id	sid	tid	token	lemma	pos
easat-224	1	1	edelweiss	edelweiss	PROPN
easat-224	1	2	applied	apply	VERB
easat-224	1	3	science	science	NOUN
easat-224	1	4	and	and	CCONJ
easat-224	1	5	technology	technology	NOUN
easat-224	1	6	issn	issn	PROPN
easat-224	1	7	:	:	PUNCT
easat-224	1	8	2576	2576	NUM
easat-224	1	9	-	-	SYM
easat-224	1	10	8484	8484	NUM
easat-224	1	11	vol	vol	NOUN
easat-224	1	12	.	.	PROPN
easat-224	2	1	2	2	NUM
easat-224	2	2	,	,	PUNCT
easat-224	2	3	no	no	INTJ
easat-224	2	4	.	.	NOUN
easat-224	2	5	1	1	NUM
easat-224	2	6	,	,	PUNCT
easat-224	2	7	1	1	NUM
easat-224	2	8	-	-	SYM
easat-224	2	9	9	9	NUM
easat-224	2	10	2018	2018	NUM
easat-224	2	11	doi	doi	NOUN
easat-224	2	12	:	:	PUNCT
easat-224	2	13	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	2	14	©	©	PROPN
easat-224	2	15	2018	2018	NUM
easat-224	2	16	by	by	ADP
easat-224	2	17	the	the	DET
easat-224	2	18	authors	author	NOUN
easat-224	2	19	©	©	PROPN
easat-224	2	20	2018	2018	NUM
easat-224	2	21	by	by	ADP
easat-224	2	22	the	the	DET
easat-224	2	23	authors	author	NOUN
easat-224	2	24	history	history	NOUN
easat-224	2	25	:	:	PUNCT
easat-224	2	26	received	receive	VERB
easat-224	2	27	:	:	PUNCT
easat-224	2	28	11	11	NUM
easat-224	2	29	november	november	PROPN
easat-224	2	30	2017	2017	NUM
easat-224	2	31	;	;	PUNCT
easat-224	2	32	accepted	accept	VERB
easat-224	2	33	:	:	PUNCT
easat-224	2	34	18	18	NUM
easat-224	2	35	december	december	PROPN
easat-224	2	36	2017	2017	NUM
easat-224	2	37	;	;	PUNCT
easat-224	2	38	published	publish	VERB
easat-224	2	39	:	:	PUNCT
easat-224	2	40	1	1	NUM
easat-224	2	41	january	january	PROPN
easat-224	2	42	2018	2018	NUM
easat-224	2	43	.	.	PUNCT
easat-224	3	1	*	*	PUNCT
easat-224	3	2	correspondence	correspondence	NOUN
easat-224	3	3	:	:	PUNCT
easat-224	4	1	samueladebola84@gmail.com	samueladebola84@gmail.com	X
easat-224	4	2	dynamic	dynamic	ADJ
easat-224	4	3	response	response	NOUN
easat-224	4	4	to	to	ADP
easat-224	4	5	moving	move	VERB
easat-224	4	6	distributed	distribute	VERB
easat-224	4	7	masses	masse	NOUN
easat-224	4	8	of	of	ADP
easat-224	4	9	pre	pre	ADJ
easat-224	4	10	-	-	ADJ
easat-224	4	11	stressed	stressed	ADJ
easat-224	4	12	uniform	uniform	ADJ
easat-224	4	13	rayleigh	rayleigh	PROPN
easat-224	4	14	beam	beam	PROPN
easat-224	4	15	resting	rest	VERB
easat-224	4	16	on	on	ADP
easat-224	4	17	variable	variable	ADJ
easat-224	4	18	elastic	elastic	ADJ
easat-224	4	19	pasternak	pasternak	PROPN
easat-224	4	20	foundation	foundation	PROPN
easat-224	4	21	adeoye	adeoye	PROPN
easat-224	4	22	as1	as1	PROPN
easat-224	4	23	*	*	PROPN
easat-224	4	24	,	,	PUNCT
easat-224	4	25	awodola	awodola	PROPN
easat-224	4	26	to1	to1	PROPN
easat-224	4	27	1department	1department	NUM
easat-224	4	28	of	of	ADP
easat-224	4	29	mathematical	mathematical	ADJ
easat-224	4	30	sciences	sciences	PROPN
easat-224	4	31	,	,	PUNCT
easat-224	4	32	federal	federal	ADJ
easat-224	4	33	university	university	NOUN
easat-224	4	34	of	of	ADP
easat-224	4	35	technology	technology	NOUN
easat-224	4	36	,	,	PUNCT
easat-224	4	37	akure	akure	NOUN
easat-224	4	38	,	,	PUNCT
easat-224	4	39	nigeria	nigeria	PROPN
easat-224	4	40	;	;	PUNCT
easat-224	4	41	samueladebola84@gmail.com	samueladebola84@gmail.com	X
easat-224	4	42	(	(	PUNCT
easat-224	4	43	a.a	a.a	PROPN
easat-224	4	44	.	.	PROPN
easat-224	4	45	)	)	PUNCT
easat-224	4	46	.	.	PUNCT
easat-224	5	1	abstract	abstract	ADV
easat-224	5	2	:	:	PUNCT
easat-224	5	3	the	the	DET
easat-224	5	4	dynamic	dynamic	ADJ
easat-224	5	5	response	response	NOUN
easat-224	5	6	to	to	ADP
easat-224	5	7	moving	move	VERB
easat-224	5	8	distributed	distribute	VERB
easat-224	5	9	masses	masse	NOUN
easat-224	5	10	of	of	ADP
easat-224	5	11	pre	pre	ADJ
easat-224	5	12	-	-	ADJ
easat-224	5	13	stressed	stressed	ADJ
easat-224	5	14	uniform	uniform	ADJ
easat-224	5	15	rayleigh	rayleigh	PROPN
easat-224	5	16	beam	beam	PROPN
easat-224	5	17	resting	rest	VERB
easat-224	5	18	on	on	ADP
easat-224	5	19	variable	variable	ADJ
easat-224	5	20	elastic	elastic	ADJ
easat-224	5	21	pasternak	pasternak	PROPN
easat-224	5	22	foundation	foundation	PROPN
easat-224	5	23	is	be	AUX
easat-224	5	24	examined	examine	VERB
easat-224	5	25	.	.	PUNCT
easat-224	6	1	the	the	DET
easat-224	6	2	equation	equation	NOUN
easat-224	6	3	governing	govern	VERB
easat-224	6	4	this	this	DET
easat-224	6	5	problem	problem	NOUN
easat-224	6	6	is	be	AUX
easat-224	6	7	a	a	DET
easat-224	6	8	fourth	fourth	ADJ
easat-224	6	9	order	order	NOUN
easat-224	6	10	partial	partial	ADJ
easat-224	6	11	differential	differential	NOUN
easat-224	6	12	equation	equation	NOUN
easat-224	6	13	with	with	ADP
easat-224	6	14	variable	variable	NOUN
easat-224	6	15	and	and	CCONJ
easat-224	6	16	singular	singular	ADJ
easat-224	6	17	co	co	NOUN
easat-224	6	18	-	-	NOUN
easat-224	6	19	efficients	efficient	NOUN
easat-224	6	20	.	.	PUNCT
easat-224	7	1	to	to	PART
easat-224	7	2	solve	solve	VERB
easat-224	7	3	this	this	DET
easat-224	7	4	cumbersome	cumbersome	ADJ
easat-224	7	5	equation	equation	NOUN
easat-224	7	6	,	,	PUNCT
easat-224	7	7	the	the	DET
easat-224	7	8	method	method	NOUN
easat-224	7	9	of	of	ADP
easat-224	7	10	galerkin	galerkin	ADJ
easat-224	7	11	approach	approach	NOUN
easat-224	7	12	is	be	AUX
easat-224	7	13	adopted	adopt	VERB
easat-224	7	14	to	to	PART
easat-224	7	15	reduce	reduce	VERB
easat-224	7	16	the	the	DET
easat-224	7	17	governing	govern	VERB
easat-224	7	18	differential	differential	ADJ
easat-224	7	19	equation	equation	NOUN
easat-224	7	20	to	to	ADP
easat-224	7	21	a	a	DET
easat-224	7	22	sequence	sequence	NOUN
easat-224	7	23	of	of	ADP
easat-224	7	24	coupled	couple	VERB
easat-224	7	25	second	second	ADJ
easat-224	7	26	order	order	NOUN
easat-224	7	27	ordinary	ordinary	ADJ
easat-224	7	28	differential	differential	ADJ
easat-224	7	29	equation	equation	NOUN
easat-224	7	30	which	which	PRON
easat-224	7	31	is	be	AUX
easat-224	7	32	then	then	ADV
easat-224	7	33	simplified	simplify	VERB
easat-224	7	34	further	far	ADV
easat-224	7	35	with	with	ADP
easat-224	7	36	modified	modify	VERB
easat-224	7	37	asymptotic	asymptotic	ADJ
easat-224	7	38	method	method	NOUN
easat-224	7	39	of	of	ADP
easat-224	7	40	struble	struble	ADJ
easat-224	7	41	.	.	PUNCT
easat-224	8	1	the	the	DET
easat-224	8	2	more	more	ADV
easat-224	8	3	simplified	simplified	ADJ
easat-224	8	4	equation	equation	NOUN
easat-224	8	5	is	be	AUX
easat-224	8	6	solved	solve	VERB
easat-224	8	7	using	use	VERB
easat-224	8	8	the	the	DET
easat-224	8	9	laplace	laplace	NOUN
easat-224	8	10	transformation	transformation	NOUN
easat-224	8	11	technique	technique	NOUN
easat-224	8	12	.	.	PUNCT
easat-224	9	1	the	the	DET
easat-224	9	2	closed	close	VERB
easat-224	9	3	form	form	NOUN
easat-224	9	4	solutions	solution	NOUN
easat-224	9	5	obtained	obtain	VERB
easat-224	9	6	are	be	AUX
easat-224	9	7	analyzed	analyze	VERB
easat-224	9	8	in	in	ADP
easat-224	9	9	order	order	NOUN
easat-224	9	10	to	to	PART
easat-224	9	11	show	show	VERB
easat-224	9	12	the	the	DET
easat-224	9	13	conditions	condition	NOUN
easat-224	9	14	of	of	ADP
easat-224	9	15	resonance	resonance	NOUN
easat-224	9	16	,	,	PUNCT
easat-224	9	17	and	and	CCONJ
easat-224	9	18	to	to	PART
easat-224	9	19	show	show	VERB
easat-224	9	20	that	that	DET
easat-224	9	21	resonance	resonance	NOUN
easat-224	9	22	is	be	AUX
easat-224	9	23	attained	attain	VERB
easat-224	9	24	earlier	early	ADV
easat-224	9	25	in	in	ADP
easat-224	9	26	moving	move	VERB
easat-224	9	27	mass	mass	ADJ
easat-224	9	28	system	system	NOUN
easat-224	9	29	than	than	ADP
easat-224	9	30	in	in	ADP
easat-224	9	31	the	the	DET
easat-224	9	32	moving	move	VERB
easat-224	9	33	force	force	NOUN
easat-224	9	34	system	system	NOUN
easat-224	9	35	.	.	PUNCT
easat-224	10	1	the	the	DET
easat-224	10	2	results	result	NOUN
easat-224	10	3	in	in	ADP
easat-224	10	4	plotted	plotted	ADJ
easat-224	10	5	graphs	graph	NOUN
easat-224	10	6	show	show	VERB
easat-224	10	7	that	that	SCONJ
easat-224	10	8	as	as	SCONJ
easat-224	10	9	the	the	DET
easat-224	10	10	axial	axial	ADJ
easat-224	10	11	force	force	NOUN
easat-224	10	12	,	,	PUNCT
easat-224	10	13	the	the	DET
easat-224	10	14	rotatory	rotatory	ADJ
easat-224	10	15	inertia	inertia	NOUN
easat-224	10	16	,	,	PUNCT
easat-224	10	17	foundation	foundation	NOUN
easat-224	10	18	modulus	modulus	NOUN
easat-224	10	19	and	and	CCONJ
easat-224	10	20	shear	shear	ADJ
easat-224	10	21	modulus	modulus	ADJ
easat-224	10	22	increase	increase	NOUN
easat-224	10	23	,	,	PUNCT
easat-224	10	24	the	the	DET
easat-224	10	25	deflection	deflection	NOUN
easat-224	10	26	of	of	ADP
easat-224	10	27	the	the	DET
easat-224	10	28	elastically	elastically	ADV
easat-224	10	29	supported	support	VERB
easat-224	10	30	non	non	ADJ
easat-224	10	31	-	-	ADJ
easat-224	10	32	uniform	uniform	ADJ
easat-224	10	33	rayleigh	rayleigh	PROPN
easat-224	10	34	beam	beam	PROPN
easat-224	10	35	decreases	decrease	VERB
easat-224	10	36	in	in	ADP
easat-224	10	37	each	each	DET
easat-224	10	38	case	case	NOUN
easat-224	10	39	.	.	PUNCT
easat-224	11	1	the	the	DET
easat-224	11	2	transverse	transverse	NOUN
easat-224	11	3	deflections	deflection	NOUN
easat-224	11	4	of	of	ADP
easat-224	11	5	the	the	DET
easat-224	11	6	beam	beam	NOUN
easat-224	11	7	on	on	ADP
easat-224	11	8	variable	variable	ADJ
easat-224	11	9	pasternak	pasternak	PROPN
easat-224	11	10	elastic	elastic	ADJ
easat-224	11	11	foundation	foundation	NOUN
easat-224	11	12	are	be	AUX
easat-224	11	13	higher	high	ADJ
easat-224	11	14	under	under	ADP
easat-224	11	15	the	the	DET
easat-224	11	16	action	action	NOUN
easat-224	11	17	of	of	ADP
easat-224	11	18	moving	move	VERB
easat-224	11	19	masses	masse	NOUN
easat-224	11	20	than	than	ADP
easat-224	11	21	those	those	PRON
easat-224	11	22	when	when	SCONJ
easat-224	11	23	only	only	ADV
easat-224	11	24	the	the	DET
easat-224	11	25	force	force	NOUN
easat-224	11	26	effects	effect	NOUN
easat-224	11	27	of	of	ADP
easat-224	11	28	the	the	DET
easat-224	11	29	moving	move	VERB
easat-224	11	30	load	load	NOUN
easat-224	11	31	are	be	AUX
easat-224	11	32	considered	consider	VERB
easat-224	11	33	.	.	PUNCT
easat-224	12	1	this	this	PRON
easat-224	12	2	implies	imply	VERB
easat-224	12	3	that	that	SCONJ
easat-224	12	4	resonance	resonance	NOUN
easat-224	12	5	is	be	AUX
easat-224	12	6	reached	reach	VERB
easat-224	12	7	faster	fast	ADV
easat-224	12	8	in	in	ADP
easat-224	12	9	moving	move	VERB
easat-224	12	10	mass	mass	ADJ
easat-224	12	11	problem	problem	NOUN
easat-224	12	12	than	than	ADP
easat-224	12	13	in	in	ADP
easat-224	12	14	moving	move	VERB
easat-224	12	15	force	force	NOUN
easat-224	12	16	problem	problem	NOUN
easat-224	12	17	.	.	PUNCT
easat-224	13	1	keywords	keyword	NOUN
easat-224	13	2	:	:	PUNCT
easat-224	13	3	pasternak	pasternak	PROPN
easat-224	13	4	foundation	foundation	PROPN
easat-224	13	5	;	;	PUNCT
easat-224	13	6	shear	shear	ADJ
easat-224	13	7	deformation	deformation	NOUN
easat-224	13	8	;	;	PUNCT
easat-224	13	9	resonance	resonance	NOUN
easat-224	13	10	;	;	PUNCT
easat-224	13	11	critical	critical	ADJ
easat-224	13	12	speed	speed	NOUN
easat-224	13	13	;	;	PUNCT
easat-224	13	14	natural	natural	ADJ
easat-224	13	15	frequency	frequency	NOUN
easat-224	13	16	;	;	PUNCT
easat-224	13	17	axial	axial	ADJ
easat-224	13	18	force	force	NOUN
easat-224	13	19	;	;	PUNCT
easat-224	13	20	modified	modified	ADJ
easat-224	13	21	frequency	frequency	NOUN
easat-224	13	22	.	.	PUNCT
easat-224	14	1	1	1	X
easat-224	14	2	.	.	X
easat-224	14	3	introduction	introduction	NOUN
easat-224	14	4	transport	transport	NOUN
easat-224	14	5	structures	structure	NOUN
easat-224	14	6	such	such	ADJ
easat-224	14	7	as	as	ADP
easat-224	14	8	railway	railway	NOUN
easat-224	14	9	or	or	CCONJ
easat-224	14	10	bridges	bridge	NOUN
easat-224	14	11	are	be	AUX
easat-224	14	12	subjected	subject	VERB
easat-224	14	13	to	to	ADP
easat-224	14	14	moving	move	VERB
easat-224	14	15	vehicles	vehicle	NOUN
easat-224	14	16	(	(	PUNCT
easat-224	14	17	loads	load	NOUN
easat-224	14	18	)	)	PUNCT
easat-224	14	19	which	which	PRON
easat-224	14	20	vary	vary	VERB
easat-224	14	21	in	in	ADP
easat-224	14	22	both	both	DET
easat-224	14	23	space	space	NOUN
easat-224	14	24	and	and	CCONJ
easat-224	14	25	time	time	NOUN
easat-224	14	26	.	.	PUNCT
easat-224	15	1	the	the	DET
easat-224	15	2	branch	branch	NOUN
easat-224	15	3	of	of	ADP
easat-224	15	4	transport	transport	NOUN
easat-224	15	5	has	have	AUX
easat-224	15	6	experienced	experience	VERB
easat-224	15	7	great	great	ADJ
easat-224	15	8	advances	advance	NOUN
easat-224	15	9	,	,	PUNCT
easat-224	15	10	characterized	characterize	VERB
easat-224	15	11	by	by	ADP
easat-224	15	12	increasing	increase	VERB
easat-224	15	13	high	high	ADJ
easat-224	15	14	speed	speed	NOUN
easat-224	15	15	and	and	CCONJ
easat-224	15	16	weights	weight	NOUN
easat-224	15	17	of	of	ADP
easat-224	15	18	vehicles	vehicle	NOUN
easat-224	15	19	.	.	PUNCT
easat-224	16	1	these	these	DET
easat-224	16	2	structures	structure	NOUN
easat-224	16	3	on	on	ADP
easat-224	16	4	which	which	PRON
easat-224	16	5	the	the	DET
easat-224	16	6	vehicles	vehicle	NOUN
easat-224	16	7	move	move	VERB
easat-224	16	8	have	have	AUX
easat-224	16	9	been	be	AUX
easat-224	16	10	subjected	subject	VERB
easat-224	16	11	to	to	ADP
easat-224	16	12	vibration	vibration	NOUN
easat-224	16	13	and	and	CCONJ
easat-224	16	14	dynamic	dynamic	ADJ
easat-224	16	15	stress	stress	NOUN
easat-224	16	16	more	more	ADV
easat-224	16	17	than	than	ADP
easat-224	16	18	ever	ever	ADV
easat-224	16	19	before	before	ADV
easat-224	16	20	.	.	PUNCT
easat-224	17	1	therefore	therefore	ADV
easat-224	17	2	,	,	PUNCT
easat-224	17	3	the	the	DET
easat-224	17	4	moving	move	VERB
easat-224	17	5	load	load	NOUN
easat-224	17	6	problem	problem	NOUN
easat-224	17	7	has	have	AUX
easat-224	17	8	been	be	AUX
easat-224	17	9	a	a	DET
easat-224	17	10	fundamental	fundamental	ADJ
easat-224	17	11	problem	problem	NOUN
easat-224	17	12	in	in	ADP
easat-224	17	13	several	several	ADJ
easat-224	17	14	fields	field	NOUN
easat-224	17	15	of	of	ADP
easat-224	17	16	applied	applied	ADJ
easat-224	17	17	mathematics	mathematic	NOUN
easat-224	17	18	,	,	PUNCT
easat-224	17	19	mechanical	mechanical	ADJ
easat-224	17	20	engineering	engineering	NOUN
easat-224	17	21	,	,	PUNCT
easat-224	17	22	applied	applied	ADJ
easat-224	17	23	physics	physics	NOUN
easat-224	17	24	and	and	CCONJ
easat-224	17	25	railway	railway	NOUN
easat-224	17	26	engineering	engineering	NOUN
easat-224	17	27	.	.	PUNCT
easat-224	18	1	rails	rail	NOUN
easat-224	18	2	and	and	CCONJ
easat-224	18	3	bridges	bridge	NOUN
easat-224	18	4	are	be	AUX
easat-224	18	5	examples	example	NOUN
easat-224	18	6	of	of	ADP
easat-224	18	7	structured	structured	ADJ
easat-224	18	8	elements	element	NOUN
easat-224	18	9	to	to	PART
easat-224	18	10	be	be	AUX
easat-224	18	11	designed	design	VERB
easat-224	18	12	to	to	PART
easat-224	18	13	support	support	VERB
easat-224	18	14	moving	move	VERB
easat-224	18	15	masses	masse	NOUN
easat-224	18	16	.	.	PUNCT
easat-224	19	1	most	most	ADV
easat-224	19	2	importantly	importantly	ADV
easat-224	19	3	,	,	PUNCT
easat-224	19	4	problems	problem	NOUN
easat-224	19	5	of	of	ADP
easat-224	19	6	this	this	DET
easat-224	19	7	type	type	NOUN
easat-224	19	8	are	be	AUX
easat-224	19	9	mathematically	mathematically	ADV
easat-224	19	10	cumbersome	cumbersome	ADJ
easat-224	19	11	when	when	SCONJ
easat-224	19	12	the	the	DET
easat-224	19	13	inertial	inertial	ADJ
easat-224	19	14	effect	effect	NOUN
easat-224	19	15	of	of	ADP
easat-224	19	16	the	the	DET
easat-224	19	17	load	load	NOUN
easat-224	19	18	is	be	AUX
easat-224	19	19	taken	take	VERB
easat-224	19	20	into	into	ADP
easat-224	19	21	consideration	consideration	NOUN
easat-224	19	22	.	.	PUNCT
easat-224	20	1	the	the	DET
easat-224	20	2	challenges	challenge	NOUN
easat-224	20	3	of	of	ADP
easat-224	20	4	these	these	DET
easat-224	20	5	designs	design	NOUN
easat-224	20	6	have	have	AUX
easat-224	20	7	attracted	attract	VERB
easat-224	20	8	the	the	DET
easat-224	20	9	interest	interest	NOUN
easat-224	20	10	of	of	ADP
easat-224	20	11	many	many	ADJ
easat-224	20	12	researchers	researcher	NOUN
easat-224	20	13	in	in	ADP
easat-224	20	14	the	the	DET
easat-224	20	15	fields	field	NOUN
easat-224	20	16	of	of	ADP
easat-224	20	17	applied	applied	ADJ
easat-224	20	18	mathematics	mathematic	NOUN
easat-224	20	19	,	,	PUNCT
easat-224	20	20	mechanical	mechanical	ADJ
easat-224	20	21	engineering	engineering	NOUN
easat-224	20	22	,	,	PUNCT
easat-224	20	23	applied	applied	ADJ
easat-224	20	24	physics	physics	NOUN
easat-224	20	25	and	and	CCONJ
easat-224	20	26	railway	railway	NOUN
easat-224	20	27	engineering	engineering	NOUN
easat-224	20	28	.	.	PUNCT
easat-224	21	1	some	some	PRON
easat-224	21	2	of	of	ADP
easat-224	21	3	these	these	DET
easat-224	21	4	researchers	researcher	NOUN
easat-224	21	5	include	include	VERB
easat-224	21	6	fryba	fryba	ADJ
easat-224	21	7	[	[	X
easat-224	21	8	1	1	NUM
easat-224	21	9	]	]	PUNCT
easat-224	21	10	who	who	PRON
easat-224	21	11	studied	study	VERB
easat-224	21	12	the	the	DET
easat-224	21	13	vibration	vibration	NOUN
easat-224	21	14	of	of	ADP
easat-224	21	15	solids	solid	NOUN
easat-224	21	16	and	and	CCONJ
easat-224	21	17	structures	structure	NOUN
easat-224	21	18	under	under	ADP
easat-224	21	19	moving	move	VERB
easat-224	21	20	loads	load	NOUN
easat-224	21	21	.	.	PUNCT
easat-224	22	1	gbadeyan	gbadeyan	NOUN
easat-224	22	2	and	and	CCONJ
easat-224	22	3	dada	dada	X
easat-224	23	1	[	[	X
easat-224	23	2	2	2	NUM
easat-224	23	3	]	]	PUNCT
easat-224	23	4	examined	examine	VERB
easat-224	23	5	the	the	DET
easat-224	23	6	influence	influence	NOUN
easat-224	23	7	of	of	ADP
easat-224	23	8	elastic	elastic	ADJ
easat-224	23	9	foundation	foundation	NOUN
easat-224	23	10	on	on	ADP
easat-224	23	11	plate	plate	NOUN
easat-224	23	12	under	under	ADP
easat-224	23	13	a	a	DET
easat-224	23	14	moving	move	VERB
easat-224	23	15	load	load	NOUN
easat-224	23	16	without	without	ADP
easat-224	23	17	considering	consider	VERB
easat-224	23	18	the	the	DET
easat-224	23	19	influence	influence	NOUN
easat-224	23	20	of	of	ADP
easat-224	23	21	rotatory	rotatory	ADJ
easat-224	23	22	inertia	inertia	NOUN
easat-224	23	23	and	and	CCONJ
easat-224	23	24	shear	shear	ADJ
easat-224	23	25	deformation	deformation	NOUN
easat-224	23	26	on	on	ADP
easat-224	23	27	the	the	DET
easat-224	23	28	plate	plate	NOUN
easat-224	23	29	.	.	PUNCT
easat-224	24	1	the	the	DET
easat-224	24	2	work	work	NOUN
easat-224	24	3	of	of	ADP
easat-224	24	4	stanistic	stanistic	ADJ
easat-224	24	5	et	et	PROPN
easat-224	24	6	al	al	PROPN
easat-224	24	7	was	be	AUX
easat-224	24	8	taken	take	VERB
easat-224	24	9	up	up	ADP
easat-224	24	10	much	much	ADV
easat-224	24	11	later	later	ADV
easat-224	24	12	by	by	ADP
easat-224	24	13	gbadeyan	gbadeyan	NOUN
easat-224	24	14	and	and	CCONJ
easat-224	24	15	oni	oni	VERB
easat-224	25	1	[	[	X
easat-224	25	2	3	3	X
easat-224	25	3	]	]	PUNCT
easat-224	25	4	who	who	PRON
easat-224	25	5	investigated	investigate	VERB
easat-224	25	6	the	the	DET
easat-224	25	7	dynamic	dynamic	ADJ
easat-224	25	8	analysis	analysis	NOUN
easat-224	25	9	of	of	ADP
easat-224	25	10	an	an	DET
easat-224	25	11	elastic	elastic	ADJ
easat-224	25	12	plate	plate	NOUN
easat-224	25	13	continuously	continuously	ADV
easat-224	25	14	supported	support	VERB
easat-224	25	15	by	by	ADP
easat-224	25	16	an	an	DET
easat-224	25	17	elastic	elastic	ADJ
easat-224	25	18	foundation	foundation	NOUN
easat-224	25	19	and	and	CCONJ
easat-224	25	20	traversed	traverse	VERB
easat-224	25	21	by	by	ADP
easat-224	25	22	an	an	DET
easat-224	25	23	arbitrary	arbitrary	ADJ
easat-224	25	24	number	number	NOUN
easat-224	25	25	of	of	ADP
easat-224	25	26	concentrated	concentrated	ADJ
easat-224	25	27	moving	move	VERB
easat-224	25	28	masses	masse	NOUN
easat-224	25	29	.	.	PUNCT
easat-224	26	1	yavari	yavari	PROPN
easat-224	27	1	[	[	X
easat-224	27	2	4	4	X
easat-224	27	3	]	]	PUNCT
easat-224	27	4	studied	study	VERB
easat-224	27	5	the	the	DET
easat-224	27	6	generalized	generalized	ADJ
easat-224	27	7	solution	solution	NOUN
easat-224	27	8	of	of	ADP
easat-224	27	9	beams	beam	NOUN
easat-224	27	10	with	with	ADP
easat-224	27	11	jump	jump	NOUN
easat-224	27	12	discontinuities	discontinuity	NOUN
easat-224	27	13	on	on	ADP
easat-224	27	14	elastic	elastic	ADJ
easat-224	27	15	foundation	foundation	NOUN
easat-224	27	16	.	.	PUNCT
easat-224	28	1	yin	yin	PROPN
easat-224	29	1	[	[	X
easat-224	29	2	5	5	NUM
easat-224	29	3	]	]	PUNCT
easat-224	29	4	also	also	ADV
easat-224	29	5	investigated	investigate	VERB
easat-224	29	6	the	the	DET
easat-224	29	7	closed	closed	ADJ
easat-224	29	8	form	form	NOUN
easat-224	29	9	solution	solution	NOUN
easat-224	29	10	for	for	ADP
easat-224	29	11	reinforced	reinforce	VERB
easat-224	29	12	timoshenko	timoshenko	NOUN
easat-224	29	13	beam	beam	NOUN
easat-224	29	14	on	on	ADP
easat-224	29	15	elastic	elastic	ADJ
easat-224	29	16	foundation	foundation	NOUN
easat-224	29	17	.	.	PUNCT
easat-224	30	1	in	in	ADP
easat-224	30	2	the	the	DET
easat-224	30	3	same	same	ADJ
easat-224	30	4	vein	vein	NOUN
easat-224	30	5	,	,	PUNCT
easat-224	30	6	teodoru	teodoru	NOUN
easat-224	31	1	[	[	X
easat-224	31	2	6	6	NUM
easat-224	31	3	]	]	PUNCT
easat-224	31	4	in	in	ADP
easat-224	31	5	his	his	PRON
easat-224	31	6	work	work	NOUN
easat-224	31	7	,	,	PUNCT
easat-224	31	8	analyzed	analyze	VERB
easat-224	31	9	beam	beam	NOUN
easat-224	31	10	on	on	ADP
easat-224	31	11	elastic	elastic	ADJ
easat-224	31	12	foundation	foundation	NOUN
easat-224	31	13	by	by	ADP
easat-224	31	14	using	use	VERB
easat-224	31	15	finite	finite	ADJ
easat-224	31	16	difference	difference	NOUN
easat-224	31	17	approach	approach	NOUN
easat-224	31	18	.	.	PUNCT
easat-224	32	1	oni	oni	PROPN
easat-224	32	2	and	and	CCONJ
easat-224	32	3	awodola	awodola	PROPN
easat-224	33	1	[	[	X
easat-224	33	2	7	7	NUM
easat-224	33	3	]	]	PUNCT
easat-224	33	4	investigated	investigate	VERB
easat-224	33	5	the	the	DET
easat-224	33	6	vibrations	vibration	NOUN
easat-224	33	7	under	under	ADP
easat-224	33	8	a	a	DET
easat-224	33	9	moving	move	VERB
easat-224	33	10	load	load	NOUN
easat-224	33	11	of	of	ADP
easat-224	33	12	a	a	DET
easat-224	33	13	non	non	ADJ
easat-224	33	14	-	-	ADJ
easat-224	33	15	uniform	uniform	ADJ
easat-224	33	16	rayleigh	rayleigh	PROPN
easat-224	33	17	beam	beam	PROPN
easat-224	33	18	on	on	ADP
easat-224	33	19	variable	variable	ADJ
easat-224	33	20	elastic	elastic	ADJ
easat-224	33	21	foundation	foundation	NOUN
easat-224	33	22	.	.	PUNCT
easat-224	34	1	oni	oni	PROPN
easat-224	34	2	and	and	CCONJ
easat-224	34	3	awodola	awodola	PROPN
easat-224	35	1	[	[	X
easat-224	35	2	8	8	NUM
easat-224	35	3	]	]	PUNCT
easat-224	35	4	also	also	ADV
easat-224	35	5	analyzed	analyze	VERB
easat-224	35	6	the	the	DET
easat-224	35	7	dynamic	dynamic	ADJ
easat-224	35	8	response	response	NOUN
easat-224	35	9	under	under	ADP
easat-224	35	10	a	a	DET
easat-224	35	11	moving	move	VERB
easat-224	35	12	load	load	NOUN
easat-224	35	13	of	of	ADP
easat-224	35	14	an	an	DET
easat-224	35	15	elastically	elastically	ADV
easat-224	35	16	supported	support	VERB
