id	sid	tid	token	lemma	pos
ajst-21812	1	1	academic	academic	ADJ
ajst-21812	1	2	journal	journal	NOUN
ajst-21812	1	3	of	of	ADP
ajst-21812	1	4	science	science	NOUN
ajst-21812	1	5	and	and	CCONJ
ajst-21812	1	6	technology	technology	NOUN
ajst-21812	1	7	issn	issn	NOUN
ajst-21812	1	8	:	:	PUNCT
ajst-21812	1	9	2771	2771	NUM
ajst-21812	1	10	-	-	SYM
ajst-21812	1	11	3032	3032	NUM
ajst-21812	1	12	|	|	NOUN
ajst-21812	1	13	vol	vol	NOUN
ajst-21812	1	14	.	.	PROPN
ajst-21812	2	1	11	11	NUM
ajst-21812	2	2	,	,	PUNCT
ajst-21812	2	3	no	no	INTJ
ajst-21812	2	4	.	.	NOUN
ajst-21812	2	5	1	1	NUM
ajst-21812	2	6	,	,	PUNCT
ajst-21812	2	7	2024	2024	NUM
ajst-21812	3	1	265	265	NUM
ajst-21812	3	2	free	free	ADJ
ajst-21812	3	3	vibration	vibration	NOUN
ajst-21812	3	4	analysis	analysis	NOUN
ajst-21812	3	5	of	of	ADP
ajst-21812	3	6	beams	beam	NOUN
ajst-21812	3	7	with	with	ADP
ajst-21812	3	8	functional	functional	ADJ
ajst-21812	3	9	gradient	gradient	NOUN
ajst-21812	3	10	materials	material	NOUN
ajst-21812	3	11	with	with	ADP
ajst-21812	3	12	cracks	crack	NOUN
ajst-21812	3	13	zhenxing	zhenxe	VERB
ajst-21812	3	14	pei	pei	PROPN
ajst-21812	3	15	*	*	PROPN
ajst-21812	3	16	school	school	NOUN
ajst-21812	3	17	of	of	ADP
ajst-21812	3	18	mechanical	mechanical	ADJ
ajst-21812	3	19	and	and	CCONJ
ajst-21812	3	20	power	power	NOUN
ajst-21812	3	21	engineering	engineering	PROPN
ajst-21812	3	22	,	,	PUNCT
ajst-21812	3	23	henan	henan	PROPN
ajst-21812	3	24	polytechnic	polytechnic	PROPN
ajst-21812	3	25	university	university	PROPN
ajst-21812	3	26	,	,	PUNCT
ajst-21812	3	27	jiaozuo	jiaozuo	PROPN
ajst-21812	3	28	454000	454000	NUM
ajst-21812	3	29	,	,	PUNCT
ajst-21812	3	30	china	china	PROPN
ajst-21812	3	31	*	*	PUNCT
ajst-21812	3	32	corresponding	correspond	VERB
ajst-21812	3	33	author	author	NOUN
ajst-21812	3	34	email	email	NOUN
ajst-21812	3	35	:	:	PUNCT
ajst-21812	3	36	1009399503@qq.com	1009399503@qq.com	NUM
ajst-21812	3	37	abstract	abstract	NOUN
ajst-21812	3	38	:	:	PUNCT
ajst-21812	3	39	the	the	DET
ajst-21812	3	40	article	article	NOUN
ajst-21812	3	41	presents	present	VERB
ajst-21812	3	42	the	the	DET
ajst-21812	3	43	development	development	NOUN
ajst-21812	3	44	of	of	ADP
ajst-21812	3	45	a	a	DET
ajst-21812	3	46	dynamic	dynamic	ADJ
ajst-21812	3	47	model	model	NOUN
ajst-21812	3	48	for	for	ADP
ajst-21812	3	49	a	a	DET
ajst-21812	3	50	functionally	functionally	ADV
ajst-21812	3	51	graded	grade	VERB
ajst-21812	3	52	material	material	NOUN
ajst-21812	3	53	(	(	PUNCT
ajst-21812	3	54	fgm	fgm	PROPN
ajst-21812	3	55	)	)	PUNCT
ajst-21812	3	56	beam	beam	NOUN
ajst-21812	3	57	incorporating	incorporate	VERB
ajst-21812	3	58	cracks	crack	NOUN
ajst-21812	3	59	.	.	PUNCT
ajst-21812	4	1	initially	initially	ADV
ajst-21812	4	2	,	,	PUNCT
ajst-21812	4	3	it	it	PRON
ajst-21812	4	4	assumes	assume	VERB
ajst-21812	4	5	an	an	DET
ajst-21812	4	6	exponential	exponential	ADJ
ajst-21812	4	7	distribution	distribution	NOUN
ajst-21812	4	8	of	of	ADP
ajst-21812	4	9	material	material	NOUN
ajst-21812	4	10	properties	property	NOUN
ajst-21812	4	11	along	along	ADP
ajst-21812	4	12	the	the	DET
ajst-21812	4	13	thickness	thickness	NOUN
ajst-21812	4	14	direction	direction	NOUN
ajst-21812	4	15	of	of	ADP
ajst-21812	4	16	the	the	DET
ajst-21812	4	17	beam	beam	NOUN
ajst-21812	4	18	and	and	CCONJ
ajst-21812	4	19	simulates	simulate	VERB
ajst-21812	4	20	the	the	DET
ajst-21812	4	21	opening	opening	NOUN
ajst-21812	4	22	crack	crack	NOUN
ajst-21812	4	23	using	use	VERB
ajst-21812	4	24	a	a	DET
ajst-21812	4	25	zero	zero	NUM
ajst-21812	4	26	-	-	PUNCT
ajst-21812	4	27	mass	mass	NOUN
ajst-21812	4	28	rotational	rotational	ADJ
ajst-21812	4	29	spring	spring	NOUN
ajst-21812	4	30	model	model	NOUN
ajst-21812	4	31	.	.	PUNCT
ajst-21812	5	1	this	this	DET
ajst-21812	5	2	approach	approach	NOUN
ajst-21812	5	3	enables	enable	VERB
ajst-21812	5	4	the	the	DET
ajst-21812	5	5	calculation	calculation	NOUN
ajst-21812	5	6	of	of	ADP
ajst-21812	5	7	bending	bend	VERB
ajst-21812	5	8	stiffness	stiffness	NOUN
ajst-21812	5	9	and	and	CCONJ
ajst-21812	5	10	local	local	ADJ
ajst-21812	5	11	flexibility	flexibility	NOUN
ajst-21812	5	12	at	at	ADP
ajst-21812	5	13	the	the	DET
ajst-21812	5	14	cracked	crack	VERB
ajst-21812	5	15	section	section	NOUN
ajst-21812	5	16	.	.	PUNCT
ajst-21812	6	1	subsequently	subsequently	ADV
ajst-21812	6	2	,	,	PUNCT
ajst-21812	6	3	drawing	draw	VERB
ajst-21812	6	4	upon	upon	SCONJ
ajst-21812	6	5	timoshenko	timoshenko	NOUN
ajst-21812	6	6	beam	beam	NOUN
ajst-21812	6	7	theory	theory	NOUN
ajst-21812	6	8	and	and	CCONJ
ajst-21812	6	9	von	von	PROPN
ajst-21812	6	10	kármán	kármán	PROPN
ajst-21812	6	11	geometric	geometric	PROPN
ajst-21812	6	12	nonlinear	nonlinear	PROPN
ajst-21812	6	13	theory	theory	NOUN
ajst-21812	6	14	,	,	PUNCT
ajst-21812	6	15	the	the	DET
ajst-21812	6	16	study	study	NOUN
ajst-21812	6	17	formulates	formulate	VERB
ajst-21812	6	18	the	the	DET
ajst-21812	6	19	energy	energy	NOUN
ajst-21812	6	20	equation	equation	NOUN
ajst-21812	6	21	of	of	ADP
ajst-21812	6	22	the	the	DET
ajst-21812	6	23	beam	beam	NOUN
ajst-21812	6	24	and	and	CCONJ
ajst-21812	6	25	establishes	establish	VERB
ajst-21812	6	26	the	the	DET
ajst-21812	6	27	partial	partial	ADJ
ajst-21812	6	28	differential	differential	NOUN
ajst-21812	6	29	control	control	NOUN
ajst-21812	6	30	equations	equation	NOUN
ajst-21812	6	31	for	for	ADP
ajst-21812	6	32	the	the	DET
ajst-21812	6	33	cracked	crack	VERB
ajst-21812	6	34	fgm	fgm	PROPN
ajst-21812	6	35	using	use	VERB
ajst-21812	6	36	hamilton	hamilton	PROPN
ajst-21812	6	37	's	's	PART
ajst-21812	6	38	principle	principle	NOUN
ajst-21812	6	39	.	.	PUNCT
ajst-21812	7	1	the	the	DET
ajst-21812	7	2	method	method	NOUN
ajst-21812	7	3	of	of	ADP
ajst-21812	7	4	separation	separation	NOUN
ajst-21812	7	5	of	of	ADP
ajst-21812	7	6	variables	variable	NOUN
ajst-21812	7	7	is	be	AUX
ajst-21812	7	8	employed	employ	VERB
ajst-21812	7	9	to	to	PART
ajst-21812	7	10	discretize	discretize	VERB
ajst-21812	7	11	the	the	DET
ajst-21812	7	12	partial	partial	ADJ
ajst-21812	7	13	differential	differential	NOUN
ajst-21812	7	14	motion	motion	NOUN
ajst-21812	7	15	equations	equation	NOUN
ajst-21812	7	16	into	into	ADP
ajst-21812	7	17	ordinary	ordinary	ADJ
ajst-21812	7	18	differential	differential	ADJ
ajst-21812	7	19	motion	motion	NOUN
ajst-21812	7	20	equations	equation	NOUN
ajst-21812	7	21	.	.	PUNCT
ajst-21812	8	1	beam	beam	NOUN
ajst-21812	8	2	functions	function	NOUN
ajst-21812	8	3	serve	serve	VERB
ajst-21812	8	4	as	as	ADP
ajst-21812	8	5	mode	mode	NOUN
ajst-21812	8	6	functions	function	NOUN
ajst-21812	8	7	,	,	PUNCT
ajst-21812	8	8	whose	whose	DET
ajst-21812	8	9	unknown	unknown	ADJ
ajst-21812	8	10	coefficients	coefficient	NOUN
ajst-21812	8	11	are	be	AUX
ajst-21812	8	12	determined	determine	VERB
ajst-21812	8	13	according	accord	VERB
ajst-21812	8	14	to	to	ADP
ajst-21812	8	15	the	the	DET
ajst-21812	8	16	boundary	boundary	ADJ
ajst-21812	8	17	and	and	CCONJ
ajst-21812	8	18	continuity	continuity	NOUN
ajst-21812	8	19	conditions	condition	NOUN
ajst-21812	8	20	,	,	PUNCT
ajst-21812	8	21	thereby	thereby	ADV
ajst-21812	8	22	yielding	yield	VERB
ajst-21812	8	23	the	the	DET
ajst-21812	8	24	natural	natural	ADJ
ajst-21812	8	25	frequencies	frequency	NOUN
ajst-21812	8	26	and	and	CCONJ
ajst-21812	8	27	mode	mode	NOUN
ajst-21812	8	28	shapes	shape	NOUN
ajst-21812	8	29	of	of	ADP
ajst-21812	8	30	the	the	DET
ajst-21812	8	31	cracked	crack	VERB
ajst-21812	8	32	fgm	fgm	PROPN
ajst-21812	8	33	beam	beam	NOUN
ajst-21812	8	34	.	.	PUNCT
ajst-21812	9	1	numerical	numerical	ADJ
ajst-21812	9	2	analysis	analysis	NOUN
ajst-21812	9	3	is	be	AUX
ajst-21812	9	4	conducted	conduct	VERB
ajst-21812	9	5	to	to	PART
ajst-21812	9	6	evaluate	evaluate	VERB
ajst-21812	9	7	the	the	DET
ajst-21812	9	8	impact	impact	NOUN
ajst-21812	9	9	of	of	ADP
ajst-21812	9	10	boundary	boundary	ADJ
ajst-21812	9	11	conditions	condition	NOUN
ajst-21812	9	12	,	,	PUNCT
ajst-21812	9	13	the	the	DET
ajst-21812	9	14	relative	relative	ADJ
ajst-21812	9	15	position	position	NOUN
ajst-21812	9	16	of	of	ADP
ajst-21812	9	17	cracks	crack	NOUN
ajst-21812	9	18	,	,	PUNCT
ajst-21812	9	19	and	and	CCONJ
ajst-21812	9	20	the	the	DET
ajst-21812	9	21	length	length	NOUN
ajst-21812	9	22	-	-	PUNCT
ajst-21812	9	23	to	to	ADP
ajst-21812	9	24	-	-	PUNCT
ajst-21812	9	25	thickness	thickness	NOUN
ajst-21812	9	26	ratio	ratio	NOUN
ajst-21812	9	27	on	on	ADP
ajst-21812	9	28	the	the	DET
ajst-21812	9	29	natural	natural	ADJ
ajst-21812	9	30	frequencies	frequency	NOUN
ajst-21812	9	31	of	of	ADP
ajst-21812	9	32	the	the	DET
ajst-21812	9	33	cracked	crack	VERB
ajst-21812	9	34	fgm	fgm	PROPN
ajst-21812	9	35	beam	beam	NOUN
ajst-21812	9	36	.	.	PUNCT
ajst-21812	10	1	keywords	keyword	NOUN
ajst-21812	10	2	:	:	PUNCT
ajst-21812	10	3	functional	functional	ADJ
ajst-21812	10	4	gradient	gradient	NOUN
ajst-21812	10	5	materials	material	NOUN
ajst-21812	10	6	,	,	PUNCT
ajst-21812	10	7	crack	crack	NOUN
ajst-21812	10	8	,	,	PUNCT
ajst-21812	10	9	free	free	ADJ
ajst-21812	10	10	vibration	vibration	NOUN
ajst-21812	10	11	.	.	PUNCT
ajst-21812	11	1	1	1	X
ajst-21812	11	2	.	.	X
ajst-21812	11	3	introduction	introduction	NOUN
ajst-21812	11	4	since	since	SCONJ
ajst-21812	11	5	the	the	DET
ajst-21812	11	6	1930s	1930	NOUN
ajst-21812	11	7	,	,	PUNCT
ajst-21812	11	8	the	the	DET
ajst-21812	11	9	vibration	vibration	NOUN
ajst-21812	11	10	problem	problem	NOUN
ajst-21812	11	11	of	of	ADP
ajst-21812	11	12	beams	beam	NOUN
ajst-21812	11	13	with	with	ADP
ajst-21812	11	14	cracks	crack	NOUN
ajst-21812	11	15	has	have	AUX
ajst-21812	11	16	drawn	draw	VERB
ajst-21812	11	17	the	the	DET
ajst-21812	11	18	attention	attention	NOUN
ajst-21812	11	19	of	of	ADP
ajst-21812	11	20	researchers	researcher	NOUN
ajst-21812	11	21	,	,	PUNCT
ajst-21812	11	22	and	and	CCONJ
ajst-21812	11	23	extensive	extensive	ADJ
ajst-21812	11	24	research	research	NOUN
ajst-21812	11	25	has	have	AUX
ajst-21812	11	26	been	be	AUX
ajst-21812	11	27	conducted	conduct	VERB
ajst-21812	11	28	in	in	ADP
ajst-21812	11	29	this	this	DET
ajst-21812	11	30	field	field	NOUN
ajst-21812	11	31	over	over	ADP
ajst-21812	11	32	time	time	NOUN
ajst-21812	11	33	.	.	PUNCT
ajst-21812	12	1	the	the	DET
ajst-21812	12	2	exploration	exploration	NOUN
ajst-21812	12	3	process	process	NOUN
ajst-21812	12	4	typically	typically	ADV
ajst-21812	12	5	includes	include	VERB
ajst-21812	12	6	selecting	select	VERB
ajst-21812	12	7	the	the	DET
ajst-21812	12	8	method	method	NOUN
ajst-21812	12	9	for	for	ADP
ajst-21812	12	10	modeling	modeling	NOUN
ajst-21812	12	11	cracks	crack	NOUN
ajst-21812	12	12	,	,	PUNCT
ajst-21812	12	13	establishing	establish	VERB
ajst-21812	12	14	dynamic	dynamic	ADJ
ajst-21812	12	15	equations	equation	NOUN
ajst-21812	12	16	,	,	PUNCT
ajst-21812	12	17	applying	apply	VERB
ajst-21812	12	18	various	various	ADJ
ajst-21812	12	19	algorithms	algorithm	NOUN
ajst-21812	12	20	,	,	PUNCT
ajst-21812	12	21	and	and	CCONJ
ajst-21812	12	22	investigating	investigate	VERB
ajst-21812	12	23	vibration	vibration	NOUN
ajst-21812	12	24	characteristics	characteristic	NOUN
ajst-21812	12	25	,	,	PUNCT
ajst-21812	12	26	excitation	excitation	NOUN
ajst-21812	12	27	responses	response	NOUN
ajst-21812	12	28	,	,	PUNCT
ajst-21812	12	29	stability	stability	NOUN
ajst-21812	12	30	,	,	PUNCT
ajst-21812	12	31	and	and	CCONJ
ajst-21812	12	32	crack	crack	VERB
ajst-21812	12	33	parameter	parameter	NOUN
ajst-21812	12	34	identification	identification	NOUN
ajst-21812	12	35	.	.	PUNCT
ajst-21812	13	1	irwin	irwin	PROPN
ajst-21812	13	2	gr[1	gr[1	PROPN
ajst-21812	13	3	]	]	PUNCT
ajst-21812	13	4	analyzed	analyze	VERB
ajst-21812	13	5	the	the	DET
ajst-21812	13	6	dynamic	dynamic	ADJ
ajst-21812	13	7	characteristics	characteristic	NOUN
ajst-21812	13	8	of	of	ADP
ajst-21812	13	9	metal	metal	NOUN
ajst-21812	13	10	plates	plate	NOUN
ajst-21812	13	11	with	with	ADP
ajst-21812	13	12	cracks	crack	NOUN
ajst-21812	13	13	through	through	ADP
ajst-21812	13	14	the	the	DET
ajst-21812	13	15	theory	theory	NOUN
ajst-21812	13	16	of	of	ADP
ajst-21812	13	17	local	local	ADJ
ajst-21812	13	18	flexibility	flexibility	NOUN
ajst-21812	13	19	,	,	PUNCT
ajst-21812	13	20	laying	lay	VERB
ajst-21812	13	21	the	the	DET
ajst-21812	13	22	foundation	foundation	NOUN
ajst-21812	13	23	for	for	ADP
ajst-21812	13	24	subsequent	subsequent	ADJ
ajst-21812	13	25	research	research	NOUN
ajst-21812	13	26	.	.	PUNCT
ajst-21812	14	1	sourki	sourki	NOUN
ajst-21812	14	2	r	r	PROPN
ajst-21812	14	3	et	et	PROPN
ajst-21812	14	4	al.[2	al.[2	PROPN
ajst-21812	14	5	]	]	X
ajst-21812	14	6	utilized	utilize	VERB
ajst-21812	14	7	the	the	DET
ajst-21812	14	8	classical	classical	ADJ
ajst-21812	14	9	euler	euler	NOUN
ajst-21812	14	10	-	-	PUNCT
ajst-21812	14	11	bernoulli	bernoulli	PROPN
ajst-21812	14	12	beam	beam	NOUN
ajst-21812	14	13	theory	theory	NOUN
ajst-21812	14	14	and	and	CCONJ
ajst-21812	14	15	different	different	ADJ
ajst-21812	14	16	methods	method	NOUN
ajst-21812	14	17	such	such	ADJ
ajst-21812	14	18	as	as	ADP
ajst-21812	14	19	the	the	DET
ajst-21812	14	20	modified	modify	VERB
ajst-21812	14	21	stress	stress	NOUN
ajst-21812	14	22	couple	couple	NOUN
ajst-21812	14	23	theory	theory	NOUN
ajst-21812	14	24	,	,	PUNCT
ajst-21812	14	25	fourier	fourier	ADJ
ajst-21812	14	26	series	series	NOUN
ajst-21812	14	27	,	,	PUNCT
ajst-21812	14	28	and	and	CCONJ
ajst-21812	14	29	galerkin	galerkin	PROPN
ajst-21812	14	30	method	method	NOUN
ajst-21812	14	31	to	to	PART
ajst-21812	14	32	analyze	analyze	VERB
ajst-21812	14	33	the	the	DET
ajst-21812	14	34	free	free	ADJ
ajst-21812	14	35	lateral	lateral	ADJ
ajst-21812	14	36	vibration	vibration	NOUN
ajst-21812	14	37	of	of	ADP
ajst-21812	14	38	cracked	crack	VERB
ajst-21812	14	39	beams	beam	NOUN
ajst-21812	14	40	,	,	PUNCT
ajst-21812	14	41	obtaining	obtain	VERB
ajst-21812	14	42	the	the	DET
ajst-21812	14	43	frequency	frequency	NOUN
ajst-21812	14	44	equations	equation	NOUN
ajst-21812	14	45	for	for	ADP
ajst-21812	14	46	cracked	cracked	ADJ
ajst-21812	14	47	beams	beam	NOUN
ajst-21812	14	48	.	.	PUNCT
ajst-21812	15	1	by	by	ADP
ajst-21812	15	2	employing	employ	VERB
ajst-21812	15	3	hamilton	hamilton	PROPN
ajst-21812	15	4	's	's	PART
ajst-21812	15	5	principle	principle	NOUN
ajst-21812	15	6	,	,	PUNCT
ajst-21812	15	7	they	they	PRON
ajst-21812	15	8	derived	derive	VERB
ajst-21812	15	9	control	control	NOUN
ajst-21812	15	10	equations	equation	NOUN
ajst-21812	15	11	and	and	CCONJ
ajst-21812	15	12	related	relate	VERB
ajst-21812	15	13	boundary	boundary	ADJ
ajst-21812	15	14	conditions	condition	NOUN
ajst-21812	15	15	,	,	PUNCT
ajst-21812	15	16	taking	take	VERB
ajst-21812	15	17	into	into	ADP
ajst-21812	15	18	account	account	NOUN
ajst-21812	15	19	the	the	DET
ajst-21812	15	20	additional	additional	ADJ
ajst-21812	15	21	strain	strain	NOUN
ajst-21812	15	22	energy	energy	NOUN
ajst-21812	15	23	caused	cause	VERB
ajst-21812	15	24	by	by	ADP
ajst-21812	15	25	cracks	crack	NOUN
ajst-21812	15	26	and	and	CCONJ
ajst-21812	15	27	the	the	DET
ajst-21812	15	28	discontinuity	discontinuity	NOUN
ajst-21812	15	29	in	in	ADP
ajst-21812	15	30	bending	bend	VERB
ajst-21812	15	31	slope	slope	NOUN
ajst-21812	15	32	due	due	ADP
ajst-21812	15	33	to	to	ADP
ajst-21812	15	34	cracks	crack	NOUN
ajst-21812	15	35	.	.	PUNCT
ajst-21812	16	1	the	the	DET
ajst-21812	16	2	study	study	NOUN
ajst-21812	16	3	examined	examine	VERB
ajst-21812	16	4	the	the	DET
ajst-21812	16	5	impact	impact	NOUN
ajst-21812	16	6	of	of	ADP
ajst-21812	16	7	different	different	ADJ
ajst-21812	16	8	crack	crack	NOUN
ajst-21812	16	9	positions	position	NOUN
ajst-21812	16	10	,	,	PUNCT
ajst-21812	16	11	crack	crack	NOUN
ajst-21812	16	12	depths	depth	NOUN
ajst-21812	16	13	,	,	PUNCT
ajst-21812	16	14	material	material	NOUN
ajst-21812	16	15	length	length	NOUN
ajst-21812	16	16	scale	scale	NOUN
ajst-21812	16	17	parameters	parameter	NOUN
ajst-21812	16	18	,	,	PUNCT
ajst-21812	16	19	and	and	CCONJ
ajst-21812	16	20	poisson	poisson	PROPN
ajst-21812	16	21	's	's	PART
ajst-21812	16	22	ratio	ratio	NOUN
ajst-21812	16	23	on	on	ADP
ajst-21812	16	24	the	the	DET
ajst-21812	16	25	system	system	NOUN
ajst-21812	16	26	's	's	PART
ajst-21812	16	27	natural	natural	ADJ
ajst-21812	16	28	frequencies	frequency	NOUN
ajst-21812	16	29	.	.	PUNCT
ajst-21812	17	1	based	base	VERB
ajst-21812	17	2	on	on	ADP
ajst-21812	17	3	the	the	DET
ajst-21812	17	4	first	first	ADJ
ajst-21812	17	5	-	-	PUNCT
ajst-21812	17	6	order	order	NOUN
ajst-21812	17	7	shear	shear	NOUN
ajst-21812	17	8	deformation	deformation	NOUN
