id	sid	tid	token	lemma	pos
ap-9572	1	1	acta	acta	PROPN
ap-9572	1	2	polytechnica	polytechnica	PROPN
ap-9572	1	3	https://doi.org/10.14311/ap.2024.64.0297	https://doi.org/10.14311/ap.2024.64.0297	PROPN
ap-9572	1	4	acta	acta	PROPN
ap-9572	1	5	polytechnica	polytechnica	PROPN
ap-9572	1	6	64(4):297–313	64(4):297–313	PROPN
ap-9572	1	7	,	,	PUNCT
ap-9572	1	8	2024	2024	NUM
ap-9572	1	9	©	©	ADP
ap-9572	1	10	2024	2024	NUM
ap-9572	1	11	the	the	DET
ap-9572	1	12	author(s	author(s	NOUN
ap-9572	1	13	)	)	PUNCT
ap-9572	1	14	.	.	PUNCT
ap-9572	2	1	licensed	license	VERB
ap-9572	2	2	under	under	ADP
ap-9572	2	3	a	a	DET
ap-9572	2	4	cc	cc	NOUN
ap-9572	2	5	-	-	PUNCT
ap-9572	2	6	by	by	ADP
ap-9572	2	7	4.0	4.0	NUM
ap-9572	2	8	licence	licence	NOUN
ap-9572	2	9	published	publish	VERB
ap-9572	2	10	by	by	ADP
ap-9572	2	11	the	the	DET
ap-9572	2	12	czech	czech	PROPN
ap-9572	2	13	technical	technical	PROPN
ap-9572	2	14	university	university	PROPN
ap-9572	2	15	in	in	ADP
ap-9572	2	16	prague	prague	PROPN
ap-9572	2	17	non	non	ADJ
ap-9572	2	18	-	-	ADJ
ap-9572	2	19	homogeneity	homogeneity	ADJ
ap-9572	2	20	effect	effect	NOUN
ap-9572	2	21	on	on	ADP
ap-9572	2	22	the	the	DET
ap-9572	2	23	vibration	vibration	NOUN
ap-9572	2	24	of	of	ADP
ap-9572	2	25	the	the	DET
ap-9572	2	26	rectangular	rectangular	ADJ
ap-9572	2	27	visco	visco	ADJ
ap-9572	2	28	-	-	ADJ
ap-9572	2	29	elastic	elastic	ADJ
ap-9572	2	30	plate	plate	NOUN
ap-9572	2	31	subjected	subject	VERB
ap-9572	2	32	to	to	ADP
ap-9572	2	33	the	the	DET
ap-9572	2	34	linear	linear	ADJ
ap-9572	2	35	temperature	temperature	NOUN
ap-9572	2	36	effect	effect	NOUN
ap-9572	2	37	with	with	ADP
ap-9572	2	38	quadratic	quadratic	ADJ
ap-9572	2	39	thickness	thickness	NOUN
ap-9572	2	40	variation	variation	NOUN
ap-9572	2	41	in	in	ADP
ap-9572	2	42	both	both	DET
ap-9572	2	43	directions	direction	NOUN
ap-9572	2	44	sudhanshu	sudhanshu	NOUN
ap-9572	2	45	aggarwal	aggarwal	PROPN
ap-9572	2	46	national	national	PROPN
ap-9572	2	47	post	post	PROPN
ap-9572	2	48	graduate	graduate	PROPN
ap-9572	2	49	college	college	PROPN
ap-9572	2	50	barhalganj	barhalganj	PROPN
ap-9572	2	51	,	,	PUNCT
ap-9572	2	52	department	department	NOUN
ap-9572	2	53	of	of	ADP
ap-9572	2	54	mathematics	mathematics	PROPN
ap-9572	2	55	,	,	PUNCT
ap-9572	2	56	gorakhpur-273402	gorakhpur-273402	NOUN
ap-9572	2	57	,	,	PUNCT
ap-9572	2	58	uttar	uttar	PROPN
ap-9572	2	59	pradesh	pradesh	PROPN
ap-9572	2	60	,	,	PUNCT
ap-9572	2	61	india	india	PROPN
ap-9572	2	62	correspondence	correspondence	NOUN
ap-9572	2	63	:	:	PUNCT
ap-9572	2	64	sudhanshu30187@gmail.com	sudhanshu30187@gmail.com	X
ap-9572	2	65	abstract	abstract	NOUN
ap-9572	2	66	.	.	PUNCT
ap-9572	3	1	the	the	DET
ap-9572	3	2	present	present	ADJ
ap-9572	3	3	work	work	NOUN
ap-9572	3	4	investigates	investigate	VERB
ap-9572	3	5	the	the	DET
ap-9572	3	6	effect	effect	NOUN
ap-9572	3	7	of	of	ADP
ap-9572	3	8	non	non	ADJ
ap-9572	3	9	-	-	NOUN
ap-9572	3	10	homogeneity	homogeneity	NOUN
ap-9572	3	11	on	on	ADP
ap-9572	3	12	the	the	DET
ap-9572	3	13	vibration	vibration	NOUN
ap-9572	3	14	of	of	ADP
ap-9572	3	15	a	a	DET
ap-9572	3	16	rectangular	rectangular	ADJ
ap-9572	3	17	visco	visco	ADJ
ap-9572	3	18	-	-	ADJ
ap-9572	3	19	elastic	elastic	ADJ
ap-9572	3	20	plate	plate	NOUN
ap-9572	3	21	.	.	PUNCT
ap-9572	4	1	the	the	DET
ap-9572	4	2	plate	plate	NOUN
ap-9572	4	3	is	be	AUX
ap-9572	4	4	subjected	subject	VERB
ap-9572	4	5	to	to	AUX
ap-9572	4	6	linear	linear	VERB
ap-9572	4	7	temperature	temperature	NOUN
ap-9572	4	8	variation	variation	NOUN
ap-9572	4	9	in	in	ADP
ap-9572	4	10	the	the	DET
ap-9572	4	11	x	x	NOUN
ap-9572	4	12	-	-	NOUN
ap-9572	4	13	direction	direction	NOUN
ap-9572	4	14	with	with	ADP
ap-9572	4	15	quadratic	quadratic	ADJ
ap-9572	4	16	thickness	thickness	NOUN
ap-9572	4	17	variation	variation	NOUN
ap-9572	4	18	in	in	ADP
ap-9572	4	19	both	both	DET
ap-9572	4	20	directions	direction	NOUN
ap-9572	4	21	.	.	PUNCT
ap-9572	5	1	the	the	DET
ap-9572	5	2	quadratic	quadratic	ADJ
ap-9572	5	3	variation	variation	NOUN
ap-9572	5	4	has	have	AUX
ap-9572	5	5	been	be	AUX
ap-9572	5	6	considered	consider	VERB
ap-9572	5	7	in	in	ADP
ap-9572	5	8	the	the	DET
ap-9572	5	9	material	material	NOUN
ap-9572	5	10	density	density	NOUN
ap-9572	5	11	of	of	ADP
ap-9572	5	12	the	the	DET
ap-9572	5	13	plate	plate	NOUN
ap-9572	5	14	only	only	ADV
ap-9572	5	15	along	along	ADP
ap-9572	5	16	the	the	DET
ap-9572	5	17	x	x	NOUN
ap-9572	5	18	-	-	NOUN
ap-9572	5	19	axis	axis	ADJ
ap-9572	5	20	,	,	PUNCT
ap-9572	5	21	and	and	CCONJ
ap-9572	5	22	it	it	PRON
ap-9572	5	23	is	be	AUX
ap-9572	5	24	assumed	assume	VERB
ap-9572	5	25	that	that	SCONJ
ap-9572	5	26	non	non	ADJ
ap-9572	5	27	-	-	ADJ
ap-9572	5	28	homogeneity	homogeneity	ADJ
ap-9572	5	29	transpires	transpire	NOUN
ap-9572	5	30	because	because	SCONJ
ap-9572	5	31	of	of	ADP
ap-9572	5	32	this	this	DET
ap-9572	5	33	variation	variation	NOUN
ap-9572	5	34	.	.	PUNCT
ap-9572	6	1	the	the	DET
ap-9572	6	2	governing	govern	VERB
ap-9572	6	3	differential	differential	ADJ
ap-9572	6	4	equation	equation	NOUN
ap-9572	6	5	is	be	AUX
ap-9572	6	6	solved	solve	VERB
ap-9572	6	7	using	use	VERB
ap-9572	6	8	the	the	DET
ap-9572	6	9	rayleigh	rayleigh	PROPN
ap-9572	6	10	-	-	PUNCT
ap-9572	6	11	ritz	ritz	PROPN
ap-9572	6	12	technique	technique	NOUN
ap-9572	6	13	.	.	PUNCT
ap-9572	7	1	all	all	DET
ap-9572	7	2	four	four	NUM
ap-9572	7	3	edges	edge	NOUN
ap-9572	7	4	of	of	ADP
ap-9572	7	5	the	the	DET
ap-9572	7	6	plate	plate	NOUN
ap-9572	7	7	should	should	AUX
ap-9572	7	8	be	be	AUX
ap-9572	7	9	clamped	clamp	VERB
ap-9572	7	10	to	to	PART
ap-9572	7	11	drive	drive	VERB
ap-9572	7	12	the	the	DET
ap-9572	7	13	frequency	frequency	NOUN
ap-9572	7	14	equation	equation	NOUN
ap-9572	7	15	.	.	PUNCT
ap-9572	8	1	deflection	deflection	NOUN
ap-9572	8	2	and	and	CCONJ
ap-9572	8	3	time	time	NOUN
ap-9572	8	4	period	period	NOUN
ap-9572	8	5	have	have	AUX
ap-9572	8	6	been	be	AUX
ap-9572	8	7	evaluated	evaluate	VERB
ap-9572	8	8	for	for	ADP
ap-9572	8	9	several	several	ADJ
ap-9572	8	10	combinations	combination	NOUN
ap-9572	8	11	of	of	ADP
ap-9572	8	12	values	value	NOUN
ap-9572	8	13	of	of	ADP
ap-9572	8	14	the	the	DET
ap-9572	8	15	thermal	thermal	ADJ
ap-9572	8	16	constant	constant	ADJ
ap-9572	8	17	,	,	PUNCT
ap-9572	8	18	constant	constant	ADJ
ap-9572	8	19	of	of	ADP
ap-9572	8	20	nonhomogeneity	nonhomogeneity	NOUN
ap-9572	8	21	,	,	PUNCT
ap-9572	8	22	taper	taper	NOUN
ap-9572	8	23	constants	constant	NOUN
ap-9572	8	24	,	,	PUNCT
ap-9572	8	25	and	and	CCONJ
ap-9572	8	26	length	length	NOUN
ap-9572	8	27	-	-	PUNCT
ap-9572	8	28	to	to	ADP
ap-9572	8	29	-	-	PUNCT
ap-9572	8	30	width	width	NOUN
ap-9572	8	31	ratio	ratio	NOUN
ap-9572	8	32	(	(	PUNCT
ap-9572	8	33	aspect	aspect	NOUN
ap-9572	8	34	ratio	ratio	NOUN
ap-9572	8	35	)	)	PUNCT
ap-9572	8	36	for	for	ADP
ap-9572	8	37	the	the	DET
ap-9572	8	38	first	first	ADJ
ap-9572	8	39	two	two	NUM
ap-9572	8	40	vibration	vibration	NOUN
ap-9572	8	41	modes	mode	NOUN
ap-9572	8	42	of	of	ADP
ap-9572	8	43	the	the	DET
ap-9572	8	44	clamped	clamp	VERB
ap-9572	8	45	plate	plate	NOUN
ap-9572	8	46	.	.	PUNCT
ap-9572	9	1	the	the	DET
ap-9572	9	2	results	result	NOUN
ap-9572	9	3	presented	present	VERB
ap-9572	9	4	are	be	AUX
ap-9572	9	5	compared	compare	VERB
ap-9572	9	6	with	with	ADP
ap-9572	9	7	those	those	PRON
ap-9572	9	8	found	find	VERB
ap-9572	9	9	in	in	ADP
ap-9572	9	10	the	the	DET
ap-9572	9	11	literature	literature	NOUN
ap-9572	9	12	.	.	PUNCT
ap-9572	10	1	keywords	keyword	NOUN
ap-9572	10	2	:	:	PUNCT
ap-9572	10	3	rayleigh	rayleigh	PROPN
ap-9572	10	4	-	-	PUNCT
ap-9572	10	5	ritz	ritz	PROPN
ap-9572	10	6	technique	technique	NOUN
ap-9572	10	7	,	,	PUNCT
ap-9572	10	8	taper	taper	NOUN
ap-9572	10	9	constants	constant	NOUN
ap-9572	10	10	,	,	PUNCT
ap-9572	10	11	clamped	clamp	VERB
ap-9572	10	12	plate	plate	NOUN
ap-9572	10	13	,	,	PUNCT
ap-9572	10	14	differential	differential	ADJ
ap-9572	10	15	equation	equation	NOUN
ap-9572	10	16	,	,	PUNCT
ap-9572	10	17	thermal	thermal	ADJ
ap-9572	10	18	constant	constant	ADJ
ap-9572	10	19	.	.	PUNCT
ap-9572	11	1	1	1	X
ap-9572	11	2	.	.	X
ap-9572	11	3	introduction	introduction	NOUN
ap-9572	11	4	due	due	ADP
ap-9572	11	5	to	to	ADP
ap-9572	11	6	their	their	PRON
ap-9572	11	7	practical	practical	ADJ
ap-9572	11	8	and	and	CCONJ
ap-9572	11	9	scholarly	scholarly	ADJ
ap-9572	11	10	interests	interest	NOUN
ap-9572	11	11	,	,	PUNCT
ap-9572	11	12	the	the	DET
ap-9572	11	13	vibration	vibration	NOUN
ap-9572	11	14	problems	problem	NOUN
ap-9572	11	15	of	of	ADP
ap-9572	11	16	elasticity	elasticity	NOUN
ap-9572	11	17	have	have	AUX
ap-9572	11	18	been	be	AUX
ap-9572	11	19	the	the	DET
ap-9572	11	20	subject	subject	NOUN
ap-9572	11	21	of	of	ADP
ap-9572	11	22	effort	effort	NOUN
ap-9572	11	23	or	or	CCONJ
ap-9572	11	24	research	research	NOUN
ap-9572	11	25	for	for	ADP
ap-9572	11	26	a	a	DET
ap-9572	11	27	considerable	considerable	ADJ
ap-9572	11	28	amount	amount	NOUN
ap-9572	11	29	of	of	ADP
ap-9572	11	30	time	time	NOUN
ap-9572	11	31	.	.	PUNCT
ap-9572	12	1	machines	machine	NOUN
ap-9572	12	2	often	often	ADV
ap-9572	12	3	produce	produce	VERB
ap-9572	12	4	heat	heat	NOUN
ap-9572	12	5	as	as	ADP
ap-9572	12	6	a	a	DET
ap-9572	12	7	result	result	NOUN
ap-9572	12	8	of	of	ADP
ap-9572	12	9	vibration	vibration	NOUN
ap-9572	12	10	,	,	PUNCT
ap-9572	12	11	which	which	PRON
ap-9572	12	12	reduces	reduce	VERB
ap-9572	12	13	machine	machine	NOUN
ap-9572	12	14	efficiency	efficiency	NOUN
ap-9572	12	15	.	.	PUNCT
ap-9572	13	1	as	as	ADP
ap-9572	13	2	a	a	DET
ap-9572	13	3	result	result	NOUN
ap-9572	13	4	,	,	PUNCT
ap-9572	13	5	it	it	PRON
ap-9572	13	6	is	be	AUX
ap-9572	13	7	critical	critical	ADJ
ap-9572	13	8	to	to	PART
ap-9572	13	9	investigate	investigate	VERB
ap-9572	13	10	variations	variation	NOUN
ap-9572	13	11	in	in	ADP
ap-9572	13	12	temperature	temperature	NOUN
ap-9572	13	13	on	on	ADP
ap-9572	13	14	vibration	vibration	NOUN
ap-9572	13	15	-	-	PUNCT
ap-9572	13	16	affected	affect	VERB
ap-9572	13	17	plates	plate	NOUN
ap-9572	13	18	.	.	PUNCT
ap-9572	14	1	there	there	PRON
ap-9572	14	2	are	be	VERB
ap-9572	14	3	a	a	DET
ap-9572	14	4	number	number	NOUN
ap-9572	14	5	of	of	ADP
ap-9572	14	6	materials	material	NOUN
ap-9572	14	7	,	,	PUNCT
ap-9572	14	8	found	find	VERB
ap-9572	14	9	in	in	ADP
ap-9572	14	10	nature	nature	NOUN
ap-9572	14	11	that	that	PRON
ap-9572	14	12	are	be	AUX
ap-9572	14	13	nonhomogeneous	nonhomogeneous	ADJ
ap-9572	14	14	(	(	PUNCT
ap-9572	14	15	e.g.	e.g.	ADV
ap-9572	14	16	delta	delta	NOUN
ap-9572	14	17	wood	wood	NOUN
ap-9572	14	18	,	,	PUNCT
ap-9572	14	19	plywood	plywood	NOUN
ap-9572	14	20	,	,	PUNCT
ap-9572	14	21	timber	timber	NOUN
ap-9572	14	22	,	,	PUNCT
ap-9572	14	23	fibre	fibre	NOUN
ap-9572	14	24	reinforced	reinforce	VERB
ap-9572	14	25	plastics	plastic	NOUN
ap-9572	14	26	,	,	PUNCT
ap-9572	14	27	etc	etc	X
ap-9572	14	28	.	.	X
ap-9572	14	29	)	)	PUNCT
ap-9572	14	30	.	.	PUNCT
ap-9572	15	1	the	the	DET
ap-9572	15	2	use	use	NOUN
ap-9572	15	3	of	of	ADP
ap-9572	15	4	these	these	DET
ap-9572	15	5	natural	natural	ADJ
ap-9572	15	6	nonhomogeneous	nonhomogeneous	ADJ
ap-9572	15	7	materials	material	NOUN
ap-9572	15	8	in	in	ADP
ap-9572	15	9	the	the	DET
ap-9572	15	10	industry	industry	NOUN
ap-9572	15	11	is	be	AUX
ap-9572	15	12	generally	generally	ADV
ap-9572	15	13	due	due	ADJ
ap-9572	15	14	to	to	ADP
ap-9572	15	15	their	their	PRON
ap-9572	15	16	nature	nature	NOUN
ap-9572	15	17	to	to	PART
ap-9572	15	18	strengthen	strengthen	VERB
ap-9572	15	19	the	the	DET
ap-9572	15	20	construction	construction	NOUN
ap-9572	15	21	.	.	PUNCT
ap-9572	16	1	glass	glass	NOUN
ap-9572	16	2	epoxy	epoxy	NOUN
ap-9572	16	3	and	and	CCONJ
ap-9572	16	4	boron	boron	NOUN
ap-9572	16	5	epoxy	epoxy	NOUN
ap-9572	16	6	in	in	ADP
ap-9572	16	7	the	the	DET
ap-9572	16	8	steel	steel	NOUN
ap-9572	16	9	alloys	alloy	NOUN
ap-9572	16	10	are	be	AUX
ap-9572	16	11	examples	example	NOUN
ap-9572	16	12	of	of	ADP
ap-9572	16	13	the	the	DET
ap-9572	16	14	artificial	artificial	ADJ
ap-9572	16	15	nonhomogeneous	nonhomogeneous	ADJ
ap-9572	16	16	materials	material	NOUN
ap-9572	16	17	used	use	VERB
ap-9572	16	18	in	in	ADP
ap-9572	16	19	the	the	DET
ap-9572	16	20	manufacture	manufacture	NOUN
ap-9572	16	21	of	of	ADP
ap-9572	16	22	nuclear	nuclear	ADJ
ap-9572	16	23	reactor	reactor	NOUN
ap-9572	16	24	rods	rod	NOUN
ap-9572	16	25	.	.	PUNCT
ap-9572	17	1	the	the	DET
ap-9572	17	2	non	non	NOUN
ap-9572	17	3	-	-	NOUN
ap-9572	17	4	homogeneity	homogeneity	NOUN
ap-9572	17	5	in	in	ADP
ap-9572	17	6	the	the	DET
ap-9572	17	7	materials	material	NOUN
ap-9572	17	8	arises	arise	VERB
ap-9572	17	9	due	due	ADJ
ap-9572	17	10	to	to	ADP
ap-9572	17	11	imperfections	imperfection	NOUN
ap-9572	17	12	in	in	ADP
ap-9572	17	13	the	the	DET
ap-9572	17	14	material	material	NOUN
ap-9572	17	15	,	,	PUNCT
ap-9572	17	16	them	they	PRON
ap-9572	17	17	being	be	AUX
ap-9572	17	18	composite	composite	ADJ
ap-9572	17	19	materials	material	NOUN
ap-9572	17	20	,	,	PUNCT
ap-9572	17	21	or	or	CCONJ
ap-9572	17	22	work	work	VERB
ap-9572	17	23	under	under	ADP
ap-9572	17	24	elevated	elevated	ADJ
ap-9572	17	25	temperatures	temperature	NOUN
ap-9572	17	26	[	[	X
ap-9572	17	27	1	1	NUM
ap-9572	17	28	]	]	PUNCT
ap-9572	17	29	.	.	PUNCT
ap-9572	18	1	sharma	sharma	PROPN
ap-9572	18	2	and	and	CCONJ
ap-9572	18	3	sarkar	sarkar	PROPN
ap-9572	19	1	[	[	X
ap-9572	19	2	2	2	NUM
ap-9572	19	3	,	,	PUNCT
ap-9572	19	4	3	3	NUM
ap-9572	19	5	]	]	PUNCT
ap-9572	19	6	suggested	suggest	VERB
ap-9572	19	7	another	another	DET
ap-9572	19	8	common	common	ADJ
ap-9572	19	9	way	way	NOUN
ap-9572	19	10	to	to	PART
ap-9572	19	11	introduce	introduce	VERB
ap-9572	19	12	the	the	DET
ap-9572	19	13	non	non	NOUN
ap-9572	19	14	-	-	NOUN
ap-9572	19	15	homogeneity	homogeneity	NOUN
ap-9572	19	16	in	in	ADP
ap-9572	19	17	the	the	DET
ap-9572	19	18	plate	plate	NOUN
ap-9572	19	19	by	by	ADP
ap-9572	19	20	attaching	attach	VERB
ap-9572	19	21	a	a	DET
ap-9572	19	22	mass	mass	NOUN
ap-9572	19	23	,	,	PUNCT
ap-9572	19	24	spring	spring	NOUN
ap-9572	19	25	,	,	PUNCT
ap-9572	19	26	or	or	CCONJ
ap-9572	19	27	a	a	DET
ap-9572	19	28	springmass	springmass	ADJ
ap-9572	19	29	system	system	NOUN
ap-9572	19	30	to	to	ADP
ap-9572	19	31	it	it	PRON
ap-9572	19	32	.	.	PUNCT
ap-9572	20	1	today	today	NOUN
ap-9572	20	2	,	,	PUNCT
ap-9572	20	3	scientists	scientist	NOUN
ap-9572	20	4	and	and	CCONJ
ap-9572	20	5	engineers	engineer	NOUN
ap-9572	20	6	are	be	AUX
ap-9572	20	7	developing	develop	VERB
ap-9572	20	8	new	new	ADJ
ap-9572	20	9	materials	material	NOUN
ap-9572	20	10	to	to	PART
ap-9572	20	11	meet	meet	VERB
ap-9572	20	12	the	the	DET
ap-9572	20	13	demands	demand	NOUN
ap-9572	20	14	of	of	ADP
ap-9572	20	15	high	high	ADJ
ap-9572	20	16	temperatures	temperature	NOUN
ap-9572	20	17	and	and	CCONJ
ap-9572	20	18	high	high	ADJ
ap-9572	20	19	strength	strength	NOUN
ap-9572	20	20	services	service	NOUN
ap-9572	20	21	.	.	PUNCT
ap-9572	21	1	duralium	duralium	NOUN
ap-9572	21	2	(	(	PUNCT
ap-9572	21	3	alloy	alloy	NOUN
ap-9572	21	4	of	of	ADP
ap-9572	21	5	aluminium	aluminium	NOUN
ap-9572	21	6	,	,	PUNCT
ap-9572	21	7	copper	copper	NOUN
ap-9572	21	8	,	,	PUNCT
ap-9572	21	9	magnesium	magnesium	NOUN
ap-9572	21	10	and	and	CCONJ
ap-9572	21	11	manganese	manganese	NOUN
ap-9572	21	12	)	)	PUNCT
ap-9572	21	13	is	be	AUX
ap-9572	21	14	the	the	DET
ap-9572	21	15	material	material	NOUN
ap-9572	21	16	that	that	PRON
ap-9572	21	17	is	be	AUX
ap-9572	21	18	widely	widely	ADV
ap-9572	21	19	used	use	VERB
ap-9572	21	20	in	in	ADP
ap-9572	21	21	the	the	DET
ap-9572	21	22	defence	defence	NOUN
ap-9572	21	23	industry	industry	NOUN
ap-9572	21	24	(	(	PUNCT
ap-9572	21	25	aircraft	aircraft	NOUN
ap-9572	21	26	fittings	fitting	NOUN
ap-9572	21	27	,	,	PUNCT
ap-9572	21	28	space	space	NOUN
ap-9572	21	29	booster	booster	NOUN
ap-9572	21	30	tank	tank	NOUN
ap-9572	21	31	age	age	NOUN
ap-9572	21	32	,	,	PUNCT
ap-9572	21	33	forgings	forging	NOUN
ap-9572	21	34	,	,	PUNCT
ap-9572	21	35	pistons	piston	NOUN
ap-9572	21	36	of	of	ADP
ap-9572	21	37	aircraft	aircraft	NOUN
ap-9572	21	38	engine	engine	NOUN
ap-9572	21	39	,	,	PUNCT
ap-9572	21	40	compressor	compressor	NOUN
ap-9572	21	41	rings	ring	NOUN
ap-9572	21	42	,	,	PUNCT
ap-9572	21	43	and	and	CCONJ
ap-9572	21	44	impellers	impeller	NOUN
ap-9572	21	45	of	of	ADP
ap-9572	21	46	the	the	DET
ap-9572	21	47	jet	jet	NOUN
ap-9572	21	48	engine	engine	NOUN
ap-9572	21	49	)	)	PUNCT
ap-9572	21	50	due	due	ADP
ap-9572	21	51	to	to	ADP
ap-9572	21	52	its	its	PRON
ap-9572	21	53	very	very	ADV
ap-9572	21	54	attractive	attractive	ADJ
ap-9572	21	55	idiosyncrasy	idiosyncrasy	NOUN
ap-9572	21	56	like	like	ADP
ap-9572	21	57	the	the	DET
ap-9572	21	58	high	high	ADJ
ap-9572	21	59	strength	strength	NOUN
ap-9572	21	60	,	,	PUNCT
ap-9572	21	61	and	and	CCONJ
ap-9572	21	62	the	the	DET
ap-9572	21	63	light	light	ADJ
ap-9572	21	64	weight	weight	NOUN
ap-9572	21	65	.	.	PUNCT
ap-9572	22	1	duralium	duralium	NOUN
ap-9572	22	2	material	material	NOUN
ap-9572	22	3	parameters	parameter	NOUN
ap-9572	22	4	are	be	AUX
ap-9572	22	5	used	use	VERB
ap-9572	22	6	for	for	ADP
ap-9572	22	7	the	the	DET
ap-9572	22	8	numerical	numerical	ADJ
ap-9572	22	9	computation	computation	NOUN
ap-9572	22	10	in	in	ADP
ap-9572	22	11	this	this	DET
ap-9572	22	12	study	study	NOUN
ap-9572	22	13	.	.	PUNCT
ap-9572	23	1	in	in	ADP
ap-9572	23	2	concrete	concrete	NOUN
ap-9572	23	3	,	,	PUNCT
ap-9572	23	4	most	most	ADJ
ap-9572	23	5	of	of	ADP
ap-9572	23	6	the	the	DET
ap-9572	23	7	materials	material	NOUN
ap-9572	23	8	used	use	VERB
ap-9572	23	9	in	in	ADP
ap-9572	23	10	industrial	industrial	ADJ
ap-9572	23	11	applications	application	NOUN
ap-9572	23	12	become	become	VERB
ap-9572	23	13	visco	visco	ADJ
ap-9572	23	14	-	-	ADJ
ap-9572	23	15	elastic	elastic	ADJ
ap-9572	23	16	due	due	ADP
ap-9572	23	17	to	to	ADP
ap-9572	23	18	the	the	DET
ap-9572	23	19	very	very	ADV
ap-9572	23	20	high	high	ADJ
ap-9572	23	21	temperature	temperature	NOUN
ap-9572	23	22	rise	rise	NOUN
ap-9572	23	23	and	and	CCONJ
ap-9572	23	24	these	these	DET
ap-9572	23	25	materials	material	NOUN
ap-9572	23	26	deviate	deviate	VERB
ap-9572	23	27	from	from	ADP
ap-9572	23	28	the	the	DET
ap-9572	23	29	hooke	hooke	PROPN
ap-9572	23	30	’s	’s	PART
ap-9572	23	31	law	law	NOUN
ap-9572	23	32	of	of	ADP
ap-9572	23	33	elasticity	elasticity	NOUN
ap-9572	23	34	,	,	PUNCT
ap-9572	23	35	which	which	PRON
ap-9572	23	36	states	state	VERB
ap-9572	23	37	that	that	SCONJ
ap-9572	23	38	within	within	ADP
ap-9572	23	39	the	the	DET
ap-9572	23	40	elastic	elastic	ADJ
ap-9572	23	41	limits	limit	NOUN
ap-9572	23	42	,	,	PUNCT
ap-9572	23	43	the	the	DET
ap-9572	23	44	stress	stress	NOUN
ap-9572	23	45	is	be	AUX
ap-9572	23	46	directly	directly	ADV
ap-9572	23	47	proportional	proportional	ADJ
ap-9572	23	48	to	to	ADP
ap-9572	23	49	the	the	DET
ap-9572	23	50	strain	strain	NOUN
ap-9572	23	51	.	.	PUNCT
ap-9572	24	1	the	the	DET
ap-9572	24	2	behaviour	behaviour	NOUN
ap-9572	24	3	(	(	PUNCT
ap-9572	24	4	elastic	elastic	ADJ
ap-9572	24	5	or	or	CCONJ
ap-9572	24	6	viscous	viscous	ADJ
ap-9572	24	7	)	)	PUNCT
ap-9572	24	8	of	of	ADP
ap-9572	24	9	the	the	DET
ap-9572	24	10	material	material	NOUN
ap-9572	24	11	depends	depend	VERB
ap-9572	24	12	on	on	ADP
ap-9572	24	13	the	the	DET
ap-9572	24	14	two	two	NUM
ap-9572	24	15	parameters	parameter	NOUN
ap-9572	24	16	,	,	PUNCT
ap-9572	24	17	the	the	DET
ap-9572	24	18	temperature	temperature	NOUN
ap-9572	24	19	and	and	CCONJ
ap-9572	24	20	the	the	DET
ap-9572	24	21	frequency	frequency	NOUN
ap-9572	24	22	(	(	PUNCT
ap-9572	24	23	the	the	DET
ap-9572	24	24	rate	rate	NOUN
ap-9572	24	25	of	of	ADP
ap-9572	24	26	the	the	DET
ap-9572	24	27	loading	loading	NOUN
ap-9572	24	28	)	)	PUNCT
ap-9572	24	29	.	.	PUNCT
ap-9572	25	1	ceramics	ceramic	NOUN
ap-9572	25	2	(	(	PUNCT
ap-9572	25	3	rocks	rock	NOUN
ap-9572	25	4	,	,	PUNCT
ap-9572	25	5	concrete	concrete	ADJ
ap-9572	25	6	,	,	PUNCT
ap-9572	25	7	inorganic	inorganic	ADJ
ap-9572	25	8	glassy	glassy	NOUN
ap-9572	25	9	materials	material	NOUN
ap-9572	25	10	,	,	PUNCT
ap-9572	25	11	piezoelectric	piezoelectric	NOUN
ap-9572	25	12	ceramics	ceramic	NOUN
ap-9572	25	13	)	)	PUNCT
ap-9572	25	14	,	,	PUNCT
ap-9572	25	15	biological	biological	ADJ
ap-9572	25	16	composite	composite	ADJ
ap-9572	25	17	materials	material	NOUN
ap-9572	25	18	(	(	PUNCT
ap-9572	25	19	wood	wood	NOUN
ap-9572	25	20	,	,	PUNCT
ap-9572	25	21	plant	plant	NOUN
ap-9572	25	22	seeds	seed	NOUN
ap-9572	25	23	,	,	PUNCT
ap-9572	25	24	tissue	tissue	NOUN
ap-9572	25	25	)	)	PUNCT
ap-9572	25	26	,	,	PUNCT
ap-9572	25	27	and	and	CCONJ
ap-9572	25	28	many	many	ADJ
ap-9572	25	29	polymers	polymer	NOUN
ap-9572	25	30	(	(	PUNCT
ap-9572	25	31	plastic	plastic	NOUN
ap-9572	25	32	,	,	PUNCT
ap-9572	25	33	rubber	rubber	NOUN
ap-9572	25	34	,	,	PUNCT
ap-9572	25	35	vinyl	vinyl	NOUN
ap-9572	25	36	,	,	PUNCT
ap-9572	25	37	acrylics	acrylic	NOUN
ap-9572	25	38	,	,	PUNCT
ap-9572	25	39	silicones	silicone	NOUN
ap-9572	25	40	,	,	PUNCT
ap-9572	25	41	adhesive	adhesive	NOUN
ap-9572	25	42	,	,	PUNCT
ap-9572	25	43	etc	etc	X
ap-9572	25	44	.	.	X
ap-9572	25	45	)	)	PUNCT
ap-9572	25	46	are	be	AUX
ap-9572	25	47	the	the	DET
ap-9572	25	48	generally	generally	ADV
ap-9572	25	49	used	use	VERB
ap-9572	25	50	visco	visco	ADJ
ap-9572	25	51	-	-	ADJ
ap-9572	25	52	elastic	elastic	ADJ
ap-9572	25	53	materials	material	NOUN
ap-9572	25	54	.	.	PUNCT
ap-9572	26	1	although	although	SCONJ
ap-9572	26	2	the	the	DET
ap-9572	26	3	uniform	uniform	ADJ
ap-9572	26	4	thickness	thickness	NOUN
ap-9572	26	5	plates	plate	NOUN
ap-9572	26	6	are	be	AUX
ap-9572	26	7	commonly	commonly	ADV
ap-9572	26	8	used	use	VERB
ap-9572	26	9	,	,	PUNCT
ap-9572	26	10	the	the	DET
ap-9572	26	11	use	use	NOUN
ap-9572	26	12	of	of	ADP
ap-9572	26	13	variable	variable	ADJ
ap-9572	26	14	thickness	thickness	NOUN
ap-9572	26	15	plates	plate	NOUN
ap-9572	26	16	is	be	AUX
ap-9572	26	17	also	also	ADV
ap-9572	26	18	common	common	ADJ
ap-9572	26	19	,	,	PUNCT
ap-9572	26	20	such	such	ADJ
ap-9572	26	21	as	as	ADP
ap-9572	26	22	rocket	rocket	NOUN
ap-9572	26	23	fins	fin	NOUN
ap-9572	26	24	,	,	PUNCT
ap-9572	26	25	the	the	DET
ap-9572	26	26	wing	wing	NOUN
ap-9572	26	27	panels	panel	NOUN
ap-9572	26	28	in	in	ADP
ap-9572	26	29	the	the	DET
ap-9572	26	30	aerospace	aerospace	NOUN
ap-9572	26	31	engineering	engineering	NOUN
ap-9572	26	32	,	,	PUNCT
ap-9572	26	33	disc	disc	NOUN
ap-9572	26	34	wheels	wheel	NOUN
ap-9572	26	35	and	and	CCONJ
ap-9572	26	36	car	car	NOUN
ap-9572	26	37	body	body	NOUN
ap-9572	26	38	panels	panel	NOUN
ap-9572	26	39	in	in	ADP
ap-9572	26	40	mechanical	mechanical	ADJ
ap-9572	26	41	engineering	engineering	NOUN
ap-9572	26	42	,	,	PUNCT
ap-9572	26	43	building	build	VERB
ap-9572	26	44	walls	wall	NOUN
ap-9572	26	45	,	,	PUNCT
ap-9572	26	46	and	and	CCONJ
ap-9572	26	47	floors	floor	NOUN
ap-9572	26	48	in	in	ADP
ap-9572	26	49	civil	civil	ADJ
ap-9572	26	50	engineering	engineering	NOUN
ap-9572	26	51	,	,	PUNCT
ap-9572	26	52	off	off	ADP
ap-9572	26	53	-	-	PUNCT
ap-9572	26	54	shore	shore	NOUN
ap-9572	26	55	platforms	platform	NOUN
ap-9572	26	56	,	,	PUNCT
ap-9572	26	57	and	and	CCONJ
ap-9572	26	58	ship	ship	NOUN
ap-9572	26	59	decks	deck	NOUN
ap-9572	26	60	in	in	ADP
ap-9572	26	61	marine	marine	ADJ
ap-9572	26	62	engineering	engineering	NOUN
ap-9572	26	63	,	,	PUNCT
ap-9572	26	64	and	and	CCONJ
ap-9572	26	65	printed	print	VERB
ap-9572	26	66	circuit	circuit	NOUN
ap-9572	26	67	boards	board	NOUN
ap-9572	26	68	in	in	ADP
ap-9572	26	69	electronics	electronic	NOUN
ap-9572	26	70	,	,	PUNCT
ap-9572	26	71	in	in	ADP
ap-9572	26	72	example	example	NOUN
ap-9572	26	73	.	.	PUNCT
ap-9572	27	1	plates	plate	NOUN
ap-9572	27	2	of	of	ADP
ap-9572	27	3	the	the	DET
ap-9572	27	4	variable	variable	ADJ
ap-9572	27	5	thickness	thickness	NOUN
ap-9572	27	6	have	have	VERB
ap-9572	27	7	the	the	DET
ap-9572	27	8	wide	wide	ADJ
ap-9572	27	9	practice	practice	NOUN
ap-9572	27	10	in	in	ADP
ap-9572	27	11	many	many	ADJ
ap-9572	27	12	fields	field	NOUN
ap-9572	27	13	of	of	ADP
ap-9572	27	14	the	the	DET
ap-9572	27	15	engineering	engineering	NOUN
ap-9572	27	16	due	due	ADP
ap-9572	27	17	to	to	ADP
ap-9572	27	18	the	the	DET
ap-9572	27	19	some	some	DET
ap-9572	27	20	very	very	ADV
ap-9572	27	21	attractive	attractive	ADJ
ap-9572	27	22	idiosyncrasy	idiosyncrasy	NOUN
ap-9572	27	23	of	of	ADP
ap-9572	27	24	their	their	PRON
ap-9572	27	25	like	like	ADP
ap-9572	27	26	the	the	DET
ap-9572	27	27	high	high	ADJ
ap-9572	27	28	strength	strength	NOUN
ap-9572	27	29	,	,	PUNCT
ap-9572	27	30	and	and	CCONJ
ap-9572	27	31	the	the	DET
ap-9572	27	32	stiffness	stiffness	NOUN
ap-9572	27	33	,	,	PUNCT
ap-9572	27	34	the	the	DET
ap-9572	27	35	reduction	reduction	NOUN
ap-9572	27	36	of	of	ADP
ap-9572	27	37	the	the	DET
ap-9572	27	38	cost	cost	NOUN
ap-9572	27	39	,	,	PUNCT
ap-9572	27	40	and	and	CCONJ
ap-9572	27	41	the	the	DET
ap-9572	27	42	minimizing	minimize	VERB
ap-9572	27	43	the	the	DET
ap-9572	27	44	size	size	NOUN
ap-9572	27	45	,	,	PUNCT
ap-9572	27	46	and	and	CCONJ
ap-9572	27	47	the	the	DET
ap-9572	27	48	weight	weight	NOUN
ap-9572	27	49	.	.	PUNCT
ap-9572	28	1	gupta	gupta	NOUN
ap-9572	28	2	and	and	CCONJ
ap-9572	28	3	kumar	kumar	PROPN
ap-9572	29	1	[	[	X
ap-9572	29	2	4	4	NUM
ap-9572	29	3	]	]	PUNCT
ap-9572	29	4	used	use	VERB
ap-9572	29	5	the	the	DET
ap-9572	29	6	galerkin	galerkin	PROPN
ap-9572	29	7	’s	’s	PART
ap-9572	29	8	technique	technique	NOUN
ap-9572	29	9	and	and	CCONJ
ap-9572	29	10	analysed	analyse	VERB
ap-9572	29	11	the	the	DET
ap-9572	29	12	vibration	vibration	NOUN
ap-9572	29	13	of	of	ADP
ap-9572	29	14	a	a	DET
ap-9572	29	15	non	non	ADJ
ap-9572	29	16	-	-	ADJ
ap-9572	29	17	homogeneous	homogeneous	ADJ
ap-9572	29	18	visco	visco	ADJ
ap-9572	29	19	-	-	ADJ
ap-9572	29	20	elastic	elastic	ADJ
ap-9572	29	21	plate	plate	NOUN
ap-9572	29	22	(	(	PUNCT
ap-9572	29	23	rectangular	rectangular	ADJ
ap-9572	29	24	)	)	PUNCT
ap-9572	29	25	in	in	ADP
ap-9572	29	26	the	the	DET
ap-9572	29	27	thermal	thermal	ADJ
ap-9572	29	28	environment	environment	NOUN
ap-9572	29	29	with	with	ADP
ap-9572	29	30	the	the	DET
ap-9572	29	31	linear	linear	ADJ
ap-9572	29	32	variation	variation	NOUN
ap-9572	29	33	of	of	ADP
ap-9572	29	34	the	the	DET
ap-9572	29	35	thickness	thickness	NOUN
ap-9572	29	36	.	.	PUNCT
ap-9572	30	1	gupta	gupta	NOUN
ap-9572	30	2	and	and	CCONJ
ap-9572	30	3	khanna	khanna	PROPN
ap-9572	31	1	[	[	X
ap-9572	31	2	5	5	NUM
ap-9572	31	3	,	,	PUNCT
ap-9572	31	4	6	6	NUM
ap-9572	31	5	]	]	PUNCT
ap-9572	31	6	studied	study	VERB
ap-9572	31	7	the	the	DET
ap-9572	31	8	vibration	vibration	NOUN
ap-9572	31	9	of	of	ADP
ap-9572	31	10	the	the	DET
ap-9572	31	11	variable	variable	ADJ
ap-9572	31	12	thickness	thickness	NOUN
ap-9572	31	13	rectangular	rectangular	ADJ
ap-9572	31	14	visco	visco	ADJ
ap-9572	31	15	-	-	ADJ
ap-9572	31	16	elastic	elastic	ADJ
ap-9572	31	17	plate	plate	NOUN
ap-9572	31	18	using	use	VERB
ap-9572	31	19	297	297	NUM
ap-9572	31	20	https://doi.org/10.14311/ap.2024.64.0297	https://doi.org/10.14311/ap.2024.64.0297	PROPN
ap-9572	31	21	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-9572	31	22	https://www.cvut.cz/en	https://www.cvut.cz/en	NOUN
ap-9572	31	23	sudhanshu	sudhanshu	NOUN
ap-9572	31	24	aggarwal	aggarwal	PROPN
ap-9572	31	25	acta	acta	PROPN
ap-9572	31	26	polytechnica	polytechnica	PROPN
ap-9572	31	27	the	the	DET
ap-9572	31	28	rayleigh	rayleigh	PROPN
ap-9572	31	29	-	-	PUNCT
ap-9572	31	30	ritz	ritz	PROPN
ap-9572	31	31	technique	technique	NOUN
ap-9572	31	32	.	.	PUNCT
ap-9572	32	1	gupta	gupta	PROPN
ap-9572	32	2	et	et	PROPN
ap-9572	32	3	al	al	PROPN
ap-9572	32	4	.	.	PUNCT
ap-9572	33	1	[	[	X
ap-9572	33	2	7	7	X
ap-9572	33	3	]	]	X
ap-9572	33	4	determined	determine	VERB
ap-9572	33	5	the	the	DET
ap-9572	33	6	fundamental	fundamental	ADJ
ap-9572	33	7	frequencies	frequency	NOUN
ap-9572	33	8	and	and	CCONJ
ap-9572	33	9	the	the	DET
ap-9572	33	10	deflection	deflection	NOUN
ap-9572	33	11	by	by	ADP
ap-9572	33	12	analysing	analyse	VERB
ap-9572	33	13	the	the	DET
ap-9572	33	14	vibration	vibration	NOUN
ap-9572	33	15	of	of	ADP
ap-9572	33	16	the	the	DET
ap-9572	33	17	non	non	ADJ
ap-9572	33	18	-	-	ADJ
ap-9572	33	19	homogeneous	homogeneous	ADJ
ap-9572	33	20	orthotropic	orthotropic	ADJ
ap-9572	33	21	plate	plate	NOUN
ap-9572	33	22	(	(	PUNCT
ap-9572	33	23	rectangular	rectangular	ADJ
ap-9572	33	24	)	)	PUNCT
ap-9572	33	25	having	have	VERB
ap-9572	33	26	linear	linear	PROPN
ap-9572	33	27	thickness	thickness	NOUN
ap-9572	33	28	variations	variation	NOUN
ap-9572	33	29	in	in	ADP
ap-9572	33	30	both	both	CCONJ
ap-9572	33	31	the	the	DET
ap-9572	33	32	directions	direction	NOUN
ap-9572	33	33	with	with	ADP
ap-9572	33	34	the	the	DET
ap-9572	33	35	thermal	thermal	ADJ
ap-9572	33	36	gradient	gradient	ADJ
ap-9572	33	37	effect	effect	NOUN
ap-9572	33	38	.	.	PUNCT
ap-9572	34	1	gupta	gupta	NOUN
ap-9572	34	2	and	and	CCONJ
ap-9572	34	3	kaur	kaur	NOUN
ap-9572	35	1	[	[	X
ap-9572	35	2	8	8	NUM
ap-9572	35	3	]	]	PUNCT
ap-9572	35	4	used	use	VERB
ap-9572	35	5	the	the	DET
ap-9572	35	6	rayleighritz	rayleighritz	NOUN
ap-9572	35	7	method	method	NOUN
ap-9572	35	8	to	to	PART
ap-9572	35	9	determine	determine	VERB
ap-9572	35	10	the	the	DET
ap-9572	35	11	thermal	thermal	ADJ
ap-9572	35	12	gradient	gradient	ADJ
ap-9572	35	13	effect	effect	NOUN
ap-9572	35	14	on	on	ADP
ap-9572	35	15	the	the	DET
ap-9572	35	16	vibration	vibration	NOUN
ap-9572	35	17	of	of	ADP
ap-9572	35	18	the	the	DET
ap-9572	35	19	variable	variable	ADJ
ap-9572	35	20	thickness	thickness	NOUN
ap-9572	35	21	visco	visco	ADJ
ap-9572	35	22	-	-	ADJ
ap-9572	35	23	elastic	elastic	ADJ
ap-9572	35	24	rectangular	rectangular	ADJ
ap-9572	35	25	plate	plate	NOUN
ap-9572	35	26	with	with	ADP
ap-9572	35	27	clamped	clamp	VERB
ap-9572	35	28	boundary	boundary	ADJ
ap-9572	35	29	conditions	condition	NOUN
ap-9572	35	30	.	.	PUNCT
ap-9572	36	1	the	the	DET
ap-9572	36	2	monograph	monograph	NOUN
ap-9572	36	3	of	of	ADP
ap-9572	36	4	leissa	leissa	ADJ
ap-9572	36	5	[	[	X
ap-9572	36	6	1	1	NUM
ap-9572	36	7	]	]	PUNCT
ap-9572	36	8	has	have	VERB
ap-9572	36	9	an	an	DET
ap-9572	36	10	excellent	excellent	ADJ
ap-9572	36	11	literature	literature	NOUN
ap-9572	36	12	on	on	ADP
ap-9572	36	13	the	the	DET
ap-9572	36	14	vibration	vibration	NOUN
ap-9572	36	15	of	of	ADP
ap-9572	36	16	the	the	DET
ap-9572	36	17	plates	plate	NOUN
ap-9572	36	18	for	for	ADP
ap-9572	36	19	the	the	DET
ap-9572	36	20	scholars	scholar	NOUN
ap-9572	36	21	and	and	CCONJ
ap-9572	36	22	it	it	PRON
ap-9572	36	23	is	be	AUX
ap-9572	36	24	very	very	ADV
ap-9572	36	25	convenient	convenient	ADJ
ap-9572	36	26	to	to	PART
ap-9572	36	27	curb	curb	VERB
ap-9572	36	28	the	the	DET
ap-9572	36	29	duplication	duplication	NOUN
ap-9572	36	30	of	of	ADP
ap-9572	36	31	the	the	DET
ap-9572	36	32	research	research	NOUN
ap-9572	36	33	handiwork	handiwork	NOUN
ap-9572	36	34	in	in	ADP
ap-9572	36	35	the	the	DET
ap-9572	36	36	plate	plate	NOUN
ap-9572	36	37	vibrations	vibration	NOUN
ap-9572	36	38	.	.	PUNCT
ap-9572	37	1	singh	singh	PROPN
ap-9572	37	2	and	and	CCONJ
ap-9572	37	3	saxena	saxena	PROPN
ap-9572	38	1	[	[	X
ap-9572	38	2	9	9	NUM
ap-9572	38	3	]	]	PUNCT
ap-9572	38	4	have	have	AUX
ap-9572	38	5	determined	determine	VERB
ap-9572	38	6	the	the	DET
ap-9572	38	7	vibration	vibration	NOUN
ap-9572	38	8	(	(	PUNCT
ap-9572	38	9	transverse	transverse	NOUN
ap-9572	38	10	)	)	PUNCT
ap-9572	38	11	of	of	ADP
ap-9572	38	12	the	the	DET
ap-9572	38	13	rectangular	rectangular	ADJ
ap-9572	38	14	plate	plate	NOUN
ap-9572	38	15	and	and	CCONJ
ap-9572	38	16	they	they	PRON
ap-9572	38	17	have	have	AUX
ap-9572	38	18	considered	consider	VERB
ap-9572	38	19	the	the	DET
ap-9572	38	20	bidirectional	bidirectional	ADJ
ap-9572	38	21	thickness	thickness	NOUN
ap-9572	38	22	variation	variation	NOUN
ap-9572	38	23	in	in	ADP
ap-9572	38	24	this	this	DET
ap-9572	38	25	study	study	NOUN
ap-9572	38	26	.	.	PUNCT
ap-9572	39	1	laura	laura	NOUN
ap-9572	39	2	and	and	CCONJ
ap-9572	39	3	gutierrez	gutierrez	PROPN
ap-9572	40	1	[	[	X
ap-9572	40	2	10	10	NUM
ap-9572	40	3	]	]	PUNCT
ap-9572	40	4	analysed	analyse	VERB
ap-9572	40	5	the	the	DET
ap-9572	40	6	vibration	vibration	NOUN
ap-9572	40	7	of	of	ADP
ap-9572	40	8	the	the	DET
ap-9572	40	9	rectangular	rectangular	ADJ
ap-9572	40	10	plate	plate	NOUN
ap-9572	40	11	with	with	ADP
ap-9572	40	12	the	the	DET
ap-9572	40	13	thermal	thermal	ADJ
ap-9572	40	14	gradient	gradient	ADJ
ap-9572	40	15	effect	effect	NOUN
ap-9572	40	16	.	.	PUNCT
ap-9572	41	1	gupta	gupta	NOUN
ap-9572	41	2	et	et	PROPN
ap-9572	41	3	al	al	PROPN
ap-9572	41	4	.	.	PUNCT
ap-9572	42	1	[	[	X
ap-9572	42	2	11	11	NUM
ap-9572	42	3	]	]	PUNCT
ap-9572	42	4	considered	consider	VERB
ap-9572	42	5	the	the	DET
ap-9572	42	6	rayleigh	rayleigh	PROPN
ap-9572	42	7	-	-	PUNCT
ap-9572	42	8	ritz	ritz	PROPN
ap-9572	42	9	technique	technique	NOUN
ap-9572	42	10	for	for	ADP
ap-9572	42	11	analysing	analyse	VERB
ap-9572	42	12	the	the	DET
ap-9572	42	13	vibrations	vibration	NOUN
ap-9572	42	14	of	of	ADP
ap-9572	42	15	the	the	DET
ap-9572	42	16	variable	variable	ADJ
ap-9572	42	17	thickness	thickness	NOUN
ap-9572	42	18	rectangular	rectangular	ADJ
ap-9572	42	19	visco	visco	ADJ
ap-9572	42	20	-	-	ADJ
ap-9572	42	21	elastic	elastic	ADJ
ap-9572	42	22	plate	plate	NOUN
ap-9572	42	23	.	.	PUNCT
ap-9572	43	1	gupta	gupta	NOUN
ap-9572	43	2	and	and	CCONJ
ap-9572	43	3	aggarwal	aggarwal	PROPN
ap-9572	43	4	[	[	X
ap-9572	43	5	12–14	12–14	X
ap-9572	43	6	]	]	PUNCT
ap-9572	43	7	discussed	discuss	VERB
ap-9572	43	8	the	the	DET
ap-9572	43	9	linear	linear	ADJ
ap-9572	43	10	temperature	temperature	NOUN
ap-9572	43	11	effect	effect	NOUN
ap-9572	43	12	on	on	ADP
ap-9572	43	13	the	the	DET
ap-9572	43	14	vibration	vibration	NOUN
ap-9572	43	15	of	of	ADP
ap-9572	43	16	a	a	DET
ap-9572	43	17	non	non	ADJ
ap-9572	43	18	-	-	ADJ
ap-9572	43	19	homogeneous	homogeneous	ADJ
ap-9572	43	20	viscoelastic	viscoelastic	ADJ
ap-9572	43	21	plate	plate	NOUN
ap-9572	43	22	(	(	PUNCT
ap-9572	43	23	rectangular	rectangular	ADJ
ap-9572	43	24	)	)	PUNCT
ap-9572	43	25	with	with	ADP
ap-9572	43	26	variable	variable	ADJ
ap-9572	43	27	thickness	thickness	NOUN
ap-9572	43	28	in	in	ADP
ap-9572	43	29	two	two	NUM
ap-9572	43	30	directions	direction	NOUN
ap-9572	43	31	.	.	PUNCT
ap-9572	44	1	gupta	gupta	NOUN
ap-9572	44	2	and	and	CCONJ
ap-9572	44	3	kaur	kaur	NOUN
ap-9572	45	1	[	[	X
ap-9572	45	2	15	15	NUM
ap-9572	45	3	]	]	PUNCT
ap-9572	45	4	have	have	AUX
ap-9572	45	5	considered	consider	VERB
ap-9572	45	6	the	the	DET
ap-9572	45	7	linear	linear	ADJ
ap-9572	45	8	temperature	temperature	NOUN
ap-9572	45	9	variation	variation	NOUN
ap-9572	45	10	and	and	CCONJ
ap-9572	45	11	studied	study	VERB
ap-9572	45	12	its	its	PRON
ap-9572	45	13	effect	effect	NOUN
ap-9572	45	14	on	on	ADP
ap-9572	45	15	the	the	DET
ap-9572	45	16	free	free	ADJ
ap-9572	45	17	transverse	transverse	NOUN
ap-9572	45	18	vibration	vibration	NOUN
ap-9572	45	19	of	of	ADP
ap-9572	45	20	the	the	DET
ap-9572	45	21	clamped	clamp	VERB
ap-9572	45	22	visco	visco	ADJ
ap-9572	45	23	-	-	ADJ
ap-9572	45	24	elastic	elastic	ADJ
ap-9572	45	25	rectangular	rectangular	ADJ
ap-9572	45	26	plate	plate	NOUN
ap-9572	45	27	exponential	exponential	ADJ
ap-9572	45	28	thickness	thickness	NOUN
ap-9572	45	29	variation	variation	NOUN
ap-9572	45	30	in	in	ADP
ap-9572	45	31	both	both	DET
ap-9572	45	32	directions	direction	NOUN
ap-9572	45	33	.	.	PUNCT
ap-9572	46	1	nagaya	nagaya	NOUN
ap-9572	47	1	[	[	X
ap-9572	47	2	16	16	NUM
ap-9572	47	3	]	]	PUNCT
ap-9572	47	4	found	find	VERB
ap-9572	47	5	solutions	solution	NOUN
ap-9572	47	6	to	to	ADP
ap-9572	47	7	the	the	DET
ap-9572	47	8	problems	problem	NOUN
ap-9572	47	9	of	of	ADP
ap-9572	47	10	vibration	vibration	NOUN
ap-9572	47	11	and	and	CCONJ
ap-9572	47	12	transient	transient	ADJ
ap-9572	47	13	response	response	NOUN
ap-9572	47	14	of	of	ADP
ap-9572	47	15	the	the	DET
