id	sid	tid	token	lemma	pos
american_scientific_journal-7479	1	1	332	332	NUM
american_scientific_journal-7479	1	2	american	american	ADJ
american_scientific_journal-7479	1	3	academic	academic	ADJ
american_scientific_journal-7479	1	4	scientific	scientific	ADJ
american_scientific_journal-7479	1	5	research	research	NOUN
american_scientific_journal-7479	1	6	journal	journal	NOUN
american_scientific_journal-7479	1	7	for	for	ADP
american_scientific_journal-7479	1	8	engineering	engineering	NOUN
american_scientific_journal-7479	1	9	,	,	PUNCT
american_scientific_journal-7479	1	10	technology	technology	NOUN
american_scientific_journal-7479	1	11	,	,	PUNCT
american_scientific_journal-7479	1	12	and	and	CCONJ
american_scientific_journal-7479	1	13	sciences	sciences	PROPN
american_scientific_journal-7479	1	14	issn	issn	PROPN
american_scientific_journal-7479	1	15	(	(	PUNCT
american_scientific_journal-7479	1	16	print	print	NOUN
american_scientific_journal-7479	1	17	)	)	PUNCT
american_scientific_journal-7479	1	18	2313	2313	NUM
american_scientific_journal-7479	1	19	-	-	SYM
american_scientific_journal-7479	1	20	4410	4410	NUM
american_scientific_journal-7479	1	21	,	,	PUNCT
american_scientific_journal-7479	1	22	issn	issn	PROPN
american_scientific_journal-7479	1	23	(	(	PUNCT
american_scientific_journal-7479	1	24	online	online	ADJ
american_scientific_journal-7479	1	25	)	)	PUNCT
american_scientific_journal-7479	1	26	2313	2313	NUM
american_scientific_journal-7479	1	27	-	-	SYM
american_scientific_journal-7479	1	28	4402	4402	NUM
american_scientific_journal-7479	1	29	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-7479	1	30	application	application	NOUN
american_scientific_journal-7479	1	31	the	the	DET
american_scientific_journal-7479	1	32	adomian	adomian	NOUN
american_scientific_journal-7479	1	33	decomposition	decomposition	NOUN
american_scientific_journal-7479	1	34	method	method	NOUN
american_scientific_journal-7479	1	35	to	to	ADP
american_scientific_journal-7479	1	36	the	the	DET
american_scientific_journal-7479	1	37	dynamic	dynamic	ADJ
american_scientific_journal-7479	1	38	response	response	NOUN
american_scientific_journal-7479	1	39	analysis	analysis	NOUN
american_scientific_journal-7479	1	40	of	of	ADP
american_scientific_journal-7479	1	41	cracked	crack	VERB
american_scientific_journal-7479	1	42	beam	beam	NOUN
american_scientific_journal-7479	1	43	under	under	ADP
american_scientific_journal-7479	1	44	moving	move	VERB
american_scientific_journal-7479	1	45	load	load	NOUN
american_scientific_journal-7479	1	46	naseradin	naseradin	VERB
american_scientific_journal-7479	1	47	abujnah	abujnah	PROPN
american_scientific_journal-7479	1	48	*	*	PUNCT
american_scientific_journal-7479	1	49	faculty	faculty	NOUN
american_scientific_journal-7479	1	50	of	of	ADP
american_scientific_journal-7479	1	51	technical	technical	ADJ
american_scientific_journal-7479	1	52	engineering	engineering	NOUN
american_scientific_journal-7479	1	53	mesallata	mesallata	NOUN
american_scientific_journal-7479	1	54	,	,	PUNCT
american_scientific_journal-7479	1	55	mesallata	mesallata	PROPN
american_scientific_journal-7479	1	56	,	,	PUNCT
american_scientific_journal-7479	1	57	libya	libya	PROPN
american_scientific_journal-7479	1	58	email	email	NOUN
american_scientific_journal-7479	1	59	:	:	PUNCT
american_scientific_journal-7479	1	60	naabujnah@gmail.com	naabujnah@gmail.com	X
american_scientific_journal-7479	1	61	abstract	abstract	ADJ
american_scientific_journal-7479	1	62	in	in	ADP
american_scientific_journal-7479	1	63	this	this	DET
american_scientific_journal-7479	1	64	article	article	NOUN
american_scientific_journal-7479	1	65	,	,	PUNCT
american_scientific_journal-7479	1	66	the	the	DET
american_scientific_journal-7479	1	67	adomian	adomian	NOUN
american_scientific_journal-7479	1	68	method	method	NOUN
american_scientific_journal-7479	1	69	of	of	ADP
american_scientific_journal-7479	1	70	decomposition	decomposition	NOUN
american_scientific_journal-7479	1	71	(	(	PUNCT
american_scientific_journal-7479	1	72	adm	adm	PROPN
american_scientific_journal-7479	1	73	)	)	PUNCT
american_scientific_journal-7479	1	74	is	be	AUX
american_scientific_journal-7479	1	75	used	use	VERB
american_scientific_journal-7479	1	76	to	to	PART
american_scientific_journal-7479	1	77	examine	examine	VERB
american_scientific_journal-7479	1	78	the	the	DET
american_scientific_journal-7479	1	79	vibration	vibration	NOUN
american_scientific_journal-7479	1	80	of	of	ADP
american_scientific_journal-7479	1	81	a	a	DET
american_scientific_journal-7479	1	82	simply	simply	ADV
american_scientific_journal-7479	1	83	supported	support	VERB
american_scientific_journal-7479	1	84	cracked	crack	VERB
american_scientific_journal-7479	1	85	beam	beam	NOUN
american_scientific_journal-7479	1	86	(	(	PUNCT
american_scientific_journal-7479	1	87	sscb	sscb	PROPN
american_scientific_journal-7479	1	88	)	)	PUNCT
american_scientific_journal-7479	1	89	under	under	ADP
american_scientific_journal-7479	1	90	a	a	DET
american_scientific_journal-7479	1	91	moving	move	VERB
american_scientific_journal-7479	1	92	load	load	NOUN
american_scientific_journal-7479	1	93	based	base	VERB
american_scientific_journal-7479	1	94	on	on	ADP
american_scientific_journal-7479	1	95	the	the	DET
american_scientific_journal-7479	1	96	euler	euler	PROPN
american_scientific_journal-7479	1	97	bernoulli	bernoulli	PROPN
american_scientific_journal-7479	1	98	hypothesis	hypothesis	NOUN
american_scientific_journal-7479	1	99	.	.	PUNCT
american_scientific_journal-7479	2	1	the	the	DET
american_scientific_journal-7479	2	2	system	system	NOUN
american_scientific_journal-7479	2	3	modelled	model	VERB
american_scientific_journal-7479	2	4	as	as	ADP
american_scientific_journal-7479	2	5	two	two	NUM
american_scientific_journal-7479	2	6	segments	segment	NOUN
american_scientific_journal-7479	2	7	of	of	ADP
american_scientific_journal-7479	2	8	the	the	DET
american_scientific_journal-7479	2	9	beam	beam	NOUN
american_scientific_journal-7479	2	10	are	be	AUX
american_scientific_journal-7479	2	11	to	to	PART
american_scientific_journal-7479	2	12	be	be	AUX
american_scientific_journal-7479	2	13	connected	connect	VERB
american_scientific_journal-7479	2	14	by	by	ADP
american_scientific_journal-7479	2	15	a	a	DET
american_scientific_journal-7479	2	16	massless	massless	ADJ
american_scientific_journal-7479	2	17	elastic	elastic	ADJ
american_scientific_journal-7479	2	18	rotational	rotational	ADJ
american_scientific_journal-7479	2	19	spring	spring	NOUN
american_scientific_journal-7479	2	20	.	.	PUNCT
american_scientific_journal-7479	3	1	bearing	bear	VERB
american_scientific_journal-7479	3	2	in	in	ADP
american_scientific_journal-7479	3	3	mind	mind	NOUN
american_scientific_journal-7479	3	4	each	each	DET
american_scientific_journal-7479	3	5	segment	segment	NOUN
american_scientific_journal-7479	3	6	of	of	ADP
american_scientific_journal-7479	3	7	a	a	DET
american_scientific_journal-7479	3	8	cracked	crack	VERB
american_scientific_journal-7479	3	9	beam	beam	NOUN
american_scientific_journal-7479	3	10	a	a	DET
american_scientific_journal-7479	3	11	substructure	substructure	NOUN
american_scientific_journal-7479	3	12	that	that	PRON
american_scientific_journal-7479	3	13	can	can	AUX
american_scientific_journal-7479	3	14	be	be	AUX
american_scientific_journal-7479	3	15	modeled	model	VERB
american_scientific_journal-7479	3	16	using	use	VERB
american_scientific_journal-7479	3	17	adm	adm	PROPN
american_scientific_journal-7479	3	18	.	.	PUNCT
american_scientific_journal-7479	4	1	adm	adm	PROPN
american_scientific_journal-7479	4	2	derives	derive	VERB
american_scientific_journal-7479	4	3	for	for	ADP
american_scientific_journal-7479	4	4	the	the	DET
american_scientific_journal-7479	4	5	first	first	ADJ
american_scientific_journal-7479	4	6	time	time	NOUN
american_scientific_journal-7479	4	7	on	on	ADP
american_scientific_journal-7479	4	8	the	the	DET
american_scientific_journal-7479	4	9	basis	basis	NOUN
american_scientific_journal-7479	4	10	of	of	ADP
american_scientific_journal-7479	4	11	kinematic	kinematic	ADJ
american_scientific_journal-7479	4	12	conditions	condition	NOUN
american_scientific_journal-7479	4	13	and	and	CCONJ
american_scientific_journal-7479	4	14	boundary	boundary	ADJ
american_scientific_journal-7479	4	15	conditions	condition	NOUN
american_scientific_journal-7479	4	16	the	the	DET
american_scientific_journal-7479	4	17	characteristic	characteristic	ADJ
american_scientific_journal-7479	4	18	/	/	SYM
american_scientific_journal-7479	4	19	eigenvalue	eigenvalue	NOUN
american_scientific_journal-7479	4	20	equation	equation	NOUN
american_scientific_journal-7479	4	21	and	and	CCONJ
american_scientific_journal-7479	4	22	mode	mode	NOUN
american_scientific_journal-7479	4	23	shape	shape	NOUN
american_scientific_journal-7479	4	24	functions	function	NOUN
american_scientific_journal-7479	4	25	of	of	ADP
american_scientific_journal-7479	4	26	the	the	DET
american_scientific_journal-7479	4	27	cracked	crack	VERB
american_scientific_journal-7479	4	28	beam	beam	NOUN
american_scientific_journal-7479	4	29	under	under	ADP
american_scientific_journal-7479	4	30	a	a	DET
american_scientific_journal-7479	4	31	moving	move	VERB
american_scientific_journal-7479	4	32	load	load	NOUN
american_scientific_journal-7479	4	33	.	.	PUNCT
american_scientific_journal-7479	5	1	the	the	DET
american_scientific_journal-7479	5	2	results	result	NOUN
american_scientific_journal-7479	5	3	obtained	obtain	VERB
american_scientific_journal-7479	5	4	from	from	ADP
american_scientific_journal-7479	5	5	adm	adm	PROPN
american_scientific_journal-7479	5	6	are	be	AUX
american_scientific_journal-7479	5	7	compared	compare	VERB
american_scientific_journal-7479	5	8	to	to	ADP
american_scientific_journal-7479	5	9	the	the	DET
american_scientific_journal-7479	5	10	results	result	NOUN
american_scientific_journal-7479	5	11	obtained	obtain	VERB
american_scientific_journal-7479	5	12	from	from	ADP
american_scientific_journal-7479	5	13	the	the	DET
american_scientific_journal-7479	5	14	method	method	NOUN
american_scientific_journal-7479	5	15	of	of	ADP
american_scientific_journal-7479	5	16	finite	finite	ADJ
american_scientific_journal-7479	5	17	elements	element	NOUN
american_scientific_journal-7479	5	18	(	(	PUNCT
american_scientific_journal-7479	5	19	fem	fem	PROPN
american_scientific_journal-7479	5	20	)	)	PUNCT
american_scientific_journal-7479	5	21	.	.	PUNCT
american_scientific_journal-7479	6	1	adm	adm	PROPN
american_scientific_journal-7479	6	2	results	result	NOUN
american_scientific_journal-7479	6	3	show	show	VERB
american_scientific_journal-7479	6	4	remarkable	remarkable	ADJ
american_scientific_journal-7479	6	5	superiority	superiority	NOUN
american_scientific_journal-7479	6	6	compared	compare	VERB
american_scientific_journal-7479	6	7	to	to	ADP
american_scientific_journal-7479	6	8	fem	fem	PROPN
american_scientific_journal-7479	6	9	.	.	PUNCT
american_scientific_journal-7479	7	1	keywords	keyword	NOUN
american_scientific_journal-7479	7	2	:	:	PUNCT
american_scientific_journal-7479	7	3	adomian	adomian	NOUN
american_scientific_journal-7479	7	4	decomposition	decomposition	NOUN
american_scientific_journal-7479	7	5	method	method	NOUN
american_scientific_journal-7479	7	6	;	;	PUNCT
american_scientific_journal-7479	7	7	euler	euler	NOUN
american_scientific_journal-7479	7	8	-	-	PUNCT
american_scientific_journal-7479	7	9	bernoulli	bernoulli	PROPN
american_scientific_journal-7479	7	10	beam	beam	NOUN
american_scientific_journal-7479	7	11	;	;	PUNCT
american_scientific_journal-7479	7	12	cracked	crack	VERB
american_scientific_journal-7479	7	13	beam	beam	NOUN
american_scientific_journal-7479	7	14	;	;	PUNCT
american_scientific_journal-7479	7	15	moving	move	VERB
american_scientific_journal-7479	7	16	load	load	NOUN
american_scientific_journal-7479	7	17	;	;	PUNCT
american_scientific_journal-7479	7	18	mode	mode	NOUN
american_scientific_journal-7479	7	19	shape	shape	NOUN
american_scientific_journal-7479	7	20	functions	function	NOUN
american_scientific_journal-7479	7	21	;	;	PUNCT
american_scientific_journal-7479	7	22	eigenvalue	eigenvalue	NOUN
american_scientific_journal-7479	7	23	equation	equation	NOUN
american_scientific_journal-7479	7	24	.	.	PUNCT
american_scientific_journal-7479	8	1	1	1	X
american_scientific_journal-7479	8	2	.	.	X
american_scientific_journal-7479	8	3	introduction	introduction	NOUN
american_scientific_journal-7479	8	4	an	an	DET
american_scientific_journal-7479	8	5	important	important	ADJ
american_scientific_journal-7479	8	6	topic	topic	NOUN
american_scientific_journal-7479	8	7	in	in	ADP
american_scientific_journal-7479	8	8	the	the	DET
american_scientific_journal-7479	8	9	field	field	NOUN
american_scientific_journal-7479	8	10	of	of	ADP
american_scientific_journal-7479	8	11	mechanical	mechanical	ADJ
american_scientific_journal-7479	8	12	engineering	engineering	NOUN
american_scientific_journal-7479	8	13	and	and	CCONJ
american_scientific_journal-7479	8	14	structural	structural	ADJ
american_scientific_journal-7479	8	15	engineering	engineering	NOUN
american_scientific_journal-7479	8	16	is	be	AUX
american_scientific_journal-7479	8	17	the	the	DET
american_scientific_journal-7479	8	18	analysis	analysis	NOUN
american_scientific_journal-7479	8	19	of	of	ADP
american_scientific_journal-7479	8	20	vibrations	vibration	NOUN
american_scientific_journal-7479	8	21	of	of	ADP
american_scientific_journal-7479	8	22	bridges	bridge	NOUN
american_scientific_journal-7479	8	23	under	under	ADP
american_scientific_journal-7479	8	24	moving	move	VERB
american_scientific_journal-7479	8	25	loads	load	NOUN
american_scientific_journal-7479	8	26	.	.	PUNCT
american_scientific_journal-7479	9	1	a	a	DET
american_scientific_journal-7479	9	2	moving	move	VERB
american_scientific_journal-7479	9	3	load	load	NOUN
american_scientific_journal-7479	9	4	will	will	AUX
american_scientific_journal-7479	9	5	cause	cause	VERB
american_scientific_journal-7479	9	6	larger	large	ADJ
american_scientific_journal-7479	9	7	deflections	deflection	NOUN
american_scientific_journal-7479	9	8	and	and	CCONJ
american_scientific_journal-7479	9	9	higher	high	ADJ
american_scientific_journal-7479	9	10	stresses	stress	NOUN
american_scientific_journal-7479	9	11	as	as	SCONJ
american_scientific_journal-7479	9	12	compared	compare	VERB
american_scientific_journal-7479	9	13	with	with	ADP
american_scientific_journal-7479	9	14	equivalent	equivalent	ADJ
american_scientific_journal-7479	9	15	static	static	ADJ
american_scientific_journal-7479	9	16	loads	load	NOUN
american_scientific_journal-7479	9	17	.	.	PUNCT
american_scientific_journal-7479	10	1	cracks	crack	NOUN
american_scientific_journal-7479	10	2	may	may	AUX
american_scientific_journal-7479	10	3	occur	occur	VERB
american_scientific_journal-7479	10	4	as	as	ADP
american_scientific_journal-7479	10	5	a	a	DET
american_scientific_journal-7479	10	6	result	result	NOUN
american_scientific_journal-7479	10	7	of	of	ADP
american_scientific_journal-7479	10	8	stresses	stress	NOUN
american_scientific_journal-7479	10	9	on	on	ADP
american_scientific_journal-7479	10	10	the	the	DET
american_scientific_journal-7479	10	11	bridge	bridge	NOUN
american_scientific_journal-7479	10	12	.	.	PUNCT
american_scientific_journal-7479	11	1	the	the	DET
american_scientific_journal-7479	11	2	cracks	crack	NOUN
american_scientific_journal-7479	11	3	are	be	AUX
american_scientific_journal-7479	11	4	the	the	DET
american_scientific_journal-7479	11	5	main	main	ADJ
american_scientific_journal-7479	11	6	reason	reason	NOUN
american_scientific_journal-7479	11	7	for	for	ADP
american_scientific_journal-7479	11	8	the	the	DET
american_scientific_journal-7479	11	9	failure	failure	NOUN
american_scientific_journal-7479	11	10	of	of	ADP
american_scientific_journal-7479	11	11	the	the	DET
american_scientific_journal-7479	11	12	bridge	bridge	NOUN
american_scientific_journal-7479	11	13	structure	structure	NOUN
american_scientific_journal-7479	11	14	,	,	PUNCT
american_scientific_journal-7479	11	15	and	and	CCONJ
american_scientific_journal-7479	11	16	when	when	SCONJ
american_scientific_journal-7479	11	17	a	a	DET
american_scientific_journal-7479	11	18	bridge	bridge	NOUN
american_scientific_journal-7479	11	19	structure	structure	NOUN
american_scientific_journal-7479	11	20	is	be	AUX
american_scientific_journal-7479	11	21	subjected	subject	VERB
american_scientific_journal-7479	11	22	to	to	ADP
american_scientific_journal-7479	11	23	cracks	crack	NOUN
american_scientific_journal-7479	11	24	,	,	PUNCT
american_scientific_journal-7479	11	25	its	its	PRON
american_scientific_journal-7479	11	26	stiffness	stiffness	NOUN
american_scientific_journal-7479	11	27	will	will	AUX
american_scientific_journal-7479	11	28	decrease	decrease	VERB
american_scientific_journal-7479	11	29	,	,	PUNCT
american_scientific_journal-7479	11	30	thus	thus	ADV
american_scientific_journal-7479	11	31	reducing	reduce	VERB
american_scientific_journal-7479	11	32	the	the	DET
american_scientific_journal-7479	11	33	bridge	bridge	NOUN
american_scientific_journal-7479	11	34	structure	structure	NOUN
american_scientific_journal-7479	11	35	's	's	PART
american_scientific_journal-7479	11	36	lifetime	lifetime	NOUN
american_scientific_journal-7479	11	37	.	.	PUNCT
american_scientific_journal-7479	12	1	the	the	DET
american_scientific_journal-7479	12	2	depth	depth	NOUN
american_scientific_journal-7479	12	3	and	and	CCONJ
american_scientific_journal-7479	12	4	location	location	NOUN
american_scientific_journal-7479	12	5	of	of	ADP
american_scientific_journal-7479	12	6	a	a	DET
american_scientific_journal-7479	12	7	crack	crack	NOUN
american_scientific_journal-7479	12	8	is	be	AUX
american_scientific_journal-7479	12	9	likely	likely	ADJ
american_scientific_journal-7479	12	10	to	to	PART
american_scientific_journal-7479	12	11	be	be	AUX
american_scientific_journal-7479	12	12	predicted	predict	VERB
american_scientific_journal-7479	12	13	by	by	ADP
american_scientific_journal-7479	12	14	the	the	DET
american_scientific_journal-7479	12	15	changes	change	NOUN
american_scientific_journal-7479	12	16	in	in	ADP
american_scientific_journal-7479	12	17	vibration	vibration	NOUN
american_scientific_journal-7479	12	18	parameters	parameter	NOUN
american_scientific_journal-7479	12	19	.	.	PUNCT
american_scientific_journal-7479	13	1	from	from	ADP
american_scientific_journal-7479	13	2	the	the	DET
american_scientific_journal-7479	13	3	earliest	early	ADJ
american_scientific_journal-7479	13	4	starting	starting	NOUN
american_scientific_journal-7479	13	5	point	point	NOUN
american_scientific_journal-7479	13	6	of	of	ADP
american_scientific_journal-7479	13	7	railroad	railroad	NOUN
american_scientific_journal-7479	13	8	development	development	NOUN
american_scientific_journal-7479	13	9	at	at	ADP
american_scientific_journal-7479	13	10	the	the	DET
american_scientific_journal-7479	13	11	middle	middle	NOUN
american_scientific_journal-7479	13	12	of	of	ADP
american_scientific_journal-7479	13	13	the	the	DET
american_scientific_journal-7479	13	14	last	last	ADJ
american_scientific_journal-7479	13	15	century	century	NOUN
american_scientific_journal-7479	13	16	,	,	PUNCT
american_scientific_journal-7479	13	17	the	the	DET
american_scientific_journal-7479	13	18	issue	issue	NOUN
american_scientific_journal-7479	13	19	of	of	ADP
american_scientific_journal-7479	13	20	vibrations	vibration	NOUN
american_scientific_journal-7479	13	21	of	of	ADP
american_scientific_journal-7479	13	22	bridges	bridge	NOUN
american_scientific_journal-7479	13	23	under	under	ADP
american_scientific_journal-7479	13	24	moving	move	VERB
american_scientific_journal-7479	13	25	loads	load	NOUN
american_scientific_journal-7479	13	26	has	have	AUX
american_scientific_journal-7479	13	27	pulled	pull	VERB
american_scientific_journal-7479	13	28	in	in	ADP
american_scientific_journal-7479	13	29	numerous	numerous	ADJ
american_scientific_journal-7479	13	30	researchers	researcher	NOUN
american_scientific_journal-7479	13	31	.	.	PUNCT
american_scientific_journal-7479	14	1	no	no	DET
american_scientific_journal-7479	14	2	bibliographic	bibliographic	ADJ
american_scientific_journal-7479	14	3	account	account	NOUN
american_scientific_journal-7479	14	4	of	of	ADP
american_scientific_journal-7479	14	5	previous	previous	ADJ
american_scientific_journal-7479	14	6	work	work	NOUN
american_scientific_journal-7479	14	7	on	on	ADP
american_scientific_journal-7479	14	8	this	this	DET
american_scientific_journal-7479	14	9	subject	subject	NOUN
american_scientific_journal-7479	14	10	will	will	AUX
american_scientific_journal-7479	14	11	be	be	AUX
american_scientific_journal-7479	14	12	given	give	VERB
american_scientific_journal-7479	14	13	here	here	ADV
american_scientific_journal-7479	14	14	.	.	PUNCT
american_scientific_journal-7479	15	1	here	here	ADV
american_scientific_journal-7479	15	2	.	.	PUNCT
american_scientific_journal-7479	16	1	some	some	DET
american_scientific_journal-7479	16	2	selective	selective	ADJ
american_scientific_journal-7479	16	3	new	new	ADJ
american_scientific_journal-7479	16	4	papers	paper	NOUN
american_scientific_journal-7479	16	5	[	[	X
american_scientific_journal-7479	16	6	1	1	NUM
american_scientific_journal-7479	16	7	,	,	PUNCT
american_scientific_journal-7479	16	8	2,3,4,5,6,7	2,3,4,5,6,7	NOUN
american_scientific_journal-7479	16	9	]	]	PUNCT
american_scientific_journal-7479	16	10	are	be	AUX
american_scientific_journal-7479	16	11	quoted	quote	VERB
american_scientific_journal-7479	16	12	,	,	PUNCT
american_scientific_journal-7479	16	13	providing	provide	VERB
american_scientific_journal-7479	16	14	additional	additional	ADJ
american_scientific_journal-7479	16	15	information	information	NOUN
american_scientific_journal-7479	16	16	on	on	ADP
american_scientific_journal-7479	16	17	the	the	DET
american_scientific_journal-7479	16	18	issue	issue	NOUN
american_scientific_journal-7479	16	19	.	.	PUNCT
american_scientific_journal-7479	17	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-7479	18	1	*	*	PUNCT
american_scientific_journal-7479	18	2	corresponding	correspond	VERB
american_scientific_journal-7479	18	3	author	author	NOUN
american_scientific_journal-7479	18	4	.	.	PUNCT
american_scientific_journal-7479	19	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-7479	19	2	american	american	PROPN
american_scientific_journal-7479	19	3	academic	academic	PROPN
american_scientific_journal-7479	19	4	scientific	scientific	ADJ
american_scientific_journal-7479	19	5	research	research	NOUN
american_scientific_journal-7479	19	6	journal	journal	NOUN
american_scientific_journal-7479	19	7	for	for	ADP
american_scientific_journal-7479	19	8	engineering	engineering	NOUN
american_scientific_journal-7479	19	9	,	,	PUNCT
american_scientific_journal-7479	19	10	technology	technology	NOUN
american_scientific_journal-7479	19	11	,	,	PUNCT
american_scientific_journal-7479	19	12	and	and	CCONJ
american_scientific_journal-7479	19	13	sciences	science	NOUN
american_scientific_journal-7479	19	14	(	(	PUNCT
american_scientific_journal-7479	19	15	asrjets	asrjet	NOUN
american_scientific_journal-7479	19	16	)	)	PUNCT
american_scientific_journal-7479	19	17	(	(	PUNCT
american_scientific_journal-7479	19	18	2022	2022	NUM
american_scientific_journal-7479	19	19	)	)	PUNCT
american_scientific_journal-7479	19	20	volume	volume	NOUN
american_scientific_journal-7479	19	21	88	88	NUM
american_scientific_journal-7479	19	22	,	,	PUNCT
american_scientific_journal-7479	19	23	no1	no1	PROPN
american_scientific_journal-7479	19	24	,	,	PUNCT
american_scientific_journal-7479	19	25	pp	pp	ADV
american_scientific_journal-7479	19	26	332	332	NUM
american_scientific_journal-7479	19	27	-	-	SYM
american_scientific_journal-7479	19	28	348	348	NUM
american_scientific_journal-7479	19	29	333	333	NUM
american_scientific_journal-7479	19	30	a	a	DET
american_scientific_journal-7479	19	31	relatively	relatively	ADV
american_scientific_journal-7479	19	32	new	new	ADJ
american_scientific_journal-7479	19	33	computational	computational	ADJ
american_scientific_journal-7479	19	34	method	method	NOUN
american_scientific_journal-7479	19	35	called	call	VERB
american_scientific_journal-7479	19	36	the	the	DET
american_scientific_journal-7479	19	37	adomian	adomian	NOUN
american_scientific_journal-7479	19	38	decomposition	decomposition	NOUN
american_scientific_journal-7479	19	39	method	method	NOUN
american_scientific_journal-7479	19	40	(	(	PUNCT
american_scientific_journal-7479	19	41	adm	adm	PROPN
american_scientific_journal-7479	19	42	)	)	PUNCT
american_scientific_journal-7479	20	1	[	[	X
american_scientific_journal-7479	20	2	8,9,10,11,12,13	8,9,10,11,12,13	NUM
american_scientific_journal-7479	20	3	]	]	PUNCT
american_scientific_journal-7479	20	4	is	be	AUX
american_scientific_journal-7479	20	5	applied	apply	VERB
american_scientific_journal-7479	20	6	in	in	ADP
american_scientific_journal-7479	20	7	this	this	DET
american_scientific_journal-7479	20	8	paper	paper	NOUN
american_scientific_journal-7479	20	9	to	to	PART
american_scientific_journal-7479	20	10	examine	examine	VERB
american_scientific_journal-7479	20	11	the	the	DET
american_scientific_journal-7479	20	12	problem	problem	NOUN
american_scientific_journal-7479	20	13	of	of	ADP
american_scientific_journal-7479	20	14	vibration	vibration	NOUN
american_scientific_journal-7479	20	15	for	for	ADP
american_scientific_journal-7479	20	16	a	a	DET
american_scientific_journal-7479	20	17	cracked	crack	VERB
american_scientific_journal-7479	20	18	beam	beam	NOUN
american_scientific_journal-7479	20	19	under	under	ADP
american_scientific_journal-7479	20	20	moving	move	VERB
american_scientific_journal-7479	20	21	load	load	NOUN
american_scientific_journal-7479	20	22	.	.	PUNCT
american_scientific_journal-7479	21	1	the	the	DET
american_scientific_journal-7479	21	2	adm	adm	PROPN
american_scientific_journal-7479	21	3	is	be	AUX
american_scientific_journal-7479	21	4	a	a	DET
american_scientific_journal-7479	21	5	powerful	powerful	ADJ
american_scientific_journal-7479	21	6	and	and	CCONJ
american_scientific_journal-7479	21	7	useful	useful	ADJ
american_scientific_journal-7479	21	8	way	way	NOUN
american_scientific_journal-7479	21	9	to	to	PART
american_scientific_journal-7479	21	10	solve	solve	VERB
american_scientific_journal-7479	21	11	linear	linear	ADJ
american_scientific_journal-7479	21	12	and	and	CCONJ
american_scientific_journal-7479	21	13	nonlinear	nonlinear	ADJ
american_scientific_journal-7479	21	14	differential	differential	ADJ
american_scientific_journal-7479	21	15	equations	equation	NOUN
american_scientific_journal-7479	21	16	.	.	PUNCT
american_scientific_journal-7479	22	1	the	the	DET
american_scientific_journal-7479	22	2	aim	aim	NOUN
american_scientific_journal-7479	22	3	of	of	ADP
american_scientific_journal-7479	22	4	the	the	DET
american_scientific_journal-7479	22	5	adm	adm	NOUN
american_scientific_journal-7479	22	6	is	be	AUX
american_scientific_journal-7479	22	7	to	to	PART
american_scientific_journal-7479	22	8	find	find	VERB
american_scientific_journal-7479	22	9	the	the	DET
american_scientific_journal-7479	22	10	linear	linear	ADJ
american_scientific_journal-7479	22	11	and	and	CCONJ
american_scientific_journal-7479	22	12	nonlinear	nonlinear	ADJ
american_scientific_journal-7479	22	13	,	,	PUNCT
american_scientific_journal-7479	22	14	ordinary	ordinary	ADJ
american_scientific_journal-7479	22	15	,	,	PUNCT
american_scientific_journal-7479	22	16	or	or	CCONJ
american_scientific_journal-7479	22	17	partial	partial	ADJ
american_scientific_journal-7479	22	18	differential	differential	NOUN
american_scientific_journal-7479	22	19	equation	equation	NOUN
american_scientific_journal-7479	22	20	solution	solution	NOUN
american_scientific_journal-7479	22	21	without	without	ADP
american_scientific_journal-7479	22	22	relying	rely	VERB
american_scientific_journal-7479	22	23	on	on	ADP
american_scientific_journal-7479	22	24	small	small	ADJ
american_scientific_journal-7479	22	25	parameters	parameter	NOUN
american_scientific_journal-7479	22	26	such	such	ADJ
american_scientific_journal-7479	22	27	as	as	ADP
american_scientific_journal-7479	22	28	the	the	DET
american_scientific_journal-7479	22	29	example	example	NOUN
american_scientific_journal-7479	22	30	of	of	ADP
american_scientific_journal-7479	22	31	the	the	DET
american_scientific_journal-7479	22	32	perturbation	perturbation	NOUN
american_scientific_journal-7479	22	33	method	method	NOUN
american_scientific_journal-7479	22	34	.	.	PUNCT
american_scientific_journal-7479	23	1	by	by	ADP
american_scientific_journal-7479	23	2	using	use	VERB
american_scientific_journal-7479	23	3	the	the	DET
american_scientific_journal-7479	23	4	adm	adm	NOUN
american_scientific_journal-7479	23	5	as	as	ADP
american_scientific_journal-7479	23	6	a	a	DET
american_scientific_journal-7479	23	7	sum	sum	NOUN
american_scientific_journal-7479	23	8	of	of	ADP
american_scientific_journal-7479	23	9	an	an	DET
american_scientific_journal-7479	23	10	infinite	infinite	ADJ
american_scientific_journal-7479	23	11	series	series	NOUN
american_scientific_journal-7479	23	12	and	and	CCONJ
american_scientific_journal-7479	23	13	a	a	DET
american_scientific_journal-7479	23	14	quick	quick	ADJ
american_scientific_journal-7479	23	15	convergence	convergence	NOUN
american_scientific_journal-7479	23	16	to	to	ADP
american_scientific_journal-7479	23	17	a	a	DET
american_scientific_journal-7479	23	18	particular	particular	ADJ
american_scientific_journal-7479	23	19	solution	solution	NOUN
american_scientific_journal-7479	23	20	,	,	PUNCT
american_scientific_journal-7479	23	21	the	the	DET
american_scientific_journal-7479	23	22	solution	solution	NOUN
american_scientific_journal-7479	23	23	is	be	AUX
american_scientific_journal-7479	23	24	considered	consider	VERB
american_scientific_journal-7479	23	25	[	[	PUNCT
american_scientific_journal-7479	23	26	9,10	9,10	NUM
american_scientific_journal-7479	23	27	]	]	X
american_scientific_journal-7479	23	28	.	.	PUNCT
american_scientific_journal-7479	24	1	the	the	DET
american_scientific_journal-7479	24	2	main	main	ADJ
american_scientific_journal-7479	24	3	advantages	advantage	NOUN
american_scientific_journal-7479	24	4	of	of	ADP
american_scientific_journal-7479	24	5	adm	adm	PROPN
american_scientific_journal-7479	24	6	are	be	AUX
american_scientific_journal-7479	24	7	computational	computational	ADJ
american_scientific_journal-7479	24	8	flexibility	flexibility	NOUN
american_scientific_journal-7479	24	9	and	and	CCONJ
american_scientific_journal-7479	24	10	do	do	AUX
american_scientific_journal-7479	24	11	not	not	PART
american_scientific_journal-7479	24	12	require	require	VERB
american_scientific_journal-7479	24	13	any	any	DET
american_scientific_journal-7479	24	14	linearization	linearization	NOUN
american_scientific_journal-7479	24	15	or	or	CCONJ
american_scientific_journal-7479	24	16	assumptions	assumption	NOUN
american_scientific_journal-7479	24	17	of	of	ADP
american_scientific_journal-7479	24	18	smallness	smallness	NOUN
american_scientific_journal-7479	24	19	.	.	PUNCT
american_scientific_journal-7479	25	1	the	the	DET
american_scientific_journal-7479	25	2	adm	adm	PROPN
american_scientific_journal-7479	25	3	has	have	AUX
american_scientific_journal-7479	25	4	been	be	AUX
american_scientific_journal-7479	25	5	recently	recently	ADV
american_scientific_journal-7479	25	6	applied	apply	VERB
american_scientific_journal-7479	25	7	to	to	ADP
american_scientific_journal-7479	25	8	the	the	DET
american_scientific_journal-7479	25	9	problem	problem	NOUN
american_scientific_journal-7479	25	10	of	of	ADP
american_scientific_journal-7479	25	11	vibration	vibration	NOUN
american_scientific_journal-7479	25	12	of	of	ADP
american_scientific_journal-7479	25	13	structural	structural	ADJ
american_scientific_journal-7479	25	14	and	and	CCONJ
american_scientific_journal-7479	25	15	mechanical	mechanical	ADJ
american_scientific_journal-7479	25	16	systems[9,10,11,12,13	systems[9,10,11,12,13	PROPN
american_scientific_journal-7479	25	17	]	]	PUNCT
american_scientific_journal-7479	25	18	.	.	PUNCT
american_scientific_journal-7479	26	1	the	the	DET
american_scientific_journal-7479	26	2	adm	adm	PROPN
american_scientific_journal-7479	26	3	is	be	AUX
american_scientific_journal-7479	26	4	a	a	DET
american_scientific_journal-7479	26	5	well	well	ADV
american_scientific_journal-7479	26	6	-	-	PUNCT
american_scientific_journal-7479	26	7	known	know	VERB
american_scientific_journal-7479	26	8	method	method	NOUN
american_scientific_journal-7479	26	9	of	of	ADP
american_scientific_journal-7479	26	10	systematic	systematic	ADJ
american_scientific_journal-7479	26	11	solution	solution	NOUN
american_scientific_journal-7479	26	12	of	of	ADP
american_scientific_journal-7479	26	13	linear	linear	PROPN
american_scientific_journal-7479	26	14	or	or	CCONJ
american_scientific_journal-7479	26	15	non	non	ADJ
american_scientific_journal-7479	26	16	-	-	ADJ
american_scientific_journal-7479	26	17	linear	linear	ADJ
american_scientific_journal-7479	26	18	operator	operator	NOUN
american_scientific_journal-7479	26	19	equations	equation	NOUN
american_scientific_journal-7479	26	20	and	and	CCONJ
american_scientific_journal-7479	26	21	deterministic	deterministic	ADJ
american_scientific_journal-7479	26	22	or	or	CCONJ
american_scientific_journal-7479	26	23	stochastic	stochastic	ADJ
american_scientific_journal-7479	26	24	operators	operator	NOUN
american_scientific_journal-7479	26	25	,	,	PUNCT
american_scientific_journal-7479	26	26	including	include	VERB
american_scientific_journal-7479	26	27	normal	normal	ADJ
american_scientific_journal-7479	26	28	differential	differential	ADJ
american_scientific_journal-7479	26	29	equations	equation	NOUN
american_scientific_journal-7479	26	30	,	,	PUNCT
american_scientific_journal-7479	26	31	partial	partial	ADJ
american_scientific_journal-7479	26	32	differential	differential	NOUN
american_scientific_journal-7479	26	33	equations	equation	NOUN
american_scientific_journal-7479	26	34	,	,	PUNCT
american_scientific_journal-7479	26	35	integrated	integrate	VERB
american_scientific_journal-7479	26	36	equations	equation	NOUN
american_scientific_journal-7479	26	37	,	,	PUNCT
american_scientific_journal-7479	26	38	integrated	integrate	VERB
american_scientific_journal-7479	26	39	differential	differential	ADJ
american_scientific_journal-7479	26	40	equations	equation	NOUN
american_scientific_journal-7479	26	41	,	,	PUNCT
american_scientific_journal-7479	26	42	etc	etc	X
american_scientific_journal-7479	26	43	.	.	X
american_scientific_journal-7479	27	1	the	the	DET
american_scientific_journal-7479	27	2	adm	adm	PROPN
american_scientific_journal-7479	27	3	offers	offer	VERB
american_scientific_journal-7479	27	4	an	an	DET
american_scientific_journal-7479	27	5	effective	effective	ADJ
american_scientific_journal-7479	27	6	methodology	methodology	NOUN
american_scientific_journal-7479	27	7	for	for	ADP
american_scientific_journal-7479	27	8	computational	computational	ADJ
american_scientific_journal-7479	27	9	methods	method	NOUN
american_scientific_journal-7479	27	10	and	and	CCONJ
american_scientific_journal-7479	27	11	numerical	numerical	ADJ
american_scientific_journal-7479	27	12	simulations	simulation	NOUN
american_scientific_journal-7479	27	13	in	in	ADP
american_scientific_journal-7479	27	14	the	the	DET
american_scientific_journal-7479	27	15	applied	apply	VERB
american_scientific_journal-7479	27	16	sciences	science	NOUN
american_scientific_journal-7479	27	17	and	and	CCONJ
american_scientific_journal-7479	27	18	engineering	engineering	NOUN
american_scientific_journal-7479	27	19	,	,	PUNCT
american_scientific_journal-7479	27	20	with	with	ADP
american_scientific_journal-7479	27	21	real	real	ADJ
american_scientific_journal-7479	27	22	-	-	PUNCT
american_scientific_journal-7479	27	23	world	world	NOUN
american_scientific_journal-7479	27	24	applications	application	NOUN
american_scientific_journal-7479	27	25	.	.	PUNCT
american_scientific_journal-7479	28	1	it	it	PRON
american_scientific_journal-7479	28	2	allows	allow	VERB
american_scientific_journal-7479	28	3	us	we	PRON
american_scientific_journal-7479	28	4	,	,	PUNCT
american_scientific_journal-7479	28	5	without	without	ADP
american_scientific_journal-7479	28	6	unphysically	unphysically	ADV
american_scientific_journal-7479	28	7	restrictive	restrictive	ADJ
american_scientific_journal-7479	28	8	assumptions	assumption	NOUN
american_scientific_journal-7479	28	9	,	,	PUNCT
american_scientific_journal-7479	28	10	to	to	PART
american_scientific_journal-7479	28	11	solve	solve	VERB
american_scientific_journal-7479	28	12	both	both	PRON
american_scientific_journal-7479	28	13	nonlinear	nonlinear	ADJ
american_scientific_journal-7479	28	14	initial	initial	ADJ
american_scientific_journal-7479	28	15	value	value	NOUN
american_scientific_journal-7479	28	16	problems	problem	NOUN
american_scientific_journal-7479	28	17	and	and	CCONJ
american_scientific_journal-7479	28	18	boundary	boundary	ADJ
american_scientific_journal-7479	28	19	value	value	NOUN
american_scientific_journal-7479	28	20	problems	problem	NOUN
american_scientific_journal-7479	28	21	,	,	PUNCT
american_scientific_journal-7479	28	22	including	include	VERB
american_scientific_journal-7479	28	23	the	the	DET
american_scientific_journal-7479	28	24	need	need	NOUN
american_scientific_journal-7479	28	25	for	for	ADP
american_scientific_journal-7479	28	26	linearization	linearization	NOUN
american_scientific_journal-7479	28	27	,	,	PUNCT
american_scientific_journal-7479	28	28	disturbance	disturbance	NOUN
american_scientific_journal-7479	28	29	,	,	PUNCT
american_scientific_journal-7479	28	30	ad	ad	X
american_scientific_journal-7479	28	31	hoc	hoc	X
american_scientific_journal-7479	28	32	assumptions	assumption	NOUN
american_scientific_journal-7479	28	33	,	,	PUNCT
american_scientific_journal-7479	28	34	divination	divination	NOUN
american_scientific_journal-7479	28	35	of	of	ADP
american_scientific_journal-7479	28	36	the	the	DET
american_scientific_journal-7479	28	37	initial	initial	ADJ
american_scientific_journal-7479	28	38	term	term	NOUN
american_scientific_journal-7479	28	39	or	or	CCONJ
american_scientific_journal-7479	28	40	set	set	NOUN
american_scientific_journal-7479	28	41	of	of	ADP
american_scientific_journal-7479	28	42	basic	basic	ADJ
american_scientific_journal-7479	28	43	functions	function	NOUN
american_scientific_journal-7479	28	44	,	,	PUNCT
american_scientific_journal-7479	28	45	etc	etc	X
american_scientific_journal-7479	29	1	[	[	X
american_scientific_journal-7479	29	2	14,15,16	14,15,16	NUM
american_scientific_journal-7479	29	3	]	]	PUNCT
american_scientific_journal-7479	29	4	.	.	PUNCT
american_scientific_journal-7479	30	1	using	use	VERB
american_scientific_journal-7479	30	2	the	the	DET
american_scientific_journal-7479	30	3	adm	adm	NOUN
american_scientific_journal-7479	30	4	,	,	PUNCT
american_scientific_journal-7479	30	5	the	the	DET
american_scientific_journal-7479	30	6	governing	govern	VERB
american_scientific_journal-7479	30	7	differential	differential	ADJ
american_scientific_journal-7479	30	8	equation	equation	NOUN
american_scientific_journal-7479	30	9	for	for	ADP
american_scientific_journal-7479	30	10	each	each	DET
american_scientific_journal-7479	30	11	segment	segment	NOUN
american_scientific_journal-7479	30	12	of	of	ADP
american_scientific_journal-7479	30	13	the	the	DET
american_scientific_journal-7479	30	14	cracked	crack	VERB
american_scientific_journal-7479	30	15	beam	beam	NOUN
american_scientific_journal-7479	30	16	becomes	become	VERB
american_scientific_journal-7479	30	17	a	a	DET
american_scientific_journal-7479	30	18	recursive	recursive	ADJ
american_scientific_journal-7479	30	19	algebraic	algebraic	ADJ
american_scientific_journal-7479	30	20	equation	equation	NOUN
american_scientific_journal-7479	30	21	.	.	PUNCT
american_scientific_journal-7479	31	1	the	the	DET
american_scientific_journal-7479	31	2	boundary	boundary	ADJ
american_scientific_journal-7479	31	3	conditions	condition	NOUN
american_scientific_journal-7479	31	4	and	and	CCONJ
american_scientific_journal-7479	31	5	conditions	condition	NOUN
american_scientific_journal-7479	31	6	of	of	ADP
american_scientific_journal-7479	31	7	continuity	continuity	NOUN
american_scientific_journal-7479	31	8	at	at	ADP
american_scientific_journal-7479	31	9	the	the	DET
american_scientific_journal-7479	31	10	crack	crack	NOUN
american_scientific_journal-7479	31	11	position	position	NOUN
american_scientific_journal-7479	31	12	become	become	VERB
american_scientific_journal-7479	31	13	simple	simple	ADJ
american_scientific_journal-7479	31	14	algebraic	algebraic	ADJ
american_scientific_journal-7479	31	15	frequency	frequency	NOUN
american_scientific_journal-7479	31	16	equations	equation	NOUN
american_scientific_journal-7479	31	17	which	which	PRON
american_scientific_journal-7479	31	18	are	be	AUX
american_scientific_journal-7479	31	19	appropriate	appropriate	ADJ
american_scientific_journal-7479	31	20	for	for	ADP
american_scientific_journal-7479	31	21	symbolic	symbolic	ADJ
american_scientific_journal-7479	31	22	computation	computation	NOUN
american_scientific_journal-7479	31	23	.	.	PUNCT
american_scientific_journal-7479	32	1	in	in	ADP
american_scientific_journal-7479	32	2	addition	addition	NOUN
american_scientific_journal-7479	32	3	,	,	PUNCT
american_scientific_journal-7479	32	4	after	after	ADP
american_scientific_journal-7479	32	5	some	some	DET
american_scientific_journal-7479	32	6	basic	basic	ADJ
american_scientific_journal-7479	32	7	algebraic	algebraic	ADJ
american_scientific_journal-7479	32	8	operations	operation	NOUN
american_scientific_journal-7479	32	9	on	on	ADP
american_scientific_journal-7479	32	10	these	these	DET
american_scientific_journal-7479	32	11	frequency	frequency	NOUN
american_scientific_journal-7479	32	12	equations	equation	NOUN
american_scientific_journal-7479	32	13	,	,	PUNCT
american_scientific_journal-7479	32	14	we	we	PRON
american_scientific_journal-7479	32	15	can	can	AUX
american_scientific_journal-7479	32	16	simultaneously	simultaneously	ADV
american_scientific_journal-7479	32	17	obtain	obtain	VERB
american_scientific_journal-7479	32	18	the	the	DET
american_scientific_journal-7479	32	19	natural	natural	ADJ
american_scientific_journal-7479	32	20	frequency	frequency	NOUN
american_scientific_journal-7479	32	21	and	and	CCONJ
american_scientific_journal-7479	32	22	the	the	DET
american_scientific_journal-7479	32	23	corresponding	corresponding	ADJ
american_scientific_journal-7479	32	24	mode	mode	NOUN
american_scientific_journal-7479	32	25	shape	shape	NOUN
american_scientific_journal-7479	32	26	solution	solution	NOUN
american_scientific_journal-7479	32	27	of	of	ADP
american_scientific_journal-7479	32	28	the	the	DET
american_scientific_journal-7479	32	29	closed	closed	ADJ
american_scientific_journal-7479	32	30	-	-	PUNCT
american_scientific_journal-7479	32	31	form	form	NOUN
american_scientific_journal-7479	32	32	series	series	NOUN
american_scientific_journal-7479	32	33	.	.	PUNCT
american_scientific_journal-7479	33	1	in	in	ADP
american_scientific_journal-7479	33	2	literature	literature	NOUN
american_scientific_journal-7479	33	3	has	have	AUX
american_scientific_journal-7479	33	4	been	be	AUX
american_scientific_journal-7479	33	5	used	use	VERB
american_scientific_journal-7479	33	6	this	this	DET
american_scientific_journal-7479	33	7	method	method	NOUN
american_scientific_journal-7479	33	8	for	for	ADP
american_scientific_journal-7479	33	9	free	free	ADJ
american_scientific_journal-7479	33	10	vibration	vibration	NOUN
american_scientific_journal-7479	33	11	analysis	analysis	NOUN
american_scientific_journal-7479	33	12	,	,	PUNCT
american_scientific_journal-7479	33	13	only	only	ADV
american_scientific_journal-7479	33	14	in	in	ADP
american_scientific_journal-7479	33	15	one	one	NUM
american_scientific_journal-7479	33	16	research	research	NOUN
american_scientific_journal-7479	33	17	,	,	PUNCT
american_scientific_journal-7479	33	18	bilik	bilik	NOUN
american_scientific_journal-7479	33	19	and	and	CCONJ
american_scientific_journal-7479	33	20	karaçay	karaçay	NOUN
american_scientific_journal-7479	33	21	[	[	X
american_scientific_journal-7479	33	22	17	17	NUM
american_scientific_journal-7479	33	23	]	]	PUNCT
american_scientific_journal-7479	33	24	applied	apply	VERB
american_scientific_journal-7479	33	25	modified	modify	VERB
american_scientific_journal-7479	33	26	adomian	adomian	NOUN
american_scientific_journal-7479	33	27	decomposition	decomposition	NOUN
american_scientific_journal-7479	33	28	method	method	NOUN
american_scientific_journal-7479	33	29	in	in	ADP
american_scientific_journal-7479	33	30	order	order	NOUN
american_scientific_journal-7479	33	31	to	to	PART
american_scientific_journal-7479	33	32	analysis	analysis	VERB
american_scientific_journal-7479	33	33	the	the	DET
american_scientific_journal-7479	33	34	vibration	vibration	NOUN
american_scientific_journal-7479	33	35	response	response	NOUN
american_scientific_journal-7479	33	36	of	of	ADP
american_scientific_journal-7479	33	37	intact	intact	ADJ
american_scientific_journal-7479	33	38	bridge	bridge	NOUN
american_scientific_journal-7479	33	39	subjected	subject	VERB
american_scientific_journal-7479	33	40	to	to	ADP
american_scientific_journal-7479	33	41	a	a	DET
american_scientific_journal-7479	33	42	constant	constant	ADJ
american_scientific_journal-7479	33	43	load	load	NOUN
american_scientific_journal-7479	33	44	.	.	PUNCT
american_scientific_journal-7479	34	1	2	2	X
american_scientific_journal-7479	34	2	.	.	X
american_scientific_journal-7479	34	3	theoretical	theoretical	ADJ
american_scientific_journal-7479	34	4	model	model	NOUN
american_scientific_journal-7479	34	5	using	use	VERB
american_scientific_journal-7479	34	6	adm	adm	PROPN
american_scientific_journal-7479	34	7	the	the	DET
american_scientific_journal-7479	34	8	adm	adm	PROPN
american_scientific_journal-7479	34	9	is	be	AUX
american_scientific_journal-7479	34	10	an	an	DET
american_scientific_journal-7479	34	11	efficient	efficient	ADJ
american_scientific_journal-7479	34	12	method	method	NOUN
american_scientific_journal-7479	34	13	for	for	ADP
american_scientific_journal-7479	34	14	determining	determine	VERB
american_scientific_journal-7479	34	15	the	the	DET
american_scientific_journal-7479	34	16	analytical	analytical	ADJ
american_scientific_journal-7479	34	17	solution	solution	NOUN
american_scientific_journal-7479	34	18	of	of	ADP
american_scientific_journal-7479	34	19	a	a	DET
american_scientific_journal-7479	34	20	large	large	ADJ
american_scientific_journal-7479	34	21	class	class	NOUN
american_scientific_journal-7479	34	22	of	of	ADP
american_scientific_journal-7479	34	23	vibrational	vibrational	ADJ
american_scientific_journal-7479	34	24	systems	system	NOUN
american_scientific_journal-7479	34	25	without	without	ADP
american_scientific_journal-7479	34	26	linearization	linearization	NOUN
american_scientific_journal-7479	34	27	or	or	CCONJ
american_scientific_journal-7479	34	28	weak	weak	ADJ
american_scientific_journal-7479	34	29	assumptions	assumption	NOUN
american_scientific_journal-7479	34	30	of	of	ADP
american_scientific_journal-7479	34	31	nonlinearity	nonlinearity	NOUN
american_scientific_journal-7479	34	32	,	,	PUNCT
american_scientific_journal-7479	34	33	which	which	PRON
american_scientific_journal-7479	34	34	can	can	AUX
american_scientific_journal-7479	34	35	result	result	VERB
american_scientific_journal-7479	34	36	in	in	ADP
american_scientific_journal-7479	34	37	a	a	DET
