id	sid	tid	token	lemma	pos
fumecheng-10848	1	1	10848	10848	NUM
fumecheng-10848	1	2	facta	facta	NOUN
fumecheng-10848	1	3	universitatis	universitatis	PROPN
fumecheng-10848	1	4	series	series	NOUN
fumecheng-10848	1	5	:	:	PUNCT
fumecheng-10848	1	6	mechanical	mechanical	ADJ
fumecheng-10848	1	7	engineering	engineering	NOUN
fumecheng-10848	1	8	vol	vol	NOUN
fumecheng-10848	1	9	.	.	PROPN
fumecheng-10848	1	10	23	23	NUM
fumecheng-10848	1	11	,	,	PUNCT
fumecheng-10848	1	12	no	no	DET
fumecheng-10848	1	13	2	2	NUM
fumecheng-10848	1	14	,	,	PUNCT
fumecheng-10848	1	15	2025	2025	NUM
fumecheng-10848	1	16	,	,	PUNCT
fumecheng-10848	1	17	pp	pp	ADJ
fumecheng-10848	1	18	.	.	PUNCT
fumecheng-10848	2	1	377	377	NUM
fumecheng-10848	2	2	385	385	NUM
fumecheng-10848	2	3	https://doi.org/10.22190/fume230428025f	https://doi.org/10.22190/fume230428025f	PROPN
fumecheng-10848	2	4	©	©	PROPN
fumecheng-10848	2	5	2025	2025	NUM
fumecheng-10848	2	6	by	by	ADP
fumecheng-10848	2	7	university	university	PROPN
fumecheng-10848	2	8	of	of	ADP
fumecheng-10848	2	9	niš	niš	PROPN
fumecheng-10848	2	10	,	,	PUNCT
fumecheng-10848	2	11	serbia	serbia	PROPN
fumecheng-10848	2	12	|	|	ADV
fumecheng-10848	2	13	creative	creative	ADJ
fumecheng-10848	2	14	commons	common	NOUN
fumecheng-10848	2	15	license	license	NOUN
fumecheng-10848	2	16	:	:	PUNCT
fumecheng-10848	2	17	cc	cc	VERB
fumecheng-10848	2	18	by	by	ADP
fumecheng-10848	2	19	-	-	PUNCT
fumecheng-10848	2	20	nc	nc	VERB
fumecheng-10848	2	21	-	-	PUNCT
fumecheng-10848	2	22	nd	nd	ADV
fumecheng-10848	2	23	original	original	ADJ
fumecheng-10848	2	24	scientific	scientific	NOUN
fumecheng-10848	2	25	paper	paper	VERB
fumecheng-10848	2	26	a	a	DET
fumecheng-10848	2	27	circular	circular	ADJ
fumecheng-10848	2	28	sector	sector	NOUN
fumecheng-10848	2	29	vibration	vibration	NOUN
fumecheng-10848	2	30	system	system	NOUN
fumecheng-10848	2	31	in	in	ADP
fumecheng-10848	2	32	a	a	DET
fumecheng-10848	2	33	porous	porous	ADJ
fumecheng-10848	2	34	medium	medium	NOUN
fumecheng-10848	2	35	:	:	PUNCT
fumecheng-10848	2	36	a	a	DET
fumecheng-10848	2	37	fractal	fractal	ADJ
fumecheng-10848	2	38	-	-	PUNCT
fumecheng-10848	2	39	fractional	fractional	ADJ
fumecheng-10848	2	40	model	model	NOUN
fumecheng-10848	2	41	and	and	CCONJ
fumecheng-10848	2	42	he	he	PRON
fumecheng-10848	2	43	’s	’	VERB
fumecheng-10848	2	44	frequency	frequency	NOUN
fumecheng-10848	2	45	formulation	formulation	NOUN
fumecheng-10848	2	46	guangqing	guangqe	VERB
fumecheng-10848	2	47	feng	feng	PROPN
fumecheng-10848	2	48	school	school	NOUN
fumecheng-10848	2	49	of	of	ADP
fumecheng-10848	2	50	mathematics	mathematic	NOUN
fumecheng-10848	2	51	and	and	CCONJ
fumecheng-10848	2	52	information	information	NOUN
fumecheng-10848	2	53	science	science	NOUN
fumecheng-10848	2	54	,	,	PUNCT
fumecheng-10848	2	55	henan	henan	PROPN
fumecheng-10848	2	56	polytechnic	polytechnic	PROPN
fumecheng-10848	2	57	university	university	PROPN
fumecheng-10848	2	58	,	,	PUNCT
fumecheng-10848	2	59	jiaozuo	jiaozuo	PROPN
fumecheng-10848	2	60	,	,	PUNCT
fumecheng-10848	2	61	china	china	PROPN
fumecheng-10848	2	62	orcid	orcid	PROPN
fumecheng-10848	3	1	i	i	PRON
fumecheng-10848	3	2	d	d	PROPN
fumecheng-10848	3	3	:	:	PUNCT
fumecheng-10848	3	4	guangqing	guangqe	VERB
fumecheng-10848	3	5	feng	feng	PROPN
fumecheng-10848	3	6	https://orcid.org/0000-0001-7851-1458	https://orcid.org/0000-0001-7851-1458	ADJ
fumecheng-10848	3	7	abstract	abstract	NOUN
fumecheng-10848	3	8	.	.	PUNCT
fumecheng-10848	4	1	a	a	DET
fumecheng-10848	4	2	circular	circular	ADJ
fumecheng-10848	4	3	sector	sector	NOUN
fumecheng-10848	4	4	is	be	AUX
fumecheng-10848	4	5	commonly	commonly	ADV
fumecheng-10848	4	6	used	use	VERB
fumecheng-10848	4	7	in	in	ADP
fumecheng-10848	4	8	a	a	DET
fumecheng-10848	4	9	linkage	linkage	NOUN
fumecheng-10848	4	10	mechanism	mechanism	NOUN
fumecheng-10848	4	11	,	,	PUNCT
fumecheng-10848	4	12	and	and	CCONJ
fumecheng-10848	4	13	its	its	PRON
fumecheng-10848	4	14	frequency	frequency	NOUN
fumecheng-10848	4	15	property	property	NOUN
fumecheng-10848	4	16	plays	play	VERB
fumecheng-10848	4	17	an	an	DET
fumecheng-10848	4	18	important	important	ADJ
fumecheng-10848	4	19	role	role	NOUN
fumecheng-10848	4	20	in	in	ADP
fumecheng-10848	4	21	optimization	optimization	NOUN
fumecheng-10848	4	22	of	of	ADP
fumecheng-10848	4	23	the	the	DET
fumecheng-10848	4	24	linkage	linkage	NOUN
fumecheng-10848	4	25	mechanism	mechanism	NOUN
fumecheng-10848	4	26	.	.	PUNCT
fumecheng-10848	5	1	fast	fast	ADJ
fumecheng-10848	5	2	insight	insight	NOUN
fumecheng-10848	5	3	into	into	ADP
fumecheng-10848	5	4	its	its	PRON
fumecheng-10848	5	5	vibration	vibration	NOUN
fumecheng-10848	5	6	property	property	NOUN
fumecheng-10848	5	7	with	with	ADP
fumecheng-10848	5	8	simple	simple	ADJ
fumecheng-10848	5	9	calculation	calculation	NOUN
fumecheng-10848	5	10	is	be	AUX
fumecheng-10848	5	11	very	very	ADV
fumecheng-10848	5	12	meaningful	meaningful	ADJ
fumecheng-10848	5	13	in	in	ADP
fumecheng-10848	5	14	scientific	scientific	ADJ
fumecheng-10848	5	15	research	research	NOUN
fumecheng-10848	5	16	.	.	PUNCT
fumecheng-10848	6	1	this	this	DET
fumecheng-10848	6	2	paper	paper	NOUN
fumecheng-10848	6	3	studies	study	VERB
fumecheng-10848	6	4	the	the	DET
fumecheng-10848	6	5	vibration	vibration	NOUN
fumecheng-10848	6	6	of	of	ADP
fumecheng-10848	6	7	the	the	DET
fumecheng-10848	6	8	circular	circular	ADJ
fumecheng-10848	6	9	sector	sector	NOUN
fumecheng-10848	6	10	in	in	ADP
fumecheng-10848	6	11	a	a	DET
fumecheng-10848	6	12	porous	porous	ADJ
fumecheng-10848	6	13	medium	medium	NOUN
fumecheng-10848	6	14	(	(	PUNCT
fumecheng-10848	6	15	e.g.	e.g.	ADJ
fumecheng-10848	6	16	water	water	NOUN
fumecheng-10848	6	17	)	)	PUNCT
fumecheng-10848	6	18	,	,	PUNCT
fumecheng-10848	6	19	and	and	CCONJ
fumecheng-10848	6	20	a	a	DET
fumecheng-10848	6	21	fractal	fractal	ADJ
fumecheng-10848	6	22	-	-	PUNCT
fumecheng-10848	6	23	fractional	fractional	ADJ
fumecheng-10848	6	24	oscillator	oscillator	NOUN
fumecheng-10848	6	25	is	be	AUX
fumecheng-10848	6	26	established	establish	VERB
fumecheng-10848	6	27	using	use	VERB
fumecheng-10848	6	28	the	the	DET
fumecheng-10848	6	29	two	two	NUM
fumecheng-10848	6	30	-	-	PUNCT
fumecheng-10848	6	31	scale	scale	NOUN
fumecheng-10848	6	32	fractal	fractal	ADJ
fumecheng-10848	6	33	derivative	derivative	NOUN
fumecheng-10848	6	34	.	.	PUNCT
fumecheng-10848	7	1	he	he	PRON
fumecheng-10848	7	2	’s	’	VERB
fumecheng-10848	7	3	frequency	frequency	NOUN
fumecheng-10848	7	4	formula	formula	NOUN
fumecheng-10848	7	5	and	and	CCONJ
fumecheng-10848	7	6	ma	ma	PROPN
fumecheng-10848	7	7	’s	’s	PART
fumecheng-10848	7	8	modification	modification	NOUN
fumecheng-10848	7	9	are	be	AUX
fumecheng-10848	7	10	used	use	VERB
fumecheng-10848	7	11	to	to	PART
fumecheng-10848	7	12	elucidate	elucidate	VERB
fumecheng-10848	7	13	the	the	DET
fumecheng-10848	7	14	circular	circular	ADJ
fumecheng-10848	7	15	sector	sector	NOUN
fumecheng-10848	7	16	’s	’s	PART
fumecheng-10848	7	17	periodic	periodic	ADJ
fumecheng-10848	7	18	property	property	NOUN
fumecheng-10848	7	19	in	in	ADP
fumecheng-10848	7	20	a	a	DET
fumecheng-10848	7	21	porous	porous	ADJ
fumecheng-10848	7	22	medium	medium	NOUN
fumecheng-10848	7	23	,	,	PUNCT
fumecheng-10848	7	24	the	the	DET
fumecheng-10848	7	25	results	result	NOUN
fumecheng-10848	7	26	show	show	VERB
fumecheng-10848	7	27	that	that	SCONJ
fumecheng-10848	7	28	the	the	DET
fumecheng-10848	7	29	fractal	fractal	ADJ
fumecheng-10848	7	30	dimension	dimension	NOUN
fumecheng-10848	7	31	of	of	ADP
fumecheng-10848	7	32	the	the	DET
fumecheng-10848	7	33	porous	porous	ADJ
fumecheng-10848	7	34	medium	medium	NOUN
fumecheng-10848	7	35	plays	play	VERB
fumecheng-10848	7	36	an	an	DET
fumecheng-10848	7	37	important	important	ADJ
fumecheng-10848	7	38	role	role	NOUN
fumecheng-10848	7	39	in	in	ADP
fumecheng-10848	7	40	vibration	vibration	NOUN
fumecheng-10848	7	41	attenuation	attenuation	NOUN
fumecheng-10848	7	42	.	.	PUNCT
fumecheng-10848	8	1	key	key	ADJ
fumecheng-10848	8	2	words	word	NOUN
fumecheng-10848	8	3	:	:	PUNCT
fumecheng-10848	8	4	he	he	PRON
fumecheng-10848	8	5	’s	’	VERB
fumecheng-10848	8	6	frequency	frequency	NOUN
fumecheng-10848	8	7	formula	formula	NOUN
fumecheng-10848	8	8	,	,	PUNCT
fumecheng-10848	8	9	ma	ma	PROPN
fumecheng-10848	8	10	’s	’s	PART
fumecheng-10848	8	11	modification	modification	NOUN
fumecheng-10848	8	12	,	,	PUNCT
fumecheng-10848	8	13	circular	circular	ADJ
fumecheng-10848	8	14	sector	sector	NOUN
fumecheng-10848	8	15	oscillator	oscillator	NOUN
fumecheng-10848	8	16	,	,	PUNCT
fumecheng-10848	8	17	fractal	fractal	ADJ
fumecheng-10848	8	18	variational	variational	ADJ
fumecheng-10848	8	19	theory	theory	NOUN
fumecheng-10848	8	20	,	,	PUNCT
fumecheng-10848	8	21	two	two	NUM
fumecheng-10848	8	22	-	-	PUNCT
fumecheng-10848	8	23	scale	scale	NOUN
fumecheng-10848	8	24	transform	transform	NOUN
fumecheng-10848	8	25	1	1	NUM
fumecheng-10848	8	26	.	.	PUNCT
fumecheng-10848	9	1	introduction	introduction	NOUN
fumecheng-10848	9	2	a	a	DET
fumecheng-10848	9	3	circular	circular	ADJ
fumecheng-10848	9	4	sector	sector	NOUN
fumecheng-10848	9	5	is	be	AUX
fumecheng-10848	9	6	commonly	commonly	ADV
fumecheng-10848	9	7	used	use	VERB
fumecheng-10848	9	8	in	in	ADP
fumecheng-10848	9	9	a	a	DET
fumecheng-10848	9	10	linkage	linkage	NOUN
fumecheng-10848	9	11	mechanism	mechanism	NOUN
fumecheng-10848	9	12	,	,	PUNCT
fumecheng-10848	9	13	it	it	PRON
fumecheng-10848	9	14	might	might	AUX
fumecheng-10848	9	15	vibrate	vibrate	VERB
fumecheng-10848	9	16	in	in	ADP
fumecheng-10848	9	17	water	water	NOUN
fumecheng-10848	9	18	or	or	CCONJ
fumecheng-10848	9	19	oil	oil	NOUN
fumecheng-10848	9	20	,	,	PUNCT
fumecheng-10848	9	21	and	and	CCONJ
fumecheng-10848	9	22	its	its	PRON
fumecheng-10848	9	23	vibration	vibration	NOUN
fumecheng-10848	9	24	property	property	NOUN
fumecheng-10848	9	25	has	have	AUX
fumecheng-10848	9	26	caught	catch	VERB
fumecheng-10848	9	27	much	much	ADJ
fumecheng-10848	9	28	attention	attention	NOUN
fumecheng-10848	9	29	in	in	ADP
fumecheng-10848	9	30	mechanical	mechanical	ADJ
fumecheng-10848	9	31	engineering	engineering	NOUN
fumecheng-10848	10	1	[	[	X
fumecheng-10848	10	2	1	1	NUM
fumecheng-10848	10	3	]	]	PUNCT
fumecheng-10848	10	4	.	.	PUNCT
fumecheng-10848	11	1	there	there	PRON
fumecheng-10848	11	2	are	be	VERB
fumecheng-10848	11	3	many	many	ADJ
fumecheng-10848	11	4	engineering	engineering	NOUN
fumecheng-10848	11	5	applications	application	NOUN
fumecheng-10848	11	6	in	in	ADP
fumecheng-10848	11	7	literature	literature	NOUN
fumecheng-10848	11	8	,	,	PUNCT
fumecheng-10848	11	9	such	such	ADJ
fumecheng-10848	11	10	as	as	ADP
fumecheng-10848	11	11	the	the	DET
fumecheng-10848	11	12	base	base	NOUN
fumecheng-10848	11	13	of	of	ADP
fumecheng-10848	11	14	structures	structure	NOUN
fumecheng-10848	11	15	,	,	PUNCT
fumecheng-10848	11	16	the	the	DET
fumecheng-10848	11	17	wipers	wiper	NOUN
fumecheng-10848	11	18	of	of	ADP
fumecheng-10848	11	19	cars	car	NOUN
fumecheng-10848	11	20	,	,	PUNCT
fumecheng-10848	11	21	smoothing	smooth	VERB
fumecheng-10848	11	22	filters	filter	NOUN
fumecheng-10848	11	23	and	and	CCONJ
fumecheng-10848	11	24	many	many	ADJ
fumecheng-10848	11	25	other	other	ADJ
fumecheng-10848	11	26	vibration	vibration	NOUN
fumecheng-10848	11	27	systems	system	NOUN
fumecheng-10848	11	28	[	[	X
fumecheng-10848	11	29	2	2	NUM
fumecheng-10848	11	30	-	-	SYM
fumecheng-10848	11	31	4	4	NUM
fumecheng-10848	11	32	]	]	PUNCT
fumecheng-10848	11	33	.	.	PUNCT
fumecheng-10848	12	1	the	the	DET
fumecheng-10848	12	2	traditional	traditional	ADJ
fumecheng-10848	12	3	vibration	vibration	NOUN
fumecheng-10848	12	4	theory	theory	NOUN
fumecheng-10848	12	5	can	can	AUX
fumecheng-10848	12	6	not	not	PART
fumecheng-10848	12	7	effectively	effectively	ADV
fumecheng-10848	12	8	elucidate	elucidate	VERB
fumecheng-10848	12	9	the	the	DET
fumecheng-10848	12	10	effect	effect	NOUN
fumecheng-10848	12	11	of	of	ADP
fumecheng-10848	12	12	the	the	DET
fumecheng-10848	12	13	porous	porous	ADJ
fumecheng-10848	12	14	medium	medium	NOUN
fumecheng-10848	12	15	’s	’s	NOUN
fumecheng-10848	12	16	geometry	geometry	NOUN
fumecheng-10848	12	17	on	on	ADP
fumecheng-10848	12	18	the	the	DET
fumecheng-10848	12	19	vibration	vibration	NOUN
fumecheng-10848	12	20	property	property	NOUN
fumecheng-10848	12	21	,	,	PUNCT
fumecheng-10848	12	22	now	now	ADV
fumecheng-10848	12	23	the	the	DET
fumecheng-10848	12	24	condition	condition	NOUN
fumecheng-10848	12	25	is	be	AUX
fumecheng-10848	12	26	changed	change	VERB
fumecheng-10848	12	27	,	,	PUNCT
fumecheng-10848	12	28	because	because	SCONJ
fumecheng-10848	12	29	of	of	ADP
fumecheng-10848	12	30	the	the	DET
fumecheng-10848	12	31	new	new	ADJ
fumecheng-10848	12	32	born	bear	VERB
fumecheng-10848	12	33	fractal	fractal	ADJ
fumecheng-10848	12	34	vibration	vibration	NOUN
fumecheng-10848	12	35	theory	theory	NOUN
fumecheng-10848	12	36	[	[	X
fumecheng-10848	12	37	5	5	NUM
fumecheng-10848	12	38	]	]	PUNCT
fumecheng-10848	12	39	.	.	PUNCT
fumecheng-10848	13	1	the	the	DET
fumecheng-10848	13	2	fractal	fractal	ADJ
fumecheng-10848	13	3	vibration	vibration	NOUN
fumecheng-10848	13	4	theory	theory	NOUN
fumecheng-10848	13	5	can	can	AUX
fumecheng-10848	13	6	make	make	VERB
fumecheng-10848	13	7	up	up	ADP
fumecheng-10848	13	8	for	for	ADP
fumecheng-10848	13	9	the	the	DET
fumecheng-10848	13	10	deficiency	deficiency	NOUN
fumecheng-10848	13	11	of	of	ADP
fumecheng-10848	13	12	the	the	DET
fumecheng-10848	13	13	traditional	traditional	ADJ
fumecheng-10848	13	14	vibration	vibration	NOUN
fumecheng-10848	13	15	theory	theory	NOUN
fumecheng-10848	13	16	.	.	PUNCT
fumecheng-10848	14	1	let	let	VERB
fumecheng-10848	14	2	's	us	PRON
fumecheng-10848	14	3	take	take	VERB
fumecheng-10848	14	4	the	the	DET
fumecheng-10848	14	5	vibration	vibration	NOUN
fumecheng-10848	14	6	of	of	ADP
fumecheng-10848	14	7	a	a	DET
fumecheng-10848	14	8	sector	sector	NOUN
fumecheng-10848	14	9	in	in	ADP
fumecheng-10848	14	10	the	the	DET
fumecheng-10848	14	11	air	air	NOUN
fumecheng-10848	14	12	as	as	ADP
fumecheng-10848	14	13	an	an	DET
fumecheng-10848	14	14	example	example	NOUN
fumecheng-10848	14	15	.	.	PUNCT
fumecheng-10848	15	1	in	in	ADP
fumecheng-10848	15	2	all	all	DET
fumecheng-10848	15	3	previous	previous	ADJ
fumecheng-10848	15	4	vibration	vibration	NOUN
fumecheng-10848	15	5	theories	theory	NOUN
fumecheng-10848	15	6	,	,	PUNCT
fumecheng-10848	15	7	the	the	DET
fumecheng-10848	15	8	influence	influence	NOUN
fumecheng-10848	15	9	of	of	ADP
fumecheng-10848	15	10	air	air	NOUN
fumecheng-10848	15	11	on	on	ADP
fumecheng-10848	15	12	vibration	vibration	NOUN
fumecheng-10848	15	13	characteristics	characteristic	NOUN
fumecheng-10848	15	14	is	be	AUX
fumecheng-10848	15	15	considered	consider	VERB
fumecheng-10848	15	16	as	as	ADP
fumecheng-10848	15	17	an	an	DET
fumecheng-10848	15	18	air	air	NOUN
fumecheng-10848	15	19	drag	drag	NOUN
fumecheng-10848	15	20	;	;	PUNCT
fumecheng-10848	15	21	however	however	ADV
fumecheng-10848	15	22	,	,	PUNCT
fumecheng-10848	15	23	the	the	DET
fumecheng-10848	15	24	performance	performance	NOUN
fumecheng-10848	15	25	of	of	ADP
fumecheng-10848	15	26	thin	thin	ADJ
fumecheng-10848	15	27	air	air	NOUN
fumecheng-10848	15	28	in	in	ADP
fumecheng-10848	15	29	a	a	DET
fumecheng-10848	15	30	microgravity	microgravity	NOUN
fumecheng-10848	15	31	environment	environment	NOUN
fumecheng-10848	15	32	is	be	AUX
fumecheng-10848	15	33	different	different	ADJ
fumecheng-10848	15	34	from	from	ADP
fumecheng-10848	15	35	that	that	PRON
fumecheng-10848	15	36	of	of	ADP
fumecheng-10848	15	37	near	near	ADP
fumecheng-10848	15	38	surface	surface	NOUN
fumecheng-10848	15	39	atmosphere	atmosphere	NOUN
fumecheng-10848	15	40	.	.	PUNCT
fumecheng-10848	16	1	the	the	DET
fumecheng-10848	16	2	vibration	vibration	NOUN
fumecheng-10848	16	3	received	receive	VERB
fumecheng-10848	16	4	:	:	PUNCT
fumecheng-10848	16	5	april	april	PROPN
fumecheng-10848	16	6	28	28	NUM
fumecheng-10848	16	7	,	,	PUNCT
fumecheng-10848	16	8	2023	2023	NUM
fumecheng-10848	16	9	/	/	PUNCT
fumecheng-10848	16	10	accepted	accept	VERB
fumecheng-10848	16	11	august	august	PROPN
fumecheng-10848	16	12	10	10	NUM
fumecheng-10848	16	13	,	,	PUNCT
fumecheng-10848	16	14	2023	2023	NUM
fumecheng-10848	16	15	corresponding	correspond	VERB
fumecheng-10848	16	16	author	author	NOUN
fumecheng-10848	16	17	:	:	PUNCT
fumecheng-10848	16	18	guangqing	guangqe	VERB
fumecheng-10848	16	19	feng	feng	PROPN
fumecheng-10848	16	20	school	school	NOUN
fumecheng-10848	16	21	of	of	ADP
fumecheng-10848	16	22	mathematics	mathematic	NOUN
fumecheng-10848	16	23	and	and	CCONJ
fumecheng-10848	16	24	information	information	NOUN
fumecheng-10848	16	25	science	science	NOUN
fumecheng-10848	16	26	,	,	PUNCT
fumecheng-10848	16	27	henan	henan	PROPN
fumecheng-10848	16	28	polytechnic	polytechnic	PROPN
fumecheng-10848	16	29	university	university	PROPN
fumecheng-10848	16	30	,	,	PUNCT
fumecheng-10848	16	31	shanyang	shanyang	PROPN
fumecheng-10848	16	32	district	district	PROPN
fumecheng-10848	16	33	,	,	PUNCT
fumecheng-10848	16	34	454011	454011	NUM
fumecheng-10848	16	35	jiaozuo	jiaozuo	PROPN
fumecheng-10848	16	36	,	,	PUNCT
fumecheng-10848	16	37	henan	henan	PROPN
fumecheng-10848	16	38	,	,	PUNCT
fumecheng-10848	16	39	china	china	PROPN
fumecheng-10848	16	40	e	e	PROPN
fumecheng-10848	16	41	-	-	NOUN
fumecheng-10848	16	42	mail	mail	NOUN
fumecheng-10848	16	43	:	:	PUNCT
fumecheng-10848	16	44	fgqing@hpu.edu.cn	fgqing@hpu.edu.cn	PROPN
fumecheng-10848	16	45	https://orcid.org/0000-0001-7851-1458	https://orcid.org/0000-0001-7851-1458	ADJ
fumecheng-10848	16	46	378	378	NUM
fumecheng-10848	16	47	g.	g.	PROPN
fumecheng-10848	16	48	feng	feng	PROPN
fumecheng-10848	16	49	model	model	PROPN
fumecheng-10848	16	50	constructed	construct	VERB
fumecheng-10848	16	51	by	by	ADP
fumecheng-10848	16	52	the	the	DET
fumecheng-10848	16	53	fractal	fractal	ADJ
fumecheng-10848	16	54	vibration	vibration	NOUN
fumecheng-10848	16	55	theory	theory	NOUN
fumecheng-10848	16	56	can	can	AUX
fumecheng-10848	16	57	consider	consider	VERB
fumecheng-10848	16	58	the	the	DET
fumecheng-10848	16	59	influence	influence	NOUN
fumecheng-10848	16	60	of	of	ADP
fumecheng-10848	16	61	molecules	molecule	NOUN
fumecheng-10848	16	62	’	'	PUNCT
fumecheng-10848	16	63	size	size	NOUN
fumecheng-10848	16	64	and	and	CCONJ
fumecheng-10848	16	65	distribution	distribution	NOUN
fumecheng-10848	16	66	on	on	ADP
fumecheng-10848	16	67	vibration	vibration	NOUN
fumecheng-10848	16	68	motion	motion	NOUN
fumecheng-10848	16	69	,	,	PUNCT
fumecheng-10848	16	70	the	the	DET
fumecheng-10848	16	71	acceleration	acceleration	NOUN
fumecheng-10848	16	72	in	in	ADP
fumecheng-10848	16	73	the	the	DET
fumecheng-10848	16	74	fractal	fractal	ADJ
fumecheng-10848	16	75	space	space	NOUN
fumecheng-10848	16	76	is	be	AUX
fumecheng-10848	16	77	a	a	DET
fumecheng-10848	16	78	combination	combination	NOUN
fumecheng-10848	16	79	of	of	ADP
fumecheng-10848	16	80	the	the	DET
fumecheng-10848	16	81	damping	damp	VERB
fumecheng-10848	16	82	force	force	NOUN
fumecheng-10848	16	83	and	and	CCONJ
fumecheng-10848	16	84	the	the	DET
fumecheng-10848	16	85	inertia	inertia	NOUN
fumecheng-10848	16	86	force	force	NOUN
fumecheng-10848	16	87	in	in	ADP
fumecheng-10848	16	88	the	the	DET
fumecheng-10848	16	89	traditional	traditional	ADJ
fumecheng-10848	16	90	vibration	vibration	NOUN
fumecheng-10848	16	91	system	system	NOUN
fumecheng-10848	16	92	[	[	X
fumecheng-10848	16	93	6	6	NUM
fumecheng-10848	16	94	-	-	SYM
fumecheng-10848	16	95	10	10	NUM
fumecheng-10848	16	96	]	]	PUNCT
fumecheng-10848	16	97	,	,	PUNCT
fumecheng-10848	16	98	so	so	CCONJ
fumecheng-10848	16	99	the	the	DET
fumecheng-10848	16	100	vibration	vibration	NOUN
fumecheng-10848	16	101	system	system	NOUN
fumecheng-10848	16	102	in	in	ADP
fumecheng-10848	16	103	a	a	DET
fumecheng-10848	16	104	porous	porous	ADJ
fumecheng-10848	16	105	medium(e.g	medium(e.g	PROPN
fumecheng-10848	16	106	.	.	PROPN
fumecheng-10848	16	107	air	air	PROPN
fumecheng-10848	16	108	,	,	PUNCT
fumecheng-10848	16	109	water	water	NOUN
fumecheng-10848	16	110	)	)	PUNCT
fumecheng-10848	16	111	can	can	AUX
fumecheng-10848	16	112	be	be	AUX
fumecheng-10848	16	113	modelled	model	VERB
fumecheng-10848	16	114	by	by	ADP
fumecheng-10848	16	115	a	a	DET
fumecheng-10848	16	116	fractal	fractal	ADJ
fumecheng-10848	16	117	-	-	PUNCT
fumecheng-10848	16	118	fractional	fractional	ADJ
fumecheng-10848	16	119	model	model	NOUN
fumecheng-10848	16	120	without	without	ADP
fumecheng-10848	16	121	considering	consider	VERB
fumecheng-10848	16	122	the	the	DET
fumecheng-10848	16	123	damping	damp	VERB
fumecheng-10848	16	124	effect	effect	NOUN
fumecheng-10848	16	125	.	.	PUNCT
fumecheng-10848	17	1	in	in	ADP
fumecheng-10848	17	2	general	general	ADJ
fumecheng-10848	17	3	,	,	PUNCT
fumecheng-10848	17	4	the	the	DET
fumecheng-10848	17	5	fractal	fractal	ADJ
fumecheng-10848	17	6	vibration	vibration	NOUN
fumecheng-10848	17	7	follows	follow	VERB
fumecheng-10848	17	8	a	a	DET
fumecheng-10848	17	9	fractal	fractal	ADJ
fumecheng-10848	17	10	variational	variational	ADJ
fumecheng-10848	17	11	theory	theory	NOUN
fumecheng-10848	17	12	,	,	PUNCT
fumecheng-10848	17	13	that	that	ADV
fumecheng-10848	17	14	is	is	ADV
fumecheng-10848	17	15	,	,	PUNCT
fumecheng-10848	17	16	the	the	DET
fumecheng-10848	17	17	vibration	vibration	NOUN
fumecheng-10848	17	18	system	system	NOUN
fumecheng-10848	17	19	in	in	ADP
fumecheng-10848	17	20	a	a	DET
fumecheng-10848	17	21	porous	porous	ADJ
fumecheng-10848	17	22	medium	medium	NOUN
fumecheng-10848	17	23	obeys	obey	NOUN
fumecheng-10848	17	24	the	the	DET
fumecheng-10848	17	25	fractal	fractal	ADJ
fumecheng-10848	17	26	energy	energy	NOUN
fumecheng-10848	17	27	conservation	conservation	NOUN
fumecheng-10848	17	28	law	law	NOUN
fumecheng-10848	17	29	,	,	PUNCT
fumecheng-10848	17	30	the	the	DET
fumecheng-10848	17	31	fractal	fractal	ADJ
fumecheng-10848	17	32	kinetic	kinetic	ADJ
fumecheng-10848	17	33	energy	energy	NOUN
fumecheng-10848	17	34	and	and	CCONJ
fumecheng-10848	17	35	the	the	DET
fumecheng-10848	17	36	potential	potential	ADJ
fumecheng-10848	17	37	energy	energy	NOUN
fumecheng-10848	17	38	are	be	AUX
fumecheng-10848	17	39	changed	change	VERB
fumecheng-10848	17	40	during	during	ADP
fumecheng-10848	17	41	the	the	DET
fumecheng-10848	17	42	vibrating	vibrating	NOUN
fumecheng-10848	17	43	process	process	NOUN
fumecheng-10848	17	44	,	,	PUNCT
fumecheng-10848	17	45	but	but	CCONJ
fumecheng-10848	17	46	their	their	PRON
fumecheng-10848	17	47	total	total	ADJ
fumecheng-10848	17	48	energy	energy	NOUN
fumecheng-10848	17	49	keeps	keep	VERB
fumecheng-10848	17	50	unchanged	unchanged	ADJ
fumecheng-10848	17	51	.	.	PUNCT
fumecheng-10848	18	1	fractal	fractal	PROPN
fumecheng-10848	18	2	nonlinear	nonlinear	PROPN
fumecheng-10848	18	3	systems	system	NOUN
fumecheng-10848	18	4	truly	truly	ADV
fumecheng-10848	18	5	describe	describe	VERB
fumecheng-10848	18	6	the	the	DET
fumecheng-10848	18	7	dynamic	dynamic	ADJ
fumecheng-10848	18	8	problems	problem	NOUN
fumecheng-10848	18	9	of	of	ADP
fumecheng-10848	18	10	engineering	engineering	NOUN
fumecheng-10848	18	11	science	science	NOUN
fumecheng-10848	18	12	,	,	PUNCT
fumecheng-10848	18	13	and	and	CCONJ
fumecheng-10848	18	14	its	its	PRON
fumecheng-10848	18	15	academic	academic	ADJ
fumecheng-10848	18	16	research	research	NOUN
fumecheng-10848	18	17	has	have	AUX
fumecheng-10848	18	18	greatly	greatly	ADV
fumecheng-10848	18	19	expanded	expand	VERB
fumecheng-10848	18	20	the	the	DET
fumecheng-10848	18	21	field	field	NOUN
fumecheng-10848	18	22	of	of	ADP
fumecheng-10848	18	23	human	human	ADJ
fumecheng-10848	18	24	cognition	cognition	NOUN
fumecheng-10848	18	25	.	.	PUNCT
fumecheng-10848	19	1	many	many	ADJ
fumecheng-10848	19	2	phenomena	phenomenon	NOUN
fumecheng-10848	19	3	can	can	AUX
fumecheng-10848	19	4	be	be	AUX
fumecheng-10848	19	5	explained	explain	VERB
fumecheng-10848	19	6	by	by	ADP
fumecheng-10848	19	7	the	the	DET
fumecheng-10848	19	8	fractal	fractal	ADJ
fumecheng-10848	19	9	theory	theory	NOUN
