id	sid	tid	token	lemma	pos
fumecheng-13737	1	1	13737	13737	NUM
fumecheng-13737	1	2	facta	facta	NOUN
fumecheng-13737	1	3	universitatis	universitatis	PROPN
fumecheng-13737	1	4	series	series	NOUN
fumecheng-13737	1	5	:	:	PUNCT
fumecheng-13737	1	6	mechanical	mechanical	ADJ
fumecheng-13737	1	7	engineering	engineering	NOUN
fumecheng-13737	1	8	vol	vol	NOUN
fumecheng-13737	1	9	.	.	PROPN
fumecheng-13737	1	10	23	23	NUM
fumecheng-13737	1	11	,	,	PUNCT
fumecheng-13737	1	12	no	no	DET
fumecheng-13737	1	13	4	4	NUM
fumecheng-13737	1	14	,	,	PUNCT
fumecheng-13737	1	15	2025	2025	NUM
fumecheng-13737	1	16	,	,	PUNCT
fumecheng-13737	1	17	pp	pp	ADJ
fumecheng-13737	1	18	.	.	PUNCT
fumecheng-13737	2	1	787	787	NUM
fumecheng-13737	2	2	806	806	NUM
fumecheng-13737	2	3	https://doi.org/10.22190/fume250525028h	https://doi.org/10.22190/fume250525028h	PROPN
fumecheng-13737	2	4	©	©	PROPN
fumecheng-13737	2	5	2025	2025	NUM
fumecheng-13737	2	6	by	by	ADP
fumecheng-13737	2	7	university	university	PROPN
fumecheng-13737	2	8	of	of	ADP
fumecheng-13737	2	9	niš	niš	PROPN
fumecheng-13737	2	10	,	,	PUNCT
fumecheng-13737	2	11	serbia	serbia	PROPN
fumecheng-13737	2	12	|	|	ADV
fumecheng-13737	2	13	creative	creative	ADJ
fumecheng-13737	2	14	commons	common	NOUN
fumecheng-13737	2	15	license	license	NOUN
fumecheng-13737	2	16	:	:	PUNCT
fumecheng-13737	2	17	cc	cc	VERB
fumecheng-13737	2	18	by	by	ADP
fumecheng-13737	2	19	-	-	PUNCT
fumecheng-13737	2	20	nc	nc	VERB
fumecheng-13737	2	21	-	-	PUNCT
fumecheng-13737	2	22	nd	nd	ADV
fumecheng-13737	2	23	original	original	ADJ
fumecheng-13737	2	24	scientific	scientific	NOUN
fumecheng-13737	2	25	paper	paper	VERB
fumecheng-13737	2	26	a	a	DET
fumecheng-13737	2	27	fast	fast	ADJ
fumecheng-13737	2	28	insight	insight	NOUN
fumecheng-13737	2	29	into	into	ADP
fumecheng-13737	2	30	high	high	ADJ
fumecheng-13737	2	31	-	-	PUNCT
fumecheng-13737	2	32	accuracy	accuracy	NOUN
fumecheng-13737	2	33	nonlinear	nonlinear	ADJ
fumecheng-13737	2	34	frequency	frequency	NOUN
fumecheng-13737	2	35	estimation	estimation	NOUN
fumecheng-13737	2	36	of	of	ADP
fumecheng-13737	2	37	stringer	stringer	NOUN
fumecheng-13737	2	38	-	-	PUNCT
fumecheng-13737	2	39	stiffened	stiffen	VERB
fumecheng-13737	2	40	shells	shell	NOUN
fumecheng-13737	2	41	chun	chun	PROPN
fumecheng-13737	2	42	-	-	PUNCT
fumecheng-13737	2	43	hui	hui	PROPN
fumecheng-13737	2	44	he1	he1	PROPN
fumecheng-13737	2	45	,	,	PUNCT
fumecheng-13737	2	46	mostafa	mostafa	PROPN
fumecheng-13737	2	47	mohammadian2	mohammadian2	PROPN
fumecheng-13737	3	1	1school	1school	NUM
fumecheng-13737	3	2	of	of	ADP
fumecheng-13737	3	3	civil	civil	ADJ
fumecheng-13737	3	4	engineering	engineering	NOUN
fumecheng-13737	3	5	and	and	CCONJ
fumecheng-13737	3	6	transportation	transportation	NOUN
fumecheng-13737	3	7	,	,	PUNCT
fumecheng-13737	3	8	foshan	foshan	PROPN
fumecheng-13737	3	9	university	university	PROPN
fumecheng-13737	3	10	,	,	PUNCT
fumecheng-13737	3	11	foshan	foshan	PROPN
fumecheng-13737	3	12	,	,	PUNCT
fumecheng-13737	3	13	china	china	PROPN
fumecheng-13737	3	14	2mechanical	2mechanical	ADJ
fumecheng-13737	3	15	engineering	engineering	NOUN
fumecheng-13737	3	16	department	department	NOUN
fumecheng-13737	3	17	,	,	PUNCT
fumecheng-13737	3	18	esfarayen	esfarayen	NOUN
fumecheng-13737	3	19	university	university	PROPN
fumecheng-13737	3	20	of	of	ADP
fumecheng-13737	3	21	technology	technology	NOUN
fumecheng-13737	3	22	,	,	PUNCT
fumecheng-13737	3	23	esfarayen	esfarayen	NOUN
fumecheng-13737	3	24	,	,	PUNCT
fumecheng-13737	3	25	north	north	NOUN
fumecheng-13737	3	26	khorasan	khorasan	PROPN
fumecheng-13737	3	27	,	,	PUNCT
fumecheng-13737	3	28	iran	iran	PROPN
fumecheng-13737	3	29	orcid	orcid	PROPN
fumecheng-13737	3	30	ids	id	NOUN
fumecheng-13737	3	31	:	:	PUNCT
fumecheng-13737	3	32	chun	chun	PROPN
fumecheng-13737	3	33	-	-	PUNCT
fumecheng-13737	3	34	hui	hui	PROPN
fumecheng-13737	4	1	he	he	PRON
fumecheng-13737	4	2	https://orcid.org/0000-0003-0810-5248	https://orcid.org/0000-0003-0810-5248	PROPN
fumecheng-13737	4	3	mostafa	mostafa	PROPN
fumecheng-13737	4	4	mohammadian	mohammadian	PROPN
fumecheng-13737	4	5	http://orcid.org/0000-0002-0714-2787	http://orcid.org/0000-0002-0714-2787	PROPN
fumecheng-13737	4	6	abstract	abstract	NOUN
fumecheng-13737	4	7	.	.	PUNCT
fumecheng-13737	5	1	understanding	understand	VERB
fumecheng-13737	5	2	the	the	DET
fumecheng-13737	5	3	behavior	behavior	NOUN
fumecheng-13737	5	4	of	of	ADP
fumecheng-13737	5	5	nonlinear	nonlinear	ADJ
fumecheng-13737	5	6	vibrations	vibration	NOUN
fumecheng-13737	5	7	in	in	ADP
fumecheng-13737	5	8	stringer	stringer	NOUN
fumecheng-13737	5	9	-	-	PUNCT
fumecheng-13737	5	10	stiffened	stiffen	VERB
fumecheng-13737	5	11	shell	shell	NOUN
fumecheng-13737	5	12	structures	structure	NOUN
fumecheng-13737	5	13	is	be	AUX
fumecheng-13737	5	14	crucial	crucial	ADJ
fumecheng-13737	5	15	for	for	ADP
fumecheng-13737	5	16	enhancing	enhance	VERB
fumecheng-13737	5	17	the	the	DET
fumecheng-13737	5	18	stability	stability	NOUN
fumecheng-13737	5	19	and	and	CCONJ
fumecheng-13737	5	20	efficiency	efficiency	NOUN
fumecheng-13737	5	21	of	of	ADP
fumecheng-13737	5	22	advanced	advanced	ADJ
fumecheng-13737	5	23	aerospace	aerospace	NOUN
fumecheng-13737	5	24	and	and	CCONJ
fumecheng-13737	5	25	marine	marine	ADJ
fumecheng-13737	5	26	systems	system	NOUN
fumecheng-13737	5	27	.	.	PUNCT
fumecheng-13737	6	1	these	these	DET
fumecheng-13737	6	2	systems	system	NOUN
fumecheng-13737	6	3	often	often	ADV
fumecheng-13737	6	4	exhibit	exhibit	VERB
fumecheng-13737	6	5	complex	complex	ADJ
fumecheng-13737	6	6	responses	response	NOUN
fumecheng-13737	6	7	due	due	ADJ
fumecheng-13737	6	8	to	to	ADP
fumecheng-13737	6	9	geometric	geometric	ADJ
fumecheng-13737	6	10	and	and	CCONJ
fumecheng-13737	6	11	material	material	NOUN
fumecheng-13737	6	12	intricacies	intricacy	NOUN
fumecheng-13737	6	13	,	,	PUNCT
fumecheng-13737	6	14	which	which	PRON
fumecheng-13737	6	15	require	require	VERB
fumecheng-13737	6	16	analytical	analytical	ADJ
fumecheng-13737	6	17	methods	method	NOUN
fumecheng-13737	6	18	capable	capable	ADJ
fumecheng-13737	6	19	of	of	ADP
fumecheng-13737	6	20	effectively	effectively	ADV
fumecheng-13737	6	21	capturing	capture	VERB
fumecheng-13737	6	22	critical	critical	ADJ
fumecheng-13737	6	23	dynamics	dynamic	NOUN
fumecheng-13737	6	24	.	.	PUNCT
fumecheng-13737	7	1	this	this	DET
fumecheng-13737	7	2	study	study	NOUN
fumecheng-13737	7	3	presents	present	VERB
fumecheng-13737	7	4	three	three	NUM
fumecheng-13737	7	5	efficient	efficient	ADJ
fumecheng-13737	7	6	analytical	analytical	ADJ
fumecheng-13737	7	7	methods	method	NOUN
fumecheng-13737	7	8	for	for	ADP
fumecheng-13737	7	9	deriving	derive	VERB
fumecheng-13737	7	10	closedform	closedform	NOUN
fumecheng-13737	7	11	expressions	expression	NOUN
fumecheng-13737	7	12	for	for	ADP
fumecheng-13737	7	13	the	the	DET
fumecheng-13737	7	14	nonlinear	nonlinear	ADJ
fumecheng-13737	7	15	frequency	frequency	NOUN
fumecheng-13737	7	16	of	of	ADP
fumecheng-13737	7	17	such	such	ADJ
fumecheng-13737	7	18	systems	system	NOUN
fumecheng-13737	7	19	:	:	PUNCT
fumecheng-13737	7	20	the	the	DET
fumecheng-13737	7	21	adaptive	adaptive	ADJ
fumecheng-13737	7	22	location	location	NOUN
fumecheng-13737	7	23	pointbased	pointbase	VERB
fumecheng-13737	7	24	he	he	PRON
fumecheng-13737	7	25	’s	’	VERB
fumecheng-13737	7	26	formulation	formulation	NOUN
fumecheng-13737	7	27	(	(	PUNCT
fumecheng-13737	7	28	alpf	alpf	PROPN
fumecheng-13737	7	29	)	)	PUNCT
fumecheng-13737	7	30	,	,	PUNCT
fumecheng-13737	7	31	the	the	DET
fumecheng-13737	7	32	square	square	ADJ
fumecheng-13737	7	33	error	error	NOUN
fumecheng-13737	7	34	minimizing	minimizing	NOUN
fumecheng-13737	7	35	-	-	PUNCT
fumecheng-13737	7	36	based	base	VERB
fumecheng-13737	7	37	frequency	frequency	NOUN
fumecheng-13737	7	38	formulation	formulation	NOUN
fumecheng-13737	7	39	(	(	PUNCT
fumecheng-13737	7	40	semf	semf	NOUN
fumecheng-13737	7	41	)	)	PUNCT
fumecheng-13737	7	42	,	,	PUNCT
fumecheng-13737	7	43	and	and	CCONJ
fumecheng-13737	7	44	the	the	DET
fumecheng-13737	7	45	hamiltonian	hamiltonian	NOUN
fumecheng-13737	7	46	-	-	PUNCT
fumecheng-13737	7	47	based	base	VERB
fumecheng-13737	7	48	frequency	frequency	NOUN
fumecheng-13737	7	49	-	-	PUNCT
fumecheng-13737	7	50	amplitude	amplitude	NOUN
fumecheng-13737	7	51	formulation	formulation	NOUN
fumecheng-13737	7	52	(	(	PUNCT
fumecheng-13737	7	53	hfaf	hfaf	NOUN
fumecheng-13737	7	54	)	)	PUNCT
fumecheng-13737	7	55	.	.	PUNCT
fumecheng-13737	8	1	these	these	DET
fumecheng-13737	8	2	methods	method	NOUN
fumecheng-13737	8	3	offer	offer	VERB
fumecheng-13737	8	4	efficient	efficient	ADJ
fumecheng-13737	8	5	and	and	CCONJ
fumecheng-13737	8	6	straightforward	straightforward	ADJ
fumecheng-13737	8	7	solutions	solution	NOUN
fumecheng-13737	8	8	for	for	ADP
fumecheng-13737	8	9	analyzing	analyze	VERB
fumecheng-13737	8	10	nonlinear	nonlinear	ADJ
fumecheng-13737	8	11	oscillators	oscillator	NOUN
fumecheng-13737	8	12	without	without	ADP
fumecheng-13737	8	13	requiring	require	VERB
fumecheng-13737	8	14	complex	complex	ADJ
fumecheng-13737	8	15	iterative	iterative	NOUN
fumecheng-13737	8	16	procedures	procedure	NOUN
fumecheng-13737	8	17	.	.	PUNCT
fumecheng-13737	9	1	the	the	DET
fumecheng-13737	9	2	nonlinear	nonlinear	ADJ
fumecheng-13737	9	3	frequency	frequency	NOUN
fumecheng-13737	9	4	of	of	ADP
fumecheng-13737	9	5	the	the	DET
fumecheng-13737	9	6	stringerstiffened	stringerstiffened	ADJ
fumecheng-13737	9	7	shell	shell	NOUN
fumecheng-13737	9	8	is	be	AUX
fumecheng-13737	9	9	determined	determine	VERB
fumecheng-13737	9	10	using	use	VERB
fumecheng-13737	9	11	each	each	DET
fumecheng-13737	9	12	method	method	NOUN
fumecheng-13737	9	13	and	and	CCONJ
fumecheng-13737	9	14	validated	validate	VERB
fumecheng-13737	9	15	against	against	ADP
fumecheng-13737	9	16	both	both	PRON
fumecheng-13737	9	17	exact	exact	ADJ
fumecheng-13737	9	18	analytical	analytical	ADJ
fumecheng-13737	9	19	solutions	solution	NOUN
fumecheng-13737	9	20	and	and	CCONJ
fumecheng-13737	9	21	numerical	numerical	ADJ
fumecheng-13737	9	22	results	result	NOUN
fumecheng-13737	9	23	.	.	PUNCT
fumecheng-13737	10	1	the	the	DET
fumecheng-13737	10	2	results	result	NOUN
fumecheng-13737	10	3	show	show	VERB
fumecheng-13737	10	4	that	that	SCONJ
fumecheng-13737	10	5	the	the	DET
fumecheng-13737	10	6	first	first	ADJ
fumecheng-13737	10	7	two	two	NUM
fumecheng-13737	10	8	methods	method	NOUN
fumecheng-13737	10	9	yield	yield	VERB
fumecheng-13737	10	10	high	high	ADJ
fumecheng-13737	10	11	accuracy	accuracy	NOUN
fumecheng-13737	10	12	for	for	ADP
fumecheng-13737	10	13	small	small	ADJ
fumecheng-13737	10	14	amplitudes	amplitude	NOUN
fumecheng-13737	10	15	,	,	PUNCT
fumecheng-13737	10	16	while	while	SCONJ
fumecheng-13737	10	17	their	their	PRON
fumecheng-13737	10	18	accuracy	accuracy	NOUN
fumecheng-13737	10	19	decreases	decrease	VERB
fumecheng-13737	10	20	at	at	ADP
fumecheng-13737	10	21	higher	high	ADJ
fumecheng-13737	10	22	amplitudes	amplitude	NOUN
fumecheng-13737	10	23	.	.	PUNCT
fumecheng-13737	11	1	in	in	ADP
fumecheng-13737	11	2	contrast	contrast	NOUN
fumecheng-13737	11	3	,	,	PUNCT
fumecheng-13737	11	4	the	the	DET
fumecheng-13737	11	5	hamiltonian	hamiltonian	NOUN
fumecheng-13737	11	6	-	-	PUNCT
fumecheng-13737	11	7	based	base	VERB
fumecheng-13737	11	8	method	method	NOUN
fumecheng-13737	11	9	maintains	maintain	VERB
fumecheng-13737	11	10	high	high	ADJ
fumecheng-13737	11	11	accuracy	accuracy	NOUN
fumecheng-13737	11	12	over	over	ADP
fumecheng-13737	11	13	a	a	DET
fumecheng-13737	11	14	wider	wide	ADJ
fumecheng-13737	11	15	range	range	NOUN
fumecheng-13737	11	16	of	of	ADP
fumecheng-13737	11	17	amplitudes	amplitude	NOUN
fumecheng-13737	11	18	.	.	PUNCT
fumecheng-13737	12	1	the	the	DET
fumecheng-13737	12	2	original	original	ADJ
fumecheng-13737	12	3	he	he	PRON
fumecheng-13737	12	4	's	's	PART
fumecheng-13737	12	5	formulation	formulation	NOUN
fumecheng-13737	12	6	is	be	AUX
fumecheng-13737	12	7	recognized	recognize	VERB
fumecheng-13737	12	8	for	for	ADP
fumecheng-13737	12	9	its	its	PRON
fumecheng-13737	12	10	simplicity	simplicity	NOUN
fumecheng-13737	12	11	and	and	CCONJ
fumecheng-13737	12	12	computational	computational	ADJ
fumecheng-13737	12	13	efficiency	efficiency	NOUN
fumecheng-13737	12	14	,	,	PUNCT
fumecheng-13737	12	15	making	make	VERB
fumecheng-13737	12	16	it	it	PRON
fumecheng-13737	12	17	a	a	DET
fumecheng-13737	12	18	practical	practical	ADJ
fumecheng-13737	12	19	tool	tool	NOUN
fumecheng-13737	12	20	for	for	ADP
fumecheng-13737	12	21	rapid	rapid	ADJ
fumecheng-13737	12	22	frequency	frequency	NOUN
fumecheng-13737	12	23	estimation	estimation	NOUN
fumecheng-13737	12	24	in	in	ADP
fumecheng-13737	12	25	stringer	stringer	NOUN
fumecheng-13737	12	26	-	-	PUNCT
fumecheng-13737	12	27	stiffened	stiffen	VERB
fumecheng-13737	12	28	shell	shell	NOUN
fumecheng-13737	12	29	systems	system	NOUN
fumecheng-13737	12	30	.	.	PUNCT
fumecheng-13737	13	1	this	this	DET
fumecheng-13737	13	2	comparative	comparative	ADJ
fumecheng-13737	13	3	study	study	NOUN
fumecheng-13737	13	4	offers	offer	VERB
fumecheng-13737	13	5	guidance	guidance	NOUN
fumecheng-13737	13	6	for	for	ADP
fumecheng-13737	13	7	selecting	select	VERB
fumecheng-13737	13	8	appropriate	appropriate	ADJ
fumecheng-13737	13	9	analytical	analytical	ADJ
fumecheng-13737	13	10	tools	tool	NOUN
fumecheng-13737	13	11	for	for	ADP
fumecheng-13737	13	12	nonlinear	nonlinear	ADJ
fumecheng-13737	13	13	vibration	vibration	NOUN
fumecheng-13737	13	14	analysis	analysis	NOUN
fumecheng-13737	13	15	of	of	ADP
fumecheng-13737	13	16	complex	complex	ADJ
fumecheng-13737	13	17	mechanical	mechanical	ADJ
fumecheng-13737	13	18	and	and	CCONJ
fumecheng-13737	13	19	physical	physical	ADJ
fumecheng-13737	13	20	systems	system	NOUN
fumecheng-13737	13	21	.	.	PUNCT
fumecheng-13737	14	1	key	key	ADJ
fumecheng-13737	14	2	words	word	NOUN
fumecheng-13737	14	3	:	:	PUNCT
fumecheng-13737	14	4	stringer	stringer	NOUN
fumecheng-13737	14	5	-	-	PUNCT
fumecheng-13737	14	6	stiffened	stiffen	VERB
fumecheng-13737	14	7	shell	shell	NOUN
fumecheng-13737	14	8	,	,	PUNCT
fumecheng-13737	14	9	approximate	approximate	ADJ
fumecheng-13737	14	10	analytical	analytical	ADJ
fumecheng-13737	14	11	solution	solution	NOUN
fumecheng-13737	14	12	,	,	PUNCT
fumecheng-13737	14	13	nonlinear	nonlinear	ADJ
fumecheng-13737	14	14	frequency	frequency	NOUN
fumecheng-13737	14	15	,	,	PUNCT
fumecheng-13737	14	16	frequency	frequency	NOUN
fumecheng-13737	14	17	-	-	PUNCT
fumecheng-13737	14	18	amplitude	amplitude	NOUN
fumecheng-13737	14	19	formulation	formulation	NOUN
fumecheng-13737	14	20	,	,	PUNCT
fumecheng-13737	14	21	nonlinear	nonlinear	ADJ
fumecheng-13737	14	22	vibration	vibration	NOUN
fumecheng-13737	14	23	received	receive	VERB
fumecheng-13737	14	24	:	:	PUNCT
fumecheng-13737	14	25	may	may	AUX
fumecheng-13737	14	26	25	25	NUM
fumecheng-13737	14	27	,	,	PUNCT
fumecheng-13737	14	28	2025	2025	NUM
fumecheng-13737	14	29	/	/	SYM
fumecheng-13737	14	30	accepted	accept	VERB
fumecheng-13737	14	31	july	july	PROPN
fumecheng-13737	14	32	23	23	NUM
fumecheng-13737	14	33	,	,	PUNCT
fumecheng-13737	14	34	2025	2025	NUM
fumecheng-13737	14	35	corresponding	correspond	VERB
fumecheng-13737	14	36	author	author	NOUN
fumecheng-13737	14	37	:	:	PUNCT
fumecheng-13737	14	38	mostafa	mostafa	PROPN
fumecheng-13737	14	39	mohammadian	mohammadian	PROPN
fumecheng-13737	14	40	mechanical	mechanical	PROPN
fumecheng-13737	14	41	engineering	engineering	PROPN
fumecheng-13737	14	42	department	department	PROPN
fumecheng-13737	14	43	,	,	PUNCT
fumecheng-13737	14	44	esfarayen	esfarayen	NOUN
fumecheng-13737	14	45	university	university	PROPN
fumecheng-13737	14	46	of	of	ADP
fumecheng-13737	14	47	technology	technology	PROPN
fumecheng-13737	14	48	,	,	PUNCT
fumecheng-13737	14	49	azadegan	azadegan	PROPN
fumecheng-13737	14	50	boulevard	boulevard	PROPN
fumecheng-13737	14	51	,	,	PUNCT
fumecheng-13737	14	52	corner	corner	NOUN
fumecheng-13737	14	53	of	of	ADP
fumecheng-13737	14	54	mader	mader	PROPN
fumecheng-13737	14	55	square	square	NOUN
fumecheng-13737	14	56	,	,	PUNCT
fumecheng-13737	14	57	esfarayen	esfarayen	NOUN
fumecheng-13737	14	58	,	,	PUNCT
fumecheng-13737	14	59	north	north	NOUN
fumecheng-13737	14	60	khorasan	khorasan	PROPN
fumecheng-13737	14	61	,	,	PUNCT
fumecheng-13737	14	62	iran	iran	PROPN
fumecheng-13737	14	63	,	,	PUNCT
fumecheng-13737	14	64	postal	postal	ADJ
fumecheng-13737	14	65	code	code	PROPN
fumecheng-13737	14	66	:	:	PUNCT
fumecheng-13737	14	67	9661998195	9661998195	NUM
fumecheng-13737	14	68	.	.	PUNCT
fumecheng-13737	15	1	e	e	X
fumecheng-13737	15	2	-	-	NOUN
fumecheng-13737	15	3	mail	mail	NOUN
fumecheng-13737	15	4	:	:	PUNCT
fumecheng-13737	15	5	mo.mohammadyan@gmail.com	mo.mohammadyan@gmail.com	PROPN
fumecheng-13737	15	6	,	,	PUNCT
fumecheng-13737	15	7	mo.mohammadyan@esfarayen.ac.ir	mo.mohammadyan@esfarayen.ac.ir	ADJ
fumecheng-13737	15	8	.	.	PUNCT
fumecheng-13737	16	1	mailto:mo.mohammadyan@gmail.com	mailto:mo.mohammadyan@gmail.com	PROPN
fumecheng-13737	16	2	mailto:mo.mohammadyan@esfarayen.ac.ir	mailto:mo.mohammadyan@esfarayen.ac.ir	PROPN
fumecheng-13737	17	1	788	788	NUM
fumecheng-13737	17	2	c	c	NOUN
fumecheng-13737	17	3	-	-	PUNCT
fumecheng-13737	17	4	h.	h.	NOUN
fumecheng-13737	17	5	he	he	PROPN
fumecheng-13737	17	6	,	,	PUNCT
fumecheng-13737	17	7	m.	m.	NOUN
fumecheng-13737	17	8	mohammadian	mohammadian	NOUN
fumecheng-13737	17	9	1	1	NUM
fumecheng-13737	17	10	.	.	PUNCT
fumecheng-13737	17	11	introduction	introduction	NOUN
fumecheng-13737	17	12	the	the	DET
fumecheng-13737	17	13	nonlinear	nonlinear	ADJ
fumecheng-13737	17	14	vibration	vibration	NOUN
fumecheng-13737	17	15	behavior	behavior	NOUN
fumecheng-13737	17	16	of	of	ADP
fumecheng-13737	17	17	cylindrical	cylindrical	ADJ
fumecheng-13737	17	18	shells	shell	NOUN
fumecheng-13737	17	19	constitutes	constitute	VERB
fumecheng-13737	17	20	a	a	DET
fumecheng-13737	17	21	critical	critical	ADJ
fumecheng-13737	17	22	topic	topic	NOUN
fumecheng-13737	17	23	in	in	ADP
fumecheng-13737	17	24	civil	civil	ADJ
fumecheng-13737	17	25	and	and	CCONJ
fumecheng-13737	17	26	mechanical	mechanical	ADJ
fumecheng-13737	17	27	engineering	engineering	NOUN
fumecheng-13737	17	28	.	.	PUNCT
fumecheng-13737	18	1	the	the	DET
fumecheng-13737	18	2	importance	importance	NOUN
fumecheng-13737	18	3	of	of	ADP
fumecheng-13737	18	4	nonlinear	nonlinear	ADJ
fumecheng-13737	18	5	vibrations	vibration	NOUN
fumecheng-13737	18	6	has	have	AUX
fumecheng-13737	18	7	grown	grow	VERB
fumecheng-13737	18	8	due	due	ADP
fumecheng-13737	18	9	to	to	ADP
fumecheng-13737	18	10	their	their	PRON
fumecheng-13737	18	11	impact	impact	NOUN
fumecheng-13737	18	12	across	across	ADP
fumecheng-13737	18	13	various	various	ADJ
fumecheng-13737	18	14	fields	field	NOUN
fumecheng-13737	18	15	,	,	PUNCT
fumecheng-13737	18	16	including	include	VERB
fumecheng-13737	18	17	physical	physical	ADJ
fumecheng-13737	18	18	sciences	science	NOUN
fumecheng-13737	18	19	,	,	PUNCT
fumecheng-13737	18	20	engineering	engineering	NOUN
fumecheng-13737	18	21	,	,	PUNCT
fumecheng-13737	18	22	and	and	CCONJ
fumecheng-13737	18	23	mechanical	mechanical	ADJ
fumecheng-13737	18	24	systems	system	NOUN
fumecheng-13737	18	25	.	.	PUNCT
fumecheng-13737	19	1	consequently	consequently	ADV
fumecheng-13737	19	2	,	,	PUNCT
fumecheng-13737	19	3	engineering	engineering	NOUN
fumecheng-13737	19	4	design	design	NOUN
fumecheng-13737	19	5	processes	process	NOUN
fumecheng-13737	19	6	are	be	AUX
fumecheng-13737	19	7	increasingly	increasingly	ADV
fumecheng-13737	19	8	focused	focus	VERB
fumecheng-13737	19	9	on	on	ADP
fumecheng-13737	19	10	the	the	DET
fumecheng-13737	19	11	dynamic	dynamic	ADJ
fumecheng-13737	19	12	behavior	behavior	NOUN
fumecheng-13737	19	13	of	of	ADP
fumecheng-13737	19	14	beams	beam	NOUN
fumecheng-13737	19	15	and	and	CCONJ
fumecheng-13737	19	16	shells	shell	NOUN
fumecheng-13737	19	17	.	.	PUNCT
fumecheng-13737	20	1	in	in	ADP
fumecheng-13737	20	2	particular	particular	ADJ
fumecheng-13737	20	3	,	,	PUNCT
fumecheng-13737	20	4	the	the	DET
fumecheng-13737	20	5	nonlinear	nonlinear	ADJ
fumecheng-13737	20	6	vibration	vibration	NOUN
fumecheng-13737	20	7	of	of	ADP
fumecheng-13737	20	8	cylindrical	cylindrical	ADJ
fumecheng-13737	20	9	shells	shell	NOUN
fumecheng-13737	20	10	plays	play	VERB
fumecheng-13737	20	11	a	a	DET
fumecheng-13737	20	12	vital	vital	ADJ
fumecheng-13737	20	13	role	role	NOUN
fumecheng-13737	20	14	in	in	ADP
fumecheng-13737	20	15	mechanical	mechanical	ADJ
fumecheng-13737	20	16	engineering	engineering	NOUN
fumecheng-13737	20	17	,	,	PUNCT
fumecheng-13737	20	18	especially	especially	ADV
fumecheng-13737	20	19	in	in	ADP
fumecheng-13737	20	20	aerospace	aerospace	NOUN
fumecheng-13737	20	21	and	and	CCONJ
fumecheng-13737	20	22	marine	marine	ADJ
fumecheng-13737	20	23	applications	application	NOUN
fumecheng-13737	20	24	.	.	PUNCT
fumecheng-13737	21	1	stringer	stringer	NOUN
fumecheng-13737	21	2	-	-	PUNCT
fumecheng-13737	21	3	stiffened	stiffen	VERB
fumecheng-13737	21	4	shells	shell	NOUN
fumecheng-13737	21	5	play	play	VERB
fumecheng-13737	21	6	a	a	DET
fumecheng-13737	21	7	foundational	foundational	ADJ
fumecheng-13737	21	8	role	role	NOUN
fumecheng-13737	21	9	in	in	ADP
fumecheng-13737	21	10	the	the	DET
fumecheng-13737	21	11	design	design	NOUN
fumecheng-13737	21	12	of	of	ADP
fumecheng-13737	21	13	aircraft	aircraft	NOUN
fumecheng-13737	21	14	,	,	PUNCT
fumecheng-13737	21	15	spacecraft	spacecraft	NOUN
fumecheng-13737	21	16	,	,	PUNCT
fumecheng-13737	21	17	and	and	CCONJ
fumecheng-13737	21	18	ships	ship	NOUN
fumecheng-13737	21	19	,	,	PUNCT
fumecheng-13737	21	20	which	which	PRON
fumecheng-13737	21	21	are	be	AUX
fumecheng-13737	21	22	frequently	frequently	ADV
fumecheng-13737	21	23	subjected	subject	VERB
fumecheng-13737	21	24	to	to	ADP
fumecheng-13737	21	25	dynamic	dynamic	ADJ
fumecheng-13737	21	26	loading	loading	NOUN
fumecheng-13737	21	27	conditions	condition	NOUN
fumecheng-13737	21	28	.	.	PUNCT
fumecheng-13737	22	1	a	a	DET
fumecheng-13737	22	2	deeper	deep	ADJ
fumecheng-13737	22	3	understanding	understanding	NOUN
fumecheng-13737	22	4	of	of	ADP
fumecheng-13737	22	5	their	their	PRON
fumecheng-13737	22	6	nonlinear	nonlinear	ADJ
fumecheng-13737	22	7	response	response	NOUN
fumecheng-13737	22	8	can	can	AUX
fumecheng-13737	22	9	significantly	significantly	ADV
fumecheng-13737	22	10	enhance	enhance	VERB
fumecheng-13737	22	11	performance	performance	NOUN
fumecheng-13737	22	12	and	and	CCONJ
fumecheng-13737	22	13	structural	structural	ADJ
fumecheng-13737	22	14	integrity	integrity	NOUN
fumecheng-13737	22	15	.	.	PUNCT
fumecheng-13737	23	1	this	this	DET
fumecheng-13737	23	2	study	study	NOUN
fumecheng-13737	23	3	aims	aim	VERB
fumecheng-13737	23	4	to	to	PART
fumecheng-13737	23	5	address	address	VERB
fumecheng-13737	23	6	the	the	DET
fumecheng-13737	23	7	need	need	NOUN
fumecheng-13737	23	8	for	for	ADP
fumecheng-13737	23	9	efficient	efficient	ADJ
fumecheng-13737	23	10	and	and	CCONJ
fumecheng-13737	23	11	accurate	accurate	ADJ
fumecheng-13737	23	12	methods	method	NOUN
fumecheng-13737	23	13	to	to	PART
fumecheng-13737	23	14	predict	predict	VERB
fumecheng-13737	23	15	the	the	DET
fumecheng-13737	23	16	nonlinear	nonlinear	ADJ
fumecheng-13737	23	17	frequency	frequency	NOUN
fumecheng-13737	23	18	of	of	ADP
fumecheng-13737	23	19	stringer	stringer	NOUN
fumecheng-13737	23	20	-	-	PUNCT
fumecheng-13737	23	21	stiffened	stiffen	VERB
fumecheng-13737	23	22	shells	shell	NOUN
fumecheng-13737	23	23	.	.	PUNCT
fumecheng-13737	24	1	such	such	ADJ
fumecheng-13737	24	2	methods	method	NOUN
fumecheng-13737	24	3	are	be	AUX
fumecheng-13737	24	4	essential	essential	ADJ
fumecheng-13737	24	5	for	for	ADP
fumecheng-13737	24	6	improving	improve	VERB
fumecheng-13737	24	7	structural	structural	ADJ
fumecheng-13737	24	8	safety	safety	NOUN
fumecheng-13737	24	9	and	and	CCONJ
fumecheng-13737	24	10	reliability	reliability	NOUN
fumecheng-13737	24	11	in	in	ADP
fumecheng-13737	24	12	engineering	engineering	NOUN
fumecheng-13737	24	13	applications	application	NOUN
fumecheng-13737	24	14	.	.	PUNCT
fumecheng-13737	25	1	the	the	DET
fumecheng-13737	25	2	dynamic	dynamic	ADJ
fumecheng-13737	25	3	behavior	behavior	NOUN
fumecheng-13737	25	4	and	and	CCONJ
fumecheng-13737	25	5	stability	stability	NOUN
fumecheng-13737	25	6	of	of	ADP
fumecheng-13737	25	7	shell	shell	ADJ
fumecheng-13737	25	8	structures	structure	NOUN
fumecheng-13737	25	9	have	have	AUX
fumecheng-13737	25	10	been	be	AUX
fumecheng-13737	25	11	thoroughly	thoroughly	ADV
fumecheng-13737	25	12	studied	study	VERB
fumecheng-13737	25	13	due	due	ADP
fumecheng-13737	25	14	to	to	ADP
fumecheng-13737	25	15	their	their	PRON
fumecheng-13737	25	16	critical	critical	ADJ
fumecheng-13737	25	17	role	role	NOUN
fumecheng-13737	25	18	in	in	ADP
fumecheng-13737	25	19	modern	modern	ADJ
fumecheng-13737	25	20	engineering	engineering	NOUN
fumecheng-13737	25	21	applications	application	NOUN
fumecheng-13737	25	22	.	.	PUNCT
fumecheng-13737	26	1	gavrilenko	gavrilenko	NOUN
fumecheng-13737	26	2	and	and	CCONJ
fumecheng-13737	26	3	matsner	matsner	NOUN
fumecheng-13737	27	1	[	[	X
fumecheng-13737	27	2	1	1	NUM
fumecheng-13737	27	3	]	]	PUNCT
fumecheng-13737	27	4	examined	examine	VERB
fumecheng-13737	27	5	the	the	DET
fumecheng-13737	27	6	buckling	buckle	VERB
fumecheng-13737	27	7	characteristics	characteristic	NOUN
fumecheng-13737	27	8	of	of	ADP
fumecheng-13737	27	9	stringer	stringer	NOUN
fumecheng-13737	27	10	shells	shell	NOUN
fumecheng-13737	27	11	,	,	PUNCT
fumecheng-13737	27	12	highlighting	highlight	VERB
fumecheng-13737	27	13	the	the	DET
fumecheng-13737	27	14	influence	influence	NOUN
fumecheng-13737	27	15	of	of	ADP
fumecheng-13737	27	16	stiffening	stiffen	VERB
fumecheng-13737	27	17	elements	element	NOUN
fumecheng-13737	27	18	on	on	ADP
fumecheng-13737	27	19	structural	structural	ADJ
fumecheng-13737	27	20	stability	stability	NOUN
fumecheng-13737	27	21	.	.	PUNCT
fumecheng-13737	28	1	naghsh	naghsh	VERB
fumecheng-13737	28	2	et	et	PROPN
fumecheng-13737	28	3	al	al	PROPN
fumecheng-13737	28	4	.	.	PUNCT
fumecheng-13737	29	1	[	[	X
fumecheng-13737	29	2	2	2	NUM
fumecheng-13737	29	3	]	]	PUNCT
fumecheng-13737	29	4	utilized	utilize	VERB
fumecheng-13737	29	5	a	a	DET
fumecheng-13737	29	6	meridional	meridional	ADJ
fumecheng-13737	29	7	finite	finite	NOUN
fumecheng-13737	29	8	strip	strip	NOUN
fumecheng-13737	29	9	method	method	NOUN
fumecheng-13737	29	10	to	to	PART
fumecheng-13737	29	11	analyze	analyze	VERB
fumecheng-13737	29	12	free	free	ADJ
fumecheng-13737	29	13	vibrations	vibration	NOUN
fumecheng-13737	29	14	of	of	ADP
fumecheng-13737	29	15	various	various	ADJ
fumecheng-13737	29	16	shell	shell	NOUN
fumecheng-13737	29	17	structures	structure	NOUN
fumecheng-13737	29	18	.	.	PUNCT
fumecheng-13737	30	1	golchi	golchi	PROPN
fumecheng-13737	30	2	et	et	PROPN
fumecheng-13737	30	3	al	al	PROPN
fumecheng-13737	30	4	.	.	PUNCT
fumecheng-13737	31	1	[	[	X
fumecheng-13737	31	2	3	3	NUM
fumecheng-13737	31	3	]	]	PUNCT
fumecheng-13737	31	4	explored	explore	VERB
fumecheng-13737	31	5	thermal	thermal	ADJ
fumecheng-13737	31	6	buckling	buckling	NOUN
fumecheng-13737	31	7	and	and	CCONJ
fumecheng-13737	31	8	free	free	ADJ
fumecheng-13737	31	9	vibration	vibration	NOUN
fumecheng-13737	31	10	of	of	ADP
fumecheng-13737	31	11	functionally	functionally	ADV
fumecheng-13737	31	12	graded	grade	VERB
fumecheng-13737	31	13	(	(	PUNCT
fumecheng-13737	31	14	fg	fg	NOUN
fumecheng-13737	31	15	)	)	PUNCT
fumecheng-13737	31	16	truncated	truncated	ADJ
fumecheng-13737	31	17	conical	conical	NOUN
fumecheng-13737	31	18	shells	shell	NOUN
fumecheng-13737	31	19	with	with	ADP
fumecheng-13737	31	20	stringer	stringer	NOUN
fumecheng-13737	31	21	and	and	CCONJ
fumecheng-13737	31	22	ring	ring	NOUN
fumecheng-13737	31	23	stiffeners	stiffener	NOUN
fumecheng-13737	31	24	.	.	PUNCT
fumecheng-13737	32	1	bich	bich	NOUN
fumecheng-13737	32	2	and	and	CCONJ
fumecheng-13737	32	3	ninh	ninh	ADJ
fumecheng-13737	32	4	[	[	X
fumecheng-13737	32	5	4	4	X
fumecheng-13737	32	6	]	]	PUNCT
fumecheng-13737	32	7	pioneered	pioneer	VERB
fumecheng-13737	32	8	this	this	DET
fumecheng-13737	32	9	area	area	NOUN
fumecheng-13737	32	10	by	by	ADP
fumecheng-13737	32	11	investigating	investigate	VERB
fumecheng-13737	32	12	nonlinear	nonlinear	ADJ
fumecheng-13737	32	13	vibrations	vibration	NOUN
fumecheng-13737	32	14	in	in	ADP
fumecheng-13737	32	15	imperfect	imperfect	ADJ
fumecheng-13737	32	16	stiffened	stiffen	VERB
fumecheng-13737	32	17	sandwich	sandwich	NOUN
fumecheng-13737	32	18	toroidal	toroidal	ADJ
fumecheng-13737	32	19	shells	shell	NOUN
fumecheng-13737	32	20	under	under	ADP
fumecheng-13737	32	21	thermo	thermo	NOUN
fumecheng-13737	32	22	-	-	PUNCT
fumecheng-13737	32	23	mechanical	mechanical	ADJ
fumecheng-13737	32	24	loading	loading	NOUN
fumecheng-13737	32	25	.	.	PUNCT
fumecheng-13737	33	1	they	they	PRON
fumecheng-13737	33	2	later	later	ADV
fumecheng-13737	33	3	extended	extend	VERB
fumecheng-13737	33	4	their	their	PRON
fumecheng-13737	33	5	work	work	NOUN
fumecheng-13737	33	6	[	[	X
fumecheng-13737	33	7	5	5	NUM
fumecheng-13737	33	8	]	]	PUNCT
fumecheng-13737	33	9	to	to	PART
fumecheng-13737	33	10	eccentrically	eccentrically	ADV
fumecheng-13737	33	11	stiffened	stiffen	VERB
fumecheng-13737	33	12	toroidal	toroidal	ADJ
fumecheng-13737	33	13	shell	shell	NOUN
fumecheng-13737	33	14	segments	segment	NOUN
fumecheng-13737	33	15	on	on	ADP
fumecheng-13737	33	16	elastic	elastic	ADJ
fumecheng-13737	33	17	foundations	foundation	NOUN
fumecheng-13737	33	18	.	.	PUNCT
fumecheng-13737	34	1	recent	recent	ADJ
fumecheng-13737	34	2	research	research	NOUN
fumecheng-13737	34	3	by	by	ADP
fumecheng-13737	34	4	liu	liu	PROPN
fumecheng-13737	34	5	et	et	PROPN
fumecheng-13737	34	6	al	al	PROPN
fumecheng-13737	34	7	.	.	PUNCT
fumecheng-13737	35	1	[	[	X
fumecheng-13737	35	2	6	6	NUM
fumecheng-13737	35	3	]	]	PUNCT
fumecheng-13737	35	4	focused	focus	VERB
fumecheng-13737	35	5	on	on	ADP
fumecheng-13737	35	6	nonlinear	nonlinear	ADJ
fumecheng-13737	35	7	traveling	traveling	ADJ
fumecheng-13737	35	8	-	-	PUNCT
fumecheng-13737	35	9	wave	wave	NOUN
fumecheng-13737	35	10	vibrations	vibration	NOUN
fumecheng-13737	35	11	of	of	ADP
fumecheng-13737	35	12	ring	ring	NOUN
fumecheng-13737	35	13	-	-	PUNCT
fumecheng-13737	35	14	stringer	stringer	NOUN
fumecheng-13737	35	15	stiffened	stiffen	VERB
fumecheng-13737	35	16	cylindrical	cylindrical	ADJ
fumecheng-13737	35	17	shells	shell	NOUN
fumecheng-13737	35	18	,	,	PUNCT
fumecheng-13737	35	19	highlighting	highlight	VERB
fumecheng-13737	35	20	the	the	DET
fumecheng-13737	35	21	complexity	complexity	NOUN
fumecheng-13737	35	22	introduced	introduce	VERB
fumecheng-13737	35	23	by	by	ADP
fumecheng-13737	35	24	wave	wave	NOUN
fumecheng-13737	35	25	propagation	propagation	NOUN
fumecheng-13737	35	26	.	.	PUNCT
fumecheng-13737	36	1	a	a	DET
fumecheng-13737	36	2	significant	significant	ADJ
fumecheng-13737	36	3	body	body	NOUN
fumecheng-13737	36	4	of	of	ADP
fumecheng-13737	36	5	research	research	NOUN
fumecheng-13737	36	6	has	have	AUX
fumecheng-13737	36	7	been	be	AUX
fumecheng-13737	36	8	dedicated	dedicate	VERB
fumecheng-13737	36	9	to	to	ADP
fumecheng-13737	36	10	the	the	DET
fumecheng-13737	36	11	exploration	exploration	NOUN
fumecheng-13737	36	12	of	of	ADP
fumecheng-13737	36	13	rotational	rotational	ADJ
fumecheng-13737	36	14	and	and	CCONJ
fumecheng-13737	36	15	thermal	thermal	ADJ
fumecheng-13737	36	16	effects	effect	NOUN
fumecheng-13737	36	17	on	on	ADP
fumecheng-13737	36	18	the	the	DET
fumecheng-13737	36	19	shell	shell	NOUN
fumecheng-13737	36	20	’s	’s	PART
fumecheng-13737	36	21	nonlinear	nonlinear	ADJ
fumecheng-13737	36	22	dynamics	dynamic	NOUN
fumecheng-13737	36	23	.	.	PUNCT
fumecheng-13737	37	1	liu	liu	PROPN
fumecheng-13737	37	2	et	et	PROPN
fumecheng-13737	37	3	al	al	PROPN
fumecheng-13737	37	4	.	.	PUNCT
fumecheng-13737	38	1	[	[	X
fumecheng-13737	38	2	7	7	NUM
fumecheng-13737	38	3	]	]	PUNCT
fumecheng-13737	38	4	analyzed	analyze	VERB
fumecheng-13737	38	5	nonlinear	nonlinear	ADJ
fumecheng-13737	38	6	forced	force	VERB
fumecheng-13737	38	7	vibrations	vibration	NOUN
fumecheng-13737	38	8	in	in	ADP
fumecheng-13737	38	9	rotating	rotate	VERB
fumecheng-13737	38	10	cylindrical	cylindrical	ADJ
fumecheng-13737	38	11	shells	shell	NOUN
fumecheng-13737	38	12	under	under	ADP
fumecheng-13737	38	13	multi	multi	ADJ
fumecheng-13737	38	14	-	-	ADJ
fumecheng-13737	38	15	harmonic	harmonic	ADJ
fumecheng-13737	38	16	excitations	excitation	NOUN
fumecheng-13737	38	17	in	in	ADP
fumecheng-13737	38	18	thermal	thermal	ADJ
fumecheng-13737	38	19	environments	environment	NOUN
fumecheng-13737	38	20	.	.	PUNCT
fumecheng-13737	39	1	vahidi	vahidi	NOUN
fumecheng-13737	39	2	et	et	PROPN
fumecheng-13737	39	3	al	al	PROPN
fumecheng-13737	39	4	.	.	PUNCT
fumecheng-13737	40	1	[	[	X
fumecheng-13737	40	2	8	8	NUM
fumecheng-13737	40	3	]	]	PUNCT
fumecheng-13737	40	4	investigated	investigate	VERB
fumecheng-13737	40	5	the	the	DET
fumecheng-13737	40	6	nonlinear	nonlinear	ADJ
fumecheng-13737	40	7	vibration	vibration	NOUN
fumecheng-13737	40	8	,	,	PUNCT
fumecheng-13737	40	9	stability	stability	NOUN
fumecheng-13737	40	10	,	,	PUNCT
fumecheng-13737	40	11	and	and	CCONJ
fumecheng-13737	40	12	bifurcation	bifurcation	NOUN
fumecheng-13737	40	13	of	of	ADP
fumecheng-13737	40	14	rotating	rotate	VERB
fumecheng-13737	40	15	axially	axially	ADV
fumecheng-13737	40	16	moving	move	VERB
fumecheng-13737	40	17	conical	conical	ADJ
fumecheng-13737	40	18	shells	shell	NOUN
fumecheng-13737	40	19	,	,	PUNCT
fumecheng-13737	40	20	providing	provide	VERB
fumecheng-13737	40	21	insight	insight	NOUN
fumecheng-13737	40	22	into	into	ADP
fumecheng-13737	40	23	the	the	DET
fumecheng-13737	40	24	dynamic	dynamic	ADJ
fumecheng-13737	40	25	instabilities	instability	NOUN
fumecheng-13737	40	26	induced	induce	VERB
fumecheng-13737	40	27	by	by	ADP
fumecheng-13737	40	28	axial	axial	ADJ
fumecheng-13737	40	29	motion	motion	NOUN
fumecheng-13737	40	30	and	and	CCONJ
fumecheng-13737	40	31	rotation	rotation	NOUN
fumecheng-13737	40	32	.	.	PUNCT
fumecheng-13737	41	1	mohammadrezazadeh	mohammadrezazadeh	PROPN
fumecheng-13737	41	2	and	and	CCONJ
fumecheng-13737	41	3	jafari	jafari	PROPN
fumecheng-13737	41	4	[	[	X
fumecheng-13737	41	5	9	9	NUM
fumecheng-13737	41	6	]	]	PUNCT
fumecheng-13737	41	7	proposed	propose	VERB
fumecheng-13737	41	8	vibration	vibration	NOUN
fumecheng-13737	41	9	suppression	suppression	NOUN
fumecheng-13737	41	10	in	in	ADP
fumecheng-13737	41	11	laminated	laminate	VERB
fumecheng-13737	41	12	composite	composite	ADJ
fumecheng-13737	41	13	cylindrical	cylindrical	ADJ
fumecheng-13737	41	14	shells	shell	NOUN
fumecheng-13737	41	15	employing	employ	VERB
fumecheng-13737	41	16	magneto	magneto	ADJ
fumecheng-13737	41	17	strictive	strictive	ADJ
fumecheng-13737	41	18	strips	strip	NOUN
fumecheng-13737	41	19	.	.	PUNCT
fumecheng-13737	42	1	recent	recent	ADJ
fumecheng-13737	42	2	advancements	advancement	NOUN
fumecheng-13737	42	3	include	include	VERB
fumecheng-13737	42	4	high	high	ADJ
fumecheng-13737	42	5	-	-	PUNCT
fumecheng-13737	42	6	fidelity	fidelity	NOUN
fumecheng-13737	42	7	modeling	modeling	NOUN
fumecheng-13737	42	8	and	and	CCONJ
fumecheng-13737	42	9	simulation	simulation	NOUN
fumecheng-13737	42	10	techniques	technique	NOUN
fumecheng-13737	42	11	for	for	ADP
fumecheng-13737	42	12	stiffened	stiffen	VERB
fumecheng-13737	42	13	cylindrical	cylindrical	ADJ
fumecheng-13737	42	14	shells	shell	NOUN
fumecheng-13737	42	15	under	under	ADP
fumecheng-13737	42	16	various	various	ADJ
fumecheng-13737	42	17	loading	loading	NOUN
fumecheng-13737	42	18	scenarios	scenario	NOUN
fumecheng-13737	42	19	.	.	PUNCT
fumecheng-13737	43	1	bochkarev	bochkarev	NOUN
fumecheng-13737	43	2	et	et	PROPN
fumecheng-13737	43	3	al	al	PROPN
fumecheng-13737	43	4	.	.	PUNCT
fumecheng-13737	44	1	[	[	X
fumecheng-13737	44	2	10	10	NUM
fumecheng-13737	44	3	]	]	PUNCT
fumecheng-13737	44	4	studied	study	VERB
fumecheng-13737	44	5	panel	panel	NOUN
fumecheng-13737	44	6	flutter	flutter	NOUN
fumecheng-13737	44	7	in	in	ADP
fumecheng-13737	44	8	stiffened	stiffen	VERB
fumecheng-13737	44	9	shallow	shallow	ADJ
fumecheng-13737	44	10	shell	shell	NOUN
fumecheng-13737	44	11	structures	structure	NOUN
fumecheng-13737	44	12	.	.	PUNCT
fumecheng-13737	45	1	foroutan	foroutan	PROPN
fumecheng-13737	45	2	and	and	CCONJ
fumecheng-13737	45	3	dai	dai	PROPN
fumecheng-13737	46	1	[	[	X
fumecheng-13737	46	2	11	11	NUM
fumecheng-13737	46	3	]	]	PUNCT
fumecheng-13737	46	4	investigated	investigate	VERB
fumecheng-13737	46	5	nonlinear	nonlinear	ADJ
fumecheng-13737	46	6	dynamics	dynamic	NOUN
fumecheng-13737	46	7	in	in	ADP
fumecheng-13737	46	8	spiralstiffened	spiralstiffene	VERB
fumecheng-13737	46	9	fg	fg	PROPN
fumecheng-13737	46	10	toroidal	toroidal	ADJ
fumecheng-13737	46	11	shells	shell	NOUN
fumecheng-13737	46	12	with	with	ADP
fumecheng-13737	46	13	variable	variable	ADJ
fumecheng-13737	46	14	thickness	thickness	NOUN
fumecheng-13737	46	15	.	.	PUNCT
fumecheng-13737	47	1	azzara	azzara	NOUN
fumecheng-13737	47	2	et	et	PROPN
fumecheng-13737	47	3	al	al	PROPN
fumecheng-13737	47	4	.	.	PUNCT
fumecheng-13737	48	1	[	[	X
fumecheng-13737	48	2	12	12	NUM
fumecheng-13737	48	3	]	]	PUNCT
fumecheng-13737	48	4	analyzed	analyze	VERB
fumecheng-13737	48	5	rotor	rotor	NOUN
fumecheng-13737	48	6	dynamic	dynamic	ADJ
fumecheng-13737	48	7	responses	response	NOUN
fumecheng-13737	48	8	of	of	ADP
fumecheng-13737	48	9	stiffened	stiffen	VERB
fumecheng-13737	48	10	cylindrical	cylindrical	ADJ
fumecheng-13737	48	11	structures	structure	NOUN
fumecheng-13737	48	12	using	use	VERB
fumecheng-13737	48	13	high	high	ADJ
fumecheng-13737	48	14	-	-	PUNCT
fumecheng-13737	48	15	order	order	NOUN
fumecheng-13737	48	16	shell	shell	NOUN
fumecheng-13737	48	17	models	model	NOUN
fumecheng-13737	48	18	.	.	PUNCT
fumecheng-13737	49	1	zhang	zhang	PROPN
fumecheng-13737	49	2	et	et	PROPN
fumecheng-13737	49	3	al	al	PROPN
fumecheng-13737	49	4	.	.	PUNCT
fumecheng-13737	50	1	[	[	X
fumecheng-13737	50	2	13	13	NUM
fumecheng-13737	50	3	]	]	PUNCT
fumecheng-13737	50	4	explored	explore	VERB
fumecheng-13737	50	5	frequency	frequency	NOUN
fumecheng-13737	50	6	responses	response	NOUN
fumecheng-13737	50	7	in	in	ADP
fumecheng-13737	50	8	porous	porous	ADJ
fumecheng-13737	50	9	hyperplastic	hyperplastic	ADJ
fumecheng-13737	50	10	mooney	mooney	PROPN
fumecheng-13737	50	11	-	-	PUNCT
fumecheng-13737	50	12	rivlin	rivlin	PROPN
fumecheng-13737	50	13	cylindrical	cylindrical	ADJ
fumecheng-13737	50	14	shells	shell	NOUN
fumecheng-13737	50	15	under	under	ADP
fumecheng-13737	50	16	radial	radial	ADJ
fumecheng-13737	50	17	harmonic	harmonic	ADJ
fumecheng-13737	50	18	forces	force	NOUN
fumecheng-13737	50	19	.	.	PUNCT
fumecheng-13737	51	1	du	du	PROPN
fumecheng-13737	51	2	et	et	PROPN
fumecheng-13737	51	3	al	al	PROPN
fumecheng-13737	51	4	.	.	PUNCT
fumecheng-13737	52	1	[	[	X
fumecheng-13737	52	2	14	14	NUM
fumecheng-13737	52	3	]	]	PUNCT
fumecheng-13737	52	4	developed	develop	VERB
fumecheng-13737	52	5	a	a	DET
fumecheng-13737	52	6	semi	semi	ADJ
fumecheng-13737	52	7	-	-	ADJ
fumecheng-13737	52	8	analytical	analytical	ADJ
fumecheng-13737	52	9	method	method	NOUN
fumecheng-13737	52	10	for	for	ADP
fumecheng-13737	52	11	the	the	DET
fumecheng-13737	52	12	vibration	vibration	NOUN
fumecheng-13737	52	13	control	control	NOUN
fumecheng-13737	52	14	in	in	ADP
fumecheng-13737	52	15	cylindrical	cylindrical	ADJ
fumecheng-13737	52	16	shell	shell	NOUN
fumecheng-13737	52	17	structures	structure	NOUN
fumecheng-13737	52	18	.	.	PUNCT
fumecheng-13737	53	1	chen	chen	PROPN
fumecheng-13737	53	2	et	et	PROPN
fumecheng-13737	53	3	al	al	PROPN
fumecheng-13737	53	4	.	.	PUNCT
fumecheng-13737	54	1	[	[	X
fumecheng-13737	54	2	15	15	NUM
fumecheng-13737	54	3	]	]	PUNCT
fumecheng-13737	54	4	examined	examine	VERB
fumecheng-13737	54	5	the	the	DET
fumecheng-13737	54	6	correlation	correlation	NOUN
fumecheng-13737	54	7	between	between	ADP
fumecheng-13737	54	8	welding	weld	VERB
fumecheng-13737	54	9	parameters	parameter	NOUN
fumecheng-13737	54	10	and	and	CCONJ
fumecheng-13737	54	11	vibro	vibro	NOUN
fumecheng-13737	54	12	-	-	PUNCT
fumecheng-13737	54	13	acoustic	acoustic	ADJ
fumecheng-13737	54	14	behavior	behavior	NOUN
fumecheng-13737	54	15	in	in	ADP
fumecheng-13737	54	16	stiffened	stiffen	VERB
fumecheng-13737	54	17	cylindrical	cylindrical	ADJ
fumecheng-13737	54	18	shells	shell	NOUN
fumecheng-13737	54	19	.	.	PUNCT
fumecheng-13737	55	1	tan	tan	VERB
fumecheng-13737	55	2	et	et	PROPN
fumecheng-13737	55	3	al	al	PROPN
fumecheng-13737	55	4	.	.	PUNCT
fumecheng-13737	56	1	[	[	X
fumecheng-13737	56	2	16	16	NUM
fumecheng-13737	56	3	]	]	PUNCT
fumecheng-13737	56	4	introduced	introduce	VERB
fumecheng-13737	56	5	innovative	innovative	ADJ
fumecheng-13737	56	6	sandwich	sandwich	NOUN
fumecheng-13737	56	7	composite	composite	ADJ
fumecheng-13737	56	8	shell	shell	NOUN
fumecheng-13737	56	9	structures	structure	NOUN
fumecheng-13737	56	10	and	and	CCONJ
fumecheng-13737	56	11	established	establish	VERB
fumecheng-13737	56	12	a	a	DET
fumecheng-13737	56	13	framework	framework	NOUN
fumecheng-13737	56	14	for	for	ADP
fumecheng-13737	56	15	nonlinear	nonlinear	ADJ
fumecheng-13737	56	16	geometric	geometric	ADJ
fumecheng-13737	56	17	and	and	CCONJ
fumecheng-13737	56	18	dynamic	dynamic	ADJ
fumecheng-13737	56	19	analyses	analysis	NOUN
fumecheng-13737	56	20	.	.	PUNCT
fumecheng-13737	57	1	khoddami	khoddami	PROPN
fumecheng-13737	57	2	maraghi	maraghi	PROPN
fumecheng-13737	57	3	et	et	PROPN
fumecheng-13737	57	4	al	al	PROPN
fumecheng-13737	57	5	.	.	PUNCT
fumecheng-13737	58	1	[	[	X
fumecheng-13737	58	2	17	17	NUM
fumecheng-13737	58	3	]	]	PUNCT
fumecheng-13737	58	4	investigated	investigate	VERB
fumecheng-13737	58	5	free	free	ADJ
fumecheng-13737	58	6	vibrations	vibration	NOUN
fumecheng-13737	58	7	of	of	ADP
fumecheng-13737	58	8	truncated	truncated	ADJ
fumecheng-13737	58	9	conical	conical	ADJ
fumecheng-13737	58	10	sandwich	sandwich	NOUN
fumecheng-13737	58	11	shells	shell	NOUN
fumecheng-13737	58	12	with	with	ADP
fumecheng-13737	58	13	auxetic	auxetic	ADJ
fumecheng-13737	58	14	core	core	NOUN
fumecheng-13737	58	15	and	and	CCONJ
fumecheng-13737	58	16	polymeric	polymeric	ADJ
fumecheng-13737	58	17	nanocomposite	nanocomposite	NOUN
fumecheng-13737	58	18	face	face	NOUN
fumecheng-13737	58	19	sheets	sheet	NOUN
fumecheng-13737	58	20	reinforced	reinforce	VERB
fumecheng-13737	58	21	with	with	ADP
fumecheng-13737	58	22	graphene	graphene	ADJ
fumecheng-13737	58	23	nanoplatelets	nanoplatelet	NOUN
fumecheng-13737	58	24	.	.	PUNCT
fumecheng-13737	59	1	despite	despite	SCONJ
fumecheng-13737	59	2	substantial	substantial	ADJ
fumecheng-13737	59	3	progress	progress	NOUN
fumecheng-13737	59	4	,	,	PUNCT
fumecheng-13737	59	5	further	further	ADJ
fumecheng-13737	59	6	research	research	NOUN
fumecheng-13737	59	7	is	be	AUX
fumecheng-13737	59	8	needed	need	VERB
fumecheng-13737	59	9	to	to	PART
fumecheng-13737	59	10	account	account	VERB
fumecheng-13737	59	11	for	for	ADP
fumecheng-13737	59	12	multi	multi	ADJ
fumecheng-13737	59	13	-	-	ADJ
fumecheng-13737	59	14	physical	physical	ADJ
fumecheng-13737	59	15	interactions	interaction	NOUN
fumecheng-13737	59	16	,	,	PUNCT
fumecheng-13737	59	17	enhance	enhance	VERB
fumecheng-13737	59	18	model	model	NOUN
fumecheng-13737	59	19	accuracy	accuracy	NOUN
fumecheng-13737	59	20	,	,	PUNCT
fumecheng-13737	59	21	and	and	CCONJ
fumecheng-13737	59	22	develop	develop	VERB
fumecheng-13737	59	23	efficient	efficient	ADJ
fumecheng-13737	59	24	computational	computational	ADJ
fumecheng-13737	59	25	techniques	technique	NOUN
fumecheng-13737	59	26	for	for	ADP
fumecheng-13737	59	27	design	design	NOUN
fumecheng-13737	59	28	and	and	CCONJ
fumecheng-13737	59	29	optimization	optimization	NOUN
fumecheng-13737	59	30	.	.	PUNCT
fumecheng-13737	60	1	a	a	DET
fumecheng-13737	60	2	fast	fast	ADJ
fumecheng-13737	60	3	insight	insight	NOUN
fumecheng-13737	60	4	into	into	ADP
fumecheng-13737	60	5	nonlinear	nonlinear	ADJ
fumecheng-13737	60	6	frequency	frequency	NOUN
fumecheng-13737	60	7	estimation	estimation	NOUN
fumecheng-13737	60	8	of	of	ADP
fumecheng-13737	60	9	stringer	stringer	NOUN
fumecheng-13737	60	10	-	-	PUNCT
fumecheng-13737	60	11	stiffened	stiffen	VERB
fumecheng-13737	60	12	shells	shell	NOUN
fumecheng-13737	60	13	with	with	ADP
fumecheng-13737	60	14	high	high	ADJ
fumecheng-13737	60	15	accuracy	accuracy	NOUN
fumecheng-13737	60	16	789	789	NUM
fumecheng-13737	60	17	solution	solution	NOUN
fumecheng-13737	60	18	methods	method	NOUN
fumecheng-13737	60	19	for	for	ADP
fumecheng-13737	60	20	nonlinear	nonlinear	ADJ
fumecheng-13737	60	21	differential	differential	ADJ
fumecheng-13737	60	22	equations	equation	NOUN
fumecheng-13737	60	23	are	be	AUX
fumecheng-13737	60	24	typically	typically	ADV
fumecheng-13737	60	25	categorized	categorize	VERB
fumecheng-13737	60	26	into	into	ADP
fumecheng-13737	60	27	numerical	numerical	ADJ
fumecheng-13737	60	28	and	and	CCONJ
fumecheng-13737	60	29	analytical	analytical	ADJ
fumecheng-13737	60	30	approaches	approach	NOUN
fumecheng-13737	60	31	.	.	PUNCT
fumecheng-13737	61	1	the	the	DET
fumecheng-13737	61	2	free	free	ADJ
fumecheng-13737	61	3	vibration	vibration	NOUN
fumecheng-13737	61	4	and	and	CCONJ
fumecheng-13737	61	5	stability	stability	NOUN
fumecheng-13737	61	6	of	of	ADP
fumecheng-13737	61	7	stringer	stringer	NOUN
fumecheng-13737	61	8	-	-	PUNCT
fumecheng-13737	61	9	stiffened	stiffen	VERB
fumecheng-13737	61	10	shells	shell	NOUN
fumecheng-13737	61	11	have	have	AUX
fumecheng-13737	61	12	been	be	AUX
fumecheng-13737	61	13	the	the	DET
fumecheng-13737	61	14	subject	subject	NOUN
fumecheng-13737	61	15	of	of	ADP
fumecheng-13737	61	16	various	various	ADJ
fumecheng-13737	61	17	numerical	numerical	ADJ
fumecheng-13737	61	18	investigations	investigation	NOUN
fumecheng-13737	61	19	[	[	X
fumecheng-13737	61	20	2	2	NUM
fumecheng-13737	61	21	,	,	PUNCT
fumecheng-13737	61	22	18	18	NUM
fumecheng-13737	61	23	,	,	PUNCT
fumecheng-13737	61	24	19	19	NUM
fumecheng-13737	61	25	]	]	PUNCT
fumecheng-13737	61	26	.	.	PUNCT
fumecheng-13737	62	1	in	in	ADP
fumecheng-13737	62	2	this	this	DET
fumecheng-13737	62	3	context	context	NOUN
fumecheng-13737	62	4	,	,	PUNCT
fumecheng-13737	62	5	developments	development	NOUN
fumecheng-13737	62	6	in	in	ADP
fumecheng-13737	62	7	finite	finite	ADJ
fumecheng-13737	62	8	element	element	NOUN
fumecheng-13737	62	9	methods	method	NOUN
fumecheng-13737	62	10	for	for	ADP
fumecheng-13737	62	11	laminated	laminated	ADJ
fumecheng-13737	62	12	shell	shell	NOUN
fumecheng-13737	62	13	structures	structure	NOUN
fumecheng-13737	62	14	[	[	X
fumecheng-13737	62	15	20	20	NUM
fumecheng-13737	62	16	]	]	PUNCT
fumecheng-13737	62	17	,	,	PUNCT
fumecheng-13737	62	18	as	as	ADV
fumecheng-13737	62	19	well	well	ADV
fumecheng-13737	62	20	as	as	ADP
fumecheng-13737	62	21	in	in	ADP
fumecheng-13737	62	22	isogeometric	isogeometric	ADJ
fumecheng-13737	62	23	finite	finite	NOUN
fumecheng-13737	62	24	element	element	NOUN
fumecheng-13737	62	25	formulations	formulation	NOUN
fumecheng-13737	62	26	[	[	X
fumecheng-13737	62	27	21	21	NUM
fumecheng-13737	62	28	]	]	PUNCT
fumecheng-13737	62	29	,	,	PUNCT
fumecheng-13737	62	30	have	have	AUX
fumecheng-13737	62	31	provided	provide	VERB
fumecheng-13737	62	32	highly	highly	ADV
fumecheng-13737	62	33	efficient	efficient	ADJ
fumecheng-13737	62	34	numerical	numerical	ADJ
fumecheng-13737	62	35	tools	tool	NOUN
fumecheng-13737	62	36	relevant	relevant	ADJ
fumecheng-13737	62	37	to	to	ADP
fumecheng-13737	62	38	such	such	ADJ
fumecheng-13737	62	39	analyses	analysis	NOUN
fumecheng-13737	62	40	.	.	PUNCT
fumecheng-13737	63	1	however	however	ADV
fumecheng-13737	63	2	,	,	PUNCT
fumecheng-13737	63	3	solving	solve	VERB
fumecheng-13737	63	4	nonlinear	nonlinear	ADJ
fumecheng-13737	63	5	problems	problem	NOUN
fumecheng-13737	63	6	with	with	ADP
fumecheng-13737	63	7	high	high	ADJ
fumecheng-13737	63	8	accuracy	accuracy	NOUN
fumecheng-13737	63	9	presents	present	VERB
fumecheng-13737	63	10	a	a	DET
fumecheng-13737	63	11	considerable	considerable	ADJ
fumecheng-13737	63	12	challenge	challenge	NOUN
fumecheng-13737	63	13	,	,	PUNCT
fumecheng-13737	63	14	and	and	CCONJ
fumecheng-13737	63	15	obtaining	obtain	VERB
fumecheng-13737	63	16	exact	exact	ADJ
fumecheng-13737	63	17	analytical	analytical	ADJ
fumecheng-13737	63	18	solutions	solution	NOUN
fumecheng-13737	63	19	is	be	AUX
fumecheng-13737	63	20	often	often	ADV
fumecheng-13737	63	21	even	even	ADV
fumecheng-13737	63	22	more	more	ADV
fumecheng-13737	63	23	complex	complex	ADJ
fumecheng-13737	63	24	.	.	PUNCT
fumecheng-13737	64	1	to	to	PART
fumecheng-13737	64	2	overcome	overcome	VERB
fumecheng-13737	64	3	these	these	DET
fumecheng-13737	64	4	limitations	limitation	NOUN
fumecheng-13737	64	5	,	,	PUNCT
fumecheng-13737	64	6	researchers	researcher	NOUN
fumecheng-13737	64	7	have	have	AUX
fumecheng-13737	64	8	developed	develop	VERB
fumecheng-13737	64	9	several	several	ADJ
fumecheng-13737	64	10	advanced	advanced	ADJ
fumecheng-13737	64	11	approximate	approximate	ADJ
fumecheng-13737	64	12	analytical	analytical	ADJ
fumecheng-13737	64	13	techniques	technique	NOUN
fumecheng-13737	64	14	.	.	PUNCT
fumecheng-13737	65	1	these	these	DET
fumecheng-13737	65	2	methods	method	NOUN
fumecheng-13737	65	3	include	include	VERB
fumecheng-13737	65	4	the	the	DET
fumecheng-13737	65	5	harmonic	harmonic	ADJ
fumecheng-13737	65	6	balance	balance	NOUN
fumecheng-13737	65	7	method	method	NOUN
fumecheng-13737	65	8	(	(	PUNCT
fumecheng-13737	65	9	hbm	hbm	PROPN
fumecheng-13737	65	10	)	)	PUNCT
fumecheng-13737	66	1	[	[	X
fumecheng-13737	66	2	22	22	NUM
fumecheng-13737	66	3	,	,	PUNCT
fumecheng-13737	66	4	23	23	NUM
fumecheng-13737	66	5	]	]	PUNCT
fumecheng-13737	66	6	,	,	PUNCT
fumecheng-13737	66	7	the	the	DET
fumecheng-13737	66	8	energy	energy	NOUN
fumecheng-13737	66	9	balance	balance	NOUN
fumecheng-13737	66	10	method	method	NOUN
fumecheng-13737	66	11	(	(	PUNCT
fumecheng-13737	66	12	ebm	ebm	NOUN
fumecheng-13737	66	13	)	)	PUNCT
fumecheng-13737	67	1	[	[	X
fumecheng-13737	67	2	24	24	NUM
fumecheng-13737	67	3	,	,	PUNCT
fumecheng-13737	67	4	25	25	NUM
fumecheng-13737	67	5	]	]	PUNCT
fumecheng-13737	67	6	,	,	PUNCT
fumecheng-13737	67	7	the	the	DET
fumecheng-13737	67	8	homotopy	homotopy	NOUN
fumecheng-13737	67	9	perturbation	perturbation	NOUN
fumecheng-13737	67	10	method	method	NOUN
fumecheng-13737	67	11	(	(	PUNCT
fumecheng-13737	67	12	hpm	hpm	NOUN
fumecheng-13737	67	13	)	)	PUNCT
fumecheng-13737	68	1	[	[	X
fumecheng-13737	68	2	26	26	NUM
fumecheng-13737	68	3	]	]	PUNCT
fumecheng-13737	68	4	,	,	PUNCT
fumecheng-13737	68	5	the	the	DET
fumecheng-13737	68	6	li	li	PROPN
fumecheng-13737	68	7	–	–	PUNCT
fumecheng-13737	68	8	he	he	PRON
fumecheng-13737	68	9	’s	’	VERB
fumecheng-13737	68	10	modified	modify	VERB
fumecheng-13737	68	11	homotopy	homotopy	PROPN
fumecheng-13737	68	12	perturbation	perturbation	NOUN
fumecheng-13737	68	13	method	method	NOUN
fumecheng-13737	68	14	(	(	PUNCT
fumecheng-13737	68	15	li	li	PROPN
fumecheng-13737	68	16	-	-	ADJ
fumecheng-13737	68	17	he	he	PRON
fumecheng-13737	68	18	hpm	hpm	NOUN
fumecheng-13737	68	19	)	)	PUNCT
fumecheng-13737	69	1	[	[	X
fumecheng-13737	69	2	27	27	NUM
fumecheng-13737	69	3	]	]	PUNCT
fumecheng-13737	69	4	,	,	PUNCT
fumecheng-13737	69	5	the	the	DET
fumecheng-13737	69	6	hamiltonian	hamiltonian	ADJ
fumecheng-13737	69	7	approach	approach	NOUN
fumecheng-13737	69	8	(	(	PUNCT
fumecheng-13737	69	9	ha	ha	INTJ
fumecheng-13737	69	10	)	)	PUNCT
fumecheng-13737	70	1	[	[	X
fumecheng-13737	70	2	28	28	NUM
fumecheng-13737	70	3	,	,	PUNCT
fumecheng-13737	70	4	29	29	NUM
fumecheng-13737	70	5	]	]	PUNCT
fumecheng-13737	70	6	,	,	PUNCT
fumecheng-13737	70	7	the	the	DET
fumecheng-13737	70	8	variational	variational	ADJ
fumecheng-13737	70	9	iteration	iteration	NOUN
fumecheng-13737	70	10	algorithms	algorithm	NOUN
fumecheng-13737	70	11	(	(	PUNCT
fumecheng-13737	70	12	vim	vim	NOUN
fumecheng-13737	70	13	)	)	PUNCT
fumecheng-13737	71	1	[	[	X
fumecheng-13737	71	2	30	30	NUM
fumecheng-13737	71	3	,	,	PUNCT
fumecheng-13737	71	4	31	31	NUM
fumecheng-13737	71	5	]	]	PUNCT
fumecheng-13737	71	6	,	,	PUNCT
fumecheng-13737	71	7	the	the	DET
fumecheng-13737	71	8	global	global	ADJ
fumecheng-13737	71	9	error	error	NOUN
fumecheng-13737	71	10	minimization	minimization	NOUN
fumecheng-13737	71	11	(	(	PUNCT
fumecheng-13737	71	12	gem	gem	NOUN
fumecheng-13737	71	13	)	)	PUNCT
fumecheng-13737	72	1	[	[	X
fumecheng-13737	72	2	32	32	NUM
fumecheng-13737	72	3	,	,	PUNCT
fumecheng-13737	72	4	33	33	NUM
fumecheng-13737	72	5	]	]	PUNCT
fumecheng-13737	72	6	,	,	PUNCT
fumecheng-13737	72	7	the	the	DET
fumecheng-13737	72	8	modified	modify	VERB
fumecheng-13737	72	9	algebraic	algebraic	ADJ
fumecheng-13737	72	10	method	method	NOUN
fumecheng-13737	72	11	(	(	PUNCT
fumecheng-13737	72	12	mam	mam	PROPN
fumecheng-13737	72	13	)	)	PUNCT
fumecheng-13737	72	14	[	[	X
fumecheng-13737	72	15	34	34	NUM
fumecheng-13737	72	16	,	,	PUNCT
fumecheng-13737	72	17	35	35	NUM
fumecheng-13737	72	18	]	]	PUNCT
fumecheng-13737	72	19	,	,	PUNCT
fumecheng-13737	72	20	and	and	CCONJ
fumecheng-13737	72	21	the	the	DET
fumecheng-13737	72	22	variational	variational	ADJ
fumecheng-13737	72	23	approach	approach	NOUN
fumecheng-13737	72	24	(	(	PUNCT
fumecheng-13737	72	25	va	va	NOUN
fumecheng-13737	72	26	)	)	PUNCT
fumecheng-13737	73	1	[	[	X
fumecheng-13737	73	2	36	36	NUM
fumecheng-13737	73	3	]	]	PUNCT
fumecheng-13737	73	4	.	.	PUNCT
fumecheng-13737	74	1	in	in	ADP
fumecheng-13737	74	2	recent	recent	ADJ
fumecheng-13737	74	3	studies	study	NOUN