american_scientific_journal-7479	34	38	huge	huge	ADJ
american_scientific_journal-7479	34	39	numerical	numerical	ADJ
american_scientific_journal-7479	34	40	estimation	estimation	NOUN
american_scientific_journal-7479	34	41	.	.	PUNCT
american_scientific_journal-7479	35	1	therefore	therefore	ADV
american_scientific_journal-7479	35	2	,	,	PUNCT
american_scientific_journal-7479	35	3	it	it	PRON
american_scientific_journal-7479	35	4	is	be	AUX
american_scientific_journal-7479	35	5	physically	physically	ADV
american_scientific_journal-7479	35	6	more	more	ADV
american_scientific_journal-7479	35	7	accurate	accurate	ADJ
american_scientific_journal-7479	35	8	and	and	CCONJ
american_scientific_journal-7479	35	9	practical	practical	ADJ
american_scientific_journal-7479	35	10	.	.	PUNCT
american_scientific_journal-7479	36	1	although	although	SCONJ
american_scientific_journal-7479	36	2	the	the	DET
american_scientific_journal-7479	36	3	solution	solution	NOUN
american_scientific_journal-7479	36	4	obtained	obtain	VERB
american_scientific_journal-7479	36	5	by	by	ADP
american_scientific_journal-7479	36	6	the	the	DET
american_scientific_journal-7479	36	7	adm	adm	PROPN
american_scientific_journal-7479	36	8	is	be	AUX
american_scientific_journal-7479	36	9	an	an	DET
american_scientific_journal-7479	36	10	infinite	infinite	ADJ
american_scientific_journal-7479	36	11	series	series	NOUN
american_scientific_journal-7479	36	12	,	,	PUNCT
american_scientific_journal-7479	36	13	a	a	DET
american_scientific_journal-7479	36	14	n	n	NUM
american_scientific_journal-7479	36	15	-	-	PUNCT
american_scientific_journal-7479	36	16	term	term	NOUN
american_scientific_journal-7479	36	17	approach	approach	NOUN
american_scientific_journal-7479	36	18	usually	usually	ADV
american_scientific_journal-7479	36	19	serves	serve	VERB
american_scientific_journal-7479	36	20	as	as	ADP
american_scientific_journal-7479	36	21	a	a	DET
american_scientific_journal-7479	36	22	practical	practical	ADJ
american_scientific_journal-7479	36	23	and	and	CCONJ
american_scientific_journal-7479	36	24	suitable	suitable	ADJ
american_scientific_journal-7479	36	25	solution	solution	NOUN
american_scientific_journal-7479	36	26	.	.	PUNCT
american_scientific_journal-7479	37	1	in	in	ADP
american_scientific_journal-7479	37	2	addition	addition	NOUN
american_scientific_journal-7479	37	3	,	,	PUNCT
american_scientific_journal-7479	37	4	an	an	DET
american_scientific_journal-7479	37	5	effective	effective	ADJ
american_scientific_journal-7479	37	6	solution	solution	NOUN
american_scientific_journal-7479	37	7	with	with	ADP
american_scientific_journal-7479	37	8	very	very	ADV
american_scientific_journal-7479	37	9	low	low	ADJ
american_scientific_journal-7479	37	10	values	value	NOUN
american_scientific_journal-7479	37	11	of	of	ADP
american_scientific_journal-7479	37	12	n	n	PUNCT
american_scientific_journal-7479	37	13	is	be	AUX
american_scientific_journal-7479	37	14	often	often	ADV
american_scientific_journal-7479	37	15	obtained[18	obtained[18	PRON
american_scientific_journal-7479	37	16	]	]	X
american_scientific_journal-7479	38	1	the	the	DET
american_scientific_journal-7479	38	2	solution	solution	NOUN
american_scientific_journal-7479	38	3	can	can	AUX
american_scientific_journal-7479	38	4	be	be	AUX
american_scientific_journal-7479	38	5	improved	improve	VERB
american_scientific_journal-7479	38	6	for	for	ADP
american_scientific_journal-7479	38	7	numerical	numerical	ADJ
american_scientific_journal-7479	38	8	purposes	purpose	NOUN
american_scientific_journal-7479	38	9	by	by	ADP
american_scientific_journal-7479	38	10	considering	consider	VERB
american_scientific_journal-7479	38	11	further	further	ADJ
american_scientific_journal-7479	38	12	terms	term	NOUN
american_scientific_journal-7479	38	13	,	,	PUNCT
american_scientific_journal-7479	38	14	and	and	CCONJ
american_scientific_journal-7479	38	15	if	if	SCONJ
american_scientific_journal-7479	38	16	it	it	PRON
american_scientific_journal-7479	38	17	exists	exist	VERB
american_scientific_journal-7479	38	18	,	,	PUNCT
american_scientific_journal-7479	38	19	the	the	DET
american_scientific_journal-7479	38	20	answer	answer	NOUN
american_scientific_journal-7479	38	21	will	will	AUX
american_scientific_journal-7479	38	22	be	be	AUX
american_scientific_journal-7479	38	23	the	the	DET
american_scientific_journal-7479	38	24	exact	exact	ADJ
american_scientific_journal-7479	38	25	solution	solution	NOUN
american_scientific_journal-7479	38	26	to	to	ADP
american_scientific_journal-7479	38	27	the	the	DET
american_scientific_journal-7479	38	28	problem	problem	NOUN
american_scientific_journal-7479	38	29	.	.	PUNCT
american_scientific_journal-7479	39	1	as	as	SCONJ
american_scientific_journal-7479	39	2	discussed	discuss	VERB
american_scientific_journal-7479	39	3	earlier	early	ADV
american_scientific_journal-7479	39	4	,	,	PUNCT
american_scientific_journal-7479	39	5	the	the	DET
american_scientific_journal-7479	39	6	adm	adm	NOUN
american_scientific_journal-7479	39	7	provides	provide	VERB
american_scientific_journal-7479	39	8	the	the	DET
american_scientific_journal-7479	39	9	solution	solution	NOUN
american_scientific_journal-7479	39	10	to	to	ADP
american_scientific_journal-7479	39	11	dynamic	dynamic	ADJ
american_scientific_journal-7479	39	12	problems	problem	NOUN
american_scientific_journal-7479	39	13	in	in	ADP
american_scientific_journal-7479	39	14	a	a	DET
american_scientific_journal-7479	39	15	rapidly	rapidly	ADV
american_scientific_journal-7479	39	16	convergent	convergent	ADJ
american_scientific_journal-7479	39	17	series	series	NOUN
american_scientific_journal-7479	39	18	with	with	ADP
american_scientific_journal-7479	39	19	easily	easily	ADV
american_scientific_journal-7479	39	20	computable	computable	ADJ
american_scientific_journal-7479	39	21	terms	term	NOUN
american_scientific_journal-7479	39	22	.	.	PUNCT
american_scientific_journal-7479	40	1	because	because	SCONJ
american_scientific_journal-7479	40	2	the	the	DET
american_scientific_journal-7479	40	3	methodology	methodology	NOUN
american_scientific_journal-7479	40	4	is	be	AUX
american_scientific_journal-7479	40	5	addressed	address	VERB
american_scientific_journal-7479	40	6	perfectly	perfectly	ADV
american_scientific_journal-7479	40	7	in	in	ADP
american_scientific_journal-7479	40	8	refs	ref	NOUN
american_scientific_journal-7479	40	9	[	[	X
american_scientific_journal-7479	40	10	18,19	18,19	NUM
american_scientific_journal-7479	40	11	]	]	PUNCT
american_scientific_journal-7479	40	12	,	,	PUNCT
american_scientific_journal-7479	40	13	the	the	DET
american_scientific_journal-7479	40	14	details	detail	NOUN
american_scientific_journal-7479	40	15	of	of	ADP
american_scientific_journal-7479	40	16	this	this	DET
american_scientific_journal-7479	40	17	paper	paper	NOUN
american_scientific_journal-7479	40	18	will	will	AUX
american_scientific_journal-7479	40	19	not	not	PART
american_scientific_journal-7479	40	20	be	be	AUX
american_scientific_journal-7479	40	21	discussed	discuss	VERB
american_scientific_journal-7479	40	22	.	.	PUNCT
american_scientific_journal-7479	41	1	the	the	DET
american_scientific_journal-7479	41	2	adm	adm	PROPN
american_scientific_journal-7479	41	3	is	be	AUX
american_scientific_journal-7479	41	4	used	use	VERB
american_scientific_journal-7479	41	5	to	to	PART
american_scientific_journal-7479	41	6	solve	solve	VERB
american_scientific_journal-7479	41	7	the	the	DET
american_scientific_journal-7479	41	8	dynamic	dynamic	ADJ
american_scientific_journal-7479	41	9	governing	govern	VERB
american_scientific_journal-7479	41	10	equation	equation	NOUN
american_scientific_journal-7479	41	11	of	of	ADP
american_scientific_journal-7479	41	12	an	an	DET
american_scientific_journal-7479	41	13	sscb	sscb	PROPN
american_scientific_journal-7479	41	14	beam	beam	NOUN
american_scientific_journal-7479	41	15	carrying	carry	VERB
american_scientific_journal-7479	41	16	a	a	DET
american_scientific_journal-7479	41	17	moving	move	VERB
american_scientific_journal-7479	41	18	load	load	NOUN
american_scientific_journal-7479	41	19	based	base	VERB
american_scientific_journal-7479	41	20	on	on	ADP
american_scientific_journal-7479	41	21	the	the	DET
american_scientific_journal-7479	41	22	theory	theory	NOUN
american_scientific_journal-7479	41	23	of	of	ADP
american_scientific_journal-7479	41	24	euler	euler	PROPN
american_scientific_journal-7479	41	25	–	–	PUNCT
american_scientific_journal-7479	41	26	bernoulli	bernoulli	NOUN
american_scientific_journal-7479	41	27	beams	beam	NOUN
american_scientific_journal-7479	41	28	with	with	ADP
american_scientific_journal-7479	41	29	general	general	ADJ
american_scientific_journal-7479	41	30	elastic	elastic	ADJ
american_scientific_journal-7479	41	31	boundary	boundary	ADJ
american_scientific_journal-7479	41	32	conditions	condition	NOUN
american_scientific_journal-7479	41	33	and	and	CCONJ
american_scientific_journal-7479	41	34	conditions	condition	NOUN
american_scientific_journal-7479	41	35	of	of	ADP
american_scientific_journal-7479	41	36	kinematics	kinematic	NOUN
american_scientific_journal-7479	41	37	.	.	PUNCT
american_scientific_journal-7479	42	1	consider	consider	VERB
american_scientific_journal-7479	42	2	an	an	DET
american_scientific_journal-7479	42	3	sscb	sscb	NOUN
american_scientific_journal-7479	42	4	with	with	ADP
american_scientific_journal-7479	42	5	a	a	DET
american_scientific_journal-7479	42	6	moving	move	VERB
american_scientific_journal-7479	42	7	load	load	NOUN
american_scientific_journal-7479	42	8	shown	show	VERB
american_scientific_journal-7479	42	9	in	in	ADP
american_scientific_journal-7479	42	10	fig.1	fig.1	PROPN
american_scientific_journal-7479	42	11	with	with	ADP
american_scientific_journal-7479	42	12	a	a	DET
american_scientific_journal-7479	42	13	single	single	ADJ
american_scientific_journal-7479	42	14	-	-	PUNCT
american_scientific_journal-7479	42	15	sided	sided	ADJ
american_scientific_journal-7479	42	16	transverse	transverse	NOUN
american_scientific_journal-7479	42	17	crack	crack	VERB
american_scientific_journal-7479	42	18	whose	whose	DET
american_scientific_journal-7479	42	19	depth	depth	NOUN
american_scientific_journal-7479	42	20	is	be	AUX
american_scientific_journal-7479	42	21	𝑎	𝑎	NOUN
american_scientific_journal-7479	42	22	,	,	PUNCT
american_scientific_journal-7479	42	23	the	the	DET
american_scientific_journal-7479	42	24	crack	crack	NOUN
american_scientific_journal-7479	42	25	is	be	AUX
american_scientific_journal-7479	42	26	in	in	ADP
american_scientific_journal-7479	42	27	the	the	DET
american_scientific_journal-7479	42	28	𝑥	𝑥	NOUN
american_scientific_journal-7479	42	29	!	!	PUNCT
american_scientific_journal-7479	42	30	position	position	NOUN
american_scientific_journal-7479	42	31	.	.	PUNCT
american_scientific_journal-7479	43	1	where	where	SCONJ
american_scientific_journal-7479	43	2	𝑥	𝑥	NOUN
american_scientific_journal-7479	43	3	"	"	PUNCT
american_scientific_journal-7479	43	4	and	and	CCONJ
american_scientific_journal-7479	43	5	𝑥	𝑥	PRON
american_scientific_journal-7479	43	6	#	#	NOUN
american_scientific_journal-7479	43	7	represent	represent	VERB
american_scientific_journal-7479	43	8	end	end	NOUN
american_scientific_journal-7479	43	9	points	point	NOUN
american_scientific_journal-7479	43	10	.	.	PUNCT
american_scientific_journal-7479	44	1	the	the	DET
american_scientific_journal-7479	44	2	width	width	ADJ
american_scientific_journal-7479	44	3	,	,	PUNCT
american_scientific_journal-7479	44	4	depth	depth	NOUN
american_scientific_journal-7479	44	5	and	and	CCONJ
american_scientific_journal-7479	44	6	length	length	NOUN
american_scientific_journal-7479	44	7	of	of	ADP
american_scientific_journal-7479	44	8	the	the	DET
american_scientific_journal-7479	44	9	beam	beam	NOUN
american_scientific_journal-7479	44	10	are	be	AUX
american_scientific_journal-7479	44	11	,	,	PUNCT
american_scientific_journal-7479	44	12	respectively	respectively	ADV
american_scientific_journal-7479	44	13	,	,	PUNCT
american_scientific_journal-7479	44	14	b	b	X
american_scientific_journal-7479	44	15	,	,	PUNCT
american_scientific_journal-7479	44	16	h	h	NOUN
american_scientific_journal-7479	44	17	and	and	CCONJ
american_scientific_journal-7479	44	18	l.	l.	PROPN
american_scientific_journal-7479	44	19	a	a	DET
american_scientific_journal-7479	44	20	load	load	NOUN
american_scientific_journal-7479	44	21	f	f	NOUN
american_scientific_journal-7479	44	22	with	with	ADP
american_scientific_journal-7479	44	23	constant	constant	ADJ
american_scientific_journal-7479	44	24	velocity	velocity	NOUN
american_scientific_journal-7479	44	25	is	be	AUX
american_scientific_journal-7479	44	26	moving	move	VERB
american_scientific_journal-7479	44	27	on	on	ADP
american_scientific_journal-7479	44	28	the	the	DET
american_scientific_journal-7479	44	29	beam	beam	NOUN
american_scientific_journal-7479	44	30	from	from	ADP
american_scientific_journal-7479	44	31	left	left	ADJ
american_scientific_journal-7479	44	32	edge	edge	NOUN
american_scientific_journal-7479	44	33	of	of	ADP
american_scientific_journal-7479	44	34	the	the	DET
american_scientific_journal-7479	44	35	beam	beam	NOUN
american_scientific_journal-7479	44	36	to	to	ADP
american_scientific_journal-7479	44	37	its	its	PRON
american_scientific_journal-7479	44	38	right	right	ADJ
american_scientific_journal-7479	44	39	end	end	NOUN
american_scientific_journal-7479	44	40	.	.	PUNCT
american_scientific_journal-7479	45	1	american	american	ADJ
american_scientific_journal-7479	45	2	academic	academic	ADJ
american_scientific_journal-7479	45	3	scientific	scientific	ADJ
american_scientific_journal-7479	45	4	research	research	NOUN
american_scientific_journal-7479	45	5	journal	journal	NOUN
american_scientific_journal-7479	45	6	for	for	ADP
american_scientific_journal-7479	45	7	engineering	engineering	NOUN
american_scientific_journal-7479	45	8	,	,	PUNCT
american_scientific_journal-7479	45	9	technology	technology	NOUN
american_scientific_journal-7479	45	10	,	,	PUNCT
american_scientific_journal-7479	45	11	and	and	CCONJ
american_scientific_journal-7479	45	12	sciences	science	NOUN
american_scientific_journal-7479	45	13	(	(	PUNCT
american_scientific_journal-7479	45	14	asrjets	asrjet	NOUN
american_scientific_journal-7479	45	15	)	)	PUNCT
american_scientific_journal-7479	45	16	(	(	PUNCT
american_scientific_journal-7479	45	17	2022	2022	NUM
american_scientific_journal-7479	45	18	)	)	PUNCT
american_scientific_journal-7479	45	19	volume	volume	NOUN
american_scientific_journal-7479	45	20	88	88	NUM
american_scientific_journal-7479	45	21	,	,	PUNCT
american_scientific_journal-7479	45	22	no1	no1	PROPN
american_scientific_journal-7479	45	23	,	,	PUNCT
american_scientific_journal-7479	45	24	pp	pp	ADV
american_scientific_journal-7479	45	25	332	332	NUM
american_scientific_journal-7479	45	26	-	-	SYM
american_scientific_journal-7479	45	27	348	348	NUM
american_scientific_journal-7479	45	28	334	334	NUM
american_scientific_journal-7479	45	29	figure	figure	NOUN
american_scientific_journal-7479	45	30	1	1	NUM
american_scientific_journal-7479	45	31	:	:	PUNCT
american_scientific_journal-7479	45	32	a	a	DET
american_scientific_journal-7479	45	33	simply	simply	ADV
american_scientific_journal-7479	45	34	supported	support	VERB
american_scientific_journal-7479	45	35	cracked	crack	VERB
american_scientific_journal-7479	45	36	beam	beam	NOUN
american_scientific_journal-7479	45	37	under	under	ADP
american_scientific_journal-7479	45	38	moving	move	VERB
american_scientific_journal-7479	45	39	load	load	NOUN
american_scientific_journal-7479	45	40	to	to	PART
american_scientific_journal-7479	45	41	include	include	VERB
american_scientific_journal-7479	45	42	the	the	DET
american_scientific_journal-7479	45	43	effect	effect	NOUN
american_scientific_journal-7479	45	44	of	of	ADP
american_scientific_journal-7479	45	45	crack	crack	NOUN
american_scientific_journal-7479	45	46	,	,	PUNCT
american_scientific_journal-7479	45	47	a	a	DET
american_scientific_journal-7479	45	48	massless	massless	ADJ
american_scientific_journal-7479	45	49	elastic	elastic	ADJ
american_scientific_journal-7479	45	50	rotational	rotational	ADJ
american_scientific_journal-7479	45	51	spring	spring	NOUN
american_scientific_journal-7479	45	52	is	be	AUX
american_scientific_journal-7479	45	53	to	to	PART
american_scientific_journal-7479	45	54	connect	connect	VERB
american_scientific_journal-7479	45	55	two	two	NUM
american_scientific_journal-7479	45	56	segments	segment	NOUN
american_scientific_journal-7479	45	57	of	of	ADP
american_scientific_journal-7479	45	58	the	the	DET
american_scientific_journal-7479	45	59	eulerbernoulli	eulerbernoulli	NOUN
american_scientific_journal-7479	45	60	beam	beam	NOUN
american_scientific_journal-7479	45	61	.	.	PUNCT
american_scientific_journal-7479	46	1	this	this	DET
american_scientific_journal-7479	46	2	spring	spring	NOUN
american_scientific_journal-7479	46	3	is	be	AUX
american_scientific_journal-7479	46	4	the	the	DET
american_scientific_journal-7479	46	5	flexibility	flexibility	NOUN
american_scientific_journal-7479	46	6	due	due	ADP
american_scientific_journal-7479	46	7	to	to	ADP
american_scientific_journal-7479	46	8	the	the	DET
american_scientific_journal-7479	46	9	crack	crack	NOUN
american_scientific_journal-7479	46	10	's	's	PART
american_scientific_journal-7479	46	11	compliance	compliance	NOUN
american_scientific_journal-7479	46	12	.	.	PUNCT
american_scientific_journal-7479	47	1	euler	euler	PROPN
american_scientific_journal-7479	47	2	-	-	PUNCT
american_scientific_journal-7479	47	3	bernoulli	bernoulli	PROPN
american_scientific_journal-7479	47	4	beam	beam	NOUN
american_scientific_journal-7479	47	5	theory	theory	NOUN
american_scientific_journal-7479	47	6	suggests	suggest	VERB
american_scientific_journal-7479	47	7	that	that	SCONJ
american_scientific_journal-7479	47	8	we	we	PRON
american_scientific_journal-7479	47	9	can	can	AUX
american_scientific_journal-7479	47	10	mention	mention	VERB
american_scientific_journal-7479	47	11	the	the	DET
american_scientific_journal-7479	47	12	equation	equation	NOUN
american_scientific_journal-7479	47	13	of	of	ADP
american_scientific_journal-7479	47	14	motion	motion	NOUN
american_scientific_journal-7479	47	15	for	for	ADP
american_scientific_journal-7479	47	16	forced	force	VERB
american_scientific_journal-7479	47	17	vibration	vibration	NOUN
american_scientific_journal-7479	47	18	of	of	ADP
american_scientific_journal-7479	47	19	both	both	DET
american_scientific_journal-7479	47	20	portions	portion	NOUN
american_scientific_journal-7479	47	21	as	as	SCONJ
american_scientific_journal-7479	47	22	follows	follow	VERB
american_scientific_journal-7479	47	23	:	:	PUNCT
american_scientific_journal-7479	47	24	𝐸𝐼	𝐸𝐼	PROPN
american_scientific_journal-7479	47	25	𝜕4𝑤𝑟(𝑥	𝜕4𝑤𝑟(𝑥	NOUN
american_scientific_journal-7479	47	26	,	,	PUNCT
american_scientific_journal-7479	47	27	𝑡	𝑡	NOUN
american_scientific_journal-7479	47	28	)	)	PUNCT
american_scientific_journal-7479	47	29	𝜕𝑥4	𝜕𝑥4	PROPN
american_scientific_journal-7479	47	30	+	+	NUM
american_scientific_journal-7479	47	31	𝐴	𝐴	PROPN
american_scientific_journal-7479	47	32	𝜕2𝑤𝑟(𝑥	𝜕2𝑤𝑟(𝑥	NOUN
american_scientific_journal-7479	47	33	,	,	PUNCT
american_scientific_journal-7479	47	34	𝑡	𝑡	NOUN
american_scientific_journal-7479	47	35	)	)	PUNCT
american_scientific_journal-7479	47	36	𝜕𝑡2	𝜕𝑡2	NOUN
american_scientific_journal-7479	47	37	=	=	SYM
american_scientific_journal-7479	47	38	�	�	PROPN
american_scientific_journal-7479	47	39	̅	̅	NOUN
american_scientific_journal-7479	47	40	�	�	NOUN
american_scientific_journal-7479	47	41	𝛿(𝑥	𝛿(𝑥	NOUN
american_scientific_journal-7479	47	42	−	−	PROPN
american_scientific_journal-7479	47	43	𝑣𝑡	𝑣𝑡	NOUN
american_scientific_journal-7479	47	44	)	)	PUNCT
american_scientific_journal-7479	47	45	,	,	PUNCT
american_scientific_journal-7479	47	46	𝑥𝑟−1	𝑥𝑟−1	VERB
american_scientific_journal-7479	47	47	<	<	X
american_scientific_journal-7479	47	48	𝑥	𝑥	X
american_scientific_journal-7479	47	49	<	<	X
american_scientific_journal-7479	47	50	𝑥𝑟	𝑥𝑟	X
american_scientific_journal-7479	47	51	,	,	PUNCT
american_scientific_journal-7479	47	52	𝑟	𝑟	X
american_scientific_journal-7479	47	53	=	=	SYM
american_scientific_journal-7479	47	54	1,2	1,2	NUM
american_scientific_journal-7479	47	55	(	(	PUNCT
american_scientific_journal-7479	47	56	1	1	NUM
american_scientific_journal-7479	47	57	)	)	PUNCT
american_scientific_journal-7479	47	58	where	where	SCONJ
american_scientific_journal-7479	47	59	r	r	NOUN
american_scientific_journal-7479	47	60	=	=	SYM
american_scientific_journal-7479	47	61	1	1	NUM
american_scientific_journal-7479	47	62	and	and	CCONJ
american_scientific_journal-7479	47	63	2	2	NUM
american_scientific_journal-7479	47	64	denoted	denote	VERB
american_scientific_journal-7479	47	65	the	the	DET
american_scientific_journal-7479	47	66	portion	portion	NOUN
american_scientific_journal-7479	47	67	of	of	ADP
american_scientific_journal-7479	47	68	the	the	DET
american_scientific_journal-7479	47	69	beam	beam	NOUN
american_scientific_journal-7479	47	70	on	on	ADP
american_scientific_journal-7479	47	71	the	the	DET
american_scientific_journal-7479	47	72	left	left	NOUN
american_scientific_journal-7479	47	73	of	of	ADP
american_scientific_journal-7479	47	74	the	the	DET
american_scientific_journal-7479	47	75	crack	crack	NOUN
american_scientific_journal-7479	47	76	and	and	CCONJ
american_scientific_journal-7479	47	77	the	the	DET
american_scientific_journal-7479	47	78	portion	portion	NOUN
american_scientific_journal-7479	47	79	of	of	ADP
american_scientific_journal-7479	47	80	the	the	DET
american_scientific_journal-7479	47	81	beam	beam	NOUN
american_scientific_journal-7479	47	82	on	on	ADP
american_scientific_journal-7479	47	83	the	the	DET
american_scientific_journal-7479	47	84	right	right	ADJ
american_scientific_journal-7479	47	85	side	side	NOUN
american_scientific_journal-7479	47	86	of	of	ADP
american_scientific_journal-7479	47	87	the	the	DET
american_scientific_journal-7479	47	88	crack	crack	NOUN
american_scientific_journal-7479	47	89	respectively	respectively	ADV
american_scientific_journal-7479	47	90	,	,	PUNCT
american_scientific_journal-7479	47	91	e	e	PRON
american_scientific_journal-7479	47	92	is	be	AUX
american_scientific_journal-7479	47	93	young	young	ADJ
american_scientific_journal-7479	47	94	’s	’s	PART
american_scientific_journal-7479	47	95	modulus	modulus	NOUN
american_scientific_journal-7479	47	96	of	of	ADP
american_scientific_journal-7479	47	97	the	the	DET
american_scientific_journal-7479	47	98	beam	beam	NOUN
american_scientific_journal-7479	47	99	material	material	NOUN
american_scientific_journal-7479	47	100	,	,	PUNCT
american_scientific_journal-7479	47	101	i	i	PRON
american_scientific_journal-7479	47	102	is	be	AUX
american_scientific_journal-7479	47	103	the	the	DET
american_scientific_journal-7479	47	104	moment	moment	NOUN
american_scientific_journal-7479	47	105	of	of	ADP
american_scientific_journal-7479	47	106	inertia	inertia	NOUN
american_scientific_journal-7479	47	107	of	of	ADP
american_scientific_journal-7479	47	108	the	the	DET
american_scientific_journal-7479	47	109	beam	beam	NOUN
american_scientific_journal-7479	47	110	’s	’s	PART
american_scientific_journal-7479	47	111	cross	cross	NOUN
american_scientific_journal-7479	47	112	-	-	NOUN
american_scientific_journal-7479	47	113	section	section	NOUN
american_scientific_journal-7479	47	114	,	,	PUNCT
american_scientific_journal-7479	47	115	𝜌	𝜌	X
american_scientific_journal-7479	47	116	is	be	AUX
american_scientific_journal-7479	47	117	the	the	DET
american_scientific_journal-7479	47	118	density	density	NOUN
american_scientific_journal-7479	47	119	of	of	ADP
american_scientific_journal-7479	47	120	material	material	NOUN
american_scientific_journal-7479	47	121	,	,	PUNCT
american_scientific_journal-7479	47	122	a	a	PRON
american_scientific_journal-7479	47	123	is	be	AUX
american_scientific_journal-7479	47	124	the	the	DET
american_scientific_journal-7479	47	125	cross	cross	ADJ
american_scientific_journal-7479	47	126	-	-	ADJ
american_scientific_journal-7479	47	127	sectional	sectional	ADJ
american_scientific_journal-7479	47	128	area	area	NOUN
american_scientific_journal-7479	47	129	of	of	ADP
american_scientific_journal-7479	47	130	the	the	DET
american_scientific_journal-7479	47	131	beam	beam	NOUN
american_scientific_journal-7479	47	132	,	,	PUNCT
american_scientific_journal-7479	47	133	�	�	NOUN
american_scientific_journal-7479	47	134	̅	̅	NOUN
american_scientific_journal-7479	47	135	�	�	NOUN
american_scientific_journal-7479	47	136	is	be	AUX
american_scientific_journal-7479	47	137	the	the	DET
american_scientific_journal-7479	47	138	moving	move	VERB
american_scientific_journal-7479	47	139	load	load	NOUN
american_scientific_journal-7479	47	140	and	and	CCONJ
american_scientific_journal-7479	47	141	𝛿(𝑥	𝛿(𝑥	NOUN
american_scientific_journal-7479	47	142	−	−	PROPN
american_scientific_journal-7479	47	143	v𝑡	v𝑡	NOUN
american_scientific_journal-7479	47	144	)	)	PUNCT
american_scientific_journal-7479	47	145	denoted	denote	VERB
american_scientific_journal-7479	47	146	the	the	DET
american_scientific_journal-7479	47	147	dirac	dirac	NOUN
american_scientific_journal-7479	47	148	delta	delta	NOUN
american_scientific_journal-7479	47	149	function	function	NOUN
american_scientific_journal-7479	47	150	.	.	PUNCT
american_scientific_journal-7479	48	1	the	the	DET
american_scientific_journal-7479	48	2	boundary	boundary	ADJ
american_scientific_journal-7479	48	3	conditions	condition	NOUN
american_scientific_journal-7479	48	4	requirement	requirement	NOUN
american_scientific_journal-7479	48	5	of	of	ADP
american_scientific_journal-7479	48	6	a	a	DET
american_scientific_journal-7479	48	7	sscb	sscb	NOUN
american_scientific_journal-7479	48	8	case	case	NOUN
american_scientific_journal-7479	48	9	are	be	AUX
american_scientific_journal-7479	48	10	𝑤1(0	𝑤1(0	PROPN
american_scientific_journal-7479	48	11	)	)	PUNCT
american_scientific_journal-7479	49	1	=	=	SYM
american_scientific_journal-7479	49	2	𝑤2(𝐿	𝑤2(𝐿	PROPN
american_scientific_journal-7479	49	3	)	)	PUNCT
american_scientific_journal-7479	49	4	=	=	SYM
american_scientific_journal-7479	49	5	0	0	NUM
american_scientific_journal-7479	49	6	,	,	PUNCT
american_scientific_journal-7479	49	7	𝑑2𝑤1(0	𝑑2𝑤1(0	PROPN
american_scientific_journal-7479	49	8	)	)	PUNCT
american_scientific_journal-7479	49	9	𝑑𝑥2	𝑑𝑥2	NOUN
american_scientific_journal-7479	49	10	=	=	SYM
american_scientific_journal-7479	49	11	𝑑2𝑤2(𝐿	𝑑2𝑤2(𝐿	PROPN
american_scientific_journal-7479	49	12	)	)	PUNCT
american_scientific_journal-7479	49	13	𝑑𝑥2	𝑑𝑥2	NOUN
american_scientific_journal-7479	49	14	=	=	SYM
american_scientific_journal-7479	49	15	0	0	PUNCT
american_scientific_journal-7479	49	16	(	(	PUNCT
american_scientific_journal-7479	49	17	2	2	NUM
american_scientific_journal-7479	49	18	)	)	PUNCT
american_scientific_journal-7479	49	19	while	while	SCONJ
american_scientific_journal-7479	49	20	the	the	DET
american_scientific_journal-7479	49	21	kinematics	kinematic	NOUN
american_scientific_journal-7479	49	22	conditions	condition	NOUN
american_scientific_journal-7479	49	23	are	be	AUX
american_scientific_journal-7479	49	24	given	give	VERB
american_scientific_journal-7479	49	25	by	by	ADP
american_scientific_journal-7479	49	26	𝑤1(𝐿𝑐−	𝑤1(𝐿𝑐−	NOUN
american_scientific_journal-7479	49	27	)	)	PUNCT
american_scientific_journal-7479	49	28	=	=	SYM
american_scientific_journal-7479	49	29	𝑤2(𝐿𝑐+	𝑤2(𝐿𝑐+	PROPN
american_scientific_journal-7479	49	30	)	)	PUNCT
american_scientific_journal-7479	49	31	,	,	PUNCT
american_scientific_journal-7479	49	32	,	,	PUNCT
american_scientific_journal-7479	49	33	𝑑2𝑤1(𝐿𝑐−	𝑑2𝑤1(𝐿𝑐−	NOUN
american_scientific_journal-7479	49	34	)	)	PUNCT
american_scientific_journal-7479	49	35	𝑑𝑥2	𝑑𝑥2	NOUN
american_scientific_journal-7479	49	36	=	=	SYM
american_scientific_journal-7479	49	37	𝑑2𝑤2(𝐿𝑐+	𝑑2𝑤2(𝐿𝑐+	PROPN
american_scientific_journal-7479	49	38	)	)	PUNCT
american_scientific_journal-7479	49	39	𝑑𝑥2	𝑑𝑥2	VERB
american_scientific_journal-7479	49	40	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
american_scientific_journal-7479	49	41	𝑑3𝑤1(𝐿𝑐−	𝑑3𝑤1(𝐿𝑐−	PROPN
american_scientific_journal-7479	49	42	)	)	PUNCT
american_scientific_journal-7479	49	43	𝑑𝑥3	𝑑𝑥3	NOUN
american_scientific_journal-7479	50	1	=	=	SYM
american_scientific_journal-7479	50	2	𝑑3𝑤2(𝐿𝑐+	𝑑3𝑤2(𝐿𝑐+	NOUN
american_scientific_journal-7479	50	3	)	)	PUNCT
american_scientific_journal-7479	50	4	𝑑𝑥3	𝑑𝑥3	NOUN
american_scientific_journal-7479	50	5	(	(	PUNCT
american_scientific_journal-7479	50	6	3	3	NUM
american_scientific_journal-7479	50	7	)	)	PUNCT
american_scientific_journal-7479	50	8	where	where	SCONJ
american_scientific_journal-7479	50	9	the	the	DET
american_scientific_journal-7479	50	10	𝐿𝑐−	𝐿𝑐−	PROPN
american_scientific_journal-7479	50	11	and	and	CCONJ
american_scientific_journal-7479	50	12	𝐿𝑐+	𝐿𝑐+	PROPN
american_scientific_journal-7479	50	13	symbols	symbol	NOUN
american_scientific_journal-7479	50	14	have	have	AUX
american_scientific_journal-7479	50	15	indicated	indicate	VERB
american_scientific_journal-7479	50	16	the	the	DET
american_scientific_journal-7479	50	17	positions	position	NOUN
american_scientific_journal-7479	50	18	just	just	ADV
american_scientific_journal-7479	50	19	before	before	ADP
american_scientific_journal-7479	50	20	and	and	CCONJ
american_scientific_journal-7479	50	21	after	after	ADP
american_scientific_journal-7479	50	22	the	the	DET
american_scientific_journal-7479	50	23	crack	crack	NOUN
american_scientific_journal-7479	50	24	.	.	PUNCT
american_scientific_journal-7479	51	1	the	the	DET
american_scientific_journal-7479	51	2	crack	crack	NOUN
american_scientific_journal-7479	51	3	is	be	AUX
american_scientific_journal-7479	51	4	supposed	suppose	VERB
american_scientific_journal-7479	51	5	to	to	PART
american_scientific_journal-7479	51	6	be	be	AUX
american_scientific_journal-7479	51	7	completely	completely	ADV
american_scientific_journal-7479	51	8	opened	open	VERB
american_scientific_journal-7479	51	9	during	during	ADP
american_scientific_journal-7479	51	10	the	the	DET
american_scientific_journal-7479	51	11	vibration	vibration	NOUN
american_scientific_journal-7479	51	12	phase	phase	NOUN
american_scientific_journal-7479	51	13	,	,	PUNCT
american_scientific_journal-7479	51	14	and	and	CCONJ
american_scientific_journal-7479	51	15	the	the	DET
american_scientific_journal-7479	51	16	impact	impact	NOUN
american_scientific_journal-7479	51	17	of	of	ADP
american_scientific_journal-7479	51	18	the	the	DET
american_scientific_journal-7479	51	19	crack	crack	NOUN
american_scientific_journal-7479	51	20	can	can	AUX
american_scientific_journal-7479	51	21	only	only	ADV
american_scientific_journal-7479	51	22	be	be	AUX
american_scientific_journal-7479	51	23	seen	see	VERB
american_scientific_journal-7479	51	24	at	at	ADP
american_scientific_journal-7479	51	25	the	the	DET
american_scientific_journal-7479	51	26	position	position	NOUN
american_scientific_journal-7479	51	27	of	of	ADP
american_scientific_journal-7479	51	28	the	the	DET
american_scientific_journal-7479	51	29	crack	crack	NOUN
american_scientific_journal-7479	51	30	.	.	PUNCT
american_scientific_journal-7479	52	1	the	the	DET
american_scientific_journal-7479	52	2	crack	crack	NOUN
american_scientific_journal-7479	52	3	's	's	PART
american_scientific_journal-7479	52	4	existence	existence	NOUN
american_scientific_journal-7479	52	5	induces	induce	VERB
american_scientific_journal-7479	52	6	discontinuity	discontinuity	NOUN
american_scientific_journal-7479	52	7	or	or	CCONJ
american_scientific_journal-7479	52	8	shift	shift	NOUN
american_scientific_journal-7479	52	9	in	in	ADP
american_scientific_journal-7479	52	10	the	the	DET
american_scientific_journal-7479	52	11	beam	beam	NOUN
american_scientific_journal-7479	52	12	's	's	PART
american_scientific_journal-7479	52	13	slope	slope	NOUN
american_scientific_journal-7479	52	14	at	at	ADP
american_scientific_journal-7479	52	15	the	the	DET
american_scientific_journal-7479	52	16	crack	crack	NOUN
american_scientific_journal-7479	52	17	's	's	PART
american_scientific_journal-7479	52	18	position	position	NOUN
american_scientific_journal-7479	52	19	.	.	PUNCT
american_scientific_journal-7479	53	1	that	that	PRON
american_scientific_journal-7479	53	2	can	can	AUX
american_scientific_journal-7479	53	3	be	be	AUX
american_scientific_journal-7479	53	4	expressed	express	VERB
american_scientific_journal-7479	53	5	as[20	as[20	PROPN
american_scientific_journal-7479	53	6	]	]	X
american_scientific_journal-7479	53	7	∆θ	∆θ	PROPN
american_scientific_journal-7479	53	8	=	=	SYM
american_scientific_journal-7479	53	9	𝐶𝑚𝑀	𝐶𝑚𝑀	PROPN
american_scientific_journal-7479	53	10	(	(	PUNCT
american_scientific_journal-7479	53	11	4	4	NUM
american_scientific_journal-7479	53	12	)	)	PUNCT
american_scientific_journal-7479	53	13	where	where	SCONJ
american_scientific_journal-7479	53	14	𝑀	𝑀	PROPN
american_scientific_journal-7479	53	15	and	and	CCONJ
american_scientific_journal-7479	53	16	𝐶𝑚	𝐶𝑚	PROPN
american_scientific_journal-7479	53	17	are	be	AUX
american_scientific_journal-7479	53	18	the	the	DET
american_scientific_journal-7479	53	19	bending	bend	VERB
american_scientific_journal-7479	53	20	moment	moment	NOUN
american_scientific_journal-7479	53	21	transmitted	transmit	VERB
american_scientific_journal-7479	53	22	by	by	ADP
american_scientific_journal-7479	53	23	the	the	DET
american_scientific_journal-7479	53	24	cracked	crack	VERB
american_scientific_journal-7479	53	25	section	section	NOUN
american_scientific_journal-7479	53	26	and	and	CCONJ
american_scientific_journal-7479	53	27	the	the	DET
american_scientific_journal-7479	53	28	flexibility	flexibility	NOUN
american_scientific_journal-7479	53	29	constant	constant	ADJ
american_scientific_journal-7479	53	30	respectively	respectively	ADV
american_scientific_journal-7479	53	31	.	.	PUNCT
american_scientific_journal-7479	54	1	here	here	ADV
american_scientific_journal-7479	54	2	american	american	PROPN
american_scientific_journal-7479	54	3	academic	academic	ADJ
american_scientific_journal-7479	54	4	scientific	scientific	ADJ
american_scientific_journal-7479	54	5	research	research	NOUN
american_scientific_journal-7479	54	6	journal	journal	NOUN
american_scientific_journal-7479	54	7	for	for	ADP
american_scientific_journal-7479	54	8	engineering	engineering	NOUN
american_scientific_journal-7479	54	9	,	,	PUNCT
american_scientific_journal-7479	54	10	technology	technology	NOUN
american_scientific_journal-7479	54	11	,	,	PUNCT
american_scientific_journal-7479	54	12	and	and	CCONJ
american_scientific_journal-7479	54	13	sciences	science	NOUN
american_scientific_journal-7479	54	14	(	(	PUNCT
american_scientific_journal-7479	54	15	asrjets	asrjet	NOUN
american_scientific_journal-7479	54	16	)	)	PUNCT
american_scientific_journal-7479	54	17	(	(	PUNCT
american_scientific_journal-7479	54	18	2022	2022	NUM
american_scientific_journal-7479	54	19	)	)	PUNCT
american_scientific_journal-7479	54	20	volume	volume	NOUN
american_scientific_journal-7479	54	21	88	88	NUM
american_scientific_journal-7479	54	22	,	,	PUNCT
american_scientific_journal-7479	54	23	no1	no1	PROPN
american_scientific_journal-7479	54	24	,	,	PUNCT
american_scientific_journal-7479	54	25	pp	pp	ADV
american_scientific_journal-7479	54	26	332	332	NUM
american_scientific_journal-7479	54	27	-	-	SYM
american_scientific_journal-7479	54	28	348	348	NUM
american_scientific_journal-7479	54	29	335	335	NUM
american_scientific_journal-7479	55	1	𝐶𝑚	𝐶𝑚	NOUN
american_scientific_journal-7479	55	2	=	=	PUNCT
american_scientific_journal-7479	55	3	ℎ	ℎ	PROPN
american_scientific_journal-7479	55	4	𝐸𝐼	𝐸𝐼	PROPN
american_scientific_journal-7479	55	5	𝑄(𝛼,cross	𝑄(𝛼,cross	PROPN
american_scientific_journal-7479	55	6	section	section	NOUN
american_scientific_journal-7479	55	7	geometry	geometry	NOUN
american_scientific_journal-7479	55	8	)	)	PUNCT
american_scientific_journal-7479	55	9	(	(	PUNCT
american_scientific_journal-7479	55	10	5	5	X
american_scientific_journal-7479	55	11	)	)	PUNCT
american_scientific_journal-7479	55	12	here	here	ADV
american_scientific_journal-7479	55	13	𝛼	𝛼	VERB
american_scientific_journal-7479	55	14	is	be	AUX
american_scientific_journal-7479	55	15	the	the	DET
american_scientific_journal-7479	55	16	amount	amount	NOUN
american_scientific_journal-7479	55	17	of	of	ADP
american_scientific_journal-7479	55	18	crack	crack	NOUN
american_scientific_journal-7479	55	19	depth	depth	NOUN
american_scientific_journal-7479	55	20	indicated	indicate	VERB
american_scientific_journal-7479	55	21	by	by	ADP
american_scientific_journal-7479	55	22	𝛼	𝛼	X
american_scientific_journal-7479	55	23	=	=	NOUN
american_scientific_journal-7479	55	24	𝑎	𝑎	X
american_scientific_journal-7479	55	25	ℎ	ℎ	PROPN
american_scientific_journal-7479	55	26	(	(	PUNCT
american_scientific_journal-7479	55	27	6	6	NUM
american_scientific_journal-7479	55	28	)	)	PUNCT
american_scientific_journal-7479	55	29	the	the	DET
american_scientific_journal-7479	55	30	𝑄(𝛼	𝑄(𝛼	NUM
american_scientific_journal-7479	55	31	)	)	PUNCT
american_scientific_journal-7479	55	32	function	function	NOUN
american_scientific_journal-7479	55	33	,	,	PUNCT
american_scientific_journal-7479	55	34	which	which	PRON
american_scientific_journal-7479	55	35	is	be	AUX
american_scientific_journal-7479	55	36	the	the	DET
american_scientific_journal-7479	55	37	configuration	configuration	NOUN
american_scientific_journal-7479	55	38	function	function	NOUN
american_scientific_journal-7479	55	39	for	for	ADP
american_scientific_journal-7479	55	40	the	the	DET
american_scientific_journal-7479	55	41	opening	opening	NOUN
american_scientific_journal-7479	55	42	region	region	NOUN
american_scientific_journal-7479	55	43	of	of	ADP
american_scientific_journal-7479	55	44	the	the	DET
american_scientific_journal-7479	55	45	crack	crack	NOUN
american_scientific_journal-7479	55	46	,	,	PUNCT
american_scientific_journal-7479	55	47	can	can	AUX
american_scientific_journal-7479	55	48	be	be	AUX
american_scientific_journal-7479	55	49	evaluated	evaluate	VERB
american_scientific_journal-7479	55	50	by	by	ADP
american_scientific_journal-7479	55	51	fracture	fracture	PROPN
american_scientific_journal-7479	55	52	mechanics	mechanic	NOUN
american_scientific_journal-7479	55	53	as[20][21	as[20][21	PUNCT
american_scientific_journal-7479	55	54	]	]	PUNCT
american_scientific_journal-7479	55	55	𝑄(𝛼	𝑄(𝛼	NUM
american_scientific_journal-7479	55	56	)	)	PUNCT
american_scientific_journal-7479	55	57	=	=	SYM
american_scientific_journal-7479	55	58	2	2	NUM
american_scientific_journal-7479	55	59	(	(	PUNCT
american_scientific_journal-7479	55	60	𝛼	𝛼	PROPN
american_scientific_journal-7479	55	61	1	1	NUM
american_scientific_journal-7479	55	62	−	−	PROPN
american_scientific_journal-7479	55	63	𝛼	𝛼	SYM
american_scientific_journal-7479	55	64	)	)	PUNCT
american_scientific_journal-7479	55	65	2	2	NUM
american_scientific_journal-7479	56	1	[	[	SYM
american_scientific_journal-7479	56	2	5.93	5.93	NUM
american_scientific_journal-7479	56	3	−	−	NUM
american_scientific_journal-7479	56	4	19.69𝛼	19.69𝛼	NUM
american_scientific_journal-7479	56	5	+	+	CCONJ
american_scientific_journal-7479	56	6	37.14𝛼2	37.14𝛼2	NUM
american_scientific_journal-7479	56	7	−	−	NOUN
american_scientific_journal-7479	56	8	35.84𝛼3	35.84𝛼3	NUM
american_scientific_journal-7479	56	9	+	+	CCONJ
american_scientific_journal-7479	56	10	13.12𝛼4	13.12𝛼4	NUM
american_scientific_journal-7479	56	11	]	]	X
american_scientific_journal-7479	56	12	(	(	PUNCT
american_scientific_journal-7479	56	13	7	7	X
american_scientific_journal-7479	56	14	)	)	PUNCT
american_scientific_journal-7479	56	15	we	we	PRON
american_scientific_journal-7479	56	16	rewrite	rewrite	VERB
american_scientific_journal-7479	56	17	eq	eq	ADP
american_scientific_journal-7479	56	18	.	.	PUNCT
american_scientific_journal-7479	57	1	(	(	PUNCT
american_scientific_journal-7479	57	2	4	4	NUM
american_scientific_journal-7479	57	3	)	)	PUNCT
american_scientific_journal-7479	57	4	as	as	ADP
american_scientific_journal-7479	57	5	∆θ	∆θ	PROPN
american_scientific_journal-7479	57	6	=	=	SYM
american_scientific_journal-7479	57	7	𝑑𝑤2(𝐿𝑐+	𝑑𝑤2(𝐿𝑐+	PROPN
american_scientific_journal-7479	57	8	)	)	PUNCT
american_scientific_journal-7479	57	9	𝑑𝑥	𝑑𝑥	VERB
american_scientific_journal-7479	57	10	−	−	PROPN
american_scientific_journal-7479	57	11	𝑑𝑤1(𝐿𝑐−	𝑑𝑤1(𝐿𝑐−	NOUN
american_scientific_journal-7479	57	12	)	)	PUNCT
american_scientific_journal-7479	57	13	𝑑𝑥	𝑑𝑥	ADP
american_scientific_journal-7479	57	14	=	=	SYM
american_scientific_journal-7479	57	15	ℎ𝑄(𝛼	ℎ𝑄(𝛼	NUM
american_scientific_journal-7479	57	16	)	)	PUNCT
american_scientific_journal-7479	57	17	𝑑2𝑤2(𝐿𝑐+	𝑑2𝑤2(𝐿𝑐+	NUM
american_scientific_journal-7479	57	18	)	)	PUNCT
american_scientific_journal-7479	57	19	𝑑𝑥2	𝑑𝑥2	NOUN
american_scientific_journal-7479	57	20	(	(	PUNCT
american_scientific_journal-7479	57	21	8)	8)	NUM
american_scientific_journal-7479	57	22	a	a	DET
american_scientific_journal-7479	57	23	series	series	NOUN
american_scientific_journal-7479	57	24	solution	solution	NOUN
american_scientific_journal-7479	57	25	of	of	ADP
american_scientific_journal-7479	57	26	eq	eq	PROPN
american_scientific_journal-7479	57	27	.	.	PUNCT
american_scientific_journal-7479	58	1	(	(	PUNCT
american_scientific_journal-7479	58	2	1	1	X
american_scientific_journal-7479	58	3	)	)	PUNCT
american_scientific_journal-7479	58	4	can	can	AUX
american_scientific_journal-7479	58	5	be	be	AUX
american_scientific_journal-7479	58	6	sought	seek	VERB
american_scientific_journal-7479	58	7	in	in	ADP
american_scientific_journal-7479	58	8	the	the	DET
american_scientific_journal-7479	58	9	form	form	NOUN
american_scientific_journal-7479	58	10	according	accord	VERB
american_scientific_journal-7479	58	11	to	to	ADP
american_scientific_journal-7479	58	12	modal	modal	ADJ
american_scientific_journal-7479	58	13	analysis	analysis	NOUN
american_scientific_journal-7479	58	14	approach	approach	NOUN
american_scientific_journal-7479	58	15	(	(	PUNCT
american_scientific_journal-7479	58	16	for	for	ADP
american_scientific_journal-7479	58	17	harmonic	harmonic	ADJ
american_scientific_journal-7479	58	18	free	free	ADJ
american_scientific_journal-7479	58	19	vibration	vibration	NOUN
american_scientific_journal-7479	58	20	)	)	PUNCT
american_scientific_journal-7479	58	21	,	,	PUNCT
american_scientific_journal-7479	58	22	the	the	DET
american_scientific_journal-7479	58	23	𝑤𝑟(𝑥	𝑤𝑟(𝑥	NOUN
american_scientific_journal-7479	58	24	,	,	PUNCT
american_scientific_journal-7479	58	25	𝑡	𝑡	PROPN
american_scientific_journal-7479	58	26	)	)	PUNCT
american_scientific_journal-7479	58	27	can	can	AUX
american_scientific_journal-7479	58	28	be	be	AUX
american_scientific_journal-7479	58	29	separated	separate	VERB
american_scientific_journal-7479	58	30	in	in	ADP
american_scientific_journal-7479	58	31	space	space	NOUN
american_scientific_journal-7479	58	32	and	and	CCONJ
american_scientific_journal-7479	58	33	time	time	NOUN
american_scientific_journal-7479	58	34	:	:	PUNCT
american_scientific_journal-7479	58	35	𝑤𝑟(𝑥	𝑤𝑟(𝑥	NUM
american_scientific_journal-7479	58	36	,	,	PUNCT
american_scientific_journal-7479	58	37	𝑡	𝑡	NOUN
american_scientific_journal-7479	58	38	)	)	PUNCT
american_scientific_journal-7479	59	1	=	=	SYM
american_scientific_journal-7479	59	2	𝜑𝑟(𝑥)𝑒𝑖𝜔𝑡	𝜑𝑟(𝑥)𝑒𝑖𝜔𝑡	NOUN
american_scientific_journal-7479	59	3	,	,	PUNCT
american_scientific_journal-7479	59	4	𝑖	𝑖	NOUN
american_scientific_journal-7479	59	5	=	=	PUNCT
american_scientific_journal-7479	59	6	√−1	√−1	X
american_scientific_journal-7479	59	7	(	(	PUNCT
american_scientific_journal-7479	59	8	9	9	NUM
american_scientific_journal-7479	59	9	)	)	PUNCT
american_scientific_journal-7479	59	10	substituting	substitute	VERB
american_scientific_journal-7479	59	11	the	the	DET
american_scientific_journal-7479	59	12	eq	eq	NOUN
american_scientific_journal-7479	59	13	.	.	PUNCT
american_scientific_journal-7479	60	1	(	(	PUNCT
american_scientific_journal-7479	60	2	9	9	NUM
american_scientific_journal-7479	60	3	)	)	PUNCT
american_scientific_journal-7479	60	4	into	into	ADP
american_scientific_journal-7479	60	5	the	the	DET
american_scientific_journal-7479	60	6	eq	eq	NOUN
american_scientific_journal-7479	60	7	.	.	PUNCT
american_scientific_journal-7479	61	1	(	(	PUNCT
american_scientific_journal-7479	61	2	1	1	NUM
american_scientific_journal-7479	61	3	)	)	PUNCT
american_scientific_journal-7479	61	4	and	and	CCONJ
american_scientific_journal-7479	61	5	the	the	DET
american_scientific_journal-7479	61	6	separating	separate	VERB
american_scientific_journal-7479	61	7	time	time	NOUN
american_scientific_journal-7479	61	8	t	t	NOUN
american_scientific_journal-7479	61	9	and	and	CCONJ
american_scientific_journal-7479	61	10	space	space	NOUN
american_scientific_journal-7479	61	11	x	x	SYM
american_scientific_journal-7479	61	12	variables	variable	NOUN
american_scientific_journal-7479	61	13	,	,	PUNCT
american_scientific_journal-7479	61	14	an	an	DET
american_scientific_journal-7479	61	15	ordinary	ordinary	ADJ
american_scientific_journal-7479	61	16	differential	differential	ADJ
american_scientific_journal-7479	61	17	equation	equation	NOUN
american_scientific_journal-7479	61	18	can	can	AUX
american_scientific_journal-7479	61	19	be	be	AUX
american_scientific_journal-7479	61	20	obtained	obtain	VERB
american_scientific_journal-7479	61	21	for	for	ADP
american_scientific_journal-7479	61	22	two	two	NUM
american_scientific_journal-7479	61	23	segments	segment	NOUN
american_scientific_journal-7479	61	24	of	of	ADP
american_scientific_journal-7479	61	25	the	the	DET
american_scientific_journal-7479	61	26	cracked	crack	VERB
american_scientific_journal-7479	61	27	beam	beam	NOUN
american_scientific_journal-7479	61	28	.	.	PUNCT
american_scientific_journal-7479	62	1	𝑑4𝜑𝑟(𝑥	𝑑4𝜑𝑟(𝑥	NOUN
american_scientific_journal-7479	62	2	)	)	PUNCT
american_scientific_journal-7479	62	3	𝑑𝑥4	𝑑𝑥4	PROPN
american_scientific_journal-7479	62	4	−	−	PROPN
american_scientific_journal-7479	62	5	ψ4𝜑𝑟(𝑥	ψ4𝜑𝑟(𝑥	PROPN
american_scientific_journal-7479	62	6	)	)	PUNCT
american_scientific_journal-7479	63	1	=	=	SYM
american_scientific_journal-7479	63	2	0	0	NUM
american_scientific_journal-7479	63	3	,	,	PUNCT
american_scientific_journal-7479	63	4	𝑥𝑟−1	𝑥𝑟−1	VERB
american_scientific_journal-7479	63	5	<	<	X
american_scientific_journal-7479	63	6	𝑥	𝑥	X
american_scientific_journal-7479	63	7	<	<	X
american_scientific_journal-7479	63	8	𝑥𝑟	𝑥𝑟	X
american_scientific_journal-7479	63	9	,	,	PUNCT
american_scientific_journal-7479	63	10	𝑟	𝑟	X
american_scientific_journal-7479	63	11	=	=	SYM
american_scientific_journal-7479	63	12	1,2	1,2	NUM
american_scientific_journal-7479	63	13	(	(	PUNCT
american_scientific_journal-7479	63	14	10	10	NUM
american_scientific_journal-7479	63	15	)	)	PUNCT
american_scientific_journal-7479	63	16	and	and	CCONJ
american_scientific_journal-7479	63	17	ψ4	ψ4	PROPN
american_scientific_journal-7479	63	18	=	=	SYM
american_scientific_journal-7479	63	19	𝐴𝜔2	𝐴𝜔2	PROPN
american_scientific_journal-7479	63	20	𝐸𝐼	𝐸𝐼	PROPN
american_scientific_journal-7479	63	21	(	(	PUNCT
american_scientific_journal-7479	63	22	11	11	NUM
american_scientific_journal-7479	63	23	)	)	PUNCT
american_scientific_journal-7479	63	24	where	where	SCONJ
american_scientific_journal-7479	63	25	𝜑(𝑟)(𝑥	𝜑(𝑟)(𝑥	ADV
american_scientific_journal-7479	63	26	)	)	PUNCT
american_scientific_journal-7479	63	27	is	be	AUX
american_scientific_journal-7479	63	28	the	the	DET
american_scientific_journal-7479	63	29	cracked	crack	VERB
american_scientific_journal-7479	63	30	beam	beam	NOUN
american_scientific_journal-7479	63	31	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-7479	63	32	for	for	ADP
