id	sid	tid	token	lemma	pos
cana-1540	1	1	communications	communication	NOUN
cana-1540	1	2	on	on	ADP
cana-1540	1	3	applied	apply	VERB
cana-1540	1	4	nonlinear	nonlinear	ADJ
cana-1540	1	5	analysis	analysis	NOUN
cana-1540	1	6	issn	issn	NOUN
cana-1540	1	7	:	:	PUNCT
cana-1540	1	8	1074	1074	NUM
cana-1540	1	9	-	-	PUNCT
cana-1540	1	10	133x	133x	NUM
cana-1540	1	11	vol	vol	NOUN
cana-1540	1	12	31	31	NUM
cana-1540	1	13	no	no	NOUN
cana-1540	1	14	.	.	PUNCT
cana-1540	2	1	8s	8s	PROPN
cana-1540	2	2	(	(	PUNCT
cana-1540	2	3	2024	2024	NUM
cana-1540	2	4	)	)	PUNCT
cana-1540	2	5	483	483	NUM
cana-1540	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	2	7	rayleigh	rayleigh	PROPN
cana-1540	2	8	waves	wave	NOUN
cana-1540	2	9	propagation	propagation	NOUN
cana-1540	2	10	in	in	ADP
cana-1540	2	11	a	a	DET
cana-1540	2	12	micropolar	micropolar	ADJ
cana-1540	2	13	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	2	14	halfspace	halfspace	NOUN
cana-1540	2	15	with	with	ADP
cana-1540	2	16	impedance	impedance	NOUN
cana-1540	2	17	boundary	boundary	ADJ
cana-1540	2	18	conditions	condition	NOUN
cana-1540	2	19	mamatha	mamatha	PROPN
cana-1540	2	20	kumari1	kumari1	NOUN
cana-1540	2	21	,	,	PUNCT
cana-1540	2	22	e.	e.	PROPN
cana-1540	2	23	rama2	rama2	PROPN
cana-1540	2	24	,	,	PUNCT
cana-1540	2	25	rajneesh	rajneesh	PROPN
cana-1540	2	26	kumar3	kumar3	PROPN
cana-1540	2	27	,	,	PUNCT
cana-1540	2	28	p	p	PROPN
cana-1540	2	29	vikas	vikas	NOUN
cana-1540	2	30	singh4	singh4	PROPN
cana-1540	2	31	1assistant	1assistant	PROPN
cana-1540	2	32	professor	professor	NOUN
cana-1540	2	33	,	,	PUNCT
cana-1540	2	34	st	st	PROPN
cana-1540	2	35	.	.	PROPN
cana-1540	2	36	martin	martin	PROPN
cana-1540	2	37	’s	’s	PART
cana-1540	2	38	engineering	engineering	PROPN
cana-1540	2	39	college	college	PROPN
cana-1540	2	40	,	,	PUNCT
cana-1540	2	41	hyderabad	hyderabad	PROPN
cana-1540	2	42	.	.	PUNCT
cana-1540	3	1	kumari4bu@gmail.com	kumari4bu@gmail.com	X
cana-1540	4	1	2associate	2associate	NUM
cana-1540	4	2	professor	professor	PROPN
cana-1540	4	3	,	,	PUNCT
cana-1540	4	4	osmania	osmania	PROPN
cana-1540	4	5	university	university	PROPN
cana-1540	4	6	,	,	PUNCT
cana-1540	4	7	hyderabad	hyderabad	PROPN
cana-1540	4	8	.	.	PUNCT
cana-1540	5	1	ramamathsou@gmail.com	ramamathsou@gmail.com	X
cana-1540	6	1	3department	3department	NUM
cana-1540	6	2	of	of	ADP
cana-1540	6	3	mathematics	mathematics	PROPN
cana-1540	6	4	,	,	PUNCT
cana-1540	6	5	kurukshetra	kurukshetra	PROPN
cana-1540	6	6	university	university	PROPN
cana-1540	6	7	,	,	PUNCT
cana-1540	6	8	kurukshetra	kurukshetra	PROPN
cana-1540	6	9	136119	136119	NUM
cana-1540	6	10	,	,	PUNCT
cana-1540	6	11	india	india	PROPN
cana-1540	6	12	rajneesh_kuk@rediffmail.com	rajneesh_kuk@rediffmail.com	X
cana-1540	7	1	4department	4department	NUM
cana-1540	7	2	of	of	ADP
cana-1540	7	3	mathematics	mathematics	PROPN
cana-1540	7	4	,	,	PUNCT
cana-1540	7	5	osmania	osmania	PROPN
cana-1540	7	6	university	university	PROPN
cana-1540	7	7	,	,	PUNCT
cana-1540	7	8	pulsinghvikas@gmail.com	pulsinghvikas@gmail.com	X
cana-1540	7	9	article	article	NOUN
cana-1540	7	10	history	history	NOUN
cana-1540	7	11	:	:	PUNCT
cana-1540	7	12	received	receive	VERB
cana-1540	7	13	:	:	PUNCT
cana-1540	7	14	10	10	NUM
cana-1540	7	15	-	-	SYM
cana-1540	7	16	05	05	NUM
cana-1540	7	17	-	-	PUNCT
cana-1540	7	18	2024	2024	NUM
cana-1540	7	19	revised	revise	VERB
cana-1540	7	20	:	:	PUNCT
cana-1540	7	21	28	28	NUM
cana-1540	7	22	-	-	SYM
cana-1540	7	23	06	06	NUM
cana-1540	7	24	-	-	PUNCT
cana-1540	7	25	2024	2024	NUM
cana-1540	7	26	accepted	accept	VERB
cana-1540	7	27	:	:	PUNCT
cana-1540	7	28	12	12	NUM
cana-1540	7	29	-	-	PUNCT
cana-1540	7	30	07	07	NUM
cana-1540	7	31	-	-	PUNCT
cana-1540	7	32	2024	2024	NUM
cana-1540	7	33	abstract	abstract	NOUN
cana-1540	7	34	this	this	DET
cana-1540	7	35	paper	paper	NOUN
cana-1540	7	36	deals	deal	NOUN
cana-1540	7	37	with	with	ADP
cana-1540	7	38	the	the	DET
cana-1540	7	39	propagation	propagation	NOUN
cana-1540	7	40	of	of	ADP
cana-1540	7	41	rayleigh	rayleigh	PROPN
cana-1540	7	42	waves	wave	NOUN
cana-1540	7	43	in	in	ADP
cana-1540	7	44	a	a	DET
cana-1540	7	45	micropolar	micropolar	ADJ
cana-1540	7	46	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	7	47	half	half	NOUN
cana-1540	7	48	space	space	NOUN
cana-1540	7	49	with	with	ADP
cana-1540	7	50	impedance	impedance	NOUN
cana-1540	7	51	boundary	boundary	ADJ
cana-1540	7	52	conditions	condition	NOUN
cana-1540	7	53	.	.	PUNCT
cana-1540	8	1	the	the	DET
cana-1540	8	2	boundary	boundary	NOUN
cana-1540	8	3	of	of	ADP
cana-1540	8	4	the	the	DET
cana-1540	8	5	half	half	ADJ
cana-1540	8	6	space	space	NOUN
cana-1540	8	7	is	be	AUX
cana-1540	8	8	thermally	thermally	ADV
cana-1540	8	9	insulated	insulate	VERB
cana-1540	8	10	/	/	SYM
cana-1540	8	11	isothermal	isothermal	ADJ
cana-1540	9	1	and	and	CCONJ
cana-1540	9	2	it	it	PRON
cana-1540	9	3	is	be	AUX
cana-1540	9	4	assumed	assume	VERB
cana-1540	9	5	that	that	SCONJ
cana-1540	9	6	normal	normal	ADJ
cana-1540	9	7	traction	traction	NOUN
cana-1540	9	8	,	,	PUNCT
cana-1540	9	9	shear	shear	NOUN
cana-1540	9	10	traction	traction	NOUN
cana-1540	9	11	and	and	CCONJ
cana-1540	9	12	shear	shear	ADJ
cana-1540	9	13	couple	couple	NOUN
cana-1540	9	14	traction	traction	NOUN
cana-1540	9	15	at	at	ADP
cana-1540	9	16	the	the	DET
cana-1540	9	17	surface	surface	NOUN
cana-1540	9	18	,	,	PUNCT
cana-1540	9	19	varies	vary	VERB
cana-1540	9	20	linearly	linearly	ADV
cana-1540	9	21	with	with	ADP
cana-1540	9	22	normal	normal	ADJ
cana-1540	9	23	,	,	PUNCT
cana-1540	9	24	tangential	tangential	ADJ
cana-1540	9	25	components	component	NOUN
cana-1540	9	26	of	of	ADP
cana-1540	9	27	displacement	displacement	NOUN
cana-1540	9	28	and	and	CCONJ
cana-1540	9	29	microrotation	microrotation	NOUN
cana-1540	9	30	respectively	respectively	ADV
cana-1540	9	31	.	.	PUNCT
cana-1540	10	1	the	the	DET
cana-1540	10	2	secular	secular	ADJ
cana-1540	10	3	equation	equation	NOUN
cana-1540	10	4	for	for	ADP
cana-1540	10	5	rayleigh	rayleigh	PROPN
cana-1540	10	6	wave	wave	PROPN
cana-1540	10	7	with	with	ADP
cana-1540	10	8	impedance	impedance	NOUN
cana-1540	10	9	boundary	boundary	ADJ
cana-1540	10	10	conditions	condition	NOUN
cana-1540	10	11	is	be	AUX
cana-1540	10	12	obtained	obtain	VERB
cana-1540	10	13	and	and	CCONJ
cana-1540	10	14	this	this	DET
cana-1540	10	15	equation	equation	NOUN
cana-1540	10	16	is	be	AUX
cana-1540	10	17	in	in	ADP
cana-1540	10	18	agreement	agreement	NOUN
cana-1540	10	19	with	with	ADP
cana-1540	10	20	the	the	DET
cana-1540	10	21	classical	classical	ADJ
cana-1540	10	22	secular	secular	ADJ
cana-1540	10	23	equation	equation	NOUN
cana-1540	10	24	for	for	ADP
cana-1540	10	25	elastic	elastic	ADJ
cana-1540	10	26	solid	solid	ADJ
cana-1540	10	27	with	with	ADP
cana-1540	10	28	traction	traction	NOUN
cana-1540	10	29	free	free	ADJ
cana-1540	10	30	boundary	boundary	ADJ
cana-1540	10	31	conditions	condition	NOUN
cana-1540	10	32	when	when	SCONJ
cana-1540	10	33	micropolar	micropolar	ADJ
cana-1540	10	34	,	,	PUNCT
cana-1540	10	35	thermal	thermal	ADJ
cana-1540	10	36	and	and	CCONJ
cana-1540	10	37	impedance	impedance	NOUN
cana-1540	10	38	parameters	parameter	NOUN
cana-1540	10	39	are	be	AUX
cana-1540	10	40	removed	remove	VERB
cana-1540	10	41	.	.	PUNCT
cana-1540	11	1	the	the	DET
cana-1540	11	2	non	non	ADJ
cana-1540	11	3	-	-	ADJ
cana-1540	11	4	dimensional	dimensional	ADJ
cana-1540	11	5	speed	speed	NOUN
cana-1540	11	6	of	of	ADP
cana-1540	11	7	rayleigh	rayleigh	PROPN
cana-1540	11	8	wave	wave	NOUN
cana-1540	11	9	is	be	AUX
cana-1540	11	10	computed	compute	VERB
cana-1540	11	11	as	as	ADP
cana-1540	11	12	a	a	DET
cana-1540	11	13	function	function	NOUN
cana-1540	11	14	of	of	ADP
cana-1540	11	15	impedance	impedance	NOUN
cana-1540	11	16	parameters	parameter	NOUN
cana-1540	11	17	and	and	CCONJ
cana-1540	11	18	presented	present	VERB
cana-1540	11	19	graphically	graphically	ADV
cana-1540	11	20	for	for	ADP
cana-1540	11	21	a	a	DET
cana-1540	11	22	particular	particular	ADJ
cana-1540	11	23	micropolar	micropolar	ADJ
cana-1540	11	24	thermoelastic	thermoelastic	ADJ
cana-1540	11	25	material	material	NOUN
cana-1540	11	26	.	.	PUNCT
cana-1540	12	1	keywords	keyword	NOUN
cana-1540	12	2	:	:	PUNCT
cana-1540	12	3	micropolar	micropolar	ADJ
cana-1540	12	4	thermoelasticity	thermoelasticity	NOUN
cana-1540	12	5	,	,	PUNCT
cana-1540	12	6	rayleigh	rayleigh	PROPN
cana-1540	12	7	waves	wave	NOUN
cana-1540	12	8	,	,	PUNCT
cana-1540	12	9	impedance	impedance	NOUN
cana-1540	12	10	boundary	boundary	ADJ
cana-1540	12	11	conditions	condition	NOUN
cana-1540	12	12	,	,	PUNCT
cana-1540	12	13	secular	secular	ADJ
cana-1540	12	14	equation	equation	NOUN
cana-1540	12	15	.	.	PUNCT
cana-1540	13	1	1.introduction	1.introduction	NUM
cana-1540	13	2	eringen	eringen	PROPN
cana-1540	13	3	’s	’s	PART
cana-1540	13	4	[	[	X
cana-1540	13	5	1]micropolar	1]micropolar	NUM
cana-1540	13	6	theory	theory	NOUN
cana-1540	13	7	of	of	ADP
cana-1540	13	8	elasticity	elasticity	NOUN
cana-1540	13	9	is	be	AUX
cana-1540	13	10	now	now	ADV
cana-1540	13	11	well	well	ADV
cana-1540	13	12	known	know	VERB
cana-1540	13	13	due	due	ADP
cana-1540	13	14	to	to	ADP
cana-1540	13	15	its	its	PRON
cana-1540	13	16	possible	possible	ADJ
cana-1540	13	17	utility	utility	NOUN
cana-1540	13	18	in	in	ADP
cana-1540	13	19	examining	examine	VERB
cana-1540	13	20	the	the	DET
cana-1540	13	21	deformation	deformation	NOUN
cana-1540	13	22	properties	property	NOUN
cana-1540	13	23	of	of	ADP
cana-1540	13	24	materials	material	NOUN
cana-1540	13	25	such	such	ADJ
cana-1540	13	26	as	as	ADP
cana-1540	13	27	cellular	cellular	ADJ
cana-1540	13	28	solids	solid	NOUN
cana-1540	13	29	,	,	PUNCT
cana-1540	13	30	polymers	polymer	NOUN
cana-1540	13	31	,	,	PUNCT
cana-1540	13	32	composite	composite	ADJ
cana-1540	13	33	fibrous	fibrous	ADJ
cana-1540	13	34	,	,	PUNCT
cana-1540	13	35	granular	granular	ADJ
cana-1540	13	36	material	material	NOUN
cana-1540	13	37	,	,	PUNCT
cana-1540	13	38	masonry	masonry	NOUN
cana-1540	13	39	,	,	PUNCT
cana-1540	13	40	bones	bone	NOUN
cana-1540	13	41	and	and	CCONJ
cana-1540	13	42	many	many	ADJ
cana-1540	13	43	more	more	ADJ
cana-1540	13	44	with	with	ADP
cana-1540	13	45	microstructures	microstructure	NOUN
cana-1540	13	46	.	.	PUNCT
cana-1540	14	1	this	this	DET
cana-1540	14	2	theory	theory	NOUN
cana-1540	14	3	takes	take	VERB
cana-1540	14	4	into	into	ADP
cana-1540	14	5	account	account	NOUN
cana-1540	14	6	the	the	DET
cana-1540	14	7	intrinsic	intrinsic	ADJ
cana-1540	14	8	rotation	rotation	NOUN
cana-1540	14	9	along	along	ADP
cana-1540	14	10	with	with	ADP
cana-1540	14	11	linear	linear	ADJ
cana-1540	14	12	displacement	displacement	NOUN
cana-1540	14	13	in	in	ADP
cana-1540	14	14	the	the	DET
cana-1540	14	15	materials	material	NOUN
cana-1540	14	16	possess	possess	VERB
cana-1540	14	17	microstructure	microstructure	NOUN
cana-1540	14	18	and	and	CCONJ
cana-1540	14	19	the	the	DET
cana-1540	14	20	motion	motion	NOUN
cana-1540	14	21	is	be	AUX
cana-1540	14	22	governed	govern	VERB
cana-1540	14	23	by	by	ADP
cana-1540	14	24	six	six	NUM
cana-1540	14	25	degrees	degree	NOUN
cana-1540	14	26	of	of	ADP
cana-1540	14	27	freedom	freedom	NOUN
cana-1540	14	28	,	,	PUNCT
cana-1540	14	29	three	three	NUM
cana-1540	14	30	of	of	ADP
cana-1540	14	31	microrotation	microrotation	NOUN
cana-1540	14	32	and	and	CCONJ
cana-1540	14	33	three	three	NUM
cana-1540	14	34	of	of	ADP
cana-1540	14	35	classical	classical	ADJ
cana-1540	14	36	translation	translation	NOUN
cana-1540	14	37	.	.	PUNCT
cana-1540	15	1	the	the	DET
cana-1540	15	2	classical	classical	ADJ
cana-1540	15	3	theory	theory	NOUN
cana-1540	15	4	of	of	ADP
cana-1540	15	5	elasticity	elasticity	NOUN
cana-1540	15	6	,	,	PUNCT
cana-1540	15	7	which	which	PRON
cana-1540	15	8	ignores	ignore	VERB
cana-1540	15	9	the	the	DET
cana-1540	15	10	microrotation	microrotation	NOUN
cana-1540	15	11	degrees	degree	NOUN
cana-1540	15	12	of	of	ADP
cana-1540	15	13	freedoms	freedom	NOUN
cana-1540	15	14	,	,	PUNCT
cana-1540	15	15	can	can	AUX
cana-1540	15	16	explain	explain	VERB
cana-1540	15	17	the	the	DET
cana-1540	15	18	behaviour	behaviour	NOUN
cana-1540	15	19	of	of	ADP
cana-1540	15	20	common	common	ADJ
cana-1540	15	21	solid	solid	ADJ
cana-1540	15	22	materials	material	NOUN
cana-1540	15	23	like	like	ADP
cana-1540	15	24	coal	coal	NOUN
cana-1540	15	25	,	,	PUNCT
cana-1540	15	26	concrete	concrete	ADJ
cana-1540	15	27	etc	etc	X
cana-1540	15	28	.	.	PUNCT
cana-1540	16	1	this	this	DET
cana-1540	16	2	theory	theory	NOUN
cana-1540	16	3	is	be	AUX
cana-1540	16	4	inadequate	inadequate	ADJ
cana-1540	16	5	to	to	PART
cana-1540	16	6	explain	explain	VERB
cana-1540	16	7	the	the	DET
cana-1540	16	8	behaviour	behaviour	NOUN
cana-1540	16	9	of	of	ADP
cana-1540	16	10	materials	material	NOUN
cana-1540	16	11	with	with	ADP
cana-1540	16	12	inner	inner	ADJ
cana-1540	16	13	microstructure	microstructure	NOUN
cana-1540	16	14	such	such	ADJ
cana-1540	16	15	as	as	ADP
cana-1540	16	16	polycrystalline	polycrystalline	NOUN
cana-1540	16	17	and	and	CCONJ
cana-1540	16	18	materials	material	NOUN
cana-1540	16	19	with	with	ADP
cana-1540	16	20	fibrous	fibrous	ADJ
cana-1540	16	21	or	or	CCONJ
cana-1540	16	22	coarse	coarse	ADJ
cana-1540	16	23	grain	grain	NOUN
cana-1540	16	24	.	.	PUNCT
cana-1540	17	1	therefore	therefore	ADV
cana-1540	17	2	,	,	PUNCT
cana-1540	17	3	micropolar	micropolar	ADJ
cana-1540	17	4	theory	theory	NOUN
cana-1540	17	5	was	be	AUX
cana-1540	17	6	developed	develop	VERB
cana-1540	17	7	to	to	PART
cana-1540	17	8	explain	explain	VERB
cana-1540	17	9	the	the	DET
cana-1540	17	10	microscopic	microscopic	ADJ
cana-1540	17	11	motion	motion	NOUN
cana-1540	17	12	and	and	CCONJ
cana-1540	17	13	longrange	longrange	NOUN
cana-1540	17	14	interactions	interaction	NOUN
cana-1540	17	15	in	in	ADP
cana-1540	17	16	solids	solid	NOUN
cana-1540	17	17	.	.	PUNCT
cana-1540	18	1	as	as	SCONJ
cana-1540	18	2	mechanical	mechanical	ADJ
cana-1540	18	3	and	and	CCONJ
cana-1540	18	4	thermal	thermal	ADJ
cana-1540	18	5	fields	field	NOUN
cana-1540	18	6	are	be	AUX
cana-1540	18	7	associated	associate	VERB
cana-1540	18	8	in	in	ADP
cana-1540	18	9	almost	almost	ADV
cana-1540	18	10	all	all	PRON
cana-1540	18	11	practical	practical	ADJ
cana-1540	18	12	engineering	engineering	NOUN
cana-1540	18	13	problems	problem	NOUN
cana-1540	18	14	where	where	SCONJ
cana-1540	18	15	,	,	PUNCT
cana-1540	18	16	the	the	DET
cana-1540	18	17	application	application	NOUN
cana-1540	18	18	of	of	ADP
cana-1540	18	19	mechanical	mechanical	ADJ
cana-1540	18	20	forces	force	NOUN
cana-1540	18	21	can	can	AUX
cana-1540	18	22	change	change	VERB
cana-1540	18	23	the	the	DET
cana-1540	18	24	temperature	temperature	NOUN
cana-1540	18	25	of	of	ADP
cana-1540	18	26	the	the	DET
cana-1540	18	27	system	system	NOUN
cana-1540	18	28	.	.	PUNCT
cana-1540	19	1	keeping	keep	VERB
cana-1540	19	2	this	this	DET
cana-1540	19	3	important	important	ADJ
cana-1540	19	4	interaction	interaction	NOUN
cana-1540	19	5	in	in	ADP
cana-1540	19	6	view	view	NOUN
cana-1540	19	7	,	,	PUNCT
cana-1540	19	8	nowacki[2	nowacki[2	PROPN
cana-1540	19	9	]	]	PUNCT
cana-1540	19	10	and	and	CCONJ
cana-1540	19	11	eringen[3]extended	eringen[3]extende	VERB
cana-1540	19	12	the	the	DET
cana-1540	19	13	micropolar	micropolar	PROPN
cana-1540	19	14	theory	theory	NOUN
cana-1540	19	15	by	by	ADP
cana-1540	19	16	including	include	VERB
cana-1540	19	17	thermal	thermal	ADJ
cana-1540	19	18	effects	effect	NOUN
cana-1540	19	19	and	and	CCONJ
cana-1540	19	20	presented	present	VERB
cana-1540	19	21	linear	linear	PROPN
cana-1540	19	22	theory	theory	NOUN
cana-1540	19	23	of	of	ADP
cana-1540	19	24	micropolar	micropolar	ADJ
cana-1540	19	25	thermoelasticity	thermoelasticity	NOUN
cana-1540	19	26	.	.	PUNCT
cana-1540	20	1	tauchert	tauchert	PROPN
cana-1540	20	2	,	,	PUNCT
cana-1540	20	3	claus	claus	PROPN
cana-1540	20	4	jr	jr	PROPN
cana-1540	20	5	and	and	CCONJ
cana-1540	20	6	ariman[4	ariman[4	NOUN
cana-1540	20	7	]	]	X
cana-1540	20	8	file:///c:/users	file:///c:/user	NOUN
cana-1540	20	9	/	/	SYM
cana-1540	20	10	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	20	11	/	/	SYM
cana-1540	20	12	appdata	appdata	NOUN
cana-1540	20	13	/	/	SYM
cana-1540	20	14	local	local	ADJ
cana-1540	20	15	/	/	SYM
cana-1540	20	16	microsoft	microsoft	PROPN
cana-1540	20	17	/	/	SYM
cana-1540	20	18	windows	windows	PROPN
cana-1540	20	19	/	/	SYM
cana-1540	20	20	inetcache	inetcache	NOUN
cana-1540	20	21	/	/	SYM
cana-1540	20	22	ie	ie	PROPN
cana-1540	20	23	/	/	SYM
cana-1540	20	24	a6wkhao2	a6wkhao2	PROPN
cana-1540	20	25	/	/	SYM
cana-1540	20	26	chapter-4%5b1%5d.docx%23placeholder1	chapter-4%5b1%5d.docx%23placeholder1	NOUN
cana-1540	20	27	file:///c:/users	file:///c:/user	NOUN
cana-1540	20	28	/	/	SYM
cana-1540	20	29	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	20	30	/	/	SYM
cana-1540	20	31	appdata	appdata	NOUN
cana-1540	20	32	/	/	SYM
cana-1540	20	33	local	local	ADJ
cana-1540	20	34	/	/	SYM
cana-1540	20	35	microsoft	microsoft	PROPN
cana-1540	20	36	/	/	SYM
cana-1540	20	37	windows	windows	PROPN
cana-1540	20	38	/	/	SYM
cana-1540	20	39	inetcache	inetcache	NOUN
cana-1540	20	40	/	/	SYM
cana-1540	20	41	ie	ie	PROPN
cana-1540	20	42	/	/	SYM
cana-1540	20	43	a6wkhao2	a6wkhao2	ADJ
cana-1540	20	44	/	/	SYM
cana-1540	20	45	chapter-4%5b1%5d.docx%23now68	chapter-4%5b1%5d.docx%23now68	NOUN
cana-1540	20	46	file:///c:/users	file:///c:/user	NOUN
cana-1540	20	47	/	/	SYM
cana-1540	20	48	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	20	49	/	/	SYM
cana-1540	20	50	appdata	appdata	NOUN
cana-1540	20	51	/	/	SYM
cana-1540	20	52	local	local	ADJ
cana-1540	20	53	/	/	SYM
cana-1540	20	54	microsoft	microsoft	PROPN
cana-1540	20	55	/	/	SYM
cana-1540	20	56	windows	windows	PROPN
cana-1540	20	57	/	/	SYM
cana-1540	20	58	inetcache	inetcache	NOUN
cana-1540	20	59	/	/	SYM
cana-1540	20	60	ie	ie	PROPN
cana-1540	20	61	/	/	SYM
cana-1540	20	62	a6wkhao2	a6wkhao2	PROPN
cana-1540	20	63	/	/	SYM
cana-1540	20	64	chapter-4%5b1%5d.docx%23ace70	chapter-4%5b1%5d.docx%23ace70	ADJ
cana-1540	20	65	file:///c:/users	file:///c:/users	PROPN
cana-1540	20	66	/	/	SYM
cana-1540	20	67	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	20	68	/	/	SYM
cana-1540	20	69	appdata	appdata	NOUN
cana-1540	20	70	/	/	SYM
cana-1540	20	71	local	local	ADJ
cana-1540	20	72	/	/	SYM
cana-1540	20	73	microsoft	microsoft	PROPN
cana-1540	20	74	/	/	SYM
cana-1540	20	75	windows	windows	PROPN
cana-1540	20	76	/	/	SYM
cana-1540	20	77	inetcache	inetcache	NOUN
cana-1540	20	78	/	/	SYM
cana-1540	20	79	ie	ie	PROPN
cana-1540	20	80	/	/	SYM
cana-1540	20	81	a6wkhao2	a6wkhao2	ADJ
cana-1540	20	82	/	/	SYM
cana-1540	20	83	chapter-4%5b1%5d.docx%23tau68	chapter-4%5b1%5d.docx%23tau68	NOUN
cana-1540	20	84	communications	communication	NOUN
cana-1540	20	85	on	on	ADP
cana-1540	20	86	applied	apply	VERB
cana-1540	20	87	nonlinear	nonlinear	ADJ
cana-1540	20	88	analysis	analysis	NOUN
cana-1540	20	89	issn	issn	NOUN
cana-1540	20	90	:	:	PUNCT
cana-1540	20	91	1074	1074	NUM
cana-1540	20	92	-	-	PUNCT
cana-1540	20	93	133x	133x	NUM
cana-1540	20	94	vol	vol	NOUN
cana-1540	20	95	31	31	NUM
cana-1540	20	96	no	no	NOUN
cana-1540	20	97	.	.	PUNCT
cana-1540	21	1	8s	8s	PROPN
cana-1540	21	2	(	(	PUNCT
cana-1540	21	3	2024	2024	NUM
cana-1540	21	4	)	)	PUNCT
cana-1540	21	5	484	484	NUM
cana-1540	21	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1540	21	7	developed	develop	VERB
cana-1540	21	8	the	the	DET
cana-1540	21	9	linear	linear	ADJ
cana-1540	21	10	theory	theory	NOUN
cana-1540	21	11	of	of	ADP
cana-1540	21	12	micropolar	micropolar	ADJ
cana-1540	21	13	thermoelasticity	thermoelasticity	NOUN
cana-1540	21	14	and	and	CCONJ
cana-1540	21	15	formulate	formulate	VERB
cana-1540	21	16	the	the	DET
cana-1540	21	17	constitutive	constitutive	ADJ
cana-1540	21	18	equations	equation	NOUN
cana-1540	21	19	.	.	PUNCT
cana-1540	22	1	various	various	ADJ
cana-1540	22	2	problems	problem	NOUN
cana-1540	22	3	on	on	ADP
cana-1540	22	4	micropolar	micropolar	ADJ
cana-1540	22	5	thermoelasticity	thermoelasticity	NOUN
cana-1540	22	6	have	have	AUX
cana-1540	22	7	been	be	AUX
cana-1540	22	8	investigated	investigate	VERB
cana-1540	22	9	extensively	extensively	ADV
cana-1540	22	10	by	by	ADP
cana-1540	22	11	researcher	researcher	NOUN
cana-1540	22	12	due	due	ADJ
cana-1540	22	13	its	its	PRON
cana-1540	22	14	applications	application	NOUN
cana-1540	22	15	in	in	ADP
cana-1540	22	16	various	various	ADJ
cana-1540	22	17	fields	field	NOUN
cana-1540	22	18	like	like	ADP
cana-1540	22	19	earthquake	earthquake	NOUN
cana-1540	22	20	,	,	PUNCT
cana-1540	22	21	nuclear	nuclear	ADJ
cana-1540	22	22	reactors	reactor	NOUN
cana-1540	22	23	,	,	PUNCT
cana-1540	22	24	aeronautics	aeronautic	NOUN
cana-1540	22	25	,	,	PUNCT
cana-1540	22	26	astronautics	astronautic	NOUN
cana-1540	22	27	and	and	CCONJ
cana-1540	22	28	modern	modern	ADJ
cana-1540	22	29	sensor	sensor	NOUN
cana-1540	22	30	devices	device	NOUN
cana-1540	22	31	.	.	PUNCT
cana-1540	23	1	the	the	DET
cana-1540	23	2	generalized	generalized	ADJ
cana-1540	23	3	theory	theory	NOUN
cana-1540	23	4	of	of	ADP
cana-1540	23	5	thermoelasticity	thermoelasticity	NOUN
cana-1540	23	6	is	be	AUX
cana-1540	23	7	a	a	DET
cana-1540	23	8	modified	modify	VERB
cana-1540	23	9	version	version	NOUN
cana-1540	23	10	of	of	ADP
cana-1540	23	11	classical	classical	ADJ
cana-1540	23	12	uncoupled	uncoupled	ADJ
cana-1540	23	13	and	and	CCONJ
cana-1540	23	14	coupled	couple	VERB
cana-1540	23	15	theory	theory	NOUN
cana-1540	23	16	of	of	ADP
cana-1540	23	17	thermoelasticity	thermoelasticity	NOUN
cana-1540	23	18	and	and	CCONJ
cana-1540	23	19	has	have	AUX
cana-1540	23	20	been	be	AUX
cana-1540	23	21	developed	develop	VERB
cana-1540	23	22	in	in	ADP
cana-1540	23	23	order	order	NOUN
cana-1540	23	24	to	to	PART
cana-1540	23	25	remove	remove	VERB
cana-1540	23	26	the	the	DET
cana-1540	23	27	paradox	paradox	NOUN
cana-1540	23	28	of	of	ADP
cana-1540	23	29	impossible	impossible	ADJ
cana-1540	23	30	phenomena	phenomenon	NOUN
cana-1540	23	31	of	of	ADP
cana-1540	23	32	infinite	infinite	ADJ
cana-1540	23	33	velocity	velocity	NOUN
cana-1540	23	34	of	of	ADP
cana-1540	23	35	thermal	thermal	ADJ
cana-1540	23	36	signals	signal	NOUN
cana-1540	23	37	in	in	ADP
cana-1540	23	38	the	the	DET
cana-1540	23	39	classical	classical	ADJ
cana-1540	23	40	coupled	couple	VERB
cana-1540	23	41	theory	theory	NOUN
cana-1540	23	42	of	of	ADP
cana-1540	23	43	thermoelasticity	thermoelasticity	NOUN
cana-1540	23	44	.	.	PUNCT
cana-1540	24	1	lord	lord	PROPN
cana-1540	24	2	and	and	CCONJ
cana-1540	24	3	shulman	shulman	PROPN
cana-1540	24	4	[	[	X
cana-1540	24	5	5	5	NUM
cana-1540	24	6	]	]	PUNCT
cana-1540	24	7	and	and	CCONJ
cana-1540	24	8	green	green	ADJ
cana-1540	24	9	and	and	CCONJ
cana-1540	24	10	lindsay[6]includes	lindsay[6]include	VERB
cana-1540	24	11	the	the	DET
cana-1540	24	12	concept	concept	NOUN
cana-1540	24	13	of	of	ADP
cana-1540	24	14	thermal	thermal	ADJ
cana-1540	24	15	relaxation	relaxation	NOUN
cana-1540	24	16	time	time	NOUN
cana-1540	24	17	and	and	CCONJ
cana-1540	24	18	eliminate	eliminate	VERB
cana-1540	24	19	this	this	DET
cana-1540	24	20	paradox	paradox	NOUN
cana-1540	24	21	of	of	ADP
cana-1540	24	22	infinite	infinite	ADJ
cana-1540	24	23	velocity	velocity	NOUN
cana-1540	24	24	of	of	ADP
cana-1540	24	25	thermal	thermal	ADJ
cana-1540	24	26	signals	signal	NOUN
cana-1540	24	27	.	.	PUNCT
cana-1540	25	1	based	base	VERB
cana-1540	25	2	upon	upon	SCONJ
cana-1540	25	3	generalized	generalized	ADJ
cana-1540	25	4	theory	theory	NOUN
cana-1540	25	5	of	of	ADP
cana-1540	25	6	thermoelasticity	thermoelasticity	NOUN
cana-1540	25	7	given	give	VERB
cana-1540	25	8	by	by	ADP
cana-1540	25	9	green	green	ADJ
cana-1540	25	10	and	and	CCONJ
cana-1540	25	11	lindsay	lindsay	PROPN
cana-1540	25	12	,	,	PUNCT
cana-1540	25	13	boschi	boschi	PROPN
cana-1540	25	14	and	and	CCONJ
cana-1540	25	15	ieşan	ieşan	NOUN
cana-1540	25	16	[	[	X
cana-1540	25	17	7	7	X
cana-1540	25	18	]	]	PUNCT
cana-1540	25	19	proposed	propose	VERB
cana-1540	25	20	a	a	DET
cana-1540	25	21	generalized	generalized	ADJ
cana-1540	25	22	theory	theory	NOUN
cana-1540	25	23	of	of	ADP
cana-1540	25	24	linear	linear	PROPN
cana-1540	25	25	micropolar	micropolar	ADJ
cana-1540	25	26	thermoelasticity	thermoelasticity	NOUN
cana-1540	25	27	that	that	PRON
cana-1540	25	28	admits	admit	VERB
cana-1540	25	29	the	the	DET
cana-1540	25	30	possibility	possibility	NOUN
cana-1540	25	31	of	of	ADP
cana-1540	25	32	second	second	ADJ
cana-1540	25	33	sound	sound	ADJ
cana-1540	25	34	effect	effect	NOUN
cana-1540	25	35	.	.	PUNCT
cana-1540	26	1	ciarletta[8]established	ciarletta[8]establishe	VERB