fumecheng-13737	74	4	,	,	PUNCT
fumecheng-13737	74	5	the	the	DET
fumecheng-13737	74	6	ha	ha	X
fumecheng-13737	75	1	[	[	X
fumecheng-13737	75	2	37	37	NUM
fumecheng-13737	75	3	]	]	PUNCT
fumecheng-13737	75	4	,	,	PUNCT
fumecheng-13737	75	5	the	the	DET
fumecheng-13737	75	6	hpm	hpm	NOUN
fumecheng-13737	76	1	[	[	X
fumecheng-13737	76	2	38	38	NUM
fumecheng-13737	76	3	]	]	PUNCT
fumecheng-13737	76	4	,	,	PUNCT
fumecheng-13737	76	5	and	and	CCONJ
fumecheng-13737	76	6	the	the	DET
fumecheng-13737	76	7	global	global	ADJ
fumecheng-13737	76	8	residue	residue	NOUN
fumecheng-13737	76	9	harmonic	harmonic	ADJ
fumecheng-13737	76	10	balance	balance	NOUN
fumecheng-13737	76	11	method	method	NOUN
fumecheng-13737	76	12	(	(	PUNCT
fumecheng-13737	76	13	grhbm	grhbm	PROPN
fumecheng-13737	76	14	)	)	PUNCT
fumecheng-13737	77	1	[	[	X
fumecheng-13737	77	2	39	39	NUM
fumecheng-13737	77	3	]	]	PUNCT
fumecheng-13737	77	4	have	have	AUX
fumecheng-13737	77	5	been	be	AUX
fumecheng-13737	77	6	employed	employ	VERB
fumecheng-13737	77	7	to	to	PART
fumecheng-13737	77	8	determine	determine	VERB
fumecheng-13737	77	9	the	the	DET
fumecheng-13737	77	10	nonlinear	nonlinear	ADJ
fumecheng-13737	77	11	frequency	frequency	NOUN
fumecheng-13737	77	12	of	of	ADP
fumecheng-13737	77	13	stringer	stringer	NOUN
fumecheng-13737	77	14	-	-	PUNCT
fumecheng-13737	77	15	stiffened	stiffen	VERB
fumecheng-13737	77	16	shells	shell	NOUN
fumecheng-13737	77	17	.	.	PUNCT
fumecheng-13737	78	1	despite	despite	SCONJ
fumecheng-13737	78	2	their	their	PRON
fumecheng-13737	78	3	effectiveness	effectiveness	NOUN
fumecheng-13737	78	4	,	,	PUNCT
fumecheng-13737	78	5	each	each	DET
fumecheng-13737	78	6	method	method	NOUN
fumecheng-13737	78	7	has	have	VERB
fumecheng-13737	78	8	notable	notable	ADJ
fumecheng-13737	78	9	limitations	limitation	NOUN
fumecheng-13737	78	10	when	when	SCONJ
fumecheng-13737	78	11	applied	apply	VERB
fumecheng-13737	78	12	to	to	ADP
fumecheng-13737	78	13	complex	complex	ADJ
fumecheng-13737	78	14	geometries	geometry	NOUN
fumecheng-13737	78	15	like	like	ADP
fumecheng-13737	78	16	stringer	stringer	NOUN
fumecheng-13737	78	17	-	-	PUNCT
fumecheng-13737	78	18	stiffened	stiffen	VERB
fumecheng-13737	78	19	shells	shell	NOUN
fumecheng-13737	78	20	.	.	PUNCT
fumecheng-13737	79	1	the	the	DET
fumecheng-13737	79	2	ha	ha	PROPN
fumecheng-13737	79	3	often	often	ADV
fumecheng-13737	79	4	requires	require	VERB
fumecheng-13737	79	5	complex	complex	ADJ
fumecheng-13737	79	6	energy	energy	NOUN
fumecheng-13737	79	7	formulations	formulation	NOUN
fumecheng-13737	79	8	and	and	CCONJ
fumecheng-13737	79	9	extensive	extensive	ADJ
fumecheng-13737	79	10	algebraic	algebraic	ADJ
fumecheng-13737	79	11	manipulation	manipulation	NOUN
fumecheng-13737	79	12	,	,	PUNCT
fumecheng-13737	79	13	making	make	VERB
fumecheng-13737	79	14	it	it	PRON
fumecheng-13737	79	15	computationally	computationally	ADV
fumecheng-13737	79	16	demanding	demand	VERB
fumecheng-13737	79	17	and	and	CCONJ
fumecheng-13737	79	18	less	less	ADV
fumecheng-13737	79	19	suitable	suitable	ADJ
fumecheng-13737	79	20	for	for	ADP
fumecheng-13737	79	21	systems	system	NOUN
fumecheng-13737	79	22	involving	involve	VERB
fumecheng-13737	79	23	damping	damp	VERB
fumecheng-13737	79	24	or	or	CCONJ
fumecheng-13737	79	25	external	external	ADJ
fumecheng-13737	79	26	forces	force	NOUN
fumecheng-13737	79	27	.	.	PUNCT
fumecheng-13737	80	1	the	the	DET
fumecheng-13737	80	2	hpm	hpm	NOUN
fumecheng-13737	80	3	,	,	PUNCT
fumecheng-13737	80	4	despite	despite	SCONJ
fumecheng-13737	80	5	its	its	PRON
fumecheng-13737	80	6	flexibility	flexibility	NOUN
fumecheng-13737	80	7	,	,	PUNCT
fumecheng-13737	80	8	relies	rely	VERB
fumecheng-13737	80	9	on	on	ADP
fumecheng-13737	80	10	iterative	iterative	NOUN
fumecheng-13737	80	11	series	series	NOUN
fumecheng-13737	80	12	expansions	expansion	NOUN
fumecheng-13737	80	13	and	and	CCONJ
fumecheng-13737	80	14	the	the	DET
fumecheng-13737	80	15	construction	construction	NOUN
fumecheng-13737	80	16	of	of	ADP
fumecheng-13737	80	17	a	a	DET
fumecheng-13737	80	18	suitable	suitable	ADJ
fumecheng-13737	80	19	homotopy	homotopy	NOUN
fumecheng-13737	80	20	.	.	PUNCT
fumecheng-13737	81	1	this	this	DET
fumecheng-13737	81	2	process	process	NOUN
fumecheng-13737	81	3	can	can	AUX
fumecheng-13737	81	4	be	be	AUX
fumecheng-13737	81	5	arduous	arduous	ADJ
fumecheng-13737	81	6	and	and	CCONJ
fumecheng-13737	81	7	time	time	NOUN
fumecheng-13737	81	8	-	-	PUNCT
fumecheng-13737	81	9	consuming	consume	VERB
fumecheng-13737	81	10	for	for	ADP
fumecheng-13737	81	11	higher	high	ADJ
fumecheng-13737	81	12	-	-	PUNCT
fumecheng-13737	81	13	order	order	NOUN
fumecheng-13737	81	14	nonlinear	nonlinear	ADJ
fumecheng-13737	81	15	systems	system	NOUN
fumecheng-13737	81	16	.	.	PUNCT
fumecheng-13737	82	1	furthermore	furthermore	ADV
fumecheng-13737	82	2	,	,	PUNCT
fumecheng-13737	82	3	the	the	DET
fumecheng-13737	82	4	accuracy	accuracy	NOUN
fumecheng-13737	82	5	of	of	ADP
fumecheng-13737	82	6	the	the	DET
fumecheng-13737	82	7	model	model	NOUN
fumecheng-13737	82	8	tends	tend	VERB
fumecheng-13737	82	9	to	to	PART
fumecheng-13737	82	10	decrease	decrease	VERB
fumecheng-13737	82	11	at	at	ADP
fumecheng-13737	82	12	large	large	ADJ
fumecheng-13737	82	13	amplitudes	amplitude	NOUN
fumecheng-13737	82	14	.	.	PUNCT
fumecheng-13737	83	1	the	the	DET
fumecheng-13737	83	2	grhbm	grhbm	NOUN
fumecheng-13737	83	3	is	be	AUX
fumecheng-13737	83	4	recognized	recognize	VERB
fumecheng-13737	83	5	for	for	ADP
fumecheng-13737	83	6	its	its	PRON
fumecheng-13737	83	7	precision	precision	NOUN
fumecheng-13737	83	8	;	;	PUNCT
fumecheng-13737	83	9	however	however	ADV
fumecheng-13737	83	10	,	,	PUNCT
fumecheng-13737	83	11	it	it	PRON
fumecheng-13737	83	12	requires	require	VERB
fumecheng-13737	83	13	balancing	balance	VERB
fumecheng-13737	83	14	multiple	multiple	ADJ
fumecheng-13737	83	15	harmonics	harmonic	NOUN
fumecheng-13737	83	16	and	and	CCONJ
fumecheng-13737	83	17	computing	compute	VERB
fumecheng-13737	83	18	global	global	ADJ
fumecheng-13737	83	19	residuals	residual	NOUN
fumecheng-13737	83	20	,	,	PUNCT
fumecheng-13737	83	21	which	which	PRON
fumecheng-13737	83	22	leads	lead	VERB
fumecheng-13737	83	23	to	to	ADP
fumecheng-13737	83	24	high	high	ADJ
fumecheng-13737	83	25	algebraic	algebraic	ADJ
fumecheng-13737	83	26	complexity	complexity	NOUN
fumecheng-13737	83	27	and	and	CCONJ
fumecheng-13737	83	28	necessitates	necessitate	VERB
fumecheng-13737	83	29	the	the	DET
fumecheng-13737	83	30	use	use	NOUN
fumecheng-13737	83	31	of	of	ADP
fumecheng-13737	83	32	symbolic	symbolic	ADJ
fumecheng-13737	83	33	computation	computation	NOUN
fumecheng-13737	83	34	tools	tool	NOUN
fumecheng-13737	83	35	.	.	PUNCT
fumecheng-13737	84	1	despite	despite	SCONJ
fumecheng-13737	84	2	significant	significant	ADJ
fumecheng-13737	84	3	progress	progress	NOUN
fumecheng-13737	84	4	in	in	ADP
fumecheng-13737	84	5	the	the	DET
fumecheng-13737	84	6	field	field	NOUN
fumecheng-13737	84	7	,	,	PUNCT
fumecheng-13737	84	8	existing	exist	VERB
fumecheng-13737	84	9	analytical	analytical	ADJ
fumecheng-13737	84	10	methodologies	methodology	NOUN
fumecheng-13737	84	11	continue	continue	VERB
fumecheng-13737	84	12	to	to	PART
fumecheng-13737	84	13	face	face	VERB
fumecheng-13737	84	14	challenges	challenge	NOUN
fumecheng-13737	84	15	in	in	ADP
fumecheng-13737	84	16	balancing	balance	VERB
fumecheng-13737	84	17	simplicity	simplicity	NOUN
fumecheng-13737	84	18	,	,	PUNCT
fumecheng-13737	84	19	accuracy	accuracy	NOUN
fumecheng-13737	84	20	,	,	PUNCT
fumecheng-13737	84	21	and	and	CCONJ
fumecheng-13737	84	22	applicability	applicability	NOUN
fumecheng-13737	84	23	to	to	ADP
fumecheng-13737	84	24	the	the	DET
fumecheng-13737	84	25	strongly	strongly	ADV
fumecheng-13737	84	26	nonlinear	nonlinear	ADJ
fumecheng-13737	84	27	dynamics	dynamic	NOUN
fumecheng-13737	84	28	of	of	ADP
fumecheng-13737	84	29	stringer	stringer	NOUN
fumecheng-13737	84	30	-	-	PUNCT
fumecheng-13737	84	31	stiffened	stiffen	VERB
fumecheng-13737	84	32	shells	shell	NOUN
fumecheng-13737	84	33	,	,	PUNCT
fumecheng-13737	84	34	particularly	particularly	ADV
fumecheng-13737	84	35	at	at	ADP
fumecheng-13737	84	36	large	large	ADJ
fumecheng-13737	84	37	vibration	vibration	NOUN
fumecheng-13737	84	38	amplitudes	amplitude	NOUN
fumecheng-13737	84	39	.	.	PUNCT
fumecheng-13737	85	1	the	the	DET
fumecheng-13737	85	2	cubicquintic	cubicquintic	ADJ
fumecheng-13737	85	3	nonlinearities	nonlinearitie	NOUN
fumecheng-13737	85	4	resulting	result	VERB
fumecheng-13737	85	5	from	from	ADP
fumecheng-13737	85	6	geometric	geometric	ADJ
fumecheng-13737	85	7	and	and	CCONJ
fumecheng-13737	85	8	material	material	NOUN
fumecheng-13737	85	9	effects	effect	NOUN
fumecheng-13737	85	10	demand	demand	VERB
fumecheng-13737	85	11	rapid	rapid	ADJ
fumecheng-13737	85	12	,	,	PUNCT
fumecheng-13737	85	13	non	non	ADJ
fumecheng-13737	85	14	-	-	ADJ
fumecheng-13737	85	15	iterative	iterative	ADJ
fumecheng-13737	85	16	solutions	solution	NOUN
fumecheng-13737	85	17	that	that	PRON
fumecheng-13737	85	18	retain	retain	VERB
fumecheng-13737	85	19	accuracy	accuracy	NOUN
fumecheng-13737	85	20	across	across	ADP
fumecheng-13737	85	21	a	a	DET
fumecheng-13737	85	22	wide	wide	ADJ
fumecheng-13737	85	23	amplitude	amplitude	NOUN
fumecheng-13737	85	24	range	range	NOUN
fumecheng-13737	85	25	.	.	PUNCT
fumecheng-13737	86	1	this	this	DET
fumecheng-13737	86	2	study	study	NOUN
fumecheng-13737	86	3	proposes	propose	VERB
fumecheng-13737	86	4	three	three	NUM
fumecheng-13737	86	5	novel	novel	ADJ
fumecheng-13737	86	6	analytical	analytical	ADJ
fumecheng-13737	86	7	methods	method	NOUN
fumecheng-13737	86	8	:	:	PUNCT
fumecheng-13737	86	9	the	the	DET
fumecheng-13737	86	10	adaptive	adaptive	ADJ
fumecheng-13737	86	11	location	location	NOUN
fumecheng-13737	86	12	point	point	NOUN
fumecheng-13737	86	13	-	-	PUNCT
fumecheng-13737	86	14	based	base	VERB
fumecheng-13737	86	15	he	he	PRON
fumecheng-13737	86	16	’s	’	VERB
fumecheng-13737	86	17	formulation	formulation	NOUN
fumecheng-13737	86	18	(	(	PUNCT
fumecheng-13737	86	19	alpf	alpf	PROPN
fumecheng-13737	86	20	)	)	PUNCT
fumecheng-13737	86	21	,	,	PUNCT
fumecheng-13737	86	22	the	the	DET
fumecheng-13737	86	23	square	square	ADJ
fumecheng-13737	86	24	error	error	NOUN
fumecheng-13737	86	25	minimizing	minimizing	NOUN
fumecheng-13737	86	26	-	-	PUNCT
fumecheng-13737	86	27	based	base	VERB
fumecheng-13737	86	28	frequency	frequency	NOUN
fumecheng-13737	86	29	formulation	formulation	NOUN
fumecheng-13737	86	30	(	(	PUNCT
fumecheng-13737	86	31	semf	semf	NOUN
fumecheng-13737	86	32	)	)	PUNCT
fumecheng-13737	86	33	,	,	PUNCT
fumecheng-13737	86	34	and	and	CCONJ
fumecheng-13737	86	35	the	the	DET
fumecheng-13737	86	36	hamiltonian	hamiltonian	NOUN
fumecheng-13737	86	37	-	-	PUNCT
fumecheng-13737	86	38	based	base	VERB
fumecheng-13737	86	39	frequency	frequency	NOUN
fumecheng-13737	86	40	-	-	PUNCT
fumecheng-13737	86	41	amplitude	amplitude	NOUN
fumecheng-13737	86	42	formulation	formulation	NOUN
fumecheng-13737	86	43	(	(	PUNCT
fumecheng-13737	86	44	hfaf	hfaf	NOUN
fumecheng-13737	86	45	)	)	PUNCT
fumecheng-13737	86	46	,	,	PUNCT
fumecheng-13737	86	47	to	to	PART
fumecheng-13737	86	48	derive	derive	VERB
fumecheng-13737	86	49	closed	close	VERB
fumecheng-13737	86	50	-	-	PUNCT
fumecheng-13737	86	51	form	form	NOUN
fumecheng-13737	86	52	expressions	expression	NOUN
fumecheng-13737	86	53	for	for	ADP
fumecheng-13737	86	54	the	the	DET
fumecheng-13737	86	55	nonlinear	nonlinear	ADJ
fumecheng-13737	86	56	frequency	frequency	NOUN
fumecheng-13737	86	57	of	of	ADP
fumecheng-13737	86	58	stringer	stringer	NOUN
fumecheng-13737	86	59	-	-	PUNCT
fumecheng-13737	86	60	stiffened	stiffen	VERB
fumecheng-13737	86	61	shells	shell	NOUN
fumecheng-13737	86	62	.	.	PUNCT
fumecheng-13737	87	1	these	these	DET
fumecheng-13737	87	2	approaches	approach	NOUN
fumecheng-13737	87	3	are	be	AUX
fumecheng-13737	87	4	optimized	optimize	VERB
fumecheng-13737	87	5	for	for	ADP
fumecheng-13737	87	6	simplicity	simplicity	NOUN
fumecheng-13737	87	7	and	and	CCONJ
fumecheng-13737	87	8	computational	computational	ADJ
fumecheng-13737	87	9	efficiency	efficiency	NOUN
fumecheng-13737	87	10	,	,	PUNCT
fumecheng-13737	87	11	effectively	effectively	ADV
fumecheng-13737	87	12	overcoming	overcome	VERB
fumecheng-13737	87	13	the	the	DET
fumecheng-13737	87	14	complexity	complexity	NOUN
fumecheng-13737	87	15	of	of	ADP
fumecheng-13737	87	16	earlier	early	ADJ
fumecheng-13737	87	17	methods	method	NOUN
fumecheng-13737	87	18	while	while	SCONJ
fumecheng-13737	87	19	maintaining	maintain	VERB
fumecheng-13737	87	20	high	high	ADJ
fumecheng-13737	87	21	accuracy	accuracy	NOUN
fumecheng-13737	87	22	.	.	PUNCT
fumecheng-13737	88	1	their	their	PRON
fumecheng-13737	88	2	performance	performance	NOUN
fumecheng-13737	88	3	is	be	AUX
fumecheng-13737	88	4	validated	validate	VERB
fumecheng-13737	88	5	through	through	ADP
fumecheng-13737	88	6	comparisons	comparison	NOUN
fumecheng-13737	88	7	with	with	ADP
fumecheng-13737	88	8	exact	exact	ADJ
fumecheng-13737	88	9	solutions	solution	NOUN
fumecheng-13737	88	10	and	and	CCONJ
fumecheng-13737	88	11	numerical	numerical	ADJ
fumecheng-13737	88	12	simulations	simulation	NOUN
fumecheng-13737	88	13	.	.	PUNCT
fumecheng-13737	89	1	the	the	DET
fumecheng-13737	89	2	proposed	propose	VERB
fumecheng-13737	89	3	methods	method	NOUN
fumecheng-13737	89	4	offer	offer	VERB
fumecheng-13737	89	5	practical	practical	ADJ
fumecheng-13737	89	6	tools	tool	NOUN
fumecheng-13737	89	7	for	for	ADP
fumecheng-13737	89	8	engineers	engineer	NOUN
fumecheng-13737	89	9	and	and	CCONJ
fumecheng-13737	89	10	researchers	researcher	NOUN
fumecheng-13737	89	11	studying	study	VERB
fumecheng-13737	89	12	nonlinear	nonlinear	ADJ
fumecheng-13737	89	13	vibrations	vibration	NOUN
fumecheng-13737	89	14	in	in	ADP
fumecheng-13737	89	15	complex	complex	ADJ
fumecheng-13737	89	16	shell	shell	NOUN
fumecheng-13737	89	17	structures	structure	NOUN
fumecheng-13737	89	18	.	.	PUNCT
fumecheng-13737	90	1	2	2	X
fumecheng-13737	90	2	.	.	X
fumecheng-13737	90	3	mathematical	mathematical	ADJ
fumecheng-13737	90	4	model	model	NOUN
fumecheng-13737	90	5	as	as	SCONJ
fumecheng-13737	90	6	illustrated	illustrate	VERB
fumecheng-13737	90	7	in	in	ADP
fumecheng-13737	90	8	fig	fig	NOUN
fumecheng-13737	90	9	.	.	PUNCT
fumecheng-13737	91	1	1	1	NUM
fumecheng-13737	91	2	,	,	PUNCT
fumecheng-13737	91	3	a	a	DET
fumecheng-13737	91	4	circular	circular	ADJ
fumecheng-13737	91	5	cylindrical	cylindrical	ADJ
fumecheng-13737	91	6	shell	shell	NOUN
fumecheng-13737	91	7	is	be	AUX
fumecheng-13737	91	8	stiffened	stiffen	VERB
fumecheng-13737	91	9	by	by	ADP
fumecheng-13737	91	10	uniformly	uniformly	ADV
fumecheng-13737	91	11	distributed	distribute	VERB
fumecheng-13737	91	12	external	external	ADJ
fumecheng-13737	91	13	stringers	stringer	NOUN
fumecheng-13737	91	14	.	.	PUNCT
fumecheng-13737	92	1	the	the	DET
fumecheng-13737	92	2	supports	support	NOUN
fumecheng-13737	92	3	consist	consist	VERB
fumecheng-13737	92	4	of	of	ADP
fumecheng-13737	92	5	ribs	rib	NOUN
fumecheng-13737	92	6	,	,	PUNCT
fumecheng-13737	92	7	modeled	model	VERB
fumecheng-13737	92	8	as	as	ADP
fumecheng-13737	92	9	one	one	NUM
fumecheng-13737	92	10	-	-	PUNCT
fumecheng-13737	92	11	dimensional	dimensional	ADJ
fumecheng-13737	92	12	elastic	elastic	ADJ
fumecheng-13737	92	13	elements	element	NOUN
fumecheng-13737	92	14	,	,	PUNCT
fumecheng-13737	92	15	which	which	PRON
fumecheng-13737	92	16	are	be	AUX
fumecheng-13737	92	17	evenly	evenly	ADV
fumecheng-13737	92	18	spaced	space	VERB
fumecheng-13737	92	19	along	along	ADP
fumecheng-13737	92	20	the	the	DET
fumecheng-13737	92	21	shell	shell	NOUN
fumecheng-13737	92	22	.	.	PUNCT
fumecheng-13737	93	1	to	to	PART
fumecheng-13737	93	2	determine	determine	VERB
fumecheng-13737	93	3	the	the	DET
fumecheng-13737	93	4	displacements	displacement	NOUN
fumecheng-13737	93	5	and	and	CCONJ
fumecheng-13737	93	6	vibration	vibration	NOUN
fumecheng-13737	93	7	frequencies	frequency	NOUN
fumecheng-13737	93	8	,	,	PUNCT
fumecheng-13737	93	9	it	it	PRON
fumecheng-13737	93	10	is	be	AUX
fumecheng-13737	93	11	assumed	assume	VERB
fumecheng-13737	93	12	that	that	SCONJ
fumecheng-13737	93	13	rib	rib	NOUN
fumecheng-13737	93	14	height	height	NOUN
fumecheng-13737	93	15	is	be	AUX
fumecheng-13737	93	16	much	much	ADV
fumecheng-13737	93	17	smaller	small	ADJ
fumecheng-13737	93	18	than	than	ADP
fumecheng-13737	93	19	the	the	DET
fumecheng-13737	93	20	shell	shell	NOUN
fumecheng-13737	93	21	's	's	PART
fumecheng-13737	93	22	radius	radius	NOUN
fumecheng-13737	93	23	of	of	ADP
fumecheng-13737	93	24	curvature	curvature	NOUN
fumecheng-13737	93	25	.	.	PUNCT
fumecheng-13737	94	1	moreover	moreover	ADV
fumecheng-13737	94	2	,	,	PUNCT
fumecheng-13737	94	3	interaction	interaction	NOUN
fumecheng-13737	94	4	between	between	ADP
fumecheng-13737	94	5	the	the	DET
fumecheng-13737	94	6	ribs	rib	NOUN
fumecheng-13737	94	7	in	in	ADP
fumecheng-13737	94	8	the	the	DET
fumecheng-13737	94	9	two	two	NUM
fumecheng-13737	94	10	directions	direction	NOUN
fumecheng-13737	94	11	is	be	AUX
fumecheng-13737	94	12	neglected	neglect	VERB
fumecheng-13737	94	13	.	.	PUNCT
fumecheng-13737	95	1	790	790	NUM
fumecheng-13737	95	2	c	c	X
fumecheng-13737	95	3	-	-	PUNCT
fumecheng-13737	95	4	h.	h.	NOUN
fumecheng-13737	95	5	he	he	PROPN
fumecheng-13737	95	6	,	,	PUNCT
fumecheng-13737	95	7	m.	m.	NOUN
fumecheng-13737	95	8	mohammadian	mohammadian	PROPN
fumecheng-13737	95	9	fig	fig	PROPN
fumecheng-13737	95	10	.	.	PUNCT
fumecheng-13737	95	11	1	1	NUM
fumecheng-13737	95	12	a	a	DET
fumecheng-13737	95	13	schematic	schematic	ADJ
fumecheng-13737	95	14	view	view	NOUN
fumecheng-13737	95	15	of	of	ADP
fumecheng-13737	95	16	a	a	DET
fumecheng-13737	95	17	stringer	stringer	NOUN
fumecheng-13737	95	18	-	-	PUNCT
fumecheng-13737	95	19	stiffened	stiffen	VERB
fumecheng-13737	95	20	shell	shell	NOUN
fumecheng-13737	95	21	structure	structure	NOUN
fumecheng-13737	95	22	to	to	PART
fumecheng-13737	95	23	study	study	VERB
fumecheng-13737	95	24	the	the	DET
fumecheng-13737	95	25	dynamics	dynamic	NOUN
fumecheng-13737	95	26	of	of	ADP
fumecheng-13737	95	27	the	the	DET
fumecheng-13737	95	28	orthotropic	orthotropic	ADJ
fumecheng-13737	95	29	stringer	stringer	NOUN
fumecheng-13737	95	30	-	-	PUNCT
fumecheng-13737	95	31	stiffened	stiffen	VERB
fumecheng-13737	95	32	shell	shell	NOUN
fumecheng-13737	95	33	under	under	ADP
fumecheng-13737	95	34	large	large	ADJ
fumecheng-13737	95	35	displacements	displacement	NOUN
fumecheng-13737	95	36	,	,	PUNCT
fumecheng-13737	95	37	the	the	DET
fumecheng-13737	95	38	following	follow	VERB
fumecheng-13737	95	39	governing	govern	VERB
fumecheng-13737	95	40	equations	equation	NOUN
fumecheng-13737	95	41	are	be	AUX
fumecheng-13737	95	42	employed	employ	VERB
fumecheng-13737	95	43	[	[	X
fumecheng-13737	95	44	40	40	NUM
fumecheng-13737	95	45	]	]	SYM
fumecheng-13737	95	46	:	:	PUNCT
fumecheng-13737	95	47	2	2	NUM
fumecheng-13737	95	48	2	2	NUM
fumecheng-13737	95	49	4	4	NUM
fumecheng-13737	95	50	2	2	NUM
fumecheng-13737	95	51	1	1	NUM
fumecheng-13737	95	52	2	2	NUM
fumecheng-13737	95	53	2	2	NUM
fumecheng-13737	95	54	(	(	PUNCT
fumecheng-13737	95	55	,	,	PUNCT
fumecheng-13737	95	56	)	)	PUNCT
fumecheng-13737	95	57	0	0	NUM
fumecheng-13737	95	58	,	,	PUNCT
fumecheng-13737	95	59	w	w	PROPN
fumecheng-13737	95	60	w	w	PROPN
fumecheng-13737	95	61	r	r	NOUN
fumecheng-13737	95	62	r	r	NOUN
fumecheng-13737	95	63	l	l	NOUN
fumecheng-13737	95	64	w	w	NOUN
fumecheng-13737	95	65	x	x	X
fumecheng-13737	95	66	t	t	NOUN
fumecheng-13737	95	67			PROPN
fumecheng-13737	95	68			ADP
fumecheng-13737	95	69			ADJ
fumecheng-13737	95	70			ADJ
fumecheng-13737	95	71			ADJ
fumecheng-13737	95	72			NOUN
fumecheng-13737	95	73	−	−	PROPN
fumecheng-13737	96	1	+	+	CCONJ
fumecheng-13737	97	1	−	−	PROPN
fumecheng-13737	97	2	=	=	SYM
fumecheng-13737	97	3			ADJ
fumecheng-13737	97	4			ADJ
fumecheng-13737	97	5	(	(	PUNCT
fumecheng-13737	97	6	1	1	NUM
fumecheng-13737	97	7	)	)	SYM
fumecheng-13737	97	8	4	4	NUM
fumecheng-13737	97	9	4	4	NUM
fumecheng-13737	97	10	4	4	NUM
fumecheng-13737	97	11	2	2	NUM
fumecheng-13737	97	12	2	2	NUM
fumecheng-13737	97	13	1	1	NUM
fumecheng-13737	97	14	1	1	NUM
fumecheng-13737	97	15	1	1	NUM
fumecheng-13737	97	16	1	1	NUM
fumecheng-13737	97	17	(	(	PUNCT
fumecheng-13737	97	18	,	,	PUNCT
fumecheng-13737	97	19	)	)	PUNCT
fumecheng-13737	97	20	0	0	NUM
fumecheng-13737	97	21	,	,	PUNCT
fumecheng-13737	97	22	2	2	NUM
fumecheng-13737	97	23	w	w	NOUN
fumecheng-13737	97	24	l	l	PROPN
fumecheng-13737	97	25	w	w	PROPN
fumecheng-13737	97	26	b	b	X
fumecheng-13737	97	27	ry	ry	ADJ
fumecheng-13737	97	28	x	x	SYM
fumecheng-13737	97	29	r	r	NOUN
fumecheng-13737	97	30			ADJ
fumecheng-13737	97	31			ADJ
fumecheng-13737	97	32			ADJ
fumecheng-13737	97	33			NOUN
fumecheng-13737	97	34	+	+	CCONJ
fumecheng-13737	97	35	−	−	PROPN
fumecheng-13737	97	36	=	=	SYM
fumecheng-13737	97	37			ADJ
fumecheng-13737	97	38			ADJ
fumecheng-13737	97	39	(	(	PUNCT
fumecheng-13737	97	40	2	2	NUM
fumecheng-13737	97	41	)	)	PUNCT
fumecheng-13737	97	42	where	where	SCONJ
fumecheng-13737	97	43	4	4	NUM
fumecheng-13737	97	44	4	4	NUM
fumecheng-13737	97	45	4	4	NUM
fumecheng-13737	97	46	4	4	NUM
fumecheng-13737	97	47	1	1	NUM
fumecheng-13737	97	48	1	1	NUM
fumecheng-13737	97	49	3	3	NUM
fumecheng-13737	97	50	22	22	NUM
fumecheng-13737	97	51	4	4	NUM
fumecheng-13737	97	52	2	2	NUM
fumecheng-13737	97	53	2	2	NUM
fumecheng-13737	97	54	4	4	NUM
fumecheng-13737	97	55	1	1	NUM
fumecheng-13737	97	56	2	2	NUM
fumecheng-13737	97	57	,	,	PUNCT
fumecheng-13737	97	58	w	w	PROPN
fumecheng-13737	97	59	d	d	PROPN
fumecheng-13737	97	60	d	d	PROPN
fumecheng-13737	97	61	d	d	X
fumecheng-13737	97	62	r	r	NOUN
fumecheng-13737	97	63	x	x	PUNCT
fumecheng-13737	97	64	x	x	SYM
fumecheng-13737	97	65	y	y	PROPN
fumecheng-13737	97	66	y	y	PROPN
fumecheng-13737	97	67			NOUN
fumecheng-13737	97	68			NOUN
fumecheng-13737	97	69			ADJ
fumecheng-13737	97	70			ADJ
fumecheng-13737	97	71			NOUN
fumecheng-13737	97	72	=	=	SYM
fumecheng-13737	97	73	+	+	PUNCT
fumecheng-13737	97	74	+	+	ADJ
fumecheng-13737	97	75			ADJ
fumecheng-13737	97	76			DET
fumecheng-13737	97	77			ADJ
fumecheng-13737	97	78			PROPN
fumecheng-13737	97	79			PROPN
fumecheng-13737	97	80			ADJ
fumecheng-13737	97	81			NOUN
fumecheng-13737	97	82	(	(	PUNCT
fumecheng-13737	97	83	3	3	NUM
fumecheng-13737	97	84	)	)	SYM
fumecheng-13737	97	85	2	2	NUM
fumecheng-13737	97	86	2	2	NUM
fumecheng-13737	97	87	2	2	NUM
fumecheng-13737	97	88	2	2	NUM
fumecheng-13737	97	89	2	2	NUM
fumecheng-13737	97	90	2	2	NUM
fumecheng-13737	97	91	2	2	NUM
fumecheng-13737	97	92	2	2	NUM
fumecheng-13737	97	93	2	2	NUM
fumecheng-13737	97	94	2	2	NUM
fumecheng-13737	97	95	(	(	PUNCT
fumecheng-13737	97	96	,	,	PUNCT
fumecheng-13737	97	97	)	)	PUNCT
fumecheng-13737	97	98	2	2	NUM
fumecheng-13737	97	99	,	,	PUNCT
fumecheng-13737	97	100	w	w	PROPN
fumecheng-13737	97	101	w	w	PROPN
fumecheng-13737	97	102	w	w	PROPN
fumecheng-13737	97	103	l	l	PROPN
fumecheng-13737	97	104	w	w	NOUN
fumecheng-13737	97	105	x	x	PUNCT
fumecheng-13737	97	106	y	y	NOUN
fumecheng-13737	97	107	x	x	PROPN
fumecheng-13737	97	108	yx	yx	NOUN
fumecheng-13737	97	109	y	y	PROPN
fumecheng-13737	97	110	x	x	PROPN
fumecheng-13737	97	111	y	y	PROPN
fumecheng-13737	97	112			PROPN
fumecheng-13737	97	113			PROPN
fumecheng-13737	97	114			PROPN
fumecheng-13737	97	115			ADJ
fumecheng-13737	97	116			NOUN
fumecheng-13737	97	117			NOUN
fumecheng-13737	97	118			ADJ
fumecheng-13737	97	119			ADJ
fumecheng-13737	97	120			ADJ
fumecheng-13737	97	121			ADJ
fumecheng-13737	97	122			PROPN
fumecheng-13737	97	123	=	=	PUNCT
fumecheng-13737	97	124	−	−	PROPN
fumecheng-13737	98	1	+	+	NUM
fumecheng-13737	98	2			PROPN
fumecheng-13737	98	3			PRON
fumecheng-13737	98	4			ADJ
fumecheng-13737	98	5			PROPN
fumecheng-13737	98	6			PROPN
fumecheng-13737	98	7			PROPN
fumecheng-13737	98	8			PROPN
fumecheng-13737	98	9			PROPN
fumecheng-13737	98	10			ADJ
fumecheng-13737	98	11			NOUN
fumecheng-13737	98	12	(	(	PUNCT
fumecheng-13737	98	13	4	4	NUM
fumecheng-13737	98	14	)	)	SYM
fumecheng-13737	98	15	1	1	NUM
fumecheng-13737	98	16	1	1	NUM
fumecheng-13737	98	17	0	0	NUM
fumecheng-13737	98	18	1	1	NUM
fumecheng-13737	98	19	2	2	NUM
fumecheng-13737	98	20	,	,	PUNCT
fumecheng-13737	98	21	,	,	PUNCT
fumecheng-13737	98	22	2	2	NUM
fumecheng-13737	98	23	2	2	NUM
fumecheng-13737	98	24	1	1	NUM
fumecheng-13737	98	25	n	n	PROPN
fumecheng-13737	98	26	f	f	PROPN
fumecheng-13737	98	27	ne	ne	PROPN
fumecheng-13737	98	28	f	f	PROPN
fumecheng-13737	99	1	eh	eh	INTJ
fumecheng-13737	99	2	h	h	NOUN
fumecheng-13737	100	1	b	b	NOUN
fumecheng-13737	100	2	r	r	NOUN
fumecheng-13737	100	3	r	r	NOUN
fumecheng-13737	100	4			NOUN
fumecheng-13737	100	5			ADP
fumecheng-13737	100	6			ADP
fumecheng-13737	100	7			PROPN
fumecheng-13737	100	8			NOUN
fumecheng-13737	100	9			NOUN
fumecheng-13737	100	10	=	=	SYM
fumecheng-13737	101	1	+	+	PUNCT
fumecheng-13737	101	2	=	=	SYM
fumecheng-13737	102	1	+	+	NUM
fumecheng-13737	102	2	−	−	PROPN
fumecheng-13737	102	3	(	(	PUNCT
fumecheng-13737	102	4	5	5	NUM
fumecheng-13737	102	5	)	)	PUNCT
fumecheng-13737	102	6	in	in	ADP
fumecheng-13737	102	7	which	which	PRON
fumecheng-13737	102	8	,	,	PUNCT
fumecheng-13737	102	9	w	w	PROPN
fumecheng-13737	102	10	and	and	CCONJ
fumecheng-13737	102	11	φ	φ	PROPN
fumecheng-13737	102	12	denote	denote	VERB
fumecheng-13737	102	13	the	the	DET
fumecheng-13737	102	14	lateral	lateral	ADJ
fumecheng-13737	102	15	displacement	displacement	NOUN
fumecheng-13737	102	16	and	and	CCONJ
fumecheng-13737	102	17	the	the	DET
fumecheng-13737	102	18	airy	airy	ADJ
fumecheng-13737	102	19	stress	stress	NOUN
fumecheng-13737	102	20	function	function	NOUN
fumecheng-13737	102	21	,	,	PUNCT
fumecheng-13737	102	22	respectively	respectively	ADV
fumecheng-13737	102	23	.	.	PUNCT
fumecheng-13737	103	1	r	r	NOUN
fumecheng-13737	103	2	represents	represent	VERB
fumecheng-13737	103	3	the	the	DET
fumecheng-13737	103	4	shell	shell	NOUN
fumecheng-13737	103	5	radius	radius	NOUN
fumecheng-13737	103	6	,	,	PUNCT
fumecheng-13737	103	7	and	and	CCONJ
fumecheng-13737	103	8	h	h	NOUN
fumecheng-13737	103	9	is	be	AUX
fumecheng-13737	103	10	its	its	PRON
fumecheng-13737	103	11	thickness	thickness	NOUN
fumecheng-13737	103	12	.	.	PUNCT
fumecheng-13737	104	1	ρ0	ρ0	PROPN
fumecheng-13737	104	2	and	and	CCONJ
fumecheng-13737	104	3	ρ1	ρ1	NOUN
fumecheng-13737	104	4	are	be	AUX
fumecheng-13737	104	5	the	the	DET
fumecheng-13737	104	6	densities	density	NOUN
fumecheng-13737	104	7	of	of	ADP
fumecheng-13737	104	8	the	the	DET
fumecheng-13737	104	9	shell	shell	NOUN
fumecheng-13737	104	10	and	and	CCONJ
fumecheng-13737	104	11	stringer	stringer	NOUN
fumecheng-13737	104	12	materials	material	NOUN
fumecheng-13737	104	13	,	,	PUNCT
fumecheng-13737	104	14	respectively	respectively	ADV
fumecheng-13737	104	15	.	.	PUNCT
fumecheng-13737	105	1	n	n	PRON
fumecheng-13737	105	2	denotes	denote	VERB
fumecheng-13737	105	3	the	the	DET
fumecheng-13737	105	4	number	number	NOUN
fumecheng-13737	105	5	of	of	ADP
fumecheng-13737	105	6	stringers	stringer	NOUN
fumecheng-13737	105	7	,	,	PUNCT
fumecheng-13737	105	8	and	and	CCONJ
fumecheng-13737	105	9	f	f	PROPN
fumecheng-13737	105	10	is	be	AUX
fumecheng-13737	105	11	the	the	DET
fumecheng-13737	105	12	crosssectional	crosssectional	ADJ
fumecheng-13737	105	13	area	area	NOUN
fumecheng-13737	105	14	of	of	ADP
fumecheng-13737	105	15	a	a	DET
fumecheng-13737	105	16	stringer	stringer	NOUN
fumecheng-13737	105	17	.	.	PUNCT
fumecheng-13737	106	1	e	e	NOUN
fumecheng-13737	106	2	and	and	CCONJ
fumecheng-13737	106	3	e1	e1	PROPN
fumecheng-13737	106	4	represent	represent	VERB
fumecheng-13737	106	5	the	the	DET
fumecheng-13737	106	6	elastic	elastic	ADJ
fumecheng-13737	106	7	modulus	modulus	NOUN
fumecheng-13737	106	8	of	of	ADP
fumecheng-13737	106	9	the	the	DET
fumecheng-13737	106	10	shell	shell	NOUN
fumecheng-13737	106	11	and	and	CCONJ
fumecheng-13737	106	12	stringer	stringer	NOUN
fumecheng-13737	106	13	materials	material	NOUN
fumecheng-13737	106	14	,	,	PUNCT
fumecheng-13737	106	15	respectively	respectively	ADV
fumecheng-13737	106	16	.	.	PUNCT
fumecheng-13737	107	1	additionally	additionally	ADV
fumecheng-13737	107	2	,	,	PUNCT
fumecheng-13737	107	3	v	v	X
fumecheng-13737	107	4	denotes	denote	VERB
fumecheng-13737	107	5	poisson	poisson	NOUN
fumecheng-13737	107	6	's	's	PART
fumecheng-13737	107	7	ratio	ratio	NOUN
fumecheng-13737	107	8	.	.	PUNCT
fumecheng-13737	108	1	the	the	DET
fumecheng-13737	108	2	coefficients	coefficient	NOUN
fumecheng-13737	108	3	di	di	INTJ
fumecheng-13737	108	4	(	(	PUNCT
fumecheng-13737	108	5	i	i	NOUN
fumecheng-13737	108	6	=	=	NOUN
fumecheng-13737	108	7	1	1	NUM
fumecheng-13737	108	8	,	,	PUNCT
fumecheng-13737	108	9	2	2	NUM
fumecheng-13737	108	10	,	,	PUNCT
fumecheng-13737	108	11	3	3	NUM
fumecheng-13737	108	12	)	)	PUNCT
fumecheng-13737	108	13	are	be	AUX
fumecheng-13737	108	14	material	material	ADJ
fumecheng-13737	108	15	-	-	PUNCT
fumecheng-13737	108	16	dependent	dependent	ADJ
fumecheng-13737	108	17	parameters	parameter	NOUN
fumecheng-13737	108	18	associated	associate	VERB
fumecheng-13737	108	19	with	with	ADP
fumecheng-13737	108	20	the	the	DET
fumecheng-13737	108	21	stiffened	stiffen	VERB
fumecheng-13737	108	22	shell	shell	NOUN
fumecheng-13737	108	23	,	,	PUNCT
fumecheng-13737	108	24	as	as	SCONJ
fumecheng-13737	108	25	reported	report	VERB
fumecheng-13737	108	26	in	in	ADP
fumecheng-13737	108	27	[	[	X
fumecheng-13737	108	28	41	41	NUM
fumecheng-13737	108	29	]	]	PUNCT
fumecheng-13737	108	30	.	.	PUNCT
fumecheng-13737	109	1	for	for	ADP
fumecheng-13737	109	2	simply	simply	ADV
fumecheng-13737	109	3	supported	support	VERB
fumecheng-13737	109	4	boundary	boundary	ADJ
fumecheng-13737	109	5	conditions	condition	NOUN
fumecheng-13737	109	6	(	(	PUNCT
fumecheng-13737	109	7	ss	ss	NOUN
fumecheng-13737	109	8	bcs	bcs	NOUN
fumecheng-13737	109	9	)	)	PUNCT
fumecheng-13737	109	10	,	,	PUNCT
fumecheng-13737	109	11	the	the	DET
fumecheng-13737	109	12	displacement	displacement	NOUN
fumecheng-13737	109	13	w	w	NOUN
fumecheng-13737	109	14	can	can	AUX
fumecheng-13737	109	15	be	be	AUX
fumecheng-13737	109	16	approximated	approximate	VERB
fumecheng-13737	109	17	as	as	SCONJ
fumecheng-13737	109	18	follows	follow	VERB
fumecheng-13737	109	19	[	[	X
fumecheng-13737	109	20	38	38	NUM
fumecheng-13737	109	21	]	]	X
fumecheng-13737	109	22	:	:	PUNCT
fumecheng-13737	109	23	a	a	DET
fumecheng-13737	109	24	fast	fast	ADJ
fumecheng-13737	109	25	insight	insight	NOUN
fumecheng-13737	109	26	into	into	ADP
fumecheng-13737	109	27	nonlinear	nonlinear	ADJ
fumecheng-13737	109	28	frequency	frequency	NOUN
fumecheng-13737	109	29	estimation	estimation	NOUN
fumecheng-13737	109	30	of	of	ADP
fumecheng-13737	109	31	stringer	stringer	NOUN
fumecheng-13737	109	32	-	-	PUNCT
fumecheng-13737	109	33	stiffened	stiffen	VERB
fumecheng-13737	109	34	shells	shell	NOUN
fumecheng-13737	109	35	with	with	ADP
fumecheng-13737	109	36	high	high	ADJ
fumecheng-13737	109	37	accuracy	accuracy	NOUN
fumecheng-13737	109	38	791	791	NUM
fumecheng-13737	109	39	2	2	NUM
fumecheng-13737	109	40	2	2	NUM
fumecheng-13737	109	41	21	21	NUM
fumecheng-13737	109	42	1	1	NUM
fumecheng-13737	109	43	(	(	PUNCT
fumecheng-13737	109	44	)	)	PUNCT
fumecheng-13737	109	45	(	(	PUNCT
fumecheng-13737	109	46	,	,	PUNCT
fumecheng-13737	109	47	,	,	PUNCT
fumecheng-13737	109	48	)	)	PUNCT
fumecheng-13737	109	49	(	(	PUNCT
fumecheng-13737	109	50	)	)	PUNCT
fumecheng-13737	109	51	sin	sin	PROPN
fumecheng-13737	109	52	cos	cos	PROPN
fumecheng-13737	109	53	(	(	PUNCT
fumecheng-13737	109	54	)	)	PUNCT
fumecheng-13737	109	55	sin	sin	NOUN
fumecheng-13737	109	56	,	,	PUNCT
fumecheng-13737	109	57	4	4	NUM
fumecheng-13737	109	58	f	f	NOUN
fumecheng-13737	109	59	t	t	PROPN
fumecheng-13737	109	60	nm	nm	ADV
fumecheng-13737	109	61	m	m	VERB
fumecheng-13737	109	62	w	w	NOUN
fumecheng-13737	109	63	x	x	PUNCT
fumecheng-13737	109	64	y	y	NOUN
fumecheng-13737	109	65	t	t	PROPN
fumecheng-13737	110	1	f	f	PROPN
fumecheng-13737	110	2	t	t	PROPN
fumecheng-13737	110	3	x	x	PROPN
fumecheng-13737	110	4	ny	ny	PROPN
fumecheng-13737	110	5	x	x	PUNCT
fumecheng-13737	110	6	l	l	NOUN
fumecheng-13737	110	7	r	r	NOUN
fumecheng-13737	110	8	l	l	NOUN
fumecheng-13737	110	9			NOUN
fumecheng-13737	110	10			NOUN
fumecheng-13737	110	11			NOUN
fumecheng-13737	110	12			NOUN
fumecheng-13737	110	13	=	=	PUNCT
fumecheng-13737	111	1	+	+	CCONJ
fumecheng-13737	111	2			PROPN
fumecheng-13737	111	3			PROPN
fumecheng-13737	112	1			PROPN
fumecheng-13737	112	2			PROPN
fumecheng-13737	113	1			ADJ
fumecheng-13737	113	2			PROPN
fumecheng-13737	113	3			PROPN
fumecheng-13737	113	4			NOUN
fumecheng-13737	113	5			PROPN
fumecheng-13737	113	6			PROPN
fumecheng-13737	113	7	(	(	PUNCT
fumecheng-13737	113	8	6	6	NUM
fumecheng-13737	113	9	)	)	PUNCT
fumecheng-13737	113	10	where	where	SCONJ
fumecheng-13737	113	11	m	m	VERB
fumecheng-13737	113	12	and	and	CCONJ
fumecheng-13737	113	13	n	n	ADV
fumecheng-13737	113	14	denote	denote	VERB
fumecheng-13737	113	15	the	the	DET
fumecheng-13737	113	16	wave	wave	NOUN
fumecheng-13737	113	17	numbers	number	NOUN
fumecheng-13737	113	18	in	in	ADP
fumecheng-13737	113	19	the	the	DET
fumecheng-13737	113	20	axial	axial	ADJ
fumecheng-13737	113	21	and	and	CCONJ
fumecheng-13737	113	22	circumferential	circumferential	ADJ
fumecheng-13737	113	23	directions	direction	NOUN
fumecheng-13737	113	24	,	,	PUNCT
fumecheng-13737	113	25	respectively	respectively	ADV
fumecheng-13737	113	26	.	.	PUNCT
fumecheng-13737	114	1	using	use	VERB
fumecheng-13737	114	2	eqs	eqs	PROPN
fumecheng-13737	114	3	.	.	PUNCT
fumecheng-13737	115	1	(	(	PUNCT
fumecheng-13737	115	2	1	1	X
fumecheng-13737	115	3	)	)	PUNCT
fumecheng-13737	115	4	and	and	CCONJ
fumecheng-13737	115	5	(	(	PUNCT
fumecheng-13737	115	6	6	6	NUM
fumecheng-13737	115	7	)	)	PUNCT
fumecheng-13737	115	8	,	,	PUNCT
fumecheng-13737	115	9	the	the	DET
fumecheng-13737	115	10	airy	airy	ADJ
fumecheng-13737	115	11	function	function	NOUN
fumecheng-13737	115	12	is	be	AUX
fumecheng-13737	115	13	obtained	obtain	VERB
fumecheng-13737	115	14	as	as	ADP
fumecheng-13737	115	15	follows	follow	VERB
fumecheng-13737	115	16	:	:	PUNCT
fumecheng-13737	115	17	2	2	NUM
fumecheng-13737	115	18	22	22	NUM
fumecheng-13737	115	19	2	2	NUM
fumecheng-13737	115	20	1	1	NUM
fumecheng-13737	115	21	1	1	NUM
fumecheng-13737	115	22	1	1	NUM
fumecheng-13737	115	23	1	1	NUM
fumecheng-13737	115	24	1	1	NUM
fumecheng-13737	115	25	4	4	NUM
fumecheng-13737	115	26	2	2	NUM
fumecheng-13737	115	27	2	2	NUM
fumecheng-13737	115	28	1	1	NUM
fumecheng-13737	115	29	32	32	NUM
fumecheng-13737	115	30	2	2	NUM
fumecheng-13737	115	31	1	1	NUM
fumecheng-13737	115	32	2	2	NUM
fumecheng-13737	115	33	3	3	NUM
fumecheng-13737	115	34	5	5	NUM
fumecheng-13737	115	35	sin	sin	NOUN
fumecheng-13737	115	36	cos	cos	PROPN
fumecheng-13737	115	37	(	(	PUNCT
fumecheng-13737	115	38	)	)	PUNCT
fumecheng-13737	115	39	cos(2	cos(2	NOUN
fumecheng-13737	115	40	)	)	PUNCT
fumecheng-13737	115	41	16	16	NUM
fumecheng-13737	115	42	1	1	NUM
fumecheng-13737	115	43	2	2	NUM
fumecheng-13737	115	44	sin	sin	NOUN
fumecheng-13737	115	45	cos	cos	PROPN
fumecheng-13737	115	46	cos	cos	PROPN
fumecheng-13737	115	47	(	(	PUNCT
fumecheng-13737	115	48	)	)	PUNCT
fumecheng-13737	115	49	.	.	PUNCT
fumecheng-13737	116	1	2	2	NUM
fumecheng-13737	116	2	f	f	X
fumecheng-13737	116	3	m	m	VERB
fumecheng-13737	116	4	fm	fm	NOUN
fumecheng-13737	116	5	m	m	PROPN
fumecheng-13737	116	6	b	b	PROPN
fumecheng-13737	116	7	x	x	SYM
fumecheng-13737	116	8	ny	ny	PROPN
fumecheng-13737	116	9	ny	ny	PROPN
fumecheng-13737	116	10	r	r	PROPN
fumecheng-13737	116	11	l	l	PROPN
fumecheng-13737	116	12	nn	nn	X
fumecheng-13737	116	13	l	l	NOUN
fumecheng-13737	116	14	r	r	NOUN
fumecheng-13737	116	15	fm	fm	NOUN
fumecheng-13737	116	16	m	m	VERB
fumecheng-13737	116	17	m	m	VERB
fumecheng-13737	116	18	x	x	X
fumecheng-13737	116	19	x	x	SYM
fumecheng-13737	116	20	ny	ny	PROPN
fumecheng-13737	116	21	l	l	NOUN
fumecheng-13737	116	22	ll	ll	AUX
fumecheng-13737	117	1	r	r	NOUN
fumecheng-13737	117	2	−	−	PROPN
fumecheng-13737	117	3			NOUN
fumecheng-13737	117	4			PROPN
fumecheng-13737	117	5			PROPN
fumecheng-13737	117	6	=	=	PUNCT
fumecheng-13737	118	1	−	−	PROPN
fumecheng-13737	118	2			PROPN
fumecheng-13737	118	3			NOUN
fumecheng-13737	119	1			PROPN
fumecheng-13737	120	1			ADJ
fumecheng-13737	120	2			PROPN
fumecheng-13737	120	3			PROPN
fumecheng-13737	120	4			NOUN
fumecheng-13737	120	5			NOUN
fumecheng-13737	120	6			NOUN
fumecheng-13737	120	7			NOUN
fumecheng-13737	120	8			PROPN
fumecheng-13737	121	1	+	+	CCONJ
fumecheng-13737	121	2			PROPN
fumecheng-13737	122	1			INTJ
fumecheng-13737	122	2			PROPN
fumecheng-13737	122	3			PROPN
fumecheng-13737	123	1			ADJ
fumecheng-13737	123	2			PROPN
fumecheng-13737	123	3			PROPN
fumecheng-13737	123	4			NOUN
fumecheng-13737	123	5			ADJ
fumecheng-13737	123	6			ADJ
fumecheng-13737	123	7			PROPN
fumecheng-13737	123	8			PROPN
fumecheng-13737	123	9			PROPN
fumecheng-13737	123	10			PROPN
fumecheng-13737	123	11	(	(	PUNCT
fumecheng-13737	123	12	7	7	NUM
fumecheng-13737	123	13	)	)	PUNCT
fumecheng-13737	123	14	by	by	ADP
fumecheng-13737	123	15	considering	consider	VERB
fumecheng-13737	123	16	u(t	u(t	NOUN
fumecheng-13737	123	17	)	)	PUNCT
fumecheng-13737	124	1	=	=	PUNCT
fumecheng-13737	124	2	f1(t)/r	f1(t)/r	PROPN
fumecheng-13737	124	3	and	and	CCONJ
fumecheng-13737	124	4	applying	apply	VERB
fumecheng-13737	124	5	the	the	DET
fumecheng-13737	124	6	galerkin	galerkin	ADJ
fumecheng-13737	124	7	method	method	NOUN
fumecheng-13737	124	8	,	,	PUNCT
fumecheng-13737	124	9	the	the	DET
fumecheng-13737	124	10	governing	govern	VERB
fumecheng-13737	124	11	differential	differential	ADJ
fumecheng-13737	124	12	equation	equation	NOUN
fumecheng-13737	124	13	for	for	ADP
fumecheng-13737	124	14	the	the	DET
fumecheng-13737	124	15	dynamics	dynamic	NOUN
fumecheng-13737	124	16	of	of	ADP
fumecheng-13737	124	17	the	the	DET
fumecheng-13737	124	18	stringer	stringer	NOUN
fumecheng-13737	124	19	-	-	PUNCT
fumecheng-13737	124	20	stiffened	stiffen	VERB
fumecheng-13737	124	21	shell	shell	NOUN
fumecheng-13737	124	22	is	be	AUX
fumecheng-13737	124	23	derived	derive	VERB
fumecheng-13737	124	24	as	as	ADP
fumecheng-13737	124	25	:	:	PUNCT
fumecheng-13737	124	26	22	22	NUM
fumecheng-13737	124	27	2	2	NUM
fumecheng-13737	124	28	2	2	NUM
fumecheng-13737	124	29	3	3	NUM
fumecheng-13737	124	30	5	5	NUM
fumecheng-13737	124	31	1	1	NUM
fumecheng-13737	124	32	2	2	NUM
fumecheng-13737	124	33	3	3	NUM
fumecheng-13737	124	34	42	42	NUM
fumecheng-13737	124	35	2	2	NUM
fumecheng-13737	124	36	0	0	NUM
fumecheng-13737	124	37	,	,	PUNCT
fumecheng-13737	124	38	d	d	NOUN
fumecheng-13737	124	39	u	u	X
fumecheng-13737	124	40	d	d	X
fumecheng-13737	124	41	u	u	X
fumecheng-13737	124	42	du	du	PROPN
fumecheng-13737	124	43	u	u	PROPN
fumecheng-13737	124	44	u	u	NOUN
fumecheng-13737	124	45	u	u	X
fumecheng-13737	124	46	u	u	X
fumecheng-13737	124	47	u	u	NOUN
fumecheng-13737	124	48	dtdt	dtdt	NOUN
fumecheng-13737	124	49	dt	dt	PROPN
fumecheng-13737	125	1			PROPN
fumecheng-13737	125	2			PROPN
fumecheng-13737	125	3			PROPN
fumecheng-13737	125	4			PROPN
fumecheng-13737	125	5			NOUN
fumecheng-13737	125	6			PROPN
fumecheng-13737	125	7			PROPN
fumecheng-13737	125	8	+	+	X
fumecheng-13737	126	1	+	+	PUNCT
fumecheng-13737	127	1	+	+	PUNCT
fumecheng-13737	127	2	+	+	CCONJ
fumecheng-13737	127	3	+	+	CCONJ
fumecheng-13737	127	4	=	=	NOUN
fumecheng-13737	127	5			PROPN
fumecheng-13737	127	6			NOUN
fumecheng-13737	127	7			X
fumecheng-13737	128	1			VERB
fumecheng-13737	128	2			NOUN
fumecheng-13737	128	3			NOUN
fumecheng-13737	128	4	(	(	PUNCT
fumecheng-13737	128	5	8)	8)	NUM
fumecheng-13737	128	6	where	where	SCONJ
fumecheng-13737	128	7	the	the	DET
fumecheng-13737	128	8	coefficients	coefficient	NOUN
fumecheng-13737	128	9	βi	βi	VERB
fumecheng-13737	128	10	(	(	PUNCT
fumecheng-13737	128	11	i	i	NOUN
fumecheng-13737	128	12	=	=	NOUN
fumecheng-13737	128	13	1	1	NUM
fumecheng-13737	128	14	,	,	PUNCT
fumecheng-13737	128	15	2	2	NUM
fumecheng-13737	128	16	,	,	PUNCT
fumecheng-13737	128	17	3	3	NUM
fumecheng-13737	128	18	,	,	PUNCT
fumecheng-13737	128	19	4	4	NUM
fumecheng-13737	128	20	)	)	PUNCT
fumecheng-13737	128	21	are	be	AUX
fumecheng-13737	128	22	defined	define	VERB
fumecheng-13737	128	23	as	as	SCONJ
fumecheng-13737	128	24	follows	follow	VERB
fumecheng-13737	128	25	:	:	PUNCT
fumecheng-13737	128	26	(	(	PUNCT
fumecheng-13737	128	27	)	)	PUNCT
fumecheng-13737	128	28	(	(	PUNCT
fumecheng-13737	128	29	)	)	PUNCT
fumecheng-13737	128	30	2	2	NUM
fumecheng-13737	128	31	2	2	NUM
fumecheng-13737	128	32	4	4	NUM
fumecheng-13737	128	33	4	4	NUM
fumecheng-13737	128	34	2	2	NUM
fumecheng-13737	128	35	4	4	NUM
fumecheng-13737	128	36	2	2	NUM
fumecheng-13737	128	37	2	2	NUM
fumecheng-13737	128	38	2	2	NUM
fumecheng-13737	128	39	2	2	NUM
fumecheng-13737	128	40	2	2	NUM
fumecheng-13737	128	41	1	1	NUM
fumecheng-13737	128	42	2	2	NUM
fumecheng-13737	128	43	1	1	NUM
fumecheng-13737	128	44	4	4	NUM
fumecheng-13737	128	45	1	1	NUM
fumecheng-13737	128	46	4	4	NUM
fumecheng-13737	128	47	3	3	NUM
fumecheng-13737	128	48	1	1	NUM
fumecheng-13737	128	49	4	4	NUM
fumecheng-13737	128	50	2	2	NUM
fumecheng-13737	128	51	62	62	NUM
fumecheng-13737	128	52	2	2	NUM
fumecheng-13737	128	53	4	4	NUM
fumecheng-13737	128	54	4	4	NUM
fumecheng-13737	128	55	4	4	NUM
fumecheng-13737	128	56	4	4	NUM
fumecheng-13737	128	57	2	2	NUM
fumecheng-13737	128	58	2	2	NUM
fumecheng-13737	128	59	2	2	NUM
fumecheng-13737	128	60	4	4	NUM
fumecheng-13737	128	61	3	3	NUM
fumecheng-13737	128	62	1	1	NUM
fumecheng-13737	128	63	4	4	NUM
fumecheng-13737	128	64	6	6	NUM
fumecheng-13737	128	65	4	4	NUM
fumecheng-13737	128	66	1	1	NUM
fumecheng-13737	128	67	0.09375	0.09375	NUM
fumecheng-13737	128	68	,	,	PUNCT
fumecheng-13737	128	69	2	2	NUM
fumecheng-13737	128	70	1	1	NUM
fumecheng-13737	128	71	,	,	PUNCT
fumecheng-13737	128	72	0.0625	0.0625	NUM
fumecheng-13737	128	73	0.5	0.5	NUM
fumecheng-13737	128	74	0.75	0.75	NUM
fumecheng-13737	128	75	1	1	NUM
fumecheng-13737	128	76	,	,	PUNCT
fumecheng-13737	128	77	0.25	0.25	NUM
fumecheng-13737	128	78	,	,	PUNCT
fumecheng-13737	128	79	n	n	CCONJ
fumecheng-13737	128	80	l	l	NOUN
fumecheng-13737	128	81	n	n	ADP
fumecheng-13737	128	82	l	l	NOUN
fumecheng-13737	128	83	n	n	CCONJ
fumecheng-13737	128	84	n	n	CCONJ
fumecheng-13737	128	85	m	m	VERB
fumecheng-13737	128	86	m	m	VERB
fumecheng-13737	128	87	n	n	ADP
fumecheng-13737	128	88	n	n	CCONJ
fumecheng-13737	128	89	n	n	CCONJ
fumecheng-13737	128	90	n	n	NOUN
fumecheng-13737	128	91	=	=	PUNCT
fumecheng-13737	128	92	=	=	PUNCT
fumecheng-13737	129	1	+	+	PUNCT
fumecheng-13737	129	2	+	+	PUNCT
fumecheng-13737	130	1	+	+	CCONJ
fumecheng-13737	130	2	−	−	NOUN
fumecheng-13737	130	3	=	=	SYM
fumecheng-13737	131	1	+	+	NUM
fumecheng-13737	131	2	−	−	PROPN
fumecheng-13737	132	1	−	−	PROPN
fumecheng-13737	132	2	=	=	SYM
fumecheng-13737	132	3			PROPN
fumecheng-13737	132	4			PROPN
fumecheng-13737	132	5			PROPN
fumecheng-13737	132	6			PROPN
fumecheng-13737	132	7			PROPN
fumecheng-13737	132	8			PROPN
fumecheng-13737	132	9			PROPN
fumecheng-13737	132	10			PROPN
fumecheng-13737	132	11			PROPN
fumecheng-13737	132	12			PROPN
fumecheng-13737	132	13			PROPN
fumecheng-13737	132	14			PROPN
fumecheng-13737	132	15			PROPN
fumecheng-13737	132	16			PROPN
fumecheng-13737	132	17			PROPN
fumecheng-13737	132	18			PROPN
fumecheng-13737	132	19			PROPN
fumecheng-13737	132	20			PROPN
fumecheng-13737	132	21	(	(	PUNCT
fumecheng-13737	132	22	9	9	NUM
fumecheng-13737	132	23	)	)	PUNCT
fumecheng-13737	132	24	and	and	CCONJ
fumecheng-13737	132	25	the	the	DET
fumecheng-13737	132	26	coefficients	coefficient	NOUN
fumecheng-13737	132	27	εi	εi	VERB
fumecheng-13737	132	28	(	(	PUNCT
fumecheng-13737	132	29	i	i	NOUN
fumecheng-13737	132	30	=	=	NOUN
fumecheng-13737	132	31	1	1	NUM
fumecheng-13737	132	32	,	,	PUNCT
fumecheng-13737	132	33	2	2	NUM
fumecheng-13737	132	34	,	,	PUNCT
fumecheng-13737	132	35	…	…	PUNCT
fumecheng-13737	132	36	6	6	NUM
fumecheng-13737	132	37	)	)	PUNCT
fumecheng-13737	132	38	are	be	AUX
fumecheng-13737	132	39	defined	define	VERB
fumecheng-13737	132	40	in	in	ADP
fumecheng-13737	132	41	[	[	X
fumecheng-13737	132	42	41	41	NUM
fumecheng-13737	132	43	]	]	PUNCT
fumecheng-13737	132	44	.	.	PUNCT
fumecheng-13737	133	1	for	for	ADP
fumecheng-13737	133	2	doubly	doubly	ADV
fumecheng-13737	133	3	clamped	clamp	VERB
fumecheng-13737	133	4	boundary	boundary	ADJ
fumecheng-13737	133	5	conditions	condition	NOUN
fumecheng-13737	133	6	(	(	PUNCT
fumecheng-13737	133	7	cc	cc	NOUN
fumecheng-13737	133	8	bcs	bc	NOUN
fumecheng-13737	133	9	)	)	PUNCT
fumecheng-13737	133	10	,	,	PUNCT
fumecheng-13737	133	11	the	the	DET
fumecheng-13737	133	12	displacement	displacement	NOUN
fumecheng-13737	133	13	w	w	NOUN
fumecheng-13737	133	14	can	can	AUX
fumecheng-13737	133	15	be	be	AUX
fumecheng-13737	133	16	approximated	approximate	VERB
fumecheng-13737	133	17	as	as	SCONJ
fumecheng-13737	133	18	follows	follow	VERB
fumecheng-13737	133	19	:	:	PUNCT
fumecheng-13737	133	20	2	2	NUM
fumecheng-13737	133	21	2	2	NUM
fumecheng-13737	133	22	2	2	NUM
fumecheng-13737	133	23	21	21	NUM
fumecheng-13737	133	24	1	1	NUM
fumecheng-13737	133	25	3	3	NUM
fumecheng-13737	133	26	(	(	PUNCT
fumecheng-13737	133	27	)	)	PUNCT
fumecheng-13737	133	28	(	(	PUNCT
fumecheng-13737	133	29	,	,	PUNCT
fumecheng-13737	133	30	,	,	PUNCT
fumecheng-13737	133	31	)	)	PUNCT
fumecheng-13737	133	32	(	(	PUNCT
fumecheng-13737	133	33	)	)	PUNCT
fumecheng-13737	133	34	sin	sin	PROPN
fumecheng-13737	133	35	cos	cos	PROPN
fumecheng-13737	133	36	(	(	PUNCT
fumecheng-13737	133	37	)	)	PUNCT
fumecheng-13737	133	38	sin	sin	NOUN
fumecheng-13737	133	39	.	.	PUNCT
fumecheng-13737	134	1	16	16	NUM
fumecheng-13737	134	2	f	f	NOUN
fumecheng-13737	134	3	t	t	PROPN
fumecheng-13737	134	4	nm	nm	ADV
fumecheng-13737	134	5	m	m	VERB
fumecheng-13737	134	6	w	w	NOUN
fumecheng-13737	134	7	x	x	PUNCT
fumecheng-13737	134	8	y	y	NOUN
fumecheng-13737	134	9	t	t	PROPN
fumecheng-13737	135	1	f	f	PROPN
fumecheng-13737	135	2	t	t	PROPN
fumecheng-13737	135	3	x	x	PROPN
fumecheng-13737	135	4	ny	ny	PROPN
fumecheng-13737	135	5	x	x	PUNCT
fumecheng-13737	135	6	l	l	NOUN
fumecheng-13737	135	7	r	r	NOUN
fumecheng-13737	135	8	l	l	NOUN
fumecheng-13737	135	9			NOUN
fumecheng-13737	135	10			NOUN
fumecheng-13737	135	11			NOUN
fumecheng-13737	135	12			NOUN
fumecheng-13737	135	13	=	=	PUNCT
fumecheng-13737	136	1	+	+	CCONJ
fumecheng-13737	136	2			PROPN
fumecheng-13737	136	3			PROPN
fumecheng-13737	137	1			PROPN
fumecheng-13737	137	2			PROPN
fumecheng-13737	138	1			ADJ
fumecheng-13737	138	2			PROPN
fumecheng-13737	138	3			PROPN
fumecheng-13737	138	4			NOUN
fumecheng-13737	138	5			PROPN
fumecheng-13737	138	6			PROPN
fumecheng-13737	138	7	(	(	PUNCT
fumecheng-13737	138	8	10	10	NUM
fumecheng-13737	138	9	)	)	PUNCT
fumecheng-13737	138	10	following	follow	VERB
fumecheng-13737	138	11	the	the	DET
fumecheng-13737	138	12	outlined	outline	VERB
fumecheng-13737	138	13	procedure	procedure	NOUN
fumecheng-13737	138	14	,	,	PUNCT
fumecheng-13737	138	15	the	the	DET
fumecheng-13737	138	16	values	value	NOUN
fumecheng-13737	138	17	βi	βi	X
fumecheng-13737	138	18	for	for	ADP
fumecheng-13737	138	19	cc	cc	PROPN
fumecheng-13737	138	20	bcs	bc	NOUN
fumecheng-13737	138	21	are	be	AUX
fumecheng-13737	138	22	determined	determine	VERB
fumecheng-13737	138	23	as	as	SCONJ
fumecheng-13737	138	24	follows	follow	VERB
fumecheng-13737	138	25	:	:	PUNCT
fumecheng-13737	138	26	(	(	PUNCT
fumecheng-13737	138	27	)	)	PUNCT
fumecheng-13737	138	28	(	(	PUNCT
fumecheng-13737	138	29	)	)	PUNCT
fumecheng-13737	139	1	4	4	NUM
fumecheng-13737	139	2	4	4	NUM
fumecheng-13737	139	3	2	2	NUM
fumecheng-13737	139	4	2	2	NUM
fumecheng-13737	139	5	2	2	NUM
fumecheng-13737	139	6	4	4	NUM
fumecheng-13737	139	7	1	1	NUM
fumecheng-13737	139	8	3	3	NUM
fumecheng-13737	139	9	1	1	NUM
fumecheng-13737	139	10	4	4	NUM
fumecheng-13737	139	11	6	6	NUM
fumecheng-13737	139	12	4	4	NUM
fumecheng-13737	139	13	2	2	NUM
fumecheng-13737	139	14	2	2	NUM
fumecheng-13737	139	15	4	4	NUM
fumecheng-13737	139	16	4	4	NUM
fumecheng-13737	139	17	2	2	NUM
fumecheng-13737	139	18	2	2	NUM
fumecheng-13737	139	19	2	2	NUM
fumecheng-13737	139	20	2	2	NUM
fumecheng-13737	139	21	2	2	NUM
fumecheng-13737	139	22	2	2	NUM
fumecheng-13737	139	23	2	2	NUM
fumecheng-13737	139	24	1	1	NUM
fumecheng-13737	139	25	4	4	NUM
fumecheng-13737	139	26	1	1	NUM
fumecheng-13737	139	27	4	4	NUM
fumecheng-13737	139	28	3	3	NUM
fumecheng-13737	139	29	1	1	NUM
fumecheng-13737	139	30	2	2	NUM
fumecheng-13737	139	31	62	62	NUM
fumecheng-13737	139	32	2	2	NUM
fumecheng-13737	139	33	4	4	NUM
fumecheng-13737	139	34	4	4	NUM
fumecheng-13737	139	35	4	4	NUM
fumecheng-13737	139	36	0.140625	0.140625	NUM
fumecheng-13737	139	37	,	,	PUNCT
fumecheng-13737	139	38	0.083	0.083	NUM
fumecheng-13737	139	39	0.1875	0.1875	NUM
fumecheng-13737	139	40	1.5	1.5	NUM
fumecheng-13737	139	41	1	1	NUM
fumecheng-13737	139	42	,	,	PUNCT
fumecheng-13737	139	43	0.1641	0.1641	NUM
fumecheng-13737	139	44	,	,	PUNCT
fumecheng-13737	139	45	1	1	NUM
fumecheng-13737	139	46	5.33	5.33	NUM
fumecheng-13737	139	47	2.67	2.67	NUM
fumecheng-13737	139	48	5.33	5.33	NUM
fumecheng-13737	139	49	1	1	NUM
fumecheng-13737	139	50	,	,	PUNCT
fumecheng-13737	139	51	n	n	CCONJ
fumecheng-13737	139	52	n	n	CCONJ
fumecheng-13737	139	53	n	n	CCONJ
fumecheng-13737	139	54	n	n	CCONJ
fumecheng-13737	139	55	n	n	ADP
fumecheng-13737	139	56	l	l	NOUN
fumecheng-13737	139	57	n	n	ADP
fumecheng-13737	139	58	l	l	NOUN
fumecheng-13737	139	59	n	n	VERB
fumecheng-13737	139	60	m	m	VERB
fumecheng-13737	139	61	m	m	VERB
fumecheng-13737	139	62	n	n	NOUN
fumecheng-13737	139	63	=	=	SYM
fumecheng-13737	140	1	=	=	PUNCT
fumecheng-13737	141	1	+	+	NUM
fumecheng-13737	141	2	−	−	NOUN
fumecheng-13737	141	3	−	−	PROPN
fumecheng-13737	141	4	=	=	PUNCT
fumecheng-13737	142	1	=	=	PUNCT
fumecheng-13737	143	1	+	+	PUNCT
fumecheng-13737	143	2	+	+	CCONJ
fumecheng-13737	144	1	+	+	CCONJ
fumecheng-13737	144	2	−	−	PROPN
fumecheng-13737	144	3			NOUN
fumecheng-13737	144	4			PROPN
fumecheng-13737	144	5			PROPN
fumecheng-13737	144	6			PROPN
fumecheng-13737	144	7			PROPN
fumecheng-13737	144	8			PROPN
fumecheng-13737	144	9			PROPN
fumecheng-13737	144	10			PROPN
fumecheng-13737	144	11			PROPN
fumecheng-13737	144	12			PROPN
fumecheng-13737	144	13			PROPN
fumecheng-13737	144	14			PROPN
fumecheng-13737	144	15			PROPN
fumecheng-13737	144	16			PROPN
fumecheng-13737	144	17			PROPN
fumecheng-13737	144	18			PROPN
fumecheng-13737	144	19			PROPN
fumecheng-13737	144	20	(	(	PUNCT
fumecheng-13737	144	21	11	11	NUM
fumecheng-13737	144	22	)	)	PUNCT
fumecheng-13737	144	23	where	where	SCONJ
fumecheng-13737	144	24	the	the	DET
fumecheng-13737	144	25	coefficients	coefficient	NOUN
fumecheng-13737	144	26	εi	εi	VERB
fumecheng-13737	144	27	(	(	PUNCT
fumecheng-13737	144	28	i	i	NOUN
fumecheng-13737	144	29	=	=	NOUN
fumecheng-13737	144	30	1	1	NUM
fumecheng-13737	144	31	,	,	PUNCT
fumecheng-13737	144	32	2	2	NUM
fumecheng-13737	144	33	,	,	PUNCT
fumecheng-13737	144	34	…	…	PUNCT
fumecheng-13737	144	35	6	6	NUM
fumecheng-13737	144	36	)	)	PUNCT
fumecheng-13737	144	37	can	can	AUX
fumecheng-13737	144	38	be	be	AUX
fumecheng-13737	144	39	found	find	VERB
fumecheng-13737	144	40	in	in	ADP
fumecheng-13737	144	41	[	[	X
fumecheng-13737	144	42	41	41	NUM
fumecheng-13737	144	43	]	]	PUNCT
fumecheng-13737	144	44	.	.	PUNCT
fumecheng-13737	145	1	the	the	DET
fumecheng-13737	145	2	governing	govern	VERB
fumecheng-13737	145	3	nonlinear	nonlinear	ADJ
fumecheng-13737	145	4	differential	differential	ADJ
fumecheng-13737	145	5	equation	equation	NOUN
fumecheng-13737	145	6	presented	present	VERB
fumecheng-13737	145	7	in	in	ADP
fumecheng-13737	145	8	eq	eq	ADP
fumecheng-13737	145	9	.	.	PUNCT
fumecheng-13737	146	1	(	(	PUNCT
fumecheng-13737	146	2	8)	8)	NUM
fumecheng-13737	146	3	is	be	AUX
fumecheng-13737	146	4	highly	highly	ADV
fumecheng-13737	146	5	nonlinear	nonlinear	ADJ
fumecheng-13737	146	6	due	due	ADP
fumecheng-13737	146	7	to	to	ADP
fumecheng-13737	146	8	the	the	DET
fumecheng-13737	146	9	presence	presence	NOUN
fumecheng-13737	146	10	of	of	ADP
fumecheng-13737	146	11	cubicquintic	cubicquintic	ADJ
fumecheng-13737	146	12	nonlinear	nonlinear	ADJ
fumecheng-13737	146	13	restoring	restore	VERB
fumecheng-13737	146	14	force	force	NOUN
fumecheng-13737	146	15	terms	term	NOUN
fumecheng-13737	146	16	,	,	PUNCT
fumecheng-13737	146	17	as	as	ADV
fumecheng-13737	146	18	well	well	ADV
fumecheng-13737	146	19	as	as	ADP
fumecheng-13737	146	20	displacement	displacement	NOUN
fumecheng-13737	146	21	-	-	PUNCT
fumecheng-13737	146	22	dependent	dependent	ADJ
fumecheng-13737	146	23	dynamic	dynamic	ADJ
fumecheng-13737	146	24	terms	term	NOUN
fumecheng-13737	146	25	such	such	ADJ
fumecheng-13737	146	26	as	as	ADP
fumecheng-13737	146	27	u2ü	u2ü	NOUN
fumecheng-13737	146	28	and	and	CCONJ
fumecheng-13737	146	29	uu̇2	uu̇2	NOUN
fumecheng-13737	146	30	.	.	PUNCT
fumecheng-13737	147	1	these	these	DET
fumecheng-13737	147	2	terms	term	NOUN
fumecheng-13737	147	3	introduce	introduce	VERB
fumecheng-13737	147	4	a	a	DET
fumecheng-13737	147	5	strong	strong	ADJ
fumecheng-13737	147	6	amplitude	amplitude	NOUN
fumecheng-13737	147	7	dependence	dependence	NOUN
fumecheng-13737	147	8	into	into	ADP
fumecheng-13737	147	9	the	the	DET
fumecheng-13737	147	10	system	system	NOUN
fumecheng-13737	147	11	's	's	PART
fumecheng-13737	147	12	response	response	NOUN
fumecheng-13737	147	13	,	,	PUNCT
fumecheng-13737	147	14	further	far	ADV
fumecheng-13737	147	15	complicating	complicate	VERB
fumecheng-13737	147	16	the	the	DET
