id	sid	tid	token	lemma	pos
ap-5556	1	1	acta	acta	PROPN
ap-5556	1	2	polytechnica	polytechnica	PROPN
ap-5556	1	3	doi:10.14311	doi:10.14311	PROPN
ap-5556	1	4	/	/	SYM
ap-5556	1	5	ap.2020.60.0127	ap.2020.60.0127	PROPN
ap-5556	1	6	acta	acta	PROPN
ap-5556	1	7	polytechnica	polytechnica	PROPN
ap-5556	1	8	60(2):127–144	60(2):127–144	PROPN
ap-5556	1	9	,	,	PUNCT
ap-5556	1	10	2020	2020	NUM
ap-5556	1	11	©	©	PROPN
ap-5556	1	12	czech	czech	PROPN
ap-5556	1	13	technical	technical	PROPN
ap-5556	1	14	university	university	PROPN
ap-5556	1	15	in	in	ADP
ap-5556	1	16	prague	prague	PROPN
ap-5556	1	17	,	,	PUNCT
ap-5556	1	18	2020	2020	NUM
ap-5556	1	19	available	available	ADJ
ap-5556	1	20	online	online	ADV
ap-5556	1	21	at	at	ADP
ap-5556	1	22	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-5556	1	23	investigation	investigation	NOUN
ap-5556	1	24	of	of	ADP
ap-5556	1	25	the	the	DET
ap-5556	1	26	dynamic	dynamic	ADJ
ap-5556	1	27	behaviour	behaviour	NOUN
ap-5556	1	28	of	of	ADP
ap-5556	1	29	non	non	ADJ
ap-5556	1	30	-	-	ADJ
ap-5556	1	31	uniform	uniform	ADJ
ap-5556	1	32	thickness	thickness	NOUN
ap-5556	1	33	circular	circular	ADJ
ap-5556	1	34	plates	plate	NOUN
ap-5556	1	35	resting	rest	VERB
ap-5556	1	36	on	on	ADP
ap-5556	1	37	winkler	winkler	NOUN
ap-5556	1	38	and	and	CCONJ
ap-5556	1	39	pasternak	pasternak	PROPN
ap-5556	1	40	foundations	foundation	NOUN
ap-5556	1	41	saheed	sahee	VERB
ap-5556	1	42	salawua,∗	salawua,∗	NOUN
ap-5556	1	43	,	,	PUNCT
ap-5556	1	44	gbeminiyi	gbeminiyi	NOUN
ap-5556	1	45	sobamowob	sobamowob	NOUN
ap-5556	1	46	,	,	PUNCT
ap-5556	1	47	obanishola	obanishola	PROPN
ap-5556	1	48	sadiqa	sadiqa	VERB
ap-5556	1	49	a	a	DET
ap-5556	1	50	university	university	NOUN
ap-5556	1	51	of	of	ADP
ap-5556	1	52	lagos	lagos	PROPN
ap-5556	1	53	,	,	PUNCT
ap-5556	1	54	department	department	NOUN
ap-5556	1	55	of	of	ADP
ap-5556	1	56	civil	civil	ADJ
ap-5556	1	57	and	and	CCONJ
ap-5556	1	58	environmental	environmental	ADJ
ap-5556	1	59	engineering	engineering	NOUN
ap-5556	1	60	,	,	PUNCT
ap-5556	1	61	akoka	akoka	NOUN
ap-5556	1	62	100213	100213	NUM
ap-5556	1	63	,	,	PUNCT
ap-5556	1	64	nigeria	nigeria	PROPN
ap-5556	1	65	b	b	PROPN
ap-5556	1	66	university	university	PROPN
ap-5556	1	67	of	of	ADP
ap-5556	1	68	lagos	lagos	PROPN
ap-5556	1	69	,	,	PUNCT
ap-5556	1	70	department	department	NOUN
ap-5556	1	71	of	of	ADP
ap-5556	1	72	mechanical	mechanical	ADJ
ap-5556	1	73	engineering	engineering	NOUN
ap-5556	1	74	,	,	PUNCT
ap-5556	1	75	akoka	akoka	NOUN
ap-5556	1	76	100213	100213	NUM
ap-5556	1	77	,	,	PUNCT
ap-5556	1	78	nigeria	nigeria	PROPN
ap-5556	1	79	∗	∗	VERB
ap-5556	1	80	corresponding	correspond	VERB
ap-5556	1	81	author	author	NOUN
ap-5556	1	82	:	:	PUNCT
ap-5556	1	83	safolu@outlook.com	safolu@outlook.com	X
ap-5556	2	1	abstract	abstract	ADJ
ap-5556	2	2	.	.	PUNCT
ap-5556	3	1	the	the	DET
ap-5556	3	2	study	study	NOUN
ap-5556	3	3	of	of	ADP
ap-5556	3	4	the	the	DET
ap-5556	3	5	dynamic	dynamic	ADJ
ap-5556	3	6	behaviour	behaviour	NOUN
ap-5556	3	7	of	of	ADP
ap-5556	3	8	non	non	ADJ
ap-5556	3	9	-	-	ADJ
ap-5556	3	10	uniform	uniform	ADJ
ap-5556	3	11	thickness	thickness	NOUN
ap-5556	3	12	circular	circular	ADJ
ap-5556	3	13	plate	plate	NOUN
ap-5556	3	14	resting	rest	VERB
ap-5556	3	15	on	on	ADP
ap-5556	3	16	elastic	elastic	ADJ
ap-5556	3	17	foundations	foundation	NOUN
ap-5556	3	18	is	be	AUX
ap-5556	3	19	very	very	ADV
ap-5556	3	20	imperative	imperative	ADJ
ap-5556	3	21	in	in	ADP
ap-5556	3	22	designing	design	VERB
ap-5556	3	23	structural	structural	ADJ
ap-5556	3	24	systems	system	NOUN
ap-5556	3	25	.	.	PUNCT
ap-5556	4	1	this	this	DET
ap-5556	4	2	present	present	ADJ
ap-5556	4	3	research	research	NOUN
ap-5556	4	4	investigates	investigate	VERB
ap-5556	4	5	the	the	DET
ap-5556	4	6	free	free	ADJ
ap-5556	4	7	vibration	vibration	NOUN
ap-5556	4	8	analysis	analysis	NOUN
ap-5556	4	9	of	of	ADP
ap-5556	4	10	varying	vary	VERB
ap-5556	4	11	density	density	NOUN
ap-5556	4	12	and	and	CCONJ
ap-5556	4	13	non	non	ADJ
ap-5556	4	14	-	-	ADJ
ap-5556	4	15	uniform	uniform	ADJ
ap-5556	4	16	thickness	thickness	NOUN
ap-5556	4	17	isotropic	isotropic	ADJ
ap-5556	4	18	circular	circular	ADJ
ap-5556	4	19	plates	plate	NOUN
ap-5556	4	20	resting	rest	VERB
ap-5556	4	21	on	on	ADP
ap-5556	4	22	winkler	winkler	NOUN
ap-5556	4	23	and	and	CCONJ
ap-5556	4	24	pasternak	pasternak	PROPN
ap-5556	4	25	foundations	foundation	NOUN
ap-5556	4	26	.	.	PUNCT
ap-5556	5	1	the	the	DET
ap-5556	5	2	governing	govern	VERB
ap-5556	5	3	differential	differential	ADJ
ap-5556	5	4	equation	equation	NOUN
ap-5556	5	5	is	be	AUX
ap-5556	5	6	analysed	analyse	VERB
ap-5556	5	7	using	use	VERB
ap-5556	5	8	the	the	DET
ap-5556	5	9	galerkin	galerkin	ADJ
ap-5556	5	10	method	method	NOUN
ap-5556	5	11	of	of	ADP
ap-5556	5	12	weighted	weight	VERB
ap-5556	5	13	residuals	residual	NOUN
ap-5556	5	14	.	.	PUNCT
ap-5556	6	1	linear	linear	ADJ
ap-5556	6	2	and	and	CCONJ
ap-5556	6	3	nonlinear	nonlinear	ADJ
ap-5556	6	4	case	case	NOUN
ap-5556	6	5	is	be	AUX
ap-5556	6	6	considered	consider	VERB
ap-5556	6	7	,	,	PUNCT
ap-5556	6	8	the	the	DET
ap-5556	6	9	surface	surface	NOUN
ap-5556	6	10	radial	radial	ADJ
ap-5556	6	11	and	and	CCONJ
ap-5556	6	12	circumferential	circumferential	ADJ
ap-5556	6	13	stresses	stress	NOUN
ap-5556	6	14	are	be	AUX
ap-5556	6	15	also	also	ADV
ap-5556	6	16	determined	determine	VERB
ap-5556	6	17	.	.	PUNCT
ap-5556	7	1	thereafter	thereafter	ADV
ap-5556	7	2	,	,	PUNCT
ap-5556	7	3	the	the	DET
ap-5556	7	4	accuracy	accuracy	NOUN
ap-5556	7	5	and	and	CCONJ
ap-5556	7	6	consistency	consistency	NOUN
ap-5556	7	7	of	of	ADP
ap-5556	7	8	the	the	DET
ap-5556	7	9	analytical	analytical	ADJ
ap-5556	7	10	solutions	solution	NOUN
ap-5556	7	11	obtained	obtain	VERB
ap-5556	7	12	are	be	AUX
ap-5556	7	13	ascertained	ascertain	VERB
ap-5556	7	14	by	by	ADP
ap-5556	7	15	comparing	compare	VERB
ap-5556	7	16	the	the	DET
ap-5556	7	17	existing	exist	VERB
ap-5556	7	18	results	result	NOUN
ap-5556	7	19	available	available	ADJ
ap-5556	7	20	in	in	ADP
ap-5556	7	21	pieces	piece	NOUN
ap-5556	7	22	of	of	ADP
ap-5556	7	23	literature	literature	NOUN
ap-5556	7	24	and	and	CCONJ
ap-5556	7	25	confirmed	confirm	VERB
ap-5556	7	26	to	to	PART
ap-5556	7	27	be	be	AUX
ap-5556	7	28	in	in	ADP
ap-5556	7	29	a	a	DET
ap-5556	7	30	good	good	ADJ
ap-5556	7	31	harmony	harmony	NOUN
ap-5556	7	32	.	.	PUNCT
ap-5556	8	1	also	also	ADV
ap-5556	8	2	,	,	PUNCT
ap-5556	8	3	it	it	PRON
ap-5556	8	4	is	be	AUX
ap-5556	8	5	observed	observe	VERB
ap-5556	8	6	that	that	SCONJ
ap-5556	8	7	very	very	ADV
ap-5556	8	8	accurate	accurate	ADJ
ap-5556	8	9	results	result	NOUN
ap-5556	8	10	can	can	AUX
ap-5556	8	11	be	be	AUX
ap-5556	8	12	obtained	obtain	VERB
ap-5556	8	13	with	with	ADP
ap-5556	8	14	few	few	ADJ
ap-5556	8	15	computations	computation	NOUN
ap-5556	8	16	.	.	PUNCT
ap-5556	9	1	issues	issue	NOUN
ap-5556	9	2	relating	relate	VERB
ap-5556	9	3	to	to	ADP
ap-5556	9	4	the	the	DET
ap-5556	9	5	singularity	singularity	NOUN
ap-5556	9	6	of	of	ADP
ap-5556	9	7	circular	circular	ADJ
ap-5556	9	8	plate	plate	NOUN
ap-5556	9	9	governing	govern	VERB
ap-5556	9	10	equations	equation	NOUN
ap-5556	9	11	are	be	AUX
ap-5556	9	12	handled	handle	VERB
ap-5556	9	13	with	with	ADP
ap-5556	9	14	ease	ease	NOUN
ap-5556	9	15	.	.	PUNCT
ap-5556	10	1	the	the	DET
ap-5556	10	2	analytical	analytical	ADJ
ap-5556	10	3	solutions	solution	NOUN
ap-5556	10	4	obtained	obtain	VERB
ap-5556	10	5	are	be	AUX
ap-5556	10	6	used	use	VERB
ap-5556	10	7	to	to	PART
ap-5556	10	8	determine	determine	VERB
ap-5556	10	9	the	the	DET
ap-5556	10	10	influence	influence	NOUN
ap-5556	10	11	of	of	ADP
ap-5556	10	12	elastic	elastic	ADJ
ap-5556	10	13	foundations	foundation	NOUN
ap-5556	10	14	,	,	PUNCT
ap-5556	10	15	homogeneity	homogeneity	NOUN
ap-5556	10	16	and	and	CCONJ
ap-5556	10	17	thickness	thickness	NOUN
ap-5556	10	18	variation	variation	NOUN
ap-5556	10	19	on	on	ADP
ap-5556	10	20	the	the	DET
ap-5556	10	21	dynamic	dynamic	ADJ
ap-5556	10	22	behaviour	behaviour	NOUN
ap-5556	10	23	of	of	ADP
ap-5556	10	24	the	the	DET
ap-5556	10	25	circular	circular	ADJ
ap-5556	10	26	plate	plate	NOUN
ap-5556	10	27	,	,	PUNCT
ap-5556	10	28	the	the	DET
ap-5556	10	29	effect	effect	NOUN
ap-5556	10	30	of	of	ADP
ap-5556	10	31	vibration	vibration	NOUN
ap-5556	10	32	on	on	ADP
ap-5556	10	33	a	a	DET
ap-5556	10	34	free	free	ADJ
ap-5556	10	35	surface	surface	NOUN
ap-5556	10	36	of	of	ADP
ap-5556	10	37	the	the	DET
ap-5556	10	38	foundation	foundation	NOUN
ap-5556	10	39	as	as	ADV
ap-5556	10	40	well	well	ADV
ap-5556	10	41	as	as	ADP
ap-5556	10	42	the	the	DET
ap-5556	10	43	influence	influence	NOUN
ap-5556	10	44	of	of	ADP
ap-5556	10	45	radial	radial	ADJ
ap-5556	10	46	and	and	CCONJ
ap-5556	10	47	circumferential	circumferential	ADJ
ap-5556	10	48	stress	stress	NOUN
ap-5556	10	49	on	on	ADP
ap-5556	10	50	mode	mode	NOUN
ap-5556	10	51	shapes	shape	NOUN
ap-5556	10	52	of	of	ADP
ap-5556	10	53	the	the	DET
ap-5556	10	54	circular	circular	ADJ
ap-5556	10	55	plate	plate	NOUN
ap-5556	10	56	considered	consider	VERB
ap-5556	10	57	.	.	PUNCT
ap-5556	11	1	from	from	ADP
ap-5556	11	2	the	the	DET
ap-5556	11	3	results	result	NOUN
ap-5556	11	4	,	,	PUNCT
ap-5556	11	5	it	it	PRON
ap-5556	11	6	is	be	AUX
ap-5556	11	7	observed	observe	VERB
ap-5556	11	8	that	that	SCONJ
ap-5556	11	9	a	a	DET
ap-5556	11	10	maximum	maximum	NOUN
ap-5556	11	11	of	of	ADP
ap-5556	11	12	8.1	8.1	NUM
ap-5556	11	13	%	%	NOUN
ap-5556	11	14	percentage	percentage	NOUN
ap-5556	11	15	difference	difference	NOUN
ap-5556	11	16	is	be	AUX
ap-5556	11	17	obtained	obtain	VERB
ap-5556	11	18	with	with	ADP
ap-5556	11	19	the	the	DET
ap-5556	11	20	solutions	solution	NOUN
ap-5556	11	21	obtained	obtain	VERB
ap-5556	11	22	from	from	ADP
ap-5556	11	23	other	other	ADJ
ap-5556	11	24	analytical	analytical	ADJ
ap-5556	11	25	methods	method	NOUN
ap-5556	11	26	.	.	PUNCT
ap-5556	12	1	furthermore	furthermore	ADV
ap-5556	12	2	,	,	PUNCT
ap-5556	12	3	increasing	increase	VERB
ap-5556	12	4	the	the	DET
ap-5556	12	5	elastic	elastic	ADJ
ap-5556	12	6	foundation	foundation	NOUN
ap-5556	12	7	parameter	parameter	NOUN
ap-5556	12	8	increases	increase	VERB
ap-5556	12	9	the	the	DET
ap-5556	12	10	natural	natural	ADJ
ap-5556	12	11	frequency	frequency	NOUN
ap-5556	12	12	.	.	PUNCT
ap-5556	13	1	extrema	extrema	NOUN
ap-5556	13	2	modal	modal	ADJ
ap-5556	13	3	displacement	displacement	NOUN
ap-5556	13	4	occurs	occur	VERB
ap-5556	13	5	due	due	ADJ
ap-5556	13	6	to	to	ADP
ap-5556	13	7	radial	radial	ADJ
ap-5556	13	8	and	and	CCONJ
ap-5556	13	9	circumferential	circumferential	ADJ
ap-5556	13	10	stress	stress	NOUN
ap-5556	13	11	.	.	PUNCT
ap-5556	14	1	natural	natural	ADJ
ap-5556	14	2	frequency	frequency	NOUN
ap-5556	14	3	increases	increase	NOUN
ap-5556	14	4	as	as	ADP
ap-5556	14	5	the	the	DET
ap-5556	14	6	thickness	thickness	NOUN
ap-5556	14	7	of	of	ADP
ap-5556	14	8	the	the	DET
ap-5556	14	9	circular	circular	ADJ
ap-5556	14	10	plate	plate	NOUN
ap-5556	14	11	increases	increase	NOUN
ap-5556	14	12	,	,	PUNCT
ap-5556	14	13	conversely	conversely	ADV
ap-5556	14	14	,	,	PUNCT
ap-5556	14	15	a	a	DET
ap-5556	14	16	decrease	decrease	NOUN
ap-5556	14	17	in	in	ADP
ap-5556	14	18	natural	natural	ADJ
ap-5556	14	19	frequency	frequency	NOUN
ap-5556	14	20	is	be	AUX
ap-5556	14	21	observed	observe	VERB
ap-5556	14	22	as	as	SCONJ
ap-5556	14	23	the	the	DET
ap-5556	14	24	density	density	NOUN
ap-5556	14	25	varies	vary	VERB
ap-5556	14	26	.	.	PUNCT
ap-5556	15	1	it	it	PRON
ap-5556	15	2	is	be	AUX
ap-5556	15	3	envisioned	envision	VERB
ap-5556	15	4	that	that	SCONJ
ap-5556	15	5	;	;	PUNCT
ap-5556	15	6	the	the	DET
ap-5556	15	7	present	present	ADJ
ap-5556	15	8	study	study	NOUN
ap-5556	15	9	will	will	AUX
ap-5556	15	10	contribute	contribute	VERB
ap-5556	15	11	to	to	ADP
ap-5556	15	12	the	the	DET
ap-5556	15	13	existing	exist	VERB
ap-5556	15	14	knowledge	knowledge	NOUN
ap-5556	15	15	of	of	ADP
ap-5556	15	16	the	the	DET
ap-5556	15	17	classical	classical	ADJ
ap-5556	15	18	theory	theory	NOUN
ap-5556	15	19	of	of	ADP
ap-5556	15	20	vibration	vibration	NOUN
ap-5556	15	21	.	.	PUNCT
ap-5556	16	1	keywords	keyword	NOUN
ap-5556	16	2	:	:	PUNCT
ap-5556	16	3	free	free	ADJ
ap-5556	16	4	vibration	vibration	NOUN
ap-5556	16	5	,	,	PUNCT
ap-5556	16	6	natural	natural	ADJ
ap-5556	16	7	frequency	frequency	NOUN
ap-5556	16	8	,	,	PUNCT
ap-5556	16	9	winkler	winkler	NOUN
ap-5556	16	10	and	and	CCONJ
ap-5556	16	11	pasternak	pasternak	PROPN
ap-5556	16	12	,	,	PUNCT
ap-5556	16	13	circular	circular	ADJ
ap-5556	16	14	plate	plate	NOUN
ap-5556	16	15	,	,	PUNCT
ap-5556	16	16	galerkin	galerkin	ADJ
ap-5556	16	17	method	method	NOUN
ap-5556	16	18	of	of	ADP
ap-5556	16	19	weighted	weight	VERB
ap-5556	16	20	residual	residual	ADJ
ap-5556	16	21	.	.	PUNCT
ap-5556	17	1	1	1	X
ap-5556	17	2	.	.	X
ap-5556	17	3	introduction	introduction	NOUN
ap-5556	17	4	application	application	NOUN
ap-5556	17	5	of	of	ADP
ap-5556	17	6	plates	plate	NOUN
ap-5556	17	7	is	be	AUX
ap-5556	17	8	commonly	commonly	ADV
ap-5556	17	9	found	find	VERB
ap-5556	17	10	in	in	ADP
ap-5556	17	11	a	a	DET
ap-5556	17	12	variety	variety	NOUN
ap-5556	17	13	of	of	ADP
ap-5556	17	14	contexts	context	NOUN
ap-5556	17	15	in	in	ADP
ap-5556	17	16	civil	civil	ADJ
ap-5556	17	17	,	,	PUNCT
ap-5556	17	18	mechanical	mechanical	ADJ
ap-5556	17	19	,	,	PUNCT
ap-5556	17	20	naval	naval	ADJ
ap-5556	17	21	,	,	PUNCT
ap-5556	17	22	marine	marine	ADJ
ap-5556	17	23	and	and	CCONJ
ap-5556	17	24	aeronautic	aeronautic	ADJ
ap-5556	17	25	engineering	engineering	NOUN
ap-5556	17	26	.	.	PUNCT
ap-5556	18	1	the	the	DET
ap-5556	18	2	understanding	understanding	NOUN
ap-5556	18	3	of	of	ADP
ap-5556	18	4	the	the	DET
ap-5556	18	5	dynamic	dynamic	ADJ
ap-5556	18	6	behaviour	behaviour	NOUN
ap-5556	18	7	of	of	ADP
ap-5556	18	8	the	the	DET
ap-5556	18	9	plate	plate	NOUN
ap-5556	18	10	is	be	AUX
ap-5556	18	11	germane	germane	ADJ
ap-5556	18	12	in	in	ADP
ap-5556	18	13	several	several	ADJ
ap-5556	18	14	contexts	contexts	NOUN
ap-5556	18	15	.	.	PUNCT
ap-5556	19	1	for	for	ADP
ap-5556	19	2	example	example	NOUN
ap-5556	19	3	,	,	PUNCT
ap-5556	19	4	a	a	DET
ap-5556	19	5	plate	plate	NOUN
ap-5556	19	6	resting	rest	VERB
ap-5556	19	7	on	on	ADP
ap-5556	19	8	a	a	DET
ap-5556	19	9	foundation	foundation	NOUN
ap-5556	19	10	,	,	PUNCT
ap-5556	19	11	fluid	fluid	ADJ
ap-5556	19	12	-	-	PUNCT
ap-5556	19	13	structure	structure	NOUN
ap-5556	19	14	interaction	interaction	NOUN
ap-5556	19	15	problems	problem	NOUN
ap-5556	19	16	,	,	PUNCT
ap-5556	19	17	panel	panel	NOUN
ap-5556	19	18	flutter	flutter	NOUN
ap-5556	19	19	and	and	CCONJ
ap-5556	19	20	plate	plate	NOUN
ap-5556	19	21	in	in	ADP
ap-5556	19	22	aeronautics	aeronautic	NOUN
ap-5556	19	23	,	,	PUNCT
ap-5556	19	24	also	also	ADV
ap-5556	19	25	the	the	DET
ap-5556	19	26	coupling	couple	VERB
ap-5556	19	27	effect	effect	NOUN
ap-5556	19	28	of	of	ADP
ap-5556	19	29	electro	electro	VERB
ap-5556	19	30	-	-	PUNCT
ap-5556	19	31	magnetic	magnetic	ADJ
ap-5556	19	32	and	and	CCONJ
ap-5556	19	33	thermal	thermal	ADJ
ap-5556	19	34	fields	field	NOUN
ap-5556	19	35	on	on	ADP
ap-5556	19	36	plate	plate	NOUN
ap-5556	19	37	.	.	PUNCT
ap-5556	20	1	several	several	ADJ
ap-5556	20	2	engineering	engineering	NOUN
ap-5556	20	3	structures	structure	NOUN
ap-5556	20	4	,	,	PUNCT
ap-5556	20	5	such	such	ADJ
ap-5556	20	6	as	as	ADP
ap-5556	20	7	railway	railway	NOUN
ap-5556	20	8	,	,	PUNCT
ap-5556	20	9	storage	storage	NOUN
ap-5556	20	10	tank	tank	NOUN
ap-5556	20	11	foundation	foundation	NOUN
ap-5556	20	12	and	and	CCONJ
ap-5556	20	13	telecommunication	telecommunication	NOUN
ap-5556	20	14	mast	mast	NOUN
ap-5556	20	15	require	require	VERB
ap-5556	20	16	information	information	NOUN
ap-5556	20	17	on	on	ADP
ap-5556	20	18	the	the	DET
ap-5556	20	19	vibration	vibration	NOUN
ap-5556	20	20	analysis	analysis	NOUN
ap-5556	20	21	of	of	ADP
ap-5556	20	22	plate	plate	NOUN
ap-5556	20	23	entrenched	entrench	VERB
ap-5556	20	24	on	on	ADP
ap-5556	20	25	foundation	foundation	NOUN
ap-5556	20	26	earlier	early	ADV
ap-5556	20	27	before	before	ADP
ap-5556	20	28	embarking	embark	VERB
ap-5556	20	29	on	on	ADP
ap-5556	20	30	the	the	DET
ap-5556	20	31	design	design	NOUN
ap-5556	20	32	.	.	PUNCT
ap-5556	21	1	the	the	DET
ap-5556	21	2	simplest	simple	ADJ
ap-5556	21	3	form	form	NOUN
ap-5556	21	4	of	of	ADP
ap-5556	21	5	modelling	model	VERB
ap-5556	21	6	the	the	DET
ap-5556	21	7	mechanical	mechanical	ADJ
ap-5556	21	8	behaviour	behaviour	NOUN
ap-5556	21	9	of	of	ADP
ap-5556	21	10	a	a	DET
ap-5556	21	11	soil	soil	NOUN
ap-5556	21	12	foundation	foundation	NOUN
ap-5556	21	13	interaction	interaction	NOUN
ap-5556	21	14	is	be	AUX
ap-5556	21	15	using	use	VERB
ap-5556	21	16	the	the	DET
ap-5556	21	17	winkler	winkler	PROPN
ap-5556	21	18	foundation	foundation	PROPN
ap-5556	21	19	.	.	PUNCT
ap-5556	22	1	the	the	DET
ap-5556	22	2	winkler	winkler	PROPN
ap-5556	22	3	foundation	foundation	PROPN
ap-5556	22	4	has	have	VERB
ap-5556	22	5	the	the	DET
ap-5556	22	6	limitation	limitation	NOUN
ap-5556	22	7	of	of	ADP
ap-5556	22	8	non	non	NOUN
ap-5556	22	9	-	-	NOUN
ap-5556	22	10	interaction	interaction	NOUN
ap-5556	22	11	between	between	ADP
ap-5556	22	12	the	the	DET
ap-5556	22	13	lateral	lateral	ADJ
ap-5556	22	14	spring	spring	NOUN
ap-5556	22	15	,	,	PUNCT
ap-5556	22	16	thereby	thereby	ADV
ap-5556	22	17	resulting	result	VERB
ap-5556	22	18	in	in	ADP
ap-5556	22	19	unreliable	unreliable	ADJ
ap-5556	22	20	results	result	NOUN
ap-5556	22	21	.	.	PUNCT
ap-5556	23	1	two	two	NUM
ap-5556	23	2	-	-	PUNCT
ap-5556	23	3	parameter	parameter	NOUN
ap-5556	23	4	elastic	elastic	ADJ
ap-5556	23	5	foundations	foundation	NOUN
ap-5556	23	6	are	be	AUX
ap-5556	23	7	established	establish	VERB
ap-5556	23	8	to	to	PART
ap-5556	23	9	cater	cater	VERB
ap-5556	23	10	for	for	ADP
ap-5556	23	11	this	this	DET
ap-5556	23	12	interaction	interaction	NOUN
ap-5556	23	13	.	.	PUNCT
ap-5556	24	1	the	the	DET
ap-5556	24	2	use	use	NOUN
ap-5556	24	3	of	of	ADP
ap-5556	24	4	two	two	NUM
ap-5556	24	5	-	-	PUNCT
ap-5556	24	6	parameter	parameter	NOUN
ap-5556	24	7	elastic	elastic	ADJ
ap-5556	24	8	foundations	foundation	NOUN
ap-5556	24	9	offers	offer	VERB
ap-5556	24	10	a	a	DET
ap-5556	24	11	true	true	ADJ
ap-5556	24	12	account	account	NOUN
ap-5556	24	13	of	of	ADP
ap-5556	24	14	the	the	DET
ap-5556	24	15	soil	soil	NOUN
ap-5556	24	16	foundation	foundation	NOUN
ap-5556	24	17	interaction	interaction	NOUN
ap-5556	24	18	.	.	PUNCT
ap-5556	25	1	in	in	ADP
ap-5556	25	2	the	the	DET
ap-5556	25	3	study	study	NOUN
ap-5556	25	4	of	of	ADP
ap-5556	25	5	vibration	vibration	NOUN
ap-5556	25	6	of	of	ADP
ap-5556	25	7	a	a	DET
ap-5556	25	8	plate	plate	NOUN
ap-5556	25	9	immersed	immerse	VERB
ap-5556	25	10	in	in	ADP
ap-5556	25	11	fluid	fluid	ADJ
ap-5556	25	12	,	,	PUNCT
ap-5556	25	13	kyeong	kyeong	NOUN
ap-5556	25	14	-	-	PUNCT
ap-5556	25	15	hoon	hoon	NOUN
ap-5556	25	16	et	et	NOUN
ap-5556	25	17	al	al	PROPN
ap-5556	25	18	.	.	PUNCT
ap-5556	26	1	[	[	X
ap-5556	26	2	1	1	X
ap-5556	26	3	]	]	PUNCT
ap-5556	26	4	formulate	formulate	VERB
ap-5556	26	5	a	a	DET
ap-5556	26	6	hypothetical	hypothetical	ADJ
ap-5556	26	7	approach	approach	NOUN
ap-5556	26	8	for	for	ADP
ap-5556	26	9	a	a	DET
ap-5556	26	10	hydroelastic	hydroelastic	ADJ
ap-5556	26	11	analysis	analysis	NOUN
ap-5556	26	12	of	of	ADP
ap-5556	26	13	a	a	DET
ap-5556	26	14	clamped	clamp	VERB
ap-5556	26	15	edge	edge	NOUN
ap-5556	26	16	circular	circular	ADJ
ap-5556	26	17	plate	plate	NOUN
ap-5556	26	18	partially	partially	ADV
ap-5556	26	19	in	in	ADP
ap-5556	26	20	contact	contact	NOUN
ap-5556	26	21	with	with	ADP
ap-5556	26	22	a	a	DET
ap-5556	26	23	liquid	liquid	NOUN
ap-5556	26	24	.	.	PUNCT
ap-5556	27	1	rayleigh	rayleigh	PROPN
ap-5556	27	2	-	-	PUNCT
ap-5556	27	3	ritz	ritz	PROPN
ap-5556	27	4	method	method	NOUN
ap-5556	27	5	was	be	AUX
ap-5556	27	6	adopted	adopt	VERB
ap-5556	27	7	for	for	ADP
ap-5556	27	8	obtaining	obtain	VERB
ap-5556	27	9	the	the	DET
ap-5556	27	10	eigenvalue	eigenvalue	ADJ
ap-5556	27	11	equation	equation	NOUN
ap-5556	27	12	.	.	PUNCT
ap-5556	28	1	the	the	DET
ap-5556	28	2	influences	influence	NOUN
ap-5556	28	3	of	of	ADP
ap-5556	28	4	the	the	DET
ap-5556	28	5	thickness	thickness	NOUN
ap-5556	28	6	and	and	CCONJ
ap-5556	28	7	depth	depth	NOUN
ap-5556	28	8	of	of	ADP
ap-5556	28	9	the	the	DET
ap-5556	28	10	liquid	liquid	ADJ
ap-5556	28	11	thickness	thickness	NOUN
ap-5556	28	12	on	on	ADP
ap-5556	28	13	the	the	DET
ap-5556	28	14	natural	natural	ADJ
ap-5556	28	15	frequencies	frequency	NOUN
ap-5556	28	16	were	be	AUX
ap-5556	28	17	determined	determine	VERB
ap-5556	28	18	.	.	PUNCT
ap-5556	29	1	in	in	ADP
ap-5556	29	2	another	another	DET
ap-5556	29	3	work	work	NOUN
ap-5556	29	4	,	,	PUNCT
ap-5556	29	5	sari	sari	NOUN
ap-5556	29	6	and	and	CCONJ
ap-5556	29	7	butcher	butcher	NOUN
ap-5556	29	8	[	[	X
ap-5556	29	9	2	2	X
ap-5556	29	10	]	]	PUNCT
ap-5556	29	11	proposed	propose	VERB
ap-5556	29	12	a	a	DET
ap-5556	29	13	numerical	numerical	ADJ
ap-5556	29	14	approach	approach	NOUN
ap-5556	29	15	for	for	ADP
ap-5556	29	16	analysing	analyse	VERB
ap-5556	29	17	the	the	DET
ap-5556	29	18	free	free	ADJ
ap-5556	29	19	vibration	vibration	NOUN
ap-5556	29	20	response	response	NOUN
ap-5556	29	21	of	of	ADP
ap-5556	29	22	an	an	DET
ap-5556	29	23	isotropic	isotropic	ADJ
ap-5556	29	24	rectangular	rectangular	ADJ
ap-5556	29	25	and	and	CCONJ
ap-5556	29	26	annular	annular	ADJ
ap-5556	29	27	mindlin	mindlin	NOUN
ap-5556	29	28	plates	plate	NOUN
ap-5556	29	29	under	under	ADP
ap-5556	29	30	damaged	damage	VERB
ap-5556	29	31	clamped	clamp	VERB
ap-5556	29	32	boundary	boundary	ADJ
ap-5556	29	33	conditions	condition	NOUN
ap-5556	29	34	using	use	VERB
ap-5556	29	35	the	the	DET
ap-5556	29	36	chebyshev	chebyshev	NOUN
ap-5556	29	37	collocation	collocation	NOUN
ap-5556	29	38	method	method	NOUN
ap-5556	29	39	.	.	PUNCT
ap-5556	30	1	the	the	DET
ap-5556	30	2	results	result	NOUN
ap-5556	30	3	obtained	obtain	VERB
ap-5556	30	4	show	show	VERB
ap-5556	30	5	that	that	SCONJ
ap-5556	30	6	the	the	DET
ap-5556	30	7	damaged	damage	VERB
ap-5556	30	8	boundary	boundary	ADJ
ap-5556	30	9	condition	condition	NOUN
ap-5556	30	10	influences	influence	VERB
ap-5556	30	11	the	the	DET
ap-5556	30	12	natural	natural	ADJ
ap-5556	30	13	frequency	frequency	NOUN
ap-5556	30	14	of	of	ADP
ap-5556	30	15	the	the	DET
ap-5556	30	16	plate	plate	NOUN
ap-5556	30	17	.	.	PUNCT
ap-5556	31	1	also	also	ADV
ap-5556	31	2	,	,	PUNCT
ap-5556	31	3	fletcher	fletcher	PROPN
ap-5556	32	1	[	[	X
ap-5556	32	2	3	3	NUM
ap-5556	32	3	]	]	PUNCT
ap-5556	32	4	worked	work	VERB
ap-5556	32	5	on	on	ADP
ap-5556	32	6	a	a	DET
ap-5556	32	7	finite	finite	ADJ
ap-5556	32	8	element	element	NOUN
ap-5556	32	9	formulation	formulation	NOUN
ap-5556	32	10	using	use	VERB
ap-5556	32	11	a	a	DET
ap-5556	32	12	weighted	weight	VERB
ap-5556	32	13	residual	residual	ADJ
ap-5556	32	14	method	method	NOUN
ap-5556	32	15	.	.	PUNCT
ap-5556	33	1	in	in	ADP
ap-5556	33	2	another	another	DET
ap-5556	33	3	study	study	NOUN
ap-5556	33	4	,	,	PUNCT
ap-5556	33	5	bahram	bahram	PROPN
ap-5556	33	6	et	et	PROPN
ap-5556	33	7	al	al	PROPN
ap-5556	34	1	[	[	X
ap-5556	34	2	4	4	NUM
ap-5556	34	3	]	]	PUNCT
ap-5556	34	4	investigated	investigate	VERB
ap-5556	34	5	the	the	DET
ap-5556	34	6	vibration	vibration	NOUN
ap-5556	34	7	analysis	analysis	NOUN
ap-5556	34	8	of	of	ADP
ap-5556	34	9	circular	circular	ADJ
ap-5556	34	10	plates	plate	NOUN
ap-5556	34	11	under	under	ADP
ap-5556	34	12	the	the	DET
ap-5556	34	13	influence	influence	NOUN
ap-5556	34	14	of	of	ADP
ap-5556	34	15	in	in	ADP
ap-5556	34	16	-	-	PUNCT
ap-5556	34	17	plane	plane	NOUN
ap-5556	34	18	loading	loading	NOUN
ap-5556	34	19	resting	rest	VERB
ap-5556	34	20	on	on	ADP
ap-5556	34	21	the	the	DET
ap-5556	34	22	winkler	winkler	PROPN
ap-5556	34	23	foundation	foundation	PROPN
ap-5556	34	24	.	.	PUNCT
ap-5556	35	1	the	the	DET
ap-5556	35	2	solutions	solution	NOUN
ap-5556	35	3	were	be	AUX
ap-5556	35	4	obtained	obtain	VERB
ap-5556	35	5	using	use	VERB
ap-5556	35	6	the	the	DET
ap-5556	35	7	ritz	ritz	PROPN
ap-5556	35	8	method	method	NOUN
ap-5556	35	9	,	,	PUNCT
ap-5556	35	10	it	it	PRON
ap-5556	35	11	was	be	AUX
ap-5556	35	12	observed	observe	VERB
ap-5556	35	13	that	that	SCONJ
ap-5556	35	14	the	the	DET
ap-5556	35	15	foundation	foundation	NOUN
ap-5556	35	16	stiffness	stiffness	NOUN
ap-5556	35	17	has	have	VERB
ap-5556	35	18	an	an	DET
ap-5556	35	19	increasing	increase	VERB
ap-5556	35	20	influence	influence	NOUN
ap-5556	35	21	on	on	ADP
ap-5556	35	22	the	the	DET
ap-5556	35	23	natural	natural	ADJ
ap-5556	35	24	frequencies	frequency	NOUN
ap-5556	35	25	.	.	PUNCT
ap-5556	36	1	also	also	ADV
ap-5556	36	2	,	,	PUNCT
ap-5556	36	3	critical	critical	ADJ
ap-5556	36	4	buckling	buckling	NOUN
ap-5556	36	5	load	load	NOUN
ap-5556	36	6	was	be	AUX
ap-5556	36	7	increased	increase	VERB
ap-5556	36	8	for	for	ADP
ap-5556	36	9	the	the	DET
ap-5556	36	10	laminated	laminate	VERB
ap-5556	36	11	circular	circular	ADJ
ap-5556	36	12	plate	plate	NOUN
ap-5556	36	13	.	.	PUNCT
ap-5556	37	1	on	on	ADP
ap-5556	37	2	the	the	DET
ap-5556	37	3	application	application	NOUN
ap-5556	37	4	of	of	ADP
ap-5556	37	5	the	the	DET
ap-5556	37	6	semi	semi	ADJ
ap-5556	37	7	-	-	ADJ
ap-5556	37	8	analytical	analytical	ADJ
ap-5556	37	9	127	127	NUM
ap-5556	37	10	https://doi.org/10.14311/ap.2020.60.0127	https://doi.org/10.14311/ap.2020.60.0127	PROPN
ap-5556	37	11	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-5556	37	12	s.	s.	PROPN
ap-5556	37	13	salawu	salawu	PROPN
ap-5556	37	14	,	,	PUNCT
ap-5556	37	15	g.	g.	PROPN
ap-5556	37	16	sobamowo	sobamowo	PROPN
ap-5556	37	17	,	,	PUNCT
ap-5556	37	18	o.	o.	PROPN
ap-5556	37	19	sadiq	sadiq	PROPN
ap-5556	37	20	acta	acta	PROPN
ap-5556	37	21	polytechnica	polytechnica	PROPN
ap-5556	37	22	figure	figure	NOUN
ap-5556	37	23	1	1	NUM
ap-5556	37	24	.	.	PUNCT
ap-5556	37	25	varying	vary	VERB
ap-5556	37	26	thickness	thickness	NOUN
ap-5556	37	27	circular	circular	ADJ
ap-5556	37	28	plate	plate	NOUN
ap-5556	37	29	resting	rest	VERB
ap-5556	37	30	on	on	ADP
ap-5556	37	31	two	two	NUM
ap-5556	37	32	-	-	PUNCT
ap-5556	37	33	parameter	parameter	NOUN
ap-5556	37	34	foundations	foundation	NOUN
ap-5556	37	35	.	.	PUNCT
ap-5556	38	1	method	method	PROPN
ap-5556	38	2	,	,	PUNCT
ap-5556	38	3	wei	wei	PROPN
ap-5556	38	4	-	-	PUNCT
ap-5556	38	5	ming	ming	PROPN
ap-5556	38	6	et	et	PROPN
ap-5556	38	7	al	al	PROPN
ap-5556	38	8	.	.	PUNCT
ap-5556	39	1	[	[	X
ap-5556	39	2	5	5	NUM
ap-5556	39	3	]	]	PUNCT
ap-5556	39	4	proposed	propose	VERB
ap-5556	39	5	a	a	DET
ap-5556	39	6	new	new	ADJ
ap-5556	39	7	semi	semi	ADJ
ap-5556	39	8	-	-	ADJ
ap-5556	39	9	analytical	analytical	ADJ
ap-5556	39	10	method	method	NOUN
ap-5556	39	11	for	for	ADP
ap-5556	39	12	obtaining	obtain	VERB
ap-5556	39	13	eigenvalues	eigenvalue	NOUN
ap-5556	39	14	of	of	ADP
ap-5556	39	15	vibrating	vibrate	VERB
ap-5556	39	16	circular	circular	ADJ
ap-5556	39	17	plates	plate	NOUN
ap-5556	39	18	with	with	ADP
ap-5556	39	19	several	several	ADJ
ap-5556	39	20	holes	hole	NOUN
ap-5556	39	21	,	,	PUNCT
ap-5556	39	22	the	the	DET
ap-5556	39	23	influence	influence	NOUN
ap-5556	39	24	of	of	ADP
ap-5556	39	25	the	the	DET
ap-5556	39	26	holes	hole	NOUN
ap-5556	39	27	on	on	ADP
ap-5556	39	28	the	the	DET
ap-5556	39	29	natural	natural	ADJ
ap-5556	39	30	frequencies	frequency	NOUN
ap-5556	39	31	was	be	AUX
ap-5556	39	32	determined	determine	VERB
ap-5556	39	33	.	.	PUNCT
ap-5556	40	1	previous	previous	ADJ
ap-5556	40	2	studies	study	NOUN
ap-5556	40	3	show	show	VERB
ap-5556	40	4	that	that	SCONJ
ap-5556	40	5	the	the	DET
ap-5556	40	6	inherent	inherent	ADJ
ap-5556	40	7	singularity	singularity	NOUN
ap-5556	40	8	issue	issue	NOUN
ap-5556	40	9	of	of	ADP
ap-5556	40	10	a	a	DET
ap-5556	40	11	circular	circular	ADJ
ap-5556	40	12	plate	plate	NOUN
ap-5556	40	13	is	be	AUX
ap-5556	40	14	not	not	PART
ap-5556	40	15	easy	easy	ADJ
ap-5556	40	16	to	to	PART
ap-5556	40	17	handle	handle	VERB
ap-5556	40	18	.	.	PUNCT
ap-5556	41	1	the	the	DET
ap-5556	41	2	numerical	numerical	ADJ
ap-5556	41	3	method	method	NOUN
ap-5556	41	4	is	be	AUX
ap-5556	41	5	a	a	DET
ap-5556	41	6	reliable	reliable	ADJ
ap-5556	41	7	method	method	NOUN
ap-5556	41	8	of	of	ADP
ap-5556	41	9	solution	solution	NOUN
ap-5556	41	10	for	for	ADP
ap-5556	41	11	handling	handle	VERB
ap-5556	41	12	the	the	DET
ap-5556	41	13	governing	govern	VERB
ap-5556	41	14	equations	equation	NOUN
ap-5556	41	15	of	of	ADP
ap-5556	41	16	related	related	ADJ
ap-5556	41	17	challenges	challenge	NOUN
ap-5556	41	18	but	but	CCONJ
ap-5556	41	19	,	,	PUNCT
ap-5556	41	20	the	the	DET
ap-5556	41	21	convergence	convergence	NOUN
ap-5556	41	22	,	,	PUNCT
ap-5556	41	23	volume	volume	NOUN
ap-5556	41	24	of	of	ADP
ap-5556	41	25	iterations	iteration	NOUN
ap-5556	41	26	and	and	CCONJ
ap-5556	41	27	stability	stability	NOUN
ap-5556	41	28	studies	study	NOUN
ap-5556	41	29	associated	associate	VERB
ap-5556	41	30	with	with	ADP
ap-5556	41	31	numerical	numerical	ADJ
ap-5556	41	32	increases	increase	NOUN
ap-5556	41	33	the	the	DET
ap-5556	41	34	computation	computation	NOUN
ap-5556	41	35	time	time	NOUN
ap-5556	41	36	and	and	CCONJ
ap-5556	41	37	cost	cost	NOUN
ap-5556	41	38	.	.	PUNCT
ap-5556	42	1	meanwhile	meanwhile	ADV
ap-5556	42	2	,	,	PUNCT
ap-5556	42	3	an	an	DET
ap-5556	42	4	attempt	attempt	NOUN
ap-5556	42	5	to	to	PART
ap-5556	42	6	obtain	obtain	VERB
ap-5556	42	7	a	a	DET
ap-5556	42	8	symbolic	symbolic	ADJ
ap-5556	42	9	solution	solution	NOUN
ap-5556	42	10	for	for	ADP
ap-5556	42	11	the	the	DET
ap-5556	42	12	dynamic	dynamic	ADJ
ap-5556	42	13	behaviour	behaviour	NOUN
ap-5556	42	14	of	of	ADP
ap-5556	42	15	a	a	DET
ap-5556	42	16	circular	circular	ADJ
ap-5556	42	17	plate	plate	NOUN
ap-5556	42	18	resting	rest	VERB
ap-5556	42	19	on	on	ADP
ap-5556	42	20	winkler	winkler	NOUN
ap-5556	42	21	and	and	CCONJ
ap-5556	42	22	pasternak	pasternak	PROPN
ap-5556	42	23	foundations	foundation	NOUN
ap-5556	42	24	requires	require	VERB
ap-5556	42	25	the	the	DET
ap-5556	42	26	adoption	adoption	NOUN
ap-5556	42	27	of	of	ADP
ap-5556	42	28	semi	semi	ADJ
ap-5556	42	29	-	-	ADJ
ap-5556	42	30	analytical	analytical	ADJ
ap-5556	42	31	and	and	CCONJ
ap-5556	42	32	analytical	analytical	ADJ
ap-5556	42	33	methods	method	NOUN
ap-5556	42	34	.	.	PUNCT
ap-5556	43	1	yun	yun	PROPN
ap-5556	43	2	and	and	CCONJ
ap-5556	43	3	temuer	temuer	NOUN
ap-5556	43	4	[	[	X
ap-5556	43	5	6	6	NUM
ap-5556	43	6	,	,	PUNCT
ap-5556	43	7	7	7	NUM
ap-5556	43	8	]	]	PUNCT
ap-5556	43	9	formulate	formulate	VERB
ap-5556	43	10	an	an	DET
ap-5556	43	11	improved	improved	ADJ
ap-5556	43	12	homotopy	homotopy	NOUN
ap-5556	43	13	perturbation	perturbation	NOUN
ap-5556	43	14	method	method	NOUN
ap-5556	43	15	(	(	PUNCT
ap-5556	43	16	hpm	hpm	NOUN
ap-5556	43	17	)	)	PUNCT
ap-5556	43	18	to	to	PART
ap-5556	43	19	obtain	obtain	VERB
ap-5556	43	20	a	a	DET
ap-5556	43	21	solution	solution	NOUN
ap-5556	43	22	for	for	ADP
ap-5556	43	23	large	large	ADJ
ap-5556	43	24	deflection	deflection	NOUN
ap-5556	43	25	of	of	ADP
ap-5556	43	26	a	a	DET
ap-5556	43	27	simply	simply	ADV
ap-5556	43	28	supported	support	VERB
ap-5556	43	29	circular	circular	ADJ
ap-5556	43	30	plate	plate	NOUN
ap-5556	43	31	.	.	PUNCT
ap-5556	44	1	reliable	reliable	ADJ
ap-5556	44	2	results	result	NOUN
ap-5556	44	3	were	be	AUX
ap-5556	44	4	obtained	obtain	VERB
ap-5556	44	5	.	.	PUNCT
ap-5556	45	1	in	in	ADP
ap-5556	45	2	a	a	DET
ap-5556	45	3	later	later	ADJ
ap-5556	45	4	work	work	NOUN
ap-5556	45	5	,	,	PUNCT
ap-5556	45	6	zhong	zhong	PROPN
ap-5556	45	7	and	and	CCONJ
ap-5556	45	8	liao	liao	PROPN
ap-5556	45	9	[	[	X
ap-5556	45	10	8	8	NUM
ap-5556	45	11	]	]	PUNCT
ap-5556	45	12	also	also	ADV
ap-5556	45	13	used	use	VERB
ap-5556	45	14	the	the	DET
ap-5556	45	15	homotopy	homotopy	NOUN
ap-5556	45	16	analysis	analysis	NOUN
ap-5556	45	17	method	method	NOUN
ap-5556	45	18	(	(	PUNCT
ap-5556	45	19	ham	ham	NOUN
ap-5556	45	20	)	)	PUNCT
ap-5556	45	21	to	to	PART
ap-5556	45	22	obtain	obtain	VERB
ap-5556	45	23	the	the	DET
ap-5556	45	24	solution	solution	NOUN
ap-5556	45	25	for	for	ADP
ap-5556	45	26	the	the	DET
ap-5556	45	27	non	non	ADJ
ap-5556	45	28	-	-	ADJ
ap-5556	45	29	linear	linear	ADJ
ap-5556	45	30	problems	problem	NOUN
ap-5556	45	31	.	.	PUNCT
ap-5556	46	1	in	in	ADP
ap-5556	46	2	another	another	DET
ap-5556	46	3	study	study	NOUN
ap-5556	46	4	,	,	PUNCT
ap-5556	46	5	yalcin	yalcin	PROPN
ap-5556	46	6	et	et	PROPN
ap-5556	46	7	al	al	PROPN
ap-5556	46	8	.	.	PUNCT
ap-5556	47	1	[	[	X
ap-5556	47	2	9	9	NUM
ap-5556	47	3	]	]	PUNCT
ap-5556	47	4	adopted	adopt	VERB
ap-5556	47	5	a	a	DET
ap-5556	47	6	differential	differential	ADJ
ap-5556	47	7	transform	transform	NOUN
ap-5556	47	8	method	method	NOUN
ap-5556	47	9	(	(	PUNCT
ap-5556	47	10	dtm	dtm	PROPN
ap-5556	47	11	)	)	PUNCT
ap-5556	47	12	for	for	ADP
ap-5556	47	13	the	the	DET
ap-5556	47	14	free	free	ADJ
ap-5556	47	15	vibration	vibration	NOUN
ap-5556	47	16	of	of	ADP
ap-5556	47	17	a	a	DET
ap-5556	47	18	circular	circular	ADJ
ap-5556	47	19	plate	plate	NOUN
ap-5556	47	20	.	.	PUNCT
ap-5556	48	1	also	also	ADV
ap-5556	48	2	,	,	PUNCT
ap-5556	48	3	li	li	PROPN
ap-5556	48	4	et	et	PROPN
ap-5556	48	5	al	al	PROPN
ap-5556	48	6	.	.	PUNCT
ap-5556	49	1	[	[	X
ap-5556	49	2	10	10	NUM
ap-5556	49	3	]	]	PUNCT
ap-5556	49	4	analysed	analyse	VERB
ap-5556	49	5	a	a	DET
ap-5556	49	6	bending	bend	VERB
ap-5556	49	7	large	large	ADJ
ap-5556	49	8	deflection	deflection	NOUN
ap-5556	49	9	of	of	ADP
ap-5556	49	10	a	a	DET
ap-5556	49	11	simply	simply	ADV
ap-5556	49	12	supported	support	VERB
ap-5556	49	13	circular	circular	ADJ
ap-5556	49	14	plate	plate	NOUN
ap-5556	49	15	using	use	VERB
ap-5556	49	16	an	an	DET
ap-5556	49	17	analytical	analytical	ADJ
ap-5556	49	18	method	method	NOUN
ap-5556	49	19	.	.	PUNCT
ap-5556	50	1	the	the	DET
ap-5556	50	2	dtm	dtm	PROPN
ap-5556	50	3	is	be	AUX
ap-5556	50	4	equally	equally	ADV
ap-5556	50	5	very	very	ADV
ap-5556	50	6	versatile	versatile	ADJ
ap-5556	50	7	method	method	NOUN
ap-5556	50	8	,	,	PUNCT
ap-5556	50	9	good	good	ADJ
ap-5556	50	10	in	in	ADP
ap-5556	50	11	handling	handle	VERB
ap-5556	50	12	singularity	singularity	NOUN
ap-5556	50	13	and	and	CCONJ
ap-5556	50	14	a	a	DET
ap-5556	50	15	non	non	ADJ
ap-5556	50	16	-	-	ADJ
ap-5556	50	17	trivial	trivial	ADJ
ap-5556	50	18	differential	differential	NOUN
ap-5556	50	19	system	system	NOUN
ap-5556	50	20	of	of	ADP
ap-5556	50	21	equations	equation	NOUN
ap-5556	50	22	,	,	PUNCT
ap-5556	50	23	but	but	CCONJ
ap-5556	50	24	requires	require	VERB
ap-5556	50	25	the	the	DET
ap-5556	50	26	need	need	NOUN
ap-5556	50	27	to	to	PART
ap-5556	50	28	manipulate	manipulate	VERB
ap-5556	50	29	the	the	DET
ap-5556	50	30	governing	govern	VERB
ap-5556	50	31	equation	equation	NOUN
ap-5556	50	32	before	before	SCONJ
ap-5556	50	33	the	the	DET
ap-5556	50	34	singularity	singularity	NOUN
ap-5556	50	35	problem	problem	NOUN
ap-5556	50	36	is	be	AUX
ap-5556	50	37	resolved	resolve	VERB
ap-5556	50	38	and	and	CCONJ
ap-5556	50	39	,	,	PUNCT
ap-5556	50	40	subsequently	subsequently	ADV
ap-5556	50	41	,	,	PUNCT
ap-5556	50	42	involve	involve	VERB
ap-5556	50	43	transforming	transform	VERB
ap-5556	50	44	the	the	DET
ap-5556	50	45	governing	govern	VERB
ap-5556	50	46	equation	equation	NOUN
ap-5556	50	47	to	to	ADP
ap-5556	50	48	an	an	DET
ap-5556	50	49	algebraic	algebraic	ADJ
ap-5556	50	50	form	form	NOUN
ap-5556	50	51	.	.	PUNCT
ap-5556	51	1	the	the	DET
ap-5556	51	2	number	number	NOUN
ap-5556	51	3	of	of	ADP
ap-5556	51	4	iterations	iteration	NOUN
ap-5556	51	5	in	in	ADP
ap-5556	51	6	the	the	DET
ap-5556	51	7	dtm	dtm	PROPN
ap-5556	51	8	is	be	AUX
ap-5556	51	9	very	very	ADV
ap-5556	51	10	cumbersome	cumbersome	ADJ
ap-5556	51	11	compared	compare	VERB
ap-5556	51	12	to	to	ADP
ap-5556	51	13	the	the	DET
ap-5556	51	14	galerkin	galerkin	ADJ
ap-5556	51	15	method	method	NOUN
ap-5556	51	16	of	of	ADP
ap-5556	51	17	weighted	weight	VERB
ap-5556	51	18	residual	residual	ADJ
ap-5556	51	19	.	.	PUNCT
ap-5556	52	1	meanwhile	meanwhile	ADV
ap-5556	52	2	,	,	PUNCT
ap-5556	52	3	the	the	DET
ap-5556	52	4	hpm	hpm	NOUN
ap-5556	52	5	also	also	ADV
ap-5556	52	6	suffers	suffer	VERB
ap-5556	52	7	the	the	DET
ap-5556	52	8	setback	setback	NOUN
ap-5556	52	9	of	of	ADP
ap-5556	52	10	finding	find	VERB
ap-5556	52	11	the	the	DET
ap-5556	52	12	embedded	embed	VERB
ap-5556	52	13	parameter	parameter	NOUN
ap-5556	52	14	and	and	CCONJ
ap-5556	52	15	initial	initial	ADJ
ap-5556	52	16	approximation	approximation	NOUN
ap-5556	52	17	of	of	ADP
ap-5556	52	18	the	the	DET
ap-5556	52	19	governing	govern	VERB
ap-5556	52	20	equation	equation	NOUN
ap-5556	52	21	that	that	PRON
ap-5556	52	22	satisfies	satisfy	VERB
ap-5556	52	23	the	the	DET
ap-5556	52	24	given	give	VERB
ap-5556	52	25	conditions	condition	NOUN
ap-5556	52	26	.	.	PUNCT
ap-5556	53	1	nonetheless	nonetheless	ADV
ap-5556	53	2	,	,	PUNCT
ap-5556	53	3	several	several	ADJ
ap-5556	53	4	researches	research	NOUN
ap-5556	53	5	on	on	ADP
ap-5556	53	6	a	a	DET
ap-5556	53	7	free	free	ADJ
ap-5556	53	8	vibration	vibration	NOUN
ap-5556	53	9	of	of	ADP
ap-5556	53	10	circular	circular	ADJ
ap-5556	53	11	plates	plate	NOUN
ap-5556	53	12	using	use	VERB
ap-5556	53	13	different	different	ADJ
ap-5556	53	14	methods	method	NOUN
ap-5556	53	15	have	have	AUX
ap-5556	53	16	been	be	AUX
ap-5556	53	17	presented	present	VERB
ap-5556	53	18	in	in	ADP
ap-5556	53	19	the	the	DET
ap-5556	53	20	literature	literature	NOUN
ap-5556	53	21	[	[	X
ap-5556	53	22	11–25	11–25	NUM
ap-5556	53	23	]	]	PUNCT
ap-5556	53	24	.	.	PUNCT
ap-5556	54	1	moreover	moreover	ADV
ap-5556	54	2	,	,	PUNCT
ap-5556	54	3	the	the	DET
ap-5556	54	4	reliability	reliability	NOUN
ap-5556	54	5	and	and	CCONJ
ap-5556	54	6	flexibility	flexibility	NOUN
ap-5556	54	7	of	of	ADP
ap-5556	54	8	the	the	DET
ap-5556	54	9	galerkin	galerkin	ADJ
ap-5556	54	10	method	method	NOUN
ap-5556	54	11	of	of	ADP
ap-5556	54	12	weighted	weight	VERB
ap-5556	54	13	residual	residual	ADJ
ap-5556	54	14	[	[	X
ap-5556	54	15	26	26	NUM
ap-5556	54	16	]	]	PUNCT
ap-5556	54	17	have	have	AUX
ap-5556	54	18	made	make	VERB
ap-5556	54	19	it	it	PRON
ap-5556	54	20	more	more	ADV
ap-5556	54	21	effective	effective	ADJ
ap-5556	54	22	than	than	ADP
ap-5556	54	23	any	any	DET
ap-5556	54	24	other	other	ADJ
ap-5556	54	25	semi	semi	ADJ
ap-5556	54	26	-	-	ADJ
ap-5556	54	27	numerical	numerical	ADJ
ap-5556	54	28	method	method	NOUN
ap-5556	54	29	.	.	PUNCT
ap-5556	55	1	the	the	DET
ap-5556	55	2	method	method	NOUN
ap-5556	55	3	is	be	AUX
ap-5556	55	4	much	much	ADV
ap-5556	55	5	simpler	simple	ADJ
ap-5556	55	6	than	than	ADP
ap-5556	55	7	any	any	DET
ap-5556	55	8	other	other	ADJ
ap-5556	55	9	approximating	approximate	VERB
ap-5556	55	10	method	method	NOUN
ap-5556	55	11	of	of	ADP
ap-5556	55	12	solutions	solution	NOUN
ap-5556	55	13	.	.	PUNCT
ap-5556	56	1	the	the	DET
ap-5556	56	2	galerkin	galerkin	ADJ
ap-5556	56	3	method	method	NOUN
ap-5556	56	4	of	of	ADP
ap-5556	56	5	weighted	weight	VERB
