id	sid	tid	token	lemma	pos
fumecheng-13730	1	1	13730	13730	NUM
fumecheng-13730	1	2	facta	facta	NOUN
fumecheng-13730	1	3	universitatis	universitatis	PROPN
fumecheng-13730	1	4	series	series	NOUN
fumecheng-13730	1	5	:	:	PUNCT
fumecheng-13730	1	6	mechanical	mechanical	ADJ
fumecheng-13730	1	7	engineering	engineering	NOUN
fumecheng-13730	1	8	vol	vol	NOUN
fumecheng-13730	1	9	.	.	PROPN
fumecheng-13730	1	10	23	23	NUM
fumecheng-13730	1	11	,	,	PUNCT
fumecheng-13730	1	12	no	no	DET
fumecheng-13730	1	13	2	2	NUM
fumecheng-13730	1	14	,	,	PUNCT
fumecheng-13730	1	15	2025	2025	NUM
fumecheng-13730	1	16	,	,	PUNCT
fumecheng-13730	1	17	pp	pp	ADV
fumecheng-13730	1	18	.	.	PUNCT
fumecheng-13730	2	1	197	197	NUM
fumecheng-13730	2	2	210	210	NUM
fumecheng-13730	3	1	https://doi.org/10.22190/fume250526022h	https://doi.org/10.22190/fume250526022h	NOUN
fumecheng-13730	3	2	©	©	PROPN
fumecheng-13730	3	3	2025	2025	NUM
fumecheng-13730	3	4	by	by	ADP
fumecheng-13730	3	5	university	university	PROPN
fumecheng-13730	3	6	of	of	ADP
fumecheng-13730	3	7	niš	niš	PROPN
fumecheng-13730	3	8	,	,	PUNCT
fumecheng-13730	3	9	serbia	serbia	PROPN
fumecheng-13730	3	10	|	|	ADV
fumecheng-13730	3	11	creative	creative	ADJ
fumecheng-13730	3	12	commons	common	NOUN
fumecheng-13730	3	13	license	license	NOUN
fumecheng-13730	3	14	:	:	PUNCT
fumecheng-13730	3	15	cc	cc	VERB
fumecheng-13730	3	16	by	by	ADP
fumecheng-13730	3	17	-	-	PUNCT
fumecheng-13730	3	18	nc	nc	VERB
fumecheng-13730	3	19	-	-	PUNCT
fumecheng-13730	3	20	nd	nd	ADV
fumecheng-13730	3	21	original	original	ADJ
fumecheng-13730	3	22	scientific	scientific	NOUN
fumecheng-13730	3	23	paper	paper	VERB
fumecheng-13730	3	24	a	a	DET
fumecheng-13730	3	25	modified	modify	VERB
fumecheng-13730	3	26	frequency	frequency	NOUN
fumecheng-13730	3	27	formulation	formulation	NOUN
fumecheng-13730	3	28	for	for	ADP
fumecheng-13730	3	29	nonlinear	nonlinear	ADJ
fumecheng-13730	3	30	mechanical	mechanical	ADJ
fumecheng-13730	3	31	vibrations	vibration	NOUN
fumecheng-13730	3	32	chun	chun	PROPN
fumecheng-13730	3	33	-	-	PUNCT
fumecheng-13730	3	34	hui	hui	PROPN
fumecheng-13730	3	35	he1,3	he1,3	PROPN
fumecheng-13730	3	36	,	,	PUNCT
fumecheng-13730	3	37	ji	ji	PROPN
fumecheng-13730	3	38	-	-	PROPN
fumecheng-13730	3	39	huan	huan	PROPN
fumecheng-13730	3	40	he2,4,5,6	he2,4,5,6	PROPN
fumecheng-13730	3	41	,	,	PUNCT
fumecheng-13730	3	42	jinfeng	jinfeng	PROPN
fumecheng-13730	3	43	ma7	ma7	PROPN
fumecheng-13730	3	44	,	,	PUNCT
fumecheng-13730	3	45	abdulrahman	abdulrahman	PROPN
fumecheng-13730	3	46	ali	ali	PROPN
fumecheng-13730	3	47	alsolami8	alsolami8	PROPN
fumecheng-13730	3	48	,	,	PUNCT
fumecheng-13730	3	49	xiao	xiao	PROPN
fumecheng-13730	3	50	-	-	PUNCT
fumecheng-13730	3	51	jun	jun	PROPN
fumecheng-13730	3	52	yang3	yang3	PROPN
fumecheng-13730	3	53	1	1	NUM
fumecheng-13730	3	54	school	school	NOUN
fumecheng-13730	3	55	of	of	ADP
fumecheng-13730	3	56	civil	civil	ADJ
fumecheng-13730	3	57	engineering	engineering	NOUN
fumecheng-13730	3	58	&	&	CCONJ
fumecheng-13730	3	59	transportation	transportation	PROPN
fumecheng-13730	3	60	,	,	PUNCT
fumecheng-13730	3	61	foshan	foshan	PROPN
fumecheng-13730	3	62	university	university	PROPN
fumecheng-13730	3	63	,	,	PUNCT
fumecheng-13730	3	64	foshan	foshan	PROPN
fumecheng-13730	3	65	,	,	PUNCT
fumecheng-13730	3	66	china	china	PROPN
fumecheng-13730	3	67	2department	2department	NUM
fumecheng-13730	3	68	of	of	ADP
fumecheng-13730	3	69	mathematical	mathematical	ADJ
fumecheng-13730	3	70	sciences	science	NOUN
fumecheng-13730	3	71	,	,	PUNCT
fumecheng-13730	3	72	saveetha	saveetha	PROPN
fumecheng-13730	3	73	school	school	NOUN
fumecheng-13730	3	74	of	of	ADP
fumecheng-13730	3	75	engineering	engineering	NOUN
fumecheng-13730	3	76	,	,	PUNCT
fumecheng-13730	3	77	simats	simat	NOUN
fumecheng-13730	3	78	,	,	PUNCT
fumecheng-13730	3	79	chennai	chennai	PROPN
fumecheng-13730	3	80	,	,	PUNCT
fumecheng-13730	3	81	tamil	tamil	PROPN
fumecheng-13730	3	82	nadu	nadu	PROPN
fumecheng-13730	3	83	,	,	PUNCT
fumecheng-13730	3	84	india	india	PROPN
fumecheng-13730	3	85	3school	3school	PROPN
fumecheng-13730	3	86	of	of	ADP
fumecheng-13730	3	87	mathematics	mathematics	PROPN
fumecheng-13730	3	88	,	,	PUNCT
fumecheng-13730	3	89	china	china	PROPN
fumecheng-13730	3	90	university	university	PROPN
fumecheng-13730	3	91	of	of	ADP
fumecheng-13730	3	92	mining	mining	NOUN
fumecheng-13730	3	93	and	and	CCONJ
fumecheng-13730	3	94	technology	technology	NOUN
fumecheng-13730	3	95	,	,	PUNCT
fumecheng-13730	3	96	xuzhou	xuzhou	PROPN
fumecheng-13730	3	97	china	china	PROPN
fumecheng-13730	4	1	4school	4school	PROPN
fumecheng-13730	4	2	of	of	ADP
fumecheng-13730	4	3	jia	jia	PROPN
fumecheng-13730	4	4	yang	yang	PROPN
fumecheng-13730	4	5	;	;	PUNCT
fumecheng-13730	4	6	zhejiang	zhejiang	PROPN
fumecheng-13730	4	7	shuren	shuren	PROPN
fumecheng-13730	4	8	university	university	PROPN
fumecheng-13730	4	9	,	,	PUNCT
fumecheng-13730	4	10	hangzhou	hangzhou	PROPN
fumecheng-13730	4	11	,	,	PUNCT
fumecheng-13730	4	12	china	china	PROPN
fumecheng-13730	4	13	5school	5school	NUM
fumecheng-13730	4	14	of	of	ADP
fumecheng-13730	4	15	information	information	NOUN
fumecheng-13730	4	16	engineering	engineering	NOUN
fumecheng-13730	4	17	,	,	PUNCT
fumecheng-13730	4	18	yango	yango	PROPN
fumecheng-13730	4	19	university	university	PROPN
fumecheng-13730	4	20	,	,	PUNCT
fumecheng-13730	4	21	fuzhou	fuzhou	PROPN
fumecheng-13730	4	22	,	,	PUNCT
fumecheng-13730	4	23	china	china	PROPN
fumecheng-13730	4	24	6school	6school	NUM
fumecheng-13730	4	25	of	of	ADP
fumecheng-13730	4	26	mathematics	mathematic	NOUN
fumecheng-13730	4	27	and	and	CCONJ
fumecheng-13730	4	28	big	big	ADJ
fumecheng-13730	4	29	data	datum	NOUN
fumecheng-13730	4	30	,	,	PUNCT
fumecheng-13730	4	31	hohhot	hohhot	PROPN
fumecheng-13730	4	32	minzu	minzu	PROPN
fumecheng-13730	4	33	college	college	NOUN
fumecheng-13730	4	34	,	,	PUNCT
fumecheng-13730	4	35	hohhot	hohhot	PROPN
fumecheng-13730	4	36	,	,	PUNCT
fumecheng-13730	4	37	china	china	PROPN
fumecheng-13730	4	38	7college	7college	NUM
fumecheng-13730	4	39	of	of	ADP
fumecheng-13730	4	40	civil	civil	ADJ
fumecheng-13730	4	41	engineering	engineering	NOUN
fumecheng-13730	4	42	and	and	CCONJ
fumecheng-13730	4	43	architecture	architecture	NOUN
fumecheng-13730	4	44	,	,	PUNCT
fumecheng-13730	4	45	jiaxing	jiaxing	PROPN
fumecheng-13730	4	46	university	university	PROPN
fumecheng-13730	4	47	,	,	PUNCT
fumecheng-13730	4	48	jiaxing	jiaxing	PROPN
fumecheng-13730	4	49	,	,	PUNCT
fumecheng-13730	4	50	china	china	PROPN
fumecheng-13730	4	51	8department	8department	NUM
fumecheng-13730	4	52	of	of	ADP
fumecheng-13730	4	53	mathematics	mathematic	NOUN
fumecheng-13730	4	54	,	,	PUNCT
fumecheng-13730	4	55	faculty	faculty	NOUN
fumecheng-13730	4	56	of	of	ADP
fumecheng-13730	4	57	science	science	NOUN
fumecheng-13730	4	58	,	,	PUNCT
fumecheng-13730	4	59	king	king	PROPN
fumecheng-13730	4	60	abdulaziz	abdulaziz	PROPN
fumecheng-13730	4	61	university	university	PROPN
fumecheng-13730	4	62	,	,	PUNCT
fumecheng-13730	4	63	jeddah	jeddah	PROPN
fumecheng-13730	4	64	,	,	PUNCT
fumecheng-13730	4	65	saudi	saudi	PROPN
fumecheng-13730	4	66	arabia	arabia	PROPN
fumecheng-13730	4	67	orcid	orcid	PROPN
fumecheng-13730	4	68	ids	id	NOUN
fumecheng-13730	4	69	:	:	PUNCT
fumecheng-13730	4	70	chun	chun	PROPN
fumecheng-13730	4	71	-	-	PUNCT
fumecheng-13730	4	72	hui	hui	PROPN
fumecheng-13730	5	1	he	he	PRON
fumecheng-13730	5	2	https://orcid.org/0000-0003-0810-5248	https://orcid.org/0000-0003-0810-5248	PROPN
fumecheng-13730	5	3	ji	ji	PROPN
fumecheng-13730	5	4	-	-	PROPN
fumecheng-13730	5	5	huan	huan	PROPN
fumecheng-13730	5	6	he	he	PRON
fumecheng-13730	5	7	https://orcid.org/0000-0002-1636-0559	https://orcid.org/0000-0002-1636-0559	VERB
fumecheng-13730	5	8	jinfeng	jinfeng	PROPN
fumecheng-13730	5	9	ma	ma	PROPN
fumecheng-13730	5	10	https://orcid.org/0009-0000-2348-9142	https://orcid.org/0009-0000-2348-9142	PROPN
fumecheng-13730	5	11	abdulrahman	abdulrahman	PROPN
fumecheng-13730	5	12	ali	ali	PROPN
fumecheng-13730	5	13	alsolami	alsolami	PROPN
fumecheng-13730	5	14	https://orcid.org/0000-0002-8189-4987	https://orcid.org/0000-0002-8189-4987	PROPN
fumecheng-13730	5	15	xiao	xiao	PROPN
fumecheng-13730	5	16	-	-	PUNCT
fumecheng-13730	5	17	jun	jun	PROPN
fumecheng-13730	5	18	yang	yang	PROPN
fumecheng-13730	5	19	https://orcid.org/0000-0003-0009-4599	https://orcid.org/0000-0003-0009-4599	PROPN
fumecheng-13730	5	20	abstract	abstract	PROPN
fumecheng-13730	5	21	.	.	PUNCT
fumecheng-13730	6	1	the	the	DET
fumecheng-13730	6	2	paper	paper	NOUN
fumecheng-13730	6	3	elucidates	elucidate	VERB
fumecheng-13730	6	4	the	the	DET
fumecheng-13730	6	5	characteristics	characteristic	NOUN
fumecheng-13730	6	6	of	of	ADP
fumecheng-13730	6	7	nonlinear	nonlinear	ADJ
fumecheng-13730	6	8	oscillators	oscillator	NOUN
fumecheng-13730	6	9	that	that	PRON
fumecheng-13730	6	10	contain	contain	VERB
fumecheng-13730	6	11	quasi	quasi	ADJ
fumecheng-13730	6	12	-	-	ADJ
fumecheng-13730	6	13	linear	linear	ADJ
fumecheng-13730	6	14	terms	term	NOUN
fumecheng-13730	6	15	arising	arise	VERB
fumecheng-13730	6	16	in	in	ADP
fumecheng-13730	6	17	mechanical	mechanical	ADJ
fumecheng-13730	6	18	engineering	engineering	NOUN
fumecheng-13730	6	19	.	.	PUNCT
fumecheng-13730	7	1	analytical	analytical	ADJ
fumecheng-13730	7	2	solutions	solution	NOUN
fumecheng-13730	7	3	for	for	ADP
fumecheng-13730	7	4	this	this	DET
fumecheng-13730	7	5	type	type	NOUN
fumecheng-13730	7	6	of	of	ADP
fumecheng-13730	7	7	nonlinear	nonlinear	ADJ
fumecheng-13730	7	8	oscillator	oscillator	NOUN
fumecheng-13730	7	9	are	be	AUX
fumecheng-13730	7	10	often	often	ADV
fumecheng-13730	7	11	difficult	difficult	ADJ
fumecheng-13730	7	12	to	to	PART
fumecheng-13730	7	13	obtain	obtain	VERB
fumecheng-13730	7	14	;	;	PUNCT
fumecheng-13730	7	15	they	they	PRON
fumecheng-13730	7	16	may	may	AUX
fumecheng-13730	7	17	involve	involve	VERB
fumecheng-13730	7	18	singular	singular	NOUN
fumecheng-13730	7	19	and	and	CCONJ
fumecheng-13730	7	20	discontinuous	discontinuous	ADJ
fumecheng-13730	7	21	terms	term	NOUN
fumecheng-13730	7	22	,	,	PUNCT
fumecheng-13730	7	23	which	which	PRON
fumecheng-13730	7	24	can	can	AUX
fumecheng-13730	7	25	make	make	VERB
fumecheng-13730	7	26	them	they	PRON
fumecheng-13730	7	27	significantly	significantly	ADV
fumecheng-13730	7	28	more	more	ADV
fumecheng-13730	7	29	difficult	difficult	ADJ
fumecheng-13730	7	30	to	to	PART
fumecheng-13730	7	31	obtain	obtain	VERB
fumecheng-13730	7	32	.	.	PUNCT
fumecheng-13730	8	1	in	in	ADP
fumecheng-13730	8	2	this	this	DET
fumecheng-13730	8	3	paper	paper	NOUN
fumecheng-13730	8	4	,	,	PUNCT
fumecheng-13730	8	5	a	a	DET
fumecheng-13730	8	6	modified	modify	VERB
fumecheng-13730	8	7	frequency	frequency	NOUN
fumecheng-13730	8	8	formulation	formulation	NOUN
fumecheng-13730	8	9	for	for	ADP
fumecheng-13730	8	10	this	this	DET
fumecheng-13730	8	11	type	type	NOUN
fumecheng-13730	8	12	of	of	ADP
fumecheng-13730	8	13	nonlinear	nonlinear	ADJ
fumecheng-13730	8	14	oscillator	oscillator	NOUN
fumecheng-13730	8	15	is	be	AUX
fumecheng-13730	8	16	presented	present	VERB
fumecheng-13730	8	17	.	.	PUNCT
fumecheng-13730	9	1	while	while	SCONJ
fumecheng-13730	9	2	the	the	DET
fumecheng-13730	9	3	mathematical	mathematical	ADJ
fumecheng-13730	9	4	proof	proof	NOUN
fumecheng-13730	9	5	is	be	AUX
fumecheng-13730	9	6	not	not	PART
fumecheng-13730	9	7	provided	provide	VERB
fumecheng-13730	9	8	,	,	PUNCT
fumecheng-13730	9	9	illustrative	illustrative	ADJ
fumecheng-13730	9	10	examples	example	NOUN
fumecheng-13730	9	11	are	be	AUX
fumecheng-13730	9	12	included	include	VERB
fumecheng-13730	9	13	to	to	PART
fumecheng-13730	9	14	demonstrate	demonstrate	VERB
fumecheng-13730	9	15	the	the	DET
fumecheng-13730	9	16	remarkable	remarkable	ADJ
fumecheng-13730	9	17	simplicity	simplicity	NOUN
fumecheng-13730	9	18	and	and	CCONJ
fumecheng-13730	9	19	reliability	reliability	NOUN
fumecheng-13730	9	20	of	of	ADP
fumecheng-13730	9	21	the	the	DET
fumecheng-13730	9	22	approach	approach	NOUN
fumecheng-13730	9	23	.	.	PUNCT
fumecheng-13730	10	1	this	this	DET
fumecheng-13730	10	2	paper	paper	NOUN
fumecheng-13730	10	3	challenges	challenge	VERB
fumecheng-13730	10	4	the	the	DET
fumecheng-13730	10	5	conventional	conventional	ADJ
fumecheng-13730	10	6	wisdom	wisdom	NOUN
fumecheng-13730	10	7	in	in	ADP
fumecheng-13730	10	8	analytical	analytical	ADJ
fumecheng-13730	10	9	methods	method	NOUN
fumecheng-13730	10	10	and	and	CCONJ
fumecheng-13730	10	11	offers	offer	VERB
fumecheng-13730	10	12	a	a	DET
fumecheng-13730	10	13	promising	promising	ADJ
fumecheng-13730	10	14	new	new	ADJ
fumecheng-13730	10	15	direction	direction	NOUN
fumecheng-13730	10	16	for	for	ADP
fumecheng-13730	10	17	further	further	ADJ
fumecheng-13730	10	18	investigation	investigation	NOUN
fumecheng-13730	10	19	.	.	PUNCT
fumecheng-13730	11	1	key	key	ADJ
fumecheng-13730	11	2	words	word	NOUN
fumecheng-13730	11	3	:	:	PUNCT
fumecheng-13730	11	4	nonlinear	nonlinear	ADJ
fumecheng-13730	11	5	vibration	vibration	NOUN
fumecheng-13730	11	6	,	,	PUNCT
fumecheng-13730	11	7	non	non	ADJ
fumecheng-13730	11	8	-	-	ADJ
fumecheng-13730	11	9	perturbative	perturbative	ADJ
fumecheng-13730	11	10	approach	approach	NOUN
fumecheng-13730	11	11	,	,	PUNCT
fumecheng-13730	11	12	quasi	quasi	ADJ
fumecheng-13730	11	13	-	-	ADJ
fumecheng-13730	11	14	linear	linear	ADJ
fumecheng-13730	11	15	oscillator	oscillator	NOUN
fumecheng-13730	11	16	,	,	PUNCT
fumecheng-13730	11	17	discontinuous	discontinuous	ADJ
fumecheng-13730	11	18	oscillator	oscillator	NOUN
fumecheng-13730	11	19	,	,	PUNCT
fumecheng-13730	11	20	fractional	fractional	ADJ
fumecheng-13730	11	21	potential	potential	NOUN
fumecheng-13730	11	22	,	,	PUNCT
fumecheng-13730	11	23	zigzag	zigzag	NOUN
fumecheng-13730	11	24	oscillation	oscillation	NOUN
fumecheng-13730	11	25	received	receive	VERB
fumecheng-13730	11	26	:	:	PUNCT
fumecheng-13730	11	27	may	may	AUX
fumecheng-13730	11	28	26	26	NUM
fumecheng-13730	11	29	,	,	PUNCT
fumecheng-13730	11	30	2025	2025	NUM
fumecheng-13730	11	31	/	/	SYM
fumecheng-13730	11	32	accepted	accept	VERB
fumecheng-13730	11	33	july	july	PROPN
fumecheng-13730	11	34	03	03	NUM
fumecheng-13730	11	35	,	,	PUNCT
fumecheng-13730	11	36	2025	2025	NUM
fumecheng-13730	11	37	corresponding	correspond	VERB
fumecheng-13730	11	38	author	author	NOUN
fumecheng-13730	11	39	:	:	PUNCT
fumecheng-13730	11	40	ji	ji	PROPN
fumecheng-13730	11	41	-	-	PROPN
fumecheng-13730	11	42	huan	huan	PROPN
fumecheng-13730	11	43	he	he	PRON
fumecheng-13730	11	44	,	,	PUNCT
fumecheng-13730	11	45	jinfeng	jinfeng	PROPN
fumecheng-13730	11	46	ma	ma	PROPN
fumecheng-13730	11	47	school	school	PROPN
fumecheng-13730	11	48	of	of	ADP
fumecheng-13730	11	49	jia	jia	PROPN
fumecheng-13730	11	50	yang	yang	PROPN
fumecheng-13730	11	51	,	,	PUNCT
fumecheng-13730	11	52	zhejiang	zhejiang	PROPN
fumecheng-13730	11	53	shuren	shuren	PROPN
fumecheng-13730	11	54	university	university	PROPN
fumecheng-13730	11	55	,	,	PUNCT
fumecheng-13730	11	56	hangzhou	hangzhou	PROPN
fumecheng-13730	11	57	,	,	PUNCT
fumecheng-13730	11	58	zhejiang	zhejiang	PROPN
fumecheng-13730	11	59	,	,	PUNCT
fumecheng-13730	11	60	china	china	PROPN
fumecheng-13730	11	61	college	college	PROPN
fumecheng-13730	11	62	of	of	ADP
fumecheng-13730	11	63	civil	civil	ADJ
fumecheng-13730	11	64	engineering	engineering	NOUN
fumecheng-13730	11	65	and	and	CCONJ
fumecheng-13730	11	66	architecture	architecture	NOUN
fumecheng-13730	11	67	,	,	PUNCT
fumecheng-13730	11	68	jiaxing	jiaxing	PROPN
fumecheng-13730	11	69	university	university	PROPN
fumecheng-13730	11	70	,	,	PUNCT
fumecheng-13730	11	71	jiaxing	jiaxing	PROPN
fumecheng-13730	11	72	,	,	PUNCT
fumecheng-13730	11	73	china	china	PROPN
fumecheng-13730	11	74	email	email	NOUN
fumecheng-13730	11	75	:	:	PUNCT
fumecheng-13730	11	76	hejihuan@ygu.edu.cn	hejihuan@ygu.edu.cn	PROPN
fumecheng-13730	11	77	(	(	PUNCT
fumecheng-13730	11	78	j.h	j.h	PROPN
fumecheng-13730	11	79	.	.	PUNCT
fumecheng-13730	11	80	he	he	PRON
fumecheng-13730	11	81	)	)	PUNCT
fumecheng-13730	11	82	,	,	PUNCT
fumecheng-13730	11	83	majinfenglz@163.com(j	majinfenglz@163.com(j	PROPN
fumecheng-13730	11	84	.	.	PUNCT
fumecheng-13730	11	85	m	m	PROPN
fumecheng-13730	11	86	)	)	PUNCT
fumecheng-13730	11	87	https://orcid.org/0000-0003-0810-5248	https://orcid.org/0000-0003-0810-5248	PROPN
fumecheng-13730	11	88	https://orcid.org/0000-0002-1636-0559	https://orcid.org/0000-0002-1636-0559	VERB
fumecheng-13730	11	89	https://orcid.org/0009-0000-2348-9142	https://orcid.org/0009-0000-2348-9142	PRON
fumecheng-13730	11	90	https://orcid.org/0000-0002-8189-4987	https://orcid.org/0000-0002-8189-4987	PRON
fumecheng-13730	11	91	https://orcid.org/0000-0003-0009-4599	https://orcid.org/0000-0003-0009-4599	PROPN
fumecheng-13730	11	92	198	198	NUM
fumecheng-13730	11	93	c.h	c.h	PROPN
fumecheng-13730	11	94	.	.	PUNCT
fumecheng-13730	12	1	he	he	PRON
fumecheng-13730	12	2	,	,	PUNCT
fumecheng-13730	12	3	j.h	j.h	PROPN
fumecheng-13730	12	4	.	.	PUNCT
fumecheng-13730	13	1	he	he	PRON
fumecheng-13730	13	2	,	,	PUNCT
fumecheng-13730	13	3	j.	j.	PROPN
fumecheng-13730	13	4	ma	ma	PROPN
fumecheng-13730	13	5	,	,	PUNCT
fumecheng-13730	13	6	a.a	a.a	PROPN
fumecheng-13730	13	7	.	.	PROPN
fumecheng-13730	13	8	alsolam	alsolam	PROPN
fumecheng-13730	13	9	,	,	PUNCT
fumecheng-13730	13	10	x.j	x.j	PROPN
fumecheng-13730	13	11	.	.	PROPN
fumecheng-13730	13	12	yang	yang	PROPN
fumecheng-13730	13	13	1	1	NUM
fumecheng-13730	13	14	.	.	PUNCT
fumecheng-13730	14	1	introduction	introduction	NOUN
fumecheng-13730	14	2	in	in	ADP
fumecheng-13730	14	3	the	the	DET
fumecheng-13730	14	4	ever	ever	ADV
fumecheng-13730	14	5	-	-	PUNCT
fumecheng-13730	14	6	evolving	evolve	VERB
fumecheng-13730	14	7	landscape	landscape	NOUN
fumecheng-13730	14	8	of	of	ADP
fumecheng-13730	14	9	contemporary	contemporary	ADJ
fumecheng-13730	14	10	science	science	NOUN
fumecheng-13730	14	11	and	and	CCONJ
fumecheng-13730	14	12	technology	technology	NOUN
fumecheng-13730	14	13	,	,	PUNCT
fumecheng-13730	14	14	nonlinear	nonlinear	ADJ
fumecheng-13730	14	15	vibration	vibration	NOUN
fumecheng-13730	14	16	systems	system	NOUN
fumecheng-13730	15	1	[	[	X
fumecheng-13730	15	2	1	1	NUM
fumecheng-13730	15	3	,	,	PUNCT
fumecheng-13730	15	4	2	2	NUM
fumecheng-13730	15	5	]	]	PUNCT
fumecheng-13730	15	6	have	have	AUX
fumecheng-13730	15	7	risen	rise	VERB
fumecheng-13730	15	8	to	to	ADP
fumecheng-13730	15	9	prominence	prominence	NOUN
fumecheng-13730	15	10	as	as	ADP
fumecheng-13730	15	11	a	a	DET
fumecheng-13730	15	12	foundational	foundational	ADJ
fumecheng-13730	15	13	building	building	NOUN
fumecheng-13730	15	14	block	block	NOUN
fumecheng-13730	15	15	with	with	ADP
fumecheng-13730	15	16	far	far	ADV
fumecheng-13730	15	17	-	-	PUNCT
fumecheng-13730	15	18	reaching	reach	VERB
fumecheng-13730	15	19	consequences	consequence	NOUN
fumecheng-13730	15	20	across	across	ADP
fumecheng-13730	15	21	a	a	DET
fumecheng-13730	15	22	diverse	diverse	ADJ
fumecheng-13730	15	23	array	array	NOUN
fumecheng-13730	15	24	of	of	ADP
fumecheng-13730	15	25	disciplines	discipline	NOUN
fumecheng-13730	15	26	.	.	PUNCT
fumecheng-13730	16	1	specifically	specifically	ADV
fumecheng-13730	16	2	,	,	PUNCT
fumecheng-13730	16	3	they	they	PRON
fumecheng-13730	16	4	have	have	AUX
fumecheng-13730	16	5	provided	provide	VERB
fumecheng-13730	16	6	substantial	substantial	ADJ
fumecheng-13730	16	7	support	support	NOUN
fumecheng-13730	16	8	to	to	ADP
fumecheng-13730	16	9	the	the	DET
fumecheng-13730	16	10	domain	domain	NOUN
fumecheng-13730	16	11	of	of	ADP
fumecheng-13730	16	12	mechanical	mechanical	ADJ
fumecheng-13730	16	13	engineering	engineering	NOUN
fumecheng-13730	16	14	[	[	X
fumecheng-13730	16	15	3	3	NUM
fumecheng-13730	16	16	]	]	PUNCT
fumecheng-13730	16	17	,	,	PUNCT
fumecheng-13730	16	18	particularly	particularly	ADV
fumecheng-13730	16	19	the	the	DET
fumecheng-13730	16	20	field	field	NOUN
fumecheng-13730	16	21	of	of	ADP
fumecheng-13730	16	22	micro	micro	ADJ
fumecheng-13730	16	23	-	-	ADJ
fumecheng-13730	16	24	electromechanical	electromechanical	ADJ
fumecheng-13730	16	25	systems	system	NOUN
fumecheng-13730	16	26	(	(	PUNCT
fumecheng-13730	16	27	mems	mem	NOUN
fumecheng-13730	16	28	)	)	PUNCT
fumecheng-13730	17	1	[	[	X
fumecheng-13730	17	2	4	4	NUM
fumecheng-13730	17	3	]	]	PUNCT
fumecheng-13730	17	4	.	.	PUNCT
fumecheng-13730	18	1	it	it	PRON
fumecheng-13730	18	2	is	be	AUX
fumecheng-13730	18	3	imperative	imperative	ADJ
fumecheng-13730	18	4	to	to	PART
fumecheng-13730	18	5	comprehend	comprehend	VERB
fumecheng-13730	18	6	the	the	DET
fumecheng-13730	18	7	frequency	frequency	NOUN
fumecheng-13730	18	8	-	-	PUNCT
fumecheng-13730	18	9	amplitude	amplitude	NOUN
fumecheng-13730	18	10	relationship	relationship	NOUN
fumecheng-13730	18	11	to	to	PART
fumecheng-13730	18	12	identify	identify	VERB
fumecheng-13730	18	13	novel	novel	ADJ
fumecheng-13730	18	14	prospects	prospect	NOUN
fumecheng-13730	18	15	and	and	CCONJ
fumecheng-13730	18	16	propel	propel	VERB
fumecheng-13730	18	17	the	the	DET
fumecheng-13730	18	18	advancement	advancement	NOUN
fumecheng-13730	18	19	of	of	ADP
fumecheng-13730	18	20	related	related	ADJ
fumecheng-13730	18	21	technologies	technology	NOUN
fumecheng-13730	18	22	.	.	PUNCT
fumecheng-13730	19	1	for	for	ADP
fumecheng-13730	19	2	instance	instance	NOUN
fumecheng-13730	19	3	,	,	PUNCT
fumecheng-13730	19	4	the	the	DET
fumecheng-13730	19	5	capacity	capacity	NOUN
fumecheng-13730	19	6	to	to	PART
fumecheng-13730	19	7	discern	discern	VERB
fumecheng-13730	19	8	the	the	DET
fumecheng-13730	19	9	slightest	slight	ADJ
fumecheng-13730	19	10	tremors	tremor	NOUN
fumecheng-13730	19	11	of	of	ADP
fumecheng-13730	19	12	starquakes	starquake	NOUN
fumecheng-13730	19	13	,	,	PUNCT
fumecheng-13730	19	14	a	a	DET
fumecheng-13730	19	15	capability	capability	NOUN
fumecheng-13730	19	16	of	of	ADP
fumecheng-13730	19	17	paramount	paramount	ADJ
fumecheng-13730	19	18	importance	importance	NOUN
fumecheng-13730	19	19	in	in	ADP
fumecheng-13730	19	20	the	the	DET
fumecheng-13730	19	21	realm	realm	NOUN
fumecheng-13730	19	22	of	of	ADP
fumecheng-13730	19	23	astronomy	astronomy	NOUN
fumecheng-13730	19	24	[	[	X
fumecheng-13730	19	25	5	5	NUM
fumecheng-13730	19	26	]	]	PUNCT
fumecheng-13730	19	27	,	,	PUNCT
fumecheng-13730	19	28	exemplifies	exemplify	VERB
fumecheng-13730	19	29	this	this	DET
fumecheng-13730	19	30	phenomenon	phenomenon	NOUN
fumecheng-13730	19	31	.	.	PUNCT
fumecheng-13730	20	1	these	these	DET
fumecheng-13730	20	2	seismic	seismic	ADJ
fumecheng-13730	20	3	events	event	NOUN
fumecheng-13730	20	4	offer	offer	VERB
fumecheng-13730	20	5	invaluable	invaluable	ADJ
fumecheng-13730	20	6	insights	insight	NOUN
fumecheng-13730	20	7	into	into	ADP
fumecheng-13730	20	8	the	the	DET
fumecheng-13730	20	9	internal	internal	ADJ
fumecheng-13730	20	10	structure	structure	NOUN
fumecheng-13730	20	11	and	and	CCONJ
fumecheng-13730	20	12	composition	composition	NOUN
fumecheng-13730	20	13	of	of	ADP
fumecheng-13730	20	14	stars	star	NOUN
fumecheng-13730	20	15	.	.	PUNCT
fumecheng-13730	21	1	additionally	additionally	ADV
fumecheng-13730	21	2	,	,	PUNCT
fumecheng-13730	21	3	high	high	ADJ
fumecheng-13730	21	4	-	-	PUNCT
fumecheng-13730	21	5	frequency	frequency	NOUN
fumecheng-13730	21	6	vibrations	vibration	NOUN
fumecheng-13730	21	7	have	have	AUX
fumecheng-13730	21	8	been	be	AUX
fumecheng-13730	21	9	observed	observe	VERB
fumecheng-13730	21	10	in	in	ADP
fumecheng-13730	21	11	the	the	DET
fumecheng-13730	21	12	coupling	coupling	NOUN
fumecheng-13730	21	13	of	of	ADP
fumecheng-13730	21	14	excitons	exciton	NOUN
fumecheng-13730	21	15	in	in	ADP
fumecheng-13730	21	16	π	π	PROPN
fumecheng-13730	21	17	-	-	ADJ
fumecheng-13730	21	18	conjugated	conjugate	VERB
fumecheng-13730	21	19	molecules	molecule	NOUN
fumecheng-13730	21	20	[	[	X
fumecheng-13730	21	21	6	6	NUM
fumecheng-13730	21	22	]	]	PUNCT
fumecheng-13730	21	23	.	.	PUNCT
fumecheng-13730	22	1	the	the	DET
fumecheng-13730	22	2	nonlinearity	nonlinearity	NOUN
fumecheng-13730	22	3	exhibited	exhibit	VERB
fumecheng-13730	22	4	by	by	ADP
fumecheng-13730	22	5	oscillators	oscillator	NOUN
fumecheng-13730	22	6	can	can	AUX
fumecheng-13730	22	7	have	have	VERB
fumecheng-13730	22	8	various	various	ADJ
fumecheng-13730	22	9	origins	origin	NOUN
fumecheng-13730	22	10	.	.	PUNCT
fumecheng-13730	23	1	cubic	cubic	ADJ
fumecheng-13730	23	2	-	-	PUNCT
fumecheng-13730	23	3	quintic	quintic	ADJ
fumecheng-13730	23	4	nonlinearity	nonlinearity	NOUN
fumecheng-13730	23	5	is	be	AUX
fumecheng-13730	23	6	a	a	DET
fumecheng-13730	23	7	frequently	frequently	ADV
fumecheng-13730	23	8	employed	employ	VERB
fumecheng-13730	23	9	phenomenon	phenomenon	NOUN
fumecheng-13730	23	10	in	in	ADP
fumecheng-13730	23	11	the	the	DET
fumecheng-13730	23	12	domain	domain	NOUN
fumecheng-13730	23	13	of	of	ADP
fumecheng-13730	23	14	mechanical	mechanical	ADJ
fumecheng-13730	23	15	engineering	engineering	NOUN
fumecheng-13730	23	16	[	[	X
fumecheng-13730	23	17	7	7	NUM
fumecheng-13730	23	18	-	-	SYM
fumecheng-13730	23	19	9	9	NUM
fumecheng-13730	23	20	]	]	PUNCT
fumecheng-13730	23	21	.	.	PUNCT
fumecheng-13730	24	1	however	however	ADV
fumecheng-13730	24	2	,	,	PUNCT
fumecheng-13730	24	3	there	there	PRON
fumecheng-13730	24	4	are	be	VERB
fumecheng-13730	24	5	also	also	ADV
fumecheng-13730	24	6	nonlinearities	nonlinearitie	NOUN
fumecheng-13730	24	7	of	of	ADP
fumecheng-13730	24	8	the	the	DET
fumecheng-13730	24	9	form	form	NOUN
fumecheng-13730	24	10	un	un	NOUN
fumecheng-13730	24	11	)	)	PUNCT
fumecheng-13730	24	12	,	,	PUNCT
fumecheng-13730	24	13	with	with	ADP
fumecheng-13730	24	14	n	n	X
fumecheng-13730	24	15	<	<	X
fumecheng-13730	24	16	1	1	NUM
fumecheng-13730	24	17	.	.	X
fumecheng-13730	25	1	for	for	ADP
fumecheng-13730	25	2	instance	instance	NOUN
fumecheng-13730	25	3	,	,	PUNCT
fumecheng-13730	25	4	the	the	DET
fumecheng-13730	25	5	integer	integer	NOUN
fumecheng-13730	25	6	n	n	PRON
fumecheng-13730	25	7	could	could	AUX
fumecheng-13730	25	8	be	be	AUX
fumecheng-13730	25	9	either	either	CCONJ
fumecheng-13730	25	10	1/3	1/3	NUM
fumecheng-13730	25	11	or	or	CCONJ
fumecheng-13730	25	12	-1	-1	NOUN
fumecheng-13730	25	13	.	.	PUNCT
fumecheng-13730	26	1	these	these	DET
fumecheng-13730	26	2	nonlinear	nonlinear	ADJ
fumecheng-13730	26	3	oscillators	oscillator	NOUN
fumecheng-13730	26	4	consist	consist	VERB
fumecheng-13730	26	5	of	of	ADP
fumecheng-13730	26	6	both	both	PRON
fumecheng-13730	26	7	singular	singular	ADJ
fumecheng-13730	26	8	oscillators	oscillator	NOUN
fumecheng-13730	26	9	and	and	CCONJ
fumecheng-13730	26	10	discontinuous	discontinuous	ADJ
fumecheng-13730	26	11	oscillators	oscillator	NOUN
fumecheng-13730	26	12	.	.	PUNCT
fumecheng-13730	27	1	the	the	DET
fumecheng-13730	27	2	procurement	procurement	NOUN
fumecheng-13730	27	3	of	of	ADP
fumecheng-13730	27	4	approximate	approximate	ADJ
fumecheng-13730	27	5	solutions	solution	NOUN
fumecheng-13730	27	6	for	for	ADP
fumecheng-13730	27	7	these	these	DET
fumecheng-13730	27	8	oscillatory	oscillatory	ADJ
fumecheng-13730	27	9	phenomena	phenomenon	NOUN
fumecheng-13730	27	10	poses	pose	VERB
fumecheng-13730	27	11	a	a	DET
fumecheng-13730	27	12	substantial	substantial	ADJ
fumecheng-13730	27	13	challenge	challenge	NOUN
fumecheng-13730	27	14	in	in	ADP
fumecheng-13730	27	15	the	the	DET
fumecheng-13730	27	16	realms	realm	NOUN
fumecheng-13730	27	17	of	of	ADP
fumecheng-13730	27	18	mathematics	mathematic	NOUN
fumecheng-13730	27	19	and	and	CCONJ
fumecheng-13730	27	20	mechanical	mechanical	ADJ
fumecheng-13730	27	21	engineering	engineering	NOUN
fumecheng-13730	27	22	.	.	PUNCT
fumecheng-13730	28	1	the	the	DET
fumecheng-13730	28	2	complexity	complexity	NOUN
fumecheng-13730	28	3	inherent	inherent	ADJ
fumecheng-13730	28	4	to	to	ADP
fumecheng-13730	28	5	this	this	DET
fumecheng-13730	28	6	phenomenon	phenomenon	NOUN
fumecheng-13730	28	7	stems	stem	VERB
fumecheng-13730	28	8	from	from	ADP
fumecheng-13730	28	9	the	the	DET
fumecheng-13730	28	10	fact	fact	NOUN
fumecheng-13730	28	11	that	that	SCONJ
fumecheng-13730	28	12	singular	singular	ADJ
fumecheng-13730	28	13	oscillators	oscillator	NOUN
fumecheng-13730	28	14	frequently	frequently	ADV
fumecheng-13730	28	15	possess	possess	VERB
fumecheng-13730	28	16	unique	unique	ADJ
fumecheng-13730	28	17	properties	property	NOUN
fumecheng-13730	28	18	,	,	PUNCT
fumecheng-13730	28	19	thereby	thereby	ADV
fumecheng-13730	28	20	rendering	render	VERB
fumecheng-13730	28	21	traditional	traditional	ADJ
fumecheng-13730	28	22	solution	solution	NOUN
fumecheng-13730	28	23	methods	method	NOUN
fumecheng-13730	28	24	ineffective	ineffective	ADJ
fumecheng-13730	28	25	.	.	PUNCT
fumecheng-13730	29	1	conversely	conversely	ADV
fumecheng-13730	29	2	,	,	PUNCT
fumecheng-13730	29	3	discontinuous	discontinuous	ADJ
fumecheng-13730	29	4	oscillators	oscillator	NOUN
fumecheng-13730	29	5	pose	pose	VERB
fumecheng-13730	29	6	significant	significant	ADJ
fumecheng-13730	29	7	challenges	challenge	NOUN
fumecheng-13730	29	8	due	due	ADP
fumecheng-13730	29	9	to	to	ADP
fumecheng-13730	29	10	their	their	PRON
fumecheng-13730	29	11	sudden	sudden	ADJ
fumecheng-13730	29	12	fluctuations	fluctuation	NOUN
fumecheng-13730	29	13	in	in	ADP
fumecheng-13730	29	14	behavior	behavior	NOUN
fumecheng-13730	29	15	.	.	PUNCT
fumecheng-13730	30	1	confronting	confront	VERB
fumecheng-13730	30	2	these	these	DET
fumecheng-13730	30	3	challenges	challenge	NOUN
fumecheng-13730	30	4	necessitates	necessitate	VERB
fumecheng-13730	30	5	the	the	DET
fumecheng-13730	30	6	development	development	NOUN
fumecheng-13730	30	7	of	of	ADP
fumecheng-13730	30	8	innovative	innovative	ADJ
fumecheng-13730	30	9	methodologies	methodology	NOUN
fumecheng-13730	30	10	and	and	CCONJ
fumecheng-13730	30	11	a	a	DET
fumecheng-13730	30	12	profound	profound	ADJ
fumecheng-13730	30	13	comprehension	comprehension	NOUN
fumecheng-13730	30	14	of	of	ADP
fumecheng-13730	30	15	both	both	DET
fumecheng-13730	30	16	mathematical	mathematical	ADJ
fumecheng-13730	30	17	principles	principle	NOUN
fumecheng-13730	30	18	and	and	CCONJ
fumecheng-13730	30	19	mechanical	mechanical	ADJ
fumecheng-13730	30	20	systems	system	NOUN
fumecheng-13730	30	21	.	.	PUNCT
fumecheng-13730	31	1	a	a	DET
fumecheng-13730	31	2	paucity	paucity	NOUN
fumecheng-13730	31	3	of	of	ADP
fumecheng-13730	31	4	known	know	VERB
fumecheng-13730	31	5	periodic	periodic	ADJ
fumecheng-13730	31	6	functions	function	NOUN
fumecheng-13730	31	7	exists	exist	VERB
fumecheng-13730	31	8	for	for	ADP
fumecheng-13730	31	9	the	the	DET
fumecheng-13730	31	10	approximation	approximation	NOUN
fumecheng-13730	31	11	of	of	ADP
fumecheng-13730	31	12	nonlinear	nonlinear	ADJ
fumecheng-13730	31	13	oscillators	oscillator	NOUN
fumecheng-13730	31	14	.	.	PUNCT
fumecheng-13730	32	1	in	in	ADP
fumecheng-13730	32	2	the	the	DET
fumecheng-13730	32	3	domain	domain	NOUN
fumecheng-13730	32	4	of	of	ADP
fumecheng-13730	32	5	nonlinear	nonlinear	ADJ
fumecheng-13730	32	6	vibration	vibration	NOUN
fumecheng-13730	32	7	theory	theory	NOUN
fumecheng-13730	32	8	,	,	PUNCT
fumecheng-13730	32	9	the	the	DET
fumecheng-13730	32	10	cosine	cosine	NOUN
fumecheng-13730	32	11	function	function	NOUN
fumecheng-13730	32	12	and	and	CCONJ
fumecheng-13730	32	13	the	the	DET
fumecheng-13730	32	14	sine	sine	ADJ
fumecheng-13730	32	15	function	function	NOUN
fumecheng-13730	32	16	are	be	AUX
fumecheng-13730	32	17	the	the	DET
fumecheng-13730	32	18	most	most	ADV
fumecheng-13730	32	19	frequently	frequently	ADV
fumecheng-13730	32	20	employed	employ	VERB
fumecheng-13730	32	21	.	.	PUNCT
fumecheng-13730	33	1	while	while	SCONJ
fumecheng-13730	33	2	it	it	PRON
fumecheng-13730	33	3	is	be	AUX
fumecheng-13730	33	4	possible	possible	ADJ
fumecheng-13730	33	5	to	to	PART
fumecheng-13730	33	6	theoretically	theoretically	ADV
fumecheng-13730	33	7	model	model	VERB
fumecheng-13730	33	8	a	a	DET
fumecheng-13730	33	9	zigzag	zigzag	NOUN
fumecheng-13730	33	10	periodic	periodic	ADJ
fumecheng-13730	33	11	motion	motion	NOUN
fumecheng-13730	33	12	through	through	ADP
fumecheng-13730	33	13	an	an	DET
fumecheng-13730	33	14	infinite	infinite	ADJ
fumecheng-13730	33	15	series	series	NOUN
fumecheng-13730	33	16	of	of	ADP
fumecheng-13730	33	17	cosine	cosine	NOUN
fumecheng-13730	33	18	or	or	CCONJ
fumecheng-13730	33	19	sine	sine	ADJ
fumecheng-13730	33	20	functions	function	NOUN
fumecheng-13730	33	21	,	,	PUNCT
fumecheng-13730	33	22	this	this	DET
fumecheng-13730	33	23	approach	approach	NOUN
fumecheng-13730	33	24	is	be	AUX
fumecheng-13730	33	25	mathematically	mathematically	ADV
fumecheng-13730	33	26	intricate	intricate	ADJ
fumecheng-13730	33	27	.	.	PUNCT
fumecheng-13730	34	1	engineers	engineer	NOUN
fumecheng-13730	34	2	generally	generally	ADV
fumecheng-13730	34	3	prioritize	prioritize	VERB
fumecheng-13730	34	4	the	the	DET
fumecheng-13730	34	5	key	key	ADJ
fumecheng-13730	34	6	factors	factor	NOUN
fumecheng-13730	34	7	that	that	PRON
fumecheng-13730	34	8	influence	influence	VERB
fumecheng-13730	34	9	the	the	DET
fumecheng-13730	34	10	period	period	NOUN
fumecheng-13730	34	11	or	or	CCONJ
fumecheng-13730	34	12	frequency	frequency	NOUN
fumecheng-13730	34	13	of	of	ADP
fumecheng-13730	34	14	these	these	DET
fumecheng-13730	34	15	oscillators	oscillator	NOUN
fumecheng-13730	34	16	.	.	PUNCT
fumecheng-13730	35	1	however	however	ADV
fumecheng-13730	35	2	,	,	PUNCT
fumecheng-13730	35	3	contemporary	contemporary	ADJ
fumecheng-13730	35	4	analytical	analytical	ADJ
fumecheng-13730	35	5	methodologies	methodology	NOUN
fumecheng-13730	35	6	predominantly	predominantly	ADV
fumecheng-13730	35	7	center	center	VERB
fumecheng-13730	35	8	on	on	ADP
fumecheng-13730	35	9	the	the	DET
fumecheng-13730	35	10	pursuit	pursuit	NOUN
fumecheng-13730	35	11	of	of	ADP
fumecheng-13730	35	12	an	an	DET
fumecheng-13730	35	13	approximate	approximate	ADJ
fumecheng-13730	35	14	cosine	cosine	NOUN
fumecheng-13730	35	15	or	or	CCONJ
fumecheng-13730	35	16	sine	sine	ADJ
fumecheng-13730	35	17	solution	solution	NOUN
fumecheng-13730	35	18	for	for	ADP
fumecheng-13730	35	19	a	a	DET
fumecheng-13730	35	20	complex	complex	ADJ
fumecheng-13730	35	21	nonlinear	nonlinear	ADJ
fumecheng-13730	35	22	vibration	vibration	NOUN
fumecheng-13730	35	23	system	system	NOUN
fumecheng-13730	35	24	,	,	PUNCT
fumecheng-13730	35	25	with	with	ADP