american_scientific_journal-7479	63	33	the	the	DET
american_scientific_journal-7479	63	34	region	region	NOUN
american_scientific_journal-7479	63	35	of	of	ADP
american_scientific_journal-7479	63	36	the	the	DET
american_scientific_journal-7479	63	37	beam	beam	NOUN
american_scientific_journal-7479	63	38	before	before	ADV
american_scientific_journal-7479	63	39	and	and	CCONJ
american_scientific_journal-7479	63	40	after	after	ADP
american_scientific_journal-7479	63	41	the	the	DET
american_scientific_journal-7479	63	42	crack	crack	NOUN
american_scientific_journal-7479	63	43	and	and	CCONJ
american_scientific_journal-7479	63	44	𝜔	𝜔	NOUN
american_scientific_journal-7479	63	45	is	be	AUX
american_scientific_journal-7479	63	46	the	the	DET
american_scientific_journal-7479	63	47	normal	normal	ADJ
american_scientific_journal-7479	63	48	frequency	frequency	NOUN
american_scientific_journal-7479	63	49	.	.	PUNCT
american_scientific_journal-7479	64	1	to	to	PART
american_scientific_journal-7479	64	2	derive	derive	VERB
american_scientific_journal-7479	64	3	the	the	DET
american_scientific_journal-7479	64	4	vibration	vibration	NOUN
american_scientific_journal-7479	64	5	mode	mode	NOUN
american_scientific_journal-7479	64	6	shapes	shape	NOUN
american_scientific_journal-7479	64	7	of	of	ADP
american_scientific_journal-7479	64	8	cracked	crack	VERB
american_scientific_journal-7479	64	9	beam	beam	NOUN
american_scientific_journal-7479	64	10	the	the	DET
american_scientific_journal-7479	64	11	adm	adm	PROPN
american_scientific_journal-7479	64	12	is	be	AUX
american_scientific_journal-7479	64	13	applied	apply	VERB
american_scientific_journal-7479	64	14	to	to	ADP
american_scientific_journal-7479	64	15	eq	eq	PROPN
american_scientific_journal-7479	64	16	.	.	PUNCT
american_scientific_journal-7479	65	1	(	(	PUNCT
american_scientific_journal-7479	65	2	10	10	NUM
american_scientific_journal-7479	65	3	)	)	PUNCT
american_scientific_journal-7479	65	4	.	.	PUNCT
american_scientific_journal-7479	66	1	first	first	ADV
american_scientific_journal-7479	66	2	eq	eq	ADP
american_scientific_journal-7479	66	3	.	.	PUNCT
american_scientific_journal-7479	67	1	(	(	PUNCT
american_scientific_journal-7479	67	2	10	10	NUM
american_scientific_journal-7479	67	3	)	)	PUNCT
american_scientific_journal-7479	67	4	is	be	AUX
american_scientific_journal-7479	67	5	rewritten	rewrite	VERB
american_scientific_journal-7479	67	6	as	as	ADP
american_scientific_journal-7479	67	7	an	an	DET
american_scientific_journal-7479	67	8	operator	operator	NOUN
american_scientific_journal-7479	67	9	form[14	form[14	NOUN
american_scientific_journal-7479	67	10	]	]	PUNCT
american_scientific_journal-7479	67	11	𝐻𝑥[𝜑𝑟(𝑥	𝐻𝑥[𝜑𝑟(𝑥	PROPN
american_scientific_journal-7479	67	12	)	)	PUNCT
american_scientific_journal-7479	67	13	]	]	PUNCT
american_scientific_journal-7479	68	1	−	−	PROPN
american_scientific_journal-7479	68	2	ψ4𝜑𝑟(𝑥	ψ4𝜑𝑟(𝑥	PROPN
american_scientific_journal-7479	68	3	)	)	PUNCT
american_scientific_journal-7479	68	4	=	=	SYM
american_scientific_journal-7479	68	5	0	0	PUNCT
american_scientific_journal-7479	69	1	𝑥𝑟−1	𝑥𝑟−1	ADJ
american_scientific_journal-7479	69	2	<	<	X
american_scientific_journal-7479	69	3	𝑥	𝑥	X
american_scientific_journal-7479	69	4	<	<	X
american_scientific_journal-7479	69	5	𝑥𝑟	𝑥𝑟	X
american_scientific_journal-7479	69	6	,	,	PUNCT
american_scientific_journal-7479	69	7	𝑟	𝑟	X
american_scientific_journal-7479	69	8	=	=	SYM
american_scientific_journal-7479	69	9	1,2	1,2	NUM
american_scientific_journal-7479	69	10	(	(	PUNCT
american_scientific_journal-7479	69	11	12	12	NUM
american_scientific_journal-7479	69	12	)	)	PUNCT
american_scientific_journal-7479	69	13	american	american	ADJ
american_scientific_journal-7479	69	14	academic	academic	ADJ
american_scientific_journal-7479	69	15	scientific	scientific	ADJ
american_scientific_journal-7479	69	16	research	research	NOUN
american_scientific_journal-7479	69	17	journal	journal	NOUN
american_scientific_journal-7479	69	18	for	for	ADP
american_scientific_journal-7479	69	19	engineering	engineering	NOUN
american_scientific_journal-7479	69	20	,	,	PUNCT
american_scientific_journal-7479	69	21	technology	technology	NOUN
american_scientific_journal-7479	69	22	,	,	PUNCT
american_scientific_journal-7479	69	23	and	and	CCONJ
american_scientific_journal-7479	69	24	sciences	science	NOUN
american_scientific_journal-7479	69	25	(	(	PUNCT
american_scientific_journal-7479	69	26	asrjets	asrjet	NOUN
american_scientific_journal-7479	69	27	)	)	PUNCT
american_scientific_journal-7479	69	28	(	(	PUNCT
american_scientific_journal-7479	69	29	2022	2022	NUM
american_scientific_journal-7479	69	30	)	)	PUNCT
american_scientific_journal-7479	69	31	volume	volume	NOUN
american_scientific_journal-7479	69	32	88	88	NUM
american_scientific_journal-7479	69	33	,	,	PUNCT
american_scientific_journal-7479	69	34	no1	no1	PROPN
american_scientific_journal-7479	69	35	,	,	PUNCT
american_scientific_journal-7479	69	36	pp	pp	ADV
american_scientific_journal-7479	69	37	332	332	NUM
american_scientific_journal-7479	69	38	-	-	SYM
american_scientific_journal-7479	69	39	348	348	NUM
american_scientific_journal-7479	69	40	336	336	NUM
american_scientific_journal-7479	69	41	where	where	SCONJ
american_scientific_journal-7479	69	42	𝐻𝑥	𝐻𝑥	PROPN
american_scientific_journal-7479	69	43	=	=	PUNCT
american_scientific_journal-7479	69	44	𝑑4	𝑑4	ADV
american_scientific_journal-7479	69	45	𝑑𝑥4	𝑑𝑥4	PROPN
american_scientific_journal-7479	69	46	,	,	PUNCT
american_scientific_journal-7479	69	47	the	the	DET
american_scientific_journal-7479	69	48	inverse	inverse	NOUN
american_scientific_journal-7479	69	49	operator	operator	NOUN
american_scientific_journal-7479	69	50	of	of	ADP
american_scientific_journal-7479	69	51	𝐻𝑥	𝐻𝑥	PROPN
american_scientific_journal-7479	69	52	is	be	AUX
american_scientific_journal-7479	69	53	then	then	ADV
american_scientific_journal-7479	69	54	a	a	DET
american_scientific_journal-7479	69	55	4	4	NUM
american_scientific_journal-7479	69	56	-	-	ADJ
american_scientific_journal-7479	69	57	fold	fold	ADJ
american_scientific_journal-7479	69	58	integral	integral	ADJ
american_scientific_journal-7479	69	59	operator	operator	NOUN
american_scientific_journal-7479	69	60	defined	define	VERB
american_scientific_journal-7479	69	61	by	by	ADP
american_scientific_journal-7479	69	62	𝐻𝑥	𝐻𝑥	PROPN
american_scientific_journal-7479	69	63	−1	−1	NOUN
american_scientific_journal-7479	69	64	=	=	SYM
american_scientific_journal-7479	70	1	∫	∫	PROPN
american_scientific_journal-7479	70	2	∫	∫	PROPN
american_scientific_journal-7479	70	3	∫	∫	PROPN
american_scientific_journal-7479	70	4	∫	∫	PROPN
american_scientific_journal-7479	70	5	(	(	PUNCT
american_scientific_journal-7479	70	6	⋅)𝑑𝑥𝑑𝑥𝑑𝑥𝑑𝑥	⋅)𝑑𝑥𝑑𝑥𝑑𝑥𝑑𝑥	ADP
american_scientific_journal-7479	70	7	𝑥	𝑥	X
american_scientific_journal-7479	70	8	0	0	NUM
american_scientific_journal-7479	70	9	𝑥	𝑥	NOUN
american_scientific_journal-7479	70	10	0	0	NUM
american_scientific_journal-7479	71	1	𝑥	𝑥	NOUN
american_scientific_journal-7479	71	2	0	0	NUM
american_scientific_journal-7479	71	3	𝑥	𝑥	NOUN
american_scientific_journal-7479	71	4	0	0	NUM
american_scientific_journal-7479	71	5	(	(	PUNCT
american_scientific_journal-7479	71	6	13	13	NUM
american_scientific_journal-7479	71	7	)	)	PUNCT
american_scientific_journal-7479	71	8	appling	apple	VERB
american_scientific_journal-7479	71	9	𝐻𝑥	𝐻𝑥	PROPN
american_scientific_journal-7479	71	10	−1	−1	NOUN
american_scientific_journal-7479	71	11	on	on	ADP
american_scientific_journal-7479	71	12	both	both	DET
american_scientific_journal-7479	71	13	sides	side	NOUN
american_scientific_journal-7479	71	14	of	of	ADP
american_scientific_journal-7479	71	15	eq	eq	PROPN
american_scientific_journal-7479	71	16	.	.	PUNCT
american_scientific_journal-7479	72	1	(	(	PUNCT
american_scientific_journal-7479	72	2	12	12	NUM
american_scientific_journal-7479	72	3	)	)	PUNCT
american_scientific_journal-7479	72	4	yields	yield	NOUN
american_scientific_journal-7479	72	5	𝜑𝑟(𝑥	𝜑𝑟(𝑥	NOUN
american_scientific_journal-7479	72	6	)	)	PUNCT
american_scientific_journal-7479	72	7	=	=	SYM
american_scientific_journal-7479	73	1	𝜑𝑟(0	𝜑𝑟(0	PROPN
american_scientific_journal-7479	73	2	)	)	PUNCT
american_scientific_journal-7479	73	3	+	+	NOUN
american_scientific_journal-7479	73	4	𝑥	𝑥	NOUN
american_scientific_journal-7479	74	1	1	1	X
american_scientific_journal-7479	74	2	!	!	NUM
american_scientific_journal-7479	74	3	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	74	4	(	(	PUNCT
american_scientific_journal-7479	74	5	1)(0	1)(0	NUM
american_scientific_journal-7479	74	6	)	)	PUNCT
american_scientific_journal-7479	74	7	+	+	NUM
american_scientific_journal-7479	74	8	𝑥2	𝑥2	NOUN
american_scientific_journal-7479	74	9	2	2	NUM
american_scientific_journal-7479	74	10	!	!	NUM
american_scientific_journal-7479	74	11	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	74	12	(	(	PUNCT
american_scientific_journal-7479	74	13	2)(0	2)(0	NUM
american_scientific_journal-7479	74	14	)	)	PUNCT
american_scientific_journal-7479	74	15	+	+	NUM
american_scientific_journal-7479	74	16	𝑥3	𝑥3	ADJ
american_scientific_journal-7479	74	17	3	3	NUM
american_scientific_journal-7479	74	18	!	!	SYM
american_scientific_journal-7479	74	19	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	74	20	(	(	PUNCT
american_scientific_journal-7479	74	21	3)(0	3)(0	NUM
american_scientific_journal-7479	74	22	)	)	PUNCT
american_scientific_journal-7479	74	23	+	+	NUM
american_scientific_journal-7479	74	24	𝛹4𝐻𝑥	𝛹4𝐻𝑥	VERB
american_scientific_journal-7479	74	25	−1[𝜑𝑟(𝑥	−1[𝜑𝑟(𝑥	NOUN
american_scientific_journal-7479	74	26	)	)	PUNCT
american_scientific_journal-7479	74	27	]	]	PUNCT
american_scientific_journal-7479	74	28	,	,	PUNCT
american_scientific_journal-7479	74	29	𝑥𝑟−1	𝑥𝑟−1	VERB
american_scientific_journal-7479	74	30	<	<	X
american_scientific_journal-7479	74	31	𝑥	𝑥	X
american_scientific_journal-7479	74	32	<	<	X
american_scientific_journal-7479	74	33	𝑥𝑟	𝑥𝑟	X
american_scientific_journal-7479	74	34	(	(	PUNCT
american_scientific_journal-7479	74	35	14	14	NUM
american_scientific_journal-7479	74	36	)	)	PUNCT
american_scientific_journal-7479	74	37	where	where	SCONJ
american_scientific_journal-7479	74	38	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	74	39	(	(	PUNCT
american_scientific_journal-7479	74	40	𝑖	𝑖	NOUN
american_scientific_journal-7479	74	41	)	)	PUNCT
american_scientific_journal-7479	74	42	denotes	denote	VERB
american_scientific_journal-7479	74	43	the	the	DET
american_scientific_journal-7479	74	44	ith	ith	PROPN
american_scientific_journal-7479	74	45	-	-	PUNCT
american_scientific_journal-7479	74	46	order	order	NOUN
american_scientific_journal-7479	74	47	derivative	derivative	NOUN
american_scientific_journal-7479	74	48	with	with	ADP
american_scientific_journal-7479	74	49	respect	respect	NOUN
american_scientific_journal-7479	74	50	to	to	ADP
american_scientific_journal-7479	74	51	x	x	PUNCT
american_scientific_journal-7479	74	52	and	and	CCONJ
american_scientific_journal-7479	74	53	sets	set	NOUN
american_scientific_journal-7479	74	54	𝜑𝑟(𝑥	𝜑𝑟(𝑥	NOUN
american_scientific_journal-7479	74	55	)	)	PUNCT
american_scientific_journal-7479	74	56	=	=	SYM
american_scientific_journal-7479	74	57	𝜑𝑟	𝜑𝑟	X
american_scientific_journal-7479	74	58	(	(	PUNCT
american_scientific_journal-7479	74	59	0)(𝑥	0)(𝑥	NOUN
american_scientific_journal-7479	74	60	)	)	PUNCT
american_scientific_journal-7479	74	61	based	base	VERB
american_scientific_journal-7479	74	62	on	on	ADP
american_scientific_journal-7479	74	63	the	the	DET
american_scientific_journal-7479	74	64	adm[22][2	adm[22][2	PROPN
american_scientific_journal-7479	74	65	]	]	PUNCT
american_scientific_journal-7479	74	66	,	,	PUNCT
american_scientific_journal-7479	74	67	the	the	DET
american_scientific_journal-7479	74	68	solution	solution	NOUN
american_scientific_journal-7479	74	69	of	of	ADP
american_scientific_journal-7479	74	70	the	the	DET
american_scientific_journal-7479	74	71	vibration	vibration	NOUN
american_scientific_journal-7479	74	72	mode	mode	NOUN
american_scientific_journal-7479	74	73	function	function	NOUN
american_scientific_journal-7479	74	74	can	can	AUX
american_scientific_journal-7479	74	75	be	be	AUX
american_scientific_journal-7479	74	76	expressed	express	VERB
american_scientific_journal-7479	74	77	as	as	ADP
american_scientific_journal-7479	74	78	a	a	DET
american_scientific_journal-7479	74	79	series	series	NOUN
american_scientific_journal-7479	74	80	:	:	PUNCT
american_scientific_journal-7479	74	81	𝜑𝑟(𝑥	𝜑𝑟(𝑥	NUM
american_scientific_journal-7479	74	82	)	)	PUNCT
american_scientific_journal-7479	74	83	=	=	PUNCT
american_scientific_journal-7479	74	84	∑	∑	PUNCT
american_scientific_journal-7479	74	85	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	75	1	[	[	X
american_scientific_journal-7479	75	2	𝑗](𝑥	𝑗](𝑥	NOUN
american_scientific_journal-7479	75	3	)	)	PUNCT
american_scientific_journal-7479	76	1	∞	∞	PROPN
american_scientific_journal-7479	76	2	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	76	3	,	,	PUNCT
american_scientific_journal-7479	76	4	𝑥𝑟−1	𝑥𝑟−1	VERB
american_scientific_journal-7479	76	5	<	<	X
american_scientific_journal-7479	76	6	𝑥	𝑥	X
american_scientific_journal-7479	76	7	<	<	X
american_scientific_journal-7479	76	8	𝑥𝑟	𝑥𝑟	X
american_scientific_journal-7479	76	9	,	,	PUNCT
american_scientific_journal-7479	76	10	𝑟	𝑟	X
american_scientific_journal-7479	76	11	=	=	SYM
american_scientific_journal-7479	76	12	1,2	1,2	NUM
american_scientific_journal-7479	76	13	(	(	PUNCT
american_scientific_journal-7479	76	14	15	15	NUM
american_scientific_journal-7479	76	15	)	)	PUNCT
american_scientific_journal-7479	76	16	substituting	substitute	VERB
american_scientific_journal-7479	76	17	eq	eq	PROPN
american_scientific_journal-7479	76	18	.	.	PUNCT
american_scientific_journal-7479	77	1	(	(	PUNCT
american_scientific_journal-7479	77	2	15	15	NUM
american_scientific_journal-7479	77	3	)	)	PUNCT
american_scientific_journal-7479	77	4	into	into	ADP
american_scientific_journal-7479	77	5	eq	eq	NOUN
american_scientific_journal-7479	77	6	.	.	PUNCT
american_scientific_journal-7479	78	1	(	(	PUNCT
american_scientific_journal-7479	78	2	14	14	NUM
american_scientific_journal-7479	78	3	)	)	PUNCT
american_scientific_journal-7479	78	4	by	by	ADP
american_scientific_journal-7479	78	5	assuming	assume	VERB
american_scientific_journal-7479	78	6	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	78	7	[	[	X
american_scientific_journal-7479	78	8	0](𝑥	0](𝑥	NOUN
american_scientific_journal-7479	78	9	)	)	PUNCT
american_scientific_journal-7479	79	1	=	=	PUNCT
american_scientific_journal-7479	79	2	𝜑𝑟(0	𝜑𝑟(0	PROPN
american_scientific_journal-7479	79	3	)	)	PUNCT
american_scientific_journal-7479	79	4	+	+	NUM
american_scientific_journal-7479	79	5	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	79	6	(	(	PUNCT
american_scientific_journal-7479	79	7	1)(0)𝑥	1)(0)𝑥	NUM
american_scientific_journal-7479	79	8	+	+	CCONJ
american_scientific_journal-7479	79	9	𝑥2	𝑥2	NOUN
american_scientific_journal-7479	79	10	2	2	NUM
american_scientific_journal-7479	79	11	!	!	NUM
american_scientific_journal-7479	79	12	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	79	13	(	(	PUNCT
american_scientific_journal-7479	79	14	2)(0	2)(0	NUM
american_scientific_journal-7479	79	15	)	)	PUNCT
american_scientific_journal-7479	79	16	+	+	NUM
american_scientific_journal-7479	79	17	𝑥3	𝑥3	ADJ
american_scientific_journal-7479	79	18	3	3	NUM
american_scientific_journal-7479	79	19	!	!	SYM
american_scientific_journal-7479	79	20	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	79	21	(	(	PUNCT
american_scientific_journal-7479	79	22	3)(0	3)(0	NUM
american_scientific_journal-7479	79	23	)	)	PUNCT
american_scientific_journal-7479	79	24	gives	give	VERB
american_scientific_journal-7479	79	25	∑𝜑𝑟	∑𝜑𝑟	PUNCT
american_scientific_journal-7479	80	1	[	[	X
american_scientific_journal-7479	80	2	𝑗](𝑥	𝑗](𝑥	NOUN
american_scientific_journal-7479	80	3	)	)	PUNCT
american_scientific_journal-7479	80	4	=	=	SYM
american_scientific_journal-7479	81	1	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	82	1	[	[	X
american_scientific_journal-7479	82	2	0	0	X
american_scientific_journal-7479	82	3	]	]	X
american_scientific_journal-7479	83	1	+	+	CCONJ
american_scientific_journal-7479	83	2	𝐻𝑥	𝐻𝑥	NOUN
american_scientific_journal-7479	83	3	−1	−1	NOUN
american_scientific_journal-7479	83	4	[	[	X
american_scientific_journal-7479	83	5	𝛹4	𝛹4	X
american_scientific_journal-7479	83	6	∑	∑	PROPN
american_scientific_journal-7479	83	7	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	83	8	[	[	X
american_scientific_journal-7479	83	9	𝑗](𝑥	𝑗](𝑥	NOUN
american_scientific_journal-7479	83	10	)	)	PUNCT
american_scientific_journal-7479	83	11	∞	∞	PROPN
american_scientific_journal-7479	84	1	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	84	2	]	]	PUNCT
american_scientific_journal-7479	85	1	∞	∞	PROPN
american_scientific_journal-7479	85	2	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	85	3	,	,	PUNCT
american_scientific_journal-7479	85	4	𝑥𝑟−1	𝑥𝑟−1	VERB
american_scientific_journal-7479	85	5	<	<	X
american_scientific_journal-7479	85	6	𝑥	𝑥	X
american_scientific_journal-7479	85	7	<	<	X
american_scientific_journal-7479	85	8	𝑥𝑟	𝑥𝑟	X
american_scientific_journal-7479	85	9	,	,	PUNCT
american_scientific_journal-7479	85	10	𝑟	𝑟	X
american_scientific_journal-7479	85	11	=	=	SYM
american_scientific_journal-7479	85	12	1,2	1,2	NUM
american_scientific_journal-7479	85	13	(	(	PUNCT
american_scientific_journal-7479	85	14	16	16	NUM
american_scientific_journal-7479	85	15	)	)	PUNCT
american_scientific_journal-7479	85	16	consequently	consequently	ADV
american_scientific_journal-7479	85	17	,	,	PUNCT
american_scientific_journal-7479	85	18	for	for	ADP
american_scientific_journal-7479	85	19	each	each	DET
american_scientific_journal-7479	85	20	term	term	NOUN
american_scientific_journal-7479	85	21	of	of	ADP
american_scientific_journal-7479	85	22	the	the	DET
american_scientific_journal-7479	85	23	series	series	NOUN
american_scientific_journal-7479	85	24	,	,	PUNCT
american_scientific_journal-7479	85	25	it	it	PRON
american_scientific_journal-7479	85	26	can	can	AUX
american_scientific_journal-7479	85	27	be	be	AUX
american_scientific_journal-7479	85	28	written	write	VERB
american_scientific_journal-7479	85	29	as	as	ADP
american_scientific_journal-7479	85	30	:	:	PUNCT
american_scientific_journal-7479	85	31	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	85	32	[	[	X
american_scientific_journal-7479	85	33	0](𝑥	0](𝑥	NOUN
american_scientific_journal-7479	85	34	)	)	PUNCT
american_scientific_journal-7479	86	1	=	=	PUNCT
american_scientific_journal-7479	86	2	∑	∑	PROPN
american_scientific_journal-7479	86	3	𝑥𝑢	𝑥𝑢	PROPN
american_scientific_journal-7479	87	1	𝑢	𝑢	NOUN
american_scientific_journal-7479	87	2	!	!	PROPN
american_scientific_journal-7479	87	3	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	87	4	(	(	PUNCT
american_scientific_journal-7479	87	5	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	87	6	)	)	PUNCT
american_scientific_journal-7479	87	7	3	3	NUM
american_scientific_journal-7479	87	8	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	87	9	,	,	PUNCT
american_scientific_journal-7479	87	10	(	(	PUNCT
american_scientific_journal-7479	87	11	17	17	NUM
american_scientific_journal-7479	87	12	)	)	PUNCT
american_scientific_journal-7479	87	13	as	as	ADP
american_scientific_journal-7479	87	14	the	the	DET
american_scientific_journal-7479	87	15	initial	initial	ADJ
american_scientific_journal-7479	87	16	term	term	NOUN
american_scientific_journal-7479	87	17	of	of	ADP
american_scientific_journal-7479	87	18	the	the	DET
american_scientific_journal-7479	87	19	decomposition	decomposition	NOUN
american_scientific_journal-7479	87	20	,	,	PUNCT
american_scientific_journal-7479	87	21	and	and	CCONJ
american_scientific_journal-7479	87	22	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	87	23	[	[	X
american_scientific_journal-7479	87	24	𝑗](𝑥	𝑗](𝑥	NOUN
american_scientific_journal-7479	87	25	)	)	PUNCT
american_scientific_journal-7479	87	26	=	=	PUNCT
american_scientific_journal-7479	88	1	ψ4𝐻𝑥	ψ4𝐻𝑥	VERB
american_scientific_journal-7479	88	2	−1[𝜑𝑟	−1[𝜑𝑟	VERB
american_scientific_journal-7479	89	1	[	[	X
american_scientific_journal-7479	89	2	𝑗−1](𝑥	𝑗−1](𝑥	NOUN
american_scientific_journal-7479	89	3	)	)	PUNCT
american_scientific_journal-7479	89	4	]	]	PUNCT
american_scientific_journal-7479	89	5	,	,	PUNCT
american_scientific_journal-7479	89	6	𝑗	𝑗	X
american_scientific_journal-7479	89	7	≥	≥	NOUN
american_scientific_journal-7479	89	8	1	1	NUM
american_scientific_journal-7479	89	9	,	,	PUNCT
american_scientific_journal-7479	89	10	𝑥𝑟−1	𝑥𝑟−1	VERB
american_scientific_journal-7479	89	11	<	<	X
american_scientific_journal-7479	89	12	𝑥	𝑥	X
american_scientific_journal-7479	89	13	<	<	X
american_scientific_journal-7479	89	14	𝑥𝑟	𝑥𝑟	X
american_scientific_journal-7479	89	15	,	,	PUNCT
american_scientific_journal-7479	89	16	𝑟	𝑟	X
american_scientific_journal-7479	89	17	=	=	SYM
american_scientific_journal-7479	89	18	1,2	1,2	NUM
american_scientific_journal-7479	89	19	(	(	PUNCT
american_scientific_journal-7479	89	20	18	18	NUM
american_scientific_journal-7479	89	21	)	)	PUNCT
american_scientific_journal-7479	89	22	as	as	ADP
american_scientific_journal-7479	89	23	the	the	DET
american_scientific_journal-7479	89	24	recurrence	recurrence	NOUN
american_scientific_journal-7479	89	25	relation	relation	NOUN
american_scientific_journal-7479	89	26	of	of	ADP
american_scientific_journal-7479	89	27	the	the	DET
american_scientific_journal-7479	89	28	decomposition	decomposition	NOUN
american_scientific_journal-7479	89	29	.	.	PUNCT
american_scientific_journal-7479	90	1	consequently	consequently	ADV
american_scientific_journal-7479	90	2	,	,	PUNCT
american_scientific_journal-7479	90	3	all	all	DET
american_scientific_journal-7479	90	4	components	component	NOUN
american_scientific_journal-7479	90	5	of	of	ADP
american_scientific_journal-7479	90	6	the	the	DET
american_scientific_journal-7479	90	7	decomposition	decomposition	NOUN
american_scientific_journal-7479	90	8	can	can	AUX
american_scientific_journal-7479	90	9	be	be	AUX
american_scientific_journal-7479	90	10	identified	identify	VERB
american_scientific_journal-7479	90	11	and	and	CCONJ
american_scientific_journal-7479	90	12	evaluated	evaluate	VERB
american_scientific_journal-7479	90	13	from	from	ADP
american_scientific_journal-7479	90	14	eq	eq	PROPN
american_scientific_journal-7479	90	15	.	.	PUNCT
american_scientific_journal-7479	91	1	(	(	PUNCT
american_scientific_journal-7479	91	2	18	18	NUM
american_scientific_journal-7479	91	3	)	)	PUNCT
american_scientific_journal-7479	91	4	.	.	PUNCT
american_scientific_journal-7479	92	1	this	this	PRON
american_scientific_journal-7479	92	2	is	be	AUX
american_scientific_journal-7479	92	3	,	,	PUNCT
american_scientific_journal-7479	92	4	by	by	ADP
american_scientific_journal-7479	92	5	substituting	substitute	VERB
american_scientific_journal-7479	92	6	eq	eq	ADP
american_scientific_journal-7479	92	7	.	.	PUNCT
american_scientific_journal-7479	93	1	(	(	PUNCT
american_scientific_journal-7479	93	2	17	17	NUM
american_scientific_journal-7479	93	3	)	)	PUNCT
american_scientific_journal-7479	93	4	into	into	ADP
american_scientific_journal-7479	93	5	eq	eq	NOUN
american_scientific_journal-7479	93	6	.	.	PUNCT
american_scientific_journal-7479	94	1	(	(	PUNCT
american_scientific_journal-7479	94	2	18	18	NUM
american_scientific_journal-7479	94	3	)	)	PUNCT
american_scientific_journal-7479	94	4	,	,	PUNCT
american_scientific_journal-7479	94	5	one	one	PRON
american_scientific_journal-7479	94	6	can	can	AUX
american_scientific_journal-7479	94	7	obtain	obtain	VERB
american_scientific_journal-7479	94	8	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	95	1	[	[	X
american_scientific_journal-7479	95	2	1](𝑥	1](𝑥	NUM
american_scientific_journal-7479	95	3	)	)	PUNCT
american_scientific_journal-7479	96	1	=	=	SYM
american_scientific_journal-7479	96	2	𝛹4𝐻𝑥	𝛹4𝐻𝑥	NOUN
american_scientific_journal-7479	96	3	−1[𝜑𝑟	−1[𝜑𝑟	PROPN
american_scientific_journal-7479	97	1	[	[	X
american_scientific_journal-7479	97	2	0](𝑥	0](𝑥	NOUN
american_scientific_journal-7479	97	3	)	)	PUNCT
american_scientific_journal-7479	97	4	]	]	PUNCT
american_scientific_journal-7479	98	1	=	=	PUNCT
american_scientific_journal-7479	98	2	𝛹4	𝛹4	INTJ
american_scientific_journal-7479	98	3	∑	∑	PROPN
american_scientific_journal-7479	98	4	𝑥4+𝑢	𝑥4+𝑢	X
american_scientific_journal-7479	98	5	(	(	PUNCT
american_scientific_journal-7479	98	6	4	4	NUM
american_scientific_journal-7479	98	7	+	+	SYM
american_scientific_journal-7479	98	8	𝑢	𝑢	NOUN
american_scientific_journal-7479	98	9	)	)	PUNCT
american_scientific_journal-7479	98	10	!	!	PUNCT
american_scientific_journal-7479	99	1	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	99	2	(	(	PUNCT
american_scientific_journal-7479	99	3	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	99	4	)	)	PUNCT
american_scientific_journal-7479	99	5	,	,	PUNCT
american_scientific_journal-7479	99	6	3	3	NUM
american_scientific_journal-7479	99	7	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	99	8	(	(	PUNCT
american_scientific_journal-7479	99	9	19	19	NUM
american_scientific_journal-7479	99	10	)	)	PUNCT
american_scientific_journal-7479	99	11	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	100	1	[	[	X
american_scientific_journal-7479	100	2	2](𝑥	2](𝑥	NUM
american_scientific_journal-7479	100	3	)	)	PUNCT
american_scientific_journal-7479	100	4	=	=	PUNCT
american_scientific_journal-7479	101	1	𝛹4𝐻𝑥	𝛹4𝐻𝑥	NOUN
american_scientific_journal-7479	101	2	−1[𝜑𝑟	−1[𝜑𝑟	PROPN
american_scientific_journal-7479	102	1	[	[	X
american_scientific_journal-7479	102	2	1](𝑥	1](𝑥	NUM
american_scientific_journal-7479	102	3	)	)	PUNCT
american_scientific_journal-7479	102	4	]	]	PUNCT
american_scientific_journal-7479	102	5	=	=	SYM
american_scientific_journal-7479	102	6	𝛹8	𝛹8	PROPN
american_scientific_journal-7479	102	7	∑	∑	ADV
american_scientific_journal-7479	102	8	𝑥8+𝑢	𝑥8+𝑢	PROPN
american_scientific_journal-7479	102	9	(	(	PUNCT
american_scientific_journal-7479	102	10	8	8	NUM
american_scientific_journal-7479	102	11	+	+	NUM
american_scientific_journal-7479	102	12	𝑢	𝑢	NOUN
american_scientific_journal-7479	102	13	)	)	PUNCT
american_scientific_journal-7479	102	14	!	!	PUNCT
american_scientific_journal-7479	103	1	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	103	2	(	(	PUNCT
american_scientific_journal-7479	103	3	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	103	4	)	)	PUNCT
american_scientific_journal-7479	103	5	,	,	PUNCT
american_scientific_journal-7479	103	6	3	3	NUM
american_scientific_journal-7479	103	7	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	103	8	(	(	PUNCT
american_scientific_journal-7479	103	9	20	20	NUM
american_scientific_journal-7479	103	10	)	)	PUNCT
american_scientific_journal-7479	103	11	american	american	ADJ
american_scientific_journal-7479	103	12	academic	academic	ADJ
american_scientific_journal-7479	103	13	scientific	scientific	ADJ
american_scientific_journal-7479	103	14	research	research	NOUN
american_scientific_journal-7479	103	15	journal	journal	NOUN
american_scientific_journal-7479	103	16	for	for	ADP
american_scientific_journal-7479	103	17	engineering	engineering	NOUN
american_scientific_journal-7479	103	18	,	,	PUNCT
american_scientific_journal-7479	103	19	technology	technology	NOUN
american_scientific_journal-7479	103	20	,	,	PUNCT
american_scientific_journal-7479	103	21	and	and	CCONJ
american_scientific_journal-7479	103	22	sciences	science	NOUN
american_scientific_journal-7479	103	23	(	(	PUNCT
american_scientific_journal-7479	103	24	asrjets	asrjet	NOUN
american_scientific_journal-7479	103	25	)	)	PUNCT
american_scientific_journal-7479	103	26	(	(	PUNCT
american_scientific_journal-7479	103	27	2022	2022	NUM
american_scientific_journal-7479	103	28	)	)	PUNCT
american_scientific_journal-7479	103	29	volume	volume	NOUN
american_scientific_journal-7479	103	30	88	88	NUM
american_scientific_journal-7479	103	31	,	,	PUNCT
american_scientific_journal-7479	103	32	no1	no1	PROPN
american_scientific_journal-7479	103	33	,	,	PUNCT
american_scientific_journal-7479	103	34	pp	pp	ADV
american_scientific_journal-7479	103	35	332	332	NUM
american_scientific_journal-7479	103	36	-	-	SYM
american_scientific_journal-7479	103	37	348	348	NUM
american_scientific_journal-7479	103	38	337	337	NUM
american_scientific_journal-7479	103	39	and	and	CCONJ
american_scientific_journal-7479	103	40	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	104	1	[	[	X
american_scientific_journal-7479	104	2	𝑗](𝑥	𝑗](𝑥	NOUN
american_scientific_journal-7479	104	3	)	)	PUNCT
american_scientific_journal-7479	104	4	=	=	PUNCT
american_scientific_journal-7479	105	1	𝛹4𝑗𝐻𝑥	𝛹4𝑗𝐻𝑥	ADP
american_scientific_journal-7479	105	2	−1[𝜑𝑟	−1[𝜑𝑟	PROPN
american_scientific_journal-7479	106	1	[	[	X
american_scientific_journal-7479	106	2	𝑗−1](𝑥	𝑗−1](𝑥	X
american_scientific_journal-7479	106	3	)	)	PUNCT
american_scientific_journal-7479	106	4	]	]	PUNCT
american_scientific_journal-7479	107	1	=	=	PUNCT
american_scientific_journal-7479	107	2	𝛹4𝑗	𝛹4𝑗	VERB
american_scientific_journal-7479	107	3	∑	∑	PROPN
american_scientific_journal-7479	107	4	𝑥4𝑗+𝑢	𝑥4𝑗+𝑢	PROPN
american_scientific_journal-7479	107	5	(	(	PUNCT
american_scientific_journal-7479	107	6	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	107	7	+	+	CCONJ
american_scientific_journal-7479	107	8	𝑢	𝑢	NOUN
american_scientific_journal-7479	107	9	)	)	PUNCT
american_scientific_journal-7479	107	10	!	!	PUNCT
american_scientific_journal-7479	108	1	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	108	2	(	(	PUNCT
american_scientific_journal-7479	108	3	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	108	4	)	)	PUNCT
american_scientific_journal-7479	108	5	,	,	PUNCT
american_scientific_journal-7479	108	6	3	3	NUM
american_scientific_journal-7479	108	7	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	108	8	𝑗	𝑗	X
american_scientific_journal-7479	108	9	≥	≥	NUM
american_scientific_journal-7479	108	10	1	1	NUM
american_scientific_journal-7479	108	11	(	(	PUNCT
american_scientific_journal-7479	108	12	21	21	NUM
american_scientific_journal-7479	108	13	)	)	PUNCT
american_scientific_journal-7479	108	14	in	in	ADP
american_scientific_journal-7479	108	15	practice	practice	NOUN
american_scientific_journal-7479	108	16	,	,	PUNCT
american_scientific_journal-7479	108	17	the	the	DET
american_scientific_journal-7479	108	18	solution	solution	NOUN
american_scientific_journal-7479	108	19	will	will	AUX
american_scientific_journal-7479	108	20	be	be	AUX
american_scientific_journal-7479	108	21	the	the	DET
american_scientific_journal-7479	108	22	n	n	NUM
american_scientific_journal-7479	108	23	-	-	PUNCT
american_scientific_journal-7479	108	24	term	term	NOUN
american_scientific_journal-7479	108	25	approximation	approximation	NOUN
american_scientific_journal-7479	108	26	𝜑𝑟	𝜑𝑟	ADP
american_scientific_journal-7479	108	27	𝑛(𝑥	𝑛(𝑥	PROPN
american_scientific_journal-7479	108	28	)	)	PUNCT
american_scientific_journal-7479	109	1	=	=	PUNCT
american_scientific_journal-7479	109	2	∑	∑	PUNCT
american_scientific_journal-7479	109	3	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	110	1	[	[	X
american_scientific_journal-7479	110	2	𝑗](𝑥	𝑗](𝑥	NOUN
american_scientific_journal-7479	110	3	)	)	PUNCT
american_scientific_journal-7479	111	1	=	=	PUNCT
american_scientific_journal-7479	112	1	𝑛−1	𝑛−1	PROPN
american_scientific_journal-7479	112	2	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	112	3	∑𝛹4𝑗	∑𝛹4𝑗	PUNCT
american_scientific_journal-7479	113	1	𝐽−1	𝐽−1	ADV
american_scientific_journal-7479	113	2	𝑗=0	𝑗=0	PROPN
american_scientific_journal-7479	113	3	∑	∑	PUNCT
american_scientific_journal-7479	114	1	𝑥4𝑗+𝑛	𝑥4𝑗+𝑛	NOUN
american_scientific_journal-7479	114	2	(	(	PUNCT
american_scientific_journal-7479	114	3	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	114	4	+	+	CCONJ
american_scientific_journal-7479	114	5	𝑛	𝑛	NOUN
american_scientific_journal-7479	114	6	)	)	PUNCT
american_scientific_journal-7479	114	7	!	!	PUNCT
american_scientific_journal-7479	115	1	3	3	NUM
american_scientific_journal-7479	115	2	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	115	3	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	115	4	(	(	PUNCT
american_scientific_journal-7479	115	5	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	115	6	)	)	PUNCT
american_scientific_journal-7479	115	7	(	(	PUNCT
american_scientific_journal-7479	115	8	22	22	NUM
american_scientific_journal-7479	115	9	)	)	PUNCT
american_scientific_journal-7479	115	10	and	and	CCONJ
american_scientific_journal-7479	115	11	from	from	ADP
american_scientific_journal-7479	115	12	the	the	DET
american_scientific_journal-7479	115	13	convergence	convergence	NOUN
american_scientific_journal-7479	115	14	of	of	ADP
american_scientific_journal-7479	115	15	adm[22	adm[22	PROPN
american_scientific_journal-7479	115	16	]	]	PUNCT
american_scientific_journal-7479	115	17	,	,	PUNCT
american_scientific_journal-7479	115	18	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	115	19	𝑛	𝑛	PRON
american_scientific_journal-7479	115	20	approaches	approach	VERB
american_scientific_journal-7479	115	21	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	115	22	[	[	X
american_scientific_journal-7479	115	23	𝑛](𝑥	𝑛](𝑥	NOUN
american_scientific_journal-7479	115	24	)	)	PUNCT
american_scientific_journal-7479	115	25	as	as	ADP
american_scientific_journal-7479	115	26	𝑛	𝑛	PROPN
american_scientific_journal-7479	115	27	→	→	SYM
american_scientific_journal-7479	115	28	∞	∞	NUM
american_scientific_journal-7479	115	29	𝜑𝑟(𝑥	𝜑𝑟(𝑥	NOUN
american_scientific_journal-7479	115	30	)	)	PUNCT
american_scientific_journal-7479	116	1	=	=	SYM
american_scientific_journal-7479	116	2	lim	lim	PROPN
american_scientific_journal-7479	116	3	𝑛→∞	𝑛→∞	NUM
american_scientific_journal-7479	116	4	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	116	5	𝑛(𝑥	𝑛(𝑥	PROPN
american_scientific_journal-7479	116	6	)	)	PUNCT
american_scientific_journal-7479	116	7	=	=	SYM
american_scientific_journal-7479	116	8	∑𝜑𝑟	∑𝜑𝑟	PUNCT
american_scientific_journal-7479	117	1	[	[	X
american_scientific_journal-7479	117	2	𝑗](𝑥	𝑗](𝑥	X
american_scientific_journal-7479	117	3	)	)	PUNCT
american_scientific_journal-7479	117	4	∞	∞	PROPN
american_scientific_journal-7479	117	5	𝑗=0	𝑗=0	PROPN
american_scientific_journal-7479	117	6	(	(	PUNCT
american_scientific_journal-7479	117	7	23	23	NUM
american_scientific_journal-7479	117	8	)	)	PUNCT
american_scientific_journal-7479	117	9	for	for	ADP
american_scientific_journal-7479	117	10	simplicity	simplicity	NOUN
american_scientific_journal-7479	117	11	,	,	PUNCT
american_scientific_journal-7479	117	12	the	the	DET
american_scientific_journal-7479	117	13	constants	constant	NOUN
american_scientific_journal-7479	117	14	are	be	AUX
american_scientific_journal-7479	117	15	set	set	VERB
american_scientific_journal-7479	117	16	as	as	ADP
american_scientific_journal-7479	117	17	𝑎𝑟	𝑎𝑟	NOUN
american_scientific_journal-7479	117	18	=	=	SYM
american_scientific_journal-7479	117	19	𝜑𝑟(0	𝜑𝑟(0	PROPN
american_scientific_journal-7479	117	20	)	)	PUNCT
american_scientific_journal-7479	117	21	,	,	PUNCT
american_scientific_journal-7479	117	22	𝑏𝑟	𝑏𝑟	PROPN
american_scientific_journal-7479	117	23	=	=	SYM
american_scientific_journal-7479	117	24	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	117	25	(	(	PUNCT
american_scientific_journal-7479	117	26	1)(0	1)(0	NUM
american_scientific_journal-7479	117	27	)	)	PUNCT
american_scientific_journal-7479	117	28	,	,	PUNCT
american_scientific_journal-7479	117	29	𝑐𝑟	𝑐𝑟	NOUN
american_scientific_journal-7479	117	30	=	=	SYM
american_scientific_journal-7479	117	31	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	117	32	(	(	PUNCT
american_scientific_journal-7479	117	33	2)(0	2)(0	NUM
american_scientific_journal-7479	117	34	)	)	PUNCT
american_scientific_journal-7479	117	35	,	,	PUNCT
american_scientific_journal-7479	117	36	𝑑𝑟	𝑑𝑟	NOUN
american_scientific_journal-7479	117	37	=	=	SYM
american_scientific_journal-7479	117	38	𝜑𝑟	𝜑𝑟	X
american_scientific_journal-7479	117	39	(	(	PUNCT
american_scientific_journal-7479	117	40	3)(0	3)(0	NUM
american_scientific_journal-7479	117	41	)	)	PUNCT
american_scientific_journal-7479	117	42	here	here	ADV
american_scientific_journal-7479	117	43	𝑎𝑟	𝑎𝑟	INTJ
american_scientific_journal-7479	117	44	,	,	PUNCT
american_scientific_journal-7479	117	45	𝑏𝑟	𝑏𝑟	NOUN
american_scientific_journal-7479	117	46	,	,	PUNCT
american_scientific_journal-7479	117	47	𝑐𝑟	𝑐𝑟	PROPN
american_scientific_journal-7479	117	48	and	and	CCONJ
american_scientific_journal-7479	117	49	𝑑𝑟	𝑑𝑟	PROPN
american_scientific_journal-7479	117	50	are	be	AUX
american_scientific_journal-7479	117	51	constants	constant	NOUN
american_scientific_journal-7479	117	52	associated	associate	VERB
american_scientific_journal-7479	117	53	with	with	ADP
american_scientific_journal-7479	117	54	the	the	DET
american_scientific_journal-7479	117	55	r	r	NOUN
american_scientific_journal-7479	117	56	-	-	PUNCT
american_scientific_journal-7479	117	57	th	th	VERB
american_scientific_journal-7479	117	58	segments	segment	NOUN
american_scientific_journal-7479	117	59	(	(	PUNCT
american_scientific_journal-7479	117	60	r	r	NOUN
american_scientific_journal-7479	117	61	=	=	SYM
american_scientific_journal-7479	117	62	1,2	1,2	NUM
american_scientific_journal-7479	117	63	)	)	PUNCT
american_scientific_journal-7479	117	64	.	.	PUNCT
american_scientific_journal-7479	118	1	the	the	DET
american_scientific_journal-7479	118	2	final	final	ADJ
american_scientific_journal-7479	118	3	vibration	vibration	NOUN
american_scientific_journal-7479	118	4	mode	mode	NOUN
american_scientific_journal-7479	118	5	shape	shape	NOUN
american_scientific_journal-7479	118	6	function	function	NOUN
american_scientific_journal-7479	118	7	has	have	AUX
american_scientific_journal-7479	118	8	been	be	AUX
american_scientific_journal-7479	118	9	shown	show	VERB
american_scientific_journal-7479	118	10	in	in	ADP
american_scientific_journal-7479	118	11	eq	eq	ADP
american_scientific_journal-7479	118	12	.	.	PUNCT
american_scientific_journal-7479	119	1	(	(	PUNCT
american_scientific_journal-7479	119	2	23	23	NUM
american_scientific_journal-7479	119	3	)	)	PUNCT
american_scientific_journal-7479	119	4	.	.	PUNCT
american_scientific_journal-7479	120	1	one	one	PRON
american_scientific_journal-7479	120	2	can	can	AUX
american_scientific_journal-7479	120	3	consider	consider	VERB
american_scientific_journal-7479	120	4	as	as	ADP
american_scientific_journal-7479	120	5	many	many	ADJ
american_scientific_journal-7479	120	6	terms	term	NOUN
american_scientific_journal-7479	120	7	as	as	SCONJ
american_scientific_journal-7479	120	8	needed	need	VERB
american_scientific_journal-7479	120	9	to	to	PART
american_scientific_journal-7479	120	10	obtain	obtain	VERB
american_scientific_journal-7479	120	11	a	a	DET
american_scientific_journal-7479	120	12	more	more	ADV
american_scientific_journal-7479	120	13	accurate	accurate	ADJ
american_scientific_journal-7479	120	14	deflection	deflection	NOUN
american_scientific_journal-7479	120	15	function	function	NOUN
american_scientific_journal-7479	120	16	.	.	PUNCT
american_scientific_journal-7479	121	1	if	if	SCONJ
american_scientific_journal-7479	121	2	the	the	DET
american_scientific_journal-7479	121	3	series	series	NOUN
american_scientific_journal-7479	121	4	converges	converge	VERB
american_scientific_journal-7479	121	5	,	,	PUNCT
american_scientific_journal-7479	121	6	the	the	DET
american_scientific_journal-7479	121	7	j	j	NOUN
american_scientific_journal-7479	121	8	-	-	PUNCT
american_scientific_journal-7479	121	9	term	term	NOUN
american_scientific_journal-7479	121	10	partial	partial	ADJ
american_scientific_journal-7479	121	11	sum	sum	NOUN
american_scientific_journal-7479	121	12	will	will	AUX
american_scientific_journal-7479	121	13	be	be	AUX
american_scientific_journal-7479	121	14	the	the	DET
american_scientific_journal-7479	121	15	approximate	approximate	ADJ
american_scientific_journal-7479	121	16	closed	closed	ADJ
american_scientific_journal-7479	121	17	-	-	PUNCT
american_scientific_journal-7479	121	18	form	form	NOUN
american_scientific_journal-7479	121	19	solution	solution	NOUN
american_scientific_journal-7479	121	20	of	of	ADP
american_scientific_journal-7479	121	21	the	the	DET
american_scientific_journal-7479	121	22	differential	differential	ADJ
american_scientific_journal-7479	121	23	equation[22	equation[22	NOUN
american_scientific_journal-7479	121	24	]	]	PUNCT
american_scientific_journal-7479	121	25	by	by	ADP
american_scientific_journal-7479	121	26	substituting	substitute	VERB
american_scientific_journal-7479	121	27	the	the	DET
american_scientific_journal-7479	121	28	final	final	ADJ
american_scientific_journal-7479	121	29	vibration	vibration	NOUN
american_scientific_journal-7479	121	30	mode	mode	NOUN
american_scientific_journal-7479	121	31	shape	shape	NOUN
american_scientific_journal-7479	121	32	function	function	NOUN
american_scientific_journal-7479	121	33	into	into	ADP
american_scientific_journal-7479	121	34	the	the	DET
american_scientific_journal-7479	121	35	four	four	NUM
american_scientific_journal-7479	121	36	boundary	boundary	ADJ
american_scientific_journal-7479	121	37	conditions	condition	NOUN
american_scientific_journal-7479	121	38	and	and	CCONJ
american_scientific_journal-7479	121	39	kinematics	kinematic	NOUN
american_scientific_journal-7479	121	40	conditions	condition	NOUN
american_scientific_journal-7479	121	41	of	of	ADP
american_scientific_journal-7479	121	42	the	the	DET
american_scientific_journal-7479	121	43	cracked	crack	VERB
american_scientific_journal-7479	121	44	beam	beam	NOUN
american_scientific_journal-7479	121	45	,	,	PUNCT
american_scientific_journal-7479	121	46	a	a	DET
american_scientific_journal-7479	121	47	system	system	NOUN
american_scientific_journal-7479	121	48	of	of	ADP
american_scientific_journal-7479	121	49	eight	eight	NUM
american_scientific_journal-7479	121	50	equations	equation	NOUN
american_scientific_journal-7479	121	51	with	with	ADP
american_scientific_journal-7479	121	52	unknown	unknown	ADJ
american_scientific_journal-7479	121	53	constants	constant	NOUN
american_scientific_journal-7479	121	54	is	be	AUX
american_scientific_journal-7479	121	55	given	give	VERB
american_scientific_journal-7479	121	56	as	as	ADP
american_scientific_journal-7479	121	57	𝑇𝑠1	𝑇𝑠1	NOUN
american_scientific_journal-7479	121	58	𝑛	𝑛	PROPN
american_scientific_journal-7479	121	59	(	(	PUNCT
american_scientific_journal-7479	121	60	ψ𝑛)𝑎𝑟	ψ𝑛)𝑎𝑟	SYM
american_scientific_journal-7479	121	61	+	+	NUM
american_scientific_journal-7479	121	62	𝑇𝑠2	𝑇𝑠2	NOUN
american_scientific_journal-7479	121	63	𝑛	𝑛	PROPN
american_scientific_journal-7479	121	64	(	(	PUNCT
american_scientific_journal-7479	121	65	ψ𝑛)𝑏𝑟	ψ𝑛)𝑏𝑟	PUNCT
american_scientific_journal-7479	121	66	+	+	NUM
american_scientific_journal-7479	121	67	𝑇𝑠3	𝑇𝑠3	NOUN
american_scientific_journal-7479	121	68	𝑛	𝑛	X
american_scientific_journal-7479	121	69	(	(	PUNCT
american_scientific_journal-7479	121	70	ψ𝑛)𝑐𝑟	ψ𝑛)𝑐𝑟	PUNCT
american_scientific_journal-7479	121	71	+	+	NUM
american_scientific_journal-7479	121	72	𝑇𝑠4	𝑇𝑠4	NOUN
american_scientific_journal-7479	121	73	𝑛	𝑛	X
american_scientific_journal-7479	121	74	(	(	PUNCT
american_scientific_journal-7479	121	75	ψ𝑛)𝑑𝑟	ψ𝑛)𝑑𝑟	X
american_scientific_journal-7479	121	76	=	=	SYM
american_scientific_journal-7479	121	77	0	0	NUM
american_scientific_journal-7479	121	78	(	(	PUNCT
american_scientific_journal-7479	121	79	24	24	NUM
american_scientific_journal-7479	121	80	)	)	PUNCT
american_scientific_journal-7479	121	81	where	where	SCONJ
american_scientific_journal-7479	121	82	𝑇𝑠1	𝑇𝑠1	ADJ
american_scientific_journal-7479	121	83	𝑛	𝑛	PROPN
american_scientific_journal-7479	121	84	(	(	PUNCT
american_scientific_journal-7479	121	85	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	121	86	)	)	PUNCT
american_scientific_journal-7479	121	87	,	,	PUNCT
american_scientific_journal-7479	121	88	𝑇𝑠2	𝑇𝑠2	NOUN
american_scientific_journal-7479	121	89	𝑛	𝑛	PROPN
american_scientific_journal-7479	121	90	(	(	PUNCT
american_scientific_journal-7479	121	91	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	121	92	)	)	PUNCT
american_scientific_journal-7479	121	93	,	,	PUNCT
american_scientific_journal-7479	121	94	𝑇𝑠3	𝑇𝑠3	NOUN
american_scientific_journal-7479	122	1	𝑛	𝑛	PROPN
american_scientific_journal-7479	122	2	(	(	PUNCT
american_scientific_journal-7479	122	3	ψ𝑛	ψ𝑛	INTJ
american_scientific_journal-7479	122	4	)	)	PUNCT
american_scientific_journal-7479	122	5	and	and	CCONJ
american_scientific_journal-7479	122	6	𝑇𝑠4	𝑇𝑠4	VERB
american_scientific_journal-7479	122	7	𝑛	𝑛	PROPN
american_scientific_journal-7479	122	8	(	(	PUNCT
american_scientific_journal-7479	122	9	ψ𝑛	ψ𝑛	INTJ
american_scientific_journal-7479	122	10	)	)	PUNCT
american_scientific_journal-7479	122	11	are	be	AUX
american_scientific_journal-7479	122	12	the	the	DET
american_scientific_journal-7479	122	13	coefficients	coefficient	NOUN
american_scientific_journal-7479	122	14	of	of	ADP
american_scientific_journal-7479	122	15	unknown	unknown	ADJ
american_scientific_journal-7479	122	16	constants	constant	NOUN
american_scientific_journal-7479	122	17	𝑎𝑟	𝑎𝑟	PRON
american_scientific_journal-7479	122	18	,	,	PUNCT
american_scientific_journal-7479	122	19	𝑏𝑟	𝑏𝑟	NOUN
american_scientific_journal-7479	122	20	,	,	PUNCT
american_scientific_journal-7479	122	21	𝑐𝑟	𝑐𝑟	ADJ
american_scientific_journal-7479	122	22	,	,	PUNCT
american_scientific_journal-7479	122	23	and	and	CCONJ
american_scientific_journal-7479	122	24	𝑑𝑟	𝑑𝑟	AUX
american_scientific_journal-7479	122	25	corresponding	correspond	VERB
american_scientific_journal-7479	122	26	to	to	ADP
american_scientific_journal-7479	122	27	the	the	DET
american_scientific_journal-7479	122	28	n	n	CCONJ
american_scientific_journal-7479	122	29	-	-	PUNCT
american_scientific_journal-7479	122	30	term	term	NOUN
american_scientific_journal-7479	122	31	solution	solution	NOUN
american_scientific_journal-7479	122	32	series	series	NOUN
american_scientific_journal-7479	122	33	as	as	ADP
american_scientific_journal-7479	122	34	a	a	DET
american_scientific_journal-7479	122	35	function	function	NOUN
american_scientific_journal-7479	122	36	of	of	ADP
american_scientific_journal-7479	122	37	𝛹𝑛.	𝛹𝑛.	PROPN
american_scientific_journal-7479	122	38	also	also	ADV
american_scientific_journal-7479	122	39	,	,	PUNCT
american_scientific_journal-7479	122	40	s	s	VERB
american_scientific_journal-7479	122	41	changes	change	NOUN
american_scientific_journal-7479	122	42	from	from	ADP
american_scientific_journal-7479	122	43	one	one	NUM
american_scientific_journal-7479	122	44	to	to	ADP
american_scientific_journal-7479	122	45	four	four	NUM
american_scientific_journal-7479	122	46	with	with	ADP
american_scientific_journal-7479	122	47	respect	respect	NOUN
american_scientific_journal-7479	122	48	to	to	ADP
american_scientific_journal-7479	122	49	each	each	DET
american_scientific_journal-7479	122	50	boundary	boundary	ADJ
american_scientific_journal-7479	122	51	condition	condition	NOUN
american_scientific_journal-7479	122	52	.	.	PUNCT
american_scientific_journal-7479	123	1	these	these	DET
american_scientific_journal-7479	123	2	constants	constant	NOUN
american_scientific_journal-7479	123	3	in	in	ADP
american_scientific_journal-7479	123	4	the	the	DET
american_scientific_journal-7479	123	5	second	second	ADJ
american_scientific_journal-7479	123	6	segment	segment	NOUN
american_scientific_journal-7479	123	7	(	(	PUNCT