fumecheng-10848	19	10	,	,	PUNCT
fumecheng-10848	19	11	which	which	PRON
fumecheng-10848	19	12	makes	make	VERB
fumecheng-10848	19	13	us	we	PRON
fumecheng-10848	19	14	realize	realize	VERB
fumecheng-10848	19	15	that	that	SCONJ
fumecheng-10848	19	16	the	the	DET
fumecheng-10848	19	17	world	world	NOUN
fumecheng-10848	19	18	is	be	AUX
fumecheng-10848	19	19	totally	totally	ADV
fumecheng-10848	19	20	discontinuous	discontinuous	ADJ
fumecheng-10848	19	21	and	and	CCONJ
fumecheng-10848	19	22	nonlinear	nonlinear	ADJ
fumecheng-10848	19	23	.	.	PUNCT
fumecheng-10848	20	1	the	the	DET
fumecheng-10848	20	2	fractal	fractal	ADJ
fumecheng-10848	20	3	nonlinear	nonlinear	ADJ
fumecheng-10848	20	4	vibration	vibration	NOUN
fumecheng-10848	20	5	can	can	AUX
fumecheng-10848	20	6	be	be	AUX
fumecheng-10848	20	7	closer	close	ADJ
fumecheng-10848	20	8	to	to	ADP
fumecheng-10848	20	9	practical	practical	ADJ
fumecheng-10848	20	10	problems	problem	NOUN
fumecheng-10848	20	11	in	in	ADP
fumecheng-10848	20	12	both	both	DET
fumecheng-10848	20	13	depth	depth	NOUN
fumecheng-10848	20	14	and	and	CCONJ
fumecheng-10848	20	15	breadth	breadth	NOUN
fumecheng-10848	20	16	.	.	PUNCT
fumecheng-10848	21	1	it	it	PRON
fumecheng-10848	21	2	is	be	AUX
fumecheng-10848	21	3	very	very	ADV
fumecheng-10848	21	4	important	important	ADJ
fumecheng-10848	21	5	to	to	PART
fumecheng-10848	21	6	study	study	VERB
fumecheng-10848	21	7	the	the	DET
fumecheng-10848	21	8	analytical	analytical	ADJ
fumecheng-10848	21	9	or	or	CCONJ
fumecheng-10848	21	10	approximate	approximate	ADJ
fumecheng-10848	21	11	solutions	solution	NOUN
fumecheng-10848	21	12	of	of	ADP
fumecheng-10848	21	13	nonlinear	nonlinear	ADJ
fumecheng-10848	21	14	vibration	vibration	NOUN
fumecheng-10848	21	15	equations	equation	NOUN
fumecheng-10848	21	16	that	that	PRON
fumecheng-10848	21	17	can	can	AUX
fumecheng-10848	21	18	provide	provide	VERB
fumecheng-10848	21	19	deep	deep	ADJ
fumecheng-10848	21	20	insight	insight	NOUN
fumecheng-10848	21	21	into	into	ADP
fumecheng-10848	21	22	the	the	DET
fumecheng-10848	21	23	essence	essence	NOUN
fumecheng-10848	21	24	of	of	ADP
fumecheng-10848	21	25	general	general	ADJ
fumecheng-10848	21	26	properties	property	NOUN
fumecheng-10848	21	27	of	of	ADP
fumecheng-10848	21	28	a	a	DET
fumecheng-10848	21	29	fractal	fractal	ADJ
fumecheng-10848	21	30	vibrating	vibrating	NOUN
fumecheng-10848	21	31	system	system	NOUN
fumecheng-10848	21	32	.	.	PUNCT
fumecheng-10848	22	1	so	so	ADV
fumecheng-10848	22	2	,	,	PUNCT
fumecheng-10848	22	3	there	there	PRON
fumecheng-10848	22	4	are	be	VERB
fumecheng-10848	22	5	many	many	ADJ
fumecheng-10848	22	6	analytical	analytical	ADJ
fumecheng-10848	22	7	and	and	CCONJ
fumecheng-10848	22	8	numerical	numerical	ADJ
fumecheng-10848	22	9	methods	method	NOUN
fumecheng-10848	22	10	to	to	PART
fumecheng-10848	22	11	find	find	VERB
fumecheng-10848	22	12	an	an	DET
fumecheng-10848	22	13	approximate	approximate	ADJ
fumecheng-10848	22	14	solution	solution	NOUN
fumecheng-10848	22	15	of	of	ADP
fumecheng-10848	22	16	a	a	DET
fumecheng-10848	22	17	differential	differential	ADJ
fumecheng-10848	22	18	equation	equation	NOUN
fumecheng-10848	22	19	involving	involve	VERB
fumecheng-10848	22	20	fractal	fractal	ADJ
fumecheng-10848	22	21	-	-	PUNCT
fumecheng-10848	22	22	fractional	fractional	ADJ
fumecheng-10848	22	23	derivatives	derivative	NOUN
fumecheng-10848	22	24	,	,	PUNCT
fumecheng-10848	22	25	such	such	ADJ
fumecheng-10848	22	26	as	as	ADP
fumecheng-10848	22	27	the	the	DET
fumecheng-10848	22	28	variational	variational	ADJ
fumecheng-10848	22	29	iteration	iteration	NOUN
fumecheng-10848	22	30	method	method	NOUN
fumecheng-10848	22	31	[	[	X
fumecheng-10848	22	32	11	11	NUM
fumecheng-10848	22	33	-	-	SYM
fumecheng-10848	22	34	13	13	NUM
fumecheng-10848	22	35	]	]	PUNCT
fumecheng-10848	22	36	,	,	PUNCT
fumecheng-10848	22	37	the	the	DET
fumecheng-10848	22	38	homotopy	homotopy	NOUN
fumecheng-10848	22	39	perturbation	perturbation	NOUN
fumecheng-10848	22	40	[	[	X
fumecheng-10848	22	41	14,15	14,15	NUM
fumecheng-10848	22	42	]	]	PUNCT
fumecheng-10848	22	43	,	,	PUNCT
fumecheng-10848	22	44	the	the	DET
fumecheng-10848	22	45	hamiltonian	hamiltonian	ADJ
fumecheng-10848	22	46	approach	approach	NOUN
fumecheng-10848	22	47	[	[	X
fumecheng-10848	22	48	16	16	NUM
fumecheng-10848	22	49	]	]	PUNCT
fumecheng-10848	22	50	,	,	PUNCT
fumecheng-10848	22	51	and	and	CCONJ
fumecheng-10848	22	52	the	the	DET
fumecheng-10848	22	53	taylor	taylor	PROPN
fumecheng-10848	22	54	series	series	PROPN
fumecheng-10848	22	55	method	method	NOUN
fumecheng-10848	22	56	[	[	X
fumecheng-10848	22	57	17	17	NUM
fumecheng-10848	22	58	]	]	PUNCT
fumecheng-10848	22	59	.	.	PUNCT
fumecheng-10848	23	1	the	the	DET
fumecheng-10848	23	2	most	most	ADV
fumecheng-10848	23	3	important	important	ADJ
fumecheng-10848	23	4	property	property	NOUN
fumecheng-10848	23	5	of	of	ADP
fumecheng-10848	23	6	a	a	DET
fumecheng-10848	23	7	nonlinear	nonlinear	ADJ
fumecheng-10848	23	8	system	system	NOUN
fumecheng-10848	23	9	is	be	AUX
fumecheng-10848	23	10	the	the	DET
fumecheng-10848	23	11	frequency	frequency	NOUN
fumecheng-10848	23	12	-	-	PUNCT
fumecheng-10848	23	13	amplitude	amplitude	NOUN
fumecheng-10848	23	14	relationship	relationship	NOUN
fumecheng-10848	23	15	,	,	PUNCT
fumecheng-10848	23	16	so	so	ADV
fumecheng-10848	23	17	how	how	SCONJ
fumecheng-10848	23	18	to	to	PART
fumecheng-10848	23	19	estimate	estimate	VERB
fumecheng-10848	23	20	quickly	quickly	ADV
fumecheng-10848	23	21	its	its	PRON
fumecheng-10848	23	22	relationship	relationship	NOUN
fumecheng-10848	23	23	is	be	AUX
fumecheng-10848	23	24	an	an	DET
fumecheng-10848	23	25	urgent	urgent	ADJ
fumecheng-10848	23	26	problem	problem	NOUN
fumecheng-10848	23	27	in	in	ADP
fumecheng-10848	23	28	practical	practical	ADJ
fumecheng-10848	23	29	applications	application	NOUN
fumecheng-10848	23	30	.	.	PUNCT
fumecheng-10848	24	1	many	many	ADJ
fumecheng-10848	24	2	researchers	researcher	NOUN
fumecheng-10848	24	3	devoted	devote	VERB
fumecheng-10848	24	4	their	their	PRON
fumecheng-10848	24	5	efforts	effort	NOUN
fumecheng-10848	24	6	to	to	ADP
fumecheng-10848	24	7	studying	study	VERB
fumecheng-10848	24	8	fractal	fractal	ADJ
fumecheng-10848	24	9	calculus	calculus	NOUN
fumecheng-10848	24	10	that	that	PRON
fumecheng-10848	24	11	provides	provide	VERB
fumecheng-10848	24	12	a	a	DET
fumecheng-10848	24	13	powerful	powerful	ADJ
fumecheng-10848	24	14	tool	tool	NOUN
fumecheng-10848	24	15	to	to	ADP
fumecheng-10848	24	16	characterizing	characterize	VERB
fumecheng-10848	24	17	the	the	DET
fumecheng-10848	24	18	periodic	periodic	ADJ
fumecheng-10848	24	19	behavior	behavior	NOUN
fumecheng-10848	24	20	of	of	ADP
fumecheng-10848	24	21	a	a	DET
fumecheng-10848	24	22	nonlinear	nonlinear	ADJ
fumecheng-10848	24	23	oscillator	oscillator	NOUN
fumecheng-10848	24	24	[	[	X
fumecheng-10848	24	25	18	18	NUM
fumecheng-10848	24	26	-	-	SYM
fumecheng-10848	24	27	20	20	NUM
fumecheng-10848	24	28	]	]	PUNCT
fumecheng-10848	24	29	.	.	PUNCT
fumecheng-10848	25	1	chun	chun	PROPN
fumecheng-10848	25	2	-	-	PUNCT
fumecheng-10848	25	3	hui	hui	PROPN
fumecheng-10848	26	1	he	he	PRON
fumecheng-10848	26	2	suggested	suggest	VERB
fumecheng-10848	26	3	a	a	DET
fumecheng-10848	26	4	fractal	fractal	ADJ
fumecheng-10848	26	5	nano	nano	NOUN
fumecheng-10848	26	6	/	/	SYM
fumecheng-10848	26	7	microelectromechanical	microelectromechanical	ADJ
fumecheng-10848	26	8	(	(	PUNCT
fumecheng-10848	26	9	n	n	CCONJ
fumecheng-10848	26	10	/	/	SYM
fumecheng-10848	26	11	mems	mem	NOUN
fumecheng-10848	26	12	)	)	PUNCT
fumecheng-10848	26	13	system	system	NOUN
fumecheng-10848	26	14	[	[	X
fumecheng-10848	26	15	21	21	NUM
fumecheng-10848	26	16	]	]	PUNCT
fumecheng-10848	26	17	,	,	PUNCT
fumecheng-10848	26	18	ji	ji	PROPN
fumecheng-10848	26	19	-	-	PROPN
fumecheng-10848	26	20	huan	huan	PROPN
fumecheng-10848	26	21	he	he	PRON
fumecheng-10848	26	22	gave	give	VERB
fumecheng-10848	26	23	a	a	DET
fumecheng-10848	26	24	tutorial	tutorial	ADJ
fumecheng-10848	26	25	review	review	NOUN
fumecheng-10848	26	26	on	on	ADP
fumecheng-10848	26	27	fractal	fractal	ADJ
fumecheng-10848	26	28	space	space	NOUN
fumecheng-10848	26	29	and	and	CCONJ
fumecheng-10848	26	30	fractional	fractional	ADJ
fumecheng-10848	26	31	calculus	calculus	NOUN
fumecheng-10848	27	1	[	[	X
fumecheng-10848	27	2	22,23	22,23	NOUN
fumecheng-10848	27	3	]	]	PUNCT
fumecheng-10848	27	4	.	.	PUNCT
fumecheng-10848	28	1	he	he	PRON
fumecheng-10848	28	2	,	,	PUNCT
fumecheng-10848	28	3	et	et	PROPN
fumecheng-10848	28	4	al	al	PROPN
fumecheng-10848	28	5	.	.	PROPN
fumecheng-10848	28	6	studied	study	VERB
fumecheng-10848	28	7	the	the	DET
fumecheng-10848	28	8	fractal	fractal	ADJ
fumecheng-10848	28	9	duffing	duffing	NOUN
fumecheng-10848	28	10	oscillator	oscillator	NOUN
fumecheng-10848	28	11	with	with	ADP
fumecheng-10848	28	12	arbitrary	arbitrary	ADJ
fumecheng-10848	28	13	conditions	condition	NOUN
fumecheng-10848	28	14	[	[	X
fumecheng-10848	28	15	24	24	NUM
fumecheng-10848	28	16	]	]	PUNCT
fumecheng-10848	28	17	.	.	PUNCT
fumecheng-10848	29	1	ji	ji	PROPN
fumecheng-10848	29	2	-	-	PROPN
fumecheng-10848	29	3	huan	huan	PROPN
fumecheng-10848	29	4	he	he	PRON
fumecheng-10848	29	5	suggested	suggest	VERB
fumecheng-10848	29	6	a	a	DET
fumecheng-10848	29	7	frequency	frequency	NOUN
fumecheng-10848	29	8	formula	formula	NOUN
fumecheng-10848	29	9	for	for	ADP
fumecheng-10848	29	10	a	a	DET
fumecheng-10848	29	11	conservation	conservation	NOUN
fumecheng-10848	29	12	nonlinear	nonlinear	ADJ
fumecheng-10848	29	13	oscillator	oscillator	NOUN
fumecheng-10848	29	14	[	[	X
fumecheng-10848	29	15	25	25	NUM
fumecheng-10848	29	16	]	]	PUNCT
fumecheng-10848	29	17	and	and	CCONJ
fumecheng-10848	29	18	it	it	PRON
fumecheng-10848	29	19	was	be	AUX
fumecheng-10848	29	20	further	far	ADV
fumecheng-10848	29	21	improved	improve	VERB
fumecheng-10848	29	22	to	to	ADP
fumecheng-10848	29	23	an	an	DET
fumecheng-10848	29	24	extremely	extremely	ADV
fumecheng-10848	29	25	simple	simple	ADJ
fumecheng-10848	29	26	formula	formula	NOUN
fumecheng-10848	29	27	in	in	ADP
fumecheng-10848	29	28	refs	ref	NOUN
fumecheng-10848	29	29	.	.	PUNCT
fumecheng-10848	30	1	[	[	X
fumecheng-10848	30	2	26,27	26,27	NUM
fumecheng-10848	30	3	]	]	PUNCT
fumecheng-10848	30	4	,	,	PUNCT
fumecheng-10848	30	5	and	and	CCONJ
fumecheng-10848	30	6	it	it	PRON
fumecheng-10848	30	7	has	have	AUX
fumecheng-10848	30	8	been	be	AUX
fumecheng-10848	30	9	widely	widely	ADV
fumecheng-10848	30	10	used	use	VERB
fumecheng-10848	30	11	to	to	PART
fumecheng-10848	30	12	solve	solve	VERB
fumecheng-10848	30	13	nonlinear	nonlinear	ADJ
fumecheng-10848	30	14	oscillator	oscillator	NOUN
fumecheng-10848	30	15	problems	problem	NOUN
fumecheng-10848	30	16	,	,	PUNCT
fumecheng-10848	30	17	for	for	ADP
fumecheng-10848	30	18	examples	example	NOUN
fumecheng-10848	30	19	,	,	PUNCT
fumecheng-10848	30	20	the	the	DET
fumecheng-10848	30	21	n	n	CCONJ
fumecheng-10848	30	22	/	/	SYM
fumecheng-10848	30	23	mems	mems	ADJ
fumecheng-10848	30	24	oscillator	oscillator	NOUN
fumecheng-10848	30	25	[	[	X
fumecheng-10848	30	26	28	28	NUM
fumecheng-10848	30	27	]	]	PUNCT
fumecheng-10848	30	28	,	,	PUNCT
fumecheng-10848	30	29	the	the	DET
fumecheng-10848	30	30	attachment	attachment	NOUN
fumecheng-10848	30	31	oscillator	oscillator	NOUN
fumecheng-10848	30	32	[	[	X
fumecheng-10848	30	33	29	29	NUM
fumecheng-10848	30	34	]	]	PUNCT
fumecheng-10848	30	35	,	,	PUNCT
fumecheng-10848	30	36	the	the	DET
fumecheng-10848	30	37	tangent	tangent	NOUN
fumecheng-10848	30	38	oscillator	oscillator	NOUN
fumecheng-10848	30	39	[	[	X
fumecheng-10848	30	40	30	30	NUM
fumecheng-10848	30	41	]	]	PUNCT
fumecheng-10848	30	42	,	,	PUNCT
fumecheng-10848	30	43	the	the	DET
fumecheng-10848	30	44	fractal	fractal	ADJ
fumecheng-10848	30	45	undamped	undampe	VERB
fumecheng-10848	30	46	duffing	duffing	NOUN
fumecheng-10848	30	47	equation	equation	NOUN
fumecheng-10848	30	48	[	[	X
fumecheng-10848	30	49	31	31	NUM
fumecheng-10848	30	50	]	]	PUNCT
fumecheng-10848	30	51	,	,	PUNCT
fumecheng-10848	30	52	the	the	DET
fumecheng-10848	30	53	large	large	ADJ
fumecheng-10848	30	54	amplitude	amplitude	NOUN
fumecheng-10848	30	55	vibration	vibration	NOUN
fumecheng-10848	30	56	system	system	NOUN
fumecheng-10848	30	57	[	[	X
fumecheng-10848	30	58	32	32	NUM
fumecheng-10848	30	59	]	]	PUNCT
fumecheng-10848	30	60	and	and	CCONJ
fumecheng-10848	30	61	the	the	DET
fumecheng-10848	30	62	vibration	vibration	NOUN
fumecheng-10848	30	63	system	system	NOUN
fumecheng-10848	30	64	on	on	ADP
fumecheng-10848	30	65	a	a	DET
fumecheng-10848	30	66	porous	porous	ADJ
fumecheng-10848	30	67	foundation	foundation	NOUN
fumecheng-10848	31	1	[	[	X
fumecheng-10848	31	2	33	33	NUM
fumecheng-10848	31	3	]	]	PUNCT
fumecheng-10848	31	4	.	.	PUNCT
fumecheng-10848	32	1	many	many	ADJ
fumecheng-10848	32	2	modifications	modification	NOUN
fumecheng-10848	32	3	were	be	AUX
fumecheng-10848	32	4	appeared	appear	VERB
fumecheng-10848	32	5	in	in	ADP
fumecheng-10848	32	6	literature	literature	NOUN
fumecheng-10848	32	7	to	to	PART
fumecheng-10848	32	8	deal	deal	VERB
fumecheng-10848	32	9	with	with	ADP
fumecheng-10848	32	10	more	more	ADJ
fumecheng-10848	32	11	complex	complex	ADJ
fumecheng-10848	32	12	vibration	vibration	NOUN
fumecheng-10848	32	13	systems	system	NOUN
fumecheng-10848	32	14	[	[	X
fumecheng-10848	32	15	34	34	NUM
fumecheng-10848	32	16	-	-	SYM
fumecheng-10848	32	17	37	37	NUM
fumecheng-10848	32	18	]	]	PUNCT
fumecheng-10848	32	19	.	.	PUNCT
fumecheng-10848	33	1	the	the	DET
fumecheng-10848	33	2	hamiltonian	hamiltonian	NOUN
fumecheng-10848	33	3	-	-	PUNCT
fumecheng-10848	33	4	based	base	VERB
fumecheng-10848	33	5	frequency	frequency	NOUN
fumecheng-10848	33	6	formula	formula	NOUN
fumecheng-10848	33	7	is	be	AUX
fumecheng-10848	33	8	a	a	DET
fumecheng-10848	33	9	modification	modification	NOUN
fumecheng-10848	33	10	of	of	ADP
fumecheng-10848	33	11	he	he	PRON
fumecheng-10848	33	12	’s	’s	PART
fumecheng-10848	33	13	frequency	frequency	NOUN
fumecheng-10848	33	14	formula	formula	NOUN
fumecheng-10848	33	15	[	[	X
fumecheng-10848	33	16	38	38	NUM
fumecheng-10848	33	17	]	]	PUNCT
fumecheng-10848	33	18	.	.	PUNCT
fumecheng-10848	34	1	the	the	DET
fumecheng-10848	34	2	frequency	frequency	NOUN
fumecheng-10848	34	3	formula	formula	NOUN
fumecheng-10848	34	4	starts	start	VERB
fumecheng-10848	34	5	with	with	ADP
fumecheng-10848	34	6	two	two	NUM
fumecheng-10848	34	7	arbitrary	arbitrary	ADJ
fumecheng-10848	34	8	guesses	guess	NOUN
fumecheng-10848	34	9	for	for	ADP
fumecheng-10848	34	10	the	the	DET
fumecheng-10848	34	11	frequency	frequency	NOUN
fumecheng-10848	34	12	,	,	PUNCT
fumecheng-10848	34	13	and	and	CCONJ
fumecheng-10848	34	14	two	two	NUM
fumecheng-10848	34	15	residual	residual	ADJ
fumecheng-10848	34	16	integrals	integral	NOUN
fumecheng-10848	34	17	must	must	AUX
fumecheng-10848	34	18	be	be	AUX
fumecheng-10848	34	19	computed	compute	VERB
fumecheng-10848	34	20	to	to	PART
fumecheng-10848	34	21	estimate	estimate	VERB
fumecheng-10848	34	22	a	a	DET
fumecheng-10848	34	23	more	more	ADV
fumecheng-10848	34	24	accurate	accurate	ADJ
fumecheng-10848	34	25	frequency	frequency	NOUN
fumecheng-10848	34	26	.	.	PUNCT
fumecheng-10848	35	1	this	this	DET
fumecheng-10848	35	2	paper	paper	NOUN
fumecheng-10848	35	3	applies	apply	VERB
fumecheng-10848	35	4	he	he	PRON
fumecheng-10848	35	5	’s	’	VERB
fumecheng-10848	35	6	frequency	frequency	NOUN
fumecheng-10848	35	7	formula	formula	NOUN
fumecheng-10848	35	8	and	and	CCONJ
fumecheng-10848	35	9	ma	ma	PROPN
fumecheng-10848	35	10	’s	’s	PART
fumecheng-10848	35	11	modification	modification	NOUN
fumecheng-10848	35	12	to	to	PART
fumecheng-10848	35	13	study	study	VERB
fumecheng-10848	35	14	the	the	DET
fumecheng-10848	35	15	fractal	fractal	ADJ
fumecheng-10848	35	16	vibration	vibration	NOUN
fumecheng-10848	35	17	systems	system	NOUN
fumecheng-10848	35	18	and	and	CCONJ
fumecheng-10848	35	19	uses	use	VERB
fumecheng-10848	35	20	the	the	DET
fumecheng-10848	35	21	fractal	fractal	ADJ
fumecheng-10848	35	22	circular	circular	ADJ
fumecheng-10848	35	23	sector	sector	NOUN
fumecheng-10848	35	24	oscillator	oscillator	NOUN
fumecheng-10848	35	25	as	as	ADP
fumecheng-10848	35	26	an	an	DET
fumecheng-10848	35	27	example	example	NOUN
fumecheng-10848	35	28	.	.	PUNCT
fumecheng-10848	36	1	the	the	DET
fumecheng-10848	36	2	results	result	NOUN
fumecheng-10848	36	3	show	show	VERB
fumecheng-10848	36	4	that	that	SCONJ
fumecheng-10848	36	5	the	the	DET
fumecheng-10848	36	6	two	two	NUM
fumecheng-10848	36	7	methods	method	NOUN
fumecheng-10848	36	8	are	be	AUX
fumecheng-10848	36	9	very	very	ADV
fumecheng-10848	36	10	effective	effective	ADJ
fumecheng-10848	36	11	for	for	ADP
fumecheng-10848	36	12	fractal	fractal	ADJ
fumecheng-10848	36	13	nonlinear	nonlinear	ADJ
fumecheng-10848	36	14	oscillators	oscillator	NOUN
fumecheng-10848	36	15	.	.	PUNCT
fumecheng-10848	37	1	2	2	X
fumecheng-10848	37	2	.	.	X
fumecheng-10848	37	3	fractal	fractal	ADJ
fumecheng-10848	37	4	circular	circular	ADJ
fumecheng-10848	37	5	sector	sector	NOUN
fumecheng-10848	37	6	oscillator	oscillator	NOUN
fumecheng-10848	37	7	as	as	ADP
fumecheng-10848	37	8	the	the	DET
fumecheng-10848	37	9	fractal	fractal	ADJ
fumecheng-10848	37	10	variational	variational	ADJ
fumecheng-10848	37	11	theory	theory	NOUN
fumecheng-10848	37	12	is	be	AUX
fumecheng-10848	37	13	helpful	helpful	ADJ
fumecheng-10848	37	14	in	in	ADP
fumecheng-10848	37	15	establishing	establish	VERB
fumecheng-10848	37	16	a	a	DET
fumecheng-10848	37	17	governing	govern	VERB
fumecheng-10848	37	18	equation	equation	NOUN
fumecheng-10848	37	19	in	in	ADP
fumecheng-10848	37	20	a	a	DET
fumecheng-10848	37	21	fractal	fractal	ADJ
fumecheng-10848	37	22	space	space	NOUN
fumecheng-10848	37	23	,	,	PUNCT
fumecheng-10848	37	24	it	it	PRON
fumecheng-10848	37	25	has	have	AUX
fumecheng-10848	37	26	become	become	VERB
fumecheng-10848	37	27	a	a	DET
fumecheng-10848	37	28	significantly	significantly	ADV
fumecheng-10848	37	29	hot	hot	ADJ
fumecheng-10848	37	30	topic	topic	NOUN
fumecheng-10848	37	31	in	in	ADP
fumecheng-10848	37	32	both	both	DET
fumecheng-10848	37	33	mathematics	mathematic	NOUN
fumecheng-10848	37	34	and	and	CCONJ
fumecheng-10848	37	35	mechanical	mechanical	ADJ
fumecheng-10848	37	36	engineering	engineering	NOUN
fumecheng-10848	37	37	.	.	PUNCT
fumecheng-10848	38	1	many	many	ADJ
fumecheng-10848	38	2	fractal	fractal	ADJ
fumecheng-10848	38	3	variational	variational	ADJ
fumecheng-10848	38	4	principles	principle	NOUN
fumecheng-10848	38	5	were	be	AUX
fumecheng-10848	38	6	appeared	appear	VERB
fumecheng-10848	38	7	for	for	ADP
fumecheng-10848	38	8	the	the	DET
fumecheng-10848	38	9	internal	internal	ADJ
fumecheng-10848	38	10	temperature	temperature	NOUN
fumecheng-10848	38	11	response	response	NOUN
fumecheng-10848	38	12	of	of	ADP
fumecheng-10848	38	13	a	a	DET
fumecheng-10848	38	14	porous	porous	ADJ
fumecheng-10848	38	15	concrete	concrete	NOUN
fumecheng-10848	38	16	[	[	X
fumecheng-10848	38	17	39	39	NUM
fumecheng-10848	38	18	]	]	PUNCT
fumecheng-10848	38	19	,	,	PUNCT
fumecheng-10848	38	20	the	the	DET
fumecheng-10848	38	21	fractal	fractal	ADJ
fumecheng-10848	38	22	benney	benney	NOUN
fumecheng-10848	38	23	-	-	PUNCT
fumecheng-10848	38	24	lin	lin	PROPN
fumecheng-10848	38	25	equation	equation	NOUN
fumecheng-10848	38	26	[	[	X
fumecheng-10848	38	27	40	40	NUM
fumecheng-10848	38	28	]	]	PUNCT
fumecheng-10848	38	29	,	,	PUNCT
fumecheng-10848	38	30	the	the	DET
fumecheng-10848	38	31	fractal	fractal	ADJ
fumecheng-10848	38	32	shallow	shallow	ADJ
fumecheng-10848	38	33	water	water	NOUN
fumecheng-10848	38	34	wave	wave	NOUN
fumecheng-10848	39	1	[	[	X
fumecheng-10848	39	2	41	41	NUM
fumecheng-10848	39	3	]	]	PUNCT
fumecheng-10848	39	4	,	,	PUNCT
fumecheng-10848	39	5	the	the	DET
fumecheng-10848	39	6	fractal	fractal	ADJ
fumecheng-10848	39	7	bogoyavlenskii	bogoyavlenskii	ADJ
fumecheng-10848	39	8	system	system	NOUN
fumecheng-10848	40	1	[	[	X
fumecheng-10848	40	2	42	42	NUM
fumecheng-10848	40	3	]	]	PUNCT
fumecheng-10848	40	4	,	,	PUNCT
fumecheng-10848	40	5	the	the	DET
fumecheng-10848	40	6	fractal	fractal	ADJ
fumecheng-10848	40	7	schrodinger	schrodinger	PROPN
fumecheng-10848	40	8	system	system	NOUN
fumecheng-10848	40	9	[	[	X
fumecheng-10848	40	10	43	43	NUM
fumecheng-10848	40	11	]	]	PUNCT
fumecheng-10848	40	12	,	,	PUNCT
fumecheng-10848	40	13	the	the	DET
fumecheng-10848	40	14	fractal	fractal	ADJ
fumecheng-10848	40	15	solitary	solitary	ADJ
fumecheng-10848	40	16	wave	wave	NOUN
fumecheng-10848	40	17	[	[	X
fumecheng-10848	40	18	44	44	NUM
fumecheng-10848	40	19	]	]	PUNCT
fumecheng-10848	40	20	and	and	CCONJ
fumecheng-10848	40	21	the	the	DET
fumecheng-10848	40	22	fractal	fractal	ADJ
fumecheng-10848	40	23	economics	economic	NOUN
fumecheng-10848	40	24	[	[	X
fumecheng-10848	40	25	45	45	NUM
fumecheng-10848	40	26	]	]	PUNCT
fumecheng-10848	40	27	.	.	PUNCT
fumecheng-10848	41	1	a	a	DET
fumecheng-10848	41	2	circular	circular	ADJ
fumecheng-10848	41	3	sector	sector	NOUN
fumecheng-10848	41	4	vibration	vibration	NOUN
fumecheng-10848	41	5	system	system	NOUN
fumecheng-10848	41	6	in	in	ADP
fumecheng-10848	41	7	a	a	DET
fumecheng-10848	41	8	porous	porous	ADJ
fumecheng-10848	41	9	medium	medium	NOUN
fumecheng-10848	41	10	:	:	PUNCT
fumecheng-10848	41	11	a	a	DET
fumecheng-10848	41	12	fractal	fractal	ADJ
fumecheng-10848	41	13	-	-	PUNCT
fumecheng-10848	41	14	fractional	fractional	ADJ
fumecheng-10848	41	15	model	model	NOUN
fumecheng-10848	41	16	...	...	PUNCT
fumecheng-10848	41	17	379	379	NUM
fumecheng-10848	41	18	the	the	DET
fumecheng-10848	41	19	variational	variational	ADJ
fumecheng-10848	41	20	formula	formula	NOUN
fumecheng-10848	41	21	of	of	ADP
fumecheng-10848	41	22	an	an	DET
fumecheng-10848	41	23	oscillator	oscillator	NOUN
fumecheng-10848	41	24	in	in	ADP
fumecheng-10848	41	25	a	a	DET
fumecheng-10848	41	26	fractal	fractal	ADJ
fumecheng-10848	41	27	space	space	NOUN
fumecheng-10848	41	28	is	be	AUX
fumecheng-10848	41	29	in	in	ADP
fumecheng-10848	41	30	the	the	DET
fumecheng-10848	41	31	form	form	NOUN
fumecheng-10848	41	32			PROPN
fumecheng-10848	41	33			X
fumecheng-10848	41	34			PROPN
fumecheng-10848	41	35			PROPN
fumecheng-10848	41	36	duf	duf	PROPN
fumecheng-10848	41	37	d	d	PROPN
fumecheng-10848	41	38	du	du	PROPN
fumecheng-10848	41	39	uj	uj	PROPN
fumecheng-10848	41	40			X
fumecheng-10848	41	41	−=	−=	PROPN
fumecheng-10848	41	42	)	)	PUNCT
fumecheng-10848	41	43	}	}	PUNCT
fumecheng-10848	41	44	(	(	PUNCT
fumecheng-10848	41	45	)	)	PUNCT
fumecheng-10848	41	46	(	(	PUNCT
fumecheng-10848	41	47	2	2	NUM
fumecheng-10848	41	48	1	1	NUM
fumecheng-10848	41	49	{	{	PUNCT
fumecheng-10848	41	50	)	)	PUNCT
fumecheng-10848	41	51	(	(	PUNCT
fumecheng-10848	41	52	2	2	NUM
fumecheng-10848	41	53	(	(	PUNCT
fumecheng-10848	41	54	1	1	NUM
fumecheng-10848	41	55	)	)	PUNCT
fumecheng-10848	41	56	where	where	SCONJ
fumecheng-10848	41	57	(	(	PUNCT
fumecheng-10848	41	58	du	du	NOUN
fumecheng-10848	41	59	/	/	SYM
fumecheng-10848	41	60	d)2/2	d)2/2	PROPN
fumecheng-10848	41	61	is	be	AUX
fumecheng-10848	41	62	the	the	DET
fumecheng-10848	41	63	fractal	fractal	ADJ
fumecheng-10848	41	64	kinetic	kinetic	ADJ
fumecheng-10848	41	65	energy	energy	NOUN
fumecheng-10848	41	66	and	and	CCONJ
fumecheng-10848	41	67	f(u	f(u	PROPN
fumecheng-10848	41	68	)	)	PUNCT
fumecheng-10848	41	69	is	be	AUX
fumecheng-10848	41	70	the	the	DET
fumecheng-10848	41	71	potential	potential	ADJ
fumecheng-10848	41	72	energy	energy	NOUN
fumecheng-10848	41	73	.	.	PUNCT
fumecheng-10848	42	1	when	when	SCONJ
fumecheng-10848	42	2	f=-cosu	f=-cosu	NOUN
fumecheng-10848	42	3	,	,	PUNCT
fumecheng-10848	42	4	it	it	PRON
fumecheng-10848	42	5	is	be	AUX
fumecheng-10848	42	6	the	the	DET
fumecheng-10848	42	7	well	well	ADV
fumecheng-10848	42	8	-	-	PUNCT
fumecheng-10848	42	9	known	know	VERB
fumecheng-10848	42	10	pendulum	pendulum	NOUN
fumecheng-10848	42	11	oscillator	oscillator	NOUN
fumecheng-10848	42	12	[	[	X
fumecheng-10848	42	13	46,47	46,47	NUM
fumecheng-10848	42	14	]	]	X
