id	sid	tid	token	lemma	pos
ajird-524	1	1	american	american	PROPN
ajird-524	1	2	journal	journal	PROPN
ajird-524	1	3	of	of	ADP
ajird-524	1	4	interdisciplinary	interdisciplinary	ADJ
ajird-524	1	5	research	research	NOUN
ajird-524	1	6	and	and	CCONJ
ajird-524	1	7	development	development	NOUN
ajird-524	1	8	issn	issn	PROPN
ajird-524	1	9	online	online	NOUN
ajird-524	1	10	:	:	PUNCT
ajird-524	1	11	2771	2771	NUM
ajird-524	1	12	-	-	SYM
ajird-524	1	13	8948	8948	NUM
ajird-524	1	14	website	website	NOUN
ajird-524	1	15	:	:	PUNCT
ajird-524	1	16	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-524	1	17	volume	volume	NOUN
ajird-524	1	18	13	13	NUM
ajird-524	1	19	,	,	PUNCT
ajird-524	1	20	feb	feb	PROPN
ajird-524	1	21	.	.	PROPN
ajird-524	1	22	,	,	PUNCT
ajird-524	1	23	2023	2023	NUM
ajird-524	1	24	124	124	NUM
ajird-524	2	1	|	|	ADV
ajird-524	2	2	p	p	ADP
ajird-524	2	3	a	a	DET
ajird-524	2	4	g	g	PROPN
ajird-524	2	5	e	e	PROPN
ajird-524	2	6	numerical	numerical	PROPN
ajird-524	2	7	investigation	investigation	NOUN
ajird-524	2	8	of	of	ADP
ajird-524	2	9	interaction	interaction	NOUN
ajird-524	2	10	of	of	ADP
ajird-524	2	11	underground	underground	ADJ
ajird-524	2	12	structure	structure	NOUN
ajird-524	2	13	(	(	PUNCT
ajird-524	2	14	tunnels	tunnel	NOUN
ajird-524	2	15	)	)	PUNCT
ajird-524	2	16	with	with	ADP
ajird-524	2	17	elastic	elastic	ADJ
ajird-524	2	18	waves	wave	NOUN
ajird-524	2	19	propagated	propagate	VERB
ajird-524	2	20	in	in	ADP
ajird-524	2	21	ground	ground	NOUN
ajird-524	2	22	medium	medium	ADJ
ajird-524	2	23	gaynazarov	gaynazarov	PROPN
ajird-524	2	24	sultan	sultan	PROPN
ajird-524	2	25	national	national	PROPN
ajird-524	2	26	university	university	PROPN
ajird-524	2	27	of	of	ADP
ajird-524	2	28	uzbekistan	uzbekistan	PROPN
ajird-524	2	29	named	name	VERB
ajird-524	2	30	after	after	ADP
ajird-524	2	31	mirzo	mirzo	PROPN
ajird-524	2	32	ulugbek	ulugbek	PROPN
ajird-524	2	33	,	,	PUNCT
ajird-524	2	34	dr	dr	PROPN
ajird-524	2	35	.	.	PROPN
ajird-524	2	36	phys	phys	PROPN
ajird-524	2	37	.	.	PUNCT
ajird-524	3	1	math	math	NOUN
ajird-524	3	2	.	.	PUNCT
ajird-524	3	3	,	,	PUNCT
ajird-524	3	4	professor	professor	NOUN
ajird-524	3	5	of	of	ADP
ajird-524	3	6	the	the	DET
ajird-524	3	7	faculty	faculty	NOUN
ajird-524	3	8	«	«	PUNCT
ajird-524	3	9	applied	apply	VERB
ajird-524	3	10	mathematics	mathematic	NOUN
ajird-524	3	11	and	and	CCONJ
ajird-524	3	12	intellectual	intellectual	ADJ
ajird-524	3	13	technologies	technology	NOUN
ajird-524	3	14	»	»	PUNCT
ajird-524	3	15	gaynazarovsm@mail.ru	gaynazarovsm@mail.ru	AUX
ajird-524	3	16	rakhimdjanova	rakhimdjanova	VERB
ajird-524	3	17	nodira	nodira	PROPN
ajird-524	3	18	national	national	PROPN
ajird-524	3	19	university	university	PROPN
ajird-524	3	20	of	of	ADP
ajird-524	3	21	uzbekistan	uzbekistan	PROPN
ajird-524	3	22	named	name	VERB
ajird-524	3	23	after	after	ADP
ajird-524	3	24	mirzo	mirzo	NOUN
ajird-524	3	25	ulugbek	ulugbek	ADV
ajird-524	3	26	,	,	PUNCT
ajird-524	3	27	2nd	2nd	ADJ
ajird-524	3	28	year	year	NOUN
ajird-524	3	29	master	master	NOUN
ajird-524	3	30	student	student	NOUN
ajird-524	3	31	of	of	ADP
ajird-524	3	32	the	the	DET
ajird-524	3	33	faculty	faculty	NOUN
ajird-524	3	34	of	of	ADP
ajird-524	3	35	«	«	PUNCT
ajird-524	3	36	applied	applied	ADJ
ajird-524	3	37	mathematics	mathematic	NOUN
ajird-524	3	38	and	and	CCONJ
ajird-524	3	39	intellectual	intellectual	ADJ
ajird-524	3	40	technologies	technology	NOUN
ajird-524	3	41	»	»	PUNCT
ajird-524	3	42	nodiraziyo1990@gmail.ru	nodiraziyo1990@gmail.ru	VERB
ajird-524	3	43	abstract	abstract	NOUN
ajird-524	3	44	in	in	ADP
ajird-524	3	45	this	this	DET
ajird-524	3	46	article	article	NOUN
ajird-524	3	47	considers	consider	VERB
ajird-524	3	48	a	a	DET
ajird-524	3	49	dynamic	dynamic	ADJ
ajird-524	3	50	method	method	NOUN
ajird-524	3	51	for	for	ADP
ajird-524	3	52	calculating	calculate	VERB
ajird-524	3	53	the	the	DET
ajird-524	3	54	analysis	analysis	NOUN
ajird-524	3	55	of	of	ADP
ajird-524	3	56	an	an	DET
ajird-524	3	57	underground	underground	ADJ
ajird-524	3	58	structure	structure	NOUN
ajird-524	3	59	(	(	PUNCT
ajird-524	3	60	tunnels	tunnel	NOUN
ajird-524	3	61	)	)	PUNCT
ajird-524	3	62	interacting	interact	VERB
ajird-524	3	63	with	with	ADP
ajird-524	3	64	the	the	DET
ajird-524	3	65	soil	soil	NOUN
ajird-524	3	66	environment	environment	NOUN
ajird-524	3	67	.	.	PUNCT
ajird-524	4	1	on	on	ADP
ajird-524	4	2	the	the	DET
ajird-524	4	3	basis	basis	NOUN
ajird-524	4	4	of	of	ADP
ajird-524	4	5	numerical	numerical	PROPN
ajird-524	4	6	simulation	simulation	PROPN
ajird-524	4	7	,	,	PUNCT
ajird-524	4	8	a	a	DET
ajird-524	4	9	diffraction	diffraction	NOUN
ajird-524	4	10	pattern	pattern	NOUN
ajird-524	4	11	for	for	ADP
ajird-524	4	12	an	an	DET
ajird-524	4	13	underground	underground	ADJ
ajird-524	4	14	structure	structure	NOUN
ajird-524	4	15	(	(	PUNCT
ajird-524	4	16	tunnels	tunnel	NOUN
ajird-524	4	17	)	)	PUNCT
ajird-524	4	18	was	be	AUX
ajird-524	4	19	constructed	construct	VERB
ajird-524	4	20	.	.	PUNCT
ajird-524	5	1	keywords	keyword	NOUN
ajird-524	5	2	:	:	PUNCT
ajird-524	5	3	finite	finite	PROPN
ajird-524	5	4	element	element	NOUN
ajird-524	5	5	method	method	NOUN
ajird-524	5	6	,	,	PUNCT
ajird-524	5	7	newmark	newmark	NOUN
ajird-524	5	8	method	method	NOUN
ajird-524	5	9	,	,	PUNCT
ajird-524	5	10	bate	bate	NOUN
ajird-524	5	11	method	method	NOUN
ajird-524	5	12	,	,	PUNCT
ajird-524	5	13	stiffness	stiffness	ADJ
ajird-524	5	14	matrix	matrix	NOUN
ajird-524	5	15	,	,	PUNCT
ajird-524	5	16	damping	damp	VERB
ajird-524	5	17	matrix	matrix	NOUN
ajird-524	5	18	,	,	PUNCT
ajird-524	5	19	mass	mass	NOUN
ajird-524	5	20	matrix	matrix	NOUN
ajird-524	5	21	.	.	PUNCT
ajird-524	6	1	introduction	introduction	NOUN
ajird-524	6	2	seismic	seismic	ADJ
ajird-524	6	3	waves	wave	NOUN
ajird-524	6	4	vibrations	vibration	NOUN
ajird-524	6	5	of	of	ADP
ajird-524	6	6	rocks	rock	NOUN
ajird-524	6	7	in	in	ADP
ajird-524	6	8	the	the	DET
ajird-524	6	9	earth	earth	NOUN
ajird-524	6	10	,	,	PUNCT
ajird-524	6	11	resulting	result	VERB
ajird-524	6	12	from	from	ADP
ajird-524	6	13	natural	natural	ADJ
ajird-524	6	14	(	(	PUNCT
ajird-524	6	15	earthquakes	earthquake	NOUN
ajird-524	6	16	)	)	PUNCT
ajird-524	6	17	or	or	CCONJ
ajird-524	6	18	artificial	artificial	ADJ
ajird-524	6	19	processes	process	NOUN
ajird-524	6	20	of	of	ADP
ajird-524	6	21	their	their	PRON
ajird-524	6	22	excitation	excitation	NOUN
ajird-524	6	23	.	.	PUNCT
ajird-524	7	1	at	at	ADP
ajird-524	7	2	present	present	ADJ
ajird-524	7	3	,	,	PUNCT
ajird-524	7	4	the	the	DET
ajird-524	7	5	study	study	NOUN
ajird-524	7	6	of	of	ADP
ajird-524	7	7	seismic	seismic	ADJ
ajird-524	7	8	waves	wave	NOUN
ajird-524	7	9	generated	generate	VERB
ajird-524	7	10	by	by	ADP
ajird-524	7	11	earthquakes	earthquake	NOUN
ajird-524	7	12	is	be	AUX
ajird-524	7	13	necessary	necessary	ADJ
ajird-524	7	14	for	for	ADP
ajird-524	7	15	understanding	understand	VERB
ajird-524	7	16	the	the	DET
ajird-524	7	17	nature	nature	NOUN
ajird-524	7	18	of	of	ADP
ajird-524	7	19	earthquakes	earthquake	NOUN
ajird-524	7	20	and	and	CCONJ
ajird-524	7	21	their	their	PRON
ajird-524	7	22	prediction	prediction	NOUN
ajird-524	7	23	.	.	PUNCT
ajird-524	8	1	seismic	seismic	ADJ
ajird-524	8	2	waves	wave	NOUN
ajird-524	8	3	caused	cause	VERB
ajird-524	8	4	by	by	ADP
ajird-524	8	5	earthquakes	earthquake	NOUN
ajird-524	8	6	or	or	CCONJ
ajird-524	8	7	explosions	explosion	NOUN
ajird-524	8	8	elastic	elastic	ADJ
ajird-524	8	9	waves	wave	NOUN
ajird-524	8	10	propagating	propagate	VERB
ajird-524	8	11	in	in	ADP
ajird-524	8	12	the	the	DET
ajird-524	8	13	body	body	NOUN
ajird-524	8	14	of	of	ADP
ajird-524	8	15	the	the	DET
ajird-524	8	16	earth	earth	NOUN
ajird-524	8	17	whether	whether	SCONJ
ajird-524	8	18	.	.	PUNCT
ajird-524	9	1	of	of	ADP
ajird-524	9	2	the	the	DET
ajird-524	9	3	body	body	NOUN
ajird-524	9	4	waves	wave	NOUN
ajird-524	9	5	,	,	PUNCT
ajird-524	9	6	the	the	DET
ajird-524	9	7	primary	primary	NOUN
ajird-524	9	8	,	,	PUNCT
ajird-524	9	9	or	or	CCONJ
ajird-524	9	10	p	p	NOUN
ajird-524	9	11	,	,	PUNCT
ajird-524	9	12	wave	wave	NOUN
ajird-524	9	13	has	have	VERB
ajird-524	9	14	the	the	DET
ajird-524	9	15	higher	high	ADJ
ajird-524	9	16	speed	speed	NOUN
ajird-524	9	17	of	of	ADP
ajird-524	9	18	propagation	propagation	NOUN
ajird-524	9	19	and	and	CCONJ
ajird-524	9	20	so	so	ADV
ajird-524	9	21	reaches	reach	VERB
ajird-524	9	22	a	a	DET
ajird-524	9	23	seismic	seismic	ADJ
ajird-524	9	24	recording	recording	NOUN
ajird-524	9	25	station	station	NOUN
ajird-524	9	26	faster	fast	ADV
ajird-524	9	27	than	than	ADP
ajird-524	9	28	the	the	DET
ajird-524	9	29	secondary	secondary	ADJ
ajird-524	9	30	,	,	PUNCT
ajird-524	9	31	or	or	CCONJ
ajird-524	9	32	s	s	NOUN
ajird-524	9	33	,	,	PUNCT
ajird-524	9	34	wave	wave	NOUN
ajird-524	9	35	.	.	PUNCT
ajird-524	10	1	p	p	PRON
ajird-524	10	2	waves	wave	NOUN
ajird-524	10	3	,	,	PUNCT
ajird-524	10	4	also	also	ADV
ajird-524	10	5	called	call	VERB
ajird-524	10	6	compressional	compressional	ADJ
ajird-524	10	7	or	or	CCONJ
ajird-524	10	8	longitudinal	longitudinal	ADJ
ajird-524	10	9	waves	wave	NOUN
ajird-524	10	10	,	,	PUNCT
ajird-524	10	11	give	give	VERB
ajird-524	10	12	the	the	DET
ajird-524	10	13	transmitting	transmit	VERB
ajird-524	10	14	medium	medium	NOUN
ajird-524	10	15	whether	whether	SCONJ
ajird-524	10	16	liquid	liquid	ADJ
ajird-524	10	17	,	,	PUNCT
ajird-524	10	18	solid	solid	ADJ
ajird-524	10	19	,	,	PUNCT
ajird-524	10	20	or	or	CCONJ
ajird-524	10	21	gas	gas	NOUN
ajird-524	10	22	a	a	DET
ajird-524	10	23	back	back	NOUN
ajird-524	10	24	and	and	CCONJ
ajird-524	10	25	forth	forth	ADV
ajird-524	10	26	motion	motion	NOUN
ajird-524	10	27	in	in	ADP
ajird-524	10	28	the	the	DET
ajird-524	10	29	direction	direction	NOUN
ajird-524	10	30	of	of	ADP
ajird-524	10	31	the	the	DET
ajird-524	10	32	path	path	NOUN
ajird-524	10	33	of	of	ADP
ajird-524	10	34	propagation	propagation	NOUN
ajird-524	10	35	,	,	PUNCT
ajird-524	10	36	thus	thus	ADV
ajird-524	10	37	stretching	stretch	VERB
ajird-524	10	38	or	or	CCONJ
ajird-524	10	39	compressing	compress	VERB