ap-5556	56	6	residual	residual	ADJ
ap-5556	56	7	handles	handle	NOUN
ap-5556	56	8	the	the	DET
ap-5556	56	9	circular	circular	ADJ
ap-5556	56	10	plate	plate	NOUN
ap-5556	56	11	vibration	vibration	NOUN
ap-5556	56	12	problem	problem	NOUN
ap-5556	56	13	without	without	ADP
ap-5556	56	14	any	any	DET
ap-5556	56	15	manipulation	manipulation	NOUN
ap-5556	56	16	of	of	ADP
ap-5556	56	17	the	the	DET
ap-5556	56	18	governing	govern	VERB
ap-5556	56	19	equation	equation	NOUN
ap-5556	56	20	with	with	ADP
ap-5556	56	21	very	very	ADV
ap-5556	56	22	precise	precise	ADJ
ap-5556	56	23	results	result	NOUN
ap-5556	56	24	compared	compare	VERB
ap-5556	56	25	to	to	ADP
ap-5556	56	26	numerical	numerical	ADJ
ap-5556	56	27	and	and	CCONJ
ap-5556	56	28	experimental	experimental	ADJ
ap-5556	56	29	results	result	NOUN
ap-5556	56	30	.	.	PUNCT
ap-5556	57	1	the	the	DET
ap-5556	57	2	review	review	NOUN
ap-5556	57	3	of	of	ADP
ap-5556	57	4	the	the	DET
ap-5556	57	5	past	past	ADJ
ap-5556	57	6	studies	study	NOUN
ap-5556	57	7	show	show	VERB
ap-5556	57	8	that	that	SCONJ
ap-5556	57	9	the	the	DET
ap-5556	57	10	analysis	analysis	NOUN
ap-5556	57	11	of	of	ADP
ap-5556	57	12	the	the	DET
ap-5556	57	13	dynamic	dynamic	ADJ
ap-5556	57	14	behaviour	behaviour	NOUN
ap-5556	57	15	of	of	ADP
ap-5556	57	16	varying	vary	VERB
ap-5556	57	17	thickness	thickness	NOUN
ap-5556	57	18	and	and	CCONJ
ap-5556	57	19	non	non	ADJ
ap-5556	57	20	-	-	ADJ
ap-5556	57	21	homogeneous	homogeneous	ADJ
ap-5556	57	22	circular	circular	ADJ
ap-5556	57	23	plates	plate	NOUN
ap-5556	57	24	resting	rest	VERB
ap-5556	57	25	on	on	ADP
ap-5556	57	26	winkler	winkler	NOUN
ap-5556	57	27	and	and	CCONJ
ap-5556	57	28	pasternak	pasternak	PROPN
ap-5556	57	29	foundations	foundation	NOUN
ap-5556	57	30	with	with	ADP
ap-5556	57	31	the	the	DET
ap-5556	57	32	aid	aid	NOUN
ap-5556	57	33	of	of	ADP
ap-5556	57	34	the	the	DET
ap-5556	57	35	galerkin	galerkin	ADJ
ap-5556	57	36	method	method	NOUN
ap-5556	57	37	of	of	ADP
ap-5556	57	38	weighted	weight	VERB
ap-5556	57	39	residual	residual	ADJ
ap-5556	57	40	has	have	AUX
ap-5556	57	41	not	not	PART
ap-5556	57	42	been	be	AUX
ap-5556	57	43	investigated	investigate	VERB
ap-5556	57	44	.	.	PUNCT
ap-5556	58	1	therefore	therefore	ADV
ap-5556	58	2	,	,	PUNCT
ap-5556	58	3	the	the	DET
ap-5556	58	4	present	present	ADJ
ap-5556	58	5	study	study	NOUN
ap-5556	58	6	focuses	focus	VERB
ap-5556	58	7	on	on	ADP
ap-5556	58	8	the	the	DET
ap-5556	58	9	application	application	NOUN
ap-5556	58	10	of	of	ADP
ap-5556	58	11	the	the	DET
ap-5556	58	12	galerkin	galerkin	ADJ
ap-5556	58	13	method	method	NOUN
ap-5556	58	14	of	of	ADP
ap-5556	58	15	weighted	weight	VERB
ap-5556	58	16	residual	residual	ADJ
ap-5556	58	17	for	for	ADP
ap-5556	58	18	a	a	DET
ap-5556	58	19	dynamic	dynamic	ADJ
ap-5556	58	20	analysis	analysis	NOUN
ap-5556	58	21	of	of	ADP
ap-5556	58	22	a	a	DET
ap-5556	58	23	non	non	ADJ
ap-5556	58	24	-	-	ADJ
ap-5556	58	25	uniform	uniform	ADJ
ap-5556	58	26	thickness	thickness	NOUN
ap-5556	58	27	circular	circular	ADJ
ap-5556	58	28	plate	plate	NOUN
ap-5556	58	29	resting	rest	VERB
ap-5556	58	30	on	on	ADP
ap-5556	58	31	winkler	winkler	NOUN
ap-5556	58	32	and	and	CCONJ
ap-5556	58	33	pasternak	pasternak	PROPN
ap-5556	58	34	foundations	foundation	NOUN
ap-5556	58	35	.	.	PUNCT
ap-5556	59	1	the	the	DET
ap-5556	59	2	novelty	novelty	NOUN
ap-5556	59	3	of	of	ADP
ap-5556	59	4	the	the	DET
ap-5556	59	5	present	present	ADJ
ap-5556	59	6	study	study	NOUN
ap-5556	59	7	also	also	ADV
ap-5556	59	8	includes	include	VERB
ap-5556	59	9	resolving	resolve	VERB
ap-5556	59	10	the	the	DET
ap-5556	59	11	singularities	singularity	NOUN
ap-5556	59	12	problem	problem	NOUN
ap-5556	59	13	associated	associate	VERB
ap-5556	59	14	with	with	ADP
ap-5556	59	15	a	a	DET
ap-5556	59	16	circular	circular	ADJ
ap-5556	59	17	plate	plate	NOUN
ap-5556	59	18	without	without	ADP
ap-5556	59	19	modifying	modify	VERB
ap-5556	59	20	the	the	DET
ap-5556	59	21	governing	govern	VERB
ap-5556	59	22	equation	equation	NOUN
ap-5556	59	23	.	.	PUNCT
ap-5556	60	1	2	2	X
ap-5556	60	2	.	.	X
ap-5556	60	3	problem	problem	NOUN
ap-5556	60	4	formulation	formulation	NOUN
ap-5556	60	5	and	and	CCONJ
ap-5556	60	6	mathematical	mathematical	ADJ
ap-5556	60	7	analysis	analysis	NOUN
ap-5556	60	8	a	a	DET
ap-5556	60	9	circular	circular	ADJ
ap-5556	60	10	plate	plate	NOUN
ap-5556	60	11	of	of	ADP
ap-5556	60	12	a	a	DET
ap-5556	60	13	varying	vary	VERB
ap-5556	60	14	uniform	uniform	ADJ
ap-5556	60	15	thickness	thickness	NOUN
ap-5556	60	16	and	and	CCONJ
ap-5556	60	17	non	non	ADJ
ap-5556	60	18	-	-	ADJ
ap-5556	60	19	homogenous	homogenous	ADJ
ap-5556	60	20	material	material	NOUN
ap-5556	60	21	resting	rest	VERB
ap-5556	60	22	on	on	ADP
ap-5556	60	23	winkler	winkler	NOUN
ap-5556	60	24	and	and	CCONJ
ap-5556	60	25	pasternak	pasternak	PROPN
ap-5556	60	26	foundation	foundation	PROPN
ap-5556	60	27	in	in	ADP
ap-5556	60	28	fig	fig	NOUN
ap-5556	60	29	.	.	PUNCT
ap-5556	60	30	1	1	NUM
ap-5556	60	31	is	be	AUX
ap-5556	60	32	considered	consider	VERB
ap-5556	60	33	under	under	ADP
ap-5556	60	34	various	various	ADJ
ap-5556	60	35	boundary	boundary	ADJ
ap-5556	60	36	conditions	condition	NOUN
ap-5556	60	37	,	,	PUNCT
ap-5556	60	38	simply	simply	ADV
ap-5556	60	39	supported	support	VERB
ap-5556	60	40	,	,	PUNCT
ap-5556	60	41	free	free	ADJ
ap-5556	60	42	and	and	CCONJ
ap-5556	60	43	clamped	clamp	VERB
ap-5556	60	44	edge	edge	NOUN
ap-5556	60	45	conditions	condition	NOUN
ap-5556	60	46	.	.	PUNCT
ap-5556	61	1	according	accord	VERB
ap-5556	61	2	to	to	ADP
ap-5556	61	3	kirchhoff	kirchhoff	PROPN
ap-5556	61	4	plate	plate	PROPN
ap-5556	61	5	theory	theory	PROPN
ap-5556	61	6	,	,	PUNCT
ap-5556	61	7	the	the	DET
ap-5556	61	8	following	follow	VERB
ap-5556	61	9	assumptions	assumption	NOUN
ap-5556	61	10	are	be	AUX
ap-5556	61	11	considered	consider	VERB
ap-5556	61	12	in	in	ADP
ap-5556	61	13	the	the	DET
ap-5556	61	14	model	model	NOUN
ap-5556	61	15	of	of	ADP
ap-5556	61	16	the	the	DET
ap-5556	61	17	governing	govern	VERB
ap-5556	61	18	equation	equation	NOUN
ap-5556	61	19	.	.	PUNCT
ap-5556	62	1	(	(	PUNCT
ap-5556	62	2	1	1	NUM
ap-5556	62	3	.	.	PUNCT
ap-5556	62	4	)	)	PUNCT
ap-5556	62	5	plate	plate	NOUN
ap-5556	62	6	thickness	thickness	NOUN
ap-5556	62	7	is	be	AUX
ap-5556	62	8	smaller	small	ADJ
ap-5556	62	9	compared	compare	VERB
ap-5556	62	10	to	to	ADP
ap-5556	62	11	the	the	DET
ap-5556	62	12	dimension	dimension	NOUN
ap-5556	62	13	of	of	ADP
ap-5556	62	14	the	the	DET
ap-5556	62	15	circular	circular	ADJ
ap-5556	62	16	plate	plate	NOUN
ap-5556	62	17	.	.	PUNCT
ap-5556	63	1	(	(	PUNCT
ap-5556	63	2	2	2	NUM
ap-5556	63	3	.	.	PUNCT
ap-5556	63	4	)	)	PUNCT
ap-5556	63	5	normal	normal	ADJ
ap-5556	63	6	stress	stress	NOUN
ap-5556	63	7	is	be	AUX
ap-5556	63	8	assumed	assume	VERB
ap-5556	63	9	negligible	negligible	ADJ
ap-5556	63	10	in	in	ADP
ap-5556	63	11	the	the	DET
ap-5556	63	12	transverse	transverse	NOUN
ap-5556	63	13	direction	direction	NOUN
ap-5556	63	14	of	of	ADP
ap-5556	63	15	the	the	DET
ap-5556	63	16	circular	circular	ADJ
ap-5556	63	17	plate	plate	NOUN
ap-5556	63	18	.	.	PUNCT
ap-5556	64	1	(	(	PUNCT
ap-5556	64	2	3	3	NUM
ap-5556	64	3	.	.	PUNCT
ap-5556	64	4	)	)	PUNCT
ap-5556	65	1	the	the	DET
ap-5556	65	2	rotary	rotary	NOUN
ap-5556	65	3	inertia	inertia	NOUN
ap-5556	65	4	effect	effect	NOUN
ap-5556	65	5	is	be	AUX
ap-5556	65	6	negligible	negligible	ADJ
ap-5556	65	7	.	.	PUNCT
ap-5556	66	1	(	(	PUNCT
ap-5556	66	2	4	4	NUM
ap-5556	66	3	.	.	PUNCT
ap-5556	66	4	)	)	PUNCT
ap-5556	66	5	normal	normal	ADJ
ap-5556	66	6	to	to	ADP
ap-5556	66	7	the	the	DET
ap-5556	66	8	undeformed	undeformed	ADJ
ap-5556	66	9	middle	middle	ADJ
ap-5556	66	10	surface	surface	NOUN
ap-5556	66	11	remains	remain	VERB
ap-5556	66	12	straight	straight	ADJ
ap-5556	66	13	and	and	CCONJ
ap-5556	66	14	normal	normal	ADJ
ap-5556	66	15	to	to	ADP
ap-5556	66	16	the	the	DET
ap-5556	66	17	deformed	deform	VERB
ap-5556	66	18	middle	middle	ADJ
ap-5556	66	19	surface	surface	NOUN
ap-5556	66	20	without	without	ADP
ap-5556	66	21	length	length	NOUN
ap-5556	66	22	stretching	stretch	VERB
ap-5556	66	23	.	.	PUNCT
ap-5556	67	1	128	128	NUM
ap-5556	67	2	vol	vol	NOUN
ap-5556	67	3	.	.	PUNCT
ap-5556	68	1	60	60	NUM
ap-5556	68	2	no	no	NOUN
ap-5556	68	3	.	.	PUNCT
ap-5556	69	1	2/2020	2/2020	NUM
ap-5556	69	2	investigation	investigation	NOUN
ap-5556	69	3	of	of	ADP
ap-5556	69	4	the	the	DET
ap-5556	69	5	dynamic	dynamic	ADJ
ap-5556	69	6	behaviour	behaviour	NOUN
ap-5556	69	7	of	of	ADP
ap-5556	69	8	non	non	ADJ
ap-5556	69	9	-	-	ADJ
ap-5556	69	10	uniform	uniform	ADJ
ap-5556	69	11	thickness	thickness	NOUN
ap-5556	69	12	.	.	PUNCT
ap-5556	69	13	.	.	PUNCT
ap-5556	69	14	.	.	PUNCT
ap-5556	70	1	the	the	DET
ap-5556	70	2	differential	differential	ADJ
ap-5556	70	3	governing	govern	VERB
ap-5556	70	4	equation	equation	NOUN
ap-5556	70	5	for	for	ADP
ap-5556	70	6	a	a	DET
ap-5556	70	7	transverse	transverse	NOUN
ap-5556	70	8	free	free	ADJ
ap-5556	70	9	vibration	vibration	NOUN
ap-5556	70	10	of	of	ADP
ap-5556	70	11	an	an	DET
ap-5556	70	12	isotropic	isotropic	ADJ
ap-5556	70	13	circular	circular	ADJ
ap-5556	70	14	plate	plate	NOUN
ap-5556	70	15	with	with	ADP
ap-5556	70	16	a	a	DET
ap-5556	70	17	uniform	uniform	ADJ
ap-5556	70	18	thickness	thickness	NOUN
ap-5556	70	19	as	as	SCONJ
ap-5556	70	20	shown	show	VERB
ap-5556	70	21	in	in	ADP
ap-5556	70	22	fig	fig	NOUN
ap-5556	70	23	.	.	PUNCT
ap-5556	71	1	1	1	NUM
ap-5556	71	2	may	may	AUX
ap-5556	71	3	be	be	AUX
ap-5556	71	4	written	write	VERB
ap-5556	71	5	as	as	ADP
ap-5556	71	6	[	[	X
ap-5556	71	7	12	12	NUM
ap-5556	71	8	,	,	PUNCT
ap-5556	71	9	27	27	NUM
ap-5556	71	10	,	,	PUNCT
ap-5556	71	11	28	28	NUM
ap-5556	71	12	]	]	PUNCT
ap-5556	71	13	,	,	PUNCT
ap-5556	71	14	g(r	g(r	PROPN
ap-5556	71	15	)	)	PUNCT
ap-5556	71	16	{	{	PUNCT
ap-5556	71	17	∂4w(r	∂4w(r	PROPN
ap-5556	71	18	,	,	PUNCT
ap-5556	71	19	t	t	PROPN
ap-5556	71	20	)	)	PUNCT
ap-5556	71	21	∂r4	∂r4	PROPN
ap-5556	72	1	+	+	CCONJ
ap-5556	72	2	2	2	NUM
ap-5556	72	3	r	r	NOUN
ap-5556	72	4	∂3	∂3	NOUN
ap-5556	72	5	∂r3w(r	∂r3w(r	NOUN
ap-5556	72	6	,	,	PUNCT
ap-5556	72	7	t)−	t)−	PROPN
ap-5556	72	8	(	(	PUNCT
ap-5556	72	9	2m2	2m2	NUM
ap-5556	72	10	+	+	SYM
ap-5556	72	11	1	1	NUM
ap-5556	72	12	r2	r2	PROPN
ap-5556	72	13	)	)	PUNCT
ap-5556	72	14	∂2w(r	∂2w(r	PROPN
ap-5556	72	15	,	,	PUNCT
ap-5556	72	16	t	t	PROPN
ap-5556	72	17	)	)	PUNCT
ap-5556	72	18	∂r2	∂r2	PROPN
ap-5556	72	19	+	+	X
ap-5556	72	20	(	(	PUNCT
ap-5556	72	21	2m2	2m2	NUM
ap-5556	72	22	+	+	SYM
ap-5556	72	23	1	1	NUM
ap-5556	72	24	r3	r3	PROPN
ap-5556	72	25	)	)	PUNCT
ap-5556	72	26	∂w(r	∂w(r	PROPN
ap-5556	72	27	,	,	PUNCT
ap-5556	72	28	t	t	PROPN
ap-5556	72	29	)	)	PUNCT
ap-5556	73	1	∂r	∂r	NOUN
ap-5556	73	2	−	−	PROPN
ap-5556	73	3	(	(	PUNCT
ap-5556	73	4	4m2	4m2	NUM
ap-5556	73	5	−m4	−m4	NOUN
ap-5556	73	6	r4	r4	VERB
ap-5556	73	7	)	)	PUNCT
ap-5556	74	1	w(r	w(r	PROPN
ap-5556	74	2	,	,	PUNCT
ap-5556	74	3	t	t	PROPN
ap-5556	74	4	)	)	PUNCT
ap-5556	74	5	}	}	PUNCT
ap-5556	75	1	+	+	PUNCT
ap-5556	75	2	∂g(r	∂g(r	NOUN
ap-5556	75	3	)	)	PUNCT
ap-5556	76	1	∂r	∂r	PROPN
ap-5556	76	2	{	{	PUNCT
ap-5556	76	3	2∂	2∂	PROPN
ap-5556	76	4	3w(r	3w(r	PROPN
ap-5556	76	5	,	,	PUNCT
ap-5556	76	6	t	t	PROPN
ap-5556	76	7	)	)	PUNCT
ap-5556	76	8	∂r3	∂r3	NOUN
ap-5556	76	9	+	+	CCONJ
ap-5556	76	10	2	2	NUM
ap-5556	76	11	+	+	CCONJ
ap-5556	76	12	ν	ν	NOUN
ap-5556	76	13	r	r	NOUN
ap-5556	76	14	∂2w(r	∂2w(r	PROPN
ap-5556	76	15	,	,	PUNCT
ap-5556	76	16	t	t	PROPN
ap-5556	76	17	)	)	PUNCT
ap-5556	76	18	∂r2	∂r2	PROPN
ap-5556	76	19	−	−	ADP
ap-5556	76	20	2m2	2m2	NUM
ap-5556	76	21	+	+	SYM
ap-5556	76	22	1	1	NUM
ap-5556	76	23	r2	r2	PROPN
ap-5556	76	24	∂w(r	∂w(r	PROPN
ap-5556	76	25	,	,	PUNCT
ap-5556	76	26	t	t	PROPN
ap-5556	76	27	)	)	PUNCT
ap-5556	77	1	∂r	∂r	PROPN
ap-5556	78	1	+	+	NUM
ap-5556	78	2	3m2	3m2	NUM
ap-5556	78	3	r3	r3	PROPN
ap-5556	78	4	w(r	w(r	PROPN
ap-5556	78	5	,	,	PUNCT
ap-5556	78	6	t	t	PROPN
ap-5556	78	7	)	)	PUNCT
ap-5556	78	8	}	}	PUNCT
ap-5556	79	1	+	+	CCONJ
ap-5556	79	2	∂2g(r	∂2g(r	X
ap-5556	79	3	)	)	PUNCT
ap-5556	79	4	∂r2	∂r2	PROPN
ap-5556	79	5	{	{	PUNCT
ap-5556	79	6	∂2w(r	∂2w(r	PROPN
ap-5556	79	7	,	,	PUNCT
ap-5556	79	8	t	t	PROPN
ap-5556	79	9	)	)	PUNCT
ap-5556	79	10	∂r2	∂r2	PROPN
ap-5556	79	11	+	+	CCONJ
ap-5556	79	12	ν	ν	X
ap-5556	79	13	(	(	PUNCT
ap-5556	79	14	1	1	NUM
ap-5556	79	15	r	r	NOUN
ap-5556	79	16	∂w(r	∂w(r	PROPN
ap-5556	79	17	,	,	PUNCT
ap-5556	79	18	t	t	PROPN
ap-5556	79	19	)	)	PUNCT
ap-5556	80	1	∂r	∂r	PROPN
ap-5556	80	2	−	−	PROPN
ap-5556	80	3	m2	m2	PROPN
ap-5556	80	4	r2	r2	PROPN
ap-5556	80	5	w(r	w(r	PROPN
ap-5556	80	6	,	,	PUNCT
ap-5556	80	7	t	t	PROPN
ap-5556	80	8	)	)	PUNCT
ap-5556	80	9	)	)	PUNCT
ap-5556	80	10	}	}	PUNCT
ap-5556	80	11	−	−	PROPN
ap-5556	80	12	ks	ks	PROPN
ap-5556	80	13	∂2w(r	∂2w(r	PROPN
ap-5556	80	14	,	,	PUNCT
ap-5556	80	15	t	t	PROPN
ap-5556	80	16	)	)	PUNCT
ap-5556	80	17	∂r2	∂r2	PROPN
ap-5556	80	18	−	−	PROPN
ap-5556	80	19	ks	ks	NOUN
ap-5556	80	20	1	1	NUM
ap-5556	80	21	r	r	NOUN
ap-5556	80	22	∂w(r	∂w(r	PROPN
ap-5556	80	23	,	,	PUNCT
ap-5556	80	24	t	t	PROPN
ap-5556	80	25	)	)	PUNCT
ap-5556	80	26	∂r	∂r	PROPN
ap-5556	81	1	+	+	NUM
ap-5556	81	2	ks	ks	PROPN
ap-5556	81	3	m2	m2	PROPN
ap-5556	81	4	r2	r2	PROPN
ap-5556	81	5	w(r	w(r	PROPN
ap-5556	81	6	,	,	PUNCT
ap-5556	81	7	t	t	PROPN
ap-5556	81	8	)	)	PUNCT
ap-5556	82	1	+	+	CCONJ
ap-5556	83	1	kww(r	kww(r	PROPN
ap-5556	83	2	,	,	PUNCT
ap-5556	83	3	t	t	PROPN
ap-5556	83	4	)	)	PUNCT
ap-5556	83	5	+	+	CCONJ
ap-5556	83	6	ρh	ρh	PROPN
ap-5556	83	7	∂2w(r	∂2w(r	PROPN
ap-5556	83	8	,	,	PUNCT
ap-5556	83	9	t	t	PROPN
ap-5556	83	10	)	)	PUNCT
ap-5556	83	11	∂t2	∂t2	NOUN
ap-5556	83	12	=	=	SYM
ap-5556	83	13	0	0	NUM
ap-5556	83	14	,	,	PUNCT
ap-5556	83	15	(	(	PUNCT
ap-5556	83	16	1	1	X
ap-5556	83	17	)	)	PUNCT
ap-5556	83	18	where	where	SCONJ
ap-5556	83	19	r	r	NOUN
ap-5556	83	20	and	and	CCONJ
ap-5556	83	21	θ	θ	PROPN
ap-5556	83	22	are	be	AUX
ap-5556	83	23	polar	polar	ADJ
ap-5556	83	24	coordinates	coordinate	NOUN
ap-5556	83	25	.	.	PUNCT
ap-5556	84	1	w	w	PROPN
ap-5556	84	2	is	be	AUX
ap-5556	84	3	the	the	DET
ap-5556	84	4	transverse	transverse	ADJ
ap-5556	84	5	displacement	displacement	NOUN
ap-5556	84	6	,	,	PUNCT
ap-5556	84	7	ρ	ρ	PROPN
ap-5556	84	8	is	be	AUX
ap-5556	84	9	the	the	DET
ap-5556	84	10	material	material	ADJ
ap-5556	84	11	density	density	NOUN
ap-5556	84	12	,	,	PUNCT
ap-5556	84	13	h	h	NOUN
ap-5556	84	14	is	be	AUX
ap-5556	84	15	the	the	DET
ap-5556	84	16	thickness	thickness	NOUN
ap-5556	84	17	of	of	ADP
ap-5556	84	18	the	the	DET
ap-5556	84	19	plate	plate	NOUN
ap-5556	84	20	,	,	PUNCT
ap-5556	84	21	flexural	flexural	ADJ
ap-5556	84	22	rigidity	rigidity	NOUN
ap-5556	84	23	d	d	PROPN
ap-5556	84	24	=	=	PUNCT
ap-5556	84	25	eh3/12(1−	eh3/12(1−	NOUN
ap-5556	84	26	ν2	ν2	NOUN
ap-5556	84	27	)	)	PUNCT
ap-5556	84	28	,	,	PUNCT
ap-5556	84	29	poisson	poisson	PROPN
ap-5556	84	30	’s	’s	PART
ap-5556	84	31	ratio	ratio	NOUN
ap-5556	84	32	is	be	AUX
ap-5556	84	33	ν	ν	NOUN
ap-5556	84	34	,	,	PUNCT
ap-5556	84	35	the	the	DET
ap-5556	84	36	elasticity	elasticity	NOUN
ap-5556	84	37	coefficient	coefficient	NOUN
ap-5556	84	38	is	be	AUX
ap-5556	84	39	e	e	NOUN
ap-5556	84	40	,	,	PUNCT
ap-5556	84	41	kw	kw	PROPN
ap-5556	84	42	is	be	AUX
ap-5556	84	43	the	the	DET
ap-5556	84	44	winkler	winkler	PROPN
ap-5556	84	45	foundation	foundation	PROPN
ap-5556	84	46	and	and	CCONJ
ap-5556	84	47	ks	ks	PROPN
ap-5556	84	48	is	be	AUX
ap-5556	84	49	the	the	DET
ap-5556	84	50	pasternak	pasternak	PROPN
ap-5556	84	51	foundation	foundation	PROPN
ap-5556	84	52	.	.	PUNCT
ap-5556	85	1	for	for	ADP
ap-5556	85	2	a	a	DET
ap-5556	85	3	free	free	ADJ
ap-5556	85	4	vibration	vibration	NOUN
ap-5556	85	5	equation	equation	NOUN
ap-5556	85	6	,	,	PUNCT
ap-5556	85	7	the	the	DET
ap-5556	85	8	solution	solution	NOUN
ap-5556	85	9	is	be	AUX
ap-5556	85	10	presented	present	VERB
ap-5556	85	11	in	in	ADP
ap-5556	85	12	this	this	DET
ap-5556	85	13	form	form	NOUN
ap-5556	85	14	based	base	VERB
ap-5556	85	15	on	on	ADP
ap-5556	85	16	kantorovich	kantorovich	NOUN
ap-5556	85	17	-	-	PUNCT
ap-5556	85	18	type	type	NOUN
ap-5556	85	19	approximation	approximation	NOUN
ap-5556	85	20	w(r	w(r	PROPN
ap-5556	85	21	,	,	PUNCT
ap-5556	85	22	t	t	PROPN
ap-5556	85	23	)	)	PUNCT
ap-5556	85	24	=	=	SYM
ap-5556	86	1	w(r)eiωt	w(r)eiωt	X
ap-5556	86	2	(	(	PUNCT
ap-5556	86	3	2	2	X
ap-5556	86	4	)	)	PUNCT
ap-5556	86	5	presenting	present	VERB
ap-5556	86	6	the	the	DET
ap-5556	86	7	solution	solution	NOUN
ap-5556	86	8	in	in	ADP
ap-5556	86	9	a	a	DET
ap-5556	86	10	more	more	ADV
ap-5556	86	11	general	general	ADJ
ap-5556	86	12	form	form	NOUN
ap-5556	86	13	,	,	PUNCT
ap-5556	86	14	the	the	DET
ap-5556	86	15	following	follow	VERB
ap-5556	86	16	dimensionless	dimensionless	NOUN
ap-5556	86	17	parameters	parameter	NOUN
ap-5556	86	18	are	be	AUX
ap-5556	86	19	used	use	VERB
ap-5556	86	20	r	r	NOUN
ap-5556	86	21	=	=	SYM
ap-5556	86	22	r	r	NOUN
ap-5556	86	23	a	a	PRON
ap-5556	86	24	,	,	PUNCT
ap-5556	86	25	w	w	PROPN
ap-5556	86	26	=	=	SYM
ap-5556	86	27	w	w	PROPN
ap-5556	86	28	h	h	NOUN
ap-5556	86	29	,	,	PUNCT
ap-5556	86	30	ω2	ω2	ADJ
ap-5556	86	31	=	=	SYM
ap-5556	86	32	ρ0h0a	ρ0h0a	NUM
ap-5556	86	33	4	4	NUM
ap-5556	86	34	d∗	d∗	NOUN
ap-5556	86	35	ω2,kw	ω2,kw	NOUN
ap-5556	86	36	=	=	SYM
ap-5556	86	37	kwa	kwa	PROPN
ap-5556	86	38	4	4	NUM
ap-5556	86	39	d∗	d∗	NOUN
ap-5556	86	40	,	,	PUNCT
ap-5556	86	41	ks	ks	NOUN
ap-5556	86	42	=	=	SYM
ap-5556	86	43	ksa	ksa	PROPN
ap-5556	86	44	2	2	NUM
ap-5556	86	45	d∗	d∗	NOUN
ap-5556	86	46	;	;	PUNCT
ap-5556	86	47	(	(	PUNCT
ap-5556	86	48	3	3	X
ap-5556	86	49	)	)	PUNCT
ap-5556	86	50	applying	apply	VERB
ap-5556	86	51	eq	eq	ADP
ap-5556	86	52	.	.	PUNCT
ap-5556	87	1	(	(	PUNCT
ap-5556	87	2	2	2	X
ap-5556	87	3	)	)	PUNCT
ap-5556	87	4	on	on	ADP
ap-5556	87	5	eq	eq	ADP
ap-5556	87	6	.	.	PUNCT
ap-5556	88	1	(	(	PUNCT
ap-5556	88	2	1	1	NUM
ap-5556	88	3	)	)	PUNCT
ap-5556	88	4	,	,	PUNCT
ap-5556	88	5	we	we	PRON
ap-5556	88	6	have	have	VERB
ap-5556	88	7	g(r	g(r	NOUN
ap-5556	88	8	)	)	PUNCT
ap-5556	88	9	{	{	PUNCT
ap-5556	89	1	d4w	d4w	PROPN
ap-5556	89	2	(	(	PUNCT
ap-5556	89	3	r	r	NOUN
ap-5556	89	4	)	)	PUNCT
ap-5556	89	5	dr4	dr4	NOUN
ap-5556	89	6	+	+	NOUN
ap-5556	89	7	2	2	NUM
ap-5556	89	8	r	r	NOUN
ap-5556	89	9	d3	d3	PROPN
ap-5556	89	10	dr3w	dr3w	PROPN
ap-5556	89	11	(	(	PUNCT
ap-5556	89	12	r)−	r)−	PROPN
ap-5556	89	13	(	(	PUNCT
ap-5556	89	14	2m2	2m2	NUM
ap-5556	89	15	+	+	SYM
ap-5556	89	16	1	1	NUM
ap-5556	89	17	r2	r2	PROPN
ap-5556	89	18	)	)	PUNCT
ap-5556	90	1	d2w	d2w	PROPN
ap-5556	90	2	(	(	PUNCT
ap-5556	90	3	r	r	NOUN
ap-5556	90	4	)	)	PUNCT
ap-5556	90	5	dr2	dr2	NOUN
ap-5556	91	1	+	+	X
ap-5556	91	2	(	(	PUNCT
ap-5556	91	3	2m2	2m2	NUM
ap-5556	91	4	+	+	SYM
ap-5556	91	5	1	1	NUM
ap-5556	91	6	r3	r3	PROPN
ap-5556	91	7	)	)	PUNCT
ap-5556	91	8	dw	dw	NOUN
ap-5556	91	9	(	(	PUNCT
ap-5556	91	10	r	r	NOUN
ap-5556	91	11	)	)	PUNCT
ap-5556	91	12	dr	dr	NOUN
ap-5556	91	13	−	−	PROPN
ap-5556	91	14	(	(	PUNCT
ap-5556	91	15	4m2	4m2	NUM
ap-5556	91	16	−m4	−m4	NOUN
ap-5556	91	17	r4	r4	VERB
ap-5556	91	18	)	)	PUNCT
ap-5556	91	19	w(r	w(r	PROPN
ap-5556	91	20	)	)	PUNCT
ap-5556	91	21	}	}	PUNCT
ap-5556	92	1	+	+	CCONJ
ap-5556	92	2	dg(r	dg(r	X
ap-5556	92	3	)	)	PUNCT
ap-5556	92	4	dr	dr	PROPN
ap-5556	92	5	{	{	PUNCT
ap-5556	92	6	2d	2d	NUM
ap-5556	92	7	3w	3w	NOUN
ap-5556	92	8	(	(	PUNCT
ap-5556	92	9	r	r	NOUN
ap-5556	92	10	)	)	PUNCT
ap-5556	92	11	dr3	dr3	PROPN
ap-5556	93	1	+	+	CCONJ
ap-5556	93	2	2	2	NUM
ap-5556	93	3	+	+	CCONJ
ap-5556	93	4	ν	ν	X
ap-5556	93	5	r	r	PROPN
ap-5556	93	6	d2w	d2w	PROPN
ap-5556	93	7	(	(	PUNCT
ap-5556	93	8	r	r	NOUN
ap-5556	93	9	)	)	PUNCT
ap-5556	93	10	dr2	dr2	NOUN
ap-5556	93	11	−	−	NOUN
ap-5556	94	1	2m2	2m2	NUM
ap-5556	94	2	+	+	CCONJ
ap-5556	94	3	1	1	NUM
ap-5556	94	4	r2	r2	PROPN
ap-5556	94	5	dw	dw	NOUN
ap-5556	94	6	(	(	PUNCT
ap-5556	94	7	r	r	NOUN
ap-5556	94	8	)	)	PUNCT
ap-5556	94	9	dr	dr	PROPN
ap-5556	94	10	+	+	PROPN
ap-5556	94	11	3m2	3m2	NUM
ap-5556	94	12	r3	r3	PROPN
ap-5556	94	13	w	w	PROPN
ap-5556	94	14	(	(	PUNCT
ap-5556	94	15	r	r	NOUN
ap-5556	94	16	)	)	PUNCT
ap-5556	94	17	}	}	PUNCT
ap-5556	95	1	+	+	CCONJ
ap-5556	95	2	d2g(r	d2g(r	PROPN
ap-5556	95	3	)	)	PUNCT
ap-5556	95	4	dr2	dr2	PROPN
ap-5556	95	5	{	{	PUNCT
ap-5556	95	6	d2w	d2w	PROPN
ap-5556	95	7	(	(	PUNCT
ap-5556	95	8	r	r	NOUN
ap-5556	95	9	)	)	PUNCT
ap-5556	95	10	dr2	dr2	NOUN
ap-5556	96	1	+	+	CCONJ
ap-5556	96	2	ν	ν	X
ap-5556	96	3	(	(	PUNCT
ap-5556	96	4	1	1	NUM
ap-5556	96	5	r	r	NOUN
ap-5556	96	6	dw	dw	NOUN
ap-5556	96	7	(	(	PUNCT
ap-5556	96	8	r	r	NOUN
ap-5556	96	9	)	)	PUNCT
ap-5556	96	10	dr	dr	PROPN
ap-5556	96	11	−	−	PROPN
ap-5556	96	12	m2	m2	PROPN
ap-5556	96	13	r2	r2	PROPN
ap-5556	96	14	w	w	PROPN
ap-5556	96	15	(	(	PUNCT
ap-5556	96	16	r	r	NOUN
ap-5556	96	17	)	)	PUNCT
ap-5556	96	18	)	)	PUNCT
ap-5556	96	19	}	}	PUNCT
ap-5556	96	20	−	−	ADP
ap-5556	96	21	a2ks	a2ks	X
ap-5556	96	22	d∗	d∗	PROPN
ap-5556	96	23	d2w	d2w	PROPN
ap-5556	96	24	(	(	PUNCT
ap-5556	96	25	r	r	NOUN
ap-5556	96	26	)	)	PUNCT
ap-5556	96	27	dr2	dr2	PROPN
ap-5556	96	28	−	−	NOUN
ap-5556	96	29	a2ks	a2ks	X
ap-5556	96	30	d∗r	d∗r	NOUN
ap-5556	96	31	dw	dw	NOUN
ap-5556	96	32	(	(	PUNCT
ap-5556	96	33	r	r	NOUN
ap-5556	96	34	)	)	PUNCT
ap-5556	96	35	dr	dr	PROPN
ap-5556	96	36	+	+	CCONJ
ap-5556	96	37	a2ks	a2ks	X
ap-5556	96	38	d∗	d∗	PROPN
ap-5556	96	39	m2	m2	PROPN
ap-5556	96	40	r2	r2	PROPN
ap-5556	96	41	w	w	PROPN
ap-5556	96	42	(	(	PUNCT
ap-5556	96	43	r	r	NOUN
ap-5556	96	44	)	)	PUNCT
ap-5556	96	45	+	+	NUM
ap-5556	96	46	a4kw	a4kw	PRON
ap-5556	96	47	d∗	d∗	PROPN
ap-5556	96	48	w	w	PROPN
ap-5556	96	49	(	(	PUNCT
ap-5556	96	50	r	r	NOUN
ap-5556	96	51	)	)	PUNCT
ap-5556	96	52	+	+	NUM
ap-5556	96	53	ρa4h	ρa4h	NUM
ap-5556	96	54	d∗	d∗	NOUN
ap-5556	96	55	ω2w	ω2w	NUM
ap-5556	96	56	(	(	PUNCT
ap-5556	96	57	r	r	NOUN
ap-5556	96	58	)	)	PUNCT
ap-5556	96	59	=	=	SYM
ap-5556	96	60	0	0	NUM
ap-5556	96	61	,	,	PUNCT
ap-5556	96	62	(	(	PUNCT
ap-5556	96	63	4	4	X
ap-5556	96	64	)	)	PUNCT
ap-5556	96	65	where	where	SCONJ
ap-5556	96	66	ω	ω	NOUN
ap-5556	96	67	is	be	AUX
ap-5556	96	68	natural	natural	ADJ
ap-5556	96	69	frequency	frequency	NOUN
ap-5556	96	70	respectively	respectively	ADV
ap-5556	96	71	.	.	PUNCT
ap-5556	97	1	while	while	SCONJ
ap-5556	97	2	m	m	NOUN
ap-5556	97	3	is	be	AUX
ap-5556	97	4	an	an	DET
ap-5556	97	5	integer	integer	NOUN
ap-5556	97	6	.	.	PUNCT
ap-5556	98	1	linear	linear	ADJ
ap-5556	98	2	variation	variation	NOUN
ap-5556	98	3	of	of	ADP
ap-5556	98	4	thickness	thickness	NOUN
ap-5556	98	5	is	be	AUX
ap-5556	98	6	considered	consider	VERB
ap-5556	98	7	.	.	PUNCT
ap-5556	99	1	h	h	NOUN
ap-5556	99	2	=	=	PUNCT
ap-5556	99	3	h0(1	h0(1	PROPN
ap-5556	99	4	+	+	CCONJ
ap-5556	99	5	ηr	ηr	NOUN
ap-5556	99	6	)	)	PUNCT
ap-5556	99	7	the	the	DET
ap-5556	99	8	thickness	thickness	NOUN
ap-5556	99	9	and	and	CCONJ
ap-5556	99	10	flexural	flexural	ADJ
ap-5556	99	11	rigidity	rigidity	NOUN
ap-5556	99	12	of	of	ADP
ap-5556	99	13	the	the	DET
ap-5556	99	14	plate	plate	NOUN
ap-5556	99	15	can	can	AUX
ap-5556	99	16	be	be	AUX
ap-5556	99	17	expressed	express	VERB
ap-5556	99	18	as	as	ADP
ap-5556	99	19	;	;	PUNCT
ap-5556	99	20	h	h	NOUN
ap-5556	99	21	=	=	SYM
ap-5556	99	22	h0f(r	h0f(r	NOUN
ap-5556	99	23	)	)	PUNCT
ap-5556	99	24	,	,	PUNCT
ap-5556	100	1	d	d	NOUN
ap-5556	100	2	=	=	PUNCT
ap-5556	100	3	d0f	d0f	VERB
ap-5556	100	4	3(r	3(r	NUM
ap-5556	100	5	)	)	PUNCT
ap-5556	100	6	=	=	SYM
ap-5556	100	7	d0g(r	d0g(r	PROPN
ap-5556	100	8	)	)	PUNCT
ap-5556	100	9	,	,	PUNCT
ap-5556	100	10	(	(	PUNCT
ap-5556	100	11	5	5	X
ap-5556	100	12	)	)	PUNCT
ap-5556	100	13	where	where	SCONJ
ap-5556	100	14	h0	h0	PROPN
ap-5556	100	15	is	be	AUX
ap-5556	100	16	thickness	thickness	NOUN
ap-5556	100	17	at	at	ADP
ap-5556	100	18	the	the	DET
ap-5556	100	19	center	center	NOUN
ap-5556	100	20	and	and	CCONJ
ap-5556	100	21	d0	d0	NOUN
ap-5556	100	22	=	=	SYM
ap-5556	100	23	eh3	eh3	NOUN
ap-5556	100	24	0	0	NUM
ap-5556	100	25	12−	12−	NUM
ap-5556	100	26	ν2	ν2	PROPN
ap-5556	100	27	η	η	PROPN
ap-5556	100	28	and	and	CCONJ
ap-5556	100	29	ξ	ξ	PROPN
ap-5556	100	30	are	be	AUX
ap-5556	100	31	the	the	DET
ap-5556	100	32	thickness	thickness	NOUN
ap-5556	100	33	and	and	CCONJ
ap-5556	100	34	density	density	NOUN
ap-5556	100	35	parameters	parameter	NOUN
ap-5556	100	36	respectively	respectively	ADV
ap-5556	100	37	.	.	PUNCT
ap-5556	101	1	(	(	PUNCT
ap-5556	101	2	r3η3	r3η3	X
ap-5556	101	3	+	+	NOUN
ap-5556	101	4	3r2η2	3r2η2	NUM
ap-5556	102	1	+	+	CCONJ
ap-5556	102	2	3ηr+	3ηr+	NUM
ap-5556	102	3	1	1	NUM
ap-5556	102	4	)	)	PUNCT
ap-5556	102	5			PUNCT
ap-5556	102	6	d4w	d4w	PROPN
ap-5556	102	7	(	(	PUNCT
ap-5556	102	8	r	r	NOUN
ap-5556	102	9	)	)	PUNCT
ap-5556	102	10	dr4	dr4	NOUN
ap-5556	102	11	+	+	CCONJ
ap-5556	102	12	2	2	NUM
ap-5556	102	13	r	r	NOUN
ap-5556	102	14	d3w	d3w	PROPN
ap-5556	102	15	(	(	PUNCT
ap-5556	102	16	r	r	NOUN
ap-5556	102	17	)	)	PUNCT
ap-5556	102	18	dr3	dr3	PROPN
ap-5556	102	19	−	−	PROPN
ap-5556	102	20	(	(	PUNCT
ap-5556	102	21	2m2	2m2	NUM
ap-5556	102	22	+	+	SYM
ap-5556	102	23	1	1	NUM
ap-5556	102	24	r2	r2	NOUN
ap-5556	102	25	)	)	PUNCT
ap-5556	102	26	d2w	d2w	PROPN
ap-5556	102	27	(	(	PUNCT
ap-5556	102	28	r	r	NOUN
ap-5556	102	29	)	)	PUNCT
ap-5556	102	30	dr2	dr2	NOUN
ap-5556	102	31	+	+	X
ap-5556	102	32	(	(	PUNCT
ap-5556	102	33	2m2	2m2	NUM
ap-5556	102	34	+	+	SYM
ap-5556	102	35	1	1	NUM
ap-5556	102	36	r3	r3	PROPN
ap-5556	102	37	)	)	PUNCT
ap-5556	102	38	dw	dw	NOUN
ap-5556	102	39	(	(	PUNCT
ap-5556	102	40	r	r	NOUN
ap-5556	102	41	)	)	PUNCT
ap-5556	102	42	dr	dr	NOUN
ap-5556	102	43	−	−	PROPN
ap-5556	102	44	(	(	PUNCT
ap-5556	102	45	4m2−m4	4m2−m4	ADV
ap-5556	102	46	r4	r4	PROPN
ap-5556	102	47	)	)	PUNCT
ap-5556	103	1	w	w	NOUN
ap-5556	103	2	(	(	PUNCT
ap-5556	103	3	r	r	NOUN
ap-5556	103	4	)	)	PUNCT
ap-5556	103	5	+	+	NOUN
ap-5556	103	6	(	(	PUNCT
ap-5556	103	7	3r2η3	3r2η3	NUM
ap-5556	103	8	+	+	CCONJ
ap-5556	103	9	6rη2	6rη2	NUM
ap-5556	103	10	+	+	CCONJ
ap-5556	103	11	3η	3η	NOUN
ap-5556	103	12	)	)	PUNCT
ap-5556	103	13	{	{	PUNCT
ap-5556	103	14	2d	2d	NUM
ap-5556	103	15	3w	3w	NOUN
ap-5556	103	16	(	(	PUNCT
ap-5556	103	17	r	r	NOUN
ap-5556	103	18	)	)	PUNCT
ap-5556	103	19	dr3	dr3	PROPN
ap-5556	104	1	+	+	CCONJ
ap-5556	104	2	2	2	NUM
ap-5556	104	3	+	+	CCONJ
ap-5556	104	4	ν	ν	X
ap-5556	104	5	r	r	PROPN
ap-5556	104	6	d2w	d2w	PROPN
ap-5556	104	7	(	(	PUNCT
ap-5556	104	8	r	r	NOUN
ap-5556	104	9	)	)	PUNCT
ap-5556	104	10	dr2	dr2	NOUN
ap-5556	104	11	−	−	NOUN
ap-5556	105	1	2m2	2m2	NUM
ap-5556	105	2	+	+	CCONJ
ap-5556	105	3	1	1	NUM
ap-5556	105	4	r2	r2	PROPN
ap-5556	105	5	dw	dw	NOUN
ap-5556	105	6	(	(	PUNCT
ap-5556	105	7	r	r	NOUN
ap-5556	105	8	)	)	PUNCT
ap-5556	105	9	dr	dr	PROPN
ap-5556	105	10	+	+	PROPN
ap-5556	105	11	3m2	3m2	NUM
ap-5556	105	12	r3	r3	PROPN
ap-5556	105	13	w	w	PROPN
ap-5556	105	14	(	(	PUNCT
ap-5556	105	15	r	r	NOUN
ap-5556	105	16	)	)	PUNCT
ap-5556	105	17	}	}	PUNCT
ap-5556	106	1	+	+	CCONJ
ap-5556	106	2	(	(	PUNCT
ap-5556	106	3	6rη3	6rη3	NUM
ap-5556	106	4	+	+	CCONJ
ap-5556	106	5	6η2){d2w	6η2){d2w	NUM
ap-5556	106	6	(	(	PUNCT
ap-5556	106	7	r	r	X
ap-5556	106	8	)	)	PUNCT
ap-5556	106	9	dr2	dr2	NOUN
ap-5556	106	10	+	+	CCONJ
ap-5556	106	11	ν	ν	X
ap-5556	106	12	(	(	PUNCT
ap-5556	106	13	1	1	NUM
ap-5556	106	14	r	r	NOUN
ap-5556	106	15	dw	dw	NOUN
ap-5556	106	16	(	(	PUNCT
ap-5556	106	17	r	r	NOUN
ap-5556	106	18	)	)	PUNCT
ap-5556	106	19	dr	dr	PROPN
ap-5556	106	20	−	−	PROPN
ap-5556	106	21	m2	m2	PROPN
ap-5556	106	22	r2	r2	PROPN
ap-5556	106	23	w	w	PROPN
ap-5556	106	24	(	(	PUNCT
ap-5556	106	25	r	r	NOUN
ap-5556	106	26	)	)	PUNCT
ap-5556	106	27	)	)	PUNCT
ap-5556	106	28	}	}	PUNCT
ap-5556	106	29	−ks	−ks	PROPN
ap-5556	106	30	d2w	d2w	PROPN
ap-5556	106	31	(	(	PUNCT
ap-5556	106	32	r	r	NOUN
ap-5556	106	33	)	)	PUNCT
ap-5556	106	34	dr2	dr2	PROPN
ap-5556	106	35	−	−	PROPN
ap-5556	107	1	ks	ks	NOUN
ap-5556	107	2	r	r	PROPN
ap-5556	107	3	dw	dw	PROPN
ap-5556	107	4	(	(	PUNCT
ap-5556	107	5	r	r	NOUN
ap-5556	107	6	)	)	PUNCT
ap-5556	107	7	dr	dr	PROPN
ap-5556	107	8	+	+	PROPN
ap-5556	107	9	ks	ks	PROPN
ap-5556	107	10	m2	m2	PROPN
ap-5556	107	11	r2	r2	PROPN
ap-5556	107	12	w	w	PROPN
ap-5556	107	13	(	(	PUNCT
ap-5556	107	14	r	r	NOUN
ap-5556	107	15	)	)	PUNCT
ap-5556	107	16	+	+	NOUN
ap-5556	107	17	kww	kww	NOUN
ap-5556	107	18	(	(	PUNCT
ap-5556	107	19	r	r	NOUN
ap-5556	107	20	)	)	PUNCT
ap-5556	107	21	+	+	CCONJ
ap-5556	107	22	(	(	PUNCT
ap-5556	107	23	ξr+	ξr+	NOUN
ap-5556	107	24	1	1	NUM
ap-5556	107	25	)	)	PUNCT
ap-5556	107	26	(	(	PUNCT
ap-5556	107	27	ηr+	ηr+	NOUN
ap-5556	107	28	1)ω2w	1)ω2w	NUM
ap-5556	107	29	(	(	PUNCT
ap-5556	107	30	r	r	NOUN
ap-5556	107	31	)	)	PUNCT
ap-5556	107	32	=	=	SYM
ap-5556	107	33	0	0	NUM
ap-5556	107	34	,	,	PUNCT
ap-5556	107	35	(	(	PUNCT
ap-5556	107	36	6	6	NUM
ap-5556	107	37	)	)	PUNCT
ap-5556	107	38	129	129	NUM
ap-5556	107	39	s.	s.	PROPN
ap-5556	107	40	salawu	salawu	PROPN
ap-5556	107	41	,	,	PUNCT
ap-5556	107	42	g.	g.	PROPN
ap-5556	107	43	sobamowo	sobamowo	PROPN
ap-5556	107	44	,	,	PUNCT
ap-5556	107	45	o.	o.	PROPN
ap-5556	107	46	sadiq	sadiq	PROPN
ap-5556	107	47	acta	acta	PROPN
ap-5556	107	48	polytechnica	polytechnica	PROPN
ap-5556	107	49	2.1	2.1	NUM
ap-5556	107	50	.	.	PUNCT
ap-5556	108	1	boundary	boundary	ADJ
ap-5556	108	2	conditions	condition	NOUN
ap-5556	108	3	the	the	DET
ap-5556	108	4	boundary	boundary	ADJ
ap-5556	108	5	conditions	condition	NOUN
ap-5556	108	6	considered	consider	VERB
ap-5556	108	7	as	as	SCONJ
ap-5556	108	8	earlier	early	ADV
ap-5556	108	9	stated	state	VERB
ap-5556	108	10	simply	simply	ADV
ap-5556	108	11	support	support	NOUN
ap-5556	108	12	,	,	PUNCT
ap-5556	108	13	clamped	clamp	VERB
ap-5556	108	14	and	and	CCONJ
ap-5556	108	15	free	free	ADJ
ap-5556	108	16	edge	edge	NOUN
ap-5556	108	17	conditions	condition	NOUN
ap-5556	108	18	.	.	PUNCT
ap-5556	109	1	the	the	DET
ap-5556	109	2	dimensionless	dimensionless	NOUN
ap-5556	109	3	form	form	NOUN
ap-5556	109	4	of	of	ADP
ap-5556	109	5	the	the	DET
ap-5556	109	6	boundary	boundary	ADJ
ap-5556	109	7	conditions	condition	NOUN
ap-5556	109	8	may	may	AUX
ap-5556	109	9	be	be	AUX
ap-5556	109	10	presented	present	VERB
ap-5556	109	11	in	in	ADP
ap-5556	109	12	terms	term	NOUN
ap-5556	109	13	of	of	ADP
ap-5556	109	14	the	the	DET
ap-5556	109	15	deflection	deflection	NOUN
ap-5556	109	16	w	w	NOUN
ap-5556	109	17	(	(	PUNCT
ap-5556	109	18	r	r	NOUN
ap-5556	109	19	)	)	PUNCT
ap-5556	109	20	as	as	SCONJ
ap-5556	109	21	follows	follow	VERB
ap-5556	109	22	[	[	X
ap-5556	109	23	8	8	NUM
ap-5556	109	24	]	]	SYM
ap-5556	109	25	•	•	NOUN
ap-5556	109	26	clamped	clamp	VERB
ap-5556	109	27	w	w	PROPN
ap-5556	109	28	(	(	PUNCT
ap-5556	109	29	r)|r=1	r)|r=1	PROPN
ap-5556	109	30	=	=	SYM
ap-5556	109	31	0	0	NUM
ap-5556	109	32	,	,	PUNCT
ap-5556	109	33	dw	dw	PROPN
ap-5556	109	34	dr	dr	PROPN
ap-5556	109	35	∣∣∣∣	∣∣∣∣	PROPN
ap-5556	109	36	r=1	r=1	PROPN
ap-5556	109	37	=	=	NOUN
ap-5556	109	38	0	0	NUM
ap-5556	109	39	,	,	PUNCT
ap-5556	109	40	(	(	PUNCT
ap-5556	109	41	7	7	X
ap-5556	109	42	)	)	PUNCT
ap-5556	109	43	•	•	NOUN
ap-5556	109	44	simply	simply	ADV
ap-5556	109	45	supported	support	VERB
ap-5556	109	46	w	w	PROPN
ap-5556	109	47	(	(	PUNCT
ap-5556	109	48	r)|r=1	r)|r=1	PROPN
ap-5556	109	49	=	=	SYM
ap-5556	109	50	0	0	NUM
ap-5556	109	51	,	,	PUNCT
ap-5556	109	52	mr|r=1	mr|r=1	NOUN
ap-5556	109	53	=	=	SYM
ap-5556	109	54	−d	−d	PROPN
ap-5556	109	55	[	[	PUNCT
ap-5556	109	56	d2w	d2w	PROPN
ap-5556	109	57	dr2	dr2	PROPN
ap-5556	110	1	+	+	CCONJ
ap-5556	110	2	ν	ν	X
ap-5556	110	3	(	(	PUNCT
ap-5556	110	4	1	1	NUM
ap-5556	110	5	r	r	NOUN
ap-5556	110	6	dw	dw	PROPN
ap-5556	110	7	dr	dr	PROPN
ap-5556	110	8	+	+	PROPN
ap-5556	110	9	m2	m2	PROPN
ap-5556	110	10	r2	r2	PROPN
ap-5556	110	11	w	w	PROPN
ap-5556	110	12	)	)	PUNCT
ap-5556	110	13	]	]	PUNCT
ap-5556	111	1	=	=	PUNCT
ap-5556	111	2	0	0	NUM
ap-5556	111	3	,	,	PUNCT
ap-5556	111	4	(	(	PUNCT
ap-5556	111	5	8)	8)	NUM
ap-5556	111	6	•	•	NUM
ap-5556	111	7	free	free	ADJ
ap-5556	111	8	edge	edge	NOUN
ap-5556	111	9	mr|r=1	mr|r=1	NOUN
ap-5556	111	10	=	=	SYM
ap-5556	111	11	−d	−d	PROPN
ap-5556	111	12	[	[	PUNCT
ap-5556	111	13	d2w	d2w	PROPN
ap-5556	111	14	dr2	dr2	PROPN
ap-5556	111	15	+	+	CCONJ
ap-5556	111	16	ν	ν	X
ap-5556	111	17	(	(	PUNCT
ap-5556	111	18	1	1	NUM
ap-5556	111	19	r	r	NOUN
ap-5556	111	20	dw	dw	PROPN
ap-5556	111	21	dr	dr	PROPN
ap-5556	111	22	+	+	PROPN
ap-5556	111	23	m2	m2	PROPN
ap-5556	111	24	r2	r2	PROPN
ap-5556	111	25	w	w	PROPN
ap-5556	111	26	)	)	PUNCT
ap-5556	111	27	]	]	PUNCT
ap-5556	112	1	=	=	PUNCT
ap-5556	112	2	0	0	NUM
ap-5556	112	3	,	,	PUNCT
ap-5556	112	4	vr|r=1	vr|r=1	NOUN
ap-5556	112	5	=	=	PUNCT
ap-5556	112	6	[	[	PUNCT
ap-5556	112	7	d3w	d3w	PROPN
ap-5556	112	8	dr3	dr3	PROPN
ap-5556	112	9	+	+	CCONJ
ap-5556	112	10	1	1	NUM
ap-5556	112	11	r	r	NOUN
ap-5556	112	12	d2w	d2w	PROPN
ap-5556	112	13	dr2	dr2	PROPN
ap-5556	113	1	+	+	CCONJ
ap-5556	113	2	(	(	PUNCT
ap-5556	113	3	m2ν	m2ν	NOUN
ap-5556	113	4	−	−	PROPN
ap-5556	113	5	2m2	2m2	NUM
ap-5556	113	6	−	−	SYM
ap-5556	113	7	1	1	NUM
ap-5556	113	8	r2	r2	PROPN
ap-5556	113	9	)	)	PUNCT
ap-5556	114	1	dw	dw	PROPN
ap-5556	114	2	dr	dr	PROPN
ap-5556	114	3	+	+	CCONJ
ap-5556	114	4	(	(	PUNCT
ap-5556	114	5	3m2	3m2	NUM
ap-5556	114	6	−m2ν	−m2ν	PRON
ap-5556	114	7	r3	r3	PROPN
ap-5556	114	8	)	)	PUNCT
ap-5556	114	9	w	w	ADP
ap-5556	114	10	]	]	PUNCT
ap-5556	115	1	=	=	PUNCT
ap-5556	115	2	0	0	X
ap-5556	115	3	.	.	PUNCT
ap-5556	116	1	(	(	PUNCT
ap-5556	116	2	9	9	X
ap-5556	116	3	)	)	PUNCT
ap-5556	116	4	the	the	DET
ap-5556	116	5	bending	bend	VERB
ap-5556	116	6	moment	moment	NOUN
ap-5556	116	7	is	be	AUX
ap-5556	116	8	represented	represent	VERB
ap-5556	116	9	as	as	SCONJ
ap-5556	116	10	the	the	DET
ap-5556	116	11	radial	radial	ADJ
ap-5556	116	12	shear	shear	NOUN
ap-5556	116	13	force	force	NOUN
ap-5556	116	14	per	per	ADP
ap-5556	116	15	unit	unit	NOUN
ap-5556	116	16	length	length	NOUN
ap-5556	116	17	is	be	AUX
ap-5556	116	18	represented	represent	VERB
ap-5556	116	19	as	as	ADP
ap-5556	116	20	vr	vr	PROPN
ap-5556	116	21	.	.	PROPN
ap-5556	117	1	an	an	DET
ap-5556	117	2	nth	nth	NOUN
ap-5556	117	3	-	-	PUNCT
ap-5556	117	4	order	order	NOUN
ap-5556	117	5	differential	differential	ADJ
ap-5556	117	6	equation	equation	NOUN
ap-5556	117	7	requires	require	VERB
ap-5556	117	8	n	n	CCONJ
ap-5556	117	9	-	-	PUNCT
ap-5556	117	10	number	number	NOUN
ap-5556	117	11	of	of	ADP
ap-5556	117	12	boundary	boundary	ADJ
ap-5556	117	13	condition	condition	NOUN
ap-5556	117	14	.	.	PUNCT
ap-5556	118	1	since	since	SCONJ
ap-5556	118	2	the	the	DET
ap-5556	118	3	dimensionless	dimensionless	NOUN
ap-5556	118	4	eq	eq	ADP
ap-5556	118	5	.	.	PUNCT
ap-5556	118	6	(	(	PUNCT
ap-5556	118	7	6	6	NUM
ap-5556	118	8	)	)	PUNCT
ap-5556	118	9	is	be	AUX
ap-5556	118	10	a	a	DET
ap-5556	118	11	fourth	fourth	ADJ
ap-5556	118	12	-	-	PUNCT
ap-5556	118	13	order	order	NOUN
ap-5556	118	14	governing	governing	NOUN
ap-5556	118	15	equation	equation	NOUN
ap-5556	118	16	then	then	ADV
ap-5556	118	17	,	,	PUNCT
ap-5556	118	18	four	four	NUM
ap-5556	118	19	boundary	boundary	ADJ
ap-5556	118	20	conditions	condition	NOUN
ap-5556	118	21	are	be	AUX
ap-5556	118	22	expected	expect	VERB
ap-5556	118	23	for	for	ADP
ap-5556	118	24	resolving	resolve	VERB
ap-5556	118	25	the	the	DET
ap-5556	118	26	equation	equation	NOUN
ap-5556	118	27	.	.	PUNCT
ap-5556	119	1	two	two	NUM
ap-5556	119	2	of	of	ADP
ap-5556	119	3	the	the	DET
ap-5556	119	4	conditions	condition	NOUN
ap-5556	119	5	may	may	AUX
ap-5556	119	6	be	be	AUX
ap-5556	119	7	obtained	obtain	VERB
ap-5556	119	8	from	from	ADP
ap-5556	119	9	the	the	DET
ap-5556	119	10	external	external	ADJ
ap-5556	119	11	condition	condition	NOUN
ap-5556	119	12	of	of	ADP
ap-5556	119	13	the	the	DET
ap-5556	119	14	plate	plate	NOUN
ap-5556	119	15	while	while	SCONJ
ap-5556	119	16	the	the	DET
ap-5556	119	17	rest	rest	NOUN
ap-5556	119	18	two	two	NUM
ap-5556	119	19	are	be	AUX
ap-5556	119	20	obtained	obtain	VERB
ap-5556	119	21	from	from	ADP
ap-5556	119	22	the	the	DET
ap-5556	119	23	condition	condition	NOUN
ap-5556	119	24	at	at	ADP
ap-5556	119	25	the	the	DET
ap-5556	119	26	center	center	NOUN
ap-5556	119	27	of	of	ADP
ap-5556	119	28	the	the	DET
ap-5556	119	29	plate	plate	NOUN
ap-5556	119	30	.	.	PUNCT
ap-5556	120	1	the	the	DET
ap-5556	120	2	regularity	regularity	NOUN
ap-5556	120	3	conditions	condition	NOUN
ap-5556	120	4	at	at	ADP
ap-5556	120	5	the	the	DET
ap-5556	120	6	center	center	NOUN
ap-5556	120	7	are	be	AUX
ap-5556	120	8	given	give	VERB
ap-5556	120	9	as	as	ADP
ap-5556	120	10	,	,	PUNCT
ap-5556	120	11	symmetric	symmetric	ADJ
ap-5556	120	12	case	case	NOUN
ap-5556	120	13	dw	dw	PROPN
ap-5556	120	14	dr	dr	PROPN
ap-5556	120	15	∣∣∣∣	∣∣∣∣	PROPN
ap-5556	120	16	r=0	r=0	PROPN
ap-5556	120	17	=	=	SYM
ap-5556	120	18	0	0	NUM
ap-5556	120	19	,	,	PUNCT
ap-5556	120	20	vr|r=0	vr|r=0	PROPN
ap-5556	120	21	=	=	SYM
ap-5556	120	22	d3w	d3w	PROPN
ap-5556	120	23	dr3	dr3	PROPN
ap-5556	120	24	=	=	PROPN
ap-5556	120	25	0	0	PROPN
ap-5556	120	26	,	,	PUNCT
ap-5556	120	27	for	for	ADP
ap-5556	120	28	(	(	PUNCT
ap-5556	120	29	m	m	PROPN
ap-5556	120	30	=	=	SYM
ap-5556	120	31	0	0	NUM
ap-5556	120	32	,	,	PUNCT
ap-5556	120	33	2	2	NUM
ap-5556	120	34	,	,	PUNCT
ap-5556	120	35	4	4	NUM
ap-5556	120	36	·	·	PUNCT
ap-5556	120	37	·	·	PUNCT
ap-5556	120	38	·	·	PUNCT
ap-5556	120	39	)	)	PUNCT
ap-5556	120	40	,	,	PUNCT
ap-5556	120	41	(	(	PUNCT
ap-5556	120	42	10	10	X
ap-5556	120	43	)	)	PUNCT
ap-5556	120	44	axisymmetric	axisymmetric	ADJ
ap-5556	120	45	case	case	NOUN
ap-5556	120	46	w	w	X
ap-5556	120	47	(	(	PUNCT
ap-5556	120	48	r)|r=0	r)|r=0	VERB
ap-5556	120	49	=	=	SYM
ap-5556	120	50	0	0	NUM
ap-5556	120	51	,	,	PUNCT
ap-5556	120	52	mr|r=0	mr|r=0	PROPN
ap-5556	120	53	=	=	PROPN
ap-5556	120	54	d2w	d2w	PROPN
ap-5556	120	55	dr2	dr2	PROPN
ap-5556	120	56	∣∣∣∣	∣∣∣∣	NOUN
ap-5556	121	1	r=0	r=0	PROPN
ap-5556	121	2	=	=	NOUN
ap-5556	121	3	0	0	NUM
ap-5556	121	4	for	for	ADP
ap-5556	121	5	(	(	PUNCT
ap-5556	121	6	m	m	PROPN
ap-5556	121	7	=	=	SYM
ap-5556	121	8	1	1	NUM
ap-5556	121	9	,	,	PUNCT
ap-5556	121	10	3	3	NUM
ap-5556	121	11	,	,	PUNCT
ap-5556	121	12	5	5	NUM
ap-5556	121	13	·	·	PUNCT
ap-5556	121	14	·	·	PUNCT
ap-5556	121	15	·	·	PUNCT
ap-5556	121	16	)	)	PUNCT
ap-5556	121	17	.	.	PUNCT
ap-5556	122	1	(	(	PUNCT
ap-5556	122	2	11	11	NUM
ap-5556	122	3	)	)	SYM
ap-5556	122	4	3	3	NUM
ap-5556	122	5	.	.	NOUN
ap-5556	122	6	method	method	NOUN
ap-5556	122	7	of	of	ADP
ap-5556	122	8	solution	solution	NOUN
ap-5556	122	9	:	:	PUNCT
ap-5556	122	10	principle	principle	NOUN
ap-5556	122	11	of	of	ADP
ap-5556	122	12	galerkin	galerkin	PROPN
ap-5556	122	13	weighted	weight	VERB
ap-5556	122	14	residual	residual	ADJ
ap-5556	122	15	galerkin	galerkin	ADJ
ap-5556	122	16	method	method	NOUN
ap-5556	122	17	was	be	AUX
ap-5556	122	18	first	first	ADV
ap-5556	122	19	proposed	propose	VERB
ap-5556	122	20	by	by	ADP
ap-5556	122	21	walther	walther	PROPN
ap-5556	122	22	ritz	ritz	PROPN
ap-5556	122	23	but	but	CCONJ
ap-5556	122	24	was	be	AUX
ap-5556	122	25	credited	credit	VERB
ap-5556	122	26	to	to	ADP
ap-5556	122	27	soviet	soviet	PROPN