ap-9572	47	16	non	non	ADJ
ap-9572	47	17	-	-	ADJ
ap-9572	47	18	periodic	periodic	ADJ
ap-9572	47	19	elastically	elastically	ADV
ap-9572	47	20	supported	support	VERB
ap-9572	47	21	continuous	continuous	ADJ
ap-9572	47	22	visco	visco	ADJ
ap-9572	47	23	-	-	ADJ
ap-9572	47	24	elastic	elastic	ADJ
ap-9572	47	25	plates	plate	NOUN
ap-9572	47	26	.	.	PUNCT
ap-9572	48	1	gupta	gupta	NOUN
ap-9572	48	2	et	et	PROPN
ap-9572	48	3	al	al	PROPN
ap-9572	48	4	.	.	PUNCT
ap-9572	49	1	[	[	X
ap-9572	49	2	17	17	NUM
ap-9572	49	3	]	]	PUNCT
ap-9572	49	4	analysed	analyse	VERB
ap-9572	49	5	the	the	DET
ap-9572	49	6	thermal	thermal	ADJ
ap-9572	49	7	effect	effect	NOUN
ap-9572	49	8	on	on	ADP
ap-9572	49	9	the	the	DET
ap-9572	49	10	vibration	vibration	NOUN
ap-9572	49	11	problem	problem	NOUN
ap-9572	49	12	of	of	ADP
ap-9572	49	13	the	the	DET
ap-9572	49	14	clamped	clamp	VERB
ap-9572	49	15	visco	visco	ADJ
ap-9572	49	16	-	-	ADJ
ap-9572	49	17	elastic	elastic	ADJ
ap-9572	49	18	rectangular	rectangular	ADJ
ap-9572	49	19	plate	plate	NOUN
ap-9572	49	20	.	.	PUNCT
ap-9572	50	1	bhat	bhat	PROPN
ap-9572	51	1	[	[	X
ap-9572	51	2	18	18	NUM
ap-9572	51	3	]	]	PUNCT
ap-9572	51	4	determined	determine	VERB
ap-9572	51	5	the	the	DET
ap-9572	51	6	natural	natural	ADJ
ap-9572	51	7	frequencies	frequency	NOUN
ap-9572	51	8	of	of	ADP
ap-9572	51	9	the	the	DET
ap-9572	51	10	rectangular	rectangular	ADJ
ap-9572	51	11	plates	plate	NOUN
ap-9572	51	12	using	use	VERB
ap-9572	51	13	the	the	DET
ap-9572	51	14	rayleigh	rayleigh	PROPN
ap-9572	51	15	-	-	PUNCT
ap-9572	51	16	ritz	ritz	PROPN
ap-9572	51	17	method	method	NOUN
ap-9572	51	18	.	.	PUNCT
ap-9572	52	1	tomar	tomar	NOUN
ap-9572	52	2	and	and	CCONJ
ap-9572	52	3	gupta	gupta	NOUN
ap-9572	53	1	[	[	X
ap-9572	53	2	19	19	NUM
ap-9572	53	3	]	]	PUNCT
ap-9572	53	4	studied	study	VERB
ap-9572	53	5	the	the	DET
ap-9572	53	6	vibration	vibration	NOUN
ap-9572	53	7	problem	problem	NOUN
ap-9572	53	8	of	of	ADP
ap-9572	53	9	an	an	DET
ap-9572	53	10	orthotropic	orthotropic	ADJ
ap-9572	53	11	rectangular	rectangular	ADJ
ap-9572	53	12	plate	plate	NOUN
ap-9572	53	13	with	with	ADP
ap-9572	53	14	the	the	DET
ap-9572	53	15	linearly	linearly	ADV
ap-9572	53	16	varying	vary	VERB
ap-9572	53	17	thickness	thickness	NOUN
ap-9572	53	18	and	and	CCONJ
ap-9572	53	19	determined	determine	VERB
ap-9572	53	20	the	the	DET
ap-9572	53	21	thermal	thermal	ADJ
ap-9572	53	22	effect	effect	NOUN
ap-9572	53	23	on	on	ADP
ap-9572	53	24	the	the	DET
ap-9572	53	25	frequencies	frequency	NOUN
ap-9572	53	26	of	of	ADP
ap-9572	53	27	the	the	DET
ap-9572	53	28	plate	plate	NOUN
ap-9572	53	29	considered	consider	VERB
ap-9572	53	30	.	.	PUNCT
ap-9572	54	1	saini	saini	PROPN
ap-9572	54	2	and	and	CCONJ
ap-9572	54	3	lal	lal	PROPN
ap-9572	55	1	[	[	X
ap-9572	55	2	20	20	NUM
ap-9572	55	3	]	]	PUNCT
ap-9572	55	4	used	use	VERB
ap-9572	55	5	the	the	DET
ap-9572	55	6	general	general	ADJ
ap-9572	55	7	differential	differential	ADJ
ap-9572	55	8	quadrature	quadrature	NOUN
ap-9572	55	9	(	(	PUNCT
ap-9572	55	10	gdq	gdq	NOUN
ap-9572	55	11	)	)	PUNCT
ap-9572	55	12	method	method	NOUN
ap-9572	55	13	to	to	PART
ap-9572	55	14	analyse	analyse	VERB
ap-9572	55	15	the	the	DET
ap-9572	55	16	transverse	transverse	ADJ
ap-9572	55	17	vibration	vibration	NOUN
ap-9572	55	18	of	of	ADP
ap-9572	55	19	the	the	DET
ap-9572	55	20	variable	variable	ADJ
ap-9572	55	21	thickness	thickness	NOUN
ap-9572	55	22	non	non	ADJ
ap-9572	55	23	-	-	ADJ
ap-9572	55	24	homogeneous	homogeneous	ADJ
ap-9572	55	25	rectangular	rectangular	ADJ
ap-9572	55	26	plates	plate	NOUN
ap-9572	55	27	.	.	PUNCT
ap-9572	56	1	gupta	gupta	PROPN
ap-9572	56	2	et	et	PROPN
ap-9572	56	3	al	al	PROPN
ap-9572	56	4	.	.	PUNCT
ap-9572	57	1	[	[	X
ap-9572	57	2	21	21	NUM
ap-9572	57	3	]	]	PUNCT
ap-9572	57	4	considered	consider	VERB
ap-9572	57	5	the	the	DET
ap-9572	57	6	linearly	linearly	ADV
ap-9572	57	7	varying	vary	VERB
ap-9572	57	8	thickness	thickness	NOUN
ap-9572	57	9	non	non	ADJ
ap-9572	57	10	-	-	ADJ
ap-9572	57	11	homogeneous	homogeneous	ADJ
ap-9572	57	12	rectangular	rectangular	ADJ
ap-9572	57	13	plate	plate	NOUN
ap-9572	57	14	and	and	CCONJ
ap-9572	57	15	analysed	analyse	VERB
ap-9572	57	16	its	its	PRON
ap-9572	57	17	vibration	vibration	NOUN
ap-9572	57	18	.	.	PUNCT
ap-9572	58	1	sobamowo	sobamowo	PROPN
ap-9572	58	2	et	et	PROPN
ap-9572	58	3	al	al	PROPN
ap-9572	58	4	.	.	PUNCT
ap-9572	59	1	[	[	X
ap-9572	59	2	22	22	NUM
ap-9572	59	3	]	]	PUNCT
ap-9572	59	4	applied	apply	VERB
ap-9572	59	5	the	the	DET
ap-9572	59	6	three	three	NUM
ap-9572	59	7	-	-	PUNCT
ap-9572	59	8	dimensional	dimensional	ADJ
ap-9572	59	9	differential	differential	ADJ
ap-9572	59	10	transformation	transformation	NOUN
ap-9572	59	11	method	method	NOUN
ap-9572	59	12	to	to	ADP
ap-9572	59	13	the	the	DET
ap-9572	59	14	problem	problem	NOUN
ap-9572	59	15	of	of	ADP
ap-9572	59	16	thermally	thermally	ADV
ap-9572	59	17	induced	induce	VERB
ap-9572	59	18	vibration	vibration	NOUN
ap-9572	59	19	of	of	ADP
ap-9572	59	20	the	the	DET
ap-9572	59	21	non	non	ADJ
ap-9572	59	22	-	-	ADJ
ap-9572	59	23	homogeneous	homogeneous	ADJ
ap-9572	59	24	rectangular	rectangular	ADJ
ap-9572	59	25	plate	plate	NOUN
ap-9572	59	26	with	with	ADP
ap-9572	59	27	the	the	DET
ap-9572	59	28	varying	vary	VERB
ap-9572	59	29	thickness	thickness	NOUN
ap-9572	59	30	.	.	PUNCT
ap-9572	60	1	shabnam	shabnam	PROPN
ap-9572	60	2	et	et	PROPN
ap-9572	60	3	al	al	PROPN
ap-9572	60	4	.	.	PUNCT
ap-9572	61	1	[	[	X
ap-9572	61	2	23	23	NUM
ap-9572	61	3	]	]	PUNCT
ap-9572	61	4	studied	study	VERB
ap-9572	61	5	the	the	DET
ap-9572	61	6	problem	problem	NOUN
ap-9572	61	7	of	of	ADP
ap-9572	61	8	free	free	ADJ
ap-9572	61	9	vibration	vibration	NOUN
ap-9572	61	10	of	of	ADP
ap-9572	61	11	thin	thin	ADJ
ap-9572	61	12	plates	plate	NOUN
ap-9572	61	13	with	with	ADP
ap-9572	61	14	the	the	DET
ap-9572	61	15	variable	variable	ADJ
ap-9572	61	16	thickness	thickness	NOUN
ap-9572	61	17	and	and	CCONJ
ap-9572	61	18	determined	determine	VERB
ap-9572	61	19	its	its	PRON
ap-9572	61	20	solution	solution	NOUN
ap-9572	61	21	using	use	VERB
ap-9572	61	22	the	the	DET
ap-9572	61	23	two	two	NUM
ap-9572	61	24	-	-	PUNCT
ap-9572	61	25	dimensional	dimensional	ADJ
ap-9572	61	26	differential	differential	ADJ
ap-9572	61	27	transformation	transformation	NOUN
ap-9572	61	28	method	method	NOUN
ap-9572	61	29	.	.	PUNCT
ap-9572	62	1	singhal	singhal	PROPN
ap-9572	62	2	and	and	CCONJ
ap-9572	62	3	ruby	ruby	PROPN
ap-9572	63	1	[	[	X
ap-9572	63	2	24	24	NUM
ap-9572	63	3	]	]	PUNCT
ap-9572	63	4	discussed	discuss	VERB
ap-9572	63	5	the	the	DET
ap-9572	63	6	thermally	thermally	ADV
ap-9572	63	7	induced	induced	ADJ
ap-9572	63	8	vibrations	vibration	NOUN
ap-9572	63	9	of	of	ADP
ap-9572	63	10	the	the	DET
ap-9572	63	11	tapered	tapered	ADJ
ap-9572	63	12	non	non	ADJ
ap-9572	63	13	-	-	ADJ
ap-9572	63	14	homogeneous	homogeneous	ADJ
ap-9572	63	15	rectangular	rectangular	ADJ
ap-9572	63	16	plate	plate	NOUN
ap-9572	63	17	.	.	PUNCT
ap-9572	64	1	yeh	yeh	PROPN
ap-9572	64	2	et	et	PROPN
ap-9572	64	3	al	al	PROPN
ap-9572	64	4	.	.	PUNCT
ap-9572	65	1	[	[	X
ap-9572	65	2	25	25	NUM
ap-9572	65	3	]	]	PUNCT
ap-9572	65	4	used	use	VERB
ap-9572	65	5	the	the	DET
ap-9572	65	6	finite	finite	ADJ
ap-9572	65	7	difference	difference	NOUN
ap-9572	65	8	,	,	PUNCT
ap-9572	65	9	and	and	CCONJ
ap-9572	65	10	the	the	DET
ap-9572	65	11	differential	differential	ADJ
ap-9572	65	12	transformation	transformation	NOUN
ap-9572	65	13	methods	method	NOUN
ap-9572	65	14	to	to	PART
ap-9572	65	15	determine	determine	VERB
ap-9572	65	16	the	the	DET
ap-9572	65	17	solution	solution	NOUN
ap-9572	65	18	to	to	ADP
ap-9572	65	19	the	the	DET
ap-9572	65	20	free	free	ADJ
ap-9572	65	21	vibration	vibration	NOUN
ap-9572	65	22	problem	problem	NOUN
ap-9572	65	23	of	of	ADP
ap-9572	65	24	the	the	DET
ap-9572	65	25	plate	plate	NOUN
ap-9572	65	26	.	.	PUNCT
ap-9572	66	1	khanna	khanna	PROPN
ap-9572	66	2	and	and	CCONJ
ap-9572	66	3	singhal	singhal	PROPN
ap-9572	67	1	[	[	X
ap-9572	67	2	26	26	NUM
ap-9572	67	3	]	]	PUNCT
ap-9572	67	4	studied	study	VERB
ap-9572	67	5	the	the	DET
ap-9572	67	6	vibration	vibration	NOUN
ap-9572	67	7	problem	problem	NOUN
ap-9572	67	8	of	of	ADP
ap-9572	67	9	a	a	DET
ap-9572	67	10	clamped	clamp	VERB
ap-9572	67	11	visco	visco	ADJ
ap-9572	67	12	-	-	ADJ
ap-9572	67	13	elastic	elastic	ADJ
ap-9572	67	14	thin	thin	ADJ
ap-9572	67	15	plate	plate	NOUN
ap-9572	67	16	(	(	PUNCT
ap-9572	67	17	rectangular	rectangular	ADJ
ap-9572	67	18	)	)	PUNCT
ap-9572	67	19	.	.	PUNCT
ap-9572	68	1	jafari	jafari	PROPN
ap-9572	68	2	and	and	CCONJ
ap-9572	68	3	azhari	azhari	ADJ
ap-9572	68	4	[	[	X
ap-9572	68	5	27	27	NUM
ap-9572	68	6	]	]	PUNCT
ap-9572	68	7	discussed	discuss	VERB
ap-9572	68	8	the	the	DET
ap-9572	68	9	problem	problem	NOUN
ap-9572	68	10	of	of	ADP
ap-9572	68	11	free	free	ADJ
ap-9572	68	12	vibration	vibration	NOUN
ap-9572	68	13	of	of	ADP
ap-9572	68	14	visco	visco	ADJ
ap-9572	68	15	-	-	ADJ
ap-9572	68	16	elastic	elastic	ADJ
ap-9572	68	17	plate	plate	NOUN
ap-9572	68	18	(	(	PUNCT
ap-9572	68	19	mindlin	mindlin	NOUN
ap-9572	68	20	)	)	PUNCT
ap-9572	68	21	and	and	CCONJ
ap-9572	68	22	determined	determine	VERB
ap-9572	68	23	the	the	DET
ap-9572	68	24	natural	natural	ADJ
ap-9572	68	25	frequency	frequency	NOUN
ap-9572	68	26	along	along	ADP
ap-9572	68	27	with	with	ADP
ap-9572	68	28	viscous	viscous	ADJ
ap-9572	68	29	damping	damping	NOUN
ap-9572	68	30	.	.	PUNCT
ap-9572	69	1	amabili	amabili	NOUN
ap-9572	69	2	et	et	PROPN
ap-9572	69	3	al	al	PROPN
ap-9572	69	4	.	.	PUNCT
ap-9572	70	1	[	[	X
ap-9572	70	2	28	28	NUM
ap-9572	70	3	]	]	PUNCT
ap-9572	70	4	obtained	obtain	VERB
ap-9572	70	5	the	the	DET
ap-9572	70	6	solutions	solution	NOUN
ap-9572	70	7	of	of	ADP
ap-9572	70	8	the	the	DET
ap-9572	70	9	problems	problem	NOUN
ap-9572	70	10	of	of	ADP
ap-9572	70	11	nonlinear	nonlinear	ADJ
ap-9572	70	12	vibration	vibration	NOUN
ap-9572	70	13	of	of	ADP
ap-9572	70	14	fractional	fractional	ADJ
ap-9572	70	15	viscoelastic	viscoelastic	ADJ
ap-9572	70	16	rectangular	rectangular	ADJ
ap-9572	70	17	plates	plate	NOUN
ap-9572	70	18	with	with	ADP
ap-9572	70	19	damping	damp	VERB
ap-9572	70	20	.	.	PUNCT
ap-9572	71	1	bhardwaz	bhardwaz	NOUN
ap-9572	71	2	et	et	PROPN
ap-9572	71	3	al	al	PROPN
ap-9572	71	4	.	.	PUNCT
ap-9572	72	1	[	[	X
ap-9572	72	2	29	29	NUM
ap-9572	72	3	]	]	PUNCT
ap-9572	72	4	determined	determine	VERB
ap-9572	72	5	the	the	DET
ap-9572	72	6	time	time	NOUN
ap-9572	72	7	period	period	NOUN
ap-9572	72	8	for	for	ADP
ap-9572	72	9	the	the	DET
ap-9572	72	10	vibration	vibration	NOUN
ap-9572	72	11	problem	problem	NOUN
ap-9572	72	12	of	of	ADP
ap-9572	72	13	a	a	DET
ap-9572	72	14	non	non	ADJ
ap-9572	72	15	-	-	ADJ
ap-9572	72	16	homogeneous	homogeneous	ADJ
ap-9572	72	17	parallelogram	parallelogram	NOUN
ap-9572	72	18	plate	plate	NOUN
ap-9572	72	19	(	(	PUNCT
ap-9572	72	20	skew	skew	NOUN
ap-9572	72	21	)	)	PUNCT
ap-9572	72	22	with	with	ADP
ap-9572	72	23	two	two	NUM
ap-9572	72	24	-	-	PUNCT
ap-9572	72	25	dimensional	dimensional	ADJ
ap-9572	72	26	parabolic	parabolic	ADJ
ap-9572	72	27	temperature	temperature	NOUN
ap-9572	72	28	variations	variation	NOUN
ap-9572	72	29	.	.	PUNCT
ap-9572	73	1	abdikarimov	abdikarimov	PROPN
ap-9572	73	2	et	et	PROPN
ap-9572	73	3	al	al	PROPN
ap-9572	73	4	.	.	PUNCT
ap-9572	74	1	[	[	X
ap-9572	74	2	30	30	NUM
ap-9572	74	3	]	]	PUNCT
ap-9572	74	4	discussed	discuss	VERB
ap-9572	74	5	the	the	DET
ap-9572	74	6	problem	problem	NOUN
ap-9572	74	7	of	of	ADP
ap-9572	74	8	dynamic	dynamic	ADJ
ap-9572	74	9	stability	stability	NOUN
ap-9572	74	10	of	of	ADP
ap-9572	74	11	a	a	DET
ap-9572	74	12	orthotropic	orthotropic	ADJ
ap-9572	74	13	visco	visco	ADJ
ap-9572	74	14	-	-	ADJ
ap-9572	74	15	elastic	elastic	ADJ
ap-9572	74	16	plate	plate	NOUN
ap-9572	74	17	(	(	PUNCT
ap-9572	74	18	rectangular	rectangular	ADJ
ap-9572	74	19	)	)	PUNCT
ap-9572	74	20	with	with	ADP
ap-9572	74	21	arbitrary	arbitrary	ADJ
ap-9572	74	22	thickness	thickness	NOUN
ap-9572	74	23	variation	variation	NOUN
ap-9572	74	24	.	.	PUNCT
ap-9572	75	1	this	this	DET
ap-9572	75	2	work	work	NOUN
ap-9572	75	3	aims	aim	VERB
ap-9572	75	4	to	to	PART
ap-9572	75	5	analyse	analyse	VERB
ap-9572	75	6	the	the	DET
ap-9572	75	7	non	non	ADJ
ap-9572	75	8	-	-	ADJ
ap-9572	75	9	homogeneity	homogeneity	ADJ
ap-9572	75	10	effect	effect	NOUN
ap-9572	75	11	of	of	ADP
ap-9572	75	12	vibrations	vibration	NOUN
ap-9572	75	13	on	on	ADP
ap-9572	75	14	the	the	DET
ap-9572	75	15	rectangular	rectangular	ADJ
ap-9572	75	16	visco	visco	ADJ
ap-9572	75	17	-	-	ADJ
ap-9572	75	18	elastic	elastic	ADJ
ap-9572	75	19	plate	plate	NOUN
ap-9572	75	20	subjected	subject	VERB
ap-9572	75	21	to	to	ADP
ap-9572	75	22	a	a	DET
ap-9572	75	23	linear	linear	ADJ
ap-9572	75	24	temperature	temperature	NOUN
ap-9572	75	25	effect	effect	NOUN
ap-9572	75	26	with	with	ADP
ap-9572	75	27	quadratic	quadratic	ADJ
ap-9572	75	28	thickness	thickness	NOUN
ap-9572	75	29	variation	variation	NOUN
ap-9572	75	30	in	in	ADP
ap-9572	75	31	both	both	DET
ap-9572	75	32	directions	direction	NOUN
ap-9572	75	33	.	.	PUNCT
ap-9572	76	1	the	the	DET
ap-9572	76	2	deflection	deflection	NOUN
ap-9572	76	3	(	(	PUNCT
ap-9572	76	4	w	w	NOUN
ap-9572	76	5	)	)	PUNCT
ap-9572	76	6	and	and	CCONJ
ap-9572	76	7	time	time	NOUN
ap-9572	76	8	period	period	NOUN
ap-9572	76	9	(	(	PUNCT
ap-9572	76	10	tp	tp	NOUN
ap-9572	76	11	)	)	PUNCT
ap-9572	76	12	have	have	AUX
ap-9572	76	13	been	be	AUX
ap-9572	76	14	evaluated	evaluate	VERB
ap-9572	76	15	for	for	ADP
ap-9572	76	16	several	several	ADJ
ap-9572	76	17	combinations	combination	NOUN
ap-9572	76	18	of	of	ADP
ap-9572	76	19	the	the	DET
ap-9572	76	20	values	value	NOUN
ap-9572	76	21	of	of	ADP
ap-9572	76	22	the	the	DET
ap-9572	76	23	thermal	thermal	ADJ
ap-9572	76	24	constant	constant	ADJ
ap-9572	76	25	(	(	PUNCT
ap-9572	76	26	α	α	NOUN
ap-9572	76	27	)	)	PUNCT
ap-9572	76	28	,	,	PUNCT
ap-9572	76	29	constant	constant	ADJ
ap-9572	76	30	of	of	ADP
ap-9572	76	31	the	the	DET
ap-9572	76	32	non	non	ADJ
ap-9572	76	33	-	-	NOUN
ap-9572	76	34	homogeneity	homogeneity	ADJ
ap-9572	76	35	(	(	PUNCT
ap-9572	76	36	α1	α1	PROPN
ap-9572	76	37	)	)	PUNCT
ap-9572	76	38	,	,	PUNCT
ap-9572	76	39	taper	taper	NOUN
ap-9572	76	40	constants	constant	NOUN
ap-9572	76	41	(	(	PUNCT
ap-9572	76	42	β1	β1	NOUN
ap-9572	76	43	,	,	PUNCT
ap-9572	76	44	β2	β2	PROPN
ap-9572	76	45	)	)	PUNCT
ap-9572	76	46	and	and	CCONJ
ap-9572	76	47	the	the	DET
ap-9572	76	48	length	length	NOUN
ap-9572	76	49	-	-	PUNCT
ap-9572	76	50	to	to	ADP
ap-9572	76	51	-	-	PUNCT
ap-9572	76	52	width	width	NOUN
ap-9572	76	53	ratio	ratio	NOUN
ap-9572	76	54	(	(	PUNCT
ap-9572	76	55	a	a	DET
ap-9572	76	56	b	b	NOUN
ap-9572	76	57	)	)	PUNCT
ap-9572	76	58	for	for	ADP
ap-9572	76	59	the	the	DET
ap-9572	76	60	first	first	ADJ
ap-9572	76	61	two	two	NUM
ap-9572	76	62	vibration	vibration	NOUN
ap-9572	76	63	modes	mode	NOUN
ap-9572	76	64	of	of	ADP
ap-9572	76	65	a	a	DET
ap-9572	76	66	clamped	clamp	VERB
ap-9572	76	67	plate	plate	NOUN
ap-9572	76	68	.	.	PUNCT
ap-9572	77	1	graphs	graph	NOUN
ap-9572	77	2	and	and	CCONJ
ap-9572	77	3	tables	table	NOUN
ap-9572	77	4	are	be	AUX
ap-9572	77	5	used	use	VERB
ap-9572	77	6	for	for	ADP
ap-9572	77	7	presenting	present	VERB
ap-9572	77	8	the	the	DET
ap-9572	77	9	corresponding	corresponding	ADJ
ap-9572	77	10	results	result	NOUN
ap-9572	77	11	.	.	PUNCT
ap-9572	78	1	the	the	DET
ap-9572	78	2	rest	rest	NOUN
ap-9572	78	3	of	of	ADP
ap-9572	78	4	this	this	DET
ap-9572	78	5	paper	paper	NOUN
ap-9572	78	6	is	be	AUX
ap-9572	78	7	organised	organise	VERB
ap-9572	78	8	as	as	SCONJ
ap-9572	78	9	follows	follow	VERB
ap-9572	78	10	.	.	PUNCT
ap-9572	79	1	assumptions	assumption	NOUN
ap-9572	79	2	of	of	ADP
ap-9572	79	3	the	the	DET
ap-9572	79	4	study	study	NOUN
ap-9572	79	5	are	be	AUX
ap-9572	79	6	provided	provide	VERB
ap-9572	79	7	in	in	ADP
ap-9572	79	8	section	section	NOUN
ap-9572	79	9	2	2	NUM
ap-9572	79	10	.	.	PUNCT
ap-9572	79	11	equation	equation	NOUN
ap-9572	79	12	of	of	ADP
ap-9572	79	13	the	the	DET
ap-9572	79	14	motion	motion	NOUN
ap-9572	79	15	and	and	CCONJ
ap-9572	79	16	the	the	DET
ap-9572	79	17	method	method	NOUN
ap-9572	79	18	of	of	ADP
ap-9572	79	19	the	the	DET
ap-9572	79	20	analysis	analysis	NOUN
ap-9572	79	21	are	be	AUX
ap-9572	79	22	presented	present	VERB
ap-9572	79	23	in	in	ADP
ap-9572	79	24	section	section	NOUN
ap-9572	79	25	3	3	NUM
ap-9572	79	26	.	.	PUNCT
ap-9572	80	1	we	we	PRON
ap-9572	80	2	present	present	VERB
ap-9572	80	3	differential	differential	ADJ
ap-9572	80	4	equation	equation	NOUN
ap-9572	80	5	of	of	ADP
ap-9572	80	6	the	the	DET
ap-9572	80	7	time	time	NOUN
ap-9572	80	8	function	function	NOUN
ap-9572	80	9	with	with	ADP
ap-9572	80	10	its	its	PRON
ap-9572	80	11	solution	solution	NOUN
ap-9572	80	12	in	in	ADP
ap-9572	80	13	section	section	NOUN
ap-9572	80	14	4	4	NUM
ap-9572	80	15	.	.	PUNCT
ap-9572	81	1	all	all	DET
ap-9572	81	2	the	the	DET
ap-9572	81	3	results	result	NOUN
ap-9572	81	4	and	and	CCONJ
ap-9572	81	5	discussions	discussion	NOUN
ap-9572	81	6	are	be	AUX
ap-9572	81	7	presented	present	VERB
ap-9572	81	8	in	in	ADP
ap-9572	81	9	section	section	NOUN
ap-9572	81	10	5	5	NUM
ap-9572	81	11	.	.	PUNCT
ap-9572	82	1	the	the	DET
ap-9572	82	2	comparison	comparison	NOUN
ap-9572	82	3	of	of	ADP
ap-9572	82	4	the	the	DET
ap-9572	82	5	results	result	NOUN
ap-9572	82	6	of	of	ADP
ap-9572	82	7	the	the	DET
ap-9572	82	8	present	present	ADJ
ap-9572	82	9	study	study	NOUN
ap-9572	82	10	with	with	ADP
ap-9572	82	11	the	the	DET
ap-9572	82	12	previous	previous	ADJ
ap-9572	82	13	study	study	NOUN
ap-9572	82	14	is	be	AUX
ap-9572	82	15	provided	provide	VERB
ap-9572	82	16	in	in	ADP
ap-9572	82	17	section	section	NOUN
ap-9572	82	18	6	6	NUM
ap-9572	82	19	.	.	PUNCT
ap-9572	83	1	the	the	DET
ap-9572	83	2	last	last	ADJ
ap-9572	83	3	section	section	NOUN
ap-9572	83	4	(	(	PUNCT
ap-9572	83	5	section	section	NOUN
ap-9572	83	6	7	7	NUM
ap-9572	83	7	)	)	PUNCT
ap-9572	83	8	presents	present	VERB
ap-9572	83	9	a	a	DET
ap-9572	83	10	brief	brief	ADJ
ap-9572	83	11	conclusion	conclusion	NOUN
ap-9572	83	12	.	.	PUNCT
ap-9572	84	1	2	2	X
ap-9572	84	2	.	.	X
ap-9572	84	3	assumptions	assumption	NOUN
ap-9572	84	4	of	of	ADP
ap-9572	84	5	the	the	DET
ap-9572	84	6	study	study	NOUN
ap-9572	84	7	author	author	NOUN
ap-9572	84	8	has	have	AUX
ap-9572	84	9	considered	consider	VERB
ap-9572	84	10	the	the	DET
ap-9572	84	11	following	follow	VERB
ap-9572	84	12	assumptions	assumption	NOUN
ap-9572	84	13	for	for	ADP
ap-9572	84	14	this	this	DET
ap-9572	84	15	study	study	NOUN
ap-9572	84	16	:	:	PUNCT
ap-9572	84	17	•	•	ADP
ap-9572	84	18	the	the	DET
ap-9572	84	19	quadratic	quadratic	ADJ
ap-9572	84	20	variation	variation	NOUN
ap-9572	84	21	has	have	AUX
ap-9572	84	22	been	be	AUX
ap-9572	84	23	considered	consider	VERB
ap-9572	84	24	in	in	ADP
ap-9572	84	25	the	the	DET
ap-9572	84	26	material	material	NOUN
ap-9572	84	27	density	density	NOUN
ap-9572	84	28	of	of	ADP
ap-9572	84	29	the	the	DET
ap-9572	84	30	plate	plate	NOUN
ap-9572	84	31	only	only	ADV
ap-9572	84	32	along	along	ADP
ap-9572	84	33	the	the	DET
ap-9572	84	34	x	x	NOUN
ap-9572	84	35	-	-	NOUN
ap-9572	84	36	axis	axis	ADJ
ap-9572	84	37	.	.	PUNCT
ap-9572	85	1	in	in	ADP
ap-9572	85	2	addition	addition	NOUN
ap-9572	85	3	,	,	PUNCT
ap-9572	85	4	it	it	PRON
ap-9572	85	5	is	be	AUX
ap-9572	85	6	supposed	suppose	VERB
ap-9572	85	7	that	that	SCONJ
ap-9572	85	8	the	the	DET
ap-9572	85	9	non	non	ADJ
ap-9572	85	10	-	-	ADJ
ap-9572	85	11	homogeneity	homogeneity	NOUN
ap-9572	85	12	occurs	occur	VERB
ap-9572	85	13	due	due	ADJ
ap-9572	85	14	to	to	ADP
ap-9572	85	15	this	this	DET
ap-9572	85	16	variation	variation	NOUN
ap-9572	85	17	.	.	PUNCT
ap-9572	86	1	•	•	INTJ
ap-9572	86	2	it	it	PRON
ap-9572	86	3	is	be	AUX
ap-9572	86	4	supposed	suppose	VERB
ap-9572	86	5	that	that	SCONJ
ap-9572	86	6	all	all	DET
ap-9572	86	7	the	the	DET
ap-9572	86	8	four	four	NUM
ap-9572	86	9	edges	edge	NOUN
ap-9572	86	10	of	of	ADP
ap-9572	86	11	the	the	DET
ap-9572	86	12	plate	plate	NOUN
ap-9572	86	13	are	be	AUX
ap-9572	86	14	clamped	clamp	VERB
ap-9572	86	15	for	for	ADP
ap-9572	86	16	deriving	derive	VERB
ap-9572	86	17	the	the	DET
ap-9572	86	18	frequency	frequency	NOUN
ap-9572	86	19	equation	equation	NOUN
ap-9572	86	20	with	with	ADP
ap-9572	86	21	the	the	DET
ap-9572	86	22	use	use	NOUN
ap-9572	86	23	of	of	ADP
ap-9572	86	24	the	the	DET
ap-9572	86	25	rayleigh	rayleigh	PROPN
ap-9572	86	26	-	-	PUNCT
ap-9572	86	27	ritz	ritz	PROPN
ap-9572	86	28	technique	technique	NOUN
ap-9572	86	29	.	.	PUNCT
ap-9572	87	1	according	accord	VERB
ap-9572	87	2	to	to	ADP
ap-9572	87	3	this	this	DET
ap-9572	87	4	technique	technique	NOUN
ap-9572	87	5	,	,	PUNCT
ap-9572	87	6	the	the	DET
ap-9572	87	7	maximum	maximum	ADJ
ap-9572	87	8	strain	strain	NOUN
ap-9572	87	9	energy	energy	NOUN
ap-9572	87	10	must	must	AUX
ap-9572	87	11	be	be	AUX
ap-9572	87	12	equal	equal	ADJ
ap-9572	87	13	to	to	ADP
ap-9572	87	14	the	the	DET
ap-9572	87	15	maximum	maximum	ADJ
ap-9572	87	16	kinetic	kinetic	ADJ
ap-9572	87	17	energy	energy	NOUN
ap-9572	87	18	.	.	PUNCT
ap-9572	88	1	•	•	NUM
ap-9572	88	2	the	the	DET
ap-9572	88	3	linear	linear	ADJ
ap-9572	88	4	variation	variation	NOUN
ap-9572	88	5	in	in	ADP
ap-9572	88	6	the	the	DET
ap-9572	88	7	temperature	temperature	NOUN
ap-9572	88	8	of	of	ADP
ap-9572	88	9	the	the	DET
ap-9572	88	10	plate	plate	NOUN
ap-9572	88	11	has	have	AUX
ap-9572	88	12	been	be	AUX
ap-9572	88	13	considered	consider	VERB
ap-9572	88	14	only	only	ADV
ap-9572	88	15	along	along	ADP
ap-9572	88	16	the	the	DET
ap-9572	88	17	x	x	NOUN
ap-9572	88	18	-	-	NOUN
ap-9572	88	19	axis	axis	ADJ
ap-9572	88	20	.	.	PUNCT
ap-9572	89	1	•	•	NUM
ap-9572	89	2	the	the	DET
ap-9572	89	3	quadratic	quadratic	ADJ
ap-9572	89	4	variation	variation	NOUN
ap-9572	89	5	has	have	AUX
ap-9572	89	6	been	be	AUX
ap-9572	89	7	considered	consider	VERB
ap-9572	89	8	for	for	ADP
ap-9572	89	9	the	the	DET
ap-9572	89	10	thickness	thickness	NOUN
ap-9572	89	11	of	of	ADP
ap-9572	89	12	the	the	DET
ap-9572	89	13	plate	plate	NOUN
ap-9572	89	14	along	along	ADP
ap-9572	89	15	the	the	DET
ap-9572	89	16	x	x	NOUN
ap-9572	89	17	-	-	NOUN
ap-9572	89	18	axis	axis	NOUN
ap-9572	89	19	and	and	CCONJ
ap-9572	89	20	the	the	DET
ap-9572	89	21	y	y	NOUN
ap-9572	89	22	-	-	PUNCT
ap-9572	89	23	axis	axis	NOUN
ap-9572	89	24	.	.	PUNCT
ap-9572	90	1	•	•	NUM
ap-9572	90	2	the	the	DET
ap-9572	90	3	linear	linear	ADJ
ap-9572	90	4	visco	visco	ADJ
ap-9572	90	5	-	-	ADJ
ap-9572	90	6	elastic	elastic	ADJ
ap-9572	90	7	behaviour	behaviour	NOUN
ap-9572	90	8	is	be	AUX
ap-9572	90	9	of	of	ADP
ap-9572	90	10	the	the	DET
ap-9572	90	11	kelvin	kelvin	PROPN
ap-9572	90	12	type	type	NOUN
ap-9572	90	13	.	.	PUNCT
ap-9572	91	1	•	•	NUM
ap-9572	91	2	the	the	DET
ap-9572	91	3	assumption	assumption	NOUN
ap-9572	91	4	of	of	ADP
ap-9572	91	5	the	the	DET
ap-9572	91	6	small	small	ADJ
ap-9572	91	7	deflection	deflection	NOUN
ap-9572	91	8	is	be	AUX
ap-9572	91	9	assumed	assume	VERB
ap-9572	91	10	.	.	PUNCT
ap-9572	92	1	•	•	NUM
ap-9572	92	2	duralium	duralium	NOUN
ap-9572	92	3	material	material	NOUN
ap-9572	92	4	(	(	PUNCT
ap-9572	92	5	alloy	alloy	NOUN
ap-9572	92	6	of	of	ADP
ap-9572	92	7	aluminium	aluminium	NOUN
ap-9572	92	8	,	,	PUNCT
ap-9572	92	9	copper	copper	NOUN
ap-9572	92	10	,	,	PUNCT
ap-9572	92	11	magnesium	magnesium	NOUN
ap-9572	92	12	,	,	PUNCT
ap-9572	92	13	and	and	CCONJ
ap-9572	92	14	manganese	manganese	NOUN
ap-9572	92	15	)	)	PUNCT
ap-9572	92	16	parameters	parameter	NOUN
ap-9572	92	17	are	be	AUX
ap-9572	92	18	used	use	VERB
ap-9572	92	19	for	for	ADP
ap-9572	92	20	the	the	DET
ap-9572	92	21	numerical	numerical	ADJ
ap-9572	92	22	computation	computation	NOUN
ap-9572	92	23	.	.	PUNCT
ap-9572	93	1	298	298	NUM
ap-9572	93	2	vol	vol	NOUN
ap-9572	93	3	.	.	PUNCT
ap-9572	94	1	64	64	NUM
ap-9572	94	2	no	no	NOUN
ap-9572	94	3	.	.	PUNCT
ap-9572	95	1	4/2024	4/2024	NUM
ap-9572	95	2	non	non	ADJ
ap-9572	95	3	-	-	ADJ
ap-9572	95	4	homogeneity	homogeneity	ADJ
ap-9572	95	5	effect	effect	NOUN
ap-9572	95	6	on	on	ADP
ap-9572	95	7	the	the	DET
ap-9572	95	8	vibration	vibration	NOUN
ap-9572	95	9	of	of	ADP
ap-9572	95	10	.	.	PUNCT
ap-9572	95	11	.	.	PUNCT
ap-9572	95	12	.	.	PUNCT
ap-9572	96	1	3	3	X
ap-9572	96	2	.	.	X
ap-9572	96	3	equation	equation	NOUN
ap-9572	96	4	of	of	ADP
ap-9572	96	5	the	the	DET
ap-9572	96	6	motion	motion	NOUN
ap-9572	96	7	and	and	CCONJ
ap-9572	96	8	the	the	DET
ap-9572	96	9	method	method	NOUN
ap-9572	96	10	of	of	ADP
ap-9572	96	11	the	the	DET
ap-9572	96	12	analysis	analysis	NOUN
ap-9572	96	13	the	the	DET
ap-9572	96	14	author	author	NOUN
ap-9572	96	15	discusses	discuss	VERB
ap-9572	96	16	the	the	DET
ap-9572	96	17	equation	equation	NOUN
ap-9572	96	18	of	of	ADP
ap-9572	96	19	the	the	DET
ap-9572	96	20	motion	motion	NOUN
ap-9572	96	21	and	and	CCONJ
ap-9572	96	22	the	the	DET
ap-9572	96	23	method	method	NOUN
ap-9572	96	24	of	of	ADP
ap-9572	96	25	the	the	DET
ap-9572	96	26	analysis	analysis	NOUN
ap-9572	96	27	in	in	ADP
ap-9572	96	28	this	this	DET
ap-9572	96	29	section	section	NOUN
ap-9572	96	30	.	.	PUNCT
ap-9572	97	1	for	for	ADP
ap-9572	97	2	the	the	DET
ap-9572	97	3	free	free	ADJ
ap-9572	97	4	vibration	vibration	NOUN
ap-9572	97	5	of	of	ADP
ap-9572	97	6	the	the	DET
ap-9572	97	7	plate	plate	NOUN
ap-9572	97	8	,	,	PUNCT
ap-9572	97	9	the	the	DET
ap-9572	97	10	transverse	transverse	NOUN
ap-9572	97	11	motion	motion	NOUN
ap-9572	97	12	and	and	CCONJ
ap-9572	97	13	the	the	DET
ap-9572	97	14	time	time	NOUN
ap-9572	97	15	function	function	NOUN
ap-9572	97	16	are	be	AUX
ap-9572	97	17	given	give	VERB
ap-9572	97	18	by	by	ADP
ap-9572	97	19	the	the	DET
ap-9572	97	20	following	follow	VERB
ap-9572	97	21	equations	equation	NOUN
ap-9572	97	22	,	,	PUNCT
ap-9572	97	23	respectively	respectively	ADV
ap-9572	97	24	,	,	PUNCT
ap-9572	97	25	as	as	ADP
ap-9572	97	26	[	[	X
ap-9572	97	27	15	15	NUM
ap-9572	97	28	]	]	NOUN
ap-9572	97	29	:	:	PUNCT
ap-9572	97	30			PROPN
ap-9572	97	31			PROPN
ap-9572	97	32	d	d	PROPN
ap-9572	97	33	(	(	PUNCT
ap-9572	97	34	∂4w	∂4w	ADV
ap-9572	97	35	∂x4	∂x4	VERB
ap-9572	97	36	+	+	CCONJ
ap-9572	97	37	2	2	NUM
ap-9572	97	38	∂4w	∂4w	X
ap-9572	97	39	∂x2∂y2	∂x2∂y2	NOUN
ap-9572	97	40	+	+	CCONJ
ap-9572	97	41	∂4w	∂4w	ADP
ap-9572	97	42	∂y4	∂y4	NOUN
ap-9572	97	43	)	)	PUNCT
ap-9572	97	44	+2	+2	PROPN
ap-9572	97	45	∂d	∂d	PROPN
ap-9572	97	46	∂x	∂x	PROPN
ap-9572	97	47	(	(	PUNCT
ap-9572	97	48	∂3w	∂3w	NOUN
ap-9572	97	49	∂x3	∂x3	ADV
ap-9572	97	50	+	+	CCONJ
ap-9572	97	51	∂3w	∂3w	NOUN
ap-9572	97	52	∂x∂y2	∂x∂y2	PUNCT
ap-9572	97	53	)	)	PUNCT
ap-9572	98	1	+2	+2	PROPN
ap-9572	98	2	∂d	∂d	PROPN
ap-9572	98	3	∂y	∂y	NOUN
ap-9572	98	4	(	(	PUNCT
ap-9572	98	5	∂3w	∂3w	NOUN
ap-9572	98	6	∂y3	∂y3	VERB
ap-9572	98	7	+	+	NUM
ap-9572	98	8	∂3w	∂3w	NOUN
ap-9572	98	9	∂x2∂y	∂x2∂y	PROPN
ap-9572	98	10	)	)	PUNCT
ap-9572	99	1	+	+	CCONJ
ap-9572	99	2	∂2d	∂2d	PROPN
ap-9572	99	3	∂x2	∂x2	NOUN
ap-9572	99	4	(	(	PUNCT
ap-9572	99	5	∂2w	∂2w	ADP
ap-9572	99	6	∂x2	∂x2	NOUN
ap-9572	99	7	+	+	NOUN
ap-9572	99	8	ν	ν	NOUN
ap-9572	99	9	∂2w	∂2w	VERB
ap-9572	99	10	∂y2	∂y2	NUM
ap-9572	99	11	)	)	PUNCT
ap-9572	100	1	+	+	CCONJ
ap-9572	100	2	∂2d	∂2d	PROPN
ap-9572	100	3	∂y2	∂y2	ADJ
ap-9572	100	4	(	(	PUNCT
ap-9572	100	5	∂2w	∂2w	VERB
ap-9572	100	6	∂y2	∂y2	ADJ
ap-9572	100	7	+	+	CCONJ
ap-9572	100	8	ν	ν	NOUN
ap-9572	100	9	∂2w	∂2w	VERB
ap-9572	100	10	∂x2	∂x2	NOUN
ap-9572	100	11	)	)	PUNCT
ap-9572	100	12	+2	+2	PROPN
ap-9572	100	13	(	(	PUNCT
ap-9572	100	14	1	1	NUM
ap-9572	100	15	−	−	NOUN
ap-9572	100	16	ν	ν	NOUN
ap-9572	100	17	)	)	PUNCT
ap-9572	100	18	∂2d	∂2d	PROPN
ap-9572	100	19	∂x∂y	∂x∂y	PROPN
ap-9572	100	20	∂2w	∂2w	VERB
ap-9572	100	21	∂x∂y	∂x∂y	NOUN
ap-9572	100	22			ADV
ap-9572	100	23	−	−	PROPN
ap-9572	100	24	ρhk2w	ρhk2w	PUNCT
ap-9572	101	1	=	=	SYM
ap-9572	101	2	0	0	NUM
ap-9572	101	3			NOUN
ap-9572	101	4	,	,	PUNCT
ap-9572	101	5	(	(	PUNCT
ap-9572	101	6	1	1	X
ap-9572	101	7	)	)	PUNCT
ap-9572	101	8	and	and	CCONJ
ap-9572	101	9	:	:	PUNCT
ap-9572	101	10	ẗ	ẗ	X
ap-9572	102	1	+	+	PUNCT
ap-9572	102	2	k2d̃t	k2d̃t	NOUN
ap-9572	102	3	=	=	SYM
ap-9572	102	4	0	0	PROPN
ap-9572	102	5	,	,	PUNCT
ap-9572	102	6	(	(	PUNCT
ap-9572	102	7	2	2	NUM
ap-9572	102	8	)	)	PUNCT
ap-9572	103	1	where	where	SCONJ
ap-9572	103	2	:	:	PUNCT
ap-9572	104	1	d	d	X
ap-9572	104	2	=	=	SYM
ap-9572	104	3	eh3	eh3	NOUN
ap-9572	104	4	12	12	NUM
ap-9572	104	5	(	(	PUNCT
ap-9572	104	6	1	1	NUM
ap-9572	104	7	−	−	NOUN
ap-9572	104	8	ν2	ν2	NOUN
ap-9572	104	9	)	)	PUNCT
ap-9572	104	10	,	,	PUNCT
ap-9572	104	11	(	(	PUNCT
ap-9572	104	12	3	3	X
ap-9572	104	13	)	)	PUNCT
ap-9572	104	14	is	be	AUX
ap-9572	104	15	the	the	DET
ap-9572	104	16	flexural	flexural	ADJ
ap-9572	104	17	rigidity	rigidity	NOUN
ap-9572	104	18	,	,	PUNCT
ap-9572	104	19	ν	ν	X
ap-9572	104	20	is	be	AUX
ap-9572	104	21	the	the	DET
ap-9572	104	22	poisson	poisson	NOUN
ap-9572	104	23	’s	’s	PART
ap-9572	104	24	ratio	ratio	NOUN
ap-9572	104	25	,	,	PUNCT
ap-9572	104	26	e	e	X
ap-9572	104	27	is	be	AUX
ap-9572	104	28	the	the	DET
ap-9572	104	29	young	young	ADJ
ap-9572	104	30	modulus	modulus	NOUN
ap-9572	104	31	of	of	ADP
ap-9572	104	32	elasticity	elasticity	NOUN
ap-9572	104	33	,	,	PUNCT
ap-9572	104	34	ρ	ρ	PROPN
ap-9572	104	35	is	be	AUX
ap-9572	104	36	the	the	DET
ap-9572	104	37	density	density	NOUN
ap-9572	104	38	,	,	PUNCT
ap-9572	104	39	h	h	PROPN
ap-9572	104	40	is	be	AUX
ap-9572	104	41	the	the	DET
ap-9572	104	42	thickness	thickness	NOUN
ap-9572	104	43	of	of	ADP
ap-9572	104	44	the	the	DET
ap-9572	104	45	plate	plate	NOUN
ap-9572	104	46	,	,	PUNCT
ap-9572	104	47	d̃	d̃	PROPN
ap-9572	104	48	is	be	AUX
ap-9572	104	49	the	the	DET
ap-9572	104	50	unique	unique	ADJ
ap-9572	104	51	rheological	rheological	ADJ
ap-9572	104	52	operator	operator	NOUN
ap-9572	104	53	,	,	PUNCT
ap-9572	104	54	k	k	PROPN
ap-9572	104	55	is	be	AUX
ap-9572	104	56	the	the	DET
ap-9572	104	57	frequency	frequency	NOUN
ap-9572	104	58	,	,	PUNCT
ap-9572	104	59	t	t	PROPN
ap-9572	104	60	is	be	AUX
ap-9572	104	61	the	the	DET
ap-9572	104	62	time	time	NOUN
ap-9572	104	63	function	function	NOUN
ap-9572	104	64	,	,	PUNCT
ap-9572	104	65	w	w	PROPN
ap-9572	104	66	is	be	AUX
ap-9572	104	67	the	the	DET
ap-9572	104	68	deflection	deflection	NOUN
ap-9572	104	69	function	function	NOUN
ap-9572	104	70	,	,	PUNCT
ap-9572	104	71	ẗ	ẗ	PROPN
ap-9572	104	72	is	be	AUX
ap-9572	104	73	the	the	DET
ap-9572	104	74	second	second	ADJ
ap-9572	104	75	derivative	derivative	NOUN
ap-9572	104	76	of	of	ADP
ap-9572	104	77	the	the	DET
ap-9572	104	78	time	time	NOUN
ap-9572	104	79	function	function	NOUN
ap-9572	104	80	with	with	ADP
ap-9572	104	81	respect	respect	NOUN
ap-9572	104	82	to	to	ADP
ap-9572	104	83	time	time	NOUN
ap-9572	104	84	t.	t.	PROPN
ap-9572	104	85	let	let	VERB
ap-9572	104	86	’s	’s	NOUN
ap-9572	104	87	consider	consider	VERB
ap-9572	104	88	a	a	DET
ap-9572	104	89	symmetrical	symmetrical	ADJ
ap-9572	104	90	plate	plate	NOUN
ap-9572	104	91	(	(	PUNCT
ap-9572	104	92	rectangular	rectangular	ADJ
ap-9572	104	93	)	)	PUNCT
ap-9572	104	94	with	with	ADP
ap-9572	104	95	all	all	DET
ap-9572	104	96	four	four	NUM
ap-9572	104	97	edges	edge	NOUN
ap-9572	104	98	clamped	clamp	VERB
ap-9572	104	99	at	at	ADP
ap-9572	104	100	length	length	NOUN
ap-9572	104	101	a	a	PRON
ap-9572	104	102	and	and	CCONJ
ap-9572	104	103	width	width	ADJ
ap-9572	104	104	b	b	NOUN
ap-9572	104	105	,	,	PUNCT
ap-9572	104	106	see	see	VERB
ap-9572	104	107	figure	figure	NOUN
ap-9572	104	108	1	1	NUM
ap-9572	104	109	.	.	PUNCT
ap-9572	104	110	assuming	assume	VERB
ap-9572	104	111	that	that	SCONJ
ap-9572	104	112	the	the	DET
ap-9572	104	113	plate	plate	NOUN
ap-9572	104	114	under	under	ADP
ap-9572	104	115	consideration	consideration	NOUN
ap-9572	104	116	has	have	VERB
ap-9572	104	117	the	the	DET
ap-9572	104	118	linear	linear	ADJ
ap-9572	104	119	temperature	temperature	NOUN
ap-9572	104	120	variation	variation	NOUN
ap-9572	104	121	only	only	ADV
ap-9572	104	122	along	along	ADP
ap-9572	104	123	the	the	DET
ap-9572	104	124	x	x	NOUN
ap-9572	104	125	-	-	NOUN
ap-9572	104	126	axis	axis	ADJ
ap-9572	104	127	:	:	PUNCT
ap-9572	104	128	τ	τ	PROPN
ap-9572	104	129	=	=	PROPN
ap-9572	104	130	τ0	τ0	NOUN
ap-9572	104	131	(	(	PUNCT
ap-9572	104	132	1	1	NUM
ap-9572	104	133	−	−	NOUN
ap-9572	104	134	x	x	SYM
ap-9572	104	135	a	a	NOUN
ap-9572	104	136	)	)	PUNCT
ap-9572	104	137	,	,	PUNCT
ap-9572	104	138	(	(	PUNCT
ap-9572	104	139	4	4	X
ap-9572	104	140	)	)	PUNCT
ap-9572	104	141	where	where	SCONJ
ap-9572	104	142	τ0	τ0	NOUN
ap-9572	104	143	and	and	CCONJ
ap-9572	104	144	τ	τ	PROPN
ap-9572	104	145	denote	denote	VERB
ap-9572	104	146	the	the	DET
ap-9572	104	147	temperature	temperature	NOUN
ap-9572	104	148	increment	increment	NOUN
ap-9572	104	149	above	above	ADP
ap-9572	104	150	the	the	DET
ap-9572	104	151	reference	reference	NOUN
ap-9572	104	152	temperature	temperature	NOUN
ap-9572	104	153	at	at	ADP
ap-9572	104	154	any	any	DET
ap-9572	104	155	point	point	NOUN
ap-9572	104	156	at	at	ADP
ap-9572	104	157	the	the	DET
ap-9572	104	158	end	end	NOUN
ap-9572	104	159	x	x	PUNCT
ap-9572	104	160	=	=	PUNCT
ap-9572	104	161	a	a	PRON
ap-9572	104	162	and	and	CCONJ
ap-9572	104	163	at	at	ADP
ap-9572	104	164	the	the	DET
ap-9572	104	165	distance	distance	NOUN
ap-9572	104	166	(	(	PUNCT
ap-9572	104	167	x	x	NOUN
ap-9572	104	168	a	a	NOUN
ap-9572	104	169	)	)	PUNCT
ap-9572	104	170	,	,	PUNCT
ap-9572	104	171	respectively	respectively	ADV
ap-9572	104	172	.	.	PUNCT
ap-9572	105	1	the	the	DET
ap-9572	105	2	modulus	modulus	NOUN
ap-9572	105	3	of	of	ADP
ap-9572	105	4	the	the	DET
ap-9572	105	5	elasticity	elasticity	NOUN
ap-9572	105	6	(	(	PUNCT
ap-9572	105	7	temperature	temperature	NOUN
ap-9572	105	8	dependent	dependent	ADJ
ap-9572	105	9	)	)	PUNCT
ap-9572	105	10	can	can	AUX
ap-9572	105	11	be	be	AUX
ap-9572	105	12	expressed	express	VERB
ap-9572	105	13	as	as	ADP
ap-9572	105	14	[	[	X
ap-9572	105	15	16	16	NUM
ap-9572	105	16	]	]	SYM
ap-9572	105	17	:	:	PUNCT
ap-9572	105	18	e	e	X
ap-9572	105	19	=	=	SYM
ap-9572	105	20	e0	e0	PROPN
ap-9572	105	21	(	(	PUNCT
ap-9572	105	22	1	1	NUM
ap-9572	105	23	−	−	PROPN
ap-9572	105	24	γτ	γτ	NOUN
ap-9572	105	25	)	)	PUNCT
ap-9572	105	26	,	,	PUNCT
ap-9572	105	27	(	(	PUNCT
ap-9572	105	28	5	5	X
ap-9572	105	29	)	)	PUNCT
ap-9572	105	30	where	where	SCONJ
ap-9572	105	31	e0	e0	PROPN
ap-9572	105	32	is	be	AUX
ap-9572	105	33	the	the	DET
ap-9572	105	34	modulus	modulus	NOUN
ap-9572	105	35	of	of	ADP
ap-9572	105	36	elasticity	elasticity	NOUN
ap-9572	105	37	at	at	ADP
ap-9572	105	38	τ	τ	PROPN
ap-9572	105	39	=	=	SYM
ap-9572	105	40	0	0	PUNCT
ap-9572	105	41	(	(	PUNCT
ap-9572	105	42	reference	reference	NOUN
ap-9572	105	43	temperature	temperature	NOUN
ap-9572	105	44	)	)	PUNCT
ap-9572	105	45	,	,	PUNCT
ap-9572	105	46	γ	γ	X
ap-9572	105	47	is	be	AUX
ap-9572	105	48	the	the	DET
ap-9572	105	49	slope	slope	NOUN
ap-9572	105	50	of	of	ADP
ap-9572	105	51	the	the	DET
ap-9572	105	52	variation	variation	NOUN
ap-9572	105	53	of	of	ADP
ap-9572	105	54	e	e	PROPN
ap-9572	105	55	with	with	ADP
ap-9572	105	56	τ	τ	PROPN
ap-9572	105	57	.	.	PUNCT
ap-9572	106	1	figure	figure	NOUN
ap-9572	106	2	1	1	NUM
ap-9572	106	3	.	.	X
ap-9572	106	4	rectangular	rectangular	ADJ
ap-9572	106	5	plate	plate	NOUN
ap-9572	106	6	with	with	ADP
ap-9572	106	7	length	length	NOUN
ap-9572	106	8	a	a	PRON
ap-9572	106	9	and	and	CCONJ
ap-9572	106	10	width	width	ADJ
ap-9572	106	11	b.	b.	PROPN
ap-9572	106	12	substituting	substitute	VERB
ap-9572	106	13	the	the	DET
ap-9572	106	14	equation	equation	NOUN
ap-9572	106	15	(	(	PUNCT
ap-9572	106	16	4	4	NUM
ap-9572	106	17	)	)	PUNCT
ap-9572	106	18	into	into	ADP
ap-9572	106	19	the	the	DET
ap-9572	106	20	equation	equation	NOUN
ap-9572	106	21	(	(	PUNCT
ap-9572	106	22	5	5	X
ap-9572	106	23	)	)	PUNCT
ap-9572	106	24	provides	provide	VERB
ap-9572	106	25	:	:	PUNCT
ap-9572	106	26	e	e	X
ap-9572	106	27	=	=	SYM
ap-9572	106	28	e0	e0	PROPN