ajst-21812	17	9	theory	theory	NOUN
ajst-21812	17	10	,	,	PUNCT
ajst-21812	17	11	torabi	torabi	NOUN
ajst-21812	17	12	k	k	PROPN
ajst-21812	17	13	et	et	PROPN
ajst-21812	17	14	al.[3	al.[3	PROPN
ajst-21812	17	15	]	]	PUNCT
ajst-21812	17	16	modeled	model	VERB
ajst-21812	17	17	the	the	DET
ajst-21812	17	18	free	free	ADJ
ajst-21812	17	19	lateral	lateral	ADJ
ajst-21812	17	20	vibration	vibration	NOUN
ajst-21812	17	21	of	of	ADP
ajst-21812	17	22	cracked	crack	VERB
ajst-21812	17	23	beams	beam	NOUN
ajst-21812	17	24	using	use	VERB
ajst-21812	17	25	a	a	DET
ajst-21812	17	26	generalized	generalized	ADJ
ajst-21812	17	27	delta	delta	NOUN
ajst-21812	17	28	function	function	NOUN
ajst-21812	17	29	and	and	CCONJ
ajst-21812	17	30	variation	variation	NOUN
ajst-21812	17	31	coefficients	coefficient	NOUN
ajst-21812	17	32	.	.	PUNCT
ajst-21812	18	1	they	they	PRON
ajst-21812	18	2	derived	derive	VERB
ajst-21812	18	3	the	the	DET
ajst-21812	18	4	control	control	NOUN
ajst-21812	18	5	equations	equation	NOUN
ajst-21812	18	6	for	for	ADP
ajst-21812	18	7	cracked	cracked	ADJ
ajst-21812	18	8	beams	beam	NOUN
ajst-21812	18	9	under	under	ADP
ajst-21812	18	10	both	both	CCONJ
ajst-21812	18	11	symmetric	symmetric	ADJ
ajst-21812	18	12	and	and	CCONJ
ajst-21812	18	13	asymmetric	asymmetric	ADJ
ajst-21812	18	14	boundary	boundary	ADJ
ajst-21812	18	15	conditions	condition	NOUN
ajst-21812	18	16	and	and	CCONJ
ajst-21812	18	17	analytically	analytically	ADV
ajst-21812	18	18	solved	solve	VERB
ajst-21812	18	19	these	these	DET
ajst-21812	18	20	equations	equation	NOUN
ajst-21812	18	21	using	use	VERB
ajst-21812	18	22	basic	basic	ADJ
ajst-21812	18	23	standard	standard	ADJ
ajst-21812	18	24	trigonometric	trigonometric	ADJ
ajst-21812	18	25	and	and	CCONJ
ajst-21812	18	26	hyperbolic	hyperbolic	ADJ
ajst-21812	18	27	functions	function	NOUN
ajst-21812	18	28	,	,	PUNCT
ajst-21812	18	29	analyzing	analyze	VERB
ajst-21812	18	30	the	the	DET
ajst-21812	18	31	free	free	ADJ
ajst-21812	18	32	vibration	vibration	NOUN
ajst-21812	18	33	characteristics	characteristic	NOUN
ajst-21812	18	34	of	of	ADP
ajst-21812	18	35	the	the	DET
ajst-21812	18	36	system	system	NOUN
ajst-21812	18	37	and	and	CCONJ
ajst-21812	18	38	investigating	investigate	VERB
ajst-21812	18	39	the	the	DET
ajst-21812	18	40	effects	effect	NOUN
ajst-21812	18	41	of	of	ADP
ajst-21812	18	42	different	different	ADJ
ajst-21812	18	43	system	system	NOUN
ajst-21812	18	44	conditions	condition	NOUN
ajst-21812	18	45	on	on	ADP
ajst-21812	18	46	its	its	PRON
ajst-21812	18	47	dynamic	dynamic	ADJ
ajst-21812	18	48	behavior	behavior	NOUN
ajst-21812	18	49	.	.	PUNCT
ajst-21812	19	1	taima	taima	PROPN
ajst-21812	19	2	ms	ms	PROPN
ajst-21812	19	3	and	and	CCONJ
ajst-21812	19	4	el	el	PROPN
ajst-21812	19	5	-	-	PUNCT
ajst-21812	19	6	sayed	say	VERB
ajst-21812	19	7	ta	ta	PROPN
ajst-21812	19	8	et	et	PROPN
ajst-21812	19	9	al.[4	al.[4	PROPN
ajst-21812	19	10	]	]	PUNCT
ajst-21812	19	11	studied	study	VERB
ajst-21812	19	12	the	the	DET
ajst-21812	19	13	lateral	lateral	ADJ
ajst-21812	19	14	vibration	vibration	NOUN
ajst-21812	19	15	of	of	ADP
ajst-21812	19	16	isotropic	isotropic	NOUN
ajst-21812	19	17	and	and	CCONJ
ajst-21812	19	18	thick	thick	ADJ
ajst-21812	19	19	beams	beam	NOUN
ajst-21812	19	20	with	with	ADP
ajst-21812	19	21	cracks	crack	NOUN
ajst-21812	19	22	,	,	PUNCT
ajst-21812	19	23	comparing	compare	VERB
ajst-21812	19	24	the	the	DET
ajst-21812	19	25	analysis	analysis	NOUN
ajst-21812	19	26	of	of	ADP
ajst-21812	19	27	timoshenko	timoshenko	ADJ
ajst-21812	19	28	beam	beam	NOUN
ajst-21812	19	29	theory	theory	NOUN
ajst-21812	19	30	and	and	CCONJ
ajst-21812	19	31	reddy	reddy	PROPN
ajst-21812	19	32	beam	beam	PROPN
ajst-21812	19	33	theory	theory	NOUN
ajst-21812	19	34	for	for	ADP
ajst-21812	19	35	beams	beam	NOUN
ajst-21812	19	36	with	with	ADP
ajst-21812	19	37	cracks	crack	NOUN
ajst-21812	19	38	.	.	PUNCT
ajst-21812	20	1	by	by	ADP
ajst-21812	20	2	dividing	divide	VERB
ajst-21812	20	3	the	the	DET
ajst-21812	20	4	beam	beam	NOUN
ajst-21812	20	5	into	into	ADP
ajst-21812	20	6	multiple	multiple	ADJ
ajst-21812	20	7	elements	element	NOUN
ajst-21812	20	8	and	and	CCONJ
ajst-21812	20	9	deriving	derive	VERB
ajst-21812	20	10	stiffness	stiffness	NOUN
ajst-21812	20	11	and	and	CCONJ
ajst-21812	20	12	mass	mass	ADJ
ajst-21812	20	13	matrices	matrix	NOUN
ajst-21812	20	14	for	for	ADP
ajst-21812	20	15	each	each	DET
ajst-21812	20	16	beam	beam	NOUN
ajst-21812	20	17	element	element	NOUN
ajst-21812	20	18	based	base	VERB
ajst-21812	20	19	on	on	ADP
ajst-21812	20	20	reddy	reddy	PROPN
ajst-21812	20	21	beam	beam	PROPN
ajst-21812	20	22	theory	theory	NOUN
ajst-21812	20	23	equations	equation	NOUN
ajst-21812	20	24	,	,	PUNCT
ajst-21812	20	25	they	they	PRON
ajst-21812	20	26	simulated	simulate	VERB
ajst-21812	20	27	the	the	DET
ajst-21812	20	28	impact	impact	NOUN
ajst-21812	20	29	of	of	ADP
ajst-21812	20	30	cracks	crack	NOUN
ajst-21812	20	31	and	and	CCONJ
ajst-21812	20	32	analyzed	analyze	VERB
ajst-21812	20	33	the	the	DET
ajst-21812	20	34	effects	effect	NOUN
ajst-21812	20	35	of	of	ADP
ajst-21812	20	36	boundary	boundary	ADJ
ajst-21812	20	37	conditions	condition	NOUN
ajst-21812	20	38	,	,	PUNCT
ajst-21812	20	39	slenderness	slenderness	ADJ
ajst-21812	20	40	ratio	ratio	NOUN
ajst-21812	20	41	,	,	PUNCT
ajst-21812	20	42	crack	crack	VERB
ajst-21812	20	43	position	position	NOUN
ajst-21812	20	44	,	,	PUNCT
ajst-21812	20	45	and	and	CCONJ
ajst-21812	20	46	depth	depth	NOUN
ajst-21812	20	47	on	on	ADP
ajst-21812	20	48	lateral	lateral	ADJ
ajst-21812	20	49	vibration	vibration	NOUN
ajst-21812	20	50	.	.	PUNCT
ajst-21812	21	1	the	the	DET
ajst-21812	21	2	accuracy	accuracy	NOUN
ajst-21812	21	3	of	of	ADP
ajst-21812	21	4	the	the	DET
ajst-21812	21	5	model	model	NOUN
ajst-21812	21	6	results	result	NOUN
ajst-21812	21	7	was	be	AUX
ajst-21812	21	8	validated	validate	VERB
ajst-21812	21	9	through	through	ADP
ajst-21812	21	10	experiments	experiment	NOUN
ajst-21812	21	11	and	and	CCONJ
ajst-21812	21	12	finite	finite	ADJ
ajst-21812	21	13	element	element	NOUN
ajst-21812	21	14	analysis	analysis	NOUN
ajst-21812	21	15	.	.	PUNCT
ajst-21812	22	1	zhao	zhao	NOUN
ajst-21812	22	2	et	et	NOUN
ajst-21812	22	3	al.[5	al.[5	PROPN
ajst-21812	22	4	]	]	PUNCT
ajst-21812	22	5	used	use	VERB
ajst-21812	22	6	the	the	DET
ajst-21812	22	7	green	green	NOUN
ajst-21812	22	8	's	's	PART
ajst-21812	22	9	function	function	NOUN
ajst-21812	22	10	method	method	NOUN
ajst-21812	22	11	and	and	CCONJ
ajst-21812	22	12	the	the	DET
ajst-21812	22	13	superposition	superposition	NOUN
ajst-21812	22	14	principle	principle	NOUN
ajst-21812	22	15	,	,	PUNCT
ajst-21812	22	16	combined	combine	VERB
ajst-21812	22	17	with	with	ADP
ajst-21812	22	18	the	the	DET
ajst-21812	22	19	separation	separation	NOUN
ajst-21812	22	20	of	of	ADP
ajst-21812	22	21	variables	variable	NOUN
ajst-21812	22	22	method	method	NOUN
ajst-21812	22	23	,	,	PUNCT
ajst-21812	22	24	laplace	laplace	NOUN
ajst-21812	22	25	transforms	transform	VERB
ajst-21812	22	26	,	,	PUNCT
ajst-21812	22	27	and	and	CCONJ
ajst-21812	22	28	other	other	ADJ
ajst-21812	22	29	mathematical	mathematical	ADJ
ajst-21812	22	30	methods	method	NOUN
ajst-21812	22	31	,	,	PUNCT
ajst-21812	22	32	to	to	PART
ajst-21812	22	33	obtain	obtain	VERB
ajst-21812	22	34	explicit	explicit	ADJ
ajst-21812	22	35	expressions	expression	NOUN
ajst-21812	22	36	for	for	ADP
ajst-21812	22	37	the	the	DET
ajst-21812	22	38	steady	steady	ADJ
ajst-21812	22	39	-	-	PUNCT
ajst-21812	22	40	state	state	NOUN
ajst-21812	22	41	forced	force	VERB
ajst-21812	22	42	vibration	vibration	NOUN
ajst-21812	22	43	of	of	ADP
ajst-21812	22	44	fixed	fix	VERB
ajst-21812	22	45	cross	cross	NOUN
ajst-21812	22	46	-	-	NOUN
ajst-21812	22	47	section	section	ADJ
ajst-21812	22	48	and	and	CCONJ
ajst-21812	22	49	variable	variable	ADJ
ajst-21812	22	50	cross	cross	NOUN
ajst-21812	22	51	-	-	NOUN
ajst-21812	22	52	section	section	ADJ
ajst-21812	22	53	euler	euler	NOUN
ajst-21812	22	54	-	-	PUNCT
ajst-21812	22	55	bernoulli	bernoulli	NOUN
ajst-21812	22	56	beams	beam	NOUN
ajst-21812	22	57	with	with	ADP
ajst-21812	22	58	multiple	multiple	ADJ
ajst-21812	22	59	cracks	crack	NOUN
ajst-21812	22	60	under	under	ADP
ajst-21812	22	61	harmonic	harmonic	ADJ
ajst-21812	22	62	loads	load	NOUN
ajst-21812	22	63	.	.	PUNCT
ajst-21812	23	1	they	they	PRON
ajst-21812	23	2	analyzed	analyze	VERB
ajst-21812	23	3	the	the	DET
ajst-21812	23	4	results	result	NOUN
ajst-21812	23	5	,	,	PUNCT
ajst-21812	23	6	demonstrating	demonstrate	VERB
ajst-21812	23	7	that	that	SCONJ
ajst-21812	23	8	the	the	DET
ajst-21812	23	9	geometric	geometric	ADJ
ajst-21812	23	10	shape	shape	NOUN
ajst-21812	23	11	of	of	ADP
ajst-21812	23	12	the	the	DET
ajst-21812	23	13	crack	crack	NOUN
ajst-21812	23	14	(	(	PUNCT
ajst-21812	23	15	depth	depth	NOUN
ajst-21812	23	16	and	and	CCONJ
ajst-21812	23	17	position	position	NOUN
ajst-21812	23	18	)	)	PUNCT
ajst-21812	23	19	and	and	CCONJ
ajst-21812	23	20	section	section	NOUN
ajst-21812	23	21	parameters	parameter	NOUN
ajst-21812	23	22	significantly	significantly	ADV
ajst-21812	23	23	impact	impact	VERB
ajst-21812	23	24	the	the	DET
ajst-21812	23	25	system	system	NOUN
ajst-21812	23	26	's	's	PART
ajst-21812	23	27	dynamic	dynamic	ADJ
ajst-21812	23	28	behavior	behavior	NOUN
ajst-21812	23	29	.	.	PUNCT
ajst-21812	24	1	based	base	VERB
ajst-21812	24	2	on	on	ADP
ajst-21812	24	3	this	this	PRON
ajst-21812	24	4	,	,	PUNCT
ajst-21812	24	5	x.	x.	NOUN
ajst-21812	24	6	zhao	zhao	PROPN
ajst-21812	24	7	et	et	PROPN
ajst-21812	24	8	al.[6	al.[6	PROPN
ajst-21812	24	9	]	]	PUNCT
ajst-21812	24	10	studied	study	VERB
ajst-21812	24	11	the	the	DET
ajst-21812	24	12	steady	steady	ADJ
ajst-21812	24	13	-	-	PUNCT
ajst-21812	24	14	state	state	NOUN
ajst-21812	24	15	forced	force	VERB
ajst-21812	24	16	vibration	vibration	NOUN
ajst-21812	24	17	of	of	ADP
ajst-21812	24	18	timoshenko	timoshenko	ADJ
ajst-21812	24	19	beams	beam	NOUN
ajst-21812	24	20	with	with	ADP
ajst-21812	24	21	multiple	multiple	ADJ
ajst-21812	24	22	cracks	crack	NOUN
ajst-21812	24	23	,	,	PUNCT
ajst-21812	24	24	verifying	verify	VERB
ajst-21812	24	25	that	that	SCONJ
ajst-21812	24	26	the	the	DET
ajst-21812	24	27	influence	influence	NOUN
ajst-21812	24	28	of	of	ADP
ajst-21812	24	29	shear	shear	ADJ
ajst-21812	24	30	deformation	deformation	NOUN
ajst-21812	24	31	and	and	CCONJ
ajst-21812	24	32	rotational	rotational	ADJ
ajst-21812	24	33	inertia	inertia	NOUN
ajst-21812	24	34	on	on	ADP
ajst-21812	24	35	beams	beam	NOUN
ajst-21812	24	36	with	with	ADP
ajst-21812	24	37	a	a	DET
ajst-21812	24	38	certain	certain	ADJ
ajst-21812	24	39	thickness	thickness	NOUN
ajst-21812	24	40	under	under	ADP
ajst-21812	24	41	forced	force	VERB
ajst-21812	24	42	vibration	vibration	NOUN
ajst-21812	24	43	can	can	AUX
ajst-21812	24	44	not	not	PART
ajst-21812	24	45	be	be	AUX
ajst-21812	24	46	ignored	ignore	VERB
ajst-21812	24	47	.	.	PUNCT
ajst-21812	25	1	loya	loya	PROPN
ajst-21812	25	2	ja	ja	PROPN
ajst-21812	25	3	et	et	NOUN
ajst-21812	25	4	al.[7	al.[7	PROPN
ajst-21812	25	5	]	]	PUNCT
ajst-21812	25	6	and	and	CCONJ
ajst-21812	25	7	chen	chen	PROPN
ajst-21812	25	8	et	et	PROPN
ajst-21812	25	9	al.[8	al.[8	PROPN
ajst-21812	25	10	]	]	PUNCT
ajst-21812	25	11	established	establish	VERB
ajst-21812	25	12	crack	crack	NOUN
ajst-21812	25	13	beam	beam	NOUN
ajst-21812	25	14	models	model	NOUN
ajst-21812	25	15	based	base	VERB
ajst-21812	25	16	on	on	ADP
ajst-21812	25	17	winkler	winkler	PROPN
ajst-21812	25	18	foundation	foundation	PROPN
ajst-21812	25	19	,	,	PUNCT
ajst-21812	25	20	deriving	derive	VERB
ajst-21812	25	21	the	the	DET
ajst-21812	25	22	differential	differential	ADJ
ajst-21812	25	23	equations	equation	NOUN
ajst-21812	25	24	for	for	ADP
ajst-21812	25	25	free	free	ADJ
ajst-21812	25	26	and	and	CCONJ
ajst-21812	25	27	forced	force	VERB
ajst-21812	25	28	vibration	vibration	NOUN
ajst-21812	25	29	of	of	ADP
ajst-21812	25	30	beams	beam	NOUN
ajst-21812	25	31	with	with	ADP
ajst-21812	25	32	multiple	multiple	ADJ
ajst-21812	25	33	cracks	crack	NOUN
ajst-21812	25	34	through	through	ADP
ajst-21812	25	35	corresponding	corresponding	ADJ
ajst-21812	25	36	boundary	boundary	ADJ
ajst-21812	25	37	conditions	condition	NOUN
ajst-21812	25	38	and	and	CCONJ
ajst-21812	25	39	compatibility	compatibility	NOUN
ajst-21812	25	40	conditions	condition	NOUN
ajst-21812	25	41	at	at	ADP
ajst-21812	25	42	the	the	DET
ajst-21812	25	43	crack	crack	NOUN
ajst-21812	25	44	sections	section	NOUN
ajst-21812	25	45	.	.	PUNCT
ajst-21812	26	1	they	they	PRON
ajst-21812	26	2	examined	examine	VERB
ajst-21812	26	3	the	the	DET
ajst-21812	26	4	impact	impact	NOUN
ajst-21812	26	5	of	of	ADP
ajst-21812	26	6	different	different	ADJ
ajst-21812	26	7	support	support	NOUN
ajst-21812	26	8	types	type	NOUN
ajst-21812	26	9	,	,	PUNCT
ajst-21812	26	10	support	support	NOUN
ajst-21812	26	11	stiffness	stiffness	NOUN
ajst-21812	26	12	,	,	PUNCT
ajst-21812	26	13	crack	crack	VERB
ajst-21812	26	14	position	position	NOUN
ajst-21812	26	15	,	,	PUNCT
ajst-21812	26	16	and	and	CCONJ
ajst-21812	26	17	crack	crack	VERB
ajst-21812	26	18	depth	depth	NOUN
ajst-21812	26	19	on	on	ADP
ajst-21812	26	20	the	the	DET
ajst-21812	26	21	system	system	NOUN
ajst-21812	26	22	's	's	PART
ajst-21812	26	23	natural	natural	ADJ
ajst-21812	26	24	frequencies	frequency	NOUN
ajst-21812	26	25	.	.	PUNCT
ajst-21812	27	1	all	all	DET
ajst-21812	27	2	the	the	DET
ajst-21812	27	3	above	above	ADJ
ajst-21812	27	4	studies	study	NOUN
ajst-21812	27	5	focus	focus	VERB
ajst-21812	27	6	on	on	ADP
ajst-21812	27	7	the	the	DET
ajst-21812	27	8	dynamic	dynamic	ADJ
ajst-21812	27	9	analysis	analysis	NOUN
ajst-21812	27	10	of	of	ADP
ajst-21812	27	11	beams	beam	NOUN
ajst-21812	27	12	with	with	ADP
ajst-21812	27	13	cracks	crack	NOUN
ajst-21812	27	14	made	make	VERB
ajst-21812	27	15	of	of	ADP
ajst-21812	27	16	homogeneous	homogeneous	ADJ
ajst-21812	27	17	materials	material	NOUN
ajst-21812	27	18	.	.	PUNCT
ajst-21812	28	1	this	this	DET
ajst-21812	28	2	article	article	NOUN
ajst-21812	28	3	will	will	AUX
ajst-21812	28	4	analyze	analyze	VERB
ajst-21812	28	5	the	the	DET
ajst-21812	28	6	free	free	ADJ
ajst-21812	28	7	vibration	vibration	NOUN
ajst-21812	28	8	characteristics	characteristic	NOUN
ajst-21812	28	9	of	of	ADP
ajst-21812	28	10	functionally	functionally	ADV
ajst-21812	28	11	graded	grade	VERB
ajst-21812	28	12	materials	material	NOUN
ajst-21812	28	13	with	with	ADP
ajst-21812	28	14	cracks	crack	NOUN
ajst-21812	28	15	.	.	PUNCT
ajst-21812	29	1	2	2	X
ajst-21812	29	2	.	.	NOUN
ajst-21812	29	3	material	material	NOUN
ajst-21812	29	4	properties	property	NOUN
ajst-21812	29	5	of	of	ADP
ajst-21812	29	6	functionally	functionally	ADV
ajst-21812	29	7	graded	grade	VERB
ajst-21812	29	8	beans	bean	NOUN
ajst-21812	29	9	and	and	CCONJ
ajst-21812	29	10	eauivalent	eauivalent	ADJ
ajst-21812	29	11	spring	spring	NOUN
ajst-21812	29	12	models	model	NOUN
ajst-21812	29	13	this	this	DET
ajst-21812	29	14	functionally	functionally	ADV
ajst-21812	29	15	graded	grade	VERB
ajst-21812	29	16	material	material	NOUN
ajst-21812	29	17	is	be	AUX
ajst-21812	29	18	composed	compose	VERB
ajst-21812	29	19	of	of	ADP
ajst-21812	29	20	two	two	NUM
ajst-21812	29	21	266	266	NUM
ajst-21812	29	22	different	different	ADJ
ajst-21812	29	23	constituent	constituent	NOUN
ajst-21812	29	24	materials	material	NOUN
ajst-21812	29	25	,	,	PUNCT
ajst-21812	29	26	with	with	ADP
ajst-21812	29	27	the	the	DET
ajst-21812	29	28	young	young	PROPN
ajst-21812	29	29	's	's	PART
ajst-21812	29	30	modulus	modulus	ADJ
ajst-21812	29	31	e(z)and	e(z)and	NOUN
ajst-21812	29	32	ρ(z)density	ρ(z)density	NOUN
ajst-21812	29	33	varying	vary	VERB
ajst-21812	29	34	exponentially	exponentially	ADV
ajst-21812	29	35	in	in	ADP
ajst-21812	29	36	the	the	DET
ajst-21812	29	37	thickness	thickness	NOUN
ajst-21812	29	38	direction	direction	NOUN
ajst-21812	29	39	(	(	PUNCT
ajst-21812	29	40	z	z	NOUN
ajst-21812	29	41	-	-	PUNCT
ajst-21812	29	42	direction	direction	NOUN
ajst-21812	29	43	)	)	PUNCT
ajst-21812	29	44	based	base	VERB
ajst-21812	29	45	on	on	ADP
ajst-21812	29	46	the	the	DET
ajst-21812	29	47	volume	volume	NOUN
ajst-21812	29	48	fraction	fraction	NOUN
ajst-21812	29	49	of	of	ADP
ajst-21812	29	50	each	each	DET
ajst-21812	29	51	material	material	NOUN
ajst-21812	29	52	component	component	NOUN
ajst-21812	29	53	.	.	PUNCT
ajst-21812	30	1	this	this	DET
ajst-21812	30	2	gradient	gradient	ADJ
ajst-21812	30	3	variation	variation	NOUN
ajst-21812	30	4	can	can	AUX
ajst-21812	30	5	be	be	AUX