fumecheng-13737	147	17	governing	govern	VERB
fumecheng-13737	147	18	equation	equation	NOUN
fumecheng-13737	147	19	.	.	PUNCT
fumecheng-13737	148	1	in	in	ADP
fumecheng-13737	148	2	the	the	DET
fumecheng-13737	148	3	following	following	ADJ
fumecheng-13737	148	4	section	section	NOUN
fumecheng-13737	148	5	,	,	PUNCT
fumecheng-13737	148	6	approximate	approximate	ADJ
fumecheng-13737	148	7	analytical	analytical	ADJ
fumecheng-13737	148	8	solutions	solution	NOUN
fumecheng-13737	148	9	are	be	AUX
fumecheng-13737	148	10	derived	derive	VERB
fumecheng-13737	148	11	for	for	ADP
fumecheng-13737	148	12	eq	eq	PROPN
fumecheng-13737	148	13	.	.	PUNCT
fumecheng-13737	149	1	(	(	PUNCT
fumecheng-13737	149	2	8)	8)	NUM
fumecheng-13737	149	3	,	,	PUNCT
fumecheng-13737	149	4	considering	consider	VERB
fumecheng-13737	149	5	the	the	DET
fumecheng-13737	149	6	initial	initial	ADJ
fumecheng-13737	149	7	conditions	condition	NOUN
fumecheng-13737	149	8	:	:	PUNCT
fumecheng-13737	149	9	0	0	NUM
fumecheng-13737	149	10	(	(	PUNCT
fumecheng-13737	149	11	0	0	NUM
fumecheng-13737	149	12	)	)	PUNCT
fumecheng-13737	149	13	,	,	PUNCT
fumecheng-13737	149	14	0	0	X
fumecheng-13737	149	15	.	.	X
fumecheng-13737	150	1	t	t	PROPN
fumecheng-13737	150	2	du	du	PROPN
fumecheng-13737	150	3	u	u	PROPN
fumecheng-13737	150	4	a	a	DET
fumecheng-13737	150	5	dt	dt	X
fumecheng-13737	150	6	=	=	SYM
fumecheng-13737	151	1	=	=	SYM
fumecheng-13737	151	2	=	=	SYM
fumecheng-13737	151	3	(	(	PUNCT
fumecheng-13737	151	4	12	12	NUM
fumecheng-13737	151	5	)	)	PUNCT
fumecheng-13737	151	6	792	792	NUM
fumecheng-13737	151	7	c	c	X
fumecheng-13737	151	8	-	-	PUNCT
fumecheng-13737	151	9	h.	h.	NOUN
fumecheng-13737	151	10	he	he	PROPN
fumecheng-13737	151	11	,	,	PUNCT
fumecheng-13737	151	12	m.	m.	NOUN
fumecheng-13737	151	13	mohammadian	mohammadian	NOUN
fumecheng-13737	151	14	although	although	SCONJ
fumecheng-13737	151	15	eq	eq	VERB
fumecheng-13737	151	16	.	.	PUNCT
fumecheng-13737	152	1	(	(	PUNCT
fumecheng-13737	152	2	8)	8)	NUM
fumecheng-13737	152	3	is	be	AUX
fumecheng-13737	152	4	specifically	specifically	ADV
fumecheng-13737	152	5	derived	derive	VERB
fumecheng-13737	152	6	for	for	ADP
fumecheng-13737	152	7	a	a	DET
fumecheng-13737	152	8	stringer	stringer	NOUN
fumecheng-13737	152	9	-	-	PUNCT
fumecheng-13737	152	10	stiffened	stiffen	VERB
fumecheng-13737	152	11	shell	shell	NOUN
fumecheng-13737	152	12	structure	structure	NOUN
fumecheng-13737	152	13	,	,	PUNCT
fumecheng-13737	152	14	it	it	PRON
fumecheng-13737	152	15	also	also	ADV
fumecheng-13737	152	16	represents	represent	VERB
fumecheng-13737	152	17	the	the	DET
fumecheng-13737	152	18	governing	govern	VERB
fumecheng-13737	152	19	dynamic	dynamic	ADJ
fumecheng-13737	152	20	differential	differential	NOUN
fumecheng-13737	152	21	equation	equation	NOUN
fumecheng-13737	152	22	of	of	ADP
fumecheng-13737	152	23	other	other	ADJ
fumecheng-13737	152	24	structural	structural	ADJ
fumecheng-13737	152	25	systems	system	NOUN
fumecheng-13737	152	26	.	.	PUNCT
fumecheng-13737	153	1	for	for	ADP
fumecheng-13737	153	2	example	example	NOUN
fumecheng-13737	153	3	,	,	PUNCT
fumecheng-13737	153	4	by	by	ADP
fumecheng-13737	153	5	setting	set	VERB
fumecheng-13737	153	6	β4	β4	PROPN
fumecheng-13737	153	7	=	=	SYM
fumecheng-13737	153	8	0	0	NUM
fumecheng-13737	153	9	,	,	PUNCT
fumecheng-13737	153	10	the	the	DET
fumecheng-13737	153	11	equation	equation	NOUN
fumecheng-13737	153	12	reduces	reduce	VERB
fumecheng-13737	153	13	to	to	ADP
fumecheng-13737	153	14	the	the	DET
fumecheng-13737	153	15	form	form	NOUN
fumecheng-13737	153	16	encountered	encounter	VERB
fumecheng-13737	153	17	in	in	ADP
fumecheng-13737	153	18	tapered	tapered	ADJ
fumecheng-13737	153	19	beams	beam	NOUN
fumecheng-13737	153	20	[	[	X
fumecheng-13737	153	21	42	42	NUM
fumecheng-13737	153	22	]	]	PUNCT
fumecheng-13737	153	23	.	.	PUNCT
fumecheng-13737	154	1	similarly	similarly	ADV
fumecheng-13737	154	2	,	,	PUNCT
fumecheng-13737	154	3	setting	set	VERB
fumecheng-13737	154	4	β1	β1	PROPN
fumecheng-13737	154	5	=	=	SYM
fumecheng-13737	154	6	0	0	NUM
fumecheng-13737	154	7	yields	yield	NOUN
fumecheng-13737	154	8	the	the	DET
fumecheng-13737	154	9	well	well	ADV
fumecheng-13737	154	10	-	-	PUNCT
fumecheng-13737	154	11	known	know	VERB
fumecheng-13737	154	12	duffing	duffing	NOUN
fumecheng-13737	154	13	equation	equation	NOUN
fumecheng-13737	154	14	,	,	PUNCT
fumecheng-13737	154	15	which	which	PRON
fumecheng-13737	154	16	is	be	AUX
fumecheng-13737	154	17	widely	widely	ADV
fumecheng-13737	154	18	used	use	VERB
fumecheng-13737	154	19	in	in	ADP
fumecheng-13737	154	20	engineering	engineering	NOUN
fumecheng-13737	154	21	and	and	CCONJ
fumecheng-13737	154	22	physics	physics	NOUN
fumecheng-13737	154	23	applications	application	NOUN
fumecheng-13737	154	24	,	,	PUNCT
fumecheng-13737	154	25	such	such	ADJ
fumecheng-13737	154	26	as	as	ADP
fumecheng-13737	154	27	modeling	modeling	NOUN
fumecheng-13737	154	28	undamped	undampe	VERB
fumecheng-13737	154	29	fg	fg	NOUN
fumecheng-13737	154	30	beams	beam	NOUN
fumecheng-13737	155	1	[	[	X
fumecheng-13737	155	2	43	43	NUM
fumecheng-13737	155	3	]	]	PUNCT
fumecheng-13737	155	4	.	.	PUNCT
fumecheng-13737	156	1	therefore	therefore	ADV
fumecheng-13737	156	2	,	,	PUNCT
fumecheng-13737	156	3	the	the	DET
fumecheng-13737	156	4	analytical	analytical	ADJ
fumecheng-13737	156	5	methods	method	NOUN
fumecheng-13737	156	6	proposed	propose	VERB
fumecheng-13737	156	7	herein	herein	NOUN
fumecheng-13737	156	8	are	be	AUX
fumecheng-13737	156	9	not	not	PART
fumecheng-13737	156	10	limited	limit	VERB
fumecheng-13737	156	11	to	to	ADP
fumecheng-13737	156	12	the	the	DET
fumecheng-13737	156	13	specific	specific	ADJ
fumecheng-13737	156	14	geometry	geometry	NOUN
fumecheng-13737	156	15	considered	consider	VERB
fumecheng-13737	156	16	but	but	CCONJ
fumecheng-13737	156	17	can	can	AUX
fumecheng-13737	156	18	be	be	AUX
fumecheng-13737	156	19	more	more	ADV
fumecheng-13737	156	20	broadly	broadly	ADV
fumecheng-13737	156	21	applied	apply	VERB
fumecheng-13737	156	22	to	to	PART
fumecheng-13737	156	23	estimate	estimate	VERB
fumecheng-13737	156	24	the	the	DET
fumecheng-13737	156	25	nonlinear	nonlinear	ADJ
fumecheng-13737	156	26	frequency	frequency	NOUN
fumecheng-13737	156	27	of	of	ADP
fumecheng-13737	156	28	a	a	DET
fumecheng-13737	156	29	wide	wide	ADJ
fumecheng-13737	156	30	range	range	NOUN
fumecheng-13737	156	31	of	of	ADP
fumecheng-13737	156	32	conservative	conservative	ADJ
fumecheng-13737	156	33	systems	system	NOUN
fumecheng-13737	156	34	.	.	PUNCT
fumecheng-13737	157	1	3	3	X
fumecheng-13737	157	2	.	.	X
fumecheng-13737	157	3	analytical	analytical	ADJ
fumecheng-13737	157	4	solutions	solution	NOUN
fumecheng-13737	157	5	for	for	ADP
fumecheng-13737	157	6	nonlinear	nonlinear	ADJ
fumecheng-13737	157	7	vibration	vibration	NOUN
fumecheng-13737	157	8	of	of	ADP
fumecheng-13737	157	9	the	the	DET
fumecheng-13737	157	10	stringer	stringer	NOUN
fumecheng-13737	157	11	-	-	PUNCT
fumecheng-13737	157	12	stiffened	stiffen	VERB
fumecheng-13737	157	13	shell	shell	NOUN
fumecheng-13737	157	14	this	this	DET
fumecheng-13737	157	15	section	section	NOUN
fumecheng-13737	157	16	derives	derive	VERB
fumecheng-13737	157	17	closed	closed	ADJ
fumecheng-13737	157	18	-	-	PUNCT
fumecheng-13737	157	19	form	form	NOUN
fumecheng-13737	157	20	expressions	expression	NOUN
fumecheng-13737	157	21	for	for	ADP
fumecheng-13737	157	22	the	the	DET
fumecheng-13737	157	23	nonlinear	nonlinear	ADJ
fumecheng-13737	157	24	frequency	frequency	NOUN
fumecheng-13737	157	25	of	of	ADP
fumecheng-13737	157	26	the	the	DET
fumecheng-13737	157	27	stringer	stringer	NOUN
fumecheng-13737	157	28	-	-	PUNCT
fumecheng-13737	157	29	stiffened	stiffen	VERB
fumecheng-13737	157	30	shell	shell	NOUN
fumecheng-13737	157	31	governed	govern	VERB
fumecheng-13737	157	32	in	in	ADP
fumecheng-13737	157	33	eq	eq	ADP
fumecheng-13737	157	34	.	.	PUNCT
fumecheng-13737	158	1	(	(	PUNCT
fumecheng-13737	158	2	8)	8)	NUM
fumecheng-13737	158	3	,	,	PUNCT
fumecheng-13737	158	4	by	by	ADP
fumecheng-13737	158	5	proposing	propose	VERB
fumecheng-13737	158	6	three	three	NUM
fumecheng-13737	158	7	straightforward	straightforward	ADJ
fumecheng-13737	158	8	and	and	CCONJ
fumecheng-13737	158	9	noniterative	noniterative	ADJ
fumecheng-13737	158	10	approximate	approximate	ADJ
fumecheng-13737	158	11	analytical	analytical	ADJ
fumecheng-13737	158	12	methods	method	NOUN
fumecheng-13737	158	13	.	.	PUNCT
fumecheng-13737	159	1	for	for	ADP
fumecheng-13737	159	2	validation	validation	NOUN
fumecheng-13737	159	3	purpose	purpose	NOUN
fumecheng-13737	159	4	,	,	PUNCT
fumecheng-13737	159	5	the	the	DET
fumecheng-13737	159	6	exact	exact	ADJ
fumecheng-13737	159	7	nonlinear	nonlinear	ADJ
fumecheng-13737	159	8	frequency	frequency	NOUN
fumecheng-13737	159	9	is	be	AUX
fumecheng-13737	159	10	also	also	ADV
fumecheng-13737	159	11	derived	derive	VERB
fumecheng-13737	159	12	.	.	PUNCT
fumecheng-13737	160	1	each	each	DET
fumecheng-13737	160	2	method	method	NOUN
fumecheng-13737	160	3	assumes	assume	VERB
fumecheng-13737	160	4	a	a	DET
fumecheng-13737	160	5	trial	trial	NOUN
fumecheng-13737	160	6	solution	solution	NOUN
fumecheng-13737	160	7	of	of	ADP
fumecheng-13737	160	8	the	the	DET
fumecheng-13737	160	9	form	form	NOUN
fumecheng-13737	160	10	u(t	u(t	NOUN
fumecheng-13737	160	11	)	)	PUNCT
fumecheng-13737	160	12	=	=	SYM
fumecheng-13737	160	13	acos(ωt	acos(ωt	NOUN
fumecheng-13737	160	14	)	)	PUNCT
fumecheng-13737	160	15	,	,	PUNCT
fumecheng-13737	160	16	which	which	PRON
fumecheng-13737	160	17	satisfies	satisfy	VERB
fumecheng-13737	160	18	the	the	DET
fumecheng-13737	160	19	initial	initial	ADJ
fumecheng-13737	160	20	conditions	condition	NOUN
fumecheng-13737	160	21	specified	specify	VERB
fumecheng-13737	160	22	in	in	ADP
fumecheng-13737	160	23	eq	eq	ADP
fumecheng-13737	160	24	.	.	PUNCT
fumecheng-13737	161	1	(	(	PUNCT
fumecheng-13737	161	2	12	12	NUM
fumecheng-13737	161	3	)	)	PUNCT
fumecheng-13737	162	1	and	and	CCONJ
fumecheng-13737	162	2	approximates	approximate	VERB
fumecheng-13737	162	3	the	the	DET
fumecheng-13737	162	4	periodic	periodic	ADJ
fumecheng-13737	162	5	behavior	behavior	NOUN
fumecheng-13737	162	6	of	of	ADP
fumecheng-13737	162	7	the	the	DET
fumecheng-13737	162	8	oscillator	oscillator	NOUN
fumecheng-13737	162	9	.	.	PUNCT
fumecheng-13737	163	1	3.1	3.1	NUM
fumecheng-13737	163	2	.	.	PUNCT
fumecheng-13737	164	1	adaptive	adaptive	ADJ
fumecheng-13737	164	2	location	location	NOUN
fumecheng-13737	164	3	point	point	NOUN
fumecheng-13737	164	4	-	-	PUNCT
fumecheng-13737	164	5	based	base	VERB
fumecheng-13737	164	6	he	he	PRON
fumecheng-13737	164	7	’s	’	VERB
fumecheng-13737	164	8	formulation	formulation	NOUN
fumecheng-13737	164	9	(	(	PUNCT
fumecheng-13737	164	10	alpf	alpf	PROPN
fumecheng-13737	164	11	)	)	PUNCT
fumecheng-13737	164	12	in	in	ADP
fumecheng-13737	164	13	this	this	DET
fumecheng-13737	164	14	paper	paper	NOUN
fumecheng-13737	164	15	,	,	PUNCT
fumecheng-13737	164	16	we	we	PRON
fumecheng-13737	164	17	propose	propose	VERB
fumecheng-13737	164	18	a	a	DET
fumecheng-13737	164	19	new	new	ADJ
fumecheng-13737	164	20	method	method	NOUN
fumecheng-13737	164	21	,	,	PUNCT
fumecheng-13737	164	22	namely	namely	ADV
fumecheng-13737	164	23	the	the	DET
fumecheng-13737	164	24	adaptive	adaptive	ADJ
fumecheng-13737	164	25	location	location	NOUN
fumecheng-13737	164	26	point	point	NOUN
fumecheng-13737	164	27	-	-	PUNCT
fumecheng-13737	164	28	based	base	VERB
fumecheng-13737	164	29	he	he	PRON
fumecheng-13737	164	30	’s	’	VERB
fumecheng-13737	164	31	formulation	formulation	NOUN
fumecheng-13737	164	32	(	(	PUNCT
fumecheng-13737	164	33	alpf	alpf	PROPN
fumecheng-13737	164	34	)	)	PUNCT
fumecheng-13737	164	35	,	,	PUNCT
fumecheng-13737	164	36	to	to	PART
fumecheng-13737	164	37	improve	improve	VERB
fumecheng-13737	164	38	he	he	PRON
fumecheng-13737	164	39	’s	’s	PART
fumecheng-13737	164	40	frequency	frequency	NOUN
fumecheng-13737	164	41	–	–	PUNCT
fumecheng-13737	164	42	amplitude	amplitude	NOUN
fumecheng-13737	164	43	formulation	formulation	NOUN
fumecheng-13737	164	44	.	.	PUNCT
fumecheng-13737	165	1	in	in	ADP
fumecheng-13737	165	2	the	the	DET
fumecheng-13737	165	3	original	original	ADJ
fumecheng-13737	165	4	method	method	NOUN
fumecheng-13737	165	5	,	,	PUNCT
fumecheng-13737	165	6	a	a	DET
fumecheng-13737	165	7	fixed	fix	VERB
fumecheng-13737	165	8	location	location	NOUN
fumecheng-13737	165	9	point	point	NOUN
fumecheng-13737	165	10	is	be	AUX
fumecheng-13737	165	11	selected	select	VERB
fumecheng-13737	165	12	based	base	VERB
fumecheng-13737	165	13	on	on	ADP
fumecheng-13737	165	14	he	he	PRON
fumecheng-13737	165	15	’s	’	VERB
fumecheng-13737	165	16	recommendation	recommendation	NOUN
fumecheng-13737	165	17	.	.	PUNCT
fumecheng-13737	166	1	in	in	ADP
fumecheng-13737	166	2	contrast	contrast	NOUN
fumecheng-13737	166	3	,	,	PUNCT
fumecheng-13737	166	4	alpf	alpf	PROPN
fumecheng-13737	166	5	introduces	introduce	VERB
fumecheng-13737	166	6	a	a	DET
fumecheng-13737	166	7	procedure	procedure	NOUN
fumecheng-13737	166	8	for	for	ADP
fumecheng-13737	166	9	selecting	select	VERB
fumecheng-13737	166	10	the	the	DET
fumecheng-13737	166	11	location	location	NOUN
fumecheng-13737	166	12	point	point	NOUN
fumecheng-13737	166	13	,	,	PUNCT
fumecheng-13737	166	14	according	accord	VERB
fumecheng-13737	166	15	to	to	ADP
fumecheng-13737	166	16	the	the	DET
fumecheng-13737	166	17	system	system	NOUN
fumecheng-13737	166	18	’s	’s	PART
fumecheng-13737	166	19	amplitude	amplitude	NOUN
fumecheng-13737	166	20	and	and	CCONJ
fumecheng-13737	166	21	physical	physical	ADJ
fumecheng-13737	166	22	parameters	parameter	NOUN
fumecheng-13737	166	23	.	.	PUNCT
fumecheng-13737	167	1	this	this	DET
fumecheng-13737	167	2	adaptation	adaptation	NOUN
fumecheng-13737	167	3	improves	improve	VERB
fumecheng-13737	167	4	the	the	DET
fumecheng-13737	167	5	accuracy	accuracy	NOUN
fumecheng-13737	167	6	of	of	ADP
fumecheng-13737	167	7	the	the	DET
fumecheng-13737	167	8	estimated	estimate	VERB
fumecheng-13737	167	9	frequency	frequency	NOUN
fumecheng-13737	167	10	,	,	PUNCT
fumecheng-13737	167	11	especially	especially	ADV
fumecheng-13737	167	12	in	in	ADP
fumecheng-13737	167	13	systems	system	NOUN
fumecheng-13737	167	14	with	with	ADP
fumecheng-13737	167	15	strong	strong	ADJ
fumecheng-13737	167	16	nonlinearities	nonlinearitie	NOUN
fumecheng-13737	167	17	or	or	CCONJ
fumecheng-13737	167	18	amplitude	amplitude	NOUN
fumecheng-13737	167	19	-	-	PUNCT
fumecheng-13737	167	20	dependent	dependent	ADJ
fumecheng-13737	167	21	behavior	behavior	NOUN
fumecheng-13737	167	22	.	.	PUNCT
fumecheng-13737	168	1	importantly	importantly	ADV
fumecheng-13737	168	2	,	,	PUNCT
fumecheng-13737	168	3	alpf	alpf	PROPN
fumecheng-13737	168	4	retains	retain	VERB
fumecheng-13737	168	5	the	the	DET
fumecheng-13737	168	6	simplicity	simplicity	NOUN
fumecheng-13737	168	7	and	and	CCONJ
fumecheng-13737	168	8	computational	computational	ADJ
fumecheng-13737	168	9	efficiency	efficiency	NOUN
fumecheng-13737	168	10	of	of	ADP
fumecheng-13737	168	11	the	the	DET
fumecheng-13737	168	12	original	original	ADJ
fumecheng-13737	168	13	method	method	NOUN
fumecheng-13737	168	14	.	.	PUNCT
fumecheng-13737	169	1	to	to	PART
fumecheng-13737	169	2	illustrate	illustrate	VERB
fumecheng-13737	169	3	the	the	DET
fumecheng-13737	169	4	method	method	NOUN
fumecheng-13737	169	5	,	,	PUNCT
fumecheng-13737	169	6	consider	consider	VERB
fumecheng-13737	169	7	the	the	DET
fumecheng-13737	169	8	differential	differential	ADJ
fumecheng-13737	169	9	equation	equation	NOUN
fumecheng-13737	169	10	of	of	ADP
fumecheng-13737	169	11	a	a	DET
fumecheng-13737	169	12	nonlinear	nonlinear	ADJ
fumecheng-13737	169	13	oscillator	oscillator	NOUN
fumecheng-13737	169	14	given	give	VERB
fumecheng-13737	169	15	by	by	ADP
fumecheng-13737	169	16	:	:	PUNCT
fumecheng-13737	169	17	(	(	PUNCT
fumecheng-13737	169	18	)	)	PUNCT
fumecheng-13737	169	19	0	0	NUM
fumecheng-13737	169	20	,	,	PUNCT
fumecheng-13737	169	21	(	(	PUNCT
fumecheng-13737	169	22	0	0	NUM
fumecheng-13737	169	23	)	)	PUNCT
fumecheng-13737	169	24	,	,	PUNCT
fumecheng-13737	169	25	(	(	PUNCT
fumecheng-13737	169	26	0	0	NUM
fumecheng-13737	169	27	)	)	PUNCT
fumecheng-13737	169	28	0.u	0.u	NUM
fumecheng-13737	170	1	f	f	NOUN
fumecheng-13737	170	2	u	u	X
fumecheng-13737	170	3	u	u	NOUN
fumecheng-13737	170	4	a	a	DET
fumecheng-13737	170	5	u+	u+	NOUN
fumecheng-13737	170	6	=	=	PUNCT
fumecheng-13737	170	7	=	=	SYM
fumecheng-13737	170	8	=	=	NOUN
fumecheng-13737	170	9			X
fumecheng-13737	170	10	(	(	PUNCT
fumecheng-13737	170	11	13	13	NUM
fumecheng-13737	170	12	)	)	PUNCT
fumecheng-13737	170	13	the	the	DET
fumecheng-13737	170	14	above	above	ADJ
fumecheng-13737	170	15	equation	equation	NOUN
fumecheng-13737	170	16	can	can	AUX
fumecheng-13737	170	17	be	be	AUX
fumecheng-13737	170	18	rewritten	rewrite	VERB
fumecheng-13737	170	19	as	as	ADP
fumecheng-13737	170	20	(	(	PUNCT
fumecheng-13737	170	21	)	)	PUNCT
fumecheng-13737	170	22	0	0	X
fumecheng-13737	170	23	.	.	PUNCT
fumecheng-13737	171	1	f	f	PROPN
fumecheng-13737	171	2	u	u	X
fumecheng-13737	171	3	u	u	VERB
fumecheng-13737	171	4	u	u	X
fumecheng-13737	171	5	u	u	NOUN
fumecheng-13737	171	6			NOUN
fumecheng-13737	171	7			NOUN
fumecheng-13737	171	8	+	+	CCONJ
fumecheng-13737	171	9	=	=	PROPN
fumecheng-13737	171	10			ADJ
fumecheng-13737	171	11			PROPN
fumecheng-13737	171	12			PROPN
fumecheng-13737	171	13			PROPN
fumecheng-13737	171	14			NOUN
fumecheng-13737	171	15	(	(	PUNCT
fumecheng-13737	171	16	14	14	NUM
fumecheng-13737	171	17	)	)	PUNCT
fumecheng-13737	171	18	he	he	PRON
fumecheng-13737	171	19	[	[	X
fumecheng-13737	171	20	44	44	NUM
fumecheng-13737	171	21	,	,	PUNCT
fumecheng-13737	171	22	45	45	NUM
fumecheng-13737	171	23	]	]	PUNCT
fumecheng-13737	171	24	demonstrated	demonstrate	VERB
fumecheng-13737	171	25	that	that	SCONJ
fumecheng-13737	171	26	the	the	DET
fumecheng-13737	171	27	frequency	frequency	NOUN
fumecheng-13737	171	28	of	of	ADP
fumecheng-13737	171	29	the	the	DET
fumecheng-13737	171	30	nonlinear	nonlinear	ADJ
fumecheng-13737	171	31	oscillator	oscillator	NOUN
fumecheng-13737	171	32	given	give	VERB
fumecheng-13737	171	33	in	in	ADP
fumecheng-13737	171	34	eq	eq	ADP
fumecheng-13737	171	35	.	.	PUNCT
fumecheng-13737	172	1	(	(	PUNCT
fumecheng-13737	172	2	13	13	NUM
fumecheng-13737	172	3	)	)	PUNCT
fumecheng-13737	172	4	can	can	AUX
fumecheng-13737	172	5	be	be	AUX
fumecheng-13737	172	6	easily	easily	ADV
fumecheng-13737	172	7	approximated	approximate	VERB
fumecheng-13737	172	8	as	as	SCONJ
fumecheng-13737	172	9	follows	follow	VERB
fumecheng-13737	172	10	:	:	PUNCT
fumecheng-13737	172	11	2	2	NUM
fumecheng-13737	172	12	(	(	PUNCT
fumecheng-13737	172	13	)	)	PUNCT
fumecheng-13737	172	14	,	,	PUNCT
fumecheng-13737	172	15	he	he	PRON
fumecheng-13737	172	16	u	u	VERB
fumecheng-13737	172	17	u	u	NOUN
fumecheng-13737	172	18	f	f	PROPN
fumecheng-13737	172	19	u	u	NOUN
fumecheng-13737	172	20	u	u	NOUN
fumecheng-13737	172	21			X
fumecheng-13737	172	22	=	=	PUNCT
fumecheng-13737	172	23			X
fumecheng-13737	172	24	(	(	PUNCT
fumecheng-13737	172	25	15	15	NUM
fumecheng-13737	172	26	)	)	PUNCT
fumecheng-13737	172	27	where	where	SCONJ
fumecheng-13737	172	28	ū	ū	PRON
fumecheng-13737	172	29	is	be	AUX
fumecheng-13737	172	30	the	the	DET
fumecheng-13737	172	31	location	location	NOUN
fumecheng-13737	172	32	point	point	NOUN
fumecheng-13737	172	33	,	,	PUNCT
fumecheng-13737	172	34	defined	define	VERB
fumecheng-13737	172	35	as	as	ADP
fumecheng-13737	172	36	ū	ū	X
fumecheng-13737	172	37	=	=	PUNCT
fumecheng-13737	172	38	ka	ka	PROPN
fumecheng-13737	172	39	.	.	PUNCT
fumecheng-13737	173	1	this	this	DET
fumecheng-13737	173	2	formulation	formulation	NOUN
fumecheng-13737	173	3	has	have	AUX
fumecheng-13737	173	4	been	be	AUX
fumecheng-13737	173	5	widely	widely	ADV
fumecheng-13737	173	6	applied	apply	VERB
fumecheng-13737	173	7	to	to	ADP
fumecheng-13737	173	8	various	various	ADJ
fumecheng-13737	173	9	types	type	NOUN
fumecheng-13737	173	10	of	of	ADP
fumecheng-13737	173	11	nonlinear	nonlinear	ADJ
fumecheng-13737	173	12	oscillators	oscillator	NOUN
fumecheng-13737	173	13	.	.	PUNCT
fumecheng-13737	174	1	the	the	DET
fumecheng-13737	174	2	method	method	NOUN
fumecheng-13737	174	3	is	be	AUX
fumecheng-13737	174	4	computationally	computationally	ADV
fumecheng-13737	174	5	simple	simple	ADJ
fumecheng-13737	174	6	,	,	PUNCT
fumecheng-13737	174	7	making	make	VERB
fumecheng-13737	174	8	it	it	PRON
fumecheng-13737	174	9	suitable	suitable	ADJ
fumecheng-13737	174	10	for	for	ADP
fumecheng-13737	174	11	quick	quick	ADJ
fumecheng-13737	174	12	frequency	frequency	NOUN
fumecheng-13737	174	13	estimations	estimation	NOUN
fumecheng-13737	174	14	.	.	PUNCT
fumecheng-13737	175	1	however	however	ADV
fumecheng-13737	175	2	,	,	PUNCT
fumecheng-13737	175	3	one	one	NUM
fumecheng-13737	175	4	of	of	ADP
fumecheng-13737	175	5	the	the	DET
fumecheng-13737	175	6	main	main	ADJ
fumecheng-13737	175	7	challenges	challenge	NOUN
fumecheng-13737	175	8	in	in	ADP
fumecheng-13737	175	9	applying	apply	VERB
fumecheng-13737	175	10	he	he	PRON
fumecheng-13737	175	11	’s	’s	PART
fumecheng-13737	175	12	method	method	NOUN
fumecheng-13737	175	13	is	be	AUX
fumecheng-13737	175	14	selecting	select	VERB
fumecheng-13737	175	15	an	an	DET
fumecheng-13737	175	16	appropriate	appropriate	ADJ
fumecheng-13737	175	17	value	value	NOUN
fumecheng-13737	175	18	for	for	ADP
fumecheng-13737	175	19	the	the	DET
fumecheng-13737	175	20	location	location	NOUN
fumecheng-13737	175	21	point	point	NOUN
fumecheng-13737	175	22	[	[	X
fumecheng-13737	175	23	27	27	NUM
fumecheng-13737	175	24	]	]	PUNCT
fumecheng-13737	175	25	.	.	PUNCT
fumecheng-13737	176	1	it	it	PRON
fumecheng-13737	176	2	is	be	AUX
fumecheng-13737	176	3	more	more	ADV
fumecheng-13737	176	4	a	a	DET
fumecheng-13737	176	5	fast	fast	ADJ
fumecheng-13737	176	6	insight	insight	NOUN
fumecheng-13737	176	7	into	into	ADP
fumecheng-13737	176	8	nonlinear	nonlinear	ADJ
fumecheng-13737	176	9	frequency	frequency	NOUN
fumecheng-13737	176	10	estimation	estimation	NOUN
fumecheng-13737	176	11	of	of	ADP
fumecheng-13737	176	12	stringer	stringer	NOUN
fumecheng-13737	176	13	-	-	PUNCT
fumecheng-13737	176	14	stiffened	stiffen	VERB
fumecheng-13737	176	15	shells	shell	NOUN
fumecheng-13737	176	16	with	with	ADP
fumecheng-13737	176	17	high	high	ADJ
fumecheng-13737	176	18	accuracy	accuracy	NOUN
fumecheng-13737	176	19	793	793	NUM
fumecheng-13737	176	20	appropriate	appropriate	ADJ
fumecheng-13737	176	21	to	to	PART
fumecheng-13737	176	22	express	express	VERB
fumecheng-13737	176	23	the	the	DET
fumecheng-13737	176	24	value	value	NOUN
fumecheng-13737	176	25	of	of	ADP
fumecheng-13737	176	26	k	k	PROPN
fumecheng-13737	176	27	as	as	ADP
fumecheng-13737	176	28	a	a	DET
fumecheng-13737	176	29	function	function	NOUN
fumecheng-13737	176	30	of	of	ADP
fumecheng-13737	176	31	both	both	CCONJ
fumecheng-13737	176	32	the	the	DET
fumecheng-13737	176	33	amplitude	amplitude	NOUN
fumecheng-13737	176	34	and	and	CCONJ
fumecheng-13737	176	35	system	system	NOUN
fumecheng-13737	176	36	parameters	parameter	NOUN
fumecheng-13737	176	37	.	.	PUNCT
fumecheng-13737	177	1	to	to	PART
fumecheng-13737	177	2	implement	implement	VERB
fumecheng-13737	177	3	the	the	DET
fumecheng-13737	177	4	proposed	propose	VERB
fumecheng-13737	177	5	alpf	alpf	NOUN
fumecheng-13737	177	6	method	method	PROPN
fumecheng-13737	177	7	,	,	PUNCT
fumecheng-13737	177	8	eq	eq	NOUN
fumecheng-13737	177	9	.	.	PUNCT
fumecheng-13737	178	1	(	(	PUNCT
fumecheng-13737	178	2	15	15	NUM
fumecheng-13737	178	3	)	)	PUNCT
fumecheng-13737	178	4	is	be	AUX
fumecheng-13737	178	5	substituted	substitute	VERB
fumecheng-13737	178	6	into	into	ADP
fumecheng-13737	178	7	eq	eq	PROPN
fumecheng-13737	178	8	.	.	PUNCT
fumecheng-13737	179	1	(	(	PUNCT
fumecheng-13737	179	2	13	13	NUM
fumecheng-13737	179	3	)	)	PUNCT
fumecheng-13737	179	4	,	,	PUNCT
fumecheng-13737	179	5	allowing	allow	VERB
fumecheng-13737	179	6	the	the	DET
fumecheng-13737	179	7	latter	latter	ADJ
fumecheng-13737	179	8	to	to	PART
fumecheng-13737	179	9	be	be	AUX
fumecheng-13737	179	10	rewritten	rewrite	VERB
fumecheng-13737	179	11	in	in	ADP
fumecheng-13737	179	12	the	the	DET
fumecheng-13737	179	13	following	follow	VERB
fumecheng-13737	179	14	form	form	NOUN
fumecheng-13737	179	15	:	:	PUNCT
fumecheng-13737	179	16	(	(	PUNCT
fumecheng-13737	179	17	)	)	PUNCT
fumecheng-13737	179	18	(	(	PUNCT
fumecheng-13737	179	19	)	)	PUNCT
fumecheng-13737	179	20	(	(	PUNCT
fumecheng-13737	179	21	)	)	PUNCT
fumecheng-13737	179	22	(	(	PUNCT
fumecheng-13737	179	23	)	)	PUNCT
fumecheng-13737	179	24	,	,	PUNCT
fumecheng-13737	179	25	(	(	PUNCT
fumecheng-13737	179	26	)	)	PUNCT
fumecheng-13737	179	27	.	.	PUNCT
fumecheng-13737	180	1	u	u	INTJ
fumecheng-13737	180	2	ka	ka	PROPN
fumecheng-13737	180	3	f	f	PROPN
fumecheng-13737	180	4	u	u	PROPN
fumecheng-13737	180	5	u	u	PROPN
fumecheng-13737	180	6	g	g	PROPN
fumecheng-13737	180	7	ka	ka	PROPN
fumecheng-13737	180	8	u	u	PROPN
fumecheng-13737	180	9	g	g	PROPN
fumecheng-13737	180	10	ka	ka	PROPN
fumecheng-13737	180	11	u	u	PROPN
fumecheng-13737	180	12	f	f	PROPN
fumecheng-13737	180	13	u	u	PROPN
fumecheng-13737	180	14	g	g	PROPN
fumecheng-13737	180	15	ka	ka	PROPN
fumecheng-13737	180	16	u	u	PROPN
fumecheng-13737	180	17	=	=	PROPN
fumecheng-13737	181	1	+	+	NUM
fumecheng-13737	181	2	=	=	SYM
fumecheng-13737	181	3	−	−	PROPN
fumecheng-13737	181	4	=	=	PRON
fumecheng-13737	181	5			NOUN
fumecheng-13737	181	6	(	(	PUNCT
fumecheng-13737	181	7	16	16	NUM
fumecheng-13737	181	8	)	)	PUNCT
fumecheng-13737	181	9	if	if	SCONJ
fumecheng-13737	181	10	the	the	DET
fumecheng-13737	181	11	frequency	frequency	NOUN
fumecheng-13737	181	12	obtained	obtain	VERB
fumecheng-13737	181	13	from	from	ADP
fumecheng-13737	181	14	eq	eq	PROPN
fumecheng-13737	181	15	.	.	PUNCT
fumecheng-13737	182	1	(	(	PUNCT
fumecheng-13737	182	2	15	15	NUM
fumecheng-13737	182	3	)	)	PUNCT
fumecheng-13737	182	4	is	be	AUX
fumecheng-13737	182	5	regarded	regard	VERB
fumecheng-13737	182	6	as	as	ADP
fumecheng-13737	182	7	the	the	DET
fumecheng-13737	182	8	exact	exact	ADJ
fumecheng-13737	182	9	frequency	frequency	NOUN
fumecheng-13737	182	10	,	,	PUNCT
fumecheng-13737	182	11	then	then	ADV
fumecheng-13737	182	12	the	the	DET
fumecheng-13737	182	13	right	right	ADJ
fumecheng-13737	182	14	-	-	PUNCT
fumecheng-13737	182	15	hand	hand	NOUN
fumecheng-13737	182	16	side	side	NOUN
fumecheng-13737	182	17	of	of	ADP
fumecheng-13737	182	18	eq	eq	PROPN
fumecheng-13737	182	19	.	.	PUNCT
fumecheng-13737	183	1	(	(	PUNCT
fumecheng-13737	183	2	16	16	NUM
fumecheng-13737	183	3	)	)	PUNCT
fumecheng-13737	183	4	reduces	reduce	VERB
fumecheng-13737	183	5	to	to	ADP
fumecheng-13737	183	6	zero	zero	NUM
fumecheng-13737	183	7	.	.	PUNCT
fumecheng-13737	184	1	by	by	ADP
fumecheng-13737	184	2	applying	apply	VERB
fumecheng-13737	184	3	the	the	DET
fumecheng-13737	184	4	galerkin	galerkin	ADJ
fumecheng-13737	184	5	technique	technique	NOUN
fumecheng-13737	184	6	and	and	CCONJ
fumecheng-13737	184	7	using	use	VERB
fumecheng-13737	184	8	cos	cos	PROPN
fumecheng-13737	184	9	(	(	PUNCT
fumecheng-13737	184	10	ωt	ωt	PROPN
fumecheng-13737	184	11	)	)	PUNCT
fumecheng-13737	184	12	as	as	ADP
fumecheng-13737	184	13	the	the	DET
fumecheng-13737	184	14	weighting	weighting	NOUN
fumecheng-13737	184	15	function	function	NOUN
fumecheng-13737	184	16	,	,	PUNCT
fumecheng-13737	184	17	the	the	DET
fumecheng-13737	184	18	following	follow	VERB
fumecheng-13737	184	19	equation	equation	NOUN
fumecheng-13737	184	20	is	be	AUX
fumecheng-13737	184	21	derived	derive	VERB
fumecheng-13737	184	22	:	:	PUNCT
fumecheng-13737	184	23	(	(	PUNCT
fumecheng-13737	184	24	)	)	PUNCT
fumecheng-13737	184	25	4	4	NUM
fumecheng-13737	184	26	0	0	NUM
fumecheng-13737	184	27	(	(	PUNCT
fumecheng-13737	184	28	)	)	PUNCT
fumecheng-13737	184	29	(	(	PUNCT
fumecheng-13737	184	30	)	)	PUNCT
fumecheng-13737	184	31	cos	cos	PROPN
fumecheng-13737	184	32	(	(	PUNCT
fumecheng-13737	184	33	)	)	PUNCT
fumecheng-13737	184	34	0	0	NUM
fumecheng-13737	184	35	,	,	PUNCT
fumecheng-13737	184	36	t	t	PROPN
fumecheng-13737	184	37	g	g	PROPN
fumecheng-13737	184	38	ka	ka	PROPN
fumecheng-13737	184	39	u	u	PROPN
fumecheng-13737	184	40	f	f	PROPN
fumecheng-13737	184	41	u	u	NOUN
fumecheng-13737	184	42	t	t	X
fumecheng-13737	184	43	dt−	dt−	PROPN
fumecheng-13737	184	44	=	=	X
fumecheng-13737	184	45			X
fumecheng-13737	184	46	(	(	PUNCT
fumecheng-13737	184	47	17	17	NUM
fumecheng-13737	184	48	)	)	PUNCT
fumecheng-13737	184	49	where	where	SCONJ
fumecheng-13737	184	50	t	t	NOUN
fumecheng-13737	184	51	=	=	PUNCT
fumecheng-13737	184	52	2π	2π	NOUN
fumecheng-13737	184	53	/	/	SYM
fumecheng-13737	184	54	ω	ω	NOUN
fumecheng-13737	184	55	.	.	PUNCT
fumecheng-13737	185	1	this	this	DET
fumecheng-13737	185	2	equation	equation	NOUN
fumecheng-13737	185	3	can	can	AUX
fumecheng-13737	185	4	be	be	AUX
fumecheng-13737	185	5	solved	solve	VERB
fumecheng-13737	185	6	to	to	PART
fumecheng-13737	185	7	determine	determine	VERB
fumecheng-13737	185	8	the	the	DET
fumecheng-13737	185	9	value	value	NOUN
fumecheng-13737	185	10	of	of	ADP
fumecheng-13737	185	11	k.	k.	PROPN
fumecheng-13737	185	12	for	for	ADP
fumecheng-13737	185	13	the	the	DET
fumecheng-13737	185	14	present	present	ADJ
fumecheng-13737	185	15	problem	problem	NOUN
fumecheng-13737	185	16	,	,	PUNCT
fumecheng-13737	185	17	eq	eq	NOUN
fumecheng-13737	185	18	.	.	PUNCT
fumecheng-13737	186	1	(	(	PUNCT
fumecheng-13737	186	2	8)	8)	NUM
fumecheng-13737	186	3	can	can	AUX
fumecheng-13737	186	4	be	be	AUX
fumecheng-13737	186	5	rewritten	rewrite	VERB
fumecheng-13737	186	6	as	as	ADP
fumecheng-13737	186	7	:	:	PUNCT
fumecheng-13737	186	8	(	(	PUNCT
fumecheng-13737	186	9	)	)	SYM
fumecheng-13737	186	10	2	2	NUM
fumecheng-13737	186	11	2	2	NUM
fumecheng-13737	186	12	3	3	NUM
fumecheng-13737	186	13	5	5	NUM
fumecheng-13737	186	14	1	1	NUM
fumecheng-13737	186	15	2	2	NUM
fumecheng-13737	186	16	3	3	NUM
fumecheng-13737	186	17	4	4	NUM
fumecheng-13737	186	18	0	0	NUM
fumecheng-13737	186	19	.	.	PUNCT
fumecheng-13737	187	1	u	u	PRON
fumecheng-13737	187	2	u	u	NOUN
fumecheng-13737	187	3	uu	uu	VERB
fumecheng-13737	187	4	u	u	NOUN
fumecheng-13737	187	5	u	u	X
fumecheng-13737	187	6	u	u	X
fumecheng-13737	187	7	u	u	NOUN
fumecheng-13737	187	8	u	u	NOUN
fumecheng-13737	187	9	u	u	NOUN
fumecheng-13737	187	10			PROPN
fumecheng-13737	187	11			PROPN
fumecheng-13737	187	12			PROPN
fumecheng-13737	187	13			CCONJ
fumecheng-13737	187	14	+	+	VERB
fumecheng-13737	187	15	+	+	CCONJ
fumecheng-13737	188	1	+	+	CCONJ
fumecheng-13737	189	1	+	+	CCONJ
fumecheng-13737	189	2			ADJ
fumecheng-13737	189	3	+	+	PROPN
fumecheng-13737	189	4	=	=	SYM
fumecheng-13737	189	5			PROPN
fumecheng-13737	189	6			PROPN
fumecheng-13737	189	7			PROPN
fumecheng-13737	189	8			PROPN
fumecheng-13737	189	9			NUM
fumecheng-13737	189	10			NOUN
fumecheng-13737	189	11	(	(	PUNCT
fumecheng-13737	189	12	18	18	NUM
fumecheng-13737	189	13	)	)	PUNCT
fumecheng-13737	189	14	following	follow	VERB
fumecheng-13737	189	15	eq	eq	ADP
fumecheng-13737	189	16	.	.	PUNCT
fumecheng-13737	189	17	(	(	PUNCT
fumecheng-13737	189	18	15	15	NUM
fumecheng-13737	189	19	)	)	PUNCT
fumecheng-13737	189	20	,	,	PUNCT
fumecheng-13737	189	21	the	the	DET
fumecheng-13737	189	22	nonlinear	nonlinear	ADJ
fumecheng-13737	189	23	frequency	frequency	NOUN
fumecheng-13737	189	24	is	be	AUX
fumecheng-13737	189	25	approximated	approximate	VERB
fumecheng-13737	189	26	as	as	ADP
fumecheng-13737	189	27	:	:	PUNCT
fumecheng-13737	189	28	(	(	PUNCT
fumecheng-13737	189	29	)	)	SYM
fumecheng-13737	189	30	2	2	NUM
fumecheng-13737	189	31	2	2	NUM
fumecheng-13737	189	32	3	3	NUM
fumecheng-13737	189	33	5	5	NUM
fumecheng-13737	189	34	1	1	NUM
fumecheng-13737	189	35	2	2	NUM
fumecheng-13737	189	36	3	3	NUM
fumecheng-13737	189	37	42	42	NUM
fumecheng-13737	189	38	,	,	PUNCT
fumecheng-13737	189	39	,	,	PUNCT
fumecheng-13737	189	40	.he	.he	PUNCT
fumecheng-13737	189	41	u	u	NOUN
fumecheng-13737	189	42	u	u	X
fumecheng-13737	189	43	u	u	VERB
fumecheng-13737	189	44	u	u	X
fumecheng-13737	189	45	u	u	X
fumecheng-13737	189	46	u	u	X
fumecheng-13737	189	47	u	u	X
fumecheng-13737	189	48	u	u	NOUN
fumecheng-13737	189	49	uu	uu	VERB
fumecheng-13737	189	50	u	u	NOUN
fumecheng-13737	189	51	u	u	X
fumecheng-13737	189	52	u	u	NOUN
fumecheng-13737	189	53	u	u	NOUN
fumecheng-13737	189	54	=	=	NOUN
fumecheng-13737	189	55	=	=	SYM
fumecheng-13737	189	56	=	=	PUNCT
fumecheng-13737	190	1	+	+	PUNCT
fumecheng-13737	190	2	+	+	PUNCT
fumecheng-13737	191	1	+	+	PUNCT
fumecheng-13737	191	2	+	+	NOUN
fumecheng-13737	191	3	=	=	SYM
fumecheng-13737	191	4			PROPN
fumecheng-13737	191	5			PROPN
fumecheng-13737	191	6			PROPN
fumecheng-13737	191	7			PROPN
fumecheng-13737	191	8			PROPN
fumecheng-13737	191	9			X
fumecheng-13737	191	10	(	(	PUNCT
fumecheng-13737	191	11	19	19	NUM
fumecheng-13737	191	12	)	)	PUNCT
fumecheng-13737	191	13	when	when	SCONJ
fumecheng-13737	191	14	ū	ū	X
fumecheng-13737	191	15	=	=	SYM
fumecheng-13737	191	16	ka	ka	PROPN
fumecheng-13737	191	17	,	,	PUNCT
fumecheng-13737	191	18	we	we	PRON
fumecheng-13737	191	19	have	have	VERB
fumecheng-13737	191	20	21	21	NUM
fumecheng-13737	191	21	,	,	PUNCT
fumecheng-13737	191	22	u	u	NOUN
fumecheng-13737	191	23	a	a	DET
fumecheng-13737	191	24	k=	k=	NOUN
fumecheng-13737	191	25	−	−	PROPN
fumecheng-13737	191	26	−	−	PROPN
fumecheng-13737	191	27	and	and	CCONJ
fumecheng-13737	191	28	2.u	2.u	NUM
fumecheng-13737	191	29	ka=	ka=	ADJ
fumecheng-13737	191	30	−	−	PROPN
fumecheng-13737	191	31	substituting	substitute	VERB
fumecheng-13737	191	32	these	these	DET
fumecheng-13737	191	33	values	value	NOUN
fumecheng-13737	191	34	into	into	ADP
fumecheng-13737	191	35	eq	eq	NOUN
fumecheng-13737	191	36	.	.	PUNCT
fumecheng-13737	192	1	(	(	PUNCT
fumecheng-13737	192	2	19	19	NUM
fumecheng-13737	192	3	)	)	PUNCT
fumecheng-13737	192	4	yields	yield	VERB
fumecheng-13737	192	5	the	the	DET
fumecheng-13737	192	6	approximate	approximate	ADJ
fumecheng-13737	192	7	nonlinear	nonlinear	PROPN
fumecheng-13737	192	8	frequency	frequency	NOUN
fumecheng-13737	192	9	as	as	SCONJ
fumecheng-13737	192	10	follows	follow	VERB
fumecheng-13737	192	11	:	:	PUNCT
fumecheng-13737	192	12	2	2	NUM
fumecheng-13737	192	13	2	2	NUM
fumecheng-13737	192	14	4	4	NUM
fumecheng-13737	192	15	4	4	NUM
fumecheng-13737	192	16	2	2	NUM
fumecheng-13737	192	17	3	3	NUM
fumecheng-13737	192	18	4	4	NUM
fumecheng-13737	192	19	2	2	NUM
fumecheng-13737	192	20	2	2	NUM
fumecheng-13737	192	21	2	2	NUM
fumecheng-13737	192	22	1	1	NUM
fumecheng-13737	192	23	1	1	NUM
fumecheng-13737	192	24	,	,	PUNCT
fumecheng-13737	192	25	1	1	NUM
fumecheng-13737	192	26	2	2	NUM
fumecheng-13737	193	1	he	he	PRON
fumecheng-13737	194	1	k	k	PROPN
fumecheng-13737	195	1	a	a	PRON
fumecheng-13737	195	2	k	k	X
fumecheng-13737	195	3	a	a	X
fumecheng-13737	195	4	k	k	PROPN
fumecheng-13737	195	5	a	a	DET
fumecheng-13737	195	6	a	a	DET
fumecheng-13737	195	7			PROPN
fumecheng-13737	195	8			PROPN
fumecheng-13737	195	9			PROPN
fumecheng-13737	195	10			PROPN
fumecheng-13737	195	11			PROPN
fumecheng-13737	195	12			PROPN
fumecheng-13737	195	13	+	+	PROPN
fumecheng-13737	195	14	+	+	PUNCT
fumecheng-13737	195	15	=	=	SYM
fumecheng-13737	195	16	+	+	NUM
fumecheng-13737	195	17	−	−	PROPN
fumecheng-13737	195	18	(	(	PUNCT
fumecheng-13737	195	19	20	20	NUM
fumecheng-13737	195	20	)	)	PUNCT
fumecheng-13737	195	21	and	and	CCONJ
fumecheng-13737	195	22	the	the	DET
fumecheng-13737	195	23	approximate	approximate	ADJ
fumecheng-13737	195	24	solution	solution	NOUN
fumecheng-13737	195	25	as	as	ADP
fumecheng-13737	195	26	:	:	SYM
fumecheng-13737	195	27	2	2	NUM
fumecheng-13737	195	28	2	2	NUM
fumecheng-13737	195	29	4	4	NUM
fumecheng-13737	195	30	4	4	NUM
fumecheng-13737	195	31	2	2	NUM
fumecheng-13737	195	32	3	3	NUM
fumecheng-13737	195	33	4	4	NUM
fumecheng-13737	195	34	2	2	NUM
fumecheng-13737	195	35	2	2	NUM
fumecheng-13737	195	36	2	2	NUM
fumecheng-13737	195	37	1	1	NUM
fumecheng-13737	195	38	1	1	NUM
fumecheng-13737	195	39	(	(	PUNCT
fumecheng-13737	195	40	)	)	PUNCT
fumecheng-13737	195	41	cos	cos	PROPN
fumecheng-13737	195	42	.	.	PROPN
fumecheng-13737	195	43	1	1	NUM
fumecheng-13737	195	44	2	2	NUM
fumecheng-13737	196	1	he	he	PRON
fumecheng-13737	196	2	k	k	PROPN
fumecheng-13737	197	1	a	a	DET
fumecheng-13737	197	2	k	k	PROPN
fumecheng-13737	197	3	a	a	DET
fumecheng-13737	197	4	u	u	NOUN
fumecheng-13737	197	5	t	t	PROPN
fumecheng-13737	197	6	a	a	DET
fumecheng-13737	197	7	t	t	X
fumecheng-13737	197	8	k	k	PROPN
fumecheng-13737	197	9	a	a	DET
fumecheng-13737	197	10	a	a	DET
fumecheng-13737	197	11			PROPN
fumecheng-13737	197	12			PROPN
fumecheng-13737	197	13			PROPN
fumecheng-13737	197	14			PROPN
fumecheng-13737	197	15			PROPN
fumecheng-13737	197	16			NOUN
fumecheng-13737	197	17	+	+	VERB
fumecheng-13737	197	18	+	+	CCONJ
fumecheng-13737	197	19			PROPN
fumecheng-13737	197	20	=	=	PROPN
fumecheng-13737	197	21			PROPN
fumecheng-13737	197	22	+	+	PROPN
fumecheng-13737	197	23	−	−	PROPN
fumecheng-13737	197	24			PROPN
fumecheng-13737	197	25			NOUN
fumecheng-13737	197	26	(	(	PUNCT
fumecheng-13737	197	27	21	21	NUM
fumecheng-13737	197	28	)	)	PUNCT
fumecheng-13737	197	29	using	use	VERB
fumecheng-13737	197	30	the	the	DET
fumecheng-13737	197	31	specific	specific	ADJ
fumecheng-13737	197	32	value	value	NOUN
fumecheng-13737	197	33	3	3	NUM
fumecheng-13737	197	34	2k	2k	NOUN
fumecheng-13737	197	35	=	=	PUNCT
fumecheng-13737	197	36	recommended	recommend	VERB
fumecheng-13737	197	37	in	in	ADP
fumecheng-13737	197	38	[	[	X
fumecheng-13737	197	39	46	46	NUM
fumecheng-13737	197	40	]	]	PUNCT
fumecheng-13737	197	41	,	,	PUNCT
fumecheng-13737	197	42	the	the	DET
fumecheng-13737	197	43	approximate	approximate	ADJ
fumecheng-13737	197	44	nonlinear	nonlinear	ADJ
fumecheng-13737	197	45	frequency	frequency	NOUN
fumecheng-13737	197	46	can	can	AUX
fumecheng-13737	197	47	be	be	AUX
fumecheng-13737	197	48	expressed	express	VERB
fumecheng-13737	197	49	as	as	SCONJ
fumecheng-13737	197	50	follows	follow	VERB
fumecheng-13737	197	51	:	:	PUNCT
fumecheng-13737	197	52	2	2	NUM
fumecheng-13737	197	53	4	4	NUM
fumecheng-13737	197	54	2	2	NUM
fumecheng-13737	197	55	3	3	NUM
fumecheng-13737	197	56	4	4	NUM
fumecheng-13737	197	57	2	2	NUM
fumecheng-13737	197	58	1	1	NUM
fumecheng-13737	197	59	16	16	NUM
fumecheng-13737	197	60	12	12	NUM
fumecheng-13737	197	61	9	9	NUM
fumecheng-13737	197	62	.	.	PUNCT
fumecheng-13737	198	1	16	16	NUM
fumecheng-13737	198	2	8	8	NUM
fumecheng-13737	198	3	he	he	PRON
fumecheng-13737	198	4	a	a	DET
fumecheng-13737	198	5	a	a	DET
fumecheng-13737	198	6	a	a	DET
fumecheng-13737	198	7			PROPN
fumecheng-13737	198	8			PROPN
fumecheng-13737	198	9			PROPN
fumecheng-13737	198	10			PROPN
fumecheng-13737	198	11			PROPN
fumecheng-13737	198	12	+	+	PROPN
fumecheng-13737	198	13	+	+	PUNCT
fumecheng-13737	198	14	=	=	SYM
fumecheng-13737	198	15	+	+	CCONJ
fumecheng-13737	198	16	(	(	PUNCT
fumecheng-13737	198	17	22	22	NUM
fumecheng-13737	198	18	)	)	PUNCT
fumecheng-13737	198	19	to	to	PART
fumecheng-13737	198	20	obtain	obtain	VERB
fumecheng-13737	198	21	a	a	DET
fumecheng-13737	198	22	more	more	ADV
fumecheng-13737	198	23	accurate	accurate	ADJ
fumecheng-13737	198	24	frequency	frequency	NOUN
fumecheng-13737	198	25	,	,	PUNCT
fumecheng-13737	198	26	eq	eq	NOUN
fumecheng-13737	198	27	.	.	PUNCT
fumecheng-13737	199	1	(	(	PUNCT
fumecheng-13737	199	2	8)	8)	NUM
fumecheng-13737	199	3	is	be	AUX
fumecheng-13737	199	4	reformulated	reformulate	VERB
fumecheng-13737	199	5	using	use	VERB
fumecheng-13737	199	6	the	the	DET
fumecheng-13737	199	7	proposed	propose	VERB
fumecheng-13737	199	8	alpf	alpf	PROPN
fumecheng-13737	199	9	approach	approach	PROPN
fumecheng-13737	199	10	as	as	SCONJ
fumecheng-13737	199	11	follows	follow	VERB
fumecheng-13737	199	12	:	:	PUNCT
fumecheng-13737	199	13	794	794	NUM
fumecheng-13737	199	14	c	c	X
fumecheng-13737	199	15	-	-	PUNCT
fumecheng-13737	199	16	h.	h.	NOUN
fumecheng-13737	199	17	he	he	PROPN
fumecheng-13737	199	18	,	,	PUNCT
fumecheng-13737	199	19	m.	m.	NOUN
fumecheng-13737	199	20	mohammadian	mohammadian	NOUN
fumecheng-13737	199	21	2	2	NUM
fumecheng-13737	199	22	2	2	NUM
fumecheng-13737	199	23	4	4	NUM
fumecheng-13737	199	24	42	42	NUM
fumecheng-13737	199	25	2	2	NUM
fumecheng-13737	199	26	3	3	NUM
fumecheng-13737	199	27	4	4	NUM
fumecheng-13737	199	28	2	2	NUM
fumecheng-13737	199	29	2	2	NUM
fumecheng-13737	199	30	2	2	NUM
fumecheng-13737	199	31	2	2	NUM
fumecheng-13737	199	32	1	1	NUM
fumecheng-13737	199	33	1	1	NUM
fumecheng-13737	199	34	22	22	NUM
fumecheng-13737	199	35	2	2	NUM
fumecheng-13737	199	36	4	4	NUM
fumecheng-13737	199	37	4	4	NUM
fumecheng-13737	199	38	2	2	NUM
fumecheng-13737	199	39	2	2	NUM
fumecheng-13737	199	40	3	3	NUM
fumecheng-13737	199	41	52	52	NUM
fumecheng-13737	199	42	3	3	NUM
fumecheng-13737	199	43	4	4	NUM
fumecheng-13737	199	44	1	1	NUM
fumecheng-13737	199	45	2	2	NUM
fumecheng-13737	199	46	3	3	NUM
fumecheng-13737	199	47	42	42	NUM
fumecheng-13737	199	48	2	2	NUM
fumecheng-13737	199	49	2	2	NUM
fumecheng-13737	199	50	2	2	NUM
fumecheng-13737	199	51	1	1	NUM
fumecheng-13737	199	52	1	1	NUM
fumecheng-13737	199	53	1	1	NUM
fumecheng-13737	199	54	2	2	NUM
fumecheng-13737	199	55	.	.	PUNCT
fumecheng-13737	199	56	1	1	NUM
fumecheng-13737	199	57	2	2	NUM
fumecheng-13737	199	58	k	k	NOUN
fumecheng-13737	199	59	a	a	DET
fumecheng-13737	199	60	k	k	PROPN
fumecheng-13737	199	61	ad	ad	NOUN
fumecheng-13737	199	62	u	u	X
fumecheng-13737	199	63	u	u	NOUN
fumecheng-13737	199	64	dt	dt	X
fumecheng-13737	199	65	k	k	PROPN
fumecheng-13737	199	66	a	a	PRON
fumecheng-13737	199	67	a	a	X
fumecheng-13737	199	68	k	k	X
fumecheng-13737	199	69	a	a	X
fumecheng-13737	199	70	k	k	PROPN
fumecheng-13737	199	71	a	a	X
fumecheng-13737	199	72	d	d	X
fumecheng-13737	199	73	u	u	X
fumecheng-13737	199	74	du	du	PROPN
fumecheng-13737	199	75	u	u	PROPN
fumecheng-13737	199	76	u	u	NOUN
fumecheng-13737	199	77	u	u	X
fumecheng-13737	199	78	u	u	X
fumecheng-13737	199	79	u	u	X
fumecheng-13737	199	80	u	u	PROPN
fumecheng-13737	199	81	dtk	dtk	PROPN
fumecheng-13737	199	82	a	a	DET
fumecheng-13737	199	83	a	a	DET
fumecheng-13737	199	84	dt	dt	X
fumecheng-13737	199	85			PROPN
fumecheng-13737	199	86			PROPN
fumecheng-13737	199	87			PROPN
fumecheng-13737	199	88			PROPN
fumecheng-13737	199	89			PROPN
fumecheng-13737	199	90			PROPN
fumecheng-13737	199	91			PROPN
fumecheng-13737	199	92			PROPN
fumecheng-13737	199	93			PROPN
fumecheng-13737	199	94			PROPN
fumecheng-13737	199	95			PROPN
fumecheng-13737	199	96			PROPN
fumecheng-13737	199	97			PROPN
fumecheng-13737	199	98			PROPN
fumecheng-13737	199	99			NOUN
fumecheng-13737	199	100	+	+	VERB
fumecheng-13737	199	101	+	+	CCONJ
fumecheng-13737	200	1	+	+	CCONJ
fumecheng-13737	200	2	=	=	PROPN
fumecheng-13737	200	3			ADJ
fumecheng-13737	200	4			PROPN
fumecheng-13737	201	1	+	+	CCONJ
fumecheng-13737	201	2	−	−	NUM
fumecheng-13737	201	3			NOUN
fumecheng-13737	201	4			VERB
fumecheng-13737	201	5			PROPN
fumecheng-13737	201	6	+	+	VERB
fumecheng-13737	201	7	+	+	PROPN
fumecheng-13737	201	8			NOUN
fumecheng-13737	201	9			NOUN
fumecheng-13737	201	10	−	−	PROPN
fumecheng-13737	202	1	+	+	CCONJ
fumecheng-13737	202	2	−	−	PROPN
fumecheng-13737	202	3	−	−	PROPN
fumecheng-13737	203	1	−	−	PROPN
fumecheng-13737	203	2			NOUN
fumecheng-13737	204	1			PROPN
fumecheng-13737	204	2			PROPN
fumecheng-13737	204	3			VERB
fumecheng-13737	204	4	+	+	PROPN
fumecheng-13737	204	5	−	−	PROPN
fumecheng-13737	204	6			PROPN
fumecheng-13737	204	7			NOUN
fumecheng-13737	204	8			NOUN
fumecheng-13737	204	9			PROPN
fumecheng-13737	204	10			NOUN
fumecheng-13737	204	11	(	(	PUNCT
fumecheng-13737	204	12	23	23	NUM
fumecheng-13737	204	13	)	)	PUNCT
fumecheng-13737	204	14	if	if	SCONJ
fumecheng-13737	204	15	the	the	DET
fumecheng-13737	204	16	frequency	frequency	NOUN
fumecheng-13737	204	17	obtained	obtain	VERB
fumecheng-13737	204	18	from	from	ADP
fumecheng-13737	204	19	eq	eq	PROPN
fumecheng-13737	204	20	.	.	PUNCT
fumecheng-13737	205	1	(	(	PUNCT
fumecheng-13737	205	2	18	18	NUM
fumecheng-13737	205	3	)	)	PUNCT
fumecheng-13737	205	4	is	be	AUX
fumecheng-13737	205	5	the	the	DET
fumecheng-13737	205	6	exact	exact	ADJ
fumecheng-13737	205	7	frequency	frequency	NOUN
fumecheng-13737	205	8	,	,	PUNCT
fumecheng-13737	205	9	then	then	ADV
fumecheng-13737	205	10	the	the	DET
fumecheng-13737	205	11	right	right	ADJ
fumecheng-13737	205	12	-	-	PUNCT
fumecheng-13737	205	13	hand	hand	NOUN
fumecheng-13737	205	14	side	side	NOUN
fumecheng-13737	205	15	of	of	ADP
fumecheng-13737	205	16	eq	eq	PROPN
fumecheng-13737	205	17	.	.	PUNCT
fumecheng-13737	206	1	(	(	PUNCT
fumecheng-13737	206	2	23	23	NUM
fumecheng-13737	206	3	)	)	PUNCT
fumecheng-13737	206	4	becomes	become	VERB
fumecheng-13737	206	5	zero	zero	NUM
fumecheng-13737	206	6	.	.	PUNCT
fumecheng-13737	207	1	based	base	VERB
fumecheng-13737	207	2	on	on	ADP
fumecheng-13737	207	3	eq	eq	PROPN
fumecheng-13737	207	4	.	.	PUNCT
fumecheng-13737	208	1	(	(	PUNCT
fumecheng-13737	208	2	17	17	NUM
fumecheng-13737	208	3	)	)	PUNCT
fumecheng-13737	208	4	,	,	PUNCT
fumecheng-13737	208	5	we	we	PRON
fumecheng-13737	208	6	obtain	obtain	VERB
fumecheng-13737	208	7	:	:	PUNCT
fumecheng-13737	208	8	24	24	NUM
fumecheng-13737	208	9	2	2	NUM
fumecheng-13737	208	10	2	2	NUM
fumecheng-13737	208	11	4	4	NUM
fumecheng-13737	208	12	4	4	NUM
fumecheng-13737	208	13	2	2	NUM
fumecheng-13737	208	14	2	2	NUM
fumecheng-13737	208	15	3	3	NUM
fumecheng-13737	208	16	52	52	NUM
fumecheng-13737	208	17	3	3	NUM
fumecheng-13737	208	18	4	4	NUM
fumecheng-13737	208	19	1	1	NUM
fumecheng-13737	208	20	2	2	NUM
fumecheng-13737	208	21	3	3	NUM
fumecheng-13737	208	22	42	42	NUM
fumecheng-13737	208	23	2	2	NUM
fumecheng-13737	208	24	2	2	NUM
fumecheng-13737	208	25	2	2	NUM
fumecheng-13737	208	26	1	1	NUM
fumecheng-13737	208	27	10	10	NUM
fumecheng-13737	208	28	cos	cos	PROPN
fumecheng-13737	208	29	(	(	PUNCT
fumecheng-13737	208	30	)	)	PUNCT
fumecheng-13737	208	31	0	0	NUM
fumecheng-13737	208	32	.	.	NOUN
fumecheng-13737	208	33	1	1	NUM
fumecheng-13737	208	34	2	2	NUM
fumecheng-13737	208	35	t	t	NOUN
fumecheng-13737	208	36	k	k	NOUN
fumecheng-13737	209	1	a	a	DET
fumecheng-13737	209	2	k	k	PROPN
fumecheng-13737	209	3	a	a	X
fumecheng-13737	209	4	d	d	X
fumecheng-13737	209	5	u	u	X
fumecheng-13737	209	6	du	du	PROPN
fumecheng-13737	209	7	u	u	PROPN
fumecheng-13737	209	8	u	u	NOUN
fumecheng-13737	209	9	u	u	X
fumecheng-13737	209	10	u	u	X
fumecheng-13737	209	11	u	u	X
fumecheng-13737	209	12	u	u	NOUN
fumecheng-13737	209	13	t	t	PROPN
fumecheng-13737	209	14	dt	dt	X
fumecheng-13737	209	15	dtk	dtk	PROPN
fumecheng-13737	209	16	a	a	DET
fumecheng-13737	209	17	a	a	DET
fumecheng-13737	209	18	dt	dt	X
fumecheng-13737	209	19			PROPN
fumecheng-13737	209	20			PROPN
fumecheng-13737	209	21			PROPN
fumecheng-13737	209	22			PROPN
fumecheng-13737	209	23			PROPN
fumecheng-13737	209	24			PROPN
fumecheng-13737	209	25			PROPN
fumecheng-13737	209	26			PROPN
fumecheng-13737	209	27			PROPN
fumecheng-13737	209	28			PROPN
fumecheng-13737	209	29			NOUN
fumecheng-13737	209	30			PROPN
fumecheng-13737	209	31	+	+	VERB
fumecheng-13737	209	32	+	+	PROPN
fumecheng-13737	210	1			NOUN
fumecheng-13737	211	1			NOUN
fumecheng-13737	211	2			PROPN
fumecheng-13737	211	3	−	−	PUNCT
fumecheng-13737	212	1	+	+	CCONJ
fumecheng-13737	212	2	−	−	ADP
fumecheng-13737	212	3	−	−	NOUN
fumecheng-13737	213	1	−	−	PUNCT
fumecheng-13737	213	2	=	=	SYM
fumecheng-13737	213	3			PROPN
fumecheng-13737	213	4			NOUN
fumecheng-13737	213	5			X
fumecheng-13737	213	6			X
fumecheng-13737	213	7	+	+	PROPN
fumecheng-13737	213	8	−	−	PROPN
fumecheng-13737	213	9			PROPN
fumecheng-13737	213	10			NOUN
fumecheng-13737	213	11			NOUN
fumecheng-13737	213	12			NOUN
fumecheng-13737	213	13			PUNCT
fumecheng-13737	213	14	(	(	PUNCT
fumecheng-13737	213	15	24	24	NUM
fumecheng-13737	213	16	)	)	PUNCT
fumecheng-13737	213	17	substituting	substitute	VERB
fumecheng-13737	213	18	eq	eq	PROPN
fumecheng-13737	213	19	.	.	PUNCT
fumecheng-13737	214	1	(	(	PUNCT
fumecheng-13737	214	2	21	21	NUM
fumecheng-13737	214	3	)	)	PUNCT
fumecheng-13737	214	4	into	into	ADP
fumecheng-13737	214	5	eq	eq	NOUN
fumecheng-13737	214	6	.	.	PUNCT
fumecheng-13737	215	1	(	(	PUNCT
fumecheng-13737	215	2	24	24	NUM
fumecheng-13737	215	3	)	)	PUNCT
fumecheng-13737	215	4	and	and	CCONJ
fumecheng-13737	215	5	solving	solve	VERB
fumecheng-13737	215	6	the	the	DET
fumecheng-13737	215	7	resulting	result	VERB
fumecheng-13737	215	8	equation	equation	NOUN
fumecheng-13737	215	9	yields	yield	VERB
fumecheng-13737	215	10	the	the	DET
fumecheng-13737	215	11	following	follow	VERB
fumecheng-13737	215	12	expression	expression	NOUN
fumecheng-13737	215	13	for	for	ADP
fumecheng-13737	215	14	k	k	NOUN
fumecheng-13737	215	15	:	:	SYM
fumecheng-13737	215	16	2	2	NUM
fumecheng-13737	215	17	2	2	NUM
fumecheng-13737	215	18	2	2	NUM
fumecheng-13737	215	19	1	1	NUM
fumecheng-13737	215	20	3	3	NUM
fumecheng-13737	215	21	1	1	NUM
fumecheng-13737	215	22	4	4	NUM
fumecheng-13737	215	23	,	,	PUNCT
fumecheng-13737	215	24	2	2	NUM
fumecheng-13737	215	25	k	k	NOUN
fumecheng-13737	215	26	−	−	PROPN
fumecheng-13737	216	1	+	+	CCONJ
fumecheng-13737	216	2			VERB
fumecheng-13737	216	3	−	−	PROPN
fumecheng-13737	216	4			NOUN
fumecheng-13737	216	5			VERB
fumecheng-13737	216	6	=	=	SYM
fumecheng-13737	216	7			VERB
fumecheng-13737	216	8	(	(	PUNCT
fumecheng-13737	216	9	25	25	NUM
fumecheng-13737	216	10	)	)	PUNCT
fumecheng-13737	216	11	where	where	SCONJ
fumecheng-13737	216	12	2	2	NUM
fumecheng-13737	216	13	4	4	NUM
fumecheng-13737	216	14	4	4	NUM
fumecheng-13737	216	15	2	2	NUM
fumecheng-13737	216	16	1	1	NUM
fumecheng-13737	216	17	4	4	NUM
fumecheng-13737	216	18	4	4	NUM
fumecheng-13737	216	19	1	1	NUM
fumecheng-13737	216	20	2	2	NUM
fumecheng-13737	216	21	4	4	NUM
fumecheng-13737	216	22	1	1	NUM
fumecheng-13737	216	23	3	3	NUM
fumecheng-13737	216	24	1	1	NUM
fumecheng-13737	216	25	2	2	NUM
fumecheng-13737	216	26	3	3	NUM
fumecheng-13737	216	27	1	1	NUM
fumecheng-13737	216	28	4	4	NUM
fumecheng-13737	216	29	2	2	NUM
fumecheng-13737	216	30	2	2	NUM
fumecheng-13737	216	31	3	3	NUM
fumecheng-13737	216	32	4	4	NUM
fumecheng-13737	216	33	1	1	NUM
fumecheng-13737	216	34	3	3	NUM
fumecheng-13737	216	35	1	1	NUM
fumecheng-13737	216	36	2	2	NUM
fumecheng-13737	216	37	3	3	NUM
fumecheng-13737	216	38	1	1	NUM
fumecheng-13737	216	39	4	4	NUM
fumecheng-13737	216	40	8	8	NUM
fumecheng-13737	216	41	4	4	NUM
fumecheng-13737	216	42	,	,	PUNCT
fumecheng-13737	216	43	10	10	NUM
fumecheng-13737	216	44	8	8	NUM
fumecheng-13737	216	45	16	16	NUM
fumecheng-13737	216	46	8	8	NUM
fumecheng-13737	216	47	,	,	PUNCT
fumecheng-13737	216	48	5	5	NUM
fumecheng-13737	216	49	6	6	NUM
fumecheng-13737	216	50	12	12	NUM
fumecheng-13737	216	51	6	6	NUM
fumecheng-13737	216	52	5	5	NUM
fumecheng-13737	216	53	.	.	PUNCT
fumecheng-13737	217	1	a	a	DET
fumecheng-13737	217	2	a	a	DET
fumecheng-13737	217	3	a	a	DET
fumecheng-13737	217	4	a	a	DET
fumecheng-13737	217	5	a	a	DET
fumecheng-13737	217	6	a	a	DET
fumecheng-13737	217	7	a	a	DET
fumecheng-13737	217	8			PROPN
fumecheng-13737	217	9			PROPN
fumecheng-13737	217	10			PROPN
fumecheng-13737	217	11			PROPN
fumecheng-13737	217	12			PROPN
fumecheng-13737	217	13			PROPN
fumecheng-13737	217	14			PROPN
fumecheng-13737	217	15			PROPN
fumecheng-13737	217	16			PROPN
fumecheng-13737	217	17			PROPN
fumecheng-13737	217	18			PROPN
fumecheng-13737	217	19			PROPN
fumecheng-13737	217	20			PROPN
fumecheng-13737	217	21			PROPN
fumecheng-13737	217	22			PROPN
fumecheng-13737	217	23			PROPN
fumecheng-13737	217	24			PROPN
fumecheng-13737	217	25			PROPN
fumecheng-13737	217	26			VERB
fumecheng-13737	217	27	=	=	SYM
fumecheng-13737	218	1	+	+	CCONJ
fumecheng-13737	218	2			VERB
fumecheng-13737	218	3	=	=	SYM
fumecheng-13737	218	4	−	−	PROPN
fumecheng-13737	218	5	+	+	CCONJ
fumecheng-13737	218	6	−	−	PROPN
fumecheng-13737	219	1	−	−	PROPN
fumecheng-13737	219	2			NOUN
fumecheng-13737	219	3	=	=	SYM
fumecheng-13737	219	4	−	−	PROPN
fumecheng-13737	220	1	+	+	CCONJ
fumecheng-13737	220	2	+	+	NUM
fumecheng-13737	220	3	−	−	PROPN
fumecheng-13737	220	4	(	(	PUNCT
fumecheng-13737	220	5	26	26	NUM
fumecheng-13737	220	6	)	)	PUNCT
fumecheng-13737	220	7	eq	eq	NOUN
fumecheng-13737	220	8	.	.	PUNCT
fumecheng-13737	221	1	(	(	PUNCT
fumecheng-13737	221	2	25	25	NUM
fumecheng-13737	221	3	)	)	PUNCT
fumecheng-13737	221	4	provides	provide	VERB
fumecheng-13737	221	5	an	an	DET
fumecheng-13737	221	6	appropriate	appropriate	ADJ
fumecheng-13737	221	7	location	location	NOUN
fumecheng-13737	221	8	point	point	NOUN
fumecheng-13737	221	9	that	that	PRON
fumecheng-13737	221	10	depends	depend	VERB
fumecheng-13737	221	11	on	on	ADP
fumecheng-13737	221	12	both	both	CCONJ
fumecheng-13737	221	13	the	the	DET
fumecheng-13737	221	14	amplitude	amplitude	NOUN
fumecheng-13737	221	15	and	and	CCONJ
fumecheng-13737	221	16	the	the	DET
fumecheng-13737	221	17	system	system	NOUN
fumecheng-13737	221	18	parameters	parameter	NOUN
fumecheng-13737	221	19	.	.	PUNCT
fumecheng-13737	222	1	by	by	ADP
fumecheng-13737	222	2	substituting	substitute	VERB
fumecheng-13737	222	3	the	the	DET
fumecheng-13737	222	4	value	value	NOUN
fumecheng-13737	222	5	of	of	ADP
fumecheng-13737	222	6	k	k	NOUN
fumecheng-13737	222	7	,	,	PUNCT
fumecheng-13737	222	8	calculated	calculate	VERB
fumecheng-13737	222	9	from	from	ADP
fumecheng-13737	222	10	eq	eq	PROPN
fumecheng-13737	222	11	.	.	PUNCT
fumecheng-13737	223	1	(	(	PUNCT
fumecheng-13737	223	2	25	25	NUM
fumecheng-13737	223	3	)	)	PUNCT
fumecheng-13737	223	4	,	,	PUNCT
fumecheng-13737	223	5	into	into	ADP
fumecheng-13737	223	6	eq	eq	NOUN
fumecheng-13737	223	7	.	.	PUNCT
fumecheng-13737	224	1	(	(	PUNCT
fumecheng-13737	224	2	20	20	NUM