fumecheng-13730	35	26	the	the	DET
fumecheng-13730	35	27	objective	objective	NOUN
fumecheng-13730	35	28	of	of	ADP
fumecheng-13730	35	29	deriving	derive	VERB
fumecheng-13730	35	30	an	an	DET
fumecheng-13730	35	31	expression	expression	NOUN
fumecheng-13730	35	32	for	for	ADP
fumecheng-13730	35	33	the	the	DET
fumecheng-13730	35	34	frequency	frequency	NOUN
fumecheng-13730	35	35	.	.	PUNCT
fumecheng-13730	36	1	in	in	ADP
fumecheng-13730	36	2	order	order	NOUN
fumecheng-13730	36	3	to	to	PART
fumecheng-13730	36	4	make	make	VERB
fumecheng-13730	36	5	a	a	DET
fumecheng-13730	36	6	more	more	ADV
fumecheng-13730	36	7	precise	precise	ADJ
fumecheng-13730	36	8	prediction	prediction	NOUN
fumecheng-13730	36	9	of	of	ADP
fumecheng-13730	36	10	the	the	DET
fumecheng-13730	36	11	impact	impact	NOUN
fumecheng-13730	36	12	of	of	ADP
fumecheng-13730	36	13	parameters	parameter	NOUN
fumecheng-13730	36	14	on	on	ADP
fumecheng-13730	36	15	the	the	DET
fumecheng-13730	36	16	frequency	frequency	NOUN
fumecheng-13730	36	17	,	,	PUNCT
fumecheng-13730	36	18	it	it	PRON
fumecheng-13730	36	19	is	be	AUX
fumecheng-13730	36	20	necessary	necessary	ADJ
fumecheng-13730	36	21	to	to	PART
fumecheng-13730	36	22	undertake	undertake	VERB
fumecheng-13730	36	23	a	a	DET
fumecheng-13730	36	24	cumbersome	cumbersome	ADJ
fumecheng-13730	36	25	derivation	derivation	NOUN
fumecheng-13730	36	26	process	process	NOUN
fumecheng-13730	36	27	.	.	PUNCT
fumecheng-13730	37	1	however	however	ADV
fumecheng-13730	37	2	,	,	PUNCT
fumecheng-13730	37	3	this	this	DET
fumecheng-13730	37	4	approach	approach	NOUN
fumecheng-13730	37	5	frequently	frequently	ADV
fumecheng-13730	37	6	falls	fall	VERB
fumecheng-13730	37	7	short	short	ADJ
fumecheng-13730	37	8	in	in	ADP
fumecheng-13730	37	9	providing	provide	VERB
fumecheng-13730	37	10	highly	highly	ADV
fumecheng-13730	37	11	accurate	accurate	ADJ
fumecheng-13730	37	12	results	result	NOUN
fumecheng-13730	37	13	due	due	ADP
fumecheng-13730	37	14	to	to	ADP
fumecheng-13730	37	15	the	the	DET
fumecheng-13730	37	16	inherent	inherent	ADJ
fumecheng-13730	37	17	limitations	limitation	NOUN
fumecheng-13730	37	18	of	of	ADP
fumecheng-13730	37	19	using	use	VERB
fumecheng-13730	37	20	cosine	cosine	NOUN
fumecheng-13730	37	21	and	and	CCONJ
fumecheng-13730	37	22	sine	sine	ADJ
fumecheng-13730	37	23	functions	function	NOUN
fumecheng-13730	37	24	.	.	PUNCT
fumecheng-13730	38	1	alternative	alternative	ADJ
fumecheng-13730	38	2	methods	method	NOUN
fumecheng-13730	38	3	,	,	PUNCT
fumecheng-13730	38	4	such	such	ADJ
fumecheng-13730	38	5	as	as	ADP
fumecheng-13730	38	6	numerical	numerical	ADJ
fumecheng-13730	38	7	simulations	simulation	NOUN
fumecheng-13730	38	8	or	or	CCONJ
fumecheng-13730	38	9	advanced	advanced	ADJ
fumecheng-13730	38	10	experiment	experiment	NOUN
fumecheng-13730	38	11	techniques	technique	NOUN
fumecheng-13730	38	12	[	[	X
fumecheng-13730	38	13	10	10	NUM
fumecheng-13730	38	14	]	]	PUNCT
fumecheng-13730	38	15	,	,	PUNCT
fumecheng-13730	38	16	have	have	VERB
fumecheng-13730	38	17	the	the	DET
fumecheng-13730	38	18	potential	potential	NOUN
fumecheng-13730	38	19	to	to	PART
fumecheng-13730	38	20	serve	serve	VERB
fumecheng-13730	38	21	as	as	ADP
fumecheng-13730	38	22	an	an	DET
fumecheng-13730	38	23	auxiliary	auxiliary	ADJ
fumecheng-13730	38	24	means	mean	NOUN
fumecheng-13730	38	25	of	of	ADP
fumecheng-13730	38	26	vibration	vibration	NOUN
fumecheng-13730	38	27	analysis	analysis	NOUN
fumecheng-13730	38	28	.	.	PUNCT
fumecheng-13730	39	1	however	however	ADV
fumecheng-13730	39	2	,	,	PUNCT
fumecheng-13730	39	3	these	these	DET
fumecheng-13730	39	4	approaches	approach	NOUN
fumecheng-13730	39	5	are	be	AUX
fumecheng-13730	39	6	costly	costly	ADJ
fumecheng-13730	39	7	and	and	CCONJ
fumecheng-13730	39	8	can	can	AUX
fumecheng-13730	39	9	not	not	PART
fumecheng-13730	39	10	provide	provide	VERB
fumecheng-13730	39	11	more	more	ADV
fumecheng-13730	39	12	accurate	accurate	ADJ
fumecheng-13730	39	13	predictions	prediction	NOUN
fumecheng-13730	39	14	or	or	CCONJ
fumecheng-13730	39	15	overcome	overcome	VERB
fumecheng-13730	39	16	the	the	DET
fumecheng-13730	39	17	complexity	complexity	NOUN
fumecheng-13730	39	18	associated	associate	VERB
fumecheng-13730	39	19	with	with	ADP
fumecheng-13730	39	20	traditional	traditional	ADJ
fumecheng-13730	39	21	methods	method	NOUN
fumecheng-13730	39	22	.	.	PUNCT
fumecheng-13730	40	1	another	another	DET
fumecheng-13730	40	2	periodic	periodic	ADJ
fumecheng-13730	40	3	function	function	NOUN
fumecheng-13730	40	4	that	that	PRON
fumecheng-13730	40	5	must	must	AUX
fumecheng-13730	40	6	be	be	AUX
fumecheng-13730	40	7	considered	consider	VERB
fumecheng-13730	40	8	is	be	AUX
fumecheng-13730	40	9	the	the	DET
fumecheng-13730	40	10	jacobi	jacobi	PROPN
fumecheng-13730	40	11	elliptic	elliptic	ADJ
fumecheng-13730	40	12	functions	function	NOUN
fumecheng-13730	40	13	[	[	X
fumecheng-13730	40	14	7	7	NUM
fumecheng-13730	40	15	]	]	PUNCT
fumecheng-13730	40	16	.	.	PUNCT
fumecheng-13730	41	1	these	these	DET
fumecheng-13730	41	2	functions	function	NOUN
fumecheng-13730	41	3	are	be	AUX
fumecheng-13730	41	4	particularly	particularly	ADV
fumecheng-13730	41	5	well	well	ADV
fumecheng-13730	41	6	-	-	PUNCT
fumecheng-13730	41	7	suited	suited	ADJ
fumecheng-13730	41	8	for	for	ADP
fumecheng-13730	41	9	duffing	duffing	NOUN
fumecheng-13730	41	10	-	-	PUNCT
fumecheng-13730	41	11	like	like	ADJ
fumecheng-13730	41	12	oscillators	oscillator	NOUN
fumecheng-13730	41	13	due	due	ADP
fumecheng-13730	41	14	to	to	ADP
fumecheng-13730	41	15	their	their	PRON
fumecheng-13730	41	16	specific	specific	ADJ
fumecheng-13730	41	17	mathematical	mathematical	ADJ
fumecheng-13730	41	18	properties	property	NOUN
fumecheng-13730	41	19	,	,	PUNCT
fumecheng-13730	41	20	which	which	PRON
fumecheng-13730	41	21	can	can	AUX
fumecheng-13730	41	22	accurately	accurately	ADV
fumecheng-13730	41	23	capture	capture	VERB
fumecheng-13730	41	24	the	the	DET
fumecheng-13730	41	25	behavior	behavior	NOUN
fumecheng-13730	41	26	of	of	ADP
fumecheng-13730	41	27	such	such	ADJ
fumecheng-13730	41	28	oscillators	oscillator	NOUN
fumecheng-13730	41	29	.	.	PUNCT
fumecheng-13730	42	1	however	however	ADV
fumecheng-13730	42	2	,	,	PUNCT
fumecheng-13730	42	3	the	the	DET
fumecheng-13730	42	4	differential	differential	ADJ
fumecheng-13730	42	5	operations	operation	NOUN
fumecheng-13730	42	6	of	of	ADP
fumecheng-13730	42	7	these	these	DET
fumecheng-13730	42	8	mechanisms	mechanism	NOUN
fumecheng-13730	42	9	are	be	AUX
fumecheng-13730	42	10	intricate	intricate	ADJ
fumecheng-13730	42	11	,	,	PUNCT
fumecheng-13730	42	12	posing	pose	VERB
fumecheng-13730	42	13	a	a	DET
fumecheng-13730	42	14	challenge	challenge	NOUN
fumecheng-13730	42	15	for	for	SCONJ
fumecheng-13730	42	16	engineers	engineer	NOUN
fumecheng-13730	42	17	to	to	PART
fumecheng-13730	42	18	comprehend	comprehend	VERB
fumecheng-13730	42	19	and	and	CCONJ
fumecheng-13730	42	20	utilize	utilize	VERB
fumecheng-13730	42	21	.	.	PUNCT
fumecheng-13730	43	1	the	the	DET
fumecheng-13730	43	2	primary	primary	ADJ
fumecheng-13730	43	3	concern	concern	NOUN
fumecheng-13730	43	4	of	of	ADP
fumecheng-13730	43	5	an	an	DET
fumecheng-13730	43	6	engineer	engineer	NOUN
fumecheng-13730	43	7	is	be	AUX
fumecheng-13730	43	8	not	not	PART
fumecheng-13730	43	9	the	the	DET
fumecheng-13730	43	10	approximate	approximate	ADJ
fumecheng-13730	43	11	solution	solution	NOUN
fumecheng-13730	43	12	per	per	ADP
fumecheng-13730	43	13	se	se	X
fumecheng-13730	43	14	;	;	PUNCT
fumecheng-13730	43	15	rather	rather	ADV
fumecheng-13730	43	16	,	,	PUNCT
fumecheng-13730	43	17	the	the	DET
fumecheng-13730	43	18	emphasis	emphasis	NOUN
fumecheng-13730	43	19	is	be	AUX
fumecheng-13730	43	20	placed	place	VERB
fumecheng-13730	43	21	on	on	ADP
fumecheng-13730	43	22	the	the	DET
fumecheng-13730	43	23	precision	precision	NOUN
fumecheng-13730	43	24	of	of	ADP
fumecheng-13730	43	25	the	the	DET
fumecheng-13730	43	26	frequencyamplitude	frequencyamplitude	NOUN
fumecheng-13730	43	27	relationship	relationship	NOUN
fumecheng-13730	43	28	.	.	PUNCT
fumecheng-13730	44	1	this	this	DET
fumecheng-13730	44	2	relationship	relationship	NOUN
fumecheng-13730	44	3	is	be	AUX
fumecheng-13730	44	4	of	of	ADP
fumecheng-13730	44	5	paramount	paramount	ADJ
fumecheng-13730	44	6	importance	importance	NOUN
fumecheng-13730	44	7	,	,	PUNCT
fumecheng-13730	44	8	as	as	SCONJ
fumecheng-13730	44	9	it	it	PRON
fumecheng-13730	44	10	constitutes	constitute	VERB
fumecheng-13730	44	11	the	the	DET
fumecheng-13730	44	12	a	a	DET
fumecheng-13730	44	13	modified	modify	VERB
fumecheng-13730	44	14	frequency	frequency	NOUN
fumecheng-13730	44	15	formulation	formulation	NOUN
fumecheng-13730	44	16	for	for	ADP
fumecheng-13730	44	17	nonlinear	nonlinear	ADJ
fumecheng-13730	44	18	mechanical	mechanical	ADJ
fumecheng-13730	44	19	vibrations	vibration	NOUN
fumecheng-13730	44	20	199	199	NUM
fumecheng-13730	44	21	foundation	foundation	NOUN
fumecheng-13730	44	22	for	for	ADP
fumecheng-13730	44	23	the	the	DET
fumecheng-13730	44	24	optimal	optimal	ADJ
fumecheng-13730	44	25	design	design	NOUN
fumecheng-13730	44	26	of	of	ADP
fumecheng-13730	44	27	a	a	DET
fumecheng-13730	44	28	nonlinear	nonlinear	ADJ
fumecheng-13730	44	29	vibration	vibration	NOUN
fumecheng-13730	44	30	system	system	NOUN
fumecheng-13730	44	31	.	.	PUNCT
fumecheng-13730	45	1	a	a	DET
fumecheng-13730	45	2	precise	precise	ADJ
fumecheng-13730	45	3	understanding	understanding	NOUN
fumecheng-13730	45	4	of	of	ADP
fumecheng-13730	45	5	the	the	DET
fumecheng-13730	45	6	frequency	frequency	NOUN
fumecheng-13730	45	7	-	-	PUNCT
fumecheng-13730	45	8	amplitude	amplitude	NOUN
fumecheng-13730	45	9	relationship	relationship	NOUN
fumecheng-13730	45	10	is	be	AUX
fumecheng-13730	45	11	essential	essential	ADJ
fumecheng-13730	45	12	for	for	ADP
fumecheng-13730	45	13	engineers	engineer	NOUN
fumecheng-13730	45	14	to	to	ADP
fumecheng-13730	45	15	fine	fine	ADJ
fumecheng-13730	45	16	-	-	PUNCT
fumecheng-13730	45	17	tune	tune	NOUN
fumecheng-13730	45	18	the	the	DET
fumecheng-13730	45	19	parameters	parameter	NOUN
fumecheng-13730	45	20	of	of	ADP
fumecheng-13730	45	21	the	the	DET
fumecheng-13730	45	22	system	system	NOUN
fumecheng-13730	45	23	,	,	PUNCT
fumecheng-13730	45	24	ensuring	ensure	VERB
fumecheng-13730	45	25	its	its	PRON
fumecheng-13730	45	26	optimal	optimal	ADJ
fumecheng-13730	45	27	performance	performance	NOUN
fumecheng-13730	45	28	and	and	CCONJ
fumecheng-13730	45	29	reliability	reliability	NOUN
fumecheng-13730	45	30	.	.	PUNCT
fumecheng-13730	46	1	absent	absent	ADJ
fumecheng-13730	46	2	a	a	DET
fumecheng-13730	46	3	reliable	reliable	ADJ
fumecheng-13730	46	4	estimate	estimate	NOUN
fumecheng-13730	46	5	of	of	ADP
fumecheng-13730	46	6	this	this	DET
fumecheng-13730	46	7	relationship	relationship	NOUN
fumecheng-13730	46	8	,	,	PUNCT
fumecheng-13730	46	9	the	the	DET
fumecheng-13730	46	10	design	design	NOUN
fumecheng-13730	46	11	process	process	NOUN
fumecheng-13730	46	12	becomes	become	VERB
fumecheng-13730	46	13	a	a	DET
fumecheng-13730	46	14	speculative	speculative	ADJ
fumecheng-13730	46	15	endeavor	endeavor	NOUN
fumecheng-13730	46	16	,	,	PUNCT
fumecheng-13730	46	17	with	with	ADP
fumecheng-13730	46	18	the	the	DET
fumecheng-13730	46	19	potential	potential	NOUN
fumecheng-13730	46	20	to	to	PART
fumecheng-13730	46	21	yield	yield	VERB
fumecheng-13730	46	22	suboptimal	suboptimal	ADJ
fumecheng-13730	46	23	results	result	NOUN
fumecheng-13730	46	24	and	and	CCONJ
fumecheng-13730	46	25	inefficiencies	inefficiency	NOUN
fumecheng-13730	46	26	.	.	PUNCT
fumecheng-13730	47	1	2	2	X
fumecheng-13730	47	2	.	.	X
fumecheng-13730	47	3	problem	problem	NOUN
fumecheng-13730	47	4	formulation	formulation	NOUN
fumecheng-13730	47	5	in	in	ADP
fumecheng-13730	47	6	a	a	DET
fumecheng-13730	47	7	previous	previous	ADJ
fumecheng-13730	47	8	publication	publication	NOUN
fumecheng-13730	47	9	,	,	PUNCT
fumecheng-13730	47	10	ji	ji	PROPN
fumecheng-13730	47	11	-	-	PROPN
fumecheng-13730	47	12	huan	huan	NOUN
fumecheng-13730	47	13	he	he	PRON
fumecheng-13730	48	1	[	[	X
fumecheng-13730	48	2	11	11	NUM
fumecheng-13730	48	3	]	]	PUNCT
fumecheng-13730	48	4	considered	consider	VERB
fumecheng-13730	48	5	the	the	DET
fumecheng-13730	48	6	following	following	ADJ
fumecheng-13730	48	7	nonlinear	nonlinear	ADJ
fumecheng-13730	48	8	oscillator	oscillator	NOUN
fumecheng-13730	48	9	:	:	PUNCT
fumecheng-13730	48	10	2	2	NUM
fumecheng-13730	48	11	1	1	NUM
fumecheng-13730	48	12	1	1	NUM
fumecheng-13730	48	13	2	2	NUM
fumecheng-13730	48	14	1	1	NUM
fumecheng-13730	48	15	1	1	NUM
fumecheng-13730	48	16	0	0	NUM
fumecheng-13730	48	17	n	n	CCONJ
fumecheng-13730	48	18	n	n	CCONJ
fumecheng-13730	48	19	n	n	CCONJ
fumecheng-13730	48	20	n	n	ADP
fumecheng-13730	48	21	u	u	NOUN
fumecheng-13730	48	22	a	a	DET
fumecheng-13730	48	23	u	u	NOUN
fumecheng-13730	48	24	a	a	DET
fumecheng-13730	48	25	u	u	NOUN
fumecheng-13730	49	1	+	+	PROPN
fumecheng-13730	49	2	+	+	CCONJ
fumecheng-13730	49	3	=	=	SYM
fumecheng-13730	49	4			PROPN
fumecheng-13730	49	5	+	+	SYM
fumecheng-13730	49	6	+	+	PUNCT
fumecheng-13730	49	7	=	=	NOUN
fumecheng-13730	49	8			X
fumecheng-13730	49	9	(	(	PUNCT
fumecheng-13730	49	10	1	1	NUM
fumecheng-13730	49	11	)	)	PUNCT
fumecheng-13730	50	1	and	and	CCONJ
fumecheng-13730	50	2	proposed	propose	VERB
fumecheng-13730	50	3	the	the	DET
fumecheng-13730	50	4	following	follow	VERB
fumecheng-13730	50	5	frequency	frequency	NOUN
fumecheng-13730	50	6	formulation	formulation	NOUN
fumecheng-13730	50	7	:	:	PUNCT
fumecheng-13730	51	1	2	2	NUM
fumecheng-13730	51	2	2	2	NUM
fumecheng-13730	51	3	1	1	NUM
fumecheng-13730	51	4	2	2	NUM
fumecheng-13730	51	5	1	1	NUM
fumecheng-13730	51	6	1	1	NUM
fumecheng-13730	51	7	3	3	NUM
fumecheng-13730	51	8	2	2	NUM
fumecheng-13730	51	9	2	2	NUM
fumecheng-13730	51	10	n	n	CCONJ
fumecheng-13730	51	11	n	n	CCONJ
fumecheng-13730	51	12	n	n	PROPN
fumecheng-13730	51	13	n	n	ADV
fumecheng-13730	51	14	a	a	DET
fumecheng-13730	51	15	a	a	DET
fumecheng-13730	51	16	a	a	DET
fumecheng-13730	51	17	n	n	NOUN
fumecheng-13730	51	18	+	+	NOUN
fumecheng-13730	51	19	=	=	SYM
fumecheng-13730	51	20	=	=	SYM
fumecheng-13730	52	1	+	+	PUNCT
fumecheng-13730	52	2	+	+	CCONJ
fumecheng-13730	52	3			PROPN
fumecheng-13730	52	4	(	(	PUNCT
fumecheng-13730	52	5	2	2	NUM
fumecheng-13730	52	6	)	)	PUNCT
fumecheng-13730	52	7	where	where	SCONJ
fumecheng-13730	52	8	a2n+1	a2n+1	VERB
fumecheng-13730	52	9	(	(	PUNCT
fumecheng-13730	52	10	n=0	n=0	NUM
fumecheng-13730	52	11	~	~	SYM
fumecheng-13730	52	12	n	n	CCONJ
fumecheng-13730	52	13	)	)	PUNCT
fumecheng-13730	52	14	are	be	AUX
fumecheng-13730	52	15	constants	constant	NOUN
fumecheng-13730	52	16	,	,	PUNCT
fumecheng-13730	52	17	a	a	PRON
fumecheng-13730	52	18	is	be	AUX
fumecheng-13730	52	19	the	the	DET
fumecheng-13730	52	20	amplitude	amplitude	NOUN
fumecheng-13730	52	21	.	.	PUNCT
fumecheng-13730	53	1	the	the	DET
fumecheng-13730	53	2	frequency	frequency	NOUN
fumecheng-13730	53	3	formulation	formulation	NOUN
fumecheng-13730	53	4	is	be	AUX
fumecheng-13730	53	5	effective	effective	ADJ
fumecheng-13730	53	6	for	for	ADP
fumecheng-13730	53	7	nonlinear	nonlinear	ADJ
fumecheng-13730	53	8	oscillators	oscillator	NOUN
fumecheng-13730	53	9	with	with	ADP
fumecheng-13730	53	10	high	high	ADJ
fumecheng-13730	53	11	order	order	NOUN
fumecheng-13730	53	12	nonlinearities	nonlinearitie	NOUN
fumecheng-13730	53	13	,	,	PUNCT
fumecheng-13730	53	14	for	for	ADP
fumecheng-13730	53	15	example	example	NOUN
fumecheng-13730	53	16	,	,	PUNCT
fumecheng-13730	53	17	the	the	DET
fumecheng-13730	53	18	cubicquintic	cubicquintic	ADJ
fumecheng-13730	53	19	-	-	PUNCT
fumecheng-13730	53	20	septic	septic	NOUN
fumecheng-13730	53	21	duffing	duffing	NOUN
fumecheng-13730	53	22	oscillator	oscillator	NOUN
fumecheng-13730	53	23	[	[	X
fumecheng-13730	53	24	12	12	NUM
fumecheng-13730	53	25	]	]	X
fumecheng-13730	53	26	:	:	PUNCT
fumecheng-13730	53	27	2	2	NUM
fumecheng-13730	53	28	2	2	NUM
fumecheng-13730	53	29	1	1	NUM
fumecheng-13730	53	30	2	2	NUM
fumecheng-13730	53	31	1	1	NUM
fumecheng-13730	53	32	2	2	NUM
fumecheng-13730	53	33	1	1	NUM
fumecheng-13730	53	34	1	1	NUM
fumecheng-13730	53	35	(	(	PUNCT
fumecheng-13730	53	36	)	)	PUNCT
fumecheng-13730	53	37	n	n	CCONJ
fumecheng-13730	53	38	n	n	CCONJ
fumecheng-13730	53	39	n	n	CCONJ
fumecheng-13730	53	40	n	n	CCONJ
fumecheng-13730	53	41	n	n	ADV
fumecheng-13730	53	42	a	a	DET
fumecheng-13730	53	43	a	a	DET
fumecheng-13730	53	44	u+	u+	NOUN
fumecheng-13730	53	45	+	+	NUM
fumecheng-13730	53	46	=	=	SYM
fumecheng-13730	54	1	=	=	SYM
fumecheng-13730	54	2	+	+	PUNCT
fumecheng-13730	54	3			PROPN
fumecheng-13730	54	4	(	(	PUNCT
fumecheng-13730	54	5	3	3	NUM
fumecheng-13730	54	6	)	)	PUNCT
fumecheng-13730	54	7	this	this	PRON
fumecheng-13730	54	8	is	be	AUX
fumecheng-13730	54	9	to	to	PART
fumecheng-13730	54	10	choose	choose	VERB
fumecheng-13730	54	11	a	a	DET
fumecheng-13730	54	12	location	location	NOUN
fumecheng-13730	54	13	point	point	NOUN
fumecheng-13730	54	14	for	for	ADP
fumecheng-13730	54	15	each	each	DET
fumecheng-13730	54	16	nonlinear	nonlinear	ADJ
fumecheng-13730	54	17	term	term	NOUN
fumecheng-13730	54	18	,	,	PUNCT
fumecheng-13730	54	19	u2n+1	u2n+1	NOUN
fumecheng-13730	54	20	:	:	PUNCT
fumecheng-13730	54	21	1/2	1/2	NUM
fumecheng-13730	54	22	2	2	NUM
fumecheng-13730	54	23	1	1	NUM
fumecheng-13730	54	24	3	3	NUM
fumecheng-13730	54	25	(	(	PUNCT
fumecheng-13730	54	26	)	)	PUNCT
fumecheng-13730	54	27	2	2	NUM
fumecheng-13730	54	28	2	2	NUM
fumecheng-13730	54	29	n	n	NUM
fumecheng-13730	54	30	nu	nu	NOUN
fumecheng-13730	54	31	a	a	DET
fumecheng-13730	54	32	n	n	NOUN
fumecheng-13730	54	33	+	+	CCONJ
fumecheng-13730	54	34	=	=	SYM
fumecheng-13730	55	1	+	+	CCONJ
fumecheng-13730	55	2	(	(	PUNCT
fumecheng-13730	55	3	4	4	X
fumecheng-13730	55	4	)	)	PUNCT
fumecheng-13730	55	5	this	this	DET
fumecheng-13730	55	6	frequency	frequency	NOUN
fumecheng-13730	55	7	formulation	formulation	NOUN
fumecheng-13730	55	8	holds	hold	VERB
fumecheng-13730	55	9	immense	immense	ADJ
fumecheng-13730	55	10	importance	importance	NOUN
fumecheng-13730	55	11	in	in	ADP
fumecheng-13730	55	12	the	the	DET
fumecheng-13730	55	13	realms	realm	NOUN
fumecheng-13730	55	14	of	of	ADP
fumecheng-13730	55	15	both	both	DET
fumecheng-13730	55	16	mathematics	mathematic	NOUN
fumecheng-13730	55	17	and	and	CCONJ
fumecheng-13730	55	18	nonlinear	nonlinear	ADJ
fumecheng-13730	55	19	vibration	vibration	NOUN
fumecheng-13730	55	20	theory	theory	NOUN
fumecheng-13730	55	21	.	.	PUNCT
fumecheng-13730	56	1	it	it	PRON
fumecheng-13730	56	2	offers	offer	VERB
fumecheng-13730	56	3	a	a	DET
fumecheng-13730	56	4	swift	swift	ADJ
fumecheng-13730	56	5	and	and	CCONJ
fumecheng-13730	56	6	effective	effective	ADJ
fumecheng-13730	56	7	means	mean	NOUN
fumecheng-13730	56	8	of	of	ADP
fumecheng-13730	56	9	understanding	understand	VERB
fumecheng-13730	56	10	the	the	DET
fumecheng-13730	56	11	two	two	NUM
fumecheng-13730	56	12	main	main	ADJ
fumecheng-13730	56	13	factors	factor	NOUN
fumecheng-13730	56	14	of	of	ADP
fumecheng-13730	56	15	oscillators	oscillator	NOUN
fumecheng-13730	56	16	and	and	CCONJ
fumecheng-13730	56	17	their	their	PRON
fumecheng-13730	56	18	intricate	intricate	ADJ
fumecheng-13730	56	19	relationship	relationship	NOUN
fumecheng-13730	56	20	.	.	PUNCT
fumecheng-13730	57	1	this	this	DET
fumecheng-13730	57	2	knowledge	knowledge	NOUN
fumecheng-13730	57	3	is	be	AUX
fumecheng-13730	57	4	essential	essential	ADJ
fumecheng-13730	57	5	for	for	ADP
fumecheng-13730	57	6	delving	delve	VERB
fumecheng-13730	57	7	deep	deep	ADV
fumecheng-13730	57	8	into	into	ADP
fumecheng-13730	57	9	the	the	DET
fumecheng-13730	57	10	vibration	vibration	NOUN
fumecheng-13730	57	11	properties	property	NOUN
fumecheng-13730	57	12	and	and	CCONJ
fumecheng-13730	57	13	enabling	enable	VERB
fumecheng-13730	57	14	advanced	advanced	ADJ
fumecheng-13730	57	15	applications	application	NOUN
fumecheng-13730	57	16	.	.	PUNCT
fumecheng-13730	58	1	take	take	VERB
fumecheng-13730	58	2	,	,	PUNCT
fumecheng-13730	58	3	for	for	ADP
fumecheng-13730	58	4	example	example	NOUN
fumecheng-13730	58	5	,	,	PUNCT
fumecheng-13730	58	6	for	for	ADP
fumecheng-13730	58	7	the	the	DET
fumecheng-13730	58	8	most	most	ADJ
fumecheng-13730	58	9	energy	energy	NOUN
fumecheng-13730	58	10	harvesting	harvesting	NOUN
fumecheng-13730	58	11	devices	device	NOUN
fumecheng-13730	58	12	or	or	CCONJ
fumecheng-13730	58	13	vibration	vibration	NOUN
fumecheng-13730	58	14	dampers	damper	NOUN
fumecheng-13730	58	15	,	,	PUNCT
fumecheng-13730	58	16	their	their	PRON
fumecheng-13730	58	17	low	low	ADJ
fumecheng-13730	58	18	-	-	PUNCT
fumecheng-13730	58	19	frequency	frequency	NOUN
fumecheng-13730	58	20	property	property	NOUN
fumecheng-13730	58	21	implies	imply	VERB
fumecheng-13730	58	22	a	a	DET
fumecheng-13730	58	23	large	large	ADJ
fumecheng-13730	58	24	amplitude	amplitude	NOUN
fumecheng-13730	58	25	motion	motion	NOUN
fumecheng-13730	58	26	.	.	PUNCT
fumecheng-13730	59	1	as	as	ADP
fumecheng-13730	59	2	an	an	DET
fumecheng-13730	59	3	illustration	illustration	NOUN
fumecheng-13730	59	4	,	,	PUNCT
fumecheng-13730	59	5	we	we	PRON
fumecheng-13730	59	6	now	now	ADV
fumecheng-13730	59	7	consider	consider	VERB
fumecheng-13730	59	8	the	the	DET
fumecheng-13730	59	9	following	follow	VERB
fumecheng-13730	59	10	nonlinear	nonlinear	ADJ
fumecheng-13730	59	11	oscillator	oscillator	NOUN
fumecheng-13730	59	12	[	[	X
fumecheng-13730	59	13	13	13	NUM
fumecheng-13730	59	14	]	]	PUNCT
fumecheng-13730	59	15	.	.	PUNCT
fumecheng-13730	60	1	2	2	NUM
fumecheng-13730	60	2	2	2	NUM
fumecheng-13730	60	3	2(1	2(1	NUM
fumecheng-13730	60	4	)	)	PUNCT
fumecheng-13730	60	5	(	(	PUNCT
fumecheng-13730	60	6	1	1	X
fumecheng-13730	60	7	)	)	PUNCT
fumecheng-13730	60	8	0au	0au	NOUN
fumecheng-13730	60	9	u	u	NOUN
fumecheng-13730	60	10	auu	auu	PROPN
fumecheng-13730	60	11	u	u	NOUN
fumecheng-13730	60	12	u	u	PROPN
fumecheng-13730	60	13	+	+	NOUN
fumecheng-13730	60	14	+	+	CCONJ
fumecheng-13730	60	15	−	−	ADP
fumecheng-13730	61	1	−	−	PROPN
fumecheng-13730	61	2	=	=	SYM
fumecheng-13730	61	3	(	(	PUNCT
fumecheng-13730	61	4	5	5	NUM
fumecheng-13730	61	5	)	)	PUNCT
fumecheng-13730	61	6	where	where	SCONJ
fumecheng-13730	61	7	α	α	NOUN
fumecheng-13730	61	8	is	be	AUX
fumecheng-13730	61	9	a	a	DET
fumecheng-13730	61	10	constant	constant	ADJ
fumecheng-13730	61	11	.	.	PUNCT
fumecheng-13730	62	1	it	it	PRON
fumecheng-13730	62	2	can	can	AUX
fumecheng-13730	62	3	be	be	AUX
fumecheng-13730	62	4	re	re	VERB
fumecheng-13730	62	5	-	-	VERB
fumecheng-13730	62	6	written	write	VERB
fumecheng-13730	62	7	as	as	ADP
fumecheng-13730	62	8	3	3	NUM
fumecheng-13730	62	9	2	2	NUM
fumecheng-13730	62	10	2	2	NUM
fumecheng-13730	62	11	0u	0u	ADJ
fumecheng-13730	62	12	u	u	NOUN
fumecheng-13730	62	13	u	u	NOUN
fumecheng-13730	62	14	auu	auu	PROPN
fumecheng-13730	62	15	au	au	PROPN
fumecheng-13730	62	16	u	u	PROPN
fumecheng-13730	62	17			PROPN
fumecheng-13730	62	18	−	−	VERB
fumecheng-13730	62	19	+	+	X
fumecheng-13730	63	1	+	+	PUNCT
fumecheng-13730	63	2	+	+	CCONJ
fumecheng-13730	63	3	=	=	SYM
fumecheng-13730	63	4	(	(	PUNCT
fumecheng-13730	63	5	6	6	NUM
fumecheng-13730	63	6	)	)	PUNCT
fumecheng-13730	63	7	by	by	ADP
fumecheng-13730	63	8	the	the	DET
fumecheng-13730	63	9	frequency	frequency	NOUN
fumecheng-13730	63	10	formulation	formulation	NOUN
fumecheng-13730	63	11	of	of	ADP
fumecheng-13730	63	12	eq	eq	PROPN
fumecheng-13730	63	13	.	.	PUNCT
fumecheng-13730	64	1	(	(	PUNCT
fumecheng-13730	64	2	3	3	NUM
fumecheng-13730	64	3	)	)	PUNCT
fumecheng-13730	64	4	,	,	PUNCT
fumecheng-13730	64	5	we	we	PRON
fumecheng-13730	64	6	have	have	VERB
fumecheng-13730	64	7	2	2	NUM
fumecheng-13730	64	8	2	2	NUM
fumecheng-13730	64	9	21	21	NUM
fumecheng-13730	64	10	u	u	NOUN
fumecheng-13730	64	11	au	au	PROPN
fumecheng-13730	64	12	auu	auu	PROPN
fumecheng-13730	64	13	=	=	PROPN
fumecheng-13730	64	14	−	−	PROPN
fumecheng-13730	65	1	+	+	CCONJ
fumecheng-13730	66	1	+	+	PUNCT
fumecheng-13730	66	2	+	+	ADJ
fumecheng-13730	66	3			X
fumecheng-13730	66	4	(	(	PUNCT
fumecheng-13730	66	5	7	7	NUM
fumecheng-13730	66	6	)	)	PUNCT
fumecheng-13730	66	7	the	the	DET
fumecheng-13730	66	8	location	location	NOUN
fumecheng-13730	66	9	point	point	NOUN
fumecheng-13730	66	10	is	be	AUX
fumecheng-13730	66	11	chosen	choose	VERB
fumecheng-13730	66	12	as	as	ADP
fumecheng-13730	66	13	200	200	NUM
fumecheng-13730	66	14	c.h	c.h	NOUN
fumecheng-13730	66	15	.	.	PUNCT
fumecheng-13730	67	1	he	he	PRON
fumecheng-13730	67	2	,	,	PUNCT
fumecheng-13730	67	3	j.h	j.h	PROPN
fumecheng-13730	67	4	.	.	PUNCT
fumecheng-13730	68	1	he	he	PRON
fumecheng-13730	68	2	,	,	PUNCT
fumecheng-13730	68	3	j.	j.	PROPN
fumecheng-13730	68	4	ma	ma	PROPN
fumecheng-13730	68	5	,	,	PUNCT
fumecheng-13730	68	6	a.a	a.a	PROPN
fumecheng-13730	68	7	.	.	PROPN
fumecheng-13730	68	8	alsolam	alsolam	PROPN
fumecheng-13730	68	9	,	,	PUNCT
fumecheng-13730	68	10	x.j	x.j	PROPN
fumecheng-13730	68	11	.	.	PROPN
fumecheng-13730	68	12	yang	yang	PROPN
fumecheng-13730	68	13	3	3	NUM
fumecheng-13730	68	14	2	2	NUM
fumecheng-13730	68	15	u	u	NOUN
fumecheng-13730	68	16	a=	a=	X
fumecheng-13730	68	17	(	(	PUNCT
fumecheng-13730	68	18	8)	8)	NUM
fumecheng-13730	68	19	its	its	PRON
fumecheng-13730	68	20	derivatives	derivative	NOUN
fumecheng-13730	68	21	can	can	AUX
fumecheng-13730	68	22	be	be	AUX
fumecheng-13730	68	23	approximately	approximately	ADV
fumecheng-13730	68	24	calculated	calculate	VERB
fumecheng-13730	68	25	as	as	ADP
fumecheng-13730	68	26	2	2	NUM
fumecheng-13730	68	27	2	2	NUM
fumecheng-13730	68	28	1	1	NUM
fumecheng-13730	68	29	2	2	NUM
fumecheng-13730	68	30	u	u	NOUN
fumecheng-13730	68	31	a	a	DET
fumecheng-13730	68	32	u	u	NOUN
fumecheng-13730	68	33	a	a	PROPN
fumecheng-13730	68	34	=	=	SYM
fumecheng-13730	68	35	−	−	PROPN
fumecheng-13730	68	36	=	=	PRON
fumecheng-13730	68	37			X
fumecheng-13730	68	38			X
fumecheng-13730	68	39	(	(	PUNCT
fumecheng-13730	68	40	9	9	NUM
fumecheng-13730	68	41	)	)	SYM
fumecheng-13730	68	42	2	2	NUM
fumecheng-13730	68	43	23	23	NUM
fumecheng-13730	68	44	2	2	NUM
fumecheng-13730	68	45	u	u	NOUN
fumecheng-13730	68	46	u	u	NOUN
fumecheng-13730	68	47	a	a	NOUN
fumecheng-13730	68	48	=	=	SYM
fumecheng-13730	68	49	−	−	PROPN
fumecheng-13730	68	50	=	=	PUNCT
fumecheng-13730	68	51	−	−	ADJ
fumecheng-13730	68	52			X
fumecheng-13730	68	53	(	(	PUNCT
fumecheng-13730	68	54	10	10	NUM
fumecheng-13730	68	55	)	)	PUNCT
fumecheng-13730	68	56	so	so	SCONJ
fumecheng-13730	68	57	we	we	PRON
fumecheng-13730	68	58	have	have	VERB
fumecheng-13730	68	59	2	2	NUM
fumecheng-13730	68	60	2	2	NUM
fumecheng-13730	68	61	2	2	NUM
fumecheng-13730	68	62	2	2	NUM
fumecheng-13730	68	63	2	2	NUM
fumecheng-13730	68	64	2	2	NUM
fumecheng-13730	68	65	2	2	NUM
fumecheng-13730	68	66	2	2	NUM
fumecheng-13730	68	67	23	23	NUM
fumecheng-13730	68	68	1	1	NUM
fumecheng-13730	68	69	3	3	NUM
fumecheng-13730	68	70	3	3	NUM
fumecheng-13730	68	71	1	1	NUM
fumecheng-13730	68	72	1	1	NUM
fumecheng-13730	68	73	1	1	NUM
fumecheng-13730	68	74	4	4	NUM
fumecheng-13730	68	75	4	4	NUM
fumecheng-13730	68	76	4	4	NUM
fumecheng-13730	68	77	4	4	NUM
fumecheng-13730	68	78	2	2	NUM
fumecheng-13730	68	79	a	a	DET
fumecheng-13730	68	80	a	a	DET
fumecheng-13730	68	81	a	a	DET
fumecheng-13730	68	82	a	a	DET
fumecheng-13730	68	83	a	a	DET
fumecheng-13730	68	84	a	a	DET
fumecheng-13730	68	85	aa=	aa=	NOUN
fumecheng-13730	68	86	−	−	PROPN
fumecheng-13730	69	1	+	+	CCONJ
fumecheng-13730	70	1	+	+	NUM
fumecheng-13730	70	2	−	−	NOUN
fumecheng-13730	70	3	=	=	SYM
fumecheng-13730	70	4	−	−	PROPN
fumecheng-13730	71	1	+	+	CCONJ
fumecheng-13730	71	2	+	+	ADV
fumecheng-13730	71	3			X
fumecheng-13730	71	4			X
fumecheng-13730	71	5			X
fumecheng-13730	71	6			X
fumecheng-13730	71	7	(	(	PUNCT
fumecheng-13730	71	8	11	11	NUM
fumecheng-13730	71	9	)	)	PUNCT
fumecheng-13730	71	10	after	after	ADP
fumecheng-13730	71	11	a	a	DET
fumecheng-13730	71	12	simple	simple	ADJ
fumecheng-13730	71	13	calculation	calculation	NOUN
fumecheng-13730	71	14	,	,	PUNCT
fumecheng-13730	71	15	we	we	PRON
fumecheng-13730	71	16	have	have	VERB
fumecheng-13730	71	17	3	3	NUM
fumecheng-13730	71	18	2	2	NUM
fumecheng-13730	71	19	4	4	NUM
fumecheng-13730	71	20	1	1	NUM
fumecheng-13730	71	21	2	2	NUM
fumecheng-13730	71	22	2	2	NUM
fumecheng-13730	71	23	1	1	NUM
fumecheng-13730	71	24	1	1	NUM
fumecheng-13730	71	25	a	a	DET
fumecheng-13730	71	26	aa	aa	NOUN
fumecheng-13730	71	27	−	−	PROPN
fumecheng-13730	72	1	+	+	CCONJ
fumecheng-13730	72	2	=	=	SYM
fumecheng-13730	73	1	+	+	CCONJ
fumecheng-13730	73	2			X
fumecheng-13730	73	3	(	(	PUNCT
fumecheng-13730	73	4	12	12	NUM
fumecheng-13730	73	5	)	)	PUNCT
fumecheng-13730	73	6	which	which	PRON
fumecheng-13730	73	7	is	be	AUX
fumecheng-13730	73	8	exactly	exactly	ADV
fumecheng-13730	73	9	same	same	ADJ
fumecheng-13730	73	10	as	as	ADP
fumecheng-13730	73	11	that	that	PRON
fumecheng-13730	73	12	in	in	ADP
fumecheng-13730	73	13	ref	ref	NOUN
fumecheng-13730	73	14	.	.	PUNCT
fumecheng-13730	74	1	[	[	X
fumecheng-13730	74	2	14	14	NUM
fumecheng-13730	74	3	]	]	PUNCT
fumecheng-13730	74	4	.	.	PUNCT
fumecheng-13730	75	1	there	there	PRON
fumecheng-13730	75	2	are	be	VERB
fumecheng-13730	75	3	an	an	DET
fumecheng-13730	75	4	abundant	abundant	ADJ
fumecheng-13730	75	5	number	number	NOUN
fumecheng-13730	75	6	of	of	ADP
fumecheng-13730	75	7	publications	publication	NOUN
fumecheng-13730	75	8	on	on	ADP
fumecheng-13730	75	9	the	the	DET
fumecheng-13730	75	10	applications	application	NOUN
fumecheng-13730	75	11	of	of	ADP
fumecheng-13730	75	12	the	the	DET
fumecheng-13730	75	13	original	original	ADJ
fumecheng-13730	75	14	frequency	frequency	NOUN
fumecheng-13730	75	15	-	-	PUNCT
fumecheng-13730	75	16	amplitude	amplitude	NOUN
fumecheng-13730	75	17	formulation	formulation	NOUN
fumecheng-13730	75	18	and	and	CCONJ
fumecheng-13730	75	19	its	its	PRON
fumecheng-13730	75	20	various	various	ADJ
fumecheng-13730	75	21	modifications	modification	NOUN
fumecheng-13730	75	22	.	.	PUNCT
fumecheng-13730	76	1	he	he	PRON
fumecheng-13730	76	2	and	and	CCONJ
fumecheng-13730	76	3	liu	liu	PROPN
fumecheng-13730	77	1	[	[	X
fumecheng-13730	77	2	15	15	NUM
fumecheng-13730	77	3	]	]	PUNCT
fumecheng-13730	77	4	gave	give	VERB
fumecheng-13730	77	5	a	a	DET
fumecheng-13730	77	6	rigorous	rigorous	ADJ
fumecheng-13730	77	7	mathematical	mathematical	ADJ
fumecheng-13730	77	8	perspective	perspective	NOUN
fumecheng-13730	77	9	for	for	SCONJ
fumecheng-13730	77	10	he	he	PRON
fumecheng-13730	77	11	’s	’	VERB
fumecheng-13730	77	12	frequency	frequency	NOUN
fumecheng-13730	77	13	formulation	formulation	NOUN
fumecheng-13730	77	14	.	.	PUNCT
fumecheng-13730	78	1	ismail	ismail	NOUN
fumecheng-13730	78	2	et	et	PROPN
fumecheng-13730	78	3	al	al	PROPN
fumecheng-13730	78	4	.	.	PUNCT
fumecheng-13730	79	1	[	[	X
fumecheng-13730	79	2	16	16	NUM
fumecheng-13730	79	3	]	]	PUNCT
fumecheng-13730	79	4	and	and	CCONJ
fumecheng-13730	79	5	hashemi	hashemi	NOUN
fumecheng-13730	80	1	[	[	X
fumecheng-13730	80	2	17	17	NUM
fumecheng-13730	80	3	]	]	PUNCT
fumecheng-13730	80	4	found	find	VERB
fumecheng-13730	80	5	that	that	SCONJ
fumecheng-13730	80	6	this	this	DET
fumecheng-13730	80	7	formulation	formulation	NOUN
fumecheng-13730	80	8	is	be	AUX
fumecheng-13730	80	9	extremely	extremely	ADV
fumecheng-13730	80	10	well	well	ADV
fumecheng-13730	80	11	-	-	PUNCT
fumecheng-13730	80	12	suited	suit	VERB
fumecheng-13730	80	13	for	for	ADP
fumecheng-13730	80	14	strongly	strongly	ADV
fumecheng-13730	80	15	nonlinear	nonlinear	ADJ
fumecheng-13730	80	16	oscillators	oscillator	NOUN
fumecheng-13730	80	17	.	.	PUNCT
fumecheng-13730	81	1	their	their	PRON
fumecheng-13730	81	2	studies	study	NOUN
fumecheng-13730	81	3	have	have	AUX
fumecheng-13730	81	4	demonstrated	demonstrate	VERB
fumecheng-13730	81	5	its	its	PRON
fumecheng-13730	81	6	effectiveness	effectiveness	NOUN
fumecheng-13730	81	7	in	in	ADP
fumecheng-13730	81	8	analyzing	analyzing	NOUN
fumecheng-13730	81	9	and	and	CCONJ
fumecheng-13730	81	10	understanding	understand	VERB
fumecheng-13730	81	11	the	the	DET
fumecheng-13730	81	12	complex	complex	ADJ
fumecheng-13730	81	13	periodic	periodic	ADJ
fumecheng-13730	81	14	properties	property	NOUN
fumecheng-13730	81	15	.	.	PUNCT
fumecheng-13730	82	1	kawser	kawser	NOUN
fumecheng-13730	82	2	et	et	PROPN
fumecheng-13730	82	3	al	al	PROPN
fumecheng-13730	82	4	.	.	PROPN
fumecheng-13730	82	5	conducted	conduct	VERB
fumecheng-13730	82	6	a	a	DET
fumecheng-13730	82	7	comparison	comparison	NOUN
fumecheng-13730	82	8	between	between	ADP
fumecheng-13730	82	9	the	the	DET
fumecheng-13730	82	10	frequency	frequency	NOUN
fumecheng-13730	82	11	formulation	formulation	NOUN
fumecheng-13730	82	12	and	and	CCONJ
fumecheng-13730	82	13	numerical	numerical	PROPN
fumecheng-13730	82	14	simulation	simulation	NOUN
fumecheng-13730	82	15	for	for	ADP
fumecheng-13730	82	16	the	the	DET
fumecheng-13730	82	17	analysis	analysis	NOUN
fumecheng-13730	82	18	of	of	ADP
fumecheng-13730	82	19	the	the	DET
fumecheng-13730	82	20	jet	jet	NOUN
fumecheng-13730	82	21	engine	engine	NOUN
fumecheng-13730	82	22	vibration	vibration	NOUN
fumecheng-13730	82	23	system	system	NOUN
fumecheng-13730	82	24	.	.	PUNCT
fumecheng-13730	83	1	they	they	PRON
fumecheng-13730	83	2	discovered	discover	VERB
fumecheng-13730	83	3	that	that	SCONJ
fumecheng-13730	83	4	the	the	DET
fumecheng-13730	83	5	former	former	ADJ
fumecheng-13730	83	6	is	be	AUX
fumecheng-13730	83	7	not	not	PART
fumecheng-13730	83	8	only	only	ADV
fumecheng-13730	83	9	simple	simple	ADJ
fumecheng-13730	83	10	to	to	AUX
fumecheng-13730	83	11	use	use	VERB
fumecheng-13730	83	12	but	but	CCONJ
fumecheng-13730	83	13	also	also	ADV
fumecheng-13730	83	14	highly	highly	ADV
fumecheng-13730	83	15	effective	effective	ADJ
fumecheng-13730	83	16	[	[	X
fumecheng-13730	83	17	18	18	NUM
fumecheng-13730	83	18	]	]	PUNCT
fumecheng-13730	83	19	.	.	PUNCT
fumecheng-13730	84	1	tsaltas	tsalta	NOUN
fumecheng-13730	85	1	[	[	X
fumecheng-13730	85	2	19	19	NUM
fumecheng-13730	85	3	]	]	PUNCT
fumecheng-13730	85	4	concluded	conclude	VERB
fumecheng-13730	85	5	that	that	SCONJ
fumecheng-13730	85	6	the	the	DET
fumecheng-13730	85	7	one	one	NUM
fumecheng-13730	85	8	-	-	PUNCT
fumecheng-13730	85	9	step	step	NOUN
fumecheng-13730	85	10	frequency	frequency	NOUN
fumecheng-13730	85	11	formulation	formulation	NOUN
fumecheng-13730	85	12	holds	hold	VERB