ajird-524	10	40	the	the	DET
ajird-524	10	41	medium	medium	NOUN
ajird-524	10	42	as	as	SCONJ
ajird-524	10	43	the	the	DET
ajird-524	10	44	wave	wave	NOUN
ajird-524	10	45	passes	pass	VERB
ajird-524	10	46	any	any	DET
ajird-524	10	47	one	one	NUM
ajird-524	10	48	point	point	NOUN
ajird-524	10	49	in	in	ADP
ajird-524	10	50	a	a	DET
ajird-524	10	51	manner	manner	NOUN
ajird-524	10	52	similar	similar	ADJ
ajird-524	10	53	to	to	ADP
ajird-524	10	54	that	that	PRON
ajird-524	10	55	of	of	ADP
ajird-524	10	56	sound	sound	ADJ
ajird-524	10	57	waves	wave	NOUN
ajird-524	10	58	in	in	ADP
ajird-524	10	59	air	air	NOUN
ajird-524	10	60	.	.	PUNCT
ajird-524	11	1	seismic	seismic	ADJ
ajird-524	11	2	action	action	NOUN
ajird-524	11	3	is	be	AUX
ajird-524	11	4	a	a	DET
ajird-524	11	5	special	special	ADJ
ajird-524	11	6	term	term	NOUN
ajird-524	11	7	,	,	PUNCT
ajird-524	11	8	which	which	PRON
ajird-524	11	9	in	in	ADP
ajird-524	11	10	the	the	DET
ajird-524	11	11	practice	practice	NOUN
ajird-524	11	12	of	of	ADP
ajird-524	11	13	calculating	calculate	VERB
ajird-524	11	14	structures	structure	NOUN
ajird-524	11	15	for	for	ADP
ajird-524	11	16	seismic	seismic	ADJ
ajird-524	11	17	resistance	resistance	NOUN
ajird-524	11	18	means	mean	VERB
ajird-524	11	19	the	the	DET
ajird-524	11	20	oscillatory	oscillatory	ADJ
ajird-524	11	21	movement	movement	NOUN
ajird-524	11	22	of	of	ADP
ajird-524	11	23	the	the	DET
ajird-524	11	24	soil	soil	NOUN
ajird-524	11	25	during	during	ADP
ajird-524	11	26	an	an	DET
ajird-524	11	27	earthquake	earthquake	NOUN
ajird-524	11	28	,	,	PUNCT
ajird-524	11	29	which	which	PRON
ajird-524	11	30	creates	create	VERB
ajird-524	11	31	kinematic	kinematic	ADJ
ajird-524	11	32	excitation	excitation	NOUN
ajird-524	11	33	of	of	ADP
ajird-524	11	34	vibrations	vibration	NOUN
ajird-524	11	35	of	of	ADP
ajird-524	11	36	building	build	VERB
ajird-524	11	37	structures	structure	NOUN
ajird-524	11	38	.	.	PUNCT
ajird-524	12	1	https://www.britannica.com/science/longitudinal-wave	https://www.britannica.com/science/longitudinal-wave	PROPN
ajird-524	12	2	https://www.britannica.com/science/wave-water	https://www.britannica.com/science/wave-water	PROPN
ajird-524	12	3	https://www.merriam-webster.com/dictionary/propagation	https://www.merriam-webster.com/dictionary/propagation	NOUN
ajird-524	12	4	https://www.britannica.com/science/secondary-wave	https://www.britannica.com/science/secondary-wave	PROPN
ajird-524	12	5	https://www.britannica.com/science/longitudinal-wave	https://www.britannica.com/science/longitudinal-wave	PROPN
ajird-524	12	6	https://www.britannica.com/science/motion-mechanics	https://www.britannica.com/science/motion-mechanics	PROPN
ajird-524	12	7	https://www.britannica.com/science/sound-physics	https://www.britannica.com/science/sound-physics	PROPN
ajird-524	12	8	american	american	ADJ
ajird-524	12	9	journal	journal	NOUN
ajird-524	12	10	of	of	ADP
ajird-524	12	11	interdisciplinary	interdisciplinary	ADJ
ajird-524	12	12	research	research	NOUN
ajird-524	12	13	and	and	CCONJ
ajird-524	12	14	development	development	NOUN
ajird-524	12	15	issn	issn	PROPN
ajird-524	12	16	online	online	NOUN
ajird-524	12	17	:	:	PUNCT
ajird-524	12	18	2771	2771	NUM
ajird-524	12	19	-	-	SYM
ajird-524	12	20	8948	8948	NUM
ajird-524	12	21	website	website	NOUN
ajird-524	12	22	:	:	PUNCT
ajird-524	12	23	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-524	12	24	volume	volume	NOUN
ajird-524	12	25	13	13	NUM
ajird-524	12	26	,	,	PUNCT
ajird-524	12	27	feb	feb	PROPN
ajird-524	12	28	.	.	PROPN
ajird-524	12	29	,	,	PUNCT
ajird-524	12	30	2023	2023	NUM
ajird-524	12	31	125	125	NUM
ajird-524	12	32	|	|	ADV
ajird-524	12	33	p	p	NOUN
ajird-524	12	34	a	a	DET
ajird-524	12	35	g	g	NOUN
ajird-524	12	36	e	e	X
ajird-524	12	37	literature	literature	NOUN
ajird-524	12	38	review	review	PROPN
ajird-524	12	39	o.	o.	PROPN
ajird-524	12	40	k.	k.	PROPN
ajird-524	12	41	zenkevich	zenkevich	PROPN
ajird-524	12	42	,	,	PUNCT
ajird-524	12	43	the	the	DET
ajird-524	12	44	finite	finite	ADJ
ajird-524	12	45	element	element	NOUN
ajird-524	12	46	method	method	NOUN
ajird-524	12	47	in	in	ADP
ajird-524	12	48	engineering	engineering	NOUN
ajird-524	12	49	science	science	NOUN
ajird-524	12	50	.	.	PUNCT
ajird-524	13	1	the	the	DET
ajird-524	13	2	monograph	monograph	NOUN
ajird-524	13	3	is	be	AUX
ajird-524	13	4	devoted	devote	VERB
ajird-524	13	5	to	to	ADP
ajird-524	13	6	the	the	DET
ajird-524	13	7	presentation	presentation	NOUN
ajird-524	13	8	of	of	ADP
ajird-524	13	9	the	the	DET
ajird-524	13	10	fundamentals	fundamental	NOUN
ajird-524	13	11	of	of	ADP
ajird-524	13	12	the	the	DET
ajird-524	13	13	finite	finite	ADJ
ajird-524	13	14	element	element	NOUN
ajird-524	13	15	method	method	NOUN
ajird-524	13	16	–	–	PUNCT
ajird-524	13	17	one	one	NUM
ajird-524	13	18	of	of	ADP
ajird-524	13	19	the	the	DET
ajird-524	13	20	most	most	ADV
ajird-524	13	21	effective	effective	ADJ
ajird-524	13	22	modern	modern	ADJ
ajird-524	13	23	methods	method	NOUN
ajird-524	13	24	for	for	ADP
ajird-524	13	25	the	the	DET
ajird-524	13	26	numerical	numerical	ADJ
ajird-524	13	27	solution	solution	NOUN
ajird-524	13	28	of	of	ADP
ajird-524	13	29	engineering	engineering	NOUN
ajird-524	13	30	,	,	PUNCT
ajird-524	13	31	physical	physical	ADJ
ajird-524	13	32	and	and	CCONJ
ajird-524	13	33	mathematical	mathematical	ADJ
ajird-524	13	34	problems	problem	NOUN
ajird-524	13	35	using	use	VERB
ajird-524	13	36	computers	computer	NOUN
ajird-524	13	37	.	.	PUNCT
ajird-524	14	1	l.	l.	PROPN
ajird-524	14	2	segerlind	segerlind	PROPN
ajird-524	14	3	,	,	PUNCT
ajird-524	14	4	application	application	NOUN
ajird-524	14	5	of	of	ADP
ajird-524	14	6	the	the	DET
ajird-524	14	7	finite	finite	ADJ
ajird-524	14	8	element	element	NOUN
ajird-524	14	9	method	method	NOUN
ajird-524	14	10	.	.	PUNCT
ajird-524	15	1	the	the	DET
ajird-524	15	2	monograph	monograph	NOUN
ajird-524	15	3	reflects	reflect	VERB
ajird-524	15	4	the	the	DET
ajird-524	15	5	work	work	NOUN
ajird-524	15	6	of	of	ADP
ajird-524	15	7	many	many	ADJ
ajird-524	15	8	researchers	researcher	NOUN
ajird-524	15	9	.	.	PUNCT
ajird-524	16	1	the	the	DET
ajird-524	16	2	order	order	NOUN
ajird-524	16	3	in	in	ADP
ajird-524	16	4	which	which	PRON
ajird-524	16	5	the	the	DET
ajird-524	16	6	material	material	NOUN
ajird-524	16	7	is	be	AUX
ajird-524	16	8	arranged	arrange	VERB
ajird-524	16	9	depends	depend	VERB
ajird-524	16	10	on	on	ADP
ajird-524	16	11	the	the	DET
ajird-524	16	12	results	result	NOUN
ajird-524	16	13	of	of	ADP
ajird-524	16	14	the	the	DET
ajird-524	16	15	author	author	NOUN
ajird-524	16	16	's	's	PART
ajird-524	16	17	experience	experience	NOUN
ajird-524	16	18	.	.	PUNCT
ajird-524	17	1	k.	k.	PROPN
ajird-524	17	2	bathe	bathe	PROPN
ajird-524	17	3	,	,	PUNCT
ajird-524	17	4	finite	finite	ADJ
ajird-524	17	5	element	element	NOUN
ajird-524	17	6	procedures	procedure	NOUN
ajird-524	17	7	.	.	PUNCT
ajird-524	18	1	finite	finite	PROPN
ajird-524	18	2	element	element	NOUN
ajird-524	18	3	procedures	procedure	NOUN
ajird-524	18	4	are	be	AUX
ajird-524	18	5	now	now	ADV
ajird-524	18	6	an	an	DET
ajird-524	18	7	important	important	ADJ
ajird-524	18	8	and	and	CCONJ
ajird-524	18	9	frequently	frequently	ADV
ajird-524	18	10	indispensable	indispensable	ADJ
ajird-524	18	11	part	part	NOUN
ajird-524	18	12	of	of	ADP
ajird-524	18	13	engineering	engineering	NOUN
ajird-524	18	14	analysis	analysis	NOUN
ajird-524	18	15	and	and	CCONJ
ajird-524	18	16	design	design	NOUN
ajird-524	18	17	.	.	PUNCT
ajird-524	19	1	finite	finite	PROPN
ajird-524	19	2	element	element	NOUN
ajird-524	19	3	computer	computer	NOUN
ajird-524	19	4	programs	program	NOUN
ajird-524	19	5	are	be	AUX
ajird-524	19	6	now	now	ADV
ajird-524	19	7	widely	widely	ADV
ajird-524	19	8	used	use	VERB
ajird-524	19	9	in	in	ADP
ajird-524	19	10	practically	practically	ADV
ajird-524	19	11	all	all	DET
ajird-524	19	12	branches	branch	NOUN
ajird-524	19	13	of	of	ADP
ajird-524	19	14	engineering	engineering	NOUN
ajird-524	19	15	for	for	ADP
ajird-524	19	16	the	the	DET
ajird-524	19	17	analysis	analysis	NOUN
ajird-524	19	18	of	of	ADP
ajird-524	19	19	structures	structure	NOUN
ajird-524	19	20	,	,	PUNCT
ajird-524	19	21	solids	solid	NOUN
ajird-524	19	22	,	,	PUNCT
ajird-524	19	23	and	and	CCONJ
ajird-524	19	24	fluids	fluid	NOUN
ajird-524	19	25	.	.	PUNCT
ajird-524	20	1	formulation	formulation	NOUN
ajird-524	20	2	of	of	ADP
ajird-524	20	3	the	the	DET
ajird-524	20	4	problem	problem	NOUN
ajird-524	20	5	.	.	PUNCT
ajird-524	21	1	the	the	DET
ajird-524	21	2	movement	movement	NOUN
ajird-524	21	3	of	of	ADP
ajird-524	21	4	an	an	DET
ajird-524	21	5	underground	underground	ADJ
ajird-524	21	6	structure	structure	NOUN
ajird-524	21	7	(	(	PUNCT
ajird-524	21	8	tunnel	tunnel	NOUN
ajird-524	21	9	)	)	PUNCT
ajird-524	21	10	and	and	CCONJ
ajird-524	21	11	its	its	PRON
ajird-524	21	12	surrounding	surround	VERB
ajird-524	21	13	elastic	elastic	ADJ
ajird-524	21	14	medium	medium	NOUN
ajird-524	21	15	(	(	PUNCT
ajird-524	21	16	soil	soil	NOUN
ajird-524	21	17	)	)	PUNCT
ajird-524	21	18	is	be	AUX
ajird-524	21	19	caused	cause	VERB
ajird-524	21	20	by	by	ADP
ajird-524	21	21	the	the	DET
ajird-524	21	22	propagation	propagation	NOUN
ajird-524	21	23	of	of	ADP
ajird-524	21	24	a	a	DET
ajird-524	21	25	longitudinal	longitudinal	ADJ
ajird-524	21	26	seismic	seismic	ADJ
ajird-524	21	27	wave	wave	NOUN
ajird-524	21	28	in	in	ADP
ajird-524	21	29	the	the	DET
ajird-524	21	30	medium	medium	NOUN
ajird-524	21	31	in	in	ADP
ajird-524	21	32	the	the	DET
ajird-524	21	33	area	area	NOUN
ajird-524	21	34	𝛺	𝛺	PROPN
ajird-524	21	35	=	=	SYM
ajird-524	21	36	{	{	PUNCT
ajird-524	21	37	(	(	PUNCT
ajird-524	21	38	𝑥	𝑥	NOUN
ajird-524	21	39	,	,	PUNCT
ajird-524	21	40	𝑦	𝑦	NOUN
ajird-524	21	41	):	):	PUNCT
ajird-524	21	42	𝑥	𝑥	PROPN
ajird-524	21	43	∈	∈	PROPN
ajird-524	22	1	[	[	X
ajird-524	22	2	0	0	NUM
ajird-524	22	3	,	,	PUNCT
ajird-524	22	4	𝐿	𝐿	PROPN
ajird-524	22	5	]	]	X
ajird-524	22	6	,	,	PUNCT
ajird-524	22	7	𝑦	𝑦	NOUN
ajird-524	22	8	∈	∈	NOUN
ajird-524	23	1	[	[	X
ajird-524	23	2	0	0	NUM
ajird-524	23	3	,	,	PUNCT