ajst-21812	30	6	expressed	express	VERB
ajst-21812	30	7	specifically	specifically	ADV
ajst-21812	30	8	as	as	ADP
ajst-21812	30	9	:	:	PUNCT
ajst-21812	30	10	0	0	NUM
ajst-21812	30	11	0	0	NUM
ajst-21812	30	12	(	(	PUNCT
ajst-21812	30	13	)	)	PUNCT
ajst-21812	30	14	,	,	PUNCT
ajst-21812	30	15	(	(	PUNCT
ajst-21812	30	16	)	)	PUNCT
ajst-21812	30	17	z	z	NOUN
ajst-21812	30	18	ze	ze	NOUN
ajst-21812	30	19	z	z	NOUN
ajst-21812	30	20	e	e	NOUN
ajst-21812	30	21	e	e	PROPN
ajst-21812	30	22	z	z	X
ajst-21812	30	23	e	e	ADP
ajst-21812	30	24			NOUN
ajst-21812	30	25			NOUN
ajst-21812	30	26			NUM
ajst-21812	30	27	(	(	PUNCT
ajst-21812	30	28	1	1	NUM
ajst-21812	30	29	)	)	PUNCT
ajst-21812	30	30	in	in	ADP
ajst-21812	30	31	the	the	DET
ajst-21812	30	32	equation	equation	NOUN
ajst-21812	30	33	,	,	PUNCT
ajst-21812	30	34	e0	e0	PROPN
ajst-21812	30	35	and	and	CCONJ
ajst-21812	30	36	ρ0	ρ0	PROPN
ajst-21812	30	37	represent	represent	VERB
ajst-21812	30	38	the	the	DET
ajst-21812	30	39	young	young	ADJ
ajst-21812	30	40	's	's	PART
ajst-21812	30	41	modulus	modulus	NOUN
ajst-21812	30	42	and	and	CCONJ
ajst-21812	30	43	density	density	NOUN
ajst-21812	30	44	at	at	ADP
ajst-21812	30	45	the	the	DET
ajst-21812	30	46	mid	mid	NOUN
ajst-21812	30	47	-	-	NOUN
ajst-21812	30	48	plane	plane	NOUN
ajst-21812	30	49	(	(	PUNCT
ajst-21812	30	50	z=0	z=0	PROPN
ajst-21812	30	51	)	)	PUNCT
ajst-21812	30	52	of	of	ADP
ajst-21812	30	53	the	the	DET
ajst-21812	30	54	functionally	functionally	ADV
ajst-21812	30	55	graded	grade	VERB
ajst-21812	30	56	beam	beam	NOUN
ajst-21812	30	57	,	,	PUNCT
ajst-21812	30	58	while	while	SCONJ
ajst-21812	30	59	e1	e1	NOUN
ajst-21812	30	60	and	and	CCONJ
ajst-21812	30	61	e2	e2	PROPN
ajst-21812	30	62	correspond	correspond	PROPN
ajst-21812	30	63	to	to	ADP
ajst-21812	30	64	the	the	DET
ajst-21812	30	65	young	young	ADJ
ajst-21812	30	66	's	's	PART
ajst-21812	30	67	modulus	modulus	NOUN
ajst-21812	30	68	of	of	ADP
ajst-21812	30	69	the	the	DET
ajst-21812	30	70	upper	upper	ADJ
ajst-21812	30	71	and	and	CCONJ
ajst-21812	30	72	lower	low	ADJ
ajst-21812	30	73	materials	material	NOUN
ajst-21812	30	74	,	,	PUNCT
ajst-21812	30	75	respectively	respectively	ADV
ajst-21812	30	76	.	.	PUNCT
ajst-21812	31	1	similarly	similarly	ADV
ajst-21812	31	2	,	,	PUNCT
ajst-21812	31	3	ρ1	ρ1	NOUN
ajst-21812	31	4	and	and	CCONJ
ajst-21812	31	5	ρ2	ρ2	NOUN
ajst-21812	31	6	correspond	correspond	NOUN
ajst-21812	31	7	to	to	ADP
ajst-21812	31	8	the	the	DET
ajst-21812	31	9	density	density	NOUN
ajst-21812	31	10	of	of	ADP
ajst-21812	31	11	the	the	DET
ajst-21812	31	12	upper	upper	ADJ
ajst-21812	31	13	and	and	CCONJ
ajst-21812	31	14	lower	low	ADJ
ajst-21812	31	15	materials	material	NOUN
ajst-21812	31	16	.	.	PUNCT
ajst-21812	32	1	the	the	DET
ajst-21812	32	2	constant	constant	ADJ
ajst-21812	32	3	denotes	denote	NOUN
ajst-21812	32	4	the	the	DET
ajst-21812	32	5	gradient	gradient	ADJ
ajst-21812	32	6	change	change	NOUN
ajst-21812	32	7	of	of	ADP
ajst-21812	32	8	material	material	NOUN
ajst-21812	32	9	properties	property	NOUN
ajst-21812	32	10	along	along	ADP
ajst-21812	32	11	the	the	DET
ajst-21812	32	12	thickness	thickness	NOUN
ajst-21812	32	13	direction	direction	NOUN
ajst-21812	32	14	,	,	PUNCT
ajst-21812	32	15	and	and	CCONJ
ajst-21812	32	16	the	the	DET
ajst-21812	32	17	beam	beam	NOUN
ajst-21812	32	18	is	be	AUX
ajst-21812	32	19	assumed	assume	VERB
ajst-21812	32	20	to	to	PART
ajst-21812	32	21	be	be	AUX
ajst-21812	32	22	isotropic	isotropic	ADJ
ajst-21812	32	23	and	and	CCONJ
ajst-21812	32	24	homogeneous	homogeneous	ADJ
ajst-21812	32	25	.	.	PUNCT
ajst-21812	33	1	since	since	SCONJ
ajst-21812	33	2	the	the	DET
ajst-21812	33	3	poisson	poisson	NOUN
ajst-21812	33	4	's	's	PART
ajst-21812	33	5	ratio	ratio	NOUN
ajst-21812	33	6	𝜈	𝜈	PROPN
ajst-21812	33	7	has	have	VERB
ajst-21812	33	8	a	a	DET
ajst-21812	33	9	minimal	minimal	ADJ
ajst-21812	33	10	effect	effect	NOUN
ajst-21812	33	11	on	on	ADP
ajst-21812	33	12	the	the	DET
ajst-21812	33	13	stress	stress	NOUN
ajst-21812	33	14	intensity	intensity	NOUN
ajst-21812	33	15	factor	factor	NOUN
ajst-21812	33	16	at	at	ADP
ajst-21812	33	17	the	the	DET
ajst-21812	33	18	crack	crack	NOUN
ajst-21812	33	19	tip	tip	NOUN
ajst-21812	33	20	,	,	PUNCT
ajst-21812	33	21	𝜈	𝜈	PROPN
ajst-21812	33	22	is	be	AUX
ajst-21812	33	23	taken	take	VERB
ajst-21812	33	24	as	as	ADP
ajst-21812	33	25	a	a	DET
ajst-21812	33	26	constant	constant	NOUN
ajst-21812	33	27	.	.	PUNCT
ajst-21812	34	1	the	the	DET
ajst-21812	34	2	cracked	crack	VERB
ajst-21812	34	3	beam	beam	NOUN
ajst-21812	34	4	can	can	AUX
ajst-21812	34	5	be	be	AUX
ajst-21812	34	6	divided	divide	VERB
ajst-21812	34	7	into	into	ADP
ajst-21812	34	8	two	two	NUM
ajst-21812	34	9	sub	sub	NOUN
ajst-21812	34	10	-	-	NOUN
ajst-21812	34	11	beams	beam	NOUN
ajst-21812	34	12	at	at	ADP
ajst-21812	34	13	the	the	DET
ajst-21812	34	14	crack	crack	NOUN
ajst-21812	34	15	location	location	NOUN
ajst-21812	34	16	,	,	PUNCT
ajst-21812	34	17	with	with	ADP
ajst-21812	34	18	the	the	DET
ajst-21812	34	19	two	two	NUM
ajst-21812	34	20	sub	sub	ADJ
ajst-21812	34	21	-	-	ADJ
ajst-21812	34	22	beams	beam	NOUN
ajst-21812	34	23	connected	connect	VERB
ajst-21812	34	24	by	by	ADP
ajst-21812	34	25	a	a	DET
ajst-21812	34	26	zeromass	zeromass	NOUN
ajst-21812	34	27	,	,	PUNCT
ajst-21812	34	28	zero	zero	NUM
ajst-21812	34	29	-	-	PUNCT
ajst-21812	34	30	length	length	NOUN
ajst-21812	34	31	rotational	rotational	ADJ
ajst-21812	34	32	spring	spring	NOUN
ajst-21812	34	33	at	at	ADP
ajst-21812	34	34	the	the	DET
ajst-21812	34	35	crack	crack	NOUN
ajst-21812	34	36	cross	cross	NOUN
ajst-21812	34	37	-	-	NOUN
ajst-21812	34	38	section	section	NOUN
ajst-21812	34	39	.	.	PUNCT
ajst-21812	35	1	therefore	therefore	ADV
ajst-21812	35	2	,	,	PUNCT
ajst-21812	35	3	the	the	DET
ajst-21812	35	4	crack	crack	VERB
ajst-21812	35	5	cross	cross	NOUN
ajst-21812	35	6	-	-	NOUN
ajst-21812	35	7	section	section	NOUN
ajst-21812	35	8	is	be	AUX
ajst-21812	35	9	modeled	model	VERB
ajst-21812	35	10	as	as	ADP
ajst-21812	35	11	a	a	DET
ajst-21812	35	12	zero	zero	NUM
ajst-21812	35	13	-	-	PUNCT
ajst-21812	35	14	mass	mass	NOUN
ajst-21812	35	15	elastic	elastic	ADJ
ajst-21812	35	16	rotational	rotational	ADJ
ajst-21812	35	17	spring	spring	NOUN
ajst-21812	35	18	,	,	PUNCT
ajst-21812	35	19	as	as	SCONJ
ajst-21812	35	20	shown	show	VERB
ajst-21812	35	21	in	in	ADP
ajst-21812	35	22	figure	figure	NOUN
ajst-21812	35	23	1	1	NUM
ajst-21812	35	24	.	.	PUNCT
ajst-21812	36	1	the	the	DET
ajst-21812	36	2	beam	beam	NOUN
ajst-21812	36	3	contains	contain	VERB
ajst-21812	36	4	a	a	DET
ajst-21812	36	5	crack	crack	NOUN
ajst-21812	36	6	of	of	ADP
ajst-21812	36	7	depth	depth	NOUN
ajst-21812	36	8	𝑎	𝑎	PUNCT
ajst-21812	36	9	located	locate	VERB
ajst-21812	36	10	at	at	ADP
ajst-21812	36	11	a	a	DET
ajst-21812	36	12	distance	distance	NOUN
ajst-21812	36	13	𝐿1	𝐿1	NOUN
ajst-21812	36	14	from	from	ADP
ajst-21812	36	15	the	the	DET
ajst-21812	36	16	left	left	ADJ
ajst-21812	36	17	end	end	NOUN
ajst-21812	36	18	,	,	PUNCT
ajst-21812	36	19	with	with	ADP
ajst-21812	36	20	a	a	DET
ajst-21812	36	21	bending	bend	VERB
ajst-21812	36	22	stiffness	stiffness	NOUN
ajst-21812	36	23	of	of	ADP
ajst-21812	36	24	:	:	PUNCT
ajst-21812	36	25	1	1	NUM
ajst-21812	36	26	tk	tk	NOUN
ajst-21812	36	27	g	g	PROPN
ajst-21812	36	28			PROPN
ajst-21812	36	29	(	(	PUNCT
ajst-21812	36	30	2	2	NUM
ajst-21812	36	31	)	)	PUNCT
ajst-21812	36	32	where	where	SCONJ
ajst-21812	36	33	g	g	PROPN
ajst-21812	36	34	represents	represent	VERB
ajst-21812	36	35	the	the	DET
ajst-21812	36	36	local	local	ADJ
ajst-21812	36	37	flexibility	flexibility	NOUN
ajst-21812	36	38	caused	cause	VERB
ajst-21812	36	39	by	by	ADP
ajst-21812	36	40	the	the	DET
ajst-21812	36	41	crack	crack	NOUN
ajst-21812	36	42	.	.	PUNCT
ajst-21812	37	1	figure	figure	NOUN
ajst-21812	37	2	1	1	NUM
ajst-21812	37	3	.	.	PUNCT
ajst-21812	37	4	functional	functional	ADJ
ajst-21812	37	5	graded	grade	VERB
ajst-21812	37	6	beam	beam	NOUN
ajst-21812	37	7	model	model	NOUN
ajst-21812	37	8	with	with	ADP
ajst-21812	37	9	crack	crack	NOUN
ajst-21812	37	10	according	accord	VERB
ajst-21812	37	11	to	to	ADP
ajst-21812	37	12	fracture	fracture	NOUN
ajst-21812	37	13	mechanics	mechanic	NOUN
ajst-21812	37	14	theory	theory	NOUN
ajst-21812	37	15	,	,	PUNCT
ajst-21812	37	16	the	the	DET
ajst-21812	37	17	flexibility	flexibility	NOUN
ajst-21812	37	18	𝐺	𝐺	NOUN
ajst-21812	37	19	caused	cause	VERB
ajst-21812	37	20	by	by	ADP
ajst-21812	37	21	the	the	DET
ajst-21812	37	22	presence	presence	NOUN
ajst-21812	37	23	of	of	ADP
ajst-21812	37	24	a	a	DET
ajst-21812	37	25	crack	crack	NOUN
ajst-21812	37	26	is	be	AUX
ajst-21812	37	27	related	relate	VERB
ajst-21812	37	28	to	to	ADP
ajst-21812	37	29	the	the	DET
ajst-21812	37	30	stress	stress	NOUN
ajst-21812	37	31	intensity	intensity	NOUN
ajst-21812	37	32	factor	factor	NOUN
ajst-21812	37	33	at	at	ADP
ajst-21812	37	34	the	the	DET
ajst-21812	37	35	crack	crack	NOUN
ajst-21812	37	36	tip	tip	NOUN
ajst-21812	37	37	.	.	PUNCT
ajst-21812	38	1	the	the	DET
ajst-21812	38	2	additional	additional	ADJ
ajst-21812	38	3	strain	strain	NOUN
ajst-21812	38	4	energy	energy	NOUN
ajst-21812	38	5	𝑈	𝑈	PROPN
ajst-21812	38	6	caused	cause	VERB
ajst-21812	38	7	by	by	ADP
ajst-21812	38	8	the	the	DET
ajst-21812	38	9	crack	crack	NOUN
ajst-21812	38	10	can	can	AUX
ajst-21812	38	11	be	be	AUX
ajst-21812	38	12	expressed	express	VERB
ajst-21812	38	13	as	as	ADP
ajst-21812	38	14	:	:	PUNCT
ajst-21812	38	15			NOUN
ajst-21812	38	16	2	2	ADJ
ajst-21812	38	17	2	2	NUM
ajst-21812	38	18	1	1	NUM
ajst-21812	38	19	1	1	NUM
ajst-21812	38	20	d	d	NOUN
ajst-21812	38	21	(	(	PUNCT
ajst-21812	38	22	)	)	PUNCT
ajst-21812	38	23	a	a	DET
ajst-21812	38	24	u	u	NOUN
ajst-21812	38	25	k	k	PROPN
ajst-21812	38	26	a	a	X
ajst-21812	38	27	e	e	X
ajst-21812	38	28	a	a	DET
ajst-21812	38	29			ADJ
ajst-21812	38	30			NOUN
ajst-21812	38	31			PUNCT
ajst-21812	38	32	(	(	PUNCT
ajst-21812	38	33	3	3	X
ajst-21812	38	34	)	)	PUNCT
ajst-21812	38	35	where	where	SCONJ
ajst-21812	38	36	𝐴	𝐴	PROPN
ajst-21812	38	37	is	be	AUX
ajst-21812	38	38	the	the	DET
ajst-21812	38	39	cross	cross	ADJ
ajst-21812	38	40	-	-	ADJ
ajst-21812	38	41	sectional	sectional	ADJ
ajst-21812	38	42	area	area	NOUN
ajst-21812	38	43	,	,	PUNCT
ajst-21812	38	44	𝐾𝐼	𝐾𝐼	PROPN
ajst-21812	38	45	represents	represent	VERB
ajst-21812	38	46	the	the	DET
ajst-21812	38	47	stress	stress	NOUN
ajst-21812	38	48	intensity	intensity	NOUN
ajst-21812	38	49	factor	factor	NOUN
ajst-21812	38	50	(	(	PUNCT
ajst-21812	38	51	sif	sif	PROPN
ajst-21812	38	52	)	)	PUNCT
ajst-21812	38	53	at	at	ADP
ajst-21812	38	54	the	the	DET
ajst-21812	38	55	crack	crack	NOUN
ajst-21812	38	56	tip	tip	NOUN
ajst-21812	38	57	under	under	ADP
ajst-21812	38	58	bending	bend	VERB
ajst-21812	38	59	load	load	NOUN
ajst-21812	38	60	in	in	ADP
ajst-21812	38	61	a	a	DET
ajst-21812	38	62	mode	mode	NOUN
ajst-21812	38	63	i	i	PRON
ajst-21812	38	64	crack	crack	VERB
ajst-21812	38	65	state	state	NOUN
ajst-21812	38	66	,	,	PUNCT
ajst-21812	38	67	and	and	CCONJ
ajst-21812	38	68	𝑀	𝑀	PROPN
ajst-21812	38	69	is	be	AUX
ajst-21812	38	70	the	the	DET
ajst-21812	38	71	bending	bend	VERB
ajst-21812	38	72	moment	moment	NOUN
ajst-21812	38	73	at	at	ADP
ajst-21812	38	74	the	the	DET
ajst-21812	38	75	crack	crack	NOUN
ajst-21812	38	76	cross	cross	NOUN
ajst-21812	38	77	-	-	NOUN
ajst-21812	38	78	section	section	NOUN
ajst-21812	38	79	.	.	PUNCT
ajst-21812	39	1	the	the	DET
ajst-21812	39	2	local	local	ADJ
ajst-21812	39	3	flexibility	flexibility	NOUN
ajst-21812	39	4	𝐺	𝐺	PROPN
ajst-21812	39	5	at	at	ADP
ajst-21812	39	6	the	the	DET
ajst-21812	39	7	material	material	NOUN
ajst-21812	39	8	’s	’s	PART
ajst-21812	39	9	crack	crack	VERB
ajst-21812	39	10	cross	cross	NOUN
ajst-21812	39	11	-	-	NOUN
ajst-21812	39	12	section	section	NOUN
ajst-21812	39	13	can	can	AUX
ajst-21812	39	14	be	be	AUX
ajst-21812	39	15	expressed	express	VERB
ajst-21812	39	16	as	as	ADP
ajst-21812	39	17	:	:	SYM
ajst-21812	39	18	2	2	NUM
ajst-21812	39	19	2	2	NUM
ajst-21812	39	20	u	u	NOUN
ajst-21812	39	21	g	g	PROPN
ajst-21812	39	22	m	m	PROPN
ajst-21812	39	23			ADJ
ajst-21812	39	24			PROPN
ajst-21812	39	25			ADJ
ajst-21812	39	26	(	(	PUNCT
ajst-21812	39	27	4	4	NUM
ajst-21812	39	28	)	)	PUNCT
ajst-21812	39	29	for	for	ADP
ajst-21812	39	30	a	a	DET
ajst-21812	39	31	functionally	functionally	ADV
ajst-21812	39	32	graded	grade	VERB
ajst-21812	39	33	beam	beam	NOUN
ajst-21812	39	34	system	system	NOUN
ajst-21812	39	35	with	with	ADP
ajst-21812	39	36	a	a	DET
ajst-21812	39	37	mode	mode	NOUN
ajst-21812	39	38	i	i	PRON
ajst-21812	39	39	crack	crack	VERB
ajst-21812	39	40	,	,	PUNCT
ajst-21812	39	41	the	the	DET
ajst-21812	39	42	magnitude	magnitude	NOUN
ajst-21812	39	43	of	of	ADP
ajst-21812	39	44	the	the	DET
ajst-21812	39	45	stress	stress	NOUN
ajst-21812	39	46	intensity	intensity	NOUN
ajst-21812	39	47	factor	factor	NOUN
ajst-21812	39	48	is	be	AUX
ajst-21812	39	49	obtained	obtain	VERB
ajst-21812	39	50	from	from	ADP
ajst-21812	39	51	the	the	DET
ajst-21812	39	52	data	datum	NOUN
ajst-21812	39	53	provided	provide	VERB
ajst-21812	39	54	by	by	ADP
ajst-21812	39	55	erdogan	erdogan	ADJ
ajst-21812	39	56	and	and	CCONJ
ajst-21812	39	57	wu[9	wu[9	NOUN
ajst-21812	39	58	]	]	PUNCT
ajst-21812	39	59	using	use	VERB
ajst-21812	39	60	lagrange	lagrange	NOUN
ajst-21812	39	61	interpolation	interpolation	NOUN
ajst-21812	39	62	techniques	technique	NOUN
ajst-21812	39	63	.	.	PUNCT
ajst-21812	40	1	1	1	NUM
ajst-21812	40	2	2	2	NUM
ajst-21812	40	3	6	6	NUM
ajst-21812	40	4	(	(	PUNCT
ajst-21812	40	5	)	)	PUNCT
ajst-21812	40	6	,	,	PUNCT
ajst-21812	40	7	(	(	PUNCT
ajst-21812	40	8	0.7	0.7	NUM
ajst-21812	40	9	)	)	PUNCT
ajst-21812	40	10	m	m	VERB
ajst-21812	40	11	h	h	NOUN
ajst-21812	41	1	a	a	PRON
ajst-21812	41	2	k	k	X
ajst-21812	41	3	f	f	X
ajst-21812	41	4	hh	hh	PROPN
ajst-21812	42	1			PROPN
ajst-21812	42	2			PROPN
ajst-21812	43	1			PROPN
ajst-21812	43	2			PROPN
ajst-21812	43	3			PROPN
ajst-21812	44	1			NUM
ajst-21812	44	2			NOUN
ajst-21812	44	3	(	(	PUNCT
ajst-21812	44	4	5	5	NUM
ajst-21812	44	5	)	)	PUNCT
ajst-21812	44	6	3	3	NUM
ajst-21812	44	7	.	.	PUNCT
ajst-21812	45	1	the	the	DET
ajst-21812	45	2	equations	equation	NOUN
ajst-21812	45	3	of	of	ADP
ajst-21812	45	4	motion	motion	NOUN
ajst-21812	45	5	for	for	ADP
ajst-21812	45	6	functionally	functionally	ADV
ajst-21812	45	7	graded	grade	VERB
ajst-21812	45	8	beams	beam	NOUN
ajst-21812	45	9	with	with	ADP
ajst-21812	45	10	crack	crack	NOUN
ajst-21812	45	11	according	accord	VERB
ajst-21812	45	12	to	to	ADP
ajst-21812	45	13	timoshenko	timoshenko	NOUN
ajst-21812	45	14	theory	theory	NOUN
ajst-21812	45	15	,	,	PUNCT
ajst-21812	45	16	the	the	DET
ajst-21812	45	17	displacements	displacement	NOUN
ajst-21812	45	18	along	along	ADP
ajst-21812	45	19	the	the	DET
ajst-21812	45	20	x	x	NOUN
ajst-21812	45	21	-	-	NOUN
ajst-21812	45	22	axis	axis	ADJ
ajst-21812	45	23	and	and	CCONJ
ajst-21812	45	24	z	z	NOUN
ajst-21812	45	25	-	-	PUNCT
ajst-21812	45	26	axis	axis	NOUN
ajst-21812	45	27	at	at	ADP
ajst-21812	45	28	any	any	DET
ajst-21812	45	29	point	point	NOUN
ajst-21812	45	30	in	in	ADP
ajst-21812	45	31	a	a	DET
ajst-21812	45	32	functionally	functionally	ADV
ajst-21812	45	33	graded	grade	VERB
ajst-21812	45	34	beam	beam	NOUN
ajst-21812	45	35	with	with	ADP
ajst-21812	45	36	cracks	crack	NOUN
ajst-21812	45	37	can	can	AUX
ajst-21812	45	38	be	be	AUX
ajst-21812	45	39	expressed	express	VERB
ajst-21812	45	40	:	:	PUNCT
ajst-21812	45	41	(	(	PUNCT
ajst-21812	45	42	,	,	PUNCT
ajst-21812	45	43	,	,	PUNCT
ajst-21812	45	44	)	)	PUNCT
ajst-21812	45	45	(	(	PUNCT
ajst-21812	45	46	,	,	PUNCT
ajst-21812	45	47	)	)	PUNCT
ajst-21812	45	48	(	(	PUNCT
ajst-21812	45	49	,	,	PUNCT
ajst-21812	45	50	)	)	PUNCT
ajst-21812	45	51	(	(	PUNCT
ajst-21812	45	52	,	,	PUNCT
ajst-21812	45	53	,	,	PUNCT
ajst-21812	45	54	)	)	PUNCT
ajst-21812	45	55	(	(	PUNCT
ajst-21812	45	56	,	,	PUNCT
ajst-21812	45	57	)	)	PUNCT
ajst-21812	45	58	u	u	NOUN
ajst-21812	45	59	x	x	X
ajst-21812	45	60	z	z	NOUN
ajst-21812	45	61	t	t	X
ajst-21812	45	62	u	u	X
ajst-21812	45	63	x	x	PROPN
ajst-21812	45	64	t	t	PROPN
ajst-21812	45	65	z	z	PROPN
ajst-21812	45	66	x	x	PROPN
ajst-21812	45	67	t	t	PROPN
ajst-21812	45	68	w	w	NOUN
ajst-21812	45	69	x	x	PROPN
ajst-21812	45	70	z	z	PROPN
ajst-21812	45	71	t	t	PROPN
ajst-21812	45	72	w	w	PROPN
ajst-21812	45	73	x	x	PROPN
ajst-21812	45	74	t	t	PROPN
ajst-21812	46	1			PROPN
ajst-21812	47	1			ADV
ajst-21812	48	1			PROPN
ajst-21812	48	2			PROPN
ajst-21812	48	3	(	(	PUNCT
ajst-21812	48	4	6	6	NUM
ajst-21812	48	5	)	)	PUNCT