ap-5556	122	28	engineer	engineer	NOUN
ap-5556	122	29	called	call	VERB
ap-5556	122	30	boris	boris	PROPN
ap-5556	122	31	galerkin	galerkin	PROPN
ap-5556	123	1	[	[	X
ap-5556	123	2	26	26	NUM
ap-5556	123	3	]	]	PUNCT
ap-5556	123	4	.	.	PUNCT
ap-5556	124	1	the	the	DET
ap-5556	124	2	method	method	NOUN
ap-5556	124	3	is	be	AUX
ap-5556	124	4	used	use	VERB
ap-5556	124	5	for	for	ADP
ap-5556	124	6	handling	handle	VERB
ap-5556	124	7	differential	differential	ADJ
ap-5556	124	8	equations	equation	NOUN
ap-5556	124	9	.	.	PUNCT
ap-5556	125	1	the	the	DET
ap-5556	125	2	approximate	approximate	ADJ
ap-5556	125	3	solutions	solution	NOUN
ap-5556	125	4	of	of	ADP
ap-5556	125	5	the	the	DET
ap-5556	125	6	differential	differential	ADJ
ap-5556	125	7	equations	equation	NOUN
ap-5556	125	8	are	be	AUX
ap-5556	125	9	presumed	presume	VERB
ap-5556	125	10	to	to	PART
ap-5556	125	11	be	be	AUX
ap-5556	125	12	thoroughly	thoroughly	ADV
ap-5556	125	13	approximated	approximate	VERB
ap-5556	125	14	by	by	ADP
ap-5556	125	15	a	a	DET
ap-5556	125	16	finite	finite	ADJ
ap-5556	125	17	sum	sum	NOUN
ap-5556	125	18	of	of	ADP
ap-5556	125	19	test	test	NOUN
ap-5556	125	20	functions	function	NOUN
ap-5556	125	21	.	.	PUNCT
ap-5556	126	1	however	however	ADV
ap-5556	126	2	,	,	PUNCT
ap-5556	126	3	the	the	DET
ap-5556	126	4	chosen	choose	VERB
ap-5556	126	5	method	method	NOUN
ap-5556	126	6	of	of	ADP
ap-5556	126	7	weighted	weight	VERB
ap-5556	126	8	residuals	residual	NOUN
ap-5556	126	9	are	be	AUX
ap-5556	126	10	used	use	VERB
ap-5556	126	11	to	to	PART
ap-5556	126	12	obtain	obtain	VERB
ap-5556	126	13	the	the	DET
ap-5556	126	14	value	value	NOUN
ap-5556	126	15	of	of	ADP
ap-5556	126	16	the	the	DET
ap-5556	126	17	coefficients	coefficient	NOUN
ap-5556	126	18	of	of	ADP
ap-5556	126	19	each	each	DET
ap-5556	126	20	resulting	result	VERB
ap-5556	126	21	test	test	NOUN
ap-5556	126	22	function	function	NOUN
ap-5556	126	23	ϕi	ϕi	ADP
ap-5556	126	24	.	.	PUNCT
ap-5556	127	1	the	the	DET
ap-5556	127	2	corresponding	corresponding	ADJ
ap-5556	127	3	coefficients	coefficient	NOUN
ap-5556	127	4	are	be	AUX
ap-5556	127	5	made	make	VERB
ap-5556	127	6	to	to	PART
ap-5556	127	7	reduce	reduce	VERB
ap-5556	127	8	the	the	DET
ap-5556	127	9	error	error	NOUN
ap-5556	127	10	between	between	ADP
ap-5556	127	11	the	the	DET
ap-5556	127	12	linear	linear	ADJ
ap-5556	127	13	combination	combination	NOUN
ap-5556	127	14	of	of	ADP
ap-5556	127	15	test	test	NOUN
ap-5556	127	16	functions	function	NOUN
ap-5556	127	17	,	,	PUNCT
ap-5556	127	18	and	and	CCONJ
ap-5556	127	19	actual	actual	ADJ
ap-5556	127	20	solution	solution	NOUN
ap-5556	127	21	,	,	PUNCT
ap-5556	127	22	in	in	ADP
ap-5556	127	23	a	a	DET
ap-5556	127	24	chosen	choose	VERB
ap-5556	127	25	standard	standard	NOUN
ap-5556	127	26	.	.	PUNCT
ap-5556	128	1	the	the	DET
ap-5556	128	2	technique	technique	NOUN
ap-5556	128	3	is	be	AUX
ap-5556	128	4	a	a	DET
ap-5556	128	5	reliable	reliable	ADJ
ap-5556	128	6	estimated	estimate	VERB
ap-5556	128	7	solution	solution	NOUN
ap-5556	128	8	capable	capable	ADJ
ap-5556	128	9	of	of	ADP
ap-5556	128	10	solving	solve	VERB
ap-5556	128	11	a	a	DET
ap-5556	128	12	series	series	NOUN
ap-5556	128	13	of	of	ADP
ap-5556	128	14	problems	problem	NOUN
ap-5556	128	15	that	that	PRON
ap-5556	128	16	eliminate	eliminate	VERB
ap-5556	128	17	the	the	DET
ap-5556	128	18	search	search	NOUN
ap-5556	128	19	for	for	ADP
ap-5556	128	20	vibrational	vibrational	ADJ
ap-5556	128	21	formulation	formulation	NOUN
ap-5556	128	22	.	.	PUNCT
ap-5556	129	1	assuming	assume	VERB
ap-5556	129	2	the	the	DET
ap-5556	129	3	governing	govern	VERB
ap-5556	129	4	equation	equation	NOUN
ap-5556	129	5	to	to	PART
ap-5556	129	6	be	be	AUX
ap-5556	129	7	l(ϕs(r	l(ϕs(r	ADJ
ap-5556	129	8	)	)	PUNCT
ap-5556	129	9	+	+	SYM
ap-5556	129	10	g(r	g(r	NOUN
ap-5556	129	11	)	)	PUNCT
ap-5556	129	12	)	)	PUNCT
ap-5556	130	1	=	=	PUNCT
ap-5556	130	2	0	0	NUM
ap-5556	130	3	,	,	PUNCT
ap-5556	130	4	r	r	NOUN
ap-5556	130	5	∈	∈	PROPN
ap-5556	130	6	φ	φ	NOUN
ap-5556	130	7	.	.	PUNCT
ap-5556	131	1	(	(	PUNCT
ap-5556	131	2	12	12	NUM
ap-5556	131	3	)	)	PUNCT
ap-5556	131	4	with	with	ADP
ap-5556	131	5	the	the	DET
ap-5556	131	6	following	follow	VERB
ap-5556	131	7	boundary	boundary	ADJ
ap-5556	131	8	conditions	condition	NOUN
ap-5556	131	9	b	b	PROPN
ap-5556	131	10	(	(	PUNCT
ap-5556	131	11	ϕs(r	ϕs(r	NUM
ap-5556	131	12	)	)	PUNCT
ap-5556	131	13	,	,	PUNCT
ap-5556	131	14	dϕs(r	dϕs(r	ADJ
ap-5556	131	15	)	)	PUNCT
ap-5556	131	16	dr	dr	NOUN
ap-5556	131	17	)	)	PUNCT
ap-5556	132	1	=	=	PUNCT
ap-5556	132	2	0	0	NUM
ap-5556	132	3	,	,	PUNCT
ap-5556	132	4	r	r	NOUN
ap-5556	132	5	∈	∈	PROPN
ap-5556	132	6	∂φ	∂φ	PROPN
ap-5556	132	7	,	,	PUNCT
ap-5556	132	8	(	(	PUNCT
ap-5556	132	9	13	13	NUM
ap-5556	132	10	)	)	PUNCT
ap-5556	132	11	where	where	SCONJ
ap-5556	132	12	l	l	NOUN
ap-5556	132	13	is	be	AUX
ap-5556	132	14	the	the	DET
ap-5556	132	15	linear	linear	ADJ
ap-5556	132	16	operator	operator	NOUN
ap-5556	132	17	,	,	PUNCT
ap-5556	132	18	r	r	NOUN
ap-5556	132	19	is	be	AUX
ap-5556	132	20	the	the	DET
ap-5556	132	21	independent	independent	ADJ
ap-5556	132	22	variable	variable	NOUN
ap-5556	132	23	,	,	PUNCT
ap-5556	132	24	ϕs(r	ϕs(r	NUM
ap-5556	132	25	)	)	PUNCT
ap-5556	133	1	is	be	AUX
ap-5556	133	2	the	the	DET
ap-5556	133	3	unknown	unknown	ADJ
ap-5556	133	4	function	function	NOUN
ap-5556	133	5	,	,	PUNCT
ap-5556	133	6	φ	φ	PROPN
ap-5556	133	7	is	be	AUX
ap-5556	133	8	the	the	DET
ap-5556	133	9	domain	domain	NOUN
ap-5556	133	10	,	,	PUNCT
ap-5556	133	11	b	b	PROPN
ap-5556	133	12	is	be	AUX
ap-5556	133	13	the	the	DET
ap-5556	133	14	boundary	boundary	ADJ
ap-5556	133	15	operator	operator	NOUN
ap-5556	133	16	and	and	CCONJ
ap-5556	133	17	∂φ	∂φ	PROPN
ap-5556	133	18	represents	represent	VERB
ap-5556	133	19	the	the	DET
ap-5556	133	20	boundary	boundary	NOUN
ap-5556	133	21	of	of	ADP
ap-5556	133	22	the	the	DET
ap-5556	133	23	domain	domain	NOUN
ap-5556	133	24	.	.	PUNCT
ap-5556	134	1	residual	residual	ADJ
ap-5556	134	2	l(ϕs(r	l(ϕs(r	NOUN
ap-5556	134	3	)	)	PUNCT
ap-5556	134	4	+	+	SYM
ap-5556	134	5	g(r	g(r	NOUN
ap-5556	134	6	)	)	PUNCT
ap-5556	134	7	)	)	PUNCT
ap-5556	135	1	=	=	SYM
ap-5556	135	2	r̃(r	r̃(r	PROPN
ap-5556	135	3	)	)	PUNCT
ap-5556	135	4	(	(	PUNCT
ap-5556	135	5	residual	residual	ADJ
ap-5556	135	6	)	)	PUNCT
ap-5556	135	7	.	.	PUNCT
ap-5556	136	1	(	(	PUNCT
ap-5556	136	2	14	14	X
ap-5556	136	3	)	)	PUNCT
ap-5556	136	4	minimize	minimize	VERB
ap-5556	136	5	the	the	DET
ap-5556	136	6	residual	residual	ADJ
ap-5556	136	7	by	by	ADP
ap-5556	136	8	multiplying	multiply	VERB
ap-5556	136	9	with	with	ADP
ap-5556	136	10	a	a	DET
ap-5556	136	11	weight	weight	NOUN
ap-5556	136	12	w	w	NOUN
ap-5556	136	13	and	and	CCONJ
ap-5556	136	14	integrate	integrate	VERB
ap-5556	136	15	over	over	ADP
ap-5556	136	16	the	the	DET
ap-5556	136	17	domain	domain	NOUN
ap-5556	136	18	.	.	PUNCT
ap-5556	137	1	1∫	1∫	NUM
ap-5556	137	2	0	0	NUM
ap-5556	137	3	r̃(r)w	r̃(r)w	NOUN
ap-5556	137	4	(	(	PUNCT
ap-5556	137	5	r)dr	r)dr	NOUN
ap-5556	137	6	=	=	SYM
ap-5556	137	7	0	0	NUM
ap-5556	137	8	(	(	PUNCT
ap-5556	137	9	15	15	NUM
ap-5556	137	10	)	)	PUNCT
ap-5556	137	11	wr	wr	NOUN
ap-5556	137	12	is	be	AUX
ap-5556	137	13	the	the	DET
ap-5556	137	14	weight	weight	NOUN
ap-5556	137	15	function	function	NOUN
ap-5556	137	16	,	,	PUNCT
ap-5556	137	17	which	which	PRON
ap-5556	137	18	is	be	AUX
ap-5556	137	19	found	find	VERB
ap-5556	137	20	through	through	ADP
ap-5556	137	21	either	either	ADV
ap-5556	137	22	,	,	PUNCT
ap-5556	137	23	galerkin	galerkin	ADJ
ap-5556	137	24	of	of	ADP
ap-5556	137	25	weighted	weight	VERB
ap-5556	137	26	residual	residual	ADJ
ap-5556	137	27	,	,	PUNCT
ap-5556	137	28	collocation	collocation	NOUN
ap-5556	137	29	,	,	PUNCT
ap-5556	137	30	sub	sub	NOUN
ap-5556	137	31	-	-	NOUN
ap-5556	137	32	domain	domain	ADJ
ap-5556	137	33	,	,	PUNCT
ap-5556	137	34	or	or	CCONJ
ap-5556	137	35	least	least	ADJ
ap-5556	137	36	square	square	ADJ
ap-5556	137	37	method	method	NOUN
ap-5556	137	38	.	.	PUNCT
ap-5556	138	1	for	for	ADP
ap-5556	138	2	this	this	DET
ap-5556	138	3	study	study	NOUN
ap-5556	138	4	galerkin	galerkin	ADJ
ap-5556	138	5	approach	approach	NOUN
ap-5556	138	6	is	be	AUX
ap-5556	138	7	adopted	adopt	VERB
ap-5556	138	8	.	.	PUNCT
ap-5556	139	1	130	130	NUM
ap-5556	139	2	vol	vol	NOUN
ap-5556	139	3	.	.	PUNCT
ap-5556	140	1	60	60	NUM
ap-5556	140	2	no	no	NOUN
ap-5556	140	3	.	.	PUNCT
ap-5556	141	1	2/2020	2/2020	NUM
ap-5556	141	2	investigation	investigation	NOUN
ap-5556	141	3	of	of	ADP
ap-5556	141	4	the	the	DET
ap-5556	141	5	dynamic	dynamic	ADJ
ap-5556	141	6	behaviour	behaviour	NOUN
ap-5556	141	7	of	of	ADP
ap-5556	141	8	non	non	ADJ
ap-5556	141	9	-	-	ADJ
ap-5556	141	10	uniform	uniform	ADJ
ap-5556	141	11	thickness	thickness	NOUN
ap-5556	141	12	.	.	PUNCT
ap-5556	141	13	.	.	PUNCT
ap-5556	141	14	.	.	PUNCT
ap-5556	142	1	the	the	DET
ap-5556	142	2	approximate	approximate	ADJ
ap-5556	142	3	solution	solution	NOUN
ap-5556	142	4	u(r	u(r	PROPN
ap-5556	142	5	)	)	PUNCT
ap-5556	142	6	is	be	AUX
ap-5556	142	7	a	a	DET
ap-5556	142	8	linear	linear	ADJ
ap-5556	142	9	combination	combination	NOUN
ap-5556	142	10	of	of	ADP
ap-5556	142	11	trial	trial	NOUN
ap-5556	142	12	functions	function	NOUN
ap-5556	142	13	which	which	PRON
ap-5556	142	14	must	must	AUX
ap-5556	142	15	satisfy	satisfy	VERB
ap-5556	142	16	the	the	DET
ap-5556	142	17	essential	essential	ADJ
ap-5556	142	18	boundary	boundary	ADJ
ap-5556	142	19	condition	condition	NOUN
ap-5556	142	20	ū(r	ū(r	NOUN
ap-5556	142	21	)	)	PUNCT
ap-5556	143	1	≈	≈	PROPN
ap-5556	143	2	n∑	n∑	PROPN
ap-5556	143	3	i=1	i=1	PROPN
ap-5556	144	1	ciφi	ciφi	PROPN
ap-5556	144	2	(	(	PUNCT
ap-5556	144	3	r	r	NOUN
ap-5556	144	4	)	)	PUNCT
ap-5556	144	5	,	,	PUNCT
ap-5556	144	6	(	(	PUNCT
ap-5556	144	7	16	16	NUM
ap-5556	144	8	)	)	PUNCT
ap-5556	144	9	φi(r	φi(r	NOUN
ap-5556	144	10	)	)	PUNCT
ap-5556	144	11	is	be	AUX
ap-5556	144	12	the	the	DET
ap-5556	144	13	trial	trial	NOUN
ap-5556	144	14	function	function	NOUN
ap-5556	144	15	,	,	PUNCT
ap-5556	144	16	while	while	SCONJ
ap-5556	144	17	the	the	DET
ap-5556	144	18	weight	weight	NOUN
ap-5556	144	19	function	function	NOUN
ap-5556	144	20	trial	trial	NOUN
ap-5556	144	21	function	function	NOUN
ap-5556	144	22	is	be	AUX
ap-5556	144	23	n	n	ADJ
ap-5556	144	24	and	and	CCONJ
ap-5556	144	25	i	i	PRON
ap-5556	144	26	is	be	AUX
ap-5556	144	27	the	the	DET
ap-5556	144	28	node	node	NOUN
ap-5556	144	29	in	in	ADP
ap-5556	144	30	the	the	DET
ap-5556	144	31	domain	domain	NOUN
ap-5556	144	32	1∫	1∫	NUM
ap-5556	144	33	0	0	NUM
ap-5556	144	34	r̃(r)φi(r)dr	r̃(r)φi(r)dr	NOUN
ap-5556	144	35	=	=	SYM
ap-5556	144	36	0	0	NUM
ap-5556	144	37	where	where	SCONJ
ap-5556	144	38	i	i	PRON
ap-5556	144	39	=	=	NOUN
ap-5556	144	40	1	1	NUM
ap-5556	144	41	,	,	PUNCT
ap-5556	144	42	2	2	NUM
ap-5556	144	43	,	,	PUNCT
ap-5556	144	44	.	.	PUNCT
ap-5556	144	45	.	.	PUNCT
ap-5556	144	46	.	.	PUNCT
ap-5556	144	47	.	.	PUNCT
ap-5556	144	48	.	.	PUNCT
ap-5556	145	1	.	.	PUNCT
ap-5556	146	1	,	,	PUNCT
ap-5556	146	2	n	n	CCONJ
ap-5556	146	3	,	,	PUNCT
ap-5556	146	4	3.1	3.1	NUM
ap-5556	146	5	.	.	PUNCT
ap-5556	146	6	application	application	NOUN
ap-5556	146	7	of	of	ADP
ap-5556	146	8	galerkin	galerkin	ADJ
ap-5556	146	9	method	method	NOUN
ap-5556	146	10	of	of	ADP
ap-5556	146	11	weighted	weight	VERB
ap-5556	146	12	residual	residual	ADJ
ap-5556	146	13	to	to	ADP
ap-5556	146	14	the	the	DET
ap-5556	146	15	governing	govern	VERB
ap-5556	146	16	equation	equation	NOUN
ap-5556	146	17	for	for	ADP
ap-5556	146	18	the	the	DET
ap-5556	146	19	sake	sake	NOUN
ap-5556	146	20	of	of	ADP
ap-5556	146	21	brevity	brevity	NOUN
ap-5556	146	22	,	,	PUNCT
ap-5556	146	23	symmetric	symmetric	ADJ
ap-5556	146	24	case	case	NOUN
ap-5556	146	25	regularity	regularity	NOUN
ap-5556	146	26	condition	condition	NOUN
ap-5556	146	27	and	and	CCONJ
ap-5556	146	28	simply	simply	ADV
ap-5556	146	29	supported	support	VERB
ap-5556	146	30	edge	edge	NOUN
ap-5556	146	31	condition	condition	NOUN
ap-5556	146	32	is	be	AUX
ap-5556	146	33	presented	present	VERB
ap-5556	146	34	here	here	ADV
ap-5556	146	35	while	while	SCONJ
ap-5556	146	36	the	the	DET
ap-5556	146	37	same	same	ADJ
ap-5556	146	38	approach	approach	NOUN
ap-5556	146	39	is	be	AUX
ap-5556	146	40	used	use	VERB
ap-5556	146	41	to	to	PART
ap-5556	146	42	determine	determine	VERB
ap-5556	146	43	the	the	DET
ap-5556	146	44	other	other	ADJ
ap-5556	146	45	conditions	condition	NOUN
ap-5556	146	46	treated	treat	VERB
ap-5556	146	47	in	in	ADP
ap-5556	146	48	this	this	DET
ap-5556	146	49	study	study	NOUN
ap-5556	146	50	.	.	PUNCT
ap-5556	147	1	the	the	DET
ap-5556	147	2	choice	choice	NOUN
ap-5556	147	3	of	of	ADP
ap-5556	147	4	the	the	DET
ap-5556	147	5	polynomial	polynomial	ADJ
ap-5556	147	6	solution	solution	NOUN
ap-5556	147	7	is	be	AUX
ap-5556	147	8	based	base	VERB
ap-5556	147	9	on	on	ADP
ap-5556	147	10	the	the	DET
ap-5556	147	11	highest	high	ADJ
ap-5556	147	12	order	order	NOUN
ap-5556	147	13	of	of	ADP
ap-5556	147	14	the	the	DET
ap-5556	147	15	derivative	derivative	NOUN
ap-5556	147	16	of	of	ADP
ap-5556	147	17	the	the	DET
ap-5556	147	18	governing	govern	VERB
ap-5556	147	19	equation	equation	NOUN
ap-5556	147	20	.	.	PUNCT
ap-5556	148	1	this	this	PRON
ap-5556	148	2	is	be	AUX
ap-5556	148	3	a	a	DET
ap-5556	148	4	fourth	fourth	ADJ
ap-5556	148	5	-	-	PUNCT
ap-5556	148	6	order	order	NOUN
ap-5556	148	7	derivative	derivative	ADJ
ap-5556	148	8	equation	equation	NOUN
ap-5556	148	9	so	so	ADV
ap-5556	148	10	;	;	PUNCT
ap-5556	148	11	the	the	DET
ap-5556	148	12	chosen	choose	VERB
ap-5556	148	13	polynomial	polynomial	NOUN
ap-5556	148	14	is	be	AUX
ap-5556	148	15	of	of	ADP
ap-5556	148	16	the	the	DET
ap-5556	148	17	order	order	NOUN
ap-5556	148	18	five	five	NUM
ap-5556	148	19	.	.	PUNCT
ap-5556	149	1	assume	assume	VERB
ap-5556	149	2	a	a	DET
ap-5556	149	3	polynomial	polynomial	ADJ
ap-5556	149	4	solution	solution	NOUN
ap-5556	149	5	for	for	ADP
ap-5556	149	6	order	order	NOUN
ap-5556	149	7	four	four	NUM
ap-5556	149	8	differential	differential	ADJ
ap-5556	149	9	equation	equation	NOUN
ap-5556	149	10	w	w	NOUN
ap-5556	149	11	(	(	PUNCT
ap-5556	149	12	r	r	NOUN
ap-5556	149	13	)	)	PUNCT
ap-5556	149	14	=	=	SYM
ap-5556	149	15	a+	a+	PUNCT
ap-5556	149	16	br+	br+	NOUN
ap-5556	149	17	cr2	cr2	NOUN
ap-5556	149	18	2	2	NUM
ap-5556	149	19	!	!	PUNCT
ap-5556	150	1	+	+	CCONJ
ap-5556	150	2	dr3	dr3	PROPN
ap-5556	150	3	3	3	NUM
ap-5556	150	4	!	!	PUNCT
ap-5556	151	1	+	+	CCONJ
ap-5556	151	2	er4	er4	PROPN
ap-5556	151	3	4	4	NUM
ap-5556	151	4	!	!	PUNCT
ap-5556	152	1	+	+	CCONJ
ap-5556	152	2	gr5	gr5	AUX
ap-5556	152	3	5	5	NUM
ap-5556	152	4	!	!	NUM
ap-5556	152	5	,	,	PUNCT
ap-5556	152	6	(	(	PUNCT
ap-5556	152	7	17	17	X
ap-5556	152	8	)	)	PUNCT
ap-5556	152	9	applying	apply	VERB
ap-5556	152	10	the	the	DET
ap-5556	152	11	boundary	boundary	ADJ
ap-5556	152	12	conditions	condition	NOUN
ap-5556	152	13	at	at	ADP
ap-5556	152	14	r	r	NOUN
ap-5556	152	15	=	=	SYM
ap-5556	152	16	0	0	NUM
ap-5556	152	17	,	,	PUNCT
ap-5556	152	18	symmetric	symmetric	ADJ
ap-5556	152	19	case	case	NOUN
ap-5556	152	20	in	in	ADP
ap-5556	152	21	eq	eq	NOUN
ap-5556	152	22	.	.	PUNCT
ap-5556	153	1	(	(	PUNCT
ap-5556	153	2	10	10	NUM
ap-5556	153	3	)	)	PUNCT
ap-5556	153	4	•	•	NOUN
ap-5556	153	5	simply	simply	ADV
ap-5556	153	6	supported	support	VERB
ap-5556	153	7	edge	edge	NOUN
ap-5556	153	8	w	w	NOUN
ap-5556	153	9	′	′	NUM
ap-5556	153	10	(	(	PUNCT
ap-5556	153	11	0	0	NUM
ap-5556	153	12	)	)	PUNCT
ap-5556	154	1	=	=	SYM
ap-5556	154	2	b	b	X
ap-5556	154	3	=	=	SYM
ap-5556	154	4	0	0	PROPN
ap-5556	154	5	,	,	PUNCT
ap-5556	154	6	(	(	PUNCT
ap-5556	154	7	18	18	NUM
ap-5556	154	8	)	)	PUNCT
ap-5556	154	9	w	w	PROPN
ap-5556	154	10	′′′	′′′	PROPN
ap-5556	154	11	(	(	PUNCT
ap-5556	154	12	0	0	NUM
ap-5556	154	13	)	)	PUNCT
ap-5556	154	14	=	=	SYM
ap-5556	155	1	d	d	NOUN
ap-5556	155	2	=	=	SYM
ap-5556	155	3	0	0	NUM
ap-5556	155	4	,	,	PUNCT
ap-5556	155	5	(	(	PUNCT
ap-5556	155	6	19	19	NUM
ap-5556	155	7	)	)	PUNCT
ap-5556	155	8	w	w	NOUN
ap-5556	155	9	(	(	PUNCT
ap-5556	155	10	1	1	NUM
ap-5556	155	11	)	)	PUNCT
ap-5556	155	12	=	=	PRON
ap-5556	155	13	a+	a+	PUNCT
ap-5556	155	14	c	c	NOUN
ap-5556	155	15	2	2	NUM
ap-5556	155	16	+	+	CCONJ
ap-5556	155	17	e	e	X
ap-5556	155	18	24	24	NUM
ap-5556	155	19	+	+	CCONJ
ap-5556	155	20	g	g	PROPN
ap-5556	155	21	120	120	NUM
ap-5556	155	22	=	=	SYM
ap-5556	155	23	0	0	NUM
ap-5556	155	24	,	,	PUNCT
ap-5556	155	25	(	(	PUNCT
ap-5556	155	26	20	20	X
ap-5556	155	27	)	)	PUNCT
ap-5556	155	28	−d	−d	PROPN
ap-5556	155	29	[	[	PUNCT
ap-5556	155	30	w	w	PROPN
ap-5556	155	31	′′	′′	PROPN
ap-5556	155	32	(	(	PUNCT
ap-5556	155	33	1	1	NUM
ap-5556	155	34	)	)	PUNCT
ap-5556	156	1	+	+	NUM
ap-5556	156	2	ν	ν	X
ap-5556	156	3	(	(	PUNCT
ap-5556	156	4	1	1	NUM
ap-5556	156	5	r	r	NOUN
ap-5556	156	6	w	w	NOUN
ap-5556	156	7	′	′	NUM
ap-5556	156	8	(	(	PUNCT
ap-5556	156	9	1	1	NUM
ap-5556	156	10	)	)	PUNCT
ap-5556	156	11	+	+	CCONJ
ap-5556	156	12	m2	m2	PROPN
ap-5556	156	13	r2	r2	PROPN
ap-5556	156	14	w	w	PROPN
ap-5556	156	15	(	(	PUNCT
ap-5556	156	16	1	1	NUM
ap-5556	156	17	)	)	PUNCT
ap-5556	156	18	)	)	PUNCT
ap-5556	156	19	]	]	PUNCT
ap-5556	156	20	⇒	⇒	NOUN
ap-5556	156	21	−221793c	−221793c	NUM
ap-5556	156	22	1000	1000	NUM
ap-5556	156	23	−	−	NOUN
ap-5556	156	24	187671e	187671e	NOUN
ap-5556	156	25	2000	2000	NUM
ap-5556	156	26	−	−	NOUN
ap-5556	156	27	244541f	244541f	NUM
ap-5556	156	28	8000	8000	NUM
ap-5556	156	29	=	=	SYM
ap-5556	156	30	0	0	NUM
ap-5556	156	31	,	,	PUNCT
ap-5556	156	32	(	(	PUNCT
ap-5556	156	33	21	21	NUM
ap-5556	156	34	)	)	PUNCT
ap-5556	156	35	for	for	ADP
ap-5556	156	36	the	the	DET
ap-5556	156	37	symmetric	symmetric	ADJ
ap-5556	156	38	case	case	NOUN
ap-5556	156	39	m	m	NOUN
ap-5556	156	40	=	=	SYM
ap-5556	156	41	0	0	NUM
ap-5556	156	42	and	and	CCONJ
ap-5556	156	43	asymmetric	asymmetric	ADJ
ap-5556	156	44	case	case	NOUN
ap-5556	156	45	m	m	NOUN
ap-5556	156	46	=	=	NOUN
ap-5556	156	47	1	1	X
ap-5556	156	48	.	.	X
ap-5556	156	49	solving	solve	VERB
ap-5556	156	50	the	the	DET
ap-5556	156	51	simultaneous	simultaneous	ADJ
ap-5556	156	52	equation	equation	NOUN
ap-5556	156	53	[	[	X
ap-5556	156	54	eqs	eqs	X
ap-5556	156	55	.	.	PUNCT
ap-5556	157	1	(	(	PUNCT
ap-5556	157	2	20	20	NUM
ap-5556	157	3	)	)	PUNCT
ap-5556	157	4	and	and	CCONJ
ap-5556	157	5	(	(	PUNCT
ap-5556	157	6	21	21	NUM
ap-5556	157	7	)	)	PUNCT
ap-5556	157	8	]	]	PUNCT
ap-5556	157	9	to	to	PART
ap-5556	157	10	find	find	VERB
ap-5556	157	11	the	the	DET
ap-5556	157	12	unknowns	unknown	NOUN
ap-5556	157	13	and	and	CCONJ
ap-5556	157	14	substitute	substitute	NOUN
ap-5556	157	15	back	back	ADV
ap-5556	157	16	to	to	ADP
ap-5556	157	17	eq	eq	PROPN
ap-5556	157	18	.	.	PUNCT
ap-5556	158	1	(	(	PUNCT
ap-5556	158	2	17	17	NUM
ap-5556	158	3	)	)	PUNCT
ap-5556	158	4	.	.	PUNCT
ap-5556	159	1	w	w	NOUN
ap-5556	159	2	⇒	⇒	NOUN
ap-5556	159	3	a+	a+	PUNCT
ap-5556	159	4	1	1	NUM
ap-5556	159	5	2	2	NUM
ap-5556	159	6	cr	cr	ADP
ap-5556	159	7	2	2	NUM
ap-5556	159	8	+	+	CCONJ
ap-5556	159	9	1	1	NUM
ap-5556	159	10	24	24	NUM
ap-5556	159	11	(	(	PUNCT
ap-5556	159	12	−5160a	−5160a	PROPN
ap-5556	159	13	83	83	NUM
ap-5556	159	14	−	−	PROPN
ap-5556	159	15	2268c	2268c	NUM
ap-5556	159	16	83	83	NUM
ap-5556	159	17	)	)	PUNCT
ap-5556	159	18	r4	r4	NOUN
ap-5556	159	19	+	+	CCONJ
ap-5556	159	20	(	(	PUNCT
ap-5556	159	21	6360c	6360c	NUM
ap-5556	159	22	83	83	NUM
ap-5556	159	23	+	+	NUM
ap-5556	159	24	15840a	15840a	NUM
ap-5556	159	25	83	83	NUM
ap-5556	159	26	)	)	PUNCT
ap-5556	159	27	r5	r5	PROPN
ap-5556	159	28	120	120	NUM
ap-5556	159	29	,	,	PUNCT
ap-5556	159	30	(	(	PUNCT
ap-5556	159	31	22	22	NUM
ap-5556	159	32	)	)	PUNCT
ap-5556	159	33	chain	chain	NOUN
ap-5556	159	34	function	function	NOUN
ap-5556	159	35	ni(r	ni(r	PRON
ap-5556	159	36	)	)	PUNCT
ap-5556	159	37	in	in	ADP
ap-5556	159	38	eq	eq	ADP
ap-5556	159	39	.	.	PUNCT
ap-5556	160	1	(	(	PUNCT
ap-5556	160	2	22	22	NUM
ap-5556	160	3	)	)	PUNCT
ap-5556	160	4	are	be	AUX
ap-5556	160	5	a	a	PRON
ap-5556	160	6	and	and	CCONJ
ap-5556	160	7	c	c	NOUN
ap-5556	160	8	,	,	PUNCT
ap-5556	160	9	as	as	SCONJ
ap-5556	160	10	reported	report	VERB
ap-5556	160	11	in	in	ADP
ap-5556	160	12	eqs	eqs	PROPN
ap-5556	160	13	.	.	PUNCT
ap-5556	161	1	(	(	PUNCT
ap-5556	161	2	7	7	NUM
ap-5556	161	3	-	-	SYM
ap-5556	161	4	9	9	NUM
ap-5556	161	5	)	)	PUNCT
ap-5556	161	6	)	)	PUNCT
ap-5556	162	1	the	the	DET
ap-5556	162	2	boundary	boundary	ADJ
ap-5556	162	3	condition	condition	NOUN
ap-5556	162	4	range	range	NOUN
ap-5556	162	5	is	be	AUX
ap-5556	162	6	0	0	NUM
ap-5556	162	7	=	=	NOUN
ap-5556	162	8	⇒	⇒	NOUN
ap-5556	162	9	1	1	NUM
ap-5556	162	10	,	,	PUNCT
ap-5556	162	11	invariably	invariably	ADV
ap-5556	162	12	the	the	DET
ap-5556	162	13	integral	integral	ADJ
ap-5556	162	14	limit	limit	NOUN
ap-5556	162	15	for	for	ADP
ap-5556	162	16	this	this	DET
ap-5556	162	17	galerkin	galerkin	ADJ
ap-5556	162	18	method	method	NOUN
ap-5556	162	19	is	be	AUX
ap-5556	162	20	0	0	NUM
ap-5556	162	21	to	to	PART
ap-5556	162	22	1	1	NUM
ap-5556	162	23	.	.	PUNCT
ap-5556	163	1	galerkin	galerkin	ADJ
ap-5556	163	2	equation	equation	NOUN
ap-5556	163	3	1∫	1∫	NUM
ap-5556	163	4	0	0	NUM
ap-5556	163	5	ni	ni	PROPN
ap-5556	163	6	(	(	PUNCT
ap-5556	163	7	r)r̃dr	r)r̃dr	NOUN
ap-5556	163	8	=	=	SYM
ap-5556	163	9	0	0	PROPN
ap-5556	163	10	,	,	PUNCT
ap-5556	163	11	(	(	PUNCT
ap-5556	163	12	23	23	NUM
ap-5556	163	13	)	)	PUNCT
ap-5556	163	14	•	•	NOUN
ap-5556	163	15	chain	chain	NOUN
ap-5556	163	16	function	function	NOUN
ap-5556	163	17	n1	n1	PROPN
ap-5556	163	18	=	=	SYM
ap-5556	163	19	dw	dw	PROPN
ap-5556	163	20	da	da	PROPN
ap-5556	163	21	⇒	⇒	PROPN
ap-5556	163	22	1−	1−	NUM
ap-5556	163	23	215r4	215r4	NUM
ap-5556	163	24	83	83	NUM
ap-5556	163	25	+	+	CCONJ
ap-5556	163	26	132r5	132r5	NUM
ap-5556	163	27	83	83	NUM
ap-5556	163	28	,	,	PUNCT
ap-5556	163	29	(	(	PUNCT
ap-5556	163	30	24	24	NUM
ap-5556	163	31	)	)	PUNCT
ap-5556	163	32	n2	n2	NOUN
ap-5556	163	33	=	=	SYM
ap-5556	163	34	dw	dw	PROPN
ap-5556	163	35	dc	dc	PROPN
ap-5556	163	36	⇒	⇒	VERB
ap-5556	163	37	1	1	NUM
ap-5556	163	38	2r	2r	NUM
ap-5556	163	39	2	2	NUM
ap-5556	163	40	−	−	PROPN
ap-5556	163	41	189r4	189r4	NUM
ap-5556	163	42	166	166	NUM
ap-5556	163	43	+	+	CCONJ
ap-5556	163	44	53r5	53r5	NUM
ap-5556	163	45	83	83	NUM
ap-5556	163	46	,	,	PUNCT
ap-5556	163	47	(	(	PUNCT
ap-5556	163	48	25	25	NUM
ap-5556	163	49	)	)	PUNCT
ap-5556	163	50	applying	apply	VERB
ap-5556	163	51	eq	eq	ADP
ap-5556	163	52	.	.	PUNCT
ap-5556	164	1	(	(	PUNCT
ap-5556	164	2	23	23	NUM
ap-5556	164	3	)	)	PUNCT
ap-5556	164	4	and	and	CCONJ
ap-5556	164	5	obtain	obtain	VERB
ap-5556	164	6	simultaneous	simultaneous	ADJ
ap-5556	164	7	equations	equation	NOUN
ap-5556	164	8	based	base	VERB
ap-5556	164	9	on	on	ADP
ap-5556	164	10	the	the	DET
ap-5556	164	11	chain	chain	NOUN
ap-5556	164	12	function	function	NOUN
ap-5556	164	13	.	.	PUNCT
ap-5556	165	1	1∫	1∫	NUM
ap-5556	165	2	0	0	NUM
ap-5556	165	3	(	(	PUNCT
ap-5556	165	4	1−	1−	NUM
ap-5556	165	5	215r4	215r4	NUM
ap-5556	165	6	83	83	NUM
ap-5556	165	7	+	+	CCONJ
ap-5556	165	8	132r5	132r5	NUM
ap-5556	165	9	83	83	NUM
ap-5556	165	10	)	)	PUNCT
ap-5556	165	11			NOUN
ap-5556	165	12	(	(	PUNCT
ap-5556	165	13	r3η3	r3η3	X
ap-5556	165	14	+	+	NOUN
ap-5556	165	15	3r2η2	3r2η2	NUM
ap-5556	165	16	+	+	CCONJ
ap-5556	165	17	3ηr+	3ηr+	NUM
ap-5556	165	18	1	1	NUM
ap-5556	165	19	)	)	PUNCT
ap-5556	165	20			PUNCT
ap-5556	165	21	d4w	d4w	PROPN
ap-5556	165	22	dr4	dr4	NOUN
ap-5556	165	23	+	+	CCONJ
ap-5556	165	24	2	2	NUM
ap-5556	165	25	r	r	NOUN
ap-5556	165	26	d3w	d3w	PROPN
ap-5556	165	27	dr3	dr3	PROPN
ap-5556	165	28	−	−	PROPN
ap-5556	165	29	(	(	PUNCT
ap-5556	165	30	2m2	2m2	NUM
ap-5556	165	31	+	+	SYM
ap-5556	165	32	1	1	NUM
ap-5556	165	33	r2	r2	NOUN
ap-5556	165	34	)	)	PUNCT
ap-5556	166	1	d2w	d2w	PROPN
ap-5556	166	2	dr2	dr2	PROPN
ap-5556	166	3	+	+	X
ap-5556	166	4	(	(	PUNCT
ap-5556	166	5	2m2	2m2	NUM
ap-5556	166	6	+	+	SYM
ap-5556	166	7	1	1	NUM
ap-5556	166	8	r3	r3	PROPN
ap-5556	166	9	)	)	PUNCT
ap-5556	166	10	dw	dw	PROPN
ap-5556	166	11	dr	dr	PROPN
ap-5556	166	12	−	−	PROPN
ap-5556	167	1	(	(	PUNCT
ap-5556	167	2	4m2−m4	4m2−m4	ADV
ap-5556	167	3	r4	r4	PROPN
ap-5556	167	4	)	)	PUNCT
ap-5556	168	1	w	w	ADP
ap-5556	168	2			NOUN
ap-5556	168	3	+	+	CCONJ
ap-5556	168	4	(	(	PUNCT
ap-5556	168	5	3r2η3	3r2η3	NUM
ap-5556	168	6	+	+	CCONJ
ap-5556	168	7	6rη2	6rη2	NUM
ap-5556	168	8	+	+	CCONJ
ap-5556	168	9	3η	3η	NOUN
ap-5556	168	10	)	)	PUNCT
ap-5556	168	11	{	{	PUNCT
ap-5556	168	12	2d	2d	NUM
ap-5556	168	13	3w	3w	NUM
ap-5556	168	14	dr3	dr3	PROPN
ap-5556	168	15	+	+	CCONJ
ap-5556	168	16	2+ν	2+ν	NUM
ap-5556	168	17	r	r	NOUN
ap-5556	168	18	d2w	d2w	PROPN
ap-5556	168	19	dr2	dr2	PROPN
ap-5556	168	20	−	−	ADP
ap-5556	168	21	2m2	2m2	NUM
ap-5556	168	22	+	+	SYM
ap-5556	168	23	1	1	NUM
ap-5556	168	24	r2	r2	PROPN
ap-5556	168	25	dw	dw	PROPN
ap-5556	168	26	dr	dr	PROPN
ap-5556	168	27	+	+	PROPN
ap-5556	168	28	3m2	3m2	NUM
ap-5556	168	29	r3	r3	PROPN
ap-5556	168	30	w	w	PROPN
ap-5556	168	31	}	}	PUNCT
ap-5556	168	32	+	+	PROPN
ap-5556	168	33	(	(	PUNCT
ap-5556	168	34	6rη3	6rη3	NUM
ap-5556	168	35	+	+	CCONJ
ap-5556	168	36	6η2){d2w	6η2){d2w	NUM
ap-5556	168	37	dr2	dr2	NOUN
ap-5556	168	38	+	+	CCONJ
ap-5556	168	39	ν	ν	X
ap-5556	168	40	(	(	PUNCT
ap-5556	168	41	1	1	NUM
ap-5556	168	42	r	r	NOUN
ap-5556	168	43	dw	dw	PROPN
ap-5556	168	44	dr	dr	PROPN
ap-5556	168	45	−	−	PROPN
ap-5556	168	46	m2	m2	PROPN
ap-5556	168	47	r2	r2	PROPN
ap-5556	168	48	w	w	PROPN
ap-5556	168	49	)	)	PUNCT
ap-5556	168	50	}	}	PUNCT
ap-5556	168	51	−ks	−ks	PROPN
ap-5556	169	1	d2w	d2w	PROPN
ap-5556	169	2	dr2	dr2	PROPN
ap-5556	169	3	−	−	PROPN
ap-5556	170	1	ks	ks	NOUN
ap-5556	170	2	r	r	PROPN
ap-5556	170	3	dw	dw	PROPN
ap-5556	170	4	dr	dr	PROPN
ap-5556	170	5	+	+	PROPN
ap-5556	170	6	ks	ks	PROPN
ap-5556	170	7	m2	m2	PROPN
ap-5556	170	8	r2	r2	PROPN
ap-5556	170	9	w	w	PROPN
ap-5556	171	1	+	+	PROPN
ap-5556	171	2	kww	kww	PROPN
ap-5556	171	3	+	+	CCONJ
ap-5556	171	4	(	(	PUNCT
ap-5556	171	5	ξr+	ξr+	NOUN
ap-5556	171	6	1	1	NUM
ap-5556	171	7	)	)	PUNCT
ap-5556	171	8	(	(	PUNCT
ap-5556	171	9	ηr+	ηr+	NOUN
ap-5556	171	10	1)ω2w	1)ω2w	NUM
ap-5556	172	1			PROPN
ap-5556	172	2	dr	dr	PROPN
ap-5556	172	3	=	=	PROPN
ap-5556	172	4	0	0	PROPN
ap-5556	172	5	,	,	PUNCT
ap-5556	172	6	(	(	PUNCT
ap-5556	172	7	26	26	NUM
ap-5556	172	8	)	)	PUNCT
ap-5556	172	9	131	131	NUM
ap-5556	172	10	s.	s.	PROPN
ap-5556	172	11	salawu	salawu	PROPN
ap-5556	172	12	,	,	PUNCT
ap-5556	172	13	g.	g.	PROPN
ap-5556	172	14	sobamowo	sobamowo	PROPN
ap-5556	172	15	,	,	PUNCT
ap-5556	172	16	o.	o.	PROPN
ap-5556	172	17	sadiq	sadiq	PROPN
ap-5556	172	18	acta	acta	PROPN
ap-5556	172	19	polytechnica	polytechnica	PROPN
ap-5556	172	20	validating	validate	VERB
ap-5556	172	21	the	the	DET
ap-5556	172	22	analytical	analytical	ADJ
ap-5556	172	23	solutions	solution	NOUN
ap-5556	172	24	requires	require	VERB
ap-5556	172	25	assign	assign	VERB
ap-5556	172	26	values	value	NOUN
ap-5556	172	27	for	for	ADP
ap-5556	172	28	the	the	DET
ap-5556	172	29	thickness	thickness	NOUN
ap-5556	172	30	parameter	parameter	NOUN
ap-5556	172	31	.	.	PUNCT
ap-5556	173	1	solution	solution	NOUN
ap-5556	173	2	of	of	ADP
ap-5556	173	3	eq	eq	PROPN
ap-5556	173	4	.	.	PUNCT
ap-5556	174	1	(	(	PUNCT
ap-5556	174	2	26	26	NUM
ap-5556	174	3	)	)	PUNCT
ap-5556	174	4	becomes	become	VERB
ap-5556	174	5	:	:	PUNCT
ap-5556	174	6	−	−	PROPN
ap-5556	174	7	104333c	104333c	NUM
ap-5556	174	8	8709	8709	NUM
ap-5556	174	9	−	−	NOUN
ap-5556	175	1	−21153a	−21153a	NOUN
ap-5556	175	2	1168	1168	NUM
ap-5556	175	3	+	+	CCONJ
ap-5556	175	4	2114ω2cξ	2114ω2cξ	NUM
ap-5556	175	5	33391	33391	NUM
ap-5556	175	6	+	+	CCONJ
ap-5556	175	7	30621aks	30621aks	NUM
ap-5556	175	8	33884	33884	NUM
ap-5556	175	9	+	+	CCONJ
ap-5556	175	10	7544ckw	7544ckw	NUM
ap-5556	175	11	226609	226609	NUM
ap-5556	175	12	+	+	CCONJ
ap-5556	175	13	7544ω2c	7544ω2c	NUM
ap-5556	175	14	226609	226609	NUM
ap-5556	175	15	+	+	CCONJ
ap-5556	175	16	38892cks	38892cks	NUM
ap-5556	175	17	79283	79283	NUM
ap-5556	175	18	+	+	CCONJ
ap-5556	175	19	+	+	CCONJ
ap-5556	175	20	19625akw	19625akw	NUM
ap-5556	175	21	30401	30401	NUM
ap-5556	175	22	+	+	CCONJ
ap-5556	175	23	19625ω2a	19625ω2a	NUM
ap-5556	175	24	30401	30401	NUM
ap-5556	175	25	=	=	SYM
ap-5556	175	26	0	0	NUM
ap-5556	175	27	(	(	PUNCT
ap-5556	175	28	27	27	NUM
ap-5556	175	29	)	)	PUNCT
ap-5556	175	30	1∫	1∫	NUM
ap-5556	175	31	0	0	NUM
ap-5556	175	32	(	(	PUNCT
ap-5556	175	33	1	1	NUM
ap-5556	175	34	2r	2r	NUM
ap-5556	175	35	2	2	NUM
ap-5556	175	36	−	−	PROPN
ap-5556	175	37	189r4	189r4	NUM
ap-5556	175	38	166	166	NUM
ap-5556	175	39	+	+	CCONJ
ap-5556	175	40	53r5	53r5	NUM
ap-5556	175	41	83	83	NUM
ap-5556	175	42	)	)	PUNCT
ap-5556	175	43			NOUN
ap-5556	175	44	(	(	PUNCT
ap-5556	175	45	r3η3	r3η3	X
ap-5556	175	46	+	+	NOUN
ap-5556	175	47	3r2η2	3r2η2	NUM
ap-5556	176	1	+	+	CCONJ
ap-5556	176	2	3ηr+	3ηr+	NUM
ap-5556	176	3	1	1	NUM
ap-5556	176	4	)	)	PUNCT
ap-5556	176	5			PUNCT
ap-5556	176	6	d4w	d4w	PROPN
ap-5556	176	7	dr4	dr4	NOUN
ap-5556	176	8	+	+	CCONJ
ap-5556	176	9	2	2	NUM
ap-5556	176	10	r	r	NOUN
ap-5556	176	11	d3w	d3w	PROPN
ap-5556	176	12	dr3	dr3	PROPN
ap-5556	176	13	−	−	PROPN
ap-5556	176	14	(	(	PUNCT
ap-5556	176	15	2m2	2m2	NUM
ap-5556	176	16	+	+	SYM
ap-5556	176	17	1	1	NUM
ap-5556	176	18	r2	r2	NOUN
ap-5556	176	19	)	)	PUNCT
ap-5556	177	1	d2w	d2w	PROPN
ap-5556	177	2	dr2	dr2	PROPN
ap-5556	177	3	+	+	X
ap-5556	177	4	(	(	PUNCT
ap-5556	177	5	2m2	2m2	NUM
ap-5556	177	6	+	+	SYM
ap-5556	177	7	1	1	NUM
ap-5556	177	8	r3	r3	PROPN
ap-5556	177	9	)	)	PUNCT
ap-5556	177	10	dw	dw	PROPN
ap-5556	177	11	dr	dr	PROPN
ap-5556	177	12	−	−	PROPN
ap-5556	178	1	(	(	PUNCT
ap-5556	178	2	4m2−m4	4m2−m4	ADV
ap-5556	178	3	r4	r4	PROPN
ap-5556	178	4	)	)	PUNCT
ap-5556	179	1	w	w	ADP
ap-5556	179	2			NOUN
ap-5556	179	3	+	+	CCONJ
ap-5556	179	4	(	(	PUNCT
ap-5556	179	5	3r2η3	3r2η3	NUM
ap-5556	179	6	+	+	CCONJ
ap-5556	179	7	6rη2	6rη2	NUM
ap-5556	179	8	+	+	CCONJ
ap-5556	179	9	3η	3η	NOUN
ap-5556	179	10	)	)	PUNCT
ap-5556	179	11	{	{	PUNCT
ap-5556	179	12	2d	2d	NUM
ap-5556	179	13	3w	3w	NUM
ap-5556	179	14	dr3	dr3	PROPN
ap-5556	179	15	+	+	CCONJ
ap-5556	179	16	2+ν	2+ν	NUM
ap-5556	179	17	r	r	NOUN
ap-5556	179	18	d2w	d2w	PROPN
ap-5556	179	19	dr2	dr2	PROPN
ap-5556	179	20	−	−	ADP
ap-5556	179	21	2m2	2m2	NUM
ap-5556	179	22	+	+	SYM
ap-5556	179	23	1	1	NUM
ap-5556	179	24	r2	r2	PROPN
ap-5556	179	25	dw	dw	PROPN
ap-5556	179	26	dr	dr	PROPN
ap-5556	179	27	+	+	PROPN
ap-5556	179	28	3m2	3m2	NUM
ap-5556	179	29	r3	r3	PROPN
ap-5556	179	30	w	w	PROPN
ap-5556	179	31	}	}	PUNCT
ap-5556	179	32	+	+	PROPN
ap-5556	179	33	(	(	PUNCT
ap-5556	179	34	6rη3	6rη3	NUM
ap-5556	179	35	+	+	CCONJ
ap-5556	179	36	6η2){d2w	6η2){d2w	NUM
ap-5556	179	37	dr2	dr2	NOUN
ap-5556	179	38	+	+	CCONJ
ap-5556	179	39	ν	ν	X
ap-5556	179	40	(	(	PUNCT
ap-5556	179	41	1	1	NUM
ap-5556	179	42	r	r	NOUN
ap-5556	179	43	dw	dw	PROPN
ap-5556	179	44	dr	dr	PROPN
ap-5556	179	45	−	−	PROPN
ap-5556	179	46	m2	m2	PROPN
ap-5556	179	47	r2	r2	PROPN
ap-5556	179	48	w	w	PROPN
ap-5556	179	49	)	)	PUNCT
ap-5556	179	50	}	}	PUNCT
ap-5556	179	51	−ks	−ks	PROPN
ap-5556	180	1	d2w	d2w	PROPN
ap-5556	180	2	dr2	dr2	PROPN
ap-5556	180	3	−	−	PROPN
ap-5556	181	1	ks	ks	NOUN
ap-5556	181	2	r	r	PROPN
ap-5556	181	3	dw	dw	PROPN
ap-5556	181	4	dr	dr	PROPN
ap-5556	181	5	+	+	PROPN
ap-5556	181	6	ks	ks	PROPN
ap-5556	181	7	m2	m2	PROPN
ap-5556	181	8	r2	r2	PROPN
ap-5556	181	9	w	w	PROPN
ap-5556	182	1	+	+	PROPN
ap-5556	182	2	kww	kww	PROPN
ap-5556	182	3	+	+	CCONJ
ap-5556	182	4	(	(	PUNCT
ap-5556	182	5	ξr+	ξr+	NOUN
ap-5556	182	6	1	1	NUM
ap-5556	182	7	)	)	PUNCT
ap-5556	182	8	(	(	PUNCT
ap-5556	182	9	ηr+	ηr+	NOUN
ap-5556	182	10	1)ω2w	1)ω2w	NUM
ap-5556	183	1			PROPN
ap-5556	183	2	dr	dr	PROPN
ap-5556	183	3	=	=	PROPN
ap-5556	183	4	0	0	PROPN
ap-5556	183	5	,	,	PUNCT
ap-5556	183	6	(	(	PUNCT
ap-5556	183	7	28	28	NUM
ap-5556	183	8	)	)	PUNCT
ap-5556	183	9	solution	solution	NOUN
ap-5556	183	10	of	of	ADP
ap-5556	183	11	eq	eq	PROPN
ap-5556	183	12	.	.	PUNCT
ap-5556	184	1	(	(	PUNCT
ap-5556	184	2	28	28	NUM
ap-5556	184	3	)	)	PUNCT
ap-5556	184	4	becomes	become	VERB
ap-5556	184	5	:	:	PUNCT
ap-5556	184	6	21524c	21524c	NUM
ap-5556	184	7	43463	43463	NUM
ap-5556	184	8	+	+	NUM
ap-5556	184	9	52591a	52591a	NUM
ap-5556	184	10	27028	27028	NUM
ap-5556	184	11	+	+	CCONJ
ap-5556	184	12	3406ω2cξ	3406ω2cξ	NUM
ap-5556	184	13	1979425	1979425	NUM
ap-5556	184	14	+	+	CCONJ
ap-5556	184	15	2114ω2aξ	2114ω2aξ	NUM
ap-5556	184	16	120859	120859	NUM
ap-5556	184	17	+	+	CCONJ
ap-5556	184	18	1939aks	1939aks	NUM
ap-5556	184	19	27556	27556	NUM
ap-5556	184	20	+	+	CCONJ
ap-5556	184	21	1737ckw	1737ckw	NUM
ap-5556	184	22	606232	606232	NUM
ap-5556	184	23	+	+	CCONJ
ap-5556	184	24	1737ω2c	1737ω2c	NUM
ap-5556	184	25	606232	606232	NUM
ap-5556	185	1	+	+	NUM
ap-5556	185	2	3617cks	3617ck	NOUN
ap-5556	185	3	86573	86573	NUM
ap-5556	185	4	+	+	CCONJ
ap-5556	185	5	2767akw	2767akw	NUM
ap-5556	185	6	83116	83116	NUM
ap-5556	185	7	+	+	CCONJ
ap-5556	185	8	2767ω2a	2767ω2a	NUM
ap-5556	185	9	83116	83116	NUM
ap-5556	185	10	=	=	SYM
ap-5556	185	11	0	0	PUNCT
ap-5556	185	12	(	(	PUNCT
ap-5556	185	13	29	29	NUM
ap-5556	185	14	)	)	PUNCT
ap-5556	185	15	eq	eq	NOUN
ap-5556	185	16	.	.	PUNCT
ap-5556	186	1	(	(	PUNCT
ap-5556	186	2	27	27	NUM
ap-5556	186	3	)	)	PUNCT
ap-5556	186	4	and	and	CCONJ
ap-5556	186	5	eq	eq	NOUN
ap-5556	186	6	.	.	PUNCT
ap-5556	187	1	(	(	PUNCT
ap-5556	187	2	29	29	NUM
ap-5556	187	3	)	)	PUNCT
ap-5556	187	4	represent	represent	VERB
ap-5556	187	5	series	series	NOUN
ap-5556	187	6	expression	expression	NOUN
ap-5556	187	7	obtained	obtain	VERB
ap-5556	187	8	after	after	ADP
ap-5556	187	9	resolving	resolve	VERB
ap-5556	187	10	eq	eq	ADP
ap-5556	187	11	.	.	PUNCT
ap-5556	188	1	(	(	PUNCT
ap-5556	188	2	26	26	NUM
ap-5556	188	3	)	)	PUNCT
ap-5556	188	4	and	and	CCONJ
ap-5556	188	5	eq	eq	NOUN
ap-5556	188	6	.	.	PUNCT
ap-5556	189	1	(	(	PUNCT
ap-5556	189	2	28	28	NUM
ap-5556	189	3	)	)	PUNCT
ap-5556	189	4	.	.	PUNCT
ap-5556	190	1	the	the	DET
ap-5556	190	2	resulting	result	VERB
ap-5556	190	3	simultaneous	simultaneous	ADJ
ap-5556	190	4	equation	equation	NOUN
ap-5556	190	5	obtained	obtain	VERB
ap-5556	190	6	may	may	AUX
ap-5556	190	7	be	be	AUX
ap-5556	190	8	written	write	VERB
ap-5556	190	9	in	in	ADP
ap-5556	190	10	this	this	DET
ap-5556	190	11	form	form	NOUN
ap-5556	190	12	(	(	PUNCT
ap-5556	190	13	−	−	PROPN
ap-5556	190	14	104333	104333	NUM
ap-5556	190	15	8709	8709	NUM
ap-5556	191	1	+	+	CCONJ
ap-5556	191	2	2114ω2ξ	2114ω2ξ	NUM
ap-5556	191	3	120859	120859	NUM
ap-5556	191	4	+	+	CCONJ
ap-5556	192	1	7544kw	7544kw	PROPN
ap-5556	192	2	226609	226609	NUM
ap-5556	192	3	+	+	CCONJ
ap-5556	192	4	7544ω2	7544ω2	NUM
ap-5556	192	5	226609	226609	NUM
ap-5556	192	6	+	+	NUM
ap-5556	192	7	38892ks	38892k	NOUN
ap-5556	192	8	79283	79283	NUM
ap-5556	192	9	)	)	PUNCT
ap-5556	192	10	c+	c+	VERB
ap-5556	192	11	(	(	PUNCT
ap-5556	192	12	−	−	PROPN
ap-5556	192	13	21153	21153	NUM
ap-5556	192	14	1168	1168	NUM
ap-5556	192	15	+	+	CCONJ
ap-5556	192	16	7469ω2ξ	7469ω2ξ	NUM
ap-5556	192	17	33391	33391	NUM
ap-5556	192	18	+	+	CCONJ
ap-5556	192	19	30621ks	30621ks	ADJ
ap-5556	192	20	33884	33884	NUM
ap-5556	192	21	+	+	SYM
ap-5556	192	22	19625kw	19625kw	NOUN
ap-5556	192	23	30401	30401	NUM
ap-5556	192	24	+	+	CCONJ
ap-5556	192	25	19625ω2	19625ω2	NUM
ap-5556	192	26	30401	30401	NUM
ap-5556	192	27	)	)	PUNCT
ap-5556	193	1	a	a	DET
ap-5556	193	2	=	=	SYM
ap-5556	193	3	0	0	NUM
ap-5556	193	4	(	(	PUNCT
ap-5556	193	5	21524	21524	NUM
ap-5556	193	6	43463	43463	NUM
ap-5556	193	7	+	+	CCONJ
ap-5556	193	8	3406ω2ξ	3406ω2ξ	NUM
ap-5556	193	9	1979425	1979425	NUM
ap-5556	193	10	+	+	SYM
ap-5556	193	11	1737kw	1737kw	PROPN
ap-5556	193	12	606232	606232	NUM
ap-5556	194	1	+	+	CCONJ
ap-5556	194	2	1737ω2	1737ω2	NOUN
ap-5556	194	3	606232	606232	NUM
ap-5556	195	1	+	+	CCONJ
ap-5556	195	2	3617ks	3617ks	PROPN
ap-5556	195	3	86573	86573	NUM
ap-5556	195	4	)	)	PUNCT
ap-5556	195	5	c+	c+	VERB
ap-5556	195	6	(	(	PUNCT
ap-5556	195	7	52591	52591	NUM
ap-5556	195	8	27028	27028	NUM
ap-5556	195	9	+	+	CCONJ
ap-5556	195	10	2114ω2ξ	2114ω2ξ	NUM
ap-5556	195	11	120859	120859	NUM
ap-5556	195	12	+	+	CCONJ
ap-5556	195	13	1939ks	1939ks	ADJ
ap-5556	195	14	27556	27556	NUM
ap-5556	195	15	+	+	CCONJ
ap-5556	195	16	2767kw	2767kw	NOUN
ap-5556	195	17	83116	83116	NUM
ap-5556	195	18	+	+	CCONJ
ap-5556	195	19	2767ω2	2767ω2	NOUN
ap-5556	195	20	83116	83116	NUM
ap-5556	195	21	)	)	PUNCT
ap-5556	195	22	a	a	DET
ap-5556	195	23	=	=	SYM
ap-5556	195	24	0	0	NUM
ap-5556	195	25	(	(	PUNCT
ap-5556	195	26	30	30	NUM
ap-5556	195	27	)	)	PUNCT
ap-5556	195	28	the	the	DET
ap-5556	195	29	solutions	solution	NOUN
ap-5556	195	30	are	be	AUX
ap-5556	195	31	represented	represent	VERB
ap-5556	195	32	in	in	ADP
ap-5556	195	33	terms	term	NOUN
ap-5556	195	34	of	of	ADP
ap-5556	195	35	the	the	DET
ap-5556	195	36	natural	natural	ADJ
ap-5556	195	37	frequency	frequency	NOUN
ap-5556	195	38	ω	ω	NOUN
ap-5556	195	39	and	and	CCONJ
ap-5556	195	40	the	the	DET
ap-5556	195	41	controlling	control	VERB
ap-5556	195	42	parameters	parameter	NOUN
ap-5556	195	43	.	.	PUNCT
ap-5556	196	1	therefore	therefore	ADV
ap-5556	196	2	,	,	PUNCT
ap-5556	196	3	eq	eq	ADJ
ap-5556	196	4	.	.	PUNCT
ap-5556	197	1	(	(	PUNCT
ap-5556	197	2	30	30	NUM
ap-5556	197	3	)	)	PUNCT
ap-5556	197	4	maybe	maybe	ADV
ap-5556	197	5	written	write	VERB
ap-5556	197	6	in	in	ADP
ap-5556	197	7	matrix	matrix	NOUN
ap-5556	197	8	form	form	NOUN
ap-5556	197	9	as	as	PROPN
ap-5556	197	10	(	(	PUNCT
ap-5556	197	11	−	−	PROPN
ap-5556	197	12	104333	104333	NUM
ap-5556	197	13	8709	8709	NUM
ap-5556	198	1	+	+	CCONJ
ap-5556	198	2	2114ω2ξ	2114ω2ξ	NUM
ap-5556	198	3	120859	120859	NUM
ap-5556	198	4	+	+	CCONJ
ap-5556	199	1	7544kw	7544kw	PROPN
ap-5556	199	2	226609	226609	NUM
ap-5556	199	3	+	+	CCONJ
ap-5556	199	4	7544ω2	7544ω2	NUM
ap-5556	199	5	226609	226609	NUM
ap-5556	199	6	+	+	NUM
ap-5556	199	7	38892ks	38892k	NOUN
ap-5556	199	8	79283	79283	NUM
ap-5556	199	9	)	)	PUNCT
ap-5556	199	10	(	(	PUNCT
ap-5556	199	11	−	−	PROPN
ap-5556	199	12	21153	21153	NUM
ap-5556	199	13	1168	1168	NUM
ap-5556	199	14	+	+	CCONJ
ap-5556	199	15	7469ω2ξ	7469ω2ξ	NUM
ap-5556	199	16	33391	33391	NUM
ap-5556	199	17	+	+	CCONJ
ap-5556	199	18	30621ks	30621ks	ADJ
ap-5556	199	19	33884	33884	NUM
ap-5556	199	20	+	+	SYM
ap-5556	199	21	19625kw	19625kw	NOUN
ap-5556	199	22	30401	30401	NUM
ap-5556	199	23	+	+	CCONJ
ap-5556	199	24	19625ω2	19625ω2	NOUN
ap-5556	199	25	30401	30401	NUM
ap-5556	199	26	)	)	PUNCT
ap-5556	199	27	(	(	PUNCT
ap-5556	199	28	21524	21524	NUM
ap-5556	199	29	43463	43463	NUM
ap-5556	200	1	+	+	CCONJ
ap-5556	200	2	3406ω2ξ	3406ω2ξ	NUM
ap-5556	200	3	1979425	1979425	NUM
ap-5556	200	4	+	+	SYM
ap-5556	200	5	1737kw	1737kw	PROPN
ap-5556	200	6	606232	606232	NUM
ap-5556	201	1	+	+	CCONJ
ap-5556	201	2	1737ω2	1737ω2	NOUN
ap-5556	201	3	606232	606232	NUM
ap-5556	202	1	+	+	CCONJ
ap-5556	202	2	3617ks	3617ks	PROPN
ap-5556	202	3	86573	86573	NUM
ap-5556	202	4	)	)	PUNCT
ap-5556	202	5	(	(	PUNCT
ap-5556	202	6	52591	52591	NUM