easat-224	35	17	non	non	ADJ
easat-224	35	18	-	-	ADJ
easat-224	35	19	prismatic	prismatic	ADJ
easat-224	35	20	bernoullieuler	bernoullieuler	NOUN
easat-224	35	21	beam	beam	NOUN
easat-224	35	22	on	on	ADP
easat-224	35	23	variable	variable	NOUN
easat-224	35	24	.	.	PUNCT
easat-224	36	1	elastic	elastic	ADJ
easat-224	36	2	foundation	foundation	NOUN
easat-224	36	3	.	.	PUNCT
easat-224	37	1	in	in	ADP
easat-224	37	2	the	the	DET
easat-224	37	3	work	work	NOUN
easat-224	37	4	of	of	ADP
easat-224	37	5	oni	oni	NOUN
easat-224	37	6	and	and	CCONJ
easat-224	37	7	omolofe	omolofe	VERB
easat-224	37	8	[	[	X
easat-224	37	9	9	9	NUM
easat-224	37	10	]	]	X
easat-224	37	11	the	the	DET
easat-224	37	12	dynamic	dynamic	ADJ
easat-224	37	13	analysis	analysis	NOUN
easat-224	37	14	of	of	ADP
easat-224	37	15	a	a	DET
easat-224	37	16	pre	pre	ADJ
easat-224	37	17	-	-	ADJ
easat-224	37	18	stressed	stressed	ADJ
easat-224	37	19	elastic	elastic	ADJ
easat-224	37	20	beam	beam	NOUN
easat-224	37	21	with	with	ADP
easat-224	37	22	general	general	ADJ
easat-224	37	23	boundary	boundary	ADJ
easat-224	37	24	conditions	condition	NOUN
easat-224	37	25	under	under	ADP
easat-224	37	26	moving	move	VERB
easat-224	37	27	loads	load	NOUN
easat-224	37	28	at	at	ADP
easat-224	37	29	varying	vary	VERB
easat-224	37	30	velocities	velocity	NOUN
easat-224	37	31	was	be	AUX
easat-224	37	32	investigated	investigate	VERB
easat-224	37	33	.	.	PUNCT
easat-224	38	1	the	the	DET
easat-224	38	2	study	study	NOUN
easat-224	38	3	on	on	ADP
easat-224	38	4	exact	exact	ADJ
easat-224	38	5	series	series	NOUN
easat-224	38	6	solution	solution	NOUN
easat-224	38	7	for	for	ADP
easat-224	38	8	the	the	DET
easat-224	38	9	transverse	transverse	NOUN
easat-224	38	10	vibrations	vibration	NOUN
easat-224	38	11	of	of	ADP
easat-224	38	12	rectangular	rectangular	ADJ
easat-224	38	13	plates	plate	NOUN
easat-224	38	14	with	with	ADP
easat-224	38	15	elastic	elastic	ADJ
easat-224	38	16	boundary	boundary	ADJ
easat-224	38	17	supports	support	NOUN
easat-224	38	18	was	be	AUX
easat-224	38	19	carried	carry	VERB
easat-224	38	20	out	out	ADP
easat-224	38	21	by	by	ADP
easat-224	38	22	li	li	PROPN
easat-224	39	1	[	[	X
easat-224	39	2	10	10	NUM
easat-224	39	3	]	]	PUNCT
easat-224	39	4	.	.	PUNCT
easat-224	40	1	hsu	hsu	PROPN
easat-224	41	1	[	[	X
easat-224	41	2	11	11	NUM
easat-224	41	3	]	]	PUNCT
easat-224	41	4	studied	study	VERB
easat-224	41	5	the	the	DET
easat-224	41	6	vibration	vibration	NOUN
easat-224	41	7	analysis	analysis	NOUN
easat-224	41	8	of	of	ADP
easat-224	41	9	non	non	ADJ
easat-224	41	10	-	-	ADJ
easat-224	41	11	uniform	uniform	ADJ
easat-224	41	12	beams	beam	NOUN
easat-224	41	13	resting	rest	VERB
easat-224	41	14	on	on	ADP
easat-224	41	15	elastic	elastic	ADJ
easat-224	41	16	foundation	foundation	NOUN
easat-224	41	17	.	.	PUNCT
easat-224	42	1	the	the	DET
easat-224	42	2	work	work	NOUN
easat-224	42	3	of	of	ADP
easat-224	42	4	ismail	ismail	NOUN
easat-224	42	5	[	[	X
easat-224	42	6	12	12	NUM
easat-224	42	7	]	]	PUNCT
easat-224	42	8	on	on	ADP
easat-224	42	9	dynamic	dynamic	ADJ
easat-224	42	10	response	response	NOUN
easat-224	42	11	of	of	ADP
easat-224	42	12	a	a	DET
easat-224	42	13	beam	beam	NOUN
easat-224	42	14	due	due	ADP
easat-224	42	15	to	to	ADP
easat-224	42	16	an	an	DET
easat-224	42	17	accelerating	accelerate	VERB
easat-224	42	18	moving	move	VERB
easat-224	42	19	mass	mass	NOUN
easat-224	42	20	using	use	VERB
easat-224	42	21	moving	move	VERB
easat-224	42	22	finite	finite	ADJ
easat-224	42	23	element	element	NOUN
easat-224	42	24	approximation	approximation	NOUN
easat-224	42	25	can	can	AUX
easat-224	42	26	not	not	PART
easat-224	42	27	be	be	AUX
easat-224	42	28	ignored	ignore	VERB
easat-224	42	29	.	.	PUNCT
easat-224	43	1	kargarmovin	kargarmovin	PROPN
easat-224	43	2	and	and	CCONJ
easat-224	43	3	younesian	younesian	NOUN
easat-224	44	1	[	[	X
easat-224	44	2	13	13	NUM
easat-224	44	3	]	]	PUNCT
easat-224	44	4	took	take	VERB
easat-224	44	5	further	further	ADJ
easat-224	44	6	study	study	NOUN
easat-224	44	7	on	on	ADP
easat-224	44	8	dynamic	dynamic	ADJ
easat-224	44	9	of	of	ADP
easat-224	44	10	timoshenko	timoshenko	ADJ
easat-224	44	11	beams	beam	NOUN
easat-224	44	12	on	on	ADP
easat-224	44	13	pasternak	pasternak	PROPN
easat-224	44	14	foundation	foundation	PROPN
easat-224	44	15	under	under	ADP
easat-224	44	16	moving	move	VERB
easat-224	44	17	load	load	NOUN
easat-224	44	18	.	.	PUNCT
easat-224	45	1	recently	recently	ADV
easat-224	45	2	,	,	PUNCT
easat-224	45	3	adeoye	adeoye	VERB
easat-224	45	4	and	and	CCONJ
easat-224	45	5	awodola	awodola	PROPN
easat-224	46	1	[	[	X
easat-224	46	2	14	14	NUM
easat-224	46	3	]	]	PUNCT
easat-224	46	4	took	take	VERB
easat-224	46	5	a	a	DET
easat-224	46	6	close	close	NOUN
easat-224	46	7	studied	study	VERB
easat-224	46	8	on	on	ADP
easat-224	46	9	influence	influence	NOUN
easat-224	46	10	of	of	ADP
easat-224	46	11	rotatory	rotatory	ADJ
easat-224	46	12	inertial	inertial	ADJ
easat-224	46	13	correction	correction	NOUN
easat-224	46	14	factor	factor	NOUN
easat-224	46	15	on	on	ADP
easat-224	46	16	the	the	DET
easat-224	46	17	vibration	vibration	NOUN
easat-224	46	18	of	of	ADP
easat-224	46	19	elastically	elastically	ADV
easat-224	46	20	supported	support	VERB
easat-224	46	21	non	non	ADJ
easat-224	46	22	-	-	ADJ
easat-224	46	23	uniform	uniform	ADJ
easat-224	46	24	rayleigh	rayleigh	PROPN
easat-224	46	25	beam	beam	NOUN
easat-224	46	26	using	use	VERB
easat-224	46	27	galerkin	galerkin	ADJ
easat-224	46	28	method	method	NOUN
easat-224	46	29	and	and	CCONJ
easat-224	46	30	struble	struble	ADJ
easat-224	46	31	technique	technique	NOUN
easat-224	46	32	.	.	PUNCT
easat-224	47	1	adeoye	adeoye	PROPN
easat-224	47	2	and	and	CCONJ
easat-224	47	3	akintomide	akintomide	VERB
easat-224	47	4	[	[	X
easat-224	47	5	15	15	NUM
easat-224	47	6	]	]	PUNCT
easat-224	47	7	investigated	investigate	VERB
easat-224	47	8	dynamic	dynamic	ADJ
easat-224	47	9	behavior	behavior	NOUN
easat-224	47	10	of	of	ADP
easat-224	47	11	bernoulli	bernoulli	PROPN
easat-224	47	12	-	-	PUNCT
easat-224	47	13	euler	euler	NOUN
easat-224	47	14	beam	beam	NOUN
easat-224	47	15	with	with	ADP
easat-224	47	16	elastically	elastically	ADV
easat-224	47	17	supported	support	VERB
easat-224	47	18	boundary	boundary	ADJ
easat-224	47	19	conditions	condition	NOUN
easat-224	47	20	under	under	ADP
easat-224	47	21	moving	move	VERB
easat-224	47	22	distributed	distribute	VERB
easat-224	47	23	masses	masse	NOUN
easat-224	47	24	on	on	ADP
easat-224	47	25	constant	constant	ADJ
easat-224	47	26	bi	bi	ADJ
easat-224	47	27	-	-	ADJ
easat-224	47	28	parametric	parametric	ADJ
easat-224	47	29	foundation	foundation	NOUN
easat-224	47	30	using	use	VERB
easat-224	47	31	galerkin	galerkin	ADJ
easat-224	47	32	method	method	NOUN
easat-224	47	33	and	and	CCONJ
easat-224	47	34	struble	struble	ADJ
easat-224	47	35	technique	technique	NOUN
easat-224	47	36	.	.	PUNCT
easat-224	48	1	akintomide	akintomide	PROPN
easat-224	48	2	and	and	CCONJ
easat-224	48	3	awodola	awodola	PROPN
easat-224	49	1	[	[	X
easat-224	49	2	16	16	NUM
easat-224	49	3	]	]	PUNCT
easat-224	49	4	analyzed	analyze	VERB
easat-224	49	5	the	the	DET
easat-224	49	6	dynamic	dynamic	ADJ
easat-224	49	7	response	response	NOUN
easat-224	49	8	to	to	ADP
easat-224	49	9	variable	variable	ADJ
easat-224	49	10	-	-	PUNCT
easat-224	49	11	magnitude	magnitude	NOUN
easat-224	49	12	moving	move	VERB
easat-224	49	13	distributed	distribute	VERB
easat-224	49	14	masses	masse	NOUN
easat-224	49	15	of	of	ADP
easat-224	49	16	bernoulli	bernoulli	PROPN
easat-224	49	17	-	-	PUNCT
easat-224	49	18	euler	euler	NOUN
easat-224	49	19	beam	beam	NOUN
easat-224	49	20	on	on	ADP
easat-224	49	21	bi	bi	ADJ
easat-224	49	22	-	-	ADJ
easat-224	49	23	parametric	parametric	ADJ
easat-224	49	24	foundation	foundation	NOUN
easat-224	49	25	and	and	CCONJ
easat-224	49	26	they	they	PRON
easat-224	49	27	obtained	obtain	VERB
easat-224	49	28	the	the	DET
easat-224	49	29	closed	closed	ADJ
easat-224	49	30	form	form	NOUN
easat-224	49	31	solution	solution	NOUN
easat-224	49	32	using	use	VERB
easat-224	49	33	runge	runge	NOUN
easat-224	49	34	-	-	PUNCT
easat-224	49	35	kutta	kutta	NOUN
easat-224	49	36	technique	technique	NOUN
easat-224	49	37	.	.	PUNCT
easat-224	50	1	in	in	ADP
easat-224	50	2	our	our	PRON
easat-224	50	3	recent	recent	ADJ
easat-224	50	4	research	research	NOUN
easat-224	50	5	work	work	NOUN
easat-224	50	6	,	,	PUNCT
easat-224	50	7	adeoye	adeoye	VERB
easat-224	50	8	and	and	CCONJ
easat-224	50	9	awodola	awodola	PROPN
easat-224	51	1	[	[	X
easat-224	51	2	14	14	NUM
easat-224	51	3	]	]	SYM
easat-224	51	4	effort	effort	NOUN
easat-224	51	5	was	be	AUX
easat-224	51	6	made	make	VERB
easat-224	51	7	to	to	PART
easat-224	51	8	investigate	investigate	VERB
easat-224	51	9	the	the	DET
easat-224	51	10	influence	influence	NOUN
easat-224	51	11	of	of	ADP
easat-224	51	12	rotatory	rotatory	ADJ
easat-224	51	13	inertial	inertial	ADJ
easat-224	51	14	correction	correction	NOUN
easat-224	51	15	factor	factor	NOUN
easat-224	51	16	on	on	ADP
easat-224	51	17	the	the	DET
easat-224	51	18	vibration	vibration	NOUN
easat-224	51	19	of	of	ADP
easat-224	51	20	elastically	elastically	ADV
easat-224	51	21	supported	support	VERB
easat-224	51	22	non	non	ADJ
easat-224	51	23	-	-	ADJ
easat-224	51	24	uniform	uniform	ADJ
easat-224	51	25	rayleigh	rayleigh	PROPN
easat-224	51	26	beam	beam	PROPN
easat-224	51	27	on	on	ADP
easat-224	51	28	variable	variable	ADJ
easat-224	51	29	foundation	foundation	NOUN
easat-224	51	30	.	.	PUNCT
easat-224	52	1	the	the	DET
easat-224	52	2	objective	objective	NOUN
easat-224	52	3	of	of	ADP
easat-224	52	4	this	this	DET
easat-224	52	5	paper	paper	NOUN
easat-224	52	6	is	be	AUX
easat-224	52	7	to	to	PART
easat-224	52	8	extend	extend	VERB
easat-224	52	9	this	this	DET
easat-224	52	10	research	research	NOUN
easat-224	52	11	work	work	NOUN
easat-224	52	12	to	to	PART
easat-224	52	13	elastically	elastically	ADV
easat-224	52	14	supported	support	VERB
easat-224	52	15	uniform	uniform	ADJ
easat-224	52	16	rayleigh	rayleigh	PROPN
easat-224	52	17	beam	beam	PROPN
easat-224	52	18	on	on	ADP
easat-224	52	19	variable	variable	ADJ
easat-224	52	20	elastic	elastic	ADJ
easat-224	52	21	bi	bi	ADJ
easat-224	52	22	-	-	ADJ
easat-224	52	23	parametric	parametric	ADJ
easat-224	52	24	foundation	foundation	NOUN
easat-224	52	25	.	.	PUNCT
easat-224	53	1	this	this	DET
easat-224	53	2	paper	paper	NOUN
easat-224	53	3	therefore	therefore	ADV
easat-224	53	4	investigates	investigate	VERB
easat-224	53	5	dynamic	dynamic	ADJ
easat-224	53	6	response	response	NOUN
easat-224	53	7	to	to	ADP
easat-224	53	8	moving	move	VERB
easat-224	53	9	distributed	distribute	VERB
easat-224	53	10	masses	masse	NOUN
easat-224	53	11	of	of	ADP
easat-224	53	12	pre	pre	ADJ
easat-224	53	13	-	-	ADJ
easat-224	53	14	stressed	stressed	ADJ
easat-224	53	15	uniform	uniform	ADJ
easat-224	53	16	rayleigh	rayleigh	PROPN
easat-224	53	17	beam	beam	PROPN
easat-224	53	18	resting	rest	VERB
easat-224	53	19	on	on	ADP
easat-224	53	20	variable	variable	ADJ
easat-224	53	21	elastic	elastic	ADJ
easat-224	53	22	pasternak	pasternak	PROPN
easat-224	53	23	foundation	foundation	NOUN
easat-224	53	24	.	.	PUNCT
easat-224	54	1	1.1	1.1	NUM
easat-224	54	2	.	.	PUNCT
easat-224	55	1	governing	govern	VERB
easat-224	55	2	equation	equation	NOUN
easat-224	55	3	considering	consider	VERB
easat-224	55	4	the	the	DET
easat-224	55	5	dynamic	dynamic	ADJ
easat-224	55	6	response	response	NOUN
easat-224	55	7	to	to	ADP
easat-224	55	8	moving	move	VERB
easat-224	55	9	distributed	distribute	VERB
easat-224	55	10	masses	masse	NOUN
easat-224	55	11	of	of	ADP
easat-224	55	12	pre	pre	ADJ
easat-224	55	13	-	-	ADJ
easat-224	55	14	stressed	stressed	ADJ
easat-224	55	15	uniform	uniform	ADJ
easat-224	55	16	rayleigh	rayleigh	PROPN
easat-224	55	17	beam	beam	PROPN
easat-224	55	18	on	on	ADP
easat-224	55	19	variable	variable	ADJ
easat-224	55	20	elastic	elastic	ADJ
easat-224	55	21	pasternak	pasternak	PROPN
easat-224	55	22	foundation	foundation	PROPN
easat-224	55	23	;	;	PUNCT
easat-224	55	24	the	the	DET
easat-224	55	25	governing	govern	VERB
easat-224	55	26	equation	equation	NOUN
easat-224	55	27	of	of	ADP
easat-224	55	28	motion	motion	NOUN
easat-224	55	29	is	be	AUX
easat-224	55	30	given	give	VERB
easat-224	55	31	by	by	ADP
easat-224	55	32	the	the	DET
easat-224	55	33	fourth	fourth	ADJ
easat-224	55	34	order	order	NOUN
easat-224	55	35	partial	partial	ADJ
easat-224	55	36	differential	differential	NOUN
easat-224	55	37	equation	equation	NOUN
easat-224	55	38	fryba	fryba	ADJ
easat-224	55	39	[	[	X
easat-224	55	40	1	1	NUM
easat-224	55	41	]	]	PUNCT
easat-224	55	42	.	.	PUNCT
easat-224	56	1	𝒜𝐼	𝒜𝐼	PROPN
easat-224	56	2	𝜕4	𝜕4	PROPN
easat-224	56	3	𝜕𝑥4	𝜕𝑥4	PROPN
easat-224	56	4	𝒷(𝑥	𝒷(𝑥	PROPN
easat-224	56	5	,	,	PUNCT
easat-224	56	6	𝑡	𝑡	NOUN
easat-224	56	7	)	)	PUNCT
easat-224	56	8	𝜕	𝜕	NOUN
easat-224	56	9	𝜕𝑥	𝜕𝑥	X
easat-224	57	1	[	[	X
easat-224	57	2	𝒩𝑜	𝒩𝑜	ADP
easat-224	57	3	𝜕	𝜕	NOUN
easat-224	57	4	𝜕𝑥	𝜕𝑥	X
easat-224	57	5	𝒷(𝑥	𝒷(𝑥	PROPN
easat-224	57	6	,	,	PUNCT
easat-224	57	7	𝑡	𝑡	NOUN
easat-224	57	8	)	)	PUNCT
easat-224	57	9	]	]	PUNCT
easat-224	57	10	𝔅(𝑥	𝔅(𝑥	NOUN
easat-224	57	11	)	)	PUNCT
easat-224	57	12	𝜕2	𝜕2	NOUN
easat-224	57	13	𝜕𝑡	𝜕𝑡	NOUN
easat-224	57	14	2	2	NUM
easat-224	57	15	𝒷(𝑥	𝒷(𝑥	PROPN
easat-224	57	16	,	,	PUNCT
easat-224	57	17	𝑡	𝑡	NOUN
easat-224	57	18	)	)	PUNCT
easat-224	57	19	𝔅(𝑥)ℛ	𝔅(𝑥)ℛ	VERB
easat-224	57	20	𝑜	𝑜	X
easat-224	57	21	𝜕4	𝜕4	PROPN
easat-224	57	22	𝜕𝑥2𝜕𝑡	𝜕𝑥2𝜕𝑡	ADP
easat-224	57	23	2	2	NUM
easat-224	57	24	𝒷(𝑥	𝒷(𝑥	NOUN
easat-224	57	25	,	,	PUNCT
easat-224	57	26	𝑡	𝑡	NOUN
easat-224	57	27	)	)	PUNCT
easat-224	57	28	+	+	CCONJ
easat-224	58	1	𝛿(𝑥	𝛿(𝑥	PROPN
easat-224	58	2	,	,	PUNCT
easat-224	58	3	𝑡	𝑡	NOUN
easat-224	58	4	)	)	PUNCT
easat-224	58	5	=	=	SYM
easat-224	59	1	𝒫(𝑥	𝒫(𝑥	NOUN
easat-224	59	2	,	,	PUNCT
easat-224	59	3	𝑡	𝑡	NOUN
easat-224	59	4	)	)	PUNCT
easat-224	59	5	(	(	PUNCT
easat-224	59	6	1	1	X
easat-224	59	7	)	)	PUNCT
easat-224	59	8	where	where	SCONJ
easat-224	59	9	𝑥	𝑥	PROPN
easat-224	59	10	is	be	AUX
easat-224	59	11	the	the	DET
easat-224	59	12	spatial	spatial	ADJ
easat-224	59	13	co	co	NOUN
easat-224	59	14	-	-	NOUN
easat-224	59	15	ordinate	ordinate	NOUN
easat-224	59	16	,	,	PUNCT
easat-224	59	17	t	t	PROPN
easat-224	59	18	is	be	AUX
easat-224	59	19	the	the	DET
easat-224	59	20	time	time	NOUN
easat-224	59	21	co	co	NOUN
easat-224	59	22	-	-	NOUN
easat-224	59	23	ordinate	ordinate	ADJ
easat-224	59	24	,	,	PUNCT
easat-224	59	25	𝒷(𝑥	𝒷(𝑥	PROPN
easat-224	59	26	,	,	PUNCT
easat-224	59	27	𝑡	𝑡	NOUN
easat-224	59	28	)	)	PUNCT
easat-224	59	29	is	be	AUX
easat-224	59	30	the	the	DET
easat-224	59	31	transverse	transverse	ADJ
easat-224	59	32	displacement	displacement	NOUN
easat-224	59	33	,	,	PUNCT
easat-224	59	34	𝒜𝐼	𝒜𝐼	PROPN
easat-224	59	35	is	be	AUX
easat-224	59	36	the	the	DET
easat-224	59	37	flexural	flexural	ADJ
easat-224	59	38	rigidity	rigidity	NOUN
easat-224	59	39	of	of	ADP
easat-224	59	40	the	the	DET
easat-224	59	41	structure	structure	NOUN
easat-224	59	42	,	,	PUNCT
easat-224	59	43	𝔅(𝑥	𝔅(𝑥	NOUN
easat-224	59	44	)	)	PUNCT
easat-224	59	45	is	be	AUX
easat-224	59	46	the	the	DET
easat-224	59	47	variable	variable	ADJ
easat-224	59	48	mass	mass	NOUN
easat-224	59	49	per	per	ADP
easat-224	59	50	unit	unit	NOUN
easat-224	59	51	length	length	NOUN
easat-224	59	52	of	of	ADP
easat-224	59	53	the	the	DET
easat-224	59	54	non	non	ADJ
easat-224	59	55	-	-	ADJ
easat-224	59	56	uniform	uniform	ADJ
easat-224	59	57	beam	beam	NOUN
easat-224	59	58	,	,	PUNCT
easat-224	60	1	𝒩𝑜is	𝒩𝑜is	PROPN
easat-224	60	2	the	the	DET
easat-224	60	3	constant	constant	ADJ
easat-224	60	4	axial	axial	ADJ
easat-224	60	5	force	force	NOUN
easat-224	60	6	,	,	PUNCT
easat-224	60	7	ℛ	ℛ	PROPN
easat-224	60	8	𝑜	𝑜	NOUN
easat-224	60	9	is	be	AUX
easat-224	60	10	the	the	DET
easat-224	60	11	rotatory	rotatory	ADJ
easat-224	60	12	inertial	inertial	ADJ
easat-224	60	13	correction	correction	NOUN
easat-224	60	14	factor	factor	NOUN
easat-224	60	15	,	,	PUNCT
easat-224	60	16	𝛿(𝑥	𝛿(𝑥	PROPN
easat-224	60	17	,	,	PUNCT
easat-224	60	18	𝑡	𝑡	X
easat-224	60	19	)	)	PUNCT
easat-224	60	20	is	be	AUX
easat-224	60	21	the	the	DET
easat-224	60	22	variable	variable	ADJ
easat-224	60	23	foundation	foundation	NOUN
easat-224	60	24	reaction	reaction	PROPN
easat-224	60	25	𝒫(𝑥	𝒫(𝑥	NOUN
easat-224	60	26	,	,	PUNCT
easat-224	60	27	𝑡	𝑡	X
easat-224	60	28	)	)	PUNCT
easat-224	60	29	is	be	AUX
easat-224	60	30	the	the	DET
easat-224	60	31	moving	move	VERB
easat-224	60	32	distributed	distribute	VERB
easat-224	60	33	load	load	NOUN
easat-224	60	34	.	.	PUNCT
easat-224	61	1	the	the	DET
easat-224	61	2	relationship	relationship	NOUN
easat-224	61	3	between	between	ADP
easat-224	61	4	the	the	DET
easat-224	61	5	foundation	foundation	NOUN
easat-224	61	6	reaction	reaction	NOUN
easat-224	61	7	and	and	CCONJ
easat-224	61	8	lateral	lateral	ADJ
easat-224	61	9	deflection	deflection	NOUN
easat-224	61	10	𝒷(𝑥	𝒷(𝑥	NOUN
easat-224	61	11	,	,	PUNCT
easat-224	61	12	𝑡	𝑡	NOUN
easat-224	61	13	)	)	PUNCT
easat-224	61	14	is	be	AUX
easat-224	61	15	𝛿(𝑥	𝛿(𝑥	NOUN
easat-224	61	16	,	,	PUNCT
easat-224	61	17	𝑡	𝑡	NOUN
easat-224	61	18	)	)	PUNCT
easat-224	61	19	=	=	SYM
easat-224	61	20	𝒮(𝑥)𝒷(𝑥	𝒮(𝑥)𝒷(𝑥	NOUN
easat-224	61	21	,	,	PUNCT
easat-224	61	22	𝑡	𝑡	PROPN
easat-224	61	23	)	)	PUNCT
easat-224	61	24	−	−	PROPN
easat-224	61	25	𝜕	𝜕	NOUN
easat-224	61	26	𝜕𝑥	𝜕𝑥	X
easat-224	61	27	[	[	X
easat-224	61	28	ℋ(𝑥	ℋ(𝑥	X
easat-224	61	29	)	)	PUNCT
easat-224	61	30	𝜕	𝜕	NOUN
easat-224	61	31	𝜕𝑥	𝜕𝑥	X
easat-224	61	32	𝒷(𝑥	𝒷(𝑥	PROPN
easat-224	61	33	,	,	PUNCT
easat-224	61	34	𝑡	𝑡	NOUN
easat-224	61	35	)	)	PUNCT
easat-224	61	36	]	]	PUNCT
easat-224	61	37	(	(	PUNCT
easat-224	61	38	2	2	X
easat-224	61	39	)	)	PUNCT
easat-224	61	40	where	where	SCONJ
easat-224	61	41	,	,	PUNCT
easat-224	61	42	𝒮(𝑥	𝒮(𝑥	NOUN
easat-224	61	43	)	)	PUNCT
easat-224	61	44	and	and	CCONJ
easat-224	61	45	ℋ(𝑥	ℋ(𝑥	NUM
easat-224	61	46	)	)	PUNCT
easat-224	61	47	are	be	AUX
easat-224	61	48	two	two	NUM
easat-224	61	49	variable	variable	ADJ
easat-224	61	50	parameters	parameter	NOUN
easat-224	61	51	of	of	ADP
easat-224	61	52	the	the	DET
easat-224	61	53	elastic	elastic	ADJ
easat-224	61	54	foundation	foundation	NOUN
easat-224	61	55	.	.	PUNCT
easat-224	62	1	that	that	PRON
easat-224	62	2	is	is	ADV
easat-224	62	3	,	,	PUNCT
easat-224	62	4	𝒮(𝑥	𝒮(𝑥	NOUN
easat-224	62	5	)	)	PUNCT
easat-224	62	6	is	be	AUX
easat-224	62	7	the	the	DET
easat-224	62	8	variable	variable	ADJ
easat-224	62	9	foundation	foundation	NOUN
easat-224	62	10	stiffness	stiffness	NOUN
easat-224	62	11	(	(	PUNCT
easat-224	62	12	foundation	foundation	NOUN
easat-224	62	13	modulus	modulus	NOUN
easat-224	62	14	)	)	PUNCT
easat-224	62	15	and	and	CCONJ
easat-224	62	16	ℋ(𝑥	ℋ(𝑥	NUM
easat-224	62	17	)	)	PUNCT
easat-224	62	18	is	be	AUX
easat-224	62	19	the	the	DET
easat-224	62	20	variable	variable	ADJ
easat-224	62	21	shear	shear	NOUN
easat-224	62	22	modulus	modulus	NOUN
easat-224	62	23	.	.	PUNCT
easat-224	63	1	where	where	SCONJ
easat-224	63	2	𝒮(𝑥	𝒮(𝑥	VERB
easat-224	63	3	)	)	PUNCT
easat-224	63	4	=	=	PUNCT
easat-224	64	1	𝒮𝑂(4𝑥	𝒮𝑂(4𝑥	PROPN
easat-224	65	1	−	−	NUM
easat-224	65	2	3𝑥2	3𝑥2	NUM
easat-224	65	3	+	+	NOUN
easat-224	65	4	𝑥3	𝑥3	NOUN
easat-224	65	5	)	)	PUNCT
easat-224	65	6	(	(	PUNCT
easat-224	65	7	3	3	X
easat-224	65	8	)	)	SYM
easat-224	65	9	2	2	NUM
easat-224	65	10	edelweiss	edelweiss	PROPN
easat-224	65	11	applied	apply	VERB
easat-224	65	12	science	science	NOUN
easat-224	65	13	and	and	CCONJ
easat-224	65	14	technology	technology	NOUN
easat-224	65	15	issn	issn	PROPN
easat-224	65	16	:	:	PUNCT
easat-224	65	17	2576	2576	NUM
easat-224	65	18	-	-	SYM
easat-224	65	19	8484	8484	NUM
easat-224	65	20	vol	vol	NOUN
easat-224	65	21	.	.	PROPN
easat-224	66	1	2	2	NUM
easat-224	66	2	,	,	PUNCT
easat-224	66	3	no	no	INTJ
easat-224	66	4	.	.	NOUN
easat-224	66	5	1	1	NUM
easat-224	66	6	:	:	SYM
easat-224	66	7	1	1	NUM
easat-224	66	8	-	-	SYM
easat-224	66	9	9	9	NUM
easat-224	66	10	,	,	PUNCT
easat-224	66	11	2018	2018	NUM
easat-224	66	12	doi	doi	NOUN
easat-224	66	13	:	:	PUNCT
easat-224	66	14	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	67	1	©	©	PROPN
easat-224	67	2	2018	2018	NUM
easat-224	67	3	by	by	ADP
easat-224	67	4	the	the	DET
easat-224	67	5	authors	author	NOUN
easat-224	67	6	ℋ(𝑥	ℋ(𝑥	NOUN
easat-224	67	7	)	)	PUNCT
easat-224	67	8	=	=	NUM
easat-224	67	9	ℋ𝑂(12	ℋ𝑂(12	NUM
easat-224	67	10	−	−	NUM
easat-224	67	11	13𝑥	13𝑥	NUM
easat-224	68	1	+	+	CCONJ
easat-224	68	2	6𝑥2	6𝑥2	NUM
easat-224	68	3	+	+	CCONJ
easat-224	68	4	𝑥3	𝑥3	NOUN
easat-224	68	5	)	)	PUNCT
easat-224	68	6	(	(	PUNCT
easat-224	68	7	4	4	X
easat-224	68	8	)	)	PUNCT
easat-224	68	9	𝔅(𝑥	𝔅(𝑥	NOUN
easat-224	68	10	)	)	PUNCT
easat-224	68	11	=	=	SYM
easat-224	69	1	𝔅𝑜	𝔅𝑜	PROPN
easat-224	69	2	(	(	PUNCT
easat-224	69	3	1	1	NUM
easat-224	69	4	+	+	NUM
easat-224	69	5	sin	sin	NOUN
easat-224	69	6	𝜋𝑥	𝜋𝑥	X
easat-224	69	7	𝐿	𝐿	PROPN
easat-224	69	8	)	)	PUNCT
easat-224	69	9	(	(	PUNCT
easat-224	69	10	5	5	X
easat-224	69	11	)	)	PUNCT
easat-224	69	12	substituting	substitute	VERB
easat-224	69	13	equations	equation	NOUN
easat-224	69	14	(	(	PUNCT
easat-224	69	15	3	3	NUM
easat-224	69	16	)	)	PUNCT
easat-224	69	17	,	,	PUNCT
easat-224	69	18	(	(	PUNCT
easat-224	69	19	4	4	NUM
easat-224	69	20	)	)	PUNCT
easat-224	69	21	and	and	CCONJ
easat-224	69	22	(	(	PUNCT
easat-224	69	23	5	5	NUM
easat-224	69	24	)	)	PUNCT
easat-224	69	25	into	into	ADP
easat-224	69	26	equation	equation	NOUN
easat-224	69	27	(	(	PUNCT
easat-224	69	28	1	1	NUM
easat-224	69	29	)	)	PUNCT
easat-224	69	30	,	,	PUNCT
easat-224	69	31	one	one	NUM
easat-224	69	32	obtains	obtain	VERB
easat-224	69	33	(	(	PUNCT
easat-224	69	34	)	)	PUNCT
easat-224	69	35	(	(	PUNCT
easat-224	69	36	)	)	PUNCT
easat-224	69	37	(	(	PUNCT
easat-224	69	38	)	)	PUNCT
easat-224	69	39	(	(	PUNCT
easat-224	69	40	)	)	PUNCT
easat-224	69	41	(	(	PUNCT
easat-224	69	42	)	)	PUNCT
easat-224	69	43	(	(	PUNCT
easat-224	69	44	)	)	PUNCT
easat-224	69	45	(	(	PUNCT
easat-224	69	46	)	)	PUNCT
easat-224	69	47	(	(	PUNCT
easat-224	69	48	)	)	PUNCT
easat-224	69	49	(	(	PUNCT
easat-224	69	50	)	)	PUNCT
easat-224	69	51	(	(	PUNCT
easat-224	69	52	)	)	PUNCT
easat-224	69	53	4	4	NUM
easat-224	69	54	2	2	NUM
easat-224	69	55	2	2	NUM
easat-224	69	56	4	4	NUM
easat-224	69	57	2	2	NUM
easat-224	69	58	2	2	NUM
easat-224	69	59	4	4	NUM
easat-224	69	60	2	2	NUM
easat-224	69	61	3	3	NUM
easat-224	69	62	2	2	NUM
easat-224	69	63	2	2	NUM
easat-224	69	64	2	2	NUM
easat-224	69	65	2	2	NUM
easat-224	69	66	3	3	NUM
easat-224	69	67	2	2	NUM
easat-224	69	68	1	1	NUM
easat-224	69	69	  	  	SPACE
easat-224	69	70	,	,	PUNCT
easat-224	69	71	,	,	PUNCT
easat-224	69	72	1	1	NUM
easat-224	69	73	sin	sin	NOUN
easat-224	69	74	,	,	PUNCT
easat-224	69	75	   	   	SPACE
easat-224	69	76	1	1	NUM
easat-224	69	77	sin	sin	NOUN
easat-224	69	78	  	  	SPACE
easat-224	69	79	,	,	PUNCT
easat-224	69	80	4	4	NUM
easat-224	69	81	3	3	NUM
easat-224	69	82	,	,	PUNCT
easat-224	69	83	1	1	NUM
easat-224	69	84	[	[	PUNCT