fumecheng-10848	42	15	;	;	PUNCT
fumecheng-10848	42	16	when	when	SCONJ
fumecheng-10848	42	17	f	f	PROPN
fumecheng-10848	42	18	=	=	SYM
fumecheng-10848	42	19	u2/2+au4/4	u2/2+au4/4	PROPN
fumecheng-10848	42	20	,	,	PUNCT
fumecheng-10848	42	21	it	it	PRON
fumecheng-10848	42	22	is	be	AUX
fumecheng-10848	42	23	the	the	DET
fumecheng-10848	42	24	well	well	ADV
fumecheng-10848	42	25	-	-	PUNCT
fumecheng-10848	42	26	known	know	VERB
fumecheng-10848	42	27	duffing	duffing	NOUN
fumecheng-10848	42	28	oscillator	oscillator	NOUN
fumecheng-10848	42	29	[	[	X
fumecheng-10848	42	30	48	48	NUM
fumecheng-10848	42	31	]	]	PUNCT
fumecheng-10848	42	32	.	.	PUNCT
fumecheng-10848	43	1	when	when	SCONJ
fumecheng-10848	43	2	f	f	X
fumecheng-10848	43	3	=	=	ADJ
fumecheng-10848	43	4	gln(3r2/2	gln(3r2/2	VERB
fumecheng-10848	43	5	-	-	PUNCT
fumecheng-10848	43	6	2rkcosu)/(2r	2rkcosu)/(2r	NUM
fumecheng-10848	43	7	)	)	PUNCT
fumecheng-10848	43	8	,	,	PUNCT
fumecheng-10848	43	9	its	its	PRON
fumecheng-10848	43	10	variational	variational	ADJ
fumecheng-10848	43	11	formula	formula	NOUN
fumecheng-10848	43	12	is	be	AUX
fumecheng-10848	43	13	:	:	PUNCT
fumecheng-10848	43	14			X
fumecheng-10848	43	15			X
fumecheng-10848	44	1			PROPN
fumecheng-10848	44	2			NOUN
fumecheng-10848	44	3	durkr	durkr	ADJ
fumecheng-10848	44	4	r	r	NOUN
fumecheng-10848	44	5	g	g	PROPN
fumecheng-10848	44	6	d	d	X
fumecheng-10848	44	7	du	du	PROPN
fumecheng-10848	44	8	uj	uj	PROPN
fumecheng-10848	44	9			X
fumecheng-10848	44	10	−−=	−−=	PROPN
fumecheng-10848	44	11	)	)	PUNCT
fumecheng-10848	44	12	}	}	PUNCT
fumecheng-10848	44	13	cos2	cos2	NOUN
fumecheng-10848	44	14	2	2	NUM
fumecheng-10848	44	15	3	3	NUM
fumecheng-10848	44	16	ln	ln	ADJ
fumecheng-10848	44	17	(	(	PUNCT
fumecheng-10848	44	18	2	2	NUM
fumecheng-10848	44	19	)	)	PUNCT
fumecheng-10848	44	20	(	(	PUNCT
fumecheng-10848	44	21	2	2	NUM
fumecheng-10848	44	22	1	1	NUM
fumecheng-10848	44	23	{	{	PUNCT
fumecheng-10848	44	24	)	)	PUNCT
fumecheng-10848	44	25	(	(	PUNCT
fumecheng-10848	44	26	22	22	NUM
fumecheng-10848	44	27	(	(	PUNCT
fumecheng-10848	44	28	2	2	NUM
fumecheng-10848	44	29	)	)	PUNCT
fumecheng-10848	44	30	it	it	PRON
fumecheng-10848	44	31	meets	meet	VERB
fumecheng-10848	44	32	the	the	DET
fumecheng-10848	44	33	following	follow	VERB
fumecheng-10848	44	34	energy	energy	NOUN
fumecheng-10848	44	35	balance	balance	NOUN
fumecheng-10848	44	36	equation	equation	NOUN
fumecheng-10848	44	37	hurkr	hurkr	ADV
fumecheng-10848	44	38	r	r	NOUN
fumecheng-10848	44	39	g	g	PROPN
fumecheng-10848	44	40	d	d	X
fumecheng-10848	44	41	du	du	PROPN
fumecheng-10848	44	42	=	=	PROPN
fumecheng-10848	44	43	−+	−+	PROPN
fumecheng-10848	44	44	)	)	PUNCT
fumecheng-10848	44	45	cos2	cos2	PROPN
fumecheng-10848	44	46	2	2	NUM
fumecheng-10848	44	47	3	3	NUM
fumecheng-10848	44	48	ln	ln	ADJ
fumecheng-10848	44	49	(	(	PUNCT
fumecheng-10848	44	50	2	2	NUM
fumecheng-10848	44	51	)	)	PUNCT
fumecheng-10848	44	52	(	(	PUNCT
fumecheng-10848	44	53	2	2	NUM
fumecheng-10848	44	54	1	1	NUM
fumecheng-10848	44	55	22	22	NUM
fumecheng-10848	44	56			NOUN
fumecheng-10848	44	57	(	(	PUNCT
fumecheng-10848	44	58	3	3	NUM
fumecheng-10848	44	59	)	)	PUNCT
fumecheng-10848	44	60	where	where	SCONJ
fumecheng-10848	44	61	h	h	NOUN
fumecheng-10848	44	62	is	be	AUX
fumecheng-10848	44	63	the	the	DET
fumecheng-10848	44	64	hamiltonian	hamiltonian	ADJ
fumecheng-10848	44	65	constant	constant	ADJ
fumecheng-10848	44	66	.	.	PUNCT
fumecheng-10848	45	1	the	the	DET
fumecheng-10848	45	2	fractal	fractal	PROPN
fumecheng-10848	45	3	nonlinear	nonlinear	PROPN
fumecheng-10848	45	4	oscillator	oscillator	NOUN
fumecheng-10848	45	5	can	can	AUX
fumecheng-10848	45	6	be	be	AUX
fumecheng-10848	45	7	obtained	obtain	VERB
fumecheng-10848	45	8	as	as	SCONJ
fumecheng-10848	45	9	follows	follow	VERB
fumecheng-10848	45	10	0	0	NUM
fumecheng-10848	45	11	cos2	cos2	PROPN
fumecheng-10848	45	12	2	2	NUM
fumecheng-10848	45	13	3	3	NUM
fumecheng-10848	45	14	sin	sin	NOUN
fumecheng-10848	45	15	)	)	PUNCT
fumecheng-10848	45	16	(	(	PUNCT
fumecheng-10848	45	17	2	2	NUM
fumecheng-10848	45	18	=	=	SYM
fumecheng-10848	45	19	−	−	PROPN
fumecheng-10848	46	1	+	+	CCONJ
fumecheng-10848	46	2	urkr	urkr	ADJ
fumecheng-10848	46	3	ugk	ugk	PROPN
fumecheng-10848	46	4	d	d	X
fumecheng-10848	46	5	du	du	PROPN
fumecheng-10848	46	6	d	d	PROPN
fumecheng-10848	46	7	d	d	PROPN
fumecheng-10848	46	8			X
fumecheng-10848	46	9			PROPN
fumecheng-10848	46	10	(	(	PUNCT
fumecheng-10848	46	11	4	4	X
fumecheng-10848	46	12	)	)	PUNCT
fumecheng-10848	46	13	it	it	PRON
fumecheng-10848	46	14	is	be	AUX
fumecheng-10848	46	15	the	the	DET
fumecheng-10848	46	16	fractal	fractal	ADJ
fumecheng-10848	46	17	circular	circular	ADJ
fumecheng-10848	46	18	sector	sector	NOUN
fumecheng-10848	46	19	oscillator	oscillator	NOUN
fumecheng-10848	46	20	[	[	X
fumecheng-10848	46	21	49	49	NUM
fumecheng-10848	46	22	]	]	PUNCT
fumecheng-10848	46	23	,	,	PUNCT
fumecheng-10848	46	24	where	where	SCONJ
fumecheng-10848	46	25	u	u	NOUN
fumecheng-10848	46	26	is	be	AUX
fumecheng-10848	46	27	the	the	DET
fumecheng-10848	46	28	angular	angular	ADJ
fumecheng-10848	46	29	displacement	displacement	NOUN
fumecheng-10848	46	30	,	,	PUNCT
fumecheng-10848	46	31	r	r	NOUN
fumecheng-10848	46	32	is	be	AUX
fumecheng-10848	46	33	the	the	DET
fumecheng-10848	46	34	semicircular	semicircular	ADJ
fumecheng-10848	46	35	radius	radius	NOUN
fumecheng-10848	46	36	,	,	PUNCT
fumecheng-10848	46	37	g	g	PROPN
fumecheng-10848	46	38	is	be	AUX
fumecheng-10848	46	39	the	the	DET
fumecheng-10848	46	40	gravity	gravity	NOUN
fumecheng-10848	46	41	acceleration	acceleration	NOUN
fumecheng-10848	46	42	,	,	PUNCT
fumecheng-10848	46	43	r̅	r̅	X
fumecheng-10848	46	44	is	be	AUX
fumecheng-10848	46	45	the	the	DET
fumecheng-10848	46	46	height	height	NOUN
fumecheng-10848	46	47	of	of	ADP
fumecheng-10848	46	48	mass	mass	ADJ
fumecheng-10848	46	49	center	center	NOUN
fumecheng-10848	46	50	,	,	PUNCT
fumecheng-10848	46	51	r̅=2rsin/(3	r̅=2rsin/(3	PROPN
fumecheng-10848	46	52	)	)	PUNCT
fumecheng-10848	46	53	,	,	PUNCT
fumecheng-10848	46	54			PRON
fumecheng-10848	46	55	indicates	indicate	VERB
fumecheng-10848	46	56	the	the	DET
fumecheng-10848	46	57	semicircular	semicircular	ADJ
fumecheng-10848	46	58	angle	angle	NOUN
fumecheng-10848	46	59	,	,	PUNCT
fumecheng-10848	46	60	k	k	PROPN
fumecheng-10848	46	61	is	be	AUX
fumecheng-10848	46	62	the	the	DET
fumecheng-10848	46	63	dimensionless	dimensionless	ADJ
fumecheng-10848	46	64	geometrical	geometrical	ADJ
fumecheng-10848	46	65	parameter	parameter	NOUN
fumecheng-10848	46	66	,	,	PUNCT
fumecheng-10848	46	67	k=	k=	X
fumecheng-10848	46	68	r̅/r=2sin/(3	r̅/r=2sin/(3	PROPN
fumecheng-10848	46	69	)	)	PUNCT
fumecheng-10848	46	70	,	,	PUNCT
fumecheng-10848	46	71	as	as	SCONJ
fumecheng-10848	46	72	illustrated	illustrate	VERB
fumecheng-10848	46	73	in	in	ADP
fumecheng-10848	46	74	fig	fig	NOUN
fumecheng-10848	46	75	.	.	PUNCT
fumecheng-10848	47	1	1	1	X
fumecheng-10848	47	2	.	.	X
fumecheng-10848	47	3	fig	fig	NOUN
fumecheng-10848	47	4	.	.	PUNCT
fumecheng-10848	48	1	1	1	NUM
fumecheng-10848	48	2	circular	circular	ADJ
fumecheng-10848	48	3	sector	sector	NOUN
fumecheng-10848	48	4	oscillator	oscillator	NOUN
fumecheng-10848	48	5	in	in	ADP
fumecheng-10848	48	6	water	water	NOUN
fumecheng-10848	48	7	by	by	ADP
fumecheng-10848	48	8	the	the	DET
fumecheng-10848	48	9	two	two	NUM
fumecheng-10848	48	10	-	-	PUNCT
fumecheng-10848	48	11	scale	scale	NOUN
fumecheng-10848	48	12	transform	transform	NOUN
fumecheng-10848	48	13	[	[	X
fumecheng-10848	48	14	50	50	NUM
fumecheng-10848	48	15	]	]	PUNCT
fumecheng-10848	48	16	,	,	PUNCT
fumecheng-10848	48	17	t=	t=	PROPN
fumecheng-10848	48	18	,	,	PUNCT
fumecheng-10848	48	19	the	the	DET
fumecheng-10848	48	20	fractal	fractal	ADJ
fumecheng-10848	48	21	circular	circular	ADJ
fumecheng-10848	48	22	sector	sector	NOUN
fumecheng-10848	48	23	oscillator	oscillator	NOUN
fumecheng-10848	48	24	of	of	ADP
fumecheng-10848	48	25	eq	eq	PROPN
fumecheng-10848	48	26	.	.	PUNCT
fumecheng-10848	49	1	(	(	PUNCT
fumecheng-10848	49	2	4	4	X
fumecheng-10848	49	3	)	)	PUNCT
fumecheng-10848	49	4	can	can	AUX
fumecheng-10848	49	5	be	be	AUX
fumecheng-10848	49	6	converted	convert	VERB
fumecheng-10848	49	7	to	to	ADP
fumecheng-10848	49	8	an	an	DET
fumecheng-10848	49	9	ordinary	ordinary	ADJ
fumecheng-10848	49	10	form	form	NOUN
fumecheng-10848	49	11	as	as	SCONJ
fumecheng-10848	49	12	follows	follow	VERB
fumecheng-10848	49	13	0)0(,)0(,0	0)0(,)0(,0	ADP
fumecheng-10848	49	14	cos2	cos2	NOUN
fumecheng-10848	49	15	2	2	NUM
fumecheng-10848	49	16	3	3	NUM
fumecheng-10848	49	17	sin	sin	NOUN
fumecheng-10848	49	18	2	2	NUM
fumecheng-10848	49	19	=	=	NOUN
fumecheng-10848	49	20	==	==	NOUN
fumecheng-10848	49	21	−	−	NOUN
fumecheng-10848	50	1	+	+	NOUN
fumecheng-10848	50	2			PROPN
fumecheng-10848	50	3	uau	uau	NOUN
fumecheng-10848	50	4	urkr	urkr	PROPN
fumecheng-10848	50	5	ugk	ugk	PROPN
fumecheng-10848	50	6	u	u	PROPN
fumecheng-10848	50	7	(	(	PUNCT
fumecheng-10848	50	8	5	5	NUM
fumecheng-10848	50	9	)	)	PUNCT
fumecheng-10848	50	10	where	where	SCONJ
fumecheng-10848	50	11	the	the	DET
fumecheng-10848	50	12	derivative	derivative	NOUN
fumecheng-10848	50	13	of	of	ADP
fumecheng-10848	50	14	the	the	DET
fumecheng-10848	50	15	function	function	NOUN
fumecheng-10848	50	16	u	u	NOUN
fumecheng-10848	50	17	with	with	ADP
fumecheng-10848	50	18	respect	respect	NOUN
fumecheng-10848	50	19	to	to	ADP
fumecheng-10848	50	20	t.	t.	PROPN
fumecheng-10848	50	21	380	380	PROPN
fumecheng-10848	50	22	g.	g.	PROPN
fumecheng-10848	50	23	feng	feng	PROPN
fumecheng-10848	50	24	3	3	X
fumecheng-10848	50	25	.	.	PUNCT
fumecheng-10848	51	1	he	he	PRON
fumecheng-10848	51	2	’s	’	VERB
fumecheng-10848	51	3	frequency	frequency	NOUN
fumecheng-10848	51	4	formula	formula	NOUN
fumecheng-10848	51	5	he	he	PRON
fumecheng-10848	51	6	’s	’	VERB
fumecheng-10848	51	7	frequency	frequency	NOUN
fumecheng-10848	51	8	formula	formula	NOUN
fumecheng-10848	51	9	[	[	X
fumecheng-10848	51	10	26,27	26,27	NUM
fumecheng-10848	51	11	]	]	PUNCT
fumecheng-10848	51	12	is	be	AUX
fumecheng-10848	51	13	an	an	DET
fumecheng-10848	51	14	effective	effective	ADJ
fumecheng-10848	51	15	tool	tool	NOUN
fumecheng-10848	51	16	to	to	PART
fumecheng-10848	51	17	learn	learn	VERB
fumecheng-10848	51	18	the	the	DET
fumecheng-10848	51	19	frequency	frequency	NOUN
fumecheng-10848	51	20	-	-	PUNCT
fumecheng-10848	51	21	amplitude	amplitude	NOUN
fumecheng-10848	51	22	relationship	relationship	NOUN
fumecheng-10848	51	23	of	of	ADP
fumecheng-10848	51	24	fractal	fractal	ADJ
fumecheng-10848	51	25	oscillators	oscillator	NOUN
fumecheng-10848	51	26	in	in	ADP
fumecheng-10848	51	27	a	a	DET
fumecheng-10848	51	28	timely	timely	ADJ
fumecheng-10848	51	29	and	and	CCONJ
fumecheng-10848	51	30	efficient	efficient	ADJ
fumecheng-10848	51	31	way	way	NOUN
fumecheng-10848	51	32	.	.	PUNCT
fumecheng-10848	52	1	consider	consider	VERB
fumecheng-10848	52	2	the	the	DET
fumecheng-10848	52	3	following	follow	VERB
fumecheng-10848	52	4	nonlinear	nonlinear	ADJ
fumecheng-10848	52	5	oscillator	oscillator	NOUN
fumecheng-10848	52	6	0)0(,)0(,0	0)0(,)0(,0	PROPN
fumecheng-10848	52	7	)	)	PUNCT
fumecheng-10848	52	8	(	(	PUNCT
fumecheng-10848	53	1	=	=	NOUN
fumecheng-10848	53	2	==+	==+	NOUN
fumecheng-10848	53	3	uauuhu	uauuhu	NOUN
fumecheng-10848	53	4	(	(	PUNCT
fumecheng-10848	53	5	6	6	NUM
fumecheng-10848	53	6	)	)	PUNCT
fumecheng-10848	53	7	where	where	SCONJ
fumecheng-10848	53	8	h(u	h(u	PROPN
fumecheng-10848	53	9	)	)	PUNCT
fumecheng-10848	53	10	is	be	AUX
fumecheng-10848	53	11	a	a	DET
fumecheng-10848	53	12	nonlinear	nonlinear	ADJ
fumecheng-10848	53	13	function	function	NOUN
fumecheng-10848	53	14	,	,	PUNCT
fumecheng-10848	53	15	and	and	CCONJ
fumecheng-10848	53	16	it	it	PRON
fumecheng-10848	53	17	satisfies	satisfy	VERB
fumecheng-10848	53	18	h(u)/u>0	h(u)/u>0	PROPN
fumecheng-10848	53	19	.	.	PUNCT
fumecheng-10848	54	1	he	he	PRON
fumecheng-10848	54	2	’s	’	VERB
fumecheng-10848	54	3	frequency	frequency	NOUN
fumecheng-10848	54	4	formula	formula	NOUN
fumecheng-10848	54	5	is	be	AUX
fumecheng-10848	54	6	：	：	PUNCT
fumecheng-10848	54	7	audu	audu	ADJ
fumecheng-10848	54	8	udh	udh	NOUN
fumecheng-10848	54	9	5.0	5.0	NUM
fumecheng-10848	54	10	2	2	NUM
fumecheng-10848	54	11	)	)	PUNCT
fumecheng-10848	54	12	(	(	PUNCT
fumecheng-10848	54	13	=	=	PUNCT
fumecheng-10848	54	14	=	=	NOUN
fumecheng-10848	54	15			X
fumecheng-10848	54	16	(	(	PUNCT
fumecheng-10848	54	17	7	7	NUM
fumecheng-10848	54	18	)	)	PUNCT
fumecheng-10848	54	19	or	or	CCONJ
fumecheng-10848	54	20	na	na	INTJ
fumecheng-10848	54	21	nah	nah	INTJ
fumecheng-10848	54	22	)	)	PUNCT
fumecheng-10848	54	23	(	(	PUNCT
fumecheng-10848	54	24	2	2	NUM
fumecheng-10848	54	25	=	=	NUM
fumecheng-10848	54	26			X
fumecheng-10848	54	27	(	(	PUNCT
fumecheng-10848	54	28	8)	8)	NUM
fumecheng-10848	54	29	where	where	SCONJ
fumecheng-10848	54	30	n	n	PRON
fumecheng-10848	54	31	is	be	AUX
fumecheng-10848	54	32	a	a	DET
fumecheng-10848	54	33	constant	constant	ADJ
fumecheng-10848	54	34	,	,	PUNCT
fumecheng-10848	54	35	0	0	NUM
fumecheng-10848	54	36	<	<	X
fumecheng-10848	54	37	n≤1	n≤1	X
fumecheng-10848	54	38	.	.	PUNCT
fumecheng-10848	55	1	n	n	PRON
fumecheng-10848	55	2	is	be	AUX
fumecheng-10848	55	3	recommended	recommend	VERB
fumecheng-10848	55	4	as√3/2	as√3/2	INTJ
fumecheng-10848	55	5	for	for	ADP
fumecheng-10848	55	6	nonlinear	nonlinear	ADJ
fumecheng-10848	55	7	oscillators	oscillator	NOUN
fumecheng-10848	55	8	in	in	ADP
fumecheng-10848	55	9	[	[	X
fumecheng-10848	55	10	26	26	NUM
fumecheng-10848	55	11	,	,	PUNCT
fumecheng-10848	55	12	27	27	NUM
fumecheng-10848	55	13	]	]	PUNCT
fumecheng-10848	55	14	.	.	PUNCT
fumecheng-10848	56	1	convert	convert	VERB
fumecheng-10848	56	2	eq	eq	ADP
fumecheng-10848	56	3	.	.	PUNCT
fumecheng-10848	57	1	(	(	PUNCT
fumecheng-10848	57	2	5	5	NUM
fumecheng-10848	57	3	)	)	PUNCT
fumecheng-10848	57	4	to	to	ADP
fumecheng-10848	57	5	the	the	DET
fumecheng-10848	57	6	following	follow	VERB
fumecheng-10848	57	7	approximate	approximate	ADJ
fumecheng-10848	57	8	form	form	NOUN
fumecheng-10848	57	9	02	02	NUM
fumecheng-10848	58	1	=	=	NOUN
fumecheng-10848	58	2	+	+	NOUN
fumecheng-10848	58	3			X
fumecheng-10848	58	4	uu	uu	PRON
fumecheng-10848	58	5			X
fumecheng-10848	58	6	(	(	PUNCT
fumecheng-10848	58	7	9	9	NUM
fumecheng-10848	58	8	)	)	PUNCT
fumecheng-10848	58	9	where	where	SCONJ
fumecheng-10848	58	10	the	the	DET
fumecheng-10848	58	11	square	square	NOUN
fumecheng-10848	58	12	of	of	ADP
fumecheng-10848	58	13	the	the	DET
fumecheng-10848	58	14	frequency	frequency	NOUN
fumecheng-10848	58	15	can	can	AUX
fumecheng-10848	58	16	be	be	AUX
fumecheng-10848	58	17	calculated	calculate	VERB
fumecheng-10848	58	18	by	by	ADP
fumecheng-10848	58	19	eq.(8	eq.(8	ADV
fumecheng-10848	58	20	):	):	PUNCT
fumecheng-10848	58	21	)	)	PUNCT
fumecheng-10848	58	22	]	]	PUNCT
fumecheng-10848	58	23	2	2	NUM
fumecheng-10848	58	24	3	3	NUM
fumecheng-10848	58	25	cos(2	cos(2	NOUN
fumecheng-10848	58	26	2	2	NUM
fumecheng-10848	58	27	3	3	NUM
fumecheng-10848	58	28	[	[	PUNCT
fumecheng-10848	58	29	2	2	NUM
fumecheng-10848	58	30	3	3	NUM
fumecheng-10848	58	31	)	)	PUNCT
fumecheng-10848	58	32	2	2	NUM
fumecheng-10848	58	33	3	3	NUM
fumecheng-10848	58	34	sin	sin	NOUN
fumecheng-10848	58	35	(	(	PUNCT
fumecheng-10848	58	36	2	2	NUM
fumecheng-10848	58	37	2	2	NUM
fumecheng-10848	58	38	arkra	arkra	NOUN
fumecheng-10848	58	39	agk	agk	PROPN
fumecheng-10848	58	40	−	−	PROPN
fumecheng-10848	59	1	=	=	PRON
fumecheng-10848	59	2			X
fumecheng-10848	59	3	(	(	PUNCT
fumecheng-10848	59	4	10	10	NUM
fumecheng-10848	59	5	)	)	PUNCT
fumecheng-10848	59	6	the	the	DET
fumecheng-10848	59	7	approximate	approximate	ADJ
fumecheng-10848	59	8	solution	solution	NOUN
fumecheng-10848	59	9	of	of	ADP
fumecheng-10848	59	10	eq	eq	PROPN
fumecheng-10848	59	11	.	.	PUNCT
fumecheng-10848	60	1	(	(	PUNCT
fumecheng-10848	60	2	4	4	X
fumecheng-10848	60	3	)	)	PUNCT
fumecheng-10848	60	4	can	can	AUX
fumecheng-10848	60	5	be	be	AUX
fumecheng-10848	60	6	formed	form	VERB
fumecheng-10848	60	7	as	as	SCONJ
fumecheng-10848	60	8	follows	follow	NOUN
fumecheng-10848	60	9	)	)	PUNCT
fumecheng-10848	60	10	cos	cos	PROPN
fumecheng-10848	60	11	(	(	PUNCT
fumecheng-10848	60	12	)	)	PUNCT
fumecheng-10848	60	13	(	(	PUNCT
fumecheng-10848	60	14			X
fumecheng-10848	60	15			PROPN
fumecheng-10848	60	16	au	au	PROPN
fumecheng-10848	61	1	=	=	PUNCT
fumecheng-10848	61	2	(	(	PUNCT
fumecheng-10848	61	3	11	11	NUM
fumecheng-10848	61	4	)	)	SYM
fumecheng-10848	61	5	4	4	NUM
fumecheng-10848	61	6	.	.	PUNCT
fumecheng-10848	62	1	ma	ma	PROPN
fumecheng-10848	62	2	’s	’s	PART
fumecheng-10848	62	3	modification	modification	PROPN
fumecheng-10848	62	4	ma	ma	PROPN
fumecheng-10848	62	5	obtained	obtain	VERB
fumecheng-10848	62	6	a	a	DET
fumecheng-10848	62	7	simplified	simplified	ADJ
fumecheng-10848	62	8	form	form	NOUN
fumecheng-10848	62	9	of	of	ADP
fumecheng-10848	62	10	hamiltonian	hamiltonian	ADJ
fumecheng-10848	62	11	-	-	PUNCT
fumecheng-10848	62	12	based	base	VERB
fumecheng-10848	62	13	frequency	frequency	NOUN
fumecheng-10848	62	14	formula	formula	NOUN
fumecheng-10848	62	15	as	as	SCONJ
fumecheng-10848	62	16	follows	follow	VERB
fumecheng-10848	62	17	[	[	X
fumecheng-10848	62	18	38	38	NUM
fumecheng-10848	62	19	]	]	SYM
fumecheng-10848	62	20	:	:	PUNCT
fumecheng-10848	62	21	22	22	NUM
fumecheng-10848	62	22	2	2	NUM
fumecheng-10848	62	23	)	)	PUNCT
fumecheng-10848	62	24	1(5.0	1(5.0	NUM
fumecheng-10848	62	25	)	)	PUNCT
fumecheng-10848	62	26	(	(	PUNCT
fumecheng-10848	62	27	)	)	PUNCT
fumecheng-10848	62	28	(	(	PUNCT
fumecheng-10848	62	29	al	al	PROPN
fumecheng-10848	62	30	lahah	lahah	NOUN
fumecheng-10848	62	31	−	−	PROPN
fumecheng-10848	63	1	−	−	PROPN
fumecheng-10848	64	1	=	=	PRON
fumecheng-10848	65	1			PROPN
fumecheng-10848	66	1	(	(	PUNCT
fumecheng-10848	66	2	12	12	NUM
fumecheng-10848	66	3	)	)	PUNCT
fumecheng-10848	66	4	where	where	SCONJ
fumecheng-10848	66	5	dh(u)/du	dh(u)/du	NOUN
fumecheng-10848	66	6	=	=	SYM
fumecheng-10848	66	7	h(u	h(u	PROPN
fumecheng-10848	66	8	)	)	PUNCT
fumecheng-10848	66	9	,	,	PUNCT
fumecheng-10848	66	10	and	and	CCONJ
fumecheng-10848	66	11	l	l	NOUN
fumecheng-10848	66	12	is	be	AUX
fumecheng-10848	66	13	recommend	recommend	VERB
fumecheng-10848	66	14	as	as	ADP
fumecheng-10848	66	15	2	2	NUM
fumecheng-10848	66	16	-	-	SYM
fumecheng-10848	66	17	0.5	0.5	NUM
fumecheng-10848	67	1	[	[	PUNCT
fumecheng-10848	67	2	38	38	NUM
fumecheng-10848	67	3	]	]	PUNCT
fumecheng-10848	67	4	,	,	PUNCT
fumecheng-10848	67	5	the	the	DET
fumecheng-10848	67	6	simplified	simplified	ADJ
fumecheng-10848	67	7	hamiltonian	hamiltonian	NOUN
fumecheng-10848	67	8	-	-	PUNCT
fumecheng-10848	67	9	based	base	VERB
fumecheng-10848	67	10	frequency	frequency	NOUN
fumecheng-10848	67	11	formula	formula	NOUN
fumecheng-10848	67	12	converts	convert	NOUN
fumecheng-10848	67	13	to	to	ADP
fumecheng-10848	67	14	)	)	PUNCT
fumecheng-10848	67	15	]	]	PUNCT
fumecheng-10848	67	16	2	2	NUM
fumecheng-10848	67	17	(	(	PUNCT
fumecheng-10848	67	18	)	)	PUNCT
fumecheng-10848	67	19	(	(	PUNCT
fumecheng-10848	67	20	[	[	PUNCT
fumecheng-10848	67	21	4	4	NUM
fumecheng-10848	67	22	2	2	NUM
fumecheng-10848	67	23	2	2	NUM
fumecheng-10848	67	24	a	a	DET
fumecheng-10848	67	25	hah	hah	INTJ
fumecheng-10848	67	26	a	a	DET
fumecheng-10848	67	27	−=	−=	NOUN
fumecheng-10848	67	28	(	(	PUNCT
fumecheng-10848	67	29	13	13	NUM
fumecheng-10848	67	30	)	)	PUNCT
fumecheng-10848	67	31	according	accord	VERB
fumecheng-10848	67	32	to	to	ADP
fumecheng-10848	67	33	eq.(5	eq.(5	NOUN
fumecheng-10848	67	34	)	)	PUNCT
fumecheng-10848	67	35	,	,	PUNCT
fumecheng-10848	67	36	we	we	PRON
fumecheng-10848	67	37	have	have	VERB
fumecheng-10848	67	38	)	)	PUNCT
fumecheng-10848	67	39	cos2	cos2	PROPN
fumecheng-10848	67	40	2	2	NUM
fumecheng-10848	67	41	3	3	NUM
fumecheng-10848	67	42	ln	ln	ADJ
fumecheng-10848	67	43	(	(	PUNCT
fumecheng-10848	67	44	2	2	NUM
fumecheng-10848	67	45	)	)	PUNCT
fumecheng-10848	67	46	(	(	PUNCT
fumecheng-10848	67	47	2	2	NUM
fumecheng-10848	67	48	urkr	urkr	ADJ
fumecheng-10848	67	49	r	r	NOUN
fumecheng-10848	67	50	g	g	NOUN
fumecheng-10848	67	51	uh	uh	INTJ
fumecheng-10848	67	52	−=	−=	VERB
fumecheng-10848	67	53	(	(	PUNCT
fumecheng-10848	67	54	14	14	NUM
fumecheng-10848	67	55	)	)	PUNCT
fumecheng-10848	67	56	a	a	DET
fumecheng-10848	67	57	circular	circular	ADJ
fumecheng-10848	67	58	sector	sector	NOUN
fumecheng-10848	67	59	vibration	vibration	NOUN
fumecheng-10848	67	60	system	system	NOUN
fumecheng-10848	67	61	in	in	ADP
fumecheng-10848	67	62	a	a	DET
fumecheng-10848	67	63	porous	porous	ADJ
fumecheng-10848	67	64	medium	medium	NOUN
fumecheng-10848	67	65	:	:	PUNCT
fumecheng-10848	67	66	a	a	DET
fumecheng-10848	67	67	fractal	fractal	ADJ
fumecheng-10848	67	68	-	-	PUNCT
fumecheng-10848	67	69	fractional	fractional	ADJ
fumecheng-10848	67	70	model	model	NOUN
fumecheng-10848	67	71	...	...	PUNCT
fumecheng-10848	67	72	381	381	NUM
fumecheng-10848	67	73	ma	ma	PROPN
fumecheng-10848	67	74	’s	’s	PART
fumecheng-10848	67	75	modification	modification	NOUN
fumecheng-10848	67	76	leads	lead	VERB
fumecheng-10848	67	77	to	to	ADP
fumecheng-10848	67	78	the	the	DET
fumecheng-10848	67	79	following	following	ADJ
fumecheng-10848	67	80	result	result	NOUN
fumecheng-10848	67	81	)	)	PUNCT
fumecheng-10848	67	82	2	2	NUM
fumecheng-10848	67	83	/	/	SYM
fumecheng-10848	67	84	cos(2	cos(2	NOUN
fumecheng-10848	67	85	2	2	NUM
fumecheng-10848	67	86	3	3	NUM
fumecheng-10848	67	87	)	)	PUNCT
fumecheng-10848	67	88	cos(2	cos(2	VERB
fumecheng-10848	67	89	2	2	NUM
fumecheng-10848	67	90	3	3	NUM
fumecheng-10848	67	91	ln	ln	NOUN
fumecheng-10848	67	92	2	2	NUM
fumecheng-10848	67	93	2	2	NUM
fumecheng-10848	67	94	2	2	NUM
fumecheng-10848	67	95	akr	akr	NOUN
fumecheng-10848	67	96	akr	akr	NOUN
fumecheng-10848	67	97	ra	ra	PROPN
fumecheng-10848	67	98	g	g	PROPN
fumecheng-10848	67	99	−	−	PROPN
fumecheng-10848	67	100	−	−	PROPN
fumecheng-10848	68	1	=	=	PRON
fumecheng-10848	68	2			X
fumecheng-10848	68	3	(	(	PUNCT
fumecheng-10848	68	4	15	15	NUM
fumecheng-10848	68	5	)	)	PUNCT
fumecheng-10848	68	6	the	the	DET
fumecheng-10848	68	7	approximate	approximate	ADJ
fumecheng-10848	68	8	solution	solution	NOUN
fumecheng-10848	68	9	of	of	ADP
fumecheng-10848	68	10	eq	eq	PROPN
fumecheng-10848	68	11	.	.	PUNCT
fumecheng-10848	69	1	(	(	PUNCT
fumecheng-10848	69	2	4	4	X
fumecheng-10848	69	3	)	)	PUNCT
fumecheng-10848	69	4	can	can	AUX
fumecheng-10848	69	5	be	be	AUX
fumecheng-10848	69	6	formed	form	VERB
fumecheng-10848	69	7	as	as	ADP
fumecheng-10848	69	8	following	follow	VERB
fumecheng-10848	69	9	)	)	PUNCT
fumecheng-10848	69	10	cos	cos	PROPN
fumecheng-10848	69	11	(	(	PUNCT
fumecheng-10848	69	12	)	)	PUNCT
fumecheng-10848	69	13	(	(	PUNCT
fumecheng-10848	69	14			X
fumecheng-10848	69	15			PROPN
fumecheng-10848	69	16	=	=	PROPN
fumecheng-10848	69	17	au	au	NOUN
fumecheng-10848	69	18	(	(	PUNCT
fumecheng-10848	69	19	16	16	NUM
fumecheng-10848	69	20	)	)	PUNCT
fumecheng-10848	69	21	the	the	DET
fumecheng-10848	69	22	obtained	obtain	VERB
fumecheng-10848	69	23	approximate	approximate	ADJ
fumecheng-10848	69	24	analytical	analytical	ADJ
fumecheng-10848	69	25	solution	solution	NOUN
fumecheng-10848	69	26	must	must	AUX
fumecheng-10848	69	27	be	be	AUX
fumecheng-10848	69	28	compared	compare	VERB
fumecheng-10848	69	29	with	with	ADP
fumecheng-10848	69	30	the	the	DET
fumecheng-10848	69	31	numerical	numerical	ADJ
fumecheng-10848	69	32	ones	one	NOUN
fumecheng-10848	69	33	to	to	PART
fumecheng-10848	69	34	demonstrate	demonstrate	VERB
fumecheng-10848	69	35	the	the	DET
fumecheng-10848	69	36	validity	validity	NOUN
fumecheng-10848	69	37	of	of	ADP
fumecheng-10848	69	38	the	the	DET
fumecheng-10848	69	39	above	above	ADJ
fumecheng-10848	69	40	approaches	approach	NOUN
fumecheng-10848	69	41	.	.	PUNCT
fumecheng-10848	70	1	therefore	therefore	ADV
fumecheng-10848	70	2	,	,	PUNCT
fumecheng-10848	70	3	figs	fig	NOUN
fumecheng-10848	70	4	.	.	PUNCT
fumecheng-10848	71	1	2	2	NUM
fumecheng-10848	71	2	-	-	SYM
fumecheng-10848	71	3	4	4	NUM
fumecheng-10848	71	4	demonstrate	demonstrate	VERB