fumecheng-13730	85	13	great	great	ADJ
fumecheng-13730	85	14	promise	promise	NOUN
fumecheng-13730	85	15	as	as	ADP
fumecheng-13730	85	16	a	a	DET
fumecheng-13730	85	17	new	new	ADJ
fumecheng-13730	85	18	approach	approach	NOUN
fumecheng-13730	85	19	for	for	ADP
fumecheng-13730	85	20	nonlinear	nonlinear	ADJ
fumecheng-13730	85	21	oscillators	oscillator	NOUN
fumecheng-13730	85	22	.	.	PUNCT
fumecheng-13730	86	1	additionally	additionally	ADV
fumecheng-13730	86	2	,	,	PUNCT
fumecheng-13730	86	3	other	other	ADJ
fumecheng-13730	86	4	applications	application	NOUN
fumecheng-13730	86	5	of	of	ADP
fumecheng-13730	86	6	the	the	DET
fumecheng-13730	86	7	frequency	frequency	NOUN
fumecheng-13730	86	8	formulation	formulation	NOUN
fumecheng-13730	86	9	are	be	AUX
fumecheng-13730	86	10	equally	equally	ADV
fumecheng-13730	86	11	captivating	captivating	ADJ
fumecheng-13730	86	12	[	[	X
fumecheng-13730	86	13	20,21	20,21	NUM
fumecheng-13730	86	14	]	]	PUNCT
fumecheng-13730	86	15	.	.	PUNCT
fumecheng-13730	87	1	these	these	DET
fumecheng-13730	87	2	applications	application	NOUN
fumecheng-13730	87	3	span	span	VERB
fumecheng-13730	87	4	different	different	ADJ
fumecheng-13730	87	5	fields	field	NOUN
fumecheng-13730	87	6	and	and	CCONJ
fumecheng-13730	87	7	highlight	highlight	VERB
fumecheng-13730	87	8	the	the	DET
fumecheng-13730	87	9	versatility	versatility	NOUN
fumecheng-13730	87	10	and	and	CCONJ
fumecheng-13730	87	11	importance	importance	NOUN
fumecheng-13730	87	12	of	of	ADP
fumecheng-13730	87	13	the	the	DET
fumecheng-13730	87	14	frequency	frequency	NOUN
fumecheng-13730	87	15	formulation	formulation	NOUN
fumecheng-13730	87	16	in	in	ADP
fumecheng-13730	87	17	understanding	understanding	NOUN
fumecheng-13730	87	18	and	and	CCONJ
fumecheng-13730	87	19	solving	solve	VERB
fumecheng-13730	87	20	a	a	DET
fumecheng-13730	87	21	wide	wide	ADJ
fumecheng-13730	87	22	range	range	NOUN
fumecheng-13730	87	23	of	of	ADP
fumecheng-13730	87	24	problems	problem	NOUN
fumecheng-13730	87	25	related	relate	VERB
fumecheng-13730	87	26	to	to	ADP
fumecheng-13730	87	27	nonlinear	nonlinear	ADJ
fumecheng-13730	87	28	oscillators	oscillator	NOUN
fumecheng-13730	87	29	.	.	PUNCT
fumecheng-13730	88	1	although	although	SCONJ
fumecheng-13730	88	2	significant	significant	ADJ
fumecheng-13730	88	3	achievements	achievement	NOUN
fumecheng-13730	88	4	have	have	AUX
fumecheng-13730	88	5	been	be	AUX
fumecheng-13730	88	6	attained	attain	VERB
fumecheng-13730	88	7	,	,	PUNCT
fumecheng-13730	88	8	there	there	PRON
fumecheng-13730	88	9	is	be	VERB
fumecheng-13730	88	10	still	still	ADV
fumecheng-13730	88	11	ample	ample	ADJ
fumecheng-13730	88	12	room	room	NOUN
fumecheng-13730	88	13	for	for	ADP
fumecheng-13730	88	14	further	further	ADJ
fumecheng-13730	88	15	improvement	improvement	NOUN
fumecheng-13730	88	16	,	,	PUNCT
fumecheng-13730	88	17	particularly	particularly	ADV
fumecheng-13730	88	18	for	for	ADP
fumecheng-13730	88	19	nonlinear	nonlinear	ADJ
fumecheng-13730	88	20	oscillators	oscillator	NOUN
fumecheng-13730	88	21	with	with	ADP
fumecheng-13730	88	22	a	a	DET
fumecheng-13730	88	23	nonlinear	nonlinear	ADJ
fumecheng-13730	88	24	term	term	NOUN
fumecheng-13730	88	25	of	of	ADP
fumecheng-13730	88	26	the	the	DET
fumecheng-13730	88	27	form	form	NOUN
fumecheng-13730	88	28	un	un	PROPN
fumecheng-13730	88	29	where	where	SCONJ
fumecheng-13730	88	30	n<1	n<1	PROPN
fumecheng-13730	88	31	.	.	PUNCT
fumecheng-13730	89	1	this	this	DET
fumecheng-13730	89	2	type	type	NOUN
fumecheng-13730	89	3	of	of	ADP
fumecheng-13730	89	4	oscillator	oscillator	NOUN
fumecheng-13730	89	5	encompasses	encompass	VERB
fumecheng-13730	89	6	singular	singular	ADJ
fumecheng-13730	89	7	oscillators	oscillator	NOUN
fumecheng-13730	89	8	and	and	CCONJ
fumecheng-13730	89	9	zigzag	zigzag	NOUN
fumecheng-13730	89	10	oscillators	oscillator	NOUN
fumecheng-13730	89	11	,	,	PUNCT
fumecheng-13730	89	12	which	which	PRON
fumecheng-13730	89	13	are	be	AUX
fumecheng-13730	89	14	extremely	extremely	ADV
fumecheng-13730	89	15	challenging	challenging	ADJ
fumecheng-13730	89	16	to	to	PART
fumecheng-13730	89	17	solve	solve	VERB
fumecheng-13730	89	18	analytically	analytically	ADV
fumecheng-13730	89	19	.	.	PUNCT
fumecheng-13730	90	1	3	3	X
fumecheng-13730	90	2	.	.	NOUN
fumecheng-13730	90	3	frequency	frequency	NOUN
fumecheng-13730	90	4	formulation	formulation	NOUN
fumecheng-13730	90	5	for	for	ADP
fumecheng-13730	90	6	quasi	quasi	ADJ
fumecheng-13730	90	7	-	-	ADJ
fumecheng-13730	90	8	linear	linear	ADJ
fumecheng-13730	90	9	oscillator	oscillator	NOUN
fumecheng-13730	90	10	and	and	CCONJ
fumecheng-13730	90	11	singular	singular	NOUN
fumecheng-13730	90	12	oscillators	oscillator	NOUN
fumecheng-13730	90	13	the	the	DET
fumecheng-13730	90	14	aforementioned	aforementioned	ADJ
fumecheng-13730	90	15	frequency	frequency	NOUN
fumecheng-13730	90	16	formulation	formulation	NOUN
fumecheng-13730	90	17	is	be	AUX
fumecheng-13730	90	18	applicable	applicable	ADJ
fumecheng-13730	90	19	to	to	ADP
fumecheng-13730	90	20	n>1	n>1	PROPN
fumecheng-13730	90	21	.	.	PUNCT
fumecheng-13730	91	1	it	it	PRON
fumecheng-13730	91	2	is	be	AUX
fumecheng-13730	91	3	evident	evident	ADJ
fumecheng-13730	91	4	that	that	SCONJ
fumecheng-13730	91	5	:	:	PUNCT
fumecheng-13730	91	6	2	2	NUM
fumecheng-13730	91	7	1	1	NUM
fumecheng-13730	91	8	,	,	PUNCT
fumecheng-13730	91	9	for	for	ADP
fumecheng-13730	91	10	1/	1/	NUM
fumecheng-13730	91	11	2nu	2nu	NOUN
fumecheng-13730	91	12	a	a	PROPN
fumecheng-13730	91	13	n+	n+	PRON
fumecheng-13730	91	14			INTJ
fumecheng-13730	91	15			PROPN
fumecheng-13730	91	16	.	.	PUNCT
fumecheng-13730	92	1	(	(	PUNCT
fumecheng-13730	92	2	13	13	NUM
fumecheng-13730	92	3	)	)	PUNCT
fumecheng-13730	92	4	however	however	ADV
fumecheng-13730	92	5	,	,	PUNCT
fumecheng-13730	92	6	this	this	PRON
fumecheng-13730	92	7	is	be	AUX
fumecheng-13730	92	8	incompatible	incompatible	ADJ
fumecheng-13730	92	9	with	with	ADP
fumecheng-13730	92	10	the	the	DET
fumecheng-13730	92	11	characteristics	characteristic	NOUN
fumecheng-13730	92	12	of	of	ADP
fumecheng-13730	92	13	a	a	DET
fumecheng-13730	92	14	conservative	conservative	ADJ
fumecheng-13730	92	15	oscillator	oscillator	NOUN
fumecheng-13730	92	16	,	,	PUNCT
fumecheng-13730	92	17	which	which	PRON
fumecheng-13730	92	18	exhibits	exhibit	VERB
fumecheng-13730	92	19	vibrations	vibration	NOUN
fumecheng-13730	92	20	from	from	ADP
fumecheng-13730	92	21	u	u	NOUN
fumecheng-13730	92	22	=	=	NOUN
fumecheng-13730	92	23	a	a	PRON
fumecheng-13730	92	24	to	to	PART
fumecheng-13730	92	25	u=-a	u=-a	VERB
fumecheng-13730	92	26	.	.	PUNCT
fumecheng-13730	93	1	there	there	PRON
fumecheng-13730	93	2	exists	exist	VERB
fumecheng-13730	93	3	a	a	DET
fumecheng-13730	93	4	large	large	ADJ
fumecheng-13730	93	5	set	set	NOUN
fumecheng-13730	93	6	of	of	ADP
fumecheng-13730	93	7	nonlinear	nonlinear	ADJ
fumecheng-13730	93	8	oscillators	oscillator	NOUN
fumecheng-13730	93	9	a	a	DET
fumecheng-13730	93	10	modified	modify	VERB
fumecheng-13730	93	11	frequency	frequency	NOUN
fumecheng-13730	93	12	formulation	formulation	NOUN
fumecheng-13730	93	13	for	for	ADP
fumecheng-13730	93	14	nonlinear	nonlinear	ADJ
fumecheng-13730	93	15	mechanical	mechanical	ADJ
fumecheng-13730	93	16	vibrations	vibration	NOUN
fumecheng-13730	93	17	201	201	NUM
fumecheng-13730	93	18	with	with	ADP
fumecheng-13730	93	19	an	an	DET
fumecheng-13730	93	20	irrational	irrational	ADJ
fumecheng-13730	93	21	term	term	NOUN
fumecheng-13730	93	22	[	[	X
fumecheng-13730	93	23	22	22	NUM
fumecheng-13730	93	24	]	]	PUNCT
fumecheng-13730	93	25	or	or	CCONJ
fumecheng-13730	93	26	a	a	DET
fumecheng-13730	93	27	term	term	NOUN
fumecheng-13730	93	28	of	of	ADP
fumecheng-13730	93	29	the	the	DET
fumecheng-13730	93	30	form	form	NOUN
fumecheng-13730	93	31	u1/(2n	u1/(2n	X
fumecheng-13730	93	32	+	+	NOUN
fumecheng-13730	93	33	1	1	X
fumecheng-13730	93	34	)	)	PUNCT
fumecheng-13730	94	1	[	[	X
fumecheng-13730	94	2	23	23	NUM
fumecheng-13730	94	3	]	]	PUNCT
fumecheng-13730	94	4	.	.	PUNCT
fumecheng-13730	95	1	though	though	SCONJ
fumecheng-13730	95	2	there	there	PRON
fumecheng-13730	95	3	were	be	VERB
fumecheng-13730	95	4	some	some	DET
fumecheng-13730	95	5	effective	effective	ADJ
fumecheng-13730	95	6	modifications	modification	NOUN
fumecheng-13730	95	7	of	of	ADP
fumecheng-13730	95	8	the	the	DET
fumecheng-13730	95	9	frequency	frequency	NOUN
fumecheng-13730	95	10	formulation	formulation	NOUN
fumecheng-13730	95	11	[	[	X
fumecheng-13730	95	12	24	24	NUM
fumecheng-13730	95	13	,	,	PUNCT
fumecheng-13730	95	14	25	25	NUM
fumecheng-13730	95	15	]	]	PUNCT
fumecheng-13730	95	16	,	,	PUNCT
fumecheng-13730	95	17	here	here	ADV
fumecheng-13730	95	18	a	a	DET
fumecheng-13730	95	19	more	more	ADV
fumecheng-13730	95	20	effective	effective	ADJ
fumecheng-13730	95	21	formulation	formulation	NOUN
fumecheng-13730	95	22	will	will	AUX
fumecheng-13730	95	23	be	be	AUX
fumecheng-13730	95	24	recommended	recommend	VERB
fumecheng-13730	95	25	.	.	PUNCT
fumecheng-13730	96	1	the	the	DET
fumecheng-13730	96	2	following	follow	VERB
fumecheng-13730	96	3	nonlinear	nonlinear	ADJ
fumecheng-13730	96	4	oscillator	oscillator	NOUN
fumecheng-13730	96	5	is	be	AUX
fumecheng-13730	96	6	now	now	ADV
fumecheng-13730	96	7	considered	consider	VERB
fumecheng-13730	96	8	.	.	PUNCT
fumecheng-13730	97	1	1	1	NUM
fumecheng-13730	97	2	0	0	NUM
fumecheng-13730	97	3	,	,	PUNCT
fumecheng-13730	97	4	2i	2i	NUM
fumecheng-13730	97	5	n	n	CCONJ
fumecheng-13730	97	6	n	n	NOUN
fumecheng-13730	98	1	i	i	PRON
fumecheng-13730	98	2	i	i	PRON
fumecheng-13730	99	1	i	i	VERB
fumecheng-13730	99	2	u	u	VERB
fumecheng-13730	99	3	b	b	PROPN
fumecheng-13730	99	4	u	u	NOUN
fumecheng-13730	99	5	n	n	PROPN
fumecheng-13730	99	6	=	=	SYM
fumecheng-13730	99	7			PROPN
fumecheng-13730	99	8	+	+	PROPN
fumecheng-13730	99	9	=	=	SYM
fumecheng-13730	99	10			PROPN
fumecheng-13730	99	11	(	(	PUNCT
fumecheng-13730	99	12	14	14	NUM
fumecheng-13730	99	13	)	)	PUNCT
fumecheng-13730	99	14	where	where	SCONJ
fumecheng-13730	99	15	bi	bi	NOUN
fumecheng-13730	99	16	(	(	PUNCT
fumecheng-13730	99	17	i=1	i=1	PROPN
fumecheng-13730	99	18	~	~	SYM
fumecheng-13730	99	19	n	n	CCONJ
fumecheng-13730	99	20	)	)	PUNCT
fumecheng-13730	99	21	are	be	AUX
fumecheng-13730	99	22	constants	constant	NOUN
fumecheng-13730	99	23	.	.	PUNCT
fumecheng-13730	100	1	for	for	ADP
fumecheng-13730	100	2	periodic	periodic	ADJ
fumecheng-13730	100	3	solutions	solution	NOUN
fumecheng-13730	100	4	,	,	PUNCT
fumecheng-13730	100	5	it	it	PRON
fumecheng-13730	100	6	requires	require	VERB
fumecheng-13730	100	7	(	(	PUNCT
fumecheng-13730	100	8	1	1	X
fumecheng-13730	100	9	)	)	PUNCT
fumecheng-13730	100	10	1	1	NUM
fumecheng-13730	100	11	0i	0i	NOUN
fumecheng-13730	100	12	n	n	CCONJ
fumecheng-13730	101	1	n	n	NOUN
fumecheng-13730	102	1	i	i	PRON
fumecheng-13730	102	2	i	i	NOUN
fumecheng-13730	102	3	b	b	VERB
fumecheng-13730	102	4	u	u	NOUN
fumecheng-13730	102	5	−	−	PROPN
fumecheng-13730	102	6	=	=	SYM
fumecheng-13730	102	7			PROPN
fumecheng-13730	102	8	(	(	PUNCT
fumecheng-13730	102	9	15	15	NUM
fumecheng-13730	102	10	)	)	PUNCT
fumecheng-13730	102	11	the	the	DET
fumecheng-13730	102	12	previous	previous	ADJ
fumecheng-13730	102	13	approaches	approach	NOUN
fumecheng-13730	102	14	to	to	ADP
fumecheng-13730	102	15	this	this	DET
fumecheng-13730	102	16	type	type	NOUN
fumecheng-13730	102	17	of	of	ADP
fumecheng-13730	102	18	nonlinear	nonlinear	ADJ
fumecheng-13730	102	19	oscillators	oscillator	NOUN
fumecheng-13730	102	20	are	be	AUX
fumecheng-13730	102	21	some	some	DET
fumecheng-13730	102	22	famous	famous	ADJ
fumecheng-13730	102	23	analytical	analytical	ADJ
fumecheng-13730	102	24	methods	method	NOUN
fumecheng-13730	102	25	,	,	PUNCT
fumecheng-13730	102	26	e.g.	e.g.	ADV
fumecheng-13730	102	27	,	,	PUNCT
fumecheng-13730	102	28	the	the	DET
fumecheng-13730	102	29	variational	variational	ADJ
fumecheng-13730	102	30	iteration	iteration	NOUN
fumecheng-13730	102	31	method	method	NOUN
fumecheng-13730	102	32	[	[	X
fumecheng-13730	102	33	26	26	NUM
fumecheng-13730	102	34	]	]	PUNCT
fumecheng-13730	102	35	and	and	CCONJ
fumecheng-13730	102	36	the	the	DET
fumecheng-13730	102	37	homotopy	homotopy	NOUN
fumecheng-13730	102	38	perturbation	perturbation	NOUN
fumecheng-13730	102	39	method	method	NOUN
fumecheng-13730	102	40	[	[	X
fumecheng-13730	102	41	27	27	NUM
fumecheng-13730	102	42	,	,	PUNCT
fumecheng-13730	102	43	28	28	NUM
fumecheng-13730	102	44	]	]	PUNCT
fumecheng-13730	102	45	,	,	PUNCT
fumecheng-13730	102	46	all	all	DET
fumecheng-13730	102	47	these	these	DET
fumecheng-13730	102	48	methods	method	NOUN
fumecheng-13730	102	49	require	require	VERB
fumecheng-13730	102	50	sophisticated	sophisticated	ADJ
fumecheng-13730	102	51	technology	technology	NOUN
fumecheng-13730	102	52	with	with	ADP
fumecheng-13730	102	53	complex	complex	ADJ
fumecheng-13730	102	54	calculation	calculation	NOUN
fumecheng-13730	102	55	,	,	PUNCT
fumecheng-13730	102	56	however	however	ADV
fumecheng-13730	102	57	,	,	PUNCT
fumecheng-13730	102	58	in	in	ADP
fumecheng-13730	102	59	the	the	DET
fumecheng-13730	102	60	practical	practical	ADJ
fumecheng-13730	102	61	applications	application	NOUN
fumecheng-13730	102	62	,	,	PUNCT
fumecheng-13730	102	63	the	the	DET
fumecheng-13730	102	64	frequency	frequency	NOUN
fumecheng-13730	102	65	-	-	PUNCT
fumecheng-13730	102	66	amplitude	amplitude	NOUN
fumecheng-13730	102	67	relationship	relationship	NOUN
fumecheng-13730	102	68	is	be	AUX
fumecheng-13730	102	69	the	the	DET
fumecheng-13730	102	70	most	most	ADV
fumecheng-13730	102	71	important	important	ADJ
fumecheng-13730	102	72	factor	factor	NOUN
fumecheng-13730	102	73	.	.	PUNCT
fumecheng-13730	103	1	a	a	DET
fumecheng-13730	103	2	simple	simple	ADJ
fumecheng-13730	103	3	yet	yet	CCONJ
fumecheng-13730	103	4	reliable	reliable	ADJ
fumecheng-13730	103	5	approach	approach	NOUN
fumecheng-13730	103	6	is	be	AUX
fumecheng-13730	103	7	always	always	ADV
fumecheng-13730	103	8	highly	highly	ADV
fumecheng-13730	103	9	welcome	welcome	ADJ
fumecheng-13730	103	10	.	.	PUNCT
fumecheng-13730	104	1	now	now	ADV
fumecheng-13730	104	2	,	,	PUNCT
fumecheng-13730	104	3	this	this	DET
fumecheng-13730	104	4	paper	paper	NOUN
fumecheng-13730	104	5	presents	present	VERB
fumecheng-13730	104	6	the	the	DET
fumecheng-13730	104	7	following	follow	VERB
fumecheng-13730	104	8	frequency	frequency	NOUN
fumecheng-13730	104	9	formulation	formulation	NOUN
fumecheng-13730	104	10	:	:	PUNCT
fumecheng-13730	104	11	(	(	PUNCT
fumecheng-13730	104	12	1)2	1)2	NUM
fumecheng-13730	104	13	1	1	NUM
fumecheng-13730	104	14	6	6	NUM
fumecheng-13730	104	15	5	5	NUM
fumecheng-13730	104	16	i	i	PRON
fumecheng-13730	104	17	n	n	VERB
fumecheng-13730	105	1	n	n	NOUN
fumecheng-13730	106	1	i	i	PRON
fumecheng-13730	106	2	i	i	PRON
fumecheng-13730	106	3	i	i	PRON
fumecheng-13730	106	4	b	b	PROPN
fumecheng-13730	106	5	a	a	DET
fumecheng-13730	106	6	n	n	NOUN
fumecheng-13730	106	7	−	−	NOUN
fumecheng-13730	106	8	=	=	SYM
fumecheng-13730	107	1	=	=	PUNCT
fumecheng-13730	107	2	+	+	NUM
fumecheng-13730	107	3			PROPN
fumecheng-13730	107	4	(	(	PUNCT
fumecheng-13730	107	5	16	16	NUM
fumecheng-13730	107	6	)	)	PUNCT
fumecheng-13730	107	7	it	it	PRON
fumecheng-13730	107	8	can	can	AUX
fumecheng-13730	107	9	be	be	AUX
fumecheng-13730	107	10	also	also	ADV
fumecheng-13730	107	11	written	write	VERB
fumecheng-13730	107	12	in	in	ADP
fumecheng-13730	107	13	the	the	DET
fumecheng-13730	107	14	form	form	NOUN
fumecheng-13730	107	15	(	(	PUNCT
fumecheng-13730	107	16	1)2	1)2	NUM
fumecheng-13730	107	17	1	1	NUM
fumecheng-13730	107	18	(	(	PUNCT
fumecheng-13730	107	19	)	)	PUNCT
fumecheng-13730	107	20	i	i	PRON
fumecheng-13730	107	21	i	i	VERB
fumecheng-13730	107	22	n	n	VERB
fumecheng-13730	107	23	n	n	CCONJ
fumecheng-13730	107	24	i	i	PRON
fumecheng-13730	108	1	n	n	VERB
fumecheng-13730	109	1	i	i	NOUN
fumecheng-13730	109	2	b	b	NOUN
fumecheng-13730	109	3	u	u	NOUN
fumecheng-13730	109	4	−	−	PROPN
fumecheng-13730	110	1	=	=	PUNCT
fumecheng-13730	110	2	=	=	NUM
fumecheng-13730	110	3			PROPN
fumecheng-13730	110	4	(	(	PUNCT
fumecheng-13730	110	5	17	17	NUM
fumecheng-13730	110	6	)	)	PUNCT
fumecheng-13730	110	7	where	where	SCONJ
fumecheng-13730	110	8	the	the	DET
fumecheng-13730	110	9	location	location	NOUN
fumecheng-13730	110	10	point	point	NOUN
fumecheng-13730	110	11	for	for	ADP
fumecheng-13730	110	12	each	each	DET
fumecheng-13730	110	13	nonlinear	nonlinear	ADJ
fumecheng-13730	110	14	term	term	NOUN
fumecheng-13730	110	15	is	be	AUX
fumecheng-13730	110	16	given	give	VERB
fumecheng-13730	110	17	as	as	ADP
fumecheng-13730	110	18	(	(	PUNCT
fumecheng-13730	110	19	1)1/6	1)1/6	PROPN
fumecheng-13730	110	20	(	(	PUNCT
fumecheng-13730	110	21	)	)	PUNCT
fumecheng-13730	110	22	5	5	NUM
fumecheng-13730	111	1	i	i	PRON
fumecheng-13730	111	2	i	i	PRON
fumecheng-13730	111	3	n	n	VERB
fumecheng-13730	111	4	n	n	NOUN
fumecheng-13730	111	5	i	i	PRON
fumecheng-13730	111	6	u	u	VERB
fumecheng-13730	111	7	a	a	PRON
fumecheng-13730	111	8	n	n	NOUN
fumecheng-13730	111	9	−	−	PROPN
fumecheng-13730	112	1	=	=	SYM
fumecheng-13730	113	1	+	+	CCONJ
fumecheng-13730	113	2	(	(	PUNCT
fumecheng-13730	113	3	18	18	NUM
fumecheng-13730	113	4	)	)	PUNCT
fumecheng-13730	113	5	the	the	DET
fumecheng-13730	113	6	new	new	ADJ
fumecheng-13730	113	7	frequency	frequency	NOUN
fumecheng-13730	113	8	formulation	formulation	NOUN
fumecheng-13730	113	9	is	be	AUX
fumecheng-13730	113	10	extremely	extremely	ADV
fumecheng-13730	113	11	simple	simple	ADJ
fumecheng-13730	113	12	.	.	PUNCT
fumecheng-13730	114	1	a	a	DET
fumecheng-13730	114	2	more	more	ADV
fumecheng-13730	114	3	straightforward	straightforward	ADJ
fumecheng-13730	114	4	approach	approach	NOUN
fumecheng-13730	114	5	is	be	AUX
fumecheng-13730	114	6	always	always	ADV
fumecheng-13730	114	7	advantageous	advantageous	ADJ
fumecheng-13730	114	8	for	for	ADP
fumecheng-13730	114	9	engineers	engineer	NOUN
fumecheng-13730	114	10	.	.	PUNCT
fumecheng-13730	115	1	the	the	DET
fumecheng-13730	115	2	frequency	frequency	NOUN
fumecheng-13730	115	3	formulation	formulation	NOUN
fumecheng-13730	115	4	demonstrates	demonstrate	VERB
fumecheng-13730	115	5	considerable	considerable	ADJ
fumecheng-13730	115	6	promise	promise	NOUN
fumecheng-13730	115	7	for	for	ADP
fumecheng-13730	115	8	a	a	DET
fumecheng-13730	115	9	diverse	diverse	ADJ
fumecheng-13730	115	10	array	array	NOUN
fumecheng-13730	115	11	of	of	ADP
fumecheng-13730	115	12	prospective	prospective	ADJ
fumecheng-13730	115	13	applications	application	NOUN
fumecheng-13730	115	14	.	.	PUNCT
fumecheng-13730	116	1	this	this	DET
fumecheng-13730	116	2	novel	novel	ADJ
fumecheng-13730	116	3	approach	approach	NOUN
fumecheng-13730	116	4	has	have	VERB
fumecheng-13730	116	5	the	the	DET
fumecheng-13730	116	6	potential	potential	NOUN
fumecheng-13730	116	7	to	to	PART
fumecheng-13730	116	8	transform	transform	VERB
fumecheng-13730	116	9	analytical	analytical	ADJ
fumecheng-13730	116	10	techniques	technique	NOUN
fumecheng-13730	116	11	within	within	ADP
fumecheng-13730	116	12	the	the	DET
fumecheng-13730	116	13	domain	domain	NOUN
fumecheng-13730	116	14	of	of	ADP
fumecheng-13730	116	15	vibration	vibration	NOUN
fumecheng-13730	116	16	theory	theory	NOUN
fumecheng-13730	116	17	.	.	PUNCT
fumecheng-13730	117	1	the	the	DET
fumecheng-13730	117	2	method	method	NOUN
fumecheng-13730	117	3	provides	provide	VERB
fumecheng-13730	117	4	a	a	DET
fumecheng-13730	117	5	rapid	rapid	ADJ
fumecheng-13730	117	6	yet	yet	CCONJ
fumecheng-13730	117	7	reliable	reliable	ADJ
fumecheng-13730	117	8	comprehension	comprehension	NOUN
fumecheng-13730	117	9	of	of	ADP
fumecheng-13730	117	10	intricate	intricate	ADJ
fumecheng-13730	117	11	vibration	vibration	NOUN
fumecheng-13730	117	12	systems	system	NOUN
fumecheng-13730	117	13	through	through	ADP
fumecheng-13730	117	14	a	a	DET
fumecheng-13730	117	15	straightforward	straightforward	ADJ
fumecheng-13730	117	16	step	step	NOUN
fumecheng-13730	117	17	that	that	PRON
fumecheng-13730	117	18	is	be	AUX
fumecheng-13730	117	19	more	more	ADV
fumecheng-13730	117	20	efficient	efficient	ADJ
fumecheng-13730	117	21	than	than	ADP
fumecheng-13730	117	22	traditional	traditional	ADJ
fumecheng-13730	117	23	analytical	analytical	ADJ
fumecheng-13730	117	24	methods	method	NOUN
fumecheng-13730	117	25	,	,	PUNCT
fumecheng-13730	117	26	which	which	PRON
fumecheng-13730	117	27	entail	entail	VERB
fumecheng-13730	117	28	complex	complex	ADJ
fumecheng-13730	117	29	and	and	CCONJ
fumecheng-13730	117	30	detailed	detailed	ADJ
fumecheng-13730	117	31	calculations	calculation	NOUN
fumecheng-13730	117	32	.	.	PUNCT
fumecheng-13730	118	1	it	it	PRON
fumecheng-13730	118	2	can	can	AUX
fumecheng-13730	118	3	be	be	AUX
fumecheng-13730	118	4	utilized	utilize	VERB
fumecheng-13730	118	5	for	for	ADP
fumecheng-13730	118	6	the	the	DET
fumecheng-13730	118	7	optimization	optimization	NOUN
fumecheng-13730	118	8	of	of	ADP
fumecheng-13730	118	9	complex	complex	ADJ
fumecheng-13730	118	10	vibration	vibration	NOUN
fumecheng-13730	118	11	systems	system	NOUN
fumecheng-13730	118	12	without	without	ADP
fumecheng-13730	118	13	the	the	DET
fumecheng-13730	118	14	necessity	necessity	NOUN
fumecheng-13730	118	15	for	for	ADP
fumecheng-13730	118	16	onerous	onerous	ADJ
fumecheng-13730	118	17	computations	computation	NOUN
fumecheng-13730	118	18	.	.	PUNCT
fumecheng-13730	119	1	the	the	DET
fumecheng-13730	119	2	remarkable	remarkable	ADJ
fumecheng-13730	119	3	versatility	versatility	NOUN
fumecheng-13730	119	4	of	of	ADP
fumecheng-13730	119	5	this	this	DET
fumecheng-13730	119	6	new	new	ADJ
fumecheng-13730	119	7	formulation	formulation	NOUN
fumecheng-13730	119	8	represents	represent	VERB
fumecheng-13730	119	9	a	a	DET
fumecheng-13730	119	10	significant	significant	ADJ
fumecheng-13730	119	11	advancement	advancement	NOUN
fumecheng-13730	119	12	in	in	ADP
fumecheng-13730	119	13	the	the	DET
fumecheng-13730	119	14	field	field	NOUN
fumecheng-13730	119	15	of	of	ADP
fumecheng-13730	119	16	nonlinear	nonlinear	ADJ
fumecheng-13730	119	17	vibration	vibration	NOUN
fumecheng-13730	119	18	theory	theory	NOUN
fumecheng-13730	119	19	.	.	PUNCT
fumecheng-13730	120	1	it	it	PRON
fumecheng-13730	120	2	is	be	AUX
fumecheng-13730	120	3	adaptable	adaptable	ADJ
fumecheng-13730	120	4	to	to	ADP
fumecheng-13730	120	5	a	a	DET
fumecheng-13730	120	6	variety	variety	NOUN
fumecheng-13730	120	7	of	of	ADP
fumecheng-13730	120	8	situations	situation	NOUN
fumecheng-13730	120	9	and	and	CCONJ
fumecheng-13730	120	10	requirements	requirement	NOUN
fumecheng-13730	120	11	,	,	PUNCT
fumecheng-13730	120	12	thereby	thereby	ADV
fumecheng-13730	120	13	facilitating	facilitate	VERB
fumecheng-13730	120	14	the	the	DET
fumecheng-13730	120	15	realization	realization	NOUN
fumecheng-13730	120	16	of	of	ADP
fumecheng-13730	120	17	novel	novel	ADJ
fumecheng-13730	120	18	possibilities	possibility	NOUN
fumecheng-13730	120	19	and	and	CCONJ
fumecheng-13730	120	20	opportunities	opportunity	NOUN
fumecheng-13730	120	21	.	.	PUNCT
fumecheng-13730	121	1	as	as	SCONJ
fumecheng-13730	121	2	research	research	NOUN
fumecheng-13730	121	3	and	and	CCONJ
fumecheng-13730	121	4	development	development	NOUN
fumecheng-13730	121	5	continue	continue	VERB
fumecheng-13730	121	6	,	,	PUNCT
fumecheng-13730	121	7	the	the	DET
fumecheng-13730	121	8	potential	potential	ADJ
fumecheng-13730	121	9	applications	application	NOUN
fumecheng-13730	121	10	of	of	ADP
fumecheng-13730	121	11	this	this	DET
fumecheng-13730	121	12	approach	approach	NOUN
fumecheng-13730	121	13	are	be	AUX
fumecheng-13730	121	14	likely	likely	ADJ
fumecheng-13730	121	15	to	to	PART
fumecheng-13730	121	16	expand	expand	VERB
fumecheng-13730	121	17	,	,	PUNCT
fumecheng-13730	121	18	with	with	ADP
fumecheng-13730	121	19	the	the	DET
fumecheng-13730	121	20	prospect	prospect	NOUN
fumecheng-13730	121	21	of	of	ADP
fumecheng-13730	121	22	substantial	substantial	ADJ
fumecheng-13730	121	23	benefits	benefit	NOUN
fumecheng-13730	121	24	for	for	ADP
fumecheng-13730	121	25	the	the	DET
fumecheng-13730	121	26	field	field	NOUN
fumecheng-13730	121	27	of	of	ADP
fumecheng-13730	121	28	nonlinear	nonlinear	ADJ
fumecheng-13730	121	29	science	science	NOUN
fumecheng-13730	121	30	.	.	PUNCT
fumecheng-13730	122	1	the	the	DET
fumecheng-13730	122	2	following	follow	VERB
fumecheng-13730	122	3	examples	example	NOUN
fumecheng-13730	122	4	demonstrate	demonstrate	VERB
fumecheng-13730	122	5	the	the	DET
fumecheng-13730	122	6	efficacy	efficacy	NOUN
fumecheng-13730	122	7	and	and	CCONJ
fumecheng-13730	122	8	simplicity	simplicity	NOUN
fumecheng-13730	122	9	of	of	ADP
fumecheng-13730	122	10	this	this	DET
fumecheng-13730	122	11	approach	approach	NOUN
fumecheng-13730	122	12	.	.	PUNCT
fumecheng-13730	123	1	202	202	NUM
fumecheng-13730	123	2	c.h	c.h	NOUN
fumecheng-13730	123	3	.	.	PUNCT
fumecheng-13730	124	1	he	he	PRON
fumecheng-13730	124	2	,	,	PUNCT
fumecheng-13730	124	3	j.h	j.h	PROPN
fumecheng-13730	124	4	.	.	PUNCT
fumecheng-13730	125	1	he	he	PRON
fumecheng-13730	125	2	,	,	PUNCT
fumecheng-13730	125	3	j.	j.	PROPN
fumecheng-13730	125	4	ma	ma	PROPN
fumecheng-13730	125	5	,	,	PUNCT
fumecheng-13730	125	6	a.a	a.a	PROPN
fumecheng-13730	125	7	.	.	PROPN
fumecheng-13730	125	8	alsolam	alsolam	PROPN
fumecheng-13730	125	9	,	,	PUNCT
fumecheng-13730	125	10	x.j	x.j	PROPN
fumecheng-13730	125	11	.	.	PROPN
fumecheng-13730	125	12	yang	yang	PROPN
fumecheng-13730	125	13	4	4	NUM
fumecheng-13730	125	14	.	.	PUNCT
fumecheng-13730	125	15	examples	example	NOUN
fumecheng-13730	125	16	4.1	4.1	NUM
fumecheng-13730	125	17	.	.	PUNCT
fumecheng-13730	125	18	example	example	NOUN
fumecheng-13730	126	1	1	1	NUM
fumecheng-13730	126	2	.	.	PUNCT
fumecheng-13730	126	3	nonlinear	nonlinear	ADJ
fumecheng-13730	126	4	oscillator	oscillator	NOUN
fumecheng-13730	126	5	with	with	ADP
fumecheng-13730	126	6	fractional	fractional	ADJ
fumecheng-13730	126	7	potential	potential	ADJ
fumecheng-13730	126	8	nonlinear	nonlinear	ADJ
fumecheng-13730	126	9	oscillators	oscillator	NOUN
fumecheng-13730	126	10	with	with	ADP
fumecheng-13730	126	11	fractional	fractional	ADJ
fumecheng-13730	126	12	potential	potential	NOUN
fumecheng-13730	126	13	are	be	AUX
fumecheng-13730	126	14	also	also	ADV
fumecheng-13730	126	15	called	call	VERB
fumecheng-13730	126	16	as	as	ADP
fumecheng-13730	126	17	quasi	quasi	ADJ
fumecheng-13730	126	18	-	-	ADJ
fumecheng-13730	126	19	linear	linear	ADJ
fumecheng-13730	126	20	oscillators	oscillator	NOUN
fumecheng-13730	126	21	,	,	PUNCT
fumecheng-13730	126	22	the	the	DET
fumecheng-13730	126	23	nonlinear	nonlinear	ADJ
fumecheng-13730	126	24	term	term	NOUN
fumecheng-13730	126	25	is	be	AUX
fumecheng-13730	126	26	always	always	ADV
fumecheng-13730	126	27	in	in	ADP
fumecheng-13730	126	28	the	the	DET
fumecheng-13730	126	29	form	form	NOUN
fumecheng-13730	126	30	,	,	PUNCT
fumecheng-13730	126	31	u1/(2n+1	u1/(2n+1	NOUN
fumecheng-13730	126	32	)	)	PUNCT
fumecheng-13730	126	33	,	,	PUNCT
fumecheng-13730	126	34	where	where	SCONJ
fumecheng-13730	126	35	n	n	PRON
fumecheng-13730	126	36	is	be	AUX
fumecheng-13730	126	37	a	a	DET
fumecheng-13730	126	38	natural	natural	ADJ
fumecheng-13730	126	39	number	number	NOUN
fumecheng-13730	126	40	.	.	PUNCT
fumecheng-13730	127	1	in	in	ADP
fumecheng-13730	127	2	this	this	DET
fumecheng-13730	127	3	example	example	NOUN
fumecheng-13730	127	4	,	,	PUNCT
fumecheng-13730	127	5	we	we	PRON
fumecheng-13730	127	6	consider	consider	VERB
fumecheng-13730	127	7	the	the	DET
fumecheng-13730	127	8	following	follow	VERB
fumecheng-13730	127	9	oscillator	oscillator	NOUN
fumecheng-13730	127	10	.	.	PUNCT
fumecheng-13730	128	1	1/3	1/3	NUM
fumecheng-13730	128	2	0u	0u	ADJ
fumecheng-13730	128	3	u	u	PROPN
fumecheng-13730	128	4	+	+	CCONJ
fumecheng-13730	129	1	=	=	X
fumecheng-13730	129	2			PROPN
fumecheng-13730	129	3	(	(	PUNCT
fumecheng-13730	129	4	19	19	NUM
fumecheng-13730	129	5	)	)	PUNCT
fumecheng-13730	129	6	where	where	SCONJ
fumecheng-13730	129	7	β	β	PROPN
fumecheng-13730	129	8	is	be	AUX
fumecheng-13730	129	9	a	a	DET
fumecheng-13730	129	10	positive	positive	ADJ
fumecheng-13730	129	11	constant	constant	NOUN
fumecheng-13730	129	12	.	.	PUNCT
fumecheng-13730	130	1	its	its	PRON
fumecheng-13730	130	2	variational	variational	ADJ
fumecheng-13730	130	3	formulation	formulation	NOUN
fumecheng-13730	130	4	is	be	AUX
fumecheng-13730	130	5	2	2	NUM
fumecheng-13730	130	6	4/31	4/31	NUM
fumecheng-13730	130	7	3	3	NUM
fumecheng-13730	130	8	(	(	PUNCT
fumecheng-13730	130	9	)	)	PUNCT
fumecheng-13730	130	10	2	2	NUM
fumecheng-13730	130	11	4	4	NUM
fumecheng-13730	130	12	j	j	NOUN
fumecheng-13730	130	13	u	u	NOUN
fumecheng-13730	130	14	u	u	X
fumecheng-13730	130	15	u	u	X
fumecheng-13730	130	16	dt	dt	X
fumecheng-13730	130	17			NOUN
fumecheng-13730	130	18			PROPN
fumecheng-13730	130	19	=	=	PROPN
fumecheng-13730	130	20	−	−	NOUN
fumecheng-13730	131	1			INTJ
fumecheng-13730	132	1			PROPN
fumecheng-13730	132	2			PROPN
fumecheng-13730	132	3			PUNCT
fumecheng-13730	133	1			NOUN
fumecheng-13730	133	2	(	(	PUNCT
fumecheng-13730	133	3	20	20	NUM
fumecheng-13730	133	4	)	)	PUNCT
fumecheng-13730	133	5	the	the	DET
fumecheng-13730	133	6	potential	potential	NOUN
fumecheng-13730	133	7	is	be	AUX
fumecheng-13730	133	8	represented	represent	VERB
fumecheng-13730	133	9	by	by	ADP
fumecheng-13730	133	10	a	a	DET
fumecheng-13730	133	11	fractional	fractional	ADJ
fumecheng-13730	133	12	exponent	exponent	NOUN
fumecheng-13730	133	13	,	,	PUNCT
fumecheng-13730	133	14	and	and	CCONJ
fumecheng-13730	133	15	thus	thus	ADV
fumecheng-13730	133	16	eq	eq	ADJ
fumecheng-13730	133	17	.	.	PUNCT
fumecheng-13730	134	1	(	(	PUNCT
fumecheng-13730	134	2	20	20	NUM
fumecheng-13730	134	3	)	)	PUNCT
fumecheng-13730	134	4	is	be	AUX
fumecheng-13730	134	5	designated	designate	VERB
fumecheng-13730	134	6	as	as	ADP
fumecheng-13730	134	7	a	a	DET
fumecheng-13730	134	8	nonlinear	nonlinear	ADJ
fumecheng-13730	134	9	oscillator	oscillator	NOUN
fumecheng-13730	134	10	with	with	ADP
fumecheng-13730	134	11	fractional	fractional	ADJ
fumecheng-13730	134	12	potential	potential	NOUN
fumecheng-13730	134	13	.	.	PUNCT
fumecheng-13730	135	1	this	this	DET
fumecheng-13730	135	2	nonlinear	nonlinear	ADJ
fumecheng-13730	135	3	oscillator	oscillator	NOUN
fumecheng-13730	135	4	has	have	AUX
fumecheng-13730	135	5	been	be	AUX
fumecheng-13730	135	6	the	the	DET
fumecheng-13730	135	7	subject	subject	NOUN
fumecheng-13730	135	8	of	of	ADP
fumecheng-13730	135	9	extensive	extensive	ADJ
fumecheng-13730	135	10	attention	attention	NOUN
fumecheng-13730	135	11	in	in	ADP
fumecheng-13730	135	12	the	the	DET
fumecheng-13730	135	13	open	open	ADJ
fumecheng-13730	135	14	literature	literature	NOUN
fumecheng-13730	135	15	,	,	PUNCT
fumecheng-13730	135	16	as	as	SCONJ
fumecheng-13730	135	17	evidenced	evidence	VERB
fumecheng-13730	135	18	by	by	ADP
fumecheng-13730	135	19	references	reference	NOUN
fumecheng-13730	135	20	[	[	X
fumecheng-13730	135	21	29	29	NUM
fumecheng-13730	135	22	,	,	PUNCT
fumecheng-13730	135	23	30	30	NUM
fumecheng-13730	135	24	]	]	PUNCT
fumecheng-13730	135	25	.	.	PUNCT
fumecheng-13730	136	1	the	the	DET
fumecheng-13730	136	2	nonlinear	nonlinear	ADJ
fumecheng-13730	136	3	nature	nature	NOUN
fumecheng-13730	136	4	of	of	ADP
fumecheng-13730	136	5	the	the	DET
fumecheng-13730	136	6	system	system	NOUN
fumecheng-13730	136	7	presents	present	VERB
fumecheng-13730	136	8	a	a	DET
fumecheng-13730	136	9	considerable	considerable	ADJ
fumecheng-13730	136	10	challenge	challenge	NOUN
fumecheng-13730	136	11	in	in	ADP
fumecheng-13730	136	12	attempting	attempt	VERB
fumecheng-13730	136	13	to	to	PART
fumecheng-13730	136	14	find	find	VERB
fumecheng-13730	136	15	a	a	DET
fumecheng-13730	136	16	general	general	ADJ
fumecheng-13730	136	17	closed	closed	ADJ
fumecheng-13730	136	18	-	-	PUNCT
fumecheng-13730	136	19	form	form	NOUN
fumecheng-13730	136	20	solution	solution	NOUN
fumecheng-13730	136	21	through	through	ADP
fumecheng-13730	136	22	analytical	analytical	ADJ
fumecheng-13730	136	23	means	mean	NOUN
fumecheng-13730	136	24	.	.	PUNCT
fumecheng-13730	137	1	the	the	DET
fumecheng-13730	137	2	nonlinear	nonlinear	ADJ
fumecheng-13730	137	3	characteristics	characteristic	NOUN
fumecheng-13730	137	4	introduce	introduce	VERB
fumecheng-13730	137	5	intricate	intricate	ADJ
fumecheng-13730	137	6	interactions	interaction	NOUN
fumecheng-13730	137	7	and	and	CCONJ
fumecheng-13730	137	8	behaviors	behavior	NOUN
fumecheng-13730	137	9	that	that	PRON
fumecheng-13730	137	10	render	render	VERB
fumecheng-13730	137	11	the	the	DET
fumecheng-13730	137	12	derivation	derivation	NOUN
fumecheng-13730	137	13	of	of	ADP
fumecheng-13730	137	14	an	an	DET
fumecheng-13730	137	15	approximate	approximate	ADJ
fumecheng-13730	137	16	solution	solution	NOUN
fumecheng-13730	137	17	an	an	DET
fumecheng-13730	137	18	exceptionally	exceptionally	ADV
fumecheng-13730	137	19	challenging	challenging	ADJ
fumecheng-13730	137	20	endeavor	endeavor	NOUN
fumecheng-13730	137	21	.	.	PUNCT
fumecheng-13730	138	1	following	follow	VERB
fumecheng-13730	138	2	meticulous	meticulous	ADJ
fumecheng-13730	138	3	and	and	CCONJ
fumecheng-13730	138	4	comprehensive	comprehensive	ADJ
fumecheng-13730	138	5	calculations	calculation	NOUN
fumecheng-13730	138	6	,	,	PUNCT
fumecheng-13730	138	7	a	a	DET
fumecheng-13730	138	8	notable	notable	ADJ
fumecheng-13730	138	9	accomplishment	accomplishment	NOUN
fumecheng-13730	138	10	is	be	AUX
fumecheng-13730	138	11	the	the	DET
fumecheng-13730	138	12	derivation	derivation	NOUN
fumecheng-13730	138	13	of	of	ADP
fumecheng-13730	138	14	the	the	DET
fumecheng-13730	138	15	frequency	frequency	NOUN
fumecheng-13730	138	16	-	-	PUNCT
fumecheng-13730	138	17	amplitude	amplitude	NOUN
fumecheng-13730	138	18	relationship	relationship	NOUN
fumecheng-13730	138	19	for	for	ADP
fumecheng-13730	138	20	eq	eq	PROPN
fumecheng-13730	138	21	.	.	PUNCT
fumecheng-13730	139	1	(	(	PUNCT
fumecheng-13730	139	2	20	20	NUM
fumecheng-13730	139	3	)	)	PUNCT
fumecheng-13730	139	4	,	,	PUNCT
fumecheng-13730	139	5	as	as	SCONJ
fumecheng-13730	139	6	documented	document	VERB
fumecheng-13730	139	7	in	in	ADP
fumecheng-13730	139	8	[	[	X
fumecheng-13730	139	9	29	29	NUM
fumecheng-13730	139	10	,	,	PUNCT
fumecheng-13730	139	11	30	30	NUM
fumecheng-13730	139	12	]	]	PUNCT
fumecheng-13730	139	13	,	,	PUNCT
fumecheng-13730	139	14	which	which	PRON