ajird-524	23	4	𝐻	𝐻	PROPN
ajird-524	23	5	]	]	PUNCT
ajird-524	23	6	}	}	PUNCT
ajird-524	23	7	,	,	PUNCT
ajird-524	23	8	and	and	CCONJ
ajird-524	23	9	with	with	ADP
ajird-524	23	10	external	external	ADJ
ajird-524	23	11	borders	border	NOUN
ajird-524	23	12	𝛤𝑙	𝛤𝑙	NOUN
ajird-524	23	13	=	=	SYM
ajird-524	23	14	{	{	PUNCT
ajird-524	23	15	(	(	PUNCT
ajird-524	23	16	𝑥	𝑥	PROPN
ajird-524	23	17	,	,	PUNCT
ajird-524	23	18	𝑦	𝑦	NOUN
ajird-524	23	19	):	):	PUNCT
ajird-524	23	20	𝑥	𝑥	PROPN
ajird-524	23	21	=	=	SYM
ajird-524	23	22	0	0	NUM
ajird-524	23	23	,	,	PUNCT
ajird-524	23	24	𝑦	𝑦	NOUN
ajird-524	23	25	∈	∈	NOUN
ajird-524	24	1	[	[	X
ajird-524	24	2	0	0	NUM
ajird-524	24	3	,	,	PUNCT
ajird-524	24	4	𝐻	𝐻	PROPN
ajird-524	24	5	]	]	PUNCT
ajird-524	24	6	}	}	PUNCT
ajird-524	24	7	,	,	PUNCT
ajird-524	24	8	𝛤𝑟	𝛤𝑟	PROPN
ajird-524	24	9	=	=	PUNCT
ajird-524	24	10	{	{	PUNCT
ajird-524	24	11	(	(	PUNCT
ajird-524	24	12	𝑥	𝑥	NOUN
ajird-524	24	13	,	,	PUNCT
ajird-524	24	14	𝑦	𝑦	NOUN
ajird-524	24	15	):	):	PUNCT
ajird-524	24	16	𝑥	𝑥	PROPN
ajird-524	24	17	=	=	SYM
ajird-524	24	18	𝐿	𝐿	PROPN
ajird-524	24	19	,	,	PUNCT
ajird-524	24	20	𝑦	𝑦	NOUN
ajird-524	24	21	∈	∈	NOUN
ajird-524	25	1	[	[	X
ajird-524	25	2	0	0	NUM
ajird-524	25	3	,	,	PUNCT
ajird-524	25	4	𝐻	𝐻	PROPN
ajird-524	25	5	]	]	PUNCT
ajird-524	25	6	}	}	PUNCT
ajird-524	25	7	,	,	PUNCT
ajird-524	26	1	𝛤𝑡	𝛤𝑡	PROPN
ajird-524	26	2	=	=	SYM
ajird-524	26	3	{	{	PUNCT
ajird-524	26	4	(	(	PUNCT
ajird-524	26	5	𝑥	𝑥	NOUN
ajird-524	26	6	,	,	PUNCT
ajird-524	26	7	𝑦	𝑦	NOUN
ajird-524	26	8	):	):	PUNCT
ajird-524	26	9	𝑥	𝑥	PROPN
ajird-524	26	10	∈	∈	PROPN
ajird-524	26	11	[	[	X
ajird-524	26	12	0	0	NUM
ajird-524	26	13	,	,	PUNCT
ajird-524	26	14	𝐿	𝐿	PROPN
ajird-524	26	15	]	]	X
ajird-524	26	16	,	,	PUNCT
ajird-524	26	17	𝑦	𝑦	NOUN
ajird-524	26	18	=	=	SYM
ajird-524	26	19	𝐻	𝐻	PROPN
ajird-524	26	20	}	}	PUNCT
ajird-524	26	21	,	,	PUNCT
ajird-524	26	22	𝛤𝑏	𝛤𝑏	X
ajird-524	26	23	=	=	SYM
ajird-524	26	24	{	{	PUNCT
ajird-524	26	25	(	(	PUNCT
ajird-524	26	26	𝑥	𝑥	NOUN
ajird-524	26	27	,	,	PUNCT
ajird-524	26	28	𝑦	𝑦	NOUN
ajird-524	26	29	):	):	PUNCT
ajird-524	26	30	𝑥	𝑥	PROPN
ajird-524	26	31	∈	∈	PROPN
ajird-524	27	1	[	[	X
ajird-524	27	2	0	0	NUM
ajird-524	27	3	,	,	PUNCT
ajird-524	27	4	𝐿	𝐿	PROPN
ajird-524	27	5	]	]	X
ajird-524	27	6	,	,	PUNCT
ajird-524	27	7	𝑦	𝑦	NOUN
ajird-524	27	8	=	=	NOUN
ajird-524	27	9	0	0	NUM
ajird-524	27	10	}	}	PUNCT
ajird-524	27	11	,	,	PUNCT
ajird-524	27	12	as	as	ADV
ajird-524	27	13	well	well	ADV
ajird-524	27	14	as	as	ADP
ajird-524	27	15	with	with	ADP
ajird-524	27	16	the	the	DET
ajird-524	27	17	boundaries	boundary	NOUN
ajird-524	27	18	of	of	ADP
ajird-524	27	19	an	an	DET
ajird-524	27	20	underground	underground	ADJ
ajird-524	27	21	structure	structure	NOUN
ajird-524	27	22	(	(	PUNCT
ajird-524	27	23	tunnel	tunnel	NOUN
ajird-524	27	24	)	)	PUNCT
ajird-524	27	25	of	of	ADP
ajird-524	27	26	a	a	DET
ajird-524	27	27	rectangular	rectangular	ADJ
ajird-524	27	28	area	area	NOUN
ajird-524	28	1	𝛤𝑙𝑖𝑛	𝛤𝑙𝑖𝑛	PROPN
ajird-524	28	2	=	=	SYM
ajird-524	28	3	{	{	PUNCT
ajird-524	28	4	(	(	PUNCT
ajird-524	28	5	𝑥	𝑥	NOUN
ajird-524	28	6	,	,	PUNCT
ajird-524	28	7	𝑦	𝑦	NOUN
ajird-524	28	8	):	):	PUNCT
ajird-524	28	9	𝑥	𝑥	PROPN
ajird-524	28	10	=	=	SYM
ajird-524	28	11	𝐿1	𝐿1	PROPN
ajird-524	28	12	,	,	PUNCT
ajird-524	28	13	𝑦	𝑦	NOUN
ajird-524	28	14	∈	∈	NOUN
ajird-524	29	1	[	[	X
ajird-524	29	2	0	0	NUM
ajird-524	29	3	,	,	PUNCT
ajird-524	29	4	𝐻1	𝐻1	NOUN
ajird-524	29	5	+	+	CCONJ
ajird-524	29	6	𝐻2	𝐻2	PROPN
ajird-524	29	7	]	]	PUNCT
ajird-524	29	8	}	}	PUNCT
ajird-524	29	9	,	,	PUNCT
ajird-524	29	10	𝛤𝑟𝑖𝑛	𝛤𝑟𝑖𝑛	PROPN
ajird-524	29	11	=	=	SYM
ajird-524	29	12	{	{	PUNCT
ajird-524	29	13	(	(	PUNCT
ajird-524	29	14	𝑥	𝑥	NOUN
ajird-524	29	15	,	,	PUNCT
ajird-524	29	16	𝑦	𝑦	NOUN
ajird-524	29	17	):	):	PUNCT
ajird-524	29	18	𝑥	𝑥	NOUN
ajird-524	29	19	=	=	PUNCT
ajird-524	30	1	[	[	X
ajird-524	30	2	𝐿1	𝐿1	X
ajird-524	30	3	+	+	CCONJ
ajird-524	30	4	𝐿2	𝐿2	NUM
ajird-524	30	5	]	]	X
ajird-524	30	6	,	,	PUNCT
ajird-524	30	7	𝑦	𝑦	NOUN
ajird-524	30	8	∈	∈	NOUN
ajird-524	31	1	[	[	X
ajird-524	31	2	0	0	NUM
ajird-524	31	3	,	,	PUNCT
ajird-524	31	4	𝐻1	𝐻1	NOUN
ajird-524	31	5	+	+	CCONJ
ajird-524	31	6	𝐻2	𝐻2	PROPN
ajird-524	31	7	]	]	PUNCT
ajird-524	31	8	}	}	PUNCT
ajird-524	31	9	,	,	PUNCT
ajird-524	31	10	𝛤𝑡𝑖𝑛	𝛤𝑡𝑖𝑛	PROPN
ajird-524	31	11	=	=	PUNCT
ajird-524	31	12	{	{	PUNCT
ajird-524	31	13	(	(	PUNCT
ajird-524	31	14	𝑥	𝑥	NOUN
ajird-524	31	15	,	,	PUNCT
ajird-524	31	16	𝑦	𝑦	NOUN
ajird-524	31	17	):	):	PUNCT
ajird-524	31	18	𝑥	𝑥	PROPN
ajird-524	31	19	∈	∈	PROPN
ajird-524	32	1	[	[	X
ajird-524	32	2	0	0	NUM
ajird-524	32	3	,	,	PUNCT
ajird-524	32	4	𝐿1	𝐿1	VERB
ajird-524	33	1	+	+	CCONJ
ajird-524	33	2	𝐿2	𝐿2	NUM
ajird-524	33	3	]	]	X
ajird-524	33	4	,	,	PUNCT
ajird-524	33	5	𝑦	𝑦	NOUN
ajird-524	33	6	=	=	PUNCT
ajird-524	34	1	[	[	X
ajird-524	34	2	𝐻1	𝐻1	X
ajird-524	34	3	+	+	CCONJ
ajird-524	34	4	𝐻2	𝐻2	PROPN
ajird-524	34	5	]	]	PUNCT
ajird-524	34	6	}	}	PUNCT
ajird-524	34	7	,	,	PUNCT
ajird-524	34	8	𝛤𝑏𝑖𝑛	𝛤𝑏𝑖𝑛	PROPN
ajird-524	34	9	=	=	PRON
ajird-524	34	10	{	{	PUNCT
ajird-524	34	11	(	(	PUNCT
ajird-524	34	12	𝑥	𝑥	NOUN
ajird-524	34	13	,	,	PUNCT
ajird-524	34	14	𝑦	𝑦	NOUN
ajird-524	34	15	):	):	PUNCT
ajird-524	34	16	𝑥	𝑥	PROPN
ajird-524	34	17	∈	∈	PROPN
ajird-524	35	1	[	[	X
ajird-524	35	2	0	0	NUM
ajird-524	35	3	,	,	PUNCT
ajird-524	35	4	𝐿1	𝐿1	VERB
ajird-524	36	1	+	+	CCONJ
ajird-524	36	2	𝐿2	𝐿2	NUM
ajird-524	36	3	]	]	X
ajird-524	36	4	,	,	PUNCT
ajird-524	36	5	𝑦	𝑦	NOUN
ajird-524	36	6	=	=	PUNCT
ajird-524	37	1	[	[	X
ajird-524	37	2	0	0	NUM
ajird-524	37	3	,	,	PUNCT
ajird-524	37	4	𝐻1	𝐻1	NOUN
ajird-524	37	5	]	]	PUNCT
ajird-524	37	6	}	}	PUNCT
ajird-524	37	7	,	,	PUNCT
ajird-524	37	8	the	the	DET
ajird-524	37	9	mathematical	mathematical	ADJ
ajird-524	37	10	model	model	NOUN
ajird-524	37	11	in	in	ADP
ajird-524	37	12	a	a	DET
ajird-524	37	13	strict	strict	ADJ
ajird-524	37	14	formulation	formulation	NOUN
ajird-524	37	15	(	(	PUNCT
ajird-524	37	16	differential	differential	NOUN
ajird-524	37	17	equation	equation	NOUN
ajird-524	37	18	)	)	PUNCT
ajird-524	37	19	has	have	VERB
ajird-524	37	20	the	the	DET
ajird-524	37	21	form	form	NOUN
ajird-524	37	22	:	:	PUNCT
ajird-524	37	23	𝜌	𝜌	PART
ajird-524	37	24	�	�	NOUN
ajird-524	37	25	̈	̈	X
ajird-524	37	26	�	�	PROPN
ajird-524	37	27	+	+	CCONJ
ajird-524	37	28	𝑐	𝑐	PROPN
ajird-524	37	29	�	�	PROPN
ajird-524	37	30	̇	̇	VERB
ajird-524	37	31	�	�	PROPN
ajird-524	37	32	−	−	PROPN
ajird-524	37	33	𝑑𝑖𝑣(𝜎	𝑑𝑖𝑣(𝜎	PROPN
ajird-524	37	34	)	)	PUNCT
ajird-524	37	35	=	=	SYM
ajird-524	38	1	𝑟	𝑟	NOUN
ajird-524	38	2	in	in	ADP
ajird-524	38	3	area	area	NOUN
ajird-524	38	4	ω	ω	PROPN
ajird-524	38	5	(	(	PUNCT
ajird-524	38	6	1	1	NUM
ajird-524	38	7	)	)	PUNCT
ajird-524	38	8	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
ajird-524	38	9	=	=	SYM
ajird-524	38	10	𝑐𝑝𝜌	𝑐𝑝𝜌	NOUN
ajird-524	38	11	�	�	PROPN
ajird-524	38	12	̇	̇	PROPN
ajird-524	38	13	�	�	PROPN
ajird-524	38	14	,	,	PUNCT
ajird-524	38	15	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
ajird-524	38	16	=	=	SYM
ajird-524	38	17	𝑐𝑠𝜌	𝑐𝑠𝜌	PROPN
ajird-524	38	18	�	�	PROPN
ajird-524	38	19	̇	̇	PROPN
ajird-524	38	20	�	�	PROPN
ajird-524	38	21	,	,	PUNCT
ajird-524	38	22	𝜎𝑥𝑦	𝜎𝑥𝑦	NOUN
ajird-524	38	23	=	=	SYM
ajird-524	38	24	0	0	NUM
ajird-524	38	25	at	at	ADP
ajird-524	38	26	the	the	DET
ajird-524	38	27	borders	border	NOUN
ajird-524	38	28	γt	γt	NOUN
ajird-524	38	29	and	and	CCONJ
ajird-524	38	30	γb	γb	PROPN
ajird-524	38	31	(	(	PUNCT
ajird-524	38	32	2	2	NUM
ajird-524	38	33	)	)	PUNCT
ajird-524	38	34	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
ajird-524	38	35	=	=	SYM
ajird-524	38	36	2𝑐𝑝𝜌𝑓(𝑡)𝑛𝑥	2𝑐𝑝𝜌𝑓(𝑡)𝑛𝑥	NOUN
ajird-524	38	37	,	,	PUNCT
ajird-524	38	38	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
ajird-524	38	39	=	=	SYM
ajird-524	38	40	2𝑐𝑝𝜌𝑓(𝑡)𝑛𝑦	2𝑐𝑝𝜌𝑓(𝑡)𝑛𝑦	NUM
ajird-524	38	41	,	,	PUNCT
ajird-524	38	42	𝜎𝑥𝑦	𝜎𝑥𝑦	PROPN
ajird-524	38	43	=	=	SYM
ajird-524	38	44	0	0	NUM
ajird-524	38	45	at	at	ADP
ajird-524	38	46	the	the	DET
ajird-524	38	47	border	border	NOUN
ajird-524	38	48	γl	γl	NOUN
ajird-524	38	49	(	(	PUNCT
ajird-524	38	50	3	3	NUM
ajird-524	38	51	)	)	PUNCT
ajird-524	38	52	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
ajird-524	38	53	=	=	SYM
ajird-524	38	54	𝑐𝑝𝜌	𝑐𝑝𝜌	NOUN
ajird-524	38	55	�	�	PROPN
ajird-524	38	56	̇	̇	PROPN
ajird-524	38	57	�	�	PROPN
ajird-524	38	58	,	,	PUNCT
ajird-524	38	59	𝜎𝑦𝑦	𝜎𝑦𝑦	NOUN
ajird-524	38	60	=	=	SYM
ajird-524	38	61	𝑐𝑠𝜌	𝑐𝑠𝜌	PROPN
ajird-524	38	62	�	�	PROPN
ajird-524	38	63	̇	̇	PROPN
ajird-524	38	64	�	�	PROPN
ajird-524	38	65	,	,	PUNCT
ajird-524	38	66	𝜎𝑥𝑦	𝜎𝑥𝑦	NOUN
ajird-524	38	67	=	=	SYM
ajird-524	38	68	0	0	NUM
ajird-524	38	69	at	at	ADP
ajird-524	38	70	the	the	DET
ajird-524	38	71	border	border	NOUN
ajird-524	38	72	γr	γr	NOUN
ajird-524	38	73	(	(	PUNCT
ajird-524	38	74	4	4	NUM
ajird-524	38	75	)	)	PUNCT
ajird-524	38	76	𝑢	𝑢	NOUN
ajird-524	38	77	=	=	SYM
ajird-524	38	78	0	0	NUM
ajird-524	38	79	,	,	PUNCT
ajird-524	38	80	�	�	PROPN
ajird-524	38	81	̇	̇	PROPN
ajird-524	38	82	�	�	PROPN
ajird-524	38	83	=	=	SYM
ajird-524	38	84	0	0	NUM
ajird-524	38	85	при	при	PROPN
ajird-524	38	86	t=0	t=0	PROPN
ajird-524	38	87	(	(	PUNCT
ajird-524	38	88	5	5	NUM
ajird-524	38	89	)	)	PUNCT
ajird-524	38	90	given	give	VERB
ajird-524	38	91	the	the	DET
ajird-524	38	92	koshi	koshi	PROPN
ajird-524	38	93	relation	relation	PROPN
ajird-524	38	94	휀𝑥𝑥	휀𝑥𝑥	X
ajird-524	38	95	=	=	SYM
ajird-524	38	96	𝜕𝑢𝑥/𝜕𝑥	𝜕𝑢𝑥/𝜕𝑥	NOUN
ajird-524	38	97	;	;	PUNCT
ajird-524	38	98	휀𝑦𝑦	휀𝑦𝑦	NOUN
ajird-524	38	99	=	=	SYM
ajird-524	38	100	𝜕𝑢𝑦/𝜕𝑦	𝜕𝑢𝑦/𝜕𝑦	NOUN
ajird-524	38	101	;	;	PUNCT
ajird-524	38	102	휀𝑥𝑦	휀𝑥𝑦	NOUN
ajird-524	38	103	=	=	SYM
ajird-524	38	104	𝜕𝑢𝑥/𝜕𝑦	𝜕𝑢𝑥/𝜕𝑦	PROPN
ajird-524	38	105	+	+	X
ajird-524	38	106	𝜕𝑢𝑦/𝜕𝑥	𝜕𝑢𝑦/𝜕𝑥	NOUN
ajird-524	38	107	(	(	PUNCT
ajird-524	38	108	6	6	NUM
ajird-524	38	109	)	)	PUNCT
ajird-524	38	110	and	and	CCONJ
ajird-524	38	111	hooke	hooke	PROPN
ajird-524	38	112	's	's	PART
ajird-524	38	113	law	law	NOUN
ajird-524	38	114	𝜎	𝜎	NOUN
ajird-524	39	1	=	=	SYM
ajird-524	39	2	𝐵휀	𝐵휀	PROPN
ajird-524	39	3	,	,	PUNCT
ajird-524	39	4	𝐵	𝐵	NOUN
ajird-524	39	5	=	=	PUNCT
ajird-524	39	6	[	[	PUNCT
ajird-524	39	7	𝜆	𝜆	NOUN