fumecheng-10848	71	5	the	the	DET
fumecheng-10848	71	6	analytical	analytical	ADJ
fumecheng-10848	71	7	solution	solution	NOUN
fumecheng-10848	71	8	from	from	ADP
fumecheng-10848	71	9	the	the	DET
fumecheng-10848	71	10	simplified	simplified	ADJ
fumecheng-10848	71	11	hamiltonian	hamiltonian	NOUN
fumecheng-10848	71	12	-	-	PUNCT
fumecheng-10848	71	13	based	base	VERB
fumecheng-10848	71	14	frequency	frequency	NOUN
fumecheng-10848	71	15	method	method	NOUN
fumecheng-10848	71	16	(	(	PUNCT
fumecheng-10848	71	17	shf	shf	NOUN
fumecheng-10848	71	18	)	)	PUNCT
fumecheng-10848	71	19	,	,	PUNCT
fumecheng-10848	71	20	together	together	ADV
fumecheng-10848	71	21	with	with	ADP
fumecheng-10848	71	22	the	the	DET
fumecheng-10848	71	23	numerical	numerical	ADJ
fumecheng-10848	71	24	solution	solution	NOUN
fumecheng-10848	71	25	(	(	PUNCT
fumecheng-10848	71	26	ns	ns	NUM
fumecheng-10848	71	27	)	)	PUNCT
fumecheng-10848	71	28	and	and	CCONJ
fumecheng-10848	71	29	the	the	DET
fumecheng-10848	71	30	solution	solution	NOUN
fumecheng-10848	71	31	from	from	ADP
fumecheng-10848	71	32	he	he	PRON
fumecheng-10848	71	33	’s	’s	PART
fumecheng-10848	71	34	frequency	frequency	NOUN
fumecheng-10848	71	35	method	method	NOUN
fumecheng-10848	71	36	(	(	PUNCT
fumecheng-10848	71	37	hf	hf	NOUN
fumecheng-10848	71	38	)	)	PUNCT
fumecheng-10848	71	39	for	for	ADP
fumecheng-10848	71	40	different	different	ADJ
fumecheng-10848	71	41	values	value	NOUN
fumecheng-10848	71	42	of	of	ADP
fumecheng-10848	71	43	a	a	PRON
fumecheng-10848	71	44	,	,	PUNCT
fumecheng-10848	71	45	r	r	NOUN
fumecheng-10848	71	46	and	and	CCONJ
fumecheng-10848	71	47	α	α	NOUN
fumecheng-10848	71	48	.	.	PUNCT
fumecheng-10848	72	1	the	the	DET
fumecheng-10848	72	2	approximate	approximate	ADJ
fumecheng-10848	72	3	periodic	periodic	ADJ
fumecheng-10848	72	4	solutions	solution	NOUN
fumecheng-10848	72	5	agree	agree	VERB
fumecheng-10848	72	6	well	well	ADV
fumecheng-10848	72	7	with	with	ADP
fumecheng-10848	72	8	exact	exact	ADJ
fumecheng-10848	72	9	numerical	numerical	ADJ
fumecheng-10848	72	10	results	result	NOUN
fumecheng-10848	72	11	.	.	PUNCT
fumecheng-10848	73	1	the	the	DET
fumecheng-10848	73	2	value	value	NOUN
fumecheng-10848	73	3	of	of	ADP
fumecheng-10848	73	4	α	α	NOUN
fumecheng-10848	73	5	changes	change	NOUN
fumecheng-10848	73	6	from	from	ADP
fumecheng-10848	73	7	/6	/6	ADJ
fumecheng-10848	73	8	to	to	ADP
fumecheng-10848	73	9	/3	/3	NOUN
fumecheng-10848	73	10	,	,	PUNCT
fumecheng-10848	73	11	the	the	DET
fumecheng-10848	73	12	change	change	NOUN
fumecheng-10848	73	13	amount	amount	NOUN
fumecheng-10848	73	14	is	be	AUX
fumecheng-10848	73	15	=/6	=/6	ADJ
fumecheng-10848	73	16	,	,	PUNCT
fumecheng-10848	73	17	and	and	CCONJ
fumecheng-10848	73	18	the	the	DET
fumecheng-10848	73	19	period	period	NOUN
fumecheng-10848	73	20	increment	increment	NOUN
fumecheng-10848	73	21	is	be	AUX
fumecheng-10848	73	22	t=4.5	t=4.5	PROPN
fumecheng-10848	73	23	in	in	ADP
fumecheng-10848	73	24	fig	fig	NOUN
fumecheng-10848	73	25	.	.	PUNCT
fumecheng-10848	74	1	2	2	X
fumecheng-10848	74	2	.	.	X
fumecheng-10848	74	3	the	the	DET
fumecheng-10848	74	4	value	value	NOUN
fumecheng-10848	74	5	of	of	ADP
fumecheng-10848	74	6	α	α	NOUN
fumecheng-10848	74	7	changes	change	NOUN
fumecheng-10848	74	8	from	from	ADP
fumecheng-10848	74	9	/2	/2	PROPN
fumecheng-10848	74	10	to	to	ADP
fumecheng-10848	74	11	2/3	2/3	NUM
fumecheng-10848	74	12	,	,	PUNCT
fumecheng-10848	74	13	the	the	DET
fumecheng-10848	74	14	change	change	NOUN
fumecheng-10848	74	15	amount	amount	NOUN
fumecheng-10848	74	16	is	be	AUX
fumecheng-10848	74	17	=/6	=/6	ADJ
fumecheng-10848	74	18	,	,	PUNCT
fumecheng-10848	74	19	and	and	CCONJ
fumecheng-10848	74	20	the	the	DET
fumecheng-10848	74	21	period	period	NOUN
fumecheng-10848	74	22	increment	increment	NOUN
fumecheng-10848	74	23	is	be	AUX
fumecheng-10848	74	24	t=14	t=14	NOUN
fumecheng-10848	74	25	in	in	ADP
fumecheng-10848	74	26	fig	fig	NOUN
fumecheng-10848	74	27	.	.	PUNCT
fumecheng-10848	75	1	3	3	X
fumecheng-10848	75	2	.	.	X
fumecheng-10848	76	1	the	the	PRON
fumecheng-10848	76	2	larger	large	ADJ
fumecheng-10848	76	3	the	the	DET
fumecheng-10848	76	4	value	value	NOUN
fumecheng-10848	76	5	of	of	ADP
fumecheng-10848	76	6	α	α	NOUN
fumecheng-10848	76	7	,	,	PUNCT
fumecheng-10848	76	8	the	the	DET
fumecheng-10848	76	9	more	more	ADV
fumecheng-10848	76	10	obvious	obvious	ADJ
fumecheng-10848	76	11	the	the	DET
fumecheng-10848	76	12	period	period	NOUN
fumecheng-10848	76	13	change	change	NOUN
fumecheng-10848	76	14	.	.	PUNCT
fumecheng-10848	77	1	it	it	PRON
fumecheng-10848	77	2	concludes	conclude	VERB
fumecheng-10848	77	3	that	that	SCONJ
fumecheng-10848	77	4	by	by	ADP
fumecheng-10848	77	5	increasing	increase	VERB
fumecheng-10848	77	6	the	the	DET
fumecheng-10848	77	7	semicircular	semicircular	ADJ
fumecheng-10848	77	8	angle	angle	NOUN
fumecheng-10848	77	9	α	α	NOUN
fumecheng-10848	77	10	with	with	ADP
fumecheng-10848	77	11	constant	constant	ADJ
fumecheng-10848	77	12	semicircular	semicircular	ADJ
fumecheng-10848	77	13	radius	radius	NOUN
fumecheng-10848	77	14	r	r	NOUN
fumecheng-10848	77	15	,	,	PUNCT
fumecheng-10848	77	16	the	the	DET
fumecheng-10848	77	17	period	period	NOUN
fumecheng-10848	77	18	of	of	ADP
fumecheng-10848	77	19	the	the	DET
fumecheng-10848	77	20	oscillation	oscillation	NOUN
fumecheng-10848	77	21	will	will	AUX
fumecheng-10848	77	22	increase	increase	VERB
fumecheng-10848	77	23	considerably	considerably	ADV
fumecheng-10848	77	24	.	.	PUNCT
fumecheng-10848	78	1	in	in	ADP
fumecheng-10848	78	2	fig	fig	NOUN
fumecheng-10848	78	3	.	.	PUNCT
fumecheng-10848	79	1	4	4	NUM
fumecheng-10848	79	2	,	,	PUNCT
fumecheng-10848	79	3	the	the	DET
fumecheng-10848	79	4	value	value	NOUN
fumecheng-10848	79	5	of	of	ADP
fumecheng-10848	79	6	the	the	DET
fumecheng-10848	79	7	amplitude	amplitude	NOUN
fumecheng-10848	79	8	a	a	DET
fumecheng-10848	79	9	determines	determine	NOUN
fumecheng-10848	79	10	the	the	DET
fumecheng-10848	79	11	maximum	maximum	ADJ
fumecheng-10848	79	12	value	value	NOUN
fumecheng-10848	79	13	of	of	ADP
fumecheng-10848	79	14	u.	u.	NOUN
fumecheng-10848	79	15	by	by	ADP
fumecheng-10848	79	16	comparing	compare	VERB
fumecheng-10848	79	17	figs	fig	NOUN
fumecheng-10848	79	18	.	.	PUNCT
fumecheng-10848	80	1	3	3	NUM
fumecheng-10848	80	2	and	and	CCONJ
fumecheng-10848	80	3	4	4	NUM
fumecheng-10848	80	4	,	,	PUNCT
fumecheng-10848	80	5	it	it	PRON
fumecheng-10848	80	6	is	be	AUX
fumecheng-10848	80	7	found	find	VERB
fumecheng-10848	80	8	that	that	SCONJ
fumecheng-10848	80	9	by	by	ADP
fumecheng-10848	80	10	reducing	reduce	VERB
fumecheng-10848	80	11	the	the	DET
fumecheng-10848	80	12	semicircular	semicircular	ADJ
fumecheng-10848	80	13	radius	radius	NOUN
fumecheng-10848	80	14	r	r	NOUN
fumecheng-10848	80	15	,	,	PUNCT
fumecheng-10848	80	16	the	the	DET
fumecheng-10848	80	17	period	period	NOUN
fumecheng-10848	80	18	of	of	ADP
fumecheng-10848	80	19	the	the	DET
fumecheng-10848	80	20	oscillation	oscillation	NOUN
fumecheng-10848	80	21	will	will	AUX
fumecheng-10848	80	22	decrease	decrease	VERB
fumecheng-10848	80	23	.	.	PUNCT
fumecheng-10848	81	1	fig	fig	NOUN
fumecheng-10848	81	2	.	.	PUNCT
fumecheng-10848	82	1	2	2	NUM
fumecheng-10848	82	2	comparisons	comparison	NOUN
fumecheng-10848	82	3	of	of	ADP
fumecheng-10848	82	4	the	the	DET
fumecheng-10848	82	5	exact	exact	ADJ
fumecheng-10848	82	6	solutions	solution	NOUN
fumecheng-10848	82	7	(	(	PUNCT
fumecheng-10848	82	8	ns	ns	CCONJ
fumecheng-10848	82	9	)	)	PUNCT
fumecheng-10848	82	10	with	with	ADP
fumecheng-10848	82	11	the	the	DET
fumecheng-10848	82	12	approximate	approximate	ADJ
fumecheng-10848	82	13	solutions	solution	NOUN
fumecheng-10848	82	14	based	base	VERB
fumecheng-10848	82	15	on	on	ADP
fumecheng-10848	82	16	eqs	eqs	PROPN
fumecheng-10848	82	17	.	.	PUNCT
fumecheng-10848	83	1	(	(	PUNCT
fumecheng-10848	83	2	11	11	NUM
fumecheng-10848	83	3	)	)	PUNCT
fumecheng-10848	83	4	(	(	PUNCT
fumecheng-10848	83	5	hf	hf	NOUN
fumecheng-10848	83	6	)	)	PUNCT
fumecheng-10848	83	7	and	and	CCONJ
fumecheng-10848	83	8	(	(	PUNCT
fumecheng-10848	83	9	16	16	NUM
fumecheng-10848	83	10	)	)	PUNCT
fumecheng-10848	83	11	(	(	PUNCT
fumecheng-10848	83	12	shf	shf	NOUN
fumecheng-10848	83	13	)	)	PUNCT
fumecheng-10848	83	14	for	for	ADP
fumecheng-10848	83	15	α	α	NOUN
fumecheng-10848	83	16	ranging	range	VERB
fumecheng-10848	83	17	from	from	ADP
fumecheng-10848	83	18	/6	/6	ADJ
fumecheng-10848	83	19	to	to	ADP
fumecheng-10848	83	20	/3	/3	NOUN
fumecheng-10848	83	21	0	0	NUM
fumecheng-10848	83	22	10	10	NUM
fumecheng-10848	83	23	20	20	NUM
fumecheng-10848	83	24	30	30	NUM
fumecheng-10848	83	25	40	40	NUM
fumecheng-10848	83	26	50	50	NUM
fumecheng-10848	83	27	60	60	NUM
fumecheng-10848	83	28	70	70	NUM
fumecheng-10848	83	29	80	80	NUM
fumecheng-10848	83	30	-0.4	-0.4	NUM
fumecheng-10848	83	31	-0.3	-0.3	PROPN
fumecheng-10848	83	32	-0.2	-0.2	PROPN
fumecheng-10848	83	33	-0.1	-0.1	PROPN
fumecheng-10848	83	34	0	0	NUM
fumecheng-10848	83	35	0.1	0.1	NUM
fumecheng-10848	83	36	0.2	0.2	NUM
fumecheng-10848	83	37	0.3	0.3	NUM
fumecheng-10848	83	38	0.4	0.4	NUM
fumecheng-10848	83	39	t	t	PROPN
fumecheng-10848	83	40	u	u	NOUN
fumecheng-10848	83	41	r	r	NOUN
fumecheng-10848	83	42	=	=	SYM
fumecheng-10848	83	43	15	15	NUM
fumecheng-10848	83	44	,	,	PUNCT
fumecheng-10848	83	45	a	a	DET
fumecheng-10848	83	46	=	=	X
fumecheng-10848	83	47			PROPN
fumecheng-10848	83	48	/	/	SYM
fumecheng-10848	83	49	8	8	NUM
fumecheng-10848	83	50	,	,	PUNCT
fumecheng-10848	83	51			X
fumecheng-10848	83	52	=	=	SYM
fumecheng-10848	83	53			PROPN
fumecheng-10848	83	54	/	/	SYM
fumecheng-10848	83	55	6	6	NUM
fumecheng-10848	83	56	n	n	NOUN
fumecheng-10848	83	57	s	s	NOUN
fumecheng-10848	83	58	h	h	NOUN
fumecheng-10848	84	1	f	f	PROPN
fumecheng-10848	84	2	s	s	PROPN
fumecheng-10848	84	3	h	h	NOUN
fumecheng-10848	84	4	f	f	NOUN
fumecheng-10848	84	5	0	0	NUM
fumecheng-10848	84	6	10	10	NUM
fumecheng-10848	84	7	20	20	NUM
fumecheng-10848	84	8	30	30	NUM
fumecheng-10848	84	9	40	40	NUM
fumecheng-10848	84	10	50	50	NUM
fumecheng-10848	84	11	60	60	NUM
fumecheng-10848	84	12	70	70	NUM
fumecheng-10848	84	13	80	80	NUM
fumecheng-10848	84	14	-0.4	-0.4	NUM
fumecheng-10848	84	15	-0.3	-0.3	PROPN
fumecheng-10848	84	16	-0.2	-0.2	PROPN
fumecheng-10848	84	17	-0.1	-0.1	PROPN
fumecheng-10848	84	18	0	0	NUM
fumecheng-10848	84	19	0.1	0.1	NUM
fumecheng-10848	84	20	0.2	0.2	NUM
fumecheng-10848	84	21	0.3	0.3	NUM
fumecheng-10848	84	22	0.4	0.4	NUM
fumecheng-10848	84	23	t	t	PROPN
fumecheng-10848	84	24	u	u	NOUN
fumecheng-10848	84	25	r	r	NOUN
fumecheng-10848	84	26	=	=	SYM
fumecheng-10848	84	27	15	15	NUM
fumecheng-10848	84	28	,	,	PUNCT
fumecheng-10848	84	29	a	a	DET
fumecheng-10848	84	30	=	=	X
fumecheng-10848	84	31			PROPN
fumecheng-10848	84	32	/	/	SYM
fumecheng-10848	84	33	8	8	NUM
fumecheng-10848	84	34	,	,	PUNCT
fumecheng-10848	84	35			X
fumecheng-10848	84	36	=	=	SYM
fumecheng-10848	84	37			PROPN
fumecheng-10848	84	38	/	/	SYM
fumecheng-10848	84	39	3	3	NUM
fumecheng-10848	84	40	n	n	NOUN
fumecheng-10848	84	41	s	s	NOUN
fumecheng-10848	84	42	h	h	NOUN
fumecheng-10848	84	43	f	f	PROPN
fumecheng-10848	84	44	s	s	PROPN
fumecheng-10848	84	45	h	h	NOUN
fumecheng-10848	84	46	f	f	PROPN
fumecheng-10848	84	47	382	382	NUM
fumecheng-10848	84	48	g.	g.	PROPN
fumecheng-10848	84	49	feng	feng	PROPN
fumecheng-10848	84	50	fig	fig	PROPN
fumecheng-10848	84	51	.	.	PUNCT
fumecheng-10848	85	1	3	3	NUM
fumecheng-10848	85	2	comparisons	comparison	NOUN
fumecheng-10848	85	3	of	of	ADP
fumecheng-10848	85	4	the	the	DET
fumecheng-10848	85	5	exact	exact	ADJ
fumecheng-10848	85	6	solutions	solution	NOUN
fumecheng-10848	85	7	(	(	PUNCT
fumecheng-10848	85	8	ns	ns	CCONJ
fumecheng-10848	85	9	)	)	PUNCT
fumecheng-10848	85	10	with	with	ADP
fumecheng-10848	85	11	the	the	DET
fumecheng-10848	85	12	approximate	approximate	ADJ
fumecheng-10848	85	13	solutions	solution	NOUN
fumecheng-10848	85	14	based	base	VERB
fumecheng-10848	85	15	on	on	ADP
fumecheng-10848	85	16	eqs	eqs	PROPN
fumecheng-10848	85	17	.	.	PUNCT
fumecheng-10848	86	1	(	(	PUNCT
fumecheng-10848	86	2	11	11	NUM
fumecheng-10848	86	3	)	)	PUNCT
fumecheng-10848	86	4	(	(	PUNCT
fumecheng-10848	86	5	hf	hf	NOUN
fumecheng-10848	86	6	)	)	PUNCT
fumecheng-10848	86	7	and	and	CCONJ
fumecheng-10848	86	8	(	(	PUNCT
fumecheng-10848	86	9	16	16	NUM
fumecheng-10848	86	10	)	)	PUNCT
fumecheng-10848	86	11	(	(	PUNCT
fumecheng-10848	86	12	shf	shf	NOUN
fumecheng-10848	86	13	)	)	PUNCT
fumecheng-10848	86	14	for	for	ADP
fumecheng-10848	86	15	α	α	NOUN
fumecheng-10848	86	16	ranging	range	VERB
fumecheng-10848	86	17	from	from	ADP
fumecheng-10848	86	18	/2	/2	PRON
fumecheng-10848	86	19	to	to	ADP
fumecheng-10848	86	20	2/3	2/3	NUM
fumecheng-10848	86	21	fig	fig	NOUN
fumecheng-10848	86	22	.	.	PUNCT
fumecheng-10848	87	1	4	4	NUM
fumecheng-10848	87	2	comparisons	comparison	NOUN
fumecheng-10848	87	3	of	of	ADP
fumecheng-10848	87	4	the	the	DET
fumecheng-10848	87	5	exact	exact	ADJ
fumecheng-10848	87	6	solutions	solution	NOUN
fumecheng-10848	87	7	(	(	PUNCT
fumecheng-10848	87	8	ns	ns	CCONJ
fumecheng-10848	87	9	)	)	PUNCT
fumecheng-10848	87	10	with	with	ADP
fumecheng-10848	87	11	the	the	DET
fumecheng-10848	87	12	approximate	approximate	ADJ
fumecheng-10848	87	13	solutions	solution	NOUN
fumecheng-10848	87	14	based	base	VERB
fumecheng-10848	87	15	on	on	ADP
fumecheng-10848	87	16	eqs	eqs	PROPN
fumecheng-10848	87	17	.	.	PUNCT
fumecheng-10848	88	1	(	(	PUNCT
fumecheng-10848	88	2	11	11	NUM
fumecheng-10848	88	3	)	)	PUNCT
fumecheng-10848	88	4	(	(	PUNCT
fumecheng-10848	88	5	hf	hf	NOUN
fumecheng-10848	88	6	)	)	PUNCT
fumecheng-10848	88	7	and	and	CCONJ
fumecheng-10848	88	8	(	(	PUNCT
fumecheng-10848	88	9	16	16	NUM
fumecheng-10848	88	10	)	)	PUNCT
fumecheng-10848	88	11	(	(	PUNCT
fumecheng-10848	88	12	shf	shf	NOUN
fumecheng-10848	88	13	)	)	PUNCT
fumecheng-10848	88	14	for	for	ADP
fumecheng-10848	88	15	amplitude	amplitude	NOUN
fumecheng-10848	88	16	a	a	DET
fumecheng-10848	88	17	ranging	ranging	NOUN
fumecheng-10848	88	18	from	from	ADP
fumecheng-10848	88	19	/8	/8	NOUN
fumecheng-10848	88	20	to	to	ADP
fumecheng-10848	88	21	/6	/6	ADJ
fumecheng-10848	88	22	based	base	VERB
fumecheng-10848	88	23	on	on	ADP
fumecheng-10848	88	24	eqs	eqs	PROPN
fumecheng-10848	88	25	.	.	PUNCT
fumecheng-10848	89	1	(	(	PUNCT
fumecheng-10848	89	2	10	10	NUM
fumecheng-10848	89	3	)	)	PUNCT
fumecheng-10848	89	4	and	and	CCONJ
fumecheng-10848	89	5	(	(	PUNCT
fumecheng-10848	89	6	15	15	NUM
fumecheng-10848	89	7	)	)	PUNCT
fumecheng-10848	89	8	,	,	PUNCT
fumecheng-10848	89	9	results	result	NOUN
fumecheng-10848	89	10	are	be	AUX
fumecheng-10848	89	11	extracted	extract	VERB
fumecheng-10848	89	12	from	from	ADP
fumecheng-10848	89	13	the	the	DET
fumecheng-10848	89	14	analytical	analytical	ADJ
fumecheng-10848	89	15	solution	solution	NOUN
fumecheng-10848	89	16	and	and	CCONJ
fumecheng-10848	89	17	are	be	AUX
fumecheng-10848	89	18	shown	show	VERB
fumecheng-10848	89	19	in	in	ADP
fumecheng-10848	89	20	fig	fig	NOUN
fumecheng-10848	89	21	.	.	PUNCT
fumecheng-10848	90	1	5	5	X
fumecheng-10848	90	2	.	.	X
fumecheng-10848	90	3	it	it	PRON
fumecheng-10848	90	4	visually	visually	ADV
fumecheng-10848	90	5	shows	show	VERB
fumecheng-10848	90	6	the	the	DET
fumecheng-10848	90	7	relationship	relationship	NOUN
fumecheng-10848	90	8	between	between	ADP
fumecheng-10848	90	9	a	a	DET
fumecheng-10848	90	10	,	,	PUNCT
fumecheng-10848	90	11	α	α	NOUN
fumecheng-10848	90	12	and	and	CCONJ
fumecheng-10848	90	13	the	the	DET
fumecheng-10848	90	14	frequency	frequency	NOUN
fumecheng-10848	90	15	when	when	SCONJ
fumecheng-10848	90	16	the	the	DET
fumecheng-10848	90	17	value	value	NOUN
fumecheng-10848	90	18	of	of	ADP
fumecheng-10848	90	19	r	r	NOUN
fumecheng-10848	90	20	is	be	AUX
fumecheng-10848	90	21	fixed	fix	VERB
fumecheng-10848	90	22	.	.	PUNCT
fumecheng-10848	91	1	an	an	DET
fumecheng-10848	91	2	increase	increase	NOUN
fumecheng-10848	91	3	in	in	ADP
fumecheng-10848	91	4	the	the	DET
fumecheng-10848	91	5	semicircle	semicircle	NOUN
fumecheng-10848	91	6	radius	radius	NOUN
fumecheng-10848	91	7	r	r	NOUN
fumecheng-10848	91	8	or	or	CCONJ
fumecheng-10848	91	9	semicircle	semicircle	NOUN
fumecheng-10848	91	10	α	α	PROPN
fumecheng-10848	91	11	results	result	VERB
fumecheng-10848	91	12	in	in	ADP
fumecheng-10848	91	13	a	a	DET
fumecheng-10848	91	14	decrease	decrease	NOUN
fumecheng-10848	91	15	in	in	ADP
fumecheng-10848	91	16	frequency	frequency	NOUN
fumecheng-10848	91	17	,	,	PUNCT
fumecheng-10848	91	18	which	which	PRON
fumecheng-10848	91	19	implies	imply	VERB
fumecheng-10848	91	20	an	an	DET
fumecheng-10848	91	21	increase	increase	NOUN
fumecheng-10848	91	22	in	in	ADP
fumecheng-10848	91	23	the	the	DET
fumecheng-10848	91	24	oscillation	oscillation	NOUN
fumecheng-10848	91	25	period	period	NOUN
fumecheng-10848	91	26	.	.	PUNCT
fumecheng-10848	92	1	five	five	NUM
fumecheng-10848	92	2	sequences	sequence	NOUN
fumecheng-10848	92	3	of	of	ADP
fumecheng-10848	92	4	the	the	DET
fumecheng-10848	92	5	fractal	fractal	ADJ
fumecheng-10848	92	6	parameter	parameter	PROPN
fumecheng-10848	92	7	θ	θ	PROPN
fumecheng-10848	92	8	are	be	AUX
fumecheng-10848	92	9	considered	consider	VERB
fumecheng-10848	92	10	for	for	ADP
fumecheng-10848	92	11	eq	eq	PROPN
fumecheng-10848	92	12	.	.	PUNCT
fumecheng-10848	93	1	(	(	PUNCT
fumecheng-10848	93	2	4	4	NUM
fumecheng-10848	93	3	)	)	PUNCT
fumecheng-10848	93	4	with	with	ADP
fumecheng-10848	93	5	the	the	DET
fumecheng-10848	93	6	fixed	fix	VERB
fumecheng-10848	93	7	parameters	parameter	NOUN
fumecheng-10848	93	8	r=10	r=10	NOUN
fumecheng-10848	93	9	,	,	PUNCT
fumecheng-10848	93	10	a	a	DET
fumecheng-10848	93	11	=	=	NOUN
fumecheng-10848	93	12	π/6	π/6	X
fumecheng-10848	93	13	,	,	PUNCT
fumecheng-10848	93	14	α	α	NOUN
fumecheng-10848	93	15	=	=	NOUN
fumecheng-10848	93	16	π/4	π/4	PUNCT
fumecheng-10848	93	17	and	and	CCONJ
fumecheng-10848	93	18	shown	show	VERB
fumecheng-10848	93	19	together	together	ADV
fumecheng-10848	93	20	in	in	ADP
fumecheng-10848	93	21	fig	fig	NOUN
fumecheng-10848	93	22	.	.	PUNCT
fumecheng-10848	94	1	6	6	NUM
fumecheng-10848	94	2	.	.	X
fumecheng-10848	94	3	numerical	numerical	ADJ
fumecheng-10848	94	4	simulations	simulation	NOUN
fumecheng-10848	94	5	indicate	indicate	VERB
fumecheng-10848	94	6	that	that	SCONJ
fumecheng-10848	94	7	the	the	DET
fumecheng-10848	94	8	oscillation	oscillation	NOUN
fumecheng-10848	94	9	frequency	frequency	NOUN
fumecheng-10848	94	10	becomes	become	VERB
fumecheng-10848	94	11	faster	fast	ADV
fumecheng-10848	94	12	and	and	CCONJ
fumecheng-10848	94	13	the	the	DET
fumecheng-10848	94	14	vibration	vibration	NOUN
fumecheng-10848	94	15	attenuation	attenuation	NOUN
fumecheng-10848	94	16	occurs	occur	VERB
fumecheng-10848	94	17	greater	great	ADJ
fumecheng-10848	94	18	for	for	ADP
fumecheng-10848	94	19	increasing	increase	VERB
fumecheng-10848	94	20	the	the	DET
fumecheng-10848	94	21	values	value	NOUN
fumecheng-10848	94	22	of	of	ADP
fumecheng-10848	94	23	the	the	DET
fumecheng-10848	94	24	fractal	fractal	ADJ
fumecheng-10848	94	25	exponent	exponent	PROPN
fumecheng-10848	94	26	θ	θ	PROPN
fumecheng-10848	94	27	.	.	PROPN
fumecheng-10848	94	28	0	0	NUM
fumecheng-10848	94	29	10	10	NUM
fumecheng-10848	94	30	20	20	NUM
fumecheng-10848	94	31	30	30	NUM
fumecheng-10848	94	32	40	40	NUM
fumecheng-10848	94	33	50	50	NUM
fumecheng-10848	94	34	60	60	NUM
fumecheng-10848	94	35	70	70	NUM
fumecheng-10848	94	36	80	80	NUM
fumecheng-10848	94	37	-0.4	-0.4	NUM
fumecheng-10848	94	38	-0.3	-0.3	PROPN
fumecheng-10848	94	39	-0.2	-0.2	PROPN
fumecheng-10848	94	40	-0.1	-0.1	PROPN
fumecheng-10848	94	41	0	0	NUM
fumecheng-10848	94	42	0.1	0.1	NUM
fumecheng-10848	94	43	0.2	0.2	NUM
fumecheng-10848	94	44	0.3	0.3	NUM
fumecheng-10848	94	45	0.4	0.4	NUM
fumecheng-10848	94	46	t	t	PROPN
fumecheng-10848	94	47	u	u	NOUN
fumecheng-10848	94	48	r	r	NOUN
fumecheng-10848	94	49	=	=	SYM
fumecheng-10848	94	50	15	15	NUM
fumecheng-10848	94	51	,	,	PUNCT
fumecheng-10848	94	52	a	a	DET
fumecheng-10848	94	53	=	=	X
fumecheng-10848	94	54			PROPN
fumecheng-10848	94	55	/	/	SYM
fumecheng-10848	94	56	8	8	NUM
fumecheng-10848	94	57	,	,	PUNCT
fumecheng-10848	94	58			X
fumecheng-10848	94	59	=	=	SYM
fumecheng-10848	94	60			PROPN
fumecheng-10848	94	61	/	/	SYM
fumecheng-10848	94	62	2	2	NUM
fumecheng-10848	94	63	n	n	NOUN
fumecheng-10848	94	64	s	s	NOUN
fumecheng-10848	94	65	h	h	NOUN
fumecheng-10848	95	1	f	f	PROPN
fumecheng-10848	95	2	s	s	PROPN
fumecheng-10848	95	3	h	h	NOUN
fumecheng-10848	95	4	f	f	NOUN
fumecheng-10848	95	5	0	0	NUM
fumecheng-10848	95	6	10	10	NUM
fumecheng-10848	95	7	20	20	NUM
fumecheng-10848	95	8	30	30	NUM
fumecheng-10848	95	9	40	40	NUM
fumecheng-10848	95	10	50	50	NUM
fumecheng-10848	95	11	60	60	NUM
fumecheng-10848	95	12	70	70	NUM
fumecheng-10848	95	13	80	80	NUM
fumecheng-10848	95	14	-0.4	-0.4	NUM
fumecheng-10848	95	15	-0.3	-0.3	PROPN
fumecheng-10848	95	16	-0.2	-0.2	PROPN
fumecheng-10848	95	17	-0.1	-0.1	PROPN
fumecheng-10848	95	18	0	0	NUM
fumecheng-10848	95	19	0.1	0.1	NUM
fumecheng-10848	95	20	0.2	0.2	NUM
fumecheng-10848	95	21	0.3	0.3	NUM
fumecheng-10848	95	22	0.4	0.4	NUM
fumecheng-10848	95	23	t	t	PROPN
fumecheng-10848	95	24	u	u	PROPN
fumecheng-10848	95	25	r=	r=	ADJ
fumecheng-10848	95	26	15	15	NUM
fumecheng-10848	95	27	,	,	PUNCT
fumecheng-10848	95	28	a	a	DET
fumecheng-10848	95	29	=	=	X
fumecheng-10848	95	30			PROPN
fumecheng-10848	95	31	/	/	SYM
fumecheng-10848	95	32	8	8	NUM
fumecheng-10848	95	33	,	,	PUNCT
fumecheng-10848	95	34			X
fumecheng-10848	95	35	=	=	SYM
fumecheng-10848	95	36	2	2	NUM
fumecheng-10848	95	37			NOUN
fumecheng-10848	95	38	/	/	SYM
fumecheng-10848	95	39	3	3	NUM
fumecheng-10848	95	40	n	n	NOUN
fumecheng-10848	95	41	s	s	NOUN
fumecheng-10848	95	42	h	h	NOUN
fumecheng-10848	96	1	f	f	PROPN
fumecheng-10848	96	2	s	s	PROPN
fumecheng-10848	96	3	h	h	NOUN
fumecheng-10848	96	4	f	f	NOUN
fumecheng-10848	96	5	0	0	NUM
fumecheng-10848	96	6	10	10	NUM
fumecheng-10848	96	7	20	20	NUM
fumecheng-10848	96	8	30	30	NUM
fumecheng-10848	96	9	40	40	NUM
fumecheng-10848	96	10	50	50	NUM
fumecheng-10848	96	11	60	60	NUM
fumecheng-10848	96	12	70	70	NUM
fumecheng-10848	96	13	80	80	NUM
fumecheng-10848	96	14	-0.4	-0.4	NUM
fumecheng-10848	96	15	-0.3	-0.3	PROPN
fumecheng-10848	96	16	-0.2	-0.2	PROPN
fumecheng-10848	96	17	-0.1	-0.1	PROPN
fumecheng-10848	96	18	0	0	NUM
fumecheng-10848	96	19	0.1	0.1	NUM
fumecheng-10848	96	20	0.2	0.2	NUM
fumecheng-10848	96	21	0.3	0.3	NUM
fumecheng-10848	96	22	0.4	0.4	NUM
fumecheng-10848	96	23	t	t	PROPN
fumecheng-10848	96	24	u	u	NOUN
fumecheng-10848	96	25	r	r	NOUN
fumecheng-10848	96	26	=	=	SYM
fumecheng-10848	96	27	10	10	NUM
fumecheng-10848	96	28	,	,	PUNCT
fumecheng-10848	96	29	a	a	DET
fumecheng-10848	96	30	=	=	X
fumecheng-10848	96	31			PROPN
fumecheng-10848	96	32	/	/	SYM
fumecheng-10848	96	33	8	8	NUM
fumecheng-10848	96	34	,	,	PUNCT
fumecheng-10848	96	35			X
fumecheng-10848	96	36	=	=	SYM
fumecheng-10848	96	37			PROPN
fumecheng-10848	96	38	/	/	SYM
fumecheng-10848	96	39	4	4	NUM
fumecheng-10848	96	40	r=10	r=10	NOUN
fumecheng-10848	96	41	,	,	PUNCT
fumecheng-10848	96	42	a=/6	a=/6	ADJ
fumecheng-10848	96	43	,	,	PUNCT
fumecheng-10848	96	44	=/4r=10	=/4r=10	NOUN
fumecheng-10848	96	45	,	,	PUNCT
fumecheng-10848	96	46	a=/6	a=/6	ADJ
fumecheng-10848	96	47	,	,	PUNCT
fumecheng-10848	96	48	=/4	=/4	PROPN
fumecheng-10848	96	49	n	n	PART
fumecheng-10848	96	50	s	s	NOUN
fumecheng-10848	96	51	h	h	NOUN
fumecheng-10848	97	1	f	f	PROPN
fumecheng-10848	97	2	s	s	PROPN
fumecheng-10848	97	3	h	h	NOUN
fumecheng-10848	97	4	f	f	NOUN
fumecheng-10848	97	5	0	0	NUM
fumecheng-10848	97	6	10	10	NUM
fumecheng-10848	97	7	20	20	NUM
fumecheng-10848	97	8	30	30	NUM
fumecheng-10848	97	9	40	40	NUM
fumecheng-10848	97	10	50	50	NUM
fumecheng-10848	97	11	60	60	NUM
fumecheng-10848	97	12	70	70	NUM
fumecheng-10848	97	13	80	80	NUM
fumecheng-10848	97	14	-0.5	-0.5	PROPN
fumecheng-10848	97	15	-0.4	-0.4	PROPN
fumecheng-10848	97	16	-0.3	-0.3	PROPN
fumecheng-10848	97	17	-0.2	-0.2	PROPN
fumecheng-10848	97	18	-0.1	-0.1	PROPN
fumecheng-10848	97	19	0	0	NUM