cana-1540	26	2	the	the	DET
cana-1540	26	3	finite	finite	ADJ
cana-1540	26	4	speed	speed	NOUN
cana-1540	26	5	of	of	ADP
cana-1540	26	6	thermal	thermal	ADJ
cana-1540	26	7	waves	wave	NOUN
cana-1540	26	8	by	by	ADP
cana-1540	26	9	using	use	VERB
cana-1540	26	10	theory	theory	NOUN
cana-1540	26	11	of	of	ADP
cana-1540	26	12	micropolar	micropolar	ADJ
cana-1540	26	13	thermoelasticity	thermoelasticity	NOUN
cana-1540	26	14	without	without	ADP
cana-1540	26	15	energy	energy	NOUN
cana-1540	26	16	dissipation	dissipation	NOUN
cana-1540	26	17	.	.	PUNCT
cana-1540	27	1	based	base	VERB
cana-1540	27	2	upon	upon	SCONJ
cana-1540	27	3	lord	lord	PROPN
cana-1540	27	4	and	and	CCONJ
cana-1540	27	5	shulman	shulman	PROPN
cana-1540	27	6	theory[5]sherief	theory[5]sherief	PROPN
cana-1540	27	7	,	,	PUNCT
cana-1540	27	8	hamza	hamza	PROPN
cana-1540	27	9	and	and	CCONJ
cana-1540	27	10	ei	ei	NOUN
cana-1540	27	11	-	-	PUNCT
cana-1540	27	12	sayed	sayed	PROPN
cana-1540	28	1	[	[	X
cana-1540	28	2	9],derived	9],derive	VERB
cana-1540	28	3	the	the	DET
cana-1540	28	4	generalized	generalized	ADJ
cana-1540	28	5	equation	equation	NOUN
cana-1540	28	6	for	for	ADP
cana-1540	28	7	the	the	DET
cana-1540	28	8	linear	linear	PROPN
cana-1540	28	9	theory	theory	NOUN
cana-1540	28	10	of	of	ADP
cana-1540	28	11	micropolar	micropolar	ADJ
cana-1540	28	12	thermoelasticity	thermoelasticity	NOUN
cana-1540	28	13	.	.	PUNCT
cana-1540	29	1	a	a	DET
cana-1540	29	2	comprehensive	comprehensive	ADJ
cana-1540	29	3	study	study	NOUN
cana-1540	29	4	is	be	AUX
cana-1540	29	5	available	available	ADJ
cana-1540	29	6	on	on	ADP
cana-1540	29	7	the	the	DET
cana-1540	29	8	phenomenon	phenomenon	NOUN
cana-1540	29	9	of	of	ADP
cana-1540	29	10	wave	wave	NOUN
cana-1540	29	11	propagation	propagation	NOUN
cana-1540	29	12	in	in	ADP
cana-1540	29	13	micropolargeneralized	micropolargeneralized	ADJ
cana-1540	29	14	thermoelastic	thermoelastic	ADJ
cana-1540	29	15	solid	solid	ADJ
cana-1540	29	16	because	because	SCONJ
cana-1540	29	17	of	of	ADP
cana-1540	29	18	their	their	PRON
cana-1540	29	19	practical	practical	ADJ
cana-1540	29	20	applicability	applicability	NOUN
cana-1540	29	21	in	in	ADP
cana-1540	29	22	the	the	DET
cana-1540	29	23	various	various	ADJ
cana-1540	29	24	fields	field	NOUN
cana-1540	29	25	of	of	ADP
cana-1540	29	26	science	science	NOUN
cana-1540	29	27	and	and	CCONJ
cana-1540	29	28	technology	technology	NOUN
cana-1540	29	29	such	such	ADJ
cana-1540	29	30	as	as	ADP
cana-1540	29	31	,	,	PUNCT
cana-1540	29	32	seismology	seismology	NOUN
cana-1540	29	33	,	,	PUNCT
cana-1540	29	34	acoustics	acoustic	NOUN
cana-1540	29	35	,	,	PUNCT
cana-1540	29	36	aerospace	aerospace	NOUN
cana-1540	29	37	and	and	CCONJ
cana-1540	29	38	submarine	submarine	NOUN
cana-1540	29	39	structures	structure	NOUN
cana-1540	29	40	.	.	PUNCT
cana-1540	30	1	surface	surface	NOUN
cana-1540	30	2	waves	wave	NOUN
cana-1540	30	3	due	due	ADP
cana-1540	30	4	to	to	ADP
cana-1540	30	5	their	their	PRON
cana-1540	30	6	destructive	destructive	ADJ
cana-1540	30	7	nature	nature	NOUN
cana-1540	30	8	during	during	ADP
cana-1540	30	9	earthquake	earthquake	NOUN
cana-1540	30	10	are	be	AUX
cana-1540	30	11	of	of	ADP
cana-1540	30	12	particular	particular	ADJ
cana-1540	30	13	importance	importance	NOUN
cana-1540	30	14	in	in	ADP
cana-1540	30	15	the	the	DET
cana-1540	30	16	study	study	NOUN
cana-1540	30	17	of	of	ADP
cana-1540	30	18	seismology	seismology	NOUN
cana-1540	30	19	.	.	PUNCT
cana-1540	31	1	lord	lord	PROPN
cana-1540	31	2	rayleigh[10]was	rayleigh[10]wa	VERB
cana-1540	31	3	the	the	DET
cana-1540	31	4	first	first	ADJ
cana-1540	31	5	to	to	PART
cana-1540	31	6	study	study	VERB
cana-1540	31	7	the	the	DET
cana-1540	31	8	wave	wave	NOUN
cana-1540	31	9	propagating	propagate	VERB
cana-1540	31	10	along	along	ADP
cana-1540	31	11	the	the	DET
cana-1540	31	12	isotropic	isotropic	ADJ
cana-1540	31	13	elastic	elastic	ADJ
cana-1540	31	14	solid	solid	ADJ
cana-1540	31	15	and	and	CCONJ
cana-1540	31	16	such	such	ADJ
cana-1540	31	17	waves	wave	NOUN
cana-1540	31	18	after	after	SCONJ
cana-1540	31	19	his	his	PRON
cana-1540	31	20	name	name	NOUN
cana-1540	31	21	are	be	AUX
cana-1540	31	22	known	know	VERB
cana-1540	31	23	as	as	ADP
cana-1540	31	24	rayleigh	rayleigh	PROPN
cana-1540	31	25	waves	wave	NOUN
cana-1540	31	26	.	.	PUNCT
cana-1540	32	1	several	several	ADJ
cana-1540	32	2	researchers	researcher	NOUN
cana-1540	32	3	have	have	AUX
cana-1540	32	4	explored	explore	VERB
cana-1540	32	5	the	the	DET
cana-1540	32	6	concept	concept	NOUN
cana-1540	32	7	of	of	ADP
cana-1540	32	8	rayleigh	rayleigh	PROPN
cana-1540	32	9	waves	wave	NOUN
cana-1540	32	10	in	in	ADP
cana-1540	32	11	different	different	ADJ
cana-1540	32	12	type	type	NOUN
cana-1540	32	13	of	of	ADP
cana-1540	32	14	elastic	elastic	ADJ
cana-1540	32	15	materials	material	NOUN
cana-1540	32	16	.	.	PUNCT
cana-1540	33	1	for	for	ADP
cana-1540	33	2	example	example	NOUN
cana-1540	33	3	,	,	PUNCT
cana-1540	33	4	lockett	lockett	PROPN
cana-1540	34	1	[	[	X
cana-1540	34	2	11]discussed	11]discusse	VERB
cana-1540	34	3	the	the	DET
cana-1540	34	4	effects	effect	NOUN
cana-1540	34	5	of	of	ADP
cana-1540	34	6	thermal	thermal	ADJ
cana-1540	34	7	properties	property	NOUN
cana-1540	34	8	of	of	ADP
cana-1540	34	9	an	an	DET
cana-1540	34	10	isotropic	isotropic	ADJ
cana-1540	34	11	thermoelastic	thermoelastic	ADJ
cana-1540	34	12	material	material	NOUN
cana-1540	34	13	on	on	ADP
cana-1540	34	14	velocity	velocity	NOUN
cana-1540	34	15	of	of	ADP
cana-1540	34	16	rayleigh	rayleigh	PROPN
cana-1540	34	17	waves	wave	NOUN
cana-1540	34	18	.	.	PUNCT
cana-1540	35	1	kumar	kumar	PROPN
cana-1540	35	2	and	and	CCONJ
cana-1540	35	3	singh[12	singh[12	PROPN
cana-1540	35	4	]	]	PUNCT
cana-1540	35	5	discussed	discuss	VERB
cana-1540	35	6	about	about	ADP
cana-1540	35	7	the	the	DET
cana-1540	35	8	existence	existence	NOUN
cana-1540	35	9	rayleigh	rayleigh	PROPN
cana-1540	35	10	wave	wave	NOUN
cana-1540	35	11	in	in	ADP
cana-1540	35	12	micropolar	micropolar	ADJ
cana-1540	35	13	generalized	generalize	VERB
cana-1540	35	14	thermoelastic	thermoelastic	ADJ
cana-1540	35	15	half	half	ADJ
cana-1540	35	16	space	space	NOUN
cana-1540	35	17	with	with	ADP
cana-1540	35	18	stretch	stretch	NOUN
cana-1540	35	19	.	.	PUNCT
cana-1540	36	1	rao	rao	PROPN
cana-1540	36	2	and	and	CCONJ
cana-1540	36	3	reddy[13]studied	reddy[13]studie	VERB
cana-1540	36	4	the	the	DET
cana-1540	36	5	rayleigh	rayleigh	PROPN
cana-1540	36	6	type	type	NOUN
cana-1540	36	7	wave	wave	NOUN
cana-1540	36	8	propagation	propagation	NOUN
cana-1540	36	9	in	in	ADP
cana-1540	36	10	a	a	DET
cana-1540	36	11	micropolar	micropolar	ADJ
cana-1540	36	12	cylindrical	cylindrical	ADJ
cana-1540	36	13	surface	surface	NOUN
cana-1540	36	14	.	.	PUNCT
cana-1540	37	1	kumar	kumar	PROPN
cana-1540	37	2	,	,	PUNCT
cana-1540	37	3	kaur	kaur	PROPN
cana-1540	37	4	and	and	CCONJ
cana-1540	37	5	rajvanshi[14]investigated	rajvanshi[14]investigate	VERB
cana-1540	37	6	the	the	DET
cana-1540	37	7	propagation	propagation	NOUN
cana-1540	37	8	of	of	ADP
cana-1540	37	9	lamb	lamb	NOUN
cana-1540	37	10	waves	wave	NOUN
cana-1540	37	11	in	in	ADP
cana-1540	37	12	micropolar	micropolar	NOUN
cana-1540	37	13	-	-	PUNCT
cana-1540	37	14	generalized	generalize	VERB
cana-1540	37	15	thermoelastic	thermoelastic	ADJ
cana-1540	37	16	solid	solid	ADJ
cana-1540	37	17	with	with	ADP
cana-1540	37	18	two	two	NUM
cana-1540	37	19	temperatures	temperature	NOUN
cana-1540	37	20	bordered	border	VERB
cana-1540	37	21	with	with	ADP
cana-1540	37	22	layer	layer	NOUN
cana-1540	37	23	of	of	ADP
cana-1540	37	24	inviscid	inviscid	ADJ
cana-1540	37	25	liquid	liquid	NOUN
cana-1540	37	26	.	.	PUNCT
cana-1540	38	1	kumar	kumar	PROPN
cana-1540	38	2	and	and	CCONJ
cana-1540	38	3	partap[15	partap[15	NOUN
cana-1540	38	4	]	]	PUNCT
cana-1540	38	5	studied	study	VERB
cana-1540	38	6	propagation	propagation	NOUN
cana-1540	38	7	of	of	ADP
cana-1540	38	8	rayleigh	rayleigh	PROPN
cana-1540	38	9	lamb	lamb	PROPN
cana-1540	38	10	waves	wave	NOUN
cana-1540	38	11	in	in	ADP
cana-1540	38	12	a	a	DET
cana-1540	38	13	micropolar	micropolar	ADJ
cana-1540	38	14	elastic	elastic	ADJ
cana-1540	38	15	cylindrical	cylindrical	ADJ
cana-1540	38	16	plate	plate	NOUN
cana-1540	38	17	.	.	PUNCT
cana-1540	39	1	sharma	sharma	PROPN
cana-1540	39	2	and	and	CCONJ
cana-1540	39	3	khator	khator	NOUN
cana-1540	40	1	[	[	X
cana-1540	40	2	22,24	22,24	NUM
cana-1540	40	3	]	]	X
cana-1540	40	4	examined	examine	VERB
cana-1540	40	5	some	some	DET
cana-1540	40	6	problems	problem	NOUN
cana-1540	40	7	of	of	ADP
cana-1540	40	8	power	power	NOUN
cana-1540	40	9	generation	generation	NOUN
cana-1540	40	10	due	due	ADP
cana-1540	40	11	to	to	ADP
cana-1540	40	12	renewable	renewable	ADJ
cana-1540	40	13	sources	source	NOUN
cana-1540	40	14	.	.	PUNCT
cana-1540	41	1	m.marin	m.marin	PROPN
cana-1540	42	1	[	[	X
cana-1540	42	2	23,25	23,25	NUM
cana-1540	42	3	,	,	PUNCT
cana-1540	42	4	]	]	PUNCT
cana-1540	42	5	explored	explore	VERB
cana-1540	42	6	some	some	DET
cana-1540	42	7	problems	problem	NOUN
cana-1540	42	8	in	in	ADP
cana-1540	42	9	bioheat	bioheat	ADJ
cana-1540	42	10	thermoelastic	thermoelastic	ADJ
cana-1540	42	11	,	,	PUNCT
cana-1540	42	12	cosserat	cosserat	NOUN
cana-1540	42	13	thermoelastic	thermoelastic	ADJ
cana-1540	42	14	media	medium	NOUN
cana-1540	42	15	and	and	CCONJ
cana-1540	42	16	non	non	ADJ
cana-1540	42	17	-	-	ADJ
cana-1540	42	18	local	local	ADJ
cana-1540	42	19	thermoelastic	thermoelastic	ADJ
cana-1540	42	20	materials	material	NOUN
cana-1540	42	21	.	.	PUNCT
cana-1540	43	1	kaushal	kaushal	PROPN
cana-1540	43	2	et	et	PROPN
cana-1540	43	3	al	al	PROPN
cana-1540	44	1	[	[	X
cana-1540	44	2	26	26	NUM
cana-1540	44	3	]	]	PUNCT
cana-1540	44	4	investigated	investigate	VERB
cana-1540	44	5	boundary	boundary	ADJ
cana-1540	44	6	value	value	NOUN
cana-1540	44	7	problem	problem	NOUN
cana-1540	44	8	in	in	ADP
cana-1540	44	9	frequency	frequency	NOUN
cana-1540	44	10	domain	domain	NOUN
cana-1540	44	11	by	by	ADP
cana-1540	44	12	considering	consider	VERB
cana-1540	44	13	modified	modify	VERB
cana-1540	44	14	greenlindsay	greenlindsay	VERB
cana-1540	44	15	thermoelastic	thermoelastic	ADJ
cana-1540	44	16	medium	medium	NOUN
cana-1540	44	17	.	.	PUNCT
cana-1540	45	1	kumar	kumar	PROPN
cana-1540	45	2	and	and	CCONJ
cana-1540	45	3	devi	devi	PROPN
cana-1540	45	4	[	[	X
cana-1540	45	5	27	27	NUM
cana-1540	45	6	]	]	PUNCT
cana-1540	45	7	analysed	analyse	VERB
cana-1540	45	8	interaction	interaction	NOUN
cana-1540	45	9	due	due	ADP
cana-1540	45	10	to	to	ADP
cana-1540	45	11	hall	hall	VERB
cana-1540	45	12	current	current	ADJ
cana-1540	45	13	and	and	CCONJ
cana-1540	45	14	rotation	rotation	NOUN
cana-1540	45	15	in	in	ADP
cana-1540	45	16	modified	modify	VERB
cana-1540	45	17	couple	couple	NOUN
cana-1540	45	18	stress	stress	NOUN
cana-1540	45	19	elastic	elastic	ADJ
cana-1540	45	20	half	half	ADJ
cana-1540	45	21	-	-	PUNCT
cana-1540	45	22	space	space	NOUN
cana-1540	45	23	subjected	subject	VERB
cana-1540	45	24	to	to	ADP
cana-1540	45	25	ramp	ramp	NOUN
cana-1540	45	26	-	-	PUNCT
cana-1540	45	27	type	type	NOUN
cana-1540	45	28	loading	loading	NOUN
cana-1540	45	29	.	.	PUNCT
cana-1540	46	1	the	the	DET
cana-1540	46	2	boundary	boundary	ADJ
cana-1540	46	3	conditions	condition	NOUN
cana-1540	46	4	in	in	ADP
cana-1540	46	5	almost	almost	ADV
cana-1540	46	6	all	all	DET
cana-1540	46	7	the	the	DET
cana-1540	46	8	problems	problem	NOUN
cana-1540	46	9	related	relate	VERB
cana-1540	46	10	to	to	ADP
cana-1540	46	11	rayleigh	rayleigh	PROPN
cana-1540	46	12	waves	wave	NOUN
cana-1540	46	13	are	be	AUX
cana-1540	46	14	considered	consider	VERB
cana-1540	46	15	as	as	SCONJ
cana-1540	46	16	a	a	DET
cana-1540	46	17	traction	traction	NOUN
cana-1540	46	18	free	free	ADJ
cana-1540	46	19	surface	surface	NOUN
cana-1540	46	20	that	that	PRON
cana-1540	46	21	is	be	AUX
cana-1540	46	22	stresses	stress	NOUN
cana-1540	46	23	vanishes	vanish	VERB
cana-1540	46	24	on	on	ADP
cana-1540	46	25	the	the	DET
cana-1540	46	26	surface	surface	NOUN
cana-1540	46	27	.	.	PUNCT
cana-1540	47	1	the	the	DET
cana-1540	47	2	possibilities	possibility	NOUN
cana-1540	47	3	of	of	ADP
cana-1540	47	4	other	other	ADJ
cana-1540	47	5	type	type	NOUN
cana-1540	47	6	of	of	ADP
cana-1540	47	7	boundary	boundary	ADJ
cana-1540	47	8	conditions	condition	NOUN
cana-1540	47	9	are	be	AUX
cana-1540	47	10	rarely	rarely	ADV
cana-1540	47	11	consider	consider	VERB
cana-1540	47	12	in	in	ADP
cana-1540	47	13	seismology	seismology	NOUN
cana-1540	47	14	or	or	CCONJ
cana-1540	47	15	geophysics	geophysic	NOUN
cana-1540	47	16	but	but	CCONJ
cana-1540	47	17	there	there	PRON
cana-1540	47	18	are	be	VERB
cana-1540	47	19	other	other	ADJ
cana-1540	47	20	fields	field	NOUN
cana-1540	47	21	of	of	ADP
cana-1540	47	22	physics	physics	NOUN
cana-1540	47	23	like	like	ADP
cana-1540	47	24	electromagnetism	electromagnetism	NOUN
cana-1540	47	25	and	and	CCONJ
cana-1540	47	26	acoustics	acoustic	NOUN
cana-1540	47	27	,	,	PUNCT
cana-1540	47	28	where	where	SCONJ
cana-1540	47	29	it	it	PRON
cana-1540	47	30	is	be	AUX
cana-1540	47	31	common	common	ADJ
cana-1540	47	32	to	to	PART
cana-1540	47	33	use	use	VERB
cana-1540	47	34	impedance	impedance	NOUN
cana-1540	47	35	boundary	boundary	ADJ
cana-1540	47	36	conditions	condition	NOUN
cana-1540	47	37	.	.	PUNCT
cana-1540	48	1	the	the	DET
cana-1540	48	2	impedance	impedance	NOUN
cana-1540	48	3	boundary	boundary	ADJ
cana-1540	48	4	conditions	condition	NOUN
cana-1540	48	5	prescribed	prescribe	VERB
cana-1540	48	6	on	on	ADP
cana-1540	48	7	the	the	DET
cana-1540	48	8	boundary	boundary	NOUN
cana-1540	48	9	is	be	AUX
cana-1540	48	10	the	the	DET
cana-1540	48	11	linear	linear	ADJ
cana-1540	48	12	combination	combination	NOUN
cana-1540	48	13	of	of	ADP
cana-1540	48	14	the	the	DET
cana-1540	48	15	unknown	unknown	ADJ
cana-1540	48	16	function	function	NOUN
cana-1540	48	17	and	and	CCONJ
cana-1540	48	18	their	their	PRON
cana-1540	48	19	derivatives	derivative	NOUN
cana-1540	48	20	.	.	PUNCT
cana-1540	49	1	tiersten	tiersten	VERB
cana-1540	50	1	[	[	X
cana-1540	50	2	16]encountered	16]encountered	NUM
cana-1540	50	3	these	these	DET
cana-1540	50	4	types	type	NOUN
cana-1540	50	5	of	of	ADP
cana-1540	50	6	boundary	boundary	ADJ
cana-1540	50	7	conditions	condition	NOUN
cana-1540	50	8	while	while	SCONJ
cana-1540	50	9	studying	study	VERB
cana-1540	50	10	the	the	DET
cana-1540	50	11	wave	wave	NOUN
cana-1540	50	12	propagation	propagation	NOUN
cana-1540	50	13	in	in	ADP
cana-1540	50	14	an	an	DET
cana-1540	50	15	isotropic	isotropic	ADJ
cana-1540	50	16	elastic	elastic	ADJ
cana-1540	50	17	solid	solid	NOUN
cana-1540	50	18	coated	coat	VERB
cana-1540	50	19	with	with	ADP
cana-1540	50	20	thin	thin	ADJ
cana-1540	50	21	film	film	NOUN
cana-1540	50	22	of	of	ADP
cana-1540	50	23	different	different	ADJ
cana-1540	50	24	material	material	NOUN
cana-1540	50	25	.	.	PUNCT
cana-1540	51	1	malischewsky	malischewsky	NOUN
cana-1540	52	1	[	[	X
cana-1540	52	2	17]modified	17]modified	NUM
cana-1540	52	3	the	the	DET
cana-1540	52	4	tiersten	tiersten	NOUN
cana-1540	52	5	’s	’s	PART
cana-1540	52	6	conditions	condition	NOUN
cana-1540	52	7	in	in	ADP
cana-1540	52	8	terms	term	NOUN
cana-1540	52	9	of	of	ADP
cana-1540	52	10	stresses	stress	NOUN
cana-1540	52	11	and	and	CCONJ
cana-1540	52	12	displacement	displacement	NOUN
cana-1540	52	13	and	and	CCONJ
cana-1540	52	14	file:///c:/users	file:///c:/user	NOUN
cana-1540	52	15	/	/	SYM
cana-1540	52	16	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	17	/	/	SYM
cana-1540	52	18	appdata	appdata	NOUN
cana-1540	52	19	/	/	SYM
cana-1540	52	20	local	local	ADJ
cana-1540	52	21	/	/	SYM
cana-1540	52	22	microsoft	microsoft	PROPN
cana-1540	52	23	/	/	SYM
cana-1540	52	24	windows	windows	PROPN
cana-1540	52	25	/	/	SYM
cana-1540	52	26	inetcache	inetcache	NOUN
cana-1540	52	27	/	/	SYM
cana-1540	52	28	ie	ie	PROPN
cana-1540	52	29	/	/	SYM
cana-1540	52	30	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	31	/	/	SYM
cana-1540	52	32	chapter-4%5b1%5d.docx%23hwl671	chapter-4%5b1%5d.docx%23hwl671	VERB
cana-1540	52	33	file:///c:/users	file:///c:/user	NOUN
cana-1540	52	34	/	/	SYM
cana-1540	52	35	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	36	/	/	SYM
cana-1540	52	37	appdata	appdata	NOUN
cana-1540	52	38	/	/	SYM
cana-1540	52	39	local	local	ADJ
cana-1540	52	40	/	/	SYM
cana-1540	52	41	microsoft	microsoft	PROPN
cana-1540	52	42	/	/	SYM
cana-1540	52	43	windows	windows	PROPN
cana-1540	52	44	/	/	SYM
cana-1540	52	45	inetcache	inetcache	NOUN
cana-1540	52	46	/	/	SYM
cana-1540	52	47	ie	ie	PROPN
cana-1540	52	48	/	/	SYM
cana-1540	52	49	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	50	/	/	SYM
cana-1540	52	51	chapter-4%5b1%5d.docx%23aeg72	chapter-4%5b1%5d.docx%23aeg72	PROPN
cana-1540	52	52	file:///c:/users	file:///c:/user	NOUN
cana-1540	52	53	/	/	SYM
cana-1540	52	54	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	55	/	/	SYM
cana-1540	52	56	appdata	appdata	NOUN
cana-1540	52	57	/	/	SYM
cana-1540	52	58	local	local	ADJ
cana-1540	52	59	/	/	SYM
cana-1540	52	60	microsoft	microsoft	PROPN
cana-1540	52	61	/	/	SYM
cana-1540	52	62	windows	windows	PROPN
cana-1540	52	63	/	/	SYM
cana-1540	52	64	inetcache	inetcache	NOUN
cana-1540	52	65	/	/	SYM
cana-1540	52	66	ie	ie	PROPN
cana-1540	52	67	/	/	SYM
cana-1540	52	68	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	69	/	/	SYM
cana-1540	52	70	chapter-4%5b1%5d.docx%23bos73	chapter-4%5b1%5d.docx%23bos73	PROPN
cana-1540	52	71	file:///c:/users	file:///c:/users	PROPN
cana-1540	52	72	/	/	SYM
cana-1540	52	73	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	74	/	/	SYM
cana-1540	52	75	appdata	appdata	NOUN
cana-1540	52	76	/	/	SYM
cana-1540	52	77	local	local	ADJ
cana-1540	52	78	/	/	SYM
cana-1540	52	79	microsoft	microsoft	PROPN
cana-1540	52	80	/	/	SYM
cana-1540	52	81	windows	windows	PROPN
cana-1540	52	82	/	/	SYM
cana-1540	52	83	inetcache	inetcache	NOUN
cana-1540	52	84	/	/	SYM
cana-1540	52	85	ie	ie	PROPN
cana-1540	52	86	/	/	SYM
cana-1540	52	87	a6wkhao2	a6wkhao2	ADJ
cana-1540	52	88	/	/	SYM
cana-1540	52	89	chapter-4%5b1%5d.docx%23cia99	chapter-4%5b1%5d.docx%23cia99	PROPN
cana-1540	52	90	file:///c:/users	file:///c:/users	PROPN
cana-1540	52	91	/	/	SYM
cana-1540	52	92	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	93	/	/	SYM
cana-1540	52	94	appdata	appdata	NOUN
cana-1540	52	95	/	/	SYM
cana-1540	52	96	local	local	ADJ
cana-1540	52	97	/	/	SYM
cana-1540	52	98	microsoft	microsoft	PROPN
cana-1540	52	99	/	/	SYM
cana-1540	52	100	windows	windows	PROPN
cana-1540	52	101	/	/	SYM
cana-1540	52	102	inetcache	inetcache	NOUN
cana-1540	52	103	/	/	SYM
cana-1540	52	104	ie	ie	PROPN
cana-1540	52	105	/	/	SYM
cana-1540	52	106	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	107	/	/	SYM
cana-1540	52	108	chapter-4%5b1%5d.docx%23hwl671	chapter-4%5b1%5d.docx%23hwl671	VERB
cana-1540	52	109	file:///c:/users	file:///c:/user	NOUN
cana-1540	52	110	/	/	SYM
cana-1540	52	111	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	112	/	/	SYM
cana-1540	52	113	appdata	appdata	NOUN
cana-1540	52	114	/	/	SYM
cana-1540	52	115	local	local	ADJ
cana-1540	52	116	/	/	SYM
cana-1540	52	117	microsoft	microsoft	PROPN
cana-1540	52	118	/	/	SYM
cana-1540	52	119	windows	windows	PROPN
cana-1540	52	120	/	/	SYM
cana-1540	52	121	inetcache	inetcache	NOUN
cana-1540	52	122	/	/	SYM
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cana-1540	52	124	/	/	SYM
cana-1540	52	125	a6wkhao2	a6wkhao2	PROPN
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cana-1540	52	127	chapter-4%5b1%5d.docx%23hhs05	chapter-4%5b1%5d.docx%23hhs05	PROPN
cana-1540	52	128	file:///c:/users	file:///c:/users	PROPN
cana-1540	52	129	/	/	SYM
cana-1540	52	130	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	131	/	/	SYM
cana-1540	52	132	appdata	appdata	NOUN
cana-1540	52	133	/	/	SYM
cana-1540	52	134	local	local	ADJ
cana-1540	52	135	/	/	SYM
cana-1540	52	136	microsoft	microsoft	PROPN
cana-1540	52	137	/	/	SYM
cana-1540	52	138	windows	windows	PROPN
cana-1540	52	139	/	/	SYM
cana-1540	52	140	inetcache	inetcache	NOUN
cana-1540	52	141	/	/	SYM
cana-1540	52	142	ie	ie	PROPN
cana-1540	52	143	/	/	SYM
cana-1540	52	144	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	145	/	/	SYM
cana-1540	52	146	chapter-4%5b1%5d.docx%23ray85	chapter-4%5b1%5d.docx%23ray85	PROPN
cana-1540	52	147	file:///c:/users	file:///c:/user	NOUN
cana-1540	52	148	/	/	SYM
cana-1540	52	149	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	150	/	/	SYM
cana-1540	52	151	appdata	appdata	NOUN
cana-1540	52	152	/	/	SYM
cana-1540	52	153	local	local	ADJ
cana-1540	52	154	/	/	SYM
cana-1540	52	155	microsoft	microsoft	PROPN
cana-1540	52	156	/	/	SYM
cana-1540	52	157	windows	windows	PROPN
cana-1540	52	158	/	/	SYM
cana-1540	52	159	inetcache	inetcache	NOUN
cana-1540	52	160	/	/	SYM
cana-1540	52	161	ie	ie	PROPN
cana-1540	52	162	/	/	SYM
cana-1540	52	163	a6wkhao2	a6wkhao2	PROPN
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cana-1540	52	165	chapter-4%5b1%5d.docx%23loc58	chapter-4%5b1%5d.docx%23loc58	PROPN
cana-1540	52	166	file:///c:/users	file:///c:/users	PROPN
cana-1540	52	167	/	/	SYM
cana-1540	52	168	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	169	/	/	SYM
cana-1540	52	170	appdata	appdata	NOUN
cana-1540	52	171	/	/	SYM
cana-1540	52	172	local	local	ADJ
cana-1540	52	173	/	/	SYM
cana-1540	52	174	microsoft	microsoft	PROPN
cana-1540	52	175	/	/	SYM
cana-1540	52	176	windows	windows	PROPN
cana-1540	52	177	/	/	SYM
cana-1540	52	178	inetcache	inetcache	NOUN
cana-1540	52	179	/	/	SYM
cana-1540	52	180	ie	ie	PROPN
cana-1540	52	181	/	/	SYM
cana-1540	52	182	a6wkhao2	a6wkhao2	ADJ
cana-1540	52	183	/	/	SYM
cana-1540	52	184	chapter-4%5b1%5d.docx%23kum96	chapter-4%5b1%5d.docx%23kum96	ADJ
cana-1540	52	185	file:///c:/users	file:///c:/user	NOUN
cana-1540	52	186	/	/	SYM
cana-1540	52	187	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	188	/	/	SYM
cana-1540	52	189	appdata	appdata	NOUN
cana-1540	52	190	/	/	SYM
cana-1540	52	191	local	local	ADJ
cana-1540	52	192	/	/	SYM
cana-1540	52	193	microsoft	microsoft	PROPN
cana-1540	52	194	/	/	SYM
cana-1540	52	195	windows	windows	PROPN
cana-1540	52	196	/	/	SYM
cana-1540	52	197	inetcache	inetcache	NOUN
cana-1540	52	198	/	/	SYM
cana-1540	52	199	ie	ie	PROPN
cana-1540	52	200	/	/	SYM
cana-1540	52	201	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	202	/	/	SYM
cana-1540	52	203	chapter-4%5b1%5d.docx%23rao93	chapter-4%5b1%5d.docx%23rao93	PROPN
cana-1540	52	204	file:///c:/users	file:///c:/users	PROPN
cana-1540	52	205	/	/	SYM
cana-1540	52	206	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	207	/	/	SYM
cana-1540	52	208	appdata	appdata	NOUN
cana-1540	52	209	/	/	SYM
cana-1540	52	210	local	local	ADJ
cana-1540	52	211	/	/	SYM
cana-1540	52	212	microsoft	microsoft	PROPN
cana-1540	52	213	/	/	SYM
cana-1540	52	214	windows	windows	PROPN
cana-1540	52	215	/	/	SYM
cana-1540	52	216	inetcache	inetcache	NOUN
cana-1540	52	217	/	/	SYM
cana-1540	52	218	ie	ie	PROPN
cana-1540	52	219	/	/	SYM
cana-1540	52	220	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	221	/	/	SYM
cana-1540	52	222	chapter-4%5b1%5d.docx%23kum14	chapter-4%5b1%5d.docx%23kum14	PROPN
cana-1540	52	223	file:///c:/users	file:///c:/users	PROPN
cana-1540	52	224	/	/	SYM
cana-1540	52	225	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	226	/	/	SYM
cana-1540	52	227	appdata	appdata	NOUN
cana-1540	52	228	/	/	SYM
cana-1540	52	229	local	local	ADJ
cana-1540	52	230	/	/	SYM
cana-1540	52	231	microsoft	microsoft	PROPN
cana-1540	52	232	/	/	SYM
cana-1540	52	233	windows	windows	PROPN
cana-1540	52	234	/	/	SYM
cana-1540	52	235	inetcache	inetcache	NOUN
cana-1540	52	236	/	/	SYM
cana-1540	52	237	ie	ie	PROPN
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cana-1540	52	241	chapter-4%5b1%5d.docx%23kum06	chapter-4%5b1%5d.docx%23kum06	PROPN
cana-1540	52	242	file:///c:/users	file:///c:/users	PROPN
cana-1540	52	243	/	/	SYM
cana-1540	52	244	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	245	/	/	SYM
cana-1540	52	246	appdata	appdata	NOUN
cana-1540	52	247	/	/	SYM
cana-1540	52	248	local	local	ADJ
cana-1540	52	249	/	/	SYM
cana-1540	52	250	microsoft	microsoft	PROPN
cana-1540	52	251	/	/	SYM
cana-1540	52	252	windows	windows	PROPN
cana-1540	52	253	/	/	SYM
cana-1540	52	254	inetcache	inetcache	NOUN
cana-1540	52	255	/	/	SYM
cana-1540	52	256	ie	ie	PROPN
cana-1540	52	257	/	/	SYM
cana-1540	52	258	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	259	/	/	SYM
cana-1540	52	260	chapter-4%5b1%5d.docx%23tie69	chapter-4%5b1%5d.docx%23tie69	PROPN
cana-1540	52	261	file:///c:/users	file:///c:/users	PROPN
