id	sid	tid	token	lemma	pos
fumecheng-7223	1	1	facta	facta	PROPN
fumecheng-7223	1	2	universitatis	universitatis	PROPN
fumecheng-7223	1	3	series	series	NOUN
fumecheng-7223	1	4	:	:	PUNCT
fumecheng-7223	1	5	mechanical	mechanical	ADJ
fumecheng-7223	1	6	engineering	engineering	NOUN
fumecheng-7223	1	7	vol	vol	NOUN
fumecheng-7223	1	8	.	.	PROPN
fumecheng-7223	2	1	19	19	NUM
fumecheng-7223	2	2	,	,	PUNCT
fumecheng-7223	2	3	no	no	DET
fumecheng-7223	2	4	2	2	NUM
fumecheng-7223	2	5	,	,	PUNCT
fumecheng-7223	2	6	2021	2021	NUM
fumecheng-7223	2	7	,	,	PUNCT
fumecheng-7223	2	8	pp	pp	ADV
fumecheng-7223	2	9	.	.	PUNCT
fumecheng-7223	3	1	199	199	NUM
fumecheng-7223	3	2	208	208	NUM
fumecheng-7223	3	3	https://doi.org/10.22190/fume201205002h	https://doi.org/10.22190/fume201205002h	NOUN
fumecheng-7223	3	4	©	©	PROPN
fumecheng-7223	3	5	2021	2021	NUM
fumecheng-7223	3	6	by	by	ADP
fumecheng-7223	3	7	university	university	PROPN
fumecheng-7223	3	8	of	of	ADP
fumecheng-7223	3	9	niš	niš	PROPN
fumecheng-7223	3	10	,	,	PUNCT
fumecheng-7223	3	11	serbia	serbia	PROPN
fumecheng-7223	3	12	|	|	ADV
fumecheng-7223	3	13	creative	creative	ADJ
fumecheng-7223	3	14	commons	common	NOUN
fumecheng-7223	3	15	license	license	NOUN
fumecheng-7223	3	16	:	:	PUNCT
fumecheng-7223	3	17	cc	cc	VERB
fumecheng-7223	3	18	by	by	ADP
fumecheng-7223	3	19	-	-	PUNCT
fumecheng-7223	3	20	nc	nc	VERB
fumecheng-7223	3	21	-	-	PUNCT
fumecheng-7223	3	22	nd	nd	ADV
fumecheng-7223	3	23	original	original	ADJ
fumecheng-7223	3	24	scientific	scientific	ADJ
fumecheng-7223	3	25	paper	paper	ADJ
fumecheng-7223	3	26	hamiltonian	hamiltonian	ADJ
fumecheng-7223	3	27	-	-	PUNCT
fumecheng-7223	3	28	based	base	VERB
fumecheng-7223	3	29	frequency	frequency	NOUN
fumecheng-7223	3	30	-	-	PUNCT
fumecheng-7223	3	31	amplitude	amplitude	NOUN
fumecheng-7223	3	32	formulation	formulation	NOUN
fumecheng-7223	3	33	for	for	ADP
fumecheng-7223	3	34	nonlinear	nonlinear	ADJ
fumecheng-7223	3	35	oscillators	oscillator	NOUN
fumecheng-7223	3	36	ji	ji	PROPN
fumecheng-7223	3	37	-	-	PROPN
fumecheng-7223	3	38	huan	huan	PROPN
fumecheng-7223	3	39	he1,2,3	he1,2,3	PROPN
fumecheng-7223	3	40	,	,	PUNCT
fumecheng-7223	3	41	wei	wei	PROPN
fumecheng-7223	3	42	-	-	PUNCT
fumecheng-7223	3	43	fan	fan	PROPN
fumecheng-7223	3	44	hou1	hou1	PROPN
fumecheng-7223	3	45	,	,	PUNCT
fumecheng-7223	3	46	na	na	ADP
fumecheng-7223	3	47	qie1	qie1	PROPN
fumecheng-7223	3	48	,	,	PUNCT
fumecheng-7223	4	1	khaled	khaled	PROPN
fumecheng-7223	4	2	a.	a.	PROPN
fumecheng-7223	4	3	gepreel4,5	gepreel4,5	PROPN
fumecheng-7223	4	4	,	,	PUNCT
fumecheng-7223	4	5	ali	ali	PROPN
fumecheng-7223	4	6	heidari	heidari	PROPN
fumecheng-7223	4	7	shirazi6	shirazi6	PROPN
fumecheng-7223	4	8	,	,	PUNCT
fumecheng-7223	4	9	hamid	hamid	PROPN
fumecheng-7223	4	10	mohammad	mohammad	PROPN
fumecheng-7223	4	11	-	-	PROPN
fumecheng-7223	4	12	sedighi6,7	sedighi6,7	PROPN
fumecheng-7223	4	13	1school	1school	NUM
fumecheng-7223	4	14	of	of	ADP
fumecheng-7223	4	15	science	science	NOUN
fumecheng-7223	4	16	,	,	PUNCT
fumecheng-7223	4	17	xi'an	xi'an	PROPN
fumecheng-7223	4	18	university	university	PROPN
fumecheng-7223	4	19	of	of	ADP
fumecheng-7223	4	20	architecture	architecture	NOUN
fumecheng-7223	4	21	and	and	CCONJ
fumecheng-7223	4	22	technology	technology	NOUN
fumecheng-7223	4	23	,	,	PUNCT
fumecheng-7223	4	24	xi’an	xi’an	PROPN
fumecheng-7223	4	25	,	,	PUNCT
fumecheng-7223	4	26	china	china	PROPN
fumecheng-7223	4	27	2school	2school	NUM
fumecheng-7223	4	28	of	of	ADP
fumecheng-7223	4	29	mathematics	mathematic	NOUN
fumecheng-7223	4	30	and	and	CCONJ
fumecheng-7223	4	31	information	information	NOUN
fumecheng-7223	4	32	science	science	NOUN
fumecheng-7223	4	33	,	,	PUNCT
fumecheng-7223	4	34	henan	henan	PROPN
fumecheng-7223	4	35	polytechnic	polytechnic	PROPN
fumecheng-7223	4	36	university	university	PROPN
fumecheng-7223	4	37	,	,	PUNCT
fumecheng-7223	4	38	jiaozuo	jiaozuo	PROPN
fumecheng-7223	4	39	,	,	PUNCT
fumecheng-7223	4	40	china	china	PROPN
fumecheng-7223	4	41	3national	3national	NUM
fumecheng-7223	4	42	engineering	engineering	NOUN
fumecheng-7223	4	43	laboratory	laboratory	NOUN
fumecheng-7223	4	44	for	for	ADP
fumecheng-7223	4	45	modern	modern	ADJ
fumecheng-7223	4	46	silk	silk	NOUN
fumecheng-7223	4	47	,	,	PUNCT
fumecheng-7223	4	48	college	college	NOUN
fumecheng-7223	4	49	of	of	ADP
fumecheng-7223	4	50	textile	textile	NOUN
fumecheng-7223	4	51	and	and	CCONJ
fumecheng-7223	4	52	clothing	clothing	NOUN
fumecheng-7223	4	53	engineering	engineering	NOUN
fumecheng-7223	4	54	,	,	PUNCT
fumecheng-7223	4	55	soochow	soochow	PROPN
fumecheng-7223	4	56	university	university	PROPN
fumecheng-7223	4	57	,	,	PUNCT
fumecheng-7223	4	58	suzhou	suzhou	PROPN
fumecheng-7223	4	59	,	,	PUNCT
fumecheng-7223	4	60	china	china	PROPN
fumecheng-7223	4	61	4math	4math	PROPN
fumecheng-7223	4	62	.	.	PUNCT
fumecheng-7223	5	1	depart	depart	PROPN
fumecheng-7223	5	2	.	.	PUNCT
fumecheng-7223	6	1	faculty	faculty	NOUN
fumecheng-7223	6	2	of	of	ADP
fumecheng-7223	6	3	science	science	NOUN
fumecheng-7223	6	4	,	,	PUNCT
fumecheng-7223	6	5	taif	taif	PROPN
fumecheng-7223	6	6	university	university	PROPN
fumecheng-7223	6	7	,	,	PUNCT
fumecheng-7223	6	8	saudi	saudi	PROPN
fumecheng-7223	6	9	arabia	arabia	PROPN
fumecheng-7223	6	10	5mathematics	5mathematics	NUM
fumecheng-7223	6	11	department	department	NOUN
fumecheng-7223	6	12	,	,	PUNCT
fumecheng-7223	6	13	faculty	faculty	NOUN
fumecheng-7223	6	14	of	of	ADP
fumecheng-7223	6	15	science	science	PROPN
fumecheng-7223	6	16	zagazig	zagazig	PROPN
fumecheng-7223	6	17	university	university	PROPN
fumecheng-7223	6	18	egypt	egypt	PROPN
fumecheng-7223	6	19	6mechanical	6mechanical	NUM
fumecheng-7223	6	20	engineering	engineering	NOUN
fumecheng-7223	6	21	department	department	NOUN
fumecheng-7223	6	22	,	,	PUNCT
fumecheng-7223	6	23	faculty	faculty	NOUN
fumecheng-7223	6	24	of	of	ADP
fumecheng-7223	6	25	engineering	engineering	NOUN
fumecheng-7223	6	26	,	,	PUNCT
fumecheng-7223	6	27	shahid	shahid	PROPN
fumecheng-7223	6	28	chamran	chamran	PROPN
fumecheng-7223	6	29	university	university	PROPN
fumecheng-7223	6	30	of	of	ADP
fumecheng-7223	6	31	ahvaz	ahvaz	PROPN
fumecheng-7223	6	32	,	,	PUNCT
fumecheng-7223	6	33	ahvaz	ahvaz	PROPN
fumecheng-7223	6	34	,	,	PUNCT
fumecheng-7223	6	35	iran	iran	PROPN
fumecheng-7223	6	36	7drilling	7drilling	NUM
fumecheng-7223	6	37	center	center	NOUN
fumecheng-7223	6	38	of	of	ADP
fumecheng-7223	6	39	excellence	excellence	NOUN
fumecheng-7223	6	40	and	and	CCONJ
fumecheng-7223	6	41	research	research	NOUN
fumecheng-7223	6	42	center	center	NOUN
fumecheng-7223	6	43	,	,	PUNCT
fumecheng-7223	6	44	shahid	shahid	PROPN
fumecheng-7223	6	45	chamran	chamran	PROPN
fumecheng-7223	6	46	university	university	PROPN
fumecheng-7223	6	47	of	of	ADP
fumecheng-7223	6	48	ahvaz	ahvaz	PROPN
fumecheng-7223	6	49	,	,	PUNCT
fumecheng-7223	6	50	ahvaz	ahvaz	ADJ
fumecheng-7223	6	51	,	,	PUNCT
fumecheng-7223	6	52	iran	iran	PROPN
fumecheng-7223	6	53	abstract	abstract	NOUN
fumecheng-7223	6	54	.	.	PUNCT
fumecheng-7223	7	1	complex	complex	ADJ
fumecheng-7223	7	2	mechanical	mechanical	ADJ
fumecheng-7223	7	3	systems	system	NOUN
fumecheng-7223	7	4	usually	usually	ADV
fumecheng-7223	7	5	include	include	VERB
fumecheng-7223	7	6	nonlinear	nonlinear	ADJ
fumecheng-7223	7	7	interactions	interaction	NOUN
fumecheng-7223	7	8	between	between	ADP
fumecheng-7223	7	9	their	their	PRON
fumecheng-7223	7	10	components	component	NOUN
fumecheng-7223	7	11	which	which	PRON
fumecheng-7223	7	12	can	can	AUX
fumecheng-7223	7	13	be	be	AUX
fumecheng-7223	7	14	modeled	model	VERB
fumecheng-7223	7	15	by	by	ADP
fumecheng-7223	7	16	nonlinear	nonlinear	ADJ
fumecheng-7223	7	17	equations	equation	NOUN
fumecheng-7223	7	18	that	that	PRON
fumecheng-7223	7	19	describe	describe	VERB
fumecheng-7223	7	20	the	the	DET
fumecheng-7223	7	21	sophisticated	sophisticated	ADJ
fumecheng-7223	7	22	motion	motion	NOUN
fumecheng-7223	7	23	of	of	ADP
fumecheng-7223	7	24	the	the	DET
fumecheng-7223	7	25	system	system	NOUN
fumecheng-7223	7	26	.	.	PUNCT
fumecheng-7223	8	1	in	in	ADP
fumecheng-7223	8	2	order	order	NOUN
fumecheng-7223	8	3	to	to	PART
fumecheng-7223	8	4	interpret	interpret	VERB
fumecheng-7223	8	5	the	the	DET
fumecheng-7223	8	6	nonlinear	nonlinear	ADJ
fumecheng-7223	8	7	dynamics	dynamic	NOUN
fumecheng-7223	8	8	of	of	ADP
fumecheng-7223	8	9	these	these	DET
fumecheng-7223	8	10	systems	system	NOUN
fumecheng-7223	8	11	,	,	PUNCT
fumecheng-7223	8	12	it	it	PRON
fumecheng-7223	8	13	is	be	AUX
fumecheng-7223	8	14	necessary	necessary	ADJ
fumecheng-7223	8	15	to	to	PART
fumecheng-7223	8	16	compute	compute	VERB
fumecheng-7223	8	17	their	their	PRON
fumecheng-7223	8	18	nonlinear	nonlinear	ADJ
fumecheng-7223	8	19	frequencies	frequency	NOUN
fumecheng-7223	8	20	more	more	ADV
fumecheng-7223	8	21	precisely	precisely	ADV
fumecheng-7223	8	22	.	.	PUNCT
fumecheng-7223	9	1	the	the	DET
fumecheng-7223	9	2	nonlinear	nonlinear	ADJ
fumecheng-7223	9	3	vibration	vibration	NOUN
fumecheng-7223	9	4	process	process	NOUN
fumecheng-7223	9	5	of	of	ADP
fumecheng-7223	9	6	a	a	DET
fumecheng-7223	9	7	conservative	conservative	ADJ
fumecheng-7223	9	8	oscillator	oscillator	NOUN
fumecheng-7223	9	9	always	always	ADV
fumecheng-7223	9	10	follows	follow	VERB
fumecheng-7223	9	11	the	the	DET
fumecheng-7223	9	12	law	law	NOUN
fumecheng-7223	9	13	of	of	ADP
fumecheng-7223	9	14	energy	energy	NOUN
fumecheng-7223	9	15	conservation	conservation	NOUN
fumecheng-7223	9	16	.	.	PUNCT
fumecheng-7223	10	1	a	a	DET
fumecheng-7223	10	2	variational	variational	ADJ
fumecheng-7223	10	3	formulation	formulation	NOUN
fumecheng-7223	10	4	is	be	AUX
fumecheng-7223	10	5	constructed	construct	VERB
fumecheng-7223	10	6	and	and	CCONJ
fumecheng-7223	10	7	its	its	PRON
fumecheng-7223	10	8	hamiltonian	hamiltonian	ADJ
fumecheng-7223	10	9	invariant	invariant	NOUN
fumecheng-7223	10	10	is	be	AUX
fumecheng-7223	10	11	obtained	obtain	VERB
fumecheng-7223	10	12	.	.	PUNCT
fumecheng-7223	11	1	this	this	DET
fumecheng-7223	11	2	paper	paper	NOUN
fumecheng-7223	11	3	suggests	suggest	VERB
fumecheng-7223	11	4	a	a	DET
fumecheng-7223	11	5	hamiltonian	hamiltonian	NOUN
fumecheng-7223	11	6	-	-	PUNCT
fumecheng-7223	11	7	based	base	VERB
fumecheng-7223	11	8	formulation	formulation	NOUN
fumecheng-7223	11	9	to	to	PART
fumecheng-7223	11	10	quickly	quickly	ADV
fumecheng-7223	11	11	determine	determine	VERB
fumecheng-7223	11	12	the	the	DET
fumecheng-7223	11	13	frequency	frequency	NOUN
fumecheng-7223	11	14	property	property	NOUN
fumecheng-7223	11	15	of	of	ADP
fumecheng-7223	11	16	the	the	DET
fumecheng-7223	11	17	nonlinear	nonlinear	ADJ
fumecheng-7223	11	18	oscillator	oscillator	NOUN
fumecheng-7223	11	19	.	.	PUNCT
fumecheng-7223	12	1	an	an	DET
fumecheng-7223	12	2	example	example	NOUN
fumecheng-7223	12	3	is	be	AUX
fumecheng-7223	12	4	given	give	VERB
fumecheng-7223	12	5	to	to	PART
fumecheng-7223	12	6	explicate	explicate	VERB
fumecheng-7223	12	7	the	the	DET
fumecheng-7223	12	8	solution	solution	NOUN
fumecheng-7223	12	9	process	process	NOUN
fumecheng-7223	12	10	.	.	PUNCT
fumecheng-7223	13	1	key	key	ADJ
fumecheng-7223	13	2	words	word	NOUN
fumecheng-7223	13	3	:	:	PUNCT
fumecheng-7223	13	4	he	he	PRON
fumecheng-7223	13	5	’s	’	VERB
fumecheng-7223	13	6	frequency	frequency	NOUN
fumecheng-7223	13	7	formulation	formulation	NOUN
fumecheng-7223	13	8	,	,	PUNCT
fumecheng-7223	13	9	ancient	ancient	ADJ
fumecheng-7223	13	10	chinese	chinese	ADJ
fumecheng-7223	13	11	mathematics	mathematic	NOUN
fumecheng-7223	13	12	,	,	PUNCT
fumecheng-7223	13	13	semi	semi	ADJ
fumecheng-7223	13	14	-	-	ADJ
fumecheng-7223	13	15	inverse	inverse	ADJ
fumecheng-7223	13	16	method	method	NOUN
fumecheng-7223	13	17	,	,	PUNCT
fumecheng-7223	13	18	periodic	periodic	ADJ
fumecheng-7223	13	19	solution	solution	NOUN
fumecheng-7223	13	20	received	receive	VERB
fumecheng-7223	13	21	december	december	PROPN
fumecheng-7223	13	22	05	05	NUM
fumecheng-7223	13	23	,	,	PUNCT
fumecheng-7223	13	24	2020	2020	NUM
fumecheng-7223	13	25	/	/	SYM
fumecheng-7223	13	26	accepted	accept	VERB
fumecheng-7223	13	27	january	january	PROPN
fumecheng-7223	13	28	06	06	NUM
fumecheng-7223	13	29	,	,	PUNCT
fumecheng-7223	13	30	2021	2021	NUM
fumecheng-7223	13	31	corresponding	correspond	VERB
fumecheng-7223	13	32	author	author	NOUN
fumecheng-7223	13	33	:	:	PUNCT
fumecheng-7223	13	34	ji	ji	PROPN
fumecheng-7223	13	35	-	-	PROPN
fumecheng-7223	13	36	huan	huan	PROPN
fumecheng-7223	13	37	he	he	PRON
fumecheng-7223	13	38	a	a	DET
fumecheng-7223	13	39	school	school	NOUN
fumecheng-7223	13	40	of	of	ADP
fumecheng-7223	13	41	mathematics	mathematic	NOUN
fumecheng-7223	13	42	and	and	CCONJ
fumecheng-7223	13	43	information	information	NOUN
fumecheng-7223	13	44	science	science	NOUN
fumecheng-7223	13	45	,	,	PUNCT
fumecheng-7223	13	46	henan	henan	PROPN
fumecheng-7223	13	47	polytechnic	polytechnic	PROPN
fumecheng-7223	13	48	university	university	PROPN
fumecheng-7223	13	49	,	,	PUNCT
fumecheng-7223	13	50	jiaozuo	jiaozuo	PROPN
fumecheng-7223	13	51	,	,	PUNCT
fumecheng-7223	13	52	china	china	PROPN
fumecheng-7223	13	53	;	;	PUNCT
fumecheng-7223	13	54	and	and	CCONJ
fumecheng-7223	13	55	national	national	ADJ
fumecheng-7223	13	56	engineering	engineering	NOUN
fumecheng-7223	13	57	laboratory	laboratory	NOUN
fumecheng-7223	13	58	for	for	ADP
fumecheng-7223	13	59	modern	modern	ADJ
fumecheng-7223	13	60	silk	silk	NOUN
fumecheng-7223	13	61	,	,	PUNCT
fumecheng-7223	13	62	college	college	NOUN
fumecheng-7223	13	63	of	of	ADP
fumecheng-7223	13	64	textile	textile	NOUN
fumecheng-7223	13	65	and	and	CCONJ
fumecheng-7223	13	66	clothing	clothing	NOUN
fumecheng-7223	13	67	engineering	engineering	NOUN
fumecheng-7223	13	68	,	,	PUNCT
fumecheng-7223	13	69	soochow	soochow	NOUN
fumecheng-7223	13	70	university,199	university,199	VERB
fumecheng-7223	13	71	ren	ren	PROPN
fumecheng-7223	13	72	-	-	PUNCT
fumecheng-7223	13	73	ai	ai	PROPN
fumecheng-7223	13	74	road	road	NOUN
fumecheng-7223	13	75	,	,	PUNCT
fumecheng-7223	13	76	suzhou	suzhou	PROPN
fumecheng-7223	13	77	,	,	PUNCT
fumecheng-7223	13	78	china	china	PROPN
fumecheng-7223	13	79	e	e	PROPN
fumecheng-7223	13	80	-	-	NOUN
fumecheng-7223	13	81	mail	mail	NOUN
fumecheng-7223	13	82	:	:	PUNCT
fumecheng-7223	13	83	hejihuan@suda.edu.cn	hejihuan@suda.edu.cn	NOUN
fumecheng-7223	13	84	200	200	NUM
fumecheng-7223	13	85	j.-h	j.-h	NOUN
fumecheng-7223	13	86	.	.	PUNCT
fumecheng-7223	14	1	he	he	PRON
fumecheng-7223	14	2	,	,	PUNCT
fumecheng-7223	14	3	w.-f	w.-f	PROPN
fumecheng-7223	14	4	.	.	PUNCT
fumecheng-7223	15	1	hou	hou	PROPN
fumecheng-7223	15	2	,	,	PUNCT
fumecheng-7223	15	3	n.	n.	PROPN
fumecheng-7223	15	4	qie	qie	PROPN
fumecheng-7223	15	5	,	,	PUNCT
fumecheng-7223	15	6	k.a	k.a	PROPN
fumecheng-7223	15	7	.	.	PROPN
fumecheng-7223	15	8	gepreel	gepreel	PROPN
fumecheng-7223	15	9	,	,	PUNCT
fumecheng-7223	15	10	a.h	a.h	PROPN
fumecheng-7223	15	11	.	.	PROPN
fumecheng-7223	15	12	shirazi	shirazi	PROPN
fumecheng-7223	15	13	,	,	PUNCT
fumecheng-7223	15	14	h.m	h.m	PROPN
fumecheng-7223	15	15	.	.	PROPN
fumecheng-7223	15	16	sedighi	sedighi	PROPN
fumecheng-7223	15	17	1	1	NUM
fumecheng-7223	15	18	.	.	PUNCT
fumecheng-7223	15	19	introduction	introduction	NOUN
fumecheng-7223	15	20	small	small	ADJ
fumecheng-7223	15	21	amplitude	amplitude	NOUN
fumecheng-7223	15	22	oscillation	oscillation	NOUN
fumecheng-7223	15	23	of	of	ADP
fumecheng-7223	15	24	a	a	DET
fumecheng-7223	15	25	pendulum	pendulum	NOUN
fumecheng-7223	15	26	or	or	CCONJ
fumecheng-7223	15	27	vibration	vibration	NOUN
fumecheng-7223	15	28	in	in	ADP
fumecheng-7223	15	29	a	a	DET
fumecheng-7223	15	30	long	long	ADJ
fumecheng-7223	15	31	slender	slender	NOUN
fumecheng-7223	15	32	beam	beam	NOUN
fumecheng-7223	15	33	with	with	ADP
fumecheng-7223	15	34	low	low	ADJ
fumecheng-7223	15	35	amplitude	amplitude	NOUN
fumecheng-7223	15	36	represent	represent	VERB
fumecheng-7223	15	37	examples	example	NOUN
fumecheng-7223	15	38	of	of	ADP
fumecheng-7223	15	39	the	the	DET
fumecheng-7223	15	40	systems	system	NOUN
fumecheng-7223	15	41	that	that	PRON
fumecheng-7223	15	42	can	can	AUX
fumecheng-7223	15	43	be	be	AUX
fumecheng-7223	15	44	well	well	ADV
fumecheng-7223	15	45	described	describe	VERB
fumecheng-7223	15	46	using	use	VERB
fumecheng-7223	15	47	linear	linear	ADJ
fumecheng-7223	15	48	vibration	vibration	NOUN
fumecheng-7223	15	49	theories	theory	NOUN
fumecheng-7223	15	50	.	.	PUNCT
fumecheng-7223	16	1	however	however	ADV
fumecheng-7223	16	2	,	,	PUNCT
fumecheng-7223	16	3	as	as	SCONJ
fumecheng-7223	16	4	the	the	DET
fumecheng-7223	16	5	system	system	NOUN
fumecheng-7223	16	6	components	component	NOUN
fumecheng-7223	16	7	shift	shift	VERB
fumecheng-7223	16	8	toward	toward	ADP
fumecheng-7223	16	9	more	more	ADV
fumecheng-7223	16	10	sophisticated	sophisticated	ADJ
fumecheng-7223	16	11	interactions	interaction	NOUN
fumecheng-7223	16	12	,	,	PUNCT
fumecheng-7223	16	13	both	both	CCONJ
fumecheng-7223	16	14	nonlinear	nonlinear	ADJ
fumecheng-7223	16	15	oscillators	oscillator	NOUN
fumecheng-7223	16	16	and	and	CCONJ
fumecheng-7223	16	17	their	their	PRON
fumecheng-7223	16	18	nonlinear	nonlinear	ADJ
fumecheng-7223	16	19	characteristic	characteristic	ADJ
fumecheng-7223	16	20	equations	equation	NOUN
fumecheng-7223	16	21	play	play	VERB
fumecheng-7223	16	22	a	a	DET
fumecheng-7223	16	23	vital	vital	ADJ
fumecheng-7223	16	24	role	role	NOUN
fumecheng-7223	16	25	in	in	ADP
fumecheng-7223	16	26	explaining	explain	VERB
fumecheng-7223	16	27	the	the	DET
fumecheng-7223	16	28	behavior	behavior	NOUN
fumecheng-7223	16	29	of	of	ADP
fumecheng-7223	16	30	complex	complex	ADJ
fumecheng-7223	16	31	systems	system	NOUN
fumecheng-7223	16	32	.	.	PUNCT
fumecheng-7223	17	1	the	the	DET
fumecheng-7223	17	2	unique	unique	ADJ
fumecheng-7223	17	3	phenomenon	phenomenon	NOUN
fumecheng-7223	17	4	that	that	PRON
fumecheng-7223	17	5	can	can	AUX
fumecheng-7223	17	6	be	be	AUX
fumecheng-7223	17	7	modeled	model	VERB
fumecheng-7223	17	8	only	only	ADV
fumecheng-7223	17	9	through	through	ADP
fumecheng-7223	17	10	nonlinear	nonlinear	ADJ
fumecheng-7223	17	11	systems	system	NOUN
fumecheng-7223	17	12	,	,	PUNCT
fumecheng-7223	17	13	such	such	ADJ
fumecheng-7223	17	14	as	as	ADP
fumecheng-7223	17	15	jump	jump	NOUN
fumecheng-7223	17	16	phenomenon	phenomenon	NOUN
fumecheng-7223	17	17	,	,	PUNCT
fumecheng-7223	17	18	chaos	chaos	NOUN
fumecheng-7223	17	19	,	,	PUNCT
fumecheng-7223	17	20	multiple	multiple	ADJ
fumecheng-7223	17	21	steady	steady	ADJ
fumecheng-7223	17	22	-	-	PUNCT
fumecheng-7223	17	23	state	state	NOUN
fumecheng-7223	17	24	solutions	solution	NOUN
fumecheng-7223	17	25	,	,	PUNCT
fumecheng-7223	17	26	etc	etc	X
fumecheng-7223	17	27	.	.	X
fumecheng-7223	17	28	,	,	PUNCT
fumecheng-7223	17	29	are	be	AUX
fumecheng-7223	17	30	the	the	DET
fumecheng-7223	17	31	main	main	ADJ
fumecheng-7223	17	32	significance	significance	NOUN
fumecheng-7223	17	33	of	of	ADP
fumecheng-7223	17	34	using	use	VERB
fumecheng-7223	17	35	the	the	DET
fumecheng-7223	17	36	nonlinear	nonlinear	ADJ
fumecheng-7223	17	37	oscillators	oscillator	NOUN
fumecheng-7223	17	38	in	in	ADP
fumecheng-7223	17	39	the	the	DET
fumecheng-7223	17	40	vast	vast	ADJ
fumecheng-7223	17	41	majority	majority	NOUN
fumecheng-7223	17	42	of	of	ADP
fumecheng-7223	17	43	fields	field	NOUN
fumecheng-7223	17	44	,	,	PUNCT
fumecheng-7223	17	45	especially	especially	ADV
fumecheng-7223	17	46	in	in	ADP
fumecheng-7223	17	47	engineering	engineering	NOUN
fumecheng-7223	17	48	structures	structure	NOUN
fumecheng-7223	17	49	.	.	PUNCT
fumecheng-7223	18	1	nonlinear	nonlinear	ADJ
fumecheng-7223	18	2	stiffness	stiffness	NOUN
fumecheng-7223	18	3	and	and	CCONJ
fumecheng-7223	18	4	friction	friction	NOUN
fumecheng-7223	18	5	in	in	ADP
fumecheng-7223	18	6	dynamical	dynamical	ADJ
fumecheng-7223	18	7	systems	system	NOUN
fumecheng-7223	19	1	[	[	X
fumecheng-7223	19	2	1	1	NUM
fumecheng-7223	19	3	]	]	PUNCT
fumecheng-7223	19	4	,	,	PUNCT
fumecheng-7223	19	5	complex	complex	ADJ
fumecheng-7223	19	6	beam	beam	NOUN
fumecheng-7223	19	7	and	and	CCONJ
fumecheng-7223	19	8	piezoelectric	piezoelectric	ADJ
fumecheng-7223	19	9	plate	plate	NOUN
fumecheng-7223	19	10	-	-	PUNCT
fumecheng-7223	19	11	based	base	VERB
fumecheng-7223	19	12	self	self	NOUN
fumecheng-7223	19	13	-	-	PUNCT
fumecheng-7223	19	14	sustainable	sustainable	ADJ
fumecheng-7223	19	15	electromechanical	electromechanical	ADJ
fumecheng-7223	19	16	models	model	NOUN
fumecheng-7223	19	17	[	[	X
fumecheng-7223	19	18	2,3	2,3	NUM
fumecheng-7223	19	19	]	]	PUNCT
fumecheng-7223	19	20	,	,	PUNCT
fumecheng-7223	19	21	nonlinear	nonlinear	ADJ
fumecheng-7223	19	22	reinforced	reinforce	VERB
fumecheng-7223	19	23	nanofibers	nanofiber	NOUN
fumecheng-7223	19	24	[	[	X
fumecheng-7223	19	25	4	4	NUM
fumecheng-7223	19	26	]	]	PUNCT
fumecheng-7223	19	27	,	,	PUNCT
fumecheng-7223	19	28	vibration	vibration	NOUN
fumecheng-7223	19	29	caused	cause	VERB
fumecheng-7223	19	30	by	by	ADP
fumecheng-7223	19	31	the	the	DET
fumecheng-7223	19	32	interaction	interaction	NOUN
fumecheng-7223	19	33	between	between	ADP
fumecheng-7223	19	34	vehicle	vehicle	NOUN
fumecheng-7223	19	35	and	and	CCONJ