fumecheng-13737	224	3	)	)	PUNCT
fumecheng-13737	224	4	,	,	PUNCT
fumecheng-13737	224	5	the	the	DET
fumecheng-13737	224	6	approximate	approximate	ADJ
fumecheng-13737	224	7	frequency	frequency	NOUN
fumecheng-13737	224	8	denoted	denote	VERB
fumecheng-13737	224	9	as	as	ADP
fumecheng-13737	224	10	ωalpf	ωalpf	ADJ
fumecheng-13737	224	11	is	be	AUX
fumecheng-13737	224	12	determined	determine	VERB
fumecheng-13737	224	13	using	use	VERB
fumecheng-13737	224	14	the	the	DET
fumecheng-13737	224	15	proposed	propose	VERB
fumecheng-13737	224	16	alpf	alpf	NOUN
fumecheng-13737	224	17	method	method	PROPN
fumecheng-13737	224	18	.	.	PUNCT
fumecheng-13737	225	1	3.2	3.2	NUM
fumecheng-13737	225	2	.	.	PUNCT
fumecheng-13737	226	1	square	square	ADJ
fumecheng-13737	226	2	error	error	NOUN
fumecheng-13737	226	3	minimizing	minimizing	NOUN
fumecheng-13737	226	4	-	-	PUNCT
fumecheng-13737	226	5	based	base	VERB
fumecheng-13737	226	6	frequency	frequency	NOUN
fumecheng-13737	226	7	formulation	formulation	NOUN
fumecheng-13737	226	8	(	(	PUNCT
fumecheng-13737	226	9	semf	semf	NOUN
fumecheng-13737	226	10	)	)	PUNCT
fumecheng-13737	226	11	the	the	DET
fumecheng-13737	226	12	square	square	ADJ
fumecheng-13737	226	13	error	error	NOUN
fumecheng-13737	226	14	minimizing	minimizing	NOUN
fumecheng-13737	226	15	-	-	PUNCT
fumecheng-13737	226	16	based	base	VERB
fumecheng-13737	226	17	frequency	frequency	NOUN
fumecheng-13737	226	18	formulation	formulation	NOUN
fumecheng-13737	226	19	(	(	PUNCT
fumecheng-13737	226	20	semf	semf	NOUN
fumecheng-13737	226	21	)	)	PUNCT
fumecheng-13737	226	22	,	,	PUNCT
fumecheng-13737	226	23	proposed	propose	VERB
fumecheng-13737	226	24	in	in	ADP
fumecheng-13737	226	25	[	[	X
fumecheng-13737	226	26	47	47	NUM
fumecheng-13737	226	27	]	]	PUNCT
fumecheng-13737	226	28	,	,	PUNCT
fumecheng-13737	226	29	is	be	AUX
fumecheng-13737	226	30	a	a	DET
fumecheng-13737	226	31	mathematical	mathematical	ADJ
fumecheng-13737	226	32	refinement	refinement	NOUN
fumecheng-13737	226	33	of	of	ADP
fumecheng-13737	226	34	he	he	PRON
fumecheng-13737	226	35	's	's	PART
fumecheng-13737	226	36	frequency	frequency	NOUN
fumecheng-13737	226	37	formulation	formulation	NOUN
fumecheng-13737	226	38	.	.	PUNCT
fumecheng-13737	227	1	it	it	PRON
fumecheng-13737	227	2	provides	provide	VERB
fumecheng-13737	227	3	a	a	DET
fumecheng-13737	227	4	modified	modified	ADJ
fumecheng-13737	227	5	approach	approach	NOUN
fumecheng-13737	227	6	that	that	PRON
fumecheng-13737	227	7	enhances	enhance	VERB
fumecheng-13737	227	8	the	the	DET
fumecheng-13737	227	9	accuracy	accuracy	NOUN
fumecheng-13737	227	10	of	of	ADP
fumecheng-13737	227	11	the	the	DET
fumecheng-13737	227	12	approximate	approximate	ADJ
fumecheng-13737	227	13	frequency	frequency	NOUN
fumecheng-13737	227	14	by	by	ADP
fumecheng-13737	227	15	minimizing	minimize	VERB
fumecheng-13737	227	16	a	a	DET
fumecheng-13737	227	17	square	square	ADJ
fumecheng-13737	227	18	error	error	NOUN
fumecheng-13737	227	19	function	function	NOUN
fumecheng-13737	227	20	.	.	PUNCT
fumecheng-13737	228	1	the	the	DET
fumecheng-13737	228	2	error	error	NOUN
fumecheng-13737	228	3	function	function	NOUN
fumecheng-13737	228	4	e(ω2	e(ω2	X
fumecheng-13737	228	5	)	)	PUNCT
fumecheng-13737	228	6	,	,	PUNCT
fumecheng-13737	228	7	corresponding	correspond	VERB
fumecheng-13737	228	8	to	to	ADP
fumecheng-13737	228	9	eq	eq	PROPN
fumecheng-13737	228	10	.	.	PUNCT
fumecheng-13737	229	1	(	(	PUNCT
fumecheng-13737	229	2	13	13	NUM
fumecheng-13737	229	3	)	)	PUNCT
fumecheng-13737	229	4	,	,	PUNCT
fumecheng-13737	229	5	is	be	AUX
fumecheng-13737	229	6	defined	define	VERB
fumecheng-13737	229	7	as	as	SCONJ
fumecheng-13737	229	8	follows	follow	VERB
fumecheng-13737	229	9	:	:	PUNCT
fumecheng-13737	229	10	2	2	NUM
fumecheng-13737	229	11	2	2	NUM
fumecheng-13737	229	12	(	(	PUNCT
fumecheng-13737	229	13	)	)	PUNCT
fumecheng-13737	229	14	(	(	PUNCT
fumecheng-13737	229	15	)	)	PUNCT
fumecheng-13737	229	16	(	(	PUNCT
fumecheng-13737	229	17	)	)	PUNCT
fumecheng-13737	229	18	(	(	PUNCT
fumecheng-13737	229	19	)	)	PUNCT
fumecheng-13737	229	20	.e	.e	PUNCT
fumecheng-13737	230	1	f	f	X
fumecheng-13737	230	2	u	u	PROPN
fumecheng-13737	230	3	a	a	DET
fumecheng-13737	230	4	u	u	NOUN
fumecheng-13737	230	5	t	t	DET
fumecheng-13737	230	6	=	=	PROPN
fumecheng-13737	230	7	−	−	PROPN
fumecheng-13737	230	8	(	(	PUNCT
fumecheng-13737	230	9	27	27	NUM
fumecheng-13737	230	10	)	)	PUNCT
fumecheng-13737	230	11	we	we	PRON
fumecheng-13737	230	12	define	define	VERB
fumecheng-13737	230	13	the	the	DET
fumecheng-13737	230	14	mean	mean	ADJ
fumecheng-13737	230	15	square	square	ADJ
fumecheng-13737	230	16	error	error	NOUN
fumecheng-13737	230	17	as	as	SCONJ
fumecheng-13737	230	18	follows	follow	VERB
fumecheng-13737	230	19	:	:	PUNCT
fumecheng-13737	230	20	(	(	PUNCT
fumecheng-13737	230	21	)	)	PUNCT
fumecheng-13737	230	22	/4	/4	NOUN
fumecheng-13737	230	23	2	2	NUM
fumecheng-13737	230	24	2	2	NUM
fumecheng-13737	230	25	2	2	NUM
fumecheng-13737	230	26	2	2	NUM
fumecheng-13737	230	27	0	0	NUM
fumecheng-13737	230	28	(	(	PUNCT
fumecheng-13737	230	29	)	)	PUNCT
fumecheng-13737	230	30	(	(	PUNCT
fumecheng-13737	230	31	)	)	PUNCT
fumecheng-13737	230	32	(	(	PUNCT
fumecheng-13737	230	33	)	)	PUNCT
fumecheng-13737	230	34	(	(	PUNCT
fumecheng-13737	230	35	)	)	PUNCT
fumecheng-13737	230	36	.	.	PUNCT
fumecheng-13737	231	1	t	t	PROPN
fumecheng-13737	231	2	e	e	X
fumecheng-13737	231	3	f	f	PROPN
fumecheng-13737	231	4	u	u	PROPN
fumecheng-13737	231	5	a	a	DET
fumecheng-13737	231	6	u	u	NOUN
fumecheng-13737	231	7	t	t	PROPN
fumecheng-13737	231	8	dt	dt	NOUN
fumecheng-13737	231	9	=	=	PROPN
fumecheng-13737	231	10	−	−	X
fumecheng-13737	231	11	(	(	PUNCT
fumecheng-13737	231	12	28	28	NUM
fumecheng-13737	231	13	)	)	PUNCT
fumecheng-13737	231	14	to	to	PART
fumecheng-13737	231	15	minimize	minimize	VERB
fumecheng-13737	231	16	the	the	DET
fumecheng-13737	231	17	error	error	NOUN
fumecheng-13737	231	18	,	,	PUNCT
fumecheng-13737	231	19	it	it	PRON
fumecheng-13737	231	20	is	be	AUX
fumecheng-13737	231	21	required	require	VERB
fumecheng-13737	231	22	that	that	SCONJ
fumecheng-13737	231	23	(	(	PUNCT
fumecheng-13737	231	24	)	)	PUNCT
fumecheng-13737	231	25	/42	/42	PUNCT
fumecheng-13737	231	26	2	2	NUM
fumecheng-13737	231	27	2	2	NUM
fumecheng-13737	231	28	2	2	NUM
fumecheng-13737	231	29	4	4	NUM
fumecheng-13737	231	30	2	2	NUM
fumecheng-13737	231	31	2	2	NUM
fumecheng-13737	231	32	2	2	NUM
fumecheng-13737	231	33	0	0	NUM
fumecheng-13737	231	34	(	(	PUNCT
fumecheng-13737	231	35	)	)	PUNCT
fumecheng-13737	231	36	(	(	PUNCT
fumecheng-13737	231	37	)	)	PUNCT
fumecheng-13737	231	38	2	2	NUM
fumecheng-13737	231	39	(	(	PUNCT
fumecheng-13737	231	40	)	)	PUNCT
fumecheng-13737	231	41	(	(	PUNCT
fumecheng-13737	231	42	)	)	PUNCT
fumecheng-13737	231	43	(	(	PUNCT
fumecheng-13737	231	44	)	)	PUNCT
fumecheng-13737	231	45	(	(	PUNCT
fumecheng-13737	231	46	)	)	PUNCT
fumecheng-13737	231	47	(	(	PUNCT
fumecheng-13737	231	48	)	)	PUNCT
fumecheng-13737	231	49	0	0	X
fumecheng-13737	231	50	.	.	PUNCT
fumecheng-13737	232	1	(	(	PUNCT
fumecheng-13737	232	2	)	)	PUNCT
fumecheng-13737	232	3	(	(	PUNCT
fumecheng-13737	232	4	)	)	PUNCT
fumecheng-13737	232	5	t	t	PROPN
fumecheng-13737	232	6	de	de	PROPN
fumecheng-13737	232	7	d	d	X
fumecheng-13737	232	8	f	f	PROPN
fumecheng-13737	232	9	u	u	PROPN
fumecheng-13737	232	10	a	a	DET
fumecheng-13737	232	11	u	u	NOUN
fumecheng-13737	232	12	t	t	NOUN
fumecheng-13737	232	13	f	f	PROPN
fumecheng-13737	232	14	u	u	PROPN
fumecheng-13737	232	15	a	a	DET
fumecheng-13737	232	16	u	u	NOUN
fumecheng-13737	232	17	t	t	NOUN
fumecheng-13737	232	18	dt	dt	X
fumecheng-13737	233	1	d	d	X
fumecheng-13737	233	2	d	d	X
fumecheng-13737	233	3			X
fumecheng-13737	233	4			X
fumecheng-13737	233	5			X
fumecheng-13737	233	6			X
fumecheng-13737	233	7			X
fumecheng-13737	233	8	=	=	PUNCT
fumecheng-13737	233	9	−	−	PROPN
fumecheng-13737	234	1	+	+	CCONJ
fumecheng-13737	234	2	=	=	NOUN
fumecheng-13737	234	3			X
fumecheng-13737	234	4	(	(	PUNCT
fumecheng-13737	234	5	29	29	NUM
fumecheng-13737	234	6	)	)	PUNCT
fumecheng-13737	234	7	a	a	DET
fumecheng-13737	234	8	fast	fast	ADJ
fumecheng-13737	234	9	insight	insight	NOUN
fumecheng-13737	234	10	into	into	ADP
fumecheng-13737	234	11	nonlinear	nonlinear	ADJ
fumecheng-13737	234	12	frequency	frequency	NOUN
fumecheng-13737	234	13	estimation	estimation	NOUN
fumecheng-13737	234	14	of	of	ADP
fumecheng-13737	234	15	stringer	stringer	NOUN
fumecheng-13737	234	16	-	-	PUNCT
fumecheng-13737	234	17	stiffened	stiffen	VERB
fumecheng-13737	234	18	shells	shell	NOUN
fumecheng-13737	234	19	with	with	ADP
fumecheng-13737	234	20	high	high	ADJ
fumecheng-13737	234	21	accuracy	accuracy	NOUN
fumecheng-13737	234	22	795	795	NUM
fumecheng-13737	234	23	by	by	ADP
fumecheng-13737	234	24	solving	solve	VERB
fumecheng-13737	234	25	eq	eq	ADJ
fumecheng-13737	234	26	.	.	PUNCT
fumecheng-13737	235	1	(	(	PUNCT
fumecheng-13737	235	2	29	29	NUM
fumecheng-13737	235	3	)	)	PUNCT
fumecheng-13737	235	4	,	,	PUNCT
fumecheng-13737	235	5	an	an	DET
fumecheng-13737	235	6	approximate	approximate	ADJ
fumecheng-13737	235	7	expression	expression	NOUN
fumecheng-13737	235	8	for	for	ADP
fumecheng-13737	235	9	the	the	DET
fumecheng-13737	235	10	nonlinear	nonlinear	ADJ
fumecheng-13737	235	11	oscillator	oscillator	NOUN
fumecheng-13737	235	12	frequency	frequency	NOUN
fumecheng-13737	235	13	given	give	VERB
fumecheng-13737	235	14	in	in	ADP
fumecheng-13737	235	15	eq	eq	ADP
fumecheng-13737	235	16	.	.	PUNCT
fumecheng-13737	236	1	(	(	PUNCT
fumecheng-13737	236	2	13	13	NUM
fumecheng-13737	236	3	)	)	PUNCT
fumecheng-13737	236	4	is	be	AUX
fumecheng-13737	236	5	obtained	obtain	VERB
fumecheng-13737	236	6	as	as	ADP
fumecheng-13737	236	7	[	[	X
fumecheng-13737	236	8	47	47	NUM
fumecheng-13737	236	9	]	]	NUM
fumecheng-13737	236	10	:	:	PUNCT
fumecheng-13737	236	11	/4	/4	NOUN
fumecheng-13737	236	12	2	2	NUM
fumecheng-13737	236	13	0	0	NUM
fumecheng-13737	236	14	/4	/4	NOUN
fumecheng-13737	236	15	2	2	NUM
fumecheng-13737	236	16	0	0	NUM
fumecheng-13737	236	17	(	(	PUNCT
fumecheng-13737	236	18	)	)	PUNCT
fumecheng-13737	236	19	(	(	PUNCT
fumecheng-13737	236	20	)	)	PUNCT
fumecheng-13737	236	21	.	.	PUNCT
fumecheng-13737	237	1	(	(	PUNCT
fumecheng-13737	237	2	)	)	PUNCT
fumecheng-13737	237	3	semf	semf	PROPN
fumecheng-13737	237	4	t	t	PROPN
fumecheng-13737	237	5	t	t	PROPN
fumecheng-13737	237	6	u	u	NOUN
fumecheng-13737	238	1	t	t	PROPN
fumecheng-13737	238	2	f	f	X
fumecheng-13737	238	3	u	u	INTJ
fumecheng-13737	238	4	dt	dt	X
fumecheng-13737	238	5	u	u	NOUN
fumecheng-13737	238	6	t	t	X
fumecheng-13737	238	7	dt	dt	X
fumecheng-13737	238	8			PROPN
fumecheng-13737	238	9	=	=	PUNCT
fumecheng-13737	238	10			X
fumecheng-13737	238	11			X
fumecheng-13737	238	12	(	(	PUNCT
fumecheng-13737	238	13	30	30	NUM
fumecheng-13737	238	14	)	)	PUNCT
fumecheng-13737	238	15	for	for	ADP
fumecheng-13737	238	16	the	the	DET
fumecheng-13737	238	17	present	present	ADJ
fumecheng-13737	238	18	problem	problem	NOUN
fumecheng-13737	238	19	,	,	PUNCT
fumecheng-13737	238	20	eq	eq	X
fumecheng-13737	238	21	(	(	PUNCT
fumecheng-13737	238	22	30	30	NUM
fumecheng-13737	238	23	)	)	PUNCT
fumecheng-13737	238	24	can	can	AUX
fumecheng-13737	238	25	be	be	AUX
fumecheng-13737	238	26	formulated	formulate	VERB
fumecheng-13737	238	27	as	as	ADP
fumecheng-13737	238	28	follows	follow	VERB
fumecheng-13737	238	29	(	(	PUNCT
fumecheng-13737	238	30	)	)	PUNCT
fumecheng-13737	238	31	(	(	PUNCT
fumecheng-13737	238	32	)	)	PUNCT
fumecheng-13737	238	33	/4	/4	NOUN
fumecheng-13737	238	34	2	2	NUM
fumecheng-13737	238	35	2	2	NUM
fumecheng-13737	238	36	3	3	NUM
fumecheng-13737	238	37	5	5	NUM
fumecheng-13737	238	38	1	1	NUM
fumecheng-13737	238	39	2	2	NUM
fumecheng-13737	238	40	3	3	NUM
fumecheng-13737	238	41	4	4	NUM
fumecheng-13737	238	42	2	2	NUM
fumecheng-13737	238	43	0	0	NUM
fumecheng-13737	238	44	/4	/4	NOUN
fumecheng-13737	238	45	2	2	NUM
fumecheng-13737	238	46	0	0	NUM
fumecheng-13737	238	47	(	(	PUNCT
fumecheng-13737	238	48	)	)	PUNCT
fumecheng-13737	238	49	.	.	PUNCT
fumecheng-13737	239	1	(	(	PUNCT
fumecheng-13737	239	2	)	)	PUNCT
fumecheng-13737	239	3	f	f	PROPN
fumecheng-13737	239	4	t	t	NOUN
fumecheng-13737	239	5	tsem	tsem	PROPN
fumecheng-13737	239	6	u	u	PROPN
fumecheng-13737	239	7	t	t	PROPN
fumecheng-13737	239	8	u	u	X
fumecheng-13737	239	9	u	u	X
fumecheng-13737	239	10	uu	uu	VERB
fumecheng-13737	239	11	u	u	NOUN
fumecheng-13737	239	12	u	u	X
fumecheng-13737	239	13	u	u	NOUN
fumecheng-13737	239	14	dt	dt	X
fumecheng-13737	239	15	u	u	NOUN
fumecheng-13737	239	16	t	t	PROPN
fumecheng-13737	239	17	dt	dt	PROPN
fumecheng-13737	239	18			PROPN
fumecheng-13737	239	19			PROPN
fumecheng-13737	239	20			PROPN
fumecheng-13737	239	21			PROPN
fumecheng-13737	239	22			PROPN
fumecheng-13737	240	1	+	+	PUNCT
fumecheng-13737	241	1	+	+	PUNCT
fumecheng-13737	241	2	+	+	PUNCT
fumecheng-13737	241	3	+	+	NUM
fumecheng-13737	241	4	=	=	NOUN
fumecheng-13737	241	5			X
fumecheng-13737	241	6			X
fumecheng-13737	241	7			NUM
fumecheng-13737	241	8	(	(	PUNCT
fumecheng-13737	241	9	31	31	NUM
fumecheng-13737	241	10	)	)	PUNCT
fumecheng-13737	241	11	by	by	ADP
fumecheng-13737	241	12	substituting	substitute	VERB
fumecheng-13737	241	13	u(t)=acos(ωt	u(t)=acos(ωt	NOUN
fumecheng-13737	241	14	)	)	PUNCT
fumecheng-13737	241	15	into	into	ADP
fumecheng-13737	241	16	eq	eq	NOUN
fumecheng-13737	241	17	.	.	PUNCT
fumecheng-13737	242	1	(	(	PUNCT
fumecheng-13737	242	2	31	31	NUM
fumecheng-13737	242	3	)	)	PUNCT
fumecheng-13737	242	4	,	,	PUNCT
fumecheng-13737	242	5	the	the	DET
fumecheng-13737	242	6	following	follow	VERB
fumecheng-13737	242	7	expression	expression	NOUN
fumecheng-13737	242	8	is	be	AUX
fumecheng-13737	242	9	obtained	obtain	VERB
fumecheng-13737	242	10	:	:	PUNCT
fumecheng-13737	242	11	(	(	PUNCT
fumecheng-13737	242	12	)	)	PUNCT
fumecheng-13737	242	13	(	(	PUNCT
fumecheng-13737	242	14	)	)	PUNCT
fumecheng-13737	242	15	/4	/4	NOUN
fumecheng-13737	242	16	3	3	NUM
fumecheng-13737	242	17	2	2	NUM
fumecheng-13737	242	18	3	3	NUM
fumecheng-13737	242	19	3	3	NUM
fumecheng-13737	242	20	2	2	NUM
fumecheng-13737	242	21	2	2	NUM
fumecheng-13737	242	22	1	1	NUM
fumecheng-13737	242	23	2	2	NUM
fumecheng-13737	242	24	0	0	NUM
fumecheng-13737	242	25	/4	/4	NOUN
fumecheng-13737	242	26	2	2	NUM
fumecheng-13737	242	27	2	2	NUM
fumecheng-13737	242	28	0	0	NUM
fumecheng-13737	242	29	/4	/4	NOUN
fumecheng-13737	242	30	3	3	NUM
fumecheng-13737	242	31	3	3	NUM
fumecheng-13737	242	32	5	5	NUM
fumecheng-13737	242	33	5	5	NUM
fumecheng-13737	242	34	2	2	NUM
fumecheng-13737	242	35	3	3	NUM
fumecheng-13737	242	36	4	4	NUM
fumecheng-13737	242	37	0	0	NUM
fumecheng-13737	242	38	/4	/4	NOUN
fumecheng-13737	242	39	2	2	NUM
fumecheng-13737	242	40	2	2	NUM
fumecheng-13737	242	41	0	0	NUM
fumecheng-13737	242	42	cos	cos	PROPN
fumecheng-13737	242	43	(	(	PUNCT
fumecheng-13737	242	44	)	)	PUNCT
fumecheng-13737	242	45	cos	cos	PROPN
fumecheng-13737	242	46	(	(	PUNCT
fumecheng-13737	242	47	)	)	PUNCT
fumecheng-13737	242	48	cos	cos	PROPN
fumecheng-13737	242	49	(	(	PUNCT
fumecheng-13737	242	50	)	)	PUNCT
fumecheng-13737	242	51	sin	sin	NOUN
fumecheng-13737	242	52	(	(	PUNCT
fumecheng-13737	242	53	)	)	PUNCT
fumecheng-13737	242	54	cos	cos	PROPN
fumecheng-13737	242	55	(	(	PUNCT
fumecheng-13737	242	56	)	)	PUNCT
fumecheng-13737	242	57	cos	cos	PROPN
fumecheng-13737	242	58	(	(	PUNCT
fumecheng-13737	242	59	)	)	PUNCT
fumecheng-13737	242	60	cos	cos	PROPN
fumecheng-13737	242	61	(	(	PUNCT
fumecheng-13737	242	62	)	)	PUNCT
fumecheng-13737	242	63	cos	cos	PROPN
fumecheng-13737	242	64	(	(	PUNCT
fumecheng-13737	242	65	)	)	PUNCT
fumecheng-13737	242	66	cos	cos	PROPN
fumecheng-13737	242	67	(	(	PUNCT
fumecheng-13737	242	68	)	)	PUNCT
fumecheng-13737	242	69	.	.	PUNCT
fumecheng-13737	243	1	cos	cos	PROPN
fumecheng-13737	243	2	(	(	PUNCT
fumecheng-13737	243	3	)	)	PUNCT
fumecheng-13737	243	4	t	t	NOUN
fumecheng-13737	243	5	t	t	PROPN
fumecheng-13737	243	6	t	t	PROPN
fumecheng-13737	243	7	s	s	X
fumecheng-13737	243	8	mf	mf	PRON
fumecheng-13737	243	9	t	t	PROPN
fumecheng-13737	243	10	e	e	PROPN
fumecheng-13737	243	11	a	a	PROPN
fumecheng-13737	243	12	t	t	NOUN
fumecheng-13737	243	13	a	a	DET
fumecheng-13737	243	14	t	t	NOUN
fumecheng-13737	243	15	a	a	DET
fumecheng-13737	243	16	t	t	NOUN
fumecheng-13737	243	17	t	t	X
fumecheng-13737	243	18	dt	dt	X
fumecheng-13737	243	19	a	a	DET
fumecheng-13737	243	20	t	t	X
fumecheng-13737	243	21	dt	dt	X
fumecheng-13737	243	22	a	a	DET
fumecheng-13737	243	23	t	t	NOUN
fumecheng-13737	243	24	a	a	DET
fumecheng-13737	243	25	t	t	NOUN
fumecheng-13737	243	26	a	a	DET
fumecheng-13737	243	27	t	t	NOUN
fumecheng-13737	243	28	a	a	DET
fumecheng-13737	243	29	t	t	NOUN
fumecheng-13737	243	30	dt	dt	X
fumecheng-13737	243	31	a	a	DET
fumecheng-13737	243	32	t	t	NOUN
fumecheng-13737	243	33	dt	dt	X
fumecheng-13737	243	34	−	−	PROPN
fumecheng-13737	244	1	+	+	CCONJ
fumecheng-13737	244	2	=	=	PUNCT
fumecheng-13737	245	1	+	+	PUNCT
fumecheng-13737	245	2	+	+	PUNCT
fumecheng-13737	246	1	+	+	NUM
fumecheng-13737	246	2			NOUN
fumecheng-13737	246	3			NOUN
fumecheng-13737	246	4			PUNCT
fumecheng-13737	246	5			PUNCT
fumecheng-13737	247	1			NOUN
fumecheng-13737	247	2			X
fumecheng-13737	247	3			X
fumecheng-13737	247	4			X
fumecheng-13737	247	5			X
fumecheng-13737	247	6			X
fumecheng-13737	247	7			X
fumecheng-13737	247	8			X
fumecheng-13737	247	9			X
fumecheng-13737	247	10			PROPN
fumecheng-13737	247	11			PROPN
fumecheng-13737	247	12			PROPN
fumecheng-13737	247	13			PROPN
fumecheng-13737	247	14			PROPN
fumecheng-13737	247	15			PROPN
fumecheng-13737	247	16			X
fumecheng-13737	247	17			X
fumecheng-13737	247	18	(	(	PUNCT
fumecheng-13737	247	19	32	32	NUM
fumecheng-13737	247	20	)	)	PUNCT
fumecheng-13737	247	21	after	after	ADP
fumecheng-13737	247	22	simplification	simplification	NOUN
fumecheng-13737	247	23	,	,	PUNCT
fumecheng-13737	247	24	the	the	DET
fumecheng-13737	247	25	expression	expression	NOUN
fumecheng-13737	247	26	for	for	ADP
fumecheng-13737	247	27	the	the	DET
fumecheng-13737	247	28	nonlinear	nonlinear	ADJ
fumecheng-13737	247	29	frequency	frequency	NOUN
fumecheng-13737	247	30	of	of	ADP
fumecheng-13737	247	31	the	the	DET
fumecheng-13737	247	32	stringer	stringer	NOUN
fumecheng-13737	247	33	-	-	PUNCT
fumecheng-13737	247	34	stiffened	stiffen	VERB
fumecheng-13737	247	35	shell	shell	NOUN
fumecheng-13737	247	36	can	can	AUX
fumecheng-13737	247	37	be	be	AUX
fumecheng-13737	247	38	written	write	VERB
fumecheng-13737	247	39	as	as	ADP
fumecheng-13737	247	40	:	:	PUNCT
fumecheng-13737	247	41	2	2	NUM
fumecheng-13737	247	42	4	4	NUM
fumecheng-13737	247	43	2	2	NUM
fumecheng-13737	247	44	3	3	NUM
fumecheng-13737	247	45	4	4	NUM
fumecheng-13737	247	46	2	2	NUM
fumecheng-13737	247	47	1	1	NUM
fumecheng-13737	247	48	16	16	NUM
fumecheng-13737	247	49	12	12	NUM
fumecheng-13737	247	50	10	10	NUM
fumecheng-13737	247	51	,	,	PUNCT
fumecheng-13737	247	52	16	16	NUM
fumecheng-13737	247	53	8	8	NUM
fumecheng-13737	247	54	semf	semf	NOUN
fumecheng-13737	247	55	a	a	DET
fumecheng-13737	247	56	a	a	DET
fumecheng-13737	247	57	a	a	DET
fumecheng-13737	247	58			PROPN
fumecheng-13737	247	59			PROPN
fumecheng-13737	247	60			PROPN
fumecheng-13737	247	61			PROPN
fumecheng-13737	247	62			PROPN
fumecheng-13737	247	63	+	+	PROPN
fumecheng-13737	247	64	+	+	PUNCT
fumecheng-13737	247	65	=	=	SYM
fumecheng-13737	248	1	+	+	CCONJ
fumecheng-13737	248	2	(	(	PUNCT
fumecheng-13737	248	3	33	33	NUM
fumecheng-13737	248	4	)	)	PUNCT
fumecheng-13737	248	5	and	and	CCONJ
fumecheng-13737	248	6	the	the	DET
fumecheng-13737	248	7	approximate	approximate	ADJ
fumecheng-13737	248	8	solution	solution	NOUN
fumecheng-13737	248	9	as	as	ADP
fumecheng-13737	248	10	2	2	NUM
fumecheng-13737	248	11	4	4	NUM
fumecheng-13737	248	12	2	2	NUM
fumecheng-13737	248	13	3	3	NUM
fumecheng-13737	248	14	4	4	NUM
fumecheng-13737	248	15	2	2	NUM
fumecheng-13737	248	16	1	1	NUM
fumecheng-13737	248	17	16	16	NUM
fumecheng-13737	248	18	12	12	NUM
fumecheng-13737	248	19	10	10	NUM
fumecheng-13737	248	20	(	(	PUNCT
fumecheng-13737	248	21	)	)	PUNCT
fumecheng-13737	248	22	cos	cos	PROPN
fumecheng-13737	248	23	.	.	PUNCT
fumecheng-13737	249	1	16	16	NUM
fumecheng-13737	249	2	8	8	NUM
fumecheng-13737	249	3	semf	semf	NOUN
fumecheng-13737	249	4	a	a	DET
fumecheng-13737	249	5	a	a	DET
fumecheng-13737	249	6	u	u	NOUN
fumecheng-13737	249	7	t	t	PROPN
fumecheng-13737	249	8	a	a	DET
fumecheng-13737	249	9	t	t	PROPN
fumecheng-13737	249	10	a	a	DET
fumecheng-13737	249	11			PROPN
fumecheng-13737	249	12			PROPN
fumecheng-13737	249	13			PROPN
fumecheng-13737	249	14			PROPN
fumecheng-13737	249	15			NOUN
fumecheng-13737	249	16	+	+	VERB
fumecheng-13737	249	17	+	+	CCONJ
fumecheng-13737	249	18			PROPN
fumecheng-13737	249	19	=	=	PROPN
fumecheng-13737	249	20			PROPN
fumecheng-13737	249	21	+	+	PROPN
fumecheng-13737	249	22			PROPN
fumecheng-13737	249	23			NOUN
fumecheng-13737	249	24	(	(	PUNCT
fumecheng-13737	249	25	34	34	NUM
fumecheng-13737	249	26	)	)	PUNCT
fumecheng-13737	249	27	this	this	DET
fumecheng-13737	249	28	method	method	NOUN
fumecheng-13737	249	29	achieves	achieve	VERB
fumecheng-13737	249	30	a	a	DET
fumecheng-13737	249	31	balance	balance	NOUN
fumecheng-13737	249	32	between	between	ADP
fumecheng-13737	249	33	accuracy	accuracy	NOUN
fumecheng-13737	249	34	and	and	CCONJ
fumecheng-13737	249	35	simplicity	simplicity	NOUN
fumecheng-13737	249	36	by	by	ADP
fumecheng-13737	249	37	optimizing	optimize	VERB
fumecheng-13737	249	38	the	the	DET
fumecheng-13737	249	39	error	error	NOUN
fumecheng-13737	249	40	and	and	CCONJ
fumecheng-13737	249	41	demonstrates	demonstrate	VERB
fumecheng-13737	249	42	robustness	robustness	NOUN
fumecheng-13737	249	43	for	for	ADP
fumecheng-13737	249	44	amplitudes	amplitude	NOUN
fumecheng-13737	249	45	ranging	range	VERB
fumecheng-13737	249	46	from	from	ADP
fumecheng-13737	249	47	small	small	ADJ
fumecheng-13737	249	48	to	to	PART
fumecheng-13737	249	49	moderate	moderate	VERB
fumecheng-13737	249	50	.	.	PUNCT
fumecheng-13737	250	1	it	it	PRON
fumecheng-13737	250	2	should	should	AUX
fumecheng-13737	250	3	be	be	AUX
fumecheng-13737	250	4	noted	note	VERB
fumecheng-13737	250	5	that	that	SCONJ
fumecheng-13737	250	6	the	the	DET
fumecheng-13737	250	7	frequency	frequency	NOUN
fumecheng-13737	250	8	derived	derive	VERB
fumecheng-13737	250	9	in	in	ADP
fumecheng-13737	250	10	eq	eq	ADP
fumecheng-13737	250	11	.	.	PUNCT
fumecheng-13737	251	1	(	(	PUNCT
fumecheng-13737	251	2	33	33	NUM
fumecheng-13737	251	3	)	)	PUNCT
fumecheng-13737	251	4	can	can	AUX
fumecheng-13737	251	5	also	also	ADV
fumecheng-13737	251	6	be	be	AUX
fumecheng-13737	251	7	obtained	obtain	VERB
fumecheng-13737	251	8	using	use	VERB
fumecheng-13737	251	9	the	the	DET
fumecheng-13737	251	10	ha	ha	INTJ
fumecheng-13737	252	1	[	[	X
fumecheng-13737	252	2	37	37	NUM
fumecheng-13737	252	3	]	]	PUNCT
fumecheng-13737	252	4	,	,	PUNCT
fumecheng-13737	252	5	the	the	DET
fumecheng-13737	252	6	hpm	hpm	NOUN
fumecheng-13737	253	1	[	[	X
fumecheng-13737	253	2	38	38	NUM
fumecheng-13737	253	3	]	]	PUNCT
fumecheng-13737	253	4	,	,	PUNCT
fumecheng-13737	253	5	and	and	CCONJ
fumecheng-13737	253	6	the	the	DET
fumecheng-13737	253	7	first	first	ADJ
fumecheng-13737	253	8	-	-	PUNCT
fumecheng-13737	253	9	order	order	NOUN
fumecheng-13737	253	10	grhbm	grhbm	NOUN
fumecheng-13737	253	11	[	[	X
fumecheng-13737	253	12	39	39	NUM
fumecheng-13737	253	13	]	]	PUNCT
fumecheng-13737	253	14	.	.	PUNCT
fumecheng-13737	254	1	796	796	NUM
fumecheng-13737	254	2	c	c	X
fumecheng-13737	254	3	-	-	PUNCT
fumecheng-13737	254	4	h.	h.	NOUN
fumecheng-13737	254	5	he	he	PROPN
fumecheng-13737	254	6	,	,	PUNCT
fumecheng-13737	254	7	m.	m.	NOUN
fumecheng-13737	254	8	mohammadian	mohammadian	NOUN
fumecheng-13737	254	9	3.3	3.3	NUM
fumecheng-13737	254	10	.	.	PUNCT
fumecheng-13737	254	11	hamiltonian	hamiltonian	ADJ
fumecheng-13737	254	12	-	-	PUNCT
fumecheng-13737	254	13	based	base	VERB
fumecheng-13737	254	14	frequency	frequency	NOUN
fumecheng-13737	254	15	-	-	PUNCT
fumecheng-13737	254	16	amplitude	amplitude	NOUN
fumecheng-13737	254	17	formulation	formulation	NOUN
fumecheng-13737	254	18	(	(	PUNCT
fumecheng-13737	254	19	hfaf	hfaf	PROPN
fumecheng-13737	254	20	)	)	PUNCT
fumecheng-13737	254	21	the	the	DET
fumecheng-13737	254	22	hamiltonian	hamiltonian	NOUN
fumecheng-13737	254	23	-	-	PUNCT
fumecheng-13737	254	24	based	base	VERB
fumecheng-13737	254	25	method	method	NOUN
fumecheng-13737	254	26	[	[	X
fumecheng-13737	254	27	48	48	NUM
fumecheng-13737	254	28	]	]	PUNCT
fumecheng-13737	254	29	utilizes	utilize	VERB
fumecheng-13737	254	30	energy	energy	NOUN
fumecheng-13737	254	31	conservation	conservation	NOUN
fumecheng-13737	254	32	to	to	PART
fumecheng-13737	254	33	estimate	estimate	VERB
fumecheng-13737	254	34	the	the	DET
fumecheng-13737	254	35	frequency	frequency	NOUN
fumecheng-13737	254	36	.	.	PUNCT
fumecheng-13737	255	1	for	for	ADP
fumecheng-13737	255	2	the	the	DET
fumecheng-13737	255	3	nonlinear	nonlinear	ADJ
fumecheng-13737	255	4	oscillator	oscillator	NOUN
fumecheng-13737	255	5	given	give	VERB
fumecheng-13737	255	6	in	in	ADP
fumecheng-13737	255	7	eq	eq	ADP
fumecheng-13737	255	8	.	.	PUNCT
fumecheng-13737	256	1	(	(	PUNCT
fumecheng-13737	256	2	13	13	NUM
fumecheng-13737	256	3	)	)	PUNCT
fumecheng-13737	256	4	,	,	PUNCT
fumecheng-13737	256	5	the	the	DET
fumecheng-13737	256	6	hamiltonian	hamiltonian	ADJ
fumecheng-13737	256	7	constant	constant	ADJ
fumecheng-13737	256	8	h	h	NOUN
fumecheng-13737	256	9	is	be	AUX
fumecheng-13737	256	10	defined	define	VERB
fumecheng-13737	256	11	as	as	SCONJ
fumecheng-13737	256	12	follows	follow	VERB
fumecheng-13737	256	13	:	:	PUNCT
fumecheng-13737	256	14	2	2	NUM
fumecheng-13737	256	15	1	1	NUM
fumecheng-13737	256	16	(	(	PUNCT
fumecheng-13737	256	17	)	)	PUNCT
fumecheng-13737	256	18	,	,	PUNCT
fumecheng-13737	256	19	2	2	NUM
fumecheng-13737	256	20	du	du	NOUN
fumecheng-13737	256	21	h	h	NOUN
fumecheng-13737	256	22	p	p	PROPN
fumecheng-13737	256	23	u	u	X
fumecheng-13737	257	1	dt	dt	NOUN
fumecheng-13737	257	2			NOUN
fumecheng-13737	257	3			NOUN
fumecheng-13737	257	4	=	=	PUNCT
fumecheng-13737	258	1	+	+	CCONJ
fumecheng-13737	258	2			PROPN
fumecheng-13737	258	3			CCONJ
fumecheng-13737	258	4			PROPN
fumecheng-13737	258	5			NOUN
fumecheng-13737	258	6	(	(	PUNCT
fumecheng-13737	258	7	35	35	NUM
fumecheng-13737	258	8	)	)	PUNCT
fumecheng-13737	258	9	where	where	SCONJ
fumecheng-13737	258	10	(	(	PUNCT
fumecheng-13737	258	11	)	)	PUNCT
fumecheng-13737	258	12	(	(	PUNCT
fumecheng-13737	258	13	)	)	PUNCT
fumecheng-13737	258	14	.p	.p	PROPN
fumecheng-13737	258	15	u	u	NOUN
fumecheng-13737	258	16	f	f	PROPN
fumecheng-13737	258	17	u	u	NOUN
fumecheng-13737	258	18	du=	du=	VERB
fumecheng-13737	258	19			PUNCT
fumecheng-13737	258	20	for	for	ADP
fumecheng-13737	258	21	a	a	DET
fumecheng-13737	258	22	conservative	conservative	ADJ
fumecheng-13737	258	23	system	system	NOUN
fumecheng-13737	258	24	,	,	PUNCT
fumecheng-13737	258	25	the	the	DET
fumecheng-13737	258	26	hamiltonian	hamiltonian	NOUN
fumecheng-13737	258	27	remains	remain	VERB
fumecheng-13737	258	28	constant	constant	ADJ
fumecheng-13737	258	29	during	during	ADP
fumecheng-13737	258	30	the	the	DET
fumecheng-13737	258	31	entire	entire	ADJ
fumecheng-13737	258	32	oscillation	oscillation	NOUN
fumecheng-13737	258	33	process	process	NOUN
fumecheng-13737	258	34	.	.	PUNCT
fumecheng-13737	259	1	therefore	therefore	ADV
fumecheng-13737	259	2	,	,	PUNCT
fumecheng-13737	259	3	we	we	PRON
fumecheng-13737	259	4	have	have	VERB
fumecheng-13737	259	5	:	:	PUNCT
fumecheng-13737	259	6	2	2	NUM
fumecheng-13737	259	7	1	1	NUM
fumecheng-13737	259	8	(	(	PUNCT
fumecheng-13737	259	9	)	)	PUNCT
fumecheng-13737	259	10	(	(	PUNCT
fumecheng-13737	259	11	)	)	PUNCT
fumecheng-13737	259	12	0	0	X
fumecheng-13737	259	13	.	.	X
fumecheng-13737	259	14	2	2	NUM
fumecheng-13737	259	15	du	du	PROPN
fumecheng-13737	259	16	p	p	PROPN
fumecheng-13737	259	17	u	u	PROPN
fumecheng-13737	259	18	p	p	NOUN
fumecheng-13737	259	19	a	a	DET
fumecheng-13737	259	20	dt	dt	NOUN
fumecheng-13737	259	21			NOUN
fumecheng-13737	259	22			NOUN
fumecheng-13737	259	23	+	+	CCONJ
fumecheng-13737	259	24	−	−	PROPN
fumecheng-13737	260	1	=	=	SYM
fumecheng-13737	260	2			PROPN
fumecheng-13737	260	3			PROPN
fumecheng-13737	260	4			PROPN
fumecheng-13737	260	5			NOUN
fumecheng-13737	260	6	(	(	PUNCT
fumecheng-13737	260	7	36	36	NUM
fumecheng-13737	260	8	)	)	PUNCT
fumecheng-13737	260	9	by	by	ADP
fumecheng-13737	260	10	substituting	substitute	VERB
fumecheng-13737	260	11	the	the	DET
fumecheng-13737	260	12	approximate	approximate	ADJ
fumecheng-13737	260	13	solution	solution	NOUN
fumecheng-13737	260	14	u(t)=acos(ωt	u(t)=acos(ωt	NOUN
fumecheng-13737	260	15	)	)	PUNCT
fumecheng-13737	260	16	into	into	ADP
fumecheng-13737	260	17	eq	eq	NOUN
fumecheng-13737	260	18	.	.	PUNCT
fumecheng-13737	260	19	(	(	PUNCT
fumecheng-13737	260	20	36	36	NUM
fumecheng-13737	260	21	)	)	PUNCT
fumecheng-13737	260	22	,	,	PUNCT
fumecheng-13737	260	23	the	the	DET
fumecheng-13737	260	24	corresponding	corresponding	ADJ
fumecheng-13737	260	25	residual	residual	ADJ
fumecheng-13737	260	26	function	function	NOUN
fumecheng-13737	260	27	is	be	AUX
fumecheng-13737	260	28	obtained	obtain	VERB
fumecheng-13737	260	29	as	as	SCONJ
fumecheng-13737	260	30	follows	follow	VERB
fumecheng-13737	260	31	:	:	PUNCT
fumecheng-13737	260	32	(	(	PUNCT
fumecheng-13737	260	33	)	)	PUNCT
fumecheng-13737	260	34	(	(	PUNCT
fumecheng-13737	260	35	)	)	PUNCT
fumecheng-13737	260	36	(	(	PUNCT
fumecheng-13737	260	37	)	)	SYM
fumecheng-13737	260	38	2	2	NUM
fumecheng-13737	260	39	2	2	NUM
fumecheng-13737	260	40	21	21	NUM
fumecheng-13737	260	41	sin	sin	NOUN
fumecheng-13737	260	42	(	(	PUNCT
fumecheng-13737	260	43	)	)	PUNCT
fumecheng-13737	260	44	cos	cos	PROPN
fumecheng-13737	260	45	(	(	PUNCT
fumecheng-13737	260	46	)	)	PUNCT
fumecheng-13737	260	47	.	.	PUNCT
fumecheng-13737	261	1	2	2	NUM
fumecheng-13737	261	2	r	r	NOUN
fumecheng-13737	261	3	t	t	NOUN
fumecheng-13737	261	4	a	a	DET
fumecheng-13737	261	5	t	t	NOUN
fumecheng-13737	261	6	p	p	NOUN
fumecheng-13737	261	7	a	a	DET
fumecheng-13737	261	8	t	t	NOUN
fumecheng-13737	261	9	p	p	NOUN
fumecheng-13737	261	10	a	a	ADV
fumecheng-13737	261	11			X
fumecheng-13737	261	12	=	=	NOUN
fumecheng-13737	261	13	+	+	CCONJ
fumecheng-13737	261	14	−	−	PROPN
fumecheng-13737	261	15	(	(	PUNCT
fumecheng-13737	261	16	37	37	NUM
fumecheng-13737	261	17	)	)	PUNCT
fumecheng-13737	261	18	by	by	ADP
fumecheng-13737	261	19	defining	define	VERB
fumecheng-13737	261	20	two	two	NUM
fumecheng-13737	261	21	average	average	ADJ
fumecheng-13737	261	22	residuals	residual	NOUN
fumecheng-13737	261	23	1	1	NUM
fumecheng-13737	261	24	/4	/4	NOUN
fumecheng-13737	261	25	1	1	NUM
fumecheng-13737	261	26	1	1	NUM
fumecheng-13737	261	27	1	1	NUM
fumecheng-13737	261	28	1	1	NUM
fumecheng-13737	261	29	0	0	NUM
fumecheng-13737	261	30	4	4	NUM
fumecheng-13737	261	31	cos	cos	PROPN
fumecheng-13737	261	32	(	(	PUNCT
fumecheng-13737	261	33	)	)	PUNCT
fumecheng-13737	261	34	,	,	PUNCT
fumecheng-13737	261	35	t	t	NOUN
fumecheng-13737	261	36	r	r	NOUN
fumecheng-13737	261	37	r	r	NOUN
fumecheng-13737	261	38	t	t	NOUN
fumecheng-13737	261	39	dt	dt	X
fumecheng-13737	261	40	t	t	PROPN
fumecheng-13737	261	41	=	=	PROPN
fumecheng-13737	261	42			X
fumecheng-13737	261	43	(	(	PUNCT
fumecheng-13737	261	44	38	38	NUM
fumecheng-13737	261	45	)	)	SYM
fumecheng-13737	261	46	2	2	NUM
fumecheng-13737	261	47	/4	/4	NOUN
fumecheng-13737	261	48	2	2	NUM
fumecheng-13737	261	49	2	2	NUM
fumecheng-13737	261	50	2	2	NUM
fumecheng-13737	261	51	2	2	NUM
fumecheng-13737	261	52	0	0	NUM
fumecheng-13737	261	53	4	4	NUM
fumecheng-13737	261	54	cos	cos	PROPN
fumecheng-13737	261	55	(	(	PUNCT
fumecheng-13737	261	56	)	)	PUNCT
fumecheng-13737	261	57	,	,	PUNCT
fumecheng-13737	261	58	t	t	NOUN
fumecheng-13737	261	59	r	r	NOUN
fumecheng-13737	261	60	r	r	NOUN
fumecheng-13737	261	61	t	t	NOUN
fumecheng-13737	261	62	dt	dt	X
fumecheng-13737	261	63	t	t	PROPN
fumecheng-13737	261	64	=	=	PROPN
fumecheng-13737	261	65			X
fumecheng-13737	261	66	(	(	PUNCT
fumecheng-13737	261	67	39	39	NUM
fumecheng-13737	261	68	)	)	PUNCT
fumecheng-13737	261	69	the	the	DET
fumecheng-13737	261	70	hamiltonian	hamiltonian	NOUN
fumecheng-13737	261	71	-	-	PUNCT
fumecheng-13737	261	72	based	base	VERB
fumecheng-13737	261	73	nonlinear	nonlinear	ADJ
fumecheng-13737	261	74	frequency	frequency	NOUN
fumecheng-13737	261	75	is	be	AUX
fumecheng-13737	261	76	obtained	obtain	VERB
fumecheng-13737	261	77	as	as	ADP
fumecheng-13737	261	78	[	[	X
fumecheng-13737	261	79	48	48	NUM
fumecheng-13737	261	80	]	]	SYM
fumecheng-13737	261	81	:	:	PUNCT
fumecheng-13737	261	82	2	2	NUM
fumecheng-13737	261	83	2	2	NUM
fumecheng-13737	261	84	2	2	NUM
fumecheng-13737	261	85	2	2	NUM
fumecheng-13737	261	86	1	1	NUM
fumecheng-13737	261	87	1	1	NUM
fumecheng-13737	261	88	2	2	NUM
fumecheng-13737	261	89	1	1	NUM
fumecheng-13737	261	90	2	2	NUM
fumecheng-13737	261	91	,	,	PUNCT
fumecheng-13737	261	92	hfaf	hfaf	VERB
fumecheng-13737	261	93	r	r	NOUN
fumecheng-13737	261	94	r	r	NOUN
fumecheng-13737	261	95	r	r	NOUN
fumecheng-13737	261	96	r	r	NOUN
fumecheng-13737	261	97			X
fumecheng-13737	261	98			X
fumecheng-13737	261	99			X
fumecheng-13737	261	100	−	−	PROPN
fumecheng-13737	261	101	=	=	SYM
fumecheng-13737	262	1	−	−	PROPN
fumecheng-13737	262	2	(	(	PUNCT
fumecheng-13737	262	3	40	40	NUM
fumecheng-13737	262	4	)	)	PUNCT
fumecheng-13737	262	5	where	where	SCONJ
fumecheng-13737	262	6	ω1	ω1	PROPN
fumecheng-13737	262	7	and	and	CCONJ
fumecheng-13737	262	8	ω2	ω2	NOUN
fumecheng-13737	262	9	are	be	AUX
fumecheng-13737	262	10	typically	typically	ADV
fumecheng-13737	262	11	chosen	choose	VERB
fumecheng-13737	262	12	as	as	ADP
fumecheng-13737	262	13	ω1	ω1	PROPN
fumecheng-13737	262	14	=	=	SYM
fumecheng-13737	262	15	1	1	NUM
fumecheng-13737	262	16	and	and	CCONJ
fumecheng-13737	262	17	ω2	ω2	NOUN
fumecheng-13737	262	18	=	=	SYM
fumecheng-13737	262	19	2	2	X
fumecheng-13737	262	20	.	.	PUNCT
fumecheng-13737	263	1	the	the	DET
fumecheng-13737	263	2	hamiltonian	hamiltonian	ADJ
fumecheng-13737	263	3	formulation	formulation	NOUN
fumecheng-13737	263	4	of	of	ADP
fumecheng-13737	263	5	the	the	DET
fumecheng-13737	263	6	present	present	ADJ
fumecheng-13737	263	7	problem	problem	NOUN
fumecheng-13737	263	8	is	be	AUX
fumecheng-13737	263	9	expressed	express	VERB
fumecheng-13737	263	10	as	as	ADP
fumecheng-13737	263	11	2	2	NUM
fumecheng-13737	263	12	2	2	NUM
fumecheng-13737	263	13	2	2	NUM
fumecheng-13737	263	14	2	2	NUM
fumecheng-13737	263	15	4	4	NUM
fumecheng-13737	263	16	6	6	NUM
fumecheng-13737	263	17	1	1	NUM
fumecheng-13737	263	18	2	2	NUM
fumecheng-13737	263	19	3	3	NUM
fumecheng-13737	263	20	4	4	NUM
fumecheng-13737	263	21	1	1	NUM
fumecheng-13737	263	22	1	1	NUM
fumecheng-13737	263	23	1	1	NUM
fumecheng-13737	263	24	1	1	NUM
fumecheng-13737	263	25	1	1	NUM
fumecheng-13737	263	26	.	.	SYM
fumecheng-13737	263	27	2	2	NUM
fumecheng-13737	263	28	2	2	NUM
fumecheng-13737	263	29	2	2	NUM
fumecheng-13737	263	30	4	4	NUM
fumecheng-13737	263	31	6	6	NUM
fumecheng-13737	263	32	du	du	X
fumecheng-13737	263	33	du	du	PROPN
fumecheng-13737	263	34	h	h	PROPN
fumecheng-13737	263	35	u	u	PROPN
fumecheng-13737	263	36	u	u	X
fumecheng-13737	263	37	u	u	X
fumecheng-13737	263	38	u	u	NOUN
fumecheng-13737	263	39	dt	dt	X
fumecheng-13737	263	40	dt	dt	PUNCT
fumecheng-13737	263	41			PROPN
fumecheng-13737	263	42			PROPN
fumecheng-13737	263	43			PROPN
fumecheng-13737	263	44			PROPN
fumecheng-13737	263	45			NOUN
fumecheng-13737	263	46			NOUN
fumecheng-13737	263	47			NOUN
fumecheng-13737	263	48			NOUN
fumecheng-13737	264	1	=	=	PUNCT
fumecheng-13737	265	1	+	+	PUNCT
fumecheng-13737	265	2	+	+	PUNCT
fumecheng-13737	265	3	+	+	CCONJ
fumecheng-13737	265	4	+	+	ADJ
fumecheng-13737	265	5			PROPN
fumecheng-13737	265	6			PROPN
fumecheng-13737	266	1			PROPN
fumecheng-13737	266	2			PROPN
fumecheng-13737	267	1			ADJ
fumecheng-13737	267	2			PROPN
fumecheng-13737	267	3			PROPN
fumecheng-13737	267	4			NOUN
fumecheng-13737	267	5	(	(	PUNCT
fumecheng-13737	267	6	41	41	NUM
fumecheng-13737	267	7	)	)	PUNCT
fumecheng-13737	267	8	considering	consider	VERB
fumecheng-13737	267	9	the	the	DET
fumecheng-13737	267	10	initial	initial	ADJ
fumecheng-13737	267	11	conditions	condition	NOUN
fumecheng-13737	267	12	given	give	VERB
fumecheng-13737	267	13	in	in	ADP
fumecheng-13737	267	14	eq	eq	ADP
fumecheng-13737	267	15	.	.	PUNCT
fumecheng-13737	268	1	(	(	PUNCT
fumecheng-13737	268	2	12	12	NUM
fumecheng-13737	268	3	)	)	PUNCT
fumecheng-13737	268	4	and	and	CCONJ
fumecheng-13737	268	5	applying	apply	VERB
fumecheng-13737	268	6	eq	eq	ADP
fumecheng-13737	268	7	.	.	PUNCT
fumecheng-13737	269	1	(	(	PUNCT
fumecheng-13737	269	2	37	37	NUM
fumecheng-13737	269	3	)	)	PUNCT
fumecheng-13737	269	4	,	,	PUNCT
fumecheng-13737	269	5	the	the	DET
fumecheng-13737	269	6	residual	residual	ADJ
fumecheng-13737	269	7	function	function	NOUN
fumecheng-13737	269	8	is	be	AUX
fumecheng-13737	269	9	constructed	construct	VERB
fumecheng-13737	269	10	as	as	SCONJ
fumecheng-13737	269	11	follows	follow	VERB
fumecheng-13737	269	12	:	:	PUNCT
fumecheng-13737	269	13	(	(	PUNCT
fumecheng-13737	269	14	)	)	PUNCT
fumecheng-13737	269	15	(	(	PUNCT
fumecheng-13737	269	16	)	)	PUNCT
fumecheng-13737	269	17	(	(	PUNCT
fumecheng-13737	269	18	)	)	PUNCT
fumecheng-13737	269	19	(	(	PUNCT
fumecheng-13737	269	20	)	)	PUNCT
fumecheng-13737	269	21	(	(	PUNCT
fumecheng-13737	269	22	)	)	PUNCT
fumecheng-13737	269	23	2	2	NUM
fumecheng-13737	269	24	22	22	NUM
fumecheng-13737	269	25	2	2	NUM
fumecheng-13737	269	26	2	2	NUM
fumecheng-13737	269	27	2	2	NUM
fumecheng-13737	269	28	1	1	NUM
fumecheng-13737	269	29	2	2	NUM
fumecheng-13737	269	30	4	4	NUM
fumecheng-13737	269	31	4	4	NUM
fumecheng-13737	269	32	6	6	NUM
fumecheng-13737	269	33	6	6	NUM
fumecheng-13737	269	34	3	3	NUM
fumecheng-13737	269	35	4	4	NUM
fumecheng-13737	269	36	1	1	NUM
fumecheng-13737	269	37	1	1	NUM
fumecheng-13737	269	38	1	1	NUM
fumecheng-13737	269	39	(	(	PUNCT
fumecheng-13737	269	40	)	)	PUNCT
fumecheng-13737	269	41	sin	sin	NOUN
fumecheng-13737	269	42	(	(	PUNCT
fumecheng-13737	269	43	)	)	PUNCT
fumecheng-13737	269	44	sin	sin	NOUN
fumecheng-13737	269	45	(	(	PUNCT
fumecheng-13737	269	46	)	)	PUNCT
fumecheng-13737	269	47	cos	cos	PROPN
fumecheng-13737	269	48	(	(	PUNCT
fumecheng-13737	269	49	)	)	PUNCT
fumecheng-13737	269	50	cos	cos	PROPN
fumecheng-13737	269	51	(	(	PUNCT
fumecheng-13737	269	52	)	)	PUNCT
fumecheng-13737	269	53	1	1	NUM
fumecheng-13737	269	54	2	2	NUM
fumecheng-13737	269	55	2	2	NUM
fumecheng-13737	269	56	2	2	NUM
fumecheng-13737	269	57	1	1	NUM
fumecheng-13737	269	58	1	1	NUM
fumecheng-13737	269	59	cos	cos	PROPN
fumecheng-13737	269	60	(	(	PUNCT
fumecheng-13737	269	61	)	)	PUNCT
fumecheng-13737	269	62	1	1	NUM
fumecheng-13737	269	63	cos	cos	NOUN
fumecheng-13737	269	64	(	(	PUNCT
fumecheng-13737	269	65	)	)	PUNCT
fumecheng-13737	269	66	1	1	NUM
fumecheng-13737	269	67	.	.	SYM
fumecheng-13737	269	68	4	4	NUM
fumecheng-13737	269	69	6	6	NUM
fumecheng-13737	269	70	r	r	NOUN
fumecheng-13737	269	71	t	t	NOUN
fumecheng-13737	269	72	a	a	DET
fumecheng-13737	269	73	t	t	NOUN
fumecheng-13737	269	74	a	a	PRON
fumecheng-13737	269	75	a	a	DET
fumecheng-13737	269	76	t	t	NOUN
fumecheng-13737	269	77	t	t	NOUN
fumecheng-13737	269	78	a	a	DET
fumecheng-13737	269	79	t	t	NOUN
fumecheng-13737	269	80	a	a	DET
fumecheng-13737	269	81	t	t	NOUN
fumecheng-13737	269	82	a	a	DET
fumecheng-13737	269	83	t	t	NOUN
fumecheng-13737	269	84			INTJ
fumecheng-13737	269	85			PROPN
fumecheng-13737	269	86			PROPN
fumecheng-13737	269	87			X
fumecheng-13737	269	88			X
fumecheng-13737	269	89			PROPN
fumecheng-13737	269	90			PROPN
fumecheng-13737	269	91			PROPN
fumecheng-13737	269	92			PROPN
fumecheng-13737	269	93			PROPN
fumecheng-13737	269	94			PROPN
fumecheng-13737	269	95			X
fumecheng-13737	269	96	=	=	PUNCT
fumecheng-13737	269	97	−	−	PROPN
fumecheng-13737	270	1	+	+	CCONJ
fumecheng-13737	270	2	−	−	PROPN
fumecheng-13737	271	1	+	+	CCONJ
fumecheng-13737	271	2	−	−	PROPN
fumecheng-13737	272	1	+	+	CCONJ
fumecheng-13737	272	2	−	−	PROPN
fumecheng-13737	273	1	+	+	CCONJ
fumecheng-13737	273	2	−	−	PROPN
fumecheng-13737	273	3	(	(	PUNCT
fumecheng-13737	273	4	42	42	NUM
fumecheng-13737	273	5	)	)	PUNCT
fumecheng-13737	273	6	a	a	DET
fumecheng-13737	273	7	fast	fast	ADJ
fumecheng-13737	273	8	insight	insight	NOUN
fumecheng-13737	273	9	into	into	ADP
fumecheng-13737	273	10	nonlinear	nonlinear	ADJ
fumecheng-13737	273	11	frequency	frequency	NOUN
fumecheng-13737	273	12	estimation	estimation	NOUN
fumecheng-13737	273	13	of	of	ADP
fumecheng-13737	273	14	stringer	stringer	NOUN
fumecheng-13737	273	15	-	-	PUNCT
fumecheng-13737	273	16	stiffened	stiffen	VERB
fumecheng-13737	273	17	shells	shell	NOUN
fumecheng-13737	273	18	with	with	ADP
fumecheng-13737	273	19	high	high	ADJ
fumecheng-13737	273	20	accuracy	accuracy	NOUN
fumecheng-13737	273	21	797	797	NUM
fumecheng-13737	273	22	assuming	assume	VERB
fumecheng-13737	273	23	ω1	ω1	PROPN
fumecheng-13737	273	24	=	=	SYM
fumecheng-13737	273	25	1	1	NUM
fumecheng-13737	273	26	and	and	CCONJ
fumecheng-13737	273	27	ω2	ω2	ADJ
fumecheng-13737	273	28	=	=	SYM
fumecheng-13737	273	29	2	2	NUM
fumecheng-13737	273	30	,	,	PUNCT
fumecheng-13737	273	31	the	the	DET
fumecheng-13737	273	32	corresponding	corresponding	ADJ
fumecheng-13737	273	33	average	average	ADJ
fumecheng-13737	273	34	residuals	residual	NOUN
fumecheng-13737	273	35	are	be	AUX
fumecheng-13737	273	36	obtained	obtain	VERB
fumecheng-13737	273	37	as	as	SCONJ
fumecheng-13737	273	38	follows	follow	VERB
fumecheng-13737	273	39	:	:	PUNCT
fumecheng-13737	273	40	4	4	NUM
fumecheng-13737	273	41	2	2	NUM
fumecheng-13737	273	42	4	4	NUM
fumecheng-13737	273	43	6	6	NUM
fumecheng-13737	273	44	2	2	NUM
fumecheng-13737	273	45	1	1	NUM
fumecheng-13737	273	46	1	1	NUM
fumecheng-13737	273	47	2	2	NUM
fumecheng-13737	273	48	3	3	NUM
fumecheng-13737	273	49	4	4	NUM
fumecheng-13737	273	50	2	2	NUM
fumecheng-13737	273	51	1	1	NUM
fumecheng-13737	273	52	7	7	NUM
fumecheng-13737	273	53	19	19	NUM
fumecheng-13737	273	54	1	1	NUM
fumecheng-13737	273	55	.	.	PUNCT
fumecheng-13737	274	1	15	15	NUM
fumecheng-13737	274	2	3	3	NUM
fumecheng-13737	274	3	30	30	NUM
fumecheng-13737	274	4	105	105	NUM
fumecheng-13737	274	5	3	3	NUM
fumecheng-13737	274	6	r	r	NOUN
fumecheng-13737	274	7	a	a	PRON
fumecheng-13737	274	8	a	a	PRON
fumecheng-13737	274	9	a	a	PRON
fumecheng-13737	274	10	a	a	PRON
fumecheng-13737	274	11	a	a	PRON
fumecheng-13737	274	12			PROPN
fumecheng-13737	274	13			PROPN
fumecheng-13737	274	14			PROPN
fumecheng-13737	274	15			PROPN
fumecheng-13737	274	16			PROPN
fumecheng-13737	274	17			PROPN
fumecheng-13737	274	18			PROPN
fumecheng-13737	274	19			NOUN
fumecheng-13737	274	20	=	=	SYM
fumecheng-13737	274	21	−	−	PROPN
fumecheng-13737	274	22	−	−	PROPN
fumecheng-13737	274	23	−	−	PROPN
fumecheng-13737	274	24	+	+	CCONJ
fumecheng-13737	274	25	(	(	PUNCT
fumecheng-13737	274	26	43	43	NUM
fumecheng-13737	274	27	)	)	PUNCT
fumecheng-13737	274	28	4	4	NUM
fumecheng-13737	274	29	2	2	NUM
fumecheng-13737	274	30	4	4	NUM
fumecheng-13737	274	31	6	6	NUM
fumecheng-13737	274	32	2	2	NUM
fumecheng-13737	274	33	2	2	NUM
fumecheng-13737	274	34	1	1	NUM
fumecheng-13737	274	35	2	2	NUM
fumecheng-13737	274	36	3	3	NUM
fumecheng-13737	274	37	4	4	NUM
fumecheng-13737	274	38	8	8	NUM
fumecheng-13737	274	39	1	1	NUM
fumecheng-13737	274	40	7	7	NUM
fumecheng-13737	274	41	19	19	NUM
fumecheng-13737	274	42	4	4	NUM
fumecheng-13737	274	43	.	.	PUNCT
fumecheng-13737	275	1	15	15	NUM
fumecheng-13737	275	2	3	3	NUM
fumecheng-13737	275	3	30	30	NUM
fumecheng-13737	275	4	105	105	NUM
fumecheng-13737	275	5	3	3	NUM
fumecheng-13737	275	6	r	r	NOUN
fumecheng-13737	275	7	a	a	PRON
fumecheng-13737	275	8	a	a	PRON
fumecheng-13737	275	9	a	a	PRON
fumecheng-13737	275	10	a	a	PRON
fumecheng-13737	275	11	a	a	PRON
fumecheng-13737	275	12			PROPN
fumecheng-13737	275	13			PROPN
fumecheng-13737	275	14			PROPN
fumecheng-13737	275	15			PROPN
fumecheng-13737	275	16			PROPN
fumecheng-13737	275	17			PROPN
fumecheng-13737	275	18			PROPN
fumecheng-13737	275	19			NOUN
fumecheng-13737	275	20	=	=	SYM
fumecheng-13737	275	21	−	−	PROPN
fumecheng-13737	275	22	−	−	PROPN
fumecheng-13737	275	23	−	−	PROPN
fumecheng-13737	276	1	+	+	CCONJ
fumecheng-13737	276	2	(	(	PUNCT
fumecheng-13737	276	3	44	44	NUM
fumecheng-13737	276	4	)	)	PUNCT
fumecheng-13737	276	5	following	follow	VERB
fumecheng-13737	276	6	eq	eq	PRON
fumecheng-13737	276	7	.	.	PUNCT
fumecheng-13737	277	1	(	(	PUNCT
fumecheng-13737	277	2	40	40	NUM
fumecheng-13737	277	3	)	)	PUNCT
fumecheng-13737	277	4	,	,	PUNCT
fumecheng-13737	277	5	the	the	DET
fumecheng-13737	277	6	hamiltonian	hamiltonian	NOUN
fumecheng-13737	277	7	-	-	PUNCT
fumecheng-13737	277	8	based	base	VERB
fumecheng-13737	277	9	expression	expression	NOUN
fumecheng-13737	277	10	for	for	ADP
fumecheng-13737	277	11	the	the	DET
fumecheng-13737	277	12	nonlinear	nonlinear	ADJ
fumecheng-13737	277	13	frequency	frequency	NOUN
fumecheng-13737	277	14	of	of	ADP
fumecheng-13737	277	15	the	the	DET
fumecheng-13737	277	16	stringer	stringer	NOUN
fumecheng-13737	277	17	-	-	PUNCT
fumecheng-13737	277	18	stiffened	stiffen	VERB
fumecheng-13737	277	19	shell	shell	NOUN
fumecheng-13737	277	20	is	be	AUX
fumecheng-13737	277	21	obtained	obtain	VERB
fumecheng-13737	277	22	as	as	ADP
fumecheng-13737	277	23	:	:	SYM
fumecheng-13737	277	24	2	2	NUM
fumecheng-13737	277	25	4	4	NUM
fumecheng-13737	277	26	2	2	NUM
fumecheng-13737	277	27	3	3	NUM
fumecheng-13737	277	28	4	4	NUM
fumecheng-13737	277	29	2	2	NUM
fumecheng-13737	277	30	1	1	NUM
fumecheng-13737	277	31	70	70	NUM
fumecheng-13737	277	32	49	49	NUM
fumecheng-13737	277	33	38	38	NUM
fumecheng-13737	277	34	,	,	PUNCT
fumecheng-13737	277	35	70	70	NUM
fumecheng-13737	277	36	28	28	NUM
fumecheng-13737	277	37	hfaf	hfaf	VERB
fumecheng-13737	277	38	a	a	DET
fumecheng-13737	277	39	a	a	DET
fumecheng-13737	277	40	a	a	DET
fumecheng-13737	277	41			PROPN
fumecheng-13737	277	42			PROPN
fumecheng-13737	277	43			PROPN
fumecheng-13737	277	44			PROPN
fumecheng-13737	277	45			PROPN
fumecheng-13737	277	46	+	+	PROPN
fumecheng-13737	278	1	+	+	PUNCT
fumecheng-13737	278	2	=	=	SYM
fumecheng-13737	278	3	+	+	CCONJ
fumecheng-13737	278	4	(	(	PUNCT
fumecheng-13737	278	5	45	45	NUM
fumecheng-13737	278	6	)	)	PUNCT
fumecheng-13737	278	7	and	and	CCONJ
fumecheng-13737	278	8	the	the	DET
fumecheng-13737	278	9	approximate	approximate	ADJ
fumecheng-13737	278	10	solution	solution	NOUN
fumecheng-13737	278	11	as	as	ADP
fumecheng-13737	278	12	:	:	SYM
fumecheng-13737	278	13	2	2	NUM
fumecheng-13737	278	14	4	4	NUM
fumecheng-13737	278	15	2	2	NUM
fumecheng-13737	278	16	3	3	NUM
fumecheng-13737	278	17	4	4	NUM
fumecheng-13737	278	18	2	2	NUM
fumecheng-13737	278	19	1	1	NUM
fumecheng-13737	278	20	70	70	NUM
fumecheng-13737	278	21	49	49	NUM
fumecheng-13737	278	22	38	38	NUM
fumecheng-13737	278	23	(	(	PUNCT
fumecheng-13737	278	24	)	)	PUNCT
fumecheng-13737	278	25	cos	cos	PROPN
fumecheng-13737	278	26	.	.	PUNCT
fumecheng-13737	279	1	70	70	NUM
fumecheng-13737	279	2	28	28	NUM
fumecheng-13737	279	3	hfaf	hfaf	VERB
fumecheng-13737	279	4	a	a	DET
fumecheng-13737	279	5	a	a	DET
fumecheng-13737	279	6	u	u	NOUN
fumecheng-13737	279	7	t	t	PROPN
fumecheng-13737	279	8	a	a	DET
fumecheng-13737	279	9	t	t	PROPN
fumecheng-13737	279	10	a	a	DET
fumecheng-13737	279	11			PROPN
fumecheng-13737	279	12			PROPN
fumecheng-13737	279	13			PROPN
fumecheng-13737	279	14			PROPN
fumecheng-13737	279	15			NOUN
fumecheng-13737	279	16	+	+	VERB
fumecheng-13737	279	17	+	+	CCONJ
fumecheng-13737	279	18			PROPN
fumecheng-13737	279	19	=	=	PROPN
fumecheng-13737	279	20			PROPN
fumecheng-13737	279	21	+	+	PROPN
fumecheng-13737	279	22			PROPN
fumecheng-13737	279	23			NOUN
fumecheng-13737	279	24	(	(	PUNCT
fumecheng-13737	279	25	46	46	NUM
fumecheng-13737	279	26	)	)	PUNCT
fumecheng-13737	279	27	this	this	DET
fumecheng-13737	279	28	method	method	NOUN
fumecheng-13737	279	29	performs	perform	VERB
fumecheng-13737	279	30	well	well	ADV
fumecheng-13737	279	31	at	at	ADP
fumecheng-13737	279	32	large	large	ADJ
fumecheng-13737	279	33	amplitudes	amplitude	NOUN
fumecheng-13737	279	34	due	due	ADP
fumecheng-13737	279	35	to	to	ADP
fumecheng-13737	279	36	its	its	PRON
fumecheng-13737	279	37	foundation	foundation	NOUN
fumecheng-13737	279	38	in	in	ADP
fumecheng-13737	279	39	energy	energy	NOUN
fumecheng-13737	279	40	principles	principle	NOUN
fumecheng-13737	279	41	.	.	PUNCT
fumecheng-13737	280	1	its	its	PRON
fumecheng-13737	280	2	energy	energy	NOUN
fumecheng-13737	280	3	-	-	PUNCT
fumecheng-13737	280	4	based	base	VERB
fumecheng-13737	280	5	formulation	formulation	NOUN
fumecheng-13737	280	6	enables	enable	VERB
fumecheng-13737	280	7	more	more	ADV
fumecheng-13737	280	8	accurate	accurate	ADJ
fumecheng-13737	280	9	capture	capture	NOUN
fumecheng-13737	280	10	of	of	ADP
fumecheng-13737	280	11	nonlinear	nonlinear	ADJ
fumecheng-13737	280	12	effects	effect	NOUN
fumecheng-13737	280	13	within	within	ADP
fumecheng-13737	280	14	this	this	DET
fumecheng-13737	280	15	range	range	NOUN
fumecheng-13737	280	16	.	.	PUNCT
fumecheng-13737	281	1	3.4	3.4	NUM
fumecheng-13737	281	2	.	.	PUNCT
fumecheng-13737	281	3	exact	exact	ADJ
fumecheng-13737	281	4	nonlinear	nonlinear	ADJ
fumecheng-13737	281	5	frequency	frequency	NOUN
fumecheng-13737	281	6	to	to	PART
fumecheng-13737	281	7	obtain	obtain	VERB
fumecheng-13737	281	8	the	the	DET
fumecheng-13737	281	9	exact	exact	ADJ
fumecheng-13737	281	10	nonlinear	nonlinear	ADJ
fumecheng-13737	281	11	frequency	frequency	NOUN
fumecheng-13737	281	12	of	of	ADP
fumecheng-13737	281	13	the	the	DET
fumecheng-13737	281	14	stringer	stringer	NOUN
fumecheng-13737	281	15	-	-	PUNCT
fumecheng-13737	281	16	stiffened	stiffen	VERB
fumecheng-13737	281	17	shell	shell	NOUN
fumecheng-13737	281	18	,	,	PUNCT
fumecheng-13737	281	19	the	the	DET
fumecheng-13737	281	20	hamiltonian	hamiltonian	ADJ
fumecheng-13737	281	21	form	form	NOUN
fumecheng-13737	281	22	derived	derive	VERB
fumecheng-13737	281	23	in	in	ADP
fumecheng-13737	281	24	eq	eq	ADP
fumecheng-13737	281	25	.	.	PUNCT
fumecheng-13737	282	1	(	(	PUNCT
fumecheng-13737	282	2	41	41	NUM
fumecheng-13737	282	3	)	)	PUNCT
fumecheng-13737	282	4	is	be	AUX
fumecheng-13737	282	5	employed	employ	VERB
fumecheng-13737	282	6	.	.	PUNCT
fumecheng-13737	283	1	using	use	VERB
fumecheng-13737	283	2	the	the	DET
fumecheng-13737	283	3	initial	initial	ADJ
fumecheng-13737	283	4	conditions	condition	NOUN
fumecheng-13737	283	5	given	give	VERB
fumecheng-13737	283	6	in	in	ADP
fumecheng-13737	283	7	eq	eq	ADP
fumecheng-13737	283	8	.	.	PUNCT
fumecheng-13737	284	1	(	(	PUNCT
fumecheng-13737	284	2	12	12	NUM
fumecheng-13737	284	3	)	)	PUNCT
fumecheng-13737	284	4	,	,	PUNCT
fumecheng-13737	284	5	and	and	CCONJ
fumecheng-13737	284	6	considering	consider	VERB
fumecheng-13737	284	7	that	that	SCONJ
fumecheng-13737	284	8	the	the	DET
fumecheng-13737	284	9	hamiltonian	hamiltonian	NOUN
fumecheng-13737	284	10	remains	remain	VERB
fumecheng-13737	284	11	constant	constant	ADJ
fumecheng-13737	284	12	in	in	ADP
fumecheng-13737	284	13	a	a	DET
fumecheng-13737	284	14	conservative	conservative	ADJ
fumecheng-13737	284	15	system	system	NOUN
fumecheng-13737	284	16	,	,	PUNCT
fumecheng-13737	284	17	the	the	DET
fumecheng-13737	284	18	following	follow	VERB
fumecheng-13737	284	19	relation	relation	NOUN
fumecheng-13737	284	20	is	be	AUX
fumecheng-13737	284	21	obtained	obtain	VERB
fumecheng-13737	284	22	:	:	PUNCT
fumecheng-13737	284	23	2	2	NUM
fumecheng-13737	284	24	2	2	NUM
fumecheng-13737	284	25	2	2	NUM
fumecheng-13737	284	26	2	2	NUM
fumecheng-13737	284	27	4	4	NUM
fumecheng-13737	284	28	6	6	NUM
fumecheng-13737	284	29	2	2	NUM
fumecheng-13737	284	30	4	4	NUM
fumecheng-13737	284	31	6	6	NUM
fumecheng-13737	284	32	1	1	NUM
fumecheng-13737	284	33	2	2	NUM
fumecheng-13737	284	34	3	3	NUM
fumecheng-13737	284	35	4	4	NUM
fumecheng-13737	284	36	2	2	NUM
fumecheng-13737	284	37	3	3	NUM
fumecheng-13737	284	38	4	4	NUM
fumecheng-13737	284	39	1	1	NUM
fumecheng-13737	284	40	1	1	NUM
fumecheng-13737	284	41	1	1	NUM
fumecheng-13737	284	42	1	1	NUM
fumecheng-13737	284	43	1	1	NUM
fumecheng-13737	284	44	1	1	NUM
fumecheng-13737	284	45	1	1	NUM
fumecheng-13737	284	46	1	1	NUM
fumecheng-13737	284	47	.	.	SYM
fumecheng-13737	284	48	2	2	NUM
fumecheng-13737	284	49	2	2	NUM
fumecheng-13737	284	50	2	2	NUM
fumecheng-13737	284	51	4	4	NUM
fumecheng-13737	284	52	6	6	NUM
fumecheng-13737	284	53	2	2	NUM
fumecheng-13737	284	54	4	4	NUM
fumecheng-13737	284	55	6	6	NUM
fumecheng-13737	284	56	du	du	X
fumecheng-13737	284	57	du	du	PROPN
fumecheng-13737	284	58	u	u	PROPN
fumecheng-13737	284	59	u	u	PROPN
fumecheng-13737	284	60	u	u	NOUN
fumecheng-13737	284	61	u	u	NOUN
fumecheng-13737	284	62	a	a	DET
fumecheng-13737	284	63	a	a	DET
fumecheng-13737	284	64	a	a	DET
fumecheng-13737	284	65	dt	dt	NOUN
fumecheng-13737	284	66	dt	dt	NOUN
fumecheng-13737	284	67			PROPN
fumecheng-13737	284	68			PROPN
fumecheng-13737	284	69			PROPN
fumecheng-13737	284	70			PROPN
fumecheng-13737	284	71			PROPN
fumecheng-13737	284	72			PROPN
fumecheng-13737	284	73			PROPN
fumecheng-13737	284	74			NOUN
fumecheng-13737	284	75			NOUN
fumecheng-13737	284	76			NOUN
fumecheng-13737	284	77			NOUN
fumecheng-13737	284	78	+	+	X
fumecheng-13737	285	1	+	+	PUNCT
fumecheng-13737	285	2	+	+	PUNCT
fumecheng-13737	285	3	+	+	PUNCT
fumecheng-13737	285	4	=	=	SYM
fumecheng-13737	286	1	+	+	CCONJ
fumecheng-13737	287	1	+	+	ADJ
fumecheng-13737	287	2			PROPN
fumecheng-13737	288	1			PROPN
fumecheng-13737	289	1			PROPN
fumecheng-13737	289	2			PROPN
fumecheng-13737	290	1			ADJ