fumecheng-13730	139	15	is	be	AUX
fumecheng-13730	139	16	:	:	PUNCT
fumecheng-13730	139	17	1/3	1/3	NUM
fumecheng-13730	139	18	1.0768a−=	1.0768a−=	NUM
fumecheng-13730	139	19	.	.	PUNCT
fumecheng-13730	140	1	(	(	PUNCT
fumecheng-13730	140	2	21	21	NUM
fumecheng-13730	140	3	)	)	PUNCT
fumecheng-13730	140	4	this	this	DET
fumecheng-13730	140	5	relationship	relationship	NOUN
fumecheng-13730	140	6	,	,	PUNCT
fumecheng-13730	140	7	with	with	ADP
fumecheng-13730	140	8	a	a	DET
fumecheng-13730	140	9	relative	relative	ADJ
fumecheng-13730	140	10	error	error	NOUN
fumecheng-13730	140	11	of	of	ADP
fumecheng-13730	140	12	0.59	0.59	NUM
fumecheng-13730	140	13	%	%	NOUN
fumecheng-13730	140	14	,	,	PUNCT
fumecheng-13730	140	15	provides	provide	VERB
fumecheng-13730	140	16	a	a	DET
fumecheng-13730	140	17	crucial	crucial	ADJ
fumecheng-13730	140	18	link	link	NOUN
fumecheng-13730	140	19	between	between	ADP
fumecheng-13730	140	20	two	two	NUM
fumecheng-13730	140	21	fundamental	fundamental	ADJ
fumecheng-13730	140	22	properties	property	NOUN
fumecheng-13730	140	23	of	of	ADP
fumecheng-13730	140	24	the	the	DET
fumecheng-13730	140	25	oscillator	oscillator	NOUN
fumecheng-13730	140	26	and	and	CCONJ
fumecheng-13730	140	27	serves	serve	VERB
fumecheng-13730	140	28	as	as	ADP
fumecheng-13730	140	29	a	a	DET
fumecheng-13730	140	30	valuable	valuable	ADJ
fumecheng-13730	140	31	resource	resource	NOUN
fumecheng-13730	140	32	for	for	ADP
fumecheng-13730	140	33	further	further	ADJ
fumecheng-13730	140	34	studies	study	NOUN
fumecheng-13730	140	35	and	and	CCONJ
fumecheng-13730	140	36	applications	application	NOUN
fumecheng-13730	140	37	.	.	PUNCT
fumecheng-13730	141	1	this	this	PRON
fumecheng-13730	141	2	provides	provide	VERB
fumecheng-13730	141	3	a	a	DET
fumecheng-13730	141	4	basis	basis	NOUN
fumecheng-13730	141	5	for	for	ADP
fumecheng-13730	141	6	analyzing	analyze	VERB
fumecheng-13730	141	7	and	and	CCONJ
fumecheng-13730	141	8	predicting	predict	VERB
fumecheng-13730	141	9	the	the	DET
fumecheng-13730	141	10	behavior	behavior	NOUN
fumecheng-13730	141	11	of	of	ADP
fumecheng-13730	141	12	the	the	DET
fumecheng-13730	141	13	oscillator	oscillator	NOUN
fumecheng-13730	141	14	in	in	ADP
fumecheng-13730	141	15	different	different	ADJ
fumecheng-13730	141	16	scenarios	scenario	NOUN
fumecheng-13730	141	17	,	,	PUNCT
fumecheng-13730	141	18	thereby	thereby	ADV
fumecheng-13730	141	19	opening	open	VERB
fumecheng-13730	141	20	up	up	ADP
fumecheng-13730	141	21	new	new	ADJ
fumecheng-13730	141	22	avenues	avenue	NOUN
fumecheng-13730	141	23	for	for	ADP
fumecheng-13730	141	24	research	research	NOUN
fumecheng-13730	141	25	and	and	CCONJ
fumecheng-13730	141	26	practical	practical	ADJ
fumecheng-13730	141	27	applications	application	NOUN
fumecheng-13730	141	28	in	in	ADP
fumecheng-13730	141	29	a	a	DET
fumecheng-13730	141	30	variety	variety	NOUN
fumecheng-13730	141	31	of	of	ADP
fumecheng-13730	141	32	fields	field	NOUN
fumecheng-13730	141	33	.	.	PUNCT
fumecheng-13730	142	1	notwithstanding	notwithstanding	ADP
fumecheng-13730	142	2	the	the	DET
fumecheng-13730	142	3	significant	significant	ADJ
fumecheng-13730	142	4	advancements	advancement	NOUN
fumecheng-13730	142	5	achieved	achieve	VERB
fumecheng-13730	142	6	through	through	ADP
fumecheng-13730	142	7	meticulous	meticulous	ADJ
fumecheng-13730	142	8	and	and	CCONJ
fumecheng-13730	142	9	intricate	intricate	ADJ
fumecheng-13730	142	10	computations	computation	NOUN
fumecheng-13730	142	11	,	,	PUNCT
fumecheng-13730	142	12	engineers	engineer	NOUN
fumecheng-13730	142	13	have	have	AUX
fumecheng-13730	142	14	been	be	AUX
fumecheng-13730	142	15	keenly	keenly	ADV
fumecheng-13730	142	16	awaiting	await	VERB
fumecheng-13730	142	17	a	a	DET
fumecheng-13730	142	18	straightforward	straightforward	ADJ
fumecheng-13730	142	19	yet	yet	CCONJ
fumecheng-13730	142	20	efficacious	efficacious	ADJ
fumecheng-13730	142	21	methodology	methodology	NOUN
fumecheng-13730	142	22	to	to	PART
fumecheng-13730	142	23	swiftly	swiftly	ADV
fumecheng-13730	142	24	and	and	CCONJ
fumecheng-13730	142	25	dependably	dependably	ADV
fumecheng-13730	142	26	comprehend	comprehend	VERB
fumecheng-13730	142	27	the	the	DET
fumecheng-13730	142	28	vibration	vibration	NOUN
fumecheng-13730	142	29	characteristics	characteristic	NOUN
fumecheng-13730	142	30	.	.	PUNCT
fumecheng-13730	143	1	the	the	DET
fumecheng-13730	143	2	time	time	NOUN
fumecheng-13730	143	3	has	have	AUX
fumecheng-13730	143	4	now	now	ADV
fumecheng-13730	143	5	come	come	VERB
fumecheng-13730	143	6	to	to	PART
fumecheng-13730	143	7	seize	seize	VERB
fumecheng-13730	143	8	this	this	DET
fumecheng-13730	143	9	opportunity	opportunity	NOUN
fumecheng-13730	143	10	.	.	PUNCT
fumecheng-13730	144	1	by	by	ADP
fumecheng-13730	144	2	employing	employ	VERB
fumecheng-13730	144	3	the	the	DET
fumecheng-13730	144	4	frequency	frequency	NOUN
fumecheng-13730	144	5	formulation	formulation	NOUN
fumecheng-13730	144	6	of	of	ADP
fumecheng-13730	144	7	equation	equation	NOUN
fumecheng-13730	144	8	(	(	PUNCT
fumecheng-13730	144	9	17	17	NUM
fumecheng-13730	144	10	)	)	PUNCT
fumecheng-13730	144	11	,	,	PUNCT
fumecheng-13730	144	12	the	the	DET
fumecheng-13730	144	13	desired	desire	VERB
fumecheng-13730	144	14	results	result	NOUN
fumecheng-13730	144	15	can	can	AUX
fumecheng-13730	144	16	be	be	AUX
fumecheng-13730	144	17	obtained	obtain	VERB
fumecheng-13730	144	18	with	with	ADP
fumecheng-13730	144	19	immediate	immediate	ADJ
fumecheng-13730	144	20	effect	effect	NOUN
fumecheng-13730	144	21	.	.	PUNCT
fumecheng-13730	145	1	2	2	NUM
fumecheng-13730	145	2	2/3	2/3	NUM
fumecheng-13730	145	3	2/3	2/3	NUM
fumecheng-13730	145	4	1	1	NUM
fumecheng-13730	145	5	3	3	NUM
fumecheng-13730	145	6	6	6	NUM
fumecheng-13730	145	7	18	18	NUM
fumecheng-13730	145	8	5	5	NUM
fumecheng-13730	145	9	16	16	NUM
fumecheng-13730	145	10	a	a	DET
fumecheng-13730	145	11	a−	a−	PROPN
fumecheng-13730	145	12	−=	−=	NOUN
fumecheng-13730	145	13	=	=	PUNCT
fumecheng-13730	146	1	+	+	CCONJ
fumecheng-13730	146	2			PROPN
fumecheng-13730	146	3			PROPN
fumecheng-13730	146	4			PROPN
fumecheng-13730	146	5	(	(	PUNCT
fumecheng-13730	146	6	22	22	NUM
fumecheng-13730	146	7	)	)	PUNCT
fumecheng-13730	146	8	or	or	CCONJ
fumecheng-13730	146	9	1/2	1/2	NUM
fumecheng-13730	146	10	1/3	1/3	NUM
fumecheng-13730	146	11	1.060660	1.060660	NUM
fumecheng-13730	146	12	a−=	a−=	NOUN
fumecheng-13730	146	13			NOUN
fumecheng-13730	146	14	(	(	PUNCT
fumecheng-13730	146	15	23	23	NUM
fumecheng-13730	146	16	)	)	PUNCT
fumecheng-13730	146	17	it	it	PRON
fumecheng-13730	146	18	is	be	AUX
fumecheng-13730	146	19	noteworthy	noteworthy	ADJ
fumecheng-13730	146	20	that	that	SCONJ
fumecheng-13730	146	21	it	it	PRON
fumecheng-13730	146	22	exhibits	exhibit	VERB
fumecheng-13730	146	23	the	the	DET
fumecheng-13730	146	24	same	same	ADJ
fumecheng-13730	146	25	form	form	NOUN
fumecheng-13730	146	26	as	as	ADP
fumecheng-13730	146	27	that	that	PRON
fumecheng-13730	146	28	of	of	ADP
fumecheng-13730	146	29	eq	eq	PROPN
fumecheng-13730	146	30	.	.	PUNCT
fumecheng-13730	147	1	(	(	PUNCT
fumecheng-13730	147	2	22	22	NUM
fumecheng-13730	147	3	)	)	PUNCT
fumecheng-13730	147	4	.	.	PUNCT
fumecheng-13730	148	1	given	give	VERB
fumecheng-13730	148	2	its	its	PRON
fumecheng-13730	148	3	simplicity	simplicity	NOUN
fumecheng-13730	148	4	,	,	PUNCT
fumecheng-13730	148	5	the	the	DET
fumecheng-13730	148	6	frequency	frequency	NOUN
fumecheng-13730	148	7	formulation	formulation	NOUN
fumecheng-13730	148	8	represents	represent	VERB
fumecheng-13730	148	9	a	a	DET
fumecheng-13730	148	10	significant	significant	ADJ
fumecheng-13730	148	11	accomplishment	accomplishment	NOUN
fumecheng-13730	148	12	in	in	ADP
fumecheng-13730	148	13	the	the	DET
fumecheng-13730	148	14	field	field	NOUN
fumecheng-13730	148	15	.	.	PUNCT
fumecheng-13730	149	1	the	the	DET
fumecheng-13730	149	2	accuracy	accuracy	NOUN
fumecheng-13730	149	3	of	of	ADP
fumecheng-13730	149	4	this	this	DET
fumecheng-13730	149	5	method	method	NOUN
fumecheng-13730	149	6	is	be	AUX
fumecheng-13730	149	7	comparable	comparable	ADJ
fumecheng-13730	149	8	to	to	ADP
fumecheng-13730	149	9	that	that	PRON
fumecheng-13730	149	10	attained	attain	VERB
fumecheng-13730	149	11	by	by	ADP
fumecheng-13730	149	12	the	the	DET
fumecheng-13730	149	13	variational	variational	ADJ
fumecheng-13730	149	14	iteration	iteration	NOUN
fumecheng-13730	149	15	method	method	NOUN
fumecheng-13730	149	16	or	or	CCONJ
fumecheng-13730	149	17	the	the	DET
fumecheng-13730	149	18	homotopy	homotopy	NOUN
fumecheng-13730	149	19	perturbation	perturbation	NOUN
fumecheng-13730	149	20	method	method	NOUN
fumecheng-13730	149	21	.	.	PUNCT
fumecheng-13730	150	1	the	the	DET
fumecheng-13730	150	2	one	one	NUM
fumecheng-13730	150	3	-	-	PUNCT
fumecheng-13730	150	4	step	step	NOUN
fumecheng-13730	150	5	approach	approach	NOUN
fumecheng-13730	150	6	is	be	AUX
fumecheng-13730	150	7	a	a	DET
fumecheng-13730	150	8	highly	highly	ADV
fumecheng-13730	150	9	attractive	attractive	ADJ
fumecheng-13730	150	10	proposition	proposition	NOUN
fumecheng-13730	150	11	.	.	PUNCT
fumecheng-13730	151	1	the	the	DET
fumecheng-13730	151	2	simplicity	simplicity	NOUN
fumecheng-13730	151	3	and	and	CCONJ
fumecheng-13730	151	4	efficiency	efficiency	NOUN
fumecheng-13730	151	5	of	of	ADP
fumecheng-13730	151	6	this	this	DET
fumecheng-13730	151	7	approach	approach	NOUN
fumecheng-13730	151	8	render	render	VERB
fumecheng-13730	151	9	it	it	PRON
fumecheng-13730	151	10	an	an	DET
fumecheng-13730	151	11	attractive	attractive	ADJ
fumecheng-13730	151	12	option	option	NOUN
fumecheng-13730	151	13	,	,	PUNCT
fumecheng-13730	151	14	particularly	particularly	ADV
fumecheng-13730	151	15	in	in	ADP
fumecheng-13730	151	16	situations	situation	NOUN
fumecheng-13730	151	17	where	where	SCONJ
fumecheng-13730	151	18	rapid	rapid	ADJ
fumecheng-13730	151	19	insights	insight	NOUN
fumecheng-13730	151	20	and	and	CCONJ
fumecheng-13730	151	21	the	the	DET
fumecheng-13730	151	22	frequency	frequency	NOUN
fumecheng-13730	151	23	-	-	PUNCT
fumecheng-13730	151	24	amplitude	amplitude	NOUN
fumecheng-13730	151	25	relationship	relationship	NOUN
fumecheng-13730	151	26	are	be	AUX
fumecheng-13730	151	27	required	require	VERB
fumecheng-13730	151	28	without	without	ADP
fumecheng-13730	151	29	the	the	DET
fumecheng-13730	151	30	intricacy	intricacy	NOUN
fumecheng-13730	151	31	of	of	ADP
fumecheng-13730	151	32	more	more	ADV
fumecheng-13730	151	33	elaborate	elaborate	ADJ
fumecheng-13730	151	34	methods	method	NOUN
fumecheng-13730	151	35	.	.	PUNCT
fumecheng-13730	152	1	https://baike.baidu.com/item/%e5%b8%8c%e8%85%8a%e5%ad%97%e6%af%8d/4428067#3-2	https://baike.baidu.com/item/%e5%b8%8c%e8%85%8a%e5%ad%97%e6%af%8d/4428067#3-2	PROPN
fumecheng-13730	152	2	a	a	DET
fumecheng-13730	152	3	modified	modify	VERB
fumecheng-13730	152	4	frequency	frequency	NOUN
fumecheng-13730	152	5	formulation	formulation	NOUN
fumecheng-13730	152	6	for	for	ADP
fumecheng-13730	152	7	nonlinear	nonlinear	ADJ
fumecheng-13730	152	8	mechanical	mechanical	ADJ
fumecheng-13730	152	9	vibrations	vibration	NOUN
fumecheng-13730	152	10	203	203	NUM
fumecheng-13730	152	11	the	the	DET
fumecheng-13730	152	12	exact	exact	ADJ
fumecheng-13730	152	13	frequency	frequency	NOUN
fumecheng-13730	152	14	is	be	AUX
fumecheng-13730	152	15	[	[	X
fumecheng-13730	152	16	29	29	NUM
fumecheng-13730	152	17	,	,	PUNCT
fumecheng-13730	152	18	30	30	NUM
fumecheng-13730	152	19	]	]	SYM
fumecheng-13730	152	20	1/2	1/2	NUM
fumecheng-13730	152	21	1/31.070451exact	1/31.070451exact	PROPN
fumecheng-13730	152	22	a−=	a−=	PUNCT
fumecheng-13730	153	1			PROPN
fumecheng-13730	153	2	(	(	PUNCT
fumecheng-13730	153	3	24	24	NUM
fumecheng-13730	153	4	)	)	PUNCT
fumecheng-13730	153	5	the	the	DET
fumecheng-13730	153	6	relative	relative	ADJ
fumecheng-13730	153	7	error	error	NOUN
fumecheng-13730	153	8	is	be	AUX
fumecheng-13730	153	9	0.91	0.91	NUM
fumecheng-13730	153	10	%	%	NOUN
fumecheng-13730	153	11	,	,	PUNCT
fumecheng-13730	153	12	which	which	PRON
fumecheng-13730	153	13	is	be	AUX
fumecheng-13730	153	14	deemed	deem	VERB
fumecheng-13730	153	15	to	to	PART
fumecheng-13730	153	16	be	be	AUX
fumecheng-13730	153	17	within	within	ADP
fumecheng-13730	153	18	an	an	DET
fumecheng-13730	153	19	acceptable	acceptable	ADJ
fumecheng-13730	153	20	range	range	NOUN
fumecheng-13730	153	21	for	for	ADP
fumecheng-13730	153	22	engineering	engineering	NOUN
fumecheng-13730	153	23	applications	application	NOUN
fumecheng-13730	153	24	.	.	PUNCT
fumecheng-13730	154	1	4.2	4.2	NUM
fumecheng-13730	154	2	.	.	PUNCT
fumecheng-13730	154	3	example	example	NOUN
fumecheng-13730	155	1	2	2	NUM
fumecheng-13730	155	2	.	.	PUNCT
fumecheng-13730	155	3	discontinuous	discontinuous	ADJ
fumecheng-13730	155	4	oscillator	oscillator	NOUN
fumecheng-13730	155	5	with	with	ADP
fumecheng-13730	155	6	sign	sign	NOUN
fumecheng-13730	155	7	function	function	VERB
fumecheng-13730	155	8	the	the	DET
fumecheng-13730	155	9	study	study	NOUN
fumecheng-13730	155	10	of	of	ADP
fumecheng-13730	155	11	nonlinear	nonlinear	ADJ
fumecheng-13730	155	12	oscillators	oscillator	NOUN
fumecheng-13730	155	13	with	with	ADP
fumecheng-13730	155	14	discontinuous	discontinuous	ADJ
fumecheng-13730	155	15	terms	term	NOUN
fumecheng-13730	155	16	represents	represent	VERB
fumecheng-13730	155	17	a	a	DET
fumecheng-13730	155	18	fascinating	fascinating	ADJ
fumecheng-13730	155	19	and	and	CCONJ
fumecheng-13730	155	20	rich	rich	ADJ
fumecheng-13730	155	21	area	area	NOUN
fumecheng-13730	155	22	of	of	ADP
fumecheng-13730	155	23	inquiry	inquiry	NOUN
fumecheng-13730	155	24	within	within	ADP
fumecheng-13730	155	25	the	the	DET
fumecheng-13730	155	26	broader	broad	ADJ
fumecheng-13730	155	27	fields	field	NOUN
fumecheng-13730	155	28	of	of	ADP
fumecheng-13730	155	29	physics	physics	NOUN
fumecheng-13730	155	30	and	and	CCONJ
fumecheng-13730	155	31	mechanical	mechanical	ADJ
fumecheng-13730	155	32	engineering	engineering	NOUN
fumecheng-13730	155	33	.	.	PUNCT
fumecheng-13730	156	1	discontinuous	discontinuous	ADJ
fumecheng-13730	156	2	terms	term	NOUN
fumecheng-13730	156	3	may	may	AUX
fumecheng-13730	156	4	originate	originate	VERB
fumecheng-13730	156	5	from	from	ADP
fumecheng-13730	156	6	impacts	impact	NOUN
fumecheng-13730	156	7	,	,	PUNCT
fumecheng-13730	156	8	switches	switch	NOUN
fumecheng-13730	156	9	,	,	PUNCT
fumecheng-13730	156	10	or	or	CCONJ
fumecheng-13730	156	11	sudden	sudden	ADJ
fumecheng-13730	156	12	alterations	alteration	NOUN
fumecheng-13730	156	13	in	in	ADP
fumecheng-13730	156	14	system	system	NOUN
fumecheng-13730	156	15	parameters	parameter	NOUN
fumecheng-13730	156	16	.	.	PUNCT
fumecheng-13730	157	1	the	the	DET
fumecheng-13730	157	2	aforementioned	aforementione	VERB
fumecheng-13730	157	3	discontinuities	discontinuity	NOUN
fumecheng-13730	157	4	present	present	VERB
fumecheng-13730	157	5	considerable	considerable	ADJ
fumecheng-13730	157	6	difficulties	difficulty	NOUN
fumecheng-13730	157	7	in	in	ADP
fumecheng-13730	157	8	the	the	DET
fumecheng-13730	157	9	analysis	analysis	NOUN
fumecheng-13730	157	10	and	and	CCONJ
fumecheng-13730	157	11	comprehension	comprehension	NOUN
fumecheng-13730	157	12	of	of	ADP
fumecheng-13730	157	13	the	the	DET
fumecheng-13730	157	14	oscillator	oscillator	NOUN
fumecheng-13730	157	15	's	's	PART
fumecheng-13730	157	16	behavior	behavior	NOUN
fumecheng-13730	157	17	.	.	PUNCT
fumecheng-13730	158	1	for	for	ADP
fumecheng-13730	158	2	example	example	NOUN
fumecheng-13730	158	3	,	,	PUNCT
fumecheng-13730	158	4	a	a	DET
fumecheng-13730	158	5	nonlinear	nonlinear	ADJ
fumecheng-13730	158	6	term	term	NOUN
fumecheng-13730	158	7	with	with	ADP
fumecheng-13730	158	8	the	the	DET
fumecheng-13730	158	9	sign	sign	NOUN
fumecheng-13730	158	10	function	function	NOUN
fumecheng-13730	158	11	frequently	frequently	ADV
fumecheng-13730	158	12	plays	play	VERB
fumecheng-13730	158	13	a	a	DET
fumecheng-13730	158	14	pivotal	pivotal	ADJ
fumecheng-13730	158	15	role	role	NOUN
fumecheng-13730	158	16	in	in	ADP
fumecheng-13730	158	17	such	such	ADJ
fumecheng-13730	158	18	systems	system	NOUN
fumecheng-13730	158	19	,	,	PUNCT
fumecheng-13730	158	20	as	as	SCONJ
fumecheng-13730	158	21	it	it	PRON
fumecheng-13730	158	22	can	can	AUX
fumecheng-13730	158	23	represent	represent	VERB
fumecheng-13730	158	24	abrupt	abrupt	ADJ
fumecheng-13730	158	25	changes	change	NOUN
fumecheng-13730	158	26	in	in	ADP
fumecheng-13730	158	27	direction	direction	NOUN
fumecheng-13730	158	28	or	or	CCONJ
fumecheng-13730	158	29	state	state	NOUN
fumecheng-13730	158	30	.	.	PUNCT
fumecheng-13730	159	1	the	the	DET
fumecheng-13730	159	2	study	study	NOUN
fumecheng-13730	159	3	of	of	ADP
fumecheng-13730	159	4	nonlinear	nonlinear	ADJ
fumecheng-13730	159	5	oscillators	oscillator	NOUN
fumecheng-13730	159	6	with	with	ADP
fumecheng-13730	159	7	discontinuous	discontinuous	ADJ
fumecheng-13730	159	8	terms	term	NOUN
fumecheng-13730	159	9	represents	represent	VERB
fumecheng-13730	159	10	a	a	DET
fumecheng-13730	159	11	vibrant	vibrant	ADJ
fumecheng-13730	159	12	and	and	CCONJ
fumecheng-13730	159	13	multifaceted	multifaceted	ADJ
fumecheng-13730	159	14	research	research	NOUN
fumecheng-13730	159	15	domain	domain	NOUN
fumecheng-13730	159	16	,	,	PUNCT
fumecheng-13730	159	17	with	with	ADP
fumecheng-13730	159	18	implications	implication	NOUN
fumecheng-13730	159	19	that	that	PRON
fumecheng-13730	159	20	extend	extend	VERB
fumecheng-13730	159	21	far	far	ADV
fumecheng-13730	159	22	beyond	beyond	ADP
fumecheng-13730	159	23	the	the	DET
fumecheng-13730	159	24	immediate	immediate	ADJ
fumecheng-13730	159	25	field	field	NOUN
fumecheng-13730	159	26	of	of	ADP
fumecheng-13730	159	27	inquiry	inquiry	NOUN
fumecheng-13730	159	28	and	and	CCONJ
fumecheng-13730	159	29	have	have	VERB
fumecheng-13730	159	30	the	the	DET
fumecheng-13730	159	31	potential	potential	NOUN
fumecheng-13730	159	32	to	to	PART
fumecheng-13730	159	33	inform	inform	VERB
fumecheng-13730	159	34	a	a	DET
fumecheng-13730	159	35	vast	vast	ADJ
fumecheng-13730	159	36	array	array	NOUN
fumecheng-13730	159	37	of	of	ADP
fumecheng-13730	159	38	practical	practical	ADJ
fumecheng-13730	159	39	applications	application	NOUN
fumecheng-13730	159	40	.	.	PUNCT
fumecheng-13730	160	1	an	an	DET
fumecheng-13730	160	2	investigation	investigation	NOUN
fumecheng-13730	160	3	of	of	ADP
fumecheng-13730	160	4	the	the	DET
fumecheng-13730	160	5	frequency	frequency	NOUN
fumecheng-13730	160	6	-	-	PUNCT
fumecheng-13730	160	7	amplitude	amplitude	NOUN
fumecheng-13730	160	8	relationship	relationship	NOUN
fumecheng-13730	160	9	may	may	AUX
fumecheng-13730	160	10	facilitate	facilitate	VERB
fumecheng-13730	160	11	the	the	DET
fumecheng-13730	160	12	discovery	discovery	NOUN
fumecheng-13730	160	13	of	of	ADP
fumecheng-13730	160	14	new	new	ADJ
fumecheng-13730	160	15	possibilities	possibility	NOUN
fumecheng-13730	160	16	for	for	ADP
fumecheng-13730	160	17	engineering	engineering	NOUN
fumecheng-13730	160	18	and	and	CCONJ
fumecheng-13730	160	19	scientific	scientific	ADJ
fumecheng-13730	160	20	advancement	advancement	NOUN
fumecheng-13730	160	21	.	.	PUNCT
fumecheng-13730	161	1	researchers	researcher	NOUN
fumecheng-13730	161	2	are	be	AUX
fumecheng-13730	161	3	engaged	engage	VERB
fumecheng-13730	161	4	in	in	ADP
fumecheng-13730	161	5	ongoing	ongoing	ADJ
fumecheng-13730	161	6	efforts	effort	NOUN
fumecheng-13730	161	7	to	to	PART
fumecheng-13730	161	8	develop	develop	VERB
fumecheng-13730	161	9	new	new	ADJ
fumecheng-13730	161	10	methods	method	NOUN
fumecheng-13730	161	11	for	for	ADP
fumecheng-13730	161	12	the	the	DET
fumecheng-13730	161	13	analysis	analysis	NOUN
fumecheng-13730	161	14	and	and	CCONJ
fumecheng-13730	161	15	control	control	NOUN
fumecheng-13730	161	16	of	of	ADP
fumecheng-13730	161	17	these	these	DET
fumecheng-13730	161	18	oscillators	oscillator	NOUN
fumecheng-13730	161	19	.	.	PUNCT
fumecheng-13730	162	1	this	this	PRON
fumecheng-13730	162	2	includes	include	VERB
fumecheng-13730	162	3	the	the	DET
fumecheng-13730	162	4	creation	creation	NOUN
fumecheng-13730	162	5	of	of	ADP
fumecheng-13730	162	6	novel	novel	ADJ
fumecheng-13730	162	7	theoretical	theoretical	ADJ
fumecheng-13730	162	8	models	model	NOUN
fumecheng-13730	162	9	and	and	CCONJ
fumecheng-13730	162	10	experimental	experimental	ADJ
fumecheng-13730	162	11	techniques	technique	NOUN
fumecheng-13730	162	12	,	,	PUNCT
fumecheng-13730	162	13	with	with	ADP
fumecheng-13730	162	14	the	the	DET
fumecheng-13730	162	15	aim	aim	NOUN
fumecheng-13730	162	16	of	of	ADP
fumecheng-13730	162	17	gaining	gain	VERB
fumecheng-13730	162	18	deeper	deep	ADJ
fumecheng-13730	162	19	insights	insight	NOUN
fumecheng-13730	162	20	into	into	ADP
fumecheng-13730	162	21	their	their	PRON
fumecheng-13730	162	22	behavior	behavior	NOUN
fumecheng-13730	162	23	and	and	CCONJ
fumecheng-13730	162	24	the	the	DET
fumecheng-13730	162	25	design	design	NOUN
fumecheng-13730	162	26	of	of	ADP
fumecheng-13730	162	27	more	more	ADV
fumecheng-13730	162	28	efficient	efficient	ADJ
fumecheng-13730	162	29	and	and	CCONJ
fumecheng-13730	162	30	reliable	reliable	ADJ
fumecheng-13730	162	31	systems	system	NOUN
fumecheng-13730	162	32	.	.	PUNCT
fumecheng-13730	163	1	in	in	ADP
fumecheng-13730	163	2	this	this	DET
fumecheng-13730	163	3	example	example	NOUN
fumecheng-13730	163	4	,	,	PUNCT
fumecheng-13730	163	5	we	we	PRON
fumecheng-13730	163	6	consider	consider	VERB
fumecheng-13730	163	7	a	a	DET
fumecheng-13730	163	8	nonlinear	nonlinear	ADJ
fumecheng-13730	163	9	oscillator	oscillator	NOUN
fumecheng-13730	163	10	subjected	subject	VERB
fumecheng-13730	163	11	to	to	ADP
fumecheng-13730	163	12	a	a	DET
fumecheng-13730	163	13	constant	constant	ADJ
fumecheng-13730	163	14	force	force	NOUN
fumecheng-13730	163	15	,	,	PUNCT
fumecheng-13730	163	16	as	as	SCONJ
fumecheng-13730	163	17	illustrated	illustrate	VERB
fumecheng-13730	163	18	in	in	ADP
fumecheng-13730	163	19	fig	fig	NOUN
fumecheng-13730	163	20	.	.	PUNCT
fumecheng-13730	164	1	1	1	X
fumecheng-13730	164	2	.	.	X
fumecheng-13730	164	3	fig	fig	NOUN
fumecheng-13730	164	4	.	.	PUNCT
fumecheng-13730	165	1	1	1	NUM
fumecheng-13730	165	2	discontinuous	discontinuous	ADJ
fumecheng-13730	165	3	oscillator	oscillator	NOUN
fumecheng-13730	165	4	with	with	ADP
fumecheng-13730	165	5	discontinuous	discontinuous	ADJ
fumecheng-13730	165	6	restoring	restoring	NOUN
fumecheng-13730	165	7	force	force	NOUN
fumecheng-13730	165	8	the	the	DET
fumecheng-13730	165	9	restoring	restore	VERB
fumecheng-13730	165	10	force	force	NOUN
fumecheng-13730	165	11	follows	follow	VERB
fumecheng-13730	165	12	:	:	PUNCT
fumecheng-13730	165	13	when	when	SCONJ
fumecheng-13730	165	14	u>0	u>0	NOUN
fumecheng-13730	165	15	,	,	PUNCT
fumecheng-13730	165	16	f(u)=1	f(u)=1	NOUN
fumecheng-13730	165	17	;	;	PUNCT
fumecheng-13730	165	18	when	when	SCONJ
fumecheng-13730	165	19	u<0	u<0	NOUN
fumecheng-13730	165	20	,	,	PUNCT
fumecheng-13730	165	21	f(u)=−1	f(u)=−1	PROPN
fumecheng-13730	165	22	.	.	PUNCT
fumecheng-13730	166	1	the	the	DET
fumecheng-13730	166	2	governing	govern	VERB
fumecheng-13730	166	3	equation	equation	NOUN
fumecheng-13730	166	4	can	can	AUX
fumecheng-13730	166	5	be	be	AUX
fumecheng-13730	166	6	expressed	express	VERB
fumecheng-13730	166	7	as	as	ADP
fumecheng-13730	166	8	sgn	sgn	NOUN
fumecheng-13730	166	9	(	(	PUNCT
fumecheng-13730	166	10	)	)	PUNCT
fumecheng-13730	166	11	0u	0u	ADJ
fumecheng-13730	166	12	u	u	NOUN
fumecheng-13730	166	13	+	+	CCONJ
fumecheng-13730	167	1	=	=	X
fumecheng-13730	167	2			PROPN
fumecheng-13730	167	3	(	(	PUNCT
fumecheng-13730	167	4	25	25	NUM
fumecheng-13730	167	5	)	)	PUNCT
fumecheng-13730	167	6	where	where	SCONJ
fumecheng-13730	167	7	β=1	β=1	ADP
fumecheng-13730	167	8	/	/	SYM
fumecheng-13730	167	9	m	m	PROPN
fumecheng-13730	167	10	,	,	PUNCT
fumecheng-13730	167	11	m	m	VERB
fumecheng-13730	167	12	is	be	AUX
fumecheng-13730	167	13	the	the	DET
fumecheng-13730	167	14	mass	mass	NOUN
fumecheng-13730	167	15	of	of	ADP
fumecheng-13730	167	16	the	the	DET
fumecheng-13730	167	17	oscillator	oscillator	NOUN
fumecheng-13730	167	18	,	,	PUNCT
fumecheng-13730	167	19	and	and	CCONJ
fumecheng-13730	167	20	sgn(u	sgn(u	NOUN
fumecheng-13730	167	21	)	)	PUNCT
fumecheng-13730	167	22	is	be	AUX
fumecheng-13730	167	23	defined	define	VERB
fumecheng-13730	167	24	as	as	ADP
fumecheng-13730	167	25	0	0	NUM
fumecheng-13730	167	26	0	0	NUM
fumecheng-13730	167	27	,	,	PUNCT
fumecheng-13730	167	28	0	0	NUM
fumecheng-13730	167	29	1	1	NUM
fumecheng-13730	167	30	,	,	PUNCT
fumecheng-13730	167	31	0	0	NUM
fumecheng-13730	167	32	sgn	sgn	NOUN
fumecheng-13730	167	33	(	(	PUNCT
fumecheng-13730	167	34	)	)	PUNCT
fumecheng-13730	167	35	0	0	NUM
fumecheng-13730	167	36	,	,	PUNCT
fumecheng-13730	167	37	0	0	NUM
fumecheng-13730	167	38	0	0	NUM
fumecheng-13730	167	39	,	,	PUNCT
fumecheng-13730	167	40	0	0	NUM
fumecheng-13730	167	41	1	1	NUM
fumecheng-13730	167	42	,	,	PUNCT
fumecheng-13730	167	43	0	0	NUM
fumecheng-13730	167	44	,	,	PUNCT
fumecheng-13730	167	45	0	0	NUM
fumecheng-13730	167	46	u	u	NOUN
fumecheng-13730	167	47	u	u	PROPN
fumecheng-13730	167	48	u	u	X
fumecheng-13730	167	49	u	u	X
fumecheng-13730	167	50	u	u	X
fumecheng-13730	167	51	u	u	NOUN
fumecheng-13730	167	52	uu	uu	VERB
fumecheng-13730	167	53	u	u	NOUN
fumecheng-13730	167	54			VERB
fumecheng-13730	167	55			PROPN
fumecheng-13730	167	56			NOUN
fumecheng-13730	167	57			NUM
fumecheng-13730	167	58			NUM
fumecheng-13730	167	59	=	=	SYM
fumecheng-13730	167	60	=	=	SYM
fumecheng-13730	167	61	=	=	PUNCT
fumecheng-13730	168	1	=	=	NOUN
fumecheng-13730	168	2			NOUN
fumecheng-13730	168	3			NUM
fumecheng-13730	168	4			NUM
fumecheng-13730	168	5	−	−	NOUN
fumecheng-13730	168	6	−	−	PROPN
fumecheng-13730	168	7			PROPN
fumecheng-13730	168	8			PROPN
fumecheng-13730	168	9	.	.	PUNCT
fumecheng-13730	169	1	(	(	PUNCT
fumecheng-13730	169	2	26	26	NUM
fumecheng-13730	169	3	)	)	PUNCT
fumecheng-13730	169	4	204	204	NUM
fumecheng-13730	169	5	c.h	c.h	NOUN
fumecheng-13730	169	6	.	.	PUNCT
fumecheng-13730	170	1	he	he	PRON
fumecheng-13730	170	2	,	,	PUNCT
fumecheng-13730	170	3	j.h	j.h	PROPN
fumecheng-13730	170	4	.	.	PUNCT
fumecheng-13730	171	1	he	he	PRON
fumecheng-13730	171	2	,	,	PUNCT
fumecheng-13730	171	3	j.	j.	PROPN
fumecheng-13730	171	4	ma	ma	PROPN
fumecheng-13730	171	5	,	,	PUNCT
fumecheng-13730	171	6	a.a	a.a	PROPN
fumecheng-13730	171	7	.	.	PROPN
fumecheng-13730	171	8	alsolam	alsolam	PROPN
fumecheng-13730	171	9	,	,	PUNCT
fumecheng-13730	171	10	x.j	x.j	PROPN
fumecheng-13730	171	11	.	.	PROPN
fumecheng-13730	171	12	yang	yang	PROPN
fumecheng-13730	171	13	considerable	considerable	ADJ
fumecheng-13730	171	14	effort	effort	NOUN
fumecheng-13730	171	15	has	have	AUX
fumecheng-13730	171	16	been	be	AUX
fumecheng-13730	171	17	dedicated	dedicate	VERB
fumecheng-13730	171	18	to	to	ADP
fumecheng-13730	171	19	seeking	seek	VERB
fumecheng-13730	171	20	an	an	DET
fumecheng-13730	171	21	accurate	accurate	ADJ
fumecheng-13730	171	22	analytical	analytical	ADJ
fumecheng-13730	171	23	approximation	approximation	NOUN
fumecheng-13730	171	24	for	for	ADP
fumecheng-13730	171	25	equation	equation	NOUN
fumecheng-13730	171	26	(	(	PUNCT
fumecheng-13730	171	27	26	26	NUM
fumecheng-13730	171	28	)	)	PUNCT
fumecheng-13730	171	29	,	,	PUNCT
fumecheng-13730	171	30	as	as	SCONJ
fumecheng-13730	171	31	referenced	reference	VERB
fumecheng-13730	171	32	in	in	ADP
fumecheng-13730	171	33	[	[	PUNCT
fumecheng-13730	171	34	31	31	NUM
fumecheng-13730	171	35	-	-	SYM
fumecheng-13730	171	36	33	33	NUM
fumecheng-13730	171	37	]	]	PUNCT
fumecheng-13730	171	38	.	.	PUNCT
fumecheng-13730	172	1	the	the	DET
fumecheng-13730	172	2	primary	primary	ADJ
fumecheng-13730	172	3	mathematical	mathematical	ADJ
fumecheng-13730	172	4	tool	tool	NOUN
fumecheng-13730	172	5	utilized	utilize	VERB
fumecheng-13730	172	6	is	be	AUX
fumecheng-13730	172	7	the	the	DET
fumecheng-13730	172	8	homotopy	homotopy	NOUN
fumecheng-13730	172	9	perturbation	perturbation	NOUN
fumecheng-13730	172	10	method	method	NOUN
fumecheng-13730	172	11	.	.	PUNCT
fumecheng-13730	173	1	in	in	ADP
fumecheng-13730	173	2	the	the	DET
fumecheng-13730	173	3	application	application	NOUN
fumecheng-13730	173	4	of	of	ADP
fumecheng-13730	173	5	this	this	DET
fumecheng-13730	173	6	method	method	NOUN
fumecheng-13730	173	7	to	to	PART
fumecheng-13730	173	8	nonlinear	nonlinear	ADJ
fumecheng-13730	173	9	vibration	vibration	NOUN
fumecheng-13730	173	10	systems	system	NOUN
fumecheng-13730	173	11	,	,	PUNCT
fumecheng-13730	173	12	the	the	DET
fumecheng-13730	173	13	construction	construction	NOUN
fumecheng-13730	173	14	of	of	ADP
fumecheng-13730	173	15	the	the	DET
fumecheng-13730	173	16	homotopy	homotopy	NOUN
fumecheng-13730	173	17	equation	equation	NOUN
fumecheng-13730	173	18	,	,	PUNCT
fumecheng-13730	173	19	the	the	DET
fumecheng-13730	173	20	selection	selection	NOUN
fumecheng-13730	173	21	of	of	ADP
fumecheng-13730	173	22	the	the	DET
fumecheng-13730	173	23	initial	initial	ADJ
fumecheng-13730	173	24	guess	guess	NOUN
fumecheng-13730	173	25	,	,	PUNCT
fumecheng-13730	173	26	and	and	CCONJ
fumecheng-13730	173	27	the	the	DET
fumecheng-13730	173	28	elimination	elimination	NOUN
fumecheng-13730	173	29	of	of	ADP
fumecheng-13730	173	30	secular	secular	ADJ
fumecheng-13730	173	31	terms	term	NOUN
fumecheng-13730	173	32	during	during	ADP
fumecheng-13730	173	33	the	the	DET
fumecheng-13730	173	34	lengthy	lengthy	ADJ
fumecheng-13730	173	35	calculation	calculation	NOUN
fumecheng-13730	173	36	process	process	NOUN
fumecheng-13730	173	37	represent	represent	VERB
fumecheng-13730	173	38	the	the	DET
fumecheng-13730	173	39	primary	primary	ADJ
fumecheng-13730	173	40	focal	focal	ADJ
fumecheng-13730	173	41	points	point	NOUN
fumecheng-13730	174	1	[	[	X
fumecheng-13730	174	2	34	34	NUM
fumecheng-13730	174	3	]	]	PUNCT
fumecheng-13730	174	4	.	.	PUNCT
fumecheng-13730	175	1	these	these	DET
fumecheng-13730	175	2	aspects	aspect	NOUN
fumecheng-13730	175	3	are	be	AUX
fumecheng-13730	175	4	of	of	ADP
fumecheng-13730	175	5	paramount	paramount	ADJ
fumecheng-13730	175	6	importance	importance	NOUN
fumecheng-13730	175	7	in	in	ADP
fumecheng-13730	175	8	guaranteeing	guarantee	VERB
fumecheng-13730	175	9	the	the	DET
fumecheng-13730	175	10	efficacy	efficacy	NOUN
fumecheng-13730	175	11	and	and	CCONJ
fumecheng-13730	175	12	precision	precision	NOUN
fumecheng-13730	175	13	of	of	ADP
fumecheng-13730	175	14	the	the	DET
fumecheng-13730	175	15	method	method	NOUN
fumecheng-13730	175	16	in	in	ADP
fumecheng-13730	175	17	analyzing	analyze	VERB
fumecheng-13730	175	18	and	and	CCONJ
fumecheng-13730	175	19	approximating	approximate	VERB
fumecheng-13730	175	20	nonlinear	nonlinear	ADJ
fumecheng-13730	175	21	vibration	vibration	NOUN
fumecheng-13730	175	22	phenomena	phenomenon	NOUN
fumecheng-13730	175	23	.	.	PUNCT
fumecheng-13730	176	1	after	after	ADP
fumecheng-13730	176	2	a	a	DET
fumecheng-13730	176	3	complex	complex	ADJ
fumecheng-13730	176	4	calculation	calculation	NOUN
fumecheng-13730	176	5	,	,	PUNCT
fumecheng-13730	176	6	belendez	belendez	PROPN
fumecheng-13730	176	7	et	et	PROPN
fumecheng-13730	176	8	al	al	PROPN
fumecheng-13730	176	9	.	.	PUNCT
fumecheng-13730	177	1	[	[	X
fumecheng-13730	177	2	30	30	NUM
fumecheng-13730	177	3	]	]	PUNCT
fumecheng-13730	177	4	obtained	obtain	VERB
fumecheng-13730	177	5	high	high	ADJ
fumecheng-13730	177	6	-	-	PUNCT
fumecheng-13730	177	7	accuracy	accuracy	NOUN
fumecheng-13730	177	8	analytical	analytical	ADJ
fumecheng-13730	177	9	approximations	approximation	NOUN
fumecheng-13730	177	10	by	by	ADP
fumecheng-13730	177	11	the	the	DET
fumecheng-13730	177	12	homotopy	homotopy	NOUN
fumecheng-13730	177	13	perturbation	perturbation	NOUN
fumecheng-13730	177	14	method	method	NOUN
fumecheng-13730	177	15	,	,	PUNCT
fumecheng-13730	177	16	resulting	result	VERB
fumecheng-13730	177	17	in	in	ADP
fumecheng-13730	177	18	the	the	DET
fumecheng-13730	177	19	following	follow	VERB
fumecheng-13730	177	20	frequencies	frequency	NOUN
fumecheng-13730	177	21	1/2	1/2	NUM
fumecheng-13730	177	22	1	1	NUM
fumecheng-13730	177	23	1.128379=	1.128379=	NUM
fumecheng-13730	177	24	a−	a−	NOUN
fumecheng-13730	177	25	,	,	PUNCT
fumecheng-13730	177	26	(	(	PUNCT
fumecheng-13730	177	27	27	27	NUM
fumecheng-13730	177	28	)	)	PUNCT
fumecheng-13730	177	29	and	and	CCONJ
fumecheng-13730	177	30	1/2	1/2	NUM
fumecheng-13730	177	31	2	2	NUM
fumecheng-13730	177	32	1.107452=	1.107452=	NUM
fumecheng-13730	177	33	a−	a−	NOUN
fumecheng-13730	177	34	.	.	PUNCT
fumecheng-13730	178	1	(	(	PUNCT
fumecheng-13730	178	2	28	28	NUM
fumecheng-13730	178	3	)	)	PUNCT
fumecheng-13730	178	4	the	the	DET
fumecheng-13730	178	5	relative	relative	ADJ
fumecheng-13730	178	6	errors	error	NOUN
fumecheng-13730	178	7	are	be	AUX
fumecheng-13730	178	8	1.59	1.59	NUM
fumecheng-13730	178	9	%	%	NOUN
fumecheng-13730	178	10	and	and	CCONJ
fumecheng-13730	178	11	0.29	0.29	NUM
fumecheng-13730	178	12	%	%	NOUN
fumecheng-13730	178	13	,	,	PUNCT
fumecheng-13730	178	14	respectively	respectively	ADV
fumecheng-13730	178	15	.	.	PUNCT
fumecheng-13730	179	1	liu	liu	PROPN
fumecheng-13730	179	2	obtained	obtain	VERB
fumecheng-13730	179	3	the	the	DET
fumecheng-13730	179	4	same	same	ADJ
fumecheng-13730	179	5	result	result	NOUN
fumecheng-13730	179	6	of	of	ADP
fumecheng-13730	179	7	eq	eq	PROPN
fumecheng-13730	179	8	.	.	PUNCT
fumecheng-13730	180	1	(	(	PUNCT
fumecheng-13730	180	2	28	28	NUM
fumecheng-13730	180	3	)	)	PUNCT
fumecheng-13730	180	4	by	by	ADP
fumecheng-13730	180	5	the	the	DET
fumecheng-13730	180	6	modified	modify	VERB
fumecheng-13730	180	7	lindstedt	lindstedt	PROPN
fumecheng-13730	180	8	–	–	PUNCT
fumecheng-13730	180	9	poincaré	poincaré	PROPN
fumecheng-13730	180	10	method	method	NOUN
fumecheng-13730	180	11	[	[	X
fumecheng-13730	180	12	33	33	NUM
fumecheng-13730	180	13	]	]	PUNCT
fumecheng-13730	180	14	.	.	PUNCT
fumecheng-13730	181	1	although	although	SCONJ
fumecheng-13730	181	2	the	the	DET
fumecheng-13730	181	3	achievement	achievement	NOUN
fumecheng-13730	181	4	has	have	AUX
fumecheng-13730	181	5	been	be	AUX
fumecheng-13730	181	6	attained	attain	VERB
fumecheng-13730	181	7	,	,	PUNCT
fumecheng-13730	181	8	engineers	engineer	NOUN
fumecheng-13730	181	9	are	be	AUX
fumecheng-13730	181	10	currently	currently	ADV
fumecheng-13730	181	11	seeking	seek	VERB
fumecheng-13730	181	12	a	a	DET