fumecheng-7223	19	36	bridge	bridge	NOUN
fumecheng-7223	19	37	[	[	X
fumecheng-7223	19	38	5	5	NUM
fumecheng-7223	19	39	]	]	PUNCT
fumecheng-7223	19	40	,	,	PUNCT
fumecheng-7223	19	41	large	large	ADJ
fumecheng-7223	19	42	amplitude	amplitude	NOUN
fumecheng-7223	19	43	vibration	vibration	NOUN
fumecheng-7223	19	44	of	of	ADP
fumecheng-7223	19	45	beams	beam	NOUN
fumecheng-7223	19	46	[	[	PUNCT
fumecheng-7223	19	47	6	6	NUM
fumecheng-7223	19	48	-	-	SYM
fumecheng-7223	19	49	12	12	NUM
fumecheng-7223	19	50	]	]	PUNCT
fumecheng-7223	19	51	and	and	CCONJ
fumecheng-7223	19	52	dynamics	dynamic	NOUN
fumecheng-7223	19	53	of	of	ADP
fumecheng-7223	19	54	micro	micro	ADJ
fumecheng-7223	19	55	/	/	PROPN
fumecheng-7223	19	56	nanoelectromechanical	nanoelectromechanical	ADJ
fumecheng-7223	19	57	systems	system	NOUN
fumecheng-7223	19	58	[	[	X
fumecheng-7223	19	59	13	13	NUM
fumecheng-7223	19	60	-	-	SYM
fumecheng-7223	19	61	18	18	NUM
fumecheng-7223	19	62	]	]	PUNCT
fumecheng-7223	19	63	are	be	AUX
fumecheng-7223	19	64	a	a	DET
fumecheng-7223	19	65	few	few	ADJ
fumecheng-7223	19	66	examples	example	NOUN
fumecheng-7223	19	67	of	of	ADP
fumecheng-7223	19	68	nonlinear	nonlinear	ADJ
fumecheng-7223	19	69	systems	system	NOUN
fumecheng-7223	19	70	in	in	ADP
fumecheng-7223	19	71	the	the	DET
fumecheng-7223	19	72	field	field	NOUN
fumecheng-7223	19	73	of	of	ADP
fumecheng-7223	19	74	mechanical	mechanical	ADJ
fumecheng-7223	19	75	engineering	engineering	NOUN
fumecheng-7223	19	76	.	.	PUNCT
fumecheng-7223	20	1	from	from	ADP
fumecheng-7223	20	2	the	the	DET
fumecheng-7223	20	3	mathematical	mathematical	ADJ
fumecheng-7223	20	4	point	point	NOUN
fumecheng-7223	20	5	of	of	ADP
fumecheng-7223	20	6	view	view	NOUN
fumecheng-7223	20	7	,	,	PUNCT
fumecheng-7223	20	8	the	the	DET
fumecheng-7223	20	9	duffing	duffing	NOUN
fumecheng-7223	20	10	oscillator	oscillator	NOUN
fumecheng-7223	20	11	,	,	PUNCT
fumecheng-7223	20	12	van	van	PROPN
fumecheng-7223	20	13	der	der	ADJ
fumecheng-7223	20	14	pol	pol	PROPN
fumecheng-7223	20	15	and	and	CCONJ
fumecheng-7223	20	16	mathieu	mathieu	PROPN
fumecheng-7223	20	17	are	be	AUX
fumecheng-7223	20	18	well	well	ADV
fumecheng-7223	20	19	-	-	PUNCT
fumecheng-7223	20	20	known	know	VERB
fumecheng-7223	20	21	nonlinear	nonlinear	ADJ
fumecheng-7223	20	22	equations	equation	NOUN
fumecheng-7223	20	23	.	.	PUNCT
fumecheng-7223	21	1	several	several	ADJ
fumecheng-7223	21	2	nonlinear	nonlinear	ADJ
fumecheng-7223	21	3	systems	system	NOUN
fumecheng-7223	21	4	can	can	AUX
fumecheng-7223	21	5	be	be	AUX
fumecheng-7223	21	6	described	describe	VERB
fumecheng-7223	21	7	by	by	ADP
fumecheng-7223	21	8	utilizing	utilize	VERB
fumecheng-7223	21	9	the	the	DET
fumecheng-7223	21	10	duffing	duffing	NOUN
fumecheng-7223	21	11	equation	equation	NOUN
fumecheng-7223	21	12	,	,	PUNCT
fumecheng-7223	21	13	from	from	ADP
fumecheng-7223	21	14	a	a	DET
fumecheng-7223	21	15	simple	simple	ADJ
fumecheng-7223	21	16	pendulum	pendulum	NOUN
fumecheng-7223	21	17	with	with	ADP
fumecheng-7223	21	18	harmonic	harmonic	ADJ
fumecheng-7223	21	19	motion	motion	NOUN
fumecheng-7223	21	20	to	to	ADP
fumecheng-7223	21	21	the	the	DET
fumecheng-7223	21	22	vibration	vibration	NOUN
fumecheng-7223	21	23	of	of	ADP
fumecheng-7223	21	24	arched	arch	VERB
fumecheng-7223	21	25	structures	structure	NOUN
fumecheng-7223	21	26	[	[	X
fumecheng-7223	21	27	19	19	NUM
fumecheng-7223	21	28	]	]	PUNCT
fumecheng-7223	21	29	.	.	PUNCT
fumecheng-7223	22	1	the	the	DET
fumecheng-7223	22	2	duffing	duffing	NOUN
fumecheng-7223	22	3	equation	equation	NOUN
fumecheng-7223	22	4	especially	especially	ADV
fumecheng-7223	22	5	emerges	emerge	VERB
fumecheng-7223	22	6	in	in	ADP
fumecheng-7223	22	7	mechanical	mechanical	ADJ
fumecheng-7223	22	8	systems	system	NOUN
fumecheng-7223	22	9	with	with	ADP
fumecheng-7223	22	10	the	the	DET
fumecheng-7223	22	11	presence	presence	NOUN
fumecheng-7223	22	12	of	of	ADP
fumecheng-7223	22	13	nonlinear	nonlinear	ADJ
fumecheng-7223	22	14	stiffness	stiffness	ADJ
fumecheng-7223	22	15	springs	spring	NOUN
fumecheng-7223	22	16	.	.	PUNCT
fumecheng-7223	23	1	in	in	ADP
fumecheng-7223	23	2	many	many	ADJ
fumecheng-7223	23	3	cases	case	NOUN
fumecheng-7223	23	4	,	,	PUNCT
fumecheng-7223	23	5	stiffness	stiffness	NOUN
fumecheng-7223	23	6	is	be	AUX
fumecheng-7223	23	7	a	a	DET
fumecheng-7223	23	8	function	function	NOUN
fumecheng-7223	23	9	of	of	ADP
fumecheng-7223	23	10	displacement	displacement	NOUN
fumecheng-7223	23	11	,	,	PUNCT
fumecheng-7223	23	12	which	which	PRON
fumecheng-7223	23	13	leads	lead	VERB
fumecheng-7223	23	14	to	to	ADP
fumecheng-7223	23	15	cubic	cubic	ADJ
fumecheng-7223	23	16	terms	term	NOUN
fumecheng-7223	23	17	in	in	ADP
fumecheng-7223	23	18	the	the	DET
fumecheng-7223	23	19	governing	govern	VERB
fumecheng-7223	23	20	equations	equation	NOUN
fumecheng-7223	23	21	.	.	PUNCT
fumecheng-7223	24	1	ultimately	ultimately	ADV
fumecheng-7223	24	2	,	,	PUNCT
fumecheng-7223	24	3	this	this	PRON
fumecheng-7223	24	4	forms	form	VERB
fumecheng-7223	24	5	a	a	DET
fumecheng-7223	24	6	nonlinear	nonlinear	ADJ
fumecheng-7223	24	7	relation	relation	NOUN
fumecheng-7223	24	8	between	between	ADP
fumecheng-7223	24	9	the	the	DET
fumecheng-7223	24	10	applied	applied	ADJ
fumecheng-7223	24	11	force	force	NOUN
fumecheng-7223	24	12	to	to	ADP
fumecheng-7223	24	13	the	the	DET
fumecheng-7223	24	14	spring	spring	NOUN
fumecheng-7223	24	15	and	and	CCONJ
fumecheng-7223	24	16	the	the	DET
fumecheng-7223	24	17	resulting	result	VERB
fumecheng-7223	24	18	displacement	displacement	NOUN
fumecheng-7223	24	19	.	.	PUNCT
fumecheng-7223	25	1	for	for	ADP
fumecheng-7223	25	2	instance	instance	NOUN
fumecheng-7223	25	3	,	,	PUNCT
fumecheng-7223	25	4	fig	fig	NOUN
fumecheng-7223	25	5	.	.	PUNCT
fumecheng-7223	25	6	1	1	NUM
fumecheng-7223	25	7	shows	show	VERB
fumecheng-7223	25	8	a	a	DET
fumecheng-7223	25	9	truck	truck	NOUN
fumecheng-7223	25	10	's	's	PART
fumecheng-7223	25	11	rear	rear	ADJ
fumecheng-7223	25	12	leaf	leaf	NOUN
fumecheng-7223	25	13	suspension	suspension	NOUN
fumecheng-7223	25	14	.	.	PUNCT
fumecheng-7223	26	1	the	the	DET
fumecheng-7223	26	2	chaotic	chaotic	ADJ
fumecheng-7223	26	3	vibration	vibration	NOUN
fumecheng-7223	26	4	caused	cause	VERB
fumecheng-7223	26	5	by	by	ADP
fumecheng-7223	26	6	road	road	NOUN
fumecheng-7223	26	7	excitation	excitation	NOUN
fumecheng-7223	26	8	in	in	ADP
fumecheng-7223	26	9	vehicles	vehicle	NOUN
fumecheng-7223	26	10	can	can	AUX
fumecheng-7223	26	11	be	be	AUX
fumecheng-7223	26	12	studied	study	VERB
fumecheng-7223	26	13	by	by	ADP
fumecheng-7223	26	14	modeling	model	VERB
fumecheng-7223	26	15	the	the	DET
fumecheng-7223	26	16	leaf	leaf	NOUN
fumecheng-7223	26	17	spring	spring	NOUN
fumecheng-7223	26	18	with	with	ADP
fumecheng-7223	26	19	magnets	magnet	NOUN
fumecheng-7223	26	20	as	as	ADP
fumecheng-7223	26	21	a	a	DET
fumecheng-7223	26	22	double	double	ADJ
fumecheng-7223	26	23	-	-	PUNCT
fumecheng-7223	26	24	potential	potential	ADJ
fumecheng-7223	26	25	-	-	PUNCT
fumecheng-7223	26	26	well	well	ADV
fumecheng-7223	26	27	duffing	duffing	NOUN
fumecheng-7223	26	28	oscillator	oscillator	NOUN
fumecheng-7223	26	29	[	[	X
fumecheng-7223	26	30	20	20	NUM
fumecheng-7223	26	31	]	]	PUNCT
fumecheng-7223	26	32	.	.	PUNCT
fumecheng-7223	27	1	fig	fig	NOUN
fumecheng-7223	27	2	.	.	PUNCT
fumecheng-7223	28	1	1	1	NUM
fumecheng-7223	28	2	leaf	leaf	NOUN
fumecheng-7223	28	3	spring	spring	NOUN
fumecheng-7223	28	4	(	(	PUNCT
fumecheng-7223	28	5	left	left	ADJ
fumecheng-7223	28	6	)	)	PUNCT
fumecheng-7223	28	7	and	and	CCONJ
fumecheng-7223	28	8	quarter	quarter	NOUN
fumecheng-7223	28	9	car	car	NOUN
fumecheng-7223	28	10	diagram	diagram	NOUN
fumecheng-7223	28	11	of	of	ADP
fumecheng-7223	28	12	a	a	DET
fumecheng-7223	28	13	nonlinear	nonlinear	ADJ
fumecheng-7223	28	14	suspension	suspension	NOUN
fumecheng-7223	28	15	(	(	PUNCT
fumecheng-7223	28	16	right	right	ADJ
fumecheng-7223	28	17	)	)	PUNCT
fumecheng-7223	28	18	van	van	PROPN
fumecheng-7223	28	19	der	der	ADJ
fumecheng-7223	28	20	pol	pol	NOUN
fumecheng-7223	28	21	is	be	AUX
fumecheng-7223	28	22	another	another	DET
fumecheng-7223	28	23	example	example	NOUN
fumecheng-7223	28	24	of	of	ADP
fumecheng-7223	28	25	nonlinear	nonlinear	ADJ
fumecheng-7223	28	26	self	self	NOUN
fumecheng-7223	28	27	-	-	PUNCT
fumecheng-7223	28	28	excited	excite	VERB
fumecheng-7223	28	29	limit	limit	NOUN
fumecheng-7223	28	30	cycle	cycle	NOUN
fumecheng-7223	28	31	oscillators	oscillator	NOUN
fumecheng-7223	28	32	that	that	PRON
fumecheng-7223	28	33	is	be	AUX
fumecheng-7223	28	34	widely	widely	ADV
fumecheng-7223	28	35	used	use	VERB
fumecheng-7223	28	36	to	to	PART
fumecheng-7223	28	37	describe	describe	VERB
fumecheng-7223	28	38	various	various	ADJ
fumecheng-7223	28	39	systems	system	NOUN
fumecheng-7223	28	40	in	in	ADP
fumecheng-7223	28	41	electrical	electrical	ADJ
fumecheng-7223	28	42	and	and	CCONJ
fumecheng-7223	28	43	mechanical	mechanical	ADJ
fumecheng-7223	28	44	engineering	engineering	NOUN
fumecheng-7223	28	45	,	,	PUNCT
fumecheng-7223	28	46	seismology	seismology	NOUN
fumecheng-7223	28	47	,	,	PUNCT
fumecheng-7223	28	48	economics	economic	NOUN
fumecheng-7223	28	49	,	,	PUNCT
fumecheng-7223	28	50	etc	etc	X
fumecheng-7223	28	51	.	.	X
fumecheng-7223	28	52	a	a	DET
fumecheng-7223	28	53	classical	classical	ADJ
fumecheng-7223	28	54	representation	representation	NOUN
fumecheng-7223	28	55	of	of	ADP
fumecheng-7223	28	56	the	the	DET
fumecheng-7223	28	57	van	van	PROPN
fumecheng-7223	28	58	der	der	PROPN
fumecheng-7223	28	59	pol	pol	PROPN
fumecheng-7223	28	60	oscillator	oscillator	NOUN
fumecheng-7223	28	61	is	be	AUX
fumecheng-7223	28	62	in	in	ADP
fumecheng-7223	28	63	oscillator	oscillator	NOUN
fumecheng-7223	28	64	triode	triode	NOUN
fumecheng-7223	28	65	circuits	circuit	NOUN
fumecheng-7223	28	66	[	[	X
fumecheng-7223	28	67	21	21	NUM
fumecheng-7223	28	68	]	]	PUNCT
fumecheng-7223	28	69	.	.	PUNCT
fumecheng-7223	29	1	this	this	DET
fumecheng-7223	29	2	equation	equation	NOUN
fumecheng-7223	29	3	is	be	AUX
fumecheng-7223	29	4	also	also	ADV
fumecheng-7223	29	5	used	use	VERB
fumecheng-7223	29	6	to	to	PART
fumecheng-7223	29	7	describe	describe	VERB
fumecheng-7223	29	8	the	the	DET
fumecheng-7223	29	9	cardiac	cardiac	ADJ
fumecheng-7223	29	10	pulse	pulse	NOUN
fumecheng-7223	29	11	modeling	modeling	NOUN
fumecheng-7223	30	1	[	[	X
fumecheng-7223	30	2	22	22	NUM
fumecheng-7223	30	3	]	]	PUNCT
fumecheng-7223	30	4	.	.	PUNCT
fumecheng-7223	31	1	another	another	DET
fumecheng-7223	31	2	well	well	ADV
fumecheng-7223	31	3	-	-	PUNCT
fumecheng-7223	31	4	known	know	VERB
fumecheng-7223	31	5	nonlinear	nonlinear	ADJ
fumecheng-7223	31	6	equation	equation	NOUN
fumecheng-7223	31	7	is	be	AUX
fumecheng-7223	31	8	mathieu	mathieu	PROPN
fumecheng-7223	31	9	's	's	PART
fumecheng-7223	31	10	equation	equation	NOUN
fumecheng-7223	31	11	.	.	PUNCT
fumecheng-7223	32	1	this	this	DET
fumecheng-7223	32	2	equation	equation	NOUN
fumecheng-7223	32	3	was	be	AUX
fumecheng-7223	32	4	firstly	firstly	ADV
fumecheng-7223	32	5	encountered	encounter	VERB
fumecheng-7223	32	6	by	by	ADP
fumecheng-7223	32	7	émile	émile	ADJ
fumecheng-7223	32	8	léonard	léonard	PROPN
fumecheng-7223	32	9	mathieu	mathieu	PROPN
fumecheng-7223	32	10	when	when	SCONJ
fumecheng-7223	32	11	he	he	PRON
fumecheng-7223	32	12	was	be	AUX
fumecheng-7223	32	13	studying	study	VERB
fumecheng-7223	32	14	vibrating	vibrate	VERB
fumecheng-7223	32	15	elliptical	elliptical	ADJ
fumecheng-7223	32	16	drumheads	drumhead	NOUN
fumecheng-7223	32	17	.	.	PUNCT
fumecheng-7223	33	1	mathieu	mathieu	PROPN
fumecheng-7223	33	2	’s	’s	PART
fumecheng-7223	33	3	equation	equation	NOUN
fumecheng-7223	33	4	tends	tend	VERB
fumecheng-7223	33	5	to	to	PART
fumecheng-7223	33	6	appear	appear	VERB
fumecheng-7223	33	7	in	in	ADP
fumecheng-7223	33	8	the	the	DET
fumecheng-7223	33	9	systems	system	NOUN
fumecheng-7223	33	10	with	with	ADP
fumecheng-7223	33	11	hamiltonian	hamiltonian	ADJ
fumecheng-7223	33	12	-	-	PUNCT
fumecheng-7223	33	13	based	base	VERB
fumecheng-7223	33	14	frequency	frequency	NOUN
fumecheng-7223	33	15	-	-	PUNCT
fumecheng-7223	33	16	amplitude	amplitude	NOUN
fumecheng-7223	33	17	formulation	formulation	NOUN
fumecheng-7223	33	18	for	for	ADP
fumecheng-7223	33	19	nonlinear	nonlinear	ADJ
fumecheng-7223	33	20	oscillators	oscillator	NOUN
fumecheng-7223	33	21	201	201	NUM
fumecheng-7223	33	22	harmonic	harmonic	ADJ
fumecheng-7223	33	23	motion	motion	NOUN
fumecheng-7223	33	24	and	and	CCONJ
fumecheng-7223	33	25	is	be	AUX
fumecheng-7223	33	26	a	a	DET
fumecheng-7223	33	27	powerful	powerful	ADJ
fumecheng-7223	33	28	tool	tool	NOUN
fumecheng-7223	33	29	for	for	ADP
fumecheng-7223	33	30	modeling	model	VERB
fumecheng-7223	33	31	systems	system	NOUN
fumecheng-7223	33	32	with	with	ADP
fumecheng-7223	33	33	elliptic	elliptic	ADJ
fumecheng-7223	33	34	boundary	boundary	ADJ
fumecheng-7223	33	35	conditions	condition	NOUN
fumecheng-7223	33	36	.	.	PUNCT
fumecheng-7223	34	1	for	for	ADP
fumecheng-7223	34	2	instance	instance	NOUN
fumecheng-7223	34	3	,	,	PUNCT
fumecheng-7223	34	4	a	a	DET
fumecheng-7223	34	5	wind	wind	NOUN
fumecheng-7223	34	6	turbine	turbine	NOUN
fumecheng-7223	34	7	blade	blade	NOUN
fumecheng-7223	34	8	under	under	ADP
fumecheng-7223	34	9	influence	influence	NOUN
fumecheng-7223	34	10	of	of	ADP
fumecheng-7223	34	11	wind	wind	NOUN
fumecheng-7223	34	12	shear	shear	NOUN
fumecheng-7223	34	13	force	force	NOUN
fumecheng-7223	34	14	and	and	CCONJ
fumecheng-7223	34	15	gravitational	gravitational	ADJ
fumecheng-7223	34	16	cyclic	cyclic	ADJ
fumecheng-7223	34	17	force	force	NOUN
fumecheng-7223	34	18	(	(	PUNCT
fumecheng-7223	34	19	fig	fig	NOUN
fumecheng-7223	34	20	.	.	NOUN
fumecheng-7223	35	1	2	2	NUM
fumecheng-7223	35	2	)	)	PUNCT
fumecheng-7223	35	3	can	can	AUX
fumecheng-7223	35	4	be	be	AUX
fumecheng-7223	35	5	expressed	express	VERB
fumecheng-7223	35	6	using	use	VERB
fumecheng-7223	35	7	the	the	DET
fumecheng-7223	35	8	forced	force	VERB
fumecheng-7223	35	9	mathieu	mathieu	NOUN
fumecheng-7223	35	10	equation	equation	NOUN
fumecheng-7223	35	11	[	[	X
fumecheng-7223	35	12	23	23	NUM
fumecheng-7223	35	13	]	]	PUNCT
fumecheng-7223	35	14	.	.	PUNCT
fumecheng-7223	36	1	fig	fig	NOUN
fumecheng-7223	36	2	.	.	PUNCT
fumecheng-7223	37	1	2	2	NUM
fumecheng-7223	37	2	wind	wind	NOUN
fumecheng-7223	37	3	turbine	turbine	NOUN
fumecheng-7223	37	4	(	(	PUNCT
fumecheng-7223	37	5	left	left	ADJ
fumecheng-7223	37	6	)	)	PUNCT
fumecheng-7223	37	7	and	and	CCONJ
fumecheng-7223	37	8	cyclic	cyclic	ADJ
fumecheng-7223	37	9	gravitational	gravitational	ADJ
fumecheng-7223	37	10	force	force	NOUN
fumecheng-7223	37	11	on	on	ADP
fumecheng-7223	37	12	a	a	DET
fumecheng-7223	37	13	blade	blade	NOUN
fumecheng-7223	37	14	(	(	PUNCT
fumecheng-7223	37	15	right	right	ADJ
fumecheng-7223	37	16	)	)	PUNCT
fumecheng-7223	37	17	in	in	ADP
fumecheng-7223	37	18	this	this	DET
fumecheng-7223	37	19	paper	paper	NOUN
fumecheng-7223	37	20	,	,	PUNCT
fumecheng-7223	37	21	based	base	VERB
fumecheng-7223	37	22	on	on	ADP
fumecheng-7223	37	23	the	the	DET
fumecheng-7223	37	24	energy	energy	NOUN
fumecheng-7223	37	25	conservation	conservation	NOUN
fumecheng-7223	37	26	,	,	PUNCT
fumecheng-7223	37	27	a	a	DET
fumecheng-7223	37	28	modification	modification	NOUN
fumecheng-7223	37	29	of	of	ADP
fumecheng-7223	37	30	the	the	DET
fumecheng-7223	37	31	frequency	frequency	NOUN
fumecheng-7223	37	32	formulation	formulation	NOUN
fumecheng-7223	37	33	is	be	AUX
fumecheng-7223	37	34	proposed	propose	VERB
fumecheng-7223	37	35	in	in	ADP
fumecheng-7223	37	36	order	order	NOUN
fumecheng-7223	37	37	to	to	PART
fumecheng-7223	37	38	obtain	obtain	VERB
fumecheng-7223	37	39	the	the	DET
fumecheng-7223	37	40	frequency	frequency	NOUN
fumecheng-7223	37	41	-	-	PUNCT
fumecheng-7223	37	42	amplitude	amplitude	NOUN
fumecheng-7223	37	43	formulation	formulation	NOUN
fumecheng-7223	37	44	of	of	ADP
fumecheng-7223	37	45	nonlinear	nonlinear	ADJ
fumecheng-7223	37	46	systems	system	NOUN
fumecheng-7223	37	47	.	.	PUNCT
fumecheng-7223	38	1	it	it	PRON
fumecheng-7223	38	2	is	be	AUX
fumecheng-7223	38	3	demonstrated	demonstrate	VERB
fumecheng-7223	38	4	that	that	SCONJ
fumecheng-7223	38	5	the	the	DET
fumecheng-7223	38	6	proposed	propose	VERB
fumecheng-7223	38	7	formulation	formulation	NOUN
fumecheng-7223	38	8	is	be	AUX
fumecheng-7223	38	9	accurate	accurate	ADJ
fumecheng-7223	38	10	enough	enough	ADV
fumecheng-7223	38	11	for	for	ADP
fumecheng-7223	38	12	highly	highly	ADV
fumecheng-7223	38	13	nonlinear	nonlinear	ADJ
fumecheng-7223	38	14	differential	differential	ADJ
fumecheng-7223	38	15	equations	equation	NOUN
fumecheng-7223	38	16	containing	contain	VERB
fumecheng-7223	38	17	large	large	ADJ
fumecheng-7223	38	18	nonlinear	nonlinear	ADJ
fumecheng-7223	38	19	terms	term	NOUN
fumecheng-7223	38	20	.	.	PUNCT
fumecheng-7223	39	1	several	several	ADJ
fumecheng-7223	39	2	examples	example	NOUN
fumecheng-7223	39	3	are	be	AUX
fumecheng-7223	39	4	also	also	ADV
fumecheng-7223	39	5	provided	provide	VERB
fumecheng-7223	39	6	to	to	PART
fumecheng-7223	39	7	exhibit	exhibit	VERB
fumecheng-7223	39	8	the	the	DET
fumecheng-7223	39	9	integrity	integrity	NOUN
fumecheng-7223	39	10	of	of	ADP
fumecheng-7223	39	11	the	the	DET
fumecheng-7223	39	12	introduced	introduce	VERB
fumecheng-7223	39	13	formulation	formulation	NOUN
fumecheng-7223	39	14	.	.	PUNCT
fumecheng-7223	40	1	2	2	X
fumecheng-7223	40	2	.	.	X
fumecheng-7223	40	3	problem	problem	NOUN
fumecheng-7223	40	4	statement	statement	NOUN
fumecheng-7223	40	5	this	this	DET
fumecheng-7223	40	6	paper	paper	NOUN
fumecheng-7223	40	7	focuses	focus	VERB
fumecheng-7223	40	8	itself	itself	PRON
fumecheng-7223	40	9	on	on	ADP
fumecheng-7223	40	10	the	the	DET
fumecheng-7223	40	11	following	follow	VERB
fumecheng-7223	40	12	conservative	conservative	ADJ
fumecheng-7223	40	13	oscillator	oscillator	NOUN
fumecheng-7223	40	14	(	(	PUNCT
fumecheng-7223	40	15	)	)	PUNCT
fumecheng-7223	40	16	0	0	NUM
fumecheng-7223	40	17	,	,	PUNCT
fumecheng-7223	40	18	(	(	PUNCT
fumecheng-7223	40	19	0	0	NUM
fumecheng-7223	40	20	)	)	PUNCT
fumecheng-7223	40	21	0	0	NUM
fumecheng-7223	41	1	(	(	PUNCT
fumecheng-7223	41	2	0)w	0)w	NOUN
fumecheng-7223	41	3	p	p	X
fumecheng-7223	41	4	w	w	PROPN
fumecheng-7223	41	5	w	w	PROPN
fumecheng-7223	41	6	w	w	PROPN
fumecheng-7223	41	7	b	b	NOUN
fumecheng-7223	41	8	+	+	NOUN
fumecheng-7223	41	9	=	=	PUNCT
fumecheng-7223	42	1	=	=	SYM
fumecheng-7223	42	2	=	=	SYM
fumecheng-7223	42	3	(	(	PUNCT
fumecheng-7223	42	4	1	1	NUM
fumecheng-7223	42	5	)	)	PUNCT
fumecheng-7223	42	6	for	for	ADP
fumecheng-7223	42	7	a	a	DET
fumecheng-7223	42	8	periodic	periodic	ADJ
fumecheng-7223	42	9	solution	solution	NOUN
fumecheng-7223	42	10	,	,	PUNCT
fumecheng-7223	42	11	it	it	PRON
fumecheng-7223	42	12	requires	require	VERB
fumecheng-7223	42	13	p(w	p(w	NOUN
fumecheng-7223	42	14	)	)	PUNCT
fumecheng-7223	42	15	/	/	PUNCT
fumecheng-7223	43	1	w	w	ADP
fumecheng-7223	43	2	>	>	X
fumecheng-7223	43	3	0	0	X
fumecheng-7223	43	4	.	.	PUNCT
fumecheng-7223	44	1	there	there	PRON
fumecheng-7223	44	2	are	be	VERB
fumecheng-7223	44	3	many	many	ADJ
fumecheng-7223	44	4	analytical	analytical	ADJ
fumecheng-7223	44	5	methods	method	NOUN
fumecheng-7223	44	6	available	available	ADJ
fumecheng-7223	44	7	for	for	ADP
fumecheng-7223	44	8	solving	solve	VERB
fumecheng-7223	44	9	eq	eq	ADJ
fumecheng-7223	44	10	.	.	PUNCT
fumecheng-7223	45	1	(	(	PUNCT
fumecheng-7223	45	2	1	1	NUM
fumecheng-7223	45	3	)	)	PUNCT
fumecheng-7223	45	4	,	,	PUNCT
fumecheng-7223	45	5	see	see	VERB
fumecheng-7223	45	6	some	some	DET
fumecheng-7223	45	7	review	review	NOUN
fumecheng-7223	45	8	articles	article	NOUN
fumecheng-7223	45	9	in	in	ADP
fumecheng-7223	45	10	refs	ref	NOUN
fumecheng-7223	45	11	.	.	PUNCT
fumecheng-7223	46	1	[	[	X
fumecheng-7223	46	2	24	24	NUM
fumecheng-7223	46	3	-	-	SYM
fumecheng-7223	46	4	26	26	NUM
fumecheng-7223	46	5	]	]	PUNCT
fumecheng-7223	46	6	.	.	PUNCT
fumecheng-7223	47	1	this	this	DET
fumecheng-7223	47	2	paper	paper	NOUN
fumecheng-7223	47	3	will	will	AUX
fumecheng-7223	47	4	discuss	discuss	VERB
fumecheng-7223	47	5	the	the	DET
fumecheng-7223	47	6	frequency	frequency	NOUN
fumecheng-7223	47	7	-	-	PUNCT
fumecheng-7223	47	8	amplitude	amplitude	NOUN
fumecheng-7223	47	9	formulation	formulation	NOUN
fumecheng-7223	47	10	,	,	PUNCT
fumecheng-7223	47	11	which	which	PRON
fumecheng-7223	47	12	was	be	AUX
fumecheng-7223	47	13	first	first	ADV
fumecheng-7223	47	14	proposed	propose	VERB
fumecheng-7223	47	15	in	in	ADP
fumecheng-7223	47	16	2006	2006	NUM
fumecheng-7223	47	17	;	;	PUNCT
fumecheng-7223	47	18	it	it	PRON
fumecheng-7223	47	19	was	be	AUX
fumecheng-7223	47	20	obtained	obtain	VERB
fumecheng-7223	47	21	according	accord	VERB
fumecheng-7223	47	22	to	to	ADP
fumecheng-7223	47	23	an	an	DET
fumecheng-7223	47	24	ancient	ancient	ADJ
fumecheng-7223	47	25	chinese	chinese	ADJ
fumecheng-7223	47	26	algorithm	algorithm	NOUN
fumecheng-7223	47	27	[	[	X
fumecheng-7223	47	28	27	27	NUM
fumecheng-7223	47	29	-	-	SYM
fumecheng-7223	47	30	29	29	NUM
fumecheng-7223	47	31	]	]	PUNCT
fumecheng-7223	47	32	.	.	PUNCT