ap-9572	106	29	[	[	PUNCT
ap-9572	106	30	1	1	NUM
ap-9572	106	31	−	−	PROPN
ap-9572	106	32	α	α	NOUN
ap-9572	106	33	(	(	PUNCT
ap-9572	106	34	1	1	NUM
ap-9572	106	35	−	−	NOUN
ap-9572	106	36	x	x	SYM
ap-9572	106	37	a	a	NOUN
ap-9572	106	38	)	)	PUNCT
ap-9572	106	39	]	]	PUNCT
ap-9572	106	40	,	,	PUNCT
ap-9572	106	41	(	(	PUNCT
ap-9572	106	42	6	6	NUM
ap-9572	106	43	)	)	PUNCT
ap-9572	107	1	where	where	SCONJ
ap-9572	107	2	the	the	DET
ap-9572	107	3	parameter	parameter	NOUN
ap-9572	107	4	α	α	PROPN
ap-9572	107	5	=	=	PUNCT
ap-9572	107	6	γτ0	γτ0	PROPN
ap-9572	107	7	is	be	AUX
ap-9572	107	8	called	call	VERB
ap-9572	107	9	the	the	DET
ap-9572	107	10	thermal	thermal	ADJ
ap-9572	107	11	gradient	gradient	NOUN
ap-9572	107	12	and	and	CCONJ
ap-9572	107	13	has	have	VERB
ap-9572	107	14	a	a	DET
ap-9572	107	15	value	value	NOUN
ap-9572	107	16	in	in	ADP
ap-9572	107	17	the	the	DET
ap-9572	107	18	interval	interval	NOUN
ap-9572	107	19	[	[	X
ap-9572	107	20	0	0	NUM
ap-9572	107	21	,	,	PUNCT
ap-9572	107	22	1	1	NUM
ap-9572	107	23	]	]	PUNCT
ap-9572	107	24	.	.	PUNCT
ap-9572	108	1	suppose	suppose	VERB
ap-9572	108	2	that	that	SCONJ
ap-9572	108	3	the	the	DET
ap-9572	108	4	plate	plate	NOUN
ap-9572	108	5	under	under	ADP
ap-9572	108	6	consideration	consideration	NOUN
ap-9572	108	7	has	have	VERB
ap-9572	108	8	a	a	DET
ap-9572	108	9	quadratic	quadratic	ADJ
ap-9572	108	10	thickness	thickness	NOUN
ap-9572	108	11	variation	variation	NOUN
ap-9572	108	12	in	in	ADP
ap-9572	108	13	both	both	DET
ap-9572	108	14	directions	direction	NOUN
ap-9572	108	15	:	:	PUNCT
ap-9572	108	16	h	h	NOUN
ap-9572	108	17	=	=	PROPN
ap-9572	108	18	h0	h0	PROPN
ap-9572	108	19	(	(	PUNCT
ap-9572	108	20	1	1	NUM
ap-9572	108	21	+	+	CCONJ
ap-9572	108	22	β1	β1	PROPN
ap-9572	108	23	x2	x2	PROPN
ap-9572	108	24	a2	a2	PROPN
ap-9572	108	25	)	)	PUNCT
ap-9572	108	26	(	(	PUNCT
ap-9572	108	27	1	1	NUM
ap-9572	108	28	+	+	NUM
ap-9572	108	29	β2	β2	ADJ
ap-9572	108	30	y2	y2	NOUN
ap-9572	108	31	b2	b2	PROPN
ap-9572	108	32	)	)	PUNCT
ap-9572	108	33	,	,	PUNCT
ap-9572	108	34	(	(	PUNCT
ap-9572	108	35	7	7	X
ap-9572	108	36	)	)	PUNCT
ap-9572	108	37	where	where	SCONJ
ap-9572	108	38	β1	β1	PROPN
ap-9572	108	39	is	be	AUX
ap-9572	108	40	the	the	DET
ap-9572	108	41	taper	taper	NOUN
ap-9572	108	42	constant	constant	ADJ
ap-9572	108	43	along	along	ADP
ap-9572	108	44	the	the	DET
ap-9572	108	45	x	x	NOUN
ap-9572	108	46	-	-	NOUN
ap-9572	108	47	axis	axis	ADJ
ap-9572	108	48	,	,	PUNCT
ap-9572	108	49	β2	β2	PROPN
ap-9572	108	50	is	be	AUX
ap-9572	108	51	the	the	DET
ap-9572	108	52	taper	taper	NOUN
ap-9572	108	53	constant	constant	ADJ
ap-9572	108	54	along	along	ADP
ap-9572	108	55	the	the	DET
ap-9572	108	56	y	y	NOUN
ap-9572	108	57	-	-	PUNCT
ap-9572	108	58	axis	axis	NOUN
ap-9572	108	59	,	,	PUNCT
ap-9572	108	60	h0	h0	PROPN
ap-9572	108	61	is	be	AUX
ap-9572	108	62	the	the	DET
ap-9572	108	63	thickness	thickness	NOUN
ap-9572	108	64	of	of	ADP
ap-9572	108	65	the	the	DET
ap-9572	108	66	plate	plate	NOUN
ap-9572	108	67	at	at	ADP
ap-9572	108	68	x	x	X
ap-9572	108	69	=	=	PUNCT
ap-9572	108	70	y	y	PROPN
ap-9572	108	71	=	=	SYM
ap-9572	108	72	0	0	X
ap-9572	108	73	.	.	PUNCT
ap-9572	109	1	assuming	assume	VERB
ap-9572	109	2	that	that	SCONJ
ap-9572	109	3	the	the	DET
ap-9572	109	4	density	density	NOUN
ap-9572	109	5	ρ	ρ	PROPN
ap-9572	109	6	of	of	ADP
ap-9572	109	7	the	the	DET
ap-9572	109	8	plate	plate	NOUN
ap-9572	109	9	under	under	ADP
ap-9572	109	10	consideration	consideration	NOUN
ap-9572	109	11	has	have	VERB
ap-9572	109	12	the	the	DET
ap-9572	109	13	parabolic	parabolic	ADJ
ap-9572	109	14	variation	variation	NOUN
ap-9572	109	15	along	along	ADP
ap-9572	109	16	the	the	DET
ap-9572	109	17	x	x	NOUN
ap-9572	109	18	-	-	NOUN
ap-9572	109	19	axis	axis	ADJ
ap-9572	109	20	,	,	PUNCT
ap-9572	109	21	given	give	VERB
ap-9572	109	22	by	by	ADP
ap-9572	109	23	:	:	PUNCT
ap-9572	109	24	ρ	ρ	PROPN
ap-9572	109	25	=	=	SYM
ap-9572	109	26	ρ0	ρ0	PROPN
ap-9572	109	27	(	(	PUNCT
ap-9572	109	28	1	1	NUM
ap-9572	109	29	+	+	NUM
ap-9572	109	30	α1	α1	PROPN
ap-9572	109	31	x2	x2	PROPN
ap-9572	109	32	a2	a2	PROPN
ap-9572	109	33	)	)	PUNCT
ap-9572	109	34	,	,	PUNCT
ap-9572	109	35	(	(	PUNCT
ap-9572	109	36	8)	8)	NUM
ap-9572	109	37	where	where	SCONJ
ap-9572	109	38	α1	α1	PROPN
ap-9572	109	39	is	be	AUX
ap-9572	109	40	the	the	DET
ap-9572	109	41	non	non	ADJ
ap-9572	109	42	-	-	ADJ
ap-9572	109	43	homogeneity	homogeneity	ADJ
ap-9572	109	44	constant	constant	ADJ
ap-9572	109	45	,	,	PUNCT
ap-9572	109	46	ρ0	ρ0	PROPN
ap-9572	109	47	is	be	AUX
ap-9572	109	48	the	the	DET
ap-9572	109	49	value	value	NOUN
ap-9572	109	50	of	of	ADP
ap-9572	109	51	the	the	DET
ap-9572	109	52	density	density	NOUN
ap-9572	109	53	at	at	ADP
ap-9572	109	54	x	x	X
ap-9572	109	55	=	=	NOUN
ap-9572	109	56	0	0	NUM
ap-9572	109	57	.	.	PUNCT
ap-9572	110	1	the	the	DET
ap-9572	110	2	deflection	deflection	NOUN
ap-9572	110	3	function	function	NOUN
ap-9572	110	4	(	(	PUNCT
ap-9572	110	5	w	w	NOUN
ap-9572	110	6	)	)	PUNCT
ap-9572	110	7	can	can	AUX
ap-9572	110	8	be	be	AUX
ap-9572	110	9	considered	consider	VERB
ap-9572	110	10	in	in	ADP
ap-9572	110	11	the	the	DET
ap-9572	110	12	following	follow	VERB
ap-9572	110	13	form	form	NOUN
ap-9572	110	14	for	for	ADP
ap-9572	110	15	the	the	DET
ap-9572	110	16	free	free	ADJ
ap-9572	110	17	vibrations	vibration	NOUN
ap-9572	110	18	(	(	PUNCT
ap-9572	110	19	transverse	transverse	NOUN
ap-9572	110	20	)	)	PUNCT
ap-9572	110	21	of	of	ADP
ap-9572	110	22	the	the	DET
ap-9572	110	23	plate	plate	NOUN
ap-9572	111	1	[	[	X
ap-9572	111	2	12	12	NUM
ap-9572	111	3	]	]	X
ap-9572	111	4	:	:	PUNCT
ap-9572	111	5	w(x	w(x	PROPN
ap-9572	111	6	,	,	PUNCT
ap-9572	111	7	y	y	PROPN
ap-9572	111	8	,	,	PUNCT
ap-9572	111	9	t	t	PROPN
ap-9572	111	10	)	)	PUNCT
ap-9572	111	11	=	=	SYM
ap-9572	111	12	t	t	PROPN
ap-9572	111	13	(	(	PUNCT
ap-9572	111	14	t	t	PROPN
ap-9572	111	15	)	)	PUNCT
ap-9572	111	16	w	w	PROPN
ap-9572	111	17	(	(	PUNCT
ap-9572	111	18	x	x	NOUN
ap-9572	111	19	,	,	PUNCT
ap-9572	111	20	y	y	PROPN
ap-9572	111	21	)	)	PUNCT
ap-9572	111	22	.	.	PUNCT
ap-9572	112	1	(	(	PUNCT
ap-9572	112	2	9	9	X
ap-9572	112	3	)	)	PUNCT
ap-9572	112	4	leissa	leissa	ADJ
ap-9572	112	5	[	[	X
ap-9572	112	6	1	1	NUM
ap-9572	112	7	]	]	PUNCT
ap-9572	112	8	defined	define	VERB
ap-9572	112	9	the	the	DET
ap-9572	112	10	strain	strain	NOUN
ap-9572	112	11	energy	energy	NOUN
ap-9572	112	12	s	s	NOUN
ap-9572	112	13	and	and	CCONJ
ap-9572	112	14	the	the	DET
ap-9572	112	15	kinetic	kinetic	ADJ
ap-9572	112	16	energy	energy	NOUN
ap-9572	112	17	p	p	NOUN
ap-9572	112	18	as	as	ADP
ap-9572	112	19	:	:	PUNCT
ap-9572	112	20	s	s	X
ap-9572	112	21	=	=	SYM
ap-9572	112	22	1	1	NUM
ap-9572	112	23	2	2	NUM
ap-9572	112	24	∫	∫	NOUN
ap-9572	112	25	a	a	DET
ap-9572	112	26	0	0	NUM
ap-9572	112	27	∫	∫	PROPN
ap-9572	112	28	b	b	PROPN
ap-9572	112	29	0	0	NUM
ap-9572	112	30	d	d	NOUN
ap-9572	112	31	[	[	PUNCT
ap-9572	112	32	(	(	PUNCT
ap-9572	112	33	∂2w	∂2w	VERB
ap-9572	112	34	∂y2	∂y2	NUM
ap-9572	112	35	)	)	PUNCT
ap-9572	112	36	2	2	NUM
ap-9572	113	1	+	+	CCONJ
ap-9572	113	2	(	(	PUNCT
ap-9572	113	3	∂2w	∂2w	VERB
ap-9572	113	4	∂x2	∂x2	NOUN
ap-9572	113	5	)	)	PUNCT
ap-9572	113	6	2	2	NUM
ap-9572	113	7	+	+	NUM
ap-9572	113	8	2	2	NUM
ap-9572	113	9	(	(	PUNCT
ap-9572	113	10	1	1	NUM
ap-9572	113	11	−	−	NOUN
ap-9572	113	12	ν	ν	NOUN
ap-9572	113	13	)	)	PUNCT
ap-9572	113	14	(	(	PUNCT
ap-9572	113	15	∂2w	∂2w	VERB
ap-9572	113	16	∂x∂y	∂x∂y	NOUN
ap-9572	113	17	)	)	PUNCT
ap-9572	113	18	2	2	NUM
ap-9572	113	19	+	+	NUM
ap-9572	113	20	2ν	2ν	NUM
ap-9572	113	21	∂2w	∂2w	VERB
ap-9572	113	22	∂x2	∂x2	NOUN
ap-9572	113	23	∂2w	∂2w	VERB
ap-9572	113	24	∂y2	∂y2	PROPN
ap-9572	113	25	]	]	PUNCT
ap-9572	113	26	dxdy	dxdy	PROPN
ap-9572	113	27	,	,	PUNCT
ap-9572	113	28	(	(	PUNCT
ap-9572	113	29	10	10	NUM
ap-9572	113	30	)	)	PUNCT
ap-9572	113	31	and	and	CCONJ
ap-9572	113	32	p	p	NOUN
ap-9572	113	33	=	=	NOUN
ap-9572	113	34	1	1	NUM
ap-9572	113	35	2k2	2k2	NUM
ap-9572	113	36	∫	∫	NOUN
ap-9572	113	37	a	a	DET
ap-9572	113	38	0	0	NUM
ap-9572	113	39	∫	∫	PROPN
ap-9572	113	40	b	b	PROPN
ap-9572	113	41	0	0	NUM
ap-9572	113	42	ρhw	ρhw	NOUN
ap-9572	113	43	2dxdy	2dxdy	NUM
ap-9572	113	44	.	.	PUNCT
ap-9572	114	1	(	(	PUNCT
ap-9572	114	2	11	11	NUM
ap-9572	114	3	)	)	SYM
ap-9572	114	4	299	299	NUM
ap-9572	114	5	sudhanshu	sudhanshu	NOUN
ap-9572	114	6	aggarwal	aggarwal	PROPN
ap-9572	114	7	acta	acta	PROPN
ap-9572	114	8	polytechnica	polytechnica	PROPN
ap-9572	114	9	the	the	DET
ap-9572	114	10	expression	expression	NOUN
ap-9572	114	11	of	of	ADP
ap-9572	114	12	the	the	DET
ap-9572	114	13	flexural	flexural	ADJ
ap-9572	114	14	rigidity	rigidity	NOUN
ap-9572	114	15	using	use	VERB
ap-9572	114	16	the	the	DET
ap-9572	114	17	equations	equation	NOUN
ap-9572	114	18	(	(	PUNCT
ap-9572	114	19	6	6	NUM
ap-9572	114	20	)	)	PUNCT
ap-9572	114	21	and	and	CCONJ
ap-9572	114	22	(	(	PUNCT
ap-9572	114	23	7	7	X
ap-9572	114	24	)	)	PUNCT
ap-9572	114	25	(	(	PUNCT
ap-9572	114	26	assuming	assume	VERB
ap-9572	114	27	ν	ν	NOUN
ap-9572	114	28	is	be	AUX
ap-9572	114	29	the	the	DET
ap-9572	114	30	constant	constant	ADJ
ap-9572	114	31	)	)	PUNCT
ap-9572	114	32	in	in	ADP
ap-9572	114	33	the	the	DET
ap-9572	114	34	equation	equation	NOUN
ap-9572	114	35	(	(	PUNCT
ap-9572	114	36	3	3	X
ap-9572	114	37	)	)	PUNCT
ap-9572	114	38	can	can	AUX
ap-9572	114	39	be	be	AUX
ap-9572	114	40	written	write	VERB
ap-9572	114	41	as	as	ADP
ap-9572	114	42	:	:	PUNCT
ap-9572	114	43	d	d	NOUN
ap-9572	114	44	=	=	SYM
ap-9572	114	45	1	1	NUM
ap-9572	114	46	12	12	NUM
ap-9572	114	47	(	(	PUNCT
ap-9572	114	48	1	1	NUM
ap-9572	114	49	−	−	NOUN
ap-9572	114	50	ν2	ν2	NOUN
ap-9572	114	51	)	)	PUNCT
ap-9572	114	52	[	[	PUNCT
ap-9572	114	53	e0h0	e0h0	NUM
ap-9572	114	54	3	3	NUM
ap-9572	114	55	{	{	PUNCT
ap-9572	114	56	1	1	NUM
ap-9572	114	57	−	−	PROPN
ap-9572	114	58	α	α	NOUN
ap-9572	114	59	(	(	PUNCT
ap-9572	114	60	1	1	NUM
ap-9572	114	61	−	−	NOUN
ap-9572	114	62	x	x	SYM
ap-9572	114	63	a	a	X
ap-9572	114	64	)	)	PUNCT
ap-9572	114	65	}	}	PUNCT
ap-9572	114	66	(	(	PUNCT
ap-9572	114	67	1	1	X
ap-9572	114	68	+	+	CCONJ
ap-9572	114	69	β1	β1	PROPN
ap-9572	114	70	x2	x2	PROPN
ap-9572	114	71	a2	a2	PROPN
ap-9572	114	72	)	)	PUNCT
ap-9572	114	73	3	3	NUM
ap-9572	114	74	(	(	PUNCT
ap-9572	114	75	1	1	NUM
ap-9572	114	76	+	+	NUM
ap-9572	114	77	β2	β2	ADJ
ap-9572	114	78	y2	y2	NOUN
ap-9572	114	79	b2	b2	NOUN
ap-9572	114	80	)	)	PUNCT
ap-9572	114	81	3	3	NUM
ap-9572	114	82	]	]	PUNCT
ap-9572	114	83	.	.	PUNCT
ap-9572	115	1	(	(	PUNCT
ap-9572	115	2	12	12	X
ap-9572	115	3	)	)	PUNCT
ap-9572	115	4	substituting	substitute	VERB
ap-9572	115	5	equations	equation	NOUN
ap-9572	115	6	(	(	PUNCT
ap-9572	115	7	7	7	NUM
ap-9572	115	8	)	)	PUNCT
ap-9572	115	9	and	and	CCONJ
ap-9572	115	10	(	(	PUNCT
ap-9572	115	11	8)	8)	NUM
ap-9572	115	12	into	into	ADP
ap-9572	115	13	the	the	DET
ap-9572	115	14	equation	equation	NOUN
ap-9572	115	15	(	(	PUNCT
ap-9572	115	16	11	11	NUM
ap-9572	115	17	)	)	PUNCT
ap-9572	115	18	gives	give	VERB
ap-9572	115	19	:	:	PUNCT
ap-9572	115	20	p	p	NOUN
ap-9572	115	21	=	=	SYM
ap-9572	115	22	1	1	NUM
ap-9572	115	23	2ρ0h0k2	2ρ0h0k2	NUM
ap-9572	115	24	∫	∫	NOUN
ap-9572	115	25	a	a	DET
ap-9572	115	26	0	0	NUM
ap-9572	115	27	∫	∫	PROPN
ap-9572	115	28	b	b	PROPN
ap-9572	115	29	0	0	NUM
ap-9572	115	30	(	(	PUNCT
ap-9572	115	31	1	1	NUM
ap-9572	115	32	+	+	NUM
ap-9572	115	33	α1	α1	PROPN
ap-9572	115	34	x2	x2	PROPN
ap-9572	115	35	a2	a2	PROPN
ap-9572	115	36	)	)	PUNCT
ap-9572	115	37	(	(	PUNCT
ap-9572	115	38	1	1	X
ap-9572	115	39	+	+	CCONJ
ap-9572	115	40	β1	β1	PROPN
ap-9572	115	41	x2	x2	PROPN
ap-9572	115	42	a2	a2	PROPN
ap-9572	115	43	)	)	PUNCT
ap-9572	115	44	(	(	PUNCT
ap-9572	115	45	1	1	NUM
ap-9572	115	46	+	+	NUM
ap-9572	115	47	β2	β2	ADJ
ap-9572	115	48	y2	y2	NOUN
ap-9572	115	49	b2	b2	PROPN
ap-9572	115	50	)	)	PUNCT
ap-9572	115	51	w	w	ADP
ap-9572	115	52	2dxdy	2dxdy	NUM
ap-9572	115	53	.	.	PUNCT
ap-9572	116	1	(	(	PUNCT
ap-9572	116	2	13	13	NUM
ap-9572	116	3	)	)	PUNCT
ap-9572	116	4	the	the	DET
ap-9572	116	5	principle	principle	NOUN
ap-9572	116	6	of	of	ADP
ap-9572	116	7	the	the	DET
ap-9572	116	8	rayleigh	rayleigh	PROPN
ap-9572	116	9	-	-	PUNCT
ap-9572	116	10	ritz	ritz	PROPN
ap-9572	116	11	technique	technique	NOUN
ap-9572	116	12	[	[	X
ap-9572	116	13	14	14	NUM
ap-9572	116	14	]	]	PUNCT
ap-9572	116	15	provides	provide	VERB
ap-9572	116	16	:	:	PUNCT
ap-9572	116	17	δ(s	δ(s	PROPN
ap-9572	116	18	−	−	PROPN
ap-9572	116	19	p	p	NOUN
ap-9572	116	20	)	)	PUNCT
ap-9572	116	21	=	=	SYM
ap-9572	116	22	0	0	NUM
ap-9572	116	23	,	,	PUNCT
ap-9572	116	24	(	(	PUNCT
ap-9572	116	25	14	14	NUM
ap-9572	116	26	)	)	PUNCT
ap-9572	116	27	the	the	DET
ap-9572	116	28	assumption	assumption	NOUN
ap-9572	116	29	that	that	SCONJ
ap-9572	116	30	the	the	DET
ap-9572	116	31	four	four	NUM
ap-9572	116	32	edges	edge	NOUN
ap-9572	116	33	of	of	ADP
ap-9572	116	34	the	the	DET
ap-9572	116	35	rectangular	rectangular	ADJ
ap-9572	116	36	plate	plate	NOUN
ap-9572	116	37	are	be	AUX
ap-9572	116	38	clamped	clamp	VERB
ap-9572	116	39	gives:	gives:	PROPN
ap-9572	116	40	(	(	PUNCT
ap-9572	116	41	w	w	NOUN
ap-9572	116	42	)	)	PUNCT
ap-9572	116	43	x=0	x=0	PUNCT
ap-9572	117	1	=	=	SYM
ap-9572	117	2	(	(	PUNCT
ap-9572	117	3	w	w	NOUN
ap-9572	117	4	)	)	PUNCT
ap-9572	117	5	x	x	X
ap-9572	117	6	=	=	NOUN
ap-9572	117	7	a	a	X
ap-9572	117	8	=	=	PUNCT
ap-9572	117	9	(	(	PUNCT
ap-9572	117	10	∂w	∂w	PROPN
ap-9572	117	11	∂x	∂x	PROPN
ap-9572	117	12	)	)	PUNCT
ap-9572	117	13	x=0	x=0	PUNCT
ap-9572	118	1	=	=	SYM
ap-9572	118	2	(	(	PUNCT
ap-9572	118	3	∂w	∂w	PROPN
ap-9572	118	4	∂x	∂x	PROPN
ap-9572	118	5	)	)	PUNCT
ap-9572	118	6	x	x	X
ap-9572	119	1	=	=	NOUN
ap-9572	119	2	a	a	X
ap-9572	119	3	=	=	SYM
ap-9572	119	4	0	0	NUM
ap-9572	119	5	,	,	PUNCT
ap-9572	119	6	(	(	PUNCT
ap-9572	119	7	w	w	NOUN
ap-9572	119	8	)	)	PUNCT
ap-9572	119	9	y=0	y=0	X
ap-9572	119	10	=	=	SYM
ap-9572	119	11	(	(	PUNCT
ap-9572	119	12	w	w	NOUN
ap-9572	119	13	)	)	PUNCT
ap-9572	119	14	y	y	PROPN
ap-9572	120	1	=	=	SYM
ap-9572	120	2	b	b	PROPN
ap-9572	120	3	=	=	PRON
ap-9572	120	4	(	(	PUNCT
ap-9572	120	5	∂w	∂w	PROPN
ap-9572	120	6	∂y	∂y	PROPN
ap-9572	120	7	)	)	PUNCT
ap-9572	120	8	y=0	y=0	X
ap-9572	121	1	=	=	PUNCT
ap-9572	121	2	(	(	PUNCT
ap-9572	121	3	∂w	∂w	PROPN
ap-9572	121	4	∂y	∂y	PROPN
ap-9572	121	5	)	)	PUNCT
ap-9572	121	6	y	y	PROPN
ap-9572	121	7	=	=	SYM
ap-9572	121	8	b	b	NOUN
ap-9572	121	9	=	=	SYM
ap-9572	121	10	0	0	PROPN
ap-9572	121	11	.	.	PUNCT
ap-9572	122	1	(	(	PUNCT
ap-9572	122	2	15	15	X
ap-9572	122	3	)	)	PUNCT
ap-9572	122	4	taking	take	VERB
ap-9572	122	5	the	the	DET
ap-9572	122	6	deflection	deflection	NOUN
ap-9572	122	7	function	function	NOUN
ap-9572	122	8	w	w	PROPN
ap-9572	122	9	(	(	PUNCT
ap-9572	122	10	x	x	NOUN
ap-9572	122	11	,	,	PUNCT
ap-9572	122	12	y	y	NOUN
ap-9572	122	13	)	)	PUNCT
ap-9572	122	14	as	as	ADP
ap-9572	122	15	[	[	X
ap-9572	122	16	13	13	NUM
ap-9572	122	17	]	]	SYM
ap-9572	122	18	:	:	PUNCT
ap-9572	122	19	w	w	X
ap-9572	122	20	(	(	PUNCT
ap-9572	122	21	x	x	NOUN
ap-9572	122	22	,	,	PUNCT
ap-9572	122	23	y	y	NOUN
ap-9572	122	24	)	)	PUNCT
ap-9572	122	25	=	=	PRON
ap-9572	123	1	{	{	PUNCT
ap-9572	123	2	[	[	X
ap-9572	123	3	(	(	PUNCT
ap-9572	123	4	y	y	PROPN
ap-9572	123	5	b	b	PROPN
ap-9572	123	6	)	)	PUNCT
ap-9572	123	7	(	(	PUNCT
ap-9572	123	8	x	x	SYM
ap-9572	123	9	a	a	X
ap-9572	123	10	)	)	PUNCT
ap-9572	123	11	(	(	PUNCT
ap-9572	123	12	1	1	NUM
ap-9572	123	13	−	−	PROPN
ap-9572	123	14	y	y	PROPN
ap-9572	123	15	b	b	PROPN
ap-9572	123	16	)	)	PUNCT
ap-9572	123	17	(	(	PUNCT
ap-9572	123	18	1	1	NUM
ap-9572	123	19	−	−	NOUN
ap-9572	123	20	x	x	SYM
ap-9572	123	21	a	a	X
ap-9572	123	22	)	)	PUNCT
ap-9572	123	23	]	]	SYM
ap-9572	123	24	2	2	NUM
ap-9572	123	25	[	[	PUNCT
ap-9572	123	26	l1	l1	X
ap-9572	123	27	+	+	CCONJ
ap-9572	123	28	l2	l2	NOUN
ap-9572	123	29	(	(	PUNCT
ap-9572	123	30	y	y	PROPN
ap-9572	123	31	b	b	PROPN
ap-9572	123	32	)	)	PUNCT
ap-9572	123	33	(	(	PUNCT
ap-9572	123	34	x	x	SYM
ap-9572	123	35	a	a	X
ap-9572	123	36	)	)	PUNCT
ap-9572	123	37	(	(	PUNCT
ap-9572	123	38	1	1	NUM
ap-9572	123	39	−	−	PROPN
ap-9572	123	40	y	y	PROPN
ap-9572	123	41	b	b	PROPN
ap-9572	123	42	)	)	PUNCT
ap-9572	123	43	(	(	PUNCT
ap-9572	123	44	1	1	NUM
ap-9572	123	45	−	−	NOUN
ap-9572	123	46	x	x	SYM
ap-9572	123	47	a	a	NOUN
ap-9572	123	48	)	)	PUNCT
ap-9572	123	49	]	]	PUNCT
ap-9572	123	50	}	}	PUNCT
ap-9572	123	51	,	,	PUNCT
ap-9572	123	52	(	(	PUNCT
ap-9572	123	53	16	16	NUM
ap-9572	123	54	)	)	PUNCT
ap-9572	123	55	where	where	SCONJ
ap-9572	123	56	both	both	PRON
ap-9572	123	57	constants	constant	VERB
ap-9572	123	58	l1	l1	PROPN
ap-9572	123	59	and	and	CCONJ
ap-9572	123	60	l2	l2	NOUN
ap-9572	123	61	are	be	AUX
ap-9572	123	62	satisfied	satisfied	ADJ
ap-9572	123	63	by	by	ADP
ap-9572	123	64	the	the	DET
ap-9572	123	65	equation	equation	NOUN
ap-9572	123	66	(	(	PUNCT
ap-9572	123	67	15	15	NUM
ap-9572	123	68	)	)	PUNCT
ap-9572	123	69	.	.	PUNCT
ap-9572	124	1	now	now	ADV
ap-9572	124	2	,	,	PUNCT
ap-9572	124	3	taking	take	VERB
ap-9572	124	4	the	the	DET
ap-9572	124	5	non	non	ADJ
ap-9572	124	6	-	-	ADJ
ap-9572	124	7	dimensional	dimensional	ADJ
ap-9572	124	8	quantities	quantity	NOUN
ap-9572	124	9	in	in	ADP
ap-9572	124	10	the	the	DET
ap-9572	124	11	capital	capital	NOUN
ap-9572	124	12	letters	letter	NOUN
ap-9572	124	13	as	as	ADP
ap-9572	124	14	[	[	X
ap-9572	124	15	13]:	13]:	NUM
ap-9572	124	16	h̄	h̄	NOUN
ap-9572	125	1	=	=	SYM
ap-9572	125	2	(	(	PUNCT
ap-9572	125	3	h	h	NOUN
ap-9572	125	4	a	a	NOUN
ap-9572	125	5	)	)	PUNCT
ap-9572	125	6	,	,	PUNCT
ap-9572	125	7	w̄	w̄	NOUN
ap-9572	125	8	=	=	PUNCT
ap-9572	125	9	(	(	PUNCT
ap-9572	125	10	w	w	NOUN
ap-9572	125	11	a	a	NOUN
ap-9572	125	12	)	)	PUNCT
ap-9572	125	13	,	,	PUNCT
ap-9572	125	14	x	x	PUNCT
ap-9572	125	15	=	=	PUNCT
ap-9572	125	16	(	(	PUNCT
ap-9572	125	17	x	x	NOUN
ap-9572	125	18	a	a	NOUN
ap-9572	125	19	)	)	PUNCT
ap-9572	125	20	,	,	PUNCT
ap-9572	125	21	y	y	PROPN
ap-9572	125	22	=	=	PUNCT
ap-9572	125	23	(	(	PUNCT
ap-9572	125	24	y	y	PROPN
ap-9572	125	25	a	a	PRON
ap-9572	125	26	)	)	PUNCT
ap-9572	125	27	.	.	PUNCT
ap-9572	126	1	(	(	PUNCT
ap-9572	126	2	17	17	NUM
ap-9572	126	3	)	)	PUNCT
ap-9572	126	4	using	use	VERB
ap-9572	126	5	equation	equation	NOUN
ap-9572	126	6	(	(	PUNCT
ap-9572	126	7	17	17	NUM
ap-9572	126	8	)	)	PUNCT
ap-9572	126	9	in	in	ADP
ap-9572	126	10	equation	equation	NOUN
ap-9572	126	11	(	(	PUNCT
ap-9572	126	12	16	16	NUM
ap-9572	126	13	)	)	PUNCT
ap-9572	126	14	gives	give	VERB
ap-9572	126	15	:	:	PUNCT
ap-9572	126	16	w	w	X
ap-9572	126	17	=	=	PUNCT
ap-9572	126	18	[	[	PUNCT
ap-9572	126	19	y	y	PROPN
ap-9572	126	20	(	(	PUNCT
ap-9572	126	21	a	a	DET
ap-9572	126	22	b	b	NOUN
ap-9572	126	23	)	)	PUNCT
ap-9572	126	24	x	x	X
ap-9572	127	1	(	(	PUNCT
ap-9572	127	2	1	1	NUM
ap-9572	127	3	−	−	PROPN
ap-9572	127	4	y	y	PROPN
ap-9572	127	5	(	(	PUNCT
ap-9572	127	6	a	a	DET
ap-9572	127	7	b	b	NOUN
ap-9572	127	8	)	)	PUNCT
ap-9572	127	9	)	)	PUNCT
ap-9572	127	10	(	(	PUNCT
ap-9572	127	11	1	1	NUM
ap-9572	127	12	−	−	PROPN
ap-9572	127	13	y	y	PROPN
ap-9572	127	14	)	)	PUNCT
ap-9572	127	15	]	]	PUNCT
ap-9572	127	16	2	2	NUM
ap-9572	127	17	[	[	PUNCT
ap-9572	127	18	l1	l1	PROPN
ap-9572	127	19	+	+	CCONJ
ap-9572	127	20	l2y	l2y	PROPN
ap-9572	127	21	(	(	PUNCT
ap-9572	127	22	a	a	DET
ap-9572	127	23	b	b	NOUN
ap-9572	127	24	)	)	PUNCT
ap-9572	127	25	x	x	X
ap-9572	127	26	(	(	PUNCT
ap-9572	127	27	1	1	NUM
ap-9572	127	28	−	−	PROPN
ap-9572	127	29	y	y	PROPN
ap-9572	127	30	(	(	PUNCT
ap-9572	127	31	a	a	DET
ap-9572	127	32	b	b	NOUN
ap-9572	127	33	)	)	PUNCT
ap-9572	127	34	)	)	PUNCT
ap-9572	127	35	(	(	PUNCT
ap-9572	127	36	1	1	NUM
ap-9572	127	37	−	−	NOUN
ap-9572	127	38	x	x	NOUN
ap-9572	127	39	)	)	PUNCT
ap-9572	127	40	]	]	PUNCT
ap-9572	127	41	.	.	PUNCT
ap-9572	128	1	(	(	PUNCT
ap-9572	128	2	18	18	NUM
ap-9572	128	3	)	)	PUNCT
ap-9572	128	4	using	use	VERB
ap-9572	128	5	equations	equation	NOUN
ap-9572	128	6	(	(	PUNCT
ap-9572	128	7	12	12	NUM
ap-9572	128	8	)	)	PUNCT
ap-9572	128	9	,	,	PUNCT
ap-9572	128	10	and	and	CCONJ
ap-9572	128	11	(	(	PUNCT
ap-9572	128	12	17	17	NUM
ap-9572	128	13	)	)	PUNCT
ap-9572	128	14	in	in	ADP
ap-9572	128	15	equations	equation	NOUN
ap-9572	128	16	(	(	PUNCT
ap-9572	128	17	10	10	NUM
ap-9572	128	18	)	)	PUNCT
ap-9572	128	19	and	and	CCONJ
ap-9572	128	20	(	(	PUNCT
ap-9572	128	21	13	13	NUM
ap-9572	128	22	)	)	PUNCT
ap-9572	128	23	gives	give	VERB
ap-9572	128	24	:	:	PUNCT
ap-9572	128	25	s	s	PART
ap-9572	129	1	=	=	X
ap-9572	129	2	c	c	X
ap-9572	129	3	∫	∫	NOUN
ap-9572	129	4	1	1	NUM
ap-9572	129	5	0	0	NUM
ap-9572	129	6	∫	∫	PROPN
ap-9572	129	7	b	b	PROPN
ap-9572	129	8	a	a	DET
ap-9572	129	9	0	0	NUM
ap-9572	129	10	[	[	PUNCT
ap-9572	129	11	[	[	PUNCT
ap-9572	129	12	{	{	PUNCT
ap-9572	129	13	1	1	NUM
ap-9572	129	14	−	−	PROPN
ap-9572	129	15	α	α	NOUN
ap-9572	129	16	(	(	PUNCT
ap-9572	129	17	1	1	NUM
ap-9572	129	18	−	−	NOUN
ap-9572	129	19	x	x	NOUN
ap-9572	129	20	)	)	PUNCT
ap-9572	129	21	}	}	PUNCT
ap-9572	129	22	(	(	PUNCT
ap-9572	129	23	1	1	NUM
ap-9572	129	24	+	+	CCONJ
ap-9572	129	25	β1x2)3	β1x2)3	NOUN
ap-9572	129	26	(	(	PUNCT
ap-9572	129	27	1	1	NUM
ap-9572	129	28	+	+	NUM
ap-9572	129	29	β2y	β2y	SYM
ap-9572	129	30	2	2	NUM
ap-9572	129	31	a2	a2	PROPN
ap-9572	129	32	b2	b2	NOUN
ap-9572	129	33	)	)	PUNCT
ap-9572	129	34	3	3	X
ap-9572	129	35	]	]	X
ap-9572	129	36	[	[	PUNCT
ap-9572	129	37	(	(	PUNCT
ap-9572	129	38	∂2w̄	∂2w̄	NOUN
ap-9572	129	39	∂y	∂y	NOUN
ap-9572	129	40	2	2	NUM
ap-9572	129	41	)	)	SYM
ap-9572	129	42	2	2	NUM
ap-9572	129	43	+	+	CCONJ
ap-9572	129	44	(	(	PUNCT
ap-9572	129	45	∂2w̄	∂2w̄	NOUN
ap-9572	129	46	∂x2	∂x2	NOUN
ap-9572	129	47	)	)	PUNCT
ap-9572	129	48	2	2	NUM
ap-9572	129	49	+	+	NUM
ap-9572	129	50	2	2	NUM
ap-9572	129	51	(	(	PUNCT
ap-9572	129	52	1	1	NUM
ap-9572	129	53	−	−	NOUN
ap-9572	129	54	ν	ν	NOUN
ap-9572	129	55	)	)	PUNCT
ap-9572	129	56	(	(	PUNCT
ap-9572	129	57	∂2w̄	∂2w̄	NOUN
ap-9572	129	58	∂x∂y	∂x∂y	PROPN
ap-9572	129	59	)	)	PUNCT
ap-9572	129	60	2	2	NUM
ap-9572	129	61	+	+	NUM
ap-9572	129	62	2ν	2ν	NOUN
ap-9572	129	63	∂2w̄	∂2w̄	PUNCT
ap-9572	129	64	∂x2	∂x2	NOUN
ap-9572	129	65	∂2w̄	∂2w̄	NOUN
ap-9572	129	66	∂y	∂y	X
ap-9572	129	67	2	2	X
ap-9572	129	68	]	]	PUNCT
ap-9572	129	69	]	]	PUNCT
ap-9572	129	70	dxdy	dxdy	PROPN
ap-9572	129	71	,	,	PUNCT
ap-9572	129	72	(	(	PUNCT
ap-9572	129	73	19	19	NUM
ap-9572	129	74	)	)	PUNCT
ap-9572	129	75	where	where	SCONJ
ap-9572	129	76	c	c	NOUN
ap-9572	129	77	=	=	SYM
ap-9572	129	78	e0h̄0	e0h̄0	NOUN
ap-9572	129	79	3	3	NUM
ap-9572	129	80	a3	a3	NOUN
ap-9572	129	81	24(1−ν2	24(1−ν2	NUM
ap-9572	129	82	)	)	PUNCT
ap-9572	129	83	and	and	CCONJ
ap-9572	129	84	:	:	PUNCT
ap-9572	129	85	p	p	X
ap-9572	129	86	=	=	NOUN
ap-9572	129	87	1	1	NUM
ap-9572	129	88	2ρ0h̄0k2a5	2ρ0h̄0k2a5	NUM
ap-9572	129	89	∫	∫	NOUN
ap-9572	129	90	1	1	NUM
ap-9572	129	91	0	0	NUM
ap-9572	129	92	∫	∫	PROPN
ap-9572	129	93	b	b	PROPN
ap-9572	129	94	a	a	DET
ap-9572	129	95	0	0	NUM
ap-9572	129	96	(	(	PUNCT
ap-9572	129	97	1	1	NUM
ap-9572	129	98	+	+	CCONJ
ap-9572	129	99	α1x2	α1x2	X
ap-9572	129	100	)	)	PUNCT
ap-9572	129	101	(	(	PUNCT
ap-9572	129	102	1	1	NUM
ap-9572	129	103	+	+	CCONJ
ap-9572	129	104	β1x2	β1x2	X
ap-9572	129	105	)	)	PUNCT
ap-9572	129	106	(	(	PUNCT
ap-9572	129	107	1	1	NUM
ap-9572	129	108	+	+	CCONJ
ap-9572	129	109	β2y	β2y	SYM
ap-9572	129	110	2	2	NUM
ap-9572	129	111	a2	a2	PROPN
ap-9572	129	112	b2	b2	NOUN
ap-9572	129	113	)	)	PUNCT
ap-9572	129	114	w̄	w̄	NOUN
ap-9572	129	115	2dxdy	2dxdy	X
ap-9572	129	116	.	.	PUNCT
ap-9572	129	117	(	(	PUNCT
ap-9572	129	118	20	20	NUM
ap-9572	129	119	)	)	PUNCT
ap-9572	129	120	using	use	VERB
ap-9572	129	121	equations	equation	NOUN
ap-9572	129	122	(	(	PUNCT
ap-9572	129	123	19	19	NUM
ap-9572	129	124	)	)	PUNCT
ap-9572	129	125	and	and	CCONJ
ap-9572	129	126	(	(	PUNCT
ap-9572	129	127	3	3	X
ap-9572	129	128	)	)	PUNCT
ap-9572	129	129	in	in	ADP
ap-9572	129	130	equation	equation	NOUN
ap-9572	129	131	(	(	PUNCT
ap-9572	129	132	14	14	NUM
ap-9572	129	133	)	)	PUNCT
ap-9572	129	134	gives	give	VERB
ap-9572	129	135	:	:	PUNCT
ap-9572	129	136	δ	δ	PROPN
ap-9572	129	137	(	(	PUNCT
ap-9572	129	138	s1	s1	PROPN
ap-9572	129	139	−	−	PROPN
ap-9572	129	140	n2k2p1	n2k2p1	NOUN
ap-9572	129	141	)	)	PUNCT
ap-9572	129	142	=	=	SYM
ap-9572	129	143	0	0	NUM
ap-9572	129	144	,	,	PUNCT
ap-9572	129	145	(	(	PUNCT
ap-9572	129	146	21	21	NUM
ap-9572	129	147	)	)	PUNCT
ap-9572	130	1	where	where	SCONJ
ap-9572	130	2	:	:	PUNCT
ap-9572	131	1	s1	s1	NOUN
ap-9572	131	2	=	=	SYM
ap-9572	131	3	∫	∫	PROPN
ap-9572	131	4	1	1	NUM
ap-9572	131	5	0	0	NUM
ap-9572	131	6	∫	∫	PROPN
ap-9572	131	7	b	b	X
ap-9572	131	8	/	/	SYM
ap-9572	131	9	a	a	DET
ap-9572	131	10	0	0	NUM
ap-9572	131	11	[	[	PUNCT
ap-9572	131	12	[	[	PUNCT
ap-9572	131	13	{	{	PUNCT
ap-9572	131	14	1	1	NUM
ap-9572	131	15	−	−	PROPN
ap-9572	131	16	α	α	NOUN
ap-9572	131	17	(	(	PUNCT
ap-9572	131	18	1	1	NUM
ap-9572	131	19	−	−	NOUN
ap-9572	131	20	x	x	NOUN
ap-9572	131	21	)	)	PUNCT
ap-9572	131	22	}	}	PUNCT
ap-9572	131	23	(	(	PUNCT
ap-9572	131	24	1	1	NUM
ap-9572	131	25	+	+	CCONJ
ap-9572	131	26	β1x2)3	β1x2)3	NOUN
ap-9572	131	27	(	(	PUNCT
ap-9572	131	28	1	1	NUM
ap-9572	131	29	+	+	NUM
ap-9572	131	30	β2y	β2y	SYM
ap-9572	131	31	2	2	NUM
ap-9572	131	32	a2	a2	PROPN
ap-9572	131	33	b2	b2	NOUN
ap-9572	131	34	)	)	PUNCT
ap-9572	131	35	3	3	X
ap-9572	131	36	]	]	X
ap-9572	131	37	[	[	PUNCT
ap-9572	131	38	(	(	PUNCT
ap-9572	131	39	∂2w̄	∂2w̄	NOUN
ap-9572	131	40	∂y	∂y	NOUN
ap-9572	131	41	2	2	NUM
ap-9572	131	42	)	)	SYM
ap-9572	131	43	2	2	NUM
ap-9572	131	44	+	+	CCONJ
ap-9572	131	45	(	(	PUNCT
ap-9572	131	46	∂2w̄	∂2w̄	NOUN
ap-9572	131	47	∂x2	∂x2	NOUN
ap-9572	131	48	)	)	PUNCT
ap-9572	131	49	2	2	NUM
ap-9572	131	50	+	+	NUM
ap-9572	131	51	2	2	NUM
ap-9572	131	52	(	(	PUNCT
ap-9572	131	53	1	1	NUM
ap-9572	131	54	−	−	NOUN
ap-9572	131	55	ν	ν	NOUN
ap-9572	131	56	)	)	PUNCT
ap-9572	131	57	(	(	PUNCT
ap-9572	131	58	∂2w̄	∂2w̄	NOUN
ap-9572	131	59	∂x∂y	∂x∂y	PROPN
ap-9572	131	60	)	)	PUNCT
ap-9572	131	61	2	2	NUM
ap-9572	131	62	+	+	NUM
ap-9572	131	63	2ν	2ν	NOUN
ap-9572	131	64	∂2w̄	∂2w̄	PUNCT
ap-9572	131	65	∂x2	∂x2	NOUN
ap-9572	131	66	∂2w̄	∂2w̄	NOUN
ap-9572	131	67	∂y	∂y	X
ap-9572	131	68	2	2	X
ap-9572	131	69	]	]	PUNCT
ap-9572	131	70	]	]	PUNCT
ap-9572	131	71	dxdy	dxdy	PROPN
ap-9572	131	72	,	,	PUNCT
ap-9572	131	73	(	(	PUNCT
ap-9572	131	74	22	22	NUM
ap-9572	131	75	)	)	PUNCT
ap-9572	131	76	and	and	CCONJ
ap-9572	131	77	:	:	PUNCT
ap-9572	131	78	p1	p1	PROPN
ap-9572	131	79	=	=	SYM
ap-9572	131	80	∫	∫	PROPN
ap-9572	131	81	1	1	NUM
ap-9572	131	82	0	0	NUM
ap-9572	131	83	∫	∫	PROPN
ap-9572	131	84	b	b	X
ap-9572	131	85	/	/	SYM
ap-9572	131	86	a	a	PRON
ap-9572	131	87	0	0	NUM
ap-9572	131	88	(	(	PUNCT
ap-9572	131	89	1	1	NUM
ap-9572	131	90	+	+	CCONJ
ap-9572	131	91	α1x2	α1x2	X
ap-9572	131	92	)	)	PUNCT
ap-9572	131	93	(	(	PUNCT
ap-9572	131	94	1	1	NUM
ap-9572	131	95	+	+	CCONJ
ap-9572	131	96	β1x2	β1x2	X
ap-9572	131	97	)	)	PUNCT
ap-9572	131	98	(	(	PUNCT
ap-9572	131	99	1	1	NUM
ap-9572	131	100	+	+	CCONJ
ap-9572	131	101	β2y	β2y	SYM
ap-9572	131	102	2	2	NUM
ap-9572	131	103	a2	a2	PROPN
ap-9572	131	104	b2	b2	NOUN
ap-9572	131	105	)	)	PUNCT
ap-9572	131	106	w̄	w̄	NOUN
ap-9572	131	107	2dxdy	2dxdy	X
ap-9572	131	108	.	.	PUNCT
ap-9572	131	109	(	(	PUNCT
ap-9572	131	110	23	23	NUM
ap-9572	131	111	)	)	PUNCT
ap-9572	131	112	here	here	ADV
ap-9572	131	113	:	:	PUNCT
ap-9572	131	114	n2	n2	NOUN
ap-9572	131	115	=	=	PUNCT
ap-9572	131	116	{	{	PUNCT
ap-9572	131	117	12ρ0	12ρ0	NUM
ap-9572	131	118	(	(	PUNCT
ap-9572	131	119	1	1	NUM
ap-9572	131	120	−	−	NOUN
ap-9572	131	121	ν2	ν2	PROPN
ap-9572	131	122	)	)	PUNCT
ap-9572	131	123	a2	a2	PROPN
ap-9572	131	124	e0h0	e0h0	VERB
ap-9572	131	125	2	2	NUM
ap-9572	131	126	}	}	PUNCT
ap-9572	131	127	.	.	PUNCT
ap-9572	132	1	(	(	PUNCT
ap-9572	132	2	24	24	NUM
ap-9572	132	3	)	)	PUNCT
ap-9572	132	4	the	the	DET
ap-9572	132	5	two	two	NUM
ap-9572	132	6	unknown	unknown	ADJ
ap-9572	132	7	parameters	parameter	NOUN
ap-9572	132	8	l1	l1	PROPN
ap-9572	132	9	and	and	CCONJ
ap-9572	132	10	l2	l2	NOUN
ap-9572	132	11	that	that	PRON
ap-9572	132	12	are	be	AUX
ap-9572	132	13	appearing	appear	VERB
ap-9572	132	14	by	by	ADP
ap-9572	132	15	substituting	substitute	VERB
ap-9572	132	16	w	w	NOUN
ap-9572	132	17	from	from	ADP
ap-9572	132	18	equation	equation	NOUN
ap-9572	132	19	(	(	PUNCT
ap-9572	132	20	16	16	NUM
ap-9572	132	21	)	)	PUNCT
ap-9572	132	22	into	into	ADP
ap-9572	132	23	equation	equation	NOUN
ap-9572	132	24	(	(	PUNCT
ap-9572	132	25	21	21	NUM
ap-9572	132	26	)	)	PUNCT
ap-9572	132	27	can	can	AUX
ap-9572	132	28	be	be	AUX
ap-9572	132	29	computed	compute	VERB
ap-9572	132	30	as:	as:	NUM
ap-9572	132	31	∂	∂	NUM
ap-9572	132	32	∂b1	∂b1	PROPN
ap-9572	132	33	(	(	PUNCT
ap-9572	132	34	s1	s1	PROPN
ap-9572	132	35	−	−	PROPN
ap-9572	132	36	n2k2p	n2k2p	NUM
ap-9572	132	37	1	1	NUM
ap-9572	132	38	)	)	PUNCT
ap-9572	132	39	=	=	SYM
ap-9572	132	40	0	0	NUM
ap-9572	132	41	,	,	PUNCT
ap-9572	132	42	and	and	CCONJ
ap-9572	132	43	∂	∂	NUM
ap-9572	132	44	∂b2	∂b2	NOUN
ap-9572	132	45	(	(	PUNCT
ap-9572	132	46	s1	s1	PROPN
ap-9572	132	47	−	−	PROPN
ap-9572	132	48	n2k2p	n2k2p	NUM
ap-9572	132	49	1	1	NUM
ap-9572	132	50	)	)	PUNCT
ap-9572	132	51	=	=	SYM
ap-9572	133	1	0	0	X
ap-9572	133	2	.	.	PUNCT
ap-9572	134	1	(	(	PUNCT
ap-9572	134	2	25	25	NUM
ap-9572	134	3	)	)	PUNCT
ap-9572	134	4	solution	solution	NOUN
ap-9572	134	5	of	of	ADP
ap-9572	134	6	equation	equation	NOUN
ap-9572	134	7	(	(	PUNCT
ap-9572	134	8	25	25	NUM
ap-9572	134	9	)	)	PUNCT
ap-9572	134	10	provides	provide	VERB
ap-9572	134	11	:	:	PUNCT
ap-9572	134	12	{	{	PUNCT
ap-9572	134	13	d11l1	d11l1	NOUN
ap-9572	134	14	+	+	CCONJ
ap-9572	134	15	d12l2	d12l2	PROPN
ap-9572	134	16	=	=	SYM
ap-9572	134	17	0	0	NUM
ap-9572	134	18	,	,	PUNCT
ap-9572	134	19	d21l1	d21l1	NOUN
ap-9572	134	20	+	+	CCONJ
ap-9572	134	21	d22l2	d22l2	X
ap-9572	134	22	=	=	SYM
ap-9572	134	23	0	0	NUM
ap-9572	134	24	,	,	PUNCT
ap-9572	134	25	(	(	PUNCT
ap-9572	134	26	26	26	NUM
ap-9572	134	27	)	)	PUNCT
ap-9572	134	28	300	300	NUM
ap-9572	134	29	vol	vol	NOUN
ap-9572	134	30	.	.	PUNCT
ap-9572	135	1	64	64	NUM
ap-9572	135	2	no	no	NOUN
ap-9572	135	3	.	.	PUNCT
ap-9572	136	1	4/2024	4/2024	NUM
ap-9572	136	2	non	non	ADJ
ap-9572	136	3	-	-	ADJ
ap-9572	136	4	homogeneity	homogeneity	ADJ
ap-9572	136	5	effect	effect	NOUN
ap-9572	136	6	on	on	ADP
ap-9572	136	7	the	the	DET
ap-9572	136	8	vibration	vibration	NOUN
ap-9572	136	9	of	of	ADP
ap-9572	136	10	.	.	PUNCT
ap-9572	136	11	.	.	PUNCT
ap-9572	136	12	.	.	PUNCT
ap-9572	137	1	s.n	s.n	PROPN
ap-9572	137	2	.	.	PROPN
ap-9572	137	3	parameters	parameter	NOUN
ap-9572	137	4	values	value	VERB
ap-9572	137	5	1	1	NUM
ap-9572	137	6	.	.	PUNCT
ap-9572	137	7	young	young	ADJ
ap-9572	137	8	modulus	modulus	NOUN
ap-9572	137	9	of	of	ADP
ap-9572	137	10	the	the	DET
ap-9572	137	11	elasticity	elasticity	NOUN
ap-9572	137	12	(	(	PUNCT
ap-9572	137	13	n	n	DET
ap-9572	137	14	m−2	m−2	NUM
ap-9572	137	15	)	)	PUNCT
ap-9572	137	16	,	,	PUNCT
ap-9572	138	1	e	e	PROPN
ap-9572	138	2	7.08	7.08	NUM
ap-9572	138	3	×	×	NOUN
ap-9572	138	4	1010	1010	NUM
ap-9572	138	5	2	2	NUM
ap-9572	138	6	.	.	PUNCT
ap-9572	138	7	shear	shear	NOUN
ap-9572	138	8	modulus	modulus	NOUN
ap-9572	138	9	(	(	PUNCT
ap-9572	138	10	n	n	PRON
ap-9572	138	11	m−2	m−2	NUM
ap-9572	138	12	)	)	PUNCT
ap-9572	138	13	,	,	PUNCT
ap-9572	138	14	g	g	PROPN
ap-9572	138	15	2.682	2.682	NUM
ap-9572	138	16	×	×	NOUN
ap-9572	138	17	1010	1010	NUM
ap-9572	138	18	3	3	NUM
ap-9572	138	19	.	.	PUNCT
ap-9572	138	20	visco	visco	ADJ
ap-9572	138	21	-	-	ADJ
ap-9572	138	22	elastic	elastic	ADJ
ap-9572	138	23	constant	constant	ADJ
ap-9572	138	24	(	(	PUNCT
ap-9572	138	25	ns	ns	NUM
ap-9572	138	26	m−2	m−2	NOUN
ap-9572	138	27	)	)	PUNCT
ap-9572	138	28	,	,	PUNCT
ap-9572	138	29	η	η	PROPN
ap-9572	138	30	1.4612	1.4612	NUM
ap-9572	138	31	×	×	NOUN
ap-9572	138	32	106	106	NUM
ap-9572	138	33	4	4	NUM
ap-9572	138	34	.	.	PUNCT
ap-9572	139	1	density	density	NOUN
ap-9572	139	2	(	(	PUNCT
ap-9572	139	3	kg	kg	PROPN
ap-9572	139	4	m−3	m−3	PROPN
ap-9572	139	5	)	)	PUNCT
ap-9572	139	6	,	,	PUNCT
ap-9572	139	7	ρ	ρ	PROPN
ap-9572	139	8	2.80	2.80	NUM
ap-9572	139	9	×	×	NOUN
ap-9572	139	10	103	103	NUM
ap-9572	139	11	5	5	NUM
ap-9572	139	12	.	.	PUNCT
ap-9572	140	1	poisson	poisson	PROPN
ap-9572	140	2	’s	’s	PART
ap-9572	140	3	ratio	ratio	NOUN
ap-9572	140	4	,	,	PUNCT
ap-9572	140	5	ν	ν	ADP
ap-9572	140	6	0.345	0.345	NUM
ap-9572	140	7	table	table	NOUN
ap-9572	140	8	1	1	NUM
ap-9572	140	9	.	.	PUNCT
ap-9572	140	10	duralium	duralium	NOUN
ap-9572	140	11	material	material	NOUN
ap-9572	140	12	(	(	PUNCT
ap-9572	140	13	alloy	alloy	NOUN
ap-9572	140	14	of	of	ADP
ap-9572	140	15	aluminum	aluminum	NOUN
ap-9572	140	16	,	,	PUNCT
ap-9572	140	17	copper	copper	NOUN
ap-9572	140	18	,	,	PUNCT
ap-9572	140	19	magnesium	magnesium	NOUN
ap-9572	140	20	,	,	PUNCT
ap-9572	140	21	and	and	CCONJ
ap-9572	140	22	manganese	manganese	ADJ
ap-9572	140	23	)	)	PUNCT
ap-9572	140	24	parameters	parameter	NOUN
ap-9572	140	25	that	that	PRON
ap-9572	140	26	are	be	AUX
ap-9572	140	27	used	use	VERB
ap-9572	140	28	for	for	ADP
ap-9572	140	29	the	the	DET
ap-9572	140	30	numerical	numerical	ADJ
ap-9572	140	31	computation	computation	NOUN
ap-9572	140	32	[	[	X
ap-9572	140	33	16	16	NUM
ap-9572	140	34	]	]	PUNCT
ap-9572	140	35	.	.	PUNCT
ap-9572	141	1	where	where	SCONJ
ap-9572	141	2	d11	d11	PROPN
ap-9572	141	3	,	,	PUNCT
ap-9572	141	4	d12	d12	PROPN
ap-9572	141	5	,	,	PUNCT
ap-9572	141	6	d21	d21	PROPN
ap-9572	141	7	,	,	PUNCT
ap-9572	141	8	d22	d22	NOUN
ap-9572	141	9	involve	involve	VERB
ap-9572	141	10	the	the	DET
ap-9572	141	11	frequency	frequency	NOUN
ap-9572	141	12	parameter	parameter	NOUN
ap-9572	141	13	and	and	CCONJ
ap-9572	141	14	the	the	DET
ap-9572	141	15	parametric	parametric	ADJ
ap-9572	141	16	constants	constant	NOUN
ap-9572	141	17	.	.	PUNCT
ap-9572	142	1	the	the	DET
ap-9572	142	2	non	non	ADJ
ap-9572	142	3	-	-	ADJ
ap-9572	142	4	trivial	trivial	ADJ
ap-9572	142	5	solution	solution	NOUN
ap-9572	142	6	of	of	ADP
ap-9572	142	7	the	the	DET
ap-9572	142	8	equation	equation	NOUN
ap-9572	142	9	(	(	PUNCT
ap-9572	142	10	26	26	NUM
ap-9572	142	11	)	)	PUNCT
ap-9572	142	12	is	be	AUX
ap-9572	142	13	obtained	obtain	VERB
ap-9572	142	14	by	by	ADP
ap-9572	142	15	:	:	PUNCT
ap-9572	142	16	∣∣∣∣d11	∣∣∣∣d11	PROPN
ap-9572	142	17	d12	d12	PROPN
ap-9572	142	18	d21	d21	PROPN
ap-9572	142	19	d22	d22	PROPN
ap-9572	142	20	∣∣∣∣	∣∣∣∣	PROPN
ap-9572	142	21	=	=	NOUN
ap-9572	143	1	0	0	PROPN
ap-9572	143	2	.	.	PUNCT
ap-9572	144	1	(	(	PUNCT
ap-9572	144	2	27	27	NUM
ap-9572	144	3	)	)	PUNCT
ap-9572	144	4	equation	equation	NOUN
ap-9572	144	5	(	(	PUNCT
ap-9572	144	6	27	27	NUM
ap-9572	144	7	)	)	PUNCT
ap-9572	144	8	is	be	AUX
ap-9572	144	9	a	a	DET
ap-9572	144	10	quadratic	quadratic	ADJ
ap-9572	144	11	equation	equation	NOUN
ap-9572	144	12	in	in	ADP
ap-9572	144	13	k2	k2	NOUN
ap-9572	144	14	and	and	CCONJ
ap-9572	144	15	it	it	PRON
ap-9572	144	16	is	be	AUX
ap-9572	144	17	known	know	VERB
ap-9572	144	18	as	as	ADP
ap-9572	144	19	the	the	DET
ap-9572	144	20	frequency	frequency	NOUN
ap-9572	144	21	equation	equation	NOUN
ap-9572	144	22	.	.	PUNCT
ap-9572	145	1	solving	solve	VERB
ap-9572	145	2	equation	equation	NOUN
ap-9572	145	3	(	(	PUNCT
ap-9572	145	4	27	27	NUM
ap-9572	145	5	)	)	PUNCT
ap-9572	145	6	gives	give	VERB
ap-9572	145	7	the	the	DET
ap-9572	145	8	two	two	NUM
ap-9572	145	9	values	value	NOUN
ap-9572	145	10	of	of	ADP
ap-9572	145	11	k2	k2	NOUN
ap-9572	145	12	.	.	PUNCT
ap-9572	146	1	now	now	ADV
ap-9572	146	2	,	,	PUNCT
ap-9572	146	3	if	if	SCONJ
ap-9572	146	4	we	we	PRON
ap-9572	146	5	choose	choose	VERB
ap-9572	146	6	l1	l1	PROPN
ap-9572	146	7	=	=	SYM
ap-9572	146	8	1	1	NUM
ap-9572	146	9	and	and	CCONJ
ap-9572	146	10	substitute	substitute	VERB
ap-9572	146	11	it	it	PRON
ap-9572	146	12	into	into	ADP
ap-9572	146	13	equation	equation	NOUN
ap-9572	146	14	(	(	PUNCT
ap-9572	146	15	26	26	NUM
ap-9572	146	16	)	)	PUNCT
ap-9572	146	17	,	,	PUNCT
ap-9572	146	18	we	we	PRON