ap-5556	202	7	27028	27028	NUM
ap-5556	202	8	+	+	CCONJ
ap-5556	202	9	2114ω2ξ	2114ω2ξ	NUM
ap-5556	202	10	120859	120859	NUM
ap-5556	202	11	+	+	CCONJ
ap-5556	202	12	1939ks	1939ks	ADJ
ap-5556	202	13	27556	27556	NUM
ap-5556	203	1	+	+	CCONJ
ap-5556	203	2	2767kw	2767kw	NOUN
ap-5556	203	3	83116	83116	NUM
ap-5556	203	4	+	+	CCONJ
ap-5556	203	5	2767ω2	2767ω2	NOUN
ap-5556	203	6	83116	83116	NUM
ap-5556	203	7	)	)	PUNCT
ap-5556	203	8			NOUN
ap-5556	203	9	{	{	PUNCT
ap-5556	204	1	c	c	NOUN
ap-5556	204	2	a	a	PRON
ap-5556	204	3	}	}	PUNCT
ap-5556	204	4	=	=	SYM
ap-5556	204	5	{	{	PUNCT
ap-5556	204	6	0	0	NUM
ap-5556	204	7	0	0	NUM
ap-5556	204	8	}	}	PUNCT
ap-5556	204	9	,	,	PUNCT
ap-5556	204	10	(	(	PUNCT
ap-5556	204	11	31	31	NUM
ap-5556	204	12	)	)	PUNCT
ap-5556	204	13	the	the	DET
ap-5556	204	14	following	follow	VERB
ap-5556	204	15	characteristic	characteristic	ADJ
ap-5556	204	16	determinant	determinant	ADJ
ap-5556	204	17	is	be	AUX
ap-5556	204	18	obtained	obtain	VERB
ap-5556	204	19	applying	apply	VERB
ap-5556	204	20	the	the	DET
ap-5556	204	21	non	non	ADJ
ap-5556	204	22	-	-	ADJ
ap-5556	204	23	trivial	trivial	ADJ
ap-5556	204	24	condition	condition	NOUN
ap-5556	204	25	(	(	PUNCT
ap-5556	204	26	−	−	PROPN
ap-5556	204	27	104333	104333	NUM
ap-5556	204	28	8709	8709	NUM
ap-5556	205	1	+	+	CCONJ
ap-5556	205	2	2114ω2ξ	2114ω2ξ	NUM
ap-5556	205	3	120859	120859	NUM
ap-5556	205	4	+	+	CCONJ
ap-5556	206	1	7544kw	7544kw	PROPN
ap-5556	206	2	226609	226609	NUM
ap-5556	206	3	+	+	CCONJ
ap-5556	206	4	7544ω2	7544ω2	NUM
ap-5556	206	5	226609	226609	NUM
ap-5556	206	6	+	+	NUM
ap-5556	206	7	38892ks	38892k	NOUN
ap-5556	206	8	79283	79283	NUM
ap-5556	206	9	)	)	PUNCT
ap-5556	206	10	(	(	PUNCT
ap-5556	206	11	−	−	PROPN
ap-5556	206	12	21153	21153	NUM
ap-5556	206	13	1168	1168	NUM
ap-5556	206	14	+	+	CCONJ
ap-5556	206	15	7469ω2ξ	7469ω2ξ	NUM
ap-5556	206	16	33391	33391	NUM
ap-5556	206	17	+	+	CCONJ
ap-5556	206	18	30621ks	30621ks	ADJ
ap-5556	206	19	33884	33884	NUM
ap-5556	206	20	+	+	SYM
ap-5556	206	21	19625kw	19625kw	NOUN
ap-5556	206	22	30401	30401	NUM
ap-5556	206	23	+	+	CCONJ
ap-5556	206	24	19625ω2	19625ω2	NOUN
ap-5556	206	25	30401	30401	NUM
ap-5556	206	26	)	)	PUNCT
ap-5556	206	27	(	(	PUNCT
ap-5556	206	28	21524	21524	NUM
ap-5556	206	29	43463	43463	NUM
ap-5556	207	1	+	+	CCONJ
ap-5556	207	2	3406ω2ξ	3406ω2ξ	NUM
ap-5556	207	3	1979425	1979425	NUM
ap-5556	207	4	+	+	SYM
ap-5556	207	5	1737kw	1737kw	PROPN
ap-5556	207	6	606232	606232	NUM
ap-5556	208	1	+	+	CCONJ
ap-5556	208	2	1737ω2	1737ω2	NOUN
ap-5556	208	3	606232	606232	NUM
ap-5556	209	1	+	+	CCONJ
ap-5556	209	2	3617ks	3617ks	PROPN
ap-5556	209	3	86573	86573	NUM
ap-5556	209	4	)	)	PUNCT
ap-5556	209	5	(	(	PUNCT
ap-5556	209	6	52591	52591	NUM
ap-5556	209	7	27028	27028	NUM
ap-5556	209	8	+	+	CCONJ
ap-5556	209	9	2114ω2ξ	2114ω2ξ	NUM
ap-5556	209	10	120859	120859	NUM
ap-5556	209	11	+	+	CCONJ
ap-5556	209	12	1939ks	1939ks	ADJ
ap-5556	209	13	27556	27556	NUM
ap-5556	210	1	+	+	CCONJ
ap-5556	210	2	2767kw	2767kw	NOUN
ap-5556	210	3	83116	83116	NUM
ap-5556	210	4	+	+	CCONJ
ap-5556	210	5	2767ω2	2767ω2	NOUN
ap-5556	210	6	83116	83116	NUM
ap-5556	210	7	)	)	PUNCT
ap-5556	211	1			PROPN
ap-5556	211	2	=	=	SYM
ap-5556	211	3	0	0	NUM
ap-5556	211	4	,	,	PUNCT
ap-5556	211	5	(	(	PUNCT
ap-5556	211	6	32	32	NUM
ap-5556	211	7	)	)	PUNCT
ap-5556	211	8	solving	solve	VERB
ap-5556	211	9	eq	eq	NOUN
ap-5556	211	10	.	.	PUNCT
ap-5556	212	1	(	(	PUNCT
ap-5556	212	2	32	32	NUM
ap-5556	212	3	)	)	PUNCT
ap-5556	212	4	,	,	PUNCT
ap-5556	212	5	one	one	PRON
ap-5556	212	6	gets	get	VERB
ap-5556	212	7	(	(	PUNCT
ap-5556	212	8	−	−	PROPN
ap-5556	212	9	5975	5975	NUM
ap-5556	212	10	8059706	8059706	NUM
ap-5556	213	1	−	−	PROPN
ap-5556	213	2	72ξ2	72ξ2	NUM
ap-5556	213	3	912077	912077	NUM
ap-5556	214	1	−	−	PROPN
ap-5556	214	2	545ξ	545ξ	NOUN
ap-5556	214	3	928333	928333	NUM
ap-5556	214	4	)	)	PUNCT
ap-5556	215	1	ω4	ω4	NOUN
ap-5556	215	2	+	+	CCONJ
ap-5556	215	3	(	(	PUNCT
ap-5556	215	4	(	(	PUNCT
ap-5556	215	5	−	−	PROPN
ap-5556	215	6	857ξ	857ξ	PROPN
ap-5556	215	7	786779	786779	NUM
ap-5556	215	8	−	−	PROPN
ap-5556	215	9	2995	2995	NUM
ap-5556	215	10	275111	275111	NUM
ap-5556	215	11	)	)	PUNCT
ap-5556	216	1	ks	ks	NOUN
ap-5556	216	2	+	+	CCONJ
ap-5556	216	3	(	(	PUNCT
ap-5556	216	4	−	−	PROPN
ap-5556	216	5	545ξ	545ξ	NOUN
ap-5556	216	6	928333	928333	NUM
ap-5556	216	7	−	−	PROPN
ap-5556	216	8	5975	5975	NUM
ap-5556	216	9	4029853	4029853	NUM
ap-5556	216	10	)	)	PUNCT
ap-5556	217	1	kw−	kw−	PROPN
ap-5556	217	2	−17466	−17466	VERB
ap-5556	217	3	29021	29021	NUM
ap-5556	217	4	−	−	NUM
ap-5556	217	5	21131ξ	21131ξ	NUM
ap-5556	217	6	82827	82827	NUM
ap-5556	217	7	)	)	PUNCT
ap-5556	218	1	ω2	ω2	ADV
ap-5556	218	2	−	−	PROPN
ap-5556	218	3	1074ks	1074ks	NOUN
ap-5556	218	4	2	2	NUM
ap-5556	218	5	331613	331613	NUM
ap-5556	218	6	+	+	CCONJ
ap-5556	218	7	(	(	PUNCT
ap-5556	218	8	15438	15438	NUM
ap-5556	218	9	36701	36701	NUM
ap-5556	218	10	−	−	PROPN
ap-5556	218	11	2995kw	2995kw	ADJ
ap-5556	218	12	275111	275111	NUM
ap-5556	218	13	)	)	PUNCT
ap-5556	219	1	ks	ks	ADP
ap-5556	219	2	−	−	PROPN
ap-5556	219	3	130782	130782	NUM
ap-5556	219	4	9119	9119	NUM
ap-5556	219	5	−	−	PROPN
ap-5556	219	6	17466kw	17466kw	NOUN
ap-5556	219	7	29021	29021	NUM
ap-5556	219	8	−	−	PROPN
ap-5556	220	1	5975kw	5975kw	ADJ
ap-5556	220	2	2	2	NUM
ap-5556	220	3	8059706	8059706	NUM
ap-5556	220	4	;	;	PUNCT
ap-5556	220	5	(	(	PUNCT
ap-5556	220	6	33	33	NUM
ap-5556	220	7	)	)	PUNCT
ap-5556	220	8	132	132	NUM
ap-5556	220	9	vol	vol	NOUN
ap-5556	220	10	.	.	PUNCT
ap-5556	221	1	60	60	NUM
ap-5556	221	2	no	no	NOUN
ap-5556	221	3	.	.	PUNCT
ap-5556	222	1	2/2020	2/2020	NUM
ap-5556	222	2	investigation	investigation	NOUN
ap-5556	222	3	of	of	ADP
ap-5556	222	4	the	the	DET
ap-5556	222	5	dynamic	dynamic	ADJ
ap-5556	222	6	behaviour	behaviour	NOUN
ap-5556	222	7	of	of	ADP
ap-5556	222	8	non	non	ADJ
ap-5556	222	9	-	-	ADJ
ap-5556	222	10	uniform	uniform	ADJ
ap-5556	222	11	thickness	thickness	NOUN
ap-5556	222	12	.	.	PUNCT
ap-5556	222	13	.	.	PUNCT
ap-5556	222	14	.	.	PUNCT
ap-5556	223	1	the	the	DET
ap-5556	223	2	eigenvalues	eigenvalue	NOUN
ap-5556	223	3	are	be	AUX
ap-5556	223	4	obtained	obtain	VERB
ap-5556	223	5	resolving	resolve	VERB
ap-5556	223	6	the	the	DET
ap-5556	223	7	quartic	quartic	ADJ
ap-5556	223	8	equation	equation	NOUN
ap-5556	223	9	eq	eq	ADJ
ap-5556	223	10	.	.	PUNCT
ap-5556	224	1	(	(	PUNCT
ap-5556	224	2	33	33	NUM
ap-5556	224	3	)	)	PUNCT
ap-5556	224	4	above	above	ADV
ap-5556	224	5	.	.	PUNCT
ap-5556	225	1	ω	ω	NOUN
ap-5556	225	2	=	=	NOUN
ap-5556	226	1	√√√√√√√√√	√√√√√√√√√	NOUN
ap-5556	226	2	(	(	PUNCT
ap-5556	226	3	1.57	1.57	NUM
ap-5556	226	4	×	×	NOUN
ap-5556	226	5	108ξ2	108ξ2	NUM
ap-5556	226	6	+1.17	+1.17	PROPN
ap-5556	226	7	×	×	NOUN
ap-5556	226	8	109ξ	109ξ	NUM
ap-5556	227	1	+1.48	+1.48	NUM
ap-5556	227	2	×	×	NOUN
ap-5556	227	3	109	109	NUM
ap-5556	227	4	)	)	PUNCT
ap-5556	227	5			NOUN
ap-5556	227	6	√√√√√√√	√√√√√√√	PROPN
ap-5556	227	7			PROPN
ap-5556	227	8	1.63	1.63	NUM
ap-5556	227	9	×	×	NOUN
ap-5556	227	10	1017ks2ξ2	1017ks2ξ2	NUM
ap-5556	227	11	−	−	PROPN
ap-5556	227	12	2.15	2.15	NUM
ap-5556	227	13	×	×	NOUN
ap-5556	227	14	1018kskwξ2	1018kskwξ2	NUM
ap-5556	227	15	+	+	CCONJ
ap-5556	227	16	1.10	1.10	NUM
ap-5556	227	17	×	×	NOUN
ap-5556	227	18	1017kw2ξ2	1017kw2ξ2	NUM
ap-5556	227	19	+1.61	+1.61	PROPN
ap-5556	227	20	×	×	PROPN
ap-5556	227	21	1019ks2ξ	1019ks2ξ	PROPN
ap-5556	227	22	−	−	PROPN
ap-5556	227	23	9.55	9.55	NUM
ap-5556	227	24	×	×	NOUN
ap-5556	227	25	1018kskwξ	1018kskwξ	NUM
ap-5556	227	26	+	+	CCONJ
ap-5556	227	27	6.88	6.88	NUM
ap-5556	227	28	×	×	NOUN
ap-5556	227	29	1020ksξ2	1020ksξ2	NUM
ap-5556	227	30	+1.09	+1.09	PROPN
ap-5556	227	31	×	×	NOUN
ap-5556	227	32	1020kwξ2	1020kwξ2	NUM
ap-5556	227	33	+	+	CCONJ
ap-5556	227	34	1.08	1.08	NUM
ap-5556	227	35	×	×	NOUN
ap-5556	227	36	1020ks2	1020ks2	NOUN
ap-5556	227	37	+	+	CCONJ
ap-5556	227	38	7.85	7.85	NUM
ap-5556	227	39	×	×	NOUN
ap-5556	227	40	1021ksξ	1021ksξ	NUM
ap-5556	228	1	+4.98	+4.98	PROPN
ap-5556	228	2	×	×	NOUN
ap-5556	228	3	1019kwξ	1019kwξ	NOUN
ap-5556	228	4	+	+	CCONJ
ap-5556	228	5	6.05	6.05	NUM
ap-5556	228	6	×	×	NOUN
ap-5556	228	7	1022ξ2	1022ξ2	NOUN
ap-5556	228	8	+	+	CCONJ
ap-5556	228	9	1.43	1.43	NUM
ap-5556	228	10	×	×	PROPN
ap-5556	228	11	1022ks	1022ks	NOUN
ap-5556	228	12	+	+	CCONJ
ap-5556	228	13	2.73	2.73	NUM
ap-5556	228	14	×	×	NOUN
ap-5556	228	15	1023ξ	1023ξ	NUM
ap-5556	228	16	+3.19	+3.19	ADP
ap-5556	228	17	×	×	NOUN
ap-5556	228	18	1023	1023	NUM
ap-5556	228	19	−	−	NOUN
ap-5556	229	1	−1.08	−1.08	INTJ
ap-5556	229	2	×	×	NOUN
ap-5556	229	3	109ksξ	109ksξ	NUM
ap-5556	229	4	−	−	NUM
ap-5556	229	5	5.8	5.8	NUM
ap-5556	229	6	×	×	NOUN
ap-5556	229	7	108kwξ	108kwξ	NUM
ap-5556	229	8	+	+	CCONJ
ap-5556	229	9	1.08	1.08	NUM
ap-5556	229	10	×	×	NOUN
ap-5556	229	11	1010ks	1010ks	NOUN
ap-5556	229	12	−	−	PROPN
ap-5556	229	13	1.48	1.48	NUM
ap-5556	229	14	×	×	NOUN
ap-5556	229	15	109kw	109kw	NOUN
ap-5556	229	16	+	+	X
ap-5556	229	17	.	.	PUNCT
ap-5556	229	18	.	.	PUNCT
ap-5556	229	19	.	.	PUNCT
ap-5556	230	1			NOUN
ap-5556	230	2	(	(	PUNCT
ap-5556	230	3	1.57	1.57	NUM
ap-5556	230	4	×	×	NOUN
ap-5556	230	5	108ξ2	108ξ2	NUM
ap-5556	230	6	+	+	CCONJ
ap-5556	230	7	1.17	1.17	NUM
ap-5556	230	8	×	×	PROPN
ap-5556	230	9	109ξ	109ξ	NUM
ap-5556	230	10	+	+	CCONJ
ap-5556	230	11	1.48	1.48	NUM
ap-5556	230	12	×	×	NOUN
ap-5556	230	13	109	109	NUM
ap-5556	230	14	)	)	PUNCT
ap-5556	230	15	;	;	PUNCT
ap-5556	230	16	(	(	PUNCT
ap-5556	230	17	34	34	NUM
ap-5556	230	18	)	)	PUNCT
ap-5556	230	19	ω	ω	NOUN
ap-5556	230	20	=	=	SYM
ap-5556	230	21	−	−	PROPN
ap-5556	230	22	√√√√√√√√√	√√√√√√√√√	NOUN
ap-5556	230	23	(	(	PUNCT
ap-5556	230	24	1.57	1.57	NUM
ap-5556	230	25	×	×	NOUN
ap-5556	230	26	108ξ2	108ξ2	NUM
ap-5556	230	27	+1.17	+1.17	PROPN
ap-5556	230	28	×	×	NOUN
ap-5556	230	29	109ξ	109ξ	NUM
ap-5556	231	1	+1.48	+1.48	NUM
ap-5556	231	2	×	×	NOUN
ap-5556	231	3	109	109	NUM
ap-5556	231	4	)	)	PUNCT
ap-5556	231	5	1	1	NOUN
ap-5556	231	6	×	×	PROPN
ap-5556	231	7			NOUN
ap-5556	231	8	√√√√√√√	√√√√√√√	PROPN
ap-5556	231	9			PROPN
ap-5556	231	10	1.63	1.63	NUM
ap-5556	231	11	×	×	NOUN
ap-5556	231	12	1017ks2ξ2	1017ks2ξ2	NUM
ap-5556	231	13	−	−	PROPN
ap-5556	231	14	2.15	2.15	NUM
ap-5556	231	15	×	×	NOUN
ap-5556	231	16	1018kskwξ2	1018kskwξ2	NUM
ap-5556	231	17	+	+	CCONJ
ap-5556	231	18	1.10	1.10	NUM
ap-5556	231	19	×	×	NOUN
ap-5556	231	20	1017kw2ξ2	1017kw2ξ2	NUM
ap-5556	231	21	+1.61	+1.61	PROPN
ap-5556	231	22	×	×	PROPN
ap-5556	231	23	1019ks2ξ	1019ks2ξ	PROPN
ap-5556	231	24	−	−	PROPN
ap-5556	231	25	9.55	9.55	NUM
ap-5556	231	26	×	×	NOUN
ap-5556	231	27	1018kskwξ	1018kskwξ	NUM
ap-5556	231	28	+	+	CCONJ
ap-5556	231	29	6.88	6.88	NUM
ap-5556	231	30	×	×	NOUN
ap-5556	231	31	1020ksξ2	1020ksξ2	NUM
ap-5556	231	32	+1.09	+1.09	PROPN
ap-5556	231	33	×	×	NOUN
ap-5556	231	34	1020kwξ2	1020kwξ2	NUM
ap-5556	231	35	+	+	CCONJ
ap-5556	231	36	1.08	1.08	NUM
ap-5556	231	37	×	×	NOUN
ap-5556	231	38	1020ks2	1020ks2	NOUN
ap-5556	231	39	+	+	CCONJ
ap-5556	231	40	7.85	7.85	NUM
ap-5556	231	41	×	×	NOUN
ap-5556	231	42	1021ksξ	1021ksξ	NUM
ap-5556	232	1	+4.98	+4.98	PROPN
ap-5556	232	2	×	×	NOUN
ap-5556	232	3	1019kwξ	1019kwξ	NOUN
ap-5556	232	4	+	+	CCONJ
ap-5556	232	5	6.05	6.05	NUM
ap-5556	232	6	×	×	NOUN
ap-5556	232	7	1022ξ2	1022ξ2	NOUN
ap-5556	232	8	+	+	CCONJ
ap-5556	232	9	1.43	1.43	NUM
ap-5556	232	10	×	×	PROPN
ap-5556	232	11	1022ks	1022ks	NOUN
ap-5556	233	1	+2.73	+2.73	PROPN
ap-5556	233	2	×	×	NOUN
ap-5556	233	3	1023ξ	1023ξ	NUM
ap-5556	233	4	+	+	CCONJ
ap-5556	233	5	3.19	3.19	NUM
ap-5556	233	6	×	×	NOUN
ap-5556	233	7	1023	1023	NUM
ap-5556	233	8	−	−	NOUN
ap-5556	234	1	−1.08	−1.08	INTJ
ap-5556	234	2	×	×	NOUN
ap-5556	234	3	109ksξ	109ksξ	NUM
ap-5556	234	4	−	−	NUM
ap-5556	234	5	5.8	5.8	NUM
ap-5556	234	6	×	×	NOUN
ap-5556	234	7	108kwξ	108kwξ	NUM
ap-5556	234	8	+	+	CCONJ
ap-5556	234	9	1.08	1.08	NUM
ap-5556	234	10	×	×	NOUN
ap-5556	234	11	1010ks	1010ks	NOUN
ap-5556	234	12	−	−	PROPN
ap-5556	234	13	1.48	1.48	NUM
ap-5556	234	14	×	×	NOUN
ap-5556	234	15	109kw	109kw	NOUN
ap-5556	234	16	+	+	X
ap-5556	234	17	.	.	PUNCT
ap-5556	234	18	.	.	PUNCT
ap-5556	234	19	.	.	PUNCT
ap-5556	235	1			NOUN
ap-5556	235	2			NOUN
ap-5556	235	3	(	(	PUNCT
ap-5556	235	4	1.57	1.57	NUM
ap-5556	235	5	×	×	NOUN
ap-5556	235	6	108ξ2	108ξ2	NUM
ap-5556	235	7	+	+	CCONJ
ap-5556	235	8	1.17	1.17	NUM
ap-5556	235	9	×	×	PROPN
ap-5556	235	10	109ξ	109ξ	NUM
ap-5556	235	11	+	+	CCONJ
ap-5556	235	12	1.48	1.48	NUM
ap-5556	235	13	×	×	NOUN
ap-5556	235	14	109	109	NUM
ap-5556	235	15	)	)	PUNCT
ap-5556	235	16	;	;	PUNCT
ap-5556	235	17	(	(	PUNCT
ap-5556	235	18	35	35	NUM
ap-5556	235	19	)	)	PUNCT
ap-5556	235	20	ω	ω	NOUN
ap-5556	235	21	=	=	SYM
ap-5556	235	22	√√√√√√√√√	√√√√√√√√√	NOUN
ap-5556	235	23	(	(	PUNCT
ap-5556	235	24	1.57	1.57	NUM
ap-5556	235	25	×	×	NOUN
ap-5556	235	26	108ξ2	108ξ2	NUM
ap-5556	235	27	+1.17	+1.17	PROPN
ap-5556	235	28	×	×	NOUN
ap-5556	235	29	109ξ	109ξ	NUM
ap-5556	236	1	+1.48	+1.48	NUM
ap-5556	236	2	×	×	NOUN
ap-5556	236	3	109	109	NUM
ap-5556	236	4	)	)	PUNCT
ap-5556	236	5	−1	−1	PROPN
ap-5556	236	6	×	×	PROPN
ap-5556	236	7			NOUN
ap-5556	236	8	√√√√√√√	√√√√√√√	PROPN
ap-5556	236	9			PROPN
ap-5556	236	10	1.63	1.63	NUM
ap-5556	236	11	×	×	NOUN
ap-5556	236	12	1017ks2ξ2	1017ks2ξ2	NUM
ap-5556	236	13	−	−	PROPN
ap-5556	236	14	2.15	2.15	NUM
ap-5556	236	15	×	×	NOUN
ap-5556	236	16	1018kskwξ2	1018kskwξ2	NUM
ap-5556	236	17	+	+	CCONJ
ap-5556	236	18	1.10	1.10	NUM
ap-5556	236	19	×	×	NOUN
ap-5556	236	20	1017kw2ξ2	1017kw2ξ2	NUM
ap-5556	236	21	+1.61	+1.61	PROPN
ap-5556	236	22	×	×	PROPN
ap-5556	236	23	1019ks2ξ	1019ks2ξ	PROPN
ap-5556	236	24	−	−	PROPN
ap-5556	236	25	9.55	9.55	NUM
ap-5556	236	26	×	×	NOUN
ap-5556	236	27	1018kskwξ	1018kskwξ	NUM
ap-5556	236	28	+	+	CCONJ
ap-5556	236	29	6.88	6.88	NUM
ap-5556	236	30	×	×	NOUN
ap-5556	236	31	1020ksξ2	1020ksξ2	NUM
ap-5556	236	32	+1.09	+1.09	PROPN
ap-5556	236	33	×	×	NOUN
ap-5556	236	34	1020kwξ2	1020kwξ2	NUM
ap-5556	236	35	+	+	CCONJ
ap-5556	236	36	1.08	1.08	NUM
ap-5556	236	37	×	×	NOUN
ap-5556	236	38	1020ks2	1020ks2	NOUN
ap-5556	236	39	+	+	CCONJ
ap-5556	236	40	7.85	7.85	NUM
ap-5556	236	41	×	×	NOUN
ap-5556	236	42	1021ksξ	1021ksξ	NUM
ap-5556	237	1	+4.98	+4.98	PROPN
ap-5556	237	2	×	×	NOUN
ap-5556	237	3	1019kwξ	1019kwξ	NOUN
ap-5556	237	4	+	+	CCONJ
ap-5556	237	5	6.05	6.05	NUM
ap-5556	237	6	×	×	NOUN
ap-5556	237	7	1022ξ2	1022ξ2	NOUN
ap-5556	237	8	+	+	CCONJ
ap-5556	237	9	1.43	1.43	NUM
ap-5556	237	10	×	×	PROPN
ap-5556	237	11	1022ks	1022ks	NOUN
ap-5556	237	12	+	+	CCONJ
ap-5556	237	13	2.73	2.73	NUM
ap-5556	237	14	×	×	NOUN
ap-5556	237	15	1023ξ	1023ξ	NUM
ap-5556	237	16	+3.19	+3.19	ADP
ap-5556	237	17	×	×	NOUN
ap-5556	237	18	1023	1023	NUM
ap-5556	237	19	−	−	NOUN
ap-5556	238	1	−1.08	−1.08	INTJ
ap-5556	238	2	×	×	NOUN
ap-5556	238	3	109ksξ	109ksξ	NUM
ap-5556	238	4	−	−	NUM
ap-5556	238	5	5.8	5.8	NUM
ap-5556	238	6	×	×	NOUN
ap-5556	238	7	108kwξ	108kwξ	NUM
ap-5556	238	8	+	+	CCONJ
ap-5556	238	9	1.08	1.08	NUM
ap-5556	238	10	×	×	NOUN
ap-5556	238	11	1010ks	1010ks	NOUN
ap-5556	238	12	−	−	PROPN
ap-5556	238	13	1.48	1.48	NUM
ap-5556	238	14	×	×	NOUN
ap-5556	238	15	109kw	109kw	NOUN
ap-5556	238	16	+	+	X
ap-5556	238	17	.	.	PUNCT
ap-5556	238	18	.	.	PUNCT
ap-5556	238	19	.	.	PUNCT
ap-5556	239	1			NOUN
ap-5556	239	2			NOUN
ap-5556	239	3	(	(	PUNCT
ap-5556	239	4	1.57	1.57	NUM
ap-5556	239	5	×	×	NOUN
ap-5556	239	6	108ξ2	108ξ2	NUM
ap-5556	239	7	+	+	CCONJ
ap-5556	239	8	1.17	1.17	NUM
ap-5556	239	9	×	×	PROPN
ap-5556	239	10	109ξ	109ξ	NUM
ap-5556	239	11	+	+	CCONJ
ap-5556	239	12	1.48	1.48	NUM
ap-5556	239	13	×	×	NOUN
ap-5556	239	14	109	109	NUM
ap-5556	239	15	)	)	PUNCT
ap-5556	239	16	;	;	PUNCT
ap-5556	239	17	(	(	PUNCT
ap-5556	239	18	36	36	NUM
ap-5556	239	19	)	)	PUNCT
ap-5556	239	20	ω	ω	NOUN
ap-5556	239	21	=	=	SYM
ap-5556	240	1	−	−	PROPN
ap-5556	240	2	√√√√√√√√√	√√√√√√√√√	NOUN
ap-5556	240	3	(	(	PUNCT
ap-5556	240	4	1.57	1.57	NUM
ap-5556	240	5	×	×	NOUN
ap-5556	240	6	108ξ2	108ξ2	NUM
ap-5556	240	7	+1.17	+1.17	PROPN
ap-5556	240	8	×	×	NOUN
ap-5556	240	9	109ξ	109ξ	NUM
ap-5556	241	1	+1.48	+1.48	NUM
ap-5556	241	2	×	×	NOUN
ap-5556	241	3	109	109	NUM
ap-5556	241	4	)	)	PUNCT
ap-5556	241	5	1	1	NOUN
ap-5556	241	6	×	×	NOUN
ap-5556	241	7	−1	−1	PROPN
ap-5556	241	8	×	×	PROPN
ap-5556	241	9			NOUN
ap-5556	241	10	√√√√√√√	√√√√√√√	PROPN
ap-5556	241	11			PROPN
ap-5556	241	12	1.63	1.63	NUM
ap-5556	241	13	×	×	NOUN
ap-5556	241	14	1017ks2ξ2	1017ks2ξ2	NUM
ap-5556	241	15	−	−	PROPN
ap-5556	241	16	2.15	2.15	NUM
ap-5556	241	17	×	×	NOUN
ap-5556	241	18	1018kskwξ2	1018kskwξ2	NUM
ap-5556	241	19	+	+	CCONJ
ap-5556	241	20	1.10	1.10	NUM
ap-5556	241	21	×	×	NOUN
ap-5556	241	22	1017kw2ξ2	1017kw2ξ2	NUM
ap-5556	241	23	+1.61	+1.61	PROPN
ap-5556	241	24	×	×	PROPN
ap-5556	241	25	1019ks2ξ	1019ks2ξ	PROPN
ap-5556	241	26	−	−	PROPN
ap-5556	241	27	9.55	9.55	NUM
ap-5556	241	28	×	×	NOUN
ap-5556	241	29	1018kskwξ	1018kskwξ	NUM
ap-5556	241	30	+	+	CCONJ
ap-5556	241	31	6.88	6.88	NUM
ap-5556	241	32	×	×	NOUN
ap-5556	241	33	1020ksξ2	1020ksξ2	NUM
ap-5556	241	34	+1.09	+1.09	PROPN
ap-5556	241	35	×	×	NOUN
ap-5556	241	36	1020kwξ2	1020kwξ2	NUM
ap-5556	241	37	+	+	CCONJ
ap-5556	241	38	1.08	1.08	NUM
ap-5556	241	39	×	×	NOUN
ap-5556	241	40	1020ks2	1020ks2	NOUN
ap-5556	241	41	+	+	CCONJ
ap-5556	241	42	7.85	7.85	NUM
ap-5556	241	43	×	×	NOUN
ap-5556	241	44	1021ksξ	1021ksξ	NUM
ap-5556	242	1	+4.98	+4.98	PROPN
ap-5556	242	2	×	×	NOUN
ap-5556	242	3	1019kwξ	1019kwξ	NOUN
ap-5556	242	4	+	+	CCONJ
ap-5556	242	5	6.05	6.05	NUM
ap-5556	242	6	×	×	NOUN
ap-5556	242	7	1022ξ2	1022ξ2	NOUN
ap-5556	242	8	+	+	CCONJ
ap-5556	242	9	1.43	1.43	NUM
ap-5556	242	10	×	×	PROPN
ap-5556	242	11	1022ks	1022ks	NOUN
ap-5556	243	1	+2.73	+2.73	PROPN
ap-5556	243	2	×	×	NOUN
ap-5556	243	3	1023ξ	1023ξ	NUM
ap-5556	243	4	+	+	CCONJ
ap-5556	243	5	3.19	3.19	NUM
ap-5556	243	6	×	×	NOUN
ap-5556	243	7	1023	1023	NUM
ap-5556	243	8	−	−	NOUN
ap-5556	244	1	−1.08	−1.08	INTJ
ap-5556	244	2	×	×	NOUN
ap-5556	244	3	109ksξ	109ksξ	NUM
ap-5556	244	4	−	−	NUM
ap-5556	244	5	5.8	5.8	NUM
ap-5556	244	6	×	×	NOUN
ap-5556	244	7	108kwξ	108kwξ	NUM
ap-5556	244	8	+	+	CCONJ
ap-5556	244	9	1.08	1.08	NUM
ap-5556	244	10	×	×	NOUN
ap-5556	244	11	1010ks	1010ks	NOUN
ap-5556	244	12	+	+	X
ap-5556	244	13	.	.	PUNCT
ap-5556	244	14	.	.	PUNCT
ap-5556	244	15	.	.	PUNCT
ap-5556	245	1			NOUN
ap-5556	245	2			NOUN
ap-5556	245	3			NOUN
ap-5556	245	4	(	(	PUNCT
ap-5556	245	5	1.57	1.57	NUM
ap-5556	245	6	×	×	NOUN
ap-5556	245	7	108ξ2	108ξ2	NUM
ap-5556	245	8	+	+	CCONJ
ap-5556	245	9	1.17	1.17	NUM
ap-5556	245	10	×	×	PROPN
ap-5556	245	11	109ξ	109ξ	NUM
ap-5556	245	12	+	+	CCONJ
ap-5556	245	13	1.48	1.48	NUM
ap-5556	245	14	×	×	NOUN
ap-5556	245	15	109	109	NUM
ap-5556	245	16	)	)	PUNCT
ap-5556	245	17	;	;	PUNCT
ap-5556	245	18	(	(	PUNCT
ap-5556	245	19	37	37	NUM
ap-5556	245	20	)	)	PUNCT
ap-5556	245	21	the	the	DET
ap-5556	245	22	numerical	numerical	ADJ
ap-5556	245	23	computation	computation	NOUN
ap-5556	245	24	of	of	ADP
ap-5556	245	25	the	the	DET
ap-5556	245	26	natural	natural	ADJ
ap-5556	245	27	frequencies	frequency	NOUN
ap-5556	245	28	requires	require	VERB
ap-5556	245	29	substituting	substitute	VERB
ap-5556	245	30	values	value	NOUN
ap-5556	245	31	to	to	ADP
ap-5556	245	32	solutions	solution	NOUN
ap-5556	245	33	obtained	obtain	VERB
ap-5556	245	34	in	in	ADP
ap-5556	245	35	eq	eq	ADP
ap-5556	245	36	.	.	PUNCT
ap-5556	246	1	(	(	PUNCT
ap-5556	246	2	34	34	NUM
ap-5556	246	3	-	-	SYM
ap-5556	246	4	37	37	NUM
ap-5556	246	5	)	)	PUNCT
ap-5556	246	6	−	−	PROPN
ap-5556	246	7	14923ω2	14923ω2	NUM
ap-5556	246	8	46030	46030	NUM
ap-5556	247	1	−	−	NOUN
ap-5556	247	2	28704	28704	NUM
ap-5556	247	3	3259	3259	NUM
ap-5556	248	1	+	+	CCONJ
ap-5556	248	2	√	√	PROPN
ap-5556	248	3	(	(	PUNCT
ap-5556	248	4	4.17×	4.17×	NUM
ap-5556	248	5	1019ω4	1019ω4	NUM
ap-5556	248	6	+	+	CCONJ
ap-5556	248	7	2.52×	2.52×	NUM
ap-5556	248	8	1021ω2	1021ω2	NUM
ap-5556	248	9	+	+	CCONJ
ap-5556	248	10	2.52×	2.52×	NUM
ap-5556	248	11	1022	1022	NUM
ap-5556	248	12	)	)	PUNCT
ap-5556	248	13	2.00×	2.00×	NUM
ap-5556	248	14	108	108	NUM
ap-5556	248	15	,	,	PUNCT
ap-5556	248	16	(	(	PUNCT
ap-5556	248	17	38	38	NUM
ap-5556	248	18	)	)	PUNCT
ap-5556	248	19	solving	solve	VERB
ap-5556	248	20	the	the	DET
ap-5556	248	21	quadratic	quadratic	ADJ
ap-5556	248	22	eq	eq	NOUN
ap-5556	248	23	.	.	PUNCT
ap-5556	249	1	(	(	PUNCT
ap-5556	249	2	38	38	NUM
ap-5556	249	3	)	)	PUNCT
ap-5556	249	4	gives	give	VERB
ap-5556	249	5	the	the	DET
ap-5556	249	6	natural	natural	ADJ
ap-5556	249	7	frequency	frequency	NOUN
ap-5556	249	8	.	.	PUNCT
ap-5556	250	1	ω	ω	X
ap-5556	250	2	=	=	SYM
ap-5556	250	3	4.957175854	4.957175854	NUM
ap-5556	250	4	,	,	PUNCT
ap-5556	250	5	−	−	PROPN
ap-5556	250	6	4.957175854	4.957175854	NUM
ap-5556	250	7	,	,	PUNCT
ap-5556	250	8	(	(	PUNCT
ap-5556	250	9	39	39	NUM
ap-5556	250	10	)	)	PUNCT
ap-5556	250	11	substitute	substitute	NOUN
ap-5556	250	12	the	the	DET
ap-5556	250	13	positive	positive	ADJ
ap-5556	250	14	root	root	NOUN
ap-5556	250	15	obtained	obtain	VERB
ap-5556	250	16	in	in	ADP
ap-5556	250	17	eq	eq	ADP
ap-5556	250	18	.	.	PUNCT
ap-5556	251	1	(	(	PUNCT
ap-5556	251	2	39	39	NUM
ap-5556	251	3	)	)	PUNCT
ap-5556	251	4	into	into	ADP
ap-5556	251	5	eq	eq	NOUN
ap-5556	251	6	.	.	PUNCT
ap-5556	252	1	(	(	PUNCT
ap-5556	252	2	31	31	NUM
ap-5556	252	3	)	)	PUNCT
ap-5556	252	4	gives	give	VERB
ap-5556	252	5	,	,	PUNCT
ap-5556	252	6	[	[	PUNCT
ap-5556	252	7	−	−	PROPN
ap-5556	252	8	137865	137865	NUM
ap-5556	252	9	4058	4058	NUM
ap-5556	252	10	−	−	PROPN
ap-5556	252	11	111560	111560	NUM
ap-5556	252	12	871735062	871735062	NUM
ap-5556	252	13	31091	31091	NUM
ap-5556	252	14	22757	22757	NUM
ap-5556	252	15	53569	53569	NUM
ap-5556	252	16	]	]	X
ap-5556	252	17	{	{	PUNCT
ap-5556	252	18	a	a	DET
ap-5556	252	19	c	c	NOUN
ap-5556	252	20	}	}	PUNCT
ap-5556	252	21	(	(	PUNCT
ap-5556	252	22	1	1	X
ap-5556	252	23	)	)	PUNCT
ap-5556	252	24	=	=	NOUN
ap-5556	252	25	{	{	PUNCT
ap-5556	252	26	0	0	NUM
ap-5556	252	27	0	0	NUM
ap-5556	252	28	}	}	PUNCT
ap-5556	252	29	,	,	PUNCT
ap-5556	252	30	(	(	PUNCT
ap-5556	252	31	40	40	NUM
ap-5556	252	32	)	)	PUNCT
ap-5556	252	33	putting	put	VERB
ap-5556	252	34	c	c	NOUN
ap-5556	252	35	=	=	SYM
ap-5556	252	36	1	1	NUM
ap-5556	252	37	in	in	ADP
ap-5556	252	38	eq	eq	ADP
ap-5556	252	39	.	.	PUNCT
ap-5556	253	1	(	(	PUNCT
ap-5556	253	2	40	40	NUM
ap-5556	253	3	)	)	PUNCT
ap-5556	253	4	,	,	PUNCT
ap-5556	253	5	then	then	ADV
ap-5556	253	6	a	a	PRON
ap-5556	253	7	is	be	AUX
ap-5556	253	8	calculated	calculate	VERB
ap-5556	253	9	as	as	ADP
ap-5556	253	10	,	,	PUNCT
ap-5556	253	11	{	{	PUNCT
ap-5556	253	12	a	a	DET
ap-5556	253	13	c	c	NOUN
ap-5556	253	14	}	}	PUNCT
ap-5556	253	15	(	(	PUNCT
ap-5556	253	16	1	1	X
ap-5556	253	17	)	)	PUNCT
ap-5556	253	18	=	=	PRON
ap-5556	253	19	{	{	PUNCT
ap-5556	253	20	−2.654608759	−2.654608759	NOUN
ap-5556	253	21	1	1	NUM
ap-5556	253	22	}	}	PUNCT
ap-5556	253	23	,	,	PUNCT
ap-5556	253	24	(	(	PUNCT
ap-5556	253	25	41	41	NUM
ap-5556	253	26	)	)	PUNCT
ap-5556	253	27	therefore	therefore	ADV
ap-5556	253	28	,	,	PUNCT
ap-5556	253	29	the	the	DET
ap-5556	253	30	deflection	deflection	NOUN
ap-5556	253	31	solution	solution	NOUN
ap-5556	253	32	of	of	ADP
ap-5556	253	33	the	the	DET
ap-5556	253	34	governing	governing	NOUN
ap-5556	253	35	eq	eq	X
ap-5556	253	36	.	.	PUNCT
ap-5556	254	1	(	(	PUNCT
ap-5556	254	2	1	1	X
ap-5556	254	3	)	)	PUNCT
ap-5556	254	4	gives	give	VERB
ap-5556	254	5	w	w	PROPN
ap-5556	254	6	(	(	PUNCT
ap-5556	254	7	r	r	NOUN
ap-5556	254	8	)	)	PUNCT
ap-5556	254	9	=	=	SYM
ap-5556	254	10	1−	1−	NUM
ap-5556	254	11	25785r2	25785r2	NUM
ap-5556	254	12	20356	20356	NUM
ap-5556	254	13	+	+	CCONJ
ap-5556	254	14	32609r4	32609r4	NUM
ap-5556	254	15	93147	93147	NUM
ap-5556	254	16	−	−	NOUN
ap-5556	254	17	9721r5	9721r5	NOUN
ap-5556	254	18	116589	116589	NUM
ap-5556	254	19	,	,	PUNCT
ap-5556	254	20	(	(	PUNCT
ap-5556	254	21	42	42	NUM
ap-5556	254	22	)	)	PUNCT
ap-5556	254	23	3.2	3.2	NUM
ap-5556	254	24	.	.	PUNCT
ap-5556	255	1	application	application	NOUN
ap-5556	255	2	of	of	ADP
ap-5556	255	3	galerkin	galerkin	ADJ
ap-5556	255	4	method	method	NOUN
ap-5556	255	5	of	of	ADP
ap-5556	255	6	weighted	weight	VERB
ap-5556	255	7	residual	residual	ADJ
ap-5556	255	8	to	to	ADP
ap-5556	255	9	nonlinear	nonlinear	ADJ
ap-5556	255	10	governing	govern	VERB
ap-5556	255	11	equation	equation	NOUN
ap-5556	255	12	considering	consider	VERB
ap-5556	255	13	a	a	DET
ap-5556	255	14	non	non	ADJ
ap-5556	255	15	-	-	ADJ
ap-5556	255	16	uniform	uniform	ADJ
ap-5556	255	17	thickness	thickness	NOUN
ap-5556	255	18	circular	circular	ADJ
ap-5556	255	19	plate	plate	NOUN
ap-5556	255	20	resting	rest	VERB
ap-5556	255	21	on	on	ADP
ap-5556	255	22	nonlinear	nonlinear	ADJ
ap-5556	255	23	foundation	foundation	NOUN
ap-5556	255	24	in	in	ADP
ap-5556	255	25	fig	fig	NOUN
ap-5556	255	26	.	.	PUNCT
ap-5556	256	1	2	2	NUM
ap-5556	256	2	,	,	PUNCT
ap-5556	256	3	vonkármán	vonkármán	NOUN
ap-5556	256	4	analogue	analogue	NOUN
ap-5556	256	5	is	be	AUX
ap-5556	256	6	employed	employ	VERB
ap-5556	256	7	due	due	ADP
ap-5556	256	8	to	to	ADP
ap-5556	256	9	geometric	geometric	ADJ
ap-5556	256	10	nonlinearity	nonlinearity	NOUN
ap-5556	256	11	condition	condition	NOUN
ap-5556	256	12	involved	involve	VERB
ap-5556	256	13	.	.	PUNCT
ap-5556	257	1	133	133	NUM
ap-5556	257	2	s.	s.	PROPN
ap-5556	257	3	salawu	salawu	PROPN
ap-5556	257	4	,	,	PUNCT
ap-5556	257	5	g.	g.	PROPN
ap-5556	257	6	sobamowo	sobamowo	PROPN
ap-5556	257	7	,	,	PUNCT
ap-5556	257	8	o.	o.	PROPN
ap-5556	257	9	sadiq	sadiq	PROPN
ap-5556	257	10	acta	acta	PROPN
ap-5556	257	11	polytechnica	polytechnica	PROPN
ap-5556	257	12	figure	figure	NOUN
ap-5556	257	13	2	2	NUM
ap-5556	257	14	.	.	PUNCT
ap-5556	257	15	varying	vary	VERB
ap-5556	257	16	thickness	thickness	NOUN
ap-5556	257	17	circular	circular	ADJ
ap-5556	257	18	plate	plate	NOUN
ap-5556	257	19	resting	rest	VERB
ap-5556	257	20	on	on	ADP
ap-5556	257	21	three	three	NUM
ap-5556	257	22	-	-	PUNCT
ap-5556	257	23	parameter	parameter	NOUN
ap-5556	257	24	foundations	foundation	NOUN
ap-5556	257	25	.	.	PUNCT
ap-5556	258	1	g(r	g(r	NOUN
ap-5556	258	2	)	)	PUNCT
ap-5556	258	3			PUNCT
ap-5556	258	4	∂4w	∂4w	PROPN
ap-5556	258	5	(	(	PUNCT
ap-5556	258	6	r	r	NOUN
ap-5556	258	7	,	,	PUNCT
ap-5556	258	8	t	t	PROPN
ap-5556	258	9	)	)	PUNCT
ap-5556	258	10	∂r4	∂r4	PROPN
ap-5556	259	1	+	+	CCONJ
ap-5556	259	2	2	2	NUM
ap-5556	259	3	r	r	NOUN
ap-5556	259	4	∂3	∂3	NOUN
ap-5556	259	5	∂r3w	∂r3w	NOUN
ap-5556	259	6	(	(	PUNCT
ap-5556	259	7	r	r	NOUN
ap-5556	259	8	,	,	PUNCT
ap-5556	259	9	t)−	t)−	PROPN
ap-5556	259	10	(	(	PUNCT
ap-5556	259	11	2m2	2m2	NUM
ap-5556	259	12	+	+	SYM
ap-5556	259	13	1	1	NUM
ap-5556	259	14	r2	r2	NOUN
ap-5556	259	15	)	)	PUNCT
ap-5556	259	16	∂2w	∂2w	VERB
ap-5556	259	17	(	(	PUNCT
ap-5556	259	18	r	r	NOUN
ap-5556	259	19	,	,	PUNCT
ap-5556	259	20	t	t	PROPN
ap-5556	259	21	)	)	PUNCT
ap-5556	259	22	∂r2	∂r2	PROPN
ap-5556	259	23	+	+	X
ap-5556	259	24	(	(	PUNCT
ap-5556	259	25	2m2	2m2	NUM
ap-5556	259	26	+	+	SYM
ap-5556	259	27	1	1	NUM
ap-5556	259	28	r3	r3	PROPN
ap-5556	259	29	)	)	PUNCT
ap-5556	260	1	∂w	∂w	PROPN
ap-5556	260	2	(	(	PUNCT
ap-5556	260	3	r	r	NOUN
ap-5556	260	4	,	,	PUNCT
ap-5556	260	5	t	t	PROPN
ap-5556	260	6	)	)	PUNCT
ap-5556	260	7	∂r	∂r	PROPN
ap-5556	260	8	−	−	PROPN
ap-5556	260	9	(	(	PUNCT
ap-5556	260	10	4m2−m4	4m2−m4	NOUN
ap-5556	260	11	r4	r4	PROPN
ap-5556	260	12	)	)	PUNCT
ap-5556	261	1	w(r	w(r	PROPN
ap-5556	261	2	,	,	PUNCT
ap-5556	261	3	t	t	PROPN
ap-5556	261	4	)	)	PUNCT
ap-5556	261	5	+	+	VERB
ap-5556	261	6	∂g(r	∂g(r	NOUN
ap-5556	261	7	)	)	PUNCT
ap-5556	262	1	∂r	∂r	PROPN
ap-5556	262	2	{	{	PUNCT
ap-5556	262	3	2∂	2∂	NUM
ap-5556	262	4	3w	3w	NOUN
ap-5556	262	5	(	(	PUNCT
ap-5556	262	6	r	r	NOUN
ap-5556	262	7	,	,	PUNCT
ap-5556	262	8	t	t	PROPN
ap-5556	262	9	)	)	PUNCT
ap-5556	262	10	∂r3	∂r3	NOUN
ap-5556	262	11	+	+	CCONJ
ap-5556	262	12	2	2	NUM
ap-5556	262	13	+	+	CCONJ
ap-5556	262	14	ν	ν	NOUN
ap-5556	262	15	r	r	NOUN
ap-5556	262	16	∂2w	∂2w	NOUN
ap-5556	262	17	(	(	PUNCT
ap-5556	262	18	r	r	NOUN
ap-5556	262	19	,	,	PUNCT
ap-5556	262	20	t	t	PROPN
ap-5556	262	21	)	)	PUNCT
ap-5556	262	22	∂r2	∂r2	PROPN
ap-5556	262	23	−	−	ADP
ap-5556	262	24	2m2	2m2	NUM
ap-5556	262	25	+	+	SYM
ap-5556	262	26	1	1	NUM
ap-5556	262	27	r2	r2	NOUN
ap-5556	262	28	∂w	∂w	PROPN
ap-5556	262	29	(	(	PUNCT
ap-5556	262	30	r	r	NOUN
ap-5556	262	31	,	,	PUNCT
ap-5556	262	32	t	t	NOUN
ap-5556	262	33	)	)	PUNCT
ap-5556	263	1	∂r	∂r	PROPN
ap-5556	264	1	+	+	NUM
ap-5556	264	2	3m2	3m2	NUM
ap-5556	264	3	r3	r3	PROPN
ap-5556	264	4	w	w	PROPN
ap-5556	264	5	(	(	PUNCT
ap-5556	264	6	r	r	NOUN
ap-5556	264	7	,	,	PUNCT
ap-5556	264	8	t	t	PROPN
ap-5556	264	9	)	)	PUNCT
ap-5556	264	10	}	}	PUNCT
ap-5556	265	1	+	+	CCONJ
ap-5556	265	2	∂2g(r	∂2g(r	X
ap-5556	265	3	)	)	PUNCT
ap-5556	265	4	∂r2	∂r2	PROPN
ap-5556	265	5	{	{	PUNCT
ap-5556	265	6	∂2w	∂2w	X
ap-5556	265	7	(	(	PUNCT
ap-5556	265	8	r	r	NOUN
ap-5556	265	9	,	,	PUNCT
ap-5556	265	10	t	t	PROPN
ap-5556	265	11	)	)	PUNCT
ap-5556	265	12	∂r2	∂r2	PROPN
ap-5556	265	13	+	+	CCONJ
ap-5556	265	14	ν	ν	X
ap-5556	265	15	(	(	PUNCT
ap-5556	265	16	1	1	NUM
ap-5556	265	17	r	r	NOUN
ap-5556	265	18	∂w	∂w	PROPN
ap-5556	265	19	(	(	PUNCT
ap-5556	265	20	r	r	NOUN
ap-5556	265	21	,	,	PUNCT
ap-5556	265	22	t	t	PROPN
ap-5556	265	23	)	)	PUNCT
ap-5556	265	24	∂r	∂r	PROPN
ap-5556	265	25	−	−	NUM
ap-5556	265	26	m2	m2	PROPN
ap-5556	265	27	r2	r2	PROPN
ap-5556	265	28	w	w	PROPN
ap-5556	265	29	(	(	PUNCT
ap-5556	265	30	r	r	NOUN
ap-5556	265	31	,	,	PUNCT
ap-5556	265	32	t	t	PROPN
ap-5556	265	33	)	)	PUNCT
ap-5556	265	34	)	)	PUNCT
ap-5556	265	35	}	}	PUNCT
ap-5556	265	36	−	−	ADP
ap-5556	265	37	a2ks	a2ks	X
ap-5556	265	38	d∗	d∗	VERB
ap-5556	265	39	∂2w	∂2w	ADJ
ap-5556	265	40	(	(	PUNCT
ap-5556	265	41	r	r	NOUN
ap-5556	265	42	,	,	PUNCT
ap-5556	265	43	t	t	PROPN
ap-5556	265	44	)	)	PUNCT
ap-5556	265	45	∂r2	∂r2	PROPN
ap-5556	265	46	−	−	ADP
ap-5556	265	47	a2ks	a2ks	X
ap-5556	265	48	d∗r	d∗r	NOUN
ap-5556	265	49	∂w	∂w	PROPN
ap-5556	265	50	(	(	PUNCT
ap-5556	265	51	r	r	NOUN
ap-5556	265	52	,	,	PUNCT
ap-5556	265	53	t	t	NOUN
ap-5556	265	54	)	)	PUNCT
ap-5556	266	1	∂r	∂r	NOUN
ap-5556	267	1	+	+	CCONJ
ap-5556	267	2	a2ks	a2ks	X
ap-5556	267	3	d∗	d∗	PROPN
ap-5556	267	4	m2	m2	PROPN
ap-5556	267	5	r2	r2	PROPN
ap-5556	267	6	w	w	PROPN
ap-5556	267	7	(	(	PUNCT
ap-5556	267	8	r	r	NOUN
ap-5556	267	9	,	,	PUNCT
ap-5556	267	10	t)−	t)−	PROPN
ap-5556	267	11	3	3	NUM
ap-5556	267	12	4	4	NUM
ap-5556	267	13	a4kp	a4kp	PUNCT
ap-5556	267	14	d∗	d∗	PROPN
ap-5556	267	15	(	(	PUNCT
ap-5556	267	16	w	w	NOUN
ap-5556	267	17	(	(	PUNCT
ap-5556	267	18	r	r	NOUN
ap-5556	267	19	,	,	PUNCT
ap-5556	267	20	t))3	t))3	NOUN
ap-5556	267	21	+	+	CCONJ
ap-5556	267	22	a4kw	a4kw	VERB
ap-5556	267	23	d∗	d∗	PROPN
ap-5556	267	24	w	w	PROPN
ap-5556	267	25	(	(	PUNCT
ap-5556	267	26	r	r	NOUN
ap-5556	267	27	,	,	PUNCT
ap-5556	267	28	t	t	PROPN
ap-5556	267	29	)	)	PUNCT
ap-5556	268	1	+	+	NUM
ap-5556	268	2	ρa4h	ρa4h	NUM
ap-5556	268	3	d∗	d∗	NOUN
ap-5556	268	4	∂2w	∂2w	VERB
ap-5556	268	5	(	(	PUNCT
ap-5556	268	6	r	r	NOUN
ap-5556	268	7	,	,	PUNCT
ap-5556	268	8	t	t	NOUN
ap-5556	268	9	)	)	PUNCT
ap-5556	268	10	∂t2	∂t2	NOUN
ap-5556	268	11	−	−	NOUN
ap-5556	268	12	1	1	NUM
ap-5556	268	13	r	r	NOUN
ap-5556	268	14	∂	∂	NOUN
ap-5556	268	15	∂r	∂r	NOUN
ap-5556	268	16	(	(	PUNCT
ap-5556	268	17	ϕ	ϕ	PROPN
ap-5556	268	18	∂w	∂w	PROPN
ap-5556	268	19	(	(	PUNCT
ap-5556	268	20	r	r	PROPN
ap-5556	268	21	,	,	PUNCT
ap-5556	268	22	t	t	PROPN
ap-5556	268	23	)	)	PUNCT
ap-5556	268	24	∂r	∂r	PROPN
ap-5556	268	25	)	)	PUNCT
ap-5556	269	1	=	=	SYM
ap-5556	269	2	0	0	NUM
ap-5556	269	3	,	,	PUNCT
ap-5556	269	4	(	(	PUNCT
ap-5556	269	5	43	43	NUM
ap-5556	269	6	)	)	PUNCT
ap-5556	269	7	∂2ϕ	∂2ϕ	NOUN
ap-5556	270	1	∂r2	∂r2	NOUN
ap-5556	270	2	+	+	CCONJ
ap-5556	270	3	1	1	NUM
ap-5556	270	4	r	r	NOUN
ap-5556	270	5	∂ϕ	∂ϕ	PROPN
ap-5556	271	1	∂r	∂r	NOUN
ap-5556	271	2	−	−	PROPN
ap-5556	271	3	ϕ	ϕ	PROPN
ap-5556	271	4	r2	r2	PROPN
ap-5556	271	5	+	+	CCONJ
ap-5556	271	6	eh	eh	INTJ
ap-5556	271	7	2r	2r	NUM
ap-5556	271	8	(	(	PUNCT
ap-5556	271	9	∂w	∂w	PROPN
ap-5556	271	10	(	(	PUNCT
ap-5556	271	11	r	r	NOUN
ap-5556	271	12	,	,	PUNCT
ap-5556	271	13	t	t	PROPN
ap-5556	271	14	)	)	PUNCT
ap-5556	272	1	∂r	∂r	VERB
ap-5556	272	2	)	)	PUNCT
ap-5556	272	3	2	2	NUM
ap-5556	272	4	=	=	SYM
ap-5556	272	5	0	0	NUM
ap-5556	272	6	(	(	PUNCT
ap-5556	272	7	44	44	NUM
ap-5556	272	8	)	)	PUNCT
ap-5556	272	9	where	where	SCONJ
ap-5556	272	10	kp	kp	PROPN
ap-5556	272	11	is	be	AUX
ap-5556	272	12	the	the	DET
ap-5556	272	13	nonlinear	nonlinear	ADJ
ap-5556	272	14	winkler	winkler	PROPN
ap-5556	272	15	foundation	foundation	PROPN
ap-5556	272	16	and	and	CCONJ
ap-5556	272	17	ϕ	ϕ	NOUN
ap-5556	272	18	is	be	AUX
ap-5556	272	19	the	the	DET
ap-5556	272	20	airy	airy	ADJ
ap-5556	272	21	stress	stress	NOUN
ap-5556	272	22	function	function	NOUN
ap-5556	272	23	.	.	PUNCT
ap-5556	273	1	an	an	DET
ap-5556	273	2	approximate	approximate	ADJ
ap-5556	273	3	solution	solution	NOUN
ap-5556	273	4	is	be	AUX
ap-5556	273	5	obtained	obtain	VERB
ap-5556	273	6	by	by	ADP
ap-5556	273	7	assuming	assume	VERB
ap-5556	273	8	the	the	DET
ap-5556	273	9	non	non	ADJ
ap-5556	273	10	-	-	ADJ
ap-5556	273	11	linear	linear	ADJ
ap-5556	273	12	free	free	ADJ
ap-5556	273	13	vibrations	vibration	NOUN
ap-5556	273	14	to	to	PART
ap-5556	273	15	have	have	VERB
ap-5556	273	16	the	the	DET
ap-5556	273	17	same	same	ADJ
ap-5556	273	18	spatial	spatial	ADJ
ap-5556	273	19	shape	shape	NOUN
ap-5556	273	20	,	,	PUNCT
ap-5556	273	21	i.e.	i.e.	X
ap-5556	273	22	,	,	PUNCT
ap-5556	273	23	w	w	X
ap-5556	273	24	(	(	PUNCT
ap-5556	273	25	r	r	NOUN
ap-5556	273	26	,	,	PUNCT
ap-5556	273	27	t	t	PROPN
ap-5556	273	28	)	)	PUNCT
ap-5556	273	29	=	=	PUNCT
ap-5556	274	1	(	(	PUNCT
ap-5556	274	2	c4r	c4r	PROPN
ap-5556	274	3	4	4	NUM
ap-5556	274	4	+	+	CCONJ
ap-5556	274	5	c2r	c2r	NOUN
ap-5556	274	6	2	2	NUM
ap-5556	274	7	+	+	CCONJ
ap-5556	274	8	1	1	NUM
ap-5556	274	9	)	)	PUNCT
ap-5556	274	10	φ	φ	PROPN
ap-5556	274	11	(	(	PUNCT
ap-5556	274	12	t	t	PROPN
ap-5556	274	13	)	)	PUNCT
ap-5556	274	14	(	(	PUNCT
ap-5556	274	15	45	45	NUM
ap-5556	274	16	)	)	PUNCT
ap-5556	274	17	substitute	substitute	NOUN
ap-5556	274	18	eq	eq	NOUN
ap-5556	274	19	.	.	PUNCT
ap-5556	275	1	(	(	PUNCT
ap-5556	275	2	45	45	NUM
ap-5556	275	3	)	)	PUNCT
ap-5556	275	4	into	into	ADP
ap-5556	275	5	eq	eq	NOUN
ap-5556	275	6	.	.	PUNCT
ap-5556	276	1	(	(	PUNCT
ap-5556	276	2	44	44	NUM
ap-5556	276	3	)	)	PUNCT
ap-5556	276	4	and	and	CCONJ
ap-5556	276	5	solve	solve	VERB
ap-5556	276	6	the	the	DET
ap-5556	276	7	ode	ode	ADJ
ap-5556	276	8	ϕ(r	ϕ(r	PROPN
ap-5556	276	9	,	,	PUNCT
ap-5556	276	10	t	t	PROPN
ap-5556	276	11	)	)	PUNCT
ap-5556	277	1	=	=	SYM
ap-5556	277	2	c1	c1	PROPN
ap-5556	277	3	r	r	NOUN
ap-5556	277	4	−	−	PROPN
ap-5556	277	5	c3r+	c3r+	NOUN
ap-5556	277	6	(	(	PUNCT
ap-5556	277	7	φ(t))2r3	φ(t))2r3	PROPN
ap-5556	277	8	(	(	PUNCT
ap-5556	277	9	2c42r4	2c42r4	NUM
ap-5556	277	10	+	+	NUM
ap-5556	277	11	4c2c4r2	4c2c4r2	NUM
ap-5556	277	12	+	+	CCONJ
ap-5556	277	13	3c22	3c22	NUM
ap-5556	277	14	)	)	PUNCT
ap-5556	277	15	6	6	NUM
ap-5556	277	16	,	,	PUNCT
ap-5556	277	17	(	(	PUNCT
ap-5556	277	18	46	46	NUM
ap-5556	277	19	)	)	PUNCT
ap-5556	277	20	the	the	DET
ap-5556	277	21	value	value	NOUN
ap-5556	277	22	of	of	ADP
ap-5556	277	23	ϕ	ϕ	NOUN
ap-5556	277	24	is	be	AUX
ap-5556	277	25	accordingly	accordingly	ADV
ap-5556	277	26	found	find	VERB
ap-5556	277	27	to	to	PART
ap-5556	277	28	be	be	AUX
ap-5556	277	29	finite	finite	ADJ
ap-5556	277	30	at	at	ADP
ap-5556	277	31	the	the	DET
ap-5556	277	32	origin	origin	NOUN
ap-5556	277	33	c1	c1	NOUN
ap-5556	277	34	=	=	PROPN
ap-5556	278	1	0	0	X
ap-5556	278	2	.	.	PUNCT
ap-5556	278	3	additionally	additionally	ADV
ap-5556	278	4	,	,	PUNCT
ap-5556	278	5	is	be	AUX
ap-5556	278	6	the	the	DET
ap-5556	278	7	constant	constant	ADJ
ap-5556	278	8	of	of	ADP
ap-5556	278	9	integration	integration	NOUN
ap-5556	278	10	is	be	AUX
ap-5556	278	11	to	to	PART
ap-5556	278	12	be	be	AUX
ap-5556	278	13	determined	determine	VERB
ap-5556	278	14	from	from	ADP
ap-5556	278	15	in	in	ADP
ap-5556	278	16	plane	plane	NOUN
ap-5556	278	17	boundary	boundary	ADJ
ap-5556	278	18	conditions	condition	NOUN
ap-5556	278	19	.	.	PUNCT
ap-5556	279	1	maximum	maximum	ADJ
ap-5556	279	2	value	value	NOUN
ap-5556	279	3	of	of	ADP
ap-5556	279	4	phi(t	phi(t	NOUN
ap-5556	279	5	)	)	PUNCT
ap-5556	279	6	coincides	coincide	VERB
ap-5556	279	7	with	with	ADP
ap-5556	279	8	the	the	DET
ap-5556	279	9	maximum	maximum	ADJ
ap-5556	279	10	deflection	deflection	NOUN
ap-5556	279	11	wmax	wmax	VERB
ap-5556	279	12	divided	divide	VERB
ap-5556	279	13	by	by	ADP
ap-5556	279	14	plate	plate	NOUN
ap-5556	279	15	thickness	thickness	NOUN
ap-5556	279	16	h.	h.	PROPN
ap-5556	279	17	the	the	DET
ap-5556	279	18	substitution	substitution	NOUN
ap-5556	279	19	of	of	ADP
ap-5556	279	20	the	the	DET
ap-5556	279	21	expressions	expression	NOUN
ap-5556	279	22	for	for	ADP
ap-5556	279	23	w	w	PROPN
ap-5556	279	24	and	and	CCONJ
ap-5556	279	25	ϕ	ϕ	PROPN
ap-5556	279	26	given	give	VERB
ap-5556	279	27	by	by	ADP
ap-5556	279	28	eqs	eqs	PROPN
ap-5556	279	29	.	.	PUNCT
ap-5556	280	1	(	(	PUNCT
ap-5556	280	2	45	45	NUM
ap-5556	280	3	)	)	PUNCT
ap-5556	280	4	and	and	CCONJ
ap-5556	280	5	(	(	PUNCT
ap-5556	280	6	46	46	NUM
ap-5556	280	7	)	)	PUNCT
ap-5556	280	8	respectively	respectively	ADV
ap-5556	280	9	into	into	ADP
ap-5556	280	10	eq	eq	NOUN
ap-5556	280	11	.	.	PUNCT
ap-5556	281	1	(	(	PUNCT
ap-5556	281	2	44	44	NUM
ap-5556	281	3	)	)	PUNCT
ap-5556	281	4	and	and	CCONJ
ap-5556	281	5	the	the	DET
ap-5556	281	6	application	application	NOUN
ap-5556	281	7	of	of	ADP
ap-5556	281	8	the	the	DET
ap-5556	281	9	galerkin	galerkin	ADJ
ap-5556	281	10	procedure	procedure	NOUN
ap-5556	281	11	in	in	ADP
ap-5556	281	12	the	the	DET
ap-5556	281	13	nonlinear	nonlinear	ADJ
ap-5556	281	14	time	time	NOUN
ap-5556	281	15	differential	differential	ADJ
ap-5556	281	16	equation	equation	NOUN
ap-5556	281	17	obtained	obtain	VERB
ap-5556	281	18	in	in	ADP
ap-5556	281	19	the	the	DET
ap-5556	281	20	form∫	form∫	ADJ
ap-5556	281	21	1	1	NUM
ap-5556	281	22	0	0	NUM
ap-5556	281	23	l′(w,ϕ)wrdr	l′(w,ϕ)wrdr	PROPN
ap-5556	281	24	=	=	SYM
ap-5556	281	25	0	0	PUNCT
ap-5556	281	26	(	(	PUNCT
ap-5556	281	27	47	47	NUM
ap-5556	281	28	)	)	PUNCT
ap-5556	281	29	l′(w,ϕ	l′(w,ϕ	NOUN
ap-5556	281	30	)	)	PUNCT
ap-5556	281	31	=	=	SYM
ap-5556	282	1	(	(	PUNCT
ap-5556	282	2	r3η3	r3η3	X
ap-5556	282	3	+	+	NOUN
ap-5556	282	4	3r2η2	3r2η2	NUM
ap-5556	283	1	+	+	CCONJ
ap-5556	283	2	3ηr+	3ηr+	NUM
ap-5556	283	3	1	1	NUM
ap-5556	283	4	)	)	PUNCT
ap-5556	283	5	(	(	PUNCT
ap-5556	283	6	72c4φ	72c4φ	NUM
ap-5556	283	7	(	(	PUNCT
ap-5556	283	8	t)−	t)−	PROPN
ap-5556	283	9	(	(	PUNCT
ap-5556	283	10	12c4r2	12c4r2	NOUN
ap-5556	283	11	+	+	CCONJ
ap-5556	283	12	2c2	2c2	NUM
ap-5556	283	13	)	)	PUNCT
ap-5556	283	14	φ	φ	PROPN
ap-5556	283	15	(	(	PUNCT
ap-5556	283	16	t	t	PROPN
ap-5556	283	17	)	)	PUNCT
ap-5556	283	18	r2	r2	PROPN
ap-5556	283	19	+	+	CCONJ
ap-5556	283	20	(	(	PUNCT