easat-224	69	85	12	12	NUM
easat-224	69	86	13	13	NUM
easat-224	69	87	6	6	NUM
easat-224	69	88	,	,	PUNCT
easat-224	69	89	]	]	PUNCT
easat-224	70	1	[	[	X
easat-224	70	2	1	1	NUM
easat-224	70	3	,	,	PUNCT
easat-224	70	4	]	]	PUNCT
easat-224	70	5	     	     	SPACE
easat-224	70	6	(	(	PUNCT
easat-224	70	7	6	6	NUM
easat-224	70	8	)	)	PUNCT
easat-224	71	1	o	o	NOUN
easat-224	72	1	o	o	NOUN
easat-224	73	1	o	o	X
easat-224	73	2	o	o	NOUN
easat-224	73	3	n	n	X
easat-224	73	4	o	o	INTJ
easat-224	74	1	i	i	NOUN
easat-224	74	2	x	x	VERB
easat-224	75	1	i	i	NOUN
easat-224	75	2	b	b	PROPN
easat-224	75	3	x	x	SYM
easat-224	75	4	t	t	PROPN
easat-224	75	5	b	b	PROPN
easat-224	75	6	x	x	SYM
easat-224	75	7	t	t	PROPN
easat-224	75	8	b	b	PROPN
easat-224	75	9	x	x	SYM
easat-224	75	10	t	t	NOUN
easat-224	75	11	x	x	PUNCT
easat-224	75	12	x	x	PUNCT
easat-224	75	13	l	l	NOUN
easat-224	75	14	t	t	NOUN
easat-224	75	15	x	x	SYM
easat-224	75	16	b	b	X
easat-224	75	17	x	x	SYM
easat-224	75	18	t	t	NOUN
easat-224	75	19	x	x	PUNCT
easat-224	75	20	x	x	PUNCT
easat-224	76	1	x	x	SYM
easat-224	76	2	b	b	X
easat-224	76	3	x	x	SYM
easat-224	76	4	t	t	NOUN
easat-224	76	5	l	l	NOUN
easat-224	76	6	x	x	PUNCT
easat-224	76	7	t	t	NOUN
easat-224	76	8	d	d	X
easat-224	76	9	x	x	PUNCT
easat-224	76	10	x	x	PUNCT
easat-224	76	11	x	x	SYM
easat-224	76	12	b	b	X
easat-224	76	13	x	x	SYM
easat-224	76	14	t	t	PROPN
easat-224	76	15	mgh	mgh	NOUN
easat-224	76	16	x	x	PROPN
easat-224	76	17	vt	vt	PROPN
easat-224	76	18	b	b	PROPN
easat-224	76	19	x	x	SYM
easat-224	76	20	t	t	NOUN
easat-224	76	21	x	x	X
easat-224	76	22	x	x	X
easat-224	76	23	g	g	NOUN
easat-224	76	24	dt	dt	X
easat-224	76	25			PROPN
easat-224	76	26			PROPN
easat-224	76	27	=	=	SYM
easat-224	76	28			ADJ
easat-224	76	29			PROPN
easat-224	76	30			SYM
easat-224	76	31			PROPN
easat-224	76	32	−	−	PROPN
easat-224	77	1	+	+	CCONJ
easat-224	77	2	+	+	ADJ
easat-224	77	3			ADJ
easat-224	77	4			PROPN
easat-224	77	5			ADJ
easat-224	77	6			PROPN
easat-224	77	7			VERB
easat-224	77	8			NOUN
easat-224	77	9			NOUN
easat-224	77	10			NOUN
easat-224	77	11	−	−	PROPN
easat-224	78	1	+	+	CCONJ
easat-224	79	1	+	+	CCONJ
easat-224	80	1	−	−	X
easat-224	80	2	+	+	ADJ
easat-224	80	3			PROPN
easat-224	80	4			PROPN
easat-224	80	5			PROPN
easat-224	80	6			ADJ
easat-224	80	7			NOUN
easat-224	80	8			ADJ
easat-224	80	9			ADJ
easat-224	80	10	−	−	PROPN
easat-224	80	11	−	−	PROPN
easat-224	81	1	+	+	CCONJ
easat-224	81	2	+	+	NUM
easat-224	81	3	=	=	SYM
easat-224	81	4	−	−	NOUN
easat-224	81	5	−	−	ADP
easat-224	81	6			ADJ
easat-224	81	7			ADJ
easat-224	81	8			X
easat-224	81	9	b	b	X
easat-224	81	10	b	b	X
easat-224	81	11	a	a	PRON
easat-224	81	12	n	n	NOUN
easat-224	81	13	r	r	NOUN
easat-224	81	14	s	s	NOUN
easat-224	81	15	h	h	NOUN
easat-224	81	16	the	the	DET
easat-224	81	17	boundary	boundary	ADJ
easat-224	81	18	condition	condition	NOUN
easat-224	81	19	of	of	ADP
easat-224	81	20	the	the	DET
easat-224	81	21	structure	structure	NOUN
easat-224	81	22	under	under	ADP
easat-224	81	23	consideration	consideration	NOUN
easat-224	81	24	is	be	AUX
easat-224	81	25	first	first	ADV
easat-224	81	26	taken	take	VERB
easat-224	81	27	to	to	PART
easat-224	81	28	be	be	AUX
easat-224	81	29	arbitrary	arbitrary	ADJ
easat-224	81	30	and	and	CCONJ
easat-224	81	31	the	the	DET
easat-224	81	32	initial	initial	ADJ
easat-224	81	33	condition	condition	NOUN
easat-224	81	34	without	without	ADP
easat-224	81	35	any	any	DET
easat-224	81	36	loss	loss	NOUN
easat-224	81	37	of	of	ADP
easat-224	81	38	generality	generality	NOUN
easat-224	81	39	is	be	AUX
easat-224	81	40	taken	take	VERB
easat-224	81	41	as	as	ADP
easat-224	81	42	𝒷(𝑥	𝒷(𝑥	NOUN
easat-224	81	43	,	,	PUNCT
easat-224	81	44	0	0	NUM
easat-224	81	45	)	)	PUNCT
easat-224	81	46	=	=	SYM
easat-224	81	47	0	0	PUNCT
easat-224	82	1	=	=	SYM
easat-224	82	2	𝜕	𝜕	PROPN
easat-224	82	3	𝜕𝑡	𝜕𝑡	PROPN
easat-224	82	4	𝒷(𝑥	𝒷(𝑥	PROPN
easat-224	82	5	,	,	PUNCT
easat-224	82	6	𝑜	𝑜	NOUN
easat-224	82	7	)	)	PUNCT
easat-224	82	8	(	(	PUNCT
easat-224	82	9	7	7	NUM
easat-224	82	10	)	)	SYM
easat-224	82	11	2	2	NUM
easat-224	82	12	.	.	PUNCT
easat-224	82	13	analytical	analytical	ADJ
easat-224	82	14	approximate	approximate	ADJ
easat-224	82	15	solution	solution	NOUN
easat-224	82	16	due	due	ADJ
easat-224	82	17	to	to	ADP
easat-224	82	18	complex	complex	ADJ
easat-224	82	19	nature	nature	NOUN
easat-224	82	20	of	of	ADP
easat-224	82	21	equation	equation	NOUN
easat-224	82	22	(	(	PUNCT
easat-224	82	23	1	1	NUM
easat-224	82	24	)	)	PUNCT
easat-224	82	25	,	,	PUNCT
easat-224	82	26	no	no	DET
easat-224	82	27	conventional	conventional	ADJ
easat-224	82	28	method	method	NOUN
easat-224	82	29	can	can	AUX
easat-224	82	30	be	be	AUX
easat-224	82	31	used	use	VERB
easat-224	82	32	to	to	PART
easat-224	82	33	solve	solve	VERB
easat-224	82	34	the	the	DET
easat-224	82	35	partial	partial	ADJ
easat-224	82	36	differential	differential	NOUN
easat-224	82	37	equation	equation	NOUN
easat-224	82	38	and	and	CCONJ
easat-224	82	39	till	till	SCONJ
easat-224	82	40	this	this	DET
easat-224	82	41	moment	moment	NOUN
easat-224	82	42	,	,	PUNCT
easat-224	82	43	there	there	PRON
easat-224	82	44	is	be	VERB
easat-224	82	45	no	no	DET
easat-224	82	46	exact	exact	ADJ
easat-224	82	47	closed	closed	ADJ
easat-224	82	48	form	form	NOUN
easat-224	82	49	solution	solution	NOUN
easat-224	82	50	to	to	ADP
easat-224	82	51	equation(1	equation(1	PROPN
easat-224	82	52	)	)	PUNCT
easat-224	82	53	.	.	PUNCT
easat-224	83	1	therefore	therefore	ADV
easat-224	83	2	,	,	PUNCT
easat-224	83	3	an	an	DET
easat-224	83	4	approximate	approximate	ADJ
easat-224	83	5	solution	solution	NOUN
easat-224	83	6	is	be	AUX
easat-224	83	7	sought	seek	VERB
easat-224	83	8	.	.	PUNCT
easat-224	84	1	the	the	DET
easat-224	84	2	method	method	NOUN
easat-224	84	3	of	of	ADP
easat-224	84	4	galerkin	galerkin	ADJ
easat-224	84	5	is	be	AUX
easat-224	84	6	used	use	VERB
easat-224	84	7	to	to	PART
easat-224	84	8	reduce	reduce	VERB
easat-224	84	9	equation(1	equation(1	NOUN
easat-224	84	10	)	)	PUNCT
easat-224	84	11	to	to	AUX
easat-224	84	12	second	second	ADJ
easat-224	84	13	order	order	NOUN
easat-224	84	14	coupled	couple	VERB
easat-224	84	15	ordinary	ordinary	ADJ
easat-224	84	16	differential	differential	ADJ
easat-224	84	17	equations	equation	NOUN
easat-224	84	18	,	,	PUNCT
easat-224	84	19	and	and	CCONJ
easat-224	84	20	this	this	PRON
easat-224	84	21	takes	take	VERB
easat-224	84	22	the	the	DET
easat-224	84	23	form	form	NOUN
easat-224	84	24	𝒷𝑖(𝑥	𝒷𝑖(𝑥	NOUN
easat-224	84	25	,	,	PUNCT
easat-224	84	26	𝑡	𝑡	NOUN
easat-224	84	27	)	)	PUNCT
easat-224	84	28	=	=	PUNCT
easat-224	84	29	∑	∑	PUNCT
easat-224	84	30	𝓌𝑖	𝓌𝑖	ADP
easat-224	84	31	(	(	PUNCT
easat-224	84	32	𝑡)𝒰𝑖(𝑥	𝑡)𝒰𝑖(𝑥	NOUN
easat-224	84	33	)	)	PUNCT
easat-224	84	34	𝑁	𝑁	PROPN
easat-224	84	35	𝑖=1	𝑖=1	PROPN
easat-224	85	1	(	(	PUNCT
easat-224	85	2	8)	8)	NUM
easat-224	85	3	where	where	SCONJ
easat-224	85	4	𝒰𝑖(𝑥	𝒰𝑖(𝑥	ADJ
easat-224	85	5	)	)	PUNCT
easat-224	85	6	=	=	PUNCT
easat-224	85	7	sin	sin	VERB
easat-224	85	8	𝔇𝑖𝑥	𝔇𝑖𝑥	PROPN
easat-224	85	9	𝐿	𝐿	PROPN
easat-224	85	10	+	+	CCONJ
easat-224	85	11	𝐴𝑖	𝐴𝑖	PROPN
easat-224	85	12	cos	cos	PROPN
easat-224	85	13	𝔇𝑖𝑥	𝔇𝑖𝑥	PROPN
easat-224	85	14	𝐿	𝐿	PROPN
easat-224	85	15	+	+	PROPN
easat-224	85	16	𝐵𝑖	𝐵𝑖	PROPN
easat-224	85	17	sinh	sinh	NOUN
easat-224	85	18	𝔇𝑖𝑥	𝔇𝑖𝑥	PROPN
easat-224	85	19	𝐿	𝐿	PROPN
easat-224	85	20	+	+	CCONJ
easat-224	85	21	𝐶𝑖	𝐶𝑖	PROPN
easat-224	85	22	cosh	cosh	NOUN
easat-224	85	23	𝔇𝑖𝑥	𝔇𝑖𝑥	PROPN
easat-224	85	24	𝐿	𝐿	PROPN
easat-224	85	25	(	(	PUNCT
easat-224	85	26	9	9	NUM
easat-224	85	27	)	)	PUNCT
easat-224	85	28	(	(	PUNCT
easat-224	85	29	)	)	PUNCT
easat-224	85	30	(	(	PUNCT
easat-224	85	31	)	)	PUNCT
easat-224	85	32	(	(	PUNCT
easat-224	85	33	)	)	PUNCT
easat-224	85	34	(	(	PUNCT
easat-224	85	35	)	)	PUNCT
easat-224	85	36	(	(	PUNCT
easat-224	85	37	)	)	PUNCT
easat-224	85	38	(	(	PUNCT
easat-224	85	39	)	)	PUNCT
easat-224	85	40	(	(	PUNCT
easat-224	85	41	)	)	PUNCT
easat-224	85	42	(	(	PUNCT
easat-224	85	43	)	)	PUNCT
easat-224	85	44	(	(	PUNCT
easat-224	85	45	)	)	PUNCT
easat-224	85	46	(	(	PUNCT
easat-224	85	47	)	)	PUNCT
easat-224	85	48	(	(	PUNCT
easat-224	85	49	)	)	PUNCT
easat-224	85	50	(	(	PUNCT
easat-224	85	51	)	)	PUNCT
easat-224	85	52	(	(	PUNCT
easat-224	85	53	)	)	PUNCT
easat-224	85	54	(	(	PUNCT
easat-224	85	55	)	)	PUNCT
easat-224	85	56	(	(	PUNCT
easat-224	85	57	)	)	PUNCT
easat-224	85	58	(	(	PUNCT
easat-224	85	59	)	)	PUNCT
easat-224	85	60	(	(	PUNCT
easat-224	85	61	)	)	PUNCT
easat-224	85	62	(	(	PUNCT
easat-224	85	63	)	)	PUNCT
easat-224	85	64	¨	¨	NOUN
easat-224	85	65	''	''	PUNCT
easat-224	85	66	''	''	PUNCT
easat-224	85	67	1	1	NUM
easat-224	85	68	''	''	SYM
easat-224	85	69	2	2	NUM
easat-224	85	70	3	3	NUM
easat-224	85	71	0	0	NUM
easat-224	85	72	'	'	PUNCT
easat-224	85	73	'	'	NUM
easat-224	85	74	2	2	NUM
easat-224	85	75	'	'	PUNCT
easat-224	85	76	''	''	PUNCT
easat-224	85	77	''	''	PUNCT
easat-224	85	78	2	2	NUM
easat-224	85	79	''	''	SYM
easat-224	85	80	3	3	NUM
easat-224	85	81	''	''	PUNCT
easat-224	85	82	sin	sin	NOUN
easat-224	85	83	  	  	SPACE
easat-224	85	84	sin	sin	NOUN
easat-224	85	85	  	  	SPACE
easat-224	85	86	4	4	NUM
easat-224	85	87	3	3	NUM
easat-224	85	88	4	4	NUM
easat-224	85	89	13	13	NUM
easat-224	85	90	12	12	NUM
easat-224	85	91	3	3	NUM
easat-224	85	92	12	12	NUM
easat-224	85	93	13	13	NUM
easat-224	85	94	6	6	NUM
easat-224	85	95	(	(	PUNCT
easat-224	85	96	)	)	PUNCT
easat-224	85	97	n	n	NOUN
easat-224	85	98	ii	ii	NOUN
easat-224	86	1	i	i	PRON
easat-224	86	2	o	o	INTJ
easat-224	87	1	i	i	PRON
easat-224	87	2	i	i	PRON
easat-224	87	3	m	m	VERB
easat-224	87	4	iv	iv	VERB
easat-224	88	1	o	o	NOUN
easat-224	88	2	o	o	INTJ
easat-224	89	1	i	i	PRON
easat-224	89	2	i	i	PRON
easat-224	90	1	i	i	PRON
easat-224	90	2	i	i	PRON
easat-224	91	1	i	i	PRON
easat-224	92	1	o	o	VERB
easat-224	93	1	o	o	VERB
easat-224	94	1	i	i	PRON
easat-224	94	2	i	i	INTJ
easat-224	94	3	io	io	VERB
easat-224	95	1	o	o	INTJ
easat-224	96	1	i	i	PRON
easat-224	96	2	i	i	PRON
easat-224	97	1	i	i	PRON
easat-224	97	2	i	i	PRON
easat-224	97	3	i	i	VERB
easat-224	97	4	x	x	VERB
easat-224	98	1	x	x	PUNCT
easat-224	98	2	x	x	PUNCT
easat-224	98	3	x	x	PUNCT
easat-224	98	4	x	x	PUNCT
easat-224	98	5	x	x	X
easat-224	98	6	t	t	NOUN
easat-224	98	7	l	l	NOUN
easat-224	98	8	l	l	NOUN
easat-224	99	1	i	i	NOUN
easat-224	99	2	x	x	X
easat-224	99	3	x	x	PUNCT
easat-224	99	4	x	x	PUNCT
easat-224	99	5	x	x	PUNCT
easat-224	99	6	x	x	PUNCT
easat-224	99	7	x	x	PUNCT
easat-224	99	8	w	w	NOUN
easat-224	99	9	x	x	X
easat-224	99	10	x	x	PUNCT
easat-224	99	11	x	x	PUNCT
easat-224	99	12	x	x	PUNCT
easat-224	99	13	x	x	PUNCT
easat-224	99	14	x	x	PUNCT
easat-224	99	15	x	x	PUNCT
easat-224	99	16	x	x	PUNCT
easat-224	99	17	x	x	PUNCT
easat-224	99	18	x	x	PUNCT
easat-224	99	19	x	x	PUNCT
easat-224	99	20	x	x	PUNCT
easat-224	99	21	x	x	PUNCT
easat-224	99	22	x	x	X
easat-224	99	23	w	w	PROPN
easat-224	99	24	t	t	PROPN
easat-224	99	25			PROPN
easat-224	99	26			ADJ
easat-224	99	27			NOUN
easat-224	99	28	=	=	SYM
easat-224	99	29			NOUN
easat-224	99	30			PROPN
easat-224	99	31			PROPN
easat-224	99	32	+	+	CCONJ
easat-224	99	33	−	−	X
easat-224	100	1	+	+	CCONJ
easat-224	100	2	+	+	ADJ
easat-224	100	3			NOUN
easat-224	100	4			PROPN
easat-224	100	5			NOUN
easat-224	100	6			PROPN
easat-224	101	1			PROPN
easat-224	101	2			NOUN
easat-224	101	3			PROPN
easat-224	101	4			NOUN
easat-224	101	5			NUM
easat-224	101	6	−	−	PROPN
easat-224	102	1	+	+	CCONJ
easat-224	103	1	−	−	PROPN
easat-224	103	2	+	+	ADJ
easat-224	103	3			PROPN
easat-224	103	4			PROPN
easat-224	103	5			PROPN
easat-224	103	6			PROPN
easat-224	104	1			PROPN
easat-224	104	2			PROPN
easat-224	105	1			PROPN
easat-224	105	2	−	−	NOUN
easat-224	105	3	+	+	CCONJ
easat-224	105	4	−	−	PROPN
easat-224	105	5	−	−	X
easat-224	105	6			PROPN
easat-224	105	7			NOUN
easat-224	106	1			X
easat-224	106	2			X
easat-224	107	1	+	+	CCONJ
easat-224	107	2	−	−	PROPN
easat-224	108	1	+	+	CCONJ
easat-224	108	2	−	−	ADJ
easat-224	108	3			NOUN
easat-224	108	4			NOUN
easat-224	108	5	+	+	CCONJ
easat-224	108	6			X
easat-224	108	7	b	b	X
easat-224	108	8	b	b	X
easat-224	108	9	b	b	X
easat-224	108	10	u	u	X
easat-224	108	11	u	u	NOUN
easat-224	108	12	r	r	NOUN
easat-224	108	13	u	u	NOUN
easat-224	108	14	u	u	NOUN
easat-224	108	15	n	n	NOUN
easat-224	108	16	sa	sa	NOUN
easat-224	108	17	u	u	NOUN
easat-224	108	18	u	u	PROPN
easat-224	108	19	u	u	X
easat-224	108	20	u	u	X
easat-224	108	21	u	u	X
easat-224	108	22	u	u	X
easat-224	108	23	u	u	NOUN
easat-224	108	24	uh	uh	INTJ
easat-224	108	25	u	u	NOUN
easat-224	108	26	u	u	X
easat-224	108	27	u	u	NOUN
easat-224	108	28	u	u	NOUN
easat-224	108	29	(	(	PUNCT
easat-224	108	30	)	)	PUNCT
easat-224	108	31	(	(	PUNCT
easat-224	108	32	)	)	PUNCT
easat-224	108	33	(	(	PUNCT
easat-224	108	34	)	)	PUNCT
easat-224	108	35	(	(	PUNCT
easat-224	108	36	)	)	PUNCT
easat-224	108	37	(	(	PUNCT
easat-224	108	38	)	)	PUNCT
easat-224	108	39	(	(	PUNCT
easat-224	108	40	)	)	PUNCT
easat-224	108	41	(	(	PUNCT
easat-224	108	42	)	)	PUNCT
easat-224	108	43	¨	¨	NOUN
easat-224	108	44	'	'	NUM
easat-224	108	45	2	2	NUM
easat-224	108	46	''	''	PUNCT
easat-224	108	47	(	(	PUNCT
easat-224	108	48	)	)	PUNCT
easat-224	108	49	  	  	SPACE
easat-224	108	50	2	2	NUM
easat-224	108	51	0	0	NUM
easat-224	108	52	ii	ii	X
easat-224	109	1	i	i	PRON
easat-224	109	2	i	i	PRON
easat-224	110	1	i	i	PRON
easat-224	110	2	i	i	PRON
easat-224	111	1	o	o	VERB
easat-224	111	2	o	o	VERB
easat-224	112	1	m	m	VERB
easat-224	112	2	h	h	NOUN
easat-224	113	1	wx	wx	PROPN
easat-224	113	2	vt	vt	PROPN
easat-224	113	3	x	x	PROPN
easat-224	114	1	t	t	PROPN
easat-224	114	2	v	v	NUM
easat-224	114	3	x	x	PROPN
easat-224	114	4	w	w	PROPN
easat-224	114	5	t	t	PROPN
easat-224	114	6	v	v	NOUN
easat-224	114	7	x	x	SYM
easat-224	114	8	w	w	PROPN
easat-224	114	9	t	t	PROPN
easat-224	114	10	mg	mg	PROPN
easat-224	115	1	h	h	PROPN
easat-224	115	2	x	x	PROPN
easat-224	115	3	vt	vt	PROPN
easat-224	115	4			NOUN
easat-224	115	5			PROPN
easat-224	115	6	−	−	PROPN
easat-224	116	1	+	+	CCONJ
easat-224	117	1	+	+	ADJ
easat-224	117	2			ADJ
easat-224	117	3			PROPN
easat-224	117	4			ADJ
easat-224	117	5			NOUN
easat-224	117	6			VERB
easat-224	117	7	−	−	PROPN
easat-224	117	8	−	−	PROPN
easat-224	118	1	=	=	SYM
easat-224	118	2			PROPN
easat-224	118	3			PROPN
easat-224	118	4	b	b	PROPN
easat-224	118	5	b	b	X
easat-224	118	6	u	u	X
easat-224	118	7	u	u	NOUN
easat-224	118	8	u	u	NOUN
easat-224	118	9	equation	equation	NOUN
easat-224	118	10	(	(	PUNCT
easat-224	118	11	11	11	NUM
easat-224	118	12	)	)	PUNCT
easat-224	118	13	can	can	AUX
easat-224	118	14	be	be	AUX
easat-224	118	15	re	re	VERB
easat-224	118	16	-	-	VERB
easat-224	118	17	written	write	VERB
easat-224	118	18	as	as	ADP
easat-224	118	19	where	where	SCONJ
easat-224	118	20	𝐹𝐴	𝐹𝐴	NOUN
easat-224	118	21	=	=	SYM
easat-224	118	22	𝒜𝐼	𝒜𝐼	PROPN
easat-224	118	23	4𝔅𝑜	4𝔅𝑜	NUM
easat-224	118	24	,	,	PUNCT
easat-224	118	25	𝐸1(𝑖	𝐸1(𝑖	PROPN
easat-224	118	26	,	,	PUNCT
easat-224	118	27	𝑗	𝑗	X
easat-224	118	28	)	)	PUNCT
easat-224	118	29	=	=	SYM
easat-224	119	1	∫	∫	PROPN
easat-224	120	1	𝒰𝑖	𝒰𝑖	PROPN
easat-224	120	2	(	(	PUNCT
easat-224	120	3	𝑥)𝒰𝑗(𝑥)𝑑𝑥	𝑥)𝒰𝑗(𝑥)𝑑𝑥	PUNCT
easat-224	120	4	𝐿	𝐿	PROPN
easat-224	120	5	0	0	NUM
easat-224	120	6	,	,	PUNCT
easat-224	120	7	𝐸2(𝑖	𝐸2(𝑖	NOUN
easat-224	120	8	,	,	PUNCT
easat-224	120	9	𝑗	𝑗	X
easat-224	120	10	)	)	PUNCT
easat-224	120	11	=	=	SYM
easat-224	120	12	∫	∫	PROPN
easat-224	120	13	sin	sin	PROPN
easat-224	120	14	𝜋𝑥	𝜋𝑥	PROPN
easat-224	120	15	𝐿	𝐿	PROPN
easat-224	120	16	𝐿	𝐿	PROPN
easat-224	120	17	0	0	NUM
easat-224	120	18	𝒰𝑖(𝑥)𝒰𝑗(𝑥)𝑑𝑥	𝒰𝑖(𝑥)𝒰𝑗(𝑥)𝑑𝑥	NOUN
easat-224	120	19	(	(	PUNCT
easat-224	120	20	13	13	NUM
easat-224	120	21	)	)	PUNCT
easat-224	120	22	3	3	NUM
easat-224	120	23	edelweiss	edelweiss	PROPN
easat-224	120	24	applied	apply	VERB
easat-224	120	25	science	science	NOUN
easat-224	120	26	and	and	CCONJ
easat-224	120	27	technology	technology	NOUN
easat-224	120	28	issn	issn	PROPN
easat-224	120	29	:	:	PUNCT
easat-224	120	30	2576	2576	NUM
easat-224	120	31	-	-	SYM
easat-224	120	32	8484	8484	NUM
easat-224	120	33	vol	vol	NOUN
easat-224	120	34	.	.	PROPN
easat-224	121	1	2	2	NUM
easat-224	121	2	,	,	PUNCT
easat-224	121	3	no	no	INTJ
easat-224	121	4	.	.	NOUN
easat-224	121	5	1	1	NUM
easat-224	121	6	:	:	SYM
easat-224	121	7	1	1	NUM
easat-224	121	8	-	-	SYM
easat-224	121	9	9	9	NUM
easat-224	121	10	,	,	PUNCT
easat-224	121	11	2018	2018	NUM
easat-224	121	12	doi	doi	NOUN
easat-224	121	13	:	:	PUNCT
easat-224	121	14	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	122	1	©	©	PROPN
easat-224	122	2	2018	2018	NUM
easat-224	122	3	by	by	ADP
easat-224	122	4	the	the	DET
easat-224	122	5	authors	author	NOUN
easat-224	122	6	in	in	ADP
easat-224	122	7	order	order	NOUN
easat-224	122	8	to	to	PART
easat-224	122	9	evaluate	evaluate	VERB
easat-224	122	10	the	the	DET
easat-224	122	11	integrals	integral	NOUN
easat-224	122	12	in	in	ADP
easat-224	122	13	e_17	e_17	X
easat-224	122	14	(	(	PUNCT
easat-224	122	15	i	i	PRON
easat-224	122	16	,	,	PUNCT
easat-224	122	17	j),e_18	j),e_18	PROPN
easat-224	122	18	(	(	PUNCT
easat-224	122	19	i	i	PRON
easat-224	122	20	,	,	PUNCT
easat-224	122	21	j	j	PROPN
easat-224	122	22	)	)	PUNCT
easat-224	122	23	and	and	CCONJ
easat-224	122	24	e_19	e_19	X
easat-224	122	25	(	(	PUNCT
easat-224	122	26	i	i	PROPN
easat-224	122	27	,	,	PUNCT
easat-224	122	28	j	j	PROPN
easat-224	122	29	)	)	PUNCT
easat-224	122	30	,	,	PUNCT
easat-224	122	31	one	one	PRON
easat-224	122	32	makes	make	VERB
easat-224	122	33	use	use	NOUN
easat-224	122	34	of	of	ADP
easat-224	122	35	the	the	DET
easat-224	122	36	fourier	fourier	NOUN
easat-224	122	37	series	series	NOUN
easat-224	122	38	representation	representation	NOUN
easat-224	122	39	for	for	ADP
easat-224	122	40	the	the	DET
easat-224	122	41	heaviside	heaviside	ADJ
easat-224	122	42	function	function	NOUN
easat-224	122	43	in	in	ADP
easat-224	122	44	the	the	DET
easat-224	122	45	form	form	NOUN
easat-224	122	46	;	;	PUNCT
easat-224	122	47	𝐻(𝑥	𝐻(𝑥	NUM
easat-224	122	48	−	−	PROPN
easat-224	122	49	𝑣𝑡	𝑣𝑡	NOUN
easat-224	122	50	)	)	PUNCT
easat-224	122	51	=	=	SYM
easat-224	122	52	1	1	NUM
easat-224	122	53	4	4	NUM
easat-224	122	54	+	+	SYM
easat-224	122	55	1	1	NUM
easat-224	122	56	𝜋	𝜋	NOUN
easat-224	122	57	∑	∑	PROPN
easat-224	122	58	sin(2𝑛	sin(2𝑛	NOUN
easat-224	122	59	+	+	CCONJ
easat-224	122	60	1)𝜋(𝑥	1)𝜋(𝑥	NUM
easat-224	122	61	−	−	PROPN
easat-224	122	62	𝑣𝑡	𝑣𝑡	NOUN
easat-224	122	63	)	)	PUNCT
easat-224	122	64	2𝑛	2𝑛	PROPN
easat-224	123	1	+	+	CCONJ
easat-224	123	2	1	1	NUM
easat-224	123	3	∞	∞	NUM
easat-224	123	4	𝑛=1	𝑛=1	NOUN
easat-224	123	5	,	,	PUNCT
easat-224	123	6	0	0	PUNCT
easat-224	123	7	<	<	X
easat-224	123	8	𝑥	𝑥	X
easat-224	123	9	<	<	X
easat-224	123	10	1	1	NUM
easat-224	123	11	(	(	PUNCT
easat-224	123	12	23	23	NUM
easat-224	123	13	)	)	PUNCT
easat-224	123	14	to	to	PART
easat-224	123	15	solve	solve	VERB
easat-224	123	16	e20(i	e20(i	NOUN
easat-224	123	17	,	,	PUNCT
easat-224	123	18	j	j	PROPN
easat-224	123	19	)	)	PUNCT
easat-224	123	20	,	,	PUNCT
easat-224	123	21	one	one	PRON
easat-224	123	22	makes	make	VERB
easat-224	123	23	use	use	NOUN
easat-224	123	24	of	of	ADP
easat-224	123	25	the	the	DET
easat-224	123	26	definition	definition	NOUN
easat-224	123	27	of	of	ADP
easat-224	123	28	heaviside	heaviside	ADJ
easat-224	123	29	function	function	NOUN
easat-224	123	30	and	and	CCONJ
easat-224	123	31	substitute	substitute	VERB
easat-224	123	32	the	the	DET
easat-224	123	33	result	result	NOUN
easat-224	123	34	into	into	ADP
easat-224	123	35	(	(	PUNCT
easat-224	123	36	12	12	NUM
easat-224	123	37	)	)	PUNCT
easat-224	123	38	,	,	PUNCT
easat-224	123	39	one	one	NUM
easat-224	123	40	obtains	obtain	VERB
easat-224	123	41	,	,	PUNCT
easat-224	123	42	therefore	therefore	ADV
easat-224	123	43	,	,	PUNCT
easat-224	123	44	equation	equation	NOUN
easat-224	123	45	(	(	PUNCT
easat-224	123	46	24	24	NUM
easat-224	123	47	)	)	PUNCT
easat-224	123	48	becomes	become	VERB
easat-224	123	49	where	where	SCONJ
easat-224	123	50	equation	equation	NOUN
easat-224	123	51	(	(	PUNCT
easat-224	123	52	25	25	NUM
easat-224	123	53	)	)	PUNCT
easat-224	123	54	is	be	AUX
easat-224	123	55	re	re	VERB
easat-224	123	56	-	-	VERB
easat-224	123	57	written	write	VERB
easat-224	123	58	as	as	ADP
easat-224	123	59	equation	equation	NOUN
easat-224	123	60	(	(	PUNCT
easat-224	123	61	29	29	NUM
easat-224	123	62	)	)	PUNCT
easat-224	123	63	is	be	AUX
easat-224	123	64	the	the	DET
easat-224	123	65	transformed	transform	VERB
easat-224	123	66	equation	equation	NOUN
easat-224	123	67	governing	govern	VERB
easat-224	123	68	the	the	DET
easat-224	123	69	problem	problem	NOUN
easat-224	123	70	of	of	ADP
easat-224	123	71	supported	support	VERB
easat-224	123	72	beam	beam	NOUN
easat-224	123	73	on	on	ADP
easat-224	123	74	variable	variable	ADJ
easat-224	123	75	bi	bi	ADJ
easat-224	123	76	-	-	ADJ
easat-224	123	77	parametric	parametric	ADJ
easat-224	123	78	elastic	elastic	ADJ
easat-224	123	79	foundation	foundation	NOUN
easat-224	123	80	.	.	PUNCT
easat-224	124	1	this	this	PRON
easat-224	124	2	coupled	couple	VERB
easat-224	124	3	non	non	ADJ
easat-224	124	4	-	-	ADJ
easat-224	124	5	homogeneous	homogeneous	ADJ
easat-224	124	6	second	second	ADJ
easat-224	124	7	order	order	NOUN
easat-224	124	8	ordinary	ordinary	ADJ
easat-224	124	9	differential	differential	ADJ
easat-224	124	10	equation	equation	NOUN
easat-224	124	11	is	be	AUX
easat-224	124	12	assumed	assume	VERB
easat-224	124	13	to	to	PART
easat-224	124	14	have	have	VERB
easat-224	124	15	arbitrary	arbitrary	ADJ
easat-224	124	16	boundary	boundary	ADJ
easat-224	124	17	conditions	condition	NOUN
easat-224	124	18	.	.	PUNCT
easat-224	125	1	2.1	2.1	NUM
easat-224	125	2	.	.	PUNCT
easat-224	125	3	case	case	NOUN
easat-224	126	1	i	i	PRON
easat-224	126	2	:	:	PUNCT
easat-224	126	3	moving	move	VERB
easat-224	126	4	force	force	NOUN
easat-224	126	5	problem	problem	NOUN
easat-224	126	6	in	in	ADP
easat-224	126	7	moving	move	VERB
easat-224	126	8	force	force	NOUN
easat-224	126	9	problem	problem	NOUN
easat-224	126	10	,	,	PUNCT
easat-224	126	11	only	only	ADV
easat-224	126	12	the	the	DET
easat-224	126	13	load	load	NOUN
easat-224	126	14	is	be	AUX
easat-224	126	15	being	be	AUX
easat-224	126	16	transferred	transfer	VERB
easat-224	126	17	to	to	ADP
easat-224	126	18	the	the	DET
easat-224	126	19	structure	structure	NOUN
easat-224	126	20	.	.	PUNCT
easat-224	127	1	in	in	ADP
easat-224	127	2	this	this	DET
easat-224	127	3	case	case	NOUN
easat-224	127	4	,	,	PUNCT
easat-224	127	5	the	the	DET
easat-224	127	6	inertia	inertia	NOUN
easat-224	127	7	effect	effect	NOUN
easat-224	127	8	is	be	AUX
easat-224	127	9	negligible	negligible	ADJ
easat-224	127	10	.	.	PUNCT
easat-224	128	1	setting	set	VERB
easat-224	128	2	ϖ=0	ϖ=0	PUNCT
easat-224	128	3	in	in	ADP
easat-224	128	4	the	the	DET
easat-224	128	5	transformed	transform	VERB
easat-224	128	6	equation	equation	NOUN
easat-224	128	7	(	(	PUNCT
easat-224	128	8	27	27	NUM
easat-224	128	9	)	)	PUNCT
easat-224	128	10	,	,	PUNCT
easat-224	128	11	one	one	NOUN
easat-224	128	12	obtains	obtain	VERB