ap-9572	146	19	have	have	VERB
ap-9572	146	20	l2	l2	NOUN
ap-9572	146	21	=	=	SYM
ap-9572	146	22	−	−	PROPN
ap-9572	147	1	(	(	PUNCT
ap-9572	147	2	d11	d11	PROPN
ap-9572	147	3	d12	d12	PROPN
ap-9572	147	4	)	)	PUNCT
ap-9572	147	5	.	.	PUNCT
ap-9572	148	1	using	use	VERB
ap-9572	148	2	the	the	DET
ap-9572	148	3	above	above	ADJ
ap-9572	148	4	values	value	NOUN
ap-9572	148	5	for	for	ADP
ap-9572	148	6	l1	l1	PROPN
ap-9572	148	7	,	,	PUNCT
ap-9572	148	8	and	and	CCONJ
ap-9572	148	9	l2	l2	NOUN
ap-9572	148	10	in	in	ADP
ap-9572	148	11	equation	equation	NOUN
ap-9572	148	12	(	(	PUNCT
ap-9572	148	13	18	18	NUM
ap-9572	148	14	)	)	PUNCT
ap-9572	148	15	suggests	suggest	VERB
ap-9572	148	16	that	that	SCONJ
ap-9572	148	17	:	:	PUNCT
ap-9572	149	1	w	w	X
ap-9572	149	2	=	=	PUNCT
ap-9572	149	3	[	[	PUNCT
ap-9572	149	4	y	y	PROPN
ap-9572	149	5	(	(	PUNCT
ap-9572	149	6	a	a	DET
ap-9572	149	7	b	b	NOUN
ap-9572	149	8	)	)	PUNCT
ap-9572	149	9	x	x	X
ap-9572	149	10	(	(	PUNCT
ap-9572	149	11	1	1	NUM
ap-9572	149	12	−	−	PROPN
ap-9572	149	13	y	y	PROPN
ap-9572	149	14	(	(	PUNCT
ap-9572	149	15	a	a	DET
ap-9572	149	16	b	b	NOUN
ap-9572	149	17	)	)	PUNCT
ap-9572	149	18	)	)	PUNCT
ap-9572	149	19	(	(	PUNCT
ap-9572	149	20	1	1	NUM
ap-9572	149	21	−	−	NOUN
ap-9572	149	22	x	x	NOUN
ap-9572	149	23	)	)	PUNCT
ap-9572	149	24	]	]	PUNCT
ap-9572	149	25	2	2	NUM
ap-9572	149	26	[	[	PUNCT
ap-9572	149	27	1	1	NUM
ap-9572	149	28	+	+	CCONJ
ap-9572	149	29	(	(	PUNCT
ap-9572	149	30	−d11	−d11	X
ap-9572	149	31	d12	d12	NOUN
ap-9572	149	32	)	)	PUNCT
ap-9572	149	33	y	y	PROPN
ap-9572	149	34	(	(	PUNCT
ap-9572	149	35	a	a	DET
ap-9572	149	36	b	b	NOUN
ap-9572	149	37	)	)	PUNCT
ap-9572	149	38	x	x	X
ap-9572	149	39	(	(	PUNCT
ap-9572	149	40	1	1	NUM
ap-9572	149	41	−	−	PROPN
ap-9572	149	42	y	y	PROPN
ap-9572	149	43	(	(	PUNCT
ap-9572	149	44	a	a	DET
ap-9572	149	45	b	b	NOUN
ap-9572	149	46	)	)	PUNCT
ap-9572	149	47	)	)	PUNCT
ap-9572	149	48	(	(	PUNCT
ap-9572	149	49	1	1	NUM
ap-9572	149	50	−	−	NOUN
ap-9572	149	51	x	x	NOUN
ap-9572	149	52	)	)	PUNCT
ap-9572	149	53	]	]	PUNCT
ap-9572	149	54	.	.	PUNCT
ap-9572	150	1	(	(	PUNCT
ap-9572	150	2	28	28	NUM
ap-9572	150	3	)	)	PUNCT
ap-9572	150	4	4	4	NUM
ap-9572	150	5	.	.	PUNCT
ap-9572	150	6	differential	differential	ADJ
ap-9572	150	7	equation	equation	NOUN
ap-9572	150	8	of	of	ADP
ap-9572	150	9	the	the	DET
ap-9572	150	10	time	time	NOUN
ap-9572	150	11	function	function	NOUN
ap-9572	150	12	with	with	ADP
ap-9572	150	13	its	its	PRON
ap-9572	150	14	solution	solution	NOUN
ap-9572	150	15	the	the	DET
ap-9572	150	16	author	author	NOUN
ap-9572	150	17	has	have	AUX
ap-9572	150	18	derived	derive	VERB
ap-9572	150	19	the	the	DET
ap-9572	150	20	differential	differential	ADJ
ap-9572	150	21	equation	equation	NOUN
ap-9572	150	22	of	of	ADP
ap-9572	150	23	the	the	DET
ap-9572	150	24	time	time	NOUN
ap-9572	150	25	function	function	NOUN
ap-9572	150	26	and	and	CCONJ
ap-9572	150	27	then	then	ADV
ap-9572	150	28	he	he	PRON
ap-9572	150	29	has	have	AUX
ap-9572	150	30	given	give	VERB
ap-9572	150	31	its	its	PRON
ap-9572	150	32	solution	solution	NOUN
ap-9572	150	33	in	in	ADP
ap-9572	150	34	this	this	DET
ap-9572	150	35	section	section	NOUN
ap-9572	150	36	.	.	PUNCT
ap-9572	151	1	the	the	DET
ap-9572	151	2	unique	unique	ADJ
ap-9572	151	3	rheological	rheological	ADJ
ap-9572	151	4	operator	operator	NOUN
ap-9572	151	5	d̃	d̃	PROPN
ap-9572	151	6	for	for	ADP
ap-9572	151	7	the	the	DET
ap-9572	151	8	consideration	consideration	NOUN
ap-9572	151	9	of	of	ADP
ap-9572	151	10	linear	linear	PROPN
ap-9572	151	11	visco	visco	ADJ
ap-9572	151	12	-	-	ADJ
ap-9572	151	13	elastic	elastic	ADJ
ap-9572	151	14	model	model	NOUN
ap-9572	151	15	(	(	PUNCT
ap-9572	151	16	model	model	NOUN
ap-9572	151	17	of	of	ADP
ap-9572	151	18	the	the	DET
ap-9572	151	19	kelvin	kelvin	PROPN
ap-9572	151	20	)	)	PUNCT
ap-9572	151	21	is	be	AUX
ap-9572	151	22	given	give	VERB
ap-9572	151	23	as	as	ADP
ap-9572	151	24	[	[	X
ap-9572	151	25	13	13	NUM
ap-9572	151	26	]	]	SYM
ap-9572	151	27	:	:	PUNCT
ap-9572	151	28	d̃	d̃	PROPN
ap-9572	151	29	≡	≡	PROPN
ap-9572	151	30	[	[	PUNCT
ap-9572	151	31	1	1	NUM
ap-9572	151	32	+	+	CCONJ
ap-9572	151	33	(	(	PUNCT
ap-9572	151	34	η	η	PROPN
ap-9572	151	35	g	g	PROPN
ap-9572	151	36	)	)	PUNCT
ap-9572	151	37	(	(	PUNCT
ap-9572	151	38	d	d	X
ap-9572	151	39	dt	dt	NOUN
ap-9572	151	40	)	)	PUNCT
ap-9572	151	41	]	]	PUNCT
ap-9572	151	42	,	,	PUNCT
ap-9572	151	43	(	(	PUNCT
ap-9572	151	44	29	29	NUM
ap-9572	151	45	)	)	PUNCT
ap-9572	151	46	where	where	SCONJ
ap-9572	151	47	η	η	PROPN
ap-9572	151	48	is	be	AUX
ap-9572	151	49	visco	visco	ADJ
ap-9572	151	50	-	-	ADJ
ap-9572	151	51	elastic	elastic	ADJ
ap-9572	151	52	constant	constant	NOUN
ap-9572	151	53	,	,	PUNCT
ap-9572	151	54	g	g	PROPN
ap-9572	151	55	is	be	AUX
ap-9572	151	56	shear	shear	ADJ
ap-9572	151	57	modulus	modulus	NOUN
ap-9572	151	58	.	.	PUNCT
ap-9572	152	1	using	use	VERB
ap-9572	152	2	equation	equation	NOUN
ap-9572	152	3	(	(	PUNCT
ap-9572	152	4	29	29	NUM
ap-9572	152	5	)	)	PUNCT
ap-9572	152	6	in	in	ADP
ap-9572	152	7	equation	equation	NOUN
ap-9572	152	8	(	(	PUNCT
ap-9572	152	9	2	2	X
ap-9572	152	10	)	)	PUNCT
ap-9572	152	11	gives	give	VERB
ap-9572	152	12	:	:	PUNCT
ap-9572	152	13	ẗ	ẗ	PUNCT
ap-9572	153	1	+	+	NUM
ap-9572	153	2	k2	k2	PROPN
ap-9572	153	3	(	(	PUNCT
ap-9572	153	4	η	η	PROPN
ap-9572	153	5	g	g	PROPN
ap-9572	153	6	)	)	PUNCT
ap-9572	153	7	ṫ	ṫ	PROPN
ap-9572	154	1	+	+	CCONJ
ap-9572	154	2	k2	k2	PROPN
ap-9572	154	3	t	t	NOUN
ap-9572	154	4	=	=	SYM
ap-9572	154	5	0	0	PROPN
ap-9572	154	6	.	.	PUNCT
ap-9572	155	1	(	(	PUNCT
ap-9572	155	2	30	30	NUM
ap-9572	155	3	)	)	PUNCT
ap-9572	155	4	the	the	DET
ap-9572	155	5	solution	solution	NOUN
ap-9572	155	6	of	of	ADP
ap-9572	155	7	the	the	DET
ap-9572	155	8	equation	equation	NOUN
ap-9572	155	9	(	(	PUNCT
ap-9572	155	10	30	30	NUM
ap-9572	155	11	)	)	PUNCT
ap-9572	155	12	will	will	AUX
ap-9572	155	13	be	be	AUX
ap-9572	155	14	of	of	ADP
ap-9572	155	15	the	the	DET
ap-9572	155	16	form	form	NOUN
ap-9572	155	17	:	:	PUNCT
ap-9572	155	18	t	t	PROPN
ap-9572	155	19	(	(	PUNCT
ap-9572	155	20	t	t	PROPN
ap-9572	155	21	)	)	PUNCT
ap-9572	155	22	=	=	PUNCT
ap-9572	156	1	ea1t(a	ea1t(a	PROPN
ap-9572	156	2	cos	cos	PROPN
ap-9572	156	3	b1	b1	PROPN
ap-9572	156	4	t	t	PROPN
ap-9572	156	5	+	+	CCONJ
ap-9572	156	6	b	b	PROPN
ap-9572	156	7	sin	sin	NOUN
ap-9572	156	8	b1	b1	PROPN
ap-9572	156	9	t	t	PROPN
ap-9572	156	10	)	)	PUNCT
ap-9572	156	11	,	,	PUNCT
ap-9572	156	12	(	(	PUNCT
ap-9572	156	13	31	31	NUM
ap-9572	156	14	)	)	PUNCT
ap-9572	157	1	where	where	SCONJ
ap-9572	157	2	:	:	PUNCT
ap-9572	157	3			NUM
ap-9572	157	4	a1	a1	NOUN
ap-9572	157	5	=	=	SYM
ap-9572	157	6	−k2	−k2	PROPN
ap-9572	157	7	2	2	NUM
ap-9572	157	8	(	(	PUNCT
ap-9572	157	9	η	η	NOUN
ap-9572	157	10	g	g	PROPN
ap-9572	157	11	)	)	PUNCT
ap-9572	157	12	,	,	PUNCT
ap-9572	157	13	b1	b1	NOUN
ap-9572	157	14	=	=	SYM
ap-9572	157	15	k	k	NOUN
ap-9572	157	16	√	√	ADP
ap-9572	157	17	1	1	NUM
ap-9572	157	18	−	−	PROPN
ap-9572	157	19	(	(	PUNCT
ap-9572	157	20	ρη	ρη	NOUN
ap-9572	157	21	2	2	NUM
ap-9572	157	22	g	g	NOUN
ap-9572	157	23	)	)	PUNCT
ap-9572	157	24	2	2	NUM
ap-9572	157	25	,	,	PUNCT
ap-9572	157	26	a	a	PRON
ap-9572	157	27	,	,	PUNCT
ap-9572	157	28	b	b	NOUN
ap-9572	157	29	=	=	NOUN
ap-9572	157	30	constants	constant	NOUN
ap-9572	157	31	.	.	PUNCT
ap-9572	158	1	(	(	PUNCT
ap-9572	158	2	32	32	NUM
ap-9572	158	3	)	)	PUNCT
ap-9572	158	4	consider	consider	VERB
ap-9572	158	5	the	the	DET
ap-9572	158	6	following	follow	VERB
ap-9572	158	7	initial	initial	ADJ
ap-9572	158	8	conditions	condition	NOUN
ap-9572	158	9	for	for	ADP
ap-9572	158	10	determining	determine	VERB
ap-9572	158	11	the	the	DET
ap-9572	158	12	values	value	NOUN
ap-9572	158	13	of	of	ADP
ap-9572	158	14	a	a	PRON
ap-9572	158	15	and	and	CCONJ
ap-9572	158	16	b	b	NOUN
ap-9572	158	17	:	:	PUNCT
ap-9572	158	18	at	at	ADP
ap-9572	158	19	t	t	NOUN
ap-9572	158	20	=	=	SYM
ap-9572	158	21	0	0	NUM
ap-9572	158	22	,	,	PUNCT
ap-9572	158	23	t	t	NOUN
ap-9572	158	24	=	=	SYM
ap-9572	158	25	1	1	NUM
ap-9572	158	26	and	and	CCONJ
ap-9572	158	27	ṫ	ṫ	PROPN
ap-9572	158	28	=	=	SYM
ap-9572	158	29	0	0	PROPN
ap-9572	158	30	.	.	PUNCT
ap-9572	159	1	(	(	PUNCT
ap-9572	159	2	33	33	NUM
ap-9572	159	3	)	)	PUNCT
ap-9572	159	4	using	use	VERB
ap-9572	159	5	equation	equation	NOUN
ap-9572	159	6	(	(	PUNCT
ap-9572	159	7	33	33	NUM
ap-9572	159	8	)	)	PUNCT
ap-9572	159	9	in	in	ADP
ap-9572	159	10	equation	equation	NOUN
ap-9572	159	11	(	(	PUNCT
ap-9572	159	12	31	31	NUM
ap-9572	159	13	)	)	PUNCT
ap-9572	159	14	provides:a	provides:a	NOUN
ap-9572	159	15	=	=	SYM
ap-9572	159	16	1	1	NUM
ap-9572	159	17	,	,	PUNCT
ap-9572	159	18	b	b	X
ap-9572	159	19	=	=	SYM
ap-9572	159	20	−a1	−a1	PROPN
ap-9572	159	21	b1	b1	NOUN
ap-9572	159	22	.	.	PUNCT
ap-9572	160	1	(	(	PUNCT
ap-9572	160	2	34	34	NUM
ap-9572	160	3	)	)	PUNCT
ap-9572	160	4	after	after	ADP
ap-9572	160	5	substituting	substitute	VERB
ap-9572	160	6	the	the	DET
ap-9572	160	7	values	value	NOUN
ap-9572	160	8	of	of	ADP
ap-9572	160	9	a	a	DET
ap-9572	160	10	,	,	PUNCT
ap-9572	160	11	b	b	NOUN
ap-9572	160	12	into	into	ADP
ap-9572	160	13	equation	equation	NOUN
ap-9572	160	14	(	(	PUNCT
ap-9572	160	15	31	31	NUM
ap-9572	160	16	)	)	PUNCT
ap-9572	160	17	,	,	PUNCT
ap-9572	160	18	one	one	PRON
ap-9572	160	19	obtains	obtain	VERB
ap-9572	160	20	:	:	PUNCT
ap-9572	160	21	t	t	PROPN
ap-9572	160	22	(	(	PUNCT
ap-9572	160	23	t	t	PROPN
ap-9572	160	24	)	)	PUNCT
ap-9572	160	25	=	=	PUNCT
ap-9572	161	1	ea1	ea1	PROPN
ap-9572	161	2	t	t	PROPN
ap-9572	161	3	(	(	PUNCT
ap-9572	161	4	cos	cos	PROPN
ap-9572	161	5	b1	b1	PROPN
ap-9572	161	6	t	t	PROPN
ap-9572	161	7	−	−	PROPN
ap-9572	161	8	a1	a1	NOUN
ap-9572	161	9	b1	b1	NOUN
ap-9572	161	10	sin	sin	PROPN
ap-9572	161	11	b1	b1	PROPN
ap-9572	161	12	t	t	PROPN
ap-9572	161	13	)	)	PUNCT
ap-9572	161	14	.	.	PUNCT
ap-9572	162	1	(	(	PUNCT
ap-9572	162	2	35	35	NUM
ap-9572	162	3	)	)	PUNCT
ap-9572	162	4	thus	thus	ADV
ap-9572	162	5	,	,	PUNCT
ap-9572	162	6	w(x	w(x	PROPN
ap-9572	162	7	,	,	PUNCT
ap-9572	162	8	y	y	PROPN
ap-9572	162	9	,	,	PUNCT
ap-9572	162	10	t	t	PROPN
ap-9572	162	11	)	)	PUNCT
ap-9572	162	12	can	can	AUX
ap-9572	162	13	be	be	AUX
ap-9572	162	14	expressed	express	VERB
ap-9572	162	15	using	use	VERB
ap-9572	162	16	equations	equation	NOUN
ap-9572	162	17	(	(	PUNCT
ap-9572	162	18	28	28	NUM
ap-9572	162	19	)	)	PUNCT
ap-9572	162	20	and	and	CCONJ
ap-9572	162	21	(	(	PUNCT
ap-9572	162	22	35	35	NUM
ap-9572	162	23	)	)	PUNCT
ap-9572	162	24	in	in	ADP
ap-9572	162	25	equation	equation	NOUN
ap-9572	162	26	(	(	PUNCT
ap-9572	162	27	9	9	NUM
ap-9572	162	28	)	)	PUNCT
ap-9572	162	29	as	as	ADP
ap-9572	162	30	:	:	PUNCT
ap-9572	162	31	w	w	X
ap-9572	162	32	=	=	SYM
ap-9572	162	33	{	{	PUNCT
ap-9572	162	34	y	y	PROPN
ap-9572	162	35	(	(	PUNCT
ap-9572	162	36	a	a	DET
ap-9572	162	37	b	b	NOUN
ap-9572	162	38	)	)	PUNCT
ap-9572	162	39	x	x	X
ap-9572	162	40	(	(	PUNCT
ap-9572	162	41	1	1	NUM
ap-9572	162	42	−	−	PROPN
ap-9572	162	43	y	y	PROPN
ap-9572	162	44	(	(	PUNCT
ap-9572	162	45	a	a	DET
ap-9572	162	46	b	b	NOUN
ap-9572	162	47	)	)	PUNCT
ap-9572	162	48	)	)	PUNCT
ap-9572	162	49	(	(	PUNCT
ap-9572	162	50	1	1	NUM
ap-9572	162	51	−	−	NOUN
ap-9572	162	52	x	x	NOUN
ap-9572	162	53	)	)	PUNCT
ap-9572	162	54	}	}	PUNCT
ap-9572	162	55	2	2	NUM
ap-9572	162	56	{	{	PUNCT
ap-9572	162	57	1	1	NUM
ap-9572	162	58	−	−	PROPN
ap-9572	162	59	(	(	PUNCT
ap-9572	162	60	b11	b11	PROPN
ap-9572	162	61	b12	b12	NOUN
ap-9572	162	62	)	)	PUNCT
ap-9572	162	63	y	y	PROPN
ap-9572	162	64	(	(	PUNCT
ap-9572	162	65	a	a	DET
ap-9572	162	66	b	b	NOUN
ap-9572	162	67	)	)	PUNCT
ap-9572	162	68	x	x	X
ap-9572	162	69	(	(	PUNCT
ap-9572	162	70	1	1	NUM
ap-9572	162	71	−	−	PROPN
ap-9572	162	72	y	y	PROPN
ap-9572	162	73	(	(	PUNCT
ap-9572	162	74	a	a	DET
ap-9572	162	75	b	b	NOUN
ap-9572	162	76	)	)	PUNCT
ap-9572	162	77	)	)	PUNCT
ap-9572	162	78	(	(	PUNCT
ap-9572	162	79	1	1	NUM
ap-9572	162	80	−	−	NOUN
ap-9572	162	81	x	x	NOUN
ap-9572	162	82	)	)	PUNCT
ap-9572	162	83	}	}	PUNCT
ap-9572	162	84	{	{	PUNCT
ap-9572	162	85	ea1	ea1	NOUN
ap-9572	162	86	t	t	PROPN
ap-9572	162	87	(	(	PUNCT
ap-9572	162	88	cosb1	cosb1	PROPN
ap-9572	162	89	t	t	PROPN
ap-9572	162	90	−	−	PROPN
ap-9572	163	1	(	(	PUNCT
ap-9572	163	2	a1	a1	NOUN
ap-9572	163	3	b1	b1	NOUN
ap-9572	163	4	)	)	PUNCT
ap-9572	163	5	sinb1	sinb1	PROPN
ap-9572	163	6	t	t	PROPN
ap-9572	163	7	)	)	PUNCT
ap-9572	163	8	}	}	PUNCT
ap-9572	163	9	.	.	PUNCT
ap-9572	164	1	(	(	PUNCT
ap-9572	164	2	36	36	NUM
ap-9572	164	3	)	)	PUNCT
ap-9572	164	4	for	for	ADP
ap-9572	164	5	the	the	DET
ap-9572	164	6	vibration	vibration	NOUN
ap-9572	164	7	of	of	ADP
ap-9572	164	8	the	the	DET
ap-9572	164	9	plate	plate	NOUN
ap-9572	164	10	,	,	PUNCT
ap-9572	164	11	the	the	DET
ap-9572	164	12	relation	relation	NOUN
ap-9572	164	13	of	of	ADP
ap-9572	164	14	the	the	DET
ap-9572	164	15	time	time	NOUN
ap-9572	164	16	period	period	NOUN
ap-9572	164	17	(	(	PUNCT
ap-9572	164	18	tp	tp	NOUN
ap-9572	164	19	)	)	PUNCT
ap-9572	164	20	with	with	ADP
ap-9572	164	21	the	the	DET
ap-9572	164	22	frequency	frequency	NOUN
ap-9572	164	23	(	(	PUNCT
ap-9572	164	24	k	k	X
ap-9572	164	25	)	)	PUNCT
ap-9572	164	26	is	be	AUX
ap-9572	164	27	expressed	express	VERB
ap-9572	164	28	by	by	ADP
ap-9572	164	29	[	[	PUNCT
ap-9572	164	30	13	13	NUM
ap-9572	164	31	]	]	SYM
ap-9572	164	32	:	:	PUNCT
ap-9572	164	33	tp	tp	X
ap-9572	164	34	=	=	PUNCT
ap-9572	164	35	2π	2π	PROPN
ap-9572	164	36	k	k	NOUN
ap-9572	164	37	,	,	PUNCT
ap-9572	164	38	(	(	PUNCT
ap-9572	164	39	37	37	NUM
ap-9572	164	40	)	)	PUNCT
ap-9572	164	41	where	where	SCONJ
ap-9572	164	42	the	the	DET
ap-9572	164	43	frequency	frequency	NOUN
ap-9572	164	44	k	k	NOUN
ap-9572	164	45	is	be	AUX
ap-9572	164	46	easily	easily	ADV
ap-9572	164	47	determined	determine	VERB
ap-9572	164	48	using	use	VERB
ap-9572	164	49	equation	equation	NOUN
ap-9572	164	50	(	(	PUNCT
ap-9572	164	51	27	27	NUM
ap-9572	164	52	)	)	PUNCT
ap-9572	164	53	.	.	PUNCT
ap-9572	165	1	5	5	X
ap-9572	165	2	.	.	NOUN
ap-9572	165	3	results	result	NOUN
ap-9572	165	4	and	and	CCONJ
ap-9572	165	5	discussions	discussion	NOUN
ap-9572	165	6	in	in	ADP
ap-9572	165	7	the	the	DET
ap-9572	165	8	present	present	ADJ
ap-9572	165	9	work	work	NOUN
ap-9572	165	10	,	,	PUNCT
ap-9572	165	11	the	the	DET
ap-9572	165	12	time	time	NOUN
ap-9572	165	13	period	period	NOUN
ap-9572	165	14	(	(	PUNCT
ap-9572	165	15	tp	tp	NOUN
ap-9572	165	16	)	)	PUNCT
ap-9572	165	17	and	and	CCONJ
ap-9572	165	18	the	the	DET
ap-9572	165	19	deflection	deflection	NOUN
ap-9572	165	20	(	(	PUNCT
ap-9572	165	21	w	w	NOUN
ap-9572	165	22	)	)	PUNCT
ap-9572	165	23	are	be	AUX
ap-9572	165	24	determined	determine	VERB
ap-9572	165	25	for	for	ADP
ap-9572	165	26	various	various	ADJ
ap-9572	165	27	combinations	combination	NOUN
ap-9572	165	28	of	of	ADP
ap-9572	165	29	the	the	DET
ap-9572	165	30	values	value	NOUN
ap-9572	165	31	of	of	ADP
ap-9572	165	32	(	(	PUNCT
ap-9572	165	33	α	α	NOUN
ap-9572	165	34	)	)	PUNCT
ap-9572	165	35	,	,	PUNCT
ap-9572	165	36	(	(	PUNCT
ap-9572	165	37	a	a	DET
ap-9572	165	38	b	b	NOUN
ap-9572	165	39	)	)	PUNCT
ap-9572	165	40	,	,	PUNCT
ap-9572	165	41	(	(	PUNCT
ap-9572	165	42	β1	β1	NOUN
ap-9572	165	43	,	,	PUNCT
ap-9572	165	44	β2	β2	NOUN
ap-9572	165	45	)	)	PUNCT
ap-9572	165	46	,	,	PUNCT
ap-9572	165	47	and	and	CCONJ
ap-9572	165	48	(	(	PUNCT
ap-9572	165	49	α1	α1	PROPN
ap-9572	165	50	)	)	PUNCT
ap-9572	165	51	for	for	ADP
ap-9572	165	52	the	the	DET
ap-9572	165	53	first	first	ADJ
ap-9572	165	54	two	two	NUM
ap-9572	165	55	modes	mode	NOUN
ap-9572	165	56	of	of	ADP
ap-9572	165	57	vibration	vibration	NOUN
ap-9572	165	58	and	and	CCONJ
ap-9572	165	59	are	be	AUX
ap-9572	165	60	given	give	VERB
ap-9572	165	61	in	in	ADP
ap-9572	165	62	tables	table	NOUN
ap-9572	165	63	2–12	2–12	ADJ
ap-9572	165	64	.	.	PUNCT
ap-9572	166	1	the	the	DET
ap-9572	166	2	quadratic	quadratic	ADJ
ap-9572	166	3	variation	variation	NOUN
ap-9572	166	4	has	have	AUX
ap-9572	166	5	been	be	AUX
ap-9572	166	6	considered	consider	VERB
ap-9572	166	7	in	in	ADP
ap-9572	166	8	the	the	DET
ap-9572	166	9	material	material	NOUN
ap-9572	166	10	density	density	NOUN
ap-9572	166	11	of	of	ADP
ap-9572	166	12	the	the	DET
ap-9572	166	13	plate	plate	NOUN
ap-9572	166	14	only	only	ADV
ap-9572	166	15	along	along	ADP
ap-9572	166	16	the	the	DET
ap-9572	166	17	x	x	NOUN
ap-9572	166	18	-	-	NOUN
ap-9572	166	19	axis	axis	ADJ
ap-9572	166	20	.	.	PUNCT
ap-9572	167	1	in	in	ADP
ap-9572	167	2	the	the	DET
ap-9572	167	3	calculation	calculation	NOUN
ap-9572	167	4	,	,	PUNCT
ap-9572	167	5	the	the	DET
ap-9572	167	6	thickness	thickness	NOUN
ap-9572	167	7	at	at	ADP
ap-9572	167	8	the	the	DET
ap-9572	167	9	centre	centre	NOUN
ap-9572	167	10	of	of	ADP
ap-9572	167	11	the	the	DET
ap-9572	167	12	rectangular	rectangular	ADJ
ap-9572	167	13	plate	plate	NOUN
ap-9572	167	14	was	be	AUX
ap-9572	167	15	taken	take	VERB
ap-9572	167	16	as	as	ADP
ap-9572	167	17	0.01	0.01	NUM
ap-9572	167	18	m.	m.	NOUN
ap-9572	167	19	the	the	DET
ap-9572	167	20	material	material	NOUN
ap-9572	167	21	(	(	PUNCT
ap-9572	167	22	duralium	duralium	NOUN
ap-9572	167	23	)	)	PUNCT
ap-9572	167	24	parameters	parameter	NOUN
ap-9572	167	25	used	use	VERB
ap-9572	167	26	for	for	ADP
ap-9572	167	27	the	the	DET
ap-9572	167	28	computational	computational	ADJ
ap-9572	167	29	work	work	NOUN
ap-9572	167	30	are	be	AUX
ap-9572	167	31	presented	present	VERB
ap-9572	167	32	in	in	ADP
ap-9572	167	33	table	table	NOUN
ap-9572	167	34	1	1	NUM
ap-9572	167	35	.	.	PUNCT
ap-9572	167	36	table	table	NOUN
ap-9572	167	37	2	2	NUM
ap-9572	167	38	deals	deal	NOUN
ap-9572	167	39	with	with	ADP
ap-9572	167	40	the	the	DET
ap-9572	167	41	variation	variation	NOUN
ap-9572	167	42	of	of	ADP
ap-9572	167	43	tp	tp	X
ap-9572	167	44	(	(	PUNCT
ap-9572	167	45	*	*	NOUN
ap-9572	167	46	10−6	10−6	NUM
ap-9572	167	47	in	in	ADP
ap-9572	167	48	seconds	second	NOUN
ap-9572	167	49	)	)	PUNCT
ap-9572	167	50	with	with	ADP
ap-9572	167	51	different	different	ADJ
ap-9572	167	52	values	value	NOUN
ap-9572	167	53	of	of	ADP
ap-9572	167	54	α	α	PROPN
ap-9572	167	55	(	(	PUNCT
ap-9572	167	56	0.0	0.0	NUM
ap-9572	167	57	,	,	PUNCT
ap-9572	167	58	0.2	0.2	NUM
ap-9572	167	59	,	,	PUNCT
ap-9572	167	60	0.4	0.4	NUM
ap-9572	167	61	,	,	PUNCT
ap-9572	167	62	0.6	0.6	NUM
ap-9572	167	63	,	,	PUNCT
ap-9572	167	64	0.8	0.8	NUM
ap-9572	167	65	,	,	PUNCT
ap-9572	167	66	1.0	1.0	NUM
ap-9572	167	67	)	)	PUNCT
ap-9572	167	68	,	,	PUNCT
ap-9572	167	69	and	and	CCONJ
ap-9572	167	70	constant	constant	VERB
ap-9572	167	71	a	a	DET
ap-9572	167	72	b	b	NOUN
ap-9572	167	73	=	=	SYM
ap-9572	167	74	1.5	1.5	NUM
ap-9572	167	75	for	for	ADP
ap-9572	167	76	all	all	DET
ap-9572	167	77	x	x	SYM
ap-9572	167	78	and	and	CCONJ
ap-9572	167	79	y	y	PROPN
ap-9572	167	80	.	.	PUNCT
ap-9572	168	1	the	the	DET
ap-9572	168	2	continuous	continuous	ADJ
ap-9572	168	3	increments	increment	NOUN
ap-9572	168	4	are	be	AUX
ap-9572	168	5	observed	observe	VERB
ap-9572	168	6	in	in	ADP
ap-9572	168	7	the	the	DET
ap-9572	168	8	values	value	NOUN
ap-9572	168	9	of	of	ADP
ap-9572	168	10	301	301	NUM
ap-9572	168	11	sudhanshu	sudhanshu	NOUN
ap-9572	168	12	aggarwal	aggarwal	PROPN
ap-9572	168	13	acta	acta	PROPN
ap-9572	168	14	polytechnica	polytechnica	PROPN
ap-9572	168	15	α1	α1	PROPN
ap-9572	168	16	=	=	SYM
ap-9572	168	17	0.0	0.0	NUM
ap-9572	168	18	α1	α1	NOUN
ap-9572	168	19	=	=	SYM
ap-9572	168	20	0.4	0.4	NUM
ap-9572	168	21	β1	β1	NOUN
ap-9572	168	22	=	=	PUNCT
ap-9572	168	23	0.0	0.0	NUM
ap-9572	168	24	β2	β2	NOUN
ap-9572	168	25	=	=	SYM
ap-9572	168	26	0.0	0.0	NUM
ap-9572	168	27	β1	β1	NOUN
ap-9572	168	28	=	=	PUNCT
ap-9572	168	29	0.4	0.4	NUM
ap-9572	168	30	β2	β2	NOUN
ap-9572	168	31	=	=	PROPN
ap-9572	168	32	0.2	0.2	NUM
ap-9572	168	33	β1	β1	NOUN
ap-9572	168	34	=	=	PUNCT
ap-9572	168	35	0.0	0.0	NUM
ap-9572	168	36	β2	β2	NOUN
ap-9572	168	37	=	=	SYM
ap-9572	168	38	0.0	0.0	NUM
ap-9572	168	39	β1	β1	NOUN
ap-9572	168	40	=	=	PUNCT
ap-9572	168	41	0.4	0.4	NUM
ap-9572	168	42	β2	β2	NOUN
ap-9572	168	43	=	=	NOUN
ap-9572	168	44	0.2	0.2	NUM
ap-9572	168	45	mode	mode	NOUN
ap-9572	168	46	→	→	PUNCT
ap-9572	169	1	i	i	NOUN
ap-9572	169	2	ii	ii	VERB
ap-9572	170	1	i	i	PRON
ap-9572	170	2	ii	ii	VERB
ap-9572	171	1	i	i	PRON
ap-9572	171	2	ii	ii	VERB
ap-9572	172	1	i	i	PRON
ap-9572	172	2	ii	ii	VERB
ap-9572	173	1	α	α	PRON
ap-9572	173	2	↓	↓	NOUN
ap-9572	173	3	0.0	0.0	NUM
ap-9572	173	4	6	6	NUM
ap-9572	173	5	462	462	NUM
ap-9572	173	6	1	1	NUM
ap-9572	173	7	623	623	NUM
ap-9572	173	8	5	5	NUM
ap-9572	173	9	324	324	NUM
ap-9572	173	10	1	1	NUM
ap-9572	173	11	332	332	NUM
ap-9572	173	12	6	6	NUM
ap-9572	173	13	897	897	NUM
ap-9572	173	14	1	1	NUM
ap-9572	173	15	728	728	NUM
ap-9572	173	16	5	5	NUM
ap-9572	173	17	543	543	NUM
ap-9572	173	18	1	1	NUM
ap-9572	173	19	433	433	NUM
ap-9572	173	20	0.2	0.2	NUM
ap-9572	173	21	6	6	NUM
ap-9572	173	22	823	823	NUM
ap-9572	173	23	1	1	NUM
ap-9572	173	24	731	731	NUM
ap-9572	173	25	5	5	NUM
ap-9572	173	26	513	513	NUM
ap-9572	173	27	1	1	NUM
ap-9572	173	28	438	438	NUM
ap-9572	173	29	7	7	NUM
ap-9572	173	30	246	246	NUM
ap-9572	173	31	1	1	NUM
ap-9572	173	32	856	856	NUM
ap-9572	173	33	5	5	NUM
ap-9572	173	34	849	849	NUM
ap-9572	173	35	1	1	NUM
ap-9572	173	36	496	496	NUM
ap-9572	173	37	0.4	0.4	NUM
ap-9572	173	38	7	7	NUM
ap-9572	173	39	236	236	NUM
ap-9572	173	40	1	1	NUM
ap-9572	173	41	863	863	NUM
ap-9572	173	42	5	5	NUM
ap-9572	173	43	874	874	NUM
ap-9572	173	44	1	1	NUM
ap-9572	173	45	497	497	NUM
ap-9572	173	46	7	7	NUM
ap-9572	173	47	733	733	NUM
ap-9572	173	48	2	2	NUM
ap-9572	173	49	002	002	NUM
ap-9572	173	50	6	6	NUM
ap-9572	173	51	194	194	NUM
ap-9572	173	52	1	1	NUM
ap-9572	173	53	617	617	NUM
ap-9572	173	54	0.6	0.6	NUM
ap-9572	173	55	7	7	NUM
ap-9572	173	56	737	737	NUM
ap-9572	173	57	2	2	NUM
ap-9572	173	58	002	002	NUM
ap-9572	173	59	6	6	NUM
ap-9572	173	60	213	213	NUM
ap-9572	173	61	1	1	NUM
ap-9572	173	62	603	603	NUM
ap-9572	173	63	8	8	NUM
ap-9572	173	64	497	497	NUM
ap-9572	173	65	2	2	NUM
ap-9572	173	66	176	176	NUM
ap-9572	173	67	6	6	NUM
ap-9572	173	68	626	626	NUM
ap-9572	173	69	1	1	NUM
ap-9572	173	70	759	759	NUM
ap-9572	173	71	0.8	0.8	NUM
ap-9572	173	72	8	8	NUM
ap-9572	173	73	443	443	NUM
ap-9572	173	74	2	2	NUM
ap-9572	173	75	168	168	NUM
ap-9572	173	76	6	6	NUM
ap-9572	173	77	584	584	NUM
ap-9572	173	78	1	1	NUM
ap-9572	173	79	737	737	NUM
ap-9572	173	80	9	9	NUM
ap-9572	173	81	220	220	NUM
ap-9572	173	82	2	2	NUM
ap-9572	173	83	285	285	NUM
ap-9572	173	84	7	7	NUM
ap-9572	173	85	082	082	NUM
ap-9572	173	86	1	1	NUM
ap-9572	173	87	846	846	NUM
ap-9572	173	88	1.0	1.0	NUM
ap-9572	173	89	9	9	NUM
ap-9572	173	90	231	231	NUM
ap-9572	173	91	2	2	NUM
ap-9572	173	92	304	304	NUM
ap-9572	173	93	7	7	NUM
ap-9572	173	94	117	117	NUM
ap-9572	173	95	1	1	NUM
ap-9572	173	96	863	863	NUM
ap-9572	173	97	9	9	NUM
ap-9572	173	98	668	668	NUM
ap-9572	173	99	2	2	NUM
ap-9572	173	100	439	439	NUM
ap-9572	173	101	7	7	NUM
ap-9572	173	102	530	530	NUM
ap-9572	173	103	1	1	NUM
ap-9572	173	104	988	988	NUM
ap-9572	173	105	table	table	NOUN
ap-9572	173	106	2	2	NUM
ap-9572	173	107	.	.	PUNCT
ap-9572	173	108	variation	variation	NOUN
ap-9572	173	109	of	of	ADP
ap-9572	173	110	tp	tp	X
ap-9572	173	111	(	(	PUNCT
ap-9572	173	112	*	*	NOUN
ap-9572	173	113	10−6	10−6	NUM
ap-9572	173	114	in	in	ADP
ap-9572	173	115	seconds	second	NOUN
ap-9572	173	116	)	)	PUNCT
ap-9572	173	117	with	with	ADP
ap-9572	173	118	different	different	ADJ
ap-9572	173	119	α	α	NOUN
ap-9572	173	120	and	and	CCONJ
ap-9572	173	121	constant	constant	ADJ
ap-9572	173	122	a	a	DET
ap-9572	173	123	b	b	NOUN
ap-9572	173	124	=	=	SYM
ap-9572	173	125	1.5	1.5	NUM
ap-9572	173	126	for	for	ADP
ap-9572	173	127	all	all	DET
ap-9572	173	128	x	x	PUNCT
ap-9572	173	129	and	and	CCONJ
ap-9572	173	130	y	y	PROPN
ap-9572	173	131	see	see	VERB
ap-9572	173	132	figure	figure	NOUN
ap-9572	173	133	2	2	NUM
ap-9572	173	134	.	.	NOUN
ap-9572	173	135	0	0	NUM
ap-9572	173	136	2000	2000	NUM
ap-9572	173	137	4000	4000	NUM
ap-9572	173	138	6000	6000	NUM
ap-9572	173	139	8000	8000	NUM
ap-9572	173	140	10000	10000	NUM
ap-9572	173	141	12000	12000	NUM
ap-9572	173	142	0	0	NUM
ap-9572	173	143	0.2	0.2	NUM
ap-9572	173	144	0.4	0.4	NUM
ap-9572	173	145	0.6	0.6	NUM
ap-9572	173	146	0.8	0.8	NUM
ap-9572	173	147	1	1	NUM
ap-9572	173	148	first	first	ADJ
ap-9572	173	149	mode	mode	NOUN
ap-9572	173	150	α1=0,β1=0,β2=0	α1=0,β1=0,β2=0	PROPN
ap-9572	173	151	second	second	ADJ
ap-9572	173	152	mode	mode	NOUN
ap-9572	173	153	α1=0,β1=0,β2=0	α1=0,β1=0,β2=0	PROPN
ap-9572	173	154	first	first	ADJ
ap-9572	173	155	mode	mode	NOUN
ap-9572	173	156	α1=0,β1=0.4,β2=0.2	α1=0,β1=0.4,β2=0.2	NUM
ap-9572	173	157	second	second	ADJ
ap-9572	173	158	mode	mode	NOUN
ap-9572	173	159	α1=0,β1=0.4,β2=0.2	α1=0,β1=0.4,β2=0.2	NUM
ap-9572	173	160	first	first	ADJ
ap-9572	173	161	mode	mode	NOUN
ap-9572	173	162	α1=0.4,β1=0,β2=0	α1=0.4,β1=0,β2=0	PROPN
ap-9572	173	163	second	second	ADJ
ap-9572	173	164	mode	mode	NOUN
ap-9572	173	165	α1=0.4,β1=0,β2=0	α1=0.4,β1=0,β2=0	PROPN
ap-9572	173	166	first	first	ADJ
ap-9572	173	167	mode	mode	PROPN
ap-9572	173	168	α1=0.4,β1=0.4,β2=0.2	α1=0.4,β1=0.4,β2=0.2	PART
ap-9572	173	169	second	second	ADJ
ap-9572	173	170	mode	mode	NOUN
ap-9572	173	171	α1=0.4,β1=0.4,β2=0.2	α1=0.4,β1=0.4,β2=0.2	NUM
ap-9572	173	172	figure	figure	NOUN
ap-9572	173	173	2	2	NUM
ap-9572	173	174	.	.	PUNCT
ap-9572	173	175	variation	variation	NOUN
ap-9572	173	176	of	of	ADP
ap-9572	173	177	tp	tp	X
ap-9572	173	178	(	(	PUNCT
ap-9572	173	179	*	*	NOUN
ap-9572	173	180	10−6	10−6	NUM
ap-9572	173	181	in	in	ADP
ap-9572	173	182	seconds	second	NOUN
ap-9572	173	183	)	)	PUNCT
ap-9572	173	184	with	with	ADP
ap-9572	173	185	different	different	ADJ
ap-9572	173	186	α	α	NOUN
ap-9572	173	187	and	and	CCONJ
ap-9572	173	188	constant	constant	ADJ
ap-9572	173	189	a	a	DET
ap-9572	173	190	b	b	NOUN
ap-9572	173	191	=	=	SYM
ap-9572	173	192	1.5	1.5	NUM
ap-9572	173	193	for	for	ADP
ap-9572	173	194	all	all	DET
ap-9572	173	195	x	x	SYM
ap-9572	173	196	and	and	CCONJ
ap-9572	173	197	y	y	PROPN
ap-9572	173	198	.	.	PUNCT
ap-9572	174	1	α1	α1	PROPN
ap-9572	174	2	=	=	PUNCT
ap-9572	174	3	0.0	0.0	NUM
ap-9572	174	4	α1	α1	NOUN
ap-9572	174	5	=	=	SYM
ap-9572	174	6	0.4	0.4	NUM
ap-9572	174	7	β1	β1	NOUN
ap-9572	174	8	=	=	PUNCT
ap-9572	174	9	0.0	0.0	NUM
ap-9572	174	10	β2	β2	NOUN
ap-9572	174	11	=	=	NOUN
ap-9572	174	12	0.0	0.0	NUM
ap-9572	174	13	α	α	NOUN
ap-9572	174	14	=	=	SYM
ap-9572	174	15	0.0	0.0	NUM
ap-9572	174	16	β1	β1	NOUN
ap-9572	174	17	=	=	PUNCT
ap-9572	174	18	0.4	0.4	NUM
ap-9572	174	19	β2	β2	NOUN
ap-9572	174	20	=	=	NOUN
ap-9572	174	21	0.2	0.2	NUM
ap-9572	174	22	α	α	NOUN
ap-9572	174	23	=	=	SYM
ap-9572	174	24	0.3	0.3	NUM
ap-9572	174	25	β1	β1	NOUN
ap-9572	174	26	=	=	PUNCT
ap-9572	174	27	0.0	0.0	NUM
ap-9572	174	28	β2	β2	NOUN
ap-9572	174	29	=	=	NOUN
ap-9572	174	30	0.0	0.0	NUM
ap-9572	174	31	α	α	NOUN
ap-9572	174	32	=	=	SYM
ap-9572	174	33	0.0	0.0	NUM
ap-9572	174	34	β1	β1	NOUN
ap-9572	174	35	=	=	PUNCT
ap-9572	174	36	0.4	0.4	NUM
ap-9572	174	37	β2	β2	NOUN
ap-9572	174	38	=	=	NOUN
ap-9572	174	39	0.2	0.2	NUM
ap-9572	174	40	α	α	NOUN
ap-9572	174	41	=	=	SYM
ap-9572	174	42	0.3	0.3	NUM
ap-9572	174	43	mode	mode	NOUN
ap-9572	174	44	→	→	PUNCT
ap-9572	175	1	i	i	NOUN
ap-9572	175	2	ii	ii	VERB
ap-9572	176	1	i	i	PRON
ap-9572	176	2	ii	ii	VERB
ap-9572	177	1	i	i	PRON
ap-9572	177	2	ii	ii	VERB
ap-9572	178	1	i	i	PRON
ap-9572	178	2	ii	ii	VERB
ap-9572	178	3	a	a	DET
ap-9572	178	4	b	b	PROPN
ap-9572	178	5	↓	↓	NOUN
ap-9572	178	6	0.5	0.5	NUM
ap-9572	178	7	15	15	NUM
ap-9572	178	8	559	559	NUM
ap-9572	178	9	3	3	NUM
ap-9572	178	10	878	878	NUM
ap-9572	178	11	13	13	NUM
ap-9572	178	12	873	873	NUM
ap-9572	178	13	3	3	NUM
ap-9572	178	14	417	417	NUM
ap-9572	178	15	16	16	NUM
ap-9572	178	16	023	023	NUM
ap-9572	178	17	4	4	NUM
ap-9572	178	18	008	008	NUM
ap-9572	178	19	14	14	NUM
ap-9572	178	20	296	296	NUM
ap-9572	178	21	3	3	NUM
ap-9572	178	22	557	557	NUM
ap-9572	178	23	1.0	1.0	NUM
ap-9572	178	24	10	10	NUM
ap-9572	178	25	411	411	NUM
ap-9572	178	26	2	2	NUM
ap-9572	178	27	638	638	NUM
ap-9572	178	28	9	9	NUM
ap-9572	178	29	657	657	NUM
ap-9572	178	30	2	2	NUM
ap-9572	178	31	471	471	NUM
ap-9572	178	32	10	10	NUM
ap-9572	178	33	860	860	NUM
ap-9572	178	34	2	2	NUM
ap-9572	178	35	747	747	NUM
ap-9572	178	36	9	9	NUM
ap-9572	178	37	971	971	NUM
ap-9572	178	38	2	2	NUM
ap-9572	178	39	588	588	NUM
ap-9572	178	40	1.5	1.5	NUM
ap-9572	178	41	6	6	NUM
ap-9572	178	42	462	462	NUM
ap-9572	178	43	1	1	NUM
ap-9572	178	44	623	623	NUM
ap-9572	178	45	5	5	NUM
ap-9572	178	46	697	697	NUM
ap-9572	178	47	1	1	NUM
ap-9572	178	48	465	465	NUM
ap-9572	178	49	6	6	NUM
ap-9572	178	50	897	897	NUM
ap-9572	178	51	1	1	NUM
ap-9572	178	52	728	728	NUM
ap-9572	178	53	6	6	NUM
ap-9572	178	54	021	021	NUM
ap-9572	178	55	1	1	NUM
ap-9572	178	56	515	515	NUM
ap-9572	178	57	2.0	2.0	NUM
ap-9572	178	58	3	3	NUM
ap-9572	178	59	724	724	NUM
ap-9572	178	60	905	905	NUM
ap-9572	178	61	3	3	NUM
ap-9572	178	62	513	513	NUM
ap-9572	178	63	873	873	NUM
ap-9572	178	64	4	4	NUM
ap-9572	178	65	082	082	NUM
ap-9572	178	66	961	961	NUM
ap-9572	178	67	3	3	NUM
ap-9572	178	68	864	864	NUM
ap-9572	178	69	957	957	NUM
ap-9572	178	70	2.5	2.5	NUM
ap-9572	178	71	2	2	NUM
ap-9572	178	72	451	451	NUM
ap-9572	178	73	576	576	NUM
ap-9572	178	74	2	2	NUM
ap-9572	178	75	391	391	NUM
ap-9572	178	76	560	560	NUM
ap-9572	178	77	2	2	NUM
ap-9572	178	78	771	771	NUM
ap-9572	178	79	658	658	NUM
ap-9572	178	80	2	2	NUM
ap-9572	178	81	739	739	NUM
ap-9572	178	82	651	651	NUM
ap-9572	178	83	table	table	NOUN
ap-9572	178	84	3	3	NUM
ap-9572	178	85	.	.	PUNCT
ap-9572	179	1	variation	variation	NOUN
ap-9572	179	2	of	of	ADP
ap-9572	179	3	tp	tp	X
ap-9572	179	4	(	(	PUNCT
ap-9572	179	5	*	*	NOUN
ap-9572	179	6	10−6	10−6	NUM
ap-9572	179	7	in	in	ADP
ap-9572	179	8	seconds	second	NOUN
ap-9572	179	9	)	)	PUNCT
ap-9572	179	10	with	with	ADP
ap-9572	179	11	different	different	ADJ
ap-9572	179	12	a	a	DET
ap-9572	179	13	b	b	NOUN
ap-9572	179	14	for	for	ADP
ap-9572	179	15	all	all	DET
ap-9572	179	16	x	x	SYM
ap-9572	179	17	and	and	CCONJ
ap-9572	179	18	y	y	PROPN
ap-9572	179	19	,	,	PUNCT
ap-9572	179	20	see	see	VERB
ap-9572	179	21	figure	figure	NOUN
ap-9572	179	22	3	3	NUM
ap-9572	179	23	.	.	PUNCT
ap-9572	179	24	tp	tp	NOUN
ap-9572	179	25	as	as	ADP
ap-9572	179	26	α	α	PROPN
ap-9572	179	27	increases	increase	VERB
ap-9572	179	28	from	from	ADP
ap-9572	179	29	0.0	0.0	NUM
ap-9572	179	30	to	to	ADP
ap-9572	179	31	1.0	1.0	NUM
ap-9572	179	32	for	for	ADP
ap-9572	179	33	both	both	DET
ap-9572	179	34	modes	mode	NOUN
ap-9572	179	35	of	of	ADP
ap-9572	179	36	vibration	vibration	NOUN
ap-9572	179	37	.	.	PUNCT
ap-9572	180	1	the	the	DET
ap-9572	180	2	graph	graph	NOUN
ap-9572	180	3	shown	show	VERB
ap-9572	180	4	in	in	ADP
ap-9572	180	5	figure	figure	NOUN
ap-9572	180	6	2	2	NUM
ap-9572	180	7	supports	support	VERB
ap-9572	180	8	the	the	DET
ap-9572	180	9	results	result	NOUN
ap-9572	180	10	of	of	ADP
ap-9572	180	11	table	table	NOUN
ap-9572	180	12	2	2	NUM
ap-9572	180	13	.	.	PUNCT
ap-9572	180	14	table	table	NOUN
ap-9572	180	15	3	3	NUM
ap-9572	180	16	is	be	AUX
ap-9572	180	17	concerned	concern	VERB
ap-9572	180	18	with	with	ADP
ap-9572	180	19	the	the	DET
ap-9572	180	20	variation	variation	NOUN
ap-9572	180	21	of	of	ADP
ap-9572	180	22	tp	tp	X
ap-9572	180	23	(	(	PUNCT
ap-9572	180	24	*	*	NOUN
ap-9572	180	25	10−6	10−6	NUM
ap-9572	180	26	in	in	ADP
ap-9572	180	27	seconds	second	NOUN
ap-9572	180	28	)	)	PUNCT
ap-9572	180	29	with	with	ADP
ap-9572	180	30	different	different	ADJ
ap-9572	180	31	a	a	DET
ap-9572	180	32	b	b	PROPN
ap-9572	180	33	(	(	PUNCT
ap-9572	180	34	0.5	0.5	NUM
ap-9572	180	35	,	,	PUNCT
ap-9572	180	36	1.0	1.0	NUM
ap-9572	180	37	,	,	PUNCT
ap-9572	180	38	1.5	1.5	NUM
ap-9572	180	39	,	,	PUNCT
ap-9572	180	40	2.0	2.0	NUM
ap-9572	180	41	,	,	PUNCT
ap-9572	180	42	2.5	2.5	NUM
ap-9572	180	43	)	)	PUNCT
ap-9572	180	44	for	for	ADP
ap-9572	180	45	all	all	DET
ap-9572	180	46	x	x	SYM
ap-9572	180	47	and	and	CCONJ
ap-9572	180	48	y	y	PROPN
ap-9572	180	49	.	.	PUNCT
ap-9572	181	1	the	the	DET
ap-9572	181	2	continuous	continuous	ADJ
ap-9572	181	3	decrements	decrement	NOUN
ap-9572	181	4	are	be	AUX
ap-9572	181	5	observed	observe	VERB
ap-9572	181	6	in	in	ADP
ap-9572	181	7	the	the	DET
ap-9572	181	8	values	value	NOUN
ap-9572	181	9	of	of	ADP
ap-9572	181	10	tp	tp	PRON
ap-9572	181	11	as	as	ADP
ap-9572	181	12	a	a	DET
ap-9572	181	13	b	b	NOUN
ap-9572	181	14	increases	increase	NOUN
ap-9572	181	15	from	from	ADP
ap-9572	181	16	0.5	0.5	NUM
ap-9572	181	17	to	to	ADP
ap-9572	181	18	2.5	2.5	NUM
ap-9572	181	19	for	for	ADP
ap-9572	181	20	modes	mode	NOUN
ap-9572	181	21	of	of	ADP
ap-9572	181	22	vibration	vibration	NOUN
ap-9572	181	23	.	.	PUNCT
ap-9572	182	1	the	the	DET
ap-9572	182	2	results	result	NOUN
ap-9572	182	3	of	of	ADP
ap-9572	182	4	table	table	NOUN
ap-9572	182	5	3	3	NUM
ap-9572	182	6	are	be	AUX
ap-9572	182	7	supported	support	VERB
ap-9572	182	8	by	by	ADP
ap-9572	182	9	the	the	DET
ap-9572	182	10	graph	graph	NOUN
ap-9572	182	11	shown	show	VERB
ap-9572	182	12	in	in	ADP
ap-9572	182	13	figure	figure	NOUN
ap-9572	182	14	3	3	NUM
ap-9572	182	15	.	.	PUNCT
ap-9572	182	16	table	table	NOUN
ap-9572	182	17	4	4	NUM
ap-9572	182	18	shows	show	VERB
ap-9572	182	19	the	the	DET
ap-9572	182	20	variation	variation	NOUN
ap-9572	182	21	of	of	ADP
ap-9572	182	22	tp	tp	X
ap-9572	182	23	(	(	PUNCT
ap-9572	182	24	*	*	NOUN
ap-9572	182	25	10−6	10−6	NUM
ap-9572	182	26	in	in	ADP
ap-9572	182	27	seconds	second	NOUN
ap-9572	182	28	)	)	PUNCT
ap-9572	182	29	with	with	ADP
ap-9572	182	30	different	different	ADJ
ap-9572	182	31	β1(0.0	β1(0.0	ADJ
ap-9572	182	32	,	,	PUNCT
ap-9572	182	33	0.2	0.2	NUM
ap-9572	182	34	,	,	PUNCT
ap-9572	182	35	0.4	0.4	NUM
ap-9572	182	36	,	,	PUNCT
ap-9572	182	37	0.6	0.6	NUM
ap-9572	182	38	,	,	PUNCT
ap-9572	182	39	0.8	0.8	NUM
ap-9572	182	40	,	,	PUNCT
ap-9572	182	41	1.0	1.0	NUM
ap-9572	182	42	)	)	PUNCT
ap-9572	182	43	and	and	CCONJ
ap-9572	182	44	constant	constant	ADJ
ap-9572	182	45	a	a	DET
ap-9572	182	46	b	b	NOUN
ap-9572	182	47	=	=	SYM
ap-9572	182	48	1.5	1.5	NUM
ap-9572	182	49	for	for	ADP
ap-9572	182	50	all	all	DET
ap-9572	182	51	x	x	NOUN
ap-9572	182	52	and	and	CCONJ
ap-9572	182	53	y	y	PROPN
ap-9572	182	54	.	.	PUNCT
ap-9572	183	1	it	it	PRON
ap-9572	183	2	is	be	AUX
ap-9572	183	3	observed	observe	VERB
ap-9572	183	4	that	that	SCONJ
ap-9572	183	5	as	as	ADP
ap-9572	183	6	the	the	DET
ap-9572	183	7	value	value	NOUN
ap-9572	183	8	of	of	ADP
ap-9572	183	9	β1	β1	PROPN
ap-9572	183	10	increases	increase	VERB
ap-9572	183	11	from	from	ADP
ap-9572	183	12	0.0	0.0	NUM
ap-9572	183	13	to	to	ADP
ap-9572	183	14	1.0	1.0	NUM
ap-9572	183	15	,	,	PUNCT
ap-9572	183	16	the	the	DET
ap-9572	183	17	value	value	NOUN
ap-9572	183	18	of	of	ADP
ap-9572	183	19	tp	tp	NOUN
ap-9572	183	20	decreases	decrease	NOUN
ap-9572	183	21	for	for	ADP
ap-9572	183	22	both	both	DET
ap-9572	183	23	modes	mode	NOUN
ap-9572	183	24	of	of	ADP
ap-9572	183	25	vibration	vibration	NOUN
ap-9572	183	26	.	.	PUNCT
ap-9572	184	1	the	the	DET
ap-9572	184	2	graph	graph	NOUN
ap-9572	184	3	in	in	ADP
ap-9572	184	4	figure	figure	NOUN
ap-9572	184	5	4	4	NUM
ap-9572	184	6	supports	support	VERB
ap-9572	184	7	the	the	DET
ap-9572	184	8	results	result	NOUN
ap-9572	184	9	of	of	ADP
ap-9572	184	10	table	table	NOUN
ap-9572	184	11	4	4	NUM
ap-9572	184	12	.	.	PUNCT
ap-9572	184	13	table	table	NOUN
ap-9572	184	14	5	5	NUM
ap-9572	184	15	shows	show	VERB
ap-9572	184	16	the	the	DET
ap-9572	184	17	variation	variation	NOUN
ap-9572	184	18	of	of	ADP
ap-9572	184	19	tp	tp	X
ap-9572	184	20	(	(	PUNCT
ap-9572	184	21	*	*	NOUN
ap-9572	184	22	10−6	10−6	NUM
ap-9572	184	23	in	in	ADP
ap-9572	184	24	seconds	second	NOUN
ap-9572	184	25	)	)	PUNCT
ap-9572	184	26	with	with	ADP
ap-9572	184	27	different	different	ADJ
ap-9572	184	28	β2(0.0	β2(0.0	PROPN
ap-9572	184	29	,	,	PUNCT
ap-9572	184	30	0.2	0.2	NUM
ap-9572	184	31	,	,	PUNCT