fumecheng-13730	181	13	straightforward	straightforward	ADJ
fumecheng-13730	181	14	yet	yet	CCONJ
fumecheng-13730	181	15	impactful	impactful	ADJ
fumecheng-13730	181	16	methodology	methodology	NOUN
fumecheng-13730	181	17	.	.	PUNCT
fumecheng-13730	182	1	by	by	ADP
fumecheng-13730	182	2	employing	employ	VERB
fumecheng-13730	182	3	the	the	DET
fumecheng-13730	182	4	frequency	frequency	NOUN
fumecheng-13730	182	5	formulation	formulation	NOUN
fumecheng-13730	182	6	,	,	PUNCT
fumecheng-13730	182	7	we	we	PRON
fumecheng-13730	182	8	have	have	AUX
fumecheng-13730	182	9	promptly	promptly	ADV
fumecheng-13730	182	10	derived	derive	VERB
fumecheng-13730	182	11	the	the	DET
fumecheng-13730	182	12	following	follow	VERB
fumecheng-13730	182	13	outcome	outcome	NOUN
fumecheng-13730	182	14	.	.	PUNCT
fumecheng-13730	183	1	2	2	NUM
fumecheng-13730	183	2	1	1	NUM
fumecheng-13730	183	3	16	16	NUM
fumecheng-13730	183	4	6	6	NUM
fumecheng-13730	183	5	0	0	NUM
fumecheng-13730	183	6	5	5	NUM
fumecheng-13730	183	7	5	5	NUM
fumecheng-13730	183	8	a	a	DET
fumecheng-13730	183	9	a−	a−	PROPN
fumecheng-13730	183	10	−=	−=	NOUN
fumecheng-13730	183	11	=	=	PUNCT
fumecheng-13730	184	1	+	+	CCONJ
fumecheng-13730	184	2			PROPN
fumecheng-13730	184	3			PROPN
fumecheng-13730	184	4			PROPN
fumecheng-13730	184	5	,	,	PUNCT
fumecheng-13730	184	6	(	(	PUNCT
fumecheng-13730	184	7	29	29	NUM
fumecheng-13730	184	8	)	)	PUNCT
fumecheng-13730	184	9	or	or	CCONJ
fumecheng-13730	184	10	1/2	1/2	NUM
fumecheng-13730	184	11	1/21.0954	1/21.0954	NUM
fumecheng-13730	184	12	a−=	a−=	ADV
fumecheng-13730	184	13			ADJ
fumecheng-13730	184	14	.	.	PUNCT
fumecheng-13730	185	1	(	(	PUNCT
fumecheng-13730	185	2	30	30	NUM
fumecheng-13730	185	3	)	)	PUNCT
fumecheng-13730	185	4	this	this	DET
fumecheng-13730	185	5	result	result	NOUN
fumecheng-13730	185	6	is	be	AUX
fumecheng-13730	185	7	comparable	comparable	ADJ
fumecheng-13730	185	8	to	to	ADP
fumecheng-13730	185	9	those	those	PRON
fumecheng-13730	185	10	produced	produce	VERB
fumecheng-13730	185	11	by	by	ADP
fumecheng-13730	185	12	the	the	DET
fumecheng-13730	185	13	homotopy	homotopy	NOUN
fumecheng-13730	185	14	perturbation	perturbation	NOUN
fumecheng-13730	185	15	method	method	NOUN
fumecheng-13730	185	16	[	[	X
fumecheng-13730	185	17	31	31	NUM
fumecheng-13730	185	18	]	]	PUNCT
fumecheng-13730	185	19	and	and	CCONJ
fumecheng-13730	185	20	the	the	DET
fumecheng-13730	185	21	modified	modify	VERB
fumecheng-13730	185	22	lindstedt	lindstedt	PROPN
fumecheng-13730	185	23	–	–	PUNCT
fumecheng-13730	185	24	poincaré	poincaré	PROPN
fumecheng-13730	185	25	method	method	NOUN
fumecheng-13730	185	26	[	[	X
fumecheng-13730	185	27	33	33	NUM
fumecheng-13730	185	28	]	]	PUNCT
fumecheng-13730	185	29	.	.	PUNCT
fumecheng-13730	186	1	the	the	DET
fumecheng-13730	186	2	exact	exact	ADJ
fumecheng-13730	186	3	frequency	frequency	NOUN
fumecheng-13730	186	4	is	be	AUX
fumecheng-13730	186	5	:	:	PUNCT
fumecheng-13730	186	6	1/2	1/2	NUM
fumecheng-13730	186	7	ex	ex	NOUN
fumecheng-13730	186	8	1.1107=	1.1107=	NUM
fumecheng-13730	186	9	a−	a−	ADV
fumecheng-13730	186	10	.	.	PUNCT
fumecheng-13730	187	1	(	(	PUNCT
fumecheng-13730	187	2	31	31	NUM
fumecheng-13730	187	3	)	)	PUNCT
fumecheng-13730	187	4	the	the	DET
fumecheng-13730	187	5	relative	relative	ADJ
fumecheng-13730	187	6	error	error	NOUN
fumecheng-13730	187	7	is	be	AUX
fumecheng-13730	187	8	1.37	1.37	NUM
fumecheng-13730	187	9	%	%	NOUN
fumecheng-13730	187	10	,	,	PUNCT
fumecheng-13730	187	11	which	which	PRON
fumecheng-13730	187	12	is	be	AUX
fumecheng-13730	187	13	comparable	comparable	ADJ
fumecheng-13730	187	14	to	to	ADP
fumecheng-13730	187	15	the	the	DET
fumecheng-13730	187	16	results	result	NOUN
fumecheng-13730	187	17	presented	present	VERB
fumecheng-13730	187	18	in	in	ADP
fumecheng-13730	187	19	refs	ref	NOUN
fumecheng-13730	187	20	.	.	PUNCT
fumecheng-13730	188	1	[	[	X
fumecheng-13730	188	2	37	37	NUM
fumecheng-13730	188	3	,	,	PUNCT
fumecheng-13730	188	4	39	39	NUM
fumecheng-13730	188	5	]	]	PUNCT
fumecheng-13730	188	6	,	,	PUNCT
fumecheng-13730	188	7	where	where	SCONJ
fumecheng-13730	188	8	a	a	DET
fumecheng-13730	188	9	length	length	NOUN
fumecheng-13730	188	10	calculation	calculation	NOUN
fumecheng-13730	188	11	and	and	CCONJ
fumecheng-13730	188	12	specialized	specialized	ADJ
fumecheng-13730	188	13	skills	skill	NOUN
fumecheng-13730	188	14	are	be	AUX
fumecheng-13730	188	15	required	require	VERB
fumecheng-13730	188	16	.	.	PUNCT
fumecheng-13730	189	1	in	in	ADP
fumecheng-13730	189	2	contrast	contrast	NOUN
fumecheng-13730	189	3	,	,	PUNCT
fumecheng-13730	189	4	the	the	DET
fumecheng-13730	189	5	present	present	ADJ
fumecheng-13730	189	6	approach	approach	NOUN
fumecheng-13730	189	7	is	be	AUX
fumecheng-13730	189	8	notable	notable	ADJ
fumecheng-13730	189	9	for	for	ADP
fumecheng-13730	189	10	its	its	PRON
fumecheng-13730	189	11	simplicity	simplicity	NOUN
fumecheng-13730	189	12	.	.	PUNCT
fumecheng-13730	190	1	in	in	ADP
fumecheng-13730	190	2	nonlinear	nonlinear	ADJ
fumecheng-13730	190	3	theoretical	theoretical	ADJ
fumecheng-13730	190	4	analysis	analysis	NOUN
fumecheng-13730	190	5	,	,	PUNCT
fumecheng-13730	190	6	a	a	DET
fumecheng-13730	190	7	minimal	minimal	ADJ
fumecheng-13730	190	8	calculation	calculation	NOUN
fumecheng-13730	190	9	with	with	ADP
fumecheng-13730	190	10	one	one	NUM
fumecheng-13730	190	11	or	or	CCONJ
fumecheng-13730	190	12	two	two	NUM
fumecheng-13730	190	13	lines	line	NOUN
fumecheng-13730	190	14	can	can	AUX
fumecheng-13730	190	15	have	have	VERB
fumecheng-13730	190	16	maximal	maximal	ADJ
fumecheng-13730	190	17	influence	influence	NOUN
fumecheng-13730	190	18	in	in	ADP
fumecheng-13730	190	19	the	the	DET
fumecheng-13730	190	20	academic	academic	ADJ
fumecheng-13730	190	21	community	community	NOUN
fumecheng-13730	190	22	,	,	PUNCT
fumecheng-13730	190	23	as	as	SCONJ
fumecheng-13730	190	24	ludwig	ludwig	PROPN
fumecheng-13730	190	25	mies	mies	PROPN
fumecheng-13730	190	26	van	van	PROPN
fumecheng-13730	190	27	der	der	PROPN
fumecheng-13730	190	28	rohe	rohe	PROPN
fumecheng-13730	190	29	(	(	PUNCT
fumecheng-13730	190	30	1886–1969	1886–1969	NUM
fumecheng-13730	190	31	)	)	PUNCT
fumecheng-13730	190	32	said	say	VERB
fumecheng-13730	190	33	,	,	PUNCT
fumecheng-13730	190	34	"	"	PUNCT
fumecheng-13730	190	35	less	less	ADJ
fumecheng-13730	190	36	is	be	AUX
fumecheng-13730	190	37	more	more	ADJ
fumecheng-13730	190	38	"	"	PUNCT
fumecheng-13730	190	39	.	.	PUNCT
fumecheng-13730	191	1	4.3	4.3	NUM
fumecheng-13730	191	2	.	.	PUNCT
fumecheng-13730	191	3	example	example	NOUN
fumecheng-13730	191	4	3	3	NUM
fumecheng-13730	191	5	.	.	PUNCT
fumecheng-13730	191	6	discontinuous	discontinuous	ADJ
fumecheng-13730	191	7	oscillator	oscillator	NOUN
fumecheng-13730	191	8	with	with	ADP
fumecheng-13730	191	9	absolute	absolute	ADJ
fumecheng-13730	191	10	value	value	NOUN
fumecheng-13730	191	11	symbols	symbol	NOUN
fumecheng-13730	191	12	the	the	DET
fumecheng-13730	191	13	study	study	NOUN
fumecheng-13730	191	14	of	of	ADP
fumecheng-13730	191	15	discontinuous	discontinuous	ADJ
fumecheng-13730	191	16	oscillators	oscillator	NOUN
fumecheng-13730	191	17	with	with	ADP
fumecheng-13730	191	18	absolute	absolute	ADJ
fumecheng-13730	191	19	value	value	NOUN
fumecheng-13730	191	20	symbols	symbol	NOUN
fumecheng-13730	191	21	represents	represent	VERB
fumecheng-13730	191	22	a	a	DET
fumecheng-13730	191	23	fascinating	fascinating	ADJ
fumecheng-13730	191	24	area	area	NOUN
fumecheng-13730	191	25	of	of	ADP
fumecheng-13730	191	26	inquiry	inquiry	NOUN
fumecheng-13730	191	27	within	within	ADP
fumecheng-13730	191	28	the	the	DET
fumecheng-13730	191	29	field	field	NOUN
fumecheng-13730	191	30	of	of	ADP
fumecheng-13730	191	31	nonlinear	nonlinear	ADJ
fumecheng-13730	191	32	dynamics	dynamic	NOUN
fumecheng-13730	191	33	.	.	PUNCT
fumecheng-13730	192	1	the	the	DET
fumecheng-13730	192	2	introduction	introduction	NOUN
fumecheng-13730	192	3	of	of	ADP
fumecheng-13730	192	4	absolute	absolute	ADJ
fumecheng-13730	192	5	value	value	NOUN
fumecheng-13730	192	6	symbols	symbol	NOUN
fumecheng-13730	192	7	can	can	AUX
fumecheng-13730	192	8	result	result	VERB
fumecheng-13730	192	9	in	in	ADP
fumecheng-13730	192	10	the	the	DET
fumecheng-13730	192	11	emergence	emergence	NOUN
fumecheng-13730	192	12	of	of	ADP
fumecheng-13730	192	13	intricate	intricate	ADJ
fumecheng-13730	192	14	dynamics	dynamic	NOUN
fumecheng-13730	192	15	,	,	PUNCT
fumecheng-13730	192	16	which	which	PRON
fumecheng-13730	192	17	in	in	ADP
fumecheng-13730	192	18	turn	turn	NOUN
fumecheng-13730	192	19	presents	present	VERB
fumecheng-13730	192	20	significant	significant	ADJ
fumecheng-13730	192	21	analytical	analytical	ADJ
fumecheng-13730	192	22	challenges	challenge	NOUN
fumecheng-13730	192	23	.	.	PUNCT
fumecheng-13730	193	1	researchers	researcher	NOUN
fumecheng-13730	193	2	employ	employ	VERB
fumecheng-13730	193	3	a	a	DET
fumecheng-13730	193	4	range	range	NOUN
fumecheng-13730	193	5	of	of	ADP
fumecheng-13730	193	6	analytical	analytical	ADJ
fumecheng-13730	193	7	techniques	technique	NOUN
fumecheng-13730	193	8	to	to	PART
fumecheng-13730	193	9	examine	examine	VERB
fumecheng-13730	193	10	these	these	DET
fumecheng-13730	193	11	oscillators	oscillator	NOUN
fumecheng-13730	193	12	,	,	PUNCT
fumecheng-13730	193	13	undertaking	undertake	VERB
fumecheng-13730	193	14	significant	significant	ADJ
fumecheng-13730	193	15	efforts	effort	NOUN
fumecheng-13730	193	16	in	in	ADP
fumecheng-13730	193	17	this	this	DET
fumecheng-13730	193	18	regard	regard	NOUN
fumecheng-13730	193	19	.	.	PUNCT
fumecheng-13730	194	1	such	such	ADJ
fumecheng-13730	194	2	techniques	technique	NOUN
fumecheng-13730	194	3	may	may	AUX
fumecheng-13730	194	4	include	include	VERB
fumecheng-13730	194	5	numerical	numerical	ADJ
fumecheng-13730	194	6	simulations	simulation	NOUN
fumecheng-13730	194	7	and	and	CCONJ
fumecheng-13730	194	8	analytical	analytical	ADJ
fumecheng-13730	194	9	approximations	approximation	NOUN
fumecheng-13730	194	10	.	.	PUNCT
fumecheng-13730	195	1	in	in	ADP
fumecheng-13730	195	2	this	this	DET
fumecheng-13730	195	3	example	example	NOUN
fumecheng-13730	195	4	,	,	PUNCT
fumecheng-13730	195	5	we	we	PRON
fumecheng-13730	195	6	consider	consider	VERB
fumecheng-13730	195	7	a	a	DET
fumecheng-13730	195	8	discontinuous	discontinuous	ADJ
fumecheng-13730	195	9	oscillator	oscillator	NOUN
fumecheng-13730	195	10	with	with	ADP
fumecheng-13730	195	11	absolute	absolute	ADJ
fumecheng-13730	195	12	value	value	NOUN
fumecheng-13730	195	13	terms	term	NOUN
fumecheng-13730	195	14	,	,	PUNCT
fumecheng-13730	195	15	as	as	SCONJ
fumecheng-13730	195	16	illustrated	illustrate	VERB
fumecheng-13730	195	17	in	in	ADP
fumecheng-13730	195	18	fig	fig	NOUN
fumecheng-13730	195	19	.	.	PUNCT
fumecheng-13730	196	1	2	2	X
fumecheng-13730	196	2	.	.	X
fumecheng-13730	196	3	a	a	DET
fumecheng-13730	196	4	modified	modify	VERB
fumecheng-13730	196	5	frequency	frequency	NOUN
fumecheng-13730	196	6	formulation	formulation	NOUN
fumecheng-13730	196	7	for	for	ADP
fumecheng-13730	196	8	nonlinear	nonlinear	ADJ
fumecheng-13730	196	9	mechanical	mechanical	ADJ
fumecheng-13730	196	10	vibrations	vibration	NOUN
fumecheng-13730	196	11	205	205	NUM
fumecheng-13730	196	12	fig	fig	NOUN
fumecheng-13730	196	13	.	.	PUNCT
fumecheng-13730	197	1	2	2	NUM
fumecheng-13730	197	2	schematic	schematic	ADJ
fumecheng-13730	197	3	of	of	ADP
fumecheng-13730	197	4	a	a	DET
fumecheng-13730	197	5	discontinuous	discontinuous	ADJ
fumecheng-13730	197	6	oscillator	oscillator	NOUN
fumecheng-13730	197	7	with	with	ADP
fumecheng-13730	197	8	absolute	absolute	ADJ
fumecheng-13730	197	9	value	value	NOUN
fumecheng-13730	197	10	terms	term	NOUN
fumecheng-13730	197	11	it	it	PRON
fumecheng-13730	197	12	is	be	AUX
fumecheng-13730	197	13	assumed	assume	VERB
fumecheng-13730	197	14	that	that	SCONJ
fumecheng-13730	197	15	the	the	DET
fumecheng-13730	197	16	equivalent	equivalent	ADJ
fumecheng-13730	197	17	elastic	elastic	ADJ
fumecheng-13730	197	18	coefficient	coefficient	NOUN
fumecheng-13730	197	19	is	be	AUX
fumecheng-13730	197	20	proportional	proportional	ADJ
fumecheng-13730	197	21	to	to	ADP
fumecheng-13730	197	22	the	the	DET
fumecheng-13730	197	23	magnitude	magnitude	NOUN
fumecheng-13730	197	24	of	of	ADP
fumecheng-13730	197	25	displacement	displacement	NOUN
fumecheng-13730	197	26	,	,	PUNCT
fumecheng-13730	197	27	and	and	CCONJ
fumecheng-13730	197	28	the	the	DET
fumecheng-13730	197	29	oscillator	oscillator	NOUN
fumecheng-13730	197	30	can	can	AUX
fumecheng-13730	197	31	be	be	AUX
fumecheng-13730	197	32	expressed	express	VERB
fumecheng-13730	197	33	as	as	ADP
fumecheng-13730	197	34	:	:	PUNCT
fumecheng-13730	197	35	0u	0u	ADJ
fumecheng-13730	197	36	u	u	NOUN
fumecheng-13730	197	37	u	u	PROPN
fumecheng-13730	197	38	+	+	X
fumecheng-13730	197	39	=	=	PUNCT
fumecheng-13730	197	40	.	.	PUNCT
fumecheng-13730	198	1	(	(	PUNCT
fumecheng-13730	198	2	32	32	NUM
fumecheng-13730	198	3	)	)	PUNCT
fumecheng-13730	198	4	by	by	ADP
fumecheng-13730	198	5	the	the	DET
fumecheng-13730	198	6	frequency	frequency	NOUN
fumecheng-13730	198	7	formulation	formulation	NOUN
fumecheng-13730	198	8	,	,	PUNCT
fumecheng-13730	198	9	we	we	PRON
fumecheng-13730	198	10	have	have	VERB
fumecheng-13730	198	11	:	:	PUNCT
fumecheng-13730	198	12	2	2	NUM
fumecheng-13730	198	13	6	6	NUM
fumecheng-13730	198	14	6	6	NUM
fumecheng-13730	198	15	2	2	NUM
fumecheng-13730	198	16	5	5	NUM
fumecheng-13730	198	17	7	7	NUM
fumecheng-13730	198	18	a	a	DET
fumecheng-13730	198	19	a=	a=	NOUN
fumecheng-13730	199	1	=	=	SYM
fumecheng-13730	200	1	+	+	CCONJ
fumecheng-13730	200	2			X
fumecheng-13730	200	3	,	,	PUNCT
fumecheng-13730	200	4	(	(	PUNCT
fumecheng-13730	200	5	33	33	NUM
fumecheng-13730	200	6	)	)	PUNCT
fumecheng-13730	200	7	or	or	CCONJ
fumecheng-13730	200	8	0.92582	0.92582	NUM
fumecheng-13730	200	9	a=	a=	NOUN
fumecheng-13730	200	10	,	,	PUNCT
fumecheng-13730	200	11	(	(	PUNCT
fumecheng-13730	200	12	34	34	NUM
fumecheng-13730	200	13	)	)	PUNCT
fumecheng-13730	200	14	while	while	SCONJ
fumecheng-13730	200	15	the	the	DET
fumecheng-13730	200	16	exact	exact	ADJ
fumecheng-13730	200	17	one	one	PRON
fumecheng-13730	200	18	is	be	AUX
fumecheng-13730	200	19	[	[	X
fumecheng-13730	200	20	35	35	NUM
fumecheng-13730	200	21	]	]	SYM
fumecheng-13730	200	22	:	:	PUNCT
fumecheng-13730	201	1	0.914681exact	0.914681exact	NOUN
fumecheng-13730	201	2	a=	a=	NOUN
fumecheng-13730	201	3	.	.	PUNCT
fumecheng-13730	202	1	(	(	PUNCT
fumecheng-13730	202	2	35	35	NUM
fumecheng-13730	202	3	)	)	PUNCT
fumecheng-13730	202	4	the	the	DET
fumecheng-13730	202	5	relative	relative	ADJ
fumecheng-13730	202	6	error	error	NOUN
fumecheng-13730	202	7	is	be	AUX
fumecheng-13730	202	8	1.21	1.21	NUM
fumecheng-13730	202	9	%	%	NOUN
fumecheng-13730	202	10	,	,	PUNCT
fumecheng-13730	202	11	which	which	PRON
fumecheng-13730	202	12	is	be	AUX
fumecheng-13730	202	13	an	an	DET
fumecheng-13730	202	14	acceptable	acceptable	ADJ
fumecheng-13730	202	15	level	level	NOUN
fumecheng-13730	202	16	of	of	ADP
fumecheng-13730	202	17	precision	precision	NOUN
fumecheng-13730	202	18	given	give	VERB
fumecheng-13730	202	19	the	the	DET
fumecheng-13730	202	20	simplicity	simplicity	NOUN
fumecheng-13730	202	21	of	of	ADP
fumecheng-13730	202	22	the	the	DET
fumecheng-13730	202	23	method	method	NOUN
fumecheng-13730	202	24	employed	employ	VERB
fumecheng-13730	202	25	.	.	PUNCT
fumecheng-13730	203	1	wang	wang	PROPN
fumecheng-13730	203	2	and	and	CCONJ
fumecheng-13730	203	3	he	he	PRON
fumecheng-13730	204	1	[	[	X
fumecheng-13730	204	2	36	36	NUM
fumecheng-13730	204	3	]	]	PUNCT
fumecheng-13730	204	4	achieved	achieve	VERB
fumecheng-13730	204	5	a	a	DET
fumecheng-13730	204	6	notable	notable	ADJ
fumecheng-13730	204	7	result	result	NOUN
fumecheng-13730	204	8	through	through	ADP
fumecheng-13730	204	9	a	a	DET
fumecheng-13730	204	10	combination	combination	NOUN
fumecheng-13730	204	11	of	of	ADP
fumecheng-13730	204	12	sophisticated	sophisticated	ADJ
fumecheng-13730	204	13	techniques	technique	NOUN
fumecheng-13730	204	14	and	and	CCONJ
fumecheng-13730	204	15	meticulous	meticulous	ADJ
fumecheng-13730	204	16	calculations	calculation	NOUN
fumecheng-13730	204	17	,	,	PUNCT
fumecheng-13730	204	18	which	which	PRON
fumecheng-13730	204	19	is	be	AUX
fumecheng-13730	204	20	8	8	NUM
fumecheng-13730	204	21	0.9214	0.9214	NUM
fumecheng-13730	204	22	3	3	NUM
fumecheng-13730	204	23	a	a	DET
fumecheng-13730	204	24	a=	a=	NOUN
fumecheng-13730	205	1	=	=	SYM
fumecheng-13730	205	2			PROPN
fumecheng-13730	205	3			PROPN
fumecheng-13730	205	4	.	.	PUNCT
fumecheng-13730	206	1	(	(	PUNCT
fumecheng-13730	206	2	36	36	NUM
fumecheng-13730	206	3	)	)	PUNCT
fumecheng-13730	206	4	this	this	DET
fumecheng-13730	206	5	achievement	achievement	NOUN
fumecheng-13730	206	6	was	be	AUX
fumecheng-13730	206	7	of	of	ADP
fumecheng-13730	206	8	tremendous	tremendous	ADJ
fumecheng-13730	206	9	significance	significance	NOUN
fumecheng-13730	206	10	because	because	SCONJ
fumecheng-13730	206	11	,	,	PUNCT
fumecheng-13730	206	12	prior	prior	ADV
fumecheng-13730	206	13	to	to	ADP
fumecheng-13730	206	14	this	this	PRON
fumecheng-13730	206	15	,	,	PUNCT
fumecheng-13730	206	16	there	there	PRON
fumecheng-13730	206	17	was	be	VERB
fumecheng-13730	206	18	no	no	DET
fumecheng-13730	206	19	analytical	analytical	ADJ
fumecheng-13730	206	20	method	method	NOUN
fumecheng-13730	206	21	that	that	PRON
fumecheng-13730	206	22	could	could	AUX
fumecheng-13730	206	23	effectively	effectively	ADV
fumecheng-13730	206	24	solve	solve	VERB
fumecheng-13730	206	25	eq	eq	ADP
fumecheng-13730	206	26	.	.	PUNCT
fumecheng-13730	207	1	(	(	PUNCT
fumecheng-13730	207	2	33	33	NUM
fumecheng-13730	207	3	)	)	PUNCT
fumecheng-13730	207	4	.	.	PUNCT
fumecheng-13730	208	1	reference	reference	NOUN
fumecheng-13730	208	2	[	[	X
fumecheng-13730	208	3	36	36	NUM
fumecheng-13730	208	4	]	]	PUNCT
fumecheng-13730	208	5	made	make	VERB
fumecheng-13730	208	6	significant	significant	ADJ
fumecheng-13730	208	7	advancements	advancement	NOUN
fumecheng-13730	208	8	in	in	ADP
fumecheng-13730	208	9	nonlinear	nonlinear	ADJ
fumecheng-13730	208	10	science	science	NOUN
fumecheng-13730	208	11	and	and	CCONJ
fumecheng-13730	208	12	nonlinear	nonlinear	ADJ
fumecheng-13730	208	13	vibration	vibration	NOUN
fumecheng-13730	208	14	theory	theory	NOUN
fumecheng-13730	208	15	.	.	PUNCT
fumecheng-13730	209	1	it	it	PRON
fumecheng-13730	209	2	provides	provide	VERB
fumecheng-13730	209	3	an	an	DET
fumecheng-13730	209	4	excellent	excellent	ADJ
fumecheng-13730	209	5	illustration	illustration	NOUN
fumecheng-13730	209	6	of	of	ADP
fumecheng-13730	209	7	the	the	DET
fumecheng-13730	209	8	efficacy	efficacy	NOUN
fumecheng-13730	209	9	of	of	ADP
fumecheng-13730	209	10	meticulous	meticulous	ADJ
fumecheng-13730	209	11	analysis	analysis	NOUN
fumecheng-13730	209	12	and	and	CCONJ
fumecheng-13730	209	13	innovative	innovative	ADJ
fumecheng-13730	209	14	thinking	thinking	NOUN
fumecheng-13730	209	15	in	in	ADP
fumecheng-13730	209	16	addressing	address	VERB
fumecheng-13730	209	17	complex	complex	ADJ
fumecheng-13730	209	18	problems	problem	NOUN
fumecheng-13730	209	19	and	and	CCONJ
fumecheng-13730	209	20	makes	make	VERB
fumecheng-13730	209	21	a	a	DET
fumecheng-13730	209	22	valuable	valuable	ADJ
fumecheng-13730	209	23	contribution	contribution	NOUN
fumecheng-13730	209	24	to	to	ADP
fumecheng-13730	209	25	the	the	DET
fumecheng-13730	209	26	expanding	expand	VERB
fumecheng-13730	209	27	body	body	NOUN
fumecheng-13730	209	28	of	of	ADP
fumecheng-13730	209	29	knowledge	knowledge	NOUN
fumecheng-13730	209	30	in	in	ADP
fumecheng-13730	209	31	the	the	DET
fumecheng-13730	209	32	relevant	relevant	ADJ
fumecheng-13730	209	33	discipline	discipline	NOUN
fumecheng-13730	209	34	.	.	PUNCT
fumecheng-13730	210	1	the	the	DET
fumecheng-13730	210	2	current	current	ADJ
fumecheng-13730	210	3	approach	approach	NOUN
fumecheng-13730	210	4	allows	allow	VERB
fumecheng-13730	210	5	for	for	ADP
fumecheng-13730	210	6	a	a	DET
fumecheng-13730	210	7	straightforward	straightforward	ADJ
fumecheng-13730	210	8	and	and	CCONJ
fumecheng-13730	210	9	effective	effective	ADJ
fumecheng-13730	210	10	solution	solution	NOUN
fumecheng-13730	210	11	,	,	PUNCT
fumecheng-13730	210	12	demonstrating	demonstrate	VERB
fumecheng-13730	210	13	the	the	DET
fumecheng-13730	210	14	value	value	NOUN
fumecheng-13730	210	15	of	of	ADP
fumecheng-13730	210	16	simplicity	simplicity	NOUN
fumecheng-13730	210	17	in	in	ADP
fumecheng-13730	210	18	achieving	achieve	VERB
fumecheng-13730	210	19	comparable	comparable	ADJ
fumecheng-13730	210	20	outcomes	outcome	NOUN
fumecheng-13730	210	21	.	.	PUNCT
fumecheng-13730	211	1	the	the	DET
fumecheng-13730	211	2	new	new	ADJ
fumecheng-13730	211	3	frequency	frequency	NOUN
fumecheng-13730	211	4	formulation	formulation	NOUN
fumecheng-13730	211	5	provides	provide	VERB
fumecheng-13730	211	6	a	a	DET
fumecheng-13730	211	7	novel	novel	ADJ
fumecheng-13730	211	8	avenue	avenue	NOUN
fumecheng-13730	211	9	for	for	ADP
fumecheng-13730	211	10	future	future	ADJ
fumecheng-13730	211	11	research	research	NOUN
fumecheng-13730	211	12	in	in	ADP
fumecheng-13730	211	13	nonlinear	nonlinear	ADJ
fumecheng-13730	211	14	vibration	vibration	NOUN
fumecheng-13730	211	15	theory	theory	NOUN
fumecheng-13730	211	16	and	and	CCONJ
fumecheng-13730	211	17	nonlinear	nonlinear	ADJ
fumecheng-13730	211	18	studies	study	NOUN
fumecheng-13730	211	19	.	.	PUNCT
fumecheng-13730	212	1	the	the	DET
fumecheng-13730	212	2	optimal	optimal	ADJ
fumecheng-13730	212	3	approach	approach	NOUN
fumecheng-13730	212	4	is	be	AUX
fumecheng-13730	212	5	to	to	PART
fumecheng-13730	212	6	employ	employ	VERB
fumecheng-13730	212	7	a	a	DET
fumecheng-13730	212	8	method	method	NOUN
fumecheng-13730	212	9	that	that	PRON
fumecheng-13730	212	10	is	be	AUX
fumecheng-13730	212	11	both	both	CCONJ
fumecheng-13730	212	12	straightforward	straightforward	ADJ
fumecheng-13730	212	13	and	and	CCONJ
fumecheng-13730	212	14	efficacious	efficacious	ADJ
fumecheng-13730	212	15	.	.	PUNCT
fumecheng-13730	213	1	4.4	4.4	NUM
fumecheng-13730	213	2	.	.	PUNCT
fumecheng-13730	213	3	example	example	NOUN
fumecheng-13730	213	4	4	4	NUM
fumecheng-13730	213	5	.	.	PUNCT
fumecheng-13730	213	6	singular	singular	PROPN
fumecheng-13730	213	7	oscillator	oscillator	VERB
fumecheng-13730	213	8	a	a	DET
fumecheng-13730	213	9	singular	singular	ADJ
fumecheng-13730	213	10	oscillator	oscillator	NOUN
fumecheng-13730	213	11	represents	represent	VERB
fumecheng-13730	213	12	a	a	DET
fumecheng-13730	213	13	distinctive	distinctive	ADJ
fumecheng-13730	213	14	category	category	NOUN
fumecheng-13730	213	15	of	of	ADP
fumecheng-13730	213	16	dynamical	dynamical	ADJ
fumecheng-13730	213	17	systems	system	NOUN
fumecheng-13730	213	18	that	that	PRON
fumecheng-13730	213	19	display	display	VERB
fumecheng-13730	213	20	a	a	DET
fumecheng-13730	213	21	range	range	NOUN
fumecheng-13730	213	22	of	of	ADP
fumecheng-13730	213	23	intriguing	intriguing	ADJ
fumecheng-13730	213	24	and	and	CCONJ
fumecheng-13730	213	25	frequently	frequently	ADV
fumecheng-13730	213	26	intricate	intricate	ADJ
fumecheng-13730	213	27	behaviors	behavior	NOUN
fumecheng-13730	213	28	.	.	PUNCT
fumecheng-13730	214	1	these	these	DET
fumecheng-13730	214	2	oscillators	oscillator	NOUN
fumecheng-13730	214	3	possess	possess	VERB
fumecheng-13730	214	4	singularities	singularity	NOUN
fumecheng-13730	214	5	,	,	PUNCT
fumecheng-13730	214	6	which	which	PRON
fumecheng-13730	214	7	give	give	VERB
fumecheng-13730	214	8	rise	rise	NOUN
fumecheng-13730	214	9	to	to	ADP
fumecheng-13730	214	10	distinctive	distinctive	ADJ
fumecheng-13730	214	11	characteristics	characteristic	NOUN
fumecheng-13730	214	12	that	that	PRON
fumecheng-13730	214	13	are	be	AUX
fumecheng-13730	214	14	not	not	PART
fumecheng-13730	214	15	observed	observe	VERB
fumecheng-13730	214	16	in	in	ADP
fumecheng-13730	214	17	traditional	traditional	ADJ
fumecheng-13730	214	18	oscillators	oscillator	NOUN
fumecheng-13730	214	19	.	.	PUNCT
fumecheng-13730	215	1	the	the	DET
fumecheng-13730	215	2	study	study	NOUN
fumecheng-13730	215	3	of	of	ADP
fumecheng-13730	215	4	singular	singular	PROPN
fumecheng-13730	215	5	oscillators	oscillator	NOUN
fumecheng-13730	215	6	is	be	AUX
fumecheng-13730	215	7	of	of	ADP
fumecheng-13730	215	8	significant	significant	ADJ
fumecheng-13730	215	9	importance	importance	NOUN
fumecheng-13730	215	10	in	in	ADP
fumecheng-13730	215	11	a	a	DET
fumecheng-13730	215	12	number	number	NOUN
fumecheng-13730	215	13	of	of	ADP
fumecheng-13730	215	14	fields	field	NOUN
fumecheng-13730	215	15	,	,	PUNCT
fumecheng-13730	215	16	including	include	VERB
fumecheng-13730	215	17	physics	physics	NOUN
fumecheng-13730	215	18	,	,	PUNCT
fumecheng-13730	215	19	engineering	engineering	NOUN
fumecheng-13730	215	20	,	,	PUNCT
fumecheng-13730	215	21	and	and	CCONJ
fumecheng-13730	215	22	mathematics	mathematic	NOUN
fumecheng-13730	215	23	.	.	PUNCT
fumecheng-13730	216	1	it	it	PRON
fumecheng-13730	216	2	facilitates	facilitate	VERB
fumecheng-13730	216	3	comprehension	comprehension	NOUN
fumecheng-13730	216	4	of	of	ADP
fumecheng-13730	216	5	complex	complex	ADJ
fumecheng-13730	216	6	206	206	NUM
fumecheng-13730	216	7	c.h	c.h	NOUN
fumecheng-13730	216	8	.	.	PUNCT
fumecheng-13730	217	1	he	he	PRON
fumecheng-13730	217	2	,	,	PUNCT
fumecheng-13730	217	3	j.h	j.h	PROPN
fumecheng-13730	217	4	.	.	PUNCT
fumecheng-13730	218	1	he	he	PRON
fumecheng-13730	218	2	,	,	PUNCT
fumecheng-13730	218	3	j.	j.	PROPN
fumecheng-13730	218	4	ma	ma	PROPN
fumecheng-13730	218	5	,	,	PUNCT
fumecheng-13730	218	6	a.a	a.a	PROPN
fumecheng-13730	218	7	.	.	PROPN
fumecheng-13730	218	8	alsolam	alsolam	PROPN
fumecheng-13730	218	9	,	,	PUNCT
fumecheng-13730	218	10	x.j	x.j	PROPN
fumecheng-13730	218	11	.	.	PROPN
fumecheng-13730	218	12	yang	yang	PROPN
fumecheng-13730	218	13	systems	systems	PROPN
fumecheng-13730	218	14	and	and	CCONJ
fumecheng-13730	218	15	may	may	AUX
fumecheng-13730	218	16	yield	yield	VERB
fumecheng-13730	218	17	novel	novel	ADJ
fumecheng-13730	218	18	insights	insight	NOUN
fumecheng-13730	218	19	and	and	CCONJ
fumecheng-13730	218	20	applications	application	NOUN
fumecheng-13730	218	21	.	.	PUNCT
fumecheng-13730	219	1	researchers	researcher	NOUN
fumecheng-13730	219	2	are	be	AUX
fumecheng-13730	219	3	engaged	engage	VERB
fumecheng-13730	219	4	in	in	ADP
fumecheng-13730	219	5	ongoing	ongoing	ADJ
fumecheng-13730	219	6	investigations	investigation	NOUN
fumecheng-13730	219	7	into	into	ADP
fumecheng-13730	219	8	the	the	DET
fumecheng-13730	219	9	properties	property	NOUN
fumecheng-13730	219	10	and	and	CCONJ
fumecheng-13730	219	11	behaviors	behavior	NOUN
fumecheng-13730	219	12	of	of	ADP
fumecheng-13730	219	13	singular	singular	ADJ
fumecheng-13730	219	14	oscillators	oscillator	NOUN
fumecheng-13730	219	15	,	,	PUNCT
fumecheng-13730	219	16	with	with	ADP
fumecheng-13730	219	17	the	the	DET
fumecheng-13730	219	18	objective	objective	NOUN
fumecheng-13730	219	19	of	of	ADP
fumecheng-13730	219	20	unlocking	unlock	VERB
fumecheng-13730	219	21	their	their	PRON
fumecheng-13730	219	22	potential	potential	NOUN
fumecheng-13730	219	23	for	for	ADP
fumecheng-13730	219	24	innovative	innovative	ADJ
fumecheng-13730	219	25	technologies	technology	NOUN
fumecheng-13730	219	26	and	and	CCONJ
fumecheng-13730	219	27	scientific	scientific	ADJ
fumecheng-13730	219	28	discoveries	discovery	NOUN
fumecheng-13730	219	29	[	[	X
fumecheng-13730	219	30	37	37	NUM
fumecheng-13730	219	31	]	]	PUNCT
fumecheng-13730	219	32	.	.	PUNCT
fumecheng-13730	220	1	the	the	DET
fumecheng-13730	220	2	following	following	ADJ
fumecheng-13730	220	3	example	example	NOUN
fumecheng-13730	220	4	considers	consider	VERB
fumecheng-13730	220	5	a	a	DET
fumecheng-13730	220	6	singular	singular	ADJ
fumecheng-13730	220	7	oscillator	oscillator	NOUN
fumecheng-13730	220	8	:	:	PUNCT
fumecheng-13730	220	9	1	1	NUM
fumecheng-13730	220	10	0u	0u	ADJ
fumecheng-13730	220	11	u−	u−	PROPN
fumecheng-13730	220	12	+	+	PUNCT
fumecheng-13730	221	1	=	=	X
fumecheng-13730	221	2			PROPN
fumecheng-13730	221	3	(	(	PUNCT
fumecheng-13730	221	4	37	37	NUM
fumecheng-13730	221	5	)	)	PUNCT
fumecheng-13730	221	6	according	accord	VERB
fumecheng-13730	221	7	to	to	ADP
fumecheng-13730	221	8	the	the	DET
fumecheng-13730	221	9	frequency	frequency	NOUN
fumecheng-13730	221	10	formulation	formulation	NOUN
fumecheng-13730	221	11	,	,	PUNCT
fumecheng-13730	221	12	we	we	PRON
fumecheng-13730	221	13	have	have	VERB
fumecheng-13730	221	14	:	:	PUNCT
fumecheng-13730	221	15	2	2	NUM
fumecheng-13730	221	16	2	2	NUM
fumecheng-13730	221	17	2	2	NUM
fumecheng-13730	221	18	.	.	NOUN
fumecheng-13730	221	19	6	6	NUM
fumecheng-13730	221	20	1	1	NUM
fumecheng-13730	221	21	5	5	NUM
fumecheng-13730	221	22	1	1	NUM
fumecheng-13730	221	23	5a	5a	NUM
fumecheng-13730	221	24	a−	a−	PROPN
fumecheng-13730	221	25	−=	−=	NOUN
fumecheng-13730	221	26	=	=	PUNCT
fumecheng-13730	221	27	−	−	PROPN
fumecheng-13730	222	1	+	+	CCONJ
fumecheng-13730	222	2			PROPN
fumecheng-13730	222	3			PROPN
fumecheng-13730	222	4			PROPN
fumecheng-13730	222	5	,	,	PUNCT
fumecheng-13730	222	6	(	(	PUNCT
fumecheng-13730	222	7	38	38	NUM
fumecheng-13730	222	8	)	)	PUNCT
fumecheng-13730	222	9	or	or	CCONJ
fumecheng-13730	222	10	1/2	1/2	NUM
fumecheng-13730	222	11	11.2247	11.2247	NUM
fumecheng-13730	222	12	a−=	a−=	NOUN
fumecheng-13730	222	13			NOUN
fumecheng-13730	222	14	.	.	PUNCT
fumecheng-13730	223	1	(	(	PUNCT
fumecheng-13730	223	2	39	39	NUM
fumecheng-13730	223	3	)	)	PUNCT
fumecheng-13730	223	4	the	the	DET
fumecheng-13730	223	5	exact	exact	ADJ
fumecheng-13730	223	6	one	one	NOUN
fumecheng-13730	223	7	is	be	AUX
fumecheng-13730	223	8	[	[	X
fumecheng-13730	223	9	37	37	NUM
fumecheng-13730	223	10	]	]	SYM
fumecheng-13730	223	11	:	:	PUNCT
fumecheng-13730	223	12	exact	exact	VERB
fumecheng-13730	223	13	1.2533	1.2533	NUM
fumecheng-13730	223	14	=	=	PUNCT
fumecheng-13730	223	15	a	a	DET
fumecheng-13730	223	16			X
fumecheng-13730	223	17	.	.	PUNCT
fumecheng-13730	224	1	(	(	PUNCT
fumecheng-13730	224	2	40	40	NUM
fumecheng-13730	224	3	)	)	PUNCT
fumecheng-13730	224	4	the	the	DET
fumecheng-13730	224	5	relative	relative	ADJ
fumecheng-13730	224	6	error	error	NOUN
fumecheng-13730	224	7	is	be	AUX
fumecheng-13730	224	8	2.28	2.28	NUM
fumecheng-13730	224	9	%	%	NOUN
fumecheng-13730	224	10	.	.	PUNCT
fumecheng-13730	225	1	the	the	DET
fumecheng-13730	225	2	singularity	singularity	NOUN
fumecheng-13730	225	3	presents	present	VERB
fumecheng-13730	225	4	a	a	DET
fumecheng-13730	225	5	challenge	challenge	NOUN
fumecheng-13730	225	6	for	for	ADP
fumecheng-13730	225	7	both	both	CCONJ
fumecheng-13730	225	8	analytical	analytical	ADJ
fumecheng-13730	225	9	and	and	CCONJ
fumecheng-13730	225	10	numerical	numerical	ADJ
fumecheng-13730	225	11	methods	method	NOUN
fumecheng-13730	225	12	.	.	PUNCT
fumecheng-13730	226	1	however	however	ADV
fumecheng-13730	226	2	,	,	PUNCT
fumecheng-13730	226	3	the	the	DET
fumecheng-13730	226	4	one	one	NUM
fumecheng-13730	226	5	-	-	PUNCT
fumecheng-13730	226	6	step	step	NOUN
fumecheng-13730	226	7	frequency	frequency	NOUN
fumecheng-13730	226	8	formulation	formulation	NOUN
fumecheng-13730	226	9	offers	offer	VERB
fumecheng-13730	226	10	a	a	DET
fumecheng-13730	226	11	solution	solution	NOUN
fumecheng-13730	226	12	that	that	PRON
fumecheng-13730	226	13	produces	produce	VERB
fumecheng-13730	226	14	optimal	optimal	ADJ
fumecheng-13730	226	15	results	result	NOUN
fumecheng-13730	226	16	with	with	ADP
fumecheng-13730	226	17	minimal	minimal	ADJ
fumecheng-13730	226	18	calculation	calculation	NOUN
fumecheng-13730	226	19	.	.	PUNCT
fumecheng-13730	227	1	4.5	4.5	NUM
fumecheng-13730	227	2	.	.	PUNCT
fumecheng-13730	227	3	example	example	NOUN
fumecheng-13730	227	4	5	5	NUM
fumecheng-13730	227	5	.	.	PUNCT
fumecheng-13730	227	6	nonlinear	nonlinear	ADJ
fumecheng-13730	227	7	oscillator	oscillator	NOUN
fumecheng-13730	227	8	with	with	ADP
fumecheng-13730	227	9	fraction	fraction	NOUN
fumecheng-13730	227	10	term	term	NOUN
fumecheng-13730	227	11	the	the	DET
fumecheng-13730	227	12	study	study	NOUN
fumecheng-13730	227	13	of	of	ADP
fumecheng-13730	227	14	nonlinear	nonlinear	ADJ
fumecheng-13730	227	15	oscillators	oscillator	NOUN
fumecheng-13730	227	16	with	with	ADP
fumecheng-13730	227	17	fraction	fraction	NOUN
fumecheng-13730	227	18	terms	term	NOUN
fumecheng-13730	227	19	represents	represent	VERB
fumecheng-13730	227	20	a	a	DET
fumecheng-13730	227	21	fascinating	fascinating	ADJ
fumecheng-13730	227	22	and	and	CCONJ
fumecheng-13730	227	23	promising	promising	ADJ
fumecheng-13730	227	24	area	area	NOUN
fumecheng-13730	227	25	of	of	ADP
fumecheng-13730	227	26	mathematical	mathematical	ADJ
fumecheng-13730	227	27	inquiry	inquiry	NOUN
fumecheng-13730	227	28	.	.	PUNCT
fumecheng-13730	228	1	it	it	PRON
fumecheng-13730	228	2	presents	present	VERB
fumecheng-13730	228	3	a	a	DET
fumecheng-13730	228	4	challenge	challenge	NOUN
fumecheng-13730	228	5	to	to	ADP
fumecheng-13730	228	6	traditional	traditional	ADJ
fumecheng-13730	228	7	analytical	analytical	ADJ
fumecheng-13730	228	8	methods	method	NOUN
fumecheng-13730	228	9	,	,	PUNCT
fumecheng-13730	228	10	as	as	SCONJ
fumecheng-13730	228	11	it	it	PRON
fumecheng-13730	228	12	may	may	AUX
fumecheng-13730	228	13	not	not	PART
fumecheng-13730	228	14	conform	conform	VERB
fumecheng-13730	228	15	to	to	ADP
fumecheng-13730	228	16	the	the	DET
fumecheng-13730	228	17	standard	standard	ADJ
fumecheng-13730	228	18	mathematical	mathematical	ADJ
fumecheng-13730	228	19	models	model	NOUN
fumecheng-13730	228	20	that	that	PRON
fumecheng-13730	228	21	are	be	AUX
fumecheng-13730	228	22	typically	typically	ADV
fumecheng-13730	228	23	employed	employ	VERB
fumecheng-13730	228	24	.	.	PUNCT
fumecheng-13730	229	1	researchers	researcher	NOUN
fumecheng-13730	229	2	employ	employ	VERB
fumecheng-13730	229	3	sophisticated	sophisticated	ADJ
fumecheng-13730	229	4	techniques	technique	NOUN
fumecheng-13730	229	5	to	to	PART
fumecheng-13730	229	6	comprehend	comprehend	VERB
fumecheng-13730	229	7	and	and	CCONJ
fumecheng-13730	229	8	anticipate	anticipate	VERB
fumecheng-13730	229	9	the	the	DET
fumecheng-13730	229	10	behavior	behavior	NOUN
fumecheng-13730	229	11	of	of	ADP
fumecheng-13730	229	12	these	these	DET
fumecheng-13730	229	13	oscillators	oscillator	NOUN
fumecheng-13730	229	14	.	.	PUNCT
