fumecheng-7253	323	2	.	.	PUNCT
fumecheng-7253	324	1	14	14	NUM
fumecheng-7253	324	2	-	-	SYM
fumecheng-7253	324	3	17	17	NUM
fumecheng-7253	324	4	indicate	indicate	VERB
fumecheng-7253	324	5	that	that	SCONJ
fumecheng-7253	324	6	there	there	PRON
fumecheng-7253	324	7	is	be	VERB
fumecheng-7253	324	8	a	a	DET
fumecheng-7253	324	9	greater	great	ADJ
fumecheng-7253	324	10	discrepancy	discrepancy	NOUN
fumecheng-7253	324	11	between	between	ADP
fumecheng-7253	324	12	u	u	NOUN
fumecheng-7253	324	13	and	and	CCONJ
fumecheng-7253	324	14	w	w	NOUN
fumecheng-7253	324	15	quantities	quantity	NOUN
fumecheng-7253	324	16	by	by	ADP
fumecheng-7253	324	17	increasing	increase	VERB
fumecheng-7253	324	18	the	the	DET
fumecheng-7253	324	19	point	point	NOUN
fumecheng-7253	324	20	load	load	NOUN
fumecheng-7253	324	21	compared	compare	VERB
fumecheng-7253	324	22	to	to	ADP
fumecheng-7253	324	23	those	those	PRON
fumecheng-7253	324	24	for	for	ADP
fumecheng-7253	324	25	bending	bend	VERB
fumecheng-7253	324	26	moment	moment	NOUN
fumecheng-7253	324	27	and	and	CCONJ
fumecheng-7253	324	28	temperature	temperature	NOUN
fumecheng-7253	324	29	gradient	gradient	NOUN
fumecheng-7253	324	30	.	.	PUNCT
fumecheng-7253	325	1	it	it	PRON
fumecheng-7253	325	2	is	be	AUX
fumecheng-7253	325	3	also	also	ADV
fumecheng-7253	325	4	noted	note	VERB
fumecheng-7253	325	5	from	from	ADP
fumecheng-7253	325	6	these	these	DET
fumecheng-7253	325	7	figures	figure	NOUN
fumecheng-7253	325	8	that	that	SCONJ
fumecheng-7253	325	9	the	the	DET
fumecheng-7253	325	10	absolute	absolute	ADJ
fumecheng-7253	325	11	values	value	NOUN
fumecheng-7253	325	12	of	of	ADP
fumecheng-7253	325	13	the	the	DET
fumecheng-7253	325	14	field	field	NOUN
fumecheng-7253	325	15	variables	variable	NOUN
fumecheng-7253	325	16	become	become	VERB
fumecheng-7253	325	17	larger	large	ADJ
fumecheng-7253	325	18	when	when	SCONJ
fumecheng-7253	325	19	the	the	DET
fumecheng-7253	325	20	exponential	exponential	ADJ
fumecheng-7253	325	21	decay	decay	NOUN
fumecheng-7253	325	22	with	with	ADP
fumecheng-7253	325	23	respect	respect	NOUN
fumecheng-7253	325	24	to	to	ADP
fumecheng-7253	325	25	time	time	NOUN
fumecheng-7253	325	26	is	be	AUX
fumecheng-7253	325	27	considered	consider	VERB
fumecheng-7253	325	28	for	for	ADP
fumecheng-7253	325	29	point	point	NOUN
fumecheng-7253	325	30	load	load	NOUN
fumecheng-7253	325	31	𝑞0	𝑞0	NOUN
fumecheng-7253	325	32	[	[	X
fumecheng-7253	325	33	58	58	NUM
fumecheng-7253	325	34	,	,	PUNCT
fumecheng-7253	325	35	59	59	NUM
fumecheng-7253	325	36	]	]	PUNCT
fumecheng-7253	325	37	.	.	PUNCT
fumecheng-7253	326	1	fig	fig	NOUN
fumecheng-7253	326	2	.	.	PUNCT
fumecheng-7253	327	1	14	14	NUM
fumecheng-7253	327	2	deflection	deflection	NOUN
fumecheng-7253	327	3	𝑤	𝑤	ADP
fumecheng-7253	327	4	under	under	ADP
fumecheng-7253	327	5	the	the	DET
fumecheng-7253	327	6	influence	influence	NOUN
fumecheng-7253	327	7	of	of	ADP
fumecheng-7253	327	8	point	point	NOUN
fumecheng-7253	327	9	load	load	NOUN
fumecheng-7253	327	10	𝑞0	𝑞0	PROPN
fumecheng-7253	327	11	fig	fig	PROPN
fumecheng-7253	327	12	.	.	PUNCT
fumecheng-7253	328	1	15	15	NUM
fumecheng-7253	328	2	temperature	temperature	NOUN
fumecheng-7253	328	3	𝜃	𝜃	NOUN
fumecheng-7253	328	4	under	under	ADP
fumecheng-7253	328	5	the	the	DET
fumecheng-7253	328	6	influence	influence	NOUN
fumecheng-7253	328	7	of	of	ADP
fumecheng-7253	328	8	point	point	NOUN
fumecheng-7253	328	9	load	load	NOUN
fumecheng-7253	328	10	𝑞0	𝑞0	NOUN
fumecheng-7253	328	11	652	652	NUM
fumecheng-7253	328	12	a.	a.	PROPN
fumecheng-7253	328	13	e.	e.	PROPN
fumecheng-7253	328	14	abouelregal	abouelregal	PROPN
fumecheng-7253	328	15	,	,	PUNCT
fumecheng-7253	328	16	h.	h.	PROPN
fumecheng-7253	328	17	m.	m.	PROPN
fumecheng-7253	328	18	sedighi	sedighi	PROPN
fumecheng-7253	328	19	,	,	PUNCT
fumecheng-7253	328	20	s.	s.	PROPN
fumecheng-7253	328	21	a.	a.	PROPN
fumecheng-7253	328	22	faghidian	faghidian	PROPN
fumecheng-7253	328	23	,	,	PUNCT
fumecheng-7253	328	24	a.	a.	PROPN
fumecheng-7253	328	25	h.	h.	PROPN
fumecheng-7253	328	26	shirazi	shirazi	PROPN
fumecheng-7253	328	27	fig	fig	PROPN
fumecheng-7253	328	28	.	.	PUNCT
fumecheng-7253	329	1	16	16	NUM
fumecheng-7253	329	2	displacement	displacement	NOUN
fumecheng-7253	329	3	𝑢	𝑢	NOUN
fumecheng-7253	329	4	under	under	ADP
fumecheng-7253	329	5	the	the	DET
fumecheng-7253	329	6	influence	influence	NOUN
fumecheng-7253	329	7	of	of	ADP
fumecheng-7253	329	8	point	point	NOUN
fumecheng-7253	329	9	load	load	NOUN
fumecheng-7253	329	10	𝑞0	𝑞0	PROPN
fumecheng-7253	329	11	fig	fig	PROPN
fumecheng-7253	329	12	.	.	PUNCT
fumecheng-7253	330	1	17	17	NUM
fumecheng-7253	330	2	bending	bend	VERB
fumecheng-7253	330	3	moment	moment	NOUN
fumecheng-7253	330	4	𝑀	𝑀	PROPN
fumecheng-7253	330	5	under	under	ADP
fumecheng-7253	330	6	the	the	DET
fumecheng-7253	330	7	influence	influence	NOUN
fumecheng-7253	330	8	of	of	ADP
fumecheng-7253	330	9	point	point	NOUN
fumecheng-7253	330	10	load	load	NOUN
fumecheng-7253	330	11	𝑞0	𝑞0	NOUN
fumecheng-7253	330	12	9	9	NUM
fumecheng-7253	330	13	.	.	PUNCT
fumecheng-7253	331	1	conclusions	conclusion	NOUN
fumecheng-7253	331	2	this	this	DET
fumecheng-7253	331	3	research	research	NOUN
fumecheng-7253	331	4	focused	focus	VERB
fumecheng-7253	331	5	on	on	ADP
fumecheng-7253	331	6	the	the	DET
fumecheng-7253	331	7	wave	wave	NOUN
fumecheng-7253	331	8	dispersion	dispersion	NOUN
fumecheng-7253	331	9	behavior	behavior	NOUN
fumecheng-7253	331	10	of	of	ADP
fumecheng-7253	331	11	rotating	rotate	VERB
fumecheng-7253	331	12	nanobeam	nanobeam	NOUN
fumecheng-7253	331	13	on	on	ADP
fumecheng-7253	331	14	the	the	DET
fumecheng-7253	331	15	basis	basis	NOUN
fumecheng-7253	331	16	of	of	ADP
fumecheng-7253	331	17	the	the	DET
fumecheng-7253	331	18	nonlocal	nonlocal	ADJ
fumecheng-7253	331	19	elasticity	elasticity	NOUN
fumecheng-7253	331	20	theory	theory	NOUN
fumecheng-7253	331	21	in	in	ADP
fumecheng-7253	331	22	conjunction	conjunction	NOUN
fumecheng-7253	331	23	with	with	ADP
fumecheng-7253	331	24	generalized	generalized	ADJ
fumecheng-7253	331	25	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	331	26	with	with	ADP
fumecheng-7253	331	27	phase	phase	NOUN
fumecheng-7253	331	28	-	-	PUNCT
fumecheng-7253	331	29	lag	lag	NOUN
fumecheng-7253	331	30	.	.	PUNCT
fumecheng-7253	332	1	the	the	DET
fumecheng-7253	332	2	systems	system	NOUN
fumecheng-7253	332	3	of	of	ADP
fumecheng-7253	332	4	governing	govern	VERB
fumecheng-7253	332	5	equations	equation	NOUN
fumecheng-7253	332	6	were	be	AUX
fumecheng-7253	332	7	derived	derive	VERB
fumecheng-7253	332	8	in	in	ADP
fumecheng-7253	332	9	the	the	DET
fumecheng-7253	332	10	context	context	NOUN
fumecheng-7253	332	11	of	of	ADP
fumecheng-7253	332	12	the	the	DET
fumecheng-7253	332	13	euler	euler	PROPN
fumecheng-7253	332	14	-	-	PUNCT
fumecheng-7253	332	15	bernoulli	bernoulli	PROPN
fumecheng-7253	332	16	beam	beam	NOUN
fumecheng-7253	332	17	theory	theory	NOUN
fumecheng-7253	332	18	.	.	PUNCT
fumecheng-7253	333	1	the	the	DET
fumecheng-7253	333	2	thermal	thermal	ADJ
fumecheng-7253	333	3	conductivity	conductivity	NOUN
fumecheng-7253	333	4	of	of	ADP
fumecheng-7253	333	5	nanobeam	nanobeam	NOUN
fumecheng-7253	333	6	and	and	CCONJ
fumecheng-7253	333	7	modulus	modulus	NOUN
fumecheng-7253	333	8	of	of	ADP
fumecheng-7253	333	9	elasticity	elasticity	NOUN
fumecheng-7253	333	10	were	be	AUX
fumecheng-7253	333	11	considered	consider	VERB
fumecheng-7253	333	12	to	to	PART
fumecheng-7253	333	13	be	be	AUX
fumecheng-7253	333	14	temperature	temperature	NOUN
fumecheng-7253	333	15	-	-	PUNCT
fumecheng-7253	333	16	dependent	dependent	ADJ
fumecheng-7253	333	17	.	.	PUNCT
fumecheng-7253	334	1	for	for	ADP
fumecheng-7253	334	2	a	a	DET
fumecheng-7253	334	3	uniform	uniform	ADJ
fumecheng-7253	334	4	rotating	rotate	VERB
fumecheng-7253	334	5	nanobeam	nanobeam	NOUN
fumecheng-7253	334	6	,	,	PUNCT
fumecheng-7253	334	7	the	the	DET
fumecheng-7253	334	8	governing	govern	VERB
fumecheng-7253	334	9	equations	equation	NOUN
fumecheng-7253	334	10	were	be	AUX
fumecheng-7253	334	11	extracted	extract	VERB
fumecheng-7253	334	12	considering	consider	VERB
fumecheng-7253	334	13	the	the	DET
fumecheng-7253	334	14	variability	variability	NOUN
fumecheng-7253	334	15	of	of	ADP
fumecheng-7253	334	16	thermal	thermal	ADJ
fumecheng-7253	334	17	conductivity	conductivity	NOUN
fumecheng-7253	334	18	and	and	CCONJ
fumecheng-7253	334	19	nonlocal	nonlocal	ADJ
fumecheng-7253	334	20	scale	scale	NOUN
fumecheng-7253	334	21	effect	effect	NOUN
fumecheng-7253	334	22	.	.	PUNCT
fumecheng-7253	335	1	the	the	DET
fumecheng-7253	335	2	nanobeam	nanobeam	ADJ
fumecheng-7253	335	3	surface	surface	NOUN
fumecheng-7253	335	4	was	be	AUX
fumecheng-7253	335	5	assumed	assume	VERB
fumecheng-7253	335	6	to	to	PART
fumecheng-7253	335	7	be	be	AUX
fumecheng-7253	335	8	thermally	thermally	ADV
fumecheng-7253	335	9	loaded	load	VERB
fumecheng-7253	335	10	with	with	ADP
fumecheng-7253	335	11	uniformly	uniformly	ADJ
fumecheng-7253	335	12	heat	heat	NOUN
fumecheng-7253	335	13	source	source	NOUN
fumecheng-7253	335	14	by	by	ADP
fumecheng-7253	335	15	considering	consider	VERB
fumecheng-7253	335	16	the	the	DET
fumecheng-7253	335	17	exponential	exponential	ADJ
fumecheng-7253	335	18	decay	decay	NOUN
fumecheng-7253	335	19	with	with	ADP
fumecheng-7253	335	20	time	time	NOUN
fumecheng-7253	335	21	.	.	PUNCT
fumecheng-7253	336	1	the	the	DET
fumecheng-7253	336	2	effects	effect	NOUN
fumecheng-7253	336	3	of	of	ADP
fumecheng-7253	336	4	dynamic	dynamic	ADJ
fumecheng-7253	336	5	load	load	NOUN
fumecheng-7253	336	6	,	,	PUNCT
fumecheng-7253	336	7	nonlocal	nonlocal	ADJ
fumecheng-7253	336	8	parameter	parameter	NOUN
fumecheng-7253	336	9	,	,	PUNCT
fumecheng-7253	336	10	rotating	rotate	VERB
fumecheng-7253	336	11	speed	speed	NOUN
fumecheng-7253	336	12	and	and	CCONJ
fumecheng-7253	336	13	thermal	thermal	ADJ
fumecheng-7253	336	14	conductivity	conductivity	NOUN
fumecheng-7253	336	15	variations	variation	NOUN
fumecheng-7253	336	16	on	on	ADP
fumecheng-7253	336	17	the	the	DET
fumecheng-7253	336	18	field	field	NOUN
fumecheng-7253	336	19	variables	variable	NOUN
fumecheng-7253	336	20	were	be	AUX
fumecheng-7253	336	21	graphically	graphically	ADV
fumecheng-7253	336	22	described	describe	VERB
fumecheng-7253	336	23	and	and	CCONJ
fumecheng-7253	336	24	examined	examine	VERB
fumecheng-7253	336	25	.	.	PUNCT
fumecheng-7253	337	1	our	our	PRON
fumecheng-7253	337	2	findings	finding	NOUN
fumecheng-7253	337	3	showed	show	VERB
fumecheng-7253	337	4	the	the	DET
fumecheng-7253	337	5	following	follow	VERB
fumecheng-7253	337	6	important	important	ADJ
fumecheng-7253	337	7	results	result	NOUN
fumecheng-7253	337	8	:	:	PUNCT
fumecheng-7253	337	9	temperature	temperature	NOUN
fumecheng-7253	337	10	-	-	PUNCT
fumecheng-7253	337	11	dependent	dependent	ADJ
fumecheng-7253	337	12	physical	physical	ADJ
fumecheng-7253	337	13	characteristics	characteristic	NOUN
fumecheng-7253	337	14	of	of	ADP
fumecheng-7253	337	15	rotating	rotate	VERB
fumecheng-7253	337	16	nonlocal	nonlocal	ADJ
fumecheng-7253	337	17	nanobeams	nanobeam	NOUN
fumecheng-7253	337	18	subject	subject	ADJ
fumecheng-7253	337	19	to	to	ADP
fumecheng-7253	337	20	...	...	PUNCT
fumecheng-7253	337	21	653	653	NUM
fumecheng-7253	337	22	▪	▪	NOUN
fumecheng-7253	337	23	the	the	DET
fumecheng-7253	337	24	variation	variation	NOUN
fumecheng-7253	337	25	of	of	ADP
fumecheng-7253	337	26	the	the	DET
fumecheng-7253	337	27	thermal	thermal	ADJ
fumecheng-7253	337	28	conductivity	conductivity	NOUN
fumecheng-7253	337	29	affects	affect	VERB
fumecheng-7253	337	30	the	the	DET
fumecheng-7253	337	31	wave	wave	NOUN
fumecheng-7253	337	32	propagation	propagation	NOUN
fumecheng-7253	337	33	rate	rate	NOUN
fumecheng-7253	337	34	of	of	ADP
fumecheng-7253	337	35	all	all	PRON
fumecheng-7253	337	36	of	of	ADP
fumecheng-7253	337	37	field	field	NOUN
fumecheng-7253	337	38	variables	variable	NOUN
fumecheng-7253	337	39	.	.	PUNCT
fumecheng-7253	338	1	physical	physical	ADJ
fumecheng-7253	338	2	fields	field	NOUN
fumecheng-7253	338	3	strongly	strongly	ADV
fumecheng-7253	338	4	depend	depend	VERB
fumecheng-7253	338	5	on	on	ADP
fumecheng-7253	338	6	the	the	DET
fumecheng-7253	338	7	variation	variation	NOUN
fumecheng-7253	338	8	of	of	ADP
fumecheng-7253	338	9	the	the	DET
fumecheng-7253	338	10	thermal	thermal	ADJ
fumecheng-7253	338	11	conductivity	conductivity	NOUN
fumecheng-7253	338	12	.	.	PUNCT
fumecheng-7253	339	1	▪	▪	NOUN
fumecheng-7253	339	2	the	the	DET
fumecheng-7253	339	3	dependency	dependency	NOUN
fumecheng-7253	339	4	of	of	ADP
fumecheng-7253	339	5	the	the	DET
fumecheng-7253	339	6	thermal	thermal	ADJ
fumecheng-7253	339	7	conductivity	conductivity	NOUN
fumecheng-7253	339	8	on	on	ADP
fumecheng-7253	339	9	the	the	DET
fumecheng-7253	339	10	temperature	temperature	NOUN
fumecheng-7253	339	11	causes	cause	VERB
fumecheng-7253	339	12	a	a	DET
fumecheng-7253	339	13	significant	significant	ADJ
fumecheng-7253	339	14	influence	influence	NOUN
fumecheng-7253	339	15	on	on	ADP
fumecheng-7253	339	16	the	the	DET
fumecheng-7253	339	17	mechanical	mechanical	ADJ
fumecheng-7253	339	18	and	and	CCONJ
fumecheng-7253	339	19	thermal	thermal	ADJ
fumecheng-7253	339	20	interactions	interaction	NOUN
fumecheng-7253	339	21	.	.	PUNCT
fumecheng-7253	340	1	▪	▪	NOUN
fumecheng-7253	340	2	the	the	DET