ap-9572	184	32	0.4	0.4	NUM
ap-9572	184	33	,	,	PUNCT
ap-9572	184	34	0.6	0.6	NUM
ap-9572	184	35	,	,	PUNCT
ap-9572	184	36	0.8	0.8	NUM
ap-9572	184	37	,	,	PUNCT
ap-9572	184	38	1.0	1.0	NUM
ap-9572	184	39	)	)	PUNCT
ap-9572	184	40	and	and	CCONJ
ap-9572	184	41	constant	constant	ADJ
ap-9572	184	42	a	a	DET
ap-9572	184	43	b	b	NOUN
ap-9572	184	44	=	=	SYM
ap-9572	184	45	1.5	1.5	NUM
ap-9572	184	46	for	for	ADP
ap-9572	184	47	all	all	DET
ap-9572	184	48	x	x	NOUN
ap-9572	184	49	and	and	CCONJ
ap-9572	184	50	y	y	PROPN
ap-9572	184	51	.	.	PUNCT
ap-9572	185	1	from	from	ADP
ap-9572	185	2	this	this	DET
ap-9572	185	3	table	table	NOUN
ap-9572	185	4	,	,	PUNCT
ap-9572	185	5	it	it	PRON
ap-9572	185	6	can	can	AUX
ap-9572	185	7	clearly	clearly	ADV
ap-9572	185	8	be	be	AUX
ap-9572	185	9	seen	see	VERB
ap-9572	185	10	that	that	SCONJ
ap-9572	185	11	the	the	DET
ap-9572	185	12	value	value	NOUN
ap-9572	185	13	of	of	ADP
ap-9572	185	14	tp	tp	NOUN
ap-9572	185	15	decreases	decrease	NOUN
ap-9572	185	16	as	as	SCONJ
ap-9572	185	17	β2	β2	VERB
ap-9572	185	18	increases	increase	VERB
ap-9572	185	19	from	from	ADP
ap-9572	185	20	0.0	0.0	NUM
ap-9572	185	21	to	to	ADP
ap-9572	185	22	1.0	1.0	NUM
ap-9572	185	23	for	for	ADP
ap-9572	185	24	both	both	CCONJ
ap-9572	185	25	the	the	DET
ap-9572	185	26	vibration	vibration	NOUN
ap-9572	185	27	302	302	NUM
ap-9572	185	28	vol	vol	NOUN
ap-9572	185	29	.	.	PROPN
ap-9572	186	1	64	64	NUM
ap-9572	186	2	no	no	NOUN
ap-9572	186	3	.	.	PUNCT
ap-9572	187	1	4/2024	4/2024	NUM
ap-9572	187	2	non	non	ADJ
ap-9572	187	3	-	-	ADJ
ap-9572	187	4	homogeneity	homogeneity	ADJ
ap-9572	187	5	effect	effect	NOUN
ap-9572	187	6	on	on	ADP
ap-9572	187	7	the	the	DET
ap-9572	187	8	vibration	vibration	NOUN
ap-9572	187	9	of	of	ADP
ap-9572	187	10	.	.	PUNCT
ap-9572	187	11	.	.	PUNCT
ap-9572	188	1	.	.	PUNCT
ap-9572	189	1	0	0	NUM
ap-9572	190	1	2000	2000	NUM
ap-9572	190	2	4000	4000	NUM
ap-9572	190	3	6000	6000	NUM
ap-9572	190	4	8000	8000	NUM
ap-9572	190	5	10000	10000	NUM
ap-9572	190	6	12000	12000	NUM
ap-9572	190	7	14000	14000	NUM
ap-9572	190	8	16000	16000	NUM
ap-9572	190	9	18000	18000	NUM
ap-9572	190	10	0.5	0.5	NUM
ap-9572	190	11	1	1	NUM
ap-9572	190	12	1.5	1.5	NUM
ap-9572	190	13	2	2	NUM
ap-9572	190	14	2.5	2.5	NUM
ap-9572	190	15	first	first	ADJ
ap-9572	190	16	mode	mode	NOUN
ap-9572	190	17	α1=0,β1=0,β2=0,α=0	α1=0,β1=0,β2=0,α=0	ADJ
ap-9572	190	18	second	second	ADJ
ap-9572	190	19	mode	mode	NOUN
ap-9572	190	20	α1=0,β1=0,β2=0	α1=0,β1=0,β2=0	PROPN
ap-9572	190	21	,	,	PUNCT
ap-9572	190	22	α=0	α=0	PROPN
ap-9572	190	23	first	first	ADJ
ap-9572	190	24	mode	mode	NOUN
ap-9572	190	25	α1=0,β1=0.4,β2=0.2,α=0.3	α1=0,β1=0.4,β2=0.2,α=0.3	ADP
ap-9572	190	26	second	second	ADJ
ap-9572	190	27	mode	mode	NOUN
ap-9572	190	28	α1=0,β1=0.4,β2=0.2,α=0.3	α1=0,β1=0.4,β2=0.2,α=0.3	ADP
ap-9572	190	29	first	first	ADJ
ap-9572	190	30	mode	mode	NOUN
ap-9572	190	31	α1=0.4,β1=0,β2=0,α=0	α1=0.4,β1=0,β2=0,α=0	CCONJ
ap-9572	190	32	second	second	ADJ
ap-9572	190	33	mode	mode	NOUN
ap-9572	190	34	α1=0.4,β1=0,β2=0,α=0	α1=0.4,β1=0,β2=0,α=0	CCONJ
ap-9572	190	35	first	first	ADJ
ap-9572	190	36	mode	mode	NOUN
ap-9572	190	37	α1=0.4,β1=0.4,β2=0.2,α=0.3	α1=0.4,β1=0.4,β2=0.2,α=0.3	PROPN
ap-9572	190	38	second	second	ADJ
ap-9572	190	39	mode	mode	NOUN
ap-9572	190	40	α1=0.4,β1=0.4,β2=0.2,α=0.3	α1=0.4,β1=0.4,β2=0.2,α=0.3	ADJ
ap-9572	190	41	figure	figure	NOUN
ap-9572	190	42	3	3	NUM
ap-9572	190	43	.	.	PUNCT
ap-9572	190	44	variation	variation	NOUN
ap-9572	190	45	of	of	ADP
ap-9572	190	46	tp	tp	X
ap-9572	190	47	(	(	PUNCT
ap-9572	190	48	*	*	NOUN
ap-9572	190	49	10−6	10−6	NUM
ap-9572	190	50	in	in	ADP
ap-9572	190	51	seconds	second	NOUN
ap-9572	190	52	)	)	PUNCT
ap-9572	190	53	with	with	ADP
ap-9572	190	54	different	different	ADJ
ap-9572	190	55	a	a	DET
ap-9572	190	56	b	b	NOUN
ap-9572	190	57	for	for	ADP
ap-9572	190	58	all	all	DET
ap-9572	190	59	x	x	SYM
ap-9572	190	60	and	and	CCONJ
ap-9572	190	61	y	y	PROPN
ap-9572	190	62	.	.	PUNCT
ap-9572	191	1	α1	α1	PROPN
ap-9572	191	2	=	=	PUNCT
ap-9572	191	3	0.0	0.0	NUM
ap-9572	191	4	α1	α1	NOUN
ap-9572	191	5	=	=	SYM
ap-9572	191	6	0.4	0.4	NUM
ap-9572	191	7	β2	β2	NOUN
ap-9572	191	8	=	=	PROPN
ap-9572	191	9	0.0	0.0	NUM
ap-9572	191	10	α	α	NOUN
ap-9572	191	11	=	=	SYM
ap-9572	191	12	0.0	0.0	NUM
ap-9572	191	13	β2	β2	NOUN
ap-9572	191	14	=	=	NOUN
ap-9572	191	15	0.2	0.2	NUM
ap-9572	191	16	α	α	NOUN
ap-9572	191	17	=	=	SYM
ap-9572	191	18	0.3	0.3	NUM
ap-9572	191	19	β2	β2	NOUN
ap-9572	191	20	=	=	PUNCT
ap-9572	191	21	0.0	0.0	NUM
ap-9572	191	22	α	α	NOUN
ap-9572	191	23	=	=	SYM
ap-9572	191	24	0.0	0.0	NUM
ap-9572	191	25	β2	β2	NOUN
ap-9572	191	26	=	=	NOUN
ap-9572	191	27	0.2	0.2	NUM
ap-9572	191	28	α	α	NOUN
ap-9572	191	29	=	=	SYM
ap-9572	191	30	0.3	0.3	NUM
ap-9572	191	31	mode	mode	NOUN
ap-9572	191	32	→	→	PUNCT
ap-9572	192	1	i	i	NOUN
ap-9572	192	2	ii	ii	VERB
ap-9572	193	1	i	i	PRON
ap-9572	193	2	ii	ii	VERB
ap-9572	194	1	i	i	PRON
ap-9572	194	2	ii	ii	VERB
ap-9572	195	1	i	i	NOUN
ap-9572	195	2	ii	ii	PROPN
ap-9572	195	3	β1	β1	PROPN
ap-9572	195	4	↓	↓	NOUN
ap-9572	195	5	0.0	0.0	NUM
ap-9572	195	6	6	6	NUM
ap-9572	195	7	462	462	NUM
ap-9572	195	8	1	1	NUM
ap-9572	195	9	623	623	NUM
ap-9572	195	10	6	6	NUM
ap-9572	195	11	360	360	NUM
ap-9572	195	12	1	1	NUM
ap-9572	195	13	564	564	NUM
ap-9572	195	14	6	6	NUM
ap-9572	195	15	897	897	NUM
ap-9572	195	16	1	1	NUM
ap-9572	195	17	728	728	NUM
ap-9572	195	18	6	6	NUM
ap-9572	195	19	702	702	NUM
ap-9572	195	20	1	1	NUM
ap-9572	195	21	701	701	NUM
ap-9572	195	22	0.2	0.2	NUM
ap-9572	195	23	6	6	NUM
ap-9572	195	24	123	123	NUM
ap-9572	195	25	1	1	NUM
ap-9572	195	26	566	566	NUM
ap-9572	195	27	6	6	NUM
ap-9572	195	28	011	011	NUM
ap-9572	195	29	1	1	NUM
ap-9572	195	30	503	503	NUM
ap-9572	195	31	6	6	NUM
ap-9572	195	32	543	543	NUM
ap-9572	195	33	1	1	NUM
ap-9572	195	34	618	618	NUM
ap-9572	195	35	6	6	NUM
ap-9572	195	36	336	336	NUM
ap-9572	195	37	1	1	NUM
ap-9572	195	38	600	600	NUM
ap-9572	195	39	0.4	0.4	NUM
ap-9572	195	40	5	5	NUM
ap-9572	195	41	784	784	NUM
ap-9572	195	42	1	1	NUM
ap-9572	195	43	489	489	NUM
ap-9572	195	44	5	5	NUM
ap-9572	195	45	697	697	NUM
ap-9572	195	46	1	1	NUM
ap-9572	195	47	465	465	NUM
ap-9572	195	48	6	6	NUM
ap-9572	195	49	216	216	NUM
ap-9572	195	50	1	1	NUM
ap-9572	195	51	568	568	NUM
ap-9572	195	52	6	6	NUM
ap-9572	195	53	021	021	NUM
ap-9572	195	54	1	1	NUM
ap-9572	195	55	515	515	NUM
ap-9572	195	56	0.6	0.6	NUM
ap-9572	195	57	5	5	NUM
ap-9572	195	58	402	402	NUM
ap-9572	195	59	1	1	NUM
ap-9572	195	60	373	373	NUM
ap-9572	195	61	5	5	NUM
ap-9572	195	62	278	278	NUM
ap-9572	195	63	1	1	NUM
ap-9572	195	64	327	327	NUM
ap-9572	195	65	5	5	NUM
ap-9572	195	66	930	930	NUM
ap-9572	195	67	1	1	NUM
ap-9572	195	68	453	453	NUM
ap-9572	195	69	5	5	NUM
ap-9572	195	70	591	591	NUM
ap-9572	195	71	1	1	NUM
ap-9572	195	72	437	437	NUM
ap-9572	195	73	0.8	0.8	NUM
ap-9572	195	74	5	5	NUM
ap-9572	195	75	087	087	NUM
ap-9572	195	76	1	1	NUM
ap-9572	195	77	285	285	NUM
ap-9572	195	78	4	4	NUM
ap-9572	195	79	923	923	NUM
ap-9572	195	80	1	1	NUM
ap-9572	195	81	213	213	NUM
ap-9572	195	82	5	5	NUM
ap-9572	195	83	433	433	NUM
ap-9572	195	84	1	1	NUM
ap-9572	195	85	365	365	NUM
ap-9572	195	86	5	5	NUM
ap-9572	195	87	242	242	NUM
ap-9572	195	88	1	1	NUM
ap-9572	195	89	343	343	NUM
ap-9572	195	90	1.0	1.0	NUM
ap-9572	195	91	4	4	NUM
ap-9572	195	92	736	736	NUM
ap-9572	195	93	1	1	NUM
ap-9572	195	94	207	207	NUM
ap-9572	195	95	4	4	NUM
ap-9572	195	96	642	642	NUM
ap-9572	195	97	1	1	NUM
ap-9572	195	98	128	128	NUM
ap-9572	195	99	5	5	NUM
ap-9572	195	100	141	141	NUM
ap-9572	195	101	1	1	NUM
ap-9572	195	102	297	297	NUM
ap-9572	195	103	4	4	NUM
ap-9572	195	104	971	971	NUM
ap-9572	195	105	1	1	NUM
ap-9572	195	106	260	260	NUM
ap-9572	195	107	table	table	NOUN
ap-9572	195	108	4	4	NUM
ap-9572	195	109	.	.	PUNCT
ap-9572	196	1	variation	variation	NOUN
ap-9572	196	2	of	of	ADP
ap-9572	196	3	tp	tp	X
ap-9572	196	4	(	(	PUNCT
ap-9572	196	5	*	*	NOUN
ap-9572	196	6	10−6	10−6	NUM
ap-9572	196	7	in	in	ADP
ap-9572	196	8	seconds	second	NOUN
ap-9572	196	9	)	)	PUNCT
ap-9572	196	10	with	with	ADP
ap-9572	196	11	different	different	ADJ
ap-9572	196	12	β1	β1	NOUN
ap-9572	196	13	and	and	CCONJ
ap-9572	196	14	constant	constant	VERB
ap-9572	196	15	a	a	DET
ap-9572	196	16	b	b	NOUN
ap-9572	196	17	=	=	SYM
ap-9572	196	18	1.5	1.5	NUM
ap-9572	196	19	for	for	ADP
ap-9572	196	20	all	all	DET
ap-9572	196	21	x	x	PUNCT
ap-9572	196	22	and	and	CCONJ
ap-9572	196	23	y	y	PROPN
ap-9572	196	24	,	,	PUNCT
ap-9572	196	25	see	see	VERB
ap-9572	196	26	figure	figure	NOUN
ap-9572	196	27	4	4	NUM
ap-9572	196	28	.	.	NOUN
ap-9572	196	29	0	0	NUM
ap-9572	197	1	1000	1000	NUM
ap-9572	197	2	2000	2000	NUM
ap-9572	197	3	3000	3000	NUM
ap-9572	197	4	4000	4000	NUM
ap-9572	197	5	5000	5000	NUM
ap-9572	197	6	6000	6000	NUM
ap-9572	197	7	7000	7000	NUM
ap-9572	197	8	8000	8000	NUM
ap-9572	197	9	0	0	NUM
ap-9572	197	10	0.2	0.2	NUM
ap-9572	197	11	0.4	0.4	NUM
ap-9572	197	12	0.6	0.6	NUM
ap-9572	197	13	0.8	0.8	NUM
ap-9572	197	14	1	1	NUM
ap-9572	197	15	first	first	ADJ
ap-9572	197	16	mode	mode	NOUN
ap-9572	197	17	α1=0,β2=0,α=0	α1=0,β2=0,α=0	PROPN
ap-9572	198	1	second	second	ADJ
ap-9572	198	2	mode	mode	NOUN
ap-9572	198	3	α1=0,β2=0	α1=0,β2=0	PROPN
ap-9572	198	4	,	,	PUNCT
ap-9572	198	5	α=0	α=0	PROPN
ap-9572	198	6	first	first	ADJ
ap-9572	198	7	mode	mode	NOUN
ap-9572	198	8	α1=0,β2=0.2,α=0.3	α1=0,β2=0.2,α=0.3	DET
ap-9572	198	9	second	second	ADJ
ap-9572	198	10	mode	mode	NOUN
ap-9572	198	11	α1=0,β2=0.2,α=0.3	α1=0,β2=0.2,α=0.3	PRON
ap-9572	198	12	first	first	ADJ
ap-9572	198	13	mode	mode	NOUN
ap-9572	198	14	α1=0.4,β2=0,α=0	α1=0.4,β2=0,α=0	NOUN
ap-9572	198	15	second	second	ADJ
ap-9572	198	16	mode	mode	NOUN
ap-9572	198	17	α1=0.4,β2=0,α=0	α1=0.4,β2=0,α=0	NOUN
ap-9572	198	18	first	first	ADJ
ap-9572	198	19	mode	mode	NOUN
ap-9572	198	20	α1=0.4,β2=0.2,α=0.3	α1=0.4,β2=0.2,α=0.3	PROPN
ap-9572	198	21	second	second	ADJ
ap-9572	198	22	mode	mode	NOUN
ap-9572	198	23	α1=0.4,β2=0.2,α=0.3	α1=0.4,β2=0.2,α=0.3	PROPN
ap-9572	198	24	figure	figure	VERB
ap-9572	198	25	4	4	NUM
ap-9572	198	26	.	.	PUNCT
ap-9572	198	27	variation	variation	NOUN
ap-9572	198	28	of	of	ADP
ap-9572	198	29	tp	tp	X
ap-9572	198	30	(	(	PUNCT
ap-9572	198	31	*	*	NOUN
ap-9572	198	32	10−6	10−6	NUM
ap-9572	198	33	in	in	ADP
ap-9572	198	34	seconds	second	NOUN
ap-9572	198	35	)	)	PUNCT
ap-9572	198	36	with	with	ADP
ap-9572	198	37	different	different	ADJ
ap-9572	198	38	β1	β1	NOUN
ap-9572	198	39	and	and	CCONJ
ap-9572	198	40	constant	constant	VERB
ap-9572	198	41	a	a	DET
ap-9572	198	42	b	b	NOUN
ap-9572	198	43	=	=	SYM
ap-9572	198	44	1.5	1.5	NUM
ap-9572	198	45	for	for	ADP
ap-9572	198	46	all	all	DET
ap-9572	198	47	x	x	NOUN
ap-9572	198	48	and	and	CCONJ
ap-9572	198	49	y	y	PROPN
ap-9572	198	50	.	.	PUNCT
ap-9572	199	1	303	303	NUM
ap-9572	199	2	sudhanshu	sudhanshu	NOUN
ap-9572	199	3	aggarwal	aggarwal	PROPN
ap-9572	199	4	acta	acta	PROPN
ap-9572	199	5	polytechnica	polytechnica	PROPN
ap-9572	199	6	α1	α1	PROPN
ap-9572	199	7	=	=	SYM
ap-9572	199	8	0.0	0.0	NUM
ap-9572	199	9	α1	α1	NOUN
ap-9572	199	10	=	=	SYM
ap-9572	199	11	0.4	0.4	NUM
ap-9572	199	12	β1	β1	NOUN
ap-9572	199	13	=	=	PUNCT
ap-9572	199	14	0.0	0.0	NUM
ap-9572	199	15	α	α	NOUN
ap-9572	199	16	=	=	SYM
ap-9572	199	17	0.0	0.0	NUM
ap-9572	199	18	β1	β1	NOUN
ap-9572	199	19	=	=	PUNCT
ap-9572	199	20	0.4	0.4	NUM
ap-9572	199	21	α	α	NOUN
ap-9572	199	22	=	=	SYM
ap-9572	199	23	0.3	0.3	NUM
ap-9572	199	24	β1	β1	NOUN
ap-9572	199	25	=	=	PUNCT
ap-9572	199	26	0.0	0.0	NUM
ap-9572	199	27	α	α	NOUN
ap-9572	199	28	=	=	SYM
ap-9572	199	29	0.0	0.0	NUM
ap-9572	199	30	β1	β1	NOUN
ap-9572	199	31	=	=	PUNCT
ap-9572	199	32	0.4	0.4	NUM
ap-9572	199	33	α	α	NOUN
ap-9572	199	34	=	=	SYM
ap-9572	199	35	0.3	0.3	NUM
ap-9572	199	36	mode	mode	NOUN
ap-9572	199	37	→	→	PUNCT
ap-9572	199	38	i	i	NOUN
ap-9572	199	39	ii	ii	VERB
ap-9572	200	1	i	i	PRON
ap-9572	200	2	ii	ii	VERB
ap-9572	201	1	i	i	PRON
ap-9572	201	2	ii	ii	VERB
ap-9572	202	1	i	i	NOUN
ap-9572	202	2	ii	ii	PROPN
ap-9572	202	3	β2	β2	VERB
ap-9572	202	4	↓	↓	PROPN
ap-9572	202	5	0.0	0.0	NUM
ap-9572	202	6	6	6	NUM
ap-9572	202	7	462	462	NUM
ap-9572	202	8	1	1	NUM
ap-9572	202	9	623	623	NUM
ap-9572	202	10	6	6	NUM
ap-9572	202	11	033	033	NUM
ap-9572	202	12	1	1	NUM
ap-9572	202	13	512	512	NUM
ap-9572	202	14	6	6	NUM
ap-9572	202	15	897	897	NUM
ap-9572	202	16	1	1	NUM
ap-9572	202	17	728	728	NUM
ap-9572	202	18	6	6	NUM
ap-9572	202	19	504	504	NUM
ap-9572	202	20	1	1	NUM
ap-9572	202	21	681	681	NUM
ap-9572	202	22	0.2	0.2	NUM
ap-9572	202	23	6	6	NUM
ap-9572	202	24	102	102	NUM
ap-9572	202	25	1	1	NUM
ap-9572	202	26	543	543	NUM
ap-9572	202	27	5	5	NUM
ap-9572	202	28	697	697	NUM
ap-9572	202	29	1	1	NUM
ap-9572	202	30	465	465	NUM
ap-9572	202	31	6	6	NUM
ap-9572	202	32	537	537	NUM
ap-9572	202	33	1	1	NUM
ap-9572	202	34	609	609	NUM
ap-9572	202	35	6	6	NUM
ap-9572	202	36	021	021	NUM
ap-9572	202	37	1	1	NUM
ap-9572	202	38	515	515	NUM
ap-9572	202	39	0.4	0.4	NUM
ap-9572	202	40	5	5	NUM
ap-9572	202	41	761	761	NUM
ap-9572	202	42	1	1	NUM
ap-9572	202	43	462	462	NUM
ap-9572	202	44	5	5	NUM
ap-9572	202	45	318	318	NUM
ap-9572	202	46	1	1	NUM
ap-9572	202	47	324	324	NUM
ap-9572	202	48	6	6	NUM
ap-9572	202	49	193	193	NUM
ap-9572	202	50	1	1	NUM
ap-9572	202	51	537	537	NUM
ap-9572	202	52	5	5	NUM
ap-9572	202	53	576	576	NUM
ap-9572	202	54	1	1	NUM
ap-9572	202	55	446	446	NUM
ap-9572	202	56	0.6	0.6	NUM
ap-9572	202	57	5	5	NUM
ap-9572	202	58	384	384	NUM
ap-9572	202	59	1	1	NUM
ap-9572	202	60	356	356	NUM
ap-9572	202	61	4	4	NUM
ap-9572	202	62	866	866	NUM
ap-9572	202	63	1	1	NUM
ap-9572	202	64	243	243	NUM
ap-9572	202	65	5	5	NUM
ap-9572	202	66	903	903	NUM
ap-9572	202	67	1	1	NUM
ap-9572	202	68	429	429	NUM
ap-9572	202	69	5	5	NUM
ap-9572	202	70	167	167	NUM
ap-9572	202	71	1	1	NUM
ap-9572	202	72	333	333	NUM
ap-9572	202	73	0.8	0.8	NUM
ap-9572	202	74	5	5	NUM
ap-9572	202	75	049	049	NUM
ap-9572	202	76	1	1	NUM
ap-9572	202	77	253	253	NUM
ap-9572	202	78	4	4	NUM
ap-9572	202	79	613	613	NUM
ap-9572	202	80	1	1	NUM
ap-9572	202	81	117	117	NUM
ap-9572	202	82	5	5	NUM
ap-9572	202	83	413	413	NUM
ap-9572	202	84	1	1	NUM
ap-9572	202	85	316	316	NUM
ap-9572	202	86	4	4	NUM
ap-9572	202	87	791	791	NUM
ap-9572	202	88	1	1	NUM
ap-9572	202	89	211	211	NUM
ap-9572	202	90	1.0	1.0	NUM
ap-9572	202	91	4	4	NUM
ap-9572	202	92	703	703	NUM
ap-9572	202	93	1	1	NUM
ap-9572	202	94	184	184	NUM
ap-9572	202	95	4	4	NUM
ap-9572	202	96	264	264	NUM
ap-9572	202	97	1	1	NUM
ap-9572	202	98	058	058	NUM
ap-9572	202	99	4	4	NUM
ap-9572	202	100	998	998	NUM
ap-9572	202	101	1	1	NUM
ap-9572	202	102	251	251	NUM
ap-9572	202	103	4	4	NUM
ap-9572	202	104	448	448	NUM
ap-9572	202	105	1	1	NUM
ap-9572	202	106	135	135	NUM
ap-9572	202	107	table	table	NOUN
ap-9572	202	108	5	5	NUM
ap-9572	202	109	.	.	PUNCT
ap-9572	202	110	variation	variation	NOUN
ap-9572	202	111	of	of	ADP
ap-9572	202	112	tp	tp	X
ap-9572	202	113	(	(	PUNCT
ap-9572	202	114	*	*	NOUN
ap-9572	202	115	10−6	10−6	NUM
ap-9572	202	116	in	in	ADP
ap-9572	202	117	seconds	second	NOUN
ap-9572	202	118	)	)	PUNCT
ap-9572	202	119	with	with	ADP
ap-9572	202	120	different	different	ADJ
ap-9572	202	121	β2	β2	NOUN
ap-9572	202	122	and	and	CCONJ
ap-9572	202	123	constant	constant	ADJ
ap-9572	202	124	a	a	DET
ap-9572	202	125	b	b	NOUN
ap-9572	202	126	=	=	SYM
ap-9572	202	127	1.5	1.5	NUM
ap-9572	202	128	for	for	ADP
ap-9572	202	129	all	all	DET
ap-9572	202	130	x	x	PUNCT
ap-9572	202	131	and	and	CCONJ
ap-9572	202	132	y	y	PROPN
ap-9572	202	133	,	,	PUNCT
ap-9572	202	134	see	see	VERB
ap-9572	202	135	figure	figure	NOUN
ap-9572	202	136	5	5	NUM
ap-9572	202	137	.	.	NOUN
ap-9572	202	138	0	0	NUM
ap-9572	203	1	1000	1000	NUM
ap-9572	203	2	2000	2000	NUM
ap-9572	203	3	3000	3000	NUM
ap-9572	203	4	4000	4000	NUM
ap-9572	203	5	5000	5000	NUM
ap-9572	203	6	6000	6000	NUM
ap-9572	203	7	7000	7000	NUM
ap-9572	203	8	8000	8000	NUM
ap-9572	203	9	0	0	NUM
ap-9572	203	10	0.2	0.2	NUM
ap-9572	203	11	0.4	0.4	NUM
ap-9572	203	12	0.6	0.6	NUM
ap-9572	203	13	0.8	0.8	NUM
ap-9572	203	14	1	1	NUM
ap-9572	203	15	first	first	ADJ
ap-9572	203	16	mode	mode	NOUN
ap-9572	203	17	α1=0,β1=0,α=0	α1=0,β1=0,α=0	NUM
ap-9572	203	18	second	second	ADJ
ap-9572	203	19	mode	mode	PROPN
ap-9572	203	20	α1=0,β1=0	α1=0,β1=0	PROPN
ap-9572	203	21	,	,	PUNCT
ap-9572	203	22	α=0	α=0	PROPN
ap-9572	203	23	first	first	ADJ
ap-9572	203	24	mode	mode	VERB
ap-9572	203	25	α1=0,β1=0.4,α=0.3	α1=0,β1=0.4,α=0.3	DET
ap-9572	203	26	second	second	ADJ
ap-9572	203	27	mode	mode	NOUN
ap-9572	203	28	α1=0,β1=0.4,α=0.3	α1=0,β1=0.4,α=0.3	PRON
ap-9572	203	29	first	first	ADJ
ap-9572	203	30	mode	mode	NOUN
ap-9572	203	31	α1=0.4,β1=0,α=0	α1=0.4,β1=0,α=0	DET
ap-9572	203	32	second	second	ADJ
ap-9572	203	33	mode	mode	NOUN
ap-9572	203	34	α1=0.4,β1=0,α=0	α1=0.4,β1=0,α=0	DET
ap-9572	203	35	first	first	ADJ
ap-9572	203	36	mode	mode	NOUN
ap-9572	203	37	α1=0.4,β1=0.4,α=0.3	α1=0.4,β1=0.4,α=0.3	DET
ap-9572	203	38	second	second	ADJ
ap-9572	203	39	mode	mode	NOUN
ap-9572	203	40	α1=0.4,β1=0.4,α=0.3	α1=0.4,β1=0.4,α=0.3	DET
ap-9572	203	41	figure	figure	NOUN
ap-9572	203	42	5	5	NUM
ap-9572	203	43	.	.	PUNCT
ap-9572	203	44	variation	variation	NOUN
ap-9572	203	45	of	of	ADP
ap-9572	203	46	tp	tp	X
ap-9572	203	47	(	(	PUNCT
ap-9572	203	48	*	*	NOUN
ap-9572	203	49	10−6	10−6	NUM
ap-9572	203	50	in	in	ADP
ap-9572	203	51	seconds	second	NOUN
ap-9572	203	52	)	)	PUNCT
ap-9572	203	53	with	with	ADP
ap-9572	203	54	different	different	ADJ
ap-9572	203	55	β2	β2	NOUN
ap-9572	203	56	and	and	CCONJ
ap-9572	203	57	constant	constant	ADJ
ap-9572	203	58	a	a	DET
ap-9572	203	59	b	b	NOUN
ap-9572	203	60	=	=	SYM
ap-9572	203	61	1.5	1.5	NUM
ap-9572	203	62	for	for	ADP
ap-9572	203	63	all	all	DET
ap-9572	203	64	x	x	SYM
ap-9572	203	65	and	and	CCONJ
ap-9572	203	66	y	y	PROPN
ap-9572	203	67	.	.	PUNCT
ap-9572	204	1	α	α	X
ap-9572	204	2	=	=	NOUN
ap-9572	204	3	0.0	0.0	NUM
ap-9572	204	4	α	α	NOUN
ap-9572	204	5	=	=	SYM
ap-9572	204	6	0.3	0.3	NUM
ap-9572	204	7	β1	β1	NOUN
ap-9572	204	8	=	=	PUNCT
ap-9572	204	9	0.0	0.0	NUM
ap-9572	204	10	β2	β2	NOUN
ap-9572	204	11	=	=	SYM
ap-9572	204	12	0.0	0.0	NUM
ap-9572	204	13	β1	β1	NOUN
ap-9572	204	14	=	=	PUNCT
ap-9572	204	15	0.4	0.4	NUM
ap-9572	204	16	β2	β2	NOUN
ap-9572	204	17	=	=	PROPN
ap-9572	204	18	0.2	0.2	NUM
ap-9572	204	19	β1	β1	NOUN
ap-9572	204	20	=	=	PUNCT
ap-9572	204	21	0.0	0.0	NUM
ap-9572	204	22	β2	β2	NOUN
ap-9572	204	23	=	=	SYM
ap-9572	204	24	0.0	0.0	NUM
ap-9572	204	25	β1	β1	NOUN
ap-9572	204	26	=	=	PUNCT
ap-9572	204	27	0.4	0.4	NUM
ap-9572	204	28	β2	β2	NOUN
ap-9572	204	29	=	=	NOUN
ap-9572	204	30	0.2	0.2	NUM
ap-9572	204	31	mode	mode	NOUN
ap-9572	204	32	→	→	PUNCT
ap-9572	205	1	i	i	NOUN
ap-9572	205	2	ii	ii	VERB
ap-9572	206	1	i	i	PRON
ap-9572	206	2	ii	ii	VERB
ap-9572	207	1	i	i	PRON
ap-9572	207	2	ii	ii	VERB
ap-9572	208	1	i	i	NOUN
ap-9572	208	2	ii	ii	PROPN
ap-9572	208	3	α1	α1	PROPN
ap-9572	208	4	↓	↓	NOUN
ap-9572	208	5	0.0	0.0	NUM
ap-9572	208	6	6	6	NUM
ap-9572	208	7	462	462	NUM
ap-9572	208	8	1	1	NUM
ap-9572	208	9	623	623	NUM
ap-9572	208	10	5	5	NUM
ap-9572	208	11	324	324	NUM
ap-9572	208	12	1	1	NUM
ap-9572	208	13	332	332	NUM
ap-9572	208	14	7	7	NUM
ap-9572	208	15	083	083	NUM
ap-9572	208	16	1	1	NUM
ap-9572	208	17	833	833	NUM
ap-9572	208	18	5	5	NUM
ap-9572	208	19	697	697	NUM
ap-9572	208	20	1	1	NUM
ap-9572	208	21	465	465	NUM
ap-9572	208	22	0.2	0.2	NUM
ap-9572	208	23	6	6	NUM
ap-9572	209	1	695	695	NUM
ap-9572	209	2	1	1	NUM
ap-9572	209	3	687	687	NUM
ap-9572	209	4	5	5	NUM
ap-9572	209	5	511	511	NUM
ap-9572	209	6	1	1	NUM
ap-9572	209	7	426	426	NUM
ap-9572	209	8	7	7	NUM
ap-9572	209	9	291	291	NUM
ap-9572	209	10	1	1	NUM
ap-9572	209	11	890	890	NUM
ap-9572	209	12	5	5	NUM
ap-9572	209	13	889	889	NUM
ap-9572	209	14	1	1	NUM
ap-9572	209	15	504	504	NUM
ap-9572	209	16	0.4	0.4	NUM
ap-9572	209	17	6	6	NUM
ap-9572	209	18	897	897	NUM
ap-9572	209	19	1	1	NUM
ap-9572	209	20	728	728	NUM
ap-9572	209	21	5	5	NUM
ap-9572	209	22	543	543	NUM
ap-9572	209	23	1	1	NUM
ap-9572	209	24	433	433	NUM
ap-9572	209	25	7	7	NUM
ap-9572	209	26	489	489	NUM
ap-9572	209	27	1	1	NUM
ap-9572	209	28	930	930	NUM
ap-9572	209	29	6	6	NUM
ap-9572	209	30	021	021	NUM
ap-9572	209	31	1	1	NUM
ap-9572	209	32	515	515	NUM
ap-9572	209	33	0.6	0.6	NUM
ap-9572	209	34	7	7	NUM
ap-9572	209	35	096	096	NUM
ap-9572	209	36	1	1	NUM
ap-9572	209	37	786	786	NUM
ap-9572	209	38	5	5	NUM
ap-9572	209	39	747	747	NUM
ap-9572	209	40	1	1	NUM
ap-9572	209	41	522	522	NUM
ap-9572	209	42	7	7	NUM
ap-9572	209	43	714	714	NUM
ap-9572	209	44	1	1	NUM
ap-9572	209	45	996	996	NUM
ap-9572	209	46	6	6	NUM
ap-9572	209	47	172	172	NUM
ap-9572	209	48	1	1	NUM
ap-9572	209	49	607	607	NUM
ap-9572	209	50	0.8	0.8	NUM
ap-9572	209	51	7	7	NUM
ap-9572	209	52	321	321	NUM
ap-9572	209	53	1	1	NUM
ap-9572	209	54	834	834	NUM
ap-9572	209	55	5	5	NUM
ap-9572	209	56	864	864	NUM
ap-9572	209	57	1	1	NUM
ap-9572	209	58	597	597	NUM
ap-9572	209	59	7	7	NUM
ap-9572	209	60	973	973	NUM
ap-9572	209	61	2	2	NUM
ap-9572	209	62	066	066	NUM
ap-9572	209	63	6	6	NUM
ap-9572	209	64	290	290	NUM
ap-9572	209	65	1	1	NUM
ap-9572	209	66	673	673	NUM
ap-9572	209	67	1.0	1.0	NUM
ap-9572	209	68	7	7	NUM
ap-9572	209	69	509	509	NUM
ap-9572	209	70	1	1	NUM
ap-9572	209	71	888	888	NUM
ap-9572	209	72	5	5	NUM
ap-9572	209	73	933	933	NUM
ap-9572	209	74	1	1	NUM
ap-9572	209	75	654	654	NUM
ap-9572	209	76	8	8	NUM
ap-9572	209	77	211	211	NUM
ap-9572	209	78	2	2	NUM
ap-9572	209	79	127	127	NUM
ap-9572	209	80	6	6	NUM
ap-9572	209	81	443	443	NUM
ap-9572	209	82	1	1	NUM
ap-9572	209	83	741	741	NUM
ap-9572	209	84	table	table	NOUN
ap-9572	209	85	6	6	NUM
ap-9572	209	86	.	.	PUNCT
ap-9572	209	87	variation	variation	NOUN
ap-9572	209	88	of	of	ADP
ap-9572	209	89	tp	tp	X
ap-9572	209	90	(	(	PUNCT
ap-9572	209	91	*	*	NOUN
ap-9572	209	92	10−6	10−6	NUM
ap-9572	209	93	in	in	ADP
ap-9572	209	94	seconds	second	NOUN
ap-9572	209	95	)	)	PUNCT
ap-9572	209	96	with	with	ADP
ap-9572	209	97	different	different	ADJ
ap-9572	209	98	α1	α1	PROPN
ap-9572	209	99	and	and	CCONJ
ap-9572	209	100	constant	constant	ADJ
ap-9572	209	101	a	a	DET
ap-9572	209	102	b	b	NOUN
ap-9572	209	103	=	=	SYM
ap-9572	209	104	1.5	1.5	NUM
ap-9572	209	105	for	for	ADP
ap-9572	209	106	all	all	DET
ap-9572	209	107	x	x	PUNCT
ap-9572	209	108	and	and	CCONJ
ap-9572	209	109	y	y	PROPN
ap-9572	209	110	,	,	PUNCT
ap-9572	209	111	see	see	VERB
ap-9572	209	112	figure	figure	NOUN
ap-9572	209	113	6	6	NUM
ap-9572	209	114	.	.	PUNCT
ap-9572	209	115	modes	mode	NOUN
ap-9572	209	116	.	.	PUNCT
ap-9572	210	1	the	the	DET
ap-9572	210	2	graph	graph	NOUN
ap-9572	210	3	shown	show	VERB
ap-9572	210	4	in	in	ADP
ap-9572	210	5	figure	figure	NOUN
ap-9572	210	6	5	5	NUM
ap-9572	210	7	shows	show	VERB
ap-9572	210	8	that	that	SCONJ
ap-9572	210	9	the	the	DET
ap-9572	210	10	period	period	NOUN
ap-9572	210	11	(	(	PUNCT
ap-9572	210	12	tp	tp	NOUN
ap-9572	210	13	)	)	PUNCT
ap-9572	210	14	decreases	decrease	NOUN
ap-9572	210	15	as	as	SCONJ
ap-9572	210	16	β2	β2	VERB
ap-9572	210	17	increases	increase	NOUN
ap-9572	210	18	for	for	ADP
ap-9572	210	19	both	both	DET
ap-9572	210	20	modes	mode	NOUN
ap-9572	210	21	of	of	ADP
ap-9572	210	22	vibration	vibration	NOUN
ap-9572	210	23	.	.	PUNCT
ap-9572	211	1	table	table	NOUN
ap-9572	211	2	6	6	NUM
ap-9572	211	3	deals	deal	NOUN
ap-9572	211	4	with	with	ADP
ap-9572	211	5	the	the	DET
ap-9572	211	6	variation	variation	NOUN
ap-9572	211	7	of	of	ADP
ap-9572	211	8	tp	tp	X
ap-9572	211	9	(	(	PUNCT
ap-9572	211	10	*	*	NOUN
ap-9572	211	11	10−6	10−6	NUM
ap-9572	211	12	in	in	ADP
ap-9572	211	13	seconds	second	NOUN
ap-9572	211	14	)	)	PUNCT
ap-9572	211	15	with	with	ADP
ap-9572	211	16	different	different	ADJ
ap-9572	211	17	α1(0.0	α1(0.0	NUM
ap-9572	211	18	,	,	PUNCT
ap-9572	211	19	0.2	0.2	NUM
ap-9572	211	20	,	,	PUNCT
ap-9572	211	21	0.4	0.4	NUM
ap-9572	211	22	,	,	PUNCT
ap-9572	211	23	0.6	0.6	NUM
ap-9572	211	24	,	,	PUNCT
ap-9572	211	25	0.8	0.8	NUM
ap-9572	211	26	,	,	PUNCT
ap-9572	211	27	1.0	1.0	NUM
ap-9572	211	28	)	)	PUNCT
ap-9572	211	29	and	and	CCONJ
ap-9572	211	30	constant	constant	ADJ
ap-9572	211	31	a	a	DET
ap-9572	211	32	b	b	NOUN
ap-9572	211	33	=	=	SYM
ap-9572	211	34	1.5	1.5	NUM
ap-9572	211	35	for	for	ADP
ap-9572	211	36	all	all	DET
ap-9572	211	37	x	x	NOUN
ap-9572	211	38	and	and	CCONJ
ap-9572	211	39	y	y	PROPN
ap-9572	211	40	.	.	PUNCT
ap-9572	212	1	it	it	PRON
ap-9572	212	2	is	be	AUX
ap-9572	212	3	observed	observe	VERB
ap-9572	212	4	that	that	SCONJ
ap-9572	212	5	the	the	DET
ap-9572	212	6	value	value	NOUN
ap-9572	212	7	of	of	ADP
ap-9572	212	8	tp	tp	NOUN
ap-9572	212	9	increases	increase	NOUN
ap-9572	212	10	as	as	ADP
ap-9572	212	11	α1	α1	PROPN
ap-9572	212	12	increases	increase	NOUN
ap-9572	212	13	from	from	ADP
ap-9572	212	14	0.0	0.0	NUM
ap-9572	212	15	to	to	ADP
ap-9572	212	16	1.0	1.0	NUM
ap-9572	212	17	for	for	ADP
ap-9572	212	18	both	both	DET
ap-9572	212	19	modes	mode	NOUN
ap-9572	212	20	of	of	ADP
ap-9572	212	21	vibration	vibration	NOUN
ap-9572	212	22	.	.	PUNCT
ap-9572	213	1	the	the	DET
ap-9572	213	2	results	result	NOUN
ap-9572	213	3	shown	show	VERB
ap-9572	213	4	in	in	ADP
ap-9572	213	5	table	table	NOUN
ap-9572	213	6	6	6	NUM
ap-9572	213	7	are	be	AUX
ap-9572	213	8	supported	support	VERB
ap-9572	213	9	by	by	ADP
ap-9572	213	10	the	the	DET
ap-9572	213	11	graph	graph	NOUN
ap-9572	213	12	shown	show	VERB
ap-9572	213	13	in	in	ADP
ap-9572	213	14	figure	figure	NOUN
ap-9572	213	15	6	6	NUM
ap-9572	213	16	.	.	PUNCT
ap-9572	214	1	tables	table	NOUN
ap-9572	214	2	7–9	7–9	PRON
ap-9572	214	3	show	show	VERB
ap-9572	214	4	the	the	DET
ap-9572	214	5	value	value	NOUN
ap-9572	214	6	of	of	ADP
ap-9572	214	7	w	w	PROPN
ap-9572	214	8	(	(	PUNCT
ap-9572	214	9	*	*	NOUN
ap-9572	214	10	10−5	10−5	NUM
ap-9572	214	11	)	)	PUNCT
ap-9572	214	12	for	for	ADP
ap-9572	214	13	the	the	DET
ap-9572	214	14	constant	constant	ADJ
ap-9572	214	15	a	a	DET
ap-9572	214	16	b	b	NOUN
ap-9572	214	17	=	=	SYM
ap-9572	214	18	1.5	1.5	NUM
ap-9572	214	19	and	and	CCONJ
ap-9572	214	20	for	for	ADP
ap-9572	214	21	different	different	ADJ
ap-9572	214	22	x	x	NOUN
ap-9572	214	23	and	and	CCONJ
ap-9572	214	24	y	y	PROPN
ap-9572	214	25	with	with	ADP
ap-9572	214	26	three	three	NUM
ap-9572	214	27	different	different	ADJ
ap-9572	214	28	variations	variation	NOUN
ap-9572	214	29	of	of	ADP
ap-9572	214	30	the	the	DET
ap-9572	214	31	values	value	NOUN
ap-9572	214	32	of	of	ADP
ap-9572	214	33	α	α	NOUN
ap-9572	214	34	,	,	PUNCT
ap-9572	214	35	β1	β1	PROPN
ap-9572	214	36	,	,	PUNCT
ap-9572	214	37	β2	β2	NOUN
ap-9572	214	38	and	and	CCONJ
ap-9572	214	39	α1	α1	PROPN
ap-9572	214	40	given	give	VERB
ap-9572	214	41	by	by	ADP
ap-9572	214	42	(	(	PUNCT
ap-9572	214	43	α	α	NOUN
ap-9572	214	44	=	=	SYM
ap-9572	214	45	β1	β1	PROPN
ap-9572	214	46	=	=	SYM
ap-9572	214	47	β2	β2	NOUN
ap-9572	214	48	=	=	SYM
ap-9572	214	49	α1	α1	PROPN
ap-9572	214	50	=	=	SYM
ap-9572	214	51	0.0	0.0	NUM
ap-9572	214	52	)	)	PUNCT
ap-9572	214	53	,	,	PUNCT
ap-9572	214	54	(	(	PUNCT
ap-9572	214	55	α	α	NOUN
ap-9572	214	56	=	=	SYM
ap-9572	214	57	β1	β1	PROPN
ap-9572	214	58	=	=	SYM
ap-9572	214	59	β2	β2	NOUN
ap-9572	214	60	=	=	NOUN
ap-9572	214	61	0.0	0.0	NUM
ap-9572	214	62	,	,	PUNCT
ap-9572	214	63	α1	α1	PROPN
ap-9572	214	64	=	=	SYM
ap-9572	214	65	0.4	0.4	NUM
ap-9572	214	66	)	)	PUNCT
ap-9572	214	67	,	,	PUNCT
ap-9572	214	68	(	(	PUNCT
ap-9572	214	69	α	α	NOUN
ap-9572	214	70	=	=	NOUN
ap-9572	214	71	0.2	0.2	NUM
ap-9572	214	72	,	,	PUNCT
ap-9572	214	73	β1	β1	PROPN
ap-9572	214	74	=	=	PUNCT
ap-9572	214	75	0.3	0.3	NUM
ap-9572	214	76	,	,	PUNCT
ap-9572	214	77	β2	β2	NOUN
ap-9572	214	78	=	=	NOUN
ap-9572	214	79	0.4	0.4	NUM
ap-9572	214	80	,	,	PUNCT
ap-9572	214	81	α1	α1	PROPN
ap-9572	214	82	=	=	SYM
ap-9572	214	83	0.4	0.4	NUM
ap-9572	214	84	)	)	PUNCT
ap-9572	214	85	,	,	PUNCT
ap-9572	214	86	respectively	respectively	ADV
ap-9572	214	87	.	.	PUNCT
ap-9572	215	1	from	from	ADP
ap-9572	215	2	these	these	DET
ap-9572	215	3	tables	table	NOUN
ap-9572	215	4	,	,	PUNCT
ap-9572	215	5	it	it	PRON
ap-9572	215	6	can	can	AUX
ap-9572	215	7	clearly	clearly	ADV
ap-9572	215	8	be	be	AUX
ap-9572	215	9	seen	see	VERB
ap-9572	215	10	that	that	SCONJ
ap-9572	215	11	as	as	SCONJ
ap-9572	215	12	x̄	x̄	NOUN
ap-9572	215	13	increases	increase	VERB
ap-9572	215	14	for	for	ADP
ap-9572	215	15	different	different	ADJ
ap-9572	215	16	values	value	NOUN
ap-9572	215	17	of	of	ADP
ap-9572	215	18	ȳ	ȳ	PROPN
ap-9572	215	19	,	,	PUNCT
ap-9572	215	20	the	the	DET
ap-9572	215	21	value	value	NOUN
ap-9572	215	22	of	of	ADP
ap-9572	215	23	w	w	PROPN
ap-9572	215	24	first	first	ADJ
ap-9572	215	25	increases	increase	NOUN
ap-9572	215	26	and	and	CCONJ
ap-9572	215	27	then	then	ADV
ap-9572	215	28	decreases	decrease	VERB
ap-9572	215	29	to	to	ADP
ap-9572	215	30	zero	zero	NUM
ap-9572	215	31	for	for	ADP
ap-9572	215	32	the	the	DET
ap-9572	215	33	first	first	ADJ
ap-9572	215	34	mode	mode	NOUN
ap-9572	215	35	of	of	ADP
ap-9572	215	36	vibration	vibration	NOUN
ap-9572	215	37	.	.	PUNCT
ap-9572	216	1	for	for	ADP
ap-9572	216	2	the	the	DET
ap-9572	216	3	second	second	ADJ
ap-9572	216	4	mode	mode	NOUN
ap-9572	216	5	of	of	ADP
ap-9572	216	6	vibration	vibration	NOUN
ap-9572	216	7	,	,	PUNCT
ap-9572	216	8	it	it	PRON
ap-9572	216	9	can	can	AUX
ap-9572	216	10	be	be	AUX
ap-9572	216	11	seen	see	VERB
ap-9572	216	12	that	that	SCONJ
ap-9572	216	13	the	the	DET
ap-9572	216	14	304	304	NUM
ap-9572	216	15	vol	vol	NOUN
ap-9572	216	16	.	.	PUNCT
ap-9572	217	1	64	64	NUM
ap-9572	217	2	no	no	NOUN
ap-9572	217	3	.	.	PUNCT
ap-9572	218	1	4/2024	4/2024	NUM
ap-9572	218	2	non	non	ADJ
ap-9572	218	3	-	-	ADJ
ap-9572	218	4	homogeneity	homogeneity	ADJ
ap-9572	218	5	effect	effect	NOUN
ap-9572	218	6	on	on	ADP
ap-9572	218	7	the	the	DET
ap-9572	218	8	vibration	vibration	NOUN
ap-9572	218	9	of	of	ADP
ap-9572	218	10	.	.	PUNCT
ap-9572	218	11	.	.	PUNCT
ap-9572	219	1	.	.	PUNCT
ap-9572	220	1	0	0	NUM
ap-9572	221	1	1000	1000	NUM
ap-9572	221	2	2000	2000	NUM
ap-9572	221	3	3000	3000	NUM
ap-9572	221	4	4000	4000	NUM
ap-9572	221	5	5000	5000	NUM
ap-9572	221	6	6000	6000	NUM
ap-9572	221	7	7000	7000	NUM
ap-9572	221	8	8000	8000	NUM
ap-9572	221	9	9000	9000	NUM
ap-9572	221	10	0	0	NUM
ap-9572	221	11	0.2	0.2	NUM
ap-9572	221	12	0.4	0.4	NUM
ap-9572	221	13	0.6	0.6	NUM
ap-9572	221	14	0.8	0.8	NUM
ap-9572	221	15	1	1	NUM
ap-9572	221	16	first	first	ADJ
ap-9572	221	17	mode	mode	NOUN
ap-9572	221	18	α=0,β1=0,β2=0	α=0,β1=0,β2=0	PROPN
ap-9572	221	19	second	second	ADJ
ap-9572	221	20	mode	mode	NOUN
ap-9572	221	21	α=0,β1=0,β2=0	α=0,β1=0,β2=0	PROPN
ap-9572	221	22	first	first	ADJ
ap-9572	221	23	mode	mode	PROPN
ap-9572	221	24	α=0,β1=0.4,β2=0.2	α=0,β1=0.4,β2=0.2	PROPN
ap-9572	221	25	second	second	ADJ
ap-9572	221	26	mode	mode	PROPN
ap-9572	221	27	α=0,β1=0.4,β2=0.2	α=0,β1=0.4,β2=0.2	PROPN
ap-9572	221	28	first	first	ADJ
ap-9572	221	29	mode	mode	PROPN
ap-9572	221	30	α=0.3,β1=0,β2=0	α=0.3,β1=0,β2=0	X
ap-9572	221	31	second	second	ADJ
ap-9572	221	32	mode	mode	NOUN
ap-9572	221	33	α=0.3,β1=0,β2=0	α=0.3,β1=0,β2=0	NUM
ap-9572	221	34	first	first	ADJ
ap-9572	221	35	mode	mode	NOUN
ap-9572	221	36	α=0.3,β1=0.4,β2=0.2	α=0.3,β1=0.4,β2=0.2	NUM
ap-9572	221	37	second	second	ADJ
ap-9572	221	38	mode	mode	NOUN
ap-9572	221	39	α=0.3,β1=0.4,β2=0.2	α=0.3,β1=0.4,β2=0.2	NUM
ap-9572	221	40	figure	figure	NOUN
ap-9572	221	41	6	6	NUM
ap-9572	221	42	.	.	PUNCT
ap-9572	221	43	variation	variation	NOUN
ap-9572	221	44	of	of	ADP
ap-9572	221	45	tp	tp	X
ap-9572	221	46	(	(	PUNCT
ap-9572	221	47	*	*	NOUN
ap-9572	221	48	10−6	10−6	NUM
ap-9572	221	49	in	in	ADP
ap-9572	221	50	seconds	second	NOUN
ap-9572	221	51	)	)	PUNCT
ap-9572	221	52	with	with	ADP
ap-9572	221	53	different	different	ADJ
ap-9572	221	54	α1	α1	PROPN
ap-9572	221	55	and	and	CCONJ
ap-9572	221	56	constant	constant	ADJ
ap-9572	221	57	a	a	DET
ap-9572	221	58	b	b	NOUN
ap-9572	221	59	=	=	SYM
ap-9572	221	60	1.5	1.5	NUM
ap-9572	221	61	for	for	ADP
ap-9572	221	62	all	all	DET
ap-9572	221	63	x	x	NOUN
ap-9572	221	64	and	and	CCONJ
ap-9572	221	65	y	y	PROPN
ap-9572	221	66	.	.	PUNCT
ap-9572	222	1	y	y	PROPN
ap-9572	222	2	=	=	PUNCT
ap-9572	222	3	0.20	0.20	NUM
ap-9572	222	4	y	y	NOUN
ap-9572	222	5	=	=	SYM
ap-9572	222	6	0.60	0.60	NUM
ap-9572	222	7	mode	mode	NOUN
ap-9572	222	8	→	→	PUNCT
ap-9572	223	1	i	i	NOUN
ap-9572	223	2	ii	ii	VERB
ap-9572	224	1	i	i	NOUN
ap-9572	224	2	ii	ii	PROPN
ap-9572	225	1	x̄	x̄	PROPN
ap-9572	225	2	↓	↓	PROPN
ap-9572	226	1	t	t	PROPN
ap-9572	226	2	i	i	PRON
ap-9572	226	3	m	m	VERB
ap-9572	226	4	e	e	NOUN
ap-9572	226	5	=	=	PUNCT
ap-9572	226	6	0	0	NUM
ap-9572	226	7	.	.	NOUN
ap-9572	226	8	0	0	NUM
ap-9572	227	1	×	×	PROPN
ap-9572	227	2	t	t	NOUN
ap-9572	227	3	p	p	NOUN
ap-9572	227	4	0.0	0.0	NUM
ap-9572	227	5	0.0	0.0	NUM
ap-9572	227	6	0.0	0.0	NUM
ap-9572	227	7	0.0	0.0	NUM
ap-9572	227	8	0.0	0.0	NUM
ap-9572	227	9	0.2	0.2	NUM
ap-9572	227	10	126.32	126.32	NUM
ap-9572	227	11	38.87	38.87	NUM
ap-9572	227	12	427.32	427.32	NUM
ap-9572	227	13	14.52	14.52	NUM
ap-9572	227	14	0.4	0.4	NUM
ap-9572	227	15	303.71	303.71	NUM
ap-9572	227	16	6.12	6.12	NUM
ap-9572	227	17	1420.12	1420.12	NUM
ap-9572	227	18	26.73	26.73	NUM
ap-9572	227	19	0.6	0.6	NUM
ap-9572	227	20	303.71	303.71	NUM
ap-9572	227	21	6.12	6.12	NUM
ap-9572	227	22	1420.12	1420.12	NUM
ap-9572	227	23	26.73	26.73	NUM
ap-9572	227	24	0.8	0.8	NUM
ap-9572	227	25	126.32	126.32	NUM
ap-9572	227	26	38.87	38.87	NUM
ap-9572	227	27	427.32	427.32	NUM
ap-9572	227	28	14.52	14.52	NUM
ap-9572	227	29	1.0	1.0	NUM
ap-9572	227	30	0.0	0.0	NUM
ap-9572	227	31	0.0	0.0	NUM
ap-9572	227	32	0.0	0.0	NUM
ap-9572	227	33	0.0	0.0	NUM
ap-9572	227	34	t	t	NOUN
ap-9572	227	35	i	i	PRON
ap-9572	227	36	m	m	VERB
ap-9572	227	37	e	e	NOUN
ap-9572	227	38	=	=	SYM
ap-9572	227	39	5	5	NUM
ap-9572	227	40	.	.	NOUN
ap-9572	227	41	0	0	NUM
ap-9572	228	1	×	×	PROPN
ap-9572	228	2	t	t	NOUN
ap-9572	228	3	p	p	NOUN
ap-9572	228	4	0.0	0.0	NUM
ap-9572	228	5	0.0	0.0	NUM
ap-9572	228	6	0.0	0.0	NUM
ap-9572	228	7	0.0	0.0	NUM
ap-9572	228	8	0.0	0.0	NUM
ap-9572	228	9	0.2	0.2	NUM
ap-9572	228	10	55.12	55.12	NUM
ap-9572	228	11	1.38	1.38	NUM
ap-9572	228	12	187.31	187.31	NUM
ap-9572	228	13	0.53	0.53	NUM
ap-9572	228	14	0.4	0.4	NUM
ap-9572	228	15	132.32	132.32	NUM
ap-9572	228	16	0.21	0.21	NUM
ap-9572	228	17	623.16	623.16	NUM
ap-9572	228	18	1.01	1.01	NUM
ap-9572	228	19	0.6	0.6	NUM
ap-9572	228	20	132.32	132.32	NUM
ap-9572	228	21	0.21	0.21	NUM
ap-9572	228	22	623.16	623.16	NUM
ap-9572	228	23	1.01	1.01	NUM
ap-9572	228	24	0.8	0.8	NUM
ap-9572	228	25	55.12	55.12	NUM
ap-9572	228	26	1.38	1.38	NUM
ap-9572	228	27	187.31	187.31	NUM
ap-9572	228	28	0.53	0.53	NUM
ap-9572	228	29	1.0	1.0	NUM
ap-9572	228	30	0.0	0.0	NUM
ap-9572	228	31	0.0	0.0	NUM
ap-9572	228	32	0.0	0.0	NUM
ap-9572	228	33	0.0	0.0	NUM
ap-9572	228	34	table	table	NOUN
ap-9572	228	35	7	7	NUM
ap-9572	228	36	.	.	PUNCT
ap-9572	228	37	w(*10−5	w(*10−5	NUM
ap-9572	228	38	)	)	PUNCT
ap-9572	228	39	for	for	ADP
ap-9572	228	40	constant	constant	ADJ
ap-9572	228	41	a	a	DET
ap-9572	228	42	b	b	NOUN
ap-9572	228	43	=	=	SYM
ap-9572	228	44	1.5	1.5	NUM
ap-9572	228	45	and	and	CCONJ
ap-9572	228	46	α	α	NOUN
ap-9572	228	47	=	=	SYM
ap-9572	228	48	β1	β1	PROPN
ap-9572	228	49	=	=	SYM
ap-9572	228	50	β2	β2	NOUN
ap-9572	228	51	=	=	SYM
ap-9572	228	52	α1	α1	PROPN
ap-9572	228	53	=	=	SYM
ap-9572	228	54	0.0	0.0	NUM
ap-9572	228	55	and	and	CCONJ
ap-9572	228	56	for	for	ADP
ap-9572	228	57	different	different	ADJ
ap-9572	228	58	x	x	X
ap-9572	228	59	and	and	CCONJ
ap-9572	228	60	y	y	PROPN
ap-9572	228	61	,	,	PUNCT
ap-9572	228	62	see	see	VERB
ap-9572	228	63	figure	figure	NOUN
ap-9572	228	64	7	7	NUM
ap-9572	228	65	.	.	NOUN
ap-9572	228	66	value	value	NOUN
ap-9572	228	67	of	of	ADP
ap-9572	228	68	w	w	PROPN
ap-9572	228	69	for	for	ADP
ap-9572	228	70	y	y	PROPN
ap-9572	228	71	=	=	SYM
ap-9572	228	72	0.2	0.2	NUM
ap-9572	228	73	,	,	PUNCT
ap-9572	228	74	the	the	DET
ap-9572	228	75	value	value	NOUN
ap-9572	228	76	changes	change	VERB
ap-9572	228	77	frequently	frequently	ADV