easat-224	128	13	equation	equation	NOUN
easat-224	128	14	(	(	PUNCT
easat-224	128	15	28	28	NUM
easat-224	128	16	)	)	PUNCT
easat-224	128	17	can	can	AUX
easat-224	128	18	be	be	AUX
easat-224	128	19	rewritten	rewrite	VERB
easat-224	128	20	as	as	ADP
easat-224	128	21	,	,	PUNCT
easat-224	128	22	where	where	SCONJ
easat-224	128	23	equation	equation	NOUN
easat-224	128	24	(	(	PUNCT
easat-224	128	25	29	29	NUM
easat-224	128	26	)	)	PUNCT
easat-224	128	27	is	be	AUX
easat-224	128	28	an	an	DET
easat-224	128	29	approximate	approximate	ADJ
easat-224	128	30	model	model	NOUN
easat-224	128	31	,	,	PUNCT
easat-224	128	32	which	which	PRON
easat-224	128	33	assumes	assume	VERB
easat-224	128	34	the	the	DET
easat-224	128	35	inertia	inertia	NOUN
easat-224	128	36	effect	effect	NOUN
easat-224	128	37	of	of	ADP
easat-224	128	38	the	the	DET
easat-224	128	39	moving	move	VERB
easat-224	128	40	mass	mass	NOUN
easat-224	128	41	as	as	ADP
easat-224	128	42	negligible	negligible	ADJ
easat-224	128	43	.	.	PUNCT
easat-224	129	1	further	further	ADJ
easat-224	129	2	rearrangement	rearrangement	NOUN
easat-224	129	3	of	of	ADP
easat-224	129	4	(	(	PUNCT
easat-224	129	5	29	29	NUM
easat-224	129	6	)	)	PUNCT
easat-224	129	7	yields	yield	NOUN
easat-224	129	8	where	where	SCONJ
easat-224	129	9	𝛺𝑗	𝛺𝑗	PROPN
easat-224	129	10	=	=	SYM
easat-224	129	11	𝔇𝑗𝑣	𝔇𝑗𝑣	PROPN
easat-224	129	12	𝐿	𝐿	PROPN
easat-224	129	13	(	(	PUNCT
easat-224	129	14	32	32	NUM
easat-224	129	15	)	)	PUNCT
easat-224	129	16	solving	solve	VERB
easat-224	129	17	equation	equation	NOUN
easat-224	129	18	(	(	PUNCT
easat-224	129	19	31	31	NUM
easat-224	129	20	)	)	PUNCT
easat-224	129	21	using	use	VERB
easat-224	129	22	laplace	laplace	NOUN
easat-224	129	23	transformation	transformation	NOUN
easat-224	129	24	techniques	technique	NOUN
easat-224	129	25	and	and	CCONJ
easat-224	129	26	taking	take	VERB
easat-224	129	27	into	into	ADP
easat-224	129	28	account	account	NOUN
easat-224	129	29	equation	equation	NOUN
easat-224	129	30	(	(	PUNCT
easat-224	129	31	7	7	X
easat-224	129	32	)	)	PUNCT
easat-224	129	33	one	one	NOUN
easat-224	129	34	obtains	obtain	VERB
easat-224	129	35	equation	equation	NOUN
easat-224	129	36	(	(	PUNCT
easat-224	129	37	33	33	NUM
easat-224	129	38	)	)	PUNCT
easat-224	129	39	represents	represent	VERB
easat-224	129	40	the	the	DET
easat-224	129	41	transverse	transverse	NOUN
easat-224	129	42	deflection	deflection	NOUN
easat-224	129	43	of	of	ADP
easat-224	129	44	uniform	uniform	ADJ
easat-224	129	45	rayleigh	rayleigh	PROPN
easat-224	129	46	beam	beam	PROPN
easat-224	129	47	under	under	ADP
easat-224	129	48	moving	move	VERB
easat-224	129	49	distributed	distribute	VERB
easat-224	129	50	force	force	NOUN
easat-224	129	51	and	and	CCONJ
easat-224	129	52	resting	rest	VERB
easat-224	129	53	on	on	ADP
easat-224	129	54	variable	variable	ADJ
easat-224	129	55	pasternak	pasternak	PROPN
easat-224	129	56	elastic	elastic	ADJ
easat-224	129	57	foundation	foundation	NOUN
easat-224	129	58	.	.	PUNCT
easat-224	130	1	4	4	NUM
easat-224	130	2	edelweiss	edelweiss	PROPN
easat-224	130	3	applied	apply	VERB
easat-224	130	4	science	science	NOUN
easat-224	130	5	and	and	CCONJ
easat-224	130	6	technology	technology	NOUN
easat-224	130	7	issn	issn	PROPN
easat-224	130	8	:	:	PUNCT
easat-224	130	9	2576	2576	NUM
easat-224	130	10	-	-	SYM
easat-224	130	11	8484	8484	NUM
easat-224	130	12	vol	vol	NOUN
easat-224	130	13	.	.	PROPN
easat-224	131	1	2	2	NUM
easat-224	131	2	,	,	PUNCT
easat-224	131	3	no	no	INTJ
easat-224	131	4	.	.	NOUN
easat-224	131	5	1	1	NUM
easat-224	131	6	:	:	SYM
easat-224	131	7	1	1	NUM
easat-224	131	8	-	-	SYM
easat-224	131	9	9	9	NUM
easat-224	131	10	,	,	PUNCT
easat-224	131	11	2018	2018	NUM
easat-224	131	12	doi	doi	NOUN
easat-224	131	13	:	:	PUNCT
easat-224	131	14	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	132	1	©	©	PROPN
easat-224	132	2	2018	2018	NUM
easat-224	132	3	by	by	ADP
easat-224	132	4	the	the	DET
easat-224	132	5	authors	author	NOUN
easat-224	132	6	2.2	2.2	NUM
easat-224	132	7	.	.	PUNCT
easat-224	133	1	case	case	NOUN
easat-224	133	2	ii	ii	PROPN
easat-224	133	3	:	:	PUNCT
easat-224	133	4	moving	move	VERB
easat-224	133	5	mass	mass	ADJ
easat-224	133	6	problem	problem	NOUN
easat-224	133	7	in	in	ADP
easat-224	133	8	moving	move	VERB
easat-224	133	9	mass	mass	ADJ
easat-224	133	10	problem	problem	NOUN
easat-224	133	11	,	,	PUNCT
easat-224	133	12	the	the	DET
easat-224	133	13	moving	move	VERB
easat-224	133	14	load	load	NOUN
easat-224	133	15	is	be	AUX
easat-224	133	16	assumed	assume	VERB
easat-224	133	17	to	to	PART
easat-224	133	18	be	be	AUX
easat-224	133	19	rigid	rigid	ADJ
easat-224	133	20	,	,	PUNCT
easat-224	133	21	and	and	CCONJ
easat-224	133	22	the	the	DET
easat-224	133	23	weight	weight	NOUN
easat-224	133	24	and	and	CCONJ
easat-224	133	25	as	as	ADV
easat-224	133	26	well	well	ADV
easat-224	133	27	as	as	ADP
easat-224	133	28	inertia	inertia	NOUN
easat-224	133	29	forces	force	NOUN
easat-224	133	30	are	be	AUX
easat-224	133	31	transferred	transfer	VERB
easat-224	133	32	to	to	ADP
easat-224	133	33	the	the	DET
easat-224	133	34	moving	move	VERB
easat-224	133	35	load	load	NOUN
easat-224	133	36	.	.	PUNCT
easat-224	134	1	that	that	PRON
easat-224	134	2	is	be	AUX
easat-224	134	3	the	the	DET
easat-224	134	4	inertia	inertia	NOUN
easat-224	134	5	effect	effect	NOUN
easat-224	134	6	is	be	AUX
easat-224	134	7	not	not	PART
easat-224	134	8	negligible	negligible	ADJ
easat-224	134	9	.	.	PUNCT
easat-224	135	1	thus	thus	ADV
easat-224	135	2	ϖ≠0	ϖ≠0	X
easat-224	135	3	and	and	CCONJ
easat-224	135	4	so	so	ADV
easat-224	135	5	it	it	PRON
easat-224	135	6	is	be	AUX
easat-224	135	7	required	require	VERB
easat-224	135	8	to	to	PART
easat-224	135	9	solve	solve	VERB
easat-224	135	10	the	the	DET
easat-224	135	11	entire	entire	ADJ
easat-224	135	12	equation	equation	NOUN
easat-224	135	13	(	(	PUNCT
easat-224	135	14	27	27	NUM
easat-224	135	15	)	)	PUNCT
easat-224	135	16	.	.	PUNCT
easat-224	136	1	thus	thus	ADV
easat-224	136	2	,	,	PUNCT
easat-224	136	3	equation	equation	NOUN
easat-224	136	4	(	(	PUNCT
easat-224	136	5	27	27	NUM
easat-224	136	6	)	)	PUNCT
easat-224	136	7	takes	take	VERB
easat-224	136	8	the	the	DET
easat-224	136	9	form	form	NOUN
easat-224	136	10	on	on	ADP
easat-224	136	11	further	further	ADJ
easat-224	136	12	rearrangements	rearrangement	NOUN
easat-224	136	13	,	,	PUNCT
easat-224	136	14	one	one	NUM
easat-224	136	15	obtains	obtain	VERB
easat-224	136	16	obviously	obviously	ADV
easat-224	136	17	,	,	PUNCT
easat-224	136	18	unlike	unlike	ADP
easat-224	136	19	the	the	DET
easat-224	136	20	moving	move	VERB
easat-224	136	21	force	force	NOUN
easat-224	136	22	problem	problem	NOUN
easat-224	136	23	,	,	PUNCT
easat-224	136	24	an	an	DET
easat-224	136	25	exact	exact	ADJ
easat-224	136	26	analytical	analytical	ADJ
easat-224	136	27	solution	solution	NOUN
easat-224	136	28	to	to	ADP
easat-224	136	29	equation	equation	NOUN
easat-224	136	30	(	(	PUNCT
easat-224	136	31	35	35	NUM
easat-224	136	32	)	)	PUNCT
easat-224	136	33	is	be	AUX
easat-224	136	34	not	not	PART
easat-224	136	35	possible	possible	ADJ
easat-224	136	36	.	.	PUNCT
easat-224	137	1	in	in	ADP
easat-224	137	2	order	order	NOUN
easat-224	137	3	to	to	PART
easat-224	137	4	obtain	obtain	VERB
easat-224	137	5	approximate	approximate	ADJ
easat-224	137	6	analytical	analytical	ADJ
easat-224	137	7	solution	solution	NOUN
easat-224	137	8	,	,	PUNCT
easat-224	137	9	one	one	PRON
easat-224	137	10	makes	make	VERB
easat-224	137	11	use	use	NOUN
easat-224	137	12	of	of	ADP
easat-224	137	13	a	a	DET
easat-224	137	14	modification	modification	NOUN
easat-224	137	15	of	of	ADP
easat-224	137	16	the	the	DET
easat-224	137	17	asymptotic	asymptotic	ADJ
easat-224	137	18	method	method	NOUN
easat-224	137	19	of	of	ADP
easat-224	137	20	struble	struble	ADJ
easat-224	137	21	.	.	PUNCT
easat-224	138	1	by	by	ADP
easat-224	138	2	this	this	DET
easat-224	138	3	method	method	NOUN
easat-224	138	4	,	,	PUNCT
easat-224	138	5	one	one	PRON
easat-224	138	6	seeks	seek	VERB
easat-224	138	7	the	the	DET
easat-224	138	8	modified	modify	VERB
easat-224	138	9	frequency	frequency	NOUN
easat-224	138	10	corresponding	correspond	VERB
easat-224	138	11	to	to	ADP
easat-224	138	12	the	the	DET
easat-224	138	13	frequency	frequency	NOUN
easat-224	138	14	of	of	ADP
easat-224	138	15	the	the	DET
easat-224	138	16	free	free	ADJ
easat-224	138	17	system	system	NOUN
easat-224	138	18	due	due	ADP
easat-224	138	19	to	to	ADP
easat-224	138	20	the	the	DET
easat-224	138	21	presence	presence	NOUN
easat-224	138	22	of	of	ADP
easat-224	138	23	the	the	DET
easat-224	138	24	effect	effect	NOUN
easat-224	138	25	of	of	ADP
easat-224	138	26	the	the	DET
easat-224	138	27	moving	move	VERB
easat-224	138	28	mass	mass	NOUN
easat-224	138	29	.	.	PUNCT
easat-224	139	1	an	an	DET
easat-224	139	2	equivalent	equivalent	ADJ
easat-224	139	3	system	system	NOUN
easat-224	139	4	operator	operator	NOUN
easat-224	139	5	defined	define	VERB
easat-224	139	6	by	by	ADP
easat-224	139	7	the	the	DET
easat-224	139	8	modified	modify	VERB
easat-224	139	9	frequency	frequency	NOUN
easat-224	139	10	then	then	ADV
easat-224	139	11	replaces	replace	VERB
easat-224	139	12	equation	equation	NOUN
easat-224	139	13	(	(	PUNCT
easat-224	139	14	35	35	NUM
easat-224	139	15	)	)	PUNCT
easat-224	139	16	.	.	PUNCT
easat-224	140	1	we	we	PRON
easat-224	140	2	shall	shall	AUX
easat-224	140	3	consider	consider	VERB
easat-224	140	4	a	a	DET
easat-224	140	5	parameter	parameter	NOUN
easat-224	140	6	ϖ0	ϖ0	NOUN
easat-224	140	7	<	<	X
easat-224	140	8	1	1	NUM
easat-224	140	9	for	for	ADP
easat-224	140	10	any	any	DET
easat-224	140	11	arbitrary	arbitrary	ADJ
easat-224	140	12	mass	mass	NOUN
easat-224	140	13	ratio	ratio	NOUN
easat-224	140	14	defined	define	VERB
easat-224	140	15	by	by	ADP
easat-224	140	16	𝜛0	𝜛0	NOUN
easat-224	140	17	=	=	PUNCT
easat-224	141	1	𝜛	𝜛	PROPN
easat-224	141	2	1	1	NUM
easat-224	142	1	+	+	NUM
easat-224	142	2	𝜛	𝜛	X
easat-224	142	3	(	(	PUNCT
easat-224	142	4	36	36	NUM
easat-224	142	5	)	)	PUNCT
easat-224	142	6	by	by	ADP
easat-224	142	7	using	use	VERB
easat-224	142	8	binomial	binomial	ADJ
easat-224	142	9	theorem	theorem	NOUN
easat-224	142	10	and	and	CCONJ
easat-224	142	11	truncating	truncating	NOUN
easat-224	142	12	after	after	ADP
easat-224	142	13	second	second	ADJ
easat-224	142	14	terms	term	NOUN
easat-224	142	15	,	,	PUNCT
easat-224	142	16	one	one	PRON
easat-224	142	17	obtains	obtain	VERB
easat-224	142	18	𝜛0	𝜛0	NOUN
easat-224	142	19	=	=	PUNCT
easat-224	142	20	𝜛	𝜛	PROPN
easat-224	142	21	−	−	PROPN
easat-224	142	22	o(𝜛2	o(𝜛2	PROPN
easat-224	142	23	)	)	PUNCT
easat-224	142	24	(	(	PUNCT
easat-224	142	25	37	37	NUM
easat-224	142	26	)	)	PUNCT
easat-224	142	27	equation	equation	NOUN
easat-224	142	28	(	(	PUNCT
easat-224	142	29	45	45	NUM
easat-224	142	30	)	)	PUNCT
easat-224	142	31	becomes	become	VERB
easat-224	142	32	𝜛	𝜛	NOUN
easat-224	142	33	=	=	PROPN
easat-224	142	34	𝜛0	𝜛0	PROPN
easat-224	142	35	(	(	PUNCT
easat-224	142	36	38	38	NUM
easat-224	142	37	)	)	PUNCT
easat-224	142	38	to	to	ADP
easat-224	142	39	𝑜(𝜛	𝑜(𝜛	PROPN
easat-224	142	40	)	)	PUNCT
easat-224	142	41	only	only	ADV
easat-224	142	42	and	and	CCONJ
easat-224	142	43	from	from	ADP
easat-224	142	44	equation	equation	NOUN
easat-224	142	45	(	(	PUNCT
easat-224	142	46	38	38	NUM
easat-224	142	47	)	)	PUNCT
easat-224	142	48	1	1	NUM
easat-224	142	49	1	1	NUM
easat-224	142	50	+	+	CCONJ
easat-224	142	51	𝜛o	𝜛o	ADJ
easat-224	142	52	(	(	PUNCT
easat-224	142	53	1	1	NUM
easat-224	142	54	4	4	NUM
easat-224	142	55	𝒢1(𝑖,𝑗	𝒢1(𝑖,𝑗	NOUN
easat-224	142	56	)	)	PUNCT
easat-224	142	57	ҕo(𝑖,𝑗	ҕo(𝑖,𝑗	NOUN
easat-224	142	58	)	)	PUNCT
easat-224	143	1	+	+	CCONJ
easat-224	143	2	1	1	NUM
easat-224	143	3	𝜋	𝜋	NOUN
easat-224	143	4	∑	∑	PROPN
easat-224	143	5	cos	cos	PROPN
easat-224	143	6	(	(	PUNCT
easat-224	143	7	2𝑛+1)𝜋𝑣𝑡	2𝑛+1)𝜋𝑣𝑡	PROPN
easat-224	143	8	2𝑛+1	2𝑛+1	NUM
easat-224	143	9	𝒢2(𝑖,𝑗	𝒢2(𝑖,𝑗	NOUN
easat-224	143	10	)	)	PUNCT
easat-224	143	11	ҕo(𝑖,j	ҕo(𝑖,j	NOUN
easat-224	143	12	)	)	PUNCT
easat-224	144	1	−	−	NOUN
easat-224	144	2	1	1	NUM
easat-224	144	3	𝜋	𝜋	NOUN
easat-224	144	4	∑	∑	ADV
easat-224	144	5	sin	sin	NOUN
easat-224	144	6	(	(	PUNCT
easat-224	144	7	2𝑛+1)𝜋𝑣𝑡	2𝑛+1)𝜋𝑣𝑡	NUM
easat-224	144	8	2𝑛+1	2𝑛+1	NUM
easat-224	144	9	𝒢3(𝑖,𝑗	𝒢3(𝑖,𝑗	NOUN
easat-224	144	10	)	)	PUNCT
easat-224	144	11	ҕo(𝑖,𝑗	ҕo(𝑖,𝑗	NOUN
easat-224	144	12	)	)	PUNCT
easat-224	145	1	∞	∞	NUM
easat-224	145	2	𝑛=0	𝑛=0	PROPN
easat-224	145	3	∞	∞	NUM
easat-224	145	4	𝑛=0	𝑛=0	PROPN
easat-224	145	5	)	)	PUNCT
easat-224	145	6	(	(	PUNCT
easat-224	145	7	39	39	NUM
easat-224	145	8	)	)	PUNCT
easat-224	146	1	[	[	X
easat-224	146	2	1	1	NUM
easat-224	146	3	−	−	NUM
easat-224	146	4	𝜛o	𝜛o	PROPN
easat-224	146	5	(	(	PUNCT
easat-224	146	6	1	1	NUM
easat-224	146	7	4	4	NUM
easat-224	146	8	𝒢1(𝑖,𝑗	𝒢1(𝑖,𝑗	NOUN
easat-224	146	9	)	)	PUNCT
easat-224	146	10	ҕo(𝑖,𝑗	ҕo(𝑖,𝑗	NOUN
easat-224	146	11	)	)	PUNCT
easat-224	147	1	+	+	CCONJ
easat-224	147	2	1	1	NUM
easat-224	147	3	𝜋	𝜋	NOUN
easat-224	147	4	∑	∑	PROPN
easat-224	147	5	cos	cos	PROPN
easat-224	147	6	(	(	PUNCT
easat-224	147	7	2𝑛+1)𝜋𝑣𝑡	2𝑛+1)𝜋𝑣𝑡	PROPN
easat-224	147	8	2𝑛+1	2𝑛+1	NUM
easat-224	147	9	𝒢2(𝑖,𝑗	𝒢2(𝑖,𝑗	NOUN
easat-224	147	10	)	)	PUNCT
easat-224	147	11	ҕo(𝑖,j	ҕo(𝑖,j	NOUN
easat-224	147	12	)	)	PUNCT
easat-224	148	1	−	−	NOUN
easat-224	149	1	1	1	NUM
easat-224	149	2	𝜋	𝜋	NOUN
easat-224	149	3	1	1	NUM
easat-224	149	4	𝜋	𝜋	NOUN
easat-224	149	5	∑	∑	ADV
easat-224	149	6	sin	sin	NOUN
easat-224	149	7	(	(	PUNCT
easat-224	149	8	2𝑛+1)𝜋𝑣𝑡	2𝑛+1)𝜋𝑣𝑡	NUM
easat-224	149	9	2𝑛+1	2𝑛+1	NUM
easat-224	149	10	𝒢3(𝑖,𝑗	𝒢3(𝑖,𝑗	NOUN
easat-224	149	11	)	)	PUNCT
easat-224	149	12	ҕo(𝑖,𝑗	ҕo(𝑖,𝑗	NOUN
easat-224	149	13	)	)	PUNCT
easat-224	149	14	∞	∞	NUM
easat-224	150	1	𝑛=0	𝑛=0	PROPN
easat-224	150	2	∞	∞	NUM
easat-224	150	3	𝑛=0	𝑛=0	PROPN
easat-224	150	4	)	)	PUNCT
easat-224	151	1	+	+	CCONJ
easat-224	151	2	⋯	⋯	ADP
easat-224	151	3	]	]	X
easat-224	151	4	(	(	PUNCT
easat-224	151	5	40	40	NUM
easat-224	151	6	)	)	PUNCT
easat-224	151	7	where	where	SCONJ
easat-224	151	8	|𝜛	|𝜛	PROPN
easat-224	151	9	(	(	PUNCT
easat-224	151	10	1	1	NUM
easat-224	151	11	4	4	NUM
easat-224	151	12	𝒢1(𝑖	𝒢1(𝑖	NUM
easat-224	151	13	,	,	PUNCT
easat-224	151	14	𝑗	𝑗	NOUN
easat-224	151	15	)	)	PUNCT
easat-224	151	16	ҕo(𝑖	ҕo(𝑖	PROPN
easat-224	151	17	,	,	PUNCT
easat-224	151	18	𝑗	𝑗	NOUN
easat-224	151	19	)	)	PUNCT
easat-224	151	20	+	+	CCONJ
easat-224	151	21	1	1	NUM
easat-224	151	22	𝜋	𝜋	NOUN
easat-224	151	23	∑	∑	PROPN
easat-224	151	24	cos	cos	PROPN
easat-224	151	25	(	(	PUNCT
easat-224	151	26	2𝑛	2𝑛	PROPN
easat-224	151	27	+	+	CCONJ
easat-224	151	28	1)𝜋𝑣𝑡	1)𝜋𝑣𝑡	NUM
easat-224	151	29	2𝑛	2𝑛	NOUN
easat-224	151	30	+	+	CCONJ
easat-224	151	31	1	1	NUM
easat-224	151	32	𝒢2(𝑖	𝒢2(𝑖	NOUN
easat-224	151	33	,	,	PUNCT
easat-224	151	34	𝑗	𝑗	NOUN
easat-224	151	35	)	)	PUNCT
easat-224	151	36	ҕo(𝑖	ҕo(𝑖	PROPN
easat-224	151	37	,	,	PUNCT
easat-224	151	38	j	j	PROPN
easat-224	151	39	)	)	PUNCT
easat-224	151	40	−	−	PROPN
easat-224	151	41	1	1	NUM
easat-224	151	42	𝜋	𝜋	NOUN
easat-224	151	43	∑	∑	ADV
easat-224	151	44	sin	sin	NOUN
easat-224	151	45	(	(	PUNCT
easat-224	151	46	2𝑛	2𝑛	NOUN
easat-224	151	47	+	+	CCONJ
easat-224	151	48	1)𝜋𝑣𝑡	1)𝜋𝑣𝑡	NUM
easat-224	151	49	2𝑛	2𝑛	NOUN
easat-224	151	50	+	+	CCONJ
easat-224	151	51	1	1	NUM
easat-224	151	52	𝒢3(𝑖	𝒢3(𝑖	ADJ
easat-224	151	53	,	,	PUNCT
easat-224	151	54	𝑗	𝑗	NOUN
easat-224	151	55	)	)	PUNCT
easat-224	151	56	ҕo(𝑖	ҕo(𝑖	PROPN
easat-224	151	57	,	,	PUNCT
easat-224	151	58	𝑗	𝑗	NOUN
easat-224	151	59	)	)	PUNCT
easat-224	151	60	∞	∞	NUM
easat-224	152	1	𝑛=0	𝑛=0	PROPN
easat-224	152	2	∞	∞	NUM
easat-224	152	3	𝑛=0	𝑛=0	PROPN
easat-224	152	4	)	)	PUNCT
easat-224	153	1	|	|	CCONJ
easat-224	153	2	<	<	X
easat-224	153	3	1	1	NUM
easat-224	153	4	(	(	PUNCT
easat-224	153	5	41	41	NUM
easat-224	153	6	)	)	PUNCT
easat-224	153	7	substituting	substitute	VERB
easat-224	153	8	equations	equation	NOUN
easat-224	153	9	(	(	PUNCT
easat-224	153	10	40	40	NUM
easat-224	153	11	)	)	PUNCT
easat-224	153	12	and	and	CCONJ
easat-224	153	13	(	(	PUNCT
easat-224	153	14	41	41	NUM
easat-224	153	15	)	)	PUNCT
easat-224	153	16	into	into	ADP
easat-224	153	17	equation	equation	NOUN
easat-224	153	18	(	(	PUNCT
easat-224	153	19	35	35	NUM
easat-224	153	20	)	)	PUNCT
easat-224	153	21	,	,	PUNCT
easat-224	153	22	one	one	PRON
easat-224	153	23	obtains	obtain	VERB
easat-224	153	24	to	to	ADP
easat-224	153	25	0(𝜛0	0(𝜛0	NUM
easat-224	153	26	)	)	PUNCT
easat-224	153	27	only	only	ADV
easat-224	153	28	applying	apply	VERB
easat-224	153	29	method	method	NOUN
easat-224	153	30	of	of	ADP
easat-224	153	31	struble	struble	ADJ
easat-224	153	32	technique	technique	NOUN
easat-224	153	33	to	to	ADP
easat-224	153	34	eqation	eqation	NOUN
easat-224	153	35	(	(	PUNCT
easat-224	153	36	42	42	NUM
easat-224	153	37	)	)	PUNCT
easat-224	153	38	one	one	NOUN
easat-224	153	39	obtains	obtain	VERB
easat-224	153	40	where	where	SCONJ
easat-224	153	41	𝜎𝑖𝑖	𝜎𝑖𝑖	ADJ
easat-224	153	42	=	=	NOUN
easat-224	153	43	𝜎𝑖	𝜎𝑖	PRON
easat-224	153	44	−	−	PROPN
easat-224	153	45	𝜛0	𝜛0	NOUN
easat-224	153	46	2	2	NUM
easat-224	153	47	[	[	PUNCT
easat-224	153	48	𝒢1(𝑖	𝒢1(𝑖	NUM
easat-224	153	49	,	,	PUNCT
easat-224	153	50	𝑗)𝜎𝑖	𝑗)𝜎𝑖	PROPN
easat-224	153	51	2	2	NUM
easat-224	154	1	−	−	PRON
easat-224	154	2	𝑣2𝒢7(𝑖	𝑣2𝒢7(𝑖	NOUN
easat-224	154	3	,	,	PUNCT
easat-224	154	4	𝑗	𝑗	NOUN
easat-224	154	5	)	)	PUNCT
easat-224	154	6	4𝜎𝑖ҕo(𝑖	4𝜎𝑖ҕo(𝑖	NUM
easat-224	154	7	,	,	PUNCT
easat-224	154	8	𝑗	𝑗	NOUN
easat-224	154	9	)	)	PUNCT
easat-224	154	10	]	]	PUNCT
easat-224	154	11	(	(	PUNCT
easat-224	154	12	44	44	X
easat-224	154	13	)	)	PUNCT
easat-224	154	14	solving	solve	VERB
easat-224	154	15	equation	equation	NOUN
easat-224	154	16	(	(	PUNCT
easat-224	154	17	43	43	NUM
easat-224	154	18	)	)	PUNCT
easat-224	154	19	using	use	VERB
easat-224	154	20	laplace	laplace	NOUN
easat-224	154	21	transformation	transformation	NOUN
easat-224	154	22	techniques	technique	NOUN
easat-224	154	23	and	and	CCONJ
easat-224	154	24	taking	take	VERB
easat-224	154	25	into	into	ADP
easat-224	154	26	account	account	NOUN
easat-224	154	27	equation	equation	NOUN
easat-224	154	28	(	(	PUNCT
easat-224	154	29	7	7	X
easat-224	154	30	)	)	PUNCT
easat-224	154	31	one	one	NOUN
easat-224	154	32	obtains	obtain	VERB
easat-224	154	33	equation	equation	NOUN
easat-224	154	34	(	(	PUNCT
easat-224	154	35	45	45	NUM
easat-224	154	36	)	)	PUNCT
easat-224	154	37	represents	represent	VERB
easat-224	154	38	the	the	DET
easat-224	154	39	transverse	transverse	NOUN
easat-224	154	40	deflection	deflection	NOUN
easat-224	154	41	of	of	ADP
easat-224	154	42	uniform	uniform	ADJ
easat-224	154	43	rayleigh	rayleigh	PROPN
easat-224	154	44	beam	beam	PROPN
easat-224	154	45	under	under	ADP
easat-224	154	46	moving	move	VERB
easat-224	154	47	distributed	distribute	VERB
easat-224	154	48	mass	mass	NOUN
easat-224	154	49	and	and	CCONJ
easat-224	154	50	resting	rest	VERB
easat-224	154	51	on	on	ADP
easat-224	154	52	variable	variable	ADJ
easat-224	154	53	pasternak	pasternak	PROPN
easat-224	154	54	elastic	elastic	ADJ
easat-224	154	55	foundation	foundation	NOUN
easat-224	154	56	.	.	PUNCT
easat-224	155	1	3	3	X
easat-224	155	2	.	.	X
easat-224	155	3	discussion	discussion	NOUN
easat-224	155	4	of	of	ADP
easat-224	155	5	the	the	DET
easat-224	155	6	analytical	analytical	ADJ
easat-224	155	7	solutions	solution	NOUN
easat-224	155	8	for	for	ADP
easat-224	155	9	this	this	DET
easat-224	155	10	undamped	undampe	VERB
easat-224	155	11	system	system	NOUN
easat-224	155	12	,	,	PUNCT
easat-224	155	13	it	it	PRON
easat-224	155	14	is	be	AUX
easat-224	155	15	desirable	desirable	ADJ
easat-224	155	16	to	to	PART
easat-224	155	17	examine	examine	VERB
easat-224	155	18	the	the	DET
easat-224	155	19	phenomenon	phenomenon	NOUN
easat-224	155	20	of	of	ADP
easat-224	155	21	resonance	resonance	NOUN
easat-224	155	22	.	.	PUNCT
easat-224	156	1	from	from	ADP
easat-224	156	2	equation(33	equation(33	NUM
easat-224	156	3	)	)	PUNCT
easat-224	156	4	,	,	PUNCT
easat-224	156	5	it	it	PRON
easat-224	156	6	is	be	AUX
easat-224	156	7	clearly	clearly	ADV
easat-224	156	8	shown	show	VERB
easat-224	156	9	that	that	SCONJ
easat-224	156	10	the	the	DET
easat-224	156	11	beam	beam	NOUN
easat-224	156	12	resting	rest	VERB
easat-224	156	13	on	on	ADP
easat-224	156	14	variable	variable	ADJ
easat-224	156	15	bi	bi	ADJ
easat-224	156	16	-	-	ADJ
easat-224	156	17	parametric	parametric	ADJ
easat-224	156	18	elastic	elastic	ADJ
easat-224	156	19	foundation	foundation	NOUN
easat-224	156	20	and	and	CCONJ
easat-224	156	21	traversed	traverse	VERB
easat-224	156	22	by	by	ADP
easat-224	156	23	a	a	DET
easat-224	156	24	moving	move	VERB
easat-224	156	25	distributed	distribute	VERB
easat-224	156	26	force	force	NOUN
easat-224	156	27	reaches	reach	VERB
easat-224	156	28	a	a	DET
easat-224	156	29	state	state	NOUN
easat-224	156	30	of	of	ADP
easat-224	156	31	resonance	resonance	NOUN
easat-224	156	32	whenever	whenever	SCONJ
easat-224	156	33	𝜎𝑖	𝜎𝑖	PRON
easat-224	156	34	=	=	SYM
easat-224	156	35	𝛺𝑗	𝛺𝑗	PROPN
easat-224	156	36	(	(	PUNCT
easat-224	156	37	46	46	NUM
easat-224	156	38	)	)	PUNCT
easat-224	156	39	where	where	SCONJ
easat-224	156	40	𝛺𝑗	𝛺𝑗	PROPN
easat-224	156	41	=	=	SYM
easat-224	156	42	𝔇𝑗𝑣	𝔇𝑗𝑣	PROPN
easat-224	156	43	𝐿	𝐿	PROPN
easat-224	156	44	(	(	PUNCT
easat-224	156	45	47	47	NUM
easat-224	156	46	)	)	PUNCT
easat-224	156	47	that	that	PRON
easat-224	156	48	is	be	AUX
easat-224	156	49	𝜎𝑖	𝜎𝑖	DET
easat-224	156	50	=	=	SYM
easat-224	156	51	𝔇𝑗𝑣	𝔇𝑗𝑣	PROPN
easat-224	156	52	𝐿	𝐿	PROPN
easat-224	156	53	(	(	PUNCT
easat-224	156	54	48	48	NUM
easat-224	156	55	)	)	PUNCT
easat-224	156	56	equation	equation	NOUN
easat-224	156	57	(	(	PUNCT
easat-224	156	58	45	45	NUM
easat-224	156	59	)	)	PUNCT
easat-224	156	60	shows	show	VERB
easat-224	156	61	that	that	SCONJ
easat-224	156	62	the	the	DET
easat-224	156	63	same	same	ADJ
easat-224	156	64	beam	beam	NOUN
easat-224	156	65	under	under	ADP
easat-224	156	66	the	the	DET
easat-224	156	67	action	action	NOUN
easat-224	156	68	of	of	ADP
easat-224	156	69	moving	move	VERB
easat-224	156	70	distributed	distribute	VERB
easat-224	156	71	mass	mass	NOUN
easat-224	156	72	experiences	experience	NOUN
easat-224	156	73	resonance	resonance	NOUN
easat-224	156	74	effect	effect	NOUN
easat-224	156	75	whenever	whenever	SCONJ
easat-224	156	76	𝜎𝑖𝑖	𝜎𝑖𝑖	ADJ
easat-224	156	77	=	=	PUNCT
easat-224	156	78	𝔇𝑗𝑣	𝔇𝑗𝑣	PROPN
easat-224	156	79	𝐿	𝐿	PROPN
easat-224	156	80	(	(	PUNCT
easat-224	156	81	49	49	NUM
easat-224	156	82	)	)	PUNCT
easat-224	156	83	from	from	ADP
easat-224	156	84	equation	equation	NOUN
easat-224	156	85	(	(	PUNCT
easat-224	156	86	44	44	NUM
easat-224	156	87	)	)	SYM
easat-224	156	88	5	5	NUM
easat-224	156	89	edelweiss	edelweiss	PROPN
easat-224	156	90	applied	apply	VERB
easat-224	156	91	science	science	NOUN
easat-224	156	92	and	and	CCONJ
easat-224	156	93	technology	technology	NOUN
easat-224	156	94	issn	issn	PROPN
easat-224	156	95	:	:	PUNCT
easat-224	156	96	2576	2576	NUM
easat-224	156	97	-	-	SYM
easat-224	156	98	8484	8484	NUM
easat-224	156	99	vol	vol	NOUN