ajird-524	39	8	+	+	NUM
ajird-524	39	9	2𝜇	2𝜇	NUM
ajird-524	39	10	𝜆	𝜆	ADP
ajird-524	39	11	0	0	NUM
ajird-524	39	12	𝜆	𝜆	PRON
ajird-524	39	13	𝜆	𝜆	PROPN
ajird-524	39	14	+	+	NUM
ajird-524	39	15	2𝜇	2𝜇	NUM
ajird-524	39	16	0	0	NUM
ajird-524	39	17	0	0	NUM
ajird-524	39	18	0	0	NUM
ajird-524	39	19	𝜇	𝜇	X
ajird-524	39	20	]	]	X
ajird-524	39	21	(	(	PUNCT
ajird-524	39	22	7	7	NUM
ajird-524	39	23	)	)	PUNCT
ajird-524	39	24	𝜆	𝜆	NOUN
ajird-524	39	25	and	and	CCONJ
ajird-524	39	26	𝜇	𝜇	ADP
ajird-524	39	27	lame	lame	ADJ
ajird-524	39	28	coefficients	coefficient	NOUN
ajird-524	39	29	.	.	PUNCT
ajird-524	40	1	american	american	ADJ
ajird-524	40	2	journal	journal	PROPN
ajird-524	40	3	of	of	ADP
ajird-524	40	4	interdisciplinary	interdisciplinary	ADJ
ajird-524	40	5	research	research	NOUN
ajird-524	40	6	and	and	CCONJ
ajird-524	40	7	development	development	NOUN
ajird-524	40	8	issn	issn	PROPN
ajird-524	40	9	online	online	NOUN
ajird-524	40	10	:	:	PUNCT
ajird-524	40	11	2771	2771	NUM
ajird-524	40	12	-	-	SYM
ajird-524	40	13	8948	8948	NUM
ajird-524	40	14	website	website	NOUN
ajird-524	40	15	:	:	PUNCT
ajird-524	40	16	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-524	40	17	volume	volume	NOUN
ajird-524	40	18	13	13	NUM
ajird-524	40	19	,	,	PUNCT
ajird-524	40	20	feb	feb	PROPN
ajird-524	40	21	.	.	PROPN
ajird-524	40	22	,	,	PUNCT
ajird-524	40	23	2023	2023	NUM
ajird-524	40	24	126	126	NUM
ajird-524	41	1	|	|	ADV
ajird-524	41	2	p	p	NOUN
ajird-524	41	3	a	a	DET
ajird-524	41	4	g	g	NOUN
ajird-524	41	5	e	e	NOUN
ajird-524	41	6	in	in	ADP
ajird-524	41	7	this	this	DET
ajird-524	41	8	problem	problem	NOUN
ajird-524	41	9	,	,	PUNCT
ajird-524	41	10	a	a	DET
ajird-524	41	11	longitudinal	longitudinal	ADJ
ajird-524	41	12	wave	wave	NOUN
ajird-524	41	13	falls	fall	VERB
ajird-524	41	14	on	on	ADP
ajird-524	41	15	the	the	DET
ajird-524	41	16	left	left	ADJ
ajird-524	41	17	edge	edge	NOUN
ajird-524	41	18	at	at	ADP
ajird-524	41	19	a	a	DET
ajird-524	41	20	given	give	VERB
ajird-524	41	21	angle	angle	NOUN
ajird-524	41	22	,	,	PUNCT
ajird-524	41	23	with	with	ADP
ajird-524	41	24	an	an	DET
ajird-524	41	25	initial	initial	ADJ
ajird-524	41	26	impulse	impulse	ADJ
ajird-524	41	27	.	.	PUNCT
ajird-524	42	1	conditions	condition	NOUN
ajird-524	42	2	for	for	ADP
ajird-524	42	3	the	the	DET
ajird-524	42	4	transparency	transparency	NOUN
ajird-524	42	5	of	of	ADP
ajird-524	42	6	borders	border	NOUN
ajird-524	42	7	have	have	AUX
ajird-524	42	8	been	be	AUX
ajird-524	42	9	established	establish	VERB
ajird-524	42	10	on	on	ADP
ajird-524	42	11	all	all	DET
ajird-524	42	12	sides	side	NOUN
ajird-524	42	13	.	.	PUNCT
ajird-524	43	1	since	since	SCONJ
ajird-524	43	2	the	the	DET
ajird-524	43	3	problem	problem	NOUN
ajird-524	43	4	is	be	AUX
ajird-524	43	5	solved	solve	VERB
ajird-524	43	6	by	by	ADP
ajird-524	43	7	the	the	DET
ajird-524	43	8	finite	finite	PROPN
ajird-524	43	9	element	element	NOUN
ajird-524	43	10	method	method	NOUN
ajird-524	43	11	,	,	PUNCT
ajird-524	43	12	which	which	PRON
ajird-524	43	13	involves	involve	VERB
ajird-524	43	14	setting	set	VERB
ajird-524	43	15	a	a	DET
ajird-524	43	16	weak	weak	ADJ
ajird-524	43	17	form	form	NOUN
ajird-524	43	18	(	(	PUNCT
ajird-524	43	19	variational	variational	ADJ
ajird-524	43	20	form	form	NOUN
ajird-524	43	21	)	)	PUNCT
ajird-524	43	22	of	of	ADP
ajird-524	43	23	the	the	DET
ajird-524	43	24	equilibrium	equilibrium	NOUN
ajird-524	43	25	equations	equation	NOUN
ajird-524	43	26	,	,	PUNCT
ajird-524	43	27	we	we	PRON
ajird-524	43	28	will	will	AUX
ajird-524	43	29	use	use	VERB
ajird-524	43	30	the	the	DET
ajird-524	43	31	lagrange	lagrange	ADJ
ajird-524	43	32	variational	variational	ADJ
ajird-524	43	33	principle	principle	NOUN
ajird-524	43	34	,	,	PUNCT
ajird-524	43	35	as	as	ADV
ajird-524	43	36	well	well	ADV
ajird-524	43	37	as	as	ADP
ajird-524	43	38	the	the	DET
ajird-524	43	39	d'alembert	d'alembert	PROPN
ajird-524	43	40	principle	principle	NOUN
ajird-524	43	41	.	.	PUNCT
ajird-524	44	1	as	as	ADP
ajird-524	44	2	a	a	DET
ajird-524	44	3	result	result	NOUN
ajird-524	44	4	,	,	PUNCT
ajird-524	44	5	the	the	DET
ajird-524	44	6	variational	variational	ADJ
ajird-524	44	7	equilibrium	equilibrium	NOUN
ajird-524	44	8	equation	equation	NOUN
ajird-524	44	9	for	for	ADP
ajird-524	44	10	an	an	DET
ajird-524	44	11	isotropic	isotropic	ADJ
ajird-524	44	12	body	body	NOUN
ajird-524	44	13	has	have	VERB
ajird-524	44	14	the	the	DET
ajird-524	44	15	form	form	NOUN
ajird-524	44	16	:	:	PUNCT
ajird-524	44	17	∫	∫	PROPN
ajird-524	44	18	𝜆𝑑𝑖𝑣(𝑢)𝑑𝑖𝑣(𝛿𝑢	𝜆𝑑𝑖𝑣(𝑢)𝑑𝑖𝑣(𝛿𝑢	NUM
ajird-524	44	19	)	)	PUNCT
ajird-524	45	1	+	+	CCONJ
ajird-524	45	2	2𝜇휀𝑇휀	2𝜇휀𝑇휀	NUM
ajird-524	45	3	−	−	NOUN
ajird-524	45	4	(	(	PUNCT
ajird-524	45	5	𝑟	𝑟	NOUN
ajird-524	45	6	−	−	ADP
ajird-524	45	7	𝛺	𝛺	PROPN
ajird-524	45	8	𝜌	𝜌	ADP
ajird-524	45	9	�	�	NOUN
ajird-524	45	10	̈	̈	X
ajird-524	45	11	�	�	PROPN
ajird-524	45	12	−	−	ADP
ajird-524	45	13	𝑐	𝑐	PROPN
ajird-524	45	14	�	�	PROPN
ajird-524	45	15	̇	̇	PROPN
ajird-524	45	16	�	�	PROPN
ajird-524	45	17	)𝛿𝑢𝑑𝛺	)𝛿𝑢𝑑𝛺	PART
ajird-524	45	18	−	−	NOUN
ajird-524	45	19	∫	∫	PROPN
ajird-524	45	20	𝑃	𝑃	NOUN
ajird-524	45	21	𝛤	𝛤	PROPN
ajird-524	45	22	𝛿𝑢𝑑𝛤	𝛿𝑢𝑑𝛤	NOUN
ajird-524	45	23	=	=	SYM
ajird-524	45	24	0	0	PUNCT
ajird-524	45	25	(	(	PUNCT
ajird-524	45	26	8)	8)	NUM
ajird-524	45	27	where	where	SCONJ
ajird-524	45	28	𝑟	𝑟	X
ajird-524	45	29	–	–	PUNCT
ajird-524	45	30	volume	volume	NOUN
ajird-524	45	31	load	load	NOUN
ajird-524	45	32	vector	vector	NOUN
ajird-524	45	33	,	,	PUNCT
ajird-524	45	34	𝑃	𝑃	NOUN
ajird-524	45	35	–	–	PUNCT
ajird-524	45	36	surface	surface	NOUN
ajird-524	45	37	load	load	NOUN
ajird-524	45	38	vector	vector	NOUN
ajird-524	45	39	.	.	PUNCT
ajird-524	46	1	applying	apply	VERB
ajird-524	46	2	the	the	DET
ajird-524	46	3	method	method	NOUN
ajird-524	46	4	of	of	ADP
ajird-524	46	5	partial	partial	ADJ
ajird-524	46	6	discretization	discretization	NOUN
ajird-524	46	7	by	by	ADP
ajird-524	46	8	finite	finite	ADJ
ajird-524	46	9	elements	element	NOUN
ajird-524	46	10	i.e.	i.e.	X
ajird-524	46	11	movements	movement	NOUN
ajird-524	46	12	in	in	ADP
ajird-524	46	13	the	the	DET
ajird-524	46	14	element	element	NOUN
ajird-524	46	15	,	,	PUNCT
ajird-524	46	16	representing	represent	VERB
ajird-524	46	17	in	in	ADP
ajird-524	46	18	the	the	DET
ajird-524	46	19	form	form	NOUN
ajird-524	46	20	:	:	PUNCT
ajird-524	46	21	𝑢𝑒	𝑢𝑒	X
ajird-524	46	22	=	=	SYM
ajird-524	46	23	∑	∑	PUNCT
ajird-524	46	24	𝑢𝑖(𝑡)𝜑(𝑥	𝑢𝑖(𝑡)𝜑(𝑥	ADJ
ajird-524	46	25	,	,	PUNCT
ajird-524	46	26	𝑦)𝑖	𝑦)𝑖	ADJ
ajird-524	46	27	𝑛	𝑛	PRON
ajird-524	46	28	𝑖=1	𝑖=1	PROPN
ajird-524	46	29	(	(	PUNCT
ajird-524	46	30	9	9	NUM
ajird-524	46	31	)	)	PUNCT
ajird-524	46	32	where	where	SCONJ
ajird-524	46	33	𝑛	𝑛	X
ajird-524	46	34	–	–	PUNCT
ajird-524	46	35	the	the	DET
ajird-524	46	36	number	number	NOUN
ajird-524	46	37	of	of	ADP
ajird-524	46	38	degrees	degree	NOUN
ajird-524	46	39	of	of	ADP
ajird-524	46	40	freedom	freedom	NOUN
ajird-524	46	41	in	in	ADP
ajird-524	46	42	the	the	DET
ajird-524	46	43	element	element	NOUN
ajird-524	46	44	𝑒	𝑒	NOUN
ajird-524	46	45	,	,	PUNCT
ajird-524	46	46	𝑢𝑖(𝑡	𝑢𝑖(𝑡	NUM
ajird-524	46	47	)	)	PUNCT
ajird-524	46	48	–	–	PUNCT
ajird-524	46	49	desired	desire	VERB
ajird-524	46	50	nodal	nodal	NOUN
ajird-524	46	51	displacements	displacement	NOUN
ajird-524	46	52	depending	depend	VERB
ajird-524	46	53	on	on	ADP
ajird-524	46	54	time	time	NOUN
ajird-524	46	55	,	,	PUNCT
ajird-524	46	56	𝜑(𝑥	𝜑(𝑥	PROPN
ajird-524	46	57	,	,	PUNCT
ajird-524	46	58	𝑦)𝑖	𝑦)𝑖	ADJ
ajird-524	46	59	–	–	PUNCT
ajird-524	46	60	form	form	NOUN
ajird-524	46	61	functions	function	NOUN
ajird-524	46	62	on	on	ADP
ajird-524	46	63	the	the	DET
ajird-524	46	64	element	element	NOUN
ajird-524	46	65	.	.	PUNCT
ajird-524	47	1	we	we	PRON
ajird-524	47	2	obtain	obtain	VERB
ajird-524	47	3	a	a	DET
ajird-524	47	4	system	system	NOUN
ajird-524	47	5	of	of	ADP
ajird-524	47	6	linear	linear	ADJ
ajird-524	47	7	ordinary	ordinary	ADJ
ajird-524	47	8	equations	equation	NOUN
ajird-524	47	9	:	:	PUNCT
ajird-524	47	10	𝑀	𝑀	PROPN
ajird-524	47	11	�	�	PROPN
ajird-524	47	12	̈	̈	NUM
ajird-524	47	13	�	�	PROPN
ajird-524	47	14	+	+	CCONJ
ajird-524	47	15	𝐶	𝐶	PROPN
ajird-524	47	16	�	�	PROPN
ajird-524	47	17	̇	̇	PROPN
ajird-524	47	18	�	�	PROPN
ajird-524	47	19	+	+	CCONJ
ajird-524	47	20	𝐾𝑈	𝐾𝑈	PROPN
ajird-524	47	21	=	=	PROPN
ajird-524	47	22	𝑅	𝑅	PROPN
ajird-524	47	23	(	(	PUNCT
ajird-524	47	24	10	10	NUM
ajird-524	47	25	)	)	PUNCT
ajird-524	47	26	with	with	ADP
ajird-524	47	27	initial	initial	ADJ
ajird-524	47	28	conditions	condition	NOUN
ajird-524	47	29	𝑈	𝑈	NOUN
ajird-524	47	30	=	=	SYM
ajird-524	47	31	0	0	NUM
ajird-524	47	32	,	,	PUNCT
ajird-524	47	33	�	�	PROPN
ajird-524	47	34	̇	̇	PROPN
ajird-524	47	35	�	�	PROPN
ajird-524	47	36	=	=	SYM
ajird-524	47	37	0	0	NUM
ajird-524	47	38	at	at	ADP
ajird-524	47	39	t=0	t=0	PROPN
ajird-524	47	40	(	(	PUNCT
ajird-524	47	41	11	11	NUM
ajird-524	47	42	)	)	PUNCT
ajird-524	47	43	equations	equation	NOUN
ajird-524	47	44	(	(	PUNCT
ajird-524	47	45	11	11	NUM
ajird-524	47	46	)	)	PUNCT
ajird-524	47	47	obtained	obtain	VERB
ajird-524	47	48	from	from	ADP
ajird-524	47	49	the	the	DET
ajird-524	47	50	consideration	consideration	NOUN
ajird-524	47	51	of	of	ADP
ajird-524	47	52	static	static	ADJ
ajird-524	47	53	equilibrium	equilibrium	NOUN
ajird-524	47	54	at	at	ADP
ajird-524	47	55	time	time	NOUN
ajird-524	47	56	t	t	PROPN
ajird-524	47	57	can	can	AUX
ajird-524	47	58	be	be	AUX
ajird-524	47	59	written	write	VERB
ajird-524	47	60	as	as	ADP
ajird-524	47	61	:	:	PUNCT
ajird-524	47	62	𝐹𝑖(𝑡	𝐹𝑖(𝑡	NUM
ajird-524	47	63	)	)	PUNCT
ajird-524	47	64	+	+	CCONJ
ajird-524	47	65	𝐹𝑑(𝑡	𝐹𝑑(𝑡	NUM
ajird-524	47	66	)	)	PUNCT
ajird-524	48	1	+	+	NUM
ajird-524	48	2	𝐹𝑒(𝑡	𝐹𝑒(𝑡	NOUN
ajird-524	48	3	)	)	PUNCT
ajird-524	48	4	=	=	SYM
ajird-524	48	5	𝑅(𝑡	𝑅(𝑡	NOUN
ajird-524	48	6	)	)	PUNCT
ajird-524	48	7	(	(	PUNCT
ajird-524	48	8	12	12	NUM
ajird-524	48	9	)	)	PUNCT
ajird-524	48	10	to	to	PART
ajird-524	48	11	solve	solve	VERB
ajird-524	48	12	systems	system	NOUN
ajird-524	48	13	of	of	ADP
ajird-524	48	14	equations	equation	NOUN
ajird-524	48	15	(	(	PUNCT