ap-9572	228	78	as	as	SCONJ
ap-9572	228	79	it	it	PRON
ap-9572	228	80	first	first	ADV
ap-9572	228	81	increases	increase	VERB
ap-9572	228	82	and	and	CCONJ
ap-9572	228	83	then	then	ADV
ap-9572	228	84	decreases	decrease	VERB
ap-9572	228	85	,	,	PUNCT
ap-9572	228	86	then	then	ADV
ap-9572	228	87	repeats	repeat	VERB
ap-9572	228	88	this	this	DET
ap-9572	228	89	trend	trend	NOUN
ap-9572	228	90	by	by	ADP
ap-9572	228	91	increasing	increase	VERB
ap-9572	228	92	again	again	ADV
ap-9572	228	93	and	and	CCONJ
ap-9572	228	94	finally	finally	ADV
ap-9572	228	95	becoming	become	VERB
ap-9572	228	96	zero	zero	NUM
ap-9572	228	97	as	as	SCONJ
ap-9572	228	98	x̄	x̄	NOUN
ap-9572	228	99	increases	increase	VERB
ap-9572	228	100	but	but	CCONJ
ap-9572	228	101	for	for	ADP
ap-9572	228	102	y	y	PROPN
ap-9572	228	103	=	=	SYM
ap-9572	228	104	0.6	0.6	NUM
ap-9572	228	105	,	,	PUNCT
ap-9572	228	106	with	with	ADP
ap-9572	228	107	the	the	DET
ap-9572	228	108	increase	increase	NOUN
ap-9572	228	109	in	in	ADP
ap-9572	228	110	x	x	X
ap-9572	228	111	,	,	PUNCT
ap-9572	228	112	the	the	DET
ap-9572	228	113	value	value	NOUN
ap-9572	228	114	of	of	ADP
ap-9572	228	115	w	w	NOUN
ap-9572	228	116	varies	varie	NOUN
ap-9572	228	117	as	as	SCONJ
ap-9572	228	118	it	it	PRON
ap-9572	228	119	first	first	ADV
ap-9572	228	120	increases	increase	VERB
ap-9572	228	121	and	and	CCONJ
ap-9572	228	122	then	then	ADV
ap-9572	228	123	it	it	PRON
ap-9572	228	124	decreases	decrease	VERB
ap-9572	228	125	until	until	SCONJ
ap-9572	228	126	it	it	PRON
ap-9572	228	127	reaches	reach	VERB
ap-9572	228	128	zero	zero	NUM
ap-9572	228	129	.	.	PUNCT
ap-9572	229	1	the	the	DET
ap-9572	229	2	graphs	graph	NOUN
ap-9572	229	3	in	in	ADP
ap-9572	229	4	figures	figure	NOUN
ap-9572	229	5	7	7	NUM
ap-9572	229	6	,	,	PUNCT
ap-9572	229	7	8	8	NUM
ap-9572	229	8	and	and	CCONJ
ap-9572	229	9	9	9	NUM
ap-9572	229	10	support	support	VERB
ap-9572	229	11	the	the	DET
ap-9572	229	12	results	result	NOUN
ap-9572	229	13	of	of	ADP
ap-9572	229	14	tables	table	NOUN
ap-9572	229	15	7–9	7–9	NUM
ap-9572	229	16	.	.	PUNCT
ap-9572	230	1	tables	table	NOUN
ap-9572	230	2	10–12	10–12	PROPN
ap-9572	230	3	represent	represent	VERB
ap-9572	230	4	the	the	DET
ap-9572	230	5	deflection	deflection	NOUN
ap-9572	230	6	w	w	ADP
ap-9572	230	7	(	(	PUNCT
ap-9572	230	8	*	*	NOUN
ap-9572	230	9	10−5	10−5	NUM
ap-9572	230	10	)	)	PUNCT
ap-9572	230	11	for	for	ADP
ap-9572	230	12	x	x	X
ap-9572	230	13	=	=	PUNCT
ap-9572	230	14	y	y	PROPN
ap-9572	230	15	=	=	PUNCT
ap-9572	230	16	0.2	0.2	NUM
ap-9572	230	17	and	and	CCONJ
ap-9572	230	18	for	for	ADP
ap-9572	230	19	three	three	NUM
ap-9572	230	20	different	different	ADJ
ap-9572	230	21	cases	case	NOUN
ap-9572	230	22	,	,	PUNCT
ap-9572	230	23	namely	namely	ADV
ap-9572	230	24	(	(	PUNCT
ap-9572	230	25	for	for	ADP
ap-9572	230	26	different	different	ADJ
ap-9572	230	27	a	a	DET
ap-9572	230	28	b	b	NOUN
ap-9572	230	29	and	and	CCONJ
ap-9572	230	30	α	α	NOUN
ap-9572	230	31	=	=	SYM
ap-9572	230	32	β1	β1	PROPN
ap-9572	230	33	=	=	SYM
ap-9572	230	34	β2	β2	NOUN
ap-9572	230	35	=	=	SYM
ap-9572	230	36	α1	α1	PROPN
ap-9572	230	37	=	=	SYM
ap-9572	230	38	0.0	0.0	NUM
ap-9572	230	39	)	)	PUNCT
ap-9572	230	40	,	,	PUNCT
ap-9572	230	41	(	(	PUNCT
ap-9572	230	42	for	for	ADP
ap-9572	230	43	different	different	ADJ
ap-9572	230	44	a	a	DET
ap-9572	230	45	b	b	NOUN
ap-9572	230	46	and	and	CCONJ
ap-9572	230	47	α	α	NOUN
ap-9572	230	48	=	=	SYM
ap-9572	230	49	β1	β1	PROPN
ap-9572	230	50	=	=	SYM
ap-9572	230	51	β2	β2	NOUN
ap-9572	230	52	=	=	NOUN
ap-9572	230	53	0.0	0.0	NUM
ap-9572	230	54	,	,	PUNCT
ap-9572	230	55	α1	α1	PROPN
ap-9572	230	56	=	=	SYM
ap-9572	230	57	0.4	0.4	NUM
ap-9572	230	58	)	)	PUNCT
ap-9572	230	59	and	and	CCONJ
ap-9572	230	60	(	(	PUNCT
ap-9572	230	61	for	for	ADP
ap-9572	230	62	different	different	ADJ
ap-9572	230	63	a	a	DET
ap-9572	230	64	b	b	NOUN
ap-9572	230	65	and	and	CCONJ
ap-9572	230	66	α	α	NOUN
ap-9572	230	67	=	=	NOUN
ap-9572	230	68	0.3	0.3	NUM
ap-9572	230	69	,	,	PUNCT
ap-9572	230	70	β1	β1	PROPN
ap-9572	230	71	=	=	PUNCT
ap-9572	230	72	0.3	0.3	NUM
ap-9572	230	73	,	,	PUNCT
ap-9572	230	74	β2	β2	NOUN
ap-9572	230	75	=	=	NOUN
ap-9572	230	76	0.4	0.4	NUM
ap-9572	230	77	,	,	PUNCT
ap-9572	230	78	α1	α1	PROPN
ap-9572	230	79	=	=	SYM
ap-9572	230	80	0.4	0.4	NUM
ap-9572	230	81	)	)	PUNCT
ap-9572	230	82	respectively	respectively	ADV
ap-9572	230	83	.	.	PUNCT
ap-9572	231	1	from	from	ADP
ap-9572	231	2	these	these	DET
ap-9572	231	3	tables	table	NOUN
ap-9572	231	4	,	,	PUNCT
ap-9572	231	5	it	it	PRON
ap-9572	231	6	can	can	AUX
ap-9572	231	7	be	be	AUX
ap-9572	231	8	seen	see	VERB
ap-9572	231	9	that	that	SCONJ
ap-9572	231	10	the	the	DET
ap-9572	231	11	value	value	NOUN
ap-9572	231	12	of	of	ADP
ap-9572	231	13	w	w	NOUN
ap-9572	231	14	increases	increase	NOUN
ap-9572	231	15	continuously	continuously	ADV
ap-9572	231	16	at	at	ADP
ap-9572	231	17	time	time	NOUN
ap-9572	231	18	0.0×	0.0×	NUM
ap-9572	231	19	tp	tp	NOUN
ap-9572	231	20	,	,	PUNCT
ap-9572	231	21	it	it	PRON
ap-9572	231	22	is	be	AUX
ap-9572	231	23	also	also	ADV
ap-9572	231	24	observed	observe	VERB
ap-9572	231	25	that	that	SCONJ
ap-9572	231	26	with	with	ADP
ap-9572	231	27	the	the	DET
ap-9572	231	28	increase	increase	NOUN
ap-9572	231	29	there	there	PRON
ap-9572	231	30	is	be	VERB
ap-9572	231	31	slight	slight	ADJ
ap-9572	231	32	decrease	decrease	NOUN
ap-9572	231	33	at	at	ADP
ap-9572	231	34	the	the	DET
ap-9572	231	35	time	time	NOUN
ap-9572	231	36	5.0	5.0	NUM
ap-9572	231	37	×	×	NOUN
ap-9572	231	38	tp	tp	NOUN
ap-9572	231	39	for	for	ADP
ap-9572	231	40	the	the	DET
ap-9572	231	41	first	first	ADJ
ap-9572	231	42	mode	mode	NOUN
ap-9572	231	43	of	of	ADP
ap-9572	231	44	vibration	vibration	NOUN
ap-9572	231	45	but	but	CCONJ
ap-9572	231	46	it	it	PRON
ap-9572	231	47	is	be	AUX
ap-9572	231	48	also	also	ADV
ap-9572	231	49	noticed	notice	VERB
ap-9572	231	50	that	that	SCONJ
ap-9572	231	51	the	the	DET
ap-9572	231	52	decrease	decrease	NOUN
ap-9572	231	53	follows	follow	VERB
ap-9572	231	54	the	the	DET
ap-9572	231	55	increase	increase	NOUN
ap-9572	231	56	in	in	ADP
ap-9572	231	57	the	the	DET
ap-9572	231	58	value	value	NOUN
ap-9572	231	59	of	of	ADP
ap-9572	231	60	a	a	DET
ap-9572	231	61	b	b	NOUN
ap-9572	231	62	from	from	ADP
ap-9572	231	63	0.5	0.5	NUM
ap-9572	231	64	to	to	ADP
ap-9572	231	65	2.5	2.5	NUM
ap-9572	231	66	,	,	PUNCT
ap-9572	231	67	at	at	ADP
ap-9572	231	68	time	time	NOUN
ap-9572	231	69	0.0	0.0	NUM
ap-9572	231	70	×	×	NOUN
ap-9572	231	71	tp	tp	NOUN
ap-9572	231	72	and	and	CCONJ
ap-9572	231	73	at	at	ADP
ap-9572	231	74	time	time	NOUN
ap-9572	231	75	5.0	5.0	NUM
ap-9572	231	76	×	×	NOUN
ap-9572	231	77	tp	tp	NOUN
ap-9572	231	78	for	for	ADP
ap-9572	231	79	the	the	DET
ap-9572	231	80	second	second	ADJ
ap-9572	231	81	mode	mode	NOUN
ap-9572	231	82	of	of	ADP
ap-9572	231	83	vibration	vibration	NOUN
ap-9572	231	84	.	.	PUNCT
ap-9572	232	1	these	these	DET
ap-9572	232	2	results	result	NOUN
ap-9572	232	3	are	be	AUX
ap-9572	232	4	also	also	ADV
ap-9572	232	5	supported	support	VERB
ap-9572	232	6	by	by	ADP
ap-9572	232	7	the	the	DET
ap-9572	232	8	graphs	graph	NOUN
ap-9572	232	9	shown	show	VERB
ap-9572	232	10	in	in	ADP
ap-9572	232	11	figures	figure	NOUN
ap-9572	232	12	10–12	10–12	NUM
ap-9572	232	13	.	.	PUNCT
ap-9572	233	1	6	6	NUM
ap-9572	233	2	.	.	X
ap-9572	233	3	comparison	comparison	NOUN
ap-9572	233	4	of	of	ADP
ap-9572	233	5	the	the	DET
ap-9572	233	6	results	result	NOUN
ap-9572	233	7	of	of	ADP
ap-9572	233	8	the	the	DET
ap-9572	233	9	present	present	ADJ
ap-9572	233	10	study	study	NOUN
ap-9572	233	11	with	with	ADP
ap-9572	233	12	the	the	DET
ap-9572	233	13	previous	previous	ADJ
ap-9572	233	14	study	study	NOUN
ap-9572	233	15	the	the	DET
ap-9572	233	16	time	time	NOUN
ap-9572	233	17	function	function	NOUN
ap-9572	233	18	and	and	CCONJ
ap-9572	233	19	the	the	DET
ap-9572	233	20	deflection	deflection	NOUN
ap-9572	233	21	results	result	NOUN
ap-9572	233	22	obtained	obtain	VERB
ap-9572	233	23	in	in	ADP
ap-9572	233	24	the	the	DET
ap-9572	233	25	present	present	ADJ
ap-9572	233	26	study	study	NOUN
ap-9572	233	27	are	be	AUX
ap-9572	233	28	compared	compare	VERB
ap-9572	233	29	with	with	ADP
ap-9572	233	30	those	those	PRON
ap-9572	233	31	of	of	ADP
ap-9572	233	32	the	the	DET
ap-9572	233	33	reference	reference	NOUN
ap-9572	233	34	[	[	X
ap-9572	233	35	13	13	NUM
ap-9572	233	36	]	]	PUNCT
ap-9572	233	37	.	.	PUNCT
ap-9572	234	1	the	the	DET
ap-9572	234	2	comparison	comparison	NOUN
ap-9572	234	3	of	of	ADP
ap-9572	234	4	the	the	DET
ap-9572	234	5	results	result	NOUN
ap-9572	234	6	of	of	ADP
ap-9572	234	7	these	these	DET
ap-9572	234	8	305	305	NUM
ap-9572	234	9	sudhanshu	sudhanshu	NOUN
ap-9572	234	10	aggarwal	aggarwal	PROPN
ap-9572	234	11	acta	acta	PROPN
ap-9572	234	12	polytechnica	polytechnica	PROPN
ap-9572	234	13	0	0	NUM
ap-9572	234	14	200	200	NUM
ap-9572	234	15	400	400	NUM
ap-9572	234	16	600	600	NUM
ap-9572	234	17	800	800	NUM
ap-9572	234	18	1000	1000	NUM
ap-9572	234	19	1200	1200	NUM
ap-9572	234	20	1400	1400	NUM
ap-9572	234	21	1600	1600	NUM
ap-9572	234	22	1800	1800	NUM
ap-9572	234	23	0	0	NUM
ap-9572	234	24	0.2	0.2	NUM
ap-9572	234	25	0.4	0.4	NUM
ap-9572	234	26	0.6	0.6	NUM
ap-9572	234	27	0.8	0.8	NUM
ap-9572	234	28	1	1	NUM
ap-9572	234	29	first	first	ADJ
ap-9572	234	30	mode	mode	NOUN
ap-9572	234	31	time=0.k	time=0.k	PROPN
ap-9572	234	32	y=0.2	y=0.2	NOUN
ap-9572	234	33	first	first	PROPN
ap-9572	234	34	mode	mode	PROPN
ap-9572	234	35	time=0.k	time=0.k	X
ap-9572	234	36	y=0.6	y=0.6	NOUN
ap-9572	234	37	first	first	ADJ
ap-9572	234	38	mode	mode	PROPN
ap-9572	234	39	time=5.k	time=5.k	NOUN
ap-9572	234	40	y=0.2	y=0.2	NOUN
ap-9572	234	41	first	first	ADJ
ap-9572	234	42	mode	mode	PROPN
ap-9572	234	43	time=5.k	time=5.k	NOUN
ap-9572	234	44	y=0.6	y=0.6	NOUN
ap-9572	234	45	(	(	PUNCT
ap-9572	234	46	a	a	NOUN
ap-9572	234	47	)	)	PUNCT
ap-9572	234	48	.	.	PUNCT
ap-9572	235	1	first	first	ADJ
ap-9572	235	2	mode	mode	NOUN
ap-9572	235	3	.	.	PUNCT
ap-9572	236	1	0	0	NUM
ap-9572	237	1	5	5	NUM
ap-9572	237	2	10	10	NUM
ap-9572	237	3	15	15	NUM
ap-9572	237	4	20	20	NUM
ap-9572	237	5	25	25	NUM
ap-9572	237	6	30	30	NUM
ap-9572	237	7	35	35	NUM
ap-9572	237	8	40	40	NUM
ap-9572	237	9	45	45	NUM
ap-9572	237	10	0	0	NUM
ap-9572	237	11	0.2	0.2	NUM
ap-9572	237	12	0.4	0.4	NUM
ap-9572	237	13	0.6	0.6	NUM
ap-9572	237	14	0.8	0.8	NUM
ap-9572	237	15	1	1	NUM
ap-9572	237	16	second	second	ADJ
ap-9572	237	17	mode	mode	NOUN
ap-9572	237	18	time=0.k	time=0.k	PROPN
ap-9572	237	19	y=0.2	y=0.2	PROPN
ap-9572	237	20	second	second	ADJ
ap-9572	237	21	mode	mode	NOUN
ap-9572	237	22	time=0.k	time=0.k	X
ap-9572	237	23	y=0.6	y=0.6	NOUN
ap-9572	237	24	second	second	ADJ
ap-9572	237	25	mode	mode	NOUN
ap-9572	237	26	time=5.k	time=5.k	NOUN
ap-9572	237	27	y=0.2	y=0.2	NOUN
ap-9572	237	28	second	second	ADJ
ap-9572	237	29	mode	mode	NOUN
ap-9572	237	30	time=5.k	time=5.k	NOUN
ap-9572	237	31	y=0.6	y=0.6	NOUN
ap-9572	237	32	(	(	PUNCT
ap-9572	237	33	b	b	NOUN
ap-9572	237	34	)	)	PUNCT
ap-9572	237	35	.	.	PUNCT
ap-9572	238	1	second	second	ADJ
ap-9572	238	2	mode	mode	NOUN
ap-9572	238	3	.	.	PUNCT
ap-9572	239	1	figure	figure	VERB
ap-9572	239	2	7	7	NUM
ap-9572	239	3	.	.	PUNCT
ap-9572	239	4	variation	variation	NOUN
ap-9572	239	5	of	of	ADP
ap-9572	239	6	w(*10−5	w(*10−5	PROPN
ap-9572	239	7	)	)	PUNCT
ap-9572	239	8	with	with	ADP
ap-9572	239	9	different	different	ADJ
ap-9572	239	10	x	x	NOUN
ap-9572	239	11	for	for	ADP
ap-9572	239	12	constant	constant	ADJ
ap-9572	239	13	a	a	DET
ap-9572	239	14	b	b	NOUN
ap-9572	239	15	=	=	SYM
ap-9572	239	16	1.5	1.5	NUM
ap-9572	239	17	and	and	CCONJ
ap-9572	239	18	α	α	NOUN
ap-9572	240	1	=	=	SYM
ap-9572	240	2	β1	β1	PROPN
ap-9572	240	3	=	=	SYM
ap-9572	240	4	β2	β2	NOUN
ap-9572	240	5	=	=	SYM
ap-9572	240	6	α1	α1	PROPN
ap-9572	240	7	=	=	SYM
ap-9572	240	8	0.0	0.0	NUM
ap-9572	240	9	and	and	CCONJ
ap-9572	240	10	for	for	ADP
ap-9572	240	11	different	different	ADJ
ap-9572	240	12	y	y	PROPN
ap-9572	240	13	.	.	PUNCT
ap-9572	241	1	y	y	PROPN
ap-9572	241	2	=	=	PUNCT
ap-9572	241	3	0.20	0.20	NUM
ap-9572	241	4	y	y	NOUN
ap-9572	241	5	=	=	SYM
ap-9572	241	6	0.60	0.60	NUM
ap-9572	241	7	mode	mode	NOUN
ap-9572	241	8	→	→	PUNCT
ap-9572	242	1	i	i	NOUN
ap-9572	242	2	ii	ii	VERB
ap-9572	243	1	i	i	NOUN
ap-9572	243	2	ii	ii	PROPN
ap-9572	244	1	x̄	x̄	PROPN
ap-9572	244	2	↓	↓	PROPN
ap-9572	245	1	t	t	PROPN
ap-9572	245	2	i	i	PRON
ap-9572	245	3	m	m	VERB
ap-9572	245	4	e	e	NOUN
ap-9572	245	5	=	=	PUNCT
ap-9572	245	6	0	0	NUM
ap-9572	245	7	.	.	NOUN
ap-9572	245	8	0	0	NUM
ap-9572	246	1	×	×	PROPN
ap-9572	246	2	t	t	NOUN
ap-9572	246	3	p	p	NOUN
ap-9572	246	4	0.0	0.0	NUM
ap-9572	246	5	0.0	0.0	NUM
ap-9572	246	6	0.0	0.0	NUM
ap-9572	246	7	0.0	0.0	NUM
ap-9572	246	8	0.0	0.0	NUM
ap-9572	246	9	0.2	0.2	NUM
ap-9572	246	10	130.43	130.43	NUM
ap-9572	246	11	40.12	40.12	NUM
ap-9572	246	12	431.01	431.01	NUM
ap-9572	246	13	15.93	15.93	NUM
ap-9572	246	14	0.4	0.4	NUM
ap-9572	246	15	307.69	307.69	NUM
ap-9572	246	16	6.96	6.96	NUM
ap-9572	246	17	1	1	NUM
ap-9572	246	18	424.07	424.07	NUM
ap-9572	246	19	28.12	28.12	NUM
ap-9572	246	20	0.6	0.6	NUM
ap-9572	246	21	307.69	307.69	NUM
ap-9572	246	22	6.96	6.96	NUM
ap-9572	246	23	1	1	NUM
ap-9572	246	24	424.07	424.07	NUM
ap-9572	246	25	28.12	28.12	NUM
ap-9572	246	26	0.8	0.8	NUM
ap-9572	246	27	130.43	130.43	NUM
ap-9572	246	28	40.12	40.12	NUM
ap-9572	246	29	431.01	431.01	NUM
ap-9572	246	30	15.93	15.93	NUM
ap-9572	246	31	1.0	1.0	NUM
ap-9572	246	32	0.0	0.0	NUM
ap-9572	246	33	0.0	0.0	NUM
ap-9572	246	34	0.0	0.0	NUM
ap-9572	246	35	0.0	0.0	NUM
ap-9572	246	36	t	t	NOUN
ap-9572	246	37	i	i	PRON
ap-9572	246	38	m	m	VERB
ap-9572	246	39	e	e	NOUN
ap-9572	246	40	=	=	SYM
ap-9572	246	41	5	5	NUM
ap-9572	246	42	.	.	NOUN
ap-9572	246	43	0	0	NUM
ap-9572	247	1	×	×	PROPN
ap-9572	247	2	t	t	NOUN
ap-9572	247	3	p	p	NOUN
ap-9572	247	4	0.0	0.0	NUM
ap-9572	247	5	0.0	0.0	NUM
ap-9572	247	6	0.0	0.0	NUM
ap-9572	247	7	0.0	0.0	NUM
ap-9572	247	8	0.0	0.0	NUM
ap-9572	247	9	0.2	0.2	NUM
ap-9572	247	10	59.13	59.13	NUM
ap-9572	247	11	1.93	1.93	NUM
ap-9572	247	12	190.34	190.34	NUM
ap-9572	247	13	0.83	0.83	NUM
ap-9572	247	14	0.4	0.4	NUM
ap-9572	247	15	136.32	136.32	NUM
ap-9572	247	16	0.43	0.43	NUM
ap-9572	247	17	627.65	627.65	NUM
ap-9572	247	18	1.17	1.17	NUM
ap-9572	247	19	0.6	0.6	NUM
ap-9572	247	20	136.32	136.32	NUM
ap-9572	247	21	0.43	0.43	NUM
ap-9572	247	22	627.65	627.65	NUM
ap-9572	247	23	1.17	1.17	NUM
ap-9572	247	24	0.8	0.8	NUM
ap-9572	247	25	59.13	59.13	NUM
ap-9572	247	26	1.93	1.93	NUM
ap-9572	247	27	190.34	190.34	NUM
ap-9572	247	28	0.83	0.83	NUM
ap-9572	247	29	1.0	1.0	NUM
ap-9572	247	30	0.0	0.0	NUM
ap-9572	247	31	0.0	0.0	NUM
ap-9572	247	32	0.0	0.0	NUM
ap-9572	247	33	0.0	0.0	NUM
ap-9572	247	34	table	table	NOUN
ap-9572	247	35	8	8	NUM
ap-9572	247	36	.	.	PUNCT
ap-9572	247	37	w(*10−5	w(*10−5	NUM
ap-9572	247	38	)	)	PUNCT
ap-9572	247	39	for	for	ADP
ap-9572	247	40	constant	constant	ADJ
ap-9572	247	41	a	a	DET
ap-9572	247	42	b	b	NOUN
ap-9572	247	43	=	=	SYM
ap-9572	247	44	1.5	1.5	NUM
ap-9572	247	45	and	and	CCONJ
ap-9572	247	46	α	α	NOUN
ap-9572	247	47	=	=	SYM
ap-9572	247	48	β1	β1	PROPN
ap-9572	247	49	=	=	SYM
ap-9572	247	50	β2	β2	NOUN
ap-9572	247	51	=	=	NOUN
ap-9572	247	52	0.0	0.0	NUM
ap-9572	247	53	,	,	PUNCT
ap-9572	247	54	α1	α1	PROPN
ap-9572	247	55	=	=	SYM
ap-9572	247	56	0.4	0.4	NUM
ap-9572	247	57	and	and	CCONJ
ap-9572	247	58	for	for	ADP
ap-9572	247	59	different	different	ADJ
ap-9572	247	60	x	x	X
ap-9572	247	61	and	and	CCONJ
ap-9572	247	62	y	y	PROPN
ap-9572	247	63	,	,	PUNCT
ap-9572	247	64	see	see	VERB
ap-9572	247	65	figure	figure	NOUN
ap-9572	247	66	8	8	NUM
ap-9572	247	67	.	.	NOUN
ap-9572	247	68	306	306	NUM
ap-9572	247	69	vol	vol	NOUN
ap-9572	247	70	.	.	PUNCT
ap-9572	248	1	64	64	NUM
ap-9572	248	2	no	no	NOUN
ap-9572	248	3	.	.	PUNCT
ap-9572	249	1	4/2024	4/2024	NUM
ap-9572	249	2	non	non	ADJ
ap-9572	249	3	-	-	ADJ
ap-9572	249	4	homogeneity	homogeneity	ADJ
ap-9572	249	5	effect	effect	NOUN
ap-9572	249	6	on	on	ADP
ap-9572	249	7	the	the	DET
ap-9572	249	8	vibration	vibration	NOUN
ap-9572	249	9	of	of	ADP
ap-9572	249	10	.	.	PUNCT
ap-9572	249	11	.	.	PUNCT
ap-9572	250	1	.	.	PUNCT
ap-9572	251	1	0	0	NUM
ap-9572	252	1	200	200	NUM
ap-9572	252	2	400	400	NUM
ap-9572	252	3	600	600	NUM
ap-9572	252	4	800	800	NUM
ap-9572	252	5	1000	1000	NUM
ap-9572	252	6	1200	1200	NUM
ap-9572	252	7	1400	1400	NUM
ap-9572	252	8	1600	1600	NUM
ap-9572	252	9	1800	1800	NUM
ap-9572	252	10	0	0	NUM
ap-9572	252	11	0.2	0.2	NUM
ap-9572	252	12	0.4	0.4	NUM
ap-9572	252	13	0.6	0.6	NUM
ap-9572	252	14	0.8	0.8	NUM
ap-9572	252	15	1	1	NUM
ap-9572	252	16	first	first	ADJ
ap-9572	252	17	mode	mode	NOUN
ap-9572	252	18	time=0.k	time=0.k	PROPN
ap-9572	252	19	y=0.2	y=0.2	NOUN
ap-9572	252	20	first	first	PROPN
ap-9572	252	21	mode	mode	PROPN
ap-9572	252	22	time=0.k	time=0.k	X
ap-9572	252	23	y=0.6	y=0.6	NOUN
ap-9572	252	24	first	first	ADJ
ap-9572	252	25	mode	mode	PROPN
ap-9572	252	26	time=5.k	time=5.k	NOUN
ap-9572	252	27	y=0.2	y=0.2	NOUN
ap-9572	252	28	first	first	ADJ
ap-9572	252	29	mode	mode	PROPN
ap-9572	252	30	time=5.k	time=5.k	NOUN
ap-9572	252	31	y=0.6	y=0.6	NOUN
ap-9572	252	32	(	(	PUNCT
ap-9572	252	33	a	a	NOUN
ap-9572	252	34	)	)	PUNCT
ap-9572	252	35	.	.	PUNCT
ap-9572	253	1	first	first	ADJ
ap-9572	253	2	mode	mode	NOUN
ap-9572	253	3	.	.	PUNCT
ap-9572	254	1	0	0	NUM
ap-9572	255	1	5	5	NUM
ap-9572	255	2	10	10	NUM
ap-9572	255	3	15	15	NUM
ap-9572	255	4	20	20	NUM
ap-9572	255	5	25	25	NUM
ap-9572	255	6	30	30	NUM
ap-9572	255	7	35	35	NUM
ap-9572	255	8	40	40	NUM
ap-9572	255	9	45	45	NUM
ap-9572	255	10	0	0	NUM
ap-9572	255	11	0.2	0.2	NUM
ap-9572	255	12	0.4	0.4	NUM
ap-9572	255	13	0.6	0.6	NUM
ap-9572	255	14	0.8	0.8	NUM
ap-9572	255	15	1	1	NUM
ap-9572	255	16	second	second	ADJ
ap-9572	255	17	mode	mode	NOUN
ap-9572	255	18	time=0.k	time=0.k	PROPN
ap-9572	255	19	y=0.2	y=0.2	PROPN
ap-9572	255	20	second	second	ADJ
ap-9572	255	21	mode	mode	NOUN
ap-9572	255	22	time=0.k	time=0.k	X
ap-9572	255	23	y=0.6	y=0.6	NOUN
ap-9572	255	24	second	second	ADJ
ap-9572	255	25	mode	mode	NOUN
ap-9572	255	26	time=5.k	time=5.k	NOUN
ap-9572	255	27	y=0.2	y=0.2	NOUN
ap-9572	255	28	second	second	ADJ
ap-9572	255	29	mode	mode	NOUN
ap-9572	255	30	time=5.k	time=5.k	NOUN
ap-9572	255	31	y=0.6	y=0.6	NOUN
ap-9572	255	32	(	(	PUNCT
ap-9572	255	33	b	b	NOUN
ap-9572	255	34	)	)	PUNCT
ap-9572	255	35	.	.	PUNCT
ap-9572	256	1	second	second	ADJ
ap-9572	256	2	mode	mode	NOUN
ap-9572	256	3	.	.	PUNCT
ap-9572	257	1	figure	figure	NOUN
ap-9572	257	2	8	8	NUM
ap-9572	257	3	.	.	PUNCT
ap-9572	258	1	variation	variation	NOUN
ap-9572	258	2	of	of	ADP
ap-9572	258	3	w(*10−5	w(*10−5	PROPN
ap-9572	258	4	)	)	PUNCT
ap-9572	258	5	with	with	ADP
ap-9572	258	6	different	different	ADJ
ap-9572	258	7	x	x	NOUN
ap-9572	258	8	for	for	ADP
ap-9572	258	9	constant	constant	ADJ
ap-9572	258	10	a	a	DET
ap-9572	258	11	b	b	NOUN
ap-9572	258	12	=	=	SYM
ap-9572	258	13	1.5	1.5	NUM
ap-9572	258	14	and	and	CCONJ
ap-9572	258	15	α	α	NOUN
ap-9572	258	16	=	=	SYM
ap-9572	258	17	β1	β1	PROPN
ap-9572	258	18	=	=	SYM
ap-9572	258	19	β2	β2	NOUN
ap-9572	258	20	=	=	NOUN
ap-9572	258	21	0.0	0.0	NUM
ap-9572	258	22	,	,	PUNCT
ap-9572	258	23	α1	α1	PROPN
ap-9572	258	24	=	=	SYM
ap-9572	258	25	0.4	0.4	NUM
ap-9572	258	26	and	and	CCONJ
ap-9572	258	27	for	for	ADP
ap-9572	258	28	different	different	ADJ
ap-9572	258	29	y	y	PROPN
ap-9572	258	30	.	.	PUNCT
ap-9572	259	1	y	y	PROPN
ap-9572	259	2	=	=	PUNCT
ap-9572	259	3	0.20	0.20	NUM
ap-9572	259	4	y	y	NOUN
ap-9572	259	5	=	=	SYM
ap-9572	259	6	0.60	0.60	NUM
ap-9572	259	7	mode	mode	NOUN
ap-9572	259	8	→	→	PUNCT
ap-9572	260	1	i	i	NOUN
ap-9572	260	2	ii	ii	VERB
ap-9572	261	1	i	i	NOUN
ap-9572	261	2	ii	ii	PROPN
ap-9572	262	1	x̄	x̄	PROPN
ap-9572	262	2	↓	↓	PROPN
ap-9572	263	1	t	t	PROPN
ap-9572	263	2	i	i	PRON
ap-9572	263	3	m	m	VERB
ap-9572	263	4	e	e	NOUN
ap-9572	263	5	=	=	PUNCT
ap-9572	263	6	0	0	NUM
ap-9572	263	7	.	.	NOUN
ap-9572	263	8	0	0	NUM
ap-9572	264	1	×	×	PROPN
ap-9572	264	2	t	t	NOUN
ap-9572	264	3	p	p	NOUN
ap-9572	264	4	0.0	0.0	NUM
ap-9572	264	5	0.0	0.0	NUM
ap-9572	264	6	0.0	0.0	NUM
ap-9572	264	7	0.0	0.0	NUM
ap-9572	264	8	0.0	0.0	NUM
ap-9572	264	9	0.2	0.2	NUM
ap-9572	264	10	233.72	233.72	NUM
ap-9572	264	11	40.12	40.12	NUM
ap-9572	264	12	3	3	NUM
ap-9572	264	13	196.18	196.18	NUM
ap-9572	264	14	15.22	15.22	NUM
ap-9572	264	15	0.4	0.4	NUM
ap-9572	264	16	654.68	654.68	NUM
ap-9572	264	17	6.94	6.94	NUM
ap-9572	264	18	10	10	NUM
ap-9572	264	19	753.11	753.11	NUM
ap-9572	264	20	27.83	27.83	NUM
ap-9572	264	21	0.6	0.6	NUM
ap-9572	264	22	654.68	654.68	NUM
ap-9572	264	23	6.94	6.94	NUM
ap-9572	264	24	10	10	NUM
ap-9572	264	25	753.11	753.11	NUM
ap-9572	264	26	27.83	27.83	NUM
ap-9572	264	27	0.8	0.8	NUM
ap-9572	264	28	233.72	233.72	NUM
ap-9572	264	29	40.12	40.12	NUM
ap-9572	264	30	3	3	NUM
ap-9572	264	31	196.18	196.18	NUM
ap-9572	264	32	15.22	15.22	NUM
ap-9572	264	33	1.0	1.0	NUM
ap-9572	264	34	0.0	0.0	NUM
ap-9572	264	35	0.0	0.0	NUM
ap-9572	264	36	0.0	0.0	NUM
ap-9572	264	37	0.0	0.0	NUM
ap-9572	264	38	t	t	NOUN
ap-9572	264	39	i	i	PRON
ap-9572	264	40	m	m	VERB
ap-9572	264	41	e	e	NOUN
ap-9572	264	42	=	=	SYM
ap-9572	264	43	5	5	NUM
ap-9572	264	44	.	.	NOUN
ap-9572	264	45	0	0	NUM
ap-9572	265	1	×	×	PROPN
ap-9572	265	2	t	t	NOUN
ap-9572	265	3	p	p	NOUN
ap-9572	265	4	0.0	0.0	NUM
ap-9572	265	5	0.0	0.0	NUM
ap-9572	265	6	0.0	0.0	NUM
ap-9572	265	7	0.0	0.0	NUM
ap-9572	265	8	0.0	0.0	NUM
ap-9572	265	9	0.2	0.2	NUM
ap-9572	265	10	96.12	96.12	NUM
ap-9572	265	11	1.13	1.13	NUM
ap-9572	265	12	1	1	NUM
ap-9572	265	13	290.07	290.07	NUM
ap-9572	265	14	0.47	0.47	NUM
ap-9572	265	15	0.4	0.4	NUM
ap-9572	265	16	258.24	258.24	NUM
ap-9572	265	17	0.21	0.21	NUM
ap-9572	265	18	4	4	NUM
ap-9572	265	19	209.84	209.84	NUM
ap-9572	265	20	0.69	0.69	NUM
ap-9572	265	21	0.6	0.6	NUM
ap-9572	265	22	258.24	258.24	NUM
ap-9572	265	23	0.21	0.21	NUM
ap-9572	265	24	4	4	NUM
ap-9572	265	25	209.84	209.84	NUM
ap-9572	265	26	0.69	0.69	NUM
ap-9572	265	27	0.8	0.8	NUM
ap-9572	265	28	96.12	96.12	NUM
ap-9572	265	29	1.13	1.13	NUM
ap-9572	265	30	1	1	NUM
ap-9572	265	31	290.07	290.07	NUM
ap-9572	265	32	0.47	0.47	NUM
ap-9572	265	33	1.0	1.0	NUM
ap-9572	265	34	0.0	0.0	NUM
ap-9572	265	35	0.0	0.0	NUM
ap-9572	265	36	0.0	0.0	NUM
ap-9572	265	37	0.0	0.0	NUM
ap-9572	265	38	table	table	NOUN
ap-9572	265	39	9	9	NUM
ap-9572	265	40	.	.	PUNCT
ap-9572	265	41	w(*10−5	w(*10−5	NUM
ap-9572	265	42	)	)	PUNCT
ap-9572	265	43	for	for	ADP
ap-9572	265	44	constant	constant	ADJ
ap-9572	265	45	a	a	DET
ap-9572	265	46	b	b	NOUN
ap-9572	265	47	=	=	SYM
ap-9572	265	48	1.5	1.5	NUM
ap-9572	265	49	and	and	CCONJ
ap-9572	265	50	α	α	NOUN
ap-9572	265	51	=	=	NOUN
ap-9572	265	52	0.2	0.2	NUM
ap-9572	265	53	,	,	PUNCT
ap-9572	265	54	β1	β1	PROPN
ap-9572	265	55	=	=	PUNCT
ap-9572	265	56	0.3	0.3	NUM
ap-9572	265	57	,	,	PUNCT
ap-9572	265	58	β2	β2	NOUN
ap-9572	265	59	=	=	SYM
ap-9572	265	60	α1	α1	PROPN
ap-9572	265	61	=	=	SYM
ap-9572	265	62	0.4	0.4	NUM
ap-9572	265	63	and	and	CCONJ
ap-9572	265	64	for	for	ADP
ap-9572	265	65	different	different	ADJ
ap-9572	265	66	x	x	X
ap-9572	265	67	and	and	CCONJ
ap-9572	265	68	y	y	PROPN
ap-9572	265	69	,	,	PUNCT
ap-9572	265	70	see	see	VERB
ap-9572	265	71	figure	figure	NOUN
ap-9572	265	72	9	9	NUM
ap-9572	265	73	.	.	X
ap-9572	265	74	307	307	NUM
ap-9572	265	75	sudhanshu	sudhanshu	NOUN
ap-9572	265	76	aggarwal	aggarwal	PROPN
ap-9572	265	77	acta	acta	PROPN
ap-9572	265	78	polytechnica	polytechnica	PROPN
ap-9572	265	79	0	0	NUM
ap-9572	265	80	2000	2000	NUM
ap-9572	265	81	4000	4000	NUM
ap-9572	265	82	6000	6000	NUM
ap-9572	265	83	8000	8000	NUM
ap-9572	265	84	10000	10000	NUM
ap-9572	265	85	12000	12000	NUM
ap-9572	265	86	14000	14000	NUM
ap-9572	265	87	0	0	NUM
ap-9572	265	88	0.2	0.2	NUM
ap-9572	265	89	0.4	0.4	NUM
ap-9572	265	90	0.6	0.6	NUM
ap-9572	265	91	0.8	0.8	NUM
ap-9572	265	92	1	1	NUM
ap-9572	265	93	first	first	ADJ
ap-9572	265	94	mode	mode	NOUN
ap-9572	265	95	time=0.k	time=0.k	PROPN
ap-9572	265	96	y=0.2	y=0.2	NOUN
ap-9572	265	97	first	first	PROPN
ap-9572	265	98	mode	mode	PROPN
ap-9572	265	99	time=0.k	time=0.k	X
ap-9572	265	100	y=0.6	y=0.6	NOUN
ap-9572	265	101	first	first	ADJ
ap-9572	265	102	mode	mode	PROPN
ap-9572	265	103	time=5.k	time=5.k	NOUN
ap-9572	265	104	y=0.2	y=0.2	NOUN
ap-9572	265	105	first	first	ADJ
ap-9572	265	106	mode	mode	PROPN
ap-9572	265	107	time=5.k	time=5.k	NOUN
ap-9572	265	108	y=0.6	y=0.6	NOUN
ap-9572	265	109	(	(	PUNCT
ap-9572	265	110	a	a	NOUN
ap-9572	265	111	)	)	PUNCT
ap-9572	265	112	.	.	PUNCT
ap-9572	266	1	first	first	ADJ
ap-9572	266	2	mode	mode	NOUN
ap-9572	266	3	.	.	PUNCT
ap-9572	267	1	0	0	NUM
ap-9572	268	1	5	5	NUM
ap-9572	268	2	10	10	NUM
ap-9572	268	3	15	15	NUM
ap-9572	268	4	20	20	NUM
ap-9572	268	5	25	25	NUM
ap-9572	268	6	30	30	NUM
ap-9572	268	7	35	35	NUM
ap-9572	268	8	40	40	NUM
ap-9572	268	9	45	45	NUM
ap-9572	268	10	0	0	NUM
ap-9572	268	11	0.2	0.2	NUM
ap-9572	268	12	0.4	0.4	NUM
ap-9572	268	13	0.6	0.6	NUM
ap-9572	268	14	0.8	0.8	NUM
ap-9572	268	15	1	1	NUM
ap-9572	268	16	second	second	ADJ
ap-9572	268	17	mode	mode	NOUN
ap-9572	268	18	time=0.k	time=0.k	PROPN
ap-9572	268	19	y=0.2	y=0.2	PROPN
ap-9572	268	20	second	second	ADJ
ap-9572	268	21	mode	mode	NOUN
ap-9572	268	22	time=0.k	time=0.k	X
ap-9572	268	23	y=0.6	y=0.6	NOUN
ap-9572	268	24	second	second	ADJ
ap-9572	268	25	mode	mode	NOUN
ap-9572	268	26	time=5.k	time=5.k	NOUN
ap-9572	268	27	y=0.2	y=0.2	NOUN
ap-9572	268	28	second	second	ADJ
ap-9572	268	29	mode	mode	NOUN
ap-9572	268	30	time=5.k	time=5.k	NOUN
ap-9572	268	31	y=0.6	y=0.6	NOUN
ap-9572	268	32	(	(	PUNCT
ap-9572	268	33	b	b	NOUN
ap-9572	268	34	)	)	PUNCT
ap-9572	268	35	.	.	PUNCT
ap-9572	269	1	second	second	ADJ
ap-9572	269	2	mode	mode	NOUN
ap-9572	269	3	.	.	PUNCT
ap-9572	270	1	figure	figure	NOUN
ap-9572	270	2	9	9	NUM
ap-9572	270	3	.	.	PUNCT
ap-9572	271	1	variation	variation	NOUN
ap-9572	271	2	of	of	ADP
ap-9572	271	3	w(*10−5	w(*10−5	PROPN
ap-9572	271	4	)	)	PUNCT
ap-9572	271	5	with	with	ADP
ap-9572	271	6	different	different	ADJ
ap-9572	271	7	x	x	NOUN
ap-9572	271	8	for	for	ADP
ap-9572	271	9	constant	constant	ADJ
ap-9572	271	10	a	a	DET
ap-9572	271	11	b	b	NOUN
ap-9572	271	12	=	=	SYM
ap-9572	271	13	1.5	1.5	NUM
ap-9572	271	14	and	and	CCONJ
ap-9572	271	15	α	α	NOUN
ap-9572	271	16	=	=	NOUN
ap-9572	271	17	0.2	0.2	NUM
ap-9572	271	18	,	,	PUNCT
ap-9572	271	19	β1	β1	PROPN
ap-9572	271	20	=	=	PUNCT
ap-9572	271	21	0.3	0.3	NUM
ap-9572	271	22	,	,	PUNCT
ap-9572	271	23	β2	β2	NOUN
ap-9572	271	24	=	=	SYM
ap-9572	271	25	α1	α1	PROPN
ap-9572	271	26	=	=	SYM
ap-9572	271	27	0.4	0.4	NUM
ap-9572	271	28	and	and	CCONJ
ap-9572	271	29	for	for	ADP
ap-9572	271	30	different	different	ADJ
ap-9572	271	31	y	y	PROPN
ap-9572	271	32	.	.	PUNCT
ap-9572	272	1	time	time	NOUN
ap-9572	273	1	=	=	SYM
ap-9572	273	2	0.0	0.0	NUM
ap-9572	273	3	×	×	NOUN
ap-9572	273	4	tp	tp	NOUN
ap-9572	273	5	time	time	NOUN
ap-9572	273	6	=	=	SYM
ap-9572	273	7	5.0	5.0	NUM
ap-9572	273	8	×	×	NOUN
ap-9572	273	9	tp	tp	NOUN
ap-9572	273	10	mode	mode	NOUN
ap-9572	273	11	→	→	PUNCT
ap-9572	274	1	i	i	NOUN
ap-9572	274	2	ii	ii	VERB
ap-9572	275	1	i	i	PRON
ap-9572	275	2	ii	ii	VERB
ap-9572	275	3	a	a	DET
ap-9572	275	4	b	b	PROPN
ap-9572	275	5	↓	↓	NOUN
ap-9572	275	6	0.5	0.5	NUM
ap-9572	275	7	20.93	20.93	NUM
ap-9572	275	8	14.02	14.02	NUM
ap-9572	275	9	14.34	14.34	NUM
ap-9572	275	10	3.63	3.63	NUM
ap-9572	275	11	1.0	1.0	NUM
ap-9572	275	12	63.12	63.12	NUM
ap-9572	275	13	32.41	32.41	NUM
ap-9572	275	14	38.67	38.67	NUM
ap-9572	275	15	4.84	4.84	NUM
ap-9572	275	16	1.5	1.5	NUM
ap-9572	275	17	126.32	126.32	NUM
ap-9572	275	18	38.87	38.87	NUM
ap-9572	275	19	55.12	55.12	NUM
ap-9572	275	20	1.38	1.38	NUM
ap-9572	275	21	2.0	2.0	NUM
ap-9572	275	22	233.96	233.96	NUM
ap-9572	275	23	37.37	37.37	NUM
ap-9572	275	24	61.42	61.42	NUM
ap-9572	275	25	0.14	0.14	NUM
ap-9572	275	26	2.5	2.5	NUM
ap-9572	275	27	398.28	398.28	NUM
ap-9572	275	28	36.09	36.09	NUM
ap-9572	275	29	53.21	53.21	NUM
ap-9572	275	30	0.003	0.003	NUM
ap-9572	275	31	table	table	NOUN
ap-9572	275	32	10	10	NUM
ap-9572	275	33	.	.	PUNCT
ap-9572	276	1	w(*10−5	w(*10−5	NUM
ap-9572	276	2	)	)	PUNCT
ap-9572	277	1	for	for	ADP
ap-9572	277	2	different	different	ADJ
ap-9572	277	3	a	a	DET
ap-9572	277	4	b	b	NOUN
ap-9572	277	5	and	and	CCONJ
ap-9572	277	6	α	α	NOUN
ap-9572	277	7	=	=	SYM
ap-9572	277	8	β1	β1	PROPN
ap-9572	277	9	=	=	SYM
ap-9572	277	10	β2	β2	NOUN
ap-9572	277	11	=	=	SYM
ap-9572	277	12	α1	α1	PROPN
ap-9572	277	13	=	=	SYM
ap-9572	277	14	0.0	0.0	NUM
ap-9572	277	15	and	and	CCONJ
ap-9572	277	16	for	for	ADP
ap-9572	277	17	x	x	X
ap-9572	277	18	=	=	PUNCT
ap-9572	277	19	y	y	PROPN
ap-9572	277	20	=	=	SYM
ap-9572	277	21	0.2	0.2	NUM
ap-9572	277	22	,	,	PUNCT
ap-9572	277	23	see	see	VERB
ap-9572	277	24	figure	figure	NOUN
ap-9572	277	25	10	10	NUM
ap-9572	277	26	.	.	PUNCT
ap-9572	278	1	308	308	NUM
ap-9572	278	2	vol	vol	NOUN
ap-9572	278	3	.	.	PUNCT
ap-9572	279	1	64	64	NUM
ap-9572	279	2	no	no	NOUN
ap-9572	279	3	.	.	PUNCT
ap-9572	280	1	4/2024	4/2024	NUM
ap-9572	280	2	non	non	ADJ
ap-9572	280	3	-	-	ADJ
ap-9572	280	4	homogeneity	homogeneity	ADJ
ap-9572	280	5	effect	effect	NOUN
ap-9572	280	6	on	on	ADP
ap-9572	280	7	the	the	DET
ap-9572	280	8	vibration	vibration	NOUN
ap-9572	280	9	of	of	ADP
ap-9572	280	10	.	.	PUNCT
ap-9572	280	11	.	.	PUNCT
ap-9572	280	12	.	.	PUNCT
ap-9572	281	1	-50	-50	PUNCT
ap-9572	281	2	0	0	NUM
ap-9572	282	1	50	50	NUM
ap-9572	282	2	100	100	NUM
ap-9572	282	3	150	150	NUM
ap-9572	282	4	200	200	NUM
ap-9572	282	5	250	250	NUM
ap-9572	282	6	300	300	NUM
ap-9572	282	7	350	350	NUM
ap-9572	282	8	400	400	NUM
ap-9572	282	9	450	450	NUM
ap-9572	282	10	0.5	0.5	NUM
ap-9572	282	11	1	1	NUM
ap-9572	282	12	1.5	1.5	NUM
ap-9572	282	13	2	2	NUM
ap-9572	282	14	2.5	2.5	NUM
ap-9572	282	15	first	first	ADJ
ap-9572	282	16	mode	mode	NOUN
ap-9572	282	17	time=0.k	time=0.k	X
ap-9572	282	18	second	second	ADJ
ap-9572	282	19	mode	mode	NOUN
ap-9572	282	20	time=0.k	time=0.k	PART
ap-9572	282	21	first	first	ADJ
ap-9572	282	22	mode	mode	PROPN
ap-9572	282	23	time=5.k	time=5.k	NOUN
ap-9572	282	24	second	second	ADJ
ap-9572	282	25	mode	mode	NOUN
ap-9572	282	26	time=5.k	time=5.k	NOUN
ap-9572	282	27	figure	figure	NOUN
ap-9572	282	28	10	10	NUM
ap-9572	282	29	.	.	PUNCT
ap-9572	282	30	variation	variation	NOUN
ap-9572	282	31	of	of	ADP
ap-9572	282	32	w(*10−5	w(*10−5	PROPN
ap-9572	282	33	)	)	PUNCT
ap-9572	282	34	for	for	ADP
ap-9572	282	35	different	different	ADJ
ap-9572	282	36	a	a	DET
ap-9572	282	37	b	b	NOUN
ap-9572	282	38	and	and	CCONJ
ap-9572	282	39	α	α	NOUN
ap-9572	282	40	=	=	SYM
ap-9572	282	41	β1	β1	PROPN
ap-9572	282	42	=	=	SYM
ap-9572	282	43	β2	β2	NOUN
ap-9572	282	44	=	=	SYM
ap-9572	282	45	α1	α1	PROPN
ap-9572	282	46	=	=	SYM
ap-9572	282	47	0.0	0.0	NUM
ap-9572	282	48	and	and	CCONJ
ap-9572	282	49	for	for	ADP
ap-9572	282	50	x	x	X
ap-9572	282	51	=	=	PUNCT
ap-9572	282	52	y	y	PROPN
ap-9572	282	53	=	=	SYM
ap-9572	282	54	0.2	0.2	NUM
ap-9572	282	55	.	.	PUNCT
ap-9572	282	56	time	time	NOUN
ap-9572	283	1	=	=	SYM
ap-9572	283	2	0.0	0.0	NUM
ap-9572	283	3	×	×	NOUN
ap-9572	283	4	tp	tp	NOUN
ap-9572	283	5	time	time	NOUN
ap-9572	283	6	=	=	SYM
ap-9572	283	7	5.0	5.0	NUM
ap-9572	283	8	×	×	NOUN
ap-9572	283	9	tp	tp	NOUN
ap-9572	283	10	mode	mode	NOUN
ap-9572	283	11	→	→	PUNCT
ap-9572	284	1	i	i	NOUN
ap-9572	284	2	ii	ii	VERB
ap-9572	285	1	i	i	PRON
ap-9572	285	2	ii	ii	VERB
ap-9572	285	3	a	a	DET
ap-9572	285	4	b	b	PROPN
ap-9572	285	5	↓	↓	NOUN
ap-9572	285	6	0.5	0.5	NUM
ap-9572	285	7	24.23	24.23	NUM
ap-9572	285	8	15.33	15.33	NUM
ap-9572	285	9	17.68	17.68	NUM
ap-9572	285	10	4.37	4.37	NUM
ap-9572	285	11	1.0	1.0	NUM
ap-9572	285	12	66.84	66.84	NUM
ap-9572	285	13	33.97	33.97	NUM
ap-9572	285	14	41.32	41.32	NUM
ap-9572	285	15	5.60	5.60	NUM
ap-9572	285	16	1.5	1.5	NUM
ap-9572	285	17	130.43	130.43	NUM
ap-9572	285	18	40.12	40.12	NUM
ap-9572	285	19	59.13	59.13	NUM
ap-9572	285	20	1.93	1.93	NUM
ap-9572	285	21	2.0	2.0	NUM
ap-9572	285	22	238.27	238.27	NUM
ap-9572	285	23	39.11	39.11	NUM
ap-9572	285	24	64.92	64.92	NUM
ap-9572	285	25	0.21	0.21	NUM
ap-9572	285	26	2.5	2.5	NUM
ap-9572	285	27	403.03	403.03	NUM
ap-9572	285	28	37.28	37.28	NUM
ap-9572	285	29	57.16	57.16	NUM
ap-9572	285	30	0.006	0.006	NUM
ap-9572	285	31	table	table	NOUN
ap-9572	285	32	11	11	NUM
ap-9572	285	33	.	.	PUNCT
ap-9572	286	1	w(*10−5	w(*10−5	NUM
ap-9572	286	2	)	)	PUNCT
ap-9572	287	1	for	for	ADP
ap-9572	287	2	different	different	ADJ
ap-9572	287	3	a	a	DET
ap-9572	287	4	b	b	NOUN
ap-9572	287	5	and	and	CCONJ
ap-9572	287	6	α	α	NOUN
ap-9572	287	7	=	=	SYM
ap-9572	287	8	β1	β1	PROPN
ap-9572	287	9	=	=	SYM
ap-9572	287	10	β2	β2	NOUN
ap-9572	287	11	=	=	NOUN
ap-9572	287	12	0.0	0.0	NUM
ap-9572	287	13	,	,	PUNCT
ap-9572	287	14	α1	α1	PROPN
ap-9572	287	15	=	=	SYM
ap-9572	287	16	0.4	0.4	NUM
ap-9572	287	17	and	and	CCONJ
ap-9572	287	18	for	for	ADP
ap-9572	287	19	x	x	X
ap-9572	287	20	=	=	PUNCT
ap-9572	287	21	y	y	PROPN
ap-9572	287	22	=	=	SYM
ap-9572	287	23	0.2	0.2	NUM
ap-9572	287	24	,	,	PUNCT
ap-9572	287	25	see	see	VERB
ap-9572	287	26	figure	figure	NOUN
ap-9572	287	27	11	11	NUM
ap-9572	287	28	.	.	PUNCT
ap-9572	288	1	-50	-50	PUNCT
ap-9572	288	2	0	0	NUM
ap-9572	288	3	50	50	NUM
ap-9572	288	4	100	100	NUM
ap-9572	288	5	150	150	NUM
ap-9572	288	6	200	200	NUM
ap-9572	288	7	250	250	NUM
ap-9572	288	8	300	300	NUM
ap-9572	288	9	350	350	NUM
ap-9572	288	10	400	400	NUM
ap-9572	288	11	450	450	NUM
ap-9572	288	12	0.5	0.5	NUM
ap-9572	288	13	1	1	NUM
ap-9572	288	14	1.5	1.5	NUM
ap-9572	288	15	2	2	NUM
ap-9572	288	16	2.5	2.5	NUM
ap-9572	288	17	first	first	ADJ
ap-9572	288	18	mode	mode	NOUN
ap-9572	288	19	time=0.k	time=0.k	X
ap-9572	288	20	second	second	ADJ
ap-9572	288	21	mode	mode	NOUN
ap-9572	288	22	time=0.k	time=0.k	PART
ap-9572	288	23	first	first	ADJ
ap-9572	288	24	mode	mode	PROPN
ap-9572	288	25	time=5.k	time=5.k	NOUN
ap-9572	288	26	second	second	ADJ
ap-9572	288	27	mode	mode	NOUN
ap-9572	288	28	time=5.k	time=5.k	NOUN
ap-9572	288	29	figure	figure	NOUN
ap-9572	288	30	11	11	NUM
ap-9572	288	31	.	.	PUNCT
ap-9572	289	1	variation	variation	NOUN
ap-9572	289	2	of	of	ADP
ap-9572	289	3	w(*10−5	w(*10−5	PROPN
ap-9572	289	4	)	)	PUNCT
ap-9572	289	5	for	for	ADP
ap-9572	289	6	different	different	ADJ
ap-9572	289	7	a	a	DET
ap-9572	289	8	b	b	NOUN
ap-9572	289	9	and	and	CCONJ
ap-9572	289	10	α	α	NOUN
ap-9572	289	11	=	=	SYM
ap-9572	289	12	β1	β1	PROPN
ap-9572	289	13	=	=	SYM
ap-9572	289	14	β2	β2	NOUN
ap-9572	289	15	=	=	NOUN
ap-9572	289	16	0.0	0.0	NUM
ap-9572	289	17	,	,	PUNCT
ap-9572	289	18	α1	α1	PROPN
ap-9572	289	19	=	=	SYM
ap-9572	289	20	0.4	0.4	NUM
ap-9572	289	21	and	and	CCONJ
ap-9572	289	22	for	for	ADP
ap-9572	289	23	x	x	X
ap-9572	289	24	=	=	PUNCT
ap-9572	289	25	y	y	PROPN
ap-9572	289	26	=	=	SYM
ap-9572	289	27	0.2	0.2	NUM
ap-9572	289	28	.	.	PUNCT
ap-9572	290	1	309	309	NUM
ap-9572	290	2	sudhanshu	sudhanshu	NOUN
ap-9572	290	3	aggarwal	aggarwal	PROPN
ap-9572	290	4	acta	acta	PROPN
ap-9572	290	5	polytechnica	polytechnica	PROPN
ap-9572	290	6	time	time	NOUN
ap-9572	290	7	=	=	SYM
ap-9572	290	8	0.0	0.0	NUM
ap-9572	290	9	×	×	NOUN
ap-9572	290	10	tp	tp	NOUN
ap-9572	290	11	time	time	NOUN
ap-9572	290	12	=	=	SYM
ap-9572	290	13	5.0	5.0	NUM
ap-9572	290	14	×	×	NOUN
ap-9572	290	15	tp	tp	NOUN
ap-9572	290	16	mode	mode	NOUN
ap-9572	290	17	→	→	PUNCT
ap-9572	290	18	i	i	NOUN
ap-9572	290	19	ii	ii	VERB
ap-9572	291	1	i	i	PRON
ap-9572	291	2	ii	ii	VERB
ap-9572	291	3	a	a	DET
ap-9572	291	4	b	b	PROPN
ap-9572	291	5	↓	↓	NOUN
ap-9572	291	6	0.5	0.5	NUM
ap-9572	291	7	28.03	28.03	NUM
ap-9572	291	8	15.73	15.73	NUM
ap-9572	291	9	21.53	21.53	NUM
ap-9572	291	10	3.64	3.64	NUM
ap-9572	291	11	1.0	1.0	NUM
ap-9572	291	12	96.67	96.67	NUM
ap-9572	291	13	33.78	33.78	NUM
ap-9572	291	14	58.45	58.45	NUM
ap-9572	291	15	4.34	4.34	NUM
ap-9572	291	16	1.5	1.5	NUM
ap-9572	291	17	235.72	235.72	NUM