fumecheng-10848	97	20	0.1	0.1	NUM
fumecheng-10848	97	21	0.2	0.2	NUM
fumecheng-10848	97	22	0.3	0.3	NUM
fumecheng-10848	97	23	0.4	0.4	NUM
fumecheng-10848	97	24	0.5	0.5	NUM
fumecheng-10848	97	25	t	t	NOUN
fumecheng-10848	97	26	u	u	NOUN
fumecheng-10848	97	27	r	r	NOUN
fumecheng-10848	97	28	=	=	SYM
fumecheng-10848	97	29	10	10	NUM
fumecheng-10848	97	30	,	,	PUNCT
fumecheng-10848	97	31	a	a	DET
fumecheng-10848	97	32	=	=	X
fumecheng-10848	97	33			PROPN
fumecheng-10848	97	34	/	/	SYM
fumecheng-10848	97	35	6	6	NUM
fumecheng-10848	97	36	,	,	PUNCT
fumecheng-10848	97	37			X
fumecheng-10848	97	38	=	=	SYM
fumecheng-10848	97	39			PROPN
fumecheng-10848	97	40	/	/	SYM
fumecheng-10848	97	41	4	4	NUM
fumecheng-10848	97	42	n	n	NOUN
fumecheng-10848	97	43	s	s	NOUN
fumecheng-10848	97	44	h	h	NOUN
fumecheng-10848	97	45	f	f	PROPN
fumecheng-10848	97	46	s	s	PROPN
fumecheng-10848	97	47	h	h	NOUN
fumecheng-10848	97	48	f	f	PROPN
fumecheng-10848	97	49	a	a	DET
fumecheng-10848	97	50	circular	circular	ADJ
fumecheng-10848	97	51	sector	sector	NOUN
fumecheng-10848	97	52	vibration	vibration	NOUN
fumecheng-10848	97	53	system	system	NOUN
fumecheng-10848	97	54	in	in	ADP
fumecheng-10848	97	55	a	a	DET
fumecheng-10848	97	56	porous	porous	ADJ
fumecheng-10848	97	57	medium	medium	NOUN
fumecheng-10848	97	58	:	:	PUNCT
fumecheng-10848	97	59	a	a	DET
fumecheng-10848	97	60	fractal	fractal	ADJ
fumecheng-10848	97	61	-	-	PUNCT
fumecheng-10848	97	62	fractional	fractional	ADJ
fumecheng-10848	97	63	model	model	NOUN
fumecheng-10848	97	64	...	...	PUNCT
fumecheng-10848	97	65	383	383	NUM
fumecheng-10848	97	66	fig	fig	NOUN
fumecheng-10848	97	67	.	.	PUNCT
fumecheng-10848	98	1	5	5	NUM
fumecheng-10848	98	2	sensitivity	sensitivity	NOUN
fumecheng-10848	98	3	analysis	analysis	NOUN
fumecheng-10848	98	4	of	of	ADP
fumecheng-10848	98	5	frequency	frequency	NOUN
fumecheng-10848	98	6	(	(	PUNCT
fumecheng-10848	98	7	0	0	NUM
fumecheng-10848	98	8	<	<	X
fumecheng-10848	98	9	a	a	DET
fumecheng-10848	98	10	<	<	X
fumecheng-10848	98	11	π/4	π/4	PROPN
fumecheng-10848	98	12	,	,	PUNCT
fumecheng-10848	98	13	0	0	NUM
fumecheng-10848	98	14	<	<	X
fumecheng-10848	98	15	α	α	X
fumecheng-10848	98	16	<	<	X
fumecheng-10848	98	17	π/2	π/2	NUM
fumecheng-10848	98	18	)	)	PUNCT
fumecheng-10848	98	19	with	with	ADP
fumecheng-10848	98	20	r	r	NOUN
fumecheng-10848	98	21	=	=	SYM
fumecheng-10848	98	22	10	10	NUM
fumecheng-10848	98	23	(	(	PUNCT
fumecheng-10848	98	24	left	left	ADJ
fumecheng-10848	98	25	)	)	PUNCT
fumecheng-10848	98	26	and	and	CCONJ
fumecheng-10848	98	27	r	r	NOUN
fumecheng-10848	98	28	=	=	SYM
fumecheng-10848	98	29	15	15	NUM
fumecheng-10848	98	30	(	(	PUNCT
fumecheng-10848	98	31	right	right	ADJ
fumecheng-10848	98	32	)	)	PUNCT
fumecheng-10848	98	33	fig	fig	NOUN
fumecheng-10848	98	34	.	.	PUNCT
fumecheng-10848	99	1	6	6	NUM
fumecheng-10848	99	2	eq	eq	NOUN
fumecheng-10848	99	3	.	.	PUNCT
fumecheng-10848	100	1	(	(	PUNCT
fumecheng-10848	100	2	4	4	NUM
fumecheng-10848	100	3	)	)	PUNCT
fumecheng-10848	100	4	at	at	ADP
fumecheng-10848	100	5	different	different	ADJ
fumecheng-10848	100	6			NOUN
fumecheng-10848	100	7	values	value	NOUN
fumecheng-10848	100	8	for	for	ADP
fumecheng-10848	100	9	r=10	r=10	NOUN
fumecheng-10848	100	10	,	,	PUNCT
fumecheng-10848	100	11	a	a	DET
fumecheng-10848	100	12	=	=	NOUN
fumecheng-10848	100	13	π/6	π/6	X
fumecheng-10848	100	14	,	,	PUNCT
fumecheng-10848	100	15	α	α	NOUN
fumecheng-10848	100	16	=	=	NOUN
fumecheng-10848	100	17	π/4	π/4	PROPN
fumecheng-10848	100	18	5	5	NUM
fumecheng-10848	100	19	.	.	X
fumecheng-10848	100	20	conclusion	conclusion	NOUN
fumecheng-10848	100	21	the	the	DET
fumecheng-10848	100	22	most	most	ADV
fumecheng-10848	100	23	important	important	ADJ
fumecheng-10848	100	24	property	property	NOUN
fumecheng-10848	100	25	of	of	ADP
fumecheng-10848	100	26	a	a	DET
fumecheng-10848	100	27	fractal	fractal	ADJ
fumecheng-10848	100	28	nonlinear	nonlinear	ADJ
fumecheng-10848	100	29	system	system	NOUN
fumecheng-10848	100	30	is	be	AUX
fumecheng-10848	100	31	the	the	DET
fumecheng-10848	100	32	relationship	relationship	NOUN
fumecheng-10848	100	33	between	between	ADP
fumecheng-10848	100	34	frequency	frequency	NOUN
fumecheng-10848	100	35	and	and	CCONJ
fumecheng-10848	100	36	amplitude	amplitude	NOUN
fumecheng-10848	100	37	,	,	PUNCT
fumecheng-10848	100	38	which	which	PRON
fumecheng-10848	100	39	plays	play	VERB
fumecheng-10848	100	40	a	a	DET
fumecheng-10848	100	41	crucial	crucial	ADJ
fumecheng-10848	100	42	role	role	NOUN
fumecheng-10848	100	43	in	in	ADP
fumecheng-10848	100	44	construction	construction	NOUN
fumecheng-10848	100	45	engineering	engineering	NOUN
fumecheng-10848	100	46	.	.	PUNCT
fumecheng-10848	101	1	this	this	DET
fumecheng-10848	101	2	paper	paper	NOUN
fumecheng-10848	101	3	presents	present	VERB
fumecheng-10848	101	4	he	he	PRON
fumecheng-10848	101	5	’s	’	VERB
fumecheng-10848	101	6	frequency	frequency	NOUN
fumecheng-10848	101	7	formula	formula	NOUN
fumecheng-10848	101	8	and	and	CCONJ
fumecheng-10848	101	9	ma	ma	PROPN
fumecheng-10848	101	10	’s	’s	PART
fumecheng-10848	101	11	modification	modification	NOUN
fumecheng-10848	101	12	of	of	ADP
fumecheng-10848	101	13	hamiltonian	hamiltonian	NOUN
fumecheng-10848	101	14	-	-	PUNCT
fumecheng-10848	101	15	based	base	VERB
fumecheng-10848	101	16	frequency	frequency	NOUN
fumecheng-10848	101	17	formula	formula	NOUN
fumecheng-10848	101	18	and	and	CCONJ
fumecheng-10848	101	19	discusses	discuss	VERB
fumecheng-10848	101	20	how	how	SCONJ
fumecheng-10848	101	21	to	to	PART
fumecheng-10848	101	22	quickly	quickly	ADV
fumecheng-10848	101	23	calculate	calculate	VERB
fumecheng-10848	101	24	the	the	DET
fumecheng-10848	101	25	approximate	approximate	ADJ
fumecheng-10848	101	26	frequency	frequency	NOUN
fumecheng-10848	101	27	of	of	ADP
fumecheng-10848	101	28	the	the	DET
fumecheng-10848	101	29	fractal	fractal	ADJ
fumecheng-10848	101	30	circular	circular	ADJ
fumecheng-10848	101	31	sector	sector	NOUN
fumecheng-10848	101	32	in	in	ADP
fumecheng-10848	101	33	a	a	DET
fumecheng-10848	101	34	porous	porous	ADJ
fumecheng-10848	101	35	medium	medium	NOUN
fumecheng-10848	101	36	.	.	PUNCT
fumecheng-10848	102	1	the	the	DET
fumecheng-10848	102	2	result	result	NOUN
fumecheng-10848	102	3	shows	show	VERB
fumecheng-10848	102	4	that	that	SCONJ
fumecheng-10848	102	5	two	two	NUM
fumecheng-10848	102	6	methods	method	NOUN
fumecheng-10848	102	7	are	be	AUX
fumecheng-10848	102	8	accurate	accurate	ADJ
fumecheng-10848	102	9	tools	tool	NOUN
fumecheng-10848	102	10	to	to	PART
fumecheng-10848	102	11	quickly	quickly	ADV
fumecheng-10848	102	12	calculating	calculate	VERB
fumecheng-10848	102	13	the	the	DET
fumecheng-10848	102	14	periodic	periodic	ADJ
fumecheng-10848	102	15	properties	property	NOUN
fumecheng-10848	102	16	of	of	ADP
fumecheng-10848	102	17	fractal	fractal	ADJ
fumecheng-10848	102	18	nonlinear	nonlinear	ADJ
fumecheng-10848	102	19	oscillators	oscillator	NOUN
fumecheng-10848	102	20	,	,	PUNCT
fumecheng-10848	102	21	and	and	CCONJ
fumecheng-10848	102	22	that	that	SCONJ
fumecheng-10848	102	23	the	the	DET
fumecheng-10848	102	24	fractal	fractal	ADJ
fumecheng-10848	102	25	dimension	dimension	NOUN
fumecheng-10848	102	26	of	of	ADP
fumecheng-10848	102	27	a	a	DET
fumecheng-10848	102	28	porous	porous	ADJ
fumecheng-10848	102	29	medium	medium	NOUN
fumecheng-10848	102	30	plays	play	VERB
fumecheng-10848	102	31	an	an	DET
fumecheng-10848	102	32	important	important	ADJ
fumecheng-10848	102	33	role	role	NOUN
fumecheng-10848	102	34	in	in	ADP
fumecheng-10848	102	35	vibration	vibration	NOUN
fumecheng-10848	102	36	attenuation	attenuation	NOUN
fumecheng-10848	102	37	.	.	PUNCT
fumecheng-10848	103	1	both	both	DET
fumecheng-10848	103	2	the	the	DET
fumecheng-10848	103	3	frequency	frequency	NOUN
fumecheng-10848	103	4	formulations	formulation	NOUN
fumecheng-10848	103	5	will	will	AUX
fumecheng-10848	103	6	play	play	VERB
fumecheng-10848	103	7	an	an	DET
fumecheng-10848	103	8	important	important	ADJ
fumecheng-10848	103	9	role	role	NOUN
fumecheng-10848	103	10	in	in	ADP
fumecheng-10848	103	11	the	the	DET
fumecheng-10848	103	12	fractal	fractal	ADJ
fumecheng-10848	103	13	nonlinear	nonlinear	ADJ
fumecheng-10848	103	14	vibration	vibration	NOUN
fumecheng-10848	103	15	theory	theory	NOUN
fumecheng-10848	103	16	and	and	CCONJ
fumecheng-10848	103	17	open	open	VERB
fumecheng-10848	103	18	up	up	ADP
fumecheng-10848	103	19	numerous	numerous	ADJ
fumecheng-10848	103	20	opportunities	opportunity	NOUN
fumecheng-10848	103	21	to	to	PART
fumecheng-10848	103	22	elucidate	elucidate	VERB
fumecheng-10848	103	23	the	the	DET
fumecheng-10848	103	24	effect	effect	NOUN
fumecheng-10848	103	25	of	of	ADP
fumecheng-10848	103	26	the	the	DET
fumecheng-10848	103	27	porous	porous	ADJ
fumecheng-10848	103	28	medium	medium	NOUN
fumecheng-10848	103	29	’s	’s	NOUN
fumecheng-10848	103	30	geometry	geometry	NOUN
fumecheng-10848	103	31	on	on	ADP
fumecheng-10848	103	32	the	the	DET
fumecheng-10848	103	33	vibration	vibration	NOUN
fumecheng-10848	103	34	property	property	NOUN
fumecheng-10848	103	35	,	,	PUNCT
fumecheng-10848	103	36	and	and	CCONJ
fumecheng-10848	103	37	also	also	ADV
fumecheng-10848	103	38	probably	probably	ADV
fumecheng-10848	103	39	pave	pave	VERB
fumecheng-10848	103	40	a	a	DET
fumecheng-10848	103	41	new	new	ADJ
fumecheng-10848	103	42	avenue	avenue	NOUN
fumecheng-10848	103	43	for	for	ADP
fumecheng-10848	103	44	optimizing	optimize	VERB
fumecheng-10848	103	45	the	the	DET
fumecheng-10848	103	46	circular	circular	ADJ
fumecheng-10848	103	47	sector	sector	NOUN
fumecheng-10848	103	48	in	in	ADP
fumecheng-10848	103	49	a	a	DET
fumecheng-10848	103	50	nanofluid	nanofluid	NOUN
fumecheng-10848	103	51	[	[	X
fumecheng-10848	103	52	51	51	NUM
fumecheng-10848	103	53	]	]	PUNCT
fumecheng-10848	103	54	where	where	SCONJ
fumecheng-10848	103	55	the	the	DET
fumecheng-10848	103	56	nanoparticles	nanoparticle	NOUN
fumecheng-10848	103	57	’	'	PUNCT
fumecheng-10848	103	58	size	size	NOUN
fumecheng-10848	103	59	and	and	CCONJ
fumecheng-10848	103	60	distribution	distribution	NOUN
fumecheng-10848	103	61	can	can	AUX
fumecheng-10848	103	62	be	be	AUX
fumecheng-10848	103	63	effectively	effectively	ADV
fumecheng-10848	103	64	modelled	model	VERB
fumecheng-10848	103	65	by	by	ADP
fumecheng-10848	103	66	the	the	DET
fumecheng-10848	103	67	fractal	fractal	ADJ
fumecheng-10848	103	68	-	-	PUNCT
fumecheng-10848	103	69	fractional	fractional	ADJ
fumecheng-10848	103	70	model	model	NOUN
fumecheng-10848	103	71	.	.	PUNCT
fumecheng-10848	104	1	0	0	NUM
fumecheng-10848	104	2	0.2	0.2	NUM
fumecheng-10848	104	3	0.4	0.4	NUM
fumecheng-10848	104	4	0.6	0.6	NUM
fumecheng-10848	104	5	0.8	0.8	NUM
fumecheng-10848	104	6	0	0	NUM
fumecheng-10848	104	7	0.4	0.4	NUM
fumecheng-10848	104	8	0.8	0.8	NUM
fumecheng-10848	104	9	1.2	1.2	NUM
fumecheng-10848	104	10	1.6	1.6	NUM
fumecheng-10848	104	11	0.16	0.16	NUM
fumecheng-10848	104	12	0.17	0.17	NUM
fumecheng-10848	104	13	0.18	0.18	NUM
fumecheng-10848	104	14	0.19	0.19	NUM
fumecheng-10848	104	15	0.2	0.2	NUM
fumecheng-10848	104	16	0.21	0.21	NUM
fumecheng-10848	104	17	0.22	0.22	NUM
fumecheng-10848	104	18	aα	aα	NOUN
fumecheng-10848	105	1	fr	fr	NOUN
fumecheng-10848	105	2	e	e	NOUN
fumecheng-10848	105	3	q	q	PUNCT
fumecheng-10848	105	4	u	u	X
fumecheng-10848	105	5	e	e	PROPN
fumecheng-10848	105	6	n	n	NOUN
fumecheng-10848	105	7	cy	cy	PROPN
fumecheng-10848	105	8	0.17	0.17	NUM
fumecheng-10848	105	9	0.18	0.18	NUM
fumecheng-10848	105	10	0.19	0.19	NUM
fumecheng-10848	105	11	0.2	0.2	NUM
fumecheng-10848	105	12	0.21	0.21	NUM
fumecheng-10848	105	13	0	0	NUM
fumecheng-10848	105	14	0.2	0.2	NUM
fumecheng-10848	105	15	0.4	0.4	NUM
fumecheng-10848	105	16	0.6	0.6	NUM
fumecheng-10848	105	17	0	0	NUM
fumecheng-10848	105	18	0.4	0.4	NUM
fumecheng-10848	105	19	0.8	0.8	NUM
fumecheng-10848	105	20	1.2	1.2	NUM
fumecheng-10848	105	21	1.6	1.6	NUM
fumecheng-10848	105	22	0.1	0.1	NUM
fumecheng-10848	105	23	0.11	0.11	NUM
fumecheng-10848	105	24	0.12	0.12	NUM
fumecheng-10848	105	25	0.13	0.13	NUM
fumecheng-10848	105	26	0.14	0.14	NUM
fumecheng-10848	105	27	0.15	0.15	NUM
fumecheng-10848	105	28	aα	aα	NOUN
fumecheng-10848	105	29	fre	fre	ADJ
fumecheng-10848	105	30	qu	qu	X
fumecheng-10848	105	31	en	en	PROPN
fumecheng-10848	105	32	cy	cy	PROPN
fumecheng-10848	105	33	0.11	0.11	NUM
fumecheng-10848	105	34	0.115	0.115	NUM
fumecheng-10848	105	35	0.12	0.12	NUM
fumecheng-10848	105	36	0.125	0.125	NUM
fumecheng-10848	105	37	0.13	0.13	NUM
fumecheng-10848	105	38	0.135	0.135	NUM
fumecheng-10848	105	39	0	0	NUM
fumecheng-10848	105	40	5	5	NUM
fumecheng-10848	105	41	10	10	NUM
fumecheng-10848	105	42	15	15	NUM
fumecheng-10848	105	43	20	20	NUM
fumecheng-10848	105	44	25	25	NUM
fumecheng-10848	105	45	30	30	NUM
fumecheng-10848	105	46	35	35	NUM
fumecheng-10848	105	47	40	40	NUM
fumecheng-10848	105	48	-0.4	-0.4	NUM
fumecheng-10848	105	49	-0.2	-0.2	PROPN
fumecheng-10848	105	50	0	0	NUM
fumecheng-10848	105	51	0.2	0.2	NUM
fumecheng-10848	105	52	0.4	0.4	NUM
fumecheng-10848	105	53	0.6	0.6	NUM
fumecheng-10848	105	54			NOUN
fumecheng-10848	105	55	u	u	NOUN
fumecheng-10848	105	56	θ=0.7	θ=0.7	X
fumecheng-10848	105	57	θ=0.9	θ=0.9	VERB
fumecheng-10848	105	58	θ=1	θ=1	ADP
fumecheng-10848	105	59	θ=1.1	θ=1.1	NOUN
fumecheng-10848	105	60	θ=1.3	θ=1.3	PROPN
fumecheng-10848	105	61	384	384	NUM
fumecheng-10848	105	62	g.	g.	PROPN
fumecheng-10848	105	63	feng	feng	PROPN
fumecheng-10848	105	64	references	reference	NOUN
fumecheng-10848	105	65	1	1	NUM
fumecheng-10848	105	66	.	.	PUNCT
fumecheng-10848	105	67	ahad	ahad	PROPN
fumecheng-10848	105	68	,	,	PUNCT
fumecheng-10848	105	69	f.e	f.e	PROPN
fumecheng-10848	105	70	.	.	PROPN
fumecheng-10848	105	71	,	,	PUNCT
fumecheng-10848	105	72	shi	shi	PROPN
fumecheng-10848	105	73	,	,	PUNCT
fumecheng-10848	105	74	d.	d.	PROPN
fumecheng-10848	105	75	,	,	PUNCT
fumecheng-10848	105	76	aftab	aftab	PROPN
fumecheng-10848	105	77	,	,	PUNCT
fumecheng-10848	105	78	s.m	s.m	PROPN
fumecheng-10848	105	79	.	.	PROPN
fumecheng-10848	105	80	,	,	PUNCT
fumecheng-10848	105	81	waqas	waqas	PROPN
fumecheng-10848	105	82	,	,	PUNCT
fumecheng-10848	105	83	h.m	h.m	PROPN
fumecheng-10848	105	84	.	.	PROPN
fumecheng-10848	105	85	,	,	PUNCT
fumecheng-10848	105	86	2019	2019	NUM
fumecheng-10848	105	87	,	,	PUNCT
fumecheng-10848	105	88	an	an	DET
fumecheng-10848	105	89	improved	improved	ADJ
fumecheng-10848	105	90	fourier	fourier	NOUN
fumecheng-10848	105	91	series	series	NOUN
fumecheng-10848	105	92	method	method	NOUN
fumecheng-10848	105	93	for	for	ADP
fumecheng-10848	105	94	vibration	vibration	NOUN
fumecheng-10848	105	95	analysis	analysis	NOUN
fumecheng-10848	105	96	of	of	ADP
fumecheng-10848	105	97	moderately	moderately	ADV
fumecheng-10848	105	98	thick	thick	ADJ
fumecheng-10848	105	99	annular	annular	ADJ
fumecheng-10848	105	100	and	and	CCONJ
fumecheng-10848	105	101	circular	circular	ADJ
fumecheng-10848	105	102	sector	sector	NOUN
fumecheng-10848	105	103	plates	plate	NOUN
fumecheng-10848	105	104	subjected	subject	VERB
fumecheng-10848	105	105	to	to	ADP
fumecheng-10848	105	106	elastic	elastic	ADJ
fumecheng-10848	105	107	boundary	boundary	ADJ
fumecheng-10848	105	108	conditions	condition	NOUN
fumecheng-10848	105	109	,	,	PUNCT
fumecheng-10848	105	110	journal	journal	NOUN
fumecheng-10848	105	111	of	of	ADP
fumecheng-10848	105	112	vibroengineering	vibroengineere	VERB
fumecheng-10848	105	113	,	,	PUNCT
fumecheng-10848	105	114	18(6	18(6	NOUN
fumecheng-10848	105	115	)	)	PUNCT
fumecheng-10848	105	116	,	,	PUNCT
fumecheng-10848	105	117	pp.3841	pp.3841	PROPN
fumecheng-10848	105	118	-	-	PUNCT
fumecheng-10848	105	119	3857	3857	NUM
fumecheng-10848	105	120	.	.	PUNCT
fumecheng-10848	106	1	2	2	X
fumecheng-10848	106	2	.	.	X
fumecheng-10848	106	3	aboutalebi	aboutalebi	PROPN
fumecheng-10848	106	4	,	,	PUNCT
fumecheng-10848	106	5	r.	r.	PROPN
fumecheng-10848	106	6	,	,	PUNCT
fumecheng-10848	106	7	eshaghi	eshaghi	PROPN
fumecheng-10848	106	8	,	,	PUNCT
fumecheng-10848	106	9	m.	m.	NOUN
fumecheng-10848	106	10	,	,	PUNCT
fumecheng-10848	106	11	taghvaeipour	taghvaeipour	ADJ
fumecheng-10848	106	12	,	,	PUNCT
fumecheng-10848	106	13	a.	a.	NOUN
fumecheng-10848	106	14	,	,	PUNCT
fumecheng-10848	106	15	2021	2021	NUM
fumecheng-10848	106	16	,	,	PUNCT
fumecheng-10848	106	17	nonlinear	nonlinear	ADJ
fumecheng-10848	106	18	vibration	vibration	NOUN
fumecheng-10848	106	19	analysis	analysis	NOUN
fumecheng-10848	106	20	of	of	ADP
fumecheng-10848	106	21	circular	circular	ADJ
fumecheng-10848	106	22	/	/	SYM
fumecheng-10848	106	23	annular	annular	ADJ
fumecheng-10848	106	24	/	/	SYM
fumecheng-10848	106	25	sector	sector	NOUN
fumecheng-10848	106	26	sandwich	sandwich	NOUN
fumecheng-10848	106	27	panels	panel	NOUN
fumecheng-10848	106	28	incorporating	incorporate	VERB
fumecheng-10848	106	29	magnetorheological	magnetorheological	ADJ
fumecheng-10848	106	30	fluid	fluid	NOUN
fumecheng-10848	106	31	operating	operating	NOUN
fumecheng-10848	106	32	in	in	ADP
fumecheng-10848	106	33	the	the	DET
fumecheng-10848	106	34	post	post	ADJ
fumecheng-10848	106	35	-	-	ADJ
fumecheng-10848	106	36	yield	yield	ADJ
fumecheng-10848	106	37	region	region	NOUN
fumecheng-10848	106	38	,	,	PUNCT
fumecheng-10848	106	39	journal	journal	NOUN
fumecheng-10848	106	40	of	of	ADP
fumecheng-10848	106	41	intelligent	intelligent	ADJ
fumecheng-10848	106	42	material	material	NOUN
fumecheng-10848	106	43	systems	system	NOUN
fumecheng-10848	106	44	and	and	CCONJ
fumecheng-10848	106	45	structures	structure	NOUN
fumecheng-10848	106	46	,	,	PUNCT
fumecheng-10848	106	47	32(7	32(7	NOUN
fumecheng-10848	106	48	)	)	PUNCT
fumecheng-10848	106	49	,	,	PUNCT
fumecheng-10848	106	50	pp	pp	ADJ
fumecheng-10848	106	51	.	.	PUNCT
fumecheng-10848	107	1	781	781	NUM
fumecheng-10848	107	2	-	-	SYM
fumecheng-10848	107	3	796	796	NUM
fumecheng-10848	107	4	.	.	PUNCT
fumecheng-10848	108	1	3	3	NUM
fumecheng-10848	108	2	.	.	NUM
fumecheng-10848	108	3	hiraoka	hiraoka	NOUN
fumecheng-10848	108	4	,	,	PUNCT
fumecheng-10848	108	5	t.	t.	PROPN
fumecheng-10848	108	6	,	,	PUNCT
fumecheng-10848	108	7	2020	2020	NUM
fumecheng-10848	108	8	,	,	PUNCT
fumecheng-10848	108	9	generation	generation	NOUN
fumecheng-10848	108	10	of	of	ADP
fumecheng-10848	108	11	arbitrarily	arbitrarily	ADV
fumecheng-10848	108	12	-	-	PUNCT
fumecheng-10848	108	13	oriented	orient	VERB
fumecheng-10848	108	14	ripple	ripple	ADJ
fumecheng-10848	108	15	images	image	NOUN
fumecheng-10848	108	16	using	use	VERB
fumecheng-10848	108	17	circular	circular	ADJ
fumecheng-10848	108	18	-	-	PUNCT
fumecheng-10848	108	19	sector	sector	NOUN
fumecheng-10848	108	20	-	-	PUNCT
fumecheng-10848	108	21	type	type	NOUN
fumecheng-10848	108	22	smoothing	smooth	VERB
fumecheng-10848	108	23	filter	filter	NOUN
fumecheng-10848	108	24	and	and	CCONJ
fumecheng-10848	108	25	inverse	inverse	NOUN
fumecheng-10848	108	26	filter	filter	NOUN
fumecheng-10848	108	27	,	,	PUNCT
fumecheng-10848	108	28	journal	journal	NOUN
fumecheng-10848	108	29	of	of	ADP
fumecheng-10848	108	30	robotics	robotic	NOUN
fumecheng-10848	108	31	networking	networking	NOUN
fumecheng-10848	108	32	and	and	CCONJ
fumecheng-10848	108	33	artificial	artificial	ADJ
fumecheng-10848	108	34	life	life	NOUN
fumecheng-10848	108	35	,	,	PUNCT
fumecheng-10848	108	36	6(4	6(4	NOUN
fumecheng-10848	108	37	)	)	PUNCT
fumecheng-10848	108	38	,	,	PUNCT
fumecheng-10848	108	39	pp	pp	PROPN
fumecheng-10848	108	40	.	.	PUNCT
fumecheng-10848	109	1	213	213	NUM
fumecheng-10848	109	2	-	-	SYM
fumecheng-10848	109	3	216	216	NUM
fumecheng-10848	109	4	.	.	NOUN
fumecheng-10848	109	5	4	4	NUM
fumecheng-10848	109	6	.	.	X
fumecheng-10848	109	7	tang	tang	PROPN
fumecheng-10848	109	8	,	,	PUNCT
fumecheng-10848	109	9	w.s	w.s	PROPN
fumecheng-10848	109	10	.	.	PROPN
fumecheng-10848	109	11	,	,	PUNCT
fumecheng-10848	109	12	xiang	xiang	PROPN
fumecheng-10848	109	13	,	,	PUNCT
fumecheng-10848	109	14	b.j	b.j	PROPN
fumecheng-10848	109	15	.	.	PROPN
fumecheng-10848	109	16	,	,	PUNCT
fumecheng-10848	109	17	zheng	zheng	PROPN
fumecheng-10848	109	18	,	,	PUNCT
fumecheng-10848	109	19	s.y	s.y	PROPN
fumecheng-10848	109	20	.	.	PROPN
fumecheng-10848	109	21	,	,	PUNCT
fumecheng-10848	109	22	long	long	ADV
fumecheng-10848	109	23	,	,	PUNCT
fumecheng-10848	109	24	y.l	y.l	PROPN
fumecheng-10848	109	25	.	.	PROPN
fumecheng-10848	109	26	,	,	PUNCT
fumecheng-10848	109	27	2021	2021	NUM
fumecheng-10848	109	28	,	,	PUNCT
fumecheng-10848	109	29	design	design	NOUN
fumecheng-10848	109	30	of	of	ADP
fumecheng-10848	109	31	wideband	wideband	NOUN
fumecheng-10848	109	32	/	/	SYM
fumecheng-10848	109	33	dual	dual	ADJ
fumecheng-10848	109	34	-	-	PUNCT
fumecheng-10848	109	35	band	band	NOUN
fumecheng-10848	109	36	bandpass	bandpass	NOUN
fumecheng-10848	109	37	filter	filter	NOUN
fumecheng-10848	109	38	using	use	VERB
fumecheng-10848	109	39	a	a	DET
fumecheng-10848	109	40	vias	via	NOUN
fumecheng-10848	109	41	and	and	CCONJ
fumecheng-10848	109	42	slots	slot	NOUN
fumecheng-10848	109	43	loaded	load	VERB
fumecheng-10848	109	44	sector	sector	NOUN
fumecheng-10848	109	45	circular	circular	ADJ
fumecheng-10848	109	46	patch	patch	NOUN
fumecheng-10848	109	47	resonator	resonator	NOUN
fumecheng-10848	109	48	,	,	PUNCT
fumecheng-10848	109	49	international	international	ADJ
fumecheng-10848	109	50	journal	journal	NOUN
fumecheng-10848	109	51	of	of	ADP
fumecheng-10848	109	52	rf	rf	NOUN
fumecheng-10848	109	53	and	and	CCONJ
fumecheng-10848	109	54	microwave	microwave	NOUN
fumecheng-10848	109	55	computeraided	computeraide	VERB
fumecheng-10848	109	56	engineering	engineering	NOUN
fumecheng-10848	109	57	,	,	PUNCT
fumecheng-10848	109	58	31(7	31(7	NUM
fumecheng-10848	109	59	)	)	PUNCT
fumecheng-10848	109	60	,	,	PUNCT
fumecheng-10848	109	61	e22681	e22681	ADV
fumecheng-10848	109	62	.	.	PUNCT
fumecheng-10848	110	1	5	5	X
fumecheng-10848	110	2	.	.	X
fumecheng-10848	110	3	he	he	PRON
fumecheng-10848	110	4	,	,	PUNCT
fumecheng-10848	110	5	j.h	j.h	PROPN
fumecheng-10848	110	6	.	.	PROPN
fumecheng-10848	110	7	,	,	PUNCT
fumecheng-10848	110	8	kou	kou	PROPN
fumecheng-10848	110	9	,	,	PUNCT
fumecheng-10848	110	10	s.j	s.j	PROPN
fumecheng-10848	110	11	.	.	PROPN
fumecheng-10848	110	12	,	,	PUNCT
fumecheng-10848	110	13	he	he	PRON
fumecheng-10848	110	14	,	,	PUNCT
fumecheng-10848	110	15	c.h	c.h	PROPN
fumecheng-10848	110	16	.	.	PROPN
fumecheng-10848	110	17	,	,	PUNCT
fumecheng-10848	110	18	zhang	zhang	PROPN
fumecheng-10848	110	19	,	,	PUNCT
fumecheng-10848	110	20	z.w	z.w	PROPN
fumecheng-10848	110	21	.	.	PROPN
fumecheng-10848	110	22	,	,	PUNCT
fumecheng-10848	110	23	gepreel	gepreel	PROPN
fumecheng-10848	110	24	,	,	PUNCT
fumecheng-10848	110	25	k.a	k.a	PROPN
fumecheng-10848	110	26	.	.	PROPN
fumecheng-10848	110	27	,	,	PUNCT
fumecheng-10848	110	28	2021	2021	NUM
fumecheng-10848	110	29	,	,	PUNCT
fumecheng-10848	110	30	fractal	fractal	ADJ
fumecheng-10848	110	31	oscillation	oscillation	NOUN
fumecheng-10848	110	32	and	and	CCONJ
fumecheng-10848	110	33	its	its	PRON
fumecheng-10848	110	34	frequency	frequency	NOUN
fumecheng-10848	110	35	-	-	PUNCT
fumecheng-10848	110	36	amplitude	amplitude	NOUN
fumecheng-10848	110	37	property	property	NOUN
fumecheng-10848	110	38	,	,	PUNCT
fumecheng-10848	110	39	fractals	fractal	NOUN
fumecheng-10848	110	40	,	,	PUNCT
fumecheng-10848	110	41	29(4	29(4	NOUN
fumecheng-10848	110	42	)	)	PUNCT
fumecheng-10848	110	43	,	,	PUNCT
fumecheng-10848	110	44	2150105	2150105	NUM
fumecheng-10848	110	45	.	.	PUNCT
fumecheng-10848	111	1	6	6	NUM
fumecheng-10848	111	2	.	.	X
fumecheng-10848	111	3	chen	chen	PROPN
fumecheng-10848	111	4	,	,	PUNCT
fumecheng-10848	111	5	l.c	l.c	PROPN
fumecheng-10848	111	6	.	.	PROPN
fumecheng-10848	111	7	,	,	PUNCT
fumecheng-10848	111	8	wang	wang	PROPN
fumecheng-10848	111	9	,	,	PUNCT
fumecheng-10848	111	10	w.h	w.h	PROPN
fumecheng-10848	111	11	.	.	PROPN
fumecheng-10848	111	12	,	,	PUNCT
fumecheng-10848	111	13	li	li	PROPN
fumecheng-10848	111	14	,	,	PUNCT
fumecheng-10848	111	15	z.s	z.s	PROPN
fumecheng-10848	111	16	.	.	PROPN
fumecheng-10848	111	17	,	,	PUNCT
fumecheng-10848	111	18	zhu	zhu	PROPN