cana-1540	52	262	/	/	SYM
cana-1540	52	263	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	52	264	/	/	SYM
cana-1540	52	265	appdata	appdata	NOUN
cana-1540	52	266	/	/	SYM
cana-1540	52	267	local	local	ADJ
cana-1540	52	268	/	/	SYM
cana-1540	52	269	microsoft	microsoft	PROPN
cana-1540	52	270	/	/	SYM
cana-1540	52	271	windows	windows	PROPN
cana-1540	52	272	/	/	SYM
cana-1540	52	273	inetcache	inetcache	NOUN
cana-1540	52	274	/	/	SYM
cana-1540	52	275	ie	ie	PROPN
cana-1540	52	276	/	/	SYM
cana-1540	52	277	a6wkhao2	a6wkhao2	PROPN
cana-1540	52	278	/	/	SYM
cana-1540	52	279	chapter-4%5b1%5d.docx%23mal88	chapter-4%5b1%5d.docx%23mal88	PROPN
cana-1540	52	280	communications	communication	NOUN
cana-1540	52	281	on	on	ADP
cana-1540	52	282	applied	apply	VERB
cana-1540	52	283	nonlinear	nonlinear	ADJ
cana-1540	52	284	analysis	analysis	NOUN
cana-1540	52	285	issn	issn	NOUN
cana-1540	52	286	:	:	PUNCT
cana-1540	52	287	1074	1074	NUM
cana-1540	52	288	-	-	PUNCT
cana-1540	52	289	133x	133x	NUM
cana-1540	52	290	vol	vol	NOUN
cana-1540	52	291	31	31	NUM
cana-1540	52	292	no	no	NOUN
cana-1540	52	293	.	.	PUNCT
cana-1540	53	1	8s	8s	PROPN
cana-1540	53	2	(	(	PUNCT
cana-1540	53	3	2024	2024	NUM
cana-1540	53	4	)	)	PUNCT
cana-1540	53	5	485	485	NUM
cana-1540	53	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	53	7	obtained	obtain	VERB
cana-1540	53	8	the	the	DET
cana-1540	53	9	secular	secular	ADJ
cana-1540	53	10	equation	equation	NOUN
cana-1540	53	11	for	for	ADP
cana-1540	53	12	rayleigh	rayleigh	PROPN
cana-1540	53	13	waves	wave	NOUN
cana-1540	53	14	.	.	PUNCT
cana-1540	54	1	godoy	godoy	PROPN
cana-1540	54	2	,	,	PUNCT
cana-1540	54	3	duran	duran	NOUN
cana-1540	54	4	and	and	CCONJ
cana-1540	54	5	nedelec	nedelec	NOUN
cana-1540	55	1	[	[	X
cana-1540	55	2	18]proved	18]proved	NUM
cana-1540	55	3	the	the	DET
cana-1540	55	4	existence	existence	NOUN
cana-1540	55	5	of	of	ADP
cana-1540	55	6	surface	surface	NOUN
cana-1540	55	7	waves	wave	NOUN
cana-1540	55	8	in	in	ADP
cana-1540	55	9	an	an	DET
cana-1540	55	10	elastic	elastic	ADJ
cana-1540	55	11	half	half	NOUN
cana-1540	55	12	space	space	NOUN
cana-1540	55	13	with	with	ADP
cana-1540	55	14	impedance	impedance	NOUN
cana-1540	55	15	boundary	boundary	ADJ
cana-1540	55	16	conditions	condition	NOUN
cana-1540	55	17	and	and	CCONJ
cana-1540	55	18	derived	derive	VERB
cana-1540	55	19	the	the	DET
cana-1540	55	20	secular	secular	ADJ
cana-1540	55	21	equation	equation	NOUN
cana-1540	55	22	with	with	ADP
cana-1540	55	23	these	these	DET
cana-1540	55	24	conditions	condition	NOUN
cana-1540	55	25	.	.	PUNCT
cana-1540	56	1	vinh	vinh	PROPN
cana-1540	56	2	and	and	CCONJ
cana-1540	56	3	hue[19	hue[19	PROPN
cana-1540	56	4	]	]	PUNCT
cana-1540	56	5	used	use	VERB
cana-1540	56	6	impedance	impedance	NOUN
cana-1540	56	7	boundary	boundary	ADJ
cana-1540	56	8	conditions	condition	NOUN
cana-1540	56	9	to	to	PART
cana-1540	56	10	investigate	investigate	VERB
cana-1540	56	11	rayleigh	rayleigh	PROPN
cana-1540	56	12	waves	wave	NOUN
cana-1540	56	13	in	in	ADP
cana-1540	56	14	an	an	DET
cana-1540	56	15	orthotropic	orthotropic	ADJ
cana-1540	56	16	and	and	CCONJ
cana-1540	56	17	monoclinic	monoclinic	ADJ
cana-1540	56	18	half	half	NOUN
cana-1540	56	19	space	space	NOUN
cana-1540	56	20	.	.	PUNCT
cana-1540	57	1	recently	recently	ADV
cana-1540	57	2	singh[20	singh[20	NOUN
cana-1540	57	3	]	]	PUNCT
cana-1540	57	4	studied	study	VERB
cana-1540	57	5	about	about	ADP
cana-1540	57	6	the	the	DET
cana-1540	57	7	rayleigh	rayleigh	PROPN
cana-1540	57	8	wave	wave	NOUN
cana-1540	57	9	in	in	ADP
cana-1540	57	10	a	a	DET
cana-1540	57	11	thermoelastic	thermoelastic	ADJ
cana-1540	57	12	solid	solid	ADJ
cana-1540	57	13	half	half	ADJ
cana-1540	57	14	space	space	NOUN
cana-1540	57	15	subjected	subject	VERB
cana-1540	57	16	to	to	ADP
cana-1540	57	17	impedance	impedance	NOUN
cana-1540	57	18	boundary	boundary	ADJ
cana-1540	57	19	conditions	condition	NOUN
cana-1540	57	20	.	.	PUNCT
cana-1540	58	1	sharma	sharma	PROPN
cana-1540	58	2	and	and	CCONJ
cana-1540	58	3	khator	khator	NOUN
cana-1540	59	1	[	[	X
cana-1540	59	2	22,24	22,24	NUM
cana-1540	59	3	]	]	X
cana-1540	59	4	examined	examine	VERB
cana-1540	59	5	some	some	DET
cana-1540	59	6	problems	problem	NOUN
cana-1540	59	7	of	of	ADP
cana-1540	59	8	power	power	NOUN
cana-1540	59	9	generation	generation	NOUN
cana-1540	59	10	due	due	ADP
cana-1540	59	11	to	to	ADP
cana-1540	59	12	renewable	renewable	ADJ
cana-1540	59	13	sources	source	NOUN
cana-1540	59	14	.	.	PUNCT
cana-1540	60	1	m.marin	m.marin	PROPN
cana-1540	61	1	[	[	X
cana-1540	61	2	23,25,27	23,25,27	NUM
cana-1540	61	3	]	]	PUNCT
cana-1540	61	4	explored	explore	VERB
cana-1540	61	5	some	some	DET
cana-1540	61	6	problems	problem	NOUN
cana-1540	61	7	in	in	ADP
cana-1540	61	8	bioheat	bioheat	ADJ
cana-1540	61	9	thermoelastic	thermoelastic	ADJ
cana-1540	61	10	,	,	PUNCT
cana-1540	61	11	cosserat	cosserat	NOUN
cana-1540	61	12	thermoelastic	thermoelastic	ADJ
cana-1540	61	13	media	medium	NOUN
cana-1540	61	14	and	and	CCONJ
cana-1540	61	15	non	non	ADJ
cana-1540	61	16	-	-	ADJ
cana-1540	61	17	local	local	ADJ
cana-1540	61	18	thermoelastic	thermoelastic	ADJ
cana-1540	61	19	materials	material	NOUN
cana-1540	61	20	.	.	PUNCT
cana-1540	62	1	kaushal	kaushal	PROPN
cana-1540	62	2	et	et	PROPN
cana-1540	62	3	al	al	PROPN
cana-1540	63	1	[	[	X
cana-1540	63	2	31	31	NUM
cana-1540	63	3	]	]	PUNCT
cana-1540	63	4	investigated	investigate	VERB
cana-1540	63	5	boundary	boundary	ADJ
cana-1540	63	6	value	value	NOUN
cana-1540	63	7	problem	problem	NOUN
cana-1540	63	8	in	in	ADP
cana-1540	63	9	frequency	frequency	NOUN
cana-1540	63	10	domain	domain	NOUN
cana-1540	63	11	by	by	ADP
cana-1540	63	12	considering	consider	VERB
cana-1540	63	13	modified	modify	VERB
cana-1540	63	14	greenlindsay	greenlindsay	VERB
cana-1540	63	15	thermoelastic	thermoelastic	ADJ
cana-1540	63	16	medium	medium	NOUN
cana-1540	63	17	.	.	PUNCT
cana-1540	64	1	kumar	kumar	PROPN
cana-1540	64	2	and	and	CCONJ
cana-1540	64	3	devi	devi	PROPN
cana-1540	64	4	[	[	X
cana-1540	64	5	26	26	NUM
cana-1540	64	6	]	]	PUNCT
cana-1540	64	7	analyzed	analyze	VERB
cana-1540	64	8	interaction	interaction	NOUN
cana-1540	64	9	due	due	ADP
cana-1540	64	10	to	to	ADP
cana-1540	64	11	hall	hall	VERB
cana-1540	64	12	current	current	ADJ
cana-1540	64	13	and	and	CCONJ
cana-1540	64	14	rotation	rotation	NOUN
cana-1540	64	15	in	in	ADP
cana-1540	64	16	modified	modify	VERB
cana-1540	64	17	couple	couple	NOUN
cana-1540	64	18	stress	stress	NOUN
cana-1540	64	19	elastic	elastic	ADJ
cana-1540	64	20	half	half	ADJ
cana-1540	64	21	-	-	PUNCT
cana-1540	64	22	space	space	NOUN
cana-1540	64	23	subjected	subject	VERB
cana-1540	64	24	to	to	ADP
cana-1540	64	25	ramp	ramp	NOUN
cana-1540	64	26	-	-	PUNCT
cana-1540	64	27	type	type	NOUN
cana-1540	64	28	loading	loading	NOUN
cana-1540	64	29	.	.	PUNCT
cana-1540	65	1	rayleigh	rayleigh	PROPN
cana-1540	65	2	waves	wave	NOUN
cana-1540	65	3	are	be	AUX
cana-1540	65	4	extremely	extremely	ADV
cana-1540	65	5	useful	useful	ADJ
cana-1540	65	6	for	for	ADP
cana-1540	65	7	material	material	NOUN
cana-1540	65	8	characterization	characterization	NOUN
cana-1540	65	9	and	and	CCONJ
cana-1540	65	10	to	to	PART
cana-1540	65	11	remove	remove	VERB
cana-1540	65	12	defects	defect	NOUN
cana-1540	65	13	in	in	ADP
cana-1540	65	14	the	the	DET
cana-1540	65	15	objects	object	NOUN
cana-1540	65	16	,	,	PUNCT
cana-1540	65	17	as	as	SCONJ
cana-1540	65	18	these	these	PRON
cana-1540	65	19	are	be	AUX
cana-1540	65	20	very	very	ADV
cana-1540	65	21	sensitive	sensitive	ADJ
cana-1540	65	22	to	to	ADP
cana-1540	65	23	surface	surface	NOUN
cana-1540	65	24	defects	defect	NOUN
cana-1540	65	25	.	.	PUNCT
cana-1540	66	1	very	very	ADV
cana-1540	66	2	few	few	ADJ
cana-1540	66	3	papers	paper	NOUN
cana-1540	66	4	on	on	ADP
cana-1540	66	5	rayleigh	rayleigh	PROPN
cana-1540	66	6	waves	wave	NOUN
cana-1540	66	7	with	with	ADP
cana-1540	66	8	impedance	impedance	NOUN
cana-1540	66	9	boundary	boundary	ADJ
cana-1540	66	10	conditions	condition	NOUN
cana-1540	66	11	are	be	AUX
cana-1540	66	12	available	available	ADJ
cana-1540	66	13	but	but	CCONJ
cana-1540	66	14	this	this	DET
cana-1540	66	15	concept	concept	NOUN
cana-1540	66	16	has	have	AUX
cana-1540	66	17	not	not	PART
cana-1540	66	18	been	be	AUX
cana-1540	66	19	used	use	VERB
cana-1540	66	20	in	in	ADP
cana-1540	66	21	micropolar	micropolar	ADJ
cana-1540	66	22	thermoelastic	thermoelastic	ADJ
cana-1540	66	23	material	material	NOUN
cana-1540	66	24	.	.	PUNCT
cana-1540	67	1	in	in	ADP
cana-1540	67	2	this	this	DET
cana-1540	67	3	paper	paper	NOUN
cana-1540	67	4	the	the	DET
cana-1540	67	5	propagation	propagation	NOUN
cana-1540	67	6	rayleigh	rayleigh	NOUN
cana-1540	67	7	waves	wave	NOUN
cana-1540	67	8	in	in	ADP
cana-1540	67	9	a	a	DET
cana-1540	67	10	micropolar	micropolar	ADJ
cana-1540	67	11	thermoelastic	thermoelastic	ADJ
cana-1540	67	12	half	half	ADJ
cana-1540	67	13	space	space	NOUN
cana-1540	67	14	with	with	ADP
cana-1540	67	15	impedance	impedance	NOUN
cana-1540	67	16	boundary	boundary	ADJ
cana-1540	67	17	condition	condition	NOUN
cana-1540	67	18	has	have	AUX
cana-1540	67	19	been	be	AUX
cana-1540	67	20	investigated	investigate	VERB
cana-1540	67	21	.	.	PUNCT
cana-1540	68	1	secular	secular	ADJ
cana-1540	68	2	equation	equation	NOUN
cana-1540	68	3	for	for	ADP
cana-1540	68	4	thermally	thermally	ADV
cana-1540	68	5	insulated	insulate	VERB
cana-1540	68	6	and	and	CCONJ
cana-1540	68	7	isothermal	isothermal	ADJ
cana-1540	68	8	surface	surface	NOUN
cana-1540	68	9	is	be	AUX
cana-1540	68	10	obtained	obtain	VERB
cana-1540	68	11	and	and	CCONJ
cana-1540	68	12	this	this	DET
cana-1540	68	13	equation	equation	NOUN
cana-1540	68	14	coincides	coincide	VERB
cana-1540	68	15	with	with	ADP
cana-1540	68	16	the	the	DET
cana-1540	68	17	secular	secular	ADJ
cana-1540	68	18	equation	equation	NOUN
cana-1540	68	19	of	of	ADP
cana-1540	68	20	rayleigh	rayleigh	PROPN
cana-1540	68	21	waves	wave	NOUN
cana-1540	68	22	in	in	ADP
cana-1540	68	23	thermoelastic	thermoelastic	ADJ
cana-1540	68	24	solid	solid	ADJ
cana-1540	68	25	when	when	SCONJ
cana-1540	68	26	the	the	DET
cana-1540	68	27	micropolar	micropolar	ADJ
cana-1540	68	28	effect	effect	NOUN
cana-1540	68	29	is	be	AUX
cana-1540	68	30	removed	remove	VERB
cana-1540	68	31	.	.	PUNCT
cana-1540	69	1	on	on	ADP
cana-1540	69	2	removing	remove	VERB
cana-1540	69	3	the	the	DET
cana-1540	69	4	micropolar	micropolar	ADJ
cana-1540	69	5	effects	effect	NOUN
cana-1540	69	6	,	,	PUNCT
cana-1540	69	7	impedance	impedance	NOUN
cana-1540	69	8	parameters	parameter	NOUN
cana-1540	69	9	and	and	CCONJ
cana-1540	69	10	thermal	thermal	ADJ
cana-1540	69	11	effects	effect	NOUN
cana-1540	69	12	this	this	DET
cana-1540	69	13	equation	equation	NOUN
cana-1540	69	14	reduces	reduce	VERB
cana-1540	69	15	to	to	ADP
cana-1540	69	16	famous	famous	ADJ
cana-1540	69	17	secular	secular	ADJ
cana-1540	69	18	equation	equation	NOUN
cana-1540	69	19	of	of	ADP
cana-1540	69	20	rayleigh	rayleigh	PROPN
cana-1540	69	21	wave	wave	PROPN
cana-1540	69	22	in	in	ADP
cana-1540	69	23	isotropic	isotropic	ADJ
cana-1540	69	24	elastic	elastic	ADJ
cana-1540	69	25	solid	solid	NOUN
cana-1540	69	26	with	with	ADP
cana-1540	69	27	traction	traction	NOUN
cana-1540	69	28	free	free	ADJ
cana-1540	69	29	boundary	boundary	ADJ
cana-1540	69	30	conditions	condition	NOUN
cana-1540	69	31	.	.	PUNCT
cana-1540	70	1	effect	effect	NOUN
cana-1540	70	2	of	of	ADP
cana-1540	70	3	micropolarity	micropolarity	NOUN
cana-1540	70	4	present	present	ADJ
cana-1540	70	5	in	in	ADP
cana-1540	70	6	the	the	DET
cana-1540	70	7	medium	medium	NOUN
cana-1540	70	8	on	on	ADP
cana-1540	70	9	the	the	DET
cana-1540	70	10	phase	phase	NOUN
cana-1540	70	11	velocity	velocity	NOUN
cana-1540	70	12	is	be	AUX
cana-1540	70	13	highlighted	highlight	VERB
cana-1540	70	14	through	through	ADP
cana-1540	70	15	comparative	comparative	ADJ
cana-1540	70	16	study	study	NOUN
cana-1540	70	17	with	with	ADP
cana-1540	70	18	respect	respect	NOUN
cana-1540	70	19	impedance	impedance	NOUN
cana-1540	70	20	parameter	parameter	NOUN
cana-1540	70	21	.	.	PUNCT
cana-1540	71	1	2	2	X
cana-1540	71	2	.	.	NUM
cana-1540	71	3	basic	basic	ADJ
cana-1540	71	4	equations	equation	NOUN
cana-1540	71	5	following	follow	VERB
cana-1540	71	6	eringen[1	eringen[1	PROPN
cana-1540	71	7	]	]	PUNCT
cana-1540	71	8	,	,	PUNCT
cana-1540	71	9	the	the	DET
cana-1540	71	10	governing	govern	VERB
cana-1540	71	11	equations	equation	NOUN
cana-1540	71	12	for	for	ADP
cana-1540	71	13	homogeneous	homogeneous	ADJ
cana-1540	71	14	,	,	PUNCT
cana-1540	71	15	isotropic	isotropic	ADJ
cana-1540	71	16	micropolar	micropolar	ADJ
cana-1540	71	17	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	71	18	solid	solid	ADJ
cana-1540	71	19	in	in	ADP
cana-1540	71	20	absence	absence	NOUN
cana-1540	71	21	of	of	ADP
cana-1540	71	22	body	body	NOUN
cana-1540	71	23	forces	force	NOUN
cana-1540	71	24	and	and	CCONJ
cana-1540	71	25	body	body	NOUN
cana-1540	71	26	couples	couple	NOUN
cana-1540	71	27	are	be	AUX
cana-1540	71	28	(	(	PUNCT
cana-1540	71	29	𝜇∗	𝜇∗	NOUN
cana-1540	71	30	+	+	CCONJ
cana-1540	71	31	𝐾∗)∇2	𝐾∗)∇2	PROPN
cana-1540	71	32	�	�	NOUN
cana-1540	71	33	⃗	⃗	NOUN
cana-1540	71	34	�	�	PROPN
cana-1540	71	35	+	+	CCONJ
cana-1540	71	36	(	(	PUNCT
cana-1540	71	37	𝜆∗	𝜆∗	NOUN
cana-1540	71	38	+	+	CCONJ
cana-1540	71	39	𝜇∗)∇(∇.	𝜇∗)∇(∇.	PROPN
cana-1540	71	40	�	�	NOUN
cana-1540	71	41	⃗	⃗	PROPN
cana-1540	71	42	�	�	PROPN
cana-1540	71	43	)	)	PUNCT
cana-1540	72	1	+	+	CCONJ
cana-1540	72	2	𝑘∗(∇	𝑘∗(∇	VERB
cana-1540	72	3	×	×	NOUN
cana-1540	72	4	𝜙)⃗⃗	𝜙)⃗⃗	NUM
cana-1540	72	5	⃗⃗	⃗⃗	NOUN
cana-1540	72	6	−	−	PROPN
cana-1540	72	7	𝜈∇t	𝜈∇t	NUM
cana-1540	72	8	=	=	SYM
cana-1540	72	9	ρ	ρ	PROPN
cana-1540	72	10	(	(	PUNCT
cana-1540	72	11	𝜕2	𝜕2	NOUN
cana-1540	72	12	�	�	NOUN
cana-1540	72	13	⃗	⃗	NOUN
cana-1540	72	14	�	�	PROPN
cana-1540	72	15	𝜕𝑡2	𝜕𝑡2	PROPN
cana-1540	72	16	)	)	PUNCT
cana-1540	72	17	(	(	PUNCT
cana-1540	72	18	1	1	X
cana-1540	72	19	)	)	PUNCT
cana-1540	72	20	(	(	PUNCT
cana-1540	72	21	α∗	α∗	NOUN
cana-1540	72	22	+	+	NUM
cana-1540	72	23	β∗	β∗	NOUN
cana-1540	72	24	+	+	CCONJ
cana-1540	72	25	γ∗	γ∗	NOUN
cana-1540	72	26	)	)	PUNCT
cana-1540	73	1	∇(∇.	∇(∇.	PROPN
cana-1540	73	2	�	�	NOUN
cana-1540	73	3	⃗	⃗	X
cana-1540	73	4	�	�	PROPN
cana-1540	73	5	)	)	PUNCT
cana-1540	73	6	−	−	PROPN
cana-1540	73	7	γ∗∇	γ∗∇	PROPN
cana-1540	73	8	×	×	NOUN
cana-1540	73	9	(	(	PUNCT
cana-1540	73	10	∇	∇	X
cana-1540	73	11	×	×	PROPN
cana-1540	73	12	�	�	PROPN
cana-1540	73	13	⃗	⃗	NOUN
cana-1540	73	14	�	�	PROPN
cana-1540	73	15	)	)	PUNCT
cana-1540	74	1	+	+	CCONJ
cana-1540	74	2	𝑘∗(∇	𝑘∗(∇	VERB
cana-1540	74	3	×	×	PROPN
cana-1540	74	4	�	�	SYM
cana-1540	74	5	⃗	⃗	X
cana-1540	74	6	�	�	PROPN
cana-1540	74	7	)	)	PUNCT
cana-1540	75	1	−	−	PROPN
cana-1540	75	2	2𝑘∗	2𝑘∗	NUM
cana-1540	75	3	�	�	NOUN
cana-1540	75	4	⃗	⃗	NOUN
cana-1540	75	5	�	�	NOUN
cana-1540	75	6	=	=	SYM
cana-1540	75	7	ρj	ρj	PROPN
cana-1540	75	8	(	(	PUNCT
cana-1540	75	9	𝜕2	𝜕2	NOUN
cana-1540	75	10	�	�	NOUN
cana-1540	75	11	⃗	⃗	NOUN
cana-1540	75	12	�	�	PROPN
cana-1540	75	13	𝜕𝑡2	𝜕𝑡2	PROPN
cana-1540	75	14	)	)	PUNCT
cana-1540	75	15	(	(	PUNCT
cana-1540	75	16	2	2	X
cana-1540	75	17	)	)	PUNCT
cana-1540	75	18	where	where	SCONJ
cana-1540	75	19	�	�	NOUN
cana-1540	75	20	⃗	⃗	NOUN
cana-1540	75	21	�	�	PROPN
cana-1540	75	22	is	be	AUX
cana-1540	75	23	the	the	DET
cana-1540	75	24	displacement	displacement	ADJ
cana-1540	75	25	vector	vector	NOUN
cana-1540	75	26	,	,	PUNCT
cana-1540	75	27	𝜌	𝜌	X
cana-1540	75	28	is	be	AUX
cana-1540	75	29	the	the	DET
cana-1540	75	30	density	density	NOUN
cana-1540	75	31	of	of	ADP
cana-1540	75	32	the	the	DET
cana-1540	75	33	material	material	NOUN
cana-1540	75	34	,	,	PUNCT
cana-1540	75	35	j	j	PROPN
cana-1540	75	36	is	be	AUX
cana-1540	75	37	the	the	DET
cana-1540	75	38	microinertia,	microinertia,	PROPN
cana-1540	75	39	�	�	PROPN
cana-1540	75	40	⃗	⃗	NOUN
cana-1540	75	41	�	�	PROPN
cana-1540	75	42	is	be	AUX
cana-1540	75	43	the	the	DET
cana-1540	75	44	microrotation	microrotation	NOUN
cana-1540	75	45	vector	vector	NOUN
cana-1540	75	46	,	,	PUNCT
cana-1540	75	47	𝜆	𝜆	NOUN
cana-1540	75	48	,	,	PUNCT
cana-1540	75	49	𝜇	𝜇	X
cana-1540	75	50	,	,	PUNCT
cana-1540	75	51	𝑘	𝑘	INTJ
cana-1540	75	52	,	,	PUNCT
cana-1540	75	53	𝛼	𝛼	INTJ
cana-1540	75	54	,	,	PUNCT
cana-1540	75	55	𝛽	𝛽	PROPN
cana-1540	75	56	,	,	PUNCT
cana-1540	75	57	𝛾	𝛾	PROPN
cana-1540	75	58	,	,	PUNCT
cana-1540	75	59	𝜆∗	𝜆∗	PROPN
cana-1540	75	60	,	,	PUNCT
cana-1540	75	61	𝜇∗	𝜇∗	NOUN
cana-1540	75	62	,	,	PUNCT
cana-1540	75	63	𝑘∗	𝑘∗	PROPN
cana-1540	75	64	,	,	PUNCT
cana-1540	75	65	α∗	α∗	NOUN
cana-1540	75	66	,	,	PUNCT
cana-1540	75	67	β∗	β∗	NOUN
cana-1540	75	68	,	,	PUNCT
cana-1540	75	69	γ∗are	γ∗are	PROPN
cana-1540	75	70	material	material	NOUN
cana-1540	75	71	constants	constant	NOUN
cana-1540	75	72	and	and	CCONJ
cana-1540	75	73	𝜆∗	𝜆∗	NOUN
cana-1540	75	74	=	=	SYM
cana-1540	76	1	𝜆	𝜆	PROPN
cana-1540	77	1	+	+	CCONJ
cana-1540	77	2	𝜆𝜈	𝜆𝜈	NUM
cana-1540	77	3	𝜕	𝜕	PROPN
cana-1540	77	4	𝜕𝑡	𝜕𝑡	PROPN
cana-1540	77	5	,	,	PUNCT
cana-1540	77	6	𝜇∗	𝜇∗	NOUN
cana-1540	77	7	=	=	SYM
cana-1540	77	8	𝜇	𝜇	X
cana-1540	77	9	+	+	ADP
cana-1540	77	10	𝜇𝜈	𝜇𝜈	ADP
cana-1540	77	11	𝜕	𝜕	PROPN
cana-1540	77	12	𝜕𝑡	𝜕𝑡	PROPN
cana-1540	77	13	,	,	PUNCT
cana-1540	77	14	𝑘∗	𝑘∗	PROPN
cana-1540	77	15	=	=	SYM
cana-1540	77	16	𝜅	𝜅	PROPN
cana-1540	77	17	+	+	NOUN
cana-1540	77	18	𝜅𝜈	𝜅𝜈	ADP
cana-1540	77	19	𝜕	𝜕	PROPN
cana-1540	77	20	𝜕𝑡	𝜕𝑡	PROPN
cana-1540	77	21	,	,	PUNCT
cana-1540	77	22	α∗	α∗	VERB
cana-1540	77	23	=	=	PUNCT
cana-1540	77	24	α	α	PROPN
cana-1540	78	1	+	+	CCONJ
cana-1540	78	2	α𝜈	α𝜈	ADV
cana-1540	78	3	𝜕	𝜕	PROPN
cana-1540	78	4	𝜕𝑡	𝜕𝑡	PROPN
cana-1540	78	5	,	,	PUNCT
cana-1540	78	6	β∗	β∗	NOUN
cana-1540	78	7	=	=	SYM
cana-1540	78	8	β	β	X
cana-1540	78	9	+	+	CCONJ
cana-1540	78	10	β𝜈	β𝜈	PROPN
cana-1540	78	11	𝜕	𝜕	PROPN
cana-1540	78	12	𝜕𝑡	𝜕𝑡	PROPN
cana-1540	78	13	,	,	PUNCT
cana-1540	78	14	γ∗	γ∗	PROPN
cana-1540	78	15	=	=	PUNCT
cana-1540	78	16	γ	γ	X
cana-1540	78	17	+	+	PROPN
cana-1540	78	18	γ𝜈	γ𝜈	NUM
cana-1540	78	19	𝜕	𝜕	NOUN
cana-1540	78	20	𝜕𝑡	𝜕𝑡	NOUN
cana-1540	78	21	file:///c:/users	file:///c:/users	PROPN
cana-1540	78	22	/	/	SYM
cana-1540	78	23	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	78	24	/	/	SYM
cana-1540	78	25	appdata	appdata	NOUN
cana-1540	78	26	/	/	SYM
cana-1540	78	27	local	local	ADJ
cana-1540	78	28	/	/	SYM
cana-1540	78	29	microsoft	microsoft	PROPN
cana-1540	78	30	/	/	SYM
cana-1540	78	31	windows	windows	PROPN
cana-1540	78	32	/	/	SYM
cana-1540	78	33	inetcache	inetcache	NOUN
cana-1540	78	34	/	/	SYM
cana-1540	78	35	ie	ie	PROPN
cana-1540	78	36	/	/	SYM
cana-1540	78	37	a6wkhao2	a6wkhao2	PROPN
cana-1540	78	38	/	/	SYM
cana-1540	78	39	chapter-4%5b1%5d.docx%23god12	chapter-4%5b1%5d.docx%23god12	PROPN
cana-1540	78	40	file:///c:/users	file:///c:/users	PROPN
cana-1540	78	41	/	/	SYM
cana-1540	78	42	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	78	43	/	/	SYM
cana-1540	78	44	appdata	appdata	NOUN
cana-1540	78	45	/	/	SYM
cana-1540	78	46	local	local	ADJ
cana-1540	78	47	/	/	SYM
cana-1540	78	48	microsoft	microsoft	PROPN
cana-1540	78	49	/	/	SYM
cana-1540	78	50	windows	windows	PROPN
cana-1540	78	51	/	/	SYM
cana-1540	78	52	inetcache	inetcache	NOUN
cana-1540	78	53	/	/	SYM
cana-1540	78	54	ie	ie	PROPN
cana-1540	78	55	/	/	SYM
cana-1540	78	56	a6wkhao2	a6wkhao2	PROPN
cana-1540	78	57	/	/	SYM
cana-1540	78	58	chapter-4%5b1%5d.docx%23vin14	chapter-4%5b1%5d.docx%23vin14	PROPN
cana-1540	78	59	file:///c:/users	file:///c:/users	PROPN
cana-1540	78	60	/	/	SYM
cana-1540	78	61	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	78	62	/	/	SYM
cana-1540	78	63	appdata	appdata	NOUN
cana-1540	78	64	/	/	SYM
cana-1540	78	65	local	local	ADJ
cana-1540	78	66	/	/	SYM
cana-1540	78	67	microsoft	microsoft	PROPN
cana-1540	78	68	/	/	SYM
cana-1540	78	69	windows	windows	PROPN
cana-1540	78	70	/	/	SYM
cana-1540	78	71	inetcache	inetcache	NOUN
cana-1540	78	72	/	/	SYM
cana-1540	78	73	ie	ie	PROPN
cana-1540	78	74	/	/	SYM
cana-1540	78	75	a6wkhao2	a6wkhao2	PROPN
cana-1540	78	76	/	/	SYM
cana-1540	78	77	chapter-4%5b1%5d.docx%23sin15	chapter-4%5b1%5d.docx%23sin15	PROPN
cana-1540	78	78	file:///c:/users	file:///c:/user	NOUN
cana-1540	78	79	/	/	SYM
cana-1540	78	80	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	78	81	/	/	SYM
cana-1540	78	82	appdata	appdata	NOUN
cana-1540	78	83	/	/	SYM
cana-1540	78	84	local	local	ADJ
cana-1540	78	85	/	/	SYM
cana-1540	78	86	microsoft	microsoft	PROPN
cana-1540	78	87	/	/	SYM
cana-1540	78	88	windows	windows	PROPN
cana-1540	78	89	/	/	SYM
cana-1540	78	90	inetcache	inetcache	NOUN
cana-1540	78	91	/	/	SYM
cana-1540	78	92	ie	ie	PROPN
cana-1540	78	93	/	/	SYM
cana-1540	78	94	a6wkhao2	a6wkhao2	PROPN
cana-1540	78	95	/	/	SYM
cana-1540	78	96	chapter-4%5b1%5d.docx%23placeholder1	chapter-4%5b1%5d.docx%23placeholder1	NOUN
cana-1540	78	97	communications	communication	NOUN
cana-1540	78	98	on	on	ADP
cana-1540	78	99	applied	apply	VERB
cana-1540	78	100	nonlinear	nonlinear	ADJ
cana-1540	78	101	analysis	analysis	NOUN
cana-1540	78	102	issn	issn	NOUN
cana-1540	78	103	:	:	PUNCT
cana-1540	78	104	1074	1074	NUM
cana-1540	78	105	-	-	PUNCT
cana-1540	78	106	133x	133x	NUM
cana-1540	78	107	vol	vol	NOUN
cana-1540	78	108	31	31	NUM
cana-1540	78	109	no	no	NOUN
cana-1540	78	110	.	.	PUNCT
cana-1540	79	1	8s	8s	PROPN
cana-1540	79	2	(	(	PUNCT
cana-1540	79	3	2024	2024	NUM
cana-1540	79	4	)	)	PUNCT
cana-1540	79	5	486	486	NUM
cana-1540	79	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	79	7	the	the	DET
cana-1540	79	8	constitutive	constitutive	ADJ
cana-1540	79	9	relations	relation	NOUN
cana-1540	79	10	are	be	AUX
cana-1540	79	11	given	give	VERB
cana-1540	79	12	by	by	ADP
cana-1540	79	13	𝜎𝑖𝑗	𝜎𝑖𝑗	PROPN
cana-1540	79	14	=	=	PROPN
cana-1540	80	1	𝜆	𝜆	DET
cana-1540	80	2	∗𝑢𝑟,𝑟𝛿𝑖𝑗	∗𝑢𝑟,𝑟𝛿𝑖𝑗	PROPN
cana-1540	80	3	+	+	PROPN
cana-1540	80	4	𝜇	𝜇	ADP
cana-1540	80	5	∗(𝑢𝑖,𝑗	∗(𝑢𝑖,𝑗	PROPN
cana-1540	80	6	+	+	CCONJ
cana-1540	80	7	𝑢𝑗,𝑖	𝑢𝑗,𝑖	PUNCT
cana-1540	80	8	)	)	PUNCT
cana-1540	81	1	+	+	CCONJ
cana-1540	81	2	𝑘	𝑘	DET
cana-1540	81	3	∗(𝑢𝑗,𝑖	∗(𝑢𝑗,𝑖	NOUN
cana-1540	81	4	−	−	NOUN
cana-1540	81	5	𝜖𝑖𝑗𝑟𝜙𝑟	𝜖𝑖𝑗𝑟𝜙𝑟	NOUN
cana-1540	81	6	)	)	PUNCT
cana-1540	81	7	−	−	PROPN
cana-1540	82	1	𝜈𝑇𝛿𝑖𝑗	𝜈𝑇𝛿𝑖𝑗	PROPN
cana-1540	82	2	(	(	PUNCT
cana-1540	82	3	3	3	NUM
cana-1540	82	4	)	)	PUNCT
cana-1540	82	5	𝑚𝑖𝑗	𝑚𝑖𝑗	NOUN
cana-1540	82	6	=	=	PUNCT
cana-1540	82	7	α	α	NOUN
cana-1540	83	1	∗𝜙𝑟,𝑟𝛿𝑖𝑗	∗𝜙𝑟,𝑟𝛿𝑖𝑗	PROPN
cana-1540	83	2	+	+	NUM
cana-1540	83	3	β	β	X
cana-1540	83	4	∗𝜙𝑖,𝑗	∗𝜙𝑖,𝑗	NOUN
cana-1540	83	5	+	+	CCONJ
cana-1540	83	6	γ	γ	X
cana-1540	83	7	∗𝜙𝑗,𝑖	∗𝜙𝑗,𝑖	X
cana-1540	83	8	(	(	PUNCT
cana-1540	83	9	4	4	NUM
cana-1540	83	10	)	)	PUNCT
cana-1540	83	11	where	where	SCONJ
cana-1540	83	12	(	(	PUNCT
cana-1540	83	13	𝑖	𝑖	SYM
cana-1540	83	14	,	,	PUNCT
cana-1540	83	15	𝑗	𝑗	INTJ
cana-1540	83	16	,	,	PUNCT
cana-1540	83	17	𝑟	𝑟	NOUN
cana-1540	83	18	=	=	SYM
cana-1540	83	19	1,2,3	1,2,3	NUM
cana-1540	83	20	)	)	PUNCT
cana-1540	83	21	,	,	PUNCT
cana-1540	83	22	𝜎𝑖𝑗	𝜎𝑖𝑗	PROPN
cana-1540	83	23	is	be	AUX
cana-1540	83	24	the	the	DET
cana-1540	83	25	stress	stress	PROPN
cana-1540	83	26	tensor,𝑚𝑖𝑗	tensor,𝑚𝑖𝑗	PROPN
cana-1540	83	27	is	be	AUX
cana-1540	83	28	the	the	DET
cana-1540	83	29	couple	couple	NOUN
cana-1540	83	30	stress	stress	NOUN
cana-1540	83	31	tensor	tensor	NOUN
cana-1540	83	32	and	and	CCONJ
cana-1540	83	33	𝛿𝑖𝑗	𝛿𝑖𝑗	NOUN
cana-1540	83	34	is	be	AUX
cana-1540	83	35	the	the	DET
cana-1540	83	36	kronecker	kronecker	NOUN
cana-1540	83	37	delta	delta	NOUN
cana-1540	83	38	.	.	PUNCT
cana-1540	84	1	following	follow	VERB
cana-1540	84	2	lord	lord	PROPN
cana-1540	84	3	and	and	CCONJ
cana-1540	84	4	shulman	shulman	PROPN
cana-1540	84	5	(	(	PUNCT
cana-1540	84	6	1967	1967	NUM
cana-1540	84	7	)	)	PUNCT
cana-1540	84	8	,	,	PUNCT
cana-1540	84	9	the	the	DET
cana-1540	84	10	heat	heat	NOUN
cana-1540	84	11	conduction	conduction	NOUN
cana-1540	84	12	equation	equation	NOUN
cana-1540	84	13	is	be	AUX
cana-1540	84	14	𝐾∗∇2𝑇	𝐾∗∇2𝑇	NOUN
cana-1540	84	15	=	=	SYM
cana-1540	84	16	𝜌𝐶∗	𝜌𝐶∗	X
cana-1540	84	17	(	(	PUNCT
cana-1540	84	18	𝜕	𝜕	PROPN
cana-1540	84	19	𝜕𝑡	𝜕𝑡	PROPN
cana-1540	84	20	+	+	CCONJ
cana-1540	84	21	𝜏0	𝜏0	PROPN
cana-1540	84	22	𝜕2	𝜕2	ADJ
cana-1540	84	23	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	84	24	)	)	PUNCT
cana-1540	84	25	𝑇	𝑇	PROPN
cana-1540	84	26	+	+	PUNCT
cana-1540	84	27	𝜈𝑇0	𝜈𝑇0	PROPN
cana-1540	84	28	(	(	PUNCT
cana-1540	84	29	𝜕	𝜕	PROPN
cana-1540	84	30	𝜕𝑡	𝜕𝑡	PROPN
cana-1540	84	31	+	+	CCONJ
cana-1540	84	32	𝜏0	𝜏0	PROPN
cana-1540	84	33	𝜕2	𝜕2	ADJ
cana-1540	84	34	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	84	35	)	)	PUNCT
cana-1540	84	36	∇.	∇.	NUM
cana-1540	84	37	�	�	NOUN
cana-1540	84	38	⃗	⃗	X
cana-1540	84	39	�	�	PROPN