ap-5556	283	21	4c4r3	4c4r3	NOUN
ap-5556	283	22	+	+	CCONJ
ap-5556	283	23	2c2r	2c2r	NOUN
ap-5556	283	24	)	)	PUNCT
ap-5556	284	1	φ	φ	PROPN
ap-5556	284	2	(	(	PUNCT
ap-5556	284	3	t	t	PROPN
ap-5556	284	4	)	)	PUNCT
ap-5556	284	5	r3	r3	PROPN
ap-5556	284	6	)	)	PUNCT
ap-5556	285	1	+	+	CCONJ
ap-5556	285	2	+	+	CCONJ
ap-5556	285	3	(	(	PUNCT
ap-5556	285	4	3r3η3	3r3η3	NUM
ap-5556	285	5	+	+	NUM
ap-5556	285	6	6rη2	6rη2	NUM
ap-5556	285	7	+	+	CCONJ
ap-5556	285	8	3η	3η	NOUN
ap-5556	285	9	)	)	PUNCT
ap-5556	285	10	(	(	PUNCT
ap-5556	285	11	48c4rφ	48c4rφ	X
ap-5556	285	12	(	(	PUNCT
ap-5556	285	13	t	t	NOUN
ap-5556	285	14	)	)	PUNCT
ap-5556	285	15	+	+	CCONJ
ap-5556	285	16	(	(	PUNCT
ap-5556	285	17	2	2	NUM
ap-5556	285	18	+	+	NUM
ap-5556	285	19	ν	ν	NOUN
ap-5556	285	20	)	)	PUNCT
ap-5556	285	21	(	(	PUNCT
ap-5556	285	22	12c4r2	12c4r2	NOUN
ap-5556	285	23	+	+	CCONJ
ap-5556	285	24	2c2	2c2	NUM
ap-5556	285	25	)	)	PUNCT
ap-5556	285	26	φ	φ	PROPN
ap-5556	285	27	(	(	PUNCT
ap-5556	285	28	t	t	PROPN
ap-5556	285	29	)	)	PUNCT
ap-5556	285	30	r	r	NOUN
ap-5556	285	31	−	−	PROPN
ap-5556	285	32	(	(	PUNCT
ap-5556	285	33	4c4r3	4c4r3	NOUN
ap-5556	285	34	+	+	CCONJ
ap-5556	285	35	2c2r	2c2r	NOUN
ap-5556	285	36	)	)	PUNCT
ap-5556	286	1	φ	φ	PROPN
ap-5556	286	2	(	(	PUNCT
ap-5556	286	3	t	t	PROPN
ap-5556	286	4	)	)	PUNCT
ap-5556	286	5	r2	r2	PROPN
ap-5556	286	6	)	)	PUNCT
ap-5556	287	1	+	+	CCONJ
ap-5556	288	1	+	+	CCONJ
ap-5556	288	2	(	(	PUNCT
ap-5556	288	3	6rη3	6rη3	NUM
ap-5556	288	4	+	+	CCONJ
ap-5556	288	5	6η2)((12c4r2	6η2)((12c4r2	NUM
ap-5556	288	6	+	+	SYM
ap-5556	288	7	2c2	2c2	NUM
ap-5556	288	8	)	)	PUNCT
ap-5556	288	9	φ	φ	PROPN
ap-5556	288	10	(	(	PUNCT
ap-5556	288	11	t	t	PROPN
ap-5556	288	12	)	)	PUNCT
ap-5556	288	13	+	+	NUM
ap-5556	288	14	ν	ν	X
ap-5556	288	15	(	(	PUNCT
ap-5556	288	16	4c4r3	4c4r3	NOUN
ap-5556	288	17	+	+	CCONJ
ap-5556	288	18	2c2r	2c2r	NOUN
ap-5556	288	19	)	)	PUNCT
ap-5556	288	20	φ	φ	PROPN
ap-5556	288	21	(	(	PUNCT
ap-5556	288	22	t	t	PROPN
ap-5556	288	23	)	)	PUNCT
ap-5556	288	24	r	r	NOUN
ap-5556	288	25	)	)	PUNCT
ap-5556	289	1	+	+	CCONJ
ap-5556	289	2	3	3	NUM
ap-5556	289	3	4kp	4kp	NOUN
ap-5556	289	4	(	(	PUNCT
ap-5556	289	5	c4r	c4r	PROPN
ap-5556	289	6	4	4	NUM
ap-5556	289	7	+	+	CCONJ
ap-5556	289	8	c2r	c2r	NOUN
ap-5556	289	9	2	2	NUM
ap-5556	289	10	+	+	CCONJ
ap-5556	289	11	1	1	NUM
ap-5556	289	12	)	)	PUNCT
ap-5556	289	13	3(φ	3(φ	NUM
ap-5556	289	14	(	(	PUNCT
ap-5556	289	15	t))3−	t))3−	NOUN
ap-5556	289	16	−	−	PROPN
ap-5556	290	1	kw	kw	INTJ
ap-5556	290	2	(	(	PUNCT
ap-5556	290	3	c4r	c4r	PROPN
ap-5556	290	4	4	4	NUM
ap-5556	290	5	+	+	CCONJ
ap-5556	290	6	c2r	c2r	NOUN
ap-5556	290	7	2	2	NUM
ap-5556	290	8	+	+	CCONJ
ap-5556	290	9	1	1	NUM
ap-5556	290	10	)	)	PUNCT
ap-5556	290	11	φ	φ	NOUN
ap-5556	290	12	(	(	PUNCT
ap-5556	290	13	t)−	t)−	PROPN
ap-5556	290	14	(	(	PUNCT
ap-5556	290	15	rc3	rc3	NOUN
ap-5556	290	16	−	−	NUM
ap-5556	290	17	1	1	NUM
ap-5556	290	18	6	6	NUM
ap-5556	290	19	(	(	PUNCT
ap-5556	290	20	φ	φ	PROPN
ap-5556	290	21	(	(	PUNCT
ap-5556	290	22	t))2	t))2	PROPN
ap-5556	290	23	r3	r3	PROPN
ap-5556	290	24	(	(	PUNCT
ap-5556	290	25	2c42r4	2c42r4	NUM
ap-5556	290	26	+	+	NUM
ap-5556	290	27	4c2c4r2	4c2c4r2	NUM
ap-5556	290	28	+	+	CCONJ
ap-5556	290	29	3c22	3c22	NUM
ap-5556	290	30	)	)	PUNCT
ap-5556	290	31	)	)	PUNCT
ap-5556	290	32	(	(	PUNCT
ap-5556	290	33	12c4r2	12c4r2	NOUN
ap-5556	290	34	+	+	CCONJ
ap-5556	290	35	2c2	2c2	NUM
ap-5556	290	36	)	)	PUNCT
ap-5556	290	37	φ	φ	PROPN
ap-5556	290	38	(	(	PUNCT
ap-5556	290	39	t	t	PROPN
ap-5556	290	40	)	)	PUNCT
ap-5556	290	41	r	r	NOUN
ap-5556	290	42	−	−	NOUN
ap-5556	290	43	−	−	PROPN
ap-5556	291	1	(	(	PUNCT
ap-5556	291	2	c3	c3	NOUN
ap-5556	291	3	−	−	PROPN
ap-5556	291	4	1	1	NUM
ap-5556	291	5	2	2	NUM
ap-5556	291	6	(	(	PUNCT
ap-5556	291	7	φ	φ	PROPN
ap-5556	291	8	(	(	PUNCT
ap-5556	291	9	t))2	t))2	PROPN
ap-5556	291	10	r2	r2	PROPN
ap-5556	291	11	(	(	PUNCT
ap-5556	291	12	2c42r4	2c42r4	NUM
ap-5556	292	1	+	+	NUM
ap-5556	292	2	4c2c4r2	4c2c4r2	NUM
ap-5556	292	3	+	+	CCONJ
ap-5556	292	4	3c22)−	3c22)−	NUM
ap-5556	292	5	1	1	NUM
ap-5556	292	6	6	6	NUM
ap-5556	292	7	(	(	PUNCT
ap-5556	292	8	φ	φ	PROPN
ap-5556	292	9	(	(	PUNCT
ap-5556	292	10	t))2	t))2	PROPN
ap-5556	292	11	r3	r3	PROPN
ap-5556	292	12	(	(	PUNCT
ap-5556	292	13	8c42r3	8c42r3	NUM
ap-5556	292	14	+	+	X
ap-5556	292	15	8c2c4r	8c2c4r	NUM
ap-5556	292	16	)	)	PUNCT
ap-5556	292	17	)	)	PUNCT
ap-5556	293	1	(	(	PUNCT
ap-5556	293	2	4c4r3	4c4r3	NOUN
ap-5556	293	3	+	+	CCONJ
ap-5556	293	4	2c2r	2c2r	NOUN
ap-5556	293	5	)	)	PUNCT
ap-5556	294	1	φ	φ	PROPN
ap-5556	294	2	(	(	PUNCT
ap-5556	294	3	t	t	PROPN
ap-5556	294	4	)	)	PUNCT
ap-5556	294	5	r	r	NOUN
ap-5556	294	6	+	+	CCONJ
ap-5556	294	7	+	+	CCONJ
ap-5556	294	8	ks	ks	X
ap-5556	294	9	(	(	PUNCT
ap-5556	294	10	12c4r2	12c4r2	PROPN
ap-5556	294	11	+	+	CCONJ
ap-5556	294	12	2c2	2c2	NUM
ap-5556	294	13	)	)	PUNCT
ap-5556	294	14	φ	φ	PROPN
ap-5556	294	15	(	(	PUNCT
ap-5556	294	16	t	t	PROPN
ap-5556	294	17	)	)	PUNCT
ap-5556	295	1	+	+	CCONJ
ap-5556	295	2	ks	ks	PROPN
ap-5556	295	3	(	(	PUNCT
ap-5556	295	4	4c4r3	4c4r3	NOUN
ap-5556	295	5	+	+	CCONJ
ap-5556	295	6	2c2r	2c2r	NOUN
ap-5556	295	7	)	)	PUNCT
ap-5556	296	1	φ	φ	PROPN
ap-5556	296	2	(	(	PUNCT
ap-5556	296	3	t	t	PROPN
ap-5556	296	4	)	)	PUNCT
ap-5556	296	5	r	r	NOUN
ap-5556	296	6	−	−	PROPN
ap-5556	296	7	(	(	PUNCT
ap-5556	296	8	ξr+	ξr+	NOUN
ap-5556	296	9	1	1	NUM
ap-5556	296	10	)	)	PUNCT
ap-5556	296	11	(	(	PUNCT
ap-5556	296	12	ηr+	ηr+	NOUN
ap-5556	296	13	1	1	NUM
ap-5556	296	14	)	)	PUNCT
ap-5556	296	15	(	(	PUNCT
ap-5556	296	16	c4r	c4r	PROPN
ap-5556	296	17	4	4	NUM
ap-5556	296	18	+	+	CCONJ
ap-5556	296	19	c2r	c2r	NOUN
ap-5556	296	20	2	2	NUM
ap-5556	296	21	+	+	CCONJ
ap-5556	296	22	1	1	NUM
ap-5556	296	23	)	)	PUNCT
ap-5556	296	24	d2	d2	NOUN
ap-5556	296	25	dt2φ	dt2φ	PROPN
ap-5556	296	26	(	(	PUNCT
ap-5556	296	27	t	t	PROPN
ap-5556	296	28	)	)	PUNCT
ap-5556	296	29	,	,	PUNCT
ap-5556	296	30	(	(	PUNCT
ap-5556	296	31	48	48	NUM
ap-5556	296	32	)	)	PUNCT
ap-5556	296	33	134	134	NUM
ap-5556	296	34	vol	vol	NOUN
ap-5556	296	35	.	.	PUNCT
ap-5556	297	1	60	60	NUM
ap-5556	297	2	no	no	NOUN
ap-5556	297	3	.	.	PUNCT
ap-5556	298	1	2/2020	2/2020	NUM
ap-5556	298	2	investigation	investigation	NOUN
ap-5556	298	3	of	of	ADP
ap-5556	298	4	the	the	DET
ap-5556	298	5	dynamic	dynamic	ADJ
ap-5556	298	6	behaviour	behaviour	NOUN
ap-5556	298	7	of	of	ADP
ap-5556	298	8	non	non	ADJ
ap-5556	298	9	-	-	ADJ
ap-5556	298	10	uniform	uniform	ADJ
ap-5556	298	11	thickness	thickness	NOUN
ap-5556	298	12	.	.	PUNCT
ap-5556	298	13	.	.	PUNCT
ap-5556	299	1	.	.	PUNCT
ap-5556	300	1	we	we	PRON
ap-5556	300	2	have	have	VERB
ap-5556	300	3	[	[	X
ap-5556	300	4	m	m	X
ap-5556	300	5	]	]	X
ap-5556	300	6	{	{	PUNCT
ap-5556	300	7	d2φ̈s	d2φ̈s	PROPN
ap-5556	300	8	dt2	dt2	PROPN
ap-5556	300	9	}	}	PUNCT
ap-5556	300	10	+	+	PROPN
ap-5556	301	1	[	[	X
ap-5556	301	2	k	k	X
ap-5556	301	3	]	]	X
ap-5556	301	4	{	{	PUNCT
ap-5556	301	5	φs	φs	NOUN
ap-5556	301	6	}	}	PUNCT
ap-5556	301	7	−	−	PROPN
ap-5556	302	1	[	[	X
ap-5556	302	2	v	v	X
ap-5556	302	3	]	]	PUNCT
ap-5556	302	4	{	{	PUNCT
ap-5556	302	5	φ3	φ3	NOUN
ap-5556	302	6	s	s	PART
ap-5556	302	7	}	}	PUNCT
ap-5556	302	8	=	=	PUNCT
ap-5556	302	9	{	{	PUNCT
ap-5556	302	10	0	0	NUM
ap-5556	302	11	}	}	PUNCT
ap-5556	302	12	,	,	PUNCT
ap-5556	302	13	(	(	PUNCT
ap-5556	302	14	49	49	NUM
ap-5556	302	15	)	)	PUNCT
ap-5556	302	16	where	where	SCONJ
ap-5556	302	17	m	m	VERB
ap-5556	302	18	=(	=(	ADJ
ap-5556	302	19	(	(	PUNCT
ap-5556	302	20	(	(	PUNCT
ap-5556	302	21	−11088ξ	−11088ξ	NUM
ap-5556	302	22	−	−	PROPN
ap-5556	302	23	12320	12320	NUM
ap-5556	302	24	)	)	PUNCT
ap-5556	302	25	η	η	PROPN
ap-5556	302	26	−	−	PROPN
ap-5556	302	27	12320ξ	12320ξ	PROPN
ap-5556	302	28	−	−	PROPN
ap-5556	302	29	13860	13860	NUM
ap-5556	302	30	)	)	PUNCT
ap-5556	303	1	c2	c2	PROPN
ap-5556	303	2	+	+	CCONJ
ap-5556	303	3	(	(	PUNCT
ap-5556	303	4	−13860ξ	−13860ξ	NUM
ap-5556	303	5	−	−	NOUN
ap-5556	303	6	15840	15840	NUM
ap-5556	303	7	)	)	PUNCT
ap-5556	303	8	η	η	PROPN
ap-5556	303	9	−	−	PROPN
ap-5556	303	10	15840ξ	15840ξ	NUM
ap-5556	303	11	−	−	PROPN
ap-5556	303	12	18480	18480	NUM
ap-5556	303	13	)	)	PUNCT
ap-5556	303	14	c4	c4	NOUN
ap-5556	303	15	55440	55440	NUM
ap-5556	303	16	+	+	CCONJ
ap-5556	304	1	+	+	CCONJ
ap-5556	304	2	(	(	PUNCT
ap-5556	304	3	(	(	PUNCT
ap-5556	304	4	−6930ξ	−6930ξ	ADJ
ap-5556	304	5	−	−	PROPN
ap-5556	304	6	7920	7920	NUM
ap-5556	304	7	)	)	PUNCT
ap-5556	304	8	η	η	PROPN
ap-5556	304	9	−	−	PROPN
ap-5556	304	10	7920ξ	7920ξ	PROPN
ap-5556	304	11	−	−	ADP
ap-5556	304	12	9240	9240	NUM
ap-5556	304	13	)	)	PUNCT
ap-5556	304	14	c22	c22	NOUN
ap-5556	304	15	55440	55440	NUM
ap-5556	304	16	+	+	CCONJ
ap-5556	304	17	(	(	PUNCT
ap-5556	304	18	(	(	PUNCT
ap-5556	304	19	−18480ξ	−18480ξ	NOUN
ap-5556	304	20	−	−	NOUN
ap-5556	304	21	22176	22176	NUM
ap-5556	304	22	)	)	PUNCT
ap-5556	304	23	η	η	PROPN
ap-5556	304	24	−	−	PROPN
ap-5556	304	25	22176ξ	22176ξ	NUM
ap-5556	304	26	−	−	PROPN
ap-5556	304	27	27720	27720	NUM
ap-5556	304	28	)	)	PUNCT
ap-5556	304	29	c2	c2	PROPN
ap-5556	304	30	55440	55440	NUM
ap-5556	305	1	+	+	PUNCT
ap-5556	305	2	+	+	CCONJ
ap-5556	305	3	(	(	PUNCT
ap-5556	305	4	(	(	PUNCT
ap-5556	305	5	−4620ξ	−4620ξ	NUM
ap-5556	305	6	−	−	PROPN
ap-5556	305	7	5040	5040	NUM
ap-5556	305	8	)	)	PUNCT
ap-5556	305	9	η	η	PROPN
ap-5556	305	10	−	−	PROPN
ap-5556	305	11	5040ξ	5040ξ	PROPN
ap-5556	305	12	−	−	PROPN
ap-5556	305	13	5544	5544	NUM
ap-5556	305	14	)	)	PUNCT
ap-5556	305	15	c24	c24	NOUN
ap-5556	305	16	55440	55440	NUM
ap-5556	305	17	+	+	CCONJ
ap-5556	305	18	(	(	PUNCT
ap-5556	305	19	−13860ξ	−13860ξ	NOUN
ap-5556	305	20	−	−	NOUN
ap-5556	305	21	18480	18480	NUM
ap-5556	305	22	)	)	PUNCT
ap-5556	305	23	η	η	PROPN
ap-5556	305	24	55440	55440	NUM
ap-5556	305	25	−	−	PROPN
ap-5556	305	26	ξ	ξ	SYM
ap-5556	305	27	3	3	NUM
ap-5556	305	28	−	−	NOUN
ap-5556	305	29	1	1	NUM
ap-5556	305	30	2	2	NUM
ap-5556	305	31	,	,	PUNCT
ap-5556	305	32	(	(	PUNCT
ap-5556	305	33	50	50	NUM
ap-5556	305	34	)	)	PUNCT
ap-5556	306	1	k	k	X
ap-5556	307	1	=	=	PUNCT
ap-5556	307	2	−	−	PROPN
ap-5556	307	3	(	(	PUNCT
ap-5556	307	4	(	(	PUNCT
ap-5556	307	5	−	−	PROPN
ap-5556	307	6	188ν	188ν	NUM
ap-5556	307	7	5	5	NUM
ap-5556	307	8	−	−	PROPN
ap-5556	307	9	3196	3196	NUM
ap-5556	307	10	15	15	NUM
ap-5556	307	11	)	)	PUNCT
ap-5556	307	12	η3	η3	NOUN
ap-5556	307	13	+	+	CCONJ
ap-5556	307	14	(	(	PUNCT
ap-5556	307	15	−72ν	−72ν	ADV
ap-5556	307	16	−	−	NUM
ap-5556	307	17	504	504	NUM
ap-5556	307	18	)	)	PUNCT
ap-5556	307	19	η2	η2	NOUN
ap-5556	307	20	+	+	CCONJ
ap-5556	307	21	(	(	PUNCT
ap-5556	307	22	−	−	PROPN
ap-5556	307	23	216ν	216ν	NUM
ap-5556	307	24	7	7	NUM
ap-5556	307	25	−	−	NOUN
ap-5556	307	26	2376	2376	NUM
ap-5556	307	27	7	7	NUM
ap-5556	307	28	)	)	PUNCT
ap-5556	307	29	η	η	PROPN
ap-5556	307	30	+	+	PROPN
ap-5556	307	31	3kw	3kw	NOUN
ap-5556	307	32	5	5	NUM
ap-5556	307	33	+	+	CCONJ
ap-5556	307	34	12c3	12c3	NUM
ap-5556	307	35	−	−	NOUN
ap-5556	307	36	12ks	12ks	NOUN
ap-5556	307	37	−	−	PROPN
ap-5556	307	38	64	64	NUM
ap-5556	307	39	)	)	PUNCT
ap-5556	307	40	6	6	NUM
ap-5556	307	41	c24−	c24−	NOUN
ap-5556	307	42	−	−	PROPN
ap-5556	307	43	(	(	PUNCT
ap-5556	307	44	(	(	PUNCT
ap-5556	307	45	(	(	PUNCT
ap-5556	307	46	−	−	PROPN
ap-5556	307	47	3981	3981	NUM
ap-5556	307	48	14	14	NUM
ap-5556	307	49	−	−	PROPN
ap-5556	307	50	873ν	873ν	NOUN
ap-5556	307	51	14	14	NUM
ap-5556	307	52	)	)	PUNCT
ap-5556	307	53	η3+(−696−120ν)η2+(−	η3+(−696−120ν)η2+(−	NOUN
ap-5556	307	54	2412	2412	NUM
ap-5556	307	55	5	5	NUM
ap-5556	307	56	−	−	NUM
ap-5556	307	57	252ν	252ν	NOUN
ap-5556	307	58	5	5	NUM
ap-5556	307	59	)	)	PUNCT
ap-5556	307	60	η+	η+	X
ap-5556	307	61	3kw	3kw	NOUN
ap-5556	307	62	2	2	NUM
ap-5556	307	63	+20c3−20ks−96	+20c3−20ks−96	NUM
ap-5556	307	64	)	)	PUNCT
ap-5556	307	65	6	6	NUM
ap-5556	307	66	c2	c2	PROPN
ap-5556	307	67	+	+	CCONJ
ap-5556	307	68	(	(	PUNCT
ap-5556	307	69	−	−	PROPN
ap-5556	307	70	324ν	324ν	NOUN
ap-5556	307	71	5	5	NUM
ap-5556	307	72	−	−	PROPN
ap-5556	307	73	1836	1836	NUM
ap-5556	307	74	5	5	NUM
ap-5556	307	75	)	)	PUNCT
ap-5556	307	76	η3	η3	NOUN
ap-5556	307	77	+	+	CCONJ
ap-5556	307	78	(	(	PUNCT
ap-5556	307	79	−144ν	−144ν	VERB
ap-5556	307	80	−	−	PROPN
ap-5556	307	81	1008	1008	NUM
ap-5556	307	82	)	)	PUNCT
ap-5556	307	83	η2	η2	PROPN
ap-5556	307	84	+	+	CCONJ
ap-5556	307	85	(	(	PUNCT
ap-5556	307	86	−72ν	−72ν	ADV
ap-5556	307	87	−	−	NUM
ap-5556	307	88	792	792	NUM
ap-5556	307	89	)	)	PUNCT
ap-5556	307	90	η	η	PROPN
ap-5556	307	91	−	−	PROPN
ap-5556	307	92	192	192	NUM
ap-5556	307	93	+	+	CCONJ
ap-5556	307	94	2kw	2kw	ADJ
ap-5556	307	95	+	+	CCONJ
ap-5556	307	96	24c3	24c3	NUM
ap-5556	307	97	−	−	NUM
ap-5556	307	98	24ks	24ks	NOUN
ap-5556	307	99	)	)	PUNCT
ap-5556	307	100	c4−	c4−	PROPN
ap-5556	307	101	−	−	PROPN
ap-5556	308	1	(	(	PUNCT
ap-5556	308	2	(	(	PUNCT
ap-5556	308	3	−	−	PROPN
ap-5556	308	4	102ν	102ν	NUM
ap-5556	308	5	5	5	NUM
ap-5556	308	6	−	−	NOUN
ap-5556	308	7	102	102	NUM
ap-5556	308	8	5	5	NUM
ap-5556	308	9	)	)	PUNCT
ap-5556	308	10	η3	η3	NOUN
ap-5556	308	11	+	+	CCONJ
ap-5556	308	12	(	(	PUNCT
ap-5556	308	13	−36ν	−36ν	NUM
ap-5556	308	14	−	−	NUM
ap-5556	308	15	36	36	NUM
ap-5556	308	16	)	)	PUNCT
ap-5556	308	17	η2	η2	NOUN
ap-5556	308	18	+	+	CCONJ
ap-5556	309	1	(	(	PUNCT
ap-5556	309	2	−12ν	−12ν	NOUN
ap-5556	309	3	−	−	NOUN
ap-5556	309	4	12	12	NUM
ap-5556	309	5	)	)	PUNCT
ap-5556	309	6	η	η	PROPN
ap-5556	309	7	+	+	PROPN
ap-5556	309	8	6c3	6c3	NUM
ap-5556	309	9	−	−	NOUN
ap-5556	309	10	6ks	6ks	NOUN
ap-5556	309	11	+	+	CCONJ
ap-5556	309	12	kw	kw	INTJ
ap-5556	309	13	)	)	PUNCT
ap-5556	309	14	6	6	NUM
ap-5556	309	15	c2	c2	PROPN
ap-5556	309	16	2−	2−	NUM
ap-5556	309	17	−	−	PROPN
ap-5556	309	18	(	(	PUNCT
ap-5556	309	19	(	(	PUNCT
ap-5556	309	20	−33ν	−33ν	NUM
ap-5556	309	21	−	−	PROPN
ap-5556	309	22	33	33	NUM
ap-5556	309	23	)	)	PUNCT
ap-5556	309	24	η3	η3	NOUN
ap-5556	309	25	+	+	CCONJ
ap-5556	309	26	(	(	PUNCT
ap-5556	309	27	−72ν	−72ν	ADV
ap-5556	309	28	−	−	NUM
ap-5556	309	29	72	72	NUM
ap-5556	309	30	)	)	PUNCT
ap-5556	309	31	η2	η2	NOUN
ap-5556	309	32	+	+	CCONJ
ap-5556	309	33	(	(	PUNCT
ap-5556	309	34	−36ν	−36ν	NUM
ap-5556	309	35	−	−	NUM
ap-5556	309	36	36	36	NUM
ap-5556	309	37	)	)	PUNCT
ap-5556	309	38	η	η	PROPN
ap-5556	309	39	+	+	PROPN
ap-5556	309	40	3kw	3kw	ADJ
ap-5556	309	41	+	+	PUNCT
ap-5556	309	42	12c3	12c3	NUM
ap-5556	309	43	−	−	PROPN
ap-5556	309	44	12ks	12ks	NOUN
ap-5556	309	45	)	)	PUNCT
ap-5556	309	46	6	6	NUM
ap-5556	309	47	c2	c2	PROPN
ap-5556	309	48	−	−	PROPN
ap-5556	309	49	kw	kw	INTJ
ap-5556	309	50	2	2	NUM
ap-5556	309	51	,	,	PUNCT
ap-5556	309	52	(	(	PUNCT
ap-5556	309	53	51	51	NUM
ap-5556	309	54	)	)	PUNCT
ap-5556	309	55	v	v	NOUN
ap-5556	309	56	=	=	SYM
ap-5556	309	57	−	−	PROPN
ap-5556	309	58	(	(	PUNCT
ap-5556	309	59	−kp4	−kp4	PROPN
ap-5556	309	60	−	−	NUM
ap-5556	309	61	40	40	NUM
ap-5556	309	62	7	7	NUM
ap-5556	309	63	)	)	PUNCT
ap-5556	309	64	c44	c44	VERB
ap-5556	309	65	6	6	NUM
ap-5556	309	66	−	−	NOUN
ap-5556	309	67	(	(	PUNCT
ap-5556	309	68	(	(	PUNCT
ap-5556	309	69	−20−	−20−	NUM
ap-5556	309	70	9kp	9kp	ADJ
ap-5556	309	71	8	8	NUM
ap-5556	309	72	)	)	PUNCT
ap-5556	309	73	c2	c2	PROPN
ap-5556	309	74	−	−	PROPN
ap-5556	309	75	9kp	9kp	ADJ
ap-5556	309	76	7	7	NUM
ap-5556	309	77	−	−	NOUN
ap-5556	309	78	8	8	NUM
ap-5556	309	79	)	)	PUNCT
ap-5556	309	80	c34	c34	VERB
ap-5556	309	81	6	6	NUM
ap-5556	309	82	−	−	NOUN
ap-5556	309	83	(	(	PUNCT
ap-5556	309	84	(	(	PUNCT
ap-5556	309	85	−28−	−28−	NUM
ap-5556	309	86	27kp	27kp	NOUN
ap-5556	309	87	14	14	NUM
ap-5556	309	88	)	)	PUNCT
ap-5556	309	89	c22	c22	NOUN
ap-5556	309	90	+	+	CCONJ
ap-5556	309	91	(	(	PUNCT
ap-5556	309	92	−20−	−20−	NUM
ap-5556	309	93	9kp	9kp	ADJ
ap-5556	309	94	2	2	NUM
ap-5556	309	95	)	)	PUNCT
ap-5556	309	96	c2	c2	PROPN
ap-5556	309	97	−	−	PROPN
ap-5556	309	98	27kp	27kp	NOUN
ap-5556	309	99	10	10	NUM
ap-5556	309	100	)	)	PUNCT
ap-5556	309	101	c24	c24	NOUN
ap-5556	309	102	6	6	NUM
ap-5556	309	103	−	−	NOUN
ap-5556	309	104	−	−	PROPN
ap-5556	310	1	(	(	PUNCT
ap-5556	310	2	(	(	PUNCT
ap-5556	310	3	−18−	−18−	PROPN
ap-5556	310	4	3kp	3kp	ADJ
ap-5556	310	5	2	2	X
ap-5556	310	6	)	)	PUNCT
ap-5556	310	7	c32	c32	NOUN
ap-5556	310	8	+	+	CCONJ
ap-5556	310	9	(	(	PUNCT
ap-5556	310	10	−20−	−20−	NUM
ap-5556	310	11	27kp	27kp	NOUN
ap-5556	310	12	5	5	NUM
ap-5556	310	13	)	)	PUNCT
ap-5556	310	14	c22	c22	NOUN
ap-5556	310	15	−	−	PROPN
ap-5556	310	16	27c2kp	27c2kp	ADJ
ap-5556	310	17	4	4	NUM
ap-5556	310	18	−	−	NOUN
ap-5556	310	19	3kp	3kp	NOUN
ap-5556	310	20	)	)	PUNCT
ap-5556	310	21	6	6	NUM
ap-5556	310	22	c4	c4	NOUN
ap-5556	310	23	−	−	PROPN
ap-5556	311	1	(	(	PUNCT
ap-5556	311	2	−	−	PROPN
ap-5556	311	3	9kp	9kp	ADJ
ap-5556	311	4	20	20	NUM
ap-5556	311	5	−	−	NOUN
ap-5556	311	6	4	4	NUM
ap-5556	311	7	)	)	PUNCT
ap-5556	311	8	6	6	NUM
ap-5556	311	9	c42	c42	NOUN
ap-5556	311	10	−	−	PROPN
ap-5556	312	1	(	(	PUNCT
ap-5556	312	2	−	−	PROPN
ap-5556	312	3	9kp	9kp	NOUN
ap-5556	312	4	4	4	NUM
ap-5556	312	5	−	−	NOUN
ap-5556	312	6	6	6	NUM
ap-5556	312	7	)	)	PUNCT
ap-5556	312	8	6	6	NUM
ap-5556	312	9	c32	c32	NOUN
ap-5556	312	10	+	+	CCONJ
ap-5556	312	11	+	+	NUM
ap-5556	312	12	3c22kp	3c22kp	NUM
ap-5556	312	13	4	4	NUM
ap-5556	312	14	+	+	CCONJ
ap-5556	312	15	3c2kp	3c2kp	NUM
ap-5556	312	16	4	4	NUM
ap-5556	312	17	+	+	CCONJ
ap-5556	312	18	3kp	3kp	ADJ
ap-5556	312	19	8	8	NUM
ap-5556	312	20	,	,	PUNCT
ap-5556	312	21	(	(	PUNCT
ap-5556	312	22	52	52	NUM
ap-5556	312	23	)	)	PUNCT
ap-5556	312	24	3.3	3.3	NUM
ap-5556	312	25	.	.	PUNCT
ap-5556	313	1	application	application	NOUN
ap-5556	313	2	of	of	ADP
ap-5556	313	3	galerkin	galerkin	ADJ
ap-5556	313	4	method	method	NOUN
ap-5556	313	5	of	of	ADP
ap-5556	313	6	weighted	weight	VERB
ap-5556	313	7	residual	residual	ADJ
ap-5556	313	8	to	to	PART
ap-5556	313	9	foundation	foundation	VERB
ap-5556	313	10	free	free	ADJ
ap-5556	313	11	surface	surface	NOUN
ap-5556	313	12	considering	consider	VERB
ap-5556	313	13	the	the	DET
ap-5556	313	14	vibration	vibration	NOUN
ap-5556	313	15	influence	influence	NOUN
ap-5556	313	16	of	of	ADP
ap-5556	313	17	foundation	foundation	NOUN
ap-5556	313	18	on	on	ADP
ap-5556	313	19	the	the	DET
ap-5556	313	20	plate	plate	NOUN
ap-5556	313	21	beyond	beyond	ADP
ap-5556	313	22	the	the	DET
ap-5556	313	23	domain	domain	NOUN
ap-5556	313	24	of	of	ADP
ap-5556	313	25	the	the	DET
ap-5556	313	26	plate	plate	NOUN
ap-5556	313	27	.	.	PUNCT
ap-5556	314	1	same	same	ADJ
ap-5556	314	2	procedure	procedure	NOUN
ap-5556	314	3	from	from	ADP
ap-5556	314	4	eq	eq	NOUN
ap-5556	314	5	.	.	PUNCT
ap-5556	315	1	(	(	PUNCT
ap-5556	315	2	43	43	NUM
ap-5556	315	3	)	)	PUNCT
ap-5556	315	4	applies	apply	VERB
ap-5556	315	5	.	.	PUNCT
ap-5556	316	1	the	the	DET
ap-5556	316	2	galerkin	galerkin	ADJ
ap-5556	316	3	procedure	procedure	NOUN
ap-5556	316	4	eq	eq	ADP
ap-5556	316	5	.	.	PUNCT
ap-5556	317	1	(	(	PUNCT
ap-5556	317	2	47	47	NUM
ap-5556	317	3	)	)	PUNCT
ap-5556	317	4	in	in	ADP
ap-5556	317	5	the	the	DET
ap-5556	317	6	nonlinear	nonlinear	ADJ
ap-5556	317	7	time	time	NOUN
ap-5556	317	8	differential	differential	NOUN
ap-5556	317	9	equation	equation	NOUN
ap-5556	317	10	now	now	ADV
ap-5556	317	11	becomes∫	becomes∫	VERB
ap-5556	317	12	a	a	DET
ap-5556	317	13	0	0	NUM
ap-5556	317	14	l(w,ϕ)wrdr−	l(w,ϕ)wrdr−	SYM
ap-5556	317	15	∫	∫	PROPN
ap-5556	317	16	a2	a2	PROPN
ap-5556	317	17	a1	a1	PROPN
ap-5556	317	18	l′(w,ϕ)wrdr	l′(w,ϕ)wrdr	ADV
ap-5556	317	19	=	=	SYM
ap-5556	317	20	0	0	PUNCT
ap-5556	317	21	(	(	PUNCT
ap-5556	317	22	53	53	NUM
ap-5556	317	23	)	)	PUNCT
ap-5556	317	24	where	where	SCONJ
ap-5556	317	25	l(w,ϕ	l(w,ϕ	NOUN
ap-5556	317	26	)	)	PUNCT
ap-5556	317	27	is	be	AUX
ap-5556	317	28	the	the	DET
ap-5556	317	29	foundation	foundation	NOUN
ap-5556	317	30	equation	equation	NOUN
ap-5556	317	31	.	.	PUNCT
ap-5556	318	1	we	we	PRON
ap-5556	318	2	have	have	VERB
ap-5556	318	3	[	[	X
ap-5556	318	4	m	m	X
ap-5556	318	5	]	]	X
ap-5556	318	6	{	{	PUNCT
ap-5556	318	7	d2φ̈s	d2φ̈s	PROPN
ap-5556	318	8	dt2	dt2	PROPN
ap-5556	318	9	}	}	PUNCT
ap-5556	318	10	+	+	PROPN
ap-5556	319	1	[	[	X
ap-5556	319	2	k	k	X
ap-5556	319	3	]	]	X
ap-5556	319	4	{	{	PUNCT
ap-5556	319	5	φs	φs	NOUN
ap-5556	319	6	}	}	PUNCT
ap-5556	319	7	−	−	PROPN
ap-5556	320	1	[	[	X
ap-5556	320	2	v	v	X
ap-5556	320	3	]	]	PUNCT
ap-5556	320	4	{	{	PUNCT
ap-5556	320	5	φ3	φ3	NOUN
ap-5556	320	6	s	s	PART
ap-5556	320	7	}	}	PUNCT
ap-5556	320	8	=	=	PUNCT
ap-5556	320	9	{	{	PUNCT
ap-5556	320	10	0	0	NUM
ap-5556	320	11	}	}	PUNCT
ap-5556	320	12	,	,	PUNCT
ap-5556	320	13	(	(	PUNCT
ap-5556	320	14	54	54	NUM
ap-5556	320	15	)	)	PUNCT
ap-5556	320	16	where	where	SCONJ
ap-5556	320	17	m	m	NOUN
ap-5556	320	18	=	=	VERB
ap-5556	320	19	c4	c4	NOUN
ap-5556	320	20	2	2	NUM
ap-5556	320	21	55440	55440	NUM
ap-5556	320	22	(	(	PUNCT
ap-5556	320	23	−4620ξηa1	−4620ξηa1	NOUN
ap-5556	320	24	12	12	NUM
ap-5556	320	25	+	+	CCONJ
ap-5556	320	26	(	(	PUNCT
ap-5556	320	27	−5040ξ	−5040ξ	NOUN
ap-5556	320	28	−	−	NOUN
ap-5556	320	29	5040η	5040η	NUM
ap-5556	320	30	)	)	PUNCT
ap-5556	320	31	a1	a1	NOUN
ap-5556	320	32	11	11	NUM
ap-5556	320	33	−	−	NOUN
ap-5556	320	34	5544a1	5544a1	NOUN
ap-5556	320	35	10	10	NUM
ap-5556	321	1	+	+	CCONJ
ap-5556	321	2	4620a2	4620a2	NOUN
ap-5556	321	3	10	10	NUM
ap-5556	321	4	(	(	PUNCT
ap-5556	321	5	6	6	NUM
ap-5556	321	6	5	5	NUM
ap-5556	321	7	+	+	CCONJ
ap-5556	321	8	ξηa2	ξηa2	PROPN
ap-5556	321	9	2	2	NUM
ap-5556	321	10	+	+	PROPN
ap-5556	321	11	(	(	PUNCT
ap-5556	321	12	12ξ	12ξ	NOUN
ap-5556	321	13	11	11	NUM
ap-5556	321	14	+	+	NUM
ap-5556	321	15	12η	12η	NOUN
ap-5556	321	16	11	11	NUM
ap-5556	321	17	)	)	PUNCT
ap-5556	321	18	a2	a2	PROPN
ap-5556	321	19	)	)	PUNCT
ap-5556	321	20	)	)	PUNCT
ap-5556	322	1	+	+	CCONJ
ap-5556	322	2	+	+	CCONJ
ap-5556	322	3	c4	c4	ADJ
ap-5556	322	4	55440	55440	NUM
ap-5556	322	5			PROPN
ap-5556	322	6	(	(	PUNCT
ap-5556	322	7	−11088ξηa1	−11088ξηa1	PROPN
ap-5556	322	8	10	10	NUM
ap-5556	322	9	+	+	CCONJ
ap-5556	322	10	(	(	PUNCT
ap-5556	322	11	−12320ξ	−12320ξ	NUM
ap-5556	322	12	−	−	PROPN
ap-5556	322	13	12320η	12320η	NUM
ap-5556	322	14	)	)	PUNCT
ap-5556	322	15	a1	a1	NOUN
ap-5556	322	16	9	9	NUM
ap-5556	322	17	−	−	PROPN
ap-5556	322	18	13860a1	13860a1	NOUN
ap-5556	322	19	8	8	NUM
ap-5556	322	20	+	+	CCONJ
ap-5556	322	21	11088a2	11088a2	NUM
ap-5556	322	22	8	8	NUM
ap-5556	322	23	(	(	PUNCT
ap-5556	322	24	5	5	NUM
ap-5556	322	25	4	4	NUM
ap-5556	322	26	+	+	CCONJ
ap-5556	322	27	ξηa2	ξηa2	PROPN
ap-5556	322	28	2	2	NUM
ap-5556	322	29	+	+	CCONJ
ap-5556	322	30	(	(	PUNCT
ap-5556	322	31	10ξ	10ξ	NOUN
ap-5556	322	32	9	9	NUM
ap-5556	322	33	+	+	CCONJ
ap-5556	322	34	10η	10η	NOUN
ap-5556	322	35	9	9	NUM
ap-5556	322	36	)	)	PUNCT
ap-5556	322	37	a2	a2	PROPN
ap-5556	322	38	)	)	PUNCT
ap-5556	322	39	)	)	PUNCT
ap-5556	323	1	c2	c2	PROPN
ap-5556	323	2	−13860ξηa1	−13860ξηa1	VERB
ap-5556	323	3	8	8	NUM
ap-5556	323	4	+	+	CCONJ
ap-5556	323	5	(	(	PUNCT
ap-5556	323	6	−15840ξ	−15840ξ	NOUN
ap-5556	323	7	−	−	NUM
ap-5556	323	8	15840η	15840η	NUM
ap-5556	323	9	)	)	PUNCT
ap-5556	323	10	a1	a1	NOUN
ap-5556	323	11	7	7	NUM
ap-5556	323	12	−	−	PROPN
ap-5556	323	13	18480a1	18480a1	NUM
ap-5556	323	14	6	6	NUM
ap-5556	323	15	+	+	NUM
ap-5556	323	16	13860a2	13860a2	NUM
ap-5556	323	17	6	6	NUM
ap-5556	323	18	(	(	PUNCT
ap-5556	323	19	4	4	NUM
ap-5556	323	20	3	3	NUM
ap-5556	323	21	+	+	CCONJ
ap-5556	323	22	ξηa2	ξηa2	PROPN
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ap-5556	323	24	+	+	CCONJ
ap-5556	323	25	(	(	PUNCT
ap-5556	323	26	8ξ	8ξ	NUM
ap-5556	323	27	7	7	NUM
ap-5556	323	28	+	+	NUM
ap-5556	323	29	8η	8η	NUM
ap-5556	323	30	7	7	NUM
ap-5556	323	31	)	)	PUNCT
ap-5556	323	32	a2	a2	PROPN
ap-5556	323	33	)	)	PUNCT
ap-5556	323	34	+	+	PROPN
ap-5556	324	1	+	+	CCONJ
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ap-5556	324	3	2	2	NUM
ap-5556	324	4	55440	55440	NUM
ap-5556	324	5	(	(	PUNCT
ap-5556	324	6	−6930ξηa1	−6930ξηa1	NOUN
ap-5556	324	7	8	8	NUM
ap-5556	324	8	+	+	CCONJ
ap-5556	324	9	(	(	PUNCT
ap-5556	324	10	−7920ξ	−7920ξ	NOUN
ap-5556	324	11	−	−	NOUN
ap-5556	324	12	7920η	7920η	NUM
ap-5556	324	13	)	)	PUNCT
ap-5556	324	14	a1	a1	NOUN
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ap-5556	324	16	−	−	NOUN
ap-5556	324	17	9240a1	9240a1	NOUN
ap-5556	324	18	6	6	NUM
ap-5556	325	1	+	+	CCONJ
ap-5556	325	2	6930a2	6930a2	NUM
ap-5556	325	3	6	6	NUM
ap-5556	325	4	(	(	PUNCT
ap-5556	325	5	4	4	NUM
ap-5556	325	6	3	3	NUM
ap-5556	325	7	+	+	CCONJ
ap-5556	325	8	ξηa2	ξηa2	PROPN
ap-5556	325	9	2	2	NUM
ap-5556	325	10	+	+	CCONJ
ap-5556	325	11	(	(	PUNCT
ap-5556	325	12	8ξ	8ξ	NUM
ap-5556	325	13	7	7	NUM
ap-5556	325	14	+	+	NUM
ap-5556	325	15	8η	8η	NUM
ap-5556	325	16	7	7	NUM
ap-5556	325	17	)	)	PUNCT
ap-5556	325	18	a2	a2	PROPN
ap-5556	325	19	)	)	PUNCT
ap-5556	325	20	)	)	PUNCT
ap-5556	326	1	+	+	CCONJ
ap-5556	326	2	+	+	CCONJ
ap-5556	326	3	(	(	PUNCT
ap-5556	326	4	−18480ξηa1	−18480ξηa1	SYM
ap-5556	326	5	6	6	NUM
ap-5556	326	6	+	+	CCONJ
ap-5556	326	7	(	(	PUNCT
ap-5556	326	8	−22176ξ	−22176ξ	NUM
ap-5556	326	9	−	−	PROPN
ap-5556	326	10	22176η	22176η	NUM
ap-5556	326	11	)	)	PUNCT
ap-5556	326	12	a1	a1	NOUN
ap-5556	326	13	5	5	NUM
ap-5556	326	14	−	−	NOUN
ap-5556	326	15	27720a1	27720a1	NUM
ap-5556	326	16	4	4	NUM
ap-5556	326	17	+	+	NUM
ap-5556	326	18	18480a2	18480a2	NUM
ap-5556	326	19	4	4	NUM
ap-5556	326	20	(	(	PUNCT
ap-5556	326	21	3	3	NUM
ap-5556	326	22	2	2	NUM
ap-5556	326	23	+	+	CCONJ
ap-5556	326	24	ξηa2	ξηa2	PROPN
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ap-5556	326	26	+	+	CCONJ
ap-5556	326	27	(	(	PUNCT
ap-5556	326	28	6	6	NUM
ap-5556	326	29	5ξ	5ξ	NOUN
ap-5556	326	30	+	+	CCONJ
ap-5556	326	31	6	6	NUM
ap-5556	326	32	5η	5η	NUM
ap-5556	326	33	)	)	PUNCT
ap-5556	326	34	a2	a2	PROPN
ap-5556	326	35	)	)	PUNCT
ap-5556	326	36	)	)	PUNCT
ap-5556	327	1	c2	c2	PROPN
ap-5556	327	2	55440	55440	NUM
ap-5556	328	1	−	−	NOUN
ap-5556	329	1	−	−	NUM
ap-5556	329	2	1	1	NUM
ap-5556	329	3	4a1	4a1	NUM
ap-5556	329	4	4ηξ	4ηξ	NOUN
ap-5556	329	5	+	+	CCONJ
ap-5556	329	6	(	(	PUNCT
ap-5556	329	7	−18480ξ	−18480ξ	NUM
ap-5556	329	8	−	−	NOUN
ap-5556	329	9	18480η	18480η	NUM
ap-5556	329	10	)	)	PUNCT
ap-5556	329	11	a1	a1	NOUN
ap-5556	329	12	3	3	NUM
ap-5556	329	13	55440	55440	NUM
ap-5556	329	14	−	−	NOUN
ap-5556	329	15	1	1	NUM
ap-5556	329	16	2a1	2a1	NUM
ap-5556	329	17	2	2	NUM
ap-5556	329	18	+	+	CCONJ
ap-5556	329	19	1	1	NUM
ap-5556	329	20	4	4	NUM
ap-5556	329	21	(	(	PUNCT
ap-5556	329	22	ξηa2	ξηa2	NOUN
ap-5556	329	23	2	2	NUM
ap-5556	329	24	+	+	NUM
ap-5556	329	25	2	2	NUM
ap-5556	329	26	+	+	CCONJ
ap-5556	329	27	(	(	PUNCT
ap-5556	329	28	4	4	NUM
ap-5556	329	29	3ξ	3ξ	NOUN
ap-5556	329	30	+	+	CCONJ
ap-5556	329	31	4	4	NUM
ap-5556	329	32	3η	3η	NUM
ap-5556	329	33	)	)	PUNCT
ap-5556	329	34	a2	a2	PROPN
ap-5556	329	35	)	)	PUNCT
ap-5556	329	36	a2	a2	PROPN
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ap-5556	329	38	,	,	PUNCT
ap-5556	329	39	(	(	PUNCT
ap-5556	329	40	55	55	NUM
ap-5556	329	41	)	)	PUNCT
ap-5556	329	42	135	135	NUM
ap-5556	329	43	s.	s.	PROPN
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ap-5556	329	45	,	,	PUNCT
ap-5556	329	46	g.	g.	PROPN
ap-5556	329	47	sobamowo	sobamowo	PROPN
ap-5556	329	48	,	,	PUNCT
ap-5556	329	49	o.	o.	PROPN
ap-5556	329	50	sadiq	sadiq	PROPN
ap-5556	329	51	acta	acta	PROPN
ap-5556	329	52	polytechnica	polytechnica	PROPN
ap-5556	330	1	k	k	PROPN
ap-5556	331	1	=	=	SYM
ap-5556	332	1	1	1	NUM
ap-5556	332	2	24	24	NUM
ap-5556	332	3			NOUN
ap-5556	332	4	(	(	PUNCT
ap-5556	332	5	(	(	PUNCT
ap-5556	332	6	432ν	432ν	PROPN
ap-5556	332	7	5	5	NUM
ap-5556	332	8	+	+	CCONJ
ap-5556	332	9	2448	2448	NUM
ap-5556	332	10	5	5	NUM
ap-5556	332	11	)	)	PUNCT
ap-5556	332	12	η3	η3	NOUN
ap-5556	332	13	−	−	PROPN
ap-5556	332	14	12kw	12kw	ADJ
ap-5556	332	15	5	5	X
ap-5556	332	16	)	)	PUNCT
ap-5556	332	17	a1	a1	NOUN
ap-5556	332	18	10	10	NUM
ap-5556	332	19	+	+	NOUN
ap-5556	332	20	64η3	64η3	NUM
ap-5556	332	21	(	(	PUNCT
ap-5556	332	22	ν	ν	X
ap-5556	332	23	+	+	CCONJ
ap-5556	332	24	17	17	NUM
ap-5556	332	25	3	3	NUM
ap-5556	332	26	)	)	PUNCT
ap-5556	332	27	a1	a1	NOUN
ap-5556	332	28	9	9	NUM
ap-5556	332	29	+	+	CCONJ
ap-5556	332	30	(	(	PUNCT
ap-5556	332	31	(	(	PUNCT
ap-5556	332	32	288ν	288ν	NUM
ap-5556	332	33	+	+	NOUN
ap-5556	332	34	2016	2016	NUM
ap-5556	332	35	)	)	PUNCT
ap-5556	332	36	η2	η2	PROPN
ap-5556	332	37	+	+	CCONJ
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ap-5556	332	39	−	−	PROPN
ap-5556	332	40	48c3	48c3	NUM
ap-5556	332	41	)	)	PUNCT
ap-5556	332	42	a1	a1	NOUN
ap-5556	332	43	8	8	NUM
ap-5556	333	1	+	+	NOUN
ap-5556	333	2	864η(11+ν)a1	864η(11+ν)a1	NUM
ap-5556	333	3	7	7	NUM
ap-5556	333	4	7	7	NUM
ap-5556	333	5	+	+	CCONJ
ap-5556	333	6	256a1	256a1	NUM
ap-5556	333	7	6	6	NUM
ap-5556	333	8	+	+	CCONJ
ap-5556	333	9	(	(	PUNCT
ap-5556	333	10	(	(	PUNCT
ap-5556	333	11	−	−	PROPN
ap-5556	333	12	432ν	432ν	PROPN
ap-5556	333	13	5	5	NUM
ap-5556	333	14	−	−	NOUN
ap-5556	333	15	2448	2448	NUM
ap-5556	333	16	5	5	NUM
ap-5556	333	17	)	)	PUNCT
ap-5556	333	18	η3	η3	NOUN
ap-5556	333	19	+	+	CCONJ
ap-5556	333	20	12kw	12kw	ADJ
ap-5556	333	21	5	5	NUM
ap-5556	333	22	)	)	PUNCT
ap-5556	333	23	a2	a2	PROPN
ap-5556	333	24	10	10	NUM
ap-5556	333	25	−	−	PROPN
ap-5556	333	26	64η3	64η3	NUM
ap-5556	333	27	(	(	PUNCT
ap-5556	333	28	ν	ν	X
ap-5556	333	29	+	+	CCONJ
ap-5556	333	30	17	17	NUM
ap-5556	333	31	3	3	NUM
ap-5556	333	32	)	)	PUNCT
ap-5556	333	33	a2	a2	PROPN
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ap-5556	333	35	+	+	CCONJ
ap-5556	333	36	(	(	PUNCT
ap-5556	333	37	(	(	PUNCT
ap-5556	333	38	−288ν	−288ν	NOUN
ap-5556	333	39	−	−	PROPN
ap-5556	333	40	2016	2016	NUM
ap-5556	333	41	)	)	PUNCT
ap-5556	333	42	η2	η2	NOUN
ap-5556	333	43	−	−	NOUN
ap-5556	333	44	48ks	48ks	NOUN
ap-5556	333	45	+	+	CCONJ
ap-5556	333	46	48c3	48c3	NUM
ap-5556	333	47	)	)	PUNCT
ap-5556	333	48	a2	a2	PROPN
ap-5556	333	49	8	8	NUM
ap-5556	333	50	−	−	NOUN
ap-5556	333	51	864η(11+ν)a2	864η(11+ν)a2	NUM
ap-5556	333	52	7	7	NUM
ap-5556	333	53	7	7	NUM
ap-5556	333	54	−	−	NUM
ap-5556	333	55	256a2	256a2	NUM
ap-5556	333	56	6	6	NUM
ap-5556	333	57	−	−	NUM
ap-5556	333	58	12a8(a2kw−20ks	12a8(a2kw−20ks	NUM
ap-5556	333	59	)	)	PUNCT
ap-5556	333	60	5	5	NUM
ap-5556	333	61			PROPN
ap-5556	333	62	c24	c24	NOUN
ap-5556	333	63	+	+	X
ap-5556	334	1	+	+	CCONJ
ap-5556	334	2	1	1	NUM
ap-5556	334	3	24	24	NUM
ap-5556	334	4	(	(	PUNCT
ap-5556	334	5	(	(	PUNCT
ap-5556	334	6	126ν	126ν	ADJ
ap-5556	334	7	+	+	CCONJ
ap-5556	334	8	630	630	NUM
ap-5556	334	9	)	)	PUNCT
ap-5556	334	10	η3	η3	NOUN
ap-5556	334	11	−	−	PROPN
ap-5556	334	12	6kw	6kw	NOUN
ap-5556	334	13	)	)	PUNCT
ap-5556	334	14	a1	a1	NOUN
ap-5556	334	15	8	8	NUM
ap-5556	334	16	+	+	NOUN
ap-5556	334	17	864η3a1	864η3a1	NOUN
ap-5556	334	18	7	7	NUM
ap-5556	334	19	7	7	NUM
ap-5556	334	20	(	(	PUNCT
ap-5556	334	21	37	37	NUM
ap-5556	334	22	9	9	NUM
ap-5556	334	23	+	+	CCONJ
ap-5556	334	24	ν	ν	NOUN
ap-5556	334	25	)	)	PUNCT
ap-5556	335	1	+	+	CCONJ
ap-5556	335	2	(	(	PUNCT
ap-5556	335	3	(	(	PUNCT
ap-5556	335	4	480ν	480ν	NOUN
ap-5556	335	5	+	+	CCONJ
ap-5556	335	6	2784	2784	NUM
ap-5556	335	7	)	)	PUNCT
ap-5556	335	8	η2	η2	PROPN
ap-5556	335	9	+	+	CCONJ
ap-5556	335	10	80ks	80ks	ADJ
ap-5556	335	11	−	−	PROPN
ap-5556	336	1	80c3	80c3	NUM
ap-5556	336	2	)	)	PUNCT
ap-5556	336	3	a1	a1	NOUN
ap-5556	336	4	6	6	NUM
ap-5556	336	5	+	+	CCONJ
ap-5556	336	6	+	+	NUM
ap-5556	336	7	1008a1	1008a1	NUM
ap-5556	336	8	5η	5η	NOUN
ap-5556	336	9	5	5	NUM
ap-5556	336	10	(	(	PUNCT
ap-5556	336	11	67	67	NUM
ap-5556	336	12	7	7	NUM
ap-5556	336	13	+	+	NUM
ap-5556	336	14	ν	ν	NOUN
ap-5556	336	15	)	)	PUNCT
ap-5556	337	1	+	+	CCONJ
ap-5556	337	2	·	·	PUNCT
ap-5556	337	3	·	·	PUNCT
ap-5556	337	4	·	·	PUNCT
ap-5556	337	5	,	,	PUNCT
ap-5556	337	6	(	(	PUNCT
ap-5556	337	7	56	56	NUM
ap-5556	337	8	)	)	PUNCT
ap-5556	337	9	v	v	NOUN
ap-5556	337	10	=	=	SYM
ap-5556	337	11	1	1	NUM
ap-5556	337	12	24	24	NUM
ap-5556	337	13	(	(	PUNCT
ap-5556	337	14	−160a2	−160a2	PROPN
ap-5556	337	15	14	14	NUM
ap-5556	337	16	7	7	NUM
ap-5556	337	17	+	+	CCONJ
ap-5556	337	18	160a1	160a1	NUM
ap-5556	337	19	14	14	NUM
ap-5556	337	20	7	7	NUM
ap-5556	337	21	+	+	CCONJ
ap-5556	337	22	kpa1	kpa1	PROPN
ap-5556	337	23	18	18	NUM
ap-5556	337	24	−	−	PROPN
ap-5556	337	25	kpa2	kpa2	NOUN
ap-5556	337	26	18	18	NUM
ap-5556	337	27	+	+	NUM
ap-5556	337	28	a18kp	a18kp	PROPN
ap-5556	337	29	)	)	PUNCT
ap-5556	337	30	c4	c4	VERB
ap-5556	337	31	4	4	NUM
ap-5556	337	32	+	+	CCONJ
ap-5556	337	33	1	1	NUM
ap-5556	337	34	24	24	NUM
ap-5556	337	35	(	(	PUNCT
ap-5556	337	36	6a12kp	6a12kp	NUM
ap-5556	337	37	+	+	CCONJ
ap-5556	337	38	6a1	6a1	NUM
ap-5556	337	39	12kp	12kp	ADJ
ap-5556	337	40	−6a2	−6a2	NUM
ap-5556	337	41	12kp	12kp	ADJ
ap-5556	337	42	+	+	CCONJ
ap-5556	337	43	72a1	72a1	NUM
ap-5556	337	44	8	8	NUM
ap-5556	337	45	−	−	NUM
ap-5556	337	46	72a2	72a2	NUM
ap-5556	337	47	8	8	NUM
ap-5556	337	48	)	)	PUNCT
ap-5556	337	49	c32	c32	NOUN
ap-5556	337	50	+	+	CCONJ
ap-5556	338	1	+	+	CCONJ
ap-5556	338	2	1	1	NUM
ap-5556	338	3	24	24	NUM
ap-5556	338	4	(	(	PUNCT
ap-5556	338	5	(	(	PUNCT
ap-5556	338	6	80a1	80a1	NUM
ap-5556	338	7	12	12	NUM
ap-5556	338	8	−	−	NOUN
ap-5556	338	9	80a2	80a2	NUM
ap-5556	338	10	12	12	NUM
ap-5556	338	11	−	−	NUM
ap-5556	338	12	9	9	NUM
ap-5556	338	13	2kpa2	2kpa2	NUM
ap-5556	338	14	16	16	NUM
ap-5556	338	15	+	+	CCONJ
ap-5556	338	16	9	9	NUM
ap-5556	338	17	2kpa1	2kpa1	NUM
ap-5556	338	18	16	16	NUM
ap-5556	338	19	+	+	CCONJ
ap-5556	338	20	9	9	NUM
ap-5556	338	21	2a	2a	NUM
ap-5556	338	22	16kp	16kp	NOUN
ap-5556	338	23	)	)	PUNCT
ap-5556	339	1	c2	c2	PROPN
ap-5556	339	2	−	−	PROPN
ap-5556	340	1	32a2	32a2	NUM
ap-5556	340	2	10	10	NUM
ap-5556	341	1	+	+	CCONJ
ap-5556	341	2	32a1	32a1	NUM
ap-5556	341	3	10	10	NUM
ap-5556	341	4	+	+	NUM
ap-5556	341	5	36a1	36a1	NUM
ap-5556	341	6	14kp	14kp	NOUN
ap-5556	341	7	7	7	NUM
ap-5556	341	8	−	−	PROPN
ap-5556	342	1	36a2	36a2	NUM
ap-5556	342	2	14kp	14kp	NOUN
ap-5556	342	3	7	7	NUM
ap-5556	343	1	+	+	CCONJ
ap-5556	343	2	36a14kp	36a14kp	NUM
ap-5556	343	3	7	7	NUM
ap-5556	343	4	)	)	PUNCT
ap-5556	343	5	c34	c34	NOUN
ap-5556	343	6	+	+	CCONJ
ap-5556	343	7	+	+	CCONJ
ap-5556	343	8	1	1	NUM
ap-5556	343	9	24	24	NUM
ap-5556	343	10			PROPN
ap-5556	343	11	(	(	PUNCT
ap-5556	343	12	112a1	112a1	NUM
ap-5556	343	13	10	10	NUM
ap-5556	343	14	−	−	NUM
ap-5556	343	15	112a2	112a2	NUM
ap-5556	343	16	10	10	NUM
ap-5556	343	17	+	+	NUM
ap-5556	343	18	54a14kp	54a14kp	NUM
ap-5556	343	19	7	7	NUM
ap-5556	343	20	−	−	NUM
ap-5556	343	21	54a2	54a2	NUM
ap-5556	343	22	14kp	14kp	NOUN
ap-5556	343	23	7	7	NUM
ap-5556	343	24	+	+	CCONJ
ap-5556	343	25	54a1	54a1	NUM
ap-5556	343	26	14kp	14kp	NOUN
ap-5556	343	27	7	7	X
ap-5556	343	28	)	)	PUNCT
ap-5556	343	29	c2	c2	PROPN
ap-5556	343	30	2	2	NUM
ap-5556	343	31	+	+	CCONJ
ap-5556	343	32	(	(	PUNCT
ap-5556	343	33	18a12kp	18a12kp	PROPN
ap-5556	343	34	+	+	PROPN
ap-5556	343	35	18a1	18a1	NUM
ap-5556	343	36	12kp	12kp	ADJ
ap-5556	343	37	−	−	PROPN
ap-5556	343	38	18a2	18a2	NUM
ap-5556	343	39	12kp	12kp	ADJ
ap-5556	343	40	+	+	CCONJ
ap-5556	343	41	80a1	80a1	NUM
ap-5556	343	42	8	8	NUM
ap-5556	343	43	−	−	PROPN
ap-5556	343	44	80a2	80a2	NUM
ap-5556	343	45	8)	8)	NUM
ap-5556	343	46	c2	c2	PROPN
ap-5556	343	47	+	+	CCONJ
ap-5556	343	48	54kp(a10+a1	54kp(a10+a1	NUM
ap-5556	343	49	10−a2	10−a2	NUM
ap-5556	343	50	10	10	NUM
ap-5556	343	51	)	)	PUNCT
ap-5556	343	52	5	5	NUM
ap-5556	343	53			NOUN
ap-5556	343	54	c4	c4	NOUN
ap-5556	343	55	2	2	NUM
ap-5556	343	56	+	+	CCONJ
ap-5556	343	57	80a1	80a1	NUM
ap-5556	343	58	6	6	NUM
ap-5556	343	59	−	−	NOUN
ap-5556	343	60	80a2	80a2	NUM
ap-5556	343	61	6	6	NUM
ap-5556	343	62	+	+	CCONJ
ap-5556	343	63	·	·	PUNCT
ap-5556	343	64	·	·	PUNCT
ap-5556	343	65	·	·	PUNCT
ap-5556	343	66	,	,	PUNCT
ap-5556	343	67	(	(	PUNCT
ap-5556	343	68	57	57	NUM
ap-5556	343	69	)	)	PUNCT
ap-5556	343	70	3.4	3.4	NUM
ap-5556	343	71	.	.	PUNCT
ap-5556	344	1	the	the	DET
ap-5556	344	2	stress	stress	NOUN
ap-5556	344	3	-	-	PUNCT
ap-5556	344	4	deflection	deflection	NOUN
ap-5556	344	5	expression	expression	NOUN
ap-5556	344	6	is	be	AUX
ap-5556	344	7	[	[	X
ap-5556	344	8	12	12	NUM
ap-5556	344	9	]	]	PUNCT
ap-5556	344	10	to	to	PART
ap-5556	344	11	determine	determine	VERB
ap-5556	344	12	the	the	DET
ap-5556	344	13	radial	radial	ADJ
ap-5556	344	14	and	and	CCONJ
ap-5556	344	15	circumferential	circumferential	ADJ
ap-5556	344	16	stress	stress	NOUN
ap-5556	344	17	for	for	ADP
ap-5556	344	18	the	the	DET
ap-5556	344	19	circular	circular	ADJ
ap-5556	344	20	plate	plate	NOUN
ap-5556	344	21	,	,	PUNCT
ap-5556	344	22	the	the	DET
ap-5556	344	23	following	follow	VERB
ap-5556	344	24	dimensionless	dimensionless	NOUN
ap-5556	344	25	expression	expression	NOUN
ap-5556	344	26	may	may	AUX
ap-5556	344	27	be	be	AUX
ap-5556	344	28	used	use	VERB
ap-5556	344	29	σrr	σrr	NOUN
ap-5556	345	1	=	=	SYM
ap-5556	345	2	e	e	X
ap-5556	345	3	(	(	PUNCT
ap-5556	345	4	r	r	NOUN
ap-5556	345	5	,	,	PUNCT
ap-5556	345	6	z	z	NOUN
ap-5556	345	7	)	)	PUNCT
ap-5556	345	8	z	z	NOUN
ap-5556	345	9	1−	1−	NUM
ap-5556	345	10	ν2	ν2	NOUN
ap-5556	345	11	(	(	PUNCT
ap-5556	345	12	d2w	d2w	PROPN
ap-5556	345	13	dr2	dr2	PROPN
ap-5556	345	14	+	+	CCONJ
ap-5556	345	15	ν	ν	X
ap-5556	345	16	r	r	PROPN
ap-5556	345	17	dw	dw	PROPN
ap-5556	345	18	dr	dr	PROPN
ap-5556	345	19	)	)	PUNCT
ap-5556	345	20	,	,	PUNCT
ap-5556	345	21	σθθ	σθθ	X
ap-5556	345	22	=	=	SYM
ap-5556	345	23	e	e	X
ap-5556	345	24	(	(	PUNCT
ap-5556	345	25	r	r	NOUN
ap-5556	345	26	,	,	PUNCT
ap-5556	345	27	z	z	NOUN
ap-5556	345	28	)	)	PUNCT
ap-5556	345	29	z	z	NOUN
ap-5556	345	30	1−	1−	NUM
ap-5556	345	31	ν2	ν2	NOUN
ap-5556	345	32	(	(	PUNCT
ap-5556	345	33	1	1	NUM
ap-5556	345	34	r	r	NOUN
ap-5556	345	35	dw	dw	PROPN
ap-5556	345	36	dr	dr	PROPN
ap-5556	345	37	+	+	PROPN
ap-5556	345	38	ν	ν	PROPN
ap-5556	345	39	d2w	d2w	PROPN
ap-5556	345	40	dr2	dr2	PROPN
ap-5556	345	41	)	)	PUNCT
ap-5556	345	42	,	,	PUNCT
ap-5556	345	43	(	(	PUNCT
ap-5556	345	44	58	58	X
ap-5556	345	45	)	)	PUNCT
ap-5556	345	46	where	where	SCONJ
ap-5556	345	47	e	e	NOUN
ap-5556	345	48	is	be	AUX
ap-5556	345	49	the	the	DET
ap-5556	345	50	young	young	ADJ
ap-5556	345	51	modulus	modulus	NOUN
ap-5556	345	52	of	of	ADP
ap-5556	345	53	the	the	DET
ap-5556	345	54	circular	circular	ADJ
ap-5556	345	55	plate	plate	NOUN
ap-5556	345	56	,	,	PUNCT
ap-5556	345	57	ν	ν	X
ap-5556	345	58	is	be	AUX
ap-5556	345	59	the	the	DET
ap-5556	345	60	poisons	poison	NOUN
ap-5556	345	61	ratio	ratio	NOUN
ap-5556	345	62	and	and	CCONJ
ap-5556	345	63	z	z	NOUN
ap-5556	345	64	is	be	AUX
ap-5556	345	65	the	the	DET
ap-5556	345	66	mid	mid	NOUN
ap-5556	345	67	-	-	NOUN
ap-5556	345	68	plane	plane	NOUN
ap-5556	345	69	of	of	ADP
ap-5556	345	70	the	the	DET
ap-5556	345	71	plate	plate	NOUN
ap-5556	345	72	.	.	PUNCT
ap-5556	346	1	4	4	X
ap-5556	346	2	.	.	NOUN
ap-5556	346	3	results	result	NOUN
ap-5556	346	4	and	and	CCONJ
ap-5556	346	5	discussion	discussion	VERB
ap-5556	346	6	the	the	DET
ap-5556	346	7	analytical	analytical	ADJ
ap-5556	346	8	solution	solution	NOUN
ap-5556	346	9	of	of	ADP
ap-5556	346	10	the	the	DET
ap-5556	346	11	governing	govern	VERB
ap-5556	346	12	equation	equation	NOUN
ap-5556	346	13	of	of	ADP
ap-5556	346	14	motion	motion	NOUN