fumecheng-10848	111	19	,	,	PUNCT
fumecheng-10848	111	20	w.q	w.q	PROPN
fumecheng-10848	111	21	.	.	PROPN
fumecheng-10848	111	22	,	,	PUNCT
fumecheng-10848	111	23	2013	2013	NUM
fumecheng-10848	111	24	,	,	PUNCT
fumecheng-10848	111	25	stationary	stationary	ADJ
fumecheng-10848	111	26	response	response	NOUN
fumecheng-10848	111	27	of	of	ADP
fumecheng-10848	111	28	duffing	duffe	VERB
fumecheng-10848	111	29	oscillator	oscillator	NOUN
fumecheng-10848	111	30	with	with	ADP
fumecheng-10848	111	31	hardening	harden	VERB
fumecheng-10848	111	32	stiffness	stiffness	NOUN
fumecheng-10848	111	33	and	and	CCONJ
fumecheng-10848	111	34	fractional	fractional	ADJ
fumecheng-10848	111	35	derivative	derivative	ADJ
fumecheng-10848	111	36	,	,	PUNCT
fumecheng-10848	111	37	international	international	ADJ
fumecheng-10848	111	38	journal	journal	NOUN
fumecheng-10848	111	39	of	of	ADP
fumecheng-10848	111	40	non	non	ADJ
fumecheng-10848	111	41	-	-	ADJ
fumecheng-10848	111	42	linear	linear	ADJ
fumecheng-10848	111	43	mechanics	mechanic	NOUN
fumecheng-10848	111	44	,	,	PUNCT
fumecheng-10848	111	45	48	48	NUM
fumecheng-10848	111	46	,	,	PUNCT
fumecheng-10848	111	47	pp	pp	ADJ
fumecheng-10848	111	48	.	.	PUNCT
fumecheng-10848	112	1	44	44	NUM
fumecheng-10848	112	2	-	-	SYM
fumecheng-10848	112	3	50	50	NUM
fumecheng-10848	112	4	.	.	PUNCT
fumecheng-10848	113	1	7	7	X
fumecheng-10848	113	2	.	.	X
fumecheng-10848	113	3	chen	chen	PROPN
fumecheng-10848	113	4	,	,	PUNCT
fumecheng-10848	113	5	l.c	l.c	PROPN
fumecheng-10848	113	6	.	.	PROPN
fumecheng-10848	113	7	,	,	PUNCT
fumecheng-10848	113	8	li	li	PROPN
fumecheng-10848	113	9	,	,	PUNCT
fumecheng-10848	113	10	z.s	z.s	PROPN
fumecheng-10848	113	11	.	.	PROPN
fumecheng-10848	113	12	,	,	PUNCT
fumecheng-10848	113	13	zhuang	zhuang	PROPN
fumecheng-10848	113	14	,	,	PUNCT
fumecheng-10848	113	15	q.q	q.q	PROPN
fumecheng-10848	113	16	.	.	PROPN
fumecheng-10848	113	17	,	,	PUNCT
fumecheng-10848	113	18	zhu	zhu	PROPN
fumecheng-10848	113	19	,	,	PUNCT
fumecheng-10848	113	20	w.q	w.q	PROPN
fumecheng-10848	113	21	.	.	PROPN
fumecheng-10848	113	22	,	,	PUNCT
fumecheng-10848	113	23	2013	2013	NUM
fumecheng-10848	113	24	,	,	PUNCT
fumecheng-10848	113	25	first	first	ADJ
fumecheng-10848	113	26	-	-	PUNCT
fumecheng-10848	113	27	passage	passage	NOUN
fumecheng-10848	113	28	failure	failure	NOUN
fumecheng-10848	113	29	of	of	ADP
fumecheng-10848	113	30	single	single	ADJ
fumecheng-10848	113	31	-	-	PUNCT
fumecheng-10848	113	32	degree	degree	NOUN
fumecheng-10848	113	33	-	-	PUNCT
fumecheng-10848	113	34	of	of	ADP
fumecheng-10848	113	35	-	-	PUNCT
fumecheng-10848	113	36	freedom	freedom	NOUN
fumecheng-10848	113	37	nonlinear	nonlinear	ADJ
fumecheng-10848	113	38	oscillators	oscillator	NOUN
fumecheng-10848	113	39	with	with	ADP
fumecheng-10848	113	40	fractional	fractional	ADJ
fumecheng-10848	113	41	derivative	derivative	ADJ
fumecheng-10848	113	42	,	,	PUNCT
fumecheng-10848	113	43	journal	journal	NOUN
fumecheng-10848	113	44	of	of	ADP
fumecheng-10848	113	45	vibration	vibration	NOUN
fumecheng-10848	113	46	and	and	CCONJ
fumecheng-10848	113	47	control	control	NOUN
fumecheng-10848	113	48	,	,	PUNCT
fumecheng-10848	113	49	19(14	19(14	NOUN
fumecheng-10848	113	50	)	)	PUNCT
fumecheng-10848	113	51	,	,	PUNCT
fumecheng-10848	113	52	pp	pp	ADP
fumecheng-10848	113	53	.	.	PUNCT
fumecheng-10848	114	1	2154	2154	NUM
fumecheng-10848	114	2	-	-	SYM
fumecheng-10848	114	3	2163	2163	NUM
fumecheng-10848	114	4	.	.	PUNCT
fumecheng-10848	115	1	8	8	NUM
fumecheng-10848	115	2	.	.	X
fumecheng-10848	115	3	shen	shen	PROPN
fumecheng-10848	115	4	,	,	PUNCT
fumecheng-10848	115	5	y.j	y.j	PROPN
fumecheng-10848	115	6	.	.	PROPN
fumecheng-10848	115	7	,	,	PUNCT
fumecheng-10848	115	8	yang	yang	PROPN
fumecheng-10848	115	9	,	,	PUNCT
fumecheng-10848	115	10	s.p	s.p	PROPN
fumecheng-10848	115	11	.	.	PROPN
fumecheng-10848	115	12	,	,	PUNCT
fumecheng-10848	115	13	xing	xing	PROPN
fumecheng-10848	115	14	,	,	PUNCT
fumecheng-10848	115	15	h.j	h.j	PROPN
fumecheng-10848	115	16	.	.	PROPN
fumecheng-10848	115	17	,	,	PUNCT
fumecheng-10848	115	18	ma	ma	PROPN
fumecheng-10848	115	19	,	,	PUNCT
fumecheng-10848	115	20	h.x	h.x	PROPN
fumecheng-10848	115	21	.	.	PROPN
fumecheng-10848	115	22	,	,	PUNCT
fumecheng-10848	115	23	2012	2012	NUM
fumecheng-10848	115	24	,	,	PUNCT
fumecheng-10848	115	25	primary	primary	ADJ
fumecheng-10848	115	26	resonance	resonance	NOUN
fumecheng-10848	115	27	of	of	ADP
fumecheng-10848	115	28	duffing	duffe	VERB
fumecheng-10848	115	29	oscillator	oscillator	NOUN
fumecheng-10848	115	30	with	with	ADP
fumecheng-10848	115	31	two	two	NUM
fumecheng-10848	115	32	kinds	kind	NOUN
fumecheng-10848	115	33	of	of	ADP
fumecheng-10848	115	34	fractional	fractional	ADJ
fumecheng-10848	115	35	-	-	PUNCT
fumecheng-10848	115	36	order	order	NOUN
fumecheng-10848	115	37	derivatives	derivative	NOUN
fumecheng-10848	115	38	,	,	PUNCT
fumecheng-10848	115	39	international	international	ADJ
fumecheng-10848	115	40	journal	journal	NOUN
fumecheng-10848	115	41	of	of	ADP
fumecheng-10848	115	42	non	non	ADJ
fumecheng-10848	115	43	-	-	ADJ
fumecheng-10848	115	44	linear	linear	ADJ
fumecheng-10848	115	45	mechanics	mechanic	NOUN
fumecheng-10848	115	46	,	,	PUNCT
fumecheng-10848	115	47	47	47	NUM
fumecheng-10848	115	48	,	,	PUNCT
fumecheng-10848	115	49	pp	pp	ADJ
fumecheng-10848	115	50	.	.	PUNCT
fumecheng-10848	116	1	975	975	NUM
fumecheng-10848	116	2	-	-	SYM
fumecheng-10848	116	3	983	983	NUM
fumecheng-10848	116	4	.	.	PUNCT
fumecheng-10848	117	1	9	9	X
fumecheng-10848	117	2	.	.	X
fumecheng-10848	118	1	he	he	PRON
fumecheng-10848	118	2	,	,	PUNCT
fumecheng-10848	118	3	c.h	c.h	PROPN
fumecheng-10848	118	4	.	.	PROPN
fumecheng-10848	118	5	,	,	PUNCT
fumecheng-10848	118	6	liu	liu	PROPN
fumecheng-10848	118	7	,	,	PUNCT
fumecheng-10848	118	8	c.	c.	PROPN
fumecheng-10848	118	9	,	,	PUNCT
fumecheng-10848	118	10	2022	2022	NUM
fumecheng-10848	118	11	,	,	PUNCT
fumecheng-10848	118	12	a	a	DET
fumecheng-10848	118	13	modified	modify	VERB
fumecheng-10848	118	14	frequency	frequency	NOUN
fumecheng-10848	118	15	-	-	PUNCT
fumecheng-10848	118	16	amplitude	amplitude	NOUN
fumecheng-10848	118	17	formulation	formulation	NOUN
fumecheng-10848	118	18	for	for	ADP
fumecheng-10848	118	19	fractal	fractal	ADJ
fumecheng-10848	118	20	vibration	vibration	NOUN
fumecheng-10848	118	21	systems	system	NOUN
fumecheng-10848	118	22	,	,	PUNCT
fumecheng-10848	118	23	fractals	fractal	NOUN
fumecheng-10848	118	24	,	,	PUNCT
fumecheng-10848	118	25	30(3	30(3	NUM
fumecheng-10848	118	26	)	)	PUNCT
fumecheng-10848	118	27	,	,	PUNCT
fumecheng-10848	118	28	2250046	2250046	NUM
fumecheng-10848	118	29	.	.	PUNCT
fumecheng-10848	119	1	10	10	NUM
fumecheng-10848	119	2	.	.	PUNCT
fumecheng-10848	120	1	feng	feng	PROPN
fumecheng-10848	120	2	,	,	PUNCT
fumecheng-10848	120	3	g.q	g.q	PROPN
fumecheng-10848	120	4	.	.	PROPN
fumecheng-10848	120	5	,	,	PUNCT
fumecheng-10848	120	6	niu	niu	PROPN
fumecheng-10848	120	7	,	,	PUNCT
fumecheng-10848	120	8	j.y	j.y	PROPN
fumecheng-10848	120	9	.	.	PROPN
fumecheng-10848	120	10	,	,	PUNCT
fumecheng-10848	120	11	2023	2023	NUM
fumecheng-10848	120	12	,	,	PUNCT
fumecheng-10848	120	13	an	an	DET
fumecheng-10848	120	14	analytical	analytical	ADJ
fumecheng-10848	120	15	solution	solution	NOUN
fumecheng-10848	120	16	of	of	ADP
fumecheng-10848	120	17	the	the	DET
fumecheng-10848	120	18	fractal	fractal	ADJ
fumecheng-10848	120	19	toda	toda	PROPN
fumecheng-10848	120	20	oscillator	oscillator	PROPN
fumecheng-10848	120	21	,	,	PUNCT
fumecheng-10848	120	22	results	result	NOUN
fumecheng-10848	120	23	in	in	ADP
fumecheng-10848	120	24	physics	physics	NOUN
fumecheng-10848	120	25	,	,	PUNCT
fumecheng-10848	120	26	44,106208	44,106208	NOUN
fumecheng-10848	120	27	.	.	PUNCT
fumecheng-10848	121	1	11	11	NUM
fumecheng-10848	121	2	.	.	PUNCT
fumecheng-10848	122	1	he	he	PRON
fumecheng-10848	122	2	,	,	PUNCT
fumecheng-10848	122	3	j.h	j.h	PROPN
fumecheng-10848	122	4	.	.	PROPN
fumecheng-10848	122	5	,	,	PUNCT
fumecheng-10848	122	6	2007	2007	NUM
fumecheng-10848	122	7	,	,	PUNCT
fumecheng-10848	122	8	variational	variational	ADJ
fumecheng-10848	122	9	iteration	iteration	NOUN
fumecheng-10848	122	10	method	method	NOUN
fumecheng-10848	122	11	-	-	PUNCT
fumecheng-10848	122	12	some	some	DET
fumecheng-10848	122	13	recent	recent	ADJ
fumecheng-10848	122	14	results	result	NOUN
fumecheng-10848	122	15	and	and	CCONJ
fumecheng-10848	122	16	new	new	ADJ
fumecheng-10848	122	17	interpretations	interpretation	NOUN
fumecheng-10848	122	18	,	,	PUNCT
fumecheng-10848	122	19	journal	journal	NOUN
fumecheng-10848	122	20	of	of	ADP
fumecheng-10848	122	21	computation	computation	NOUN
fumecheng-10848	122	22	and	and	CCONJ
fumecheng-10848	122	23	applied	apply	VERB
fumecheng-10848	122	24	mathematics	mathematic	NOUN
fumecheng-10848	122	25	,	,	PUNCT
fumecheng-10848	122	26	207	207	NUM
fumecheng-10848	122	27	,	,	PUNCT
fumecheng-10848	122	28	pp	pp	ADJ
fumecheng-10848	122	29	.	.	PUNCT
fumecheng-10848	123	1	3	3	NUM
fumecheng-10848	123	2	-	-	SYM
fumecheng-10848	123	3	17	17	NUM
fumecheng-10848	123	4	.	.	PUNCT
fumecheng-10848	124	1	12	12	NUM
fumecheng-10848	124	2	.	.	PUNCT
fumecheng-10848	125	1	wang	wang	PROPN
fumecheng-10848	125	2	,	,	PUNCT
fumecheng-10848	125	3	s.q	s.q	PROPN
fumecheng-10848	125	4	.	.	PROPN
fumecheng-10848	125	5	,	,	PUNCT
fumecheng-10848	125	6	he	he	PRON
fumecheng-10848	125	7	,	,	PUNCT
fumecheng-10848	125	8	j.h	j.h	PROPN
fumecheng-10848	125	9	.	.	PROPN
fumecheng-10848	125	10	,	,	PUNCT
fumecheng-10848	125	11	2007	2007	NUM
fumecheng-10848	125	12	,	,	PUNCT
fumecheng-10848	125	13	variational	variational	ADJ
fumecheng-10848	125	14	iteration	iteration	NOUN
fumecheng-10848	125	15	method	method	NOUN
fumecheng-10848	125	16	for	for	ADP
fumecheng-10848	125	17	solving	solve	VERB
fumecheng-10848	125	18	integro	integro	ADJ
fumecheng-10848	125	19	-	-	PUNCT
fumecheng-10848	125	20	differential	differential	NOUN
fumecheng-10848	125	21	equations	equation	NOUN
fumecheng-10848	125	22	,	,	PUNCT
fumecheng-10848	125	23	physics	physics	NOUN
fumecheng-10848	125	24	letters	letter	NOUN
fumecheng-10848	125	25	a	a	DET
fumecheng-10848	125	26	,	,	PUNCT
fumecheng-10848	125	27	367(3	367(3	NUM
fumecheng-10848	125	28	)	)	PUNCT
fumecheng-10848	125	29	,	,	PUNCT
fumecheng-10848	125	30	pp	pp	ADP
fumecheng-10848	125	31	.	.	PUNCT
fumecheng-10848	126	1	188	188	NUM
fumecheng-10848	126	2	-	-	SYM
fumecheng-10848	126	3	191	191	NUM
fumecheng-10848	126	4	.	.	PUNCT
fumecheng-10848	126	5	13	13	NUM
fumecheng-10848	126	6	.	.	X
fumecheng-10848	127	1	wang	wang	PROPN
fumecheng-10848	127	2	,	,	PUNCT
fumecheng-10848	127	3	s.q	s.q	PROPN
fumecheng-10848	127	4	.	.	PROPN
fumecheng-10848	127	5	,	,	PUNCT
fumecheng-10848	127	6	2009	2009	NUM
fumecheng-10848	127	7	,	,	PUNCT
fumecheng-10848	127	8	a	a	DET
fumecheng-10848	127	9	variational	variational	ADJ
fumecheng-10848	127	10	approach	approach	NOUN
fumecheng-10848	127	11	to	to	PART
fumecheng-10848	127	12	nonlinear	nonlinear	VERB
fumecheng-10848	127	13	two	two	NUM
fumecheng-10848	127	14	-	-	PUNCT
fumecheng-10848	127	15	point	point	NOUN
fumecheng-10848	127	16	boundary	boundary	ADJ
fumecheng-10848	127	17	value	value	NOUN
fumecheng-10848	127	18	problems	problem	NOUN
fumecheng-10848	127	19	,	,	PUNCT
fumecheng-10848	127	20	computers	computer	NOUN
fumecheng-10848	127	21	&	&	CCONJ
fumecheng-10848	127	22	mathematics	mathematics	PROPN
fumecheng-10848	127	23	with	with	ADP
fumecheng-10848	127	24	applications	application	NOUN
fumecheng-10848	127	25	,	,	PUNCT
fumecheng-10848	127	26	58(11	58(11	NUM
fumecheng-10848	127	27	)	)	PUNCT
fumecheng-10848	127	28	,	,	PUNCT
fumecheng-10848	127	29	pp	pp	ADJ
fumecheng-10848	127	30	.	.	PUNCT
fumecheng-10848	128	1	2452	2452	NUM
fumecheng-10848	128	2	-	-	SYM
fumecheng-10848	128	3	2455	2455	NUM
fumecheng-10848	128	4	.	.	PUNCT
fumecheng-10848	129	1	14	14	NUM
fumecheng-10848	129	2	.	.	X
fumecheng-10848	130	1	nadeem	nadeem	PROPN
fumecheng-10848	130	2	,	,	PUNCT
fumecheng-10848	130	3	m.	m.	NOUN
fumecheng-10848	130	4	,	,	PUNCT
fumecheng-10848	130	5	he	he	PRON
fumecheng-10848	130	6	,	,	PUNCT
fumecheng-10848	130	7	j.h	j.h	PROPN
fumecheng-10848	130	8	.	.	PROPN
fumecheng-10848	130	9	,	,	PUNCT
fumecheng-10848	130	10	islam	islam	PROPN
fumecheng-10848	130	11	,	,	PUNCT
fumecheng-10848	130	12	a.	a.	NOUN
fumecheng-10848	130	13	,	,	PUNCT
fumecheng-10848	130	14	2021	2021	NUM
fumecheng-10848	130	15	,	,	PUNCT
fumecheng-10848	130	16	the	the	DET
fumecheng-10848	130	17	homotopy	homotopy	NOUN
fumecheng-10848	130	18	perturbation	perturbation	NOUN
fumecheng-10848	130	19	method	method	NOUN
fumecheng-10848	130	20	for	for	ADP
fumecheng-10848	130	21	fractional	fractional	ADJ
fumecheng-10848	130	22	differential	differential	ADJ
fumecheng-10848	130	23	equations	equation	NOUN
fumecheng-10848	130	24	:	:	PUNCT
fumecheng-10848	130	25	part	part	NOUN
fumecheng-10848	130	26	1	1	NUM
fumecheng-10848	130	27	mohand	mohand	NOUN
fumecheng-10848	130	28	transform	transform	NOUN
fumecheng-10848	130	29	,	,	PUNCT
fumecheng-10848	130	30	international	international	ADJ
fumecheng-10848	130	31	journal	journal	NOUN
fumecheng-10848	130	32	of	of	ADP
fumecheng-10848	130	33	numerical	numerical	ADJ
fumecheng-10848	130	34	methods	method	NOUN
fumecheng-10848	130	35	for	for	ADP
fumecheng-10848	130	36	heat	heat	NOUN
fumecheng-10848	130	37	&	&	CCONJ
fumecheng-10848	130	38	fluid	fluid	ADJ
fumecheng-10848	130	39	flow	flow	NOUN
fumecheng-10848	130	40	,	,	PUNCT
fumecheng-10848	130	41	31(11	31(11	NUM
fumecheng-10848	130	42	)	)	PUNCT
fumecheng-10848	130	43	,	,	PUNCT
fumecheng-10848	130	44	pp	pp	ADP
fumecheng-10848	130	45	.	.	PUNCT
fumecheng-10848	131	1	3490	3490	NUM
fumecheng-10848	131	2	-	-	SYM
fumecheng-10848	131	3	3504	3504	NUM
fumecheng-10848	131	4	.	.	PUNCT
fumecheng-10848	132	1	15	15	NUM
fumecheng-10848	132	2	.	.	PUNCT
fumecheng-10848	133	1	he	he	PRON
fumecheng-10848	133	2	,	,	PUNCT
fumecheng-10848	133	3	c.h	c.h	PROPN
fumecheng-10848	133	4	.	.	PROPN
fumecheng-10848	133	5	,	,	PUNCT
fumecheng-10848	133	6	el	el	PROPN
fumecheng-10848	133	7	-	-	PUNCT
fumecheng-10848	133	8	dib	dib	PROPN
fumecheng-10848	133	9	,	,	PUNCT
fumecheng-10848	133	10	y.o	y.o	PROPN
fumecheng-10848	133	11	.	.	PROPN
fumecheng-10848	133	12	,	,	PUNCT
fumecheng-10848	133	13	2022	2022	NUM
fumecheng-10848	133	14	,	,	PUNCT
fumecheng-10848	133	15	a	a	DET
fumecheng-10848	133	16	heuristic	heuristic	ADJ
fumecheng-10848	133	17	review	review	NOUN
fumecheng-10848	133	18	on	on	ADP
fumecheng-10848	133	19	the	the	DET
fumecheng-10848	133	20	homotopy	homotopy	NOUN
fumecheng-10848	133	21	perturbation	perturbation	NOUN
fumecheng-10848	133	22	method	method	NOUN
fumecheng-10848	133	23	for	for	ADP
fumecheng-10848	133	24	non	non	ADJ
fumecheng-10848	133	25	-	-	ADJ
fumecheng-10848	133	26	conservative	conservative	ADJ
fumecheng-10848	133	27	oscillators	oscillator	NOUN
fumecheng-10848	133	28	,	,	PUNCT
fumecheng-10848	133	29	journal	journal	NOUN
fumecheng-10848	133	30	of	of	ADP
fumecheng-10848	133	31	low	low	ADJ
fumecheng-10848	133	32	frequency	frequency	NOUN
fumecheng-10848	133	33	noise	noise	NOUN
fumecheng-10848	133	34	,	,	PUNCT
fumecheng-10848	133	35	vibration	vibration	NOUN
fumecheng-10848	133	36	&	&	CCONJ
fumecheng-10848	133	37	active	active	ADJ
fumecheng-10848	133	38	control	control	NOUN
fumecheng-10848	133	39	,	,	PUNCT
fumecheng-10848	133	40	41	41	NUM
fumecheng-10848	133	41	(	(	PUNCT
fumecheng-10848	133	42	2	2	NUM
fumecheng-10848	133	43	)	)	PUNCT
fumecheng-10848	133	44	,	,	PUNCT
fumecheng-10848	133	45	pp.572	pp.572	NOUN
fumecheng-10848	133	46	-	-	PUNCT
fumecheng-10848	133	47	603	603	NUM
fumecheng-10848	133	48	.	.	PUNCT
fumecheng-10848	133	49	16	16	NUM
fumecheng-10848	133	50	.	.	PUNCT
fumecheng-10848	134	1	he	he	PRON
fumecheng-10848	134	2	,	,	PUNCT
fumecheng-10848	134	3	j.h	j.h	PROPN
fumecheng-10848	134	4	.	.	PROPN
fumecheng-10848	134	5	,	,	PUNCT
fumecheng-10848	134	6	2010	2010	NUM
fumecheng-10848	134	7	,	,	PUNCT
fumecheng-10848	134	8	hamiltonian	hamiltonian	ADJ
fumecheng-10848	134	9	approach	approach	NOUN
fumecheng-10848	134	10	to	to	ADP
fumecheng-10848	134	11	nonlinear	nonlinear	ADJ
fumecheng-10848	134	12	oscillators	oscillator	NOUN
fumecheng-10848	134	13	,	,	PUNCT
fumecheng-10848	134	14	physics	physics	NOUN
fumecheng-10848	134	15	letters	letter	NOUN
fumecheng-10848	134	16	a	a	PRON
fumecheng-10848	134	17	,	,	PUNCT
fumecheng-10848	134	18	374	374	NUM
fumecheng-10848	134	19	,	,	PUNCT
fumecheng-10848	134	20	pp	pp	ADJ
fumecheng-10848	134	21	.	.	PUNCT
fumecheng-10848	134	22	2312–2314	2312–2314	NUM
fumecheng-10848	134	23	.	.	PUNCT
fumecheng-10848	135	1	17	17	NUM
fumecheng-10848	135	2	.	.	PUNCT
fumecheng-10848	136	1	he	he	PRON
fumecheng-10848	136	2	,	,	PUNCT
fumecheng-10848	136	3	c.h	c.h	PROPN
fumecheng-10848	136	4	.	.	PROPN
fumecheng-10848	136	5	,	,	PUNCT
fumecheng-10848	136	6	shen	shen	PROPN
fumecheng-10848	136	7	,	,	PUNCT
fumecheng-10848	136	8	y.	y.	PROPN
fumecheng-10848	136	9	,	,	PUNCT
fumecheng-10848	136	10	ji	ji	PROPN
fumecheng-10848	136	11	,	,	PUNCT
fumecheng-10848	136	12	f.y	f.y	PROPN
fumecheng-10848	136	13	.	.	PROPN
fumecheng-10848	136	14	,	,	PUNCT
fumecheng-10848	136	15	he	he	PRON
fumecheng-10848	136	16	,	,	PUNCT
fumecheng-10848	136	17	j.h	j.h	PROPN
fumecheng-10848	136	18	.	.	PROPN
fumecheng-10848	136	19	,	,	PUNCT
fumecheng-10848	136	20	2020	2020	NUM
fumecheng-10848	136	21	,	,	PUNCT
fumecheng-10848	136	22	taylor	taylor	PROPN
fumecheng-10848	136	23	series	series	PROPN
fumecheng-10848	136	24	solution	solution	NOUN
fumecheng-10848	136	25	for	for	ADP
fumecheng-10848	136	26	fractal	fractal	ADJ
fumecheng-10848	136	27	bratu	bratu	ADJ
fumecheng-10848	136	28	-	-	PUNCT
fumecheng-10848	136	29	type	type	NOUN
fumecheng-10848	136	30	equation	equation	NOUN
fumecheng-10848	136	31	arising	arise	VERB
fumecheng-10848	136	32	in	in	ADP
fumecheng-10848	136	33	electrospinning	electrospinne	VERB
fumecheng-10848	136	34	process	process	NOUN
fumecheng-10848	136	35	,	,	PUNCT
fumecheng-10848	136	36	fractals	fractal	NOUN
fumecheng-10848	136	37	,	,	PUNCT
fumecheng-10848	136	38	28(1	28(1	NOUN
fumecheng-10848	136	39	)	)	PUNCT
fumecheng-10848	136	40	,	,	PUNCT
fumecheng-10848	136	41	2050011	2050011	NUM
fumecheng-10848	136	42	.	.	PUNCT
fumecheng-10848	137	1	18	18	NUM
fumecheng-10848	137	2	.	.	X
fumecheng-10848	137	3	ain	ain	PROPN
fumecheng-10848	137	4	,	,	PUNCT
fumecheng-10848	137	5	q.t	q.t	PROPN
fumecheng-10848	137	6	.	.	PROPN
fumecheng-10848	137	7	,	,	PUNCT
fumecheng-10848	137	8	ji	ji	PROPN
fumecheng-10848	137	9	,	,	PUNCT
fumecheng-10848	137	10	f.y	f.y	PROPN
fumecheng-10848	137	11	.	.	PROPN
fumecheng-10848	137	12	,	,	PUNCT
fumecheng-10848	137	13	2019	2019	NUM
fumecheng-10848	137	14	,	,	PUNCT
fumecheng-10848	137	15	on	on	ADP
fumecheng-10848	137	16	two	two	NUM
fumecheng-10848	137	17	-	-	PUNCT
fumecheng-10848	137	18	scale	scale	NOUN
fumecheng-10848	137	19	dimension	dimension	NOUN
fumecheng-10848	137	20	and	and	CCONJ
fumecheng-10848	137	21	its	its	PRON
fumecheng-10848	137	22	applications	application	NOUN
fumecheng-10848	137	23	,	,	PUNCT
fumecheng-10848	137	24	thermal	thermal	ADJ
fumecheng-10848	137	25	science	science	NOUN
fumecheng-10848	137	26	,	,	PUNCT
fumecheng-10848	137	27	23	23	NUM
fumecheng-10848	137	28	,	,	PUNCT
fumecheng-10848	137	29	pp	pp	ADJ
fumecheng-10848	137	30	.	.	PUNCT
fumecheng-10848	137	31	1707	1707	NUM
fumecheng-10848	137	32	-	-	SYM
fumecheng-10848	137	33	1712	1712	NUM
fumecheng-10848	137	34	.	.	PUNCT
fumecheng-10848	138	1	19	19	NUM
fumecheng-10848	138	2	.	.	PUNCT
fumecheng-10848	139	1	he	he	PRON
fumecheng-10848	139	2	,	,	PUNCT
fumecheng-10848	139	3	j.h	j.h	PROPN
fumecheng-10848	139	4	.	.	PROPN
fumecheng-10848	139	5	,	,	PUNCT
fumecheng-10848	139	6	ji	ji	PROPN
fumecheng-10848	139	7	,	,	PUNCT
fumecheng-10848	139	8	f.y	f.y	PROPN
fumecheng-10848	139	9	.	.	PROPN
fumecheng-10848	139	10	,	,	PUNCT
fumecheng-10848	139	11	2019	2019	NUM
fumecheng-10848	139	12	,	,	PUNCT
fumecheng-10848	139	13	two	two	NUM
fumecheng-10848	139	14	-	-	PUNCT
fumecheng-10848	139	15	scale	scale	NOUN
fumecheng-10848	139	16	mathematics	mathematic	NOUN
fumecheng-10848	139	17	and	and	CCONJ
fumecheng-10848	139	18	fractional	fractional	ADJ
fumecheng-10848	139	19	calculus	calculus	NOUN
fumecheng-10848	139	20	for	for	ADP
fumecheng-10848	139	21	thermodynamics	thermodynamic	NOUN
fumecheng-10848	139	22	,	,	PUNCT
fumecheng-10848	139	23	thermal	thermal	ADJ
fumecheng-10848	139	24	science	science	NOUN
fumecheng-10848	139	25	,	,	PUNCT
fumecheng-10848	139	26	23	23	NUM
fumecheng-10848	139	27	,	,	PUNCT
fumecheng-10848	139	28	pp	pp	ADJ
fumecheng-10848	139	29	.	.	PUNCT
fumecheng-10848	139	30	2131	2131	NUM
fumecheng-10848	139	31	-	-	SYM
fumecheng-10848	139	32	2134	2134	NUM
fumecheng-10848	139	33	.	.	PUNCT
fumecheng-10848	140	1	20	20	NUM
fumecheng-10848	140	2	.	.	PUNCT
fumecheng-10848	141	1	he	he	PRON
fumecheng-10848	141	2	,	,	PUNCT
fumecheng-10848	141	3	j.h	j.h	PROPN
fumecheng-10848	141	4	.	.	PROPN
fumecheng-10848	141	5	,	,	PUNCT
fumecheng-10848	141	6	ain	ain	PROPN
fumecheng-10848	141	7	,	,	PUNCT
fumecheng-10848	141	8	q.t	q.t	PROPN
fumecheng-10848	141	9	.	.	PROPN
fumecheng-10848	141	10	,	,	PUNCT
fumecheng-10848	141	11	2019	2019	NUM
fumecheng-10848	141	12	,	,	PUNCT
fumecheng-10848	141	13	new	new	ADJ
fumecheng-10848	141	14	promises	promise	NOUN
fumecheng-10848	141	15	and	and	CCONJ
fumecheng-10848	141	16	future	future	ADJ
fumecheng-10848	141	17	challenges	challenge	NOUN
fumecheng-10848	141	18	of	of	ADP
fumecheng-10848	141	19	fractal	fractal	ADJ
fumecheng-10848	141	20	calculus	calculus	NOUN
fumecheng-10848	141	21	:	:	PUNCT
fumecheng-10848	141	22	from	from	ADP
fumecheng-10848	141	23	two	two	NUM
fumecheng-10848	141	24	-	-	PUNCT
fumecheng-10848	141	25	scale	scale	NOUN
fumecheng-10848	141	26	thermodynamics	thermodynamic	NOUN
fumecheng-10848	141	27	to	to	ADP
fumecheng-10848	141	28	fractal	fractal	ADJ
fumecheng-10848	141	29	variational	variational	ADJ
fumecheng-10848	141	30	principle	principle	NOUN
fumecheng-10848	141	31	,	,	PUNCT
fumecheng-10848	141	32	thermal	thermal	ADJ
fumecheng-10848	141	33	science	science	NOUN
fumecheng-10848	141	34	,	,	PUNCT
fumecheng-10848	141	35	24	24	NUM
fumecheng-10848	141	36	,	,	PUNCT
fumecheng-10848	141	37	pp	pp	ADJ
fumecheng-10848	141	38	.	.	PUNCT
fumecheng-10848	141	39	659	659	NUM
fumecheng-10848	141	40	-	-	SYM
fumecheng-10848	141	41	681	681	NUM
fumecheng-10848	141	42	.	.	PUNCT
fumecheng-10848	141	43	21	21	NUM
fumecheng-10848	141	44	.	.	PUNCT
fumecheng-10848	142	1	he	he	PRON
fumecheng-10848	142	2	,	,	PUNCT
fumecheng-10848	142	3	c.h	c.h	PROPN
fumecheng-10848	142	4	.	.	PROPN
fumecheng-10848	142	5	,	,	PUNCT
fumecheng-10848	142	6	2023	2023	NUM
fumecheng-10848	142	7	,	,	PUNCT
fumecheng-10848	142	8	a	a	DET
fumecheng-10848	142	9	variational	variational	ADJ
fumecheng-10848	142	10	principle	principle	NOUN
fumecheng-10848	142	11	for	for	ADP
fumecheng-10848	142	12	a	a	DET
fumecheng-10848	142	13	fractal	fractal	ADJ
fumecheng-10848	142	14	nano	nano	NOUN
fumecheng-10848	142	15	/	/	SYM
fumecheng-10848	142	16	microelectromechanical	microelectromechanical	ADJ
fumecheng-10848	142	17	(	(	PUNCT
fumecheng-10848	142	18	n	n	CCONJ
fumecheng-10848	142	19	/	/	SYM
fumecheng-10848	142	20	mems	mem	NOUN
fumecheng-10848	142	21	)	)	PUNCT
fumecheng-10848	142	22	system	system	NOUN
fumecheng-10848	142	23	,	,	PUNCT
fumecheng-10848	142	24	international	international	ADJ
fumecheng-10848	142	25	journal	journal	NOUN
fumecheng-10848	142	26	of	of	ADP
fumecheng-10848	142	27	numerical	numerical	ADJ
fumecheng-10848	142	28	methods	method	NOUN
fumecheng-10848	142	29	for	for	ADP
fumecheng-10848	142	30	heat	heat	NOUN
fumecheng-10848	142	31	&	&	CCONJ
fumecheng-10848	142	32	fluid	fluid	ADJ
fumecheng-10848	142	33	flow	flow	NOUN
fumecheng-10848	142	34	,	,	PUNCT
fumecheng-10848	142	35	33	33	NUM
fumecheng-10848	142	36	(	(	PUNCT
fumecheng-10848	142	37	1	1	NUM
fumecheng-10848	142	38	)	)	PUNCT
fumecheng-10848	142	39	,	,	PUNCT