ajird-524	48	16	12	12	NUM
ajird-524	48	17	)	)	PUNCT
ajird-524	48	18	with	with	ADP
ajird-524	48	19	initial	initial	ADJ
ajird-524	48	20	conditions	condition	NOUN
ajird-524	48	21	(	(	PUNCT
ajird-524	48	22	11	11	NUM
ajird-524	48	23	)	)	PUNCT
ajird-524	48	24	,	,	PUNCT
ajird-524	48	25	the	the	DET
ajird-524	48	26	implicit	implicit	ADJ
ajird-524	48	27	difference	difference	NOUN
ajird-524	48	28	methods	method	NOUN
ajird-524	48	29	of	of	ADP
ajird-524	48	30	newmark	newmark	PROPN
ajird-524	48	31	and	and	CCONJ
ajird-524	48	32	bate	bate	NOUN
ajird-524	48	33	are	be	AUX
ajird-524	48	34	used	use	VERB
ajird-524	48	35	.	.	PUNCT
ajird-524	49	1	step	step	NOUN
ajird-524	49	2	-	-	PUNCT
ajird-524	49	3	by	by	ADP
ajird-524	49	4	-	-	PUNCT
ajird-524	49	5	step	step	NOUN
ajird-524	49	6	solution	solution	NOUN
ajird-524	49	7	using	use	VERB
ajird-524	49	8	newmark	newmark	NOUN
ajird-524	49	9	integration	integration	NOUN
ajird-524	49	10	method	method	NOUN
ajird-524	49	11	.	.	PUNCT
ajird-524	50	1	a.	a.	NOUN
ajird-524	50	2	initial	initial	ADJ
ajird-524	50	3	calculations	calculation	NOUN
ajird-524	50	4	:	:	PUNCT
ajird-524	50	5	1	1	X
ajird-524	50	6	.	.	X
ajird-524	50	7	form	form	NOUN
ajird-524	50	8	stiffness	stiffness	NOUN
ajird-524	50	9	matrix	matrix	NOUN
ajird-524	50	10	𝐾	𝐾	NOUN
ajird-524	50	11	,	,	PUNCT
ajird-524	50	12	mass	mass	ADJ
ajird-524	50	13	matrix	matrix	NOUN
ajird-524	50	14	𝑀	𝑀	PROPN
ajird-524	50	15	and	and	CCONJ
ajird-524	50	16	damping	damp	VERB
ajird-524	50	17	constant	constant	ADJ
ajird-524	50	18	𝐶.	𝐶.	PROPN
ajird-524	50	19	2	2	NUM
ajird-524	50	20	.	.	PUNCT
ajird-524	50	21	initialize	initialize	NOUN
ajird-524	50	22	𝑈0	𝑈0	NOUN
ajird-524	50	23	,	,	PUNCT
ajird-524	50	24	�	�	PROPN
ajird-524	50	25	̇	̇	PROPN
ajird-524	50	26	�	�	PROPN
ajird-524	50	27	0	0	NUM
ajird-524	50	28	and	and	CCONJ
ajird-524	50	29	�	�	PROPN
ajird-524	50	30	̈	̈	X
ajird-524	50	31	�	�	NOUN
ajird-524	50	32	0	0	NUM
ajird-524	50	33	.	.	NOUN
ajird-524	51	1	3	3	NUM
ajird-524	51	2	.	.	NOUN
ajird-524	51	3	select	select	ADJ
ajird-524	51	4	time	time	NOUN
ajird-524	51	5	step	step	NOUN
ajird-524	51	6	∆𝑡	∆𝑡	PROPN
ajird-524	51	7	,	,	PUNCT
ajird-524	51	8	and	and	CCONJ
ajird-524	51	9	parameters	parameter	NOUN
ajird-524	51	10	𝛼	𝛼	NOUN
ajird-524	51	11	and	and	CCONJ
ajird-524	51	12	𝛿	𝛿	ADJ
ajird-524	51	13	and	and	CCONJ
ajird-524	51	14	calculate	calculate	ADJ
ajird-524	51	15	integration	integration	NOUN
ajird-524	51	16	constants	constant	NOUN
ajird-524	51	17	:	:	PUNCT
ajird-524	51	18	𝛿	𝛿	PRON
ajird-524	51	19	≥	≥	NOUN
ajird-524	51	20	0,50	0,50	NOUN
ajird-524	51	21	;	;	PUNCT
ajird-524	51	22	𝛼	𝛼	PRON
ajird-524	51	23	≥	≥	NOUN
ajird-524	51	24	0,25(0,5	0,25(0,5	NOUN
ajird-524	52	1	+	+	CCONJ
ajird-524	53	1	𝛿)2	𝛿)2	ADJ
ajird-524	53	2	;	;	PUNCT
ajird-524	53	3	𝑎0	𝑎0	PROPN
ajird-524	53	4	=	=	SYM
ajird-524	53	5	1	1	NUM
ajird-524	53	6	𝛼∆𝑡2	𝛼∆𝑡2	NOUN
ajird-524	53	7	;	;	PUNCT
ajird-524	53	8	𝑎1	𝑎1	PROPN
ajird-524	53	9	=	=	VERB
ajird-524	53	10	𝛿	𝛿	DET
ajird-524	53	11	𝛼∆𝑡	𝛼∆𝑡	NOUN
ajird-524	53	12	;	;	PUNCT
ajird-524	53	13	𝑎2	𝑎2	NOUN
ajird-524	53	14	=	=	SYM
ajird-524	53	15	1	1	NUM
ajird-524	53	16	𝛼∆𝑡	𝛼∆𝑡	NOUN
ajird-524	53	17	;	;	PUNCT
ajird-524	53	18	𝑎3	𝑎3	PROPN
ajird-524	53	19	=	=	SYM
ajird-524	53	20	1	1	NUM
ajird-524	53	21	2𝛼	2𝛼	NUM
ajird-524	53	22	−	−	NOUN
ajird-524	53	23	1	1	NUM
ajird-524	53	24	;	;	PUNCT
ajird-524	53	25	𝑎4	𝑎4	PROPN
ajird-524	53	26	=	=	PUNCT
ajird-524	53	27	𝛿	𝛿	ADJ
ajird-524	53	28	𝛼	𝛼	ADJ
ajird-524	53	29	−	−	PROPN
ajird-524	53	30	1	1	NUM
ajird-524	53	31	;	;	PUNCT
ajird-524	53	32	𝑎5	𝑎5	PROPN
ajird-524	53	33	=	=	SYM
ajird-524	53	34	∆𝑡	∆𝑡	PROPN
ajird-524	53	35	2	2	NUM
ajird-524	53	36	(	(	PUNCT
ajird-524	53	37	𝛿	𝛿	PRON
ajird-524	53	38	𝛼	𝛼	PRON
ajird-524	53	39	−	−	PROPN
ajird-524	53	40	2	2	NUM
ajird-524	53	41	)	)	PUNCT
ajird-524	53	42	;	;	PUNCT
ajird-524	53	43	𝑎6	𝑎6	NOUN
ajird-524	53	44	=	=	SYM
ajird-524	53	45	∆𝑡(1	∆𝑡(1	PROPN
ajird-524	53	46	−	−	PROPN
ajird-524	53	47	𝛿	𝛿	NOUN
ajird-524	53	48	)	)	PUNCT
ajird-524	53	49	;	;	PUNCT
ajird-524	53	50	𝑎7	𝑎7	NOUN
ajird-524	53	51	=	=	NOUN
ajird-524	53	52	𝛿∆𝑡.	𝛿∆𝑡.	NOUN
ajird-524	53	53	4	4	NUM
ajird-524	53	54	.	.	PUNCT
ajird-524	53	55	form	form	VERB
ajird-524	53	56	effective	effective	ADJ
ajird-524	53	57	stiffness	stiffness	NOUN
ajird-524	53	58	matrix	matrix	NOUN
ajird-524	53	59	�	�	NOUN
ajird-524	53	60	̂	̂	SYM
ajird-524	53	61	�	�	PROPN
ajird-524	53	62	:	:	PUNCT
ajird-524	53	63	�	�	PROPN
ajird-524	53	64	̂	̂	VERB
ajird-524	53	65	�	�	NOUN
ajird-524	53	66	=	=	SYM
ajird-524	53	67	𝐾	𝐾	NOUN
ajird-524	53	68	+	+	NOUN
ajird-524	53	69	𝑎0𝑀	𝑎0𝑀	NUM
ajird-524	53	70	+	+	CCONJ
ajird-524	53	71	𝑎1𝐶.	𝑎1𝐶.	PROPN
ajird-524	53	72	5	5	X
ajird-524	53	73	.	.	X
ajird-524	53	74	triangularize	triangularize	PROPN
ajird-524	53	75	�	�	PROPN
ajird-524	53	76	̂	̂	PROPN
ajird-524	53	77	�	�	PROPN
ajird-524	53	78	:	:	PUNCT
ajird-524	53	79	�	�	PROPN
ajird-524	53	80	̂	̂	SYM
ajird-524	53	81	�	�	NOUN
ajird-524	53	82	=	=	SYM
ajird-524	53	83	𝐿𝐷𝐿𝑡.	𝐿𝐷𝐿𝑡.	PROPN
ajird-524	53	84	american	american	PROPN
ajird-524	53	85	journal	journal	PROPN
ajird-524	53	86	of	of	ADP
ajird-524	53	87	interdisciplinary	interdisciplinary	ADJ
ajird-524	53	88	research	research	NOUN
ajird-524	53	89	and	and	CCONJ
ajird-524	53	90	development	development	NOUN
ajird-524	53	91	issn	issn	PROPN
ajird-524	53	92	online	online	NOUN
ajird-524	53	93	:	:	PUNCT
ajird-524	53	94	2771	2771	NUM
ajird-524	53	95	-	-	SYM
ajird-524	53	96	8948	8948	NUM
ajird-524	53	97	website	website	NOUN
ajird-524	53	98	:	:	PUNCT
ajird-524	53	99	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-524	53	100	volume	volume	NOUN
ajird-524	53	101	13	13	NUM
ajird-524	53	102	,	,	PUNCT
ajird-524	53	103	feb	feb	PROPN
ajird-524	53	104	.	.	PROPN
ajird-524	53	105	,	,	PUNCT
ajird-524	53	106	2023	2023	NUM
ajird-524	53	107	127	127	NUM
ajird-524	54	1	|	|	ADV
ajird-524	54	2	p	p	NOUN
ajird-524	54	3	a	a	DET
ajird-524	54	4	g	g	PROPN
ajird-524	54	5	e	e	PROPN
ajird-524	54	6	b.	b.	PROPN
ajird-524	54	7	for	for	ADP
ajird-524	54	8	each	each	DET
ajird-524	54	9	time	time	NOUN
ajird-524	54	10	step	step	NOUN
ajird-524	54	11	:	:	PUNCT
ajird-524	54	12	1	1	X
ajird-524	54	13	.	.	X
ajird-524	54	14	calculate	calculate	VERB
ajird-524	54	15	effective	effective	ADJ
ajird-524	54	16	loads	load	NOUN
ajird-524	54	17	at	at	ADP
ajird-524	54	18	time	time	NOUN
ajird-524	54	19	𝑡	𝑡	X
ajird-524	55	1	+	+	PROPN
ajird-524	55	2	∆𝑡	∆𝑡	NOUN
ajird-524	55	3	:	:	PUNCT
ajird-524	55	4	�	�	PROPN
ajird-524	55	5	̂	̂	SYM
ajird-524	55	6	�	�	NOUN
ajird-524	55	7	𝑡+∆𝑡	𝑡+∆𝑡	NOUN
ajird-524	55	8	=	=	PUNCT
ajird-524	55	9	𝑅𝑡+∆𝑡	𝑅𝑡+∆𝑡	PUNCT
ajird-524	55	10	+	+	NUM
ajird-524	55	11	𝑀(𝑎0𝑈𝑡	𝑀(𝑎0𝑈𝑡	NOUN
ajird-524	55	12	+	+	CCONJ
ajird-524	55	13	𝑎2	𝑎2	PROPN
ajird-524	55	14	�	�	PROPN
ajird-524	55	15	̇	̇	NOUN
ajird-524	55	16	�	�	PROPN
ajird-524	55	17	𝑡	𝑡	PROPN
ajird-524	55	18	+	+	X
ajird-524	55	19	𝑎3	𝑎3	PROPN
ajird-524	55	20	�	�	PROPN
ajird-524	55	21	̈	̈	SYM
ajird-524	55	22	�	�	NOUN
ajird-524	55	23	𝑡	𝑡	NOUN
ajird-524	55	24	)	)	PUNCT
ajird-524	55	25	+	+	CCONJ
ajird-524	55	26	𝐶(𝑎1𝑈𝑡	𝐶(𝑎1𝑈𝑡	NOUN
ajird-524	55	27	+	+	CCONJ
ajird-524	55	28	𝑎4	𝑎4	PROPN
ajird-524	55	29	�	�	PROPN
ajird-524	55	30	̇	̇	PROPN
ajird-524	55	31	�	�	PROPN
ajird-524	55	32	𝑡	𝑡	PROPN
ajird-524	55	33	+	+	PROPN
ajird-524	55	34	𝑎5	𝑎5	PROPN
ajird-524	55	35	�	�	PROPN
ajird-524	55	36	̈	̈	SYM
ajird-524	55	37	�	�	NOUN
ajird-524	55	38	𝑡	𝑡	NOUN
ajird-524	55	39	)	)	PUNCT
ajird-524	55	40	.	.	PUNCT
ajird-524	56	1	2	2	X
ajird-524	56	2	.	.	X
ajird-524	56	3	solve	solve	VERB
ajird-524	56	4	for	for	ADP
ajird-524	56	5	displacements	displacement	NOUN
ajird-524	56	6	at	at	ADP
ajird-524	56	7	time	time	NOUN
ajird-524	56	8	𝑡	𝑡	X
ajird-524	56	9	+	+	PROPN
ajird-524	56	10	∆𝑡	∆𝑡	NOUN
ajird-524	56	11	:	:	PUNCT
ajird-524	56	12	𝐿𝐷𝐿𝑡𝑈𝑡+∆𝑡	𝐿𝐷𝐿𝑡𝑈𝑡+∆𝑡	NOUN
ajird-524	56	13	=	=	SYM
ajird-524	56	14	�	�	PROPN
ajird-524	56	15	̂	̂	NOUN
ajird-524	56	16	�	�	NOUN
ajird-524	56	17	𝑡+∆𝑡.	𝑡+∆𝑡.	NOUN
ajird-524	56	18	3	3	NUM
ajird-524	56	19	.	.	NOUN
ajird-524	56	20	calculate	calculate	NOUN
ajird-524	56	21	accelerations	acceleration	NOUN
ajird-524	56	22	and	and	CCONJ
ajird-524	56	23	velocities	velocity	NOUN
ajird-524	56	24	at	at	ADP
ajird-524	56	25	time	time	NOUN
ajird-524	56	26	𝑡	𝑡	X
ajird-524	56	27	+	+	PROPN
ajird-524	56	28	∆𝑡	∆𝑡	NOUN
ajird-524	56	29	:	:	PUNCT
ajird-524	56	30	�	�	PROPN
ajird-524	56	31	̈	̈	NOUN
ajird-524	56	32	�	�	NOUN
ajird-524	56	33	𝑡+∆𝑡	𝑡+∆𝑡	NOUN
ajird-524	56	34	=	=	SYM
ajird-524	56	35	𝑎0(𝑈𝑡+∆𝑡	𝑎0(𝑈𝑡+∆𝑡	NOUN
ajird-524	56	36	−	−	PROPN
ajird-524	56	37	𝑈𝑡	𝑈𝑡	NOUN
ajird-524	56	38	)	)	PUNCT
ajird-524	56	39	−	−	PROPN
ajird-524	56	40	𝑎2	𝑎2	PROPN
ajird-524	56	41	�	�	PROPN
ajird-524	56	42	̇	̇	NOUN
ajird-524	56	43	�	�	PROPN
ajird-524	56	44	𝑡	𝑡	PROPN
ajird-524	56	45	−	−	PROPN
ajird-524	56	46	𝑎3	𝑎3	PROPN
ajird-524	56	47	�	�	PROPN
ajird-524	56	48	̈	̈	SYM
ajird-524	56	49	�	�	NOUN
ajird-524	56	50	𝑡	𝑡	NOUN
ajird-524	56	51	;	;	PUNCT
ajird-524	56	52	�	�	PROPN
ajird-524	56	53	̇	̇	PROPN
ajird-524	56	54	�	�	NOUN
ajird-524	56	55	𝑡+∆𝑡	𝑡+∆𝑡	PROPN
ajird-524	56	56	=	=	SYM
ajird-524	56	57	�	�	PROPN
ajird-524	56	58	̇	̇	PROPN
ajird-524	56	59	�	�	PROPN
ajird-524	56	60	𝑡	𝑡	PROPN
ajird-524	56	61	+	+	X
ajird-524	56	62	𝑎6	𝑎6	NOUN
ajird-524	56	63	�	�	PROPN
ajird-524	56	64	̈	̈	SYM
ajird-524	56	65	�	�	NOUN
ajird-524	56	66	𝑡	𝑡	PROPN
ajird-524	56	67	+	+	PROPN
ajird-524	56	68	𝑎7	𝑎7	NOUN
ajird-524	56	69	�	�	PROPN
ajird-524	56	70	̈	̈	SYM
ajird-524	56	71	�	�	NOUN
ajird-524	56	72	𝑡+∆𝑡	𝑡+∆𝑡	NOUN
ajird-524	56	73	.	.	PUNCT
ajird-524	57	1	step	step	NOUN
ajird-524	57	2	-	-	PUNCT
ajird-524	57	3	by	by	ADP
ajird-524	57	4	-	-	PUNCT
ajird-524	57	5	step	step	NOUN
ajird-524	57	6	solution	solution	NOUN
ajird-524	57	7	using	use	VERB
ajird-524	57	8	the	the	DET
ajird-524	57	9	bathe	bathe	NOUN
ajird-524	57	10	integration	integration	NOUN
ajird-524	57	11	method	method	NOUN
ajird-524	57	12	.	.	PUNCT
ajird-524	58	1	a.	a.	NOUN
ajird-524	58	2	initial	initial	ADJ
ajird-524	58	3	calculations	calculation	NOUN
ajird-524	58	4	:	:	PUNCT
ajird-524	58	5	1	1	X
ajird-524	58	6	.	.	X