fumecheng-7223	48	1	due	due	ADP
fumecheng-7223	48	2	to	to	ADP
fumecheng-7223	48	3	its	its	PRON
fumecheng-7223	48	4	simplicity	simplicity	NOUN
fumecheng-7223	48	5	and	and	CCONJ
fumecheng-7223	48	6	accuracy	accuracy	NOUN
fumecheng-7223	48	7	,	,	PUNCT
fumecheng-7223	48	8	the	the	DET
fumecheng-7223	48	9	formulation	formulation	NOUN
fumecheng-7223	48	10	has	have	AUX
fumecheng-7223	48	11	been	be	AUX
fumecheng-7223	48	12	widely	widely	ADV
fumecheng-7223	48	13	applied	apply	VERB
fumecheng-7223	48	14	to	to	ADP
fumecheng-7223	48	15	solving	solve	VERB
fumecheng-7223	48	16	various	various	ADJ
fumecheng-7223	48	17	nonlinear	nonlinear	ADJ
fumecheng-7223	48	18	oscillators	oscillator	NOUN
fumecheng-7223	48	19	;	;	PUNCT
fumecheng-7223	48	20	various	various	ADJ
fumecheng-7223	48	21	modifications	modification	NOUN
fumecheng-7223	48	22	appeared	appear	VERB
fumecheng-7223	48	23	in	in	ADP
fumecheng-7223	48	24	literature	literature	NOUN
fumecheng-7223	48	25	[	[	X
fumecheng-7223	48	26	30	30	NUM
fumecheng-7223	48	27	-	-	SYM
fumecheng-7223	48	28	38	38	NUM
fumecheng-7223	48	29	]	]	PUNCT
fumecheng-7223	48	30	.	.	PUNCT
fumecheng-7223	49	1	the	the	DET
fumecheng-7223	49	2	formulation	formulation	NOUN
fumecheng-7223	49	3	is	be	AUX
fumecheng-7223	49	4	to	to	PART
fumecheng-7223	49	5	find	find	VERB
fumecheng-7223	49	6	a	a	DET
fumecheng-7223	49	7	suitable	suitable	ADJ
fumecheng-7223	49	8	solution	solution	NOUN
fumecheng-7223	49	9	in	in	ADP
fumecheng-7223	49	10	the	the	DET
fumecheng-7223	49	11	form	form	NOUN
fumecheng-7223	49	12	tbw	tbw	PROPN
fumecheng-7223	49	13	cos=	cos=	X
fumecheng-7223	49	14	(	(	PUNCT
fumecheng-7223	49	15	2	2	NUM
fumecheng-7223	49	16	)	)	PUNCT
fumecheng-7223	49	17	where	where	SCONJ
fumecheng-7223	49	18			PROPN
fumecheng-7223	49	19	is	be	AUX
fumecheng-7223	49	20	the	the	DET
fumecheng-7223	49	21	frequency	frequency	NOUN
fumecheng-7223	49	22	to	to	PART
fumecheng-7223	49	23	be	be	AUX
fumecheng-7223	49	24	further	far	ADV
fumecheng-7223	49	25	determined	determine	VERB
fumecheng-7223	49	26	.	.	PUNCT
fumecheng-7223	50	1	b	b	PRON
fumecheng-7223	50	2	residual	residual	ADJ
fumecheng-7223	50	3	equation	equation	NOUN
fumecheng-7223	50	4	is	be	AUX
fumecheng-7223	50	5	obtained	obtain	VERB
fumecheng-7223	50	6	by	by	ADP
fumecheng-7223	50	7	introducing	introduce	VERB
fumecheng-7223	50	8	eq	eq	ADP
fumecheng-7223	50	9	.	.	PUNCT
fumecheng-7223	51	1	(	(	PUNCT
fumecheng-7223	51	2	2	2	NUM
fumecheng-7223	51	3	)	)	PUNCT
fumecheng-7223	51	4	into	into	ADP
fumecheng-7223	51	5	eq	eq	NOUN
fumecheng-7223	51	6	.	.	PUNCT
fumecheng-7223	52	1	(	(	PUNCT
fumecheng-7223	52	2	1	1	NUM
fumecheng-7223	52	3	)	)	PUNCT
fumecheng-7223	52	4	,	,	PUNCT
fumecheng-7223	52	5	which	which	PRON
fumecheng-7223	52	6	results	result	VERB
fumecheng-7223	52	7	in	in	ADP
fumecheng-7223	52	8	)	)	PUNCT
fumecheng-7223	52	9	cos(cos	cos(co	NOUN
fumecheng-7223	52	10	)	)	PUNCT
fumecheng-7223	52	11	(	(	PUNCT
fumecheng-7223	52	12	2	2	NUM
fumecheng-7223	52	13	tbptbtr	tbptbtr	VERB
fumecheng-7223	52	14			PROPN
fumecheng-7223	53	1	+	+	ADJ
fumecheng-7223	53	2	−=	−=	X
fumecheng-7223	53	3	(	(	PUNCT
fumecheng-7223	53	4	3	3	NUM
fumecheng-7223	53	5	)	)	PUNCT
fumecheng-7223	53	6	202	202	NUM
fumecheng-7223	53	7	j.-h	j.-h	NOUN
fumecheng-7223	53	8	.	.	PUNCT
fumecheng-7223	54	1	he	he	PRON
fumecheng-7223	54	2	,	,	PUNCT
fumecheng-7223	54	3	w.-f	w.-f	PROPN
fumecheng-7223	54	4	.	.	PUNCT
fumecheng-7223	55	1	hou	hou	PROPN
fumecheng-7223	55	2	,	,	PUNCT
fumecheng-7223	55	3	n.	n.	PROPN
fumecheng-7223	55	4	qie	qie	PROPN
fumecheng-7223	55	5	,	,	PUNCT
fumecheng-7223	55	6	k.a	k.a	PROPN
fumecheng-7223	55	7	.	.	PROPN
fumecheng-7223	55	8	gepreel	gepreel	PROPN
fumecheng-7223	55	9	,	,	PUNCT
fumecheng-7223	55	10	a.h	a.h	PROPN
fumecheng-7223	55	11	.	.	PROPN
fumecheng-7223	55	12	shirazi	shirazi	PROPN
fumecheng-7223	55	13	,	,	PUNCT
fumecheng-7223	55	14	h.m	h.m	PROPN
fumecheng-7223	55	15	.	.	PROPN
fumecheng-7223	55	16	sedighi	sedighi	PROPN
fumecheng-7223	55	17	the	the	DET
fumecheng-7223	55	18	average	average	ADJ
fumecheng-7223	55	19	residual	residual	NOUN
fumecheng-7223	55	20	can	can	AUX
fumecheng-7223	55	21	be	be	AUX
fumecheng-7223	55	22	calculated	calculate	VERB
fumecheng-7223	55	23	as	as	ADP
fumecheng-7223	55	24	=	=	PROPN
fumecheng-7223	55	25	4/	4/	PROPN
fumecheng-7223	55	26	0	0	NUM
fumecheng-7223	56	1	cos	cos	PROPN
fumecheng-7223	56	2	4~	4~	PROPN
fumecheng-7223	57	1	t	t	PROPN
fumecheng-7223	57	2	tdtr	tdtr	INTJ
fumecheng-7223	57	3	t	t	PROPN
fumecheng-7223	57	4	r	r	PROPN
fumecheng-7223	57	5			X
fumecheng-7223	57	6	(	(	PUNCT
fumecheng-7223	57	7	4	4	NUM
fumecheng-7223	57	8	)	)	PUNCT
fumecheng-7223	57	9	where	where	SCONJ
fumecheng-7223	57	10			ADV
fumecheng-7223	57	11	/2	/2	PUNCT
fumecheng-7223	58	1	=	=	NOUN
fumecheng-7223	58	2	t	t	PROPN
fumecheng-7223	58	3	.	.	PUNCT
fumecheng-7223	59	1	the	the	DET
fumecheng-7223	59	2	formulation	formulation	NOUN
fumecheng-7223	59	3	is	be	AUX
fumecheng-7223	59	4	to	to	PART
fumecheng-7223	59	5	choose	choose	VERB
fumecheng-7223	59	6	two	two	NUM
fumecheng-7223	59	7	trial	trial	NOUN
fumecheng-7223	59	8	frequencies	frequency	NOUN
fumecheng-7223	59	9	,	,	PUNCT
fumecheng-7223	59	10	e.g.	e.g.	ADV
fumecheng-7223	59	11	,	,	PUNCT
fumecheng-7223	59	12	1	1	NUM
fumecheng-7223	59	13	1	1	NUM
fumecheng-7223	59	14	=	=	NOUN
fumecheng-7223	59	15			X
fumecheng-7223	59	16	and	and	CCONJ
fumecheng-7223	59	17	2	2	NUM
fumecheng-7223	59	18	2	2	NUM
fumecheng-7223	59	19	=	=	NOUN
fumecheng-7223	59	20			X
fumecheng-7223	59	21	,	,	PUNCT
fumecheng-7223	59	22	and	and	CCONJ
fumecheng-7223	59	23	their	their	PRON
fumecheng-7223	59	24	residuals	residual	NOUN
fumecheng-7223	59	25	are	be	AUX
fumecheng-7223	59	26	respectively	respectively	ADV
fumecheng-7223	59	27	calculated	calculate	VERB
fumecheng-7223	59	28	as	as	ADP
fumecheng-7223	59	29	tdtr	tdtr	PROPN
fumecheng-7223	59	30	t	t	NOUN
fumecheng-7223	59	31	r	r	NOUN
fumecheng-7223	59	32	t	t	PROPN
fumecheng-7223	59	33	1	1	NUM
fumecheng-7223	59	34	4/	4/	NUM
fumecheng-7223	59	35	0	0	NUM
fumecheng-7223	59	36	1	1	NUM
fumecheng-7223	59	37	1	1	NUM
fumecheng-7223	59	38	1	1	NUM
fumecheng-7223	59	39	cos	cos	NOUN
fumecheng-7223	59	40	4~	4~	NOUN
fumecheng-7223	59	41	1	1	NUM
fumecheng-7223	59	42	=	=	NOUN
fumecheng-7223	59	43	(	(	PUNCT
fumecheng-7223	59	44	5	5	NUM
fumecheng-7223	59	45	)	)	PUNCT
fumecheng-7223	59	46	tdtr	tdtr	PROPN
fumecheng-7223	59	47	t	t	NOUN
fumecheng-7223	59	48	r	r	NOUN
fumecheng-7223	59	49	t	t	PROPN
fumecheng-7223	59	50	2	2	NUM
fumecheng-7223	59	51	4/	4/	NUM
fumecheng-7223	59	52	0	0	NUM
fumecheng-7223	59	53	2	2	NUM
fumecheng-7223	59	54	2	2	NUM
fumecheng-7223	59	55	2	2	NUM
fumecheng-7223	59	56	cos	cos	NOUN
fumecheng-7223	59	57	4~	4~	NOUN
fumecheng-7223	59	58	2	2	NUM
fumecheng-7223	59	59	=	=	NOUN
fumecheng-7223	59	60	(	(	PUNCT
fumecheng-7223	59	61	6	6	NUM
fumecheng-7223	59	62	)	)	PUNCT
fumecheng-7223	59	63	the	the	DET
fumecheng-7223	59	64	frequency	frequency	NOUN
fumecheng-7223	59	65	-	-	PUNCT
fumecheng-7223	59	66	amplitude	amplitude	NOUN
fumecheng-7223	59	67	formulation	formulation	NOUN
fumecheng-7223	59	68	is	be	AUX
fumecheng-7223	59	69	obtained	obtain	VERB
fumecheng-7223	59	70	as	as	SCONJ
fumecheng-7223	59	71	follows	follow	VERB
fumecheng-7223	59	72	[	[	X
fumecheng-7223	59	73	27	27	NUM
fumecheng-7223	59	74	-	-	SYM
fumecheng-7223	59	75	29	29	NUM
fumecheng-7223	59	76	]	]	SYM
fumecheng-7223	60	1	21	21	NUM
fumecheng-7223	60	2	2	2	NUM
fumecheng-7223	60	3	2	2	NUM
fumecheng-7223	60	4	11	11	NUM
fumecheng-7223	60	5	2	2	NUM
fumecheng-7223	60	6	22	22	NUM
fumecheng-7223	60	7	~~	~~	NUM
fumecheng-7223	60	8	~~	~~	NUM
fumecheng-7223	60	9	rr	rr	PROPN
fumecheng-7223	60	10	rr	rr	NOUN
fumecheng-7223	61	1	−	−	NOUN
fumecheng-7223	61	2	−	−	PROPN
fumecheng-7223	62	1	=	=	SYM
fumecheng-7223	62	2			X
fumecheng-7223	62	3			X
fumecheng-7223	62	4	(	(	PUNCT
fumecheng-7223	62	5	7	7	NUM
fumecheng-7223	62	6	)	)	PUNCT
fumecheng-7223	62	7	there	there	PRON
fumecheng-7223	62	8	are	be	VERB
fumecheng-7223	62	9	many	many	ADJ
fumecheng-7223	62	10	modifications	modification	NOUN
fumecheng-7223	62	11	of	of	ADP
fumecheng-7223	62	12	eq	eq	NOUN
fumecheng-7223	62	13	.	.	PUNCT
fumecheng-7223	63	1	(	(	PUNCT
fumecheng-7223	63	2	7	7	NUM
fumecheng-7223	63	3	)	)	PUNCT
fumecheng-7223	63	4	,	,	PUNCT
fumecheng-7223	63	5	see	see	VERB
fumecheng-7223	63	6	for	for	ADP
fumecheng-7223	63	7	examples	example	NOUN
fumecheng-7223	63	8	,	,	PUNCT
fumecheng-7223	63	9	refs	ref	NOUN
fumecheng-7223	63	10	[	[	X
fumecheng-7223	63	11	30	30	NUM
fumecheng-7223	63	12	-	-	SYM
fumecheng-7223	63	13	38	38	NUM
fumecheng-7223	63	14	]	]	PUNCT
fumecheng-7223	63	15	.	.	PUNCT
fumecheng-7223	64	1	this	this	DET
fumecheng-7223	64	2	paper	paper	NOUN
fumecheng-7223	64	3	will	will	AUX
fumecheng-7223	64	4	suggest	suggest	VERB
fumecheng-7223	64	5	an	an	DET
fumecheng-7223	64	6	effective	effective	ADJ
fumecheng-7223	64	7	modification	modification	NOUN
fumecheng-7223	64	8	based	base	VERB
fumecheng-7223	64	9	on	on	ADP
fumecheng-7223	64	10	the	the	DET
fumecheng-7223	64	11	hamiltonian	hamiltonian	ADJ
fumecheng-7223	64	12	invariant	invariant	PROPN
fumecheng-7223	64	13	.	.	PUNCT
fumecheng-7223	65	1	3	3	X
fumecheng-7223	65	2	.	.	X
fumecheng-7223	65	3	hamiltonian	hamiltonian	ADJ
fumecheng-7223	65	4	-	-	PUNCT
fumecheng-7223	65	5	based	base	VERB
fumecheng-7223	65	6	frequency	frequency	NOUN
fumecheng-7223	65	7	-	-	PUNCT
fumecheng-7223	65	8	amplitude	amplitude	NOUN
fumecheng-7223	65	9	formulation	formulation	NOUN
fumecheng-7223	65	10	the	the	DET
fumecheng-7223	65	11	above	above	ADJ
fumecheng-7223	65	12	frequency	frequency	NOUN
fumecheng-7223	65	13	formulation	formulation	NOUN
fumecheng-7223	65	14	is	be	AUX
fumecheng-7223	65	15	derived	derive	VERB
fumecheng-7223	65	16	from	from	ADP
fumecheng-7223	65	17	a	a	DET
fumecheng-7223	65	18	differential	differential	ADJ
fumecheng-7223	65	19	equation	equation	NOUN
fumecheng-7223	65	20	,	,	PUNCT
fumecheng-7223	65	21	here	here	ADV
fumecheng-7223	65	22	we	we	PRON
fumecheng-7223	65	23	suggests	suggest	VERB
fumecheng-7223	65	24	a	a	DET
fumecheng-7223	65	25	modification	modification	NOUN
fumecheng-7223	65	26	from	from	ADP
fumecheng-7223	65	27	an	an	DET
fumecheng-7223	65	28	energy	energy	NOUN
fumecheng-7223	65	29	form	form	NOUN
fumecheng-7223	65	30	.	.	PUNCT
fumecheng-7223	66	1	the	the	DET
fumecheng-7223	66	2	kinetic	kinetic	ADJ
fumecheng-7223	66	3	energy	energy	NOUN
fumecheng-7223	66	4	and	and	CCONJ
fumecheng-7223	66	5	the	the	DET
fumecheng-7223	66	6	potential	potential	ADJ
fumecheng-7223	66	7	energy	energy	NOUN
fumecheng-7223	66	8	are	be	AUX
fumecheng-7223	66	9	changed	change	VERB
fumecheng-7223	66	10	during	during	ADP
fumecheng-7223	66	11	the	the	DET
fumecheng-7223	66	12	oscillation	oscillation	NOUN
fumecheng-7223	66	13	process	process	NOUN
fumecheng-7223	66	14	,	,	PUNCT
fumecheng-7223	66	15	but	but	CCONJ
fumecheng-7223	66	16	the	the	DET
fumecheng-7223	66	17	total	total	ADJ
fumecheng-7223	66	18	energy	energy	NOUN
fumecheng-7223	66	19	will	will	AUX
fumecheng-7223	66	20	keep	keep	VERB
fumecheng-7223	66	21	unchanged	unchanged	ADJ
fumecheng-7223	66	22	for	for	ADP
fumecheng-7223	66	23	a	a	DET
fumecheng-7223	66	24	conservative	conservative	ADJ
fumecheng-7223	66	25	oscillator	oscillator	NOUN
fumecheng-7223	66	26	.	.	PUNCT
fumecheng-7223	67	1	in	in	ADP
fumecheng-7223	67	2	2002	2002	NUM
fumecheng-7223	67	3	,	,	PUNCT
fumecheng-7223	67	4	an	an	DET
fumecheng-7223	67	5	energy	energy	NOUN
fumecheng-7223	67	6	approach	approach	NOUN
fumecheng-7223	67	7	to	to	ADP
fumecheng-7223	67	8	nonlinear	nonlinear	ADJ
fumecheng-7223	67	9	oscillations	oscillation	NOUN
fumecheng-7223	67	10	was	be	AUX
fumecheng-7223	67	11	suggested	suggest	VERB
fumecheng-7223	67	12	[	[	X
fumecheng-7223	67	13	39	39	NUM
fumecheng-7223	67	14	]	]	PUNCT
fumecheng-7223	67	15	.	.	PUNCT
fumecheng-7223	68	1	the	the	DET
fumecheng-7223	68	2	variational	variational	ADJ
fumecheng-7223	68	3	principle	principle	NOUN
fumecheng-7223	68	4	of	of	ADP
fumecheng-7223	68	5	eq	eq	PROPN
fumecheng-7223	68	6	.	.	PUNCT
fumecheng-7223	69	1	(	(	PUNCT
fumecheng-7223	69	2	1	1	X
fumecheng-7223	69	3	)	)	PUNCT
fumecheng-7223	69	4	can	can	AUX
fumecheng-7223	69	5	be	be	AUX
fumecheng-7223	69	6	constructed	construct	VERB
fumecheng-7223	69	7	by	by	ADP
fumecheng-7223	69	8	the	the	DET
fumecheng-7223	69	9	semi	semi	ADJ
fumecheng-7223	69	10	-	-	ADJ
fumecheng-7223	69	11	inverse	inverse	ADJ
fumecheng-7223	69	12	method	method	NOUN
fumecheng-7223	70	1	[	[	X
fumecheng-7223	70	2	40	40	NUM
fumecheng-7223	70	3	-	-	SYM
fumecheng-7223	70	4	43	43	NUM
fumecheng-7223	70	5	]	]	PUNCT
fumecheng-7223	70	6	,	,	PUNCT
fumecheng-7223	70	7	which	which	PRON
fumecheng-7223	70	8	is	be	AUX
fumecheng-7223	70	9	dtwpwwj	dtwpwwj	ADV
fumecheng-7223	70	10			PUNCT
fumecheng-7223	71	1			PROPN
fumecheng-7223	71	2			INTJ
fumecheng-7223	72	1			PROPN
fumecheng-7223	72	2			INTJ
fumecheng-7223	72	3			NUM
fumecheng-7223	72	4			ADP
fumecheng-7223	73	1	−=	−=	NUM
fumecheng-7223	73	2	)	)	PUNCT
fumecheng-7223	73	3	(	(	PUNCT
fumecheng-7223	73	4	2	2	NUM
fumecheng-7223	73	5	1	1	NUM
fumecheng-7223	73	6	)	)	PUNCT
fumecheng-7223	73	7	(	(	PUNCT
fumecheng-7223	73	8	2	2	NUM
fumecheng-7223	73	9	(	(	PUNCT
fumecheng-7223	73	10	8)	8)	NUM
fumecheng-7223	73	11	where	where	SCONJ
fumecheng-7223	73	12	p(w	p(w	NOUN
fumecheng-7223	73	13	)	)	PUNCT
fumecheng-7223	73	14	is	be	AUX
fumecheng-7223	73	15	the	the	DET
fumecheng-7223	73	16	potential	potential	NOUN
fumecheng-7223	73	17	,	,	PUNCT
fumecheng-7223	73	18	satisfying	satisfy	VERB
fumecheng-7223	73	19	the	the	DET
fumecheng-7223	73	20	following	follow	VERB
fumecheng-7223	73	21	relation	relation	NOUN
fumecheng-7223	73	22	:	:	PUNCT
fumecheng-7223	73	23	)	)	PUNCT
fumecheng-7223	74	1	(	(	PUNCT
fumecheng-7223	74	2	)	)	PUNCT
fumecheng-7223	74	3	(	(	PUNCT
fumecheng-7223	74	4	wpwp	wpwp	NOUN
fumecheng-7223	74	5	dw	dw	PROPN
fumecheng-7223	74	6	d	d	PROPN
fumecheng-7223	74	7	=	=	PUNCT
fumecheng-7223	74	8	(	(	PUNCT
fumecheng-7223	74	9	9	9	NUM
fumecheng-7223	74	10	)	)	PUNCT
fumecheng-7223	74	11	in	in	ADP
fumecheng-7223	74	12	the	the	DET
fumecheng-7223	74	13	variational	variational	ADJ
fumecheng-7223	74	14	formulation	formulation	NOUN
fumecheng-7223	74	15	given	give	VERB
fumecheng-7223	74	16	in	in	ADP
fumecheng-7223	74	17	eq	eq	ADP
fumecheng-7223	74	18	.	.	PUNCT
fumecheng-7223	75	1	(	(	PUNCT
fumecheng-7223	75	2	8)	8)	NUM
fumecheng-7223	75	3	,	,	PUNCT
fumecheng-7223	75	4	2	2	NUM
fumecheng-7223	75	5	2	2	NUM
fumecheng-7223	75	6	1	1	NUM
fumecheng-7223	75	7	w	w	NOUN
fumecheng-7223	75	8	is	be	AUX
fumecheng-7223	75	9	the	the	DET
fumecheng-7223	75	10	kinetic	kinetic	ADJ
fumecheng-7223	75	11	energy	energy	NOUN
fumecheng-7223	75	12	,	,	PUNCT
fumecheng-7223	75	13	and	and	CCONJ
fumecheng-7223	75	14	p(w	p(w	NOUN
fumecheng-7223	75	15	)	)	PUNCT
fumecheng-7223	75	16	is	be	AUX
fumecheng-7223	75	17	the	the	DET
fumecheng-7223	75	18	potential	potential	ADJ
fumecheng-7223	75	19	energy	energy	NOUN
fumecheng-7223	75	20	.	.	PUNCT
fumecheng-7223	76	1	the	the	DET
fumecheng-7223	76	2	total	total	ADJ
fumecheng-7223	76	3	energy	energy	NOUN
fumecheng-7223	76	4	keeps	keep	VERB
fumecheng-7223	76	5	unchanged	unchanged	ADJ
fumecheng-7223	76	6	during	during	ADP
fumecheng-7223	76	7	the	the	DET
fumecheng-7223	76	8	oscillation	oscillation	NOUN
fumecheng-7223	76	9	:	:	PUNCT
fumecheng-7223	76	10	hwpw	hwpw	PROPN
fumecheng-7223	76	11	=	=	PUNCT
fumecheng-7223	76	12	+	+	PROPN
fumecheng-7223	76	13			ADJ
fumecheng-7223	76	14	)	)	PUNCT
fumecheng-7223	76	15	(	(	PUNCT
fumecheng-7223	76	16	2	2	NUM
fumecheng-7223	76	17	1	1	NUM
fumecheng-7223	76	18	2	2	NUM
fumecheng-7223	76	19	(	(	PUNCT
fumecheng-7223	76	20	10	10	NUM
fumecheng-7223	76	21	)	)	PUNCT
fumecheng-7223	76	22	hamiltonian	hamiltonian	ADJ
fumecheng-7223	76	23	-	-	PUNCT
fumecheng-7223	76	24	based	base	VERB
fumecheng-7223	76	25	frequency	frequency	NOUN
fumecheng-7223	76	26	-	-	PUNCT
fumecheng-7223	76	27	amplitude	amplitude	NOUN
fumecheng-7223	76	28	formulation	formulation	NOUN
fumecheng-7223	76	29	for	for	ADP
fumecheng-7223	76	30	nonlinear	nonlinear	ADJ
fumecheng-7223	76	31	oscillators	oscillator	NOUN
fumecheng-7223	76	32	203	203	NUM
fumecheng-7223	76	33	where	where	SCONJ
fumecheng-7223	76	34	h	h	NOUN
fumecheng-7223	76	35	is	be	AUX
fumecheng-7223	76	36	the	the	DET
fumecheng-7223	76	37	hamiltonian	hamiltonian	ADJ
fumecheng-7223	76	38	constant	constant	NOUN
fumecheng-7223	76	39	,	,	PUNCT
fumecheng-7223	76	40	which	which	PRON
fumecheng-7223	76	41	can	can	AUX
fumecheng-7223	76	42	be	be	AUX
fumecheng-7223	76	43	identified	identify	VERB
fumecheng-7223	76	44	by	by	ADP
fumecheng-7223	76	45	the	the	DET
fumecheng-7223	76	46	initial	initial	ADJ
fumecheng-7223	76	47	conditions	condition	NOUN
fumecheng-7223	76	48	given	give	VERB
fumecheng-7223	76	49	in	in	ADP
fumecheng-7223	76	50	eq	eq	ADP
fumecheng-7223	76	51	.	.	PUNCT
fumecheng-7223	77	1	(	(	PUNCT
fumecheng-7223	77	2	1	1	NUM
fumecheng-7223	77	3	)	)	PUNCT
fumecheng-7223	77	4	.	.	PUNCT
fumecheng-7223	78	1	finally	finally	ADV
fumecheng-7223	78	2	we	we	PRON
fumecheng-7223	78	3	obtain	obtain	VERB
fumecheng-7223	78	4	the	the	DET
fumecheng-7223	78	5	following	follow	VERB
fumecheng-7223	78	6	first	first	ADJ
fumecheng-7223	78	7	order	order	NOUN
fumecheng-7223	78	8	differential	differential	NOUN
fumecheng-7223	78	9	equation	equation	NOUN
fumecheng-7223	78	10	,	,	PUNCT
fumecheng-7223	78	11	0	0	NUM
fumecheng-7223	78	12	)	)	PUNCT
fumecheng-7223	78	13	(	(	PUNCT
fumecheng-7223	78	14	)	)	PUNCT
fumecheng-7223	78	15	(	(	PUNCT
fumecheng-7223	78	16	2	2	NUM
fumecheng-7223	78	17	1	1	NUM
fumecheng-7223	78	18	2	2	NUM
fumecheng-7223	78	19	=	=	NUM
fumecheng-7223	78	20	−+	−+	NOUN
fumecheng-7223	78	21	bpwpw	bpwpw	PROPN
fumecheng-7223	78	22	(	(	PUNCT
fumecheng-7223	78	23	11	11	NUM
fumecheng-7223	78	24	)	)	PUNCT
fumecheng-7223	78	25	we	we	PRON
fumecheng-7223	78	26	use	use	VERB
fumecheng-7223	78	27	eq	eq	ADP
fumecheng-7223	78	28	.	.	PUNCT
fumecheng-7223	79	1	(	(	PUNCT
fumecheng-7223	79	2	11	11	NUM
fumecheng-7223	79	3	)	)	PUNCT
fumecheng-7223	79	4	instead	instead	ADV
fumecheng-7223	79	5	of	of	ADP
fumecheng-7223	79	6	eq	eq	NOUN
fumecheng-7223	79	7	.	.	PUNCT
fumecheng-7223	80	1	(	(	PUNCT
fumecheng-7223	80	2	1	1	X
fumecheng-7223	80	3	)	)	PUNCT
fumecheng-7223	80	4	to	to	PART
fumecheng-7223	80	5	re	re	VERB
fumecheng-7223	80	6	-	-	VERB
fumecheng-7223	80	7	build	build	VERB
fumecheng-7223	80	8	the	the	DET
fumecheng-7223	80	9	frequency	frequency	NOUN
fumecheng-7223	80	10	-	-	PUNCT
fumecheng-7223	80	11	amplitude	amplitude	NOUN
fumecheng-7223	80	12	formulations	formulation	NOUN
fumecheng-7223	80	13	.	.	PUNCT
fumecheng-7223	81	1	substituting	substitute	VERB
fumecheng-7223	81	2	eq	eq	ADP
fumecheng-7223	81	3	.	.	PUNCT
fumecheng-7223	82	1	(	(	PUNCT
fumecheng-7223	82	2	2	2	NUM
fumecheng-7223	82	3	)	)	PUNCT
fumecheng-7223	82	4	into	into	ADP
fumecheng-7223	82	5	eq	eq	NOUN
fumecheng-7223	82	6	.	.	PUNCT
fumecheng-7223	83	1	(	(	PUNCT
fumecheng-7223	83	2	11	11	NUM
fumecheng-7223	83	3	)	)	PUNCT
fumecheng-7223	83	4	results	result	NOUN
fumecheng-7223	83	5	in	in	ADP
fumecheng-7223	83	6	the	the	DET
fumecheng-7223	83	7	following	follow	VERB
fumecheng-7223	83	8	residual	residual	ADJ
fumecheng-7223	83	9	equation	equation	NOUN
fumecheng-7223	83	10	,	,	PUNCT
fumecheng-7223	83	11	)	)	PUNCT
fumecheng-7223	83	12	(	(	PUNCT
fumecheng-7223	83	13	)	)	PUNCT
fumecheng-7223	83	14	cos(sin	cos(sin	PROPN
fumecheng-7223	83	15	)	)	PUNCT
fumecheng-7223	83	16	(	(	PUNCT
fumecheng-7223	83	17	222	222	NUM
fumecheng-7223	83	18	bptbptbtr	bptbptbtr	ADJ
fumecheng-7223	83	19	−+=	−+=	X
fumecheng-7223	83	20			PROPN
fumecheng-7223	84	1	(	(	PUNCT
fumecheng-7223	84	2	12	12	NUM
fumecheng-7223	84	3	)	)	PUNCT
fumecheng-7223	84	4	similarly	similarly	ADV
fumecheng-7223	84	5	we	we	PRON
fumecheng-7223	84	6	define	define	VERB
fumecheng-7223	84	7	two	two	NUM
fumecheng-7223	84	8	average	average	ADJ
fumecheng-7223	84	9	residuals	residual	NOUN
fumecheng-7223	84	10	tdtr	tdtr	NOUN
fumecheng-7223	84	11	t	t	NOUN
fumecheng-7223	84	12	r	r	NOUN
fumecheng-7223	84	13	t	t	PROPN
fumecheng-7223	84	14	1	1	NUM
fumecheng-7223	84	15	4/	4/	NUM
fumecheng-7223	84	16	0	0	NUM
fumecheng-7223	84	17	1	1	NUM
fumecheng-7223	84	18	1	1	NUM
fumecheng-7223	84	19	1	1	NUM
fumecheng-7223	84	20	cos	cos	NOUN
fumecheng-7223	84	21	4~	4~	NOUN
fumecheng-7223	84	22	1	1	NUM
fumecheng-7223	84	23	=	=	NOUN
fumecheng-7223	84	24	(	(	PUNCT
fumecheng-7223	84	25	13	13	NUM
fumecheng-7223	84	26	)	)	PUNCT
fumecheng-7223	84	27	tdtr	tdtr	PROPN
fumecheng-7223	84	28	t	t	NOUN
fumecheng-7223	84	29	r	r	NOUN
fumecheng-7223	84	30	t	t	PROPN
fumecheng-7223	84	31	2	2	NUM
fumecheng-7223	84	32	4/	4/	NUM
fumecheng-7223	84	33	0	0	NUM
fumecheng-7223	84	34	2	2	NUM
fumecheng-7223	84	35	2	2	NUM
fumecheng-7223	84	36	2	2	NUM
fumecheng-7223	84	37	cos	cos	NOUN
fumecheng-7223	84	38	4~	4~	NOUN
fumecheng-7223	84	39	2	2	NUM
fumecheng-7223	84	40	=	=	NOUN
fumecheng-7223	84	41	(	(	PUNCT
fumecheng-7223	84	42	14	14	NUM
fumecheng-7223	84	43	)	)	PUNCT