american_scientific_journal-7479	123	8	𝑎2	𝑎2	PROPN
american_scientific_journal-7479	123	9	,	,	PUNCT
american_scientific_journal-7479	123	10	𝑏2	𝑏2	PROPN
american_scientific_journal-7479	123	11	,	,	PUNCT
american_scientific_journal-7479	123	12	𝑐2	𝑐2	NOUN
american_scientific_journal-7479	123	13	and	and	CCONJ
american_scientific_journal-7479	123	14	𝑑2	𝑑2	VERB
american_scientific_journal-7479	123	15	)	)	PUNCT
american_scientific_journal-7479	123	16	are	be	AUX
american_scientific_journal-7479	123	17	related	relate	VERB
american_scientific_journal-7479	123	18	to	to	ADP
american_scientific_journal-7479	123	19	those	those	PRON
american_scientific_journal-7479	123	20	in	in	ADP
american_scientific_journal-7479	123	21	the	the	DET
american_scientific_journal-7479	123	22	first	first	ADJ
american_scientific_journal-7479	123	23	segment	segment	NOUN
american_scientific_journal-7479	123	24	(	(	PUNCT
american_scientific_journal-7479	123	25	𝑎1	𝑎1	ADJ
american_scientific_journal-7479	123	26	,	,	PUNCT
american_scientific_journal-7479	123	27	𝑏1	𝑏1	ADJ
american_scientific_journal-7479	123	28	,	,	PUNCT
american_scientific_journal-7479	123	29	𝑐1	𝑐1	NOUN
american_scientific_journal-7479	123	30	and	and	CCONJ
american_scientific_journal-7479	123	31	𝑑1	𝑑1	NOUN
american_scientific_journal-7479	123	32	)	)	PUNCT
american_scientific_journal-7479	123	33	through	through	ADP
american_scientific_journal-7479	123	34	the	the	DET
american_scientific_journal-7479	123	35	compatibility	compatibility	NOUN
american_scientific_journal-7479	123	36	conditions	condition	NOUN
american_scientific_journal-7479	123	37	in	in	ADP
american_scientific_journal-7479	123	38	eqs	eqs	PROPN
american_scientific_journal-7479	123	39	.	.	PUNCT
american_scientific_journal-7479	124	1	(	(	PUNCT
american_scientific_journal-7479	124	2	3	3	X
american_scientific_journal-7479	124	3	)	)	PUNCT
american_scientific_journal-7479	124	4	and	and	CCONJ
american_scientific_journal-7479	124	5	(	(	PUNCT
american_scientific_journal-7479	124	6	4	4	NUM
american_scientific_journal-7479	124	7	)	)	PUNCT
american_scientific_journal-7479	124	8	and	and	CCONJ
american_scientific_journal-7479	124	9	cab	cab	NOUN
american_scientific_journal-7479	124	10	be	be	AUX
american_scientific_journal-7479	124	11	expressed	express	VERB
american_scientific_journal-7479	124	12	as	as	ADP
american_scientific_journal-7479	124	13	{	{	PUNCT
american_scientific_journal-7479	124	14	𝑎2	𝑎2	PROPN
american_scientific_journal-7479	124	15	𝑏2	𝑏2	PROPN
american_scientific_journal-7479	124	16	𝑐2	𝑐2	NOUN
american_scientific_journal-7479	124	17	𝑑2	𝑑2	NOUN
american_scientific_journal-7479	124	18	}	}	PUNCT
american_scientific_journal-7479	124	19	=	=	PUNCT
american_scientific_journal-7479	124	20	[	[	PUNCT
american_scientific_journal-7479	124	21	𝑧11	𝑧11	X
american_scientific_journal-7479	124	22	𝑛	𝑛	PROPN
american_scientific_journal-7479	124	23	(	(	PUNCT
american_scientific_journal-7479	124	24	ψ𝑛	ψ𝑛	NOUN
american_scientific_journal-7479	124	25	)	)	PUNCT
american_scientific_journal-7479	124	26	⋯	⋯	ADP
american_scientific_journal-7479	124	27	𝑧14	𝑧14	NOUN
american_scientific_journal-7479	124	28	𝑛	𝑛	PROPN
american_scientific_journal-7479	124	29	(	(	PUNCT
american_scientific_journal-7479	124	30	ψ𝑛	ψ𝑛	NOUN
american_scientific_journal-7479	124	31	)	)	PUNCT
american_scientific_journal-7479	124	32	⋮	⋮	NOUN
american_scientific_journal-7479	124	33	⋱	⋱	PUNCT
american_scientific_journal-7479	124	34	⋮	⋮	NOUN
american_scientific_journal-7479	124	35	𝑧41	𝑧41	VERB
american_scientific_journal-7479	124	36	𝑛	𝑛	PROPN
american_scientific_journal-7479	124	37	(	(	PUNCT
american_scientific_journal-7479	124	38	ψ𝑛	ψ𝑛	NOUN
american_scientific_journal-7479	124	39	)	)	PUNCT
american_scientific_journal-7479	124	40	⋯	⋯	VERB
american_scientific_journal-7479	124	41	𝑧44	𝑧44	PROPN
american_scientific_journal-7479	124	42	𝑛	𝑛	PROPN
american_scientific_journal-7479	124	43	(	(	PUNCT
american_scientific_journal-7479	124	44	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	124	45	)	)	PUNCT
american_scientific_journal-7479	124	46	]	]	PUNCT
american_scientific_journal-7479	125	1	{	{	PUNCT
american_scientific_journal-7479	125	2	𝑎1	𝑎1	ADP
american_scientific_journal-7479	125	3	𝑏1	𝑏1	ADJ
american_scientific_journal-7479	125	4	𝑐1	𝑐1	NOUN
american_scientific_journal-7479	125	5	𝑑1	𝑑1	NOUN
american_scientific_journal-7479	125	6	}	}	PUNCT
american_scientific_journal-7479	125	7	=	=	SYM
american_scientific_journal-7479	125	8	𝑍4×4	𝑍4×4	NUM
american_scientific_journal-7479	125	9	{	{	PUNCT
american_scientific_journal-7479	125	10	𝑎1	𝑎1	ADP
american_scientific_journal-7479	125	11	𝑏1	𝑏1	ADJ
american_scientific_journal-7479	125	12	𝑐1	𝑐1	NOUN
american_scientific_journal-7479	125	13	𝑑1	𝑑1	NOUN
american_scientific_journal-7479	125	14	}	}	PUNCT
american_scientific_journal-7479	125	15	(	(	PUNCT
american_scientific_journal-7479	125	16	25𝑎	25𝑎	NOUN
american_scientific_journal-7479	125	17	)	)	PUNCT
american_scientific_journal-7479	125	18	where	where	SCONJ
american_scientific_journal-7479	125	19	𝑍4×4	𝑍4×4	PROPN
american_scientific_journal-7479	125	20	is	be	AUX
american_scientific_journal-7479	125	21	a	a	DET
american_scientific_journal-7479	125	22	4	4	NUM
american_scientific_journal-7479	125	23	×	×	NOUN
american_scientific_journal-7479	125	24	4	4	NUM
american_scientific_journal-7479	125	25	transfer	transfer	NOUN
american_scientific_journal-7479	125	26	matrix	matrix	NOUN
american_scientific_journal-7479	125	27	which	which	PRON
american_scientific_journal-7479	125	28	depends	depend	VERB
american_scientific_journal-7479	125	29	on	on	ADP
american_scientific_journal-7479	125	30	eigenvalue	eigenvalue	PROPN
american_scientific_journal-7479	125	31	ψ𝑗	ψ𝑗	ADP
american_scientific_journal-7479	125	32	after	after	ADP
american_scientific_journal-7479	125	33	applying	apply	VERB
american_scientific_journal-7479	125	34	the	the	DET
american_scientific_journal-7479	125	35	boundary	boundary	ADJ
american_scientific_journal-7479	125	36	conditions	condition	NOUN
american_scientific_journal-7479	125	37	,	,	PUNCT
american_scientific_journal-7479	125	38	the	the	DET
american_scientific_journal-7479	125	39	following	follow	VERB
american_scientific_journal-7479	125	40	equation	equation	NOUN
american_scientific_journal-7479	125	41	can	can	AUX
american_scientific_journal-7479	125	42	be	be	AUX
american_scientific_journal-7479	125	43	obtained	obtain	VERB
american_scientific_journal-7479	125	44	as	as	ADP
american_scientific_journal-7479	125	45	:	:	PUNCT
american_scientific_journal-7479	125	46	american	american	ADJ
american_scientific_journal-7479	125	47	academic	academic	ADJ
american_scientific_journal-7479	125	48	scientific	scientific	ADJ
american_scientific_journal-7479	125	49	research	research	NOUN
american_scientific_journal-7479	125	50	journal	journal	NOUN
american_scientific_journal-7479	125	51	for	for	ADP
american_scientific_journal-7479	125	52	engineering	engineering	NOUN
american_scientific_journal-7479	125	53	,	,	PUNCT
american_scientific_journal-7479	125	54	technology	technology	NOUN
american_scientific_journal-7479	125	55	,	,	PUNCT
american_scientific_journal-7479	125	56	and	and	CCONJ
american_scientific_journal-7479	125	57	sciences	science	NOUN
american_scientific_journal-7479	125	58	(	(	PUNCT
american_scientific_journal-7479	125	59	asrjets	asrjet	NOUN
american_scientific_journal-7479	125	60	)	)	PUNCT
american_scientific_journal-7479	125	61	(	(	PUNCT
american_scientific_journal-7479	125	62	2022	2022	NUM
american_scientific_journal-7479	125	63	)	)	PUNCT
american_scientific_journal-7479	125	64	volume	volume	NOUN
american_scientific_journal-7479	125	65	88	88	NUM
american_scientific_journal-7479	125	66	,	,	PUNCT
american_scientific_journal-7479	125	67	no1	no1	PROPN
american_scientific_journal-7479	125	68	,	,	PUNCT
american_scientific_journal-7479	125	69	pp	pp	ADV
american_scientific_journal-7479	125	70	332	332	NUM
american_scientific_journal-7479	125	71	-	-	SYM
american_scientific_journal-7479	125	72	348	348	NUM
american_scientific_journal-7479	125	73	338	338	NUM
american_scientific_journal-7479	125	74	{	{	PUNCT
american_scientific_journal-7479	125	75	0	0	NUM
american_scientific_journal-7479	125	76	0	0	NUM
american_scientific_journal-7479	125	77	}	}	PUNCT
american_scientific_journal-7479	125	78	=	=	PUNCT
american_scientific_journal-7479	125	79	𝑇2×4	𝑇2×4	NOUN
american_scientific_journal-7479	125	80	{	{	PUNCT
american_scientific_journal-7479	125	81	𝑎2	𝑎2	PROPN
american_scientific_journal-7479	125	82	𝑏2	𝑏2	PROPN
american_scientific_journal-7479	125	83	𝑐2	𝑐2	NOUN
american_scientific_journal-7479	125	84	𝑑2	𝑑2	NOUN
american_scientific_journal-7479	125	85	}	}	PUNCT
american_scientific_journal-7479	125	86	=	=	PUNCT
american_scientific_journal-7479	125	87	𝑇2×4	𝑇2×4	X
american_scientific_journal-7479	125	88	𝑍4×4	𝑍4×4	NOUN
american_scientific_journal-7479	125	89	{	{	PUNCT
american_scientific_journal-7479	125	90	𝑎1	𝑎1	ADP
american_scientific_journal-7479	125	91	𝑏1	𝑏1	ADJ
american_scientific_journal-7479	125	92	𝑐1	𝑐1	NOUN
american_scientific_journal-7479	125	93	𝑑1	𝑑1	NOUN
american_scientific_journal-7479	125	94	}	}	PUNCT
american_scientific_journal-7479	126	1	=	=	SYM
american_scientific_journal-7479	127	1	𝑄2×4	𝑄2×4	PRON
american_scientific_journal-7479	127	2	{	{	PUNCT
american_scientific_journal-7479	127	3	𝑎1	𝑎1	ADP
american_scientific_journal-7479	127	4	𝑏1	𝑏1	ADJ
american_scientific_journal-7479	127	5	𝑐1	𝑐1	NOUN
american_scientific_journal-7479	127	6	𝑑1	𝑑1	NOUN
american_scientific_journal-7479	127	7	}	}	PUNCT
american_scientific_journal-7479	127	8	(	(	PUNCT
american_scientific_journal-7479	127	9	25𝑏	25𝑏	NOUN
american_scientific_journal-7479	127	10	)	)	PUNCT
american_scientific_journal-7479	127	11	where	where	SCONJ
american_scientific_journal-7479	127	12	where	where	SCONJ
american_scientific_journal-7479	127	13	𝑇2×4	𝑇2×4	NOUN
american_scientific_journal-7479	127	14	=	=	SYM
american_scientific_journal-7479	127	15	[	[	PUNCT
american_scientific_journal-7479	127	16	𝑡11	𝑡11	PROPN
american_scientific_journal-7479	127	17	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	18	(	(	PUNCT
american_scientific_journal-7479	127	19	ψ𝑛	ψ𝑛	INTJ
american_scientific_journal-7479	127	20	)	)	PUNCT
american_scientific_journal-7479	127	21	𝑡21	𝑡21	NOUN
american_scientific_journal-7479	127	22	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	23	(	(	PUNCT
american_scientific_journal-7479	127	24	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	25	)	)	PUNCT
american_scientific_journal-7479	127	26	𝑡12	𝑡12	NOUN
american_scientific_journal-7479	127	27	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	28	(	(	PUNCT
american_scientific_journal-7479	127	29	ψ𝑛	ψ𝑛	INTJ
american_scientific_journal-7479	127	30	)	)	PUNCT
american_scientific_journal-7479	127	31	𝑇22	𝑇22	PROPN
american_scientific_journal-7479	127	32	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	33	(	(	PUNCT
american_scientific_journal-7479	127	34	ψ𝑛	ψ𝑛	NOUN
american_scientific_journal-7479	127	35	)	)	PUNCT
american_scientific_journal-7479	127	36	𝑡13	𝑡13	NOUN
american_scientific_journal-7479	127	37	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	38	(	(	PUNCT
american_scientific_journal-7479	127	39	ψ𝑛	ψ𝑛	NOUN
american_scientific_journal-7479	127	40	)	)	PUNCT
american_scientific_journal-7479	127	41	𝑡23	𝑡23	NOUN
american_scientific_journal-7479	127	42	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	43	(	(	PUNCT
american_scientific_journal-7479	127	44	ψ𝑛	ψ𝑛	NOUN
american_scientific_journal-7479	127	45	)	)	PUNCT
american_scientific_journal-7479	127	46	𝑡14	𝑡14	NOUN
american_scientific_journal-7479	127	47	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	48	(	(	PUNCT
american_scientific_journal-7479	127	49	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	50	)	)	PUNCT
american_scientific_journal-7479	127	51	𝑡24	𝑡24	NOUN
american_scientific_journal-7479	127	52	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	53	(	(	PUNCT
american_scientific_journal-7479	127	54	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	55	)	)	PUNCT
american_scientific_journal-7479	127	56	]	]	PUNCT
american_scientific_journal-7479	127	57	(	(	PUNCT
american_scientific_journal-7479	127	58	25𝑐	25𝑐	NOUN
american_scientific_journal-7479	127	59	)	)	PUNCT
american_scientific_journal-7479	127	60	𝑄2×4	𝑄2×4	NOUN
american_scientific_journal-7479	127	61	=	=	PUNCT
american_scientific_journal-7479	127	62	𝑇2×4	𝑇2×4	X
american_scientific_journal-7479	127	63	𝑍4×4	𝑍4×4	NOUN
american_scientific_journal-7479	127	64	=	=	PUNCT
american_scientific_journal-7479	127	65	[	[	PUNCT
american_scientific_journal-7479	127	66	𝑞11	𝑞11	NOUN
american_scientific_journal-7479	127	67	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	68	(	(	PUNCT
american_scientific_journal-7479	127	69	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	70	)	)	PUNCT
american_scientific_journal-7479	127	71	𝑞21	𝑞21	NUM
american_scientific_journal-7479	127	72	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	73	(	(	PUNCT
american_scientific_journal-7479	127	74	ψ𝑛	ψ𝑛	NOUN
american_scientific_journal-7479	127	75	)	)	PUNCT
american_scientific_journal-7479	127	76	𝑞12	𝑞12	NOUN
american_scientific_journal-7479	127	77	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	78	(	(	PUNCT
american_scientific_journal-7479	127	79	ψ𝑛	ψ𝑛	NOUN
american_scientific_journal-7479	127	80	)	)	PUNCT
american_scientific_journal-7479	127	81	𝑞22	𝑞22	NOUN
american_scientific_journal-7479	127	82	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	83	(	(	PUNCT
american_scientific_journal-7479	127	84	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	85	)	)	PUNCT
american_scientific_journal-7479	127	86	𝑞13	𝑞13	NOUN
american_scientific_journal-7479	127	87	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	88	(	(	PUNCT
american_scientific_journal-7479	127	89	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	90	)	)	PUNCT
american_scientific_journal-7479	127	91	𝑞23	𝑞23	NOUN
american_scientific_journal-7479	127	92	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	93	(	(	PUNCT
american_scientific_journal-7479	127	94	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	95	)	)	PUNCT
american_scientific_journal-7479	127	96	𝑞14	𝑞14	NOUN
american_scientific_journal-7479	127	97	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	98	(	(	PUNCT
american_scientific_journal-7479	127	99	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	100	)	)	PUNCT
american_scientific_journal-7479	127	101	𝑞24	𝑞24	NOUN
american_scientific_journal-7479	127	102	𝑛	𝑛	PROPN
american_scientific_journal-7479	127	103	(	(	PUNCT
american_scientific_journal-7479	127	104	ψ𝑛	ψ𝑛	PROPN
american_scientific_journal-7479	127	105	)	)	PUNCT
american_scientific_journal-7479	127	106	]	]	PUNCT
american_scientific_journal-7479	127	107	(	(	PUNCT
american_scientific_journal-7479	127	108	25𝑑	25𝑑	NUM
american_scientific_journal-7479	127	109	)	)	PUNCT
american_scientific_journal-7479	127	110	thus	thus	ADV
american_scientific_journal-7479	127	111	,	,	PUNCT
american_scientific_journal-7479	127	112	the	the	DET
american_scientific_journal-7479	127	113	existence	existence	NOUN
american_scientific_journal-7479	127	114	of	of	ADP
american_scientific_journal-7479	127	115	nontrivial	nontrivial	ADJ
american_scientific_journal-7479	127	116	solution	solution	NOUN
american_scientific_journal-7479	127	117	requires	require	VERB
american_scientific_journal-7479	127	118	|	|	ADV
american_scientific_journal-7479	127	119	𝑞11	𝑞11	VERB
american_scientific_journal-7479	128	1	𝑛	𝑛	PROPN
american_scientific_journal-7479	128	2	(	(	PUNCT
american_scientific_journal-7479	128	3	𝛹𝑛	𝛹𝑛	PROPN
american_scientific_journal-7479	128	4	)	)	PUNCT
american_scientific_journal-7479	128	5	𝑞13	𝑞13	NOUN
american_scientific_journal-7479	128	6	𝑛	𝑛	PROPN
american_scientific_journal-7479	128	7	(	(	PUNCT
american_scientific_journal-7479	128	8	𝛹𝑛	𝛹𝑛	PROPN
american_scientific_journal-7479	128	9	)	)	PUNCT
american_scientific_journal-7479	128	10	𝑞21	𝑞21	NUM
american_scientific_journal-7479	128	11	𝑛	𝑛	PROPN
american_scientific_journal-7479	128	12	(	(	PUNCT
american_scientific_journal-7479	128	13	𝛹𝑛	𝛹𝑛	PROPN
american_scientific_journal-7479	128	14	)	)	PUNCT
american_scientific_journal-7479	128	15	𝑞23	𝑞23	NOUN
american_scientific_journal-7479	128	16	𝑛	𝑛	PROPN
american_scientific_journal-7479	128	17	(	(	PUNCT
american_scientific_journal-7479	128	18	𝛹𝑛	𝛹𝑛	NOUN
american_scientific_journal-7479	128	19	)	)	PUNCT
american_scientific_journal-7479	128	20	|	|	ADV
american_scientific_journal-7479	128	21	=	=	SYM
american_scientific_journal-7479	128	22	0	0	NUM
american_scientific_journal-7479	129	1	(	(	PUNCT
american_scientific_journal-7479	129	2	26	26	NUM
american_scientific_journal-7479	129	3	)	)	PUNCT
american_scientific_journal-7479	129	4	equation	equation	NOUN
american_scientific_journal-7479	129	5	(	(	PUNCT
american_scientific_journal-7479	129	6	26	26	NUM
american_scientific_journal-7479	129	7	)	)	PUNCT
american_scientific_journal-7479	129	8	leads	lead	VERB
american_scientific_journal-7479	129	9	to	to	ADP
american_scientific_journal-7479	129	10	the	the	DET
american_scientific_journal-7479	129	11	eigenvalues	eigenvalue	NOUN
american_scientific_journal-7479	129	12	equation	equation	NOUN
american_scientific_journal-7479	129	13	solving	solve	VERB
american_scientific_journal-7479	129	14	𝛹𝑛	𝛹𝑛	PROPN
american_scientific_journal-7479	129	15	,	,	PUNCT
american_scientific_journal-7479	129	16	which	which	PRON
american_scientific_journal-7479	129	17	is	be	AUX
american_scientific_journal-7479	129	18	the	the	DET
american_scientific_journal-7479	129	19	n	n	ADV
american_scientific_journal-7479	129	20	-	-	PUNCT
american_scientific_journal-7479	129	21	th	th	VERB
american_scientific_journal-7479	129	22	eigenvalue	eigenvalue	NOUN
american_scientific_journal-7479	129	23	related	relate	VERB
american_scientific_journal-7479	129	24	with	with	ADP
american_scientific_journal-7479	129	25	the	the	DET
american_scientific_journal-7479	129	26	n	n	CCONJ
american_scientific_journal-7479	129	27	-	-	PUNCT
american_scientific_journal-7479	129	28	th	th	X
american_scientific_journal-7479	129	29	natural	natural	ADJ
american_scientific_journal-7479	129	30	frequency	frequency	NOUN
american_scientific_journal-7479	129	31	of	of	ADP
american_scientific_journal-7479	129	32	the	the	DET
american_scientific_journal-7479	129	33	beam	beam	NOUN
american_scientific_journal-7479	129	34	.	.	PUNCT
american_scientific_journal-7479	130	1	substituting	substitute	VERB
american_scientific_journal-7479	130	2	𝛹𝑛	𝛹𝑛	PROPN
american_scientific_journal-7479	130	3	into	into	ADP
american_scientific_journal-7479	130	4	eq	eq	ADP
american_scientific_journal-7479	130	5	.	.	PUNCT
american_scientific_journal-7479	131	1	(	(	PUNCT
american_scientific_journal-7479	131	2	26	26	NUM
american_scientific_journal-7479	131	3	)	)	PUNCT
american_scientific_journal-7479	131	4	and	and	CCONJ
american_scientific_journal-7479	131	5	choosing	choose	VERB
american_scientific_journal-7479	131	6	an	an	DET
american_scientific_journal-7479	131	7	arbitrary	arbitrary	ADJ
american_scientific_journal-7479	131	8	constant	constant	ADJ
american_scientific_journal-7479	131	9	,	,	PUNCT
american_scientific_journal-7479	131	10	other	other	ADJ
american_scientific_journal-7479	131	11	three	three	NUM
american_scientific_journal-7479	131	12	unknown	unknown	ADJ
american_scientific_journal-7479	131	13	constants	constant	NOUN
american_scientific_journal-7479	131	14	can	can	AUX
american_scientific_journal-7479	131	15	be	be	AUX
american_scientific_journal-7479	131	16	evaluated	evaluate	VERB
american_scientific_journal-7479	131	17	.	.	PUNCT
american_scientific_journal-7479	132	1	then	then	ADV
american_scientific_journal-7479	132	2	eq	eq	X
american_scientific_journal-7479	132	3	.	.	PUNCT
american_scientific_journal-7479	133	1	(	(	PUNCT
american_scientific_journal-7479	133	2	23	23	NUM
american_scientific_journal-7479	133	3	)	)	PUNCT
american_scientific_journal-7479	133	4	gives	give	VERB
american_scientific_journal-7479	133	5	the	the	DET
american_scientific_journal-7479	133	6	vibration	vibration	NOUN
american_scientific_journal-7479	133	7	mode	mode	NOUN
american_scientific_journal-7479	133	8	shapes	shape	NOUN
american_scientific_journal-7479	133	9	function	function	VERB
american_scientific_journal-7479	133	10	for	for	ADP
american_scientific_journal-7479	133	11	both	both	DET
american_scientific_journal-7479	133	12	span	span	NOUN
american_scientific_journal-7479	133	13	segments	segment	NOUN
american_scientific_journal-7479	133	14	(	(	PUNCT
american_scientific_journal-7479	133	15	the	the	DET
american_scientific_journal-7479	133	16	region	region	NOUN
american_scientific_journal-7479	133	17	before	before	ADV
american_scientific_journal-7479	133	18	and	and	CCONJ
american_scientific_journal-7479	133	19	after	after	ADP
american_scientific_journal-7479	133	20	crack	crack	NOUN
american_scientific_journal-7479	133	21	)	)	PUNCT
american_scientific_journal-7479	133	22	.	.	PUNCT
american_scientific_journal-7479	134	1	2	2	X
american_scientific_journal-7479	134	2	.	.	X
american_scientific_journal-7479	134	3	forced	force	VERB
american_scientific_journal-7479	134	4	responses	response	NOUN
american_scientific_journal-7479	134	5	the	the	DET
american_scientific_journal-7479	134	6	original	original	ADJ
american_scientific_journal-7479	134	7	equation	equation	NOUN
american_scientific_journal-7479	134	8	of	of	ADP
american_scientific_journal-7479	134	9	motion	motion	NOUN
american_scientific_journal-7479	134	10	(	(	PUNCT
american_scientific_journal-7479	134	11	eq	eq	NOUN
american_scientific_journal-7479	134	12	.	.	PUNCT
american_scientific_journal-7479	135	1	(	(	PUNCT
american_scientific_journal-7479	135	2	1	1	NUM
american_scientific_journal-7479	135	3	)	)	PUNCT
american_scientific_journal-7479	135	4	)	)	PUNCT
american_scientific_journal-7479	135	5	can	can	AUX
american_scientific_journal-7479	135	6	be	be	AUX
american_scientific_journal-7479	135	7	expressed	express	VERB
american_scientific_journal-7479	135	8	as	as	ADP
american_scientific_journal-7479	135	9	𝜕4𝑤𝑟(𝑥	𝜕4𝑤𝑟(𝑥	NOUN
american_scientific_journal-7479	135	10	,	,	PUNCT
american_scientific_journal-7479	135	11	𝑡	𝑡	NOUN
american_scientific_journal-7479	135	12	)	)	PUNCT
american_scientific_journal-7479	135	13	𝜕𝑥4	𝜕𝑥4	PROPN
american_scientific_journal-7479	135	14	+	+	NUM
american_scientific_journal-7479	135	15	𝐴	𝐴	PROPN
american_scientific_journal-7479	135	16	𝐸𝐼	𝐸𝐼	PROPN
american_scientific_journal-7479	135	17	𝜕2𝑤𝑟(𝑥	𝜕2𝑤𝑟(𝑥	PROPN
american_scientific_journal-7479	135	18	,	,	PUNCT
american_scientific_journal-7479	135	19	𝑡	𝑡	NOUN
american_scientific_journal-7479	135	20	)	)	PUNCT
american_scientific_journal-7479	135	21	𝜕𝑡2	𝜕𝑡2	NOUN
american_scientific_journal-7479	135	22	=	=	SYM
american_scientific_journal-7479	135	23	�	�	PROPN
american_scientific_journal-7479	135	24	̅	̅	NOUN
american_scientific_journal-7479	135	25	�	�	PROPN
american_scientific_journal-7479	135	26	𝐸𝐼	𝐸𝐼	PROPN
american_scientific_journal-7479	135	27	𝛿(𝑥	𝛿(𝑥	PROPN
american_scientific_journal-7479	135	28	−	−	PROPN
american_scientific_journal-7479	135	29	v𝑡	v𝑡	NOUN
american_scientific_journal-7479	135	30	)	)	PUNCT
american_scientific_journal-7479	135	31	,	,	PUNCT
american_scientific_journal-7479	135	32	𝑟	𝑟	X
american_scientific_journal-7479	136	1	=	=	SYM
american_scientific_journal-7479	136	2	1,2	1,2	NUM
american_scientific_journal-7479	136	3	(	(	PUNCT
american_scientific_journal-7479	136	4	27	27	NUM
american_scientific_journal-7479	136	5	)	)	PUNCT
american_scientific_journal-7479	136	6	using	use	VERB
american_scientific_journal-7479	136	7	the	the	DET
american_scientific_journal-7479	136	8	modal	modal	ADJ
american_scientific_journal-7479	136	9	expansion	expansion	NOUN
american_scientific_journal-7479	136	10	theory	theory	NOUN
american_scientific_journal-7479	136	11	,	,	PUNCT
american_scientific_journal-7479	136	12	the	the	DET
american_scientific_journal-7479	136	13	forced	force	VERB
american_scientific_journal-7479	136	14	response	response	NOUN
american_scientific_journal-7479	136	15	𝑤𝑟(𝑥	𝑤𝑟(𝑥	NOUN
american_scientific_journal-7479	136	16	,	,	PUNCT
american_scientific_journal-7479	136	17	𝑡	𝑡	PROPN
american_scientific_journal-7479	136	18	)	)	PUNCT
american_scientific_journal-7479	136	19	can	can	AUX
american_scientific_journal-7479	136	20	be	be	AUX
american_scientific_journal-7479	136	21	expressed	express	VERB
american_scientific_journal-7479	136	22	as	as	ADP
american_scientific_journal-7479	136	23	𝑤𝑟(𝑥	𝑤𝑟(𝑥	NOUN
american_scientific_journal-7479	136	24	,	,	PUNCT
american_scientific_journal-7479	136	25	𝑡	𝑡	NOUN
american_scientific_journal-7479	136	26	)	)	PUNCT
american_scientific_journal-7479	136	27	=	=	SYM
american_scientific_journal-7479	136	28	∑𝜑𝑟	∑𝜑𝑟	NOUN
american_scientific_journal-7479	136	29	𝑛(𝑥	𝑛(𝑥	PROPN
american_scientific_journal-7479	136	30	)	)	PUNCT
american_scientific_journal-7479	137	1	𝑛	𝑛	PROPN
american_scientific_journal-7479	137	2	𝑗=1	𝑗=1	PROPN
american_scientific_journal-7479	137	3	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	137	4	𝑛(𝑡	𝑛(𝑡	PROPN
american_scientific_journal-7479	137	5	)	)	PUNCT
american_scientific_journal-7479	137	6	,	,	PUNCT
american_scientific_journal-7479	137	7	𝑟	𝑟	X
american_scientific_journal-7479	137	8	=	=	SYM
american_scientific_journal-7479	137	9	1,2	1,2	NUM
american_scientific_journal-7479	137	10	(	(	PUNCT
american_scientific_journal-7479	137	11	28	28	NUM
american_scientific_journal-7479	137	12	)	)	PUNCT
american_scientific_journal-7479	137	13	where	where	SCONJ
american_scientific_journal-7479	137	14	𝜑𝑟	𝜑𝑟	PROPN
american_scientific_journal-7479	137	15	𝑛(𝑥	𝑛(𝑥	PROPN
american_scientific_journal-7479	137	16	)	)	PUNCT
american_scientific_journal-7479	137	17	are	be	AUX
american_scientific_journal-7479	137	18	eigenfunctions	eigenfunction	NOUN
american_scientific_journal-7479	137	19	of	of	ADP
american_scientific_journal-7479	137	20	the	the	DET
american_scientific_journal-7479	137	21	cracked	crack	VERB
american_scientific_journal-7479	137	22	beam	beam	NOUN
american_scientific_journal-7479	137	23	and	and	CCONJ
american_scientific_journal-7479	137	24	which	which	PRON
american_scientific_journal-7479	137	25	are	be	AUX
american_scientific_journal-7479	137	26	obtained	obtain	VERB
american_scientific_journal-7479	137	27	from	from	ADP
american_scientific_journal-7479	137	28	the	the	DET
american_scientific_journal-7479	137	29	above	above	ADJ
american_scientific_journal-7479	137	30	section	section	NOUN
american_scientific_journal-7479	137	31	(	(	PUNCT
american_scientific_journal-7479	137	32	section	section	NOUN
american_scientific_journal-7479	137	33	2),𝜂𝑟	2),𝜂𝑟	NUM
american_scientific_journal-7479	137	34	𝑛(𝑡	𝑛(𝑡	PROPN
american_scientific_journal-7479	137	35	)	)	PUNCT
american_scientific_journal-7479	137	36	are	be	AUX
american_scientific_journal-7479	137	37	generalized	generalized	ADJ
american_scientific_journal-7479	137	38	coordinates	coordinate	NOUN
american_scientific_journal-7479	137	39	and	and	CCONJ
american_scientific_journal-7479	137	40	n	n	PRON
american_scientific_journal-7479	137	41	is	be	AUX
american_scientific_journal-7479	137	42	the	the	DET
american_scientific_journal-7479	137	43	number	number	NOUN
american_scientific_journal-7479	137	44	of	of	ADP
american_scientific_journal-7479	137	45	terms	term	NOUN
american_scientific_journal-7479	137	46	used	use	VERB
american_scientific_journal-7479	137	47	to	to	PART
american_scientific_journal-7479	137	48	approximate	approximate	VERB
american_scientific_journal-7479	137	49	the	the	DET
american_scientific_journal-7479	137	50	solution	solution	NOUN
american_scientific_journal-7479	137	51	.	.	PUNCT
american_scientific_journal-7479	138	1	substitute	substitute	PROPN
american_scientific_journal-7479	138	2	eq	eq	PROPN
american_scientific_journal-7479	138	3	.	.	PUNCT
american_scientific_journal-7479	139	1	(	(	PUNCT
american_scientific_journal-7479	139	2	28	28	NUM
american_scientific_journal-7479	139	3	)	)	PUNCT
american_scientific_journal-7479	139	4	into	into	ADP
american_scientific_journal-7479	139	5	eq	eq	NOUN
american_scientific_journal-7479	139	6	.	.	PUNCT
american_scientific_journal-7479	140	1	(	(	PUNCT
american_scientific_journal-7479	140	2	27	27	NUM
american_scientific_journal-7479	140	3	)	)	PUNCT
american_scientific_journal-7479	140	4	,	,	PUNCT
american_scientific_journal-7479	140	5	multiplying	multiply	VERB
american_scientific_journal-7479	140	6	by	by	ADP
american_scientific_journal-7479	140	7	𝜑𝑟(𝑥	𝜑𝑟(𝑥	NOUN
american_scientific_journal-7479	140	8	)	)	PUNCT
american_scientific_journal-7479	140	9	,	,	PUNCT
american_scientific_journal-7479	140	10	and	and	CCONJ
american_scientific_journal-7479	140	11	integrating	integrate	VERB
american_scientific_journal-7479	140	12	from	from	ADP
american_scientific_journal-7479	140	13	0	0	NUM
american_scientific_journal-7479	140	14	to	to	ADP
american_scientific_journal-7479	140	15	l	l	NOUN
american_scientific_journal-7479	140	16	leads	lead	VERB
american_scientific_journal-7479	140	17	to	to	ADP
american_scientific_journal-7479	140	18	𝑑2𝜂𝑟(𝑡	𝑑2𝜂𝑟(𝑡	PROPN
american_scientific_journal-7479	140	19	)	)	PUNCT
american_scientific_journal-7479	140	20	𝑑𝑡2	𝑑𝑡2	NOUN
american_scientific_journal-7479	141	1	+	+	CCONJ
american_scientific_journal-7479	141	2	𝜔2𝜂𝑟(𝑡	𝜔2𝜂𝑟(𝑡	PROPN
american_scientific_journal-7479	141	3	)	)	PUNCT
american_scientific_journal-7479	141	4	=	=	SYM
american_scientific_journal-7479	141	5	𝐹𝑠𝜑𝑟(v𝑡	𝐹𝑠𝜑𝑟(v𝑡	NOUN
american_scientific_journal-7479	141	6	)	)	PUNCT
american_scientific_journal-7479	141	7	,	,	PUNCT
american_scientific_journal-7479	141	8	𝑟	𝑟	X
american_scientific_journal-7479	141	9	=	=	SYM
american_scientific_journal-7479	141	10	1,2	1,2	NUM
american_scientific_journal-7479	141	11	(	(	PUNCT
american_scientific_journal-7479	141	12	29	29	NUM
american_scientific_journal-7479	141	13	)	)	PUNCT
american_scientific_journal-7479	141	14	american	american	ADJ
american_scientific_journal-7479	141	15	academic	academic	ADJ
american_scientific_journal-7479	141	16	scientific	scientific	ADJ
american_scientific_journal-7479	141	17	research	research	NOUN
american_scientific_journal-7479	141	18	journal	journal	NOUN
american_scientific_journal-7479	141	19	for	for	ADP
american_scientific_journal-7479	141	20	engineering	engineering	NOUN
american_scientific_journal-7479	141	21	,	,	PUNCT
american_scientific_journal-7479	141	22	technology	technology	NOUN
american_scientific_journal-7479	141	23	,	,	PUNCT
american_scientific_journal-7479	141	24	and	and	CCONJ
american_scientific_journal-7479	141	25	sciences	science	NOUN
american_scientific_journal-7479	141	26	(	(	PUNCT
american_scientific_journal-7479	141	27	asrjets	asrjet	NOUN
american_scientific_journal-7479	141	28	)	)	PUNCT
american_scientific_journal-7479	141	29	(	(	PUNCT
american_scientific_journal-7479	141	30	2022	2022	NUM
american_scientific_journal-7479	141	31	)	)	PUNCT
american_scientific_journal-7479	141	32	volume	volume	NOUN
american_scientific_journal-7479	141	33	88	88	NUM
american_scientific_journal-7479	141	34	,	,	PUNCT
american_scientific_journal-7479	141	35	no1	no1	PROPN
american_scientific_journal-7479	141	36	,	,	PUNCT
american_scientific_journal-7479	141	37	pp	pp	ADV
american_scientific_journal-7479	141	38	332	332	NUM
american_scientific_journal-7479	141	39	-	-	SYM
american_scientific_journal-7479	141	40	348	348	NUM
american_scientific_journal-7479	141	41	339	339	NUM
american_scientific_journal-7479	141	42	where	where	SCONJ
american_scientific_journal-7479	141	43	𝐹𝑠	𝐹𝑠	PROPN
american_scientific_journal-7479	141	44	=	=	PUNCT
american_scientific_journal-7479	141	45	�	�	PROPN
american_scientific_journal-7479	141	46	̅	̅	NOUN
american_scientific_journal-7479	141	47	�	�	NOUN
american_scientific_journal-7479	141	48	𝜌𝐴	𝜌𝐴	PRON
american_scientific_journal-7479	141	49	to	to	PART
american_scientific_journal-7479	141	50	derive	derive	VERB
american_scientific_journal-7479	141	51	the	the	DET
american_scientific_journal-7479	141	52	generalized	generalized	ADJ
american_scientific_journal-7479	141	53	coordinates	coordinate	NOUN
american_scientific_journal-7479	141	54	of	of	ADP
american_scientific_journal-7479	141	55	cracked	crack	VERB
american_scientific_journal-7479	141	56	beam	beam	NOUN
american_scientific_journal-7479	141	57	the	the	DET
american_scientific_journal-7479	141	58	adm	adm	PROPN
american_scientific_journal-7479	141	59	is	be	AUX
american_scientific_journal-7479	141	60	applied	apply	VERB
american_scientific_journal-7479	141	61	to	to	ADP
american_scientific_journal-7479	141	62	eq	eq	PROPN
american_scientific_journal-7479	141	63	.	.	PUNCT
american_scientific_journal-7479	142	1	(	(	PUNCT
american_scientific_journal-7479	142	2	29	29	NUM
american_scientific_journal-7479	142	3	)	)	PUNCT
american_scientific_journal-7479	142	4	.	.	PUNCT
american_scientific_journal-7479	143	1	first	first	ADV
american_scientific_journal-7479	143	2	eq	eq	ADP
american_scientific_journal-7479	143	3	.	.	PUNCT
american_scientific_journal-7479	144	1	(	(	PUNCT
american_scientific_journal-7479	144	2	29	29	NUM
american_scientific_journal-7479	144	3	)	)	PUNCT
american_scientific_journal-7479	144	4	is	be	AUX
american_scientific_journal-7479	144	5	rewritten	rewrite	VERB
american_scientific_journal-7479	144	6	as	as	ADP
american_scientific_journal-7479	144	7	an	an	DET
american_scientific_journal-7479	144	8	operator	operator	NOUN
american_scientific_journal-7479	144	9	form	form	NOUN
american_scientific_journal-7479	144	10	.	.	PUNCT
american_scientific_journal-7479	145	1	𝐺𝑡[𝜂𝑟(𝑡	𝐺𝑡[𝜂𝑟(𝑡	NOUN
american_scientific_journal-7479	145	2	)	)	PUNCT
american_scientific_journal-7479	145	3	]	]	PUNCT
american_scientific_journal-7479	146	1	+	+	CCONJ
american_scientific_journal-7479	146	2	𝜔2𝜂𝑟(𝑡	𝜔2𝜂𝑟(𝑡	PROPN
american_scientific_journal-7479	146	3	)	)	PUNCT
american_scientific_journal-7479	146	4	=	=	SYM
american_scientific_journal-7479	146	5	𝐹𝑠𝜑𝑟(v𝑡	𝐹𝑠𝜑𝑟(v𝑡	NOUN
american_scientific_journal-7479	146	6	)	)	PUNCT
american_scientific_journal-7479	146	7	,	,	PUNCT
american_scientific_journal-7479	146	8	𝑟	𝑟	X
american_scientific_journal-7479	146	9	=	=	SYM
american_scientific_journal-7479	146	10	1,2	1,2	NUM
american_scientific_journal-7479	146	11	(	(	PUNCT
american_scientific_journal-7479	146	12	30	30	NUM
american_scientific_journal-7479	146	13	)	)	PUNCT
american_scientific_journal-7479	147	1	where	where	SCONJ
american_scientific_journal-7479	147	2	𝐺𝑡	𝐺𝑡	NOUN
american_scientific_journal-7479	147	3	=	=	PUNCT
american_scientific_journal-7479	147	4	𝑑4	𝑑4	ADP
american_scientific_journal-7479	147	5	𝑑𝑡4	𝑑𝑡4	NOUN
american_scientific_journal-7479	147	6	,	,	PUNCT
american_scientific_journal-7479	147	7	the	the	DET
american_scientific_journal-7479	147	8	inverse	inverse	NOUN
american_scientific_journal-7479	147	9	operator	operator	NOUN
american_scientific_journal-7479	147	10	of	of	ADP
american_scientific_journal-7479	147	11	𝐺𝑡	𝐺𝑡	PROPN
american_scientific_journal-7479	147	12	−1	−1	NOUN
american_scientific_journal-7479	147	13	is	be	AUX
american_scientific_journal-7479	147	14	then	then	ADV
american_scientific_journal-7479	147	15	a	a	DET
american_scientific_journal-7479	147	16	2	2	NUM
american_scientific_journal-7479	147	17	-	-	ADJ
american_scientific_journal-7479	147	18	fold	fold	ADJ
american_scientific_journal-7479	147	19	integral	integral	ADJ
american_scientific_journal-7479	147	20	operator	operator	NOUN
american_scientific_journal-7479	147	21	defined	define	VERB
american_scientific_journal-7479	147	22	by	by	ADP
american_scientific_journal-7479	147	23	𝐺𝑡	𝐺𝑡	PROPN
american_scientific_journal-7479	147	24	−1	−1	NOUN
american_scientific_journal-7479	148	1	=	=	SYM
american_scientific_journal-7479	149	1	∫	∫	PROPN
american_scientific_journal-7479	150	1	∫	∫	PROPN
american_scientific_journal-7479	151	1	(	(	PUNCT
american_scientific_journal-7479	151	2	⋅)𝑑𝑡𝑑𝑡	⋅)𝑑𝑡𝑑𝑡	PROPN
american_scientific_journal-7479	151	3	𝑡	𝑡	PROPN
american_scientific_journal-7479	151	4	0	0	NUM
american_scientific_journal-7479	151	5	𝑡	𝑡	NOUN
american_scientific_journal-7479	151	6	0	0	NUM
american_scientific_journal-7479	151	7	(	(	PUNCT
american_scientific_journal-7479	151	8	31	31	NUM
american_scientific_journal-7479	151	9	)	)	PUNCT
american_scientific_journal-7479	151	10	appling	appling	NOUN
american_scientific_journal-7479	151	11	𝐺𝑡	𝐺𝑡	PROPN
american_scientific_journal-7479	151	12	−1	−1	NOUN
american_scientific_journal-7479	151	13	on	on	ADP
american_scientific_journal-7479	151	14	both	both	DET
american_scientific_journal-7479	151	15	sides	side	NOUN
american_scientific_journal-7479	151	16	of	of	ADP
american_scientific_journal-7479	151	17	eq	eq	PROPN
american_scientific_journal-7479	151	18	.	.	PUNCT
american_scientific_journal-7479	152	1	(	(	PUNCT
american_scientific_journal-7479	152	2	30	30	NUM
american_scientific_journal-7479	152	3	)	)	PUNCT
american_scientific_journal-7479	152	4	yields	yield	NOUN
american_scientific_journal-7479	152	5	𝜂𝑟(𝑡	𝜂𝑟(𝑡	NUM
american_scientific_journal-7479	152	6	)	)	PUNCT
american_scientific_journal-7479	152	7	=	=	PUNCT
american_scientific_journal-7479	153	1	𝜂𝑟(0	𝜂𝑟(0	PROPN
american_scientific_journal-7479	153	2	)	)	PUNCT
american_scientific_journal-7479	153	3	+	+	NUM
american_scientific_journal-7479	153	4	𝑡𝜂𝑟	𝑡𝜂𝑟	NOUN
american_scientific_journal-7479	153	5	(	(	PUNCT
american_scientific_journal-7479	153	6	1)(0	1)(0	NUM
american_scientific_journal-7479	153	7	)	)	PUNCT
american_scientific_journal-7479	153	8	−	−	PROPN
american_scientific_journal-7479	154	1	𝐺𝑡	𝐺𝑡	PROPN
american_scientific_journal-7479	154	2	−1[𝜔𝑗	−1[𝜔𝑗	PROPN
american_scientific_journal-7479	154	3	2𝜂𝑟(𝑡	2𝜂𝑟(𝑡	NUM
american_scientific_journal-7479	154	4	)	)	PUNCT
american_scientific_journal-7479	154	5	−	−	PROPN
american_scientific_journal-7479	154	6	𝐹𝑠𝜑𝑟(v𝑡	𝐹𝑠𝜑𝑟(v𝑡	NOUN
american_scientific_journal-7479	154	7	)	)	PUNCT
american_scientific_journal-7479	154	8	]	]	PUNCT
american_scientific_journal-7479	154	9	(	(	PUNCT
american_scientific_journal-7479	154	10	32	32	NUM
american_scientific_journal-7479	154	11	)	)	PUNCT
american_scientific_journal-7479	154	12	based	base	VERB
american_scientific_journal-7479	154	13	on	on	ADP
american_scientific_journal-7479	154	14	the	the	DET
american_scientific_journal-7479	154	15	adm	adm	PROPN
american_scientific_journal-7479	154	16	,	,	PUNCT
american_scientific_journal-7479	154	17	the	the	DET
american_scientific_journal-7479	154	18	solution	solution	NOUN
american_scientific_journal-7479	154	19	of	of	ADP
american_scientific_journal-7479	154	20	the	the	DET
american_scientific_journal-7479	154	21	vibration	vibration	NOUN
american_scientific_journal-7479	154	22	mode	mode	NOUN
american_scientific_journal-7479	154	23	function	function	NOUN
american_scientific_journal-7479	154	24	can	can	AUX
american_scientific_journal-7479	154	25	be	be	AUX
american_scientific_journal-7479	154	26	expressed	express	VERB
american_scientific_journal-7479	154	27	as	as	ADP
american_scientific_journal-7479	154	28	a	a	DET
american_scientific_journal-7479	154	29	series	series	NOUN
american_scientific_journal-7479	154	30	:	:	PUNCT
american_scientific_journal-7479	154	31	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	154	32	𝑛(𝑡	𝑛(𝑡	PROPN
american_scientific_journal-7479	154	33	)	)	PUNCT
american_scientific_journal-7479	155	1	=	=	PUNCT
american_scientific_journal-7479	155	2	∑	∑	PUNCT
american_scientific_journal-7479	155	3	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	155	4	[	[	X
american_scientific_journal-7479	155	5	𝑗](𝑡	𝑗](𝑡	NOUN
american_scientific_journal-7479	155	6	)	)	PUNCT
american_scientific_journal-7479	155	7	∞	∞	PROPN
american_scientific_journal-7479	156	1	𝑗=0	𝑗=0	PROPN
american_scientific_journal-7479	156	2	(	(	PUNCT
american_scientific_journal-7479	156	3	33	33	NUM
american_scientific_journal-7479	156	4	)	)	PUNCT
american_scientific_journal-7479	156	5	consequently	consequently	ADV
american_scientific_journal-7479	156	6	,	,	PUNCT
american_scientific_journal-7479	156	7	for	for	ADP
american_scientific_journal-7479	156	8	each	each	DET
american_scientific_journal-7479	156	9	term	term	NOUN
american_scientific_journal-7479	156	10	of	of	ADP
american_scientific_journal-7479	156	11	the	the	DET
american_scientific_journal-7479	156	12	series	series	NOUN
american_scientific_journal-7479	156	13	,	,	PUNCT
american_scientific_journal-7479	156	14	it	it	PRON
american_scientific_journal-7479	156	15	can	can	AUX
american_scientific_journal-7479	156	16	be	be	AUX
american_scientific_journal-7479	156	17	written	write	VERB
american_scientific_journal-7479	156	18	as	as	ADP
american_scientific_journal-7479	156	19	:	:	PUNCT
american_scientific_journal-7479	156	20	𝜂𝑟	𝜂𝑟	X
american_scientific_journal-7479	157	1	[	[	X
american_scientific_journal-7479	157	2	0](𝑡	0](𝑡	NOUN
american_scientific_journal-7479	157	3	)	)	PUNCT
american_scientific_journal-7479	157	4	=	=	PUNCT
american_scientific_journal-7479	158	1	∑	∑	PUNCT
american_scientific_journal-7479	158	2	[	[	PUNCT
american_scientific_journal-7479	158	3	𝑡𝑢	𝑡𝑢	X
american_scientific_journal-7479	158	4	𝑢	𝑢	PROPN
american_scientific_journal-7479	158	5	!	!	PUNCT
american_scientific_journal-7479	158	6	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	158	7	(	(	PUNCT
american_scientific_journal-7479	158	8	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	158	9	)	)	PUNCT
american_scientific_journal-7479	158	10	]	]	PUNCT
american_scientific_journal-7479	158	11	1	1	NUM
american_scientific_journal-7479	158	12	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	158	13	+	+	CCONJ
american_scientific_journal-7479	158	14	𝐺𝑡	𝐺𝑡	PROPN
american_scientific_journal-7479	158	15	−1[𝐹𝑠𝜑𝑟(v𝑡	−1[𝐹𝑠𝜑𝑟(v𝑡	PROPN
american_scientific_journal-7479	158	16	)	)	PUNCT
american_scientific_journal-7479	158	17	]	]	PUNCT
american_scientific_journal-7479	158	18	(	(	PUNCT
american_scientific_journal-7479	158	19	34	34	NUM
american_scientific_journal-7479	158	20	)	)	PUNCT
american_scientific_journal-7479	158	21	substituting	substitute	VERB
american_scientific_journal-7479	158	22	eq	eq	PROPN
american_scientific_journal-7479	158	23	.	.	PUNCT
american_scientific_journal-7479	159	1	(	(	PUNCT
american_scientific_journal-7479	159	2	22	22	NUM
american_scientific_journal-7479	159	3	)	)	PUNCT
american_scientific_journal-7479	159	4	into	into	ADP
american_scientific_journal-7479	159	5	eq	eq	NOUN
american_scientific_journal-7479	159	6	.	.	PUNCT
american_scientific_journal-7479	160	1	(	(	PUNCT
american_scientific_journal-7479	160	2	34	34	NUM
american_scientific_journal-7479	160	3	)	)	PUNCT
american_scientific_journal-7479	160	4	gives	give	VERB
american_scientific_journal-7479	160	5	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	160	6	[	[	X
american_scientific_journal-7479	160	7	0](𝑡	0](𝑡	NOUN
american_scientific_journal-7479	160	8	)	)	PUNCT
american_scientific_journal-7479	160	9	=	=	PUNCT
american_scientific_journal-7479	161	1	∑	∑	PUNCT
american_scientific_journal-7479	161	2	[	[	PUNCT
american_scientific_journal-7479	161	3	𝑡𝑢	𝑡𝑢	X
american_scientific_journal-7479	161	4	𝑢	𝑢	PROPN
american_scientific_journal-7479	161	5	!	!	PUNCT
american_scientific_journal-7479	161	6	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	161	7	(	(	PUNCT
american_scientific_journal-7479	161	8	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	161	9	)	)	PUNCT
american_scientific_journal-7479	161	10	]	]	PUNCT
american_scientific_journal-7479	161	11	1	1	NUM
american_scientific_journal-7479	161	12	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	161	13	+	+	CCONJ
american_scientific_journal-7479	162	1	𝐹𝑠𝐺𝑡	𝐹𝑠𝐺𝑡	PROPN
american_scientific_journal-7479	162	2	−1	−1	NOUN
american_scientific_journal-7479	163	1	[	[	X
american_scientific_journal-7479	163	2	∑𝛹4𝑗	∑𝛹4𝑗	VERB
american_scientific_journal-7479	163	3	∑	∑	INTJ
american_scientific_journal-7479	163	4	(	(	PUNCT
american_scientific_journal-7479	163	5	v𝑡)4𝑗+𝑛	v𝑡)4𝑗+𝑛	PROPN
american_scientific_journal-7479	163	6	(	(	PUNCT
american_scientific_journal-7479	163	7	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	163	8	+	+	CCONJ
american_scientific_journal-7479	163	9	𝑛	𝑛	NOUN
american_scientific_journal-7479	163	10	)	)	PUNCT
american_scientific_journal-7479	163	11	!	!	PUNCT
american_scientific_journal-7479	164	1	3	3	NUM
american_scientific_journal-7479	164	2	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	164	3	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	164	4	(	(	PUNCT
american_scientific_journal-7479	164	5	𝑢)(0	𝑢)(0	NOUN
american_scientific_journal-7479	164	6	)	)	PUNCT
american_scientific_journal-7479	164	7	𝐽−1	𝐽−1	NOUN
american_scientific_journal-7479	164	8	𝑗=0	𝑗=0	X
american_scientific_journal-7479	164	9	]	]	PUNCT
american_scientific_journal-7479	165	1	=	=	PUNCT
american_scientific_journal-7479	165	2	∑	∑	PUNCT
american_scientific_journal-7479	165	3	[	[	PUNCT
american_scientific_journal-7479	165	4	𝑡𝑢	𝑡𝑢	X
american_scientific_journal-7479	165	5	𝑢	𝑢	PROPN
american_scientific_journal-7479	165	6	!	!	PUNCT
american_scientific_journal-7479	165	7	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	165	8	(	(	PUNCT
american_scientific_journal-7479	165	9	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	165	10	)	)	PUNCT
american_scientific_journal-7479	165	11	]	]	PUNCT
american_scientific_journal-7479	165	12	1	1	NUM
american_scientific_journal-7479	165	13	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	165	14	+	+	CCONJ
american_scientific_journal-7479	165	15	𝐹𝑠	𝐹𝑠	PROPN
american_scientific_journal-7479	165	16	[	[	PUNCT
american_scientific_journal-7479	165	17	∑	∑	ADV
american_scientific_journal-7479	165	18	𝛹4𝑗	𝛹4𝑗	VERB
american_scientific_journal-7479	165	19	𝐽−1	𝐽−1	ADV
american_scientific_journal-7479	165	20	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	165	21	∑	∑	PUNCT
american_scientific_journal-7479	165	22	v4𝑗+𝑛.	v4𝑗+𝑛.	VERB
american_scientific_journal-7479	165	23	𝑡4𝑗+𝑛+2	𝑡4𝑗+𝑛+2	NUM
american_scientific_journal-7479	165	24	(	(	PUNCT
american_scientific_journal-7479	165	25	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	165	26	+	+	CCONJ
american_scientific_journal-7479	165	27	𝑛	𝑛	PRON
american_scientific_journal-7479	165	28	+	+	NOUN
american_scientific_journal-7479	165	29	2	2	NUM
american_scientific_journal-7479	165	30	)	)	PUNCT
american_scientific_journal-7479	165	31	!	!	PUNCT
american_scientific_journal-7479	166	1	3	3	NUM
american_scientific_journal-7479	166	2	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	166	3	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	166	4	(	(	PUNCT
american_scientific_journal-7479	166	5	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	166	6	)	)	PUNCT
american_scientific_journal-7479	166	7	]	]	PUNCT
american_scientific_journal-7479	166	8	(	(	PUNCT
american_scientific_journal-7479	166	9	35	35	NUM
american_scientific_journal-7479	166	10	)	)	PUNCT
american_scientific_journal-7479	166	11	as	as	ADP
american_scientific_journal-7479	166	12	the	the	DET
american_scientific_journal-7479	166	13	initial	initial	ADJ
american_scientific_journal-7479	166	14	term	term	NOUN
american_scientific_journal-7479	166	15	of	of	ADP
american_scientific_journal-7479	166	16	the	the	DET
american_scientific_journal-7479	166	17	decomposition	decomposition	NOUN
american_scientific_journal-7479	166	18	,	,	PUNCT
american_scientific_journal-7479	166	19	and	and	CCONJ
american_scientific_journal-7479	166	20	𝜂𝑟	𝜂𝑟	X
american_scientific_journal-7479	167	1	[	[	X
american_scientific_journal-7479	167	2	𝑗](𝑡	𝑗](𝑡	NOUN
american_scientific_journal-7479	167	3	)	)	PUNCT