fumecheng-13730	230	1	consider	consider	VERB
fumecheng-13730	230	2	the	the	DET
fumecheng-13730	230	3	following	follow	VERB
fumecheng-13730	230	4	nonlinear	nonlinear	ADJ
fumecheng-13730	230	5	oscillator	oscillator	NOUN
fumecheng-13730	230	6	with	with	ADP
fumecheng-13730	230	7	a	a	DET
fumecheng-13730	230	8	fraction	fraction	NOUN
fumecheng-13730	230	9	term	term	NOUN
fumecheng-13730	230	10	:	:	PUNCT
fumecheng-13730	230	11	2	2	NUM
fumecheng-13730	230	12	0	0	NUM
fumecheng-13730	230	13	2	2	NUM
fumecheng-13730	230	14	1	1	NUM
fumecheng-13730	230	15	0	0	NUM
fumecheng-13730	230	16	n	n	CCONJ
fumecheng-13730	230	17	n	n	CCONJ
fumecheng-13730	230	18	n	n	CCONJ
fumecheng-13730	230	19	n	n	CCONJ
fumecheng-13730	230	20	u	u	NOUN
fumecheng-13730	230	21	u	u	NOUN
fumecheng-13730	230	22	c	c	NOUN
fumecheng-13730	230	23	c	c	NOUN
fumecheng-13730	230	24	u	u	X
fumecheng-13730	230	25	=	=	PUNCT
fumecheng-13730	230	26			PROPN
fumecheng-13730	230	27	+	+	SYM
fumecheng-13730	230	28	=	=	SYM
fumecheng-13730	230	29	+	+	ADJ
fumecheng-13730	230	30			X
fumecheng-13730	230	31	.	.	PUNCT
fumecheng-13730	231	1	(	(	PUNCT
fumecheng-13730	231	2	41	41	NUM
fumecheng-13730	231	3	)	)	PUNCT
fumecheng-13730	231	4	in	in	ADP
fumecheng-13730	231	5	order	order	NOUN
fumecheng-13730	231	6	to	to	PART
fumecheng-13730	231	7	utilize	utilize	VERB
fumecheng-13730	231	8	the	the	DET
fumecheng-13730	231	9	aforementioned	aforementioned	ADJ
fumecheng-13730	231	10	frequency	frequency	NOUN
fumecheng-13730	231	11	formulation	formulation	NOUN
fumecheng-13730	231	12	,	,	PUNCT
fumecheng-13730	231	13	we	we	PRON
fumecheng-13730	231	14	assume	assume	VERB
fumecheng-13730	231	15	that	that	SCONJ
fumecheng-13730	231	16	a	a	PRON
fumecheng-13730	231	17	tends	tend	VERB
fumecheng-13730	231	18	to	to	PART
fumecheng-13730	231	19	infinity	infinity	VERB
fumecheng-13730	231	20	.	.	PUNCT
fumecheng-13730	232	1	under	under	ADP
fumecheng-13730	232	2	this	this	DET
fumecheng-13730	232	3	assumption	assumption	NOUN
fumecheng-13730	232	4	,	,	PUNCT
fumecheng-13730	232	5	eq	eq	NOUN
fumecheng-13730	232	6	.	.	PUNCT
fumecheng-13730	233	1	(	(	PUNCT
fumecheng-13730	233	2	41	41	NUM
fumecheng-13730	233	3	)	)	PUNCT
fumecheng-13730	233	4	becomes	become	VERB
fumecheng-13730	233	5	:	:	PUNCT
fumecheng-13730	233	6	1	1	NUM
fumecheng-13730	233	7	2	2	NUM
fumecheng-13730	233	8	2	2	NUM
fumecheng-13730	233	9	1	1	NUM
fumecheng-13730	233	10	0	0	NUM
fumecheng-13730	233	11	n	n	CCONJ
fumecheng-13730	233	12	n	n	CCONJ
fumecheng-13730	233	13	n	n	CCONJ
fumecheng-13730	233	14	n	n	CCONJ
fumecheng-13730	233	15	u	u	NOUN
fumecheng-13730	233	16	c	c	NOUN
fumecheng-13730	233	17	u	u	NOUN
fumecheng-13730	233	18	−	−	NOUN
fumecheng-13730	233	19	=	=	SYM
fumecheng-13730	233	20			PROPN
fumecheng-13730	233	21	+	+	CCONJ
fumecheng-13730	233	22	=	=	NOUN
fumecheng-13730	233	23			X
fumecheng-13730	233	24	.	.	PUNCT
fumecheng-13730	234	1	(	(	PUNCT
fumecheng-13730	234	2	42	42	X
fumecheng-13730	234	3	)	)	PUNCT
fumecheng-13730	234	4	its	its	PRON
fumecheng-13730	234	5	frequency	frequency	NOUN
fumecheng-13730	234	6	-	-	PUNCT
fumecheng-13730	234	7	amplitude	amplitude	NOUN
fumecheng-13730	234	8	relationship	relationship	NOUN
fumecheng-13730	234	9	is	be	AUX
fumecheng-13730	234	10	2	2	NUM
fumecheng-13730	234	11	2	2	NUM
fumecheng-13730	234	12	2	2	NUM
fumecheng-13730	234	13	2	2	NUM
fumecheng-13730	234	14	2	2	NUM
fumecheng-13730	234	15	1	1	NUM
fumecheng-13730	234	16	1	1	NUM
fumecheng-13730	234	17	6	6	NUM
fumecheng-13730	234	18	3	3	NUM
fumecheng-13730	234	19	1	1	NUM
fumecheng-13730	234	20	2	2	NUM
fumecheng-13730	234	21	5	5	NUM
fumecheng-13730	234	22	3	3	NUM
fumecheng-13730	234	23	n	n	CCONJ
fumecheng-13730	234	24	n	n	CCONJ
fumecheng-13730	234	25	n	n	CCONJ
fumecheng-13730	234	26	n	n	CCONJ
fumecheng-13730	234	27	n	n	CCONJ
fumecheng-13730	234	28	n	n	CCONJ
fumecheng-13730	234	29	n	n	CCONJ
fumecheng-13730	234	30	n	n	PROPN
fumecheng-13730	234	31	b	b	PROPN
fumecheng-13730	234	32	a	a	DET
fumecheng-13730	234	33	b	b	NOUN
fumecheng-13730	234	34	a	a	DET
fumecheng-13730	234	35	n	n	CCONJ
fumecheng-13730	234	36	n	n	ADV
fumecheng-13730	234	37	−	−	NOUN
fumecheng-13730	234	38	−	−	PROPN
fumecheng-13730	235	1	=	=	PUNCT
fumecheng-13730	235	2	=	=	PUNCT
fumecheng-13730	235	3	=	=	PUNCT
fumecheng-13730	235	4	=	=	PUNCT
fumecheng-13730	236	1	−	−	PROPN
fumecheng-13730	237	1	+	+	CCONJ
fumecheng-13730	237	2	−	−	X
fumecheng-13730	237	3			X
fumecheng-13730	237	4			PROPN
fumecheng-13730	237	5	(	(	PUNCT
fumecheng-13730	237	6	43	43	NUM
fumecheng-13730	237	7	)	)	PUNCT
fumecheng-13730	237	8	for	for	ADP
fumecheng-13730	237	9	eq	eq	PROPN
fumecheng-13730	237	10	.	.	PUNCT
fumecheng-13730	238	1	(	(	PUNCT
fumecheng-13730	238	2	42	42	NUM
fumecheng-13730	238	3	)	)	PUNCT
fumecheng-13730	238	4	the	the	DET
fumecheng-13730	238	5	frequency	frequency	NOUN
fumecheng-13730	238	6	formulation	formulation	NOUN
fumecheng-13730	238	7	should	should	AUX
fumecheng-13730	238	8	be	be	AUX
fumecheng-13730	238	9	modified	modify	VERB
fumecheng-13730	238	10	as	as	ADP
fumecheng-13730	238	11	:	:	SYM
fumecheng-13730	238	12	2	2	NUM
fumecheng-13730	238	13	2	2	NUM
fumecheng-13730	238	14	0	0	NUM
fumecheng-13730	238	15	2	2	NUM
fumecheng-13730	238	16	1	1	NUM
fumecheng-13730	238	17	1	1	NUM
fumecheng-13730	238	18	3	3	NUM
fumecheng-13730	238	19	3	3	NUM
fumecheng-13730	238	20	n	n	CCONJ
fumecheng-13730	238	21	n	n	CCONJ
fumecheng-13730	238	22	n	n	CCONJ
fumecheng-13730	238	23	n	n	CCONJ
fumecheng-13730	238	24	n	n	PROPN
fumecheng-13730	238	25	c	c	PROPN
fumecheng-13730	238	26	b	b	PROPN
fumecheng-13730	238	27	a	a	PRON
fumecheng-13730	238	28	=	=	SYM
fumecheng-13730	238	29	=	=	SYM
fumecheng-13730	239	1	−	−	PROPN
fumecheng-13730	240	1	+	+	NOUN
fumecheng-13730	240	2			X
fumecheng-13730	240	3			X
fumecheng-13730	240	4	.	.	PUNCT
fumecheng-13730	241	1	(	(	PUNCT
fumecheng-13730	241	2	44	44	NUM
fumecheng-13730	241	3	)	)	PUNCT
fumecheng-13730	241	4	a	a	DET
fumecheng-13730	241	5	modified	modify	VERB
fumecheng-13730	241	6	frequency	frequency	NOUN
fumecheng-13730	241	7	formulation	formulation	NOUN
fumecheng-13730	241	8	for	for	ADP
fumecheng-13730	241	9	nonlinear	nonlinear	ADJ
fumecheng-13730	241	10	mechanical	mechanical	ADJ
fumecheng-13730	241	11	vibrations	vibration	NOUN
fumecheng-13730	241	12	207	207	NUM
fumecheng-13730	241	13	in	in	ADP
fumecheng-13730	241	14	this	this	DET
fumecheng-13730	241	15	modification	modification	NOUN
fumecheng-13730	241	16	,	,	PUNCT
fumecheng-13730	241	17	the	the	DET
fumecheng-13730	241	18	case	case	NOUN
fumecheng-13730	241	19	of	of	ADP
fumecheng-13730	241	20	c0=0	c0=0	PROPN
fumecheng-13730	241	21	and	and	CCONJ
fumecheng-13730	241	22	n=1	n=1	PROPN
fumecheng-13730	241	23	can	can	AUX
fumecheng-13730	241	24	be	be	AUX
fumecheng-13730	241	25	transformed	transform	VERB
fumecheng-13730	241	26	into	into	ADP
fumecheng-13730	241	27	the	the	DET
fumecheng-13730	241	28	form	form	NOUN
fumecheng-13730	241	29	of	of	ADP
fumecheng-13730	241	30	eq	eq	PROPN
fumecheng-13730	241	31	.	.	PUNCT
fumecheng-13730	242	1	(	(	PUNCT
fumecheng-13730	242	2	44	44	NUM
fumecheng-13730	242	3	)	)	PUNCT
fumecheng-13730	242	4	.	.	PUNCT
fumecheng-13730	243	1	so	so	ADV
fumecheng-13730	243	2	it	it	PRON
fumecheng-13730	243	3	is	be	AUX
fumecheng-13730	243	4	suitable	suitable	ADJ
fumecheng-13730	243	5	for	for	ADP
fumecheng-13730	243	6	large	large	ADJ
fumecheng-13730	243	7	amplitude	amplitude	NOUN
fumecheng-13730	243	8	oscillation	oscillation	NOUN
fumecheng-13730	243	9	.	.	PUNCT
fumecheng-13730	244	1	in	in	ADP
fumecheng-13730	244	2	order	order	NOUN
fumecheng-13730	244	3	to	to	PART
fumecheng-13730	244	4	show	show	VERB
fumecheng-13730	244	5	its	its	PRON
fumecheng-13730	244	6	effectiveness	effectiveness	NOUN
fumecheng-13730	244	7	,	,	PUNCT
fumecheng-13730	244	8	we	we	PRON
fumecheng-13730	244	9	consider	consider	VERB
fumecheng-13730	244	10	a	a	DET
fumecheng-13730	244	11	simple	simple	ADJ
fumecheng-13730	244	12	case	case	NOUN
fumecheng-13730	244	13	:	:	PUNCT
fumecheng-13730	244	14	2	2	NUM
fumecheng-13730	244	15	0	0	NUM
fumecheng-13730	244	16	1	1	NUM
fumecheng-13730	244	17	u	u	NOUN
fumecheng-13730	244	18	u	u	NOUN
fumecheng-13730	244	19	u	u	NOUN
fumecheng-13730	244	20			PROPN
fumecheng-13730	244	21	+	+	CCONJ
fumecheng-13730	244	22	=	=	SYM
fumecheng-13730	245	1	+	+	CCONJ
fumecheng-13730	245	2	.	.	PUNCT
fumecheng-13730	246	1	(	(	PUNCT
fumecheng-13730	246	2	45	45	NUM
fumecheng-13730	246	3	)	)	PUNCT
fumecheng-13730	246	4	by	by	ADP
fumecheng-13730	246	5	the	the	DET
fumecheng-13730	246	6	frequency	frequency	NOUN
fumecheng-13730	246	7	formulation	formulation	NOUN
fumecheng-13730	246	8	of	of	ADP
fumecheng-13730	246	9	eq	eq	PROPN
fumecheng-13730	246	10	.	.	PUNCT
fumecheng-13730	247	1	(	(	PUNCT
fumecheng-13730	247	2	45	45	NUM
fumecheng-13730	247	3	)	)	PUNCT
fumecheng-13730	247	4	,	,	PUNCT
fumecheng-13730	247	5	the	the	DET
fumecheng-13730	247	6	following	following	ADJ
fumecheng-13730	247	7	result	result	NOUN
fumecheng-13730	247	8	is	be	AUX
fumecheng-13730	247	9	obtained	obtain	VERB
fumecheng-13730	247	10	:	:	PUNCT
fumecheng-13730	247	11	2	2	NUM
fumecheng-13730	247	12	1	1	NUM
fumecheng-13730	247	13	2	2	NUM
fumecheng-13730	247	14	1	1	NUM
fumecheng-13730	247	15	3	3	NUM
fumecheng-13730	247	16	a	a	PRON
fumecheng-13730	247	17	=	=	PUNCT
fumecheng-13730	248	1	+	+	CCONJ
fumecheng-13730	248	2			X
fumecheng-13730	248	3	.	.	PUNCT
fumecheng-13730	249	1	(	(	PUNCT
fumecheng-13730	249	2	46	46	NUM
fumecheng-13730	249	3	)	)	PUNCT
fumecheng-13730	249	4	the	the	DET
fumecheng-13730	249	5	exact	exact	ADJ
fumecheng-13730	249	6	period	period	NOUN
fumecheng-13730	249	7	can	can	AUX
fumecheng-13730	249	8	be	be	AUX
fumecheng-13730	249	9	calculated	calculate	VERB
fumecheng-13730	249	10	as	as	ADP
fumecheng-13730	249	11	:	:	SYM
fumecheng-13730	249	12	0	0	NUM
fumecheng-13730	249	13	2	2	NUM
fumecheng-13730	249	14	2	2	NUM
fumecheng-13730	249	15	1	1	NUM
fumecheng-13730	249	16	4	4	NUM
fumecheng-13730	249	17	ln(1	ln(1	NOUN
fumecheng-13730	249	18	)	)	PUNCT
fumecheng-13730	249	19	ln(1	ln(1	NOUN
fumecheng-13730	249	20	)	)	PUNCT
fumecheng-13730	249	21	a	a	DET
fumecheng-13730	249	22	t	t	X
fumecheng-13730	249	23	du	du	NOUN
fumecheng-13730	249	24	a	a	DET
fumecheng-13730	249	25	u	u	NOUN
fumecheng-13730	249	26	=	=	X
fumecheng-13730	250	1	+	+	NUM
fumecheng-13730	250	2	−	−	PROPN
fumecheng-13730	251	1	+	+	CCONJ
fumecheng-13730	251	2			X
fumecheng-13730	251	3	.	.	PUNCT
fumecheng-13730	252	1	(	(	PUNCT
fumecheng-13730	252	2	47	47	NUM
fumecheng-13730	252	3	)	)	PUNCT
fumecheng-13730	252	4	for	for	ADP
fumecheng-13730	252	5	the	the	DET
fumecheng-13730	252	6	case	case	NOUN
fumecheng-13730	252	7	a	a	DET
fumecheng-13730	252	8	tends	tend	VERB
fumecheng-13730	252	9	to	to	PART
fumecheng-13730	252	10	infinity	infinity	VERB
fumecheng-13730	252	11	,	,	PUNCT
fumecheng-13730	252	12	we	we	PRON
fumecheng-13730	252	13	have	have	VERB
fumecheng-13730	252	14	:	:	PUNCT
fumecheng-13730	252	15	0	0	NUM
fumecheng-13730	252	16	2	2	NUM
fumecheng-13730	252	17	2	2	NUM
fumecheng-13730	252	18	0	0	NUM
fumecheng-13730	252	19	2	2	NUM
fumecheng-13730	252	20	2	2	NUM
fumecheng-13730	252	21	1	1	NUM
fumecheng-13730	252	22	lim	lim	PROPN
fumecheng-13730	252	23	4	4	NUM
fumecheng-13730	253	1	lim	lim	PROPN
fumecheng-13730	253	2	ln(1	ln(1	PROPN
fumecheng-13730	253	3	)	)	PUNCT
fumecheng-13730	253	4	ln(1	ln(1	NOUN
fumecheng-13730	253	5	)	)	PUNCT
fumecheng-13730	253	6	1	1	NUM
fumecheng-13730	253	7	4	4	NUM
fumecheng-13730	253	8	2	2	NUM
fumecheng-13730	253	9	2	2	NUM
fumecheng-13730	253	10	ln	ln	ADJ
fumecheng-13730	253	11	(	(	PUNCT
fumecheng-13730	253	12	)	)	PUNCT
fumecheng-13730	253	13	ln	ln	ADJ
fumecheng-13730	253	14	(	(	PUNCT
fumecheng-13730	253	15	)	)	PUNCT
fumecheng-13730	253	16	a	a	DET
fumecheng-13730	253	17	a	a	DET
fumecheng-13730	253	18	a	a	DET
fumecheng-13730	253	19	a	a	DET
fumecheng-13730	253	20	t	t	X
fumecheng-13730	253	21	du	du	NOUN
fumecheng-13730	253	22	a	a	DET
fumecheng-13730	253	23	u	u	X
fumecheng-13730	253	24	du	du	PROPN
fumecheng-13730	253	25	a	a	DET
fumecheng-13730	253	26	a	a	DET
fumecheng-13730	253	27	u	u	NOUN
fumecheng-13730	253	28	→	→	PUNCT
fumecheng-13730	253	29	→	→	PUNCT
fumecheng-13730	253	30	=	=	NOUN
fumecheng-13730	254	1	+	+	CCONJ
fumecheng-13730	254	2	−	−	PROPN
fumecheng-13730	254	3	+	+	NOUN
fumecheng-13730	254	4	=	=	SYM
fumecheng-13730	254	5	=	=	SYM
fumecheng-13730	254	6	−	−	NOUN
fumecheng-13730	254	7			X
fumecheng-13730	255	1			X
fumecheng-13730	255	2			PROPN
fumecheng-13730	255	3	(	(	PUNCT
fumecheng-13730	255	4	48	48	NUM
fumecheng-13730	255	5	)	)	PUNCT
fumecheng-13730	255	6	so	so	SCONJ
fumecheng-13730	255	7	we	we	PRON
fumecheng-13730	255	8	have	have	VERB
fumecheng-13730	255	9	:	:	PUNCT
fumecheng-13730	255	10	1	1	NUM
fumecheng-13730	255	11	12	12	NUM
fumecheng-13730	255	12	lim	lim	PROPN
fumecheng-13730	255	13	lim	lim	PROPN
fumecheng-13730	255	14	1.2533	1.2533	NUM
fumecheng-13730	255	15	2	2	NUM
fumecheng-13730	255	16	exact	exact	NOUN
fumecheng-13730	255	17	a	a	DET
fumecheng-13730	255	18	a	a	DET
fumecheng-13730	255	19	a	a	DET
fumecheng-13730	255	20	a	a	DET
fumecheng-13730	255	21	t	t	NOUN
fumecheng-13730	255	22	−	−	NOUN
fumecheng-13730	255	23	−	−	PROPN
fumecheng-13730	255	24	→	→	PUNCT
fumecheng-13730	255	25	→	→	PUNCT
fumecheng-13730	255	26	=	=	NOUN
fumecheng-13730	256	1	=	=	PUNCT
fumecheng-13730	256	2	=	=	PUNCT
fumecheng-13730	256	3			PROPN
fumecheng-13730	256	4			PROPN
fumecheng-13730	256	5			X
fumecheng-13730	256	6	,	,	PUNCT
fumecheng-13730	256	7	(	(	PUNCT
fumecheng-13730	256	8	49	49	NUM
fumecheng-13730	256	9	)	)	PUNCT
fumecheng-13730	256	10	while	while	SCONJ
fumecheng-13730	256	11	from	from	ADP
fumecheng-13730	256	12	eq	eq	NOUN
fumecheng-13730	256	13	.	.	PUNCT
fumecheng-13730	257	1	(	(	PUNCT
fumecheng-13730	257	2	28	28	NUM
fumecheng-13730	257	3	)	)	PUNCT
fumecheng-13730	257	4	,	,	PUNCT
fumecheng-13730	257	5	we	we	PRON
fumecheng-13730	257	6	have	have	VERB
fumecheng-13730	257	7	:	:	PUNCT
fumecheng-13730	257	8	1	1	NUM
fumecheng-13730	257	9	2	2	NUM
fumecheng-13730	257	10	1	1	NUM
fumecheng-13730	257	11	l	l	NOUN
fumecheng-13730	257	12	4im	4im	NOUN
fumecheng-13730	257	13	1.22	1.22	NUM
fumecheng-13730	257	14	2	2	NUM
fumecheng-13730	257	15	3	3	NUM
fumecheng-13730	257	16	7	7	NUM
fumecheng-13730	257	17	a	a	PRON
fumecheng-13730	257	18	a	a	DET
fumecheng-13730	257	19	a	a	DET
fumecheng-13730	257	20	−	−	NOUN
fumecheng-13730	257	21	→	→	PUNCT
fumecheng-13730	257	22	=	=	PUNCT
fumecheng-13730	258	1	=	=	NOUN
fumecheng-13730	258	2			X
fumecheng-13730	258	3	.	.	PUNCT
fumecheng-13730	259	1	(	(	PUNCT
fumecheng-13730	259	2	50	50	NUM
fumecheng-13730	259	3	)	)	PUNCT
fumecheng-13730	259	4	the	the	DET
fumecheng-13730	259	5	relative	relative	ADJ
fumecheng-13730	259	6	error	error	NOUN
fumecheng-13730	259	7	is	be	AUX
fumecheng-13730	259	8	2.28	2.28	NUM
fumecheng-13730	259	9	%	%	NOUN
fumecheng-13730	259	10	.	.	PUNCT
fumecheng-13730	260	1	it	it	PRON
fumecheng-13730	260	2	should	should	AUX
fumecheng-13730	260	3	be	be	AUX
fumecheng-13730	260	4	note	note	VERB
fumecheng-13730	260	5	that	that	SCONJ
fumecheng-13730	260	6	eq	eq	ADP
fumecheng-13730	260	7	.	.	PUNCT
fumecheng-13730	261	1	(	(	PUNCT
fumecheng-13730	261	2	48	48	NUM
fumecheng-13730	261	3	)	)	PUNCT
fumecheng-13730	261	4	is	be	AUX
fumecheng-13730	261	5	valid	valid	ADJ
fumecheng-13730	261	6	for	for	ADP
fumecheng-13730	261	7	large	large	ADJ
fumecheng-13730	261	8	amplitude	amplitude	NOUN
fumecheng-13730	261	9	.	.	PUNCT
fumecheng-13730	262	1	for	for	ADP
fumecheng-13730	262	2	the	the	DET
fumecheng-13730	262	3	small	small	ADJ
fumecheng-13730	262	4	values	value	NOUN
fumecheng-13730	262	5	of	of	ADP
fumecheng-13730	262	6	a	a	DET
fumecheng-13730	262	7	,	,	PUNCT
fumecheng-13730	262	8	eq	eq	NOUN
fumecheng-13730	262	9	.	.	PUNCT
fumecheng-13730	262	10	(	(	PUNCT
fumecheng-13730	262	11	46	46	NUM
fumecheng-13730	262	12	)	)	PUNCT
fumecheng-13730	262	13	can	can	AUX
fumecheng-13730	262	14	be	be	AUX
fumecheng-13730	262	15	approximated	approximate	VERB
fumecheng-13730	262	16	as	as	ADP
fumecheng-13730	262	17	:	:	PUNCT
fumecheng-13730	262	18	3	3	NUM
fumecheng-13730	262	19	0u	0u	ADJ
fumecheng-13730	262	20	u	u	NOUN
fumecheng-13730	262	21	u	u	PROPN
fumecheng-13730	262	22	+	+	CCONJ
fumecheng-13730	262	23	−	−	PROPN
fumecheng-13730	262	24	=	=	X
fumecheng-13730	262	25	.	.	PUNCT
fumecheng-13730	263	1	(	(	PUNCT
fumecheng-13730	263	2	51	51	NUM
fumecheng-13730	263	3	)	)	PUNCT
fumecheng-13730	263	4	by	by	ADP
fumecheng-13730	263	5	the	the	DET
fumecheng-13730	263	6	frequency	frequency	NOUN
fumecheng-13730	263	7	formulation	formulation	NOUN
fumecheng-13730	263	8	given	give	VERB
fumecheng-13730	263	9	in	in	ADP
fumecheng-13730	263	10	eq	eq	ADP
fumecheng-13730	263	11	.	.	PUNCT
fumecheng-13730	264	1	(	(	PUNCT
fumecheng-13730	264	2	2	2	NUM
fumecheng-13730	264	3	)	)	PUNCT
fumecheng-13730	264	4	,	,	PUNCT
fumecheng-13730	264	5	we	we	PRON
fumecheng-13730	264	6	have	have	VERB
fumecheng-13730	264	7	:	:	PUNCT
fumecheng-13730	264	8	2	2	NUM
fumecheng-13730	264	9	2	2	NUM
fumecheng-13730	264	10	23	23	NUM
fumecheng-13730	264	11	3	3	NUM
fumecheng-13730	264	12	1	1	NUM
fumecheng-13730	264	13	1	1	NUM
fumecheng-13730	264	14	(	(	PUNCT
fumecheng-13730	264	15	)	)	PUNCT
fumecheng-13730	264	16	2	2	NUM
fumecheng-13730	264	17	4	4	NUM
fumecheng-13730	264	18	a	a	PRON
fumecheng-13730	264	19	a	a	DET
fumecheng-13730	264	20	o	o	NOUN
fumecheng-13730	264	21	a=	a=	NOUN
fumecheng-13730	264	22	−	−	NOUN
fumecheng-13730	265	1	=	=	PUNCT
fumecheng-13730	266	1	−	−	PROPN
fumecheng-13730	267	1	+	+	ADV
fumecheng-13730	267	2			X
fumecheng-13730	267	3	.	.	PUNCT
fumecheng-13730	268	1	(	(	PUNCT
fumecheng-13730	268	2	52	52	NUM
fumecheng-13730	268	3	)	)	PUNCT
fumecheng-13730	268	4	considering	consider	VERB
fumecheng-13730	268	5	eqs	eqs	PROPN
fumecheng-13730	268	6	.	.	PUNCT
fumecheng-13730	269	1	(	(	PUNCT
fumecheng-13730	269	2	48	48	NUM
fumecheng-13730	269	3	)	)	PUNCT
fumecheng-13730	269	4	and	and	CCONJ
fumecheng-13730	269	5	(	(	PUNCT
fumecheng-13730	269	6	49	49	NUM
fumecheng-13730	269	7	)	)	PUNCT
fumecheng-13730	269	8	,	,	PUNCT
fumecheng-13730	269	9	we	we	PRON
fumecheng-13730	269	10	recommend	recommend	VERB
fumecheng-13730	269	11	the	the	DET
fumecheng-13730	269	12	following	follow	VERB
fumecheng-13730	269	13	matching	match	VERB
fumecheng-13730	269	14	one	one	NUM
fumecheng-13730	269	15	:	:	SYM
fumecheng-13730	269	16	2	2	NUM
fumecheng-13730	269	17	1	1	NUM
fumecheng-13730	269	18	2	2	NUM
fumecheng-13730	269	19	3(1	3(1	NUM
fumecheng-13730	269	20	)	)	PUNCT
fumecheng-13730	269	21	1	1	NUM
fumecheng-13730	269	22	3	3	NUM
fumecheng-13730	269	23	2(1	2(1	NUM
fumecheng-13730	269	24	)	)	PUNCT
fumecheng-13730	270	1	m	m	VERB
fumecheng-13730	270	2	m	m	VERB
fumecheng-13730	270	3	a	a	PRON
fumecheng-13730	270	4	m	m	NOUN
fumecheng-13730	270	5	m	m	NOUN
fumecheng-13730	270	6	=	=	ADJ
fumecheng-13730	271	1	+	+	CCONJ
fumecheng-13730	271	2	−	−	PROPN
fumecheng-13730	272	1	+	+	CCONJ
fumecheng-13730	273	1	+	+	CCONJ
fumecheng-13730	273	2	−	−	PROPN
fumecheng-13730	273	3			X
fumecheng-13730	273	4	,	,	PUNCT
fumecheng-13730	273	5	(	(	PUNCT
fumecheng-13730	273	6	53	53	NUM
fumecheng-13730	273	7	)	)	PUNCT
fumecheng-13730	273	8	208	208	NUM
fumecheng-13730	273	9	c.h	c.h	NOUN
fumecheng-13730	273	10	.	.	PUNCT
fumecheng-13730	274	1	he	he	PRON
fumecheng-13730	274	2	,	,	PUNCT
fumecheng-13730	274	3	j.h	j.h	PROPN
fumecheng-13730	274	4	.	.	PUNCT
fumecheng-13730	275	1	he	he	PRON
fumecheng-13730	275	2	,	,	PUNCT
fumecheng-13730	275	3	j.	j.	PROPN
fumecheng-13730	275	4	ma	ma	PROPN
fumecheng-13730	275	5	,	,	PUNCT
fumecheng-13730	275	6	a.a	a.a	PROPN
fumecheng-13730	275	7	.	.	PROPN
fumecheng-13730	275	8	alsolam	alsolam	PROPN
fumecheng-13730	275	9	,	,	PUNCT
fumecheng-13730	275	10	x.j	x.j	PROPN
fumecheng-13730	275	11	.	.	PROPN
fumecheng-13730	275	12	yang	yang	PROPN
fumecheng-13730	275	13	where	where	SCONJ
fumecheng-13730	275	14	m	m	PROPN
fumecheng-13730	275	15	is	be	AUX
fumecheng-13730	275	16	the	the	DET
fumecheng-13730	275	17	weighting	weighting	NOUN
fumecheng-13730	275	18	factor	factor	NOUN
fumecheng-13730	275	19	,	,	PUNCT
fumecheng-13730	275	20	m=0	m=0	PROPN
fumecheng-13730	275	21	for	for	ADP
fumecheng-13730	275	22	a<1	a<1	NOUN
fumecheng-13730	275	23	and	and	CCONJ
fumecheng-13730	275	24	m=1	m=1	PROPN
fumecheng-13730	275	25	for	for	ADP
fumecheng-13730	275	26	a>1	a>1	ADJ
fumecheng-13730	275	27	,	,	PUNCT
fumecheng-13730	275	28	and	and	CCONJ
fumecheng-13730	275	29	the	the	DET
fumecheng-13730	275	30	value	value	NOUN
fumecheng-13730	275	31	of	of	ADP
fumecheng-13730	275	32	m	m	PROPN
fumecheng-13730	275	33	can	can	AUX
fumecheng-13730	275	34	be	be	AUX
fumecheng-13730	275	35	determined	determine	VERB
fumecheng-13730	275	36	by	by	ADP
fumecheng-13730	275	37	matching	match	VERB
fumecheng-13730	275	38	eq	eq	ADP
fumecheng-13730	275	39	.	.	PUNCT
fumecheng-13730	276	1	(	(	PUNCT
fumecheng-13730	276	2	53	53	NUM
fumecheng-13730	276	3	)	)	PUNCT
fumecheng-13730	276	4	with	with	ADP
fumecheng-13730	276	5	the	the	DET
fumecheng-13730	276	6	exact	exact	ADJ
fumecheng-13730	276	7	one	one	NOUN
fumecheng-13730	276	8	when	when	SCONJ
fumecheng-13730	276	9	a=1	a=1	X
fumecheng-13730	276	10	.	.	PUNCT
fumecheng-13730	277	1	now	now	ADV
fumecheng-13730	277	2	this	this	DET
fumecheng-13730	277	3	paper	paper	NOUN
fumecheng-13730	277	4	challenges	challenge	VERB
fumecheng-13730	277	5	the	the	DET
fumecheng-13730	277	6	following	following	ADJ
fumecheng-13730	277	7	nonlinear	nonlinear	ADJ
fumecheng-13730	277	8	oscillators	oscillator	NOUN
fumecheng-13730	277	9	:	:	PUNCT
fumecheng-13730	277	10	1/3	1/3	NUM
fumecheng-13730	277	11	1/5	1/5	NUM
fumecheng-13730	277	12	3	3	NUM
fumecheng-13730	277	13	5	5	NUM
fumecheng-13730	277	14	1	1	NUM
fumecheng-13730	277	15	2	2	NUM
fumecheng-13730	277	16	3	3	NUM
fumecheng-13730	277	17	4	4	NUM
fumecheng-13730	277	18	5sgn	5sgn	NUM
fumecheng-13730	277	19	(	(	PUNCT
fumecheng-13730	277	20	)	)	PUNCT
fumecheng-13730	277	21	0u	0u	ADJ
fumecheng-13730	277	22	u	u	NOUN
fumecheng-13730	277	23	b	b	X
fumecheng-13730	277	24	u	u	PROPN
fumecheng-13730	277	25	b	b	PROPN
fumecheng-13730	277	26	u	u	PROPN
fumecheng-13730	277	27	b	b	PROPN
fumecheng-13730	277	28	u	u	PROPN
fumecheng-13730	277	29	b	b	PROPN
fumecheng-13730	277	30	u	u	X
fumecheng-13730	277	31	b	b	PROPN
fumecheng-13730	277	32	u	u	PROPN
fumecheng-13730	277	33	+	+	PROPN
fumecheng-13730	278	1	+	+	PUNCT
fumecheng-13730	279	1	+	+	PUNCT
fumecheng-13730	279	2	+	+	PUNCT
fumecheng-13730	279	3	+	+	PUNCT
fumecheng-13730	279	4	+	+	CCONJ
fumecheng-13730	279	5	=	=	NOUN
fumecheng-13730	279	6	,	,	PUNCT
fumecheng-13730	279	7	(	(	PUNCT
fumecheng-13730	279	8	54	54	NUM
fumecheng-13730	279	9	)	)	PUNCT
fumecheng-13730	279	10	with	with	ADP
fumecheng-13730	279	11	arbitrary	arbitrary	ADJ
fumecheng-13730	279	12	initial	initial	ADJ
fumecheng-13730	279	13	conditions	condition	NOUN
fumecheng-13730	279	14	:	:	PUNCT
fumecheng-13730	279	15	(	(	PUNCT
fumecheng-13730	279	16	0	0	NUM
fumecheng-13730	279	17	)	)	PUNCT
fumecheng-13730	279	18	,	,	PUNCT
fumecheng-13730	279	19	(	(	PUNCT
fumecheng-13730	279	20	0)u	0)u	ADP
fumecheng-13730	279	21	u=	u=	ADP
fumecheng-13730	279	22	=	=	NOUN
fumecheng-13730	279	23			NOUN
fumecheng-13730	279	24			NOUN
fumecheng-13730	279	25	.	.	PUNCT
fumecheng-13730	280	1	(	(	PUNCT
fumecheng-13730	280	2	55	55	NUM
fumecheng-13730	280	3	)	)	PUNCT
fumecheng-13730	280	4	and	and	CCONJ
fumecheng-13730	280	5	this	this	DET
fumecheng-13730	280	6	paper	paper	NOUN
fumecheng-13730	280	7	gives	give	VERB
fumecheng-13730	280	8	the	the	DET
fumecheng-13730	280	9	following	following	ADJ
fumecheng-13730	280	10	result	result	NOUN
fumecheng-13730	280	11	without	without	ADP
fumecheng-13730	280	12	proof	proof	NOUN
fumecheng-13730	280	13	:	:	PUNCT
fumecheng-13730	280	14	2	2	NUM
fumecheng-13730	280	15	2/3	2/3	NUM
fumecheng-13730	280	16	4/5	4/5	NUM
fumecheng-13730	280	17	1	1	NUM
fumecheng-13730	280	18	2	2	NUM
fumecheng-13730	280	19	4	4	NUM
fumecheng-13730	280	20	1	1	NUM
fumecheng-13730	280	21	2	2	NUM
fumecheng-13730	280	22	3	3	NUM
fumecheng-13730	280	23	4	4	NUM
fumecheng-13730	280	24	51	51	NUM
fumecheng-13730	280	25	1	1	NUM
fumecheng-13730	280	26	3	3	NUM
fumecheng-13730	280	27	5	5	NUM
fumecheng-13730	280	28	2/3	2/3	NUM
fumecheng-13730	280	29	4/5	4/5	NUM
fumecheng-13730	280	30	1	1	NUM
fumecheng-13730	280	31	2	2	NUM
fumecheng-13730	280	32	4	4	NUM
fumecheng-13730	280	33	1	1	NUM
fumecheng-13730	280	34	2	2	NUM
fumecheng-13730	280	35	3	3	NUM
fumecheng-13730	280	36	4	4	NUM
fumecheng-13730	280	37	5	5	NUM
fumecheng-13730	280	38	6	6	NUM
fumecheng-13730	280	39	6	6	NUM
fumecheng-13730	280	40	6	6	NUM
fumecheng-13730	280	41	3	3	NUM
fumecheng-13730	280	42	3	3	NUM
fumecheng-13730	280	43	1	1	NUM
fumecheng-13730	280	44	5	5	NUM
fumecheng-13730	280	45	5	5	NUM
fumecheng-13730	280	46	0	0	NUM
fumecheng-13730	280	47	5	5	NUM
fumecheng-13730	280	48	2	2	NUM
fumecheng-13730	280	49	2	2	NUM
fumecheng-13730	280	50	2	2	NUM
fumecheng-13730	280	51	4	4	NUM
fumecheng-13730	280	52	9	9	NUM
fumecheng-13730	280	53	15	15	NUM
fumecheng-13730	280	54	6	6	NUM
fumecheng-13730	280	55	3	3	NUM
fumecheng-13730	280	56	1	1	NUM
fumecheng-13730	280	57	1	1	NUM
fumecheng-13730	280	58	8	8	NUM
fumecheng-13730	280	59	13	13	NUM
fumecheng-13730	280	60	5	5	NUM
fumecheng-13730	280	61	4	4	NUM
fumecheng-13730	280	62	2	2	NUM
fumecheng-13730	280	63	b	b	PROPN
fumecheng-13730	280	64	a	a	DET
fumecheng-13730	280	65	b	b	X
fumecheng-13730	280	66	u	u	PROPN
fumecheng-13730	280	67	b	b	PROPN
fumecheng-13730	280	68	a	a	PRON
fumecheng-13730	280	69	b	b	NOUN
fumecheng-13730	280	70	a	a	DET
fumecheng-13730	280	71	b	b	NOUN
fumecheng-13730	280	72	a	a	DET
fumecheng-13730	280	73	b	b	NOUN
fumecheng-13730	280	74	a	a	DET
fumecheng-13730	280	75	b	b	X
fumecheng-13730	280	76	u	u	PROPN
fumecheng-13730	280	77	b	b	PROPN
fumecheng-13730	280	78	a	a	PRON
fumecheng-13730	280	79	b	b	NOUN
fumecheng-13730	280	80	a	a	DET
fumecheng-13730	280	81	b	b	NOUN
fumecheng-13730	280	82	a	a	PRON
fumecheng-13730	280	83	−	−	NOUN
fumecheng-13730	280	84	−	−	NOUN
fumecheng-13730	280	85	−	−	PROPN
fumecheng-13730	280	86	−	−	PROPN
fumecheng-13730	280	87	−	−	NOUN
fumecheng-13730	280	88	−	−	PROPN
fumecheng-13730	281	1	=	=	PUNCT
fumecheng-13730	282	1	+	+	PUNCT
fumecheng-13730	282	2	+	+	PUNCT
fumecheng-13730	282	3	+	+	PUNCT
fumecheng-13730	282	4	+	+	PUNCT
fumecheng-13730	282	5	+	+	PUNCT
fumecheng-13730	282	6	+	+	PUNCT
fumecheng-13730	282	7	+	+	PUNCT
fumecheng-13730	282	8	+	+	PUNCT
fumecheng-13730	282	9	+	+	PUNCT
fumecheng-13730	282	10	+	+	PUNCT
fumecheng-13730	282	11	=	=	X
fumecheng-13730	283	1	+	+	PUNCT
fumecheng-13730	283	2	+	+	PUNCT
fumecheng-13730	283	3	+	+	PUNCT
fumecheng-13730	283	4	+	+	PUNCT
fumecheng-13730	283	5	+	+	CCONJ
fumecheng-13730	283	6			X
fumecheng-13730	283	7	(	(	PUNCT
fumecheng-13730	283	8	56	56	NUM
fumecheng-13730	283	9	)	)	PUNCT
fumecheng-13730	283	10	and	and	CCONJ
fumecheng-13730	283	11	2	2	NUM
fumecheng-13730	283	12	2	2	NUM
fumecheng-13730	283	13	2	2	NUM
fumecheng-13730	283	14	2	2	NUM
fumecheng-13730	283	15	a+	a+	PRON
fumecheng-13730	283	16	=	=	NOUN
fumecheng-13730	283	17			PROPN
fumecheng-13730	283	18			NUM
fumecheng-13730	283	19			X
fumecheng-13730	283	20	.	.	PUNCT
fumecheng-13730	283	21	(	(	PUNCT
fumecheng-13730	283	22	57	57	NUM
fumecheng-13730	283	23	)	)	PUNCT
fumecheng-13730	283	24	5	5	NUM
fumecheng-13730	283	25	.	.	PUNCT
fumecheng-13730	283	26	discussion	discussion	NOUN
fumecheng-13730	283	27	and	and	CCONJ
fumecheng-13730	283	28	conclusion	conclusion	NOUN
fumecheng-13730	283	29	dozens	dozen	NOUN
fumecheng-13730	283	30	of	of	ADP
fumecheng-13730	283	31	research	research	NOUN
fumecheng-13730	283	32	groups	group	NOUN
fumecheng-13730	283	33	around	around	ADP
fumecheng-13730	283	34	the	the	DET
fumecheng-13730	283	35	world	world	NOUN
fumecheng-13730	283	36	are	be	AUX
fumecheng-13730	283	37	engaged	engage	VERB
fumecheng-13730	283	38	in	in	ADP
fumecheng-13730	283	39	the	the	DET
fumecheng-13730	283	40	development	development	NOUN
fumecheng-13730	283	41	of	of	ADP
fumecheng-13730	283	42	analytical	analytical	ADJ
fumecheng-13730	283	43	methods	method	NOUN
fumecheng-13730	283	44	for	for	ADP
fumecheng-13730	283	45	the	the	DET
fumecheng-13730	283	46	study	study	NOUN
fumecheng-13730	283	47	of	of	ADP
fumecheng-13730	283	48	the	the	DET
fumecheng-13730	283	49	frequency	frequency	NOUN
fumecheng-13730	283	50	-	-	PUNCT
fumecheng-13730	283	51	amplitude	amplitude	NOUN
fumecheng-13730	283	52	relationship	relationship	NOUN
fumecheng-13730	283	53	of	of	ADP
fumecheng-13730	283	54	complex	complex	ADJ
fumecheng-13730	283	55	nonlinear	nonlinear	ADJ
fumecheng-13730	283	56	oscillators	oscillator	NOUN
fumecheng-13730	283	57	[	[	X
fumecheng-13730	283	58	38	38	NUM
fumecheng-13730	283	59	]	]	PUNCT
fumecheng-13730	283	60	.	.	PUNCT
fumecheng-13730	284	1	the	the	DET
fumecheng-13730	284	2	nonlinear	nonlinear	ADJ
fumecheng-13730	284	3	vibration	vibration	NOUN
fumecheng-13730	284	4	theory	theory	NOUN
fumecheng-13730	284	5	is	be	AUX
fumecheng-13730	284	6	cheaper	cheap	ADJ
fumecheng-13730	284	7	and	and	CCONJ
fumecheng-13730	284	8	greener	green	ADJ
fumecheng-13730	284	9	than	than	ADP
fumecheng-13730	284	10	other	other	ADJ
fumecheng-13730	284	11	artificial	artificial	ADJ
fumecheng-13730	284	12	methods	method	NOUN
fumecheng-13730	284	13	,	,	PUNCT
fumecheng-13730	284	14	including	include	VERB
fumecheng-13730	284	15	sophisticated	sophisticated	ADJ
fumecheng-13730	284	16	experiments	experiment	NOUN
fumecheng-13730	284	17	,	,	PUNCT
fumecheng-13730	284	18	precise	precise	ADJ
fumecheng-13730	284	19	measurements	measurement	NOUN
fumecheng-13730	284	20	,	,	PUNCT
fumecheng-13730	284	21	and	and	CCONJ
fumecheng-13730	284	22	time	time	NOUN
fumecheng-13730	284	23	-	-	PUNCT
fumecheng-13730	284	24	consuming	consume	VERB
fumecheng-13730	284	25	simulations	simulation	NOUN
fumecheng-13730	284	26	.	.	PUNCT
fumecheng-13730	285	1	the	the	DET
fumecheng-13730	285	2	nonlinear	nonlinear	ADJ
fumecheng-13730	285	3	vibration	vibration	NOUN
fumecheng-13730	285	4	theory	theory	NOUN
fumecheng-13730	285	5	has	have	VERB
fumecheng-13730	285	6	the	the	DET
fumecheng-13730	285	7	potential	potential	NOUN
fumecheng-13730	285	8	to	to	PART
fumecheng-13730	285	9	enhance	enhance	VERB
fumecheng-13730	285	10	the	the	DET
fumecheng-13730	285	11	efficiency	efficiency	NOUN
fumecheng-13730	285	12	of	of	ADP
fumecheng-13730	285	13	energy	energy	NOUN
fumecheng-13730	285	14	harvester	harvester	NOUN
fumecheng-13730	285	15	devices	device	NOUN
fumecheng-13730	285	16	or	or	CCONJ
fumecheng-13730	285	17	to	to	PART
fumecheng-13730	285	18	facilitate	facilitate	VERB
fumecheng-13730	285	19	the	the	DET
fumecheng-13730	285	20	conservation	conservation	NOUN
fumecheng-13730	285	21	of	of	ADP
fumecheng-13730	285	22	mechanical	mechanical	ADJ
fumecheng-13730	285	23	vibrations	vibration	NOUN
fumecheng-13730	285	24	,	,	PUNCT
fumecheng-13730	285	25	thereby	thereby	ADV
fumecheng-13730	285	26	reducing	reduce	VERB
fumecheng-13730	285	27	the	the	DET
fumecheng-13730	285	28	emission	emission	NOUN
fumecheng-13730	285	29	of	of	ADP
fumecheng-13730	285	30	greenhouse	greenhouse	NOUN
fumecheng-13730	285	31	gases	gas	NOUN
fumecheng-13730	285	32	.	.	PUNCT
fumecheng-13730	286	1	furthermore	furthermore	ADV
fumecheng-13730	286	2	,	,	PUNCT
fumecheng-13730	286	3	the	the	DET
fumecheng-13730	286	4	frequency	frequency	NOUN
fumecheng-13730	286	5	formulation	formulation	NOUN
fumecheng-13730	286	6	can	can	AUX
fumecheng-13730	286	7	assist	assist	VERB
fumecheng-13730	286	8	in	in	ADP
fumecheng-13730	286	9	the	the	DET
fumecheng-13730	286	10	identification	identification	NOUN
fumecheng-13730	286	11	and	and	CCONJ
fumecheng-13730	286	12	search	search	NOUN
fumecheng-13730	286	13	for	for	ADP
fumecheng-13730	286	14	optimal	optimal	ADJ
fumecheng-13730	286	15	parameters	parameter	NOUN
fumecheng-13730	286	16	for	for	ADP
fumecheng-13730	286	17	the	the	DET
fumecheng-13730	286	18	devices	device	NOUN
fumecheng-13730	286	19	currently	currently	ADV
fumecheng-13730	286	20	under	under	ADP
fumecheng-13730	286	21	development	development	NOUN
fumecheng-13730	286	22	.	.	PUNCT
fumecheng-13730	287	1	to	to	ADP
fumecheng-13730	287	2	date	date	NOUN
fumecheng-13730	287	3	,	,	PUNCT
fumecheng-13730	287	4	a	a	DET
fumecheng-13730	287	5	number	number	NOUN
fumecheng-13730	287	6	of	of	ADP
fumecheng-13730	287	7	analytical	analytical	ADJ
fumecheng-13730	287	8	methods	method	NOUN
fumecheng-13730	287	9	have	have	AUX
fumecheng-13730	287	10	been	be	AUX
fumecheng-13730	287	11	proposed	propose	VERB
fumecheng-13730	287	12	for	for	ADP
fumecheng-13730	287	13	this	this	DET
fumecheng-13730	287	14	purpose	purpose	NOUN
fumecheng-13730	287	15	,	,	PUNCT
fumecheng-13730	287	16	with	with	ADP
fumecheng-13730	287	17	the	the	DET
fumecheng-13730	287	18	homotopy	homotopy	NOUN
fumecheng-13730	287	19	perturbation	perturbation	NOUN
fumecheng-13730	287	20	method	method	NOUN
fumecheng-13730	287	21	and	and	CCONJ
fumecheng-13730	287	22	the	the	DET
fumecheng-13730	287	23	variational	variational	ADJ
fumecheng-13730	287	24	iteration	iteration	NOUN
fumecheng-13730	287	25	method	method	NOUN
fumecheng-13730	287	26	representing	represent	VERB
fumecheng-13730	287	27	the	the	DET
fumecheng-13730	287	28	most	most	ADV
fumecheng-13730	287	29	commonly	commonly	ADV
fumecheng-13730	287	30	used	use	VERB
fumecheng-13730	287	31	mathematical	mathematical	ADJ
fumecheng-13730	287	32	tools	tool	NOUN
fumecheng-13730	287	33	.	.	PUNCT
fumecheng-13730	288	1	the	the	DET
fumecheng-13730	288	2	frequency	frequency	NOUN
fumecheng-13730	288	3	formulation	formulation	NOUN
fumecheng-13730	288	4	represents	represent	VERB
fumecheng-13730	288	5	a	a	DET
fumecheng-13730	288	6	particularly	particularly	ADV
fumecheng-13730	288	7	simple	simple	ADJ
fumecheng-13730	288	8	method	method	NOUN
fumecheng-13730	288	9	.	.	PUNCT
fumecheng-13730	289	1	this	this	DET
fumecheng-13730	289	2	paper	paper	NOUN
fumecheng-13730	289	3	identifies	identify	VERB
fumecheng-13730	289	4	the	the	DET
fumecheng-13730	289	5	most	most	ADV
fumecheng-13730	289	6	fascinating	fascinating	ADJ
fumecheng-13730	289	7	aspect	aspect	NOUN
fumecheng-13730	289	8	of	of	ADP