fumecheng-7253	340	3	nonlocal	nonlocal	ADJ
fumecheng-7253	340	4	parameter	parameter	NOUN
fumecheng-7253	340	5	effects	effect	NOUN
fumecheng-7253	340	6	are	be	AUX
fumecheng-7253	340	7	considered	consider	VERB
fumecheng-7253	340	8	to	to	PART
fumecheng-7253	340	9	be	be	AUX
fumecheng-7253	340	10	significant	significant	ADJ
fumecheng-7253	340	11	on	on	ADP
fumecheng-7253	340	12	all	all	DET
fumecheng-7253	340	13	fields	field	NOUN
fumecheng-7253	340	14	studied	study	VERB
fumecheng-7253	340	15	.	.	PUNCT
fumecheng-7253	341	1	▪	▪	NOUN
fumecheng-7253	341	2	the	the	DET
fumecheng-7253	341	3	presence	presence	NOUN
fumecheng-7253	341	4	of	of	ADP
fumecheng-7253	341	5	dynamic	dynamic	ADJ
fumecheng-7253	341	6	load	load	NOUN
fumecheng-7253	341	7	has	have	VERB
fumecheng-7253	341	8	a	a	DET
fumecheng-7253	341	9	considerable	considerable	ADJ
fumecheng-7253	341	10	impact	impact	NOUN
fumecheng-7253	341	11	on	on	ADP
fumecheng-7253	341	12	the	the	DET
fumecheng-7253	341	13	results	result	NOUN
fumecheng-7253	341	14	of	of	ADP
fumecheng-7253	341	15	all	all	DET
fumecheng-7253	341	16	physical	physical	ADJ
fumecheng-7253	341	17	quantities	quantity	NOUN
fumecheng-7253	341	18	.	.	PUNCT
fumecheng-7253	342	1	▪	▪	NOUN
fumecheng-7253	342	2	there	there	PRON
fumecheng-7253	342	3	are	be	VERB
fumecheng-7253	342	4	significant	significant	ADJ
fumecheng-7253	342	5	differences	difference	NOUN
fumecheng-7253	342	6	between	between	ADP
fumecheng-7253	342	7	the	the	DET
fumecheng-7253	342	8	results	result	NOUN
fumecheng-7253	342	9	of	of	ADP
fumecheng-7253	342	10	point	point	NOUN
fumecheng-7253	342	11	load	load	NOUN
fumecheng-7253	342	12	with	with	ADP
fumecheng-7253	342	13	exponential	exponential	ADJ
fumecheng-7253	342	14	decay	decay	NOUN
fumecheng-7253	342	15	and	and	CCONJ
fumecheng-7253	342	16	those	those	PRON
fumecheng-7253	342	17	obtained	obtain	VERB
fumecheng-7253	342	18	in	in	ADP
fumecheng-7253	342	19	the	the	DET
fumecheng-7253	342	20	case	case	NOUN
fumecheng-7253	342	21	of	of	ADP
fumecheng-7253	342	22	uniformly	uniformly	ADV
fumecheng-7253	342	23	distributed	distribute	VERB
fumecheng-7253	342	24	one	one	NUM
fumecheng-7253	342	25	.	.	PUNCT
fumecheng-7253	343	1	the	the	DET
fumecheng-7253	343	2	thermoelastic	thermoelastic	ADJ
fumecheng-7253	343	3	stresses	stress	NOUN
fumecheng-7253	343	4	and	and	CCONJ
fumecheng-7253	343	5	temperature	temperature	NOUN
fumecheng-7253	343	6	gradient	gradient	NOUN
fumecheng-7253	343	7	,	,	PUNCT
fumecheng-7253	343	8	on	on	ADP
fumecheng-7253	343	9	the	the	DET
fumecheng-7253	343	10	other	other	ADJ
fumecheng-7253	343	11	hand	hand	NOUN
fumecheng-7253	343	12	,	,	PUNCT
fumecheng-7253	343	13	are	be	AUX
fumecheng-7253	343	14	highly	highly	ADV
fumecheng-7253	343	15	dependent	dependent	ADJ
fumecheng-7253	343	16	on	on	ADP
fumecheng-7253	343	17	the	the	DET
fumecheng-7253	343	18	angular	angular	ADJ
fumecheng-7253	343	19	frequency	frequency	NOUN
fumecheng-7253	343	20	of	of	ADP
fumecheng-7253	343	21	the	the	DET
fumecheng-7253	343	22	thermal	thermal	ADJ
fumecheng-7253	343	23	loading	loading	NOUN
fumecheng-7253	343	24	.	.	PUNCT
fumecheng-7253	344	1	current	current	ADJ
fumecheng-7253	344	2	research	research	NOUN
fumecheng-7253	344	3	may	may	AUX
fumecheng-7253	344	4	be	be	AUX
fumecheng-7253	344	5	used	use	VERB
fumecheng-7253	344	6	in	in	ADP
fumecheng-7253	344	7	applications	application	NOUN
fumecheng-7253	344	8	including	include	VERB
fumecheng-7253	344	9	micro	micro	ADJ
fumecheng-7253	344	10	and	and	CCONJ
fumecheng-7253	344	11	nano	nano	ADJ
fumecheng-7253	344	12	mechanical	mechanical	ADJ
fumecheng-7253	344	13	gears	gear	NOUN
fumecheng-7253	344	14	,	,	PUNCT
fumecheng-7253	344	15	micro	micro	NOUN
fumecheng-7253	344	16	-	-	NOUN
fumecheng-7253	344	17	mirrors	mirror	NOUN
fumecheng-7253	344	18	for	for	ADP
fumecheng-7253	344	19	light	light	ADJ
fumecheng-7253	344	20	guiding	guide	VERB
fumecheng-7253	344	21	purposes	purpose	NOUN
fumecheng-7253	344	22	in	in	ADP
fumecheng-7253	344	23	image	image	NOUN
fumecheng-7253	344	24	projection	projection	NOUN
fumecheng-7253	344	25	devises	devise	NOUN
fumecheng-7253	344	26	,	,	PUNCT
fumecheng-7253	344	27	micro	micro	ADJ
fumecheng-7253	344	28	-	-	NOUN
fumecheng-7253	344	29	turbine	turbine	ADJ
fumecheng-7253	344	30	blades	blade	NOUN
fumecheng-7253	344	31	,	,	PUNCT
fumecheng-7253	344	32	micro	micro	ADJ
fumecheng-7253	344	33	accelerometers	accelerometer	NOUN
fumecheng-7253	344	34	(	(	PUNCT
fumecheng-7253	344	35	fig	fig	NOUN
fumecheng-7253	344	36	.	.	PUNCT
fumecheng-7253	344	37	18	18	NUM
fumecheng-7253	344	38	)	)	PUNCT
fumecheng-7253	344	39	,	,	PUNCT
fumecheng-7253	344	40	resonators	resonator	NOUN
fumecheng-7253	344	41	,	,	PUNCT
fumecheng-7253	344	42	frequency	frequency	NOUN
fumecheng-7253	344	43	filters	filter	NOUN
fumecheng-7253	344	44	and	and	CCONJ
fumecheng-7253	344	45	relay	relay	NOUN
fumecheng-7253	344	46	switches	switch	NOUN
fumecheng-7253	344	47	.	.	PUNCT
fumecheng-7253	345	1	fig	fig	NOUN
fumecheng-7253	345	2	.	.	PUNCT
fumecheng-7253	346	1	18	18	NUM
fumecheng-7253	346	2	(	(	PUNCT
fumecheng-7253	346	3	a	a	NOUN
fumecheng-7253	346	4	)	)	PUNCT
fumecheng-7253	346	5	micro	micro	ADJ
fumecheng-7253	346	6	scale	scale	NOUN
fumecheng-7253	346	7	mechanical	mechanical	ADJ
fumecheng-7253	346	8	gear	gear	NOUN
fumecheng-7253	346	9	,	,	PUNCT
fumecheng-7253	346	10	(	(	PUNCT
fumecheng-7253	346	11	b)micro	b)micro	NOUN
fumecheng-7253	346	12	-	-	NOUN
fumecheng-7253	346	13	mirror	mirror	NOUN
fumecheng-7253	346	14	,	,	PUNCT
fumecheng-7253	346	15	(	(	PUNCT
fumecheng-7253	346	16	c	c	NOUN
fumecheng-7253	346	17	)	)	PUNCT
fumecheng-7253	346	18	micro	micro	NOUN
fumecheng-7253	346	19	-	-	NOUN
fumecheng-7253	346	20	turbine	turbine	ADJ
fumecheng-7253	346	21	,	,	PUNCT
fumecheng-7253	346	22	(	(	PUNCT
fumecheng-7253	346	23	d	d	NOUN
fumecheng-7253	346	24	)	)	PUNCT
fumecheng-7253	346	25	micro	micro	ADJ
fumecheng-7253	346	26	scale	scale	NOUN
fumecheng-7253	346	27	accelerometer	accelerometer	NOUN
fumecheng-7253	346	28	acknowledgements	acknowledgement	NOUN
fumecheng-7253	346	29	:	:	PUNCT
fumecheng-7253	346	30	h.m	h.m	PROPN
fumecheng-7253	346	31	.	.	PROPN
fumecheng-7253	346	32	sedighi	sedighi	PROPN
fumecheng-7253	346	33	is	be	AUX
fumecheng-7253	346	34	grateful	grateful	ADJ
fumecheng-7253	346	35	to	to	ADP
fumecheng-7253	346	36	the	the	DET
fumecheng-7253	346	37	research	research	NOUN
fumecheng-7253	346	38	council	council	PROPN
fumecheng-7253	346	39	of	of	ADP
fumecheng-7253	346	40	shahid	shahid	PROPN
fumecheng-7253	346	41	chamran	chamran	PROPN
fumecheng-7253	346	42	university	university	PROPN
fumecheng-7253	346	43	of	of	ADP
fumecheng-7253	346	44	ahvaz	ahvaz	NOUN
fumecheng-7253	346	45	for	for	ADP
fumecheng-7253	346	46	its	its	PRON
fumecheng-7253	346	47	financial	financial	ADJ
fumecheng-7253	346	48	support	support	NOUN
fumecheng-7253	346	49	(	(	PUNCT
fumecheng-7253	346	50	grant	grant	VERB
fumecheng-7253	346	51	no	no	INTJ
fumecheng-7253	346	52	.	.	PUNCT
fumecheng-7253	346	53	scu.em99.98	scu.em99.98	NOUN
fumecheng-7253	346	54	)	)	PUNCT
fumecheng-7253	346	55	.	.	PUNCT
fumecheng-7253	347	1	654	654	NUM
fumecheng-7253	347	2	a.	a.	NOUN
fumecheng-7253	347	3	e.	e.	PROPN
fumecheng-7253	347	4	abouelregal	abouelregal	PROPN
fumecheng-7253	347	5	,	,	PUNCT
fumecheng-7253	347	6	h.	h.	PROPN
fumecheng-7253	347	7	m.	m.	PROPN
fumecheng-7253	347	8	sedighi	sedighi	PROPN
fumecheng-7253	347	9	,	,	PUNCT
fumecheng-7253	347	10	s.	s.	PROPN
fumecheng-7253	347	11	a.	a.	PROPN
fumecheng-7253	347	12	faghidian	faghidian	PROPN
fumecheng-7253	347	13	,	,	PUNCT
fumecheng-7253	347	14	a.	a.	PROPN
fumecheng-7253	347	15	h.	h.	PROPN
fumecheng-7253	347	16	shirazi	shirazi	PROPN
fumecheng-7253	347	17	references	reference	NOUN
fumecheng-7253	347	18	1	1	NUM
fumecheng-7253	347	19	.	.	PUNCT
fumecheng-7253	348	1	lord	lord	PROPN
fumecheng-7253	348	2	,	,	PUNCT
fumecheng-7253	348	3	h.w	h.w	PROPN
fumecheng-7253	348	4	.	.	PROPN
fumecheng-7253	348	5	,	,	PUNCT
fumecheng-7253	348	6	shulman	shulman	PROPN
fumecheng-7253	348	7	,	,	PUNCT
fumecheng-7253	348	8	y.h	y.h	PROPN
fumecheng-7253	348	9	.	.	PROPN
fumecheng-7253	348	10	,1967	,1967	PROPN
fumecheng-7253	348	11	,	,	PUNCT
fumecheng-7253	348	12	a	a	DET
fumecheng-7253	348	13	generalized	generalize	VERB
fumecheng-7253	348	14	dynamical	dynamical	ADJ
fumecheng-7253	348	15	theory	theory	NOUN
fumecheng-7253	348	16	of	of	ADP
fumecheng-7253	348	17	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	348	18	,	,	PUNCT
fumecheng-7253	348	19	j.	j.	PROPN
fumecheng-7253	348	20	mech	mech	PROPN
fumecheng-7253	348	21	.	.	PUNCT
fumecheng-7253	349	1	phys	phy	NOUN
fumecheng-7253	349	2	.	.	PUNCT
fumecheng-7253	350	1	solids,15(5	solids,15(5	PROPN
fumecheng-7253	350	2	)	)	PUNCT
fumecheng-7253	350	3	,	,	PUNCT
fumecheng-7253	350	4	pp	pp	ADJ
fumecheng-7253	350	5	.	.	PUNCT
fumecheng-7253	351	1	299–309	299–309	NUM
fumecheng-7253	351	2	.	.	X
fumecheng-7253	352	1	2	2	NUM
fumecheng-7253	352	2	.	.	X
fumecheng-7253	352	3	tzou	tzou	PROPN
fumecheng-7253	352	4	,	,	PUNCT
fumecheng-7253	352	5	d.y	d.y	PROPN
fumecheng-7253	352	6	.	.	PROPN
fumecheng-7253	352	7	,1992	,1992	ADJ
fumecheng-7253	352	8	,	,	PUNCT
fumecheng-7253	352	9	thermal	thermal	ADJ
fumecheng-7253	352	10	shock	shock	NOUN
fumecheng-7253	352	11	phenomena	phenomenon	NOUN
fumecheng-7253	352	12	under	under	ADP
fumecheng-7253	352	13	high	high	ADJ
fumecheng-7253	352	14	rate	rate	NOUN
fumecheng-7253	352	15	response	response	NOUN
fumecheng-7253	352	16	in	in	ADP
fumecheng-7253	352	17	solids	solid	NOUN
fumecheng-7253	352	18	,	,	PUNCT
fumecheng-7253	352	19	annual	annual	ADJ
fumecheng-7253	352	20	rev	rev	X
fumecheng-7253	352	21	.	.	PROPN
fumecheng-7253	352	22	heat	heat	PROPN
fumecheng-7253	352	23	transf	transf	PROPN
fumecheng-7253	352	24	.	.	PUNCT
fumecheng-7253	352	25	,	,	PUNCT
fumecheng-7253	352	26	4(4	4(4	NUM
fumecheng-7253	352	27	)	)	PUNCT
fumecheng-7253	352	28	,	,	PUNCT
fumecheng-7253	352	29	pp	pp	ADJ
fumecheng-7253	352	30	.	.	PUNCT
fumecheng-7253	353	1	111–185	111–185	NUM
fumecheng-7253	353	2	.	.	PUNCT
fumecheng-7253	354	1	3	3	X
fumecheng-7253	354	2	.	.	X
fumecheng-7253	354	3	tzou	tzou	PROPN
fumecheng-7253	354	4	,	,	PUNCT
fumecheng-7253	354	5	d.y	d.y	PROPN
fumecheng-7253	354	6	.	.	PROPN
fumecheng-7253	354	7	,1995	,1995	PROPN
fumecheng-7253	354	8	,	,	PUNCT
fumecheng-7253	354	9	a	a	DET
fumecheng-7253	354	10	unified	unified	ADJ
fumecheng-7253	354	11	field	field	NOUN
fumecheng-7253	354	12	approach	approach	NOUN
fumecheng-7253	354	13	for	for	ADP
fumecheng-7253	354	14	heat	heat	NOUN
fumecheng-7253	354	15	conduction	conduction	NOUN
fumecheng-7253	354	16	from	from	ADP
fumecheng-7253	354	17	macro	macro	NOUN
fumecheng-7253	354	18	-	-	PUNCT
fumecheng-7253	354	19	to	to	ADP
fumecheng-7253	354	20	micro	micro	NOUN
fumecheng-7253	354	21	-	-	NOUN
fumecheng-7253	354	22	scales	scale	NOUN
fumecheng-7253	354	23	,	,	PUNCT
fumecheng-7253	354	24	j.	j.	PROPN
fumecheng-7253	354	25	heat	heat	PROPN
fumecheng-7253	354	26	transf	transf	PROPN
fumecheng-7253	354	27	.	.	PUNCT
fumecheng-7253	354	28	,	,	PUNCT
fumecheng-7253	354	29	117(1	117(1	NUM
fumecheng-7253	354	30	)	)	PUNCT
fumecheng-7253	354	31	,	,	PUNCT
fumecheng-7253	354	32	pp	pp	PROPN
fumecheng-7253	354	33	.	.	PUNCT
fumecheng-7253	355	1	8–16	8–16	PROPN
fumecheng-7253	355	2	.	.	PROPN
fumecheng-7253	356	1	4	4	NUM
fumecheng-7253	356	2	.	.	X
fumecheng-7253	356	3	tzou	tzou	PROPN
fumecheng-7253	356	4	,	,	PUNCT
fumecheng-7253	356	5	d.y	d.y	PROPN
fumecheng-7253	356	6	.	.	PROPN
fumecheng-7253	356	7	,1995	,1995	PROPN
fumecheng-7253	356	8	,	,	PUNCT
fumecheng-7253	356	9	the	the	DET
fumecheng-7253	356	10	generalized	generalized	ADJ
fumecheng-7253	356	11	lagging	lagging	ADJ
fumecheng-7253	356	12	response	response	NOUN
fumecheng-7253	356	13	in	in	ADP
fumecheng-7253	356	14	small	small	ADJ
fumecheng-7253	356	15	-	-	PUNCT
fumecheng-7253	356	16	scale	scale	NOUN
fumecheng-7253	356	17	and	and	CCONJ
fumecheng-7253	356	18	high	high	ADJ
fumecheng-7253	356	19	-	-	PUNCT
fumecheng-7253	356	20	rate	rate	NOUN
fumecheng-7253	356	21	heating	heating	NOUN
fumecheng-7253	356	22	,	,	PUNCT
fumecheng-7253	356	23	int	int	NOUN
fumecheng-7253	356	24	.	.	PUNCT
fumecheng-7253	357	1	j.	j.	PROPN
fumecheng-7253	357	2	heat	heat	PROPN
fumecheng-7253	357	3	mass	mass	PROPN
fumecheng-7253	357	4	transf	transf	PROPN
fumecheng-7253	357	5	.	.	PUNCT
fumecheng-7253	357	6	,	,	PUNCT
fumecheng-7253	357	7	38(17	38(17	PROPN
fumecheng-7253	357	8	)	)	PUNCT
fumecheng-7253	357	9	,	,	PUNCT
fumecheng-7253	357	10	pp	pp	ADP
fumecheng-7253	357	11	.	.	PUNCT
fumecheng-7253	358	1	3231–3240	3231–3240	NUM
fumecheng-7253	358	2	.	.	PUNCT
fumecheng-7253	359	1	5	5	NUM
fumecheng-7253	359	2	.	.	X
fumecheng-7253	359	3	abouelregal	abouelregal	ADJ
fumecheng-7253	359	4	,	,	PUNCT
fumecheng-7253	359	5	a.e	a.e	PROPN
fumecheng-7253	359	6	.	.	PROPN
fumecheng-7253	359	7	2019	2019	NUM
fumecheng-7253	359	8	,	,	PUNCT
fumecheng-7253	359	9	two	two	NUM
fumecheng-7253	359	10	-	-	PUNCT
fumecheng-7253	359	11	temperature	temperature	NOUN
fumecheng-7253	359	12	thermoelastic	thermoelastic	ADJ
fumecheng-7253	359	13	model	model	NOUN
fumecheng-7253	359	14	without	without	ADP
fumecheng-7253	359	15	energy	energy	NOUN
fumecheng-7253	359	16	dissipation	dissipation	NOUN