american_scientific_journal-7479	167	4	=	=	PUNCT
american_scientific_journal-7479	168	1	−𝜔2𝑗𝐺𝑡	−𝜔2𝑗𝐺𝑡	NUM
american_scientific_journal-7479	168	2	−1[𝜂𝑟	−1[𝜂𝑟	ADJ
american_scientific_journal-7479	168	3	[	[	NOUN
american_scientific_journal-7479	168	4	𝑗−1](𝑡	𝑗−1](𝑡	NOUN
american_scientific_journal-7479	168	5	)	)	PUNCT
american_scientific_journal-7479	168	6	]	]	PUNCT
american_scientific_journal-7479	168	7	,	,	PUNCT
american_scientific_journal-7479	168	8	𝑗	𝑗	X
american_scientific_journal-7479	168	9	≥	≥	NUM
american_scientific_journal-7479	168	10	1	1	NUM
american_scientific_journal-7479	168	11	,	,	PUNCT
american_scientific_journal-7479	168	12	𝑟	𝑟	NOUN
american_scientific_journal-7479	168	13	=	=	SYM
american_scientific_journal-7479	168	14	1,2	1,2	NUM
american_scientific_journal-7479	168	15	(	(	PUNCT
american_scientific_journal-7479	168	16	36	36	NUM
american_scientific_journal-7479	168	17	)	)	PUNCT
american_scientific_journal-7479	168	18	as	as	ADP
american_scientific_journal-7479	168	19	the	the	DET
american_scientific_journal-7479	168	20	recurrence	recurrence	NOUN
american_scientific_journal-7479	168	21	relation	relation	NOUN
american_scientific_journal-7479	168	22	of	of	ADP
american_scientific_journal-7479	168	23	the	the	DET
american_scientific_journal-7479	168	24	decomposition	decomposition	NOUN
american_scientific_journal-7479	168	25	.	.	PUNCT
american_scientific_journal-7479	169	1	consequently	consequently	ADV
american_scientific_journal-7479	169	2	,	,	PUNCT
american_scientific_journal-7479	169	3	all	all	DET
american_scientific_journal-7479	169	4	components	component	NOUN
american_scientific_journal-7479	169	5	of	of	ADP
american_scientific_journal-7479	169	6	the	the	DET
american_scientific_journal-7479	169	7	decomposition	decomposition	NOUN
american_scientific_journal-7479	169	8	can	can	AUX
american_scientific_journal-7479	169	9	be	be	AUX
american_scientific_journal-7479	169	10	american	american	ADJ
american_scientific_journal-7479	169	11	academic	academic	ADJ
american_scientific_journal-7479	169	12	scientific	scientific	ADJ
american_scientific_journal-7479	169	13	research	research	NOUN
american_scientific_journal-7479	169	14	journal	journal	NOUN
american_scientific_journal-7479	169	15	for	for	ADP
american_scientific_journal-7479	169	16	engineering	engineering	NOUN
american_scientific_journal-7479	169	17	,	,	PUNCT
american_scientific_journal-7479	169	18	technology	technology	NOUN
american_scientific_journal-7479	169	19	,	,	PUNCT
american_scientific_journal-7479	169	20	and	and	CCONJ
american_scientific_journal-7479	169	21	sciences	science	NOUN
american_scientific_journal-7479	169	22	(	(	PUNCT
american_scientific_journal-7479	169	23	asrjets	asrjet	NOUN
american_scientific_journal-7479	169	24	)	)	PUNCT
american_scientific_journal-7479	169	25	(	(	PUNCT
american_scientific_journal-7479	169	26	2022	2022	NUM
american_scientific_journal-7479	169	27	)	)	PUNCT
american_scientific_journal-7479	169	28	volume	volume	NOUN
american_scientific_journal-7479	169	29	88	88	NUM
american_scientific_journal-7479	169	30	,	,	PUNCT
american_scientific_journal-7479	169	31	no1	no1	PROPN
american_scientific_journal-7479	169	32	,	,	PUNCT
american_scientific_journal-7479	169	33	pp	pp	ADV
american_scientific_journal-7479	169	34	332	332	NUM
american_scientific_journal-7479	169	35	-	-	SYM
american_scientific_journal-7479	169	36	348	348	NUM
american_scientific_journal-7479	169	37	340	340	NUM
american_scientific_journal-7479	169	38	identified	identify	VERB
american_scientific_journal-7479	169	39	and	and	CCONJ
american_scientific_journal-7479	169	40	evaluated	evaluate	VERB
american_scientific_journal-7479	169	41	from	from	ADP
american_scientific_journal-7479	169	42	eq	eq	PROPN
american_scientific_journal-7479	169	43	.	.	PUNCT
american_scientific_journal-7479	170	1	(	(	PUNCT
american_scientific_journal-7479	170	2	36	36	NUM
american_scientific_journal-7479	170	3	)	)	PUNCT
american_scientific_journal-7479	170	4	.	.	PUNCT
american_scientific_journal-7479	171	1	this	this	PRON
american_scientific_journal-7479	171	2	is	be	AUX
american_scientific_journal-7479	171	3	,	,	PUNCT
american_scientific_journal-7479	171	4	by	by	ADP
american_scientific_journal-7479	171	5	substituting	substitute	VERB
american_scientific_journal-7479	171	6	eq	eq	ADP
american_scientific_journal-7479	171	7	.	.	PUNCT
american_scientific_journal-7479	172	1	(	(	PUNCT
american_scientific_journal-7479	172	2	35	35	NUM
american_scientific_journal-7479	172	3	)	)	PUNCT
american_scientific_journal-7479	172	4	into	into	ADP
american_scientific_journal-7479	172	5	eq	eq	NOUN
american_scientific_journal-7479	172	6	.	.	PUNCT
american_scientific_journal-7479	173	1	(	(	PUNCT
american_scientific_journal-7479	173	2	36	36	NUM
american_scientific_journal-7479	173	3	)	)	PUNCT
american_scientific_journal-7479	173	4	,	,	PUNCT
american_scientific_journal-7479	173	5	one	one	PRON
american_scientific_journal-7479	173	6	can	can	AUX
american_scientific_journal-7479	173	7	obtain	obtain	VERB
american_scientific_journal-7479	173	8	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	174	1	[	[	X
american_scientific_journal-7479	174	2	1](𝑡	1](𝑡	NOUN
american_scientific_journal-7479	174	3	)	)	PUNCT
american_scientific_journal-7479	174	4	=	=	SYM
american_scientific_journal-7479	175	1	−𝜔2𝐺𝑡	−𝜔2𝐺𝑡	NOUN
american_scientific_journal-7479	175	2	−1[𝜂𝑟	−1[𝜂𝑟	PROPN
american_scientific_journal-7479	176	1	[	[	X
american_scientific_journal-7479	176	2	0](𝑡	0](𝑡	NOUN
american_scientific_journal-7479	176	3	)	)	PUNCT
american_scientific_journal-7479	176	4	]	]	PUNCT
american_scientific_journal-7479	177	1	=	=	PUNCT
american_scientific_journal-7479	177	2	−𝜔2	−𝜔2	PROPN
american_scientific_journal-7479	178	1	[	[	X
american_scientific_journal-7479	178	2	∑	∑	INTJ
american_scientific_journal-7479	178	3	[	[	PUNCT
american_scientific_journal-7479	178	4	𝑡𝑢+2	𝑡𝑢+2	NUM
american_scientific_journal-7479	178	5	(	(	PUNCT
american_scientific_journal-7479	178	6	𝑢	𝑢	X
american_scientific_journal-7479	178	7	+	+	NOUN
american_scientific_journal-7479	178	8	2	2	NUM
american_scientific_journal-7479	178	9	)	)	PUNCT
american_scientific_journal-7479	178	10	!	!	PUNCT
american_scientific_journal-7479	179	1	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	179	2	(	(	PUNCT
american_scientific_journal-7479	179	3	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	179	4	)	)	PUNCT
american_scientific_journal-7479	179	5	]	]	PUNCT
american_scientific_journal-7479	179	6	1	1	NUM
american_scientific_journal-7479	179	7	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	179	8	+	+	CCONJ
american_scientific_journal-7479	179	9	𝐹𝑠	𝐹𝑠	PROPN
american_scientific_journal-7479	179	10	[	[	PUNCT
american_scientific_journal-7479	179	11	∑	∑	ADV
american_scientific_journal-7479	179	12	𝛹4𝑗	𝛹4𝑗	VERB
american_scientific_journal-7479	179	13	𝐽−1	𝐽−1	ADV
american_scientific_journal-7479	179	14	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	179	15	∑	∑	PUNCT
american_scientific_journal-7479	179	16	v4𝑗+𝑛.	v4𝑗+𝑛.	VERB
american_scientific_journal-7479	179	17	𝑡4𝑗+𝑛+4	𝑡4𝑗+𝑛+4	NUM
american_scientific_journal-7479	179	18	(	(	PUNCT
american_scientific_journal-7479	179	19	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	179	20	+	+	CCONJ
american_scientific_journal-7479	179	21	𝑛	𝑛	PRON
american_scientific_journal-7479	179	22	+	+	NOUN
american_scientific_journal-7479	179	23	4	4	NUM
american_scientific_journal-7479	179	24	)	)	PUNCT
american_scientific_journal-7479	179	25	!	!	PUNCT
american_scientific_journal-7479	180	1	3	3	NUM
american_scientific_journal-7479	180	2	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	180	3	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	180	4	(	(	PUNCT
american_scientific_journal-7479	180	5	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	180	6	)	)	PUNCT
american_scientific_journal-7479	180	7	]	]	X
american_scientific_journal-7479	180	8	]	]	PUNCT
american_scientific_journal-7479	180	9	,	,	PUNCT
american_scientific_journal-7479	180	10	(	(	PUNCT
american_scientific_journal-7479	180	11	37	37	NUM
american_scientific_journal-7479	180	12	)	)	PUNCT
american_scientific_journal-7479	180	13	𝜂𝑟	𝜂𝑟	NOUN
american_scientific_journal-7479	181	1	[	[	X
american_scientific_journal-7479	181	2	2](𝑡	2](𝑡	NUM
american_scientific_journal-7479	181	3	)	)	PUNCT
american_scientific_journal-7479	182	1	=	=	SYM
american_scientific_journal-7479	182	2	−𝜔4𝐺𝑡	−𝜔4𝐺𝑡	PROPN
american_scientific_journal-7479	182	3	−1[𝜂𝑟	−1[𝜂𝑟	PROPN
american_scientific_journal-7479	183	1	[	[	X
american_scientific_journal-7479	183	2	1](𝑡	1](𝑡	NOUN
american_scientific_journal-7479	183	3	)	)	PUNCT
american_scientific_journal-7479	183	4	]	]	PUNCT
american_scientific_journal-7479	184	1	=	=	PUNCT
american_scientific_journal-7479	184	2	𝜔4	𝜔4	X
american_scientific_journal-7479	185	1	[	[	X
american_scientific_journal-7479	185	2	∑	∑	PROPN
american_scientific_journal-7479	185	3	[	[	PUNCT
american_scientific_journal-7479	185	4	𝑡𝑢+4	𝑡𝑢+4	NUM
american_scientific_journal-7479	185	5	(	(	PUNCT
american_scientific_journal-7479	185	6	𝑢	𝑢	NOUN
american_scientific_journal-7479	185	7	+	+	NOUN
american_scientific_journal-7479	185	8	4	4	NUM
american_scientific_journal-7479	185	9	)	)	PUNCT
american_scientific_journal-7479	185	10	!	!	PUNCT
american_scientific_journal-7479	186	1	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	186	2	(	(	PUNCT
american_scientific_journal-7479	186	3	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	186	4	)	)	PUNCT
american_scientific_journal-7479	186	5	]	]	PUNCT
american_scientific_journal-7479	186	6	1	1	NUM
american_scientific_journal-7479	186	7	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	186	8	+	+	CCONJ
american_scientific_journal-7479	186	9	𝐹𝑠	𝐹𝑠	PROPN
american_scientific_journal-7479	186	10	[	[	PUNCT
american_scientific_journal-7479	186	11	∑	∑	ADV
american_scientific_journal-7479	186	12	𝛹4𝑗	𝛹4𝑗	VERB
american_scientific_journal-7479	186	13	𝐽−1	𝐽−1	ADV
american_scientific_journal-7479	186	14	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	186	15	∑	∑	PUNCT
american_scientific_journal-7479	186	16	v4𝑗+𝑛.	v4𝑗+𝑛.	VERB
american_scientific_journal-7479	186	17	𝑡4𝑗+𝑛+6	𝑡4𝑗+𝑛+6	NUM
american_scientific_journal-7479	186	18	(	(	PUNCT
american_scientific_journal-7479	186	19	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	186	20	+	+	CCONJ
american_scientific_journal-7479	186	21	𝑛	𝑛	PRON
american_scientific_journal-7479	186	22	+	+	NOUN
american_scientific_journal-7479	186	23	6	6	NUM
american_scientific_journal-7479	186	24	)	)	PUNCT
american_scientific_journal-7479	186	25	!	!	PUNCT
american_scientific_journal-7479	187	1	3	3	NUM
american_scientific_journal-7479	187	2	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	187	3	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	187	4	(	(	PUNCT
american_scientific_journal-7479	187	5	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	187	6	)	)	PUNCT
american_scientific_journal-7479	187	7	]	]	X
american_scientific_journal-7479	187	8	]	]	PUNCT
american_scientific_journal-7479	187	9	,	,	PUNCT
american_scientific_journal-7479	187	10	(	(	PUNCT
american_scientific_journal-7479	187	11	38	38	NUM
american_scientific_journal-7479	187	12	)	)	PUNCT
american_scientific_journal-7479	187	13	𝜂𝑟	𝜂𝑟	NOUN
american_scientific_journal-7479	188	1	[	[	X
american_scientific_journal-7479	188	2	3](𝑡	3](𝑡	NUM
american_scientific_journal-7479	188	3	)	)	PUNCT
american_scientific_journal-7479	189	1	=	=	SYM
american_scientific_journal-7479	189	2	−𝜔4𝐺𝑡	−𝜔4𝐺𝑡	PROPN
american_scientific_journal-7479	189	3	−1[𝜂𝑟	−1[𝜂𝑟	PROPN
american_scientific_journal-7479	190	1	[	[	X
american_scientific_journal-7479	190	2	2](𝑡	2](𝑡	NUM
american_scientific_journal-7479	190	3	)	)	PUNCT
american_scientific_journal-7479	190	4	]	]	PUNCT
american_scientific_journal-7479	191	1	=	=	PUNCT
american_scientific_journal-7479	191	2	−𝜔6	−𝜔6	PROPN
american_scientific_journal-7479	192	1	[	[	X
american_scientific_journal-7479	192	2	∑	∑	PROPN
american_scientific_journal-7479	192	3	[	[	PUNCT
american_scientific_journal-7479	192	4	𝑡𝑢+6	𝑡𝑢+6	X
american_scientific_journal-7479	192	5	(	(	PUNCT
american_scientific_journal-7479	192	6	𝑢	𝑢	X
american_scientific_journal-7479	192	7	+	+	PROPN
american_scientific_journal-7479	192	8	6	6	NUM
american_scientific_journal-7479	192	9	)	)	PUNCT
american_scientific_journal-7479	192	10	!	!	PUNCT
american_scientific_journal-7479	193	1	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	193	2	(	(	PUNCT
american_scientific_journal-7479	193	3	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	193	4	)	)	PUNCT
american_scientific_journal-7479	193	5	]	]	PUNCT
american_scientific_journal-7479	193	6	1	1	NUM
american_scientific_journal-7479	193	7	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	193	8	+	+	CCONJ
american_scientific_journal-7479	193	9	𝐹𝑠	𝐹𝑠	PROPN
american_scientific_journal-7479	193	10	[	[	PUNCT
american_scientific_journal-7479	193	11	∑	∑	ADV
american_scientific_journal-7479	193	12	𝛹4𝑗	𝛹4𝑗	VERB
american_scientific_journal-7479	193	13	𝐽−1	𝐽−1	ADV
american_scientific_journal-7479	193	14	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	193	15	∑	∑	PUNCT
american_scientific_journal-7479	193	16	v4𝑗+𝑛.	v4𝑗+𝑛.	VERB
american_scientific_journal-7479	193	17	𝑡4𝑗+𝑛+8	𝑡4𝑗+𝑛+8	NUM
american_scientific_journal-7479	193	18	(	(	PUNCT
american_scientific_journal-7479	193	19	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	193	20	+	+	CCONJ
american_scientific_journal-7479	193	21	𝑛	𝑛	DET
american_scientific_journal-7479	193	22	+	+	NOUN
american_scientific_journal-7479	193	23	8)	8)	NUM
american_scientific_journal-7479	193	24	!	!	NOUN
american_scientific_journal-7479	193	25	3	3	NUM
american_scientific_journal-7479	193	26	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	193	27	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	193	28	(	(	PUNCT
american_scientific_journal-7479	193	29	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	193	30	)	)	PUNCT
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american_scientific_journal-7479	193	35	39	39	NUM
american_scientific_journal-7479	193	36	)	)	PUNCT
american_scientific_journal-7479	193	37	and	and	CCONJ
american_scientific_journal-7479	193	38	𝜂𝑟	𝜂𝑟	X
american_scientific_journal-7479	194	1	[	[	X
american_scientific_journal-7479	194	2	𝑚](𝑡	𝑚](𝑡	NOUN
american_scientific_journal-7479	194	3	)	)	PUNCT
american_scientific_journal-7479	194	4	=	=	PUNCT
american_scientific_journal-7479	194	5	−𝜔2𝑚𝐺𝑡	−𝜔2𝑚𝐺𝑡	VERB
american_scientific_journal-7479	194	6	−1[𝜂𝑟	−1[𝜂𝑟	PROPN
american_scientific_journal-7479	194	7	[	[	X
american_scientific_journal-7479	194	8	𝑚−1](𝑡)]=	𝑚−1](𝑡)]=	X
american_scientific_journal-7479	194	9	−𝜔2𝑚	−𝜔2𝑚	PROPN
american_scientific_journal-7479	195	1	[	[	X
american_scientific_journal-7479	195	2	∑	∑	X
american_scientific_journal-7479	195	3	[	[	PUNCT
american_scientific_journal-7479	195	4	𝑡𝑢+2𝑚	𝑡𝑢+2𝑚	X
american_scientific_journal-7479	195	5	(	(	PUNCT
american_scientific_journal-7479	195	6	𝑢	𝑢	X
american_scientific_journal-7479	195	7	+	+	NOUN
american_scientific_journal-7479	195	8	2𝑚	2𝑚	NUM
american_scientific_journal-7479	195	9	)	)	PUNCT
american_scientific_journal-7479	195	10	!	!	PUNCT
american_scientific_journal-7479	196	1	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	196	2	(	(	PUNCT
american_scientific_journal-7479	196	3	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	196	4	)	)	PUNCT
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american_scientific_journal-7479	196	6	1	1	NUM
american_scientific_journal-7479	196	7	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	196	8	+	+	CCONJ
american_scientific_journal-7479	196	9	𝐹𝑠	𝐹𝑠	PROPN
american_scientific_journal-7479	196	10	[	[	PUNCT
american_scientific_journal-7479	196	11	∑	∑	ADV
american_scientific_journal-7479	196	12	𝛹4𝑗	𝛹4𝑗	VERB
american_scientific_journal-7479	196	13	𝐽−1	𝐽−1	ADV
american_scientific_journal-7479	196	14	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	196	15	∑	∑	PUNCT
american_scientific_journal-7479	196	16	v4𝑗+𝑛	v4𝑗+𝑛	PROPN
american_scientific_journal-7479	196	17	.	.	PUNCT
american_scientific_journal-7479	197	1	𝑡4𝑗+𝑛+2𝑚+2	𝑡4𝑗+𝑛+2𝑚+2	NOUN
american_scientific_journal-7479	197	2	(	(	PUNCT
american_scientific_journal-7479	197	3	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	197	4	+	+	CCONJ
american_scientific_journal-7479	197	5	𝑛	𝑛	DET
american_scientific_journal-7479	197	6	+	+	NUM
american_scientific_journal-7479	197	7	2𝑚	2𝑚	NOUN
american_scientific_journal-7479	197	8	+	+	CCONJ
american_scientific_journal-7479	197	9	2	2	NUM
american_scientific_journal-7479	197	10	)	)	PUNCT
american_scientific_journal-7479	197	11	!	!	PUNCT
american_scientific_journal-7479	198	1	3	3	NUM
american_scientific_journal-7479	198	2	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	198	3	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	198	4	(	(	PUNCT
american_scientific_journal-7479	198	5	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	198	6	)	)	PUNCT
american_scientific_journal-7479	198	7	]	]	X
american_scientific_journal-7479	198	8	]	]	PUNCT
american_scientific_journal-7479	198	9	,	,	PUNCT
american_scientific_journal-7479	198	10	𝑚	𝑚	X
american_scientific_journal-7479	198	11	≥	≥	NUM
american_scientific_journal-7479	198	12	1	1	NUM
american_scientific_journal-7479	198	13	(	(	PUNCT
american_scientific_journal-7479	198	14	40	40	NUM
american_scientific_journal-7479	198	15	)	)	PUNCT
american_scientific_journal-7479	198	16	in	in	ADP
american_scientific_journal-7479	198	17	practice	practice	NOUN
american_scientific_journal-7479	198	18	,	,	PUNCT
american_scientific_journal-7479	198	19	the	the	DET
american_scientific_journal-7479	198	20	solution	solution	NOUN
american_scientific_journal-7479	198	21	will	will	AUX
american_scientific_journal-7479	198	22	be	be	AUX
american_scientific_journal-7479	198	23	the	the	DET
american_scientific_journal-7479	198	24	n	n	NUM
american_scientific_journal-7479	198	25	-	-	PUNCT
american_scientific_journal-7479	198	26	term	term	NOUN
american_scientific_journal-7479	198	27	approximation	approximation	NOUN
american_scientific_journal-7479	198	28	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	198	29	𝑛	𝑛	PROPN
american_scientific_journal-7479	198	30	=	=	PUNCT
american_scientific_journal-7479	198	31	∑	∑	PUNCT
american_scientific_journal-7479	198	32	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	198	33	[	[	X
american_scientific_journal-7479	198	34	𝑚](𝑡	𝑚](𝑡	NOUN
american_scientific_journal-7479	198	35	)	)	PUNCT
american_scientific_journal-7479	198	36	𝑛−1	𝑛−1	NUM
american_scientific_journal-7479	198	37	𝑚=0	𝑚=0	PUNCT
american_scientific_journal-7479	198	38	=	=	SYM
american_scientific_journal-7479	198	39	∑	∑	PUNCT
american_scientific_journal-7479	198	40	[	[	PUNCT
american_scientific_journal-7479	198	41	−𝜔2𝑚	−𝜔2𝑚	PROPN
american_scientific_journal-7479	198	42	[	[	X
american_scientific_journal-7479	198	43	∑	∑	X
american_scientific_journal-7479	198	44	[	[	PUNCT
american_scientific_journal-7479	198	45	𝑡𝑢+2𝑚	𝑡𝑢+2𝑚	X
american_scientific_journal-7479	198	46	(	(	PUNCT
american_scientific_journal-7479	198	47	𝑢	𝑢	X
american_scientific_journal-7479	198	48	+	+	NOUN
american_scientific_journal-7479	198	49	2𝑚	2𝑚	NUM
american_scientific_journal-7479	198	50	)	)	PUNCT
american_scientific_journal-7479	198	51	!	!	PUNCT
american_scientific_journal-7479	199	1	𝜂𝑟	𝜂𝑟	PROPN
american_scientific_journal-7479	199	2	(	(	PUNCT
american_scientific_journal-7479	199	3	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	199	4	)	)	PUNCT
american_scientific_journal-7479	199	5	]	]	PUNCT
american_scientific_journal-7479	199	6	1	1	NUM
american_scientific_journal-7479	199	7	𝑢=0	𝑢=0	NOUN
american_scientific_journal-7479	199	8	+	+	CCONJ
american_scientific_journal-7479	199	9	𝐹𝑠	𝐹𝑠	PROPN
american_scientific_journal-7479	199	10	[	[	X
american_scientific_journal-7479	199	11	∑𝛹4𝑗	∑𝛹4𝑗	X
american_scientific_journal-7479	199	12	𝐽−1	𝐽−1	NOUN
american_scientific_journal-7479	199	13	𝑗=0	𝑗=0	PUNCT
american_scientific_journal-7479	199	14	∑	∑	PUNCT
american_scientific_journal-7479	199	15	v4𝑗+𝑛.	v4𝑗+𝑛.	VERB
american_scientific_journal-7479	199	16	𝑡4𝑗+𝑛+2𝑚+2	𝑡4𝑗+𝑛+2𝑚+2	NOUN
american_scientific_journal-7479	199	17	(	(	PUNCT
american_scientific_journal-7479	199	18	4𝑗	4𝑗	NOUN
american_scientific_journal-7479	199	19	+	+	CCONJ
american_scientific_journal-7479	199	20	𝑛	𝑛	DET
american_scientific_journal-7479	199	21	+	+	NUM
american_scientific_journal-7479	199	22	2𝑚	2𝑚	NOUN
american_scientific_journal-7479	199	23	+	+	CCONJ
american_scientific_journal-7479	199	24	2	2	NUM
american_scientific_journal-7479	199	25	)	)	PUNCT
american_scientific_journal-7479	199	26	!	!	PUNCT
american_scientific_journal-7479	200	1	3	3	NUM
american_scientific_journal-7479	200	2	𝑢=0	𝑢=0	PROPN
american_scientific_journal-7479	200	3	𝜑𝑟	𝜑𝑟	INTJ
american_scientific_journal-7479	200	4	(	(	PUNCT
american_scientific_journal-7479	200	5	𝑢)(0	𝑢)(0	PROPN
american_scientific_journal-7479	200	6	)	)	PUNCT
american_scientific_journal-7479	200	7	]	]	PUNCT
american_scientific_journal-7479	200	8	]	]	X
american_scientific_journal-7479	200	9	]	]	X
american_scientific_journal-7479	201	1	𝑛−1	𝑛−1	NUM
american_scientific_journal-7479	201	2	𝑚=0	𝑚=0	PUNCT
american_scientific_journal-7479	201	3	,	,	PUNCT
american_scientific_journal-7479	201	4	𝑚	𝑚	X
american_scientific_journal-7479	201	5	≥	≥	NUM
american_scientific_journal-7479	201	6	1	1	NUM
american_scientific_journal-7479	201	7	(	(	PUNCT
american_scientific_journal-7479	201	8	41	41	NUM
american_scientific_journal-7479	201	9	)	)	PUNCT
american_scientific_journal-7479	201	10	american	american	ADJ
american_scientific_journal-7479	201	11	academic	academic	ADJ
american_scientific_journal-7479	201	12	scientific	scientific	ADJ
american_scientific_journal-7479	201	13	research	research	NOUN
american_scientific_journal-7479	201	14	journal	journal	NOUN
american_scientific_journal-7479	201	15	for	for	ADP
american_scientific_journal-7479	201	16	engineering	engineering	NOUN
american_scientific_journal-7479	201	17	,	,	PUNCT
american_scientific_journal-7479	201	18	technology	technology	NOUN
american_scientific_journal-7479	201	19	,	,	PUNCT
american_scientific_journal-7479	201	20	and	and	CCONJ
american_scientific_journal-7479	201	21	sciences	science	NOUN
american_scientific_journal-7479	201	22	(	(	PUNCT
american_scientific_journal-7479	201	23	asrjets	asrjet	NOUN
american_scientific_journal-7479	201	24	)	)	PUNCT
american_scientific_journal-7479	201	25	(	(	PUNCT
american_scientific_journal-7479	201	26	2022	2022	NUM
american_scientific_journal-7479	201	27	)	)	PUNCT
american_scientific_journal-7479	201	28	volume	volume	NOUN
american_scientific_journal-7479	201	29	88	88	NUM
american_scientific_journal-7479	201	30	,	,	PUNCT
american_scientific_journal-7479	201	31	no1	no1	PROPN
american_scientific_journal-7479	201	32	,	,	PUNCT
american_scientific_journal-7479	201	33	pp	pp	ADV
american_scientific_journal-7479	201	34	332	332	NUM
american_scientific_journal-7479	201	35	-	-	SYM
american_scientific_journal-7479	201	36	348	348	NUM
american_scientific_journal-7479	201	37	341	341	NUM
american_scientific_journal-7479	201	38	and	and	CCONJ
american_scientific_journal-7479	201	39	from	from	ADP
american_scientific_journal-7479	201	40	the	the	DET
american_scientific_journal-7479	201	41	convergence	convergence	NOUN
american_scientific_journal-7479	201	42	of	of	ADP
american_scientific_journal-7479	201	43	adm	adm	PROPN
american_scientific_journal-7479	201	44	[	[	PUNCT
american_scientific_journal-7479	201	45	]	]	X
american_scientific_journal-7479	201	46	,	,	PUNCT
american_scientific_journal-7479	201	47	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	201	48	𝑛	𝑛	VERB
american_scientific_journal-7479	201	49	approaches	approach	VERB
american_scientific_journal-7479	201	50	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	201	51	[	[	X
american_scientific_journal-7479	201	52	𝑚](𝑡	𝑚](𝑡	NOUN
american_scientific_journal-7479	201	53	)	)	PUNCT
american_scientific_journal-7479	201	54	as	as	ADP
american_scientific_journal-7479	201	55	𝑛	𝑛	PROPN
american_scientific_journal-7479	201	56	→	→	SYM
american_scientific_journal-7479	201	57	∞	∞	NUM
american_scientific_journal-7479	201	58	𝜂𝑟(𝑡	𝜂𝑟(𝑡	X
american_scientific_journal-7479	201	59	)	)	PUNCT
american_scientific_journal-7479	202	1	=	=	SYM
american_scientific_journal-7479	202	2	lim	lim	PROPN
american_scientific_journal-7479	202	3	𝑛→∞	𝑛→∞	NUM
american_scientific_journal-7479	202	4	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	202	5	𝑛(𝑡	𝑛(𝑡	PROPN
american_scientific_journal-7479	202	6	)	)	PUNCT
american_scientific_journal-7479	203	1	=	=	PUNCT
american_scientific_journal-7479	203	2	∑	∑	PUNCT
american_scientific_journal-7479	203	3	𝜂𝑟	𝜂𝑟	ADP
american_scientific_journal-7479	204	1	[	[	X
american_scientific_journal-7479	204	2	𝑚](𝑡	𝑚](𝑡	NOUN
american_scientific_journal-7479	204	3	)	)	PUNCT
american_scientific_journal-7479	204	4	∞	∞	NUM
american_scientific_journal-7479	204	5	𝑚=0	𝑚=0	PUNCT
american_scientific_journal-7479	204	6	,	,	PUNCT
american_scientific_journal-7479	204	7	𝑟	𝑟	X
american_scientific_journal-7479	204	8	=	=	SYM
american_scientific_journal-7479	204	9	1,2	1,2	NUM
american_scientific_journal-7479	204	10	(	(	PUNCT
american_scientific_journal-7479	204	11	42	42	NUM
american_scientific_journal-7479	204	12	)	)	PUNCT
american_scientific_journal-7479	204	13	the	the	DET
american_scientific_journal-7479	204	14	final	final	ADJ
american_scientific_journal-7479	204	15	generalized	generalized	ADJ
american_scientific_journal-7479	204	16	coordinates	coordinate	NOUN
american_scientific_journal-7479	204	17	function	function	VERB
american_scientific_journal-7479	204	18	for	for	ADP
american_scientific_journal-7479	204	19	two	two	NUM
american_scientific_journal-7479	204	20	segments	segment	NOUN
american_scientific_journal-7479	204	21	(	(	PUNCT
american_scientific_journal-7479	204	22	the	the	DET
american_scientific_journal-7479	204	23	region	region	NOUN
american_scientific_journal-7479	204	24	before	before	ADV
american_scientific_journal-7479	204	25	and	and	CCONJ
american_scientific_journal-7479	204	26	after	after	ADP
american_scientific_journal-7479	204	27	the	the	DET
american_scientific_journal-7479	204	28	crack	crack	NOUN
american_scientific_journal-7479	204	29	)	)	PUNCT
american_scientific_journal-7479	204	30	has	have	AUX
american_scientific_journal-7479	204	31	been	be	AUX
american_scientific_journal-7479	204	32	shown	show	VERB
american_scientific_journal-7479	204	33	in	in	ADP
american_scientific_journal-7479	204	34	eq	eq	ADP
american_scientific_journal-7479	204	35	.	.	PUNCT
american_scientific_journal-7479	205	1	(	(	PUNCT
american_scientific_journal-7479	205	2	42	42	NUM
american_scientific_journal-7479	205	3	)	)	PUNCT
american_scientific_journal-7479	205	4	one	one	PRON
american_scientific_journal-7479	205	5	can	can	AUX
american_scientific_journal-7479	205	6	consider	consider	VERB
american_scientific_journal-7479	205	7	as	as	ADP
american_scientific_journal-7479	205	8	many	many	ADJ
american_scientific_journal-7479	205	9	terms	term	NOUN
american_scientific_journal-7479	205	10	as	as	SCONJ
american_scientific_journal-7479	205	11	needed	need	VERB
american_scientific_journal-7479	205	12	to	to	PART
american_scientific_journal-7479	205	13	obtain	obtain	VERB
american_scientific_journal-7479	205	14	a	a	DET
american_scientific_journal-7479	205	15	more	more	ADV
american_scientific_journal-7479	205	16	accurate	accurate	ADJ
american_scientific_journal-7479	205	17	deflection	deflection	NOUN
american_scientific_journal-7479	205	18	function	function	NOUN
american_scientific_journal-7479	205	19	.	.	PUNCT
american_scientific_journal-7479	206	1	if	if	SCONJ
american_scientific_journal-7479	206	2	the	the	DET
american_scientific_journal-7479	206	3	series	series	NOUN
american_scientific_journal-7479	206	4	converges	converge	VERB
american_scientific_journal-7479	206	5	,	,	PUNCT
american_scientific_journal-7479	206	6	the	the	DET
american_scientific_journal-7479	206	7	j	j	NOUN
american_scientific_journal-7479	206	8	-	-	PUNCT
american_scientific_journal-7479	206	9	term	term	NOUN
american_scientific_journal-7479	206	10	partial	partial	ADJ
american_scientific_journal-7479	206	11	sum	sum	NOUN
american_scientific_journal-7479	206	12	will	will	AUX
american_scientific_journal-7479	206	13	be	be	AUX
american_scientific_journal-7479	206	14	the	the	DET
american_scientific_journal-7479	206	15	approximate	approximate	ADJ
american_scientific_journal-7479	206	16	closed	closed	ADJ
american_scientific_journal-7479	206	17	-	-	PUNCT
american_scientific_journal-7479	206	18	form	form	NOUN
american_scientific_journal-7479	206	19	solution	solution	NOUN
american_scientific_journal-7479	206	20	of	of	ADP
american_scientific_journal-7479	206	21	the	the	DET
american_scientific_journal-7479	206	22	differential	differential	ADJ
american_scientific_journal-7479	206	23	equation	equation	NOUN
american_scientific_journal-7479	206	24	.	.	PUNCT
american_scientific_journal-7479	207	1	the	the	DET
american_scientific_journal-7479	207	2	constants	constant	NOUN
american_scientific_journal-7479	207	3	have	have	AUX
american_scientific_journal-7479	207	4	been	be	AUX
american_scientific_journal-7479	207	5	found	find	VERB
american_scientific_journal-7479	207	6	by	by	ADP
american_scientific_journal-7479	207	7	applying	apply	VERB
american_scientific_journal-7479	207	8	the	the	DET
american_scientific_journal-7479	207	9	four	four	NUM
american_scientific_journal-7479	207	10	boundary	boundary	ADJ
american_scientific_journal-7479	207	11	conditions	condition	NOUN
american_scientific_journal-7479	207	12	and	and	CCONJ
american_scientific_journal-7479	207	13	kinematics	kinematic	NOUN
american_scientific_journal-7479	207	14	conditions	condition	NOUN
american_scientific_journal-7479	207	15	of	of	ADP
american_scientific_journal-7479	207	16	the	the	DET
american_scientific_journal-7479	207	17	cracked	crack	VERB
american_scientific_journal-7479	207	18	beam	beam	NOUN
american_scientific_journal-7479	207	19	.	.	PUNCT
american_scientific_journal-7479	208	1	the	the	DET
american_scientific_journal-7479	208	2	dynamic	dynamic	ADJ
american_scientific_journal-7479	208	3	response	response	NOUN
american_scientific_journal-7479	208	4	of	of	ADP
american_scientific_journal-7479	208	5	cracked	crack	VERB
american_scientific_journal-7479	208	6	beam	beam	NOUN
american_scientific_journal-7479	208	7	under	under	ADP
american_scientific_journal-7479	208	8	moving	move	VERB
american_scientific_journal-7479	208	9	load	load	NOUN
american_scientific_journal-7479	208	10	can	can	AUX
american_scientific_journal-7479	208	11	be	be	AUX
american_scientific_journal-7479	208	12	found	find	VERB
american_scientific_journal-7479	208	13	from	from	ADP
american_scientific_journal-7479	208	14	substituting	substitute	VERB
american_scientific_journal-7479	208	15	eq	eq	ADP
american_scientific_journal-7479	208	16	.	.	PUNCT
american_scientific_journal-7479	209	1	(	(	PUNCT
american_scientific_journal-7479	209	2	23	23	NUM
american_scientific_journal-7479	209	3	)	)	PUNCT
american_scientific_journal-7479	209	4	and	and	CCONJ
american_scientific_journal-7479	209	5	eq	eq	NOUN
american_scientific_journal-7479	209	6	.	.	PUNCT
american_scientific_journal-7479	210	1	(	(	PUNCT
american_scientific_journal-7479	210	2	42	42	NUM
american_scientific_journal-7479	210	3	)	)	PUNCT
american_scientific_journal-7479	210	4	into	into	ADP
american_scientific_journal-7479	210	5	eq	eq	NOUN
american_scientific_journal-7479	210	6	.	.	PUNCT
american_scientific_journal-7479	211	1	(	(	PUNCT
american_scientific_journal-7479	211	2	28	28	NUM
american_scientific_journal-7479	211	3	)	)	PUNCT
american_scientific_journal-7479	211	4	.	.	PUNCT
american_scientific_journal-7479	212	1	4	4	X
american_scientific_journal-7479	212	2	.	.	X
american_scientific_journal-7479	212	3	numerical	numerical	ADJ
american_scientific_journal-7479	212	4	results	result	NOUN
american_scientific_journal-7479	212	5	and	and	CCONJ
american_scientific_journal-7479	212	6	discussion	discussion	NOUN
american_scientific_journal-7479	212	7	4.1	4.1	NUM
american_scientific_journal-7479	212	8	.	.	PUNCT
american_scientific_journal-7479	213	1	validation	validation	NOUN
american_scientific_journal-7479	213	2	in	in	ADP
american_scientific_journal-7479	213	3	this	this	DET
american_scientific_journal-7479	213	4	subsection	subsection	NOUN
american_scientific_journal-7479	213	5	,	,	PUNCT
american_scientific_journal-7479	213	6	the	the	DET
american_scientific_journal-7479	213	7	accuracy	accuracy	NOUN
american_scientific_journal-7479	213	8	and	and	CCONJ
american_scientific_journal-7479	213	9	efficiency	efficiency	NOUN
american_scientific_journal-7479	213	10	of	of	ADP
american_scientific_journal-7479	213	11	adm	adm	PROPN
american_scientific_journal-7479	213	12	solutions	solution	NOUN
american_scientific_journal-7479	213	13	are	be	AUX
american_scientific_journal-7479	213	14	investigated	investigate	VERB
american_scientific_journal-7479	213	15	through	through	ADP
american_scientific_journal-7479	213	16	a	a	DET
american_scientific_journal-7479	213	17	comparison	comparison	NOUN
american_scientific_journal-7479	213	18	with	with	ADP
american_scientific_journal-7479	213	19	those	those	PRON
american_scientific_journal-7479	213	20	obtained	obtain	VERB
american_scientific_journal-7479	213	21	from	from	ADP
american_scientific_journal-7479	213	22	fem	fem	PROPN
american_scientific_journal-7479	213	23	.	.	PUNCT
american_scientific_journal-7479	214	1	the	the	DET
american_scientific_journal-7479	214	2	adm	adm	PROPN
american_scientific_journal-7479	214	3	model	model	NOUN
american_scientific_journal-7479	214	4	developed	develop	VERB
american_scientific_journal-7479	214	5	in	in	ADP
american_scientific_journal-7479	214	6	this	this	DET
american_scientific_journal-7479	214	7	article	article	NOUN
american_scientific_journal-7479	214	8	is	be	AUX
american_scientific_journal-7479	214	9	applied	apply	VERB
american_scientific_journal-7479	214	10	to	to	ADP
american_scientific_journal-7479	214	11	a	a	DET
american_scientific_journal-7479	214	12	sscb	sscb	NOUN
american_scientific_journal-7479	214	13	under	under	ADP
american_scientific_journal-7479	214	14	a	a	DET
american_scientific_journal-7479	214	15	moving	move	VERB
american_scientific_journal-7479	214	16	load	load	NOUN
american_scientific_journal-7479	214	17	.	.	PUNCT
american_scientific_journal-7479	215	1	the	the	DET
american_scientific_journal-7479	215	2	numerical	numerical	ADJ
american_scientific_journal-7479	215	3	values	value	NOUN
american_scientific_journal-7479	215	4	of	of	ADP
american_scientific_journal-7479	215	5	geometrical	geometrical	ADJ
american_scientific_journal-7479	215	6	and	and	CCONJ
american_scientific_journal-7479	215	7	material	material	NOUN
american_scientific_journal-7479	215	8	parameters	parameter	NOUN
american_scientific_journal-7479	215	9	of	of	ADP
american_scientific_journal-7479	215	10	the	the	DET
american_scientific_journal-7479	215	11	euler	euler	PROPN
american_scientific_journal-7479	215	12	bernoulli	bernoulli	PROPN
american_scientific_journal-7479	215	13	beam	beam	PROPN
american_scientific_journal-7479	215	14	are	be	AUX
american_scientific_journal-7479	215	15	:	:	PUNCT
american_scientific_journal-7479	215	16	length	length	NOUN
american_scientific_journal-7479	215	17	l	l	NOUN
american_scientific_journal-7479	215	18	=	=	SYM
american_scientific_journal-7479	215	19	5(m	5(m	NUM
american_scientific_journal-7479	215	20	)	)	PUNCT
american_scientific_journal-7479	215	21	,	,	PUNCT
american_scientific_journal-7479	215	22	young	young	PROPN
american_scientific_journal-7479	215	23	’s	’s	PART
american_scientific_journal-7479	215	24	modulus	modulus	ADJ
american_scientific_journal-7479	215	25	e	e	NOUN
american_scientific_journal-7479	215	26	=	=	PUNCT
american_scientific_journal-7479	215	27	2.1×1011(gpa	2.1×1011(gpa	NOUN
american_scientific_journal-7479	215	28	)	)	PUNCT
american_scientific_journal-7479	215	29	,	,	PUNCT
american_scientific_journal-7479	215	30	cross	cross	ADJ
american_scientific_journal-7479	215	31	-	-	ADJ
american_scientific_journal-7479	215	32	sectional	sectional	ADJ
american_scientific_journal-7479	215	33	second	second	ADJ
american_scientific_journal-7479	215	34	moment	moment	NOUN
american_scientific_journal-7479	215	35	of	of	ADP
american_scientific_journal-7479	215	36	inertia	inertia	NOUN
american_scientific_journal-7479	216	1	i	i	PRON
american_scientific_journal-7479	216	2	=	=	PUNCT
american_scientific_journal-7479	216	3	𝑏×ℎ3	𝑏×ℎ3	ADV
american_scientific_journal-7479	216	4	12	12	NUM
american_scientific_journal-7479	216	5	(	(	PUNCT
american_scientific_journal-7479	216	6	𝑚4),width	𝑚4),width	NUM
american_scientific_journal-7479	216	7	b	b	X
american_scientific_journal-7479	216	8	=	=	NOUN
american_scientific_journal-7479	216	9	0.5(m	0.5(m	NUM
american_scientific_journal-7479	216	10	)	)	PUNCT
american_scientific_journal-7479	216	11	,	,	PUNCT
american_scientific_journal-7479	216	12	height	height	NOUN
american_scientific_journal-7479	216	13	h	h	NOUN
american_scientific_journal-7479	216	14	=	=	NOUN
american_scientific_journal-7479	216	15	1(m	1(m	NUM
american_scientific_journal-7479	216	16	)	)	PUNCT
american_scientific_journal-7479	216	17	,	,	PUNCT
american_scientific_journal-7479	216	18	mass	mass	NOUN
american_scientific_journal-7479	216	19	density	density	NOUN
american_scientific_journal-7479	216	20	ρ	ρ	PROPN
american_scientific_journal-7479	216	21	=	=	SYM
american_scientific_journal-7479	216	22	7860(kg/𝑚3	7860(kg/𝑚3	NUM
american_scientific_journal-7479	216	23	)	)	PUNCT
american_scientific_journal-7479	216	24	(	(	PUNCT
american_scientific_journal-7479	216	25	mahmoud	mahmoud	PROPN
american_scientific_journal-7479	216	26	,	,	PUNCT
american_scientific_journal-7479	216	27	2001	2001	NUM
american_scientific_journal-7479	216	28	)	)	PUNCT
american_scientific_journal-7479	216	29	.	.	PUNCT
american_scientific_journal-7479	217	1	to	to	PART
american_scientific_journal-7479	217	2	obtain	obtain	VERB
american_scientific_journal-7479	217	3	the	the	DET
american_scientific_journal-7479	217	4	dynamic	dynamic	ADJ
american_scientific_journal-7479	217	5	response	response	NOUN
american_scientific_journal-7479	217	6	of	of	ADP
american_scientific_journal-7479	217	7	cracked	crack	VERB
american_scientific_journal-7479	217	8	beams	beam	NOUN
american_scientific_journal-7479	217	9	under	under	ADP
american_scientific_journal-7479	217	10	a	a	DET
american_scientific_journal-7479	217	11	moving	move	VERB
american_scientific_journal-7479	217	12	load	load	NOUN
american_scientific_journal-7479	217	13	,	,	PUNCT
american_scientific_journal-7479	217	14	equations	equation	NOUN
american_scientific_journal-7479	217	15	(	(	PUNCT
american_scientific_journal-7479	217	16	23	23	NUM
american_scientific_journal-7479	217	17	)	)	PUNCT
american_scientific_journal-7479	217	18	,	,	PUNCT
american_scientific_journal-7479	217	19	(	(	PUNCT
american_scientific_journal-7479	217	20	28	28	NUM
american_scientific_journal-7479	217	21	)	)	PUNCT
american_scientific_journal-7479	217	22	and	and	CCONJ
american_scientific_journal-7479	217	23	(	(	PUNCT
american_scientific_journal-7479	217	24	42	42	NUM
american_scientific_journal-7479	217	25	)	)	PUNCT
american_scientific_journal-7479	217	26	is	be	AUX
american_scientific_journal-7479	217	27	used	use	VERB
american_scientific_journal-7479	217	28	for	for	ADP
american_scientific_journal-7479	217	29	an	an	DET
american_scientific_journal-7479	217	30	adm	adm	NOUN
american_scientific_journal-7479	217	31	analysis	analysis	NOUN
american_scientific_journal-7479	217	32	,	,	PUNCT
american_scientific_journal-7479	217	33	the	the	DET
american_scientific_journal-7479	217	34	corresponding	corresponding	ADJ
american_scientific_journal-7479	217	35	numerical	numerical	ADJ
american_scientific_journal-7479	217	36	results	result	NOUN
american_scientific_journal-7479	217	37	are	be	AUX
american_scientific_journal-7479	217	38	denoted	denote	VERB
american_scientific_journal-7479	217	39	by	by	ADP
american_scientific_journal-7479	217	40	adm	adm	PROPN
american_scientific_journal-7479	217	41	.	.	PUNCT
american_scientific_journal-7479	218	1	on	on	ADP
american_scientific_journal-7479	218	2	the	the	DET
american_scientific_journal-7479	218	3	other	other	ADJ
american_scientific_journal-7479	218	4	hand	hand	NOUN
american_scientific_journal-7479	218	5	,	,	PUNCT
american_scientific_journal-7479	218	6	for	for	ADP
american_scientific_journal-7479	218	7	an	an	DET
american_scientific_journal-7479	218	8	fem	fem	NOUN
american_scientific_journal-7479	218	9	analysis	analysis	NOUN
american_scientific_journal-7479	218	10	,	,	PUNCT
american_scientific_journal-7479	218	11	the	the	DET
american_scientific_journal-7479	218	12	total	total	ADJ
american_scientific_journal-7479	218	13	number	number	NOUN
american_scientific_journal-7479	218	14	of	of	ADP
american_scientific_journal-7479	218	15	finite	finite	ADJ
american_scientific_journal-7479	218	16	elements	element	NOUN
american_scientific_journal-7479	218	17	used	use	VERB
american_scientific_journal-7479	218	18	in	in	ADP
american_scientific_journal-7479	218	19	the	the	DET
american_scientific_journal-7479	218	20	analysis	analysis	NOUN
american_scientific_journal-7479	218	21	is	be	AUX
american_scientific_journal-7479	218	22	varied	varied	ADJ
american_scientific_journal-7479	218	23	in	in	ADP
american_scientific_journal-7479	218	24	order	order	NOUN
american_scientific_journal-7479	218	25	to	to	PART
american_scientific_journal-7479	218	26	improve	improve	VERB
american_scientific_journal-7479	218	27	the	the	DET
american_scientific_journal-7479	218	28	numerical	numerical	ADJ
american_scientific_journal-7479	218	29	accuracy	accuracy	NOUN
american_scientific_journal-7479	218	30	;	;	PUNCT
american_scientific_journal-7479	218	31	and	and	CCONJ
american_scientific_journal-7479	218	32	the	the	DET
american_scientific_journal-7479	218	33	corresponding	corresponding	ADJ
american_scientific_journal-7479	218	34	results	result	NOUN
american_scientific_journal-7479	218	35	are	be	AUX
american_scientific_journal-7479	218	36	denoted	denote	VERB
american_scientific_journal-7479	218	37	by	by	ADP
american_scientific_journal-7479	218	38	fem	fem	PROPN
american_scientific_journal-7479	218	39	.	.	PUNCT
american_scientific_journal-7479	219	1	the	the	DET
american_scientific_journal-7479	219	2	dynamic	dynamic	ADJ
american_scientific_journal-7479	219	3	transverse	transverse	NOUN
american_scientific_journal-7479	219	4	deflections	deflection	NOUN
american_scientific_journal-7479	219	5	against	against	ADP
american_scientific_journal-7479	219	6	time	time	NOUN
american_scientific_journal-7479	219	7	response	response	NOUN
american_scientific_journal-7479	219	8	are	be	AUX
american_scientific_journal-7479	219	9	normalized	normalize	VERB
american_scientific_journal-7479	219	10	relative	relative	ADJ
american_scientific_journal-7479	219	11	to	to	ADP
american_scientific_journal-7479	219	12	the	the	DET
american_scientific_journal-7479	219	13	value	value	NOUN
american_scientific_journal-7479	219	14	,	,	PUNCT
american_scientific_journal-7479	219	15	𝐹𝐿3	𝐹𝐿3	PROPN
american_scientific_journal-7479	219	16	48𝐸𝐼	48𝐸𝐼	NUM
american_scientific_journal-7479	219	17	,	,	PUNCT
american_scientific_journal-7479	219	18	which	which	PRON
american_scientific_journal-7479	219	19	is	be	AUX
american_scientific_journal-7479	219	20	the	the	DET
american_scientific_journal-7479	219	21	related	relate	VERB
american_scientific_journal-7479	219	22	static	static	ADJ
american_scientific_journal-7479	219	23	deflection	deflection	NOUN
american_scientific_journal-7479	219	24	was	be	AUX
american_scientific_journal-7479	219	25	applied	apply	VERB
american_scientific_journal-7479	219	26	to	to	ADP
american_scientific_journal-7479	219	27	the	the	DET
american_scientific_journal-7479	219	28	mid	mid	ADJ
american_scientific_journal-7479	219	29	-	-	ADJ
american_scientific_journal-7479	219	30	span	span	NOUN
american_scientific_journal-7479	219	31	beam	beam	NOUN
american_scientific_journal-7479	219	32	due	due	ADP
american_scientific_journal-7479	219	33	to	to	PART
american_scientific_journal-7479	219	34	load	load	VERB
american_scientific_journal-7479	219	35	amplitude	amplitude	NOUN
american_scientific_journal-7479	219	36	f.	f.	NOUN
american_scientific_journal-7479	219	37	4.2	4.2	NUM
american_scientific_journal-7479	219	38	moving	move	VERB
american_scientific_journal-7479	219	39	load	load	NOUN
american_scientific_journal-7479	219	40	with	with	ADP
american_scientific_journal-7479	219	41	constant	constant	ADJ
american_scientific_journal-7479	219	42	velocity	velocity	NOUN
american_scientific_journal-7479	219	43	for	for	ADP
american_scientific_journal-7479	219	44	example	example	NOUN
american_scientific_journal-7479	219	45	,	,	PUNCT
american_scientific_journal-7479	219	46	a	a	DET
american_scientific_journal-7479	219	47	moveable	moveable	ADJ
american_scientific_journal-7479	219	48	load	load	NOUN
american_scientific_journal-7479	219	49	with	with	ADP
american_scientific_journal-7479	219	50	a	a	DET
american_scientific_journal-7479	219	51	constant	constant	ADJ
american_scientific_journal-7479	219	52	load	load	NOUN
american_scientific_journal-7479	219	53	amplitude	amplitude	NOUN
american_scientific_journal-7479	219	54	f	f	NOUN
american_scientific_journal-7479	219	55	=	=	SYM
american_scientific_journal-7479	219	56	2000(n	2000(n	X
american_scientific_journal-7479	219	57	)	)	PUNCT
american_scientific_journal-7479	219	58	,	,	PUNCT
american_scientific_journal-7479	219	59	a	a	DET
american_scientific_journal-7479	219	60	constant	constant	ADJ
american_scientific_journal-7479	219	61	velocity	velocity	NOUN
american_scientific_journal-7479	219	62	v	v	ADP
american_scientific_journal-7479	219	63	=	=	SYM
american_scientific_journal-7479	219	64	80(m	80(m	NUM
american_scientific_journal-7479	219	65	/	/	SYM
american_scientific_journal-7479	219	66	s	s	NOUN
american_scientific_journal-7479	219	67	)	)	PUNCT
american_scientific_journal-7479	219	68	and	and	CCONJ
american_scientific_journal-7479	219	69	initial	initial	ADJ
american_scientific_journal-7479	219	70	zero	zero	NUM
american_scientific_journal-7479	219	71	conditions	condition	NOUN
american_scientific_journal-7479	219	72	0	0	NUM
american_scientific_journal-7479	219	73	are	be	AUX
american_scientific_journal-7479	219	74	taken	take	VERB
american_scientific_journal-7479	219	75	into	into	ADP
american_scientific_journal-7479	219	76	consideration	consideration	NOUN
american_scientific_journal-7479	219	77	.	.	PUNCT
american_scientific_journal-7479	220	1	fig.2	fig.2	PROPN
american_scientific_journal-7479	220	2	,	,	PUNCT
american_scientific_journal-7479	220	3	indicates	indicate	VERB
american_scientific_journal-7479	220	4	the	the	DET
american_scientific_journal-7479	220	5	normalized	normalized	ADJ
american_scientific_journal-7479	220	6	deflection	deflection	NOUN
american_scientific_journal-7479	220	7	for	for	ADP
american_scientific_journal-7479	220	8	mid	mid	NOUN
american_scientific_journal-7479	220	9	-	-	NOUN
american_scientific_journal-7479	220	10	point	point	NOUN
american_scientific_journal-7479	220	11	of	of	ADP
american_scientific_journal-7479	220	12	the	the	DET
american_scientific_journal-7479	220	13	beam	beam	NOUN
american_scientific_journal-7479	220	14	.	.	PUNCT
american_scientific_journal-7479	221	1	in	in	ADP
american_scientific_journal-7479	221	2	this	this	DET