ajst-21812	48	6	where	where	SCONJ
ajst-21812	48	7	𝑢0	𝑢0	PROPN
ajst-21812	48	8	and	and	CCONJ
ajst-21812	48	9	𝑤0	𝑤0	NOUN
ajst-21812	48	10	are	be	AUX
ajst-21812	48	11	the	the	DET
ajst-21812	48	12	longitudinal	longitudinal	ADJ
ajst-21812	48	13	and	and	CCONJ
ajst-21812	48	14	lateral	lateral	ADJ
ajst-21812	48	15	displacement	displacement	ADJ
ajst-21812	48	16	components	component	NOUN
ajst-21812	48	17	at	at	ADP
ajst-21812	48	18	the	the	DET
ajst-21812	48	19	mid	mid	NOUN
ajst-21812	48	20	-	-	NOUN
ajst-21812	48	21	plane	plane	NOUN
ajst-21812	48	22	(	(	PUNCT
ajst-21812	48	23	z=0	z=0	PROPN
ajst-21812	48	24	)	)	PUNCT
ajst-21812	48	25	,	,	PUNCT
ajst-21812	48	26	and	and	CCONJ
ajst-21812	48	27	𝜙	𝜙	PRON
ajst-21812	48	28	is	be	AUX
ajst-21812	48	29	the	the	DET
ajst-21812	48	30	rotation	rotation	NOUN
ajst-21812	48	31	angle	angle	NOUN
ajst-21812	48	32	of	of	ADP
ajst-21812	48	33	the	the	DET
ajst-21812	48	34	beam	beam	NOUN
ajst-21812	48	35	cross	cross	NOUN
ajst-21812	48	36	-	-	NOUN
ajst-21812	48	37	section	section	NOUN
ajst-21812	48	38	,	,	PUNCT
ajst-21812	48	39	with	with	ADP
ajst-21812	48	40	𝑡	𝑡	PRON
ajst-21812	48	41	representing	represent	VERB
ajst-21812	48	42	time	time	NOUN
ajst-21812	48	43	.	.	PUNCT
ajst-21812	49	1	according	accord	VERB
ajst-21812	49	2	to	to	ADP
ajst-21812	49	3	von	von	PROPN
ajst-21812	49	4	kármán	kármán	PROPN
ajst-21812	49	5	’s	’s	PART
ajst-21812	49	6	nonlinear	nonlinear	ADJ
ajst-21812	49	7	strain	strain	NOUN
ajst-21812	49	8	-	-	PUNCT
ajst-21812	49	9	displacement	displacement	NOUN
ajst-21812	49	10	relationship	relationship	NOUN
ajst-21812	49	11	,	,	PUNCT
ajst-21812	49	12	the	the	DET
ajst-21812	49	13	normal	normal	ADJ
ajst-21812	49	14	strain	strain	NOUN
ajst-21812	49	15	and	and	CCONJ
ajst-21812	49	16	shear	shear	NOUN
ajst-21812	49	17	strain	strain	NOUN
ajst-21812	49	18	can	can	AUX
ajst-21812	49	19	be	be	AUX
ajst-21812	49	20	derived	derive	VERB
ajst-21812	49	21	as	as	SCONJ
ajst-21812	49	22	follows	follow	VERB
ajst-21812	49	23	:	:	PUNCT
ajst-21812	49	24	2	2	NUM
ajst-21812	49	25	1	1	NUM
ajst-21812	49	26	,	,	PUNCT
ajst-21812	49	27	2x	2x	NUM
ajst-21812	49	28	xz	xz	PROPN
ajst-21812	49	29	u	u	PROPN
ajst-21812	49	30	w	w	PROPN
ajst-21812	49	31	w	w	PROPN
ajst-21812	49	32	z	z	PROPN
ajst-21812	49	33	x	x	SYM
ajst-21812	49	34	x	x	PUNCT
ajst-21812	49	35	x	x	SYM
ajst-21812	49	36	x	x	X
ajst-21812	49	37			NOUN
ajst-21812	49	38			PUNCT
ajst-21812	49	39			NOUN
ajst-21812	49	40			PROPN
ajst-21812	49	41			PROPN
ajst-21812	49	42			PROPN
ajst-21812	49	43			PROPN
ajst-21812	49	44			PROPN
ajst-21812	49	45			PROPN
ajst-21812	49	46			ADJ
ajst-21812	49	47			PROPN
ajst-21812	49	48			PROPN
ajst-21812	49	49			PROPN
ajst-21812	49	50			PROPN
ajst-21812	49	51			ADJ
ajst-21812	49	52			NOUN
ajst-21812	49	53	(	(	PUNCT
ajst-21812	49	54	7	7	NUM
ajst-21812	49	55	)	)	PUNCT
ajst-21812	49	56	according	accord	VERB
ajst-21812	49	57	to	to	ADP
ajst-21812	49	58	the	the	DET
ajst-21812	49	59	linear	linear	ADJ
ajst-21812	49	60	elastic	elastic	ADJ
ajst-21812	49	61	constitutive	constitutive	ADJ
ajst-21812	49	62	relations	relation	NOUN
ajst-21812	49	63	,	,	PUNCT
ajst-21812	49	64	the	the	DET
ajst-21812	49	65	normal	normal	ADJ
ajst-21812	49	66	stress	stress	NOUN
ajst-21812	49	67	𝜎	𝜎	NOUN
ajst-21812	49	68	and	and	CCONJ
ajst-21812	49	69	shear	shear	ADJ
ajst-21812	49	70	stress	stress	NOUN
ajst-21812	49	71	𝜏	𝜏	NOUN
ajst-21812	49	72	can	can	AUX
ajst-21812	49	73	be	be	AUX
ajst-21812	49	74	expressed	express	VERB
ajst-21812	49	75	as	as	ADP
ajst-21812	49	76	:	:	PUNCT
ajst-21812	49	77	2	2	NUM
ajst-21812	49	78	11	11	NUM
ajst-21812	49	79	55	55	NUM
ajst-21812	49	80	1	1	NUM
ajst-21812	49	81	(	(	PUNCT
ajst-21812	49	82	)	)	PUNCT
ajst-21812	49	83	,	,	PUNCT
ajst-21812	49	84	2	2	NUM
ajst-21812	49	85	(	(	PUNCT
ajst-21812	49	86	)	)	PUNCT
ajst-21812	50	1	xx	xx	NUM
ajst-21812	51	1	xz	xz	PROPN
ajst-21812	51	2	u	u	PROPN
ajst-21812	51	3	w	w	PROPN
ajst-21812	51	4	q	q	PROPN
ajst-21812	51	5	z	z	NOUN
ajst-21812	51	6	z	z	NOUN
ajst-21812	51	7	x	x	SYM
ajst-21812	51	8	x	x	PUNCT
ajst-21812	51	9	x	x	PUNCT
ajst-21812	51	10	w	w	NOUN
ajst-21812	51	11	q	q	X
ajst-21812	51	12	z	z	PROPN
ajst-21812	51	13	x	x	X
ajst-21812	51	14			PROPN
ajst-21812	51	15			NOUN
ajst-21812	51	16			NOUN
ajst-21812	51	17			VERB
ajst-21812	51	18			PROPN
ajst-21812	51	19			NUM
ajst-21812	51	20			PROPN
ajst-21812	51	21			PROPN
ajst-21812	51	22			PROPN
ajst-21812	51	23			NOUN
ajst-21812	51	24			X
ajst-21812	52	1			X
ajst-21812	52	2			ADV
ajst-21812	52	3			VERB
ajst-21812	52	4			NOUN
ajst-21812	52	5			NOUN
ajst-21812	52	6			NUM
ajst-21812	52	7			NOUN
ajst-21812	52	8			PROPN
ajst-21812	52	9			NOUN
ajst-21812	52	10			NOUN
ajst-21812	52	11	(	(	PUNCT
ajst-21812	52	12	8)	8)	NUM
ajst-21812	52	13	where	where	SCONJ
ajst-21812	52	14	:	:	PUNCT
ajst-21812	52	15	11	11	NUM
ajst-21812	52	16	552	552	NUM
ajst-21812	52	17	(	(	PUNCT
ajst-21812	52	18	)	)	PUNCT
ajst-21812	52	19	(	(	PUNCT
ajst-21812	52	20	)	)	PUNCT
ajst-21812	52	21	(	(	PUNCT
ajst-21812	52	22	)	)	PUNCT
ajst-21812	52	23	,	,	PUNCT
ajst-21812	52	24	(	(	PUNCT
ajst-21812	52	25	)	)	PUNCT
ajst-21812	52	26	2(1	2(1	NUM
ajst-21812	52	27	)	)	PUNCT
ajst-21812	52	28	1	1	NUM
ajst-21812	53	1	e	e	NOUN
ajst-21812	53	2	z	z	NOUN
ajst-21812	53	3	e	e	NOUN
ajst-21812	53	4	z	z	NOUN
ajst-21812	53	5	q	q	PROPN
ajst-21812	53	6	z	z	X
ajst-21812	53	7	q	q	NOUN
ajst-21812	53	8	z	z	NOUN
ajst-21812	53	9	vv	vv	ADP
ajst-21812	53	10			NOUN
ajst-21812	53	11			PROPN
ajst-21812	53	12			NOUN
ajst-21812	53	13	(	(	PUNCT
ajst-21812	53	14	9	9	NUM
ajst-21812	53	15	)	)	PUNCT
ajst-21812	53	16	the	the	DET
ajst-21812	53	17	axial	axial	ADJ
ajst-21812	53	18	force	force	NOUN
ajst-21812	53	19	𝑁	𝑁	PROPN
ajst-21812	53	20	,	,	PUNCT
ajst-21812	53	21	bending	bend	VERB
ajst-21812	53	22	moment	moment	NOUN
ajst-21812	53	23	𝑀	𝑀	PROPN
ajst-21812	53	24	,	,	PUNCT
ajst-21812	53	25	and	and	CCONJ
ajst-21812	53	26	transverse	transverse	ADJ
ajst-21812	53	27	shear	shear	NOUN
ajst-21812	53	28	force	force	NOUN
ajst-21812	53	29	𝑉	𝑉	PROPN
ajst-21812	53	30	acting	act	VERB
ajst-21812	53	31	on	on	ADP
ajst-21812	53	32	the	the	DET
ajst-21812	53	33	functionally	functionally	ADV
ajst-21812	53	34	graded	grade	VERB
ajst-21812	53	35	material	material	NOUN
ajst-21812	53	36	beam	beam	NOUN
ajst-21812	53	37	with	with	ADP
ajst-21812	53	38	cracks	crack	NOUN
ajst-21812	53	39	can	can	AUX
ajst-21812	53	40	be	be	AUX
ajst-21812	53	41	expressed	express	VERB
ajst-21812	53	42	in	in	ADP
ajst-21812	53	43	the	the	DET
ajst-21812	53	44	following	follow	VERB
ajst-21812	53	45	forms	form	NOUN
ajst-21812	53	46	:	:	PUNCT
ajst-21812	53	47	/2	/2	PROPN
ajst-21812	53	48	/	/	SYM
ajst-21812	53	49	2	2	NUM
ajst-21812	53	50	/2	/2	NUM
ajst-21812	53	51	/	/	SYM
ajst-21812	53	52	2	2	NUM
ajst-21812	53	53	/	/	SYM
ajst-21812	53	54	2	2	NUM
ajst-21812	53	55	/2	/2	NOUN
ajst-21812	54	1	d	d	X
ajst-21812	54	2	zd	zd	PROPN
ajst-21812	54	3	d	d	PROPN
ajst-21812	54	4	h	h	PROPN
ajst-21812	54	5	xxh	xxh	PROPN
ajst-21812	55	1	h	h	PROPN
ajst-21812	55	2	xxx	xxx	NOUN
ajst-21812	56	1	h	h	PROPN
ajst-21812	56	2	h	h	NOUN
ajst-21812	57	1	xz	xz	PROPN
ajst-21812	57	2	x	x	PUNCT
ajst-21812	58	1	x	x	SYM
ajst-21812	58	2	h	h	NOUN
ajst-21812	58	3	n	n	NOUN
ajst-21812	58	4	z	z	NOUN
ajst-21812	58	5	m	m	VERB
ajst-21812	58	6	z	z	NOUN
ajst-21812	58	7	q	q	PROPN
ajst-21812	58	8	z	z	PROPN
ajst-21812	58	9			X
ajst-21812	58	10			X
ajst-21812	58	11			X
ajst-21812	58	12			PROPN
ajst-21812	58	13			PROPN
ajst-21812	58	14			PROPN
ajst-21812	58	15			VERB
ajst-21812	58	16			PROPN
ajst-21812	59	1			PRON
ajst-21812	59	2			NOUN
ajst-21812	60	1			NOUN
ajst-21812	60	2			X
ajst-21812	60	3			X
ajst-21812	60	4	(	(	PUNCT
ajst-21812	60	5	10	10	NUM
ajst-21812	60	6	)	)	PUNCT
ajst-21812	60	7	267	267	NUM
ajst-21812	60	8	by	by	ADP
ajst-21812	60	9	substituting	substitute	VERB
ajst-21812	60	10	equation	equation	NOUN
ajst-21812	60	11	6	6	NUM
ajst-21812	60	12	into	into	ADP
ajst-21812	60	13	equation	equation	NOUN
ajst-21812	60	14	11	11	NUM
ajst-21812	60	15	,	,	PUNCT
ajst-21812	60	16	we	we	PRON
ajst-21812	60	17	obtain	obtain	VERB
ajst-21812	60	18	:	:	PUNCT
ajst-21812	60	19	2	2	NUM
ajst-21812	60	20	11	11	NUM
ajst-21812	60	21	11	11	NUM
ajst-21812	60	22	11	11	NUM
ajst-21812	60	23	2	2	NUM
ajst-21812	60	24	11	11	NUM
ajst-21812	60	25	11	11	NUM
ajst-21812	60	26	11	11	NUM
ajst-21812	60	27	55	55	NUM
ajst-21812	60	28	1	1	NUM
ajst-21812	60	29	2	2	NUM
ajst-21812	60	30	1	1	NUM
ajst-21812	60	31	2	2	NUM
ajst-21812	61	1	i	i	PRON
ajst-21812	61	2	i	i	PRON
ajst-21812	62	1	i	i	PRON
ajst-21812	62	2	i	i	PRON
ajst-21812	63	1	i	i	PRON
ajst-21812	63	2	i	i	PRON
ajst-21812	64	1	i	i	PRON
ajst-21812	64	2	i	i	PRON
ajst-21812	64	3	ix	ix	INTJ
ajst-21812	65	1	i	i	INTJ
ajst-21812	65	2	x	x	NOUN
ajst-21812	66	1	x	x	VERB
ajst-21812	66	2	i	i	PRON
ajst-21812	66	3	u	u	VERB
ajst-21812	66	4	w	w	VERB
ajst-21812	66	5	n	n	DET
ajst-21812	66	6	a	a	DET
ajst-21812	66	7	a	a	DET
ajst-21812	66	8	b	b	NOUN
ajst-21812	66	9	x	x	SYM
ajst-21812	66	10	x	x	SYM
ajst-21812	66	11	x	x	PUNCT
ajst-21812	66	12	u	u	NOUN
ajst-21812	66	13	w	w	PROPN
ajst-21812	66	14	m	m	PROPN
ajst-21812	66	15	b	b	PROPN
ajst-21812	66	16	b	b	PROPN
ajst-21812	66	17	d	d	NOUN
ajst-21812	66	18	x	x	SYM
ajst-21812	66	19	x	x	X
ajst-21812	66	20	x	x	X
ajst-21812	66	21	w	w	ADP
ajst-21812	66	22	q	q	NOUN
ajst-21812	66	23	a	a	PRON
ajst-21812	66	24	x	x	X
ajst-21812	66	25			VERB
ajst-21812	66	26			PROPN
ajst-21812	66	27			PROPN
ajst-21812	66	28			PROPN
ajst-21812	66	29			PROPN
ajst-21812	66	30			PROPN
ajst-21812	66	31			PROPN
ajst-21812	66	32			PROPN
ajst-21812	66	33			ADJ
ajst-21812	66	34			ADJ
ajst-21812	66	35			NOUN
ajst-21812	66	36			ADJ
ajst-21812	66	37			PROPN
ajst-21812	66	38			PROPN
ajst-21812	66	39			PROPN
ajst-21812	66	40			PROPN
ajst-21812	66	41			PROPN
ajst-21812	66	42			PROPN
ajst-21812	66	43			ADJ
ajst-21812	66	44			ADJ
ajst-21812	66	45			NOUN
ajst-21812	66	46			NUM
ajst-21812	66	47			NOUN
ajst-21812	66	48			ADV
ajst-21812	66	49			PROPN
ajst-21812	67	1			NUM
ajst-21812	67	2			NOUN
ajst-21812	67	3	(	(	PUNCT
ajst-21812	67	4	11	11	NUM
ajst-21812	67	5	)	)	PUNCT
ajst-21812	67	6	in	in	ADP
ajst-21812	67	7	the	the	DET
ajst-21812	67	8	equation	equation	NOUN
ajst-21812	67	9	,	,	PUNCT
ajst-21812	67	10	𝜅κ	𝜅κ	PRON
ajst-21812	67	11	represents	represent	VERB
ajst-21812	67	12	the	the	DET
ajst-21812	67	13	shear	shear	NOUN
ajst-21812	67	14	correction	correction	NOUN
ajst-21812	67	15	factor	factor	NOUN
ajst-21812	67	16	for	for	ADP
ajst-21812	67	17	the	the	DET
ajst-21812	67	18	timoshenko	timoshenko	ADJ
ajst-21812	67	19	beam	beam	NOUN
ajst-21812	67	20	,	,	PUNCT
ajst-21812	67	21	the	the	DET
ajst-21812	67	22	precise	precise	ADJ
ajst-21812	67	23	value	value	NOUN
ajst-21812	67	24	of	of	ADP
ajst-21812	67	25	which	which	PRON
ajst-21812	67	26	is	be	AUX
ajst-21812	67	27	calculated	calculate	VERB
ajst-21812	67	28	as	as	ADP
ajst-21812	67	29	a	a	DET
ajst-21812	67	30	function	function	NOUN
ajst-21812	67	31	of	of	ADP
ajst-21812	67	32	material	material	NOUN
ajst-21812	67	33	properties	property	NOUN
ajst-21812	67	34	and	and	CCONJ
ajst-21812	67	35	beam	beam	VERB
ajst-21812	67	36	cross	cross	ADJ
ajst-21812	67	37	-	-	ADJ
ajst-21812	67	38	sectional	sectional	ADJ
ajst-21812	67	39	parameters	parameter	NOUN
ajst-21812	67	40	and	and	CCONJ
ajst-21812	67	41	requires	require	VERB
ajst-21812	67	42	complex	complex	ADJ
ajst-21812	67	43	computations	computation	NOUN
ajst-21812	67	44	.	.	PUNCT
ajst-21812	68	1	for	for	ADP
ajst-21812	68	2	functionally	functionally	ADV
ajst-21812	68	3	graded	grade	VERB
ajst-21812	68	4	material	material	NOUN
ajst-21812	68	5	beams	beam	NOUN
ajst-21812	68	6	with	with	ADP
ajst-21812	68	7	rectangular	rectangular	ADJ
ajst-21812	68	8	cross	cross	NOUN
ajst-21812	68	9	-	-	NOUN
ajst-21812	68	10	section	section	NOUN
ajst-21812	68	11	,	,	PUNCT
ajst-21812	68	12	the	the	DET
ajst-21812	68	13	value	value	NOUN
ajst-21812	68	14	is	be	AUX
ajst-21812	68	15	typically	typically	ADV
ajst-21812	68	16	taken	take	VERB
ajst-21812	68	17	as	as	ADP
ajst-21812	68	18	𝜅=5/6	𝜅=5/6	PROPN
ajst-21812	68	19	.	.	PUNCT
ajst-21812	69	1	the	the	DET
ajst-21812	69	2	stiffness	stiffness	ADJ
ajst-21812	69	3	coefficients	coefficient	NOUN
ajst-21812	69	4	and	and	CCONJ
ajst-21812	69	5	inertia	inertia	NOUN
ajst-21812	69	6	terms	term	NOUN
ajst-21812	69	7	for	for	ADP
ajst-21812	69	8	functionally	functionally	ADV
ajst-21812	69	9	graded	grade	VERB
ajst-21812	69	10	timoshenko	timoshenko	NOUN
ajst-21812	69	11	beams	beam	NOUN
ajst-21812	69	12	with	with	ADP
ajst-21812	69	13	cracks	crack	NOUN
ajst-21812	69	14	can	can	AUX
ajst-21812	69	15	be	be	AUX
ajst-21812	69	16	defined	define	VERB
ajst-21812	69	17	as	as	ADP
ajst-21812	69	18	:	:	PUNCT
ajst-21812	69	19			NOUN
ajst-21812	69	20			PROPN
ajst-21812	69	21			PROPN
ajst-21812	69	22	/	/	PUNCT
ajst-21812	69	23	2	2	NUM
ajst-21812	69	24	2	2	NUM
ajst-21812	69	25	11	11	NUM
ajst-21812	69	26	11	11	NUM
ajst-21812	69	27	11	11	NUM
ajst-21812	69	28	11/2	11/2	NUM
ajst-21812	69	29	,	,	PUNCT
ajst-21812	69	30	,	,	PUNCT
ajst-21812	69	31	(	(	PUNCT
ajst-21812	69	32	)	)	PUNCT
ajst-21812	69	33	1	1	NUM
ajst-21812	69	34	,	,	PUNCT
ajst-21812	69	35	,	,	PUNCT
ajst-21812	69	36	d	d	PROPN
ajst-21812	69	37	h	h	NOUN
ajst-21812	69	38	h	h	NOUN
ajst-21812	69	39	a	a	DET
ajst-21812	69	40	b	b	NOUN
ajst-21812	70	1	d	d	X
ajst-21812	70	2	q	q	PROPN
ajst-21812	70	3	z	z	NOUN
ajst-21812	70	4	z	z	NOUN
ajst-21812	70	5	z	z	NOUN
ajst-21812	70	6	z	z	NOUN
ajst-21812	70	7			NOUN
ajst-21812	70	8			PRON
ajst-21812	70	9			NOUN
ajst-21812	70	10	/	/	SYM
ajst-21812	70	11	2	2	NUM
ajst-21812	70	12	55	55	NUM
ajst-21812	70	13	55/	55/	NUM
ajst-21812	70	14	2	2	NUM
ajst-21812	70	15	(	(	PUNCT
ajst-21812	70	16	)	)	PUNCT
ajst-21812	71	1	d	d	NOUN
ajst-21812	71	2	h	h	NOUN
ajst-21812	71	3	h	h	NOUN
ajst-21812	71	4	a	a	DET
ajst-21812	71	5	q	q	X
ajst-21812	71	6	z	z	NOUN
ajst-21812	71	7	z	z	NOUN
ajst-21812	71	8			NOUN
ajst-21812	71	9			PRON
ajst-21812	71	10			PUNCT
ajst-21812	71	11	(	(	PUNCT
ajst-21812	71	12	12	12	NUM
ajst-21812	71	13	)	)	PUNCT
ajst-21812	71	14			NOUN
ajst-21812	72	1			PROPN
ajst-21812	72	2			PROPN
ajst-21812	72	3	/	/	ADP
ajst-21812	72	4	2	2	NUM
ajst-21812	72	5	2	2	NUM
ajst-21812	72	6	1	1	NUM
ajst-21812	72	7	2	2	NUM
ajst-21812	72	8	3	3	NUM
ajst-21812	72	9	/2	/2	NUM
ajst-21812	72	10	,	,	PUNCT
ajst-21812	72	11	,	,	PUNCT
ajst-21812	72	12	(	(	PUNCT
ajst-21812	72	13	)	)	PUNCT
ajst-21812	72	14	1	1	NUM
ajst-21812	72	15	,	,	PUNCT
ajst-21812	72	16	z	z	NOUN
ajst-21812	72	17	,	,	PUNCT
ajst-21812	72	18	z	z	NOUN
ajst-21812	73	1	d	d	NOUN
ajst-21812	73	2	h	h	NOUN
ajst-21812	73	3	h	h	NOUN
ajst-21812	74	1	i	i	PRON
ajst-21812	74	2	i	i	PRON
ajst-21812	75	1	i	i	VERB
ajst-21812	75	2	z	z	NOUN
ajst-21812	75	3	z	z	NUM
ajst-21812	75	4			NOUN
ajst-21812	75	5			PRON
ajst-21812	75	6			ADP
ajst-21812	75	7	based	base	VERB
ajst-21812	75	8	on	on	ADP
ajst-21812	75	9	hamilton	hamilton	PROPN
ajst-21812	75	10	's	's	PART
ajst-21812	75	11	principle	principle	NOUN
ajst-21812	75	12	,	,	PUNCT
ajst-21812	75	13	continuity	continuity	NOUN
ajst-21812	75	14	conditions	condition	NOUN
ajst-21812	75	15	of	of	ADP
ajst-21812	75	16	force	force	NOUN
ajst-21812	75	17	and	and	CCONJ
ajst-21812	75	18	displacement	displacement	NOUN
ajst-21812	75	19	,	,	PUNCT
ajst-21812	75	20	and	and	CCONJ
ajst-21812	75	21	the	the	DET
ajst-21812	75	22	relationship	relationship	NOUN
ajst-21812	75	23	between	between	ADP
ajst-21812	75	24	crackinduced	crackinduce	VERB
ajst-21812	75	25	additional	additional	ADJ
ajst-21812	75	26	rotation	rotation	NOUN
ajst-21812	75	27	,	,	PUNCT
ajst-21812	75	28	and	and	CCONJ
ajst-21812	75	29	by	by	ADP
ajst-21812	75	30	non	non	ADJ
ajst-21812	75	31	-	-	ADJ
ajst-21812	75	32	dimensionalizing	dimensionalize	VERB
ajst-21812	75	33	the	the	DET
ajst-21812	75	34	equations	equation	NOUN
ajst-21812	75	35	,	,	PUNCT
ajst-21812	75	36	the	the	DET
ajst-21812	75	37	system	system	NOUN
ajst-21812	75	38	's	's	PART
ajst-21812	75	39	free	free	ADJ
ajst-21812	75	40	vibration	vibration	NOUN
ajst-21812	75	41	equation	equation	NOUN
ajst-21812	75	42	is	be	AUX
ajst-21812	75	43	derived	derive	VERB
ajst-21812	75	44	as	as	ADP
ajst-21812	75	45	:	:	SYM
ajst-21812	75	46	2	2	NUM
ajst-21812	75	47	2	2	NUM
ajst-21812	75	48	11	11	NUM
ajst-21812	75	49	11	11	NUM
ajst-21812	75	50	12	12	NUM
ajst-21812	75	51	2	2	NUM
ajst-21812	75	52	2	2	NUM
ajst-21812	75	53	2	2	NUM
ajst-21812	75	54	2	2	NUM
ajst-21812	75	55	22	22	NUM