fumecheng-7223	84	44	a	a	DET
fumecheng-7223	84	45	modification	modification	NOUN
fumecheng-7223	84	46	of	of	ADP
fumecheng-7223	84	47	the	the	DET
fumecheng-7223	84	48	frequencyamplitude	frequencyamplitude	NOUN
fumecheng-7223	84	49	formulation	formulation	NOUN
fumecheng-7223	84	50	is	be	AUX
fumecheng-7223	84	51	given	give	VERB
fumecheng-7223	84	52	as	as	SCONJ
fumecheng-7223	84	53	follows	follow	VERB
fumecheng-7223	84	54	21	21	NUM
fumecheng-7223	84	55	2	2	NUM
fumecheng-7223	84	56	2	2	NUM
fumecheng-7223	84	57	11	11	NUM
fumecheng-7223	84	58	2	2	NUM
fumecheng-7223	84	59	22	22	NUM
fumecheng-7223	84	60	~~	~~	NUM
fumecheng-7223	84	61	~~	~~	NUM
fumecheng-7223	84	62	rr	rr	PROPN
fumecheng-7223	84	63	rr	rr	NOUN
fumecheng-7223	85	1	−	−	NOUN
fumecheng-7223	85	2	−	−	PROPN
fumecheng-7223	86	1	=	=	SYM
fumecheng-7223	86	2			X
fumecheng-7223	86	3			X
fumecheng-7223	86	4	(	(	PUNCT
fumecheng-7223	86	5	15	15	NUM
fumecheng-7223	86	6	)	)	SYM
fumecheng-7223	86	7	4	4	NUM
fumecheng-7223	86	8	.	.	PUNCT
fumecheng-7223	86	9	example	example	NOUN
fumecheng-7223	86	10	consider	consider	VERB
fumecheng-7223	86	11	the	the	DET
fumecheng-7223	86	12	following	follow	VERB
fumecheng-7223	86	13	well	well	ADV
fumecheng-7223	86	14	-	-	PUNCT
fumecheng-7223	86	15	known	know	VERB
fumecheng-7223	86	16	duffing	duffing	NOUN
fumecheng-7223	86	17	equation	equation	NOUN
fumecheng-7223	86	18	,	,	PUNCT
fumecheng-7223	86	19	bwwwww	bwwwww	NOUN
fumecheng-7223	86	20	=	=	NOUN
fumecheng-7223	86	21	=	=	NOUN
fumecheng-7223	86	22	=++	=++	NOUN
fumecheng-7223	86	23	)	)	PUNCT
fumecheng-7223	86	24	0(0)0(,03	0(0)0(,03	NOUN
fumecheng-7223	86	25	(	(	PUNCT
fumecheng-7223	86	26	16	16	NUM
fumecheng-7223	86	27	)	)	PUNCT
fumecheng-7223	86	28	eq	eq	NOUN
fumecheng-7223	86	29	.	.	PUNCT
fumecheng-7223	87	1	(	(	PUNCT
fumecheng-7223	87	2	16	16	NUM
fumecheng-7223	87	3	)	)	PUNCT
fumecheng-7223	87	4	can	can	AUX
fumecheng-7223	87	5	be	be	AUX
fumecheng-7223	87	6	reduced	reduce	VERB
fumecheng-7223	87	7	to	to	ADP
fumecheng-7223	87	8	the	the	DET
fumecheng-7223	87	9	following	follow	VERB
fumecheng-7223	87	10	first	first	ADJ
fumecheng-7223	87	11	-	-	PUNCT
fumecheng-7223	87	12	order	order	NOUN
fumecheng-7223	87	13	differential	differential	ADJ
fumecheng-7223	87	14	equation	equation	NOUN
fumecheng-7223	87	15	,	,	PUNCT
fumecheng-7223	87	16	0	0	NUM
fumecheng-7223	87	17	4	4	NUM
fumecheng-7223	87	18	1	1	NUM
fumecheng-7223	87	19	2	2	NUM
fumecheng-7223	87	20	1	1	NUM
fumecheng-7223	87	21	4	4	NUM
fumecheng-7223	87	22	1	1	NUM
fumecheng-7223	87	23	2	2	NUM
fumecheng-7223	87	24	1	1	NUM
fumecheng-7223	87	25	2	2	NUM
fumecheng-7223	87	26	1	1	NUM
fumecheng-7223	87	27	42422	42422	NUM
fumecheng-7223	87	28	=	=	SYM
fumecheng-7223	87	29	−−++	−−++	PROPN
fumecheng-7223	87	30	bbwww	bbwww	PROPN
fumecheng-7223	87	31			PROPN
fumecheng-7223	87	32	(	(	PUNCT
fumecheng-7223	87	33	17	17	NUM
fumecheng-7223	87	34	)	)	PUNCT
fumecheng-7223	87	35	we	we	PRON
fumecheng-7223	87	36	choose	choose	VERB
fumecheng-7223	87	37	two	two	NUM
fumecheng-7223	87	38	arbitrary	arbitrary	ADJ
fumecheng-7223	87	39	frequencies	frequency	NOUN
fumecheng-7223	87	40	,	,	PUNCT
fumecheng-7223	87	41	e.g.	e.g.	ADV
fumecheng-7223	87	42	,	,	PUNCT
fumecheng-7223	87	43	1	1	NUM
fumecheng-7223	87	44	=	=	SYM
fumecheng-7223	87	45	1ω	1ω	NUM
fumecheng-7223	87	46	and	and	CCONJ
fumecheng-7223	87	47	2	2	NUM
fumecheng-7223	87	48	=	=	SYM
fumecheng-7223	87	49	2ω	2ω	NUM
fumecheng-7223	87	50	,	,	PUNCT
fumecheng-7223	87	51	and	and	CCONJ
fumecheng-7223	87	52	obtain	obtain	VERB
fumecheng-7223	87	53	the	the	DET
fumecheng-7223	87	54	following	following	ADJ
fumecheng-7223	87	55	residual	residual	ADJ
fumecheng-7223	87	56	equations	equation	NOUN
fumecheng-7223	87	57	,	,	PUNCT
fumecheng-7223	87	58	respectively	respectively	ADV
fumecheng-7223	87	59	.	.	PUNCT
fumecheng-7223	88	1	42442222	42442222	NUM
fumecheng-7223	88	2	1	1	NUM
fumecheng-7223	88	3	4	4	NUM
fumecheng-7223	88	4	1	1	NUM
fumecheng-7223	88	5	2	2	NUM
fumecheng-7223	88	6	1	1	NUM
fumecheng-7223	88	7	cos	cos	ADP
fumecheng-7223	88	8	4	4	NUM
fumecheng-7223	88	9	1	1	NUM
fumecheng-7223	88	10	cos	cos	NOUN
fumecheng-7223	88	11	2	2	NUM
fumecheng-7223	88	12	1	1	NUM
fumecheng-7223	88	13	sin	sin	NOUN
fumecheng-7223	88	14	2	2	NUM
fumecheng-7223	88	15	1	1	NUM
fumecheng-7223	88	16	bbtbtbtbr	bbtbtbtbr	NOUN
fumecheng-7223	88	17			PROPN
fumecheng-7223	88	18	−−++=	−−++=	PUNCT
fumecheng-7223	88	19	(	(	PUNCT
fumecheng-7223	88	20	18	18	NUM
fumecheng-7223	88	21	)	)	PUNCT
fumecheng-7223	88	22	42442222	42442222	NUM
fumecheng-7223	88	23	2	2	NUM
fumecheng-7223	88	24	4	4	NUM
fumecheng-7223	88	25	1	1	NUM
fumecheng-7223	88	26	2	2	NUM
fumecheng-7223	88	27	1	1	NUM
fumecheng-7223	88	28	2cos	2co	NOUN
fumecheng-7223	88	29	4	4	NUM
fumecheng-7223	88	30	1	1	NUM
fumecheng-7223	88	31	2cos	2co	NOUN
fumecheng-7223	88	32	2	2	NUM
fumecheng-7223	88	33	1	1	NUM
fumecheng-7223	88	34	2sin2	2sin2	NUM
fumecheng-7223	88	35	bbtbtbtbr	bbtbtbtbr	NOUN
fumecheng-7223	88	36			NOUN
fumecheng-7223	88	37	−−++=	−−++=	PUNCT
fumecheng-7223	88	38	(	(	PUNCT
fumecheng-7223	88	39	19	19	NUM
fumecheng-7223	88	40	)	)	PUNCT
fumecheng-7223	88	41	their	their	PRON
fumecheng-7223	88	42	average	average	ADJ
fumecheng-7223	88	43	residuals	residual	NOUN
fumecheng-7223	88	44	can	can	AUX
fumecheng-7223	88	45	be	be	AUX
fumecheng-7223	88	46	easily	easily	ADV
fumecheng-7223	88	47	calculated	calculate	VERB
fumecheng-7223	88	48	:	:	PUNCT
fumecheng-7223	88	49			ADJ
fumecheng-7223	88	50			NOUN
fumecheng-7223	88	51	30	30	NUM
fumecheng-7223	88	52	7	7	NUM
fumecheng-7223	88	53	cos	cos	ADP
fumecheng-7223	88	54	4~	4~	NOUN
fumecheng-7223	88	55	4	4	NUM
fumecheng-7223	88	56	4/	4/	NUM
fumecheng-7223	88	57	0	0	NUM
fumecheng-7223	88	58	1	1	NUM
fumecheng-7223	88	59	1	1	NUM
fumecheng-7223	88	60	1	1	NUM
fumecheng-7223	88	61	1	1	NUM
fumecheng-7223	88	62	b	b	X
fumecheng-7223	88	63	tdtr	tdtr	NOUN
fumecheng-7223	88	64	t	t	NOUN
fumecheng-7223	88	65	r	r	NOUN
fumecheng-7223	88	66	t	t	NOUN
fumecheng-7223	88	67	−	−	NOUN
fumecheng-7223	89	1	=	=	NOUN
fumecheng-7223	89	2	=	=	SYM
fumecheng-7223	89	3			X
fumecheng-7223	89	4	(	(	PUNCT
fumecheng-7223	89	5	20	20	NUM
fumecheng-7223	89	6	)	)	PUNCT
fumecheng-7223	89	7			ADJ
fumecheng-7223	89	8			NOUN
fumecheng-7223	89	9	30	30	NUM
fumecheng-7223	89	10	307	307	NUM
fumecheng-7223	89	11	2cos	2co	NOUN
fumecheng-7223	89	12	4~	4~	NOUN
fumecheng-7223	89	13	24	24	NUM
fumecheng-7223	89	14	4/	4/	NUM
fumecheng-7223	89	15	0	0	NUM
fumecheng-7223	89	16	2	2	NUM
fumecheng-7223	89	17	2	2	NUM
fumecheng-7223	89	18	2	2	NUM
fumecheng-7223	89	19	2	2	NUM
fumecheng-7223	89	20	bb	bb	NUM
fumecheng-7223	89	21	tdtr	tdtr	NOUN
fumecheng-7223	89	22	t	t	NOUN
fumecheng-7223	89	23	r	r	NOUN
fumecheng-7223	89	24	t	t	NOUN
fumecheng-7223	89	25	+	+	NOUN
fumecheng-7223	89	26	−	−	PROPN
fumecheng-7223	89	27	=	=	NOUN
fumecheng-7223	89	28	=	=	NOUN
fumecheng-7223	89	29			X
fumecheng-7223	89	30	(	(	PUNCT
fumecheng-7223	89	31	21	21	NUM
fumecheng-7223	89	32	)	)	PUNCT
fumecheng-7223	89	33	204	204	NUM
fumecheng-7223	89	34	j.-h	j.-h	NOUN
fumecheng-7223	89	35	.	.	PUNCT
fumecheng-7223	90	1	he	he	PRON
fumecheng-7223	90	2	,	,	PUNCT
fumecheng-7223	90	3	w.-f	w.-f	PROPN
fumecheng-7223	90	4	.	.	PUNCT
fumecheng-7223	91	1	hou	hou	PROPN
fumecheng-7223	91	2	,	,	PUNCT
fumecheng-7223	91	3	n.	n.	PROPN
fumecheng-7223	91	4	qie	qie	PROPN
fumecheng-7223	91	5	,	,	PUNCT
fumecheng-7223	91	6	k.a	k.a	PROPN
fumecheng-7223	91	7	.	.	PROPN
fumecheng-7223	91	8	gepreel	gepreel	PROPN
fumecheng-7223	91	9	,	,	PUNCT
fumecheng-7223	91	10	a.h	a.h	PROPN
fumecheng-7223	91	11	.	.	PROPN
fumecheng-7223	91	12	shirazi	shirazi	PROPN
fumecheng-7223	91	13	,	,	PUNCT
fumecheng-7223	91	14	h.m	h.m	PROPN
fumecheng-7223	91	15	.	.	PROPN
fumecheng-7223	91	16	sedighi	sedighi	PROPN
fumecheng-7223	91	17	according	accord	VERB
fumecheng-7223	91	18	to	to	ADP
fumecheng-7223	91	19	the	the	DET
fumecheng-7223	91	20	modified	modify	VERB
fumecheng-7223	91	21	frequency	frequency	NOUN
fumecheng-7223	91	22	-	-	PUNCT
fumecheng-7223	91	23	amplitude	amplitude	NOUN
fumecheng-7223	91	24	formulation	formulation	NOUN
fumecheng-7223	91	25	,	,	PUNCT
fumecheng-7223	91	26	we	we	PRON
fumecheng-7223	91	27	obtain	obtain	VERB
fumecheng-7223	91	28	2	2	NUM
fumecheng-7223	91	29	21	21	NUM
fumecheng-7223	91	30	2	2	NUM
fumecheng-7223	91	31	12	12	NUM
fumecheng-7223	91	32	2	2	NUM
fumecheng-7223	91	33	21	21	NUM
fumecheng-7223	91	34	10	10	NUM
fumecheng-7223	91	35	7	7	NUM
fumecheng-7223	91	36	1~~	1~~	NUM
fumecheng-7223	91	37	~~	~~	PUNCT
fumecheng-7223	91	38	b	b	X
fumecheng-7223	91	39	rr	rr	PROPN
fumecheng-7223	91	40	rr	rr	PROPN
fumecheng-7223	91	41			PROPN
fumecheng-7223	91	42			CCONJ
fumecheng-7223	91	43			PROPN
fumecheng-7223	91	44	+	+	PROPN
fumecheng-7223	91	45	=	=	NOUN
fumecheng-7223	91	46	−	−	NOUN
fumecheng-7223	92	1	−	−	PROPN
fumecheng-7223	93	1	=	=	SYM
fumecheng-7223	94	1	(	(	PUNCT
fumecheng-7223	94	2	22	22	NUM
fumecheng-7223	94	3	)	)	PUNCT
fumecheng-7223	94	4	to	to	PART
fumecheng-7223	94	5	show	show	VERB
fumecheng-7223	94	6	its	its	PRON
fumecheng-7223	94	7	accuracy	accuracy	NOUN
fumecheng-7223	94	8	given	give	VERB
fumecheng-7223	94	9	in	in	ADP
fumecheng-7223	94	10	eq	eq	ADP
fumecheng-7223	94	11	.	.	PUNCT
fumecheng-7223	95	1	(	(	PUNCT
fumecheng-7223	95	2	22	22	NUM
fumecheng-7223	95	3	)	)	PUNCT
fumecheng-7223	95	4	,	,	PUNCT
fumecheng-7223	95	5	we	we	PRON
fumecheng-7223	95	6	consider	consider	VERB
fumecheng-7223	95	7	two	two	NUM
fumecheng-7223	95	8	extremes	extreme	NOUN
fumecheng-7223	95	9	when	when	SCONJ
fumecheng-7223	95	10	02	02	NUM
fumecheng-7223	95	11	→b	→b	NOUN
fumecheng-7223	95	12	and	and	CCONJ
fumecheng-7223	95	13	→2b	→2b	PROPN
fumecheng-7223	95	14	.	.	PUNCT
fumecheng-7223	96	1	when	when	SCONJ
fumecheng-7223	96	2	12	12	NUM
fumecheng-7223	96	3	b	b	PROPN
fumecheng-7223	96	4	eq	eq	NOUN
fumecheng-7223	96	5	.	.	PUNCT
fumecheng-7223	96	6	(	(	PUNCT
fumecheng-7223	96	7	22	22	NUM
fumecheng-7223	96	8	)	)	PUNCT
fumecheng-7223	96	9	can	can	AUX
fumecheng-7223	96	10	be	be	AUX
fumecheng-7223	96	11	approximated	approximate	VERB
fumecheng-7223	96	12	as	as	ADP
fumecheng-7223	96	13	2	2	NUM
fumecheng-7223	96	14	20	20	NUM
fumecheng-7223	96	15	7	7	NUM
fumecheng-7223	96	16	1	1	NUM
fumecheng-7223	96	17	b	b	ADP
fumecheng-7223	96	18	+	+	PROPN
fumecheng-7223	96	19	=	=	SYM
fumecheng-7223	96	20	(	(	PUNCT
fumecheng-7223	96	21	23	23	NUM
fumecheng-7223	96	22	)	)	PUNCT
fumecheng-7223	96	23	while	while	SCONJ
fumecheng-7223	96	24	the	the	DET
fumecheng-7223	96	25	perturbation	perturbation	NOUN
fumecheng-7223	96	26	solution	solution	NOUN
fumecheng-7223	96	27	is	be	AUX
fumecheng-7223	96	28	[	[	X
fumecheng-7223	96	29	32	32	NUM
fumecheng-7223	96	30	]	]	SYM
fumecheng-7223	96	31	2	2	NUM
fumecheng-7223	96	32	8	8	NUM
fumecheng-7223	96	33	3	3	NUM
fumecheng-7223	96	34	1	1	NUM
fumecheng-7223	96	35	b	b	ADP
fumecheng-7223	96	36	+	+	PROPN
fumecheng-7223	96	37	=	=	SYM
fumecheng-7223	96	38	(	(	PUNCT
fumecheng-7223	96	39	24	24	NUM
fumecheng-7223	96	40	)	)	PUNCT
fumecheng-7223	96	41	table	table	NOUN
fumecheng-7223	96	42	1	1	NUM
fumecheng-7223	96	43	shows	show	VERB
fumecheng-7223	96	44	that	that	SCONJ
fumecheng-7223	96	45	both	both	PRON
fumecheng-7223	96	46	eq	eq	ADP
fumecheng-7223	96	47	.	.	PUNCT
fumecheng-7223	97	1	(	(	PUNCT
fumecheng-7223	97	2	23	23	NUM
fumecheng-7223	97	3	)	)	PUNCT
fumecheng-7223	97	4	and	and	CCONJ
fumecheng-7223	97	5	eq	eq	NOUN
fumecheng-7223	97	6	.	.	PUNCT
fumecheng-7223	98	1	(	(	PUNCT
fumecheng-7223	98	2	24	24	NUM
fumecheng-7223	98	3	)	)	PUNCT
fumecheng-7223	98	4	see	see	VERB
fumecheng-7223	98	5	good	good	ADJ
fumecheng-7223	98	6	accuracy	accuracy	NOUN
fumecheng-7223	98	7	when	when	SCONJ
fumecheng-7223	98	8	12	12	NUM
fumecheng-7223	98	9	b	b	PROPN
fumecheng-7223	98	10	.	.	PUNCT
fumecheng-7223	99	1	fig	fig	NOUN
fumecheng-7223	99	2	.	.	PUNCT
fumecheng-7223	100	1	3	3	NUM
fumecheng-7223	100	2	also	also	ADV
fumecheng-7223	100	3	shows	show	VERB
fumecheng-7223	100	4	the	the	DET
fumecheng-7223	100	5	good	good	ADJ
fumecheng-7223	100	6	agreement	agreement	NOUN
fumecheng-7223	100	7	between	between	ADP
fumecheng-7223	100	8	the	the	DET
fumecheng-7223	100	9	approximate	approximate	NOUN
fumecheng-7223	100	10	and	and	CCONJ
fumecheng-7223	100	11	the	the	DET
fumecheng-7223	100	12	exact	exact	ADJ
fumecheng-7223	100	13	solutions	solution	NOUN
fumecheng-7223	100	14	.	.	PUNCT
fumecheng-7223	101	1	fig	fig	NOUN
fumecheng-7223	101	2	.	.	PUNCT
fumecheng-7223	102	1	3	3	NUM
fumecheng-7223	102	2	comparison	comparison	NOUN
fumecheng-7223	102	3	of	of	ADP
fumecheng-7223	102	4	the	the	DET
fumecheng-7223	102	5	approximate	approximate	ADJ
fumecheng-7223	102	6	solution	solution	NOUN
fumecheng-7223	102	7	,	,	PUNCT
fumecheng-7223	102	8	the	the	DET
fumecheng-7223	102	9	red	red	ADJ
fumecheng-7223	102	10	continuous	continuous	ADJ
fumecheng-7223	102	11	line	line	NOUN
fumecheng-7223	102	12	is	be	AUX
fumecheng-7223	102	13	the	the	DET
fumecheng-7223	102	14	exact	exact	ADJ
fumecheng-7223	102	15	solution	solution	NOUN
fumecheng-7223	102	16	,	,	PUNCT
fumecheng-7223	102	17	the	the	DET
fumecheng-7223	102	18	black	black	ADJ
fumecheng-7223	102	19	discontinuous	discontinuous	ADJ
fumecheng-7223	102	20	line	line	NOUN
fumecheng-7223	102	21	is	be	AUX
fumecheng-7223	102	22	the	the	DET
fumecheng-7223	102	23	approximate	approximate	ADJ
fumecheng-7223	102	24	solution	solution	NOUN
fumecheng-7223	102	25	,	,	PUNCT
fumecheng-7223	102	26	and	and	CCONJ
fumecheng-7223	102	27	the	the	DET
fumecheng-7223	102	28	blue	blue	ADJ
fumecheng-7223	102	29	circles	circle	NOUN
fumecheng-7223	102	30	are	be	AUX
fumecheng-7223	102	31	perturbation	perturbation	NOUN
fumecheng-7223	102	32	solution	solution	NOUN
fumecheng-7223	102	33	hamiltonian	hamiltonian	NOUN
fumecheng-7223	102	34	-	-	PUNCT
fumecheng-7223	102	35	based	base	VERB
fumecheng-7223	102	36	frequency	frequency	NOUN
fumecheng-7223	102	37	-	-	PUNCT
fumecheng-7223	102	38	amplitude	amplitude	NOUN
fumecheng-7223	102	39	formulation	formulation	NOUN
fumecheng-7223	102	40	for	for	ADP
fumecheng-7223	102	41	nonlinear	nonlinear	ADJ
fumecheng-7223	102	42	oscillators	oscillator	NOUN
fumecheng-7223	102	43	205	205	NUM
fumecheng-7223	102	44	table	table	NOUN
fumecheng-7223	102	45	1	1	NUM
fumecheng-7223	102	46	.	.	PUNCT
fumecheng-7223	102	47	comparison	comparison	NOUN
fumecheng-7223	102	48	of	of	ADP
fumecheng-7223	102	49	the	the	DET
fumecheng-7223	102	50	approximate	approximate	ADJ
fumecheng-7223	102	51	frequency	frequency	NOUN
fumecheng-7223	102	52	of	of	ADP
fumecheng-7223	102	53	eq	eq	PROPN
fumecheng-7223	102	54	.	.	PUNCT
fumecheng-7223	103	1	(	(	PUNCT
fumecheng-7223	103	2	23	23	NUM
fumecheng-7223	103	3	)	)	PUNCT
fumecheng-7223	103	4	with	with	ADP
fumecheng-7223	103	5	the	the	DET
fumecheng-7223	103	6	exact	exact	ADJ
fumecheng-7223	103	7	one	one	NUM
fumecheng-7223	103	8	and	and	CCONJ
fumecheng-7223	103	9	the	the	DET
fumecheng-7223	103	10	perturbation	perturbation	NOUN
fumecheng-7223	103	11	solution	solution	NOUN
fumecheng-7223	103	12	b2	b2	NOUN
fumecheng-7223	103	13	0	0	NUM
fumecheng-7223	103	14	0.001	0.001	NUM
fumecheng-7223	103	15	0.0025	0.0025	NUM
fumecheng-7223	103	16	0.003	0.003	NUM
fumecheng-7223	103	17	0.005	0.005	NUM
fumecheng-7223	103	18	0.007	0.007	NUM
fumecheng-7223	103	19	0.009	0.009	NUM
fumecheng-7223	103	20	eq.(23	eq.(23	NOUN
fumecheng-7223	103	21	)	)	PUNCT
fumecheng-7223	103	22	1	1	NUM
fumecheng-7223	103	23	1.00035	1.00035	NUM
fumecheng-7223	103	24	1.000875	1.000875	NUM
fumecheng-7223	103	25	1.00105	1.00105	NUM
fumecheng-7223	103	26	1.00175	1.00175	NUM
fumecheng-7223	103	27	1.00245	1.00245	NUM
fumecheng-7223	103	28	1.00315	1.00315	NUM
fumecheng-7223	103	29	eq.(24	eq.(24	NOUN
fumecheng-7223	103	30	)	)	PUNCT
fumecheng-7223	103	31	1	1	NUM
fumecheng-7223	103	32	1.000375	1.000375	NUM
fumecheng-7223	103	33	1.0009375	1.0009375	NUM
fumecheng-7223	103	34	1.001125	1.001125	NUM
fumecheng-7223	103	35	1.001875	1.001875	NUM
fumecheng-7223	103	36	1.002625	1.002625	NUM
fumecheng-7223	103	37	1.003375	1.003375	NUM
fumecheng-7223	103	38	exact	exact	ADJ
fumecheng-7223	103	39	frequency	frequency	NOUN
fumecheng-7223	103	40	1	1	NUM
fumecheng-7223	103	41	1.000380	1.000380	NUM
fumecheng-7223	103	42	1.0009442	1.0009442	NUM
fumecheng-7223	103	43	1.00113	1.00113	NUM
fumecheng-7223	103	44	1.0018726	1.0018726	NUM
fumecheng-7223	103	45	1.002613	1.002613	NUM
fumecheng-7223	103	46	1.003369	1.003369	NUM
fumecheng-7223	103	47	when	when	SCONJ
fumecheng-7223	103	48	→2b	→2b	NOUN
fumecheng-7223	103	49	,	,	PUNCT
fumecheng-7223	103	50	its	its	PRON
fumecheng-7223	103	51	approximate	approximate	ADJ
fumecheng-7223	103	52	period	period	NOUN
fumecheng-7223	103	53	becomes	become	VERB
fumecheng-7223	103	54	2	2	NUM
fumecheng-7223	103	55	2	2	NUM
fumecheng-7223	103	56	5098.7	5098.7	NUM
fumecheng-7223	103	57	10	10	NUM
fumecheng-7223	103	58	7	7	NUM
fumecheng-7223	103	59	1	1	NUM
fumecheng-7223	103	60	2	2	NUM
fumecheng-7223	103	61	lim	lim	NOUN
fumecheng-7223	103	62	2	2	NUM
fumecheng-7223	103	63	lim	lim	PROPN
fumecheng-7223	103	64	22	22	NUM
fumecheng-7223	103	65	b	b	PROPN
fumecheng-7223	103	66	b	b	PROPN
fumecheng-7223	103	67	t	t	PROPN
fumecheng-7223	103	68	b	b	PROPN
fumecheng-7223	103	69	app	app	PROPN
fumecheng-7223	103	70	b	b	PROPN
fumecheng-7223	103	71			PROPN
fumecheng-7223	103	72			PROPN
fumecheng-7223	103	73			PROPN
fumecheng-7223	103	74			PROPN
fumecheng-7223	103	75			PROPN
fumecheng-7223	103	76			PROPN
fumecheng-7223	103	77	=	=	PUNCT
fumecheng-7223	104	1	+	+	PUNCT
fumecheng-7223	105	1	=	=	PUNCT
fumecheng-7223	105	2	=	=	SYM
fumecheng-7223	105	3	→→	→→	PROPN
fumecheng-7223	105	4	(	(	PUNCT
fumecheng-7223	105	5	25	25	NUM
fumecheng-7223	105	6	)	)	PUNCT
fumecheng-7223	105	7	the	the	DET
fumecheng-7223	105	8	exact	exact	ADJ
fumecheng-7223	105	9	period	period	NOUN
fumecheng-7223	105	10	,	,	PUNCT
fumecheng-7223	105	11	when	when	SCONJ
fumecheng-7223	105	12	→2b	→2b	NOUN
fumecheng-7223	105	13	,	,	PUNCT
fumecheng-7223	105	14	is	be	AUX
fumecheng-7223	105	15	2	2	NUM
fumecheng-7223	105	16	2/	2/	NUM
fumecheng-7223	105	17	0	0	NUM
fumecheng-7223	105	18	2	2	NUM
fumecheng-7223	105	19	2	2	NUM
fumecheng-7223	105	20	4164.7	4164.7	NUM
fumecheng-7223	105	21	sin5.01	sin5.01	PROPN
fumecheng-7223	105	22	4	4	NUM
fumecheng-7223	105	23	b	b	NOUN
fumecheng-7223	105	24	x	x	X
fumecheng-7223	105	25	dx	dx	PROPN
fumecheng-7223	105	26	b	b	PROPN
fumecheng-7223	105	27	tex	tex	PROPN
fumecheng-7223	105	28			PROPN
fumecheng-7223	105	29			PROPN
fumecheng-7223	105	30	=	=	NOUN
fumecheng-7223	105	31	−=	−=	X
fumecheng-7223	105	32			X
fumecheng-7223	105	33	(	(	PUNCT
fumecheng-7223	105	34	26	26	NUM
fumecheng-7223	105	35	)	)	PUNCT
fumecheng-7223	105	36	it	it	PRON
fumecheng-7223	105	37	is	be	AUX
fumecheng-7223	105	38	obvious	obvious	ADJ
fumecheng-7223	105	39	that	that	SCONJ
fumecheng-7223	105	40	987.0lim	987.0lim	NUM
fumecheng-7223	105	41	=	=	SYM
fumecheng-7223	105	42	→	→	PROPN
fumecheng-7223	105	43	app	app	NOUN
fumecheng-7223	105	44	ex	ex	X
fumecheng-7223	105	45	t	t	PROPN
fumecheng-7223	105	46	t	t	PROPN
fumecheng-7223	105	47			PROPN
fumecheng-7223	105	48	(	(	PUNCT
fumecheng-7223	105	49	27	27	NUM
fumecheng-7223	105	50	)	)	PUNCT
fumecheng-7223	105	51	the	the	DET
fumecheng-7223	105	52	relative	relative	ADJ
fumecheng-7223	105	53	error	error	NOUN
fumecheng-7223	105	54	is	be	AUX
fumecheng-7223	105	55	1.317	1.317	NUM
fumecheng-7223	105	56	%	%	NOUN
fumecheng-7223	105	57	when	when	SCONJ
fumecheng-7223	105	58	→2b	→2b	PRON
fumecheng-7223	105	59	.	.	PUNCT
fumecheng-7223	106	1	the	the	DET
fumecheng-7223	106	2	approximate	approximate	ADJ
fumecheng-7223	106	3	period	period	NOUN
fumecheng-7223	106	4	by	by	ADP
fumecheng-7223	106	5	the	the	DET
fumecheng-7223	106	6	homotopy	homotopy	NOUN
fumecheng-7223	106	7	perturbation	perturbation	NOUN
fumecheng-7223	106	8	method	method	NOUN
fumecheng-7223	106	9	is	be	AUX
fumecheng-7223	106	10	2	2	NUM
fumecheng-7223	106	11	2	2	NUM
fumecheng-7223	106	12	homotopy	homotopy	NOUN
fumecheng-7223	106	13	2552.7	2552.7	NUM
fumecheng-7223	106	14	4	4	NUM
fumecheng-7223	106	15	3	3	NUM
fumecheng-7223	106	16	1	1	NUM
fumecheng-7223	106	17	2	2	NUM
fumecheng-7223	106	18	lim	lim	NOUN
fumecheng-7223	106	19	2	2	NUM
fumecheng-7223	106	20	lim	lim	PROPN
fumecheng-7223	107	1	22	22	NUM
fumecheng-7223	107	2	b	b	PROPN
fumecheng-7223	107	3	b	b	PROPN
fumecheng-7223	107	4	t	t	NOUN
fumecheng-7223	107	5	bb	bb	NUM
fumecheng-7223	107	6			PROPN
fumecheng-7223	107	7			PROPN
fumecheng-7223	107	8			PROPN
fumecheng-7223	107	9			PROPN
fumecheng-7223	107	10			PROPN
fumecheng-7223	107	11			PROPN
fumecheng-7223	107	12	=	=	PUNCT
fumecheng-7223	108	1	+	+	PUNCT
fumecheng-7223	108	2	=	=	PUNCT
fumecheng-7223	108	3	=	=	SYM
fumecheng-7223	108	4	→→	→→	PROPN
fumecheng-7223	108	5	(	(	PUNCT
fumecheng-7223	108	6	28	28	NUM
fumecheng-7223	108	7	)	)	PUNCT
fumecheng-7223	108	8	022.1lim	022.1lim	NUM
fumecheng-7223	108	9	homotopy	homotopy	NOUN
fumecheng-7223	108	10	=	=	SYM
fumecheng-7223	108	11	→	→	PROPN
fumecheng-7223	108	12	t	t	NOUN
fumecheng-7223	108	13	tex	tex	PROPN