cana-1540	84	40	(	(	PUNCT
cana-1540	84	41	5	5	NUM
cana-1540	84	42	)	)	PUNCT
cana-1540	84	43	where	where	SCONJ
cana-1540	84	44	𝐾∗	𝐾∗	PROPN
cana-1540	84	45	is	be	AUX
cana-1540	84	46	the	the	DET
cana-1540	84	47	coefficient	coefficient	NOUN
cana-1540	84	48	of	of	ADP
cana-1540	84	49	thermal	thermal	ADJ
cana-1540	84	50	conductivity	conductivity	NOUN
cana-1540	84	51	,	,	PUNCT
cana-1540	84	52	𝜈	𝜈	X
cana-1540	84	53	=	=	SYM
cana-1540	84	54	(	(	PUNCT
cana-1540	84	55	3𝜆	3𝜆	ADJ
cana-1540	84	56	+	+	CCONJ
cana-1540	84	57	2	2	NUM
cana-1540	84	58	𝜇	𝜇	ADP
cana-1540	84	59	+	+	X
cana-1540	84	60	𝐾)𝛼𝑡	𝐾)𝛼𝑡	ADJ
cana-1540	84	61	,	,	PUNCT
cana-1540	84	62	𝐶	𝐶	PROPN
cana-1540	84	63	∗	∗	NOUN
cana-1540	84	64	is	be	AUX
cana-1540	84	65	the	the	DET
cana-1540	84	66	specific	specific	ADJ
cana-1540	84	67	heat	heat	NOUN
cana-1540	84	68	at	at	ADP
cana-1540	84	69	constant	constant	ADJ
cana-1540	84	70	strain	strain	NOUN
cana-1540	84	71	,	,	PUNCT
cana-1540	84	72	𝛼𝑡	𝛼𝑡	X
cana-1540	84	73	is	be	AUX
cana-1540	84	74	the	the	DET
cana-1540	84	75	coefficient	coefficient	NOUN
cana-1540	84	76	of	of	ADP
cana-1540	84	77	thermal	thermal	ADJ
cana-1540	84	78	linear	linear	ADJ
cana-1540	84	79	expansion	expansion	NOUN
cana-1540	84	80	,	,	PUNCT
cana-1540	84	81	t	t	PROPN
cana-1540	84	82	is	be	AUX
cana-1540	84	83	the	the	DET
cana-1540	84	84	change	change	NOUN
cana-1540	84	85	in	in	ADP
cana-1540	84	86	temperature	temperature	NOUN
cana-1540	84	87	of	of	ADP
cana-1540	84	88	the	the	DET
cana-1540	84	89	medium	medium	NOUN
cana-1540	84	90	at	at	ADP
cana-1540	84	91	any	any	DET
cana-1540	84	92	time	time	NOUN
cana-1540	84	93	,	,	PUNCT
cana-1540	84	94	𝑇0	𝑇0	NOUN
cana-1540	84	95	is	be	AUX
cana-1540	84	96	the	the	DET
cana-1540	84	97	reference	reference	NOUN
cana-1540	84	98	temperature	temperature	NOUN
cana-1540	84	99	of	of	ADP
cana-1540	84	100	the	the	DET
cana-1540	84	101	body	body	NOUN
cana-1540	84	102	and𝜏0is	and𝜏0is	VERB
cana-1540	84	103	the	the	DET
cana-1540	84	104	thermal	thermal	ADJ
cana-1540	84	105	relaxation	relaxation	NOUN
cana-1540	84	106	time	time	NOUN
cana-1540	84	107	3	3	NUM
cana-1540	84	108	.	.	PUNCT
cana-1540	85	1	formulation	formulation	NOUN
cana-1540	85	2	of	of	ADP
cana-1540	85	3	the	the	DET
cana-1540	85	4	problem	problem	NOUN
cana-1540	85	5	we	we	PRON
cana-1540	85	6	consider	consider	VERB
cana-1540	85	7	a	a	DET
cana-1540	85	8	homogeneous	homogeneous	ADJ
cana-1540	85	9	and	and	CCONJ
cana-1540	85	10	isotropic	isotropic	ADJ
cana-1540	85	11	micropolar	micropolar	ADJ
cana-1540	85	12	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	85	13	half	half	NOUN
cana-1540	85	14	space	space	NOUN
cana-1540	85	15	at	at	ADP
cana-1540	85	16	uniform	uniform	ADJ
cana-1540	85	17	temperature	temperature	NOUN
cana-1540	85	18	𝑇0	𝑇0	NOUN
cana-1540	85	19	in	in	ADP
cana-1540	85	20	the	the	DET
cana-1540	85	21	undeformed	undeformed	ADJ
cana-1540	85	22	state	state	NOUN
cana-1540	85	23	.	.	PUNCT
cana-1540	86	1	origin	origin	NOUN
cana-1540	86	2	is	be	AUX
cana-1540	86	3	placed	place	VERB
cana-1540	86	4	at	at	ADP
cana-1540	86	5	the	the	DET
cana-1540	86	6	plane	plane	NOUN
cana-1540	86	7	surface	surface	NOUN
cana-1540	86	8	and	and	CCONJ
cana-1540	86	9	𝑦-axis	𝑦-axis	ADJ
cana-1540	86	10	pointing	pointing	NOUN
cana-1540	86	11	vertically	vertically	ADV
cana-1540	86	12	downward	downward	ADV
cana-1540	86	13	into	into	ADP
cana-1540	86	14	the	the	DET
cana-1540	86	15	half	half	ADJ
cana-1540	86	16	space	space	NOUN
cana-1540	86	17	.	.	PUNCT
cana-1540	87	1	the	the	DET
cana-1540	87	2	direction	direction	NOUN
cana-1540	87	3	of	of	ADP
cana-1540	87	4	propagation	propagation	NOUN
cana-1540	87	5	of	of	ADP
cana-1540	87	6	the	the	DET
cana-1540	87	7	waves	wave	NOUN
cana-1540	87	8	is	be	AUX
cana-1540	87	9	considered	consider	VERB
cana-1540	87	10	along	along	ADP
cana-1540	87	11	𝑥-axis	𝑥-axis	NOUN
cana-1540	87	12	so	so	SCONJ
cana-1540	87	13	that	that	SCONJ
cana-1540	87	14	all	all	DET
cana-1540	87	15	particles	particle	NOUN
cana-1540	87	16	vibrating	vibrate	VERB
cana-1540	87	17	on	on	ADP
cana-1540	87	18	a	a	DET
cana-1540	87	19	line	line	NOUN
cana-1540	87	20	parallel	parallel	NOUN
cana-1540	87	21	to	to	ADP
cana-1540	87	22	z	z	NOUN
cana-1540	87	23	-	-	PUNCT
cana-1540	87	24	axis	axis	NOUN
cana-1540	87	25	are	be	AUX
cana-1540	87	26	equally	equally	ADV
cana-1540	87	27	displaced	displace	VERB
cana-1540	87	28	.	.	PUNCT
cana-1540	88	1	therefore	therefore	ADV
cana-1540	88	2	,	,	PUNCT
cana-1540	88	3	all	all	DET
cana-1540	88	4	the	the	DET
cana-1540	88	5	field	field	NOUN
cana-1540	88	6	quantities	quantity	NOUN
cana-1540	88	7	will	will	AUX
cana-1540	88	8	be	be	AUX
cana-1540	88	9	independent	independent	ADJ
cana-1540	88	10	of	of	ADP
cana-1540	88	11	z	z	NOUN
cana-1540	88	12	-	-	PUNCT
cana-1540	88	13	coordinates	coordinate	NOUN
cana-1540	88	14	.	.	PUNCT
cana-1540	89	1	for	for	ADP
cana-1540	89	2	the	the	DET
cana-1540	89	3	two	two	NUM
cana-1540	89	4	-	-	PUNCT
cana-1540	89	5	dimensional	dimensional	ADJ
cana-1540	89	6	problem	problem	NOUN
cana-1540	89	7	,	,	PUNCT
cana-1540	89	8	we	we	PRON
cana-1540	89	9	assume	assume	VERB
cana-1540	89	10	the	the	DET
cana-1540	89	11	components	component	NOUN
cana-1540	89	12	of	of	ADP
cana-1540	89	13	the	the	DET
cana-1540	89	14	displacement	displacement	ADJ
cana-1540	89	15	�	�	PROPN
cana-1540	89	16	⃗	⃗	NOUN
cana-1540	89	17	�	�	PROPN
cana-1540	89	18	and	and	CCONJ
cana-1540	89	19	microrotation	microrotation	NOUN
cana-1540	89	20	vector	vector	PROPN
cana-1540	89	21	�	�	PROPN
cana-1540	89	22	⃗	⃗	PROPN
cana-1540	89	23	�	�	PROPN
cana-1540	89	24	of	of	ADP
cana-1540	89	25	the	the	DET
cana-1540	89	26	form	form	NOUN
cana-1540	89	27	�	�	NOUN
cana-1540	89	28	⃗	⃗	NOUN
cana-1540	89	29	�	�	NOUN
cana-1540	89	30	=	=	SYM
cana-1540	89	31	(	(	PUNCT
cana-1540	89	32	𝑢	𝑢	NOUN
cana-1540	89	33	,	,	PUNCT
cana-1540	89	34	𝑣	𝑣	X
cana-1540	89	35	,	,	PUNCT
cana-1540	89	36	0	0	NUM
cana-1540	89	37	)	)	PUNCT
cana-1540	89	38	,	,	PUNCT
cana-1540	89	39	�	�	PROPN
cana-1540	89	40	⃗	⃗	NOUN
cana-1540	89	41	�	�	X
cana-1540	89	42	=	=	SYM
cana-1540	89	43	(	(	PUNCT
cana-1540	89	44	0	0	NUM
cana-1540	89	45	,	,	PUNCT
cana-1540	89	46	0	0	NUM
cana-1540	89	47	,	,	PUNCT
cana-1540	89	48	𝜙	𝜙	NOUN
cana-1540	89	49	)	)	PUNCT
cana-1540	89	50	(	(	PUNCT
cana-1540	89	51	6	6	X
cana-1540	89	52	)	)	PUNCT
cana-1540	89	53	using	use	VERB
cana-1540	89	54	(	(	PUNCT
cana-1540	89	55	6	6	NUM
cana-1540	89	56	)	)	PUNCT
cana-1540	89	57	,	,	PUNCT
cana-1540	89	58	equation	equation	NOUN
cana-1540	89	59	(	(	PUNCT
cana-1540	89	60	1	1	NUM
cana-1540	89	61	)	)	PUNCT
cana-1540	89	62	and	and	CCONJ
cana-1540	89	63	(	(	PUNCT
cana-1540	89	64	2	2	X
cana-1540	89	65	)	)	PUNCT
cana-1540	89	66	can	can	AUX
cana-1540	89	67	be	be	AUX
cana-1540	89	68	written	write	VERB
cana-1540	89	69	as	as	ADP
cana-1540	89	70	(	(	PUNCT
cana-1540	89	71	𝜆∗	𝜆∗	NOUN
cana-1540	89	72	+	+	CCONJ
cana-1540	89	73	2𝜇∗	2𝜇∗	NUM
cana-1540	89	74	+	+	CCONJ
cana-1540	89	75	𝑘∗	𝑘∗	ADJ
cana-1540	89	76	)	)	PUNCT
cana-1540	89	77	𝜕2𝑢	𝜕2𝑢	PROPN
cana-1540	89	78	𝜕𝑥2	𝜕𝑥2	NOUN
cana-1540	89	79	+	+	CCONJ
cana-1540	89	80	(	(	PUNCT
cana-1540	89	81	𝜇∗	𝜇∗	NOUN
cana-1540	89	82	+	+	CCONJ
cana-1540	89	83	𝑘∗	𝑘∗	ADJ
cana-1540	89	84	)	)	PUNCT
cana-1540	89	85	𝜕2𝑢	𝜕2𝑢	PROPN
cana-1540	89	86	𝜕𝑦2	𝜕𝑦2	PROPN
cana-1540	89	87	+	+	CCONJ
cana-1540	89	88	(	(	PUNCT
cana-1540	89	89	𝜆∗	𝜆∗	NOUN
cana-1540	89	90	+	+	CCONJ
cana-1540	89	91	𝜇∗	𝜇∗	NOUN
cana-1540	89	92	)	)	PUNCT
cana-1540	89	93	𝜕2𝑣	𝜕2𝑣	NOUN
cana-1540	89	94	𝜕𝑥𝜕𝑦	𝜕𝑥𝜕𝑦	NOUN
cana-1540	89	95	+	+	CCONJ
cana-1540	89	96	𝑘∗	𝑘∗	ADJ
cana-1540	89	97	𝜕𝜙	𝜕𝜙	ADJ
cana-1540	89	98	𝜕𝑦	𝜕𝑦	NOUN
cana-1540	89	99	−	−	NOUN
cana-1540	89	100	𝜈	𝜈	X
cana-1540	89	101	𝜕𝑇	𝜕𝑇	X
cana-1540	89	102	𝜕𝑥	𝜕𝑥	X
cana-1540	89	103	=	=	PUNCT
cana-1540	89	104	𝜌	𝜌	ADP
cana-1540	89	105	𝜕2𝑢	𝜕2𝑢	PROPN
cana-1540	89	106	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	89	107	(	(	PUNCT
cana-1540	89	108	7	7	NUM
cana-1540	89	109	)	)	PUNCT
cana-1540	89	110	(	(	PUNCT
cana-1540	89	111	𝜆∗	𝜆∗	NOUN
cana-1540	89	112	+	+	CCONJ
cana-1540	89	113	2𝜇∗	2𝜇∗	NUM
cana-1540	89	114	+	+	CCONJ
cana-1540	89	115	𝑘∗	𝑘∗	ADJ
cana-1540	89	116	)	)	PUNCT
cana-1540	89	117	𝜕2𝑣	𝜕2𝑣	NOUN
cana-1540	89	118	𝜕𝑦2	𝜕𝑦2	PROPN
cana-1540	89	119	+	+	CCONJ
cana-1540	89	120	(	(	PUNCT
cana-1540	89	121	𝜇∗	𝜇∗	NOUN
cana-1540	89	122	+	+	CCONJ
cana-1540	89	123	𝑘∗	𝑘∗	PROPN
cana-1540	89	124	)	)	PUNCT
cana-1540	89	125	𝜕2𝑣	𝜕2𝑣	NOUN
cana-1540	89	126	𝜕𝑥2	𝜕𝑥2	NOUN
cana-1540	90	1	+	+	CCONJ
cana-1540	90	2	(	(	PUNCT
cana-1540	90	3	𝜆∗	𝜆∗	PROPN
cana-1540	90	4	+	+	CCONJ
cana-1540	90	5	𝜇∗	𝜇∗	NOUN
cana-1540	90	6	)	)	PUNCT
cana-1540	90	7	𝜕2𝑢	𝜕2𝑢	PROPN
cana-1540	90	8	𝜕𝑥𝜕𝑦	𝜕𝑥𝜕𝑦	NOUN
cana-1540	90	9	−	−	ADP
cana-1540	90	10	𝑘∗	𝑘∗	ADJ
cana-1540	90	11	𝜕𝜙	𝜕𝜙	ADJ
cana-1540	90	12	𝜕𝑥	𝜕𝑥	NOUN
cana-1540	90	13	−	−	NOUN
cana-1540	90	14	𝜈	𝜈	X
cana-1540	90	15	𝜕𝑇	𝜕𝑇	NOUN
cana-1540	90	16	𝜕𝑦	𝜕𝑦	NOUN
cana-1540	90	17	=	=	PUNCT
cana-1540	90	18	𝜌	𝜌	ADP
cana-1540	90	19	𝜕2𝑣	𝜕2𝑣	PROPN
cana-1540	90	20	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	90	21	(	(	PUNCT
cana-1540	90	22	8)	8)	NUM
cana-1540	90	23	𝛾∗	𝛾∗	NOUN
cana-1540	90	24	(	(	PUNCT
cana-1540	90	25	𝜕2𝜙	𝜕2𝜙	NOUN
cana-1540	90	26	𝜕𝑥2	𝜕𝑥2	NOUN
cana-1540	90	27	+	+	CCONJ
cana-1540	90	28	𝜕2𝜙	𝜕2𝜙	NOUN
cana-1540	90	29	𝜕𝑦2	𝜕𝑦2	NOUN
cana-1540	90	30	)	)	PUNCT
cana-1540	91	1	+	+	CCONJ
cana-1540	91	2	𝑘∗	𝑘∗	ADJ
cana-1540	91	3	(	(	PUNCT
cana-1540	91	4	𝜕𝑣	𝜕𝑣	NOUN
cana-1540	91	5	𝜕𝑥	𝜕𝑥	X
cana-1540	91	6	−	−	ADP
cana-1540	91	7	𝜕𝑢	𝜕𝑢	NOUN
cana-1540	91	8	𝜕𝑦	𝜕𝑦	NOUN
cana-1540	91	9	)	)	PUNCT
cana-1540	92	1	−	−	PROPN
cana-1540	93	1	2𝑘∗𝜙	2𝑘∗𝜙	NUM
cana-1540	93	2	=	=	SYM
cana-1540	93	3	𝜌𝑗	𝜌𝑗	ADP
cana-1540	93	4	𝜕2𝜙	𝜕2𝜙	NOUN
cana-1540	93	5	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	93	6	(	(	PUNCT
cana-1540	93	7	9	9	X
cana-1540	93	8	)	)	PUNCT
cana-1540	93	9	using	use	VERB
cana-1540	93	10	helmholtz	helmholtz	NOUN
cana-1540	93	11	’s	’s	PART
cana-1540	93	12	representation	representation	NOUN
cana-1540	93	13	,	,	PUNCT
cana-1540	93	14	the	the	DET
cana-1540	93	15	displacement	displacement	NOUN
cana-1540	93	16	components	component	NOUN
cana-1540	93	17	𝑢	𝑢	NOUN
cana-1540	93	18	and	and	CCONJ
cana-1540	93	19	𝑣can	𝑣can	PROPN
cana-1540	93	20	be	be	AUX
cana-1540	93	21	written	write	VERB
cana-1540	93	22	in	in	ADP
cana-1540	93	23	terms	term	NOUN
cana-1540	93	24	of	of	ADP
cana-1540	93	25	potential	potential	ADJ
cana-1540	93	26	functions	function	NOUN
cana-1540	93	27	as	as	ADP
cana-1540	93	28	𝑢	𝑢	NOUN
cana-1540	93	29	=	=	SYM
cana-1540	93	30	𝜕𝜙1	𝜕𝜙1	NOUN
cana-1540	93	31	𝜕𝑥	𝜕𝑥	NOUN
cana-1540	93	32	+	+	CCONJ
cana-1540	93	33	𝜕𝜓1	𝜕𝜓1	ADJ
cana-1540	93	34	𝜕𝑦	𝜕𝑦	NOUN
cana-1540	93	35	,	,	PUNCT
cana-1540	93	36	𝑣	𝑣	X
cana-1540	93	37	=	=	PUNCT
cana-1540	93	38	𝜕𝜙1	𝜕𝜙1	PROPN
cana-1540	93	39	𝜕𝑦	𝜕𝑦	NOUN
cana-1540	93	40	−	−	ADP
cana-1540	93	41	𝜕𝜓1	𝜕𝜓1	ADJ
cana-1540	93	42	𝜕𝑥	𝜕𝑥	X
cana-1540	93	43	(	(	PUNCT
cana-1540	93	44	10	10	NUM
cana-1540	93	45	)	)	PUNCT
cana-1540	93	46	substituting	substitute	VERB
cana-1540	93	47	(	(	PUNCT
cana-1540	93	48	10	10	NUM
cana-1540	93	49	)	)	PUNCT
cana-1540	93	50	in	in	ADP
cana-1540	93	51	equations	equation	NOUN
cana-1540	93	52	(	(	PUNCT
cana-1540	93	53	5	5	NUM
cana-1540	93	54	)	)	PUNCT
cana-1540	93	55	and	and	CCONJ
cana-1540	93	56	(	(	PUNCT
cana-1540	93	57	7)-(9	7)-(9	NOUN
cana-1540	93	58	)	)	PUNCT
cana-1540	93	59	,	,	PUNCT
cana-1540	93	60	we	we	PRON
cana-1540	93	61	obtained	obtain	VERB
cana-1540	93	62	(	(	PUNCT
cana-1540	93	63	𝜆∗	𝜆∗	NOUN
cana-1540	93	64	+	+	CCONJ
cana-1540	93	65	2𝜇∗	2𝜇∗	NUM
cana-1540	93	66	+	+	CCONJ
cana-1540	93	67	𝑘∗)∇2𝜙1	𝑘∗)∇2𝜙1	PROPN
cana-1540	93	68	−	−	PROPN
cana-1540	93	69	𝜈𝑇	𝜈𝑇	NOUN
cana-1540	93	70	=	=	SYM
cana-1540	94	1	𝜌	𝜌	X
cana-1540	94	2	𝜕2𝜙1	𝜕2𝜙1	PUNCT
cana-1540	94	3	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	94	4	(	(	PUNCT
cana-1540	94	5	11	11	NUM
cana-1540	94	6	)	)	PUNCT
cana-1540	94	7	communications	communication	NOUN
cana-1540	94	8	on	on	ADP
cana-1540	94	9	applied	apply	VERB
cana-1540	94	10	nonlinear	nonlinear	ADJ
cana-1540	94	11	analysis	analysis	NOUN
cana-1540	94	12	issn	issn	NOUN
cana-1540	94	13	:	:	PUNCT
cana-1540	94	14	1074	1074	NUM
cana-1540	94	15	-	-	PUNCT
cana-1540	94	16	133x	133x	NUM
cana-1540	94	17	vol	vol	NOUN
cana-1540	94	18	31	31	NUM
cana-1540	94	19	no	no	NOUN
cana-1540	94	20	.	.	PUNCT
cana-1540	95	1	8s	8s	PROPN
cana-1540	95	2	(	(	PUNCT
cana-1540	95	3	2024	2024	NUM
cana-1540	95	4	)	)	PUNCT
cana-1540	95	5	487	487	NUM
cana-1540	95	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	95	7	(	(	PUNCT
cana-1540	95	8	𝜇∗	𝜇∗	NOUN
cana-1540	95	9	+	+	CCONJ
cana-1540	95	10	𝑘∗)∇2𝜓1	𝑘∗)∇2𝜓1	NOUN
cana-1540	95	11	+	+	CCONJ
cana-1540	95	12	𝑘	𝑘	DET
cana-1540	95	13	∗𝜙	∗𝜙	PROPN
cana-1540	95	14	=	=	PUNCT
cana-1540	95	15	𝜌	𝜌	ADP
cana-1540	95	16	𝜕2𝜓1	𝜕2𝜓1	ADV
cana-1540	95	17	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	95	18	(	(	PUNCT
cana-1540	95	19	12	12	NUM
cana-1540	95	20	)	)	PUNCT
cana-1540	95	21	𝛾∗∇2𝜙	𝛾∗∇2𝜙	NOUN
cana-1540	95	22	−	−	PROPN
cana-1540	96	1	2𝑘∗𝜙	2𝑘∗𝜙	NUM
cana-1540	96	2	−	−	PROPN
cana-1540	96	3	𝑘∗∇2𝜓1	𝑘∗∇2𝜓1	ADJ
cana-1540	96	4	=	=	NOUN
cana-1540	96	5	𝜌𝑗	𝜌𝑗	ADP
cana-1540	96	6	𝜕2𝜙	𝜕2𝜙	NOUN
cana-1540	96	7	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	96	8	(	(	PUNCT
cana-1540	96	9	13	13	NUM
cana-1540	96	10	)	)	PUNCT
cana-1540	96	11	𝐾∗∇2𝑇	𝐾∗∇2𝑇	NOUN
cana-1540	97	1	=	=	SYM
cana-1540	97	2	(	(	PUNCT
cana-1540	97	3	𝜕	𝜕	PROPN
cana-1540	97	4	𝜕𝑡	𝜕𝑡	PROPN
cana-1540	97	5	+	+	CCONJ
cana-1540	97	6	𝜏0	𝜏0	PROPN
cana-1540	97	7	𝜕2	𝜕2	ADJ
cana-1540	97	8	𝜕𝑡2	𝜕𝑡2	NOUN
cana-1540	97	9	)	)	PUNCT
cana-1540	97	10	(	(	PUNCT
cana-1540	97	11	𝜌𝐶∗𝑇	𝜌𝐶∗𝑇	NOUN
cana-1540	97	12	+	+	CCONJ
cana-1540	97	13	𝜈𝑇0∇	𝜈𝑇0∇	PROPN
cana-1540	97	14	2𝜙1	2𝜙1	NUM
cana-1540	97	15	)	)	PUNCT
cana-1540	97	16	(	(	PUNCT
cana-1540	97	17	14	14	NUM
cana-1540	97	18	)	)	PUNCT
cana-1540	97	19	4	4	NUM
cana-1540	97	20	.	.	PUNCT
cana-1540	97	21	solution	solution	NOUN
cana-1540	97	22	of	of	ADP
cana-1540	97	23	the	the	DET
cana-1540	97	24	problem	problem	NOUN
cana-1540	97	25	the	the	DET
cana-1540	97	26	surface	surface	NOUN
cana-1540	97	27	wave	wave	NOUN
cana-1540	97	28	solutions	solution	NOUN
cana-1540	97	29	of	of	ADP
cana-1540	97	30	the	the	DET
cana-1540	97	31	equations	equation	NOUN
cana-1540	97	32	(	(	PUNCT
cana-1540	97	33	11)-(14	11)-(14	NOUN
cana-1540	97	34	)	)	PUNCT
cana-1540	97	35	may	may	AUX
cana-1540	97	36	be	be	AUX
cana-1540	97	37	consider	consider	VERB
cana-1540	97	38	as	as	ADP
cana-1540	97	39	{	{	PUNCT
cana-1540	97	40	𝜙1	𝜙1	NOUN
cana-1540	97	41	,	,	PUNCT
cana-1540	97	42	𝜓1	𝜓1	NOUN
cana-1540	97	43	,	,	PUNCT
cana-1540	97	44	𝑇	𝑇	PROPN
cana-1540	97	45	,	,	PUNCT
cana-1540	97	46	𝜙	𝜙	NOUN
cana-1540	97	47	}	}	PUNCT
cana-1540	97	48	=	=	SYM
cana-1540	97	49	{	{	PUNCT
cana-1540	97	50	𝜙1̅̅̅̅	𝜙1̅̅̅̅	PROPN
cana-1540	97	51	(	(	PUNCT
cana-1540	97	52	𝑦	𝑦	NOUN
cana-1540	97	53	)	)	PUNCT
cana-1540	97	54	,	,	PUNCT
cana-1540	97	55	𝜓1̅̅̅̅	𝜓1̅̅̅̅	PROPN
cana-1540	97	56	(	(	PUNCT
cana-1540	97	57	𝑦	𝑦	NOUN
cana-1540	97	58	)	)	PUNCT
cana-1540	97	59	,	,	PUNCT
cana-1540	97	60	�	�	NOUN
cana-1540	97	61	̅	̅	NOUN
cana-1540	97	62	�	�	NOUN
cana-1540	97	63	(𝑦	(𝑦	NOUN
cana-1540	97	64	)	)	PUNCT
cana-1540	97	65	,	,	PUNCT
cana-1540	97	66	�	�	PROPN
cana-1540	97	67	̅	̅	NOUN
cana-1540	97	68	�	�	NOUN
cana-1540	97	69	(𝑦)}𝑒	(𝑦)}𝑒	NOUN
cana-1540	97	70	𝑖𝐾(𝑥−𝑐𝑡	𝑖𝐾(𝑥−𝑐𝑡	NOUN
cana-1540	97	71	)	)	PUNCT
cana-1540	97	72	(	(	PUNCT
cana-1540	97	73	15	15	X
cana-1540	97	74	)	)	PUNCT
cana-1540	97	75	where𝑐	where𝑐	NOUN
cana-1540	97	76	is	be	AUX
cana-1540	97	77	the	the	DET
cana-1540	97	78	phase	phase	NOUN
cana-1540	97	79	velocity	velocity	NOUN
cana-1540	97	80	,	,	PUNCT
cana-1540	97	81	𝐾	𝐾	PROPN
cana-1540	97	82	is	be	AUX
cana-1540	97	83	the	the	DET
cana-1540	97	84	wave	wave	NOUN
cana-1540	97	85	number	number	NOUN
cana-1540	97	86	,	,	PUNCT
cana-1540	97	87	𝜔	𝜔	PUNCT
cana-1540	97	88	=	=	PUNCT
cana-1540	97	89	𝐾𝑐	𝐾𝑐	VERB
cana-1540	97	90	is	be	AUX
cana-1540	97	91	the	the	DET
cana-1540	97	92	circular	circular	ADJ
cana-1540	97	93	frequency	frequency	NOUN
cana-1540	97	94	.	.	PUNCT
cana-1540	98	1	it	it	PRON
cana-1540	98	2	is	be	AUX
cana-1540	98	3	assumed	assume	VERB
cana-1540	98	4	that	that	SCONJ
cana-1540	98	5	the	the	DET
cana-1540	98	6	rayleigh	rayleigh	PROPN
cana-1540	98	7	surface	surface	NOUN
cana-1540	98	8	waves	wave	NOUN
cana-1540	98	9	possibly	possibly	ADV
cana-1540	98	10	damped	damp	VERB
cana-1540	98	11	in	in	ADP
cana-1540	98	12	time	time	NOUN
cana-1540	98	13	,	,	PUNCT
cana-1540	98	14	propagating	propagate	VERB
cana-1540	98	15	along	along	ADP
cana-1540	98	16	𝑥-axis	𝑥-axis	NOUN
cana-1540	98	17	with	with	ADP
cana-1540	98	18	wave	wave	NOUN
cana-1540	98	19	speed	speed	NOUN
cana-1540	98	20	𝑅𝑒(𝑐	𝑅𝑒(𝑐	NOUN
cana-1540	98	21	)	)	PUNCT
cana-1540	98	22	=	=	SYM
cana-1540	98	23	𝑉	𝑉	PROPN
cana-1540	98	24	>	>	X
cana-1540	98	25	0and	0and	PROPN
cana-1540	98	26	𝐼𝑚(𝑐	𝐼𝑚(𝑐	NOUN
cana-1540	98	27	)	)	PUNCT
cana-1540	98	28	≤	≤	NOUN
cana-1540	98	29	0	0	NUM
cana-1540	98	30	.	.	PUNCT
cana-1540	99	1	using	use	VERB
cana-1540	99	2	(	(	PUNCT
cana-1540	99	3	15	15	NUM
cana-1540	99	4	)	)	PUNCT
cana-1540	99	5	in	in	ADP
cana-1540	99	6	the	the	DET
cana-1540	99	7	equations	equation	NOUN
cana-1540	99	8	(	(	PUNCT
cana-1540	99	9	11	11	NUM
cana-1540	99	10	)	)	PUNCT
cana-1540	99	11	–	–	PUNCT
cana-1540	99	12	(	(	PUNCT
cana-1540	99	13	14	14	NUM
cana-1540	99	14	)	)	PUNCT
cana-1540	99	15	,	,	PUNCT
cana-1540	99	16	we	we	PRON
cana-1540	99	17	have	have	VERB
cana-1540	99	18	[	[	X
cana-1540	99	19	𝐷4	𝐷4	NOUN
cana-1540	99	20	−	−	NOUN
cana-1540	100	1	𝐴𝐷2	𝐴𝐷2	PROPN
cana-1540	101	1	+	+	CCONJ
cana-1540	101	2	𝐵](𝜙1̅̅̅̅	𝐵](𝜙1̅̅̅̅	PROPN
cana-1540	101	3	(	(	PUNCT
cana-1540	101	4	𝑦	𝑦	NOUN
cana-1540	101	5	)	)	PUNCT
cana-1540	101	6	,	,	PUNCT
cana-1540	101	7	�	�	NOUN
cana-1540	101	8	̅	̅	NOUN
cana-1540	101	9	�	�	NOUN
cana-1540	101	10	(𝑦	(𝑦	NOUN
cana-1540	101	11	)	)	PUNCT
cana-1540	101	12	)	)	PUNCT
cana-1540	102	1	=	=	SYM
cana-1540	102	2	0	0	NUM
cana-1540	102	3	(	(	PUNCT
cana-1540	102	4	16	16	NUM
cana-1540	102	5	)	)	PUNCT
cana-1540	102	6	[	[	X
cana-1540	102	7	𝐷4	𝐷4	NOUN
cana-1540	102	8	−	−	PROPN
cana-1540	102	9	𝐴′𝐷2	𝐴′𝐷2	NOUN
cana-1540	102	10	+	+	CCONJ
cana-1540	102	11	𝐵′](𝜓1̅̅̅̅	𝐵′](𝜓1̅̅̅̅	PROPN
cana-1540	102	12	(	(	PUNCT
cana-1540	102	13	𝑦	𝑦	NOUN
cana-1540	102	14	)	)	PUNCT
cana-1540	102	15	,	,	PUNCT
cana-1540	102	16	�	�	NOUN
cana-1540	102	17	̅	̅	NOUN
cana-1540	102	18	�	�	NOUN
cana-1540	102	19	(𝑦	(𝑦	NOUN
cana-1540	102	20	)	)	PUNCT
cana-1540	102	21	)	)	PUNCT
cana-1540	103	1	=	=	SYM
cana-1540	103	2	0	0	NUM
cana-1540	103	3	(	(	PUNCT
cana-1540	103	4	17	17	NUM
cana-1540	103	5	)	)	PUNCT
cana-1540	103	6	here	here	ADV
cana-1540	103	7	𝐷	𝐷	PROPN
cana-1540	103	8	=	=	PUNCT
cana-1540	103	9	𝑑	𝑑	PROPN
cana-1540	103	10	𝑑𝑦	𝑑𝑦	NOUN
cana-1540	103	11	,	,	PUNCT
cana-1540	103	12	𝐴	𝐴	PROPN
cana-1540	103	13	=	=	PUNCT
cana-1540	103	14	𝐾2	𝐾2	NOUN
cana-1540	104	1	[	[	X
cana-1540	104	2	2	2	NUM
cana-1540	104	3	−	−	NOUN
cana-1540	104	4	𝑐2(1+𝐴2	𝑐2(1+𝐴2	SYM
cana-1540	104	5	+	+	NUM
cana-1540	104	6	𝐴1	𝐴1	PROPN
cana-1540	104	7	𝑐1	𝑐1	NOUN
cana-1540	104	8	2	2	NUM
cana-1540	104	9	)	)	PUNCT
cana-1540	104	10	𝐴1	𝐴1	PROPN
cana-1540	104	11	]	]	PUNCT
cana-1540	104	12	,	,	PUNCT
cana-1540	104	13	𝐵	𝐵	NOUN
cana-1540	104	14	=	=	NOUN
cana-1540	104	15	𝐾4	𝐾4	NOUN
cana-1540	104	16	[	[	PUNCT
cana-1540	104	17	𝐴1−𝑐	𝐴1−𝑐	NOUN
cana-1540	104	18	2(1+𝐴2	2(1+𝐴2	NOUN
cana-1540	104	19	+	+	NUM
cana-1540	104	20	𝐴1	𝐴1	PROPN
cana-1540	104	21	𝑐1	𝑐1	NOUN
cana-1540	104	22	2)+	2)+	NUM
cana-1540	104	23	𝑐4	𝑐4	NOUN
cana-1540	104	24	𝑐1	𝑐1	NOUN
cana-1540	104	25	2	2	NUM
cana-1540	104	26	𝐴1	𝐴1	NOUN
cana-1540	104	27	]	]	PUNCT
cana-1540	105	1	𝐴′	𝐴′	PROPN
cana-1540	105	2	=	=	SYM
cana-1540	105	3	𝐾2	𝐾2	NOUN
cana-1540	105	4	(	(	PUNCT
cana-1540	105	5	1	1	NUM
cana-1540	105	6	−	−	NOUN
cana-1540	105	7	𝑐2	𝑐2	NOUN
cana-1540	105	8	𝑐2	𝑐2	NOUN
cana-1540	105	9	2	2	NUM
cana-1540	105	10	)	)	PUNCT
cana-1540	105	11	+	+	SYM
cana-1540	105	12	𝐾	𝐾	PROPN
cana-1540	105	13	2	2	NUM
cana-1540	105	14	−	−	NOUN
cana-1540	105	15	𝐾2𝑐2𝜌𝑗	𝐾2𝑐2𝜌𝑗	PROPN
cana-1540	105	16	𝛾	𝛾	ADP
cana-1540	105	17	+	+	ADJ
cana-1540	105	18	2𝑘∗	2𝑘∗	NUM
cana-1540	105	19	𝛾	𝛾	ADP
cana-1540	105	20	−	−	NOUN
cana-1540	105	21	𝑘∗2	𝑘∗2	ADJ
cana-1540	105	22	𝛾(𝜇	𝛾(𝜇	PROPN
cana-1540	105	23	+	+	CCONJ
cana-1540	105	24	𝐾	𝐾	PROPN
cana-1540	105	25	)	)	PUNCT
cana-1540	105	26	𝐵′	𝐵′	NUM
cana-1540	105	27	=	=	PUNCT
cana-1540	105	28	𝐾2	𝐾2	NOUN
cana-1540	105	29	(	(	PUNCT
cana-1540	105	30	𝐾2	𝐾2	NOUN
cana-1540	105	31	−	−	PROPN
cana-1540	105	32	𝐾2𝑐2𝜌𝑗	𝐾2𝑐2𝜌𝑗	NOUN
cana-1540	105	33	𝛾	𝛾	ADP
cana-1540	105	34	+	+	ADJ
cana-1540	105	35	2𝑘∗	2𝑘∗	NUM
cana-1540	105	36	𝛾	𝛾	NOUN
cana-1540	105	37	)	)	PUNCT
cana-1540	105	38	(	(	PUNCT
cana-1540	105	39	1	1	NUM
cana-1540	105	40	−	−	NOUN
cana-1540	105	41	𝑐2	𝑐2	NOUN
cana-1540	105	42	𝑐2	𝑐2	NOUN
cana-1540	105	43	2	2	NUM
cana-1540	105	44	)	)	PUNCT
cana-1540	105	45	−	−	NOUN
cana-1540	106	1	𝐾2𝑘∗2	𝐾2𝑘∗2	PROPN
cana-1540	106	2	𝛾(𝜇	𝛾(𝜇	PROPN
cana-1540	106	3	+	+	CCONJ
cana-1540	106	4	𝐾	𝐾	PROPN
cana-1540	106	5	)	)	PUNCT
cana-1540	106	6	𝑐1	𝑐1	NOUN
cana-1540	106	7	2	2	NUM
cana-1540	106	8	=	=	SYM
cana-1540	106	9	𝜆∗+2𝜇∗+𝑘∗	𝜆∗+2𝜇∗+𝑘∗	PART
cana-1540	106	10	𝜌	𝜌	X
cana-1540	106	11	,	,	PUNCT
cana-1540	106	12	𝑐2	𝑐2	NOUN
cana-1540	106	13	2	2	NUM
cana-1540	106	14	=	=	SYM
cana-1540	106	15	𝜇∗+𝑘∗	𝜇∗+𝑘∗	ADJ
cana-1540	106	16	𝜌	𝜌	X
cana-1540	106	17	,	,	PUNCT
cana-1540	106	18	𝜏∗	𝜏∗	NOUN
cana-1540	106	19	=	=	SYM
cana-1540	106	20	𝜏0	𝜏0	PROPN
cana-1540	106	21	+	+	CCONJ
cana-1540	106	22	𝑖	𝑖	PROPN
cana-1540	106	23	𝜔	𝜔	NOUN
cana-1540	106	24	,	,	PUNCT
cana-1540	106	25	𝐴1	𝐴1	PROPN
cana-1540	106	26	=	=	PUNCT
cana-1540	106	27	𝐾∗	𝐾∗	ADP
cana-1540	107	1	𝜌𝐶∗𝜏∗	𝜌𝐶∗𝜏∗	NOUN
cana-1540	107	2	,	,	PUNCT
cana-1540	107	3	𝐴2	𝐴2	PROPN
cana-1540	107	4	=	=	PRON
cana-1540	107	5	𝜈2𝑇0	𝜈2𝑇0	PROPN
cana-1540	107	6	𝜌2𝑐1	𝜌2𝑐1	X
cana-1540	107	7	2𝐶∗	2𝐶∗	NUM
cana-1540	107	8	(	(	PUNCT
cana-1540	107	9	𝜆∗	𝜆∗	PROPN
cana-1540	107	10	,	,	PUNCT
cana-1540	107	11	𝜇∗	𝜇∗	NOUN
cana-1540	107	12	,	,	PUNCT
cana-1540	107	13	α∗	α∗	NOUN
cana-1540	107	14	,	,	PUNCT
cana-1540	107	15	β∗	β∗	PROPN
cana-1540	107	16	,	,	PUNCT
cana-1540	107	17	γ∗	γ∗	PROPN
cana-1540	107	18	,	,	PUNCT
cana-1540	107	19	𝜅∗	𝜅∗	PROPN
cana-1540	107	20	)	)	PUNCT
cana-1540	107	21	=	=	PUNCT
cana-1540	108	1	(	(	PUNCT
cana-1540	108	2	𝜆	𝜆	NOUN
cana-1540	108	3	,	,	PUNCT
cana-1540	108	4	𝜇	𝜇	ADP
cana-1540	108	5	,	,	PUNCT
cana-1540	108	6	α	α	PROPN
cana-1540	108	7	,	,	PUNCT
cana-1540	108	8	β	β	X
cana-1540	108	9	,	,	PUNCT
cana-1540	108	10	γ	γ	PROPN
cana-1540	108	11	,	,	PUNCT
cana-1540	108	12	𝜅	𝜅	NOUN
cana-1540	108	13	)	)	PUNCT
cana-1540	108	14	∗	∗	NOUN
cana-1540	108	15	(	(	PUNCT
cana-1540	108	16	1	1	NUM
cana-1540	108	17	−	−	NOUN
cana-1540	108	18	𝜄𝑄𝑖	𝜄𝑄𝑖	NOUN
cana-1540	108	19	)	)	PUNCT
cana-1540	108	20	(	(	PUNCT
cana-1540	108	21	𝑖	𝑖	SYM
cana-1540	108	22	=	=	SYM
cana-1540	108	23	1	1	NUM
cana-1540	108	24	−	−	NUM
cana-1540	108	25	6	6	NUM
cana-1540	108	26	)	)	PUNCT
cana-1540	108	27	𝑄1	𝑄1	NOUN
cana-1540	108	28	=	=	SYM
cana-1540	108	29	𝜔	𝜔	PROPN
cana-1540	108	30	(	(	PUNCT
cana-1540	108	31	𝜆𝜈	𝜆𝜈	NOUN
cana-1540	108	32	𝜆	𝜆	X
cana-1540	108	33	)	)	PUNCT
cana-1540	109	1	,	,	PUNCT
cana-1540	109	2	𝑄2	𝑄2	X
cana-1540	109	3	=	=	PUNCT
cana-1540	110	1	𝜔	𝜔	X
cana-1540	110	2	(	(	PUNCT
cana-1540	110	3	𝜇𝜈	𝜇𝜈	ADP
cana-1540	110	4	𝜇	𝜇	NOUN
cana-1540	110	5	)	)	PUNCT
cana-1540	110	6	,	,	PUNCT
cana-1540	110	7	𝑄3	𝑄3	X
cana-1540	110	8	=	=	PUNCT
cana-1540	110	9	𝜔	𝜔	X
cana-1540	110	10	(	(	PUNCT
cana-1540	110	11	𝛼𝜈	𝛼𝜈	ADP
cana-1540	110	12	𝛼	𝛼	NOUN
cana-1540	110	13	)	)	PUNCT
cana-1540	110	14	,	,	PUNCT
cana-1540	110	15	𝑄4	𝑄4	X
cana-1540	110	16	=	=	PUNCT
cana-1540	110	17	𝜔	𝜔	PROPN
cana-1540	110	18	(	(	PUNCT
cana-1540	110	19	𝛽𝜈	𝛽𝜈	ADV
cana-1540	110	20	𝛽	𝛽	NOUN
cana-1540	110	21	)	)	PUNCT
cana-1540	110	22	,	,	PUNCT
cana-1540	110	23	𝑄5	𝑄5	PROPN
cana-1540	111	1	=	=	PUNCT
cana-1540	111	2	𝜔	𝜔	PROPN
cana-1540	111	3	(	(	PUNCT
cana-1540	111	4	𝛾𝜈	𝛾𝜈	NOUN
cana-1540	111	5	𝛾	𝛾	PROPN
cana-1540	111	6	)	)	PUNCT
cana-1540	111	7	,	,	PUNCT
cana-1540	111	8	𝑄6	𝑄6	NOUN
cana-1540	111	9	=	=	SYM
cana-1540	111	10	𝜔	𝜔	PROPN
cana-1540	111	11	(	(	PUNCT
cana-1540	111	12	𝜅𝜈	𝜅𝜈	ADP
cana-1540	111	13	𝜅	𝜅	PROPN
cana-1540	111	14	)	)	PUNCT
cana-1540	111	15	,	,	PUNCT
cana-1540	111	16	(	(	PUNCT
cana-1540	111	17	18	18	NUM
cana-1540	111	18	)	)	PUNCT
cana-1540	111	19	using	use	VERB
cana-1540	111	20	the	the	DET
cana-1540	111	21	radiation	radiation	NOUN
cana-1540	111	22	conditions	condition	NOUN
cana-1540	111	23	𝜙1̅̅̅̅	𝜙1̅̅̅̅	PROPN
cana-1540	111	24	(	(	PUNCT
cana-1540	111	25	𝑦	𝑦	NOUN
cana-1540	111	26	)	)	PUNCT
cana-1540	111	27	,	,	PUNCT
cana-1540	111	28	𝜓1̅̅̅̅	𝜓1̅̅̅̅	PROPN
cana-1540	111	29	(	(	PUNCT