ajst-21812	76	1	i	i	PRON
ajst-21812	76	2	i	i	PRON
ajst-21812	77	1	i	i	PRON
ajst-21812	77	2	iu	iu	VERB
ajst-21812	77	3	u	u	PROPN
ajst-21812	77	4	a	a	DET
ajst-21812	77	5	ib	ib	INTJ
ajst-21812	78	1	i	i	PRON
ajst-21812	78	2			NOUN
ajst-21812	78	3			NOUN
ajst-21812	78	4			NOUN
ajst-21812	78	5			NOUN
ajst-21812	79	1			NOUN
ajst-21812	80	1			X
ajst-21812	81	1			ADJ
ajst-21812	81	2			ADJ
ajst-21812	81	3			ADJ
ajst-21812	81	4			ADJ
ajst-21812	81	5			PROPN
ajst-21812	81	6			PROPN
ajst-21812	81	7			PROPN
ajst-21812	81	8			PROPN
ajst-21812	81	9			ADJ
ajst-21812	81	10	255	255	NUM
ajst-21812	81	11	1	1	NUM
ajst-21812	81	12	22	22	NUM
ajst-21812	81	13	2	2	NUM
ajst-21812	82	1	i	i	PRON
ajst-21812	82	2	i	i	PRON
ajst-21812	83	1	iww	iww	PROPN
ajst-21812	83	2	t	t	PROPN
ajst-21812	83	3	a	a	PRON
ajst-21812	83	4	i	i	PRON
ajst-21812	83	5			NOUN
ajst-21812	83	6			VERB
ajst-21812	83	7			PUNCT
ajst-21812	83	8			ADV
ajst-21812	83	9			NOUN
ajst-21812	83	10			PROPN
ajst-21812	83	11			PROPN
ajst-21812	83	12			X
ajst-21812	83	13			PUNCT
ajst-21812	83	14			PROPN
ajst-21812	83	15			PROPN
ajst-21812	83	16			PROPN
ajst-21812	83	17			NOUN
ajst-21812	83	18	(	(	PUNCT
ajst-21812	83	19	13	13	NUM
ajst-21812	83	20	)	)	SYM
ajst-21812	83	21	2	2	NUM
ajst-21812	83	22	2	2	NUM
ajst-21812	83	23	11	11	NUM
ajst-21812	83	24	11	11	NUM
ajst-21812	83	25	5	5	NUM
ajst-21812	83	26	2	2	NUM
ajst-21812	83	27	2	2	NUM
ajst-21812	83	28	2	2	NUM
ajst-21812	83	29	32	32	NUM
ajst-21812	83	30	252	252	NUM
ajst-21812	83	31	2	2	NUM
ajst-21812	84	1	i	i	PRON
ajst-21812	84	2	i	i	PRON
ajst-21812	85	1	i	i	PRON
ajst-21812	85	2	i	i	PRON
ajst-21812	86	1	iiu	iiu	INTJ
ajst-21812	86	2	w	w	PROPN
ajst-21812	86	3	b	b	PROPN
ajst-21812	87	1	i	i	PROPN
ajst-21812	87	2	d	d	PROPN
ajst-21812	87	3	a	a	DET
ajst-21812	87	4	u	u	NOUN
ajst-21812	87	5	i	i	PRON
ajst-21812	87	6	t	t	NOUN
ajst-21812	87	7	t	t	PROPN
ajst-21812	87	8			PRON
ajst-21812	87	9			NOUN
ajst-21812	87	10			PUNCT
ajst-21812	87	11			PUNCT
ajst-21812	87	12			PROPN
ajst-21812	87	13			PROPN
ajst-21812	87	14			X
ajst-21812	87	15			PROPN
ajst-21812	87	16			PROPN
ajst-21812	87	17			PROPN
ajst-21812	87	18			PROPN
ajst-21812	87	19			VERB
ajst-21812	87	20			PROPN
ajst-21812	87	21			ADV
ajst-21812	87	22			PUNCT
ajst-21812	87	23			PROPN
ajst-21812	87	24			ADJ
ajst-21812	87	25			PROPN
ajst-21812	87	26			ADJ
ajst-21812	87	27			NOUN
ajst-21812	87	28			VERB
ajst-21812	87	29			ADJ
ajst-21812	87	30			PROPN
ajst-21812	87	31	the	the	DET
ajst-21812	87	32	boundary	boundary	ADJ
ajst-21812	87	33	conditions	condition	NOUN
ajst-21812	87	34	corresponding	correspond	VERB
ajst-21812	87	35	to	to	ADP
ajst-21812	87	36	three	three	NUM
ajst-21812	87	37	different	different	ADJ
ajst-21812	87	38	support	support	NOUN
ajst-21812	87	39	types	type	NOUN
ajst-21812	87	40	can	can	AUX
ajst-21812	87	41	be	be	AUX
ajst-21812	87	42	stated	state	VERB
ajst-21812	87	43	as	as	SCONJ
ajst-21812	87	44	follows	follow	VERB
ajst-21812	87	45	:	:	PUNCT
ajst-21812	87	46	(	(	PUNCT
ajst-21812	87	47	a	a	X
ajst-21812	87	48	)	)	PUNCT
ajst-21812	87	49	one	one	NUM
ajst-21812	87	50	end	end	NOUN
ajst-21812	87	51	complained	complain	VERB
ajst-21812	87	52	,	,	PUNCT
ajst-21812	87	53	one	one	NUM
ajst-21812	87	54	end	end	VERB
ajst-21812	87	55	free	free	ADJ
ajst-21812	87	56	(	(	PUNCT
ajst-21812	87	57	c	c	NOUN
ajst-21812	87	58	-	-	SYM
ajst-21812	87	59	f	f	NOUN
ajst-21812	87	60	):	):	PUNCT
ajst-21812	87	61	1	1	NUM
ajst-21812	87	62	1	1	NUM
ajst-21812	87	63	1	1	NUM
ajst-21812	87	64	2	2	NUM
ajst-21812	87	65	2	2	NUM
ajst-21812	87	66	2	2	NUM
ajst-21812	87	67	0	0	NUM
ajst-21812	87	68	0	0	NUM
ajst-21812	87	69	,	,	PUNCT
ajst-21812	87	70	0	0	NUM
ajst-21812	87	71	,	,	PUNCT
ajst-21812	87	72	0	0	NUM
ajst-21812	87	73	1	1	NUM
ajst-21812	87	74	0	0	NUM
ajst-21812	87	75	,	,	PUNCT
ajst-21812	87	76	0	0	NUM
ajst-21812	87	77	,	,	PUNCT
ajst-21812	87	78	0x	0x	NOUN
ajst-21812	87	79	x	x	SYM
ajst-21812	87	80	x	x	PUNCT
ajst-21812	87	81	u	u	NOUN
ajst-21812	87	82	w	w	PROPN
ajst-21812	87	83	n	n	PROPN
ajst-21812	87	84	q	q	NOUN
ajst-21812	87	85	m	m	VERB
ajst-21812	87	86			NOUN
ajst-21812	88	1			NOUN
ajst-21812	88	2			NOUN
ajst-21812	89	1			NUM
ajst-21812	90	1			ADJ
ajst-21812	91	1			PRON
ajst-21812	92	1			ADJ
ajst-21812	93	1			ADJ
ajst-21812	94	1			PRON
ajst-21812	95	1			NUM
ajst-21812	95	2			NOUN
ajst-21812	95	3	在	在	PROPN
ajst-21812	95	4	处	处	NOUN
ajst-21812	95	5	：	：	PUNCT
ajst-21812	95	6	在	在	PROPN
ajst-21812	95	7	处	处	PROPN
ajst-21812	95	8	：	：	PUNCT
ajst-21812	95	9	(	(	PUNCT
ajst-21812	95	10	14	14	NUM
ajst-21812	95	11	)	)	PUNCT
ajst-21812	95	12	(	(	PUNCT
ajst-21812	95	13	b	b	X
ajst-21812	95	14	)	)	PUNCT
ajst-21812	95	15	hinged	hinge	VERB
ajst-21812	95	16	at	at	ADP
ajst-21812	95	17	both	both	DET
ajst-21812	95	18	ends	end	NOUN
ajst-21812	95	19	(	(	PUNCT
ajst-21812	95	20	h	h	NOUN
ajst-21812	95	21	-	-	PUNCT
ajst-21812	95	22	h	h	NOUN
ajst-21812	95	23	):	):	PUNCT
ajst-21812	96	1	1	1	NUM
ajst-21812	96	2	1	1	NUM
ajst-21812	96	3	1	1	NUM
ajst-21812	96	4	2	2	NUM
ajst-21812	96	5	2	2	NUM
ajst-21812	96	6	2	2	NUM
ajst-21812	96	7	0	0	NUM
ajst-21812	96	8	0	0	NUM
ajst-21812	96	9	,	,	PUNCT
ajst-21812	96	10	0	0	NUM
ajst-21812	96	11	,	,	PUNCT
ajst-21812	96	12	0	0	NUM
ajst-21812	96	13	1	1	NUM
ajst-21812	96	14	0	0	NUM
ajst-21812	96	15	,	,	PUNCT
ajst-21812	96	16	0	0	NUM
ajst-21812	96	17	,	,	PUNCT
ajst-21812	96	18	0	0	NUM
ajst-21812	96	19	x	x	SYM
ajst-21812	97	1	x	x	PUNCT
ajst-21812	97	2	u	u	NOUN
ajst-21812	97	3	w	w	NOUN
ajst-21812	97	4	m	m	VERB
ajst-21812	97	5	u	u	NOUN
ajst-21812	97	6	w	w	PROPN
ajst-21812	97	7	m	m	VERB
ajst-21812	97	8			NOUN
ajst-21812	98	1			X
ajst-21812	99	1			NOUN
ajst-21812	100	1			ADJ
ajst-21812	101	1			PRON
ajst-21812	102	1			ADJ
ajst-21812	103	1			ADJ
ajst-21812	104	1			PRON
ajst-21812	105	1			NUM
ajst-21812	105	2			NOUN
ajst-21812	105	3	在	在	PROPN
ajst-21812	105	4	处	处	NOUN
ajst-21812	105	5	：	：	PUNCT
ajst-21812	105	6	在	在	PROPN
ajst-21812	105	7	处	处	NOUN
ajst-21812	105	8	：	：	PUNCT
ajst-21812	105	9	(	(	PUNCT
ajst-21812	105	10	15	15	NUM
ajst-21812	105	11	)	)	PUNCT
ajst-21812	105	12	(	(	PUNCT
ajst-21812	105	13	c	c	X
ajst-21812	105	14	)	)	PUNCT
ajst-21812	105	15	both	both	PRON
ajst-21812	105	16	ends	end	VERB
ajst-21812	105	17	complained	complain	VERB
ajst-21812	105	18	(	(	PUNCT
ajst-21812	105	19	c	c	X
ajst-21812	105	20	-	-	SYM
ajst-21812	105	21	c	c	NOUN
ajst-21812	105	22	):	):	PUNCT
ajst-21812	105	23	1	1	NUM
ajst-21812	105	24	1	1	NUM
ajst-21812	105	25	1	1	NUM
ajst-21812	105	26	2	2	NUM
ajst-21812	105	27	2	2	NUM
ajst-21812	105	28	2	2	NUM
ajst-21812	105	29	0	0	NUM
ajst-21812	105	30	0	0	NUM
ajst-21812	105	31	,	,	PUNCT
ajst-21812	105	32	0	0	NUM
ajst-21812	105	33	,	,	PUNCT
ajst-21812	105	34	0	0	NUM
ajst-21812	105	35	1	1	NUM
ajst-21812	105	36	0	0	NUM
ajst-21812	105	37	,	,	PUNCT
ajst-21812	105	38	0	0	NUM
ajst-21812	105	39	,	,	PUNCT
ajst-21812	105	40	0	0	NUM
ajst-21812	105	41	u	u	PROPN
ajst-21812	106	1	w	w	PROPN
ajst-21812	106	2	u	u	PROPN
ajst-21812	106	3	w	w	NOUN
ajst-21812	106	4			NOUN
ajst-21812	107	1			NOUN
ajst-21812	107	2			X
ajst-21812	108	1			NOUN
ajst-21812	109	1			NOUN
ajst-21812	109	2			PRON
ajst-21812	110	1			NOUN
ajst-21812	111	1			PRON
ajst-21812	112	1			ADJ
ajst-21812	113	1			PRON
ajst-21812	114	1			NUM
ajst-21812	114	2			NOUN
ajst-21812	114	3	在	在	PROPN
ajst-21812	114	4	处	处	NOUN
ajst-21812	114	5	：	：	PUNCT
ajst-21812	114	6	在	在	PROPN
ajst-21812	114	7	处	处	PROPN
ajst-21812	114	8	：	：	PUNCT
ajst-21812	114	9	(	(	PUNCT
ajst-21812	114	10	16	16	NUM
ajst-21812	114	11	)	)	PUNCT
ajst-21812	114	12	by	by	ADP
ajst-21812	114	13	considering	consider	VERB
ajst-21812	114	14	different	different	ADJ
ajst-21812	114	15	boundary	boundary	ADJ
ajst-21812	114	16	conditions	condition	NOUN
ajst-21812	114	17	and	and	CCONJ
ajst-21812	114	18	combining	combine	VERB
ajst-21812	114	19	the	the	DET
ajst-21812	114	20	expressions	expression	NOUN
ajst-21812	114	21	for	for	ADP
ajst-21812	114	22	𝑁	𝑁	PROPN
ajst-21812	114	23	,	,	PUNCT
ajst-21812	114	24	𝑀	𝑀	PROPN
ajst-21812	114	25	,	,	PUNCT
ajst-21812	114	26	and	and	CCONJ
ajst-21812	114	27	q	q	X
ajst-21812	114	28	,	,	PUNCT
ajst-21812	114	29	12	12	NUM
ajst-21812	114	30	homogeneous	homogeneous	ADJ
ajst-21812	114	31	nonlinear	nonlinear	ADJ
ajst-21812	114	32	algebraic	algebraic	ADJ
ajst-21812	114	33	equations	equation	NOUN
ajst-21812	114	34	can	can	AUX
ajst-21812	114	35	be	be	AUX
ajst-21812	114	36	obtained	obtain	VERB
ajst-21812	114	37	,	,	PUNCT
ajst-21812	114	38	which	which	PRON
ajst-21812	114	39	can	can	AUX
ajst-21812	114	40	be	be	AUX
ajst-21812	114	41	written	write	VERB
ajst-21812	114	42	in	in	ADP
ajst-21812	114	43	matrix	matrix	NOUN
ajst-21812	114	44	form	form	NOUN
ajst-21812	114	45	as	as	ADP
ajst-21812	114	46	:	:	PUNCT
ajst-21812	114	47	(	(	PUNCT
ajst-21812	114	48	)	)	PUNCT
ajst-21812	114	49			PROPN
ajst-21812	114	50	h	h	NOUN
ajst-21812	114	51	χ	χ	NOUN
ajst-21812	114	52	0	0	NUM
ajst-21812	114	53	(	(	PUNCT
ajst-21812	114	54	17	17	NUM
ajst-21812	114	55	)	)	PUNCT
ajst-21812	114	56	in	in	ADP
ajst-21812	114	57	the	the	DET
ajst-21812	114	58	equation	equation	NOUN
ajst-21812	114	59	,	,	PUNCT
ajst-21812	114	60	h(𝜔	h(𝜔	PROPN
ajst-21812	114	61	)	)	PUNCT
ajst-21812	114	62	is	be	AUX
ajst-21812	114	63	a	a	DET
ajst-21812	114	64	matrix	matrix	NOUN
ajst-21812	114	65	that	that	PRON
ajst-21812	114	66	is	be	AUX
ajst-21812	114	67	associated	associate	VERB
ajst-21812	114	68	with	with	ADP
ajst-21812	114	69	the	the	DET
ajst-21812	114	70	system	system	NOUN
ajst-21812	114	71	's	's	PART
ajst-21812	114	72	natural	natural	ADJ
ajst-21812	114	73	frequencies	frequency	NOUN
ajst-21812	114	74	𝜔	𝜔	NOUN
ajst-21812	114	75	and	and	CCONJ
ajst-21812	114	76	exhibits	exhibit	VERB
ajst-21812	114	77	nonlinear	nonlinear	ADJ
ajst-21812	114	78	characteristics	characteristic	NOUN
ajst-21812	114	79	,	,	PUNCT
ajst-21812	114	80	while	while	SCONJ
ajst-21812	114	81	χ	χ	PRON
ajst-21812	114	82	represents	represent	VERB
ajst-21812	114	83	a	a	DET
ajst-21812	114	84	vector	vector	NOUN
ajst-21812	114	85	composed	compose	VERB
ajst-21812	114	86	of	of	ADP
ajst-21812	114	87	the	the	DET
ajst-21812	114	88	12	12	NUM
ajst-21812	114	89	unknown	unknown	ADJ
ajst-21812	114	90	coefficients	coefficient	NOUN
ajst-21812	114	91	,	,	PUNCT
ajst-21812	114	92	defined	define	VERB
ajst-21812	114	93	,	,	PUNCT
ajst-21812	114	94	in	in	ADP
ajst-21812	114	95	order	order	NOUN
ajst-21812	114	96	for	for	SCONJ
ajst-21812	114	97	the	the	DET
ajst-21812	114	98	equations	equation	NOUN
ajst-21812	114	99	to	to	PART
ajst-21812	114	100	have	have	VERB
ajst-21812	114	101	a	a	DET
ajst-21812	114	102	nontrivial	nontrivial	ADJ
ajst-21812	114	103	solution	solution	NOUN
ajst-21812	114	104	,	,	PUNCT
ajst-21812	114	105	the	the	DET
ajst-21812	114	106	determinant	determinant	NOUN
ajst-21812	114	107	of	of	ADP
ajst-21812	114	108	h(𝜔	h(𝜔	PROPN
ajst-21812	114	109	)	)	PUNCT
ajst-21812	114	110	must	must	AUX
ajst-21812	114	111	be	be	AUX
ajst-21812	114	112	zero	zero	NUM
ajst-21812	114	113	,	,	PUNCT
ajst-21812	114	114	as	as	SCONJ
ajst-21812	114	115	:	:	PUNCT
ajst-21812	114	116	det	det	PROPN
ajst-21812	114	117	[	[	PUNCT
ajst-21812	114	118	(	(	PUNCT
ajst-21812	114	119	)	)	PUNCT
ajst-21812	114	120	]	]	PUNCT
ajst-21812	114	121	0	0	PROPN
ajst-21812	114	122	h	h	PROPN
ajst-21812	114	123	(	(	PUNCT
ajst-21812	114	124	18	18	NUM
ajst-21812	114	125	)	)	PUNCT
ajst-21812	114	126	4	4	NUM
ajst-21812	114	127	.	.	PUNCT
ajst-21812	114	128	numerical	numerical	ADJ
ajst-21812	114	129	results	result	NOUN
ajst-21812	114	130	and	and	CCONJ
ajst-21812	114	131	discussion	discussion	NOUN
ajst-21812	114	132	in	in	ADP
ajst-21812	114	133	the	the	DET
ajst-21812	114	134	numerical	numerical	ADJ
ajst-21812	114	135	simulations	simulation	NOUN
ajst-21812	114	136	presented	present	VERB
ajst-21812	114	137	in	in	ADP
ajst-21812	114	138	this	this	DET
ajst-21812	114	139	paper	paper	NOUN
ajst-21812	114	140	,	,	PUNCT
ajst-21812	114	141	the	the	DET
ajst-21812	114	142	following	follow	VERB
ajst-21812	114	143	geometric	geometric	ADJ
ajst-21812	114	144	and	and	CCONJ
ajst-21812	114	145	material	material	NOUN
ajst-21812	114	146	parameters	parameter	NOUN
ajst-21812	114	147	were	be	AUX
ajst-21812	114	148	used	use	VERB
ajst-21812	114	149	:	:	PUNCT
ajst-21812	114	150	the	the	DET
ajst-21812	114	151	thickness	thickness	NOUN
ajst-21812	114	152	of	of	ADP
ajst-21812	114	153	the	the	DET
ajst-21812	114	154	beam	beam	NOUN
ajst-21812	114	155	is	be	AUX
ajst-21812	114	156	ℎ=0.1	ℎ=0.1	NOUN
ajst-21812	114	157	 	 	SPACE
ajst-21812	114	158	m	m	PROPN
ajst-21812	114	159	,	,	PUNCT
ajst-21812	114	160	and	and	CCONJ
ajst-21812	114	161	the	the	DET
ajst-21812	114	162	ratio	ratio	NOUN
ajst-21812	114	163	of	of	ADP
ajst-21812	114	164	elastic	elastic	ADJ
ajst-21812	114	165	moduli	modulus	NOUN
ajst-21812	114	166	𝐸2	𝐸2	PROPN
ajst-21812	114	167	/𝐸1	/𝐸1	PROPN
ajst-21812	114	168	is	be	AUX
ajst-21812	114	169	set	set	VERB
ajst-21812	114	170	to	to	ADP
ajst-21812	114	171	0.2	0.2	NUM
ajst-21812	114	172	,	,	PUNCT
ajst-21812	114	173	1	1	NUM
ajst-21812	114	174	,	,	PUNCT
ajst-21812	114	175	and	and	CCONJ
ajst-21812	114	176	5	5	NUM
ajst-21812	114	177	.	.	PUNCT
ajst-21812	115	1	the	the	DET
ajst-21812	115	2	case	case	NOUN
ajst-21812	115	3	𝐸2	𝐸2	PROPN
ajst-21812	115	4	/𝐸1=1	/𝐸1=1	PROPN
ajst-21812	115	5	corresponds	correspond	VERB
ajst-21812	115	6	to	to	ADP
ajst-21812	115	7	an	an	DET
ajst-21812	115	8	isotropic	isotropic	ADJ
ajst-21812	115	9	homogeneous	homogeneous	ADJ
ajst-21812	115	10	beam	beam	NOUN
ajst-21812	115	11	.	.	PUNCT
ajst-21812	116	1	the	the	DET
ajst-21812	116	2	upper	upper	ADJ
ajst-21812	116	3	surface	surface	NOUN
ajst-21812	116	4	of	of	ADP
ajst-21812	116	5	the	the	DET
ajst-21812	116	6	beam	beam	NOUN
ajst-21812	116	7	consists	consist	VERB
ajst-21812	116	8	of	of	ADP
ajst-21812	116	9	100	100	NUM
ajst-21812	116	10	%	%	NOUN
ajst-21812	116	11	aluminum	aluminum	NOUN
ajst-21812	116	12	,	,	PUNCT
ajst-21812	116	13	with	with	ADP
ajst-21812	116	14	the	the	DET
ajst-21812	116	15	material	material	NOUN
ajst-21812	116	16	properties	property	NOUN
ajst-21812	116	17	being	be	AUX
ajst-21812	116	18	.	.	PUNCT
ajst-21812	117	1	according	accord	VERB
ajst-21812	117	2	to	to	PART
ajst-21812	117	3	figure	figure	NOUN
ajst-21812	117	4	2	2	NUM
ajst-21812	117	5	,	,	PUNCT
ajst-21812	117	6	when	when	SCONJ
ajst-21812	117	7	the	the	DET
ajst-21812	117	8	functionally	functionally	ADV
ajst-21812	117	9	graded	grade	VERB
ajst-21812	117	10	beam	beam	NOUN
ajst-21812	117	11	has	have	VERB
ajst-21812	117	12	material	material	NOUN
ajst-21812	117	13	parameters	parameter	NOUN
ajst-21812	117	14	𝐸2	𝐸2	ADP
ajst-21812	117	15	/𝐸1=0.2	/𝐸1=0.2	PROPN
ajst-21812	117	16	,	,	PUNCT
ajst-21812	117	17	e2	e2	PROPN
ajst-21812	117	18	/e1	/e1	PUNCT
ajst-21812	118	1	=	=	NUM
ajst-21812	118	2	0.2	0.2	NUM
ajst-21812	118	3	,	,	PUNCT
ajst-21812	118	4	a	a	DET
ajst-21812	118	5	lengthto	lengthto	NOUN
ajst-21812	118	6	-	-	PUNCT
ajst-21812	118	7	width	width	NOUN
ajst-21812	118	8	ratio	ratio	NOUN
ajst-21812	118	9	of	of	ADP
ajst-21812	118	10	8	8	NUM
ajst-21812	118	11	,	,	PUNCT
ajst-21812	118	12	and	and	CCONJ
ajst-21812	118	13	a	a	DET
ajst-21812	118	14	relative	relative	ADJ
ajst-21812	118	15	crack	crack	NOUN
ajst-21812	118	16	depth	depth	NOUN
ajst-21812	118	17	of	of	ADP
ajst-21812	118	18	0.2	0.2	NUM
ajst-21812	118	19	,	,	PUNCT
ajst-21812	118	20	the	the	DET
ajst-21812	118	21	impact	impact	NOUN
ajst-21812	118	22	of	of	ADP
ajst-21812	118	23	different	different	ADJ
ajst-21812	118	24	crack	crack	NOUN
ajst-21812	118	25	positions	position	NOUN
ajst-21812	118	26	and	and	CCONJ
ajst-21812	118	27	different	different	ADJ
ajst-21812	118	28	boundary	boundary	ADJ
ajst-21812	118	29	conditions	condition	NOUN
ajst-21812	118	30	on	on	ADP
ajst-21812	118	31	the	the	DET
ajst-21812	118	32	first	first	ADJ
ajst-21812	118	33	three	three	NUM
ajst-21812	118	34	natural	natural	ADJ
ajst-21812	118	35	frequency	frequency	NOUN
ajst-21812	118	36	ratios	ratio	NOUN
ajst-21812	118	37	of	of	ADP
ajst-21812	118	38	the	the	DET
ajst-21812	118	39	system	system	NOUN
ajst-21812	118	40	can	can	AUX
ajst-21812	118	41	be	be	AUX
ajst-21812	118	42	observed	observe	VERB
ajst-21812	118	43	.	.	PUNCT
ajst-21812	119	1	from	from	ADP
ajst-21812	119	2	figure	figure	NOUN
ajst-21812	119	3	2(a	2(a	NUM
ajst-21812	119	4	)	)	PUNCT
ajst-21812	119	5	,	,	PUNCT
ajst-21812	119	6	it	it	PRON
ajst-21812	119	7	can	can	AUX
ajst-21812	119	8	be	be	AUX
ajst-21812	119	9	seen	see	VERB