fumecheng-7253	359	17	including	include	VERB
fumecheng-7253	359	18	higher	high	ADJ
fumecheng-7253	359	19	order	order	NOUN
fumecheng-7253	359	20	time	time	NOUN
fumecheng-7253	359	21	-	-	PUNCT
fumecheng-7253	359	22	derivatives	derivative	NOUN
fumecheng-7253	359	23	and	and	CCONJ
fumecheng-7253	359	24	two	two	NUM
fumecheng-7253	359	25	phase	phase	NOUN
fumecheng-7253	359	26	-	-	PUNCT
fumecheng-7253	359	27	lags	lag	NOUN
fumecheng-7253	359	28	,	,	PUNCT
fumecheng-7253	359	29	materials	material	NOUN
fumecheng-7253	359	30	research	research	NOUN
fumecheng-7253	359	31	express	express	ADJ
fumecheng-7253	359	32	,	,	PUNCT
fumecheng-7253	359	33	6(11	6(11	NUM
fumecheng-7253	359	34	)	)	PUNCT
fumecheng-7253	359	35	,	,	PUNCT
fumecheng-7253	359	36	116535	116535	NUM
fumecheng-7253	359	37	.	.	PUNCT
fumecheng-7253	360	1	6	6	NUM
fumecheng-7253	360	2	.	.	X
fumecheng-7253	360	3	abouelregal	abouelregal	ADJ
fumecheng-7253	360	4	,	,	PUNCT
fumecheng-7253	360	5	a.e	a.e	PROPN
fumecheng-7253	360	6	.	.	PROPN
fumecheng-7253	360	7	,2020	,2020	PROPN
fumecheng-7253	360	8	,	,	PUNCT
fumecheng-7253	360	9	on	on	ADP
fumecheng-7253	360	10	green	green	ADJ
fumecheng-7253	360	11	and	and	CCONJ
fumecheng-7253	360	12	naghdithermoelasticity	naghdithermoelasticity	NOUN
fumecheng-7253	360	13	model	model	NOUN
fumecheng-7253	360	14	without	without	ADP
fumecheng-7253	360	15	energy	energy	NOUN
fumecheng-7253	360	16	dissipation	dissipation	NOUN
fumecheng-7253	360	17	with	with	ADP
fumecheng-7253	360	18	higher	high	ADJ
fumecheng-7253	360	19	order	order	NOUN
fumecheng-7253	360	20	time	time	NOUN
fumecheng-7253	360	21	differential	differential	NOUN
fumecheng-7253	360	22	and	and	CCONJ
fumecheng-7253	360	23	phase	phase	NOUN
fumecheng-7253	360	24	-	-	PUNCT
fumecheng-7253	360	25	lags	lag	NOUN
fumecheng-7253	360	26	,	,	PUNCT
fumecheng-7253	360	27	journal	journal	NOUN
fumecheng-7253	360	28	of	of	ADP
fumecheng-7253	360	29	applied	applied	ADJ
fumecheng-7253	360	30	and	and	CCONJ
fumecheng-7253	360	31	computational	computational	ADJ
fumecheng-7253	360	32	mechanics	mechanic	NOUN
fumecheng-7253	360	33	,	,	PUNCT
fumecheng-7253	360	34	6(3),pp	6(3),pp	NUM
fumecheng-7253	360	35	.	.	PUNCT
fumecheng-7253	361	1	445–56	445–56	NUM
fumecheng-7253	361	2	.	.	PUNCT
fumecheng-7253	362	1	7	7	X
fumecheng-7253	362	2	.	.	X
fumecheng-7253	362	3	abouelregal	abouelregal	ADJ
fumecheng-7253	362	4	,	,	PUNCT
fumecheng-7253	362	5	a.e	a.e	PROPN
fumecheng-7253	362	6	.	.	PROPN
fumecheng-7253	362	7	,2019	,2019	PROPN
fumecheng-7253	362	8	,	,	PUNCT
fumecheng-7253	362	9	a	a	DET
fumecheng-7253	362	10	novel	novel	ADJ
fumecheng-7253	362	11	generalized	generalize	VERB
fumecheng-7253	362	12	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	362	13	with	with	ADP
fumecheng-7253	362	14	higher	high	ADJ
fumecheng-7253	362	15	-	-	PUNCT
fumecheng-7253	362	16	order	order	NOUN
fumecheng-7253	362	17	time	time	NOUN
fumecheng-7253	362	18	-	-	PUNCT
fumecheng-7253	362	19	derivatives	derivative	NOUN
fumecheng-7253	362	20	and	and	CCONJ
fumecheng-7253	362	21	threephase	threephase	NOUN
fumecheng-7253	362	22	lags	lag	NOUN
fumecheng-7253	362	23	,	,	PUNCT
fumecheng-7253	362	24	multidiscipline	multidiscipline	VERB
fumecheng-7253	362	25	modeling	modeling	NOUN
fumecheng-7253	362	26	in	in	ADP
fumecheng-7253	362	27	materials	material	NOUN
fumecheng-7253	362	28	and	and	CCONJ
fumecheng-7253	362	29	structures	structure	NOUN
fumecheng-7253	362	30	,	,	PUNCT
fumecheng-7253	362	31	doi	doi	NOUN
fumecheng-7253	362	32	:	:	PUNCT
fumecheng-7253	362	33	10.1108	10.1108	NUM
fumecheng-7253	362	34	/	/	SYM
fumecheng-7253	362	35	mmms-07	mmms-07	PROPN
fumecheng-7253	362	36	-	-	PUNCT
fumecheng-7253	362	37	2019	2019	NUM
fumecheng-7253	362	38	-	-	PUNCT
fumecheng-7253	362	39	0138	0138	NUM
fumecheng-7253	362	40	.	.	PUNCT
fumecheng-7253	363	1	8	8	NUM
fumecheng-7253	363	2	.	.	X
fumecheng-7253	364	1	abouelregal	abouelregal	ADJ
fumecheng-7253	364	2	,	,	PUNCT
fumecheng-7253	364	3	a.e	a.e	PROPN
fumecheng-7253	364	4	.	.	PROPN
fumecheng-7253	364	5	,2019	,2019	PUNCT
fumecheng-7253	364	6	,	,	PUNCT
fumecheng-7253	364	7	three	three	NUM
fumecheng-7253	364	8	-	-	PUNCT
fumecheng-7253	364	9	phase	phase	NOUN
fumecheng-7253	364	10	-	-	PUNCT
fumecheng-7253	364	11	lag	lag	NOUN
fumecheng-7253	364	12	thermoelastic	thermoelastic	ADJ
fumecheng-7253	364	13	heat	heat	NOUN
fumecheng-7253	364	14	conduction	conduction	NOUN
fumecheng-7253	364	15	model	model	NOUN
fumecheng-7253	364	16	with	with	ADP
fumecheng-7253	364	17	higher	high	ADJ
fumecheng-7253	364	18	-	-	PUNCT
fumecheng-7253	364	19	order	order	NOUN
fumecheng-7253	364	20	timefractional	timefractional	ADJ
fumecheng-7253	364	21	derivatives	derivative	NOUN
fumecheng-7253	364	22	,	,	PUNCT
fumecheng-7253	364	23	indian	indian	ADJ
fumecheng-7253	364	24	j.	j.	PROPN
fumecheng-7253	364	25	phys	phys	PROPN
fumecheng-7253	364	26	.	.	PUNCT
fumecheng-7253	365	1	https://doi.org/10.1007/s12648-019-01635-z	https://doi.org/10.1007/s12648-019-01635-z	INTJ
fumecheng-7253	365	2	.	.	PUNCT
fumecheng-7253	366	1	9	9	X
fumecheng-7253	366	2	.	.	X
fumecheng-7253	366	3	berman	berman	PROPN
fumecheng-7253	366	4	,	,	PUNCT
fumecheng-7253	366	5	r.	r.	PROPN
fumecheng-7253	366	6	,1953	,1953	PROPN
fumecheng-7253	366	7	,	,	PUNCT
fumecheng-7253	366	8	the	the	DET
fumecheng-7253	366	9	thermal	thermal	ADJ
fumecheng-7253	366	10	conductivity	conductivity	NOUN
fumecheng-7253	366	11	of	of	ADP
fumecheng-7253	366	12	dielectric	dielectric	ADJ
fumecheng-7253	366	13	solids	solid	NOUN
fumecheng-7253	366	14	at	at	ADP
fumecheng-7253	366	15	low	low	ADJ
fumecheng-7253	366	16	temperatures	temperature	NOUN
fumecheng-7253	366	17	,	,	PUNCT
fumecheng-7253	366	18	advances	advance	NOUN
fumecheng-7253	366	19	in	in	ADP
fumecheng-7253	366	20	physics	physics	NOUN
fumecheng-7253	366	21	,	,	PUNCT
fumecheng-7253	366	22	2(5	2(5	NUM
fumecheng-7253	366	23	)	)	PUNCT
fumecheng-7253	366	24	,	,	PUNCT
fumecheng-7253	366	25	pp	pp	ADP
fumecheng-7253	366	26	.	.	PUNCT
fumecheng-7253	367	1	103	103	NUM
fumecheng-7253	367	2	-	-	SYM
fumecheng-7253	367	3	140	140	NUM
fumecheng-7253	367	4	.	.	PUNCT
fumecheng-7253	368	1	10	10	NUM
fumecheng-7253	368	2	.	.	PUNCT
fumecheng-7253	369	1	younis	younis	PROPN
fumecheng-7253	369	2	,	,	PUNCT
fumecheng-7253	369	3	m.i	m.i	PROPN
fumecheng-7253	369	4	.	.	PROPN
fumecheng-7253	369	5	,2011	,2011	PUNCT
fumecheng-7253	369	6	,	,	PUNCT
fumecheng-7253	369	7	mems	mem	NOUN
fumecheng-7253	369	8	linear	linear	ADJ
fumecheng-7253	369	9	and	and	CCONJ
fumecheng-7253	369	10	non	non	ADJ
fumecheng-7253	369	11	-	-	ADJ
fumecheng-7253	369	12	linear	linear	ADJ
fumecheng-7253	369	13	statics	static	NOUN
fumecheng-7253	369	14	and	and	CCONJ
fumecheng-7253	369	15	dynamics	dynamic	NOUN
fumecheng-7253	369	16	,	,	PUNCT
fumecheng-7253	369	17	springer	springer	NOUN
fumecheng-7253	369	18	,	,	PUNCT
fumecheng-7253	369	19	new	new	PROPN
fumecheng-7253	369	20	york	york	PROPN
fumecheng-7253	369	21	,	,	PUNCT
fumecheng-7253	369	22	usa	usa	PROPN
fumecheng-7253	369	23	.	.	PROPN
fumecheng-7253	369	24	11	11	NUM
fumecheng-7253	369	25	.	.	PUNCT
fumecheng-7253	370	1	allameh	allameh	NOUN
fumecheng-7253	370	2	,	,	PUNCT
fumecheng-7253	370	3	s.m	s.m	PROPN
fumecheng-7253	370	4	.	.	PROPN
fumecheng-7253	370	5	,2003	,2003	PROPN
fumecheng-7253	370	6	,	,	PUNCT
fumecheng-7253	370	7	an	an	DET
fumecheng-7253	370	8	introduction	introduction	NOUN
fumecheng-7253	370	9	to	to	ADP
fumecheng-7253	370	10	mechanical	mechanical	ADJ
fumecheng-7253	370	11	-	-	PUNCT
fumecheng-7253	370	12	properties	property	NOUN
fumecheng-7253	370	13	-	-	PUNCT
fumecheng-7253	370	14	related	relate	VERB
fumecheng-7253	370	15	issues	issue	NOUN
fumecheng-7253	370	16	in	in	ADP
fumecheng-7253	370	17	mems	mems	ADJ
fumecheng-7253	370	18	structures	structure	NOUN
fumecheng-7253	370	19	,	,	PUNCT
fumecheng-7253	370	20	j.	j.	PROPN
fumecheng-7253	370	21	mater	mater	PROPN
fumecheng-7253	370	22	.	.	PUNCT
fumecheng-7253	371	1	sci	sci	PROPN
fumecheng-7253	371	2	.	.	PROPN
fumecheng-7253	371	3	,	,	PUNCT
fumecheng-7253	371	4	38	38	NUM
fumecheng-7253	371	5	,	,	PUNCT
fumecheng-7253	371	6	pp	pp	ADJ
fumecheng-7253	371	7	.	.	PUNCT
fumecheng-7253	372	1	4115–4123	4115–4123	NUM
fumecheng-7253	372	2	.	.	PUNCT
fumecheng-7253	373	1	12	12	NUM
fumecheng-7253	373	2	.	.	X
fumecheng-7253	373	3	sedighi	sedighi	PROPN
fumecheng-7253	373	4	,	,	PUNCT
fumecheng-7253	373	5	h.m	h.m	PROPN
fumecheng-7253	373	6	.	.	PROPN
fumecheng-7253	373	7	,	,	PUNCT
fumecheng-7253	373	8	bozorgmehri	bozorgmehri	PROPN
fumecheng-7253	373	9	,	,	PUNCT
fumecheng-7253	373	10	a.	a.	NOUN
fumecheng-7253	373	11	,	,	PUNCT
fumecheng-7253	373	12	2016	2016	NUM
fumecheng-7253	373	13	,	,	PUNCT
fumecheng-7253	373	14	dynamic	dynamic	ADJ
fumecheng-7253	373	15	instability	instability	NOUN
fumecheng-7253	373	16	analysis	analysis	NOUN
fumecheng-7253	373	17	of	of	ADP
fumecheng-7253	373	18	doubly	doubly	ADV
fumecheng-7253	373	19	clamped	clamp	VERB
fumecheng-7253	373	20	cylindrical	cylindrical	ADJ
fumecheng-7253	373	21	nanowires	nanowire	NOUN
fumecheng-7253	373	22	in	in	ADP
fumecheng-7253	373	23	the	the	DET
fumecheng-7253	373	24	presence	presence	NOUN
fumecheng-7253	373	25	of	of	ADP
fumecheng-7253	373	26	casimir	casimir	NOUN
fumecheng-7253	373	27	attraction	attraction	NOUN
fumecheng-7253	373	28	and	and	CCONJ
fumecheng-7253	373	29	surface	surface	NOUN
fumecheng-7253	373	30	effects	effect	NOUN
fumecheng-7253	373	31	using	use	VERB
fumecheng-7253	373	32	modified	modified	ADJ
fumecheng-7253	373	33	couple	couple	NOUN
fumecheng-7253	373	34	stress	stress	NOUN
fumecheng-7253	373	35	theory	theory	NOUN
fumecheng-7253	373	36	,	,	PUNCT
fumecheng-7253	373	37	acta	acta	PROPN
fumecheng-7253	373	38	mech	mech	PROPN
fumecheng-7253	373	39	.	.	PROPN
fumecheng-7253	373	40	,	,	PUNCT
fumecheng-7253	373	41	227	227	NUM
fumecheng-7253	373	42	,	,	PUNCT
fumecheng-7253	373	43	pp	pp	ADJ
fumecheng-7253	373	44	.	.	PUNCT
fumecheng-7253	374	1	1575	1575	NUM
fumecheng-7253	374	2	-	-	SYM
fumecheng-7253	374	3	1591	1591	NUM
fumecheng-7253	374	4	.	.	PUNCT
fumecheng-7253	375	1	13	13	NUM
fumecheng-7253	375	2	.	.	X
fumecheng-7253	375	3	malikan	malikan	PROPN
fumecheng-7253	375	4	,	,	PUNCT
fumecheng-7253	375	5	m.	m.	NOUN
fumecheng-7253	375	6	,	,	PUNCT
fumecheng-7253	375	7	uglov	uglov	NOUN
fumecheng-7253	375	8	,	,	PUNCT
fumecheng-7253	375	9	n.	n.	PROPN
fumecheng-7253	375	10	s.	s.	PROPN
fumecheng-7253	375	11	,	,	PUNCT
fumecheng-7253	375	12	eremeyev	eremeyev	PROPN
fumecheng-7253	375	13	,	,	PUNCT
fumecheng-7253	375	14	v.a	v.a	PROPN
fumecheng-7253	375	15	.	.	PROPN
fumecheng-7253	375	16	,	,	PUNCT
fumecheng-7253	375	17	2020,on	2020,on	NUM
fumecheng-7253	375	18	instabilities	instability	NOUN
fumecheng-7253	375	19	and	and	CCONJ
fumecheng-7253	375	20	post	post	ADJ
fumecheng-7253	375	21	-	-	ADJ
fumecheng-7253	375	22	buckling	buckling	NOUN
fumecheng-7253	375	23	of	of	ADP
fumecheng-7253	375	24	piezomagnetic	piezomagnetic	ADJ
fumecheng-7253	375	25	and	and	CCONJ
fumecheng-7253	375	26	flexomagnetic	flexomagnetic	ADJ
fumecheng-7253	375	27	nanostructures	nanostructure	NOUN
fumecheng-7253	375	28	,	,	PUNCT
fumecheng-7253	375	29	international	international	ADJ
fumecheng-7253	375	30	journal	journal	NOUN
fumecheng-7253	375	31	of	of	ADP
fumecheng-7253	375	32	engineering	engineering	NOUN
fumecheng-7253	375	33	science	science	NOUN
fumecheng-7253	375	34	,	,	PUNCT
fumecheng-7253	375	35	157	157	NUM
fumecheng-7253	375	36	,	,	PUNCT
fumecheng-7253	375	37	103395	103395	NUM
fumecheng-7253	375	38	.	.	PUNCT
fumecheng-7253	376	1	14	14	NUM
fumecheng-7253	376	2	.	.	PUNCT
fumecheng-7253	376	3	malikan	malikan	PROPN
fumecheng-7253	376	4	,	,	PUNCT
fumecheng-7253	376	5	m.	m.	NOUN
fumecheng-7253	376	6	,	,	PUNCT
fumecheng-7253	376	7	eremeyev	eremeyev	ADJ
fumecheng-7253	376	8	,	,	PUNCT
fumecheng-7253	376	9	v.	v.	ADP
fumecheng-7253	376	10	a.	a.	NOUN
fumecheng-7253	376	11	,żur	,żur	PUNCT
fumecheng-7253	376	12	,	,	PUNCT
fumecheng-7253	376	13	k.	k.	PROPN
fumecheng-7253	376	14	k.	k.	PROPN
fumecheng-7253	376	15	,2020,effect	,2020,effect	PUNCT
fumecheng-7253	376	16	of	of	ADP
fumecheng-7253	376	17	axial	axial	ADJ
fumecheng-7253	376	18	porosities	porosity	NOUN
fumecheng-7253	376	19	on	on	ADP
fumecheng-7253	376	20	flexomagnetic	flexomagnetic	ADJ
fumecheng-7253	376	21	response	response	NOUN
fumecheng-7253	376	22	of	of	ADP
fumecheng-7253	376	23	in	in	ADP
fumecheng-7253	376	24	-	-	PUNCT
fumecheng-7253	376	25	plane	plane	NOUN
fumecheng-7253	376	26	compressed	compress	VERB
fumecheng-7253	376	27	piezomagneticnanobeams	piezomagneticnanobeam	NOUN
fumecheng-7253	376	28	,	,	PUNCT
fumecheng-7253	376	29	symmetry	symmetry	NOUN
fumecheng-7253	376	30	,	,	PUNCT
fumecheng-7253	376	31	12(12	12(12	NUM
fumecheng-7253	376	32	)	)	PUNCT
fumecheng-7253	376	33	,	,	PUNCT
fumecheng-7253	376	34	1935	1935	NUM
fumecheng-7253	376	35	.	.	PUNCT
fumecheng-7253	377	1	15	15	NUM
fumecheng-7253	377	2	.	.	PUNCT
fumecheng-7253	377	3	malikan	malikan	PROPN
fumecheng-7253	377	4	,	,	PUNCT
fumecheng-7253	377	5	m.	m.	NOUN
fumecheng-7253	377	6	,	,	PUNCT
fumecheng-7253	377	7	&	&	CCONJ
fumecheng-7253	377	8	eremeyev	eremeyev	ADJ
fumecheng-7253	377	9	,	,	PUNCT
fumecheng-7253	377	10	v.a	v.a	PROPN
fumecheng-7253	377	11	.	.	PROPN
fumecheng-7253	377	12	,	,	PUNCT