ap-9572	291	18	40.31	40.31	NUM
ap-9572	291	19	98.27	98.27	NUM
ap-9572	291	20	1.29	1.29	NUM
ap-9572	291	21	2.0	2.0	NUM
ap-9572	291	22	501.18	501.18	NUM
ap-9572	291	23	38.92	38.92	NUM
ap-9572	291	24	121.02	121.02	NUM
ap-9572	291	25	0.099	0.099	NUM
ap-9572	291	26	2.5	2.5	NUM
ap-9572	291	27	935.23	935.23	NUM
ap-9572	291	28	37.35	37.35	NUM
ap-9572	291	29	109.33	109.33	NUM
ap-9572	291	30	0.00053	0.00053	NUM
ap-9572	291	31	table	table	NOUN
ap-9572	291	32	12	12	NUM
ap-9572	291	33	.	.	PUNCT
ap-9572	292	1	w(*10−5	w(*10−5	NUM
ap-9572	292	2	)	)	PUNCT
ap-9572	293	1	for	for	ADP
ap-9572	293	2	different	different	ADJ
ap-9572	293	3	a	a	DET
ap-9572	293	4	b	b	NOUN
ap-9572	293	5	and	and	CCONJ
ap-9572	293	6	α	α	NOUN
ap-9572	293	7	=	=	SYM
ap-9572	293	8	β1	β1	PROPN
ap-9572	293	9	=	=	PUNCT
ap-9572	293	10	0.3	0.3	NUM
ap-9572	293	11	,	,	PUNCT
ap-9572	293	12	β2	β2	NOUN
ap-9572	293	13	=	=	SYM
ap-9572	293	14	α1	α1	PROPN
ap-9572	293	15	=	=	SYM
ap-9572	293	16	0.4	0.4	NUM
ap-9572	293	17	and	and	CCONJ
ap-9572	293	18	for	for	ADP
ap-9572	293	19	x	x	X
ap-9572	293	20	=	=	PUNCT
ap-9572	293	21	y	y	PROPN
ap-9572	293	22	=	=	SYM
ap-9572	293	23	0.2	0.2	NUM
ap-9572	293	24	,	,	PUNCT
ap-9572	293	25	see	see	VERB
ap-9572	293	26	figure	figure	NOUN
ap-9572	293	27	12	12	NUM
ap-9572	293	28	.	.	PUNCT
ap-9572	294	1	-200	-200	NUM
ap-9572	294	2	0	0	NUM
ap-9572	294	3	200	200	NUM
ap-9572	294	4	400	400	NUM
ap-9572	294	5	600	600	NUM
ap-9572	294	6	800	800	NUM
ap-9572	294	7	1000	1000	NUM
ap-9572	294	8	0.5	0.5	NUM
ap-9572	294	9	1	1	NUM
ap-9572	294	10	1.5	1.5	NUM
ap-9572	294	11	2	2	NUM
ap-9572	294	12	2.5	2.5	NUM
ap-9572	294	13	first	first	ADJ
ap-9572	294	14	mode	mode	NOUN
ap-9572	294	15	time=0.k	time=0.k	X
ap-9572	294	16	second	second	ADJ
ap-9572	294	17	mode	mode	NOUN
ap-9572	294	18	time=0.k	time=0.k	PART
ap-9572	294	19	first	first	ADJ
ap-9572	294	20	mode	mode	PROPN
ap-9572	294	21	time=5.k	time=5.k	NOUN
ap-9572	294	22	second	second	ADJ
ap-9572	294	23	mode	mode	NOUN
ap-9572	294	24	time=5.k	time=5.k	NOUN
ap-9572	294	25	figure	figure	NOUN
ap-9572	294	26	12	12	NUM
ap-9572	294	27	.	.	PUNCT
ap-9572	295	1	variation	variation	NOUN
ap-9572	295	2	of	of	ADP
ap-9572	295	3	w(*10−5	w(*10−5	PROPN
ap-9572	295	4	)	)	PUNCT
ap-9572	295	5	for	for	ADP
ap-9572	295	6	different	different	ADJ
ap-9572	295	7	a	a	DET
ap-9572	295	8	b	b	NOUN
ap-9572	295	9	and	and	CCONJ
ap-9572	295	10	α	α	NOUN
ap-9572	295	11	=	=	SYM
ap-9572	295	12	β1	β1	PROPN
ap-9572	295	13	=	=	PUNCT
ap-9572	295	14	0.3	0.3	NUM
ap-9572	295	15	,	,	PUNCT
ap-9572	295	16	β2	β2	NOUN
ap-9572	295	17	=	=	SYM
ap-9572	295	18	α1	α1	PROPN
ap-9572	295	19	=	=	SYM
ap-9572	295	20	0.4	0.4	NUM
ap-9572	295	21	and	and	CCONJ
ap-9572	295	22	for	for	ADP
ap-9572	295	23	x	x	X
ap-9572	295	24	=	=	PUNCT
ap-9572	295	25	y	y	PROPN
ap-9572	295	26	=	=	SYM
ap-9572	295	27	0.2	0.2	NUM
ap-9572	295	28	.	.	PUNCT
ap-9572	296	1	α1	α1	PROPN
ap-9572	296	2	=	=	SYM
ap-9572	296	3	0.0	0.0	NUM
ap-9572	296	4	,	,	PUNCT
ap-9572	296	5	α	α	NOUN
ap-9572	296	6	=	=	SYM
ap-9572	296	7	0.0	0.0	NUM
ap-9572	296	8	,	,	PUNCT
ap-9572	296	9	a	a	DET
ap-9572	296	10	b	b	NOUN
ap-9572	296	11	=	=	SYM
ap-9572	296	12	1.5	1.5	NUM
ap-9572	296	13	α1	α1	NOUN
ap-9572	296	14	=	=	SYM
ap-9572	296	15	0.4	0.4	NUM
ap-9572	296	16	,	,	PUNCT
ap-9572	296	17	α	α	NOUN
ap-9572	296	18	=	=	SYM
ap-9572	296	19	0.0	0.0	NUM
ap-9572	296	20	,	,	PUNCT
ap-9572	296	21	a	a	DET
ap-9572	296	22	b	b	NOUN
ap-9572	296	23	=	=	SYM
ap-9572	296	24	1.5	1.5	NUM
ap-9572	296	25	β1	β1	NOUN
ap-9572	296	26	=	=	SYM
ap-9572	296	27	0.0	0.0	NUM
ap-9572	296	28	β2	β2	NOUN
ap-9572	296	29	=	=	SYM
ap-9572	296	30	0.0	0.0	NUM
ap-9572	296	31	β1	β1	NOUN
ap-9572	296	32	=	=	PUNCT
ap-9572	296	33	0.4	0.4	NUM
ap-9572	296	34	β2	β2	NOUN
ap-9572	296	35	=	=	PROPN
ap-9572	296	36	0.2	0.2	NUM
ap-9572	296	37	β1	β1	NOUN
ap-9572	296	38	=	=	PUNCT
ap-9572	296	39	0.0	0.0	NUM
ap-9572	296	40	β2	β2	NOUN
ap-9572	296	41	=	=	SYM
ap-9572	296	42	0.0	0.0	NUM
ap-9572	296	43	β1	β1	NOUN
ap-9572	296	44	=	=	PUNCT
ap-9572	296	45	0.4	0.4	NUM
ap-9572	296	46	β2	β2	NOUN
ap-9572	296	47	=	=	NOUN
ap-9572	296	48	0.2	0.2	NUM
ap-9572	296	49	mode	mode	NOUN
ap-9572	296	50	→	→	PUNCT
ap-9572	297	1	i	i	NOUN
ap-9572	297	2	ii	ii	VERB
ap-9572	298	1	i	i	PRON
ap-9572	298	2	ii	ii	VERB
ap-9572	299	1	i	i	PRON
ap-9572	299	2	ii	ii	VERB
ap-9572	300	1	i	i	PRON
ap-9572	300	2	ii	ii	PROPN
ap-9572	300	3	present	present	ADJ
ap-9572	300	4	study	study	NOUN
ap-9572	300	5	6	6	NUM
ap-9572	300	6	462	462	NUM
ap-9572	300	7	1	1	NUM
ap-9572	300	8	623	623	NUM
ap-9572	300	9	5	5	NUM
ap-9572	300	10	324	324	NUM
ap-9572	300	11	1	1	NUM
ap-9572	300	12	332	332	NUM
ap-9572	300	13	6	6	NUM
ap-9572	300	14	897	897	NUM
ap-9572	300	15	1	1	NUM
ap-9572	300	16	728	728	NUM
ap-9572	300	17	5	5	NUM
ap-9572	300	18	543	543	NUM
ap-9572	300	19	1	1	NUM
ap-9572	300	20	433	433	NUM
ap-9572	301	1	[	[	X
ap-9572	301	2	13	13	NUM
ap-9572	301	3	]	]	SYM
ap-9572	301	4	6	6	NUM
ap-9572	301	5	462	462	NUM
ap-9572	301	6	1	1	NUM
ap-9572	301	7	623	623	NUM
ap-9572	301	8	5	5	NUM
ap-9572	301	9	324	324	NUM
ap-9572	301	10	1	1	NUM
ap-9572	301	11	332	332	NUM
ap-9572	301	12	6	6	NUM
ap-9572	301	13	883	883	NUM
ap-9572	301	14	1	1	NUM
ap-9572	301	15	724	724	NUM
ap-9572	301	16	5	5	NUM
ap-9572	301	17	531	531	NUM
ap-9572	301	18	1	1	NUM
ap-9572	301	19	428	428	NUM
ap-9572	301	20	table	table	NOUN
ap-9572	301	21	13	13	NUM
ap-9572	301	22	.	.	PUNCT
ap-9572	302	1	the	the	DET
ap-9572	302	2	comparative	comparative	ADJ
ap-9572	302	3	data	datum	NOUN
ap-9572	302	4	of	of	ADP
ap-9572	302	5	the	the	DET
ap-9572	302	6	time	time	NOUN
ap-9572	302	7	period	period	NOUN
ap-9572	302	8	with	with	ADP
ap-9572	302	9	the	the	DET
ap-9572	302	10	reference	reference	NOUN
ap-9572	302	11	[	[	X
ap-9572	302	12	13	13	NUM
ap-9572	302	13	]	]	PUNCT
ap-9572	302	14	.	.	PUNCT
ap-9572	303	1	α1	α1	PROPN
ap-9572	303	2	=	=	PUNCT
ap-9572	303	3	α	α	PROPN
ap-9572	303	4	=	=	SYM
ap-9572	303	5	β1	β1	PROPN
ap-9572	303	6	=	=	SYM
ap-9572	303	7	β2	β2	NOUN
ap-9572	303	8	=	=	NOUN
ap-9572	303	9	0.0	0.0	NUM
ap-9572	303	10	α1	α1	NOUN
ap-9572	303	11	=	=	SYM
ap-9572	303	12	0.4	0.4	NUM
ap-9572	303	13	,	,	PUNCT
ap-9572	303	14	α	α	NOUN
ap-9572	303	15	=	=	SYM
ap-9572	303	16	β1	β1	PROPN
ap-9572	303	17	=	=	SYM
ap-9572	303	18	β2	β2	NOUN
ap-9572	303	19	=	=	NOUN
ap-9572	303	20	0.0	0.0	NUM
ap-9572	303	21	a	a	DET
ap-9572	303	22	b	b	NOUN
ap-9572	303	23	=	=	SYM
ap-9572	303	24	1.0	1.0	NUM
ap-9572	303	25	a	a	DET
ap-9572	303	26	b	b	NOUN
ap-9572	303	27	=	=	SYM
ap-9572	303	28	2.0	2.0	NUM
ap-9572	303	29	a	a	DET
ap-9572	303	30	b	b	NOUN
ap-9572	303	31	=	=	SYM
ap-9572	303	32	1.0	1.0	NUM
ap-9572	303	33	a	a	DET
ap-9572	303	34	b	b	NOUN
ap-9572	303	35	=	=	SYM
ap-9572	303	36	2.0	2.0	NUM
ap-9572	303	37	mode	mode	NOUN
ap-9572	303	38	→	→	PUNCT
ap-9572	304	1	i	i	NOUN
ap-9572	304	2	ii	ii	VERB
ap-9572	305	1	i	i	PRON
ap-9572	305	2	ii	ii	VERB
ap-9572	306	1	i	i	PRON
ap-9572	306	2	ii	ii	VERB
ap-9572	307	1	i	i	PRON
ap-9572	307	2	ii	ii	VERB
ap-9572	307	3	present	present	ADJ
ap-9572	307	4	study	study	NOUN
ap-9572	307	5	10	10	NUM
ap-9572	307	6	411	411	NUM
ap-9572	307	7	2	2	NUM
ap-9572	307	8	638	638	NUM
ap-9572	307	9	3	3	NUM
ap-9572	307	10	724	724	NUM
ap-9572	307	11	905	905	NUM
ap-9572	307	12	10	10	NUM
ap-9572	307	13	860	860	NUM
ap-9572	307	14	2	2	NUM
ap-9572	307	15	747	747	NUM
ap-9572	307	16	4	4	NUM
ap-9572	307	17	082	082	NUM
ap-9572	307	18	961	961	NUM
ap-9572	308	1	[	[	X
ap-9572	308	2	13	13	NUM
ap-9572	308	3	]	]	SYM
ap-9572	308	4	10	10	NUM
ap-9572	308	5	411	411	NUM
ap-9572	308	6	2	2	NUM
ap-9572	308	7	638	638	NUM
ap-9572	308	8	3	3	NUM
ap-9572	308	9	724	724	NUM
ap-9572	308	10	905	905	NUM
ap-9572	308	11	10	10	NUM
ap-9572	308	12	847	847	NUM
ap-9572	308	13	2	2	NUM
ap-9572	308	14	741	741	NUM
ap-9572	308	15	4	4	NUM
ap-9572	308	16	073	073	NUM
ap-9572	308	17	958	958	NUM
ap-9572	308	18	table	table	NOUN
ap-9572	308	19	14	14	NUM
ap-9572	308	20	.	.	PUNCT
ap-9572	309	1	the	the	DET
ap-9572	309	2	comparative	comparative	ADJ
ap-9572	309	3	data	datum	NOUN
ap-9572	309	4	of	of	ADP
ap-9572	309	5	the	the	DET
ap-9572	309	6	time	time	NOUN
ap-9572	309	7	period	period	NOUN
ap-9572	309	8	with	with	ADP
ap-9572	309	9	the	the	DET
ap-9572	309	10	reference	reference	NOUN
ap-9572	309	11	[	[	X
ap-9572	309	12	13	13	NUM
ap-9572	309	13	]	]	PUNCT
ap-9572	309	14	.	.	PUNCT
ap-9572	310	1	two	two	NUM
ap-9572	310	2	studies	study	NOUN
ap-9572	310	3	for	for	ADP
ap-9572	310	4	the	the	DET
ap-9572	310	5	time	time	NOUN
ap-9572	310	6	function	function	NOUN
ap-9572	310	7	is	be	AUX
ap-9572	310	8	shown	show	VERB
ap-9572	310	9	in	in	ADP
ap-9572	310	10	tables	table	NOUN
ap-9572	310	11	13	13	NUM
ap-9572	310	12	–	–	SYM
ap-9572	310	13	15	15	NUM
ap-9572	310	14	while	while	SCONJ
ap-9572	310	15	the	the	DET
ap-9572	310	16	comparison	comparison	NOUN
ap-9572	310	17	of	of	ADP
ap-9572	310	18	the	the	DET
ap-9572	310	19	results	result	NOUN
ap-9572	310	20	of	of	ADP
ap-9572	310	21	the	the	DET
ap-9572	310	22	deflection	deflection	NOUN
ap-9572	310	23	are	be	AUX
ap-9572	310	24	shown	show	VERB
ap-9572	310	25	in	in	ADP
ap-9572	310	26	tables	table	NOUN
ap-9572	310	27	16–21	16–21	NUM
ap-9572	310	28	.	.	PUNCT
ap-9572	311	1	the	the	DET
ap-9572	311	2	tables	table	NOUN
ap-9572	311	3	13–15	13–15	PROPN
ap-9572	311	4	show	show	VERB
ap-9572	311	5	that	that	SCONJ
ap-9572	311	6	the	the	DET
ap-9572	311	7	results	result	NOUN
ap-9572	311	8	of	of	ADP
ap-9572	311	9	the	the	DET
ap-9572	311	10	period	period	NOUN
ap-9572	311	11	for	for	ADP
ap-9572	311	12	the	the	DET
ap-9572	311	13	present	present	ADJ
ap-9572	311	14	study	study	NOUN
ap-9572	311	15	and	and	CCONJ
ap-9572	311	16	the	the	DET
ap-9572	311	17	reference	reference	NOUN
ap-9572	311	18	[	[	X
ap-9572	311	19	13	13	NUM
ap-9572	311	20	]	]	PUNCT
ap-9572	311	21	are	be	AUX
ap-9572	311	22	identical	identical	ADJ
ap-9572	311	23	when	when	SCONJ
ap-9572	311	24	the	the	DET
ap-9572	311	25	value	value	NOUN
ap-9572	311	26	of	of	ADP
ap-9572	311	27	the	the	DET
ap-9572	311	28	constant	constant	NOUN
ap-9572	311	29	of	of	ADP
ap-9572	311	30	non	non	ADJ
ap-9572	311	31	-	-	NOUN
ap-9572	311	32	homogeneity	homogeneity	ADJ
ap-9572	311	33	(	(	PUNCT
ap-9572	311	34	α1	α1	PROPN
ap-9572	311	35	)	)	PUNCT
ap-9572	311	36	is	be	AUX
ap-9572	311	37	zero	zero	NUM
ap-9572	311	38	.	.	PUNCT
ap-9572	312	1	these	these	DET
ap-9572	312	2	tables	table	NOUN
ap-9572	312	3	also	also	ADV
ap-9572	312	4	show	show	VERB
ap-9572	312	5	that	that	SCONJ
ap-9572	312	6	the	the	DET
ap-9572	312	7	quadratic	quadratic	ADJ
ap-9572	312	8	variation	variation	NOUN
ap-9572	312	9	in	in	ADP
ap-9572	312	10	the	the	DET
ap-9572	312	11	material	material	NOUN
ap-9572	312	12	density	density	NOUN
ap-9572	312	13	of	of	ADP
ap-9572	312	14	the	the	DET
ap-9572	312	15	plate	plate	NOUN
ap-9572	312	16	along	along	ADP
ap-9572	312	17	the	the	DET
ap-9572	312	18	x	x	NOUN
ap-9572	312	19	-	-	NOUN
ap-9572	312	20	axis	axis	NOUN
ap-9572	312	21	is	be	AUX
ap-9572	312	22	more	more	ADV
ap-9572	312	23	dominant	dominant	ADJ
ap-9572	312	24	as	as	ADP
ap-9572	312	25	compared	compare	VERB
ap-9572	312	26	to	to	ADP
ap-9572	312	27	that	that	PRON
ap-9572	312	28	along	along	ADP
ap-9572	312	29	the	the	DET
ap-9572	312	30	x	x	NOUN
ap-9572	312	31	-	-	NOUN
ap-9572	312	32	axis	axis	ADJ
ap-9572	312	33	.	.	PUNCT
ap-9572	313	1	tables	table	NOUN
ap-9572	313	2	16–18	16–18	NUM
ap-9572	313	3	show	show	NOUN
ap-9572	313	4	that	that	SCONJ
ap-9572	313	5	the	the	DET
ap-9572	313	6	results	result	NOUN
ap-9572	313	7	of	of	ADP
ap-9572	313	8	the	the	DET
ap-9572	313	9	deflection	deflection	NOUN
ap-9572	313	10	for	for	ADP
ap-9572	313	11	the	the	DET
ap-9572	313	12	present	present	ADJ
ap-9572	313	13	study	study	NOUN
ap-9572	313	14	and	and	CCONJ
ap-9572	313	15	the	the	DET
ap-9572	313	16	reference	reference	NOUN
ap-9572	313	17	[	[	X
ap-9572	313	18	13	13	NUM
ap-9572	313	19	]	]	PUNCT
ap-9572	313	20	are	be	AUX
ap-9572	313	21	identical	identical	ADJ
ap-9572	313	22	when	when	SCONJ
ap-9572	313	23	the	the	DET
ap-9572	313	24	value	value	NOUN
ap-9572	313	25	of	of	ADP
ap-9572	313	26	the	the	DET
ap-9572	313	27	constant	constant	NOUN
ap-9572	313	28	of	of	ADP
ap-9572	313	29	non	non	ADJ
ap-9572	313	30	-	-	NOUN
ap-9572	313	31	homogeneity	homogeneity	ADJ
ap-9572	313	32	(	(	PUNCT
ap-9572	313	33	α1	α1	PROPN
ap-9572	313	34	)	)	PUNCT
ap-9572	313	35	is	be	AUX
ap-9572	313	36	zero	zero	NUM
ap-9572	313	37	.	.	PUNCT
ap-9572	314	1	the	the	DET
ap-9572	314	2	results	result	NOUN
ap-9572	314	3	shown	show	VERB
ap-9572	314	4	in	in	ADP
ap-9572	314	5	tables	table	NOUN
ap-9572	314	6	19–21	19–21	NUM
ap-9572	314	7	indicate	indicate	VERB
ap-9572	314	8	that	that	SCONJ
ap-9572	314	9	the	the	DET
ap-9572	314	10	quadratic	quadratic	ADJ
ap-9572	314	11	variation	variation	NOUN
ap-9572	314	12	in	in	ADP
ap-9572	314	13	the	the	DET
ap-9572	314	14	material	material	NOUN
ap-9572	314	15	density	density	NOUN
ap-9572	314	16	of	of	ADP
ap-9572	314	17	the	the	DET
ap-9572	314	18	310	310	NUM
ap-9572	314	19	vol	vol	NOUN
ap-9572	314	20	.	.	PROPN
ap-9572	315	1	64	64	NUM
ap-9572	315	2	no	no	NOUN
ap-9572	315	3	.	.	PUNCT
ap-9572	316	1	4/2024	4/2024	NUM
ap-9572	316	2	non	non	ADJ
ap-9572	316	3	-	-	ADJ
ap-9572	316	4	homogeneity	homogeneity	ADJ
ap-9572	316	5	effect	effect	NOUN
ap-9572	316	6	on	on	ADP
ap-9572	316	7	the	the	DET
ap-9572	316	8	vibration	vibration	NOUN
ap-9572	316	9	of	of	ADP
ap-9572	316	10	.	.	PUNCT
ap-9572	316	11	.	.	PUNCT
ap-9572	316	12	.	.	PUNCT
ap-9572	317	1	α1	α1	PROPN
ap-9572	317	2	=	=	SYM
ap-9572	317	3	0.0	0.0	NUM
ap-9572	317	4	,	,	PUNCT
ap-9572	317	5	α	α	NOUN
ap-9572	317	6	=	=	SYM
ap-9572	317	7	0.6	0.6	NUM
ap-9572	317	8	,	,	PUNCT
ap-9572	317	9	a	a	DET
ap-9572	317	10	b	b	NOUN
ap-9572	317	11	=	=	SYM
ap-9572	317	12	1.5	1.5	NUM
ap-9572	317	13	α1	α1	NOUN
ap-9572	317	14	=	=	SYM
ap-9572	317	15	0.4	0.4	NUM
ap-9572	317	16	,	,	PUNCT
ap-9572	317	17	α	α	NOUN
ap-9572	317	18	=	=	SYM
ap-9572	317	19	0.6	0.6	NUM
ap-9572	317	20	,	,	PUNCT
ap-9572	317	21	a	a	DET
ap-9572	317	22	b	b	NOUN
ap-9572	317	23	=	=	SYM
ap-9572	317	24	1.5	1.5	NUM
ap-9572	317	25	β1	β1	NOUN
ap-9572	317	26	=	=	SYM
ap-9572	317	27	0.0	0.0	NUM
ap-9572	317	28	β2	β2	NOUN
ap-9572	317	29	=	=	SYM
ap-9572	317	30	0.0	0.0	NUM
ap-9572	317	31	β1	β1	NOUN
ap-9572	317	32	=	=	PUNCT
ap-9572	317	33	0.4	0.4	NUM
ap-9572	317	34	β2	β2	NOUN
ap-9572	317	35	=	=	PROPN
ap-9572	317	36	0.2	0.2	NUM
ap-9572	317	37	β1	β1	NOUN
ap-9572	317	38	=	=	PUNCT
ap-9572	317	39	0.0	0.0	NUM
ap-9572	317	40	β2	β2	NOUN
ap-9572	317	41	=	=	SYM
ap-9572	317	42	0.0	0.0	NUM
ap-9572	317	43	β1	β1	NOUN
ap-9572	317	44	=	=	PUNCT
ap-9572	317	45	0.4	0.4	NUM
ap-9572	317	46	β2	β2	NOUN
ap-9572	317	47	=	=	NOUN
ap-9572	317	48	0.2	0.2	NUM
ap-9572	317	49	mode	mode	NOUN
ap-9572	317	50	→	→	PUNCT
ap-9572	318	1	i	i	NOUN
ap-9572	318	2	ii	ii	VERB
ap-9572	319	1	i	i	PRON
ap-9572	319	2	ii	ii	VERB
ap-9572	320	1	i	i	PRON
ap-9572	320	2	ii	ii	VERB
ap-9572	321	1	i	i	PRON
ap-9572	321	2	ii	ii	VERB
ap-9572	321	3	present	present	ADJ
ap-9572	321	4	study	study	NOUN
ap-9572	321	5	7	7	NUM
ap-9572	321	6	737	737	NUM
ap-9572	321	7	2	2	NUM
ap-9572	321	8	002	002	NUM
ap-9572	321	9	6	6	NUM
ap-9572	321	10	213	213	NUM
ap-9572	321	11	1	1	NUM
ap-9572	321	12	603	603	NUM
ap-9572	321	13	8	8	NUM
ap-9572	321	14	497	497	NUM
ap-9572	321	15	2	2	NUM
ap-9572	321	16	176	176	NUM
ap-9572	321	17	6	6	NUM
ap-9572	321	18	626	626	NUM
ap-9572	321	19	1	1	NUM
ap-9572	321	20	759	759	NUM
ap-9572	321	21	[	[	X
ap-9572	321	22	13	13	NUM
ap-9572	321	23	]	]	SYM
ap-9572	321	24	7	7	NUM
ap-9572	321	25	737	737	NUM
ap-9572	321	26	2	2	NUM
ap-9572	321	27	002	002	NUM
ap-9572	321	28	6	6	NUM
ap-9572	321	29	213	213	NUM
ap-9572	321	30	1	1	NUM
ap-9572	321	31	603	603	NUM
ap-9572	321	32	8	8	NUM
ap-9572	321	33	486	486	NUM
ap-9572	321	34	2	2	NUM
ap-9572	321	35	173	173	NUM
ap-9572	321	36	6	6	NUM
ap-9572	321	37	617	617	NUM
ap-9572	321	38	1	1	NUM
ap-9572	321	39	756	756	NUM
ap-9572	321	40	table	table	NOUN
ap-9572	321	41	15	15	NUM
ap-9572	321	42	.	.	PUNCT
ap-9572	322	1	the	the	DET
ap-9572	322	2	comparative	comparative	ADJ
ap-9572	322	3	data	datum	NOUN
ap-9572	322	4	of	of	ADP
ap-9572	322	5	the	the	DET
ap-9572	322	6	time	time	NOUN
ap-9572	322	7	period	period	NOUN
ap-9572	322	8	with	with	ADP
ap-9572	322	9	the	the	DET
ap-9572	322	10	reference	reference	NOUN
ap-9572	322	11	[	[	X
ap-9572	322	12	13	13	NUM
ap-9572	322	13	]	]	PUNCT
ap-9572	322	14	.	.	PUNCT
ap-9572	323	1	time	time	NOUN
ap-9572	324	1	=	=	SYM
ap-9572	324	2	0.0	0.0	NUM
ap-9572	324	3	×	×	NOUN
ap-9572	324	4	tp	tp	NOUN
ap-9572	324	5	time	time	NOUN
ap-9572	324	6	=	=	SYM
ap-9572	324	7	5.0	5.0	NUM
ap-9572	324	8	×	×	NOUN
ap-9572	324	9	tp	tp	NOUN
ap-9572	324	10	mode	mode	NOUN
ap-9572	324	11	→	→	PUNCT
ap-9572	325	1	i	i	NOUN
ap-9572	325	2	ii	ii	VERB
ap-9572	326	1	i	i	PRON
ap-9572	326	2	ii	ii	VERB
ap-9572	326	3	present	present	ADJ
ap-9572	326	4	study	study	NOUN
ap-9572	326	5	126.32	126.32	NUM
ap-9572	326	6	38.87	38.87	NUM
ap-9572	326	7	55.12	55.12	NUM
ap-9572	326	8	1.38	1.38	NUM
ap-9572	326	9	[	[	X
ap-9572	326	10	13	13	NUM
ap-9572	326	11	]	]	PUNCT
ap-9572	326	12	126.32	126.32	NUM
ap-9572	326	13	38.87	38.87	NUM
ap-9572	326	14	55.12	55.12	NUM
ap-9572	326	15	1.38	1.38	NUM
ap-9572	326	16	table	table	NOUN
ap-9572	326	17	16	16	NUM
ap-9572	326	18	.	.	PUNCT
ap-9572	327	1	the	the	DET
ap-9572	327	2	comparative	comparative	ADJ
ap-9572	327	3	data	datum	NOUN
ap-9572	327	4	of	of	ADP
ap-9572	327	5	the	the	DET
ap-9572	327	6	deflection	deflection	NOUN
ap-9572	327	7	with	with	ADP
ap-9572	327	8	the	the	DET
ap-9572	327	9	reference	reference	NOUN
ap-9572	327	10	[	[	X
ap-9572	327	11	13	13	NUM
ap-9572	327	12	]	]	PUNCT
ap-9572	327	13	;	;	PUNCT
ap-9572	327	14	α	α	X
ap-9572	327	15	=	=	SYM
ap-9572	327	16	β1	β1	PROPN
ap-9572	327	17	=	=	SYM
ap-9572	327	18	β2	β2	NOUN
ap-9572	327	19	=	=	SYM
ap-9572	327	20	α1	α1	PROPN
ap-9572	327	21	=	=	SYM
ap-9572	327	22	0.0	0.0	NUM
ap-9572	327	23	,	,	PUNCT
ap-9572	327	24	a	a	DET
ap-9572	327	25	b	b	NOUN
ap-9572	327	26	=	=	SYM
ap-9572	327	27	1.5	1.5	NUM
ap-9572	327	28	,	,	PUNCT
ap-9572	327	29	x	x	PUNCT
ap-9572	327	30	=	=	PUNCT
ap-9572	327	31	y	y	PROPN
ap-9572	327	32	=	=	SYM
ap-9572	327	33	0.20	0.20	NUM
ap-9572	327	34	.	.	PUNCT
ap-9572	327	35	time	time	NOUN
ap-9572	327	36	=	=	SYM
ap-9572	327	37	0.0	0.0	NUM
ap-9572	327	38	×	×	NOUN
ap-9572	327	39	tp	tp	NOUN
ap-9572	327	40	time	time	NOUN
ap-9572	327	41	=	=	SYM
ap-9572	327	42	5.0	5.0	NUM
ap-9572	327	43	×	×	NOUN
ap-9572	327	44	tp	tp	NOUN
ap-9572	327	45	mode	mode	NOUN
ap-9572	327	46	→	→	PUNCT
ap-9572	327	47	i	i	NOUN
ap-9572	327	48	ii	ii	VERB
ap-9572	328	1	i	i	PRON
ap-9572	328	2	ii	ii	VERB
ap-9572	328	3	present	present	ADJ
ap-9572	328	4	study	study	NOUN
ap-9572	328	5	233.96	233.96	NUM
ap-9572	328	6	37.37	37.37	NUM
ap-9572	328	7	61.42	61.42	NUM
ap-9572	328	8	0.14	0.14	NUM
ap-9572	328	9	[	[	X
ap-9572	328	10	13	13	NUM
ap-9572	328	11	]	]	PUNCT
ap-9572	328	12	233.96	233.96	NUM
ap-9572	328	13	37.37	37.37	NUM
ap-9572	328	14	61.42	61.42	NUM
ap-9572	328	15	0.14	0.14	NUM
ap-9572	328	16	table	table	NOUN
ap-9572	328	17	17	17	NUM
ap-9572	328	18	.	.	PUNCT
ap-9572	329	1	the	the	DET
ap-9572	329	2	comparative	comparative	ADJ
ap-9572	329	3	data	datum	NOUN
ap-9572	329	4	of	of	ADP
ap-9572	329	5	the	the	DET
ap-9572	329	6	deflection	deflection	NOUN
ap-9572	329	7	with	with	ADP
ap-9572	329	8	the	the	DET
ap-9572	329	9	reference	reference	NOUN
ap-9572	329	10	[	[	X
ap-9572	329	11	13	13	NUM
ap-9572	329	12	]	]	PUNCT
ap-9572	329	13	;	;	PUNCT
ap-9572	329	14	α	α	X
ap-9572	329	15	=	=	SYM
ap-9572	329	16	β1	β1	PROPN
ap-9572	329	17	=	=	SYM
ap-9572	329	18	β2	β2	NOUN
ap-9572	329	19	=	=	SYM
ap-9572	329	20	α1	α1	PROPN
ap-9572	329	21	=	=	SYM
ap-9572	329	22	0.0	0.0	NUM
ap-9572	329	23	,	,	PUNCT
ap-9572	329	24	a	a	DET
ap-9572	329	25	b	b	NOUN
ap-9572	329	26	=	=	SYM
ap-9572	329	27	2.0	2.0	NUM
ap-9572	329	28	,	,	PUNCT
ap-9572	329	29	x	x	PUNCT
ap-9572	329	30	=	=	PUNCT
ap-9572	329	31	y	y	PROPN
ap-9572	329	32	=	=	SYM
ap-9572	329	33	0.20	0.20	NUM
ap-9572	329	34	.	.	PUNCT
ap-9572	329	35	time	time	NOUN
ap-9572	329	36	=	=	SYM
ap-9572	329	37	0.0	0.0	NUM
ap-9572	329	38	×	×	NOUN
ap-9572	329	39	tp	tp	NOUN
ap-9572	329	40	time	time	NOUN
ap-9572	329	41	=	=	SYM
ap-9572	329	42	5.0	5.0	NUM
ap-9572	329	43	×	×	NOUN
ap-9572	329	44	tp	tp	NOUN
ap-9572	329	45	mode	mode	NOUN
ap-9572	329	46	→	→	PUNCT
ap-9572	329	47	i	i	NOUN
ap-9572	329	48	ii	ii	VERB
ap-9572	330	1	i	i	PRON
ap-9572	330	2	ii	ii	VERB
ap-9572	330	3	present	present	ADJ
ap-9572	330	4	study	study	VERB
ap-9572	330	5	427.32	427.32	NUM
ap-9572	330	6	14.52	14.52	NUM
ap-9572	330	7	187.31	187.31	NUM
ap-9572	330	8	0.53	0.53	NUM
ap-9572	331	1	[	[	X
ap-9572	331	2	13	13	NUM
ap-9572	331	3	]	]	PUNCT
ap-9572	331	4	427.32	427.32	NUM
ap-9572	331	5	14.52	14.52	NUM
ap-9572	331	6	187.31	187.31	NUM
ap-9572	331	7	0.53	0.53	NUM
ap-9572	331	8	table	table	NOUN
ap-9572	331	9	18	18	NUM
ap-9572	331	10	.	.	PUNCT
ap-9572	332	1	the	the	DET
ap-9572	332	2	comparative	comparative	ADJ
ap-9572	332	3	data	datum	NOUN
ap-9572	332	4	of	of	ADP
ap-9572	332	5	the	the	DET
ap-9572	332	6	deflection	deflection	NOUN
ap-9572	332	7	with	with	ADP
ap-9572	332	8	the	the	DET
ap-9572	332	9	reference	reference	NOUN
ap-9572	332	10	[	[	X
ap-9572	332	11	13	13	NUM
ap-9572	332	12	]	]	PUNCT
ap-9572	332	13	;	;	PUNCT
ap-9572	332	14	α	α	X
ap-9572	332	15	=	=	SYM
ap-9572	332	16	β1	β1	PROPN
ap-9572	332	17	=	=	SYM
ap-9572	332	18	β2	β2	NOUN
ap-9572	332	19	=	=	SYM
ap-9572	332	20	α1	α1	PROPN
ap-9572	332	21	=	=	SYM
ap-9572	332	22	0.0	0.0	NUM
ap-9572	332	23	,	,	PUNCT
ap-9572	332	24	a	a	DET
ap-9572	332	25	b	b	NOUN
ap-9572	332	26	=	=	SYM
ap-9572	332	27	1.5	1.5	NUM
ap-9572	332	28	,	,	PUNCT
ap-9572	332	29	x	x	PUNCT
ap-9572	332	30	=	=	SYM
ap-9572	332	31	0.20	0.20	NUM
ap-9572	332	32	,	,	PUNCT
ap-9572	332	33	y	y	PROPN
ap-9572	332	34	=	=	NOUN
ap-9572	332	35	0.60	0.60	NUM
ap-9572	332	36	.	.	PUNCT
ap-9572	332	37	time	time	NOUN
ap-9572	332	38	=	=	SYM
ap-9572	332	39	0.0	0.0	NUM
ap-9572	332	40	×	×	NOUN
ap-9572	332	41	tp	tp	NOUN
ap-9572	332	42	time	time	NOUN
ap-9572	332	43	=	=	SYM
ap-9572	332	44	5.0	5.0	NUM
ap-9572	332	45	×	×	NOUN
ap-9572	332	46	tp	tp	NOUN
ap-9572	332	47	mode	mode	NOUN
ap-9572	332	48	→	→	PUNCT
ap-9572	332	49	i	i	NOUN
ap-9572	332	50	ii	ii	VERB
ap-9572	333	1	i	i	PRON
ap-9572	333	2	ii	ii	VERB
ap-9572	333	3	present	present	ADJ
ap-9572	333	4	study	study	NOUN
ap-9572	333	5	130.43	130.43	NUM
ap-9572	333	6	40.12	40.12	NUM
ap-9572	333	7	59.13	59.13	NUM
ap-9572	333	8	1.93	1.93	NUM
ap-9572	333	9	[	[	X
ap-9572	333	10	13	13	NUM
ap-9572	333	11	]	]	PUNCT
ap-9572	333	12	128.62	128.62	NUM
ap-9572	333	13	39.74	39.74	NUM
ap-9572	333	14	57.36	57.36	NUM
ap-9572	333	15	1.58	1.58	NUM
ap-9572	333	16	table	table	NOUN
ap-9572	333	17	19	19	NUM
ap-9572	333	18	.	.	PUNCT
ap-9572	334	1	the	the	DET
ap-9572	334	2	comparative	comparative	ADJ
ap-9572	334	3	data	datum	NOUN
ap-9572	334	4	of	of	ADP
ap-9572	334	5	the	the	DET
ap-9572	334	6	deflection	deflection	NOUN
ap-9572	334	7	with	with	ADP
ap-9572	334	8	the	the	DET
ap-9572	334	9	reference	reference	NOUN
ap-9572	334	10	[	[	X
ap-9572	334	11	13	13	NUM
ap-9572	334	12	]	]	PUNCT
ap-9572	334	13	;	;	PUNCT
ap-9572	334	14	α	α	X
ap-9572	334	15	=	=	SYM
ap-9572	334	16	β1	β1	PROPN
ap-9572	334	17	=	=	SYM
ap-9572	334	18	β2	β2	NOUN
ap-9572	334	19	=	=	PROPN
ap-9572	334	20	α1	α1	PROPN
ap-9572	334	21	=	=	SYM
ap-9572	334	22	0.4	0.4	NUM
ap-9572	334	23	,	,	PUNCT
ap-9572	334	24	a	a	DET
ap-9572	334	25	b	b	NOUN
ap-9572	334	26	=	=	SYM
ap-9572	334	27	1.5	1.5	NUM
ap-9572	334	28	,	,	PUNCT
ap-9572	334	29	x	x	PUNCT
ap-9572	334	30	=	=	PUNCT
ap-9572	334	31	y	y	PROPN
ap-9572	334	32	=	=	SYM
ap-9572	334	33	0.20	0.20	NUM
ap-9572	334	34	.	.	PUNCT
ap-9572	334	35	time	time	NOUN
ap-9572	334	36	=	=	SYM
ap-9572	334	37	0.0	0.0	NUM
ap-9572	334	38	×	×	NOUN
ap-9572	334	39	tp	tp	NOUN
ap-9572	334	40	time	time	NOUN
ap-9572	334	41	=	=	SYM
ap-9572	334	42	5.0	5.0	NUM
ap-9572	334	43	×	×	NOUN
ap-9572	334	44	tp	tp	NOUN
ap-9572	334	45	mode	mode	NOUN
ap-9572	334	46	→	→	PUNCT
ap-9572	334	47	i	i	NOUN
ap-9572	334	48	ii	ii	VERB
ap-9572	335	1	i	i	PRON
ap-9572	335	2	ii	ii	VERB
ap-9572	335	3	present	present	ADJ
ap-9572	335	4	study	study	NOUN
ap-9572	335	5	238.27	238.27	NUM
ap-9572	335	6	39.11	39.11	NUM
ap-9572	335	7	64.92	64.92	NUM
ap-9572	335	8	0.21	0.21	NUM
ap-9572	336	1	[	[	X
ap-9572	336	2	13	13	NUM
ap-9572	336	3	]	]	PUNCT
ap-9572	336	4	236.43	236.43	NUM
ap-9572	336	5	38.15	38.15	NUM
ap-9572	336	6	63.88	63.88	NUM
ap-9572	336	7	0.18	0.18	NUM
ap-9572	336	8	table	table	NOUN
ap-9572	336	9	20	20	NUM
ap-9572	336	10	.	.	PUNCT
ap-9572	337	1	the	the	DET
ap-9572	337	2	comparative	comparative	ADJ
ap-9572	337	3	data	datum	NOUN
ap-9572	337	4	of	of	ADP
ap-9572	337	5	the	the	DET
ap-9572	337	6	deflection	deflection	NOUN
ap-9572	337	7	with	with	ADP
ap-9572	337	8	the	the	DET
ap-9572	337	9	reference	reference	NOUN
ap-9572	337	10	[	[	X
ap-9572	337	11	13	13	NUM
ap-9572	337	12	]	]	PUNCT
ap-9572	337	13	;	;	PUNCT
ap-9572	337	14	α	α	X
ap-9572	337	15	=	=	SYM
ap-9572	337	16	β1	β1	PROPN
ap-9572	337	17	=	=	SYM
ap-9572	337	18	β2	β2	NOUN
ap-9572	337	19	=	=	PROPN
ap-9572	337	20	α1	α1	PROPN
ap-9572	337	21	=	=	SYM
ap-9572	337	22	0.4	0.4	NUM
ap-9572	337	23	,	,	PUNCT
ap-9572	337	24	a	a	DET
ap-9572	337	25	b	b	NOUN
ap-9572	337	26	=	=	SYM
ap-9572	337	27	2.0	2.0	NUM
ap-9572	337	28	,	,	PUNCT
ap-9572	337	29	x	x	PUNCT
ap-9572	337	30	=	=	PUNCT
ap-9572	337	31	y	y	PROPN
ap-9572	337	32	=	=	SYM
ap-9572	337	33	0.20	0.20	NUM
ap-9572	337	34	.	.	PUNCT
ap-9572	337	35	time	time	NOUN
ap-9572	337	36	=	=	SYM
ap-9572	337	37	0.0	0.0	NUM
ap-9572	337	38	×	×	NOUN
ap-9572	337	39	tp	tp	NOUN
ap-9572	337	40	time	time	NOUN
ap-9572	337	41	=	=	SYM
ap-9572	337	42	5.0	5.0	NUM
ap-9572	337	43	×	×	NOUN
ap-9572	337	44	tp	tp	NOUN
ap-9572	337	45	mode	mode	NOUN
ap-9572	337	46	→	→	PUNCT
ap-9572	337	47	i	i	NOUN
ap-9572	337	48	ii	ii	VERB
ap-9572	338	1	i	i	PRON
ap-9572	338	2	ii	ii	VERB
ap-9572	338	3	present	present	ADJ
ap-9572	338	4	study	study	VERB
ap-9572	338	5	431.01	431.01	NUM
ap-9572	338	6	15.93	15.93	NUM
ap-9572	338	7	190.34	190.34	NUM
ap-9572	338	8	0.83	0.83	NUM
ap-9572	338	9	[	[	X
ap-9572	338	10	13	13	NUM
ap-9572	338	11	]	]	PUNCT
ap-9572	338	12	428.52	428.52	NUM
ap-9572	338	13	15.02	15.02	NUM
ap-9572	338	14	188.82	188.82	NUM
ap-9572	338	15	0.64	0.64	NUM
ap-9572	338	16	table	table	NOUN
ap-9572	338	17	21	21	NUM
ap-9572	338	18	.	.	PUNCT
ap-9572	339	1	the	the	DET
ap-9572	339	2	comparative	comparative	ADJ
ap-9572	339	3	data	datum	NOUN
ap-9572	339	4	of	of	ADP
ap-9572	339	5	the	the	DET
ap-9572	339	6	deflection	deflection	NOUN
ap-9572	339	7	with	with	ADP
ap-9572	339	8	the	the	DET
ap-9572	339	9	reference	reference	NOUN
ap-9572	339	10	[	[	X
ap-9572	339	11	13	13	NUM
ap-9572	339	12	]	]	PUNCT
ap-9572	339	13	;	;	PUNCT
ap-9572	339	14	α	α	X
ap-9572	339	15	=	=	SYM
ap-9572	339	16	β1	β1	PROPN
ap-9572	339	17	=	=	SYM
ap-9572	339	18	β2	β2	NOUN
ap-9572	339	19	=	=	PROPN
ap-9572	339	20	α1	α1	PROPN
ap-9572	339	21	=	=	SYM
ap-9572	339	22	0.4	0.4	NUM
ap-9572	339	23	,	,	PUNCT
ap-9572	339	24	a	a	DET
ap-9572	339	25	b	b	NOUN
ap-9572	339	26	=	=	SYM
ap-9572	339	27	1.5	1.5	NUM
ap-9572	339	28	,	,	PUNCT
ap-9572	339	29	x	x	PUNCT
ap-9572	339	30	=	=	SYM
ap-9572	339	31	0.20	0.20	NUM
ap-9572	339	32	,	,	PUNCT
ap-9572	339	33	y	y	PROPN
ap-9572	339	34	=	=	NOUN
ap-9572	339	35	0.60	0.60	NUM
ap-9572	339	36	.	.	PUNCT
ap-9572	340	1	311	311	NUM
ap-9572	340	2	sudhanshu	sudhanshu	NOUN
ap-9572	340	3	aggarwal	aggarwal	PROPN
ap-9572	340	4	acta	acta	PROPN
ap-9572	340	5	polytechnica	polytechnica	PROPN
ap-9572	340	6	plate	plate	NOUN
ap-9572	340	7	along	along	ADP
ap-9572	340	8	the	the	DET
ap-9572	340	9	x	x	NOUN
ap-9572	340	10	-	-	NOUN
ap-9572	340	11	axis	axis	NOUN
ap-9572	340	12	is	be	AUX
ap-9572	340	13	more	more	ADV
ap-9572	340	14	dominant	dominant	ADJ
ap-9572	340	15	as	as	ADP
ap-9572	340	16	compared	compare	VERB
ap-9572	340	17	to	to	ADP
ap-9572	340	18	that	that	PRON
ap-9572	340	19	along	along	ADP
ap-9572	340	20	the	the	DET
ap-9572	340	21	x	x	NOUN
ap-9572	340	22	-	-	NOUN
ap-9572	340	23	axis	axis	NOUN
ap-9572	340	24	.	.	PUNCT
ap-9572	341	1	the	the	DET
ap-9572	341	2	comparative	comparative	ADJ
ap-9572	341	3	study	study	NOUN
ap-9572	341	4	of	of	ADP
ap-9572	341	5	the	the	DET
ap-9572	341	6	present	present	ADJ
ap-9572	341	7	results	result	NOUN
ap-9572	341	8	with	with	ADP
ap-9572	341	9	the	the	DET
ap-9572	341	10	reference	reference	NOUN
ap-9572	341	11	[	[	X
ap-9572	341	12	13	13	NUM
ap-9572	341	13	]	]	PUNCT
ap-9572	341	14	using	use	VERB
ap-9572	341	15	tables	table	NOUN
ap-9572	341	16	13–21	13–21	NUM
ap-9572	341	17	ensure	ensure	VERB
ap-9572	341	18	the	the	DET
ap-9572	341	19	accuracy	accuracy	NOUN
ap-9572	341	20	and	and	CCONJ
ap-9572	341	21	the	the	DET
ap-9572	341	22	validity	validity	NOUN
ap-9572	341	23	of	of	ADP
ap-9572	341	24	the	the	DET
ap-9572	341	25	derived	derive	VERB
ap-9572	341	26	formulas	formula	NOUN
ap-9572	341	27	and	and	CCONJ
ap-9572	341	28	the	the	DET
ap-9572	341	29	results	result	NOUN
ap-9572	341	30	of	of	ADP
ap-9572	341	31	this	this	DET
ap-9572	341	32	study	study	NOUN
ap-9572	341	33	.	.	PUNCT
ap-9572	342	1	7	7	X
ap-9572	342	2	.	.	X
ap-9572	342	3	conclusion	conclusion	NOUN
ap-9572	342	4	the	the	DET
ap-9572	342	5	author	author	NOUN
ap-9572	342	6	effectively	effectively	ADV
ap-9572	342	7	discussed	discuss	VERB
ap-9572	342	8	the	the	DET
ap-9572	342	9	non	non	ADJ
ap-9572	342	10	-	-	ADJ
ap-9572	342	11	homogeneity	homogeneity	ADJ
ap-9572	342	12	effect	effect	NOUN
ap-9572	342	13	on	on	ADP
ap-9572	342	14	the	the	DET
ap-9572	342	15	vibration	vibration	NOUN
ap-9572	342	16	of	of	ADP
ap-9572	342	17	the	the	DET
ap-9572	342	18	rectangular	rectangular	ADJ
ap-9572	342	19	visco	visco	ADJ
ap-9572	342	20	-	-	ADJ
ap-9572	342	21	elastic	elastic	ADJ
ap-9572	342	22	plate	plate	NOUN
ap-9572	342	23	subjected	subject	VERB
ap-9572	342	24	to	to	ADP
ap-9572	342	25	the	the	DET
ap-9572	342	26	linear	linear	ADJ
ap-9572	342	27	temperature	temperature	NOUN
ap-9572	342	28	effect	effect	NOUN
ap-9572	342	29	with	with	ADP
ap-9572	342	30	both	both	CCONJ
ap-9572	342	31	the	the	DET
ap-9572	342	32	directions	direction	NOUN
ap-9572	342	33	quadratic	quadratic	ADJ
ap-9572	342	34	thickness	thickness	NOUN
ap-9572	342	35	variation	variation	NOUN
ap-9572	342	36	.	.	PUNCT
ap-9572	343	1	the	the	DET
ap-9572	343	2	results	result	NOUN
ap-9572	343	3	show	show	VERB
ap-9572	343	4	that	that	SCONJ
ap-9572	343	5	as	as	ADP
ap-9572	343	6	the	the	DET
ap-9572	343	7	non	non	ADJ
ap-9572	343	8	-	-	ADJ
ap-9572	343	9	homogeneity	homogeneity	ADJ
ap-9572	343	10	constant	constant	ADJ
ap-9572	343	11	increases	increase	NOUN
ap-9572	343	12	for	for	ADP
ap-9572	343	13	both	both	DET
ap-9572	343	14	modes	mode	NOUN
ap-9572	343	15	of	of	ADP
ap-9572	343	16	vibration	vibration	NOUN
ap-9572	343	17	,	,	PUNCT
ap-9572	343	18	the	the	DET
ap-9572	343	19	time	time	NOUN
ap-9572	343	20	function	function	NOUN
ap-9572	343	21	and	and	CCONJ
ap-9572	343	22	the	the	DET
ap-9572	343	23	deflection	deflection	NOUN
ap-9572	343	24	continuously	continuously	ADV
ap-9572	343	25	increase	increase	VERB
ap-9572	343	26	(	(	PUNCT
ap-9572	343	27	frequency	frequency	NOUN
ap-9572	343	28	decreases	decrease	VERB
ap-9572	343	29	)	)	PUNCT
ap-9572	343	30	,	,	PUNCT
ap-9572	343	31	therefore	therefore	ADV
ap-9572	343	32	the	the	DET
ap-9572	343	33	effect	effect	NOUN
ap-9572	343	34	of	of	ADP
ap-9572	343	35	non	non	ADJ
ap-9572	343	36	-	-	NOUN
ap-9572	343	37	homogeneity	homogeneity	NOUN
ap-9572	343	38	on	on	ADP
ap-9572	343	39	vibrations	vibration	NOUN
ap-9572	343	40	can	can	AUX
ap-9572	343	41	not	not	PART
ap-9572	343	42	be	be	AUX
ap-9572	343	43	neglected	neglect	VERB
ap-9572	343	44	.	.	PUNCT
ap-9572	344	1	the	the	DET
ap-9572	344	2	results	result	NOUN
ap-9572	344	3	of	of	ADP
ap-9572	344	4	this	this	DET
ap-9572	344	5	paper	paper	NOUN
ap-9572	344	6	also	also	ADV
ap-9572	344	7	show	show	VERB
ap-9572	344	8	that	that	SCONJ
ap-9572	344	9	the	the	DET
ap-9572	344	10	effect	effect	NOUN
ap-9572	344	11	of	of	ADP
ap-9572	344	12	taper	taper	NOUN
ap-9572	344	13	is	be	AUX
ap-9572	344	14	more	more	ADV
ap-9572	344	15	dominant	dominant	ADJ
ap-9572	344	16	in	in	ADP
ap-9572	344	17	the	the	DET
ap-9572	344	18	x	x	NOUN
ap-9572	344	19	-	-	NOUN
ap-9572	344	20	direction	direction	NOUN
ap-9572	344	21	as	as	SCONJ
ap-9572	344	22	compared	compare	VERB
ap-9572	344	23	to	to	ADP
ap-9572	344	24	that	that	PRON
ap-9572	344	25	of	of	ADP
ap-9572	344	26	the	the	DET
ap-9572	344	27	y	y	NOUN
ap-9572	344	28	-	-	PUNCT
ap-9572	344	29	direction	direction	NOUN
ap-9572	344	30	.	.	PUNCT
ap-9572	345	1	references	reference	NOUN
ap-9572	345	2	[	[	X
ap-9572	345	3	1	1	NUM
ap-9572	345	4	]	]	PUNCT
ap-9572	345	5	a.	a.	NOUN
ap-9572	345	6	w.	w.	PROPN
ap-9572	345	7	leissa	leissa	PROPN
ap-9572	345	8	.	.	PUNCT
ap-9572	346	1	nasa	nasa	PROPN
ap-9572	346	2	sp-160	sp-160	PROPN
ap-9572	346	3	.	.	PUNCT
ap-9572	347	1	vibration	vibration	NOUN
ap-9572	347	2	of	of	ADP
ap-9572	347	3	plates	plate	NOUN
ap-9572	347	4	.	.	PUNCT
ap-9572	348	1	u.s	u.s	PROPN
ap-9572	348	2	.	.	PROPN
ap-9572	348	3	government	government	NOUN
ap-9572	348	4	printing	printing	NOUN
ap-9572	348	5	office	office	NOUN
ap-9572	348	6	,	,	PUNCT
ap-9572	348	7	washington	washington	PROPN
ap-9572	348	8	,	,	PUNCT
ap-9572	348	9	d.c	d.c	PROPN
ap-9572	348	10	.	.	PROPN
ap-9572	348	11	,	,	PUNCT
ap-9572	348	12	usa	usa	PROPN
ap-9572	348	13	,	,	PUNCT
ap-9572	348	14	1969	1969	NUM
ap-9572	348	15	.	.	PUNCT
ap-9572	349	1	[	[	X
ap-9572	349	2	2	2	X
ap-9572	349	3	]	]	X
ap-9572	349	4	g.	g.	PROPN
ap-9572	349	5	s.	s.	PROPN
ap-9572	349	6	sharma	sharma	PROPN
ap-9572	349	7	,	,	PUNCT
ap-9572	349	8	a.	a.	PROPN
ap-9572	349	9	sarkar	sarkar	PROPN
ap-9572	349	10	.	.	PUNCT
ap-9572	350	1	directivity	directivity	PROPN
ap-9572	350	2	-	-	PUNCT
ap-9572	350	3	based	base	VERB
ap-9572	350	4	passive	passive	ADJ
ap-9572	350	5	barrier	barrier	NOUN
ap-9572	350	6	for	for	ADP
ap-9572	350	7	local	local	ADJ
ap-9572	350	8	control	control	NOUN
ap-9572	350	9	of	of	ADP
ap-9572	350	10	low	low	ADJ
ap-9572	350	11	-	-	PUNCT
ap-9572	350	12	frequency	frequency	NOUN
ap-9572	350	13	noise	noise	NOUN
ap-9572	350	14	.	.	PUNCT
ap-9572	351	1	journal	journal	NOUN
ap-9572	351	2	of	of	ADP
ap-9572	351	3	theoretical	theoretical	ADJ
ap-9572	351	4	and	and	CCONJ
ap-9572	351	5	computational	computational	ADJ
ap-9572	351	6	acoustics	acoustic	NOUN
ap-9572	351	7	26(4):1850012	26(4):1850012	PROPN
ap-9572	351	8	,	,	PUNCT
ap-9572	351	9	2018	2018	NUM
ap-9572	351	10	.	.	PUNCT
ap-9572	352	1	https://doi.org/10.1142/s2591728518500123	https://doi.org/10.1142/s2591728518500123	NUM
ap-9572	352	2	[	[	X
ap-9572	352	3	3	3	X
ap-9572	352	4	]	]	X
ap-9572	352	5	g.	g.	PROPN
ap-9572	352	6	s.	s.	PROPN
ap-9572	352	7	sharma	sharma	PROPN
ap-9572	352	8	,	,	PUNCT
ap-9572	352	9	a.	a.	PROPN
ap-9572	352	10	sarkar	sarkar	PROPN
ap-9572	352	11	.	.	PUNCT
ap-9572	353	1	directivity	directivity	PROPN
ap-9572	353	2	based	base	VERB
ap-9572	353	3	control	control	NOUN
ap-9572	353	4	of	of	ADP
ap-9572	353	5	acoustic	acoustic	ADJ
ap-9572	353	6	radiation	radiation	NOUN
ap-9572	353	7	.	.	PUNCT
ap-9572	354	1	applied	apply	VERB
ap-9572	354	2	acoustics	acoustic	NOUN
ap-9572	354	3	154:226–235	154:226–235	NUM
ap-9572	354	4	,	,	PUNCT
ap-9572	354	5	2019	2019	NUM
ap-9572	354	6	.	.	PUNCT
ap-9572	355	1	https://doi.org/10.1016/j.apacoust.2019.04.031	https://doi.org/10.1016/j.apacoust.2019.04.031	NOUN
ap-9572	355	2	[	[	X
ap-9572	355	3	4	4	NUM
ap-9572	355	4	]	]	PUNCT
ap-9572	355	5	a.	a.	NOUN
ap-9572	355	6	k.	k.	PROPN
ap-9572	355	7	gupta	gupta	PROPN
ap-9572	355	8	,	,	PUNCT
ap-9572	355	9	l.	l.	PROPN
ap-9572	355	10	kumar	kumar	PROPN
ap-9572	355	11	.	.	PUNCT