cana-1540	111	30	𝑦	𝑦	NOUN
cana-1540	111	31	)	)	PUNCT
cana-1540	111	32	,	,	PUNCT
cana-1540	111	33	�	�	NOUN
cana-1540	111	34	̅	̅	NOUN
cana-1540	111	35	�	�	NOUN
cana-1540	111	36	(𝑦	(𝑦	NOUN
cana-1540	111	37	)	)	PUNCT
cana-1540	111	38	,	,	PUNCT
cana-1540	111	39	�	�	NOUN
cana-1540	111	40	̅	̅	NOUN
cana-1540	111	41	�	�	NOUN
cana-1540	111	42	(𝑦	(𝑦	NOUN
cana-1540	111	43	)	)	PUNCT
cana-1540	111	44	→	→	SYM
cana-1540	111	45	0	0	NUM
cana-1540	111	46	as	as	ADP
cana-1540	111	47	𝑦	𝑦	X
cana-1540	111	48	→	→	SYM
cana-1540	111	49	∞	∞	NUM
cana-1540	111	50	on	on	ADP
cana-1540	111	51	the	the	DET
cana-1540	111	52	general	general	ADJ
cana-1540	111	53	solutions	solution	NOUN
cana-1540	111	54	of	of	ADP
cana-1540	111	55	the	the	DET
cana-1540	111	56	equations	equation	NOUN
cana-1540	111	57	(	(	PUNCT
cana-1540	111	58	16	16	NUM
cana-1540	111	59	)	)	PUNCT
cana-1540	111	60	and	and	CCONJ
cana-1540	111	61	(	(	PUNCT
cana-1540	111	62	17	17	NUM
cana-1540	111	63	)	)	PUNCT
cana-1540	111	64	and	and	CCONJ
cana-1540	111	65	using	use	VERB
cana-1540	111	66	(	(	PUNCT
cana-1540	111	67	15	15	NUM
cana-1540	111	68	)	)	PUNCT
cana-1540	111	69	,	,	PUNCT
cana-1540	111	70	we	we	PRON
cana-1540	111	71	obtained	obtain	VERB
cana-1540	111	72	communications	communication	NOUN
cana-1540	111	73	on	on	ADP
cana-1540	111	74	applied	apply	VERB
cana-1540	111	75	nonlinear	nonlinear	ADJ
cana-1540	111	76	analysis	analysis	NOUN
cana-1540	111	77	issn	issn	NOUN
cana-1540	111	78	:	:	PUNCT
cana-1540	111	79	1074	1074	NUM
cana-1540	111	80	-	-	PUNCT
cana-1540	111	81	133x	133x	NUM
cana-1540	111	82	vol	vol	NOUN
cana-1540	111	83	31	31	NUM
cana-1540	111	84	no	no	NOUN
cana-1540	111	85	.	.	PUNCT
cana-1540	112	1	8s	8s	PROPN
cana-1540	112	2	(	(	PUNCT
cana-1540	112	3	2024	2024	NUM
cana-1540	112	4	)	)	PUNCT
cana-1540	112	5	488	488	NUM
cana-1540	112	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	112	7	𝜙1	𝜙1	NOUN
cana-1540	112	8	=	=	PUNCT
cana-1540	112	9	(	(	PUNCT
cana-1540	112	10	𝐵1𝑒	𝐵1𝑒	PROPN
cana-1540	112	11	−𝐾𝑏1𝑦	−𝐾𝑏1𝑦	PROPN
cana-1540	112	12	+	+	CCONJ
cana-1540	112	13	𝐵2𝑒	𝐵2𝑒	PROPN
cana-1540	112	14	−𝐾𝑏2𝑦)𝑒𝑖𝐾(𝑥−𝑐𝑡	−𝐾𝑏2𝑦)𝑒𝑖𝐾(𝑥−𝑐𝑡	ADJ
cana-1540	112	15	)	)	PUNCT
cana-1540	112	16	(	(	PUNCT
cana-1540	112	17	19	19	NUM
cana-1540	112	18	)	)	PUNCT
cana-1540	112	19	𝜓1	𝜓1	NOUN
cana-1540	112	20	=	=	PUNCT
cana-1540	112	21	(	(	PUNCT
cana-1540	112	22	𝐵3𝑒	𝐵3𝑒	PROPN
cana-1540	112	23	−𝐾𝑏3𝑦	−𝐾𝑏3𝑦	PROPN
cana-1540	112	24	+	+	CCONJ
cana-1540	112	25	𝐵4𝑒	𝐵4𝑒	PROPN
cana-1540	112	26	−𝐾𝑏4𝑦)𝑒𝑖𝐾(𝑥−𝑐𝑡	−𝐾𝑏4𝑦)𝑒𝑖𝐾(𝑥−𝑐𝑡	NOUN
cana-1540	112	27	)	)	PUNCT
cana-1540	112	28	(	(	PUNCT
cana-1540	112	29	20	20	X
cana-1540	112	30	)	)	PUNCT
cana-1540	112	31	𝑇	𝑇	NOUN
cana-1540	112	32	=	=	SYM
cana-1540	112	33	(	(	PUNCT
cana-1540	112	34	𝑟1𝐵1𝑒	𝑟1𝐵1𝑒	ADJ
cana-1540	112	35	−𝐾𝑏1𝑦	−𝐾𝑏1𝑦	PROPN
cana-1540	112	36	+	+	CCONJ
cana-1540	112	37	𝑟2𝐵2𝑒	𝑟2𝐵2𝑒	NOUN
cana-1540	112	38	−𝐾𝑏2𝑦)𝑒𝑖𝐾(𝑥−𝑐𝑡	−𝐾𝑏2𝑦)𝑒𝑖𝐾(𝑥−𝑐𝑡	ADJ
cana-1540	112	39	)	)	PUNCT
cana-1540	112	40	(	(	PUNCT
cana-1540	112	41	21	21	NUM
cana-1540	112	42	)	)	PUNCT
cana-1540	112	43	𝜙	𝜙	NOUN
cana-1540	112	44	=	=	SYM
cana-1540	112	45	(	(	PUNCT
cana-1540	112	46	𝑟3𝐵3𝑒	𝑟3𝐵3𝑒	NOUN
cana-1540	112	47	−𝐾𝑏3𝑦	−𝐾𝑏3𝑦	PROPN
cana-1540	112	48	+	+	CCONJ
cana-1540	112	49	𝑟4𝐵4𝑒	𝑟4𝐵4𝑒	NUM
cana-1540	112	50	−𝐾𝑏4𝑦)𝑒𝑖𝐾(𝑥−𝑐𝑡	−𝐾𝑏4𝑦)𝑒𝑖𝐾(𝑥−𝑐𝑡	NOUN
cana-1540	112	51	)	)	PUNCT
cana-1540	112	52	(	(	PUNCT
cana-1540	112	53	22	22	NUM
cana-1540	112	54	)	)	PUNCT
cana-1540	112	55	where	where	SCONJ
cana-1540	112	56	𝑏1	𝑏1	ADJ
cana-1540	112	57	2	2	NUM
cana-1540	112	58	+	+	CCONJ
cana-1540	112	59	𝑏2	𝑏2	PROPN
cana-1540	112	60	2	2	PROPN
cana-1540	112	61	=	=	SYM
cana-1540	112	62	𝐴	𝐴	PROPN
cana-1540	112	63	𝐾2	𝐾2	NOUN
cana-1540	112	64	,	,	PUNCT
cana-1540	112	65	𝑏1	𝑏1	NOUN
cana-1540	112	66	2𝑏2	2𝑏2	NUM
cana-1540	112	67	2	2	NUM
cana-1540	112	68	=	=	SYM
cana-1540	112	69	𝐵	𝐵	NOUN
cana-1540	112	70	𝐾4	𝐾4	NOUN
cana-1540	112	71	,	,	PUNCT
cana-1540	112	72	𝑏3	𝑏3	NOUN
cana-1540	112	73	2	2	NUM
cana-1540	112	74	+	+	NUM
cana-1540	112	75	𝑏4	𝑏4	PROPN
cana-1540	112	76	2	2	NUM
cana-1540	112	77	=	=	SYM
cana-1540	112	78	𝐴′	𝐴′	ADJ
cana-1540	112	79	𝐾2	𝐾2	NOUN
cana-1540	112	80	,	,	PUNCT
cana-1540	112	81	𝑏3	𝑏3	NOUN
cana-1540	112	82	2𝑏4	2𝑏4	NUM
cana-1540	112	83	2	2	NUM
cana-1540	112	84	=	=	SYM
cana-1540	112	85	𝐵′	𝐵′	NUM
cana-1540	112	86	𝐾4	𝐾4	NOUN
cana-1540	112	87	(	(	PUNCT
cana-1540	112	88	23	23	NUM
cana-1540	112	89	)	)	PUNCT
cana-1540	112	90	{	{	PUNCT
cana-1540	112	91	𝑟𝑖	𝑟𝑖	ADV
cana-1540	112	92	=	=	SYM
cana-1540	112	93	𝐾2	𝐾2	NOUN
cana-1540	112	94	[	[	PUNCT
cana-1540	112	95	(	(	PUNCT
cana-1540	112	96	𝑏𝑖	𝑏𝑖	ADP
cana-1540	112	97	2	2	NUM
cana-1540	112	98	−	−	PROPN
cana-1540	112	99	1)(𝜆∗	1)(𝜆∗	NUM
cana-1540	112	100	+	+	CCONJ
cana-1540	112	101	2𝜇∗	2𝜇∗	NUM
cana-1540	112	102	+	+	CCONJ
cana-1540	112	103	𝑘∗	𝑘∗	ADJ
cana-1540	112	104	)	)	PUNCT
cana-1540	112	105	+	+	CCONJ
cana-1540	112	106	𝜌𝑐2	𝜌𝑐2	ADJ
cana-1540	112	107	𝜈	𝜈	X
cana-1540	112	108	]	]	PUNCT
cana-1540	112	109	,	,	PUNCT
cana-1540	112	110	(	(	PUNCT
cana-1540	112	111	𝑖	𝑖	SYM
cana-1540	112	112	=	=	SYM
cana-1540	112	113	1,2	1,2	NUM
cana-1540	112	114	)	)	PUNCT
cana-1540	112	115	𝑟𝑗	𝑟𝑗	ADP
cana-1540	112	116	=	=	SYM
cana-1540	112	117	𝐾2(𝜇∗	𝐾2(𝜇∗	PROPN
cana-1540	112	118	+	+	CCONJ
cana-1540	112	119	𝑘∗	𝑘∗	ADJ
cana-1540	112	120	)	)	PUNCT
cana-1540	112	121	𝑘∗	𝑘∗	NOUN
cana-1540	113	1	[	[	X
cana-1540	113	2	1	1	NUM
cana-1540	113	3	−	−	NOUN
cana-1540	113	4	𝑐2	𝑐2	NOUN
cana-1540	113	5	𝑐2	𝑐2	NOUN
cana-1540	113	6	2	2	NUM
cana-1540	113	7	−	−	NOUN
cana-1540	113	8	𝑏𝑗	𝑏𝑗	NOUN
cana-1540	113	9	2	2	NUM
cana-1540	113	10	]	]	PUNCT
cana-1540	113	11	,	,	PUNCT
cana-1540	113	12	(	(	PUNCT
cana-1540	113	13	𝑗	𝑗	NOUN
cana-1540	113	14	=	=	SYM
cana-1540	113	15	3,4	3,4	NUM
cana-1540	113	16	)	)	PUNCT
cana-1540	113	17	(	(	PUNCT
cana-1540	113	18	24	24	NUM
cana-1540	113	19	)	)	PUNCT
cana-1540	113	20	and𝐵1	and𝐵1	PART
cana-1540	113	21	,	,	PUNCT
cana-1540	113	22	𝐵2	𝐵2	NOUN
cana-1540	113	23	,	,	PUNCT
cana-1540	113	24	𝐵3	𝐵3	PROPN
cana-1540	113	25	and	and	CCONJ
cana-1540	113	26	𝐵4	𝐵4	NOUN
cana-1540	113	27	are	be	AUX
cana-1540	113	28	arbitrary	arbitrary	ADJ
cana-1540	113	29	constants	constant	NOUN
cana-1540	113	30	.	.	PUNCT
cana-1540	114	1	5	5	X
cana-1540	114	2	.	.	NOUN
cana-1540	114	3	boundary	boundary	ADJ
cana-1540	114	4	conditions	condition	NOUN
cana-1540	114	5	and	and	CCONJ
cana-1540	114	6	secular	secular	ADJ
cana-1540	114	7	equation	equation	NOUN
cana-1540	114	8	the	the	DET
cana-1540	114	9	general	general	ADJ
cana-1540	114	10	form	form	NOUN
cana-1540	114	11	of	of	ADP
cana-1540	114	12	impedance	impedance	NOUN
cana-1540	114	13	boundary	boundary	ADJ
cana-1540	114	14	conditions	condition	NOUN
cana-1540	114	15	in	in	ADP
cana-1540	114	16	two	two	NUM
cana-1540	114	17	dimensions	dimension	NOUN
cana-1540	114	18	in	in	ADP
cana-1540	114	19	terms	term	NOUN
cana-1540	114	20	of	of	ADP
cana-1540	114	21	displacements	displacement	NOUN
cana-1540	114	22	and	and	CCONJ
cana-1540	114	23	stresses	stress	NOUN
cana-1540	114	24	given	give	VERB
cana-1540	114	25	by	by	ADP
cana-1540	114	26	malischewsky	malischewsky	NOUN
cana-1540	114	27	(	(	PUNCT
cana-1540	114	28	1988	1988	NUM
cana-1540	114	29	)	)	PUNCT
cana-1540	114	30	can	can	AUX
cana-1540	114	31	be	be	AUX
cana-1540	114	32	written	write	VERB
cana-1540	114	33	as	as	ADP
cana-1540	114	34	𝜎𝑖2	𝜎𝑖2	PROPN
cana-1540	114	35	+	+	CCONJ
cana-1540	114	36	𝜖𝑖𝑢𝑖	𝜖𝑖𝑢𝑖	NOUN
cana-1540	114	37	=	=	SYM
cana-1540	114	38	0	0	NUM
cana-1540	114	39	,	,	PUNCT
cana-1540	114	40	for	for	ADP
cana-1540	114	41	𝑦	𝑦	NOUN
cana-1540	114	42	=	=	SYM
cana-1540	114	43	0,where	0,where	ADP
cana-1540	114	44	𝜖𝑖are	𝜖𝑖are	VERB
cana-1540	114	45	the	the	DET
cana-1540	114	46	impedance	impedance	NOUN
cana-1540	114	47	parameters	parameter	NOUN
cana-1540	114	48	and	and	CCONJ
cana-1540	114	49	have	have	VERB
cana-1540	114	50	the	the	DET
cana-1540	114	51	dimensions	dimension	NOUN
cana-1540	114	52	of	of	ADP
cana-1540	114	53	stress	stress	NOUN
cana-1540	114	54	/	/	SYM
cana-1540	114	55	length	length	NOUN
cana-1540	114	56	.	.	PUNCT
cana-1540	115	1	for	for	ADP
cana-1540	115	2	elastic	elastic	ADJ
cana-1540	115	3	half	half	NOUN
cana-1540	115	4	space	space	NOUN
cana-1540	115	5	,	,	PUNCT
cana-1540	115	6	godoy	godoy	PROPN
cana-1540	115	7	,	,	PUNCT
cana-1540	115	8	duran	duran	NOUN
cana-1540	115	9	and	and	CCONJ
cana-1540	115	10	nedelec	nedelec	PROPN
cana-1540	115	11	(	(	PUNCT
cana-1540	115	12	2012	2012	NUM
cana-1540	115	13	)	)	PUNCT
cana-1540	115	14	,	,	PUNCT
cana-1540	115	15	expressed	express	VERB
cana-1540	115	16	𝜖𝑖as𝜖𝑖	𝜖𝑖as𝜖𝑖	NOUN
cana-1540	115	17	=	=	SYM
cana-1540	115	18	𝜔𝑍𝑖.	𝜔𝑍𝑖.	PROPN
cana-1540	115	19	here	here	ADV
cana-1540	116	1	𝑍𝑖	𝑍𝑖	PROPN
cana-1540	116	2	are	be	AUX
cana-1540	116	3	impedance	impedance	NOUN
cana-1540	116	4	real	real	ADV
cana-1540	116	5	valued	value	VERB
cana-1540	116	6	parameters	parameter	NOUN
cana-1540	116	7	,	,	PUNCT
cana-1540	116	8	has	have	AUX
cana-1540	116	9	dimensions	dimension	NOUN
cana-1540	116	10	of	of	ADP
cana-1540	116	11	stress	stress	NOUN
cana-1540	116	12	/	/	SYM
cana-1540	116	13	velocity	velocity	NOUN
cana-1540	116	14	and	and	CCONJ
cana-1540	116	15	𝜔	𝜔	AUX
cana-1540	116	16	=	=	PRON
cana-1540	116	17	𝑘𝑐is	𝑘𝑐is	PROPN
cana-1540	116	18	the	the	DET
cana-1540	116	19	circular	circular	ADJ
cana-1540	116	20	frequency	frequency	NOUN
cana-1540	116	21	.	.	PUNCT
cana-1540	117	1	here	here	ADV
cana-1540	117	2	the	the	DET
cana-1540	117	3	impedance	impedance	NOUN
cana-1540	117	4	boundary	boundary	ADJ
cana-1540	117	5	conditions	condition	NOUN
cana-1540	117	6	at	at	ADP
cana-1540	117	7	the	the	DET
cana-1540	117	8	surface	surface	NOUN
cana-1540	117	9	𝑦	𝑦	NOUN
cana-1540	117	10	=	=	SYM
cana-1540	117	11	0of	0of	NOUN
cana-1540	117	12	a	a	DET
cana-1540	117	13	micropolar	micropolar	ADJ
cana-1540	117	14	thermoelastic	thermoelastic	ADJ
cana-1540	117	15	solid	solid	NOUN
cana-1540	117	16	are	be	AUX
cana-1540	117	17	consider	consider	VERB
cana-1540	117	18	as	as	ADP
cana-1540	117	19	𝜎2𝑖	𝜎2𝑖	X
cana-1540	117	20	+	+	CCONJ
cana-1540	117	21	𝜔𝑍𝑖𝑢𝑖	𝜔𝑍𝑖𝑢𝑖	PROPN
cana-1540	117	22	=	=	SYM
cana-1540	117	23	0	0	NUM
cana-1540	117	24	,	,	PUNCT
cana-1540	117	25	which	which	PRON
cana-1540	117	26	can	can	AUX
cana-1540	117	27	be	be	AUX
cana-1540	117	28	written	write	VERB
cana-1540	117	29	as	as	ADP
cana-1540	117	30	𝜎21	𝜎21	NOUN
cana-1540	117	31	+	+	CCONJ
cana-1540	117	32	𝜔𝑍1𝑢	𝜔𝑍1𝑢	NOUN
cana-1540	117	33	=	=	SYM
cana-1540	117	34	0	0	NUM
cana-1540	117	35	,	,	PUNCT
cana-1540	117	36	𝜎22	𝜎22	NOUN
cana-1540	117	37	+	+	CCONJ
cana-1540	117	38	𝜔𝑍2𝑣	𝜔𝑍2𝑣	X
cana-1540	117	39	=	=	SYM
cana-1540	117	40	0	0	NUM
cana-1540	117	41	,	,	PUNCT
cana-1540	117	42	𝑚23	𝑚23	NOUN
cana-1540	117	43	+	+	CCONJ
cana-1540	117	44	𝜔𝑍3𝜙	𝜔𝑍3𝜙	NOUN
cana-1540	117	45	=	=	SYM
cana-1540	117	46	0	0	NUM
cana-1540	117	47	,	,	PUNCT
cana-1540	117	48	𝜕𝑇	𝜕𝑇	PROPN
cana-1540	117	49	𝜕𝑦	𝜕𝑦	X
cana-1540	118	1	+	+	PUNCT
cana-1540	118	2	ℎ𝑇	ℎ𝑇	NOUN
cana-1540	118	3	=	=	SYM
cana-1540	118	4	0	0	PUNCT
cana-1540	118	5	(	(	PUNCT
cana-1540	118	6	25	25	NUM
cana-1540	118	7	)	)	PUNCT
cana-1540	118	8	where	where	SCONJ
cana-1540	118	9	ℎ	ℎ	PROPN
cana-1540	118	10	→	→	SYM
cana-1540	118	11	0	0	NUM
cana-1540	118	12	corresponds	correspond	NOUN
cana-1540	118	13	to	to	PART
cana-1540	118	14	thermally	thermally	ADV
cana-1540	118	15	insulated	insulate	VERB
cana-1540	118	16	surface	surface	NOUN
cana-1540	118	17	and	and	CCONJ
cana-1540	118	18	ℎ	ℎ	PROPN
cana-1540	118	19	→	→	SYM
cana-1540	118	20	∞	∞	NUM
cana-1540	118	21	corresponds	correspond	VERB
cana-1540	118	22	to	to	ADP
cana-1540	118	23	isothermal	isothermal	ADJ
cana-1540	118	24	surface	surface	NOUN
cana-1540	118	25	.	.	PUNCT
cana-1540	119	1	imposing	impose	VERB
cana-1540	119	2	boundary	boundary	ADJ
cana-1540	119	3	conditions	condition	NOUN
cana-1540	119	4	(	(	PUNCT
cana-1540	119	5	25	25	NUM
cana-1540	119	6	)	)	PUNCT
cana-1540	119	7	on	on	ADP
cana-1540	119	8	the	the	DET
cana-1540	119	9	surface	surface	NOUN
cana-1540	119	10	𝑦	𝑦	NOUN
cana-1540	119	11	=	=	SYM
cana-1540	119	12	0	0	NUM
cana-1540	119	13	,	,	PUNCT
cana-1540	119	14	we	we	PRON
cana-1540	119	15	get	get	VERB
cana-1540	119	16	a	a	DET
cana-1540	119	17	system	system	NOUN
cana-1540	119	18	of	of	ADP
cana-1540	119	19	four	four	NUM
cana-1540	119	20	homogeneous	homogeneous	ADJ
cana-1540	119	21	equations	equation	NOUN
cana-1540	119	22	.	.	PUNCT
cana-1540	120	1	for	for	ADP
cana-1540	120	2	a	a	DET
cana-1540	120	3	non	non	ADJ
cana-1540	120	4	-	-	ADJ
cana-1540	120	5	trivial	trivial	ADJ
cana-1540	120	6	solution	solution	NOUN
cana-1540	120	7	,	,	PUNCT
cana-1540	120	8	the	the	DET
cana-1540	120	9	determinant	determinant	NOUN
cana-1540	120	10	of	of	ADP
cana-1540	120	11	the	the	DET
cana-1540	120	12	coefficients	coefficient	NOUN
cana-1540	120	13	𝐵1	𝐵1	NOUN
cana-1540	120	14	,	,	PUNCT
cana-1540	120	15	𝐵2	𝐵2	NOUN
cana-1540	120	16	,	,	PUNCT
cana-1540	120	17	𝐵3	𝐵3	PROPN
cana-1540	120	18	and	and	CCONJ
cana-1540	120	19	𝐵4	𝐵4	NOUN
cana-1540	120	20	must	must	AUX
cana-1540	120	21	vanishes	vanish	VERB
cana-1540	120	22	which	which	PRON
cana-1540	120	23	yields	yield	VERB
cana-1540	120	24	the	the	DET
cana-1540	120	25	following	follow	VERB
cana-1540	120	26	secular	secular	ADJ
cana-1540	120	27	equation	equation	NOUN
cana-1540	120	28	for	for	ADP
cana-1540	120	29	the	the	DET
cana-1540	120	30	velocity	velocity	NOUN
cana-1540	120	31	of	of	ADP
cana-1540	120	32	propagation	propagation	NOUN
cana-1540	120	33	of	of	ADP
cana-1540	120	34	the	the	DET
cana-1540	120	35	rayleigh	rayleigh	PROPN
cana-1540	120	36	waves	wave	NOUN
cana-1540	120	37	𝑚1[𝑇1(𝑙2𝑛4	𝑚1[𝑇1(𝑙2𝑛4	PUNCT
cana-1540	120	38	−	−	NOUN
cana-1540	121	1	𝑛2𝑙4	𝑛2𝑙4	NOUN
cana-1540	121	2	)	)	PUNCT
cana-1540	121	3	−	−	NOUN
cana-1540	121	4	𝑇2(𝑙1𝑛4	𝑇2(𝑙1𝑛4	NOUN
cana-1540	121	5	−	−	PROPN
cana-1540	121	6	𝑛1𝑙4	𝑛1𝑙4	PROPN
cana-1540	121	7	)	)	PUNCT
cana-1540	121	8	]	]	PUNCT
cana-1540	122	1	=	=	PUNCT
cana-1540	122	2	𝑚2[𝑇1(𝑙2𝑛3	𝑚2[𝑇1(𝑙2𝑛3	NOUN
cana-1540	122	3	−	−	X
cana-1540	122	4	𝑛2𝑙3	𝑛2𝑙3	NOUN
cana-1540	122	5	)	)	PUNCT
cana-1540	122	6	−	−	PROPN
cana-1540	122	7	𝑇2(𝑙1𝑛3	𝑇2(𝑙1𝑛3	NOUN
cana-1540	122	8	−	−	NOUN
cana-1540	122	9	𝑛1𝑙3	𝑛1𝑙3	NOUN
cana-1540	122	10	)	)	PUNCT
cana-1540	122	11	]	]	PUNCT
cana-1540	122	12	(	(	PUNCT
cana-1540	122	13	26	26	NUM
cana-1540	122	14	)	)	PUNCT
cana-1540	122	15	where	where	SCONJ
cana-1540	122	16	𝑙𝑖	𝑙𝑖	NOUN
cana-1540	122	17	=	=	SYM
cana-1540	122	18	𝑉1𝑍1	𝑉1𝑍1	NOUN
cana-1540	122	19	∗	∗	VERB
cana-1540	122	20	−	−	PUNCT
cana-1540	123	1	𝑏𝑖	𝑏𝑖	ADP
cana-1540	123	2	−	−	PROPN
cana-1540	123	3	(	(	PUNCT
cana-1540	123	4	1	1	NUM
cana-1540	123	5	+	+	NUM
cana-1540	123	6	𝑘∗	𝑘∗	ADJ
cana-1540	123	7	𝜇	𝜇	NOUN
cana-1540	123	8	)	)	PUNCT
cana-1540	123	9	𝑏𝑖	𝑏𝑖	ADP
cana-1540	123	10	,	,	PUNCT
cana-1540	123	11	(	(	PUNCT
cana-1540	123	12	𝑖	𝑖	SYM
cana-1540	123	13	=	=	SYM
cana-1540	123	14	1,2	1,2	NUM
cana-1540	123	15	)	)	PUNCT
cana-1540	123	16	𝑙𝑗	𝑙𝑗	NOUN
cana-1540	123	17	=	=	PUNCT
cana-1540	123	18	𝑉1𝑍1	𝑉1𝑍1	PROPN
cana-1540	123	19	∗𝑏𝑗	∗𝑏𝑗	NUM
cana-1540	123	20	−	−	PROPN
cana-1540	123	21	1	1	NUM
cana-1540	123	22	−	−	PROPN
cana-1540	123	23	(	(	PUNCT
cana-1540	123	24	1	1	NUM
cana-1540	123	25	+	+	NUM
cana-1540	123	26	𝑘∗	𝑘∗	PROPN
cana-1540	123	27	𝜇∗	𝜇∗	NOUN
cana-1540	123	28	)	)	PUNCT
cana-1540	123	29	(	(	PUNCT
cana-1540	123	30	1	1	NUM
cana-1540	123	31	−	−	NOUN
cana-1540	123	32	𝑐2	𝑐2	NOUN
cana-1540	123	33	𝑐2	𝑐2	NOUN
cana-1540	123	34	2	2	NUM
cana-1540	123	35	)	)	PUNCT
cana-1540	123	36	,	,	PUNCT
cana-1540	123	37	(	(	PUNCT
cana-1540	123	38	𝑗	𝑗	NOUN
cana-1540	123	39	=	=	SYM
cana-1540	123	40	3,4	3,4	NUM
cana-1540	123	41	)	)	PUNCT
cana-1540	123	42	communications	communication	NOUN
cana-1540	123	43	on	on	ADP
cana-1540	123	44	applied	apply	VERB
cana-1540	123	45	nonlinear	nonlinear	ADJ
cana-1540	123	46	analysis	analysis	NOUN
cana-1540	123	47	issn	issn	NOUN
cana-1540	123	48	:	:	PUNCT
cana-1540	123	49	1074	1074	NUM
cana-1540	123	50	-	-	PUNCT
cana-1540	123	51	133x	133x	NUM
cana-1540	123	52	vol	vol	NOUN
cana-1540	123	53	31	31	NUM
cana-1540	123	54	no	no	NOUN
cana-1540	123	55	.	.	PUNCT
cana-1540	124	1	8s	8s	PROPN
cana-1540	124	2	(	(	PUNCT
cana-1540	124	3	2024	2024	NUM
cana-1540	124	4	)	)	PUNCT
cana-1540	124	5	489	489	NUM
cana-1540	124	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	124	7	𝑛𝑖	𝑛𝑖	NOUN
cana-1540	124	8	=	=	SYM
cana-1540	124	9	2	2	NUM
cana-1540	124	10	+	+	CCONJ
cana-1540	124	11	𝑘∗	𝑘∗	PROPN
cana-1540	124	12	𝜇∗	𝜇∗	NOUN
cana-1540	124	13	−	−	PROPN
cana-1540	124	14	𝑉1	𝑉1	NOUN
cana-1540	124	15	2	2	NUM
cana-1540	124	16	−	−	NOUN
cana-1540	124	17	𝑉1𝑍2	𝑉1𝑍2	PROPN
cana-1540	124	18	∗𝑏𝑖	∗𝑏𝑖	PROPN
cana-1540	124	19	,	,	PUNCT
cana-1540	124	20	(	(	PUNCT
cana-1540	124	21	𝑖	𝑖	SYM
cana-1540	124	22	=	=	SYM
cana-1540	124	23	1,2	1,2	NUM
cana-1540	124	24	)	)	PUNCT
cana-1540	124	25	𝑛𝑗	𝑛𝑗	ADP
cana-1540	124	26	=	=	PUNCT
cana-1540	124	27	(	(	PUNCT
cana-1540	124	28	2	2	NUM
cana-1540	124	29	+	+	CCONJ
cana-1540	124	30	𝑘∗	𝑘∗	PROPN
cana-1540	124	31	𝜇∗	𝜇∗	NOUN
cana-1540	124	32	)	)	PUNCT
cana-1540	124	33	𝑏𝑗	𝑏𝑗	PROPN
cana-1540	124	34	−	−	PROPN
cana-1540	124	35	𝑉1𝑍2	𝑉1𝑍2	PROPN
cana-1540	124	36	∗	∗	VERB
cana-1540	124	37	,	,	PUNCT
cana-1540	124	38	(	(	PUNCT
cana-1540	124	39	𝑗	𝑗	NOUN
cana-1540	124	40	=	=	SYM
cana-1540	124	41	3,4	3,4	NUM
cana-1540	124	42	)	)	PUNCT
cana-1540	124	43	𝑚1	𝑚1	NOUN
cana-1540	124	44	=	=	SYM
cana-1540	124	45	(	(	PUNCT
cana-1540	124	46	𝜇	𝜇	ADP
cana-1540	124	47	∗𝑉1𝑍3	∗𝑉1𝑍3	ADJ
cana-1540	124	48	∗	∗	NOUN
cana-1540	124	49	−	−	VERB
cana-1540	124	50	𝛾∗𝑏3	𝛾∗𝑏3	NOUN
cana-1540	124	51	)	)	PUNCT
cana-1540	124	52	(	(	PUNCT
cana-1540	124	53	1	1	NUM
cana-1540	124	54	−	−	NOUN
cana-1540	124	55	𝑐2	𝑐2	NOUN
cana-1540	124	56	𝑐2	𝑐2	NOUN
cana-1540	124	57	2	2	NUM
cana-1540	124	58	−	−	NOUN
cana-1540	124	59	𝑏3	𝑏3	NOUN
cana-1540	124	60	2	2	NUM
cana-1540	124	61	)	)	PUNCT
cana-1540	124	62	,	,	PUNCT
cana-1540	124	63	𝑚2	𝑚2	NOUN
cana-1540	124	64	=	=	SYM
cana-1540	124	65	(	(	PUNCT
cana-1540	124	66	𝜇𝑉1𝑍3	𝜇𝑉1𝑍3	NOUN
cana-1540	124	67	∗	∗	NOUN
cana-1540	124	68	−	−	PROPN
cana-1540	124	69	𝛾∗𝑏4	𝛾∗𝑏4	NOUN
cana-1540	124	70	)	)	PUNCT
cana-1540	124	71	(	(	PUNCT
cana-1540	124	72	1	1	NUM
cana-1540	124	73	−	−	NOUN
cana-1540	124	74	𝑐2	𝑐2	NOUN
cana-1540	124	75	𝑐2	𝑐2	NOUN
cana-1540	124	76	2	2	NUM
cana-1540	124	77	−	−	PROPN
cana-1540	124	78	𝑏4	𝑏4	PROPN
cana-1540	124	79	2	2	NUM
cana-1540	124	80	)	)	PUNCT
cana-1540	124	81	𝑉1	𝑉1	NOUN
cana-1540	124	82	=	=	SYM
cana-1540	124	83	√	√	NOUN
cana-1540	125	1	𝜌𝑐2	𝜌𝑐2	NOUN
cana-1540	125	2	𝜇	𝜇	ADP
cana-1540	125	3	,	,	PUNCT
cana-1540	125	4	𝑍𝑖	𝑍𝑖	NOUN
cana-1540	125	5	∗	∗	NOUN
cana-1540	125	6	=	=	SYM
cana-1540	126	1	𝑍𝑖	𝑍𝑖	PROPN
cana-1540	126	2	√𝜌𝜇	√𝜌𝜇	NOUN
cana-1540	126	3	,	,	PUNCT
cana-1540	126	4	(	(	PUNCT
cana-1540	126	5	𝑖	𝑖	NOUN
cana-1540	126	6	=	=	NOUN
cana-1540	126	7	1,2,3	1,2,3	NUM
cana-1540	126	8	)	)	PUNCT
cana-1540	126	9	for	for	ADP
cana-1540	126	10	thermally	thermally	ADV
cana-1540	126	11	insulated	insulate	VERB
cana-1540	126	12	surface	surface	NOUN
cana-1540	127	1	𝑇𝑖	𝑇𝑖	PROPN
cana-1540	127	2	=	=	PUNCT
cana-1540	127	3	𝑏𝑖	𝑏𝑖	PROPN
cana-1540	127	4	[	[	X
cana-1540	127	5	(	(	PUNCT
cana-1540	127	6	2	2	NUM
cana-1540	127	7	+	+	CCONJ
cana-1540	127	8	𝜆∗+𝑘∗	𝜆∗+𝑘∗	ADJ
cana-1540	127	9	𝜇∗	𝜇∗	NOUN
cana-1540	127	10	)	)	PUNCT
cana-1540	128	1	(	(	PUNCT
cana-1540	128	2	𝑏𝑖	𝑏𝑖	ADP
cana-1540	128	3	2	2	NUM
cana-1540	128	4	−	−	NUM
cana-1540	128	5	1	1	NUM
cana-1540	128	6	)	)	PUNCT
cana-1540	128	7	+	+	CCONJ
cana-1540	128	8	𝑉1	𝑉1	NOUN
cana-1540	128	9	2	2	NUM
cana-1540	128	10	]	]	PUNCT
cana-1540	128	11	,	,	PUNCT
cana-1540	128	12	(	(	PUNCT
cana-1540	128	13	𝑖	𝑖	SYM
cana-1540	128	14	=	=	SYM
cana-1540	128	15	1,2	1,2	NUM
cana-1540	128	16	)	)	PUNCT
cana-1540	128	17	for	for	ADP
cana-1540	128	18	isothermal	isothermal	ADJ
cana-1540	128	19	surface	surface	NOUN
cana-1540	129	1	𝑇𝑖	𝑇𝑖	PROPN
cana-1540	129	2	=	=	PUNCT
cana-1540	130	1	[	[	X
cana-1540	130	2	(	(	PUNCT
cana-1540	130	3	2	2	NUM
cana-1540	130	4	+	+	CCONJ
cana-1540	130	5	𝜆∗+𝑘∗	𝜆∗+𝑘∗	ADJ
cana-1540	130	6	𝜇∗	𝜇∗	NOUN
cana-1540	130	7	)	)	PUNCT
cana-1540	130	8	(	(	PUNCT
cana-1540	130	9	𝑏𝑖	𝑏𝑖	ADP
cana-1540	130	10	2	2	NUM
cana-1540	130	11	−	−	NUM
cana-1540	130	12	1	1	NUM
cana-1540	130	13	)	)	PUNCT
cana-1540	130	14	+	+	CCONJ
cana-1540	130	15	𝑉1	𝑉1	NOUN
cana-1540	130	16	2	2	NUM
cana-1540	130	17	]	]	PUNCT
cana-1540	130	18	,	,	PUNCT
cana-1540	130	19	(	(	PUNCT
cana-1540	130	20	𝑖	𝑖	SYM
cana-1540	130	21	=	=	SYM
cana-1540	130	22	1,2	1,2	NUM
cana-1540	130	23	)	)	PUNCT
cana-1540	130	24	6	6	NUM
cana-1540	130	25	.	.	PUNCT
cana-1540	130	26	particular	particular	ADJ
cana-1540	130	27	cases	case	NOUN
cana-1540	130	28	1	1	NUM
cana-1540	130	29	)	)	PUNCT
cana-1540	130	30	in	in	ADP
cana-1540	130	31	the	the	DET
cana-1540	130	32	absence	absence	NOUN
cana-1540	130	33	of	of	ADP
cana-1540	130	34	micropolar	micropolar	ADJ
cana-1540	130	35	and	and	CCONJ
cana-1540	130	36	viscous	viscous	ADJ
cana-1540	130	37	effects	effect	NOUN
cana-1540	130	38	,	,	PUNCT
cana-1540	130	39	the	the	DET
cana-1540	130	40	equation	equation	NOUN
cana-1540	130	41	(	(	PUNCT
cana-1540	130	42	26	26	NUM
cana-1540	130	43	)	)	PUNCT
cana-1540	130	44	reduces	reduce	VERB
cana-1540	130	45	to	to	ADP
cana-1540	130	46	the	the	DET
cana-1540	130	47	secular	secular	ADJ
cana-1540	130	48	equation	equation	NOUN
cana-1540	130	49	for	for	ADP
cana-1540	130	50	the	the	DET
cana-1540	130	51	phase	phase	NOUN
cana-1540	130	52	velocity	velocity	NOUN
cana-1540	130	53	of	of	ADP
cana-1540	130	54	rayleigh	rayleigh	PROPN
cana-1540	130	55	waves	wave	NOUN
cana-1540	130	56	in	in	ADP
cana-1540	130	57	a	a	DET
cana-1540	130	58	thermoelastic	thermoelastic	ADJ
cana-1540	130	59	half	half	NOUN
cana-1540	130	60	space	space	NOUN
cana-1540	130	61	with	with	ADP
cana-1540	130	62	impedance	impedance	NOUN
cana-1540	130	63	boundary	boundary	ADJ
cana-1540	130	64	conditions	condition	NOUN
cana-1540	130	65	.	.	PUNCT
cana-1540	131	1	neglecting	neglect	VERB
cana-1540	131	2	micropolar	micropolar	ADJ
cana-1540	131	3	constants	constant	NOUN
cana-1540	131	4	(	(	PUNCT
cana-1540	131	5	𝐾	𝐾	NOUN
cana-1540	131	6	=	=	SYM
cana-1540	131	7	𝑗	𝑗	PROPN
cana-1540	131	8	=	=	NOUN
cana-1540	131	9	0	0	NUM
cana-1540	131	10	)	)	PUNCT
cana-1540	131	11	in	in	ADP
cana-1540	131	12	the	the	DET
cana-1540	131	13	condition	condition	NOUN
cana-1540	131	14	(	(	PUNCT
cana-1540	131	15	18	18	NUM
cana-1540	131	16	)	)	PUNCT
cana-1540	131	17	,	,	PUNCT
cana-1540	131	18	we	we	PRON
cana-1540	131	19	obtained	obtain	VERB
cana-1540	131	20	𝐴′	𝐴′	PROPN
cana-1540	131	21	=	=	SYM
cana-1540	131	22	𝑘2	𝑘2	PROPN
cana-1540	131	23	(	(	PUNCT
cana-1540	131	24	1	1	NUM
cana-1540	131	25	−	−	NOUN
cana-1540	131	26	𝑐2	𝑐2	NOUN
cana-1540	131	27	𝑐2	𝑐2	NOUN
cana-1540	131	28	2	2	NUM
cana-1540	131	29	)	)	PUNCT
cana-1540	131	30	+	+	CCONJ
cana-1540	131	31	𝑘	𝑘	DET
cana-1540	131	32	2	2	NUM
cana-1540	131	33	,	,	PUNCT
cana-1540	131	34	𝐵′	𝐵′	NUM
cana-1540	131	35	=	=	SYM
cana-1540	131	36	𝑘4(1	𝑘4(1	PROPN
cana-1540	131	37	−	−	PRON
cana-1540	131	38	𝑐2	𝑐2	NOUN
cana-1540	131	39	𝑐2	𝑐2	NOUN
cana-1540	131	40	2	2	NUM
cana-1540	131	41	)	)	PUNCT
cana-1540	131	42	using	use	VERB
cana-1540	131	43	equation	equation	NOUN
cana-1540	131	44	(	(	PUNCT
cana-1540	131	45	23	23	NUM
cana-1540	131	46	)	)	PUNCT
cana-1540	131	47	,	,	PUNCT
cana-1540	131	48	we	we	PRON
cana-1540	131	49	get	get	VERB
cana-1540	131	50	𝑏3	𝑏3	NOUN
cana-1540	131	51	2	2	NUM
cana-1540	131	52	=	=	SYM
cana-1540	131	53	1	1	NUM
cana-1540	131	54	−	−	NOUN
cana-1540	131	55	𝑐2	𝑐2	NOUN
cana-1540	131	56	𝑐2	𝑐2	NOUN
cana-1540	131	57	2,𝑏4	2,𝑏4	NUM
cana-1540	131	58	2	2	NUM
cana-1540	131	59	=	=	SYM
cana-1540	131	60	1	1	NUM
cana-1540	131	61	,	,	PUNCT
cana-1540	131	62	𝑚1	𝑚1	NOUN
cana-1540	131	63	=	=	SYM
cana-1540	131	64	0	0	PUNCT
cana-1540	132	1	and	and	CCONJ
cana-1540	132	2	𝑚2	𝑚2	NOUN
cana-1540	132	3	be	be	AUX
cana-1540	132	4	a	a	DET
cana-1540	132	5	non	non	ADJ
cana-1540	132	6	-	-	ADJ
cana-1540	132	7	zero	zero	NUM
cana-1540	132	8	value	value	NOUN
cana-1540	132	9	consequently	consequently	ADV
cana-1540	132	10	,	,	PUNCT
cana-1540	132	11	the	the	DET
cana-1540	132	12	secular	secular	ADJ
cana-1540	132	13	equation	equation	NOUN
cana-1540	132	14	(	(	PUNCT
cana-1540	132	15	26	26	NUM
cana-1540	132	16	)	)	PUNCT
cana-1540	132	17	reduces	reduce	VERB
cana-1540	132	18	to	to	ADP
cana-1540	132	19	𝑙3(𝑛1𝑇2	𝑙3(𝑛1𝑇2	NUM
cana-1540	132	20	−	−	PROPN
cana-1540	132	21	𝑛2𝑇1	𝑛2𝑇1	NUM
cana-1540	132	22	)	)	PUNCT
cana-1540	132	23	−	−	PROPN
cana-1540	132	24	𝑛3(𝑙1𝑇2	𝑛3(𝑙1𝑇2	NUM
cana-1540	133	1	−	−	PROPN
cana-1540	133	2	𝑙2𝑇1	𝑙2𝑇1	NUM
cana-1540	133	3	)	)	PUNCT
cana-1540	133	4	=	=	SYM
cana-1540	133	5	0	0	NUM
cana-1540	133	6	(	(	PUNCT
cana-1540	133	7	27	27	NUM
cana-1540	133	8	)	)	PUNCT
cana-1540	133	9	the	the	DET
cana-1540	133	10	equation	equation	NOUN
cana-1540	133	11	(	(	PUNCT