ajird-524	58	7	form	form	NOUN
ajird-524	58	8	stiffness	stiffness	NOUN
ajird-524	58	9	matrix	matrix	NOUN
ajird-524	58	10	𝐾	𝐾	NOUN
ajird-524	58	11	,	,	PUNCT
ajird-524	58	12	mass	mass	ADJ
ajird-524	58	13	matrix	matrix	NOUN
ajird-524	58	14	𝑀	𝑀	PROPN
ajird-524	58	15	and	and	CCONJ
ajird-524	58	16	damping	damp	VERB
ajird-524	58	17	constant	constant	ADJ
ajird-524	58	18	𝐶.	𝐶.	PROPN
ajird-524	58	19	2	2	NUM
ajird-524	58	20	.	.	PUNCT
ajird-524	58	21	initialize	initialize	NOUN
ajird-524	58	22	𝑈0	𝑈0	NOUN
ajird-524	58	23	,	,	PUNCT
ajird-524	58	24	�	�	PROPN
ajird-524	58	25	̇	̇	PROPN
ajird-524	58	26	�	�	PROPN
ajird-524	58	27	0	0	NUM
ajird-524	58	28	and	and	CCONJ
ajird-524	58	29	�	�	PROPN
ajird-524	58	30	̈	̈	X
ajird-524	58	31	�	�	NOUN
ajird-524	58	32	0	0	NUM
ajird-524	58	33	.	.	NOUN
ajird-524	59	1	3	3	NUM
ajird-524	59	2	.	.	NOUN
ajird-524	59	3	select	select	ADJ
ajird-524	59	4	time	time	NOUN
ajird-524	59	5	step	step	NOUN
ajird-524	59	6	∆𝑡	∆𝑡	PROPN
ajird-524	59	7	and	and	CCONJ
ajird-524	59	8	calculate	calculate	VERB
ajird-524	59	9	integration	integration	NOUN
ajird-524	59	10	constants	constant	NOUN
ajird-524	59	11	:	:	PUNCT
ajird-524	59	12	𝑎0	𝑎0	PROPN
ajird-524	59	13	=	=	SYM
ajird-524	59	14	16	16	NUM
ajird-524	59	15	∆𝑡2	∆𝑡2	NOUN
ajird-524	59	16	;	;	PUNCT
ajird-524	60	1	𝑎1	𝑎1	NOUN
ajird-524	60	2	=	=	SYM
ajird-524	60	3	4	4	NUM
ajird-524	60	4	∆𝑡	∆𝑡	NOUN
ajird-524	60	5	;	;	PUNCT
ajird-524	60	6	𝑎2	𝑎2	NOUN
ajird-524	60	7	=	=	NOUN
ajird-524	60	8	9	9	NUM
ajird-524	60	9	∆𝑡2	∆𝑡2	NOUN
ajird-524	60	10	;	;	PUNCT
ajird-524	60	11	𝑎3	𝑎3	PROPN
ajird-524	60	12	=	=	SYM
ajird-524	60	13	3	3	NUM
ajird-524	60	14	∆𝑡	∆𝑡	NOUN
ajird-524	60	15	;	;	PUNCT
ajird-524	60	16	𝑎4	𝑎4	PROPN
ajird-524	60	17	=	=	SYM
ajird-524	60	18	2𝑎1	2𝑎1	NUM
ajird-524	60	19	;	;	PUNCT
ajird-524	60	20	𝑎5	𝑎5	PROPN
ajird-524	60	21	=	=	SYM
ajird-524	60	22	12	12	NUM
ajird-524	60	23	∆𝑡2	∆𝑡2	NOUN
ajird-524	60	24	;	;	PUNCT
ajird-524	60	25	𝑎6	𝑎6	NOUN
ajird-524	60	26	=	=	SYM
ajird-524	60	27	−	−	PROPN
ajird-524	60	28	3	3	NUM
ajird-524	60	29	∆𝑡2	∆𝑡2	NOUN
ajird-524	60	30	;	;	PUNCT
ajird-524	60	31	𝑎7	𝑎7	NOUN
ajird-524	60	32	=	=	SYM
ajird-524	60	33	−	−	PROPN
ajird-524	60	34	1	1	NUM
ajird-524	60	35	∆𝑡	∆𝑡	NOUN
ajird-524	60	36	.	.	PUNCT
ajird-524	61	1	4	4	X
ajird-524	61	2	.	.	X
ajird-524	61	3	form	form	VERB
ajird-524	61	4	effective	effective	ADJ
ajird-524	61	5	stiffness	stiffness	ADJ
ajird-524	61	6	matrices	matrix	NOUN
ajird-524	61	7	𝐾1̂	𝐾1̂	X
ajird-524	61	8	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
ajird-524	61	9	𝐾2̂	𝐾2̂	NOUN
ajird-524	61	10	:	:	PUNCT
ajird-524	61	11	�	�	X
ajird-524	61	12	̂	̂	VERB
ajird-524	61	13	�	�	NOUN
ajird-524	61	14	1	1	NUM
ajird-524	61	15	=	=	SYM
ajird-524	61	16	𝐾	𝐾	NOUN
ajird-524	61	17	+	+	NOUN
ajird-524	61	18	𝑎0𝑀	𝑎0𝑀	NUM
ajird-524	61	19	+	+	NUM
ajird-524	61	20	𝑎1𝐶	𝑎1𝐶	NOUN
ajird-524	61	21	,	,	PUNCT
ajird-524	61	22	�	�	PROPN
ajird-524	61	23	̂	̂	NOUN
ajird-524	61	24	�	�	NOUN
ajird-524	61	25	2	2	NUM
ajird-524	61	26	=	=	SYM
ajird-524	61	27	𝐾	𝐾	NOUN
ajird-524	61	28	+	+	NOUN
ajird-524	61	29	𝑎2𝑀	𝑎2𝑀	ADV
ajird-524	61	30	+	+	CCONJ
ajird-524	61	31	𝑎3𝐶.	𝑎3𝐶.	ADJ
ajird-524	61	32	5	5	NUM
ajird-524	61	33	.	.	PUNCT
ajird-524	61	34	triangularize	triangularize	PROPN
ajird-524	61	35	𝐾1̂	𝐾1̂	PROPN
ajird-524	61	36	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
ajird-524	61	37	𝐾2̂	𝐾2̂	NOUN
ajird-524	61	38	:	:	PUNCT
ajird-524	61	39	�	�	PROPN
ajird-524	61	40	̂	̂	VERB
ajird-524	61	41	�	�	NOUN
ajird-524	61	42	1	1	NUM
ajird-524	61	43	=	=	SYM
ajird-524	61	44	𝐿1𝐷1𝐿1	𝐿1𝐷1𝐿1	PUNCT
ajird-524	61	45	𝑡	𝑡	PROPN
ajird-524	61	46	,	,	PUNCT
ajird-524	61	47	�	�	PROPN
ajird-524	61	48	̂	̂	NOUN
ajird-524	61	49	�	�	NOUN
ajird-524	61	50	2	2	NUM
ajird-524	61	51	=	=	SYM
ajird-524	61	52	𝐿2𝐷2𝐿2	𝐿2𝐷2𝐿2	PROPN
ajird-524	61	53	𝑡.	𝑡.	PROPN
ajird-524	61	54	b.	b.	PROPN
ajird-524	61	55	for	for	ADP
ajird-524	61	56	each	each	DET
ajird-524	61	57	time	time	NOUN
ajird-524	61	58	step	step	NOUN
ajird-524	61	59	:	:	PUNCT
ajird-524	61	60	first	first	ADJ
ajird-524	61	61	sub	sub	NOUN
ajird-524	61	62	-	-	NOUN
ajird-524	61	63	step	step	NOUN
ajird-524	61	64	:	:	PUNCT
ajird-524	61	65	1	1	X
ajird-524	61	66	.	.	X
ajird-524	61	67	calculate	calculate	VERB
ajird-524	61	68	effective	effective	ADJ
ajird-524	61	69	loads	load	NOUN
ajird-524	61	70	at	at	ADP
ajird-524	61	71	time	time	NOUN
ajird-524	61	72	𝑡	𝑡	PROPN
ajird-524	61	73	+	+	PROPN
ajird-524	61	74	∆𝑡	∆𝑡	PROPN
ajird-524	61	75	2	2	NUM
ajird-524	61	76	:	:	PUNCT
ajird-524	61	77	�	�	PROPN
ajird-524	61	78	̂	̂	SYM
ajird-524	61	79	�	�	PROPN
ajird-524	61	80	𝑡+	𝑡+	PUNCT
ajird-524	61	81	∆𝑡	∆𝑡	PROPN
ajird-524	61	82	2	2	NUM
ajird-524	61	83	=	=	SYM
ajird-524	61	84	𝑅	𝑅	PROPN
ajird-524	61	85	𝑡+	𝑡+	X
ajird-524	61	86	∆𝑡	∆𝑡	PROPN
ajird-524	61	87	2	2	NUM
ajird-524	61	88	+	+	NUM
ajird-524	61	89	𝑀(𝑎0𝑈𝑡	𝑀(𝑎0𝑈𝑡	NOUN
ajird-524	61	90	+	+	CCONJ
ajird-524	61	91	𝑎4	𝑎4	PROPN
ajird-524	61	92	�	�	PROPN
ajird-524	61	93	̇	̇	PROPN
ajird-524	61	94	�	�	PROPN
ajird-524	61	95	𝑡	𝑡	PROPN
ajird-524	61	96	+	+	PROPN
ajird-524	61	97	�	�	PROPN
ajird-524	61	98	̈	̈	SYM
ajird-524	61	99	�	�	NOUN
ajird-524	61	100	𝑡	𝑡	NOUN
ajird-524	61	101	)	)	PUNCT
ajird-524	62	1	+	+	CCONJ
ajird-524	62	2	𝐶(𝑎1𝑈𝑡	𝐶(𝑎1𝑈𝑡	NOUN
ajird-524	62	3	+	+	CCONJ
ajird-524	62	4	�	�	PROPN
ajird-524	62	5	̇	̇	PROPN
ajird-524	62	6	�	�	NOUN
ajird-524	62	7	𝑡	𝑡	NOUN
ajird-524	62	8	)	)	PUNCT
ajird-524	62	9	.	.	PUNCT
ajird-524	63	1	2	2	X
ajird-524	63	2	.	.	X
ajird-524	63	3	solve	solve	VERB
ajird-524	63	4	for	for	ADP
ajird-524	63	5	displacements	displacement	NOUN
ajird-524	63	6	at	at	ADP
ajird-524	63	7	time	time	NOUN
ajird-524	63	8	𝑡	𝑡	X
ajird-524	63	9	+	+	PROPN
ajird-524	63	10	∆𝑡	∆𝑡	PROPN
ajird-524	63	11	2	2	NUM
ajird-524	63	12	:	:	PUNCT
ajird-524	63	13	𝐿1𝐷1𝐿1	𝐿1𝐷1𝐿1	X
ajird-524	63	14	𝑡𝑈	𝑡𝑈	ADJ
ajird-524	63	15	𝑡+	𝑡+	PUNCT
ajird-524	63	16	∆𝑡	∆𝑡	PROPN
ajird-524	63	17	2	2	NUM
ajird-524	63	18	=	=	SYM
ajird-524	63	19	�	�	PROPN
ajird-524	63	20	̂	̂	PROPN
ajird-524	63	21	�	�	PROPN
ajird-524	63	22	𝑡+	𝑡+	PUNCT
ajird-524	63	23	∆𝑡	∆𝑡	PROPN
ajird-524	63	24	2	2	NUM
ajird-524	63	25	.	.	PUNCT
ajird-524	64	1	3	3	X
ajird-524	64	2	.	.	NOUN
ajird-524	64	3	calculate	calculate	NOUN
ajird-524	64	4	accelerations	acceleration	NOUN
ajird-524	64	5	and	and	CCONJ
ajird-524	64	6	velocities	velocity	NOUN
ajird-524	64	7	at	at	ADP
ajird-524	64	8	time	time	NOUN
ajird-524	64	9	𝑡	𝑡	PROPN
ajird-524	64	10	+	+	PROPN
ajird-524	64	11	∆𝑡	∆𝑡	PROPN
ajird-524	64	12	2	2	NUM
ajird-524	64	13	:	:	PUNCT
ajird-524	64	14	�	�	PROPN
ajird-524	64	15	̈	̈	X
ajird-524	64	16	�	�	PROPN
ajird-524	64	17	𝑡+	𝑡+	PUNCT
ajird-524	64	18	∆𝑡	∆𝑡	PROPN
ajird-524	64	19	2	2	X
ajird-524	64	20	=	=	NOUN
ajird-524	64	21	𝑎1	𝑎1	INTJ
ajird-524	64	22	(	(	PUNCT
ajird-524	64	23	�	�	PROPN
ajird-524	64	24	̇	̇	PROPN
ajird-524	64	25	�	�	PROPN
ajird-524	64	26	𝑡+	𝑡+	PUNCT
ajird-524	64	27	∆𝑡	∆𝑡	PROPN
ajird-524	64	28	2	2	NUM
ajird-524	64	29	−	−	PROPN
ajird-524	64	30	�	�	PROPN
ajird-524	64	31	̇	̇	PROPN
ajird-524	64	32	�	�	PROPN
ajird-524	64	33	𝑡	𝑡	NOUN
ajird-524	64	34	)	)	PUNCT
ajird-524	64	35	−	−	PROPN
ajird-524	64	36	�	�	PROPN
ajird-524	64	37	̈	̈	X
ajird-524	64	38	�	�	NOUN
ajird-524	64	39	𝑡	𝑡	NOUN
ajird-524	64	40	;	;	PUNCT
ajird-524	64	41	�	�	PROPN
ajird-524	64	42	̇	̇	PROPN
ajird-524	64	43	�	�	PROPN
ajird-524	64	44	𝑡+	𝑡+	PUNCT
ajird-524	64	45	∆𝑡	∆𝑡	PROPN
ajird-524	64	46	2	2	X
ajird-524	64	47	=	=	NOUN
ajird-524	64	48	𝑎1	𝑎1	INTJ
ajird-524	64	49	(	(	PUNCT
ajird-524	64	50	𝑈	𝑈	PROPN
ajird-524	64	51	𝑡+	𝑡+	PUNCT
ajird-524	64	52	∆𝑡	∆𝑡	PROPN
ajird-524	64	53	2	2	NUM
ajird-524	64	54	−	−	NOUN
ajird-524	64	55	𝑈𝑡	𝑈𝑡	NOUN
ajird-524	64	56	)	)	PUNCT
ajird-524	64	57	−	−	PROPN
ajird-524	64	58	�	�	PROPN
ajird-524	64	59	̇	̇	PROPN
ajird-524	64	60	�	�	PROPN
ajird-524	64	61	𝑡	𝑡	PROPN
ajird-524	64	62	.	.	PUNCT
ajird-524	65	1	second	second	ADJ
ajird-524	65	2	sub	sub	NOUN
ajird-524	65	3	-	-	NOUN
ajird-524	65	4	step	step	NOUN
ajird-524	65	5	:	:	PUNCT
ajird-524	65	6	1	1	X
ajird-524	65	7	.	.	X
ajird-524	65	8	calculate	calculate	VERB
ajird-524	65	9	effective	effective	ADJ
ajird-524	65	10	loads	load	NOUN
ajird-524	65	11	at	at	ADP
ajird-524	65	12	time	time	NOUN
ajird-524	65	13	𝑡	𝑡	X
ajird-524	66	1	+	+	PROPN
ajird-524	66	2	∆𝑡	∆𝑡	NOUN
ajird-524	66	3	:	:	PUNCT
ajird-524	66	4	�	�	PROPN
ajird-524	66	5	̂	̂	SYM
ajird-524	66	6	�	�	NOUN
ajird-524	66	7	𝑡+∆𝑡	𝑡+∆𝑡	NOUN
ajird-524	66	8	=	=	PUNCT
ajird-524	66	9	𝑅𝑡+∆𝑡	𝑅𝑡+∆𝑡	PUNCT
ajird-524	66	10	+	+	NUM
ajird-524	66	11	𝑀	𝑀	PROPN
ajird-524	66	12	(	(	PUNCT
ajird-524	66	13	𝑎5𝑈	𝑎5𝑈	ADJ
ajird-524	66	14	𝑡+	𝑡+	PUNCT
ajird-524	66	15	∆𝑡	∆𝑡	PROPN
ajird-524	66	16	2	2	NUM
ajird-524	66	17	+	+	CCONJ
ajird-524	66	18	𝑎6𝑈𝑡	𝑎6𝑈𝑡	NOUN
ajird-524	66	19	+	+	CCONJ
ajird-524	66	20	𝑎1	𝑎1	PROPN
ajird-524	66	21	�	�	SYM
ajird-524	66	22	̇	̇	NOUN
ajird-524	66	23	�	�	PROPN
ajird-524	66	24	𝑡+	𝑡+	PUNCT
ajird-524	66	25	∆𝑡	∆𝑡	PROPN
ajird-524	66	26	2	2	NUM
ajird-524	66	27	+	+	CCONJ
ajird-524	66	28	𝑎7	𝑎7	PROPN
ajird-524	66	29	�	�	PROPN
ajird-524	66	30	̇	̇	NOUN
ajird-524	66	31	�	�	NOUN
ajird-524	66	32	𝑡	𝑡	NOUN
ajird-524	66	33	)	)	PUNCT
ajird-524	66	34	+	+	NUM
ajird-524	66	35	𝐶(𝑎1𝑈𝑡+∆𝑡/2	𝐶(𝑎1𝑈𝑡+∆𝑡/2	NOUN
ajird-524	66	36	+	+	CCONJ
ajird-524	66	37	𝑎7𝑈𝑡	𝑎7𝑈𝑡	NOUN
ajird-524	66	38	)	)	PUNCT
ajird-524	66	39	.	.	PUNCT
ajird-524	67	1	2	2	X
ajird-524	67	2	.	.	X
ajird-524	67	3	solve	solve	VERB
ajird-524	67	4	for	for	ADP
ajird-524	67	5	displacements	displacement	NOUN
ajird-524	67	6	at	at	ADP
ajird-524	67	7	time	time	NOUN
ajird-524	67	8	𝑡	𝑡	X
ajird-524	67	9	+	+	PROPN
ajird-524	67	10	∆𝑡	∆𝑡	NOUN
ajird-524	67	11	:	:	PUNCT
ajird-524	67	12	american	american	PROPN
ajird-524	67	13	journal	journal	PROPN
ajird-524	67	14	of	of	ADP
ajird-524	67	15	interdisciplinary	interdisciplinary	ADJ
ajird-524	67	16	research	research	NOUN
ajird-524	67	17	and	and	CCONJ
ajird-524	67	18	development	development	NOUN
ajird-524	67	19	issn	issn	PROPN
ajird-524	67	20	online	online	NOUN
ajird-524	67	21	:	:	PUNCT
ajird-524	67	22	2771	2771	NUM
ajird-524	67	23	-	-	SYM
ajird-524	67	24	8948	8948	NUM
ajird-524	67	25	website	website	NOUN