fumecheng-13737	290	2			PROPN
fumecheng-13737	290	3			PROPN
fumecheng-13737	290	4			NOUN
fumecheng-13737	290	5	(	(	PUNCT
fumecheng-13737	290	6	47	47	NUM
fumecheng-13737	290	7	)	)	PUNCT
fumecheng-13737	290	8	eq	eq	NOUN
fumecheng-13737	290	9	.	.	PUNCT
fumecheng-13737	291	1	(	(	PUNCT
fumecheng-13737	291	2	47	47	NUM
fumecheng-13737	291	3	)	)	PUNCT
fumecheng-13737	291	4	can	can	AUX
fumecheng-13737	291	5	be	be	AUX
fumecheng-13737	291	6	rewritten	rewrite	VERB
fumecheng-13737	291	7	as	as	SCONJ
fumecheng-13737	291	8	follows	follow	VERB
fumecheng-13737	291	9	:	:	PUNCT
fumecheng-13737	291	10	(	(	PUNCT
fumecheng-13737	291	11	)	)	PUNCT
fumecheng-13737	291	12	(	(	PUNCT
fumecheng-13737	291	13	)	)	PUNCT
fumecheng-13737	291	14	(	(	PUNCT
fumecheng-13737	291	15	)	)	SYM
fumecheng-13737	291	16	2	2	NUM
fumecheng-13737	291	17	2	2	NUM
fumecheng-13737	291	18	4	4	NUM
fumecheng-13737	291	19	4	4	NUM
fumecheng-13737	291	20	6	6	NUM
fumecheng-13737	291	21	6	6	NUM
fumecheng-13737	291	22	2	2	NUM
fumecheng-13737	291	23	2	2	NUM
fumecheng-13737	291	24	3	3	NUM
fumecheng-13737	291	25	4	4	NUM
fumecheng-13737	291	26	2	2	NUM
fumecheng-13737	291	27	1	1	NUM
fumecheng-13737	291	28	1	1	NUM
fumecheng-13737	291	29	1	1	NUM
fumecheng-13737	291	30	2	2	NUM
fumecheng-13737	291	31	3	3	NUM
fumecheng-13737	291	32	.	.	PUNCT
fumecheng-13737	291	33	1	1	NUM
fumecheng-13737	291	34	a	a	DET
fumecheng-13737	291	35	u	u	NOUN
fumecheng-13737	291	36	a	a	DET
fumecheng-13737	291	37	u	u	NOUN
fumecheng-13737	291	38	a	a	DET
fumecheng-13737	291	39	u	u	X
fumecheng-13737	291	40	du	du	PROPN
fumecheng-13737	291	41	dt	dt	X
fumecheng-13737	291	42	u	u	PROPN
fumecheng-13737	291	43			PROPN
fumecheng-13737	291	44			PROPN
fumecheng-13737	291	45			PROPN
fumecheng-13737	291	46			NOUN
fumecheng-13737	291	47	−	−	PROPN
fumecheng-13737	291	48	+	+	CCONJ
fumecheng-13737	291	49	−	−	PROPN
fumecheng-13737	291	50	+	+	CCONJ
fumecheng-13737	291	51	−	−	PROPN
fumecheng-13737	292	1			NOUN
fumecheng-13737	292	2			NOUN
fumecheng-13737	292	3	=	=	SYM
fumecheng-13737	292	4			PROPN
fumecheng-13737	292	5			PROPN
fumecheng-13737	293	1	+	+	ADJ
fumecheng-13737	293	2			PROPN
fumecheng-13737	293	3			NOUN
fumecheng-13737	293	4	(	(	PUNCT
fumecheng-13737	293	5	48	48	NUM
fumecheng-13737	293	6	)	)	PUNCT
fumecheng-13737	293	7	solving	solve	VERB
fumecheng-13737	293	8	eq	eq	NOUN
fumecheng-13737	293	9	.	.	PUNCT
fumecheng-13737	294	1	(	(	PUNCT
fumecheng-13737	294	2	48	48	NUM
fumecheng-13737	294	3	)	)	PUNCT
fumecheng-13737	294	4	for	for	ADP
fumecheng-13737	294	5	dt	dt	PROPN
fumecheng-13737	294	6	,	,	PUNCT
fumecheng-13737	294	7	we	we	PRON
fumecheng-13737	294	8	obtain	obtain	VERB
fumecheng-13737	294	9	:	:	PUNCT
fumecheng-13737	294	10	(	(	PUNCT
fumecheng-13737	294	11	)	)	PUNCT
fumecheng-13737	294	12	(	(	PUNCT
fumecheng-13737	294	13	)	)	PUNCT
fumecheng-13737	294	14	(	(	PUNCT
fumecheng-13737	294	15	)	)	PUNCT
fumecheng-13737	295	1	2	2	NUM
fumecheng-13737	295	2	1	1	NUM
fumecheng-13737	295	3	2	2	NUM
fumecheng-13737	295	4	2	2	NUM
fumecheng-13737	295	5	4	4	NUM
fumecheng-13737	295	6	4	4	NUM
fumecheng-13737	295	7	6	6	NUM
fumecheng-13737	295	8	6	6	NUM
fumecheng-13737	295	9	2	2	NUM
fumecheng-13737	295	10	3	3	NUM
fumecheng-13737	295	11	4	4	NUM
fumecheng-13737	295	12	1	1	NUM
fumecheng-13737	295	13	.	.	PUNCT
fumecheng-13737	295	14	1	1	NUM
fumecheng-13737	295	15	1	1	NUM
fumecheng-13737	295	16	2	2	NUM
fumecheng-13737	295	17	3	3	NUM
fumecheng-13737	295	18	u	u	NOUN
fumecheng-13737	295	19	dt	dt	X
fumecheng-13737	295	20	du	du	PROPN
fumecheng-13737	295	21	a	a	DET
fumecheng-13737	295	22	u	u	NOUN
fumecheng-13737	295	23	a	a	DET
fumecheng-13737	295	24	u	u	NOUN
fumecheng-13737	295	25	a	a	DET
fumecheng-13737	295	26	u	u	NOUN
fumecheng-13737	295	27			PROPN
fumecheng-13737	295	28			PROPN
fumecheng-13737	295	29			PROPN
fumecheng-13737	295	30			PROPN
fumecheng-13737	295	31	+	+	CCONJ
fumecheng-13737	295	32	=	=	PUNCT
fumecheng-13737	295	33			PROPN
fumecheng-13737	295	34	−	−	PROPN
fumecheng-13737	296	1	+	+	CCONJ
fumecheng-13737	296	2	−	−	PROPN
fumecheng-13737	297	1	+	+	CCONJ
fumecheng-13737	297	2	−	−	PROPN
fumecheng-13737	297	3	(	(	PUNCT
fumecheng-13737	297	4	49	49	NUM
fumecheng-13737	297	5	)	)	PUNCT
fumecheng-13737	297	6	since	since	SCONJ
fumecheng-13737	297	7	the	the	DET
fumecheng-13737	297	8	period	period	NOUN
fumecheng-13737	297	9	of	of	ADP
fumecheng-13737	297	10	the	the	DET
fumecheng-13737	297	11	oscillator	oscillator	NOUN
fumecheng-13737	297	12	is	be	AUX
fumecheng-13737	297	13	four	four	NUM
fumecheng-13737	297	14	times	time	NOUN
fumecheng-13737	297	15	the	the	DET
fumecheng-13737	297	16	duration	duration	NOUN
fumecheng-13737	297	17	required	require	VERB
fumecheng-13737	297	18	to	to	PART
fumecheng-13737	297	19	move	move	VERB
fumecheng-13737	297	20	from	from	ADP
fumecheng-13737	297	21	0	0	NUM
fumecheng-13737	297	22	to	to	ADP
fumecheng-13737	297	23	a	a	PRON
fumecheng-13737	297	24	,	,	PUNCT
fumecheng-13737	297	25	we	we	PRON
fumecheng-13737	297	26	have	have	VERB
fumecheng-13737	297	27	798	798	NUM
fumecheng-13737	297	28	c	c	NOUN
fumecheng-13737	297	29	-	-	PUNCT
fumecheng-13737	297	30	h.	h.	NOUN
fumecheng-13737	297	31	he	he	PROPN
fumecheng-13737	297	32	,	,	PUNCT
fumecheng-13737	297	33	m.	m.	NOUN
fumecheng-13737	297	34	mohammadian	mohammadian	NOUN
fumecheng-13737	297	35	(	(	PUNCT
fumecheng-13737	297	36	)	)	PUNCT
fumecheng-13737	297	37	(	(	PUNCT
fumecheng-13737	297	38	)	)	PUNCT
fumecheng-13737	297	39	(	(	PUNCT
fumecheng-13737	297	40	)	)	PUNCT
fumecheng-13737	298	1	2	2	NUM
fumecheng-13737	298	2	1	1	NUM
fumecheng-13737	298	3	2	2	NUM
fumecheng-13737	298	4	2	2	NUM
fumecheng-13737	298	5	4	4	NUM
fumecheng-13737	298	6	4	4	NUM
fumecheng-13737	298	7	6	6	NUM
fumecheng-13737	298	8	60	60	NUM
fumecheng-13737	298	9	2	2	NUM
fumecheng-13737	298	10	3	3	NUM
fumecheng-13737	298	11	4	4	NUM
fumecheng-13737	298	12	1	1	NUM
fumecheng-13737	298	13	4	4	NUM
fumecheng-13737	298	14	.	.	PUNCT
fumecheng-13737	298	15	1	1	NUM
fumecheng-13737	298	16	1	1	NUM
fumecheng-13737	298	17	2	2	NUM
fumecheng-13737	298	18	3	3	NUM
fumecheng-13737	298	19	a	a	DET
fumecheng-13737	298	20	exact	exact	NOUN
fumecheng-13737	298	21	u	u	X
fumecheng-13737	299	1	t	t	X
fumecheng-13737	299	2	du	du	PROPN
fumecheng-13737	299	3	a	a	DET
fumecheng-13737	299	4	u	u	NOUN
fumecheng-13737	299	5	a	a	DET
fumecheng-13737	299	6	u	u	NOUN
fumecheng-13737	299	7	a	a	DET
fumecheng-13737	299	8	u	u	NOUN
fumecheng-13737	299	9			PROPN
fumecheng-13737	299	10			PROPN
fumecheng-13737	299	11			PROPN
fumecheng-13737	299	12			PROPN
fumecheng-13737	299	13	+	+	NUM
fumecheng-13737	299	14	=	=	SYM
fumecheng-13737	300	1	−	−	PROPN
fumecheng-13737	301	1	+	+	CCONJ
fumecheng-13737	301	2	−	−	PROPN
fumecheng-13737	302	1	+	+	CCONJ
fumecheng-13737	302	2	−	−	NOUN
fumecheng-13737	302	3			X
fumecheng-13737	302	4	(	(	PUNCT
fumecheng-13737	302	5	50	50	NUM
fumecheng-13737	302	6	)	)	PUNCT
fumecheng-13737	302	7	therefore	therefore	ADV
fumecheng-13737	302	8	,	,	PUNCT
fumecheng-13737	302	9	the	the	DET
fumecheng-13737	302	10	exact	exact	ADJ
fumecheng-13737	302	11	nonlinear	nonlinear	ADJ
fumecheng-13737	302	12	frequency	frequency	NOUN
fumecheng-13737	302	13	of	of	ADP
fumecheng-13737	302	14	the	the	DET
fumecheng-13737	302	15	stringer	stringer	NOUN
fumecheng-13737	302	16	-	-	PUNCT
fumecheng-13737	302	17	stiffened	stiffen	VERB
fumecheng-13737	302	18	shell	shell	NOUN
fumecheng-13737	302	19	is	be	AUX
fumecheng-13737	302	20	obtained	obtain	VERB
fumecheng-13737	302	21	as	as	SCONJ
fumecheng-13737	302	22	follows	follow	VERB
fumecheng-13737	302	23	:	:	PUNCT
fumecheng-13737	302	24	(	(	PUNCT
fumecheng-13737	302	25	)	)	PUNCT
fumecheng-13737	302	26	(	(	PUNCT
fumecheng-13737	302	27	)	)	PUNCT
fumecheng-13737	302	28	(	(	PUNCT
fumecheng-13737	302	29	)	)	PUNCT
fumecheng-13737	303	1	2	2	NUM
fumecheng-13737	303	2	1	1	NUM
fumecheng-13737	303	3	2	2	NUM
fumecheng-13737	303	4	2	2	NUM
fumecheng-13737	303	5	4	4	NUM
fumecheng-13737	303	6	4	4	NUM
fumecheng-13737	303	7	6	6	NUM
fumecheng-13737	303	8	60	60	NUM
fumecheng-13737	303	9	2	2	NUM
fumecheng-13737	303	10	3	3	NUM
fumecheng-13737	303	11	4	4	NUM
fumecheng-13737	303	12	2	2	NUM
fumecheng-13737	303	13	.	.	PUNCT
fumecheng-13737	303	14	1	1	NUM
fumecheng-13737	303	15	4	4	NUM
fumecheng-13737	303	16	1	1	NUM
fumecheng-13737	303	17	1	1	NUM
fumecheng-13737	303	18	2	2	NUM
fumecheng-13737	303	19	3	3	NUM
fumecheng-13737	303	20	exact	exact	NOUN
fumecheng-13737	303	21	a	a	DET
fumecheng-13737	303	22	u	u	NOUN
fumecheng-13737	303	23	du	du	PROPN
fumecheng-13737	303	24	a	a	DET
fumecheng-13737	303	25	u	u	NOUN
fumecheng-13737	303	26	a	a	DET
fumecheng-13737	303	27	u	u	NOUN
fumecheng-13737	303	28	a	a	DET
fumecheng-13737	303	29	u	u	NOUN
fumecheng-13737	303	30			PROPN
fumecheng-13737	303	31			PROPN
fumecheng-13737	303	32			PROPN
fumecheng-13737	303	33			PROPN
fumecheng-13737	303	34			PROPN
fumecheng-13737	303	35			NOUN
fumecheng-13737	303	36	=	=	PUNCT
fumecheng-13737	304	1	+	+	CCONJ
fumecheng-13737	304	2	−	−	PROPN
fumecheng-13737	305	1	+	+	CCONJ
fumecheng-13737	305	2	−	−	PROPN
fumecheng-13737	306	1	+	+	CCONJ
fumecheng-13737	306	2	−	−	NOUN
fumecheng-13737	306	3			X
fumecheng-13737	306	4	(	(	PUNCT
fumecheng-13737	306	5	51	51	NUM
fumecheng-13737	306	6	)	)	PUNCT
fumecheng-13737	306	7	this	this	DET
fumecheng-13737	306	8	integral	integral	ADJ
fumecheng-13737	306	9	typically	typically	ADV
fumecheng-13737	306	10	requires	require	VERB
fumecheng-13737	306	11	numerical	numerical	ADJ
fumecheng-13737	306	12	evaluation	evaluation	NOUN
fumecheng-13737	306	13	or	or	CCONJ
fumecheng-13737	306	14	the	the	DET
fumecheng-13737	306	15	use	use	NOUN
fumecheng-13737	306	16	of	of	ADP
fumecheng-13737	306	17	elliptic	elliptic	ADJ
fumecheng-13737	306	18	functions	function	NOUN
fumecheng-13737	306	19	,	,	PUNCT
fumecheng-13737	306	20	serving	serve	VERB
fumecheng-13737	306	21	as	as	ADP
fumecheng-13737	306	22	a	a	DET
fumecheng-13737	306	23	benchmark	benchmark	NOUN
fumecheng-13737	306	24	for	for	ADP
fumecheng-13737	306	25	approximate	approximate	ADJ
fumecheng-13737	306	26	methods	method	NOUN
fumecheng-13737	306	27	.	.	PUNCT
fumecheng-13737	307	1	4	4	X
fumecheng-13737	307	2	.	.	NOUN
fumecheng-13737	307	3	results	result	NOUN
fumecheng-13737	307	4	and	and	CCONJ
fumecheng-13737	307	5	discussion	discussion	NOUN
fumecheng-13737	307	6	this	this	DET
fumecheng-13737	307	7	section	section	NOUN
fumecheng-13737	307	8	evaluates	evaluate	VERB
fumecheng-13737	307	9	the	the	DET
fumecheng-13737	307	10	nonlinear	nonlinear	ADJ
fumecheng-13737	307	11	frequencies	frequency	NOUN
fumecheng-13737	307	12	of	of	ADP
fumecheng-13737	307	13	a	a	DET
fumecheng-13737	307	14	stringer	stringer	NOUN
fumecheng-13737	307	15	-	-	PUNCT
fumecheng-13737	307	16	stiffened	stiffen	VERB
fumecheng-13737	307	17	cylindrical	cylindrical	ADJ
fumecheng-13737	307	18	shell	shell	NOUN
fumecheng-13737	307	19	using	use	VERB
fumecheng-13737	307	20	the	the	DET
fumecheng-13737	307	21	proposed	propose	VERB
fumecheng-13737	307	22	methods	method	NOUN
fumecheng-13737	307	23	.	.	PUNCT
fumecheng-13737	308	1	the	the	DET
fumecheng-13737	308	2	results	result	NOUN
fumecheng-13737	308	3	are	be	AUX
fumecheng-13737	308	4	presented	present	VERB
fumecheng-13737	308	5	for	for	ADP
fumecheng-13737	308	6	ss	ss	NOUN
fumecheng-13737	308	7	bcs	bc	NOUN
fumecheng-13737	308	8	and	and	CCONJ
fumecheng-13737	308	9	are	be	AUX
fumecheng-13737	308	10	validated	validate	VERB
fumecheng-13737	308	11	through	through	ADP
fumecheng-13737	308	12	comparisons	comparison	NOUN
fumecheng-13737	308	13	with	with	ADP
fumecheng-13737	308	14	both	both	CCONJ
fumecheng-13737	308	15	exact	exact	ADJ
fumecheng-13737	308	16	and	and	CCONJ
fumecheng-13737	308	17	numerical	numerical	ADJ
fumecheng-13737	308	18	solutions	solution	NOUN
fumecheng-13737	308	19	.	.	PUNCT
fumecheng-13737	309	1	tables	table	NOUN
fumecheng-13737	309	2	1	1	NUM
fumecheng-13737	309	3	-	-	SYM
fumecheng-13737	309	4	3	3	NUM
fumecheng-13737	309	5	report	report	NOUN
fumecheng-13737	309	6	the	the	DET
fumecheng-13737	309	7	nonlinear	nonlinear	ADJ
fumecheng-13737	309	8	frequencies	frequency	NOUN
fumecheng-13737	309	9	and	and	CCONJ
fumecheng-13737	309	10	relative	relative	ADJ
fumecheng-13737	309	11	errors	error	NOUN
fumecheng-13737	309	12	for	for	ADP
fumecheng-13737	309	13	non	non	ADJ
fumecheng-13737	309	14	-	-	ADJ
fumecheng-13737	309	15	dimensional	dimensional	ADJ
fumecheng-13737	309	16	amplitudes	amplitude	NOUN
fumecheng-13737	309	17	a	a	DET
fumecheng-13737	309	18	ranging	ranging	NOUN
fumecheng-13737	309	19	from	from	ADP
fumecheng-13737	309	20	0.01	0.01	NUM
fumecheng-13737	309	21	to	to	ADP
fumecheng-13737	309	22	3	3	NUM
fumecheng-13737	309	23	.	.	PUNCT
fumecheng-13737	310	1	the	the	DET
fumecheng-13737	310	2	parameter	parameter	NOUN
fumecheng-13737	310	3	sets	set	NOUN
fumecheng-13737	310	4	are	be	AUX
fumecheng-13737	310	5	as	as	SCONJ
fumecheng-13737	310	6	follows	follow	VERB
fumecheng-13737	310	7	:	:	PUNCT
fumecheng-13737	310	8	table	table	NOUN
fumecheng-13737	310	9	1	1	NUM
fumecheng-13737	310	10	(	(	PUNCT
fumecheng-13737	310	11	case1	case1	PROPN
fumecheng-13737	310	12	:	:	PUNCT
fumecheng-13737	310	13	β1	β1	PROPN
fumecheng-13737	310	14	=	=	SYM
fumecheng-13737	310	15	0.5	0.5	NUM
fumecheng-13737	310	16	,	,	PUNCT
fumecheng-13737	310	17	β2	β2	NOUN
fumecheng-13737	310	18	=	=	NOUN
fumecheng-13737	310	19	2	2	NUM
fumecheng-13737	310	20	,	,	PUNCT
fumecheng-13737	310	21	β3	β3	ADJ
fumecheng-13737	310	22	=	=	NUM
fumecheng-13737	310	23	0.2	0.2	NUM
fumecheng-13737	310	24	,	,	PUNCT
fumecheng-13737	310	25	β4	β4	PROPN
fumecheng-13737	310	26	=	=	NOUN
fumecheng-13737	310	27	0.1	0.1	NUM
fumecheng-13737	310	28	)	)	PUNCT
fumecheng-13737	310	29	;	;	PUNCT
fumecheng-13737	310	30	table	table	NOUN
fumecheng-13737	310	31	2	2	NUM
fumecheng-13737	310	32	(	(	PUNCT
fumecheng-13737	310	33	case	case	NOUN
fumecheng-13737	310	34	2	2	NUM
fumecheng-13737	310	35	:	:	PUNCT
fumecheng-13737	310	36	β1	β1	NOUN
fumecheng-13737	310	37	=	=	NOUN
fumecheng-13737	310	38	0.1	0.1	NUM
fumecheng-13737	310	39	,	,	PUNCT
fumecheng-13737	310	40	β2	β2	NOUN
fumecheng-13737	310	41	=	=	NOUN
fumecheng-13737	310	42	1	1	NUM
fumecheng-13737	310	43	,	,	PUNCT
fumecheng-13737	310	44	β3	β3	VERB
fumecheng-13737	310	45	=	=	SYM
fumecheng-13737	310	46	0.5	0.5	NUM
fumecheng-13737	310	47	,	,	PUNCT
fumecheng-13737	310	48	β4	β4	PROPN
fumecheng-13737	310	49	=	=	PUNCT
fumecheng-13737	310	50	0.2	0.2	NUM
fumecheng-13737	310	51	)	)	PUNCT
fumecheng-13737	310	52	;	;	PUNCT
fumecheng-13737	310	53	and	and	CCONJ
fumecheng-13737	310	54	table	table	NOUN
fumecheng-13737	310	55	3	3	NUM
fumecheng-13737	310	56	(	(	PUNCT
fumecheng-13737	310	57	case	case	NOUN
fumecheng-13737	310	58	3	3	NUM
fumecheng-13737	310	59	:	:	PUNCT
fumecheng-13737	310	60	β1	β1	PROPN
fumecheng-13737	310	61	=	=	SYM
fumecheng-13737	310	62	0.9	0.9	NUM
fumecheng-13737	310	63	,	,	PUNCT
fumecheng-13737	310	64	β2	β2	NOUN
fumecheng-13737	310	65	=	=	NOUN
fumecheng-13737	310	66	1.5	1.5	NUM
fumecheng-13737	310	67	,	,	PUNCT
fumecheng-13737	310	68	β3	β3	VERB
fumecheng-13737	310	69	=	=	SYM
fumecheng-13737	310	70	2.5	2.5	NUM
fumecheng-13737	310	71	,	,	PUNCT
fumecheng-13737	310	72	β4	β4	PROPN
fumecheng-13737	310	73	=	=	PROPN
fumecheng-13737	310	74	3.5	3.5	NUM
fumecheng-13737	310	75	)	)	PUNCT
fumecheng-13737	310	76	,	,	PUNCT
fumecheng-13737	310	77	reflecting	reflect	VERB
fumecheng-13737	310	78	increasing	increase	VERB
fumecheng-13737	310	79	degrees	degree	NOUN
fumecheng-13737	310	80	of	of	ADP
fumecheng-13737	310	81	nonlinearity	nonlinearity	NOUN
fumecheng-13737	310	82	.	.	PUNCT
fumecheng-13737	311	1	the	the	DET
fumecheng-13737	311	2	results	result	NOUN
fumecheng-13737	311	3	are	be	AUX
fumecheng-13737	311	4	compared	compare	VERB
fumecheng-13737	311	5	with	with	ADP
fumecheng-13737	311	6	the	the	DET
fumecheng-13737	311	7	exact	exact	ADJ
fumecheng-13737	311	8	solutions	solution	NOUN
fumecheng-13737	311	9	and	and	CCONJ
fumecheng-13737	311	10	with	with	ADP
fumecheng-13737	311	11	those	those	PRON
fumecheng-13737	311	12	reported	report	VERB
fumecheng-13737	311	13	in	in	ADP
fumecheng-13737	311	14	[	[	X
fumecheng-13737	311	15	40	40	NUM
fumecheng-13737	311	16	]	]	PUNCT
fumecheng-13737	311	17	using	use	VERB
fumecheng-13737	311	18	the	the	DET
fumecheng-13737	311	19	hpm	hpm	NOUN
fumecheng-13737	311	20	.	.	PUNCT
fumecheng-13737	312	1	to	to	PART
fumecheng-13737	312	2	facilitate	facilitate	VERB
fumecheng-13737	312	3	clearer	clear	ADJ
fumecheng-13737	312	4	comparison	comparison	NOUN
fumecheng-13737	312	5	,	,	PUNCT
fumecheng-13737	312	6	the	the	DET
fumecheng-13737	312	7	relative	relative	ADJ
fumecheng-13737	312	8	errors	error	NOUN
fumecheng-13737	312	9	reported	report	VERB
fumecheng-13737	312	10	in	in	ADP
fumecheng-13737	312	11	tables	table	NOUN
fumecheng-13737	312	12	1	1	NUM
fumecheng-13737	312	13	-	-	SYM
fumecheng-13737	312	14	3	3	NUM
fumecheng-13737	312	15	are	be	AUX
fumecheng-13737	312	16	also	also	ADV
fumecheng-13737	312	17	illustrated	illustrate	VERB
fumecheng-13737	312	18	in	in	ADP
fumecheng-13737	312	19	fig	fig	NOUN
fumecheng-13737	312	20	.	.	PUNCT
fumecheng-13737	313	1	2	2	NUM
fumecheng-13737	313	2	as	as	ADP
fumecheng-13737	313	3	a	a	DET
fumecheng-13737	313	4	function	function	NOUN
fumecheng-13737	313	5	of	of	ADP
fumecheng-13737	313	6	amplitude	amplitude	NOUN
fumecheng-13737	313	7	.	.	PUNCT
fumecheng-13737	314	1	it	it	PRON
fumecheng-13737	314	2	can	can	AUX
fumecheng-13737	314	3	be	be	AUX
fumecheng-13737	314	4	observed	observe	VERB
fumecheng-13737	314	5	that	that	SCONJ
fumecheng-13737	314	6	for	for	ADP
fumecheng-13737	314	7	small	small	ADJ
fumecheng-13737	314	8	amplitudes	amplitude	NOUN
fumecheng-13737	314	9	(	(	PUNCT
fumecheng-13737	314	10	a	a	DET
fumecheng-13737	314	11	≤	≤	NUM
fumecheng-13737	314	12	0.2	0.2	NUM
fumecheng-13737	314	13	)	)	PUNCT
fumecheng-13737	314	14	,	,	PUNCT
fumecheng-13737	314	15	all	all	DET
fumecheng-13737	314	16	methods	method	NOUN
fumecheng-13737	314	17	exhibit	exhibit	VERB
fumecheng-13737	314	18	high	high	ADJ
fumecheng-13737	314	19	accuracy	accuracy	NOUN
fumecheng-13737	314	20	,	,	PUNCT
fumecheng-13737	314	21	with	with	ADP
fumecheng-13737	314	22	errors	error	NOUN
fumecheng-13737	314	23	below	below	ADP
fumecheng-13737	314	24	0.1	0.1	NUM
fumecheng-13737	314	25	%	%	NOUN
fumecheng-13737	314	26	across	across	ADP
fumecheng-13737	314	27	all	all	DET
fumecheng-13737	314	28	parameter	parameter	NOUN
fumecheng-13737	314	29	sets	set	NOUN
fumecheng-13737	314	30	.	.	PUNCT
fumecheng-13737	315	1	this	this	DET
fumecheng-13737	315	2	behavior	behavior	NOUN
fumecheng-13737	315	3	is	be	AUX
fumecheng-13737	315	4	expected	expect	VERB
fumecheng-13737	315	5	,	,	PUNCT
fumecheng-13737	315	6	as	as	ADP
fumecheng-13737	315	7	the	the	DET
fumecheng-13737	315	8	cubic	cubic	ADJ
fumecheng-13737	315	9	and	and	CCONJ
fumecheng-13737	315	10	quintic	quintic	ADJ
fumecheng-13737	315	11	terms	term	NOUN
fumecheng-13737	315	12	in	in	ADP
fumecheng-13737	315	13	eq	eq	ADP
fumecheng-13737	315	14	.	.	PUNCT
fumecheng-13737	316	1	(	(	PUNCT
fumecheng-13737	316	2	8)	8)	NUM
fumecheng-13737	316	3	contribute	contribute	VERB
fumecheng-13737	316	4	minimally	minimally	ADV
fumecheng-13737	316	5	at	at	ADP
fumecheng-13737	316	6	low	low	ADJ
fumecheng-13737	316	7	a	a	PRON
fumecheng-13737	316	8	,	,	PUNCT
fumecheng-13737	316	9	making	make	VERB
fumecheng-13737	316	10	the	the	DET
fumecheng-13737	316	11	system	system	NOUN
fumecheng-13737	316	12	nearly	nearly	ADV
fumecheng-13737	316	13	linear	linear	ADJ
fumecheng-13737	316	14	.	.	PUNCT
fumecheng-13737	317	1	the	the	DET
fumecheng-13737	317	2	results	result	NOUN
fumecheng-13737	317	3	of	of	ADP
fumecheng-13737	317	4	alpf	alpf	NOUN
fumecheng-13737	317	5	and	and	CCONJ
fumecheng-13737	317	6	semf	semf	NOUN
fumecheng-13737	317	7	methods	method	NOUN
fumecheng-13737	317	8	are	be	AUX
fumecheng-13737	317	9	identical	identical	ADJ
fumecheng-13737	317	10	to	to	ADP
fumecheng-13737	317	11	the	the	DET
fumecheng-13737	317	12	exact	exact	ADJ
fumecheng-13737	317	13	solution	solution	NOUN
fumecheng-13737	317	14	for	for	ADP
fumecheng-13737	317	15	a	a	DET
fumecheng-13737	317	16	≤	≤	NUM
fumecheng-13737	317	17	0.1	0.1	NUM
fumecheng-13737	317	18	,	,	PUNCT
fumecheng-13737	317	19	while	while	SCONJ
fumecheng-13737	317	20	the	the	DET
fumecheng-13737	317	21	hamiltonian	hamiltonian	NOUN
fumecheng-13737	317	22	-	-	PUNCT
fumecheng-13737	317	23	based	base	VERB
fumecheng-13737	317	24	method	method	NOUN
fumecheng-13737	317	25	shows	show	VERB
fumecheng-13737	317	26	slight	slight	ADJ
fumecheng-13737	317	27	deviations	deviation	NOUN
fumecheng-13737	317	28	(	(	PUNCT
fumecheng-13737	317	29	e.g.	e.g.	ADV
fumecheng-13737	317	30	,	,	PUNCT
fumecheng-13737	317	31	0.09	0.09	NUM
fumecheng-13737	317	32	%	%	NOUN
fumecheng-13737	317	33	error	error	NOUN
fumecheng-13737	317	34	at	at	ADP
fumecheng-13737	317	35	a	a	DET
fumecheng-13737	317	36	=	=	SYM
fumecheng-13737	317	37	0.2	0.2	NUM
fumecheng-13737	317	38	in	in	ADP
fumecheng-13737	317	39	table	table	NOUN
fumecheng-13737	317	40	1	1	NUM
fumecheng-13737	317	41	)	)	PUNCT
fumecheng-13737	317	42	,	,	PUNCT
fumecheng-13737	317	43	likely	likely	ADJ
fumecheng-13737	317	44	due	due	ADP
fumecheng-13737	317	45	to	to	ADP
fumecheng-13737	317	46	its	its	PRON
fumecheng-13737	317	47	sensitivity	sensitivity	NOUN
fumecheng-13737	317	48	to	to	ADP
fumecheng-13737	317	49	higher	high	ADJ
fumecheng-13737	317	50	-	-	PUNCT
fumecheng-13737	317	51	order	order	NOUN
fumecheng-13737	317	52	nonlinear	nonlinear	ADJ
fumecheng-13737	317	53	terms	term	NOUN
fumecheng-13737	317	54	.	.	PUNCT
fumecheng-13737	318	1	at	at	ADP
fumecheng-13737	318	2	large	large	ADJ
fumecheng-13737	318	3	amplitudes	amplitude	NOUN
fumecheng-13737	318	4	(	(	PUNCT
fumecheng-13737	318	5	a	a	DET
fumecheng-13737	318	6	≥	≥	NOUN
fumecheng-13737	318	7	1	1	NUM
fumecheng-13737	318	8	)	)	PUNCT
fumecheng-13737	318	9	,	,	PUNCT
fumecheng-13737	318	10	the	the	DET
fumecheng-13737	318	11	errors	error	NOUN
fumecheng-13737	318	12	increase	increase	VERB
fumecheng-13737	318	13	,	,	PUNCT
fumecheng-13737	318	14	particularly	particularly	ADV
fumecheng-13737	318	15	for	for	ADP
fumecheng-13737	318	16	he	he	PRON
fumecheng-13737	318	17	's	's	PART
fumecheng-13737	318	18	method	method	NOUN
fumecheng-13737	318	19	,	,	PUNCT
fumecheng-13737	318	20	which	which	PRON
fumecheng-13737	318	21	reaches	reach	VERB
fumecheng-13737	318	22	10.26	10.26	NUM
fumecheng-13737	318	23	%	%	NOUN
fumecheng-13737	318	24	at	at	ADP
fumecheng-13737	318	25	a	a	DET
fumecheng-13737	318	26	=	=	SYM
fumecheng-13737	318	27	3	3	NUM
fumecheng-13737	318	28	in	in	ADP
fumecheng-13737	318	29	table	table	NOUN
fumecheng-13737	318	30	3	3	NUM
fumecheng-13737	318	31	.	.	PUNCT
fumecheng-13737	319	1	in	in	ADP
fumecheng-13737	319	2	contrast	contrast	NOUN
fumecheng-13737	319	3	,	,	PUNCT
fumecheng-13737	319	4	the	the	DET
fumecheng-13737	319	5	alpf	alpf	NOUN
fumecheng-13737	319	6	and	and	CCONJ
fumecheng-13737	319	7	semf	semf	PROPN
fumecheng-13737	319	8	show	show	VERB
fumecheng-13737	319	9	improved	improved	ADJ
fumecheng-13737	319	10	performance	performance	NOUN
fumecheng-13737	319	11	,	,	PUNCT
fumecheng-13737	319	12	with	with	ADP
fumecheng-13737	319	13	errors	error	NOUN
fumecheng-13737	319	14	up	up	ADP
fumecheng-13737	319	15	to	to	PART
fumecheng-13737	319	16	5.89	5.89	NUM
fumecheng-13737	319	17	%	%	NOUN
fumecheng-13737	319	18	at	at	ADP
fumecheng-13737	319	19	a	a	DET
fumecheng-13737	319	20	=	=	SYM
fumecheng-13737	319	21	3	3	NUM
fumecheng-13737	319	22	,	,	PUNCT
fumecheng-13737	319	23	benefiting	benefit	VERB
fumecheng-13737	319	24	from	from	ADP
fumecheng-13737	319	25	their	their	PRON
fumecheng-13737	319	26	error	error	NOUN
fumecheng-13737	319	27	minimization	minimization	NOUN
fumecheng-13737	319	28	strategies	strategy	NOUN
fumecheng-13737	319	29	.	.	PUNCT
fumecheng-13737	320	1	the	the	DET
fumecheng-13737	320	2	hamiltonian	hamiltonian	ADJ
fumecheng-13737	320	3	method	method	NOUN
fumecheng-13737	320	4	consistently	consistently	ADV
fumecheng-13737	320	5	outperforms	outperform	VERB
fumecheng-13737	320	6	the	the	DET
fumecheng-13737	320	7	others	other	NOUN
fumecheng-13737	320	8	,	,	PUNCT
fumecheng-13737	320	9	maintaining	maintain	VERB
fumecheng-13737	320	10	errors	error	NOUN
fumecheng-13737	320	11	below	below	ADP
fumecheng-13737	320	12	3.92	3.92	NUM
fumecheng-13737	320	13	%	%	NOUN
fumecheng-13737	320	14	at	at	ADP
fumecheng-13737	320	15	a	a	DET
fumecheng-13737	320	16	=	=	ADJ
fumecheng-13737	320	17	3	3	NUM
fumecheng-13737	320	18	,	,	PUNCT
fumecheng-13737	320	19	as	as	SCONJ
fumecheng-13737	320	20	its	its	PRON
fumecheng-13737	320	21	energy	energy	NOUN
fumecheng-13737	320	22	-	-	PUNCT
fumecheng-13737	320	23	based	base	VERB
fumecheng-13737	320	24	framework	framework	NOUN
fumecheng-13737	320	25	more	more	ADV
fumecheng-13737	320	26	effectively	effectively	ADV
fumecheng-13737	320	27	captures	capture	VERB
fumecheng-13737	320	28	the	the	DET
fumecheng-13737	320	29	nonlinear	nonlinear	ADJ
fumecheng-13737	320	30	dynamic	dynamic	ADJ
fumecheng-13737	320	31	behavior	behavior	NOUN
fumecheng-13737	320	32	.	.	PUNCT
fumecheng-13737	321	1	it	it	PRON
fumecheng-13737	321	2	is	be	AUX
fumecheng-13737	321	3	noteworthy	noteworthy	ADJ
fumecheng-13737	321	4	that	that	SCONJ
fumecheng-13737	321	5	both	both	CCONJ
fumecheng-13737	321	6	the	the	DET
fumecheng-13737	321	7	alpf	alpf	NOUN
fumecheng-13737	321	8	and	and	CCONJ
fumecheng-13737	321	9	semf	semf	PROPN
fumecheng-13737	321	10	methods	method	NOUN
fumecheng-13737	321	11	accurately	accurately	ADV
fumecheng-13737	321	12	predict	predict	VERB
fumecheng-13737	321	13	the	the	DET
fumecheng-13737	321	14	frequencies	frequency	NOUN
fumecheng-13737	321	15	obtained	obtain	VERB
fumecheng-13737	321	16	by	by	ADP
fumecheng-13737	321	17	the	the	DET
fumecheng-13737	321	18	hpm	hpm	NOUN
fumecheng-13737	321	19	,	,	PUNCT
fumecheng-13737	321	20	while	while	SCONJ
fumecheng-13737	321	21	offering	offer	VERB
fumecheng-13737	321	22	a	a	DET
fumecheng-13737	321	23	simpler	simple	ADJ
fumecheng-13737	321	24	computational	computational	ADJ
fumecheng-13737	321	25	procedure	procedure	NOUN
fumecheng-13737	321	26	.	.	PUNCT
fumecheng-13737	322	1	furthermore	furthermore	ADV
fumecheng-13737	322	2	,	,	PUNCT
fumecheng-13737	322	3	the	the	DET
fumecheng-13737	322	4	computational	computational	ADJ
fumecheng-13737	322	5	time	time	NOUN
fumecheng-13737	322	6	required	require	VERB
fumecheng-13737	322	7	to	to	PART
fumecheng-13737	322	8	evaluate	evaluate	VERB
fumecheng-13737	322	9	the	the	DET
fumecheng-13737	322	10	frequency	frequency	NOUN
fumecheng-13737	322	11	using	use	VERB
fumecheng-13737	322	12	the	the	DET
fumecheng-13737	322	13	proposed	propose	VERB
fumecheng-13737	322	14	methods	method	NOUN
fumecheng-13737	322	15	is	be	AUX
fumecheng-13737	322	16	minimal	minimal	ADJ
fumecheng-13737	322	17	,	,	PUNCT
fumecheng-13737	322	18	demonstrating	demonstrate	VERB
fumecheng-13737	322	19	their	their	PRON
fumecheng-13737	322	20	high	high	ADJ
fumecheng-13737	322	21	efficiency	efficiency	NOUN
fumecheng-13737	322	22	.	.	PUNCT
fumecheng-13737	323	1	for	for	ADP
fumecheng-13737	323	2	instance	instance	NOUN
fumecheng-13737	323	3	,	,	PUNCT
fumecheng-13737	323	4	for	for	ADP
fumecheng-13737	323	5	the	the	DET
fumecheng-13737	323	6	case	case	NOUN
fumecheng-13737	323	7	of	of	ADP
fumecheng-13737	323	8	a	a	PRON
fumecheng-13737	323	9	=	=	SYM
fumecheng-13737	323	10	3	3	NUM
fumecheng-13737	323	11	in	in	ADP
fumecheng-13737	323	12	table	table	NOUN
fumecheng-13737	323	13	1	1	NUM
fumecheng-13737	323	14	,	,	PUNCT
fumecheng-13737	323	15	the	the	DET
fumecheng-13737	323	16	computation	computation	NOUN
fumecheng-13737	323	17	times	time	NOUN
fumecheng-13737	323	18	on	on	ADP
fumecheng-13737	323	19	a	a	DET
fumecheng-13737	323	20	system	system	NOUN
fumecheng-13737	323	21	with	with	ADP
fumecheng-13737	323	22	an	an	DET
fumecheng-13737	323	23	intel	intel	PROPN
fumecheng-13737	323	24	core	core	NOUN
fumecheng-13737	323	25	i7	i7	NOUN
fumecheng-13737	323	26	-	-	PUNCT
fumecheng-13737	323	27	7500u	7500u	NUM
fumecheng-13737	323	28	cpu	cpu	NOUN
fumecheng-13737	323	29	and	and	CCONJ
fumecheng-13737	323	30	12	12	NUM
fumecheng-13737	323	31	gb	gb	NOUN
fumecheng-13737	323	32	ram	ram	NOUN
fumecheng-13737	323	33	,	,	PUNCT
fumecheng-13737	323	34	using	use	VERB
fumecheng-13737	323	35	matlab	matlab	PROPN
fumecheng-13737	323	36	,	,	PUNCT
fumecheng-13737	323	37	are	be	AUX
fumecheng-13737	323	38	approximately	approximately	ADV
fumecheng-13737	323	39	0.1	0.1	NUM
fumecheng-13737	323	40	ms	ms	NOUN
fumecheng-13737	323	41	,	,	PUNCT
fumecheng-13737	323	42	0.03	0.03	NUM
fumecheng-13737	323	43	ms	ms	NOUN
fumecheng-13737	323	44	,	,	PUNCT
fumecheng-13737	323	45	and	and	CCONJ
fumecheng-13737	323	46	0.006	0.006	NUM
fumecheng-13737	323	47	ms	ms	NOUN
fumecheng-13737	323	48	for	for	ADP
fumecheng-13737	323	49	the	the	DET
fumecheng-13737	323	50	alpf	alpf	NOUN
fumecheng-13737	323	51	,	,	PUNCT
fumecheng-13737	323	52	seme	seme	NOUN
fumecheng-13737	323	53	,	,	PUNCT
fumecheng-13737	323	54	and	and	CCONJ
fumecheng-13737	323	55	hfaf	hfaf	VERB
fumecheng-13737	323	56	methods	method	NOUN
fumecheng-13737	323	57	,	,	PUNCT
fumecheng-13737	323	58	respectively	respectively	ADV
fumecheng-13737	323	59	.	.	PUNCT
fumecheng-13737	324	1	in	in	ADP
fumecheng-13737	324	2	comparison	comparison	NOUN
fumecheng-13737	324	3	,	,	PUNCT
fumecheng-13737	324	4	the	the	DET
fumecheng-13737	324	5	exact	exact	ADJ
fumecheng-13737	324	6	method	method	NOUN
fumecheng-13737	324	7	requires	require	VERB
fumecheng-13737	324	8	about	about	ADP
fumecheng-13737	324	9	1.3	1.3	NUM
fumecheng-13737	324	10	ms	ms	NOUN
fumecheng-13737	324	11	due	due	ADP
fumecheng-13737	324	12	to	to	ADP
fumecheng-13737	324	13	the	the	DET
fumecheng-13737	324	14	necessity	necessity	NOUN
fumecheng-13737	324	15	for	for	ADP
fumecheng-13737	324	16	numerical	numerical	ADJ
fumecheng-13737	324	17	integration	integration	NOUN
fumecheng-13737	324	18	.	.	PUNCT
fumecheng-13737	325	1	a	a	DET
fumecheng-13737	325	2	fast	fast	ADJ
fumecheng-13737	325	3	insight	insight	NOUN
fumecheng-13737	325	4	into	into	ADP
fumecheng-13737	325	5	nonlinear	nonlinear	ADJ
fumecheng-13737	325	6	frequency	frequency	NOUN
fumecheng-13737	325	7	estimation	estimation	NOUN
fumecheng-13737	325	8	of	of	ADP
fumecheng-13737	325	9	stringer	stringer	NOUN
fumecheng-13737	325	10	-	-	PUNCT
fumecheng-13737	325	11	stiffened	stiffen	VERB
fumecheng-13737	325	12	shells	shell	NOUN
fumecheng-13737	325	13	with	with	ADP
fumecheng-13737	325	14	high	high	ADJ
fumecheng-13737	325	15	accuracy	accuracy	NOUN
fumecheng-13737	325	16	799	799	NUM
fumecheng-13737	325	17	table	table	NOUN
fumecheng-13737	325	18	1	1	NUM
fumecheng-13737	325	19	comparison	comparison	NOUN
fumecheng-13737	325	20	of	of	ADP
fumecheng-13737	325	21	the	the	DET
fumecheng-13737	325	22	frequencies	frequency	NOUN
fumecheng-13737	325	23	obtained	obtain	VERB
fumecheng-13737	325	24	by	by	ADP
fumecheng-13737	325	25	the	the	DET
fumecheng-13737	325	26	proposed	propose	VERB
fumecheng-13737	325	27	three	three	NUM
fumecheng-13737	325	28	methods	method	NOUN
fumecheng-13737	325	29	with	with	ADP
fumecheng-13737	325	30	exact	exact	ADJ
fumecheng-13737	325	31	ones	one	NOUN
fumecheng-13737	325	32	for	for	ADP
fumecheng-13737	325	33	β1	β1	PROPN
fumecheng-13737	325	34	=	=	PUNCT
fumecheng-13737	325	35	0.5	0.5	NUM
fumecheng-13737	325	36	,	,	PUNCT
fumecheng-13737	325	37	β2	β2	NOUN
fumecheng-13737	325	38	=	=	NOUN
fumecheng-13737	325	39	2	2	NUM
fumecheng-13737	325	40	,	,	PUNCT
fumecheng-13737	325	41	β3	β3	ADJ
fumecheng-13737	325	42	=	=	NUM
fumecheng-13737	325	43	0.2	0.2	NUM
fumecheng-13737	325	44	,	,	PUNCT
fumecheng-13737	325	45	β4	β4	PROPN
fumecheng-13737	325	46	=	=	NOUN
fumecheng-13737	325	47	0.1	0.1	NUM
fumecheng-13737	325	48	.	.	PUNCT
fumecheng-13737	326	1	a	a	DET
fumecheng-13737	326	2	present	present	ADJ
fumecheng-13737	326	3	ωhpm	ωhpm	NOUN
fumecheng-13737	326	4	[	[	X
fumecheng-13737	326	5	38	38	NUM
fumecheng-13737	326	6	]	]	PUNCT
fumecheng-13737	326	7	ωexact	ωexact	PROPN
fumecheng-13737	326	8	ωhe	ωhe	PROPN
fumecheng-13737	326	9	ωalpf	ωalpf	ADJ
fumecheng-13737	326	10	ωsemf	ωsemf	NOUN
fumecheng-13737	326	11	ωhfaf	ωhfaf	NOUN
fumecheng-13737	327	1	0.01	0.01	NUM
fumecheng-13737	327	2	1.4142	1.4142	NUM
fumecheng-13737	327	3	1.4142	1.4142	NUM
fumecheng-13737	327	4	1.4142	1.4142	NUM
fumecheng-13737	327	5	1.4142	1.4142	NUM
fumecheng-13737	327	6	1.4142	1.4142	NUM
fumecheng-13737	327	7	1.4142	1.4142	NUM
fumecheng-13737	327	8	0.1	0.1	NUM
fumecheng-13737	327	9	1.4130	1.4130	NUM
fumecheng-13737	327	10	1.4130	1.4130	NUM
fumecheng-13737	327	11	1.4130	1.4130	NUM
fumecheng-13737	327	12	1.4130	1.4130	NUM
fumecheng-13737	327	13	1.4133	1.4133	NUM
fumecheng-13737	327	14	1.4130	1.4130	NUM
fumecheng-13737	327	15	0.2	0.2	NUM
fumecheng-13737	327	16	1.4093	1.4093	NUM
fumecheng-13737	327	17	1.4093	1.4093	NUM
fumecheng-13737	327	18	1.4093	1.4093	NUM
fumecheng-13737	327	19	1.4093	1.4093	NUM
fumecheng-13737	327	20	1.4106	1.4106	NUM
fumecheng-13737	327	21	1.4093	1.4093	NUM
fumecheng-13737	327	22	0.8	0.8	NUM
fumecheng-13737	327	23	1.3544	1.3544	NUM
fumecheng-13737	327	24	1.3516	1.3516	NUM
fumecheng-13737	327	25	1.3524	1.3524	NUM
fumecheng-13737	327	26	1.3524	1.3524	NUM
fumecheng-13737	327	27	1.3683	1.3683	NUM
fumecheng-13737	327	28	1.3524	1.3524	NUM
fumecheng-13737	327	29	1	1	NUM
fumecheng-13737	327	30	1.3347	1.3347	NUM
fumecheng-13737	327	31	1.3285	1.3285	NUM
fumecheng-13737	327	32	1.3304	1.3304	NUM
fumecheng-13737	327	33	1.3304	1.3304	NUM
fumecheng-13737	327	34	1.3522	1.3522	NUM
fumecheng-13737	327	35	1.3304	1.3304	NUM
fumecheng-13737	327	36	1.4	1.4	NUM
fumecheng-13737	327	37	1.3162	1.3162	NUM
fumecheng-13737	327	38	1.2979	1.2979	NUM
fumecheng-13737	327	39	1.3041	1.3041	NUM
fumecheng-13737	327	40	1.3041	1.3041	NUM
fumecheng-13737	327	41	1.3356	1.3356	NUM
fumecheng-13737	327	42	1.3041	1.3041	NUM
fumecheng-13737	327	43	1.8	1.8	NUM
fumecheng-13737	327	44	1.3411	1.3411	NUM
fumecheng-13737	327	45	1.3037	1.3037	NUM
fumecheng-13737	327	46	1.3176	1.3176	NUM
fumecheng-13737	327	47	1.3176	1.3176	NUM
fumecheng-13737	327	48	1.3545	1.3545	NUM
fumecheng-13737	327	49	1.3176	1.3176	NUM
fumecheng-13737	327	50	2	2	NUM
fumecheng-13737	327	51	1.3719	1.3719	NUM
fumecheng-13737	327	52	1.3229	1.3229	NUM
fumecheng-13737	327	53	1.3416	1.3416	NUM
fumecheng-13737	327	54	1.3416	1.3416	NUM
fumecheng-13737	327	55	1.3801	1.3801	NUM
fumecheng-13737	327	56	1.3416	1.3416	NUM
fumecheng-13737	327	57	2.5	2.5	NUM
fumecheng-13737	327	58	1.4985	1.4985	NUM
fumecheng-13737	327	59	1.4156	1.4156	NUM
fumecheng-13737	327	60	1.4488	1.4488	NUM
fumecheng-13737	327	61	1.4488	1.4488	NUM
fumecheng-13737	327	62	1.4900	1.4900	NUM
fumecheng-13737	327	63	1.4488	1.4488	NUM
fumecheng-13737	327	64	3	3	NUM
fumecheng-13737	327	65	1.6820	1.6820	NUM
fumecheng-13737	327	66	1.5597	1.5597	NUM
fumecheng-13737	327	67	1.6089	1.6089	NUM
fumecheng-13737	327	68	1.6089	1.6089	NUM
fumecheng-13737	327	69	1.6537	1.6537	NUM
fumecheng-13737	327	70	1.6089	1.6089	NUM
fumecheng-13737	327	71	table	table	NOUN
fumecheng-13737	327	72	2	2	NUM
fumecheng-13737	327	73	comparison	comparison	NOUN
fumecheng-13737	327	74	of	of	ADP
fumecheng-13737	327	75	the	the	DET
fumecheng-13737	327	76	frequencies	frequency	NOUN
fumecheng-13737	327	77	obtained	obtain	VERB
fumecheng-13737	327	78	by	by	ADP
fumecheng-13737	327	79	the	the	DET
fumecheng-13737	327	80	proposed	propose	VERB
fumecheng-13737	327	81	three	three	NUM
fumecheng-13737	327	82	methods	method	NOUN
fumecheng-13737	327	83	with	with	ADP
fumecheng-13737	327	84	exact	exact	ADJ
fumecheng-13737	327	85	ones	one	NOUN
fumecheng-13737	327	86	for	for	ADP
fumecheng-13737	327	87	β1	β1	PROPN
fumecheng-13737	327	88	=	=	PUNCT
fumecheng-13737	327	89	0.1	0.1	NUM
fumecheng-13737	327	90	,	,	PUNCT
fumecheng-13737	327	91	β2	β2	NOUN
fumecheng-13737	327	92	=	=	NOUN
fumecheng-13737	327	93	1	1	NUM
fumecheng-13737	327	94	,	,	PUNCT
fumecheng-13737	327	95	β3	β3	VERB
fumecheng-13737	327	96	=	=	SYM
fumecheng-13737	327	97	0.5	0.5	NUM
fumecheng-13737	327	98	,	,	PUNCT
fumecheng-13737	327	99	β4	β4	PROPN
fumecheng-13737	327	100	=	=	ADJ
fumecheng-13737	327	101	0.2	0.2	NUM
fumecheng-13737	327	102	.	.	PUNCT
fumecheng-13737	328	1	a	a	DET
fumecheng-13737	328	2	present	present	ADJ
fumecheng-13737	328	3	ωhpm	ωhpm	NOUN
fumecheng-13737	328	4	[	[	X
fumecheng-13737	328	5	38	38	NUM
fumecheng-13737	328	6	]	]	PUNCT
fumecheng-13737	328	7	ωexact	ωexact	PROPN
fumecheng-13737	328	8	ωhe	ωhe	PROPN
fumecheng-13737	328	9	ωalpf	ωalpf	ADJ
fumecheng-13737	328	10	ωsemf	ωsemf	NOUN
fumecheng-13737	328	11	ωhfaf	ωhfaf	NOUN
fumecheng-13737	328	12	0.01	0.01	NUM
fumecheng-13737	328	13	1.0000	1.0000	NUM
fumecheng-13737	328	14	1.0000	1.0000	NUM
fumecheng-13737	328	15	1.0000	1.0000	NUM
fumecheng-13737	328	16	1.0000	1.0000	NUM
fumecheng-13737	328	17	1.0000	1.0000	NUM
fumecheng-13737	328	18	1.0000	1.0000	NUM
fumecheng-13737	328	19	0.1	0.1	NUM
fumecheng-13737	328	20	1.0016	1.0016	NUM
fumecheng-13737	328	21	1.0016	1.0016	NUM
fumecheng-13737	328	22	1.0016	1.0016	NUM
fumecheng-13737	328	23	1.0016	1.0016	NUM
fumecheng-13737	328	24	1.0016	1.0016	NUM
fumecheng-13737	328	25	1.0016	1.0016	NUM
fumecheng-13737	328	26	0.2	0.2	NUM
fumecheng-13737	328	27	1.0066	1.0066	NUM
fumecheng-13737	328	28	1.0066	1.0066	NUM
fumecheng-13737	328	29	1.0066	1.0066	NUM
fumecheng-13737	328	30	1.0066	1.0066	NUM
fumecheng-13737	328	31	1.0063	1.0063	NUM
fumecheng-13737	328	32	1.0066	1.0066	NUM
fumecheng-13737	328	33	0.8	0.8	NUM
fumecheng-13737	328	34	1.1175	1.1175	NUM
fumecheng-13737	328	35	1.1163	1.1163	NUM
fumecheng-13737	328	36	1.1186	1.1186	NUM
fumecheng-13737	328	37	1.1186	1.1186	NUM
fumecheng-13737	328	38	1.1121	1.1121	NUM
fumecheng-13737	328	39	1.1186	1.1186	NUM
fumecheng-13737	328	40	1	1	NUM
fumecheng-13737	328	41	1.1926	1.1926	NUM
fumecheng-13737	328	42	1.1902	1.1902	NUM
fumecheng-13737	328	43	1.1952	1.1952	NUM
fumecheng-13737	328	44	1.1952	1.1952	NUM
fumecheng-13737	328	45	1.1843	1.1843	NUM
fumecheng-13737	328	46	1.1952	1.1952	NUM
fumecheng-13737	328	47	1.4	1.4	NUM
fumecheng-13737	328	48	1.4110	1.4110	NUM
fumecheng-13737	328	49	1.4049	1.4049	NUM
fumecheng-13737	328	50	1.4204	1.4204	NUM
fumecheng-13737	328	51	1.4204	1.4204	NUM
fumecheng-13737	328	52	1.3965	1.3965	NUM
fumecheng-13737	328	53	1.4204	1.4204	NUM
fumecheng-13737	328	54	1.8	1.8	NUM
fumecheng-13737	328	55	1.7215	1.7215	NUM
fumecheng-13737	328	56	1.7095	1.7095	NUM
fumecheng-13737	328	57	1.7423	1.7423	NUM
fumecheng-13737	328	58	1.7423	1.7423	NUM
fumecheng-13737	328	59	1.7024	1.7024	NUM
fumecheng-13737	328	60	1.7423	1.7423	NUM
fumecheng-13737	328	61	2	2	NUM
fumecheng-13737	328	62	1.9093	1.9093	NUM
fumecheng-13737	328	63	1.8930	1.8930	NUM
fumecheng-13737	328	64	1.9365	1.9365	NUM
fumecheng-13737	328	65	1.9365	1.9365	NUM
fumecheng-13737	328	66	1.8885	1.8885	NUM
fumecheng-13737	328	67	1.9365	1.9365	NUM
fumecheng-13737	328	68	2.5	2.5	NUM
fumecheng-13737	328	69	2.4621	2.4621	NUM
fumecheng-13737	328	70	2.4281	2.4281	NUM
fumecheng-13737	328	71	2.5036	2.5036	NUM
fumecheng-13737	328	72	2.5036	2.5036	NUM
fumecheng-13737	328	73	2.4378	2.4378	NUM
fumecheng-13737	328	74	2.5036	2.5036	NUM
fumecheng-13737	328	75	3	3	NUM
fumecheng-13737	328	76	3.1145	3.1145	NUM
fumecheng-13737	328	77	3.0499	3.0499	NUM
fumecheng-13737	328	78	3.1623	3.1623	NUM
fumecheng-13737	328	79	3.1623	3.1623	NUM
fumecheng-13737	328	80	3.0851	3.0851	NUM
fumecheng-13737	328	81	3.1623	3.1623	NUM
fumecheng-13737	328	82	table	table	NOUN
fumecheng-13737	328	83	3	3	NUM
fumecheng-13737	328	84	comparison	comparison	NOUN
fumecheng-13737	328	85	of	of	ADP
fumecheng-13737	328	86	the	the	DET
fumecheng-13737	328	87	frequencies	frequency	NOUN
fumecheng-13737	328	88	obtained	obtain	VERB
fumecheng-13737	328	89	by	by	ADP
fumecheng-13737	328	90	the	the	DET
fumecheng-13737	328	91	proposed	propose	VERB
fumecheng-13737	328	92	three	three	NUM
fumecheng-13737	328	93	methods	method	NOUN
fumecheng-13737	328	94	with	with	ADP
fumecheng-13737	328	95	exact	exact	ADJ
fumecheng-13737	328	96	ones	one	NOUN
fumecheng-13737	328	97	for	for	ADP
fumecheng-13737	328	98	β1	β1	PROPN
fumecheng-13737	328	99	=	=	SYM
fumecheng-13737	328	100	0.9	0.9	NUM
fumecheng-13737	328	101	,	,	PUNCT
fumecheng-13737	328	102	β2	β2	NOUN
fumecheng-13737	328	103	=	=	NOUN
fumecheng-13737	328	104	1.5	1.5	NUM
fumecheng-13737	328	105	,	,	PUNCT
fumecheng-13737	328	106	β3	β3	VERB
fumecheng-13737	328	107	=	=	SYM
fumecheng-13737	328	108	2.5	2.5	NUM
fumecheng-13737	328	109	,	,	PUNCT
fumecheng-13737	328	110	β4	β4	PROPN
fumecheng-13737	328	111	=	=	NOUN
fumecheng-13737	328	112	3.5	3.5	NUM
fumecheng-13737	328	113	.	.	PUNCT
fumecheng-13737	329	1	a	a	DET
fumecheng-13737	329	2	present	present	ADJ
fumecheng-13737	329	3	ωhpm	ωhpm	NOUN
fumecheng-13737	329	4	[	[	X
fumecheng-13737	329	5	38	38	NUM
fumecheng-13737	329	6	]	]	PUNCT
fumecheng-13737	329	7	ωexact	ωexact	PROPN
fumecheng-13737	329	8	ωhe	ωhe	PROPN
fumecheng-13737	329	9	ωalpf	ωalpf	ADJ
fumecheng-13737	329	10	ωsemf	ωsemf	NOUN
fumecheng-13737	329	11	ωhfaf	ωhfaf	NOUN
fumecheng-13737	329	12	0.01	0.01	NUM
fumecheng-13737	329	13	1.2248	1.2248	NUM
fumecheng-13737	329	14	1.2248	1.2248	NUM
fumecheng-13737	329	15	1.2248	1.2248	NUM
fumecheng-13737	329	16	1.2248	1.2248	NUM
fumecheng-13737	329	17	1.2248	1.2248	NUM
fumecheng-13737	329	18	1.2248	1.2248	NUM
fumecheng-13737	329	19	0.1	0.1	NUM
fumecheng-13737	329	20	1.2297	1.2297	NUM
fumecheng-13737	329	21	1.2297	1.2297	NUM
fumecheng-13737	329	22	1.2297	1.2297	NUM
fumecheng-13737	329	23	1.2297	1.2297	NUM
fumecheng-13737	329	24	1.2297	1.2297	NUM
fumecheng-13737	329	25	1.2297	1.2297	NUM
fumecheng-13737	329	26	0.2	0.2	NUM
fumecheng-13737	329	27	1.2452	1.2452	NUM
fumecheng-13737	329	28	1.2451	1.2451	NUM
fumecheng-13737	329	29	1.2452	1.2452	NUM
fumecheng-13737	329	30	1.2452	1.2452	NUM
fumecheng-13737	329	31	1.2453	1.2453	NUM
fumecheng-13737	329	32	1.2452	1.2452	NUM
fumecheng-13737	329	33	0.8	0.8	NUM
fumecheng-13737	329	34	1.6689	1.6689	NUM
fumecheng-13737	329	35	1.6500	1.6500	NUM
fumecheng-13737	329	36	1.6709	1.6709	NUM
fumecheng-13737	329	37	1.6709	1.6709	NUM
fumecheng-13737	329	38	1.6619	1.6619	NUM
fumecheng-13737	329	39	1.6709	1.6709	NUM
fumecheng-13737	329	40	1	1	NUM
fumecheng-13737	329	41	1.9571	1.9571	NUM
fumecheng-13737	329	42	1.9197	1.9197	NUM
fumecheng-13737	330	1	1.9586	1.9586	NUM
fumecheng-13737	330	2	1.9586	1.9586	NUM
fumecheng-13737	330	3	1.9460	1.9460	NUM
fumecheng-13737	330	4	1.9586	1.9586	NUM
fumecheng-13737	330	5	1.4	1.4	NUM
fumecheng-13737	330	6	2.7040	2.7040	NUM
fumecheng-13737	330	7	2.6016	2.6016	NUM
fumecheng-13737	330	8	2.6861	2.6861	NUM
fumecheng-13737	330	9	2.6861	2.6861	NUM
fumecheng-13737	330	10	2.6777	2.6777	NUM
fumecheng-13737	330	11	2.6861	2.6861	NUM
fumecheng-13737	330	12	1.8	1.8	NUM
fumecheng-13737	330	13	3.5965	3.5965	NUM
fumecheng-13737	330	14	3.3897	3.3897	NUM
fumecheng-13737	330	15	3.5248	3.5248	NUM
fumecheng-13737	330	16	3.5248	3.5248	NUM
fumecheng-13737	330	17	3.5378	3.5378	NUM
fumecheng-13737	330	18	3.5248	3.5248	NUM
fumecheng-13737	330	19	2	2	NUM
fumecheng-13737	330	20	4.0750	4.0750	NUM
fumecheng-13737	330	21	3.8032	3.8032	NUM
fumecheng-13737	330	22	3.9641	3.9641	NUM
fumecheng-13737	330	23	3.9641	3.9641	NUM
fumecheng-13737	330	24	3.9928	3.9928	NUM
fumecheng-13737	330	25	3.9641	3.9641	NUM
fumecheng-13737	330	26	2.5	2.5	NUM
fumecheng-13737	330	27	5.3237	5.3237	NUM
fumecheng-13737	330	28	4.8620	4.8620	NUM
fumecheng-13737	330	29	5.0873	5.0873	NUM
fumecheng-13737	330	30	5.0873	5.0873	NUM
fumecheng-13737	330	31	5.1637	5.1637	NUM
fumecheng-13737	330	32	5.0873	5.0873	NUM
fumecheng-13737	330	33	3	3	NUM
fumecheng-13737	330	34	6.6127	6.6127	NUM
fumecheng-13737	330	35	5.9344	5.9344	NUM
fumecheng-13737	330	36	6.2230	6.2230	NUM
fumecheng-13737	330	37	6.2230	6.2230	NUM
fumecheng-13737	330	38	6.3534	6.3534	NUM
fumecheng-13737	330	39	6.2230	6.2230	NUM
fumecheng-13737	330	40	800	800	NUM
fumecheng-13737	330	41	c	c	NOUN
fumecheng-13737	330	42	-	-	PUNCT
fumecheng-13737	330	43	h.	h.	NOUN
fumecheng-13737	330	44	he	he	PROPN
fumecheng-13737	330	45	,	,	PUNCT
fumecheng-13737	330	46	m.	m.	NOUN
fumecheng-13737	330	47	mohammadian	mohammadian	PROPN
fumecheng-13737	330	48	fig	fig	PROPN
fumecheng-13737	330	49	.	.	PUNCT
fumecheng-13737	330	50	2	2	NUM
fumecheng-13737	330	51	the	the	DET
fumecheng-13737	330	52	relative	relative	ADJ
fumecheng-13737	330	53	error	error	NOUN
fumecheng-13737	330	54	with	with	ADP
fumecheng-13737	330	55	respect	respect	NOUN
fumecheng-13737	330	56	to	to	ADP
fumecheng-13737	330	57	amplitude	amplitude	NOUN
fumecheng-13737	330	58	for	for	ADP
fumecheng-13737	330	59	the	the	DET
fumecheng-13737	330	60	three	three	NUM
fumecheng-13737	330	61	proposed	propose	VERB
fumecheng-13737	330	62	methods	method	NOUN
fumecheng-13737	330	63	under	under	ADP
fumecheng-13737	330	64	various	various	ADJ
fumecheng-13737	330	65	system	system	NOUN
fumecheng-13737	330	66	parameters	parameter	NOUN
fumecheng-13737	330	67	,	,	PUNCT
fumecheng-13737	330	68	(	(	PUNCT
fumecheng-13737	330	69	a	a	X
fumecheng-13737	330	70	)	)	PUNCT
fumecheng-13737	330	71	case	case	NOUN
fumecheng-13737	330	72	1	1	NUM
fumecheng-13737	330	73	,	,	PUNCT
fumecheng-13737	330	74	(	(	PUNCT
fumecheng-13737	330	75	b	b	X
fumecheng-13737	330	76	)	)	PUNCT
fumecheng-13737	330	77	case	case	NOUN
fumecheng-13737	330	78	2	2	NUM
fumecheng-13737	330	79	,	,	PUNCT
fumecheng-13737	330	80	and	and	CCONJ
fumecheng-13737	330	81	(	(	PUNCT
fumecheng-13737	330	82	c	c	NOUN
fumecheng-13737	330	83	)	)	PUNCT
fumecheng-13737	330	84	case	case	NOUN
fumecheng-13737	330	85	3	3	NUM
fumecheng-13737	330	86	fig	fig	NOUN
fumecheng-13737	330	87	.	.	PUNCT
fumecheng-13737	330	88	3	3	NUM
fumecheng-13737	330	89	illustrates	illustrate	VERB
fumecheng-13737	330	90	the	the	DET
fumecheng-13737	330	91	periodic	periodic	ADJ
fumecheng-13737	330	92	solutions	solution	NOUN
fumecheng-13737	330	93	obtained	obtain	VERB
fumecheng-13737	330	94	by	by	ADP
fumecheng-13737	330	95	the	the	DET
fumecheng-13737	330	96	proposed	propose	VERB
fumecheng-13737	330	97	methods	method	NOUN
fumecheng-13737	330	98	in	in	ADP
fumecheng-13737	330	99	comparison	comparison	NOUN
fumecheng-13737	330	100	with	with	ADP
fumecheng-13737	330	101	the	the	DET
fumecheng-13737	330	102	numerical	numerical	ADJ
fumecheng-13737	330	103	solution	solution	NOUN
fumecheng-13737	330	104	.	.	PUNCT
fumecheng-13737	331	1	all	all	DET
fumecheng-13737	331	2	methods	method	NOUN
fumecheng-13737	331	3	demonstrate	demonstrate	VERB
fumecheng-13737	331	4	acceptable	acceptable	ADJ
fumecheng-13737	331	5	accuracy	accuracy	NOUN
fumecheng-13737	331	6	and	and	CCONJ
fumecheng-13737	331	7	successfully	successfully	ADV
fumecheng-13737	331	8	capture	capture	VERB
fumecheng-13737	331	9	the	the	DET
fumecheng-13737	331	10	periodic	periodic	ADJ
fumecheng-13737	331	11	behavior	behavior	NOUN
fumecheng-13737	331	12	of	of	ADP
fumecheng-13737	331	13	the	the	DET
fumecheng-13737	331	14	stringer	stringer	NOUN
fumecheng-13737	331	15	-	-	PUNCT
fumecheng-13737	331	16	stiffened	stiffen	VERB
fumecheng-13737	331	17	shell	shell	NOUN
fumecheng-13737	331	18	.	.	PUNCT
fumecheng-13737	332	1	compared	compare	VERB
fumecheng-13737	332	2	to	to	ADP
fumecheng-13737	332	3	previous	previous	ADJ
fumecheng-13737	332	4	studies	study	NOUN
fumecheng-13737	332	5	,	,	PUNCT
fumecheng-13737	332	6	the	the	DET
fumecheng-13737	332	7	proposed	propose	VERB
fumecheng-13737	332	8	methods	method	NOUN
fumecheng-13737	332	9	offer	offer	VERB
fumecheng-13737	332	10	simpler	simple	ADJ
fumecheng-13737	332	11	alternatives	alternative	NOUN
fumecheng-13737	332	12	to	to	ADP
fumecheng-13737	332	13	iterative	iterative	NOUN
fumecheng-13737	332	14	approaches	approach	NOUN
fumecheng-13737	332	15	such	such	ADJ
fumecheng-13737	332	16	as	as	ADP
fumecheng-13737	332	17	hpm	hpm	NOUN
fumecheng-13737	332	18	[	[	X
fumecheng-13737	332	19	38	38	NUM
fumecheng-13737	332	20	]	]	PUNCT
fumecheng-13737	332	21	and	and	CCONJ
fumecheng-13737	332	22	grhbm	grhbm	VERB
fumecheng-13737	333	1	[	[	X
fumecheng-13737	333	2	39	39	NUM
fumecheng-13737	333	3	]	]	PUNCT
fumecheng-13737	333	4	,	,	PUNCT
fumecheng-13737	333	5	which	which	PRON
fumecheng-13737	333	6	involve	involve	VERB
fumecheng-13737	333	7	complex	complex	ADJ
fumecheng-13737	333	8	series	series	NOUN
fumecheng-13737	333	9	expansions	expansion	NOUN
fumecheng-13737	333	10	and	and	CCONJ
fumecheng-13737	333	11	exhibit	exhibit	NOUN
fumecheng-13737	333	12	limitations	limitation	NOUN
fumecheng-13737	333	13	at	at	ADP
fumecheng-13737	333	14	large	large	ADJ
fumecheng-13737	333	15	amplitude	amplitude	NOUN
fumecheng-13737	333	16	values	value	NOUN
fumecheng-13737	333	17	.	.	PUNCT
fumecheng-13737	334	1	accurate	accurate	ADJ
fumecheng-13737	334	2	frequency	frequency	NOUN
fumecheng-13737	334	3	prediction	prediction	NOUN
fumecheng-13737	334	4	is	be	AUX
fumecheng-13737	334	5	essential	essential	ADJ
fumecheng-13737	334	6	for	for	ADP
fumecheng-13737	334	7	avoiding	avoid	VERB
fumecheng-13737	334	8	resonance	resonance	NOUN
fumecheng-13737	334	9	in	in	ADP
fumecheng-13737	334	10	stiffened	stiffen	VERB
fumecheng-13737	334	11	shells	shell	NOUN
fumecheng-13737	334	12	,	,	PUNCT
fumecheng-13737	334	13	thereby	thereby	ADV
fumecheng-13737	334	14	enhancing	enhance	VERB
fumecheng-13737	334	15	safety	safety	NOUN
fumecheng-13737	334	16	in	in	ADP
fumecheng-13737	334	17	applications	application	NOUN
fumecheng-13737	334	18	such	such	ADJ
fumecheng-13737	334	19	as	as	ADP
fumecheng-13737	334	20	aircraft	aircraft	NOUN
fumecheng-13737	334	21	and	and	CCONJ
fumecheng-13737	334	22	submarines	submarine	NOUN
fumecheng-13737	334	23	.	.	PUNCT
fumecheng-13737	335	1	he	he	PRON
fumecheng-13737	335	2	’s	’	VERB
fumecheng-13737	335	3	method	method	NOUN
fumecheng-13737	335	4	,	,	PUNCT
fumecheng-13737	335	5	due	due	ADP
fumecheng-13737	335	6	to	to	ADP
fumecheng-13737	335	7	its	its	PRON
fumecheng-13737	335	8	simplicity	simplicity	NOUN
fumecheng-13737	335	9	and	and	CCONJ
fumecheng-13737	335	10	errors	error	NOUN
fumecheng-13737	335	11	below	below	ADP
fumecheng-13737	335	12	2	2	NUM
fumecheng-13737	335	13	%	%	NOUN
fumecheng-13737	335	14	for	for	ADP
fumecheng-13737	335	15	a	a	DET
fumecheng-13737	335	16	≤	≤	NUM
fumecheng-13737	335	17	1	1	NUM
fumecheng-13737	335	18	,	,	PUNCT
fumecheng-13737	335	19	is	be	AUX
fumecheng-13737	335	20	particularly	particularly	ADV
fumecheng-13737	335	21	suitable	suitable	ADJ
fumecheng-13737	335	22	for	for	ADP
fumecheng-13737	335	23	rapid	rapid	ADJ
fumecheng-13737	335	24	design	design	NOUN
fumecheng-13737	335	25	iterations	iteration	NOUN
fumecheng-13737	335	26	during	during	ADP
fumecheng-13737	335	27	preliminary	preliminary	ADJ
fumecheng-13737	335	28	engineering	engineering	NOUN
fumecheng-13737	335	29	analyses	analysis	NOUN
fumecheng-13737	335	30	.	.	PUNCT
fumecheng-13737	336	1	the	the	DET
fumecheng-13737	336	2	hamiltonianbased	hamiltonianbase	VERB
fumecheng-13737	336	3	method	method	NOUN
fumecheng-13737	336	4	,	,	PUNCT
fumecheng-13737	336	5	with	with	ADP
fumecheng-13737	336	6	errors	error	NOUN
fumecheng-13737	336	7	remaining	remain	VERB
fumecheng-13737	336	8	below	below	ADP
fumecheng-13737	336	9	4	4	NUM
fumecheng-13737	336	10	%	%	NOUN
fumecheng-13737	336	11	for	for	ADP
fumecheng-13737	336	12	all	all	DET
fumecheng-13737	336	13	amplitude	amplitude	NOUN
fumecheng-13737	336	14	levels	level	NOUN
fumecheng-13737	336	15	,	,	PUNCT
fumecheng-13737	336	16	is	be	AUX
fumecheng-13737	336	17	better	well	ADV
fumecheng-13737	336	18	suited	suit	VERB
fumecheng-13737	336	19	for	for	ADP
fumecheng-13737	336	20	critical	critical	ADJ
fumecheng-13737	336	21	applications	application	NOUN
fumecheng-13737	336	22	that	that	PRON
fumecheng-13737	336	23	demand	demand	VERB
fumecheng-13737	336	24	high	high	ADJ
fumecheng-13737	336	25	precision	precision	NOUN
fumecheng-13737	336	26	,	,	PUNCT
fumecheng-13737	336	27	such	such	ADJ
fumecheng-13737	336	28	as	as	ADP
fumecheng-13737	336	29	spacecraft	spacecraft	NOUN
fumecheng-13737	336	30	panels	panel	NOUN
fumecheng-13737	336	31	subjected	subject	VERB
fumecheng-13737	336	32	to	to	ADP
fumecheng-13737	336	33	large	large	ADJ
fumecheng-13737	336	34	dynamic	dynamic	ADJ
fumecheng-13737	336	35	loads	load	NOUN
fumecheng-13737	336	36	.	.	PUNCT
fumecheng-13737	337	1	these	these	DET
fumecheng-13737	337	2	methods	method	NOUN
fumecheng-13737	337	3	enable	enable	VERB
fumecheng-13737	337	4	engineers	engineer	NOUN
fumecheng-13737	337	5	to	to	PART
fumecheng-13737	337	6	optimize	optimize	VERB
fumecheng-13737	337	7	shell	shell	NOUN
fumecheng-13737	337	8	designs	design	NOUN
fumecheng-13737	337	9	more	more	ADV
fumecheng-13737	337	10	efficiently	efficiently	ADV
fumecheng-13737	337	11	,	,	PUNCT
fumecheng-13737	337	12	reducing	reduce	VERB
fumecheng-13737	337	13	costs	cost	NOUN
fumecheng-13737	337	14	and	and	CCONJ
fumecheng-13737	337	15	improving	improve	VERB
fumecheng-13737	337	16	structural	structural	ADJ
fumecheng-13737	337	17	integrity	integrity	NOUN
fumecheng-13737	337	18	.	.	PUNCT
fumecheng-13737	338	1	0	0	NUM
fumecheng-13737	338	2	0.5	0.5	NUM
fumecheng-13737	338	3	1	1	NUM
fumecheng-13737	338	4	1.5	1.5	NUM
fumecheng-13737	338	5	2	2	NUM
fumecheng-13737	338	6	2.5	2.5	NUM
fumecheng-13737	338	7	3	3	NUM
fumecheng-13737	338	8	0	0	NUM
fumecheng-13737	338	9	2	2	NUM
fumecheng-13737	338	10	4	4	NUM
fumecheng-13737	338	11	6	6	NUM
fumecheng-13737	338	12	8	8	NUM