fumecheng-7253	377	13	2020,on	2020,on	NUM
fumecheng-7253	377	14	nonlinear	nonlinear	ADJ
fumecheng-7253	377	15	bending	bend	VERB
fumecheng-7253	377	16	study	study	NOUN
fumecheng-7253	377	17	of	of	ADP
fumecheng-7253	377	18	a	a	DET
fumecheng-7253	377	19	piezo	piezo	PROPN
fumecheng-7253	377	20	-	-	ADJ
fumecheng-7253	377	21	flexomagneticnanobeam	flexomagneticnanobeam	NOUN
fumecheng-7253	377	22	based	base	VERB
fumecheng-7253	377	23	on	on	ADP
fumecheng-7253	377	24	an	an	DET
fumecheng-7253	377	25	analytical	analytical	ADJ
fumecheng-7253	377	26	-	-	PUNCT
fumecheng-7253	377	27	numerical	numerical	ADJ
fumecheng-7253	377	28	solution	solution	NOUN
fumecheng-7253	377	29	,	,	PUNCT
fumecheng-7253	377	30	nanomaterials	nanomaterial	NOUN
fumecheng-7253	377	31	,	,	PUNCT
fumecheng-7253	377	32	10(9	10(9	NUM
fumecheng-7253	377	33	)	)	PUNCT
fumecheng-7253	377	34	,	,	PUNCT
fumecheng-7253	377	35	1762	1762	NUM
fumecheng-7253	377	36	.	.	PUNCT
fumecheng-7253	378	1	16	16	NUM
fumecheng-7253	378	2	.	.	PUNCT
fumecheng-7253	378	3	malikan	malikan	PROPN
fumecheng-7253	378	4	,	,	PUNCT
fumecheng-7253	378	5	m.	m.	NOUN
fumecheng-7253	378	6	,	,	PUNCT
fumecheng-7253	378	7	eremeyev	eremeyev	PROPN
fumecheng-7253	378	8	,	,	PUNCT
fumecheng-7253	378	9	v.a	v.a	PROPN
fumecheng-7253	378	10	.	.	PROPN
fumecheng-7253	378	11	,	,	PUNCT
fumecheng-7253	378	12	2020,on	2020,on	VERB
fumecheng-7253	378	13	the	the	DET
fumecheng-7253	378	14	dynamics	dynamic	NOUN
fumecheng-7253	378	15	of	of	ADP
fumecheng-7253	378	16	a	a	DET
fumecheng-7253	378	17	visco	visco	ADJ
fumecheng-7253	378	18	–	–	PUNCT
fumecheng-7253	378	19	piezo	piezo	X
fumecheng-7253	378	20	–	–	PUNCT
fumecheng-7253	378	21	flexoelectricnanobeam	flexoelectricnanobeam	NOUN
fumecheng-7253	378	22	,	,	PUNCT
fumecheng-7253	378	23	symmetry	symmetry	NOUN
fumecheng-7253	378	24	,	,	PUNCT
fumecheng-7253	378	25	12(4	12(4	NUM
fumecheng-7253	378	26	)	)	PUNCT
fumecheng-7253	378	27	,	,	PUNCT
fumecheng-7253	378	28	643	643	NUM
fumecheng-7253	378	29	.	.	NOUN
fumecheng-7253	378	30	17	17	NUM
fumecheng-7253	378	31	.	.	PUNCT
fumecheng-7253	379	1	eringen	eringen	PROPN
fumecheng-7253	379	2	,	,	PUNCT
fumecheng-7253	379	3	a.c	a.c	PROPN
fumecheng-7253	379	4	.	.	PROPN
fumecheng-7253	379	5	,1983	,1983	PUNCT
fumecheng-7253	379	6	,	,	PUNCT
fumecheng-7253	379	7	on	on	ADP
fumecheng-7253	379	8	differential	differential	ADJ
fumecheng-7253	379	9	equations	equation	NOUN
fumecheng-7253	379	10	of	of	ADP
fumecheng-7253	379	11	nonlocal	nonlocal	ADJ
fumecheng-7253	379	12	elasticity	elasticity	NOUN
fumecheng-7253	379	13	and	and	CCONJ
fumecheng-7253	379	14	solutions	solution	NOUN
fumecheng-7253	379	15	of	of	ADP
fumecheng-7253	379	16	screw	screw	ADJ
fumecheng-7253	379	17	dislocation	dislocation	NOUN
fumecheng-7253	379	18	and	and	CCONJ
fumecheng-7253	379	19	surface	surface	NOUN
fumecheng-7253	379	20	waves	wave	NOUN
fumecheng-7253	379	21	,	,	PUNCT
fumecheng-7253	379	22	j	j	PROPN
fumecheng-7253	379	23	appl	appl	PROPN
fumecheng-7253	379	24	phys	phys	PROPN
fumecheng-7253	379	25	,	,	PUNCT
fumecheng-7253	379	26	54	54	NUM
fumecheng-7253	379	27	,	,	PUNCT
fumecheng-7253	379	28	pp	pp	ADJ
fumecheng-7253	379	29	.	.	PUNCT
fumecheng-7253	380	1	4703–4710	4703–4710	NUM
fumecheng-7253	380	2	.	.	PUNCT
fumecheng-7253	381	1	18	18	NUM
fumecheng-7253	381	2	.	.	X
fumecheng-7253	381	3	eringen	eringen	PROPN
fumecheng-7253	381	4	,	,	PUNCT
fumecheng-7253	381	5	a.c	a.c	PROPN
fumecheng-7253	381	6	.	.	PROPN
fumecheng-7253	381	7	,1972	,1972	PUNCT
fumecheng-7253	381	8	,	,	PUNCT
fumecheng-7253	381	9	nonlocal	nonlocal	ADJ
fumecheng-7253	381	10	polar	polar	ADJ
fumecheng-7253	381	11	elastic	elastic	ADJ
fumecheng-7253	381	12	continua	continuum	NOUN
fumecheng-7253	381	13	,	,	PUNCT
fumecheng-7253	381	14	int	int	PROPN
fumecheng-7253	381	15	j	j	PROPN
fumecheng-7253	381	16	engsci	engsci	PROPN
fumecheng-7253	381	17	,	,	PUNCT
fumecheng-7253	381	18	10	10	NUM
fumecheng-7253	381	19	,	,	PUNCT
fumecheng-7253	381	20	pp	pp	PROPN
fumecheng-7253	381	21	.	.	PUNCT
fumecheng-7253	382	1	1–16	1–16	PROPN
fumecheng-7253	382	2	.	.	PUNCT
fumecheng-7253	383	1	19	19	NUM
fumecheng-7253	383	2	.	.	X
fumecheng-7253	383	3	sedighi	sedighi	PROPN
fumecheng-7253	383	4	,	,	PUNCT
fumecheng-7253	383	5	h.m	h.m	PROPN
fumecheng-7253	383	6	.	.	PROPN
fumecheng-7253	383	7	,	,	PUNCT
fumecheng-7253	383	8	keivani	keivani	PROPN
fumecheng-7253	383	9	,	,	PUNCT
fumecheng-7253	383	10	m.	m.	NOUN
fumecheng-7253	383	11	,	,	PUNCT
fumecheng-7253	383	12	abadyan	abadyan	PROPN
fumecheng-7253	383	13	,	,	PUNCT
fumecheng-7253	383	14	m.r	m.r	PROPN
fumecheng-7253	383	15	.	.	PROPN
fumecheng-7253	383	16	,	,	PUNCT
fumecheng-7253	383	17	2015	2015	NUM
fumecheng-7253	383	18	,	,	PUNCT
fumecheng-7253	383	19	modified	modify	VERB
fumecheng-7253	383	20	continuum	continuum	ADJ
fumecheng-7253	383	21	model	model	NOUN
fumecheng-7253	383	22	for	for	ADP
fumecheng-7253	383	23	stability	stability	NOUN
fumecheng-7253	383	24	analysis	analysis	NOUN
fumecheng-7253	383	25	of	of	ADP
fumecheng-7253	383	26	asymmetric	asymmetric	ADJ
fumecheng-7253	383	27	fgm	fgm	PROPN
fumecheng-7253	383	28	double	double	ADJ
fumecheng-7253	383	29	-	-	PUNCT
fumecheng-7253	383	30	sided	sided	ADJ
fumecheng-7253	383	31	nems	nem	NOUN
fumecheng-7253	383	32	:	:	PUNCT
fumecheng-7253	383	33	corrections	correction	NOUN
fumecheng-7253	383	34	due	due	ADJ
fumecheng-7253	383	35	to	to	ADP
fumecheng-7253	383	36	finite	finite	VERB
fumecheng-7253	383	37	conductivity	conductivity	NOUN
fumecheng-7253	383	38	,	,	PUNCT
fumecheng-7253	383	39	surface	surface	NOUN
fumecheng-7253	383	40	energy	energy	NOUN
fumecheng-7253	383	41	and	and	CCONJ
fumecheng-7253	383	42	nonlocal	nonlocal	ADJ
fumecheng-7253	383	43	effect	effect	NOUN
fumecheng-7253	383	44	,	,	PUNCT
fumecheng-7253	383	45	composites	composite	VERB
fumecheng-7253	383	46	part	part	NOUN
fumecheng-7253	383	47	b	b	NOUN
fumecheng-7253	383	48	:	:	PUNCT
fumecheng-7253	383	49	engineering	engineering	NOUN
fumecheng-7253	383	50	,	,	PUNCT
fumecheng-7253	383	51	83	83	NUM
fumecheng-7253	383	52	,	,	PUNCT
fumecheng-7253	383	53	pp	pp	ADJ
fumecheng-7253	383	54	.	.	PUNCT
fumecheng-7253	384	1	117	117	NUM
fumecheng-7253	384	2	-	-	SYM
fumecheng-7253	384	3	133	133	NUM
fumecheng-7253	384	4	.	.	PUNCT
fumecheng-7253	385	1	20	20	NUM
fumecheng-7253	385	2	.	.	X
fumecheng-7253	386	1	abouelregal	abouelregal	ADJ
fumecheng-7253	386	2	,	,	PUNCT
fumecheng-7253	386	3	a.e	a.e	PROPN
fumecheng-7253	386	4	.	.	PROPN
fumecheng-7253	386	5	,	,	PUNCT
fumecheng-7253	386	6	marin	marin	NOUN
fumecheng-7253	386	7	,	,	PUNCT
fumecheng-7253	386	8	m.	m.	NOUN
fumecheng-7253	386	9	,2020	,2020	PUNCT
fumecheng-7253	386	10	,	,	PUNCT
fumecheng-7253	386	11	the	the	DET
fumecheng-7253	386	12	size	size	NOUN
fumecheng-7253	386	13	-	-	PUNCT
fumecheng-7253	386	14	dependent	dependent	ADJ
fumecheng-7253	386	15	thermoelastic	thermoelastic	ADJ
fumecheng-7253	386	16	vibrations	vibration	NOUN
fumecheng-7253	386	17	of	of	ADP
fumecheng-7253	386	18	nanobeams	nanobeam	NOUN
fumecheng-7253	386	19	subjected	subject	VERB
fumecheng-7253	386	20	to	to	AUX
fumecheng-7253	386	21	harmonic	harmonic	ADJ
fumecheng-7253	386	22	excitation	excitation	NOUN
fumecheng-7253	386	23	and	and	CCONJ
fumecheng-7253	386	24	rectified	rectified	ADJ
fumecheng-7253	386	25	sine	sine	ADJ
fumecheng-7253	386	26	wave	wave	NOUN
fumecheng-7253	386	27	heating	heating	NOUN
fumecheng-7253	386	28	,	,	PUNCT
fumecheng-7253	386	29	mathematics	mathematic	NOUN
fumecheng-7253	386	30	;	;	PUNCT
fumecheng-7253	386	31	8(7	8(7	NUM
fumecheng-7253	386	32	)	)	PUNCT
fumecheng-7253	386	33	,	,	PUNCT
fumecheng-7253	386	34	1128	1128	NUM
fumecheng-7253	386	35	.	.	PUNCT
fumecheng-7253	387	1	21	21	NUM
fumecheng-7253	387	2	.	.	PUNCT
fumecheng-7253	388	1	barretta	barretta	PROPN
fumecheng-7253	388	2	,	,	PUNCT
fumecheng-7253	388	3	r.	r.	PROPN
fumecheng-7253	388	4	,	,	PUNCT
fumecheng-7253	388	5	faghidian	faghidian	PROPN
fumecheng-7253	388	6	,	,	PUNCT
fumecheng-7253	388	7	s.a	s.a	PROPN
fumecheng-7253	388	8	.	.	PROPN
fumecheng-7253	388	9	,	,	PUNCT
fumecheng-7253	388	10	marotti	marotti	PROPN
fumecheng-7253	388	11	de	de	X
fumecheng-7253	388	12	sciarra	sciarra	PROPN
fumecheng-7253	388	13	,	,	PUNCT
fumecheng-7253	388	14	f.	f.	PROPN
fumecheng-7253	388	15	,	,	PUNCT
fumecheng-7253	388	16	pinnola	pinnola	PROPN
fumecheng-7253	388	17	,	,	PUNCT
fumecheng-7253	388	18	f.p	f.p	PROPN
fumecheng-7253	388	19	.	.	PROPN
fumecheng-7253	388	20	,	,	PUNCT
fumecheng-7253	388	21	2020	2020	NUM
fumecheng-7253	388	22	,	,	PUNCT
fumecheng-7253	388	23	timoshenko	timoshenko	ADJ
fumecheng-7253	388	24	nonlocal	nonlocal	ADJ
fumecheng-7253	388	25	strain	strain	NOUN
fumecheng-7253	388	26	gradient	gradient	NOUN
fumecheng-7253	388	27	nanobeams	nanobeam	NOUN
fumecheng-7253	388	28	:	:	PUNCT
fumecheng-7253	388	29	variational	variational	ADJ
fumecheng-7253	388	30	consistency	consistency	NOUN
fumecheng-7253	388	31	,	,	PUNCT
fumecheng-7253	388	32	exact	exact	ADJ
fumecheng-7253	388	33	solutions	solution	NOUN
fumecheng-7253	388	34	and	and	CCONJ
fumecheng-7253	388	35	carbon	carbon	NOUN
fumecheng-7253	388	36	nanotube	nanotube	ADJ
fumecheng-7253	388	37	young	young	ADJ
fumecheng-7253	388	38	moduli	modulus	NOUN
fumecheng-7253	388	39	,	,	PUNCT
fumecheng-7253	388	40	mechanics	mechanic	NOUN
fumecheng-7253	388	41	of	of	ADP
fumecheng-7253	388	42	advanced	advanced	ADJ
fumecheng-7253	388	43	materials	material	NOUN
fumecheng-7253	388	44	and	and	CCONJ
fumecheng-7253	388	45	structures	structure	NOUN
fumecheng-7253	388	46	,	,	PUNCT
fumecheng-7253	388	47	2020	2020	NUM
fumecheng-7253	388	48	,	,	PUNCT
fumecheng-7253	388	49	doi	doi	NOUN
fumecheng-7253	388	50	:	:	PUNCT
fumecheng-7253	388	51	10.1080/15376494.2019.1683660	10.1080/15376494.2019.1683660	NUM
fumecheng-7253	388	52	.	.	PUNCT
fumecheng-7253	388	53	22	22	NUM
fumecheng-7253	388	54	.	.	PUNCT
fumecheng-7253	389	1	abouelregal	abouelregal	ADJ
fumecheng-7253	389	2	,	,	PUNCT
fumecheng-7253	389	3	a.e	a.e	PROPN
fumecheng-7253	389	4	.	.	PROPN
fumecheng-7253	389	5	,	,	PUNCT
fumecheng-7253	389	6	mohammed	mohammed	PROPN
fumecheng-7253	389	7	,	,	PUNCT
fumecheng-7253	389	8	w.w	w.w	PROPN
fumecheng-7253	389	9	.	.	PROPN
fumecheng-7253	389	10	,	,	PUNCT
fumecheng-7253	389	11	2020	2020	NUM
fumecheng-7253	389	12	,	,	PUNCT
fumecheng-7253	389	13	effects	effect	NOUN
fumecheng-7253	389	14	of	of	ADP
fumecheng-7253	389	15	nonlocal	nonlocal	ADJ
fumecheng-7253	389	16	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	389	17	on	on	ADP
fumecheng-7253	389	18	nanoscale	nanoscale	NOUN
fumecheng-7253	389	19	beams	beam	NOUN
fumecheng-7253	389	20	based	base	VERB
fumecheng-7253	389	21	on	on	ADP
fumecheng-7253	389	22	couple	couple	NOUN
fumecheng-7253	389	23	stress	stress	NOUN
fumecheng-7253	389	24	theory	theory	NOUN
fumecheng-7253	389	25	,	,	PUNCT
fumecheng-7253	389	26	mathematical	mathematical	ADJ
fumecheng-7253	389	27	methods	method	NOUN
fumecheng-7253	389	28	in	in	ADP
fumecheng-7253	389	29	the	the	DET
fumecheng-7253	389	30	applied	apply	VERB
fumecheng-7253	389	31	sciences	science	NOUN
fumecheng-7253	389	32	,	,	PUNCT
fumecheng-7253	389	33	doi:10.1002	doi:10.1002	NOUN
fumecheng-7253	389	34	/	/	SYM
fumecheng-7253	389	35	mma.6764	mma.6764	NOUN
fumecheng-7253	389	36	.	.	NOUN
fumecheng-7253	389	37	23	23	NUM
fumecheng-7253	389	38	.	.	PUNCT
fumecheng-7253	390	1	abouelregal	abouelregal	PROPN
fumecheng-7253	390	2	a.e	a.e	PROPN
fumecheng-7253	390	3	.	.	PROPN
fumecheng-7253	390	4	,	,	PUNCT
fumecheng-7253	390	5	marin	marin	NOUN
fumecheng-7253	390	6	m.	m.	NOUN
fumecheng-7253	390	7	,2020	,2020	PROPN
fumecheng-7253	390	8	,	,	PUNCT
fumecheng-7253	390	9	the	the	DET
fumecheng-7253	390	10	response	response	NOUN
fumecheng-7253	390	11	of	of	ADP
fumecheng-7253	390	12	nanobeams	nanobeam	NOUN
fumecheng-7253	390	13	with	with	ADP
fumecheng-7253	390	14	temperature	temperature	NOUN
fumecheng-7253	390	15	-	-	PUNCT
fumecheng-7253	390	16	dependent	dependent	ADJ
fumecheng-7253	390	17	properties	property	NOUN
fumecheng-7253	390	18	using	use	VERB
fumecheng-7253	390	19	state	state	NOUN
fumecheng-7253	390	20	-	-	PUNCT
fumecheng-7253	390	21	space	space	NOUN
fumecheng-7253	390	22	method	method	NOUN
fumecheng-7253	390	23	via	via	ADP
fumecheng-7253	390	24	modified	modify	VERB
fumecheng-7253	390	25	couple	couple	NOUN
fumecheng-7253	390	26	stress	stress	NOUN
fumecheng-7253	390	27	theory	theory	NOUN
fumecheng-7253	390	28	,	,	PUNCT
fumecheng-7253	390	29	symmetry	symmetry	NOUN
fumecheng-7253	390	30	,	,	PUNCT
fumecheng-7253	390	31	12(8	12(8	NUM
fumecheng-7253	390	32	)	)	PUNCT
fumecheng-7253	390	33	,	,	PUNCT
fumecheng-7253	390	34	1276	1276	NUM
fumecheng-7253	390	35	.	.	PUNCT
fumecheng-7253	391	1	24	24	NUM
fumecheng-7253	391	2	.	.	PUNCT
fumecheng-7253	392	1	barretta	barretta	PROPN
fumecheng-7253	392	2	,	,	PUNCT
fumecheng-7253	392	3	r.	r.	PROPN
fumecheng-7253	392	4	,	,	PUNCT
fumecheng-7253	392	5	faghidian	faghidian	PROPN
fumecheng-7253	392	6	,	,	PUNCT
fumecheng-7253	392	7	s.a	s.a	PROPN
fumecheng-7253	392	8	.	.	PROPN
fumecheng-7253	392	9	,	,	PUNCT
fumecheng-7253	392	10	marotti	marotti	PROPN
fumecheng-7253	392	11	de	de	X
fumecheng-7253	392	12	sciarra	sciarra	PROPN
fumecheng-7253	392	13	,	,	PUNCT
fumecheng-7253	392	14	f.	f.	PROPN
fumecheng-7253	392	15	,	,	PUNCT