ajst-21812	119	10	that	that	SCONJ
ajst-21812	119	11	under	under	ADP
ajst-21812	119	12	one	one	NUM
ajst-21812	119	13	fixed	fix	VERB
ajst-21812	119	14	end	end	NOUN
ajst-21812	119	15	and	and	CCONJ
ajst-21812	119	16	one	one	NUM
ajst-21812	119	17	free	free	ADJ
ajst-21812	119	18	end	end	NOUN
ajst-21812	119	19	boundary	boundary	ADJ
ajst-21812	119	20	conditions	condition	NOUN
ajst-21812	119	21	,	,	PUNCT
ajst-21812	119	22	the	the	DET
ajst-21812	119	23	first	first	ADJ
ajst-21812	119	24	natural	natural	ADJ
ajst-21812	119	25	frequency	frequency	NOUN
ajst-21812	119	26	ratio	ratio	NOUN
ajst-21812	119	27	of	of	ADP
ajst-21812	119	28	the	the	DET
ajst-21812	119	29	system	system	NOUN
ajst-21812	119	30	increases	increase	VERB
ajst-21812	119	31	as	as	ADP
ajst-21812	119	32	the	the	DET
ajst-21812	119	33	relative	relative	ADJ
ajst-21812	119	34	position	position	NOUN
ajst-21812	119	35	of	of	ADP
ajst-21812	119	36	the	the	DET
ajst-21812	119	37	crack	crack	NOUN
ajst-21812	119	38	shifts	shift	NOUN
ajst-21812	119	39	from	from	ADP
ajst-21812	119	40	the	the	DET
ajst-21812	119	41	fixed	fixed	ADJ
ajst-21812	119	42	end	end	NOUN
ajst-21812	119	43	towards	towards	ADP
ajst-21812	119	44	the	the	DET
ajst-21812	119	45	free	free	ADJ
ajst-21812	119	46	end	end	NOUN
ajst-21812	119	47	,	,	PUNCT
ajst-21812	119	48	reaching	reach	VERB
ajst-21812	119	49	its	its	PRON
ajst-21812	119	50	maximum	maximum	NOUN
ajst-21812	119	51	when	when	SCONJ
ajst-21812	119	52	the	the	DET
ajst-21812	119	53	crack	crack	NOUN
ajst-21812	119	54	is	be	AUX
ajst-21812	119	55	entirely	entirely	ADV
ajst-21812	119	56	at	at	ADP
ajst-21812	119	57	the	the	DET
ajst-21812	119	58	free	free	ADJ
ajst-21812	119	59	end	end	NOUN
ajst-21812	119	60	.	.	PUNCT
ajst-21812	120	1	the	the	DET
ajst-21812	120	2	second	second	ADJ
ajst-21812	120	3	and	and	CCONJ
ajst-21812	120	4	third	third	ADJ
ajst-21812	120	5	natural	natural	ADJ
ajst-21812	120	6	frequency	frequency	NOUN
ajst-21812	120	7	ratios	ratio	NOUN
ajst-21812	120	8	show	show	VERB
ajst-21812	120	9	an	an	DET
ajst-21812	120	10	irregular	irregular	ADJ
ajst-21812	120	11	fluctuation	fluctuation	NOUN
ajst-21812	120	12	trend	trend	NOUN
ajst-21812	120	13	as	as	ADP
ajst-21812	120	14	the	the	DET
ajst-21812	120	15	crack	crack	NOUN
ajst-21812	120	16	position	position	NOUN
ajst-21812	120	17	increases	increase	NOUN
ajst-21812	120	18	,	,	PUNCT
ajst-21812	120	19	reaching	reach	VERB
ajst-21812	120	20	their	their	PRON
ajst-21812	120	21	maximum	maximum	ADJ
ajst-21812	120	22	values	value	NOUN
ajst-21812	120	23	when	when	SCONJ
ajst-21812	120	24	the	the	DET
ajst-21812	120	25	relative	relative	ADJ
ajst-21812	120	26	crack	crack	NOUN
ajst-21812	120	27	position	position	NOUN
ajst-21812	120	28	𝐿1	𝐿1	NOUN
ajst-21812	120	29	/𝐿	/𝐿	PUNCT
ajst-21812	120	30	is	be	AUX
ajst-21812	120	31	at	at	ADP
ajst-21812	120	32	0.2	0.2	NUM
ajst-21812	120	33	,	,	PUNCT
ajst-21812	120	34	1	1	NUM
ajst-21812	120	35	and	and	CCONJ
ajst-21812	120	36	0.3	0.3	NUM
ajst-21812	120	37	,	,	PUNCT
ajst-21812	120	38	0.5	0.5	NUM
ajst-21812	120	39	,	,	PUNCT
ajst-21812	120	40	1	1	NUM
ajst-21812	120	41	respectively	respectively	ADV
ajst-21812	120	42	.	.	PUNCT
ajst-21812	121	1	the	the	DET
ajst-21812	121	2	natural	natural	ADJ
ajst-21812	121	3	frequency	frequency	NOUN
ajst-21812	121	4	ratios	ratio	NOUN
ajst-21812	121	5	for	for	ADP
ajst-21812	121	6	the	the	DET
ajst-21812	121	7	first	first	ADJ
ajst-21812	121	8	three	three	NUM
ajst-21812	121	9	modes	mode	NOUN
ajst-21812	121	10	are	be	AUX
ajst-21812	121	11	all	all	PRON
ajst-21812	121	12	minimized	minimized	ADJ
ajst-21812	121	13	when	when	SCONJ
ajst-21812	121	14	the	the	DET
ajst-21812	121	15	crack	crack	NOUN
ajst-21812	121	16	is	be	AUX
ajst-21812	121	17	located	locate	VERB
ajst-21812	121	18	at	at	ADP
ajst-21812	121	19	the	the	DET
ajst-21812	121	20	fixed	fixed	ADJ
ajst-21812	121	21	end	end	NOUN
ajst-21812	121	22	,	,	PUNCT
ajst-21812	121	23	with	with	ADP
ajst-21812	121	24	the	the	DET
ajst-21812	121	25	first	first	ADJ
ajst-21812	121	26	mode	mode	NOUN
ajst-21812	121	27	being	be	AUX
ajst-21812	121	28	the	the	DET
ajst-21812	121	29	smallest	small	ADJ
ajst-21812	121	30	and	and	CCONJ
ajst-21812	121	31	the	the	DET
ajst-21812	121	32	second	second	ADJ
ajst-21812	121	33	mode	mode	NOUN
ajst-21812	121	34	following	follow	VERB
ajst-21812	121	35	closely	closely	ADV
ajst-21812	121	36	.	.	PUNCT
ajst-21812	122	1	from	from	ADP
ajst-21812	122	2	figures	figure	NOUN
ajst-21812	122	3	2(b	2(b	NUM
ajst-21812	122	4	)	)	PUNCT
ajst-21812	122	5	and	and	CCONJ
ajst-21812	122	6	2(c	2(c	NUM
ajst-21812	122	7	)	)	PUNCT
ajst-21812	122	8	,	,	PUNCT
ajst-21812	122	9	it	it	PRON
ajst-21812	122	10	can	can	AUX
ajst-21812	122	11	be	be	AUX
ajst-21812	122	12	observed	observe	VERB
ajst-21812	122	13	that	that	SCONJ
ajst-21812	122	14	when	when	SCONJ
ajst-21812	122	15	the	the	DET
ajst-21812	122	16	functionally	functionally	ADV
ajst-21812	122	17	graded	grade	VERB
ajst-21812	122	18	beam	beam	NOUN
ajst-21812	122	19	with	with	ADP
ajst-21812	122	20	cracks	crack	NOUN
ajst-21812	122	21	is	be	AUX
ajst-21812	122	22	under	under	ADP
ajst-21812	122	23	either	either	CCONJ
ajst-21812	122	24	both	both	DET
ajst-21812	122	25	ends	end	NOUN
ajst-21812	122	26	fixed	fix	VERB
ajst-21812	122	27	or	or	CCONJ
ajst-21812	122	28	both	both	PRON
ajst-21812	122	29	ends	end	VERB
ajst-21812	122	30	hinged	hinge	VERB
ajst-21812	122	31	boundary	boundary	ADJ
ajst-21812	122	32	conditions	condition	NOUN
ajst-21812	122	33	,	,	PUNCT
ajst-21812	122	34	the	the	DET
ajst-21812	122	35	curves	curve	NOUN
ajst-21812	122	36	of	of	ADP
ajst-21812	122	37	the	the	DET
ajst-21812	122	38	natural	natural	ADJ
ajst-21812	122	39	frequency	frequency	NOUN
ajst-21812	122	40	ratios	ratio	NOUN
ajst-21812	122	41	with	with	ADP
ajst-21812	122	42	respect	respect	NOUN
ajst-21812	122	43	to	to	ADP
ajst-21812	122	44	the	the	DET
ajst-21812	122	45	crack	crack	NOUN
ajst-21812	122	46	position	position	NOUN
ajst-21812	122	47	exhibit	exhibit	NOUN
ajst-21812	122	48	symmetry	symmetry	NOUN
ajst-21812	122	49	.	.	PUNCT
ajst-21812	123	1	for	for	ADP
ajst-21812	123	2	functionally	functionally	ADV
ajst-21812	123	3	graded	grade	VERB
ajst-21812	123	4	beams	beam	NOUN
ajst-21812	123	5	under	under	ADP
ajst-21812	123	6	both	both	PRON
ajst-21812	123	7	ends	end	VERB
ajst-21812	123	8	fixed	fix	VERB
ajst-21812	123	9	conditions	condition	NOUN
ajst-21812	123	10	,	,	PUNCT
ajst-21812	123	11	the	the	DET
ajst-21812	123	12	natural	natural	ADJ
ajst-21812	123	13	frequency	frequency	NOUN
ajst-21812	123	14	ratios	ratio	NOUN
ajst-21812	123	15	for	for	ADP
ajst-21812	123	16	the	the	DET
ajst-21812	123	17	first	first	ADJ
ajst-21812	123	18	three	three	NUM
ajst-21812	123	19	modes	mode	NOUN
ajst-21812	123	20	are	be	AUX
ajst-21812	123	21	minimized	minimize	VERB
ajst-21812	123	22	when	when	SCONJ
ajst-21812	123	23	the	the	DET
ajst-21812	123	24	crack	crack	NOUN
ajst-21812	123	25	is	be	AUX
ajst-21812	123	26	located	locate	VERB
ajst-21812	123	27	at	at	ADP
ajst-21812	123	28	the	the	DET
ajst-21812	123	29	fixed	fix	VERB
ajst-21812	123	30	ends	end	NOUN
ajst-21812	123	31	,	,	PUNCT
ajst-21812	123	32	following	follow	VERB
ajst-21812	123	33	a	a	DET
ajst-21812	123	34	similar	similar	ADJ
ajst-21812	123	35	trend	trend	NOUN
ajst-21812	123	36	to	to	ADP
ajst-21812	123	37	the	the	DET
ajst-21812	123	38	one	one	NUM
ajst-21812	123	39	fixed	fix	VERB
ajst-21812	123	40	end	end	NOUN
ajst-21812	123	41	condition	condition	NOUN
ajst-21812	123	42	.	.	PUNCT
ajst-21812	124	1	for	for	ADP
ajst-21812	124	2	the	the	DET
ajst-21812	124	3	both	both	DET
ajst-21812	124	4	ends	end	NOUN
ajst-21812	124	5	hinged	hinge	VERB
ajst-21812	124	6	boundary	boundary	ADJ
ajst-21812	124	7	condition	condition	NOUN
ajst-21812	124	8	,	,	PUNCT
ajst-21812	124	9	the	the	DET
ajst-21812	124	10	first	first	ADJ
ajst-21812	124	11	natural	natural	ADJ
ajst-21812	124	12	frequency	frequency	NOUN
ajst-21812	124	13	ratio	ratio	NOUN
ajst-21812	124	14	of	of	ADP
ajst-21812	124	15	the	the	DET
ajst-21812	124	16	system	system	NOUN
ajst-21812	124	17	is	be	AUX
ajst-21812	124	18	minimized	minimize	VERB
ajst-21812	124	19	when	when	SCONJ
ajst-21812	124	20	𝐿1	𝐿1	PROPN
ajst-21812	124	21	/𝐿=0.5	/𝐿=0.5	X
ajst-21812	124	22	.	.	PUNCT
ajst-21812	125	1	the	the	DET
ajst-21812	125	2	second	second	ADJ
ajst-21812	125	3	natural	natural	ADJ
ajst-21812	125	4	frequency	frequency	NOUN
ajst-21812	125	5	ratio	ratio	NOUN
ajst-21812	125	6	is	be	AUX
ajst-21812	125	7	minimized	minimize	VERB
ajst-21812	125	8	at	at	ADP
ajst-21812	125	9	𝐿1	𝐿1	PROPN
ajst-21812	125	10	/𝐿=0.25	/𝐿=0.25	PROPN
ajst-21812	125	11	and	and	CCONJ
ajst-21812	125	12	0.75	0.75	NUM
ajst-21812	125	13	,	,	PUNCT
ajst-21812	125	14	while	while	SCONJ
ajst-21812	125	15	the	the	DET
ajst-21812	125	16	third	third	ADJ
ajst-21812	125	17	natural	natural	ADJ
ajst-21812	125	18	frequency	frequency	NOUN
ajst-21812	125	19	ratio	ratio	NOUN
ajst-21812	125	20	is	be	AUX
ajst-21812	125	21	minimized	minimize	VERB
ajst-21812	125	22	when	when	SCONJ
ajst-21812	125	23	l1	l1	PROPN
ajst-21812	125	24	/l=0.15	/l=0.15	PROPN
ajst-21812	125	25	and	and	CCONJ
ajst-21812	125	26	0.85	0.85	NUM
ajst-21812	125	27	.	.	PUNCT
ajst-21812	126	1	in	in	ADP
ajst-21812	126	2	all	all	DET
ajst-21812	126	3	three	three	NUM
ajst-21812	126	4	boundary	boundary	ADJ
ajst-21812	126	5	conditions	condition	NOUN
ajst-21812	126	6	,	,	PUNCT
ajst-21812	126	7	the	the	DET
ajst-21812	126	8	pattern	pattern	NOUN
ajst-21812	126	9	remains	remain	VERB
ajst-21812	126	10	consistent	consistent	ADJ
ajst-21812	126	11	:	:	PUNCT
ajst-21812	126	12	the	the	DET
ajst-21812	126	13	first	first	ADJ
ajst-21812	126	14	mode	mode	NOUN
ajst-21812	126	15	frequency	frequency	NOUN
ajst-21812	126	16	ratio	ratio	NOUN
ajst-21812	126	17	is	be	AUX
ajst-21812	126	18	the	the	DET
ajst-21812	126	19	smallest	small	ADJ
ajst-21812	126	20	,	,	PUNCT
ajst-21812	126	21	followed	follow	VERB
ajst-21812	126	22	by	by	ADP
ajst-21812	126	23	the	the	DET
ajst-21812	126	24	second	second	ADJ
ajst-21812	126	25	mode	mode	NOUN
ajst-21812	126	26	frequency	frequency	NOUN
ajst-21812	126	27	ratio	ratio	NOUN
ajst-21812	126	28	.	.	PUNCT
ajst-21812	127	1	268	268	NUM
ajst-21812	127	2	figure	figure	NOUN
ajst-21812	127	3	2	2	NUM
ajst-21812	127	4	.	.	PUNCT
ajst-21812	128	1	the	the	DET
ajst-21812	128	2	first	first	ADJ
ajst-21812	128	3	three	three	NUM
ajst-21812	128	4	natural	natural	ADJ
ajst-21812	128	5	frequency	frequency	NOUN
ajst-21812	128	6	ratios	ratio	NOUN
ajst-21812	128	7	of	of	ADP
ajst-21812	128	8	functionally	functionally	ADV
ajst-21812	128	9	graded	grade	VERB
ajst-21812	128	10	material	material	NOUN
ajst-21812	128	11	(	(	PUNCT
ajst-21812	128	12	fgm	fgm	PROPN
ajst-21812	128	13	)	)	PUNCT
ajst-21812	128	14	beams	beam	NOUN
ajst-21812	128	15	with	with	ADP
ajst-21812	128	16	edge	edge	NOUN
ajst-21812	128	17	cracks	crack	NOUN
ajst-21812	128	18	at	at	ADP
ajst-21812	128	19	different	different	ADJ
ajst-21812	128	20	positions	position	NOUN
ajst-21812	128	21	as	as	SCONJ
ajst-21812	128	22	seen	see	VERB
ajst-21812	128	23	from	from	ADP
ajst-21812	128	24	figure	figure	NOUN
ajst-21812	128	25	3	3	NUM
ajst-21812	128	26	,	,	PUNCT
ajst-21812	128	27	when	when	SCONJ
ajst-21812	128	28	the	the	DET
ajst-21812	128	29	elastic	elastic	ADJ
ajst-21812	128	30	modulus	modulus	NOUN
ajst-21812	128	31	ratio	ratio	NOUN
ajst-21812	128	32	of	of	ADP
ajst-21812	128	33	the	the	DET
ajst-21812	128	34	functionally	functionally	ADV
ajst-21812	128	35	graded	grade	VERB
ajst-21812	128	36	beam	beam	NOUN
ajst-21812	128	37	with	with	ADP
ajst-21812	128	38	cracks	crack	NOUN
ajst-21812	128	39	is	be	AUX
ajst-21812	128	40	5	5	NUM
ajst-21812	128	41	and	and	CCONJ
ajst-21812	128	42	the	the	DET
ajst-21812	128	43	relative	relative	ADJ
ajst-21812	128	44	crack	crack	NOUN
ajst-21812	128	45	depth	depth	NOUN
ajst-21812	128	46	is	be	AUX
ajst-21812	128	47	0.2	0.2	NUM
ajst-21812	128	48	,	,	PUNCT
ajst-21812	128	49	the	the	DET
ajst-21812	128	50	impact	impact	NOUN
ajst-21812	128	51	of	of	ADP
ajst-21812	128	52	different	different	ADJ
ajst-21812	128	53	length	length	NOUN
ajst-21812	128	54	-	-	PUNCT
ajst-21812	128	55	to	to	ADP
ajst-21812	128	56	-	-	PUNCT
ajst-21812	128	57	thickness	thickness	NOUN
ajst-21812	128	58	ratios	ratio	NOUN
ajst-21812	128	59	on	on	ADP
ajst-21812	128	60	the	the	DET
ajst-21812	128	61	third	third	ADJ
ajst-21812	128	62	mode	mode	NOUN
ajst-21812	128	63	natural	natural	ADJ
ajst-21812	128	64	frequency	frequency	NOUN
ajst-21812	128	65	ratio	ratio	NOUN
ajst-21812	128	66	under	under	ADP
ajst-21812	128	67	different	different	ADJ
ajst-21812	128	68	boundary	boundary	ADJ
ajst-21812	128	69	conditions	condition	NOUN
ajst-21812	128	70	and	and	CCONJ
ajst-21812	128	71	crack	crack	VERB
ajst-21812	128	72	positions	position	NOUN
ajst-21812	128	73	can	can	AUX
ajst-21812	128	74	be	be	AUX
ajst-21812	128	75	observed	observe	VERB
ajst-21812	128	76	.	.	PUNCT
ajst-21812	129	1	in	in	ADP
ajst-21812	129	2	figure	figure	NOUN
ajst-21812	129	3	3(a	3(a	NUM
ajst-21812	129	4	)	)	PUNCT
ajst-21812	129	5	,	,	PUNCT
ajst-21812	129	6	under	under	ADP
ajst-21812	129	7	the	the	DET
ajst-21812	129	8	boundary	boundary	ADJ
ajst-21812	129	9	condition	condition	NOUN
ajst-21812	129	10	of	of	ADP
ajst-21812	129	11	one	one	NUM
ajst-21812	129	12	fixed	fix	VERB
ajst-21812	129	13	end	end	NOUN
ajst-21812	129	14	and	and	CCONJ
ajst-21812	129	15	one	one	NUM
ajst-21812	129	16	free	free	ADJ
ajst-21812	129	17	end	end	NOUN
ajst-21812	129	18	,	,	PUNCT
ajst-21812	129	19	the	the	DET
ajst-21812	129	20	natural	natural	ADJ
ajst-21812	129	21	frequency	frequency	NOUN
ajst-21812	129	22	ratio	ratio	NOUN
ajst-21812	129	23	is	be	AUX
ajst-21812	129	24	minimized	minimize	VERB
ajst-21812	129	25	when	when	SCONJ
ajst-21812	129	26	the	the	DET
ajst-21812	129	27	crack	crack	NOUN
ajst-21812	129	28	is	be	AUX
ajst-21812	129	29	located	locate	VERB
ajst-21812	129	30	at	at	ADP
ajst-21812	129	31	the	the	DET
ajst-21812	129	32	fixed	fixed	ADJ
ajst-21812	129	33	end	end	NOUN
ajst-21812	129	34	.	.	PUNCT
ajst-21812	130	1	as	as	ADP
ajst-21812	130	2	the	the	DET
ajst-21812	130	3	crack	crack	NOUN
ajst-21812	130	4	position	position	NOUN
ajst-21812	130	5	shifts	shift	NOUN
ajst-21812	130	6	towards	towards	ADP
ajst-21812	130	7	the	the	DET
ajst-21812	130	8	free	free	ADJ
ajst-21812	130	9	end	end	NOUN
ajst-21812	130	10	,	,	PUNCT
ajst-21812	130	11	the	the	DET
ajst-21812	130	12	frequency	frequency	NOUN
ajst-21812	130	13	ratio	ratio	NOUN
ajst-21812	130	14	increases	increase	VERB
ajst-21812	130	15	steadily	steadily	ADV
ajst-21812	130	16	.	.	PUNCT
ajst-21812	131	1	in	in	ADP
ajst-21812	131	2	figure	figure	NOUN
ajst-21812	131	3	3(b	3(b	NUM
ajst-21812	131	4	)	)	PUNCT
ajst-21812	131	5	,	,	PUNCT
ajst-21812	131	6	under	under	ADP
ajst-21812	131	7	both	both	DET
ajst-21812	131	8	ends	end	NOUN
ajst-21812	131	9	fixed	fix	VERB
ajst-21812	131	10	boundary	boundary	ADJ
ajst-21812	131	11	conditions	condition	NOUN
ajst-21812	131	12	,	,	PUNCT
ajst-21812	131	13	the	the	DET
ajst-21812	131	14	natural	natural	ADJ
ajst-21812	131	15	frequency	frequency	NOUN
ajst-21812	131	16	ratio	ratio	NOUN
ajst-21812	131	17	is	be	AUX
ajst-21812	131	18	also	also	ADV
ajst-21812	131	19	minimized	minimize	VERB
ajst-21812	131	20	when	when	SCONJ
ajst-21812	131	21	the	the	DET
ajst-21812	131	22	crack	crack	NOUN
ajst-21812	131	23	is	be	AUX
ajst-21812	131	24	at	at	ADP
ajst-21812	131	25	either	either	DET
ajst-21812	131	26	fixed	fix	VERB
ajst-21812	131	27	end	end	NOUN
ajst-21812	131	28	,	,	PUNCT
ajst-21812	131	29	with	with	ADP
ajst-21812	131	30	a	a	DET
ajst-21812	131	31	noticeable	noticeable	ADJ
ajst-21812	131	32	increase	increase	NOUN
ajst-21812	131	33	in	in	ADP
ajst-21812	131	34	the	the	DET
ajst-21812	131	35	minimum	minimum	ADJ
ajst-21812	131	36	frequency	frequency	NOUN
ajst-21812	131	37	ratio	ratio	NOUN
ajst-21812	131	38	compared	compare	VERB
ajst-21812	131	39	to	to	ADP
ajst-21812	131	40	the	the	DET
ajst-21812	131	41	one	one	NUM
ajst-21812	131	42	fixed	fix	VERB
ajst-21812	131	43	end	end	NOUN
ajst-21812	131	44	condition	condition	NOUN
ajst-21812	131	45	.	.	PUNCT
ajst-21812	132	1	the	the	DET
ajst-21812	132	2	frequency	frequency	NOUN
ajst-21812	132	3	ratio	ratio	NOUN
ajst-21812	132	4	fluctuates	fluctuate	NOUN
ajst-21812	132	5	as	as	ADP
ajst-21812	132	6	the	the	DET
ajst-21812	132	7	relative	relative	ADJ
ajst-21812	132	8	crack	crack	NOUN
ajst-21812	132	9	position	position	NOUN
ajst-21812	132	10	increases	increase	NOUN