ap-5556	346	15	of	of	ADP
ap-5556	346	16	the	the	DET
ap-5556	346	17	circular	circular	ADJ
ap-5556	346	18	plate	plate	NOUN
ap-5556	346	19	under	under	ADP
ap-5556	346	20	various	various	ADJ
ap-5556	346	21	boundary	boundary	ADJ
ap-5556	346	22	conditions	condition	NOUN
ap-5556	346	23	with	with	ADP
ap-5556	346	24	galerkin	galerkin	ADJ
ap-5556	346	25	method	method	NOUN
ap-5556	346	26	of	of	ADP
ap-5556	346	27	weighted	weight	VERB
ap-5556	346	28	residual	residual	ADJ
ap-5556	346	29	is	be	AUX
ap-5556	346	30	hereby	hereby	ADV
ap-5556	346	31	presented	present	VERB
ap-5556	346	32	.	.	PUNCT
ap-5556	347	1	the	the	DET
ap-5556	347	2	material	material	NOUN
ap-5556	347	3	properties	property	NOUN
ap-5556	347	4	for	for	ADP
ap-5556	347	5	the	the	DET
ap-5556	347	6	thin	thin	ADJ
ap-5556	347	7	non	non	ADJ
ap-5556	347	8	-	-	ADJ
ap-5556	347	9	uniform	uniform	ADJ
ap-5556	347	10	thickness	thickness	NOUN
ap-5556	347	11	,	,	PUNCT
ap-5556	347	12	non	non	ADJ
ap-5556	347	13	-	-	ADJ
ap-5556	347	14	homogenous	homogenous	ADJ
ap-5556	347	15	wrought	wrought	ADJ
ap-5556	347	16	iron	iron	NOUN
ap-5556	347	17	circular	circular	ADJ
ap-5556	347	18	plate	plate	NOUN
ap-5556	347	19	used	use	VERB
ap-5556	347	20	are	be	AUX
ap-5556	347	21	e	e	X
ap-5556	347	22	=	=	SYM
ap-5556	347	23	200gpa	200gpa	NUM
ap-5556	347	24	material	material	NOUN
ap-5556	347	25	density	density	NOUN
ap-5556	347	26	rho	rho	NOUN
ap-5556	347	27	=	=	NOUN
ap-5556	347	28	7.70	7.70	NUM
ap-5556	347	29	g	g	NOUN
ap-5556	347	30	/	/	SYM
ap-5556	347	31	m3	m3	PROPN
ap-5556	347	32	thickness	thickness	NOUN
ap-5556	347	33	of	of	ADP
ap-5556	347	34	the	the	DET
ap-5556	347	35	plate	plate	NOUN
ap-5556	347	36	h	h	NOUN
ap-5556	347	37	=	=	NOUN
ap-5556	347	38	0.01	0.01	NUM
ap-5556	347	39	m	m	NOUN
ap-5556	347	40	and	and	CCONJ
ap-5556	347	41	poisson	poisson	PROPN
ap-5556	347	42	’s	’s	PART
ap-5556	347	43	ratio	ratio	NOUN
ap-5556	347	44	ν	ν	NOUN
ap-5556	347	45	=	=	PUNCT
ap-5556	347	46	0.3	0.3	NUM
ap-5556	347	47	respectively	respectively	ADV
ap-5556	347	48	.	.	PUNCT
ap-5556	348	1	to	to	PART
ap-5556	348	2	validate	validate	VERB
ap-5556	348	3	the	the	DET
ap-5556	348	4	analytical	analytical	ADJ
ap-5556	348	5	solution	solution	NOUN
ap-5556	348	6	of	of	ADP
ap-5556	348	7	free	free	ADJ
ap-5556	348	8	vibration	vibration	NOUN
ap-5556	348	9	of	of	ADP
ap-5556	348	10	non	non	ADJ
ap-5556	348	11	-	-	ADJ
ap-5556	348	12	homogenous	homogenous	ADJ
ap-5556	348	13	and	and	CCONJ
ap-5556	348	14	varying	vary	VERB
ap-5556	348	15	thickness	thickness	NOUN
ap-5556	348	16	circular	circular	ADJ
ap-5556	348	17	plate	plate	NOUN
ap-5556	348	18	resting	rest	VERB
ap-5556	348	19	on	on	ADP
ap-5556	348	20	winkler	winkler	NOUN
ap-5556	348	21	and	and	CCONJ
ap-5556	348	22	pasternak	pasternak	PROPN
ap-5556	348	23	foundations	foundation	NOUN
ap-5556	348	24	using	use	VERB
ap-5556	348	25	galerkin	galerkin	ADJ
ap-5556	348	26	method	method	NOUN
ap-5556	348	27	of	of	ADP
ap-5556	348	28	weighted	weight	VERB
ap-5556	348	29	residuals	residual	NOUN
ap-5556	348	30	,	,	PUNCT
ap-5556	348	31	application	application	NOUN
ap-5556	348	32	is	be	AUX
ap-5556	348	33	made	make	VERB
ap-5556	348	34	to	to	ADP
ap-5556	348	35	the	the	DET
ap-5556	348	36	numeric	numeric	ADJ
ap-5556	348	37	data	datum	NOUN
ap-5556	348	38	stated	state	VERB
ap-5556	348	39	above	above	ADP
ap-5556	348	40	given	give	VERB
ap-5556	348	41	by	by	ADP
ap-5556	348	42	[	[	PUNCT
ap-5556	348	43	9	9	NUM
ap-5556	348	44	]	]	PUNCT
ap-5556	348	45	.	.	PUNCT
ap-5556	349	1	galerkin	galerkin	PROPN
ap-5556	349	2	method	method	NOUN
ap-5556	349	3	of	of	ADP
ap-5556	349	4	weighted	weight	VERB
ap-5556	349	5	residual	residual	ADJ
ap-5556	349	6	determined	determine	VERB
ap-5556	349	7	the	the	DET
ap-5556	349	8	natural	natural	ADJ
ap-5556	349	9	frequency	frequency	NOUN
ap-5556	349	10	in	in	ADP
ap-5556	349	11	dimensionless	dimensionless	NOUN
ap-5556	349	12	form	form	NOUN
ap-5556	349	13	.	.	PUNCT
ap-5556	350	1	however	however	ADV
ap-5556	350	2	,	,	PUNCT
ap-5556	350	3	the	the	DET
ap-5556	350	4	accuracy	accuracy	NOUN
ap-5556	350	5	of	of	ADP
ap-5556	350	6	the	the	DET
ap-5556	350	7	analytical	analytical	ADJ
ap-5556	350	8	solutions	solution	NOUN
ap-5556	350	9	obtained	obtain	VERB
ap-5556	350	10	are	be	AUX
ap-5556	350	11	compared	compare	VERB
ap-5556	350	12	with	with	ADP
ap-5556	350	13	results	result	NOUN
ap-5556	350	14	as	as	SCONJ
ap-5556	350	15	reported	report	VERB
ap-5556	350	16	in	in	ADP
ap-5556	350	17	the	the	DET
ap-5556	350	18	literature	literature	NOUN
ap-5556	350	19	[	[	X
ap-5556	350	20	25	25	NUM
ap-5556	350	21	]	]	PUNCT
ap-5556	350	22	and	and	CCONJ
ap-5556	350	23	confirm	confirm	VERB
ap-5556	350	24	in	in	ADP
ap-5556	350	25	good	good	ADJ
ap-5556	350	26	harmony	harmony	NOUN
ap-5556	350	27	along	along	ADP
ap-5556	350	28	the	the	DET
ap-5556	350	29	entire	entire	ADJ
ap-5556	350	30	values	value	NOUN
ap-5556	350	31	under	under	ADP
ap-5556	350	32	different	different	ADJ
ap-5556	350	33	boundary	boundary	ADJ
ap-5556	350	34	conditions	condition	NOUN
ap-5556	350	35	and	and	CCONJ
ap-5556	350	36	presented	present	VERB
ap-5556	350	37	in	in	ADP
ap-5556	350	38	table	table	NOUN
ap-5556	350	39	1	1	NUM
ap-5556	350	40	and	and	CCONJ
ap-5556	350	41	2	2	NUM
ap-5556	350	42	.	.	PUNCT
ap-5556	351	1	since	since	SCONJ
ap-5556	351	2	the	the	DET
ap-5556	351	3	dimensionless	dimensionless	NOUN
ap-5556	351	4	value	value	NOUN
ap-5556	351	5	of	of	ADP
ap-5556	351	6	the	the	DET
ap-5556	351	7	natural	natural	ADJ
ap-5556	351	8	frequency	frequency	NOUN
ap-5556	351	9	ω	ω	NOUN
ap-5556	351	10	is	be	AUX
ap-5556	351	11	obtained	obtain	VERB
ap-5556	351	12	in	in	ADP
ap-5556	351	13	the	the	DET
ap-5556	351	14	analysis	analysis	NOUN
ap-5556	351	15	,	,	PUNCT
ap-5556	351	16	the	the	DET
ap-5556	351	17	results	result	NOUN
ap-5556	351	18	are	be	AUX
ap-5556	351	19	valid	valid	ADJ
ap-5556	351	20	for	for	SCONJ
ap-5556	351	21	all	all	DET
ap-5556	351	22	thickness	thickness	NOUN
ap-5556	351	23	to	to	PART
ap-5556	351	24	radius	radius	NOUN
ap-5556	351	25	ratio	ratio	NOUN
ap-5556	351	26	.	.	PUNCT
ap-5556	352	1	also	also	ADV
ap-5556	352	2	,	,	PUNCT
ap-5556	352	3	the	the	DET
ap-5556	352	4	parametric	parametric	ADJ
ap-5556	352	5	studies	study	NOUN
ap-5556	352	6	of	of	ADP
ap-5556	352	7	the	the	DET
ap-5556	352	8	controlling	control	VERB
ap-5556	352	9	factors	factor	NOUN
ap-5556	352	10	are	be	AUX
ap-5556	352	11	presented	present	VERB
ap-5556	352	12	in	in	ADP
ap-5556	352	13	graphical	graphical	ADJ
ap-5556	352	14	form	form	NOUN
ap-5556	352	15	.	.	PUNCT
ap-5556	353	1	the	the	DET
ap-5556	353	2	solution	solution	NOUN
ap-5556	353	3	of	of	ADP
ap-5556	353	4	the	the	DET
ap-5556	353	5	galerkin	galerkin	ADJ
ap-5556	353	6	method	method	NOUN
ap-5556	353	7	of	of	ADP
ap-5556	353	8	weighted	weight	VERB
ap-5556	353	9	residual	residual	ADJ
ap-5556	353	10	is	be	AUX
ap-5556	353	11	a	a	DET
ap-5556	353	12	determinant	determinant	NOUN
ap-5556	353	13	of	of	ADP
ap-5556	353	14	order	order	NOUN
ap-5556	353	15	of	of	ADP
ap-5556	353	16	the	the	DET
ap-5556	353	17	assumed	assume	VERB
ap-5556	353	18	polynomial	polynomial	PROPN
ap-5556	353	19	chosen	choose	VERB
ap-5556	353	20	.	.	PUNCT
ap-5556	354	1	in	in	ADP
ap-5556	354	2	this	this	DET
ap-5556	354	3	study	study	NOUN
ap-5556	354	4	,	,	PUNCT
ap-5556	354	5	fifth	fifth	ADJ
ap-5556	354	6	-	-	PUNCT
ap-5556	354	7	order	order	NOUN
ap-5556	354	8	polynomial	polynomial	NOUN
ap-5556	354	9	is	be	AUX
ap-5556	354	10	chosen	choose	VERB
ap-5556	354	11	for	for	ADP
ap-5556	354	12	the	the	DET
ap-5556	354	13	fourth	fourth	ADJ
ap-5556	354	14	-	-	PUNCT
ap-5556	354	15	order	order	NOUN
ap-5556	354	16	governing	govern	VERB
ap-5556	354	17	differential	differential	ADJ
ap-5556	354	18	equation	equation	NOUN
ap-5556	354	19	.	.	PUNCT
ap-5556	355	1	the	the	DET
ap-5556	355	2	analytical	analytical	ADJ
ap-5556	355	3	solutions	solution	NOUN
ap-5556	355	4	obtained	obtain	VERB
ap-5556	355	5	though	though	ADV
ap-5556	355	6	are	be	AUX
ap-5556	355	7	limited	limit	VERB
ap-5556	355	8	to	to	ADP
ap-5556	355	9	the	the	DET
ap-5556	355	10	first	first	ADJ
ap-5556	355	11	two	two	NUM
ap-5556	355	12	natural	natural	ADJ
ap-5556	355	13	frequencies	frequency	NOUN
ap-5556	355	14	but	but	CCONJ
ap-5556	355	15	,	,	PUNCT
ap-5556	355	16	it	it	PRON
ap-5556	355	17	is	be	AUX
ap-5556	355	18	good	good	ADJ
ap-5556	355	19	enough	enough	ADV
ap-5556	355	20	to	to	PART
ap-5556	355	21	predict	predict	VERB
ap-5556	355	22	the	the	DET
ap-5556	355	23	behaviour	behaviour	NOUN
ap-5556	355	24	of	of	ADP
ap-5556	355	25	the	the	DET
ap-5556	355	26	plate	plate	NOUN
ap-5556	355	27	and	and	CCONJ
ap-5556	355	28	the	the	DET
ap-5556	355	29	results	result	NOUN
ap-5556	355	30	are	be	AUX
ap-5556	355	31	observed	observe	VERB
ap-5556	355	32	similar	similar	ADJ
ap-5556	355	33	to	to	ADP
ap-5556	355	34	results	result	NOUN
ap-5556	355	35	reported	report	VERB
ap-5556	355	36	in	in	ADP
ap-5556	355	37	the	the	DET
ap-5556	355	38	literature	literature	NOUN
ap-5556	356	1	[	[	X
ap-5556	356	2	27	27	NUM
ap-5556	356	3	]	]	PUNCT
ap-5556	356	4	.	.	PUNCT
ap-5556	357	1	moreso	moreso	PROPN
ap-5556	357	2	,	,	PUNCT
ap-5556	357	3	comparing	compare	VERB
ap-5556	357	4	the	the	DET
ap-5556	357	5	results	result	NOUN
ap-5556	357	6	obtained	obtain	VERB
ap-5556	357	7	using	use	VERB
ap-5556	357	8	galerkin	galerkin	ADJ
ap-5556	357	9	method	method	NOUN
ap-5556	357	10	of	of	ADP
ap-5556	357	11	weighted	weight	VERB
ap-5556	357	12	residual	residual	ADJ
ap-5556	357	13	to	to	ADP
ap-5556	357	14	results	result	NOUN
ap-5556	357	15	obtained	obtain	VERB
ap-5556	357	16	in	in	ADP
ap-5556	357	17	[	[	X
ap-5556	357	18	9	9	NUM
ap-5556	357	19	]	]	PUNCT
ap-5556	357	20	using	use	VERB
ap-5556	357	21	dtm	dtm	PROPN
ap-5556	357	22	.	.	PUNCT
ap-5556	358	1	the	the	DET
ap-5556	358	2	dtm	dtm	PROPN
ap-5556	358	3	results	result	NOUN
ap-5556	358	4	converged	converge	VERB
ap-5556	358	5	at	at	ADP
ap-5556	358	6	ten	ten	NUM
ap-5556	358	7	iterations	iteration	NOUN
ap-5556	358	8	while	while	SCONJ
ap-5556	358	9	the	the	DET
ap-5556	358	10	present	present	ADJ
ap-5556	358	11	method	method	NOUN
ap-5556	358	12	predict	predict	VERB
ap-5556	358	13	almost	almost	ADV
ap-5556	358	14	the	the	DET
ap-5556	358	15	same	same	ADJ
ap-5556	358	16	results	result	NOUN
ap-5556	358	17	with	with	ADP
ap-5556	358	18	fewer	few	ADJ
ap-5556	358	19	steps	step	NOUN
ap-5556	358	20	of	of	ADP
ap-5556	358	21	calculation	calculation	NOUN
ap-5556	358	22	using	use	VERB
ap-5556	358	23	the	the	DET
ap-5556	358	24	assumed	assume	VERB
ap-5556	358	25	polynomial	polynomial	NOUN
ap-5556	358	26	.	.	PUNCT
ap-5556	359	1	it	it	PRON
ap-5556	359	2	is	be	AUX
ap-5556	359	3	also	also	ADV
ap-5556	359	4	observed	observe	VERB
ap-5556	359	5	that	that	SCONJ
ap-5556	359	6	to	to	PART
ap-5556	359	7	obtain	obtain	VERB
ap-5556	359	8	a	a	DET
ap-5556	359	9	higher	high	ADJ
ap-5556	359	10	node	node	NOUN
ap-5556	359	11	of	of	ADP
ap-5556	359	12	natural	natural	ADJ
ap-5556	359	13	frequencies	frequency	NOUN
ap-5556	359	14	there	there	PRON
ap-5556	359	15	is	be	VERB
ap-5556	359	16	a	a	DET
ap-5556	359	17	need	need	NOUN
ap-5556	359	18	to	to	PART
ap-5556	359	19	increase	increase	VERB
ap-5556	359	20	the	the	DET
ap-5556	359	21	order	order	NOUN
ap-5556	359	22	of	of	ADP
ap-5556	359	23	the	the	DET
ap-5556	359	24	assumed	assume	VERB
ap-5556	359	25	polynomial	polynomial	NOUN
ap-5556	359	26	chosen	choose	VERB
ap-5556	359	27	at	at	ADP
ap-5556	359	28	the	the	DET
ap-5556	359	29	beginning	beginning	NOUN
ap-5556	359	30	of	of	ADP
ap-5556	359	31	the	the	DET
ap-5556	359	32	analysis	analysis	NOUN
ap-5556	359	33	.	.	PUNCT
ap-5556	360	1	results	result	NOUN
ap-5556	360	2	are	be	AUX
ap-5556	360	3	shown	show	VERB
ap-5556	360	4	in	in	ADP
ap-5556	360	5	tables	table	NOUN
ap-5556	360	6	1	1	NUM
ap-5556	360	7	and	and	CCONJ
ap-5556	360	8	2	2	NUM
ap-5556	360	9	illustrate	illustrate	VERB
ap-5556	360	10	the	the	DET
ap-5556	360	11	fundamental	fundamental	ADJ
ap-5556	360	12	natural	natural	ADJ
ap-5556	360	13	frequencies	frequency	NOUN
ap-5556	360	14	obtained	obtain	VERB
ap-5556	360	15	which	which	PRON
ap-5556	360	16	gives	give	VERB
ap-5556	360	17	a	a	DET
ap-5556	360	18	reasonable	reasonable	ADJ
ap-5556	360	19	prediction	prediction	NOUN
ap-5556	360	20	of	of	ADP
ap-5556	360	21	the	the	DET
ap-5556	360	22	circular	circular	ADJ
ap-5556	360	23	plate	plate	NOUN
ap-5556	360	24	behaviour	behaviour	NOUN
ap-5556	360	25	with	with	ADP
ap-5556	360	26	minimal	minimal	ADJ
ap-5556	360	27	iterations	iteration	NOUN
ap-5556	360	28	.	.	PUNCT
ap-5556	361	1	tables	table	NOUN
ap-5556	361	2	1	1	NUM
ap-5556	361	3	and	and	CCONJ
ap-5556	361	4	2	2	NUM
ap-5556	361	5	also	also	ADV
ap-5556	361	6	show	show	VERB
ap-5556	361	7	comparisons	comparison	NOUN
ap-5556	361	8	of	of	ADP
ap-5556	361	9	results	result	NOUN
ap-5556	361	10	for	for	ADP
ap-5556	361	11	the	the	DET
ap-5556	361	12	symmetric	symmetric	ADJ
ap-5556	361	13	and	and	CCONJ
ap-5556	361	14	asymmetric	asymmetric	ADJ
ap-5556	361	15	case	case	NOUN
ap-5556	361	16	of	of	ADP
ap-5556	361	17	the	the	DET
ap-5556	361	18	present	present	ADJ
ap-5556	361	19	study	study	NOUN
ap-5556	361	20	with	with	ADP
ap-5556	361	21	reported	report	VERB
ap-5556	361	22	work	work	NOUN
ap-5556	361	23	in	in	ADP
ap-5556	361	24	the	the	DET
ap-5556	361	25	literature	literature	NOUN
ap-5556	361	26	review	review	NOUN
ap-5556	361	27	.	.	PUNCT
ap-5556	362	1	there	there	PRON
ap-5556	362	2	is	be	VERB
ap-5556	362	3	good	good	ADJ
ap-5556	362	4	agreement	agreement	NOUN
ap-5556	362	5	between	between	ADP
ap-5556	362	6	the	the	DET
ap-5556	362	7	present	present	ADJ
ap-5556	362	8	study	study	NOUN
ap-5556	362	9	and	and	CCONJ
ap-5556	362	10	the	the	DET
ap-5556	362	11	results	result	NOUN
ap-5556	362	12	reported	report	VERB
ap-5556	362	13	[	[	X
ap-5556	362	14	27	27	NUM
ap-5556	362	15	]	]	PUNCT
ap-5556	362	16	,	,	PUNCT
ap-5556	362	17	hence	hence	ADV
ap-5556	362	18	,	,	PUNCT
ap-5556	362	19	it	it	PRON
ap-5556	362	20	can	can	AUX
ap-5556	362	21	be	be	AUX
ap-5556	362	22	concluded	conclude	VERB
ap-5556	362	23	that	that	SCONJ
ap-5556	362	24	the	the	DET
ap-5556	362	25	present	present	ADJ
ap-5556	362	26	procedure	procedure	NOUN
ap-5556	362	27	is	be	AUX
ap-5556	362	28	very	very	ADV
ap-5556	362	29	effective	effective	ADJ
ap-5556	362	30	.	.	PUNCT
ap-5556	363	1	fig	fig	NOUN
ap-5556	363	2	.	.	PUNCT
ap-5556	364	1	3	3	NUM
ap-5556	364	2	shows	show	VERB
ap-5556	364	3	comparison	comparison	NOUN
ap-5556	364	4	of	of	ADP
ap-5556	364	5	linear	linear	ADJ
ap-5556	364	6	and	and	CCONJ
ap-5556	364	7	nonlinear	nonlinear	ADJ
ap-5556	364	8	vibration	vibration	NOUN
ap-5556	364	9	.	.	PUNCT
ap-5556	365	1	it	it	PRON
ap-5556	365	2	is	be	AUX
ap-5556	365	3	observed	observe	VERB
ap-5556	365	4	that	that	SCONJ
ap-5556	365	5	the	the	DET
ap-5556	365	6	discrepancy	discrepancy	NOUN
ap-5556	365	7	become	become	VERB
ap-5556	365	8	significant	significant	ADJ
ap-5556	365	9	as	as	ADP
ap-5556	365	10	the	the	DET
ap-5556	365	11	vibration	vibration	NOUN
ap-5556	365	12	increases	increase	NOUN
ap-5556	365	13	.	.	PUNCT
ap-5556	366	1	136	136	NUM
ap-5556	366	2	vol	vol	NOUN
ap-5556	366	3	.	.	PUNCT
ap-5556	367	1	60	60	NUM
ap-5556	367	2	no	no	NOUN
ap-5556	367	3	.	.	PUNCT
ap-5556	368	1	2/2020	2/2020	NUM
ap-5556	368	2	investigation	investigation	NOUN
ap-5556	368	3	of	of	ADP
ap-5556	368	4	the	the	DET
ap-5556	368	5	dynamic	dynamic	ADJ
ap-5556	368	6	behaviour	behaviour	NOUN
ap-5556	368	7	of	of	ADP
ap-5556	368	8	non	non	ADJ
ap-5556	368	9	-	-	ADJ
ap-5556	368	10	uniform	uniform	ADJ
ap-5556	368	11	thickness	thickness	NOUN
ap-5556	368	12	.	.	PUNCT
ap-5556	368	13	.	.	PUNCT
ap-5556	368	14	.	.	PUNCT
ap-5556	369	1	edge	edge	NOUN
ap-5556	369	2	condition	condition	NOUN
ap-5556	369	3	/	/	SYM
ap-5556	369	4	dimensionless	dimensionless	NOUN
ap-5556	369	5	natural	natural	ADJ
ap-5556	369	6	frequency	frequency	NOUN
ap-5556	369	7	ω	ω	NOUN
ap-5556	369	8	simply	simply	ADV
ap-5556	369	9	supported	support	VERB
ap-5556	369	10	[	[	PUNCT
ap-5556	369	11	9	9	NUM
ap-5556	369	12	,	,	PUNCT
ap-5556	369	13	12	12	NUM
ap-5556	369	14	,	,	PUNCT
ap-5556	369	15	27	27	NUM
ap-5556	369	16	]	]	SYM
ap-5556	369	17	4.93511	4.93511	NUM
ap-5556	369	18	present	present	ADJ
ap-5556	369	19	4.95717	4.95717	NUM
ap-5556	369	20	%	%	NOUN
ap-5556	369	21	diff	diff	NOUN
ap-5556	369	22	2.206	2.206	NUM
ap-5556	369	23	clamped	clamp	VERB
ap-5556	369	24	[	[	PUNCT
ap-5556	369	25	9	9	NUM
ap-5556	369	26	,	,	PUNCT
ap-5556	369	27	12	12	NUM
ap-5556	369	28	,	,	PUNCT
ap-5556	369	29	27	27	NUM
ap-5556	369	30	]	]	SYM
ap-5556	369	31	10.21582	10.21582	NUM
ap-5556	369	32	present	present	ADJ
ap-5556	369	33	10.28571	10.28571	NUM
ap-5556	369	34	%	%	NOUN
ap-5556	369	35	diff	diff	NOUN
ap-5556	369	36	6.989	6.989	NUM
ap-5556	369	37	free	free	ADJ
ap-5556	369	38	[	[	X
ap-5556	369	39	9	9	NUM
ap-5556	369	40	,	,	PUNCT
ap-5556	369	41	12	12	NUM
ap-5556	369	42	,	,	PUNCT
ap-5556	369	43	27	27	NUM
ap-5556	369	44	]	]	SYM
ap-5556	369	45	9.00312	9.00312	NUM
ap-5556	369	46	present	present	ADJ
ap-5556	369	47	9.03381	9.03381	NUM
ap-5556	369	48	%	%	NOUN
ap-5556	369	49	diff	diff	NOUN
ap-5556	369	50	3.069	3.069	NUM
ap-5556	369	51	table	table	NOUN
ap-5556	369	52	1	1	NUM
ap-5556	369	53	.	.	PUNCT
ap-5556	369	54	validation	validation	NOUN
ap-5556	369	55	of	of	ADP
ap-5556	369	56	fundamental	fundamental	ADJ
ap-5556	369	57	natural	natural	ADJ
ap-5556	369	58	frequency	frequency	NOUN
ap-5556	369	59	for	for	ADP
ap-5556	369	60	symmetric	symmetric	ADJ
ap-5556	369	61	condition	condition	NOUN
ap-5556	369	62	.	.	PUNCT
ap-5556	370	1	edge	edge	NOUN
ap-5556	370	2	condition	condition	NOUN
ap-5556	370	3	/	/	SYM
ap-5556	370	4	dimensionless	dimensionless	NOUN
ap-5556	370	5	natural	natural	ADJ
ap-5556	370	6	frequency	frequency	NOUN
ap-5556	370	7	ω	ω	NOUN
ap-5556	370	8	simply	simply	ADV
ap-5556	370	9	supported	support	VERB
ap-5556	370	10	[	[	PUNCT
ap-5556	370	11	9	9	NUM
ap-5556	370	12	,	,	PUNCT
ap-5556	370	13	27	27	NUM
ap-5556	370	14	,	,	PUNCT
ap-5556	370	15	29	29	NUM
ap-5556	370	16	]	]	SYM
ap-5556	370	17	13.94	13.94	NUM
ap-5556	370	18	present	present	NOUN
ap-5556	370	19	13.9	13.9	NUM
ap-5556	370	20	%	%	NOUN
ap-5556	370	21	diff	diff	NOUN
ap-5556	370	22	4	4	NUM
ap-5556	370	23	clamped	clamp	VERB
ap-5556	370	24	[	[	PUNCT
ap-5556	370	25	9	9	NUM
ap-5556	370	26	,	,	PUNCT
ap-5556	370	27	27	27	NUM
ap-5556	370	28	,	,	PUNCT
ap-5556	370	29	29	29	NUM
ap-5556	370	30	]	]	SYM
ap-5556	370	31	21.26	21.26	NUM
ap-5556	370	32	present	present	ADJ
ap-5556	370	33	21.26	21.26	NUM
ap-5556	370	34	%	%	NOUN
ap-5556	370	35	diff	diff	NOUN
ap-5556	370	36	0	0	PUNCT
ap-5556	370	37	free	free	ADJ
ap-5556	370	38	[	[	X
ap-5556	370	39	9	9	NUM
ap-5556	370	40	,	,	PUNCT
ap-5556	370	41	27	27	NUM
ap-5556	370	42	,	,	PUNCT
ap-5556	370	43	29	29	NUM
ap-5556	370	44	]	]	PUNCT
ap-5556	370	45	20.475	20.475	NUM
ap-5556	370	46	present	present	ADJ
ap-5556	370	47	20.556	20.556	NUM
ap-5556	370	48	%	%	NOUN
ap-5556	370	49	diff	diff	NOUN
ap-5556	370	50	8.1	8.1	NUM
ap-5556	370	51	table	table	NOUN
ap-5556	370	52	2	2	NUM
ap-5556	370	53	.	.	PUNCT
ap-5556	370	54	validation	validation	NOUN
ap-5556	370	55	of	of	ADP
ap-5556	370	56	fundamental	fundamental	ADJ
ap-5556	370	57	natural	natural	ADJ
ap-5556	370	58	frequency	frequency	NOUN
ap-5556	370	59	for	for	ADP
ap-5556	370	60	axisymmetric	axisymmetric	ADJ
ap-5556	370	61	condition	condition	NOUN
ap-5556	370	62	.	.	PUNCT
ap-5556	371	1	figure	figure	NOUN
ap-5556	371	2	3	3	NUM
ap-5556	371	3	.	.	NOUN
ap-5556	371	4	comparison	comparison	NOUN
ap-5556	371	5	of	of	ADP
ap-5556	371	6	dflection	dflection	NOUN
ap-5556	371	7	time	time	NOUN
ap-5556	371	8	history	history	NOUN
ap-5556	371	9	for	for	ADP
ap-5556	371	10	the	the	DET
ap-5556	371	11	linear	linear	ADJ
ap-5556	371	12	and	and	CCONJ
ap-5556	371	13	nonlinear	nonlinear	ADJ
ap-5556	371	14	circular	circular	ADJ
ap-5556	371	15	plate	plate	NOUN
ap-5556	371	16	.	.	PUNCT
ap-5556	372	1	137	137	NUM
ap-5556	372	2	s.	s.	PROPN
ap-5556	372	3	salawu	salawu	PROPN
ap-5556	372	4	,	,	PUNCT
ap-5556	372	5	g.	g.	PROPN
ap-5556	372	6	sobamowo	sobamowo	PROPN
ap-5556	372	7	,	,	PUNCT
ap-5556	372	8	o.	o.	PROPN
ap-5556	372	9	sadiq	sadiq	PROPN
ap-5556	372	10	acta	acta	PROPN
ap-5556	372	11	polytechnica	polytechnica	PROPN
ap-5556	372	12	4.1	4.1	NUM
ap-5556	372	13	.	.	PUNCT
ap-5556	373	1	investigation	investigation	NOUN
ap-5556	373	2	of	of	ADP
ap-5556	373	3	plate	plate	NOUN
ap-5556	373	4	behaviour	behaviour	NOUN
ap-5556	373	5	on	on	ADP
ap-5556	373	6	foundation	foundation	NOUN
ap-5556	373	7	to	to	PART
ap-5556	373	8	further	far	ADV
ap-5556	373	9	investigate	investigate	VERB
ap-5556	373	10	the	the	DET
ap-5556	373	11	effect	effect	NOUN
ap-5556	373	12	of	of	ADP
ap-5556	373	13	plate	plate	NOUN
ap-5556	373	14	resting	rest	VERB
ap-5556	373	15	on	on	ADP
ap-5556	373	16	elastic	elastic	ADJ
ap-5556	373	17	foundation	foundation	NOUN
ap-5556	373	18	for	for	ADP
ap-5556	373	19	free	free	ADJ
ap-5556	373	20	vibration	vibration	NOUN
ap-5556	373	21	of	of	ADP
ap-5556	373	22	non	non	ADJ
ap-5556	373	23	-	-	ADJ
ap-5556	373	24	homogenous	homogenous	ADJ
ap-5556	373	25	varying	vary	VERB
ap-5556	373	26	thickness	thickness	NOUN
ap-5556	373	27	circular	circular	ADJ
ap-5556	373	28	plate	plate	NOUN
ap-5556	373	29	,	,	PUNCT
ap-5556	373	30	the	the	DET
ap-5556	373	31	natural	natural	ADJ
ap-5556	373	32	frequencies	frequency	NOUN
ap-5556	373	33	of	of	ADP
ap-5556	373	34	the	the	DET
ap-5556	373	35	solutions	solution	NOUN
ap-5556	373	36	obtained	obtain	VERB
ap-5556	373	37	are	be	AUX
ap-5556	373	38	plotted	plot	VERB
ap-5556	373	39	against	against	ADP
ap-5556	373	40	the	the	DET
ap-5556	373	41	foundation	foundation	NOUN
ap-5556	373	42	parameter	parameter	PROPN
ap-5556	373	43	variation	variation	NOUN
ap-5556	373	44	.	.	PUNCT
ap-5556	374	1	the	the	DET
ap-5556	374	2	results	result	NOUN
ap-5556	374	3	are	be	AUX
ap-5556	374	4	obtained	obtain	VERB
ap-5556	374	5	by	by	ADP
ap-5556	374	6	setting	set	VERB
ap-5556	374	7	m	m	PROPN
ap-5556	374	8	=	=	SYM
ap-5556	374	9	1	1	NUM
ap-5556	374	10	and	and	CCONJ
ap-5556	374	11	m	m	PROPN
ap-5556	374	12	=	=	NOUN
ap-5556	374	13	0	0	NUM
ap-5556	374	14	respectively	respectively	ADV
ap-5556	374	15	as	as	SCONJ
ap-5556	374	16	shown	show	VERB
ap-5556	374	17	in	in	ADP
ap-5556	374	18	figs	fig	NOUN
ap-5556	374	19	.	.	PUNCT
ap-5556	375	1	4	4	NUM
ap-5556	375	2	and	and	CCONJ
ap-5556	375	3	5	5	NUM
ap-5556	375	4	.	.	PUNCT
ap-5556	375	5	figs	fig	NOUN
ap-5556	375	6	.	.	PUNCT
ap-5556	376	1	4	4	NUM
ap-5556	376	2	and	and	CCONJ
ap-5556	376	3	5	5	NUM
ap-5556	376	4	show	show	VERB
ap-5556	376	5	that	that	SCONJ
ap-5556	376	6	as	as	ADP
ap-5556	376	7	the	the	DET
ap-5556	376	8	elastic	elastic	ADJ
ap-5556	376	9	foundation	foundation	NOUN
ap-5556	376	10	parameter	parameter	NOUN
ap-5556	376	11	(	(	PUNCT
ap-5556	376	12	shear	shear	NOUN
ap-5556	376	13	stiffness	stiffness	NOUN
ap-5556	376	14	)	)	PUNCT
ap-5556	376	15	of	of	ADP
ap-5556	376	16	the	the	DET
ap-5556	376	17	elastic	elastic	ADJ
ap-5556	376	18	medium	medium	ADJ
ap-5556	376	19	increases	increase	NOUN
ap-5556	376	20	,	,	PUNCT
ap-5556	376	21	the	the	DET
ap-5556	376	22	natural	natural	ADJ
ap-5556	376	23	frequency	frequency	NOUN
ap-5556	376	24	of	of	ADP
ap-5556	376	25	vibration	vibration	NOUN
ap-5556	376	26	of	of	ADP
ap-5556	376	27	the	the	DET
ap-5556	376	28	uniform	uniform	ADJ
ap-5556	376	29	thickness	thickness	NOUN
ap-5556	376	30	,	,	PUNCT
ap-5556	376	31	homogenous	homogenous	ADJ
ap-5556	376	32	circular	circular	ADJ
ap-5556	376	33	plate	plate	NOUN
ap-5556	376	34	increases	increase	NOUN
ap-5556	376	35	.	.	PUNCT
ap-5556	377	1	this	this	PRON
ap-5556	377	2	as	as	ADP
ap-5556	377	3	a	a	DET
ap-5556	377	4	result	result	NOUN
ap-5556	377	5	of	of	ADP
ap-5556	377	6	the	the	DET
ap-5556	377	7	increased	increase	VERB
ap-5556	377	8	value	value	NOUN
ap-5556	377	9	of	of	ADP
ap-5556	377	10	the	the	DET
ap-5556	377	11	elastic	elastic	ADJ
ap-5556	377	12	medium	medium	NOUN
ap-5556	377	13	stiffness	stiffness	NOUN
ap-5556	377	14	,	,	PUNCT
ap-5556	377	15	the	the	DET
ap-5556	377	16	shear	shear	NOUN
ap-5556	377	17	stiffness	stiffness	NOUN
ap-5556	377	18	makes	make	VERB
ap-5556	377	19	the	the	DET
ap-5556	377	20	uniform	uniform	ADJ
ap-5556	377	21	circular	circular	ADJ
ap-5556	377	22	plate	plate	NOUN
ap-5556	377	23	stronger	strong	ADJ
ap-5556	377	24	/	/	SYM
ap-5556	377	25	stiffer	stiff	ADJ
ap-5556	377	26	and	and	CCONJ
ap-5556	377	27	vibrates	vibrate	VERB
ap-5556	377	28	at	at	ADP
ap-5556	377	29	higher	high	ADJ
ap-5556	377	30	natural	natural	ADJ
ap-5556	377	31	frequency	frequency	NOUN
ap-5556	377	32	.	.	PUNCT
ap-5556	378	1	although	although	SCONJ
ap-5556	378	2	,	,	PUNCT
ap-5556	378	3	it	it	PRON
ap-5556	378	4	a	a	DET
ap-5556	378	5	known	know	VERB
ap-5556	378	6	character	character	NOUN
ap-5556	378	7	of	of	ADP
ap-5556	378	8	the	the	DET
ap-5556	378	9	plate	plate	NOUN
ap-5556	378	10	to	to	PART
ap-5556	378	11	be	be	AUX
ap-5556	378	12	affected	affect	VERB
ap-5556	378	13	by	by	ADP
ap-5556	378	14	the	the	DET
ap-5556	378	15	characteristic	characteristic	NOUN
ap-5556	378	16	of	of	ADP
ap-5556	378	17	the	the	DET
ap-5556	378	18	elastic	elastic	ADJ
ap-5556	378	19	foundation	foundation	NOUN
ap-5556	378	20	.	.	PUNCT
ap-5556	379	1	the	the	DET
ap-5556	379	2	same	same	ADJ
ap-5556	379	3	effect	effect	NOUN
ap-5556	379	4	is	be	AUX
ap-5556	379	5	also	also	ADV
ap-5556	379	6	observed	observe	VERB
ap-5556	379	7	under	under	ADP
ap-5556	379	8	the	the	DET
ap-5556	379	9	pasternak	pasternak	PROPN
ap-5556	379	10	foundation	foundation	PROPN
ap-5556	379	11	and	and	CCONJ
ap-5556	379	12	when	when	SCONJ
ap-5556	379	13	the	the	DET
ap-5556	379	14	plate	plate	NOUN
ap-5556	379	15	is	be	AUX
ap-5556	379	16	resting	rest	VERB
ap-5556	379	17	on	on	ADP
ap-5556	379	18	combined	combine	VERB
ap-5556	379	19	winkler	winkler	NOUN
ap-5556	379	20	and	and	CCONJ
ap-5556	379	21	pasternak	pasternak	PROPN
ap-5556	379	22	foundations	foundations	PROPN
ap-5556	379	23	.	.	PUNCT
ap-5556	380	1	fig	fig	NOUN
ap-5556	380	2	.	.	PUNCT
ap-5556	381	1	6	6	NUM
ap-5556	381	2	depicts	depict	VERB
ap-5556	381	3	the	the	DET
ap-5556	381	4	influence	influence	NOUN
ap-5556	381	5	of	of	ADP
ap-5556	381	6	varying	vary	VERB
ap-5556	381	7	nonlinear	nonlinear	ADJ
ap-5556	381	8	foundation	foundation	NOUN
ap-5556	381	9	on	on	ADP
ap-5556	381	10	vibration	vibration	NOUN
ap-5556	381	11	of	of	ADP
ap-5556	381	12	the	the	DET
ap-5556	381	13	circular	circular	ADJ
ap-5556	381	14	plate	plate	NOUN
ap-5556	381	15	,	,	PUNCT
ap-5556	381	16	it	it	PRON
ap-5556	381	17	is	be	AUX
ap-5556	381	18	observed	observe	VERB
ap-5556	381	19	that	that	SCONJ
ap-5556	381	20	increasing	increase	VERB
ap-5556	381	21	combine	combine	PROPN
ap-5556	381	22	foundation	foundation	NOUN
ap-5556	381	23	attenuate	attenuate	VERB
ap-5556	381	24	the	the	DET
ap-5556	381	25	deflection	deflection	NOUN
ap-5556	381	26	of	of	ADP
ap-5556	381	27	the	the	DET
ap-5556	381	28	circular	circular	ADJ
ap-5556	381	29	plate	plate	NOUN
ap-5556	381	30	.	.	PUNCT
ap-5556	382	1	fig	fig	NOUN
ap-5556	382	2	.	.	PUNCT
ap-5556	383	1	7	7	NUM
ap-5556	383	2	illustrates	illustrate	VERB
ap-5556	383	3	the	the	DET
ap-5556	383	4	influence	influence	NOUN
ap-5556	383	5	of	of	ADP
ap-5556	383	6	foundation	foundation	NOUN
ap-5556	383	7	free	free	ADJ
ap-5556	383	8	surface	surface	NOUN
ap-5556	383	9	on	on	ADP
ap-5556	383	10	the	the	DET
ap-5556	383	11	vibration	vibration	NOUN
ap-5556	383	12	characteristic	characteristic	NOUN
ap-5556	383	13	of	of	ADP
ap-5556	383	14	the	the	DET
ap-5556	383	15	circular	circular	ADJ
ap-5556	383	16	plate	plate	NOUN
ap-5556	383	17	.	.	PUNCT
ap-5556	384	1	conversely	conversely	ADV
ap-5556	384	2	,	,	PUNCT
ap-5556	384	3	it	it	PRON
ap-5556	384	4	is	be	AUX
ap-5556	384	5	observed	observe	VERB
ap-5556	384	6	that	that	SCONJ
ap-5556	384	7	as	as	ADP
ap-5556	384	8	the	the	DET
ap-5556	384	9	stiffness	stiffness	NOUN
ap-5556	384	10	of	of	ADP
ap-5556	384	11	free	free	ADJ
ap-5556	384	12	foundation	foundation	NOUN
ap-5556	384	13	increases	increase	NOUN
ap-5556	384	14	,	,	PUNCT
ap-5556	384	15	the	the	DET
ap-5556	384	16	nonlinear	nonlinear	ADJ
ap-5556	384	17	vibration	vibration	NOUN
ap-5556	384	18	frequency	frequency	NOUN
ap-5556	384	19	ratio	ratio	NOUN
ap-5556	384	20	increases	increase	NOUN
ap-5556	384	21	.	.	PUNCT
ap-5556	385	1	figure	figure	VERB
ap-5556	385	2	4	4	NUM
ap-5556	385	3	.	.	PUNCT
ap-5556	386	1	influence	influence	NOUN
ap-5556	386	2	of	of	ADP
ap-5556	386	3	pasternak	pasternak	PROPN
ap-5556	386	4	foundation	foundation	PROPN
ap-5556	386	5	variation	variation	NOUN
ap-5556	386	6	on	on	ADP
ap-5556	386	7	symmetric	symmetric	ADJ
ap-5556	386	8	and	and	CCONJ
ap-5556	386	9	asymmetric	asymmetric	ADJ
ap-5556	386	10	case	case	NOUN
ap-5556	386	11	.	.	PUNCT
ap-5556	387	1	figure	figure	NOUN
ap-5556	387	2	5	5	NUM
ap-5556	387	3	.	.	PUNCT
ap-5556	388	1	influence	influence	NOUN
ap-5556	388	2	of	of	ADP
ap-5556	388	3	winkler	winkler	PROPN
ap-5556	388	4	foundation	foundation	PROPN
ap-5556	388	5	variation	variation	NOUN
ap-5556	388	6	on	on	ADP
ap-5556	388	7	symmetric	symmetric	ADJ
ap-5556	388	8	and	and	CCONJ
ap-5556	388	9	asymmetric	asymmetric	ADJ
ap-5556	388	10	case	case	NOUN
ap-5556	388	11	.	.	PUNCT
ap-5556	389	1	figure	figure	NOUN
ap-5556	389	2	6	6	NUM
ap-5556	389	3	.	.	PUNCT
ap-5556	390	1	influence	influence	NOUN
ap-5556	390	2	of	of	ADP
ap-5556	390	3	elastic	elastic	ADJ
ap-5556	390	4	foundation	foundation	NOUN
ap-5556	390	5	variation	variation	NOUN
ap-5556	390	6	on	on	ADP
ap-5556	390	7	deflection	deflection	NOUN
ap-5556	390	8	.	.	PUNCT
ap-5556	391	1	figure	figure	NOUN
ap-5556	391	2	7	7	NUM
ap-5556	391	3	.	.	PUNCT
ap-5556	392	1	influence	influence	NOUN
ap-5556	392	2	of	of	ADP
ap-5556	392	3	foundation	foundation	NOUN
ap-5556	392	4	free	free	ADJ
ap-5556	392	5	surface	surface	NOUN
ap-5556	392	6	on	on	ADP
ap-5556	392	7	vibration	vibration	NOUN
ap-5556	392	8	of	of	ADP
ap-5556	392	9	the	the	DET
ap-5556	392	10	circular	circular	ADJ
ap-5556	392	11	plate	plate	NOUN
ap-5556	392	12	.	.	PUNCT
ap-5556	393	1	138	138	NUM
ap-5556	393	2	vol	vol	NOUN
ap-5556	393	3	.	.	PUNCT
ap-5556	394	1	60	60	NUM
ap-5556	394	2	no	no	NOUN
ap-5556	394	3	.	.	PUNCT
ap-5556	395	1	2/2020	2/2020	NUM
ap-5556	395	2	investigation	investigation	NOUN
ap-5556	395	3	of	of	ADP
ap-5556	395	4	the	the	DET
ap-5556	395	5	dynamic	dynamic	ADJ
ap-5556	395	6	behaviour	behaviour	NOUN
ap-5556	395	7	of	of	ADP
ap-5556	395	8	non	non	ADJ
ap-5556	395	9	-	-	ADJ
ap-5556	395	10	uniform	uniform	ADJ
ap-5556	395	11	thickness	thickness	NOUN
ap-5556	395	12	.	.	PUNCT
ap-5556	395	13	.	.	PUNCT
ap-5556	396	1	.	.	PUNCT
ap-5556	397	1	4.2	4.2	NUM
ap-5556	397	2	.	.	PUNCT
ap-5556	397	3	mode	mode	PROPN
ap-5556	397	4	shapes	shape	VERB
ap-5556	397	5	the	the	DET
ap-5556	397	6	mode	mode	NOUN
ap-5556	397	7	shape	shape	NOUN
ap-5556	397	8	for	for	ADP
ap-5556	397	9	the	the	DET
ap-5556	397	10	dimensionless	dimensionless	ADJ
ap-5556	397	11	natural	natural	ADJ
ap-5556	397	12	frequencies	frequency	NOUN
ap-5556	397	13	are	be	AUX
ap-5556	397	14	shown	show	VERB
ap-5556	397	15	in	in	ADP
ap-5556	397	16	figs	fig	NOUN
ap-5556	397	17	.	.	PUNCT
ap-5556	398	1	8	8	NUM
ap-5556	398	2	-	-	SYM
ap-5556	398	3	13	13	NUM
ap-5556	398	4	respectively	respectively	ADV
ap-5556	398	5	.	.	PUNCT
ap-5556	399	1	it	it	PRON
ap-5556	399	2	is	be	AUX
ap-5556	399	3	important	important	ADJ
ap-5556	399	4	to	to	PART
ap-5556	399	5	note	note	VERB
ap-5556	399	6	that	that	SCONJ
ap-5556	399	7	,	,	PUNCT
ap-5556	399	8	the	the	DET
ap-5556	399	9	mode	mode	NOUN
ap-5556	399	10	shape	shape	NOUN
ap-5556	399	11	obeys	obey	VERB
ap-5556	399	12	the	the	DET
ap-5556	399	13	classical	classical	ADJ
ap-5556	399	14	theory	theory	NOUN
ap-5556	399	15	of	of	ADP
ap-5556	399	16	vibration	vibration	NOUN
ap-5556	399	17	.	.	PUNCT
ap-5556	400	1	according	accord	VERB
ap-5556	400	2	to	to	ADP
ap-5556	400	3	[	[	X
ap-5556	400	4	12	12	NUM
ap-5556	400	5	]	]	PUNCT
ap-5556	400	6	,	,	PUNCT
ap-5556	400	7	for	for	ADP
ap-5556	400	8	transient	transient	ADJ
ap-5556	400	9	stress	stress	NOUN
ap-5556	400	10	investigation	investigation	NOUN
ap-5556	400	11	,	,	PUNCT
ap-5556	400	12	the	the	DET
ap-5556	400	13	response	response	NOUN
ap-5556	400	14	is	be	AUX
ap-5556	400	15	normally	normally	ADV
ap-5556	400	16	based	base	VERB
ap-5556	400	17	on	on	ADP
ap-5556	400	18	the	the	DET
ap-5556	400	19	modal	modal	ADJ
ap-5556	400	20	superposition	superposition	NOUN
ap-5556	400	21	principle	principle	NOUN
ap-5556	400	22	and	and	CCONJ
ap-5556	400	23	the	the	DET
ap-5556	400	24	modal	modal	ADJ
ap-5556	400	25	stress	stress	NOUN
ap-5556	400	26	which	which	PRON
ap-5556	400	27	to	to	ADP
ap-5556	400	28	a	a	DET
ap-5556	400	29	certain	certain	ADJ
ap-5556	400	30	level	level	NOUN
ap-5556	400	31	will	will	AUX
ap-5556	400	32	expose	expose	VERB
ap-5556	400	33	the	the	DET
ap-5556	400	34	characteristics	characteristic	NOUN
ap-5556	400	35	and	and	CCONJ
ap-5556	400	36	content	content	NOUN
ap-5556	400	37	of	of	ADP
ap-5556	400	38	the	the	DET
ap-5556	400	39	whole	whole	ADJ
ap-5556	400	40	response	response	NOUN
ap-5556	400	41	of	of	ADP
ap-5556	400	42	the	the	DET
ap-5556	400	43	plate	plate	NOUN
ap-5556	400	44	.	.	PUNCT
ap-5556	401	1	based	base	VERB
ap-5556	401	2	on	on	ADP
ap-5556	401	3	that	that	PRON
ap-5556	401	4	,	,	PUNCT
ap-5556	401	5	the	the	DET
ap-5556	401	6	study	study	NOUN
ap-5556	401	7	of	of	ADP
ap-5556	401	8	the	the	DET
ap-5556	401	9	non	non	ADJ
ap-5556	401	10	-	-	ADJ
ap-5556	401	11	dimension	dimension	ADJ
ap-5556	401	12	radial	radial	ADJ
ap-5556	401	13	and	and	CCONJ
ap-5556	401	14	circumferential	circumferential	ADJ
ap-5556	401	15	stress	stress	NOUN
ap-5556	401	16	is	be	AUX
ap-5556	401	17	determined	determine	VERB
ap-5556	401	18	using	use	VERB
ap-5556	401	19	eq	eq	ADP
ap-5556	401	20	.	.	PUNCT
ap-5556	402	1	(	(	PUNCT
ap-5556	402	2	58	58	NUM
ap-5556	402	3	)	)	PUNCT
ap-5556	402	4	and	and	CCONJ
ap-5556	402	5	results	result	NOUN
ap-5556	402	6	illustrated	illustrate	VERB
ap-5556	402	7	in	in	ADP
ap-5556	402	8	figs	fig	NOUN
ap-5556	402	9	.	.	PUNCT
ap-5556	403	1	14	14	NUM
ap-5556	403	2	-	-	SYM
ap-5556	403	3	17	17	NUM
ap-5556	403	4	.	.	PUNCT
ap-5556	404	1	for	for	ADP
ap-5556	404	2	radial	radial	ADJ
ap-5556	404	3	and	and	CCONJ
ap-5556	404	4	circumferential	circumferential	ADJ
ap-5556	404	5	stresses	stress	NOUN
ap-5556	404	6	,	,	PUNCT
ap-5556	404	7	figs	fig	NOUN
ap-5556	404	8	.	.	PUNCT
ap-5556	405	1	14	14	NUM
ap-5556	405	2	-	-	SYM
ap-5556	405	3	17	17	NUM
ap-5556	405	4	show	show	NOUN
ap-5556	405	5	that	that	SCONJ
ap-5556	405	6	the	the	DET
ap-5556	405	7	location	location	NOUN
ap-5556	405	8	of	of	ADP
ap-5556	405	9	the	the	DET
ap-5556	405	10	vibrating	vibrate	VERB
ap-5556	405	11	node	node	NOUN
ap-5556	405	12	and	and	CCONJ
ap-5556	405	13	antinodes	antinode	NOUN
ap-5556	405	14	are	be	AUX
ap-5556	405	15	in	in	ADP
ap-5556	405	16	-	-	PUNCT
ap-5556	405	17	away	away	ADV
ap-5556	405	18	different	different	ADJ
ap-5556	405	19	.	.	PUNCT
ap-5556	406	1	the	the	DET
ap-5556	406	2	phenomenon	phenomenon	NOUN
ap-5556	406	3	is	be	AUX
ap-5556	406	4	due	due	ADJ
ap-5556	406	5	to	to	ADP
ap-5556	406	6	the	the	DET
ap-5556	406	7	vanishing	vanish	VERB
ap-5556	406	8	mode	mode	NOUN
ap-5556	406	9	of	of	ADP
ap-5556	406	10	the	the	DET
ap-5556	406	11	boundary	boundary	ADJ
ap-5556	406	12	condition	condition	NOUN
ap-5556	406	13	.	.	PUNCT
ap-5556	407	1	it	it	PRON
ap-5556	407	2	is	be	AUX
ap-5556	407	3	clearly	clearly	ADV
ap-5556	407	4	shown	show	VERB
ap-5556	407	5	that	that	SCONJ
ap-5556	407	6	,	,	PUNCT
ap-5556	407	7	the	the	DET
ap-5556	407	8	location	location	NOUN
ap-5556	407	9	of	of	ADP
ap-5556	407	10	the	the	DET
ap-5556	407	11	node	node	NOUN
ap-5556	407	12	and	and	CCONJ
ap-5556	407	13	antinodes	antinode	NOUN
ap-5556	407	14	of	of	ADP
ap-5556	407	15	the	the	DET
ap-5556	407	16	vibrating	vibrate	VERB
ap-5556	407	17	plate	plate	NOUN
ap-5556	407	18	changes	change	NOUN
ap-5556	407	19	.	.	PUNCT
ap-5556	408	1	figs	fig	NOUN
ap-5556	408	2	.	.	PUNCT
ap-5556	409	1	14	14	NUM
ap-5556	409	2	-	-	SYM
ap-5556	409	3	17	17	NUM
ap-5556	409	4	when	when	SCONJ
ap-5556	409	5	compared	compare	VERB
ap-5556	409	6	to	to	ADP
ap-5556	409	7	figs	fig	NOUN
ap-5556	409	8	.	.	PUNCT
ap-5556	410	1	8	8	NUM
ap-5556	410	2	-	-	SYM
ap-5556	410	3	13	13	NUM
ap-5556	410	4	different	different	ADJ
ap-5556	410	5	in	in	ADP
ap-5556	410	6	the	the	DET
ap-5556	410	7	mode	mode	NOUN
ap-5556	410	8	shape	shape	NOUN
ap-5556	410	9	is	be	AUX
ap-5556	410	10	clearly	clearly	ADV
ap-5556	410	11	shown	show	VERB
ap-5556	410	12	.	.	PUNCT
ap-5556	411	1	invariably	invariably	ADV
ap-5556	411	2	,	,	PUNCT
ap-5556	411	3	the	the	DET
ap-5556	411	4	extrema	extrema	ADJ
ap-5556	411	5	mode	mode	NOUN
ap-5556	411	6	shapes	shape	NOUN
ap-5556	411	7	location	location	NOUN
ap-5556	411	8	differs	differ	NOUN
ap-5556	411	9	based	base	VERB
ap-5556	411	10	on	on	ADP
ap-5556	411	11	the	the	DET
ap-5556	411	12	boundary	boundary	ADJ
ap-5556	411	13	conditions	condition	NOUN
ap-5556	411	14	.	.	PUNCT
ap-5556	412	1	the	the	DET
ap-5556	412	2	extrema	extrema	ADJ
ap-5556	412	3	mode	mode	NOUN
ap-5556	412	4	shape	shape	NOUN
ap-5556	412	5	of	of	ADP
ap-5556	412	6	the	the	DET
ap-5556	412	7	circular	circular	ADJ
ap-5556	412	8	plate	plate	NOUN
ap-5556	412	9	is	be	AUX
ap-5556	412	10	distorted	distort	VERB
ap-5556	412	11	due	due	ADP
ap-5556	412	12	to	to	ADP
ap-5556	412	13	the	the	DET
ap-5556	412	14	presence	presence	NOUN
ap-5556	412	15	of	of	ADP
ap-5556	412	16	radial	radial	ADJ
ap-5556	412	17	and	and	CCONJ
ap-5556	412	18	circumferential	circumferential	ADJ
ap-5556	412	19	stresses	stress	NOUN
ap-5556	412	20	.	.	PUNCT
ap-5556	413	1	also	also	ADV
ap-5556	413	2	comparing	compare	VERB
ap-5556	413	3	figs	fig	NOUN
ap-5556	413	4	8	8	NUM
ap-5556	413	5	and	and	CCONJ
ap-5556	413	6	9	9	NUM
ap-5556	413	7	,	,	PUNCT
ap-5556	413	8	figs	fig	NOUN
ap-5556	413	9	.	.	PUNCT
ap-5556	414	1	10	10	NUM
ap-5556	414	2	and	and	CCONJ
ap-5556	414	3	11	11	NUM
ap-5556	414	4	likewise	likewise	ADV
ap-5556	414	5	figs	fig	NOUN
ap-5556	414	6	.	.	PUNCT
ap-5556	415	1	12	12	NUM
ap-5556	415	2	and	and	CCONJ
ap-5556	415	3	13	13	NUM
ap-5556	415	4	respectively	respectively	ADV
ap-5556	415	5	,	,	PUNCT
ap-5556	415	6	it	it	PRON
ap-5556	415	7	is	be	AUX
ap-5556	415	8	observed	observe	VERB
ap-5556	415	9	the	the	DET
ap-5556	415	10	symmetric	symmetric	ADJ
ap-5556	415	11	case	case	NOUN
ap-5556	415	12	of	of	ADP
ap-5556	415	13	circular	circular	ADJ
ap-5556	415	14	plate	plate	NOUN
ap-5556	415	15	differs	differ	VERB
ap-5556	415	16	from	from	ADP
ap-5556	415	17	the	the	DET
ap-5556	415	18	axisymmetric	axisymmetric	ADJ
ap-5556	415	19	case	case	NOUN
ap-5556	415	20	.	.	PUNCT
ap-5556	416	1	this	this	PRON
ap-5556	416	2	due	due	ADP
ap-5556	416	3	to	to	ADP
ap-5556	416	4	the	the	DET