fumecheng-13730	289	9	the	the	DET
fumecheng-13730	289	10	frequency	frequency	NOUN
fumecheng-13730	289	11	formulation	formulation	NOUN
fumecheng-13730	289	12	:	:	PUNCT
fumecheng-13730	289	13	its	its	PRON
fumecheng-13730	289	14	ability	ability	NOUN
fumecheng-13730	289	15	to	to	PART
fumecheng-13730	289	16	link	link	VERB
fumecheng-13730	289	17	two	two	NUM
fumecheng-13730	289	18	primary	primary	ADJ
fumecheng-13730	289	19	factors	factor	NOUN
fumecheng-13730	289	20	that	that	PRON
fumecheng-13730	289	21	control	control	VERB
fumecheng-13730	289	22	periodic	periodic	ADJ
fumecheng-13730	289	23	motion	motion	NOUN
fumecheng-13730	289	24	in	in	ADP
fumecheng-13730	289	25	a	a	DET
fumecheng-13730	289	26	complex	complex	ADJ
fumecheng-13730	289	27	oscillator	oscillator	NOUN
fumecheng-13730	289	28	.	.	PUNCT
fumecheng-13730	290	1	the	the	DET
fumecheng-13730	290	2	aforementioned	aforementioned	ADJ
fumecheng-13730	290	3	examples	example	NOUN
fumecheng-13730	290	4	illustrate	illustrate	VERB
fumecheng-13730	290	5	the	the	DET
fumecheng-13730	290	6	efficacy	efficacy	NOUN
fumecheng-13730	290	7	of	of	ADP
fumecheng-13730	290	8	the	the	DET
fumecheng-13730	290	9	straightforward	straightforward	ADJ
fumecheng-13730	290	10	yet	yet	CCONJ
fumecheng-13730	290	11	impactful	impactful	ADJ
fumecheng-13730	290	12	frequency	frequency	NOUN
fumecheng-13730	290	13	formulation	formulation	NOUN
fumecheng-13730	290	14	in	in	ADP
fumecheng-13730	290	15	the	the	DET
fumecheng-13730	290	16	context	context	NOUN
fumecheng-13730	290	17	of	of	ADP
fumecheng-13730	290	18	scientific	scientific	ADJ
fumecheng-13730	290	19	and	and	CCONJ
fumecheng-13730	290	20	technological	technological	ADJ
fumecheng-13730	290	21	advancement	advancement	NOUN
fumecheng-13730	290	22	.	.	PUNCT
fumecheng-13730	291	1	the	the	DET
fumecheng-13730	291	2	new	new	ADJ
fumecheng-13730	291	3	frequency	frequency	NOUN
fumecheng-13730	291	4	formulation	formulation	NOUN
fumecheng-13730	291	5	presented	present	VERB
fumecheng-13730	291	6	in	in	ADP
fumecheng-13730	291	7	this	this	DET
fumecheng-13730	291	8	paper	paper	NOUN
fumecheng-13730	291	9	represents	represent	VERB
fumecheng-13730	291	10	a	a	DET
fumecheng-13730	291	11	continuous	continuous	ADJ
fumecheng-13730	291	12	process	process	NOUN
fumecheng-13730	291	13	of	of	ADP
fumecheng-13730	291	14	improvement	improvement	NOUN
fumecheng-13730	291	15	and	and	CCONJ
fumecheng-13730	291	16	expansion	expansion	NOUN
fumecheng-13730	291	17	of	of	ADP
fumecheng-13730	291	18	its	its	PRON
fumecheng-13730	291	19	applications	application	NOUN
fumecheng-13730	291	20	.	.	PUNCT
fumecheng-13730	292	1	the	the	DET
fumecheng-13730	292	2	discovery	discovery	NOUN
fumecheng-13730	292	3	constituted	constitute	VERB
fumecheng-13730	292	4	a	a	DET
fumecheng-13730	292	5	profound	profound	ADJ
fumecheng-13730	292	6	breakthrough	breakthrough	NOUN
fumecheng-13730	292	7	that	that	PRON
fumecheng-13730	292	8	astonished	astonish	VERB
fumecheng-13730	292	9	the	the	DET
fumecheng-13730	292	10	scientific	scientific	ADJ
fumecheng-13730	292	11	community	community	NOUN
fumecheng-13730	292	12	.	.	PUNCT
fumecheng-13730	293	1	while	while	SCONJ
fumecheng-13730	293	2	the	the	DET
fumecheng-13730	293	3	effectiveness	effectiveness	NOUN
fumecheng-13730	293	4	is	be	AUX
fumecheng-13730	293	5	illustrated	illustrate	VERB
fumecheng-13730	293	6	by	by	ADP
fumecheng-13730	293	7	examples	example	NOUN
fumecheng-13730	293	8	,	,	PUNCT
fumecheng-13730	293	9	it	it	PRON
fumecheng-13730	293	10	remains	remain	VERB
fumecheng-13730	293	11	in	in	ADP
fumecheng-13730	293	12	its	its	PRON
fumecheng-13730	293	13	nascent	nascent	ADJ
fumecheng-13730	293	14	stages	stage	NOUN
fumecheng-13730	293	15	,	,	PUNCT
fumecheng-13730	293	16	and	and	CCONJ
fumecheng-13730	293	17	there	there	PRON
fumecheng-13730	293	18	are	be	VERB
fumecheng-13730	293	19	numerous	numerous	ADJ
fumecheng-13730	293	20	challenges	challenge	NOUN
fumecheng-13730	293	21	and	and	CCONJ
fumecheng-13730	293	22	prospects	prospect	NOUN
fumecheng-13730	293	23	for	for	ADP
fumecheng-13730	293	24	future	future	ADJ
fumecheng-13730	293	25	research	research	NOUN
fumecheng-13730	293	26	.	.	PUNCT
fumecheng-13730	294	1	a	a	DET
fumecheng-13730	294	2	rigorous	rigorous	ADJ
fumecheng-13730	294	3	mathematical	mathematical	ADJ
fumecheng-13730	294	4	proof	proof	NOUN
fumecheng-13730	294	5	of	of	ADP
fumecheng-13730	294	6	the	the	DET
fumecheng-13730	294	7	frequency	frequency	NOUN
fumecheng-13730	294	8	formulation	formulation	NOUN
fumecheng-13730	294	9	is	be	AUX
fumecheng-13730	294	10	required	require	VERB
fumecheng-13730	294	11	to	to	PART
fumecheng-13730	294	12	confirm	confirm	VERB
fumecheng-13730	294	13	its	its	PRON
fumecheng-13730	294	14	effectiveness	effectiveness	NOUN
fumecheng-13730	294	15	.	.	PUNCT
fumecheng-13730	295	1	the	the	DET
fumecheng-13730	295	2	formulation	formulation	NOUN
fumecheng-13730	295	3	may	may	AUX
fumecheng-13730	295	4	encounter	encounter	VERB
fumecheng-13730	295	5	counter	counter	NOUN
fumecheng-13730	295	6	-	-	NOUN
fumecheng-13730	295	7	examples	example	NOUN
fumecheng-13730	295	8	in	in	ADP
fumecheng-13730	295	9	practical	practical	ADJ
fumecheng-13730	295	10	applications	application	NOUN
fumecheng-13730	295	11	,	,	PUNCT
fumecheng-13730	295	12	which	which	PRON
fumecheng-13730	295	13	could	could	AUX
fumecheng-13730	295	14	lead	lead	VERB
fumecheng-13730	295	15	to	to	ADP
fumecheng-13730	295	16	further	further	ADJ
fumecheng-13730	295	17	technological	technological	ADJ
fumecheng-13730	295	18	developments	development	NOUN
fumecheng-13730	295	19	.	.	PUNCT
fumecheng-13730	296	1	the	the	DET
fumecheng-13730	296	2	innovation	innovation	NOUN
fumecheng-13730	296	3	represents	represent	VERB
fumecheng-13730	296	4	a	a	DET
fumecheng-13730	296	5	significant	significant	ADJ
fumecheng-13730	296	6	advancement	advancement	NOUN
fumecheng-13730	296	7	in	in	ADP
fumecheng-13730	296	8	technology	technology	NOUN
fumecheng-13730	296	9	and	and	CCONJ
fumecheng-13730	296	10	has	have	VERB
fumecheng-13730	296	11	the	the	DET
fumecheng-13730	296	12	potential	potential	NOUN
fumecheng-13730	296	13	to	to	PART
fumecheng-13730	296	14	transform	transform	VERB
fumecheng-13730	296	15	existing	exist	VERB
fumecheng-13730	296	16	practices	practice	NOUN
fumecheng-13730	296	17	.	.	PUNCT
fumecheng-13730	297	1	a	a	DET
fumecheng-13730	297	2	modified	modify	VERB
fumecheng-13730	297	3	frequency	frequency	NOUN
fumecheng-13730	297	4	formulation	formulation	NOUN
fumecheng-13730	297	5	for	for	ADP
fumecheng-13730	297	6	nonlinear	nonlinear	ADJ
fumecheng-13730	297	7	mechanical	mechanical	ADJ
fumecheng-13730	297	8	vibrations	vibration	NOUN
fumecheng-13730	297	9	209	209	NUM
fumecheng-13730	297	10	acknowledgement	acknowledgement	NOUN
fumecheng-13730	297	11	:	:	PUNCT
fumecheng-13730	297	12	the	the	DET
fumecheng-13730	297	13	work	work	NOUN
fumecheng-13730	297	14	is	be	AUX
fumecheng-13730	297	15	supported	support	VERB
fumecheng-13730	297	16	by	by	ADP
fumecheng-13730	297	17	guangdong	guangdong	PROPN
fumecheng-13730	298	1	basic	basic	ADJ
fumecheng-13730	298	2	and	and	CCONJ
fumecheng-13730	298	3	applied	apply	VERB
fumecheng-13730	298	4	basic	basic	ADJ
fumecheng-13730	298	5	research	research	NOUN
fumecheng-13730	298	6	foundation	foundation	NOUN
fumecheng-13730	298	7	(	(	PUNCT
fumecheng-13730	298	8	no.2022a1515111135	no.2022a1515111135	PROPN
fumecheng-13730	298	9	&	&	CCONJ
fumecheng-13730	298	10	no.2025a1515010407	no.2025a1515010407	PROPN
fumecheng-13730	298	11	)	)	PUNCT
fumecheng-13730	298	12	.	.	PUNCT
fumecheng-13730	299	1	references	reference	NOUN
fumecheng-13730	299	2	1	1	NUM
fumecheng-13730	299	3	.	.	PUNCT
fumecheng-13730	299	4	ipek	ipek	PROPN
fumecheng-13730	299	5	,	,	PUNCT
fumecheng-13730	299	6	c.	c.	PROPN
fumecheng-13730	299	7	,	,	PUNCT
fumecheng-13730	299	8	2023	2023	NUM
fumecheng-13730	299	9	,	,	PUNCT
fumecheng-13730	299	10	vibration	vibration	NOUN
fumecheng-13730	299	11	analysis	analysis	NOUN
fumecheng-13730	299	12	of	of	ADP
fumecheng-13730	299	13	shear	shear	ADJ
fumecheng-13730	299	14	deformable	deformable	ADJ
fumecheng-13730	299	15	cylindrical	cylindrical	ADJ
fumecheng-13730	299	16	shells	shell	NOUN
fumecheng-13730	299	17	made	make	VERB
fumecheng-13730	299	18	of	of	ADP
fumecheng-13730	299	19	heterogeneous	heterogeneous	ADJ
fumecheng-13730	299	20	anisotropic	anisotropic	NOUN
fumecheng-13730	299	21	material	material	NOUN
fumecheng-13730	299	22	with	with	ADP
fumecheng-13730	299	23	clamped	clamp	VERB
fumecheng-13730	299	24	edges	edge	NOUN
fumecheng-13730	299	25	,	,	PUNCT
fumecheng-13730	299	26	journal	journal	NOUN
fumecheng-13730	299	27	of	of	ADP
fumecheng-13730	299	28	applied	applied	ADJ
fumecheng-13730	299	29	and	and	CCONJ
fumecheng-13730	299	30	computational	computational	ADJ
fumecheng-13730	299	31	mechanics	mechanic	NOUN
fumecheng-13730	299	32	,	,	PUNCT
fumecheng-13730	299	33	9(3	9(3	NUM
fumecheng-13730	299	34	)	)	PUNCT
fumecheng-13730	299	35	,	,	PUNCT
fumecheng-13730	299	36	pp	pp	PROPN
fumecheng-13730	299	37	.	.	PUNCT
fumecheng-13730	300	1	861	861	NUM
fumecheng-13730	300	2	-	-	SYM
fumecheng-13730	300	3	869	869	NUM
fumecheng-13730	300	4	.	.	NOUN
fumecheng-13730	301	1	2	2	NUM
fumecheng-13730	301	2	.	.	X
fumecheng-13730	301	3	tekin	tekin	PROPN
fumecheng-13730	301	4	,	,	PUNCT
fumecheng-13730	301	5	g.	g.	PROPN
fumecheng-13730	301	6	,	,	PUNCT
fumecheng-13730	301	7	ecer	ecer	PROPN
fumecheng-13730	301	8	,	,	PUNCT
fumecheng-13730	301	9	s.	s.	PROPN
fumecheng-13730	301	10	,	,	PUNCT
fumecheng-13730	301	11	kadioglu	kadioglu	PROPN
fumecheng-13730	301	12	,	,	PUNCT
fumecheng-13730	301	13	f.	f.	PROPN
fumecheng-13730	301	14	,	,	PUNCT
fumecheng-13730	301	15	2023	2023	NUM
fumecheng-13730	301	16	,	,	PUNCT
fumecheng-13730	301	17	an	an	DET
fumecheng-13730	301	18	alternative	alternative	ADJ
fumecheng-13730	301	19	procedure	procedure	NOUN
fumecheng-13730	301	20	for	for	ADP
fumecheng-13730	301	21	longitudinal	longitudinal	ADJ
fumecheng-13730	301	22	vibration	vibration	NOUN
fumecheng-13730	301	23	analysis	analysis	NOUN
fumecheng-13730	301	24	of	of	ADP
fumecheng-13730	301	25	bars	bar	NOUN
fumecheng-13730	301	26	with	with	ADP
fumecheng-13730	301	27	arbitrary	arbitrary	ADJ
fumecheng-13730	301	28	boundary	boundary	ADJ
fumecheng-13730	301	29	conditions	condition	NOUN
fumecheng-13730	301	30	,	,	PUNCT
fumecheng-13730	301	31	journal	journal	NOUN
fumecheng-13730	301	32	of	of	ADP
fumecheng-13730	301	33	applied	applied	ADJ
fumecheng-13730	301	34	and	and	CCONJ
fumecheng-13730	301	35	computational	computational	ADJ
fumecheng-13730	301	36	mechanics	mechanic	NOUN
fumecheng-13730	301	37	,	,	PUNCT
fumecheng-13730	301	38	9(1	9(1	NUM
fumecheng-13730	301	39	)	)	PUNCT
fumecheng-13730	301	40	,	,	PUNCT
fumecheng-13730	301	41	pp	pp	ADJ
fumecheng-13730	301	42	.	.	PUNCT
fumecheng-13730	302	1	294	294	NUM
fumecheng-13730	302	2	-	-	SYM
fumecheng-13730	302	3	301	301	NUM
fumecheng-13730	302	4	.	.	PUNCT
fumecheng-13730	303	1	3	3	X
fumecheng-13730	303	2	.	.	X
fumecheng-13730	303	3	barbosa	barbosa	PROPN
fumecheng-13730	303	4	,	,	PUNCT
fumecheng-13730	303	5	a.	a.	PROPN
fumecheng-13730	303	6	,	,	PUNCT
fumecheng-13730	303	7	kacem	kacem	PROPN
fumecheng-13730	303	8	,	,	PUNCT
fumecheng-13730	303	9	n.	n.	NOUN
fumecheng-13730	303	10	,	,	PUNCT
fumecheng-13730	303	11	bouhaddi	bouhaddi	NOUN
fumecheng-13730	303	12	,	,	PUNCT
fumecheng-13730	303	13	n.	n.	NOUN
fumecheng-13730	303	14	,	,	PUNCT
fumecheng-13730	303	15	2024	2024	NUM
fumecheng-13730	303	16	,	,	PUNCT
fumecheng-13730	303	17	a	a	DET
fumecheng-13730	303	18	design	design	NOUN
fumecheng-13730	303	19	methodology	methodology	NOUN
fumecheng-13730	303	20	for	for	ADP
fumecheng-13730	303	21	nonlinear	nonlinear	ADJ
fumecheng-13730	303	22	oscillator	oscillator	NOUN
fumecheng-13730	303	23	chains	chain	NOUN
fumecheng-13730	303	24	enabling	enable	VERB
fumecheng-13730	303	25	energy	energy	NOUN
fumecheng-13730	303	26	localization	localization	NOUN
fumecheng-13730	303	27	tuning	tuning	NOUN
fumecheng-13730	303	28	and	and	CCONJ
fumecheng-13730	303	29	soliton	soliton	NOUN
fumecheng-13730	303	30	stability	stability	NOUN
fumecheng-13730	303	31	enhancement	enhancement	NOUN
fumecheng-13730	303	32	with	with	ADP
fumecheng-13730	303	33	optimal	optimal	ADJ
fumecheng-13730	303	34	damping	damping	NOUN
fumecheng-13730	303	35	,	,	PUNCT
fumecheng-13730	303	36	mechanical	mechanical	ADJ
fumecheng-13730	303	37	systems	system	NOUN
fumecheng-13730	303	38	and	and	CCONJ
fumecheng-13730	303	39	signal	signal	NOUN
fumecheng-13730	303	40	processing	processing	NOUN
fumecheng-13730	303	41	,	,	PUNCT
fumecheng-13730	303	42	213	213	NUM
fumecheng-13730	303	43	,	,	PUNCT
fumecheng-13730	303	44	111358	111358	NUM
fumecheng-13730	303	45	.	.	PUNCT
fumecheng-13730	304	1	4	4	X
fumecheng-13730	304	2	.	.	X
fumecheng-13730	305	1	he	he	PRON
fumecheng-13730	305	2	,	,	PUNCT
fumecheng-13730	305	3	j.-h	j.-h	PROPN
fumecheng-13730	305	4	.	.	PUNCT
fumecheng-13730	305	5	,	,	PUNCT
fumecheng-13730	305	6	bai	bai	PROPN
fumecheng-13730	305	7	,	,	PUNCT
fumecheng-13730	305	8	q.	q.	PROPN
fumecheng-13730	305	9	,	,	PUNCT
fumecheng-13730	305	10	luo	luo	PROPN
fumecheng-13730	305	11	,	,	PUNCT
fumecheng-13730	305	12	y.-c	y.-c	PROPN
fumecheng-13730	305	13	.	.	PROPN
fumecheng-13730	305	14	,	,	PUNCT
fumecheng-13730	305	15	kuangaliyeva	kuangaliyeva	PROPN
fumecheng-13730	305	16	,	,	PUNCT
fumecheng-13730	305	17	d.	d.	PROPN
fumecheng-13730	305	18	,	,	PUNCT
fumecheng-13730	305	19	ellis	ellis	PROPN
fumecheng-13730	305	20	,	,	PUNCT
fumecheng-13730	305	21	g.	g.	PROPN
fumecheng-13730	305	22	,	,	PUNCT
fumecheng-13730	305	23	yessetov	yessetov	NOUN
fumecheng-13730	305	24	,	,	PUNCT
fumecheng-13730	305	25	y.	y.	NOUN
fumecheng-13730	305	26	,	,	PUNCT
fumecheng-13730	305	27	skrzypacz	skrzypacz	NOUN
fumecheng-13730	305	28	,	,	PUNCT
fumecheng-13730	305	29	p.	p.	NOUN
fumecheng-13730	305	30	,	,	PUNCT
fumecheng-13730	305	31	2025	2025	NUM
fumecheng-13730	305	32	,	,	PUNCT
fumecheng-13730	305	33	modeling	modeling	NOUN
fumecheng-13730	305	34	and	and	CCONJ
fumecheng-13730	305	35	numerical	numerical	ADJ
fumecheng-13730	305	36	analysis	analysis	NOUN
fumecheng-13730	305	37	for	for	ADP
fumecheng-13730	305	38	an	an	DET
fumecheng-13730	305	39	mems	mem	NOUN
fumecheng-13730	305	40	graphene	graphene	NOUN
fumecheng-13730	305	41	resonator	resonator	NOUN
fumecheng-13730	305	42	,	,	PUNCT
fumecheng-13730	305	43	front	front	NOUN
fumecheng-13730	305	44	.	.	PUNCT
fumecheng-13730	306	1	phys	phy	NOUN
fumecheng-13730	306	2	.	.	PUNCT
fumecheng-13730	307	1	13	13	NUM
fumecheng-13730	307	2	,	,	PUNCT
fumecheng-13730	307	3	1551969	1551969	NUM
fumecheng-13730	307	4	.	.	PUNCT
fumecheng-13730	308	1	5	5	X
fumecheng-13730	308	2	.	.	X
fumecheng-13730	308	3	campante	campante	NOUN
fumecheng-13730	308	4	,	,	PUNCT
fumecheng-13730	308	5	t.	t.	PROPN
fumecheng-13730	308	6	,	,	PUNCT
fumecheng-13730	308	7	2024	2024	NUM
fumecheng-13730	308	8	,	,	PUNCT
fumecheng-13730	308	9	smallest	small	ADJ
fumecheng-13730	308	10	known	know	VERB
fumecheng-13730	308	11	starquakes	starquake	NOUN
fumecheng-13730	308	12	are	be	AUX
fumecheng-13730	308	13	detected	detect	VERB
fumecheng-13730	308	14	with	with	ADP
fumecheng-13730	308	15	a	a	DET
fumecheng-13730	308	16	subtle	subtle	ADJ
fumecheng-13730	308	17	shift	shift	NOUN
fumecheng-13730	308	18	of	of	ADP
fumecheng-13730	308	19	colour	colour	NOUN
fumecheng-13730	308	20	,	,	PUNCT
fumecheng-13730	308	21	nature	nature	NOUN
fumecheng-13730	308	22	,	,	PUNCT
fumecheng-13730	308	23	628	628	NUM
fumecheng-13730	308	24	,	,	PUNCT
fumecheng-13730	308	25	pp	pp	ADJ
fumecheng-13730	308	26	.	.	PUNCT
fumecheng-13730	309	1	239	239	NUM
fumecheng-13730	309	2	-	-	SYM
fumecheng-13730	309	3	239	239	NUM
fumecheng-13730	309	4	.	.	PUNCT
fumecheng-13730	310	1	6	6	NUM
fumecheng-13730	310	2	.	.	X
fumecheng-13730	310	3	maiuri	maiuri	PROPN
fumecheng-13730	310	4	,	,	PUNCT
fumecheng-13730	310	5	m.	m.	NOUN
fumecheng-13730	310	6	,	,	PUNCT
fumecheng-13730	310	7	2024	2024	NUM
fumecheng-13730	310	8	,	,	PUNCT
fumecheng-13730	310	9	vibration	vibration	NOUN
fumecheng-13730	310	10	isolation	isolation	NOUN
fumecheng-13730	310	11	could	could	AUX
fumecheng-13730	310	12	boost	boost	VERB
fumecheng-13730	310	13	performance	performance	NOUN
fumecheng-13730	310	14	of	of	ADP
fumecheng-13730	310	15	near	near	ADV
fumecheng-13730	310	16	-	-	PUNCT
fumecheng-13730	310	17	infrared	infrared	ADJ
fumecheng-13730	310	18	organic	organic	ADJ
fumecheng-13730	310	19	leds	led	NOUN
fumecheng-13730	310	20	,	,	PUNCT
fumecheng-13730	310	21	nature	nature	NOUN
fumecheng-13730	310	22	,	,	PUNCT
fumecheng-13730	310	23	629	629	NUM
fumecheng-13730	310	24	,	,	PUNCT
fumecheng-13730	310	25	pp	pp	ADJ
fumecheng-13730	310	26	.	.	PUNCT
fumecheng-13730	311	1	289	289	NUM
fumecheng-13730	311	2	-	-	SYM
fumecheng-13730	311	3	290	290	NUM
fumecheng-13730	311	4	.	.	PUNCT
fumecheng-13730	312	1	7	7	NUM
fumecheng-13730	312	2	.	.	X
fumecheng-13730	312	3	elías	elías	PROPN
fumecheng-13730	312	4	-	-	PUNCT
fumecheng-13730	312	5	zúñiga	zúñiga	PROPN
fumecheng-13730	312	6	,	,	PUNCT
fumecheng-13730	312	7	a.	a.	NOUN
fumecheng-13730	312	8	,	,	PUNCT
fumecheng-13730	312	9	2014	2014	NUM
fumecheng-13730	312	10	,	,	PUNCT
fumecheng-13730	312	11	solution	solution	NOUN
fumecheng-13730	312	12	of	of	ADP
fumecheng-13730	312	13	the	the	DET
fumecheng-13730	312	14	damped	damped	ADJ
fumecheng-13730	312	15	cubic	cubic	ADJ
fumecheng-13730	312	16	-	-	PUNCT
fumecheng-13730	312	17	quintic	quintic	ADJ
fumecheng-13730	312	18	duffing	duffing	NOUN
fumecheng-13730	312	19	oscillator	oscillator	NOUN
fumecheng-13730	312	20	by	by	ADP
fumecheng-13730	312	21	using	use	VERB
fumecheng-13730	312	22	jacobi	jacobi	PROPN
fumecheng-13730	312	23	elliptic	elliptic	ADJ
fumecheng-13730	312	24	functions	function	NOUN
fumecheng-13730	312	25	,	,	PUNCT
fumecheng-13730	312	26	applied	apply	VERB
fumecheng-13730	312	27	mathematics	mathematic	NOUN
fumecheng-13730	312	28	and	and	CCONJ
fumecheng-13730	312	29	computation	computation	NOUN
fumecheng-13730	312	30	,	,	PUNCT
fumecheng-13730	312	31	246	246	NUM
fumecheng-13730	312	32	,	,	PUNCT
fumecheng-13730	312	33	pp	pp	ADJ
fumecheng-13730	312	34	.	.	PUNCT
fumecheng-13730	313	1	474	474	NUM
fumecheng-13730	313	2	-	-	SYM
fumecheng-13730	313	3	481	481	NUM
fumecheng-13730	313	4	.	.	NOUN
fumecheng-13730	313	5	8	8	NUM
fumecheng-13730	313	6	.	.	PUNCT
fumecheng-13730	314	1	elías	elías	PROPN
fumecheng-13730	314	2	-	-	PUNCT
fumecheng-13730	314	3	zúñiga	zúñiga	PROPN
fumecheng-13730	314	4	,	,	PUNCT
fumecheng-13730	314	5	a.	a.	NOUN
fumecheng-13730	314	6	,	,	PUNCT
fumecheng-13730	314	7	2013	2013	NUM
fumecheng-13730	314	8	,	,	PUNCT
fumecheng-13730	314	9	exact	exact	ADJ
fumecheng-13730	314	10	solution	solution	NOUN
fumecheng-13730	314	11	of	of	ADP
fumecheng-13730	314	12	the	the	DET
fumecheng-13730	314	13	cubic	cubic	ADJ
fumecheng-13730	314	14	-	-	PUNCT
fumecheng-13730	314	15	quintic	quintic	ADJ
fumecheng-13730	314	16	duffing	duffing	NOUN
fumecheng-13730	314	17	oscillator	oscillator	NOUN
fumecheng-13730	314	18	,	,	PUNCT
fumecheng-13730	314	19	applied	apply	VERB
fumecheng-13730	314	20	mathematical	mathematical	ADJ
fumecheng-13730	314	21	modelling	modelling	NOUN
fumecheng-13730	314	22	,	,	PUNCT
fumecheng-13730	314	23	37(4	37(4	PROPN
fumecheng-13730	314	24	)	)	PUNCT
fumecheng-13730	314	25	,	,	PUNCT
fumecheng-13730	315	1	pp	pp	ADJ
fumecheng-13730	315	2	.	.	PUNCT
fumecheng-13730	316	1	2574	2574	NUM
fumecheng-13730	316	2	-	-	SYM
fumecheng-13730	316	3	2579	2579	NUM
fumecheng-13730	316	4	.	.	PUNCT
fumecheng-13730	317	1	9	9	X
fumecheng-13730	317	2	.	.	X
fumecheng-13730	317	3	beléndez	beléndez	PROPN
fumecheng-13730	317	4	,	,	PUNCT
fumecheng-13730	317	5	a.	a.	PROPN
fumecheng-13730	317	6	,	,	PUNCT
fumecheng-13730	317	7	alvarez	alvarez	PROPN
fumecheng-13730	317	8	,	,	PUNCT
fumecheng-13730	317	9	m.	m.	PROPN
fumecheng-13730	317	10	l.	l.	PROPN
fumecheng-13730	317	11	,	,	PUNCT
fumecheng-13730	317	12	francés	francés	PROPN
fumecheng-13730	317	13	,	,	PUNCT
fumecheng-13730	317	14	j.	j.	PROPN
fumecheng-13730	317	15	,	,	PUNCT
fumecheng-13730	317	16	bleda	bleda	PROPN
fumecheng-13730	317	17	,	,	PUNCT
fumecheng-13730	317	18	s.	s.	PROPN
fumecheng-13730	317	19	,	,	PUNCT
fumecheng-13730	317	20	beléndez	beléndez	PROPN
fumecheng-13730	317	21	,	,	PUNCT
fumecheng-13730	317	22	t.	t.	NOUN
fumecheng-13730	317	23	,	,	PUNCT
fumecheng-13730	317	24	nájera	nájera	NOUN
fumecheng-13730	317	25	,	,	PUNCT
fumecheng-13730	317	26	a.	a.	NOUN
fumecheng-13730	317	27	,	,	PUNCT
fumecheng-13730	317	28	arribas	arribas	PROPN
fumecheng-13730	317	29	,	,	PUNCT
fumecheng-13730	317	30	e.	e.	PROPN
fumecheng-13730	317	31	,2012	,2012	PROPN
fumecheng-13730	317	32	,	,	PUNCT
fumecheng-13730	317	33	analytical	analytical	ADJ
fumecheng-13730	317	34	approximate	approximate	ADJ
fumecheng-13730	317	35	solutions	solution	NOUN
fumecheng-13730	317	36	for	for	ADP
fumecheng-13730	317	37	the	the	DET
fumecheng-13730	317	38	cubic	cubic	ADJ
fumecheng-13730	317	39	-	-	PUNCT
fumecheng-13730	317	40	quintic	quintic	ADJ
fumecheng-13730	317	41	duffing	duffing	NOUN
fumecheng-13730	317	42	oscillator	oscillator	NOUN
fumecheng-13730	317	43	in	in	ADP
fumecheng-13730	317	44	terms	term	NOUN
fumecheng-13730	317	45	of	of	ADP
fumecheng-13730	317	46	elementary	elementary	ADJ
fumecheng-13730	317	47	functions	function	NOUN
fumecheng-13730	317	48	,	,	PUNCT
fumecheng-13730	317	49	journal	journal	NOUN
fumecheng-13730	317	50	of	of	ADP
fumecheng-13730	317	51	applied	apply	VERB
fumecheng-13730	317	52	mathematics	mathematic	NOUN
fumecheng-13730	317	53	,	,	PUNCT
fumecheng-13730	317	54	2012	2012	NUM
fumecheng-13730	317	55	,	,	PUNCT
fumecheng-13730	317	56	286290	286290	NUM
fumecheng-13730	317	57	.	.	PUNCT
fumecheng-13730	318	1	10	10	NUM
fumecheng-13730	318	2	.	.	PUNCT
fumecheng-13730	319	1	guo	guo	PROPN
fumecheng-13730	319	2	,	,	PUNCT
fumecheng-13730	319	3	x.t	x.t	PROPN
fumecheng-13730	319	4	.	.	PROPN
fumecheng-13730	319	5	,	,	PUNCT
fumecheng-13730	319	6	zhang	zhang	PROPN
fumecheng-13730	319	7	,	,	PUNCT
fumecheng-13730	319	8	w.	w.	PROPN
fumecheng-13730	319	9	,	,	PUNCT
fumecheng-13730	319	10	zhang	zhang	PROPN
fumecheng-13730	319	11	,	,	PUNCT
fumecheng-13730	319	12	y.f	y.f	PROPN
fumecheng-13730	319	13	.	.	PROPN
fumecheng-13730	319	14	,	,	PUNCT
fumecheng-13730	319	15	experimental	experimental	ADJ
fumecheng-13730	319	16	and	and	CCONJ
fumecheng-13730	319	17	numerical	numerical	ADJ
fumecheng-13730	319	18	investigations	investigation	NOUN
fumecheng-13730	319	19	on	on	ADP
fumecheng-13730	319	20	nonlinear	nonlinear	ADJ
fumecheng-13730	319	21	snap	snap	VERB
fumecheng-13730	319	22	-	-	PUNCT
fumecheng-13730	319	23	through	through	ADP
fumecheng-13730	319	24	vibrations	vibration	NOUN
fumecheng-13730	319	25	of	of	ADP
fumecheng-13730	319	26	an	an	DET
fumecheng-13730	319	27	asymmetrically	asymmetrically	ADV
fumecheng-13730	319	28	composite	composite	NOUN
fumecheng-13730	319	29	laminated	laminate	VERB
fumecheng-13730	319	30	bistable	bistable	ADJ
fumecheng-13730	319	31	thin	thin	ADJ
fumecheng-13730	319	32	plate	plate	NOUN
fumecheng-13730	319	33	simple	simple	NOUN
fumecheng-13730	319	34	supported	support	VERB
fumecheng-13730	319	35	at	at	ADP
fumecheng-13730	319	36	four	four	NUM
fumecheng-13730	319	37	corners	corner	NOUN
fumecheng-13730	319	38	,	,	PUNCT
fumecheng-13730	319	39	engineering	engineering	NOUN
fumecheng-13730	319	40	structures	structure	NOUN
fumecheng-13730	319	41	,	,	PUNCT
fumecheng-13730	319	42	296	296	NUM
fumecheng-13730	319	43	,	,	PUNCT
fumecheng-13730	319	44	116926	116926	NUM
fumecheng-13730	319	45	.	.	PUNCT
fumecheng-13730	320	1	11	11	NUM
fumecheng-13730	320	2	.	.	PUNCT
fumecheng-13730	321	1	he	he	PRON
fumecheng-13730	321	2	,	,	PUNCT
fumecheng-13730	321	3	j.h	j.h	PROPN
fumecheng-13730	321	4	.	.	PROPN
fumecheng-13730	321	5	,	,	PUNCT
fumecheng-13730	321	6	2024	2024	NUM
fumecheng-13730	321	7	,	,	PUNCT
fumecheng-13730	321	8	frequency	frequency	NOUN
fumecheng-13730	321	9	formulation	formulation	NOUN
fumecheng-13730	321	10	for	for	ADP
fumecheng-13730	321	11	nonlinear	nonlinear	ADJ
fumecheng-13730	321	12	oscillators	oscillator	NOUN
fumecheng-13730	321	13	(	(	PUNCT
fumecheng-13730	321	14	part	part	NOUN
fumecheng-13730	321	15	1	1	NUM
fumecheng-13730	321	16	)	)	PUNCT
fumecheng-13730	321	17	,	,	PUNCT
fumecheng-13730	321	18	sound	sound	NOUN
fumecheng-13730	321	19	&	&	CCONJ
fumecheng-13730	321	20	vibration	vibration	NOUN
fumecheng-13730	321	21	,	,	PUNCT
fumecheng-13730	321	22	59(1	59(1	NUM
fumecheng-13730	321	23	)	)	PUNCT
fumecheng-13730	321	24	,	,	PUNCT
fumecheng-13730	321	25	1687	1687	NUM
fumecheng-13730	321	26	.	.	PUNCT
fumecheng-13730	322	1	12	12	NUM
fumecheng-13730	322	2	.	.	PUNCT
fumecheng-13730	322	3	remmi	remmi	PROPN
fumecheng-13730	322	4	,	,	PUNCT
fumecheng-13730	322	5	s.k	s.k	PROPN
fumecheng-13730	322	6	.	.	PROPN
fumecheng-13730	322	7	,	,	PUNCT
fumecheng-13730	322	8	latha	latha	PROPN
fumecheng-13730	322	9	,	,	PUNCT
fumecheng-13730	322	10	m.m	m.m	PROPN
fumecheng-13730	322	11	.	.	PROPN
fumecheng-13730	322	12	,	,	PUNCT
fumecheng-13730	322	13	2018	2018	NUM
fumecheng-13730	322	14	,	,	PUNCT
fumecheng-13730	322	15	cubic	cubic	ADJ
fumecheng-13730	322	16	quintic	quintic	ADJ
fumecheng-13730	322	17	-	-	PUNCT
fumecheng-13730	322	18	septic	septic	NOUN
fumecheng-13730	322	19	duffing	duffing	NOUN
fumecheng-13730	322	20	oscillator	oscillator	NOUN
fumecheng-13730	322	21	:	:	PUNCT
fumecheng-13730	322	22	an	an	DET
fumecheng-13730	322	23	analytical	analytical	ADJ
fumecheng-13730	322	24	study	study	NOUN
fumecheng-13730	322	25	,	,	PUNCT
fumecheng-13730	322	26	chinese	chinese	ADJ
fumecheng-13730	322	27	journal	journal	PROPN
fumecheng-13730	322	28	of	of	ADP
fumecheng-13730	322	29	physics	physics	PROPN
fumecheng-13730	322	30	,	,	PUNCT
fumecheng-13730	322	31	56(5	56(5	NOUN
fumecheng-13730	322	32	)	)	PUNCT
fumecheng-13730	322	33	,	,	PUNCT
fumecheng-13730	322	34	pp	pp	ADJ
fumecheng-13730	322	35	.	.	PUNCT
fumecheng-13730	323	1	2085	2085	NUM
fumecheng-13730	323	2	-	-	SYM
fumecheng-13730	323	3	2094	2094	NUM
fumecheng-13730	323	4	.	.	PUNCT
fumecheng-13730	324	1	13	13	NUM
fumecheng-13730	324	2	.	.	PUNCT
fumecheng-13730	324	3	lev	lev	PROPN
fumecheng-13730	324	4	,	,	PUNCT
fumecheng-13730	324	5	b.i	b.i	PROPN
fumecheng-13730	324	6	.	.	PROPN
fumecheng-13730	324	7	,	,	PUNCT
fumecheng-13730	324	8	tymchyshyn	tymchyshyn	PROPN
fumecheng-13730	324	9	,	,	PUNCT
fumecheng-13730	324	10	v.b	v.b	PROPN
fumecheng-13730	324	11	.	.	PROPN
fumecheng-13730	324	12	,	,	PUNCT
fumecheng-13730	324	13	zagorodny	zagorodny	PROPN
fumecheng-13730	324	14	,	,	PUNCT
fumecheng-13730	324	15	a.g	a.g	PROPN
fumecheng-13730	324	16	.	.	PROPN
fumecheng-13730	324	17	,	,	PUNCT
fumecheng-13730	324	18	2017	2017	NUM
fumecheng-13730	324	19	,	,	PUNCT
fumecheng-13730	324	20	on	on	ADP
fumecheng-13730	324	21	certain	certain	ADJ
fumecheng-13730	324	22	properties	property	NOUN
fumecheng-13730	324	23	of	of	ADP
fumecheng-13730	324	24	nonlinear	nonlinear	ADJ
fumecheng-13730	324	25	oscillator	oscillator	NOUN
fumecheng-13730	324	26	with	with	ADP
fumecheng-13730	324	27	coordinate	coordinate	NOUN
fumecheng-13730	324	28	-	-	PUNCT
fumecheng-13730	324	29	dependent	dependent	ADJ
fumecheng-13730	324	30	mass	mass	NOUN
fumecheng-13730	324	31	,	,	PUNCT
fumecheng-13730	324	32	physics	physics	NOUN
fumecheng-13730	324	33	letters	letter	NOUN
fumecheng-13730	324	34	a	a	PRON
fumecheng-13730	324	35	,	,	PUNCT
fumecheng-13730	324	36	381	381	NUM
fumecheng-13730	324	37	,	,	PUNCT
fumecheng-13730	324	38	pp	pp	ADJ
fumecheng-13730	324	39	.	.	PUNCT
fumecheng-13730	325	1	3417	3417	NUM
fumecheng-13730	325	2	-	-	SYM
fumecheng-13730	325	3	3423	3423	NUM
fumecheng-13730	325	4	.	.	PUNCT
fumecheng-13730	326	1	14	14	NUM
fumecheng-13730	326	2	.	.	PUNCT
fumecheng-13730	327	1	ren	ren	PROPN
fumecheng-13730	327	2	,	,	PUNCT
fumecheng-13730	327	3	z.y	z.y	PROPN
fumecheng-13730	327	4	.	.	PROPN
fumecheng-13730	327	5	,	,	PUNCT
fumecheng-13730	327	6	2018	2018	NUM
fumecheng-13730	327	7	,	,	PUNCT
fumecheng-13730	327	8	the	the	DET
fumecheng-13730	327	9	frequency	frequency	NOUN
fumecheng-13730	327	10	-	-	PUNCT
fumecheng-13730	327	11	amplitude	amplitude	NOUN
fumecheng-13730	327	12	formulation	formulation	NOUN
fumecheng-13730	327	13	with	with	ADP
fumecheng-13730	327	14	ω4	ω4	NUM
fumecheng-13730	327	15	for	for	ADP
fumecheng-13730	327	16	fast	fast	ADJ
fumecheng-13730	327	17	insight	insight	NOUN
fumecheng-13730	327	18	into	into	ADP
fumecheng-13730	327	19	a	a	DET
fumecheng-13730	327	20	nonlinear	nonlinear	ADJ
fumecheng-13730	327	21	oscillator	oscillator	NOUN
fumecheng-13730	327	22	,	,	PUNCT
fumecheng-13730	327	23	results	result	NOUN
fumecheng-13730	327	24	in	in	ADP
fumecheng-13730	327	25	physics	physics	NOUN
fumecheng-13730	327	26	,	,	PUNCT
fumecheng-13730	327	27	11	11	NUM
fumecheng-13730	327	28	,	,	PUNCT
fumecheng-13730	327	29	pp	pp	ADJ
fumecheng-13730	327	30	.	.	PUNCT
fumecheng-13730	327	31	1052	1052	NUM
fumecheng-13730	327	32	-	-	SYM
fumecheng-13730	327	33	1053	1053	NUM
fumecheng-13730	327	34	.	.	PUNCT
fumecheng-13730	328	1	15	15	NUM
fumecheng-13730	328	2	.	.	PUNCT
fumecheng-13730	329	1	he	he	PRON
fumecheng-13730	329	2	,	,	PUNCT
fumecheng-13730	329	3	c.h	c.h	PROPN
fumecheng-13730	329	4	.	.	PROPN
fumecheng-13730	329	5	,	,	PUNCT
fumecheng-13730	329	6	liu	liu	PROPN
fumecheng-13730	329	7	,	,	PUNCT
fumecheng-13730	329	8	c.	c.	PROPN
fumecheng-13730	329	9	,	,	PUNCT
fumecheng-13730	329	10	2022	2022	NUM
fumecheng-13730	329	11	,	,	PUNCT
fumecheng-13730	329	12	a	a	DET
fumecheng-13730	329	13	modified	modify	VERB
fumecheng-13730	329	14	frequency	frequency	NOUN
fumecheng-13730	329	15	-	-	PUNCT
fumecheng-13730	329	16	amplitude	amplitude	NOUN
fumecheng-13730	329	17	formulation	formulation	NOUN
fumecheng-13730	329	18	for	for	ADP
fumecheng-13730	329	19	fractal	fractal	ADJ
fumecheng-13730	329	20	vibration	vibration	NOUN
fumecheng-13730	329	21	systems	system	NOUN
fumecheng-13730	329	22	,	,	PUNCT
fumecheng-13730	329	23	fractals	fractal	NOUN
fumecheng-13730	329	24	,	,	PUNCT
fumecheng-13730	329	25	30(3	30(3	NUM
fumecheng-13730	329	26	)	)	PUNCT
fumecheng-13730	329	27	,	,	PUNCT
fumecheng-13730	329	28	2250046	2250046	NUM
fumecheng-13730	329	29	.	.	PUNCT
fumecheng-13730	330	1	16	16	NUM
fumecheng-13730	330	2	.	.	PUNCT
fumecheng-13730	331	1	ismail	ismail	PROPN
fumecheng-13730	331	2	,	,	PUNCT
fumecheng-13730	331	3	g.m	g.m	PROPN
fumecheng-13730	331	4	.	.	PROPN
fumecheng-13730	331	5	,	,	PUNCT
fumecheng-13730	331	6	moatimid	moatimid	PROPN
fumecheng-13730	331	7	,	,	PUNCT
fumecheng-13730	331	8	g.m	g.m	PROPN
fumecheng-13730	331	9	.	.	PROPN
fumecheng-13730	331	10	,	,	PUNCT
fumecheng-13730	331	11	yamani	yamani	PROPN
fumecheng-13730	331	12	,	,	PUNCT
fumecheng-13730	331	13	m.i	m.i	PROPN
fumecheng-13730	331	14	.	.	PROPN
fumecheng-13730	331	15	,	,	PUNCT
fumecheng-13730	331	16	2024	2024	NUM
fumecheng-13730	331	17	,	,	PUNCT
fumecheng-13730	331	18	periodic	periodic	ADJ
fumecheng-13730	331	19	solutions	solution	NOUN
fumecheng-13730	331	20	of	of	ADP
fumecheng-13730	331	21	strongly	strongly	ADV
fumecheng-13730	331	22	nonlinear	nonlinear	ADJ
fumecheng-13730	331	23	oscillators	oscillator	NOUN
fumecheng-13730	331	24	using	use	VERB
fumecheng-13730	331	25	he	he	PRON
fumecheng-13730	331	26	's	's	PART
fumecheng-13730	331	27	frequency	frequency	NOUN
fumecheng-13730	331	28	formulation	formulation	NOUN
fumecheng-13730	331	29	,	,	PUNCT
fumecheng-13730	331	30	european	european	ADJ
fumecheng-13730	331	31	journal	journal	NOUN
fumecheng-13730	331	32	of	of	ADP
fumecheng-13730	331	33	pure	pure	ADJ
fumecheng-13730	331	34	and	and	CCONJ
fumecheng-13730	331	35	applied	applied	ADJ
fumecheng-13730	331	36	mathematics	mathematic	NOUN
fumecheng-13730	331	37	,	,	PUNCT
fumecheng-13730	331	38	17(3	17(3	NUM
fumecheng-13730	331	39	)	)	PUNCT
fumecheng-13730	331	40	,	,	PUNCT
fumecheng-13730	331	41	pp	pp	ADJ
fumecheng-13730	331	42	.	.	PUNCT
fumecheng-13730	331	43	2155	2155	NUM
fumecheng-13730	331	44	-	-	SYM
fumecheng-13730	331	45	2172	2172	NUM
fumecheng-13730	331	46	.	.	PUNCT
fumecheng-13730	332	1	17	17	NUM
fumecheng-13730	332	2	.	.	X
fumecheng-13730	332	3	hashemi	hashemi	PROPN
fumecheng-13730	332	4	,	,	PUNCT
fumecheng-13730	332	5	g.	g.	PROPN
fumecheng-13730	332	6	,	,	PUNCT
fumecheng-13730	332	7	2023	2023	NUM
fumecheng-13730	332	8	,	,	PUNCT
fumecheng-13730	332	9	a	a	DET
fumecheng-13730	332	10	novel	novel	ADJ
fumecheng-13730	332	11	analytical	analytical	ADJ
fumecheng-13730	332	12	approximation	approximation	NOUN
fumecheng-13730	332	13	approach	approach	NOUN
fumecheng-13730	332	14	for	for	ADP
fumecheng-13730	332	15	strongly	strongly	ADV
fumecheng-13730	332	16	nonlinear	nonlinear	ADJ
fumecheng-13730	332	17	oscillation	oscillation	NOUN
fumecheng-13730	332	18	systems	system	NOUN
fumecheng-13730	332	19	based	base	VERB
fumecheng-13730	332	20	on	on	ADP
fumecheng-13730	332	21	the	the	DET
fumecheng-13730	332	22	energy	energy	NOUN
fumecheng-13730	332	23	balance	balance	NOUN
fumecheng-13730	332	24	method	method	NOUN
fumecheng-13730	332	25	and	and	CCONJ
fumecheng-13730	332	26	he	he	PRON
fumecheng-13730	332	27	's	's	PART
fumecheng-13730	332	28	frequency	frequency	NOUN
fumecheng-13730	332	29	-	-	PUNCT
fumecheng-13730	332	30	amplitude	amplitude	NOUN
fumecheng-13730	332	31	formulation	formulation	NOUN
fumecheng-13730	332	32	,	,	PUNCT
fumecheng-13730	332	33	computational	computational	ADJ
fumecheng-13730	332	34	methods	method	NOUN
fumecheng-13730	332	35	for	for	ADP
fumecheng-13730	332	36	differential	differential	ADJ
fumecheng-13730	332	37	equations	equation	NOUN
fumecheng-13730	332	38	,	,	PUNCT
fumecheng-13730	332	39	11(3	11(3	NUM
fumecheng-13730	332	40	)	)	PUNCT
fumecheng-13730	332	41	,	,	PUNCT
fumecheng-13730	332	42	pp	pp	PROPN
fumecheng-13730	332	43	.	.	PUNCT
fumecheng-13730	333	1	464	464	NUM
fumecheng-13730	333	2	-	-	SYM
fumecheng-13730	333	3	477	477	NUM
fumecheng-13730	333	4	.	.	PUNCT
fumecheng-13730	334	1	18	18	NUM
fumecheng-13730	334	2	.	.	X
fumecheng-13730	334	3	kawser	kawser	PROPN
fumecheng-13730	334	4	,	,	PUNCT
fumecheng-13730	334	5	m.a	m.a	PROPN
fumecheng-13730	334	6	.	.	PROPN
fumecheng-13730	334	7	,	,	PUNCT