easat-224	156	100	.	.	PROPN
easat-224	157	1	2	2	NUM
easat-224	157	2	,	,	PUNCT
easat-224	157	3	no	no	INTJ
easat-224	157	4	.	.	NOUN
easat-224	157	5	1	1	NUM
easat-224	157	6	:	:	SYM
easat-224	157	7	1	1	NUM
easat-224	157	8	-	-	SYM
easat-224	157	9	9	9	NUM
easat-224	157	10	,	,	PUNCT
easat-224	157	11	2018	2018	NUM
easat-224	157	12	doi	doi	NOUN
easat-224	157	13	:	:	PUNCT
easat-224	157	14	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	158	1	©	©	PROPN
easat-224	158	2	2018	2018	NUM
easat-224	158	3	by	by	ADP
easat-224	158	4	the	the	DET
easat-224	158	5	authors	author	NOUN
easat-224	158	6	𝜎𝑖𝑖	𝜎𝑖𝑖	ADJ
easat-224	158	7	=	=	PUNCT
easat-224	159	1	𝜎𝑖	𝜎𝑖	NUM
easat-224	159	2	−	−	NOUN
easat-224	159	3	𝜛	𝜛	SYM
easat-224	159	4	2	2	NUM
easat-224	159	5	[	[	PUNCT
easat-224	159	6	𝒢1(𝑖	𝒢1(𝑖	NUM
easat-224	159	7	,	,	PUNCT
easat-224	159	8	𝑗)𝜎𝑖	𝑗)𝜎𝑖	PROPN
easat-224	159	9	2	2	NUM
easat-224	159	10	−	−	PRON
easat-224	159	11	𝑣2𝒢7(𝑖	𝑣2𝒢7(𝑖	NOUN
easat-224	159	12	,	,	PUNCT
easat-224	159	13	𝑗	𝑗	NOUN
easat-224	159	14	)	)	PUNCT
easat-224	159	15	4𝜎𝑖ҕo(𝑖	4𝜎𝑖ҕo(𝑖	NUM
easat-224	159	16	,	,	PUNCT
easat-224	159	17	𝑗	𝑗	NOUN
easat-224	159	18	)	)	PUNCT
easat-224	159	19	]	]	PUNCT
easat-224	160	1	=	=	PUNCT
easat-224	160	2	𝔇𝑗𝑣	𝔇𝑗𝑣	PROPN
easat-224	160	3	𝐿	𝐿	PROPN
easat-224	160	4	(	(	PUNCT
easat-224	160	5	50	50	NUM
easat-224	160	6	)	)	PUNCT
easat-224	160	7	it	it	PRON
easat-224	160	8	is	be	AUX
easat-224	160	9	therefore	therefore	ADV
easat-224	160	10	clear	clear	ADJ
easat-224	160	11	that	that	SCONJ
easat-224	160	12	for	for	ADP
easat-224	160	13	the	the	DET
easat-224	160	14	same	same	ADJ
easat-224	160	15	natural	natural	ADJ
easat-224	160	16	frequency	frequency	NOUN
easat-224	160	17	,	,	PUNCT
easat-224	160	18	the	the	DET
easat-224	160	19	critical	critical	ADJ
easat-224	160	20	speed	speed	NOUN
easat-224	160	21	for	for	ADP
easat-224	160	22	the	the	DET
easat-224	160	23	system	system	NOUN
easat-224	160	24	consisting	consist	VERB
easat-224	160	25	of	of	ADP
easat-224	160	26	elastically	elastically	ADV
easat-224	160	27	supported	support	VERB
easat-224	160	28	uniform	uniform	ADJ
easat-224	160	29	rayleigh	rayleigh	PROPN
easat-224	160	30	beam	beam	PROPN
easat-224	160	31	resting	rest	VERB
easat-224	160	32	on	on	ADP
easat-224	160	33	variable	variable	ADJ
easat-224	160	34	elastic	elastic	ADJ
easat-224	160	35	foundation	foundation	NOUN
easat-224	160	36	and	and	CCONJ
easat-224	160	37	traverse	traverse	VERB
easat-224	160	38	by	by	ADP
easat-224	160	39	moving	move	VERB
easat-224	160	40	distributed	distributed	ADJ
easat-224	160	41	force	force	NOUN
easat-224	160	42	with	with	ADP
easat-224	160	43	uniform	uniform	ADJ
easat-224	160	44	speed	speed	NOUN
easat-224	160	45	is	be	AUX
easat-224	160	46	greater	great	ADJ
easat-224	160	47	than	than	ADP
easat-224	160	48	that	that	PRON
easat-224	160	49	of	of	ADP
easat-224	160	50	moving	move	VERB
easat-224	160	51	distributed	distribute	VERB
easat-224	160	52	mass	mass	NOUN
easat-224	160	53	problem	problem	NOUN
easat-224	160	54	.	.	PUNCT
easat-224	161	1	thus	thus	ADV
easat-224	161	2	for	for	ADP
easat-224	161	3	the	the	DET
easat-224	161	4	same	same	ADJ
easat-224	161	5	natural	natural	ADJ
easat-224	161	6	frequency	frequency	NOUN
easat-224	161	7	,	,	PUNCT
easat-224	161	8	resonance	resonance	NOUN
easat-224	161	9	is	be	AUX
easat-224	161	10	reached	reach	VERB
easat-224	161	11	faster	fast	ADV
easat-224	161	12	in	in	ADP
easat-224	161	13	the	the	DET
easat-224	161	14	moving	move	VERB
easat-224	161	15	distributed	distribute	VERB
easat-224	161	16	mass	mass	NOUN
easat-224	161	17	system	system	NOUN
easat-224	161	18	than	than	ADP
easat-224	161	19	in	in	ADP
easat-224	161	20	the	the	DET
easat-224	161	21	moving	move	VERB
easat-224	161	22	distributed	distribute	VERB
easat-224	161	23	force	force	NOUN
easat-224	161	24	system	system	NOUN
easat-224	161	25	.	.	PUNCT
easat-224	162	1	3.1	3.1	NUM
easat-224	162	2	.	.	PUNCT
easat-224	162	3	illustrative	illustrative	ADJ
easat-224	162	4	examples	example	NOUN
easat-224	162	5	3.1.1	3.1.1	NUM
easat-224	162	6	.	.	PUNCT
easat-224	163	1	clamped	clamp	VERB
easat-224	163	2	-	-	PUNCT
easat-224	163	3	elastic	elastic	ADJ
easat-224	163	4	boundary	boundary	ADJ
easat-224	163	5	conditions	condition	NOUN
easat-224	163	6	at	at	ADP
easat-224	163	7	a	a	DET
easat-224	163	8	clamped	clamp	VERB
easat-224	163	9	end	end	NOUN
easat-224	163	10	,	,	PUNCT
easat-224	163	11	both	both	DET
easat-224	163	12	deflection	deflection	NOUN
easat-224	163	13	and	and	CCONJ
easat-224	163	14	slope	slope	NOUN
easat-224	163	15	vanish	vanish	NOUN
easat-224	163	16	.	.	PUNCT
easat-224	164	1	thus	thus	ADV
easat-224	164	2	,	,	PUNCT
easat-224	164	3	when	when	SCONJ
easat-224	164	4	the	the	DET
easat-224	164	5	rayleigh	rayleigh	PROPN
easat-224	164	6	beam	beam	NOUN
easat-224	164	7	is	be	AUX
easat-224	164	8	clamped	clamp	VERB
easat-224	164	9	at	at	ADP
easat-224	164	10	𝑥	𝑥	PROPN
easat-224	164	11	=	=	SYM
easat-224	164	12	0	0	NUM
easat-224	164	13	and	and	CCONJ
easat-224	164	14	elastically	elastically	ADV
easat-224	164	15	supported	support	VERB
easat-224	164	16	at	at	ADP
easat-224	164	17	𝑥	𝑥	PROPN
easat-224	164	18	=	=	SYM
easat-224	164	19	𝐿	𝐿	PROPN
easat-224	164	20	,	,	PUNCT
easat-224	164	21	the	the	DET
easat-224	164	22	conditions	condition	NOUN
easat-224	164	23	are	be	AUX
easat-224	164	24	expressed	express	VERB
easat-224	164	25	as	as	ADP
easat-224	164	26	𝒷(0	𝒷(0	PROPN
easat-224	164	27	,	,	PUNCT
easat-224	164	28	𝑡	𝑡	PROPN
easat-224	164	29	)	)	PUNCT
easat-224	164	30	=	=	SYM
easat-224	164	31	0	0	PUNCT
easat-224	164	32	=	=	PUNCT
easat-224	164	33	𝒷	𝒷	PRON
easat-224	164	34	′(0	′(0	PROPN
easat-224	164	35	,	,	PUNCT
easat-224	164	36	𝑡	𝑡	X
easat-224	164	37	)	)	PUNCT
easat-224	164	38	(	(	PUNCT
easat-224	164	39	59	59	NUM
easat-224	164	40	)	)	PUNCT
easat-224	164	41	at	at	ADP
easat-224	164	42	the	the	DET
easat-224	164	43	end	end	NOUN
easat-224	164	44	𝑥	𝑥	ADP
easat-224	164	45	=	=	SYM
easat-224	164	46	0	0	NUM
easat-224	164	47	and	and	CCONJ
easat-224	164	48	𝒷	𝒷	X
easat-224	165	1	′′	′′	PROPN
easat-224	165	2	−	−	PROPN
easat-224	165	3	𝑘1𝒷	𝑘1𝒷	PROPN
easat-224	165	4	′(𝐿	′(𝐿	NOUN
easat-224	165	5	,	,	PUNCT
easat-224	165	6	𝑡	𝑡	X
easat-224	165	7	)	)	PUNCT
easat-224	165	8	=	=	SYM
easat-224	165	9	0	0	PUNCT
easat-224	166	1	=	=	PUNCT
easat-224	166	2	𝒷	𝒷	PRON
easat-224	166	3	′′′(𝐿	′′′(𝐿	NOUN
easat-224	166	4	,	,	PUNCT
easat-224	166	5	𝑡	𝑡	X
easat-224	166	6	)	)	PUNCT
easat-224	166	7	+	+	CCONJ
easat-224	166	8	𝑘2𝒷(𝐿	𝑘2𝒷(𝐿	PROPN
easat-224	166	9	,	,	PUNCT
easat-224	166	10	𝑡	𝑡	X
easat-224	166	11	)	)	PUNCT
easat-224	166	12	(	(	PUNCT
easat-224	166	13	60	60	NUM
easat-224	166	14	)	)	PUNCT
easat-224	166	15	at	at	ADP
easat-224	166	16	the	the	DET
easat-224	166	17	end	end	NOUN
easat-224	166	18	𝑥	𝑥	X
easat-224	166	19	=	=	SYM
easat-224	166	20	𝐿	𝐿	PROPN
easat-224	166	21	and	and	CCONJ
easat-224	166	22	for	for	ADP
easat-224	166	23	the	the	DET
easat-224	166	24	normal	normal	ADJ
easat-224	166	25	modes	mode	NOUN
easat-224	166	26	𝒰𝑖(0	𝒰𝑖(0	PROPN
easat-224	166	27	)	)	PUNCT
easat-224	167	1	=	=	PUNCT
easat-224	167	2	0	0	PUNCT
easat-224	168	1	=	=	PUNCT
easat-224	168	2	𝒰𝑖	𝒰𝑖	PROPN
easat-224	168	3	′(0	′(0	NOUN
easat-224	168	4	)	)	PUNCT
easat-224	168	5	(	(	PUNCT
easat-224	168	6	61	61	NUM
easat-224	168	7	)	)	PUNCT
easat-224	168	8	at	at	ADP
easat-224	168	9	the	the	DET
easat-224	168	10	end	end	NOUN
easat-224	169	1	𝑥	𝑥	ADP
easat-224	169	2	=	=	SYM
easat-224	169	3	0	0	NUM
easat-224	169	4	and	and	CCONJ
easat-224	169	5	𝒰𝑖	𝒰𝑖	PROPN
easat-224	169	6	′′(𝐿	′′(𝐿	PROPN
easat-224	169	7	)	)	PUNCT
easat-224	169	8	−	−	PROPN
easat-224	169	9	𝑘1𝒰𝑖	𝑘1𝒰𝑖	VERB
easat-224	169	10	′(𝐿	′(𝐿	NOUN
easat-224	169	11	)	)	PUNCT
easat-224	169	12	=	=	SYM
easat-224	169	13	0	0	PUNCT
easat-224	170	1	=	=	PUNCT
easat-224	170	2	𝒰𝑖	𝒰𝑖	PROPN
easat-224	170	3	′′′(𝐿	′′′(𝐿	NOUN
easat-224	170	4	)	)	PUNCT
easat-224	171	1	+	+	NUM
easat-224	171	2	𝑘2𝒰𝑖(𝐿	𝑘2𝒰𝑖(𝐿	ADJ
easat-224	171	3	)	)	PUNCT
easat-224	171	4	(	(	PUNCT
easat-224	171	5	62	62	NUM
easat-224	171	6	)	)	PUNCT
easat-224	171	7	at	at	ADP
easat-224	171	8	end	end	NOUN
easat-224	171	9	𝑥	𝑥	X
easat-224	171	10	=	=	SYM
easat-224	171	11	𝐿	𝐿	PROPN
easat-224	171	12	which	which	PRON
easat-224	171	13	implies	imply	VERB
easat-224	171	14	that	that	SCONJ
easat-224	171	15	𝒰𝑗(0	𝒰𝑗(0	NOUN
easat-224	171	16	)	)	PUNCT
easat-224	172	1	=	=	SYM
easat-224	172	2	0	0	PUNCT
easat-224	173	1	=	=	PUNCT
easat-224	173	2	𝒰𝑗	𝒰𝑗	NOUN
easat-224	173	3	′(0	′(0	NOUN
easat-224	173	4	)	)	PUNCT
easat-224	173	5	(	(	PUNCT
easat-224	173	6	63	63	NUM
easat-224	173	7	)	)	PUNCT
easat-224	173	8	and	and	CCONJ
easat-224	173	9	𝒰𝑗	𝒰𝑗	ADP
easat-224	173	10	′′(𝐿	′′(𝐿	NOUN
easat-224	173	11	)	)	PUNCT
easat-224	173	12	−	−	NOUN
easat-224	173	13	𝑘1𝒰𝑗	𝑘1𝒰𝑗	ADJ
easat-224	173	14	′(𝐿	′(𝐿	NOUN
easat-224	173	15	)	)	PUNCT
easat-224	174	1	=	=	SYM
easat-224	174	2	0	0	PUNCT
easat-224	175	1	=	=	PUNCT
easat-224	175	2	𝒰𝑗	𝒰𝑗	ADP
easat-224	175	3	′′′(𝐿	′′′(𝐿	NOUN
easat-224	175	4	)	)	PUNCT
easat-224	175	5	+	+	NUM
easat-224	175	6	𝑘2𝒰𝑗(𝐿	𝑘2𝒰𝑗(𝐿	X
easat-224	175	7	)	)	PUNCT
easat-224	175	8	(	(	PUNCT
easat-224	175	9	64	64	NUM
easat-224	175	10	)	)	PUNCT
easat-224	175	11	using	use	VERB
easat-224	175	12	equations	equation	NOUN
easat-224	175	13	(	(	PUNCT
easat-224	175	14	59	59	NUM
easat-224	175	15	)	)	PUNCT
easat-224	175	16	and	and	CCONJ
easat-224	175	17	(	(	PUNCT
easat-224	175	18	60	60	NUM
easat-224	175	19	)	)	PUNCT
easat-224	175	20	,	,	PUNCT
easat-224	175	21	it	it	PRON
easat-224	175	22	can	can	AUX
easat-224	175	23	be	be	AUX
easat-224	175	24	shown	show	VERB
easat-224	175	25	that	that	SCONJ
easat-224	175	26	at	at	ADP
easat-224	175	27	𝑥	𝑥	NOUN
easat-224	175	28	=	=	SYM
easat-224	175	29	0	0	NUM
easat-224	175	30	,	,	PUNCT
easat-224	175	31	𝐴𝑖	𝐴𝑖	PROPN
easat-224	175	32	=	=	PUNCT
easat-224	175	33	−𝐶𝑖	−𝐶𝑖	PROPN
easat-224	175	34	and	and	CCONJ
easat-224	175	35	𝐵𝑖	𝐵𝑖	PROPN
easat-224	175	36	=	=	SYM
easat-224	175	37	−1	−1	NOUN
easat-224	175	38	(	(	PUNCT
easat-224	175	39	65	65	NUM
easat-224	175	40	)	)	PUNCT
easat-224	175	41	and	and	CCONJ
easat-224	175	42	at	at	ADP
easat-224	175	43	𝑥	𝑥	PRON
easat-224	175	44	=	=	SYM
easat-224	175	45	𝐿	𝐿	PROPN
easat-224	175	46	,	,	PUNCT
easat-224	175	47	using	use	VERB
easat-224	175	48	(	(	PUNCT
easat-224	175	49	64	64	NUM
easat-224	175	50	)	)	PUNCT
easat-224	176	1	𝐴𝑖	𝐴𝑖	PROPN
easat-224	176	2	=	=	SYM
easat-224	176	3	𝜙𝑖	𝜙𝑖	ADP
easat-224	176	4	𝐿	𝐿	PROPN
easat-224	176	5	[	[	PUNCT
easat-224	176	6	sin	sin	NOUN
easat-224	176	7	𝜙𝑖	𝜙𝑖	NOUN
easat-224	176	8	+	+	CCONJ
easat-224	176	9	sinh	sinh	VERB
easat-224	176	10	𝜙𝑖	𝜙𝑖	NOUN
easat-224	176	11	]	]	X
easat-224	176	12	+	+	NUM
easat-224	176	13	𝑘1[cos	𝑘1[cos	PROPN
easat-224	176	14	𝜙𝑖	𝜙𝑖	VERB
easat-224	176	15	−	−	PROPN
easat-224	176	16	cosh	cosh	PROPN
easat-224	176	17	𝜙𝑖	𝜙𝑖	VERB
easat-224	176	18	]	]	PUNCT
easat-224	176	19	𝜙𝑖	𝜙𝑖	ADP
easat-224	176	20	𝐿	𝐿	PROPN
easat-224	176	21	[	[	X
easat-224	176	22	cos	cos	ADP
easat-224	176	23	𝜙𝑖	𝜙𝑖	PROPN
easat-224	176	24	+	+	CCONJ
easat-224	176	25	cosh	cosh	PROPN
easat-224	176	26	𝜙𝑖	𝜙𝑖	NOUN
easat-224	176	27	]	]	X
easat-224	176	28	−	−	PROPN
easat-224	176	29	𝑘1[sin	𝑘1[sin	PROPN
easat-224	176	30	𝜙𝑖	𝜙𝑖	NOUN
easat-224	177	1	+	+	CCONJ
easat-224	177	2	sinh	sinh	PROPN
easat-224	177	3	𝜙i	𝜙i	NOUN
easat-224	177	4	]	]	X
easat-224	177	5	=	=	SYM
easat-224	177	6	𝜙𝑖	𝜙𝑖	NOUN
easat-224	177	7	3	3	NUM
easat-224	177	8	𝐿3	𝐿3	NOUN
easat-224	178	1	[	[	X
easat-224	178	2	cos	cos	ADP
easat-224	178	3	𝜙𝑖	𝜙𝑖	X
easat-224	178	4	+	+	CCONJ
easat-224	178	5	cosh	cosh	PROPN
easat-224	178	6	𝜙𝑖	𝜙𝑖	VERB
easat-224	178	7	]	]	X
easat-224	178	8	+	+	NUM
easat-224	178	9	𝑘2[sinh	𝑘2[sinh	NOUN
easat-224	178	10	𝜙𝑖	𝜙𝑖	NOUN
easat-224	178	11	−	−	PROPN
easat-224	178	12	sin	sin	NOUN
easat-224	178	13	𝜙𝑖	𝜙𝑖	NOUN
easat-224	178	14	]	]	X
easat-224	178	15	−𝜙𝑖	−𝜙𝑖	PRON
easat-224	178	16	3	3	NUM
easat-224	178	17	𝐿3	𝐿3	NOUN
easat-224	179	1	[	[	X
easat-224	179	2	sin	sin	NOUN
easat-224	179	3	𝜙𝑖	𝜙𝑖	VERB
easat-224	179	4	−	−	PROPN
easat-224	179	5	sinh	sinh	NOUN
easat-224	179	6	𝜙𝑖	𝜙𝑖	X
easat-224	179	7	]	]	X
easat-224	179	8	+	+	CCONJ
easat-224	179	9	𝑘2[cos	𝑘2[co	NOUN
easat-224	179	10	𝜙𝑖	𝜙𝑖	VERB
easat-224	179	11	−	−	PROPN
easat-224	179	12	cosh	cosh	PROPN
easat-224	179	13	𝜙𝑖	𝜙𝑖	VERB
easat-224	179	14	]	]	X
easat-224	179	15	=	=	SYM
easat-224	179	16	−𝐶𝑖	−𝐶𝑖	PROPN
easat-224	179	17	(	(	PUNCT
easat-224	179	18	66	66	NUM
easat-224	179	19	)	)	PUNCT
easat-224	179	20	from	from	ADP
easat-224	179	21	(	(	PUNCT
easat-224	179	22	66	66	NUM
easat-224	179	23	)	)	PUNCT
easat-224	179	24	one	one	NOUN
easat-224	179	25	obtains	obtain	VERB
easat-224	179	26	tan	tan	PROPN
easat-224	179	27	𝜙𝑖	𝜙𝑖	NOUN
easat-224	180	1	=	=	SYM
easat-224	180	2	tanh	tanh	PROPN
easat-224	180	3	𝜙𝑖	𝜙𝑖	X
easat-224	180	4	(	(	PUNCT
easat-224	180	5	67	67	NUM
easat-224	180	6	)	)	PUNCT
easat-224	180	7	hence	hence	ADV
easat-224	180	8	,	,	PUNCT
easat-224	180	9	we	we	PRON
easat-224	180	10	have	have	VERB
easat-224	180	11	𝜙1	𝜙1	NOUN
easat-224	180	12	=	=	SYM
easat-224	180	13	3.927,𝜙2	3.927,𝜙2	NUM
easat-224	180	14	=	=	SYM
easat-224	180	15	7.069,𝜙3	7.069,𝜙3	NUM
easat-224	180	16	=	=	SYM
easat-224	180	17	10.21	10.21	NUM
easat-224	180	18	…	…	PUNCT
easat-224	180	19	(	(	PUNCT
easat-224	180	20	68	68	NUM
easat-224	180	21	)	)	PUNCT
easat-224	180	22	putting	put	VERB
easat-224	180	23	equations	equation	NOUN
easat-224	180	24	(	(	PUNCT
easat-224	180	25	65	65	NUM
easat-224	180	26	)	)	PUNCT
easat-224	180	27	,	,	PUNCT
easat-224	180	28	(	(	PUNCT
easat-224	180	29	66	66	NUM
easat-224	180	30	)	)	PUNCT
easat-224	180	31	and	and	CCONJ
easat-224	180	32	(	(	PUNCT
easat-224	180	33	68	68	NUM
easat-224	180	34	)	)	PUNCT
easat-224	180	35	into	into	ADP
easat-224	180	36	equations	equation	NOUN
easat-224	180	37	(	(	PUNCT
easat-224	180	38	41)and	41)and	NUM
easat-224	180	39	(	(	PUNCT
easat-224	180	40	53	53	NUM
easat-224	180	41	)	)	PUNCT
easat-224	180	42	,	,	PUNCT
easat-224	180	43	one	one	PRON
easat-224	180	44	obtains	obtain	VERB
easat-224	180	45	the	the	DET
easat-224	180	46	displacement	displacement	ADJ
easat-224	180	47	response	response	NOUN
easat-224	180	48	respectively	respectively	ADV
easat-224	180	49	to	to	ADP
easat-224	180	50	a	a	DET
easat-224	180	51	moving	move	VERB
easat-224	180	52	force	force	NOUN
easat-224	180	53	and	and	CCONJ
easat-224	180	54	a	a	DET
easat-224	180	55	moving	move	VERB
easat-224	180	56	mass	mass	NOUN
easat-224	180	57	of	of	ADP
easat-224	180	58	clamped	clamp	VERB
easat-224	180	59	-	-	PUNCT
easat-224	180	60	elastic	elastic	ADJ
easat-224	180	61	ends	end	NOUN
easat-224	180	62	rayleigh	rayleigh	PROPN
easat-224	180	63	beam	beam	PROPN
easat-224	180	64	on	on	ADP
easat-224	180	65	a	a	DET
easat-224	180	66	variable	variable	ADJ
easat-224	180	67	foundation	foundation	NOUN
easat-224	180	68	.	.	PUNCT
easat-224	181	1	3.2	3.2	NUM
easat-224	181	2	.	.	PUNCT
easat-224	181	3	elastically	elastically	ADV
easat-224	181	4	supported	support	VERB
easat-224	181	5	conditions	condition	NOUN
easat-224	181	6	at	at	ADP
easat-224	181	7	both	both	DET
easat-224	181	8	ends	end	NOUN
easat-224	181	9	for	for	ADP
easat-224	181	10	the	the	DET
easat-224	181	11	case	case	NOUN
easat-224	181	12	when	when	SCONJ
easat-224	181	13	the	the	DET
easat-224	181	14	beam	beam	NOUN
easat-224	181	15	is	be	AUX
easat-224	181	16	elastically	elastically	ADV
easat-224	181	17	supported	support	VERB
easat-224	181	18	both	both	PRON
easat-224	181	19	at	at	ADP
easat-224	181	20	𝑥	𝑥	NOUN
easat-224	181	21	=	=	SYM
easat-224	181	22	0	0	NUM
easat-224	182	1	and	and	CCONJ
easat-224	182	2	𝑥	𝑥	NOUN
easat-224	182	3	=	=	SYM
easat-224	182	4	𝐿	𝐿	PROPN
easat-224	182	5	,	,	PUNCT
easat-224	182	6	the	the	DET
easat-224	182	7	conditions	condition	NOUN
easat-224	182	8	are	be	AUX
easat-224	182	9	expressed	express	VERB
easat-224	182	10	as	as	ADP
easat-224	182	11	𝒷	𝒷	PROPN
easat-224	182	12	′′(0	′′(0	NOUN
easat-224	182	13	,	,	PUNCT
easat-224	182	14	𝑡	𝑡	NOUN
easat-224	182	15	)	)	PUNCT
easat-224	182	16	−	−	PROPN
easat-224	182	17	𝑘1	𝑘1	PROPN
easat-224	182	18	𝒷	𝒷	PROPN
easat-224	182	19	′(0	′(0	PROPN
easat-224	182	20	,	,	PUNCT
easat-224	182	21	𝑡	𝑡	X
easat-224	182	22	)	)	PUNCT
easat-224	182	23	=	=	SYM
easat-224	182	24	0	0	PUNCT
easat-224	182	25	=	=	PUNCT
easat-224	182	26	𝒷	𝒷	PRON
easat-224	182	27	′′′(0	′′′(0	PROPN
easat-224	182	28	,	,	PUNCT
easat-224	182	29	𝑡	𝑡	X
easat-224	182	30	)	)	PUNCT
easat-224	182	31	+	+	CCONJ
easat-224	182	32	𝑘2	𝑘2	PROPN
easat-224	182	33	𝒷(0	𝒷(0	PROPN
easat-224	182	34	,	,	PUNCT
easat-224	182	35	𝑡	𝑡	PROPN
easat-224	182	36	)	)	PUNCT
easat-224	182	37	(	(	PUNCT
easat-224	182	38	69	69	NUM
easat-224	182	39	)	)	PUNCT
easat-224	182	40	at	at	ADP
easat-224	182	41	𝑥	𝑥	NOUN
easat-224	182	42	=	=	SYM
easat-224	182	43	0	0	PROPN
easat-224	182	44	and	and	CCONJ
easat-224	182	45	𝒷	𝒷	PRON
easat-224	182	46	′′(𝐿	′′(𝐿	PROPN
easat-224	182	47	,	,	PUNCT
easat-224	182	48	𝑡	𝑡	NOUN
easat-224	182	49	)	)	PUNCT
easat-224	182	50	−	−	PROPN
easat-224	182	51	𝑘1	𝑘1	PROPN
easat-224	182	52	𝒷	𝒷	PROPN
easat-224	182	53	′(𝐿	′(𝐿	NOUN
easat-224	182	54	,	,	PUNCT
easat-224	182	55	𝑡	𝑡	X
easat-224	182	56	)	)	PUNCT
easat-224	182	57	=	=	SYM
easat-224	182	58	0	0	PUNCT
easat-224	183	1	=	=	PUNCT
easat-224	183	2	𝒷	𝒷	PRON
easat-224	183	3	′′′(𝐿	′′′(𝐿	NOUN
easat-224	183	4	,	,	PUNCT
easat-224	183	5	𝑡	𝑡	X
easat-224	183	6	)	)	PUNCT
easat-224	183	7	+	+	CCONJ
easat-224	183	8	𝑘2	𝑘2	PROPN
easat-224	183	9	𝒷(𝐿	𝒷(𝐿	PROPN
easat-224	183	10	,	,	PUNCT
easat-224	183	11	𝑡	𝑡	X
easat-224	183	12	)	)	PUNCT
easat-224	183	13	(	(	PUNCT
easat-224	183	14	70	70	NUM
easat-224	183	15	)	)	PUNCT
easat-224	183	16	at	at	ADP
easat-224	183	17	𝑥	𝑥	NOUN
easat-224	183	18	=	=	SYM
easat-224	183	19	𝐿	𝐿	PROPN
easat-224	183	20	similarly	similarly	ADV
easat-224	183	21	,	,	PUNCT
easat-224	183	22	for	for	ADP
easat-224	183	23	normal	normal	ADJ
easat-224	183	24	modes	mode	NOUN
easat-224	183	25	𝒰𝑖	𝒰𝑖	PROPN
easat-224	183	26	′′(0	′′(0	PROPN
easat-224	183	27	)	)	PUNCT
easat-224	183	28	−	−	PROPN
easat-224	183	29	𝑘1𝒰𝑖	𝑘1𝒰𝑖	VERB
easat-224	183	30	′(0	′(0	X
easat-224	183	31	)	)	PUNCT
easat-224	183	32	=	=	SYM
easat-224	183	33	0	0	PUNCT
easat-224	184	1	=	=	PUNCT
easat-224	184	2	𝒰𝑖	𝒰𝑖	PROPN
easat-224	184	3	′′′(0	′′′(0	PROPN
easat-224	184	4	)	)	PUNCT
easat-224	184	5	+	+	NUM
easat-224	184	6	𝑘2𝒰𝑖	𝑘2𝒰𝑖	INTJ
easat-224	184	7	(	(	PUNCT
easat-224	184	8	0	0	NUM
easat-224	184	9	)	)	PUNCT
easat-224	184	10	(	(	PUNCT
easat-224	184	11	71	71	NUM
easat-224	184	12	)	)	PUNCT
easat-224	184	13	at	at	ADP
easat-224	184	14	𝑥	𝑥	NOUN
easat-224	184	15	=	=	SYM
easat-224	184	16	0	0	NUM
easat-224	184	17	and	and	CCONJ
easat-224	184	18	𝒰𝑖	𝒰𝑖	PROPN
easat-224	184	19	′′(𝐿	′′(𝐿	PROPN
easat-224	184	20	)	)	PUNCT
easat-224	184	21	−	−	PROPN
easat-224	184	22	𝑘1𝒰𝑖	𝑘1𝒰𝑖	VERB
easat-224	184	23	′(𝐿	′(𝐿	NOUN
easat-224	184	24	)	)	PUNCT
easat-224	185	1	=	=	SYM
easat-224	185	2	0	0	PUNCT
easat-224	186	1	=	=	PUNCT
easat-224	186	2	𝒰𝑖	𝒰𝑖	PROPN
easat-224	186	3	′′′(𝐿	′′′(𝐿	NOUN
easat-224	186	4	)	)	PUNCT
easat-224	187	1	+	+	NUM
easat-224	187	2	𝑘2𝒰𝑖(𝐿	𝑘2𝒰𝑖(𝐿	ADJ
easat-224	187	3	)	)	PUNCT
easat-224	187	4	(	(	PUNCT
easat-224	187	5	72	72	NUM
easat-224	187	6	)	)	PUNCT
easat-224	187	7	at	at	ADP
easat-224	187	8	𝑥	𝑥	DET
easat-224	187	9	=	=	SYM
easat-224	187	10	𝐿	𝐿	PROPN
easat-224	187	11	which	which	PRON
easat-224	187	12	implies	imply	VERB
easat-224	187	13	that	that	SCONJ
easat-224	188	1	𝒰𝑗	𝒰𝑗	ADV
easat-224	188	2	′′(0	′′(0	NOUN
easat-224	188	3	)	)	PUNCT
easat-224	188	4	−	−	NUM
easat-224	188	5	𝑘1𝒰𝑗	𝑘1𝒰𝑗	X
easat-224	188	6	′(0	′(0	PROPN
easat-224	188	7	)	)	PUNCT
easat-224	188	8	=	=	SYM
easat-224	188	9	0	0	PUNCT
easat-224	189	1	=	=	PUNCT
easat-224	189	2	𝒰𝑗	𝒰𝑗	NOUN
easat-224	189	3	′′′(0	′′′(0	X
easat-224	189	4	)	)	PUNCT
easat-224	190	1	+	+	NUM
easat-224	190	2	𝑘2𝒰𝑗(0	𝑘2𝒰𝑗(0	NOUN
easat-224	190	3	)	)	PUNCT
easat-224	190	4	(	(	PUNCT
easat-224	190	5	73	73	NUM
easat-224	190	6	)	)	PUNCT
easat-224	190	7	at	at	ADP
easat-224	190	8	𝑥	𝑥	NOUN
easat-224	190	9	=	=	SYM
easat-224	190	10	0	0	PUNCT
easat-224	190	11	and	and	CCONJ
easat-224	190	12	𝒰𝑗	𝒰𝑗	ADV
easat-224	190	13	′′(𝐿	′′(𝐿	NOUN
easat-224	190	14	)	)	PUNCT
easat-224	190	15	−	−	NOUN
easat-224	190	16	𝑘1𝒰𝑗	𝑘1𝒰𝑗	ADJ
easat-224	190	17	′(𝐿	′(𝐿	NOUN
easat-224	190	18	)	)	PUNCT
easat-224	191	1	=	=	SYM
easat-224	191	2	0	0	PUNCT
easat-224	192	1	=	=	PUNCT
easat-224	192	2	𝒰𝑗	𝒰𝑗	ADP
easat-224	192	3	′′′(𝐿	′′′(𝐿	NOUN
easat-224	192	4	)	)	PUNCT
easat-224	192	5	+	+	NUM
easat-224	192	6	𝑘2𝒰𝑗(𝐿	𝑘2𝒰𝑗(𝐿	X
easat-224	192	7	)	)	PUNCT
easat-224	192	8	(	(	PUNCT
easat-224	192	9	74	74	NUM
easat-224	192	10	)	)	PUNCT
easat-224	192	11	at	at	ADP
easat-224	192	12	𝑥	𝑥	NOUN
easat-224	192	13	=	=	SYM
easat-224	192	14	𝐿	𝐿	PROPN
easat-224	192	15	using	use	VERB
easat-224	192	16	(	(	PUNCT
easat-224	192	17	71	71	NUM
easat-224	192	18	)	)	PUNCT
easat-224	192	19	and	and	CCONJ
easat-224	192	20	(	(	PUNCT
easat-224	192	21	72	72	NUM
easat-224	192	22	)	)	PUNCT
easat-224	192	23	,	,	PUNCT
easat-224	192	24	it	it	PRON
easat-224	192	25	can	can	AUX
easat-224	192	26	be	be	AUX
easat-224	192	27	shown	show	VERB
easat-224	192	28	that	that	SCONJ
easat-224	192	29	𝐴𝑖	𝐴𝑖	PROPN
easat-224	192	30	=	=	PUNCT
easat-224	192	31	𝑟1𝐶𝑖	𝑟1𝐶𝑖	PROPN
easat-224	192	32	+	+	CCONJ
easat-224	192	33	𝑟2	𝑟2	NOUN
easat-224	192	34	and	and	CCONJ
easat-224	192	35	𝐵𝑖	𝐵𝑖	PROPN
easat-224	192	36	=	=	PRON
easat-224	192	37	𝑟3𝐶𝑖	𝑟3𝐶𝑖	VERB
easat-224	192	38	+	+	NUM
easat-224	192	39	𝑟1	𝑟1	NOUN
easat-224	192	40	(	(	PUNCT
easat-224	192	41	76	76	NUM
easat-224	192	42	)	)	PUNCT
easat-224	192	43	where	where	SCONJ
easat-224	192	44	𝑟1	𝑟1	NOUN
easat-224	192	45	=	=	PUNCT
easat-224	192	46	𝜙𝑖	𝜙𝑖	VERB
easat-224	192	47	4	4	NUM
easat-224	192	48	𝐿4+𝑘1𝑘2	𝐿4+𝑘1𝑘2	NUM
easat-224	192	49	𝜙	𝜙	NOUN
easat-224	192	50	𝑖	𝑖	SYM
easat-224	192	51	4	4	NUM
easat-224	192	52	𝐿4−𝑘1𝑘2	𝐿4−𝑘1𝑘2	NUM
easat-224	192	53	;	;	PUNCT
easat-224	192	54	𝑟2	𝑟2	NOUN
easat-224	192	55	=	=	SYM
easat-224	192	56	−	−	PROPN
easat-224	192	57	2𝑘1𝜙𝑖	2𝑘1𝜙𝑖	NUM
easat-224	192	58	3	3	NUM
easat-224	192	59	𝐿3	𝐿3	NOUN
easat-224	192	60	𝜙	𝜙	PROPN
easat-224	192	61	𝑖	𝑖	SYM
easat-224	192	62	4	4	NUM
easat-224	192	63	𝐿4−𝑘1𝑘2	𝐿4−𝑘1𝑘2	NUM
easat-224	192	64	and	and	CCONJ
easat-224	192	65	𝑟3	𝑟3	NOUN
easat-224	192	66	=	=	PUNCT
easat-224	192	67	−	−	PROPN
easat-224	192	68	2𝑘1𝜙𝑖	2𝑘1𝜙𝑖	NUM
easat-224	192	69	𝐿	𝐿	NOUN
easat-224	192	70	𝜙	𝜙	NOUN
easat-224	192	71	𝑖	𝑖	SYM
easat-224	192	72	4	4	NUM
easat-224	192	73	𝐿4−𝑘1𝑘2	𝐿4−𝑘1𝑘2	NUM
easat-224	192	74	(	(	PUNCT
easat-224	192	75	77	77	NUM
easat-224	192	76	)	)	PUNCT
easat-224	192	77	using	use	VERB
easat-224	192	78	equations	equation	NOUN
easat-224	192	79	(	(	PUNCT
easat-224	192	80	75	75	NUM
easat-224	192	81	)	)	PUNCT
easat-224	192	82	,	,	PUNCT
easat-224	192	83	(	(	PUNCT
easat-224	192	84	76	76	NUM
easat-224	192	85	)	)	PUNCT
easat-224	192	86	and	and	CCONJ
easat-224	192	87	(	(	PUNCT
easat-224	192	88	77	77	NUM
easat-224	192	89	)	)	PUNCT
easat-224	192	90	,	,	PUNCT
easat-224	192	91	the	the	DET
easat-224	192	92	frequency	frequency	NOUN
easat-224	192	93	equation	equation	NOUN
easat-224	192	94	for	for	ADP
easat-224	192	95	the	the	DET