cana-1540	133	12	27	27	NUM
cana-1540	133	13	)	)	PUNCT
cana-1540	133	14	coincides	coincide	VERB
cana-1540	133	15	with	with	ADP
cana-1540	133	16	the	the	DET
cana-1540	133	17	secular	secular	ADJ
cana-1540	133	18	equation	equation	NOUN
cana-1540	133	19	,	,	PUNCT
cana-1540	133	20	obtained	obtain	VERB
cana-1540	133	21	by	by	ADP
cana-1540	133	22	author	author	NOUN
cana-1540	133	23	singh[20	singh[20	PROPN
cana-1540	133	24	]	]	PUNCT
cana-1540	133	25	for	for	ADP
cana-1540	133	26	rayleigh	rayleigh	PROPN
cana-1540	133	27	waves	wave	NOUN
cana-1540	133	28	in	in	ADP
cana-1540	133	29	thermoelastic	thermoelastic	ADJ
cana-1540	133	30	solid	solid	ADJ
cana-1540	133	31	half	half	ADJ
cana-1540	133	32	space	space	NOUN
cana-1540	133	33	with	with	ADP
cana-1540	133	34	impedance	impedance	NOUN
cana-1540	133	35	boundary	boundary	ADJ
cana-1540	133	36	conditions	condition	NOUN
cana-1540	133	37	.	.	PUNCT
cana-1540	134	1	2	2	X
cana-1540	134	2	)	)	PUNCT
cana-1540	134	3	further	further	ADJ
cana-1540	134	4	equation	equation	NOUN
cana-1540	134	5	(	(	PUNCT
cana-1540	134	6	27	27	NUM
cana-1540	134	7	)	)	PUNCT
cana-1540	134	8	reduces	reduce	VERB
cana-1540	134	9	to	to	ADP
cana-1540	134	10	secular	secular	ADJ
cana-1540	134	11	equation	equation	NOUN
cana-1540	134	12	for	for	ADP
cana-1540	134	13	rayleigh	rayleigh	PROPN
cana-1540	134	14	wave	wave	NOUN
cana-1540	134	15	velocity	velocity	NOUN
cana-1540	134	16	with	with	ADP
cana-1540	134	17	traction	traction	NOUN
cana-1540	134	18	free	free	ADJ
cana-1540	134	19	boundary	boundary	ADJ
cana-1540	134	20	conditions	condition	NOUN
cana-1540	135	1	when	when	SCONJ
cana-1540	135	2	𝑍𝑖	𝑍𝑖	PROPN
cana-1540	135	3	∗	∗	NOUN
cana-1540	135	4	=	=	SYM
cana-1540	135	5	0	0	NUM
cana-1540	135	6	,	,	PUNCT
cana-1540	135	7	(	(	PUNCT
cana-1540	135	8	𝑖	𝑖	SYM
cana-1540	135	9	=	=	NOUN
cana-1540	135	10	1,2,3	1,2,3	NUM
cana-1540	135	11	)	)	PUNCT
cana-1540	135	12	3	3	NUM
cana-1540	135	13	)	)	PUNCT
cana-1540	135	14	if	if	SCONJ
cana-1540	135	15	we	we	PRON
cana-1540	135	16	neglect	neglect	VERB
cana-1540	135	17	the	the	DET
cana-1540	135	18	impedance	impedance	NOUN
cana-1540	135	19	parameter	parameter	NOUN
cana-1540	135	20	,	,	PUNCT
cana-1540	135	21	micropolarity	micropolarity	NOUN
cana-1540	135	22	,	,	PUNCT
cana-1540	135	23	viscosity	viscosity	NOUN
cana-1540	135	24	and	and	CCONJ
cana-1540	135	25	thermal	thermal	ADJ
cana-1540	135	26	effects	effect	NOUN
cana-1540	135	27	from	from	ADP
cana-1540	135	28	the	the	DET
cana-1540	135	29	model	model	NOUN
cana-1540	135	30	i.e.	i.e.	X
cana-1540	135	31	𝑘∗	𝑘∗	X
cana-1540	135	32	=	=	SYM
cana-1540	135	33	𝑗	𝑗	NOUN
cana-1540	135	34	=	=	X
cana-1540	135	35	𝑍1	𝑍1	NOUN
cana-1540	135	36	∗	∗	NOUN
cana-1540	135	37	=	=	PUNCT
cana-1540	135	38	𝑍2	𝑍2	VERB
cana-1540	135	39	∗	∗	NOUN
cana-1540	135	40	=	=	PUNCT
cana-1540	135	41	𝑍3	𝑍3	NOUN
cana-1540	135	42	∗	∗	NOUN
cana-1540	135	43	=	=	PUNCT
cana-1540	135	44	𝜈	𝜈	X
cana-1540	135	45	=	=	SYM
cana-1540	135	46	0	0	NUM
cana-1540	135	47	,	,	PUNCT
cana-1540	135	48	the	the	DET
cana-1540	135	49	equation	equation	NOUN
cana-1540	135	50	(	(	PUNCT
cana-1540	135	51	26	26	NUM
cana-1540	135	52	)	)	PUNCT
cana-1540	135	53	reduces	reduce	VERB
cana-1540	135	54	to	to	ADP
cana-1540	135	55	(	(	PUNCT
cana-1540	135	56	2	2	NUM
cana-1540	135	57	−	−	NOUN
cana-1540	135	58	𝑐2	𝑐2	NOUN
cana-1540	135	59	𝑐2	𝑐2	NOUN
cana-1540	135	60	2	2	NUM
cana-1540	135	61	)	)	PUNCT
cana-1540	135	62	2	2	NUM
cana-1540	136	1	=	=	SYM
cana-1540	136	2	4√1	4√1	PROPN
cana-1540	136	3	−	−	NOUN
cana-1540	136	4	𝑐2	𝑐2	NOUN
cana-1540	136	5	𝑐1	𝑐1	NOUN
cana-1540	136	6	2	2	NUM
cana-1540	136	7	√1	√1	ADV
cana-1540	136	8	−	−	PROPN
cana-1540	136	9	𝑐2	𝑐2	NOUN
cana-1540	136	10	𝑐2	𝑐2	NOUN
cana-1540	136	11	2	2	NUM
cana-1540	136	12	(	(	PUNCT
cana-1540	136	13	28	28	NUM
cana-1540	136	14	)	)	PUNCT
cana-1540	136	15	where	where	SCONJ
cana-1540	136	16	𝑐1	𝑐1	NOUN
cana-1540	136	17	2	2	NUM
cana-1540	136	18	=	=	SYM
cana-1540	136	19	𝜆∗+2𝜇∗	𝜆∗+2𝜇∗	ADP
cana-1540	136	20	𝜌	𝜌	X
cana-1540	136	21	,	,	PUNCT
cana-1540	136	22	𝑐2	𝑐2	NOUN
cana-1540	136	23	2	2	NUM
cana-1540	136	24	=	=	SYM
cana-1540	136	25	𝜇∗	𝜇∗	NOUN
cana-1540	136	26	𝜌	𝜌	ADP
cana-1540	136	27	file:///c:/users	file:///c:/user	NOUN
cana-1540	136	28	/	/	SYM
cana-1540	136	29	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	136	30	/	/	SYM
cana-1540	136	31	appdata	appdata	NOUN
cana-1540	136	32	/	/	SYM
cana-1540	136	33	local	local	ADJ
cana-1540	136	34	/	/	SYM
cana-1540	136	35	microsoft	microsoft	PROPN
cana-1540	136	36	/	/	SYM
cana-1540	136	37	windows	windows	PROPN
cana-1540	136	38	/	/	SYM
cana-1540	136	39	inetcache	inetcache	NOUN
cana-1540	136	40	/	/	SYM
cana-1540	136	41	ie	ie	PROPN
cana-1540	136	42	/	/	SYM
cana-1540	136	43	a6wkhao2	a6wkhao2	PROPN
cana-1540	136	44	/	/	SYM
cana-1540	136	45	chapter-4%5b1%5d.docx%23sin15	chapter-4%5b1%5d.docx%23sin15	PROPN
cana-1540	136	46	communications	communication	NOUN
cana-1540	136	47	on	on	ADP
cana-1540	136	48	applied	apply	VERB
cana-1540	136	49	nonlinear	nonlinear	ADJ
cana-1540	136	50	analysis	analysis	NOUN
cana-1540	136	51	issn	issn	NOUN
cana-1540	136	52	:	:	PUNCT
cana-1540	136	53	1074	1074	NUM
cana-1540	136	54	-	-	PUNCT
cana-1540	136	55	133x	133x	NUM
cana-1540	136	56	vol	vol	NOUN
cana-1540	136	57	31	31	NUM
cana-1540	136	58	no	no	NOUN
cana-1540	136	59	.	.	PUNCT
cana-1540	137	1	8s	8s	PROPN
cana-1540	137	2	(	(	PUNCT
cana-1540	137	3	2024	2024	NUM
cana-1540	137	4	)	)	PUNCT
cana-1540	137	5	490	490	NUM
cana-1540	137	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	137	7	equation	equation	NOUN
cana-1540	137	8	(	(	PUNCT
cana-1540	137	9	28	28	NUM
cana-1540	137	10	)	)	PUNCT
cana-1540	137	11	is	be	AUX
cana-1540	137	12	the	the	DET
cana-1540	137	13	well	well	ADV
cana-1540	137	14	-	-	PUNCT
cana-1540	137	15	known	know	VERB
cana-1540	137	16	dispersion	dispersion	NOUN
cana-1540	137	17	equation	equation	NOUN
cana-1540	137	18	for	for	ADP
cana-1540	137	19	the	the	DET
cana-1540	137	20	phase	phase	NOUN
cana-1540	137	21	velocity	velocity	NOUN
cana-1540	137	22	of	of	ADP
cana-1540	137	23	rayleigh	rayleigh	PROPN
cana-1540	137	24	waves	wave	NOUN
cana-1540	137	25	in	in	ADP
cana-1540	137	26	classical	classical	ADJ
cana-1540	137	27	elastic	elastic	ADJ
cana-1540	137	28	half	half	NOUN
cana-1540	137	29	space	space	NOUN
cana-1540	137	30	7	7	NUM
cana-1540	137	31	.	.	PUNCT
cana-1540	137	32	numerical	numerical	ADJ
cana-1540	137	33	results	result	NOUN
cana-1540	137	34	and	and	CCONJ
cana-1540	137	35	discussions	discussion	NOUN
cana-1540	137	36	to	to	PART
cana-1540	137	37	illustrate	illustrate	VERB
cana-1540	137	38	the	the	DET
cana-1540	137	39	theoretical	theoretical	ADJ
cana-1540	137	40	results	result	NOUN
cana-1540	137	41	numerical	numerical	ADJ
cana-1540	137	42	computations	computation	NOUN
cana-1540	137	43	have	have	AUX
cana-1540	137	44	been	be	AUX
cana-1540	137	45	carried	carry	VERB
cana-1540	137	46	out	out	ADP
cana-1540	137	47	and	and	CCONJ
cana-1540	137	48	non	non	ADJ
cana-1540	137	49	dimensional	dimensional	ADJ
cana-1540	137	50	rayleigh	rayleigh	NOUN
cana-1540	137	51	wave	wave	NOUN
cana-1540	137	52	speed	speed	NOUN
cana-1540	137	53	has	have	AUX
cana-1540	137	54	been	be	AUX
cana-1540	137	55	calculated	calculate	VERB
cana-1540	137	56	in	in	ADP
cana-1540	137	57	a	a	DET
cana-1540	137	58	micropolar	micropolar	ADJ
cana-1540	137	59	thermoelastic	thermoelastic	ADJ
cana-1540	137	60	solid	solid	NOUN
cana-1540	137	61	.	.	PUNCT
cana-1540	138	1	the	the	DET
cana-1540	138	2	aluminium	aluminium	NOUN
cana-1540	138	3	epoxy	epoxy	NOUN
cana-1540	138	4	composite	composite	NOUN
cana-1540	138	5	is	be	AUX
cana-1540	138	6	taken	take	VERB
cana-1540	138	7	as	as	ADP
cana-1540	138	8	a	a	DET
cana-1540	138	9	micropolar	micropolar	ADJ
cana-1540	138	10	thermoelastic	thermoelastic	ADJ
cana-1540	138	11	solid	solid	ADJ
cana-1540	138	12	and	and	CCONJ
cana-1540	138	13	following	follow	VERB
cana-1540	138	14	gauthier[21],the	gauthier[21],the	DET
cana-1540	138	15	values	value	NOUN
cana-1540	138	16	of	of	ADP
cana-1540	138	17	relevant	relevant	ADJ
cana-1540	138	18	physical	physical	ADJ
cana-1540	138	19	constants	constant	NOUN
cana-1540	138	20	of	of	ADP
cana-1540	138	21	this	this	DET
cana-1540	138	22	material	material	NOUN
cana-1540	138	23	are	be	AUX
cana-1540	138	24	𝜌	𝜌	X
cana-1540	138	25	=	=	SYM
cana-1540	138	26	2.19	2.19	NUM
cana-1540	138	27	×	×	NOUN
cana-1540	138	28	103𝑘𝑔/𝑚3	103𝑘𝑔/𝑚3	NUM
cana-1540	138	29	,	,	PUNCT
cana-1540	138	30	𝜆	𝜆	NOUN
cana-1540	138	31	=	=	PUNCT
cana-1540	138	32	7.59	7.59	NUM
cana-1540	138	33	×	×	PROPN
cana-1540	138	34	1010𝑁/𝑚2	1010𝑁/𝑚2	NUM
cana-1540	138	35	,	,	PUNCT
cana-1540	138	36	𝜇	𝜇	X
cana-1540	138	37	=	=	PROPN
cana-1540	138	38	1.89	1.89	NUM
cana-1540	138	39	×	×	NOUN
cana-1540	138	40	1010𝑁/𝑚2	1010𝑁/𝑚2	NUM
cana-1540	138	41	,	,	PUNCT
cana-1540	139	1	𝐾	𝐾	PROPN
cana-1540	139	2	=	=	PROPN
cana-1540	139	3	0.0149	0.0149	NUM
cana-1540	139	4	×	×	NOUN
cana-1540	139	5	1010𝑁/𝑚2	1010𝑁/𝑚2	NUM
cana-1540	139	6	𝛼	𝛼	NOUN
cana-1540	139	7	=	=	NOUN
cana-1540	139	8	0.01	0.01	NUM
cana-1540	139	9	×	×	NOUN
cana-1540	139	10	106𝑁	106𝑁	NUM
cana-1540	139	11	,	,	PUNCT
cana-1540	139	12	𝛽	𝛽	NOUN
cana-1540	139	13	=	=	SYM
cana-1540	139	14	0.015	0.015	NUM
cana-1540	139	15	×	×	NOUN
cana-1540	139	16	106𝑁	106𝑁	NUM
cana-1540	139	17	,	,	PUNCT
cana-1540	139	18	𝛾	𝛾	NOUN
cana-1540	139	19	=	=	PUNCT
cana-1540	139	20	0.268	0.268	NUM
cana-1540	139	21	×	×	NOUN
cana-1540	139	22	106𝑁	106𝑁	NUM
cana-1540	139	23	,	,	PUNCT
cana-1540	139	24	𝑗	𝑗	NOUN
cana-1540	139	25	=	=	SYM
cana-1540	139	26	0.196	0.196	NUM
cana-1540	139	27	×	×	PROPN
cana-1540	139	28	104𝑚2	104𝑚2	NUM
cana-1540	139	29	,	,	PUNCT
cana-1540	139	30	𝐾∗	𝐾∗	PROPN
cana-1540	140	1	=	=	SYM
cana-1540	140	2	0.492	0.492	NUM
cana-1540	140	3	×	×	NOUN
cana-1540	140	4	102𝑊/𝑚	102𝑊/𝑚	PROPN
cana-1540	140	5	𝐾	𝐾	PROPN
cana-1540	140	6	,	,	PUNCT
cana-1540	140	7	𝐶∗	𝐶∗	NOUN
cana-1540	140	8	=	=	NUM
cana-1540	140	9	1.89	1.89	NUM
cana-1540	140	10	×	×	NOUN
cana-1540	140	11	1010𝐽/𝑘𝑔.	1010𝐽/𝑘𝑔.	PROPN
cana-1540	140	12	𝐾.	𝐾.	PROPN
cana-1540	140	13	,	,	PUNCT
cana-1540	140	14	𝜏0	𝜏0	PROPN
cana-1540	140	15	=	=	PROPN
cana-1540	140	16	0.5	0.5	NUM
cana-1540	140	17	×	×	NOUN
cana-1540	140	18	10−10𝑠	10−10𝑠	NUM
cana-1540	140	19	,	,	PUNCT
cana-1540	140	20	𝑇0	𝑇0	NOUN
cana-1540	140	21	=	=	SYM
cana-1540	140	22	298𝐾	298𝐾	NUM
cana-1540	140	23	,	,	PUNCT
cana-1540	140	24	𝛼𝑡	𝛼𝑡	NOUN
cana-1540	140	25	=	=	SYM
cana-1540	140	26	2.36	2.36	NUM
cana-1540	140	27	×	×	NOUN
cana-1540	140	28	10−6𝐾−1	10−6𝐾−1	NUM
cana-1540	140	29	secular	secular	ADJ
cana-1540	140	30	equation	equation	NOUN
cana-1540	140	31	(	(	PUNCT
cana-1540	140	32	26	26	NUM
cana-1540	140	33	)	)	PUNCT
cana-1540	140	34	using	use	VERB
cana-1540	140	35	the	the	DET
cana-1540	140	36	functional	functional	ADJ
cana-1540	140	37	iteration	iteration	NOUN
cana-1540	140	38	method	method	NOUN
cana-1540	140	39	,	,	PUNCT
cana-1540	140	40	assuming	assume	VERB
cana-1540	140	41	that	that	SCONJ
cana-1540	140	42	c	c	PROPN
cana-1540	140	43	is	be	AUX
cana-1540	140	44	a	a	DET
cana-1540	140	45	complex	complex	ADJ
cana-1540	140	46	constant	constant	ADJ
cana-1540	140	47	parameter	parameter	NOUN
cana-1540	140	48	with	with	ADP
cana-1540	140	49	re(c)=v	re(c)=v	DET
cana-1540	140	50	≥0	≥0	NOUN
cana-1540	140	51	.	.	PUNCT
cana-1540	141	1	the	the	DET
cana-1540	141	2	graphic	graphic	ADJ
cana-1540	141	3	representations	representation	NOUN
cana-1540	141	4	of	of	ADP
cana-1540	141	5	the	the	DET
cana-1540	141	6	effects	effect	NOUN
cana-1540	141	7	of	of	ADP
cana-1540	141	8	viscosity	viscosity	NOUN
cana-1540	141	9	,	,	PUNCT
cana-1540	141	10	impedance	impedance	NOUN
cana-1540	141	11	parameters	parameter	NOUN
cana-1540	141	12	,	,	PUNCT
cana-1540	141	13	and	and	CCONJ
cana-1540	141	14	the	the	DET
cana-1540	141	15	rayleigh	rayleigh	PROPN
cana-1540	141	16	wave	wave	PROPN
cana-1540	141	17	speed	speed	NOUN
cana-1540	141	18	's	's	PART
cana-1540	141	19	dependence	dependence	NOUN
cana-1540	141	20	on	on	ADP
cana-1540	141	21	wave	wave	NOUN
cana-1540	141	22	number	number	NOUN
cana-1540	141	23	are	be	AUX
cana-1540	141	24	illustrated	illustrate	VERB
cana-1540	141	25	in	in	ADP
cana-1540	141	26	fig	fig	NOUN
cana-1540	141	27	.	.	PUNCT
cana-1540	142	1	1	1	NUM
cana-1540	142	2	through	through	ADP
cana-1540	142	3	fig	fig	NOUN
cana-1540	142	4	.	.	PUNCT
cana-1540	143	1	6.figs	6.figs	NUM
cana-1540	143	2	.	.	PUNCT
cana-1540	144	1	1–3	1–3	NUM
cana-1540	144	2	illustrate	illustrate	VERB
cana-1540	144	3	the	the	DET
cana-1540	144	4	impact	impact	NOUN
cana-1540	144	5	of	of	ADP
cana-1540	144	6	viscosity	viscosity	NOUN
cana-1540	144	7	on	on	ADP
cana-1540	144	8	the	the	DET
cana-1540	144	9	non	non	ADJ
cana-1540	144	10	-	-	ADJ
cana-1540	144	11	dimensional	dimensional	ADJ
cana-1540	144	12	rayleigh	rayleigh	NOUN
cana-1540	144	13	wave	wave	NOUN
cana-1540	144	14	speed	speed	NOUN
cana-1540	144	15	𝑉1	𝑉1	NOUN
cana-1540	144	16	in	in	ADP
cana-1540	144	17	relation	relation	NOUN
cana-1540	144	18	to	to	ADP
cana-1540	144	19	impedance	impedance	NOUN
cana-1540	144	20	parameters	parameter	NOUN
cana-1540	144	21	z.	z.	PROPN
cana-1540	144	22	figures	figure	VERB
cana-1540	144	23	4	4	NUM
cana-1540	144	24	through	through	ADP
cana-1540	144	25	6	6	NUM
cana-1540	144	26	illustrate	illustrate	VERB
cana-1540	144	27	the	the	DET
cana-1540	144	28	variations	variation	NOUN
cana-1540	144	29	in	in	ADP
cana-1540	144	30	wave	wave	NOUN
cana-1540	144	31	speed	speed	NOUN
cana-1540	144	32	𝑉1with	𝑉1with	ADP
cana-1540	144	33	regard	regard	NOUN
cana-1540	144	34	to	to	ADP
cana-1540	144	35	the	the	DET
cana-1540	144	36	impedance	impedance	NOUN
cana-1540	144	37	parameter	parameter	NOUN
cana-1540	144	38	in	in	ADP
cana-1540	144	39	a	a	DET
cana-1540	144	40	micropolar	micropolar	ADJ
cana-1540	144	41	thermoelastic	thermoelastic	ADJ
cana-1540	144	42	half	half	ADJ
cana-1540	144	43	space	space	NOUN
cana-1540	144	44	under	under	ADP
cana-1540	144	45	thermally	thermally	ADV
cana-1540	144	46	insulated	insulate	VERB
cana-1540	144	47	and	and	CCONJ
cana-1540	144	48	isothermal	isothermal	ADJ
cana-1540	144	49	boundary	boundary	ADJ
cana-1540	144	50	conditions	condition	NOUN
cana-1540	144	51	.	.	PUNCT
cana-1540	145	1	fig	fig	NOUN
cana-1540	145	2	.	.	PUNCT
cana-1540	146	1	1	1	X
cana-1540	146	2	.	.	X
cana-1540	146	3	viscosity	viscosity	NOUN
cana-1540	146	4	effects	effect	NOUN
cana-1540	146	5	w.r.t	w.r.t	VERB
cana-1540	146	6	.	.	PUNCT
cana-1540	147	1	impedance	impedance	NOUN
cana-1540	147	2	parameter	parameter	NOUN
cana-1540	147	3	𝑍2	𝑍2	VERB
cana-1540	147	4	on	on	ADP
cana-1540	147	5	non	non	ADJ
cana-1540	147	6	-	-	ADJ
cana-1540	147	7	dimensional	dimensional	ADJ
cana-1540	147	8	speed	speed	NOUN
cana-1540	147	9	𝑉1of	𝑉1of	NOUN
cana-1540	147	10	rayleigh	rayleigh	PROPN
cana-1540	147	11	wave	wave	NOUN
cana-1540	147	12	.	.	PUNCT
cana-1540	148	1	the	the	DET
cana-1540	148	2	effect	effect	NOUN
cana-1540	148	3	of	of	ADP
cana-1540	148	4	viscosity	viscosity	NOUN
cana-1540	148	5	parameter	parameter	NOUN
cana-1540	148	6	in	in	ADP
cana-1540	148	7	the	the	DET
cana-1540	148	8	non	non	ADJ
cana-1540	148	9	-	-	ADJ
cana-1540	148	10	dimensional	dimensional	ADJ
cana-1540	148	11	speed	speed	NOUN
cana-1540	148	12	𝑉1	𝑉1	NOUN
cana-1540	148	13	is	be	AUX
cana-1540	148	14	significant	significant	ADJ
cana-1540	148	15	pertinent	pertinent	NOUN
cana-1540	148	16	and	and	CCONJ
cana-1540	148	17	is	be	AUX
cana-1540	148	18	noticed	notice	VERB
cana-1540	148	19	evidently	evidently	ADV
cana-1540	148	20	from	from	ADP
cana-1540	148	21	the	the	DET
cana-1540	148	22	figs	fig	NOUN
cana-1540	148	23	(	(	PUNCT
cana-1540	148	24	1)(3	1)(3	NUM
cana-1540	148	25	)	)	PUNCT
cana-1540	148	26	in	in	ADP
cana-1540	148	27	fig	fig	NOUN
cana-1540	148	28	(	(	PUNCT
cana-1540	148	29	1	1	NUM
cana-1540	148	30	)	)	PUNCT
cana-1540	148	31	the	the	DET
cana-1540	148	32	non	non	ADJ
cana-1540	148	33	-	-	ADJ
cana-1540	148	34	dimensional	dimensional	ADJ
cana-1540	148	35	wave	wave	NOUN
cana-1540	148	36	speed	speed	NOUN
cana-1540	148	37	𝑉1	𝑉1	NOUN
cana-1540	148	38	has	have	AUX
cana-1540	148	39	been	be	AUX
cana-1540	148	40	depicted	depict	VERB
cana-1540	148	41	against	against	ADP
cana-1540	148	42	the	the	DET
cana-1540	148	43	non	non	ADJ
cana-1540	148	44	-	-	ADJ
cana-1540	148	45	dimensional	dimensional	ADJ
cana-1540	148	46	impedance	impedance	NOUN
cana-1540	148	47	parameter	parameter	NOUN
cana-1540	148	48	𝑍1	𝑍1	NOUN
cana-1540	148	49	at	at	ADP
cana-1540	148	50	constant	constant	ADJ
cana-1540	148	51	frequency	frequency	NOUN
cana-1540	148	52	𝜔	𝜔	X
cana-1540	148	53	=	=	SYM
cana-1540	148	54	10	10	NUM
cana-1540	148	55	𝑟𝑎𝑑/𝑠	𝑟𝑎𝑑/𝑠	NOUN
cana-1540	148	56	and	and	CCONJ
cana-1540	148	57	retaining	retain	VERB
cana-1540	148	58	the	the	DET
cana-1540	148	59	boundary	boundary	ADJ
cana-1540	148	60	free	free	ADJ
cana-1540	148	61	of	of	ADP
cana-1540	148	62	normal	normal	ADJ
cana-1540	148	63	and	and	CCONJ
cana-1540	148	64	tangential	tangential	ADJ
cana-1540	148	65	couple	couple	NOUN
cana-1540	148	66	traction	traction	NOUN
cana-1540	148	67	𝑍2	𝑍2	VERB
cana-1540	148	68	=	=	SYM
cana-1540	148	69	0	0	NUM
cana-1540	148	70	,	,	PUNCT
cana-1540	148	71	𝑍3	𝑍3	NOUN
cana-1540	148	72	=	=	PROPN
cana-1540	149	1	0	0	X
cana-1540	149	2	.	.	PUNCT
cana-1540	150	1	it	it	PRON
cana-1540	150	2	is	be	AUX
cana-1540	150	3	evident	evident	ADJ
cana-1540	150	4	that	that	SCONJ
cana-1540	150	5	due	due	ADP
cana-1540	150	6	to	to	ADP
cana-1540	150	7	viscosity	viscosity	NOUN
cana-1540	150	8	𝑉1	𝑉1	NOUN
cana-1540	150	9	contains	contain	VERB
cana-1540	150	10	higher	high	ADJ
cana-1540	150	11	magnitude	magnitude	NOUN
cana-1540	150	12	.	.	PUNCT
cana-1540	151	1	impedance	impedance	NOUN
cana-1540	151	2	parameter	parameter	NOUN
cana-1540	151	3	z	z	PROPN
cana-1540	151	4	1	1	NUM
cana-1540	151	5	n	n	NOUN
cana-1540	151	6	on	on	ADP
cana-1540	151	7	-d	-d	PRON
cana-1540	151	8	i	i	PRON
cana-1540	151	9	m	m	VERB
cana-1540	151	10	en	en	ADP
cana-1540	151	11	si	si	X
cana-1540	151	12	on	on	ADP
cana-1540	151	13	al	al	PROPN
cana-1540	151	14	w	w	PROPN
cana-1540	151	15	av	av	PROPN
cana-1540	151	16	e	e	PROPN
cana-1540	151	17	sp	sp	ADP
cana-1540	151	18	ee	ee	PROPN
cana-1540	151	19	d	d	PROPN
cana-1540	151	20	0	0	NUM
cana-1540	152	1	0.1	0.1	NUM
cana-1540	152	2	0.2	0.2	NUM
cana-1540	152	3	0.3	0.3	NUM
cana-1540	152	4	0.4	0.4	NUM
cana-1540	152	5	0.5	0.5	NUM
cana-1540	152	6	0.6	0.6	NUM
cana-1540	152	7	0.7	0.7	NUM
cana-1540	152	8	0.8	0.8	NUM
cana-1540	152	9	0.9	0.9	NUM
cana-1540	152	10	1	1	NUM
cana-1540	152	11	1	1	NUM
cana-1540	152	12	1.1	1.1	NUM
cana-1540	152	13	1.2	1.2	NUM
cana-1540	152	14	1.3	1.3	NUM
cana-1540	152	15	1.4	1.4	NUM
cana-1540	152	16	1.5	1.5	NUM
cana-1540	152	17	1.6	1.6	NUM
cana-1540	152	18	1.7	1.7	NUM
cana-1540	152	19	1.8	1.8	NUM
cana-1540	152	20	1.9	1.9	NUM
cana-1540	152	21	2	2	NUM
cana-1540	152	22	micropolar	micropolar	ADJ
cana-1540	152	23	thermoelastic	thermoelastic	ADJ
cana-1540	152	24	micropolar	micropolar	ADJ
cana-1540	152	25	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	152	26	file:///c:/users	file:///c:/user	NOUN
cana-1540	152	27	/	/	SYM
cana-1540	152	28	rajneesh%20kumar	rajneesh%20kumar	NOUN
cana-1540	152	29	/	/	SYM
cana-1540	152	30	appdata	appdata	NOUN
cana-1540	152	31	/	/	SYM
cana-1540	152	32	local	local	ADJ
cana-1540	152	33	/	/	SYM
cana-1540	152	34	microsoft	microsoft	PROPN
cana-1540	152	35	/	/	SYM
cana-1540	152	36	windows	windows	PROPN
cana-1540	152	37	/	/	SYM
cana-1540	152	38	inetcache	inetcache	NOUN
cana-1540	152	39	/	/	SYM
cana-1540	152	40	ie	ie	PROPN
cana-1540	152	41	/	/	SYM
cana-1540	152	42	a6wkhao2	a6wkhao2	ADJ
cana-1540	152	43	/	/	SYM
cana-1540	152	44	chapter-4%5b1%5d.docx%23gau82	chapter-4%5b1%5d.docx%23gau82	ADJ
cana-1540	152	45	communications	communication	NOUN
cana-1540	152	46	on	on	ADP
cana-1540	152	47	applied	apply	VERB
cana-1540	152	48	nonlinear	nonlinear	ADJ
cana-1540	152	49	analysis	analysis	NOUN
cana-1540	152	50	issn	issn	NOUN
cana-1540	152	51	:	:	PUNCT
cana-1540	152	52	1074	1074	NUM
cana-1540	152	53	-	-	PUNCT
cana-1540	152	54	133x	133x	NUM
cana-1540	152	55	vol	vol	NOUN
cana-1540	152	56	31	31	NUM
cana-1540	152	57	no	no	NOUN
cana-1540	152	58	.	.	PUNCT
cana-1540	153	1	8s	8s	PROPN
cana-1540	153	2	(	(	PUNCT
cana-1540	153	3	2024	2024	NUM
cana-1540	153	4	)	)	PUNCT
cana-1540	153	5	491	491	NUM
cana-1540	153	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	153	7	fig	fig	NOUN
cana-1540	153	8	.	.	PUNCT
cana-1540	154	1	2	2	X
cana-1540	154	2	.	.	X
cana-1540	154	3	viscosity	viscosity	NOUN
cana-1540	154	4	effects	effect	NOUN
cana-1540	154	5	w.r.t	w.r.t	VERB
cana-1540	154	6	.	.	PUNCT
cana-1540	155	1	impedance	impedance	NOUN
cana-1540	155	2	parameter	parameter	PROPN
cana-1540	155	3	z2	z2	PROPN
cana-1540	155	4	on	on	ADP
cana-1540	155	5	non	non	ADJ
cana-1540	155	6	-	-	ADJ
cana-1540	155	7	dimensional	dimensional	ADJ
cana-1540	155	8	speed	speed	NOUN
cana-1540	155	9	𝑉1	𝑉1	NOUN
cana-1540	155	10	of	of	ADP
cana-1540	155	11	rayleigh	rayleigh	PROPN
cana-1540	155	12	wave	wave	PROPN
cana-1540	155	13	fig	fig	PROPN
cana-1540	155	14	.	.	PUNCT
cana-1540	156	1	3	3	X
cana-1540	156	2	.	.	X
cana-1540	156	3	viscosity	viscosity	NOUN
cana-1540	156	4	effects	effect	NOUN
cana-1540	156	5	w.r.t	w.r.t	VERB
cana-1540	156	6	.	.	PUNCT
cana-1540	157	1	impedance	impedance	NOUN
cana-1540	157	2	parameter	parameter	PROPN
cana-1540	157	3	z3	z3	PROPN
cana-1540	157	4	on	on	ADP
cana-1540	157	5	non	non	ADJ
cana-1540	157	6	-	-	ADJ
cana-1540	157	7	dimensional	dimensional	ADJ
cana-1540	157	8	speed	speed	NOUN
cana-1540	157	9	𝑉1rayleigh	𝑉1rayleigh	ADJ
cana-1540	157	10	wave	wave	NOUN
cana-1540	157	11	fig	fig	NOUN
cana-1540	157	12	(	(	PUNCT
cana-1540	157	13	2	2	NUM
cana-1540	157	14	)	)	PUNCT
cana-1540	157	15	and	and	CCONJ
cana-1540	157	16	fig	fig	NOUN
cana-1540	157	17	(	(	PUNCT
cana-1540	157	18	3	3	X
cana-1540	157	19	)	)	PUNCT
cana-1540	157	20	reveals	reveal	VERB
cana-1540	157	21	the	the	DET
cana-1540	157	22	variations	variation	NOUN
cana-1540	157	23	of	of	ADP
cana-1540	157	24	wave	wave	NOUN
cana-1540	157	25	speed	speed	NOUN
cana-1540	157	26	𝑉1	𝑉1	NOUN
cana-1540	157	27	with	with	ADP
cana-1540	157	28	respect	respect	NOUN
cana-1540	157	29	to	to	ADP
cana-1540	157	30	non	non	ADJ
cana-1540	157	31	-	-	ADJ
cana-1540	157	32	dimensional	dimensional	ADJ
cana-1540	157	33	impedance	impedance	NOUN
cana-1540	157	34	parameters	parameter	NOUN
cana-1540	157	35	𝑍2𝑎𝑛𝑑	𝑍2𝑎𝑛𝑑	PROPN
cana-1540	157	36	𝑍3	𝑍3	PROPN
cana-1540	157	37	respectively	respectively	ADV
cana-1540	157	38	keeping	keep	VERB
cana-1540	157	39	the	the	DET
cana-1540	157	40	other	other	ADJ
cana-1540	157	41	two	two	NUM
cana-1540	157	42	impedance	impedance	NOUN
cana-1540	157	43	parameters	parameter	NOUN
cana-1540	157	44	fixed	fix	VERB
cana-1540	157	45	at	at	ADP
cana-1540	157	46	zero	zero	NUM
cana-1540	157	47	value	value	NOUN
cana-1540	157	48	.	.	PUNCT
cana-1540	158	1	from	from	ADP
cana-1540	158	2	both	both	CCONJ
cana-1540	158	3	the	the	DET
cana-1540	158	4	figs	fig	NOUN
cana-1540	158	5	it	it	PRON
cana-1540	158	6	is	be	AUX
cana-1540	158	7	evidently	evidently	ADV
cana-1540	158	8	visible	visible	ADJ
cana-1540	158	9	that	that	SCONJ
cana-1540	158	10	viscosity	viscosity	NOUN
cana-1540	158	11	decreases	decrease	VERB
cana-1540	158	12	and	and	CCONJ
cana-1540	158	13	increases	increase	VERB
cana-1540	158	14	the	the	DET
cana-1540	158	15	wave	wave	NOUN
cana-1540	158	16	speed	speed	NOUN
cana-1540	158	17	respectively	respectively	ADV
cana-1540	158	18	.	.	PUNCT
cana-1540	159	1	fig4.variation	fig4.variation	NOUN
cana-1540	159	2	of	of	ADP
cana-1540	159	3	non	non	ADJ
cana-1540	159	4	-	-	ADJ
cana-1540	159	5	dimensional	dimensional	ADJ
cana-1540	159	6	wave	wave	NOUN
cana-1540	159	7	speed	speed	NOUN
cana-1540	159	8	𝑉1w.r.t	𝑉1w.r.t	NOUN
cana-1540	159	9	.	.	PUNCT
cana-1540	160	1	impedance	impedance	NOUN
cana-1540	160	2	parameter	parameter	NOUN
cana-1540	160	3	𝑍1	𝑍1	PROPN
cana-1540	161	1	in	in	ADP
cana-1540	161	2	a	a	DET
cana-1540	161	3	micropolar	micropolar	NOUN
cana-1540	161	4	viscothermally	viscothermally	ADV
cana-1540	161	5	insulated	insulated	ADJ
cana-1540	161	6	and	and	CCONJ
cana-1540	161	7	isothermal	isothermal	ADJ
cana-1540	161	8	half	half	ADJ
cana-1540	161	9	space	space	NOUN
cana-1540	161	10	.	.	PUNCT
cana-1540	162	1	fig.5	fig.5	NOUN
cana-1540	162	2	.	.	PUNCT
cana-1540	162	3	variation	variation	NOUN
cana-1540	162	4	of	of	ADP
cana-1540	162	5	non	non	ADJ
cana-1540	162	6	-	-	ADJ
cana-1540	162	7	dimensional	dimensional	ADJ
cana-1540	162	8	wave	wave	NOUN
cana-1540	162	9	speed	speed	NOUN
cana-1540	162	10	𝑉1w.r.t	𝑉1w.r.t	NOUN
cana-1540	162	11	.	.	PUNCT