fumecheng-13737	338	13	10	10	NUM
fumecheng-13737	338	14			NOUN
fumecheng-13737	338	15	1	1	NUM
fumecheng-13737	338	16	=	=	SYM
fumecheng-13737	338	17	0.5	0.5	NUM
fumecheng-13737	338	18			NOUN
fumecheng-13737	338	19	2	2	NUM
fumecheng-13737	338	20	=	=	SYM
fumecheng-13737	338	21	2	2	NUM
fumecheng-13737	338	22			NOUN
fumecheng-13737	338	23	3	3	NUM
fumecheng-13737	338	24	=	=	SYM
fumecheng-13737	338	25	0.2	0.2	NUM
fumecheng-13737	338	26			NOUN
fumecheng-13737	338	27	4	4	NUM
fumecheng-13737	338	28	=	=	SYM
fumecheng-13737	338	29	0.1	0.1	NUM
fumecheng-13737	338	30	amplitude	amplitude	NOUN
fumecheng-13737	338	31	,	,	PUNCT
fumecheng-13737	338	32	a	a	DET
fumecheng-13737	338	33	r	r	NOUN
fumecheng-13737	338	34	el	el	NOUN
fumecheng-13737	338	35	at	at	ADP
fumecheng-13737	338	36	iv	iv	NUM
fumecheng-13737	338	37	e	e	NOUN
fumecheng-13737	338	38	er	er	INTJ
fumecheng-13737	338	39	ro	ro	INTJ
fumecheng-13737	338	40	r	r	NOUN
fumecheng-13737	338	41	(	(	PUNCT
fumecheng-13737	338	42	%	%	INTJ
fumecheng-13737	338	43	)	)	PUNCT
fumecheng-13737	339	1	he	he	PRON
fumecheng-13737	339	2	’s	’	VERB
fumecheng-13737	339	3	formula	formula	NOUN
fumecheng-13737	339	4	alpf	alpf	PROPN
fumecheng-13737	339	5	&	&	CCONJ
fumecheng-13737	339	6	semf	semf	PROPN
fumecheng-13737	339	7	methods	method	NOUN
fumecheng-13737	339	8	hfaf	hfaf	VERB
fumecheng-13737	339	9	method	method	NOUN
fumecheng-13737	339	10	(	(	PUNCT
fumecheng-13737	339	11	a	a	X
fumecheng-13737	339	12	)	)	PUNCT
fumecheng-13737	339	13	0	0	NUM
fumecheng-13737	339	14	0.5	0.5	NUM
fumecheng-13737	339	15	1	1	NUM
fumecheng-13737	339	16	1.5	1.5	NUM
fumecheng-13737	339	17	2	2	NUM
fumecheng-13737	339	18	2.5	2.5	NUM
fumecheng-13737	339	19	3	3	NUM
fumecheng-13737	339	20	0	0	NUM
fumecheng-13737	339	21	0.5	0.5	NUM
fumecheng-13737	339	22	1	1	NUM
fumecheng-13737	339	23	1.5	1.5	NUM
fumecheng-13737	339	24	2	2	NUM
fumecheng-13737	339	25	2.5	2.5	NUM
fumecheng-13737	339	26	3	3	NUM
fumecheng-13737	339	27	amplitude	amplitude	NOUN
fumecheng-13737	339	28	,	,	PUNCT
fumecheng-13737	339	29	a	a	DET
fumecheng-13737	339	30	r	r	NOUN
fumecheng-13737	339	31	e	e	NOUN
fumecheng-13737	339	32	la	la	X
fumecheng-13737	339	33	ti	ti	X
fumecheng-13737	339	34	v	v	NOUN
fumecheng-13737	339	35	e	e	X
fumecheng-13737	339	36	e	e	NOUN
fumecheng-13737	339	37	rr	rr	NOUN
fumecheng-13737	339	38	o	o	NOUN
fumecheng-13737	339	39	r	r	NOUN
fumecheng-13737	339	40	(	(	PUNCT
fumecheng-13737	339	41	%	%	NOUN
fumecheng-13737	339	42	)	)	PUNCT
fumecheng-13737	339	43			NOUN
fumecheng-13737	339	44	1	1	NUM
fumecheng-13737	339	45	=	=	SYM
fumecheng-13737	339	46	0.1	0.1	NUM
fumecheng-13737	339	47			NOUN
fumecheng-13737	339	48	2	2	NUM
fumecheng-13737	339	49	=	=	SYM
fumecheng-13737	339	50	1	1	NUM
fumecheng-13737	339	51			NOUN
fumecheng-13737	339	52	3	3	NUM
fumecheng-13737	339	53	=	=	SYM
fumecheng-13737	339	54	0.5	0.5	NUM
fumecheng-13737	339	55			NOUN
fumecheng-13737	339	56	4	4	NUM
fumecheng-13737	339	57	=	=	SYM
fumecheng-13737	339	58	0.2	0.2	NUM
fumecheng-13737	339	59	he	he	PRON
fumecheng-13737	339	60	’s	’	VERB
fumecheng-13737	339	61	formula	formula	NOUN
fumecheng-13737	339	62	alpf	alpf	PROPN
fumecheng-13737	339	63	&	&	CCONJ
fumecheng-13737	339	64	semf	semf	PROPN
fumecheng-13737	339	65	methods	method	NOUN
fumecheng-13737	339	66	hfaf	hfaf	VERB
fumecheng-13737	339	67	method	method	NOUN
fumecheng-13737	339	68	(	(	PUNCT
fumecheng-13737	339	69	b	b	NOUN
fumecheng-13737	339	70	)	)	PUNCT
fumecheng-13737	339	71	0	0	NUM
fumecheng-13737	340	1	0.5	0.5	NUM
fumecheng-13737	340	2	1	1	NUM
fumecheng-13737	340	3	1.5	1.5	NUM
fumecheng-13737	340	4	2	2	NUM
fumecheng-13737	340	5	2.5	2.5	NUM
fumecheng-13737	340	6	3	3	NUM
fumecheng-13737	340	7	0	0	NUM
fumecheng-13737	340	8	2	2	NUM
fumecheng-13737	340	9	4	4	NUM
fumecheng-13737	340	10	6	6	NUM
fumecheng-13737	340	11	8	8	NUM
fumecheng-13737	340	12	10	10	NUM
fumecheng-13737	340	13			NOUN
fumecheng-13737	340	14	1	1	NUM
fumecheng-13737	340	15	=	=	SYM
fumecheng-13737	340	16	0.9	0.9	NUM
fumecheng-13737	340	17			NOUN
fumecheng-13737	340	18	2	2	NUM
fumecheng-13737	340	19	=	=	SYM
fumecheng-13737	340	20	1.5	1.5	NUM
fumecheng-13737	340	21			NOUN
fumecheng-13737	340	22	3	3	NUM
fumecheng-13737	340	23	=	=	SYM
fumecheng-13737	340	24	2.5	2.5	NUM
fumecheng-13737	340	25			NOUN
fumecheng-13737	340	26	4	4	NUM
fumecheng-13737	340	27	=	=	SYM
fumecheng-13737	340	28	3.5	3.5	NUM
fumecheng-13737	340	29	amplitude	amplitude	NOUN
fumecheng-13737	340	30	,	,	PUNCT
fumecheng-13737	340	31	a	a	DET
fumecheng-13737	340	32	r	r	NOUN
fumecheng-13737	340	33	e	e	NOUN
fumecheng-13737	340	34	la	la	X
fumecheng-13737	340	35	ti	ti	X
fumecheng-13737	340	36	v	v	NOUN
fumecheng-13737	340	37	e	e	X
fumecheng-13737	340	38	e	e	NOUN
fumecheng-13737	340	39	rr	rr	NOUN
fumecheng-13737	340	40	o	o	NOUN
fumecheng-13737	340	41	r	r	NOUN
fumecheng-13737	340	42	(	(	PUNCT
fumecheng-13737	340	43	%	%	INTJ
fumecheng-13737	340	44	)	)	PUNCT
fumecheng-13737	341	1	he	he	PRON
fumecheng-13737	341	2	’s	’	VERB
fumecheng-13737	341	3	formula	formula	NOUN
fumecheng-13737	341	4	alpf	alpf	PROPN
fumecheng-13737	341	5	&	&	CCONJ
fumecheng-13737	341	6	semf	semf	PROPN
fumecheng-13737	341	7	methods	method	NOUN
fumecheng-13737	341	8	hfaf	hfaf	VERB
fumecheng-13737	341	9	method	method	NOUN
fumecheng-13737	341	10	(	(	PUNCT
fumecheng-13737	341	11	c	c	X
fumecheng-13737	341	12	)	)	PUNCT
fumecheng-13737	341	13	a	a	DET
fumecheng-13737	341	14	fast	fast	ADJ
fumecheng-13737	341	15	insight	insight	NOUN
fumecheng-13737	341	16	into	into	ADP
fumecheng-13737	341	17	nonlinear	nonlinear	ADJ
fumecheng-13737	341	18	frequency	frequency	NOUN
fumecheng-13737	341	19	estimation	estimation	NOUN
fumecheng-13737	341	20	of	of	ADP
fumecheng-13737	341	21	stringer	stringer	NOUN
fumecheng-13737	341	22	-	-	PUNCT
fumecheng-13737	341	23	stiffened	stiffen	VERB
fumecheng-13737	341	24	shells	shell	NOUN
fumecheng-13737	341	25	with	with	ADP
fumecheng-13737	341	26	high	high	ADJ
fumecheng-13737	341	27	accuracy	accuracy	NOUN
fumecheng-13737	341	28	801	801	NUM
fumecheng-13737	341	29	fig	fig	NOUN
fumecheng-13737	341	30	.	.	PUNCT
fumecheng-13737	342	1	3	3	NUM
fumecheng-13737	342	2	comparison	comparison	NOUN
fumecheng-13737	342	3	of	of	ADP
fumecheng-13737	342	4	the	the	DET
fumecheng-13737	342	5	analytical	analytical	ADJ
fumecheng-13737	342	6	solutions	solution	NOUN
fumecheng-13737	342	7	with	with	ADP
fumecheng-13737	342	8	the	the	DET
fumecheng-13737	342	9	numerical	numerical	ADJ
fumecheng-13737	342	10	solution	solution	NOUN
fumecheng-13737	342	11	for	for	ADP
fumecheng-13737	342	12	various	various	ADJ
fumecheng-13737	342	13	system	system	NOUN
fumecheng-13737	342	14	parameters	parameter	NOUN
fumecheng-13737	342	15	and	and	CCONJ
fumecheng-13737	342	16	amplitudes	amplitude	NOUN
fumecheng-13737	342	17	,	,	PUNCT
fumecheng-13737	342	18	(	(	PUNCT
fumecheng-13737	342	19	a	a	X
fumecheng-13737	342	20	)	)	PUNCT
fumecheng-13737	342	21	case	case	NOUN
fumecheng-13737	342	22	1	1	NUM
fumecheng-13737	342	23	,	,	PUNCT
fumecheng-13737	342	24	a	a	DET
fumecheng-13737	342	25	=	=	SYM
fumecheng-13737	342	26	0.5	0.5	NUM
fumecheng-13737	342	27	,	,	PUNCT
fumecheng-13737	342	28	(	(	PUNCT
fumecheng-13737	342	29	b	b	NOUN
fumecheng-13737	342	30	)	)	PUNCT
fumecheng-13737	342	31	case	case	NOUN
fumecheng-13737	342	32	1	1	NUM
fumecheng-13737	342	33	,	,	PUNCT
fumecheng-13737	342	34	a	a	DET
fumecheng-13737	342	35	=	=	SYM
fumecheng-13737	342	36	2.3	2.3	NUM
fumecheng-13737	342	37	,	,	PUNCT
fumecheng-13737	342	38	(	(	PUNCT
fumecheng-13737	342	39	c	c	NOUN
fumecheng-13737	342	40	)	)	PUNCT
fumecheng-13737	342	41	case	case	NOUN
fumecheng-13737	342	42	2	2	NUM
fumecheng-13737	342	43	,	,	PUNCT
fumecheng-13737	342	44	a=0.5	a=0.5	NUM
fumecheng-13737	342	45	,	,	PUNCT
fumecheng-13737	342	46	(	(	PUNCT
fumecheng-13737	342	47	d	d	X
fumecheng-13737	342	48	)	)	PUNCT
fumecheng-13737	342	49	case	case	NOUN
fumecheng-13737	342	50	2	2	NUM
fumecheng-13737	342	51	,	,	PUNCT
fumecheng-13737	342	52	a	a	DET
fumecheng-13737	342	53	=	=	SYM
fumecheng-13737	342	54	2	2	NUM
fumecheng-13737	342	55	,	,	PUNCT
fumecheng-13737	342	56	(	(	PUNCT
fumecheng-13737	342	57	e	e	NOUN
fumecheng-13737	342	58	)	)	PUNCT
fumecheng-13737	342	59	case	case	NOUN
fumecheng-13737	342	60	3	3	NUM
fumecheng-13737	342	61	,	,	PUNCT
fumecheng-13737	342	62	a	a	DET
fumecheng-13737	342	63	=	=	SYM
fumecheng-13737	342	64	0.5	0.5	NUM
fumecheng-13737	342	65	,	,	PUNCT
fumecheng-13737	342	66	and	and	CCONJ
fumecheng-13737	342	67	(	(	PUNCT
fumecheng-13737	342	68	f	f	X
fumecheng-13737	342	69	)	)	PUNCT
fumecheng-13737	342	70	case	case	NOUN
fumecheng-13737	342	71	3	3	NUM
fumecheng-13737	342	72	,	,	PUNCT
fumecheng-13737	342	73	a	a	DET
fumecheng-13737	342	74	=	=	SYM
fumecheng-13737	342	75	2	2	NUM
fumecheng-13737	342	76	using	use	VERB
fumecheng-13737	342	77	the	the	DET
fumecheng-13737	342	78	frequency	frequency	NOUN
fumecheng-13737	342	79	-	-	PUNCT
fumecheng-13737	342	80	amplitude	amplitude	NOUN
fumecheng-13737	342	81	relationship	relationship	NOUN
fumecheng-13737	342	82	derived	derive	VERB
fumecheng-13737	342	83	from	from	ADP
fumecheng-13737	342	84	the	the	DET
fumecheng-13737	342	85	hamiltonian	hamiltonian	NOUN
fumecheng-13737	342	86	-	-	PUNCT
fumecheng-13737	342	87	based	base	VERB
fumecheng-13737	342	88	frequency	frequency	NOUN
fumecheng-13737	342	89	-	-	PUNCT
fumecheng-13737	342	90	amplitude	amplitude	NOUN
fumecheng-13737	342	91	method	method	NOUN
fumecheng-13737	342	92	,	,	PUNCT
fumecheng-13737	342	93	fig	fig	NOUN
fumecheng-13737	342	94	.	.	PUNCT
fumecheng-13737	342	95	4	4	NUM
fumecheng-13737	342	96	illustrates	illustrate	VERB
fumecheng-13737	342	97	the	the	DET
fumecheng-13737	342	98	variation	variation	NOUN
fumecheng-13737	342	99	of	of	ADP
fumecheng-13737	342	100	the	the	DET
fumecheng-13737	342	101	frequency	frequency	NOUN
fumecheng-13737	342	102	ratio	ratio	NOUN
fumecheng-13737	342	103	(	(	PUNCT
fumecheng-13737	342	104	ωnl	ωnl	NOUN
fumecheng-13737	342	105	/	/	SYM
fumecheng-13737	342	106	ωl	ωl	NOUN
fumecheng-13737	342	107	)	)	PUNCT
fumecheng-13737	342	108	with	with	ADP
fumecheng-13737	342	109	respect	respect	NOUN
fumecheng-13737	342	110	to	to	ADP
fumecheng-13737	342	111	amplitude	amplitude	NOUN
fumecheng-13737	342	112	under	under	ADP
fumecheng-13737	342	113	various	various	ADJ
fumecheng-13737	342	114	system	system	NOUN
fumecheng-13737	342	115	parameters	parameter	NOUN
fumecheng-13737	342	116	.	.	PUNCT
fumecheng-13737	343	1	in	in	ADP
fumecheng-13737	343	2	this	this	DET
fumecheng-13737	343	3	figure	figure	NOUN
fumecheng-13737	343	4	,	,	PUNCT
fumecheng-13737	343	5	when	when	SCONJ
fumecheng-13737	343	6	the	the	DET
fumecheng-13737	343	7	effect	effect	NOUN
fumecheng-13737	343	8	of	of	ADP
fumecheng-13737	343	9	one	one	NUM
fumecheng-13737	343	10	parameter	parameter	NOUN
fumecheng-13737	343	11	is	be	AUX
fumecheng-13737	343	12	studied	study	VERB
fumecheng-13737	343	13	,	,	PUNCT
fumecheng-13737	343	14	the	the	DET
fumecheng-13737	343	15	other	other	ADJ
fumecheng-13737	343	16	three	three	NUM
fumecheng-13737	343	17	parameters	parameter	NOUN
fumecheng-13737	343	18	are	be	AUX
fumecheng-13737	343	19	fixed	fix	VERB
fumecheng-13737	343	20	at	at	ADP
fumecheng-13737	343	21	unity	unity	NOUN
fumecheng-13737	343	22	.	.	PUNCT
fumecheng-13737	344	1	it	it	PRON
fumecheng-13737	344	2	is	be	AUX
fumecheng-13737	344	3	observed	observe	VERB
fumecheng-13737	344	4	that	that	SCONJ
fumecheng-13737	344	5	parameters	parameter	NOUN
fumecheng-13737	344	6	β1	β1	PROPN
fumecheng-13737	344	7	and	and	CCONJ
fumecheng-13737	344	8	β2	β2	PROPN
fumecheng-13737	344	9	have	have	VERB
fumecheng-13737	344	10	a	a	DET
fumecheng-13737	344	11	similar	similar	ADJ
fumecheng-13737	344	12	effect	effect	NOUN
fumecheng-13737	344	13	.	.	PUNCT
fumecheng-13737	345	1	as	as	SCONJ
fumecheng-13737	345	2	their	their	PRON
fumecheng-13737	345	3	values	value	NOUN
fumecheng-13737	345	4	increase	increase	VERB
fumecheng-13737	345	5	,	,	PUNCT
fumecheng-13737	345	6	the	the	DET
fumecheng-13737	345	7	frequency	frequency	NOUN
fumecheng-13737	345	8	ratio	ratio	NOUN
fumecheng-13737	345	9	0	0	NUM
fumecheng-13737	345	10	1	1	NUM
fumecheng-13737	345	11	2	2	NUM
fumecheng-13737	345	12	3	3	NUM
fumecheng-13737	345	13	4	4	NUM
fumecheng-13737	345	14	-0.5	-0.5	NUM
fumecheng-13737	345	15	0	0	NUM
fumecheng-13737	345	16	0.5	0.5	NUM
fumecheng-13737	345	17			NOUN
fumecheng-13737	345	18	1	1	NUM
fumecheng-13737	345	19	=	=	SYM
fumecheng-13737	345	20	0.5	0.5	NUM
fumecheng-13737	345	21			NOUN
fumecheng-13737	345	22	2	2	NUM
fumecheng-13737	345	23	=	=	SYM
fumecheng-13737	345	24	2	2	NUM
fumecheng-13737	345	25			NOUN
fumecheng-13737	345	26	3	3	NUM
fumecheng-13737	345	27	=	=	SYM
fumecheng-13737	345	28	0.2	0.2	NUM
fumecheng-13737	345	29			NOUN
fumecheng-13737	345	30	4	4	NUM
fumecheng-13737	345	31	=	=	SYM
fumecheng-13737	345	32	0.1	0.1	NUM
fumecheng-13737	345	33	a	a	DET
fumecheng-13737	345	34	=	=	SYM
fumecheng-13737	345	35	0.5	0.5	NUM
fumecheng-13737	345	36	t	t	NOUN
fumecheng-13737	345	37	u	u	PROPN
fumecheng-13737	345	38	(	(	PUNCT
fumecheng-13737	345	39	t	t	PROPN
fumecheng-13737	345	40	)	)	PUNCT
fumecheng-13737	345	41	numerical	numerical	ADJ
fumecheng-13737	345	42	solution	solution	NOUN
fumecheng-13737	345	43	he	he	PRON
fumecheng-13737	345	44	’s	’	VERB
fumecheng-13737	345	45	formula	formula	NOUN
fumecheng-13737	345	46	alpf	alpf	PROPN
fumecheng-13737	345	47	&	&	CCONJ
fumecheng-13737	345	48	semf	semf	PROPN
fumecheng-13737	345	49	methods	method	NOUN
fumecheng-13737	345	50	hfaf	hfaf	VERB
fumecheng-13737	345	51	method(a	method(a	PROPN
fumecheng-13737	345	52	)	)	PUNCT
fumecheng-13737	345	53	0	0	NUM
fumecheng-13737	345	54	0.5	0.5	NUM
fumecheng-13737	345	55	1	1	NUM
fumecheng-13737	345	56	1.5	1.5	NUM
fumecheng-13737	345	57	2	2	NUM
fumecheng-13737	345	58	2.5	2.5	NUM
fumecheng-13737	345	59	3	3	NUM
fumecheng-13737	345	60	3.5	3.5	NUM
fumecheng-13737	345	61	4	4	NUM
fumecheng-13737	345	62	-2	-2	NOUN
fumecheng-13737	345	63	-1	-1	NOUN
fumecheng-13737	345	64	0	0	NUM
fumecheng-13737	345	65	1	1	NUM
fumecheng-13737	345	66	2	2	NUM
fumecheng-13737	345	67			NOUN
fumecheng-13737	345	68	1	1	NUM
fumecheng-13737	345	69	=	=	SYM
fumecheng-13737	345	70	0.5	0.5	NUM
fumecheng-13737	345	71			NOUN
fumecheng-13737	345	72	2	2	NUM
fumecheng-13737	345	73	=	=	SYM
fumecheng-13737	345	74	2	2	NUM
fumecheng-13737	345	75			NOUN
fumecheng-13737	345	76	3	3	NUM
fumecheng-13737	345	77	=	=	SYM
fumecheng-13737	345	78	0.2	0.2	NUM
fumecheng-13737	345	79			NOUN
fumecheng-13737	345	80	4	4	NUM
fumecheng-13737	345	81	=	=	SYM
fumecheng-13737	345	82	0.1	0.1	NUM
fumecheng-13737	345	83	t	t	NOUN
fumecheng-13737	345	84	u	u	PROPN
fumecheng-13737	345	85	(	(	PUNCT
fumecheng-13737	345	86	t	t	PROPN
fumecheng-13737	345	87	)	)	PUNCT
fumecheng-13737	345	88	a	a	DET
fumecheng-13737	345	89	=	=	SYM
fumecheng-13737	345	90	2.3	2.3	NUM
fumecheng-13737	345	91	numerical	numerical	ADJ
fumecheng-13737	345	92	solution	solution	NOUN
fumecheng-13737	345	93	he	he	PRON
fumecheng-13737	345	94	’s	’	VERB
fumecheng-13737	345	95	formula	formula	NOUN
fumecheng-13737	345	96	alpf	alpf	PROPN
fumecheng-13737	345	97	&	&	CCONJ
fumecheng-13737	345	98	semf	semf	PROPN
fumecheng-13737	345	99	methods	method	NOUN
fumecheng-13737	345	100	hfaf	hfaf	VERB
fumecheng-13737	345	101	method	method	NOUN
fumecheng-13737	345	102	(	(	PUNCT
fumecheng-13737	345	103	b	b	NOUN
fumecheng-13737	345	104	)	)	PUNCT
fumecheng-13737	345	105	0	0	NUM
fumecheng-13737	345	106	1	1	NUM
fumecheng-13737	345	107	2	2	NUM
fumecheng-13737	345	108	3	3	NUM
fumecheng-13737	345	109	4	4	NUM
fumecheng-13737	345	110	5	5	NUM
fumecheng-13737	345	111	6	6	NUM
fumecheng-13737	345	112	-0.5	-0.5	NUM
fumecheng-13737	345	113	0	0	NUM
fumecheng-13737	345	114	0.5	0.5	NUM
fumecheng-13737	345	115	t	t	NOUN
fumecheng-13737	345	116	u	u	PROPN
fumecheng-13737	345	117	(	(	PUNCT
fumecheng-13737	345	118	t	t	PROPN
fumecheng-13737	345	119	)	)	PUNCT
fumecheng-13737	345	120			NOUN
fumecheng-13737	345	121	1	1	NUM
fumecheng-13737	346	1	=	=	SYM
fumecheng-13737	346	2	0.1	0.1	NUM
fumecheng-13737	346	3			NOUN
fumecheng-13737	346	4	2	2	NUM
fumecheng-13737	346	5	=	=	SYM
fumecheng-13737	346	6	1	1	NUM
fumecheng-13737	346	7			NOUN
fumecheng-13737	346	8	3	3	NUM
fumecheng-13737	346	9	=	=	SYM
fumecheng-13737	346	10	0.5	0.5	NUM
fumecheng-13737	346	11			NOUN
fumecheng-13737	346	12	4	4	NUM
fumecheng-13737	346	13	=	=	SYM
fumecheng-13737	346	14	0.2	0.2	NUM
fumecheng-13737	346	15	a	a	DET
fumecheng-13737	346	16	=	=	SYM
fumecheng-13737	346	17	0.5	0.5	NUM
fumecheng-13737	346	18	numerical	numerical	ADJ
fumecheng-13737	346	19	solution	solution	NOUN
fumecheng-13737	346	20	he	he	PRON
fumecheng-13737	346	21	’s	’	VERB
fumecheng-13737	346	22	formula	formula	NOUN
fumecheng-13737	346	23	alpf	alpf	PROPN
fumecheng-13737	346	24	&	&	CCONJ
fumecheng-13737	346	25	semf	semf	PROPN
fumecheng-13737	346	26	methods	method	NOUN
fumecheng-13737	346	27	hfaf	hfaf	VERB
fumecheng-13737	346	28	method(c	method(c	PROPN
fumecheng-13737	346	29	)	)	PUNCT
fumecheng-13737	346	30	0	0	NUM
fumecheng-13737	346	31	0.5	0.5	NUM
fumecheng-13737	346	32	1	1	NUM
fumecheng-13737	346	33	1.5	1.5	NUM
fumecheng-13737	346	34	2	2	NUM
fumecheng-13737	346	35	2.5	2.5	NUM
fumecheng-13737	346	36	3	3	NUM
fumecheng-13737	346	37	-2	-2	NOUN
fumecheng-13737	346	38	-1.5	-1.5	NUM
fumecheng-13737	346	39	-1	-1	PROPN
fumecheng-13737	347	1	-0.5	-0.5	X
fumecheng-13737	347	2	0	0	NUM
fumecheng-13737	347	3	0.5	0.5	NUM
fumecheng-13737	347	4	1	1	NUM
fumecheng-13737	347	5	1.5	1.5	NUM
fumecheng-13737	347	6	2	2	NUM
fumecheng-13737	347	7	t	t	NOUN
fumecheng-13737	347	8	u	u	PROPN
fumecheng-13737	347	9	(	(	PUNCT
fumecheng-13737	347	10	t	t	PROPN
fumecheng-13737	347	11	)	)	PUNCT
fumecheng-13737	347	12			NOUN
fumecheng-13737	347	13	1	1	NUM
fumecheng-13737	347	14	=	=	SYM
fumecheng-13737	347	15	0.1	0.1	NUM
fumecheng-13737	347	16			NOUN
fumecheng-13737	347	17	2	2	NUM
fumecheng-13737	347	18	=	=	SYM
fumecheng-13737	347	19	1	1	NUM
fumecheng-13737	347	20			NOUN
fumecheng-13737	347	21	3	3	NUM
fumecheng-13737	347	22	=	=	SYM
fumecheng-13737	347	23	0.5	0.5	NUM
fumecheng-13737	347	24			NOUN
fumecheng-13737	347	25	4	4	NUM
fumecheng-13737	347	26	=	=	SYM
fumecheng-13737	347	27	0.2	0.2	NUM
fumecheng-13737	347	28	a	a	DET
fumecheng-13737	347	29	=	=	SYM
fumecheng-13737	347	30	2	2	NUM
fumecheng-13737	347	31	numerical	numerical	ADJ
fumecheng-13737	347	32	solution	solution	NOUN
fumecheng-13737	347	33	he	he	PRON
fumecheng-13737	347	34	’s	’	VERB
fumecheng-13737	347	35	formula	formula	NOUN
fumecheng-13737	347	36	alpf	alpf	PROPN
fumecheng-13737	347	37	&	&	CCONJ
fumecheng-13737	347	38	semf	semf	PROPN
fumecheng-13737	347	39	methods	method	NOUN
fumecheng-13737	347	40	hfaf	hfaf	VERB
fumecheng-13737	347	41	method(d	method(d	NOUN
fumecheng-13737	347	42	)	)	PUNCT
fumecheng-13737	347	43	0	0	NUM
fumecheng-13737	347	44	1	1	NUM
fumecheng-13737	347	45	2	2	NUM
fumecheng-13737	347	46	3	3	NUM
fumecheng-13737	347	47	4	4	NUM
fumecheng-13737	347	48	-0.5	-0.5	NUM
fumecheng-13737	347	49	0	0	NUM
fumecheng-13737	347	50	0.5	0.5	NUM
fumecheng-13737	347	51	t	t	NOUN
fumecheng-13737	347	52	u	u	PROPN
fumecheng-13737	347	53	(	(	PUNCT
fumecheng-13737	347	54	t	t	PROPN
fumecheng-13737	347	55	)	)	PUNCT
fumecheng-13737	347	56			NOUN
fumecheng-13737	347	57	2	2	NUM
fumecheng-13737	347	58	=	=	SYM
fumecheng-13737	347	59	1	1	NUM
fumecheng-13737	347	60			NOUN
fumecheng-13737	347	61	3	3	NUM
fumecheng-13737	347	62	=	=	SYM
fumecheng-13737	347	63	0.5	0.5	NUM
fumecheng-13737	347	64			NOUN
fumecheng-13737	347	65	4	4	NUM
fumecheng-13737	347	66	=	=	SYM
fumecheng-13737	347	67	0.2	0.2	NUM
fumecheng-13737	347	68	a	a	DET
fumecheng-13737	347	69	=	=	SYM
fumecheng-13737	347	70	2	2	NUM
fumecheng-13737	347	71			NOUN
fumecheng-13737	347	72	1	1	NUM
fumecheng-13737	347	73	=	=	SYM
fumecheng-13737	347	74	0.9	0.9	NUM
fumecheng-13737	347	75			NOUN
fumecheng-13737	347	76	2	2	NUM
fumecheng-13737	347	77	=	=	SYM
fumecheng-13737	347	78	1.5	1.5	NUM
fumecheng-13737	347	79			NOUN
fumecheng-13737	347	80	3	3	NUM
fumecheng-13737	347	81	=	=	SYM
fumecheng-13737	347	82	2.5	2.5	NUM
fumecheng-13737	347	83			NOUN
fumecheng-13737	347	84	4	4	NUM
fumecheng-13737	347	85	=	=	SYM
fumecheng-13737	347	86	3.5	3.5	NUM
fumecheng-13737	347	87	a	a	DET
fumecheng-13737	347	88	=	=	SYM
fumecheng-13737	347	89	0.5	0.5	NUM
fumecheng-13737	347	90	numerical	numerical	ADJ
fumecheng-13737	347	91	solution	solution	NOUN
fumecheng-13737	347	92	he	he	PRON
fumecheng-13737	347	93	’s	’	VERB
fumecheng-13737	347	94	formula	formula	NOUN
fumecheng-13737	347	95	alpf	alpf	PROPN
fumecheng-13737	347	96	&	&	CCONJ
fumecheng-13737	347	97	semf	semf	PROPN
fumecheng-13737	347	98	methods	method	NOUN
fumecheng-13737	347	99	hfaf	hfaf	VERB
fumecheng-13737	347	100	method(e	method(e	NUM
fumecheng-13737	347	101	)	)	PUNCT
fumecheng-13737	347	102	0	0	NUM
fumecheng-13737	347	103	0.5	0.5	NUM
fumecheng-13737	347	104	1	1	NUM
fumecheng-13737	347	105	1.5	1.5	NUM
fumecheng-13737	347	106	-2	-2	NOUN
fumecheng-13737	347	107	-1.5	-1.5	NUM
fumecheng-13737	347	108	-1	-1	PROPN
fumecheng-13737	348	1	-0.5	-0.5	X
fumecheng-13737	348	2	0	0	NUM
fumecheng-13737	348	3	0.5	0.5	NUM
fumecheng-13737	348	4	1	1	NUM
fumecheng-13737	348	5	1.5	1.5	NUM
fumecheng-13737	348	6	2	2	NUM
fumecheng-13737	348	7	t	t	NOUN
fumecheng-13737	348	8	u	u	PROPN
fumecheng-13737	348	9	(	(	PUNCT
fumecheng-13737	348	10	t	t	PROPN
fumecheng-13737	348	11	)	)	PUNCT
fumecheng-13737	348	12	a	a	PRON
fumecheng-13737	348	13	=	=	SYM
fumecheng-13737	348	14	2	2	NUM
fumecheng-13737	348	15			NOUN
fumecheng-13737	348	16	1	1	NUM
fumecheng-13737	348	17	=	=	SYM
fumecheng-13737	348	18	0.9	0.9	NUM
fumecheng-13737	348	19			NOUN
fumecheng-13737	348	20	2	2	NUM
fumecheng-13737	348	21	=	=	SYM
fumecheng-13737	348	22	1.5	1.5	NUM
fumecheng-13737	348	23			NOUN
fumecheng-13737	348	24	3	3	NUM
fumecheng-13737	348	25	=	=	SYM
fumecheng-13737	348	26	2.5	2.5	NUM
fumecheng-13737	348	27			NOUN
fumecheng-13737	348	28	4	4	NUM
fumecheng-13737	348	29	=	=	SYM
fumecheng-13737	348	30	3.5	3.5	NUM
fumecheng-13737	348	31	a	a	DET
fumecheng-13737	348	32	=	=	SYM
fumecheng-13737	348	33	0.5	0.5	NUM
fumecheng-13737	348	34	a	a	DET
fumecheng-13737	348	35	=	=	SYM
fumecheng-13737	348	36	2	2	NUM
fumecheng-13737	348	37	numerical	numerical	ADJ
fumecheng-13737	348	38	solution	solution	NOUN
fumecheng-13737	348	39	he	he	PRON
fumecheng-13737	348	40	’s	’	VERB
fumecheng-13737	348	41	formula	formula	NOUN
fumecheng-13737	348	42	alpf	alpf	PROPN
fumecheng-13737	348	43	&	&	CCONJ
fumecheng-13737	348	44	semf	semf	PROPN
fumecheng-13737	348	45	methods	method	NOUN
fumecheng-13737	348	46	hfaf	hfaf	VERB
fumecheng-13737	348	47	method(f	method(f	NOUN
fumecheng-13737	348	48	)	)	PUNCT
fumecheng-13737	348	49	802	802	NUM
fumecheng-13737	348	50	c	c	X
fumecheng-13737	348	51	-	-	PUNCT
fumecheng-13737	348	52	h.	h.	NOUN
fumecheng-13737	348	53	he	he	PROPN
fumecheng-13737	348	54	,	,	PUNCT
fumecheng-13737	348	55	m.	m.	NOUN
fumecheng-13737	348	56	mohammadian	mohammadian	NOUN
fumecheng-13737	348	57	decreases	decrease	VERB
fumecheng-13737	348	58	.	.	PUNCT
fumecheng-13737	349	1	in	in	ADP
fumecheng-13737	349	2	contrast	contrast	NOUN
fumecheng-13737	349	3	,	,	PUNCT
fumecheng-13737	349	4	parameters	parameter	NOUN
fumecheng-13737	349	5	β3	β3	VERB
fumecheng-13737	349	6	and	and	CCONJ
fumecheng-13737	349	7	β4	β4	PROPN
fumecheng-13737	349	8	exhibit	exhibit	VERB
fumecheng-13737	349	9	the	the	DET
fumecheng-13737	349	10	opposite	opposite	ADJ
fumecheng-13737	349	11	trend	trend	NOUN
fumecheng-13737	349	12	.	.	PUNCT
fumecheng-13737	350	1	an	an	DET
fumecheng-13737	350	2	increase	increase	NOUN
fumecheng-13737	350	3	in	in	ADP
fumecheng-13737	350	4	these	these	DET
fumecheng-13737	350	5	parameters	parameter	NOUN
fumecheng-13737	350	6	results	result	VERB
fumecheng-13737	350	7	in	in	ADP
fumecheng-13737	350	8	an	an	DET
fumecheng-13737	350	9	increase	increase	NOUN
fumecheng-13737	350	10	in	in	ADP
fumecheng-13737	350	11	the	the	DET
fumecheng-13737	350	12	nonlinear	nonlinear	NOUN
fumecheng-13737	350	13	to	to	ADP
fumecheng-13737	350	14	linear	linear	ADJ
fumecheng-13737	350	15	frequency	frequency	NOUN
fumecheng-13737	350	16	ratio	ratio	NOUN
fumecheng-13737	350	17	.	.	PUNCT
fumecheng-13737	351	1	fig	fig	NOUN
fumecheng-13737	351	2	.	.	PUNCT
fumecheng-13737	352	1	4	4	NUM
fumecheng-13737	352	2	the	the	DET
fumecheng-13737	352	3	effect	effect	NOUN
fumecheng-13737	352	4	of	of	ADP
fumecheng-13737	352	5	system	system	NOUN
fumecheng-13737	352	6	parameters	parameter	NOUN
fumecheng-13737	352	7	(	(	PUNCT
fumecheng-13737	352	8	a	a	X
fumecheng-13737	352	9	)	)	PUNCT
fumecheng-13737	352	10	β1	β1	PROPN
fumecheng-13737	352	11	,	,	PUNCT
fumecheng-13737	352	12	(	(	PUNCT
fumecheng-13737	352	13	b	b	X
fumecheng-13737	352	14	)	)	PUNCT
fumecheng-13737	352	15	β2	β2	NOUN
fumecheng-13737	352	16	,	,	PUNCT
fumecheng-13737	352	17	(	(	PUNCT
fumecheng-13737	352	18	c	c	NOUN
fumecheng-13737	352	19	)	)	PUNCT
fumecheng-13737	352	20	β3	β3	ADJ
fumecheng-13737	352	21	,	,	PUNCT
fumecheng-13737	352	22	and	and	CCONJ
fumecheng-13737	352	23	(	(	PUNCT
fumecheng-13737	352	24	d	d	X
fumecheng-13737	352	25	)	)	PUNCT
fumecheng-13737	352	26	β4	β4	PROPN
fumecheng-13737	352	27	on	on	ADP
fumecheng-13737	352	28	the	the	DET
fumecheng-13737	352	29	variation	variation	NOUN
fumecheng-13737	352	30	of	of	ADP
fumecheng-13737	352	31	frequency	frequency	NOUN
fumecheng-13737	352	32	ratio	ratio	NOUN
fumecheng-13737	352	33	with	with	ADP
fumecheng-13737	352	34	respect	respect	NOUN
fumecheng-13737	352	35	to	to	ADP
fumecheng-13737	352	36	the	the	DET
fumecheng-13737	352	37	amplitude	amplitude	NOUN
fumecheng-13737	352	38	fig	fig	NOUN
fumecheng-13737	352	39	.	.	PUNCT
fumecheng-13737	353	1	5	5	NUM
fumecheng-13737	353	2	presents	present	VERB
fumecheng-13737	353	3	a	a	DET
fumecheng-13737	353	4	sensitivity	sensitivity	NOUN
fumecheng-13737	353	5	analysis	analysis	NOUN
fumecheng-13737	353	6	of	of	ADP
fumecheng-13737	353	7	the	the	DET
fumecheng-13737	353	8	frequency	frequency	NOUN
fumecheng-13737	353	9	ratio	ratio	NOUN
fumecheng-13737	353	10	with	with	ADP
fumecheng-13737	353	11	respect	respect	NOUN
fumecheng-13737	353	12	to	to	ADP
fumecheng-13737	353	13	various	various	ADJ
fumecheng-13737	353	14	system	system	NOUN
fumecheng-13737	353	15	parameters	parameter	NOUN
fumecheng-13737	353	16	under	under	ADP
fumecheng-13737	353	17	different	different	ADJ
fumecheng-13737	353	18	amplitudes	amplitude	NOUN
fumecheng-13737	353	19	.	.	PUNCT
fumecheng-13737	354	1	as	as	SCONJ
fumecheng-13737	354	2	expected	expect	VERB
fumecheng-13737	354	3	,	,	PUNCT
fumecheng-13737	354	4	at	at	ADP
fumecheng-13737	354	5	small	small	ADJ
fumecheng-13737	354	6	amplitudes	amplitude	NOUN
fumecheng-13737	354	7	(	(	PUNCT
fumecheng-13737	354	8	here	here	ADV
fumecheng-13737	354	9	a	a	DET
fumecheng-13737	354	10	=	=	NOUN
fumecheng-13737	354	11	0.1	0.1	NUM
fumecheng-13737	354	12	)	)	PUNCT
fumecheng-13737	354	13	,	,	PUNCT
fumecheng-13737	354	14	the	the	DET
fumecheng-13737	354	15	frequency	frequency	NOUN
fumecheng-13737	354	16	ratio	ratio	NOUN
fumecheng-13737	354	17	is	be	AUX
fumecheng-13737	354	18	equal	equal	ADJ
fumecheng-13737	354	19	to	to	ADP
fumecheng-13737	354	20	unity	unity	NOUN
fumecheng-13737	354	21	,	,	PUNCT
fumecheng-13737	354	22	indicating	indicate	VERB
fumecheng-13737	354	23	the	the	DET
fumecheng-13737	354	24	negligible	negligible	ADJ
fumecheng-13737	354	25	effect	effect	NOUN
fumecheng-13737	354	26	of	of	ADP
fumecheng-13737	354	27	nonlinear	nonlinear	ADJ
fumecheng-13737	354	28	terms	term	NOUN
fumecheng-13737	354	29	.	.	PUNCT
fumecheng-13737	355	1	figs	fig	NOUN
fumecheng-13737	355	2	.	.	PUNCT
fumecheng-13737	356	1	5a	5a	NUM
fumecheng-13737	356	2	and	and	CCONJ
fumecheng-13737	356	3	5b	5b	NUM
fumecheng-13737	356	4	show	show	VERB
fumecheng-13737	356	5	that	that	SCONJ
fumecheng-13737	356	6	,	,	PUNCT
fumecheng-13737	356	7	for	for	ADP
fumecheng-13737	356	8	various	various	ADJ
fumecheng-13737	356	9	amplitudes	amplitude	NOUN
fumecheng-13737	356	10	,	,	PUNCT
fumecheng-13737	356	11	an	an	DET
fumecheng-13737	356	12	increase	increase	NOUN
fumecheng-13737	356	13	in	in	ADP
fumecheng-13737	356	14	the	the	DET
fumecheng-13737	356	15	parameters	parameter	NOUN
fumecheng-13737	356	16	β1	β1	PROPN
fumecheng-13737	356	17	and	and	CCONJ
fumecheng-13737	356	18	β2	β2	NOUN
fumecheng-13737	356	19	results	result	VERB
fumecheng-13737	356	20	in	in	ADP
fumecheng-13737	356	21	the	the	DET
fumecheng-13737	356	22	frequency	frequency	NOUN
fumecheng-13737	356	23	ratio	ratio	NOUN
fumecheng-13737	356	24	approaching	approach	VERB
fumecheng-13737	356	25	unity	unity	NOUN
fumecheng-13737	356	26	,	,	PUNCT
fumecheng-13737	356	27	thereby	thereby	ADV
fumecheng-13737	356	28	reducing	reduce	VERB
fumecheng-13737	356	29	the	the	DET
fumecheng-13737	356	30	impact	impact	NOUN
fumecheng-13737	356	31	of	of	ADP
fumecheng-13737	356	32	nonlinearities	nonlinearitie	NOUN
fumecheng-13737	356	33	.	.	PUNCT
fumecheng-13737	357	1	specifically	specifically	ADV
fumecheng-13737	357	2	,	,	PUNCT
fumecheng-13737	357	3	fig	fig	NOUN
fumecheng-13737	357	4	.	.	PUNCT
fumecheng-13737	358	1	5a	5a	NUM
fumecheng-13737	358	2	indicates	indicate	VERB
fumecheng-13737	358	3	that	that	SCONJ
fumecheng-13737	358	4	for	for	ADP
fumecheng-13737	358	5	moderate	moderate	ADJ
fumecheng-13737	358	6	amplitudes	amplitude	NOUN
fumecheng-13737	358	7	(	(	PUNCT
fumecheng-13737	358	8	here	here	ADV
fumecheng-13737	358	9	a	a	DET
fumecheng-13737	358	10	=	=	SYM
fumecheng-13737	358	11	0.5	0.5	NUM
fumecheng-13737	358	12	and	and	CCONJ
fumecheng-13737	358	13	a	a	DET
fumecheng-13737	358	14	=	=	ADJ
fumecheng-13737	358	15	1.5	1.5	NUM
fumecheng-13737	358	16	)	)	PUNCT
fumecheng-13737	358	17	,	,	PUNCT
fumecheng-13737	358	18	the	the	DET
fumecheng-13737	358	19	frequency	frequency	NOUN
fumecheng-13737	358	20	ratio	ratio	NOUN
fumecheng-13737	358	21	may	may	AUX
fumecheng-13737	358	22	be	be	AUX
fumecheng-13737	358	23	either	either	CCONJ
fumecheng-13737	358	24	greater	great	ADJ
fumecheng-13737	358	25	or	or	CCONJ
fumecheng-13737	358	26	less	less	ADJ
fumecheng-13737	358	27	than	than	ADP
fumecheng-13737	358	28	unity	unity	NOUN
fumecheng-13737	358	29	,	,	PUNCT
fumecheng-13737	358	30	depending	depend	VERB
fumecheng-13737	358	31	on	on	ADP
fumecheng-13737	358	32	the	the	DET
fumecheng-13737	358	33	value	value	NOUN
fumecheng-13737	358	34	of	of	ADP
fumecheng-13737	358	35	β1	β1	PROPN
fumecheng-13737	358	36	.	.	PUNCT
fumecheng-13737	359	1	for	for	ADP
fumecheng-13737	359	2	instance	instance	NOUN
fumecheng-13737	359	3	,	,	PUNCT
fumecheng-13737	359	4	at	at	ADP
fumecheng-13737	359	5	a	a	DET
fumecheng-13737	359	6	=	=	SYM
fumecheng-13737	359	7	1.5	1.5	NUM
fumecheng-13737	359	8	,	,	PUNCT
fumecheng-13737	359	9	the	the	DET
fumecheng-13737	359	10	frequency	frequency	NOUN
fumecheng-13737	359	11	ratio	ratio	NOUN
fumecheng-13737	359	12	is	be	AUX
fumecheng-13737	359	13	approximately	approximately	ADV
fumecheng-13737	359	14	1.2	1.2	NUM
fumecheng-13737	359	15	when	when	SCONJ
fumecheng-13737	359	16	β1	β1	PROPN
fumecheng-13737	359	17	=	=	PROPN
fumecheng-13737	359	18	2	2	NUM
fumecheng-13737	359	19	,	,	PUNCT
fumecheng-13737	359	20	while	while	SCONJ
fumecheng-13737	359	21	it	it	PRON
fumecheng-13737	359	22	decreases	decrease	VERB
fumecheng-13737	359	23	to	to	ADP
fumecheng-13737	359	24	nearly	nearly	ADV
fumecheng-13737	359	25	0.9	0.9	NUM
fumecheng-13737	359	26	when	when	SCONJ
fumecheng-13737	359	27	β1	β1	PROPN
fumecheng-13737	359	28	=	=	PROPN
fumecheng-13737	359	29	5	5	X
fumecheng-13737	359	30	.	.	PUNCT
fumecheng-13737	360	1	however	however	ADV
fumecheng-13737	360	2	,	,	PUNCT
fumecheng-13737	360	3	at	at	ADP
fumecheng-13737	360	4	higher	high	ADJ
fumecheng-13737	360	5	amplitudes	amplitude	NOUN
fumecheng-13737	360	6	,	,	PUNCT
fumecheng-13737	360	7	the	the	DET
fumecheng-13737	360	8	ratio	ratio	NOUN
fumecheng-13737	360	9	exceeds	exceed	VERB
fumecheng-13737	360	10	for	for	ADP
fumecheng-13737	360	11	all	all	DET
fumecheng-13737	360	12	values	value	NOUN
fumecheng-13737	360	13	of	of	ADP
fumecheng-13737	360	14	β1	β1	PROPN
fumecheng-13737	360	15	.	.	PUNCT
fumecheng-13737	361	1	it	it	PRON
fumecheng-13737	361	2	is	be	AUX
fumecheng-13737	361	3	important	important	ADJ
fumecheng-13737	361	4	to	to	PART
fumecheng-13737	361	5	note	note	VERB
fumecheng-13737	361	6	that	that	SCONJ
fumecheng-13737	361	7	,	,	PUNCT
fumecheng-13737	361	8	as	as	SCONJ
fumecheng-13737	361	9	defined	define	VERB
fumecheng-13737	361	10	in	in	ADP
fumecheng-13737	361	11	eq	eq	ADP
fumecheng-13737	361	12	.	.	PUNCT
fumecheng-13737	362	1	(	(	PUNCT
fumecheng-13737	362	2	8)	8)	NUM
fumecheng-13737	362	3	,	,	PUNCT
fumecheng-13737	362	4	the	the	DET
fumecheng-13737	362	5	parameter	parameter	NOUN
fumecheng-13737	362	6	β1	β1	PROPN
fumecheng-13737	362	7	quantifies	quantify	VERB
fumecheng-13737	362	8	the	the	DET
fumecheng-13737	362	9	contribution	contribution	NOUN
fumecheng-13737	362	10	of	of	ADP
fumecheng-13737	362	11	displacement	displacement	NOUN
fumecheng-13737	362	12	-	-	PUNCT
fumecheng-13737	362	13	dependent	dependent	ADJ
fumecheng-13737	362	14	terms	term	NOUN
fumecheng-13737	362	15	.	.	PUNCT
fumecheng-13737	363	1	therefore	therefore	ADV
fumecheng-13737	363	2	,	,	PUNCT
fumecheng-13737	363	3	it	it	PRON
fumecheng-13737	363	4	may	may	AUX
fumecheng-13737	363	5	be	be	AUX
fumecheng-13737	363	6	concluded	conclude	VERB
fumecheng-13737	363	7	that	that	SCONJ
fumecheng-13737	363	8	the	the	DET
fumecheng-13737	363	9	influence	influence	NOUN
fumecheng-13737	363	10	of	of	ADP
fumecheng-13737	363	11	these	these	DET
fumecheng-13737	363	12	terms	term	NOUN
fumecheng-13737	363	13	on	on	ADP
fumecheng-13737	363	14	the	the	DET
fumecheng-13737	363	15	nonlinear	nonlinear	ADJ
fumecheng-13737	363	16	frequency	frequency	NOUN
fumecheng-13737	363	17	of	of	ADP
fumecheng-13737	363	18	stringer	stringer	NOUN
fumecheng-13737	363	19	-	-	PUNCT
fumecheng-13737	363	20	stiffened	stiffen	VERB
fumecheng-13737	363	21	shell	shell	NOUN
fumecheng-13737	363	22	becomes	become	VERB
fumecheng-13737	363	23	significant	significant	ADJ
fumecheng-13737	363	24	at	at	ADP
fumecheng-13737	363	25	larger	large	ADJ
fumecheng-13737	363	26	amplitudes	amplitude	NOUN
fumecheng-13737	363	27	.	.	PUNCT
fumecheng-13737	364	1	furthermore	furthermore	ADV
fumecheng-13737	364	2	,	,	PUNCT
fumecheng-13737	364	3	figs	fig	NOUN
fumecheng-13737	364	4	.	.	PUNCT
fumecheng-13737	365	1	5c	5c	NUM
fumecheng-13737	365	2	and	and	CCONJ
fumecheng-13737	365	3	5d	5d	NUM
fumecheng-13737	365	4	reveal	reveal	VERB
fumecheng-13737	365	5	that	that	SCONJ
fumecheng-13737	365	6	the	the	DET
fumecheng-13737	365	7	frequency	frequency	NOUN
fumecheng-13737	365	8	ratio	ratio	NOUN
fumecheng-13737	365	9	increases	increase	NOUN
fumecheng-13737	365	10	with	with	ADP
fumecheng-13737	365	11	higher	high	ADJ
fumecheng-13737	365	12	values	value	NOUN
fumecheng-13737	365	13	of	of	ADP
fumecheng-13737	365	14	β3	β3	ADJ
fumecheng-13737	365	15	and	and	CCONJ
fumecheng-13737	365	16	β4	β4	PROPN
fumecheng-13737	365	17	,	,	PUNCT
fumecheng-13737	365	18	indicating	indicate	VERB
fumecheng-13737	365	19	the	the	DET
fumecheng-13737	365	20	role	role	NOUN
fumecheng-13737	365	21	of	of	ADP
fumecheng-13737	365	22	cubicquintic	cubicquintic	ADJ
fumecheng-13737	365	23	nonlinearities	nonlinearitie	NOUN
fumecheng-13737	365	24	in	in	ADP
fumecheng-13737	365	25	the	the	DET
fumecheng-13737	365	26	nonlinear	nonlinear	ADJ
fumecheng-13737	365	27	frequency	frequency	NOUN
fumecheng-13737	365	28	response	response	NOUN
fumecheng-13737	365	29	of	of	ADP
fumecheng-13737	365	30	the	the	DET
fumecheng-13737	365	31	structure	structure	NOUN
fumecheng-13737	365	32	.	.	PUNCT
fumecheng-13737	366	1	0	0	NUM
fumecheng-13737	366	2	0.5	0.5	NUM
fumecheng-13737	366	3	1	1	NUM
fumecheng-13737	366	4	1.5	1.5	NUM
fumecheng-13737	366	5	2	2	NUM
fumecheng-13737	366	6	2.5	2.5	NUM
fumecheng-13737	366	7	3	3	NUM
fumecheng-13737	366	8	0.5	0.5	NUM
fumecheng-13737	366	9	1	1	NUM
fumecheng-13737	366	10	1.5	1.5	NUM
fumecheng-13737	366	11	2	2	NUM
fumecheng-13737	366	12	2.5	2.5	NUM
fumecheng-13737	366	13	3	3	NUM
fumecheng-13737	366	14	3.5	3.5	NUM
fumecheng-13737	366	15	a	a	DET
fumecheng-13737	366	16			PROPN
fumecheng-13737	366	17	n	n	NUM
fumecheng-13737	366	18	l	l	NOUN
fumecheng-13737	366	19	/	/	PUNCT
fumecheng-13737	367	1	l	l	NOUN
fumecheng-13737	367	2			NOUN
fumecheng-13737	367	3	1	1	NUM
fumecheng-13737	367	4	=	=	SYM
fumecheng-13737	367	5	1	1	NUM
fumecheng-13737	367	6			NOUN
fumecheng-13737	367	7	1	1	NUM
fumecheng-13737	367	8	=	=	SYM
fumecheng-13737	367	9	2	2	NUM
fumecheng-13737	367	10			NOUN
fumecheng-13737	367	11	1	1	NUM
fumecheng-13737	367	12	=	=	SYM
fumecheng-13737	367	13	3	3	NUM
fumecheng-13737	367	14			NOUN
fumecheng-13737	367	15	1	1	NUM
fumecheng-13737	367	16	=	=	SYM
fumecheng-13737	367	17	4	4	NUM
fumecheng-13737	367	18			NOUN
fumecheng-13737	367	19	1	1	NUM
fumecheng-13737	367	20	=	=	SYM
fumecheng-13737	367	21	5	5	NUM
fumecheng-13737	367	22	(	(	PUNCT
fumecheng-13737	367	23	a	a	NOUN
fumecheng-13737	367	24	)	)	PUNCT
fumecheng-13737	367	25	0	0	NUM
fumecheng-13737	367	26	1	1	NUM
fumecheng-13737	367	27	2	2	NUM
fumecheng-13737	367	28	3	3	NUM
fumecheng-13737	367	29	0.5	0.5	NUM
fumecheng-13737	367	30	1	1	NUM
fumecheng-13737	367	31	1.5	1.5	NUM
fumecheng-13737	367	32	2	2	NUM
fumecheng-13737	367	33	2.5	2.5	NUM
fumecheng-13737	367	34	3	3	NUM
fumecheng-13737	367	35	3.5	3.5	NUM
fumecheng-13737	367	36	a	a	DET
fumecheng-13737	367	37			PROPN
fumecheng-13737	367	38	n	n	NUM
fumecheng-13737	367	39	l	l	NOUN
fumecheng-13737	367	40	/	/	PUNCT
fumecheng-13737	368	1	l	l	NOUN
fumecheng-13737	368	2			NOUN
fumecheng-13737	368	3	2	2	NUM
fumecheng-13737	368	4	=	=	SYM
fumecheng-13737	368	5	1	1	NUM
fumecheng-13737	368	6			NOUN
fumecheng-13737	368	7	2	2	NUM
fumecheng-13737	368	8	=	=	SYM
fumecheng-13737	368	9	2	2	NUM
fumecheng-13737	368	10			NOUN
fumecheng-13737	368	11	3	3	NUM
fumecheng-13737	368	12	=	=	SYM
fumecheng-13737	368	13	3	3	NUM
fumecheng-13737	368	14			NOUN
fumecheng-13737	368	15	4	4	NUM
fumecheng-13737	368	16	=	=	SYM
fumecheng-13737	368	17	4	4	NUM
fumecheng-13737	368	18			NOUN
fumecheng-13737	368	19	5	5	NUM
fumecheng-13737	368	20	=	=	SYM
fumecheng-13737	368	21	5	5	NUM
fumecheng-13737	368	22	(	(	PUNCT
fumecheng-13737	368	23	b	b	NOUN
fumecheng-13737	368	24	)	)	PUNCT
fumecheng-13737	368	25	0	0	NUM
fumecheng-13737	368	26	0.5	0.5	NUM
fumecheng-13737	368	27	1	1	NUM
fumecheng-13737	368	28	1.5	1.5	NUM
fumecheng-13737	368	29	2	2	NUM
fumecheng-13737	368	30	2.5	2.5	NUM
fumecheng-13737	368	31	3	3	NUM
fumecheng-13737	368	32	1	1	NUM
fumecheng-13737	368	33	2	2	NUM
fumecheng-13737	368	34	3	3	NUM
fumecheng-13737	368	35	4	4	NUM
fumecheng-13737	368	36	a	a	DET
fumecheng-13737	368	37			X
fumecheng-13737	368	38	n	n	NUM
fumecheng-13737	368	39	l	l	NOUN
fumecheng-13737	368	40	/	/	PUNCT
fumecheng-13737	369	1	l	l	NOUN
fumecheng-13737	369	2			NOUN
fumecheng-13737	369	3	3	3	NUM
fumecheng-13737	369	4	=	=	SYM
fumecheng-13737	369	5	1	1	NUM
fumecheng-13737	369	6			NOUN
fumecheng-13737	369	7	3	3	NUM
fumecheng-13737	369	8	=	=	SYM
fumecheng-13737	369	9	2	2	NUM
fumecheng-13737	369	10			NOUN
fumecheng-13737	369	11	3	3	NUM
fumecheng-13737	369	12	=	=	SYM
fumecheng-13737	369	13	3	3	NUM
fumecheng-13737	369	14			NOUN
fumecheng-13737	369	15	3	3	NUM
fumecheng-13737	369	16	=	=	SYM
fumecheng-13737	369	17	4	4	NUM
fumecheng-13737	369	18			NOUN
fumecheng-13737	369	19	3	3	NUM
fumecheng-13737	369	20	=	=	SYM
fumecheng-13737	369	21	5	5	NUM
fumecheng-13737	369	22	(	(	PUNCT
fumecheng-13737	369	23	c	c	NOUN
fumecheng-13737	369	24	)	)	PUNCT
fumecheng-13737	369	25	0	0	NUM
fumecheng-13737	369	26	0.5	0.5	NUM
fumecheng-13737	369	27	1	1	NUM
fumecheng-13737	369	28	1.5	1.5	NUM
fumecheng-13737	369	29	2	2	NUM
fumecheng-13737	369	30	2.5	2.5	NUM
fumecheng-13737	369	31	3	3	NUM
fumecheng-13737	369	32	0	0	NUM
fumecheng-13737	369	33	2	2	NUM
fumecheng-13737	369	34	4	4	NUM
fumecheng-13737	369	35	6	6	NUM
fumecheng-13737	369	36	8	8	NUM
fumecheng-13737	369	37	a	a	DET
fumecheng-13737	369	38			PROPN
fumecheng-13737	369	39	n	n	NUM
fumecheng-13737	369	40	l	l	NOUN
fumecheng-13737	369	41	/	/	PUNCT
fumecheng-13737	370	1	l	l	NOUN
fumecheng-13737	370	2			NOUN
fumecheng-13737	370	3	4	4	NUM
fumecheng-13737	370	4	=	=	SYM
fumecheng-13737	370	5	1	1	NUM
fumecheng-13737	370	6			NOUN
fumecheng-13737	370	7	4	4	NUM
fumecheng-13737	370	8	=	=	SYM
fumecheng-13737	370	9	2	2	NUM
fumecheng-13737	370	10			NOUN
fumecheng-13737	370	11	4	4	NUM
fumecheng-13737	370	12	=	=	SYM
fumecheng-13737	370	13	3	3	NUM
fumecheng-13737	370	14			NOUN
fumecheng-13737	370	15	4	4	NUM
fumecheng-13737	370	16	=	=	SYM
fumecheng-13737	370	17	4	4	NUM
fumecheng-13737	370	18			NOUN
fumecheng-13737	370	19	4	4	NUM
fumecheng-13737	370	20	=	=	SYM
fumecheng-13737	370	21	5	5	NUM
fumecheng-13737	370	22	(	(	PUNCT
fumecheng-13737	370	23	d	d	NOUN
fumecheng-13737	370	24	)	)	PUNCT
fumecheng-13737	370	25	a	a	DET
fumecheng-13737	370	26	fast	fast	ADJ
fumecheng-13737	370	27	insight	insight	NOUN
fumecheng-13737	370	28	into	into	ADP
fumecheng-13737	370	29	nonlinear	nonlinear	ADJ
fumecheng-13737	370	30	frequency	frequency	NOUN
fumecheng-13737	370	31	estimation	estimation	NOUN
fumecheng-13737	370	32	of	of	ADP
fumecheng-13737	370	33	stringer	stringer	NOUN
fumecheng-13737	370	34	-	-	PUNCT
fumecheng-13737	370	35	stiffened	stiffen	VERB
fumecheng-13737	370	36	shells	shell	NOUN
fumecheng-13737	370	37	with	with	ADP
fumecheng-13737	370	38	high	high	ADJ
fumecheng-13737	370	39	accuracy	accuracy	NOUN
fumecheng-13737	370	40	803	803	NUM
fumecheng-13737	370	41	using	use	VERB
fumecheng-13737	370	42	the	the	DET
fumecheng-13737	370	43	expressions	expression	NOUN
fumecheng-13737	370	44	derived	derive	VERB
fumecheng-13737	370	45	for	for	ADP
fumecheng-13737	370	46	the	the	DET
fumecheng-13737	370	47	nonlinear	nonlinear	ADJ
fumecheng-13737	370	48	frequency	frequency	NOUN
fumecheng-13737	370	49	of	of	ADP
fumecheng-13737	370	50	the	the	DET
fumecheng-13737	370	51	stringer	stringer	NOUN
fumecheng-13737	370	52	-	-	PUNCT
fumecheng-13737	370	53	stiffened	stiffen	VERB
fumecheng-13737	370	54	shell	shell	NOUN
fumecheng-13737	370	55	,	,	PUNCT
fumecheng-13737	370	56	the	the	DET
fumecheng-13737	370	57	influence	influence	NOUN
fumecheng-13737	370	58	of	of	ADP
fumecheng-13737	370	59	geometric	geometric	ADJ
fumecheng-13737	370	60	parameters	parameter	NOUN
fumecheng-13737	370	61	can	can	AUX
fumecheng-13737	370	62	be	be	AUX
fumecheng-13737	370	63	readily	readily	ADV
fumecheng-13737	370	64	examined	examine	VERB
fumecheng-13737	370	65	.	.	PUNCT
fumecheng-13737	371	1	for	for	ADP
fumecheng-13737	371	2	instance	instance	NOUN
fumecheng-13737	371	3	,	,	PUNCT
fumecheng-13737	371	4	fig	fig	NOUN
fumecheng-13737	371	5	.	.	PUNCT
fumecheng-13737	372	1	6	6	NUM
fumecheng-13737	372	2	illustrates	illustrate	VERB
fumecheng-13737	372	3	the	the	DET
fumecheng-13737	372	4	effects	effect	NOUN
fumecheng-13737	372	5	of	of	ADP
fumecheng-13737	372	6	the	the	DET
fumecheng-13737	372	7	number	number	NOUN
fumecheng-13737	372	8	of	of	ADP
fumecheng-13737	372	9	stringers	stringer	NOUN
fumecheng-13737	372	10	n	n	CCONJ
fumecheng-13737	372	11	and	and	CCONJ
fumecheng-13737	372	12	the	the	DET
fumecheng-13737	372	13	amplitude	amplitude	NOUN
fumecheng-13737	372	14	a	a	PRON
fumecheng-13737	372	15	on	on	ADP
fumecheng-13737	372	16	the	the	DET
fumecheng-13737	372	17	nonlinear	nonlinear	ADJ
fumecheng-13737	372	18	frequency	frequency	NOUN
fumecheng-13737	372	19	under	under	ADP
fumecheng-13737	372	20	both	both	CCONJ
fumecheng-13737	372	21	ss	ss	NOUN
fumecheng-13737	372	22	and	and	CCONJ
fumecheng-13737	372	23	cc	cc	ADP
fumecheng-13737	372	24	bcs	bc	NOUN
fumecheng-13737	372	25	.	.	PUNCT
fumecheng-13737	373	1	the	the	DET
fumecheng-13737	373	2	geometrical	geometrical	ADJ
fumecheng-13737	373	3	and	and	CCONJ
fumecheng-13737	373	4	material	material	NOUN
fumecheng-13737	373	5	properties	property	NOUN
fumecheng-13737	373	6	of	of	ADP
fumecheng-13737	373	7	the	the	DET
fumecheng-13737	373	8	shell	shell	NOUN
fumecheng-13737	373	9	are	be	AUX
fumecheng-13737	373	10	as	as	SCONJ
fumecheng-13737	373	11	follows	follow	VERB
fumecheng-13737	373	12	[	[	X
fumecheng-13737	373	13	49	49	NUM
fumecheng-13737	373	14	]	]	X
fumecheng-13737	373	15	:	:	PUNCT
fumecheng-13737	373	16	radius	radius	NOUN
fumecheng-13737	373	17	r	r	NOUN
fumecheng-13737	373	18	=	=	SYM
fumecheng-13737	373	19	242	242	NUM
fumecheng-13737	373	20	mm	mm	NOUN
fumecheng-13737	373	21	,	,	PUNCT
fumecheng-13737	373	22	thickness	thickness	NOUN
fumecheng-13737	373	23	h	h	NOUN
fumecheng-13737	373	24	=	=	NOUN
fumecheng-13737	373	25	0.65	0.65	NUM
fumecheng-13737	373	26	mm	mm	NOUN
fumecheng-13737	373	27	,	,	PUNCT
fumecheng-13737	373	28	length	length	NOUN
fumecheng-13737	373	29	l	l	NOUN
fumecheng-13737	374	1	=	=	SYM
fumecheng-13737	375	1	609	609	NUM
fumecheng-13737	375	2	mm	mm	NUM
fumecheng-13737	375	3	,	,	PUNCT
fumecheng-13737	375	4	elastic	elastic	ADJ
fumecheng-13737	375	5	modulus	modulus	NOUN
fumecheng-13737	375	6	e	e	NOUN
fumecheng-13737	375	7	=	=	SYM
fumecheng-13737	375	8	68.95	68.95	NUM
fumecheng-13737	375	9	gpa	gpa	PROPN
fumecheng-13737	375	10	,	,	PUNCT
fumecheng-13737	375	11	poisson	poisson	PROPN
fumecheng-13737	375	12	's	's	PART
fumecheng-13737	375	13	ratio	ratio	NOUN
fumecheng-13737	375	14	ν	ν	NOUN
fumecheng-13737	375	15	=	=	SYM
fumecheng-13737	375	16	0.3	0.3	NUM
fumecheng-13737	375	17	,	,	PUNCT
fumecheng-13737	375	18	and	and	CCONJ
fumecheng-13737	375	19	density	density	NOUN
fumecheng-13737	375	20	ρ	ρ	NOUN
fumecheng-13737	375	21	=	=	SYM
fumecheng-13737	375	22	2714	2714	NUM
fumecheng-13737	375	23	kg	kg	NOUN
fumecheng-13737	375	24	/	/	SYM
fumecheng-13737	375	25	m3	m3	PROPN
fumecheng-13737	375	26	.	.	PUNCT
fumecheng-13737	376	1	the	the	DET
fumecheng-13737	376	2	depth	depth	NOUN
fumecheng-13737	376	3	and	and	CCONJ
fumecheng-13737	376	4	width	width	NOUN
fumecheng-13737	376	5	of	of	ADP
fumecheng-13737	376	6	the	the	DET
fumecheng-13737	376	7	stringers	stringer	NOUN
fumecheng-13737	376	8	are	be	AUX
fumecheng-13737	376	9	taken	take	VERB
fumecheng-13737	376	10	as	as	ADP
fumecheng-13737	376	11	7.02	7.02	NUM
fumecheng-13737	376	12	mm	mm	NOUN
fumecheng-13737	376	13	and	and	CCONJ
fumecheng-13737	376	14	2.55	2.55	NUM
fumecheng-13737	376	15	mm	mm	NOUN
fumecheng-13737	376	16	,	,	PUNCT
fumecheng-13737	376	17	respectively	respectively	ADV
fumecheng-13737	376	18	,	,	PUNCT
fumecheng-13737	376	19	with	with	ADP
fumecheng-13737	376	20	the	the	DET
fumecheng-13737	376	21	assumption	assumption	NOUN
fumecheng-13737	376	22	that	that	SCONJ
fumecheng-13737	376	23	the	the	DET
fumecheng-13737	376	24	shell	shell	NOUN
fumecheng-13737	376	25	and	and	CCONJ
fumecheng-13737	376	26	stringers	stringer	NOUN
fumecheng-13737	376	27	are	be	AUX
fumecheng-13737	376	28	made	make	VERB
fumecheng-13737	376	29	of	of	ADP
fumecheng-13737	376	30	the	the	DET
fumecheng-13737	376	31	same	same	ADJ
fumecheng-13737	376	32	materials	material	NOUN
fumecheng-13737	376	33	.	.	PUNCT
fumecheng-13737	377	1	as	as	SCONJ
fumecheng-13737	377	2	shown	show	VERB
fumecheng-13737	377	3	in	in	ADP
fumecheng-13737	377	4	fig	fig	NOUN
fumecheng-13737	377	5	.	.	PUNCT
fumecheng-13737	378	1	6	6	NUM
fumecheng-13737	378	2	,	,	PUNCT
fumecheng-13737	378	3	increasing	increase	VERB
fumecheng-13737	378	4	the	the	DET
fumecheng-13737	378	5	number	number	NOUN
fumecheng-13737	378	6	of	of	ADP
fumecheng-13737	378	7	stringers	stringer	NOUN
fumecheng-13737	378	8	leads	lead	VERB
fumecheng-13737	378	9	to	to	ADP
fumecheng-13737	378	10	a	a	DET
fumecheng-13737	378	11	higher	high	ADJ
fumecheng-13737	378	12	nonlinear	nonlinear	ADJ
fumecheng-13737	378	13	frequency	frequency	NOUN
fumecheng-13737	378	14	due	due	ADP
fumecheng-13737	378	15	to	to	ADP
fumecheng-13737	378	16	the	the	DET
fumecheng-13737	378	17	corresponding	corresponding	ADJ
fumecheng-13737	378	18	increase	increase	NOUN
fumecheng-13737	378	19	in	in	ADP
fumecheng-13737	378	20	structural	structural	ADJ
fumecheng-13737	378	21	stiffness	stiffness	NOUN
fumecheng-13737	378	22	.	.	PUNCT
fumecheng-13737	379	1	additionally	additionally	ADV
fumecheng-13737	379	2	,	,	PUNCT
fumecheng-13737	379	3	as	as	ADP
fumecheng-13737	379	4	the	the	DET
fumecheng-13737	379	5	amplitude	amplitude	NOUN
fumecheng-13737	379	6	increases	increase	NOUN
fumecheng-13737	379	7	,	,	PUNCT
fumecheng-13737	379	8	the	the	DET
fumecheng-13737	379	9	frequency	frequency	NOUN
fumecheng-13737	379	10	initially	initially	ADV
fumecheng-13737	379	11	decreases	decrease	VERB
fumecheng-13737	379	12	and	and	CCONJ
fumecheng-13737	379	13	then	then	ADV
fumecheng-13737	379	14	increases	increase	VERB
fumecheng-13737	379	15	.	.	PUNCT
fumecheng-13737	380	1	this	this	DET
fumecheng-13737	380	2	initial	initial	ADJ
fumecheng-13737	380	3	drop	drop	NOUN
fumecheng-13737	380	4	in	in	ADP
fumecheng-13737	380	5	frequency	frequency	NOUN
fumecheng-13737	380	6	persists	persist	VERB
fumecheng-13737	380	7	up	up	ADP
fumecheng-13737	380	8	to	to	ADP
fumecheng-13737	380	9	higher	high	ADJ
fumecheng-13737	380	10	amplitude	amplitude	NOUN
fumecheng-13737	380	11	levels	level	NOUN
fumecheng-13737	380	12	for	for	ADP
fumecheng-13737	380	13	cc	cc	NOUN
fumecheng-13737	380	14	bcs	bc	NOUN
fumecheng-13737	380	15	compared	compare	VERB
fumecheng-13737	380	16	to	to	ADP
fumecheng-13737	380	17	ss	ss	NOUN
fumecheng-13737	380	18	ones	one	NOUN
fumecheng-13737	380	19	.	.	PUNCT
fumecheng-13737	381	1	fig	fig	NOUN
fumecheng-13737	381	2	.	.	PUNCT
fumecheng-13737	382	1	7	7	NUM
fumecheng-13737	382	2	further	far	ADV
fumecheng-13737	382	3	demonstrates	demonstrate	VERB
fumecheng-13737	382	4	that	that	SCONJ
fumecheng-13737	382	5	the	the	DET
fumecheng-13737	382	6	nonlinear	nonlinear	ADJ
fumecheng-13737	382	7	frequency	frequency	NOUN
fumecheng-13737	382	8	increases	increase	VERB
fumecheng-13737	382	9	with	with	ADP
fumecheng-13737	382	10	increasing	increase	VERB
fumecheng-13737	382	11	shell	shell	NOUN
fumecheng-13737	382	12	thickness	thickness	NOUN
fumecheng-13737	382	13	h.	h.	PROPN
fumecheng-13737	382	14	similarly	similarly	ADV
fumecheng-13737	382	15	,	,	PUNCT
fumecheng-13737	382	16	the	the	DET
fumecheng-13737	382	17	effects	effect	NOUN
fumecheng-13737	382	18	of	of	ADP
fumecheng-13737	382	19	other	other	ADJ
fumecheng-13737	382	20	geometric	geometric	ADJ
fumecheng-13737	382	21	parameters	parameter	NOUN
fumecheng-13737	382	22	can	can	AUX
fumecheng-13737	382	23	be	be	AUX
fumecheng-13737	382	24	systematically	systematically	ADV
fumecheng-13737	382	25	explored	explore	VERB
fumecheng-13737	382	26	using	use	VERB
fumecheng-13737	382	27	the	the	DET
fumecheng-13737	382	28	derived	derive	VERB
fumecheng-13737	382	29	expressions	expression	NOUN
fumecheng-13737	382	30	.	.	PUNCT
fumecheng-13737	383	1	fig	fig	NOUN
fumecheng-13737	383	2	.	.	PUNCT
fumecheng-13737	384	1	5	5	NUM
fumecheng-13737	384	2	the	the	DET
fumecheng-13737	384	3	variation	variation	NOUN
fumecheng-13737	384	4	of	of	ADP
fumecheng-13737	384	5	frequency	frequency	NOUN
fumecheng-13737	384	6	ratio	ratio	NOUN
fumecheng-13737	384	7	with	with	ADP
fumecheng-13737	384	8	respect	respect	NOUN
fumecheng-13737	384	9	to	to	ADP
fumecheng-13737	384	10	(	(	PUNCT
fumecheng-13737	384	11	a	a	X
fumecheng-13737	384	12	)	)	PUNCT
fumecheng-13737	384	13	β1	β1	NOUN
fumecheng-13737	384	14	,	,	PUNCT
fumecheng-13737	384	15	(	(	PUNCT
fumecheng-13737	384	16	b	b	X
fumecheng-13737	384	17	)	)	PUNCT
fumecheng-13737	384	18	β2	β2	NOUN
fumecheng-13737	384	19	,	,	PUNCT
fumecheng-13737	384	20	(	(	PUNCT
fumecheng-13737	384	21	c	c	NOUN
fumecheng-13737	384	22	)	)	PUNCT
fumecheng-13737	384	23	β3	β3	ADJ
fumecheng-13737	384	24	,	,	PUNCT
fumecheng-13737	384	25	and	and	CCONJ
fumecheng-13737	384	26	(	(	PUNCT
fumecheng-13737	384	27	d	d	X
fumecheng-13737	384	28	)	)	PUNCT
fumecheng-13737	384	29	β4	β4	NOUN
fumecheng-13737	384	30	under	under	ADP
fumecheng-13737	384	31	various	various	ADJ
fumecheng-13737	384	32	amplitudes	amplitude	NOUN
fumecheng-13737	384	33	0	0	NUM
fumecheng-13737	384	34	1	1	NUM
fumecheng-13737	384	35	2	2	NUM
fumecheng-13737	384	36	3	3	NUM
fumecheng-13737	384	37	4	4	NUM
fumecheng-13737	384	38	5	5	NUM
fumecheng-13737	384	39	0.5	0.5	NUM
fumecheng-13737	384	40	1	1	NUM
fumecheng-13737	384	41	1.5	1.5	NUM
fumecheng-13737	384	42	2	2	NUM
fumecheng-13737	384	43	2.5	2.5	NUM
fumecheng-13737	384	44			NOUN
fumecheng-13737	384	45	1	1	NUM
fumecheng-13737	384	46			PROPN
fumecheng-13737	384	47	n	n	PRON
fumecheng-13737	384	48	l	l	NOUN
fumecheng-13737	384	49	/	/	PUNCT
fumecheng-13737	385	1	l	l	NOUN
fumecheng-13737	385	2	a	a	X
fumecheng-13737	385	3	=	=	SYM
fumecheng-13737	385	4	0.1	0.1	NUM
fumecheng-13737	385	5	a	a	PRON
fumecheng-13737	385	6	=	=	NOUN
fumecheng-13737	385	7	0.5	0.5	NUM
fumecheng-13737	385	8	a	a	DET
fumecheng-13737	385	9	=	=	NOUN
fumecheng-13737	385	10	1.5	1.5	NUM
fumecheng-13737	385	11	a	a	PRON
fumecheng-13737	385	12	=	=	SYM
fumecheng-13737	385	13	2	2	NUM
fumecheng-13737	385	14	(	(	PUNCT
fumecheng-13737	385	15	a	a	NOUN
fumecheng-13737	385	16	)	)	PUNCT
fumecheng-13737	385	17	0	0	NUM
fumecheng-13737	385	18	1	1	NUM
fumecheng-13737	385	19	2	2	NUM
fumecheng-13737	385	20	3	3	NUM
fumecheng-13737	385	21	4	4	NUM
fumecheng-13737	385	22	5	5	NUM
fumecheng-13737	385	23	0.5	0.5	NUM
fumecheng-13737	385	24	1	1	NUM
fumecheng-13737	385	25	1.5	1.5	NUM
fumecheng-13737	385	26	2	2	NUM
fumecheng-13737	385	27	2.5	2.5	NUM
fumecheng-13737	385	28	3	3	NUM
fumecheng-13737	385	29	3.5	3.5	NUM
fumecheng-13737	385	30			NOUN