ajird-524	67	26	:	:	PUNCT
ajird-524	67	27	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-524	67	28	volume	volume	NOUN
ajird-524	67	29	13	13	NUM
ajird-524	67	30	,	,	PUNCT
ajird-524	67	31	feb	feb	PROPN
ajird-524	67	32	.	.	PROPN
ajird-524	67	33	,	,	PUNCT
ajird-524	67	34	2023	2023	NUM
ajird-524	67	35	128	128	NUM
ajird-524	68	1	|	|	ADV
ajird-524	68	2	p	p	X
ajird-524	68	3	a	a	DET
ajird-524	68	4	g	g	NOUN
ajird-524	68	5	e	e	NOUN
ajird-524	68	6	𝐿2𝐷2𝐿2	𝐿2𝐷2𝐿2	PROPN
ajird-524	68	7	𝑡𝑈𝑡+∆𝑡	𝑡𝑈𝑡+∆𝑡	X
ajird-524	68	8	=	=	SYM
ajird-524	68	9	�	�	PROPN
ajird-524	68	10	̂	̂	NOUN
ajird-524	68	11	�	�	NOUN
ajird-524	68	12	𝑡+∆𝑡.	𝑡+∆𝑡.	NOUN
ajird-524	68	13	3	3	NUM
ajird-524	68	14	.	.	NOUN
ajird-524	68	15	calculate	calculate	NOUN
ajird-524	68	16	accelerations	acceleration	NOUN
ajird-524	68	17	and	and	CCONJ
ajird-524	68	18	velocities	velocity	NOUN
ajird-524	68	19	at	at	ADP
ajird-524	68	20	time	time	NOUN
ajird-524	68	21	𝑡	𝑡	X
ajird-524	68	22	+	+	PROPN
ajird-524	68	23	∆𝑡	∆𝑡	NOUN
ajird-524	68	24	:	:	PUNCT
ajird-524	68	25	�	�	PROPN
ajird-524	68	26	̈	̈	NOUN
ajird-524	68	27	�	�	NOUN
ajird-524	68	28	𝑡+∆𝑡	𝑡+∆𝑡	NOUN
ajird-524	68	29	=	=	SYM
ajird-524	68	30	−𝑎7	−𝑎7	PROPN
ajird-524	68	31	�	�	PROPN
ajird-524	68	32	̇	̇	PROPN
ajird-524	68	33	�	�	PROPN
ajird-524	68	34	𝑡	𝑡	PROPN
ajird-524	68	35	−	−	NOUN
ajird-524	68	36	𝑎1	𝑎1	PROPN
ajird-524	68	37	�	�	PROPN
ajird-524	68	38	̇	̇	PROPN
ajird-524	68	39	�	�	PROPN
ajird-524	68	40	𝑡+	𝑡+	PUNCT
ajird-524	68	41	∆𝑡	∆𝑡	PROPN
ajird-524	68	42	2	2	NUM
ajird-524	68	43	+	+	CCONJ
ajird-524	68	44	𝑎3	𝑎3	PROPN
ajird-524	68	45	�	�	PROPN
ajird-524	68	46	̇	̇	NOUN
ajird-524	68	47	�	�	NOUN
ajird-524	68	48	𝑡+∆𝑡	𝑡+∆𝑡	PROPN
ajird-524	68	49	,	,	PUNCT
ajird-524	68	50	�	�	PROPN
ajird-524	68	51	̇	̇	NOUN
ajird-524	68	52	�	�	NOUN
ajird-524	68	53	𝑡+∆𝑡	𝑡+∆𝑡	NOUN
ajird-524	68	54	=	=	SYM
ajird-524	69	1	−𝑎7𝑈𝑡	−𝑎7𝑈𝑡	ADV
ajird-524	69	2	−	−	PROPN
ajird-524	69	3	𝑎1𝑈	𝑎1𝑈	NOUN
ajird-524	69	4	𝑡+	𝑡+	PUNCT
ajird-524	69	5	∆𝑡	∆𝑡	PROPN
ajird-524	69	6	2	2	NUM
ajird-524	69	7	+	+	NUM
ajird-524	69	8	𝑎3𝑈𝑡+∆𝑡	𝑎3𝑈𝑡+∆𝑡	NOUN
ajird-524	69	9	.	.	PUNCT
ajird-524	70	1	analysis	analysis	NOUN
ajird-524	70	2	and	and	CCONJ
ajird-524	70	3	results	result	NOUN
ajird-524	70	4	.	.	PUNCT
ajird-524	71	1	the	the	DET
ajird-524	71	2	study	study	NOUN
ajird-524	71	3	was	be	AUX
ajird-524	71	4	conducted	conduct	VERB
ajird-524	71	5	on	on	ADP
ajird-524	71	6	the	the	DET
ajird-524	71	7	following	follow	VERB
ajird-524	71	8	problem	problem	NOUN
ajird-524	71	9	:	:	PUNCT
ajird-524	71	10	meaning	mean	VERB
ajird-524	71	11	l=400	l=400	PROPN
ajird-524	71	12	m	m	PROPN
ajird-524	71	13	,	,	PUNCT
ajird-524	71	14	h=100	h=100	PROPN
ajird-524	71	15	m	m	NOUN
ajird-524	71	16	,	,	PUNCT
ajird-524	71	17	young	young	PROPN
ajird-524	71	18	's	's	PART
ajird-524	71	19	modulus	modulus	PROPN
ajird-524	71	20	e=1.e8pa	e=1.e8pa	PROPN
ajird-524	71	21	,	,	PUNCT
ajird-524	71	22	poisson	poisson	PROPN
ajird-524	71	23	's	's	PART
ajird-524	71	24	ratio	ratio	NOUN
ajird-524	71	25	ν=0.3	ν=0.3	NOUN
ajird-524	71	26	,	,	PUNCT
ajird-524	71	27	)	)	PUNCT
ajird-524	71	28	)	)	PUNCT
ajird-524	72	1	2-(1)+/((1e)),1(2/	2-(1)+/((1e)),1(2/	NUM
ajird-524	72	2	(	(	PUNCT
ajird-524	72	3			CCONJ
ajird-524	72	4	=+=	=+=	NOUN
ajird-524	72	5	e	e	NOUN
ajird-524	72	6	lame	lame	ADJ
ajird-524	72	7	coefficients	coefficient	NOUN
ajird-524	72	8	,	,	PUNCT
ajird-524	72	9	density	density	NOUN
ajird-524	72	10	ρ=1800pa	ρ=1800pa	NOUN
ajird-524	72	11	,	,	PUNCT
ajird-524	72	12	coefficient	coefficient	NOUN
ajird-524	72	13	of	of	ADP
ajird-524	72	14	the	the	DET
ajird-524	72	15	longitudinal	longitudinal	ADJ
ajird-524	72	16	and	and	CCONJ
ajird-524	72	17	transverse	transverse	NOUN
ajird-524	72	18	waves	wave	NOUN
ajird-524	72	19	of	of	ADP
ajird-524	72	20	the	the	DET
ajird-524	72	21	medium	medium	NOUN
ajird-524	72	22	were	be	AUX
ajird-524	72	23	calculated	calculate	VERB
ajird-524	72	24	by	by	ADP
ajird-524	72	25	the	the	DET
ajird-524	72	26	formula	formula	NOUN
ajird-524	72	27			NOUN
ajird-524	72	28	/)2(,/	/)2(,/	PUNCT
ajird-524	73	1	+	+	ADJ
ajird-524	73	2	=	=	SYM
ajird-524	73	3	=	=	SYM
ajird-524	73	4	sp	sp	ADP
ajird-524	73	5	cc	cc	PROPN
ajird-524	73	6	.	.	PUNCT
ajird-524	74	1	a	a	DET
ajird-524	74	2	triangular	triangular	NOUN
ajird-524	74	3	element	element	NOUN
ajird-524	74	4	with	with	ADP
ajird-524	74	5	six	six	NUM
ajird-524	74	6	nodes	node	NOUN
ajird-524	74	7	,	,	PUNCT
ajird-524	74	8	the	the	DET
ajird-524	74	9	second	second	ADJ
ajird-524	74	10	degree	degree	NOUN
ajird-524	74	11	of	of	ADP
ajird-524	74	12	accuracy	accuracy	NOUN
ajird-524	74	13	,	,	PUNCT
ajird-524	74	14	was	be	AUX
ajird-524	74	15	used	use	VERB
ajird-524	74	16	as	as	ADP
ajird-524	74	17	finite	finite	ADJ
ajird-524	74	18	elements	element	NOUN
ajird-524	74	19	.	.	PUNCT
ajird-524	75	1	a	a	DET
ajird-524	75	2	study	study	NOUN
ajird-524	75	3	was	be	AUX
ajird-524	75	4	carried	carry	VERB
ajird-524	75	5	out	out	ADP
ajird-524	75	6	on	on	ADP
ajird-524	75	7	the	the	DET
ajird-524	75	8	influence	influence	NOUN
ajird-524	75	9	of	of	ADP
ajird-524	75	10	the	the	DET
ajird-524	75	11	number	number	NOUN
ajird-524	75	12	of	of	ADP
ajird-524	75	13	elements	element	NOUN
ajird-524	75	14	on	on	ADP
ajird-524	75	15	the	the	DET
ajird-524	75	16	accuracy	accuracy	NOUN
ajird-524	75	17	of	of	ADP
ajird-524	75	18	the	the	DET
ajird-524	75	19	solution	solution	NOUN
ajird-524	75	20	,	,	PUNCT
ajird-524	75	21	the	the	DET
ajird-524	75	22	following	follow	VERB
ajird-524	75	23	table	table	NOUN
ajird-524	75	24	shows	show	VERB
ajird-524	75	25	the	the	DET
ajird-524	75	26	value	value	NOUN
ajird-524	75	27	of	of	ADP
ajird-524	75	28	the	the	DET
ajird-524	75	29	displacements	displacement	NOUN
ajird-524	75	30	in	in	ADP
ajird-524	75	31	the	the	DET
ajird-524	75	32	center	center	NOUN
ajird-524	75	33	of	of	ADP
ajird-524	75	34	the	the	DET
ajird-524	75	35	two	two	NUM
ajird-524	75	36	-	-	PUNCT
ajird-524	75	37	dimensional	dimensional	ADJ
ajird-524	75	38	region	region	NOUN
ajird-524	75	39	at	at	ADP
ajird-524	75	40	the	the	DET
ajird-524	75	41	point	point	NOUN
ajird-524	75	42	(	(	PUNCT
ajird-524	75	43	200,50	200,50	NUM
ajird-524	75	44	)	)	PUNCT
ajird-524	75	45	,	,	PUNCT
ajird-524	75	46	the	the	DET
ajird-524	75	47	calculation	calculation	NOUN
ajird-524	75	48	was	be	AUX
ajird-524	75	49	carried	carry	VERB
ajird-524	75	50	out	out	ADP
ajird-524	75	51	by	by	ADP
ajird-524	75	52	the	the	DET
ajird-524	75	53	newmark	newmark	PROPN
ajird-524	75	54	method	method	NOUN
ajird-524	75	55	,	,	PUNCT
ajird-524	75	56	with	with	ADP
ajird-524	75	57	a	a	DET
ajird-524	75	58	step	step	NOUN
ajird-524	75	59	dt=0.001sec	dt=0.001sec	NOUN
ajird-524	75	60	at	at	ADP
ajird-524	75	61	a	a	DET
ajird-524	75	62	point	point	NOUN
ajird-524	75	63	in	in	ADP
ajird-524	75	64	time	time	NOUN
ajird-524	75	65	t=1sec	t=1sec	PROPN
ajird-524	75	66	:	:	PUNCT
ajird-524	75	67	it	it	PRON
ajird-524	75	68	can	can	AUX
ajird-524	75	69	be	be	AUX
ajird-524	75	70	seen	see	VERB
ajird-524	75	71	from	from	ADP
ajird-524	75	72	the	the	DET
ajird-524	75	73	table	table	NOUN
ajird-524	75	74	that	that	SCONJ
ajird-524	75	75	with	with	ADP
ajird-524	75	76	an	an	DET
ajird-524	75	77	increase	increase	NOUN
ajird-524	75	78	in	in	ADP
ajird-524	75	79	the	the	DET
ajird-524	75	80	partition	partition	NOUN
ajird-524	75	81	,	,	PUNCT
ajird-524	75	82	the	the	DET
ajird-524	75	83	accuracy	accuracy	NOUN
ajird-524	75	84	of	of	ADP
ajird-524	75	85	the	the	DET
ajird-524	75	86	result	result	NOUN
ajird-524	75	87	increases	increase	NOUN
ajird-524	75	88	and	and	CCONJ
ajird-524	75	89	when	when	SCONJ
ajird-524	75	90	the	the	DET
ajird-524	75	91	sides	side	NOUN
ajird-524	75	92	are	be	AUX
ajird-524	75	93	divided	divide	VERB
ajird-524	75	94	into	into	ADP
ajird-524	75	95	100/25	100/25	NUM
ajird-524	75	96	we	we	PRON
ajird-524	75	97	have	have	VERB
ajird-524	75	98	4	4	NUM
ajird-524	75	99	correct	correct	ADJ
ajird-524	75	100	digits	digit	NOUN
ajird-524	75	101	.	.	PUNCT
ajird-524	76	1	next	next	ADV
ajird-524	76	2	,	,	PUNCT
ajird-524	76	3	a	a	DET
ajird-524	76	4	comparative	comparative	ADJ
ajird-524	76	5	analysis	analysis	NOUN
ajird-524	76	6	of	of	ADP
ajird-524	76	7	the	the	DET
ajird-524	76	8	calculations	calculation	NOUN
ajird-524	76	9	by	by	ADP
ajird-524	76	10	the	the	DET
ajird-524	76	11	newmark	newmark	PROPN
ajird-524	76	12	method	method	NOUN
ajird-524	76	13	and	and	CCONJ
ajird-524	76	14	the	the	DET
ajird-524	76	15	bathe	bathe	NOUN
ajird-524	76	16	method	method	NOUN
ajird-524	76	17	was	be	AUX
ajird-524	76	18	carried	carry	VERB
ajird-524	76	19	out	out	ADP
ajird-524	76	20	.	.	PUNCT
ajird-524	77	1	the	the	DET
ajird-524	77	2	following	follow	VERB
ajird-524	77	3	table	table	NOUN
ajird-524	77	4	shows	show	VERB
ajird-524	77	5	the	the	DET
ajird-524	77	6	offset	offset	ADJ
ajird-524	77	7	values	value	NOUN
ajird-524	77	8	ux	ux	INTJ
ajird-524	77	9	at	at	ADP
ajird-524	77	10	the	the	DET
ajird-524	77	11	point	point	NOUN
ajird-524	77	12	(	(	PUNCT
ajird-524	77	13	200,50	200,50	NUM
ajird-524	77	14	)	)	PUNCT
ajird-524	77	15	at	at	ADP
ajird-524	77	16	a	a	DET
ajird-524	77	17	point	point	NOUN
ajird-524	77	18	in	in	ADP
ajird-524	77	19	time	time	NOUN
ajird-524	77	20	t=1	t=1	PROPN
ajird-524	77	21	sec	sec	PROPN
ajird-524	77	22	.	.	PROPN
ajird-524	78	1	with	with	ADP
ajird-524	78	2	the	the	DET
ajird-524	78	3	same	same	ADJ
ajird-524	78	4	physical	physical	ADJ
ajird-524	78	5	parameters	parameter	NOUN
ajird-524	78	6	as	as	ADP
ajird-524	78	7	above	above	ADV
ajird-524	78	8	.	.	PUNCT
ajird-524	79	1	it	it	PRON
ajird-524	79	2	can	can	AUX
ajird-524	79	3	be	be	AUX
ajird-524	79	4	seen	see	VERB
ajird-524	79	5	from	from	ADP
ajird-524	79	6	the	the	DET
ajird-524	79	7	table	table	NOUN
ajird-524	79	8	that	that	SCONJ
ajird-524	79	9	at	at	ADP
ajird-524	79	10	a	a	DET
ajird-524	79	11	step	step	NOUN
ajird-524	79	12	0.0001	0.0001	NUM
ajird-524	79	13	newmark	newmark	NOUN
ajird-524	79	14	's	's	PART
ajird-524	79	15	method	method	NOUN
ajird-524	79	16	yields	yield	VERB
ajird-524	79	17	an	an	DET
ajird-524	79	18	exact	exact	ADJ