fumecheng-7253	392	16	penna	penna	PROPN
fumecheng-7253	392	17	,	,	PUNCT
fumecheng-7253	392	18	r.	r.	PROPN
fumecheng-7253	392	19	,	,	PUNCT
fumecheng-7253	392	20	pinnola	pinnola	PROPN
fumecheng-7253	392	21	,	,	PUNCT
fumecheng-7253	392	22	f.p	f.p	PROPN
fumecheng-7253	392	23	.	.	PROPN
fumecheng-7253	392	24	,	,	PUNCT
fumecheng-7253	392	25	2020,on	2020,on	NUM
fumecheng-7253	392	26	torsion	torsion	NOUN
fumecheng-7253	392	27	of	of	ADP
fumecheng-7253	392	28	nonlocal	nonlocal	ADJ
fumecheng-7253	392	29	lam	lam	PROPN
fumecheng-7253	392	30	strain	strain	NOUN
fumecheng-7253	392	31	gradient	gradient	NOUN
fumecheng-7253	392	32	fg	fg	PROPN
fumecheng-7253	392	33	elastic	elastic	ADJ
fumecheng-7253	392	34	beams	beam	NOUN
fumecheng-7253	392	35	,	,	PUNCT
fumecheng-7253	392	36	composite	composite	ADJ
fumecheng-7253	392	37	structures	structure	NOUN
fumecheng-7253	392	38	,	,	PUNCT
fumecheng-7253	392	39	233	233	NUM
fumecheng-7253	392	40	,	,	PUNCT
fumecheng-7253	392	41	111550	111550	NUM
fumecheng-7253	392	42	.	.	PUNCT
fumecheng-7253	393	1	25	25	NUM
fumecheng-7253	393	2	.	.	X
fumecheng-7253	393	3	shabani	shabani	PROPN
fumecheng-7253	393	4	,	,	PUNCT
fumecheng-7253	393	5	s.	s.	PROPN
fumecheng-7253	393	6	,	,	PUNCT
fumecheng-7253	393	7	cunedioglu	cunedioglu	PROPN
fumecheng-7253	393	8	,	,	PUNCT
fumecheng-7253	393	9	y.	y.	NOUN
fumecheng-7253	393	10	2020	2020	NUM
fumecheng-7253	393	11	,	,	PUNCT
fumecheng-7253	393	12	free	free	ADJ
fumecheng-7253	393	13	vibration	vibration	NOUN
fumecheng-7253	393	14	analysis	analysis	NOUN
fumecheng-7253	393	15	of	of	ADP
fumecheng-7253	393	16	cracked	crack	VERB
fumecheng-7253	393	17	functionally	functionally	ADV
fumecheng-7253	393	18	graded	grade	VERB
fumecheng-7253	393	19	non	non	ADJ
fumecheng-7253	393	20	-	-	ADJ
fumecheng-7253	393	21	uniform	uniform	ADJ
fumecheng-7253	393	22	beams	beam	NOUN
fumecheng-7253	393	23	,	,	PUNCT
fumecheng-7253	393	24	mater	mater	NOUN
fumecheng-7253	393	25	.	.	PUNCT
fumecheng-7253	394	1	res	re	NOUN
fumecheng-7253	394	2	.	.	PUNCT
fumecheng-7253	395	1	express	express	ADJ
fumecheng-7253	395	2	,	,	PUNCT
fumecheng-7253	395	3	7	7	NUM
fumecheng-7253	395	4	,	,	PUNCT
fumecheng-7253	395	5	015707	015707	NUM
fumecheng-7253	395	6	.	.	PUNCT
fumecheng-7253	396	1	26	26	NUM
fumecheng-7253	396	2	.	.	X
fumecheng-7253	397	1	romano	romano	NOUN
fumecheng-7253	397	2	,	,	PUNCT
fumecheng-7253	397	3	g.	g.	PROPN
fumecheng-7253	397	4	,	,	PUNCT
fumecheng-7253	397	5	barretta	barretta	PROPN
fumecheng-7253	397	6	,	,	PUNCT
fumecheng-7253	397	7	r.	r.	PROPN
fumecheng-7253	397	8	,	,	PUNCT
fumecheng-7253	397	9	2017	2017	NUM
fumecheng-7253	397	10	,	,	PUNCT
fumecheng-7253	397	11	nonlocal	nonlocal	ADJ
fumecheng-7253	397	12	elasticity	elasticity	NOUN
fumecheng-7253	397	13	in	in	ADP
fumecheng-7253	397	14	nanobeams	nanobeam	NOUN
fumecheng-7253	397	15	:	:	PUNCT
fumecheng-7253	397	16	the	the	DET
fumecheng-7253	397	17	stress	stress	NOUN
fumecheng-7253	397	18	-	-	PUNCT
fumecheng-7253	397	19	driven	drive	VERB
fumecheng-7253	397	20	integral	integral	ADJ
fumecheng-7253	397	21	model	model	NOUN
fumecheng-7253	397	22	,	,	PUNCT
fumecheng-7253	397	23	international	international	ADJ
fumecheng-7253	397	24	journal	journal	NOUN
fumecheng-7253	397	25	of	of	ADP
fumecheng-7253	397	26	engineering	engineering	NOUN
fumecheng-7253	397	27	science	science	NOUN
fumecheng-7253	397	28	,	,	PUNCT
fumecheng-7253	397	29	115	115	NUM
fumecheng-7253	397	30	,	,	PUNCT
fumecheng-7253	397	31	pp	pp	ADJ
fumecheng-7253	397	32	.	.	PUNCT
fumecheng-7253	398	1	14	14	NUM
fumecheng-7253	398	2	-	-	SYM
fumecheng-7253	398	3	27	27	NUM
fumecheng-7253	398	4	.	.	PUNCT
fumecheng-7253	399	1	27	27	NUM
fumecheng-7253	399	2	.	.	PUNCT
fumecheng-7253	400	1	barretta	barretta	NOUN
fumecheng-7253	400	2	,	,	PUNCT
fumecheng-7253	400	3	r.	r.	PROPN
fumecheng-7253	400	4	,	,	PUNCT
fumecheng-7253	400	5	feo	feo	PROPN
fumecheng-7253	400	6	,	,	PUNCT
fumecheng-7253	400	7	l.	l.	PROPN
fumecheng-7253	400	8	,	,	PUNCT
fumecheng-7253	400	9	luciano	luciano	PROPN
fumecheng-7253	400	10	,	,	PUNCT
fumecheng-7253	400	11	r.	r.	PROPN
fumecheng-7253	400	12	,	,	PUNCT
fumecheng-7253	400	13	marotti	marotti	PROPN
fumecheng-7253	400	14	de	de	X
fumecheng-7253	400	15	sciarra	sciarra	PROPN
fumecheng-7253	400	16	,	,	PUNCT
fumecheng-7253	400	17	f.	f.	PROPN
fumecheng-7253	400	18	,	,	PUNCT
fumecheng-7253	400	19	penna	penna	PROPN
fumecheng-7253	400	20	,	,	PUNCT
fumecheng-7253	400	21	r.	r.	PROPN
fumecheng-7253	400	22	,	,	PUNCT
fumecheng-7253	400	23	2017	2017	NUM
fumecheng-7253	400	24	,	,	PUNCT
fumecheng-7253	400	25	nano	nano	NOUN
fumecheng-7253	400	26	-	-	PUNCT
fumecheng-7253	400	27	beams	beam	NOUN
fumecheng-7253	400	28	under	under	ADP
fumecheng-7253	400	29	torsion	torsion	NOUN
fumecheng-7253	400	30	:	:	PUNCT
fumecheng-7253	400	31	a	a	DET
fumecheng-7253	400	32	stressdriven	stressdriven	ADJ
fumecheng-7253	400	33	nonlocal	nonlocal	ADJ
fumecheng-7253	400	34	approach	approach	NOUN
fumecheng-7253	400	35	,	,	PUNCT
fumecheng-7253	400	36	psu	psu	X
fumecheng-7253	400	37	research	research	NOUN
fumecheng-7253	400	38	review	review	PROPN
fumecheng-7253	400	39	,	,	PUNCT
fumecheng-7253	400	40	1(2	1(2	NUM
fumecheng-7253	400	41	)	)	PUNCT
fumecheng-7253	400	42	,	,	PUNCT
fumecheng-7253	400	43	pp	pp	ADP
fumecheng-7253	400	44	.	.	PUNCT
fumecheng-7253	401	1	164	164	NUM
fumecheng-7253	401	2	-	-	SYM
fumecheng-7253	401	3	169	169	NUM
fumecheng-7253	401	4	.	.	PUNCT
fumecheng-7253	402	1	28	28	NUM
fumecheng-7253	402	2	.	.	PUNCT
fumecheng-7253	403	1	drexler	drexler	PROPN
fumecheng-7253	403	2	,	,	PUNCT
fumecheng-7253	403	3	k.	k.	PROPN
fumecheng-7253	403	4	e.	e.	PROPN
fumecheng-7253	403	5	,	,	PUNCT
fumecheng-7253	403	6	1992	1992	NUM
fumecheng-7253	403	7	,	,	PUNCT
fumecheng-7253	403	8	nanosystems	nanosystem	VERB
fumecheng-7253	403	9	:	:	PUNCT
fumecheng-7253	403	10	molecular	molecular	ADJ
fumecheng-7253	403	11	machinery	machinery	NOUN
fumecheng-7253	403	12	,	,	PUNCT
fumecheng-7253	403	13	manufacturing	manufacturing	NOUN
fumecheng-7253	403	14	,	,	PUNCT
fumecheng-7253	403	15	and	and	CCONJ
fumecheng-7253	403	16	computation	computation	NOUN
fumecheng-7253	403	17	,	,	PUNCT
fumecheng-7253	403	18	wiley	wiley	PROPN
fumecheng-7253	403	19	,	,	PUNCT
fumecheng-7253	403	20	new	new	PROPN
fumecheng-7253	403	21	york	york	PROPN
fumecheng-7253	403	22	,	,	PUNCT
fumecheng-7253	403	23	usa	usa	PROPN
fumecheng-7253	403	24	.	.	PROPN
fumecheng-7253	404	1	https://doi.org/10.1002/mma.6764	https://doi.org/10.1002/mma.6764	ADJ
fumecheng-7253	404	2	temperature	temperature	NOUN
fumecheng-7253	404	3	-	-	PUNCT
fumecheng-7253	404	4	dependent	dependent	ADJ
fumecheng-7253	404	5	physical	physical	ADJ
fumecheng-7253	404	6	characteristics	characteristic	NOUN
fumecheng-7253	404	7	of	of	ADP
fumecheng-7253	404	8	rotating	rotate	VERB
fumecheng-7253	404	9	nonlocal	nonlocal	ADJ
fumecheng-7253	404	10	nanobeams	nanobeam	NOUN
fumecheng-7253	404	11	subject	subject	ADJ
fumecheng-7253	404	12	to	to	ADP
fumecheng-7253	404	13	...	...	PUNCT
fumecheng-7253	404	14	655	655	NUM
fumecheng-7253	404	15	29	29	NUM
fumecheng-7253	404	16	.	.	PUNCT
fumecheng-7253	405	1	han	han	PROPN
fumecheng-7253	405	2	,	,	PUNCT
fumecheng-7253	405	3	j.	j.	PROPN
fumecheng-7253	405	4	,	,	PUNCT
fumecheng-7253	405	5	globus	globus	NOUN
fumecheng-7253	405	6	,	,	PUNCT
fumecheng-7253	405	7	a.	a.	PROPN
fumecheng-7253	405	8	,	,	PUNCT
fumecheng-7253	405	9	jaffe	jaffe	PROPN
fumecheng-7253	405	10	,	,	PUNCT
fumecheng-7253	405	11	r.	r.	PROPN
fumecheng-7253	405	12	,	,	PUNCT
fumecheng-7253	405	13	deardorff	deardorff	PROPN
fumecheng-7253	405	14	,	,	PUNCT
fumecheng-7253	405	15	g.	g.	PROPN
fumecheng-7253	405	16	,	,	PUNCT
fumecheng-7253	405	17	1997	1997	NUM
fumecheng-7253	405	18	,	,	PUNCT
fumecheng-7253	405	19	molecular	molecular	ADJ
fumecheng-7253	405	20	dynamics	dynamic	NOUN
fumecheng-7253	405	21	simulations	simulation	NOUN
fumecheng-7253	405	22	of	of	ADP
fumecheng-7253	405	23	carbon	carbon	NOUN
fumecheng-7253	405	24	nanotube	nanotube	NOUN
fumecheng-7253	405	25	-	-	PUNCT
fumecheng-7253	405	26	based	base	VERB
fumecheng-7253	405	27	gears	gear	NOUN
fumecheng-7253	405	28	,	,	PUNCT
fumecheng-7253	405	29	nanotechnology	nanotechnology	NOUN
fumecheng-7253	405	30	,	,	PUNCT
fumecheng-7253	405	31	8	8	NUM
fumecheng-7253	405	32	,	,	PUNCT
fumecheng-7253	405	33	pp	pp	ADJ
fumecheng-7253	405	34	.	.	PUNCT
fumecheng-7253	406	1	95–102	95–102	NUM
fumecheng-7253	406	2	.	.	NOUN
fumecheng-7253	406	3	30	30	NUM
fumecheng-7253	406	4	.	.	PUNCT
fumecheng-7253	407	1	srivastava	srivastava	PROPN
fumecheng-7253	407	2	,	,	PUNCT
fumecheng-7253	407	3	d.	d.	PROPN
fumecheng-7253	407	4	,	,	PUNCT
fumecheng-7253	407	5	1997	1997	NUM
fumecheng-7253	407	6	,	,	PUNCT
fumecheng-7253	407	7	a	a	DET
fumecheng-7253	407	8	phenomenological	phenomenological	ADJ
fumecheng-7253	407	9	model	model	NOUN
fumecheng-7253	407	10	of	of	ADP
fumecheng-7253	407	11	the	the	DET
fumecheng-7253	407	12	rotation	rotation	NOUN
fumecheng-7253	407	13	dynamics	dynamic	NOUN
fumecheng-7253	407	14	of	of	ADP
fumecheng-7253	407	15	carbon	carbon	NOUN
fumecheng-7253	407	16	nanotube	nanotube	NOUN
fumecheng-7253	407	17	gears	gear	NOUN
fumecheng-7253	407	18	with	with	ADP
fumecheng-7253	407	19	laser	laser	NOUN
fumecheng-7253	407	20	electric	electric	ADJ
fumecheng-7253	407	21	fields	field	NOUN
fumecheng-7253	407	22	,	,	PUNCT
fumecheng-7253	407	23	nanotechnology	nanotechnology	NOUN
fumecheng-7253	407	24	,	,	PUNCT
fumecheng-7253	407	25	8	8	NUM
fumecheng-7253	407	26	,	,	PUNCT
fumecheng-7253	407	27	pp	pp	ADJ
fumecheng-7253	407	28	.	.	PUNCT
fumecheng-7253	408	1	186–192	186–192	NUM
fumecheng-7253	408	2	.	.	PUNCT
fumecheng-7253	409	1	31	31	NUM
fumecheng-7253	409	2	.	.	PUNCT
fumecheng-7253	410	1	lohrasebi	lohrasebi	NOUN
fumecheng-7253	410	2	,	,	PUNCT
fumecheng-7253	410	3	a.	a.	NOUN
fumecheng-7253	410	4	rafii	rafii	NOUN
fumecheng-7253	410	5	-	-	PUNCT
fumecheng-7253	410	6	tabar	tabar	NOUN
fumecheng-7253	410	7	,	,	PUNCT
fumecheng-7253	410	8	h.	h.	PROPN
fumecheng-7253	410	9	,	,	PUNCT
fumecheng-7253	410	10	2008	2008	NUM
fumecheng-7253	410	11	,	,	PUNCT
fumecheng-7253	410	12	computational	computational	ADJ
fumecheng-7253	410	13	modeling	modeling	NOUN
fumecheng-7253	410	14	of	of	ADP
fumecheng-7253	410	15	an	an	DET
fumecheng-7253	410	16	iondrivennanomotor	iondrivennanomotor	NOUN
fumecheng-7253	410	17	,	,	PUNCT
fumecheng-7253	410	18	j.	j.	PROPN
fumecheng-7253	410	19	mol	mol	PROPN
fumecheng-7253	410	20	.	.	PROPN
fumecheng-7253	410	21	graphics	graphics	PROPN
fumecheng-7253	410	22	modell	modell	PROPN
fumecheng-7253	410	23	.	.	PUNCT
fumecheng-7253	410	24	,	,	PUNCT
fumecheng-7253	410	25	27	27	NUM
fumecheng-7253	410	26	,	,	PUNCT
fumecheng-7253	410	27	pp	pp	ADJ
fumecheng-7253	410	28	.	.	PUNCT
fumecheng-7253	411	1	116–123	116–123	NUM
fumecheng-7253	411	2	.	.	PUNCT
fumecheng-7253	412	1	32	32	NUM
fumecheng-7253	412	2	.	.	PUNCT
fumecheng-7253	413	1	yokoyama	yokoyama	PROPN
fumecheng-7253	413	2	,	,	PUNCT
fumecheng-7253	413	3	t.	t.	PROPN
fumecheng-7253	413	4	,1988	,1988	PUNCT
fumecheng-7253	413	5	,	,	PUNCT
fumecheng-7253	413	6	free	free	ADJ
fumecheng-7253	413	7	vibration	vibration	NOUN
fumecheng-7253	413	8	characteristics	characteristic	NOUN
fumecheng-7253	413	9	of	of	ADP
fumecheng-7253	413	10	rotating	rotate	VERB
fumecheng-7253	413	11	timoshenko	timoshenko	ADJ
fumecheng-7253	413	12	beams	beam	NOUN
fumecheng-7253	413	13	,	,	PUNCT
fumecheng-7253	413	14	int	int	NOUN
fumecheng-7253	413	15	.	.	PUNCT
fumecheng-7253	414	1	j.	j.	PROPN
fumecheng-7253	414	2	mech	mech	PROPN
fumecheng-7253	414	3	.	.	PUNCT
fumecheng-7253	415	1	sci	sci	PROPN
fumecheng-7253	415	2	.	.	PROPN
fumecheng-7253	415	3	30	30	NUM
fumecheng-7253	415	4	,	,	PUNCT
fumecheng-7253	415	5	pp	pp	ADJ
fumecheng-7253	415	6	.	.	PUNCT
fumecheng-7253	416	1	743–755	743–755	NUM
fumecheng-7253	416	2	.	.	PUNCT
fumecheng-7253	417	1	33	33	NUM
fumecheng-7253	417	2	.	.	PUNCT
fumecheng-7253	418	1	gunda	gunda	PROPN
fumecheng-7253	418	2	j.b	j.b	PROPN
fumecheng-7253	418	3	.	.	PROPN
fumecheng-7253	418	4	,	,	PUNCT
fumecheng-7253	418	5	ganguli	ganguli	PROPN
fumecheng-7253	418	6	r.	r.	PROPN
fumecheng-7253	418	7	,2008	,2008	PROPN
fumecheng-7253	418	8	,	,	PUNCT
fumecheng-7253	418	9	new	new	ADJ
fumecheng-7253	418	10	rational	rational	ADJ
fumecheng-7253	418	11	interpolation	interpolation	NOUN
fumecheng-7253	418	12	functions	function	NOUN
fumecheng-7253	418	13	for	for	ADP
fumecheng-7253	418	14	finite	finite	ADJ
fumecheng-7253	418	15	element	element	NOUN
fumecheng-7253	418	16	analysis	analysis	NOUN
fumecheng-7253	418	17	of	of	ADP
fumecheng-7253	418	18	rotating	rotate	VERB
fumecheng-7253	418	19	beams	beam	NOUN
fumecheng-7253	418	20	,	,	PUNCT
fumecheng-7253	418	21	int	int	NOUN
fumecheng-7253	418	22	.	.	PUNCT
fumecheng-7253	419	1	j.	j.	PROPN
fumecheng-7253	419	2	mech	mech	PROPN
fumecheng-7253	419	3	.	.	PUNCT
fumecheng-7253	420	1	sci	sci	PROPN
fumecheng-7253	420	2	.	.	PROPN
fumecheng-7253	420	3	,	,	PUNCT
fumecheng-7253	420	4	50	50	NUM
fumecheng-7253	420	5	,	,	PUNCT
fumecheng-7253	420	6	578–588	578–588	NUM
fumecheng-7253	420	7	.	.	PUNCT
fumecheng-7253	421	1	34	34	NUM
fumecheng-7253	421	2	.	.	PUNCT
fumecheng-7253	421	3	yoo	yoo	PROPN
fumecheng-7253	421	4	,	,	PUNCT
fumecheng-7253	421	5	h.h	h.h	PROPN