easat-224	192	96	dynamical	dynamical	ADJ
easat-224	192	97	problem	problem	NOUN
easat-224	192	98	is	be	AUX
easat-224	192	99	obtained	obtain	VERB
easat-224	192	100	as	as	ADP
easat-224	192	101	tan	tan	PROPN
easat-224	192	102	𝜙𝑖	𝜙𝑖	NOUN
easat-224	192	103	=	=	SYM
easat-224	192	104	tanh	tanh	PROPN
easat-224	192	105	𝜙𝑖	𝜙𝑖	X
easat-224	192	106	(	(	PUNCT
easat-224	192	107	78	78	NUM
easat-224	192	108	)	)	PUNCT
easat-224	192	109	hence	hence	ADV
easat-224	192	110	.	.	PUNCT
easat-224	193	1	we	we	PRON
easat-224	193	2	have	have	VERB
easat-224	193	3	𝜙1	𝜙1	NOUN
easat-224	193	4	=	=	NOUN
easat-224	193	5	3.927	3.927	NUM
easat-224	193	6	,	,	PUNCT
easat-224	193	7	𝜙2	𝜙2	NOUN
easat-224	193	8	=	=	SYM
easat-224	193	9	7.069	7.069	NUM
easat-224	193	10	,	,	PUNCT
easat-224	193	11	𝜙3=	𝜙3=	PROPN
easat-224	193	12	10.21	10.21	NUM
easat-224	193	13	…	…	PUNCT
easat-224	193	14	(	(	PUNCT
easat-224	193	15	79	79	NUM
easat-224	193	16	)	)	PUNCT
easat-224	193	17	substituting	substitute	VERB
easat-224	193	18	equations	equation	NOUN
easat-224	193	19	(	(	PUNCT
easat-224	193	20	75	75	NUM
easat-224	193	21	)	)	PUNCT
easat-224	193	22	,	,	PUNCT
easat-224	193	23	(	(	PUNCT
easat-224	193	24	76	76	NUM
easat-224	193	25	)	)	PUNCT
easat-224	193	26	,	,	PUNCT
easat-224	193	27	(	(	PUNCT
easat-224	193	28	77	77	NUM
easat-224	193	29	)	)	PUNCT
easat-224	193	30	and	and	CCONJ
easat-224	193	31	(	(	PUNCT
easat-224	193	32	78	78	NUM
easat-224	193	33	)	)	PUNCT
easat-224	193	34	into	into	ADP
easat-224	193	35	equations	equation	NOUN
easat-224	193	36	(	(	PUNCT
easat-224	193	37	41	41	NUM
easat-224	193	38	)	)	PUNCT
easat-224	193	39	and	and	CCONJ
easat-224	193	40	(	(	PUNCT
easat-224	193	41	53	53	NUM
easat-224	193	42	)	)	PUNCT
easat-224	193	43	one	one	NOUN
easat-224	193	44	obtains	obtain	VERB
easat-224	193	45	the	the	DET
easat-224	193	46	displacement	displacement	ADJ
easat-224	193	47	response	response	NOUN
easat-224	193	48	respectively	respectively	ADV
easat-224	193	49	to	to	ADP
easat-224	193	50	a	a	DET
easat-224	193	51	moving	move	VERB
easat-224	193	52	force	force	NOUN
easat-224	193	53	and	and	CCONJ
easat-224	193	54	a	a	DET
easat-224	193	55	moving	move	VERB
easat-224	193	56	mass	mass	NOUN
easat-224	193	57	of	of	ADP
easat-224	193	58	rayleigh	rayleigh	PROPN
easat-224	193	59	beam	beam	PROPN
easat-224	193	60	elastically	elastically	ADV
easat-224	193	61	supported	support	VERB
easat-224	193	62	at	at	ADP
easat-224	193	63	both	both	DET
easat-224	193	64	ends	end	NOUN
easat-224	193	65	and	and	CCONJ
easat-224	193	66	resting	rest	VERB
easat-224	193	67	on	on	ADP
easat-224	193	68	a	a	DET
easat-224	193	69	variable	variable	ADJ
easat-224	193	70	foundation	foundation	NOUN
easat-224	193	71	.	.	PUNCT
easat-224	194	1	4	4	X
easat-224	194	2	.	.	X
easat-224	194	3	numerical	numerical	ADJ
easat-224	194	4	results	result	NOUN
easat-224	194	5	and	and	CCONJ
easat-224	194	6	discussions	discussion	NOUN
easat-224	194	7	to	to	PART
easat-224	194	8	illustrate	illustrate	VERB
easat-224	194	9	the	the	DET
easat-224	194	10	analysis	analysis	NOUN
easat-224	194	11	presented	present	VERB
easat-224	194	12	in	in	ADP
easat-224	194	13	this	this	DET
easat-224	194	14	work	work	NOUN
easat-224	194	15	,	,	PUNCT
easat-224	194	16	the	the	DET
easat-224	194	17	uniform	uniform	ADJ
easat-224	194	18	rayleigh	rayleigh	PROPN
easat-224	194	19	beam	beam	NOUN
easat-224	194	20	is	be	AUX
easat-224	194	21	taken	take	VERB
easat-224	194	22	to	to	PART
easat-224	194	23	be	be	AUX
easat-224	194	24	of	of	ADP
easat-224	194	25	length	length	NOUN
easat-224	194	26	l	l	NOUN
easat-224	194	27	=	=	SYM
easat-224	194	28	12.192	12.192	NUM
easat-224	194	29	m	m	NOUN
easat-224	194	30	,	,	PUNCT
easat-224	195	1	the	the	DET
easat-224	195	2	load	load	NOUN
easat-224	195	3	velocity	velocity	NOUN
easat-224	195	4	c	c	NOUN
easat-224	195	5	=	=	PUNCT
easat-224	195	6	8.128	8.128	NUM
easat-224	195	7	m	m	PROPN
easat-224	195	8	/	/	SYM
easat-224	195	9	s	s	PART
easat-224	195	10	and	and	CCONJ
easat-224	195	11	modulus	modulus	NOUN
easat-224	195	12	of	of	ADP
easat-224	195	13	elasticity	elasticity	NOUN
easat-224	195	14	𝐸	𝐸	PROPN
easat-224	195	15	=	=	SYM
easat-224	195	16	2.109	2.109	NUM
easat-224	195	17	×	×	PROPN
easat-224	195	18	109𝑘𝑔/𝑚	109𝑘𝑔/𝑚	NUM
easat-224	195	19	,	,	PUNCT
easat-224	195	20	the	the	DET
easat-224	195	21	moment	moment	NOUN
easat-224	195	22	of	of	ADP
easat-224	195	23	inertia	inertia	NOUN
easat-224	195	24	𝐼𝑜	𝐼𝑜	PROPN
easat-224	195	25	=	=	PUNCT
easat-224	196	1	2.87698	2.87698	NUM
easat-224	196	2	×	×	NOUN
easat-224	196	3	10−3𝑚4	10−3𝑚4	NUM
easat-224	196	4	.	.	PUNCT
easat-224	197	1	4.1	4.1	NUM
easat-224	197	2	graphs	graph	NOUN
easat-224	197	3	for	for	ADP
easat-224	197	4	free	free	ADJ
easat-224	197	5	-	-	PUNCT
easat-224	197	6	elastic	elastic	ADJ
easat-224	197	7	boundary	boundary	ADJ
easat-224	197	8	conditions	condition	NOUN
easat-224	197	9	figures	figure	VERB
easat-224	197	10	6.1	6.1	NUM
easat-224	197	11	and	and	CCONJ
easat-224	197	12	6.2	6.2	NUM
easat-224	197	13	display	display	NOUN
easat-224	197	14	the	the	DET
easat-224	197	15	effect	effect	NOUN
easat-224	197	16	of	of	ADP
easat-224	197	17	axial	axial	ADJ
easat-224	197	18	force	force	NOUN
easat-224	197	19	n	n	CCONJ
easat-224	197	20	on	on	ADP
easat-224	197	21	the	the	DET
easat-224	197	22	deflection	deflection	NOUN
easat-224	197	23	profile	profile	NOUN
easat-224	197	24	of	of	ADP
easat-224	197	25	free	free	ADJ
easat-224	197	26	elastic	elastic	ADJ
easat-224	197	27	rayleigh	rayleigh	NOUN
easat-224	197	28	beam	beam	NOUN
easat-224	197	29	under	under	ADP
easat-224	197	30	the	the	DET
easat-224	197	31	action	action	NOUN
easat-224	197	32	of	of	ADP
easat-224	197	33	load	load	NOUN
easat-224	197	34	moving	move	VERB
easat-224	197	35	at	at	ADP
easat-224	197	36	constant	constant	ADJ
easat-224	197	37	velocity	velocity	NOUN
easat-224	197	38	in	in	ADP
easat-224	197	39	both	both	DET
easat-224	197	40	cases	case	NOUN
easat-224	197	41	of	of	ADP
easat-224	197	42	moving	move	VERB
easat-224	197	43	distributed	distribute	VERB
easat-224	197	44	forces	force	NOUN
easat-224	197	45	and	and	CCONJ
easat-224	197	46	moving	move	VERB
easat-224	197	47	distributed	distribute	VERB
easat-224	197	48	masses	masse	NOUN
easat-224	197	49	respectively	respectively	ADV
easat-224	197	50	.	.	PUNCT
easat-224	198	1	the	the	DET
easat-224	198	2	graphs	graph	NOUN
easat-224	198	3	show	show	VERB
easat-224	198	4	that	that	SCONJ
easat-224	198	5	the	the	DET
easat-224	198	6	response	response	NOUN
easat-224	198	7	amplitude	amplitude	NOUN
easat-224	198	8	decreases	decrease	VERB
easat-224	198	9	as	as	ADP
easat-224	198	10	the	the	DET
easat-224	198	11	value	value	NOUN
easat-224	198	12	of	of	ADP
easat-224	198	13	n	n	PRON
easat-224	198	14	increases	increase	NOUN
easat-224	198	15	.	.	PUNCT
easat-224	199	1	6	6	NUM
easat-224	199	2	edelweiss	edelweiss	PROPN
easat-224	199	3	applied	apply	VERB
easat-224	199	4	science	science	NOUN
easat-224	199	5	and	and	CCONJ
easat-224	199	6	technology	technology	NOUN
easat-224	199	7	issn	issn	PROPN
easat-224	199	8	:	:	PUNCT
easat-224	199	9	2576	2576	NUM
easat-224	199	10	-	-	SYM
easat-224	199	11	8484	8484	NUM
easat-224	199	12	vol	vol	NOUN
easat-224	199	13	.	.	PROPN
easat-224	200	1	2	2	NUM
easat-224	200	2	,	,	PUNCT
easat-224	200	3	no	no	INTJ
easat-224	200	4	.	.	NOUN
easat-224	200	5	1	1	NUM
easat-224	200	6	:	:	SYM
easat-224	200	7	1	1	NUM
easat-224	200	8	-	-	SYM
easat-224	200	9	9	9	NUM
easat-224	200	10	,	,	PUNCT
easat-224	200	11	2018	2018	NUM
easat-224	200	12	doi	doi	NOUN
easat-224	200	13	:	:	PUNCT
easat-224	200	14	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	201	1	©	©	PROPN
easat-224	201	2	2018	2018	NUM
easat-224	201	3	by	by	ADP
easat-224	201	4	the	the	DET
easat-224	201	5	authors	author	NOUN
easat-224	201	6	figure	figure	VERB
easat-224	201	7	6.1	6.1	NUM
easat-224	201	8	.	.	PUNCT
easat-224	202	1	deflection	deflection	NOUN
easat-224	202	2	profile	profile	NOUN
easat-224	202	3	of	of	ADP
easat-224	202	4	a	a	DET
easat-224	202	5	free	free	ADJ
easat-224	202	6	elastic	elastic	ADJ
easat-224	202	7	uniform	uniform	NOUN
easat-224	202	8	rayleigh	rayleigh	PROPN
easat-224	202	9	beam	beam	PROPN
easat-224	202	10	on	on	ADP
easat-224	202	11	variable	variable	ADJ
easat-224	202	12	foundation	foundation	NOUN
easat-224	202	13	and	and	CCONJ
easat-224	202	14	traversed	traverse	VERB
easat-224	202	15	by	by	ADP
easat-224	202	16	moving	move	VERB
easat-224	202	17	distributed	distributed	ADJ
easat-224	202	18	force	force	NOUN
easat-224	202	19	for	for	ADP
easat-224	202	20	various	various	ADJ
easat-224	202	21	values	value	NOUN
easat-224	202	22	of	of	ADP
easat-224	202	23	𝑵.	𝑵.	PROPN
easat-224	202	24	figure	figure	NOUN
easat-224	202	25	6.2	6.2	NUM
easat-224	202	26	.	.	PUNCT
easat-224	203	1	deflection	deflection	NOUN
easat-224	203	2	profile	profile	NOUN
easat-224	203	3	of	of	ADP
easat-224	203	4	a	a	DET
easat-224	203	5	free	free	ADJ
easat-224	203	6	elastic	elastic	ADJ
easat-224	203	7	uniform	uniform	NOUN
easat-224	203	8	rayleigh	rayleigh	PROPN
easat-224	203	9	beam	beam	PROPN
easat-224	203	10	on	on	ADP
easat-224	203	11	variable	variable	ADJ
easat-224	203	12	foundation	foundation	NOUN
easat-224	203	13	and	and	CCONJ
easat-224	203	14	traversed	traverse	VERB
easat-224	203	15	by	by	ADP
easat-224	203	16	moving	move	VERB
easat-224	203	17	distributed	distribute	VERB
easat-224	203	18	mass	mass	NOUN
easat-224	203	19	for	for	ADP
easat-224	203	20	various	various	ADJ
easat-224	203	21	values	value	NOUN
easat-224	203	22	of	of	ADP
easat-224	203	23	𝑵.	𝑵.	PROPN
easat-224	203	24	figures	figure	NOUN
easat-224	203	25	6.3	6.3	NUM
easat-224	203	26	and	and	CCONJ
easat-224	203	27	6.4	6.4	NUM
easat-224	203	28	display	display	VERB
easat-224	203	29	the	the	DET
easat-224	203	30	effect	effect	NOUN
easat-224	203	31	of	of	ADP
easat-224	203	32	rotatory	rotatory	ADJ
easat-224	203	33	inertia	inertia	NOUN
easat-224	203	34	r	r	NOUN
easat-224	203	35	on	on	ADP
easat-224	203	36	the	the	DET
easat-224	203	37	deflection	deflection	NOUN
easat-224	203	38	profile	profile	NOUN
easat-224	203	39	of	of	ADP
easat-224	203	40	free	free	ADJ
easat-224	203	41	elastic	elastic	ADJ
easat-224	203	42	rayleigh	rayleigh	NOUN
easat-224	203	43	beam	beam	NOUN
easat-224	203	44	under	under	ADP
easat-224	203	45	the	the	DET
easat-224	203	46	action	action	NOUN
easat-224	203	47	of	of	ADP
easat-224	203	48	load	load	NOUN
easat-224	203	49	moving	move	VERB
easat-224	203	50	at	at	ADP
easat-224	203	51	constant	constant	ADJ
easat-224	203	52	velocity	velocity	NOUN
easat-224	203	53	in	in	ADP
easat-224	203	54	both	both	DET
easat-224	203	55	cases	case	NOUN
easat-224	203	56	of	of	ADP
easat-224	203	57	moving	move	VERB
easat-224	203	58	distributed	distribute	VERB
easat-224	203	59	forces	force	NOUN
easat-224	203	60	and	and	CCONJ
easat-224	203	61	moving	move	VERB
easat-224	203	62	distributed	distribute	VERB
easat-224	203	63	masses	masse	NOUN
easat-224	203	64	respectively	respectively	ADV
easat-224	203	65	.	.	PUNCT
easat-224	204	1	the	the	DET
easat-224	204	2	graphs	graph	NOUN
easat-224	204	3	show	show	VERB
easat-224	204	4	that	that	SCONJ
easat-224	204	5	the	the	DET
easat-224	204	6	response	response	NOUN
easat-224	204	7	amplitude	amplitude	NOUN
easat-224	204	8	decreases	decrease	VERB
easat-224	204	9	as	as	ADP
easat-224	204	10	the	the	DET
easat-224	204	11	value	value	NOUN
easat-224	204	12	of	of	ADP
easat-224	204	13	r	r	NOUN
easat-224	204	14	increases	increase	NOUN
easat-224	204	15	.	.	PUNCT
easat-224	205	1	figures	figure	NOUN
easat-224	205	2	6.5	6.5	NUM
easat-224	205	3	and	and	CCONJ
easat-224	205	4	6.6	6.6	NUM
easat-224	205	5	display	display	NOUN
easat-224	205	6	the	the	DET
easat-224	205	7	effect	effect	NOUN
easat-224	205	8	of	of	ADP
easat-224	205	9	foundation	foundation	NOUN
easat-224	205	10	modulus	modulus	NOUN
easat-224	205	11	so	so	ADV
easat-224	205	12	on	on	ADP
easat-224	205	13	the	the	DET
easat-224	205	14	deflection	deflection	NOUN
easat-224	205	15	profile	profile	NOUN
easat-224	205	16	of	of	ADP
easat-224	205	17	free	free	ADJ
easat-224	205	18	elastic	elastic	ADJ
easat-224	205	19	rayleigh	rayleigh	NOUN
easat-224	205	20	beam	beam	NOUN
easat-224	205	21	under	under	ADP
easat-224	205	22	the	the	DET
easat-224	205	23	action	action	NOUN
easat-224	205	24	of	of	ADP
easat-224	205	25	load	load	NOUN
easat-224	205	26	moving	move	VERB
easat-224	205	27	at	at	ADP
easat-224	205	28	constant	constant	ADJ
easat-224	205	29	velocity	velocity	NOUN
easat-224	205	30	in	in	ADP
easat-224	205	31	both	both	DET
easat-224	205	32	cases	case	NOUN
easat-224	205	33	of	of	ADP
easat-224	205	34	moving	move	VERB
easat-224	205	35	distributed	distribute	VERB
easat-224	205	36	forces	force	NOUN
easat-224	205	37	and	and	CCONJ
easat-224	205	38	moving	move	VERB
easat-224	205	39	distributed	distribute	VERB
easat-224	205	40	masses	masse	NOUN
easat-224	205	41	respectively	respectively	ADV
easat-224	205	42	.	.	PUNCT
easat-224	206	1	the	the	DET
easat-224	206	2	graphs	graph	NOUN
easat-224	206	3	show	show	VERB
easat-224	206	4	that	that	SCONJ
easat-224	206	5	the	the	DET
easat-224	206	6	response	response	NOUN
easat-224	206	7	amplitude	amplitude	NOUN
easat-224	206	8	decreases	decrease	VERB
easat-224	206	9	as	as	ADP
easat-224	206	10	the	the	DET
easat-224	206	11	value	value	NOUN
easat-224	206	12	of	of	ADP
easat-224	206	13	so	so	ADV
easat-224	206	14	increases	increase	NOUN
easat-224	206	15	.	.	PUNCT
easat-224	207	1	figure	figure	VERB
easat-224	207	2	6.3	6.3	NUM
easat-224	207	3	.	.	PUNCT
easat-224	208	1	deflection	deflection	NOUN
easat-224	208	2	profile	profile	NOUN
easat-224	208	3	of	of	ADP
easat-224	208	4	a	a	DET
easat-224	208	5	free	free	ADJ
easat-224	208	6	elastic	elastic	ADJ
easat-224	208	7	uniform	uniform	NOUN
easat-224	208	8	rayleigh	rayleigh	PROPN
easat-224	208	9	beam	beam	PROPN
easat-224	208	10	on	on	ADP
easat-224	208	11	variable	variable	ADJ
easat-224	208	12	foundation	foundation	NOUN
easat-224	208	13	and	and	CCONJ
easat-224	208	14	traversed	traverse	VERB
easat-224	208	15	by	by	ADP
easat-224	208	16	moving	move	VERB
easat-224	208	17	distributed	distributed	ADJ
easat-224	208	18	force	force	NOUN
easat-224	208	19	for	for	ADP
easat-224	208	20	various	various	ADJ
easat-224	208	21	values	value	NOUN
easat-224	208	22	of	of	ADP
easat-224	208	23	𝑹.	𝑹.	PROPN
easat-224	208	24	figure	figure	NOUN
easat-224	208	25	6.4	6.4	NUM
easat-224	208	26	.	.	PUNCT
easat-224	209	1	deflection	deflection	NOUN
easat-224	209	2	profile	profile	NOUN
easat-224	209	3	of	of	ADP
easat-224	209	4	a	a	DET
easat-224	209	5	free	free	ADJ
easat-224	209	6	elastic	elastic	ADJ
easat-224	209	7	uniform	uniform	NOUN
easat-224	209	8	rayleigh	rayleigh	PROPN
easat-224	209	9	beam	beam	PROPN
easat-224	209	10	on	on	ADP
easat-224	209	11	variable	variable	ADJ
easat-224	209	12	foundation	foundation	NOUN
easat-224	209	13	and	and	CCONJ
easat-224	209	14	traversed	traverse	VERB
easat-224	209	15	by	by	ADP
easat-224	209	16	moving	move	VERB
easat-224	209	17	distributed	distributed	ADJ
easat-224	209	18	force	force	NOUN
easat-224	209	19	for	for	ADP
easat-224	209	20	various	various	ADJ
easat-224	209	21	values	value	NOUN
easat-224	209	22	of	of	ADP
easat-224	209	23	𝑹.	𝑹.	PROPN
easat-224	209	24	figure	figure	NOUN
easat-224	209	25	6.5	6.5	NUM
easat-224	209	26	.	.	PUNCT
easat-224	210	1	deflection	deflection	NOUN
easat-224	210	2	profile	profile	NOUN
easat-224	210	3	of	of	ADP
easat-224	210	4	a	a	DET
easat-224	210	5	free	free	ADJ
easat-224	210	6	elastic	elastic	ADJ
easat-224	210	7	uniform	uniform	NOUN
easat-224	210	8	rayleigh	rayleigh	PROPN
easat-224	210	9	beam	beam	PROPN
easat-224	210	10	on	on	ADP
easat-224	210	11	variable	variable	ADJ
easat-224	210	12	foundation	foundation	NOUN
easat-224	210	13	and	and	CCONJ
easat-224	210	14	traversed	traverse	VERB
easat-224	210	15	by	by	ADP
easat-224	210	16	moving	move	VERB
easat-224	210	17	distributed	distribute	VERB
easat-224	210	18	forces	force	NOUN
easat-224	210	19	for	for	ADP
easat-224	210	20	various	various	ADJ
easat-224	210	21	values	value	NOUN
easat-224	210	22	of	of	ADP
easat-224	210	23	𝑺𝒐.	𝑺𝒐.	PROPN
easat-224	210	24	figure	figure	NOUN
easat-224	210	25	6.6	6.6	NUM
easat-224	210	26	.	.	PUNCT
easat-224	211	1	deflection	deflection	NOUN
easat-224	211	2	profile	profile	NOUN
easat-224	211	3	of	of	ADP
easat-224	211	4	a	a	DET
easat-224	211	5	free	free	ADJ
easat-224	211	6	elastic	elastic	ADJ
easat-224	211	7	uniform	uniform	NOUN
easat-224	211	8	rayleigh	rayleigh	PROPN
easat-224	211	9	beam	beam	PROPN
easat-224	211	10	on	on	ADP
easat-224	211	11	variable	variable	ADJ
easat-224	211	12	foundation	foundation	NOUN
easat-224	211	13	and	and	CCONJ
easat-224	211	14	traversed	traverse	VERB
easat-224	211	15	by	by	ADP
easat-224	211	16	moving	move	VERB
easat-224	211	17	distributed	distribute	VERB
easat-224	211	18	mass	mass	NOUN
easat-224	211	19	for	for	ADP
easat-224	211	20	various	various	ADJ
easat-224	211	21	values	value	NOUN
easat-224	211	22	of	of	ADP
easat-224	211	23	𝑺𝒐.	𝑺𝒐.	PROPN
easat-224	211	24	7	7	NUM
easat-224	211	25	edelweiss	edelweiss	PROPN
easat-224	211	26	applied	apply	VERB
easat-224	211	27	science	science	NOUN
easat-224	211	28	and	and	CCONJ
easat-224	211	29	technology	technology	NOUN
easat-224	211	30	issn	issn	PROPN
easat-224	211	31	:	:	PUNCT
easat-224	211	32	2576	2576	NUM
easat-224	211	33	-	-	SYM
easat-224	211	34	8484	8484	NUM
easat-224	211	35	vol	vol	NOUN
easat-224	211	36	.	.	PROPN
easat-224	212	1	2	2	NUM
easat-224	212	2	,	,	PUNCT
easat-224	212	3	no	no	INTJ
easat-224	212	4	.	.	NOUN
easat-224	212	5	1	1	NUM
easat-224	212	6	:	:	SYM
easat-224	212	7	1	1	NUM
easat-224	212	8	-	-	SYM
easat-224	212	9	9	9	NUM
easat-224	212	10	,	,	PUNCT
easat-224	212	11	2018	2018	NUM
easat-224	212	12	doi	doi	NOUN
easat-224	212	13	:	:	PUNCT
easat-224	212	14	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	213	1	©	©	PROPN
easat-224	213	2	2018	2018	NUM
easat-224	213	3	by	by	ADP
easat-224	213	4	the	the	DET
easat-224	213	5	authors	author	NOUN
easat-224	213	6	figures	figure	VERB
easat-224	213	7	6.7	6.7	NUM
easat-224	213	8	and	and	CCONJ
easat-224	213	9	6.8	6.8	NUM
easat-224	213	10	display	display	VERB
easat-224	213	11	the	the	DET
easat-224	213	12	effect	effect	NOUN
easat-224	213	13	of	of	ADP
easat-224	213	14	shear	shear	NOUN
easat-224	213	15	modulus	modulus	ADJ
easat-224	213	16	h	h	NOUN
easat-224	213	17	on	on	ADP
easat-224	213	18	the	the	DET
easat-224	213	19	deflection	deflection	NOUN
easat-224	213	20	profile	profile	NOUN
easat-224	213	21	of	of	ADP
easat-224	213	22	free	free	ADJ
easat-224	213	23	elastic	elastic	ADJ
easat-224	213	24	rayleigh	rayleigh	NOUN
easat-224	213	25	beam	beam	NOUN
easat-224	213	26	under	under	ADP
easat-224	213	27	the	the	DET
easat-224	213	28	action	action	NOUN
easat-224	213	29	of	of	ADP
easat-224	213	30	load	load	NOUN
easat-224	213	31	moving	move	VERB
easat-224	213	32	at	at	ADP
easat-224	213	33	constant	constant	ADJ
easat-224	213	34	velocity	velocity	NOUN
easat-224	213	35	in	in	ADP
easat-224	213	36	both	both	DET
easat-224	213	37	cases	case	NOUN
easat-224	213	38	of	of	ADP
easat-224	213	39	moving	move	VERB
easat-224	213	40	distributed	distribute	VERB
easat-224	213	41	forces	force	NOUN
easat-224	213	42	and	and	CCONJ
easat-224	213	43	moving	move	VERB
easat-224	213	44	distributed	distribute	VERB
easat-224	213	45	masses	masse	NOUN
easat-224	213	46	respectively	respectively	ADV
easat-224	213	47	.	.	PUNCT
easat-224	214	1	the	the	DET
easat-224	214	2	graphs	graph	NOUN
easat-224	214	3	show	show	VERB
easat-224	214	4	that	that	SCONJ
easat-224	214	5	the	the	DET
easat-224	214	6	response	response	NOUN
easat-224	214	7	amplitude	amplitude	NOUN
easat-224	214	8	decreases	decrease	VERB
easat-224	214	9	as	as	ADP
easat-224	214	10	the	the	DET
easat-224	214	11	value	value	NOUN
easat-224	214	12	of	of	ADP
easat-224	214	13	h	h	NOUN
easat-224	214	14	increases	increase	NOUN
easat-224	214	15	.	.	PUNCT
easat-224	215	1	figure	figure	VERB
easat-224	215	2	6.7	6.7	NUM
easat-224	215	3	.	.	PUNCT
easat-224	216	1	deflection	deflection	NOUN
easat-224	216	2	profile	profile	NOUN
easat-224	216	3	of	of	ADP
easat-224	216	4	a	a	DET
easat-224	216	5	free	free	ADJ
easat-224	216	6	elastic	elastic	ADJ
easat-224	216	7	uniform	uniform	NOUN
easat-224	216	8	rayleigh	rayleigh	PROPN
easat-224	216	9	beam	beam	PROPN
easat-224	216	10	on	on	ADP
easat-224	216	11	variable	variable	ADJ
easat-224	216	12	foundation	foundation	NOUN
easat-224	216	13	and	and	CCONJ
easat-224	216	14	traversed	traverse	VERB
easat-224	216	15	by	by	ADP
easat-224	216	16	moving	move	VERB
easat-224	216	17	distributed	distributed	ADJ
easat-224	216	18	force	force	NOUN
easat-224	216	19	for	for	ADP
easat-224	216	20	various	various	ADJ
easat-224	216	21	values	value	NOUN
easat-224	216	22	of	of	ADP
easat-224	216	23	h.	h.	PROPN
easat-224	216	24	figure	figure	NOUN
easat-224	216	25	6.8	6.8	NUM
easat-224	216	26	.	.	PUNCT
easat-224	217	1	deflection	deflection	NOUN
easat-224	217	2	profile	profile	NOUN
easat-224	217	3	of	of	ADP
easat-224	217	4	a	a	DET
easat-224	217	5	free	free	ADJ
easat-224	217	6	elastic	elastic	ADJ
easat-224	217	7	uniform	uniform	NOUN
easat-224	217	8	rayleigh	rayleigh	PROPN
easat-224	217	9	beam	beam	PROPN
easat-224	217	10	on	on	ADP
easat-224	217	11	variable	variable	ADJ
easat-224	217	12	foundation	foundation	NOUN
easat-224	217	13	and	and	CCONJ
easat-224	217	14	traversed	traverse	VERB
easat-224	217	15	by	by	ADP
easat-224	217	16	moving	move	VERB
easat-224	217	17	distributed	distribute	VERB
easat-224	217	18	mass	mass	NOUN
easat-224	217	19	for	for	ADP
easat-224	217	20	various	various	ADJ
easat-224	217	21	values	value	NOUN
easat-224	217	22	of	of	ADP
easat-224	217	23	𝓗.	𝓗.	ADJ
easat-224	217	24	figure	figure	NOUN
easat-224	217	25	6.9	6.9	NUM
easat-224	217	26	.	.	PUNCT
easat-224	217	27	shows	show	VERB
easat-224	217	28	the	the	DET
easat-224	217	29	comparison	comparison	NOUN
easat-224	217	30	of	of	ADP
easat-224	217	31	the	the	DET
easat-224	217	32	moving	move	VERB
easat-224	217	33	distributed	distribute	VERB
easat-224	217	34	forces	force	NOUN
easat-224	217	35	and	and	CCONJ
easat-224	217	36	moving	move	VERB
easat-224	217	37	distributed	distribute	VERB
easat-224	217	38	masses	masse	NOUN
easat-224	217	39	for	for	ADP
easat-224	217	40	fixed	fix	VERB
easat-224	217	41	values	value	NOUN
easat-224	217	42	of	of	ADP
easat-224	217	43	ho	ho	PROPN
easat-224	217	44	,	,	PUNCT
easat-224	217	45	n	n	CCONJ
easat-224	217	46	,	,	PUNCT
easat-224	217	47	so	so	ADV
easat-224	217	48	and	and	CCONJ
easat-224	217	49	r.	r.	PROPN
easat-224	217	50	figure	figure	NOUN
easat-224	217	51	6.9	6.9	NUM
easat-224	217	52	.	.	PUNCT
easat-224	218	1	comparison	comparison	NOUN
easat-224	218	2	of	of	ADP
easat-224	218	3	the	the	DET
easat-224	218	4	deflection	deflection	NOUN
easat-224	218	5	profile	profile	NOUN
easat-224	218	6	of	of	ADP
easat-224	218	7	moving	move	VERB
easat-224	218	8	force	force	NOUN