american_scientific_journal-7479	221	3	figure	figure	NOUN
american_scientific_journal-7479	221	4	,	,	PUNCT
american_scientific_journal-7479	221	5	v𝑡	v𝑡	PROPN
american_scientific_journal-7479	221	6	𝐿	𝐿	PROPN
american_scientific_journal-7479	221	7	indicate	indicate	VERB
american_scientific_journal-7479	221	8	to	to	ADP
american_scientific_journal-7479	221	9	the	the	DET
american_scientific_journal-7479	221	10	normalized	normalize	VERB
american_scientific_journal-7479	221	11	position	position	NOUN
american_scientific_journal-7479	221	12	of	of	ADP
american_scientific_journal-7479	221	13	moving	move	VERB
american_scientific_journal-7479	221	14	load	load	NOUN
american_scientific_journal-7479	221	15	once	once	ADV
american_scientific_journal-7479	221	16	over	over	ADP
american_scientific_journal-7479	221	17	the	the	DET
american_scientific_journal-7479	221	18	beam	beam	NOUN
american_scientific_journal-7479	221	19	.	.	PUNCT
american_scientific_journal-7479	222	1	fig	fig	NOUN
american_scientific_journal-7479	222	2	.	.	PUNCT
american_scientific_journal-7479	223	1	2	2	NUM
american_scientific_journal-7479	223	2	shows	show	VERB
american_scientific_journal-7479	223	3	that	that	SCONJ
american_scientific_journal-7479	223	4	the	the	DET
american_scientific_journal-7479	223	5	results	result	NOUN
american_scientific_journal-7479	223	6	predicted	predict	VERB
american_scientific_journal-7479	223	7	by	by	ADP
american_scientific_journal-7479	223	8	fem	fem	NOUN
american_scientific_journal-7479	223	9	model	model	NOUN
american_scientific_journal-7479	223	10	would	would	AUX
american_scientific_journal-7479	223	11	converge	converge	VERB
american_scientific_journal-7479	223	12	to	to	ADP
american_scientific_journal-7479	223	13	those	those	PRON
american_scientific_journal-7479	223	14	predicted	predict	VERB
american_scientific_journal-7479	223	15	by	by	ADP
american_scientific_journal-7479	223	16	the	the	DET
american_scientific_journal-7479	223	17	present	present	ADJ
american_scientific_journal-7479	223	18	adm	adm	PROPN
american_scientific_journal-7479	223	19	method	method	NOUN
american_scientific_journal-7479	223	20	provided	provide	VERB
american_scientific_journal-7479	223	21	that	that	SCONJ
american_scientific_journal-7479	223	22	the	the	DET
american_scientific_journal-7479	223	23	total	total	ADJ
american_scientific_journal-7479	223	24	number	number	NOUN
american_scientific_journal-7479	223	25	of	of	ADP
american_scientific_journal-7479	223	26	elements	element	NOUN
american_scientific_journal-7479	223	27	used	use	VERB
american_scientific_journal-7479	223	28	in	in	ADP
american_scientific_journal-7479	223	29	fem	fem	NOUN
american_scientific_journal-7479	223	30	could	could	AUX
american_scientific_journal-7479	223	31	increase	increase	VERB
american_scientific_journal-7479	223	32	beyond	beyond	ADP
american_scientific_journal-7479	223	33	100	100	NUM
american_scientific_journal-7479	223	34	.	.	PUNCT
american_scientific_journal-7479	224	1	in	in	ADP
american_scientific_journal-7479	224	2	fig	fig	NOUN
american_scientific_journal-7479	224	3	.	.	PUNCT
american_scientific_journal-7479	225	1	2	2	NUM
american_scientific_journal-7479	225	2	,	,	PUNCT
american_scientific_journal-7479	225	3	it	it	PRON
american_scientific_journal-7479	225	4	is	be	AUX
american_scientific_journal-7479	225	5	seen	see	VERB
american_scientific_journal-7479	225	6	that	that	SCONJ
american_scientific_journal-7479	225	7	the	the	DET
american_scientific_journal-7479	225	8	results	result	NOUN
american_scientific_journal-7479	225	9	of	of	ADP
american_scientific_journal-7479	225	10	adm	adm	PROPN
american_scientific_journal-7479	225	11	are	be	AUX
american_scientific_journal-7479	225	12	in	in	ADP
american_scientific_journal-7479	225	13	good	good	ADJ
american_scientific_journal-7479	225	14	agreement	agreement	NOUN
american_scientific_journal-7479	225	15	with	with	ADP
american_scientific_journal-7479	225	16	those	those	PRON
american_scientific_journal-7479	225	17	of	of	ADP
american_scientific_journal-7479	225	18	exact	exact	ADJ
american_scientific_journal-7479	225	19	solution	solution	NOUN
american_scientific_journal-7479	225	20	and	and	CCONJ
american_scientific_journal-7479	225	21	closed	close	VERB
american_scientific_journal-7479	225	22	to	to	ADP
american_scientific_journal-7479	225	23	fem	fem	NOUN
american_scientific_journal-7479	225	24	solution	solution	NOUN
american_scientific_journal-7479	225	25	.	.	PUNCT
american_scientific_journal-7479	226	1	this	this	PRON
american_scientific_journal-7479	226	2	could	could	AUX
american_scientific_journal-7479	226	3	verify	verify	VERB
american_scientific_journal-7479	226	4	the	the	DET
american_scientific_journal-7479	226	5	higher	high	ADJ
american_scientific_journal-7479	226	6	accuracy	accuracy	NOUN
american_scientific_journal-7479	226	7	of	of	ADP
american_scientific_journal-7479	226	8	the	the	DET
american_scientific_journal-7479	226	9	present	present	ADJ
american_scientific_journal-7479	226	10	adm	adm	PROPN
american_scientific_journal-7479	226	11	method	method	NOUN
american_scientific_journal-7479	226	12	.	.	PUNCT
american_scientific_journal-7479	227	1	the	the	DET
american_scientific_journal-7479	227	2	percent	percent	NOUN
american_scientific_journal-7479	227	3	proportional	proportional	ADJ
american_scientific_journal-7479	227	4	error	error	NOUN
american_scientific_journal-7479	227	5	(	(	PUNCT
american_scientific_journal-7479	227	6	ppe	ppe	PROPN
american_scientific_journal-7479	227	7	)	)	PUNCT
american_scientific_journal-7479	227	8	is	be	AUX
american_scientific_journal-7479	227	9	defined	define	VERB
american_scientific_journal-7479	227	10	in	in	ADP
american_scientific_journal-7479	227	11	eq	eq	ADP
american_scientific_journal-7479	227	12	.	.	PUNCT
american_scientific_journal-7479	228	1	(	(	PUNCT
american_scientific_journal-7479	228	2	43	43	NUM
american_scientific_journal-7479	228	3	)	)	PUNCT
american_scientific_journal-7479	229	1	and	and	CCONJ
american_scientific_journal-7479	229	2	shows	show	VERB
american_scientific_journal-7479	229	3	the	the	DET
american_scientific_journal-7479	229	4	numerical	numerical	ADJ
american_scientific_journal-7479	229	5	error	error	NOUN
american_scientific_journal-7479	229	6	of	of	ADP
american_scientific_journal-7479	229	7	adm	adm	PROPN
american_scientific_journal-7479	229	8	and	and	CCONJ
american_scientific_journal-7479	229	9	fem	fem	NOUN
american_scientific_journal-7479	229	10	methods	method	NOUN
american_scientific_journal-7479	229	11	in	in	ADP
american_scientific_journal-7479	229	12	comparison	comparison	NOUN
american_scientific_journal-7479	229	13	with	with	ADP
american_scientific_journal-7479	229	14	exact	exact	ADJ
american_scientific_journal-7479	229	15	solution	solution	NOUN
american_scientific_journal-7479	229	16	and	and	CCONJ
american_scientific_journal-7479	229	17	table	table	NOUN
american_scientific_journal-7479	229	18	1	1	NUM
american_scientific_journal-7479	229	19	american	american	ADJ
american_scientific_journal-7479	229	20	academic	academic	ADJ
american_scientific_journal-7479	229	21	scientific	scientific	ADJ
american_scientific_journal-7479	229	22	research	research	NOUN
american_scientific_journal-7479	229	23	journal	journal	NOUN
american_scientific_journal-7479	229	24	for	for	ADP
american_scientific_journal-7479	229	25	engineering	engineering	NOUN
american_scientific_journal-7479	229	26	,	,	PUNCT
american_scientific_journal-7479	229	27	technology	technology	NOUN
american_scientific_journal-7479	229	28	,	,	PUNCT
american_scientific_journal-7479	229	29	and	and	CCONJ
american_scientific_journal-7479	229	30	sciences	science	NOUN
american_scientific_journal-7479	229	31	(	(	PUNCT
american_scientific_journal-7479	229	32	asrjets	asrjet	NOUN
american_scientific_journal-7479	229	33	)	)	PUNCT
american_scientific_journal-7479	229	34	(	(	PUNCT
american_scientific_journal-7479	229	35	2022	2022	NUM
american_scientific_journal-7479	229	36	)	)	PUNCT
american_scientific_journal-7479	229	37	volume	volume	NOUN
american_scientific_journal-7479	229	38	88	88	NUM
american_scientific_journal-7479	229	39	,	,	PUNCT
american_scientific_journal-7479	229	40	no1	no1	PROPN
american_scientific_journal-7479	229	41	,	,	PUNCT
american_scientific_journal-7479	229	42	pp	pp	ADV
american_scientific_journal-7479	229	43	332	332	NUM
american_scientific_journal-7479	229	44	-	-	SYM
american_scientific_journal-7479	229	45	348	348	NUM
american_scientific_journal-7479	229	46	342	342	NUM
american_scientific_journal-7479	229	47	shows	show	VERB
american_scientific_journal-7479	229	48	this	this	DET
american_scientific_journal-7479	229	49	ratio	ratio	NOUN
american_scientific_journal-7479	229	50	of	of	ADP
american_scientific_journal-7479	229	51	the	the	DET
american_scientific_journal-7479	229	52	error	error	NOUN
american_scientific_journal-7479	229	53	.	.	PUNCT
american_scientific_journal-7479	230	1	ppe(%	ppe(%	NOUN
american_scientific_journal-7479	230	2	)	)	PUNCT
american_scientific_journal-7479	231	1	=	=	SYM
american_scientific_journal-7479	231	2	exact	exact	ADJ
american_scientific_journal-7479	231	3	solution	solution	NOUN
american_scientific_journal-7479	231	4	−	−	PROPN
american_scientific_journal-7479	231	5	adm	adm	PROPN
american_scientific_journal-7479	231	6	or	or	CCONJ
american_scientific_journal-7479	231	7	fem	fem	NOUN
american_scientific_journal-7479	231	8	response	response	NOUN
american_scientific_journal-7479	231	9	exact	exact	ADJ
american_scientific_journal-7479	231	10	solution	solution	NOUN
american_scientific_journal-7479	231	11	×	×	NOUN
american_scientific_journal-7479	231	12	100	100	NUM
american_scientific_journal-7479	231	13	(	(	PUNCT
american_scientific_journal-7479	231	14	43	43	NUM
american_scientific_journal-7479	231	15	)	)	PUNCT
american_scientific_journal-7479	231	16	although	although	SCONJ
american_scientific_journal-7479	231	17	the	the	DET
american_scientific_journal-7479	231	18	numerical	numerical	ADJ
american_scientific_journal-7479	231	19	error	error	NOUN
american_scientific_journal-7479	231	20	would	would	AUX
american_scientific_journal-7479	231	21	be	be	AUX
american_scientific_journal-7479	231	22	diminished	diminish	VERB
american_scientific_journal-7479	231	23	by	by	ADP
american_scientific_journal-7479	231	24	increasing	increase	VERB
american_scientific_journal-7479	231	25	the	the	DET
american_scientific_journal-7479	231	26	number	number	NOUN
american_scientific_journal-7479	231	27	of	of	ADP
american_scientific_journal-7479	231	28	elements	element	NOUN
american_scientific_journal-7479	231	29	,	,	PUNCT
american_scientific_journal-7479	231	30	it	it	PRON
american_scientific_journal-7479	231	31	could	could	AUX
american_scientific_journal-7479	231	32	be	be	AUX
american_scientific_journal-7479	231	33	seen	see	VERB
american_scientific_journal-7479	231	34	that	that	SCONJ
american_scientific_journal-7479	231	35	the	the	DET
american_scientific_journal-7479	231	36	efficiency	efficiency	NOUN
american_scientific_journal-7479	231	37	of	of	ADP
american_scientific_journal-7479	231	38	using	use	VERB
american_scientific_journal-7479	231	39	adm	adm	PROPN
american_scientific_journal-7479	231	40	is	be	AUX
american_scientific_journal-7479	231	41	much	much	ADV
american_scientific_journal-7479	231	42	bigger	big	ADJ
american_scientific_journal-7479	231	43	than	than	ADP
american_scientific_journal-7479	231	44	that	that	PRON
american_scientific_journal-7479	231	45	using	use	VERB
american_scientific_journal-7479	231	46	numerous	numerous	ADJ
american_scientific_journal-7479	231	47	elements	element	NOUN
american_scientific_journal-7479	231	48	in	in	ADP
american_scientific_journal-7479	231	49	fem	fem	PROPN
american_scientific_journal-7479	231	50	.	.	PUNCT
american_scientific_journal-7479	232	1	section	section	NOUN
american_scientific_journal-7479	232	2	4	4	NUM
american_scientific_journal-7479	232	3	assumes	assume	VERB
american_scientific_journal-7479	232	4	that	that	SCONJ
american_scientific_journal-7479	232	5	the	the	DET
american_scientific_journal-7479	232	6	initial	initial	ADJ
american_scientific_journal-7479	232	7	conditions	condition	NOUN
american_scientific_journal-7479	232	8	for	for	ADP
american_scientific_journal-7479	232	9	numerical	numerical	ADJ
american_scientific_journal-7479	232	10	examples	example	NOUN
american_scientific_journal-7479	232	11	are	be	AUX
american_scientific_journal-7479	232	12	zero	zero	NUM
american_scientific_journal-7479	232	13	,	,	PUNCT
american_scientific_journal-7479	232	14	whereas	whereas	SCONJ
american_scientific_journal-7479	232	15	the	the	DET
american_scientific_journal-7479	232	16	moving	move	VERB
american_scientific_journal-7479	232	17	load	load	NOUN
american_scientific_journal-7479	232	18	crosses	cross	VERB
american_scientific_journal-7479	232	19	the	the	DET
american_scientific_journal-7479	232	20	beam	beam	NOUN
american_scientific_journal-7479	232	21	for	for	ADP
american_scientific_journal-7479	232	22	once	once	ADV
american_scientific_journal-7479	232	23	and	and	CCONJ
american_scientific_journal-7479	232	24	it	it	PRON
american_scientific_journal-7479	232	25	could	could	AUX
american_scientific_journal-7479	232	26	be	be	AUX
american_scientific_journal-7479	232	27	a	a	DET
american_scientific_journal-7479	232	28	pseudo	pseudo	NOUN
american_scientific_journal-7479	232	29	initial	initial	ADJ
american_scientific_journal-7479	232	30	condition	condition	NOUN
american_scientific_journal-7479	232	31	for	for	ADP
american_scientific_journal-7479	232	32	a	a	DET
american_scientific_journal-7479	232	33	euler	euler	PROPN
american_scientific_journal-7479	232	34	bernoulli	bernoulli	PROPN
american_scientific_journal-7479	232	35	beam	beam	NOUN
american_scientific_journal-7479	232	36	.	.	PUNCT
american_scientific_journal-7479	233	1	pseudo	pseudo	NOUN
american_scientific_journal-7479	233	2	initial	initial	ADJ
american_scientific_journal-7479	233	3	speed	speed	NOUN
american_scientific_journal-7479	233	4	situation	situation	NOUN
american_scientific_journal-7479	233	5	means	mean	VERB
american_scientific_journal-7479	233	6	a	a	DET
american_scientific_journal-7479	233	7	pulse	pulse	NOUN
american_scientific_journal-7479	233	8	function	function	NOUN
american_scientific_journal-7479	233	9	that	that	PRON
american_scientific_journal-7479	233	10	limits	limit	VERB
american_scientific_journal-7479	233	11	dirac	dirac	PROPN
american_scientific_journal-7479	233	12	delta	delta	NOUN
american_scientific_journal-7479	233	13	function	function	NOUN
american_scientific_journal-7479	233	14	at	at	ADP
american_scientific_journal-7479	233	15	a	a	DET
american_scientific_journal-7479	233	16	not	not	PART
american_scientific_journal-7479	233	17	so	so	ADV
american_scientific_journal-7479	233	18	small	small	ADJ
american_scientific_journal-7479	233	19	-	-	PUNCT
american_scientific_journal-7479	233	20	time	time	NOUN
american_scientific_journal-7479	233	21	interval	interval	NOUN
american_scientific_journal-7479	233	22	that	that	PRON
american_scientific_journal-7479	233	23	might	might	AUX
american_scientific_journal-7479	233	24	mimic	mimic	VERB
american_scientific_journal-7479	233	25	the	the	DET
american_scientific_journal-7479	233	26	function	function	NOUN
american_scientific_journal-7479	233	27	of	of	ADP
american_scientific_journal-7479	233	28	theoretical	theoretical	ADJ
american_scientific_journal-7479	233	29	impulses	impulse	NOUN
american_scientific_journal-7479	233	30	but	but	CCONJ
american_scientific_journal-7479	233	31	is	be	AUX
american_scientific_journal-7479	233	32	very	very	ADV
american_scientific_journal-7479	233	33	close	close	ADJ
american_scientific_journal-7479	233	34	to	to	ADP
american_scientific_journal-7479	233	35	it	it	PRON
american_scientific_journal-7479	233	36	.	.	PUNCT
american_scientific_journal-7479	234	1	fig.3	fig.3	PROPN
american_scientific_journal-7479	234	2	shows	show	VERB
american_scientific_journal-7479	234	3	a	a	DET
american_scientific_journal-7479	234	4	normalized	normalize	VERB
american_scientific_journal-7479	234	5	dynamic	dynamic	ADJ
american_scientific_journal-7479	234	6	response	response	NOUN
american_scientific_journal-7479	234	7	for	for	ADP
american_scientific_journal-7479	234	8	different	different	ADJ
american_scientific_journal-7479	234	9	load	load	NOUN
american_scientific_journal-7479	234	10	speeds	speed	NOUN
american_scientific_journal-7479	234	11	with	with	ADP
american_scientific_journal-7479	234	12	adm	adm	PROPN
american_scientific_journal-7479	234	13	and	and	CCONJ
american_scientific_journal-7479	234	14	fem	fem	NOUN
american_scientific_journal-7479	234	15	(	(	PUNCT
american_scientific_journal-7479	234	16	100	100	NUM
american_scientific_journal-7479	234	17	elements	element	NOUN
american_scientific_journal-7479	234	18	)	)	PUNCT
american_scientific_journal-7479	234	19	at	at	ADP
american_scientific_journal-7479	234	20	the	the	DET
american_scientific_journal-7479	234	21	mid	mid	NOUN
american_scientific_journal-7479	234	22	-	-	NOUN
american_scientific_journal-7479	234	23	span	span	NOUN
american_scientific_journal-7479	234	24	of	of	ADP
american_scientific_journal-7479	234	25	a	a	DET
american_scientific_journal-7479	234	26	cracked	crack	VERB
american_scientific_journal-7479	234	27	beam	beam	NOUN
american_scientific_journal-7479	234	28	.	.	PUNCT
american_scientific_journal-7479	235	1	as	as	SCONJ
american_scientific_journal-7479	235	2	predicted	predict	VERB
american_scientific_journal-7479	235	3	,	,	PUNCT
american_scientific_journal-7479	235	4	an	an	DET
american_scientific_journal-7479	235	5	increase	increase	NOUN
american_scientific_journal-7479	235	6	in	in	ADP
american_scientific_journal-7479	235	7	load	load	NOUN
american_scientific_journal-7479	235	8	velocity	velocity	NOUN
american_scientific_journal-7479	235	9	will	will	AUX
american_scientific_journal-7479	235	10	cause	cause	VERB
american_scientific_journal-7479	235	11	the	the	DET
american_scientific_journal-7479	235	12	maximum	maximum	ADJ
american_scientific_journal-7479	235	13	dynamic	dynamic	ADJ
american_scientific_journal-7479	235	14	deflection	deflection	NOUN
american_scientific_journal-7479	235	15	to	to	PART
american_scientific_journal-7479	235	16	correspondingly	correspondingly	ADV
american_scientific_journal-7479	235	17	increase	increase	VERB
american_scientific_journal-7479	235	18	.	.	PUNCT
american_scientific_journal-7479	236	1	fig.4	fig.4	PROPN
american_scientific_journal-7479	236	2	shows	show	VERB
american_scientific_journal-7479	236	3	the	the	DET
american_scientific_journal-7479	236	4	effect	effect	NOUN
american_scientific_journal-7479	236	5	of	of	ADP
american_scientific_journal-7479	236	6	moving	move	VERB
american_scientific_journal-7479	236	7	load	load	NOUN
american_scientific_journal-7479	236	8	amplitude	amplitude	NOUN
american_scientific_journal-7479	236	9	on	on	ADP
american_scientific_journal-7479	236	10	the	the	DET
american_scientific_journal-7479	236	11	dynamic	dynamic	ADJ
american_scientific_journal-7479	236	12	deflection	deflection	NOUN
american_scientific_journal-7479	236	13	response	response	NOUN
american_scientific_journal-7479	236	14	at	at	ADP
american_scientific_journal-7479	236	15	the	the	DET
american_scientific_journal-7479	236	16	midpoint	midpoint	NOUN
american_scientific_journal-7479	236	17	of	of	ADP
american_scientific_journal-7479	236	18	a	a	DET
american_scientific_journal-7479	236	19	cracked	crack	VERB
american_scientific_journal-7479	236	20	beam	beam	NOUN
american_scientific_journal-7479	236	21	at	at	ADP
american_scientific_journal-7479	236	22	constant	constant	ADJ
american_scientific_journal-7479	236	23	velocity	velocity	NOUN
american_scientific_journal-7479	236	24	v	v	ADP
american_scientific_journal-7479	236	25	=	=	SYM
american_scientific_journal-7479	236	26	70	70	NUM
american_scientific_journal-7479	236	27	(	(	PUNCT
american_scientific_journal-7479	236	28	m	m	PROPN
american_scientific_journal-7479	236	29	/	/	SYM
american_scientific_journal-7479	236	30	s	s	PART
american_scientific_journal-7479	236	31	)	)	PUNCT
american_scientific_journal-7479	236	32	under	under	ADP
american_scientific_journal-7479	236	33	moving	move	VERB
american_scientific_journal-7479	236	34	load	load	NOUN
american_scientific_journal-7479	236	35	.	.	PUNCT
american_scientific_journal-7479	237	1	it	it	PRON
american_scientific_journal-7479	237	2	can	can	AUX
american_scientific_journal-7479	237	3	be	be	AUX
american_scientific_journal-7479	237	4	seen	see	VERB
american_scientific_journal-7479	237	5	that	that	SCONJ
american_scientific_journal-7479	237	6	by	by	ADP
american_scientific_journal-7479	237	7	increasing	increase	VERB
american_scientific_journal-7479	237	8	the	the	DET
american_scientific_journal-7479	237	9	load	load	NOUN
american_scientific_journal-7479	237	10	amplitude	amplitude	NOUN
american_scientific_journal-7479	237	11	from	from	ADP
american_scientific_journal-7479	237	12	1000	1000	NUM
american_scientific_journal-7479	237	13	(	(	PUNCT
american_scientific_journal-7479	237	14	n	n	CCONJ
american_scientific_journal-7479	237	15	)	)	PUNCT
american_scientific_journal-7479	237	16	to	to	ADP
american_scientific_journal-7479	237	17	2000	2000	NUM
american_scientific_journal-7479	237	18	(	(	PUNCT
american_scientific_journal-7479	237	19	n	n	CCONJ
american_scientific_journal-7479	237	20	)	)	PUNCT
american_scientific_journal-7479	237	21	,	,	PUNCT
american_scientific_journal-7479	237	22	the	the	DET
american_scientific_journal-7479	237	23	mid	mid	ADJ
american_scientific_journal-7479	237	24	-	-	ADJ
american_scientific_journal-7479	237	25	point	point	NOUN
american_scientific_journal-7479	237	26	deflection	deflection	NOUN
american_scientific_journal-7479	237	27	of	of	ADP
american_scientific_journal-7479	237	28	cracked	crack	VERB
american_scientific_journal-7479	237	29	beam	beam	NOUN
american_scientific_journal-7479	237	30	is	be	AUX
american_scientific_journal-7479	237	31	increased	increase	VERB
american_scientific_journal-7479	237	32	.	.	PUNCT
american_scientific_journal-7479	238	1	fig.5	fig.5	NOUN
american_scientific_journal-7479	238	2	shows	show	VERB
american_scientific_journal-7479	238	3	the	the	DET
american_scientific_journal-7479	238	4	difference	difference	NOUN
american_scientific_journal-7479	238	5	between	between	ADP
american_scientific_journal-7479	238	6	the	the	DET
american_scientific_journal-7479	238	7	mid	mid	ADJ
american_scientific_journal-7479	238	8	-	-	ADJ
american_scientific_journal-7479	238	9	point	point	NOUN
american_scientific_journal-7479	238	10	deflection	deflection	NOUN
american_scientific_journal-7479	238	11	of	of	ADP
american_scientific_journal-7479	238	12	the	the	DET
american_scientific_journal-7479	238	13	cracked	crack	VERB
american_scientific_journal-7479	238	14	beam	beam	NOUN
american_scientific_journal-7479	238	15	and	and	CCONJ
american_scientific_journal-7479	238	16	the	the	DET
american_scientific_journal-7479	238	17	same	same	ADJ
american_scientific_journal-7479	238	18	one	one	NUM
american_scientific_journal-7479	238	19	for	for	ADP
american_scientific_journal-7479	238	20	an	an	DET
american_scientific_journal-7479	238	21	intact	intact	ADJ
american_scientific_journal-7479	238	22	beam	beam	NOUN
american_scientific_journal-7479	238	23	(	(	PUNCT
american_scientific_journal-7479	238	24	uncracked	uncracked	ADJ
american_scientific_journal-7479	238	25	beam	beam	NOUN
american_scientific_journal-7479	238	26	)	)	PUNCT
american_scientific_journal-7479	238	27	.	.	PUNCT
american_scientific_journal-7479	239	1	it	it	PRON
american_scientific_journal-7479	239	2	is	be	AUX
american_scientific_journal-7479	239	3	seen	see	VERB
american_scientific_journal-7479	239	4	that	that	SCONJ
american_scientific_journal-7479	239	5	the	the	DET
american_scientific_journal-7479	239	6	maximum	maximum	ADJ
american_scientific_journal-7479	239	7	mid	mid	ADJ
american_scientific_journal-7479	239	8	-	-	ADJ
american_scientific_journal-7479	239	9	span	span	ADJ
american_scientific_journal-7479	239	10	deflection	deflection	NOUN
american_scientific_journal-7479	239	11	of	of	ADP
american_scientific_journal-7479	239	12	the	the	DET
american_scientific_journal-7479	239	13	beam	beam	NOUN
american_scientific_journal-7479	239	14	with	with	ADP
american_scientific_journal-7479	239	15	open	open	ADJ
american_scientific_journal-7479	239	16	crack	crack	NOUN
american_scientific_journal-7479	239	17	is	be	AUX
american_scientific_journal-7479	239	18	greater	great	ADJ
american_scientific_journal-7479	239	19	than	than	ADP
american_scientific_journal-7479	239	20	that	that	PRON
american_scientific_journal-7479	239	21	of	of	ADP
american_scientific_journal-7479	239	22	the	the	DET
american_scientific_journal-7479	239	23	healthy	healthy	ADJ
american_scientific_journal-7479	239	24	beam	beam	NOUN
american_scientific_journal-7479	239	25	.	.	PUNCT
american_scientific_journal-7479	240	1	in	in	ADP
american_scientific_journal-7479	240	2	addition	addition	NOUN
american_scientific_journal-7479	240	3	,	,	PUNCT
american_scientific_journal-7479	240	4	the	the	DET
american_scientific_journal-7479	240	5	time	time	NOUN
american_scientific_journal-7479	240	6	response	response	NOUN
american_scientific_journal-7479	240	7	of	of	ADP
american_scientific_journal-7479	240	8	mid	mid	ADJ
american_scientific_journal-7479	240	9	-	-	ADJ
american_scientific_journal-7479	240	10	span	span	NOUN
american_scientific_journal-7479	240	11	deflection	deflection	NOUN
american_scientific_journal-7479	240	12	causes	cause	VERB
american_scientific_journal-7479	240	13	a	a	DET
american_scientific_journal-7479	240	14	horizontal	horizontal	ADJ
american_scientific_journal-7479	240	15	shift	shift	NOUN
american_scientific_journal-7479	240	16	-	-	PUNCT
american_scientific_journal-7479	240	17	intime	intime	NOUN
american_scientific_journal-7479	240	18	.	.	PUNCT
american_scientific_journal-7479	241	1	such	such	ADJ
american_scientific_journal-7479	241	2	vertical	vertical	ADJ
american_scientific_journal-7479	241	3	and	and	CCONJ
american_scientific_journal-7479	241	4	horizontal	horizontal	ADJ
american_scientific_journal-7479	241	5	shifts	shift	NOUN
american_scientific_journal-7479	241	6	in	in	ADP
american_scientific_journal-7479	241	7	the	the	DET
american_scientific_journal-7479	241	8	response	response	NOUN
american_scientific_journal-7479	241	9	time	time	NOUN
american_scientific_journal-7479	241	10	signals	signal	NOUN
american_scientific_journal-7479	241	11	will	will	AUX
american_scientific_journal-7479	241	12	occur	occur	VERB
american_scientific_journal-7479	241	13	because	because	SCONJ
american_scientific_journal-7479	241	14	the	the	DET
american_scientific_journal-7479	241	15	stiffness	stiffness	NOUN
american_scientific_journal-7479	241	16	of	of	ADP
american_scientific_journal-7479	241	17	the	the	DET
american_scientific_journal-7479	241	18	cracked	crack	VERB
american_scientific_journal-7479	241	19	beam	beam	NOUN
american_scientific_journal-7479	241	20	is	be	AUX
american_scientific_journal-7479	241	21	lower	low	ADJ
american_scientific_journal-7479	241	22	than	than	ADP
american_scientific_journal-7479	241	23	that	that	PRON
american_scientific_journal-7479	241	24	of	of	ADP
american_scientific_journal-7479	241	25	the	the	DET
american_scientific_journal-7479	241	26	healthy	healthy	ADJ
american_scientific_journal-7479	241	27	beam	beam	NOUN
american_scientific_journal-7479	241	28	.	.	PUNCT
american_scientific_journal-7479	242	1	the	the	DET
american_scientific_journal-7479	242	2	good	good	ADJ
american_scientific_journal-7479	242	3	agreement	agreement	NOUN
american_scientific_journal-7479	242	4	between	between	ADP
american_scientific_journal-7479	242	5	the	the	DET
american_scientific_journal-7479	242	6	results	result	NOUN
american_scientific_journal-7479	242	7	from	from	ADP
american_scientific_journal-7479	242	8	adm	adm	PROPN
american_scientific_journal-7479	242	9	and	and	CCONJ
american_scientific_journal-7479	242	10	from	from	ADP
american_scientific_journal-7479	242	11	those	those	PRON
american_scientific_journal-7479	242	12	of	of	ADP
american_scientific_journal-7479	242	13	transfer	transfer	NOUN
american_scientific_journal-7479	242	14	matrix	matrix	NOUN
american_scientific_journal-7479	242	15	method	method	NOUN
american_scientific_journal-7479	242	16	(	(	PUNCT
american_scientific_journal-7479	242	17	gopalakrishnan	gopalakrishnan	NOUN
american_scientific_journal-7479	242	18	and	and	CCONJ
american_scientific_journal-7479	242	19	his	his	PRON
american_scientific_journal-7479	242	20	colleagues	colleague	NOUN
american_scientific_journal-7479	242	21	1992	1992	NUM
american_scientific_journal-7479	242	22	)	)	PUNCT
american_scientific_journal-7479	242	23	,	,	PUNCT
american_scientific_journal-7479	242	24	lead	lead	VERB
american_scientific_journal-7479	242	25	to	to	ADP
american_scientific_journal-7479	242	26	the	the	DET
american_scientific_journal-7479	242	27	utilization	utilization	NOUN
american_scientific_journal-7479	242	28	of	of	ADP
american_scientific_journal-7479	242	29	adm	adm	PROPN
american_scientific_journal-7479	242	30	for	for	ADP
american_scientific_journal-7479	242	31	this	this	DET
american_scientific_journal-7479	242	32	case	case	NOUN
american_scientific_journal-7479	242	33	study	study	NOUN
american_scientific_journal-7479	242	34	.	.	PUNCT
american_scientific_journal-7479	243	1	maximum	maximum	PROPN
american_scientific_journal-7479	243	2	normalized	normalize	VERB
american_scientific_journal-7479	243	3	relative	relative	ADJ
american_scientific_journal-7479	243	4	error	error	NOUN
american_scientific_journal-7479	243	5	deflection	deflection	NOUN
american_scientific_journal-7479	243	6	(	(	PUNCT
american_scientific_journal-7479	243	7	mnred	mnre	VERB
american_scientific_journal-7479	243	8	)	)	PUNCT
american_scientific_journal-7479	243	9	is	be	AUX
american_scientific_journal-7479	243	10	defined	define	VERB
american_scientific_journal-7479	243	11	in	in	ADP
american_scientific_journal-7479	243	12	eq	eq	ADP
american_scientific_journal-7479	243	13	.	.	PUNCT
american_scientific_journal-7479	244	1	(	(	PUNCT
american_scientific_journal-7479	244	2	44	44	NUM
american_scientific_journal-7479	244	3	)	)	PUNCT
american_scientific_journal-7479	245	1	and	and	CCONJ
american_scientific_journal-7479	245	2	shows	show	VERB
american_scientific_journal-7479	245	3	the	the	DET
american_scientific_journal-7479	245	4	numerical	numerical	ADJ
american_scientific_journal-7479	245	5	error	error	NOUN
american_scientific_journal-7479	245	6	of	of	ADP
american_scientific_journal-7479	245	7	adm	adm	PROPN
american_scientific_journal-7479	245	8	and	and	CCONJ
american_scientific_journal-7479	245	9	fem	fem	NOUN
american_scientific_journal-7479	245	10	methods	method	NOUN
american_scientific_journal-7479	245	11	in	in	ADP
american_scientific_journal-7479	245	12	comparison	comparison	NOUN
american_scientific_journal-7479	245	13	with	with	ADP
american_scientific_journal-7479	245	14	the	the	DET
american_scientific_journal-7479	245	15	transfer	transfer	NOUN
american_scientific_journal-7479	245	16	matrix	matrix	NOUN
american_scientific_journal-7479	245	17	method	method	NOUN
american_scientific_journal-7479	245	18	.	.	PUNCT
american_scientific_journal-7479	246	1	these	these	DET
american_scientific_journal-7479	246	2	numerical	numerical	ADJ
american_scientific_journal-7479	246	3	error	error	NOUN
american_scientific_journal-7479	246	4	ratios	ratio	NOUN
american_scientific_journal-7479	246	5	are	be	AUX
american_scientific_journal-7479	246	6	given	give	VERB
american_scientific_journal-7479	246	7	in	in	ADP
american_scientific_journal-7479	246	8	table	table	NOUN
american_scientific_journal-7479	246	9	2	2	NUM
american_scientific_journal-7479	246	10	.	.	PUNCT
american_scientific_journal-7479	247	1	the	the	DET
american_scientific_journal-7479	247	2	efficiency	efficiency	NOUN
american_scientific_journal-7479	247	3	of	of	ADP
american_scientific_journal-7479	247	4	using	use	VERB
american_scientific_journal-7479	247	5	adm	adm	PROPN
american_scientific_journal-7479	247	6	in	in	ADP
american_scientific_journal-7479	247	7	comparison	comparison	NOUN
american_scientific_journal-7479	247	8	with	with	ADP
american_scientific_journal-7479	247	9	fem	fem	NOUN
american_scientific_journal-7479	247	10	could	could	AUX
american_scientific_journal-7479	247	11	be	be	AUX
american_scientific_journal-7479	247	12	seen	see	VERB
american_scientific_journal-7479	247	13	again	again	ADV
american_scientific_journal-7479	247	14	in	in	ADP
american_scientific_journal-7479	247	15	this	this	DET
american_scientific_journal-7479	247	16	table	table	NOUN
american_scientific_journal-7479	247	17	.	.	PUNCT
american_scientific_journal-7479	248	1	mnred(%	mnred(%	NOUN
american_scientific_journal-7479	248	2	)	)	PUNCT
american_scientific_journal-7479	248	3	=	=	SYM
american_scientific_journal-7479	248	4	transfer	transfer	NOUN
american_scientific_journal-7479	248	5	matrix	matrix	NOUN
american_scientific_journal-7479	248	6	response	response	NOUN
american_scientific_journal-7479	248	7	−	−	PROPN
american_scientific_journal-7479	248	8	adm	adm	PROPN
american_scientific_journal-7479	248	9	or	or	CCONJ
american_scientific_journal-7479	248	10	fem	fem	NOUN
american_scientific_journal-7479	248	11	response	response	NOUN
american_scientific_journal-7479	248	12	response	response	NOUN
american_scientific_journal-7479	248	13	transfer	transfer	NOUN
american_scientific_journal-7479	248	14	matrix	matrix	NOUN
american_scientific_journal-7479	248	15	response	response	NOUN
american_scientific_journal-7479	248	16	×	×	PROPN
american_scientific_journal-7479	248	17	100	100	NUM
american_scientific_journal-7479	248	18	(	(	PUNCT
american_scientific_journal-7479	248	19	44	44	NUM
american_scientific_journal-7479	248	20	)	)	PUNCT
american_scientific_journal-7479	248	21	the	the	DET
american_scientific_journal-7479	248	22	effect	effect	NOUN
american_scientific_journal-7479	248	23	on	on	ADP
american_scientific_journal-7479	248	24	the	the	DET
american_scientific_journal-7479	248	25	mid	mid	ADJ
american_scientific_journal-7479	248	26	-	-	ADJ
american_scientific_journal-7479	248	27	point	point	NOUN
american_scientific_journal-7479	248	28	deflection	deflection	NOUN
american_scientific_journal-7479	248	29	of	of	ADP
american_scientific_journal-7479	248	30	the	the	DET
american_scientific_journal-7479	248	31	beam	beam	NOUN
american_scientific_journal-7479	248	32	is	be	AUX
american_scientific_journal-7479	248	33	shown	show	VERB
american_scientific_journal-7479	248	34	in	in	ADP
american_scientific_journal-7479	248	35	fig	fig	NOUN
american_scientific_journal-7479	248	36	.	.	PUNCT
american_scientific_journal-7479	249	1	6	6	NUM
american_scientific_journal-7479	249	2	.	.	X
american_scientific_journal-7479	249	3	in	in	ADP
american_scientific_journal-7479	249	4	this	this	DET
american_scientific_journal-7479	249	5	case	case	NOUN
american_scientific_journal-7479	249	6	,	,	PUNCT
american_scientific_journal-7479	249	7	both	both	CCONJ
american_scientific_journal-7479	249	8	the	the	DET
american_scientific_journal-7479	249	9	vertical	vertical	ADJ
american_scientific_journal-7479	249	10	and	and	CCONJ
american_scientific_journal-7479	249	11	the	the	DET
american_scientific_journal-7479	249	12	horizontal	horizontal	ADJ
american_scientific_journal-7479	249	13	changes	change	NOUN
american_scientific_journal-7479	249	14	are	be	AUX
american_scientific_journal-7479	249	15	extended	extend	VERB
american_scientific_journal-7479	249	16	to	to	ADP
american_scientific_journal-7479	249	17	the	the	DET
american_scientific_journal-7479	249	18	higher	high	ADJ
american_scientific_journal-7479	249	19	values	value	NOUN
american_scientific_journal-7479	249	20	of	of	ADP
american_scientific_journal-7479	249	21	magnitude	magnitude	NOUN
american_scientific_journal-7479	249	22	and	and	CCONJ
american_scientific_journal-7479	249	23	time	time	NOUN
american_scientific_journal-7479	249	24	for	for	ADP
american_scientific_journal-7479	249	25	the	the	DET
american_scientific_journal-7479	249	26	beam	beam	NOUN
american_scientific_journal-7479	249	27	's	's	PART
american_scientific_journal-7479	249	28	midpoint	midpoint	NOUN
american_scientific_journal-7479	249	29	deflection	deflection	NOUN
american_scientific_journal-7479	249	30	,	,	PUNCT
american_scientific_journal-7479	249	31	respectively	respectively	ADV
american_scientific_journal-7479	249	32	.	.	PUNCT
american_scientific_journal-7479	250	1	the	the	DET
american_scientific_journal-7479	250	2	horizontal	horizontal	ADJ
american_scientific_journal-7479	250	3	shift	shift	NOUN
american_scientific_journal-7479	250	4	-	-	PUNCT
american_scientific_journal-7479	250	5	in	in	ADP
american_scientific_journal-7479	250	6	-	-	PUNCT
american_scientific_journal-7479	250	7	time	time	NOUN
american_scientific_journal-7479	250	8	phenomenon	phenomenon	NOUN
american_scientific_journal-7479	250	9	demonstrates	demonstrate	VERB
american_scientific_journal-7479	250	10	the	the	DET
american_scientific_journal-7479	250	11	cracked	crack	VERB
american_scientific_journal-7479	250	12	beam	beam	NOUN
american_scientific_journal-7479	250	13	's	's	PART
american_scientific_journal-7479	250	14	fundamental	fundamental	ADJ
american_scientific_journal-7479	250	15	periodlengthening	periodlengthening	NOUN
american_scientific_journal-7479	250	16	event	event	NOUN
american_scientific_journal-7479	250	17	corresponding	correspond	VERB
american_scientific_journal-7479	250	18	to	to	ADP
american_scientific_journal-7479	250	19	the	the	DET
american_scientific_journal-7479	250	20	deficiency	deficiency	NOUN
american_scientific_journal-7479	250	21	in	in	ADP
american_scientific_journal-7479	250	22	stiffness	stiffness	NOUN
american_scientific_journal-7479	250	23	.	.	PUNCT
american_scientific_journal-7479	251	1	this	this	PRON
american_scientific_journal-7479	251	2	is	be	AUX
american_scientific_journal-7479	251	3	more	more	ADV
american_scientific_journal-7479	251	4	pronounced	pronounce	VERB
american_scientific_journal-7479	251	5	with	with	ADP
american_scientific_journal-7479	251	6	higher	high	ADJ
american_scientific_journal-7479	251	7	levels	level	NOUN
american_scientific_journal-7479	251	8	of	of	ADP
american_scientific_journal-7479	251	9	crack	crack	NOUN
american_scientific_journal-7479	251	10	depth	depth	NOUN
american_scientific_journal-7479	251	11	.	.	PUNCT
american_scientific_journal-7479	252	1	in	in	ADP
american_scientific_journal-7479	252	2	eq	eq	ADP
american_scientific_journal-7479	252	3	.	.	PROPN
american_scientific_journal-7479	252	4	45	45	NUM
american_scientific_journal-7479	252	5	,	,	PUNCT
american_scientific_journal-7479	252	6	the	the	DET
american_scientific_journal-7479	252	7	factor	factor	NOUN
american_scientific_journal-7479	252	8	of	of	ADP
american_scientific_journal-7479	252	9	crack	crack	NOUN
american_scientific_journal-7479	252	10	magnification	magnification	NOUN
american_scientific_journal-7479	252	11	(	(	PUNCT
american_scientific_journal-7479	252	12	fcm	fcm	X
american_scientific_journal-7479	252	13	)	)	PUNCT
american_scientific_journal-7479	252	14	displays	display	VERB
american_scientific_journal-7479	252	15	the	the	DET
american_scientific_journal-7479	252	16	numerical	numerical	ADJ
american_scientific_journal-7479	252	17	ratio	ratio	NOUN
american_scientific_journal-7479	252	18	of	of	ADP
american_scientific_journal-7479	252	19	the	the	DET
american_scientific_journal-7479	252	20	average	average	ADJ
american_scientific_journal-7479	252	21	deflection	deflection	NOUN
american_scientific_journal-7479	252	22	between	between	ADP
american_scientific_journal-7479	252	23	cracked	crack	VERB
american_scientific_journal-7479	252	24	and	and	CCONJ
american_scientific_journal-7479	252	25	intact	intact	ADJ
american_scientific_journal-7479	252	26	beams	beam	NOUN
american_scientific_journal-7479	252	27	subjected	subject	VERB
american_scientific_journal-7479	252	28	to	to	ADP
american_scientific_journal-7479	252	29	moving	move	VERB
american_scientific_journal-7479	252	30	load	load	NOUN
american_scientific_journal-7479	252	31	with	with	ADP
american_scientific_journal-7479	252	32	constant	constant	ADJ
american_scientific_journal-7479	252	33	velocity	velocity	NOUN
american_scientific_journal-7479	252	34	,	,	PUNCT
american_scientific_journal-7479	252	35	v	v	NOUN
american_scientific_journal-7479	252	36	=	=	SYM
american_scientific_journal-7479	252	37	70	70	NUM
american_scientific_journal-7479	252	38	(	(	PUNCT
american_scientific_journal-7479	252	39	m	m	PROPN
american_scientific_journal-7479	252	40	/	/	SYM
american_scientific_journal-7479	252	41	s	s	PART
american_scientific_journal-7479	252	42	)	)	PUNCT
american_scientific_journal-7479	252	43	.	.	PUNCT
american_scientific_journal-7479	253	1	table	table	NOUN
american_scientific_journal-7479	253	2	3	3	NUM
american_scientific_journal-7479	253	3	shows	show	VERB
american_scientific_journal-7479	253	4	these	these	DET
american_scientific_journal-7479	253	5	adm	adm	PROPN
american_scientific_journal-7479	253	6	numerical	numerical	PROPN
american_scientific_journal-7479	253	7	results	result	NOUN
american_scientific_journal-7479	253	8	.	.	PUNCT
american_scientific_journal-7479	254	1	american	american	ADJ
american_scientific_journal-7479	254	2	academic	academic	ADJ
american_scientific_journal-7479	254	3	scientific	scientific	ADJ
american_scientific_journal-7479	254	4	research	research	NOUN
american_scientific_journal-7479	254	5	journal	journal	NOUN
american_scientific_journal-7479	254	6	for	for	ADP
american_scientific_journal-7479	254	7	engineering	engineering	NOUN
american_scientific_journal-7479	254	8	,	,	PUNCT
american_scientific_journal-7479	254	9	technology	technology	NOUN
american_scientific_journal-7479	254	10	,	,	PUNCT
american_scientific_journal-7479	254	11	and	and	CCONJ
american_scientific_journal-7479	254	12	sciences	science	NOUN
american_scientific_journal-7479	254	13	(	(	PUNCT
american_scientific_journal-7479	254	14	asrjets	asrjet	NOUN
american_scientific_journal-7479	254	15	)	)	PUNCT
american_scientific_journal-7479	254	16	(	(	PUNCT
american_scientific_journal-7479	254	17	2022	2022	NUM
american_scientific_journal-7479	254	18	)	)	PUNCT
american_scientific_journal-7479	254	19	volume	volume	NOUN
american_scientific_journal-7479	254	20	88	88	NUM
american_scientific_journal-7479	254	21	,	,	PUNCT
american_scientific_journal-7479	254	22	no1	no1	PROPN
american_scientific_journal-7479	254	23	,	,	PUNCT
american_scientific_journal-7479	254	24	pp	pp	ADV
american_scientific_journal-7479	254	25	332	332	NUM
american_scientific_journal-7479	254	26	-	-	SYM
american_scientific_journal-7479	254	27	348	348	NUM
american_scientific_journal-7479	254	28	343	343	NUM
american_scientific_journal-7479	254	29	fcm	fcm	X
american_scientific_journal-7479	254	30	=	=	X
american_scientific_journal-7479	254	31	maximum	maximum	ADJ
american_scientific_journal-7479	254	32	mid	mid	ADJ
american_scientific_journal-7479	254	33	−	−	PROPN
american_scientific_journal-7479	254	34	point	point	NOUN
american_scientific_journal-7479	254	35	cracked	crack	VERB
american_scientific_journal-7479	254	36	beam	beam	NOUN
american_scientific_journal-7479	254	37	deflection	deflection	NOUN
american_scientific_journal-7479	254	38	maximum	maximum	ADJ
american_scientific_journal-7479	254	39	mid	mid	ADJ
american_scientific_journal-7479	254	40	−	−	PROPN
american_scientific_journal-7479	254	41	point	point	NOUN
american_scientific_journal-7479	254	42	intact	intact	ADJ
american_scientific_journal-7479	254	43	beam	beam	NOUN
american_scientific_journal-7479	254	44	deflection	deflection	NOUN
american_scientific_journal-7479	254	45	×	×	NOUN
american_scientific_journal-7479	254	46	100	100	NUM
american_scientific_journal-7479	254	47	(	(	PUNCT
american_scientific_journal-7479	254	48	45	45	NUM
american_scientific_journal-7479	254	49	)	)	PUNCT
american_scientific_journal-7479	254	50	the	the	DET
american_scientific_journal-7479	254	51	effect	effect	NOUN
american_scientific_journal-7479	254	52	of	of	ADP
american_scientific_journal-7479	254	53	an	an	DET
american_scientific_journal-7479	254	54	open	open	ADJ
american_scientific_journal-7479	254	55	crack	crack	NOUN
american_scientific_journal-7479	254	56	location	location	NOUN
american_scientific_journal-7479	254	57	on	on	ADP
american_scientific_journal-7479	254	58	the	the	DET
american_scientific_journal-7479	254	59	dynamic	dynamic	ADJ
american_scientific_journal-7479	254	60	response	response	NOUN
american_scientific_journal-7479	254	61	of	of	ADP
american_scientific_journal-7479	254	62	a	a	DET
american_scientific_journal-7479	254	63	sscb	sscb	NOUN
american_scientific_journal-7479	254	64	under	under	ADP
american_scientific_journal-7479	254	65	moving	move	VERB
american_scientific_journal-7479	254	66	load	load	NOUN
american_scientific_journal-7479	254	67	with	with	ADP
american_scientific_journal-7479	254	68	constant	constant	ADJ
american_scientific_journal-7479	254	69	velocity	velocity	NOUN
american_scientific_journal-7479	254	70	,	,	PUNCT
american_scientific_journal-7479	254	71	v	v	NOUN
american_scientific_journal-7479	254	72	=	=	SYM
american_scientific_journal-7479	254	73	70	70	NUM
american_scientific_journal-7479	254	74	(	(	PUNCT
american_scientific_journal-7479	254	75	m	m	PROPN
american_scientific_journal-7479	254	76	/	/	SYM
american_scientific_journal-7479	254	77	s	s	PART
american_scientific_journal-7479	254	78	)	)	PUNCT
american_scientific_journal-7479	254	79	,	,	PUNCT
american_scientific_journal-7479	254	80	is	be	AUX
american_scientific_journal-7479	254	81	investigated	investigate	VERB
american_scientific_journal-7479	254	82	in	in	ADP
american_scientific_journal-7479	254	83	fig	fig	NOUN
american_scientific_journal-7479	254	84	.	.	PUNCT
american_scientific_journal-7479	254	85	7	7	NUM
american_scientific_journal-7479	254	86	by	by	ADP
american_scientific_journal-7479	254	87	adm	adm	PROPN
american_scientific_journal-7479	254	88	.	.	PUNCT
american_scientific_journal-7479	255	1	it	it	PRON
american_scientific_journal-7479	255	2	seems	seem	VERB
american_scientific_journal-7479	255	3	that	that	SCONJ
american_scientific_journal-7479	255	4	getting	get	VERB
american_scientific_journal-7479	255	5	the	the	DET
american_scientific_journal-7479	255	6	crack	crack	NOUN
american_scientific_journal-7479	255	7	location	location	NOUN
american_scientific_journal-7479	255	8	away	away	ADV
american_scientific_journal-7479	255	9	from	from	ADP
american_scientific_journal-7479	255	10	the	the	DET
american_scientific_journal-7479	255	11	beam	beam	NOUN
american_scientific_journal-7479	255	12	's	's	PART
american_scientific_journal-7479	255	13	midpoint	midpoint	NOUN
american_scientific_journal-7479	255	14	would	would	AUX
american_scientific_journal-7479	255	15	decrease	decrease	VERB
american_scientific_journal-7479	255	16	the	the	DET
american_scientific_journal-7479	255	17	midpoint	midpoint	NOUN
american_scientific_journal-7479	255	18	deflection	deflection	NOUN
american_scientific_journal-7479	255	19	of	of	ADP
american_scientific_journal-7479	255	20	the	the	DET
american_scientific_journal-7479	255	21	beam	beam	NOUN
american_scientific_journal-7479	255	22	until	until	SCONJ
american_scientific_journal-7479	255	23	it	it	PRON
american_scientific_journal-7479	255	24	becomes	become	VERB
american_scientific_journal-7479	255	25	nil	nil	NOUN
american_scientific_journal-7479	255	26	at	at	ADP
american_scientific_journal-7479	255	27	the	the	DET
american_scientific_journal-7479	255	28	beam	beam	NOUN
american_scientific_journal-7479	255	29	's	's	PART