fumecheng-13737	385	31	2	2	NUM
fumecheng-13737	385	32			X
fumecheng-13737	385	33	n	n	PRON
fumecheng-13737	385	34	l	l	NOUN
fumecheng-13737	385	35	/	/	PUNCT
fumecheng-13737	385	36	l	l	NOUN
fumecheng-13737	385	37	a	a	X
fumecheng-13737	385	38	=	=	SYM
fumecheng-13737	385	39	0.1	0.1	NUM
fumecheng-13737	385	40	a	a	PRON
fumecheng-13737	385	41	=	=	NOUN
fumecheng-13737	385	42	0.5	0.5	NUM
fumecheng-13737	385	43	a	a	DET
fumecheng-13737	385	44	=	=	NOUN
fumecheng-13737	385	45	1.5	1.5	NUM
fumecheng-13737	385	46	a	a	DET
fumecheng-13737	385	47	=	=	SYM
fumecheng-13737	385	48	2	2	NUM
fumecheng-13737	385	49	(	(	PUNCT
fumecheng-13737	385	50	b	b	NOUN
fumecheng-13737	385	51	)	)	PUNCT
fumecheng-13737	385	52	0	0	NUM
fumecheng-13737	385	53	1	1	NUM
fumecheng-13737	385	54	2	2	NUM
fumecheng-13737	385	55	3	3	NUM
fumecheng-13737	385	56	4	4	NUM
fumecheng-13737	385	57	5	5	NUM
fumecheng-13737	385	58	0.5	0.5	NUM
fumecheng-13737	385	59	1	1	NUM
fumecheng-13737	385	60	1.5	1.5	NUM
fumecheng-13737	385	61	2	2	NUM
fumecheng-13737	385	62	2.5	2.5	NUM
fumecheng-13737	385	63			NOUN
fumecheng-13737	385	64	3	3	NUM
fumecheng-13737	385	65			PROPN
fumecheng-13737	385	66	n	n	PRON
fumecheng-13737	385	67	l	l	NOUN
fumecheng-13737	385	68	/	/	PUNCT
fumecheng-13737	385	69	l	l	NOUN
fumecheng-13737	385	70	a	a	X
fumecheng-13737	385	71	=	=	SYM
fumecheng-13737	385	72	0.1	0.1	NUM
fumecheng-13737	385	73	a	a	DET
fumecheng-13737	385	74	=	=	NOUN
fumecheng-13737	385	75	0.5	0.5	NUM
fumecheng-13737	385	76	a	a	DET
fumecheng-13737	385	77	=	=	NOUN
fumecheng-13737	385	78	1.5	1.5	NUM
fumecheng-13737	385	79	a	a	DET
fumecheng-13737	385	80	=	=	SYM
fumecheng-13737	385	81	2	2	NUM
fumecheng-13737	385	82	(	(	PUNCT
fumecheng-13737	385	83	c	c	NOUN
fumecheng-13737	385	84	)	)	PUNCT
fumecheng-13737	385	85	0	0	NUM
fumecheng-13737	385	86	1	1	NUM
fumecheng-13737	385	87	2	2	NUM
fumecheng-13737	385	88	3	3	NUM
fumecheng-13737	385	89	4	4	NUM
fumecheng-13737	385	90	5	5	NUM
fumecheng-13737	385	91	0.5	0.5	NUM
fumecheng-13737	385	92	1	1	NUM
fumecheng-13737	385	93	1.5	1.5	NUM
fumecheng-13737	385	94	2	2	NUM
fumecheng-13737	385	95	2.5	2.5	NUM
fumecheng-13737	385	96	3	3	NUM
fumecheng-13737	385	97			NOUN
fumecheng-13737	385	98	4	4	NUM
fumecheng-13737	385	99			PROPN
fumecheng-13737	385	100	n	n	PRON
fumecheng-13737	385	101	l	l	NOUN
fumecheng-13737	385	102	/	/	PUNCT
fumecheng-13737	385	103	l	l	NOUN
fumecheng-13737	385	104	a	a	X
fumecheng-13737	385	105	=	=	SYM
fumecheng-13737	385	106	0.1	0.1	NUM
fumecheng-13737	385	107	a	a	DET
fumecheng-13737	385	108	=	=	NOUN
fumecheng-13737	385	109	0.5	0.5	NUM
fumecheng-13737	385	110	a	a	DET
fumecheng-13737	385	111	=	=	NOUN
fumecheng-13737	385	112	1.5	1.5	NUM
fumecheng-13737	385	113	a	a	DET
fumecheng-13737	385	114	=	=	SYM
fumecheng-13737	385	115	2	2	NUM
fumecheng-13737	385	116	(	(	PUNCT
fumecheng-13737	385	117	d	d	NOUN
fumecheng-13737	385	118	)	)	PUNCT
fumecheng-13737	385	119	804	804	NUM
fumecheng-13737	385	120	c	c	PROPN
fumecheng-13737	385	121	-	-	PUNCT
fumecheng-13737	385	122	h.	h.	NOUN
fumecheng-13737	385	123	he	he	PROPN
fumecheng-13737	385	124	,	,	PUNCT
fumecheng-13737	385	125	m.	m.	NOUN
fumecheng-13737	385	126	mohammadian	mohammadian	PROPN
fumecheng-13737	385	127	fig	fig	PROPN
fumecheng-13737	385	128	.	.	PUNCT
fumecheng-13737	386	1	6	6	NUM
fumecheng-13737	386	2	the	the	DET
fumecheng-13737	386	3	effects	effect	NOUN
fumecheng-13737	386	4	of	of	ADP
fumecheng-13737	386	5	the	the	DET
fumecheng-13737	386	6	number	number	NOUN
fumecheng-13737	386	7	of	of	ADP
fumecheng-13737	386	8	stringers	stringer	NOUN
fumecheng-13737	386	9	n	n	ADP
fumecheng-13737	386	10	and	and	CCONJ
fumecheng-13737	386	11	amplitude	amplitude	VERB
fumecheng-13737	386	12	a	a	PRON
fumecheng-13737	386	13	on	on	ADP
fumecheng-13737	386	14	the	the	DET
fumecheng-13737	386	15	frequency	frequency	NOUN
fumecheng-13737	386	16	of	of	ADP
fumecheng-13737	386	17	a	a	DET
fumecheng-13737	386	18	stringer	stringer	NOUN
fumecheng-13737	386	19	-	-	PUNCT
fumecheng-13737	386	20	stiffened	stiffen	VERB
fumecheng-13737	386	21	shell	shell	NOUN
fumecheng-13737	386	22	when	when	SCONJ
fumecheng-13737	386	23	m	m	VERB
fumecheng-13737	386	24	=	=	SYM
fumecheng-13737	386	25	n	n	PROPN
fumecheng-13737	386	26	=	=	SYM
fumecheng-13737	386	27	1	1	X
fumecheng-13737	386	28	.	.	PUNCT
fumecheng-13737	387	1	(	(	PUNCT
fumecheng-13737	387	2	a	a	X
fumecheng-13737	387	3	)	)	PUNCT
fumecheng-13737	387	4	ss	ss	NOUN
fumecheng-13737	387	5	bcs	bc	NOUN
fumecheng-13737	387	6	,	,	PUNCT
fumecheng-13737	387	7	(	(	PUNCT
fumecheng-13737	387	8	b	b	X
fumecheng-13737	387	9	)	)	PUNCT
fumecheng-13737	387	10	cc	cc	ADP
fumecheng-13737	387	11	bcs	bcs	NOUN
fumecheng-13737	387	12	fig	fig	NOUN
fumecheng-13737	387	13	.	.	PUNCT
fumecheng-13737	388	1	7	7	NUM
fumecheng-13737	388	2	the	the	DET
fumecheng-13737	388	3	effects	effect	NOUN
fumecheng-13737	388	4	of	of	ADP
fumecheng-13737	388	5	the	the	DET
fumecheng-13737	388	6	number	number	NOUN
fumecheng-13737	388	7	of	of	ADP
fumecheng-13737	388	8	stringers	stringer	NOUN
fumecheng-13737	388	9	n	n	CCONJ
fumecheng-13737	388	10	and	and	CCONJ
fumecheng-13737	388	11	shell	shell	VERB
fumecheng-13737	388	12	thickness	thickness	NOUN
fumecheng-13737	388	13	h	h	NOUN
fumecheng-13737	388	14	on	on	ADP
fumecheng-13737	388	15	the	the	DET
fumecheng-13737	388	16	frequency	frequency	NOUN
fumecheng-13737	388	17	of	of	ADP
fumecheng-13737	388	18	a	a	DET
fumecheng-13737	388	19	stringer	stringer	NOUN
fumecheng-13737	388	20	-	-	PUNCT
fumecheng-13737	388	21	stiffened	stiffen	VERB
fumecheng-13737	388	22	shell	shell	NOUN
fumecheng-13737	388	23	under	under	ADP
fumecheng-13737	388	24	ss	ss	NOUN
fumecheng-13737	388	25	bcs	bc	NOUN
fumecheng-13737	388	26	.	.	PUNCT
fumecheng-13737	389	1	m	m	VERB
fumecheng-13737	390	1	=	=	SYM
fumecheng-13737	390	2	n	n	NOUN
fumecheng-13737	390	3	=	=	SYM
fumecheng-13737	390	4	1	1	NUM
fumecheng-13737	390	5	5	5	NUM
fumecheng-13737	390	6	.	.	PUNCT
fumecheng-13737	391	1	conclusion	conclusion	NOUN
fumecheng-13737	391	2	this	this	DET
fumecheng-13737	391	3	study	study	NOUN
fumecheng-13737	391	4	developed	develop	VERB
fumecheng-13737	391	5	three	three	NUM
fumecheng-13737	391	6	analytical	analytical	ADJ
fumecheng-13737	391	7	methods	method	NOUN
fumecheng-13737	391	8	:	:	PUNCT
fumecheng-13737	391	9	adaptive	adaptive	ADJ
fumecheng-13737	391	10	location	location	NOUN
fumecheng-13737	391	11	point	point	NOUN
fumecheng-13737	391	12	-	-	PUNCT
fumecheng-13737	391	13	based	base	VERB
fumecheng-13737	391	14	he	he	PRON
fumecheng-13737	391	15	’s	’	VERB
fumecheng-13737	391	16	formulation	formulation	NOUN
fumecheng-13737	391	17	(	(	PUNCT
fumecheng-13737	391	18	alpf	alpf	PROPN
fumecheng-13737	391	19	)	)	PUNCT
fumecheng-13737	391	20	,	,	PUNCT
fumecheng-13737	391	21	square	square	ADJ
fumecheng-13737	391	22	error	error	NOUN
fumecheng-13737	391	23	minimizing	minimizing	NOUN
fumecheng-13737	391	24	-	-	PUNCT
fumecheng-13737	391	25	based	base	VERB
fumecheng-13737	391	26	frequency	frequency	NOUN
fumecheng-13737	391	27	formulation	formulation	NOUN
fumecheng-13737	391	28	(	(	PUNCT
fumecheng-13737	391	29	semf	semf	NOUN
fumecheng-13737	391	30	)	)	PUNCT
fumecheng-13737	391	31	,	,	PUNCT
fumecheng-13737	391	32	and	and	CCONJ
fumecheng-13737	391	33	hamiltonian	hamiltonian	ADJ
fumecheng-13737	391	34	-	-	PUNCT
fumecheng-13737	391	35	based	base	VERB
fumecheng-13737	391	36	frequency	frequency	NOUN
fumecheng-13737	391	37	-	-	PUNCT
fumecheng-13737	391	38	amplitude	amplitude	NOUN
fumecheng-13737	391	39	formulation	formulation	NOUN
fumecheng-13737	391	40	(	(	PUNCT
fumecheng-13737	391	41	hfaf	hfaf	NOUN
fumecheng-13737	391	42	)	)	PUNCT
fumecheng-13737	391	43	,	,	PUNCT
fumecheng-13737	391	44	to	to	PART
fumecheng-13737	391	45	derive	derive	VERB
fumecheng-13737	391	46	closed	close	VERB
fumecheng-13737	391	47	-	-	PUNCT
fumecheng-13737	391	48	form	form	NOUN
fumecheng-13737	391	49	expressions	expression	NOUN
fumecheng-13737	391	50	for	for	ADP
fumecheng-13737	391	51	the	the	DET
fumecheng-13737	391	52	nonlinear	nonlinear	ADJ
fumecheng-13737	391	53	frequency	frequency	NOUN
fumecheng-13737	391	54	of	of	ADP
fumecheng-13737	391	55	stringer	stringer	NOUN
fumecheng-13737	391	56	-	-	PUNCT
fumecheng-13737	391	57	stiffened	stiffen	VERB
fumecheng-13737	391	58	cylindrical	cylindrical	ADJ
fumecheng-13737	391	59	shells	shell	NOUN
fumecheng-13737	391	60	.	.	PUNCT
fumecheng-13737	392	1	these	these	DET
fumecheng-13737	392	2	methods	method	NOUN
fumecheng-13737	392	3	were	be	AUX
fumecheng-13737	392	4	validated	validate	VERB
fumecheng-13737	392	5	against	against	ADP
fumecheng-13737	392	6	both	both	CCONJ
fumecheng-13737	392	7	exact	exact	ADJ
fumecheng-13737	392	8	and	and	CCONJ
fumecheng-13737	392	9	numerical	numerical	ADJ
fumecheng-13737	392	10	solutions	solution	NOUN
fumecheng-13737	392	11	.	.	PUNCT
fumecheng-13737	393	1	for	for	ADP
fumecheng-13737	393	2	small	small	ADJ
fumecheng-13737	393	3	vibration	vibration	NOUN
fumecheng-13737	393	4	amplitudes	amplitude	NOUN
fumecheng-13737	393	5	,	,	PUNCT
fumecheng-13737	393	6	they	they	PRON
fumecheng-13737	393	7	exhibited	exhibit	VERB
fumecheng-13737	393	8	errors	error	NOUN
fumecheng-13737	393	9	les	le	NOUN
fumecheng-13737	393	10	than	than	ADP
fumecheng-13737	393	11	0.1	0.1	NUM
fumecheng-13737	393	12	%	%	NOUN
fumecheng-13737	393	13	,	,	PUNCT
fumecheng-13737	393	14	while	while	SCONJ
fumecheng-13737	393	15	for	for	ADP
fumecheng-13737	393	16	larger	large	ADJ
fumecheng-13737	393	17	amplitudes	amplitude	NOUN
fumecheng-13737	393	18	,	,	PUNCT
fumecheng-13737	393	19	the	the	DET
fumecheng-13737	393	20	hamiltonianbased	hamiltonianbase	VERB
fumecheng-13737	393	21	method	method	NOUN
fumecheng-13737	393	22	maintained	maintain	VERB
fumecheng-13737	393	23	an	an	DET
fumecheng-13737	393	24	error	error	NOUN
fumecheng-13737	393	25	within	within	ADP
fumecheng-13737	393	26	to	to	ADP
fumecheng-13737	393	27	3.92	3.92	NUM
fumecheng-13737	393	28	%	%	NOUN
fumecheng-13737	393	29	.	.	PUNCT
fumecheng-13737	394	1	compared	compare	VERB
fumecheng-13737	394	2	to	to	ADP
fumecheng-13737	394	3	iterative	iterative	NOUN
fumecheng-13737	394	4	techniques	technique	NOUN
fumecheng-13737	394	5	such	such	ADJ
fumecheng-13737	394	6	as	as	ADP
fumecheng-13737	394	7	the	the	DET
fumecheng-13737	394	8	homotopy	homotopy	NOUN
fumecheng-13737	394	9	perturbation	perturbation	NOUN
fumecheng-13737	394	10	method	method	NOUN
fumecheng-13737	394	11	,	,	PUNCT
fumecheng-13737	394	12	the	the	DET
fumecheng-13737	394	13	proposed	propose	VERB
fumecheng-13737	394	14	methods	method	NOUN
fumecheng-13737	394	15	offer	offer	VERB
fumecheng-13737	394	16	efficiency	efficiency	NOUN
fumecheng-13737	394	17	and	and	CCONJ
fumecheng-13737	394	18	ease	ease	NOUN
fumecheng-13737	394	19	of	of	ADP
fumecheng-13737	394	20	application	application	NOUN
fumecheng-13737	394	21	.	.	PUNCT
fumecheng-13737	395	1	the	the	DET
fumecheng-13737	395	2	models	model	NOUN
fumecheng-13737	395	3	effectively	effectively	ADV
fumecheng-13737	395	4	address	address	VERB
fumecheng-13737	395	5	the	the	DET
fumecheng-13737	395	6	cubic	cubic	ADJ
fumecheng-13737	395	7	-	-	PUNCT
fumecheng-13737	395	8	quintic	quintic	ADJ
fumecheng-13737	395	9	nonlinearities	nonlinearitie	NOUN
fumecheng-13737	395	10	characteristic	characteristic	ADJ
fumecheng-13737	395	11	of	of	ADP
fumecheng-13737	395	12	stiffened	stiffen	VERB
fumecheng-13737	395	13	shells	shell	NOUN
fumecheng-13737	395	14	,	,	PUNCT
fumecheng-13737	395	15	offering	offer	VERB
fumecheng-13737	395	16	practical	practical	ADJ
fumecheng-13737	395	17	tools	tool	NOUN
fumecheng-13737	395	18	for	for	ADP
fumecheng-13737	395	19	fast	fast	ADJ
fumecheng-13737	395	20	and	and	CCONJ
fumecheng-13737	395	21	accurate	accurate	ADJ
fumecheng-13737	395	22	frequency	frequency	NOUN
fumecheng-13737	395	23	prediction	prediction	NOUN
fumecheng-13737	395	24	.	.	PUNCT
fumecheng-13737	396	1	these	these	DET
fumecheng-13737	396	2	findings	finding	NOUN
fumecheng-13737	396	3	are	be	AUX
fumecheng-13737	396	4	particularly	particularly	ADV
fumecheng-13737	396	5	relevant	relevant	ADJ
fumecheng-13737	396	6	to	to	ADP
fumecheng-13737	396	7	aerospace	aerospace	NOUN
fumecheng-13737	396	8	structures	structure	NOUN
fumecheng-13737	396	9	,	,	PUNCT
fumecheng-13737	396	10	spacecraft	spacecraft	NOUN
fumecheng-13737	396	11	panels	panel	NOUN
fumecheng-13737	396	12	,	,	PUNCT
fumecheng-13737	396	13	and	and	CCONJ
fumecheng-13737	396	14	marine	marine	ADJ
fumecheng-13737	396	15	hulls	hull	NOUN
fumecheng-13737	396	16	,	,	PUNCT
fumecheng-13737	396	17	where	where	SCONJ
fumecheng-13737	396	18	avoiding	avoid	VERB
fumecheng-13737	396	19	resonance	resonance	NOUN
fumecheng-13737	396	20	is	be	AUX
fumecheng-13737	396	21	essential	essential	ADJ
fumecheng-13737	396	22	for	for	ADP
fumecheng-13737	396	23	ensuring	ensure	VERB
fumecheng-13737	396	24	structural	structural	ADJ
fumecheng-13737	396	25	safety	safety	NOUN
fumecheng-13737	396	26	.	.	PUNCT
fumecheng-13737	397	1	it	it	PRON
fumecheng-13737	397	2	is	be	AUX
fumecheng-13737	397	3	important	important	ADJ
fumecheng-13737	397	4	to	to	PART
fumecheng-13737	397	5	note	note	VERB
fumecheng-13737	397	6	that	that	SCONJ
fumecheng-13737	397	7	the	the	DET
fumecheng-13737	397	8	present	present	ADJ
fumecheng-13737	397	9	study	study	NOUN
fumecheng-13737	397	10	focused	focus	VERB
fumecheng-13737	397	11	on	on	ADP
fumecheng-13737	397	12	the	the	DET
fumecheng-13737	397	13	vibration	vibration	NOUN
fumecheng-13737	397	14	response	response	NOUN
fumecheng-13737	397	15	in	in	ADP
fumecheng-13737	397	16	a	a	DET
fumecheng-13737	397	17	single	single	ADJ
fumecheng-13737	397	18	dominant	dominant	ADJ
fumecheng-13737	397	19	mode	mode	NOUN
fumecheng-13737	397	20	and	and	CCONJ
fumecheng-13737	397	21	neglected	neglect	VERB
fumecheng-13737	397	22	damping	damp	VERB
fumecheng-13737	397	23	effects	effect	NOUN
fumecheng-13737	397	24	.	.	PUNCT
fumecheng-13737	398	1	these	these	DET
fumecheng-13737	398	2	assumptions	assumption	NOUN
fumecheng-13737	398	3	were	be	AUX
fumecheng-13737	398	4	adopted	adopt	VERB
fumecheng-13737	398	5	to	to	PART
fumecheng-13737	398	6	facilitate	facilitate	VERB
fumecheng-13737	398	7	the	the	DET
fumecheng-13737	398	8	development	development	NOUN
fumecheng-13737	398	9	of	of	ADP
fumecheng-13737	398	10	simple	simple	ADJ
fumecheng-13737	398	11	,	,	PUNCT
fumecheng-13737	398	12	fast	fast	ADJ
fumecheng-13737	398	13	,	,	PUNCT
fumecheng-13737	398	14	and	and	CCONJ
fumecheng-13737	398	15	non	non	ADJ
fumecheng-13737	398	16	-	-	ADJ
fumecheng-13737	398	17	iterative	iterative	ADJ
fumecheng-13737	398	18	analytical	analytical	ADJ
fumecheng-13737	398	19	expressions	expression	NOUN
fumecheng-13737	398	20	for	for	ADP
fumecheng-13737	398	21	the	the	DET
fumecheng-13737	398	22	0	0	NUM
fumecheng-13737	398	23	0.5	0.5	NUM
fumecheng-13737	398	24	1	1	NUM
fumecheng-13737	398	25	1.5	1.5	NUM
fumecheng-13737	398	26	2	2	NUM
fumecheng-13737	398	27	2.5	2.5	NUM
fumecheng-13737	398	28	3	3	NUM
fumecheng-13737	398	29	0.4	0.4	NUM
fumecheng-13737	398	30	0.6	0.6	NUM
fumecheng-13737	398	31	0.8	0.8	NUM
fumecheng-13737	398	32	1	1	NUM
fumecheng-13737	398	33	1.2	1.2	NUM
fumecheng-13737	398	34	1.4	1.4	NUM
fumecheng-13737	398	35	1.6	1.6	NUM
fumecheng-13737	398	36	1.8	1.8	NUM
fumecheng-13737	398	37	2	2	NUM
fumecheng-13737	398	38	amplitude	amplitude	NOUN
fumecheng-13737	398	39	,	,	PUNCT
fumecheng-13737	398	40	a	a	DET
fumecheng-13737	398	41	f	f	X
fumecheng-13737	398	42	re	re	ADP
fumecheng-13737	398	43	q	q	PROPN
fumecheng-13737	398	44	u	u	PROPN
fumecheng-13737	398	45	en	en	PROPN
fumecheng-13737	398	46	cy	cy	PROPN
fumecheng-13737	399	1	(	(	PUNCT
fumecheng-13737	399	2	k	k	PROPN
fumecheng-13737	399	3	h	h	PROPN
fumecheng-13737	399	4	z	z	PROPN
fumecheng-13737	399	5	)	)	PUNCT
fumecheng-13737	399	6	n	n	NOUN
fumecheng-13737	399	7	=	=	SYM
fumecheng-13737	399	8	10	10	NUM
fumecheng-13737	399	9	n	n	NOUN
fumecheng-13737	399	10	=	=	SYM
fumecheng-13737	399	11	30	30	NUM
fumecheng-13737	399	12	n	n	NOUN
fumecheng-13737	399	13	=	=	SYM
fumecheng-13737	399	14	50	50	NUM
fumecheng-13737	399	15	n	n	NOUN
fumecheng-13737	399	16	=	=	SYM
fumecheng-13737	399	17	70	70	NUM
fumecheng-13737	399	18	(	(	PUNCT
fumecheng-13737	399	19	a	a	NOUN
fumecheng-13737	399	20	)	)	PUNCT
fumecheng-13737	399	21	ss	ss	NOUN
fumecheng-13737	399	22	bcs	bcs	NOUN
fumecheng-13737	399	23	0	0	NUM
fumecheng-13737	399	24	0.5	0.5	NUM
fumecheng-13737	399	25	1	1	NUM
fumecheng-13737	399	26	1.5	1.5	NUM
fumecheng-13737	399	27	2	2	NUM
fumecheng-13737	399	28	2.5	2.5	NUM
fumecheng-13737	399	29	3	3	NUM
fumecheng-13737	399	30	0.8	0.8	NUM
fumecheng-13737	399	31	1	1	NUM
fumecheng-13737	399	32	1.2	1.2	NUM
fumecheng-13737	399	33	1.4	1.4	NUM
fumecheng-13737	399	34	1.6	1.6	NUM
fumecheng-13737	399	35	1.8	1.8	NUM
fumecheng-13737	399	36	2	2	NUM
fumecheng-13737	399	37	amplitude	amplitude	NOUN
fumecheng-13737	399	38	,	,	PUNCT
fumecheng-13737	399	39	a	a	DET
fumecheng-13737	399	40	f	f	X
fumecheng-13737	399	41	re	re	ADP
fumecheng-13737	399	42	q	q	PROPN
fumecheng-13737	399	43	u	u	PROPN
fumecheng-13737	399	44	en	en	PROPN
fumecheng-13737	399	45	cy	cy	PROPN
fumecheng-13737	400	1	(	(	PUNCT
fumecheng-13737	400	2	k	k	PROPN
fumecheng-13737	400	3	h	h	PROPN
fumecheng-13737	400	4	z	z	PROPN
fumecheng-13737	400	5	)	)	PUNCT
fumecheng-13737	400	6	n	n	NOUN
fumecheng-13737	400	7	=	=	SYM
fumecheng-13737	400	8	10	10	NUM
fumecheng-13737	400	9	n	n	NOUN
fumecheng-13737	400	10	=	=	SYM
fumecheng-13737	400	11	30	30	NUM
fumecheng-13737	400	12	n	n	NOUN
fumecheng-13737	400	13	=	=	SYM
fumecheng-13737	400	14	50	50	NUM
fumecheng-13737	400	15	n	n	NOUN
fumecheng-13737	400	16	=	=	SYM
fumecheng-13737	400	17	70	70	NUM
fumecheng-13737	400	18	(	(	PUNCT
fumecheng-13737	400	19	b	b	NOUN
fumecheng-13737	400	20	)	)	PUNCT
fumecheng-13737	400	21	cc	cc	ADP
fumecheng-13737	400	22	bcs	bcs	NOUN
fumecheng-13737	400	23	0.4	0.4	NUM
fumecheng-13737	400	24	0.45	0.45	NUM
fumecheng-13737	400	25	0.5	0.5	NUM
fumecheng-13737	400	26	0.55	0.55	NUM
fumecheng-13737	400	27	0.6	0.6	NUM
fumecheng-13737	400	28	0.65	0.65	NUM
fumecheng-13737	400	29	0.35	0.35	NUM
fumecheng-13737	400	30	0.4	0.4	NUM
fumecheng-13737	400	31	0.45	0.45	NUM
fumecheng-13737	400	32	0.5	0.5	NUM
fumecheng-13737	400	33	0.55	0.55	NUM
fumecheng-13737	400	34	0.6	0.6	NUM
fumecheng-13737	400	35	0.65	0.65	NUM
fumecheng-13737	400	36	0.7	0.7	NUM
fumecheng-13737	400	37	shell	shell	NOUN
fumecheng-13737	400	38	thickness	thickness	NOUN
fumecheng-13737	400	39	,	,	PUNCT
fumecheng-13737	400	40	h	h	NOUN
fumecheng-13737	400	41	(	(	PUNCT
fumecheng-13737	400	42	mm	mm	INTJ
fumecheng-13737	400	43	)	)	PUNCT
fumecheng-13737	400	44	f	f	NOUN
fumecheng-13737	400	45	re	re	PRON
fumecheng-13737	400	46	q	q	PROPN
fumecheng-13737	400	47	u	u	PROPN
fumecheng-13737	400	48	en	en	PROPN
fumecheng-13737	400	49	cy	cy	PROPN
fumecheng-13737	401	1	(	(	PUNCT
fumecheng-13737	401	2	k	k	PROPN
fumecheng-13737	401	3	h	h	PROPN
fumecheng-13737	401	4	z	z	PROPN
fumecheng-13737	401	5	)	)	PUNCT
fumecheng-13737	401	6	n	n	NOUN
fumecheng-13737	401	7	=	=	SYM
fumecheng-13737	401	8	10	10	NUM
fumecheng-13737	401	9	n	n	NOUN
fumecheng-13737	401	10	=	=	SYM
fumecheng-13737	401	11	30	30	NUM
fumecheng-13737	401	12	n	n	NOUN
fumecheng-13737	401	13	=	=	SYM
fumecheng-13737	401	14	50	50	NUM
fumecheng-13737	401	15	n	n	NOUN
fumecheng-13737	401	16	=	=	SYM
fumecheng-13737	401	17	70	70	NUM
fumecheng-13737	401	18	a	a	DET
fumecheng-13737	401	19	fast	fast	ADJ
fumecheng-13737	401	20	insight	insight	NOUN
fumecheng-13737	401	21	into	into	ADP
fumecheng-13737	401	22	nonlinear	nonlinear	ADJ
fumecheng-13737	401	23	frequency	frequency	NOUN
fumecheng-13737	401	24	estimation	estimation	NOUN
fumecheng-13737	401	25	of	of	ADP
fumecheng-13737	401	26	stringer	stringer	NOUN
fumecheng-13737	401	27	-	-	PUNCT
fumecheng-13737	401	28	stiffened	stiffen	VERB
fumecheng-13737	401	29	shells	shell	NOUN
fumecheng-13737	401	30	with	with	ADP
fumecheng-13737	401	31	high	high	ADJ
fumecheng-13737	401	32	accuracy	accuracy	NOUN
fumecheng-13737	401	33	805	805	NUM
fumecheng-13737	401	34	nonlinear	nonlinear	ADJ
fumecheng-13737	401	35	frequency	frequency	NOUN
fumecheng-13737	401	36	of	of	ADP
fumecheng-13737	401	37	stringer	stringer	NOUN
fumecheng-13737	401	38	-	-	PUNCT
fumecheng-13737	401	39	stiffened	stiffen	VERB
fumecheng-13737	401	40	shells	shell	NOUN
fumecheng-13737	401	41	.	.	PUNCT
fumecheng-13737	402	1	while	while	SCONJ
fumecheng-13737	402	2	this	this	DET
fumecheng-13737	402	3	approach	approach	NOUN
fumecheng-13737	402	4	effectively	effectively	ADV
fumecheng-13737	402	5	captures	capture	VERB
fumecheng-13737	402	6	the	the	DET
fumecheng-13737	402	7	primary	primary	ADJ
fumecheng-13737	402	8	nonlinear	nonlinear	ADJ
fumecheng-13737	402	9	behavior	behavior	NOUN
fumecheng-13737	402	10	,	,	PUNCT
fumecheng-13737	402	11	it	it	PRON
fumecheng-13737	402	12	does	do	AUX
fumecheng-13737	402	13	not	not	PART
fumecheng-13737	402	14	account	account	VERB
fumecheng-13737	402	15	for	for	ADP
fumecheng-13737	402	16	potential	potential	ADJ
fumecheng-13737	402	17	multi	multi	ADJ
fumecheng-13737	402	18	-	-	ADJ
fumecheng-13737	402	19	mode	mode	ADJ
fumecheng-13737	402	20	interactions	interaction	NOUN
fumecheng-13737	402	21	or	or	CCONJ
fumecheng-13737	402	22	energy	energy	NOUN
fumecheng-13737	402	23	dissipation	dissipation	NOUN
fumecheng-13737	402	24	mechanisms	mechanism	NOUN
fumecheng-13737	402	25	,	,	PUNCT
fumecheng-13737	402	26	which	which	PRON
fumecheng-13737	402	27	may	may	AUX
fumecheng-13737	402	28	influence	influence	VERB
fumecheng-13737	402	29	the	the	DET
fumecheng-13737	402	30	dynamic	dynamic	ADJ
fumecheng-13737	402	31	response	response	NOUN
fumecheng-13737	402	32	in	in	ADP
fumecheng-13737	402	33	more	more	ADJ
fumecheng-13737	402	34	complex	complex	ADJ
fumecheng-13737	402	35	scenarios	scenario	NOUN
fumecheng-13737	402	36	.	.	PUNCT
fumecheng-13737	403	1	these	these	DET
fumecheng-13737	403	2	limitations	limitation	NOUN
fumecheng-13737	403	3	suggest	suggest	VERB
fumecheng-13737	403	4	valuable	valuable	ADJ
fumecheng-13737	403	5	directions	direction	NOUN
fumecheng-13737	403	6	for	for	ADP
fumecheng-13737	403	7	future	future	ADJ
fumecheng-13737	403	8	research	research	NOUN
fumecheng-13737	403	9	,	,	PUNCT
fumecheng-13737	403	10	including	include	VERB
fumecheng-13737	403	11	the	the	DET
fumecheng-13737	403	12	extension	extension	NOUN
fumecheng-13737	403	13	of	of	ADP
fumecheng-13737	403	14	the	the	DET
fumecheng-13737	403	15	proposed	propose	VERB
fumecheng-13737	403	16	methods	method	NOUN
fumecheng-13737	403	17	to	to	PART
fumecheng-13737	403	18	multi	multi	ADJ
fumecheng-13737	403	19	-	-	ADJ
fumecheng-13737	403	20	mode	mode	ADJ
fumecheng-13737	403	21	systems	system	NOUN
fumecheng-13737	403	22	and	and	CCONJ
fumecheng-13737	403	23	the	the	DET
fumecheng-13737	403	24	incorporation	incorporation	NOUN
fumecheng-13737	403	25	of	of	ADP
fumecheng-13737	403	26	damping	damp	VERB
fumecheng-13737	403	27	effects	effect	NOUN
fumecheng-13737	403	28	for	for	ADP
fumecheng-13737	403	29	a	a	DET
fumecheng-13737	403	30	more	more	ADV
fumecheng-13737	403	31	comprehensive	comprehensive	ADJ
fumecheng-13737	403	32	dynamic	dynamic	ADJ
fumecheng-13737	403	33	analysis	analysis	NOUN
fumecheng-13737	403	34	.	.	PUNCT
fumecheng-13737	404	1	references	reference	NOUN
fumecheng-13737	404	2	1	1	NUM
fumecheng-13737	404	3	.	.	PUNCT
fumecheng-13737	405	1	gavrilenko	gavrilenko	PROPN
fumecheng-13737	405	2	,	,	PUNCT
fumecheng-13737	405	3	g.d	g.d	PROPN
fumecheng-13737	405	4	.	.	PROPN
fumecheng-13737	405	5	,	,	PUNCT
fumecheng-13737	405	6	matsner	matsner	NOUN
fumecheng-13737	405	7	,	,	PUNCT
fumecheng-13737	405	8	v.i	v.i	PROPN
fumecheng-13737	405	9	.	.	PROPN
fumecheng-13737	405	10	,	,	PUNCT
fumecheng-13737	405	11	2006	2006	NUM
fumecheng-13737	405	12	,	,	PUNCT
fumecheng-13737	405	13	some	some	DET
fumecheng-13737	405	14	features	feature	NOUN
fumecheng-13737	405	15	of	of	ADP
fumecheng-13737	405	16	the	the	DET
fumecheng-13737	405	17	buckling	buckling	NOUN
fumecheng-13737	405	18	of	of	ADP
fumecheng-13737	405	19	stringer	stringer	NOUN
fumecheng-13737	405	20	shells	shell	NOUN
fumecheng-13737	405	21	,	,	PUNCT
fumecheng-13737	405	22	international	international	ADJ
fumecheng-13737	405	23	applied	apply	VERB
fumecheng-13737	405	24	mechanics	mechanic	NOUN
fumecheng-13737	405	25	,	,	PUNCT
fumecheng-13737	405	26	42(2	42(2	NOUN
fumecheng-13737	405	27	)	)	PUNCT
fumecheng-13737	405	28	,	,	PUNCT
fumecheng-13737	406	1	pp	pp	ADP
fumecheng-13737	406	2	.	.	PUNCT
fumecheng-13737	407	1	176	176	NUM
fumecheng-13737	407	2	-	-	SYM
fumecheng-13737	407	3	180	180	NUM
fumecheng-13737	407	4	.	.	NOUN
fumecheng-13737	408	1	2	2	NUM
fumecheng-13737	408	2	.	.	X
fumecheng-13737	408	3	naghsh	naghsh	NOUN
fumecheng-13737	408	4	,	,	PUNCT
fumecheng-13737	408	5	a.	a.	NOUN
fumecheng-13737	408	6	,	,	PUNCT
fumecheng-13737	408	7	saadatpour	saadatpour	NOUN
fumecheng-13737	408	8	,	,	PUNCT
fumecheng-13737	408	9	m.m	m.m	PROPN
fumecheng-13737	408	10	.	.	PROPN
fumecheng-13737	408	11	,	,	PUNCT
fumecheng-13737	408	12	azhari	azhari	PROPN
fumecheng-13737	408	13	,	,	PUNCT
fumecheng-13737	408	14	m.	m.	NOUN
fumecheng-13737	408	15	,	,	PUNCT
fumecheng-13737	408	16	2015	2015	NUM
fumecheng-13737	408	17	,	,	PUNCT
fumecheng-13737	408	18	free	free	ADJ
fumecheng-13737	408	19	vibration	vibration	NOUN
fumecheng-13737	408	20	analysis	analysis	NOUN
fumecheng-13737	408	21	of	of	ADP
fumecheng-13737	408	22	stringer	stringer	NOUN
fumecheng-13737	408	23	stiffened	stiffen	VERB
fumecheng-13737	408	24	general	general	ADJ
fumecheng-13737	408	25	shells	shell	NOUN
fumecheng-13737	408	26	of	of	ADP
fumecheng-13737	408	27	revolution	revolution	NOUN
fumecheng-13737	408	28	using	use	VERB
fumecheng-13737	408	29	a	a	DET
fumecheng-13737	408	30	meridional	meridional	ADJ
fumecheng-13737	408	31	finite	finite	ADJ
fumecheng-13737	408	32	strip	strip	NOUN
fumecheng-13737	408	33	method	method	NOUN
fumecheng-13737	408	34	,	,	PUNCT
fumecheng-13737	408	35	thin	thin	ADJ
fumecheng-13737	408	36	-	-	PUNCT
fumecheng-13737	408	37	walled	walled	ADJ
fumecheng-13737	408	38	structures	structure	NOUN
fumecheng-13737	408	39	,	,	PUNCT
fumecheng-13737	408	40	94	94	NUM
fumecheng-13737	408	41	,	,	PUNCT
fumecheng-13737	408	42	pp	pp	ADJ
fumecheng-13737	408	43	.	.	PUNCT
fumecheng-13737	409	1	651	651	NUM
fumecheng-13737	409	2	-	-	SYM
fumecheng-13737	409	3	662	662	NUM
fumecheng-13737	409	4	.	.	PUNCT
fumecheng-13737	410	1	3	3	X
fumecheng-13737	410	2	.	.	X
fumecheng-13737	410	3	golchi	golchi	PROPN
fumecheng-13737	410	4	,	,	PUNCT
fumecheng-13737	410	5	m.	m.	NOUN
fumecheng-13737	410	6	,	,	PUNCT
fumecheng-13737	410	7	mostafa	mostafa	PROPN
fumecheng-13737	410	8	,	,	PUNCT
fumecheng-13737	410	9	t.	t.	PROPN
fumecheng-13737	410	10	,	,	PUNCT
fumecheng-13737	410	11	talebitooti	talebitooti	PROPN
fumecheng-13737	410	12	,	,	PUNCT
fumecheng-13737	410	13	r.	r.	PROPN
fumecheng-13737	410	14	,	,	PUNCT
fumecheng-13737	410	15	2019	2019	NUM
fumecheng-13737	410	16	,	,	PUNCT
fumecheng-13737	410	17	thermal	thermal	ADJ
fumecheng-13737	410	18	buckling	buckling	NOUN
fumecheng-13737	410	19	and	and	CCONJ
fumecheng-13737	410	20	free	free	ADJ
fumecheng-13737	410	21	vibration	vibration	NOUN
fumecheng-13737	410	22	of	of	ADP
fumecheng-13737	410	23	fg	fg	PROPN
fumecheng-13737	410	24	truncated	truncated	ADJ
fumecheng-13737	410	25	conical	conical	NOUN
fumecheng-13737	410	26	shells	shell	NOUN
fumecheng-13737	410	27	with	with	ADP
fumecheng-13737	410	28	stringer	stringer	NOUN
fumecheng-13737	410	29	and	and	CCONJ
fumecheng-13737	410	30	ring	ring	NOUN
fumecheng-13737	410	31	stiffeners	stiffener	NOUN
fumecheng-13737	410	32	using	use	VERB
fumecheng-13737	410	33	differential	differential	ADJ
fumecheng-13737	410	34	quadrature	quadrature	NOUN
fumecheng-13737	410	35	method	method	NOUN
fumecheng-13737	410	36	,	,	PUNCT
fumecheng-13737	410	37	mechanics	mechanic	NOUN
fumecheng-13737	410	38	based	base	VERB
fumecheng-13737	410	39	design	design	NOUN
fumecheng-13737	410	40	of	of	ADP
fumecheng-13737	410	41	structures	structure	NOUN
fumecheng-13737	410	42	and	and	CCONJ
fumecheng-13737	410	43	machines	machine	NOUN
fumecheng-13737	410	44	,	,	PUNCT
fumecheng-13737	410	45	47(3	47(3	NOUN
fumecheng-13737	410	46	)	)	PUNCT
fumecheng-13737	410	47	,	,	PUNCT
fumecheng-13737	410	48	pp	pp	ADJ
fumecheng-13737	410	49	.	.	PUNCT
fumecheng-13737	411	1	255	255	NUM
fumecheng-13737	411	2	-	-	SYM
fumecheng-13737	411	3	282	282	NUM
fumecheng-13737	411	4	.	.	PUNCT
fumecheng-13737	412	1	4	4	NUM
fumecheng-13737	412	2	.	.	X
fumecheng-13737	412	3	bich	bich	PROPN
fumecheng-13737	412	4	,	,	PUNCT
fumecheng-13737	412	5	d.h	d.h	PROPN
fumecheng-13737	412	6	.	.	PROPN
fumecheng-13737	412	7	,	,	PUNCT
fumecheng-13737	412	8	ninh	ninh	PROPN
fumecheng-13737	412	9	,	,	PUNCT
fumecheng-13737	412	10	d.g	d.g	PROPN
fumecheng-13737	412	11	.	.	PROPN
fumecheng-13737	412	12	,	,	PUNCT
fumecheng-13737	412	13	2017	2017	NUM
fumecheng-13737	412	14	,	,	PUNCT
fumecheng-13737	412	15	an	an	DET
fumecheng-13737	412	16	analytical	analytical	ADJ
fumecheng-13737	412	17	approach	approach	NOUN
fumecheng-13737	412	18	:	:	PUNCT
fumecheng-13737	412	19	nonlinear	nonlinear	ADJ
fumecheng-13737	412	20	vibration	vibration	NOUN
fumecheng-13737	412	21	of	of	ADP
fumecheng-13737	412	22	imperfect	imperfect	NOUN
fumecheng-13737	412	23	stiffened	stiffen	VERB
fumecheng-13737	412	24	fgm	fgm	PROPN
fumecheng-13737	412	25	sandwich	sandwich	NOUN
fumecheng-13737	412	26	toroidal	toroidal	ADJ
fumecheng-13737	412	27	shell	shell	NOUN
fumecheng-13737	412	28	segments	segment	NOUN
fumecheng-13737	412	29	containing	contain	VERB
fumecheng-13737	412	30	fluid	fluid	NOUN
fumecheng-13737	412	31	under	under	ADP
fumecheng-13737	412	32	external	external	ADJ
fumecheng-13737	412	33	thermo	thermo	NOUN
fumecheng-13737	412	34	-	-	PUNCT
fumecheng-13737	412	35	mechanical	mechanical	ADJ
fumecheng-13737	412	36	loads	load	NOUN
fumecheng-13737	412	37	,	,	PUNCT
fumecheng-13737	412	38	composite	composite	ADJ
fumecheng-13737	412	39	structures	structure	NOUN
fumecheng-13737	412	40	,	,	PUNCT
fumecheng-13737	412	41	162	162	NUM
fumecheng-13737	412	42	,	,	PUNCT
fumecheng-13737	412	43	pp	pp	ADJ
fumecheng-13737	412	44	.	.	PUNCT
fumecheng-13737	412	45	164	164	NUM
fumecheng-13737	412	46	-	-	SYM
fumecheng-13737	412	47	181	181	NUM
fumecheng-13737	412	48	.	.	PUNCT
fumecheng-13737	413	1	5	5	NUM
fumecheng-13737	413	2	.	.	X
fumecheng-13737	414	1	ninh	ninh	PROPN
fumecheng-13737	414	2	,	,	PUNCT
fumecheng-13737	414	3	d.g	d.g	PROPN
fumecheng-13737	414	4	.	.	PROPN
fumecheng-13737	414	5	,	,	PUNCT
fumecheng-13737	414	6	bich	bich	PROPN
fumecheng-13737	414	7	,	,	PUNCT
fumecheng-13737	414	8	d.h	d.h	PROPN
fumecheng-13737	414	9	.	.	PROPN
fumecheng-13737	414	10	,	,	PUNCT
fumecheng-13737	414	11	2016	2016	NUM
fumecheng-13737	414	12	,	,	PUNCT
fumecheng-13737	414	13	nonlinear	nonlinear	ADJ
fumecheng-13737	414	14	thermal	thermal	ADJ
fumecheng-13737	414	15	vibration	vibration	NOUN
fumecheng-13737	414	16	of	of	ADP
fumecheng-13737	414	17	eccentrically	eccentrically	ADV
fumecheng-13737	414	18	stiffened	stiffen	VERB
fumecheng-13737	414	19	ceramic	ceramic	ADJ
fumecheng-13737	414	20	-	-	PUNCT
fumecheng-13737	414	21	fgm	fgm	ADJ
fumecheng-13737	414	22	-	-	PUNCT
fumecheng-13737	414	23	metal	metal	NOUN
fumecheng-13737	414	24	layer	layer	NOUN
fumecheng-13737	414	25	toroidal	toroidal	ADJ
fumecheng-13737	414	26	shell	shell	NOUN
fumecheng-13737	414	27	segments	segment	NOUN
fumecheng-13737	414	28	surrounded	surround	VERB
fumecheng-13737	414	29	by	by	ADP
fumecheng-13737	414	30	elastic	elastic	ADJ
fumecheng-13737	414	31	foundation	foundation	NOUN
fumecheng-13737	414	32	,	,	PUNCT
fumecheng-13737	414	33	thin	thin	ADJ
fumecheng-13737	414	34	-	-	PUNCT
fumecheng-13737	414	35	walled	walled	ADJ
fumecheng-13737	414	36	structures	structure	NOUN
fumecheng-13737	414	37	,	,	PUNCT
fumecheng-13737	414	38	104	104	NUM
fumecheng-13737	414	39	,	,	PUNCT
fumecheng-13737	414	40	pp	pp	ADJ
fumecheng-13737	414	41	.	.	PUNCT
fumecheng-13737	415	1	198	198	NUM
fumecheng-13737	415	2	-	-	SYM
fumecheng-13737	415	3	210	210	NUM
fumecheng-13737	415	4	.	.	PUNCT
fumecheng-13737	416	1	6	6	NUM
fumecheng-13737	416	2	.	.	X
fumecheng-13737	416	3	liu	liu	PROPN
fumecheng-13737	416	4	,	,	PUNCT
fumecheng-13737	416	5	l.	l.	PROPN
fumecheng-13737	416	6	,	,	PUNCT
fumecheng-13737	416	7	sun	sun	PROPN
fumecheng-13737	416	8	,	,	PUNCT
fumecheng-13737	416	9	s.	s.	PROPN
fumecheng-13737	416	10	,	,	PUNCT
fumecheng-13737	416	11	han	han	PROPN
fumecheng-13737	416	12	,	,	PUNCT
fumecheng-13737	416	13	j.	j.	PROPN
fumecheng-13737	416	14	,	,	PUNCT
fumecheng-13737	416	15	2021	2021	NUM
fumecheng-13737	416	16	,	,	PUNCT
fumecheng-13737	416	17	nonlinear	nonlinear	ADJ
fumecheng-13737	416	18	traveling	traveling	ADJ
fumecheng-13737	416	19	-	-	PUNCT
fumecheng-13737	416	20	wave	wave	NOUN
fumecheng-13737	416	21	vibration	vibration	NOUN
fumecheng-13737	416	22	of	of	ADP
fumecheng-13737	416	23	a	a	DET
fumecheng-13737	416	24	ring	ring	NOUN
fumecheng-13737	416	25	-	-	PUNCT
fumecheng-13737	416	26	stringer	stringer	NOUN
fumecheng-13737	416	27	stiffened	stiffen	VERB
fumecheng-13737	416	28	cylindrical	cylindrical	ADJ
fumecheng-13737	416	29	shell	shell	NOUN
fumecheng-13737	416	30	,	,	PUNCT
fumecheng-13737	416	31	international	international	ADJ
fumecheng-13737	416	32	journal	journal	NOUN
fumecheng-13737	416	33	of	of	ADP
fumecheng-13737	416	34	structural	structural	ADJ
fumecheng-13737	416	35	stability	stability	NOUN
fumecheng-13737	416	36	and	and	CCONJ
fumecheng-13737	416	37	dynamics	dynamic	NOUN
fumecheng-13737	416	38	,	,	PUNCT
fumecheng-13737	416	39	21(04	21(04	NUM
fumecheng-13737	416	40	)	)	PUNCT
fumecheng-13737	416	41	,	,	PUNCT
fumecheng-13737	416	42	2150059	2150059	NUM
fumecheng-13737	416	43	.	.	PUNCT
fumecheng-13737	417	1	7	7	X
fumecheng-13737	417	2	.	.	X
fumecheng-13737	417	3	liu	liu	PROPN
fumecheng-13737	417	4	,	,	PUNCT
fumecheng-13737	417	5	y.	y.	PROPN
fumecheng-13737	417	6	,	,	PUNCT
fumecheng-13737	417	7	qin	qin	PROPN
fumecheng-13737	417	8	,	,	PUNCT
fumecheng-13737	417	9	z.	z.	PROPN
fumecheng-13737	417	10	,	,	PUNCT
fumecheng-13737	417	11	chu	chu	PROPN
fumecheng-13737	417	12	,	,	PUNCT
fumecheng-13737	417	13	f.	f.	PROPN
fumecheng-13737	417	14	,	,	PUNCT
fumecheng-13737	417	15	2022	2022	NUM
fumecheng-13737	417	16	,	,	PUNCT
fumecheng-13737	417	17	nonlinear	nonlinear	ADJ
fumecheng-13737	417	18	forced	force	VERB
fumecheng-13737	417	19	vibrations	vibration	NOUN
fumecheng-13737	417	20	of	of	ADP
fumecheng-13737	417	21	rotating	rotate	VERB
fumecheng-13737	417	22	cylindrical	cylindrical	ADJ
fumecheng-13737	417	23	shells	shell	NOUN
fumecheng-13737	417	24	under	under	ADP
fumecheng-13737	417	25	multiharmonic	multiharmonic	NOUN
fumecheng-13737	417	26	excitations	excitation	NOUN
fumecheng-13737	417	27	in	in	ADP
fumecheng-13737	417	28	thermal	thermal	ADJ
fumecheng-13737	417	29	environment	environment	NOUN
fumecheng-13737	417	30	,	,	PUNCT
fumecheng-13737	417	31	nonlinear	nonlinear	ADJ
fumecheng-13737	417	32	dynamics	dynamic	NOUN
fumecheng-13737	417	33	,	,	PUNCT
fumecheng-13737	417	34	108(4	108(4	NUM
fumecheng-13737	417	35	)	)	PUNCT
fumecheng-13737	417	36	,	,	PUNCT
fumecheng-13737	417	37	pp	pp	ADJ
fumecheng-13737	417	38	.	.	PUNCT
fumecheng-13737	418	1	2977	2977	NUM
fumecheng-13737	418	2	-	-	SYM
fumecheng-13737	418	3	2991	2991	NUM
fumecheng-13737	418	4	.	.	PUNCT
fumecheng-13737	419	1	8	8	X
fumecheng-13737	419	2	.	.	X
fumecheng-13737	419	3	vahidi	vahidi	PROPN
fumecheng-13737	419	4	,	,	PUNCT
fumecheng-13737	419	5	h.	h.	PROPN
fumecheng-13737	419	6	,	,	PUNCT
fumecheng-13737	419	7	shahgholi	shahgholi	PROPN
fumecheng-13737	419	8	,	,	PUNCT
fumecheng-13737	419	9	m.	m.	NOUN
fumecheng-13737	419	10	,	,	PUNCT
fumecheng-13737	419	11	hanzaki	hanzaki	NOUN
fumecheng-13737	419	12	,	,	PUNCT
fumecheng-13737	419	13	a.r	a.r	PROPN
fumecheng-13737	419	14	.	.	PROPN
fumecheng-13737	419	15	,	,	PUNCT
fumecheng-13737	419	16	mohamadi	mohamadi	NOUN
fumecheng-13737	419	17	,	,	PUNCT
fumecheng-13737	419	18	a.	a.	NOUN
fumecheng-13737	419	19	,	,	PUNCT
fumecheng-13737	419	20	2022	2022	NUM
fumecheng-13737	419	21	,	,	PUNCT
fumecheng-13737	419	22	nonlinear	nonlinear	ADJ
fumecheng-13737	419	23	vibration	vibration	NOUN
fumecheng-13737	419	24	,	,	PUNCT
fumecheng-13737	419	25	stability	stability	NOUN
fumecheng-13737	419	26	,	,	PUNCT
fumecheng-13737	419	27	and	and	CCONJ
fumecheng-13737	419	28	bifurcation	bifurcation	NOUN
fumecheng-13737	419	29	of	of	ADP
fumecheng-13737	419	30	rotating	rotate	VERB
fumecheng-13737	419	31	axially	axially	ADV
fumecheng-13737	419	32	moving	move	VERB
fumecheng-13737	419	33	conical	conical	ADJ
fumecheng-13737	419	34	shells	shell	NOUN
fumecheng-13737	419	35	,	,	PUNCT
fumecheng-13737	419	36	acta	acta	PROPN
fumecheng-13737	419	37	mechanica	mechanica	PROPN
fumecheng-13737	419	38	,	,	PUNCT
fumecheng-13737	419	39	233(8	233(8	NUM
fumecheng-13737	419	40	)	)	PUNCT
fumecheng-13737	419	41	,	,	PUNCT
fumecheng-13737	419	42	pp	pp	PROPN
fumecheng-13737	419	43	.	.	PUNCT
fumecheng-13737	420	1	3175	3175	NUM
fumecheng-13737	420	2	-	-	SYM
fumecheng-13737	420	3	3196	3196	NUM
fumecheng-13737	420	4	.	.	PUNCT
fumecheng-13737	421	1	9	9	X
fumecheng-13737	421	2	.	.	X
fumecheng-13737	421	3	mohammadrezazadeh	mohammadrezazadeh	PROPN
fumecheng-13737	421	4	,	,	PUNCT
fumecheng-13737	421	5	s.	s.	PROPN
fumecheng-13737	421	6	,	,	PUNCT
fumecheng-13737	421	7	jafari	jafari	PROPN
fumecheng-13737	421	8	,	,	PUNCT
fumecheng-13737	421	9	a.a	a.a	PROPN
fumecheng-13737	421	10	.	.	PROPN
fumecheng-13737	421	11	,	,	PUNCT
fumecheng-13737	421	12	2023	2023	NUM
fumecheng-13737	421	13	,	,	PUNCT
fumecheng-13737	421	14	nonlinear	nonlinear	ADJ
fumecheng-13737	421	15	vibration	vibration	NOUN
fumecheng-13737	421	16	suppression	suppression	NOUN
fumecheng-13737	421	17	of	of	ADP
fumecheng-13737	421	18	s	s	NOUN
fumecheng-13737	421	19	-	-	PUNCT
fumecheng-13737	421	20	s	s	X
fumecheng-13737	421	21	and	and	CCONJ
fumecheng-13737	421	22	c	c	NOUN
fumecheng-13737	421	23	-	-	PUNCT
fumecheng-13737	421	24	c	c	NOUN
fumecheng-13737	421	25	laminated	laminate	VERB
fumecheng-13737	421	26	composite	composite	ADJ
fumecheng-13737	421	27	cylindrical	cylindrical	ADJ
fumecheng-13737	421	28	shells	shell	NOUN
fumecheng-13737	421	29	with	with	ADP
fumecheng-13737	421	30	magnetostrictive	magnetostrictive	ADJ
fumecheng-13737	421	31	strips	strip	NOUN
fumecheng-13737	421	32	,	,	PUNCT
fumecheng-13737	421	33	mechanics	mechanic	NOUN
fumecheng-13737	421	34	based	base	VERB
fumecheng-13737	421	35	design	design	NOUN
fumecheng-13737	421	36	of	of	ADP
fumecheng-13737	421	37	structures	structure	NOUN
fumecheng-13737	421	38	and	and	CCONJ
fumecheng-13737	421	39	machines	machine	NOUN
fumecheng-13737	421	40	,	,	PUNCT
fumecheng-13737	421	41	51(10	51(10	NUM
fumecheng-13737	421	42	)	)	PUNCT
fumecheng-13737	421	43	,	,	PUNCT
fumecheng-13737	421	44	pp	pp	ADP
fumecheng-13737	421	45	.	.	PUNCT
fumecheng-13737	422	1	5470	5470	NUM
fumecheng-13737	422	2	-	-	SYM
fumecheng-13737	422	3	5491	5491	NUM
fumecheng-13737	422	4	.	.	PUNCT
fumecheng-13737	423	1	10	10	NUM
fumecheng-13737	423	2	.	.	X
fumecheng-13737	423	3	bochkarev	bochkarev	PROPN
fumecheng-13737	423	4	,	,	PUNCT
fumecheng-13737	423	5	s.a	s.a	PROPN
fumecheng-13737	423	6	.	.	PROPN
fumecheng-13737	423	7	,	,	PUNCT
fumecheng-13737	423	8	lekomtsev	lekomtsev	PROPN
fumecheng-13737	423	9	,	,	PUNCT
fumecheng-13737	423	10	s.v	s.v	PROPN
fumecheng-13737	423	11	.	.	PROPN
fumecheng-13737	423	12	,	,	PUNCT
fumecheng-13737	423	13	matveenko	matveenko	PROPN
fumecheng-13737	423	14	,	,	PUNCT
fumecheng-13737	423	15	v.p	v.p	PROPN
fumecheng-13737	423	16	.	.	PROPN
fumecheng-13737	423	17	,	,	PUNCT
fumecheng-13737	423	18	2023	2023	NUM
fumecheng-13737	423	19	,	,	PUNCT
fumecheng-13737	423	20	finite	finite	NOUN
fumecheng-13737	423	21	element	element	NOUN
fumecheng-13737	423	22	analysis	analysis	NOUN
fumecheng-13737	423	23	of	of	ADP
fumecheng-13737	423	24	the	the	DET
fumecheng-13737	423	25	panel	panel	NOUN
fumecheng-13737	423	26	flutter	flutter	NOUN
fumecheng-13737	423	27	of	of	ADP
fumecheng-13737	423	28	stiffened	stiffen	VERB
fumecheng-13737	423	29	shallow	shallow	ADJ
fumecheng-13737	423	30	shells	shell	NOUN
fumecheng-13737	423	31	,	,	PUNCT
fumecheng-13737	423	32	continuum	continuum	ADJ
fumecheng-13737	423	33	mechanics	mechanic	NOUN
fumecheng-13737	423	34	and	and	CCONJ
fumecheng-13737	423	35	thermodynamics	thermodynamic	NOUN
fumecheng-13737	423	36	,	,	PUNCT
fumecheng-13737	423	37	35(4	35(4	NUM
fumecheng-13737	423	38	)	)	PUNCT
fumecheng-13737	423	39	,	,	PUNCT
fumecheng-13737	423	40	pp	pp	ADP
fumecheng-13737	423	41	.	.	PUNCT
fumecheng-13737	424	1	1275	1275	NUM
fumecheng-13737	424	2	-	-	SYM
fumecheng-13737	424	3	1290	1290	NUM
fumecheng-13737	424	4	.	.	PUNCT
fumecheng-13737	425	1	11	11	NUM
fumecheng-13737	425	2	.	.	X
fumecheng-13737	426	1	foroutan	foroutan	PROPN
fumecheng-13737	426	2	,	,	PUNCT
fumecheng-13737	426	3	k.	k.	PROPN
fumecheng-13737	426	4	,	,	PUNCT
fumecheng-13737	426	5	dai	dai	PROPN
fumecheng-13737	426	6	,	,	PUNCT
fumecheng-13737	426	7	l.	l.	PROPN
fumecheng-13737	426	8	,	,	PUNCT
fumecheng-13737	426	9	2024	2024	NUM
fumecheng-13737	426	10	,	,	PUNCT
fumecheng-13737	426	11	nonlinear	nonlinear	ADJ
fumecheng-13737	426	12	dynamic	dynamic	ADJ
fumecheng-13737	426	13	response	response	NOUN
fumecheng-13737	426	14	and	and	CCONJ
fumecheng-13737	426	15	vibration	vibration	NOUN
fumecheng-13737	426	16	of	of	ADP
fumecheng-13737	426	17	spiral	spiral	ADJ
fumecheng-13737	426	18	stiffened	stiffen	VERB
fumecheng-13737	426	19	fg	fg	ADP
fumecheng-13737	426	20	toroidal	toroidal	ADJ
fumecheng-13737	426	21	shell	shell	ADJ
fumecheng-13737	426	22	segments	segment	NOUN
fumecheng-13737	426	23	with	with	ADP
fumecheng-13737	426	24	variable	variable	ADJ
fumecheng-13737	426	25	thickness	thickness	NOUN
fumecheng-13737	426	26	,	,	PUNCT
fumecheng-13737	426	27	mechanics	mechanic	NOUN
fumecheng-13737	426	28	based	base	VERB
fumecheng-13737	426	29	design	design	NOUN
fumecheng-13737	426	30	of	of	ADP
fumecheng-13737	426	31	structures	structure	NOUN
fumecheng-13737	426	32	and	and	CCONJ
fumecheng-13737	426	33	machines	machine	NOUN
fumecheng-13737	426	34	,	,	PUNCT
fumecheng-13737	426	35	52(8	52(8	NUM
fumecheng-13737	426	36	)	)	PUNCT
fumecheng-13737	426	37	,	,	PUNCT
fumecheng-13737	426	38	pp	pp	PROPN
fumecheng-13737	426	39	.	.	PUNCT
fumecheng-13737	427	1	4930	4930	NUM
fumecheng-13737	427	2	-	-	SYM
fumecheng-13737	427	3	4952	4952	NUM
fumecheng-13737	427	4	.	.	PUNCT
fumecheng-13737	428	1	12	12	NUM
fumecheng-13737	428	2	.	.	PUNCT
fumecheng-13737	429	1	azzara	azzara	PROPN
fumecheng-13737	429	2	,	,	PUNCT
fumecheng-13737	429	3	r.	r.	PROPN
fumecheng-13737	429	4	,	,	PUNCT
fumecheng-13737	429	5	filippi	filippi	PROPN
fumecheng-13737	429	6	,	,	PUNCT
fumecheng-13737	429	7	m.	m.	NOUN
fumecheng-13737	429	8	,	,	PUNCT
fumecheng-13737	429	9	carrera	carrera	PROPN
fumecheng-13737	429	10	,	,	PUNCT
fumecheng-13737	429	11	e.	e.	PROPN
fumecheng-13737	429	12	,	,	PUNCT
fumecheng-13737	429	13	2024	2024	NUM
fumecheng-13737	429	14	,	,	PUNCT
fumecheng-13737	429	15	rotordynamic	rotordynamic	ADJ
fumecheng-13737	429	16	analyses	analysis	NOUN
fumecheng-13737	429	17	of	of	ADP
fumecheng-13737	429	18	stiffened	stiffen	VERB
fumecheng-13737	429	19	cylindrical	cylindrical	ADJ
fumecheng-13737	429	20	structures	structure	NOUN
fumecheng-13737	429	21	using	use	VERB
fumecheng-13737	429	22	high	high	ADJ
fumecheng-13737	429	23	-	-	PUNCT
fumecheng-13737	429	24	fidelity	fidelity	NOUN
fumecheng-13737	429	25	shell	shell	NOUN
fumecheng-13737	429	26	models	model	NOUN
fumecheng-13737	429	27	,	,	PUNCT
fumecheng-13737	429	28	mechanics	mechanic	NOUN
fumecheng-13737	429	29	of	of	ADP
fumecheng-13737	429	30	advanced	advanced	ADJ
fumecheng-13737	429	31	materials	material	NOUN
fumecheng-13737	429	32	and	and	CCONJ
fumecheng-13737	429	33	structures	structure	NOUN
fumecheng-13737	429	34	,	,	PUNCT
fumecheng-13737	429	35	31(29	31(29	NOUN
fumecheng-13737	429	36	)	)	PUNCT
fumecheng-13737	429	37	,	,	PUNCT
fumecheng-13737	429	38	pp	pp	PROPN
fumecheng-13737	429	39	.	.	PUNCT
fumecheng-13737	430	1	11677	11677	NUM
fumecheng-13737	430	2	-	-	SYM
fumecheng-13737	430	3	11686	11686	NUM
fumecheng-13737	430	4	.	.	PUNCT
fumecheng-13737	431	1	13	13	NUM
fumecheng-13737	431	2	.	.	X
fumecheng-13737	432	1	zhang	zhang	PROPN
fumecheng-13737	432	2	,	,	PUNCT
fumecheng-13737	432	3	j.	j.	PROPN
fumecheng-13737	432	4	,	,	PUNCT
fumecheng-13737	432	5	zhang	zhang	PROPN
fumecheng-13737	432	6	,	,	PUNCT
fumecheng-13737	432	7	w.	w.	PROPN
fumecheng-13737	432	8	,	,	PUNCT
fumecheng-13737	432	9	zhang	zhang	PROPN
fumecheng-13737	432	10	,	,	PUNCT
fumecheng-13737	432	11	y.f	y.f	PROPN
fumecheng-13737	432	12	.	.	PROPN
fumecheng-13737	432	13	,	,	PUNCT
fumecheng-13737	432	14	2024	2024	NUM
fumecheng-13737	432	15	,	,	PUNCT
fumecheng-13737	432	16	nonlinear	nonlinear	ADJ
fumecheng-13737	432	17	vibrations	vibration	NOUN
fumecheng-13737	432	18	of	of	ADP
fumecheng-13737	432	19	porous	porous	ADJ
fumecheng-13737	432	20	-	-	PUNCT
fumecheng-13737	432	21	hyperelastic	hyperelastic	ADJ
fumecheng-13737	432	22	cylindrical	cylindrical	ADJ
fumecheng-13737	432	23	shell	shell	NOUN
fumecheng-13737	432	24	under	under	ADP
fumecheng-13737	432	25	harmonic	harmonic	ADJ
fumecheng-13737	432	26	force	force	NOUN
fumecheng-13737	432	27	using	use	VERB
fumecheng-13737	432	28	harmonic	harmonic	ADJ
fumecheng-13737	432	29	balance	balance	NOUN
fumecheng-13737	432	30	and	and	CCONJ
fumecheng-13737	432	31	pseudo	pseudo	NOUN
fumecheng-13737	432	32	-	-	NOUN
fumecheng-13737	432	33	arc	arc	NOUN
fumecheng-13737	432	34	length	length	NOUN
fumecheng-13737	432	35	continuation	continuation	NOUN
fumecheng-13737	432	36	methods	method	NOUN
fumecheng-13737	432	37	,	,	PUNCT
fumecheng-13737	432	38	thin	thin	ADJ
fumecheng-13737	432	39	-	-	PUNCT
fumecheng-13737	432	40	walled	walled	ADJ
fumecheng-13737	432	41	structures	structure	NOUN
fumecheng-13737	432	42	,	,	PUNCT
fumecheng-13737	432	43	198	198	NUM
fumecheng-13737	432	44	,	,	PUNCT
fumecheng-13737	432	45	111767	111767	NUM
fumecheng-13737	432	46	.	.	PUNCT
fumecheng-13737	433	1	14	14	NUM
fumecheng-13737	433	2	.	.	X
fumecheng-13737	434	1	du	du	PROPN
fumecheng-13737	434	2	,	,	PUNCT
fumecheng-13737	434	3	y.	y.	PROPN
fumecheng-13737	434	4	,	,	PUNCT
fumecheng-13737	434	5	tang	tang	PROPN
fumecheng-13737	434	6	,	,	PUNCT
fumecheng-13737	434	7	y.	y.	PROPN
fumecheng-13737	434	8	,	,	PUNCT
fumecheng-13737	434	9	zou	zou	PROPN
fumecheng-13737	434	10	,	,	PUNCT
fumecheng-13737	434	11	y.	y.	PROPN
fumecheng-13737	434	12	,	,	PUNCT
fumecheng-13737	434	13	wang	wang	PROPN
fumecheng-13737	434	14	,	,	PUNCT
fumecheng-13737	434	15	y.	y.	PROPN
fumecheng-13737	434	16	,	,	PUNCT
fumecheng-13737	434	17	pang	pang	NOUN
fumecheng-13737	434	18	,	,	PUNCT
fumecheng-13737	434	19	f.	f.	PROPN
fumecheng-13737	434	20	,	,	PUNCT
fumecheng-13737	434	21	jia	jia	PROPN
fumecheng-13737	434	22	,	,	PUNCT
fumecheng-13737	434	23	f.	f.	PROPN
fumecheng-13737	434	24	,	,	PUNCT
fumecheng-13737	434	25	ma	ma	PROPN
fumecheng-13737	434	26	,	,	PUNCT
fumecheng-13737	434	27	y.	y.	PROPN
fumecheng-13737	434	28	,	,	PUNCT
fumecheng-13737	434	29	wang	wang	PROPN
fumecheng-13737	434	30	,	,	PUNCT
fumecheng-13737	434	31	s.	s.	PROPN
fumecheng-13737	434	32	,	,	PUNCT
fumecheng-13737	434	33	2024	2024	NUM
fumecheng-13737	434	34	,	,	PUNCT
fumecheng-13737	434	35	the	the	DET
fumecheng-13737	434	36	low	low	ADJ
fumecheng-13737	434	37	frequency	frequency	NOUN
fumecheng-13737	434	38	multi	multi	ADJ
fumecheng-13737	434	39	-	-	ADJ
fumecheng-13737	434	40	linear	linear	ADJ
fumecheng-13737	434	41	spectrum	spectrum	NOUN
fumecheng-13737	434	42	vibration	vibration	NOUN
fumecheng-13737	434	43	control	control	NOUN
fumecheng-13737	434	44	study	study	NOUN
fumecheng-13737	434	45	of	of	ADP
fumecheng-13737	434	46	cylindrical	cylindrical	ADJ
fumecheng-13737	434	47	shell	shell	NOUN
fumecheng-13737	434	48	through	through	ADP
fumecheng-13737	434	49	a	a	DET
fumecheng-13737	434	50	semi	semi	ADJ
fumecheng-13737	434	51	-	-	ADJ
fumecheng-13737	434	52	analytical	analytical	ADJ
fumecheng-13737	434	53	method	method	NOUN
fumecheng-13737	434	54	,	,	PUNCT
fumecheng-13737	434	55	thin	thin	ADJ
fumecheng-13737	434	56	-	-	PUNCT
fumecheng-13737	434	57	walled	walled	ADJ
fumecheng-13737	434	58	structures	structure	NOUN
fumecheng-13737	434	59	,	,	PUNCT
fumecheng-13737	434	60	196	196	NUM
fumecheng-13737	434	61	,	,	PUNCT
fumecheng-13737	434	62	111521	111521	NUM
fumecheng-13737	434	63	.	.	PUNCT
fumecheng-13737	435	1	15	15	NUM
fumecheng-13737	435	2	.	.	PUNCT
fumecheng-13737	436	1	chen	chen	PROPN
fumecheng-13737	436	2	,	,	PUNCT
fumecheng-13737	436	3	z.	z.	PROPN
fumecheng-13737	436	4	,	,	PUNCT
fumecheng-13737	436	5	liu	liu	PROPN
fumecheng-13737	436	6	,	,	PUNCT
fumecheng-13737	436	7	h.	h.	PROPN
fumecheng-13737	436	8	,	,	PUNCT
fumecheng-13737	436	9	ma	ma	PROPN
fumecheng-13737	436	10	,	,	PUNCT
fumecheng-13737	436	11	l.	l.	PROPN
fumecheng-13737	436	12	,	,	PUNCT
fumecheng-13737	436	13	gan	gan	PROPN
fumecheng-13737	436	14	,	,	PUNCT
fumecheng-13737	436	15	j.	j.	PROPN
fumecheng-13737	436	16	,	,	PUNCT
fumecheng-13737	436	17	wu	wu	PROPN
fumecheng-13737	436	18	,	,	PUNCT
fumecheng-13737	436	19	w.	w.	PROPN
fumecheng-13737	436	20	,	,	PUNCT
fumecheng-13737	436	21	2025	2025	NUM
fumecheng-13737	436	22	,	,	PUNCT
fumecheng-13737	436	23	investigation	investigation	NOUN
fumecheng-13737	436	24	on	on	ADP
fumecheng-13737	436	25	the	the	DET
fumecheng-13737	436	26	correlation	correlation	NOUN
fumecheng-13737	436	27	between	between	ADP
fumecheng-13737	436	28	welding	weld	VERB
fumecheng-13737	436	29	parameters	parameter	NOUN
fumecheng-13737	436	30	and	and	CCONJ
fumecheng-13737	436	31	vibro	vibro	NOUN
fumecheng-13737	436	32	-	-	PUNCT
fumecheng-13737	436	33	acoustic	acoustic	ADJ
fumecheng-13737	436	34	characteristics	characteristic	NOUN
fumecheng-13737	436	35	in	in	ADP
fumecheng-13737	436	36	the	the	DET
fumecheng-13737	436	37	stiffened	stiffen	VERB
fumecheng-13737	436	38	cylindrical	cylindrical	ADJ
fumecheng-13737	436	39	shells	shell	NOUN
fumecheng-13737	436	40	,	,	PUNCT
fumecheng-13737	436	41	ocean	ocean	NOUN
fumecheng-13737	436	42	engineering	engineering	NOUN
fumecheng-13737	436	43	,	,	PUNCT
fumecheng-13737	436	44	321	321	NUM
fumecheng-13737	436	45	,	,	PUNCT
fumecheng-13737	436	46	120355	120355	NUM
fumecheng-13737	436	47	.	.	PUNCT
fumecheng-13737	437	1	16	16	NUM
fumecheng-13737	437	2	.	.	PUNCT
fumecheng-13737	438	1	tan	tan	PROPN
fumecheng-13737	438	2	,	,	PUNCT
fumecheng-13737	438	3	n.c	n.c	PROPN
fumecheng-13737	438	4	.	.	PROPN
fumecheng-13737	438	5	,	,	PUNCT
fumecheng-13737	438	6	dzung	dzung	PROPN
fumecheng-13737	438	7	,	,	PUNCT
fumecheng-13737	438	8	n.m	n.m	PROPN
fumecheng-13737	438	9	.	.	PROPN
fumecheng-13737	438	10	,	,	PUNCT
fumecheng-13737	438	11	ha	ha	INTJ
fumecheng-13737	438	12	,	,	PUNCT
fumecheng-13737	438	13	n.h	n.h	PROPN
fumecheng-13737	438	14	.	.	PROPN
fumecheng-13737	438	15	,	,	PUNCT
fumecheng-13737	438	16	tien	tien	PROPN
fumecheng-13737	438	17	,	,	PUNCT
fumecheng-13737	438	18	n.d	n.d	PROPN
fumecheng-13737	438	19	.	.	PROPN
fumecheng-13737	438	20	,	,	PUNCT
fumecheng-13737	438	21	hung	hung	PROPN
fumecheng-13737	438	22	,	,	PUNCT
fumecheng-13737	438	23	n.c	n.c	PROPN
fumecheng-13737	438	24	.	.	PROPN
fumecheng-13737	438	25	,	,	PUNCT
fumecheng-13737	438	26	sofiyev	sofiyev	PROPN
fumecheng-13737	438	27	,	,	PUNCT
fumecheng-13737	438	28	a.h	a.h	PROPN
fumecheng-13737	438	29	.	.	PROPN
fumecheng-13737	438	30	,	,	PUNCT
fumecheng-13737	438	31	ninh	ninh	PROPN
fumecheng-13737	438	32	,	,	PUNCT
fumecheng-13737	438	33	d.g	d.g	PROPN
fumecheng-13737	438	34	.	.	PROPN
fumecheng-13737	438	35	,	,	PUNCT
fumecheng-13737	438	36	2025	2025	NUM
fumecheng-13737	438	37	,	,	PUNCT
fumecheng-13737	438	38	novel	novel	ADJ
fumecheng-13737	438	39	sandwich	sandwich	NOUN
fumecheng-13737	438	40	composite	composite	ADJ
fumecheng-13737	438	41	shell	shell	NOUN
fumecheng-13737	438	42	structures	structure	NOUN
fumecheng-13737	438	43	in	in	ADP
fumecheng-13737	438	44	nonlinear	nonlinear	ADJ
fumecheng-13737	438	45	geometric	geometric	ADJ
fumecheng-13737	438	46	and	and	CCONJ
fumecheng-13737	438	47	dynamic	dynamic	ADJ
fumecheng-13737	438	48	analyses	analysis	NOUN
fumecheng-13737	438	49	,	,	PUNCT
fumecheng-13737	438	50	aiaa	aiaa	ADJ
fumecheng-13737	438	51	journal	journal	PROPN
fumecheng-13737	438	52	,	,	PUNCT
fumecheng-13737	438	53	https://doi.org/10.2514/1.j065315	https://doi.org/10.2514/1.j065315	PROPN
fumecheng-13737	438	54	.	.	PROPN
fumecheng-13737	439	1	17	17	NUM
fumecheng-13737	439	2	.	.	PUNCT
fumecheng-13737	439	3	khoddami	khoddami	PROPN
fumecheng-13737	439	4	maraghi	maraghi	PROPN
fumecheng-13737	439	5	,	,	PUNCT
fumecheng-13737	439	6	z.	z.	PROPN
fumecheng-13737	439	7	,	,	PUNCT
fumecheng-13737	439	8	safari	safari	PROPN
fumecheng-13737	439	9	,	,	PUNCT
fumecheng-13737	439	10	i.	i.	NOUN
fumecheng-13737	439	11	,	,	PUNCT
fumecheng-13737	439	12	ghorbanpour	ghorbanpour	NOUN
fumecheng-13737	439	13	arani	arani	PROPN
fumecheng-13737	439	14	,	,	PUNCT
fumecheng-13737	439	15	a.	a.	NOUN
fumecheng-13737	439	16	,	,	PUNCT
fumecheng-13737	439	17	shekari	shekari	PROPN
fumecheng-13737	439	18	,	,	PUNCT
fumecheng-13737	439	19	a.m.	a.m.	ADV
fumecheng-13737	439	20	,	,	PUNCT
fumecheng-13737	439	21	saeidnejad	saeidnejad	PROPN
fumecheng-13737	439	22	,	,	PUNCT
fumecheng-13737	439	23	s.	s.	PROPN
fumecheng-13737	439	24	,	,	PUNCT