cana-1540	163	1	impedance	impedance	NOUN
cana-1540	163	2	parameter	parameter	NOUN
cana-1540	163	3	𝑍2	𝑍2	VERB
cana-1540	163	4	in	in	ADP
cana-1540	163	5	a	a	DET
cana-1540	163	6	micropolar	micropolar	NOUN
cana-1540	163	7	thermally	thermally	ADV
cana-1540	163	8	insulated	insulate	VERB
cana-1540	163	9	and	and	CCONJ
cana-1540	163	10	isothermal	isothermal	ADJ
cana-1540	163	11	half	half	ADJ
cana-1540	163	12	space	space	NOUN
cana-1540	163	13	fig	fig	NOUN
cana-1540	163	14	4	4	NUM
cana-1540	163	15	.	.	PUNCT
cana-1540	163	16	depicts	depict	VERB
cana-1540	163	17	the	the	DET
cana-1540	163	18	non	non	ADJ
cana-1540	163	19	-	-	ADJ
cana-1540	163	20	dimensional	dimensional	ADJ
cana-1540	163	21	wave	wave	NOUN
cana-1540	163	22	speed	speed	NOUN
cana-1540	163	23	of	of	ADP
cana-1540	163	24	rayleigh	rayleigh	PROPN
cana-1540	163	25	wave	wave	PROPN
cana-1540	163	26	as	as	ADP
cana-1540	163	27	a	a	DET
cana-1540	163	28	function	function	NOUN
cana-1540	163	29	of	of	ADP
cana-1540	163	30	impedance	impedance	NOUN
cana-1540	163	31	parameter	parameter	NOUN
cana-1540	163	32	𝑍1	𝑍1	PROPN
cana-1540	164	1	when	when	SCONJ
cana-1540	164	2	the	the	DET
cana-1540	164	3	boundary	boundary	NOUN
cana-1540	164	4	is	be	AUX
cana-1540	164	5	free	free	ADJ
cana-1540	164	6	from	from	ADP
cana-1540	164	7	normal	normal	ADJ
cana-1540	164	8	and	and	CCONJ
cana-1540	164	9	couple	couple	NOUN
cana-1540	164	10	traction	traction	NOUN
cana-1540	164	11	(	(	PUNCT
cana-1540	164	12	𝑍2	𝑍2	VERB
cana-1540	164	13	=	=	SYM
cana-1540	164	14	0	0	NUM
cana-1540	164	15	,	,	PUNCT
cana-1540	164	16	𝑍3	𝑍3	NOUN
cana-1540	164	17	=	=	PROPN
cana-1540	164	18	0	0	NUM
cana-1540	164	19	)	)	PUNCT
cana-1540	164	20	.	.	PUNCT
cana-1540	165	1	comparison	comparison	NOUN
cana-1540	165	2	of	of	ADP
cana-1540	165	3	𝑉1	𝑉1	PROPN
cana-1540	165	4	has	have	AUX
cana-1540	165	5	been	be	AUX
cana-1540	165	6	determined	determine	VERB
cana-1540	165	7	when	when	SCONJ
cana-1540	165	8	the	the	DET
cana-1540	165	9	solid	solid	ADJ
cana-1540	165	10	half	half	ADJ
cana-1540	165	11	space	space	NOUN
cana-1540	165	12	is	be	AUX
cana-1540	165	13	due	due	ADJ
cana-1540	165	14	to	to	PART
cana-1540	165	15	thermally	thermally	ADV
cana-1540	165	16	insulated	insulate	VERB
cana-1540	165	17	and	and	CCONJ
cana-1540	165	18	isothermal	isothermal	ADJ
cana-1540	165	19	boundary	boundary	ADJ
cana-1540	165	20	restrictions	restriction	NOUN
cana-1540	165	21	.	.	PUNCT
cana-1540	166	1	it	it	PRON
cana-1540	166	2	is	be	AUX
cana-1540	166	3	evident	evident	ADJ
cana-1540	166	4	that	that	SCONJ
cana-1540	166	5	wave	wave	NOUN
cana-1540	166	6	speed	speed	NOUN
cana-1540	166	7	𝑉1	𝑉1	NOUN
cana-1540	166	8	contracted	contract	VERB
cana-1540	166	9	in	in	ADP
cana-1540	166	10	case	case	NOUN
cana-1540	166	11	of	of	ADP
cana-1540	166	12	isothermal	isothermal	ADJ
cana-1540	166	13	surface(curve-2	surface(curve-2	NOUN
cana-1540	166	14	)	)	PUNCT
cana-1540	166	15	as	as	ADP
cana-1540	166	16	contrast	contrast	NOUN
cana-1540	166	17	to	to	ADP
cana-1540	166	18	thermally	thermally	ADV
cana-1540	166	19	insulated	insulate	VERB
cana-1540	166	20	surface(curve-1	surface(curve-1	NOUN
cana-1540	166	21	)	)	PUNCT
cana-1540	166	22	for	for	ADP
cana-1540	166	23	some	some	DET
cana-1540	166	24	value	value	NOUN
cana-1540	166	25	of	of	ADP
cana-1540	166	26	impedance	impedance	NOUN
cana-1540	166	27	parameter	parameter	NOUN
cana-1540	166	28	𝑍1	𝑍1	PROPN
cana-1540	166	29	where	where	SCONJ
cana-1540	166	30	(	(	PUNCT
cana-1540	166	31	𝑍2	𝑍2	VERB
cana-1540	166	32	=	=	PUNCT
cana-1540	166	33	𝑍3	𝑍3	NOUN
cana-1540	166	34	=	=	PUNCT
cana-1540	166	35	0,𝜔	0,𝜔	X
cana-1540	167	1	=	=	SYM
cana-1540	167	2	10	10	NUM
cana-1540	167	3	𝑟𝑎𝑑/sec	𝑟𝑎𝑑/sec	PROPN
cana-1540	167	4	)	)	PUNCT
cana-1540	167	5	.	.	PUNCT
cana-1540	168	1	it	it	PRON
cana-1540	168	2	is	be	AUX
cana-1540	168	3	noticed	notice	VERB
cana-1540	168	4	from	from	ADP
cana-1540	168	5	the	the	DET
cana-1540	168	6	graph	graph	NOUN
cana-1540	168	7	that	that	PRON
cana-1540	168	8	wave	wave	NOUN
cana-1540	168	9	speed	speed	NOUN
cana-1540	168	10	contracted	contract	VERB
cana-1540	168	11	gradually	gradually	ADV
cana-1540	168	12	with	with	ADP
cana-1540	168	13	the	the	DET
cana-1540	168	14	increase	increase	NOUN
cana-1540	168	15	in	in	ADP
cana-1540	168	16	impedance	impedance	NOUN
cana-1540	168	17	parameters	parameter	NOUN
cana-1540	168	18	𝑍1	𝑍1	ADJ
cana-1540	168	19	for	for	ADP
cana-1540	168	20	the	the	DET
cana-1540	168	21	region	region	NOUN
cana-1540	168	22	0≤	0≤	NUM
cana-1540	168	23	𝑍1	𝑍1	X
cana-1540	168	24	≤	≤	ADV
cana-1540	168	25	1	1	NUM
cana-1540	168	26	for	for	ADP
cana-1540	168	27	both	both	DET
cana-1540	168	28	the	the	DET
cana-1540	168	29	conditions	condition	NOUN
cana-1540	168	30	.	.	PUNCT
cana-1540	169	1	the	the	DET
cana-1540	169	2	similar	similar	ADJ
cana-1540	169	3	stencil	stencil	NOUN
cana-1540	169	4	of	of	ADP
cana-1540	169	5	variant	variant	NOUN
cana-1540	169	6	of	of	ADP
cana-1540	169	7	wave	wave	NOUN
cana-1540	169	8	speed	speed	NOUN
cana-1540	169	9	is	be	AUX
cana-1540	169	10	noticed	notice	VERB
cana-1540	169	11	with	with	ADP
cana-1540	169	12	respect	respect	NOUN
cana-1540	169	13	to	to	ADP
cana-1540	169	14	impedance	impedance	NOUN
cana-1540	169	15	parameters	parameter	NOUN
cana-1540	169	16	𝑍2	𝑍2	VERB
cana-1540	169	17	𝑎𝑛𝑑𝑍3	𝑎𝑛𝑑𝑍3	PROPN
cana-1540	169	18	as	as	ADP
cana-1540	169	19	impedance	impedance	NOUN
cana-1540	169	20	parameter	parameter	NOUN
cana-1540	169	21	z	z	PROPN
cana-1540	169	22	2	2	NUM
cana-1540	169	23	n	n	NOUN
cana-1540	169	24	on	on	ADP
cana-1540	169	25	-d	-d	PRON
cana-1540	169	26	i	i	PRON
cana-1540	169	27	m	m	VERB
cana-1540	169	28	en	en	ADP
cana-1540	169	29	si	si	X
cana-1540	169	30	on	on	ADP
cana-1540	169	31	al	al	PROPN
cana-1540	169	32	s	s	PROPN
cana-1540	169	33	pe	pe	PROPN
cana-1540	169	34	ed	ed	NOUN
cana-1540	169	35	0	0	NUM
cana-1540	169	36	0.1	0.1	NUM
cana-1540	169	37	0.2	0.2	NUM
cana-1540	169	38	0.3	0.3	NUM
cana-1540	169	39	0.4	0.4	NUM
cana-1540	169	40	0.5	0.5	NUM
cana-1540	169	41	0.6	0.6	NUM
cana-1540	169	42	0.7	0.7	NUM
cana-1540	169	43	1.75	1.75	NUM
cana-1540	169	44	1.8	1.8	NUM
cana-1540	169	45	1.85	1.85	NUM
cana-1540	169	46	1.9	1.9	NUM
cana-1540	169	47	1.95	1.95	NUM
cana-1540	169	48	micropolar	micropolar	ADJ
cana-1540	169	49	thermoelastic	thermoelastic	ADJ
cana-1540	169	50	micropolar	micropolar	ADJ
cana-1540	169	51	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	169	52	impedance	impedance	NOUN
cana-1540	169	53	parameter	parameter	NOUN
cana-1540	169	54	z	z	PROPN
cana-1540	169	55	3	3	NUM
cana-1540	169	56	n	n	NUM
cana-1540	169	57	o	o	NOUN
cana-1540	169	58	n	n	CCONJ
cana-1540	169	59	-d	-d	PROPN
cana-1540	169	60	i	i	NOUN
cana-1540	169	61	m	m	VERB
cana-1540	169	62	e	e	NOUN
cana-1540	169	63	n	n	PROPN
cana-1540	169	64	s	s	PROPN
cana-1540	169	65	io	io	X
cana-1540	169	66	n	n	ADV
cana-1540	169	67	a	a	DET
cana-1540	169	68	l	l	NOUN
cana-1540	169	69	s	s	X
cana-1540	169	70	p	p	X
cana-1540	169	71	e	e	X
cana-1540	169	72	e	e	X
cana-1540	169	73	d	d	X
cana-1540	169	74	0.1	0.1	NUM
cana-1540	169	75	0.15	0.15	NUM
cana-1540	169	76	0.2	0.2	NUM
cana-1540	169	77	0.25	0.25	NUM
cana-1540	169	78	0.3	0.3	NUM
cana-1540	169	79	0.35	0.35	NUM
cana-1540	169	80	0.4	0.4	NUM
cana-1540	169	81	0.45	0.45	NUM
cana-1540	169	82	0.5	0.5	NUM
cana-1540	169	83	1.9	1.9	NUM
cana-1540	169	84	1.905	1.905	NUM
cana-1540	169	85	1.91	1.91	NUM
cana-1540	169	86	1.915	1.915	NUM
cana-1540	169	87	1.92	1.92	NUM
cana-1540	169	88	1.925	1.925	NUM
cana-1540	169	89	1.93	1.93	NUM
cana-1540	169	90	1.935	1.935	NUM
cana-1540	169	91	1.94	1.94	NUM
cana-1540	169	92	1.945	1.945	NUM
cana-1540	169	93	1.95	1.95	NUM
cana-1540	169	94	micropolar	micropolar	ADJ
cana-1540	169	95	thermoelastic	thermoelastic	ADJ
cana-1540	169	96	micropolar	micropolar	ADJ
cana-1540	169	97	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	169	98	impedance	impedance	NOUN
cana-1540	169	99	parameter	parameter	NOUN
cana-1540	169	100	z	z	PROPN
cana-1540	169	101	1	1	NUM
cana-1540	169	102	n	n	NOUN
cana-1540	169	103	on	on	ADP
cana-1540	169	104	-d	-d	PRON
cana-1540	169	105	i	i	PRON
cana-1540	169	106	m	m	VERB
cana-1540	169	107	en	en	ADP
cana-1540	169	108	si	si	X
cana-1540	169	109	on	on	ADP
cana-1540	169	110	al	al	PROPN
cana-1540	169	111	s	s	PROPN
cana-1540	169	112	pe	pe	PROPN
cana-1540	169	113	ed	ed	NOUN
cana-1540	169	114	0	0	NUM
cana-1540	169	115	0.1	0.1	NUM
cana-1540	169	116	0.2	0.2	NUM
cana-1540	169	117	0.3	0.3	NUM
cana-1540	169	118	0.4	0.4	NUM
cana-1540	169	119	0.5	0.5	NUM
cana-1540	169	120	0.6	0.6	NUM
cana-1540	169	121	0.7	0.7	NUM
cana-1540	169	122	0.8	0.8	NUM
cana-1540	169	123	0.9	0.9	NUM
cana-1540	169	124	1	1	NUM
cana-1540	169	125	1	1	NUM
cana-1540	169	126	1.1	1.1	NUM
cana-1540	169	127	1.2	1.2	NUM
cana-1540	169	128	1.3	1.3	NUM
cana-1540	169	129	1.4	1.4	NUM
cana-1540	169	130	1.5	1.5	NUM
cana-1540	169	131	1.6	1.6	NUM
cana-1540	169	132	1.7	1.7	NUM
cana-1540	169	133	1.8	1.8	NUM
cana-1540	169	134	1.9	1.9	NUM
cana-1540	169	135	2	2	NUM
cana-1540	169	136	isothermal	isothermal	ADJ
cana-1540	169	137	insulated	insulate	VERB
cana-1540	169	138	impedance	impedance	NOUN
cana-1540	169	139	paramater	paramater	NOUN
cana-1540	169	140	z	z	PROPN
cana-1540	169	141	2	2	NUM
cana-1540	169	142	n	n	NUM
cana-1540	169	143	o	o	NOUN
cana-1540	170	1	n	n	NOUN
cana-1540	170	2	d	d	X
cana-1540	170	3	i	i	PRON
cana-1540	170	4	m	m	VERB
cana-1540	170	5	e	e	NOUN
cana-1540	170	6	n	n	PROPN
cana-1540	170	7	s	s	PROPN
cana-1540	170	8	io	io	X
cana-1540	170	9	n	n	ADV
cana-1540	170	10	a	a	DET
cana-1540	170	11	l	l	NOUN
cana-1540	170	12	s	s	X
cana-1540	170	13	p	p	X
cana-1540	170	14	e	e	X
cana-1540	170	15	e	e	X
cana-1540	170	16	d	d	X
cana-1540	170	17	0	0	NUM
cana-1540	170	18	0.5	0.5	NUM
cana-1540	170	19	1	1	NUM
cana-1540	170	20	1.5	1.5	NUM
cana-1540	170	21	1.5	1.5	NUM
cana-1540	170	22	1.55	1.55	NUM
cana-1540	170	23	1.6	1.6	NUM
cana-1540	170	24	1.65	1.65	NUM
cana-1540	170	25	1.7	1.7	NUM
cana-1540	170	26	1.75	1.75	NUM
cana-1540	170	27	1.8	1.8	NUM
cana-1540	170	28	1.85	1.85	NUM
cana-1540	170	29	1.9	1.9	NUM
cana-1540	170	30	1.95	1.95	NUM
cana-1540	170	31	2	2	NUM
cana-1540	170	32	insulated	insulate	VERB
cana-1540	170	33	isothermal	isothermal	ADJ
cana-1540	170	34	communications	communication	NOUN
cana-1540	170	35	on	on	ADP
cana-1540	170	36	applied	apply	VERB
cana-1540	170	37	nonlinear	nonlinear	ADJ
cana-1540	170	38	analysis	analysis	NOUN
cana-1540	170	39	issn	issn	NOUN
cana-1540	170	40	:	:	PUNCT
cana-1540	170	41	1074	1074	NUM
cana-1540	170	42	-	-	PUNCT
cana-1540	170	43	133x	133x	NUM
cana-1540	170	44	vol	vol	NOUN
cana-1540	170	45	31	31	NUM
cana-1540	170	46	no	no	NOUN
cana-1540	170	47	.	.	PUNCT
cana-1540	171	1	8s	8s	PROPN
cana-1540	171	2	(	(	PUNCT
cana-1540	171	3	2024	2024	NUM
cana-1540	171	4	)	)	PUNCT
cana-1540	171	5	492	492	NUM
cana-1540	171	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	171	7	revealed	reveal	VERB
cana-1540	171	8	in	in	ADP
cana-1540	171	9	fig5	fig5	NOUN
cana-1540	171	10	and	and	CCONJ
cana-1540	171	11	fig6.the	fig6.the	DET
cana-1540	171	12	wave	wave	NOUN
cana-1540	171	13	speed	speed	NOUN
cana-1540	171	14	is	be	AUX
cana-1540	171	15	more	more	ADJ
cana-1540	171	16	in	in	ADP
cana-1540	171	17	case	case	NOUN
cana-1540	171	18	of	of	ADP
cana-1540	171	19	thermally	thermally	ADV
cana-1540	171	20	insulated	insulated	ADJ
cana-1540	171	21	state	state	NOUN
cana-1540	171	22	as	as	ADP
cana-1540	171	23	contrast	contrast	NOUN
cana-1540	171	24	to	to	ADP
cana-1540	171	25	isothermal	isothermal	ADJ
cana-1540	171	26	condition	condition	NOUN
cana-1540	171	27	.	.	PUNCT
cana-1540	172	1	fig.6	fig.6	VERB
cana-1540	172	2	variation	variation	NOUN
cana-1540	172	3	of	of	ADP
cana-1540	172	4	non	non	ADJ
cana-1540	172	5	-	-	ADJ
cana-1540	172	6	dimensional	dimensional	ADJ
cana-1540	172	7	wave	wave	NOUN
cana-1540	172	8	speed	speed	NOUN
cana-1540	172	9	𝑉1w.r.t	𝑉1w.r.t	NOUN
cana-1540	172	10	.	.	PUNCT
cana-1540	173	1	impedance	impedance	NOUN
cana-1540	173	2	parameter	parameter	NOUN
cana-1540	173	3	𝑍3	𝑍3	PROPN
cana-1540	173	4	in	in	ADP
cana-1540	173	5	a	a	DET
cana-1540	173	6	micropolar	micropolar	NOUN
cana-1540	173	7	thermally	thermally	ADV
cana-1540	173	8	insulated	insulate	VERB
cana-1540	173	9	and	and	CCONJ
cana-1540	173	10	isothermal	isothermal	ADJ
cana-1540	173	11	half	half	ADJ
cana-1540	173	12	space	space	NOUN
cana-1540	173	13	7	7	NUM
cana-1540	173	14	.	.	PUNCT
cana-1540	173	15	conclusion	conclusion	NOUN
cana-1540	173	16	in	in	ADP
cana-1540	173	17	this	this	DET
cana-1540	173	18	investigation	investigation	NOUN
cana-1540	173	19	,	,	PUNCT
cana-1540	173	20	the	the	DET
cana-1540	173	21	rayleigh	rayleigh	PROPN
cana-1540	173	22	waves	wave	NOUN
cana-1540	173	23	in	in	ADP
cana-1540	173	24	a	a	DET
cana-1540	173	25	micropolar	micropolar	ADJ
cana-1540	173	26	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	173	27	half	half	NOUN
cana-1540	173	28	space	space	NOUN
cana-1540	173	29	with	with	ADP
cana-1540	173	30	impedance	impedance	NOUN
cana-1540	173	31	boundary	boundary	ADJ
cana-1540	173	32	conditions	condition	NOUN
cana-1540	173	33	for	for	ADP
cana-1540	173	34	a	a	DET
cana-1540	173	35	thermally	thermally	ADV
cana-1540	173	36	insulated	insulate	VERB
cana-1540	173	37	and	and	CCONJ
cana-1540	173	38	isothermal	isothermal	ADJ
cana-1540	173	39	surface	surface	NOUN
cana-1540	173	40	are	be	AUX
cana-1540	173	41	examined	examine	VERB
cana-1540	173	42	.	.	PUNCT
cana-1540	174	1	the	the	DET
cana-1540	174	2	secular	secular	ADJ
cana-1540	174	3	equation	equation	NOUN
cana-1540	174	4	for	for	ADP
cana-1540	174	5	rayleigh	rayleigh	PROPN
cana-1540	174	6	waves	wave	NOUN
cana-1540	174	7	that	that	PRON
cana-1540	174	8	satisfies	satisfy	VERB
cana-1540	174	9	impedance	impedance	NOUN
cana-1540	174	10	boundary	boundary	ADJ
cana-1540	174	11	conditions	condition	NOUN
cana-1540	174	12	is	be	AUX
cana-1540	174	13	obtained	obtain	VERB
cana-1540	174	14	in	in	ADP
cana-1540	174	15	the	the	DET
cana-1540	174	16	explicit	explicit	ADJ
cana-1540	174	17	form	form	NOUN
cana-1540	174	18	.	.	PUNCT
cana-1540	175	1	the	the	DET
cana-1540	175	2	secular	secular	ADJ
cana-1540	175	3	equation	equation	NOUN
cana-1540	175	4	is	be	AUX
cana-1540	175	5	consistent	consistent	ADJ
cana-1540	175	6	with	with	ADP
cana-1540	175	7	the	the	DET
cana-1540	175	8	secular	secular	ADJ
cana-1540	175	9	equation	equation	NOUN
cana-1540	175	10	of	of	ADP
cana-1540	175	11	rayleigh	rayleigh	PROPN
cana-1540	175	12	waves	wave	NOUN
cana-1540	175	13	for	for	ADP
cana-1540	175	14	thermoelastic	thermoelastic	ADJ
cana-1540	175	15	half	half	ADJ
cana-1540	175	16	space	space	NOUN
cana-1540	175	17	with	with	ADP
cana-1540	175	18	impedance	impedance	NOUN
cana-1540	175	19	boundary	boundary	ADJ
cana-1540	175	20	conditions	condition	NOUN
cana-1540	175	21	when	when	SCONJ
cana-1540	175	22	the	the	DET
cana-1540	175	23	micropolar	micropolar	ADJ
cana-1540	175	24	parameters	parameter	NOUN
cana-1540	175	25	are	be	AUX
cana-1540	175	26	eliminated	eliminate	VERB
cana-1540	175	27	.	.	PUNCT
cana-1540	176	1	moreover	moreover	ADV
cana-1540	176	2	,	,	PUNCT
cana-1540	176	3	the	the	DET
cana-1540	176	4	classical	classical	ADJ
cana-1540	176	5	equation	equation	NOUN
cana-1540	176	6	for	for	ADP
cana-1540	176	7	an	an	DET
cana-1540	176	8	elastic	elastic	ADJ
cana-1540	176	9	solid	solid	NOUN
cana-1540	176	10	,	,	PUNCT
cana-1540	176	11	as	as	SCONJ
cana-1540	176	12	determined	determine	VERB
cana-1540	176	13	by	by	ADP
cana-1540	176	14	lord	lord	PROPN
cana-1540	176	15	rayleigh	rayleigh	PROPN
cana-1540	177	1	[	[	X
cana-1540	177	2	10	10	NUM
cana-1540	177	3	]	]	PUNCT
cana-1540	177	4	,	,	PUNCT
cana-1540	177	5	is	be	AUX
cana-1540	177	6	obtained	obtain	VERB
cana-1540	177	7	by	by	ADP
cana-1540	177	8	eliminating	eliminate	VERB
cana-1540	177	9	impedance	impedance	NOUN
cana-1540	177	10	and	and	CCONJ
cana-1540	177	11	viscothermal	viscothermal	NOUN
cana-1540	177	12	effects	effect	NOUN
cana-1540	177	13	from	from	ADP
cana-1540	177	14	this	this	DET
cana-1540	177	15	equation	equation	NOUN
cana-1540	177	16	.	.	PUNCT
cana-1540	178	1	the	the	DET
cana-1540	178	2	numerical	numerical	ADJ
cana-1540	178	3	analysis	analysis	NOUN
cana-1540	178	4	yields	yield	VERB
cana-1540	178	5	the	the	DET
cana-1540	178	6	following	follow	VERB
cana-1540	178	7	conclusion	conclusion	NOUN
cana-1540	178	8	:	:	PUNCT
cana-1540	178	9	•	•	NUM
cana-1540	178	10	rayleigh	rayleigh	NOUN
cana-1540	178	11	waves	wave	NOUN
cana-1540	178	12	are	be	AUX
cana-1540	178	13	present	present	ADJ
cana-1540	178	14	in	in	ADP
cana-1540	178	15	a	a	DET
cana-1540	178	16	micropolar	micropolar	ADJ
cana-1540	178	17	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	178	18	material	material	NOUN
cana-1540	178	19	with	with	ADP
cana-1540	178	20	impedance	impedance	NOUN
cana-1540	178	21	boundary	boundary	ADJ
cana-1540	178	22	conditions	condition	NOUN
cana-1540	178	23	.	.	PUNCT
cana-1540	179	1	•	•	NUM
cana-1540	179	2	rayleigh	rayleigh	PROPN
cana-1540	179	3	waves	wave	NOUN
cana-1540	179	4	non	non	ADJ
cana-1540	179	5	-	-	ADJ
cana-1540	179	6	dimensional	dimensional	ADJ
cana-1540	179	7	speed	speed	NOUN
cana-1540	179	8	is	be	AUX
cana-1540	179	9	affected	affect	VERB
cana-1540	179	10	by	by	ADP
cana-1540	179	11	the	the	DET
cana-1540	179	12	viscosity	viscosity	NOUN
cana-1540	179	13	of	of	ADP
cana-1540	179	14	micropolar	micropolar	ADJ
cana-1540	179	15	thermoelastic	thermoelastic	ADJ
cana-1540	179	16	solids	solid	NOUN
cana-1540	179	17	in	in	ADP
cana-1540	179	18	relation	relation	NOUN
cana-1540	179	19	to	to	ADP
cana-1540	179	20	all	all	DET
cana-1540	179	21	impedance	impedance	NOUN
cana-1540	179	22	parameters	parameter	NOUN
cana-1540	179	23	,	,	PUNCT
cana-1540	179	24	with	with	ADP
cana-1540	179	25	both	both	DET
cana-1540	179	26	increases	increase	NOUN
cana-1540	179	27	and	and	CCONJ
cana-1540	179	28	decreases	decrease	NOUN
cana-1540	179	29	occurring	occur	VERB
cana-1540	179	30	.	.	PUNCT
cana-1540	180	1	the	the	DET
cana-1540	180	2	degree	degree	NOUN
cana-1540	180	3	of	of	ADP
cana-1540	180	4	dispersion	dispersion	NOUN
cana-1540	180	5	of	of	ADP
cana-1540	180	6	the	the	DET
cana-1540	180	7	non	non	ADJ
cana-1540	180	8	-	-	ADJ
cana-1540	180	9	dimensional	dimensional	ADJ
cana-1540	180	10	rayleigh	rayleigh	NOUN
cana-1540	180	11	wave	wave	NOUN
cana-1540	180	12	speed	speed	NOUN
cana-1540	180	13	is	be	AUX
cana-1540	180	14	contingent	contingent	ADJ
cana-1540	180	15	upon	upon	SCONJ
cana-1540	180	16	the	the	DET
cana-1540	180	17	wave	wave	NOUN
cana-1540	180	18	number	number	NOUN
cana-1540	180	19	and	and	CCONJ
cana-1540	180	20	the	the	DET
cana-1540	180	21	impedance	impedance	NOUN
cana-1540	180	22	parameter	parameter	NOUN
cana-1540	180	23	range	range	NOUN
cana-1540	180	24	.	.	PUNCT
cana-1540	181	1	•	•	NUM
cana-1540	181	2	the	the	DET
cana-1540	181	3	non	non	ADJ
cana-1540	181	4	-	-	ADJ
cana-1540	181	5	dimensional	dimensional	ADJ
cana-1540	181	6	wave	wave	NOUN
cana-1540	181	7	speed	speed	NOUN
cana-1540	181	8	increases	increase	NOUN
cana-1540	181	9	in	in	ADP
cana-1540	181	10	the	the	DET
cana-1540	181	11	presence	presence	NOUN
cana-1540	181	12	of	of	ADP
cana-1540	181	13	a	a	DET
cana-1540	181	14	thermally	thermally	ADV
cana-1540	181	15	insulated	insulate	VERB
cana-1540	181	16	boundary	boundary	ADJ
cana-1540	181	17	when	when	SCONJ
cana-1540	181	18	compared	compare	VERB
cana-1540	181	19	to	to	ADP
cana-1540	181	20	isothermal	isothermal	ADJ
cana-1540	181	21	boundary	boundary	ADJ
cana-1540	181	22	conditions	condition	NOUN
cana-1540	181	23	when	when	SCONJ
cana-1540	181	24	calculated	calculate	VERB
cana-1540	181	25	as	as	ADP
cana-1540	181	26	a	a	DET
cana-1540	181	27	function	function	NOUN
cana-1540	181	28	of	of	ADP
cana-1540	181	29	impedance	impedance	NOUN
cana-1540	181	30	parameters	parameter	NOUN
cana-1540	181	31	.	.	PUNCT
cana-1540	182	1	rayleigh	rayleigh	PROPN
cana-1540	182	2	waves	wave	NOUN
cana-1540	182	3	are	be	AUX
cana-1540	182	4	particularly	particularly	ADV
cana-1540	182	5	significant	significant	ADJ
cana-1540	182	6	in	in	ADP
cana-1540	182	7	the	the	DET
cana-1540	182	8	field	field	NOUN
cana-1540	182	9	of	of	ADP
cana-1540	182	10	earthquake	earthquake	NOUN
cana-1540	182	11	engineering	engineering	NOUN
cana-1540	182	12	due	due	ADP
cana-1540	182	13	to	to	ADP
cana-1540	182	14	their	their	PRON
cana-1540	182	15	destructive	destructive	ADJ
cana-1540	182	16	character	character	NOUN
cana-1540	182	17	during	during	ADP
cana-1540	182	18	earthquakes	earthquake	NOUN
cana-1540	182	19	,	,	PUNCT
cana-1540	182	20	and	and	CCONJ
cana-1540	182	21	the	the	DET
cana-1540	182	22	investigation	investigation	NOUN
cana-1540	182	23	of	of	ADP
cana-1540	182	24	waves	wave	NOUN
cana-1540	182	25	in	in	ADP
cana-1540	182	26	micropolar	micropolar	ADJ
cana-1540	182	27	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	182	28	material	material	NOUN
cana-1540	182	29	is	be	AUX
cana-1540	182	30	quite	quite	ADV
cana-1540	182	31	significant	significant	ADJ
cana-1540	182	32	.	.	PUNCT
cana-1540	183	1	waves	wave	NOUN
cana-1540	183	2	in	in	ADP
cana-1540	183	3	certain	certain	ADJ
cana-1540	183	4	rock	rock	NOUN
cana-1540	183	5	behave	behave	VERB
cana-1540	183	6	like	like	ADP
cana-1540	183	7	micropolar	micropolar	ADJ
cana-1540	183	8	viscothermoelastic	viscothermoelastic	ADJ
cana-1540	183	9	solids	solid	NOUN
cana-1540	183	10	.	.	PUNCT
cana-1540	184	1	as	as	ADP
cana-1540	184	2	a	a	DET
cana-1540	184	3	consequence	consequence	NOUN
cana-1540	184	4	,	,	PUNCT
cana-1540	184	5	the	the	DET
cana-1540	184	6	results	result	NOUN
cana-1540	184	7	of	of	ADP
cana-1540	184	8	the	the	DET
cana-1540	184	9	present	present	ADJ
cana-1540	184	10	study	study	NOUN
cana-1540	184	11	,	,	PUNCT
cana-1540	184	12	despite	despite	SCONJ
cana-1540	184	13	being	be	AUX
cana-1540	184	14	a	a	DET
cana-1540	184	15	theoretical	theoretical	ADJ
cana-1540	184	16	modal	modal	NOUN
cana-1540	184	17	,	,	PUNCT
cana-1540	184	18	are	be	AUX
cana-1540	184	19	of	of	ADP
cana-1540	184	20	paramount	paramount	ADJ
cana-1540	184	21	importance	importance	NOUN
cana-1540	184	22	to	to	ADP
cana-1540	184	23	researchers	researcher	NOUN
cana-1540	184	24	in	in	ADP
cana-1540	184	25	the	the	DET
cana-1540	184	26	fields	field	NOUN
cana-1540	184	27	of	of	ADP
cana-1540	184	28	geophysics	geophysic	NOUN
cana-1540	184	29	,	,	PUNCT
cana-1540	184	30	composite	composite	ADJ
cana-1540	184	31	materials	material	NOUN
cana-1540	184	32	,	,	PUNCT
cana-1540	184	33	geological	geological	ADJ
cana-1540	184	34	materials	material	NOUN
cana-1540	184	35	,	,	PUNCT
cana-1540	184	36	and	and	CCONJ
cana-1540	184	37	seismology	seismology	NOUN
cana-1540	184	38	.	.	PUNCT
cana-1540	185	1	references	reference	NOUN
cana-1540	185	2	[	[	X
cana-1540	185	3	1	1	NUM
cana-1540	185	4	]	]	X
cana-1540	185	5	a.c	a.c	PROPN
cana-1540	185	6	.	.	PROPN
cana-1540	185	7	eringen	eringen	PROPN
cana-1540	185	8	//	//	PROPN
cana-1540	185	9	journal	journal	PROPN
cana-1540	185	10	of	of	ADP
cana-1540	185	11	mathematics	mathematic	NOUN
cana-1540	185	12	and	and	CCONJ
cana-1540	185	13	mechanics	mechanic	NOUN
cana-1540	185	14	15	15	NUM
cana-1540	185	15	(	(	PUNCT
cana-1540	185	16	1966	1966	NUM
cana-1540	185	17	)	)	PUNCT
cana-1540	185	18	909	909	NUM
cana-1540	185	19	.	.	PUNCT
cana-1540	186	1	[	[	X
cana-1540	186	2	2	2	NUM
cana-1540	186	3	]	]	X
cana-1540	186	4	a.c	a.c	PROPN
cana-1540	186	5	.	.	PROPN
cana-1540	186	6	eringen	eringen	PROPN
cana-1540	186	7	,	,	PUNCT
cana-1540	186	8	foundations	foundation	NOUN
cana-1540	186	9	of	of	ADP
cana-1540	186	10	micropolar	micropolar	ADJ
cana-1540	186	11	thermoelasticity	thermoelasticity	NOUN
cana-1540	186	12	,	,	PUNCT
cana-1540	186	13	international	international	ADJ
cana-1540	186	14	centre	centre	NOUN
cana-1540	186	15	for	for	ADP
cana-1540	186	16	mechanical	mechanical	ADJ
cana-1540	186	17	science	science	NOUN
cana-1540	186	18	,	,	PUNCT
cana-1540	186	19	udline	udline	ADJ
cana-1540	186	20	course	course	NOUN
cana-1540	186	21	and	and	CCONJ
cana-1540	186	22	lectures	lecture	VERB
cana-1540	186	23	23	23	NUM
cana-1540	186	24	(	(	PUNCT
cana-1540	186	25	springer	springer	NOUN
cana-1540	186	26	-	-	PUNCT
cana-1540	186	27	verlag	verlag	PROPN
cana-1540	186	28	,	,	PUNCT
cana-1540	186	29	berlin	berlin	PROPN
cana-1540	186	30	,	,	PUNCT
cana-1540	186	31	1970	1970	NUM
cana-1540	186	32	)	)	PUNCT
cana-1540	186	33	.	.	PUNCT
cana-1540	187	1	impedance	impedance	NOUN
cana-1540	187	2	parameter	parameter	NOUN
cana-1540	187	3	z	z	PROPN
cana-1540	187	4	3	3	NUM
cana-1540	187	5	n	n	NOUN
cana-1540	187	6	on	on	ADP
cana-1540	187	7	-d	-d	PRON
cana-1540	187	8	i	i	PRON
cana-1540	187	9	m	m	VERB