easat-224	218	9	and	and	CCONJ
easat-224	218	10	moving	move	VERB
easat-224	218	11	mass	mass	NOUN
easat-224	218	12	for	for	ADP
easat-224	218	13	a	a	DET
easat-224	218	14	free	free	ADJ
easat-224	218	15	elastic	elastic	ADJ
easat-224	218	16	uniform	uniform	NOUN
easat-224	218	17	rayleigh	rayleigh	PROPN
easat-224	218	18	beam	beam	PROPN
easat-224	218	19	.	.	PUNCT
easat-224	219	1	4.2	4.2	NUM
easat-224	219	2	.	.	PUNCT
easat-224	219	3	graphs	graph	NOUN
easat-224	219	4	for	for	ADP
easat-224	219	5	elastic	elastic	ADJ
easat-224	219	6	-	-	PUNCT
easat-224	219	7	elastic	elastic	ADJ
easat-224	219	8	boundary	boundary	NOUN
easat-224	219	9	conditions	condition	NOUN
easat-224	219	10	figures	figure	VERB
easat-224	219	11	6.10	6.10	NUM
easat-224	219	12	and	and	CCONJ
easat-224	219	13	6.11	6.11	NUM
easat-224	219	14	display	display	VERB
easat-224	219	15	the	the	DET
easat-224	219	16	effect	effect	NOUN
easat-224	219	17	of	of	ADP
easat-224	219	18	axial	axial	ADJ
easat-224	219	19	force	force	NOUN
easat-224	219	20	n	n	CCONJ
easat-224	219	21	on	on	ADP
easat-224	219	22	the	the	DET
easat-224	219	23	deflection	deflection	NOUN
easat-224	219	24	profile	profile	NOUN
easat-224	219	25	of	of	ADP
easat-224	219	26	elasticelastic	elasticelastic	ADJ
easat-224	219	27	rayleigh	rayleigh	PROPN
easat-224	219	28	beam	beam	NOUN
easat-224	219	29	under	under	ADP
easat-224	219	30	the	the	DET
easat-224	219	31	action	action	NOUN
easat-224	219	32	of	of	ADP
easat-224	219	33	load	load	NOUN
easat-224	219	34	moving	move	VERB
easat-224	219	35	at	at	ADP
easat-224	219	36	constant	constant	ADJ
easat-224	219	37	velocity	velocity	NOUN
easat-224	219	38	in	in	ADP
easat-224	219	39	both	both	DET
easat-224	219	40	cases	case	NOUN
easat-224	219	41	of	of	ADP
easat-224	219	42	moving	move	VERB
easat-224	219	43	distributed	distribute	VERB
easat-224	219	44	forces	force	NOUN
easat-224	219	45	and	and	CCONJ
easat-224	219	46	moving	move	VERB
easat-224	219	47	distributed	distribute	VERB
easat-224	219	48	masses	masse	NOUN
easat-224	219	49	respectively	respectively	ADV
easat-224	219	50	.	.	PUNCT
easat-224	220	1	the	the	DET
easat-224	220	2	graphs	graph	NOUN
easat-224	220	3	show	show	VERB
easat-224	220	4	that	that	SCONJ
easat-224	220	5	the	the	DET
easat-224	220	6	response	response	NOUN
easat-224	220	7	amplitude	amplitude	NOUN
easat-224	220	8	decreases	decrease	VERB
easat-224	220	9	as	as	ADP
easat-224	220	10	the	the	DET
easat-224	220	11	value	value	NOUN
easat-224	220	12	of	of	ADP
easat-224	220	13	rotatory	rotatory	ADJ
easat-224	220	14	inertia	inertia	NOUN
easat-224	220	15	increases	increase	NOUN
easat-224	220	16	.	.	PUNCT
easat-224	221	1	figure	figure	NOUN
easat-224	221	2	.	.	PUNCT
easat-224	222	1	6.10	6.10	NUM
easat-224	222	2	.	.	PUNCT
easat-224	223	1	deflection	deflection	NOUN
easat-224	223	2	profile	profile	NOUN
easat-224	223	3	of	of	ADP
easat-224	223	4	an	an	DET
easat-224	223	5	elasticelastic	elasticelastic	ADJ
easat-224	223	6	uniform	uniform	ADJ
easat-224	223	7	rayleigh	rayleigh	PROPN
easat-224	223	8	beam	beam	PROPN
easat-224	223	9	on	on	ADP
easat-224	223	10	variable	variable	ADJ
easat-224	223	11	foundation	foundation	NOUN
easat-224	223	12	and	and	CCONJ
easat-224	223	13	traversed	traverse	VERB
easat-224	223	14	by	by	ADP
easat-224	223	15	moving	move	VERB
easat-224	223	16	distributed	distribute	VERB
easat-224	223	17	forces	force	NOUN
easat-224	223	18	for	for	ADP
easat-224	223	19	various	various	ADJ
easat-224	223	20	values	value	NOUN
easat-224	223	21	of	of	ADP
easat-224	223	22	𝑵.	𝑵.	PROPN
easat-224	223	23	figure	figure	NOUN
easat-224	223	24	6.11	6.11	NUM
easat-224	223	25	.	.	PUNCT
easat-224	224	1	deflection	deflection	NOUN
easat-224	224	2	profile	profile	NOUN
easat-224	224	3	of	of	ADP
easat-224	224	4	an	an	DET
easat-224	224	5	elasticelastic	elasticelastic	ADJ
easat-224	224	6	uniform	uniform	ADJ
easat-224	224	7	rayleigh	rayleigh	PROPN
easat-224	224	8	beam	beam	PROPN
easat-224	224	9	on	on	ADP
easat-224	224	10	variable	variable	ADJ
easat-224	224	11	foundation	foundation	NOUN
easat-224	224	12	and	and	CCONJ
easat-224	224	13	traversed	traverse	VERB
easat-224	224	14	by	by	ADP
easat-224	224	15	moving	move	VERB
easat-224	224	16	distributed	distribute	VERB
easat-224	224	17	forces	force	NOUN
easat-224	224	18	for	for	ADP
easat-224	224	19	various	various	ADJ
easat-224	224	20	values	value	NOUN
easat-224	224	21	of	of	ADP
easat-224	224	22	𝑵.	𝑵.	PROPN
easat-224	224	23	figures	figure	NOUN
easat-224	224	24	6.12	6.12	NUM
easat-224	224	25	and	and	CCONJ
easat-224	224	26	6.13	6.13	NUM
easat-224	224	27	display	display	VERB
easat-224	224	28	the	the	DET
easat-224	224	29	effect	effect	NOUN
easat-224	224	30	of	of	ADP
easat-224	224	31	rotatory	rotatory	ADJ
easat-224	224	32	inertia	inertia	NOUN
easat-224	224	33	r	r	NOUN
easat-224	224	34	on	on	ADP
easat-224	224	35	the	the	DET
easat-224	224	36	deflection	deflection	NOUN
easat-224	224	37	profile	profile	NOUN
easat-224	224	38	of	of	ADP
easat-224	224	39	elasticelastic	elasticelastic	ADJ
easat-224	224	40	rayleigh	rayleigh	PROPN
easat-224	224	41	beam	beam	NOUN
easat-224	224	42	under	under	ADP
easat-224	224	43	the	the	DET
easat-224	224	44	action	action	NOUN
easat-224	224	45	of	of	ADP
easat-224	224	46	load	load	NOUN
easat-224	224	47	moving	move	VERB
easat-224	224	48	at	at	ADP
easat-224	224	49	constant	constant	ADJ
easat-224	224	50	velocity	velocity	NOUN
easat-224	224	51	in	in	ADP
easat-224	224	52	both	both	DET
easat-224	224	53	cases	case	NOUN
easat-224	224	54	of	of	ADP
easat-224	224	55	moving	move	VERB
easat-224	224	56	distributed	distribute	VERB
easat-224	224	57	forces	force	NOUN
easat-224	224	58	and	and	CCONJ
easat-224	224	59	moving	move	VERB
easat-224	224	60	distributed	distribute	VERB
easat-224	224	61	masses	masse	NOUN
easat-224	224	62	respectively	respectively	ADV
easat-224	224	63	.	.	PUNCT
easat-224	225	1	the	the	DET
easat-224	225	2	graphs	graph	NOUN
easat-224	225	3	show	show	VERB
easat-224	225	4	that	that	SCONJ
easat-224	225	5	the	the	DET
easat-224	225	6	response	response	NOUN
easat-224	225	7	amplitude	amplitude	NOUN
easat-224	225	8	decreases	decrease	VERB
easat-224	225	9	as	as	ADP
easat-224	225	10	the	the	DET
easat-224	225	11	value	value	NOUN
easat-224	225	12	of	of	ADP
easat-224	225	13	rotatory	rotatory	ADJ
easat-224	225	14	inertia	inertia	NOUN
easat-224	225	15	increases	increase	NOUN
easat-224	225	16	.	.	PUNCT
easat-224	226	1	8	8	NUM
easat-224	226	2	edelweiss	edelweiss	PROPN
easat-224	226	3	applied	apply	VERB
easat-224	226	4	science	science	NOUN
easat-224	226	5	and	and	CCONJ
easat-224	226	6	technology	technology	NOUN
easat-224	226	7	issn	issn	PROPN
easat-224	226	8	:	:	PUNCT
easat-224	226	9	2576	2576	NUM
easat-224	226	10	-	-	SYM
easat-224	226	11	8484	8484	NUM
easat-224	226	12	vol	vol	NOUN
easat-224	226	13	.	.	PROPN
easat-224	227	1	2	2	NUM
easat-224	227	2	,	,	PUNCT
easat-224	227	3	no	no	INTJ
easat-224	227	4	.	.	NOUN
easat-224	227	5	1	1	NUM
easat-224	227	6	:	:	SYM
easat-224	227	7	1	1	NUM
easat-224	227	8	-	-	SYM
easat-224	227	9	9	9	NUM
easat-224	227	10	,	,	PUNCT
easat-224	227	11	2018	2018	NUM
easat-224	227	12	doi	doi	NOUN
easat-224	227	13	:	:	PUNCT
easat-224	227	14	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	228	1	©	©	PROPN
easat-224	228	2	2018	2018	NUM
easat-224	228	3	by	by	ADP
easat-224	228	4	the	the	DET
easat-224	228	5	authors	author	NOUN
easat-224	228	6	figure	figure	VERB
easat-224	228	7	6.12	6.12	NUM
easat-224	228	8	.	.	PUNCT
easat-224	229	1	deflection	deflection	NOUN
easat-224	229	2	profile	profile	NOUN
easat-224	229	3	of	of	ADP
easat-224	229	4	an	an	DET
easat-224	229	5	elasticelastic	elasticelastic	ADJ
easat-224	229	6	uniform	uniform	ADJ
easat-224	229	7	rayleigh	rayleigh	PROPN
easat-224	229	8	beam	beam	PROPN
easat-224	229	9	on	on	ADP
easat-224	229	10	variable	variable	ADJ
easat-224	229	11	foundation	foundation	NOUN
easat-224	229	12	and	and	CCONJ
easat-224	229	13	traversed	traverse	VERB
easat-224	229	14	by	by	ADP
easat-224	229	15	moving	move	VERB
easat-224	229	16	distributed	distribute	VERB
easat-224	229	17	forces	force	NOUN
easat-224	229	18	for	for	ADP
easat-224	229	19	various	various	ADJ
easat-224	229	20	values	value	NOUN
easat-224	229	21	of	of	ADP
easat-224	229	22	𝑹.	𝑹.	ADJ
easat-224	229	23	figure	figure	NOUN
easat-224	229	24	6.13	6.13	NUM
easat-224	229	25	.	.	PUNCT
easat-224	230	1	deflection	deflection	NOUN
easat-224	230	2	profile	profile	NOUN
easat-224	230	3	of	of	ADP
easat-224	230	4	an	an	DET
easat-224	230	5	elastic	elastic	ADJ
easat-224	230	6	-	-	PUNCT
easat-224	230	7	elastic	elastic	ADJ
easat-224	230	8	uniform	uniform	NOUN
easat-224	230	9	rayleigh	rayleigh	PROPN
easat-224	230	10	beam	beam	PROPN
easat-224	230	11	on	on	ADP
easat-224	230	12	variable	variable	ADJ
easat-224	230	13	foundation	foundation	NOUN
easat-224	230	14	and	and	CCONJ
easat-224	230	15	traversed	traverse	VERB
easat-224	230	16	by	by	ADP
easat-224	230	17	moving	move	VERB
easat-224	230	18	distributed	distribute	VERB
easat-224	230	19	mass	mass	NOUN
easat-224	230	20	for	for	ADP
easat-224	230	21	various	various	ADJ
easat-224	230	22	values	value	NOUN
easat-224	230	23	of	of	ADP
easat-224	230	24	𝑹.	𝑹.	PROPN
easat-224	230	25	figures	figure	NOUN
easat-224	230	26	6.14	6.14	NUM
easat-224	230	27	and	and	CCONJ
easat-224	230	28	6.15	6.15	NUM
easat-224	230	29	display	display	NOUN
easat-224	230	30	the	the	DET
easat-224	230	31	effect	effect	NOUN
easat-224	230	32	of	of	ADP
easat-224	230	33	shear	shear	NOUN
easat-224	230	34	modulus	modulus	NOUN
easat-224	230	35	𝓗	𝓗	PROPN
easat-224	230	36	on	on	ADP
easat-224	230	37	the	the	DET
easat-224	230	38	deflection	deflection	NOUN
easat-224	230	39	profile	profile	NOUN
easat-224	230	40	of	of	ADP
easat-224	230	41	clamped	clamp	VERB
easat-224	230	42	elastic	elastic	ADJ
easat-224	230	43	rayleigh	rayleigh	NOUN
easat-224	230	44	beam	beam	NOUN
easat-224	230	45	under	under	ADP
easat-224	230	46	the	the	DET
easat-224	230	47	action	action	NOUN
easat-224	230	48	of	of	ADP
easat-224	230	49	load	load	NOUN
easat-224	230	50	moving	move	VERB
easat-224	230	51	at	at	ADP
easat-224	230	52	constant	constant	ADJ
easat-224	230	53	velocity	velocity	NOUN
easat-224	230	54	in	in	ADP
easat-224	230	55	both	both	DET
easat-224	230	56	cases	case	NOUN
easat-224	230	57	of	of	ADP
easat-224	230	58	moving	move	VERB
easat-224	230	59	distributed	distribute	VERB
easat-224	230	60	forces	force	NOUN
easat-224	230	61	and	and	CCONJ
easat-224	230	62	moving	move	VERB
easat-224	230	63	distributed	distribute	VERB
easat-224	230	64	masses	masse	NOUN
easat-224	230	65	respectively	respectively	ADV
easat-224	230	66	.	.	PUNCT
easat-224	231	1	the	the	DET
easat-224	231	2	graphs	graph	NOUN
easat-224	231	3	show	show	VERB
easat-224	231	4	that	that	SCONJ
easat-224	231	5	the	the	DET
easat-224	231	6	response	response	NOUN
easat-224	231	7	amplitude	amplitude	NOUN
easat-224	231	8	decreases	decrease	VERB
easat-224	231	9	as	as	ADP
easat-224	231	10	the	the	DET
easat-224	231	11	value	value	NOUN
easat-224	231	12	of	of	ADP
easat-224	231	13	𝓗	𝓗	PROPN
easat-224	231	14	increases	increase	NOUN
easat-224	231	15	.	.	PUNCT
easat-224	232	1	figure	figure	VERB
easat-224	232	2	6.14	6.14	NUM
easat-224	232	3	.	.	PUNCT
easat-224	233	1	deflection	deflection	NOUN
easat-224	233	2	profile	profile	NOUN
easat-224	233	3	of	of	ADP
easat-224	233	4	an	an	DET
easat-224	233	5	elastic	elastic	ADJ
easat-224	233	6	-	-	PUNCT
easat-224	233	7	elastic	elastic	ADJ
easat-224	233	8	uniform	uniform	NOUN
easat-224	233	9	rayleigh	rayleigh	PROPN
easat-224	233	10	beam	beam	PROPN
easat-224	233	11	on	on	ADP
easat-224	233	12	variable	variable	ADJ
easat-224	233	13	foundation	foundation	NOUN
easat-224	233	14	and	and	CCONJ
easat-224	233	15	traversed	traverse	VERB
easat-224	233	16	by	by	ADP
easat-224	233	17	moving	move	VERB
easat-224	233	18	distributed	distributed	ADJ
easat-224	233	19	force	force	NOUN
easat-224	233	20	for	for	ADP
easat-224	233	21	various	various	ADJ
easat-224	233	22	values	value	NOUN
easat-224	233	23	of	of	ADP
easat-224	233	24	𝓗.	𝓗.	ADJ
easat-224	233	25	figure	figure	NOUN
easat-224	233	26	6.15	6.15	NUM
easat-224	233	27	.	.	PUNCT
easat-224	234	1	deflection	deflection	NOUN
easat-224	234	2	profile	profile	NOUN
easat-224	234	3	of	of	ADP
easat-224	234	4	an	an	DET
easat-224	234	5	elastic	elastic	ADJ
easat-224	234	6	-	-	PUNCT
easat-224	234	7	elastic	elastic	ADJ
easat-224	234	8	uniform	uniform	NOUN
easat-224	234	9	rayleigh	rayleigh	PROPN
easat-224	234	10	beam	beam	PROPN
easat-224	234	11	on	on	ADP
easat-224	234	12	variable	variable	ADJ
easat-224	234	13	foundation	foundation	NOUN
easat-224	234	14	and	and	CCONJ
easat-224	234	15	traversed	traverse	VERB
easat-224	234	16	by	by	ADP
easat-224	234	17	moving	move	VERB
easat-224	234	18	distributed	distribute	VERB
easat-224	234	19	masses	masse	NOUN
easat-224	234	20	for	for	ADP
easat-224	234	21	various	various	ADJ
easat-224	234	22	values	value	NOUN
easat-224	234	23	of	of	ADP
easat-224	234	24	𝓗.	𝓗.	PROPN
easat-224	234	25	figures	figure	NOUN
easat-224	234	26	6.16	6.16	NUM
easat-224	234	27	and	and	CCONJ
easat-224	234	28	6.17	6.17	NUM
easat-224	234	29	display	display	NOUN
easat-224	234	30	the	the	DET
easat-224	234	31	effect	effect	NOUN
easat-224	234	32	of	of	ADP
easat-224	234	33	foundation	foundation	NOUN
easat-224	234	34	modulus	modulus	NOUN
easat-224	234	35	𝑺𝒐	𝑺𝒐	PROPN
easat-224	234	36	on	on	ADP
easat-224	234	37	the	the	DET
easat-224	234	38	deflection	deflection	NOUN
easat-224	234	39	profile	profile	NOUN
easat-224	234	40	of	of	ADP
easat-224	234	41	clamped	clamp	VERB
easat-224	234	42	elastic	elastic	ADJ
easat-224	234	43	rayleigh	rayleigh	NOUN
easat-224	234	44	beam	beam	NOUN
easat-224	234	45	under	under	ADP
easat-224	234	46	the	the	DET
easat-224	234	47	action	action	NOUN
easat-224	234	48	of	of	ADP
easat-224	234	49	load	load	NOUN
easat-224	234	50	moving	move	VERB
easat-224	234	51	at	at	ADP
easat-224	234	52	constant	constant	ADJ
easat-224	234	53	velocity	velocity	NOUN
easat-224	234	54	in	in	ADP
easat-224	234	55	both	both	DET
easat-224	234	56	cases	case	NOUN
easat-224	234	57	of	of	ADP
easat-224	234	58	moving	move	VERB
easat-224	234	59	distributed	distribute	VERB
easat-224	234	60	forces	force	NOUN
easat-224	234	61	and	and	CCONJ
easat-224	234	62	moving	move	VERB
easat-224	234	63	distributed	distribute	VERB
easat-224	234	64	masses	masse	NOUN
easat-224	234	65	respectively	respectively	ADV
easat-224	234	66	.	.	PUNCT
easat-224	235	1	the	the	DET
easat-224	235	2	graphs	graph	NOUN
easat-224	235	3	show	show	VERB
easat-224	235	4	that	that	SCONJ
easat-224	235	5	the	the	DET
easat-224	235	6	response	response	NOUN
easat-224	235	7	amplitude	amplitude	NOUN
easat-224	235	8	decreases	decrease	VERB
easat-224	235	9	as	as	ADP
easat-224	235	10	the	the	DET
easat-224	235	11	value	value	NOUN
easat-224	235	12	of	of	ADP
easat-224	235	13	𝑺𝒐	𝑺𝒐	ADJ
easat-224	235	14	increases	increase	NOUN
easat-224	235	15	.	.	PUNCT
easat-224	236	1	figure	figure	VERB
easat-224	236	2	6.16	6.16	NUM
easat-224	236	3	.	.	PUNCT
easat-224	237	1	deflection	deflection	NOUN
easat-224	237	2	profile	profile	NOUN
easat-224	237	3	of	of	ADP
easat-224	237	4	an	an	DET
easat-224	237	5	elastic	elastic	ADJ
easat-224	237	6	-	-	PUNCT
easat-224	237	7	elastic	elastic	ADJ
easat-224	237	8	uniform	uniform	NOUN
easat-224	237	9	rayleigh	rayleigh	PROPN
easat-224	237	10	beam	beam	PROPN
easat-224	237	11	on	on	ADP
easat-224	237	12	variable	variable	ADJ
easat-224	237	13	foundation	foundation	NOUN
easat-224	237	14	and	and	CCONJ
easat-224	237	15	traversed	traverse	VERB
easat-224	237	16	by	by	ADP
easat-224	237	17	moving	move	VERB
easat-224	237	18	distributed	distributed	ADJ
easat-224	237	19	force	force	NOUN
easat-224	237	20	for	for	ADP
easat-224	237	21	various	various	ADJ
easat-224	237	22	values	value	NOUN
easat-224	237	23	of	of	ADP
easat-224	237	24	𝑺𝒐.	𝑺𝒐.	PROPN
easat-224	237	25	figure	figure	NOUN
easat-224	237	26	6.17	6.17	NUM
easat-224	237	27	.	.	PUNCT
easat-224	238	1	deflection	deflection	NOUN
easat-224	238	2	profile	profile	NOUN
easat-224	238	3	of	of	ADP
easat-224	238	4	an	an	DET
easat-224	238	5	elastic	elastic	ADJ
easat-224	238	6	-	-	PUNCT
easat-224	238	7	elastic	elastic	ADJ
easat-224	238	8	uniform	uniform	NOUN
easat-224	238	9	rayleigh	rayleigh	PROPN
easat-224	238	10	beam	beam	PROPN
easat-224	238	11	on	on	ADP
easat-224	238	12	variable	variable	ADJ
easat-224	238	13	foundation	foundation	NOUN
easat-224	238	14	and	and	CCONJ
easat-224	238	15	traversed	traverse	VERB
easat-224	238	16	by	by	ADP
easat-224	238	17	moving	move	VERB
easat-224	238	18	distributed	distribute	VERB
easat-224	238	19	mass	mass	NOUN
easat-224	238	20	for	for	ADP
easat-224	238	21	various	various	ADJ
easat-224	238	22	values	value	NOUN
easat-224	238	23	of	of	ADP
easat-224	238	24	𝑺𝒐.	𝑺𝒐.	PROPN
easat-224	238	25	9	9	NUM
easat-224	238	26	edelweiss	edelweiss	PROPN
easat-224	238	27	applied	apply	VERB
easat-224	238	28	science	science	NOUN
easat-224	238	29	and	and	CCONJ
easat-224	238	30	technology	technology	NOUN
easat-224	238	31	issn	issn	PROPN
easat-224	238	32	:	:	PUNCT
easat-224	238	33	2576	2576	NUM
easat-224	238	34	-	-	SYM
easat-224	238	35	8484	8484	NUM
easat-224	238	36	vol	vol	NOUN
easat-224	238	37	.	.	PROPN
easat-224	239	1	2	2	NUM
easat-224	239	2	,	,	PUNCT
easat-224	239	3	no	no	INTJ
easat-224	239	4	.	.	NOUN
easat-224	239	5	1	1	NUM
easat-224	239	6	:	:	SYM
easat-224	239	7	1	1	NUM
easat-224	239	8	-	-	SYM
easat-224	239	9	9	9	NUM
easat-224	239	10	,	,	PUNCT
easat-224	239	11	2018	2018	NUM
easat-224	239	12	doi	doi	NOUN
easat-224	239	13	:	:	PUNCT
easat-224	239	14	10.33805/2576.8484.106	10.33805/2576.8484.106	NUM
easat-224	240	1	©	©	PROPN
easat-224	240	2	2018	2018	NUM
easat-224	240	3	by	by	ADP
easat-224	240	4	the	the	DET
easat-224	240	5	authors	author	NOUN
easat-224	240	6	figure	figure	VERB
easat-224	240	7	6.18	6.18	NUM
easat-224	240	8	.	.	PUNCT
easat-224	241	1	shows	show	VERB
easat-224	241	2	the	the	DET
easat-224	241	3	comparison	comparison	NOUN
easat-224	241	4	of	of	ADP
easat-224	241	5	the	the	DET
easat-224	241	6	moving	move	VERB
easat-224	241	7	distributed	distribute	VERB
easat-224	241	8	forces	force	NOUN
easat-224	241	9	and	and	CCONJ
easat-224	241	10	moving	move	VERB
easat-224	241	11	distributed	distribute	VERB
easat-224	241	12	masses	masse	NOUN
easat-224	241	13	for	for	ADP
easat-224	241	14	fixed	fix	VERB
easat-224	241	15	values	value	NOUN
easat-224	241	16	of	of	ADP
easat-224	241	17	𝑺𝒐	𝑺𝒐	PROPN
easat-224	241	18	,	,	PUNCT
easat-224	241	19	𝑵	𝑵	PROPN
easat-224	241	20	,	,	PUNCT
easat-224	241	21	𝓗	𝓗	PROPN
easat-224	241	22	and	and	CCONJ
easat-224	241	23	𝑹.	𝑹.	PROPN
easat-224	241	24	figure	figure	NOUN
easat-224	241	25	6.18	6.18	NUM
easat-224	241	26	.	.	PUNCT
easat-224	242	1	comparison	comparison	NOUN
easat-224	242	2	of	of	ADP
easat-224	242	3	the	the	DET
easat-224	242	4	deflection	deflection	NOUN
easat-224	242	5	profile	profile	NOUN
easat-224	242	6	of	of	ADP
easat-224	242	7	moving	move	VERB
easat-224	242	8	force	force	NOUN
easat-224	242	9	and	and	CCONJ
easat-224	242	10	moving	move	VERB
easat-224	242	11	mass	mass	NOUN
easat-224	242	12	for	for	ADP
easat-224	242	13	elastic	elastic	ADJ
easat-224	242	14	-	-	PUNCT
easat-224	242	15	elastic	elastic	ADJ
easat-224	242	16	uniform	uniform	NOUN
easat-224	242	17	rayleigh	rayleigh	PROPN
easat-224	242	18	beam	beam	PROPN
easat-224	242	19	for	for	ADP
easat-224	242	20	fixed	fix	VERB
easat-224	242	21	values	value	NOUN
easat-224	242	22	of	of	ADP
easat-224	242	23	𝑺𝒐	𝑺𝒐	PROPN
easat-224	242	24	,	,	PUNCT
easat-224	242	25	𝑵𝒐	𝑵𝒐	PROPN
easat-224	242	26	,	,	PUNCT
easat-224	242	27	𝑹𝒐	𝑹𝒐	PROPN
easat-224	242	28	,	,	PUNCT
easat-224	242	29	and	and	CCONJ
easat-224	242	30	𝓗.	𝓗.	PROPN
easat-224	242	31	5	5	NUM
easat-224	242	32	.	.	PUNCT
easat-224	242	33	conclusion	conclusion	NOUN
easat-224	242	34	in	in	ADP
easat-224	242	35	this	this	DET
easat-224	242	36	research	research	NOUN
easat-224	242	37	work	work	NOUN
easat-224	242	38	,	,	PUNCT
easat-224	242	39	the	the	DET
easat-224	242	40	problem	problem	NOUN
easat-224	242	41	associating	associate	VERB
easat-224	242	42	with	with	ADP
easat-224	242	43	the	the	DET
easat-224	242	44	dynamic	dynamic	ADJ
easat-224	242	45	response	response	NOUN
easat-224	242	46	to	to	ADP
easat-224	242	47	moving	move	VERB
easat-224	242	48	distributed	distribute	VERB
easat-224	242	49	masses	masse	NOUN
easat-224	242	50	of	of	ADP
easat-224	242	51	pre	pre	ADJ
easat-224	242	52	-	-	ADJ
easat-224	242	53	stressed	stressed	ADJ
easat-224	242	54	uniform	uniform	ADJ
easat-224	242	55	rayleigh	rayleigh	PROPN
easat-224	242	56	beam	beam	PROPN
easat-224	242	57	resting	rest	VERB
easat-224	242	58	on	on	ADP
easat-224	242	59	variable	variable	ADJ
easat-224	242	60	elastic	elastic	ADJ
easat-224	242	61	pasternak	pasternak	PROPN
easat-224	242	62	foundation	foundation	NOUN
easat-224	242	63	has	have	AUX
easat-224	242	64	been	be	AUX
easat-224	242	65	studied	study	VERB
easat-224	242	66	.	.	PUNCT
easat-224	243	1	the	the	DET
easat-224	243	2	closed	close	VERB
easat-224	243	3	form	form	NOUN
easat-224	243	4	solutions	solution	NOUN
easat-224	243	5	of	of	ADP
easat-224	243	6	the	the	DET
easat-224	243	7	fourth	fourth	ADJ
easat-224	243	8	order	order	NOUN
easat-224	243	9	partial	partial	ADJ
easat-224	243	10	differential	differential	ADJ
easat-224	243	11	equations	equation	NOUN
easat-224	243	12	with	with	ADP
easat-224	243	13	variable	variable	NOUN
easat-224	243	14	and	and	CCONJ
easat-224	243	15	singular	singular	ADJ
easat-224	243	16	co	co	NOUN
easat-224	243	17	-	-	NOUN
easat-224	243	18	efficients	efficient	NOUN
easat-224	243	19	are	be	AUX
easat-224	243	20	obtained	obtain	VERB
easat-224	243	21	for	for	ADP
easat-224	243	22	both	both	DET
easat-224	243	23	cases	case	NOUN
easat-224	243	24	of	of	ADP
easat-224	243	25	moving	move	VERB
easat-224	243	26	force	force	NOUN
easat-224	243	27	and	and	CCONJ
easat-224	243	28	moving	move	VERB
easat-224	243	29	mass	mass	NOUN
easat-224	243	30	.	.	PUNCT
easat-224	244	1	from	from	ADP
easat-224	244	2	the	the	DET
easat-224	244	3	closed	closed	ADJ
easat-224	244	4	form	form	NOUN
easat-224	244	5	solutions	solution	NOUN
easat-224	244	6	obtained	obtain	VERB
easat-224	244	7	,	,	PUNCT
easat-224	244	8	the	the	DET
easat-224	244	9	conditions	condition	NOUN
easat-224	244	10	of	of	ADP
easat-224	244	11	resonance	resonance	NOUN
easat-224	244	12	are	be	AUX
easat-224	244	13	obtained	obtain	VERB
easat-224	244	14	for	for	ADP
easat-224	244	15	both	both	DET
easat-224	244	16	moving	move	VERB
easat-224	244	17	force	force	NOUN
easat-224	244	18	and	and	CCONJ
easat-224	244	19	moving	move	VERB
easat-224	244	20	mass	mass	NOUN
easat-224	244	21	.	.	PUNCT
easat-224	245	1	also	also	ADV
easat-224	245	2	from	from	ADP
easat-224	245	3	the	the	DET
easat-224	245	4	closed	closed	ADJ
easat-224	245	5	form	form	NOUN
easat-224	245	6	solutions	solution	NOUN
easat-224	245	7	,	,	PUNCT