ajird-524	79	19	solution	solution	NOUN
ajird-524	79	20	,	,	PUNCT
ajird-524	79	21	while	while	SCONJ
ajird-524	79	22	bathe	bathe	VERB
ajird-524	79	23	's	's	PART
ajird-524	79	24	method	method	NOUN
ajird-524	79	25	yields	yield	VERB
ajird-524	79	26	an	an	DET
ajird-524	79	27	exact	exact	ADJ
ajird-524	79	28	solution	solution	NOUN
ajird-524	79	29	with	with	ADP
ajird-524	79	30	a	a	DET
ajird-524	79	31	step	step	NOUN
ajird-524	79	32	0.001	0.001	NUM
ajird-524	79	33	.	.	PUNCT
ajird-524	80	1	thus	thus	ADV
ajird-524	80	2	,	,	PUNCT
ajird-524	80	3	the	the	DET
ajird-524	80	4	bathe	bathe	NOUN
ajird-524	80	5	method	method	NOUN
ajird-524	80	6	produces	produce	VERB
ajird-524	80	7	a	a	DET
ajird-524	80	8	more	more	ADV
ajird-524	80	9	accurate	accurate	ADJ
ajird-524	80	10	result	result	NOUN
ajird-524	80	11	with	with	ADP
ajird-524	80	12	a	a	DET
ajird-524	80	13	larger	large	ADJ
ajird-524	80	14	step	step	NOUN
ajird-524	80	15	.	.	PUNCT
ajird-524	81	1	next	next	ADV
ajird-524	81	2	,	,	PUNCT
ajird-524	81	3	consider	consider	VERB
ajird-524	81	4	the	the	DET
ajird-524	81	5	oscillation	oscillation	NOUN
ajird-524	81	6	of	of	ADP
ajird-524	81	7	the	the	DET
ajird-524	81	8	midpoint	midpoint	NOUN
ajird-524	81	9	of	of	ADP
ajird-524	81	10	a	a	DET
ajird-524	81	11	two	two	NUM
ajird-524	81	12	-	-	PUNCT
ajird-524	81	13	dimensional	dimensional	ADJ
ajird-524	81	14	body	body	NOUN
ajird-524	81	15	with	with	ADP
ajird-524	81	16	the	the	DET
ajird-524	81	17	above	above	ADJ
ajird-524	81	18	physical	physical	ADJ
ajird-524	81	19	and	and	CCONJ
ajird-524	81	20	geometric	geometric	ADJ
ajird-524	81	21	characteristics	characteristic	NOUN
ajird-524	81	22	.	.	PUNCT
ajird-524	82	1	the	the	DET
ajird-524	82	2	figure	figure	NOUN
ajird-524	82	3	shows	show	VERB
ajird-524	82	4	the	the	DET
ajird-524	82	5	movement	movement	NOUN
ajird-524	82	6	of	of	ADP
ajird-524	82	7	a	a	DET
ajird-524	82	8	point	point	NOUN
ajird-524	82	9	for	for	ADP
ajird-524	82	10	4	4	NUM
ajird-524	82	11	seconds	second	NOUN
ajird-524	82	12	.	.	PUNCT
ajird-524	83	1	amount	amount	NOUN
ajird-524	83	2	of	of	ADP
ajird-524	83	3	elements\bias	elements\bia	NOUN
ajird-524	83	4	212(20/5	212(20/5	NUM
ajird-524	83	5	)	)	PUNCT
ajird-524	83	6	858(40/10	858(40/10	NUM
ajird-524	83	7	)	)	PUNCT
ajird-524	83	8	1896(60/15	1896(60/15	NUM
ajird-524	83	9	)	)	PUNCT
ajird-524	83	10	5306(100/25	5306(100/25	NUM
ajird-524	83	11	)	)	PUNCT
ajird-524	83	12	ux	ux	ADP
ajird-524	83	13	-0.00728348	-0.00728348	PROPN
ajird-524	83	14	-0.00739348	-0.00739348	PROPN
ajird-524	83	15	-0.00742446	-0.00742446	PROPN
ajird-524	83	16	-0.00743622	-0.00743622	PUNCT
ajird-524	83	17	uy	uy	ADP
ajird-524	83	18	0.00130321	0.00130321	NUM
ajird-524	83	19	0.00126898	0.00126898	NUM
ajird-524	83	20	0.00129406	0.00129406	NUM
ajird-524	83	21	0.00129469	0.00129469	NUM
ajird-524	83	22	step\	step\	NOUN
ajird-524	83	23	method	method	NOUN
ajird-524	83	24	0.05	0.05	NUM
ajird-524	83	25	0.01	0.01	NUM
ajird-524	83	26	0.005	0.005	NUM
ajird-524	83	27	0.001	0.001	NUM
ajird-524	83	28	0.0001	0.0001	NUM
ajird-524	83	29	newmark	newmark	PROPN
ajird-524	83	30	-0.006348	-0.006348	NOUN
ajird-524	83	31	-0.007408	-0.007408	PROPN
ajird-524	83	32	-0.007421	-0.007421	PROPN
ajird-524	84	1	-0.007436	-0.007436	PRON
ajird-524	84	2	-0.007424	-0.007424	VERB
ajird-524	84	3	bathe	bathe	ADJ
ajird-524	84	4	-0.006994	-0.006994	PUNCT
ajird-524	84	5	-0.007417	-0.007417	PROPN
ajird-524	84	6	-0.007421	-0.007421	PROPN
ajird-524	84	7	-0.007424	-0.007424	PROPN
ajird-524	84	8	-0.007424	-0.007424	PROPN
ajird-524	84	9	american	american	PROPN
ajird-524	84	10	journal	journal	PROPN
ajird-524	84	11	of	of	ADP
ajird-524	84	12	interdisciplinary	interdisciplinary	ADJ
ajird-524	84	13	research	research	NOUN
ajird-524	84	14	and	and	CCONJ
ajird-524	84	15	development	development	NOUN
ajird-524	84	16	issn	issn	PROPN
ajird-524	84	17	online	online	NOUN
ajird-524	84	18	:	:	PUNCT
ajird-524	84	19	2771	2771	NUM
ajird-524	84	20	-	-	SYM
ajird-524	84	21	8948	8948	NUM
ajird-524	84	22	website	website	NOUN
ajird-524	84	23	:	:	PUNCT
ajird-524	84	24	www.ajird.journalspark.org	www.ajird.journalspark.org	ADJ
ajird-524	84	25	volume	volume	NOUN
ajird-524	84	26	13	13	NUM
ajird-524	84	27	,	,	PUNCT
ajird-524	84	28	feb	feb	PROPN
ajird-524	84	29	.	.	PROPN
ajird-524	84	30	,	,	PUNCT
ajird-524	84	31	2023	2023	NUM
ajird-524	84	32	129	129	NUM
ajird-524	85	1	|	|	ADV
ajird-524	85	2	p	p	ADP
ajird-524	85	3	a	a	DET
ajird-524	85	4	g	g	NOUN
ajird-524	85	5	e	e	NOUN
ajird-524	85	6	the	the	DET
ajird-524	85	7	dynamics	dynamic	NOUN
ajird-524	85	8	of	of	ADP
ajird-524	85	9	wave	wave	NOUN
ajird-524	85	10	propagation	propagation	NOUN
ajird-524	85	11	along	along	ADP
ajird-524	85	12	the	the	DET
ajird-524	85	13	line	line	NOUN
ajird-524	85	14	y=50	y=50	PROPN
ajird-524	85	15	is	be	AUX
ajird-524	85	16	shown	show	VERB
ajird-524	85	17	in	in	ADP
ajird-524	85	18	the	the	DET
ajird-524	85	19	following	follow	VERB
ajird-524	85	20	figure	figure	NOUN
ajird-524	85	21	conclusion	conclusion	NOUN
ajird-524	85	22	studies	study	NOUN
ajird-524	85	23	have	have	AUX
ajird-524	85	24	shown	show	VERB
ajird-524	85	25	that	that	SCONJ
ajird-524	85	26	for	for	ADP
ajird-524	85	27	dynamic	dynamic	ADJ
ajird-524	85	28	calculation	calculation	NOUN
ajird-524	85	29	it	it	PRON
ajird-524	85	30	is	be	AUX
ajird-524	85	31	not	not	PART
ajird-524	85	32	necessary	necessary	ADJ
ajird-524	85	33	to	to	PART
ajird-524	85	34	thicken	thicken	VERB
ajird-524	85	35	the	the	DET
ajird-524	85	36	mesh	mesh	NOUN
ajird-524	85	37	,	,	PUNCT
ajird-524	85	38	the	the	DET
ajird-524	85	39	use	use	NOUN
ajird-524	85	40	of	of	ADP
ajird-524	85	41	the	the	DET
ajird-524	85	42	bate	bate	NOUN
ajird-524	85	43	method	method	NOUN
ajird-524	85	44	is	be	AUX
ajird-524	85	45	preferable	preferable	ADJ
ajird-524	85	46	to	to	ADP
ajird-524	85	47	the	the	DET
ajird-524	85	48	use	use	NOUN
ajird-524	85	49	of	of	ADP
ajird-524	85	50	the	the	DET
ajird-524	85	51	newmark	newmark	NOUN
ajird-524	85	52	method	method	NOUN
ajird-524	85	53	,	,	PUNCT
ajird-524	85	54	the	the	DET
ajird-524	85	55	use	use	NOUN
ajird-524	85	56	of	of	ADP
ajird-524	85	57	the	the	DET
ajird-524	85	58	boundary	boundary	ADJ
ajird-524	85	59	transparency	transparency	NOUN
ajird-524	85	60	condition	condition	NOUN
ajird-524	85	61	correctly	correctly	ADV
ajird-524	85	62	simulates	simulate	VERB
ajird-524	85	63	the	the	DET
ajird-524	85	64	passage	passage	NOUN
ajird-524	85	65	of	of	ADP
ajird-524	85	66	the	the	DET
ajird-524	85	67	wave	wave	NOUN
ajird-524	85	68	.	.	PUNCT
ajird-524	86	1	references	reference	NOUN
ajird-524	86	2	1	1	NUM
ajird-524	86	3	.	.	PUNCT
ajird-524	87	1	сегерлинд	сегерлинд	PROPN
ajird-524	87	2	л	л	PROPN
ajird-524	87	3	.	.	PUNCT
ajird-524	88	1	применение	применение	PROPN
ajird-524	88	2	метода	метода	PROPN
ajird-524	88	3	конечных	конечных	PROPN
ajird-524	88	4	элементов	элементов	NOUN
ajird-524	88	5	–	–	PUNCT
ajird-524	88	6	москва	москва	PROPN
ajird-524	88	7	.	.	PUNCT
ajird-524	88	8	:	:	PUNCT
ajird-524	88	9	«	«	PUNCT
ajird-524	88	10	мир	мир	X
ajird-524	88	11	»	»	NOUN
ajird-524	88	12	,	,	PUNCT
ajird-524	88	13	1979	1979	NUM
ajird-524	88	14	.	.	PUNCT
ajird-524	88	15	–	–	PUNCT
ajird-524	88	16	392с	392с	NUM
ajird-524	88	17	.	.	PUNCT
ajird-524	89	1	[	[	X
ajird-524	89	2	segerlind	segerlind	NOUN
ajird-524	89	3	,	,	PUNCT
ajird-524	89	4	l.	l.	PROPN
ajird-524	89	5	1979	1979	NUM
ajird-524	89	6	.	.	PUNCT
ajird-524	90	1	application	application	NOUN
ajird-524	90	2	of	of	ADP
ajird-524	90	3	the	the	DET
ajird-524	90	4	finite	finite	ADJ
ajird-524	90	5	element	element	NOUN
ajird-524	90	6	method	method	NOUN
ajird-524	90	7	.	.	PUNCT
ajird-524	91	1	moscow	moscow	PROPN
ajird-524	91	2	.	.	PUNCT
ajird-524	92	1	mir	mir	PROPN
ajird-524	92	2	.	.	PUNCT
ajird-524	92	3	392p	392p	NUM
ajird-524	92	4	.	.	PUNCT
ajird-524	92	5	]	]	PUNCT
ajird-524	93	1	(	(	PUNCT
ajird-524	93	2	in	in	ADP
ajird-524	93	3	russian	russian	NOUN
ajird-524	93	4	)	)	PUNCT
ajird-524	93	5	.	.	PUNCT
ajird-524	94	1	2	2	X
ajird-524	94	2	.	.	X
ajird-524	94	3	зенкевич	зенкевич	NOUN
ajird-524	94	4	,	,	PUNCT
ajird-524	94	5	о	о	PROPN
ajird-524	94	6	.	.	PUNCT
ajird-524	94	7	метод	метод	PROPN
ajird-524	94	8	конечных	конечных	PROPN
ajird-524	94	9	элементов	элементов	PROPN
ajird-524	94	10	в	в	PROPN
ajird-524	94	11	технике	технике	VERB
ajird-524	94	12	.	.	PUNCT
ajird-524	95	1	–	–	PUNCT
ajird-524	95	2	москва	москва	PROPN
ajird-524	95	3	:	:	PUNCT
ajird-524	95	4	«	«	PUNCT
ajird-524	95	5	мир	мир	X
ajird-524	95	6	»	»	NOUN
ajird-524	95	7	,	,	PUNCT
ajird-524	95	8	1975	1975	NUM
ajird-524	95	9	.	.	PUNCT
ajird-524	96	1	–	–	PUNCT
ajird-524	96	2	541с	541с	NOUN
ajird-524	96	3	.	.	PUNCT
ajird-524	97	1	[	[	X
ajird-524	97	2	zienkiewicz	zienkiewicz	INTJ
ajird-524	97	3	,	,	PUNCT
ajird-524	97	4	o.	o.	NOUN
ajird-524	97	5	1975	1975	NUM
ajird-524	97	6	.	.	PUNCT
ajird-524	98	1	the	the	DET
ajird-524	98	2	finite	finite	PROPN
ajird-524	98	3	element	element	NOUN
ajird-524	98	4	method	method	NOUN
ajird-524	98	5	in	in	ADP
ajird-524	98	6	engineering	engineering	NOUN
ajird-524	98	7	science	science	NOUN
ajird-524	98	8	.	.	PUNCT
ajird-524	99	1	moscow	moscow	PROPN
ajird-524	99	2	.	.	PUNCT
ajird-524	100	1	mir	mir	PROPN
ajird-524	100	2	.	.	PUNCT
ajird-524	100	3	541p	541p	PROPN
ajird-524	100	4	.	.	PUNCT
ajird-524	100	5	]	]	PUNCT
ajird-524	101	1	(	(	PUNCT
ajird-524	101	2	in	in	ADP
ajird-524	101	3	russian	russian	NOUN
ajird-524	101	4	)	)	PUNCT
ajird-524	101	5	.	.	PUNCT
ajird-524	102	1	3	3	X
ajird-524	102	2	.	.	X
ajird-524	102	3	k.	k.	PROPN
ajird-524	102	4	bathe	bathe	PROPN
ajird-524	102	5	,	,	PUNCT
ajird-524	102	6	2014	2014	NUM
ajird-524	102	7	.	.	PUNCT
ajird-524	103	1	finite	finite	PROPN
ajird-524	103	2	element	element	NOUN
ajird-524	103	3	procedures	procedure	NOUN
ajird-524	103	4	.	.	PUNCT
ajird-524	104	1	second	second	ADJ
ajird-524	104	2	edition	edition	PROPN
ajird-524	104	3	.	.	PUNCT
ajird-524	105	1	watertown	watertown	PROPN
ajird-524	105	2	.	.	PROPN
ajird-524	105	3	1043p	1043p	NUM
ajird-524	105	4	.	.	PUNCT