ajst-21812	132	11	,	,	PUNCT
ajst-21812	132	12	reaching	reach	VERB
ajst-21812	132	13	a	a	DET
ajst-21812	132	14	minimum	minimum	NOUN
ajst-21812	132	15	when	when	SCONJ
ajst-21812	132	16	the	the	DET
ajst-21812	132	17	crack	crack	NOUN
ajst-21812	132	18	is	be	AUX
ajst-21812	132	19	at	at	ADP
ajst-21812	132	20	the	the	DET
ajst-21812	132	21	center	center	NOUN
ajst-21812	132	22	of	of	ADP
ajst-21812	132	23	the	the	DET
ajst-21812	132	24	beam	beam	NOUN
ajst-21812	132	25	.	.	PUNCT
ajst-21812	133	1	from	from	ADP
ajst-21812	133	2	figure	figure	NOUN
ajst-21812	133	3	3(c	3(c	NUM
ajst-21812	133	4	)	)	PUNCT
ajst-21812	133	5	,	,	PUNCT
ajst-21812	133	6	under	under	ADP
ajst-21812	133	7	both	both	DET
ajst-21812	133	8	ends	end	NOUN
ajst-21812	133	9	hinged	hinge	VERB
ajst-21812	133	10	boundary	boundary	ADJ
ajst-21812	133	11	conditions	condition	NOUN
ajst-21812	133	12	,	,	PUNCT
ajst-21812	133	13	the	the	DET
ajst-21812	133	14	natural	natural	ADJ
ajst-21812	133	15	frequency	frequency	NOUN
ajst-21812	133	16	ratio	ratio	NOUN
ajst-21812	133	17	is	be	AUX
ajst-21812	133	18	minimized	minimize	VERB
ajst-21812	133	19	when	when	SCONJ
ajst-21812	133	20	the	the	DET
ajst-21812	133	21	crack	crack	NOUN
ajst-21812	133	22	is	be	AUX
ajst-21812	133	23	at	at	ADP
ajst-21812	133	24	the	the	DET
ajst-21812	133	25	center	center	NOUN
ajst-21812	133	26	of	of	ADP
ajst-21812	133	27	the	the	DET
ajst-21812	133	28	beam	beam	NOUN
ajst-21812	133	29	.	.	PUNCT
ajst-21812	134	1	the	the	DET
ajst-21812	134	2	natural	natural	ADJ
ajst-21812	134	3	frequency	frequency	NOUN
ajst-21812	134	4	ratio	ratio	NOUN
ajst-21812	134	5	is	be	AUX
ajst-21812	134	6	maximized	maximize	VERB
ajst-21812	134	7	when	when	SCONJ
ajst-21812	134	8	the	the	DET
ajst-21812	134	9	crack	crack	NOUN
ajst-21812	134	10	is	be	AUX
ajst-21812	134	11	at	at	ADP
ajst-21812	134	12	either	either	DET
ajst-21812	134	13	end	end	NOUN
ajst-21812	134	14	of	of	ADP
ajst-21812	134	15	the	the	DET
ajst-21812	134	16	beam	beam	NOUN
ajst-21812	134	17	.	.	PUNCT
ajst-21812	135	1	as	as	ADP
ajst-21812	135	2	the	the	DET
ajst-21812	135	3	relative	relative	ADJ
ajst-21812	135	4	crack	crack	NOUN
ajst-21812	135	5	position	position	NOUN
ajst-21812	135	6	increases	increase	NOUN
ajst-21812	135	7	,	,	PUNCT
ajst-21812	135	8	the	the	DET
ajst-21812	135	9	natural	natural	ADJ
ajst-21812	135	10	frequency	frequency	NOUN
ajst-21812	135	11	ratio	ratio	NOUN
ajst-21812	135	12	for	for	ADP
ajst-21812	135	13	different	different	ADJ
ajst-21812	135	14	length	length	NOUN
ajst-21812	135	15	-	-	PUNCT
ajst-21812	135	16	to	to	ADP
ajst-21812	135	17	-	-	PUNCT
ajst-21812	135	18	thickness	thickness	NOUN
ajst-21812	135	19	ratios	ratio	NOUN
ajst-21812	135	20	first	first	ADJ
ajst-21812	135	21	decreases	decrease	VERB
ajst-21812	135	22	and	and	CCONJ
ajst-21812	135	23	then	then	ADV
ajst-21812	135	24	increases	increase	VERB
ajst-21812	135	25	.	.	PUNCT
ajst-21812	136	1	when	when	SCONJ
ajst-21812	136	2	the	the	DET
ajst-21812	136	3	functionally	functionally	ADV
ajst-21812	136	4	graded	grade	VERB
ajst-21812	136	5	beam	beam	NOUN
ajst-21812	136	6	with	with	ADP
ajst-21812	136	7	cracks	crack	NOUN
ajst-21812	136	8	is	be	AUX
ajst-21812	136	9	under	under	ADP
ajst-21812	136	10	either	either	CCONJ
ajst-21812	136	11	both	both	DET
ajst-21812	136	12	ends	end	NOUN
ajst-21812	136	13	hinged	hinge	VERB
ajst-21812	136	14	or	or	CCONJ
ajst-21812	136	15	both	both	PRON
ajst-21812	136	16	ends	end	VERB
ajst-21812	136	17	fixed	fix	VERB
ajst-21812	136	18	boundary	boundary	ADJ
ajst-21812	136	19	conditions	condition	NOUN
ajst-21812	136	20	,	,	PUNCT
ajst-21812	136	21	the	the	DET
ajst-21812	136	22	curves	curve	NOUN
ajst-21812	136	23	of	of	ADP
ajst-21812	136	24	different	different	ADJ
ajst-21812	136	25	relative	relative	ADJ
ajst-21812	136	26	crack	crack	NOUN
ajst-21812	136	27	depths	depth	NOUN
ajst-21812	136	28	and	and	CCONJ
ajst-21812	136	29	crack	crack	VERB
ajst-21812	136	30	positions	position	NOUN
ajst-21812	136	31	show	show	VERB
ajst-21812	136	32	geometric	geometric	ADJ
ajst-21812	136	33	symmetry	symmetry	NOUN
ajst-21812	136	34	.	.	PUNCT
ajst-21812	137	1	figure	figure	VERB
ajst-21812	137	2	3	3	NUM
ajst-21812	137	3	.	.	PUNCT
ajst-21812	137	4	variation	variation	NOUN
ajst-21812	137	5	in	in	ADP
ajst-21812	137	6	the	the	DET
ajst-21812	137	7	first	first	ADJ
ajst-21812	137	8	mode	mode	NOUN
ajst-21812	137	9	natural	natural	ADJ
ajst-21812	137	10	frequency	frequency	NOUN
ajst-21812	137	11	of	of	ADP
ajst-21812	137	12	cracked	crack	VERB
ajst-21812	137	13	functionally	functionally	ADV
ajst-21812	137	14	graded	grade	VERB
ajst-21812	137	15	material	material	NOUN
ajst-21812	137	16	(	(	PUNCT
ajst-21812	137	17	fgm	fgm	PROPN
ajst-21812	137	18	)	)	PUNCT
ajst-21812	137	19	beams	beam	NOUN
ajst-21812	137	20	with	with	ADP
ajst-21812	137	21	different	different	ADJ
ajst-21812	137	22	length	length	NOUN
ajst-21812	137	23	-	-	PUNCT
ajst-21812	137	24	tothickness	tothickness	NOUN
ajst-21812	137	25	ratios	ratio	NOUN
ajst-21812	137	26	from	from	ADP
ajst-21812	137	27	figure	figure	NOUN
ajst-21812	137	28	3	3	NUM
ajst-21812	137	29	,	,	PUNCT
ajst-21812	137	30	under	under	ADP
ajst-21812	137	31	three	three	NUM
ajst-21812	137	32	different	different	ADJ
ajst-21812	137	33	boundary	boundary	ADJ
ajst-21812	137	34	conditions	condition	NOUN
ajst-21812	137	35	,	,	PUNCT
ajst-21812	137	36	when	when	SCONJ
ajst-21812	137	37	the	the	DET
ajst-21812	137	38	crack	crack	NOUN
ajst-21812	137	39	is	be	AUX
ajst-21812	137	40	at	at	ADP
ajst-21812	137	41	any	any	DET
ajst-21812	137	42	position	position	NOUN
ajst-21812	137	43	,	,	PUNCT
ajst-21812	137	44	the	the	DET
ajst-21812	137	45	system	system	NOUN
ajst-21812	137	46	with	with	ADP
ajst-21812	137	47	a	a	DET
ajst-21812	137	48	higher	high	ADJ
ajst-21812	137	49	length	length	NOUN
ajst-21812	137	50	-	-	PUNCT
ajst-21812	137	51	to	to	ADP
ajst-21812	137	52	-	-	PUNCT
ajst-21812	137	53	thickness	thickness	NOUN
ajst-21812	137	54	ratio	ratio	NOUN
ajst-21812	137	55	tends	tend	VERB
ajst-21812	137	56	to	to	PART
ajst-21812	137	57	have	have	VERB
ajst-21812	137	58	a	a	DET
ajst-21812	137	59	lower	low	ADJ
ajst-21812	137	60	natural	natural	ADJ
ajst-21812	137	61	frequency	frequency	NOUN
ajst-21812	137	62	ratio	ratio	NOUN
ajst-21812	137	63	.	.	PUNCT
ajst-21812	138	1	when	when	SCONJ
ajst-21812	138	2	the	the	DET
ajst-21812	138	3	length	length	NOUN
ajst-21812	138	4	-	-	PUNCT
ajst-21812	138	5	to	to	ADP
ajst-21812	138	6	-	-	PUNCT
ajst-21812	138	7	thickness	thickness	NOUN
ajst-21812	138	8	ratio	ratio	NOUN
ajst-21812	138	9	of	of	ADP
ajst-21812	138	10	the	the	DET
ajst-21812	138	11	system	system	NOUN
ajst-21812	138	12	decreases	decrease	VERB
ajst-21812	138	13	from	from	ADP
ajst-21812	138	14	18	18	NUM
ajst-21812	138	15	to	to	PART
ajst-21812	138	16	8	8	NUM
ajst-21812	138	17	,	,	PUNCT
ajst-21812	138	18	there	there	PRON
ajst-21812	138	19	is	be	VERB
ajst-21812	138	20	a	a	DET
ajst-21812	138	21	significant	significant	ADJ
ajst-21812	138	22	decrease	decrease	NOUN
ajst-21812	138	23	0	0	NUM
ajst-21812	138	24	0.2	0.2	NUM
ajst-21812	138	25	0.4	0.4	NUM
ajst-21812	138	26	0.6	0.6	NUM
ajst-21812	138	27	0.8	0.8	NUM
ajst-21812	138	28	1	1	NUM
ajst-21812	138	29	0.85	0.85	NUM
ajst-21812	138	30	0.9	0.9	NUM
ajst-21812	138	31	0.95	0.95	NUM
ajst-21812	138	32	1	1	NUM
ajst-21812	138	33	l1	l1	PROPN
ajst-21812	138	34	/	/	SYM
ajst-21812	138	35	l	l	NOUN
ajst-21812	138	36	ω	ω	PROPN
ajst-21812	138	37	n/	n/	PROPN
ajst-21812	138	38	ω	ω	PROPN
ajst-21812	138	39	n0	n0	PROPN
ajst-21812	138	40	ω1	ω1	PROPN
ajst-21812	138	41	ω2	ω2	PROPN
ajst-21812	138	42	ω3	ω3	PROPN
ajst-21812	138	43	(	(	PUNCT
ajst-21812	138	44	a	a	X
ajst-21812	138	45	)	)	PUNCT
ajst-21812	138	46	c	c	NOUN
ajst-21812	138	47	-	-	PUNCT
ajst-21812	138	48	f	f	PROPN
ajst-21812	138	49	0	0	NUM
ajst-21812	138	50	0.2	0.2	NUM
ajst-21812	138	51	0.4	0.4	NUM
ajst-21812	138	52	0.6	0.6	NUM
ajst-21812	138	53	0.8	0.8	NUM
ajst-21812	138	54	1	1	NUM
ajst-21812	138	55	0.9	0.9	NUM
ajst-21812	138	56	0.92	0.92	NUM
ajst-21812	138	57	0.94	0.94	NUM
ajst-21812	138	58	0.96	0.96	NUM
ajst-21812	138	59	0.98	0.98	NUM
ajst-21812	138	60	1	1	NUM
ajst-21812	138	61	l1	l1	PROPN
ajst-21812	138	62	/	/	SYM
ajst-21812	138	63	l	l	NOUN
ajst-21812	138	64	ω	ω	PROPN
ajst-21812	138	65	n/	n/	PROPN
ajst-21812	138	66	ω	ω	PROPN
ajst-21812	138	67	n0	n0	PROPN
ajst-21812	138	68	ω1	ω1	PROPN
ajst-21812	138	69	ω2	ω2	PROPN
ajst-21812	138	70	ω3	ω3	PROPN
ajst-21812	138	71	(	(	PUNCT
ajst-21812	138	72	b	b	NOUN
ajst-21812	138	73	)	)	PUNCT
ajst-21812	138	74	c	c	NOUN
ajst-21812	138	75	-	-	PUNCT
ajst-21812	138	76	c	c	NOUN
ajst-21812	138	77	0	0	NUM
ajst-21812	138	78	0.2	0.2	NUM
ajst-21812	138	79	0.4	0.4	NUM
ajst-21812	138	80	0.6	0.6	NUM
ajst-21812	138	81	0.8	0.8	NUM
ajst-21812	138	82	1	1	NUM
ajst-21812	138	83	0.9	0.9	NUM
ajst-21812	138	84	0.92	0.92	NUM
ajst-21812	138	85	0.94	0.94	NUM
ajst-21812	138	86	0.96	0.96	NUM
ajst-21812	138	87	0.98	0.98	NUM
ajst-21812	138	88	1	1	NUM
ajst-21812	138	89	l1	l1	PROPN
ajst-21812	138	90	/	/	SYM
ajst-21812	138	91	l	l	NOUN
ajst-21812	138	92	ω	ω	PROPN
ajst-21812	138	93	n/	n/	PROPN
ajst-21812	138	94	ω	ω	PROPN
ajst-21812	138	95	n0	n0	PROPN
ajst-21812	138	96	ω1	ω1	PROPN
ajst-21812	138	97	ω2	ω2	PROPN
ajst-21812	138	98	ω3	ω3	PROPN
ajst-21812	138	99	(	(	PUNCT
ajst-21812	138	100	c	c	NOUN
ajst-21812	138	101	)	)	PUNCT
ajst-21812	138	102	h	h	NOUN
ajst-21812	138	103	-	-	PUNCT
ajst-21812	138	104	h	h	NOUN
ajst-21812	138	105	0	0	NUM
ajst-21812	138	106	0.2	0.2	NUM
ajst-21812	138	107	0.4	0.4	NUM
ajst-21812	138	108	0.6	0.6	NUM
ajst-21812	138	109	0.8	0.8	NUM
ajst-21812	138	110	1	1	NUM
ajst-21812	138	111	0.94	0.94	NUM
ajst-21812	138	112	0.95	0.95	NUM
ajst-21812	138	113	0.96	0.96	NUM
ajst-21812	138	114	0.97	0.97	NUM
ajst-21812	138	115	0.98	0.98	NUM
ajst-21812	138	116	0.99	0.99	NUM
ajst-21812	138	117	1	1	NUM
ajst-21812	138	118	l	l	NOUN
ajst-21812	138	119	/	/	SYM
ajst-21812	138	120	h=8	h=8	PROPN
ajst-21812	138	121	l	l	NOUN
ajst-21812	138	122	/	/	SYM
ajst-21812	138	123	h=18	h=18	PROPN
ajst-21812	138	124	l	l	NOUN
ajst-21812	138	125	/	/	SYM
ajst-21812	138	126	h=28	h=28	X
ajst-21812	138	127	l1	l1	PROPN
ajst-21812	138	128	/	/	SYM
ajst-21812	138	129	l	l	PROPN
ajst-21812	138	130	ω	ω	PROPN
ajst-21812	138	131	1/	1/	NUM
ajst-21812	138	132	ω	ω	NUM
ajst-21812	138	133	10	10	NUM
ajst-21812	138	134	(	(	PUNCT
ajst-21812	138	135	a	a	NOUN
ajst-21812	138	136	)	)	PUNCT
ajst-21812	138	137	c	c	NOUN
ajst-21812	138	138	-	-	PUNCT
ajst-21812	138	139	f	f	PROPN
ajst-21812	138	140	0	0	NUM
ajst-21812	138	141	0.2	0.2	NUM
ajst-21812	138	142	0.4	0.4	NUM
ajst-21812	138	143	0.6	0.6	NUM
ajst-21812	138	144	0.8	0.8	NUM
ajst-21812	138	145	1	1	NUM
ajst-21812	138	146	0.95	0.95	NUM
ajst-21812	138	147	0.96	0.96	NUM
ajst-21812	138	148	0.97	0.97	NUM
ajst-21812	138	149	0.98	0.98	NUM
ajst-21812	138	150	0.99	0.99	NUM
ajst-21812	138	151	1	1	NUM
ajst-21812	138	152	l	l	NOUN
ajst-21812	138	153	/	/	SYM
ajst-21812	138	154	h=8	h=8	PROPN
ajst-21812	138	155	l	l	NOUN
ajst-21812	138	156	/	/	SYM
ajst-21812	138	157	h=18	h=18	PROPN
ajst-21812	138	158	l	l	NOUN
ajst-21812	138	159	/	/	SYM
ajst-21812	138	160	h=28	h=28	X
ajst-21812	138	161	l1	l1	PROPN
ajst-21812	138	162	/	/	SYM
ajst-21812	138	163	l	l	PROPN
ajst-21812	138	164	ω	ω	PROPN
ajst-21812	138	165	1/	1/	NUM
ajst-21812	138	166	ω	ω	NUM
ajst-21812	138	167	10	10	NUM
ajst-21812	138	168	(	(	PUNCT
ajst-21812	138	169	b	b	NOUN
ajst-21812	138	170	)	)	PUNCT
ajst-21812	138	171	c	c	NOUN
ajst-21812	138	172	-	-	PUNCT
ajst-21812	138	173	c	c	NOUN
ajst-21812	138	174	0	0	NUM
ajst-21812	138	175	0.2	0.2	NUM
ajst-21812	138	176	0.4	0.4	NUM
ajst-21812	138	177	0.6	0.6	NUM
ajst-21812	138	178	0.8	0.8	NUM
ajst-21812	138	179	1	1	NUM
ajst-21812	138	180	0.965	0.965	NUM
ajst-21812	138	181	0.97	0.97	NUM
ajst-21812	138	182	0.975	0.975	NUM
ajst-21812	138	183	0.98	0.98	NUM
ajst-21812	138	184	0.985	0.985	NUM
ajst-21812	138	185	0.99	0.99	NUM
ajst-21812	138	186	0.995	0.995	NUM
ajst-21812	138	187	1	1	NUM
ajst-21812	138	188	l	l	NOUN
ajst-21812	138	189	/	/	SYM
ajst-21812	138	190	h=8	h=8	PROPN
ajst-21812	138	191	l	l	NOUN
ajst-21812	138	192	/	/	SYM
ajst-21812	138	193	h=18	h=18	PROPN
ajst-21812	138	194	l	l	NOUN
ajst-21812	138	195	/	/	SYM
ajst-21812	138	196	h=28	h=28	X
ajst-21812	138	197	l1	l1	PROPN
ajst-21812	138	198	/	/	SYM
ajst-21812	138	199	l	l	PROPN
ajst-21812	138	200	ω	ω	PROPN
ajst-21812	138	201	1/	1/	NUM
ajst-21812	138	202	ω	ω	NUM
ajst-21812	138	203	10	10	NUM
ajst-21812	138	204	(	(	PUNCT
ajst-21812	138	205	c	c	NOUN
ajst-21812	138	206	)	)	PUNCT
ajst-21812	138	207	h	h	NOUN
ajst-21812	138	208	-	-	PUNCT
ajst-21812	138	209	h	h	NOUN
ajst-21812	138	210	269	269	NUM
ajst-21812	138	211	in	in	ADP
ajst-21812	138	212	the	the	DET
ajst-21812	138	213	natural	natural	ADJ
ajst-21812	138	214	frequency	frequency	NOUN
ajst-21812	138	215	ratio	ratio	NOUN
ajst-21812	138	216	,	,	PUNCT
ajst-21812	138	217	indicating	indicate	VERB
ajst-21812	138	218	that	that	SCONJ
ajst-21812	138	219	the	the	DET
ajst-21812	138	220	first	first	ADJ
ajst-21812	138	221	mode	mode	NOUN
ajst-21812	138	222	natural	natural	ADJ
ajst-21812	138	223	frequency	frequency	NOUN
ajst-21812	138	224	of	of	ADP
ajst-21812	138	225	functionally	functionally	ADV
ajst-21812	138	226	graded	grade	VERB
ajst-21812	138	227	beams	beam	NOUN
ajst-21812	138	228	with	with	ADP
ajst-21812	138	229	lower	low	ADJ
ajst-21812	138	230	length	length	NOUN
ajst-21812	138	231	-	-	PUNCT
ajst-21812	138	232	to	to	ADP
ajst-21812	138	233	-	-	PUNCT
ajst-21812	138	234	thickness	thickness	NOUN
ajst-21812	138	235	ratios	ratio	NOUN
ajst-21812	138	236	is	be	AUX
ajst-21812	138	237	more	more	ADV
ajst-21812	138	238	sensitive	sensitive	ADJ
ajst-21812	138	239	to	to	ADP
ajst-21812	138	240	cracks	crack	NOUN
ajst-21812	138	241	.	.	PUNCT
ajst-21812	139	1	5	5	X
ajst-21812	139	2	.	.	X
ajst-21812	139	3	conclusion	conclusion	NOUN
ajst-21812	139	4	this	this	DET
ajst-21812	139	5	paper	paper	NOUN
ajst-21812	139	6	studies	study	NOUN
ajst-21812	139	7	the	the	DET
ajst-21812	139	8	nonlinear	nonlinear	ADJ
ajst-21812	139	9	static	static	ADJ
ajst-21812	139	10	response	response	NOUN
ajst-21812	139	11	of	of	ADP
ajst-21812	139	12	functionally	functionally	ADV
ajst-21812	139	13	graded	grade	VERB
ajst-21812	139	14	material	material	NOUN
ajst-21812	139	15	timoshenko	timoshenko	NOUN
ajst-21812	139	16	beams	beam	NOUN
ajst-21812	139	17	with	with	ADP
ajst-21812	139	18	cracks	crack	NOUN
ajst-21812	139	19	.	.	PUNCT
ajst-21812	140	1	a	a	DET
ajst-21812	140	2	nonlinear	nonlinear	ADJ
ajst-21812	140	3	mechanical	mechanical	ADJ
ajst-21812	140	4	model	model	NOUN
ajst-21812	140	5	of	of	ADP
ajst-21812	140	6	functionally	functionally	ADV
ajst-21812	140	7	graded	grade	VERB
ajst-21812	140	8	material	material	NOUN
ajst-21812	140	9	timoshenko	timoshenko	NOUN
ajst-21812	140	10	beams	beam	NOUN
ajst-21812	140	11	with	with	ADP
ajst-21812	140	12	cracks	crack	NOUN
ajst-21812	140	13	was	be	AUX
ajst-21812	140	14	established	establish	VERB
ajst-21812	140	15	using	use	VERB
ajst-21812	140	16	the	the	DET
ajst-21812	140	17	first	first	ADJ
ajst-21812	140	18	-	-	PUNCT
ajst-21812	140	19	order	order	NOUN
ajst-21812	140	20	shear	shear	NOUN
ajst-21812	140	21	deformation	deformation	NOUN
ajst-21812	140	22	theory	theory	NOUN
ajst-21812	140	23	and	and	CCONJ
ajst-21812	140	24	von	von	PROPN
ajst-21812	140	25	kármán	kármán	PROPN
ajst-21812	140	26	nonlinear	nonlinear	PROPN
ajst-21812	140	27	theory	theory	PROPN
ajst-21812	140	28	.	.	PUNCT
ajst-21812	141	1	the	the	DET
ajst-21812	141	2	influence	influence	NOUN
ajst-21812	141	3	of	of	ADP
ajst-21812	141	4	crack	crack	VERB
ajst-21812	141	5	position	position	NOUN
ajst-21812	141	6	and	and	CCONJ
ajst-21812	141	7	beam	beam	NOUN
ajst-21812	141	8	length	length	NOUN
ajst-21812	141	9	-	-	PUNCT
ajst-21812	141	10	to	to	ADP
ajst-21812	141	11	-	-	PUNCT
ajst-21812	141	12	thickness	thickness	NOUN
ajst-21812	141	13	ratio	ratio	NOUN
ajst-21812	141	14	on	on	ADP
ajst-21812	141	15	the	the	DET
ajst-21812	141	16	system	system	NOUN
ajst-21812	141	17	's	's	PART
ajst-21812	141	18	free	free	ADJ
ajst-21812	141	19	vibration	vibration	NOUN
ajst-21812	141	20	characteristics	characteristic	NOUN
ajst-21812	141	21	under	under	ADP
ajst-21812	141	22	different	different	ADJ
ajst-21812	141	23	boundary	boundary	ADJ
ajst-21812	141	24	conditions	condition	NOUN
ajst-21812	141	25	was	be	AUX
ajst-21812	141	26	analyzed	analyze	VERB
ajst-21812	141	27	.	.	PUNCT