fumecheng-7223	108	14			PROPN
fumecheng-7223	108	15	(	(	PUNCT
fumecheng-7223	108	16	29	29	NUM
fumecheng-7223	108	17	)	)	PUNCT
fumecheng-7223	108	18	the	the	DET
fumecheng-7223	108	19	relative	relative	ADJ
fumecheng-7223	108	20	error	error	NOUN
fumecheng-7223	108	21	is	be	AUX
fumecheng-7223	108	22	2.153	2.153	NUM
fumecheng-7223	108	23	%	%	NOUN
fumecheng-7223	108	24	even	even	ADV
fumecheng-7223	108	25	when	when	SCONJ
fumecheng-7223	108	26	→2b	→2b	NOUN
fumecheng-7223	108	27	,	,	PUNCT
fumecheng-7223	108	28	see	see	VERB
fumecheng-7223	108	29	fig	fig	NOUN
fumecheng-7223	108	30	.	.	PUNCT
fumecheng-7223	109	1	4	4	NUM
fumecheng-7223	109	2	and	and	CCONJ
fumecheng-7223	109	3	table	table	NOUN
fumecheng-7223	109	4	2	2	NUM
fumecheng-7223	109	5	.	.	PUNCT
fumecheng-7223	109	6	table	table	NOUN
fumecheng-7223	109	7	2	2	NUM
fumecheng-7223	109	8	.	.	PUNCT
fumecheng-7223	109	9	comparison	comparison	NOUN
fumecheng-7223	109	10	of	of	ADP
fumecheng-7223	109	11	the	the	DET
fumecheng-7223	109	12	approximate	approximate	ADJ
fumecheng-7223	109	13	period	period	NOUN
fumecheng-7223	109	14	of	of	ADP
fumecheng-7223	109	15	eq	eq	PROPN
fumecheng-7223	109	16	.	.	PUNCT
fumecheng-7223	110	1	(	(	PUNCT
fumecheng-7223	110	2	25	25	NUM
fumecheng-7223	110	3	)	)	PUNCT
fumecheng-7223	110	4	with	with	ADP
fumecheng-7223	110	5	the	the	DET
fumecheng-7223	110	6	exact	exact	ADJ
fumecheng-7223	110	7	one	one	NUM
fumecheng-7223	110	8	b2	b2	NOUN
fumecheng-7223	110	9	100	100	NUM
fumecheng-7223	110	10	500	500	NUM
fumecheng-7223	110	11	1000	1000	NUM
fumecheng-7223	110	12	1500	1500	NUM
fumecheng-7223	110	13	2000	2000	NUM
fumecheng-7223	110	14	b2	b2	NOUN
fumecheng-7223	110	15	→	→	SYM
fumecheng-7223	110	16			X
fumecheng-7223	110	17	exact	exact	ADJ
fumecheng-7223	110	18	period	period	NOUN
fumecheng-7223	110	19	0.73629	0.73629	NUM
fumecheng-7223	110	20	0.33118	0.33118	NUM
fumecheng-7223	111	1	0.23435	0.23435	NUM
fumecheng-7223	111	2	0.19140	0.19140	NUM
fumecheng-7223	111	3	0.16577	0.16577	NUM
fumecheng-7223	111	4	2/4164.7	2/4164.7	NUM
fumecheng-7223	111	5	b	b	PROPN
fumecheng-7223	111	6	eq.(25	eq.(25	NOUN
fumecheng-7223	111	7	)	)	PUNCT
fumecheng-7223	111	8	0.74568	0.74568	NUM
fumecheng-7223	111	9	0.33537	0.33537	NUM
fumecheng-7223	111	10	0.23731	0.23731	NUM
fumecheng-7223	111	11	0.19381	0.19381	NUM
fumecheng-7223	111	12	0.16787	0.16787	NUM
fumecheng-7223	111	13	2/5098.7	2/5098.7	NUM
fumecheng-7223	111	14	b	b	ADJ
fumecheng-7223	111	15	relative	relative	ADJ
fumecheng-7223	111	16	error	error	NOUN
fumecheng-7223	111	17	1.275	1.275	NUM
fumecheng-7223	111	18	%	%	NOUN
fumecheng-7223	111	19	1.265	1.265	NUM
fumecheng-7223	111	20	%	%	NOUN
fumecheng-7223	111	21	1.263	1.263	NUM
fumecheng-7223	111	22	%	%	NOUN
fumecheng-7223	111	23	1.259	1.259	NUM
fumecheng-7223	111	24	%	%	NOUN
fumecheng-7223	111	25	1.267	1.267	NUM
fumecheng-7223	111	26	%	%	NOUN
fumecheng-7223	111	27	1.317	1.317	NUM
fumecheng-7223	111	28	%	%	NOUN
fumecheng-7223	111	29	eq.(28	eq.(28	NOUN
fumecheng-7223	111	30	)	)	PUNCT
fumecheng-7223	111	31	0.72073	0.72073	NUM
fumecheng-7223	111	32	0.32403	0.32403	NUM
fumecheng-7223	111	33	0.22928	0.22928	NUM
fumecheng-7223	111	34	0.18725	0.18725	NUM
fumecheng-7223	111	35	0.16218	0.16218	NUM
fumecheng-7223	111	36	2/2552.7	2/2552.7	NUM
fumecheng-7223	111	37	b	b	ADJ
fumecheng-7223	111	38	relative	relative	ADJ
fumecheng-7223	111	39	error	error	NOUN
fumecheng-7223	111	40	2.113	2.113	NUM
fumecheng-7223	111	41	%	%	NOUN
fumecheng-7223	111	42	2.159	2.159	NUM
fumecheng-7223	111	43	%	%	NOUN
fumecheng-7223	111	44	2.163	2.163	NUM
fumecheng-7223	111	45	%	%	NOUN
fumecheng-7223	111	46	2.168	2.168	NUM
fumecheng-7223	111	47	%	%	NOUN
fumecheng-7223	111	48	2.166	2.166	NUM
fumecheng-7223	111	49	%	%	NOUN
fumecheng-7223	111	50	2.153	2.153	NUM
fumecheng-7223	111	51	%	%	NOUN
fumecheng-7223	111	52	206	206	NUM
fumecheng-7223	111	53	j.-h	j.-h	NOUN
fumecheng-7223	111	54	.	.	PUNCT
fumecheng-7223	112	1	he	he	PRON
fumecheng-7223	112	2	,	,	PUNCT
fumecheng-7223	112	3	w.-f	w.-f	PROPN
fumecheng-7223	112	4	.	.	PUNCT
fumecheng-7223	113	1	hou	hou	PROPN
fumecheng-7223	113	2	,	,	PUNCT
fumecheng-7223	113	3	n.	n.	PROPN
fumecheng-7223	113	4	qie	qie	PROPN
fumecheng-7223	113	5	,	,	PUNCT
fumecheng-7223	113	6	k.a	k.a	PROPN
fumecheng-7223	113	7	.	.	PROPN
fumecheng-7223	113	8	gepreel	gepreel	PROPN
fumecheng-7223	113	9	,	,	PUNCT
fumecheng-7223	113	10	a.h	a.h	PROPN
fumecheng-7223	113	11	.	.	PROPN
fumecheng-7223	113	12	shirazi	shirazi	PROPN
fumecheng-7223	113	13	,	,	PUNCT
fumecheng-7223	113	14	h.m	h.m	PROPN
fumecheng-7223	113	15	.	.	PROPN
fumecheng-7223	113	16	sedighi	sedighi	PROPN
fumecheng-7223	113	17	fig	fig	PROPN
fumecheng-7223	113	18	.	.	PUNCT
fumecheng-7223	114	1	4	4	NUM
fumecheng-7223	114	2	comparison	comparison	NOUN
fumecheng-7223	114	3	of	of	ADP
fumecheng-7223	114	4	the	the	DET
fumecheng-7223	114	5	approximate	approximate	ADJ
fumecheng-7223	114	6	solution	solution	NOUN
fumecheng-7223	114	7	,	,	PUNCT
fumecheng-7223	114	8	the	the	DET
fumecheng-7223	114	9	red	red	ADJ
fumecheng-7223	114	10	continuous	continuous	ADJ
fumecheng-7223	114	11	line	line	NOUN
fumecheng-7223	114	12	is	be	AUX
fumecheng-7223	114	13	the	the	DET
fumecheng-7223	114	14	exact	exact	ADJ
fumecheng-7223	114	15	solution	solution	NOUN
fumecheng-7223	114	16	,	,	PUNCT
fumecheng-7223	114	17	the	the	DET
fumecheng-7223	114	18	black	black	ADJ
fumecheng-7223	114	19	discontinuous	discontinuous	ADJ
fumecheng-7223	114	20	line	line	NOUN
fumecheng-7223	114	21	is	be	AUX
fumecheng-7223	114	22	the	the	DET
fumecheng-7223	114	23	approximate	approximate	ADJ
fumecheng-7223	114	24	solution	solution	NOUN
fumecheng-7223	114	25	,	,	PUNCT
fumecheng-7223	114	26	and	and	CCONJ
fumecheng-7223	114	27	the	the	DET
fumecheng-7223	114	28	blue	blue	ADJ
fumecheng-7223	114	29	circles	circle	NOUN
fumecheng-7223	114	30	are	be	AUX
fumecheng-7223	114	31	perturbation	perturbation	NOUN
fumecheng-7223	114	32	solution	solution	NOUN
fumecheng-7223	114	33	4	4	NUM
fumecheng-7223	114	34	.	.	PUNCT
fumecheng-7223	115	1	conclusion	conclusion	NOUN
fumecheng-7223	115	2	this	this	DET
fumecheng-7223	115	3	paper	paper	NOUN
fumecheng-7223	115	4	suggests	suggest	VERB
fumecheng-7223	115	5	a	a	DET
fumecheng-7223	115	6	modification	modification	NOUN
fumecheng-7223	115	7	of	of	ADP
fumecheng-7223	115	8	the	the	DET
fumecheng-7223	115	9	frequency	frequency	NOUN
fumecheng-7223	115	10	formulation	formulation	NOUN
fumecheng-7223	115	11	based	base	VERB
fumecheng-7223	115	12	on	on	ADP
fumecheng-7223	115	13	the	the	DET
fumecheng-7223	115	14	energy	energy	NOUN
fumecheng-7223	115	15	conservation	conservation	NOUN
fumecheng-7223	115	16	,	,	PUNCT
fumecheng-7223	115	17	the	the	DET
fumecheng-7223	115	18	obtained	obtain	VERB
fumecheng-7223	115	19	result	result	NOUN
fumecheng-7223	115	20	is	be	AUX
fumecheng-7223	115	21	globally	globally	ADV
fumecheng-7223	115	22	valid	valid	ADJ
fumecheng-7223	115	23	for	for	ADP
fumecheng-7223	115	24	0	0	NUM
fumecheng-7223	115	25			NOUN
fumecheng-7223	115	26	b2	b2	NOUN
fumecheng-7223	115	27	<	<	X
fumecheng-7223	115	28	.	.	X
fumecheng-7223	115	29	the	the	DET
fumecheng-7223	115	30	example	example	NOUN
fumecheng-7223	115	31	shows	show	VERB
fumecheng-7223	115	32	that	that	SCONJ
fumecheng-7223	115	33	our	our	PRON
fumecheng-7223	115	34	result	result	NOUN
fumecheng-7223	115	35	sees	see	VERB
fumecheng-7223	115	36	a	a	DET
fumecheng-7223	115	37	good	good	ADJ
fumecheng-7223	115	38	agreement	agreement	NOUN
fumecheng-7223	115	39	with	with	ADP
fumecheng-7223	115	40	the	the	DET
fumecheng-7223	115	41	perturbation	perturbation	NOUN
fumecheng-7223	115	42	solution	solution	NOUN
fumecheng-7223	115	43	for	for	ADP
fumecheng-7223	115	44	the	the	DET
fumecheng-7223	115	45	weak	weak	ADJ
fumecheng-7223	115	46	nonlinearity	nonlinearity	NOUN
fumecheng-7223	115	47	.	.	PUNCT
fumecheng-7223	116	1	even	even	ADV
fumecheng-7223	116	2	when	when	SCONJ
fumecheng-7223	116	3	b2	b2	PROPN
fumecheng-7223	116	4	→	→	SYM
fumecheng-7223	116	5			PROPN
fumecheng-7223	116	6	,	,	PUNCT
fumecheng-7223	116	7	our	our	PRON
fumecheng-7223	116	8	approximate	approximate	ADJ
fumecheng-7223	116	9	frequency	frequency	NOUN
fumecheng-7223	116	10	has	have	VERB
fumecheng-7223	116	11	also	also	ADV
fumecheng-7223	116	12	an	an	DET
fumecheng-7223	116	13	extremely	extremely	ADV
fumecheng-7223	116	14	high	high	ADJ
fumecheng-7223	116	15	accuracy	accuracy	NOUN
fumecheng-7223	116	16	,	,	PUNCT
fumecheng-7223	116	17	better	well	ADJ
fumecheng-7223	116	18	than	than	ADP
fumecheng-7223	116	19	those	those	PRON
fumecheng-7223	116	20	obtained	obtain	VERB
fumecheng-7223	116	21	by	by	ADP
fumecheng-7223	116	22	the	the	DET
fumecheng-7223	116	23	variational	variational	ADJ
fumecheng-7223	116	24	iteration	iteration	NOUN
fumecheng-7223	116	25	method	method	NOUN
fumecheng-7223	116	26	and	and	CCONJ
fumecheng-7223	116	27	the	the	DET
fumecheng-7223	116	28	homotopy	homotopy	NOUN
fumecheng-7223	116	29	perturbation	perturbation	NOUN
fumecheng-7223	116	30	method	method	NOUN
fumecheng-7223	116	31	.	.	PUNCT
fumecheng-7223	117	1	acknowledgements	acknowledgement	NOUN
fumecheng-7223	117	2	:	:	PUNCT
fumecheng-7223	117	3	the	the	DET
fumecheng-7223	117	4	authors	author	NOUN
fumecheng-7223	117	5	thanks	thanks	PROPN
fumecheng-7223	117	6	taif	taif	PROPN
fumecheng-7223	117	7	university	university	NOUN
fumecheng-7223	117	8	researchers	researcher	NOUN
fumecheng-7223	117	9	for	for	ADP
fumecheng-7223	117	10	supporting	support	VERB
fumecheng-7223	117	11	project	project	NOUN
fumecheng-7223	117	12	number	number	NOUN
fumecheng-7223	117	13	(	(	PUNCT
fumecheng-7223	117	14	tursp-2020/16	tursp-2020/16	NOUN
fumecheng-7223	117	15	)	)	PUNCT
fumecheng-7223	117	16	,	,	PUNCT
fumecheng-7223	117	17	taif	taif	PROPN
fumecheng-7223	117	18	university	university	PROPN
fumecheng-7223	117	19	,	,	PUNCT
fumecheng-7223	117	20	taif	taif	PROPN
fumecheng-7223	117	21	,	,	PUNCT
fumecheng-7223	117	22	saudi	saudi	PROPN
fumecheng-7223	117	23	arabia	arabia	PROPN
fumecheng-7223	117	24	.	.	PUNCT
fumecheng-7223	118	1	h.m	h.m	PROPN
fumecheng-7223	118	2	.	.	PROPN
fumecheng-7223	118	3	sedighi	sedighi	PROPN
fumecheng-7223	118	4	is	be	AUX
fumecheng-7223	118	5	grateful	grateful	ADJ
fumecheng-7223	118	6	to	to	ADP
fumecheng-7223	118	7	the	the	DET
fumecheng-7223	118	8	research	research	NOUN
fumecheng-7223	118	9	council	council	PROPN
fumecheng-7223	118	10	of	of	ADP
fumecheng-7223	118	11	shahid	shahid	PROPN
fumecheng-7223	118	12	chamran	chamran	PROPN
fumecheng-7223	118	13	university	university	PROPN
fumecheng-7223	118	14	of	of	ADP
fumecheng-7223	118	15	ahvaz	ahvaz	NOUN
fumecheng-7223	118	16	for	for	ADP
fumecheng-7223	118	17	its	its	PRON
fumecheng-7223	118	18	financial	financial	ADJ
fumecheng-7223	118	19	support	support	NOUN
fumecheng-7223	118	20	(	(	PUNCT
fumecheng-7223	118	21	grant	grant	VERB
fumecheng-7223	118	22	no	no	INTJ
fumecheng-7223	118	23	.	.	PUNCT
fumecheng-7223	118	24	scu.em99.98	scu.em99.98	NOUN
fumecheng-7223	118	25	)	)	PUNCT
fumecheng-7223	118	26	.	.	PUNCT
fumecheng-7223	119	1	hamiltonian	hamiltonian	ADJ
fumecheng-7223	119	2	-	-	PUNCT
fumecheng-7223	119	3	based	base	VERB
fumecheng-7223	119	4	frequency	frequency	NOUN
fumecheng-7223	119	5	-	-	PUNCT
fumecheng-7223	119	6	amplitude	amplitude	NOUN
fumecheng-7223	119	7	formulation	formulation	NOUN
fumecheng-7223	119	8	for	for	ADP
fumecheng-7223	119	9	nonlinear	nonlinear	ADJ
fumecheng-7223	119	10	oscillators	oscillator	NOUN
fumecheng-7223	119	11	207	207	NUM
fumecheng-7223	119	12	references	reference	NOUN
fumecheng-7223	119	13	1	1	NUM
fumecheng-7223	119	14	.	.	PUNCT
fumecheng-7223	120	1	kleyman	kleyman	PROPN
fumecheng-7223	120	2	,	,	PUNCT
fumecheng-7223	120	3	g.	g.	PROPN
fumecheng-7223	120	4	,	,	PUNCT
fumecheng-7223	120	5	paehr	paehr	NOUN
fumecheng-7223	120	6	,	,	PUNCT
fumecheng-7223	120	7	m.	m.	NOUN
fumecheng-7223	120	8	,	,	PUNCT
fumecheng-7223	120	9	tatzko	tatzko	PROPN
fumecheng-7223	120	10	,	,	PUNCT
fumecheng-7223	120	11	s.	s.	PROPN
fumecheng-7223	120	12	,	,	PUNCT
fumecheng-7223	120	13	2020	2020	NUM
fumecheng-7223	120	14	,	,	PUNCT
fumecheng-7223	120	15	application	application	NOUN
fumecheng-7223	120	16	of	of	ADP
fumecheng-7223	120	17	control	control	NOUN
fumecheng-7223	120	18	-	-	PUNCT
fumecheng-7223	120	19	based	base	VERB
fumecheng-7223	120	20	-	-	NOUN
fumecheng-7223	120	21	continuation	continuation	NOUN
fumecheng-7223	120	22	for	for	ADP
fumecheng-7223	120	23	characterization	characterization	NOUN
fumecheng-7223	120	24	of	of	ADP
fumecheng-7223	120	25	dynamic	dynamic	ADJ
fumecheng-7223	120	26	systems	system	NOUN
fumecheng-7223	120	27	with	with	ADP
fumecheng-7223	120	28	stiffness	stiffness	NOUN
fumecheng-7223	120	29	and	and	CCONJ
fumecheng-7223	120	30	friction	friction	NOUN
fumecheng-7223	120	31	nonlinearities	nonlinearitie	NOUN
fumecheng-7223	120	32	,	,	PUNCT
fumecheng-7223	120	33	mechanics	mechanic	NOUN
fumecheng-7223	120	34	research	research	NOUN
fumecheng-7223	120	35	communications	communication	NOUN
fumecheng-7223	120	36	,	,	PUNCT
fumecheng-7223	120	37	106	106	NUM
fumecheng-7223	120	38	,	,	PUNCT
fumecheng-7223	120	39	103520	103520	NUM
fumecheng-7223	120	40	.	.	PUNCT
fumecheng-7223	121	1	2	2	NUM
fumecheng-7223	121	2	.	.	X
fumecheng-7223	121	3	andrianov	andrianov	PROPN
fumecheng-7223	121	4	,	,	PUNCT
fumecheng-7223	121	5	i.i	i.i	PROPN
fumecheng-7223	121	6	.	.	PROPN
fumecheng-7223	121	7	,	,	PUNCT
fumecheng-7223	121	8	awrejcewicz	awrejcewicz	PROPN
fumecheng-7223	121	9	,	,	PUNCT
fumecheng-7223	121	10	j.	j.	PROPN
fumecheng-7223	121	11	,	,	PUNCT
fumecheng-7223	121	12	van	van	PROPN
fumecheng-7223	121	13	horssen	horssen	PROPN
fumecheng-7223	121	14	,	,	PUNCT
fumecheng-7223	121	15	w.t	w.t	PROPN
fumecheng-7223	121	16	.	.	PROPN
fumecheng-7223	121	17	,	,	PUNCT
fumecheng-7223	121	18	2020	2020	NUM
fumecheng-7223	121	19	,	,	PUNCT
fumecheng-7223	121	20	on	on	ADP
fumecheng-7223	121	21	the	the	DET
fumecheng-7223	121	22	bolotin	bolotin	PROPN
fumecheng-7223	121	23	's	's	PART
fumecheng-7223	121	24	reduced	reduce	VERB
fumecheng-7223	121	25	beam	beam	NOUN
fumecheng-7223	121	26	model	model	NOUN
fumecheng-7223	121	27	versus	versus	ADP
fumecheng-7223	121	28	various	various	ADJ
fumecheng-7223	121	29	boundary	boundary	ADJ
fumecheng-7223	121	30	conditions	condition	NOUN
fumecheng-7223	121	31	,	,	PUNCT
fumecheng-7223	121	32	mechanics	mechanic	NOUN
fumecheng-7223	121	33	research	research	NOUN
fumecheng-7223	121	34	communications	communication	NOUN
fumecheng-7223	121	35	,	,	PUNCT
fumecheng-7223	121	36	105	105	NUM
fumecheng-7223	121	37	,	,	PUNCT
fumecheng-7223	121	38	103505	103505	NUM
fumecheng-7223	121	39	.	.	PUNCT
fumecheng-7223	122	1	3	3	X
fumecheng-7223	122	2	.	.	X
fumecheng-7223	122	3	soh	soh	PROPN
fumecheng-7223	122	4	,	,	PUNCT
fumecheng-7223	122	5	g.b.m	g.b.m	PROPN
fumecheng-7223	122	6	.	.	PROPN
fumecheng-7223	122	7	,	,	PUNCT
fumecheng-7223	122	8	monkam	monkam	ADJ
fumecheng-7223	122	9	,	,	PUNCT
fumecheng-7223	122	10	y.j	y.j	PROPN
fumecheng-7223	122	11	.	.	PROPN
fumecheng-7223	122	12	,	,	PUNCT
fumecheng-7223	122	13	tuwa	tuwa	ADJ
fumecheng-7223	122	14	,	,	PUNCT
fumecheng-7223	122	15	p.r.n	p.r.n	PROPN
fumecheng-7223	122	16	.	.	PUNCT
fumecheng-7223	122	17	,	,	PUNCT
fumecheng-7223	122	18	tchitnga	tchitnga	NOUN
fumecheng-7223	122	19	,	,	PUNCT
fumecheng-7223	122	20	r.	r.	PROPN
fumecheng-7223	122	21	,	,	PUNCT
fumecheng-7223	122	22	woafo	woafo	NOUN
fumecheng-7223	122	23	,	,	PUNCT
fumecheng-7223	122	24	p.	p.	NOUN
fumecheng-7223	122	25	,	,	PUNCT
fumecheng-7223	122	26	2020	2020	NUM
fumecheng-7223	122	27	,	,	PUNCT
fumecheng-7223	122	28	study	study	NOUN
fumecheng-7223	122	29	of	of	ADP
fumecheng-7223	122	30	a	a	DET
fumecheng-7223	122	31	piezoelectric	piezoelectric	ADJ
fumecheng-7223	122	32	plate	plate	NOUN
fumecheng-7223	122	33	based	base	VERB
fumecheng-7223	122	34	self	self	NOUN
fumecheng-7223	122	35	-	-	PUNCT
fumecheng-7223	122	36	sustained	sustain	VERB
fumecheng-7223	122	37	electric	electric	ADJ
fumecheng-7223	122	38	and	and	CCONJ
fumecheng-7223	122	39	electromechanical	electromechanical	ADJ
fumecheng-7223	122	40	oscillator	oscillator	NOUN
fumecheng-7223	122	41	,	,	PUNCT
fumecheng-7223	122	42	mechanics	mechanic	NOUN
fumecheng-7223	122	43	research	research	NOUN
fumecheng-7223	122	44	communications	communication	NOUN
fumecheng-7223	122	45	,	,	PUNCT
fumecheng-7223	122	46	105	105	NUM
fumecheng-7223	122	47	,	,	PUNCT
fumecheng-7223	122	48	103504	103504	NUM
fumecheng-7223	122	49	.	.	PUNCT
fumecheng-7223	123	1	4	4	X
fumecheng-7223	123	2	.	.	X
fumecheng-7223	124	1	ji	ji	PROPN
fumecheng-7223	124	2	,	,	PUNCT
fumecheng-7223	124	3	f.	f.	PROPN
fumecheng-7223	124	4	y.	y.	PROPN
fumecheng-7223	124	5	,	,	PUNCT
fumecheng-7223	124	6	he	he	PRON
fumecheng-7223	124	7	,	,	PUNCT
fumecheng-7223	124	8	c.h	c.h	PROPN
fumecheng-7223	124	9	.	.	PROPN
fumecheng-7223	124	10	,	,	PUNCT
fumecheng-7223	124	11	zhang	zhang	PROPN
fumecheng-7223	124	12	,	,	PUNCT
fumecheng-7223	124	13	j.j	j.j	PROPN
fumecheng-7223	124	14	.	.	PROPN
fumecheng-7223	124	15	,	,	PUNCT
fumecheng-7223	124	16	2020	2020	NUM
fumecheng-7223	124	17	,	,	PUNCT
fumecheng-7223	124	18	a	a	DET
fumecheng-7223	124	19	fractal	fractal	ADJ
fumecheng-7223	124	20	boussinesq	boussinesq	ADJ
fumecheng-7223	124	21	equation	equation	NOUN
fumecheng-7223	124	22	for	for	ADP
fumecheng-7223	124	23	nonlinear	nonlinear	ADJ
fumecheng-7223	124	24	transverse	transverse	NOUN
fumecheng-7223	124	25	vibration	vibration	NOUN
fumecheng-7223	124	26	of	of	ADP
fumecheng-7223	124	27	a	a	DET
fumecheng-7223	124	28	nanofiber	nanofiber	NOUN
fumecheng-7223	124	29	-	-	PUNCT
fumecheng-7223	124	30	reinforced	reinforce	VERB
fumecheng-7223	124	31	concrete	concrete	ADJ
fumecheng-7223	124	32	pillar	pillar	NOUN
fumecheng-7223	124	33	,	,	PUNCT
fumecheng-7223	124	34	applied	apply	VERB
fumecheng-7223	124	35	mathematical	mathematical	ADJ
fumecheng-7223	124	36	modelling	modelling	NOUN
fumecheng-7223	124	37	,	,	PUNCT
fumecheng-7223	124	38	82	82	NUM
fumecheng-7223	124	39	,	,	PUNCT
fumecheng-7223	124	40	pp	pp	ADJ
fumecheng-7223	124	41	.	.	PUNCT
fumecheng-7223	125	1	437	437	NUM
fumecheng-7223	125	2	-	-	SYM
fumecheng-7223	125	3	448	448	NUM
fumecheng-7223	125	4	.	.	PUNCT
fumecheng-7223	126	1	5	5	NUM
fumecheng-7223	126	2	.	.	X
fumecheng-7223	126	3	meng	meng	PROPN
fumecheng-7223	126	4	,	,	PUNCT
fumecheng-7223	126	5	d.	d.	PROPN
fumecheng-7223	126	6	,	,	PUNCT
fumecheng-7223	126	7	xiao	xiao	PROPN
fumecheng-7223	126	8	,	,	PUNCT
fumecheng-7223	126	9	f.	f.	PROPN
fumecheng-7223	126	10	,	,	PUNCT
fumecheng-7223	126	11	zhang	zhang	PROPN
fumecheng-7223	126	12	,	,	PUNCT
fumecheng-7223	126	13	l.	l.	PROPN
fumecheng-7223	126	14	,	,	PUNCT
fumecheng-7223	126	15	xu	xu	PROPN
fumecheng-7223	126	16	,	,	PUNCT
fumecheng-7223	126	17	x.	x.	PROPN
fumecheng-7223	126	18	,	,	PUNCT
fumecheng-7223	126	19	chen	chen	PROPN
fumecheng-7223	126	20	,	,	PUNCT
fumecheng-7223	126	21	g.s	g.s	PROPN
fumecheng-7223	126	22	.	.	PROPN
fumecheng-7223	126	23	,	,	PUNCT
fumecheng-7223	126	24	zatar	zatar	PROPN
fumecheng-7223	126	25	,	,	PUNCT
fumecheng-7223	126	26	w.	w.	PROPN
fumecheng-7223	126	27	,	,	PUNCT
fumecheng-7223	126	28	hulsey	hulsey	PROPN
fumecheng-7223	126	29	,	,	PUNCT
fumecheng-7223	126	30	j.l	j.l	PROPN
fumecheng-7223	126	31	.	.	PROPN
fumecheng-7223	126	32	,	,	PUNCT
fumecheng-7223	126	33	2019	2019	NUM
fumecheng-7223	126	34	,	,	PUNCT
fumecheng-7223	126	35	nonlinear	nonlinear	ADJ
fumecheng-7223	126	36	vibration	vibration	NOUN
fumecheng-7223	126	37	analysis	analysis	NOUN
fumecheng-7223	126	38	of	of	ADP
fumecheng-7223	126	39	vehicle	vehicle	NOUN
fumecheng-7223	126	40	–	–	PUNCT
fumecheng-7223	126	41	bridge	bridge	NOUN
fumecheng-7223	126	42	interaction	interaction	NOUN
fumecheng-7223	126	43	for	for	ADP
fumecheng-7223	126	44	condition	condition	NOUN
fumecheng-7223	126	45	monitoring	monitoring	NOUN
fumecheng-7223	126	46	,	,	PUNCT
fumecheng-7223	126	47	low	low	ADJ
fumecheng-7223	126	48	frequency	frequency	NOUN
fumecheng-7223	126	49	noise	noise	NOUN
fumecheng-7223	126	50	&	&	CCONJ
fumecheng-7223	126	51	vibration	vibration	NOUN
fumecheng-7223	126	52	,	,	PUNCT
fumecheng-7223	126	53	38(3	38(3	NUM
fumecheng-7223	126	54	-	-	SYM
fumecheng-7223	126	55	4	4	NUM
fumecheng-7223	126	56	)	)	PUNCT
fumecheng-7223	126	57	,	,	PUNCT
fumecheng-7223	126	58	pp	pp	ADP
fumecheng-7223	126	59	.	.	PUNCT
fumecheng-7223	126	60	1422	1422	NUM
fumecheng-7223	126	61	-	-	SYM
fumecheng-7223	126	62	1432	1432	NUM
fumecheng-7223	126	63	.	.	PUNCT
fumecheng-7223	127	1	6	6	NUM
fumecheng-7223	127	2	.	.	PUNCT
fumecheng-7223	127	3	n.	n.	PROPN
fumecheng-7223	127	4	mohamed	mohamed	PROPN
fumecheng-7223	127	5	,	,	PUNCT
fumecheng-7223	127	6	m.a	m.a	PROPN
fumecheng-7223	127	7	.	.	PROPN
fumecheng-7223	127	8	eltaher	eltaher	PROPN
fumecheng-7223	127	9	,	,	PUNCT
fumecheng-7223	127	10	s.a	s.a	PROPN
fumecheng-7223	127	11	.	.	PROPN
fumecheng-7223	127	12	mohamed	mohamed	PROPN
fumecheng-7223	127	13	,	,	PUNCT
fumecheng-7223	127	14	l.f	l.f	PROPN
fumecheng-7223	127	15	.	.	PROPN