american_scientific_journal-7479	255	30	two	two	NUM
american_scientific_journal-7479	255	31	ends	end	NOUN
american_scientific_journal-7479	255	32	.	.	PUNCT
american_scientific_journal-7479	256	1	(	(	PUNCT
american_scientific_journal-7479	256	2	a	a	X
american_scientific_journal-7479	256	3	)	)	PUNCT
american_scientific_journal-7479	256	4	(	(	PUNCT
american_scientific_journal-7479	256	5	b	b	X
american_scientific_journal-7479	256	6	)	)	PUNCT
american_scientific_journal-7479	256	7	figure	figure	NOUN
american_scientific_journal-7479	256	8	2	2	NUM
american_scientific_journal-7479	256	9	:	:	PUNCT
american_scientific_journal-7479	256	10	(	(	PUNCT
american_scientific_journal-7479	256	11	a	a	X
american_scientific_journal-7479	256	12	)	)	PUNCT
american_scientific_journal-7479	256	13	comparison	comparison	NOUN
american_scientific_journal-7479	256	14	between	between	ADP
american_scientific_journal-7479	256	15	the	the	DET
american_scientific_journal-7479	256	16	normalized	normalize	VERB
american_scientific_journal-7479	256	17	deflection	deflection	NOUN
american_scientific_journal-7479	256	18	at	at	ADP
american_scientific_journal-7479	256	19	mid	mid	NOUN
american_scientific_journal-7479	256	20	-	-	NOUN
american_scientific_journal-7479	256	21	span	span	NOUN
american_scientific_journal-7479	256	22	of	of	ADP
american_scientific_journal-7479	256	23	a	a	DET
american_scientific_journal-7479	256	24	sscb	sscb	NOUN
american_scientific_journal-7479	256	25	subjected	subject	VERB
american_scientific_journal-7479	256	26	to	to	ADP
american_scientific_journal-7479	256	27	moving	move	VERB
american_scientific_journal-7479	256	28	load	load	NOUN
american_scientific_journal-7479	256	29	with	with	ADP
american_scientific_journal-7479	256	30	constant	constant	ADJ
american_scientific_journal-7479	256	31	velocity	velocity	NOUN
american_scientific_journal-7479	256	32	v=80	v=80	NOUN
american_scientific_journal-7479	256	33	(	(	PUNCT
american_scientific_journal-7479	256	34	m/	m/	NOUN
american_scientific_journal-7479	256	35	s	s	PART
american_scientific_journal-7479	256	36	)	)	PUNCT
american_scientific_journal-7479	256	37	,	,	PUNCT
american_scientific_journal-7479	256	38	by	by	ADP
american_scientific_journal-7479	256	39	using	use	VERB
american_scientific_journal-7479	256	40	adm	adm	PROPN
american_scientific_journal-7479	256	41	,	,	PUNCT
american_scientific_journal-7479	256	42	fem	fem	NOUN
american_scientific_journal-7479	256	43	and	and	CCONJ
american_scientific_journal-7479	256	44	exact	exact	ADJ
american_scientific_journal-7479	256	45	solution	solution	NOUN
american_scientific_journal-7479	256	46	(	(	PUNCT
american_scientific_journal-7479	256	47	80	80	NUM
american_scientific_journal-7479	256	48	and	and	CCONJ
american_scientific_journal-7479	256	49	100	100	NUM
american_scientific_journal-7479	256	50	elements	element	NOUN
american_scientific_journal-7479	256	51	)	)	PUNCT
american_scientific_journal-7479	256	52	(	(	PUNCT
american_scientific_journal-7479	256	53	b	b	X
american_scientific_journal-7479	256	54	)	)	PUNCT
american_scientific_journal-7479	256	55	zoom	zoom	NOUN
american_scientific_journal-7479	256	56	-	-	PUNCT
american_scientific_journal-7479	256	57	in	in	ADP
american_scientific_journal-7479	256	58	subfigure	subfigure	NOUN
american_scientific_journal-7479	256	59	(	(	PUNCT
american_scientific_journal-7479	256	60	a	a	PRON
american_scientific_journal-7479	256	61	)	)	PUNCT
american_scientific_journal-7479	256	62	shows	show	VERB
american_scientific_journal-7479	256	63	the	the	DET
american_scientific_journal-7479	256	64	comparison	comparison	NOUN
american_scientific_journal-7479	256	65	between	between	ADP
american_scientific_journal-7479	256	66	these	these	DET
american_scientific_journal-7479	256	67	three	three	NUM
american_scientific_journal-7479	256	68	methods	method	NOUN
american_scientific_journal-7479	256	69	table	table	NOUN
american_scientific_journal-7479	256	70	1	1	NUM
american_scientific_journal-7479	256	71	:	:	PUNCT
american_scientific_journal-7479	256	72	difference	difference	NOUN
american_scientific_journal-7479	256	73	between	between	ADP
american_scientific_journal-7479	256	74	maximum	maximum	ADV
american_scientific_journal-7479	256	75	normalized	normalize	VERB
american_scientific_journal-7479	256	76	defection	defection	NOUN
american_scientific_journal-7479	256	77	at	at	ADP
american_scientific_journal-7479	256	78	the	the	DET
american_scientific_journal-7479	256	79	mid	mid	NOUN
american_scientific_journal-7479	256	80	-	-	NOUN
american_scientific_journal-7479	256	81	point	point	NOUN
american_scientific_journal-7479	256	82	of	of	ADP
american_scientific_journal-7479	256	83	a	a	DET
american_scientific_journal-7479	256	84	simplysupported	simplysupporte	VERB
american_scientific_journal-7479	256	85	beam	beam	NOUN
american_scientific_journal-7479	256	86	for	for	ADP
american_scientific_journal-7479	256	87	adm	adm	PROPN
american_scientific_journal-7479	256	88	,	,	PUNCT
american_scientific_journal-7479	256	89	fem	fem	NOUN
american_scientific_journal-7479	256	90	,	,	PUNCT
american_scientific_journal-7479	256	91	and	and	CCONJ
american_scientific_journal-7479	256	92	exact	exact	ADJ
american_scientific_journal-7479	256	93	solution	solution	NOUN
american_scientific_journal-7479	256	94	,	,	PUNCT
american_scientific_journal-7479	256	95	v	v	NOUN
american_scientific_journal-7479	256	96	=	=	SYM
american_scientific_journal-7479	256	97	80	80	NUM
american_scientific_journal-7479	256	98	(	(	PUNCT
american_scientific_journal-7479	256	99	m	m	PROPN
american_scientific_journal-7479	256	100	/	/	SYM
american_scientific_journal-7479	256	101	s	s	PART
american_scientific_journal-7479	256	102	)	)	PUNCT
american_scientific_journal-7479	256	103	method	method	NOUN
american_scientific_journal-7479	256	104	maximum	maximum	ADV
american_scientific_journal-7479	256	105	normalized	normalize	VERB
american_scientific_journal-7479	256	106	deflection	deflection	NOUN
american_scientific_journal-7479	256	107	of	of	ADP
american_scientific_journal-7479	256	108	mid	mid	ADJ
american_scientific_journal-7479	256	109	-	-	ADJ
american_scientific_journal-7479	256	110	span	span	ADJ
american_scientific_journal-7479	256	111	ppe	ppe	NOUN
american_scientific_journal-7479	256	112	(	(	PUNCT
american_scientific_journal-7479	256	113	%	%	INTJ
american_scientific_journal-7479	256	114	)	)	PUNCT
american_scientific_journal-7479	256	115	exact	exact	ADJ
american_scientific_journal-7479	256	116	solution	solution	NOUN
american_scientific_journal-7479	256	117	-1.0361	-1.0361	NOUN
american_scientific_journal-7479	257	1	american	american	PROPN
american_scientific_journal-7479	257	2	academic	academic	ADJ
american_scientific_journal-7479	257	3	scientific	scientific	ADJ
american_scientific_journal-7479	257	4	research	research	NOUN
american_scientific_journal-7479	257	5	journal	journal	NOUN
american_scientific_journal-7479	257	6	for	for	ADP
american_scientific_journal-7479	257	7	engineering	engineering	NOUN
american_scientific_journal-7479	257	8	,	,	PUNCT
american_scientific_journal-7479	257	9	technology	technology	NOUN
american_scientific_journal-7479	257	10	,	,	PUNCT
american_scientific_journal-7479	257	11	and	and	CCONJ
american_scientific_journal-7479	257	12	sciences	science	NOUN
american_scientific_journal-7479	257	13	(	(	PUNCT
american_scientific_journal-7479	257	14	asrjets	asrjet	NOUN
american_scientific_journal-7479	257	15	)	)	PUNCT
american_scientific_journal-7479	257	16	(	(	PUNCT
american_scientific_journal-7479	257	17	2022	2022	NUM
american_scientific_journal-7479	257	18	)	)	PUNCT
american_scientific_journal-7479	257	19	volume	volume	NOUN
american_scientific_journal-7479	257	20	88	88	NUM
american_scientific_journal-7479	257	21	,	,	PUNCT
american_scientific_journal-7479	257	22	no1	no1	PROPN
american_scientific_journal-7479	257	23	,	,	PUNCT
american_scientific_journal-7479	257	24	pp	pp	ADV
american_scientific_journal-7479	257	25	332	332	NUM
american_scientific_journal-7479	257	26	-	-	SYM
american_scientific_journal-7479	257	27	348	348	NUM
american_scientific_journal-7479	257	28	344	344	NUM
american_scientific_journal-7479	257	29	adm	adm	PROPN
american_scientific_journal-7479	257	30	fem	fem	NOUN
american_scientific_journal-7479	257	31	(	(	PUNCT
american_scientific_journal-7479	257	32	80	80	NUM
american_scientific_journal-7479	257	33	elements	element	NOUN
american_scientific_journal-7479	257	34	)	)	PUNCT
american_scientific_journal-7479	257	35	fem	fem	NOUN
american_scientific_journal-7479	257	36	(	(	PUNCT
american_scientific_journal-7479	257	37	100	100	NUM
american_scientific_journal-7479	257	38	elements	element	NOUN
american_scientific_journal-7479	257	39	)	)	PUNCT
american_scientific_journal-7479	257	40	-1.0860	-1.0860	NOUN
american_scientific_journal-7479	257	41	-1.0836	-1.0836	VERB
american_scientific_journal-7479	257	42	-1.0843	-1.0843	NOUN
american_scientific_journal-7479	258	1	0.0092	0.0092	NUM
american_scientific_journal-7479	258	2	0.2302	0.2302	NUM
american_scientific_journal-7479	258	3	0.1657	0.1657	NUM
american_scientific_journal-7479	258	4	(	(	PUNCT
american_scientific_journal-7479	258	5	a	a	NOUN
american_scientific_journal-7479	258	6	)	)	PUNCT
american_scientific_journal-7479	258	7	(	(	PUNCT
american_scientific_journal-7479	258	8	b	b	X
american_scientific_journal-7479	258	9	)	)	PUNCT
american_scientific_journal-7479	258	10	figure	figure	NOUN
american_scientific_journal-7479	258	11	3	3	NUM
american_scientific_journal-7479	258	12	:	:	PUNCT
american_scientific_journal-7479	258	13	(	(	PUNCT
american_scientific_journal-7479	258	14	a	a	X
american_scientific_journal-7479	258	15	)	)	PUNCT
american_scientific_journal-7479	258	16	moving	move	VERB
american_scientific_journal-7479	258	17	load	load	NOUN
american_scientific_journal-7479	258	18	velocity	velocity	NOUN
american_scientific_journal-7479	258	19	(	(	PUNCT
american_scientific_journal-7479	258	20	70	70	NUM
american_scientific_journal-7479	258	21	,	,	PUNCT
american_scientific_journal-7479	258	22	80	80	NUM
american_scientific_journal-7479	258	23	,	,	PUNCT
american_scientific_journal-7479	258	24	90(m	90(m	NUM
american_scientific_journal-7479	258	25	/	/	SYM
american_scientific_journal-7479	258	26	s	s	NOUN
american_scientific_journal-7479	258	27	)	)	PUNCT
american_scientific_journal-7479	258	28	)	)	PUNCT
american_scientific_journal-7479	258	29	effects	effect	NOUN
american_scientific_journal-7479	258	30	on	on	ADP
american_scientific_journal-7479	258	31	the	the	DET
american_scientific_journal-7479	258	32	normalized	normalize	VERB
american_scientific_journal-7479	258	33	deflection	deflection	NOUN
american_scientific_journal-7479	258	34	at	at	ADP
american_scientific_journal-7479	258	35	mid	mid	NOUN
american_scientific_journal-7479	258	36	-	-	NOUN
american_scientific_journal-7479	258	37	span	span	NOUN
american_scientific_journal-7479	258	38	of	of	ADP
american_scientific_journal-7479	258	39	a	a	DET
american_scientific_journal-7479	258	40	sscb	sscb	NOUN
american_scientific_journal-7479	258	41	by	by	ADP
american_scientific_journal-7479	258	42	using	use	VERB
american_scientific_journal-7479	258	43	adm	adm	PROPN
american_scientific_journal-7479	258	44	and	and	CCONJ
american_scientific_journal-7479	258	45	fem	fem	X
american_scientific_journal-7479	258	46	(	(	PUNCT
american_scientific_journal-7479	258	47	100	100	NUM
american_scientific_journal-7479	258	48	elements	element	NOUN
american_scientific_journal-7479	258	49	)	)	PUNCT
american_scientific_journal-7479	258	50	(	(	PUNCT
american_scientific_journal-7479	258	51	b	b	X
american_scientific_journal-7479	258	52	)	)	PUNCT
american_scientific_journal-7479	258	53	zoom	zoom	NOUN
american_scientific_journal-7479	258	54	-	-	PUNCT
american_scientific_journal-7479	258	55	in	in	ADP
american_scientific_journal-7479	258	56	subfigure	subfigure	NOUN
american_scientific_journal-7479	258	57	(	(	PUNCT
american_scientific_journal-7479	258	58	a	a	PRON
american_scientific_journal-7479	258	59	)	)	PUNCT
american_scientific_journal-7479	258	60	shows	show	VERB
american_scientific_journal-7479	258	61	the	the	DET
american_scientific_journal-7479	258	62	comparison	comparison	NOUN
american_scientific_journal-7479	258	63	between	between	ADP
american_scientific_journal-7479	258	64	these	these	DET
american_scientific_journal-7479	258	65	two	two	NUM
american_scientific_journal-7479	258	66	method	method	ADJ
american_scientific_journal-7479	258	67	american	american	ADJ
american_scientific_journal-7479	258	68	academic	academic	ADJ
american_scientific_journal-7479	258	69	scientific	scientific	ADJ
american_scientific_journal-7479	258	70	research	research	NOUN
american_scientific_journal-7479	258	71	journal	journal	NOUN
american_scientific_journal-7479	258	72	for	for	ADP
american_scientific_journal-7479	258	73	engineering	engineering	NOUN
american_scientific_journal-7479	258	74	,	,	PUNCT
american_scientific_journal-7479	258	75	technology	technology	NOUN
american_scientific_journal-7479	258	76	,	,	PUNCT
american_scientific_journal-7479	258	77	and	and	CCONJ
american_scientific_journal-7479	258	78	sciences	science	NOUN
american_scientific_journal-7479	258	79	(	(	PUNCT
american_scientific_journal-7479	258	80	asrjets	asrjet	NOUN
american_scientific_journal-7479	258	81	)	)	PUNCT
american_scientific_journal-7479	258	82	(	(	PUNCT
american_scientific_journal-7479	258	83	2022	2022	NUM
american_scientific_journal-7479	258	84	)	)	PUNCT
american_scientific_journal-7479	258	85	volume	volume	NOUN
american_scientific_journal-7479	258	86	88	88	NUM
american_scientific_journal-7479	258	87	,	,	PUNCT
american_scientific_journal-7479	258	88	no1	no1	PROPN
american_scientific_journal-7479	258	89	,	,	PUNCT
american_scientific_journal-7479	258	90	pp	pp	ADV
american_scientific_journal-7479	258	91	332	332	NUM
american_scientific_journal-7479	258	92	-	-	SYM
american_scientific_journal-7479	258	93	348	348	NUM
american_scientific_journal-7479	258	94	345	345	NUM
american_scientific_journal-7479	258	95	figure	figure	NOUN
american_scientific_journal-7479	258	96	4	4	NUM
american_scientific_journal-7479	258	97	:	:	PUNCT
american_scientific_journal-7479	258	98	the	the	DET
american_scientific_journal-7479	258	99	effect	effect	NOUN
american_scientific_journal-7479	258	100	of	of	ADP
american_scientific_journal-7479	258	101	the	the	DET
american_scientific_journal-7479	258	102	amplitude	amplitude	NOUN
american_scientific_journal-7479	258	103	of	of	ADP
american_scientific_journal-7479	258	104	the	the	DET
american_scientific_journal-7479	258	105	moving	move	VERB
american_scientific_journal-7479	258	106	load	load	NOUN
american_scientific_journal-7479	258	107	on	on	ADP
american_scientific_journal-7479	258	108	the	the	DET
american_scientific_journal-7479	258	109	mid	mid	ADJ
american_scientific_journal-7479	258	110	-	-	ADJ
american_scientific_journal-7479	258	111	span	span	ADJ
american_scientific_journal-7479	258	112	deflection	deflection	NOUN
american_scientific_journal-7479	258	113	of	of	ADP
american_scientific_journal-7479	258	114	an	an	DET
american_scientific_journal-7479	258	115	sscb	sscb	NOUN
american_scientific_journal-7479	258	116	undergoing	undergo	VERB
american_scientific_journal-7479	258	117	a	a	DET
american_scientific_journal-7479	258	118	moving	move	VERB
american_scientific_journal-7479	258	119	load	load	NOUN
american_scientific_journal-7479	258	120	with	with	ADP
american_scientific_journal-7479	258	121	constant	constant	ADJ
american_scientific_journal-7479	258	122	velocity	velocity	NOUN
american_scientific_journal-7479	258	123	v=70	v=70	NOUN
american_scientific_journal-7479	258	124	(	(	PUNCT
american_scientific_journal-7479	258	125	m	m	NOUN
american_scientific_journal-7479	258	126	/	/	SYM
american_scientific_journal-7479	258	127	s	s	PART
american_scientific_journal-7479	258	128	)	)	PUNCT
american_scientific_journal-7479	258	129	and	and	CCONJ
american_scientific_journal-7479	258	130	α=0.25	α=0.25	NOUN
american_scientific_journal-7479	258	131	using	use	VERB
american_scientific_journal-7479	258	132	adm	adm	PROPN
american_scientific_journal-7479	258	133	(	(	PUNCT
american_scientific_journal-7479	258	134	a	a	NOUN
american_scientific_journal-7479	258	135	)	)	PUNCT
american_scientific_journal-7479	258	136	(	(	PUNCT
american_scientific_journal-7479	258	137	b	b	X
american_scientific_journal-7479	258	138	)	)	PUNCT
american_scientific_journal-7479	258	139	figure	figure	NOUN
american_scientific_journal-7479	258	140	5	5	NUM
american_scientific_journal-7479	258	141	:	:	PUNCT
american_scientific_journal-7479	258	142	(	(	PUNCT
american_scientific_journal-7479	258	143	a	a	X
american_scientific_journal-7479	258	144	)	)	PUNCT
american_scientific_journal-7479	258	145	comparison	comparison	NOUN
american_scientific_journal-7479	258	146	between	between	ADP
american_scientific_journal-7479	258	147	the	the	DET
american_scientific_journal-7479	258	148	normalized	normalize	VERB
american_scientific_journal-7479	258	149	deflection	deflection	NOUN
american_scientific_journal-7479	258	150	at	at	ADP
american_scientific_journal-7479	258	151	mid	mid	NOUN
american_scientific_journal-7479	258	152	-	-	NOUN
american_scientific_journal-7479	258	153	span	span	NOUN
american_scientific_journal-7479	258	154	of	of	ADP
american_scientific_journal-7479	258	155	a	a	DET
american_scientific_journal-7479	258	156	simply	simply	ADV
american_scientific_journal-7479	258	157	supported	support	VERB
american_scientific_journal-7479	258	158	cracked	cracked	ADJ
american_scientific_journal-7479	258	159	and	and	CCONJ
american_scientific_journal-7479	258	160	intact	intact	ADJ
american_scientific_journal-7479	258	161	beam	beam	NOUN
american_scientific_journal-7479	258	162	subjected	subject	VERB
american_scientific_journal-7479	258	163	to	to	ADP
american_scientific_journal-7479	258	164	moving	move	VERB
american_scientific_journal-7479	258	165	load	load	NOUN
american_scientific_journal-7479	258	166	with	with	ADP
american_scientific_journal-7479	258	167	constant	constant	ADJ
american_scientific_journal-7479	258	168	velocity	velocity	NOUN
american_scientific_journal-7479	258	169	v=70	v=70	NOUN
american_scientific_journal-7479	258	170	(	(	PUNCT
american_scientific_journal-7479	258	171	m/	m/	NOUN
american_scientific_journal-7479	258	172	s	s	PART
american_scientific_journal-7479	258	173	)	)	PUNCT
american_scientific_journal-7479	258	174	,	,	PUNCT
american_scientific_journal-7479	258	175	by	by	ADP
american_scientific_journal-7479	258	176	using	use	VERB
american_scientific_journal-7479	258	177	transfer	transfer	NOUN
american_scientific_journal-7479	258	178	matrix	matrix	NOUN
american_scientific_journal-7479	258	179	,	,	PUNCT
american_scientific_journal-7479	258	180	adm	adm	PROPN
american_scientific_journal-7479	258	181	and	and	CCONJ
american_scientific_journal-7479	258	182	fem	fem	NOUN
american_scientific_journal-7479	258	183	(	(	PUNCT
american_scientific_journal-7479	258	184	60	60	NUM
american_scientific_journal-7479	258	185	and	and	CCONJ
american_scientific_journal-7479	258	186	100	100	NUM
american_scientific_journal-7479	258	187	elements	element	NOUN
american_scientific_journal-7479	258	188	)	)	PUNCT
american_scientific_journal-7479	258	189	(	(	PUNCT
american_scientific_journal-7479	258	190	b	b	X
american_scientific_journal-7479	258	191	)	)	PUNCT
american_scientific_journal-7479	258	192	zoom	zoom	NOUN
american_scientific_journal-7479	258	193	-	-	PUNCT
american_scientific_journal-7479	258	194	in	in	ADP
american_scientific_journal-7479	258	195	subfigure	subfigure	NOUN
american_scientific_journal-7479	258	196	(	(	PUNCT
american_scientific_journal-7479	258	197	a	a	PRON
american_scientific_journal-7479	258	198	)	)	PUNCT
american_scientific_journal-7479	258	199	shows	show	VERB
american_scientific_journal-7479	258	200	the	the	DET
american_scientific_journal-7479	258	201	comparison	comparison	NOUN
american_scientific_journal-7479	258	202	between	between	ADP
american_scientific_journal-7479	258	203	these	these	DET
american_scientific_journal-7479	258	204	three	three	NUM
american_scientific_journal-7479	258	205	methods	method	NOUN
american_scientific_journal-7479	258	206	american	american	ADJ
american_scientific_journal-7479	258	207	academic	academic	ADJ
american_scientific_journal-7479	258	208	scientific	scientific	ADJ
american_scientific_journal-7479	258	209	research	research	NOUN
american_scientific_journal-7479	258	210	journal	journal	NOUN
american_scientific_journal-7479	258	211	for	for	ADP
american_scientific_journal-7479	258	212	engineering	engineering	NOUN
american_scientific_journal-7479	258	213	,	,	PUNCT
american_scientific_journal-7479	258	214	technology	technology	NOUN
american_scientific_journal-7479	258	215	,	,	PUNCT
american_scientific_journal-7479	258	216	and	and	CCONJ
american_scientific_journal-7479	258	217	sciences	science	NOUN
american_scientific_journal-7479	258	218	(	(	PUNCT
american_scientific_journal-7479	258	219	asrjets	asrjet	NOUN
american_scientific_journal-7479	258	220	)	)	PUNCT
american_scientific_journal-7479	258	221	(	(	PUNCT
american_scientific_journal-7479	258	222	2022	2022	NUM
american_scientific_journal-7479	258	223	)	)	PUNCT
american_scientific_journal-7479	258	224	volume	volume	NOUN
american_scientific_journal-7479	258	225	88	88	NUM
american_scientific_journal-7479	258	226	,	,	PUNCT
american_scientific_journal-7479	258	227	no1	no1	PROPN
american_scientific_journal-7479	258	228	,	,	PUNCT
american_scientific_journal-7479	258	229	pp	pp	ADV
american_scientific_journal-7479	258	230	332	332	NUM
american_scientific_journal-7479	258	231	-	-	SYM
american_scientific_journal-7479	258	232	348	348	NUM
american_scientific_journal-7479	258	233	346	346	NUM
american_scientific_journal-7479	258	234	figure	figure	NOUN
american_scientific_journal-7479	258	235	6	6	NUM
american_scientific_journal-7479	258	236	:	:	PUNCT
american_scientific_journal-7479	258	237	crack	crack	VERB
american_scientific_journal-7479	258	238	depth	depth	NOUN
american_scientific_journal-7479	258	239	ratio	ratio	NOUN
american_scientific_journal-7479	258	240	effects	effect	NOUN
american_scientific_journal-7479	258	241	on	on	ADP
american_scientific_journal-7479	258	242	the	the	DET
american_scientific_journal-7479	258	243	deflection	deflection	NOUN
american_scientific_journal-7479	258	244	at	at	ADP
american_scientific_journal-7479	258	245	mid	mid	NOUN
american_scientific_journal-7479	258	246	-	-	NOUN
american_scientific_journal-7479	258	247	span	span	NOUN
american_scientific_journal-7479	258	248	of	of	ADP
american_scientific_journal-7479	258	249	a	a	DET
american_scientific_journal-7479	258	250	sscb	sscb	NOUN
american_scientific_journal-7479	258	251	subjected	subject	VERB
american_scientific_journal-7479	258	252	to	to	ADP
american_scientific_journal-7479	258	253	moving	move	VERB
american_scientific_journal-7479	258	254	load	load	NOUN
american_scientific_journal-7479	258	255	with	with	ADP
american_scientific_journal-7479	258	256	constant	constant	ADJ
american_scientific_journal-7479	258	257	velocity(v=70	velocity(v=70	PROPN
american_scientific_journal-7479	258	258	m/s	m/s	NOUN
american_scientific_journal-7479	258	259	)	)	PUNCT
american_scientific_journal-7479	258	260	by	by	ADP
american_scientific_journal-7479	258	261	using	use	VERB
american_scientific_journal-7479	258	262	adm	adm	PROPN
american_scientific_journal-7479	258	263	table	table	NOUN
american_scientific_journal-7479	258	264	2	2	NUM
american_scientific_journal-7479	258	265	:	:	PUNCT
american_scientific_journal-7479	258	266	difference	difference	NOUN
american_scientific_journal-7479	258	267	between	between	ADP
american_scientific_journal-7479	258	268	maximum	maximum	ADV
american_scientific_journal-7479	258	269	normalized	normalize	VERB
american_scientific_journal-7479	258	270	defection	defection	NOUN
american_scientific_journal-7479	258	271	in	in	ADP
american_scientific_journal-7479	258	272	mid	mid	NOUN
american_scientific_journal-7479	258	273	-	-	NOUN
american_scientific_journal-7479	258	274	point	point	NOUN
american_scientific_journal-7479	258	275	of	of	ADP
american_scientific_journal-7479	258	276	simply	simply	ADV
american_scientific_journal-7479	258	277	supported	support	VERB
american_scientific_journal-7479	258	278	beam	beam	NOUN
american_scientific_journal-7479	258	279	in	in	ADP
american_scientific_journal-7479	258	280	adm	adm	PROPN
american_scientific_journal-7479	258	281	,	,	PUNCT
american_scientific_journal-7479	258	282	fem	fem	NOUN
american_scientific_journal-7479	258	283	and	and	CCONJ
american_scientific_journal-7479	258	284	transfer	transfer	NOUN
american_scientific_journal-7479	258	285	matrix	matrix	NOUN
american_scientific_journal-7479	258	286	method	method	NOUN
american_scientific_journal-7479	258	287	,	,	PUNCT
american_scientific_journal-7479	258	288	v=70	v=70	NOUN
american_scientific_journal-7479	258	289	(	(	PUNCT
american_scientific_journal-7479	258	290	m	m	NOUN
american_scientific_journal-7479	258	291	/	/	SYM
american_scientific_journal-7479	258	292	s	s	PART
american_scientific_journal-7479	258	293	)	)	PUNCT
american_scientific_journal-7479	258	294	and	and	CCONJ
american_scientific_journal-7479	258	295	𝛼	𝛼	X
american_scientific_journal-7479	258	296	=	=	NOUN
american_scientific_journal-7479	258	297	0.25	0.25	NUM
american_scientific_journal-7479	258	298	method	method	NOUN
american_scientific_journal-7479	258	299	maximum	maximum	ADV
american_scientific_journal-7479	258	300	normalized	normalize	VERB
american_scientific_journal-7479	258	301	deflection	deflection	NOUN
american_scientific_journal-7479	258	302	of	of	ADP
american_scientific_journal-7479	258	303	mid	mid	ADJ
american_scientific_journal-7479	258	304	-	-	NOUN
american_scientific_journal-7479	258	305	span	span	NOUN
american_scientific_journal-7479	258	306	mnred	mnre	VERB
american_scientific_journal-7479	258	307	(	(	PUNCT
american_scientific_journal-7479	258	308	%	%	INTJ
american_scientific_journal-7479	258	309	)	)	PUNCT
american_scientific_journal-7479	258	310	transfer	transfer	NOUN
american_scientific_journal-7479	258	311	matrix	matrix	NOUN
american_scientific_journal-7479	258	312	adm	adm	PROPN
american_scientific_journal-7479	258	313	fem	fem	X
american_scientific_journal-7479	258	314	(	(	PUNCT
american_scientific_journal-7479	258	315	30	30	NUM
american_scientific_journal-7479	258	316	elements	element	NOUN
american_scientific_journal-7479	258	317	)	)	PUNCT
american_scientific_journal-7479	258	318	fem	fem	NOUN
american_scientific_journal-7479	258	319	(	(	PUNCT
american_scientific_journal-7479	258	320	60	60	NUM
american_scientific_journal-7479	258	321	elements	element	NOUN
american_scientific_journal-7479	258	322	)	)	PUNCT
american_scientific_journal-7479	258	323	fem	fem	NOUN
american_scientific_journal-7479	258	324	(	(	PUNCT
american_scientific_journal-7479	258	325	90	90	NUM
american_scientific_journal-7479	258	326	elements	element	NOUN
american_scientific_journal-7479	258	327	)	)	PUNCT
american_scientific_journal-7479	258	328	-1.4269	-1.4269	PUNCT
american_scientific_journal-7479	259	1	-1.4268	-1.4268	PROPN
american_scientific_journal-7479	259	2	-1.4128	-1.4128	PUNCT
american_scientific_journal-7479	260	1	-1.4139	-1.4139	ADJ
american_scientific_journal-7479	260	2	-1.4166	-1.4166	ADJ
american_scientific_journal-7479	260	3	1	1	NUM
american_scientific_journal-7479	260	4	0.007	0.007	NUM
american_scientific_journal-7479	260	5	0.9882	0.9882	NUM
american_scientific_journal-7479	260	6	0.9111	0.9111	NUM
american_scientific_journal-7479	260	7	0.7218	0.7218	NUM
american_scientific_journal-7479	260	8	figure	figure	NOUN
american_scientific_journal-7479	260	9	7	7	NUM
american_scientific_journal-7479	260	10	:	:	PUNCT
american_scientific_journal-7479	260	11	crack	crack	VERB
american_scientific_journal-7479	260	12	location	location	NOUN
american_scientific_journal-7479	260	13	effects	effect	NOUN
american_scientific_journal-7479	260	14	on	on	ADP
american_scientific_journal-7479	260	15	the	the	DET
american_scientific_journal-7479	260	16	normalized	normalize	VERB
american_scientific_journal-7479	260	17	deflection	deflection	NOUN
american_scientific_journal-7479	260	18	at	at	ADP
american_scientific_journal-7479	260	19	mid	mid	NOUN
american_scientific_journal-7479	260	20	-	-	NOUN
american_scientific_journal-7479	260	21	span	span	NOUN
american_scientific_journal-7479	260	22	of	of	ADP
american_scientific_journal-7479	260	23	a	a	DET
american_scientific_journal-7479	260	24	sscb	sscb	NOUN
american_scientific_journal-7479	260	25	subjected	subject	VERB
american_scientific_journal-7479	260	26	to	to	ADP
american_scientific_journal-7479	260	27	moving	move	VERB
american_scientific_journal-7479	260	28	load	load	NOUN
american_scientific_journal-7479	260	29	with	with	ADP
american_scientific_journal-7479	260	30	constant	constant	ADJ
american_scientific_journal-7479	260	31	velocity(v=70	velocity(v=70	PROPN
american_scientific_journal-7479	260	32	m/s	m/s	PROPN
american_scientific_journal-7479	260	33	)	)	PUNCT
american_scientific_journal-7479	260	34	and	and	CCONJ
american_scientific_journal-7479	260	35	α=0.25	α=0.25	NOUN
american_scientific_journal-7479	260	36	,	,	PUNCT
american_scientific_journal-7479	260	37	by	by	ADP
american_scientific_journal-7479	260	38	using	use	VERB
american_scientific_journal-7479	260	39	adm	adm	PROPN
american_scientific_journal-7479	260	40	table	table	NOUN
american_scientific_journal-7479	260	41	3	3	NUM
american_scientific_journal-7479	260	42	:	:	PUNCT
american_scientific_journal-7479	260	43	effect	effect	NOUN
american_scientific_journal-7479	260	44	of	of	ADP
american_scientific_journal-7479	260	45	crack	crack	NOUN
american_scientific_journal-7479	260	46	size	size	NOUN
american_scientific_journal-7479	260	47	on	on	ADP
american_scientific_journal-7479	260	48	the	the	DET
american_scientific_journal-7479	260	49	ratio	ratio	NOUN
american_scientific_journal-7479	260	50	between	between	ADP
american_scientific_journal-7479	260	51	maximum	maximum	ADJ
american_scientific_journal-7479	260	52	normalized	normalize	VERB
american_scientific_journal-7479	260	53	deflections	deflection	NOUN
american_scientific_journal-7479	260	54	of	of	ADP
american_scientific_journal-7479	260	55	cracked	cracked	ADJ
american_scientific_journal-7479	260	56	and	and	CCONJ
american_scientific_journal-7479	260	57	healthy	healthy	ADJ
american_scientific_journal-7479	260	58	beams	beam	NOUN
american_scientific_journal-7479	260	59	under	under	ADP
american_scientific_journal-7479	260	60	moving	move	VERB
american_scientific_journal-7479	260	61	load	load	NOUN
american_scientific_journal-7479	260	62	with	with	ADP
american_scientific_journal-7479	260	63	constant	constant	ADJ
american_scientific_journal-7479	260	64	velocity	velocity	NOUN
american_scientific_journal-7479	260	65	,	,	PUNCT
american_scientific_journal-7479	260	66	v=70	v=70	NOUN
american_scientific_journal-7479	260	67	(	(	PUNCT
american_scientific_journal-7479	260	68	m	m	NOUN
american_scientific_journal-7479	260	69	/	/	SYM
american_scientific_journal-7479	260	70	s	s	PART
american_scientific_journal-7479	260	71	)	)	PUNCT
american_scientific_journal-7479	260	72	,	,	PUNCT
american_scientific_journal-7479	260	73	by	by	ADP
american_scientific_journal-7479	260	74	using	use	VERB
american_scientific_journal-7479	260	75	adm	adm	PROPN
american_scientific_journal-7479	260	76	american	american	PROPN
american_scientific_journal-7479	260	77	academic	academic	PROPN
american_scientific_journal-7479	260	78	scientific	scientific	ADJ
american_scientific_journal-7479	260	79	research	research	NOUN
american_scientific_journal-7479	260	80	journal	journal	NOUN
american_scientific_journal-7479	260	81	for	for	ADP
american_scientific_journal-7479	260	82	engineering	engineering	NOUN
american_scientific_journal-7479	260	83	,	,	PUNCT
american_scientific_journal-7479	260	84	technology	technology	NOUN
american_scientific_journal-7479	260	85	,	,	PUNCT
american_scientific_journal-7479	260	86	and	and	CCONJ
american_scientific_journal-7479	260	87	sciences	science	NOUN
american_scientific_journal-7479	260	88	(	(	PUNCT
american_scientific_journal-7479	260	89	asrjets	asrjet	NOUN
american_scientific_journal-7479	260	90	)	)	PUNCT
american_scientific_journal-7479	260	91	(	(	PUNCT
american_scientific_journal-7479	260	92	2022	2022	NUM
american_scientific_journal-7479	260	93	)	)	PUNCT
american_scientific_journal-7479	260	94	volume	volume	NOUN
american_scientific_journal-7479	260	95	88	88	NUM
american_scientific_journal-7479	260	96	,	,	PUNCT
american_scientific_journal-7479	260	97	no1	no1	PROPN
american_scientific_journal-7479	260	98	,	,	PUNCT
american_scientific_journal-7479	260	99	pp	pp	ADV
american_scientific_journal-7479	260	100	332	332	NUM
american_scientific_journal-7479	260	101	-	-	SYM
american_scientific_journal-7479	260	102	348	348	NUM
american_scientific_journal-7479	260	103	347	347	NUM
american_scientific_journal-7479	260	104	𝛼	𝛼	PRON
american_scientific_journal-7479	260	105	maximum	maximum	ADV
american_scientific_journal-7479	260	106	normalized	normalize	VERB
american_scientific_journal-7479	260	107	deflection	deflection	NOUN
american_scientific_journal-7479	260	108	of	of	ADP
american_scientific_journal-7479	260	109	mid	mid	ADJ
american_scientific_journal-7479	260	110	-	-	NOUN
american_scientific_journal-7479	260	111	span	span	NOUN
american_scientific_journal-7479	260	112	fcm	fcm	X
american_scientific_journal-7479	260	113	0	0	NUM
american_scientific_journal-7479	260	114	0.15	0.15	NUM
american_scientific_journal-7479	260	115	0.25	0.25	NUM
american_scientific_journal-7479	260	116	0.35	0.35	NUM
american_scientific_journal-7479	260	117	0.45	0.45	NUM
american_scientific_journal-7479	260	118	0.55	0.55	NUM
american_scientific_journal-7479	260	119	-1.061	-1.061	PUNCT
american_scientific_journal-7479	260	120	-1.1726	-1.1726	X
american_scientific_journal-7479	260	121	-1.4268	-1.4268	PROPN
american_scientific_journal-7479	260	122	-1.8977	-1.8977	PUNCT
american_scientific_journal-7479	260	123	-2.537	-2.537	X
american_scientific_journal-7479	260	124	-3.6196	-3.6196	NOUN
american_scientific_journal-7479	261	1	1	1	NUM
american_scientific_journal-7479	261	2	1.105	1.105	NUM
american_scientific_journal-7479	261	3	1.345	1.345	NUM
american_scientific_journal-7479	261	4	1.789	1.789	NUM
american_scientific_journal-7479	261	5	2.391	2.391	NUM
american_scientific_journal-7479	261	6	3.412	3.412	NUM
american_scientific_journal-7479	261	7	4	4	NUM
american_scientific_journal-7479	261	8	.	.	PUNCT
american_scientific_journal-7479	261	9	conclusions	conclusion	NOUN
american_scientific_journal-7479	261	10	in	in	ADP
american_scientific_journal-7479	261	11	this	this	DET
american_scientific_journal-7479	261	12	article	article	NOUN
american_scientific_journal-7479	261	13	,	,	PUNCT
american_scientific_journal-7479	261	14	the	the	DET
american_scientific_journal-7479	261	15	vibrations	vibration	NOUN
american_scientific_journal-7479	261	16	of	of	ADP
american_scientific_journal-7479	261	17	cracked	crack	VERB
american_scientific_journal-7479	261	18	euler	euler	PROPN
american_scientific_journal-7479	261	19	bernoulli	bernoulli	PROPN
american_scientific_journal-7479	261	20	beams	beam	NOUN
american_scientific_journal-7479	261	21	under	under	ADP
american_scientific_journal-7479	261	22	moving	move	VERB
american_scientific_journal-7479	261	23	load	load	NOUN
american_scientific_journal-7479	261	24	are	be	AUX
american_scientific_journal-7479	261	25	analyzed	analyze	VERB
american_scientific_journal-7479	261	26	using	use	VERB
american_scientific_journal-7479	261	27	adm	adm	PROPN
american_scientific_journal-7479	261	28	.	.	PUNCT
american_scientific_journal-7479	262	1	the	the	DET
american_scientific_journal-7479	262	2	open	open	ADJ
american_scientific_journal-7479	262	3	crack	crack	NOUN
american_scientific_journal-7479	262	4	was	be	AUX
american_scientific_journal-7479	262	5	modeled	model	VERB
american_scientific_journal-7479	262	6	by	by	ADP
american_scientific_journal-7479	262	7	a	a	DET
american_scientific_journal-7479	262	8	massless	massless	ADJ
american_scientific_journal-7479	262	9	rotational	rotational	ADJ
american_scientific_journal-7479	262	10	spring	spring	NOUN
american_scientific_journal-7479	262	11	.	.	PUNCT
american_scientific_journal-7479	263	1	the	the	DET
american_scientific_journal-7479	263	2	main	main	ADJ
american_scientific_journal-7479	263	3	characteristics	characteristic	NOUN
american_scientific_journal-7479	263	4	of	of	ADP
american_scientific_journal-7479	263	5	adm	adm	PROPN
american_scientific_journal-7479	263	6	were	be	AUX
american_scientific_journal-7479	263	7	its	its	PRON
american_scientific_journal-7479	263	8	higher	high	ADJ
american_scientific_journal-7479	263	9	accuracy	accuracy	NOUN
american_scientific_journal-7479	263	10	and	and	CCONJ
american_scientific_journal-7479	263	11	its	its	PRON
american_scientific_journal-7479	263	12	superiority	superiority	NOUN
american_scientific_journal-7479	263	13	comparison	comparison	NOUN
american_scientific_journal-7479	263	14	with	with	ADP
american_scientific_journal-7479	263	15	other	other	ADJ
american_scientific_journal-7479	263	16	methods	method	NOUN
american_scientific_journal-7479	263	17	,	,	PUNCT
american_scientific_journal-7479	263	18	such	such	ADJ
american_scientific_journal-7479	263	19	as	as	ADP
american_scientific_journal-7479	263	20	fem	fem	NOUN
american_scientific_journal-7479	263	21	.	.	PUNCT
american_scientific_journal-7479	264	1	it	it	PRON
american_scientific_journal-7479	264	2	was	be	AUX
american_scientific_journal-7479	264	3	shown	show	VERB
american_scientific_journal-7479	264	4	that	that	SCONJ
american_scientific_journal-7479	264	5	the	the	DET
american_scientific_journal-7479	264	6	present	present	ADJ
american_scientific_journal-7479	264	7	adm	adm	PROPN
american_scientific_journal-7479	264	8	could	could	AUX
american_scientific_journal-7479	264	9	provide	provide	VERB
american_scientific_journal-7479	264	10	extremely	extremely	ADV
american_scientific_journal-7479	264	11	accurate	accurate	ADJ
american_scientific_journal-7479	264	12	solutions	solution	NOUN
american_scientific_journal-7479	264	13	,	,	PUNCT
american_scientific_journal-7479	264	14	as	as	SCONJ
american_scientific_journal-7479	264	15	compared	compare	VERB
american_scientific_journal-7479	264	16	with	with	ADP
american_scientific_journal-7479	264	17	those	those	PRON
american_scientific_journal-7479	264	18	obtained	obtain	VERB
american_scientific_journal-7479	264	19	from	from	ADP
american_scientific_journal-7479	264	20	an	an	DET
american_scientific_journal-7479	264	21	fem	fem	NOUN
american_scientific_journal-7479	264	22	having	have	VERB
american_scientific_journal-7479	264	23	even	even	ADV
american_scientific_journal-7479	264	24	one	one	NUM
american_scientific_journal-7479	264	25	hundred	hundred	NUM
american_scientific_journal-7479	264	26	elements	element	NOUN
american_scientific_journal-7479	264	27	,	,	PUNCT
american_scientific_journal-7479	264	28	the	the	DET
american_scientific_journal-7479	264	29	following	follow	VERB
american_scientific_journal-7479	264	30	results	result	NOUN
american_scientific_journal-7479	264	31	were	be	AUX
american_scientific_journal-7479	264	32	observed	observe	VERB
american_scientific_journal-7479	264	33	:	:	PUNCT
american_scientific_journal-7479	264	34	vertical	vertical	ADJ
american_scientific_journal-7479	264	35	and	and	CCONJ
american_scientific_journal-7479	264	36	horizontal	horizontal	ADJ
american_scientific_journal-7479	264	37	shifts	shift	NOUN
american_scientific_journal-7479	264	38	of	of	ADP
american_scientific_journal-7479	264	39	the	the	PRON
american_scientific_journal-7479	264	40	(	(	PUNCT
american_scientific_journal-7479	264	41	both	both	CCONJ
american_scientific_journal-7479	264	42	healthy	healthy	ADJ
american_scientific_journal-7479	264	43	and	and	CCONJ
american_scientific_journal-7479	264	44	cracked	cracked	ADJ
american_scientific_journal-7479	264	45	)	)	PUNCT
american_scientific_journal-7479	264	46	beam	beam	NOUN
american_scientific_journal-7479	264	47	mid	mid	ADJ
american_scientific_journal-7479	264	48	-	-	ADJ
american_scientific_journal-7479	264	49	point	point	NOUN
american_scientific_journal-7479	264	50	deflection	deflection	NOUN
american_scientific_journal-7479	264	51	to	to	ADP
american_scientific_journal-7479	264	52	the	the	DET
american_scientific_journal-7479	264	53	higher	high	ADJ
american_scientific_journal-7479	264	54	values	value	NOUN
american_scientific_journal-7479	264	55	were	be	AUX
american_scientific_journal-7479	264	56	a	a	DET
american_scientific_journal-7479	264	57	result	result	NOUN
american_scientific_journal-7479	264	58	of	of	ADP
american_scientific_journal-7479	264	59	•	•	NOUN
american_scientific_journal-7479	264	60	increase	increase	NOUN
american_scientific_journal-7479	264	61	of	of	ADP
american_scientific_journal-7479	264	62	load	load	NOUN
american_scientific_journal-7479	264	63	movement	movement	NOUN
american_scientific_journal-7479	264	64	speed	speed	NOUN
american_scientific_journal-7479	264	65	.	.	PUNCT
american_scientific_journal-7479	265	1	(	(	PUNCT
american_scientific_journal-7479	265	2	move	move	VERB
american_scientific_journal-7479	265	3	load	load	NOUN
american_scientific_journal-7479	265	4	quicker	quick	ADV
american_scientific_journal-7479	265	5	)	)	PUNCT
american_scientific_journal-7479	265	6	•	•	NOUN
american_scientific_journal-7479	265	7	increase	increase	VERB
american_scientific_journal-7479	265	8	the	the	DET
american_scientific_journal-7479	265	9	moving	move	VERB
american_scientific_journal-7479	265	10	load	load	NOUN
american_scientific_journal-7479	265	11	amplitude	amplitude	NOUN
american_scientific_journal-7479	265	12	.	.	PUNCT
american_scientific_journal-7479	266	1	(	(	PUNCT
american_scientific_journal-7479	266	2	greater	great	ADJ
american_scientific_journal-7479	266	3	moving	moving	NOUN
american_scientific_journal-7479	266	4	load	load	NOUN
american_scientific_journal-7479	266	5	)	)	PUNCT
american_scientific_journal-7479	266	6	•	•	NUM
american_scientific_journal-7479	266	7	increased	increase	VERB
american_scientific_journal-7479	266	8	the	the	DET
american_scientific_journal-7479	266	9	height	height	NOUN
american_scientific_journal-7479	266	10	ratio	ratio	NOUN
american_scientific_journal-7479	266	11	of	of	ADP
american_scientific_journal-7479	266	12	the	the	DET
american_scientific_journal-7479	266	13	crack	crack	NOUN
american_scientific_journal-7479	266	14	depth	depth	NOUN
american_scientific_journal-7479	266	15	to	to	ADP
american_scientific_journal-7479	266	16	a	a	DET
american_scientific_journal-7479	266	17	beam	beam	NOUN
american_scientific_journal-7479	266	18	.	.	PUNCT
american_scientific_journal-7479	267	1	(	(	PUNCT
american_scientific_journal-7479	267	2	cracks	crack	NOUN
american_scientific_journal-7479	267	3	deeper	deeply	ADV
american_scientific_journal-7479	267	4	)	)	PUNCT
american_scientific_journal-7479	267	5	the	the	DET
american_scientific_journal-7479	267	6	reduction	reduction	NOUN
american_scientific_journal-7479	267	7	of	of	ADP
american_scientific_journal-7479	267	8	the	the	DET
american_scientific_journal-7479	267	9	maximum	maximum	ADJ
american_scientific_journal-7479	267	10	deflection	deflection	NOUN
american_scientific_journal-7479	267	11	at	at	ADP
american_scientific_journal-7479	267	12	the	the	DET
american_scientific_journal-7479	267	13	midpoint	midpoint	NOUN
american_scientific_journal-7479	267	14	of	of	ADP
american_scientific_journal-7479	267	15	the	the	DET
american_scientific_journal-7479	267	16	cracked	crack	VERB
american_scientific_journal-7479	267	17	euler	euler	NOUN
american_scientific_journal-7479	267	18	bernoulli	bernoulli	PROPN
american_scientific_journal-7479	267	19	beam	beam	NOUN
american_scientific_journal-7479	267	20	could	could	AUX
american_scientific_journal-7479	267	21	be	be	AUX
american_scientific_journal-7479	267	22	the	the	DET
american_scientific_journal-7479	267	23	result	result	NOUN
american_scientific_journal-7479	267	24	of	of	ADP
american_scientific_journal-7479	267	25	shifting	shift	VERB
american_scientific_journal-7479	267	26	crack	crack	NOUN
american_scientific_journal-7479	267	27	location	location	NOUN
american_scientific_journal-7479	267	28	away	away	ADV
american_scientific_journal-7479	267	29	from	from	ADP
american_scientific_journal-7479	267	30	the	the	DET
american_scientific_journal-7479	267	31	center	center	NOUN
american_scientific_journal-7479	267	32	.	.	PUNCT
american_scientific_journal-7479	268	1	references	reference	NOUN
american_scientific_journal-7479	268	2	[	[	X
american_scientific_journal-7479	268	3	1	1	NUM
american_scientific_journal-7479	268	4	]	]	PUNCT
american_scientific_journal-7479	268	5	m.	m.	NOUN
american_scientific_journal-7479	268	6	mofid	mofid	NOUN
american_scientific_journal-7479	268	7	and	and	CCONJ
american_scientific_journal-7479	268	8	m.	m.	NOUN
american_scientific_journal-7479	268	9	shadnam	shadnam	PROPN
american_scientific_journal-7479	268	10	,	,	PUNCT
american_scientific_journal-7479	268	11	“	"	PUNCT
american_scientific_journal-7479	268	12	on	on	ADP
american_scientific_journal-7479	268	13	the	the	DET
american_scientific_journal-7479	268	14	response	response	NOUN
american_scientific_journal-7479	268	15	of	of	ADP
american_scientific_journal-7479	268	16	beams	beam	NOUN
american_scientific_journal-7479	268	17	with	with	ADP
american_scientific_journal-7479	268	18	internal	internal	ADJ
american_scientific_journal-7479	268	19	hinges	hinge	NOUN
american_scientific_journal-7479	268	20	,	,	PUNCT
american_scientific_journal-7479	268	21	under	under	ADP
american_scientific_journal-7479	268	22	moving	move	VERB
american_scientific_journal-7479	268	23	mass	mass	NOUN
american_scientific_journal-7479	268	24	,	,	PUNCT
american_scientific_journal-7479	268	25	”	"	PUNCT
american_scientific_journal-7479	268	26	adv	adv	PROPN
american_scientific_journal-7479	268	27	.	.	PUNCT
american_scientific_journal-7479	269	1	eng	eng	PROPN
american_scientific_journal-7479	269	2	.	.	PUNCT
american_scientific_journal-7479	270	1	softw	softw	PROPN
american_scientific_journal-7479	270	2	.	.	PUNCT
american_scientific_journal-7479	271	1	,	,	PUNCT
american_scientific_journal-7479	271	2	vol	vol	NOUN
american_scientific_journal-7479	271	3	.	.	PROPN
american_scientific_journal-7479	272	1	31	31	NUM
american_scientific_journal-7479	272	2	,	,	PUNCT
american_scientific_journal-7479	272	3	no	no	INTJ
american_scientific_journal-7479	272	4	.	.	NOUN
american_scientific_journal-7479	272	5	5	5	NUM
american_scientific_journal-7479	272	6	,	,	PUNCT
american_scientific_journal-7479	272	7	pp	pp	ADJ
american_scientific_journal-7479	272	8	.	.	PUNCT
american_scientific_journal-7479	273	1	323–328	323–328	NUM
american_scientific_journal-7479	273	2	,	,	PUNCT
american_scientific_journal-7479	273	3	2000	2000	NUM
american_scientific_journal-7479	273	4	.	.	PUNCT
american_scientific_journal-7479	274	1	[	[	X
american_scientific_journal-7479	274	2	2	2	X
american_scientific_journal-7479	274	3	]	]	PUNCT
american_scientific_journal-7479	274	4	m.	m.	NOUN
american_scientific_journal-7479	274	5	a.	a.	PROPN
american_scientific_journal-7479	274	6	mahmoud	mahmoud	PROPN
american_scientific_journal-7479	274	7	and	and	CCONJ
american_scientific_journal-7479	274	8	m.	m.	PROPN
american_scientific_journal-7479	274	9	a.	a.	PROPN
american_scientific_journal-7479	274	10	abou	abou	PROPN
american_scientific_journal-7479	274	11	zaid	zaid	PROPN
american_scientific_journal-7479	274	12	,	,	PUNCT