ap-5556	416	5	difference	difference	NOUN
ap-5556	416	6	in	in	ADP
ap-5556	416	7	the	the	DET
ap-5556	416	8	regularity	regularity	NOUN
ap-5556	416	9	condition	condition	NOUN
ap-5556	416	10	at	at	ADP
ap-5556	416	11	the	the	DET
ap-5556	416	12	center	center	NOUN
ap-5556	416	13	.	.	PUNCT
ap-5556	417	1	figure	figure	NOUN
ap-5556	417	2	8	8	NUM
ap-5556	417	3	.	.	PUNCT
ap-5556	417	4	mode	mode	NOUN
ap-5556	417	5	shape	shape	NOUN
ap-5556	417	6	for	for	ADP
ap-5556	417	7	simply	simply	ADV
ap-5556	417	8	supported	support	VERB
ap-5556	417	9	edge	edge	NOUN
ap-5556	417	10	condition	condition	NOUN
ap-5556	417	11	symmetric	symmetric	ADJ
ap-5556	417	12	case	case	NOUN
ap-5556	417	13	.	.	PUNCT
ap-5556	418	1	figure	figure	NOUN
ap-5556	418	2	9	9	NUM
ap-5556	418	3	.	.	PUNCT
ap-5556	418	4	mode	mode	NOUN
ap-5556	418	5	shape	shape	NOUN
ap-5556	418	6	for	for	ADP
ap-5556	418	7	simply	simply	ADV
ap-5556	418	8	supported	support	VERB
ap-5556	418	9	edge	edge	NOUN
ap-5556	418	10	condition	condition	NOUN
ap-5556	418	11	asymmetric	asymmetric	NOUN
ap-5556	418	12	case	case	NOUN
ap-5556	418	13	.	.	PUNCT
ap-5556	419	1	figure	figure	NOUN
ap-5556	419	2	10	10	NUM
ap-5556	419	3	.	.	PUNCT
ap-5556	420	1	mode	mode	NOUN
ap-5556	420	2	shape	shape	NOUN
ap-5556	420	3	for	for	ADP
ap-5556	420	4	clamped	clamp	VERB
ap-5556	420	5	edge	edge	NOUN
ap-5556	420	6	condition	condition	NOUN
ap-5556	420	7	symmetric	symmetric	ADJ
ap-5556	420	8	case	case	NOUN
ap-5556	420	9	.	.	PUNCT
ap-5556	421	1	figure	figure	NOUN
ap-5556	421	2	11	11	NUM
ap-5556	421	3	.	.	PUNCT
ap-5556	422	1	mode	mode	NOUN
ap-5556	422	2	shape	shape	NOUN
ap-5556	422	3	for	for	ADP
ap-5556	422	4	clamped	clamp	VERB
ap-5556	422	5	edge	edge	NOUN
ap-5556	422	6	condition	condition	NOUN
ap-5556	422	7	asymmetric	asymmetric	ADJ
ap-5556	422	8	case	case	NOUN
ap-5556	422	9	.	.	PUNCT
ap-5556	423	1	139	139	NUM
ap-5556	423	2	s.	s.	PROPN
ap-5556	423	3	salawu	salawu	PROPN
ap-5556	423	4	,	,	PUNCT
ap-5556	423	5	g.	g.	PROPN
ap-5556	423	6	sobamowo	sobamowo	PROPN
ap-5556	423	7	,	,	PUNCT
ap-5556	423	8	o.	o.	PROPN
ap-5556	423	9	sadiq	sadiq	PROPN
ap-5556	423	10	acta	acta	PROPN
ap-5556	423	11	polytechnica	polytechnica	PROPN
ap-5556	423	12	figure	figure	NOUN
ap-5556	423	13	12	12	NUM
ap-5556	423	14	.	.	PUNCT
ap-5556	423	15	mode	mode	NOUN
ap-5556	423	16	shape	shape	NOUN
ap-5556	423	17	for	for	ADP
ap-5556	423	18	free	free	ADJ
ap-5556	423	19	edge	edge	NOUN
ap-5556	423	20	condition	condition	NOUN
ap-5556	423	21	symmetric	symmetric	ADJ
ap-5556	423	22	case	case	NOUN
ap-5556	423	23	.	.	PUNCT
ap-5556	424	1	figure	figure	NOUN
ap-5556	424	2	13	13	NUM
ap-5556	424	3	.	.	PUNCT
ap-5556	425	1	mode	mode	NOUN
ap-5556	425	2	shape	shape	NOUN
ap-5556	425	3	for	for	ADP
ap-5556	425	4	free	free	ADJ
ap-5556	425	5	edge	edge	NOUN
ap-5556	425	6	condition	condition	NOUN
ap-5556	425	7	asymmetric	asymmetric	ADJ
ap-5556	425	8	case	case	NOUN
ap-5556	425	9	.	.	PUNCT
ap-5556	426	1	figure	figure	NOUN
ap-5556	426	2	14	14	NUM
ap-5556	426	3	.	.	PUNCT
ap-5556	427	1	radial	radial	ADJ
ap-5556	427	2	stress	stress	NOUN
ap-5556	427	3	for	for	ADP
ap-5556	427	4	clamped	clamp	VERB
ap-5556	427	5	edge	edge	NOUN
ap-5556	427	6	symmetric	symmetric	ADJ
ap-5556	427	7	case	case	NOUN
ap-5556	427	8	.	.	PUNCT
ap-5556	428	1	figure	figure	NOUN
ap-5556	428	2	15	15	NUM
ap-5556	428	3	.	.	PUNCT
ap-5556	429	1	radial	radial	ADJ
ap-5556	429	2	stress	stress	NOUN
ap-5556	429	3	for	for	ADP
ap-5556	429	4	clamped	clamp	VERB
ap-5556	429	5	edge	edge	NOUN
ap-5556	429	6	asymmetric	asymmetric	ADJ
ap-5556	429	7	case	case	NOUN
ap-5556	429	8	.	.	PUNCT
ap-5556	430	1	figure	figure	NOUN
ap-5556	430	2	16	16	NUM
ap-5556	430	3	.	.	PUNCT
ap-5556	431	1	circumferential	circumferential	ADJ
ap-5556	431	2	stress	stress	NOUN
ap-5556	431	3	for	for	ADP
ap-5556	431	4	clamped	clamp	VERB
ap-5556	431	5	edge	edge	NOUN
ap-5556	431	6	symmetric	symmetric	ADJ
ap-5556	431	7	case	case	NOUN
ap-5556	431	8	.	.	PUNCT
ap-5556	432	1	figure	figure	NOUN
ap-5556	432	2	17	17	NUM
ap-5556	432	3	.	.	PUNCT
ap-5556	433	1	circumferential	circumferential	ADJ
ap-5556	433	2	stress	stress	NOUN
ap-5556	433	3	for	for	ADP
ap-5556	433	4	clamped	clamp	VERB
ap-5556	433	5	edge	edge	NOUN
ap-5556	433	6	asymmetric	asymmetric	ADJ
ap-5556	433	7	case	case	NOUN
ap-5556	433	8	.	.	PUNCT
ap-5556	434	1	140	140	NUM
ap-5556	434	2	vol	vol	NOUN
ap-5556	434	3	.	.	PUNCT
ap-5556	435	1	60	60	NUM
ap-5556	435	2	no	no	NOUN
ap-5556	435	3	.	.	PUNCT
ap-5556	436	1	2/2020	2/2020	NUM
ap-5556	436	2	investigation	investigation	NOUN
ap-5556	436	3	of	of	ADP
ap-5556	436	4	the	the	DET
ap-5556	436	5	dynamic	dynamic	ADJ
ap-5556	436	6	behaviour	behaviour	NOUN
ap-5556	436	7	of	of	ADP
ap-5556	436	8	non	non	ADJ
ap-5556	436	9	-	-	ADJ
ap-5556	436	10	uniform	uniform	ADJ
ap-5556	436	11	thickness	thickness	NOUN
ap-5556	436	12	.	.	PUNCT
ap-5556	436	13	.	.	PUNCT
ap-5556	437	1	.	.	PUNCT
ap-5556	438	1	figure	figure	NOUN
ap-5556	438	2	18	18	NUM
ap-5556	438	3	.	.	PUNCT
ap-5556	439	1	influence	influence	NOUN
ap-5556	439	2	of	of	ADP
ap-5556	439	3	thickness	thickness	NOUN
ap-5556	439	4	parameter	parameter	NOUN
ap-5556	439	5	variation	variation	NOUN
ap-5556	439	6	on	on	ADP
ap-5556	439	7	symmetric	symmetric	ADJ
ap-5556	439	8	and	and	CCONJ
ap-5556	439	9	asymmetric	asymmetric	ADJ
ap-5556	439	10	case	case	NOUN
ap-5556	439	11	circular	circular	ADJ
ap-5556	439	12	plate	plate	NOUN
ap-5556	439	13	.	.	PUNCT
ap-5556	440	1	figure	figure	NOUN
ap-5556	440	2	19	19	NUM
ap-5556	440	3	.	.	PUNCT
ap-5556	441	1	influence	influence	NOUN
ap-5556	441	2	of	of	ADP
ap-5556	441	3	thickness	thickness	NOUN
ap-5556	441	4	parameter	parameter	NOUN
ap-5556	441	5	variation	variation	NOUN
ap-5556	441	6	on	on	ADP
ap-5556	441	7	deflection	deflection	NOUN
ap-5556	441	8	of	of	ADP
ap-5556	441	9	circular	circular	ADJ
ap-5556	441	10	plate	plate	NOUN
ap-5556	441	11	for	for	ADP
ap-5556	441	12	nonlinear	nonlinear	ADJ
ap-5556	441	13	foundation	foundation	PROPN
ap-5556	441	14	.	.	PUNCT
ap-5556	442	1	figure	figure	NOUN
ap-5556	442	2	20	20	NUM
ap-5556	442	3	.	.	PUNCT
ap-5556	443	1	influence	influence	NOUN
ap-5556	443	2	of	of	ADP
ap-5556	443	3	thickness	thickness	NOUN
ap-5556	443	4	parameter	parameter	NOUN
ap-5556	443	5	variation	variation	NOUN
ap-5556	443	6	on	on	ADP
ap-5556	443	7	dynamic	dynamic	ADJ
ap-5556	443	8	behaviour	behaviour	NOUN
ap-5556	443	9	of	of	ADP
ap-5556	443	10	circular	circular	ADJ
ap-5556	443	11	plate	plate	NOUN
ap-5556	443	12	for	for	ADP
ap-5556	443	13	free	free	ADJ
ap-5556	443	14	surface	surface	NOUN
ap-5556	443	15	of	of	ADP
ap-5556	443	16	foundation	foundation	NOUN
ap-5556	443	17	.	.	PUNCT
ap-5556	444	1	4.3	4.3	NUM
ap-5556	444	2	.	.	PUNCT
ap-5556	444	3	investigation	investigation	NOUN
ap-5556	444	4	of	of	ADP
ap-5556	444	5	plate	plate	NOUN
ap-5556	444	6	thickness	thickness	NOUN
ap-5556	444	7	variation	variation	NOUN
ap-5556	444	8	on	on	ADP
ap-5556	444	9	the	the	DET
ap-5556	444	10	natural	natural	ADJ
ap-5556	444	11	frequency	frequency	NOUN
ap-5556	444	12	fig	fig	NOUN
ap-5556	444	13	.	.	PUNCT
ap-5556	445	1	18	18	NUM
ap-5556	445	2	illustrates	illustrate	VERB
ap-5556	445	3	the	the	DET
ap-5556	445	4	influence	influence	NOUN
ap-5556	445	5	of	of	ADP
ap-5556	445	6	the	the	DET
ap-5556	445	7	taper	taper	NOUN
ap-5556	445	8	variation	variation	NOUN
ap-5556	445	9	on	on	ADP
ap-5556	445	10	the	the	DET
ap-5556	445	11	natural	natural	ADJ
ap-5556	445	12	frequency	frequency	NOUN
ap-5556	445	13	.	.	PUNCT
ap-5556	446	1	an	an	DET
ap-5556	446	2	increase	increase	NOUN
ap-5556	446	3	in	in	ADP
ap-5556	446	4	taper	taper	NOUN
ap-5556	446	5	ratio	ratio	NOUN
ap-5556	446	6	along	along	ADP
ap-5556	446	7	means	mean	VERB
ap-5556	446	8	that	that	SCONJ
ap-5556	446	9	as	as	ADP
ap-5556	446	10	the	the	DET
ap-5556	446	11	thickness	thickness	NOUN
ap-5556	446	12	of	of	ADP
ap-5556	446	13	the	the	DET
ap-5556	446	14	plate	plate	NOUN
ap-5556	446	15	increase	increase	NOUN
ap-5556	446	16	,	,	PUNCT
ap-5556	446	17	the	the	DET
ap-5556	446	18	plate	plate	NOUN
ap-5556	446	19	gains	gain	VERB
ap-5556	446	20	more	more	ADJ
ap-5556	446	21	strength	strength	NOUN
ap-5556	446	22	and	and	CCONJ
ap-5556	446	23	stiffness	stiffness	NOUN
ap-5556	446	24	.	.	PUNCT
ap-5556	447	1	the	the	PRON
ap-5556	447	2	more	more	ADV
ap-5556	447	3	the	the	DET
ap-5556	447	4	stiffness	stiffness	NOUN
ap-5556	447	5	of	of	ADP
ap-5556	447	6	the	the	DET
ap-5556	447	7	plate	plate	NOUN
ap-5556	447	8	,	,	PUNCT
ap-5556	447	9	the	the	PRON
ap-5556	447	10	more	more	ADJ
ap-5556	447	11	that	that	DET
ap-5556	447	12	natural	natural	ADJ
ap-5556	447	13	frequency	frequency	NOUN
ap-5556	447	14	of	of	ADP
ap-5556	447	15	the	the	DET
ap-5556	447	16	plate	plate	NOUN
ap-5556	447	17	increase	increase	NOUN
ap-5556	447	18	.	.	PUNCT
ap-5556	448	1	this	this	PRON
ap-5556	448	2	is	be	AUX
ap-5556	448	3	an	an	DET
ap-5556	448	4	obvious	obvious	ADJ
ap-5556	448	5	result	result	NOUN
ap-5556	448	6	considering	consider	VERB
ap-5556	448	7	the	the	DET
ap-5556	448	8	classical	classical	ADJ
ap-5556	448	9	theory	theory	NOUN
ap-5556	448	10	of	of	ADP
ap-5556	448	11	vibration	vibration	NOUN
ap-5556	448	12	.	.	PUNCT
ap-5556	449	1	fig	fig	NOUN
ap-5556	449	2	.	.	PUNCT
ap-5556	450	1	19	19	NUM
ap-5556	450	2	shows	show	VERB
ap-5556	450	3	the	the	DET
ap-5556	450	4	result	result	NOUN
ap-5556	450	5	obtained	obtain	VERB
ap-5556	450	6	while	while	SCONJ
ap-5556	450	7	investigating	investigate	VERB
ap-5556	450	8	the	the	DET
ap-5556	450	9	influence	influence	NOUN
ap-5556	450	10	of	of	ADP
ap-5556	450	11	plate	plate	NOUN
ap-5556	450	12	thickness	thickness	NOUN
ap-5556	450	13	variation	variation	NOUN
ap-5556	450	14	for	for	ADP
ap-5556	450	15	the	the	DET
ap-5556	450	16	circular	circular	ADJ
ap-5556	450	17	plate	plate	NOUN
ap-5556	450	18	resting	rest	VERB
ap-5556	450	19	on	on	ADP
ap-5556	450	20	nonlinear	nonlinear	ADJ
ap-5556	450	21	foundation	foundation	PROPN
ap-5556	450	22	.	.	PUNCT
ap-5556	451	1	from	from	ADP
ap-5556	451	2	the	the	DET
ap-5556	451	3	result	result	NOUN
ap-5556	451	4	,	,	PUNCT
ap-5556	451	5	it	it	PRON
ap-5556	451	6	is	be	AUX
ap-5556	451	7	observed	observe	VERB
ap-5556	451	8	that	that	SCONJ
ap-5556	451	9	increasing	increase	VERB
ap-5556	451	10	the	the	DET
ap-5556	451	11	thickness	thickness	NOUN
ap-5556	451	12	,	,	PUNCT
ap-5556	451	13	deflection	deflection	NOUN
ap-5556	451	14	of	of	ADP
ap-5556	451	15	the	the	DET
ap-5556	451	16	circular	circular	ADJ
ap-5556	451	17	plate	plate	NOUN
ap-5556	451	18	increases	increase	NOUN
ap-5556	451	19	.	.	PUNCT
ap-5556	452	1	as	as	ADP
ap-5556	452	2	flexibility	flexibility	NOUN
ap-5556	452	3	of	of	ADP
ap-5556	452	4	the	the	DET
ap-5556	452	5	plate	plate	NOUN
ap-5556	452	6	increases	increase	NOUN
ap-5556	452	7	,	,	PUNCT
ap-5556	452	8	the	the	DET
ap-5556	452	9	deflection	deflection	NOUN
ap-5556	452	10	increases	increase	VERB
ap-5556	452	11	.	.	PUNCT
ap-5556	453	1	also	also	ADV
ap-5556	453	2	,	,	PUNCT
ap-5556	453	3	fig	fig	NOUN
ap-5556	453	4	.	.	PUNCT
ap-5556	454	1	20	20	NUM
ap-5556	454	2	depicts	depict	VERB
ap-5556	454	3	the	the	DET
ap-5556	454	4	nonlinear	nonlinear	ADJ
ap-5556	454	5	frequency	frequency	NOUN
ap-5556	454	6	response	response	NOUN
ap-5556	454	7	of	of	ADP
ap-5556	454	8	the	the	DET
ap-5556	454	9	circular	circular	NOUN
ap-5556	454	10	when	when	SCONJ
ap-5556	454	11	the	the	DET
ap-5556	454	12	plate	plate	NOUN
ap-5556	454	13	thickness	thickness	NOUN
ap-5556	454	14	is	be	AUX
ap-5556	454	15	increase	increase	NOUN
ap-5556	454	16	with	with	ADP
ap-5556	454	17	consideration	consideration	NOUN
ap-5556	454	18	to	to	ADP
ap-5556	454	19	the	the	DET
ap-5556	454	20	free	free	ADJ
ap-5556	454	21	surface	surface	NOUN
ap-5556	454	22	of	of	ADP
ap-5556	454	23	the	the	DET
ap-5556	454	24	foundation	foundation	NOUN
ap-5556	454	25	.	.	PUNCT
ap-5556	455	1	a	a	DET
ap-5556	455	2	decrease	decrease	NOUN
ap-5556	455	3	in	in	ADP
ap-5556	455	4	nonlinear	nonlinear	ADJ
ap-5556	455	5	frequency	frequency	NOUN
ap-5556	455	6	ratio	ratio	NOUN
ap-5556	455	7	is	be	AUX
ap-5556	455	8	observed	observe	VERB
ap-5556	455	9	as	as	SCONJ
ap-5556	455	10	the	the	DET
ap-5556	455	11	thickness	thickness	NOUN
ap-5556	455	12	increases	increase	VERB
ap-5556	455	13	.	.	PUNCT
ap-5556	456	1	4.4	4.4	NUM
ap-5556	456	2	.	.	PUNCT
ap-5556	456	3	investigation	investigation	NOUN
ap-5556	456	4	of	of	ADP
ap-5556	456	5	homogeneity	homogeneity	NOUN
ap-5556	456	6	parameter	parameter	NOUN
ap-5556	456	7	variation	variation	NOUN
ap-5556	456	8	on	on	ADP
ap-5556	456	9	the	the	DET
ap-5556	456	10	natural	natural	ADJ
ap-5556	456	11	frequency	frequency	NOUN
ap-5556	456	12	the	the	DET
ap-5556	456	13	effect	effect	NOUN
ap-5556	456	14	of	of	ADP
ap-5556	456	15	homogeneity	homogeneity	NOUN
ap-5556	456	16	is	be	AUX
ap-5556	456	17	determined	determine	VERB
ap-5556	456	18	and	and	CCONJ
ap-5556	456	19	shown	show	VERB
ap-5556	456	20	in	in	ADP
ap-5556	456	21	fig	fig	NOUN
ap-5556	456	22	.	.	PUNCT
ap-5556	457	1	21	21	NUM
ap-5556	457	2	.	.	X
ap-5556	457	3	homogeneity	homogeneity	NOUN
ap-5556	457	4	is	be	AUX
ap-5556	457	5	a	a	DET
ap-5556	457	6	function	function	NOUN
ap-5556	457	7	of	of	ADP
ap-5556	457	8	density	density	NOUN
ap-5556	457	9	variation	variation	NOUN
ap-5556	457	10	.	.	PUNCT
ap-5556	458	1	from	from	ADP
ap-5556	458	2	the	the	DET
ap-5556	458	3	results	result	NOUN
ap-5556	458	4	obtained	obtain	VERB
ap-5556	458	5	,	,	PUNCT
ap-5556	458	6	it	it	PRON
ap-5556	458	7	is	be	AUX
ap-5556	458	8	shown	show	VERB
ap-5556	458	9	that	that	SCONJ
ap-5556	458	10	the	the	DET
ap-5556	458	11	natural	natural	ADJ
ap-5556	458	12	frequency	frequency	NOUN
ap-5556	458	13	decreases	decrease	VERB
ap-5556	458	14	with	with	ADP
ap-5556	458	15	an	an	DET
ap-5556	458	16	increase	increase	NOUN
ap-5556	458	17	in	in	ADP
ap-5556	458	18	density	density	NOUN
ap-5556	458	19	.	.	PUNCT
ap-5556	459	1	this	this	PRON
ap-5556	459	2	implies	imply	VERB
ap-5556	459	3	that	that	SCONJ
ap-5556	459	4	,	,	PUNCT
ap-5556	459	5	as	as	SCONJ
ap-5556	459	6	the	the	DET
ap-5556	459	7	material	material	NOUN
ap-5556	459	8	properties	property	NOUN
ap-5556	459	9	are	be	AUX
ap-5556	459	10	being	be	AUX
ap-5556	459	11	increased	increase	VERB
ap-5556	459	12	,	,	PUNCT
ap-5556	459	13	the	the	DET
ap-5556	459	14	plates	plate	NOUN
ap-5556	459	15	gained	gain	VERB
ap-5556	459	16	more	more	ADJ
ap-5556	459	17	mass	mass	NOUN
ap-5556	459	18	.	.	PUNCT
ap-5556	460	1	the	the	PRON
ap-5556	460	2	more	more	ADV
ap-5556	460	3	the	the	DET
ap-5556	460	4	plate	plate	NOUN
ap-5556	460	5	mass	mass	NOUN
ap-5556	460	6	increases	increase	VERB
ap-5556	460	7	the	the	PRON
ap-5556	460	8	more	more	ADV
ap-5556	460	9	the	the	DET
ap-5556	460	10	natural	natural	ADJ
ap-5556	460	11	frequency	frequency	NOUN
ap-5556	460	12	decreases	decrease	NOUN
ap-5556	460	13	due	due	ADP
ap-5556	460	14	to	to	ADP
ap-5556	460	15	the	the	DET
ap-5556	460	16	increase	increase	NOUN
ap-5556	460	17	in	in	ADP
ap-5556	460	18	the	the	DET
ap-5556	460	19	mass	mass	NOUN
ap-5556	460	20	of	of	ADP
ap-5556	460	21	the	the	DET
ap-5556	460	22	plate	plate	NOUN
ap-5556	460	23	,	,	PUNCT
ap-5556	460	24	as	as	ADP
ap-5556	460	25	a	a	DET
ap-5556	460	26	result	result	NOUN
ap-5556	460	27	,	,	PUNCT
ap-5556	460	28	the	the	DET
ap-5556	460	29	natural	natural	ADJ
ap-5556	460	30	frequency	frequency	NOUN
ap-5556	460	31	decrease	decrease	NOUN
ap-5556	460	32	.	.	PUNCT
ap-5556	461	1	fig	fig	NOUN
ap-5556	461	2	.	.	PUNCT
ap-5556	462	1	22	22	NUM
ap-5556	462	2	illustrates	illustrate	VERB
ap-5556	462	3	that	that	SCONJ
ap-5556	462	4	,	,	PUNCT
ap-5556	462	5	increasing	increase	VERB
ap-5556	462	6	the	the	DET
ap-5556	462	7	homogeneity	homogeneity	NOUN
ap-5556	462	8	of	of	ADP
ap-5556	462	9	the	the	DET
ap-5556	462	10	circular	circular	ADJ
ap-5556	462	11	plate	plate	NOUN
ap-5556	462	12	leads	lead	VERB
ap-5556	462	13	to	to	PART
ap-5556	462	14	increase	increase	VERB
ap-5556	462	15	in	in	ADP
ap-5556	462	16	the	the	DET
ap-5556	462	17	deflection	deflection	NOUN
ap-5556	462	18	of	of	ADP
ap-5556	462	19	the	the	DET
ap-5556	462	20	circular	circular	ADJ
ap-5556	462	21	plate	plate	NOUN
ap-5556	462	22	meanwhile	meanwhile	ADV
ap-5556	462	23	,	,	PUNCT
ap-5556	462	24	from	from	ADP
ap-5556	462	25	the	the	DET
ap-5556	462	26	result	result	NOUN
ap-5556	462	27	illustrated	illustrate	VERB
ap-5556	462	28	in	in	ADP
ap-5556	462	29	fig	fig	NOUN
ap-5556	462	30	.	.	PUNCT
ap-5556	463	1	23	23	NUM
ap-5556	464	1	increasing	increase	VERB
ap-5556	464	2	the	the	DET
ap-5556	464	3	density	density	NOUN
ap-5556	464	4	lowers	lower	VERB
ap-5556	464	5	the	the	DET
ap-5556	464	6	deflection	deflection	NOUN
ap-5556	464	7	of	of	ADP
ap-5556	464	8	the	the	DET
ap-5556	464	9	circular	circular	ADJ
ap-5556	464	10	plate	plate	NOUN
ap-5556	464	11	in	in	ADP
ap-5556	464	12	relation	relation	NOUN
ap-5556	464	13	to	to	ADP
ap-5556	464	14	the	the	DET
ap-5556	464	15	free	free	ADJ
ap-5556	464	16	surface	surface	NOUN
ap-5556	464	17	of	of	ADP
ap-5556	464	18	the	the	DET
ap-5556	464	19	foundation	foundation	NOUN
ap-5556	464	20	.	.	PUNCT
ap-5556	465	1	141	141	NUM
ap-5556	465	2	s.	s.	PROPN
ap-5556	465	3	salawu	salawu	PROPN
ap-5556	465	4	,	,	PUNCT
ap-5556	465	5	g.	g.	PROPN
ap-5556	465	6	sobamowo	sobamowo	PROPN
ap-5556	465	7	,	,	PUNCT
ap-5556	465	8	o.	o.	PROPN
ap-5556	465	9	sadiq	sadiq	PROPN
ap-5556	465	10	acta	acta	PROPN
ap-5556	465	11	polytechnica	polytechnica	PROPN
ap-5556	465	12	figure	figure	NOUN
ap-5556	465	13	21	21	NUM
ap-5556	465	14	.	.	PUNCT
ap-5556	466	1	influence	influence	NOUN
ap-5556	466	2	of	of	ADP
ap-5556	466	3	density	density	NOUN
ap-5556	466	4	variation	variation	NOUN
ap-5556	466	5	on	on	ADP
ap-5556	466	6	symmetric	symmetric	ADJ
ap-5556	466	7	and	and	CCONJ
ap-5556	466	8	asymmetric	asymmetric	ADJ
ap-5556	466	9	case	case	NOUN
ap-5556	466	10	circular	circular	ADJ
ap-5556	466	11	plate	plate	NOUN
ap-5556	466	12	.	.	PUNCT
ap-5556	467	1	figure	figure	NOUN
ap-5556	467	2	22	22	NUM
ap-5556	467	3	.	.	PUNCT
ap-5556	468	1	influence	influence	NOUN
ap-5556	468	2	of	of	ADP
ap-5556	468	3	density	density	NOUN
ap-5556	468	4	variation	variation	NOUN
ap-5556	468	5	on	on	ADP
ap-5556	468	6	deflection	deflection	NOUN
ap-5556	468	7	of	of	ADP
ap-5556	468	8	circular	circular	ADJ
ap-5556	468	9	plate	plate	NOUN
ap-5556	468	10	for	for	ADP
ap-5556	468	11	nonlinear	nonlinear	ADJ
ap-5556	468	12	foundation	foundation	PROPN
ap-5556	468	13	.	.	PUNCT
ap-5556	469	1	figure	figure	NOUN
ap-5556	469	2	23	23	NUM
ap-5556	469	3	.	.	PUNCT
ap-5556	470	1	influence	influence	NOUN
ap-5556	470	2	of	of	ADP
ap-5556	470	3	density	density	NOUN
ap-5556	470	4	variation	variation	NOUN
ap-5556	470	5	on	on	ADP
ap-5556	470	6	deflection	deflection	NOUN
ap-5556	470	7	of	of	ADP
ap-5556	470	8	circular	circular	ADJ
ap-5556	470	9	plate	plate	NOUN
ap-5556	470	10	for	for	ADP
ap-5556	470	11	free	free	ADJ
ap-5556	470	12	surface	surface	NOUN
ap-5556	470	13	of	of	ADP
ap-5556	470	14	foundation	foundation	NOUN
ap-5556	470	15	.	.	PUNCT
ap-5556	471	1	5	5	X
ap-5556	471	2	.	.	X
ap-5556	471	3	conclusion	conclusion	NOUN
ap-5556	471	4	in	in	ADP
ap-5556	471	5	this	this	DET
ap-5556	471	6	study	study	NOUN
ap-5556	471	7	,	,	PUNCT
ap-5556	471	8	free	free	ADJ
ap-5556	471	9	vibration	vibration	NOUN
ap-5556	471	10	of	of	ADP
ap-5556	471	11	varying	vary	VERB
ap-5556	471	12	thickness	thickness	NOUN
ap-5556	471	13	and	and	CCONJ
ap-5556	471	14	non	non	ADJ
ap-5556	471	15	-	-	ADJ
ap-5556	471	16	homogenous	homogenous	ADJ
ap-5556	471	17	circular	circular	ADJ
ap-5556	471	18	plate	plate	NOUN
ap-5556	471	19	resting	rest	VERB
ap-5556	471	20	on	on	ADP
ap-5556	471	21	winkler	winkler	NOUN
ap-5556	471	22	and	and	CCONJ
ap-5556	471	23	pasternak	pasternak	PROPN
ap-5556	471	24	foundations	foundation	NOUN
ap-5556	471	25	using	use	VERB
ap-5556	471	26	galerkin	galerkin	NOUN
ap-5556	471	27	of	of	ADP
ap-5556	471	28	weighted	weight	VERB
ap-5556	471	29	residual	residual	ADJ
ap-5556	471	30	method	method	NOUN
ap-5556	471	31	is	be	AUX
ap-5556	471	32	investigated	investigate	VERB
ap-5556	471	33	.	.	PUNCT
ap-5556	472	1	from	from	ADP
ap-5556	472	2	the	the	DET
ap-5556	472	3	parametric	parametric	ADJ
ap-5556	472	4	studies	study	NOUN
ap-5556	472	5	,	,	PUNCT
ap-5556	472	6	it	it	PRON
ap-5556	472	7	was	be	AUX
ap-5556	472	8	established	establish	VERB
ap-5556	472	9	that	that	SCONJ
ap-5556	472	10	(	(	PUNCT
ap-5556	472	11	1	1	NUM
ap-5556	472	12	.	.	PUNCT
ap-5556	472	13	)	)	PUNCT
ap-5556	473	1	the	the	DET
ap-5556	473	2	natural	natural	ADJ
ap-5556	473	3	frequency	frequency	NOUN
ap-5556	473	4	of	of	ADP
ap-5556	473	5	circular	circular	ADJ
ap-5556	473	6	plate	plate	NOUN
ap-5556	473	7	increases	increase	VERB
ap-5556	473	8	with	with	ADP
ap-5556	473	9	increase	increase	NOUN
ap-5556	473	10	in	in	ADP
ap-5556	473	11	elastic	elastic	ADJ
ap-5556	473	12	winkler	winkler	NOUN
ap-5556	473	13	foundation	foundation	NOUN
ap-5556	473	14	parameter	parameter	NOUN
ap-5556	473	15	.	.	PUNCT
ap-5556	474	1	(	(	PUNCT
ap-5556	474	2	2	2	NUM
ap-5556	474	3	.	.	PUNCT
ap-5556	474	4	)	)	PUNCT
ap-5556	475	1	the	the	DET
ap-5556	475	2	natural	natural	ADJ
ap-5556	475	3	frequency	frequency	NOUN
ap-5556	475	4	of	of	ADP
ap-5556	475	5	circular	circular	ADJ
ap-5556	475	6	plate	plate	NOUN
ap-5556	475	7	increases	increase	VERB
ap-5556	475	8	with	with	ADP
ap-5556	475	9	an	an	DET
ap-5556	475	10	increase	increase	NOUN
ap-5556	475	11	in	in	ADP
ap-5556	475	12	elastic	elastic	ADJ
ap-5556	475	13	pasternak	pasternak	PROPN
ap-5556	475	14	foundation	foundation	NOUN
ap-5556	475	15	parameter	parameter	NOUN
ap-5556	475	16	.	.	PUNCT
ap-5556	476	1	(	(	PUNCT
ap-5556	476	2	3	3	NUM
ap-5556	476	3	.	.	PUNCT
ap-5556	476	4	)	)	PUNCT
ap-5556	476	5	extreme	extreme	ADJ
ap-5556	476	6	modal	modal	ADJ
ap-5556	476	7	displacement	displacement	NOUN
ap-5556	476	8	occurs	occur	VERB
ap-5556	476	9	on	on	ADP
ap-5556	476	10	the	the	DET
ap-5556	476	11	plate	plate	NOUN
ap-5556	476	12	due	due	ADP
ap-5556	476	13	to	to	ADP
ap-5556	476	14	radial	radial	ADJ
ap-5556	476	15	and	and	CCONJ
ap-5556	476	16	circumferential	circumferential	ADJ
ap-5556	476	17	stresses	stress	NOUN
ap-5556	476	18	.	.	PUNCT
ap-5556	477	1	(	(	PUNCT
ap-5556	477	2	4	4	NUM
ap-5556	477	3	.	.	PUNCT
ap-5556	477	4	)	)	PUNCT
ap-5556	478	1	the	the	DET
ap-5556	478	2	natural	natural	ADJ
ap-5556	478	3	frequency	frequency	NOUN
ap-5556	478	4	of	of	ADP
ap-5556	478	5	the	the	DET
ap-5556	478	6	circular	circular	ADJ
ap-5556	478	7	plate	plate	NOUN
ap-5556	478	8	increases	increase	VERB
ap-5556	478	9	with	with	ADP
ap-5556	478	10	increase	increase	NOUN
ap-5556	478	11	in	in	ADP
ap-5556	478	12	the	the	DET
ap-5556	478	13	thickness	thickness	NOUN
ap-5556	478	14	of	of	ADP
ap-5556	478	15	the	the	DET
ap-5556	478	16	circular	circular	ADJ
ap-5556	478	17	plate	plate	NOUN
ap-5556	478	18	(	(	PUNCT
ap-5556	478	19	5	5	NUM
ap-5556	478	20	.	.	PUNCT
ap-5556	478	21	)	)	PUNCT
ap-5556	479	1	the	the	DET
ap-5556	479	2	natural	natural	ADJ
ap-5556	479	3	frequency	frequency	NOUN
ap-5556	479	4	of	of	ADP
ap-5556	479	5	the	the	DET
ap-5556	479	6	circular	circular	ADJ
ap-5556	479	7	plate	plate	NOUN
ap-5556	479	8	decreases	decrease	VERB
ap-5556	479	9	with	with	ADP
ap-5556	479	10	increase	increase	NOUN
ap-5556	479	11	in	in	ADP
ap-5556	479	12	density	density	NOUN
ap-5556	479	13	of	of	ADP
ap-5556	479	14	the	the	DET
ap-5556	479	15	circular	circular	ADJ
ap-5556	479	16	plate	plate	NOUN
ap-5556	479	17	(	(	PUNCT
ap-5556	479	18	6	6	NUM
ap-5556	479	19	.	.	PUNCT
ap-5556	479	20	)	)	PUNCT
ap-5556	480	1	the	the	DET
ap-5556	480	2	nonlinear	nonlinear	ADJ
ap-5556	480	3	vibration	vibration	NOUN
ap-5556	480	4	frequency	frequency	NOUN
ap-5556	480	5	ratio	ratio	NOUN
ap-5556	480	6	increases	increase	NOUN
ap-5556	480	7	as	as	ADP
ap-5556	480	8	the	the	DET
ap-5556	480	9	stiffness	stiffness	NOUN
ap-5556	480	10	of	of	ADP
ap-5556	480	11	free	free	ADJ
ap-5556	480	12	foundation	foundation	NOUN
ap-5556	480	13	increases	increase	NOUN
ap-5556	480	14	.	.	PUNCT
ap-5556	481	1	increasing	increase	VERB
ap-5556	481	2	nonlinear	nonlinear	ADJ
ap-5556	481	3	foundation	foundation	NOUN
ap-5556	481	4	stiffness	stiffness	NOUN
ap-5556	481	5	decrease	decrease	VERB
ap-5556	481	6	the	the	DET
ap-5556	481	7	deflection	deflection	NOUN
ap-5556	481	8	of	of	ADP
ap-5556	481	9	the	the	DET
ap-5556	481	10	circular	circular	ADJ
ap-5556	481	11	plate	plate	NOUN
ap-5556	481	12	.	.	PUNCT
ap-5556	482	1	(	(	PUNCT
ap-5556	482	2	7	7	NUM
ap-5556	482	3	.	.	PUNCT
ap-5556	482	4	)	)	PUNCT
ap-5556	483	1	deflection	deflection	NOUN
ap-5556	483	2	of	of	ADP
ap-5556	483	3	the	the	DET
ap-5556	483	4	circular	circular	ADJ
ap-5556	483	5	plate	plate	NOUN
ap-5556	483	6	increases	increase	NOUN
ap-5556	483	7	as	as	SCONJ
ap-5556	483	8	the	the	DET
ap-5556	483	9	thickness	thickness	NOUN
ap-5556	483	10	increases	increase	VERB
ap-5556	483	11	for	for	ADP
ap-5556	483	12	nonlinear	nonlinear	ADJ
ap-5556	483	13	model	model	NOUN
ap-5556	483	14	.	.	PUNCT
ap-5556	484	1	conversely	conversely	ADV
ap-5556	484	2	,	,	PUNCT
ap-5556	484	3	the	the	DET
ap-5556	484	4	free	free	PROPN
ap-5556	484	5	foundation	foundation	NOUN
ap-5556	484	6	thickness	thickness	NOUN
ap-5556	484	7	increases	increase	VERB
ap-5556	484	8	the	the	DET
ap-5556	484	9	nonlinear	nonlinear	ADJ
ap-5556	484	10	frequency	frequency	NOUN
ap-5556	484	11	ratio	ratio	NOUN
ap-5556	484	12	decreases	decrease	VERB
ap-5556	484	13	.	.	PUNCT
ap-5556	485	1	(	(	PUNCT
ap-5556	485	2	8	8	NUM
ap-5556	485	3	.	.	PUNCT
ap-5556	485	4	)	)	PUNCT
ap-5556	486	1	increasing	increase	VERB
ap-5556	486	2	the	the	DET
ap-5556	486	3	homogeneity	homogeneity	NOUN
ap-5556	486	4	of	of	ADP
ap-5556	486	5	the	the	DET
ap-5556	486	6	circular	circular	ADJ
ap-5556	486	7	plate	plate	NOUN
ap-5556	486	8	leads	lead	VERB
ap-5556	486	9	to	to	PART
ap-5556	486	10	increase	increase	VERB
ap-5556	486	11	in	in	ADP
ap-5556	486	12	the	the	DET
ap-5556	486	13	deflection	deflection	NOUN
ap-5556	486	14	of	of	ADP
ap-5556	486	15	the	the	DET
ap-5556	486	16	circular	circular	ADJ
ap-5556	486	17	plate	plate	NOUN
ap-5556	486	18	.	.	PUNCT
ap-5556	487	1	the	the	DET
ap-5556	487	2	present	present	ADJ
ap-5556	487	3	study	study	NOUN
ap-5556	487	4	emphasizes	emphasize	VERB
ap-5556	487	5	the	the	DET
ap-5556	487	6	effect	effect	NOUN
ap-5556	487	7	of	of	ADP
ap-5556	487	8	elastic	elastic	ADJ
ap-5556	487	9	foundation	foundation	NOUN
ap-5556	487	10	thickness	thickness	NOUN
ap-5556	487	11	and	and	CCONJ
ap-5556	487	12	density	density	NOUN
ap-5556	487	13	variation	variation	NOUN
ap-5556	487	14	on	on	ADP
ap-5556	487	15	the	the	DET
ap-5556	487	16	dynamic	dynamic	ADJ
ap-5556	487	17	behaviour	behaviour	NOUN
ap-5556	487	18	of	of	ADP
ap-5556	487	19	a	a	DET
ap-5556	487	20	thin	thin	ADJ
ap-5556	487	21	circular	circular	ADJ
ap-5556	487	22	plate	plate	NOUN
ap-5556	487	23	.	.	PUNCT
ap-5556	488	1	also	also	ADV
ap-5556	488	2	,	,	PUNCT
ap-5556	488	3	the	the	DET
ap-5556	488	4	singularities	singularity	NOUN
ap-5556	488	5	issue	issue	NOUN
ap-5556	488	6	of	of	ADP
ap-5556	488	7	circular	circular	ADJ
ap-5556	488	8	plate	plate	NOUN
ap-5556	488	9	is	be	AUX
ap-5556	488	10	handled	handle	VERB
ap-5556	488	11	with	with	ADP
ap-5556	488	12	ease	ease	NOUN
ap-5556	488	13	using	use	VERB
ap-5556	488	14	galerkin	galerkin	NOUN
ap-5556	488	15	of	of	ADP
ap-5556	488	16	weighted	weight	VERB
ap-5556	488	17	residual	residual	ADJ
ap-5556	488	18	,	,	PUNCT
ap-5556	488	19	the	the	DET
ap-5556	488	20	ease	ease	NOUN
ap-5556	488	21	of	of	ADP
ap-5556	488	22	obtaining	obtain	VERB
ap-5556	488	23	the	the	DET
ap-5556	488	24	eigenvalue	eigenvalue	NOUN
ap-5556	488	25	without	without	ADP
ap-5556	488	26	the	the	DET
ap-5556	488	27	difficulty	difficulty	NOUN
ap-5556	488	28	of	of	ADP
ap-5556	488	29	many	many	ADJ
ap-5556	488	30	iteration	iteration	NOUN
ap-5556	488	31	and	and	CCONJ
ap-5556	488	32	complex	complex	ADJ
ap-5556	488	33	mathematics	mathematic	NOUN
ap-5556	488	34	is	be	AUX
ap-5556	488	35	a	a	DET
ap-5556	488	36	huge	huge	ADJ
ap-5556	488	37	benefit	benefit	NOUN
ap-5556	488	38	of	of	ADP
ap-5556	488	39	the	the	DET
ap-5556	488	40	method	method	NOUN
ap-5556	488	41	.	.	PUNCT
ap-5556	489	1	it	it	PRON
ap-5556	489	2	is	be	AUX
ap-5556	489	3	expected	expect	VERB
ap-5556	489	4	that	that	SCONJ
ap-5556	489	5	the	the	DET
ap-5556	489	6	present	present	ADJ
ap-5556	489	7	study	study	NOUN
ap-5556	489	8	will	will	AUX
ap-5556	489	9	contribute	contribute	VERB
ap-5556	489	10	to	to	ADP
ap-5556	489	11	the	the	DET
ap-5556	489	12	understanding	understanding	NOUN
ap-5556	489	13	of	of	ADP
ap-5556	489	14	the	the	DET
ap-5556	489	15	study	study	NOUN
ap-5556	489	16	of	of	ADP
ap-5556	489	17	the	the	DET
ap-5556	489	18	dynamic	dynamic	ADJ
ap-5556	489	19	behavior	behavior	NOUN
ap-5556	489	20	of	of	ADP
ap-5556	489	21	a	a	DET
ap-5556	489	22	circular	circular	ADJ
ap-5556	489	23	plate	plate	NOUN
ap-5556	489	24	under	under	ADP
ap-5556	489	25	various	various	ADJ
ap-5556	489	26	parameters	parameter	NOUN
ap-5556	489	27	.	.	PUNCT
ap-5556	490	1	142	142	NUM
ap-5556	490	2	vol	vol	NOUN
ap-5556	490	3	.	.	PUNCT
ap-5556	491	1	60	60	NUM
ap-5556	491	2	no	no	NOUN
ap-5556	491	3	.	.	PUNCT
ap-5556	492	1	2/2020	2/2020	NUM
ap-5556	492	2	investigation	investigation	NOUN
ap-5556	492	3	of	of	ADP
ap-5556	492	4	the	the	DET
ap-5556	492	5	dynamic	dynamic	ADJ
ap-5556	492	6	behaviour	behaviour	NOUN
ap-5556	492	7	of	of	ADP
ap-5556	492	8	non	non	ADJ
ap-5556	492	9	-	-	ADJ
ap-5556	492	10	uniform	uniform	ADJ
ap-5556	492	11	thickness	thickness	NOUN
ap-5556	492	12	.	.	PUNCT
ap-5556	492	13	.	.	PUNCT
ap-5556	493	1	.	.	PUNCT
ap-5556	494	1	6	6	X
ap-5556	494	2	.	.	X
ap-5556	494	3	data	datum	NOUN
ap-5556	494	4	availability	availability	NOUN
ap-5556	494	5	the	the	DET
ap-5556	494	6	data	datum	NOUN
ap-5556	494	7	used	use	VERB
ap-5556	494	8	to	to	PART
ap-5556	494	9	support	support	VERB
ap-5556	494	10	the	the	DET
ap-5556	494	11	findings	finding	NOUN
ap-5556	494	12	of	of	ADP
ap-5556	494	13	this	this	DET
ap-5556	494	14	study	study	NOUN
ap-5556	494	15	are	be	AUX
ap-5556	494	16	available	available	ADJ
ap-5556	494	17	from	from	ADP
ap-5556	494	18	the	the	DET
ap-5556	494	19	corresponding	corresponding	ADJ
ap-5556	494	20	author	author	NOUN
ap-5556	494	21	upon	upon	SCONJ
ap-5556	494	22	request	request	NOUN
ap-5556	494	23	.	.	PUNCT
ap-5556	495	1	7	7	X
ap-5556	495	2	.	.	X
ap-5556	495	3	conflicts	conflict	NOUN
ap-5556	495	4	of	of	ADP
ap-5556	495	5	interest	interest	NOUN
ap-5556	495	6	the	the	DET
ap-5556	495	7	author	author	NOUN
ap-5556	495	8	declares	declare	VERB
ap-5556	495	9	that	that	SCONJ
ap-5556	495	10	there	there	PRON
ap-5556	495	11	are	be	VERB
ap-5556	495	12	no	no	DET
ap-5556	495	13	conflicts	conflict	NOUN
ap-5556	495	14	of	of	ADP
ap-5556	495	15	interest	interest	NOUN
ap-5556	495	16	regarding	regard	VERB
ap-5556	495	17	the	the	DET
ap-5556	495	18	publication	publication	NOUN
ap-5556	495	19	of	of	ADP
ap-5556	495	20	this	this	DET
ap-5556	495	21	paper	paper	NOUN
ap-5556	495	22	.	.	PUNCT
ap-5556	496	1	acknowledgements	acknowledgement	VERB
ap-5556	496	2	the	the	DET
ap-5556	496	3	author	author	NOUN
ap-5556	496	4	expresses	express	VERB
ap-5556	496	5	sincere	sincere	ADJ
ap-5556	496	6	appreciation	appreciation	NOUN
ap-5556	496	7	to	to	ADP
ap-5556	496	8	the	the	DET
ap-5556	496	9	university	university	PROPN
ap-5556	496	10	of	of	ADP
ap-5556	496	11	lagos	lagos	PROPN
ap-5556	496	12	,	,	PUNCT
ap-5556	496	13	nigeria	nigeria	PROPN
ap-5556	496	14	and	and	CCONJ
ap-5556	496	15	herzer	herzer	NOUN
ap-5556	496	16	research	research	NOUN
ap-5556	496	17	group	group	NOUN
ap-5556	496	18	,	,	PUNCT
ap-5556	496	19	for	for	ADP
ap-5556	496	20	providing	provide	VERB
ap-5556	496	21	material	material	NOUN
ap-5556	496	22	supports	support	NOUN
ap-5556	496	23	and	and	CCONJ
ap-5556	496	24	a	a	DET
ap-5556	496	25	good	good	ADJ
ap-5556	496	26	environment	environment	NOUN
ap-5556	496	27	for	for	ADP
ap-5556	496	28	this	this	DET
ap-5556	496	29	work	work	NOUN
ap-5556	496	30	.	.	PUNCT
ap-5556	497	1	list	list	NOUN
ap-5556	497	2	of	of	ADP
ap-5556	497	3	symbols	symbol	NOUN
ap-5556	497	4	r	r	NOUN
ap-5556	497	5	radius	radius	NOUN
ap-5556	497	6	of	of	ADP
ap-5556	497	7	the	the	DET
ap-5556	497	8	plate	plate	NOUN
ap-5556	497	9	c	c	NOUN
ap-5556	497	10	clamped	clamp	VERB
ap-5556	497	11	edge	edge	NOUN
ap-5556	497	12	plate	plate	NOUN
ap-5556	497	13	e	e	PROPN
ap-5556	497	14	young	young	PROPN
ap-5556	497	15	’s	’s	PART
ap-5556	497	16	modulus	modulus	PROPN
ap-5556	497	17	f	f	PROPN
ap-5556	497	18	free	free	ADJ
ap-5556	497	19	edge	edge	NOUN
ap-5556	497	20	support	support	NOUN
ap-5556	497	21	s	s	PRON
ap-5556	497	22	simply	simply	ADV
ap-5556	497	23	supported	support	VERB
ap-5556	497	24	edge	edge	NOUN
ap-5556	497	25	ω	ω	NUM
ap-5556	497	26	natural	natural	ADJ
ap-5556	497	27	frequency	frequency	NOUN
ap-5556	497	28	d	d	PROPN
ap-5556	497	29	dr	dr	PROPN
ap-5556	497	30	differential	differential	PROPN
ap-5556	497	31	operator	operator	NOUN
ap-5556	497	32	f	f	PROPN
ap-5556	497	33	dynamic	dynamic	ADJ
ap-5556	497	34	deflection	deflection	NOUN
ap-5556	497	35	h	h	PROPN
ap-5556	497	36	plate	plate	NOUN
ap-5556	497	37	thickness	thickness	NOUN
ap-5556	497	38	ρ	ρ	PROPN
ap-5556	497	39	mass	mass	NOUN
ap-5556	497	40	density	density	NOUN
ap-5556	497	41	d	d	NOUN
ap-5556	497	42	modulus	modulus	NOUN
ap-5556	497	43	of	of	ADP
ap-5556	497	44	elasticity	elasticity	NOUN
ap-5556	497	45	references	reference	NOUN
ap-5556	497	46	[	[	X
ap-5556	497	47	1	1	NUM
ap-5556	497	48	]	]	X
ap-5556	497	49	k.-h	k.-h	NOUN
ap-5556	497	50	.	.	PUNCT
ap-5556	498	1	jeong	jeong	PROPN
ap-5556	498	2	,	,	PUNCT
ap-5556	498	3	g.-m	g.-m	PROPN
ap-5556	498	4	.	.	PUNCT
ap-5556	499	1	lee	lee	PROPN
ap-5556	499	2	,	,	PUNCT
ap-5556	499	3	t.-w	t.-w	PROPN
ap-5556	499	4	.	.	PUNCT
ap-5556	500	1	kim	kim	PROPN
ap-5556	500	2	.	.	PUNCT
ap-5556	501	1	free	free	ADJ
ap-5556	501	2	vibration	vibration	NOUN
ap-5556	501	3	analysis	analysis	NOUN
ap-5556	501	4	of	of	ADP
ap-5556	501	5	a	a	DET
ap-5556	501	6	circular	circular	ADJ
ap-5556	501	7	plate	plate	NOUN
ap-5556	501	8	partially	partially	ADV
ap-5556	501	9	in	in	ADP
ap-5556	501	10	contact	contact	NOUN
ap-5556	501	11	with	with	ADP
ap-5556	501	12	a	a	DET
ap-5556	501	13	liquid	liquid	NOUN
ap-5556	501	14	.	.	PUNCT
ap-5556	502	1	journal	journal	PROPN
ap-5556	502	2	of	of	ADP
ap-5556	502	3	sound	sound	NOUN
ap-5556	502	4	and	and	CCONJ
ap-5556	502	5	vibration	vibration	NOUN
ap-5556	502	6	324(1):194	324(1):194	NUM
ap-5556	502	7	–	–	PUNCT
ap-5556	502	8	208	208	NUM
ap-5556	502	9	,	,	PUNCT
ap-5556	502	10	2009	2009	NUM
ap-5556	502	11	.	.	PUNCT
ap-5556	503	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	503	2	/	/	SYM
ap-5556	503	3	j.jsv.2009.01.061	j.jsv.2009.01.061	PROPN
ap-5556	503	4	.	.	PUNCT
ap-5556	504	1	[	[	X
ap-5556	504	2	2	2	NUM
ap-5556	504	3	]	]	PUNCT
ap-5556	504	4	m.	m.	NOUN
ap-5556	504	5	sari	sari	NOUN
ap-5556	504	6	,	,	PUNCT
ap-5556	504	7	e.	e.	PROPN
ap-5556	504	8	butcher	butcher	PROPN
ap-5556	504	9	.	.	PUNCT
ap-5556	505	1	free	free	ADJ
ap-5556	505	2	vibration	vibration	NOUN
ap-5556	505	3	analysis	analysis	NOUN
ap-5556	505	4	of	of	ADP
ap-5556	505	5	rectangular	rectangular	ADJ
ap-5556	505	6	and	and	CCONJ
ap-5556	505	7	annular	annular	ADJ
ap-5556	505	8	mindlin	mindlin	NOUN
ap-5556	505	9	plates	plate	NOUN
ap-5556	505	10	with	with	ADP
ap-5556	505	11	undamaged	undamaged	ADJ
ap-5556	505	12	and	and	CCONJ
ap-5556	505	13	damaged	damaged	ADJ
ap-5556	505	14	boundaries	boundary	NOUN
ap-5556	505	15	by	by	ADP
ap-5556	505	16	the	the	DET
ap-5556	505	17	spectral	spectral	ADJ
ap-5556	505	18	collocation	collocation	NOUN
ap-5556	505	19	method	method	NOUN
ap-5556	505	20	.	.	PUNCT
ap-5556	506	1	jvc	jvc	PROPN
ap-5556	506	2	/	/	SYM
ap-5556	506	3	journal	journal	NOUN
ap-5556	506	4	of	of	ADP
ap-5556	506	5	vibration	vibration	NOUN
ap-5556	506	6	and	and	CCONJ
ap-5556	506	7	control	control	NOUN
ap-5556	506	8	18(11):1722	18(11):1722	NUM
ap-5556	506	9	–	–	PUNCT
ap-5556	506	10	1736	1736	NUM
ap-5556	506	11	,	,	PUNCT
ap-5556	506	12	2012	2012	NUM
ap-5556	506	13	.	.	PUNCT
ap-5556	507	1	doi:10.1177/1077546311422242	doi:10.1177/1077546311422242	NOUN
ap-5556	507	2	.	.	PUNCT
ap-5556	508	1	[	[	X
ap-5556	508	2	3	3	X
ap-5556	508	3	]	]	X
ap-5556	508	4	c.	c.	PROPN
ap-5556	508	5	a.	a.	PROPN
ap-5556	508	6	j.	j.	PROPN
ap-5556	508	7	fletcher	fletcher	PROPN
ap-5556	508	8	.	.	PUNCT
ap-5556	509	1	an	an	DET
ap-5556	509	2	improved	improve	VERB
ap-5556	509	3	finite	finite	ADJ
ap-5556	509	4	element	element	NOUN
ap-5556	509	5	formulation	formulation	NOUN
ap-5556	509	6	derived	derive	VERB
ap-5556	509	7	from	from	ADP
ap-5556	509	8	the	the	DET
ap-5556	509	9	method	method	NOUN
ap-5556	509	10	of	of	ADP
ap-5556	509	11	weighted	weight	VERB
ap-5556	509	12	residuals	residual	NOUN
ap-5556	509	13	.	.	PUNCT
ap-5556	510	1	computer	computer	NOUN
ap-5556	510	2	methods	method	NOUN
ap-5556	510	3	in	in	ADP
ap-5556	510	4	applied	applied	ADJ
ap-5556	510	5	mechanics	mechanic	NOUN
ap-5556	510	6	and	and	CCONJ
ap-5556	510	7	engineering	engineering	NOUN
ap-5556	510	8	15(2):207	15(2):207	NOUN
ap-5556	510	9	–	–	PUNCT
ap-5556	510	10	222	222	NUM
ap-5556	510	11	,	,	PUNCT
ap-5556	510	12	1978	1978	NUM
ap-5556	510	13	.	.	PUNCT
ap-5556	511	1	doi:10.1016/0045	doi:10.1016/0045	ADJ
ap-5556	511	2	-	-	PUNCT
ap-5556	511	3	7825(78)90024	7825(78)90024	NUM
ap-5556	511	4	-	-	SYM
ap-5556	511	5	5	5	NUM
ap-5556	511	6	.	.	PUNCT
ap-5556	512	1	[	[	X
ap-5556	512	2	4	4	X
ap-5556	512	3	]	]	X
ap-5556	512	4	b.	b.	PROPN
ap-5556	512	5	afsharmanesh	afsharmanesh	PROPN
ap-5556	512	6	,	,	PUNCT
ap-5556	512	7	a.	a.	NOUN
ap-5556	512	8	ghaheri	ghaheri	PROPN
ap-5556	512	9	,	,	PUNCT
ap-5556	512	10	f.	f.	PROPN
ap-5556	512	11	taheri	taheri	PROPN
ap-5556	512	12	-	-	PUNCT
ap-5556	512	13	behrooz	behrooz	NOUN
ap-5556	512	14	.	.	PUNCT
ap-5556	513	1	buckling	buckling	NOUN
ap-5556	513	2	and	and	CCONJ
ap-5556	513	3	vibration	vibration	NOUN
ap-5556	513	4	of	of	ADP
ap-5556	513	5	laminated	laminated	ADJ
ap-5556	513	6	composite	composite	ADJ
ap-5556	513	7	circular	circular	ADJ
ap-5556	513	8	plate	plate	NOUN
ap-5556	513	9	on	on	ADP
ap-5556	513	10	winkler	winkler	NOUN
ap-5556	513	11	-	-	PUNCT
ap-5556	513	12	type	type	NOUN
ap-5556	513	13	foundation	foundation	NOUN
ap-5556	513	14	.	.	PUNCT
ap-5556	514	1	steel	steel	NOUN
ap-5556	514	2	and	and	CCONJ
ap-5556	514	3	composite	composite	ADJ
ap-5556	514	4	structures	structure	NOUN
ap-5556	514	5	17:1	17:1	NUM
ap-5556	514	6	–	–	PUNCT
ap-5556	514	7	19	19	NUM
ap-5556	514	8	,	,	PUNCT
ap-5556	514	9	2014	2014	NUM
ap-5556	514	10	.	.	PUNCT
ap-5556	515	1	doi:10.12989	doi:10.12989	PROPN
ap-5556	515	2	/	/	SYM
ap-5556	515	3	scs.2014.17.1.001	scs.2014.17.1.001	PROPN
ap-5556	515	4	.	.	PUNCT
ap-5556	516	1	[	[	X
ap-5556	516	2	5	5	X
ap-5556	516	3	]	]	PUNCT
ap-5556	516	4	w.	w.	PROPN