fumecheng-7223	127	16	seddek	seddek	PROPN
fumecheng-7223	127	17	,	,	PUNCT
fumecheng-7223	127	18	2018	2018	NUM
fumecheng-7223	127	19	,	,	PUNCT
fumecheng-7223	127	20	numerical	numerical	ADJ
fumecheng-7223	127	21	analysis	analysis	NOUN
fumecheng-7223	127	22	of	of	ADP
fumecheng-7223	127	23	nonlinear	nonlinear	ADJ
fumecheng-7223	127	24	free	free	ADJ
fumecheng-7223	127	25	and	and	CCONJ
fumecheng-7223	127	26	forced	force	VERB
fumecheng-7223	127	27	vibrations	vibration	NOUN
fumecheng-7223	127	28	of	of	ADP
fumecheng-7223	127	29	buckled	buckled	ADJ
fumecheng-7223	127	30	curved	curved	ADJ
fumecheng-7223	127	31	beams	beam	NOUN
fumecheng-7223	127	32	resting	rest	VERB
fumecheng-7223	127	33	on	on	ADP
fumecheng-7223	127	34	nonlinear	nonlinear	ADJ
fumecheng-7223	127	35	elastic	elastic	ADJ
fumecheng-7223	127	36	foundations	foundation	NOUN
fumecheng-7223	127	37	,	,	PUNCT
fumecheng-7223	127	38	international	international	ADJ
fumecheng-7223	127	39	journal	journal	NOUN
fumecheng-7223	127	40	of	of	ADP
fumecheng-7223	127	41	non	non	ADJ
fumecheng-7223	127	42	-	-	ADJ
fumecheng-7223	127	43	linear	linear	ADJ
fumecheng-7223	127	44	mechanics	mechanic	NOUN
fumecheng-7223	127	45	,	,	PUNCT
fumecheng-7223	127	46	101	101	NUM
fumecheng-7223	127	47	,	,	PUNCT
fumecheng-7223	127	48	pp	pp	ADJ
fumecheng-7223	127	49	.	.	PUNCT
fumecheng-7223	128	1	157	157	NUM
fumecheng-7223	128	2	-	-	SYM
fumecheng-7223	128	3	173	173	NUM
fumecheng-7223	128	4	.	.	PUNCT
fumecheng-7223	129	1	7	7	X
fumecheng-7223	129	2	.	.	X
fumecheng-7223	129	3	m.a	m.a	PROPN
fumecheng-7223	129	4	.	.	PROPN
fumecheng-7223	129	5	eltaher	eltaher	PROPN
fumecheng-7223	129	6	,	,	PUNCT
fumecheng-7223	129	7	a.a	a.a	PROPN
fumecheng-7223	129	8	.	.	PROPN
fumecheng-7223	129	9	abdelrahman	abdelrahman	PROPN
fumecheng-7223	129	10	,	,	PUNCT
fumecheng-7223	129	11	a.	a.	PROPN
fumecheng-7223	129	12	al	al	PROPN
fumecheng-7223	129	13	-	-	PUNCT
fumecheng-7223	129	14	nabawy	nabawy	PROPN
fumecheng-7223	129	15	,	,	PUNCT
fumecheng-7223	129	16	m.	m.	NOUN
fumecheng-7223	129	17	khater	khater	NOUN
fumecheng-7223	129	18	,	,	PUNCT
fumecheng-7223	129	19	a.	a.	PROPN
fumecheng-7223	129	20	mansour	mansour	PROPN
fumecheng-7223	129	21	,	,	PUNCT
fumecheng-7223	129	22	2014	2014	NUM
fumecheng-7223	129	23	,	,	PUNCT
fumecheng-7223	129	24	vibration	vibration	NOUN
fumecheng-7223	129	25	of	of	ADP
fumecheng-7223	129	26	nonlinear	nonlinear	ADJ
fumecheng-7223	129	27	graduation	graduation	NOUN
fumecheng-7223	129	28	of	of	ADP
fumecheng-7223	129	29	nano	nano	NOUN
fumecheng-7223	129	30	-	-	PUNCT
fumecheng-7223	129	31	timoshenko	timoshenko	ADJ
fumecheng-7223	129	32	beam	beam	NOUN
fumecheng-7223	129	33	considering	consider	VERB
fumecheng-7223	129	34	the	the	DET
fumecheng-7223	129	35	neutral	neutral	ADJ
fumecheng-7223	129	36	axis	axis	NOUN
fumecheng-7223	129	37	position	position	NOUN
fumecheng-7223	129	38	,	,	PUNCT
fumecheng-7223	129	39	applied	apply	VERB
fumecheng-7223	129	40	mathematics	mathematic	NOUN
fumecheng-7223	129	41	and	and	CCONJ
fumecheng-7223	129	42	computation	computation	NOUN
fumecheng-7223	129	43	,	,	PUNCT
fumecheng-7223	129	44	235	235	NUM
fumecheng-7223	129	45	,	,	PUNCT
fumecheng-7223	129	46	pp	pp	ADJ
fumecheng-7223	129	47	.	.	PUNCT
fumecheng-7223	130	1	512	512	NUM
fumecheng-7223	130	2	-	-	SYM
fumecheng-7223	130	3	529	529	NUM
fumecheng-7223	130	4	.	.	NOUN
fumecheng-7223	131	1	8	8	NUM
fumecheng-7223	131	2	.	.	X
fumecheng-7223	131	3	sedighi	sedighi	PROPN
fumecheng-7223	131	4	,	,	PUNCT
fumecheng-7223	131	5	h.m	h.m	PROPN
fumecheng-7223	131	6	.	.	PROPN
fumecheng-7223	131	7	,	,	PUNCT
fumecheng-7223	131	8	shirazi	shirazi	PROPN
fumecheng-7223	131	9	,	,	PUNCT
fumecheng-7223	131	10	k.h	k.h	PROPN
fumecheng-7223	131	11	.	.	PROPN
fumecheng-7223	131	12	,	,	PUNCT
fumecheng-7223	131	13	zare	zare	PROPN
fumecheng-7223	131	14	,	,	PUNCT
fumecheng-7223	131	15	j.	j.	PROPN
fumecheng-7223	131	16	,	,	PUNCT
fumecheng-7223	131	17	2012	2012	NUM
fumecheng-7223	131	18	,	,	PUNCT
fumecheng-7223	131	19	an	an	DET
fumecheng-7223	131	20	analytic	analytic	ADJ
fumecheng-7223	131	21	solution	solution	NOUN
fumecheng-7223	131	22	of	of	ADP
fumecheng-7223	131	23	transversal	transversal	ADJ
fumecheng-7223	131	24	oscillation	oscillation	NOUN
fumecheng-7223	131	25	of	of	ADP
fumecheng-7223	131	26	quintic	quintic	ADJ
fumecheng-7223	131	27	non	non	ADJ
fumecheng-7223	131	28	-	-	ADJ
fumecheng-7223	131	29	linear	linear	ADJ
fumecheng-7223	131	30	beam	beam	NOUN
fumecheng-7223	131	31	with	with	ADP
fumecheng-7223	131	32	homotopy	homotopy	NOUN
fumecheng-7223	131	33	analysis	analysis	NOUN
fumecheng-7223	131	34	method	method	NOUN
fumecheng-7223	131	35	,	,	PUNCT
fumecheng-7223	131	36	international	international	ADJ
fumecheng-7223	131	37	journal	journal	NOUN
fumecheng-7223	131	38	of	of	ADP
fumecheng-7223	131	39	non	non	ADJ
fumecheng-7223	131	40	-	-	ADJ
fumecheng-7223	131	41	linear	linear	ADJ
fumecheng-7223	131	42	mechanics	mechanic	NOUN
fumecheng-7223	131	43	,	,	PUNCT
fumecheng-7223	131	44	47(7	47(7	NOUN
fumecheng-7223	131	45	)	)	PUNCT
fumecheng-7223	131	46	,	,	PUNCT
fumecheng-7223	131	47	pp	pp	PROPN
fumecheng-7223	131	48	.	.	PUNCT
fumecheng-7223	132	1	777	777	NUM
fumecheng-7223	132	2	-	-	SYM
fumecheng-7223	132	3	784	784	NUM
fumecheng-7223	132	4	.	.	PUNCT
fumecheng-7223	132	5	9	9	NUM
fumecheng-7223	132	6	.	.	X
fumecheng-7223	132	7	sedighi	sedighi	PROPN
fumecheng-7223	132	8	,	,	PUNCT
fumecheng-7223	132	9	h.m	h.m	PROPN
fumecheng-7223	132	10	.	.	PROPN
fumecheng-7223	132	11	,	,	PUNCT
fumecheng-7223	132	12	reza	reza	PROPN
fumecheng-7223	132	13	,	,	PUNCT
fumecheng-7223	132	14	a.	a.	NOUN
fumecheng-7223	132	15	,	,	PUNCT
fumecheng-7223	132	16	2013	2013	NUM
fumecheng-7223	132	17	,	,	PUNCT
fumecheng-7223	132	18	high	high	ADJ
fumecheng-7223	132	19	precise	precise	ADJ
fumecheng-7223	132	20	analysis	analysis	NOUN
fumecheng-7223	132	21	of	of	ADP
fumecheng-7223	132	22	lateral	lateral	ADJ
fumecheng-7223	132	23	vibration	vibration	NOUN
fumecheng-7223	132	24	of	of	ADP
fumecheng-7223	132	25	quintic	quintic	ADJ
fumecheng-7223	132	26	nonlinear	nonlinear	ADJ
fumecheng-7223	132	27	beam	beam	NOUN
fumecheng-7223	132	28	,	,	PUNCT
fumecheng-7223	132	29	latin	latin	ADJ
fumecheng-7223	132	30	american	american	ADJ
fumecheng-7223	132	31	journal	journal	PROPN
fumecheng-7223	132	32	of	of	ADP
fumecheng-7223	132	33	solids	solid	NOUN
fumecheng-7223	132	34	and	and	CCONJ
fumecheng-7223	132	35	structures	structure	NOUN
fumecheng-7223	132	36	,	,	PUNCT
fumecheng-7223	132	37	10(2	10(2	NUM
fumecheng-7223	132	38	)	)	PUNCT
fumecheng-7223	132	39	,	,	PUNCT
fumecheng-7223	132	40	pp	pp	ADJ
fumecheng-7223	132	41	.	.	PUNCT
fumecheng-7223	133	1	441	441	NUM
fumecheng-7223	133	2	-	-	SYM
fumecheng-7223	133	3	452	452	NUM
fumecheng-7223	133	4	.	.	PUNCT
fumecheng-7223	133	5	10	10	NUM
fumecheng-7223	133	6	.	.	X
fumecheng-7223	133	7	sedighi	sedighi	PROPN
fumecheng-7223	133	8	,	,	PUNCT
fumecheng-7223	133	9	h.m	h.m	PROPN
fumecheng-7223	133	10	.	.	PROPN
fumecheng-7223	133	11	,	,	PUNCT
fumecheng-7223	133	12	malikan	malikan	PROPN
fumecheng-7223	133	13	,	,	PUNCT
fumecheng-7223	133	14	m.	m.	NOUN
fumecheng-7223	133	15	,	,	PUNCT
fumecheng-7223	133	16	2020	2020	NUM
fumecheng-7223	133	17	,	,	PUNCT
fumecheng-7223	133	18	stress	stress	NOUN
fumecheng-7223	133	19	-	-	PUNCT
fumecheng-7223	133	20	driven	drive	VERB
fumecheng-7223	133	21	nonlocal	nonlocal	ADJ
fumecheng-7223	133	22	elasticity	elasticity	NOUN
fumecheng-7223	133	23	for	for	ADP
fumecheng-7223	133	24	nonlinear	nonlinear	ADJ
fumecheng-7223	133	25	vibration	vibration	NOUN
fumecheng-7223	133	26	characteristics	characteristic	NOUN
fumecheng-7223	133	27	of	of	ADP
fumecheng-7223	133	28	carbon	carbon	NOUN
fumecheng-7223	133	29	/	/	SYM
fumecheng-7223	133	30	boron	boron	NOUN
fumecheng-7223	133	31	-	-	PUNCT
fumecheng-7223	133	32	nitride	nitride	NOUN
fumecheng-7223	133	33	hetero	hetero	NOUN
fumecheng-7223	133	34	-	-	PUNCT
fumecheng-7223	133	35	nanotube	nanotube	ADJ
fumecheng-7223	133	36	subject	subject	NOUN
fumecheng-7223	133	37	to	to	ADP
fumecheng-7223	133	38	magneto	magneto	NOUN
fumecheng-7223	133	39	-	-	PUNCT
fumecheng-7223	133	40	thermal	thermal	ADJ
fumecheng-7223	133	41	environment	environment	NOUN
fumecheng-7223	133	42	,	,	PUNCT
fumecheng-7223	133	43	phys	phy	NOUN
fumecheng-7223	133	44	.	.	PUNCT
fumecheng-7223	134	1	scr	scr	PROPN
fumecheng-7223	134	2	.	.	PROPN
fumecheng-7223	134	3	,	,	PUNCT
fumecheng-7223	134	4	95	95	NUM
fumecheng-7223	134	5	,	,	PUNCT
fumecheng-7223	134	6	055218	055218	NUM
fumecheng-7223	134	7	.	.	PUNCT
fumecheng-7223	135	1	11	11	NUM
fumecheng-7223	135	2	.	.	X
fumecheng-7223	135	3	sedighi	sedighi	PROPN
fumecheng-7223	135	4	,	,	PUNCT
fumecheng-7223	135	5	h.m	h.m	PROPN
fumecheng-7223	135	6	.	.	PROPN
fumecheng-7223	135	7	,	,	PUNCT
fumecheng-7223	135	8	shirazi	shirazi	PROPN
fumecheng-7223	135	9	,	,	PUNCT
fumecheng-7223	135	10	k.h	k.h	PROPN
fumecheng-7223	135	11	.	.	PROPN
fumecheng-7223	135	12	,	,	PUNCT
fumecheng-7223	135	13	2013	2013	NUM
fumecheng-7223	135	14	,	,	PUNCT
fumecheng-7223	135	15	asymptotic	asymptotic	ADJ
fumecheng-7223	135	16	approach	approach	NOUN
fumecheng-7223	135	17	for	for	ADP
fumecheng-7223	135	18	nonlinear	nonlinear	ADJ
fumecheng-7223	135	19	vibrating	vibrating	NOUN
fumecheng-7223	135	20	beams	beam	NOUN
fumecheng-7223	135	21	with	with	ADP
fumecheng-7223	135	22	saturation	saturation	NOUN
fumecheng-7223	135	23	type	type	NOUN
fumecheng-7223	135	24	boundary	boundary	ADJ
fumecheng-7223	135	25	condition	condition	NOUN
fumecheng-7223	135	26	,	,	PUNCT
fumecheng-7223	135	27	proceedings	proceeding	NOUN
fumecheng-7223	135	28	of	of	ADP
fumecheng-7223	135	29	the	the	DET
fumecheng-7223	135	30	institution	institution	NOUN
fumecheng-7223	135	31	of	of	ADP
fumecheng-7223	135	32	mechanical	mechanical	ADJ
fumecheng-7223	135	33	engineers	engineer	NOUN
fumecheng-7223	135	34	,	,	PUNCT
fumecheng-7223	135	35	part	part	NOUN
fumecheng-7223	135	36	c	c	NOUN
fumecheng-7223	135	37	:	:	PUNCT
fumecheng-7223	135	38	journal	journal	NOUN
fumecheng-7223	135	39	of	of	ADP
fumecheng-7223	135	40	mechanical	mechanical	ADJ
fumecheng-7223	135	41	engineering	engineering	NOUN
fumecheng-7223	135	42	science	science	NOUN
fumecheng-7223	135	43	,	,	PUNCT
fumecheng-7223	135	44	227(11	227(11	NUM
fumecheng-7223	135	45	)	)	PUNCT
fumecheng-7223	135	46	,	,	PUNCT
fumecheng-7223	135	47	pp	pp	ADP
fumecheng-7223	135	48	.	.	PUNCT
fumecheng-7223	135	49	2479	2479	NUM
fumecheng-7223	135	50	-	-	SYM
fumecheng-7223	135	51	2486	2486	NUM
fumecheng-7223	135	52	.	.	PUNCT
fumecheng-7223	136	1	12	12	NUM
fumecheng-7223	136	2	.	.	X
fumecheng-7223	136	3	sedighi	sedighi	PROPN
fumecheng-7223	136	4	,	,	PUNCT
fumecheng-7223	136	5	h.m	h.m	PROPN
fumecheng-7223	136	6	.	.	PROPN
fumecheng-7223	136	7	,	,	PUNCT
fumecheng-7223	136	8	2014	2014	NUM
fumecheng-7223	136	9	,	,	PUNCT
fumecheng-7223	136	10	the	the	DET
fumecheng-7223	136	11	influence	influence	NOUN
fumecheng-7223	136	12	of	of	ADP
fumecheng-7223	136	13	small	small	ADJ
fumecheng-7223	136	14	scale	scale	NOUN
fumecheng-7223	136	15	on	on	ADP
fumecheng-7223	136	16	the	the	DET
fumecheng-7223	136	17	pull	pull	VERB
fumecheng-7223	136	18	-	-	PUNCT
fumecheng-7223	136	19	in	in	NOUN
fumecheng-7223	136	20	behavior	behavior	NOUN
fumecheng-7223	136	21	of	of	ADP
fumecheng-7223	136	22	nonlocal	nonlocal	ADJ
fumecheng-7223	136	23	nanobridges	nanobridge	NOUN
fumecheng-7223	136	24	considering	consider	VERB
fumecheng-7223	136	25	surface	surface	NOUN
fumecheng-7223	136	26	effect	effect	NOUN
fumecheng-7223	136	27	,	,	PUNCT
fumecheng-7223	136	28	casimir	casimir	NOUN
fumecheng-7223	136	29	and	and	CCONJ
fumecheng-7223	136	30	van	van	PROPN
fumecheng-7223	136	31	der	der	NOUN
fumecheng-7223	136	32	waals	waal	NOUN
fumecheng-7223	136	33	attractions	attraction	NOUN
fumecheng-7223	136	34	,	,	PUNCT
fumecheng-7223	136	35	international	international	ADJ
fumecheng-7223	136	36	journal	journal	NOUN
fumecheng-7223	136	37	of	of	ADP
fumecheng-7223	136	38	applied	apply	VERB
fumecheng-7223	136	39	mechanics	mechanic	NOUN
fumecheng-7223	136	40	,	,	PUNCT
fumecheng-7223	136	41	6(3	6(3	NUM
fumecheng-7223	136	42	)	)	PUNCT
fumecheng-7223	136	43	,	,	PUNCT
fumecheng-7223	136	44	1450030	1450030	NUM
fumecheng-7223	136	45	.	.	PUNCT
fumecheng-7223	137	1	13	13	NUM
fumecheng-7223	137	2	.	.	X
fumecheng-7223	137	3	sedighi	sedighi	PROPN
fumecheng-7223	137	4	,	,	PUNCT
fumecheng-7223	137	5	h.m	h.m	PROPN
fumecheng-7223	137	6	.	.	PROPN
fumecheng-7223	137	7	,	,	PUNCT
fumecheng-7223	137	8	2014	2014	NUM
fumecheng-7223	137	9	,	,	PUNCT
fumecheng-7223	137	10	size	size	NOUN
fumecheng-7223	137	11	-	-	PUNCT
fumecheng-7223	137	12	dependent	dependent	ADJ
fumecheng-7223	137	13	dynamic	dynamic	ADJ
fumecheng-7223	137	14	pull	pull	NOUN
fumecheng-7223	137	15	-	-	PUNCT
fumecheng-7223	137	16	in	in	ADP
fumecheng-7223	137	17	instability	instability	NOUN
fumecheng-7223	137	18	of	of	ADP
fumecheng-7223	137	19	vibrating	vibrate	VERB
fumecheng-7223	137	20	electrically	electrically	ADV
fumecheng-7223	137	21	actuated	actuate	VERB
fumecheng-7223	137	22	microbeams	microbeam	NOUN
fumecheng-7223	137	23	based	base	VERB
fumecheng-7223	137	24	on	on	ADP
fumecheng-7223	137	25	the	the	DET
fumecheng-7223	137	26	strain	strain	NOUN
fumecheng-7223	137	27	gradient	gradient	NOUN
fumecheng-7223	137	28	elasticity	elasticity	NOUN
fumecheng-7223	137	29	theory	theory	NOUN
fumecheng-7223	137	30	,	,	PUNCT
fumecheng-7223	137	31	acta	acta	PROPN
fumecheng-7223	137	32	astronautica	astronautica	PROPN
fumecheng-7223	137	33	,	,	PUNCT
fumecheng-7223	137	34	95	95	NUM
fumecheng-7223	137	35	,	,	PUNCT
fumecheng-7223	137	36	pp	pp	ADJ
fumecheng-7223	137	37	.	.	PUNCT
fumecheng-7223	137	38	111	111	NUM
fumecheng-7223	137	39	-	-	SYM
fumecheng-7223	137	40	123	123	NUM
fumecheng-7223	137	41	.	.	PUNCT
fumecheng-7223	138	1	14	14	NUM
fumecheng-7223	138	2	.	.	X
fumecheng-7223	139	1	sedighi	sedighi	PROPN
fumecheng-7223	139	2	,	,	PUNCT
fumecheng-7223	139	3	h.m	h.m	PROPN
fumecheng-7223	139	4	.	.	PROPN
fumecheng-7223	139	5	,	,	PUNCT
fumecheng-7223	139	6	shirazi	shirazi	PROPN
fumecheng-7223	139	7	,	,	PUNCT
fumecheng-7223	139	8	k.h	k.h	PROPN
fumecheng-7223	139	9	.	.	PROPN
fumecheng-7223	139	10	,	,	PUNCT
fumecheng-7223	139	11	2015	2015	NUM
fumecheng-7223	139	12	,	,	PUNCT
fumecheng-7223	139	13	dynamic	dynamic	ADJ
fumecheng-7223	139	14	pull	pull	NOUN
fumecheng-7223	139	15	-	-	PUNCT
fumecheng-7223	139	16	in	in	ADP
fumecheng-7223	139	17	instability	instability	NOUN
fumecheng-7223	139	18	of	of	ADP
fumecheng-7223	139	19	double	double	ADJ
fumecheng-7223	139	20	-	-	PUNCT
fumecheng-7223	139	21	sided	sided	ADJ
fumecheng-7223	139	22	actuated	actuate	VERB
fumecheng-7223	139	23	nano	nano	NOUN
fumecheng-7223	139	24	-	-	PUNCT
fumecheng-7223	139	25	torsional	torsional	NOUN
fumecheng-7223	139	26	switches	switch	NOUN
fumecheng-7223	139	27	,	,	PUNCT
fumecheng-7223	139	28	acta	acta	PROPN
fumecheng-7223	139	29	mechanica	mechanica	PROPN
fumecheng-7223	139	30	solida	solida	PROPN
fumecheng-7223	139	31	sinica	sinica	PROPN
fumecheng-7223	139	32	,	,	PUNCT
fumecheng-7223	139	33	28	28	NUM
fumecheng-7223	139	34	,	,	PUNCT
fumecheng-7223	139	35	pp	pp	ADJ
fumecheng-7223	139	36	.	.	PUNCT
fumecheng-7223	140	1	91	91	NUM
fumecheng-7223	140	2	-	-	SYM
fumecheng-7223	140	3	101	101	NUM
fumecheng-7223	140	4	.	.	NOUN
fumecheng-7223	141	1	15	15	NUM
fumecheng-7223	141	2	.	.	X
fumecheng-7223	142	1	ouakad	ouakad	ADJ
fumecheng-7223	142	2	,	,	PUNCT
fumecheng-7223	142	3	h.m	h.m	PROPN
fumecheng-7223	142	4	.	.	PROPN
fumecheng-7223	142	5	,	,	PUNCT
fumecheng-7223	142	6	sedighi	sedighi	PROPN
fumecheng-7223	142	7	,	,	PUNCT
fumecheng-7223	142	8	h.m	h.m	PROPN
fumecheng-7223	142	9	.	.	PROPN
fumecheng-7223	142	10	,	,	PUNCT
fumecheng-7223	142	11	2019	2019	NUM
fumecheng-7223	142	12	,	,	PUNCT
fumecheng-7223	142	13	static	static	ADJ
fumecheng-7223	142	14	response	response	NOUN
fumecheng-7223	142	15	and	and	CCONJ
fumecheng-7223	142	16	free	free	ADJ
fumecheng-7223	142	17	vibration	vibration	NOUN
fumecheng-7223	142	18	of	of	ADP
fumecheng-7223	142	19	mems	mem	NOUN
fumecheng-7223	142	20	arches	arch	NOUN
fumecheng-7223	142	21	assuming	assume	VERB
fumecheng-7223	142	22	out	out	ADP
fumecheng-7223	142	23	-	-	PUNCT
fumecheng-7223	142	24	of	of	ADP
fumecheng-7223	142	25	-	-	PUNCT
fumecheng-7223	142	26	plane	plane	NOUN
fumecheng-7223	142	27	actuation	actuation	NOUN
fumecheng-7223	142	28	pattern	pattern	NOUN
fumecheng-7223	142	29	,	,	PUNCT
fumecheng-7223	142	30	international	international	ADJ
fumecheng-7223	142	31	journal	journal	NOUN
fumecheng-7223	142	32	of	of	ADP
fumecheng-7223	142	33	non	non	ADJ
fumecheng-7223	142	34	-	-	ADJ
fumecheng-7223	142	35	linear	linear	ADJ
fumecheng-7223	142	36	mechanics	mechanic	NOUN
fumecheng-7223	142	37	,	,	PUNCT
fumecheng-7223	142	38	110	110	NUM
fumecheng-7223	142	39	,	,	PUNCT
fumecheng-7223	142	40	pp	pp	ADJ
fumecheng-7223	142	41	.	.	PUNCT
fumecheng-7223	143	1	44	44	NUM
fumecheng-7223	143	2	-	-	SYM
fumecheng-7223	143	3	57	57	NUM
fumecheng-7223	143	4	.	.	PUNCT
fumecheng-7223	144	1	16	16	NUM
fumecheng-7223	144	2	.	.	PUNCT
fumecheng-7223	145	1	ouakad	ouakad	ADJ
fumecheng-7223	145	2	,	,	PUNCT
fumecheng-7223	145	3	h.m	h.m	PROPN
fumecheng-7223	145	4	.	.	PROPN
fumecheng-7223	145	5	,	,	PUNCT
fumecheng-7223	145	6	mohammad	mohammad	PROPN
fumecheng-7223	145	7	sedighi	sedighi	PROPN
fumecheng-7223	145	8	,	,	PUNCT
fumecheng-7223	145	9	h.	h.	PROPN
fumecheng-7223	145	10	,	,	PUNCT
fumecheng-7223	145	11	2019	2019	NUM
fumecheng-7223	145	12	,	,	PUNCT
fumecheng-7223	145	13	rippling	ripple	VERB
fumecheng-7223	145	14	effect	effect	NOUN
fumecheng-7223	145	15	on	on	ADP
fumecheng-7223	145	16	the	the	DET
fumecheng-7223	145	17	structural	structural	ADJ
fumecheng-7223	145	18	response	response	NOUN
fumecheng-7223	145	19	of	of	ADP
fumecheng-7223	145	20	electrostatically	electrostatically	ADV
fumecheng-7223	145	21	actuated	actuate	VERB
fumecheng-7223	145	22	single	single	ADJ
fumecheng-7223	145	23	-	-	PUNCT
fumecheng-7223	145	24	walled	wall	VERB
fumecheng-7223	145	25	carbon	carbon	NOUN
fumecheng-7223	145	26	nanotube	nanotube	NOUN
fumecheng-7223	145	27	based	base	VERB
fumecheng-7223	145	28	nems	nem	NOUN
fumecheng-7223	145	29	actuators	actuator	NOUN
fumecheng-7223	145	30	,	,	PUNCT
fumecheng-7223	145	31	international	international	ADJ
fumecheng-7223	145	32	journal	journal	NOUN
fumecheng-7223	145	33	of	of	ADP
fumecheng-7223	145	34	non	non	ADJ
fumecheng-7223	145	35	-	-	ADJ
fumecheng-7223	145	36	linear	linear	ADJ
fumecheng-7223	145	37	mechanics	mechanic	NOUN
fumecheng-7223	145	38	,	,	PUNCT
fumecheng-7223	145	39	87	87	NUM
fumecheng-7223	145	40	,	,	PUNCT
fumecheng-7223	145	41	pp	pp	ADJ
fumecheng-7223	145	42	.	.	PUNCT
fumecheng-7223	146	1	97	97	NUM
fumecheng-7223	146	2	-	-	SYM
fumecheng-7223	146	3	108	108	NUM
fumecheng-7223	146	4	.	.	PUNCT
fumecheng-7223	147	1	17	17	NUM
fumecheng-7223	147	2	.	.	X
fumecheng-7223	148	1	sedighi	sedighi	PROPN
fumecheng-7223	148	2	,	,	PUNCT
fumecheng-7223	148	3	h.m	h.m	PROPN
fumecheng-7223	148	4	.	.	PROPN
fumecheng-7223	148	5	,	,	PUNCT
fumecheng-7223	148	6	daneshmand	daneshmand	PROPN
fumecheng-7223	148	7	,	,	PUNCT
fumecheng-7223	148	8	f.	f.	PROPN
fumecheng-7223	148	9	,	,	PUNCT
fumecheng-7223	148	10	2014	2014	NUM
fumecheng-7223	148	11	,	,	PUNCT
fumecheng-7223	148	12	static	static	ADJ
fumecheng-7223	148	13	and	and	CCONJ
fumecheng-7223	148	14	dynamic	dynamic	ADJ
fumecheng-7223	148	15	pull	pull	NOUN
fumecheng-7223	148	16	-	-	PUNCT
fumecheng-7223	148	17	in	in	ADP
fumecheng-7223	148	18	instability	instability	NOUN
fumecheng-7223	148	19	of	of	ADP
fumecheng-7223	148	20	multi	multi	ADJ
fumecheng-7223	148	21	-	-	ADJ
fumecheng-7223	148	22	walled	walled	ADJ
fumecheng-7223	148	23	carbon	carbon	NOUN
fumecheng-7223	148	24	nanotube	nanotube	NOUN
fumecheng-7223	148	25	probes	probe	NOUN
fumecheng-7223	148	26	by	by	ADP
fumecheng-7223	148	27	he	he	PRON
fumecheng-7223	148	28	’s	’	VERB
fumecheng-7223	148	29	iteration	iteration	NOUN
fumecheng-7223	148	30	perturbation	perturbation	NOUN
fumecheng-7223	148	31	method	method	NOUN
fumecheng-7223	148	32	,	,	PUNCT
fumecheng-7223	148	33	journal	journal	NOUN
fumecheng-7223	148	34	of	of	ADP
fumecheng-7223	148	35	mechanical	mechanical	ADJ
fumecheng-7223	148	36	science	science	NOUN
fumecheng-7223	148	37	and	and	CCONJ
fumecheng-7223	148	38	technology	technology	NOUN
fumecheng-7223	148	39	,	,	PUNCT
fumecheng-7223	148	40	28	28	NUM
fumecheng-7223	148	41	,	,	PUNCT
fumecheng-7223	148	42	pp	pp	ADJ
fumecheng-7223	148	43	.	.	PUNCT
fumecheng-7223	148	44	3459	3459	NUM
fumecheng-7223	148	45	-	-	SYM
fumecheng-7223	148	46	3469	3469	NUM
fumecheng-7223	148	47	.	.	PUNCT
fumecheng-7223	149	1	18	18	NUM
fumecheng-7223	149	2	.	.	X
fumecheng-7223	149	3	sedighi	sedighi	PROPN
fumecheng-7223	149	4	,	,	PUNCT
fumecheng-7223	149	5	h.m	h.m	PROPN
fumecheng-7223	149	6	.	.	PROPN
fumecheng-7223	149	7	,	,	PUNCT
fumecheng-7223	149	8	moory	moory	NOUN
fumecheng-7223	149	9	-	-	PUNCT
fumecheng-7223	149	10	shirbani	shirbani	ADJ
fumecheng-7223	149	11	,	,	PUNCT