fumecheng-7253	421	6	.	.	PROPN
fumecheng-7253	421	7	,	,	PUNCT
fumecheng-7253	421	8	park	park	PROPN
fumecheng-7253	421	9	,	,	PUNCT
fumecheng-7253	421	10	j.h	j.h	PROPN
fumecheng-7253	421	11	.	.	PROPN
fumecheng-7253	421	12	,	,	PUNCT
fumecheng-7253	421	13	park	park	PROPN
fumecheng-7253	421	14	j.	j.	PROPN
fumecheng-7253	421	15	,2001	,2001	PROPN
fumecheng-7253	421	16	,	,	PUNCT
fumecheng-7253	421	17	vibration	vibration	NOUN
fumecheng-7253	421	18	analysis	analysis	NOUN
fumecheng-7253	421	19	of	of	ADP
fumecheng-7253	421	20	rotating	rotate	VERB
fumecheng-7253	421	21	pre	pre	ADJ
fumecheng-7253	421	22	-	-	ADJ
fumecheng-7253	421	23	twisted	twisted	ADJ
fumecheng-7253	421	24	blades	blade	NOUN
fumecheng-7253	421	25	,	,	PUNCT
fumecheng-7253	421	26	comput	comput	NOUN
fumecheng-7253	421	27	.	.	PUNCT
fumecheng-7253	422	1	struct	struct	NOUN
fumecheng-7253	422	2	.	.	PUNCT
fumecheng-7253	422	3	,	,	PUNCT
fumecheng-7253	422	4	79(19	79(19	NUM
fumecheng-7253	422	5	)	)	PUNCT
fumecheng-7253	422	6	,	,	PUNCT
fumecheng-7253	422	7	pp	pp	ADP
fumecheng-7253	422	8	.	.	PUNCT
fumecheng-7253	423	1	1811–1819	1811–1819	NUM
fumecheng-7253	423	2	.	.	PUNCT
fumecheng-7253	424	1	35	35	NUM
fumecheng-7253	424	2	.	.	PUNCT
fumecheng-7253	425	1	lee	lee	PROPN
fumecheng-7253	425	2	,	,	PUNCT
fumecheng-7253	425	3	s.y	s.y	PROPN
fumecheng-7253	425	4	.	.	PROPN
fumecheng-7253	425	5	,	,	PUNCT
fumecheng-7253	425	6	lin	lin	PROPN
fumecheng-7253	425	7	,	,	PUNCT
fumecheng-7253	425	8	s.m	s.m	PROPN
fumecheng-7253	425	9	.	.	PROPN
fumecheng-7253	425	10	,	,	PUNCT
fumecheng-7253	425	11	lin	lin	PROPN
fumecheng-7253	425	12	,	,	PUNCT
fumecheng-7253	425	13	y.s	y.s	PROPN
fumecheng-7253	425	14	.	.	PROPN
fumecheng-7253	425	15	,2009	,2009	NOUN
fumecheng-7253	425	16	,	,	PUNCT
fumecheng-7253	425	17	instability	instability	NOUN
fumecheng-7253	425	18	and	and	CCONJ
fumecheng-7253	425	19	vibration	vibration	NOUN
fumecheng-7253	425	20	of	of	ADP
fumecheng-7253	425	21	a	a	DET
fumecheng-7253	425	22	rotating	rotate	VERB
fumecheng-7253	425	23	timoshenko	timoshenko	NOUN
fumecheng-7253	425	24	beam	beam	NOUN
fumecheng-7253	425	25	with	with	ADP
fumecheng-7253	425	26	precone	precone	PROPN
fumecheng-7253	425	27	,	,	PUNCT
fumecheng-7253	425	28	int	int	NOUN
fumecheng-7253	425	29	.	.	PUNCT
fumecheng-7253	426	1	j.	j.	PROPN
fumecheng-7253	426	2	mech	mech	PROPN
fumecheng-7253	426	3	.	.	PUNCT
fumecheng-7253	427	1	sci	sci	PROPN
fumecheng-7253	427	2	.	.	PROPN
fumecheng-7253	428	1	51	51	NUM
fumecheng-7253	428	2	,	,	PUNCT
fumecheng-7253	428	3	pp	pp	ADJ
fumecheng-7253	428	4	.	.	PUNCT
fumecheng-7253	429	1	114–121	114–121	NUM
fumecheng-7253	429	2	.	.	PUNCT
fumecheng-7253	430	1	36	36	NUM
fumecheng-7253	430	2	.	.	PUNCT
fumecheng-7253	431	1	avramov	avramov	PROPN
fumecheng-7253	431	2	,	,	PUNCT
fumecheng-7253	431	3	k.v	k.v	PROPN
fumecheng-7253	431	4	.	.	PROPN
fumecheng-7253	431	5	,	,	PUNCT
fumecheng-7253	431	6	pierre	pierre	PROPN
fumecheng-7253	431	7	,	,	PUNCT
fumecheng-7253	431	8	c.	c.	PROPN
fumecheng-7253	431	9	,	,	PUNCT
fumecheng-7253	431	10	shyriaieva	shyriaieva	PROPN
fumecheng-7253	431	11	,	,	PUNCT
fumecheng-7253	431	12	n.	n.	NOUN
fumecheng-7253	431	13	,2007	,2007	NOUN
fumecheng-7253	431	14	,	,	PUNCT
fumecheng-7253	431	15	flexural	flexural	ADJ
fumecheng-7253	431	16	-	-	PUNCT
fumecheng-7253	431	17	flexural	flexural	ADJ
fumecheng-7253	431	18	-	-	PUNCT
fumecheng-7253	431	19	torsional	torsional	NOUN
fumecheng-7253	431	20	nonlinear	nonlinear	ADJ
fumecheng-7253	431	21	vibrations	vibration	NOUN
fumecheng-7253	431	22	of	of	ADP
fumecheng-7253	431	23	pre	pre	ADJ
fumecheng-7253	431	24	-	-	ADJ
fumecheng-7253	431	25	twisted	twisted	ADJ
fumecheng-7253	431	26	rotating	rotating	NOUN
fumecheng-7253	431	27	beams	beam	NOUN
fumecheng-7253	431	28	with	with	ADP
fumecheng-7253	431	29	asymmetric	asymmetric	ADJ
fumecheng-7253	431	30	cross	cross	NOUN
fumecheng-7253	431	31	-	-	NOUN
fumecheng-7253	431	32	sections	section	NOUN
fumecheng-7253	431	33	,	,	PUNCT
fumecheng-7253	432	1	j.	j.	PROPN
fumecheng-7253	432	2	vib	vib	PROPN
fumecheng-7253	432	3	.	.	PUNCT
fumecheng-7253	432	4	control	control	PROPN
fumecheng-7253	432	5	.	.	PUNCT
fumecheng-7253	432	6	,	,	PUNCT
fumecheng-7253	432	7	13	13	NUM
fumecheng-7253	432	8	,	,	PUNCT
fumecheng-7253	432	9	pp	pp	ADJ
fumecheng-7253	432	10	.	.	PUNCT
fumecheng-7253	433	1	329–364	329–364	NUM
fumecheng-7253	433	2	.	.	PUNCT
fumecheng-7253	434	1	37	37	NUM
fumecheng-7253	434	2	.	.	PUNCT
fumecheng-7253	434	3	mohammadi	mohammadi	NOUN
fumecheng-7253	434	4	,	,	PUNCT
fumecheng-7253	434	5	m.	m.	NOUN
fumecheng-7253	434	6	,	,	PUNCT
fumecheng-7253	434	7	safarabadi	safarabadi	NOUN
fumecheng-7253	434	8	,	,	PUNCT
fumecheng-7253	434	9	m.	m.	NOUN
fumecheng-7253	434	10	,	,	PUNCT
fumecheng-7253	434	11	rastgoo	rastgoo	NOUN
fumecheng-7253	434	12	,	,	PUNCT
fumecheng-7253	434	13	a.	a.	NOUN
fumecheng-7253	434	14	,	,	PUNCT
fumecheng-7253	434	15	farajpour	farajpour	ADJ
fumecheng-7253	434	16	,	,	PUNCT
fumecheng-7253	434	17	a.	a.	PROPN
fumecheng-7253	434	18	,2016	,2016	PUNCT
fumecheng-7253	434	19	,	,	PUNCT
fumecheng-7253	434	20	hygro	hygro	ADJ
fumecheng-7253	434	21	-	-	PUNCT
fumecheng-7253	434	22	mechanical	mechanical	ADJ
fumecheng-7253	434	23	vibration	vibration	NOUN
fumecheng-7253	434	24	analysis	analysis	NOUN
fumecheng-7253	434	25	of	of	ADP
fumecheng-7253	434	26	a	a	DET
fumecheng-7253	434	27	rotating	rotate	VERB
fumecheng-7253	434	28	viscoelastic	viscoelastic	ADJ
fumecheng-7253	434	29	nanobeam	nanobeam	NOUN
fumecheng-7253	434	30	embedded	embed	VERB
fumecheng-7253	434	31	in	in	ADP
fumecheng-7253	434	32	a	a	DET
fumecheng-7253	434	33	visco	visco	ADJ
fumecheng-7253	434	34	-	-	ADJ
fumecheng-7253	434	35	pasternak	pasternak	ADJ
fumecheng-7253	434	36	elastic	elastic	ADJ
fumecheng-7253	434	37	medium	medium	NOUN
fumecheng-7253	434	38	and	and	CCONJ
fumecheng-7253	434	39	in	in	ADP
fumecheng-7253	434	40	a	a	DET
fumecheng-7253	434	41	nonlinear	nonlinear	ADJ
fumecheng-7253	434	42	thermal	thermal	ADJ
fumecheng-7253	434	43	environment	environment	NOUN
fumecheng-7253	434	44	,	,	PUNCT
fumecheng-7253	434	45	actamechanica	actamechanica	PROPN
fumecheng-7253	434	46	,	,	PUNCT
fumecheng-7253	434	47	227(8	227(8	NUM
fumecheng-7253	434	48	)	)	PUNCT
fumecheng-7253	434	49	,	,	PUNCT
fumecheng-7253	434	50	pp	pp	ADP
fumecheng-7253	434	51	.	.	PUNCT
fumecheng-7253	435	1	2207–2232	2207–2232	NUM
fumecheng-7253	435	2	.	.	PUNCT
fumecheng-7253	436	1	38	38	NUM
fumecheng-7253	436	2	.	.	PUNCT
fumecheng-7253	437	1	faroughia	faroughia	PROPN
fumecheng-7253	437	2	,	,	PUNCT
fumecheng-7253	437	3	s.	s.	PROPN
fumecheng-7253	437	4	,	,	PUNCT
fumecheng-7253	437	5	rahmani	rahmani	PROPN
fumecheng-7253	437	6	,	,	PUNCT
fumecheng-7253	437	7	a.	a.	NOUN
fumecheng-7253	437	8	,	,	PUNCT
fumecheng-7253	437	9	friswell	friswell	ADJ
fumecheng-7253	437	10	,	,	PUNCT
fumecheng-7253	437	11	m.i	m.i	PROPN
fumecheng-7253	437	12	.	.	PROPN
fumecheng-7253	437	13	,2020	,2020	PROPN
fumecheng-7253	437	14	,	,	PUNCT
fumecheng-7253	437	15	on	on	ADP
fumecheng-7253	437	16	wave	wave	NOUN
fumecheng-7253	437	17	propagation	propagation	NOUN
fumecheng-7253	437	18	in	in	ADP
fumecheng-7253	437	19	two	two	NUM
fumecheng-7253	437	20	-	-	PUNCT
fumecheng-7253	437	21	dimensional	dimensional	ADJ
fumecheng-7253	437	22	functionally	functionally	ADV
fumecheng-7253	437	23	graded	grade	VERB
fumecheng-7253	437	24	porous	porous	ADJ
fumecheng-7253	437	25	rotating	rotate	VERB
fumecheng-7253	437	26	nano	nano	NOUN
fumecheng-7253	437	27	-	-	PUNCT
fumecheng-7253	437	28	beams	beam	NOUN
fumecheng-7253	437	29	using	use	VERB
fumecheng-7253	437	30	a	a	DET
fumecheng-7253	437	31	general	general	ADJ
fumecheng-7253	437	32	nonlocal	nonlocal	ADJ
fumecheng-7253	437	33	higher	high	ADJ
fumecheng-7253	437	34	-	-	PUNCT
fumecheng-7253	437	35	orderbeam	orderbeam	NOUN
fumecheng-7253	437	36	model	model	NOUN
fumecheng-7253	437	37	,	,	PUNCT
fumecheng-7253	437	38	applied	apply	VERB
fumecheng-7253	437	39	mathematical	mathematical	ADJ
fumecheng-7253	437	40	modelling	modelling	NOUN
fumecheng-7253	437	41	,	,	PUNCT
fumecheng-7253	437	42	80	80	NUM
fumecheng-7253	437	43	,	,	PUNCT
fumecheng-7253	437	44	pp	pp	ADJ
fumecheng-7253	437	45	.	.	PUNCT
fumecheng-7253	438	1	169	169	NUM
fumecheng-7253	438	2	-	-	SYM
fumecheng-7253	438	3	190	190	NUM
fumecheng-7253	438	4	.	.	NOUN
fumecheng-7253	439	1	39	39	NUM
fumecheng-7253	439	2	.	.	PUNCT
fumecheng-7253	440	1	ebrahimi	ebrahimi	PROPN
fumecheng-7253	440	2	,	,	PUNCT
fumecheng-7253	440	3	f.	f.	PROPN
fumecheng-7253	440	4	,	,	PUNCT
fumecheng-7253	440	5	haghi	haghi	PROPN
fumecheng-7253	440	6	,	,	PUNCT
fumecheng-7253	440	7	p.	p.	NOUN
fumecheng-7253	440	8	,2017	,2017	PUNCT
fumecheng-7253	440	9	,	,	PUNCT
fumecheng-7253	440	10	wave	wave	VERB
fumecheng-7253	440	11	propagation	propagation	NOUN
fumecheng-7253	440	12	analysis	analysis	NOUN
fumecheng-7253	440	13	of	of	ADP
fumecheng-7253	440	14	rotating	rotate	VERB
fumecheng-7253	440	15	thermoelastically	thermoelastically	ADV
fumecheng-7253	440	16	-	-	PUNCT
fumecheng-7253	440	17	actuated	actuate	VERB
fumecheng-7253	440	18	nanobeams	nanobeam	NOUN
fumecheng-7253	440	19	based	base	VERB
fumecheng-7253	440	20	on	on	ADP
fumecheng-7253	440	21	nonlocal	nonlocal	ADJ
fumecheng-7253	440	22	strain	strain	NOUN
fumecheng-7253	440	23	gradient	gradient	NOUN
fumecheng-7253	440	24	theory	theory	NOUN
fumecheng-7253	440	25	,	,	PUNCT
fumecheng-7253	440	26	actamechanicasolidasinica	actamechanicasolidasinica	PROPN
fumecheng-7253	440	27	,	,	PUNCT
fumecheng-7253	440	28	30(6	30(6	NUM
fumecheng-7253	440	29	)	)	PUNCT
fumecheng-7253	440	30	,	,	PUNCT
fumecheng-7253	440	31	pp	pp	ADP
fumecheng-7253	440	32	.	.	PUNCT
fumecheng-7253	441	1	647–657	647–657	NUM
fumecheng-7253	441	2	.	.	PUNCT
fumecheng-7253	442	1	40	40	NUM
fumecheng-7253	442	2	.	.	PUNCT
fumecheng-7253	443	1	azimi	azimi	PROPN
fumecheng-7253	443	2	,	,	PUNCT
fumecheng-7253	443	3	m.	m.	NOUN
fumecheng-7253	443	4	,	,	PUNCT
fumecheng-7253	443	5	mirjavadi	mirjavadi	NOUN
fumecheng-7253	443	6	,	,	PUNCT
fumecheng-7253	443	7	s.	s.	PROPN
fumecheng-7253	443	8	s.	s.	PROPN
fumecheng-7253	443	9	,	,	PUNCT
fumecheng-7253	443	10	shafiei	shafiei	PROPN
fumecheng-7253	443	11	,	,	PUNCT
fumecheng-7253	443	12	n.	n.	NOUN
fumecheng-7253	443	13	,	,	PUNCT
fumecheng-7253	443	14	hamouda	hamouda	PROPN
fumecheng-7253	443	15	,	,	PUNCT
fumecheng-7253	443	16	a.	a.	NOUN
fumecheng-7253	443	17	m.	m.	PROPN
fumecheng-7253	443	18	s.	s.	PROPN
fumecheng-7253	443	19	,	,	PUNCT
fumecheng-7253	443	20	davari	davari	PROPN
fumecheng-7253	443	21	,	,	PUNCT
fumecheng-7253	443	22	e.	e.	PROPN
fumecheng-7253	443	23	,2017	,2017	PROPN
fumecheng-7253	443	24	,	,	PUNCT
fumecheng-7253	443	25	vibration	vibration	NOUN
fumecheng-7253	443	26	of	of	ADP
fumecheng-7253	443	27	rotating	rotate	VERB
fumecheng-7253	443	28	functionally	functionally	ADV
fumecheng-7253	443	29	graded	grade	VERB
fumecheng-7253	443	30	timoshenko	timoshenko	ADJ
fumecheng-7253	443	31	nano	nano	NOUN
fumecheng-7253	443	32	-	-	PUNCT
fumecheng-7253	443	33	beams	beam	NOUN
fumecheng-7253	443	34	with	with	ADP
fumecheng-7253	443	35	nonlinear	nonlinear	ADJ
fumecheng-7253	443	36	thermal	thermal	ADJ
fumecheng-7253	443	37	distribution	distribution	NOUN
fumecheng-7253	443	38	,	,	PUNCT
fumecheng-7253	443	39	mechanics	mechanic	NOUN
fumecheng-7253	443	40	of	of	ADP
fumecheng-7253	443	41	advanced	advanced	ADJ
fumecheng-7253	443	42	materials	material	NOUN
fumecheng-7253	443	43	and	and	CCONJ
fumecheng-7253	443	44	structures	structure	NOUN
fumecheng-7253	443	45	,	,	PUNCT
fumecheng-7253	443	46	25(6	25(6	NOUN
fumecheng-7253	443	47	)	)	PUNCT
fumecheng-7253	443	48	,	,	PUNCT
fumecheng-7253	443	49	pp	pp	ADP
fumecheng-7253	443	50	.	.	PUNCT
fumecheng-7253	444	1	467–480	467–480	NUM
fumecheng-7253	444	2	.	.	PUNCT
fumecheng-7253	445	1	41	41	NUM
fumecheng-7253	445	2	.	.	PUNCT
fumecheng-7253	446	1	narendar	narendar	NOUN
fumecheng-7253	446	2	,	,	PUNCT
fumecheng-7253	446	3	s.	s.	PROPN
fumecheng-7253	446	4	,	,	PUNCT
fumecheng-7253	446	5	gopalakrishnan	gopalakrishnan	NOUN
fumecheng-7253	446	6	,	,	PUNCT
fumecheng-7253	446	7	s.	s.	PROPN
fumecheng-7253	446	8	,2011	,2011	PUNCT
fumecheng-7253	446	9	,	,	PUNCT
fumecheng-7253	446	10	nonlocal	nonlocal	ADJ
fumecheng-7253	446	11	wave	wave	NOUN
fumecheng-7253	446	12	propagation	propagation	NOUN
fumecheng-7253	446	13	in	in	ADP
fumecheng-7253	446	14	rotating	rotate	VERB
fumecheng-7253	446	15	nanotube	nanotube	NOUN
fumecheng-7253	446	16	,	,	PUNCT
fumecheng-7253	446	17	results	result	NOUN
fumecheng-7253	446	18	in	in	ADP
fumecheng-7253	446	19	physics	physics	NOUN
fumecheng-7253	446	20	,	,	PUNCT
fumecheng-7253	446	21	1	1	NUM
fumecheng-7253	446	22	,	,	PUNCT
fumecheng-7253	446	23	pp	pp	ADJ
fumecheng-7253	446	24	.	.	PUNCT
fumecheng-7253	447	1	17–25	17–25	NUM
fumecheng-7253	447	2	.	.	NUM
fumecheng-7253	448	1	42	42	NUM
fumecheng-7253	448	2	.	.	PUNCT
fumecheng-7253	449	1	ebrahimi	ebrahimi	PROPN
fumecheng-7253	449	2	,	,	PUNCT
fumecheng-7253	449	3	f.	f.	PROPN
fumecheng-7253	449	4	,	,	PUNCT
fumecheng-7253	449	5	dabbagh	dabbagh	PROPN
fumecheng-7253	449	6	,	,	PUNCT
fumecheng-7253	449	7	a.	a.	NOUN
fumecheng-7253	449	8	,2018	,2018	PUNCT
fumecheng-7253	449	9	,	,	PUNCT
fumecheng-7253	449	10	wave	wave	NOUN
fumecheng-7253	449	11	dispersion	dispersion	NOUN