fumecheng-10848	142	40	pp	pp	PROPN
fumecheng-10848	142	41	.	.	PUNCT
fumecheng-10848	142	42	351	351	NUM
fumecheng-10848	142	43	-	-	SYM
fumecheng-10848	142	44	359	359	NUM
fumecheng-10848	142	45	.	.	PUNCT
fumecheng-10848	143	1	22	22	NUM
fumecheng-10848	143	2	.	.	PUNCT
fumecheng-10848	144	1	he	he	PRON
fumecheng-10848	144	2	,	,	PUNCT
fumecheng-10848	144	3	j.h	j.h	PROPN
fumecheng-10848	144	4	.	.	PROPN
fumecheng-10848	144	5	,	,	PUNCT
fumecheng-10848	144	6	2014	2014	NUM
fumecheng-10848	144	7	,	,	PUNCT
fumecheng-10848	144	8	a	a	DET
fumecheng-10848	144	9	tutorial	tutorial	ADJ
fumecheng-10848	144	10	review	review	NOUN
fumecheng-10848	144	11	on	on	ADP
fumecheng-10848	144	12	fractal	fractal	ADJ
fumecheng-10848	144	13	spacetime	spacetime	NOUN
fumecheng-10848	144	14	and	and	CCONJ
fumecheng-10848	144	15	fractional	fractional	ADJ
fumecheng-10848	144	16	calculus	calculus	NOUN
fumecheng-10848	144	17	,	,	PUNCT
fumecheng-10848	144	18	international	international	ADJ
fumecheng-10848	144	19	journal	journal	NOUN
fumecheng-10848	144	20	of	of	ADP
fumecheng-10848	144	21	theoretical	theoretical	ADJ
fumecheng-10848	144	22	physics	physics	NOUN
fumecheng-10848	144	23	,	,	PUNCT
fumecheng-10848	144	24	53	53	NUM
fumecheng-10848	144	25	,	,	PUNCT
fumecheng-10848	144	26	pp	pp	ADJ
fumecheng-10848	144	27	.	.	PUNCT
fumecheng-10848	145	1	3698	3698	NUM
fumecheng-10848	145	2	-	-	SYM
fumecheng-10848	145	3	3718	3718	NUM
fumecheng-10848	145	4	.	.	PUNCT
fumecheng-10848	146	1	23	23	NUM
fumecheng-10848	146	2	.	.	PUNCT
fumecheng-10848	147	1	he	he	PRON
fumecheng-10848	147	2	,	,	PUNCT
fumecheng-10848	147	3	j.h	j.h	PROPN
fumecheng-10848	147	4	.	.	PROPN
fumecheng-10848	147	5	,	,	PUNCT
fumecheng-10848	147	6	2018	2018	NUM
fumecheng-10848	147	7	,	,	PUNCT
fumecheng-10848	147	8	fractal	fractal	ADJ
fumecheng-10848	147	9	calculus	calculus	NOUN
fumecheng-10848	147	10	and	and	CCONJ
fumecheng-10848	147	11	its	its	PRON
fumecheng-10848	147	12	geometrical	geometrical	ADJ
fumecheng-10848	147	13	explanation	explanation	NOUN
fumecheng-10848	147	14	,	,	PUNCT
fumecheng-10848	147	15	results	result	NOUN
fumecheng-10848	147	16	in	in	ADP
fumecheng-10848	147	17	physics	physics	NOUN
fumecheng-10848	147	18	,	,	PUNCT
fumecheng-10848	147	19	10	10	NUM
fumecheng-10848	147	20	,	,	PUNCT
fumecheng-10848	147	21	pp	pp	ADJ
fumecheng-10848	147	22	.	.	PUNCT
fumecheng-10848	148	1	272	272	NUM
fumecheng-10848	148	2	-	-	SYM
fumecheng-10848	148	3	276	276	NUM
fumecheng-10848	148	4	.	.	PUNCT
fumecheng-10848	149	1	24	24	NUM
fumecheng-10848	149	2	.	.	PUNCT
fumecheng-10848	150	1	he	he	PRON
fumecheng-10848	150	2	,	,	PUNCT
fumecheng-10848	150	3	j.h	j.h	PROPN
fumecheng-10848	150	4	.	.	PROPN
fumecheng-10848	150	5	,	,	PUNCT
fumecheng-10848	150	6	jiao	jiao	PROPN
fumecheng-10848	150	7	,	,	PUNCT
fumecheng-10848	150	8	m.l	m.l	PROPN
fumecheng-10848	150	9	.	.	PROPN
fumecheng-10848	150	10	,	,	PUNCT
fumecheng-10848	150	11	he	he	PRON
fumecheng-10848	150	12	,	,	PUNCT
fumecheng-10848	150	13	c.h	c.h	PROPN
fumecheng-10848	150	14	.	.	PROPN
fumecheng-10848	150	15	,	,	PUNCT
fumecheng-10848	150	16	2022	2022	NUM
fumecheng-10848	150	17	,	,	PUNCT
fumecheng-10848	150	18	homotopy	homotopy	VERB
fumecheng-10848	150	19	perturbation	perturbation	NOUN
fumecheng-10848	150	20	method	method	NOUN
fumecheng-10848	150	21	for	for	ADP
fumecheng-10848	150	22	fractal	fractal	ADJ
fumecheng-10848	150	23	duffing	duffing	NOUN
fumecheng-10848	150	24	oscillator	oscillator	NOUN
fumecheng-10848	150	25	with	with	ADP
fumecheng-10848	150	26	arbitrary	arbitrary	ADJ
fumecheng-10848	150	27	conditions	condition	NOUN
fumecheng-10848	150	28	,	,	PUNCT
fumecheng-10848	150	29	fractals	fractal	NOUN
fumecheng-10848	150	30	,	,	PUNCT
fumecheng-10848	150	31	30(9	30(9	NOUN
fumecheng-10848	150	32	)	)	PUNCT
fumecheng-10848	150	33	,	,	PUNCT
fumecheng-10848	150	34	doi:10.1142	doi:10.1142	NOUN
fumecheng-10848	150	35	/	/	SYM
fumecheng-10848	150	36	s0218348x22501651	s0218348x22501651	NOUN
fumecheng-10848	150	37	.	.	PUNCT
fumecheng-10848	151	1	25	25	NUM
fumecheng-10848	151	2	.	.	PUNCT
fumecheng-10848	152	1	he	he	PRON
fumecheng-10848	152	2	,	,	PUNCT
fumecheng-10848	152	3	j.h	j.h	PROPN
fumecheng-10848	152	4	.	.	PROPN
fumecheng-10848	152	5	,	,	PUNCT
fumecheng-10848	152	6	2006	2006	NUM
fumecheng-10848	152	7	,	,	PUNCT
fumecheng-10848	152	8	some	some	DET
fumecheng-10848	152	9	asymptotic	asymptotic	ADJ
fumecheng-10848	152	10	methods	method	NOUN
fumecheng-10848	152	11	for	for	ADP
fumecheng-10848	152	12	strongly	strongly	ADV
fumecheng-10848	152	13	nonlinear	nonlinear	ADJ
fumecheng-10848	152	14	equations	equation	NOUN
fumecheng-10848	152	15	,	,	PUNCT
fumecheng-10848	152	16	international	international	ADJ
fumecheng-10848	152	17	journal	journal	NOUN
fumecheng-10848	152	18	of	of	ADP
fumecheng-10848	152	19	modern	modern	ADJ
fumecheng-10848	152	20	physics	physics	PROPN
fumecheng-10848	152	21	b	b	PROPN
fumecheng-10848	152	22	,	,	PUNCT
fumecheng-10848	152	23	20(10	20(10	NUM
fumecheng-10848	152	24	)	)	PUNCT
fumecheng-10848	152	25	,	,	PUNCT
fumecheng-10848	152	26	pp	pp	ADJ
fumecheng-10848	152	27	.	.	PUNCT
fumecheng-10848	152	28	1141–1199	1141–1199	NUM
fumecheng-10848	152	29	.	.	PUNCT
fumecheng-10848	153	1	26	26	NUM
fumecheng-10848	153	2	.	.	PUNCT
fumecheng-10848	154	1	he	he	PRON
fumecheng-10848	154	2	,	,	PUNCT
fumecheng-10848	154	3	j.h	j.h	PROPN
fumecheng-10848	154	4	.	.	PROPN
fumecheng-10848	154	5	,	,	PUNCT
fumecheng-10848	154	6	2019	2019	NUM
fumecheng-10848	154	7	,	,	PUNCT
fumecheng-10848	154	8	the	the	PRON
fumecheng-10848	154	9	simpler	simple	ADJ
fumecheng-10848	154	10	,	,	PUNCT
fumecheng-10848	154	11	the	the	PRON
fumecheng-10848	154	12	better	well	ADJ
fumecheng-10848	154	13	:	:	PUNCT
fumecheng-10848	154	14	analytical	analytical	ADJ
fumecheng-10848	154	15	methods	method	NOUN
fumecheng-10848	154	16	for	for	ADP
fumecheng-10848	154	17	nonlinear	nonlinear	ADJ
fumecheng-10848	154	18	oscillators	oscillator	NOUN
fumecheng-10848	154	19	and	and	CCONJ
fumecheng-10848	154	20	fractional	fractional	ADJ
fumecheng-10848	154	21	oscillators	oscillator	NOUN
fumecheng-10848	154	22	,	,	PUNCT
fumecheng-10848	154	23	journal	journal	NOUN
fumecheng-10848	154	24	of	of	ADP
fumecheng-10848	154	25	low	low	ADJ
fumecheng-10848	154	26	frequency	frequency	NOUN
fumecheng-10848	154	27	noise	noise	NOUN
fumecheng-10848	154	28	,	,	PUNCT
fumecheng-10848	154	29	vibration	vibration	NOUN
fumecheng-10848	154	30	&	&	CCONJ
fumecheng-10848	154	31	active	active	ADJ
fumecheng-10848	154	32	control	control	NOUN
fumecheng-10848	154	33	,	,	PUNCT
fumecheng-10848	154	34	38	38	NUM
fumecheng-10848	154	35	,	,	PUNCT
fumecheng-10848	154	36	pp	pp	ADJ
fumecheng-10848	154	37	.	.	PUNCT
fumecheng-10848	154	38	1252–1260	1252–1260	NUM
fumecheng-10848	154	39	.	.	PUNCT
fumecheng-10848	154	40	27	27	NUM
fumecheng-10848	154	41	.	.	PUNCT
fumecheng-10848	155	1	he	he	PRON
fumecheng-10848	155	2	,	,	PUNCT
fumecheng-10848	155	3	j.h	j.h	PROPN
fumecheng-10848	155	4	.	.	PROPN
fumecheng-10848	155	5	,	,	PUNCT
fumecheng-10848	155	6	2019	2019	NUM
fumecheng-10848	155	7	,	,	PUNCT
fumecheng-10848	155	8	the	the	DET
fumecheng-10848	155	9	simplest	simple	ADJ
fumecheng-10848	155	10	approach	approach	NOUN
fumecheng-10848	155	11	to	to	ADP
fumecheng-10848	155	12	nonlinear	nonlinear	ADJ
fumecheng-10848	155	13	oscillators	oscillator	NOUN
fumecheng-10848	155	14	,	,	PUNCT
fumecheng-10848	155	15	results	result	NOUN
fumecheng-10848	155	16	in	in	ADP
fumecheng-10848	155	17	physics	physics	NOUN
fumecheng-10848	155	18	,	,	PUNCT
fumecheng-10848	155	19	15	15	NUM
fumecheng-10848	155	20	,	,	PUNCT
fumecheng-10848	155	21	102546	102546	NUM
fumecheng-10848	155	22	.	.	PUNCT
fumecheng-10848	156	1	28	28	NUM
fumecheng-10848	156	2	.	.	X
fumecheng-10848	157	1	tian	tian	PROPN
fumecheng-10848	157	2	,	,	PUNCT
fumecheng-10848	157	3	d.	d.	PROPN
fumecheng-10848	157	4	,	,	PUNCT
fumecheng-10848	157	5	ain	ain	PROPN
fumecheng-10848	157	6	,	,	PUNCT
fumecheng-10848	157	7	q.t	q.t	PROPN
fumecheng-10848	157	8	.	.	PROPN
fumecheng-10848	157	9	,	,	PUNCT
fumecheng-10848	157	10	anjum	anjum	PROPN
fumecheng-10848	157	11	,	,	PUNCT
fumecheng-10848	157	12	n.	n.	NOUN
fumecheng-10848	157	13	,	,	PUNCT
fumecheng-10848	157	14	2020	2020	NUM
fumecheng-10848	157	15	,	,	PUNCT
fumecheng-10848	157	16	fractal	fractal	ADJ
fumecheng-10848	157	17	n	n	CCONJ
fumecheng-10848	157	18	/	/	SYM
fumecheng-10848	157	19	mems	mem	NOUN
fumecheng-10848	157	20	:	:	PUNCT
fumecheng-10848	157	21	from	from	ADP
fumecheng-10848	157	22	pull	pull	NOUN
fumecheng-10848	157	23	-	-	PUNCT
fumecheng-10848	157	24	in	in	ADP
fumecheng-10848	157	25	instability	instability	NOUN
fumecheng-10848	157	26	to	to	PART
fumecheng-10848	157	27	pull	pull	VERB
fumecheng-10848	157	28	-	-	PUNCT
fumecheng-10848	157	29	in	in	ADP
fumecheng-10848	157	30	stability	stability	NOUN
fumecheng-10848	157	31	,	,	PUNCT
fumecheng-10848	157	32	fractals	fractal	NOUN
fumecheng-10848	157	33	,	,	PUNCT
fumecheng-10848	157	34	29(2	29(2	NUM
fumecheng-10848	157	35	)	)	PUNCT
fumecheng-10848	157	36	,	,	PUNCT
fumecheng-10848	157	37	2150030	2150030	NUM
fumecheng-10848	157	38	.	.	PUNCT
fumecheng-10848	158	1	29	29	NUM
fumecheng-10848	158	2	.	.	PUNCT
fumecheng-10848	159	1	li	li	PROPN
fumecheng-10848	159	2	,	,	PUNCT
fumecheng-10848	159	3	x.x	x.x	PROPN
fumecheng-10848	159	4	.	.	PROPN
fumecheng-10848	159	5	,	,	PUNCT
fumecheng-10848	159	6	he	he	PRON
fumecheng-10848	159	7	,	,	PUNCT
fumecheng-10848	159	8	j.h	j.h	PROPN
fumecheng-10848	159	9	.	.	PROPN
fumecheng-10848	159	10	,	,	PUNCT
fumecheng-10848	159	11	2019	2019	NUM
fumecheng-10848	159	12	,	,	PUNCT
fumecheng-10848	159	13	nanoscale	nanoscale	NOUN
fumecheng-10848	159	14	adhesion	adhesion	NOUN
fumecheng-10848	159	15	and	and	CCONJ
fumecheng-10848	159	16	attachment	attachment	NOUN
fumecheng-10848	159	17	oscillation	oscillation	NOUN
fumecheng-10848	159	18	under	under	ADP
fumecheng-10848	159	19	the	the	DET
fumecheng-10848	159	20	geometric	geometric	ADJ
fumecheng-10848	159	21	potential	potential	NOUN
fumecheng-10848	159	22	.	.	PUNCT
fumecheng-10848	160	1	part	part	NOUN
fumecheng-10848	160	2	1	1	NUM
fumecheng-10848	160	3	:	:	PUNCT
fumecheng-10848	160	4	the	the	DET
fumecheng-10848	160	5	formation	formation	NOUN
fumecheng-10848	160	6	mechanism	mechanism	NOUN
fumecheng-10848	160	7	of	of	ADP
fumecheng-10848	160	8	nanofiber	nanofiber	NOUN
fumecheng-10848	160	9	membrane	membrane	NOUN
fumecheng-10848	160	10	in	in	ADP
fumecheng-10848	160	11	the	the	DET
fumecheng-10848	160	12	electrospinning	electrospinning	NOUN
fumecheng-10848	160	13	,	,	PUNCT
fumecheng-10848	160	14	results	result	NOUN
fumecheng-10848	160	15	in	in	ADP
fumecheng-10848	160	16	physics	physics	NOUN
fumecheng-10848	160	17	,	,	PUNCT
fumecheng-10848	160	18	12	12	NUM
fumecheng-10848	160	19	,	,	PUNCT
fumecheng-10848	160	20	pp	pp	ADJ
fumecheng-10848	160	21	.	.	PUNCT
fumecheng-10848	161	1	1410	1410	NUM
fumecheng-10848	161	2	-	-	SYM
fumecheng-10848	161	3	1405	1405	NUM
fumecheng-10848	161	4	.	.	PUNCT
fumecheng-10848	162	1	a	a	DET
fumecheng-10848	162	2	circular	circular	ADJ
fumecheng-10848	162	3	sector	sector	NOUN
fumecheng-10848	162	4	vibration	vibration	NOUN
fumecheng-10848	162	5	system	system	NOUN
fumecheng-10848	162	6	in	in	ADP
fumecheng-10848	162	7	a	a	DET
fumecheng-10848	162	8	porous	porous	ADJ
fumecheng-10848	162	9	medium	medium	NOUN
fumecheng-10848	162	10	:	:	PUNCT
fumecheng-10848	162	11	a	a	DET
fumecheng-10848	162	12	fractal	fractal	ADJ
fumecheng-10848	162	13	-	-	PUNCT
fumecheng-10848	162	14	fractional	fractional	ADJ
fumecheng-10848	162	15	model	model	NOUN
fumecheng-10848	162	16	...	...	PUNCT
fumecheng-10848	162	17	385	385	NUM
fumecheng-10848	162	18	30	30	NUM
fumecheng-10848	162	19	.	.	PUNCT
fumecheng-10848	163	1	he	he	PRON
fumecheng-10848	163	2	,	,	PUNCT
fumecheng-10848	163	3	j.h	j.h	PROPN
fumecheng-10848	163	4	.	.	PROPN
fumecheng-10848	163	5	,	,	PUNCT
fumecheng-10848	163	6	yang	yang	PROPN
fumecheng-10848	163	7	,	,	PUNCT
fumecheng-10848	163	8	q.	q.	PROPN
fumecheng-10848	163	9	,	,	PUNCT
fumecheng-10848	163	10	he	he	PRON
fumecheng-10848	163	11	,	,	PUNCT
fumecheng-10848	163	12	c.h	c.h	PROPN
fumecheng-10848	163	13	.	.	PROPN
fumecheng-10848	163	14	,	,	PUNCT
fumecheng-10848	163	15	khan	khan	PROPN
fumecheng-10848	163	16	,	,	PUNCT
fumecheng-10848	163	17	y.	y.	PROPN
fumecheng-10848	163	18	,	,	PUNCT
fumecheng-10848	163	19	2021	2021	NUM
fumecheng-10848	163	20	,	,	PUNCT
fumecheng-10848	163	21	a	a	DET
fumecheng-10848	163	22	simple	simple	ADJ
fumecheng-10848	163	23	frequency	frequency	NOUN
fumecheng-10848	163	24	formulation	formulation	NOUN
fumecheng-10848	163	25	for	for	ADP
fumecheng-10848	163	26	the	the	DET
fumecheng-10848	163	27	tangent	tangent	NOUN
fumecheng-10848	163	28	oscillator	oscillator	NOUN
fumecheng-10848	163	29	,	,	PUNCT
fumecheng-10848	163	30	axioms	axiom	NOUN
fumecheng-10848	163	31	,	,	PUNCT
fumecheng-10848	163	32	10(4	10(4	NUM
fumecheng-10848	163	33	)	)	PUNCT
fumecheng-10848	163	34	,	,	PUNCT
fumecheng-10848	163	35	320	320	NUM
fumecheng-10848	163	36	.	.	PUNCT
fumecheng-10848	163	37	31	31	NUM
fumecheng-10848	163	38	.	.	PUNCT
fumecheng-10848	164	1	feng	feng	PROPN
fumecheng-10848	164	2	,	,	PUNCT
fumecheng-10848	164	3	g.q	g.q	PROPN
fumecheng-10848	164	4	.	.	PROPN
fumecheng-10848	164	5	,	,	PUNCT
fumecheng-10848	164	6	2021	2021	NUM
fumecheng-10848	164	7	,	,	PUNCT
fumecheng-10848	164	8	he	he	PRON
fumecheng-10848	164	9	's	's	PART
fumecheng-10848	164	10	frequency	frequency	NOUN
fumecheng-10848	164	11	formula	formula	NOUN
fumecheng-10848	164	12	to	to	ADP
fumecheng-10848	164	13	fractal	fractal	ADJ
fumecheng-10848	164	14	undamped	undampe	VERB
fumecheng-10848	164	15	duffing	duffing	NOUN
fumecheng-10848	164	16	equation	equation	NOUN
fumecheng-10848	164	17	,	,	PUNCT
fumecheng-10848	164	18	journal	journal	NOUN
fumecheng-10848	164	19	of	of	ADP
fumecheng-10848	164	20	low	low	ADJ
fumecheng-10848	164	21	frequency	frequency	NOUN
fumecheng-10848	164	22	noise	noise	NOUN
fumecheng-10848	164	23	vibration	vibration	NOUN
fumecheng-10848	164	24	&	&	CCONJ
fumecheng-10848	164	25	active	active	ADJ
fumecheng-10848	164	26	control	control	NOUN
fumecheng-10848	164	27	,	,	PUNCT
fumecheng-10848	164	28	40(4	40(4	NUM
fumecheng-10848	164	29	)	)	PUNCT
fumecheng-10848	164	30	,	,	PUNCT
fumecheng-10848	164	31	pp	pp	ADP
fumecheng-10848	164	32	.	.	PUNCT
fumecheng-10848	164	33	1671	1671	NUM
fumecheng-10848	164	34	-	-	SYM
fumecheng-10848	164	35	1676	1676	NUM
fumecheng-10848	164	36	.	.	PUNCT
fumecheng-10848	165	1	32	32	NUM
fumecheng-10848	165	2	.	.	X
fumecheng-10848	165	3	qie	qie	PROPN
fumecheng-10848	165	4	,	,	PUNCT
fumecheng-10848	165	5	n.	n.	NOUN
fumecheng-10848	165	6	,	,	PUNCT
fumecheng-10848	165	7	houa	houa	PROPN
fumecheng-10848	165	8	,	,	PUNCT
fumecheng-10848	165	9	w.f	w.f	PROPN
fumecheng-10848	165	10	.	.	PROPN
fumecheng-10848	165	11	,	,	PUNCT
fumecheng-10848	165	12	he	he	PRON
fumecheng-10848	165	13	,	,	PUNCT
fumecheng-10848	165	14	j.h	j.h	PROPN
fumecheng-10848	165	15	.	.	PROPN
fumecheng-10848	165	16	,	,	PUNCT
fumecheng-10848	165	17	2020	2020	NUM
fumecheng-10848	165	18	,	,	PUNCT
fumecheng-10848	165	19	the	the	DET
fumecheng-10848	165	20	fastest	fast	ADJ
fumecheng-10848	165	21	insight	insight	NOUN
fumecheng-10848	165	22	into	into	ADP
fumecheng-10848	165	23	the	the	DET
fumecheng-10848	165	24	large	large	ADJ
fumecheng-10848	165	25	amplitude	amplitude	NOUN
fumecheng-10848	165	26	vibration	vibration	NOUN
fumecheng-10848	165	27	of	of	ADP
fumecheng-10848	165	28	a	a	DET
fumecheng-10848	165	29	string	string	NOUN
fumecheng-10848	165	30	,	,	PUNCT
fumecheng-10848	165	31	reports	report	NOUN
fumecheng-10848	165	32	in	in	ADP
fumecheng-10848	165	33	mechanical	mechanical	ADJ
fumecheng-10848	165	34	engineering	engineering	NOUN
fumecheng-10848	165	35	,	,	PUNCT
fumecheng-10848	165	36	2	2	NUM
fumecheng-10848	165	37	,	,	PUNCT
fumecheng-10848	165	38	pp.1–5	pp.1–5	NOUN
fumecheng-10848	165	39	.	.	PUNCT
fumecheng-10848	166	1	33	33	NUM
fumecheng-10848	166	2	.	.	PUNCT
fumecheng-10848	167	1	feng	feng	PROPN
fumecheng-10848	167	2	,	,	PUNCT
fumecheng-10848	167	3	g.q	g.q	PROPN
fumecheng-10848	167	4	.	.	PROPN
fumecheng-10848	167	5	,	,	PUNCT
fumecheng-10848	167	6	niu	niu	PROPN
fumecheng-10848	167	7	,	,	PUNCT
fumecheng-10848	167	8	j.y	j.y	PROPN
fumecheng-10848	167	9	.	.	PROPN
fumecheng-10848	167	10	,	,	PUNCT
fumecheng-10848	167	11	2021	2021	NUM
fumecheng-10848	167	12	,	,	PUNCT
fumecheng-10848	167	13	he	he	PRON
fumecheng-10848	167	14	’s	’	VERB
fumecheng-10848	167	15	frequency	frequency	NOUN
fumecheng-10848	167	16	formulation	formulation	NOUN
fumecheng-10848	167	17	for	for	ADP
fumecheng-10848	167	18	nonlinear	nonlinear	ADJ
fumecheng-10848	167	19	vibration	vibration	NOUN
fumecheng-10848	167	20	of	of	ADP
fumecheng-10848	167	21	a	a	DET
fumecheng-10848	167	22	porous	porous	ADJ
fumecheng-10848	167	23	foundation	foundation	NOUN
fumecheng-10848	167	24	with	with	ADP
fumecheng-10848	167	25	fractal	fractal	ADJ
fumecheng-10848	167	26	derivative	derivative	ADJ
fumecheng-10848	167	27	,	,	PUNCT
fumecheng-10848	167	28	gem	gem	NOUN
fumecheng-10848	167	29	-	-	PUNCT
fumecheng-10848	167	30	international	international	ADJ
fumecheng-10848	167	31	on	on	ADP
fumecheng-10848	167	32	geomathematics	geomathematic	NOUN
fumecheng-10848	167	33	,	,	PUNCT
fumecheng-10848	167	34	12(1	12(1	NUM
fumecheng-10848	167	35	)	)	PUNCT
fumecheng-10848	167	36	,	,	PUNCT
fumecheng-10848	167	37	14	14	NUM
fumecheng-10848	167	38	.	.	PUNCT
fumecheng-10848	168	1	34	34	NUM
fumecheng-10848	168	2	.	.	PUNCT
fumecheng-10848	169	1	elías	elías	NOUN
fumecheng-10848	169	2	-	-	PUNCT
fumecheng-10848	169	3	zúiga	zúiga	ADV
fumecheng-10848	169	4	,	,	PUNCT
fumecheng-10848	169	5	a.	a.	NOUN
fumecheng-10848	169	6	,	,	PUNCT
fumecheng-10848	169	7	palacios	palacio	NOUN
fumecheng-10848	169	8	-	-	PUNCT
fumecheng-10848	169	9	pineda	pineda	PROPN
fumecheng-10848	169	10	,	,	PUNCT
fumecheng-10848	169	11	l.m	l.m	PROPN
fumecheng-10848	169	12	.	.	PROPN
fumecheng-10848	169	13	,	,	PUNCT
fumecheng-10848	169	14	jiménez	jiménez	PROPN
fumecheng-10848	169	15	-	-	PUNCT
fumecheng-10848	169	16	cedeo	cedeo	PROPN
fumecheng-10848	169	17	,	,	PUNCT
fumecheng-10848	169	18	i.h	i.h	PROPN
fumecheng-10848	169	19	.	.	PROPN
fumecheng-10848	169	20	,	,	PUNCT
fumecheng-10848	169	21	martínez	martínez	PROPN
fumecheng-10848	169	22	-	-	PUNCT
fumecheng-10848	169	23	romero	romero	PROPN
fumecheng-10848	169	24	,	,	PUNCT
fumecheng-10848	169	25	o.	o.	PROPN
fumecheng-10848	169	26	,	,	PUNCT
fumecheng-10848	169	27	trejo	trejo	PROPN
fumecheng-10848	169	28	,	,	PUNCT
fumecheng-10848	169	29	d.o	d.o	PROPN
fumecheng-10848	169	30	.	.	PROPN
fumecheng-10848	169	31	,	,	PUNCT
fumecheng-10848	169	32	2020	2020	NUM
fumecheng-10848	169	33	,	,	PUNCT
fumecheng-10848	169	34	he	he	PRON
fumecheng-10848	169	35	's	's	PART
fumecheng-10848	169	36	frequency	frequency	NOUN
fumecheng-10848	169	37	–	–	PUNCT
fumecheng-10848	169	38	amplitude	amplitude	NOUN
fumecheng-10848	169	39	formulation	formulation	NOUN
fumecheng-10848	169	40	for	for	ADP
fumecheng-10848	169	41	nonlinear	nonlinear	ADJ
fumecheng-10848	169	42	oscillators	oscillator	NOUN
fumecheng-10848	169	43	using	use	VERB
fumecheng-10848	169	44	jacobi	jacobi	PROPN
fumecheng-10848	169	45	elliptic	elliptic	ADJ
fumecheng-10848	169	46	functions	function	NOUN
fumecheng-10848	169	47	,	,	PUNCT
fumecheng-10848	169	48	journal	journal	NOUN
fumecheng-10848	169	49	of	of	ADP
fumecheng-10848	169	50	low	low	ADJ
fumecheng-10848	169	51	frequency	frequency	NOUN
fumecheng-10848	169	52	noise	noise	NOUN
fumecheng-10848	169	53	,	,	PUNCT
fumecheng-10848	169	54	vibration	vibration	NOUN
fumecheng-10848	169	55	&	&	CCONJ
fumecheng-10848	169	56	active	active	ADJ
fumecheng-10848	169	57	control	control	NOUN
fumecheng-10848	169	58	,	,	PUNCT
fumecheng-10848	169	59	39(4	39(4	NOUN
fumecheng-10848	169	60	)	)	PUNCT
fumecheng-10848	169	61	,	,	PUNCT
fumecheng-10848	169	62	pp	pp	PROPN
fumecheng-10848	169	63	.	.	PUNCT
fumecheng-10848	169	64	1216	1216	NUM
fumecheng-10848	169	65	-	-	SYM
fumecheng-10848	169	66	1223	1223	NUM
fumecheng-10848	169	67	.	.	PUNCT
fumecheng-10848	170	1	35	35	NUM
fumecheng-10848	170	2	.	.	PUNCT
fumecheng-10848	171	1	wang	wang	PROPN
fumecheng-10848	171	2	,	,	PUNCT
fumecheng-10848	171	3	k.j	k.j	PROPN
fumecheng-10848	171	4	.	.	PROPN
fumecheng-10848	171	5	,	,	PUNCT
fumecheng-10848	171	6	wang	wang	PROPN
fumecheng-10848	171	7	,	,	PUNCT
fumecheng-10848	171	8	g.d	g.d	PROPN
fumecheng-10848	171	9	.	.	PROPN
fumecheng-10848	171	10	,	,	PUNCT
fumecheng-10848	171	11	2021	2021	NUM
fumecheng-10848	171	12	,	,	PUNCT
fumecheng-10848	171	13	gamma	gamma	NOUN
fumecheng-10848	171	14	function	function	NOUN
fumecheng-10848	171	15	method	method	NOUN
fumecheng-10848	171	16	for	for	ADP
fumecheng-10848	171	17	the	the	DET
fumecheng-10848	171	18	nonlinear	nonlinear	ADJ
fumecheng-10848	171	19	cubic	cubic	ADJ
fumecheng-10848	171	20	-	-	PUNCT
fumecheng-10848	171	21	quintic	quintic	ADJ
fumecheng-10848	171	22	duffing	duffing	NOUN
fumecheng-10848	171	23	oscillators	oscillator	NOUN
fumecheng-10848	171	24	,	,	PUNCT
fumecheng-10848	171	25	journal	journal	NOUN
fumecheng-10848	171	26	of	of	ADP
fumecheng-10848	171	27	low	low	ADJ
fumecheng-10848	171	28	frequency	frequency	NOUN
fumecheng-10848	171	29	noise	noise	NOUN
fumecheng-10848	171	30	vibration	vibration	NOUN
fumecheng-10848	171	31	&	&	CCONJ
fumecheng-10848	171	32	active	active	ADJ
fumecheng-10848	171	33	control	control	NOUN
fumecheng-10848	171	34	,	,	PUNCT
fumecheng-10848	171	35	41(1	41(1	NUM
fumecheng-10848	171	36	)	)	PUNCT
fumecheng-10848	171	37	,	,	PUNCT
fumecheng-10848	171	38	pp	pp	ADP
fumecheng-10848	171	39	.	.	PUNCT
fumecheng-10848	172	1	216	216	NUM
fumecheng-10848	172	2	-	-	SYM
fumecheng-10848	172	3	222	222	NUM
fumecheng-10848	172	4	.	.	PUNCT
fumecheng-10848	173	1	36	36	NUM
fumecheng-10848	173	2	.	.	PUNCT
fumecheng-10848	174	1	he	he	PRON
fumecheng-10848	174	2	,	,	PUNCT
fumecheng-10848	174	3	c.h	c.h	PROPN
fumecheng-10848	174	4	.	.	PROPN
fumecheng-10848	174	5	,	,	PUNCT
fumecheng-10848	174	6	wang	wang	PROPN
fumecheng-10848	174	7	,	,	PUNCT
fumecheng-10848	174	8	j.h	j.h	PROPN
fumecheng-10848	174	9	.	.	PROPN
fumecheng-10848	174	10	,	,	PUNCT
fumecheng-10848	174	11	yao	yao	PROPN
fumecheng-10848	174	12	,	,	PUNCT
fumecheng-10848	174	13	s.w	s.w	PROPN
fumecheng-10848	174	14	.	.	PROPN
fumecheng-10848	174	15	,	,	PUNCT
fumecheng-10848	174	16	2019	2019	NUM
fumecheng-10848	174	17	,	,	PUNCT
fumecheng-10848	174	18	a	a	DET
fumecheng-10848	174	19	complement	complement	NOUN
fumecheng-10848	174	20	to	to	ADP
fumecheng-10848	174	21	period	period	NOUN
fumecheng-10848	174	22	/	/	SYM
fumecheng-10848	174	23	frequency	frequency	NOUN
fumecheng-10848	174	24	estimation	estimation	NOUN
fumecheng-10848	174	25	of	of	ADP
fumecheng-10848	174	26	a	a	DET
fumecheng-10848	174	27	nonlinear	nonlinear	ADJ
fumecheng-10848	174	28	oscillator	oscillator	NOUN
fumecheng-10848	174	29	,	,	PUNCT
fumecheng-10848	174	30	journal	journal	NOUN
fumecheng-10848	174	31	of	of	ADP
fumecheng-10848	174	32	low	low	ADJ
fumecheng-10848	174	33	frequency	frequency	NOUN
fumecheng-10848	174	34	noise	noise	NOUN
fumecheng-10848	174	35	vibration	vibration	NOUN
fumecheng-10848	174	36	&	&	CCONJ
fumecheng-10848	174	37	active	active	ADJ
fumecheng-10848	174	38	control	control	NOUN
fumecheng-10848	174	39	,	,	PUNCT
fumecheng-10848	174	40	38	38	NUM
fumecheng-10848	174	41	,	,	PUNCT
fumecheng-10848	174	42	pp	pp	ADJ
fumecheng-10848	174	43	.	.	PUNCT
fumecheng-10848	175	1	992	992	NUM
fumecheng-10848	175	2	-	-	SYM
fumecheng-10848	175	3	995	995	NUM
fumecheng-10848	175	4	.	.	PUNCT
fumecheng-10848	176	1	37	37	NUM
fumecheng-10848	176	2	.	.	PUNCT
fumecheng-10848	177	1	tian	tian	PROPN
fumecheng-10848	177	2	,	,	PUNCT
fumecheng-10848	177	3	y.	y.	NOUN
fumecheng-10848	177	4	,	,	PUNCT
fumecheng-10848	177	5	2022	2022	NUM
fumecheng-10848	177	6	,	,	PUNCT
fumecheng-10848	177	7	frequency	frequency	NOUN
fumecheng-10848	177	8	formula	formula	NOUN