fumecheng-7223	149	12	m.	m.	NOUN
fumecheng-7223	149	13	,	,	PUNCT
fumecheng-7223	149	14	shishesaz	shishesaz	PROPN
fumecheng-7223	149	15	,	,	PUNCT
fumecheng-7223	149	16	m.	m.	NOUN
fumecheng-7223	149	17	,	,	PUNCT
fumecheng-7223	149	18	koochi	koochi	PROPN
fumecheng-7223	149	19	,	,	PUNCT
fumecheng-7223	149	20	a.	a.	NOUN
fumecheng-7223	149	21	,	,	PUNCT
fumecheng-7223	149	22	abadyan	abadyan	PROPN
fumecheng-7223	149	23	,	,	PUNCT
fumecheng-7223	149	24	m.	m.	NOUN
fumecheng-7223	149	25	,	,	PUNCT
fumecheng-7223	149	26	2016	2016	NUM
fumecheng-7223	149	27	,	,	PUNCT
fumecheng-7223	149	28	size	size	NOUN
fumecheng-7223	149	29	-	-	PUNCT
fumecheng-7223	149	30	dependent	dependent	ADJ
fumecheng-7223	149	31	dynamic	dynamic	ADJ
fumecheng-7223	149	32	behavior	behavior	NOUN
fumecheng-7223	149	33	and	and	CCONJ
fumecheng-7223	149	34	instability	instability	NOUN
fumecheng-7223	149	35	analysis	analysis	NOUN
fumecheng-7223	149	36	of	of	ADP
fumecheng-7223	149	37	nano	nano	NOUN
fumecheng-7223	149	38	-	-	PUNCT
fumecheng-7223	149	39	scale	scale	NOUN
fumecheng-7223	149	40	rotational	rotational	ADJ
fumecheng-7223	149	41	varactor	varactor	NOUN
fumecheng-7223	149	42	in	in	ADP
fumecheng-7223	149	43	the	the	DET
fumecheng-7223	149	44	presence	presence	NOUN
fumecheng-7223	149	45	of	of	ADP
fumecheng-7223	149	46	casimir	casimir	PROPN
fumecheng-7223	149	47	attraction	attraction	PROPN
fumecheng-7223	149	48	,	,	PUNCT
fumecheng-7223	149	49	international	international	ADJ
fumecheng-7223	149	50	journal	journal	NOUN
fumecheng-7223	149	51	of	of	ADP
fumecheng-7223	149	52	applied	apply	VERB
fumecheng-7223	149	53	mechanics	mechanic	NOUN
fumecheng-7223	149	54	,	,	PUNCT
fumecheng-7223	149	55	8(2	8(2	NUM
fumecheng-7223	149	56	)	)	PUNCT
fumecheng-7223	149	57	,	,	PUNCT
fumecheng-7223	149	58	1650018	1650018	NUM
fumecheng-7223	149	59	.	.	PUNCT
fumecheng-7223	150	1	19	19	NUM
fumecheng-7223	150	2	.	.	X
fumecheng-7223	150	3	kovacic	kovacic	PROPN
fumecheng-7223	150	4	,	,	PUNCT
fumecheng-7223	150	5	i.	i.	PROPN
fumecheng-7223	150	6	,	,	PUNCT
fumecheng-7223	150	7	brennan	brennan	PROPN
fumecheng-7223	150	8	,	,	PUNCT
fumecheng-7223	150	9	m.j	m.j	PROPN
fumecheng-7223	150	10	.	.	PROPN
fumecheng-7223	150	11	,	,	PUNCT
fumecheng-7223	150	12	2011	2011	NUM
fumecheng-7223	150	13	,	,	PUNCT
fumecheng-7223	150	14	the	the	DET
fumecheng-7223	150	15	duffing	duffing	NOUN
fumecheng-7223	150	16	equation	equation	NOUN
fumecheng-7223	150	17	nonlinear	nonlinear	NOUN
fumecheng-7223	150	18	oscillators	oscillator	NOUN
fumecheng-7223	150	19	and	and	CCONJ
fumecheng-7223	150	20	their	their	PRON
fumecheng-7223	150	21	behaviour	behaviour	NOUN
fumecheng-7223	150	22	,	,	PUNCT
fumecheng-7223	150	23	1st	1st	ADJ
fumecheng-7223	150	24	ed	ed	NOUN
fumecheng-7223	150	25	.	.	PROPN
fumecheng-7223	150	26	,	,	PUNCT
fumecheng-7223	150	27	john	john	PROPN
fumecheng-7223	150	28	wiley	wiley	PROPN
fumecheng-7223	150	29	&	&	CCONJ
fumecheng-7223	150	30	sons	son	NOUN
fumecheng-7223	150	31	,	,	PUNCT
fumecheng-7223	150	32	p.	p.	NOUN
fumecheng-7223	150	33	42	42	NUM
fumecheng-7223	150	34	.	.	PUNCT
fumecheng-7223	151	1	20	20	NUM
fumecheng-7223	151	2	.	.	PUNCT
fumecheng-7223	152	1	liu	liu	PROPN
fumecheng-7223	152	2	,	,	PUNCT
fumecheng-7223	152	3	s.	s.	PROPN
fumecheng-7223	152	4	,	,	PUNCT
fumecheng-7223	152	5	jian	jian	PROPN
fumecheng-7223	152	6	,	,	PUNCT
fumecheng-7223	152	7	j.	j.	PROPN
fumecheng-7223	152	8	,	,	PUNCT
fumecheng-7223	152	9	su	su	PROPN
fumecheng-7223	152	10	,	,	PUNCT
fumecheng-7223	152	11	p.	p.	PROPN
fumecheng-7223	152	12	,	,	PUNCT
fumecheng-7223	152	13	wu	wu	PROPN
fumecheng-7223	152	14	,	,	PUNCT
fumecheng-7223	152	15	j.	j.	PROPN
fumecheng-7223	152	16	,	,	PUNCT
fumecheng-7223	152	17	liu	liu	PROPN
fumecheng-7223	152	18	,	,	PUNCT
fumecheng-7223	152	19	y.	y.	PROPN
fumecheng-7223	152	20	,	,	PUNCT
fumecheng-7223	152	21	fang	fang	PROPN
fumecheng-7223	152	22	,	,	PUNCT
fumecheng-7223	152	23	y.	y.	NOUN
fumecheng-7223	152	24	,	,	PUNCT
fumecheng-7223	152	25	2017	2017	NUM
fumecheng-7223	152	26	,	,	PUNCT
fumecheng-7223	152	27	study	study	NOUN
fumecheng-7223	152	28	of	of	ADP
fumecheng-7223	152	29	double	double	ADJ
fumecheng-7223	152	30	-	-	PUNCT
fumecheng-7223	152	31	potential	potential	ADJ
fumecheng-7223	152	32	-	-	PUNCT
fumecheng-7223	152	33	well	well	NOUN
fumecheng-7223	152	34	leaf	leaf	NOUN
fumecheng-7223	152	35	spring	spring	NOUN
fumecheng-7223	152	36	system	system	NOUN
fumecheng-7223	152	37	’s	’s	PART
fumecheng-7223	152	38	chaotic	chaotic	ADJ
fumecheng-7223	152	39	vibration	vibration	NOUN
fumecheng-7223	152	40	,	,	PUNCT
fumecheng-7223	152	41	journal	journal	NOUN
fumecheng-7223	152	42	of	of	ADP
fumecheng-7223	152	43	vibroengineering	vibroengineere	VERB
fumecheng-7223	152	44	,	,	PUNCT
fumecheng-7223	152	45	19(3	19(3	NUM
fumecheng-7223	152	46	)	)	PUNCT
fumecheng-7223	152	47	,	,	PUNCT
fumecheng-7223	152	48	pp	pp	ADJ
fumecheng-7223	152	49	.	.	PUNCT
fumecheng-7223	153	1	2202–2223	2202–2223	NUM
fumecheng-7223	153	2	.	.	PUNCT
fumecheng-7223	154	1	21	21	NUM
fumecheng-7223	154	2	.	.	X
fumecheng-7223	154	3	tsatsos	tsatsos	NOUN
fumecheng-7223	154	4	,	,	PUNCT
fumecheng-7223	154	5	m.	m.	NOUN
fumecheng-7223	154	6	,	,	PUNCT
fumecheng-7223	154	7	2006	2006	NUM
fumecheng-7223	154	8	,	,	PUNCT
fumecheng-7223	154	9	theoretical	theoretical	ADJ
fumecheng-7223	154	10	and	and	CCONJ
fumecheng-7223	154	11	numerical	numerical	ADJ
fumecheng-7223	154	12	study	study	NOUN
fumecheng-7223	154	13	of	of	ADP
fumecheng-7223	154	14	the	the	DET
fumecheng-7223	154	15	van	van	PROPN
fumecheng-7223	154	16	der	der	ADJ
fumecheng-7223	154	17	pol	pol	NOUN
fumecheng-7223	154	18	equation	equation	NOUN
fumecheng-7223	154	19	,	,	PUNCT
fumecheng-7223	154	20	doctoral	doctoral	ADJ
fumecheng-7223	154	21	dissertation	dissertation	NOUN
fumecheng-7223	154	22	,	,	PUNCT
fumecheng-7223	154	23	aristotle	aristotle	PROPN
fumecheng-7223	154	24	university	university	PROPN
fumecheng-7223	154	25	of	of	ADP
fumecheng-7223	154	26	thessaloniki	thessaloniki	PROPN
fumecheng-7223	154	27	.	.	PUNCT
fumecheng-7223	155	1	22	22	NUM
fumecheng-7223	155	2	.	.	PUNCT
fumecheng-7223	156	1	lopez	lopez	NOUN
fumecheng-7223	156	2	-	-	PUNCT
fumecheng-7223	156	3	chamorro	chamorro	PROPN
fumecheng-7223	156	4	,	,	PUNCT
fumecheng-7223	156	5	f.m	f.m	PROPN
fumecheng-7223	156	6	.	.	PROPN
fumecheng-7223	156	7	,	,	PUNCT
fumecheng-7223	156	8	arciniegas	arciniegas	PROPN
fumecheng-7223	156	9	-	-	PUNCT
fumecheng-7223	156	10	mejia	mejia	PROPN
fumecheng-7223	156	11	,	,	PUNCT
fumecheng-7223	156	12	a.	a.	PROPN
fumecheng-7223	156	13	f.	f.	PROPN
fumecheng-7223	156	14	,	,	PUNCT
fumecheng-7223	156	15	imbajoa	imbajoa	NOUN
fumecheng-7223	156	16	-	-	PUNCT
fumecheng-7223	156	17	ruiz	ruiz	NOUN
fumecheng-7223	156	18	,	,	PUNCT
fumecheng-7223	156	19	d.e	d.e	PROPN
fumecheng-7223	156	20	.	.	PROPN
fumecheng-7223	156	21	,	,	PUNCT
fumecheng-7223	156	22	rosero	rosero	ADJ
fumecheng-7223	156	23	-	-	PUNCT
fumecheng-7223	156	24	montalvo	montalvo	NOUN
fumecheng-7223	156	25	,	,	PUNCT
fumecheng-7223	156	26	p.d	p.d	PROPN
fumecheng-7223	156	27	.	.	PROPN
fumecheng-7223	156	28	,	,	PUNCT
fumecheng-7223	156	29	garc´ıa	garc´ıa	PROPN
fumecheng-7223	156	30	,	,	PUNCT
fumecheng-7223	156	31	p.	p.	NOUN
fumecheng-7223	156	32	,	,	PUNCT
fumecheng-7223	156	33	castro	castro	PROPN
fumecheng-7223	156	34	-	-	PUNCT
fumecheng-7223	156	35	ospina	ospina	PROPN
fumecheng-7223	156	36	,	,	PUNCT
fumecheng-7223	156	37	a.e	a.e	PROPN
fumecheng-7223	156	38	.	.	PROPN
fumecheng-7223	156	39	,	,	PUNCT
fumecheng-7223	156	40	acosta	acosta	PROPN
fumecheng-7223	156	41	,	,	PUNCT
fumecheng-7223	156	42	a.	a.	NOUN
fumecheng-7223	156	43	,	,	PUNCT
fumecheng-7223	156	44	peluffo	peluffo	PROPN
fumecheng-7223	156	45	-	-	PUNCT
fumecheng-7223	156	46	ord´o˜nez	ord´o˜nez	PROPN
fumecheng-7223	156	47	,	,	PUNCT
fumecheng-7223	156	48	d.h	d.h	PROPN
fumecheng-7223	156	49	.	.	PROPN
fumecheng-7223	156	50	,	,	PUNCT
fumecheng-7223	156	51	2018	2018	NUM
fumecheng-7223	156	52	,	,	PUNCT
fumecheng-7223	156	53	cardiac	cardiac	ADJ
fumecheng-7223	156	54	pulse	pulse	NOUN
fumecheng-7223	156	55	modeling	modeling	NOUN
fumecheng-7223	156	56	using	use	VERB
fumecheng-7223	156	57	a	a	DET
fumecheng-7223	156	58	modified	modify	VERB
fumecheng-7223	156	59	van	van	PROPN
fumecheng-7223	156	60	der	der	ADJ
fumecheng-7223	156	61	pol	pol	NOUN
fumecheng-7223	156	62	oscillator	oscillator	NOUN
fumecheng-7223	156	63	and	and	CCONJ
fumecheng-7223	156	64	genetic	genetic	ADJ
fumecheng-7223	156	65	algorithms	algorithm	NOUN
fumecheng-7223	156	66	,	,	PUNCT
fumecheng-7223	156	67	in	in	ADP
fumecheng-7223	156	68	in	in	ADP
fumecheng-7223	156	69	:	:	PUNCT
fumecheng-7223	156	70	rojas	rojas	PROPN
fumecheng-7223	156	71	,	,	PUNCT
fumecheng-7223	156	72	i.	i.	PROPN
fumecheng-7223	156	73	,	,	PUNCT
fumecheng-7223	156	74	ortuño	ortuño	PROPN
fumecheng-7223	156	75	,	,	PUNCT
fumecheng-7223	156	76	f.	f.	PROPN
fumecheng-7223	156	77	(	(	PUNCT
fumecheng-7223	156	78	eds	eds	PROPN
fumecheng-7223	156	79	.	.	PUNCT
fumecheng-7223	156	80	)	)	PUNCT
fumecheng-7223	156	81	,	,	PUNCT
fumecheng-7223	156	82	bioinformatics	bioinformatics	NOUN
fumecheng-7223	156	83	and	and	CCONJ
fumecheng-7223	156	84	biomedical	biomedical	ADJ
fumecheng-7223	156	85	engineering	engineering	NOUN
fumecheng-7223	156	86	,	,	PUNCT
fumecheng-7223	156	87	iwbbio	iwbbio	NOUN
fumecheng-7223	156	88	2018	2018	NUM
fumecheng-7223	156	89	,	,	PUNCT
fumecheng-7223	156	90	lecture	lecture	NOUN
fumecheng-7223	156	91	notes	note	NOUN
fumecheng-7223	156	92	in	in	ADP
fumecheng-7223	156	93	computer	computer	NOUN
fumecheng-7223	156	94	science	science	NOUN
fumecheng-7223	156	95	,	,	PUNCT
fumecheng-7223	156	96	vol	vol	NOUN
fumecheng-7223	156	97	.	.	PROPN
fumecheng-7223	156	98	10813	10813	NUM
fumecheng-7223	156	99	,	,	PUNCT
fumecheng-7223	156	100	springer	springer	NOUN
fumecheng-7223	156	101	,	,	PUNCT
fumecheng-7223	156	102	cham	cham	NOUN
fumecheng-7223	156	103	.	.	PUNCT
fumecheng-7223	157	1	23	23	NUM
fumecheng-7223	157	2	.	.	PUNCT
fumecheng-7223	158	1	ramakrishnan	ramakrishnan	PROPN
fumecheng-7223	158	2	,	,	PUNCT
fumecheng-7223	158	3	v.	v.	ADV
fumecheng-7223	158	4	,	,	PUNCT
fumecheng-7223	158	5	feeny	feeny	PROPN
fumecheng-7223	158	6	,	,	PUNCT
fumecheng-7223	158	7	b.f	b.f	PROPN
fumecheng-7223	158	8	.	.	PROPN
fumecheng-7223	158	9	,	,	PUNCT
fumecheng-7223	158	10	2012	2012	NUM
fumecheng-7223	158	11	,	,	PUNCT
fumecheng-7223	158	12	resonances	resonance	NOUN
fumecheng-7223	158	13	of	of	ADP
fumecheng-7223	158	14	a	a	DET
fumecheng-7223	158	15	forced	force	VERB
fumecheng-7223	158	16	mathieu	mathieu	NOUN
fumecheng-7223	158	17	equation	equation	NOUN
fumecheng-7223	158	18	with	with	ADP
fumecheng-7223	158	19	reference	reference	NOUN
fumecheng-7223	158	20	to	to	ADP
fumecheng-7223	158	21	wind	wind	NOUN
fumecheng-7223	158	22	turbine	turbine	NOUN
fumecheng-7223	158	23	blades	blade	NOUN
fumecheng-7223	158	24	,	,	PUNCT
fumecheng-7223	158	25	journal	journal	NOUN
fumecheng-7223	158	26	of	of	ADP
fumecheng-7223	158	27	vibration	vibration	NOUN
fumecheng-7223	158	28	and	and	CCONJ
fumecheng-7223	158	29	acoustics	acoustic	NOUN
fumecheng-7223	158	30	,	,	PUNCT
fumecheng-7223	158	31	134(6	134(6	NUM
fumecheng-7223	158	32	)	)	PUNCT
fumecheng-7223	158	33	,	,	PUNCT
fumecheng-7223	158	34	064501	064501	NUM
fumecheng-7223	158	35	.	.	PUNCT
fumecheng-7223	159	1	24	24	NUM
fumecheng-7223	159	2	.	.	PUNCT
fumecheng-7223	160	1	he	he	PRON
fumecheng-7223	160	2	,	,	PUNCT
fumecheng-7223	160	3	j.	j.	PROPN
fumecheng-7223	160	4	,	,	PUNCT
fumecheng-7223	160	5	jin	jin	PROPN
fumecheng-7223	160	6	,	,	PUNCT
fumecheng-7223	160	7	x.	x.	NOUN
fumecheng-7223	160	8	,	,	PUNCT
fumecheng-7223	160	9	2020	2020	NUM
fumecheng-7223	160	10	,	,	PUNCT
fumecheng-7223	160	11	a	a	DET
fumecheng-7223	160	12	short	short	ADJ
fumecheng-7223	160	13	review	review	NOUN
fumecheng-7223	160	14	on	on	ADP
fumecheng-7223	160	15	analytical	analytical	ADJ
fumecheng-7223	160	16	methods	method	NOUN
fumecheng-7223	160	17	for	for	ADP
fumecheng-7223	160	18	the	the	DET
fumecheng-7223	160	19	capillary	capillary	ADJ
fumecheng-7223	160	20	oscillator	oscillator	NOUN
fumecheng-7223	160	21	in	in	ADP
fumecheng-7223	160	22	a	a	DET
fumecheng-7223	160	23	nanoscale	nanoscale	ADJ
fumecheng-7223	160	24	deformable	deformable	ADJ
fumecheng-7223	160	25	tube	tube	NOUN
fumecheng-7223	160	26	,	,	PUNCT
fumecheng-7223	160	27	mathematical	mathematical	ADJ
fumecheng-7223	160	28	methods	method	NOUN
fumecheng-7223	160	29	in	in	ADP
fumecheng-7223	160	30	the	the	DET
fumecheng-7223	160	31	applied	apply	VERB
fumecheng-7223	160	32	sciences	science	NOUN
fumecheng-7223	160	33	,	,	PUNCT
fumecheng-7223	160	34	doi:10.1002	doi:10.1002	NOUN
fumecheng-7223	160	35	/	/	SYM
fumecheng-7223	160	36	mma.6321	mma.6321	PROPN
fumecheng-7223	160	37	.	.	PUNCT
fumecheng-7223	160	38	https://www.worldscientific.com/worldscinet/ijam	https://www.worldscientific.com/worldscinet/ijam	PROPN
fumecheng-7223	160	39	https://www.worldscientific.com/toc/ijam/06/03	https://www.worldscientific.com/toc/ijam/06/03	PROPN
fumecheng-7223	160	40	https://link.springer.com/journal/12206	https://link.springer.com/journal/12206	PROPN
fumecheng-7223	160	41	208	208	NUM
fumecheng-7223	160	42	j.-h	j.-h	NOUN
fumecheng-7223	160	43	.	.	PUNCT
fumecheng-7223	161	1	he	he	PRON
fumecheng-7223	161	2	,	,	PUNCT
fumecheng-7223	161	3	w.-f	w.-f	PROPN
fumecheng-7223	161	4	.	.	PUNCT
fumecheng-7223	162	1	hou	hou	PROPN
fumecheng-7223	162	2	,	,	PUNCT
fumecheng-7223	162	3	n.	n.	PROPN
fumecheng-7223	162	4	qie	qie	PROPN
fumecheng-7223	162	5	,	,	PUNCT
fumecheng-7223	162	6	k.a	k.a	PROPN
fumecheng-7223	162	7	.	.	PROPN
fumecheng-7223	162	8	gepreel	gepreel	PROPN
fumecheng-7223	162	9	,	,	PUNCT
fumecheng-7223	162	10	a.h	a.h	PROPN
fumecheng-7223	162	11	.	.	PROPN
fumecheng-7223	162	12	shirazi	shirazi	PROPN
fumecheng-7223	162	13	,	,	PUNCT
fumecheng-7223	162	14	h.m	h.m	PROPN
fumecheng-7223	162	15	.	.	PROPN
fumecheng-7223	162	16	sedighi	sedighi	PROPN
fumecheng-7223	162	17	25	25	NUM
fumecheng-7223	162	18	.	.	PUNCT
fumecheng-7223	163	1	he	he	PRON
fumecheng-7223	163	2	,	,	PUNCT
fumecheng-7223	163	3	j.-h	j.-h	PROPN
fumecheng-7223	163	4	.	.	PUNCT
fumecheng-7223	163	5	,	,	PUNCT
fumecheng-7223	163	6	2020	2020	NUM
fumecheng-7223	163	7	,	,	PUNCT
fumecheng-7223	163	8	a	a	DET
fumecheng-7223	163	9	short	short	ADJ
fumecheng-7223	163	10	review	review	NOUN
fumecheng-7223	163	11	on	on	ADP
fumecheng-7223	163	12	analytical	analytical	ADJ
fumecheng-7223	163	13	methods	method	NOUN
fumecheng-7223	163	14	for	for	ADP
fumecheng-7223	163	15	a	a	DET
fumecheng-7223	163	16	fully	fully	ADV
fumecheng-7223	163	17	fourth	fourth	ADJ
fumecheng-7223	163	18	-	-	PUNCT
fumecheng-7223	163	19	order	order	NOUN
fumecheng-7223	163	20	nonlinear	nonlinear	ADJ
fumecheng-7223	163	21	integral	integral	ADJ
fumecheng-7223	163	22	boundary	boundary	ADJ
fumecheng-7223	163	23	value	value	NOUN
fumecheng-7223	163	24	problem	problem	NOUN
fumecheng-7223	163	25	with	with	ADP
fumecheng-7223	163	26	fractal	fractal	ADJ
fumecheng-7223	163	27	derivatives	derivative	NOUN
fumecheng-7223	163	28	,	,	PUNCT
fumecheng-7223	163	29	international	international	ADJ
fumecheng-7223	163	30	journal	journal	NOUN
fumecheng-7223	163	31	of	of	ADP
fumecheng-7223	163	32	numerical	numerical	ADJ
fumecheng-7223	163	33	methods	method	NOUN
fumecheng-7223	163	34	for	for	ADP
fumecheng-7223	163	35	heat	heat	NOUN
fumecheng-7223	163	36	&	&	CCONJ
fumecheng-7223	163	37	fluid	fluid	ADJ
fumecheng-7223	163	38	flow	flow	NOUN
fumecheng-7223	163	39	,	,	PUNCT
fumecheng-7223	163	40	30(11	30(11	NUM
fumecheng-7223	163	41	)	)	PUNCT
fumecheng-7223	163	42	,	,	PUNCT
fumecheng-7223	163	43	pp	pp	PROPN
fumecheng-7223	163	44	.	.	PUNCT
fumecheng-7223	163	45	4933–4943	4933–4943	NUM
fumecheng-7223	163	46	.	.	PROPN
fumecheng-7223	163	47	26	26	NUM
fumecheng-7223	163	48	.	.	PUNCT
fumecheng-7223	164	1	he	he	PRON
fumecheng-7223	164	2	,	,	PUNCT
fumecheng-7223	164	3	j.-h	j.-h	PROPN
fumecheng-7223	164	4	.	.	PUNCT
fumecheng-7223	164	5	,	,	PUNCT
fumecheng-7223	164	6	2006	2006	NUM
fumecheng-7223	164	7	,	,	PUNCT
fumecheng-7223	164	8	some	some	DET
fumecheng-7223	164	9	asymptotic	asymptotic	ADJ
fumecheng-7223	164	10	methods	method	NOUN
fumecheng-7223	164	11	for	for	ADP
fumecheng-7223	164	12	strongly	strongly	ADV
fumecheng-7223	164	13	nonlinear	nonlinear	ADJ
fumecheng-7223	164	14	equations	equation	NOUN
fumecheng-7223	164	15	,	,	PUNCT
fumecheng-7223	164	16	international	international	ADJ
fumecheng-7223	164	17	journal	journal	NOUN
fumecheng-7223	164	18	of	of	ADP
fumecheng-7223	164	19	modern	modern	ADJ
fumecheng-7223	164	20	physics	physics	PROPN
fumecheng-7223	164	21	b	b	PROPN
fumecheng-7223	164	22	,	,	PUNCT
fumecheng-7223	164	23	20(10	20(10	NUM
fumecheng-7223	164	24	)	)	PUNCT
fumecheng-7223	164	25	,	,	PUNCT
fumecheng-7223	164	26	pp	pp	ADJ
fumecheng-7223	164	27	.	.	PUNCT
fumecheng-7223	165	1	1141–1199	1141–1199	NUM
fumecheng-7223	165	2	.	.	PUNCT
fumecheng-7223	166	1	27	27	NUM
fumecheng-7223	166	2	.	.	PUNCT
fumecheng-7223	167	1	he	he	PRON
fumecheng-7223	167	2	,	,	PUNCT
fumecheng-7223	167	3	j.-h	j.-h	PROPN
fumecheng-7223	167	4	.	.	PROPN
fumecheng-7223	167	5	,	,	PUNCT
fumecheng-7223	167	6	2008	2008	NUM
fumecheng-7223	167	7	,	,	PUNCT
fumecheng-7223	167	8	comment	comment	NOUN
fumecheng-7223	167	9	on	on	ADP
fumecheng-7223	167	10	‘	'	PUNCT
fumecheng-7223	167	11	he	he	PRON
fumecheng-7223	167	12	’s	’s	PART
fumecheng-7223	167	13	frequency	frequency	NOUN
fumecheng-7223	167	14	formulation	formulation	NOUN
fumecheng-7223	167	15	for	for	ADP
fumecheng-7223	167	16	nonlinear	nonlinear	ADJ
fumecheng-7223	167	17	oscillators	oscillator	NOUN
fumecheng-7223	167	18	,	,	PUNCT
fumecheng-7223	167	19	european	european	PROPN
fumecheng-7223	167	20	journal	journal	PROPN
fumecheng-7223	167	21	of	of	ADP
fumecheng-7223	167	22	physics	physics	PROPN
fumecheng-7223	167	23	,	,	PUNCT
fumecheng-7223	167	24	29(4	29(4	NOUN
fumecheng-7223	167	25	)	)	PUNCT
fumecheng-7223	167	26	,	,	PUNCT
fumecheng-7223	167	27	pp	pp	PROPN
fumecheng-7223	167	28	.	.	PUNCT
fumecheng-7223	168	1	l19	l19	NOUN
fumecheng-7223	168	2	–	–	PUNCT
fumecheng-7223	168	3	l22	l22	NOUN
fumecheng-7223	168	4	.	.	PUNCT
fumecheng-7223	169	1	28	28	NUM
fumecheng-7223	169	2	.	.	PUNCT
fumecheng-7223	170	1	he	he	PRON
fumecheng-7223	170	2	,	,	PUNCT
fumecheng-7223	170	3	j.-h	j.-h	PROPN
fumecheng-7223	170	4	.	.	PROPN
fumecheng-7223	170	5	,	,	PUNCT
fumecheng-7223	170	6	2019	2019	NUM
fumecheng-7223	170	7	,	,	PUNCT
fumecheng-7223	170	8	the	the	PRON
fumecheng-7223	170	9	simpler	simple	ADJ
fumecheng-7223	170	10	,	,	PUNCT
fumecheng-7223	170	11	the	the	PRON
fumecheng-7223	170	12	better	well	ADJ
fumecheng-7223	170	13	:	:	PUNCT
fumecheng-7223	170	14	analytical	analytical	ADJ
fumecheng-7223	170	15	methods	method	NOUN
fumecheng-7223	170	16	for	for	ADP
fumecheng-7223	170	17	nonlinear	nonlinear	ADJ
fumecheng-7223	170	18	oscillators	oscillator	NOUN
fumecheng-7223	170	19	and	and	CCONJ
fumecheng-7223	170	20	fractional	fractional	ADJ
fumecheng-7223	170	21	oscillators	oscillator	NOUN
fumecheng-7223	170	22	,	,	PUNCT
fumecheng-7223	170	23	journal	journal	NOUN
fumecheng-7223	170	24	of	of	ADP
fumecheng-7223	170	25	low	low	ADJ
fumecheng-7223	170	26	frequency	frequency	NOUN
fumecheng-7223	170	27	noise	noise	NOUN
fumecheng-7223	170	28	,	,	PUNCT
fumecheng-7223	170	29	vibration	vibration	NOUN
fumecheng-7223	170	30	and	and	CCONJ
fumecheng-7223	170	31	active	active	ADJ
fumecheng-7223	170	32	control	control	NOUN
fumecheng-7223	170	33	,	,	PUNCT
fumecheng-7223	170	34	38(3–4	38(3–4	PROPN
fumecheng-7223	170	35	)	)	PUNCT
fumecheng-7223	170	36	,	,	PUNCT
fumecheng-7223	170	37	pp	pp	PROPN
fumecheng-7223	170	38	.	.	PUNCT
fumecheng-7223	170	39	1252–1260	1252–1260	NUM
fumecheng-7223	170	40	.	.	PUNCT
fumecheng-7223	170	41	29	29	NUM
fumecheng-7223	170	42	.	.	PUNCT
fumecheng-7223	171	1	he	he	PRON
fumecheng-7223	171	2	,	,	PUNCT
fumecheng-7223	171	3	j.-h	j.-h	PROPN
fumecheng-7223	171	4	.	.	PROPN
fumecheng-7223	171	5	,	,	PUNCT
fumecheng-7223	171	6	2019	2019	NUM
fumecheng-7223	171	7	,	,	PUNCT
fumecheng-7223	171	8	the	the	DET
fumecheng-7223	171	9	simplest	simple	ADJ
fumecheng-7223	171	10	approach	approach	NOUN
fumecheng-7223	171	11	to	to	ADP
fumecheng-7223	171	12	nonlinear	nonlinear	ADJ
fumecheng-7223	171	13	oscillators	oscillator	NOUN
fumecheng-7223	171	14	,	,	PUNCT
fumecheng-7223	171	15	results	result	NOUN
fumecheng-7223	171	16	in	in	ADP
fumecheng-7223	171	17	physics	physics	NOUN
fumecheng-7223	171	18	,	,	PUNCT
fumecheng-7223	171	19	15	15	NUM
fumecheng-7223	171	20	,	,	PUNCT
fumecheng-7223	171	21	102546	102546	NUM
fumecheng-7223	171	22	.	.	PUNCT
fumecheng-7223	172	1	30	30	NUM
fumecheng-7223	172	2	.	.	PUNCT
fumecheng-7223	173	1	he	he	PRON
fumecheng-7223	173	2	,	,	PUNCT
fumecheng-7223	173	3	c.-h	c.-h	PROPN
fumecheng-7223	173	4	.	.	PROPN
fumecheng-7223	173	5	,	,	PUNCT
fumecheng-7223	173	6	wang	wang	PROPN
fumecheng-7223	173	7	,	,	PUNCT
fumecheng-7223	173	8	j.-h	j.-h	PROPN
fumecheng-7223	173	9	.	.	PUNCT
fumecheng-7223	173	10	,	,	PUNCT