fumecheng-7253	449	12	characteristics	characteristic	NOUN
fumecheng-7253	449	13	of	of	ADP
fumecheng-7253	449	14	rotating	rotate	VERB
fumecheng-7253	449	15	heterogeneous	heterogeneous	ADJ
fumecheng-7253	449	16	magneto	magneto	ADJ
fumecheng-7253	449	17	-	-	PUNCT
fumecheng-7253	449	18	electroelastic	electroelastic	ADJ
fumecheng-7253	449	19	nanobeams	nanobeam	NOUN
fumecheng-7253	449	20	based	base	VERB
fumecheng-7253	449	21	on	on	ADP
fumecheng-7253	449	22	nonlocal	nonlocal	ADJ
fumecheng-7253	449	23	strain	strain	NOUN
fumecheng-7253	449	24	gradient	gradient	NOUN
fumecheng-7253	449	25	elasticity	elasticity	NOUN
fumecheng-7253	449	26	theory	theory	NOUN
fumecheng-7253	449	27	,	,	PUNCT
fumecheng-7253	449	28	j.	j.	PROPN
fumecheng-7253	449	29	electromag	electromag	PROPN
fumecheng-7253	449	30	.	.	PUNCT
fumecheng-7253	450	1	waves	wave	NOUN
fumecheng-7253	450	2	appl	appl	PROPN
fumecheng-7253	450	3	.	.	PROPN
fumecheng-7253	450	4	,	,	PUNCT
fumecheng-7253	450	5	32(2	32(2	NUM
fumecheng-7253	450	6	)	)	PUNCT
fumecheng-7253	450	7	,	,	PUNCT
fumecheng-7253	451	1	pp	pp	PROPN
fumecheng-7253	451	2	.	.	PUNCT
fumecheng-7253	452	1	138	138	NUM
fumecheng-7253	452	2	-	-	SYM
fumecheng-7253	452	3	169	169	NUM
fumecheng-7253	452	4	.	.	PUNCT
fumecheng-7253	453	1	43	43	NUM
fumecheng-7253	453	2	.	.	PUNCT
fumecheng-7253	454	1	noda	noda	PROPN
fumecheng-7253	454	2	,	,	PUNCT
fumecheng-7253	454	3	n.	n.	NOUN
fumecheng-7253	454	4	,1986	,1986	PUNCT
fumecheng-7253	454	5	,	,	PUNCT
fumecheng-7253	454	6	thermal	thermal	ADJ
fumecheng-7253	454	7	stress	stress	NOUN
fumecheng-7253	454	8	in	in	ADP
fumecheng-7253	454	9	material	material	NOUN
fumecheng-7253	454	10	with	with	ADP
fumecheng-7253	454	11	temperature	temperature	NOUN
fumecheng-7253	454	12	dependent	dependent	ADJ
fumecheng-7253	454	13	properties	property	NOUN
fumecheng-7253	454	14	,	,	PUNCT
fumecheng-7253	454	15	in	in	ADP
fumecheng-7253	454	16	:	:	PUNCT
fumecheng-7253	454	17	r.b	r.b	PROPN
fumecheng-7253	454	18	.	.	PROPN
fumecheng-7253	454	19	hetnarski	hetnarski	PROPN
fumecheng-7253	454	20	(	(	PUNCT
fumecheng-7253	454	21	ed	ed	NOUN
fumecheng-7253	454	22	.	.	PUNCT
fumecheng-7253	454	23	)	)	PUNCT
fumecheng-7253	454	24	,	,	PUNCT
fumecheng-7253	454	25	thermal	thermal	ADJ
fumecheng-7253	454	26	stresses	stress	NOUN
fumecheng-7253	454	27	,	,	PUNCT
fumecheng-7253	454	28	elsevier	elsevier	PROPN
fumecheng-7253	454	29	science	science	PROPN
fumecheng-7253	454	30	,	,	PUNCT
fumecheng-7253	454	31	north	north	NOUN
fumecheng-7253	454	32	holland	holland	PROPN
fumecheng-7253	454	33	,	,	PUNCT
fumecheng-7253	454	34	amsterdam	amsterdam	PROPN
fumecheng-7253	454	35	,	,	PUNCT
fumecheng-7253	454	36	pp	pp	ADJ
fumecheng-7253	454	37	.	.	PUNCT
fumecheng-7253	455	1	391	391	NUM
fumecheng-7253	455	2	-	-	SYM
fumecheng-7253	455	3	483	483	NUM
fumecheng-7253	455	4	.	.	PUNCT
fumecheng-7253	456	1	44	44	NUM
fumecheng-7253	456	2	.	.	PUNCT
fumecheng-7253	457	1	berman	berman	PROPN
fumecheng-7253	457	2	,	,	PUNCT
fumecheng-7253	457	3	r.	r.	PROPN
fumecheng-7253	457	4	,1953	,1953	PROPN
fumecheng-7253	457	5	,	,	PUNCT
fumecheng-7253	457	6	the	the	DET
fumecheng-7253	457	7	thermal	thermal	ADJ
fumecheng-7253	457	8	conductivity	conductivity	NOUN
fumecheng-7253	457	9	of	of	ADP
fumecheng-7253	457	10	dielectric	dielectric	ADJ
fumecheng-7253	457	11	solids	solid	NOUN
fumecheng-7253	457	12	at	at	ADP
fumecheng-7253	457	13	low	low	ADJ
fumecheng-7253	457	14	temperatures	temperature	NOUN
fumecheng-7253	457	15	,	,	PUNCT
fumecheng-7253	457	16	advances	advance	NOUN
fumecheng-7253	457	17	in	in	ADP
fumecheng-7253	457	18	physics	physics	NOUN
fumecheng-7253	457	19	,	,	PUNCT
fumecheng-7253	457	20	2(5	2(5	NUM
fumecheng-7253	457	21	)	)	PUNCT
fumecheng-7253	457	22	,	,	PUNCT
fumecheng-7253	457	23	pp	pp	ADP
fumecheng-7253	457	24	.	.	PUNCT
fumecheng-7253	458	1	103	103	NUM
fumecheng-7253	458	2	-	-	SYM
fumecheng-7253	458	3	140	140	NUM
fumecheng-7253	458	4	.	.	NOUN
fumecheng-7253	459	1	45	45	NUM
fumecheng-7253	459	2	.	.	PUNCT
fumecheng-7253	459	3	sharma	sharma	PROPN
fumecheng-7253	459	4	,	,	PUNCT
fumecheng-7253	459	5	j.n	j.n	PROPN
fumecheng-7253	459	6	.	.	PROPN
fumecheng-7253	459	7	,	,	PUNCT
fumecheng-7253	459	8	kaur	kaur	PROPN
fumecheng-7253	459	9	,	,	PUNCT
fumecheng-7253	459	10	r.	r.	PROPN
fumecheng-7253	459	11	,2015	,2015	PUNCT
fumecheng-7253	459	12	,	,	PUNCT
fumecheng-7253	459	13	response	response	NOUN
fumecheng-7253	459	14	of	of	ADP
fumecheng-7253	459	15	anisotropic	anisotropic	NOUN
fumecheng-7253	459	16	thermoelastic	thermoelastic	ADJ
fumecheng-7253	459	17	micro	micro	ADJ
fumecheng-7253	459	18	-	-	ADJ
fumecheng-7253	459	19	beam	beam	ADJ
fumecheng-7253	459	20	resonators	resonator	NOUN
fumecheng-7253	459	21	under	under	ADP
fumecheng-7253	459	22	dynamic	dynamic	ADJ
fumecheng-7253	459	23	loads	load	NOUN
fumecheng-7253	459	24	,	,	PUNCT
fumecheng-7253	459	25	applied	apply	VERB
fumecheng-7253	459	26	mathematical	mathematical	ADJ
fumecheng-7253	459	27	modelling	modelling	NOUN
fumecheng-7253	459	28	,	,	PUNCT
fumecheng-7253	459	29	39	39	NUM
fumecheng-7253	459	30	,	,	PUNCT
fumecheng-7253	459	31	pp	pp	ADJ
fumecheng-7253	459	32	.	.	PUNCT
fumecheng-7253	460	1	2929–2941	2929–2941	NUM
fumecheng-7253	460	2	.	.	PUNCT
fumecheng-7253	461	1	46	46	NUM
fumecheng-7253	461	2	.	.	PUNCT
fumecheng-7253	462	1	honig	honig	PROPN
fumecheng-7253	462	2	,	,	PUNCT
fumecheng-7253	462	3	g.	g.	PROPN
fumecheng-7253	462	4	,	,	PUNCT
fumecheng-7253	462	5	hirdes	hirde	VERB
fumecheng-7253	462	6	,	,	PUNCT
fumecheng-7253	462	7	u.	u.	PROPN
fumecheng-7253	462	8	,1984	,1984	PROPN
fumecheng-7253	462	9	,	,	PUNCT
fumecheng-7253	462	10	a	a	DET
fumecheng-7253	462	11	method	method	NOUN
fumecheng-7253	462	12	for	for	ADP
fumecheng-7253	462	13	the	the	DET
fumecheng-7253	462	14	numerical	numerical	ADJ
fumecheng-7253	462	15	inversion	inversion	NOUN
fumecheng-7253	462	16	of	of	ADP
fumecheng-7253	462	17	laplace	laplace	NOUN
fumecheng-7253	462	18	transform	transform	NOUN
fumecheng-7253	462	19	,	,	PUNCT
fumecheng-7253	462	20	j.	j.	PROPN
fumecheng-7253	462	21	comp	comp	PROPN
fumecheng-7253	462	22	.	.	PUNCT
fumecheng-7253	463	1	appl	appl	PROPN
fumecheng-7253	463	2	.	.	PROPN
fumecheng-7253	463	3	math	math	PROPN
fumecheng-7253	463	4	.	.	PUNCT
fumecheng-7253	464	1	,	,	PUNCT
fumecheng-7253	464	2	10	10	NUM
fumecheng-7253	464	3	,	,	PUNCT
fumecheng-7253	464	4	113	113	NUM
fumecheng-7253	464	5	-	-	SYM
fumecheng-7253	464	6	132	132	NUM
fumecheng-7253	464	7	.	.	PUNCT
fumecheng-7253	465	1	47	47	NUM
fumecheng-7253	465	2	.	.	PUNCT
fumecheng-7253	466	1	tzou	tzou	PROPN
fumecheng-7253	466	2	,	,	PUNCT
fumecheng-7253	466	3	d.y	d.y	PROPN
fumecheng-7253	466	4	.	.	PROPN
fumecheng-7253	466	5	,1995	,1995	ADJ
fumecheng-7253	466	6	,	,	PUNCT
fumecheng-7253	466	7	experimental	experimental	ADJ
fumecheng-7253	466	8	support	support	NOUN
fumecheng-7253	466	9	for	for	ADP
fumecheng-7253	466	10	the	the	DET
fumecheng-7253	466	11	lagging	lag	VERB
fumecheng-7253	466	12	behavior	behavior	NOUN
fumecheng-7253	466	13	in	in	ADP
fumecheng-7253	466	14	heat	heat	NOUN
fumecheng-7253	466	15	propagation	propagation	NOUN
fumecheng-7253	466	16	,	,	PUNCT
fumecheng-7253	466	17	j.	j.	PROPN
fumecheng-7253	466	18	thermophys	thermophys	PROPN
fumecheng-7253	466	19	.	.	PUNCT
fumecheng-7253	467	1	heat	heat	PROPN
fumecheng-7253	467	2	transf	transf	NOUN
fumecheng-7253	467	3	.	.	PUNCT
fumecheng-7253	468	1	9(4	9(4	NUM
fumecheng-7253	468	2	)	)	PUNCT
fumecheng-7253	468	3	,	,	PUNCT
fumecheng-7253	468	4	pp	pp	ADJ
fumecheng-7253	468	5	.	.	PUNCT
fumecheng-7253	469	1	686–693	686–693	NUM
fumecheng-7253	469	2	.	.	PUNCT
fumecheng-7253	470	1	48	48	NUM
fumecheng-7253	470	2	.	.	PUNCT
fumecheng-7253	471	1	wang	wang	PROPN
fumecheng-7253	471	2	,	,	PUNCT
fumecheng-7253	471	3	y.	y.	PROPN
fumecheng-7253	471	4	,	,	PUNCT
fumecheng-7253	471	5	liu	liu	PROPN
fumecheng-7253	471	6	,	,	PUNCT
fumecheng-7253	471	7	d.	d.	PROPN
fumecheng-7253	471	8	wang	wang	PROPN
fumecheng-7253	471	9	,	,	PUNCT
fumecheng-7253	471	10	q.	q.	PROPN
fumecheng-7253	471	11	,	,	PUNCT
fumecheng-7253	471	12	zhou	zhou	PROPN
fumecheng-7253	471	13	,	,	PUNCT
fumecheng-7253	471	14	j.	j.	PROPN
fumecheng-7253	471	15	,2016	,2016	PUNCT
fumecheng-7253	471	16	,	,	PUNCT
fumecheng-7253	471	17	asymptotic	asymptotic	ADJ
fumecheng-7253	471	18	solutions	solution	NOUN
fumecheng-7253	471	19	for	for	ADP
fumecheng-7253	471	20	generalized	generalized	ADJ
fumecheng-7253	471	21	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	471	22	with	with	ADP
fumecheng-7253	471	23	variable	variable	ADJ
fumecheng-7253	471	24	thermal	thermal	ADJ
fumecheng-7253	471	25	material	material	NOUN
fumecheng-7253	471	26	properties	property	NOUN
fumecheng-7253	471	27	,	,	PUNCT
fumecheng-7253	471	28	archives	archive	NOUN
fumecheng-7253	471	29	of	of	ADP
fumecheng-7253	471	30	mechanics	mechanic	NOUN
fumecheng-7253	471	31	,	,	PUNCT
fumecheng-7253	471	32	68(3	68(3	NOUN
fumecheng-7253	471	33	)	)	PUNCT
fumecheng-7253	471	34	,	,	PUNCT
fumecheng-7253	471	35	pp	pp	ADP
fumecheng-7253	471	36	.	.	PUNCT
fumecheng-7253	472	1	181–202	181–202	NUM
fumecheng-7253	472	2	.	.	PUNCT
fumecheng-7253	473	1	49	49	NUM
fumecheng-7253	473	2	.	.	PUNCT
fumecheng-7253	474	1	abo‐dahab	abo‐dahab	PROPN
fumecheng-7253	474	2	,	,	PUNCT
fumecheng-7253	474	3	s.m	s.m	PROPN
fumecheng-7253	474	4	.	.	PROPN
fumecheng-7253	474	5	,	,	PUNCT
fumecheng-7253	474	6	abouelregal	abouelregal	PROPN
fumecheng-7253	474	7	,	,	PUNCT
fumecheng-7253	474	8	a.e	a.e	PROPN
fumecheng-7253	474	9	.	.	PROPN
fumecheng-7253	474	10	,	,	PUNCT
fumecheng-7253	474	11	ahmad	ahmad	PROPN
fumecheng-7253	474	12	,	,	PUNCT
fumecheng-7253	474	13	h.	h.	PROPN
fumecheng-7253	474	14	,2020	,2020	PROPN
fumecheng-7253	474	15	,	,	PUNCT
fumecheng-7253	474	16	fractional	fractional	ADJ
fumecheng-7253	474	17	heat	heat	NOUN
fumecheng-7253	474	18	conduction	conduction	NOUN
fumecheng-7253	474	19	model	model	NOUN
fumecheng-7253	474	20	with	with	ADP
fumecheng-7253	474	21	phase	phase	NOUN
fumecheng-7253	474	22	lags	lag	VERB
fumecheng-7253	474	23	for	for	ADP
fumecheng-7253	474	24	a	a	DET
fumecheng-7253	474	25	half‐space	half‐space	NOUN
fumecheng-7253	474	26	with	with	ADP
fumecheng-7253	474	27	thermal	thermal	ADJ
fumecheng-7253	474	28	conductivity	conductivity	NOUN
fumecheng-7253	474	29	and	and	CCONJ
fumecheng-7253	474	30	temperature	temperature	NOUN
fumecheng-7253	474	31	dependent	dependent	ADJ
fumecheng-7253	474	32	,	,	PUNCT
fumecheng-7253	474	33	mathematical	mathematical	ADJ
fumecheng-7253	474	34	methods	method	NOUN
fumecheng-7253	474	35	in	in	ADP
fumecheng-7253	474	36	the	the	DET
fumecheng-7253	474	37	applied	apply	VERB
fumecheng-7253	474	38	sciences	science	NOUN
fumecheng-7253	474	39	,	,	PUNCT
fumecheng-7253	474	40	doi:10.1002	doi:10.1002	NOUN
fumecheng-7253	474	41	/	/	SYM
fumecheng-7253	474	42	mma.6614	mma.6614	SYM
fumecheng-7253	474	43	50	50	NUM
fumecheng-7253	474	44	.	.	PUNCT
fumecheng-7253	475	1	ebrahimi	ebrahimi	PROPN
fumecheng-7253	475	2	,	,	PUNCT
fumecheng-7253	475	3	f.	f.	PROPN
fumecheng-7253	475	4	haghi	haghi	PROPN
fumecheng-7253	475	5	,	,	PUNCT
fumecheng-7253	475	6	p.	p.	NOUN
fumecheng-7253	475	7	2018	2018	NUM
fumecheng-7253	475	8	,	,	PUNCT
fumecheng-7253	475	9	elastic	elastic	ADJ
fumecheng-7253	475	10	wave	wave	NOUN
fumecheng-7253	475	11	dispersion	dispersion	NOUN
fumecheng-7253	475	12	modelling	modelling	NOUN
fumecheng-7253	475	13	within	within	ADP
fumecheng-7253	475	14	rotating	rotate	VERB
fumecheng-7253	475	15	functionally	functionally	ADV
fumecheng-7253	475	16	graded	grade	VERB
fumecheng-7253	475	17	nanobeams	nanobeam	NOUN
fumecheng-7253	475	18	in	in	ADP
fumecheng-7253	475	19	thermal	thermal	ADJ
fumecheng-7253	475	20	environment	environment	NOUN
fumecheng-7253	475	21	,	,	PUNCT
fumecheng-7253	475	22	advances	advance	NOUN
fumecheng-7253	475	23	in	in	ADP
fumecheng-7253	475	24	nano	nano	NOUN
fumecheng-7253	475	25	research	research	NOUN
fumecheng-7253	475	26	,	,	PUNCT
fumecheng-7253	475	27	6(3	6(3	NUM
fumecheng-7253	475	28	)	)	PUNCT
fumecheng-7253	475	29	,	,	PUNCT
fumecheng-7253	475	30	pp	pp	PROPN
fumecheng-7253	475	31	.	.	PUNCT
fumecheng-7253	475	32	201	201	NUM
fumecheng-7253	475	33	-	-	SYM
fumecheng-7253	475	34	217	217	NUM
fumecheng-7253	475	35	.	.	PUNCT
fumecheng-7253	476	1	51	51	NUM
fumecheng-7253	476	2	.	.	PUNCT
fumecheng-7253	477	1	shafiei	shafiei	PROPN
fumecheng-7253	477	2	,	,	PUNCT
fumecheng-7253	477	3	n.	n.	PROPN
fumecheng-7253	477	4	,	,	PUNCT
fumecheng-7253	477	5	kazemi	kazemi	PROPN
fumecheng-7253	477	6	,	,	PUNCT
fumecheng-7253	477	7	m.	m.	NOUN
fumecheng-7253	477	8	,	,	PUNCT
fumecheng-7253	477	9	ghadiri	ghadiri	NOUN
fumecheng-7253	477	10	,	,	PUNCT
fumecheng-7253	477	11	m.	m.	NOUN
fumecheng-7253	477	12	,2016	,2016	PUNCT
fumecheng-7253	477	13	,	,	PUNCT
fumecheng-7253	477	14	comparison	comparison	NOUN
fumecheng-7253	477	15	of	of	ADP
fumecheng-7253	477	16	modeling	modeling	NOUN
fumecheng-7253	477	17	of	of	ADP
fumecheng-7253	477	18	the	the	DET
fumecheng-7253	477	19	rotating	rotate	VERB
fumecheng-7253	477	20	tapered	tapered	NOUN
fumecheng-7253	477	21	axially	axially	ADV
fumecheng-7253	477	22	functionally	functionally	ADV
fumecheng-7253	477	23	graded	grade	VERB
fumecheng-7253	477	24	timoshenko	timoshenko	NOUN