ap-9572	355	12	thermal	thermal	ADJ
ap-9572	355	13	effect	effect	NOUN
ap-9572	355	14	on	on	ADP
ap-9572	355	15	vibration	vibration	NOUN
ap-9572	355	16	of	of	ADP
ap-9572	355	17	non	non	ADJ
ap-9572	355	18	-	-	ADJ
ap-9572	355	19	homogenous	homogenous	ADJ
ap-9572	355	20	visco	visco	ADJ
ap-9572	355	21	-	-	ADJ
ap-9572	355	22	elastic	elastic	ADJ
ap-9572	355	23	rectangular	rectangular	ADJ
ap-9572	355	24	plate	plate	NOUN
ap-9572	355	25	of	of	ADP
ap-9572	355	26	linearly	linearly	ADV
ap-9572	355	27	varying	vary	VERB
ap-9572	355	28	thickness	thickness	NOUN
ap-9572	355	29	.	.	PUNCT
ap-9572	356	1	meccanica	meccanica	PROPN
ap-9572	356	2	43(1):47–54	43(1):47–54	NUM
ap-9572	356	3	,	,	PUNCT
ap-9572	356	4	2008	2008	NUM
ap-9572	356	5	.	.	PUNCT
ap-9572	357	1	https://doi.org/10.1007/s11012-007-9093-3	https://doi.org/10.1007/s11012-007-9093-3	NUM
ap-9572	358	1	[	[	X
ap-9572	358	2	5	5	NUM
ap-9572	358	3	]	]	PUNCT
ap-9572	358	4	a.	a.	NOUN
ap-9572	358	5	k.	k.	PROPN
ap-9572	358	6	gupta	gupta	PROPN
ap-9572	358	7	,	,	PUNCT
ap-9572	358	8	a.	a.	NOUN
ap-9572	358	9	khanna	khanna	PROPN
ap-9572	358	10	.	.	PUNCT
ap-9572	359	1	vibration	vibration	NOUN
ap-9572	359	2	of	of	ADP
ap-9572	359	3	visco	visco	ADJ
ap-9572	359	4	-	-	ADJ
ap-9572	359	5	elastic	elastic	ADJ
ap-9572	359	6	rectangular	rectangular	ADJ
ap-9572	359	7	plate	plate	NOUN
ap-9572	359	8	with	with	ADP
ap-9572	359	9	linearly	linearly	ADV
ap-9572	359	10	thickness	thickness	NOUN
ap-9572	359	11	variations	variation	NOUN
ap-9572	359	12	in	in	ADP
ap-9572	359	13	both	both	DET
ap-9572	359	14	directions	direction	NOUN
ap-9572	359	15	.	.	PUNCT
ap-9572	360	1	journal	journal	NOUN
ap-9572	360	2	of	of	ADP
ap-9572	360	3	sound	sound	NOUN
ap-9572	360	4	and	and	CCONJ
ap-9572	360	5	vibration	vibration	NOUN
ap-9572	360	6	301(3–5):450–457	301(3–5):450–457	NUM
ap-9572	360	7	,	,	PUNCT
ap-9572	360	8	2007	2007	NUM
ap-9572	360	9	.	.	PUNCT
ap-9572	361	1	https://doi.org/10.1016/j.jsv.2006.01.074	https://doi.org/10.1016/j.jsv.2006.01.074	PROPN
ap-9572	362	1	[	[	X
ap-9572	362	2	6	6	X
ap-9572	362	3	]	]	PUNCT
ap-9572	362	4	p.	p.	NOUN
ap-9572	362	5	a.	a.	NOUN
ap-9572	362	6	a.	a.	PROPN
ap-9572	362	7	laura	laura	PROPN
ap-9572	362	8	,	,	PUNCT
ap-9572	362	9	r.	r.	PROPN
ap-9572	362	10	h.	h.	PROPN
ap-9572	362	11	gutierrez	gutierrez	PROPN
ap-9572	362	12	.	.	PUNCT
ap-9572	363	1	comments	comment	NOUN
ap-9572	363	2	on	on	ADP
ap-9572	363	3	“	"	PUNCT
ap-9572	363	4	vibration	vibration	NOUN
ap-9572	363	5	analysis	analysis	NOUN
ap-9572	363	6	of	of	ADP
ap-9572	363	7	a	a	DET
ap-9572	363	8	rectangular	rectangular	ADJ
ap-9572	363	9	plate	plate	NOUN
ap-9572	363	10	subjected	subject	VERB
ap-9572	363	11	to	to	ADP
ap-9572	363	12	a	a	DET
ap-9572	363	13	thermal	thermal	ADJ
ap-9572	363	14	gradient	gradient	NOUN
ap-9572	363	15	”	"	PUNCT
ap-9572	363	16	.	.	PUNCT
ap-9572	364	1	journal	journal	PROPN
ap-9572	364	2	of	of	ADP
ap-9572	364	3	sound	sound	NOUN
ap-9572	364	4	and	and	CCONJ
ap-9572	364	5	vibration	vibration	NOUN
ap-9572	364	6	72(2):263	72(2):263	NUM
ap-9572	364	7	,	,	PUNCT
ap-9572	364	8	1980	1980	NUM
ap-9572	364	9	.	.	PUNCT
ap-9572	365	1	https://doi.org/10.1016/0022-460x(80)90656-2	https://doi.org/10.1016/0022-460x(80)90656-2	PROPN
ap-9572	366	1	[	[	X
ap-9572	366	2	7	7	NUM
ap-9572	366	3	]	]	PUNCT
ap-9572	366	4	a.	a.	NOUN
ap-9572	366	5	k.	k.	PROPN
ap-9572	366	6	gupta	gupta	PROPN
ap-9572	366	7	,	,	PUNCT
ap-9572	366	8	t.	t.	PROPN
ap-9572	366	9	johri	johri	PROPN
ap-9572	366	10	,	,	PUNCT
ap-9572	366	11	r.	r.	PROPN
ap-9572	366	12	p.	p.	NOUN
ap-9572	366	13	vats	vat	NOUN
ap-9572	366	14	.	.	PUNCT
ap-9572	367	1	study	study	NOUN
ap-9572	367	2	of	of	ADP
ap-9572	367	3	thermal	thermal	ADJ
ap-9572	367	4	gradient	gradient	ADJ
ap-9572	367	5	effect	effect	NOUN
ap-9572	367	6	on	on	ADP
ap-9572	367	7	vibrations	vibration	NOUN
ap-9572	367	8	of	of	ADP
ap-9572	367	9	a	a	DET
ap-9572	367	10	non	non	ADJ
ap-9572	367	11	-	-	ADJ
ap-9572	367	12	homogeneous	homogeneous	ADJ
ap-9572	367	13	orthotropic	orthotropic	ADJ
ap-9572	367	14	rectangular	rectangular	ADJ
ap-9572	367	15	plate	plate	NOUN
ap-9572	367	16	having	have	VERB
ap-9572	367	17	bi	bi	NOUN
ap-9572	367	18	-	-	NOUN
ap-9572	367	19	direction	direction	NOUN
ap-9572	367	20	linearly	linearly	ADV
ap-9572	367	21	thickness	thickness	NOUN
ap-9572	367	22	variations	variation	NOUN
ap-9572	367	23	.	.	PUNCT
ap-9572	368	1	meccanica	meccanica	PROPN
ap-9572	368	2	45(3):393–400	45(3):393–400	PROPN
ap-9572	368	3	,	,	PUNCT
ap-9572	368	4	2010	2010	NUM
ap-9572	368	5	.	.	PUNCT
ap-9572	369	1	https://doi.org/10.1007/s11012-009-9258-3	https://doi.org/10.1007/s11012-009-9258-3	NUM
ap-9572	370	1	[	[	X
ap-9572	370	2	8	8	NUM
ap-9572	370	3	]	]	PUNCT
ap-9572	370	4	a.	a.	NOUN
ap-9572	370	5	k.	k.	PROPN
ap-9572	370	6	gupta	gupta	PROPN
ap-9572	370	7	,	,	PUNCT
ap-9572	370	8	h.	h.	PROPN
ap-9572	370	9	kaur	kaur	PROPN
ap-9572	370	10	.	.	PUNCT
ap-9572	371	1	study	study	NOUN
ap-9572	371	2	of	of	ADP
ap-9572	371	3	the	the	DET
ap-9572	371	4	effect	effect	NOUN
ap-9572	371	5	of	of	ADP
ap-9572	371	6	thermal	thermal	ADJ
ap-9572	371	7	gradient	gradient	NOUN
ap-9572	371	8	on	on	ADP
ap-9572	371	9	free	free	ADJ
ap-9572	371	10	vibration	vibration	NOUN
ap-9572	371	11	of	of	ADP
ap-9572	371	12	clamped	clamp	VERB
ap-9572	371	13	visco	visco	ADJ
ap-9572	371	14	-	-	ADJ
ap-9572	371	15	elastic	elastic	ADJ
ap-9572	371	16	rectangular	rectangular	ADJ
ap-9572	371	17	plates	plate	NOUN
ap-9572	371	18	with	with	ADP
ap-9572	371	19	linearly	linearly	ADV
ap-9572	371	20	thickness	thickness	NOUN
ap-9572	371	21	variation	variation	NOUN
ap-9572	371	22	in	in	ADP
ap-9572	371	23	both	both	DET
ap-9572	371	24	directions	direction	NOUN
ap-9572	371	25	.	.	PUNCT
ap-9572	372	1	meccanica	meccanica	PROPN
ap-9572	372	2	43(4):449–458	43(4):449–458	PROPN
ap-9572	372	3	,	,	PUNCT
ap-9572	372	4	2008	2008	NUM
ap-9572	372	5	.	.	PUNCT
ap-9572	372	6	https://doi.org/10.1007/s11012-008-9110-1	https://doi.org/10.1007/s11012-008-9110-1	X
ap-9572	373	1	[	[	X
ap-9572	373	2	9	9	NUM
ap-9572	373	3	]	]	X
ap-9572	373	4	b.	b.	PROPN
ap-9572	373	5	singh	singh	PROPN
ap-9572	373	6	,	,	PUNCT
ap-9572	373	7	v.	v.	CCONJ
ap-9572	373	8	saxena	saxena	PROPN
ap-9572	373	9	.	.	PUNCT
ap-9572	374	1	transverse	transverse	NOUN
ap-9572	374	2	vibration	vibration	NOUN
ap-9572	374	3	of	of	ADP
ap-9572	374	4	a	a	DET
ap-9572	374	5	rectangular	rectangular	ADJ
ap-9572	374	6	plate	plate	NOUN
ap-9572	374	7	with	with	ADP
ap-9572	374	8	bidirectional	bidirectional	ADJ
ap-9572	374	9	thickness	thickness	NOUN
ap-9572	374	10	variation	variation	NOUN
ap-9572	374	11	.	.	PUNCT
ap-9572	375	1	journal	journal	NOUN
ap-9572	375	2	of	of	ADP
ap-9572	375	3	sound	sound	NOUN
ap-9572	375	4	and	and	CCONJ
ap-9572	375	5	vibration	vibration	NOUN
ap-9572	375	6	198(1):51–65	198(1):51–65	NOUN
ap-9572	375	7	,	,	PUNCT
ap-9572	375	8	1996	1996	NUM
ap-9572	375	9	.	.	PUNCT
ap-9572	376	1	https://doi.org/10.1006/jsvi.1996.0556	https://doi.org/10.1006/jsvi.1996.0556	PROPN
ap-9572	377	1	[	[	X
ap-9572	377	2	10	10	NUM
ap-9572	377	3	]	]	PUNCT
ap-9572	377	4	m.	m.	NOUN
ap-9572	377	5	s.	s.	PROPN
ap-9572	377	6	dhotarad	dhotarad	PROPN
ap-9572	377	7	,	,	PUNCT
ap-9572	377	8	n.	n.	PROPN
ap-9572	377	9	ganesan	ganesan	PROPN
ap-9572	377	10	.	.	PUNCT
ap-9572	378	1	vibration	vibration	NOUN
ap-9572	378	2	analysis	analysis	NOUN
ap-9572	378	3	of	of	ADP
ap-9572	378	4	a	a	DET
ap-9572	378	5	rectangular	rectangular	ADJ
ap-9572	378	6	plate	plate	NOUN
ap-9572	378	7	subjected	subject	VERB
ap-9572	378	8	to	to	ADP
ap-9572	378	9	a	a	DET
ap-9572	378	10	thermal	thermal	ADJ
ap-9572	378	11	gradient	gradient	NOUN
ap-9572	378	12	.	.	PUNCT
ap-9572	379	1	journal	journal	NOUN
ap-9572	379	2	of	of	ADP
ap-9572	379	3	sound	sound	NOUN
ap-9572	379	4	and	and	CCONJ
ap-9572	379	5	vibration	vibration	NOUN
ap-9572	379	6	60(4):481–497	60(4):481–497	NUM
ap-9572	379	7	,	,	PUNCT
ap-9572	379	8	1978	1978	NUM
ap-9572	379	9	.	.	PUNCT
ap-9572	380	1	https://doi.org/10.1016/s0022-460x(78)80087-x	https://doi.org/10.1016/s0022-460x(78)80087-x	VERB
ap-9572	380	2	[	[	X
ap-9572	380	3	11	11	NUM
ap-9572	380	4	]	]	PUNCT
ap-9572	380	5	a.	a.	NOUN
ap-9572	380	6	k.	k.	PROPN
ap-9572	380	7	gupta	gupta	PROPN
ap-9572	380	8	,	,	PUNCT
ap-9572	380	9	a.	a.	NOUN
ap-9572	380	10	khanna	khanna	PROPN
ap-9572	380	11	,	,	PUNCT
ap-9572	380	12	s.	s.	PROPN
ap-9572	380	13	kumar	kumar	PROPN
ap-9572	380	14	,	,	PUNCT
ap-9572	380	15	et	et	PROPN
ap-9572	380	16	al	al	PROPN
ap-9572	380	17	.	.	PROPN
ap-9572	381	1	vibration	vibration	NOUN
ap-9572	381	2	analysis	analysis	NOUN
ap-9572	381	3	of	of	ADP
ap-9572	381	4	visco	visco	ADJ
ap-9572	381	5	-	-	ADJ
ap-9572	381	6	elastic	elastic	ADJ
ap-9572	381	7	rectangular	rectangular	ADJ
ap-9572	381	8	plate	plate	NOUN
ap-9572	381	9	with	with	ADP
ap-9572	381	10	thickness	thickness	NOUN
ap-9572	381	11	varies	vary	VERB
ap-9572	381	12	linearly	linearly	ADV
ap-9572	381	13	in	in	ADP
ap-9572	381	14	one	one	NUM
ap-9572	381	15	and	and	CCONJ
ap-9572	381	16	parabolically	parabolically	ADV
ap-9572	381	17	in	in	ADP
ap-9572	381	18	other	other	ADJ
ap-9572	381	19	direction	direction	NOUN
ap-9572	381	20	.	.	PUNCT
ap-9572	382	1	advanced	advanced	ADJ
ap-9572	382	2	studies	study	NOUN
ap-9572	382	3	in	in	ADP
ap-9572	382	4	theoretical	theoretical	ADJ
ap-9572	382	5	physics	physics	NOUN
ap-9572	382	6	4(15):743–758	4(15):743–758	NUM
ap-9572	382	7	,	,	PUNCT
ap-9572	382	8	2010	2010	NUM
ap-9572	382	9	.	.	PUNCT
ap-9572	383	1	[	[	X
ap-9572	383	2	12	12	NUM
ap-9572	383	3	]	]	PUNCT
ap-9572	383	4	a.	a.	PROPN
ap-9572	383	5	k.	k.	PROPN
ap-9572	383	6	gupta	gupta	PROPN
ap-9572	383	7	,	,	PUNCT
ap-9572	383	8	s.	s.	PROPN
ap-9572	383	9	aggarwal	aggarwal	PROPN
ap-9572	383	10	.	.	PUNCT
ap-9572	384	1	vibration	vibration	NOUN
ap-9572	384	2	of	of	ADP
ap-9572	384	3	non	non	ADJ
ap-9572	384	4	-	-	ADJ
ap-9572	384	5	homogeneous	homogeneous	ADJ
ap-9572	384	6	visco	visco	ADJ
ap-9572	384	7	-	-	ADJ
ap-9572	384	8	elastic	elastic	ADJ
ap-9572	384	9	rectangular	rectangular	ADJ
ap-9572	384	10	plate	plate	NOUN
ap-9572	384	11	having	having	AUX
ap-9572	384	12	linearly	linearly	ADV
ap-9572	384	13	varying	vary	VERB
ap-9572	384	14	thickness	thickness	NOUN
ap-9572	384	15	in	in	ADP
ap-9572	384	16	both	both	DET
ap-9572	384	17	directions	direction	NOUN
ap-9572	384	18	with	with	ADP
ap-9572	384	19	thermal	thermal	ADJ
ap-9572	384	20	gradient	gradient	ADJ
ap-9572	384	21	effect	effect	NOUN
ap-9572	384	22	.	.	PUNCT
ap-9572	385	1	journal	journal	NOUN
ap-9572	385	2	of	of	ADP
ap-9572	385	3	advanced	advanced	ADJ
ap-9572	385	4	research	research	NOUN
ap-9572	385	5	in	in	ADP
ap-9572	385	6	applied	apply	VERB
ap-9572	385	7	mathematics	mathematic	NOUN
ap-9572	385	8	and	and	CCONJ
ap-9572	385	9	statistics	statistic	NOUN
ap-9572	385	10	3(1–2):19–28	3(1–2):19–28	NUM
ap-9572	385	11	,	,	PUNCT
ap-9572	385	12	2018	2018	NUM
ap-9572	385	13	.	.	PUNCT
ap-9572	386	1	[	[	X
ap-9572	386	2	13	13	NUM
ap-9572	386	3	]	]	PUNCT
ap-9572	386	4	a.	a.	NOUN
ap-9572	386	5	k.	k.	PROPN
ap-9572	386	6	gupta	gupta	PROPN
ap-9572	386	7	,	,	PUNCT
ap-9572	386	8	s.	s.	PROPN
ap-9572	386	9	aggarwal	aggarwal	PROPN
ap-9572	386	10	.	.	PUNCT
ap-9572	387	1	non	non	ADJ
ap-9572	387	2	-	-	ADJ
ap-9572	387	3	homogeneous	homogeneous	ADJ
ap-9572	387	4	effect	effect	NOUN
ap-9572	387	5	on	on	ADP
ap-9572	387	6	vibration	vibration	NOUN
ap-9572	387	7	of	of	ADP
ap-9572	387	8	visco	visco	ADJ
ap-9572	387	9	-	-	ADJ
ap-9572	387	10	elastic	elastic	ADJ
ap-9572	387	11	rectangular	rectangular	ADJ
ap-9572	387	12	plate	plate	NOUN
ap-9572	387	13	having	having	AUX
ap-9572	387	14	parabolically	parabolically	ADV
ap-9572	387	15	varying	vary	VERB
ap-9572	387	16	thickness	thickness	NOUN
ap-9572	387	17	in	in	ADP
ap-9572	387	18	both	both	DET
ap-9572	387	19	directions	direction	NOUN
ap-9572	387	20	.	.	PUNCT
ap-9572	388	1	journal	journal	NOUN
ap-9572	388	2	of	of	ADP
ap-9572	388	3	experimental	experimental	PROPN
ap-9572	388	4	&	&	CCONJ
ap-9572	388	5	applied	apply	VERB
ap-9572	388	6	mechanics	mechanic	NOUN
ap-9572	388	7	9(3):1–17	9(3):1–17	NUM
ap-9572	388	8	,	,	PUNCT
ap-9572	388	9	2018	2018	NUM
ap-9572	388	10	.	.	PUNCT
ap-9572	389	1	[	[	X
ap-9572	389	2	14	14	NUM
ap-9572	389	3	]	]	PUNCT
ap-9572	389	4	a.	a.	PROPN
ap-9572	389	5	k.	k.	PROPN
ap-9572	389	6	gupta	gupta	PROPN
ap-9572	389	7	,	,	PUNCT
ap-9572	389	8	s.	s.	PROPN
ap-9572	389	9	aggarwal	aggarwal	PROPN
ap-9572	389	10	.	.	PUNCT
ap-9572	389	11	thermally	thermally	ADV
ap-9572	389	12	induced	induce	VERB
ap-9572	389	13	vibration	vibration	NOUN
ap-9572	389	14	of	of	ADP
ap-9572	389	15	non	non	ADJ
ap-9572	389	16	-	-	ADJ
ap-9572	389	17	homogeneous	homogeneous	ADJ
ap-9572	389	18	visco	visco	ADJ
ap-9572	389	19	-	-	ADJ
ap-9572	389	20	elastic	elastic	ADJ
ap-9572	389	21	rectangular	rectangular	ADJ
ap-9572	389	22	plate	plate	NOUN
ap-9572	389	23	of	of	ADP
ap-9572	389	24	variable	variable	ADJ
ap-9572	389	25	thickness	thickness	NOUN
ap-9572	389	26	.	.	PUNCT
ap-9572	390	1	international	international	ADJ
ap-9572	390	2	journal	journal	PROPN
ap-9572	390	3	of	of	ADP
ap-9572	390	4	research	research	NOUN
ap-9572	390	5	in	in	ADP
ap-9572	390	6	advent	advent	PROPN
ap-9572	390	7	technology	technology	NOUN
ap-9572	390	8	6(5):768–777	6(5):768–777	PROPN
ap-9572	390	9	,	,	PUNCT
ap-9572	390	10	2018	2018	NUM
ap-9572	390	11	.	.	PUNCT
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ap-9572	391	2	15	15	NUM
ap-9572	391	3	]	]	X
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ap-9572	391	5	k.	k.	PROPN
ap-9572	391	6	gupta	gupta	PROPN
ap-9572	391	7	,	,	PUNCT
ap-9572	391	8	h.	h.	PROPN
ap-9572	391	9	kaur	kaur	PROPN
ap-9572	391	10	.	.	PUNCT
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ap-9572	392	2	of	of	ADP
ap-9572	392	3	thermal	thermal	ADJ
ap-9572	392	4	gradient	gradient	NOUN
ap-9572	392	5	on	on	ADP
ap-9572	392	6	vibration	vibration	NOUN
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ap-9572	392	8	clamped	clamp	VERB
ap-9572	392	9	visco	visco	ADJ
ap-9572	392	10	-	-	ADJ
ap-9572	392	11	elastic	elastic	ADJ
ap-9572	392	12	rectangular	rectangular	ADJ
ap-9572	392	13	plate	plate	NOUN
ap-9572	392	14	with	with	ADP
ap-9572	392	15	exponentially	exponentially	ADV
ap-9572	392	16	thickness	thickness	NOUN
ap-9572	392	17	variation	variation	NOUN
ap-9572	392	18	in	in	ADP
ap-9572	392	19	both	both	CCONJ
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ap-9572	392	21	directions	direction	NOUN
ap-9572	392	22	.	.	PUNCT
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ap-9572	393	2	journal	journal	PROPN
ap-9572	393	3	of	of	ADP
ap-9572	393	4	computational	computational	ADJ
ap-9572	393	5	and	and	CCONJ
ap-9572	393	6	applied	apply	VERB
ap-9572	393	7	mathematics	mathematic	NOUN
ap-9572	393	8	3(1):36–45	3(1):36–45	NUM
ap-9572	393	9	,	,	PUNCT
ap-9572	393	10	2013	2013	NUM
ap-9572	393	11	.	.	PUNCT
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ap-9572	395	2	16	16	NUM
ap-9572	395	3	]	]	PUNCT
ap-9572	395	4	k.	k.	PROPN
ap-9572	395	5	nagaya	nagaya	PROPN
ap-9572	395	6	.	.	PUNCT
ap-9572	396	1	vibrations	vibration	NOUN
ap-9572	396	2	and	and	CCONJ
ap-9572	396	3	dynamic	dynamic	ADJ
ap-9572	396	4	response	response	NOUN
ap-9572	396	5	of	of	ADP
ap-9572	396	6	viscoelastic	viscoelastic	ADJ
ap-9572	396	7	plates	plate	NOUN
ap-9572	396	8	on	on	ADP
ap-9572	396	9	nonperiodic	nonperiodic	ADJ
ap-9572	396	10	elastic	elastic	ADJ
ap-9572	396	11	supports	support	NOUN
ap-9572	396	12	.	.	PUNCT
ap-9572	397	1	journal	journal	NOUN
ap-9572	397	2	of	of	ADP
ap-9572	397	3	manufacturing	manufacturing	NOUN
ap-9572	397	4	science	science	NOUN
ap-9572	397	5	and	and	CCONJ
ap-9572	397	6	engineering	engineering	NOUN
ap-9572	397	7	99(2):404–409	99(2):404–409	PROPN
ap-9572	397	8	,	,	PUNCT
ap-9572	397	9	1977	1977	NUM
ap-9572	397	10	.	.	PUNCT
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ap-9572	399	2	17	17	NUM
ap-9572	399	3	]	]	PUNCT
ap-9572	399	4	a.	a.	PROPN
ap-9572	399	5	k.	k.	PROPN
ap-9572	399	6	gupta	gupta	PROPN
ap-9572	399	7	,	,	PUNCT
ap-9572	399	8	h.	h.	PROPN
ap-9572	399	9	kaur	kaur	PROPN
ap-9572	399	10	,	,	PUNCT
ap-9572	399	11	s.	s.	PROPN
ap-9572	399	12	kumar	kumar	PROPN
ap-9572	399	13	.	.	PUNCT
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ap-9572	400	2	effect	effect	NOUN
ap-9572	400	3	on	on	ADP
ap-9572	400	4	vibration	vibration	NOUN
ap-9572	400	5	of	of	ADP
ap-9572	400	6	clamped	clamp	VERB
ap-9572	400	7	visco	visco	ADJ
ap-9572	400	8	-	-	ADJ
ap-9572	400	9	elastic	elastic	ADJ
ap-9572	400	10	rectangular	rectangular	ADJ
ap-9572	400	11	plate	plate	NOUN
ap-9572	400	12	with	with	ADP
ap-9572	400	13	parabolic	parabolic	ADJ
ap-9572	400	14	thickness	thickness	NOUN
ap-9572	400	15	variation	variation	NOUN
ap-9572	400	16	in	in	ADP
ap-9572	400	17	both	both	DET
ap-9572	400	18	directions	direction	NOUN
ap-9572	400	19	.	.	PUNCT
ap-9572	401	1	shock	shock	NOUN
ap-9572	401	2	and	and	CCONJ
ap-9572	401	3	vibration	vibration	NOUN
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ap-9572	401	5	,	,	PUNCT
ap-9572	401	6	2010	2010	NUM
ap-9572	401	7	.	.	PUNCT
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ap-9572	403	2	18	18	NUM
ap-9572	403	3	]	]	X
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ap-9572	403	5	b.	b.	PROPN
ap-9572	403	6	bhat	bhat	PROPN
ap-9572	403	7	.	.	PUNCT
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ap-9572	404	4	rectangular	rectangular	ADJ
ap-9572	404	5	plates	plate	NOUN
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ap-9572	404	8	orthogonal	orthogonal	ADJ
ap-9572	404	9	polynomials	polynomial	NOUN
ap-9572	404	10	in	in	ADP
ap-9572	404	11	rayleigh	rayleigh	PROPN
ap-9572	404	12	-	-	PUNCT
ap-9572	404	13	ritz	ritz	PROPN
ap-9572	404	14	method	method	NOUN
ap-9572	404	15	.	.	PUNCT
ap-9572	405	1	journal	journal	NOUN
ap-9572	405	2	of	of	ADP
ap-9572	405	3	sound	sound	NOUN
ap-9572	405	4	and	and	CCONJ
ap-9572	405	5	vibration	vibration	NOUN
ap-9572	405	6	102(4):493–499	102(4):493–499	NUM
ap-9572	405	7	,	,	PUNCT
ap-9572	405	8	1985	1985	NUM
ap-9572	405	9	.	.	PUNCT
ap-9572	406	1	https://doi.org/10.1016/s0022-460x(85)80109-7	https://doi.org/10.1016/s0022-460x(85)80109-7	PROPN
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ap-9572	406	3	19	19	NUM
ap-9572	406	4	]	]	PUNCT
ap-9572	406	5	j.	j.	PROPN
ap-9572	406	6	s.	s.	PROPN
ap-9572	406	7	tomar	tomar	PROPN
ap-9572	406	8	,	,	PUNCT
ap-9572	406	9	a.	a.	PROPN
ap-9572	406	10	k.	k.	PROPN
ap-9572	406	11	gupta	gupta	PROPN
ap-9572	406	12	.	.	PUNCT
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ap-9572	407	2	effect	effect	NOUN
ap-9572	407	3	on	on	ADP
ap-9572	407	4	frequencies	frequency	NOUN
ap-9572	407	5	of	of	ADP
ap-9572	407	6	an	an	DET
ap-9572	407	7	orthotropic	orthotropic	ADJ
ap-9572	407	8	rectangular	rectangular	ADJ
ap-9572	407	9	plate	plate	NOUN
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ap-9572	407	11	linearly	linearly	ADV
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ap-9572	407	14	.	.	PUNCT
ap-9572	408	1	journal	journal	PROPN
ap-9572	408	2	of	of	ADP
ap-9572	408	3	sound	sound	NOUN
ap-9572	408	4	and	and	CCONJ
ap-9572	408	5	vibration	vibration	NOUN
ap-9572	408	6	90(3):325–331	90(3):325–331	NUM
ap-9572	408	7	,	,	PUNCT
ap-9572	408	8	1983	1983	NUM
ap-9572	408	9	.	.	PUNCT
ap-9572	409	1	https://doi.org/10.1016/0022-460x(83)90715-0	https://doi.org/10.1016/0022-460x(83)90715-0	PROPN
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ap-9572	410	2	20	20	NUM
ap-9572	410	3	]	]	PUNCT
ap-9572	410	4	r.	r.	PROPN
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ap-9572	410	6	,	,	PUNCT
ap-9572	410	7	r.	r.	PROPN
ap-9572	410	8	lal	lal	PROPN
ap-9572	410	9	.	.	PUNCT
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ap-9572	411	2	vibration	vibration	NOUN
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ap-9572	411	14	.	.	PUNCT
ap-9572	412	1	international	international	ADJ
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ap-9572	412	4	engineering	engineering	PROPN
ap-9572	412	5	,	,	PUNCT
ap-9572	412	6	mathematical	mathematical	ADJ
ap-9572	412	7	and	and	CCONJ
ap-9572	412	8	physical	physical	ADJ
ap-9572	412	9	sciences	science	NOUN
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ap-9572	412	11	,	,	PUNCT
ap-9572	412	12	2014	2014	NUM
ap-9572	412	13	.	.	PUNCT
ap-9572	413	1	[	[	X
ap-9572	413	2	21	21	NUM
ap-9572	413	3	]	]	PUNCT
ap-9572	413	4	a.	a.	PROPN
ap-9572	413	5	k.	k.	PROPN
ap-9572	413	6	gupta	gupta	PROPN
ap-9572	413	7	,	,	PUNCT
ap-9572	413	8	m.	m.	PROPN
ap-9572	413	9	saini	saini	PROPN
ap-9572	413	10	,	,	PUNCT
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ap-9572	413	13	,	,	PUNCT
ap-9572	413	14	r.	r.	PROPN
ap-9572	413	15	kumar	kumar	PROPN
ap-9572	413	16	.	.	PROPN
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ap-9572	414	5	-	-	ADJ
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ap-9572	414	13	.	.	PUNCT
ap-9572	415	1	journal	journal	NOUN
ap-9572	415	2	of	of	ADP
ap-9572	415	3	vibration	vibration	NOUN
ap-9572	415	4	and	and	CCONJ
ap-9572	415	5	control	control	NOUN
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ap-9572	415	7	,	,	PUNCT
ap-9572	415	8	2014	2014	NUM
ap-9572	415	9	.	.	PUNCT
ap-9572	416	1	https://doi.org/10.1177/1077546312466883	https://doi.org/10.1177/1077546312466883	ADP
ap-9572	416	2	312	312	NUM
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ap-9572	416	4	https://doi.org/10.1016/j.apacoust.2019.04.031	https://doi.org/10.1016/j.apacoust.2019.04.031	PROPN
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ap-9572	416	6	https://doi.org/10.1016/j.jsv.2006.01.074	https://doi.org/10.1016/j.jsv.2006.01.074	PROPN
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ap-9572	416	8	https://doi.org/10.1007/s11012-009-9258-3	https://doi.org/10.1007/s11012-009-9258-3	PROPN
ap-9572	416	9	https://doi.org/10.1007/s11012-008-9110-1	https://doi.org/10.1007/s11012-008-9110-1	NUM
ap-9572	416	10	https://doi.org/10.1006/jsvi.1996.0556	https://doi.org/10.1006/jsvi.1996.0556	PROPN
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ap-9572	417	1	https://doi.org/10.1016/0022-460x(83)90715-0	https://doi.org/10.1016/0022-460x(83)90715-0	PROPN
ap-9572	417	2	https://doi.org/10.1177/1077546312466883	https://doi.org/10.1177/1077546312466883	NUM
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ap-9572	417	4	.	.	PUNCT
ap-9572	418	1	64	64	NUM
ap-9572	418	2	no	no	NOUN
ap-9572	418	3	.	.	PUNCT
ap-9572	419	1	4/2024	4/2024	NUM
ap-9572	419	2	non	non	ADJ
ap-9572	419	3	-	-	ADJ
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ap-9572	419	5	effect	effect	NOUN
ap-9572	419	6	on	on	ADP
ap-9572	419	7	the	the	DET
ap-9572	419	8	vibration	vibration	NOUN
ap-9572	419	9	of	of	ADP
ap-9572	419	10	.	.	PUNCT
ap-9572	419	11	.	.	PUNCT
ap-9572	419	12	.	.	PUNCT
ap-9572	420	1	[	[	X
ap-9572	420	2	22	22	NUM
ap-9572	420	3	]	]	PUNCT
ap-9572	420	4	m.	m.	NOUN
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ap-9572	420	8	s.	s.	PROPN
ap-9572	420	9	a.	a.	PROPN
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ap-9572	420	11	,	,	PUNCT
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ap-9572	420	13	a.	a.	PROPN
ap-9572	420	14	yinusa	yinusa	PROPN
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ap-9572	420	16	o.	o.	PROPN
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ap-9572	421	5	analysis	analysis	NOUN
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ap-9572	421	8	-	-	ADJ
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ap-9572	421	10	rectangular	rectangular	ADJ
ap-9572	421	11	plate	plate	NOUN
ap-9572	421	12	with	with	ADP
ap-9572	421	13	varying	vary	VERB
ap-9572	421	14	thickness	thickness	NOUN
ap-9572	421	15	using	use	VERB
ap-9572	421	16	three	three	NUM
ap-9572	421	17	-	-	PUNCT
ap-9572	421	18	dimensional	dimensional	ADJ
ap-9572	421	19	differential	differential	ADJ
ap-9572	421	20	transform	transform	NOUN
ap-9572	421	21	method	method	NOUN
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ap-9572	422	2	scientific	scientific	ADJ
ap-9572	422	3	news	news	PROPN
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ap-9572	422	5	,	,	PUNCT
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ap-9572	422	7	.	.	PUNCT
ap-9572	423	1	[	[	X
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ap-9572	423	3	]	]	PUNCT
ap-9572	423	4	a.	a.	PROPN
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ap-9572	423	6	gupta	gupta	PROPN
ap-9572	423	7	,	,	PUNCT
ap-9572	423	8	j.	j.	PROPN
ap-9572	423	9	mamta	mamta	PROPN
ap-9572	423	10	.	.	PUNCT
ap-9572	424	1	exponential	exponential	ADJ
ap-9572	424	2	temperature	temperature	NOUN
ap-9572	424	3	effect	effect	NOUN
ap-9572	424	4	on	on	ADP
ap-9572	424	5	frequencies	frequency	NOUN
ap-9572	424	6	of	of	ADP
ap-9572	424	7	a	a	DET
ap-9572	424	8	rectangular	rectangular	ADJ
ap-9572	424	9	plate	plate	NOUN
ap-9572	424	10	of	of	ADP
ap-9572	424	11	non	non	ADJ
ap-9572	424	12	-	-	ADJ
ap-9572	424	13	linear	linear	ADJ
ap-9572	424	14	varying	vary	VERB
ap-9572	424	15	thickness	thickness	NOUN
ap-9572	424	16	:	:	PUNCT
ap-9572	424	17	a	a	DET
ap-9572	424	18	quintic	quintic	ADJ
ap-9572	424	19	spline	spline	NOUN
ap-9572	424	20	technique	technique	NOUN
ap-9572	424	21	.	.	PUNCT
ap-9572	425	1	journal	journal	NOUN
ap-9572	425	2	of	of	ADP
ap-9572	425	3	theoretical	theoretical	ADJ
ap-9572	425	4	and	and	CCONJ
ap-9572	425	5	applied	apply	VERB
ap-9572	425	6	mechanics	mechanic	NOUN
ap-9572	425	7	52(1):15–24	52(1):15–24	NUM
ap-9572	425	8	,	,	PUNCT
ap-9572	425	9	2014	2014	NUM
ap-9572	425	10	.	.	PUNCT
ap-9572	426	1	[	[	X
ap-9572	426	2	24	24	NUM
ap-9572	426	3	]	]	X
ap-9572	426	4	p.	p.	NOUN
ap-9572	426	5	singhal	singhal	PROPN
ap-9572	426	6	,	,	PUNCT
ap-9572	426	7	ruby	ruby	PROPN
ap-9572	426	8	.	.	PUNCT
ap-9572	427	1	a	a	DET
ap-9572	427	2	scientific	scientific	ADJ
ap-9572	427	3	approach	approach	NOUN
ap-9572	427	4	on	on	ADP
ap-9572	427	5	thermally	thermally	ADV
ap-9572	427	6	induced	induce	VERB
ap-9572	427	7	vibrations	vibration	NOUN
ap-9572	427	8	of	of	ADP
ap-9572	427	9	non	non	ADJ
ap-9572	427	10	-	-	ADJ
ap-9572	427	11	homogeneous	homogeneous	ADJ
ap-9572	427	12	tapered	taper	VERB
ap-9572	427	13	rectangular	rectangular	ADJ
ap-9572	427	14	plate	plate	NOUN
ap-9572	427	15	.	.	PUNCT
ap-9572	428	1	a	a	DET
ap-9572	428	2	journal	journal	NOUN
ap-9572	428	3	of	of	ADP
ap-9572	428	4	composition	composition	NOUN
ap-9572	428	5	theory	theory	NOUN
ap-9572	428	6	12(7):875–882	12(7):875–882	PROPN
ap-9572	428	7	,	,	PUNCT
ap-9572	428	8	2023	2023	NUM
ap-9572	428	9	.	.	PUNCT
ap-9572	429	1	[	[	X
ap-9572	429	2	25	25	NUM
ap-9572	429	3	]	]	PUNCT
ap-9572	429	4	y.-l	y.-l	NOUN
ap-9572	429	5	.	.	PUNCT
ap-9572	430	1	yeh	yeh	PROPN
ap-9572	430	2	,	,	PUNCT
ap-9572	430	3	m.-j	m.-j	PROPN
ap-9572	430	4	.	.	PUNCT
ap-9572	431	1	jang	jang	PROPN
ap-9572	431	2	,	,	PUNCT
ap-9572	431	3	c.	c.	PROPN
ap-9572	431	4	c.	c.	PROPN
ap-9572	431	5	wang	wang	PROPN
ap-9572	431	6	.	.	PUNCT
ap-9572	432	1	analyzing	analyze	VERB
ap-9572	432	2	the	the	DET
ap-9572	432	3	free	free	ADJ
ap-9572	432	4	vibrations	vibration	NOUN
ap-9572	432	5	of	of	ADP
ap-9572	432	6	a	a	DET
ap-9572	432	7	plate	plate	NOUN
ap-9572	432	8	using	use	VERB
ap-9572	432	9	finite	finite	ADJ
ap-9572	432	10	difference	difference	NOUN
ap-9572	432	11	and	and	CCONJ
ap-9572	432	12	differential	differential	ADJ
ap-9572	432	13	transformation	transformation	NOUN
ap-9572	432	14	method	method	NOUN
ap-9572	432	15	.	.	PUNCT
ap-9572	433	1	applied	apply	VERB
ap-9572	433	2	mathematics	mathematic	NOUN
ap-9572	433	3	and	and	CCONJ
ap-9572	433	4	computation	computation	NOUN
ap-9572	433	5	178(2):493–501	178(2):493–501	NUM
ap-9572	433	6	,	,	PUNCT
ap-9572	433	7	2006	2006	NUM
ap-9572	433	8	.	.	PUNCT
ap-9572	434	1	https://doi.org/10.1016/j.amc.2005.11.068	https://doi.org/10.1016/j.amc.2005.11.068	X
ap-9572	435	1	[	[	X
ap-9572	435	2	26	26	NUM
ap-9572	435	3	]	]	PUNCT
ap-9572	435	4	a.	a.	NOUN
ap-9572	435	5	khanna	khanna	PROPN
ap-9572	435	6	,	,	PUNCT
ap-9572	435	7	a.	a.	NOUN
ap-9572	435	8	singhal	singhal	PROPN
ap-9572	435	9	.	.	PUNCT
ap-9572	436	1	influence	influence	NOUN
ap-9572	436	2	of	of	ADP
ap-9572	436	3	temperature	temperature	NOUN
ap-9572	436	4	variation	variation	NOUN
ap-9572	436	5	on	on	ADP
ap-9572	436	6	vibration	vibration	NOUN
ap-9572	436	7	of	of	ADP
ap-9572	436	8	rectangular	rectangular	ADJ
ap-9572	436	9	plate	plate	NOUN
ap-9572	436	10	of	of	ADP
ap-9572	436	11	visco	visco	ADJ
ap-9572	436	12	-	-	ADJ
ap-9572	436	13	elastic	elastic	ADJ
ap-9572	436	14	material	material	NOUN
ap-9572	436	15	.	.	PUNCT
ap-9572	437	1	world	world	NOUN
ap-9572	437	2	scientific	scientific	ADJ
ap-9572	437	3	news	news	NOUN
ap-9572	437	4	139(2):61–75	139(2):61–75	NOUN
ap-9572	437	5	,	,	PUNCT
ap-9572	437	6	2020	2020	NUM
ap-9572	437	7	.	.	PUNCT
ap-9572	438	1	[	[	X
ap-9572	438	2	27	27	NUM
ap-9572	438	3	]	]	X
ap-9572	438	4	n.	n.	PROPN
ap-9572	438	5	jafari	jafari	PROPN
ap-9572	438	6	,	,	PUNCT
ap-9572	438	7	m.	m.	NOUN
ap-9572	438	8	azhari	azhari	PROPN
ap-9572	438	9	.	.	PUNCT
ap-9572	439	1	free	free	ADJ
ap-9572	439	2	vibration	vibration	NOUN
ap-9572	439	3	analysis	analysis	NOUN
ap-9572	439	4	of	of	ADP
ap-9572	439	5	viscoelastic	viscoelastic	ADJ
ap-9572	439	6	plates	plate	NOUN
ap-9572	439	7	with	with	ADP
ap-9572	439	8	simultaneous	simultaneous	ADJ
ap-9572	439	9	calculation	calculation	NOUN
ap-9572	439	10	of	of	ADP
ap-9572	439	11	natural	natural	ADJ
ap-9572	439	12	frequency	frequency	NOUN
ap-9572	439	13	and	and	CCONJ
ap-9572	439	14	viscous	viscous	ADJ
ap-9572	439	15	damping	damping	NOUN
ap-9572	439	16	.	.	PUNCT
ap-9572	440	1	mathematics	mathematic	NOUN
ap-9572	440	2	and	and	CCONJ
ap-9572	440	3	computers	computer	NOUN
ap-9572	440	4	in	in	ADP
ap-9572	440	5	simulation	simulation	NOUN
ap-9572	440	6	185:646–659	185:646–659	NUM
ap-9572	440	7	,	,	PUNCT
ap-9572	440	8	2021	2021	NUM
ap-9572	440	9	.	.	PUNCT
ap-9572	441	1	https://doi.org/10.1016/j.matcom.2021.01.019	https://doi.org/10.1016/j.matcom.2021.01.019	PROPN
ap-9572	442	1	[	[	X
ap-9572	442	2	28	28	NUM
ap-9572	442	3	]	]	X
ap-9572	442	4	m.	m.	NOUN
ap-9572	442	5	amabili	amabili	NOUN
ap-9572	442	6	,	,	PUNCT
ap-9572	442	7	p.	p.	PROPN
ap-9572	442	8	balasubramanian	balasubramanian	PROPN
ap-9572	442	9	,	,	PUNCT
ap-9572	442	10	g.	g.	PROPN
ap-9572	442	11	ferrari	ferrari	PROPN
ap-9572	442	12	.	.	PUNCT
ap-9572	443	1	nonlinear	nonlinear	ADJ
ap-9572	443	2	vibrations	vibration	NOUN
ap-9572	443	3	and	and	CCONJ
ap-9572	443	4	damping	damp	VERB
ap-9572	443	5	of	of	ADP
ap-9572	443	6	fractional	fractional	ADJ
ap-9572	443	7	viscoelastic	viscoelastic	ADJ
ap-9572	443	8	rectangular	rectangular	ADJ
ap-9572	443	9	plates	plate	NOUN
ap-9572	443	10	.	.	PUNCT
ap-9572	444	1	nonlinear	nonlinear	ADJ
ap-9572	444	2	dynamics	dynamic	NOUN
ap-9572	444	3	103(4):3581–3609	103(4):3581–3609	PROPN
ap-9572	444	4	,	,	PUNCT
ap-9572	444	5	2021	2021	NUM
ap-9572	444	6	.	.	PUNCT
ap-9572	445	1	https://doi.org/10.1007/s11071-020-05892-0	https://doi.org/10.1007/s11071-020-05892-0	NUM
ap-9572	446	1	[	[	X
ap-9572	446	2	29	29	NUM
ap-9572	446	3	]	]	PUNCT
ap-9572	446	4	r.	r.	PROPN
ap-9572	446	5	bhardwaj	bhardwaj	PROPN
ap-9572	446	6	,	,	PUNCT
ap-9572	446	7	n.	n.	PROPN
ap-9572	446	8	mani	mani	PROPN
ap-9572	446	9	,	,	PUNCT
ap-9572	446	10	a.	a.	PROPN
ap-9572	446	11	sharma	sharma	PROPN
ap-9572	446	12	.	.	PROPN
ap-9572	446	13	time	time	NOUN
ap-9572	446	14	period	period	NOUN
ap-9572	446	15	of	of	ADP
ap-9572	446	16	transverse	transverse	NOUN
ap-9572	446	17	vibration	vibration	NOUN
ap-9572	446	18	of	of	ADP
ap-9572	446	19	skew	skew	ADJ
ap-9572	446	20	plate	plate	NOUN
ap-9572	446	21	with	with	ADP
ap-9572	446	22	parabolic	parabolic	ADJ
ap-9572	446	23	temperature	temperature	NOUN
ap-9572	446	24	variation	variation	NOUN
ap-9572	446	25	.	.	PUNCT
ap-9572	447	1	journal	journal	NOUN
ap-9572	447	2	of	of	ADP
ap-9572	447	3	vibration	vibration	NOUN
ap-9572	447	4	and	and	CCONJ
ap-9572	447	5	control	control	NOUN
ap-9572	447	6	27(3–4):323–331	27(3–4):323–331	NUM
ap-9572	447	7	,	,	PUNCT
ap-9572	447	8	2021	2021	NUM
ap-9572	447	9	.	.	PUNCT
ap-9572	447	10	https://doi.org/10.1177/1077546320926887	https://doi.org/10.1177/1077546320926887	VERB
ap-9572	448	1	[	[	X
ap-9572	448	2	30	30	NUM
ap-9572	448	3	]	]	X
ap-9572	448	4	r.	r.	PROPN
ap-9572	448	5	abdikarimov	abdikarimov	PROPN
ap-9572	448	6	,	,	PUNCT
ap-9572	448	7	m.	m.	NOUN
ap-9572	448	8	amabili	amabili	NOUN
ap-9572	448	9	,	,	PUNCT
ap-9572	448	10	n.	n.	PROPN
ap-9572	448	11	i.	i.	PROPN
ap-9572	448	12	vatin	vatin	PROPN
ap-9572	448	13	,	,	PUNCT
ap-9572	448	14	d.	d.	PROPN
ap-9572	448	15	khodzhaev	khodzhaev	PROPN
ap-9572	448	16	.	.	PUNCT
ap-9572	449	1	dynamic	dynamic	ADJ
ap-9572	449	2	stability	stability	NOUN
ap-9572	449	3	of	of	ADP
ap-9572	449	4	orthotropic	orthotropic	ADJ
ap-9572	449	5	viscoelastic	viscoelastic	ADJ
ap-9572	449	6	rectangular	rectangular	ADJ
ap-9572	449	7	plate	plate	NOUN
ap-9572	449	8	of	of	ADP
ap-9572	449	9	an	an	DET
ap-9572	449	10	arbitrarily	arbitrarily	ADV
ap-9572	449	11	varying	vary	VERB
ap-9572	449	12	thickness	thickness	NOUN
ap-9572	449	13	.	.	PUNCT
ap-9572	450	1	applied	apply	VERB
ap-9572	450	2	sciences	science	NOUN
ap-9572	450	3	11(13):6029	11(13):6029	NUM
ap-9572	450	4	,	,	PUNCT
ap-9572	450	5	2021	2021	NUM
ap-9572	450	6	.	.	PUNCT
ap-9572	451	1	https://doi.org/10.3390/app11136029	https://doi.org/10.3390/app11136029	PROPN
ap-9572	451	2	313	313	NUM
ap-9572	451	3	https://doi.org/10.1016/j.amc.2005.11.068	https://doi.org/10.1016/j.amc.2005.11.068	PROPN
ap-9572	451	4	https://doi.org/10.1016/j.matcom.2021.01.019	https://doi.org/10.1016/j.matcom.2021.01.019	PROPN
ap-9572	451	5	https://doi.org/10.1007/s11071-020-05892-0	https://doi.org/10.1007/s11071-020-05892-0	NUM
ap-9572	451	6	https://doi.org/10.1177/1077546320926887	https://doi.org/10.1177/1077546320926887	VERB
ap-9572	451	7	https://doi.org/10.3390/app11136029	https://doi.org/10.3390/app11136029	PROPN
ap-9572	451	8	acta	acta	PROPN
ap-9572	451	9	polytechnica	polytechnica	PROPN
ap-9572	451	10	64(4):297–313	64(4):297–313	PROPN
ap-9572	451	11	,	,	PUNCT
ap-9572	451	12	2024	2024	NUM
ap-9572	451	13	1	1	NUM
ap-9572	451	14	introduction	introduction	NOUN
ap-9572	451	15	2	2	NUM
ap-9572	451	16	assumptions	assumption	NOUN
ap-9572	451	17	of	of	ADP
ap-9572	451	18	the	the	DET
ap-9572	451	19	study	study	NOUN
ap-9572	451	20	3	3	NUM
ap-9572	451	21	equation	equation	NOUN
ap-9572	451	22	of	of	ADP
ap-9572	451	23	the	the	DET
ap-9572	451	24	motion	motion	NOUN
ap-9572	451	25	and	and	CCONJ
ap-9572	451	26	the	the	DET
ap-9572	451	27	method	method	NOUN
ap-9572	451	28	of	of	ADP
ap-9572	451	29	the	the	DET
ap-9572	451	30	analysis	analysis	NOUN
ap-9572	451	31	4	4	NUM
ap-9572	451	32	differential	differential	ADJ
ap-9572	451	33	equation	equation	NOUN
ap-9572	451	34	of	of	ADP
ap-9572	451	35	the	the	DET
ap-9572	451	36	time	time	NOUN
ap-9572	451	37	function	function	NOUN
ap-9572	451	38	with	with	ADP
ap-9572	451	39	its	its	PRON
ap-9572	451	40	solution	solution	NOUN
ap-9572	451	41	5	5	NUM
ap-9572	451	42	results	result	NOUN
ap-9572	451	43	and	and	CCONJ
ap-9572	451	44	discussions	discussion	NOUN
ap-9572	451	45	6	6	NUM
ap-9572	451	46	comparison	comparison	NOUN
ap-9572	451	47	of	of	ADP
ap-9572	451	48	the	the	DET
ap-9572	451	49	results	result	NOUN
ap-9572	451	50	of	of	ADP
ap-9572	451	51	the	the	DET
ap-9572	451	52	present	present	ADJ
ap-9572	451	53	study	study	NOUN
ap-9572	451	54	with	with	ADP
ap-9572	451	55	the	the	DET
ap-9572	451	56	previous	previous	ADJ
ap-9572	451	57	study	study	NOUN
ap-9572	451	58	7	7	NUM
ap-9572	451	59	conclusion	conclusion	NOUN
ap-9572	451	60	references	reference	NOUN