fumecheng-7223	173	11	yao	yao	NOUN
fumecheng-7223	173	12	,	,	PUNCT
fumecheng-7223	173	13	s.-w	s.-w	PROPN
fumecheng-7223	173	14	.	.	PROPN
fumecheng-7223	173	15	,	,	PUNCT
fumecheng-7223	173	16	2019	2019	NUM
fumecheng-7223	173	17	,	,	PUNCT
fumecheng-7223	173	18	a	a	DET
fumecheng-7223	173	19	complement	complement	NOUN
fumecheng-7223	173	20	to	to	ADP
fumecheng-7223	173	21	period	period	NOUN
fumecheng-7223	173	22	/	/	SYM
fumecheng-7223	173	23	frequency	frequency	NOUN
fumecheng-7223	173	24	estimation	estimation	NOUN
fumecheng-7223	173	25	of	of	ADP
fumecheng-7223	173	26	a	a	DET
fumecheng-7223	173	27	nonlinear	nonlinear	ADJ
fumecheng-7223	173	28	oscillator	oscillator	NOUN
fumecheng-7223	173	29	,	,	PUNCT
fumecheng-7223	173	30	journal	journal	NOUN
fumecheng-7223	173	31	of	of	ADP
fumecheng-7223	173	32	low	low	ADJ
fumecheng-7223	173	33	frequency	frequency	NOUN
fumecheng-7223	173	34	noise	noise	NOUN
fumecheng-7223	173	35	,	,	PUNCT
fumecheng-7223	173	36	vibration	vibration	NOUN
fumecheng-7223	173	37	and	and	CCONJ
fumecheng-7223	173	38	active	active	ADJ
fumecheng-7223	173	39	control	control	NOUN
fumecheng-7223	173	40	,	,	PUNCT
fumecheng-7223	173	41	38(3–4	38(3–4	PROPN
fumecheng-7223	173	42	)	)	PUNCT
fumecheng-7223	173	43	,	,	PUNCT
fumecheng-7223	173	44	pp	pp	ADP
fumecheng-7223	173	45	.	.	PUNCT
fumecheng-7223	174	1	992–995	992–995	NUM
fumecheng-7223	174	2	.	.	PUNCT
fumecheng-7223	175	1	31	31	NUM
fumecheng-7223	175	2	.	.	X
fumecheng-7223	176	1	tao	tao	PROPN
fumecheng-7223	176	2	,	,	PUNCT
fumecheng-7223	176	3	z.-l	z.-l	PROPN
fumecheng-7223	176	4	.	.	PUNCT
fumecheng-7223	176	5	,	,	PUNCT
fumecheng-7223	176	6	chen	chen	PROPN
fumecheng-7223	176	7	,	,	PUNCT
fumecheng-7223	176	8	g.-h	g.-h	PROPN
fumecheng-7223	176	9	.	.	PUNCT
fumecheng-7223	176	10	,	,	PUNCT
fumecheng-7223	176	11	xue	xue	PROPN
fumecheng-7223	176	12	,	,	PUNCT
fumecheng-7223	176	13	y.-m	y.-m	NOUN
fumecheng-7223	176	14	.	.	PROPN
fumecheng-7223	176	15	,	,	PUNCT
fumecheng-7223	176	16	2019	2019	NUM
fumecheng-7223	176	17	,	,	PUNCT
fumecheng-7223	176	18	frequency	frequency	NOUN
fumecheng-7223	176	19	and	and	CCONJ
fumecheng-7223	176	20	solution	solution	NOUN
fumecheng-7223	176	21	of	of	ADP
fumecheng-7223	176	22	an	an	DET
fumecheng-7223	176	23	oscillator	oscillator	NOUN
fumecheng-7223	176	24	with	with	ADP
fumecheng-7223	176	25	a	a	DET
fumecheng-7223	176	26	damping	damp	VERB
fumecheng-7223	176	27	,	,	PUNCT
fumecheng-7223	176	28	journal	journal	NOUN
fumecheng-7223	176	29	of	of	ADP
fumecheng-7223	176	30	low	low	ADJ
fumecheng-7223	176	31	frequency	frequency	NOUN
fumecheng-7223	176	32	noise	noise	NOUN
fumecheng-7223	176	33	,	,	PUNCT
fumecheng-7223	176	34	vibration	vibration	NOUN
fumecheng-7223	176	35	and	and	CCONJ
fumecheng-7223	176	36	active	active	ADJ
fumecheng-7223	176	37	control	control	NOUN
fumecheng-7223	176	38	,	,	PUNCT
fumecheng-7223	176	39	38(3–4	38(3–4	PROPN
fumecheng-7223	176	40	)	)	PUNCT
fumecheng-7223	176	41	,	,	PUNCT
fumecheng-7223	176	42	pp	pp	ADJ
fumecheng-7223	176	43	.	.	PUNCT
fumecheng-7223	177	1	1699–1702	1699–1702	NUM
fumecheng-7223	177	2	.	.	PUNCT
fumecheng-7223	178	1	32	32	NUM
fumecheng-7223	178	2	.	.	PUNCT
fumecheng-7223	179	1	wu	wu	PROPN
fumecheng-7223	179	2	,	,	PUNCT
fumecheng-7223	179	3	y.	y.	PROPN
fumecheng-7223	179	4	,	,	PUNCT
fumecheng-7223	179	5	liu	liu	PROPN
fumecheng-7223	179	6	,	,	PUNCT
fumecheng-7223	179	7	y.-p	y.-p	PROPN
fumecheng-7223	179	8	.	.	PROPN
fumecheng-7223	179	9	,	,	PUNCT
fumecheng-7223	179	10	2020	2020	NUM
fumecheng-7223	179	11	,	,	PUNCT
fumecheng-7223	179	12	residual	residual	ADJ
fumecheng-7223	179	13	calculation	calculation	NOUN
fumecheng-7223	179	14	in	in	ADP
fumecheng-7223	179	15	he	he	PRON
fumecheng-7223	179	16	’s	’s	PART
fumecheng-7223	179	17	frequency	frequency	NOUN
fumecheng-7223	179	18	–	–	PUNCT
fumecheng-7223	179	19	amplitude	amplitude	NOUN
fumecheng-7223	179	20	formulation	formulation	NOUN
fumecheng-7223	179	21	,	,	PUNCT
fumecheng-7223	179	22	journal	journal	NOUN
fumecheng-7223	179	23	of	of	ADP
fumecheng-7223	179	24	low	low	ADJ
fumecheng-7223	179	25	frequency	frequency	NOUN
fumecheng-7223	179	26	noise	noise	NOUN
fumecheng-7223	179	27	,	,	PUNCT
fumecheng-7223	179	28	vibration	vibration	NOUN
fumecheng-7223	179	29	and	and	CCONJ
fumecheng-7223	179	30	active	active	ADJ
fumecheng-7223	179	31	control	control	NOUN
fumecheng-7223	179	32	,	,	PUNCT
fumecheng-7223	179	33	doi	doi	NOUN
fumecheng-7223	179	34	:	:	PUNCT
fumecheng-7223	179	35	10.1177/1461348420913662	10.1177/1461348420913662	NUM
fumecheng-7223	179	36	.	.	PUNCT
fumecheng-7223	180	1	33	33	NUM
fumecheng-7223	180	2	.	.	PUNCT
fumecheng-7223	181	1	ren	ren	PROPN
fumecheng-7223	181	2	,	,	PUNCT
fumecheng-7223	181	3	z.f	z.f	PROPN
fumecheng-7223	181	4	.	.	PROPN
fumecheng-7223	181	5	,	,	PUNCT
fumecheng-7223	181	6	hu	hu	PROPN
fumecheng-7223	181	7	,	,	PUNCT
fumecheng-7223	181	8	g.f	g.f	PROPN
fumecheng-7223	181	9	.	.	PROPN
fumecheng-7223	181	10	,	,	PUNCT
fumecheng-7223	181	11	2019	2019	NUM
fumecheng-7223	181	12	,	,	PUNCT
fumecheng-7223	181	13	he	he	PRON
fumecheng-7223	181	14	’s	’	VERB
fumecheng-7223	181	15	frequency	frequency	NOUN
fumecheng-7223	181	16	-	-	PUNCT
fumecheng-7223	181	17	amplitude	amplitude	NOUN
fumecheng-7223	181	18	formulation	formulation	NOUN
fumecheng-7223	181	19	with	with	ADP
fumecheng-7223	181	20	average	average	ADJ
fumecheng-7223	181	21	residuals	residual	NOUN
fumecheng-7223	181	22	for	for	ADP
fumecheng-7223	181	23	nonlinear	nonlinear	ADJ
fumecheng-7223	181	24	oscillators	oscillator	NOUN
fumecheng-7223	181	25	,	,	PUNCT
fumecheng-7223	181	26	journal	journal	NOUN
fumecheng-7223	181	27	of	of	ADP
fumecheng-7223	181	28	low	low	ADJ
fumecheng-7223	181	29	frequency	frequency	NOUN
fumecheng-7223	181	30	noise	noise	NOUN
fumecheng-7223	181	31	vibration	vibration	NOUN
fumecheng-7223	181	32	and	and	CCONJ
fumecheng-7223	181	33	active	active	ADJ
fumecheng-7223	181	34	control	control	NOUN
fumecheng-7223	181	35	,	,	PUNCT
fumecheng-7223	181	36	38	38	NUM
fumecheng-7223	181	37	,	,	PUNCT
fumecheng-7223	181	38	pp	pp	ADJ
fumecheng-7223	181	39	.	.	PUNCT
fumecheng-7223	182	1	1050–1059	1050–1059	NUM
fumecheng-7223	182	2	34	34	NUM
fumecheng-7223	182	3	.	.	PUNCT
fumecheng-7223	183	1	ren	ren	PROPN
fumecheng-7223	183	2	,	,	PUNCT
fumecheng-7223	183	3	z.f	z.f	PROPN
fumecheng-7223	183	4	.	.	PROPN
fumecheng-7223	183	5	,	,	PUNCT
fumecheng-7223	183	6	hu	hu	PROPN
fumecheng-7223	183	7	,	,	PUNCT
fumecheng-7223	183	8	g.f	g.f	PROPN
fumecheng-7223	183	9	.	.	PROPN
fumecheng-7223	183	10	,	,	PUNCT
fumecheng-7223	183	11	2019	2019	NUM
fumecheng-7223	183	12	,	,	PUNCT
fumecheng-7223	183	13	discussion	discussion	NOUN
fumecheng-7223	183	14	on	on	ADP
fumecheng-7223	183	15	the	the	DET
fumecheng-7223	183	16	accuracies	accuracy	NOUN
fumecheng-7223	183	17	of	of	ADP
fumecheng-7223	183	18	he	he	PRON
fumecheng-7223	183	19	’s	’s	PART
fumecheng-7223	183	20	frequency	frequency	NOUN
fumecheng-7223	183	21	–	–	PUNCT
fumecheng-7223	183	22	amplitude	amplitude	NOUN
fumecheng-7223	183	23	formulation	formulation	NOUN
fumecheng-7223	183	24	and	and	CCONJ
fumecheng-7223	183	25	its	its	PRON
fumecheng-7223	183	26	modification	modification	NOUN
fumecheng-7223	183	27	with	with	ADP
fumecheng-7223	183	28	average	average	ADJ
fumecheng-7223	183	29	residuals	residual	NOUN
fumecheng-7223	183	30	,	,	PUNCT
fumecheng-7223	183	31	journal	journal	NOUN
fumecheng-7223	183	32	of	of	ADP
fumecheng-7223	183	33	low	low	ADJ
fumecheng-7223	183	34	frequency	frequency	NOUN
fumecheng-7223	183	35	noise	noise	NOUN
fumecheng-7223	183	36	vibration	vibration	NOUN
fumecheng-7223	183	37	and	and	CCONJ
fumecheng-7223	183	38	active	active	ADJ
fumecheng-7223	183	39	control	control	NOUN
fumecheng-7223	183	40	,	,	PUNCT
fumecheng-7223	183	41	38(3–4	38(3–4	PROPN
fumecheng-7223	183	42	)	)	PUNCT
fumecheng-7223	183	43	,	,	PUNCT
fumecheng-7223	183	44	pp	pp	PROPN
fumecheng-7223	183	45	.	.	PUNCT
fumecheng-7223	183	46	1713–1715	1713–1715	NUM
fumecheng-7223	183	47	.	.	PUNCT
fumecheng-7223	183	48	35	35	NUM
fumecheng-7223	183	49	.	.	PUNCT
fumecheng-7223	184	1	ren	ren	PROPN
fumecheng-7223	184	2	,	,	PUNCT
fumecheng-7223	184	3	z.f	z.f	PROPN
fumecheng-7223	184	4	.	.	PROPN
fumecheng-7223	184	5	,	,	PUNCT
fumecheng-7223	184	6	liu	liu	PROPN
fumecheng-7223	184	7	,	,	PUNCT
fumecheng-7223	184	8	g.q	g.q	PROPN
fumecheng-7223	184	9	.	.	PROPN
fumecheng-7223	184	10	,	,	PUNCT
fumecheng-7223	184	11	kang	kang	PROPN
fumecheng-7223	184	12	,	,	PUNCT
fumecheng-7223	184	13	y.x	y.x	PROPN
fumecheng-7223	184	14	.	.	PROPN
fumecheng-7223	184	15	,	,	PUNCT
fumecheng-7223	184	16	2009	2009	NUM
fumecheng-7223	184	17	,	,	PUNCT
fumecheng-7223	184	18	application	application	NOUN
fumecheng-7223	184	19	of	of	ADP
fumecheng-7223	184	20	he	he	PRON
fumecheng-7223	184	21	’s	’s	PART
fumecheng-7223	184	22	amplitude	amplitude	NOUN
fumecheng-7223	184	23	-	-	PUNCT
fumecheng-7223	184	24	frequency	frequency	NOUN
fumecheng-7223	184	25	formulation	formulation	NOUN
fumecheng-7223	184	26	to	to	AUX
fumecheng-7223	184	27	nonlinear	nonlinear	ADJ
fumecheng-7223	184	28	oscillators	oscillator	NOUN
fumecheng-7223	184	29	with	with	ADP
fumecheng-7223	184	30	discontinuities	discontinuity	NOUN
fumecheng-7223	184	31	,	,	PUNCT
fumecheng-7223	184	32	physica	physica	PROPN
fumecheng-7223	184	33	scripta	scripta	PROPN
fumecheng-7223	184	34	,	,	PUNCT
fumecheng-7223	184	35	80	80	NUM
fumecheng-7223	184	36	,	,	PUNCT
fumecheng-7223	184	37	045003	045003	NUM
fumecheng-7223	184	38	.	.	PUNCT
fumecheng-7223	185	1	36	36	NUM
fumecheng-7223	185	2	.	.	PUNCT
fumecheng-7223	186	1	liu	liu	PROPN
fumecheng-7223	186	2	,	,	PUNCT
fumecheng-7223	186	3	c.x	c.x	PROPN
fumecheng-7223	186	4	.	.	PROPN
fumecheng-7223	186	5	,	,	PUNCT
fumecheng-7223	186	6	2020	2020	NUM
fumecheng-7223	186	7	,	,	PUNCT
fumecheng-7223	186	8	a	a	DET
fumecheng-7223	186	9	short	short	ADJ
fumecheng-7223	186	10	remark	remark	NOUN
fumecheng-7223	186	11	on	on	ADP
fumecheng-7223	186	12	he	he	PRON
fumecheng-7223	186	13	’s	’s	PART
fumecheng-7223	186	14	frequency	frequency	NOUN
fumecheng-7223	186	15	formulation	formulation	NOUN
fumecheng-7223	186	16	,	,	PUNCT
fumecheng-7223	186	17	journal	journal	NOUN
fumecheng-7223	186	18	of	of	ADP
fumecheng-7223	186	19	low	low	ADJ
fumecheng-7223	186	20	frequency	frequency	NOUN
fumecheng-7223	186	21	noise	noise	NOUN
fumecheng-7223	186	22	,	,	PUNCT
fumecheng-7223	186	23	vibration	vibration	NOUN
fumecheng-7223	186	24	and	and	CCONJ
fumecheng-7223	186	25	active	active	ADJ
fumecheng-7223	186	26	control	control	NOUN
fumecheng-7223	186	27	,	,	PUNCT
fumecheng-7223	186	28	doi	doi	NOUN
fumecheng-7223	186	29	:	:	PUNCT
fumecheng-7223	186	30	10.1177/1461348420926331	10.1177/1461348420926331	NUM
fumecheng-7223	186	31	.	.	NOUN
fumecheng-7223	186	32	37	37	NUM
fumecheng-7223	186	33	.	.	PUNCT
fumecheng-7223	187	1	wang	wang	PROPN
fumecheng-7223	187	2	,	,	PUNCT
fumecheng-7223	187	3	y.	y.	PROPN
fumecheng-7223	187	4	,	,	PUNCT
fumecheng-7223	187	5	an	an	PRON
fumecheng-7223	187	6	,	,	PUNCT
fumecheng-7223	187	7	j.y	j.y	PROPN
fumecheng-7223	187	8	.	.	PROPN
fumecheng-7223	187	9	,	,	PUNCT
fumecheng-7223	187	10	2019	2019	NUM
fumecheng-7223	187	11	,	,	PUNCT
fumecheng-7223	187	12	amplitude	amplitude	NOUN
fumecheng-7223	187	13	-	-	PUNCT
fumecheng-7223	187	14	frequency	frequency	NOUN
fumecheng-7223	187	15	relationship	relationship	NOUN
fumecheng-7223	187	16	to	to	ADP
fumecheng-7223	187	17	a	a	DET
fumecheng-7223	187	18	fractional	fractional	ADJ
fumecheng-7223	187	19	duffing	duffing	NOUN
fumecheng-7223	187	20	oscillator	oscillator	NOUN
fumecheng-7223	187	21	arising	arise	VERB
fumecheng-7223	187	22	in	in	ADP
fumecheng-7223	187	23	microphysics	microphysic	NOUN
fumecheng-7223	187	24	and	and	CCONJ
fumecheng-7223	187	25	tsunami	tsunami	NOUN
fumecheng-7223	187	26	motion	motion	NOUN
fumecheng-7223	187	27	,	,	PUNCT
fumecheng-7223	187	28	journal	journal	NOUN
fumecheng-7223	187	29	of	of	ADP
fumecheng-7223	187	30	low	low	ADJ
fumecheng-7223	187	31	frequency	frequency	NOUN
fumecheng-7223	187	32	noise	noise	NOUN
fumecheng-7223	187	33	vibration	vibration	NOUN
fumecheng-7223	187	34	and	and	CCONJ
fumecheng-7223	187	35	active	active	ADJ
fumecheng-7223	187	36	control	control	NOUN
fumecheng-7223	187	37	,	,	PUNCT
fumecheng-7223	187	38	38	38	NUM
fumecheng-7223	187	39	,	,	PUNCT
fumecheng-7223	187	40	pp	pp	ADJ
fumecheng-7223	187	41	.	.	PUNCT
fumecheng-7223	187	42	1008–1012	1008–1012	NUM
fumecheng-7223	187	43	.	.	PUNCT
fumecheng-7223	188	1	38	38	NUM
fumecheng-7223	188	2	.	.	PUNCT
fumecheng-7223	189	1	wang	wang	PROPN
fumecheng-7223	189	2	,	,	PUNCT
fumecheng-7223	189	3	q.	q.	PROPN
fumecheng-7223	189	4	,	,	PUNCT
fumecheng-7223	189	5	shi	shi	PROPN
fumecheng-7223	189	6	,	,	PUNCT
fumecheng-7223	189	7	x.	x.	PROPN
fumecheng-7223	189	8	,	,	PUNCT
fumecheng-7223	189	9	li	li	PROPN
fumecheng-7223	189	10	,	,	PUNCT
fumecheng-7223	189	11	z.	z.	PROPN
fumecheng-7223	189	12	,	,	PUNCT
fumecheng-7223	189	13	2019	2019	NUM
fumecheng-7223	189	14	,	,	PUNCT
fumecheng-7223	189	15	a	a	DET
fumecheng-7223	189	16	short	short	ADJ
fumecheng-7223	189	17	remark	remark	NOUN
fumecheng-7223	189	18	on	on	ADP
fumecheng-7223	189	19	ren	ren	PROPN
fumecheng-7223	189	20	–	–	PUNCT
fumecheng-7223	189	21	hu	hu	PROPN
fumecheng-7223	189	22	’s	’s	PART
fumecheng-7223	189	23	modification	modification	NOUN
fumecheng-7223	189	24	of	of	ADP
fumecheng-7223	189	25	he	he	PRON
fumecheng-7223	189	26	’s	’s	PART
fumecheng-7223	189	27	frequency	frequency	NOUN
fumecheng-7223	189	28	–	–	PUNCT
fumecheng-7223	189	29	amplitude	amplitude	NOUN
fumecheng-7223	189	30	formulation	formulation	NOUN
fumecheng-7223	189	31	and	and	CCONJ
fumecheng-7223	189	32	the	the	DET
fumecheng-7223	189	33	temperature	temperature	NOUN
fumecheng-7223	189	34	oscillation	oscillation	NOUN
fumecheng-7223	189	35	in	in	ADP
fumecheng-7223	189	36	a	a	DET
fumecheng-7223	189	37	polar	polar	ADJ
fumecheng-7223	189	38	bear	bear	NOUN
fumecheng-7223	189	39	hair	hair	NOUN
fumecheng-7223	189	40	,	,	PUNCT
fumecheng-7223	189	41	low	low	ADJ
fumecheng-7223	189	42	frequency	frequency	NOUN
fumecheng-7223	189	43	noise	noise	NOUN
fumecheng-7223	189	44	&	&	CCONJ
fumecheng-7223	189	45	vibration	vibration	NOUN
fumecheng-7223	189	46	,	,	PUNCT
fumecheng-7223	189	47	38(3–4	38(3–4	PROPN
fumecheng-7223	189	48	)	)	PUNCT
fumecheng-7223	189	49	,	,	PUNCT
fumecheng-7223	189	50	pp	pp	ADJ
fumecheng-7223	189	51	.	.	PUNCT
fumecheng-7223	189	52	1374–1377	1374–1377	X
fumecheng-7223	189	53	.	.	PUNCT
fumecheng-7223	189	54	39	39	NUM
fumecheng-7223	189	55	.	.	PUNCT
fumecheng-7223	190	1	he	he	PRON
fumecheng-7223	190	2	,	,	PUNCT
fumecheng-7223	190	3	j.-h	j.-h	PROPN
fumecheng-7223	190	4	.	.	PROPN
fumecheng-7223	190	5	,	,	PUNCT
fumecheng-7223	190	6	2002	2002	NUM
fumecheng-7223	190	7	,	,	PUNCT
fumecheng-7223	190	8	preliminary	preliminary	ADJ
fumecheng-7223	190	9	report	report	NOUN
fumecheng-7223	190	10	on	on	ADP
fumecheng-7223	190	11	the	the	DET
fumecheng-7223	190	12	energy	energy	NOUN
fumecheng-7223	190	13	balance	balance	NOUN
fumecheng-7223	190	14	for	for	ADP
fumecheng-7223	190	15	nonlinear	nonlinear	ADJ
fumecheng-7223	190	16	oscillations	oscillation	NOUN
fumecheng-7223	190	17	,	,	PUNCT
fumecheng-7223	190	18	mechanics	mechanic	NOUN
fumecheng-7223	190	19	research	research	NOUN
fumecheng-7223	190	20	communications	communication	NOUN
fumecheng-7223	190	21	,	,	PUNCT
fumecheng-7223	190	22	29(2–3	29(2–3	NUM
fumecheng-7223	190	23	)	)	PUNCT
fumecheng-7223	190	24	,	,	PUNCT
fumecheng-7223	190	25	pp	pp	ADP
fumecheng-7223	190	26	.	.	PUNCT
fumecheng-7223	191	1	107–111	107–111	NUM
fumecheng-7223	191	2	.	.	PUNCT
fumecheng-7223	192	1	40	40	NUM
fumecheng-7223	192	2	.	.	PUNCT
fumecheng-7223	193	1	he	he	PRON
fumecheng-7223	193	2	,	,	PUNCT
fumecheng-7223	193	3	j.-h	j.-h	PROPN
fumecheng-7223	193	4	.	.	PUNCT
fumecheng-7223	193	5	,	,	PUNCT
fumecheng-7223	193	6	2020	2020	NUM
fumecheng-7223	193	7	,	,	PUNCT
fumecheng-7223	193	8	variational	variational	ADJ
fumecheng-7223	193	9	principle	principle	NOUN
fumecheng-7223	193	10	and	and	CCONJ
fumecheng-7223	193	11	periodic	periodic	ADJ
fumecheng-7223	193	12	solution	solution	NOUN
fumecheng-7223	193	13	of	of	ADP
fumecheng-7223	193	14	the	the	DET
fumecheng-7223	193	15	kundu	kundu	NOUN
fumecheng-7223	193	16	–	–	PUNCT
fumecheng-7223	193	17	mukherjee	mukherjee	NOUN
fumecheng-7223	193	18	–	–	PUNCT
fumecheng-7223	193	19	naskar	naskar	NOUN
fumecheng-7223	193	20	equation	equation	NOUN
fumecheng-7223	193	21	,	,	PUNCT
fumecheng-7223	193	22	results	result	NOUN
fumecheng-7223	193	23	in	in	ADP
fumecheng-7223	193	24	physics	physics	NOUN
fumecheng-7223	193	25	,	,	PUNCT
fumecheng-7223	193	26	17	17	NUM
fumecheng-7223	193	27	,	,	PUNCT
fumecheng-7223	193	28	103031	103031	NUM
fumecheng-7223	193	29	.	.	PUNCT
fumecheng-7223	194	1	41	41	NUM
fumecheng-7223	194	2	.	.	PUNCT
fumecheng-7223	195	1	he	he	PRON
fumecheng-7223	195	2	,	,	PUNCT
fumecheng-7223	195	3	j.-h	j.-h	PROPN
fumecheng-7223	195	4	.	.	PUNCT
fumecheng-7223	195	5	,	,	PUNCT
fumecheng-7223	195	6	2020	2020	NUM
fumecheng-7223	195	7	,	,	PUNCT
fumecheng-7223	195	8	on	on	ADP
fumecheng-7223	195	9	the	the	DET
fumecheng-7223	195	10	fractal	fractal	ADJ
fumecheng-7223	195	11	variational	variational	ADJ
fumecheng-7223	195	12	principle	principle	NOUN
fumecheng-7223	195	13	for	for	ADP
fumecheng-7223	195	14	the	the	DET
fumecheng-7223	195	15	telegraph	telegraph	NOUN
fumecheng-7223	195	16	equation	equation	NOUN
fumecheng-7223	195	17	,	,	PUNCT
fumecheng-7223	195	18	fractals	fractal	NOUN
fumecheng-7223	195	19	,	,	PUNCT
fumecheng-7223	195	20	doi:10.1142	doi:10.1142	NOUN
fumecheng-7223	195	21	/	/	SYM
fumecheng-7223	195	22	s0218348x21500225	s0218348x21500225	NOUN
fumecheng-7223	195	23	42	42	NUM
fumecheng-7223	195	24	.	.	PUNCT
fumecheng-7223	196	1	liu	liu	PROPN
fumecheng-7223	196	2	,	,	PUNCT
fumecheng-7223	196	3	h.-y	h.-y	NOUN
fumecheng-7223	196	4	.	.	PUNCT
fumecheng-7223	196	5	,	,	PUNCT
fumecheng-7223	196	6	li	li	PROPN
fumecheng-7223	196	7	,	,	PUNCT
fumecheng-7223	196	8	z.-m	z.-m	PROPN
fumecheng-7223	196	9	.	.	PROPN
fumecheng-7223	196	10	,	,	PUNCT
fumecheng-7223	196	11	yao	yao	PROPN
fumecheng-7223	196	12	,	,	PUNCT
fumecheng-7223	196	13	s.-w	s.-w	PROPN
fumecheng-7223	196	14	.	.	PUNCT
fumecheng-7223	196	15	,	,	PUNCT
fumecheng-7223	196	16	yao	yao	PROPN
fumecheng-7223	196	17	,	,	PUNCT
fumecheng-7223	196	18	y.-j	y.-j	PROPN
fumecheng-7223	196	19	.	.	PROPN
fumecheng-7223	196	20	,	,	PUNCT
fumecheng-7223	196	21	liu	liu	PROPN
fumecheng-7223	196	22	,	,	PUNCT
fumecheng-7223	196	23	j.	j.	PROPN
fumecheng-7223	196	24	,	,	PUNCT
fumecheng-7223	196	25	2020	2020	NUM
fumecheng-7223	196	26	,	,	PUNCT
fumecheng-7223	196	27	a	a	DET
fumecheng-7223	196	28	variational	variational	ADJ
fumecheng-7223	196	29	principle	principle	NOUN
fumecheng-7223	196	30	for	for	ADP
fumecheng-7223	196	31	the	the	DET
fumecheng-7223	196	32	photocatalytic	photocatalytic	ADJ
fumecheng-7223	196	33	nox	nox	NOUN
fumecheng-7223	196	34	abatement	abatement	NOUN
fumecheng-7223	196	35	,	,	PUNCT
fumecheng-7223	196	36	thermal	thermal	ADJ
fumecheng-7223	196	37	science	science	NOUN
fumecheng-7223	196	38	,	,	PUNCT
fumecheng-7223	196	39	24(4	24(4	NUM
fumecheng-7223	196	40	)	)	PUNCT
fumecheng-7223	196	41	,	,	PUNCT
fumecheng-7223	196	42	pp	pp	ADJ
fumecheng-7223	196	43	.	.	PUNCT
fumecheng-7223	196	44	2515–2518	2515–2518	NUM
fumecheng-7223	196	45	.	.	PUNCT
fumecheng-7223	197	1	43	43	NUM
fumecheng-7223	197	2	.	.	PUNCT
fumecheng-7223	198	1	he	he	PRON
fumecheng-7223	198	2	,	,	PUNCT
fumecheng-7223	198	3	j.-h	j.-h	PROPN
fumecheng-7223	198	4	.	.	PROPN
fumecheng-7223	198	5	,	,	PUNCT
fumecheng-7223	198	6	ain	ain	PROPN
fumecheng-7223	198	7	,	,	PUNCT
fumecheng-7223	198	8	q.-t	q.-t	NOUN
fumecheng-7223	198	9	.	.	PUNCT
fumecheng-7223	198	10	,	,	PUNCT
fumecheng-7223	198	11	2020	2020	NUM
fumecheng-7223	198	12	,	,	PUNCT
fumecheng-7223	198	13	new	new	ADJ
fumecheng-7223	198	14	promises	promise	NOUN
fumecheng-7223	198	15	and	and	CCONJ
fumecheng-7223	198	16	future	future	ADJ
fumecheng-7223	198	17	challenges	challenge	NOUN
fumecheng-7223	198	18	of	of	ADP
fumecheng-7223	198	19	fractal	fractal	ADJ
fumecheng-7223	198	20	calculus	calculus	NOUN
fumecheng-7223	198	21	:	:	PUNCT
fumecheng-7223	198	22	from	from	ADP
fumecheng-7223	198	23	two	two	NUM
fumecheng-7223	198	24	-	-	PUNCT
fumecheng-7223	198	25	scale	scale	NOUN
fumecheng-7223	198	26	thermodynamics	thermodynamic	NOUN
fumecheng-7223	198	27	to	to	ADP
fumecheng-7223	198	28	fractal	fractal	ADJ
fumecheng-7223	198	29	variational	variational	ADJ
fumecheng-7223	198	30	principle	principle	NOUN
fumecheng-7223	198	31	,	,	PUNCT
fumecheng-7223	198	32	thermal	thermal	ADJ
fumecheng-7223	198	33	science	science	NOUN
fumecheng-7223	198	34	,	,	PUNCT
fumecheng-7223	198	35	24(2	24(2	NUM
fumecheng-7223	198	36	part	part	NOUN
fumecheng-7223	198	37	a	a	X
fumecheng-7223	198	38	)	)	PUNCT
fumecheng-7223	198	39	,	,	PUNCT
fumecheng-7223	198	40	pp	pp	ADJ
fumecheng-7223	198	41	.	.	PUNCT
fumecheng-7223	199	1	659–681	659–681	NUM
fumecheng-7223	199	2	.	.	PUNCT