fumecheng-7253	477	25	and	and	CCONJ
fumecheng-7253	477	26	euler	euler	PROPN
fumecheng-7253	477	27	–	–	PUNCT
fumecheng-7253	477	28	bernoulli	bernoulli	NOUN
fumecheng-7253	477	29	microbeams	microbeam	NOUN
fumecheng-7253	477	30	,	,	PUNCT
fumecheng-7253	477	31	physica	physica	NOUN
fumecheng-7253	477	32	e	e	NOUN
fumecheng-7253	477	33	:	:	PUNCT
fumecheng-7253	477	34	lowdimensional	lowdimensional	ADJ
fumecheng-7253	477	35	systems	system	NOUN
fumecheng-7253	477	36	and	and	CCONJ
fumecheng-7253	477	37	nanostructures	nanostructure	NOUN
fumecheng-7253	477	38	,	,	PUNCT
fumecheng-7253	477	39	83	83	NUM
fumecheng-7253	477	40	,	,	PUNCT
fumecheng-7253	477	41	pp	pp	ADJ
fumecheng-7253	477	42	.	.	PUNCT
fumecheng-7253	478	1	74	74	NUM
fumecheng-7253	478	2	-	-	SYM
fumecheng-7253	478	3	87	87	NUM
fumecheng-7253	478	4	.	.	PUNCT
fumecheng-7253	479	1	52	52	NUM
fumecheng-7253	479	2	.	.	PUNCT
fumecheng-7253	479	3	younesian	younesian	PROPN
fumecheng-7253	479	4	,	,	PUNCT
fumecheng-7253	479	5	d.	d.	PROPN
fumecheng-7253	479	6	,	,	PUNCT
fumecheng-7253	479	7	esmailzadeh	esmailzadeh	PROPN
fumecheng-7253	479	8	,	,	PUNCT
fumecheng-7253	479	9	e.	e.	PROPN
fumecheng-7253	479	10	,2011	,2011	PUNCT
fumecheng-7253	479	11	,	,	PUNCT
fumecheng-7253	479	12	vibration	vibration	NOUN
fumecheng-7253	479	13	suppression	suppression	NOUN
fumecheng-7253	479	14	of	of	ADP
fumecheng-7253	479	15	rotating	rotate	VERB
fumecheng-7253	479	16	beams	beam	NOUN
fumecheng-7253	479	17	using	use	VERB
fumecheng-7253	479	18	timevarying	timevarye	VERB
fumecheng-7253	479	19	internal	internal	ADJ
fumecheng-7253	479	20	tensile	tensile	NOUN
fumecheng-7253	479	21	force	force	NOUN
fumecheng-7253	479	22	,	,	PUNCT
fumecheng-7253	479	23	journal	journal	NOUN
fumecheng-7253	479	24	of	of	ADP
fumecheng-7253	479	25	sound	sound	NOUN
fumecheng-7253	479	26	and	and	CCONJ
fumecheng-7253	479	27	vibration	vibration	NOUN
fumecheng-7253	479	28	,	,	PUNCT
fumecheng-7253	479	29	330(2	330(2	NUM
fumecheng-7253	479	30	)	)	PUNCT
fumecheng-7253	479	31	,	,	PUNCT
fumecheng-7253	479	32	pp	pp	ADP
fumecheng-7253	479	33	.	.	PUNCT
fumecheng-7253	480	1	308	308	NUM
fumecheng-7253	480	2	-	-	SYM
fumecheng-7253	480	3	320	320	NUM
fumecheng-7253	480	4	.	.	PUNCT
fumecheng-7253	481	1	53	53	NUM
fumecheng-7253	481	2	.	.	PUNCT
fumecheng-7253	482	1	khaniki	khaniki	PROPN
fumecheng-7253	482	2	,	,	PUNCT
fumecheng-7253	482	3	h.b	h.b	PROPN
fumecheng-7253	482	4	.	.	PROPN
fumecheng-7253	482	5	,2018	,2018	NOUN
fumecheng-7253	482	6	,	,	PUNCT
fumecheng-7253	482	7	vibration	vibration	VERB
fumecheng-7253	482	8	analysis	analysis	NOUN
fumecheng-7253	482	9	of	of	ADP
fumecheng-7253	482	10	rotating	rotate	VERB
fumecheng-7253	482	11	nanobeam	nanobeam	NOUN
fumecheng-7253	482	12	systems	system	NOUN
fumecheng-7253	482	13	using	use	VERB
fumecheng-7253	482	14	eringen	eringen	PROPN
fumecheng-7253	482	15	’s	’s	PART
fumecheng-7253	482	16	two	two	NUM
fumecheng-7253	482	17	-	-	PUNCT
fumecheng-7253	482	18	phase	phase	NOUN
fumecheng-7253	482	19	local	local	ADJ
fumecheng-7253	482	20	/	/	SYM
fumecheng-7253	482	21	nonlocal	nonlocal	ADJ
fumecheng-7253	482	22	model	model	NOUN
fumecheng-7253	482	23	,	,	PUNCT
fumecheng-7253	482	24	physica	physica	NOUN
fumecheng-7253	482	25	e	e	NOUN
fumecheng-7253	482	26	:	:	PUNCT
fumecheng-7253	482	27	low	low	ADJ
fumecheng-7253	482	28	-	-	PUNCT
fumecheng-7253	482	29	dimensional	dimensional	ADJ
fumecheng-7253	482	30	systems	system	NOUN
fumecheng-7253	482	31	and	and	CCONJ
fumecheng-7253	482	32	nanostructures	nanostructure	NOUN
fumecheng-7253	482	33	,	,	PUNCT
fumecheng-7253	482	34	99	99	NUM
fumecheng-7253	482	35	,	,	PUNCT
fumecheng-7253	482	36	pp	pp	ADJ
fumecheng-7253	482	37	.	.	PUNCT
fumecheng-7253	483	1	310–319	310–319	NUM
fumecheng-7253	483	2	.	.	PUNCT
fumecheng-7253	484	1	54	54	NUM
fumecheng-7253	484	2	.	.	PUNCT
fumecheng-7253	485	1	safarabadi	safarabadi	NOUN
fumecheng-7253	485	2	,	,	PUNCT
fumecheng-7253	485	3	m.	m.	NOUN
fumecheng-7253	485	4	,	,	PUNCT
fumecheng-7253	485	5	mohammadi	mohammadi	NOUN
fumecheng-7253	485	6	,	,	PUNCT
fumecheng-7253	485	7	m.	m.	NOUN
fumecheng-7253	485	8	,	,	PUNCT
fumecheng-7253	485	9	farajpour	farajpour	ADJ
fumecheng-7253	485	10	,	,	PUNCT
fumecheng-7253	485	11	a.	a.	PROPN
fumecheng-7253	485	12	,	,	PUNCT
fumecheng-7253	485	13	goodarz	goodarz	PROPN
fumecheng-7253	485	14	,	,	PUNCT
fumecheng-7253	485	15	m.	m.	NOUN
fumecheng-7253	485	16	,2015	,2015	PUNCT
fumecheng-7253	485	17	,	,	PUNCT
fumecheng-7253	485	18	effect	effect	NOUN
fumecheng-7253	485	19	of	of	ADP
fumecheng-7253	485	20	surface	surface	NOUN
fumecheng-7253	485	21	energy	energy	NOUN
fumecheng-7253	485	22	on	on	ADP
fumecheng-7253	485	23	the	the	DET
fumecheng-7253	485	24	vibration	vibration	NOUN
fumecheng-7253	485	25	analysis	analysis	NOUN
fumecheng-7253	485	26	of	of	ADP
fumecheng-7253	485	27	rotating	rotate	VERB
fumecheng-7253	485	28	nanobeam	nanobeam	NOUN
fumecheng-7253	485	29	,	,	PUNCT
fumecheng-7253	485	30	journal	journal	NOUN
fumecheng-7253	485	31	of	of	ADP
fumecheng-7253	485	32	solid	solid	ADJ
fumecheng-7253	485	33	mechanics	mechanic	NOUN
fumecheng-7253	485	34	,	,	PUNCT
fumecheng-7253	485	35	7(3	7(3	NUM
fumecheng-7253	485	36	)	)	PUNCT
fumecheng-7253	485	37	pp	pp	ADV
fumecheng-7253	485	38	.	.	PUNCT
fumecheng-7253	486	1	299	299	NUM
fumecheng-7253	486	2	-	-	SYM
fumecheng-7253	486	3	311	311	NUM
fumecheng-7253	486	4	.	.	PUNCT
fumecheng-7253	487	1	656	656	NUM
fumecheng-7253	487	2	a.	a.	NOUN
fumecheng-7253	487	3	e.	e.	PROPN
fumecheng-7253	487	4	abouelregal	abouelregal	PROPN
fumecheng-7253	487	5	,	,	PUNCT
fumecheng-7253	487	6	h.	h.	PROPN
fumecheng-7253	487	7	m.	m.	PROPN
fumecheng-7253	487	8	sedighi	sedighi	PROPN
fumecheng-7253	487	9	,	,	PUNCT
fumecheng-7253	487	10	s.	s.	PROPN
fumecheng-7253	487	11	a.	a.	PROPN
fumecheng-7253	487	12	faghidian	faghidian	PROPN
fumecheng-7253	487	13	,	,	PUNCT
fumecheng-7253	487	14	a.	a.	PROPN
fumecheng-7253	487	15	h.	h.	PROPN
fumecheng-7253	487	16	shirazi	shirazi	PROPN
fumecheng-7253	487	17	55	55	NUM
fumecheng-7253	487	18	.	.	PUNCT
fumecheng-7253	487	19	fang	fang	PROPN
fumecheng-7253	487	20	,	,	PUNCT
fumecheng-7253	487	21	j.	j.	PROPN
fumecheng-7253	487	22	,	,	PUNCT
fumecheng-7253	487	23	gu	gu	PROPN
fumecheng-7253	487	24	,	,	PUNCT
fumecheng-7253	487	25	j.	j.	PROPN
fumecheng-7253	487	26	,	,	PUNCT
fumecheng-7253	487	27	wang	wang	PROPN
fumecheng-7253	487	28	,	,	PUNCT
fumecheng-7253	487	29	h.	h.	PROPN
fumecheng-7253	487	30	,2018	,2018	PUNCT
fumecheng-7253	487	31	,	,	PUNCT
fumecheng-7253	487	32	size	size	NOUN
fumecheng-7253	487	33	-	-	PUNCT
fumecheng-7253	487	34	dependent	dependent	ADJ
fumecheng-7253	487	35	three	three	NUM
fumecheng-7253	487	36	-	-	PUNCT
fumecheng-7253	487	37	dimensional	dimensional	ADJ
fumecheng-7253	487	38	free	free	ADJ
fumecheng-7253	487	39	vibration	vibration	NOUN
fumecheng-7253	487	40	of	of	ADP
fumecheng-7253	487	41	rotating	rotate	VERB
fumecheng-7253	487	42	functionally	functionally	ADV
fumecheng-7253	487	43	graded	grade	VERB
fumecheng-7253	487	44	microbeams	microbeam	NOUN
fumecheng-7253	487	45	based	base	VERB
fumecheng-7253	487	46	on	on	ADP
fumecheng-7253	487	47	a	a	DET
fumecheng-7253	487	48	modified	modify	VERB
fumecheng-7253	487	49	couple	couple	NOUN
fumecheng-7253	487	50	stress	stress	NOUN
fumecheng-7253	487	51	theory	theory	NOUN
fumecheng-7253	487	52	,	,	PUNCT
fumecheng-7253	487	53	international	international	ADJ
fumecheng-7253	487	54	journal	journal	NOUN
fumecheng-7253	487	55	of	of	ADP
fumecheng-7253	487	56	mechanical	mechanical	ADJ
fumecheng-7253	487	57	sciences	science	NOUN
fumecheng-7253	487	58	,	,	PUNCT
fumecheng-7253	487	59	136	136	NUM
fumecheng-7253	487	60	,	,	PUNCT
fumecheng-7253	487	61	pp	pp	ADJ
fumecheng-7253	487	62	.	.	PUNCT
fumecheng-7253	488	1	188	188	NUM
fumecheng-7253	488	2	-	-	SYM
fumecheng-7253	488	3	199	199	NUM
fumecheng-7253	488	4	.	.	PUNCT
fumecheng-7253	489	1	56	56	NUM
fumecheng-7253	489	2	.	.	PUNCT
fumecheng-7253	490	1	abouelregal	abouelregal	ADJ
fumecheng-7253	490	2	,	,	PUNCT
fumecheng-7253	490	3	a.e	a.e	PROPN
fumecheng-7253	490	4	.	.	PROPN
fumecheng-7253	490	5	2020	2020	NUM
fumecheng-7253	490	6	,	,	PUNCT
fumecheng-7253	490	7	a	a	DET
fumecheng-7253	490	8	novel	novel	ADJ
fumecheng-7253	490	9	model	model	NOUN
fumecheng-7253	490	10	of	of	ADP
fumecheng-7253	490	11	nonlocal	nonlocal	ADJ
fumecheng-7253	490	12	thermoelasticity	thermoelasticity	NOUN
fumecheng-7253	490	13	with	with	ADP
fumecheng-7253	490	14	time	time	NOUN
fumecheng-7253	490	15	derivatives	derivative	NOUN
fumecheng-7253	490	16	of	of	ADP
fumecheng-7253	490	17	higher	high	ADJ
fumecheng-7253	490	18	order	order	NOUN
fumecheng-7253	490	19	,	,	PUNCT
fumecheng-7253	490	20	mathematical	mathematical	ADJ
fumecheng-7253	490	21	methods	method	NOUN
fumecheng-7253	490	22	in	in	ADP
fumecheng-7253	490	23	the	the	DET
fumecheng-7253	490	24	applied	apply	VERB
fumecheng-7253	490	25	sciences	science	NOUN
fumecheng-7253	490	26	,	,	PUNCT
fumecheng-7253	490	27	doi:10.1002	doi:10.1002	NOUN
fumecheng-7253	490	28	/	/	SYM
fumecheng-7253	491	1	mma.6416	mma.6416	NOUN
fumecheng-7253	491	2	.	.	NOUN
fumecheng-7253	491	3	57	57	NUM
fumecheng-7253	491	4	.	.	PUNCT
fumecheng-7253	492	1	borjalilou	borjalilou	NOUN
fumecheng-7253	492	2	,	,	PUNCT
fumecheng-7253	492	3	v.	v.	ADV
fumecheng-7253	492	4	,	,	PUNCT
fumecheng-7253	492	5	asghari	asghari	ADJ
fumecheng-7253	492	6	,	,	PUNCT
fumecheng-7253	492	7	m.	m.	NOUN
fumecheng-7253	492	8	,	,	PUNCT
fumecheng-7253	492	9	taati	taati	PROPN
fumecheng-7253	492	10	,	,	PUNCT
fumecheng-7253	492	11	e.	e.	PROPN
fumecheng-7253	492	12	,2020	,2020	PROPN
fumecheng-7253	492	13	,	,	PUNCT
fumecheng-7253	492	14	thermoelastic	thermoelastic	ADJ
fumecheng-7253	492	15	damping	damping	NOUN
fumecheng-7253	492	16	in	in	ADP
fumecheng-7253	492	17	nonlocal	nonlocal	ADJ
fumecheng-7253	492	18	nanobeams	nanobeam	NOUN
fumecheng-7253	492	19	considering	consider	VERB
fumecheng-7253	492	20	dualphase	dualphase	NOUN
fumecheng-7253	492	21	-	-	PUNCT
fumecheng-7253	492	22	lagging	lag	VERB
fumecheng-7253	492	23	effect	effect	NOUN
fumecheng-7253	492	24	,	,	PUNCT
fumecheng-7253	492	25	journal	journal	NOUN
fumecheng-7253	492	26	of	of	ADP
fumecheng-7253	492	27	vibration	vibration	NOUN
fumecheng-7253	492	28	and	and	CCONJ
fumecheng-7253	492	29	control	control	NOUN
fumecheng-7253	492	30	,	,	PUNCT
fumecheng-7253	492	31	26(11–12	26(11–12	NUM
fumecheng-7253	492	32	)	)	PUNCT
fumecheng-7253	492	33	,	,	PUNCT
fumecheng-7253	492	34	pp	pp	PROPN
fumecheng-7253	492	35	.	.	PUNCT
fumecheng-7253	493	1	1042–1053	1042–1053	VERB
fumecheng-7253	493	2	.	.	PUNCT
fumecheng-7253	494	1	58	58	NUM
fumecheng-7253	494	2	.	.	PUNCT
fumecheng-7253	495	1	abouelregal	abouelregal	ADJ
fumecheng-7253	495	2	,	,	PUNCT
fumecheng-7253	495	3	a.e	a.e	PROPN
fumecheng-7253	495	4	.	.	PROPN
fumecheng-7253	495	5	,	,	PUNCT
fumecheng-7253	495	6	zenkour	zenkour	NOUN
fumecheng-7253	495	7	,	,	PUNCT
fumecheng-7253	495	8	a.m.	a.m.	ADV
fumecheng-7253	495	9	,2017	,2017	PUNCT
fumecheng-7253	495	10	,	,	PUNCT
fumecheng-7253	495	11	thermoelastic	thermoelastic	ADJ
fumecheng-7253	495	12	response	response	NOUN
fumecheng-7253	495	13	of	of	ADP
fumecheng-7253	495	14	nanobeam	nanobeam	ADJ
fumecheng-7253	495	15	resonators	resonator	NOUN
fumecheng-7253	495	16	subjected	subject	VERB
fumecheng-7253	495	17	to	to	ADP
fumecheng-7253	495	18	exponential	exponential	ADJ
fumecheng-7253	495	19	decaying	decay	VERB
fumecheng-7253	495	20	time	time	NOUN
fumecheng-7253	495	21	varying	vary	VERB
fumecheng-7253	495	22	load	load	NOUN
fumecheng-7253	495	23	,	,	PUNCT
fumecheng-7253	495	24	journal	journal	NOUN
fumecheng-7253	495	25	of	of	ADP
fumecheng-7253	495	26	theoretical	theoretical	ADJ
fumecheng-7253	495	27	and	and	CCONJ
fumecheng-7253	495	28	applied	applied	ADJ
fumecheng-7253	495	29	mechanics	mechanic	NOUN
fumecheng-7253	495	30	,	,	PUNCT
fumecheng-7253	495	31	55(3	55(3	NUM
fumecheng-7253	495	32	)	)	PUNCT
fumecheng-7253	495	33	,	,	PUNCT
fumecheng-7253	495	34	pp	pp	PROPN
fumecheng-7253	495	35	.	.	PUNCT
fumecheng-7253	496	1	937	937	NUM
fumecheng-7253	496	2	-	-	SYM
fumecheng-7253	496	3	948	948	NUM
fumecheng-7253	496	4	,	,	PUNCT
fumecheng-7253	496	5	warsaw	warsaw	PROPN
fumecheng-7253	496	6	.	.	PUNCT
fumecheng-7253	497	1	59	59	NUM
fumecheng-7253	497	2	.	.	PUNCT
fumecheng-7253	497	3	hahn	hahn	PROPN
fumecheng-7253	497	4	,	,	PUNCT
fumecheng-7253	497	5	d.w	d.w	PROPN
fumecheng-7253	497	6	.	.	PROPN
fumecheng-7253	497	7	,özişik	,özişik	PROPN
fumecheng-7253	497	8	,	,	PUNCT
fumecheng-7253	497	9	m.	m.	NOUN
fumecheng-7253	497	10	n.	n.	PROPN
fumecheng-7253	497	11	,	,	PUNCT
fumecheng-7253	497	12	2012	2012	NUM
fumecheng-7253	497	13	,	,	PUNCT
fumecheng-7253	497	14	heat	heat	NOUN
fumecheng-7253	497	15	conduction	conduction	NOUN
fumecheng-7253	497	16	,	,	PUNCT
fumecheng-7253	497	17	(	(	PUNCT
fumecheng-7253	497	18	3rd	3rd	PROPN
fumecheng-7253	497	19	ed.),hoboken	ed.),hoboken	PROPN
fumecheng-7253	497	20	,	,	PUNCT
fumecheng-7253	497	21	n.j	n.j	PROPN
fumecheng-7253	497	22	.	.	PROPN
fumecheng-7253	497	23	,	,	PUNCT
fumecheng-7253	497	24	wiley	wiley	PROPN
fumecheng-7253	497	25	.	.	PUNCT
fumecheng-7253	498	1	https://www.sciencedirect.com/science/journal/00207403/136/supp/c	https://www.sciencedirect.com/science/journal/00207403/136/supp/c	PROPN