ajst-21812	142	1	numerical	numerical	PROPN
ajst-21812	142	2	results	result	NOUN
ajst-21812	142	3	indicate	indicate	VERB
ajst-21812	142	4	:	:	PUNCT
ajst-21812	142	5	under	under	ADP
ajst-21812	142	6	three	three	NUM
ajst-21812	142	7	different	different	ADJ
ajst-21812	142	8	boundary	boundary	ADJ
ajst-21812	142	9	conditions	condition	NOUN
ajst-21812	142	10	,	,	PUNCT
ajst-21812	142	11	the	the	DET
ajst-21812	142	12	first	first	ADJ
ajst-21812	142	13	mode	mode	NOUN
ajst-21812	142	14	natural	natural	ADJ
ajst-21812	142	15	frequency	frequency	NOUN
ajst-21812	142	16	is	be	AUX
ajst-21812	142	17	always	always	ADV
ajst-21812	142	18	less	less	ADJ
ajst-21812	142	19	than	than	ADP
ajst-21812	142	20	the	the	DET
ajst-21812	142	21	second	second	ADJ
ajst-21812	142	22	mode	mode	NOUN
ajst-21812	142	23	natural	natural	ADJ
ajst-21812	142	24	frequency	frequency	NOUN
ajst-21812	142	25	,	,	PUNCT
ajst-21812	142	26	which	which	PRON
ajst-21812	142	27	in	in	ADP
ajst-21812	142	28	turn	turn	NOUN
ajst-21812	142	29	is	be	AUX
ajst-21812	142	30	less	less	ADJ
ajst-21812	142	31	than	than	ADP
ajst-21812	142	32	the	the	DET
ajst-21812	142	33	third	third	ADJ
ajst-21812	142	34	mode	mode	NOUN
ajst-21812	142	35	natural	natural	ADJ
ajst-21812	142	36	frequency	frequency	NOUN
ajst-21812	142	37	for	for	ADP
ajst-21812	142	38	different	different	ADJ
ajst-21812	142	39	relative	relative	ADJ
ajst-21812	142	40	crack	crack	NOUN
ajst-21812	142	41	positions	position	NOUN
ajst-21812	142	42	in	in	ADP
ajst-21812	142	43	the	the	DET
ajst-21812	142	44	cracked	crack	VERB
ajst-21812	142	45	beam	beam	NOUN
ajst-21812	142	46	.	.	PUNCT
ajst-21812	143	1	additionally	additionally	ADV
ajst-21812	143	2	,	,	PUNCT
ajst-21812	143	3	when	when	SCONJ
ajst-21812	143	4	the	the	DET
ajst-21812	143	5	relative	relative	ADJ
ajst-21812	143	6	crack	crack	NOUN
ajst-21812	143	7	position	position	NOUN
ajst-21812	143	8	takes	take	VERB
ajst-21812	143	9	specific	specific	ADJ
ajst-21812	143	10	values	value	NOUN
ajst-21812	143	11	,	,	PUNCT
ajst-21812	143	12	the	the	DET
ajst-21812	143	13	natural	natural	ADJ
ajst-21812	143	14	frequency	frequency	NOUN
ajst-21812	143	15	ratio	ratio	NOUN
ajst-21812	143	16	equals	equal	VERB
ajst-21812	143	17	1	1	NUM
ajst-21812	143	18	,	,	PUNCT
ajst-21812	143	19	indicating	indicate	VERB
ajst-21812	143	20	that	that	SCONJ
ajst-21812	143	21	the	the	DET
ajst-21812	143	22	crack	crack	NOUN
ajst-21812	143	23	at	at	ADP
ajst-21812	143	24	the	the	DET
ajst-21812	143	25	current	current	ADJ
ajst-21812	143	26	position	position	NOUN
ajst-21812	143	27	does	do	AUX
ajst-21812	143	28	not	not	PART
ajst-21812	143	29	impact	impact	VERB
ajst-21812	143	30	a	a	DET
ajst-21812	143	31	certain	certain	ADJ
ajst-21812	143	32	mode	mode	NOUN
ajst-21812	143	33	of	of	ADP
ajst-21812	143	34	natural	natural	ADJ
ajst-21812	143	35	frequency	frequency	NOUN
ajst-21812	143	36	in	in	ADP
ajst-21812	143	37	the	the	DET
ajst-21812	143	38	beam	beam	NOUN
ajst-21812	143	39	.	.	PUNCT
ajst-21812	144	1	the	the	DET
ajst-21812	144	2	increase	increase	NOUN
ajst-21812	144	3	in	in	ADP
ajst-21812	144	4	the	the	DET
ajst-21812	144	5	length	length	NOUN
ajst-21812	144	6	-	-	PUNCT
ajst-21812	144	7	to	to	ADP
ajst-21812	144	8	-	-	PUNCT
ajst-21812	144	9	thickness	thickness	NOUN
ajst-21812	144	10	ratio	ratio	NOUN
ajst-21812	144	11	also	also	ADV
ajst-21812	144	12	does	do	AUX
ajst-21812	144	13	not	not	PART
ajst-21812	144	14	change	change	VERB
ajst-21812	144	15	the	the	DET
ajst-21812	144	16	relative	relative	ADJ
ajst-21812	144	17	crack	crack	NOUN
ajst-21812	144	18	positions	position	NOUN
ajst-21812	144	19	at	at	ADP
ajst-21812	144	20	which	which	PRON
ajst-21812	144	21	the	the	DET
ajst-21812	144	22	minimum	minimum	ADJ
ajst-21812	144	23	and	and	CCONJ
ajst-21812	144	24	maximum	maximum	ADJ
ajst-21812	144	25	natural	natural	ADJ
ajst-21812	144	26	frequency	frequency	NOUN
ajst-21812	144	27	ratios	ratio	NOUN
ajst-21812	144	28	occur	occur	VERB
ajst-21812	144	29	for	for	ADP
ajst-21812	144	30	each	each	DET
ajst-21812	144	31	mode	mode	NOUN
ajst-21812	144	32	.	.	PUNCT
ajst-21812	145	1	references	reference	NOUN
ajst-21812	145	2	[	[	X
ajst-21812	145	3	1	1	NUM
ajst-21812	145	4	]	]	PUNCT
ajst-21812	145	5	irwin	irwin	PROPN
ajst-21812	145	6	g	g	PROPN
ajst-21812	145	7	r.	r.	PROPN
ajst-21812	145	8	analyses	analysis	NOUN
ajst-21812	145	9	of	of	ADP
ajst-21812	145	10	stresses	stress	NOUN
ajst-21812	145	11	and	and	CCONJ
ajst-21812	145	12	strains	strain	NOUN
ajst-21812	145	13	near	near	ADP
ajst-21812	145	14	the	the	DET
ajst-21812	145	15	end	end	NOUN
ajst-21812	145	16	of	of	ADP
ajst-21812	145	17	a	a	DET
ajst-21812	145	18	crack	crack	NOUN
ajst-21812	145	19	transversing	transverse	VERB
ajst-21812	145	20	a	a	DET
ajst-21812	145	21	plate[j	plate[j	NOUN
ajst-21812	145	22	]	]	PUNCT
ajst-21812	145	23	.	.	PUNCT
ajst-21812	146	1	appl	appl	PROPN
ajst-21812	146	2	mech	mech	PROPN
ajst-21812	146	3	,	,	PUNCT
ajst-21812	146	4	1957	1957	NUM
ajst-21812	146	5	,	,	PUNCT
ajst-21812	146	6	24	24	NUM
ajst-21812	146	7	:	:	SYM
ajst-21812	146	8	361	361	NUM
ajst-21812	146	9	-	-	SYM
ajst-21812	146	10	364	364	NUM
ajst-21812	146	11	.	.	PUNCT
ajst-21812	147	1	[	[	X
ajst-21812	147	2	2	2	X
ajst-21812	147	3	]	]	PUNCT
ajst-21812	147	4	sourki	sourki	NOUN
ajst-21812	147	5	r	r	NOUN
ajst-21812	147	6	,	,	PUNCT
ajst-21812	147	7	hoseini	hoseini	NOUN
ajst-21812	147	8	s	s	PROPN
ajst-21812	147	9	a	a	DET
ajst-21812	147	10	h.	h.	NOUN
ajst-21812	147	11	free	free	ADJ
ajst-21812	147	12	vibration	vibration	NOUN
ajst-21812	147	13	analysis	analysis	NOUN
ajst-21812	147	14	of	of	ADP
ajst-21812	147	15	sizedependent	sizedependent	NOUN
ajst-21812	147	16	cracked	crack	VERB
ajst-21812	147	17	microbeam	microbeam	NOUN
ajst-21812	147	18	based	base	VERB
ajst-21812	147	19	on	on	ADP
ajst-21812	147	20	the	the	DET
ajst-21812	147	21	modified	modify	VERB
ajst-21812	147	22	couple	couple	NOUN
ajst-21812	147	23	stress	stress	NOUN
ajst-21812	147	24	theory[j	theory[j	NOUN
ajst-21812	147	25	]	]	PUNCT
ajst-21812	147	26	.	.	PUNCT
ajst-21812	148	1	applied	apply	VERB
ajst-21812	148	2	physics	physics	PROPN
ajst-21812	148	3	a	a	PRON
ajst-21812	148	4	,	,	PUNCT
ajst-21812	148	5	2016	2016	NUM
ajst-21812	148	6	,	,	PUNCT
ajst-21812	148	7	122(4	122(4	NUM
ajst-21812	148	8	):	):	PUNCT
ajst-21812	148	9	413	413	NUM
ajst-21812	148	10	.	.	PUNCT
ajst-21812	149	1	[	[	X
ajst-21812	149	2	3	3	NUM
ajst-21812	149	3	]	]	PUNCT
ajst-21812	149	4	torabi	torabi	NOUN
ajst-21812	149	5	k	k	NOUN
ajst-21812	149	6	,	,	PUNCT
ajst-21812	149	7	dastgerdi	dastgerdi	PROPN
ajst-21812	149	8	j	j	PROPN
ajst-21812	149	9	n.	n.	PROPN
ajst-21812	149	10	an	an	DET
ajst-21812	149	11	analytical	analytical	ADJ
ajst-21812	149	12	method	method	NOUN
ajst-21812	149	13	for	for	ADP
ajst-21812	149	14	free	free	ADJ
ajst-21812	149	15	vibration	vibration	NOUN
ajst-21812	149	16	analysis	analysis	NOUN
ajst-21812	149	17	of	of	ADP
ajst-21812	149	18	timoshenko	timoshenko	ADJ
ajst-21812	149	19	beam	beam	NOUN
ajst-21812	149	20	theory	theory	NOUN
ajst-21812	149	21	applied	apply	VERB
ajst-21812	149	22	to	to	ADP
ajst-21812	149	23	cracked	crack	VERB
ajst-21812	149	24	nanobeams	nanobeam	NOUN
ajst-21812	149	25	using	use	VERB
ajst-21812	149	26	a	a	DET
ajst-21812	149	27	nonlocal	nonlocal	ADJ
ajst-21812	149	28	elasticity	elasticity	NOUN
ajst-21812	149	29	model[j	model[j	PROPN
ajst-21812	149	30	]	]	PUNCT
ajst-21812	149	31	.	.	PUNCT
ajst-21812	150	1	thin	thin	ADJ
ajst-21812	150	2	solid	solid	ADJ
ajst-21812	150	3	films	film	NOUN
ajst-21812	150	4	,	,	PUNCT
ajst-21812	150	5	2012	2012	NUM
ajst-21812	150	6	,	,	PUNCT
ajst-21812	150	7	520(21	520(21	NUM
ajst-21812	150	8	):	):	PUNCT
ajst-21812	150	9	6595	6595	NUM
ajst-21812	150	10	-	-	SYM
ajst-21812	150	11	6602	6602	NUM
ajst-21812	150	12	.	.	PUNCT
ajst-21812	151	1	[	[	X
ajst-21812	151	2	4	4	X
ajst-21812	151	3	]	]	X
ajst-21812	151	4	taima	taima	PROPN
ajst-21812	151	5	m	m	PROPN
ajst-21812	151	6	s	s	PROPN
ajst-21812	151	7	,	,	PUNCT
ajst-21812	151	8	el	el	PROPN
ajst-21812	151	9	-	-	PUNCT
ajst-21812	151	10	sayed	sayed	PROPN
ajst-21812	151	11	t	t	PROPN
ajst-21812	151	12	a	a	X
ajst-21812	151	13	,	,	PUNCT
ajst-21812	151	14	shehab	shehab	PROPN
ajst-21812	151	15	m	m	PROPN
ajst-21812	151	16	b	b	NOUN
ajst-21812	151	17	,	,	PUNCT
ajst-21812	151	18	et	et	PROPN
ajst-21812	151	19	al	al	PROPN
ajst-21812	151	20	.	.	PROPN
ajst-21812	151	21	vibration	vibration	NOUN
ajst-21812	151	22	analysis	analysis	NOUN
ajst-21812	151	23	of	of	ADP
ajst-21812	151	24	cracked	crack	VERB
ajst-21812	151	25	beam	beam	NOUN
ajst-21812	151	26	based	base	VERB
ajst-21812	151	27	on	on	ADP
ajst-21812	151	28	reddy	reddy	PROPN
ajst-21812	151	29	beam	beam	PROPN
ajst-21812	151	30	theory	theory	NOUN
ajst-21812	151	31	by	by	ADP
ajst-21812	151	32	finite	finite	PROPN
ajst-21812	151	33	element	element	PROPN
ajst-21812	151	34	method[j	method[j	PROPN
ajst-21812	151	35	]	]	PUNCT
ajst-21812	151	36	.	.	PUNCT
ajst-21812	152	1	journal	journal	PROPN
ajst-21812	152	2	of	of	ADP
ajst-21812	152	3	vibration	vibration	NOUN
ajst-21812	152	4	and	and	CCONJ
ajst-21812	152	5	control	control	NOUN
ajst-21812	152	6	,	,	PUNCT
ajst-21812	152	7	2023	2023	NUM
ajst-21812	152	8	,	,	PUNCT
ajst-21812	152	9	29(19	29(19	NUM
ajst-21812	152	10	-	-	PUNCT
ajst-21812	152	11	20):4589	20):4589	NUM
ajst-21812	152	12	-	-	PUNCT
ajst-21812	152	13	4606	4606	NUM
ajst-21812	152	14	.	.	PUNCT
ajst-21812	153	1	[	[	X
ajst-21812	153	2	5	5	NUM
ajst-21812	153	3	]	]	X
ajst-21812	153	4	zhao	zhao	PROPN
ajst-21812	153	5	x	x	PROPN
ajst-21812	153	6	,	,	PUNCT
ajst-21812	153	7	zhao	zhao	PROPN
ajst-21812	153	8	y	y	PROPN
ajst-21812	153	9	r	r	PROPN
ajst-21812	153	10	,	,	PUNCT
ajst-21812	153	11	gao	gao	PROPN
ajst-21812	153	12	x	x	PROPN
ajst-21812	153	13	z	z	PROPN
ajst-21812	153	14	,	,	PUNCT
ajst-21812	153	15	et	et	PROPN
ajst-21812	153	16	al	al	PROPN
ajst-21812	153	17	.	.	PUNCT
ajst-21812	153	18	green׳	green׳	PROPN
ajst-21812	153	19	s	s	NOUN
ajst-21812	153	20	functions	function	NOUN
ajst-21812	153	21	for	for	ADP
ajst-21812	153	22	the	the	DET
ajst-21812	153	23	forced	force	VERB
ajst-21812	153	24	vibrations	vibration	NOUN
ajst-21812	153	25	of	of	ADP
ajst-21812	153	26	cracked	crack	VERB
ajst-21812	153	27	euler	euler	NOUN
ajst-21812	153	28	–	–	PUNCT
ajst-21812	153	29	bernoulli	bernoulli	PROPN
ajst-21812	153	30	beams[j	beams[j	NOUN
ajst-21812	153	31	]	]	PUNCT
ajst-21812	153	32	.	.	PUNCT
ajst-21812	154	1	mechanical	mechanical	ADJ
ajst-21812	154	2	systems	system	NOUN
ajst-21812	154	3	and	and	CCONJ
ajst-21812	154	4	signal	signal	NOUN
ajst-21812	154	5	processing	processing	NOUN
ajst-21812	154	6	,	,	PUNCT
ajst-21812	154	7	201668	201668	NUM
ajst-21812	154	8	:	:	PUNCT
ajst-21812	154	9	155	155	NUM
ajst-21812	154	10	-	-	SYM
ajst-21812	154	11	175	175	NUM
ajst-21812	154	12	.	.	PUNCT
ajst-21812	155	1	[	[	X
ajst-21812	155	2	6	6	NUM
ajst-21812	155	3	]	]	X
ajst-21812	155	4	zhao	zhao	PROPN
ajst-21812	155	5	x	x	PROPN
ajst-21812	155	6	,	,	PUNCT
ajst-21812	155	7	chen	chen	PROPN
ajst-21812	155	8	b	b	PROPN
ajst-21812	155	9	,	,	PUNCT
ajst-21812	155	10	li	li	PROPN
ajst-21812	155	11	y	y	PROPN
ajst-21812	155	12	h	h	PROPN
ajst-21812	155	13	,	,	PUNCT
ajst-21812	155	14	et	et	PROPN
ajst-21812	155	15	al	al	PROPN
ajst-21812	155	16	.	.	PROPN
ajst-21812	155	17	forced	force	VERB
ajst-21812	155	18	vibration	vibration	NOUN
ajst-21812	155	19	analysis	analysis	NOUN
ajst-21812	155	20	of	of	ADP
ajst-21812	155	21	timoshenko	timoshenko	ADJ
ajst-21812	155	22	double	double	ADJ
ajst-21812	155	23	-	-	PUNCT
ajst-21812	155	24	beam	beam	NOUN
ajst-21812	155	25	system	system	NOUN
ajst-21812	155	26	under	under	ADP
ajst-21812	155	27	compressive	compressive	ADJ
ajst-21812	155	28	axial	axial	ADJ
ajst-21812	155	29	load	load	NOUN
ajst-21812	155	30	by	by	ADP
ajst-21812	155	31	means	mean	NOUN
ajst-21812	155	32	of	of	ADP
ajst-21812	155	33	green's	green's	PROPN
ajst-21812	155	34	functions[j	functions[j	PROPN
ajst-21812	155	35	]	]	PUNCT
ajst-21812	155	36	.	.	PUNCT
ajst-21812	156	1	journal	journal	PROPN
ajst-21812	156	2	of	of	ADP
ajst-21812	156	3	sound	sound	NOUN
ajst-21812	156	4	and	and	CCONJ
ajst-21812	156	5	vibration	vibration	NOUN
ajst-21812	156	6	,	,	PUNCT
ajst-21812	156	7	2020	2020	NUM
ajst-21812	156	8	,	,	PUNCT
ajst-21812	156	9	464	464	NUM
ajst-21812	156	10	:	:	PUNCT
ajst-21812	156	11	11500	11500	NUM
ajst-21812	156	12	.	.	PUNCT
ajst-21812	157	1	[	[	X
ajst-21812	157	2	7	7	X
ajst-21812	157	3	]	]	X
ajst-21812	157	4	loya	loya	PROPN
ajst-21812	157	5	j	j	PROPN
ajst-21812	157	6	a	a	PROPN
ajst-21812	157	7	,	,	PUNCT
ajst-21812	157	8	aranda	aranda	NOUN
ajst-21812	157	9	-	-	PUNCT
ajst-21812	157	10	ruiz	ruiz	PROPN
ajst-21812	157	11	j	j	PROPN
ajst-21812	157	12	,	,	PUNCT
ajst-21812	157	13	zaera	zaera	PROPN
ajst-21812	157	14	r.	r.	PROPN
ajst-21812	157	15	natural	natural	ADJ
ajst-21812	157	16	frequencies	frequency	NOUN
ajst-21812	157	17	of	of	ADP
ajst-21812	157	18	vibration	vibration	NOUN
ajst-21812	157	19	in	in	ADP
ajst-21812	157	20	cracked	crack	VERB
ajst-21812	157	21	timoshenko	timoshenko	NOUN
ajst-21812	157	22	beams	beam	NOUN
ajst-21812	157	23	within	within	ADP
ajst-21812	157	24	an	an	DET
ajst-21812	157	25	elastic	elastic	ADJ
ajst-21812	157	26	medium[j	medium[j	NOUN
ajst-21812	157	27	]	]	PUNCT
ajst-21812	157	28	.	.	PUNCT
ajst-21812	158	1	theoretical	theoretical	ADJ
ajst-21812	158	2	and	and	CCONJ
ajst-21812	158	3	applied	apply	VERB
ajst-21812	158	4	fracture	fracture	NOUN
ajst-21812	158	5	mechanics	mechanic	NOUN
ajst-21812	158	6	,	,	PUNCT
ajst-21812	158	7	2022	2022	NUM
ajst-21812	158	8	,	,	PUNCT
ajst-21812	158	9	118	118	NUM
ajst-21812	158	10	:	:	SYM
ajst-21812	158	11	103257	103257	NUM
ajst-21812	158	12	.	.	PUNCT
ajst-21812	159	1	[	[	X
ajst-21812	159	2	8	8	NUM
ajst-21812	159	3	]	]	X
ajst-21812	159	4	chen	chen	PROPN
ajst-21812	159	5	b	b	PROPN
ajst-21812	159	6	,	,	PUNCT
ajst-21812	159	7	lin	lin	PROPN
ajst-21812	159	8	b	b	PROPN
ajst-21812	159	9	,	,	PUNCT
ajst-21812	159	10	zhao	zhao	PROPN
ajst-21812	159	11	x	x	PROPN
ajst-21812	159	12	,	,	PUNCT
ajst-21812	159	13	et	et	PROPN
ajst-21812	159	14	al	al	PROPN
ajst-21812	159	15	.	.	PROPN
ajst-21812	159	16	closed	close	VERB
ajst-21812	159	17	-	-	PUNCT
ajst-21812	159	18	form	form	NOUN
ajst-21812	159	19	solutions	solution	NOUN
ajst-21812	159	20	for	for	ADP
ajst-21812	159	21	forced	force	VERB
ajst-21812	159	22	vibrations	vibration	NOUN
ajst-21812	159	23	of	of	ADP
ajst-21812	159	24	a	a	DET
ajst-21812	159	25	cracked	crack	VERB
ajst-21812	159	26	doublebeam	doublebeam	NOUN
ajst-21812	159	27	system	system	NOUN
ajst-21812	159	28	interconnected	interconnect	VERB
ajst-21812	159	29	by	by	ADP
ajst-21812	159	30	a	a	DET
ajst-21812	159	31	viscoelastic	viscoelastic	ADJ
ajst-21812	159	32	layer	layer	NOUN
ajst-21812	159	33	resting	rest	VERB
ajst-21812	159	34	on	on	ADP
ajst-21812	159	35	winkler	winkler	NOUN
ajst-21812	159	36	–	–	PUNCT
ajst-21812	159	37	pasternak	pasternak	NOUN
ajst-21812	159	38	elastic	elastic	ADJ
ajst-21812	159	39	foundation[j	foundation[j	PROPN
ajst-21812	159	40	]	]	PUNCT
ajst-21812	159	41	.	.	PUNCT
ajst-21812	160	1	thin	thin	ADJ
ajst-21812	160	2	-	-	PUNCT
ajst-21812	160	3	walled	walled	ADJ
ajst-21812	160	4	structures	structure	NOUN
ajst-21812	160	5	,	,	PUNCT
ajst-21812	160	6	2021	2021	NUM
ajst-21812	160	7	,	,	PUNCT
ajst-21812	160	8	163	163	NUM
ajst-21812	160	9	:	:	SYM
ajst-21812	160	10	107688	107688	NUM
ajst-21812	160	11	.	.	PUNCT
ajst-21812	161	1	[	[	X
ajst-21812	161	2	9	9	NUM
ajst-21812	161	3	]	]	PUNCT
ajst-21812	161	4	erdogan	erdogan	NOUN
ajst-21812	161	5	f	f	X
ajst-21812	161	6	,	,	PUNCT
ajst-21812	161	7	wu	wu	PROPN
ajst-21812	161	8	b	b	PROPN
ajst-21812	161	9	h.	h.	PROPN
ajst-21812	161	10	the	the	DET
ajst-21812	161	11	surface	surface	NOUN
ajst-21812	161	12	crack	crack	NOUN
ajst-21812	161	13	problem	problem	NOUN
ajst-21812	161	14	for	for	ADP
ajst-21812	161	15	a	a	DET
ajst-21812	161	16	plate	plate	NOUN
ajst-21812	161	17	with	with	ADP
ajst-21812	161	18	functionally	functionally	ADV
ajst-21812	161	19	graded	grade	VERB
ajst-21812	161	20	properties[j].journal	properties[j].journal	ADJ
ajst-21812	161	21	of	of	ADP
ajst-21812	161	22	applied	applied	ADJ
ajst-21812	161	23	mechanics	mechanic	NOUN
ajst-21812	161	24	,	,	PUNCT
ajst-21812	161	25	1997	1997	NUM
ajst-21812	161	26	,	,	PUNCT
ajst-21812	161	27	64(3	64(3	NUM
ajst-21812	161	28	):	):	PUNCT
ajst-21812	161	29	449	449	NUM
ajst-21812	161	30	-	-	NOUN
ajst-21812	161	31	456	456	NUM
ajst-21812	161	32	.	.	PUNCT