cana-1540	187	10	en	en	ADP
cana-1540	187	11	si	si	X
cana-1540	187	12	on	on	ADP
cana-1540	187	13	al	al	PROPN
cana-1540	187	14	s	s	PROPN
cana-1540	187	15	pe	pe	PROPN
cana-1540	187	16	ed	ed	NOUN
cana-1540	187	17	0.1	0.1	NUM
cana-1540	187	18	0.15	0.15	NUM
cana-1540	187	19	0.2	0.2	NUM
cana-1540	187	20	0.25	0.25	NUM
cana-1540	187	21	0.3	0.3	NUM
cana-1540	187	22	0.35	0.35	NUM
cana-1540	187	23	0.4	0.4	NUM
cana-1540	187	24	0.45	0.45	NUM
cana-1540	187	25	0.5	0.5	NUM
cana-1540	187	26	1.9	1.9	NUM
cana-1540	187	27	1.905	1.905	NUM
cana-1540	187	28	1.91	1.91	NUM
cana-1540	187	29	1.915	1.915	NUM
cana-1540	187	30	1.92	1.92	NUM
cana-1540	187	31	1.925	1.925	NUM
cana-1540	187	32	1.93	1.93	NUM
cana-1540	187	33	1.935	1.935	NUM
cana-1540	187	34	1.94	1.94	NUM
cana-1540	187	35	1.945	1.945	NUM
cana-1540	187	36	1.95	1.95	NUM
cana-1540	187	37	insulated	insulated	ADJ
cana-1540	187	38	isothermal	isothermal	ADJ
cana-1540	187	39	communications	communication	NOUN
cana-1540	187	40	on	on	ADP
cana-1540	187	41	applied	apply	VERB
cana-1540	187	42	nonlinear	nonlinear	ADJ
cana-1540	187	43	analysis	analysis	NOUN
cana-1540	187	44	issn	issn	NOUN
cana-1540	187	45	:	:	PUNCT
cana-1540	187	46	1074	1074	NUM
cana-1540	187	47	-	-	PUNCT
cana-1540	187	48	133x	133x	NUM
cana-1540	187	49	vol	vol	NOUN
cana-1540	187	50	31	31	NUM
cana-1540	187	51	no	no	NOUN
cana-1540	187	52	.	.	PUNCT
cana-1540	188	1	8s	8s	PROPN
cana-1540	188	2	(	(	PUNCT
cana-1540	188	3	2024	2024	NUM
cana-1540	188	4	)	)	PUNCT
cana-1540	188	5	493	493	NUM
cana-1540	188	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1540	189	1	[	[	X
cana-1540	189	2	3	3	X
cana-1540	189	3	]	]	X
cana-1540	189	4	a.e	a.e	PROPN
cana-1540	189	5	.	.	PROPN
cana-1540	189	6	green	green	PROPN
cana-1540	189	7	and	and	CCONJ
cana-1540	189	8	k.a	k.a	PROPN
cana-1540	189	9	.	.	PROPN
cana-1540	189	10	lindsay	lindsay	PROPN
cana-1540	189	11	//	//	PROPN
cana-1540	189	12	journal	journal	PROPN
cana-1540	189	13	of	of	ADP
cana-1540	189	14	elasticity	elasticity	NOUN
cana-1540	189	15	2(1	2(1	NUM
cana-1540	189	16	)	)	PUNCT
cana-1540	189	17	(	(	PUNCT
cana-1540	189	18	1972	1972	NUM
cana-1540	189	19	)	)	PUNCT
cana-1540	189	20	1	1	NUM
cana-1540	189	21	.	.	PUNCT
cana-1540	190	1	[	[	X
cana-1540	190	2	4	4	X
cana-1540	190	3	]	]	PUNCT
cana-1540	190	4	b.	b.	PROPN
cana-1540	190	5	singh	singh	PROPN
cana-1540	190	6	//	//	PROPN
cana-1540	190	7	meccanica	meccanica	PROPN
cana-1540	190	8	51(5	51(5	NUM
cana-1540	190	9	)	)	PUNCT
cana-1540	190	10	(	(	PUNCT
cana-1540	190	11	2016	2016	NUM
cana-1540	190	12	)	)	PUNCT
cana-1540	190	13	1135	1135	NUM
cana-1540	190	14	.	.	PUNCT
cana-1540	191	1	[	[	X
cana-1540	191	2	5	5	NUM
cana-1540	191	3	]	]	X
cana-1540	191	4	e.	e.	PROPN
cana-1540	191	5	boschi	boschi	PROPN
cana-1540	191	6	and	and	CCONJ
cana-1540	191	7	d.	d.	PROPN
cana-1540	191	8	ieşan	ieşan	PROPN
cana-1540	191	9	//	//	PROPN
cana-1540	191	10	meccanica	meccanica	PROPN
cana-1540	191	11	8(3	8(3	NUM
cana-1540	191	12	)	)	PUNCT
cana-1540	191	13	(	(	PUNCT
cana-1540	191	14	1973	1973	NUM
cana-1540	191	15	)	)	PUNCT
cana-1540	191	16	154	154	NUM
cana-1540	191	17	.	.	PUNCT
cana-1540	192	1	[	[	X
cana-1540	192	2	6	6	NUM
cana-1540	192	3	]	]	PUNCT
cana-1540	192	4	e.	e.	PROPN
cana-1540	192	5	godoy	godoy	PROPN
cana-1540	192	6	,	,	PUNCT
cana-1540	192	7	m.	m.	NOUN
cana-1540	192	8	duran	duran	PROPN
cana-1540	192	9	,	,	PUNCT
cana-1540	192	10	and	and	CCONJ
cana-1540	192	11	j.c	j.c	PROPN
cana-1540	192	12	.	.	PROPN
cana-1540	192	13	nedelec	nedelec	PROPN
cana-1540	192	14	//	//	PROPN
cana-1540	192	15	wave	wave	PROPN
cana-1540	192	16	motion	motion	NOUN
cana-1540	192	17	49(6	49(6	NOUN
cana-1540	192	18	)	)	PUNCT
cana-1540	192	19	(	(	PUNCT
cana-1540	192	20	2012	2012	NUM
cana-1540	192	21	)	)	PUNCT
cana-1540	192	22	585	585	NUM
cana-1540	192	23	.	.	PUNCT
cana-1540	193	1	[	[	X
cana-1540	193	2	7	7	X
cana-1540	193	3	]	]	X
cana-1540	193	4	f.j	f.j	PROPN
cana-1540	193	5	.	.	PROPN
cana-1540	193	6	lockett	lockett	PROPN
cana-1540	193	7	//	//	PROPN
cana-1540	193	8	journal	journal	PROPN
cana-1540	193	9	of	of	ADP
cana-1540	193	10	mechanics	mechanic	NOUN
cana-1540	193	11	and	and	CCONJ
cana-1540	193	12	physics	physic	NOUN
cana-1540	193	13	of	of	ADP
cana-1540	193	14	solids	solid	NOUN
cana-1540	193	15	7(1	7(1	NUM
cana-1540	193	16	)	)	PUNCT
cana-1540	193	17	(	(	PUNCT
cana-1540	193	18	1958	1958	NUM
cana-1540	193	19	)	)	PUNCT
cana-1540	193	20	71	71	NUM
cana-1540	193	21	.	.	PUNCT
cana-1540	194	1	[	[	X
cana-1540	194	2	8	8	NUM
cana-1540	194	3	]	]	X
cana-1540	194	4	h.f	h.f	PROPN
cana-1540	194	5	.	.	PROPN
cana-1540	194	6	tiersten	tiersten	PROPN
cana-1540	194	7	//	//	SYM
cana-1540	194	8	journal	journal	NOUN
cana-1540	194	9	of	of	ADP
cana-1540	194	10	applied	apply	VERB
cana-1540	194	11	physics	physics	NOUN
cana-1540	194	12	40(2	40(2	NUM
cana-1540	194	13	)	)	PUNCT
cana-1540	194	14	(	(	PUNCT
cana-1540	194	15	1969	1969	NUM
cana-1540	194	16	)	)	PUNCT
cana-1540	194	17	770	770	NUM
cana-1540	194	18	.	.	PUNCT
cana-1540	195	1	[	[	X
cana-1540	195	2	9	9	NUM
cana-1540	195	3	]	]	X
cana-1540	195	4	h.h	h.h	PROPN
cana-1540	195	5	.	.	PROPN
cana-1540	195	6	sherief	sherief	NOUN
cana-1540	195	7	,	,	PUNCT
cana-1540	195	8	f.a	f.a	PROPN
cana-1540	195	9	.	.	PROPN
cana-1540	195	10	hamza	hamza	PROPN
cana-1540	195	11	,	,	PUNCT
cana-1540	195	12	and	and	CCONJ
cana-1540	195	13	a.m.	a.m.	PROPN
cana-1540	195	14	ei	ei	PROPN
cana-1540	195	15	-	-	PUNCT
cana-1540	195	16	sayed	say	VERB
cana-1540	195	17	//	//	PROPN
cana-1540	195	18	journal	journal	PROPN
cana-1540	195	19	of	of	ADP
cana-1540	195	20	thermal	thermal	ADJ
cana-1540	195	21	stresses	stress	NOUN
cana-1540	195	22	28(4	28(4	NUM
cana-1540	195	23	)	)	PUNCT
cana-1540	195	24	(	(	PUNCT
cana-1540	195	25	2005	2005	NUM
cana-1540	195	26	)	)	PUNCT
cana-1540	195	27	409	409	NUM
cana-1540	195	28	.	.	PUNCT
cana-1540	196	1	[	[	X
cana-1540	196	2	10	10	NUM
cana-1540	196	3	]	]	X
cana-1540	196	4	h.w	h.w	PROPN
cana-1540	196	5	.	.	PROPN
cana-1540	196	6	lord	lord	PROPN
cana-1540	196	7	and	and	CCONJ
cana-1540	196	8	y.	y.	PROPN
cana-1540	196	9	shulman	shulman	PROPN
cana-1540	196	10	//	//	PROPN
cana-1540	196	11	journal	journal	PROPN
cana-1540	196	12	of	of	ADP
cana-1540	196	13	the	the	DET
cana-1540	196	14	mechanics	mechanic	NOUN
cana-1540	196	15	and	and	CCONJ
cana-1540	196	16	physics	physic	NOUN
cana-1540	196	17	of	of	ADP
cana-1540	196	18	solids	solid	NOUN
cana-1540	196	19	15(5	15(5	NUM
cana-1540	196	20	)	)	PUNCT
cana-1540	196	21	(	(	PUNCT
cana-1540	196	22	1967	1967	NUM
cana-1540	196	23	)	)	PUNCT
cana-1540	196	24	299	299	NUM
cana-1540	196	25	.	.	PUNCT
cana-1540	197	1	[	[	X
cana-1540	197	2	11	11	NUM
cana-1540	197	3	]	]	X
cana-1540	197	4	k.m	k.m	PROPN
cana-1540	197	5	.	.	PROPN
cana-1540	197	6	rao	rao	PROPN
cana-1540	197	7	and	and	CCONJ
cana-1540	197	8	m.p	m.p	PROPN
cana-1540	197	9	.	.	PROPN
cana-1540	197	10	reddy	reddy	PROPN
cana-1540	197	11	//	//	PROPN
cana-1540	197	12	journal	journal	PROPN
cana-1540	197	13	of	of	ADP
cana-1540	197	14	applied	apply	VERB
cana-1540	197	15	mechanics	mechanic	NOUN
cana-1540	197	16	60(4	60(4	NUM
cana-1540	197	17	)	)	PUNCT
cana-1540	197	18	(	(	PUNCT
cana-1540	197	19	1993	1993	NUM
cana-1540	197	20	)	)	PUNCT
cana-1540	197	21	857	857	NUM
cana-1540	197	22	.	.	PUNCT
cana-1540	198	1	[	[	X
cana-1540	198	2	12	12	NUM
cana-1540	198	3	]	]	X
cana-1540	198	4	l.	l.	PROPN
cana-1540	198	5	rayleigh	rayleigh	PROPN
cana-1540	198	6	in	in	ADP
cana-1540	198	7	proceedings	proceeding	NOUN
cana-1540	198	8	of	of	ADP
cana-1540	198	9	royal	royal	ADJ
cana-1540	198	10	society	society	NOUN
cana-1540	198	11	of	of	ADP
cana-1540	198	12	london	london	PROPN
cana-1540	198	13	,	,	PUNCT
cana-1540	198	14	series	series	PROPN
cana-1540	198	15	a	a	PROPN
cana-1540	198	16	,	,	PUNCT
cana-1540	198	17	london	london	PROPN
cana-1540	198	18	,	,	PUNCT
cana-1540	198	19	1885	1885	NUM
cana-1540	198	20	,	,	PUNCT
cana-1540	198	21	pp	pp	ADJ
cana-1540	198	22	.	.	PUNCT
cana-1540	199	1	4	4	NUM
cana-1540	199	2	-	-	SYM
cana-1540	199	3	11	11	NUM
cana-1540	199	4	.	.	PUNCT
cana-1540	200	1	[	[	X
cana-1540	200	2	13	13	NUM
cana-1540	200	3	]	]	PUNCT
cana-1540	200	4	m.	m.	NOUN
cana-1540	200	5	ciarletta	ciarletta	PROPN
cana-1540	200	6	//	//	PROPN
cana-1540	200	7	journal	journal	PROPN
cana-1540	200	8	of	of	ADP
cana-1540	200	9	thermal	thermal	ADJ
cana-1540	200	10	stresses	stress	NOUN
cana-1540	200	11	22(6	22(6	NUM
cana-1540	200	12	)	)	PUNCT
cana-1540	200	13	(	(	PUNCT
cana-1540	200	14	1999	1999	NUM
cana-1540	200	15	)	)	PUNCT
cana-1540	200	16	581	581	NUM
cana-1540	200	17	.	.	PUNCT
cana-1540	201	1	[	[	X
cana-1540	201	2	14	14	NUM
cana-1540	201	3	]	]	PUNCT
cana-1540	201	4	m.	m.	NOUN
cana-1540	201	5	marin	marin	NOUN
cana-1540	201	6	,	,	PUNCT
cana-1540	201	7	a	a	DET
cana-1540	201	8	hobiny	hobiny	NOUN
cana-1540	201	9	and	and	CCONJ
cana-1540	201	10	i	i	PROPN
cana-1540	201	11	abbas	abbas	PROPN
cana-1540	201	12	,	,	PUNCT
cana-1540	201	13	finite	finite	PROPN
cana-1540	201	14	element	element	NOUN
cana-1540	201	15	analysis	analysis	NOUN
cana-1540	201	16	of	of	ADP
cana-1540	201	17	nonlinear	nonlinear	ADJ
cana-1540	201	18	bioheat	bioheat	ADJ
cana-1540	201	19	model	model	NOUN
cana-1540	201	20	in	in	ADP
cana-1540	201	21	skin	skin	NOUN
cana-1540	201	22	tissue	tissue	NOUN
cana-1540	201	23	due	due	ADP
cana-1540	201	24	to	to	ADP
cana-1540	201	25	external	external	ADJ
cana-1540	201	26	thermal	thermal	ADJ
cana-1540	201	27	sources	source	NOUN
cana-1540	201	28	,	,	PUNCT
cana-1540	201	29	mathematics	mathematic	NOUN
cana-1540	201	30	,	,	PUNCT
cana-1540	201	31	9(13	9(13	NUM
cana-1540	201	32	):	):	PUNCT
cana-1540	201	33	art.no.1459	art.no.1459	X
cana-1540	201	34	(	(	PUNCT
cana-1540	201	35	2021	2021	NUM
cana-1540	201	36	)	)	PUNCT
cana-1540	201	37	.	.	PUNCT
cana-1540	202	1	[	[	X
cana-1540	202	2	15	15	NUM
cana-1540	202	3	]	]	X
cana-1540	202	4	m.	m.	NOUN
cana-1540	202	5	marin	marin	NOUN
cana-1540	202	6	,	,	PUNCT
cana-1540	202	7	a	a	DET
cana-1540	202	8	seadawy	seadawy	PROPN
cana-1540	202	9	,	,	PUNCT
cana-1540	202	10	s	s	PART
cana-1540	202	11	vlase	vlase	NOUN
cana-1540	202	12	,	,	PUNCT
cana-1540	202	13	a	a	DET
cana-1540	202	14	chirila	chirila	NOUN
cana-1540	202	15	,	,	PUNCT
cana-1540	202	16	on	on	ADP
cana-1540	202	17	mixed	mixed	ADJ
cana-1540	202	18	problem	problem	NOUN
cana-1540	202	19	in	in	ADP
cana-1540	202	20	thermo	thermo	NOUN
cana-1540	202	21	-	-	PUNCT
cana-1540	202	22	elasticity	elasticity	NOUN
cana-1540	202	23	of	of	ADP
cana-1540	202	24	type	type	NOUN
cana-1540	202	25	iii	iii	NOUN
cana-1540	202	26	for	for	ADP
cana-1540	202	27	cosserat	cosserat	NOUN
cana-1540	202	28	media	medium	NOUN
cana-1540	202	29	,	,	PUNCT
cana-1540	202	30	journal	journal	NOUN
cana-1540	202	31	of	of	ADP
cana-1540	202	32	taibah	taibah	PROPN
cana-1540	202	33	university	university	PROPN
cana-1540	202	34	for	for	ADP
cana-1540	202	35	science	science	NOUN
cana-1540	202	36	,	,	PUNCT
cana-1540	202	37	16(1):1264	16(1):1264	NUM
cana-1540	202	38	-	-	SYM
cana-1540	202	39	1274	1274	NUM
cana-1540	202	40	(	(	PUNCT
cana-1540	202	41	2022	2022	NUM
cana-1540	202	42	)	)	PUNCT
cana-1540	202	43	.	.	PUNCT
cana-1540	203	1	[	[	X
cana-1540	203	2	16	16	NUM
cana-1540	203	3	]	]	PUNCT
cana-1540	203	4	p.	p.	NOUN
cana-1540	203	5	malischewsky	malischewsky	NOUN
cana-1540	203	6	,	,	PUNCT
cana-1540	203	7	surface	surface	NOUN
cana-1540	203	8	waves	wave	NOUN
cana-1540	203	9	and	and	CCONJ
cana-1540	203	10	discontinuities	discontinuity	NOUN
cana-1540	203	11	(	(	PUNCT
cana-1540	203	12	elsevier	elsevier	NOUN
cana-1540	203	13	,	,	PUNCT
cana-1540	203	14	amsterdam	amsterdam	PROPN
cana-1540	203	15	,	,	PUNCT
cana-1540	203	16	1988	1988	NUM
cana-1540	203	17	)	)	PUNCT
cana-1540	203	18	.	.	PUNCT
cana-1540	204	1	[	[	X
cana-1540	204	2	17	17	NUM
cana-1540	204	3	]	]	X
cana-1540	204	4	p.c	p.c	PROPN
cana-1540	204	5	.	.	PROPN
cana-1540	204	6	vinh	vinh	PROPN
cana-1540	204	7	and	and	CCONJ
cana-1540	204	8	t.t.t	t.t.t	PROPN
cana-1540	204	9	.	.	PUNCT
cana-1540	204	10	hue	hue	PROPN
cana-1540	204	11	//	//	NUM
cana-1540	204	12	wave	wave	NOUN
cana-1540	204	13	motion	motion	NOUN
cana-1540	204	14	51(7	51(7	PROPN
cana-1540	204	15	)	)	PUNCT
cana-1540	204	16	(	(	PUNCT
cana-1540	204	17	2014	2014	NUM
cana-1540	204	18	)	)	PUNCT
cana-1540	204	19	1082	1082	NUM
cana-1540	204	20	.	.	PUNCT
cana-1540	205	1	[	[	X
cana-1540	205	2	18	18	NUM
cana-1540	205	3	]	]	X
cana-1540	205	4	r.	r.	PROPN
cana-1540	205	5	kumar	kumar	PROPN
cana-1540	205	6	and	and	CCONJ
cana-1540	205	7	b.	b.	PROPN
cana-1540	205	8	singh	singh	PROPN
cana-1540	205	9	proceedings	proceeding	NOUN
cana-1540	205	10	of	of	ADP
cana-1540	205	11	the	the	DET
cana-1540	205	12	indian	indian	PROPN
cana-1540	205	13	academy	academy	PROPN
cana-1540	205	14	of	of	ADP
cana-1540	205	15	sciences	sciences	PROPN
cana-1540	205	16	mathematical	mathematical	PROPN
cana-1540	205	17	sciences	sciences	PROPN
cana-1540	205	18	,	,	PUNCT
cana-1540	205	19	106(2	106(2	NUM
cana-1540	205	20	)	)	PUNCT
cana-1540	205	21	(	(	PUNCT
cana-1540	205	22	1996	1996	NUM
cana-1540	205	23	)	)	PUNCT
cana-1540	205	24	183	183	NUM
cana-1540	205	25	.	.	PUNCT
cana-1540	206	1	[	[	X
cana-1540	206	2	19	19	NUM
cana-1540	206	3	]	]	X
cana-1540	206	4	r.	r.	PROPN
cana-1540	206	5	kumar	kumar	PROPN
cana-1540	206	6	,	,	PUNCT
cana-1540	206	7	m.	m.	NOUN
cana-1540	206	8	kaur	kaur	PROPN
cana-1540	206	9	,	,	PUNCT
cana-1540	206	10	and	and	CCONJ
cana-1540	206	11	s.c	s.c	PROPN
cana-1540	206	12	.	.	PROPN
cana-1540	206	13	rajvanshi	rajvanshi	PROPN
cana-1540	206	14	//	//	PROPN
cana-1540	206	15	latin	latin	PROPN
cana-1540	206	16	american	american	PROPN
cana-1540	206	17	journal	journal	PROPN
cana-1540	206	18	of	of	ADP
cana-1540	206	19	solids	solid	NOUN
cana-1540	206	20	and	and	CCONJ
cana-1540	206	21	structures	structure	NOUN
cana-1540	206	22	2(7	2(7	NUM
cana-1540	206	23	)	)	PUNCT
cana-1540	206	24	(	(	PUNCT
cana-1540	206	25	2014	2014	NUM
cana-1540	206	26	)	)	PUNCT
cana-1540	206	27	1091	1091	NUM
cana-1540	206	28	.	.	PUNCT
cana-1540	207	1	[	[	X
cana-1540	207	2	20	20	NUM
cana-1540	207	3	]	]	PUNCT
cana-1540	207	4	r.	r.	PROPN
cana-1540	207	5	kumar	kumar	PROPN
cana-1540	207	6	and	and	CCONJ
cana-1540	207	7	g.	g.	PROPN
cana-1540	207	8	partap	partap	PROPN
cana-1540	207	9	//	//	PROPN
cana-1540	207	10	applied	apply	VERB
cana-1540	207	11	mathematics	mathematic	NOUN
cana-1540	207	12	and	and	CCONJ
cana-1540	207	13	mechanics	mechanic	NOUN
cana-1540	207	14	27(8	27(8	NUM
cana-1540	207	15	)	)	PUNCT
cana-1540	207	16	(	(	PUNCT
cana-1540	207	17	2006	2006	NUM
cana-1540	207	18	)	)	PUNCT
cana-1540	207	19	1049	1049	NUM
cana-1540	207	20	.	.	PUNCT
cana-1540	208	1	[	[	X
cana-1540	208	2	21	21	NUM
cana-1540	208	3	]	]	X
cana-1540	208	4	rajneesh	rajneesh	PROPN
cana-1540	208	5	kumar	kumar	PROPN
cana-1540	208	6	,	,	PUNCT
cana-1540	208	7	kulwinder	kulwinder	PROPN
cana-1540	208	8	singh	singh	PROPN
cana-1540	208	9	,	,	PUNCT
cana-1540	208	10	and	and	CCONJ
cana-1540	208	11	devinder	devinder	PROPN
cana-1540	208	12	singh	singh	PROPN
cana-1540	208	13	pathania	pathania	NOUN
cana-1540	208	14	,	,	PUNCT
cana-1540	208	15	"	"	PUNCT
cana-1540	208	16	interactions	interaction	NOUN
cana-1540	208	17	due	due	ADJ
cana-1540	208	18	to	to	ADP
cana-1540	208	19	hall	hall	NOUN
cana-1540	208	20	current	current	ADJ
cana-1540	208	21	and	and	CCONJ
cana-1540	208	22	rotation	rotation	NOUN
cana-1540	208	23	in	in	ADP
cana-1540	208	24	a	a	DET
cana-1540	208	25	magneto	magneto	ADJ
cana-1540	208	26	micropolar	micropolar	ADJ
cana-1540	208	27	thermoelastic	thermoelastic	ADJ
cana-1540	208	28	half	half	ADJ
cana-1540	208	29	-	-	PUNCT
cana-1540	208	30	space	space	NOUN
cana-1540	208	31	subjected	subject	VERB
cana-1540	208	32	to	to	ADP
cana-1540	208	33	ramp	ramp	NOUN
cana-1540	208	34	-	-	PUNCT
cana-1540	208	35	type	type	NOUN
cana-1540	208	36	heating	heating	NOUN
cana-1540	208	37	"	"	PUNCT
cana-1540	208	38	,	,	PUNCT
cana-1540	208	39	multidiscipline	multidiscipline	VERB
cana-1540	208	40	modelling	modelling	NOUN
cana-1540	208	41	in	in	ADP
cana-1540	208	42	materials	material	NOUN
cana-1540	208	43	and	and	CCONJ
cana-1540	208	44	structures	structure	NOUN
cana-1540	208	45	,	,	PUNCT
cana-1540	208	46	vol.12	vol.12	NOUN
cana-1540	208	47	,	,	PUNCT
cana-1540	208	48	no.1	no.1	NUM
cana-1540	208	49	,	,	PUNCT
cana-1540	208	50	pp.133	pp.133	NOUN
cana-1540	208	51	-	-	ADJ
cana-1540	208	52	150	150	NUM
cana-1540	208	53	,	,	PUNCT
cana-1540	208	54	2016	2016	NUM
cana-1540	208	55	.	.	PUNCT
cana-1540	209	1	[	[	X
cana-1540	209	2	22	22	NUM
cana-1540	209	3	]	]	X
cana-1540	209	4	s.	s.	PROPN
cana-1540	209	5	kaushal	kaushal	PROPN
cana-1540	209	6	,	,	PUNCT
cana-1540	209	7	r.	r.	PROPN
cana-1540	209	8	kumar	kumar	PROPN
cana-1540	209	9	,	,	PUNCT
cana-1540	209	10	kh	kh	PROPN
cana-1540	209	11	.	.	PROPN
cana-1540	209	12	lofty	lofty	ADJ
cana-1540	209	13	and	and	CCONJ
cana-1540	209	14	i.	i.	PROPN
cana-1540	209	15	bala	bala	PROPN
cana-1540	209	16	,	,	PUNCT
cana-1540	209	17	response	response	NOUN
cana-1540	209	18	of	of	ADP
cana-1540	209	19	frequency	frequency	NOUN
cana-1540	209	20	domain	domain	NOUN
cana-1540	209	21	in	in	ADP
cana-1540	209	22	generalized	generalized	ADJ
cana-1540	209	23	thermoelastic	thermoelastic	ADJ
cana-1540	209	24	half	half	ADJ
cana-1540	209	25	-	-	PUNCT
cana-1540	209	26	space	space	NOUN
cana-1540	209	27	under	under	ADP
cana-1540	209	28	modified	modify	VERB
cana-1540	209	29	green	green	ADJ
cana-1540	209	30	-	-	PUNCT
cana-1540	209	31	lindsay	lindsay	PROPN
cana-1540	209	32	with	with	ADP
cana-1540	209	33	non	non	ADJ
cana-1540	209	34	-	-	ADJ
cana-1540	209	35	local	local	ADJ
cana-1540	209	36	and	and	CCONJ
cana-1540	209	37	two	two	NUM
cana-1540	209	38	temperature	temperature	NOUN
cana-1540	209	39	,	,	PUNCT
cana-1540	209	40	zamm	zamm	PROPN
cana-1540	209	41	-	-	PUNCT
cana-1540	209	42	journal	journal	PROPN
cana-1540	209	43	of	of	ADP
cana-1540	209	44	applied	apply	VERB
cana-1540	209	45	mathematics	mathematic	NOUN
cana-1540	209	46	and	and	CCONJ
cana-1540	209	47	mechanics	mechanic	NOUN
cana-1540	209	48	,	,	PUNCT
cana-1540	209	49	2024	2024	NUM
cana-1540	209	50	,	,	PUNCT
cana-1540	209	51	doi:10.1002	doi:10.1002	NOUN
cana-1540	209	52	/	/	SYM
cana-1540	209	53	zamm.202301012	zamm.202301012	PROPN
cana-1540	209	54	.	.	PUNCT
cana-1540	210	1	[	[	X
cana-1540	210	2	23	23	NUM
cana-1540	210	3	]	]	PUNCT
cana-1540	210	4	s.	s.	PROPN
cana-1540	210	5	sharma	sharma	PROPN
cana-1540	210	6	and	and	CCONJ
cana-1540	210	7	s.	s.	PROPN
cana-1540	210	8	khator	khator	PROPN
cana-1540	210	9	,	,	PUNCT
cana-1540	210	10	power	power	NOUN
cana-1540	210	11	generation	generation	NOUN
cana-1540	210	12	planning	planning	NOUN
cana-1540	210	13	with	with	ADP
cana-1540	210	14	reserve	reserve	NOUN
cana-1540	210	15	dispatch	dispatch	NOUN
cana-1540	210	16	and	and	CCONJ
cana-1540	210	17	weather	weather	NOUN
cana-1540	210	18	uncertainties	uncertainty	NOUN
cana-1540	210	19	including	include	VERB
cana-1540	210	20	penetration	penetration	NOUN
cana-1540	210	21	of	of	ADP
cana-1540	210	22	renewable	renewable	ADJ
cana-1540	210	23	sources	source	NOUN
cana-1540	210	24	,	,	PUNCT
cana-1540	210	25	international	international	ADJ
cana-1540	210	26	journal	journal	NOUN
cana-1540	210	27	of	of	ADP
cana-1540	210	28	smart	smart	ADJ
cana-1540	210	29	grid	grid	NOUN
cana-1540	210	30	and	and	CCONJ
cana-1540	210	31	clean	clean	ADJ
cana-1540	210	32	energy	energy	NOUN
cana-1540	210	33	,	,	PUNCT
cana-1540	210	34	2021	2021	NUM
cana-1540	210	35	,	,	PUNCT
cana-1540	210	36	doi:10.12720	doi:10.12720	NOUN
cana-1540	210	37	/	/	SYM
cana-1540	210	38	sgce.10.4.292	sgce.10.4.292	NOUN
cana-1540	210	39	-	-	X
cana-1540	210	40	303	303	NUM
cana-1540	210	41	.	.	PUNCT
cana-1540	211	1	[	[	X
cana-1540	211	2	24	24	NUM
cana-1540	211	3	]	]	PUNCT
cana-1540	211	4	s.	s.	PROPN
cana-1540	211	5	sharma	sharma	PROPN
cana-1540	211	6	and	and	CCONJ
cana-1540	211	7	s.	s.	PROPN
cana-1540	211	8	khator	khator	PROPN
cana-1540	211	9	,	,	PUNCT
cana-1540	211	10	micro	micro	ADJ
cana-1540	211	11	-	-	NOUN
cana-1540	211	12	grid	grid	ADJ
cana-1540	211	13	planning	planning	NOUN
cana-1540	211	14	with	with	ADP
cana-1540	211	15	aggregator	aggregator	NOUN
cana-1540	211	16	’s	’s	PART
cana-1540	211	17	role	role	NOUN
cana-1540	211	18	in	in	ADP
cana-1540	211	19	the	the	DET
cana-1540	211	20	renewable	renewable	ADJ
cana-1540	211	21	inclusive	inclusive	ADJ
cana-1540	211	22	prosumer	prosumer	NOUN
cana-1540	211	23	market	market	NOUN
cana-1540	211	24	.	.	PUNCT
cana-1540	212	1	journal	journal	PROPN
cana-1540	212	2	of	of	ADP
cana-1540	212	3	power	power	NOUN
cana-1540	212	4	and	and	CCONJ
cana-1540	212	5	energy	energy	NOUN
cana-1540	212	6	engineering	engineering	NOUN
cana-1540	212	7	,	,	PUNCT
cana-1540	212	8	2022	2022	NUM
cana-1540	212	9	,	,	PUNCT
cana-1540	212	10	doi:10.4236	doi:10.4236	X
cana-1540	212	11	/	/	SYM
cana-1540	212	12	jpee.2022.104004	jpee.2022.104004	PROPN
cana-1540	212	13	.	.	PUNCT
cana-1540	213	1	[	[	X
cana-1540	213	2	25	25	NUM
cana-1540	213	3	]	]	PUNCT
cana-1540	213	4	s.	s.	PROPN
cana-1540	213	5	sharma	sharma	PROPN
cana-1540	213	6	,	,	PUNCT
cana-1540	213	7	s.	s.	PROPN
cana-1540	213	8	devi	devi	PROPN
cana-1540	213	9	,	,	PUNCT
cana-1540	213	10	r.	r.	PROPN
cana-1540	213	11	kumar	kumar	PROPN
cana-1540	213	12	and	and	CCONJ
cana-1540	213	13	m.	m.	PROPN
cana-1540	213	14	marin	marin	PROPN
cana-1540	213	15	,	,	PUNCT
cana-1540	213	16	“	"	PUNCT
cana-1540	213	17	examining	examine	VERB
cana-1540	213	18	basic	basic	ADJ
cana-1540	213	19	theorems	theorem	NOUN
cana-1540	213	20	and	and	CCONJ
cana-1540	213	21	plane	plane	NOUN
cana-1540	213	22	waves	wave	NOUN
cana-1540	213	23	in	in	ADP
cana-1540	213	24	the	the	DET
cana-1540	213	25	context	context	NOUN
cana-1540	213	26	of	of	ADP
cana-1540	213	27	thermoelastic	thermoelastic	ADJ
cana-1540	213	28	diffusion	diffusion	NOUN
cana-1540	213	29	using	use	VERB
cana-1540	213	30	a	a	DET
cana-1540	213	31	multi	multi	ADJ
cana-1540	213	32	-	-	ADJ
cana-1540	213	33	phase	phase	NOUN
cana-1540	213	34	-	-	PUNCT
cana-1540	213	35	lag	lag	NOUN
cana-1540	213	36	model	model	NOUN
cana-1540	213	37	with	with	ADP
cana-1540	213	38	temperature	temperature	NOUN
cana-1540	213	39	dependence	dependence	NOUN
cana-1540	213	40	,	,	PUNCT
cana-1540	213	41	2024	2024	NUM
cana-1540	213	42	,	,	PUNCT
cana-1540	213	43	https://doi.org/10.1080/15376494.2024.2370523	https://doi.org/10.1080/15376494.2024.2370523	PROPN
cana-1540	213	44	.	.	PUNCT
cana-1540	214	1	[	[	X
cana-1540	214	2	26	26	NUM
cana-1540	214	3	]	]	X
cana-1540	214	4	t.r	t.r	PROPN
cana-1540	214	5	.	.	PROPN
cana-1540	214	6	tauchert	tauchert	PROPN
cana-1540	214	7	,	,	PUNCT
cana-1540	214	8	w.d	w.d	PROPN
cana-1540	214	9	.	.	PROPN
cana-1540	214	10	claus	claus	PROPN
cana-1540	214	11	jr	jr	PROPN
cana-1540	214	12	,	,	PUNCT
cana-1540	214	13	and	and	CCONJ
cana-1540	214	14	t.	t.	PROPN
cana-1540	214	15	ariman	ariman	PROPN
cana-1540	214	16	//	//	PROPN
cana-1540	214	17	international	international	PROPN
cana-1540	214	18	journal	journal	PROPN
cana-1540	214	19	of	of	ADP
cana-1540	214	20	engineering	engineering	NOUN
cana-1540	214	21	science	science	NOUN
cana-1540	214	22	6(1	6(1	NUM
cana-1540	214	23	)	)	PUNCT
cana-1540	214	24	(	(	PUNCT
cana-1540	214	25	1968	1968	NUM
cana-1540	214	26	)	)	PUNCT
cana-1540	214	27	37	37	NUM
cana-1540	214	28	.	.	PUNCT
cana-1540	215	1	[	[	X
cana-1540	215	2	27	27	NUM
cana-1540	215	3	]	]	X
cana-1540	215	4	w.	w.	PROPN
cana-1540	215	5	nowacki	nowacki	PROPN
cana-1540	215	6	//	//	PROPN
cana-1540	215	7	couple	couple	NOUN
cana-1540	215	8	-	-	PUNCT
cana-1540	215	9	stresses	stress	NOUN
cana-1540	215	10	in	in	ADP
cana-1540	215	11	the	the	DET
cana-1540	215	12	theory	theory	NOUN
cana-1540	215	13	of	of	ADP
cana-1540	215	14	thermoelasticity	thermoelasticity	NOUN
cana-1540	215	15	in	in	ADP
cana-1540	215	16	irreversible	irreversible	ADJ
cana-1540	215	17	aspects	aspect	NOUN
cana-1540	215	18	of	of	ADP
cana-1540	215	19	continuum	continuum	ADJ
cana-1540	215	20	mechanics	mechanic	NOUN
cana-1540	215	21	and	and	CCONJ
cana-1540	215	22	characteristics	characteristic	NOUN
cana-1540	215	23	in	in	ADP
cana-1540	215	24	moving	move	VERB
cana-1540	215	25	fluids	fluid	NOUN
cana-1540	215	26	(	(	PUNCT
cana-1540	215	27	springer	springer	NOUN
cana-1540	215	28	vienna	vienna	PROPN
cana-1540	215	29	,	,	PUNCT
cana-1540	215	30	new	new	PROPN
cana-1540	215	31	york	york	PROPN
cana-1540	215	32	,	,	PUNCT
cana-1540	215	33	1968	1968	NUM
cana-1540	215	34	)	)	PUNCT
cana-1540	215	35	.	.	PUNCT
cana-1540	216	1	https://doi.org/10.1080/15376494.2024.2370523	https://doi.org/10.1080/15376494.2024.2370523	PROPN