ap-5556	516	5	lee	lee	PROPN
ap-5556	516	6	,	,	PUNCT
ap-5556	516	7	j.	j.	PROPN
ap-5556	516	8	chen	chen	PROPN
ap-5556	516	9	,	,	PUNCT
ap-5556	516	10	y.	y.	PROPN
ap-5556	516	11	lee	lee	PROPN
ap-5556	516	12	.	.	PUNCT
ap-5556	517	1	free	free	ADJ
ap-5556	517	2	vibration	vibration	NOUN
ap-5556	517	3	analysis	analysis	NOUN
ap-5556	517	4	of	of	ADP
ap-5556	517	5	circular	circular	ADJ
ap-5556	517	6	plates	plate	NOUN
ap-5556	517	7	with	with	ADP
ap-5556	517	8	multiple	multiple	ADJ
ap-5556	517	9	circular	circular	ADJ
ap-5556	517	10	holes	hole	NOUN
ap-5556	517	11	using	use	VERB
ap-5556	517	12	indirect	indirect	ADJ
ap-5556	517	13	biems	biem	NOUN
ap-5556	517	14	.	.	PUNCT
ap-5556	518	1	journal	journal	NOUN
ap-5556	518	2	of	of	ADP
ap-5556	518	3	sound	sound	NOUN
ap-5556	518	4	and	and	CCONJ
ap-5556	518	5	vibration	vibration	NOUN
ap-5556	518	6	304(3):811	304(3):811	NUM
ap-5556	518	7	–	–	PUNCT
ap-5556	518	8	830	830	NUM
ap-5556	518	9	,	,	PUNCT
ap-5556	518	10	2007	2007	NUM
ap-5556	518	11	.	.	PUNCT
ap-5556	519	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	519	2	/	/	SYM
ap-5556	519	3	j.jsv.2007.03.026	j.jsv.2007.03.026	PROPN
ap-5556	519	4	.	.	PUNCT
ap-5556	520	1	[	[	X
ap-5556	520	2	6	6	NUM
ap-5556	520	3	]	]	X
ap-5556	520	4	y.	y.	PROPN
ap-5556	520	5	shan	shan	PROPN
ap-5556	520	6	yun	yun	PROPN
ap-5556	520	7	,	,	PUNCT
ap-5556	520	8	c.	c.	PROPN
ap-5556	520	9	temuer	temuer	PROPN
ap-5556	520	10	.	.	PUNCT
ap-5556	521	1	application	application	NOUN
ap-5556	521	2	of	of	ADP
ap-5556	521	3	the	the	DET
ap-5556	521	4	homotopy	homotopy	NOUN
ap-5556	521	5	perturbation	perturbation	NOUN
ap-5556	521	6	method	method	NOUN
ap-5556	521	7	for	for	ADP
ap-5556	521	8	the	the	DET
ap-5556	521	9	large	large	ADJ
ap-5556	521	10	deflection	deflection	NOUN
ap-5556	521	11	problem	problem	NOUN
ap-5556	521	12	of	of	ADP
ap-5556	521	13	a	a	DET
ap-5556	521	14	circular	circular	ADJ
ap-5556	521	15	plate	plate	NOUN
ap-5556	521	16	.	.	PUNCT
ap-5556	522	1	applied	apply	VERB
ap-5556	522	2	mathematical	mathematical	ADJ
ap-5556	522	3	modelling	modelling	NOUN
ap-5556	522	4	39(3):1308	39(3):1308	NUM
ap-5556	522	5	–	–	PUNCT
ap-5556	522	6	1316	1316	NUM
ap-5556	522	7	,	,	PUNCT
ap-5556	522	8	2015	2015	NUM
ap-5556	522	9	.	.	PUNCT
ap-5556	523	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	523	2	/	/	SYM
ap-5556	523	3	j.apm.2014.09.001	j.apm.2014.09.001	PROPN
ap-5556	523	4	.	.	PUNCT
ap-5556	524	1	[	[	X
ap-5556	524	2	7	7	X
ap-5556	524	3	]	]	X
ap-5556	524	4	y.	y.	PROPN
ap-5556	524	5	shan	shan	PROPN
ap-5556	524	6	yun	yun	PROPN
ap-5556	524	7	,	,	PUNCT
ap-5556	524	8	c.	c.	PROPN
ap-5556	524	9	temuer	temuer	PROPN
ap-5556	524	10	.	.	PUNCT
ap-5556	525	1	application	application	NOUN
ap-5556	525	2	of	of	ADP
ap-5556	525	3	the	the	DET
ap-5556	525	4	homotopy	homotopy	NOUN
ap-5556	525	5	perturbation	perturbation	NOUN
ap-5556	525	6	method	method	NOUN
ap-5556	525	7	for	for	ADP
ap-5556	525	8	the	the	DET
ap-5556	525	9	large	large	ADJ
ap-5556	525	10	deflection	deflection	NOUN
ap-5556	525	11	problem	problem	NOUN
ap-5556	525	12	of	of	ADP
ap-5556	525	13	a	a	DET
ap-5556	525	14	circular	circular	ADJ
ap-5556	525	15	plate	plate	NOUN
ap-5556	525	16	.	.	PUNCT
ap-5556	526	1	applied	apply	VERB
ap-5556	526	2	mathematical	mathematical	ADJ
ap-5556	526	3	modelling	modelling	NOUN
ap-5556	526	4	39(3):1308	39(3):1308	NUM
ap-5556	526	5	–	–	PUNCT
ap-5556	526	6	1316	1316	NUM
ap-5556	526	7	,	,	PUNCT
ap-5556	526	8	2015	2015	NUM
ap-5556	526	9	.	.	PUNCT
ap-5556	527	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	527	2	/	/	SYM
ap-5556	527	3	j.apm.2014.09.001	j.apm.2014.09.001	PROPN
ap-5556	527	4	.	.	PUNCT
ap-5556	528	1	[	[	X
ap-5556	528	2	8	8	NUM
ap-5556	528	3	]	]	PUNCT
ap-5556	528	4	x.	x.	NOUN
ap-5556	528	5	zhong	zhong	PROPN
ap-5556	528	6	,	,	PUNCT
ap-5556	528	7	s.	s.	PROPN
ap-5556	528	8	liao	liao	PROPN
ap-5556	528	9	.	.	PUNCT
ap-5556	529	1	analytic	analytic	ADJ
ap-5556	529	2	solutions	solution	NOUN
ap-5556	529	3	of	of	ADP
ap-5556	529	4	von	von	PROPN
ap-5556	529	5	karman	karman	PROPN
ap-5556	529	6	plate	plate	PROPN
ap-5556	529	7	under	under	ADP
ap-5556	529	8	arbitrary	arbitrary	ADJ
ap-5556	529	9	uniform	uniform	ADJ
ap-5556	529	10	pressure	pressure	NOUN
ap-5556	529	11	(	(	PUNCT
ap-5556	529	12	i	i	NOUN
ap-5556	529	13	):	):	PUNCT
ap-5556	529	14	equations	equation	NOUN
ap-5556	529	15	in	in	ADP
ap-5556	529	16	differential	differential	ADJ
ap-5556	529	17	form	form	NOUN
ap-5556	529	18	.	.	PUNCT
ap-5556	530	1	studies	study	NOUN
ap-5556	530	2	in	in	ADP
ap-5556	530	3	applied	applied	ADJ
ap-5556	530	4	mathematics	mathematic	NOUN
ap-5556	530	5	138	138	NUM
ap-5556	530	6	,	,	PUNCT
ap-5556	530	7	2016	2016	NUM
ap-5556	530	8	.	.	PUNCT
ap-5556	531	1	doi:10.1111	doi:10.1111	PROPN
ap-5556	531	2	/	/	SYM
ap-5556	531	3	sapm.12158	sapm.12158	PROPN
ap-5556	531	4	.	.	PUNCT
ap-5556	532	1	[	[	X
ap-5556	532	2	9	9	NUM
ap-5556	532	3	]	]	PUNCT
ap-5556	532	4	h.	h.	PROPN
ap-5556	532	5	s.	s.	PROPN
ap-5556	532	6	yalcin	yalcin	PROPN
ap-5556	532	7	,	,	PUNCT
ap-5556	532	8	a.	a.	NOUN
ap-5556	532	9	arikoglu	arikoglu	PROPN
ap-5556	532	10	,	,	PUNCT
ap-5556	532	11	i.	i.	PROPN
ap-5556	532	12	ozkol	ozkol	PROPN
ap-5556	532	13	.	.	PUNCT
ap-5556	533	1	free	free	ADJ
ap-5556	533	2	vibration	vibration	NOUN
ap-5556	533	3	analysis	analysis	NOUN
ap-5556	533	4	of	of	ADP
ap-5556	533	5	circular	circular	ADJ
ap-5556	533	6	plates	plate	NOUN
ap-5556	533	7	by	by	ADP
ap-5556	533	8	differential	differential	ADJ
ap-5556	533	9	transformation	transformation	NOUN
ap-5556	533	10	method	method	NOUN
ap-5556	533	11	.	.	PUNCT
ap-5556	534	1	applied	apply	VERB
ap-5556	534	2	mathematics	mathematic	NOUN
ap-5556	534	3	and	and	CCONJ
ap-5556	534	4	computation	computation	NOUN
ap-5556	534	5	212(2):377	212(2):377	NUM
ap-5556	534	6	–	–	PUNCT
ap-5556	534	7	386	386	NUM
ap-5556	534	8	,	,	PUNCT
ap-5556	534	9	2009	2009	NUM
ap-5556	534	10	.	.	PUNCT
ap-5556	535	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	535	2	/	/	SYM
ap-5556	535	3	j.amc.2009.02.032	j.amc.2009.02.032	PROPN
ap-5556	535	4	.	.	PUNCT
ap-5556	536	1	[	[	X
ap-5556	536	2	10	10	NUM
ap-5556	536	3	]	]	X
ap-5556	536	4	q.	q.	PROPN
ap-5556	536	5	li	li	PROPN
ap-5556	536	6	,	,	PUNCT
ap-5556	536	7	j.	j.	PROPN
ap-5556	536	8	liu	liu	PROPN
ap-5556	536	9	,	,	PUNCT
ap-5556	536	10	h.	h.	PROPN
ap-5556	536	11	xiao	xiao	PROPN
ap-5556	536	12	.	.	PUNCT
ap-5556	537	1	a	a	DET
ap-5556	537	2	new	new	ADJ
ap-5556	537	3	approach	approach	NOUN
ap-5556	537	4	for	for	ADP
ap-5556	537	5	bending	bend	VERB
ap-5556	537	6	analysis	analysis	NOUN
ap-5556	537	7	of	of	ADP
ap-5556	537	8	thin	thin	ADJ
ap-5556	537	9	circular	circular	ADJ
ap-5556	537	10	plates	plate	NOUN
ap-5556	537	11	with	with	ADP
ap-5556	537	12	large	large	ADJ
ap-5556	537	13	deflection	deflection	NOUN
ap-5556	537	14	.	.	PUNCT
ap-5556	538	1	international	international	ADJ
ap-5556	538	2	journal	journal	PROPN
ap-5556	538	3	of	of	ADP
ap-5556	538	4	mechanical	mechanical	ADJ
ap-5556	538	5	sciences	science	NOUN
ap-5556	538	6	46(2):173	46(2):173	PROPN
ap-5556	538	7	–	–	PUNCT
ap-5556	538	8	180	180	NUM
ap-5556	538	9	,	,	PUNCT
ap-5556	538	10	2004	2004	NUM
ap-5556	538	11	.	.	PUNCT
ap-5556	539	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	539	2	/	/	SYM
ap-5556	539	3	j.ijmecsci.2004.03.012	j.ijmecsci.2004.03.012	PROPN
ap-5556	539	4	.	.	PUNCT
ap-5556	540	1	[	[	X
ap-5556	540	2	11	11	NUM
ap-5556	540	3	]	]	PUNCT
ap-5556	540	4	z.	z.	PROPN
ap-5556	540	5	liangchi	liangchi	PROPN
ap-5556	540	6	,	,	PUNCT
ap-5556	540	7	d.	d.	PROPN
ap-5556	540	8	haojiang	haojiang	PROPN
ap-5556	540	9	.	.	PUNCT
ap-5556	541	1	the	the	DET
ap-5556	541	2	method	method	NOUN
ap-5556	541	3	of	of	ADP
ap-5556	541	4	weighted	weight	VERB
ap-5556	541	5	residuals	residual	NOUN
ap-5556	541	6	for	for	ADP
ap-5556	541	7	transversely	transversely	ADJ
ap-5556	541	8	isotropic	isotropic	NOUN
ap-5556	541	9	axisymmetric	axisymmetric	ADJ
ap-5556	541	10	problems	problem	NOUN
ap-5556	541	11	and	and	CCONJ
ap-5556	541	12	its	its	PRON
ap-5556	541	13	applications	application	NOUN
ap-5556	541	14	to	to	ADP
ap-5556	541	15	engineering	engineering	NOUN
ap-5556	541	16	.	.	PUNCT
ap-5556	542	1	acta	acta	PROPN
ap-5556	542	2	mechanica	mechanica	PROPN
ap-5556	542	3	sinica	sinica	PROPN
ap-5556	542	4	3:261	3:261	PROPN
ap-5556	542	5	–	–	PUNCT
ap-5556	542	6	267	267	NUM
ap-5556	542	7	,	,	PUNCT
ap-5556	542	8	1987	1987	NUM
ap-5556	542	9	.	.	PUNCT
ap-5556	543	1	doi:10.1007	doi:10.1007	PROPN
ap-5556	543	2	/	/	SYM
ap-5556	543	3	bf02486772	bf02486772	NOUN
ap-5556	543	4	.	.	PUNCT
ap-5556	544	1	[	[	X
ap-5556	544	2	12	12	NUM
ap-5556	544	3	]	]	PUNCT
ap-5556	544	4	m.	m.	NOUN
ap-5556	544	5	shariyat	shariyat	PROPN
ap-5556	544	6	.	.	PUNCT
ap-5556	544	7	differential	differential	ADJ
ap-5556	544	8	transform	transform	VERB
ap-5556	544	9	vibration	vibration	NOUN
ap-5556	544	10	and	and	CCONJ
ap-5556	544	11	modal	modal	NOUN
ap-5556	544	12	stress	stress	NOUN
ap-5556	544	13	analyses	analysis	NOUN
ap-5556	544	14	of	of	ADP
ap-5556	544	15	circular	circular	ADJ
ap-5556	544	16	plates	plate	NOUN
ap-5556	544	17	made	make	VERB
ap-5556	544	18	of	of	ADP
ap-5556	544	19	two	two	NUM
ap-5556	544	20	-	-	PUNCT
ap-5556	544	21	directional	directional	NOUN
ap-5556	544	22	functionally	functionally	ADV
ap-5556	544	23	graded	grade	VERB
ap-5556	544	24	materials	material	NOUN
ap-5556	544	25	resting	rest	VERB
ap-5556	544	26	on	on	ADP
ap-5556	544	27	elastic	elastic	ADJ
ap-5556	544	28	foundations	foundation	NOUN
ap-5556	544	29	.	.	PUNCT
ap-5556	545	1	archive	archive	NOUN
ap-5556	545	2	of	of	ADP
ap-5556	545	3	applied	apply	VERB
ap-5556	545	4	mechanics	mechanic	NOUN
ap-5556	545	5	81:1289	81:1289	NUM
ap-5556	545	6	–	–	PUNCT
ap-5556	545	7	1306	1306	NUM
ap-5556	545	8	,	,	PUNCT
ap-5556	545	9	2011	2011	NUM
ap-5556	545	10	.	.	PUNCT
ap-5556	546	1	doi:10.1007	doi:10.1007	VERB
ap-5556	546	2	/	/	SYM
ap-5556	546	3	s00419	s00419	PROPN
ap-5556	546	4	-	-	PUNCT
ap-5556	546	5	010	010	NUM
ap-5556	546	6	-	-	PUNCT
ap-5556	546	7	0484	0484	NUM
ap-5556	546	8	-	-	PUNCT
ap-5556	546	9	x.	x.	NOUN
ap-5556	547	1	[	[	X
ap-5556	547	2	13	13	NUM
ap-5556	547	3	]	]	X
ap-5556	547	4	d.	d.	PROPN
ap-5556	547	5	shi	shi	PROPN
ap-5556	547	6	,	,	PUNCT
ap-5556	547	7	h.	h.	PROPN
ap-5556	547	8	zhang	zhang	PROPN
ap-5556	547	9	,	,	PUNCT
ap-5556	547	10	q.	q.	PROPN
ap-5556	547	11	wang	wang	PROPN
ap-5556	547	12	,	,	PUNCT
ap-5556	547	13	s.	s.	PROPN
ap-5556	547	14	zha	zha	PROPN
ap-5556	547	15	.	.	PROPN
ap-5556	547	16	free	free	ADJ
ap-5556	547	17	and	and	CCONJ
ap-5556	547	18	forced	force	VERB
ap-5556	547	19	vibration	vibration	NOUN
ap-5556	547	20	of	of	ADP
ap-5556	547	21	the	the	DET
ap-5556	547	22	moderately	moderately	ADV
ap-5556	547	23	thick	thick	ADJ
ap-5556	547	24	laminated	laminated	ADJ
ap-5556	547	25	composite	composite	ADJ
ap-5556	547	26	rectangular	rectangular	ADJ
ap-5556	547	27	plate	plate	NOUN
ap-5556	547	28	on	on	ADP
ap-5556	547	29	various	various	ADJ
ap-5556	547	30	elastic	elastic	ADJ
ap-5556	547	31	winkler	winkler	NOUN
ap-5556	547	32	and	and	CCONJ
ap-5556	547	33	pasternak	pasternak	PROPN
ap-5556	547	34	foundations	foundation	NOUN
ap-5556	547	35	.	.	PUNCT
ap-5556	548	1	shock	shock	NOUN
ap-5556	548	2	and	and	CCONJ
ap-5556	548	3	vibration	vibration	NOUN
ap-5556	548	4	2017	2017	NUM
ap-5556	548	5	,	,	PUNCT
ap-5556	548	6	2017	2017	NUM
ap-5556	548	7	.	.	PUNCT
ap-5556	549	1	[	[	X
ap-5556	549	2	14	14	NUM
ap-5556	549	3	]	]	PUNCT
ap-5556	549	4	ömer	ömer	NOUN
ap-5556	549	5	civalek	civalek	NOUN
ap-5556	549	6	,	,	PUNCT
ap-5556	549	7	m.	m.	NOUN
ap-5556	549	8	h.	h.	PROPN
ap-5556	549	9	acar	acar	PROPN
ap-5556	549	10	.	.	PUNCT
ap-5556	550	1	discrete	discrete	ADJ
ap-5556	550	2	singular	singular	ADJ
ap-5556	550	3	convolution	convolution	NOUN
ap-5556	550	4	method	method	NOUN
ap-5556	550	5	for	for	ADP
ap-5556	550	6	the	the	DET
ap-5556	550	7	analysis	analysis	NOUN
ap-5556	550	8	of	of	ADP
ap-5556	550	9	mindlin	mindlin	NOUN
ap-5556	550	10	plates	plate	NOUN
ap-5556	550	11	on	on	ADP
ap-5556	550	12	elastic	elastic	ADJ
ap-5556	550	13	foundations	foundation	NOUN
ap-5556	550	14	.	.	PUNCT
ap-5556	551	1	international	international	ADJ
ap-5556	551	2	journal	journal	NOUN
ap-5556	551	3	of	of	ADP
ap-5556	551	4	pressure	pressure	NOUN
ap-5556	551	5	vessels	vessel	NOUN
ap-5556	551	6	and	and	CCONJ
ap-5556	551	7	piping	pipe	VERB
ap-5556	551	8	84(9):527	84(9):527	NUM
ap-5556	551	9	–	–	PUNCT
ap-5556	551	10	535	535	NUM
ap-5556	551	11	,	,	PUNCT
ap-5556	551	12	2007	2007	NUM
ap-5556	551	13	.	.	PUNCT
ap-5556	552	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	552	2	/	/	SYM
ap-5556	552	3	j.ijpvp.2007.07.001	j.ijpvp.2007.07.001	PROPN
ap-5556	552	4	.	.	PUNCT
ap-5556	553	1	143	143	NUM
ap-5556	553	2	http://dx.doi.org/10.1016/j.jsv.2009.01.061	http://dx.doi.org/10.1016/j.jsv.2009.01.061	PROPN
ap-5556	553	3	http://dx.doi.org/10.1177/1077546311422242	http://dx.doi.org/10.1177/1077546311422242	NOUN
ap-5556	553	4	http://dx.doi.org/10.1016/0045-7825(78)90024-5	http://dx.doi.org/10.1016/0045-7825(78)90024-5	VERB
ap-5556	553	5	http://dx.doi.org/10.12989/scs.2014.17.1.001	http://dx.doi.org/10.12989/scs.2014.17.1.001	NOUN
ap-5556	554	1	http://dx.doi.org/10.1016/j.jsv.2007.03.026	http://dx.doi.org/10.1016/j.jsv.2007.03.026	PROPN
ap-5556	554	2	http://dx.doi.org/10.1016/j.apm.2014.09.001	http://dx.doi.org/10.1016/j.apm.2014.09.001	PROPN
ap-5556	554	3	http://dx.doi.org/10.1016/j.apm.2014.09.001	http://dx.doi.org/10.1016/j.apm.2014.09.001	PROPN
ap-5556	554	4	http://dx.doi.org/10.1111/sapm.12158	http://dx.doi.org/10.1111/sapm.12158	NOUN
ap-5556	555	1	http://dx.doi.org/10.1016/j.amc.2009.02.032	http://dx.doi.org/10.1016/j.amc.2009.02.032	NOUN
ap-5556	555	2	http://dx.doi.org/10.1016/j.ijmecsci.2004.03.012	http://dx.doi.org/10.1016/j.ijmecsci.2004.03.012	NOUN
ap-5556	555	3	http://dx.doi.org/10.1007/bf02486772	http://dx.doi.org/10.1007/bf02486772	ADV
ap-5556	555	4	http://dx.doi.org/10.1007/s00419-010-0484-x	http://dx.doi.org/10.1007/s00419-010-0484-x	PROPN
ap-5556	555	5	http://dx.doi.org/10.1016/j.ijpvp.2007.07.001	http://dx.doi.org/10.1016/j.ijpvp.2007.07.001	PROPN
ap-5556	555	6	s.	s.	PROPN
ap-5556	555	7	salawu	salawu	PROPN
ap-5556	555	8	,	,	PUNCT
ap-5556	555	9	g.	g.	PROPN
ap-5556	555	10	sobamowo	sobamowo	PROPN
ap-5556	555	11	,	,	PUNCT
ap-5556	555	12	o.	o.	PROPN
ap-5556	555	13	sadiq	sadiq	PROPN
ap-5556	555	14	acta	acta	PROPN
ap-5556	555	15	polytechnica	polytechnica	PROPN
ap-5556	555	16	[	[	X
ap-5556	555	17	15	15	NUM
ap-5556	555	18	]	]	X
ap-5556	556	1	b.	b.	PROPN
ap-5556	556	2	akgöz	akgöz	PROPN
ap-5556	556	3	,	,	PUNCT
ap-5556	556	4	o.	o.	PROPN
ap-5556	556	5	civalek	civalek	PROPN
ap-5556	556	6	.	.	PUNCT
ap-5556	557	1	nonlinear	nonlinear	ADJ
ap-5556	557	2	vibration	vibration	NOUN
ap-5556	557	3	analysis	analysis	NOUN
ap-5556	557	4	of	of	ADP
ap-5556	557	5	laminated	laminated	ADJ
ap-5556	557	6	plates	plate	NOUN
ap-5556	557	7	resting	rest	VERB
ap-5556	557	8	on	on	ADP
ap-5556	557	9	nonlinear	nonlinear	ADJ
ap-5556	557	10	two	two	NUM
ap-5556	557	11	-	-	PUNCT
ap-5556	557	12	parameters	parameter	NOUN
ap-5556	557	13	elastic	elastic	ADJ
ap-5556	557	14	foundations	foundation	NOUN
ap-5556	557	15	.	.	PUNCT
ap-5556	558	1	steel	steel	NOUN
ap-5556	558	2	and	and	CCONJ
ap-5556	558	3	composite	composite	ADJ
ap-5556	558	4	structures	structure	NOUN
ap-5556	558	5	11:403	11:403	NUM
ap-5556	558	6	–	–	PUNCT
ap-5556	558	7	421	421	NUM
ap-5556	558	8	,	,	PUNCT
ap-5556	558	9	2011	2011	NUM
ap-5556	558	10	.	.	PUNCT
ap-5556	559	1	doi:10.12989	doi:10.12989	PROPN
ap-5556	559	2	/	/	SYM
ap-5556	559	3	scs.2011.11.5.403	scs.2011.11.5.403	PROPN
ap-5556	559	4	.	.	PUNCT
ap-5556	560	1	[	[	X
ap-5556	560	2	16	16	NUM
ap-5556	560	3	]	]	PUNCT
ap-5556	560	4	m.	m.	NOUN
ap-5556	560	5	bodaghi	bodaghi	PROPN
ap-5556	560	6	,	,	PUNCT
ap-5556	560	7	a.	a.	PROPN
ap-5556	560	8	saidi	saidi	PROPN
ap-5556	560	9	.	.	PUNCT
ap-5556	561	1	stability	stability	NOUN
ap-5556	561	2	analysis	analysis	NOUN
ap-5556	561	3	of	of	ADP
ap-5556	561	4	functionally	functionally	ADV
ap-5556	561	5	graded	grade	VERB
ap-5556	561	6	rectangular	rectangular	ADJ
ap-5556	561	7	plates	plate	NOUN
ap-5556	561	8	under	under	ADP
ap-5556	561	9	nonlinearly	nonlinearly	ADV
ap-5556	561	10	varying	vary	VERB
ap-5556	561	11	in	in	ADP
ap-5556	561	12	-	-	PUNCT
ap-5556	561	13	plane	plane	NOUN
ap-5556	561	14	loading	loading	NOUN
ap-5556	561	15	resting	rest	VERB
ap-5556	561	16	on	on	ADP
ap-5556	561	17	elastic	elastic	ADJ
ap-5556	561	18	foundation	foundation	NOUN
ap-5556	561	19	.	.	PUNCT
ap-5556	562	1	archive	archive	NOUN
ap-5556	562	2	of	of	ADP
ap-5556	562	3	applied	apply	VERB
ap-5556	562	4	mechanics	mechanic	NOUN
ap-5556	562	5	81:765	81:765	NUM
ap-5556	562	6	–	–	PUNCT
ap-5556	562	7	780	780	NUM
ap-5556	562	8	,	,	PUNCT
ap-5556	562	9	2011	2011	NUM
ap-5556	562	10	.	.	PUNCT
ap-5556	563	1	doi:10.1007	doi:10.1007	VERB
ap-5556	563	2	/	/	SYM
ap-5556	563	3	s00419	s00419	PROPN
ap-5556	563	4	-	-	PUNCT
ap-5556	563	5	010	010	NUM
ap-5556	563	6	-	-	PUNCT
ap-5556	563	7	0449	0449	NUM
ap-5556	563	8	-	-	PUNCT
ap-5556	563	9	0	0	NUM
ap-5556	563	10	.	.	PUNCT
ap-5556	564	1	[	[	X
ap-5556	564	2	17	17	NUM
ap-5556	564	3	]	]	X
ap-5556	564	4	o.	o.	PROPN
ap-5556	564	5	civalek	civalek	PROPN
ap-5556	564	6	,	,	PUNCT
ap-5556	564	7	c.	c.	PROPN
ap-5556	564	8	demir	demir	PROPN
ap-5556	564	9	.	.	PUNCT
ap-5556	565	1	buckling	buckle	VERB
ap-5556	565	2	and	and	CCONJ
ap-5556	565	3	bending	bend	VERB
ap-5556	565	4	analyses	analysis	NOUN
ap-5556	565	5	of	of	ADP
ap-5556	565	6	cantilever	cantilever	NOUN
ap-5556	565	7	carbon	carbon	NOUN
ap-5556	565	8	nanotubes	nanotube	NOUN
ap-5556	565	9	using	use	VERB
ap-5556	565	10	the	the	DET
ap-5556	565	11	euler	euler	VERB
ap-5556	565	12	-	-	PUNCT
ap-5556	565	13	bernoulli	bernoulli	PROPN
ap-5556	565	14	beam	beam	NOUN
ap-5556	565	15	theory	theory	NOUN
ap-5556	565	16	based	base	VERB
ap-5556	565	17	on	on	ADP
ap-5556	565	18	non	non	ADJ
ap-5556	565	19	-	-	ADJ
ap-5556	565	20	local	local	ADJ
ap-5556	565	21	continuum	continuum	ADJ
ap-5556	565	22	model	model	NOUN
ap-5556	565	23	.	.	PUNCT
ap-5556	566	1	asian	asian	ADJ
ap-5556	566	2	journal	journal	NOUN
ap-5556	566	3	of	of	ADP
ap-5556	566	4	civil	civil	ADJ
ap-5556	566	5	engineering	engineering	NOUN
ap-5556	566	6	12:651	12:651	NUM
ap-5556	566	7	–	–	PUNCT
ap-5556	566	8	–	–	PUNCT
ap-5556	566	9	661	661	NUM
ap-5556	566	10	,	,	PUNCT
ap-5556	566	11	2011	2011	NUM
ap-5556	566	12	.	.	PUNCT
ap-5556	567	1	[	[	X
ap-5556	567	2	18	18	NUM
ap-5556	567	3	]	]	PUNCT
ap-5556	567	4	k.	k.	PROPN
ap-5556	567	5	k.	k.	PROPN
ap-5556	567	6	żur	żur	PROPN
ap-5556	567	7	.	.	PROPN
ap-5556	567	8	quasi	quasi	ADJ
ap-5556	567	9	-	-	ADJ
ap-5556	567	10	green	green	ADJ
ap-5556	567	11	’s	’s	PART
ap-5556	567	12	function	function	NOUN
ap-5556	567	13	approach	approach	NOUN
ap-5556	567	14	to	to	ADP
ap-5556	567	15	free	free	ADJ
ap-5556	567	16	vibration	vibration	NOUN
ap-5556	567	17	analysis	analysis	NOUN
ap-5556	567	18	of	of	ADP
ap-5556	567	19	elastically	elastically	ADV
ap-5556	567	20	supported	support	VERB
ap-5556	567	21	functionally	functionally	ADV
ap-5556	567	22	graded	grade	VERB
ap-5556	567	23	circular	circular	ADJ
ap-5556	567	24	plates	plate	NOUN
ap-5556	567	25	.	.	PUNCT
ap-5556	568	1	composite	composite	ADJ
ap-5556	568	2	structures	structure	NOUN
ap-5556	568	3	183:600	183:600	NUM
ap-5556	568	4	–	–	PUNCT
ap-5556	568	5	610	610	NUM
ap-5556	568	6	,	,	PUNCT
ap-5556	568	7	2018	2018	NUM
ap-5556	568	8	.	.	PUNCT
ap-5556	569	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	569	2	/	/	SYM
ap-5556	569	3	j.compstruct.2017.07.012	j.compstruct.2017.07.012	PROPN
ap-5556	569	4	.	.	PUNCT
ap-5556	570	1	[	[	X
ap-5556	570	2	19	19	NUM
ap-5556	570	3	]	]	PUNCT
ap-5556	570	4	k.	k.	PROPN
ap-5556	570	5	k.	k.	PROPN
ap-5556	570	6	żur	żur	PROPN
ap-5556	570	7	.	.	PROPN
ap-5556	570	8	free	free	ADJ
ap-5556	570	9	vibration	vibration	NOUN
ap-5556	570	10	analysis	analysis	NOUN
ap-5556	570	11	of	of	ADP
ap-5556	570	12	elastically	elastically	ADV
ap-5556	570	13	supported	support	VERB
ap-5556	570	14	functionally	functionally	ADV
ap-5556	570	15	graded	grade	VERB
ap-5556	570	16	annular	annular	ADJ
ap-5556	570	17	plates	plate	NOUN
ap-5556	570	18	via	via	ADP
ap-5556	570	19	quasi	quasi	ADJ
ap-5556	570	20	-	-	ADJ
ap-5556	570	21	green	green	ADJ
ap-5556	570	22	’s	’s	PART
ap-5556	570	23	function	function	NOUN
ap-5556	570	24	method	method	NOUN
ap-5556	570	25	.	.	PUNCT
ap-5556	571	1	composites	composite	VERB
ap-5556	571	2	part	part	NOUN
ap-5556	571	3	b	b	NOUN
ap-5556	571	4	:	:	PUNCT
ap-5556	571	5	engineering	engineer	VERB
ap-5556	571	6	144:37	144:37	NUM
ap-5556	571	7	–	–	PUNCT
ap-5556	571	8	55	55	NUM
ap-5556	571	9	,	,	PUNCT
ap-5556	571	10	2018	2018	NUM
ap-5556	571	11	.	.	PUNCT
ap-5556	572	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	572	2	/	/	SYM
ap-5556	572	3	j.compositesb.2018.02.019	j.compositesb.2018.02.019	PROPN
ap-5556	572	4	.	.	PUNCT
ap-5556	573	1	[	[	X
ap-5556	573	2	20	20	NUM
ap-5556	573	3	]	]	PUNCT
ap-5556	573	4	k.	k.	PROPN
ap-5556	573	5	k.	k.	PROPN
ap-5556	573	6	żur	żur	PROPN
ap-5556	573	7	,	,	PUNCT
ap-5556	573	8	p.	p.	PROPN
ap-5556	573	9	jankowski	jankowski	PROPN
ap-5556	573	10	.	.	PUNCT
ap-5556	574	1	multiparametric	multiparametric	ADJ
ap-5556	574	2	analytical	analytical	ADJ
ap-5556	574	3	solution	solution	NOUN
ap-5556	574	4	for	for	ADP
ap-5556	574	5	the	the	DET
ap-5556	574	6	eigenvalue	eigenvalue	ADJ
ap-5556	574	7	problem	problem	NOUN
ap-5556	574	8	of	of	ADP
ap-5556	574	9	fgm	fgm	PROPN
ap-5556	574	10	porous	porous	ADJ
ap-5556	574	11	circular	circular	ADJ
ap-5556	574	12	plates	plate	NOUN
ap-5556	574	13	.	.	PUNCT
ap-5556	575	1	symmetry	symmetry	PROPN
ap-5556	575	2	11:429	11:429	NUM
ap-5556	575	3	,	,	PUNCT
ap-5556	575	4	2019	2019	NUM
ap-5556	575	5	.	.	PUNCT
ap-5556	576	1	[	[	X
ap-5556	576	2	21	21	NUM
ap-5556	576	3	]	]	PUNCT
ap-5556	576	4	k.	k.	PROPN
ap-5556	576	5	k.	k.	PROPN
ap-5556	576	6	żur	żur	PROPN
ap-5556	576	7	.	.	PROPN
ap-5556	576	8	free	free	ADJ
ap-5556	576	9	vibration	vibration	NOUN
ap-5556	576	10	analysis	analysis	NOUN
ap-5556	576	11	of	of	ADP
ap-5556	576	12	discrete	discrete	NOUN
ap-5556	576	13	-	-	PUNCT
ap-5556	576	14	continuous	continuous	ADJ
ap-5556	576	15	functionally	functionally	ADV
ap-5556	576	16	graded	grade	VERB
ap-5556	576	17	circular	circular	ADJ
ap-5556	576	18	plate	plate	NOUN
ap-5556	576	19	via	via	ADP
ap-5556	576	20	the	the	DET
ap-5556	576	21	neumann	neumann	PROPN
ap-5556	576	22	series	series	PROPN
ap-5556	576	23	method	method	PROPN
ap-5556	576	24	.	.	PUNCT
ap-5556	577	1	applied	apply	VERB
ap-5556	577	2	mathematical	mathematical	ADJ
ap-5556	577	3	modelling	model	VERB
ap-5556	577	4	73:166	73:166	NUM
ap-5556	577	5	–	–	PUNCT
ap-5556	577	6	189	189	NUM
ap-5556	577	7	,	,	PUNCT
ap-5556	577	8	2019	2019	NUM
ap-5556	577	9	.	.	PUNCT
ap-5556	578	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	578	2	/	/	SYM
ap-5556	578	3	j.apm.2019.02.047	j.apm.2019.02.047	PROPN
ap-5556	578	4	.	.	PUNCT
ap-5556	579	1	[	[	X
ap-5556	579	2	22	22	NUM
ap-5556	579	3	]	]	PUNCT
ap-5556	579	4	k.	k.	PROPN
ap-5556	579	5	k.	k.	PROPN
ap-5556	579	6	żur	żur	PROPN
ap-5556	579	7	.	.	PROPN
ap-5556	579	8	green	green	PROPN
ap-5556	579	9	’s	’s	PART
ap-5556	579	10	function	function	NOUN
ap-5556	579	11	approach	approach	NOUN
ap-5556	579	12	to	to	AUX
ap-5556	579	13	frequency	frequency	VERB
ap-5556	579	14	analysis	analysis	NOUN
ap-5556	579	15	of	of	ADP
ap-5556	579	16	thin	thin	ADJ
ap-5556	579	17	circular	circular	ADJ
ap-5556	579	18	plates	plate	NOUN
ap-5556	579	19	.	.	PUNCT
ap-5556	580	1	bulletin	bulletin	NOUN
ap-5556	580	2	of	of	ADP
ap-5556	580	3	the	the	DET
ap-5556	580	4	polish	polish	PROPN
ap-5556	580	5	academy	academy	PROPN
ap-5556	580	6	of	of	ADP
ap-5556	580	7	sciences	sciences	PROPN
ap-5556	580	8	technical	technical	PROPN
ap-5556	580	9	sciences	sciences	PROPN
ap-5556	580	10	64(1	64(1	NUM
ap-5556	580	11	)	)	PUNCT
ap-5556	580	12	,	,	PUNCT
ap-5556	580	13	2016	2016	NUM
ap-5556	580	14	.	.	PUNCT
ap-5556	581	1	doi:10.1515	doi:10.1515	NOUN
ap-5556	581	2	/	/	SYM
ap-5556	581	3	bpasts-2016	bpasts-2016	NOUN
ap-5556	581	4	-	-	PUNCT
ap-5556	581	5	0020	0020	NUM
ap-5556	581	6	.	.	PUNCT
ap-5556	582	1	[	[	X
ap-5556	582	2	23	23	NUM
ap-5556	582	3	]	]	PUNCT
ap-5556	582	4	k.	k.	PROPN
ap-5556	582	5	k.	k.	PROPN
ap-5556	582	6	żur	żur	PROPN
ap-5556	582	7	.	.	PROPN
ap-5556	582	8	green	green	PROPN
ap-5556	582	9	’s	’s	PART
ap-5556	582	10	function	function	NOUN
ap-5556	582	11	in	in	ADP
ap-5556	582	12	frequency	frequency	NOUN
ap-5556	582	13	analysis	analysis	NOUN
ap-5556	582	14	of	of	ADP
ap-5556	582	15	circular	circular	ADJ
ap-5556	582	16	thin	thin	ADJ
ap-5556	582	17	plates	plate	NOUN
ap-5556	582	18	of	of	ADP
ap-5556	582	19	variable	variable	ADJ
ap-5556	582	20	thickness	thickness	NOUN
ap-5556	582	21	53:873	53:873	NUM
ap-5556	582	22	–	–	PUNCT
ap-5556	582	23	884	884	NUM
ap-5556	582	24	,	,	PUNCT
ap-5556	582	25	2015	2015	NUM
ap-5556	582	26	.	.	PUNCT
ap-5556	583	1	doi:10.15632	doi:10.15632	PROPN
ap-5556	583	2	/	/	SYM
ap-5556	583	3	jtam	jtam	NOUN
ap-5556	583	4	-	-	PUNCT
ap-5556	583	5	pl.53.4.873	pl.53.4.873	PROPN
ap-5556	583	6	.	.	PUNCT
ap-5556	584	1	[	[	X
ap-5556	584	2	24	24	NUM
ap-5556	584	3	]	]	X
ap-5556	584	4	s.	s.	PROPN
ap-5556	584	5	salawu	salawu	PROPN
ap-5556	584	6	,	,	PUNCT
ap-5556	584	7	g.	g.	PROPN
ap-5556	584	8	sobamowo	sobamowo	PROPN
ap-5556	584	9	.	.	PUNCT
ap-5556	585	1	assessment	assessment	NOUN
ap-5556	585	2	of	of	ADP
ap-5556	585	3	hybrid	hybrid	ADJ
ap-5556	585	4	method	method	NOUN
ap-5556	585	5	on	on	ADP
ap-5556	585	6	investigation	investigation	NOUN
ap-5556	585	7	of	of	ADP
ap-5556	585	8	dynamic	dynamic	ADJ
ap-5556	585	9	behaviour	behaviour	NOUN
ap-5556	585	10	of	of	ADP
ap-5556	585	11	isotropic	isotropic	ADJ
ap-5556	585	12	rectangular	rectangular	ADJ
ap-5556	585	13	plates	plate	NOUN
ap-5556	585	14	resting	rest	VERB
ap-5556	585	15	on	on	ADP
ap-5556	585	16	two	two	NUM
ap-5556	585	17	-	-	PUNCT
ap-5556	585	18	parameters	parameter	NOUN
ap-5556	585	19	foundation	foundation	NOUN
ap-5556	585	20	under	under	ADP
ap-5556	585	21	a	a	DET
ap-5556	585	22	creative	creative	ADJ
ap-5556	585	23	commons	common	NOUN
ap-5556	585	24	attribution	attribution	NOUN
ap-5556	585	25	-	-	PUNCT
ap-5556	585	26	noncommercial	noncommercial	ADJ
ap-5556	585	27	4.0	4.0	NUM
ap-5556	585	28	international	international	ADJ
ap-5556	585	29	license	license	NOUN
ap-5556	585	30	(	(	PUNCT
ap-5556	585	31	cc	cc	NOUN
ap-5556	585	32	by	by	ADP
ap-5556	585	33	-	-	PUNCT
ap-5556	585	34	nc	nc	PROPN
ap-5556	585	35	4	4	NUM
ap-5556	585	36	13:169	13:169	NUM
ap-5556	585	37	–	–	PUNCT
ap-5556	585	38	181	181	NUM
ap-5556	585	39	,	,	PUNCT
ap-5556	585	40	2020	2020	NUM
ap-5556	585	41	.	.	PUNCT
ap-5556	586	1	doi:10.17516/1999	doi:10.17516/1999	NOUN
ap-5556	586	2	-	-	PUNCT
ap-5556	586	3	494x-0213	494x-0213	NUM
ap-5556	586	4	.	.	PUNCT
ap-5556	587	1	[	[	X
ap-5556	587	2	25	25	NUM
ap-5556	587	3	]	]	X
ap-5556	587	4	s.	s.	PROPN
ap-5556	587	5	salawu	salawu	PROPN
ap-5556	587	6	,	,	PUNCT
ap-5556	587	7	g.	g.	PROPN
ap-5556	587	8	sobamowo	sobamowo	PROPN
ap-5556	587	9	,	,	PUNCT
ap-5556	587	10	o.	o.	PROPN
ap-5556	587	11	sadiq	sadiq	PROPN
ap-5556	587	12	.	.	PUNCT
ap-5556	588	1	dynamic	dynamic	ADJ
ap-5556	588	2	analysis	analysis	NOUN
ap-5556	588	3	of	of	ADP
ap-5556	588	4	non	non	ADJ
ap-5556	588	5	-	-	ADJ
ap-5556	588	6	homogenous	homogenous	ADJ
ap-5556	588	7	varying	vary	VERB
ap-5556	588	8	thickness	thickness	NOUN
ap-5556	588	9	rectangular	rectangular	ADJ
ap-5556	588	10	plates	plate	NOUN
ap-5556	588	11	resting	rest	VERB
ap-5556	588	12	on	on	ADP
ap-5556	588	13	pasternak	pasternak	PROPN
ap-5556	588	14	and	and	CCONJ
ap-5556	588	15	winkler	winkler	PROPN
ap-5556	588	16	foundations	foundation	NOUN
ap-5556	588	17	.	.	PUNCT
ap-5556	589	1	engineering	engineering	NOUN
ap-5556	589	2	and	and	CCONJ
ap-5556	589	3	applied	apply	VERB
ap-5556	589	4	science	science	NOUN
ap-5556	589	5	letters	letter	NOUN
ap-5556	589	6	3:1	3:1	NUM
ap-5556	589	7	–	–	PUNCT
ap-5556	589	8	20	20	NUM
ap-5556	589	9	,	,	PUNCT
ap-5556	589	10	2020	2020	NUM
ap-5556	589	11	.	.	PUNCT
ap-5556	590	1	doi:10.30538	doi:10.30538	NOUN
ap-5556	590	2	/	/	SYM
ap-5556	590	3	psrp	psrp	PROPN
ap-5556	590	4	-	-	PUNCT
ap-5556	590	5	easl2020.0031	easl2020.0031	NOUN
ap-5556	590	6	.	.	PUNCT
ap-5556	591	1	[	[	X
ap-5556	591	2	26	26	NUM
ap-5556	591	3	]	]	X
ap-5556	591	4	c.	c.	NOUN
ap-5556	591	5	vendhan	vendhan	NOUN
ap-5556	591	6	,	,	PUNCT
ap-5556	591	7	y.	y.	PROPN
ap-5556	591	8	das	das	PROPN
ap-5556	591	9	.	.	PUNCT
ap-5556	591	10	application	application	NOUN
ap-5556	591	11	of	of	ADP
ap-5556	591	12	rayleigh	rayleigh	PROPN
ap-5556	591	13	-	-	PUNCT
ap-5556	591	14	ritz	ritz	PROPN
ap-5556	591	15	and	and	CCONJ
ap-5556	591	16	galerkin	galerkin	ADJ
ap-5556	591	17	methods	method	NOUN
ap-5556	591	18	to	to	ADP
ap-5556	591	19	non	non	ADJ
ap-5556	591	20	-	-	ADJ
ap-5556	591	21	linear	linear	ADJ
ap-5556	591	22	vibration	vibration	NOUN
ap-5556	591	23	of	of	ADP
ap-5556	591	24	plates	plate	NOUN
ap-5556	591	25	.	.	PUNCT
ap-5556	592	1	journal	journal	PROPN
ap-5556	592	2	of	of	ADP
ap-5556	592	3	sound	sound	NOUN
ap-5556	592	4	and	and	CCONJ
ap-5556	592	5	vibration	vibration	NOUN
ap-5556	592	6	39(2):147	39(2):147	NUM
ap-5556	592	7	–	–	PUNCT
ap-5556	592	8	157	157	NUM
ap-5556	592	9	,	,	PUNCT
ap-5556	592	10	1975	1975	NUM
ap-5556	592	11	.	.	PUNCT
ap-5556	593	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	593	2	/	/	SYM
ap-5556	593	3	s0022	s0022	PROPN
ap-5556	593	4	-	-	PUNCT
ap-5556	593	5	460x(75)80214	460x(75)80214	NUM
ap-5556	593	6	-	-	PUNCT
ap-5556	593	7	8	8	NUM
ap-5556	593	8	.	.	PUNCT
ap-5556	594	1	[	[	X
ap-5556	594	2	27	27	NUM
ap-5556	594	3	]	]	PUNCT
ap-5556	594	4	t.	t.	PROPN
ap-5556	594	5	wu	wu	PROPN
ap-5556	594	6	,	,	PUNCT
ap-5556	595	1	g.	g.	PROPN
ap-5556	595	2	liu	liu	PROPN
ap-5556	595	3	.	.	PUNCT
ap-5556	596	1	free	free	ADJ
ap-5556	596	2	vibration	vibration	NOUN
ap-5556	596	3	analysis	analysis	NOUN
ap-5556	596	4	of	of	ADP
ap-5556	596	5	circular	circular	ADJ
ap-5556	596	6	plates	plate	NOUN
ap-5556	596	7	with	with	ADP
ap-5556	596	8	variable	variable	ADJ
ap-5556	596	9	thickness	thickness	NOUN
ap-5556	596	10	by	by	ADP
ap-5556	596	11	the	the	DET
ap-5556	596	12	generalized	generalize	VERB
ap-5556	596	13	differential	differential	ADJ
ap-5556	596	14	quadrature	quadrature	NOUN
ap-5556	596	15	rule	rule	NOUN
ap-5556	596	16	.	.	PUNCT
ap-5556	597	1	international	international	ADJ
ap-5556	597	2	journal	journal	PROPN
ap-5556	597	3	of	of	ADP
ap-5556	597	4	solids	solid	NOUN
ap-5556	597	5	and	and	CCONJ
ap-5556	597	6	structures	structure	NOUN
ap-5556	597	7	38(44):7967	38(44):7967	NUM
ap-5556	597	8	–	–	PUNCT
ap-5556	597	9	7980	7980	NUM
ap-5556	597	10	,	,	PUNCT
ap-5556	597	11	2001	2001	NUM
ap-5556	597	12	.	.	PUNCT
ap-5556	598	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	598	2	/	/	SYM
ap-5556	598	3	s0020	s0020	ADV
ap-5556	598	4	-	-	PUNCT
ap-5556	598	5	7683(01)00077	7683(01)00077	NUM
ap-5556	598	6	-	-	PUNCT
ap-5556	598	7	4	4	NUM
ap-5556	598	8	.	.	PUNCT
ap-5556	599	1	[	[	X
ap-5556	599	2	28	28	NUM
ap-5556	599	3	]	]	X
ap-5556	599	4	d.	d.	PROPN
ap-5556	599	5	zhou	zhou	PROPN
ap-5556	599	6	,	,	PUNCT
ap-5556	599	7	s.	s.	PROPN
ap-5556	599	8	lo	lo	PROPN
ap-5556	599	9	,	,	PUNCT
ap-5556	599	10	f.	f.	PROPN
ap-5556	599	11	au	au	PROPN
ap-5556	599	12	,	,	PUNCT
ap-5556	599	13	y.	y.	PROPN
ap-5556	599	14	cheung	cheung	PROPN
ap-5556	599	15	.	.	PUNCT
ap-5556	600	1	three	three	NUM
ap-5556	600	2	-	-	PUNCT
ap-5556	600	3	dimensional	dimensional	ADJ
ap-5556	600	4	free	free	ADJ
ap-5556	600	5	vibration	vibration	NOUN
ap-5556	600	6	of	of	ADP
ap-5556	600	7	thick	thick	ADJ
ap-5556	600	8	circular	circular	ADJ
ap-5556	600	9	plates	plate	NOUN
ap-5556	600	10	on	on	ADP
ap-5556	600	11	pasternak	pasternak	PROPN
ap-5556	600	12	foundation	foundation	PROPN
ap-5556	600	13	.	.	PUNCT
ap-5556	601	1	journal	journal	PROPN
ap-5556	601	2	of	of	ADP
ap-5556	601	3	sound	sound	NOUN
ap-5556	601	4	and	and	CCONJ
ap-5556	601	5	vibration	vibration	NOUN
ap-5556	601	6	292(3):726	292(3):726	NUM
ap-5556	601	7	–	–	PUNCT
ap-5556	601	8	741	741	NUM
ap-5556	601	9	,	,	PUNCT
ap-5556	601	10	2006	2006	NUM
ap-5556	601	11	.	.	PUNCT
ap-5556	602	1	doi:10.1016	doi:10.1016	PROPN
ap-5556	602	2	/	/	SYM
ap-5556	602	3	j.jsv.2005.08.028	j.jsv.2005.08.028	PROPN
ap-5556	602	4	.	.	PUNCT
ap-5556	603	1	[	[	X
ap-5556	603	2	29	29	NUM
ap-5556	603	3	]	]	PUNCT
ap-5556	603	4	a.	a.	NOUN
ap-5556	603	5	w.	w.	PROPN
ap-5556	603	6	leissa	leissa	PROPN
ap-5556	603	7	.	.	PUNCT
ap-5556	604	1	vibration	vibration	NOUN
ap-5556	604	2	of	of	ADP
ap-5556	604	3	plates	plate	NOUN
ap-5556	604	4	.	.	PUNCT
ap-5556	605	1	tech	tech	NOUN
ap-5556	605	2	.	.	PUNCT
ap-5556	606	1	rep	rep	PROPN
ap-5556	606	2	.	.	PROPN
ap-5556	606	3	,	,	PUNCT
ap-5556	606	4	national	national	ADJ
ap-5556	606	5	aeronautics	aeronautics	PROPN
ap-5556	606	6	and	and	CCONJ
ap-5556	606	7	space	space	NOUN
ap-5556	606	8	administration	administration	PROPN
ap-5556	606	9	,	,	PUNCT
ap-5556	606	10	washington	washington	PROPN
ap-5556	606	11	d.c	d.c	PROPN
ap-5556	606	12	.	.	PROPN
ap-5556	606	13	,	,	PUNCT
ap-5556	606	14	1970	1970	NUM
ap-5556	606	15	.	.	PUNCT
ap-5556	607	1	144	144	NUM
ap-5556	607	2	http://dx.doi.org/10.12989/scs.2011.11.5.403	http://dx.doi.org/10.12989/scs.2011.11.5.403	PROPN
ap-5556	607	3	http://dx.doi.org/10.1007/s00419-010-0449-0	http://dx.doi.org/10.1007/s00419-010-0449-0	PUNCT
ap-5556	608	1	http://dx.doi.org/10.1016/j.compstruct.2017.07.012	http://dx.doi.org/10.1016/j.compstruct.2017.07.012	NOUN
ap-5556	608	2	http://dx.doi.org/10.1016/j.compositesb.2018.02.019	http://dx.doi.org/10.1016/j.compositesb.2018.02.019	PROPN
ap-5556	608	3	http://dx.doi.org/10.1016/j.apm.2019.02.047	http://dx.doi.org/10.1016/j.apm.2019.02.047	PROPN
ap-5556	608	4	http://dx.doi.org/10.1515/bpasts-2016-0020	http://dx.doi.org/10.1515/bpasts-2016-0020	PROPN
ap-5556	608	5	http://dx.doi.org/10.15632/jtam-pl.53.4.873	http://dx.doi.org/10.15632/jtam-pl.53.4.873	VERB
ap-5556	608	6	http://dx.doi.org/10.17516/1999-494x-0213	http://dx.doi.org/10.17516/1999-494x-0213	PROPN
ap-5556	608	7	http://dx.doi.org/10.30538/psrp-easl2020.0031	http://dx.doi.org/10.30538/psrp-easl2020.0031	NOUN
ap-5556	608	8	http://dx.doi.org/10.1016/s0022-460x(75)80214-8	http://dx.doi.org/10.1016/s0022-460x(75)80214-8	PROPN
ap-5556	608	9	http://dx.doi.org/10.1016/s0020-7683(01)00077-4	http://dx.doi.org/10.1016/s0020-7683(01)00077-4	PROPN
ap-5556	608	10	http://dx.doi.org/10.1016/j.jsv.2005.08.028	http://dx.doi.org/10.1016/j.jsv.2005.08.028	PROPN
ap-5556	608	11	acta	acta	PROPN
ap-5556	608	12	polytechnica	polytechnica	PROPN
ap-5556	608	13	60(2):127–144	60(2):127–144	PROPN
ap-5556	608	14	,	,	PUNCT
ap-5556	608	15	2020	2020	NUM
ap-5556	608	16	1	1	NUM
ap-5556	608	17	introduction	introduction	NOUN
ap-5556	608	18	2	2	NUM
ap-5556	608	19	problem	problem	NOUN
ap-5556	608	20	formulation	formulation	NOUN
ap-5556	608	21	and	and	CCONJ
ap-5556	608	22	mathematical	mathematical	ADJ
ap-5556	608	23	analysis	analysis	NOUN
ap-5556	608	24	2.1	2.1	NUM
ap-5556	608	25	boundary	boundary	ADJ
ap-5556	608	26	conditions	condition	NOUN
ap-5556	608	27	3	3	NUM
ap-5556	608	28	method	method	NOUN
ap-5556	608	29	of	of	ADP
ap-5556	608	30	solution	solution	NOUN
ap-5556	608	31	:	:	PUNCT
ap-5556	608	32	principle	principle	NOUN
ap-5556	608	33	of	of	ADP
ap-5556	608	34	galerkin	galerkin	PROPN
ap-5556	608	35	weighted	weight	VERB
ap-5556	608	36	residual	residual	ADJ
ap-5556	608	37	3.1	3.1	NUM
ap-5556	608	38	application	application	NOUN
ap-5556	608	39	of	of	ADP
ap-5556	608	40	galerkin	galerkin	ADJ
ap-5556	608	41	method	method	NOUN
ap-5556	608	42	of	of	ADP
ap-5556	608	43	weighted	weight	VERB
ap-5556	608	44	residual	residual	ADJ
ap-5556	608	45	to	to	ADP
ap-5556	608	46	the	the	DET
ap-5556	608	47	governing	govern	VERB
ap-5556	608	48	equation	equation	NOUN
ap-5556	608	49	3.2	3.2	NUM
ap-5556	608	50	application	application	NOUN
ap-5556	608	51	of	of	ADP
ap-5556	608	52	galerkin	galerkin	ADJ
ap-5556	608	53	method	method	NOUN
ap-5556	608	54	of	of	ADP
ap-5556	608	55	weighted	weight	VERB
ap-5556	608	56	residual	residual	ADJ
ap-5556	608	57	to	to	ADP
ap-5556	608	58	nonlinear	nonlinear	ADJ
ap-5556	608	59	governing	govern	VERB
ap-5556	608	60	equation	equation	NOUN
ap-5556	608	61	3.3	3.3	NUM
ap-5556	608	62	application	application	NOUN
ap-5556	608	63	of	of	ADP
ap-5556	608	64	galerkin	galerkin	ADJ
ap-5556	608	65	method	method	NOUN
ap-5556	608	66	of	of	ADP
ap-5556	608	67	weighted	weight	VERB
ap-5556	608	68	residual	residual	ADJ
ap-5556	608	69	to	to	PART
ap-5556	608	70	foundation	foundation	VERB
ap-5556	608	71	free	free	PROPN
ap-5556	608	72	surface	surface	PROPN
ap-5556	608	73	3.4	3.4	NUM
ap-5556	608	74	the	the	DET
ap-5556	608	75	stress	stress	NOUN
ap-5556	608	76	-	-	PUNCT
ap-5556	608	77	deflection	deflection	NOUN
ap-5556	608	78	expression	expression	NOUN
ap-5556	608	79	is	be	AUX
ap-5556	608	80	12	12	NUM
ap-5556	608	81	4	4	NUM
ap-5556	608	82	results	result	NOUN
ap-5556	608	83	and	and	CCONJ
ap-5556	608	84	discussion	discussion	NOUN
ap-5556	608	85	4.1	4.1	NUM
ap-5556	608	86	investigation	investigation	NOUN
ap-5556	608	87	of	of	ADP
ap-5556	608	88	plate	plate	NOUN
ap-5556	608	89	behaviour	behaviour	NOUN
ap-5556	608	90	on	on	ADP
ap-5556	608	91	foundation	foundation	NOUN
ap-5556	608	92	4.2	4.2	NUM
ap-5556	608	93	mode	mode	NOUN
ap-5556	608	94	shapes	shape	VERB
ap-5556	608	95	4.3	4.3	NUM
ap-5556	608	96	investigation	investigation	NOUN
ap-5556	608	97	of	of	ADP
ap-5556	608	98	plate	plate	NOUN
ap-5556	608	99	thickness	thickness	NOUN
ap-5556	608	100	variation	variation	NOUN
ap-5556	608	101	on	on	ADP
ap-5556	608	102	the	the	DET
ap-5556	608	103	natural	natural	ADJ
ap-5556	608	104	frequency	frequency	NOUN
ap-5556	608	105	4.4	4.4	NUM
ap-5556	608	106	investigation	investigation	NOUN
ap-5556	608	107	of	of	ADP
ap-5556	608	108	homogeneity	homogeneity	NOUN
ap-5556	608	109	parameter	parameter	NOUN
ap-5556	608	110	variation	variation	NOUN
ap-5556	608	111	on	on	ADP
ap-5556	608	112	the	the	DET
ap-5556	608	113	natural	natural	ADJ
ap-5556	608	114	frequency	frequency	NOUN
ap-5556	608	115	5	5	NUM
ap-5556	608	116	conclusion	conclusion	NOUN
ap-5556	608	117	6	6	NUM
ap-5556	608	118	data	datum	NOUN
ap-5556	608	119	availability	availability	NOUN
ap-5556	608	120	7	7	NUM
ap-5556	608	121	conflicts	conflict	NOUN
ap-5556	608	122	of	of	ADP
ap-5556	608	123	interest	interest	NOUN
ap-5556	608	124	acknowledgements	acknowledgement	NOUN
ap-5556	608	125	list	list	NOUN
ap-5556	608	126	of	of	ADP
ap-5556	608	127	symbols	symbol	NOUN
ap-5556	608	128	references	reference	NOUN