fumecheng-13730	334	8	alim	alim	NOUN
fumecheng-13730	334	9	,	,	PUNCT
fumecheng-13730	334	10	m.a	m.a	PROPN
fumecheng-13730	334	11	.	.	PROPN
fumecheng-13730	334	12	,	,	PUNCT
fumecheng-13730	334	13	sharif	sharif	PROPN
fumecheng-13730	334	14	,	,	PUNCT
fumecheng-13730	334	15	n.	n.	NOUN
fumecheng-13730	334	16	,	,	PUNCT
fumecheng-13730	334	17	2024	2024	NUM
fumecheng-13730	334	18	,	,	PUNCT
fumecheng-13730	334	19	analyzing	analyze	VERB
fumecheng-13730	334	20	nonlinear	nonlinear	ADJ
fumecheng-13730	334	21	oscillations	oscillation	NOUN
fumecheng-13730	334	22	with	with	ADP
fumecheng-13730	334	23	he	he	PRON
fumecheng-13730	334	24	's	's	PART
fumecheng-13730	334	25	frequency	frequency	NOUN
fumecheng-13730	334	26	-	-	PUNCT
fumecheng-13730	334	27	amplitude	amplitude	NOUN
fumecheng-13730	334	28	method	method	NOUN
fumecheng-13730	334	29	and	and	CCONJ
fumecheng-13730	334	30	numerical	numerical	ADJ
fumecheng-13730	334	31	comparison	comparison	NOUN
fumecheng-13730	334	32	in	in	ADP
fumecheng-13730	334	33	jet	jet	NOUN
fumecheng-13730	334	34	engine	engine	NOUN
fumecheng-13730	334	35	vibration	vibration	NOUN
fumecheng-13730	334	36	system	system	NOUN
fumecheng-13730	334	37	,	,	PUNCT
fumecheng-13730	334	38	heliyon	heliyon	NOUN
fumecheng-13730	334	39	,	,	PUNCT
fumecheng-13730	334	40	10(2	10(2	NUM
fumecheng-13730	334	41	)	)	PUNCT
fumecheng-13730	334	42	,	,	PUNCT
fumecheng-13730	334	43	e24261	e24261	NOUN
fumecheng-13730	334	44	.	.	NOUN
fumecheng-13730	334	45	19	19	NUM
fumecheng-13730	334	46	.	.	PUNCT
fumecheng-13730	334	47	tsaltas	tsalta	NOUN
fumecheng-13730	334	48	,	,	PUNCT
fumecheng-13730	334	49	k.	k.	PROPN
fumecheng-13730	334	50	,	,	PUNCT
fumecheng-13730	334	51	2023	2023	NUM
fumecheng-13730	334	52	,	,	PUNCT
fumecheng-13730	334	53	an	an	DET
fumecheng-13730	334	54	improved	improved	ADJ
fumecheng-13730	334	55	one	one	NUM
fumecheng-13730	334	56	-	-	PUNCT
fumecheng-13730	334	57	step	step	NOUN
fumecheng-13730	334	58	amplitude	amplitude	NOUN
fumecheng-13730	334	59	-	-	PUNCT
fumecheng-13730	334	60	frequency	frequency	NOUN
fumecheng-13730	334	61	relation	relation	NOUN
fumecheng-13730	334	62	for	for	ADP
fumecheng-13730	334	63	nonlinear	nonlinear	ADJ
fumecheng-13730	334	64	oscillators	oscillator	NOUN
fumecheng-13730	334	65	,	,	PUNCT
fumecheng-13730	334	66	results	result	NOUN
fumecheng-13730	334	67	in	in	ADP
fumecheng-13730	334	68	physics	physics	NOUN
fumecheng-13730	334	69	,	,	PUNCT
fumecheng-13730	334	70	54	54	NUM
fumecheng-13730	334	71	,	,	PUNCT
fumecheng-13730	334	72	107090	107090	NUM
fumecheng-13730	334	73	.	.	PUNCT
fumecheng-13730	335	1	20	20	NUM
fumecheng-13730	335	2	.	.	X
fumecheng-13730	336	1	tian	tian	PROPN
fumecheng-13730	336	2	,	,	PUNCT
fumecheng-13730	336	3	y.	y.	PROPN
fumecheng-13730	336	4	,	,	PUNCT
fumecheng-13730	336	5	shao	shao	PROPN
fumecheng-13730	336	6	,	,	PUNCT
fumecheng-13730	336	7	y.b	y.b	PROPN
fumecheng-13730	336	8	.	.	PROPN
fumecheng-13730	336	9	,	,	PUNCT
fumecheng-13730	336	10	2024	2024	NUM
fumecheng-13730	336	11	,	,	PUNCT
fumecheng-13730	336	12	mini	mini	NOUN
fumecheng-13730	336	13	-	-	NOUN
fumecheng-13730	336	14	review	review	NOUN
fumecheng-13730	336	15	on	on	ADP
fumecheng-13730	336	16	periodic	periodic	ADJ
fumecheng-13730	336	17	properties	property	NOUN
fumecheng-13730	336	18	of	of	ADP
fumecheng-13730	336	19	mems	mem	NOUN
fumecheng-13730	336	20	oscillators	oscillator	NOUN
fumecheng-13730	336	21	,	,	PUNCT
fumecheng-13730	336	22	frontiers	frontier	NOUN
fumecheng-13730	336	23	in	in	ADP
fumecheng-13730	336	24	physics	physics	NOUN
fumecheng-13730	336	25	,	,	PUNCT
fumecheng-13730	336	26	12	12	NUM
fumecheng-13730	336	27	,	,	PUNCT
fumecheng-13730	336	28	1498185	1498185	NUM
fumecheng-13730	336	29	.	.	PUNCT
fumecheng-13730	337	1	21	21	NUM
fumecheng-13730	337	2	.	.	PUNCT
fumecheng-13730	338	1	he	he	PRON
fumecheng-13730	338	2	,	,	PUNCT
fumecheng-13730	338	3	j.h	j.h	PROPN
fumecheng-13730	338	4	.	.	PROPN
fumecheng-13730	338	5	,	,	PUNCT
fumecheng-13730	338	6	2024	2024	NUM
fumecheng-13730	338	7	,	,	PUNCT
fumecheng-13730	338	8	an	an	DET
fumecheng-13730	338	9	old	old	ADJ
fumecheng-13730	338	10	babylonian	babylonian	ADJ
fumecheng-13730	338	11	algorithm	algorithm	NOUN
fumecheng-13730	338	12	and	and	CCONJ
fumecheng-13730	338	13	its	its	PRON
fumecheng-13730	338	14	modern	modern	ADJ
fumecheng-13730	338	15	applications	application	NOUN
fumecheng-13730	338	16	,	,	PUNCT
fumecheng-13730	338	17	symmetry	symmetry	NOUN
fumecheng-13730	338	18	,	,	PUNCT
fumecheng-13730	338	19	16	16	NUM
fumecheng-13730	338	20	,	,	PUNCT
fumecheng-13730	338	21	1467	1467	NUM
fumecheng-13730	338	22	.	.	PUNCT
fumecheng-13730	339	1	22	22	NUM
fumecheng-13730	339	2	.	.	PUNCT
fumecheng-13730	340	1	zhao	zhao	PROPN
fumecheng-13730	340	2	,	,	PUNCT
fumecheng-13730	340	3	l.	l.	PROPN
fumecheng-13730	340	4	,	,	PUNCT
fumecheng-13730	340	5	2009	2009	NUM
fumecheng-13730	340	6	,	,	PUNCT
fumecheng-13730	340	7	he	he	PRON
fumecheng-13730	340	8	's	's	PART
fumecheng-13730	340	9	frequency	frequency	NOUN
fumecheng-13730	340	10	-	-	PUNCT
fumecheng-13730	340	11	amplitude	amplitude	NOUN
fumecheng-13730	340	12	formulation	formulation	NOUN
fumecheng-13730	340	13	for	for	ADP
fumecheng-13730	340	14	nonlinear	nonlinear	ADJ
fumecheng-13730	340	15	oscillators	oscillator	NOUN
fumecheng-13730	340	16	with	with	ADP
fumecheng-13730	340	17	an	an	DET
fumecheng-13730	340	18	irrational	irrational	ADJ
fumecheng-13730	340	19	force	force	NOUN
fumecheng-13730	340	20	,	,	PUNCT
fumecheng-13730	340	21	computers	computer	NOUN
fumecheng-13730	340	22	and	and	CCONJ
fumecheng-13730	340	23	mathematics	mathematic	NOUN
fumecheng-13730	340	24	with	with	ADP
fumecheng-13730	340	25	applications	application	NOUN
fumecheng-13730	340	26	,	,	PUNCT
fumecheng-13730	340	27	58(11	58(11	NUM
fumecheng-13730	340	28	-	-	SYM
fumecheng-13730	340	29	12	12	NUM
fumecheng-13730	340	30	)	)	PUNCT
fumecheng-13730	340	31	,	,	PUNCT
fumecheng-13730	340	32	pp	pp	ADJ
fumecheng-13730	340	33	.	.	PUNCT
fumecheng-13730	341	1	2477	2477	NUM
fumecheng-13730	341	2	-	-	SYM
fumecheng-13730	341	3	2479	2479	NUM
fumecheng-13730	341	4	.	.	PUNCT
fumecheng-13730	342	1	23	23	NUM
fumecheng-13730	342	2	.	.	X
fumecheng-13730	343	1	ebaid	ebaid	PROPN
fumecheng-13730	343	2	,	,	PUNCT
fumecheng-13730	343	3	a.e	a.e	PROPN
fumecheng-13730	343	4	.	.	PROPN
fumecheng-13730	343	5	,	,	PUNCT
fumecheng-13730	343	6	2009	2009	NUM
fumecheng-13730	343	7	,	,	PUNCT
fumecheng-13730	343	8	oscillations	oscillation	NOUN
fumecheng-13730	343	9	in	in	ADP
fumecheng-13730	343	10	an	an	DET
fumecheng-13730	343	11	x(2n+2)/(2n+1	x(2n+2)/(2n+1	PROPN
fumecheng-13730	343	12	)	)	PUNCT
fumecheng-13730	343	13	potential	potential	NOUN
fumecheng-13730	343	14	via	via	ADP
fumecheng-13730	343	15	he	he	PRON
fumecheng-13730	343	16	's	's	PART
fumecheng-13730	343	17	frequency	frequency	NOUN
fumecheng-13730	343	18	-	-	PUNCT
fumecheng-13730	343	19	amplitude	amplitude	NOUN
fumecheng-13730	343	20	formulation	formulation	NOUN
fumecheng-13730	343	21	,	,	PUNCT
fumecheng-13730	343	22	zeitschrift	zeitschrift	NOUN
fumecheng-13730	343	23	fur	fur	NOUN
fumecheng-13730	343	24	naturforschung	naturforschung	PROPN
fumecheng-13730	343	25	a	a	ADP
fumecheng-13730	343	26	,	,	PUNCT
fumecheng-13730	343	27	64	64	NUM
fumecheng-13730	343	28	(	(	PUNCT
fumecheng-13730	343	29	12	12	NUM
fumecheng-13730	343	30	)	)	PUNCT
fumecheng-13730	343	31	,	,	PUNCT
fumecheng-13730	343	32	pp	pp	PROPN
fumecheng-13730	343	33	.	.	PUNCT
fumecheng-13730	344	1	877	877	NUM
fumecheng-13730	344	2	-	-	SYM
fumecheng-13730	344	3	878	878	NUM
fumecheng-13730	344	4	.	.	PUNCT
fumecheng-13730	345	1	24	24	NUM
fumecheng-13730	345	2	.	.	PUNCT
fumecheng-13730	346	1	elías	elías	PROPN
fumecheng-13730	346	2	-	-	PUNCT
fumecheng-13730	346	3	zúñiga	zúñiga	PROPN
fumecheng-13730	346	4	,	,	PUNCT
fumecheng-13730	346	5	a.	a.	NOUN
fumecheng-13730	346	6	,	,	PUNCT
fumecheng-13730	346	7	palacios	palacio	NOUN
fumecheng-13730	346	8	-	-	PUNCT
fumecheng-13730	346	9	pineda	pineda	PROPN
fumecheng-13730	346	10	,	,	PUNCT
fumecheng-13730	346	11	l.m	l.m	PROPN
fumecheng-13730	346	12	.	.	PROPN
fumecheng-13730	346	13	,	,	PUNCT
fumecheng-13730	346	14	jiménez	jiménez	PROPN
fumecheng-13730	346	15	-	-	PUNCT
fumecheng-13730	346	16	cedeño	cedeño	PROPN
fumecheng-13730	346	17	,	,	PUNCT
fumecheng-13730	346	18	i.h	i.h	PROPN
fumecheng-13730	346	19	.	.	PROPN
fumecheng-13730	346	20	,	,	PUNCT
fumecheng-13730	346	21	martínez	martínez	PROPN
fumecheng-13730	346	22	-	-	PUNCT
fumecheng-13730	346	23	romero	romero	PROPN
fumecheng-13730	346	24	,	,	PUNCT
fumecheng-13730	346	25	o.	o.	PROPN
fumecheng-13730	346	26	,	,	PUNCT
fumecheng-13730	346	27	olvera	olvera	PROPN
fumecheng-13730	346	28	-	-	PUNCT
fumecheng-13730	346	29	trejo	trejo	PROPN
fumecheng-13730	346	30	,	,	PUNCT
fumecheng-13730	346	31	d.	d.	PROPN
fumecheng-13730	346	32	,	,	PUNCT
fumecheng-13730	346	33	2020	2020	NUM
fumecheng-13730	346	34	,	,	PUNCT
fumecheng-13730	346	35	enhanced	enhance	VERB
fumecheng-13730	346	36	he	he	PRON
fumecheng-13730	346	37	's	's	PART
fumecheng-13730	346	38	frequency	frequency	NOUN
fumecheng-13730	346	39	-	-	PUNCT
fumecheng-13730	346	40	amplitude	amplitude	NOUN
fumecheng-13730	346	41	formulation	formulation	NOUN
fumecheng-13730	346	42	for	for	ADP
fumecheng-13730	346	43	nonlinear	nonlinear	ADJ
fumecheng-13730	346	44	oscillators	oscillator	NOUN
fumecheng-13730	346	45	,	,	PUNCT
fumecheng-13730	346	46	results	result	NOUN
fumecheng-13730	346	47	in	in	ADP
fumecheng-13730	346	48	physics	physics	NOUN
fumecheng-13730	346	49	,	,	PUNCT
fumecheng-13730	346	50	19	19	NUM
fumecheng-13730	346	51	,	,	PUNCT
fumecheng-13730	346	52	103626	103626	NUM
fumecheng-13730	346	53	.	.	PUNCT
fumecheng-13730	347	1	210	210	NUM
fumecheng-13730	347	2	c.h	c.h	NOUN
fumecheng-13730	347	3	.	.	PUNCT
fumecheng-13730	348	1	he	he	PRON
fumecheng-13730	348	2	,	,	PUNCT
fumecheng-13730	348	3	j.h	j.h	PROPN
fumecheng-13730	348	4	.	.	PUNCT
fumecheng-13730	349	1	he	he	PRON
fumecheng-13730	349	2	,	,	PUNCT
fumecheng-13730	349	3	j.	j.	PROPN
fumecheng-13730	349	4	ma	ma	PROPN
fumecheng-13730	349	5	,	,	PUNCT
fumecheng-13730	349	6	a.a	a.a	PROPN
fumecheng-13730	349	7	.	.	PROPN
fumecheng-13730	349	8	alsolam	alsolam	PROPN
fumecheng-13730	349	9	,	,	PUNCT
fumecheng-13730	349	10	x.j	x.j	PROPN
fumecheng-13730	349	11	.	.	PROPN
fumecheng-13730	349	12	yang	yang	PROPN
fumecheng-13730	349	13	25	25	NUM
fumecheng-13730	349	14	.	.	PUNCT
fumecheng-13730	350	1	mohammadian	mohammadian	NOUN
fumecheng-13730	350	2	,	,	PUNCT
fumecheng-13730	350	3	m.	m.	NOUN
fumecheng-13730	350	4	,	,	PUNCT
fumecheng-13730	350	5	2024	2024	NUM
fumecheng-13730	350	6	,	,	PUNCT
fumecheng-13730	350	7	application	application	NOUN
fumecheng-13730	350	8	of	of	ADP
fumecheng-13730	351	1	he	he	PRON
fumecheng-13730	351	2	's	be	AUX
fumecheng-13730	351	3	new	new	ADJ
fumecheng-13730	351	4	frequency	frequency	NOUN
fumecheng-13730	351	5	-	-	PUNCT
fumecheng-13730	351	6	amplitude	amplitude	NOUN
fumecheng-13730	351	7	formulation	formulation	NOUN
fumecheng-13730	351	8	for	for	ADP
fumecheng-13730	351	9	the	the	DET
fumecheng-13730	351	10	nonlinear	nonlinear	ADJ
fumecheng-13730	351	11	oscillators	oscillator	NOUN
fumecheng-13730	351	12	by	by	ADP
fumecheng-13730	351	13	introducing	introduce	VERB
fumecheng-13730	351	14	a	a	DET
fumecheng-13730	351	15	new	new	ADJ
fumecheng-13730	351	16	trend	trend	NOUN
fumecheng-13730	351	17	for	for	ADP
fumecheng-13730	351	18	determining	determine	VERB
fumecheng-13730	351	19	the	the	DET
fumecheng-13730	351	20	location	location	NOUN
fumecheng-13730	351	21	points	point	NOUN
fumecheng-13730	351	22	,	,	PUNCT
fumecheng-13730	351	23	chinese	chinese	ADJ
fumecheng-13730	351	24	journal	journal	PROPN
fumecheng-13730	351	25	of	of	ADP
fumecheng-13730	351	26	physics	physics	PROPN
fumecheng-13730	351	27	,	,	PUNCT
fumecheng-13730	351	28	89	89	NUM
fumecheng-13730	351	29	,	,	PUNCT
fumecheng-13730	351	30	pp	pp	ADJ
fumecheng-13730	351	31	.	.	PUNCT
fumecheng-13730	352	1	1024	1024	NUM
fumecheng-13730	352	2	-	-	SYM
fumecheng-13730	352	3	1040	1040	NUM
fumecheng-13730	352	4	.	.	PUNCT
fumecheng-13730	353	1	26	26	NUM
fumecheng-13730	353	2	.	.	PUNCT
fumecheng-13730	354	1	li	li	PROPN
fumecheng-13730	354	2	,	,	PUNCT
fumecheng-13730	354	3	y.d	y.d	PROPN
fumecheng-13730	354	4	.	.	PROPN
fumecheng-13730	354	5	,	,	PUNCT
fumecheng-13730	354	6	yang	yang	PROPN
fumecheng-13730	354	7	,	,	PUNCT
fumecheng-13730	354	8	y.r	y.r	PROPN
fumecheng-13730	354	9	.	.	PROPN
fumecheng-13730	354	10	,	,	PUNCT
fumecheng-13730	354	11	2017	2017	NUM
fumecheng-13730	354	12	,	,	PUNCT
fumecheng-13730	354	13	vibration	vibration	NOUN
fumecheng-13730	354	14	analysis	analysis	NOUN
fumecheng-13730	354	15	of	of	ADP
fumecheng-13730	354	16	conveying	convey	VERB
fumecheng-13730	354	17	fluid	fluid	ADJ
fumecheng-13730	354	18	pipe	pipe	NOUN
fumecheng-13730	354	19	via	via	ADP
fumecheng-13730	354	20	he	he	PRON
fumecheng-13730	354	21	’s	’	VERB
fumecheng-13730	354	22	variational	variational	ADJ
fumecheng-13730	354	23	iteration	iteration	NOUN
fumecheng-13730	354	24	method	method	NOUN
fumecheng-13730	354	25	,	,	PUNCT
fumecheng-13730	354	26	applied	apply	VERB
fumecheng-13730	354	27	mathematical	mathematical	ADJ
fumecheng-13730	354	28	modelling	modelling	NOUN
fumecheng-13730	354	29	,	,	PUNCT
fumecheng-13730	354	30	43	43	NUM
fumecheng-13730	354	31	,	,	PUNCT
fumecheng-13730	354	32	pp	pp	ADJ
fumecheng-13730	354	33	.	.	PUNCT
fumecheng-13730	355	1	409	409	NUM
fumecheng-13730	355	2	-	-	SYM
fumecheng-13730	355	3	420	420	NUM
fumecheng-13730	355	4	.	.	PUNCT
fumecheng-13730	356	1	27	27	NUM
fumecheng-13730	356	2	.	.	PUNCT
fumecheng-13730	357	1	brodsky	brodsky	PROPN
fumecheng-13730	357	2	,	,	PUNCT
fumecheng-13730	357	3	y.	y.	PROPN
fumecheng-13730	357	4	,	,	PUNCT
fumecheng-13730	357	5	2024	2024	NUM
fumecheng-13730	357	6	,	,	PUNCT
fumecheng-13730	357	7	analyzing	analyze	VERB
fumecheng-13730	357	8	and	and	CCONJ
fumecheng-13730	357	9	simulating	simulate	VERB
fumecheng-13730	357	10	the	the	DET
fumecheng-13730	357	11	oscillation	oscillation	NOUN
fumecheng-13730	357	12	in	in	ADP
fumecheng-13730	357	13	multidimensional	multidimensional	ADJ
fumecheng-13730	357	14	odd	odd	ADJ
fumecheng-13730	357	15	competitive	competitive	ADJ
fumecheng-13730	357	16	systems	system	NOUN
fumecheng-13730	357	17	,	,	PUNCT
fumecheng-13730	357	18	advances	advance	NOUN
fumecheng-13730	357	19	in	in	ADP
fumecheng-13730	357	20	differential	differential	ADJ
fumecheng-13730	357	21	equations	equation	NOUN
fumecheng-13730	357	22	and	and	CCONJ
fumecheng-13730	357	23	control	control	NOUN
fumecheng-13730	357	24	processes	process	NOUN
fumecheng-13730	357	25	,	,	PUNCT
fumecheng-13730	357	26	31	31	NUM
fumecheng-13730	357	27	(	(	PUNCT
fumecheng-13730	357	28	3	3	NUM
fumecheng-13730	357	29	)	)	PUNCT
fumecheng-13730	357	30	,	,	PUNCT
fumecheng-13730	357	31	2441	2441	NUM
fumecheng-13730	357	32	.	.	PUNCT
fumecheng-13730	358	1	28	28	NUM
fumecheng-13730	358	2	.	.	PUNCT
fumecheng-13730	358	3	alshomrani	alshomrani	PROPN
fumecheng-13730	358	4	,	,	PUNCT
fumecheng-13730	358	5	n.	n.	NOUN
fumecheng-13730	358	6	,	,	PUNCT
fumecheng-13730	358	7	g.	g.	PROPN
fumecheng-13730	358	8	,	,	PUNCT
fumecheng-13730	358	9	alharbi	alharbi	PROPN
fumecheng-13730	358	10	,	,	PUNCT
fumecheng-13730	358	11	w.	w.	PROPN
fumecheng-13730	358	12	,	,	PUNCT
fumecheng-13730	358	13	alanazi	alanazi	PROPN
fumecheng-13730	358	14	,	,	PUNCT
fumecheng-13730	358	15	i.	i.	PROPN
fumecheng-13730	358	16	,	,	PUNCT
fumecheng-13730	358	17	alyasi	alyasi	PROPN
fumecheng-13730	358	18	,	,	PUNCT
fumecheng-13730	358	19	l.	l.	PROPN
fumecheng-13730	358	20	,	,	PUNCT
fumecheng-13730	358	21	alrefaei	alrefaei	NOUN
fumecheng-13730	358	22	,	,	PUNCT
fumecheng-13730	358	23	g.	g.	PROPN
fumecheng-13730	358	24	,	,	PUNCT
fumecheng-13730	358	25	a.al’amri	a.al’amri	PROPN
fumecheng-13730	358	26	,	,	PUNCT
fumecheng-13730	358	27	s.	s.	PROPN
fumecheng-13730	358	28	,	,	PUNCT
fumecheng-13730	358	29	alanzi	alanzi	PROPN
fumecheng-13730	358	30	,	,	PUNCT
fumecheng-13730	358	31	a.	a.	NOUN
fumecheng-13730	358	32	,	,	PUNCT
fumecheng-13730	358	33	2024	2024	NUM
fumecheng-13730	358	34	,	,	PUNCT
fumecheng-13730	358	35	homotopy	homotopy	VERB
fumecheng-13730	358	36	perturbation	perturbation	NOUN
fumecheng-13730	358	37	method	method	NOUN
fumecheng-13730	358	38	for	for	ADP
fumecheng-13730	358	39	solving	solve	VERB
fumecheng-13730	358	40	a	a	DET
fumecheng-13730	358	41	nonlinear	nonlinear	ADJ
fumecheng-13730	358	42	system	system	NOUN
fumecheng-13730	358	43	for	for	ADP
fumecheng-13730	358	44	an	an	DET
fumecheng-13730	358	45	epidemic	epidemic	NOUN
fumecheng-13730	358	46	,	,	PUNCT
fumecheng-13730	358	47	advances	advance	NOUN
fumecheng-13730	358	48	in	in	ADP
fumecheng-13730	358	49	differential	differential	ADJ
fumecheng-13730	358	50	equations	equation	NOUN
fumecheng-13730	358	51	and	and	CCONJ
fumecheng-13730	358	52	control	control	NOUN
fumecheng-13730	358	53	processes	process	NOUN
fumecheng-13730	358	54	,	,	PUNCT
fumecheng-13730	358	55	31(3	31(3	NUM
fumecheng-13730	358	56	)	)	PUNCT
fumecheng-13730	358	57	,	,	PUNCT
fumecheng-13730	358	58	2442	2442	NUM
fumecheng-13730	358	59	.	.	PUNCT
fumecheng-13730	359	1	29	29	NUM
fumecheng-13730	359	2	.	.	X
fumecheng-13730	360	1	öziş	öziş	NOUN
fumecheng-13730	360	2	,	,	PUNCT
fumecheng-13730	360	3	t.	t.	PROPN
fumecheng-13730	360	4	,	,	PUNCT
fumecheng-13730	360	5	yıldırım	yıldırım	PROPN
fumecheng-13730	360	6	,	,	PUNCT
fumecheng-13730	360	7	a.	a.	NOUN
fumecheng-13730	360	8	,	,	PUNCT
fumecheng-13730	360	9	2007	2007	NUM
fumecheng-13730	360	10	,	,	PUNCT
fumecheng-13730	360	11	a	a	DET
fumecheng-13730	360	12	study	study	NOUN
fumecheng-13730	360	13	of	of	ADP
fumecheng-13730	360	14	nonlinear	nonlinear	ADJ
fumecheng-13730	360	15	oscillators	oscillator	NOUN
fumecheng-13730	360	16	with	with	ADP
fumecheng-13730	360	17	u1/3	u1/3	PROPN
fumecheng-13730	360	18	force	force	NOUN
fumecheng-13730	360	19	by	by	ADP
fumecheng-13730	360	20	he	he	PRON
fumecheng-13730	360	21	's	's	PART
fumecheng-13730	360	22	variational	variational	ADJ
fumecheng-13730	360	23	iteration	iteration	NOUN
fumecheng-13730	360	24	method	method	NOUN
fumecheng-13730	360	25	,	,	PUNCT
fumecheng-13730	360	26	journal	journal	NOUN
fumecheng-13730	360	27	of	of	ADP
fumecheng-13730	360	28	sound	sound	NOUN
fumecheng-13730	360	29	and	and	CCONJ
fumecheng-13730	360	30	vibration	vibration	NOUN
fumecheng-13730	360	31	,	,	PUNCT
fumecheng-13730	360	32	306(1–2	306(1–2	NUM
fumecheng-13730	360	33	)	)	PUNCT
fumecheng-13730	360	34	,	,	PUNCT
fumecheng-13730	360	35	pp	pp	PROPN
fumecheng-13730	360	36	.	.	PUNCT
fumecheng-13730	361	1	372	372	NUM
fumecheng-13730	361	2	-	-	SYM
fumecheng-13730	361	3	376	376	NUM
fumecheng-13730	361	4	.	.	PUNCT
fumecheng-13730	362	1	30	30	NUM
fumecheng-13730	362	2	.	.	PUNCT
fumecheng-13730	363	1	belendez	belendez	PROPN
fumecheng-13730	363	2	,	,	PUNCT
fumecheng-13730	363	3	a.	a.	NOUN
fumecheng-13730	363	4	,	,	PUNCT
fumecheng-13730	363	5	pascual	pascual	NOUN
fumecheng-13730	363	6	,	,	PUNCT
fumecheng-13730	363	7	c.	c.	NOUN
fumecheng-13730	363	8	,	,	PUNCT
fumecheng-13730	363	9	gallego	gallego	NOUN
fumecheng-13730	363	10	,	,	PUNCT
fumecheng-13730	363	11	s.	s.	PROPN
fumecheng-13730	363	12	,	,	PUNCT
fumecheng-13730	363	13	ortuño	ortuño	PROPN
fumecheng-13730	363	14	,	,	PUNCT
fumecheng-13730	363	15	m.	m.	NOUN
fumecheng-13730	363	16	,	,	PUNCT
fumecheng-13730	363	17	neipp	neipp	PROPN
fumecheng-13730	363	18	,	,	PUNCT
fumecheng-13730	363	19	c.	c.	PROPN
fumecheng-13730	363	20	,	,	PUNCT
fumecheng-13730	363	21	2007	2007	NUM
fumecheng-13730	363	22	,	,	PUNCT
fumecheng-13730	363	23	application	application	NOUN
fumecheng-13730	363	24	of	of	ADP
fumecheng-13730	363	25	a	a	DET
fumecheng-13730	363	26	modified	modify	VERB
fumecheng-13730	363	27	he	he	PRON
fumecheng-13730	363	28	's	's	PART
fumecheng-13730	363	29	homotopy	homotopy	NOUN
fumecheng-13730	363	30	perturbation	perturbation	NOUN
fumecheng-13730	363	31	method	method	NOUN
fumecheng-13730	363	32	to	to	PART
fumecheng-13730	363	33	obtain	obtain	VERB
fumecheng-13730	363	34	higher	high	ADJ
fumecheng-13730	363	35	-	-	PUNCT
fumecheng-13730	363	36	order	order	NOUN
fumecheng-13730	363	37	approximations	approximation	NOUN
fumecheng-13730	363	38	of	of	ADP
fumecheng-13730	363	39	an	an	DET
fumecheng-13730	363	40	x1/3	x1/3	PROPN
fumecheng-13730	363	41	force	force	PROPN
fumecheng-13730	363	42	nonlinear	nonlinear	PROPN
fumecheng-13730	363	43	oscillator	oscillator	NOUN
fumecheng-13730	363	44	,	,	PUNCT
fumecheng-13730	363	45	physics	physics	NOUN
fumecheng-13730	363	46	letters	letter	NOUN
fumecheng-13730	363	47	a	a	DET
fumecheng-13730	363	48	,	,	PUNCT
fumecheng-13730	363	49	371(5–6	371(5–6	NUM
fumecheng-13730	363	50	)	)	PUNCT
fumecheng-13730	363	51	,	,	PUNCT
fumecheng-13730	363	52	pp	pp	ADP
fumecheng-13730	363	53	.	.	PUNCT
fumecheng-13730	364	1	421	421	NUM
fumecheng-13730	364	2	-	-	SYM
fumecheng-13730	364	3	426	426	NUM
fumecheng-13730	364	4	.	.	PROPN
fumecheng-13730	365	1	31	31	NUM
fumecheng-13730	365	2	.	.	PUNCT
fumecheng-13730	366	1	beléndez	beléndez	PROPN
fumecheng-13730	366	2	,	,	PUNCT
fumecheng-13730	366	3	a.	a.	PROPN
fumecheng-13730	366	4	,	,	PUNCT
fumecheng-13730	366	5	hernández	hernández	PROPN
fumecheng-13730	366	6	,	,	PUNCT
fumecheng-13730	366	7	a.	a.	NOUN
fumecheng-13730	366	8	,	,	PUNCT
fumecheng-13730	366	9	beléndez	beléndez	PROPN
fumecheng-13730	366	10	,	,	PUNCT
fumecheng-13730	366	11	t.	t.	PROPN
fumecheng-13730	366	12	,	,	PUNCT
fumecheng-13730	366	13	neipp	neipp	PROPN
fumecheng-13730	366	14	,	,	PUNCT
fumecheng-13730	366	15	c.	c.	PROPN
fumecheng-13730	366	16	,	,	PUNCT
fumecheng-13730	366	17	márquez	márquez	PROPN
fumecheng-13730	366	18	,	,	PUNCT
fumecheng-13730	366	19	a.	a.	NOUN
fumecheng-13730	366	20	,	,	PUNCT
fumecheng-13730	366	21	2008	2008	NUM
fumecheng-13730	366	22	,	,	PUNCT
fumecheng-13730	366	23	higher	high	ADJ
fumecheng-13730	366	24	accuracy	accuracy	NOUN
fumecheng-13730	366	25	analytical	analytical	ADJ
fumecheng-13730	366	26	approximations	approximation	NOUN
fumecheng-13730	366	27	to	to	ADP
fumecheng-13730	366	28	a	a	DET
fumecheng-13730	366	29	nonlinear	nonlinear	ADJ
fumecheng-13730	366	30	oscillator	oscillator	NOUN
fumecheng-13730	366	31	with	with	ADP
fumecheng-13730	366	32	discontinuity	discontinuity	NOUN
fumecheng-13730	366	33	by	by	ADP
fumecheng-13730	366	34	he	he	PRON
fumecheng-13730	366	35	's	's	PART
fumecheng-13730	366	36	homotopy	homotopy	NOUN
fumecheng-13730	366	37	perturbation	perturbation	NOUN
fumecheng-13730	366	38	method	method	NOUN
fumecheng-13730	366	39	,	,	PUNCT
fumecheng-13730	366	40	physics	physics	NOUN
fumecheng-13730	366	41	letters	letter	NOUN
fumecheng-13730	366	42	a	a	PRON
fumecheng-13730	366	43	,	,	PUNCT
fumecheng-13730	366	44	372(12	372(12	NUM
fumecheng-13730	366	45	)	)	PUNCT
fumecheng-13730	366	46	,	,	PUNCT
fumecheng-13730	366	47	pp	pp	PROPN
fumecheng-13730	366	48	.	.	PUNCT
fumecheng-13730	367	1	2010	2010	NUM
fumecheng-13730	367	2	-	-	SYM
fumecheng-13730	367	3	2016	2016	NUM
fumecheng-13730	367	4	.	.	PUNCT
fumecheng-13730	368	1	32	32	NUM
fumecheng-13730	368	2	.	.	PUNCT
fumecheng-13730	369	1	bayat	bayat	PROPN
fumecheng-13730	369	2	,	,	PUNCT
fumecheng-13730	369	3	m.	m.	NOUN
fumecheng-13730	369	4	,	,	PUNCT
fumecheng-13730	369	5	bayat	bayat	PROPN
fumecheng-13730	369	6	,	,	PUNCT
fumecheng-13730	369	7	m.	m.	NOUN
fumecheng-13730	369	8	,	,	PUNCT
fumecheng-13730	369	9	pakar	pakar	PROPN
fumecheng-13730	369	10	,	,	PUNCT
fumecheng-13730	369	11	i.	i.	PROPN
fumecheng-13730	369	12	,	,	PUNCT
fumecheng-13730	369	13	2014	2014	NUM
fumecheng-13730	369	14	,	,	PUNCT
fumecheng-13730	369	15	accurate	accurate	ADJ
fumecheng-13730	369	16	analytical	analytical	ADJ
fumecheng-13730	369	17	solutions	solution	NOUN
fumecheng-13730	369	18	for	for	ADP
fumecheng-13730	369	19	nonlinear	nonlinear	ADJ
fumecheng-13730	369	20	oscillators	oscillator	NOUN
fumecheng-13730	369	21	with	with	ADP
fumecheng-13730	369	22	discontinuous	discontinuous	ADJ
fumecheng-13730	369	23	,	,	PUNCT
fumecheng-13730	369	24	structural	structural	ADJ
fumecheng-13730	369	25	engineering	engineering	NOUN
fumecheng-13730	369	26	and	and	CCONJ
fumecheng-13730	369	27	mechanics	mechanic	NOUN
fumecheng-13730	369	28	,	,	PUNCT
fumecheng-13730	369	29	51(2	51(2	NUM
fumecheng-13730	369	30	)	)	PUNCT
fumecheng-13730	369	31	,	,	PUNCT
fumecheng-13730	369	32	pp	pp	ADJ
fumecheng-13730	369	33	.	.	PUNCT
fumecheng-13730	370	1	349	349	NUM
fumecheng-13730	370	2	-	-	SYM
fumecheng-13730	370	3	360	360	NUM
fumecheng-13730	370	4	.	.	PUNCT
fumecheng-13730	371	1	33	33	NUM
fumecheng-13730	371	2	.	.	PUNCT
fumecheng-13730	372	1	liu	liu	PROPN
fumecheng-13730	372	2	,	,	PUNCT
fumecheng-13730	372	3	h.m	h.m	PROPN
fumecheng-13730	372	4	.	.	PROPN
fumecheng-13730	372	5	,	,	PUNCT
fumecheng-13730	372	6	2005	2005	NUM
fumecheng-13730	372	7	,	,	PUNCT
fumecheng-13730	372	8	approximate	approximate	ADJ
fumecheng-13730	372	9	period	period	NOUN
fumecheng-13730	372	10	of	of	ADP
fumecheng-13730	372	11	nonlinear	nonlinear	ADJ
fumecheng-13730	372	12	oscillators	oscillator	NOUN
fumecheng-13730	372	13	with	with	ADP
fumecheng-13730	372	14	discontinuities	discontinuity	NOUN
fumecheng-13730	372	15	by	by	ADP
fumecheng-13730	372	16	modified	modified	ADJ
fumecheng-13730	372	17	lindstedt	lindstedt	PROPN
fumecheng-13730	372	18	–	–	PUNCT
fumecheng-13730	372	19	poincare	poincare	PROPN
fumecheng-13730	372	20	method	method	NOUN
fumecheng-13730	372	21	,	,	PUNCT
fumecheng-13730	372	22	chaos	chaos	NOUN
fumecheng-13730	372	23	,	,	PUNCT
fumecheng-13730	372	24	solitons	soliton	NOUN
fumecheng-13730	372	25	&	&	CCONJ
fumecheng-13730	372	26	fractals	fractal	NOUN
fumecheng-13730	372	27	,	,	PUNCT
fumecheng-13730	372	28	23(2	23(2	NUM
fumecheng-13730	372	29	)	)	PUNCT
fumecheng-13730	372	30	,	,	PUNCT
fumecheng-13730	372	31	pp	pp	ADP
fumecheng-13730	372	32	.	.	PUNCT
fumecheng-13730	373	1	577	577	NUM
fumecheng-13730	373	2	-	-	SYM
fumecheng-13730	373	3	579	579	NUM
fumecheng-13730	373	4	.	.	PUNCT
fumecheng-13730	374	1	34	34	NUM
fumecheng-13730	374	2	.	.	PUNCT
fumecheng-13730	375	1	ji	ji	PROPN
fumecheng-13730	375	2	,	,	PUNCT
fumecheng-13730	375	3	q.p	q.p	PROPN
fumecheng-13730	375	4	.	.	PROPN
fumecheng-13730	375	5	,	,	PUNCT
fumecheng-13730	375	6	wang	wang	PROPN
fumecheng-13730	375	7	,	,	PUNCT
fumecheng-13730	375	8	j.	j.	PROPN
fumecheng-13730	375	9	,	,	PUNCT
fumecheng-13730	375	10	lu	lu	PROPN
fumecheng-13730	375	11	,	,	PUNCT
fumecheng-13730	375	12	l.x	l.x	PROPN
fumecheng-13730	375	13	.	.	PROPN
fumecheng-13730	375	14	,	,	PUNCT
fumecheng-13730	375	15	ge	ge	PROPN
fumecheng-13730	375	16	,	,	PUNCT
fumecheng-13730	375	17	c.f	c.f	PROPN
fumecheng-13730	375	18	.	.	PROPN
fumecheng-13730	375	19	,	,	PUNCT
fumecheng-13730	375	20	2021	2021	NUM
fumecheng-13730	375	21	,	,	PUNCT
fumecheng-13730	375	22	li	li	PROPN
fumecheng-13730	375	23	-	-	PROPN
fumecheng-13730	375	24	he	he	PRON
fumecheng-13730	375	25	's	's	PART
fumecheng-13730	375	26	modified	modify	VERB
fumecheng-13730	375	27	homotopy	homotopy	NOUN
fumecheng-13730	375	28	perturbation	perturbation	NOUN
fumecheng-13730	375	29	method	method	NOUN
fumecheng-13730	375	30	coupled	couple	VERB
fumecheng-13730	375	31	with	with	ADP
fumecheng-13730	375	32	the	the	DET
fumecheng-13730	375	33	energy	energy	NOUN
fumecheng-13730	375	34	method	method	NOUN
fumecheng-13730	375	35	for	for	ADP
fumecheng-13730	375	36	the	the	DET
fumecheng-13730	375	37	dropping	drop	VERB
fumecheng-13730	375	38	shock	shock	NOUN
fumecheng-13730	375	39	response	response	NOUN
fumecheng-13730	375	40	of	of	ADP
fumecheng-13730	375	41	a	a	DET
fumecheng-13730	375	42	tangent	tangent	ADJ
fumecheng-13730	375	43	nonlinear	nonlinear	ADJ
fumecheng-13730	375	44	packaging	packaging	NOUN
fumecheng-13730	375	45	system	system	NOUN
fumecheng-13730	375	46	,	,	PUNCT
fumecheng-13730	375	47	journal	journal	NOUN
fumecheng-13730	375	48	of	of	ADP
fumecheng-13730	375	49	low	low	ADJ
fumecheng-13730	375	50	frequency	frequency	NOUN
fumecheng-13730	375	51	noise	noise	NOUN
fumecheng-13730	375	52	,	,	PUNCT
fumecheng-13730	375	53	vibration	vibration	NOUN
fumecheng-13730	375	54	&	&	CCONJ
fumecheng-13730	375	55	active	active	ADJ
fumecheng-13730	375	56	control	control	NOUN
fumecheng-13730	375	57	,	,	PUNCT
fumecheng-13730	375	58	40(2	40(2	NUM
fumecheng-13730	375	59	)	)	PUNCT
fumecheng-13730	375	60	,	,	PUNCT
fumecheng-13730	376	1	pp	pp	ADJ
fumecheng-13730	376	2	.	.	PUNCT
fumecheng-13730	377	1	675	675	NUM
fumecheng-13730	377	2	-	-	SYM
fumecheng-13730	377	3	682	682	NUM
fumecheng-13730	377	4	.	.	PUNCT
fumecheng-13730	378	1	35	35	NUM
fumecheng-13730	378	2	.	.	X
fumecheng-13730	379	1	zhang	zhang	PROPN
fumecheng-13730	379	2	,	,	PUNCT
fumecheng-13730	379	3	h.l	h.l	PROPN
fumecheng-13730	379	4	.	.	PROPN
fumecheng-13730	379	5	,	,	PUNCT
fumecheng-13730	379	6	2008	2008	NUM
fumecheng-13730	379	7	,	,	PUNCT
fumecheng-13730	379	8	application	application	NOUN
fumecheng-13730	379	9	of	of	ADP
fumecheng-13730	379	10	he	he	PRON
fumecheng-13730	379	11	’s	’s	PART
fumecheng-13730	379	12	amplitude	amplitude	NOUN
fumecheng-13730	379	13	–	–	PUNCT
fumecheng-13730	379	14	frequency	frequency	NOUN
fumecheng-13730	379	15	formulation	formulation	NOUN
fumecheng-13730	379	16	to	to	ADP
fumecheng-13730	379	17	a	a	DET
fumecheng-13730	379	18	nonlinear	nonlinear	ADJ
fumecheng-13730	379	19	oscillator	oscillator	NOUN
fumecheng-13730	379	20	with	with	ADP
fumecheng-13730	379	21	discontinuity	discontinuity	NOUN
fumecheng-13730	379	22	,	,	PUNCT
fumecheng-13730	379	23	computers	computer	NOUN
fumecheng-13730	379	24	&	&	CCONJ
fumecheng-13730	379	25	mathematics	mathematics	PROPN
fumecheng-13730	379	26	with	with	ADP
fumecheng-13730	379	27	applications	application	NOUN
fumecheng-13730	379	28	,	,	PUNCT
fumecheng-13730	379	29	58(11–12	58(11–12	NUM
fumecheng-13730	379	30	)	)	PUNCT
fumecheng-13730	379	31	,	,	PUNCT
fumecheng-13730	379	32	pp	pp	ADJ
fumecheng-13730	379	33	.	.	PUNCT
fumecheng-13730	379	34	2197	2197	NUM
fumecheng-13730	379	35	-	-	SYM
fumecheng-13730	379	36	2198	2198	NUM
fumecheng-13730	379	37	.	.	PUNCT
fumecheng-13730	380	1	36	36	NUM
fumecheng-13730	380	2	.	.	X
fumecheng-13730	381	1	wang	wang	PROPN
fumecheng-13730	381	2	,	,	PUNCT
fumecheng-13730	381	3	s.q	s.q	PROPN
fumecheng-13730	381	4	.	.	PROPN
fumecheng-13730	381	5	,	,	PUNCT
fumecheng-13730	381	6	he	he	PRON
fumecheng-13730	381	7	,	,	PUNCT
fumecheng-13730	381	8	j.h	j.h	PROPN
fumecheng-13730	381	9	.	.	PROPN
fumecheng-13730	381	10	,	,	PUNCT
fumecheng-13730	381	11	2008	2008	NUM
fumecheng-13730	381	12	,	,	PUNCT
fumecheng-13730	381	13	nonlinear	nonlinear	ADJ
fumecheng-13730	381	14	oscillator	oscillator	NOUN
fumecheng-13730	381	15	with	with	ADP
fumecheng-13730	381	16	discontinuity	discontinuity	NOUN
fumecheng-13730	381	17	by	by	ADP
fumecheng-13730	381	18	parameter	parameter	NOUN
fumecheng-13730	381	19	-	-	PUNCT
fumecheng-13730	381	20	expansion	expansion	NOUN
fumecheng-13730	381	21	method	method	NOUN
fumecheng-13730	381	22	,	,	PUNCT
fumecheng-13730	381	23	chaos	chaos	NOUN
fumecheng-13730	381	24	solitons	soliton	NOUN
fumecheng-13730	381	25	and	and	CCONJ
fumecheng-13730	381	26	fractals	fractal	NOUN
fumecheng-13730	381	27	,	,	PUNCT
fumecheng-13730	381	28	35(2008	35(2008	NOUN
fumecheng-13730	381	29	)	)	PUNCT
fumecheng-13730	381	30	,	,	PUNCT
fumecheng-13730	381	31	pp	pp	PROPN
fumecheng-13730	381	32	.	.	PUNCT
fumecheng-13730	382	1	688	688	NUM
fumecheng-13730	382	2	-	-	SYM
fumecheng-13730	382	3	691	691	NUM
fumecheng-13730	382	4	.	.	PUNCT
fumecheng-13730	383	1	37	37	NUM
fumecheng-13730	383	2	.	.	PUNCT
fumecheng-13730	384	1	shou	shou	PROPN
fumecheng-13730	384	2	,	,	PUNCT
fumecheng-13730	384	3	d.h	d.h	PROPN
fumecheng-13730	384	4	.	.	PROPN
fumecheng-13730	384	5	,	,	PUNCT
fumecheng-13730	384	6	2009	2009	NUM
fumecheng-13730	384	7	,	,	PUNCT
fumecheng-13730	384	8	variational	variational	ADJ
fumecheng-13730	384	9	approach	approach	NOUN
fumecheng-13730	384	10	for	for	ADP
fumecheng-13730	384	11	nonlinear	nonlinear	ADJ
fumecheng-13730	384	12	oscillators	oscillator	NOUN
fumecheng-13730	384	13	with	with	ADP
fumecheng-13730	384	14	discontinuities	discontinuity	NOUN
fumecheng-13730	384	15	,	,	PUNCT
fumecheng-13730	384	16	computers	computer	NOUN
fumecheng-13730	384	17	&	&	CCONJ
fumecheng-13730	384	18	mathematics	mathematics	PROPN
fumecheng-13730	384	19	with	with	ADP
fumecheng-13730	384	20	applications	application	NOUN
fumecheng-13730	384	21	,	,	PUNCT
fumecheng-13730	384	22	58(11–12	58(11–12	NUM
fumecheng-13730	384	23	)	)	PUNCT
fumecheng-13730	384	24	,	,	PUNCT
fumecheng-13730	384	25	pp	pp	ADP
fumecheng-13730	384	26	.	.	PUNCT
fumecheng-13730	385	1	2416	2416	NUM
fumecheng-13730	385	2	-	-	SYM
fumecheng-13730	385	3	2419	2419	NUM
fumecheng-13730	385	4	.	.	PUNCT
fumecheng-13730	386	1	38	38	NUM
fumecheng-13730	386	2	.	.	PUNCT
fumecheng-13730	387	1	he	he	PRON
fumecheng-13730	387	2	,	,	PUNCT
fumecheng-13730	387	3	j.-h	j.-h	PROPN
fumecheng-13730	387	4	.	.	PUNCT
fumecheng-13730	387	5	,	,	PUNCT
fumecheng-13730	387	6	2025	2025	NUM
fumecheng-13730	387	7	,	,	PUNCT
fumecheng-13730	387	8	frequency	frequency	NOUN
fumecheng-13730	387	9	-	-	PUNCT
fumecheng-13730	387	10	amplitude	amplitude	NOUN
fumecheng-13730	387	11	relationship	relationship	NOUN
fumecheng-13730	387	12	in	in	ADP
fumecheng-13730	387	13	nonlinear	nonlinear	ADJ
fumecheng-13730	387	14	oscillators	oscillator	NOUN
fumecheng-13730	387	15	with	with	ADP
fumecheng-13730	387	16	irrational	irrational	ADJ
fumecheng-13730	387	17	nonlinearities	nonlinearitie	NOUN
fumecheng-13730	387	18	,	,	PUNCT
fumecheng-13730	387	19	spectrum	spectrum	NOUN
fumecheng-13730	387	20	of	of	ADP
fumecheng-13730	387	21	mechanical	mechanical	ADJ
fumecheng-13730	387	22	engineering	engineering	NOUN
fumecheng-13730	387	23	and	and	CCONJ
fumecheng-13730	387	24	operational	operational	ADJ
fumecheng-13730	387	25	research	research	NOUN
fumecheng-13730	387	26	,	,	PUNCT
fumecheng-13730	387	27	2(1	2(1	NUM
fumecheng-13730	387	28	)	)	PUNCT
fumecheng-13730	387	29	,	,	PUNCT
fumecheng-13730	387	30	pp	pp	PROPN
fumecheng-13730	387	31	.	.	PUNCT
fumecheng-13730	388	1	121	121	NUM
fumecheng-13730	388	2	-	-	SYM
fumecheng-13730	388	3	129	129	NUM
fumecheng-13730	388	4	.	.	PUNCT