fumecheng-13737	439	25	zahedi	zahedi	PROPN
fumecheng-13737	439	26	bidgoli	bidgoli	PROPN
fumecheng-13737	439	27	,	,	PUNCT
fumecheng-13737	439	28	a.	a.	NOUN
fumecheng-13737	439	29	,	,	PUNCT
fumecheng-13737	439	30	2025	2025	NUM
fumecheng-13737	439	31	,	,	PUNCT
fumecheng-13737	439	32	free	free	ADJ
fumecheng-13737	439	33	vibration	vibration	NOUN
fumecheng-13737	439	34	analysis	analysis	NOUN
fumecheng-13737	439	35	of	of	ADP
fumecheng-13737	439	36	sandwich	sandwich	NOUN
fumecheng-13737	439	37	graphene	graphene	NOUN
fumecheng-13737	439	38	-	-	PUNCT
fumecheng-13737	439	39	reinforced	reinforce	VERB
fumecheng-13737	439	40	nanocomposite	nanocomposite	NOUN
fumecheng-13737	439	41	truncated	truncate	VERB
fumecheng-13737	439	42	conical	conical	NOUN
fumecheng-13737	439	43	shells	shell	NOUN
fumecheng-13737	439	44	with	with	ADP
fumecheng-13737	439	45	auxetic	auxetic	ADJ
fumecheng-13737	439	46	honeycomb	honeycomb	NOUN
fumecheng-13737	439	47	core	core	NOUN
fumecheng-13737	439	48	,	,	PUNCT
fumecheng-13737	439	49	the	the	DET
fumecheng-13737	439	50	journal	journal	NOUN
fumecheng-13737	439	51	of	of	ADP
fumecheng-13737	439	52	strain	strain	ADJ
fumecheng-13737	439	53	analysis	analysis	NOUN
fumecheng-13737	439	54	for	for	ADP
fumecheng-13737	439	55	engineering	engineering	NOUN
fumecheng-13737	439	56	design	design	NOUN
fumecheng-13737	439	57	,	,	PUNCT
fumecheng-13737	439	58	https://doi.org/10.1177/03093247241311390	https://doi.org/10.1177/03093247241311390	X
fumecheng-13737	439	59	.	.	PROPN
fumecheng-13737	439	60	18	18	NUM
fumecheng-13737	439	61	.	.	X
fumecheng-13737	440	1	jiang	jiang	PROPN
fumecheng-13737	440	2	,	,	PUNCT
fumecheng-13737	440	3	j.	j.	PROPN
fumecheng-13737	440	4	,	,	PUNCT
fumecheng-13737	440	5	olson	olson	PROPN
fumecheng-13737	440	6	,	,	PUNCT
fumecheng-13737	440	7	m.d	m.d	PROPN
fumecheng-13737	440	8	.	.	PROPN
fumecheng-13737	440	9	,	,	PUNCT
fumecheng-13737	440	10	1994	1994	NUM
fumecheng-13737	440	11	,	,	PUNCT
fumecheng-13737	440	12	vibration	vibration	NOUN
fumecheng-13737	440	13	analysis	analysis	NOUN
fumecheng-13737	440	14	of	of	ADP
fumecheng-13737	440	15	orthogonally	orthogonally	ADV
fumecheng-13737	440	16	stiffened	stiffen	VERB
fumecheng-13737	440	17	cylindrical	cylindrical	ADJ
fumecheng-13737	440	18	shells	shell	NOUN
fumecheng-13737	440	19	using	use	VERB
fumecheng-13737	440	20	super	super	ADJ
fumecheng-13737	440	21	finite	finite	ADJ
fumecheng-13737	440	22	elements	element	NOUN
fumecheng-13737	440	23	,	,	PUNCT
fumecheng-13737	440	24	journal	journal	NOUN
fumecheng-13737	440	25	of	of	ADP
fumecheng-13737	440	26	sound	sound	NOUN
fumecheng-13737	440	27	and	and	CCONJ
fumecheng-13737	440	28	vibration	vibration	NOUN
fumecheng-13737	440	29	,	,	PUNCT
fumecheng-13737	440	30	173(1	173(1	NUM
fumecheng-13737	440	31	)	)	PUNCT
fumecheng-13737	440	32	,	,	PUNCT
fumecheng-13737	440	33	pp	pp	ADP
fumecheng-13737	440	34	.	.	PUNCT
fumecheng-13737	441	1	73	73	NUM
fumecheng-13737	441	2	-	-	SYM
fumecheng-13737	441	3	83	83	NUM
fumecheng-13737	441	4	.	.	PUNCT
fumecheng-13737	442	1	19	19	NUM
fumecheng-13737	442	2	.	.	X
fumecheng-13737	442	3	stanley	stanley	PROPN
fumecheng-13737	442	4	,	,	PUNCT
fumecheng-13737	442	5	a.j	a.j	PROPN
fumecheng-13737	442	6	.	.	PROPN
fumecheng-13737	442	7	,	,	PUNCT
fumecheng-13737	442	8	ganesan	ganesan	PROPN
fumecheng-13737	442	9	,	,	PUNCT
fumecheng-13737	442	10	n.	n.	NOUN
fumecheng-13737	442	11	,	,	PUNCT
fumecheng-13737	442	12	1997	1997	NUM
fumecheng-13737	442	13	,	,	PUNCT
fumecheng-13737	442	14	free	free	ADJ
fumecheng-13737	442	15	vibration	vibration	NOUN
fumecheng-13737	442	16	characteristics	characteristic	NOUN
fumecheng-13737	442	17	of	of	ADP
fumecheng-13737	442	18	stiffened	stiffen	VERB
fumecheng-13737	442	19	cylindrical	cylindrical	ADJ
fumecheng-13737	442	20	shells	shell	NOUN
fumecheng-13737	442	21	,	,	PUNCT
fumecheng-13737	442	22	computers	computer	NOUN
fumecheng-13737	442	23	&	&	CCONJ
fumecheng-13737	442	24	structures	structure	NOUN
fumecheng-13737	442	25	,	,	PUNCT
fumecheng-13737	442	26	65(1	65(1	NOUN
fumecheng-13737	442	27	)	)	PUNCT
fumecheng-13737	442	28	,	,	PUNCT
fumecheng-13737	442	29	pp	pp	PROPN
fumecheng-13737	442	30	.	.	PUNCT
fumecheng-13737	443	1	33	33	NUM
fumecheng-13737	443	2	-	-	SYM
fumecheng-13737	443	3	45	45	NUM
fumecheng-13737	443	4	.	.	NOUN
fumecheng-13737	443	5	20	20	NUM
fumecheng-13737	443	6	.	.	PUNCT
fumecheng-13737	444	1	rama	rama	PROPN
fumecheng-13737	444	2	,	,	PUNCT
fumecheng-13737	444	3	g.	g.	PROPN
fumecheng-13737	444	4	,	,	PUNCT
fumecheng-13737	444	5	marinković	marinković	PROPN
fumecheng-13737	444	6	,	,	PUNCT
fumecheng-13737	444	7	d.	d.	PROPN
fumecheng-13737	444	8	,	,	PUNCT
fumecheng-13737	444	9	zehn	zehn	PROPN
fumecheng-13737	444	10	,	,	PUNCT
fumecheng-13737	444	11	m.	m.	NOUN
fumecheng-13737	444	12	,	,	PUNCT
fumecheng-13737	444	13	2018	2018	NUM
fumecheng-13737	444	14	,	,	PUNCT
fumecheng-13737	444	15	efficient	efficient	ADJ
fumecheng-13737	444	16	three	three	NUM
fumecheng-13737	444	17	-	-	PUNCT
fumecheng-13737	444	18	node	node	ADJ
fumecheng-13737	444	19	finite	finite	PROPN
fumecheng-13737	444	20	shell	shell	NOUN
fumecheng-13737	444	21	element	element	NOUN
fumecheng-13737	444	22	for	for	ADP
fumecheng-13737	444	23	linear	linear	PROPN
fumecheng-13737	444	24	and	and	CCONJ
fumecheng-13737	444	25	geometrically	geometrically	ADV
fumecheng-13737	444	26	nonlinear	nonlinear	ADJ
fumecheng-13737	444	27	analyses	analysis	NOUN
fumecheng-13737	444	28	of	of	ADP
fumecheng-13737	444	29	piezoelectric	piezoelectric	ADJ
fumecheng-13737	444	30	laminated	laminate	VERB
fumecheng-13737	444	31	structures	structure	NOUN
fumecheng-13737	444	32	,	,	PUNCT
fumecheng-13737	444	33	journal	journal	NOUN
fumecheng-13737	444	34	of	of	ADP
fumecheng-13737	444	35	intelligent	intelligent	ADJ
fumecheng-13737	444	36	material	material	NOUN
fumecheng-13737	444	37	systems	system	NOUN
fumecheng-13737	444	38	and	and	CCONJ
fumecheng-13737	444	39	structures	structure	NOUN
fumecheng-13737	444	40	,	,	PUNCT
fumecheng-13737	444	41	29(3	29(3	NUM
fumecheng-13737	444	42	)	)	PUNCT
fumecheng-13737	444	43	,	,	PUNCT
fumecheng-13737	444	44	pp	pp	ADJ
fumecheng-13737	444	45	.	.	PUNCT
fumecheng-13737	445	1	345	345	NUM
fumecheng-13737	445	2	-	-	SYM
fumecheng-13737	445	3	357	357	NUM
fumecheng-13737	445	4	.	.	PUNCT
fumecheng-13737	446	1	https://doi.org/10.1177/03093247241311390	https://doi.org/10.1177/03093247241311390	X
fumecheng-13737	447	1	806	806	NUM
fumecheng-13737	447	2	c	c	X
fumecheng-13737	447	3	-	-	PUNCT
fumecheng-13737	447	4	h.	h.	NOUN
fumecheng-13737	447	5	he	he	PROPN
fumecheng-13737	447	6	,	,	PUNCT
fumecheng-13737	447	7	m.	m.	NOUN
fumecheng-13737	447	8	mohammadian	mohammadian	NOUN
fumecheng-13737	447	9	21	21	NUM
fumecheng-13737	447	10	.	.	PUNCT
fumecheng-13737	447	11	milić	milić	PROPN
fumecheng-13737	447	12	,	,	PUNCT
fumecheng-13737	447	13	p.	p.	NOUN
fumecheng-13737	447	14	,	,	PUNCT
fumecheng-13737	447	15	marinković	marinković	PROPN
fumecheng-13737	447	16	,	,	PUNCT
fumecheng-13737	447	17	d.	d.	PROPN
fumecheng-13737	447	18	,	,	PUNCT
fumecheng-13737	447	19	klinge	klinge	PROPN
fumecheng-13737	447	20	,	,	PUNCT
fumecheng-13737	447	21	s.	s.	PROPN
fumecheng-13737	447	22	,	,	PUNCT
fumecheng-13737	447	23	ćojbašić	ćojbašić	PROPN
fumecheng-13737	447	24	,	,	PUNCT
fumecheng-13737	447	25	ž	ž	PROPN
fumecheng-13737	447	26	.	.	PROPN
fumecheng-13737	447	27	,	,	PUNCT
fumecheng-13737	447	28	2023	2023	NUM
fumecheng-13737	447	29	,	,	PUNCT
fumecheng-13737	447	30	reissner	reissner	NOUN
fumecheng-13737	447	31	-	-	PUNCT
fumecheng-13737	447	32	mindlin	mindlin	NOUN
fumecheng-13737	447	33	based	base	VERB
fumecheng-13737	447	34	isogeometric	isogeometric	ADJ
fumecheng-13737	447	35	finite	finite	PROPN
fumecheng-13737	447	36	element	element	NOUN
fumecheng-13737	447	37	formulation	formulation	NOUN
fumecheng-13737	447	38	for	for	ADP
fumecheng-13737	447	39	piezoelectric	piezoelectric	ADJ
fumecheng-13737	447	40	active	active	ADJ
fumecheng-13737	447	41	laminated	laminated	ADJ
fumecheng-13737	447	42	shells	shell	NOUN
fumecheng-13737	447	43	,	,	PUNCT
fumecheng-13737	447	44	tehnički	tehnički	PROPN
fumecheng-13737	447	45	vjesnik	vjesnik	PROPN
fumecheng-13737	447	46	,	,	PUNCT
fumecheng-13737	447	47	30(2	30(2	NUM
fumecheng-13737	447	48	)	)	PUNCT
fumecheng-13737	447	49	,	,	PUNCT
fumecheng-13737	447	50	pp	pp	PROPN
fumecheng-13737	447	51	.	.	PUNCT
fumecheng-13737	448	1	416	416	NUM
fumecheng-13737	448	2	-	-	SYM
fumecheng-13737	448	3	425	425	NUM
fumecheng-13737	448	4	.	.	PUNCT
fumecheng-13737	449	1	22	22	NUM
fumecheng-13737	449	2	.	.	PUNCT
fumecheng-13737	450	1	mohammadian	mohammadian	NOUN
fumecheng-13737	450	2	,	,	PUNCT
fumecheng-13737	450	3	m.	m.	NOUN
fumecheng-13737	450	4	,	,	PUNCT
fumecheng-13737	450	5	ismail	ismail	PROPN
fumecheng-13737	450	6	,	,	PUNCT
fumecheng-13737	450	7	g.m	g.m	PROPN
fumecheng-13737	450	8	.	.	PROPN
fumecheng-13737	450	9	,	,	PUNCT
fumecheng-13737	450	10	2024	2024	NUM
fumecheng-13737	450	11	,	,	PUNCT
fumecheng-13737	450	12	improved	improve	VERB
fumecheng-13737	450	13	harmonic	harmonic	ADJ
fumecheng-13737	450	14	balance	balance	NOUN
fumecheng-13737	450	15	method	method	NOUN
fumecheng-13737	450	16	for	for	ADP
fumecheng-13737	450	17	analyzing	analyze	VERB
fumecheng-13737	450	18	asymmetric	asymmetric	ADJ
fumecheng-13737	450	19	restoring	restore	VERB
fumecheng-13737	450	20	force	force	NOUN
fumecheng-13737	450	21	functions	function	NOUN
fumecheng-13737	450	22	in	in	ADP
fumecheng-13737	450	23	nonlinear	nonlinear	ADJ
fumecheng-13737	450	24	vibration	vibration	NOUN
fumecheng-13737	450	25	of	of	ADP
fumecheng-13737	450	26	mechanical	mechanical	ADJ
fumecheng-13737	450	27	systems	system	NOUN
fumecheng-13737	450	28	,	,	PUNCT
fumecheng-13737	450	29	physica	physica	PROPN
fumecheng-13737	450	30	scripta	scripta	PROPN
fumecheng-13737	450	31	,	,	PUNCT
fumecheng-13737	450	32	99(7	99(7	NUM
fumecheng-13737	450	33	)	)	PUNCT
fumecheng-13737	450	34	,	,	PUNCT
fumecheng-13737	450	35	075280	075280	NUM
fumecheng-13737	450	36	.	.	PUNCT
fumecheng-13737	451	1	23	23	NUM
fumecheng-13737	451	2	.	.	PUNCT
fumecheng-13737	452	1	chen	chen	PROPN
fumecheng-13737	452	2	,	,	PUNCT
fumecheng-13737	452	3	y.	y.	PROPN
fumecheng-13737	452	4	,	,	PUNCT
fumecheng-13737	452	5	hou	hou	PROPN
fumecheng-13737	452	6	,	,	PUNCT
fumecheng-13737	452	7	l.	l.	PROPN
fumecheng-13737	452	8	,	,	PUNCT
fumecheng-13737	452	9	lin	lin	PROPN
fumecheng-13737	452	10	,	,	PUNCT
fumecheng-13737	452	11	r.	r.	PROPN
fumecheng-13737	452	12	,	,	PUNCT
fumecheng-13737	452	13	toh	toh	PROPN
fumecheng-13737	452	14	,	,	PUNCT
fumecheng-13737	452	15	w.	w.	PROPN
fumecheng-13737	452	16	,	,	PUNCT
fumecheng-13737	452	17	ng	ng	PROPN
fumecheng-13737	452	18	,	,	PUNCT
fumecheng-13737	452	19	t.	t.	PROPN
fumecheng-13737	452	20	,	,	PUNCT
fumecheng-13737	452	21	chen	chen	PROPN
fumecheng-13737	452	22	,	,	PUNCT
fumecheng-13737	452	23	y.	y.	PROPN
fumecheng-13737	452	24	,	,	PUNCT
fumecheng-13737	452	25	2024	2024	NUM
fumecheng-13737	452	26	,	,	PUNCT
fumecheng-13737	452	27	a	a	DET
fumecheng-13737	452	28	general	general	ADJ
fumecheng-13737	452	29	and	and	CCONJ
fumecheng-13737	452	30	efficient	efficient	ADJ
fumecheng-13737	452	31	harmonic	harmonic	ADJ
fumecheng-13737	452	32	balance	balance	NOUN
fumecheng-13737	452	33	method	method	NOUN
fumecheng-13737	452	34	for	for	ADP
fumecheng-13737	452	35	nonlinear	nonlinear	ADJ
fumecheng-13737	452	36	dynamic	dynamic	ADJ
fumecheng-13737	452	37	simulation	simulation	NOUN
fumecheng-13737	452	38	,	,	PUNCT
fumecheng-13737	452	39	international	international	ADJ
fumecheng-13737	452	40	journal	journal	NOUN
fumecheng-13737	452	41	of	of	ADP
fumecheng-13737	452	42	mechanical	mechanical	ADJ
fumecheng-13737	452	43	sciences	science	NOUN
fumecheng-13737	452	44	,	,	PUNCT
fumecheng-13737	452	45	276	276	NUM
fumecheng-13737	452	46	,	,	PUNCT
fumecheng-13737	452	47	109388	109388	NUM
fumecheng-13737	452	48	.	.	PUNCT
fumecheng-13737	453	1	24	24	NUM
fumecheng-13737	453	2	.	.	PUNCT
fumecheng-13737	453	3	fu	fu	PROPN
fumecheng-13737	453	4	,	,	PUNCT
fumecheng-13737	453	5	y.	y.	PROPN
fumecheng-13737	453	6	,	,	PUNCT
fumecheng-13737	453	7	zhang	zhang	PROPN
fumecheng-13737	453	8	,	,	PUNCT
fumecheng-13737	453	9	j.	j.	PROPN
fumecheng-13737	453	10	,	,	PUNCT
fumecheng-13737	453	11	wan	wan	PROPN
fumecheng-13737	453	12	,	,	PUNCT
fumecheng-13737	453	13	l.	l.	PROPN
fumecheng-13737	453	14	,	,	PUNCT
fumecheng-13737	453	15	2011	2011	NUM
fumecheng-13737	453	16	,	,	PUNCT
fumecheng-13737	453	17	application	application	NOUN
fumecheng-13737	453	18	of	of	ADP
fumecheng-13737	453	19	the	the	DET
fumecheng-13737	453	20	energy	energy	NOUN
fumecheng-13737	453	21	balance	balance	NOUN
fumecheng-13737	453	22	method	method	NOUN
fumecheng-13737	453	23	to	to	ADP
fumecheng-13737	453	24	a	a	DET
fumecheng-13737	453	25	nonlinear	nonlinear	ADJ
fumecheng-13737	453	26	oscillator	oscillator	NOUN
fumecheng-13737	453	27	arising	arise	VERB
fumecheng-13737	453	28	in	in	ADP
fumecheng-13737	453	29	the	the	DET
fumecheng-13737	453	30	microelectromechanical	microelectromechanical	ADJ
fumecheng-13737	453	31	system	system	NOUN
fumecheng-13737	453	32	(	(	PUNCT
fumecheng-13737	453	33	mems	mems	PROPN
fumecheng-13737	453	34	)	)	PUNCT
fumecheng-13737	453	35	,	,	PUNCT
fumecheng-13737	453	36	current	current	ADJ
fumecheng-13737	453	37	applied	applied	ADJ
fumecheng-13737	453	38	physics	physic	NOUN
fumecheng-13737	453	39	,	,	PUNCT
fumecheng-13737	453	40	11(3	11(3	NUM
fumecheng-13737	453	41	)	)	PUNCT
fumecheng-13737	453	42	,	,	PUNCT
fumecheng-13737	453	43	pp	pp	ADP
fumecheng-13737	453	44	.	.	PUNCT
fumecheng-13737	454	1	482	482	NUM
fumecheng-13737	454	2	-	-	SYM
fumecheng-13737	454	3	485	485	NUM
fumecheng-13737	454	4	.	.	X
fumecheng-13737	454	5	25	25	NUM
fumecheng-13737	454	6	.	.	X
fumecheng-13737	454	7	molla	molla	PROPN
fumecheng-13737	454	8	,	,	PUNCT
fumecheng-13737	454	9	m.h.u	m.h.u	NOUN
fumecheng-13737	454	10	.	.	PUNCT
fumecheng-13737	454	11	,	,	PUNCT
fumecheng-13737	454	12	alam	alam	PROPN
fumecheng-13737	454	13	,	,	PUNCT
fumecheng-13737	454	14	m.s	m.s	PROPN
fumecheng-13737	454	15	.	.	PROPN
fumecheng-13737	454	16	,	,	PUNCT
fumecheng-13737	454	17	2017	2017	NUM
fumecheng-13737	454	18	,	,	PUNCT
fumecheng-13737	454	19	higher	high	ADJ
fumecheng-13737	454	20	accuracy	accuracy	NOUN
fumecheng-13737	454	21	analytical	analytical	ADJ
fumecheng-13737	454	22	approximations	approximation	NOUN
fumecheng-13737	454	23	to	to	PART
fumecheng-13737	454	24	nonlinear	nonlinear	ADJ
fumecheng-13737	454	25	oscillators	oscillator	NOUN
fumecheng-13737	454	26	with	with	ADP
fumecheng-13737	454	27	discontinuity	discontinuity	NOUN
fumecheng-13737	454	28	by	by	ADP
fumecheng-13737	454	29	energy	energy	NOUN
fumecheng-13737	454	30	balance	balance	NOUN
fumecheng-13737	454	31	method	method	NOUN
fumecheng-13737	454	32	,	,	PUNCT
fumecheng-13737	454	33	results	result	NOUN
fumecheng-13737	454	34	in	in	ADP
fumecheng-13737	454	35	physics	physics	NOUN
fumecheng-13737	454	36	,	,	PUNCT
fumecheng-13737	454	37	7	7	NUM
fumecheng-13737	454	38	,	,	PUNCT
fumecheng-13737	454	39	pp	pp	ADJ
fumecheng-13737	454	40	.	.	PUNCT
fumecheng-13737	455	1	2104	2104	NUM
fumecheng-13737	455	2	-	-	SYM
fumecheng-13737	455	3	2110	2110	NUM
fumecheng-13737	455	4	.	.	PUNCT
fumecheng-13737	456	1	26	26	NUM
fumecheng-13737	456	2	.	.	PUNCT
fumecheng-13737	457	1	he	he	PRON
fumecheng-13737	457	2	,	,	PUNCT
fumecheng-13737	457	3	j.-h	j.-h	PROPN
fumecheng-13737	457	4	.	.	PROPN
fumecheng-13737	457	5	,	,	PUNCT
fumecheng-13737	457	6	2003	2003	NUM
fumecheng-13737	457	7	,	,	PUNCT
fumecheng-13737	457	8	homotopy	homotopy	VERB
fumecheng-13737	457	9	perturbation	perturbation	NOUN
fumecheng-13737	457	10	method	method	NOUN
fumecheng-13737	457	11	:	:	PUNCT
fumecheng-13737	457	12	a	a	DET
fumecheng-13737	457	13	new	new	ADJ
fumecheng-13737	457	14	nonlinear	nonlinear	ADJ
fumecheng-13737	457	15	analytical	analytical	ADJ
fumecheng-13737	457	16	technique	technique	NOUN
fumecheng-13737	457	17	,	,	PUNCT
fumecheng-13737	457	18	applied	apply	VERB
fumecheng-13737	457	19	mathematics	mathematic	NOUN
fumecheng-13737	457	20	and	and	CCONJ
fumecheng-13737	457	21	computation	computation	NOUN
fumecheng-13737	457	22	,	,	PUNCT
fumecheng-13737	457	23	135(1	135(1	NUM
fumecheng-13737	457	24	)	)	PUNCT
fumecheng-13737	457	25	,	,	PUNCT
fumecheng-13737	457	26	pp	pp	ADP
fumecheng-13737	457	27	.	.	PUNCT
fumecheng-13737	458	1	73	73	NUM
fumecheng-13737	458	2	-	-	SYM
fumecheng-13737	458	3	79	79	NUM
fumecheng-13737	458	4	.	.	PUNCT
fumecheng-13737	459	1	27	27	NUM
fumecheng-13737	459	2	.	.	X
fumecheng-13737	460	1	mohammadian	mohammadian	NOUN
fumecheng-13737	460	2	,	,	PUNCT
fumecheng-13737	460	3	m.	m.	NOUN
fumecheng-13737	460	4	,	,	PUNCT
fumecheng-13737	460	5	2024	2024	NUM
fumecheng-13737	460	6	,	,	PUNCT
fumecheng-13737	460	7	application	application	NOUN
fumecheng-13737	460	8	of	of	ADP
fumecheng-13737	461	1	he	he	PRON
fumecheng-13737	461	2	's	be	AUX
fumecheng-13737	461	3	new	new	ADJ
fumecheng-13737	461	4	frequency	frequency	NOUN
fumecheng-13737	461	5	-	-	PUNCT
fumecheng-13737	461	6	amplitude	amplitude	NOUN
fumecheng-13737	461	7	formulation	formulation	NOUN
fumecheng-13737	461	8	for	for	ADP
fumecheng-13737	461	9	the	the	DET
fumecheng-13737	461	10	nonlinear	nonlinear	ADJ
fumecheng-13737	461	11	oscillators	oscillator	NOUN
fumecheng-13737	461	12	by	by	ADP
fumecheng-13737	461	13	introducing	introduce	VERB
fumecheng-13737	461	14	a	a	DET
fumecheng-13737	461	15	new	new	ADJ
fumecheng-13737	461	16	trend	trend	NOUN
fumecheng-13737	461	17	for	for	ADP
fumecheng-13737	461	18	determining	determine	VERB
fumecheng-13737	461	19	the	the	DET
fumecheng-13737	461	20	location	location	NOUN
fumecheng-13737	461	21	points	point	NOUN
fumecheng-13737	461	22	,	,	PUNCT
fumecheng-13737	461	23	chinese	chinese	ADJ
fumecheng-13737	461	24	journal	journal	PROPN
fumecheng-13737	461	25	of	of	ADP
fumecheng-13737	461	26	physics	physics	PROPN
fumecheng-13737	461	27	,	,	PUNCT
fumecheng-13737	461	28	89	89	NUM
fumecheng-13737	461	29	,	,	PUNCT
fumecheng-13737	461	30	pp	pp	ADJ
fumecheng-13737	461	31	.	.	PUNCT
fumecheng-13737	461	32	1024	1024	NUM
fumecheng-13737	461	33	-	-	SYM
fumecheng-13737	461	34	1040	1040	NUM
fumecheng-13737	461	35	.	.	PUNCT
fumecheng-13737	462	1	28	28	NUM
fumecheng-13737	462	2	.	.	PUNCT
fumecheng-13737	463	1	he	he	PRON
fumecheng-13737	463	2	,	,	PUNCT
fumecheng-13737	463	3	j.-h	j.-h	PROPN
fumecheng-13737	463	4	.	.	PUNCT
fumecheng-13737	463	5	,	,	PUNCT
fumecheng-13737	463	6	2010	2010	NUM
fumecheng-13737	463	7	,	,	PUNCT
fumecheng-13737	463	8	hamiltonian	hamiltonian	ADJ
fumecheng-13737	463	9	approach	approach	NOUN
fumecheng-13737	463	10	to	to	ADP
fumecheng-13737	463	11	nonlinear	nonlinear	ADJ
fumecheng-13737	463	12	oscillators	oscillator	NOUN
fumecheng-13737	463	13	,	,	PUNCT
fumecheng-13737	463	14	physics	physics	NOUN
fumecheng-13737	463	15	letters	letter	NOUN
fumecheng-13737	463	16	a	a	PRON
fumecheng-13737	463	17	,	,	PUNCT
fumecheng-13737	463	18	374(23	374(23	NOUN
fumecheng-13737	463	19	)	)	PUNCT
fumecheng-13737	463	20	,	,	PUNCT
fumecheng-13737	463	21	pp	pp	ADP
fumecheng-13737	463	22	.	.	PUNCT
fumecheng-13737	464	1	2312	2312	NUM
fumecheng-13737	464	2	-	-	SYM
fumecheng-13737	464	3	2314	2314	NUM
fumecheng-13737	464	4	.	.	PUNCT
fumecheng-13737	465	1	29	29	NUM
fumecheng-13737	465	2	.	.	X
fumecheng-13737	465	3	akter	akter	PROPN
fumecheng-13737	465	4	,	,	PUNCT
fumecheng-13737	465	5	r.	r.	PROPN
fumecheng-13737	465	6	,	,	PUNCT
fumecheng-13737	465	7	2024	2024	NUM
fumecheng-13737	465	8	,	,	PUNCT
fumecheng-13737	465	9	soliton	soliton	NOUN
fumecheng-13737	465	10	dynamics	dynamic	NOUN
fumecheng-13737	465	11	and	and	CCONJ
fumecheng-13737	465	12	multistability	multistability	NOUN
fumecheng-13737	465	13	analysis	analysis	NOUN
fumecheng-13737	465	14	of	of	ADP
fumecheng-13737	465	15	the	the	DET
fumecheng-13737	465	16	hamiltonian	hamiltonian	ADJ
fumecheng-13737	465	17	amplitude	amplitude	NOUN
fumecheng-13737	465	18	model	model	NOUN
fumecheng-13737	465	19	,	,	PUNCT
fumecheng-13737	465	20	results	result	NOUN
fumecheng-13737	465	21	in	in	ADP
fumecheng-13737	465	22	physics	physics	NOUN
fumecheng-13737	465	23	,	,	PUNCT
fumecheng-13737	465	24	63	63	NUM
fumecheng-13737	465	25	,	,	PUNCT
fumecheng-13737	465	26	107878	107878	NUM
fumecheng-13737	465	27	.	.	PUNCT
fumecheng-13737	466	1	30	30	NUM
fumecheng-13737	466	2	.	.	X
fumecheng-13737	467	1	mohammadian	mohammadian	NOUN
fumecheng-13737	467	2	,	,	PUNCT
fumecheng-13737	467	3	m.	m.	NOUN
fumecheng-13737	467	4	,	,	PUNCT
fumecheng-13737	467	5	2017	2017	NUM
fumecheng-13737	467	6	,	,	PUNCT
fumecheng-13737	467	7	application	application	NOUN
fumecheng-13737	467	8	of	of	ADP
fumecheng-13737	467	9	the	the	DET
fumecheng-13737	467	10	variational	variational	ADJ
fumecheng-13737	467	11	iteration	iteration	NOUN
fumecheng-13737	467	12	method	method	NOUN
fumecheng-13737	467	13	to	to	PART
fumecheng-13737	467	14	nonlinear	nonlinear	ADJ
fumecheng-13737	467	15	vibrations	vibration	NOUN
fumecheng-13737	467	16	of	of	ADP
fumecheng-13737	467	17	nanobeams	nanobeam	NOUN
fumecheng-13737	467	18	induced	induce	VERB
fumecheng-13737	467	19	by	by	ADP
fumecheng-13737	467	20	the	the	DET
fumecheng-13737	467	21	van	van	PROPN
fumecheng-13737	467	22	der	der	NOUN
fumecheng-13737	467	23	waals	waal	NOUN
fumecheng-13737	467	24	force	force	VERB
fumecheng-13737	467	25	under	under	ADP
fumecheng-13737	467	26	different	different	ADJ
fumecheng-13737	467	27	boundary	boundary	ADJ
fumecheng-13737	467	28	conditions	condition	NOUN
fumecheng-13737	467	29	,	,	PUNCT
fumecheng-13737	467	30	the	the	DET
fumecheng-13737	467	31	european	european	PROPN
fumecheng-13737	467	32	physical	physical	PROPN
fumecheng-13737	467	33	journal	journal	PROPN
fumecheng-13737	467	34	plus	plus	CCONJ
fumecheng-13737	467	35	,	,	PUNCT
fumecheng-13737	467	36	132(4	132(4	NUM
fumecheng-13737	467	37	)	)	PUNCT
fumecheng-13737	467	38	,	,	PUNCT
fumecheng-13737	467	39	169	169	NUM
fumecheng-13737	467	40	.	.	PUNCT
fumecheng-13737	467	41	31	31	NUM
fumecheng-13737	467	42	.	.	PUNCT
fumecheng-13737	468	1	ahmad	ahmad	PROPN
fumecheng-13737	468	2	,	,	PUNCT
fumecheng-13737	468	3	h.	h.	PROPN
fumecheng-13737	468	4	,	,	PUNCT
fumecheng-13737	468	5	ozsahin	ozsahin	PROPN
fumecheng-13737	468	6	,	,	PUNCT
fumecheng-13737	468	7	d.u	d.u	PROPN
fumecheng-13737	468	8	.	.	PROPN
fumecheng-13737	468	9	,	,	PUNCT
fumecheng-13737	468	10	farooq	farooq	PROPN
fumecheng-13737	468	11	,	,	PUNCT
fumecheng-13737	468	12	u.	u.	PROPN
fumecheng-13737	468	13	,	,	PUNCT
fumecheng-13737	468	14	fahmy	fahmy	PROPN
fumecheng-13737	468	15	,	,	PUNCT
fumecheng-13737	468	16	m.a	m.a	PROPN
fumecheng-13737	468	17	.	.	PROPN
fumecheng-13737	468	18	,	,	PUNCT
fumecheng-13737	468	19	albalwi	albalwi	PROPN
fumecheng-13737	468	20	,	,	PUNCT
fumecheng-13737	468	21	m.d	m.d	PROPN
fumecheng-13737	468	22	.	.	PROPN
fumecheng-13737	468	23	,	,	PUNCT
fumecheng-13737	468	24	abu	abu	PROPN
fumecheng-13737	468	25	-	-	PUNCT
fumecheng-13737	468	26	zinadah	zinadah	PROPN
fumecheng-13737	468	27	,	,	PUNCT
fumecheng-13737	468	28	h.	h.	PROPN
fumecheng-13737	468	29	,	,	PUNCT
fumecheng-13737	468	30	2023	2023	NUM
fumecheng-13737	468	31	,	,	PUNCT
fumecheng-13737	468	32	comparative	comparative	ADJ
fumecheng-13737	468	33	analysis	analysis	NOUN
fumecheng-13737	468	34	of	of	ADP
fumecheng-13737	468	35	new	new	ADJ
fumecheng-13737	468	36	approximate	approximate	ADJ
fumecheng-13737	468	37	analytical	analytical	ADJ
fumecheng-13737	468	38	method	method	NOUN
fumecheng-13737	468	39	and	and	CCONJ
fumecheng-13737	468	40	mohand	mohand	ADJ
fumecheng-13737	468	41	variational	variational	ADJ
fumecheng-13737	468	42	transform	transform	NOUN
fumecheng-13737	468	43	method	method	NOUN
fumecheng-13737	468	44	for	for	ADP
fumecheng-13737	468	45	the	the	DET
fumecheng-13737	468	46	solution	solution	NOUN
fumecheng-13737	468	47	of	of	ADP
fumecheng-13737	468	48	wave	wave	NOUN
fumecheng-13737	468	49	-	-	PUNCT
fumecheng-13737	468	50	like	like	ADJ
fumecheng-13737	468	51	equations	equation	NOUN
fumecheng-13737	468	52	with	with	ADP
fumecheng-13737	468	53	variable	variable	ADJ
fumecheng-13737	468	54	coefficients	coefficient	NOUN
fumecheng-13737	468	55	,	,	PUNCT
fumecheng-13737	468	56	results	result	NOUN
fumecheng-13737	468	57	in	in	ADP
fumecheng-13737	468	58	physics	physics	NOUN
fumecheng-13737	468	59	,	,	PUNCT
fumecheng-13737	468	60	51	51	NUM
fumecheng-13737	468	61	,	,	PUNCT
fumecheng-13737	468	62	106623	106623	NUM
fumecheng-13737	468	63	.	.	PUNCT
fumecheng-13737	469	1	32	32	NUM
fumecheng-13737	469	2	.	.	PUNCT
fumecheng-13737	470	1	farzaneh	farzaneh	PROPN
fumecheng-13737	470	2	,	,	PUNCT
fumecheng-13737	470	3	y.	y.	PROPN
fumecheng-13737	470	4	,	,	PUNCT
fumecheng-13737	470	5	akbarzadeh	akbarzadeh	PROPN
fumecheng-13737	470	6	tootoonchi	tootoonchi	PROPN
fumecheng-13737	470	7	,	,	PUNCT
fumecheng-13737	470	8	a.	a.	NOUN
fumecheng-13737	470	9	,	,	PUNCT
fumecheng-13737	470	10	2010	2010	NUM
fumecheng-13737	470	11	,	,	PUNCT
fumecheng-13737	470	12	global	global	ADJ
fumecheng-13737	470	13	mrror	mrror	NOUN
fumecheng-13737	470	14	minimization	minimization	NOUN
fumecheng-13737	470	15	method	method	NOUN
fumecheng-13737	470	16	for	for	ADP
fumecheng-13737	470	17	solving	solve	VERB
fumecheng-13737	470	18	strongly	strongly	ADV
fumecheng-13737	470	19	nonlinear	nonlinear	ADJ
fumecheng-13737	470	20	oscillator	oscillator	NOUN
fumecheng-13737	470	21	differential	differential	NOUN
fumecheng-13737	470	22	equations	equation	NOUN
fumecheng-13737	470	23	,	,	PUNCT
fumecheng-13737	470	24	computers	computer	NOUN
fumecheng-13737	470	25	&	&	CCONJ
fumecheng-13737	470	26	mathematics	mathematics	PROPN
fumecheng-13737	470	27	with	with	ADP
fumecheng-13737	470	28	applications	application	NOUN
fumecheng-13737	470	29	,	,	PUNCT
fumecheng-13737	470	30	59(8	59(8	NUM
fumecheng-13737	470	31	)	)	PUNCT
fumecheng-13737	470	32	,	,	PUNCT
fumecheng-13737	470	33	pp	pp	ADP
fumecheng-13737	470	34	.	.	PUNCT
fumecheng-13737	471	1	2887	2887	NUM
fumecheng-13737	471	2	-	-	SYM
fumecheng-13737	471	3	2895	2895	NUM
fumecheng-13737	471	4	.	.	PUNCT
fumecheng-13737	472	1	33	33	NUM
fumecheng-13737	472	2	.	.	PUNCT
fumecheng-13737	473	1	ismail	ismail	PROPN
fumecheng-13737	473	2	,	,	PUNCT
fumecheng-13737	473	3	g.m	g.m	PROPN
fumecheng-13737	473	4	.	.	PROPN
fumecheng-13737	473	5	,	,	PUNCT
fumecheng-13737	473	6	abu	abu	PROPN
fumecheng-13737	473	7	-	-	PUNCT
fumecheng-13737	473	8	zinadah	zinadah	PROPN
fumecheng-13737	473	9	,	,	PUNCT
fumecheng-13737	473	10	h.	h.	PROPN
fumecheng-13737	473	11	,	,	PUNCT
fumecheng-13737	473	12	2021	2021	NUM
fumecheng-13737	473	13	,	,	PUNCT
fumecheng-13737	473	14	analytic	analytic	ADJ
fumecheng-13737	473	15	approximations	approximation	NOUN
fumecheng-13737	473	16	to	to	ADP
fumecheng-13737	473	17	non	non	ADJ
fumecheng-13737	473	18	-	-	ADJ
fumecheng-13737	473	19	linear	linear	ADJ
fumecheng-13737	473	20	third	third	ADJ
fumecheng-13737	473	21	order	order	NOUN
fumecheng-13737	473	22	jerk	jerk	NOUN
fumecheng-13737	473	23	equations	equation	NOUN
fumecheng-13737	473	24	via	via	ADP
fumecheng-13737	473	25	modified	modify	VERB
fumecheng-13737	473	26	global	global	ADJ
fumecheng-13737	473	27	error	error	NOUN
fumecheng-13737	473	28	minimization	minimization	NOUN
fumecheng-13737	473	29	method	method	NOUN
fumecheng-13737	473	30	,	,	PUNCT
fumecheng-13737	473	31	journal	journal	NOUN
fumecheng-13737	473	32	of	of	ADP
fumecheng-13737	473	33	king	king	PROPN
fumecheng-13737	473	34	saud	saud	PROPN
fumecheng-13737	473	35	university	university	PROPN
fumecheng-13737	473	36	science	science	NOUN
fumecheng-13737	473	37	,	,	PUNCT
fumecheng-13737	473	38	33(1	33(1	NUM
fumecheng-13737	473	39	)	)	PUNCT
fumecheng-13737	473	40	,	,	PUNCT
fumecheng-13737	473	41	101219	101219	NUM
fumecheng-13737	473	42	.	.	PUNCT
fumecheng-13737	474	1	34	34	NUM
fumecheng-13737	474	2	.	.	PUNCT
fumecheng-13737	474	3	mohammadian	mohammadian	NOUN
fumecheng-13737	474	4	,	,	PUNCT
fumecheng-13737	474	5	m.	m.	NOUN
fumecheng-13737	474	6	,	,	PUNCT
fumecheng-13737	474	7	shariati	shariati	PROPN
fumecheng-13737	474	8	,	,	PUNCT
fumecheng-13737	474	9	m.	m.	NOUN
fumecheng-13737	474	10	,	,	PUNCT
fumecheng-13737	474	11	2020	2020	NUM
fumecheng-13737	474	12	,	,	PUNCT
fumecheng-13737	474	13	application	application	NOUN
fumecheng-13737	474	14	of	of	ADP
fumecheng-13737	474	15	ag	ag	PROPN
fumecheng-13737	474	16	method	method	NOUN
fumecheng-13737	474	17	and	and	CCONJ
fumecheng-13737	474	18	its	its	PRON
fumecheng-13737	474	19	improvement	improvement	NOUN
fumecheng-13737	474	20	to	to	PART
fumecheng-13737	474	21	nonlinear	nonlinear	VERB
fumecheng-13737	474	22	damped	damped	ADJ
fumecheng-13737	474	23	oscillators	oscillator	NOUN
fumecheng-13737	474	24	,	,	PUNCT
fumecheng-13737	474	25	scientia	scientia	PROPN
fumecheng-13737	474	26	iranica	iranica	PROPN
fumecheng-13737	474	27	,	,	PUNCT
fumecheng-13737	474	28	27(1	27(1	NUM
fumecheng-13737	474	29	)	)	PUNCT
fumecheng-13737	474	30	,	,	PUNCT
fumecheng-13737	474	31	pp	pp	ADP
fumecheng-13737	474	32	.	.	PUNCT
fumecheng-13737	475	1	203	203	NUM
fumecheng-13737	475	2	-	-	SYM
fumecheng-13737	475	3	214	214	NUM
fumecheng-13737	475	4	.	.	PUNCT
fumecheng-13737	476	1	35	35	NUM
fumecheng-13737	476	2	.	.	PUNCT
fumecheng-13737	476	3	mohammadian	mohammadian	NOUN
fumecheng-13737	476	4	,	,	PUNCT
fumecheng-13737	476	5	m.	m.	NOUN
fumecheng-13737	476	6	,	,	PUNCT
fumecheng-13737	476	7	2021	2021	NUM
fumecheng-13737	476	8	,	,	PUNCT
fumecheng-13737	476	9	approximate	approximate	ADJ
fumecheng-13737	476	10	analytical	analytical	ADJ
fumecheng-13737	476	11	solutions	solution	NOUN
fumecheng-13737	476	12	to	to	PART
fumecheng-13737	476	13	nonlinear	nonlinear	VERB
fumecheng-13737	476	14	damped	damp	VERB
fumecheng-13737	476	15	oscillatory	oscillatory	ADJ
fumecheng-13737	476	16	systems	system	NOUN
fumecheng-13737	476	17	using	use	VERB
fumecheng-13737	476	18	a	a	DET
fumecheng-13737	476	19	modified	modify	VERB
fumecheng-13737	476	20	algebraic	algebraic	ADJ
fumecheng-13737	476	21	method	method	NOUN
fumecheng-13737	476	22	,	,	PUNCT
fumecheng-13737	476	23	journal	journal	NOUN
fumecheng-13737	476	24	of	of	ADP
fumecheng-13737	476	25	applied	apply	VERB
fumecheng-13737	476	26	mechanics	mechanic	NOUN
fumecheng-13737	476	27	and	and	CCONJ
fumecheng-13737	476	28	technical	technical	ADJ
fumecheng-13737	476	29	physics	physic	NOUN
fumecheng-13737	476	30	,	,	PUNCT
fumecheng-13737	476	31	62(1	62(1	NOUN
fumecheng-13737	476	32	)	)	PUNCT
fumecheng-13737	476	33	,	,	PUNCT
fumecheng-13737	476	34	pp	pp	PROPN
fumecheng-13737	476	35	.	.	PUNCT
fumecheng-13737	477	1	70	70	NUM
fumecheng-13737	477	2	-	-	SYM
fumecheng-13737	477	3	78	78	NUM
fumecheng-13737	477	4	.	.	PUNCT
fumecheng-13737	478	1	36	36	NUM
fumecheng-13737	478	2	.	.	PUNCT
fumecheng-13737	479	1	he	he	PRON
fumecheng-13737	479	2	,	,	PUNCT
fumecheng-13737	479	3	j.-h	j.-h	PROPN
fumecheng-13737	479	4	.	.	PUNCT
fumecheng-13737	479	5	,	,	PUNCT
fumecheng-13737	479	6	2007	2007	NUM
fumecheng-13737	479	7	,	,	PUNCT
fumecheng-13737	479	8	variational	variational	ADJ
fumecheng-13737	479	9	approach	approach	NOUN
fumecheng-13737	479	10	for	for	ADP
fumecheng-13737	479	11	nonlinear	nonlinear	ADJ
fumecheng-13737	479	12	oscillators	oscillator	NOUN
fumecheng-13737	479	13	,	,	PUNCT
fumecheng-13737	479	14	chaos	chaos	NOUN
fumecheng-13737	479	15	,	,	PUNCT
fumecheng-13737	479	16	solitons	soliton	NOUN
fumecheng-13737	479	17	&	&	CCONJ
fumecheng-13737	479	18	fractals	fractal	NOUN
fumecheng-13737	479	19	,	,	PUNCT
fumecheng-13737	479	20	34(5	34(5	NUM
fumecheng-13737	479	21	)	)	PUNCT
fumecheng-13737	479	22	,	,	PUNCT
fumecheng-13737	479	23	pp	pp	ADP
fumecheng-13737	479	24	.	.	PUNCT
fumecheng-13737	480	1	1430	1430	NUM
fumecheng-13737	480	2	-	-	SYM
fumecheng-13737	480	3	1439	1439	NUM
fumecheng-13737	480	4	.	.	PUNCT
fumecheng-13737	481	1	37	37	NUM
fumecheng-13737	481	2	.	.	PUNCT
fumecheng-13737	482	1	bayat	bayat	PROPN
fumecheng-13737	482	2	,	,	PUNCT
fumecheng-13737	482	3	m.	m.	NOUN
fumecheng-13737	482	4	,	,	PUNCT
fumecheng-13737	482	5	pakar	pakar	PROPN
fumecheng-13737	482	6	,	,	PUNCT
fumecheng-13737	482	7	i.	i.	PROPN
fumecheng-13737	482	8	,	,	PUNCT
fumecheng-13737	482	9	cveticanin	cveticanin	PROPN
fumecheng-13737	482	10	,	,	PUNCT
fumecheng-13737	482	11	l.	l.	PROPN
fumecheng-13737	482	12	,	,	PUNCT
fumecheng-13737	482	13	2014	2014	NUM
fumecheng-13737	482	14	,	,	PUNCT
fumecheng-13737	482	15	nonlinear	nonlinear	ADJ
fumecheng-13737	482	16	vibration	vibration	NOUN
fumecheng-13737	482	17	of	of	ADP
fumecheng-13737	482	18	stringer	stringer	NOUN
fumecheng-13737	482	19	shell	shell	NOUN
fumecheng-13737	482	20	by	by	ADP
fumecheng-13737	482	21	means	mean	NOUN
fumecheng-13737	482	22	of	of	ADP
fumecheng-13737	482	23	extended	extended	ADJ
fumecheng-13737	482	24	hamiltonian	hamiltonian	ADJ
fumecheng-13737	482	25	approach	approach	NOUN
fumecheng-13737	482	26	,	,	PUNCT
fumecheng-13737	482	27	archive	archive	NOUN
fumecheng-13737	482	28	of	of	ADP
fumecheng-13737	482	29	applied	apply	VERB
fumecheng-13737	482	30	mechanics	mechanic	NOUN
fumecheng-13737	482	31	,	,	PUNCT
fumecheng-13737	482	32	84(1	84(1	NUM
fumecheng-13737	482	33	)	)	PUNCT
fumecheng-13737	482	34	,	,	PUNCT
fumecheng-13737	482	35	pp	pp	ADP
fumecheng-13737	482	36	.	.	PUNCT
fumecheng-13737	483	1	43	43	NUM
fumecheng-13737	483	2	-	-	SYM
fumecheng-13737	483	3	50	50	NUM
fumecheng-13737	483	4	.	.	PUNCT
fumecheng-13737	484	1	38	38	NUM
fumecheng-13737	484	2	.	.	PUNCT
fumecheng-13737	485	1	pakar	pakar	PROPN
fumecheng-13737	485	2	,	,	PUNCT
fumecheng-13737	485	3	i.	i.	PROPN
fumecheng-13737	485	4	,	,	PUNCT
fumecheng-13737	485	5	bayat	bayat	PROPN
fumecheng-13737	485	6	,	,	PUNCT
fumecheng-13737	485	7	m.	m.	NOUN
fumecheng-13737	485	8	,	,	PUNCT
fumecheng-13737	485	9	2015	2015	NUM
fumecheng-13737	485	10	,	,	PUNCT
fumecheng-13737	485	11	nonlinear	nonlinear	ADJ
fumecheng-13737	485	12	vibration	vibration	NOUN
fumecheng-13737	485	13	of	of	ADP
fumecheng-13737	485	14	stringer	stringer	NOUN
fumecheng-13737	485	15	shell	shell	NOUN
fumecheng-13737	485	16	:	:	PUNCT
fumecheng-13737	485	17	an	an	DET
fumecheng-13737	485	18	analytical	analytical	ADJ
fumecheng-13737	485	19	approach	approach	NOUN
fumecheng-13737	485	20	,	,	PUNCT
fumecheng-13737	485	21	proceedings	proceeding	NOUN
fumecheng-13737	485	22	of	of	ADP
fumecheng-13737	485	23	the	the	DET
fumecheng-13737	485	24	institution	institution	NOUN
fumecheng-13737	485	25	of	of	ADP
fumecheng-13737	485	26	mechanical	mechanical	ADJ
fumecheng-13737	485	27	engineers	engineer	NOUN
fumecheng-13737	485	28	,	,	PUNCT
fumecheng-13737	485	29	part	part	NOUN
fumecheng-13737	485	30	e	e	NOUN
fumecheng-13737	485	31	:	:	PUNCT
fumecheng-13737	485	32	journal	journal	NOUN
fumecheng-13737	485	33	of	of	ADP
fumecheng-13737	485	34	process	process	NOUN
fumecheng-13737	485	35	mechanical	mechanical	ADJ
fumecheng-13737	485	36	engineering	engineering	NOUN
fumecheng-13737	485	37	,	,	PUNCT
fumecheng-13737	485	38	229(1	229(1	NUM
fumecheng-13737	485	39	)	)	PUNCT
fumecheng-13737	485	40	,	,	PUNCT
fumecheng-13737	485	41	pp	pp	PROPN
fumecheng-13737	485	42	.	.	PUNCT
fumecheng-13737	486	1	44	44	NUM
fumecheng-13737	486	2	-	-	SYM
fumecheng-13737	486	3	51	51	NUM
fumecheng-13737	486	4	.	.	NOUN
fumecheng-13737	487	1	39	39	NUM
fumecheng-13737	487	2	.	.	PUNCT
fumecheng-13737	488	1	farea	farea	PROPN
fumecheng-13737	488	2	,	,	PUNCT
fumecheng-13737	488	3	n.m	n.m	PROPN
fumecheng-13737	488	4	.	.	PROPN
fumecheng-13737	488	5	,	,	PUNCT
fumecheng-13737	488	6	ismail	ismail	PROPN
fumecheng-13737	488	7	,	,	PUNCT
fumecheng-13737	488	8	g.m	g.m	PROPN
fumecheng-13737	488	9	.	.	PROPN
fumecheng-13737	488	10	,	,	PUNCT
fumecheng-13737	488	11	2025	2025	NUM
fumecheng-13737	488	12	,	,	PUNCT
fumecheng-13737	488	13	analytical	analytical	ADJ
fumecheng-13737	488	14	solution	solution	NOUN
fumecheng-13737	488	15	for	for	ADP
fumecheng-13737	488	16	strongly	strongly	ADV
fumecheng-13737	488	17	nonlinear	nonlinear	ADJ
fumecheng-13737	488	18	vibration	vibration	NOUN
fumecheng-13737	488	19	of	of	ADP
fumecheng-13737	488	20	a	a	DET
fumecheng-13737	488	21	stringer	stringer	NOUN
fumecheng-13737	488	22	shell	shell	NOUN
fumecheng-13737	488	23	,	,	PUNCT
fumecheng-13737	488	24	journal	journal	NOUN
fumecheng-13737	488	25	of	of	ADP
fumecheng-13737	488	26	low	low	ADJ
fumecheng-13737	488	27	frequency	frequency	NOUN
fumecheng-13737	488	28	noise	noise	NOUN
fumecheng-13737	488	29	,	,	PUNCT
fumecheng-13737	488	30	vibration	vibration	NOUN
fumecheng-13737	488	31	and	and	CCONJ
fumecheng-13737	488	32	active	active	ADJ
fumecheng-13737	488	33	control	control	NOUN
fumecheng-13737	488	34	,	,	PUNCT
fumecheng-13737	488	35	44(1	44(1	PROPN
fumecheng-13737	488	36	)	)	PUNCT
fumecheng-13737	488	37	,	,	PUNCT
fumecheng-13737	488	38	pp	pp	PROPN
fumecheng-13737	488	39	.	.	PUNCT
fumecheng-13737	489	1	81	81	NUM
fumecheng-13737	489	2	-	-	SYM
fumecheng-13737	489	3	87	87	NUM
fumecheng-13737	489	4	.	.	PUNCT
fumecheng-13737	490	1	40	40	NUM
fumecheng-13737	490	2	.	.	PUNCT
fumecheng-13737	491	1	evkin	evkin	X
fumecheng-13737	491	2	,	,	PUNCT
fumecheng-13737	491	3	a.y	a.y	PROPN
fumecheng-13737	491	4	.	.	PROPN
fumecheng-13737	491	5	,	,	PUNCT
fumecheng-13737	491	6	kalamkarov	kalamkarov	PROPN
fumecheng-13737	491	7	,	,	PUNCT
fumecheng-13737	491	8	a.l	a.l	PROPN
fumecheng-13737	491	9	.	.	PROPN
fumecheng-13737	491	10	,	,	PUNCT
fumecheng-13737	491	11	2001	2001	NUM
fumecheng-13737	491	12	,	,	PUNCT
fumecheng-13737	491	13	analysis	analysis	NOUN
fumecheng-13737	491	14	of	of	ADP
fumecheng-13737	491	15	large	large	ADJ
fumecheng-13737	491	16	deflection	deflection	NOUN
fumecheng-13737	491	17	equilibrium	equilibrium	NOUN
fumecheng-13737	491	18	states	state	NOUN
fumecheng-13737	491	19	of	of	ADP
fumecheng-13737	491	20	composite	composite	ADJ
fumecheng-13737	491	21	shells	shell	NOUN
fumecheng-13737	491	22	of	of	ADP
fumecheng-13737	491	23	revolution	revolution	NOUN
fumecheng-13737	491	24	.	.	PUNCT
fumecheng-13737	492	1	part	part	NOUN
fumecheng-13737	492	2	1	1	NUM
fumecheng-13737	492	3	.	.	PUNCT
fumecheng-13737	492	4	general	general	ADJ
fumecheng-13737	492	5	model	model	NOUN
fumecheng-13737	492	6	and	and	CCONJ
fumecheng-13737	492	7	singular	singular	ADJ
fumecheng-13737	492	8	perturbation	perturbation	NOUN
fumecheng-13737	492	9	analysis	analysis	NOUN
fumecheng-13737	492	10	,	,	PUNCT
fumecheng-13737	492	11	international	international	ADJ
fumecheng-13737	492	12	journal	journal	NOUN
fumecheng-13737	492	13	of	of	ADP
fumecheng-13737	492	14	solids	solid	NOUN
fumecheng-13737	492	15	and	and	CCONJ
fumecheng-13737	492	16	structures	structure	NOUN
fumecheng-13737	492	17	,	,	PUNCT
fumecheng-13737	492	18	38(50	38(50	NUM
fumecheng-13737	492	19	-	-	SYM
fumecheng-13737	492	20	51	51	NUM
fumecheng-13737	492	21	)	)	PUNCT
fumecheng-13737	492	22	,	,	PUNCT
fumecheng-13737	492	23	pp	pp	PROPN
fumecheng-13737	492	24	.	.	PUNCT
fumecheng-13737	493	1	8961	8961	NUM
fumecheng-13737	493	2	-	-	SYM
fumecheng-13737	493	3	8974	8974	NUM
fumecheng-13737	493	4	.	.	PUNCT
fumecheng-13737	494	1	41	41	NUM
fumecheng-13737	494	2	.	.	PUNCT
fumecheng-13737	495	1	awrejcewicz	awrejcewicz	PROPN
fumecheng-13737	495	2	,	,	PUNCT
fumecheng-13737	495	3	j.	j.	PROPN
fumecheng-13737	495	4	,	,	PUNCT
fumecheng-13737	495	5	andrianov	andrianov	PROPN
fumecheng-13737	495	6	,	,	PUNCT
fumecheng-13737	495	7	i.v	i.v	PROPN
fumecheng-13737	495	8	.	.	PROPN
fumecheng-13737	495	9	,	,	PUNCT
fumecheng-13737	495	10	manevitch	manevitch	PROPN
fumecheng-13737	495	11	,	,	PUNCT
fumecheng-13737	495	12	l.i	l.i	PROPN
fumecheng-13737	495	13	.	.	PROPN
fumecheng-13737	495	14	,	,	PUNCT
fumecheng-13737	495	15	2012	2012	NUM
fumecheng-13737	495	16	,	,	PUNCT
fumecheng-13737	495	17	asymptotic	asymptotic	ADJ
fumecheng-13737	495	18	approaches	approach	NOUN
fumecheng-13737	495	19	in	in	ADP
fumecheng-13737	495	20	nonlinear	nonlinear	ADJ
fumecheng-13737	495	21	dynamics	dynamic	NOUN
fumecheng-13737	495	22	:	:	PUNCT
fumecheng-13737	495	23	new	new	ADJ
fumecheng-13737	495	24	trends	trend	NOUN
fumecheng-13737	495	25	and	and	CCONJ
fumecheng-13737	495	26	applications	application	NOUN
fumecheng-13737	495	27	,	,	PUNCT
fumecheng-13737	495	28	springer	springer	NOUN
fumecheng-13737	495	29	science	science	PROPN
fumecheng-13737	495	30	&	&	CCONJ
fumecheng-13737	495	31	business	business	NOUN
fumecheng-13737	495	32	media	medium	NOUN
fumecheng-13737	495	33	,	,	PUNCT
fumecheng-13737	495	34	berlin	berlin	PROPN
fumecheng-13737	495	35	.	.	PUNCT
fumecheng-13737	496	1	42	42	NUM
fumecheng-13737	496	2	.	.	PUNCT
fumecheng-13737	497	1	bayat	bayat	PROPN
fumecheng-13737	497	2	,	,	PUNCT
fumecheng-13737	497	3	m.	m.	NOUN
fumecheng-13737	497	4	,	,	PUNCT
fumecheng-13737	497	5	pakar	pakar	PROPN
fumecheng-13737	497	6	,	,	PUNCT
fumecheng-13737	497	7	i.	i.	PROPN
fumecheng-13737	497	8	,	,	PUNCT
fumecheng-13737	497	9	bayat	bayat	PROPN
fumecheng-13737	497	10	,	,	PUNCT
fumecheng-13737	497	11	m.	m.	NOUN
fumecheng-13737	497	12	,	,	PUNCT
fumecheng-13737	497	13	2011	2011	NUM
fumecheng-13737	497	14	.	.	PUNCT
fumecheng-13737	498	1	analytical	analytical	ADJ
fumecheng-13737	498	2	study	study	NOUN
fumecheng-13737	498	3	on	on	ADP
fumecheng-13737	498	4	the	the	DET
fumecheng-13737	498	5	vibration	vibration	NOUN
fumecheng-13737	498	6	frequencies	frequency	NOUN
fumecheng-13737	498	7	of	of	ADP
fumecheng-13737	498	8	tapered	tapered	ADJ
fumecheng-13737	498	9	beams	beam	NOUN
fumecheng-13737	498	10	,	,	PUNCT
fumecheng-13737	498	11	latin	latin	ADJ
fumecheng-13737	498	12	american	american	ADJ
fumecheng-13737	498	13	journal	journal	PROPN
fumecheng-13737	498	14	of	of	ADP
fumecheng-13737	498	15	solids	solid	NOUN
fumecheng-13737	498	16	and	and	CCONJ
fumecheng-13737	498	17	structures	structure	NOUN
fumecheng-13737	498	18	,	,	PUNCT
fumecheng-13737	498	19	8	8	NUM
fumecheng-13737	498	20	,	,	PUNCT
fumecheng-13737	498	21	pp	pp	ADJ
fumecheng-13737	498	22	.	.	PUNCT
fumecheng-13737	499	1	149	149	NUM
fumecheng-13737	499	2	-	-	SYM
fumecheng-13737	499	3	162	162	NUM
fumecheng-13737	499	4	.	.	PUNCT
fumecheng-13737	500	1	43	43	NUM
fumecheng-13737	500	2	.	.	PUNCT
fumecheng-13737	501	1	mohammadian	mohammadian	NOUN
fumecheng-13737	501	2	,	,	PUNCT
fumecheng-13737	501	3	m.	m.	NOUN
fumecheng-13737	501	4	,	,	PUNCT
fumecheng-13737	501	5	2021	2021	NUM
fumecheng-13737	501	6	,	,	PUNCT
fumecheng-13737	501	7	nonlinear	nonlinear	ADJ
fumecheng-13737	501	8	free	free	ADJ
fumecheng-13737	501	9	vibration	vibration	NOUN
fumecheng-13737	501	10	of	of	ADP
fumecheng-13737	501	11	damped	damped	NOUN
fumecheng-13737	501	12	and	and	CCONJ
fumecheng-13737	501	13	undamped	undampe	VERB
fumecheng-13737	501	14	bi	bi	ADJ
fumecheng-13737	501	15	-	-	ADJ
fumecheng-13737	501	16	directional	directional	ADJ
fumecheng-13737	501	17	functionally	functionally	ADV
fumecheng-13737	501	18	graded	grade	VERB
fumecheng-13737	501	19	beams	beam	NOUN
fumecheng-13737	501	20	using	use	VERB
fumecheng-13737	501	21	a	a	DET
fumecheng-13737	501	22	cubic	cubic	ADJ
fumecheng-13737	501	23	-	-	PUNCT
fumecheng-13737	501	24	quintic	quintic	ADJ
fumecheng-13737	501	25	nonlinear	nonlinear	ADJ
fumecheng-13737	501	26	model	model	NOUN
fumecheng-13737	501	27	,	,	PUNCT
fumecheng-13737	501	28	composite	composite	ADJ
fumecheng-13737	501	29	structures	structure	NOUN
fumecheng-13737	501	30	,	,	PUNCT
fumecheng-13737	501	31	255	255	NUM
fumecheng-13737	501	32	,	,	PUNCT
fumecheng-13737	501	33	112866	112866	NUM
fumecheng-13737	501	34	.	.	PUNCT
fumecheng-13737	502	1	44	44	NUM
fumecheng-13737	502	2	.	.	PUNCT
fumecheng-13737	503	1	he	he	PRON
fumecheng-13737	503	2	,	,	PUNCT
fumecheng-13737	503	3	j.-h	j.-h	PROPN
fumecheng-13737	503	4	.	.	PUNCT
fumecheng-13737	503	5	,	,	PUNCT
fumecheng-13737	503	6	2025	2025	NUM
fumecheng-13737	503	7	,	,	PUNCT
fumecheng-13737	503	8	frequency	frequency	NOUN
fumecheng-13737	503	9	-	-	PUNCT
fumecheng-13737	503	10	amplitude	amplitude	NOUN
fumecheng-13737	503	11	relationship	relationship	NOUN
fumecheng-13737	503	12	in	in	ADP
fumecheng-13737	503	13	nonlinear	nonlinear	ADJ
fumecheng-13737	503	14	oscillators	oscillator	NOUN
fumecheng-13737	503	15	with	with	ADP
fumecheng-13737	503	16	irrational	irrational	ADJ
fumecheng-13737	503	17	nonlinearities	nonlinearitie	NOUN
fumecheng-13737	503	18	,	,	PUNCT
fumecheng-13737	503	19	spectrum	spectrum	NOUN
fumecheng-13737	503	20	of	of	ADP
fumecheng-13737	503	21	mechanical	mechanical	ADJ
fumecheng-13737	503	22	engineering	engineering	NOUN
fumecheng-13737	503	23	and	and	CCONJ
fumecheng-13737	503	24	operational	operational	ADJ
fumecheng-13737	503	25	research	research	NOUN
fumecheng-13737	503	26	,	,	PUNCT
fumecheng-13737	503	27	2(1	2(1	NUM
fumecheng-13737	503	28	)	)	PUNCT
fumecheng-13737	503	29	,	,	PUNCT
fumecheng-13737	503	30	pp	pp	PROPN
fumecheng-13737	503	31	.	.	PUNCT
fumecheng-13737	504	1	121	121	NUM
fumecheng-13737	504	2	-	-	SYM
fumecheng-13737	504	3	129	129	NUM
fumecheng-13737	504	4	.	.	PUNCT
fumecheng-13737	505	1	45	45	NUM
fumecheng-13737	505	2	.	.	PUNCT
fumecheng-13737	506	1	he	he	PRON
fumecheng-13737	506	2	,	,	PUNCT
fumecheng-13737	506	3	j.-h	j.-h	PROPN
fumecheng-13737	506	4	.	.	PROPN
fumecheng-13737	506	5	,	,	PUNCT
fumecheng-13737	506	6	2019	2019	NUM
fumecheng-13737	506	7	,	,	PUNCT
fumecheng-13737	506	8	the	the	PRON
fumecheng-13737	506	9	simpler	simple	ADJ
fumecheng-13737	506	10	,	,	PUNCT
fumecheng-13737	506	11	the	the	PRON
fumecheng-13737	506	12	better	well	ADJ
fumecheng-13737	506	13	:	:	PUNCT
fumecheng-13737	506	14	analytical	analytical	ADJ
fumecheng-13737	506	15	methods	method	NOUN
fumecheng-13737	506	16	for	for	ADP
fumecheng-13737	506	17	nonlinear	nonlinear	ADJ
fumecheng-13737	506	18	oscillators	oscillator	NOUN
fumecheng-13737	506	19	and	and	CCONJ
fumecheng-13737	506	20	fractional	fractional	ADJ
fumecheng-13737	506	21	oscillators	oscillator	NOUN
fumecheng-13737	506	22	,	,	PUNCT
fumecheng-13737	506	23	journal	journal	NOUN
fumecheng-13737	506	24	of	of	ADP
fumecheng-13737	506	25	low	low	ADJ
fumecheng-13737	506	26	frequency	frequency	NOUN
fumecheng-13737	506	27	noise	noise	NOUN
fumecheng-13737	506	28	,	,	PUNCT
fumecheng-13737	506	29	vibration	vibration	NOUN
fumecheng-13737	506	30	and	and	CCONJ
fumecheng-13737	506	31	active	active	ADJ
fumecheng-13737	506	32	control	control	NOUN
fumecheng-13737	506	33	,	,	PUNCT
fumecheng-13737	506	34	38(3	38(3	NUM
fumecheng-13737	506	35	-	-	SYM
fumecheng-13737	506	36	4	4	NUM
fumecheng-13737	506	37	)	)	PUNCT
fumecheng-13737	506	38	,	,	PUNCT
fumecheng-13737	506	39	pp	pp	ADJ
fumecheng-13737	506	40	.	.	PUNCT
fumecheng-13737	506	41	1252	1252	NUM
fumecheng-13737	506	42	-	-	SYM
fumecheng-13737	506	43	1260	1260	NUM
fumecheng-13737	506	44	.	.	PUNCT
fumecheng-13737	507	1	46	46	NUM
fumecheng-13737	507	2	.	.	X
fumecheng-13737	508	1	zhang	zhang	PROPN
fumecheng-13737	508	2	,	,	PUNCT
fumecheng-13737	508	3	y.	y.	PROPN
fumecheng-13737	508	4	,	,	PUNCT
fumecheng-13737	508	5	tian	tian	PROPN
fumecheng-13737	508	6	,	,	PUNCT
fumecheng-13737	508	7	d.	d.	PROPN
fumecheng-13737	508	8	,	,	PUNCT
fumecheng-13737	508	9	pang	pang	NOUN
fumecheng-13737	508	10	,	,	PUNCT
fumecheng-13737	508	11	j.	j.	PROPN
fumecheng-13737	508	12	,	,	PUNCT
fumecheng-13737	508	13	2022	2022	NUM
fumecheng-13737	508	14	,	,	PUNCT
fumecheng-13737	508	15	a	a	DET
fumecheng-13737	508	16	fast	fast	ADJ
fumecheng-13737	508	17	estimation	estimation	NOUN
fumecheng-13737	508	18	of	of	ADP
fumecheng-13737	508	19	the	the	DET
fumecheng-13737	508	20	frequency	frequency	NOUN
fumecheng-13737	508	21	property	property	NOUN
fumecheng-13737	508	22	of	of	ADP
fumecheng-13737	508	23	the	the	DET
fumecheng-13737	508	24	microelectromechanical	microelectromechanical	ADJ
fumecheng-13737	508	25	system	system	NOUN
fumecheng-13737	508	26	oscillator	oscillator	NOUN
fumecheng-13737	508	27	,	,	PUNCT
fumecheng-13737	508	28	journal	journal	NOUN
fumecheng-13737	508	29	of	of	ADP
fumecheng-13737	508	30	low	low	ADJ
fumecheng-13737	508	31	frequency	frequency	NOUN
fumecheng-13737	508	32	noise	noise	NOUN
fumecheng-13737	508	33	,	,	PUNCT
fumecheng-13737	508	34	vibration	vibration	NOUN
fumecheng-13737	508	35	and	and	CCONJ
fumecheng-13737	508	36	active	active	ADJ
fumecheng-13737	508	37	control	control	NOUN
fumecheng-13737	508	38	,	,	PUNCT
fumecheng-13737	508	39	41(1	41(1	NUM
fumecheng-13737	508	40	)	)	PUNCT
fumecheng-13737	508	41	,	,	PUNCT
fumecheng-13737	508	42	pp	pp	ADP
fumecheng-13737	508	43	.	.	PUNCT
fumecheng-13737	509	1	160	160	NUM
fumecheng-13737	509	2	-	-	SYM
fumecheng-13737	509	3	166	166	NUM
fumecheng-13737	509	4	.	.	PUNCT
fumecheng-13737	510	1	47	47	NUM
fumecheng-13737	510	2	.	.	PUNCT
fumecheng-13737	511	1	he	he	PRON
fumecheng-13737	511	2	,	,	PUNCT
fumecheng-13737	511	3	c.-h	c.-h	PROPN
fumecheng-13737	511	4	.	.	PROPN
fumecheng-13737	511	5	,	,	PUNCT
fumecheng-13737	511	6	liu	liu	PROPN
fumecheng-13737	511	7	,	,	PUNCT
fumecheng-13737	511	8	c.	c.	PROPN
fumecheng-13737	511	9	,	,	PUNCT
fumecheng-13737	511	10	2022	2022	NUM
fumecheng-13737	511	11	,	,	PUNCT
fumecheng-13737	511	12	a	a	DET
fumecheng-13737	511	13	modified	modify	VERB
fumecheng-13737	511	14	frequency	frequency	NOUN
fumecheng-13737	511	15	–	–	PUNCT
fumecheng-13737	511	16	amplitude	amplitude	NOUN
fumecheng-13737	511	17	formulation	formulation	NOUN
fumecheng-13737	511	18	for	for	ADP
fumecheng-13737	511	19	fractal	fractal	ADJ
fumecheng-13737	511	20	vibration	vibration	NOUN
fumecheng-13737	511	21	systems	system	NOUN
fumecheng-13737	511	22	,	,	PUNCT
fumecheng-13737	511	23	fractals	fractal	NOUN
fumecheng-13737	511	24	,	,	PUNCT
fumecheng-13737	511	25	30(03	30(03	NOUN
fumecheng-13737	511	26	)	)	PUNCT
fumecheng-13737	511	27	,	,	PUNCT
fumecheng-13737	511	28	2250046	2250046	NUM
fumecheng-13737	511	29	.	.	PUNCT
fumecheng-13737	512	1	48	48	NUM
fumecheng-13737	512	2	.	.	PUNCT
fumecheng-13737	513	1	wang	wang	PROPN
fumecheng-13737	513	2	,	,	PUNCT
fumecheng-13737	513	3	k.-j	k.-j	PROPN
fumecheng-13737	513	4	.	.	PROPN
fumecheng-13737	513	5	,	,	PUNCT
fumecheng-13737	513	6	wang	wang	PROPN
fumecheng-13737	513	7	,	,	PUNCT
fumecheng-13737	513	8	g.-d	g.-d	PROPN
fumecheng-13737	513	9	.	.	PUNCT
fumecheng-13737	513	10	,	,	PUNCT
fumecheng-13737	513	11	2021	2021	NUM
fumecheng-13737	513	12	,	,	PUNCT
fumecheng-13737	513	13	study	study	NOUN
fumecheng-13737	513	14	on	on	ADP
fumecheng-13737	513	15	the	the	DET
fumecheng-13737	513	16	nonlinear	nonlinear	ADJ
fumecheng-13737	513	17	vibration	vibration	NOUN
fumecheng-13737	513	18	of	of	ADP
fumecheng-13737	513	19	embedded	embed	VERB
fumecheng-13737	513	20	carbon	carbon	NOUN
fumecheng-13737	513	21	nanotube	nanotube	NOUN
fumecheng-13737	513	22	via	via	ADP
fumecheng-13737	513	23	the	the	DET
fumecheng-13737	513	24	hamiltonian	hamiltonian	NOUN
fumecheng-13737	513	25	-	-	PUNCT
fumecheng-13737	513	26	based	base	VERB
fumecheng-13737	513	27	method	method	NOUN
fumecheng-13737	513	28	,	,	PUNCT
fumecheng-13737	513	29	journal	journal	NOUN
fumecheng-13737	513	30	of	of	ADP
fumecheng-13737	513	31	low	low	ADJ
fumecheng-13737	513	32	frequency	frequency	NOUN
fumecheng-13737	513	33	noise	noise	NOUN
fumecheng-13737	513	34	,	,	PUNCT
fumecheng-13737	513	35	vibration	vibration	NOUN
fumecheng-13737	513	36	and	and	CCONJ
fumecheng-13737	513	37	active	active	ADJ
fumecheng-13737	513	38	control	control	NOUN
fumecheng-13737	513	39	,	,	PUNCT
fumecheng-13737	513	40	41(1	41(1	NUM
fumecheng-13737	513	41	)	)	PUNCT
fumecheng-13737	513	42	,	,	PUNCT
fumecheng-13737	513	43	pp	pp	ADP
fumecheng-13737	513	44	.	.	PUNCT
fumecheng-13737	514	1	112	112	NUM
fumecheng-13737	514	2	-	-	SYM
fumecheng-13737	514	3	117	117	NUM
fumecheng-13737	514	4	.	.	PUNCT
fumecheng-13737	514	5	49	49	NUM
fumecheng-13737	514	6	.	.	PUNCT
fumecheng-13737	515	1	zhao	zhao	PROPN
fumecheng-13737	515	2	,	,	PUNCT
fumecheng-13737	515	3	x.	x.	PROPN
fumecheng-13737	515	4	,	,	PUNCT
fumecheng-13737	515	5	liew	liew	PROPN
fumecheng-13737	515	6	,	,	PUNCT
fumecheng-13737	515	7	k.m	k.m	PROPN
fumecheng-13737	515	8	.	.	PROPN
fumecheng-13737	515	9	,	,	PUNCT
fumecheng-13737	515	10	ng	ng	PROPN
fumecheng-13737	515	11	,	,	PUNCT
fumecheng-13737	515	12	t.y	t.y	PROPN
fumecheng-13737	515	13	.	.	PROPN
fumecheng-13737	515	14	,	,	PUNCT
fumecheng-13737	515	15	2002	2002	NUM
fumecheng-13737	515	16	,	,	PUNCT
fumecheng-13737	515	17	vibrations	vibration	NOUN
fumecheng-13737	515	18	of	of	ADP
fumecheng-13737	515	19	rotating	rotate	VERB
fumecheng-13737	515	20	cross	cross	ADJ
fumecheng-13737	515	21	-	-	ADJ
fumecheng-13737	515	22	ply	ply	ADJ
fumecheng-13737	515	23	laminated	laminate	VERB
fumecheng-13737	515	24	circular	circular	ADJ
fumecheng-13737	515	25	cylindrical	cylindrical	ADJ
fumecheng-13737	515	26	shells	shell	NOUN
fumecheng-13737	515	27	with	with	ADP
fumecheng-13737	515	28	stringer	stringer	NOUN
fumecheng-13737	515	29	and	and	CCONJ
fumecheng-13737	515	30	ring	ring	NOUN
fumecheng-13737	515	31	stiffeners	stiffener	NOUN
fumecheng-13737	515	32	,	,	PUNCT
fumecheng-13737	515	33	international	international	ADJ
fumecheng-13737	515	34	journal	journal	NOUN
fumecheng-13737	515	35	of	of	ADP
fumecheng-13737	515	36	solids	solid	NOUN
fumecheng-13737	515	37	and	and	CCONJ
fumecheng-13737	515	38	structures	structure	NOUN
fumecheng-13737	515	39	,	,	PUNCT
fumecheng-13737	515	40	39	39	NUM
fumecheng-13737	515	41	,	,	PUNCT
fumecheng-13737	515	42	pp	pp	ADJ
fumecheng-13737	515	43	.	.	PUNCT
fumecheng-13737	516	1	529	529	NUM
fumecheng-13737	516	2	-	-	SYM
fumecheng-13737	516	3	545	545	NUM
fumecheng-13737	516	4	.	.	PUNCT