easat-224	245	8	the	the	DET
easat-224	245	9	effects	effect	NOUN
easat-224	245	10	of	of	ADP
easat-224	245	11	beam	beam	NOUN
easat-224	245	12	parameters	parameter	NOUN
easat-224	245	13	such	such	ADJ
easat-224	245	14	as	as	ADP
easat-224	245	15	rotatory	rotatory	ADJ
easat-224	245	16	inertia	inertia	NOUN
easat-224	245	17	,	,	PUNCT
easat-224	245	18	axial	axial	ADJ
easat-224	245	19	force	force	NOUN
easat-224	245	20	,	,	PUNCT
easat-224	245	21	shear	shear	NOUN
easat-224	245	22	modulus	modulus	NOUN
easat-224	245	23	and	and	CCONJ
easat-224	245	24	foundation	foundation	NOUN
easat-224	245	25	modulus	modulus	NOUN
easat-224	245	26	on	on	ADP
easat-224	245	27	the	the	DET
easat-224	245	28	beam	beam	NOUN
easat-224	245	29	for	for	ADP
easat-224	245	30	both	both	DET
easat-224	245	31	cases	case	NOUN
easat-224	245	32	of	of	ADP
easat-224	245	33	moving	move	VERB
easat-224	245	34	distributed	distribute	VERB
easat-224	245	35	force	force	NOUN
easat-224	245	36	and	and	CCONJ
easat-224	245	37	moving	move	VERB
easat-224	245	38	distributed	distribute	VERB
easat-224	245	39	mass	mass	NOUN
easat-224	245	40	were	be	AUX
easat-224	245	41	investigated	investigate	VERB
easat-224	245	42	.	.	PUNCT
easat-224	246	1	references	reference	NOUN
easat-224	246	2	[	[	X
easat-224	246	3	1	1	NUM
easat-224	246	4	]	]	X
easat-224	246	5	l.	l.	PROPN
easat-224	246	6	fryba	fryba	PROPN
easat-224	246	7	,	,	PUNCT
easat-224	246	8	vibration	vibration	NOUN
easat-224	246	9	of	of	ADP
easat-224	246	10	solids	solid	NOUN
easat-224	246	11	and	and	CCONJ
easat-224	246	12	structures	structure	NOUN
easat-224	246	13	under	under	ADP
easat-224	246	14	moving	move	VERB
easat-224	246	15	loads	load	NOUN
easat-224	246	16	groningen	groningen	X
easat-224	246	17	,	,	PUNCT
easat-224	246	18	netherlands	netherlands	PROPN
easat-224	246	19	:	:	PUNCT
easat-224	246	20	noordhoff	noordhoff	PROPN
easat-224	246	21	international	international	PROPN
easat-224	246	22	publishing	publishing	PROPN
easat-224	246	23	groningen	groningen	PROPN
easat-224	246	24	,	,	PUNCT
easat-224	246	25	1972	1972	NUM
easat-224	246	26	.	.	PUNCT
easat-224	247	1	[	[	X
easat-224	247	2	2	2	X
easat-224	247	3	]	]	PUNCT
easat-224	247	4	j.	j.	PROPN
easat-224	247	5	gbedeyan	gbedeyan	PROPN
easat-224	247	6	and	and	CCONJ
easat-224	247	7	m.	m.	PROPN
easat-224	247	8	dada	dada	PROPN
easat-224	247	9	,	,	PUNCT
easat-224	247	10	"	"	PUNCT
easat-224	247	11	dynamic	dynamic	ADJ
easat-224	247	12	response	response	NOUN
easat-224	247	13	of	of	ADP
easat-224	247	14	plates	plate	NOUN
easat-224	247	15	on	on	ADP
easat-224	247	16	pasternak	pasternak	PROPN
easat-224	247	17	foundation	foundation	PROPN
easat-224	247	18	to	to	PART
easat-224	247	19	distributed	distribute	VERB
easat-224	247	20	moving	moving	NOUN
easat-224	247	21	load	load	NOUN
easat-224	247	22	,	,	PUNCT
easat-224	247	23	"	"	PUNCT
easat-224	247	24	journal	journal	NOUN
easat-224	247	25	of	of	ADP
easat-224	247	26	the	the	DET
easat-224	247	27	nigerian	nigerian	PROPN
easat-224	247	28	association	association	PROPN
easat-224	247	29	of	of	ADP
easat-224	247	30	mathematical	mathematical	ADJ
easat-224	247	31	physics	physics	NOUN
easat-224	247	32	,	,	PUNCT
easat-224	247	33	vol	vol	NOUN
easat-224	247	34	.	.	PROPN
easat-224	247	35	5	5	NUM
easat-224	247	36	,	,	PUNCT
easat-224	247	37	pp	pp	ADJ
easat-224	247	38	.	.	PUNCT
easat-224	248	1	185	185	NUM
easat-224	248	2	-	-	SYM
easat-224	248	3	200	200	NUM
easat-224	248	4	,	,	PUNCT
easat-224	248	5	2001	2001	NUM
easat-224	248	6	.	.	PUNCT
easat-224	249	1	[	[	X
easat-224	249	2	3	3	X
easat-224	249	3	]	]	X
easat-224	249	4	j.	j.	PROPN
easat-224	249	5	gbadeyan	gbadeyan	PROPN
easat-224	249	6	and	and	CCONJ
easat-224	249	7	s.	s.	PROPN
easat-224	249	8	oni	oni	PROPN
easat-224	249	9	,	,	PUNCT
easat-224	249	10	"	"	PUNCT
easat-224	249	11	dynamic	dynamic	ADJ
easat-224	249	12	behaviour	behaviour	NOUN
easat-224	249	13	of	of	ADP
easat-224	249	14	beams	beam	NOUN
easat-224	249	15	and	and	CCONJ
easat-224	249	16	rectangular	rectangular	ADJ
easat-224	249	17	plates	plate	NOUN
easat-224	249	18	under	under	ADP
easat-224	249	19	moving	move	VERB
easat-224	249	20	loads	load	NOUN
easat-224	249	21	,	,	PUNCT
easat-224	249	22	"	"	PUNCT
easat-224	249	23	journal	journal	NOUN
easat-224	249	24	of	of	ADP
easat-224	249	25	sound	sound	NOUN
easat-224	249	26	and	and	CCONJ
easat-224	249	27	vibration	vibration	NOUN
easat-224	249	28	,	,	PUNCT
easat-224	249	29	vol	vol	NOUN
easat-224	249	30	.	.	PROPN
easat-224	249	31	182	182	NUM
easat-224	249	32	,	,	PUNCT
easat-224	249	33	no	no	INTJ
easat-224	249	34	.	.	NOUN
easat-224	249	35	5	5	NUM
easat-224	249	36	,	,	PUNCT
easat-224	249	37	pp	pp	ADJ
easat-224	249	38	.	.	PUNCT
easat-224	250	1	677	677	NUM
easat-224	250	2	-	-	SYM
easat-224	250	3	695	695	NUM
easat-224	250	4	,	,	PUNCT
easat-224	250	5	1995	1995	NUM
easat-224	250	6	.	.	PUNCT
easat-224	251	1	https://doi.org/10.1006/jsvi.1995.0226	https://doi.org/10.1006/jsvi.1995.0226	PROPN
easat-224	252	1	[	[	X
easat-224	252	2	4	4	X
easat-224	252	3	]	]	PUNCT
easat-224	252	4	a.	a.	NOUN
easat-224	252	5	yavari	yavari	PROPN
easat-224	252	6	,	,	PUNCT
easat-224	252	7	s.	s.	PROPN
easat-224	252	8	sarkani	sarkani	PROPN
easat-224	252	9	,	,	PUNCT
easat-224	252	10	and	and	CCONJ
easat-224	252	11	j.	j.	PROPN
easat-224	252	12	reddy	reddy	PROPN
easat-224	252	13	,	,	PUNCT
easat-224	252	14	"	"	PUNCT
easat-224	252	15	generalized	generalized	ADJ
easat-224	252	16	solutions	solution	NOUN
easat-224	252	17	of	of	ADP
easat-224	252	18	beams	beam	NOUN
easat-224	252	19	with	with	ADP
easat-224	252	20	jump	jump	NOUN
easat-224	252	21	discontinuities	discontinuity	NOUN
easat-224	252	22	on	on	ADP
easat-224	252	23	elastic	elastic	ADJ
easat-224	252	24	foundations	foundation	NOUN
easat-224	252	25	,	,	PUNCT
easat-224	252	26	"	"	PUNCT
easat-224	252	27	archive	archive	NOUN
easat-224	252	28	of	of	ADP
easat-224	252	29	applied	apply	VERB
easat-224	252	30	mechanics	mechanic	NOUN
easat-224	252	31	,	,	PUNCT
easat-224	252	32	vol	vol	NOUN
easat-224	252	33	.	.	PROPN
easat-224	252	34	71	71	NUM
easat-224	252	35	,	,	PUNCT
easat-224	252	36	pp	pp	ADJ
easat-224	252	37	.	.	PUNCT
easat-224	252	38	625	625	NUM
easat-224	252	39	-	-	SYM
easat-224	252	40	639	639	NUM
easat-224	252	41	,	,	PUNCT
easat-224	252	42	2001	2001	NUM
easat-224	252	43	.	.	PUNCT
easat-224	252	44	https://doi.org/10.1007/s004190100169	https://doi.org/10.1007/s004190100169	PUNCT
easat-224	253	1	[	[	X
easat-224	253	2	5	5	NUM
easat-224	253	3	]	]	X
easat-224	253	4	j.-h	j.-h	NOUN
easat-224	253	5	.	.	PUNCT
easat-224	253	6	yin	yin	NOUN
easat-224	253	7	,	,	PUNCT
easat-224	253	8	"	"	PUNCT
easat-224	253	9	closed	closed	ADJ
easat-224	253	10	-	-	PUNCT
easat-224	253	11	form	form	NOUN
easat-224	253	12	solution	solution	NOUN
easat-224	253	13	for	for	ADP
easat-224	253	14	reinforced	reinforce	VERB
easat-224	253	15	timoshenko	timoshenko	NOUN
easat-224	253	16	beam	beam	NOUN
easat-224	253	17	on	on	ADP
easat-224	253	18	elastic	elastic	ADJ
easat-224	253	19	foundation	foundation	NOUN
easat-224	253	20	,	,	PUNCT
easat-224	253	21	"	"	PUNCT
easat-224	253	22	journal	journal	NOUN
easat-224	253	23	of	of	ADP
easat-224	253	24	engineering	engineering	NOUN
easat-224	253	25	mechanics	mechanic	NOUN
easat-224	253	26	,	,	PUNCT
easat-224	253	27	vol	vol	NOUN
easat-224	253	28	.	.	PROPN
easat-224	253	29	126	126	NUM
easat-224	253	30	,	,	PUNCT
easat-224	253	31	no	no	INTJ
easat-224	253	32	.	.	NOUN
easat-224	253	33	8	8	NUM
easat-224	253	34	,	,	PUNCT
easat-224	253	35	pp	pp	ADJ
easat-224	253	36	.	.	PUNCT
easat-224	254	1	868	868	NUM
easat-224	254	2	-	-	SYM
easat-224	254	3	874	874	NUM
easat-224	254	4	,	,	PUNCT
easat-224	254	5	2000	2000	NUM
easat-224	254	6	.	.	PUNCT
easat-224	255	1	https://doi.org/10.1061/(asce)0733-9399(2000)126:8(868	https://doi.org/10.1061/(asce)0733-9399(2000)126:8(868	VERB
easat-224	255	2	)	)	PUNCT
easat-224	256	1	[	[	X
easat-224	256	2	6	6	NUM
easat-224	256	3	]	]	PUNCT
easat-224	256	4	i.	i.	NOUN
easat-224	256	5	teodoru	teodoru	NOUN
easat-224	256	6	,	,	PUNCT
easat-224	256	7	"	"	PUNCT
easat-224	256	8	analysis	analysis	NOUN
easat-224	256	9	of	of	ADP
easat-224	256	10	beams	beam	NOUN
easat-224	256	11	on	on	ADP
easat-224	256	12	elastic	elastic	ADJ
easat-224	256	13	foundation	foundation	NOUN
easat-224	256	14	:	:	PUNCT
easat-224	256	15	the	the	DET
easat-224	256	16	finite	finite	ADJ
easat-224	256	17	difference	difference	NOUN
easat-224	256	18	approach	approach	NOUN
easat-224	256	19	,	,	PUNCT
easat-224	256	20	"	"	PUNCT
easat-224	256	21	presented	present	VERB
easat-224	256	22	at	at	ADP
easat-224	256	23	the	the	DET
easat-224	256	24	9th	9th	ADJ
easat-224	256	25	technical	technical	ADJ
easat-224	256	26	conference	conference	NOUN
easat-224	256	27	for	for	ADP
easat-224	256	28	doctoral	doctoral	ADJ
easat-224	256	29	study	study	NOUN
easat-224	256	30	,	,	PUNCT
easat-224	256	31	brno	brno	PROPN
easat-224	256	32	university	university	PROPN
easat-224	256	33	of	of	ADP
easat-224	256	34	technology	technology	NOUN
easat-224	256	35	,	,	PUNCT
easat-224	256	36	czech	czech	PROPN
easat-224	256	37	republic	republic	NOUN
easat-224	256	38	,	,	PUNCT
easat-224	256	39	2007	2007	NUM
easat-224	256	40	.	.	PUNCT
easat-224	257	1	[	[	X
easat-224	257	2	7	7	X
easat-224	257	3	]	]	X
easat-224	257	4	s.	s.	PROPN
easat-224	257	5	oni	oni	PROPN
easat-224	257	6	and	and	CCONJ
easat-224	257	7	t.	t.	PROPN
easat-224	257	8	awodola	awodola	PROPN
easat-224	257	9	,	,	PUNCT
easat-224	257	10	"	"	PUNCT
easat-224	257	11	vibrations	vibration	NOUN
easat-224	257	12	under	under	ADP
easat-224	257	13	a	a	DET
easat-224	257	14	moving	move	VERB
easat-224	257	15	load	load	NOUN
easat-224	257	16	of	of	ADP
easat-224	257	17	a	a	DET
easat-224	257	18	non	non	ADJ
easat-224	257	19	-	-	ADJ
easat-224	257	20	uniform	uniform	ADJ
easat-224	257	21	rayleigh	rayleigh	PROPN
easat-224	257	22	beam	beam	PROPN
easat-224	257	23	on	on	ADP
easat-224	257	24	variable	variable	ADJ
easat-224	257	25	elastic	elastic	ADJ
easat-224	257	26	foundation	foundation	NOUN
easat-224	257	27	,	,	PUNCT
easat-224	257	28	"	"	PUNCT
easat-224	257	29	journal	journal	NOUN
easat-224	257	30	of	of	ADP
easat-224	257	31	nigerian	nigerian	PROPN
easat-224	257	32	association	association	PROPN
easat-224	257	33	of	of	ADP
easat-224	257	34	mathematical	mathematical	ADJ
easat-224	257	35	physics	physics	NOUN
easat-224	257	36	,	,	PUNCT
easat-224	257	37	vol	vol	NOUN
easat-224	257	38	.	.	PROPN
easat-224	257	39	7	7	NUM
easat-224	257	40	,	,	PUNCT
easat-224	257	41	pp	pp	ADJ
easat-224	257	42	.	.	PUNCT
easat-224	258	1	191	191	NUM
easat-224	258	2	-	-	SYM
easat-224	258	3	206	206	NUM
easat-224	258	4	,	,	PUNCT
easat-224	258	5	2003	2003	NUM
easat-224	258	6	.	.	PUNCT
easat-224	259	1	[	[	X
easat-224	259	2	8	8	X
easat-224	259	3	]	]	PUNCT
easat-224	259	4	t.	t.	PROPN
easat-224	259	5	awodola	awodola	PROPN
easat-224	259	6	and	and	CCONJ
easat-224	259	7	s.	s.	PROPN
easat-224	259	8	oni	oni	PROPN
easat-224	259	9	,	,	PUNCT
easat-224	259	10	"	"	PUNCT
easat-224	259	11	dynamic	dynamic	ADJ
easat-224	259	12	response	response	NOUN
easat-224	259	13	to	to	ADP
easat-224	259	14	moving	move	VERB
easat-224	259	15	masses	masse	NOUN
easat-224	259	16	of	of	ADP
easat-224	259	17	rectangular	rectangular	ADJ
easat-224	259	18	plates	plate	NOUN
easat-224	259	19	with	with	ADP
easat-224	259	20	general	general	ADJ
easat-224	259	21	boundary	boundary	ADJ
easat-224	259	22	conditions	condition	NOUN
easat-224	259	23	and	and	CCONJ
easat-224	259	24	resting	rest	VERB
easat-224	259	25	on	on	ADP
easat-224	259	26	variable	variable	ADJ
easat-224	259	27	winkler	winkler	PROPN
easat-224	259	28	foundation	foundation	PROPN
easat-224	259	29	,	,	PUNCT
easat-224	259	30	"	"	PUNCT
easat-224	259	31	latin	latin	ADJ
easat-224	259	32	american	american	ADJ
easat-224	259	33	journal	journal	PROPN
easat-224	259	34	of	of	ADP
easat-224	259	35	solids	solid	NOUN
easat-224	259	36	and	and	CCONJ
easat-224	259	37	structures	structure	NOUN
easat-224	259	38	,	,	PUNCT
easat-224	259	39	vol	vol	NOUN
easat-224	259	40	.	.	PROPN
easat-224	259	41	10	10	NUM
easat-224	259	42	,	,	PUNCT
easat-224	259	43	pp	pp	ADJ
easat-224	259	44	.	.	PUNCT
easat-224	260	1	301	301	NUM
easat-224	260	2	-	-	SYM
easat-224	260	3	322	322	NUM
easat-224	260	4	,	,	PUNCT
easat-224	260	5	2013	2013	NUM
easat-224	260	6	.	.	PUNCT
easat-224	261	1	https://doi.org/10.1590/s1679-78252013000200005	https://doi.org/10.1590/s1679-78252013000200005	PROPN
easat-224	262	1	[	[	X
easat-224	262	2	9	9	NUM
easat-224	262	3	]	]	PUNCT
easat-224	262	4	s.	s.	PROPN
easat-224	262	5	oni	oni	PROPN
easat-224	262	6	and	and	CCONJ
easat-224	262	7	b.	b.	PROPN
easat-224	262	8	omolofe	omolofe	VERB
easat-224	262	9	,	,	PUNCT
easat-224	262	10	"	"	PUNCT
easat-224	262	11	dynamic	dynamic	ADJ
easat-224	262	12	analysis	analysis	NOUN
easat-224	262	13	of	of	ADP
easat-224	262	14	a	a	DET
easat-224	262	15	prestressed	prestressed	ADJ
easat-224	262	16	elastic	elastic	ADJ
easat-224	262	17	beam	beam	NOUN
easat-224	262	18	with	with	ADP
easat-224	262	19	general	general	ADJ
easat-224	262	20	boundary	boundary	ADJ
easat-224	262	21	conditions	condition	NOUN
easat-224	262	22	under	under	ADP
easat-224	262	23	moving	move	VERB
easat-224	262	24	loads	load	NOUN
easat-224	262	25	at	at	ADP
easat-224	262	26	varying	vary	VERB
easat-224	262	27	velocities	velocity	NOUN
easat-224	262	28	,	,	PUNCT
easat-224	262	29	"	"	PUNCT
easat-224	262	30	journal	journal	NOUN
easat-224	262	31	of	of	ADP
easat-224	262	32	engineering	engineering	NOUN
easat-224	262	33	and	and	CCONJ
easat-224	262	34	engineering	engineering	NOUN
easat-224	262	35	technology	technology	NOUN
easat-224	262	36	,	,	PUNCT
easat-224	262	37	futa	futa	PROPN
easat-224	262	38	,	,	PUNCT
easat-224	262	39	vol	vol	NOUN
easat-224	262	40	.	.	PROPN
easat-224	263	1	4	4	NUM
easat-224	263	2	,	,	PUNCT
easat-224	263	3	no	no	INTJ
easat-224	263	4	.	.	NOUN
easat-224	263	5	1	1	NUM
easat-224	263	6	,	,	PUNCT
easat-224	263	7	pp	pp	ADJ
easat-224	263	8	.	.	PUNCT
easat-224	264	1	55	55	NUM
easat-224	264	2	-	-	SYM
easat-224	264	3	72	72	NUM
easat-224	264	4	,	,	PUNCT
easat-224	264	5	2005	2005	NUM
easat-224	264	6	.	.	PUNCT
easat-224	265	1	[	[	X
easat-224	265	2	10	10	NUM
easat-224	265	3	]	]	X
easat-224	265	4	w.	w.	PROPN
easat-224	265	5	li	li	PROPN
easat-224	265	6	,	,	PUNCT
easat-224	265	7	x.	x.	PROPN
easat-224	265	8	zhang	zhang	PROPN
easat-224	265	9	,	,	PUNCT
easat-224	265	10	j.	j.	PROPN
easat-224	265	11	du	du	PROPN
easat-224	265	12	,	,	PUNCT
easat-224	265	13	and	and	CCONJ
easat-224	265	14	z.	z.	PROPN
easat-224	265	15	liu	liu	PROPN
easat-224	265	16	,	,	PUNCT
easat-224	265	17	"	"	PUNCT
easat-224	265	18	an	an	DET
easat-224	265	19	exact	exact	ADJ
easat-224	265	20	series	series	NOUN
easat-224	265	21	solution	solution	NOUN
easat-224	265	22	for	for	ADP
easat-224	265	23	the	the	DET
easat-224	265	24	transverse	transverse	ADJ
easat-224	265	25	vibration	vibration	NOUN
easat-224	265	26	of	of	ADP
easat-224	265	27	rectangular	rectangular	ADJ
easat-224	265	28	plates	plate	NOUN
easat-224	265	29	with	with	ADP
easat-224	265	30	general	general	ADJ
easat-224	265	31	elastic	elastic	ADJ
easat-224	265	32	boundary	boundary	NOUN
easat-224	265	33	supports	support	NOUN
easat-224	265	34	,	,	PUNCT
easat-224	265	35	"	"	PUNCT
easat-224	265	36	journal	journal	NOUN
easat-224	265	37	of	of	ADP
easat-224	265	38	sound	sound	NOUN
easat-224	265	39	and	and	CCONJ
easat-224	265	40	vibration	vibration	NOUN
easat-224	265	41	,	,	PUNCT
easat-224	265	42	vol	vol	NOUN
easat-224	265	43	.	.	PROPN
easat-224	265	44	321	321	NUM
easat-224	265	45	,	,	PUNCT
easat-224	265	46	no	no	NOUN
easat-224	265	47	.	.	NOUN
easat-224	265	48	1	1	NUM
easat-224	265	49	-	-	SYM
easat-224	265	50	2	2	NUM
easat-224	265	51	,	,	PUNCT
easat-224	265	52	pp	pp	ADJ
easat-224	265	53	.	.	PUNCT
easat-224	266	1	254	254	NUM
easat-224	266	2	-	-	SYM
easat-224	266	3	269	269	NUM
easat-224	266	4	,	,	PUNCT
easat-224	266	5	2009	2009	NUM
easat-224	266	6	.	.	PUNCT
easat-224	267	1	https://doi.org/10.1016/j.jsv.2008.09.035	https://doi.org/10.1016/j.jsv.2008.09.035	X
easat-224	268	1	[	[	X
easat-224	268	2	11	11	NUM
easat-224	268	3	]	]	PUNCT
easat-224	268	4	m.-h	m.-h	NOUN
easat-224	268	5	.	.	PUNCT
easat-224	269	1	hsu	hsu	PROPN
easat-224	269	2	,	,	PUNCT
easat-224	269	3	"	"	PUNCT
easat-224	269	4	vibration	vibration	NOUN
easat-224	269	5	analysis	analysis	NOUN
easat-224	269	6	of	of	ADP
easat-224	269	7	non	non	ADJ
easat-224	269	8	-	-	ADJ
easat-224	269	9	uniform	uniform	ADJ
easat-224	269	10	beams	beam	NOUN
easat-224	269	11	resting	rest	VERB
easat-224	269	12	on	on	ADP
easat-224	269	13	elastic	elastic	ADJ
easat-224	269	14	foundations	foundation	NOUN
easat-224	269	15	using	use	VERB
easat-224	269	16	the	the	DET
easat-224	269	17	spline	spline	NOUN
easat-224	269	18	collocation	collocation	NOUN
easat-224	269	19	method	method	NOUN
easat-224	269	20	,	,	PUNCT
easat-224	269	21	"	"	PUNCT
easat-224	269	22	journal	journal	NOUN
easat-224	269	23	of	of	ADP
easat-224	269	24	applied	apply	VERB
easat-224	269	25	science	science	NOUN
easat-224	269	26	and	and	CCONJ
easat-224	269	27	engineering	engineering	NOUN
easat-224	269	28	,	,	PUNCT
easat-224	269	29	vol	vol	NOUN
easat-224	269	30	.	.	PROPN
easat-224	269	31	12	12	NUM
easat-224	269	32	,	,	PUNCT
easat-224	269	33	no	no	INTJ
easat-224	269	34	.	.	NOUN
easat-224	269	35	2	2	NUM
easat-224	269	36	,	,	PUNCT
easat-224	269	37	pp	pp	ADJ
easat-224	269	38	.	.	PUNCT
easat-224	270	1	113	113	NUM
easat-224	270	2	-	-	SYM
easat-224	270	3	122	122	NUM
easat-224	270	4	,	,	PUNCT
easat-224	270	5	2009	2009	NUM
easat-224	270	6	.	.	PUNCT
easat-224	271	1	https://doi.org/10.51400/27096998.1964	https://doi.org/10.51400/27096998.1964	PRON
easat-224	272	1	[	[	X
easat-224	272	2	12	12	NUM
easat-224	272	3	]	]	X
easat-224	272	4	i.	i.	NOUN
easat-224	272	5	esen	esen	PROPN
easat-224	272	6	,	,	PUNCT
easat-224	272	7	"	"	PUNCT
easat-224	272	8	dynamic	dynamic	ADJ
easat-224	272	9	response	response	NOUN
easat-224	272	10	of	of	ADP
easat-224	272	11	a	a	DET
easat-224	272	12	beam	beam	NOUN
easat-224	272	13	due	due	ADP
easat-224	272	14	to	to	ADP
easat-224	272	15	an	an	DET
easat-224	272	16	accelerating	accelerate	VERB
easat-224	272	17	moving	move	VERB
easat-224	272	18	mass	mass	NOUN
easat-224	272	19	using	use	VERB
easat-224	272	20	moving	move	VERB
easat-224	272	21	finite	finite	ADJ
easat-224	272	22	element	element	NOUN
easat-224	272	23	approximation	approximation	NOUN
easat-224	272	24	,	,	PUNCT
easat-224	272	25	"	"	PUNCT
easat-224	272	26	mathematical	mathematical	ADJ
easat-224	272	27	and	and	CCONJ
easat-224	272	28	computational	computational	ADJ
easat-224	272	29	applications	application	NOUN
easat-224	272	30	,	,	PUNCT
easat-224	272	31	vol	vol	NOUN
easat-224	272	32	.	.	PROPN
easat-224	272	33	16	16	NUM
easat-224	272	34	,	,	PUNCT
easat-224	272	35	no	no	INTJ
easat-224	272	36	.	.	NOUN
easat-224	272	37	1	1	NUM
easat-224	272	38	,	,	PUNCT
easat-224	272	39	pp	pp	ADJ
easat-224	272	40	.	.	PUNCT
easat-224	273	1	171	171	NUM
easat-224	273	2	-	-	SYM
easat-224	273	3	182	182	NUM
easat-224	273	4	,	,	PUNCT
easat-224	273	5	2011	2011	NUM
easat-224	273	6	.	.	PUNCT
easat-224	274	1	https://doi.org/10.3390/mca16010171	https://doi.org/10.3390/mca16010171	PRON
easat-224	275	1	[	[	X
easat-224	275	2	13	13	NUM
easat-224	275	3	]	]	PUNCT
easat-224	275	4	m.	m.	NOUN
easat-224	275	5	kargarnovin	kargarnovin	PROPN
easat-224	275	6	and	and	CCONJ
easat-224	275	7	d.	d.	PROPN
easat-224	275	8	younesian	younesian	PROPN
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easat-224	275	17	foundation	foundation	PROPN
easat-224	275	18	under	under	ADP
easat-224	275	19	moving	move	VERB
easat-224	275	20	load	load	NOUN
easat-224	275	21	,	,	PUNCT
easat-224	275	22	"	"	PUNCT
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easat-224	275	24	research	research	NOUN
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easat-224	276	2	,	,	PUNCT
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easat-224	276	4	.	.	NOUN
easat-224	276	5	6	6	NUM
easat-224	276	6	,	,	PUNCT
easat-224	276	7	pp	pp	ADJ
easat-224	276	8	.	.	PUNCT
easat-224	277	1	713	713	NUM
easat-224	277	2	-	-	SYM
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easat-224	277	4	,	,	PUNCT
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easat-224	277	6	.	.	PUNCT
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easat-224	279	2	14	14	NUM
easat-224	279	3	]	]	PUNCT
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easat-224	279	7	a.	a.	NOUN
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easat-224	279	9	,	,	PUNCT
easat-224	279	10	"	"	PUNCT
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easat-224	279	14	inertial	inertial	ADJ
easat-224	279	15	correction	correction	NOUN
easat-224	279	16	factor	factor	NOUN
easat-224	279	17	on	on	ADP
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easat-224	279	46	,	,	PUNCT
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easat-224	280	1	1	1	NUM
easat-224	280	2	-	-	SYM
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easat-224	282	7	a.	a.	NOUN
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easat-224	282	9	,	,	PUNCT
easat-224	282	10	"	"	PUNCT
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easat-224	282	12	response	response	NOUN
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easat-224	282	15	-	-	PUNCT
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easat-224	282	31	"	"	PUNCT
easat-224	282	32	asian	asian	ADJ
easat-224	282	33	research	research	NOUN
easat-224	282	34	journal	journal	NOUN
easat-224	282	35	of	of	ADP
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easat-224	283	2	,	,	PUNCT
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easat-224	283	4	.	.	NOUN
easat-224	283	5	1	1	NUM
easat-224	283	6	,	,	PUNCT
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easat-224	283	8	.	.	PROPN
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easat-224	284	2	,	,	PUNCT
easat-224	284	3	2017	2017	NUM
easat-224	284	4	.	.	PUNCT
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easat-224	286	17	beam	beam	NOUN
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easat-224	286	23	under	under	ADP
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easat-224	286	38	mathematics	mathematics	PROPN
easat-224	286	39	,	,	PUNCT
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easat-224	286	41	.	.	PROPN
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easat-224	287	2	-	-	SYM
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easat-224	287	4	,	,	PUNCT
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easat-224	289	9	https://doi.org/10.1016/j.mechrescom.2004.05.002	https://doi.org/10.1016/j.mechrescom.2004.05.002	VERB
easat-224	289	10	https://doi.org/10.9734/arjom/2017/31271	https://doi.org/10.9734/arjom/2017/31271	PROPN
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