fumecheng-10848	177	9	for	for	ADP
fumecheng-10848	177	10	a	a	DET
fumecheng-10848	177	11	class	class	NOUN
fumecheng-10848	177	12	of	of	ADP
fumecheng-10848	177	13	fractal	fractal	ADJ
fumecheng-10848	177	14	vibration	vibration	NOUN
fumecheng-10848	177	15	system	system	NOUN
fumecheng-10848	177	16	,	,	PUNCT
fumecheng-10848	177	17	reports	report	NOUN
fumecheng-10848	177	18	in	in	ADP
fumecheng-10848	177	19	mechanical	mechanical	ADJ
fumecheng-10848	177	20	engineering	engineering	NOUN
fumecheng-10848	177	21	,	,	PUNCT
fumecheng-10848	177	22	3(1	3(1	NUM
fumecheng-10848	177	23	)	)	PUNCT
fumecheng-10848	177	24	,	,	PUNCT
fumecheng-10848	177	25	pp	pp	ADP
fumecheng-10848	177	26	.	.	PUNCT
fumecheng-10848	178	1	55	55	NUM
fumecheng-10848	178	2	-	-	SYM
fumecheng-10848	178	3	61	61	NUM
fumecheng-10848	178	4	.	.	PUNCT
fumecheng-10848	179	1	38	38	NUM
fumecheng-10848	179	2	.	.	PUNCT
fumecheng-10848	180	1	ma	ma	PROPN
fumecheng-10848	180	2	,	,	PUNCT
fumecheng-10848	180	3	h.j	h.j	PROPN
fumecheng-10848	180	4	.	.	PROPN
fumecheng-10848	180	5	,	,	PUNCT
fumecheng-10848	180	6	2022	2022	NUM
fumecheng-10848	180	7	,	,	PUNCT
fumecheng-10848	180	8	simplified	simplified	ADJ
fumecheng-10848	180	9	hamiltonian	hamiltonian	ADJ
fumecheng-10848	180	10	-	-	PUNCT
fumecheng-10848	180	11	based	base	VERB
fumecheng-10848	180	12	frequency	frequency	NOUN
fumecheng-10848	180	13	-	-	PUNCT
fumecheng-10848	180	14	amplitude	amplitude	NOUN
fumecheng-10848	180	15	formulation	formulation	NOUN
fumecheng-10848	180	16	for	for	ADP
fumecheng-10848	180	17	nonlinear	nonlinear	ADJ
fumecheng-10848	180	18	vibration	vibration	NOUN
fumecheng-10848	180	19	systems	system	NOUN
fumecheng-10848	180	20	,	,	PUNCT
fumecheng-10848	180	21	facta	facta	PROPN
fumecheng-10848	180	22	universitatis	universitatis	PROPN
fumecheng-10848	180	23	-	-	PUNCT
fumecheng-10848	180	24	series	series	NOUN
fumecheng-10848	180	25	mechanical	mechanical	ADJ
fumecheng-10848	180	26	engineering	engineering	NOUN
fumecheng-10848	180	27	,	,	PUNCT
fumecheng-10848	180	28	20(2	20(2	NUM
fumecheng-10848	180	29	)	)	PUNCT
fumecheng-10848	180	30	,	,	PUNCT
fumecheng-10848	180	31	pp	pp	PROPN
fumecheng-10848	180	32	.	.	PUNCT
fumecheng-10848	181	1	445	445	NUM
fumecheng-10848	181	2	-	-	SYM
fumecheng-10848	181	3	455	455	NUM
fumecheng-10848	181	4	.	.	PUNCT
fumecheng-10848	182	1	39	39	NUM
fumecheng-10848	182	2	.	.	PUNCT
fumecheng-10848	183	1	he	he	PRON
fumecheng-10848	183	2	,	,	PUNCT
fumecheng-10848	183	3	c.h	c.h	PROPN
fumecheng-10848	183	4	.	.	PROPN
fumecheng-10848	183	5	,	,	PUNCT
fumecheng-10848	183	6	liu	liu	PROPN
fumecheng-10848	183	7	,	,	PUNCT
fumecheng-10848	183	8	c.	c.	PROPN
fumecheng-10848	183	9	,	,	PUNCT
fumecheng-10848	183	10	he	he	PRON
fumecheng-10848	183	11	,	,	PUNCT
fumecheng-10848	183	12	j.h	j.h	PROPN
fumecheng-10848	183	13	.	.	PROPN
fumecheng-10848	183	14	,	,	PUNCT
fumecheng-10848	183	15	sedighi	sedighi	PROPN
fumecheng-10848	183	16	,	,	PUNCT
fumecheng-10848	183	17	h.m	h.m	PROPN
fumecheng-10848	183	18	.	.	PROPN
fumecheng-10848	183	19	,	,	PUNCT
fumecheng-10848	183	20	shokri	shokri	PROPN
fumecheng-10848	183	21	,	,	PUNCT
fumecheng-10848	183	22	a.	a.	NOUN
fumecheng-10848	183	23	,	,	PUNCT
fumecheng-10848	183	24	gepreel	gepreel	ADJ
fumecheng-10848	183	25	,	,	PUNCT
fumecheng-10848	183	26	k.a	k.a	PROPN
fumecheng-10848	183	27	.	.	PROPN
fumecheng-10848	183	28	,	,	PUNCT
fumecheng-10848	183	29	2022	2022	NUM
fumecheng-10848	183	30	,	,	PUNCT
fumecheng-10848	183	31	a	a	DET
fumecheng-10848	183	32	fractal	fractal	ADJ
fumecheng-10848	183	33	model	model	NOUN
fumecheng-10848	183	34	for	for	ADP
fumecheng-10848	183	35	the	the	DET
fumecheng-10848	183	36	internal	internal	ADJ
fumecheng-10848	183	37	temperature	temperature	NOUN
fumecheng-10848	183	38	response	response	NOUN
fumecheng-10848	183	39	of	of	ADP
fumecheng-10848	183	40	a	a	DET
fumecheng-10848	183	41	porous	porous	ADJ
fumecheng-10848	183	42	concrete	concrete	NOUN
fumecheng-10848	183	43	,	,	PUNCT
fumecheng-10848	183	44	applied	apply	VERB
fumecheng-10848	183	45	and	and	CCONJ
fumecheng-10848	183	46	computational	computational	ADJ
fumecheng-10848	183	47	mathematics	mathematic	NOUN
fumecheng-10848	183	48	,	,	PUNCT
fumecheng-10848	183	49	21(1	21(1	NUM
fumecheng-10848	183	50	)	)	PUNCT
fumecheng-10848	183	51	,	,	PUNCT
fumecheng-10848	183	52	pp	pp	ADJ
fumecheng-10848	183	53	.	.	PUNCT
fumecheng-10848	184	1	71	71	NUM
fumecheng-10848	184	2	-	-	SYM
fumecheng-10848	184	3	77	77	NUM
fumecheng-10848	184	4	.	.	PUNCT
fumecheng-10848	185	1	40	40	NUM
fumecheng-10848	185	2	.	.	PUNCT
fumecheng-10848	186	1	wang	wang	PROPN
fumecheng-10848	186	2	,	,	PUNCT
fumecheng-10848	186	3	k.j	k.j	PROPN
fumecheng-10848	186	4	.	.	PROPN
fumecheng-10848	186	5	,	,	PUNCT
fumecheng-10848	186	6	wang	wang	PROPN
fumecheng-10848	186	7	,	,	PUNCT
fumecheng-10848	186	8	j.f	j.f	PROPN
fumecheng-10848	186	9	.	.	PROPN
fumecheng-10848	186	10	,	,	PUNCT
fumecheng-10848	186	11	2021	2021	NUM
fumecheng-10848	186	12	,	,	PUNCT
fumecheng-10848	186	13	generalized	generalize	VERB
fumecheng-10848	186	14	variational	variational	ADJ
fumecheng-10848	186	15	principles	principle	NOUN
fumecheng-10848	186	16	of	of	ADP
fumecheng-10848	186	17	the	the	DET
fumecheng-10848	186	18	benney	benney	NOUN
fumecheng-10848	186	19	-	-	PUNCT
fumecheng-10848	186	20	lin	lin	PROPN
fumecheng-10848	186	21	equation	equation	NOUN
fumecheng-10848	186	22	arising	arise	VERB
fumecheng-10848	186	23	in	in	ADP
fumecheng-10848	186	24	fluid	fluid	ADJ
fumecheng-10848	186	25	dynamics	dynamic	NOUN
fumecheng-10848	186	26	,	,	PUNCT
fumecheng-10848	186	27	epl	epl	PROPN
fumecheng-10848	186	28	,	,	PUNCT
fumecheng-10848	186	29	doi	doi	PROPN
fumecheng-10848	186	30	:	:	PUNCT
fumecheng-10848	186	31	10.1209/0295	10.1209/0295	NUM
fumecheng-10848	186	32	-	-	PUNCT
fumecheng-10848	186	33	5075	5075	NUM
fumecheng-10848	186	34	/	/	SYM
fumecheng-10848	186	35	ac3cce	ac3cce	NOUN
fumecheng-10848	186	36	.	.	PUNCT
fumecheng-10848	187	1	41	41	NUM
fumecheng-10848	187	2	.	.	PUNCT
fumecheng-10848	188	1	wang	wang	PROPN
fumecheng-10848	188	2	,	,	PUNCT
fumecheng-10848	188	3	k.l	k.l	PROPN
fumecheng-10848	188	4	.	.	PROPN
fumecheng-10848	188	5	,	,	PUNCT
fumecheng-10848	188	6	2022	2022	NUM
fumecheng-10848	188	7	,	,	PUNCT
fumecheng-10848	188	8	exact	exact	ADJ
fumecheng-10848	188	9	solitary	solitary	ADJ
fumecheng-10848	188	10	wave	wave	NOUN
fumecheng-10848	188	11	solution	solution	NOUN
fumecheng-10848	188	12	for	for	ADP
fumecheng-10848	188	13	fractal	fractal	ADJ
fumecheng-10848	188	14	shallow	shallow	ADJ
fumecheng-10848	188	15	water	water	NOUN
fumecheng-10848	188	16	wave	wave	NOUN
fumecheng-10848	188	17	model	model	NOUN
fumecheng-10848	188	18	by	by	ADP
fumecheng-10848	188	19	he	he	PRON
fumecheng-10848	188	20	’s	’	VERB
fumecheng-10848	188	21	variational	variational	ADJ
fumecheng-10848	188	22	method	method	NOUN
fumecheng-10848	188	23	,	,	PUNCT
fumecheng-10848	188	24	modern	modern	ADJ
fumecheng-10848	188	25	physics	physics	NOUN
fumecheng-10848	188	26	letters	letters	PROPN
fumecheng-10848	188	27	b	b	NOUN
fumecheng-10848	188	28	,	,	PUNCT
fumecheng-10848	188	29	36(7	36(7	NUM
fumecheng-10848	188	30	)	)	PUNCT
fumecheng-10848	188	31	,	,	PUNCT
fumecheng-10848	188	32	2150602	2150602	NUM
fumecheng-10848	188	33	.	.	PUNCT
fumecheng-10848	189	1	42	42	NUM
fumecheng-10848	189	2	.	.	PUNCT
fumecheng-10848	190	1	wang	wang	PROPN
fumecheng-10848	190	2	,	,	PUNCT
fumecheng-10848	190	3	k.l	k.l	PROPN
fumecheng-10848	190	4	.	.	PROPN
fumecheng-10848	190	5	,	,	PUNCT
fumecheng-10848	190	6	2022	2022	NUM
fumecheng-10848	190	7	,	,	PUNCT
fumecheng-10848	190	8	solitary	solitary	ADJ
fumecheng-10848	190	9	wave	wave	NOUN
fumecheng-10848	190	10	solution	solution	NOUN
fumecheng-10848	190	11	of	of	ADP
fumecheng-10848	190	12	nonlinear	nonlinear	ADJ
fumecheng-10848	190	13	bogoyavlenskii	bogoyavlenskii	ADJ
fumecheng-10848	190	14	system	system	NOUN
fumecheng-10848	190	15	by	by	ADP
fumecheng-10848	190	16	variational	variational	ADJ
fumecheng-10848	190	17	analysis	analysis	NOUN
fumecheng-10848	190	18	method	method	NOUN
fumecheng-10848	190	19	,	,	PUNCT
fumecheng-10848	190	20	international	international	ADJ
fumecheng-10848	190	21	journal	journal	NOUN
fumecheng-10848	190	22	of	of	ADP
fumecheng-10848	190	23	modern	modern	ADJ
fumecheng-10848	190	24	physics	physics	PROPN
fumecheng-10848	190	25	b	b	PROPN
fumecheng-10848	190	26	,	,	PUNCT
fumecheng-10848	190	27	36(2	36(2	NUM
fumecheng-10848	190	28	)	)	PUNCT
fumecheng-10848	190	29	,	,	PUNCT
fumecheng-10848	190	30	2250015	2250015	NUM
fumecheng-10848	190	31	.	.	PUNCT
fumecheng-10848	191	1	43	43	NUM
fumecheng-10848	191	2	.	.	PUNCT
fumecheng-10848	192	1	wang	wang	PROPN
fumecheng-10848	192	2	,	,	PUNCT
fumecheng-10848	192	3	k.l	k.l	PROPN
fumecheng-10848	192	4	.	.	PROPN
fumecheng-10848	192	5	,	,	PUNCT
fumecheng-10848	192	6	2022	2022	NUM
fumecheng-10848	192	7	,	,	PUNCT
fumecheng-10848	192	8	new	new	ADJ
fumecheng-10848	192	9	variational	variational	ADJ
fumecheng-10848	192	10	theory	theory	NOUN
fumecheng-10848	192	11	for	for	ADP
fumecheng-10848	192	12	coupled	couple	VERB
fumecheng-10848	192	13	nonlinear	nonlinear	ADJ
fumecheng-10848	192	14	fractal	fractal	PROPN
fumecheng-10848	192	15	schrodinger	schrodinger	PROPN
fumecheng-10848	192	16	system	system	PROPN
fumecheng-10848	192	17	,	,	PUNCT
fumecheng-10848	192	18	international	international	ADJ
fumecheng-10848	192	19	journal	journal	NOUN
fumecheng-10848	192	20	of	of	ADP
fumecheng-10848	192	21	numerical	numerical	ADJ
fumecheng-10848	192	22	methods	method	NOUN
fumecheng-10848	192	23	for	for	ADP
fumecheng-10848	192	24	heat	heat	NOUN
fumecheng-10848	192	25	&	&	CCONJ
fumecheng-10848	192	26	fluid	fluid	ADJ
fumecheng-10848	192	27	flow	flow	NOUN
fumecheng-10848	192	28	,	,	PUNCT
fumecheng-10848	192	29	32(2	32(2	NUM
fumecheng-10848	192	30	)	)	PUNCT
fumecheng-10848	192	31	,	,	PUNCT
fumecheng-10848	192	32	pp	pp	ADP
fumecheng-10848	192	33	.	.	PUNCT
fumecheng-10848	193	1	589	589	NUM
fumecheng-10848	193	2	-	-	SYM
fumecheng-10848	193	3	597	597	NUM
fumecheng-10848	193	4	.	.	NUM
fumecheng-10848	194	1	44	44	NUM
fumecheng-10848	194	2	.	.	PUNCT
fumecheng-10848	195	1	he	he	PRON
fumecheng-10848	195	2	,	,	PUNCT
fumecheng-10848	195	3	j.h	j.h	PROPN
fumecheng-10848	195	4	.	.	PROPN
fumecheng-10848	195	5	,	,	PUNCT
fumecheng-10848	195	6	hou	hou	PROPN
fumecheng-10848	195	7	,	,	PUNCT
fumecheng-10848	195	8	w.f	w.f	PROPN
fumecheng-10848	195	9	.	.	PROPN
fumecheng-10848	195	10	,	,	PUNCT
fumecheng-10848	195	11	he	he	PRON
fumecheng-10848	195	12	,	,	PUNCT
fumecheng-10848	195	13	c.h	c.h	PROPN
fumecheng-10848	195	14	.	.	PROPN
fumecheng-10848	195	15	,	,	PUNCT
fumecheng-10848	195	16	saeed	saeed	PROPN
fumecheng-10848	195	17	,	,	PUNCT
fumecheng-10848	195	18	t.	t.	PROPN
fumecheng-10848	195	19	,	,	PUNCT
fumecheng-10848	195	20	2021	2021	NUM
fumecheng-10848	195	21	,	,	PUNCT
fumecheng-10848	195	22	variational	variational	ADJ
fumecheng-10848	195	23	approach	approach	NOUN
fumecheng-10848	195	24	to	to	ADP
fumecheng-10848	195	25	fractal	fractal	ADJ
fumecheng-10848	195	26	solitary	solitary	ADJ
fumecheng-10848	195	27	waves	wave	NOUN
fumecheng-10848	195	28	,	,	PUNCT
fumecheng-10848	195	29	fractals	fractal	NOUN
fumecheng-10848	195	30	,	,	PUNCT
fumecheng-10848	195	31	29(7	29(7	NUM
fumecheng-10848	195	32	)	)	PUNCT
fumecheng-10848	195	33	,	,	PUNCT
fumecheng-10848	195	34	2150199	2150199	NUM
fumecheng-10848	195	35	.	.	PUNCT
fumecheng-10848	196	1	45	45	NUM
fumecheng-10848	196	2	.	.	PUNCT
fumecheng-10848	197	1	he	he	PRON
fumecheng-10848	197	2	,	,	PUNCT
fumecheng-10848	197	3	j.h	j.h	PROPN
fumecheng-10848	197	4	.	.	PROPN
fumecheng-10848	197	5	,	,	PUNCT
fumecheng-10848	197	6	he	he	PRON
fumecheng-10848	197	7	,	,	PUNCT
fumecheng-10848	197	8	c.h	c.h	PROPN
fumecheng-10848	197	9	.	.	PROPN
fumecheng-10848	197	10	,	,	PUNCT
fumecheng-10848	197	11	sedighi	sedighi	PROPN
fumecheng-10848	197	12	,	,	PUNCT
fumecheng-10848	197	13	h.m	h.m	PROPN
fumecheng-10848	197	14	.	.	PROPN
fumecheng-10848	197	15	,	,	PUNCT
fumecheng-10848	197	16	2021	2021	NUM
fumecheng-10848	197	17	,	,	PUNCT
fumecheng-10848	197	18	evans	evans	PROPN
fumecheng-10848	197	19	model	model	PROPN
fumecheng-10848	197	20	for	for	ADP
fumecheng-10848	197	21	dynamic	dynamic	ADJ
fumecheng-10848	197	22	economics	economic	NOUN
fumecheng-10848	197	23	revised	revise	VERB
fumecheng-10848	197	24	,	,	PUNCT
fumecheng-10848	197	25	aims	aim	VERB
fumecheng-10848	197	26	mathematics	mathematic	NOUN
fumecheng-10848	197	27	,	,	PUNCT
fumecheng-10848	197	28	6(9	6(9	NUM
fumecheng-10848	197	29	)	)	PUNCT
fumecheng-10848	197	30	,	,	PUNCT
fumecheng-10848	197	31	pp	pp	ADP
fumecheng-10848	197	32	.	.	PUNCT
fumecheng-10848	198	1	9194	9194	NUM
fumecheng-10848	198	2	-	-	SYM
fumecheng-10848	198	3	9206	9206	NUM
fumecheng-10848	198	4	.	.	PUNCT
fumecheng-10848	199	1	46	46	NUM
fumecheng-10848	199	2	.	.	PUNCT
fumecheng-10848	200	1	he	he	PRON
fumecheng-10848	200	2	,	,	PUNCT
fumecheng-10848	200	3	j.h	j.h	PROPN
fumecheng-10848	200	4	.	.	PROPN
fumecheng-10848	200	5	,	,	PUNCT
fumecheng-10848	200	6	amer	amer	PROPN
fumecheng-10848	200	7	,	,	PUNCT
fumecheng-10848	200	8	t.s	t.s	PROPN
fumecheng-10848	200	9	.	.	PROPN
fumecheng-10848	200	10	,	,	PUNCT
fumecheng-10848	200	11	elnaggar	elnaggar	PROPN
fumecheng-10848	200	12	,	,	PUNCT
fumecheng-10848	200	13	s.	s.	PROPN
fumecheng-10848	200	14	,	,	PUNCT
fumecheng-10848	200	15	galal	galal	PROPN
fumecheng-10848	200	16	,	,	PUNCT
fumecheng-10848	200	17	a.a	a.a	PROPN
fumecheng-10848	200	18	.	.	PROPN
fumecheng-10848	200	19	,	,	PUNCT
fumecheng-10848	200	20	2021	2021	NUM
fumecheng-10848	200	21	,	,	PUNCT
fumecheng-10848	200	22	periodic	periodic	ADJ
fumecheng-10848	200	23	property	property	NOUN
fumecheng-10848	200	24	and	and	CCONJ
fumecheng-10848	200	25	instability	instability	NOUN
fumecheng-10848	200	26	of	of	ADP
fumecheng-10848	200	27	a	a	DET
fumecheng-10848	200	28	rotating	rotate	VERB
fumecheng-10848	200	29	pendulum	pendulum	NOUN
fumecheng-10848	200	30	system	system	NOUN
fumecheng-10848	200	31	,	,	PUNCT
fumecheng-10848	200	32	axioms	axiom	NOUN
fumecheng-10848	200	33	,	,	PUNCT
fumecheng-10848	200	34	10(3	10(3	NUM
fumecheng-10848	200	35	)	)	PUNCT
fumecheng-10848	200	36	,	,	PUNCT
fumecheng-10848	200	37	191	191	NUM
fumecheng-10848	200	38	.	.	PUNCT
fumecheng-10848	200	39	47	47	NUM
fumecheng-10848	200	40	.	.	PUNCT
fumecheng-10848	201	1	he	he	PRON
fumecheng-10848	201	2	,	,	PUNCT
fumecheng-10848	201	3	c.h	c.h	PROPN
fumecheng-10848	201	4	.	.	PROPN
fumecheng-10848	201	5	,	,	PUNCT
fumecheng-10848	201	6	amer	amer	PROPN
fumecheng-10848	201	7	,	,	PUNCT
fumecheng-10848	201	8	t.s	t.s	PROPN
fumecheng-10848	201	9	.	.	PROPN
fumecheng-10848	201	10	,	,	PUNCT
fumecheng-10848	201	11	tian	tian	PROPN
fumecheng-10848	201	12	,	,	PUNCT
fumecheng-10848	201	13	d.	d.	PROPN
fumecheng-10848	201	14	,	,	PUNCT
fumecheng-10848	201	15	abolila	abolila	PROPN
fumecheng-10848	201	16	,	,	PUNCT
fumecheng-10848	201	17	a.f	a.f	PROPN
fumecheng-10848	201	18	.	.	PROPN
fumecheng-10848	201	19	,	,	PUNCT
fumecheng-10848	201	20	galal	galal	PROPN
fumecheng-10848	201	21	,	,	PUNCT
fumecheng-10848	201	22	a.a	a.a	PROPN
fumecheng-10848	201	23	.	.	PROPN
fumecheng-10848	201	24	,	,	PUNCT
fumecheng-10848	201	25	2022	2022	NUM
fumecheng-10848	201	26	,	,	PUNCT
fumecheng-10848	201	27	controlling	control	VERB
fumecheng-10848	201	28	the	the	DET
fumecheng-10848	201	29	kinematics	kinematic	NOUN
fumecheng-10848	201	30	of	of	ADP
fumecheng-10848	201	31	a	a	DET
fumecheng-10848	201	32	spring	spring	NOUN
fumecheng-10848	201	33	-	-	PUNCT
fumecheng-10848	201	34	pendulum	pendulum	NOUN
fumecheng-10848	201	35	system	system	NOUN
fumecheng-10848	201	36	using	use	VERB
fumecheng-10848	201	37	an	an	DET
fumecheng-10848	201	38	energy	energy	NOUN
fumecheng-10848	201	39	harvesting	harvesting	NOUN
fumecheng-10848	201	40	device	device	NOUN
fumecheng-10848	201	41	,	,	PUNCT
fumecheng-10848	201	42	journal	journal	NOUN
fumecheng-10848	201	43	of	of	ADP
fumecheng-10848	201	44	low	low	ADJ
fumecheng-10848	201	45	frequency	frequency	NOUN
fumecheng-10848	201	46	noise	noise	NOUN
fumecheng-10848	201	47	,	,	PUNCT
fumecheng-10848	201	48	vibration	vibration	NOUN
fumecheng-10848	201	49	&	&	CCONJ
fumecheng-10848	201	50	active	active	ADJ
fumecheng-10848	201	51	control	control	NOUN
fumecheng-10848	201	52	,	,	PUNCT
fumecheng-10848	201	53	41(3	41(3	NUM
fumecheng-10848	201	54	)	)	PUNCT
fumecheng-10848	201	55	,	,	PUNCT
fumecheng-10848	201	56	pp	pp	PROPN
fumecheng-10848	201	57	.	.	PUNCT
fumecheng-10848	201	58	1234	1234	NUM
fumecheng-10848	201	59	-	-	SYM
fumecheng-10848	201	60	1257	1257	NUM
fumecheng-10848	201	61	.	.	PUNCT
fumecheng-10848	202	1	48	48	NUM
fumecheng-10848	202	2	.	.	PUNCT
fumecheng-10848	203	1	he	he	PRON
fumecheng-10848	203	2	,	,	PUNCT
fumecheng-10848	203	3	c.h	c.h	PROPN
fumecheng-10848	203	4	.	.	PROPN
fumecheng-10848	203	5	,	,	PUNCT
fumecheng-10848	203	6	tian	tian	PROPN
fumecheng-10848	203	7	,	,	PUNCT
fumecheng-10848	203	8	d.	d.	PROPN
fumecheng-10848	203	9	,	,	PUNCT
fumecheng-10848	203	10	moatimid	moatimid	PROPN
fumecheng-10848	203	11	,	,	PUNCT
fumecheng-10848	203	12	g.m	g.m	PROPN
fumecheng-10848	203	13	.	.	PROPN
fumecheng-10848	203	14	,	,	PUNCT
fumecheng-10848	203	15	salman	salman	PROPN
fumecheng-10848	203	16	,	,	PUNCT
fumecheng-10848	203	17	h.f	h.f	PROPN
fumecheng-10848	203	18	.	.	PROPN
fumecheng-10848	203	19	,	,	PUNCT
fumecheng-10848	203	20	zekry	zekry	PROPN
fumecheng-10848	203	21	,	,	PUNCT
fumecheng-10848	203	22	m.h	m.h	PROPN
fumecheng-10848	203	23	.	.	PROPN
fumecheng-10848	203	24	,	,	PUNCT
fumecheng-10848	203	25	2022	2022	NUM
fumecheng-10848	203	26	,	,	PUNCT
fumecheng-10848	203	27	hybrid	hybrid	ADJ
fumecheng-10848	203	28	rayleigh	rayleigh	PROPN
fumecheng-10848	203	29	-van	-van	PROPN
fumecheng-10848	203	30	der	der	ADJ
fumecheng-10848	203	31	pol	pol	NOUN
fumecheng-10848	203	32	-	-	PUNCT
fumecheng-10848	203	33	duffing	duffe	VERB
fumecheng-10848	203	34	oscillator	oscillator	NOUN
fumecheng-10848	203	35	(	(	PUNCT
fumecheng-10848	203	36	hrvd	hrvd	NOUN
fumecheng-10848	203	37	):	):	PUNCT
fumecheng-10848	203	38	stability	stability	NOUN
fumecheng-10848	203	39	analysis	analysis	NOUN
fumecheng-10848	203	40	and	and	CCONJ
fumecheng-10848	203	41	controller	controller	NOUN
fumecheng-10848	203	42	,	,	PUNCT
fumecheng-10848	203	43	journal	journal	NOUN
fumecheng-10848	203	44	of	of	ADP
fumecheng-10848	203	45	low	low	ADJ
fumecheng-10848	203	46	frequency	frequency	NOUN
fumecheng-10848	203	47	noise	noise	NOUN
fumecheng-10848	203	48	,	,	PUNCT
fumecheng-10848	203	49	vibration	vibration	NOUN
fumecheng-10848	203	50	&	&	CCONJ
fumecheng-10848	203	51	active	active	ADJ
fumecheng-10848	203	52	control	control	NOUN
fumecheng-10848	203	53	,	,	PUNCT
fumecheng-10848	203	54	41(1	41(1	NUM
fumecheng-10848	203	55	)	)	PUNCT
fumecheng-10848	203	56	,	,	PUNCT
fumecheng-10848	203	57	pp	pp	PROPN
fumecheng-10848	203	58	.	.	PUNCT
fumecheng-10848	204	1	244	244	NUM
fumecheng-10848	204	2	-	-	SYM
fumecheng-10848	204	3	268	268	NUM
fumecheng-10848	204	4	.	.	PUNCT
fumecheng-10848	205	1	49	49	NUM
fumecheng-10848	205	2	.	.	PUNCT
fumecheng-10848	206	1	shaban	shaban	PROPN
fumecheng-10848	206	2	,	,	PUNCT
fumecheng-10848	206	3	m.	m.	NOUN
fumecheng-10848	206	4	,	,	PUNCT
fumecheng-10848	206	5	ganji	ganji	X
fumecheng-10848	206	6	,	,	PUNCT
fumecheng-10848	206	7	d.d	d.d	PROPN
fumecheng-10848	206	8	.	.	PROPN
fumecheng-10848	206	9	,	,	PUNCT
fumecheng-10848	206	10	alipour	alipour	PROPN
fumecheng-10848	206	11	,	,	PUNCT
fumecheng-10848	206	12	m.m	m.m	PROPN
fumecheng-10848	206	13	.	.	PROPN
fumecheng-10848	206	14	,	,	PUNCT
fumecheng-10848	206	15	2010	2010	NUM
fumecheng-10848	206	16	,	,	PUNCT
fumecheng-10848	206	17	nonlinear	nonlinear	ADJ
fumecheng-10848	206	18	fluctuation	fluctuation	NOUN
fumecheng-10848	206	19	,	,	PUNCT
fumecheng-10848	206	20	frequency	frequency	NOUN
fumecheng-10848	206	21	and	and	CCONJ
fumecheng-10848	206	22	stability	stability	NOUN
fumecheng-10848	206	23	analyses	analysis	NOUN
fumecheng-10848	206	24	in	in	ADP
fumecheng-10848	206	25	free	free	ADJ
fumecheng-10848	206	26	vibration	vibration	NOUN
fumecheng-10848	206	27	of	of	ADP
fumecheng-10848	206	28	circular	circular	ADJ
fumecheng-10848	206	29	sector	sector	NOUN
fumecheng-10848	206	30	oscillation	oscillation	NOUN
fumecheng-10848	206	31	systems	system	NOUN
fumecheng-10848	206	32	,	,	PUNCT
fumecheng-10848	206	33	journal	journal	NOUN
fumecheng-10848	206	34	of	of	ADP
fumecheng-10848	206	35	current	current	ADJ
fumecheng-10848	206	36	applied	applied	ADJ
fumecheng-10848	206	37	physics	physic	NOUN
fumecheng-10848	206	38	,	,	PUNCT
fumecheng-10848	206	39	10	10	NUM
fumecheng-10848	206	40	,	,	PUNCT
fumecheng-10848	206	41	pp	pp	ADJ
fumecheng-10848	206	42	.	.	PUNCT
fumecheng-10848	207	1	1267	1267	NUM
fumecheng-10848	207	2	-	-	SYM
fumecheng-10848	207	3	1285	1285	NUM
fumecheng-10848	207	4	.	.	PUNCT
fumecheng-10848	208	1	50	50	NUM
fumecheng-10848	208	2	.	.	PUNCT
fumecheng-10848	209	1	qian	qian	PROPN
fumecheng-10848	209	2	,	,	PUNCT
fumecheng-10848	209	3	m.y	m.y	PROPN
fumecheng-10848	209	4	.	.	PROPN
fumecheng-10848	209	5	,	,	PUNCT
fumecheng-10848	209	6	he	he	PRON
fumecheng-10848	209	7	,	,	PUNCT
fumecheng-10848	209	8	j.h	j.h	PROPN
fumecheng-10848	209	9	.	.	PROPN
fumecheng-10848	209	10	,	,	PUNCT
fumecheng-10848	209	11	2022	2022	NUM
fumecheng-10848	209	12	,	,	PUNCT
fumecheng-10848	209	13	two	two	NUM
fumecheng-10848	209	14	-	-	PUNCT
fumecheng-10848	209	15	scale	scale	NOUN
fumecheng-10848	209	16	thermal	thermal	ADJ
fumecheng-10848	209	17	science	science	NOUN
fumecheng-10848	209	18	for	for	ADP
fumecheng-10848	209	19	modern	modern	ADJ
fumecheng-10848	209	20	life	life	NOUN
fumecheng-10848	209	21	–	–	PUNCT
fumecheng-10848	209	22	making	make	VERB
fumecheng-10848	209	23	the	the	DET
fumecheng-10848	209	24	impossible	impossible	ADJ
fumecheng-10848	209	25	possible	possible	ADJ
fumecheng-10848	209	26	,	,	PUNCT
fumecheng-10848	209	27	thermal	thermal	ADJ
fumecheng-10848	209	28	science	science	NOUN
fumecheng-10848	209	29	,	,	PUNCT
fumecheng-10848	209	30	26(3b	26(3b	NUM
fumecheng-10848	209	31	)	)	PUNCT
fumecheng-10848	209	32	,	,	PUNCT
fumecheng-10848	209	33	pp	pp	ADP
fumecheng-10848	209	34	.	.	PUNCT
fumecheng-10848	210	1	2409	2409	NUM
fumecheng-10848	210	2	-	-	SYM
fumecheng-10848	210	3	2412	2412	NUM
fumecheng-10848	210	4	.	.	PUNCT
fumecheng-10848	211	1	51	51	NUM
fumecheng-10848	211	2	.	.	PUNCT
fumecheng-10848	212	1	he	he	PRON
fumecheng-10848	212	2	,	,	PUNCT
fumecheng-10848	212	3	j.h	j.h	PROPN
fumecheng-10848	212	4	.	.	PROPN
fumecheng-10848	212	5	,	,	PUNCT
fumecheng-10848	212	6	elazem	elazem	NOUN
fumecheng-10848	212	7	,	,	PUNCT
fumecheng-10848	212	8	n.y.a	n.y.a	NOUN
fumecheng-10848	212	9	.	.	PROPN
fumecheng-10848	212	10	,	,	PUNCT
fumecheng-10848	212	11	2022	2022	NUM
fumecheng-10848	212	12	,	,	PUNCT
fumecheng-10848	212	13	the	the	DET
fumecheng-10848	212	14	carbon	carbon	NOUN
fumecheng-10848	212	15	nanotube	nanotube	NOUN
fumecheng-10848	212	16	-	-	PUNCT
fumecheng-10848	212	17	embedded	embed	VERB
fumecheng-10848	212	18	boundary	boundary	ADJ
fumecheng-10848	212	19	layer	layer	NOUN
fumecheng-10848	212	20	theory	theory	NOUN
fumecheng-10848	212	21	for	for	ADP
fumecheng-10848	212	22	energy	energy	NOUN
fumecheng-10848	212	23	harvesting	harvesting	NOUN
fumecheng-10848	212	24	,	,	PUNCT
fumecheng-10848	212	25	facta	facta	PROPN
fumecheng-10848	212	26	universitatis	universitatis	PROPN
fumecheng-10848	212	27	-	-	PUNCT
fumecheng-10848	212	28	series	series	NOUN
fumecheng-10848	212	29	mechanical	mechanical	ADJ
fumecheng-10848	212	30	engineering	engineering	NOUN
fumecheng-10848	212	31	,	,	PUNCT
fumecheng-10848	212	32	20(2	20(2	NUM
fumecheng-10848	212	33	)	)	PUNCT
fumecheng-10848	212	34	,	,	PUNCT
fumecheng-10848	212	35	pp	pp	PROPN
fumecheng-10848	212	36	.	.	PUNCT
fumecheng-10848	213	1	211	211	NUM
fumecheng-10848	213	2	-	-	SYM
fumecheng-10848	213	3	235	235	NUM
fumecheng-10848	213	4	.	.	PUNCT