american_scientific_journal-7479	274	13	“	"	PUNCT
american_scientific_journal-7479	274	14	dynamic	dynamic	ADJ
american_scientific_journal-7479	274	15	response	response	NOUN
american_scientific_journal-7479	274	16	of	of	ADP
american_scientific_journal-7479	274	17	a	a	DET
american_scientific_journal-7479	274	18	beam	beam	NOUN
american_scientific_journal-7479	274	19	with	with	ADP
american_scientific_journal-7479	274	20	a	a	DET
american_scientific_journal-7479	274	21	crack	crack	NOUN
american_scientific_journal-7479	274	22	subject	subject	NOUN
american_scientific_journal-7479	274	23	to	to	ADP
american_scientific_journal-7479	274	24	a	a	DET
american_scientific_journal-7479	274	25	moving	move	VERB
american_scientific_journal-7479	274	26	mass	mass	NOUN
american_scientific_journal-7479	274	27	,	,	PUNCT
american_scientific_journal-7479	274	28	”	"	PUNCT
american_scientific_journal-7479	274	29	j.	j.	PROPN
american_scientific_journal-7479	274	30	sound	sound	PROPN
american_scientific_journal-7479	274	31	vib	vib	PROPN
american_scientific_journal-7479	274	32	.	.	PROPN
american_scientific_journal-7479	274	33	,	,	PUNCT
american_scientific_journal-7479	274	34	vol	vol	NOUN
american_scientific_journal-7479	274	35	.	.	PROPN
american_scientific_journal-7479	274	36	256	256	NUM
american_scientific_journal-7479	274	37	,	,	PUNCT
american_scientific_journal-7479	274	38	no	no	INTJ
american_scientific_journal-7479	274	39	.	.	NOUN
american_scientific_journal-7479	274	40	4	4	NUM
american_scientific_journal-7479	274	41	,	,	PUNCT
american_scientific_journal-7479	274	42	pp	pp	ADJ
american_scientific_journal-7479	274	43	.	.	PUNCT
american_scientific_journal-7479	275	1	591–603	591–603	NUM
american_scientific_journal-7479	275	2	,	,	PUNCT
american_scientific_journal-7479	275	3	2002	2002	NUM
american_scientific_journal-7479	275	4	.	.	PUNCT
american_scientific_journal-7479	276	1	[	[	X
american_scientific_journal-7479	276	2	3	3	X
american_scientific_journal-7479	276	3	]	]	X
american_scientific_journal-7479	276	4	j.-j	j.-j	PROPN
american_scientific_journal-7479	276	5	.	.	PUNCT
american_scientific_journal-7479	276	6	wu	wu	PROPN
american_scientific_journal-7479	276	7	,	,	PUNCT
american_scientific_journal-7479	276	8	a.	a.	PROPN
american_scientific_journal-7479	276	9	r.	r.	PROPN
american_scientific_journal-7479	276	10	whittaker	whittaker	PROPN
american_scientific_journal-7479	276	11	,	,	PUNCT
american_scientific_journal-7479	276	12	and	and	CCONJ
american_scientific_journal-7479	276	13	m.	m.	NOUN
american_scientific_journal-7479	276	14	p.	p.	PROPN
american_scientific_journal-7479	276	15	cartmell	cartmell	PROPN
american_scientific_journal-7479	276	16	,	,	PUNCT
american_scientific_journal-7479	276	17	“	"	PUNCT
american_scientific_journal-7479	276	18	the	the	DET
american_scientific_journal-7479	276	19	use	use	NOUN
american_scientific_journal-7479	276	20	of	of	ADP
american_scientific_journal-7479	276	21	finite	finite	ADJ
american_scientific_journal-7479	276	22	element	element	NOUN
american_scientific_journal-7479	276	23	techniques	technique	NOUN
american_scientific_journal-7479	276	24	for	for	ADP
american_scientific_journal-7479	276	25	calculating	calculate	VERB
american_scientific_journal-7479	276	26	the	the	DET
american_scientific_journal-7479	276	27	dynamic	dynamic	ADJ
american_scientific_journal-7479	276	28	response	response	NOUN
american_scientific_journal-7479	276	29	of	of	ADP
american_scientific_journal-7479	276	30	structures	structure	NOUN
american_scientific_journal-7479	276	31	to	to	ADP
american_scientific_journal-7479	276	32	moving	move	VERB
american_scientific_journal-7479	276	33	loads	load	NOUN
american_scientific_journal-7479	276	34	,	,	PUNCT
american_scientific_journal-7479	276	35	”	"	PUNCT
american_scientific_journal-7479	276	36	comput	comput	NOUN
american_scientific_journal-7479	276	37	.	.	PUNCT
american_scientific_journal-7479	276	38	struct	struct	NOUN
american_scientific_journal-7479	276	39	.	.	PUNCT
american_scientific_journal-7479	276	40	,	,	PUNCT
american_scientific_journal-7479	276	41	vol	vol	NOUN
american_scientific_journal-7479	276	42	.	.	PROPN
american_scientific_journal-7479	277	1	78	78	NUM
american_scientific_journal-7479	277	2	,	,	PUNCT
american_scientific_journal-7479	277	3	no	no	INTJ
american_scientific_journal-7479	277	4	.	.	NOUN
american_scientific_journal-7479	277	5	6	6	NUM
american_scientific_journal-7479	277	6	,	,	PUNCT
american_scientific_journal-7479	277	7	pp	pp	ADJ
american_scientific_journal-7479	277	8	.	.	PUNCT
american_scientific_journal-7479	278	1	789–799	789–799	NUM
american_scientific_journal-7479	278	2	,	,	PUNCT
american_scientific_journal-7479	278	3	2000	2000	NUM
american_scientific_journal-7479	278	4	.	.	PUNCT
american_scientific_journal-7479	279	1	[	[	X
american_scientific_journal-7479	279	2	4	4	NUM
american_scientific_journal-7479	279	3	]	]	PUNCT
american_scientific_journal-7479	279	4	h.-p	h.-p	NOUN
american_scientific_journal-7479	279	5	.	.	PUNCT
american_scientific_journal-7479	280	1	lin	lin	PROPN
american_scientific_journal-7479	280	2	and	and	CCONJ
american_scientific_journal-7479	280	3	s.-c	s.-c	PROPN
american_scientific_journal-7479	280	4	.	.	PUNCT
american_scientific_journal-7479	281	1	chang	chang	PROPN
american_scientific_journal-7479	281	2	,	,	PUNCT
american_scientific_journal-7479	281	3	“	"	PUNCT
american_scientific_journal-7479	281	4	forced	force	VERB
american_scientific_journal-7479	281	5	responses	response	NOUN
american_scientific_journal-7479	281	6	of	of	ADP
american_scientific_journal-7479	281	7	cracked	crack	VERB
american_scientific_journal-7479	281	8	cantilever	cantilever	NOUN
american_scientific_journal-7479	281	9	beams	beam	NOUN
american_scientific_journal-7479	281	10	subjected	subject	VERB
american_scientific_journal-7479	281	11	to	to	ADP
american_scientific_journal-7479	281	12	a	a	DET
american_scientific_journal-7479	281	13	concentrated	concentrated	ADJ
american_scientific_journal-7479	281	14	moving	moving	NOUN
american_scientific_journal-7479	281	15	load	load	NOUN
american_scientific_journal-7479	281	16	,	,	PUNCT
american_scientific_journal-7479	281	17	”	"	PUNCT
american_scientific_journal-7479	281	18	int	int	NOUN
american_scientific_journal-7479	281	19	.	.	PUNCT
american_scientific_journal-7479	282	1	j.	j.	PROPN
american_scientific_journal-7479	282	2	mech	mech	PROPN
american_scientific_journal-7479	282	3	.	.	PUNCT
american_scientific_journal-7479	283	1	sci	sci	PROPN
american_scientific_journal-7479	283	2	.	.	PROPN
american_scientific_journal-7479	283	3	,	,	PUNCT
american_scientific_journal-7479	283	4	vol	vol	NOUN
american_scientific_journal-7479	283	5	.	.	PROPN
american_scientific_journal-7479	284	1	48	48	NUM
american_scientific_journal-7479	284	2	,	,	PUNCT
american_scientific_journal-7479	284	3	no	no	INTJ
american_scientific_journal-7479	284	4	.	.	NOUN
american_scientific_journal-7479	284	5	12	12	NUM
american_scientific_journal-7479	284	6	,	,	PUNCT
american_scientific_journal-7479	284	7	pp	pp	ADJ
american_scientific_journal-7479	284	8	.	.	PUNCT
american_scientific_journal-7479	285	1	1456–1463	1456–1463	NUM
american_scientific_journal-7479	285	2	,	,	PUNCT
american_scientific_journal-7479	285	3	2006	2006	NUM
american_scientific_journal-7479	285	4	.	.	PUNCT
american_scientific_journal-7479	286	1	[	[	X
american_scientific_journal-7479	286	2	5	5	X
american_scientific_journal-7479	286	3	]	]	PUNCT
american_scientific_journal-7479	286	4	s.	s.	PROPN
american_scientific_journal-7479	286	5	zhong	zhong	PROPN
american_scientific_journal-7479	286	6	and	and	CCONJ
american_scientific_journal-7479	286	7	s.	s.	PROPN
american_scientific_journal-7479	286	8	o.	o.	PROPN
american_scientific_journal-7479	286	9	oyadiji	oyadiji	PROPN
american_scientific_journal-7479	286	10	,	,	PUNCT
american_scientific_journal-7479	286	11	“	"	PUNCT
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american_scientific_journal-7479	286	14	of	of	ADP
american_scientific_journal-7479	286	15	natural	natural	ADJ
american_scientific_journal-7479	286	16	frequencies	frequency	NOUN
american_scientific_journal-7479	286	17	of	of	ADP
american_scientific_journal-7479	286	18	cracked	crack	VERB
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american_scientific_journal-7479	286	20	supported	support	VERB
american_scientific_journal-7479	286	21	beams	beam	NOUN
american_scientific_journal-7479	286	22	with	with	ADP
american_scientific_journal-7479	286	23	a	a	DET
american_scientific_journal-7479	286	24	stationary	stationary	ADJ
american_scientific_journal-7479	286	25	roving	rove	VERB
american_scientific_journal-7479	286	26	mass	mass	NOUN
american_scientific_journal-7479	286	27	,	,	PUNCT
american_scientific_journal-7479	286	28	”	"	PUNCT
american_scientific_journal-7479	286	29	j.	j.	PROPN
american_scientific_journal-7479	286	30	sound	sound	PROPN
american_scientific_journal-7479	286	31	vib	vib	PROPN
american_scientific_journal-7479	286	32	.	.	PROPN
american_scientific_journal-7479	286	33	,	,	PUNCT
american_scientific_journal-7479	286	34	vol	vol	NOUN
american_scientific_journal-7479	286	35	.	.	PROPN
american_scientific_journal-7479	286	36	311	311	NUM
american_scientific_journal-7479	286	37	,	,	PUNCT
american_scientific_journal-7479	286	38	no	no	INTJ
american_scientific_journal-7479	286	39	.	.	PUNCT
american_scientific_journal-7479	287	1	1–2	1–2	NUM
american_scientific_journal-7479	287	2	,	,	PUNCT
american_scientific_journal-7479	287	3	pp	pp	ADJ
american_scientific_journal-7479	287	4	.	.	PUNCT
american_scientific_journal-7479	288	1	328–352	328–352	NUM
american_scientific_journal-7479	288	2	,	,	PUNCT
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american_scientific_journal-7479	288	4	.	.	PUNCT
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american_scientific_journal-7479	289	2	6	6	NUM
american_scientific_journal-7479	289	3	]	]	PUNCT
american_scientific_journal-7479	289	4	s.	s.	PROPN
american_scientific_journal-7479	289	5	s.	s.	PROPN
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american_scientific_journal-7479	289	11	,	,	PUNCT
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american_scientific_journal-7479	289	13	dynamic	dynamic	ADJ
american_scientific_journal-7479	289	14	behavior	behavior	NOUN
american_scientific_journal-7479	289	15	of	of	ADP
american_scientific_journal-7479	289	16	damaged	damage	VERB
american_scientific_journal-7479	289	17	concrete	concrete	ADJ
american_scientific_journal-7479	289	18	bridge	bridge	NOUN
american_scientific_journal-7479	289	19	structures	structure	NOUN
american_scientific_journal-7479	289	20	under	under	ADP
american_scientific_journal-7479	289	21	moving	move	VERB
american_scientific_journal-7479	289	22	vehicular	vehicular	ADJ
american_scientific_journal-7479	289	23	loads	load	NOUN
american_scientific_journal-7479	289	24	,	,	PUNCT
american_scientific_journal-7479	289	25	”	"	PUNCT
american_scientific_journal-7479	289	26	eng	eng	PROPN
american_scientific_journal-7479	289	27	.	.	PROPN
american_scientific_journal-7479	289	28	struct	struct	PROPN
american_scientific_journal-7479	289	29	.	.	PUNCT
american_scientific_journal-7479	289	30	,	,	PUNCT
american_scientific_journal-7479	289	31	vol	vol	NOUN
american_scientific_journal-7479	289	32	.	.	PROPN
american_scientific_journal-7479	289	33	26	26	NUM
american_scientific_journal-7479	289	34	,	,	PUNCT
american_scientific_journal-7479	289	35	no	no	INTJ
american_scientific_journal-7479	289	36	.	.	NOUN
american_scientific_journal-7479	289	37	9	9	NUM
american_scientific_journal-7479	289	38	,	,	PUNCT
american_scientific_journal-7479	289	39	pp	pp	ADJ
american_scientific_journal-7479	289	40	.	.	PUNCT
american_scientific_journal-7479	289	41	1279–1293	1279–1293	NUM
american_scientific_journal-7479	289	42	,	,	PUNCT
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american_scientific_journal-7479	289	44	.	.	PUNCT
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american_scientific_journal-7479	290	3	scientific	scientific	ADJ
american_scientific_journal-7479	290	4	research	research	NOUN
american_scientific_journal-7479	290	5	journal	journal	NOUN
american_scientific_journal-7479	290	6	for	for	ADP
american_scientific_journal-7479	290	7	engineering	engineering	NOUN
american_scientific_journal-7479	290	8	,	,	PUNCT
american_scientific_journal-7479	290	9	technology	technology	NOUN
american_scientific_journal-7479	290	10	,	,	PUNCT
american_scientific_journal-7479	290	11	and	and	CCONJ
american_scientific_journal-7479	290	12	sciences	science	NOUN
american_scientific_journal-7479	290	13	(	(	PUNCT
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american_scientific_journal-7479	290	15	)	)	PUNCT
american_scientific_journal-7479	290	16	(	(	PUNCT
american_scientific_journal-7479	290	17	2022	2022	NUM
american_scientific_journal-7479	290	18	)	)	PUNCT
american_scientific_journal-7479	290	19	volume	volume	NOUN
american_scientific_journal-7479	290	20	88	88	NUM
american_scientific_journal-7479	290	21	,	,	PUNCT
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american_scientific_journal-7479	290	23	,	,	PUNCT
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american_scientific_journal-7479	290	25	332	332	NUM
american_scientific_journal-7479	290	26	-	-	SYM
american_scientific_journal-7479	290	27	348	348	NUM
american_scientific_journal-7479	290	28	348	348	NUM
american_scientific_journal-7479	290	29	[	[	X
american_scientific_journal-7479	290	30	7	7	NUM
american_scientific_journal-7479	290	31	]	]	X
american_scientific_journal-7479	290	32	c.	c.	PROPN
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american_scientific_journal-7479	290	34	and	and	CCONJ
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american_scientific_journal-7479	290	36	a.	a.	PROPN
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american_scientific_journal-7479	290	38	,	,	PUNCT
american_scientific_journal-7479	290	39	“	"	PUNCT
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american_scientific_journal-7479	290	41	of	of	ADP
american_scientific_journal-7479	290	42	damaged	damage	VERB
american_scientific_journal-7479	290	43	beams	beam	NOUN
american_scientific_journal-7479	290	44	under	under	ADP
american_scientific_journal-7479	290	45	a	a	DET
american_scientific_journal-7479	290	46	moving	move	VERB
american_scientific_journal-7479	290	47	mass	mass	NOUN
american_scientific_journal-7479	290	48	:	:	PUNCT
american_scientific_journal-7479	290	49	theory	theory	NOUN
american_scientific_journal-7479	290	50	and	and	CCONJ
american_scientific_journal-7479	290	51	experimental	experimental	ADJ
american_scientific_journal-7479	290	52	validation	validation	NOUN
american_scientific_journal-7479	290	53	,	,	PUNCT
american_scientific_journal-7479	290	54	”	"	PUNCT
american_scientific_journal-7479	290	55	j.	j.	PROPN
american_scientific_journal-7479	290	56	sound	sound	PROPN
american_scientific_journal-7479	290	57	vib	vib	PROPN
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american_scientific_journal-7479	290	59	,	,	PUNCT
american_scientific_journal-7479	290	60	vol	vol	NOUN
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american_scientific_journal-7479	290	62	274	274	NUM
american_scientific_journal-7479	290	63	,	,	PUNCT
american_scientific_journal-7479	290	64	no	no	INTJ
american_scientific_journal-7479	290	65	.	.	PUNCT
american_scientific_journal-7479	291	1	3–5	3–5	NUM
american_scientific_journal-7479	291	2	,	,	PUNCT
american_scientific_journal-7479	291	3	pp	pp	ADJ
american_scientific_journal-7479	291	4	.	.	PUNCT
american_scientific_journal-7479	292	1	567–582	567–582	NUM
american_scientific_journal-7479	292	2	,	,	PUNCT
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american_scientific_journal-7479	292	4	.	.	PUNCT
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american_scientific_journal-7479	293	3	]	]	PUNCT
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american_scientific_journal-7479	293	14	of	of	ADP
american_scientific_journal-7479	293	15	physics	physics	NOUN
american_scientific_journal-7479	293	16	by	by	ADP
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american_scientific_journal-7479	293	20	a	a	DET
american_scientific_journal-7479	293	21	new	new	ADJ
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american_scientific_journal-7479	293	23	,	,	PUNCT
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american_scientific_journal-7479	293	25	kybernetes	kybernete	NOUN
american_scientific_journal-7479	293	26	,	,	PUNCT
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american_scientific_journal-7479	293	28	.	.	PUNCT
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american_scientific_journal-7479	294	4	a.-m	a.-m	NOUN
american_scientific_journal-7479	294	5	.	.	PUNCT
american_scientific_journal-7479	295	1	wazwaz	wazwaz	NOUN
american_scientific_journal-7479	295	2	,	,	PUNCT
american_scientific_journal-7479	295	3	“	"	PUNCT
american_scientific_journal-7479	295	4	analytic	analytic	ADJ
american_scientific_journal-7479	295	5	treatment	treatment	NOUN
american_scientific_journal-7479	295	6	for	for	ADP
american_scientific_journal-7479	295	7	variable	variable	ADJ
american_scientific_journal-7479	295	8	coefficient	coefficient	NOUN
american_scientific_journal-7479	295	9	fourth	fourth	ADJ
american_scientific_journal-7479	295	10	-	-	PUNCT
american_scientific_journal-7479	295	11	order	order	NOUN
american_scientific_journal-7479	295	12	parabolic	parabolic	ADJ
american_scientific_journal-7479	295	13	partial	partial	ADJ
american_scientific_journal-7479	295	14	differential	differential	NOUN
american_scientific_journal-7479	295	15	equations	equation	NOUN
american_scientific_journal-7479	295	16	,	,	PUNCT
american_scientific_journal-7479	295	17	”	"	PUNCT
american_scientific_journal-7479	295	18	appl	appl	NOUN
american_scientific_journal-7479	295	19	.	.	PROPN
american_scientific_journal-7479	295	20	math	math	NOUN
american_scientific_journal-7479	295	21	.	.	PUNCT
american_scientific_journal-7479	296	1	comput	comput	NOUN
american_scientific_journal-7479	296	2	.	.	PUNCT
american_scientific_journal-7479	296	3	,	,	PUNCT
american_scientific_journal-7479	296	4	vol	vol	NOUN
american_scientific_journal-7479	296	5	.	.	PROPN
american_scientific_journal-7479	297	1	123	123	NUM
american_scientific_journal-7479	297	2	,	,	PUNCT
american_scientific_journal-7479	297	3	no	no	INTJ
american_scientific_journal-7479	297	4	.	.	NOUN
american_scientific_journal-7479	297	5	2	2	NUM
american_scientific_journal-7479	297	6	,	,	PUNCT
american_scientific_journal-7479	297	7	pp	pp	ADJ
american_scientific_journal-7479	297	8	.	.	PUNCT
american_scientific_journal-7479	298	1	219–227	219–227	NUM
american_scientific_journal-7479	298	2	,	,	PUNCT
american_scientific_journal-7479	298	3	2001	2001	NUM
american_scientific_journal-7479	298	4	.	.	PUNCT
american_scientific_journal-7479	299	1	[	[	X
american_scientific_journal-7479	299	2	10	10	NUM
american_scientific_journal-7479	299	3	]	]	X
american_scientific_journal-7479	299	4	h.	h.	PROPN
american_scientific_journal-7479	299	5	haddadpour	haddadpour	PROPN
american_scientific_journal-7479	299	6	,	,	PUNCT
american_scientific_journal-7479	299	7	“	"	PUNCT
american_scientific_journal-7479	299	8	an	an	DET
american_scientific_journal-7479	299	9	exact	exact	ADJ
american_scientific_journal-7479	299	10	solution	solution	NOUN
american_scientific_journal-7479	299	11	for	for	ADP
american_scientific_journal-7479	299	12	variable	variable	ADJ
american_scientific_journal-7479	299	13	coefficients	coefficient	NOUN
american_scientific_journal-7479	299	14	fourth	fourth	ADJ
american_scientific_journal-7479	299	15	-	-	PUNCT
american_scientific_journal-7479	299	16	order	order	NOUN
american_scientific_journal-7479	299	17	wave	wave	NOUN
american_scientific_journal-7479	299	18	equation	equation	NOUN
american_scientific_journal-7479	299	19	using	use	VERB
american_scientific_journal-7479	299	20	the	the	DET
american_scientific_journal-7479	299	21	adomian	adomian	NOUN
american_scientific_journal-7479	299	22	method	method	NOUN
american_scientific_journal-7479	299	23	,	,	PUNCT
american_scientific_journal-7479	299	24	”	"	PUNCT
american_scientific_journal-7479	299	25	math	math	NOUN
american_scientific_journal-7479	299	26	.	.	PUNCT
american_scientific_journal-7479	300	1	comput	comput	NOUN
american_scientific_journal-7479	300	2	.	.	PUNCT
american_scientific_journal-7479	301	1	model	model	PROPN
american_scientific_journal-7479	301	2	.	.	PUNCT
american_scientific_journal-7479	302	1	,	,	PUNCT
american_scientific_journal-7479	302	2	vol	vol	NOUN
american_scientific_journal-7479	302	3	.	.	PROPN
american_scientific_journal-7479	303	1	44	44	NUM
american_scientific_journal-7479	303	2	,	,	PUNCT
american_scientific_journal-7479	303	3	no	no	INTJ
american_scientific_journal-7479	303	4	.	.	PUNCT
american_scientific_journal-7479	304	1	11–12	11–12	NUM
american_scientific_journal-7479	304	2	,	,	PUNCT
american_scientific_journal-7479	304	3	pp	pp	ADJ
american_scientific_journal-7479	304	4	.	.	PUNCT
american_scientific_journal-7479	305	1	1144–1152	1144–1152	NUM
american_scientific_journal-7479	305	2	,	,	PUNCT
american_scientific_journal-7479	305	3	2006	2006	NUM
american_scientific_journal-7479	305	4	.	.	PUNCT
american_scientific_journal-7479	306	1	[	[	X
american_scientific_journal-7479	306	2	11	11	NUM
american_scientific_journal-7479	306	3	]	]	PUNCT
american_scientific_journal-7479	306	4	h.-y	h.-y	NOUN
american_scientific_journal-7479	306	5	.	.	PUNCT
american_scientific_journal-7479	307	1	lai	lai	PROPN
american_scientific_journal-7479	307	2	and	and	CCONJ
american_scientific_journal-7479	307	3	j.-c	j.-c	PROPN
american_scientific_journal-7479	307	4	.	.	PUNCT
american_scientific_journal-7479	308	1	hsu	hsu	PROPN
american_scientific_journal-7479	308	2	,	,	PUNCT
american_scientific_journal-7479	308	3	“	"	PUNCT
american_scientific_journal-7479	308	4	an	an	DET
american_scientific_journal-7479	308	5	innovative	innovative	ADJ
american_scientific_journal-7479	308	6	eigenvalue	eigenvalue	NOUN
american_scientific_journal-7479	308	7	problem	problem	NOUN
american_scientific_journal-7479	308	8	solver	solver	VERB
american_scientific_journal-7479	308	9	for	for	ADP
american_scientific_journal-7479	308	10	free	free	ADJ
american_scientific_journal-7479	308	11	vibration	vibration	NOUN
american_scientific_journal-7479	308	12	of	of	ADP
american_scientific_journal-7479	308	13	euler	euler	PROPN
american_scientific_journal-7479	308	14	–	–	PUNCT
american_scientific_journal-7479	308	15	bernoulli	bernoulli	NOUN
american_scientific_journal-7479	308	16	beam	beam	NOUN
american_scientific_journal-7479	308	17	by	by	ADP
american_scientific_journal-7479	308	18	using	use	VERB
american_scientific_journal-7479	308	19	the	the	DET
american_scientific_journal-7479	308	20	adomian	adomian	NOUN
american_scientific_journal-7479	308	21	decomposition	decomposition	NOUN
american_scientific_journal-7479	308	22	method	method	NOUN
american_scientific_journal-7479	308	23	,	,	PUNCT
american_scientific_journal-7479	308	24	”	"	PUNCT
american_scientific_journal-7479	308	25	comput	comput	NOUN
american_scientific_journal-7479	308	26	.	.	PUNCT
american_scientific_journal-7479	309	1	math	math	NOUN
american_scientific_journal-7479	309	2	.	.	PUNCT
american_scientific_journal-7479	310	1	appl	appl	PROPN
american_scientific_journal-7479	310	2	.	.	PROPN
american_scientific_journal-7479	310	3	,	,	PUNCT
american_scientific_journal-7479	310	4	vol	vol	NOUN
american_scientific_journal-7479	310	5	.	.	PROPN
american_scientific_journal-7479	311	1	56	56	NUM
american_scientific_journal-7479	311	2	,	,	PUNCT
american_scientific_journal-7479	311	3	no	no	INTJ
american_scientific_journal-7479	311	4	.	.	NOUN
american_scientific_journal-7479	311	5	12	12	NUM
american_scientific_journal-7479	311	6	,	,	PUNCT
american_scientific_journal-7479	311	7	pp	pp	ADJ
american_scientific_journal-7479	311	8	.	.	PUNCT
american_scientific_journal-7479	311	9	3204–3220	3204–3220	NUM
american_scientific_journal-7479	311	10	,	,	PUNCT
american_scientific_journal-7479	311	11	2008	2008	NUM
american_scientific_journal-7479	311	12	.	.	PUNCT
american_scientific_journal-7479	312	1	[	[	X
american_scientific_journal-7479	312	2	12	12	NUM
american_scientific_journal-7479	312	3	]	]	X
american_scientific_journal-7479	312	4	q.	q.	PROPN
american_scientific_journal-7479	312	5	mao	mao	PROPN
american_scientific_journal-7479	312	6	,	,	PUNCT
american_scientific_journal-7479	312	7	“	"	PUNCT
american_scientific_journal-7479	312	8	free	free	ADJ
american_scientific_journal-7479	312	9	vibration	vibration	NOUN
american_scientific_journal-7479	312	10	analysis	analysis	NOUN
american_scientific_journal-7479	312	11	of	of	ADP
american_scientific_journal-7479	312	12	uniform	uniform	ADJ
american_scientific_journal-7479	312	13	beams	beam	NOUN
american_scientific_journal-7479	312	14	with	with	ADP
american_scientific_journal-7479	312	15	arbitrary	arbitrary	ADJ
american_scientific_journal-7479	312	16	number	number	NOUN
american_scientific_journal-7479	312	17	of	of	ADP
american_scientific_journal-7479	312	18	cracks	crack	NOUN
american_scientific_journal-7479	312	19	by	by	ADP
american_scientific_journal-7479	312	20	using	use	VERB
american_scientific_journal-7479	312	21	adomian	adomian	NOUN
american_scientific_journal-7479	312	22	decomposition	decomposition	NOUN
american_scientific_journal-7479	312	23	method	method	NOUN
american_scientific_journal-7479	312	24	,	,	PUNCT
american_scientific_journal-7479	312	25	”	"	PUNCT
american_scientific_journal-7479	312	26	world	world	NOUN
american_scientific_journal-7479	312	27	appl	appl	NOUN
american_scientific_journal-7479	312	28	.	.	PUNCT
american_scientific_journal-7479	313	1	sci	sci	PROPN
american_scientific_journal-7479	313	2	.	.	PUNCT
american_scientific_journal-7479	314	1	j.	j.	PROPN
american_scientific_journal-7479	314	2	,	,	PUNCT
american_scientific_journal-7479	314	3	vol	vol	NOUN
american_scientific_journal-7479	314	4	.	.	PROPN
american_scientific_journal-7479	314	5	1	1	NUM
american_scientific_journal-7479	314	6	,	,	PUNCT
american_scientific_journal-7479	314	7	no	no	INTJ
american_scientific_journal-7479	314	8	.	.	NOUN
american_scientific_journal-7479	314	9	19	19	NUM
american_scientific_journal-7479	314	10	,	,	PUNCT
american_scientific_journal-7479	314	11	pp	pp	ADJ
american_scientific_journal-7479	314	12	.	.	PUNCT
american_scientific_journal-7479	314	13	1721–1723	1721–1723	NUM
american_scientific_journal-7479	314	14	,	,	PUNCT
american_scientific_journal-7479	314	15	2012	2012	NUM
american_scientific_journal-7479	314	16	.	.	PUNCT
american_scientific_journal-7479	315	1	[	[	X
american_scientific_journal-7479	315	2	13	13	NUM
american_scientific_journal-7479	315	3	]	]	PUNCT
american_scientific_journal-7479	315	4	q.	q.	PROPN
american_scientific_journal-7479	315	5	mao	mao	PROPN
american_scientific_journal-7479	315	6	and	and	CCONJ
american_scientific_journal-7479	315	7	s.	s.	PROPN
american_scientific_journal-7479	315	8	pietrzko	pietrzko	PROPN
american_scientific_journal-7479	315	9	,	,	PUNCT
american_scientific_journal-7479	315	10	“	"	PUNCT
american_scientific_journal-7479	315	11	design	design	NOUN
american_scientific_journal-7479	315	12	of	of	ADP
american_scientific_journal-7479	315	13	shaped	shape	VERB
american_scientific_journal-7479	315	14	piezoelectric	piezoelectric	NOUN
american_scientific_journal-7479	315	15	modal	modal	NOUN
american_scientific_journal-7479	315	16	sensor	sensor	NOUN
american_scientific_journal-7479	315	17	for	for	ADP
american_scientific_journal-7479	315	18	beam	beam	NOUN
american_scientific_journal-7479	315	19	with	with	ADP
american_scientific_journal-7479	315	20	arbitrary	arbitrary	ADJ
american_scientific_journal-7479	315	21	boundary	boundary	ADJ
american_scientific_journal-7479	315	22	conditions	condition	NOUN
american_scientific_journal-7479	315	23	by	by	ADP
american_scientific_journal-7479	315	24	using	use	VERB
american_scientific_journal-7479	315	25	adomian	adomian	NOUN
american_scientific_journal-7479	315	26	decomposition	decomposition	NOUN
american_scientific_journal-7479	315	27	method	method	NOUN
american_scientific_journal-7479	315	28	,	,	PUNCT
american_scientific_journal-7479	315	29	”	"	PUNCT
american_scientific_journal-7479	315	30	j.	j.	PROPN
american_scientific_journal-7479	315	31	sound	sound	PROPN
american_scientific_journal-7479	315	32	vib	vib	PROPN
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american_scientific_journal-7479	315	34	,	,	PUNCT
american_scientific_journal-7479	315	35	vol	vol	NOUN
american_scientific_journal-7479	315	36	.	.	PROPN
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american_scientific_journal-7479	315	38	,	,	PUNCT
american_scientific_journal-7479	315	39	no	no	INTJ
american_scientific_journal-7479	315	40	.	.	NOUN
american_scientific_journal-7479	315	41	11	11	NUM
american_scientific_journal-7479	315	42	,	,	PUNCT
american_scientific_journal-7479	315	43	pp	pp	ADJ
american_scientific_journal-7479	315	44	.	.	PUNCT
american_scientific_journal-7479	315	45	2068–2082	2068–2082	NUM
american_scientific_journal-7479	315	46	,	,	PUNCT
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american_scientific_journal-7479	315	48	.	.	PUNCT
american_scientific_journal-7479	316	1	[	[	X
american_scientific_journal-7479	316	2	14	14	NUM
american_scientific_journal-7479	316	3	]	]	X
american_scientific_journal-7479	316	4	d.	d.	PROPN
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american_scientific_journal-7479	316	6	and	and	CCONJ
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american_scientific_journal-7479	316	8	riganti	riganti	PROPN
american_scientific_journal-7479	316	9	,	,	PUNCT
american_scientific_journal-7479	316	10	“	"	PUNCT
american_scientific_journal-7479	316	11	solutions	solution	NOUN
american_scientific_journal-7479	316	12	of	of	ADP
american_scientific_journal-7479	316	13	nonlinear	nonlinear	ADJ
american_scientific_journal-7479	316	14	boundary	boundary	ADJ
american_scientific_journal-7479	316	15	value	value	NOUN
american_scientific_journal-7479	316	16	problems	problem	NOUN
american_scientific_journal-7479	316	17	by	by	ADP
american_scientific_journal-7479	316	18	the	the	DET
american_scientific_journal-7479	316	19	decomposition	decomposition	NOUN
american_scientific_journal-7479	316	20	method	method	NOUN
american_scientific_journal-7479	316	21	,	,	PUNCT
american_scientific_journal-7479	316	22	”	"	PUNCT
american_scientific_journal-7479	316	23	appl	appl	NOUN
american_scientific_journal-7479	316	24	.	.	PROPN
american_scientific_journal-7479	316	25	math	math	PROPN
american_scientific_journal-7479	316	26	.	.	PUNCT
american_scientific_journal-7479	317	1	model	model	PROPN
american_scientific_journal-7479	317	2	.	.	PUNCT
american_scientific_journal-7479	317	3	,	,	PUNCT
american_scientific_journal-7479	317	4	vol	vol	NOUN
american_scientific_journal-7479	317	5	.	.	PROPN
american_scientific_journal-7479	318	1	10	10	NUM
american_scientific_journal-7479	318	2	,	,	PUNCT
american_scientific_journal-7479	318	3	no	no	INTJ
american_scientific_journal-7479	318	4	.	.	NOUN
american_scientific_journal-7479	318	5	1	1	NUM
american_scientific_journal-7479	318	6	,	,	PUNCT
american_scientific_journal-7479	318	7	pp	pp	ADJ
american_scientific_journal-7479	318	8	.	.	PUNCT
american_scientific_journal-7479	319	1	49–52	49–52	NUM
american_scientific_journal-7479	319	2	,	,	PUNCT
american_scientific_journal-7479	319	3	1986	1986	NUM
american_scientific_journal-7479	319	4	.	.	PUNCT
american_scientific_journal-7479	320	1	[	[	X
american_scientific_journal-7479	320	2	15	15	NUM
american_scientific_journal-7479	320	3	]	]	X
american_scientific_journal-7479	320	4	a.-m	a.-m	NOUN
american_scientific_journal-7479	320	5	.	.	PUNCT
american_scientific_journal-7479	321	1	wazwaz	wazwaz	NOUN
american_scientific_journal-7479	321	2	,	,	PUNCT
american_scientific_journal-7479	321	3	“	"	PUNCT
american_scientific_journal-7479	321	4	the	the	DET
american_scientific_journal-7479	321	5	modified	modified	ADJ
american_scientific_journal-7479	321	6	adomian	adomian	NOUN
american_scientific_journal-7479	321	7	decomposition	decomposition	NOUN
american_scientific_journal-7479	321	8	method	method	NOUN
american_scientific_journal-7479	321	9	for	for	ADP
american_scientific_journal-7479	321	10	solving	solve	VERB
american_scientific_journal-7479	321	11	linear	linear	NOUN
american_scientific_journal-7479	321	12	and	and	CCONJ
american_scientific_journal-7479	321	13	nonlinear	nonlinear	ADJ
american_scientific_journal-7479	321	14	boundary	boundary	ADJ
american_scientific_journal-7479	321	15	value	value	NOUN
american_scientific_journal-7479	321	16	problems	problem	NOUN
american_scientific_journal-7479	321	17	of	of	ADP
american_scientific_journal-7479	321	18	tenth	tenth	ADJ
american_scientific_journal-7479	321	19	-	-	PUNCT
american_scientific_journal-7479	321	20	order	order	NOUN
american_scientific_journal-7479	321	21	and	and	CCONJ
american_scientific_journal-7479	321	22	twelfth	twelfth	ADJ
american_scientific_journal-7479	321	23	-	-	PUNCT
american_scientific_journal-7479	321	24	order	order	NOUN
american_scientific_journal-7479	321	25	,	,	PUNCT
american_scientific_journal-7479	321	26	”	"	PUNCT
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american_scientific_journal-7479	321	28	.	.	PUNCT
american_scientific_journal-7479	322	1	j.	j.	PROPN
american_scientific_journal-7479	322	2	nonlinear	nonlinear	PROPN
american_scientific_journal-7479	322	3	sci	sci	PROPN
american_scientific_journal-7479	322	4	.	.	PUNCT
american_scientific_journal-7479	322	5	numer	numer	PROPN
american_scientific_journal-7479	322	6	.	.	PUNCT
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american_scientific_journal-7479	323	2	.	.	PROPN
american_scientific_journal-7479	323	3	,	,	PUNCT
american_scientific_journal-7479	323	4	vol	vol	NOUN
american_scientific_journal-7479	323	5	.	.	PROPN
american_scientific_journal-7479	323	6	1	1	NUM
american_scientific_journal-7479	323	7	,	,	PUNCT
american_scientific_journal-7479	323	8	no	no	INTJ
american_scientific_journal-7479	323	9	.	.	NOUN
american_scientific_journal-7479	323	10	1	1	NUM
american_scientific_journal-7479	323	11	,	,	PUNCT
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american_scientific_journal-7479	323	13	.	.	PUNCT
american_scientific_journal-7479	324	1	17–24	17–24	NUM
american_scientific_journal-7479	324	2	,	,	PUNCT
american_scientific_journal-7479	324	3	2000	2000	NUM
american_scientific_journal-7479	324	4	.	.	PUNCT
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american_scientific_journal-7479	325	2	16	16	NUM
american_scientific_journal-7479	325	3	]	]	PUNCT
american_scientific_journal-7479	325	4	w.	w.	PROPN
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american_scientific_journal-7479	325	6	-	-	PUNCT
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american_scientific_journal-7479	325	8	and	and	CCONJ
american_scientific_journal-7479	325	9	l.	l.	PROPN
american_scientific_journal-7479	325	10	casasús	casasús	PROPN
american_scientific_journal-7479	325	11	,	,	PUNCT
american_scientific_journal-7479	325	12	“	"	PUNCT
american_scientific_journal-7479	325	13	approximate	approximate	ADJ
american_scientific_journal-7479	325	14	analytical	analytical	ADJ
american_scientific_journal-7479	325	15	solution	solution	NOUN
american_scientific_journal-7479	325	16	of	of	ADP
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american_scientific_journal-7479	325	19	boundary	boundary	ADJ
american_scientific_journal-7479	325	20	value	value	NOUN
american_scientific_journal-7479	325	21	problems	problem	NOUN
american_scientific_journal-7479	325	22	,	,	PUNCT
american_scientific_journal-7479	325	23	”	"	PUNCT
american_scientific_journal-7479	325	24	numer	numer	NOUN
american_scientific_journal-7479	325	25	.	.	PUNCT
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american_scientific_journal-7479	326	2	,	,	PUNCT
american_scientific_journal-7479	326	3	vol	vol	NOUN
american_scientific_journal-7479	326	4	.	.	PROPN
american_scientific_journal-7479	326	5	40	40	NUM
american_scientific_journal-7479	326	6	,	,	PUNCT
american_scientific_journal-7479	326	7	no	no	INTJ
american_scientific_journal-7479	326	8	.	.	NOUN
american_scientific_journal-7479	326	9	1	1	NUM
american_scientific_journal-7479	326	10	,	,	PUNCT
american_scientific_journal-7479	326	11	pp	pp	ADJ
american_scientific_journal-7479	326	12	.	.	PUNCT
american_scientific_journal-7479	327	1	67–78	67–78	NOUN
american_scientific_journal-7479	327	2	,	,	PUNCT
american_scientific_journal-7479	327	3	2005	2005	NUM
american_scientific_journal-7479	327	4	.	.	PUNCT
american_scientific_journal-7479	328	1	[	[	X
american_scientific_journal-7479	328	2	17	17	NUM
american_scientific_journal-7479	328	3	]	]	X
american_scientific_journal-7479	328	4	f.	f.	NOUN
american_scientific_journal-7479	328	5	bi̇li̇k	bi̇li̇k	PROPN
american_scientific_journal-7479	328	6	and	and	CCONJ
american_scientific_journal-7479	328	7	t.	t.	PROPN
american_scientific_journal-7479	328	8	karaçay	karaçay	NOUN
american_scientific_journal-7479	328	9	,	,	PUNCT
american_scientific_journal-7479	328	10	“	"	PUNCT
american_scientific_journal-7479	328	11	vibration	vibration	NOUN
american_scientific_journal-7479	328	12	analysis	analysis	NOUN
american_scientific_journal-7479	328	13	of	of	ADP
american_scientific_journal-7479	328	14	a	a	DET
american_scientific_journal-7479	328	15	high	high	ADJ
american_scientific_journal-7479	328	16	speed	speed	NOUN
american_scientific_journal-7479	328	17	railway	railway	NOUN
american_scientific_journal-7479	328	18	bridge	bridge	NOUN
american_scientific_journal-7479	328	19	modelled	model	VERB
american_scientific_journal-7479	328	20	as	as	ADP
american_scientific_journal-7479	328	21	simply	simply	ADV
american_scientific_journal-7479	328	22	supported	support	VERB
american_scientific_journal-7479	328	23	euler	euler	PROPN
american_scientific_journal-7479	328	24	bernoulli	bernoulli	PROPN
american_scientific_journal-7479	328	25	beam	beam	PROPN
american_scientific_journal-7479	328	26	”	"	PUNCT
american_scientific_journal-7479	328	27	.	.	PUNCT
american_scientific_journal-7479	329	1	[	[	X
american_scientific_journal-7479	329	2	18	18	NUM
american_scientific_journal-7479	329	3	]	]	X
american_scientific_journal-7479	329	4	g.	g.	PROPN
american_scientific_journal-7479	329	5	adomian	adomian	PROPN
american_scientific_journal-7479	329	6	,	,	PUNCT
american_scientific_journal-7479	329	7	“	"	PUNCT
american_scientific_journal-7479	329	8	a	a	DET
american_scientific_journal-7479	329	9	review	review	NOUN
american_scientific_journal-7479	329	10	of	of	ADP
american_scientific_journal-7479	329	11	the	the	DET
american_scientific_journal-7479	329	12	decomposition	decomposition	NOUN
american_scientific_journal-7479	329	13	method	method	NOUN
american_scientific_journal-7479	329	14	in	in	ADP
american_scientific_journal-7479	329	15	applied	applied	ADJ
american_scientific_journal-7479	329	16	mathematics	mathematic	NOUN
american_scientific_journal-7479	329	17	,	,	PUNCT
american_scientific_journal-7479	329	18	”	"	PUNCT
american_scientific_journal-7479	329	19	j.	j.	PROPN
american_scientific_journal-7479	329	20	math	math	PROPN
american_scientific_journal-7479	329	21	.	.	PUNCT
american_scientific_journal-7479	330	1	anal	anal	PROPN
american_scientific_journal-7479	330	2	.	.	PUNCT
american_scientific_journal-7479	331	1	appl	appl	PROPN
american_scientific_journal-7479	331	2	.	.	PROPN
american_scientific_journal-7479	331	3	,	,	PUNCT
american_scientific_journal-7479	331	4	vol	vol	NOUN
american_scientific_journal-7479	331	5	.	.	PROPN
american_scientific_journal-7479	331	6	135	135	NUM
american_scientific_journal-7479	331	7	,	,	PUNCT
american_scientific_journal-7479	331	8	no	no	INTJ
american_scientific_journal-7479	331	9	.	.	NOUN
american_scientific_journal-7479	331	10	2	2	NUM
american_scientific_journal-7479	331	11	,	,	PUNCT
american_scientific_journal-7479	331	12	pp	pp	ADJ
american_scientific_journal-7479	331	13	.	.	PUNCT
american_scientific_journal-7479	332	1	501–544	501–544	NUM
american_scientific_journal-7479	332	2	,	,	PUNCT
american_scientific_journal-7479	332	3	1988	1988	NUM
american_scientific_journal-7479	332	4	.	.	PUNCT
american_scientific_journal-7479	333	1	[	[	X
american_scientific_journal-7479	333	2	19	19	NUM
american_scientific_journal-7479	333	3	]	]	X
american_scientific_journal-7479	333	4	g.	g.	PROPN
american_scientific_journal-7479	333	5	adomian	adomian	PROPN
american_scientific_journal-7479	333	6	,	,	PUNCT
american_scientific_journal-7479	333	7	solving	solve	VERB
american_scientific_journal-7479	333	8	frontier	frontier	NOUN
american_scientific_journal-7479	333	9	problems	problem	NOUN
american_scientific_journal-7479	333	10	of	of	ADP
american_scientific_journal-7479	333	11	physics	physics	NOUN
american_scientific_journal-7479	333	12	:	:	PUNCT
american_scientific_journal-7479	333	13	the	the	DET
american_scientific_journal-7479	333	14	decomposition	decomposition	NOUN
american_scientific_journal-7479	333	15	method	method	NOUN
american_scientific_journal-7479	333	16	,	,	PUNCT
american_scientific_journal-7479	333	17	vol	vol	NOUN
american_scientific_journal-7479	333	18	.	.	PROPN
american_scientific_journal-7479	333	19	60	60	NUM
american_scientific_journal-7479	333	20	.	.	PUNCT
american_scientific_journal-7479	334	1	springer	springer	NOUN
american_scientific_journal-7479	334	2	science	science	PROPN
american_scientific_journal-7479	334	3	&	&	CCONJ
american_scientific_journal-7479	334	4	business	business	NOUN
american_scientific_journal-7479	334	5	media	medium	NOUN
american_scientific_journal-7479	334	6	,	,	PUNCT
american_scientific_journal-7479	334	7	2013	2013	NUM
american_scientific_journal-7479	334	8	.	.	PUNCT
american_scientific_journal-7479	335	1	[	[	X
american_scientific_journal-7479	335	2	20	20	NUM
american_scientific_journal-7479	335	3	]	]	PUNCT
american_scientific_journal-7479	335	4	s.	s.	PROPN
american_scientific_journal-7479	335	5	zhong	zhong	PROPN
american_scientific_journal-7479	335	6	and	and	CCONJ
american_scientific_journal-7479	335	7	s.	s.	PROPN
american_scientific_journal-7479	335	8	o.	o.	PROPN
american_scientific_journal-7479	335	9	oyadiji	oyadiji	PROPN
american_scientific_journal-7479	335	10	,	,	PUNCT
american_scientific_journal-7479	335	11	“	"	PUNCT
american_scientific_journal-7479	335	12	detection	detection	NOUN
american_scientific_journal-7479	335	13	of	of	ADP
american_scientific_journal-7479	335	14	cracks	crack	NOUN
american_scientific_journal-7479	335	15	in	in	ADP
american_scientific_journal-7479	335	16	simply	simply	ADV
american_scientific_journal-7479	335	17	-	-	PUNCT
american_scientific_journal-7479	335	18	supported	support	VERB
american_scientific_journal-7479	335	19	beams	beam	NOUN
american_scientific_journal-7479	335	20	by	by	ADP
american_scientific_journal-7479	335	21	continuous	continuous	ADJ
american_scientific_journal-7479	335	22	wavelet	wavelet	NOUN
american_scientific_journal-7479	335	23	american	american	PROPN
american_scientific_journal-7479	335	24	academic	academic	PROPN
american_scientific_journal-7479	335	25	scientific	scientific	ADJ
american_scientific_journal-7479	335	26	research	research	NOUN
american_scientific_journal-7479	335	27	journal	journal	NOUN
american_scientific_journal-7479	335	28	for	for	ADP
american_scientific_journal-7479	335	29	engineering	engineering	NOUN
american_scientific_journal-7479	335	30	,	,	PUNCT
american_scientific_journal-7479	335	31	technology	technology	NOUN
american_scientific_journal-7479	335	32	,	,	PUNCT
american_scientific_journal-7479	335	33	and	and	CCONJ
american_scientific_journal-7479	335	34	sciences	science	NOUN
american_scientific_journal-7479	335	35	(	(	PUNCT
american_scientific_journal-7479	335	36	asrjets	asrjet	NOUN
american_scientific_journal-7479	335	37	)	)	PUNCT
american_scientific_journal-7479	335	38	(	(	PUNCT
american_scientific_journal-7479	335	39	2022	2022	NUM
american_scientific_journal-7479	335	40	)	)	PUNCT
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american_scientific_journal-7479	335	43	,	,	PUNCT
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american_scientific_journal-7479	335	45	,	,	PUNCT
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american_scientific_journal-7479	335	47	332	332	NUM
american_scientific_journal-7479	335	48	-	-	SYM
american_scientific_journal-7479	335	49	348	348	NUM
american_scientific_journal-7479	335	50	349	349	NUM
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american_scientific_journal-7479	335	52	of	of	ADP
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american_scientific_journal-7479	335	54	modal	modal	ADJ
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american_scientific_journal-7479	335	56	,	,	PUNCT
american_scientific_journal-7479	335	57	”	"	PUNCT
american_scientific_journal-7479	335	58	comput	comput	NOUN
american_scientific_journal-7479	335	59	.	.	PUNCT
american_scientific_journal-7479	335	60	struct	struct	NOUN
american_scientific_journal-7479	335	61	.	.	PUNCT
american_scientific_journal-7479	335	62	,	,	PUNCT
american_scientific_journal-7479	335	63	vol	vol	NOUN
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american_scientific_journal-7479	335	65	89	89	NUM
american_scientific_journal-7479	335	66	,	,	PUNCT
american_scientific_journal-7479	335	67	no	no	INTJ
american_scientific_journal-7479	335	68	.	.	PUNCT
american_scientific_journal-7479	336	1	1–2	1–2	NUM
american_scientific_journal-7479	336	2	,	,	PUNCT
american_scientific_journal-7479	336	3	pp	pp	ADJ
american_scientific_journal-7479	336	4	.	.	PUNCT
american_scientific_journal-7479	337	1	127–148	127–148	NUM
american_scientific_journal-7479	337	2	,	,	PUNCT
american_scientific_journal-7479	337	3	2011	2011	NUM
american_scientific_journal-7479	337	4	.	.	PUNCT
american_scientific_journal-7479	338	1	[	[	X
american_scientific_journal-7479	338	2	21	21	NUM
american_scientific_journal-7479	338	3	]	]	X
american_scientific_journal-7479	338	4	h.	h.	PROPN
american_scientific_journal-7479	338	5	tada	tada	PROPN
american_scientific_journal-7479	338	6	,	,	PUNCT
american_scientific_journal-7479	338	7	p.	p.	PROPN
american_scientific_journal-7479	338	8	c.	c.	PROPN
american_scientific_journal-7479	338	9	paris	paris	PROPN
american_scientific_journal-7479	338	10	,	,	PUNCT
american_scientific_journal-7479	338	11	and	and	CCONJ
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american_scientific_journal-7479	338	13	r.	r.	PROPN
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american_scientific_journal-7479	338	15	,	,	PUNCT
american_scientific_journal-7479	338	16	“	"	PUNCT
american_scientific_journal-7479	338	17	the	the	DET
american_scientific_journal-7479	338	18	stress	stress	NOUN
american_scientific_journal-7479	338	19	analysis	analysis	NOUN
american_scientific_journal-7479	338	20	of	of	ADP
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american_scientific_journal-7479	338	22	,	,	PUNCT
american_scientific_journal-7479	338	23	”	"	PUNCT
american_scientific_journal-7479	338	24	handb	handb	NOUN
american_scientific_journal-7479	338	25	.	.	PUNCT
american_scientific_journal-7479	339	1	res	res	PROPN
american_scientific_journal-7479	339	2	.	.	PROPN
american_scientific_journal-7479	339	3	corp	corp	PROPN
american_scientific_journal-7479	339	4	.	.	PROPN
american_scientific_journal-7479	339	5	,	,	PUNCT
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american_scientific_journal-7479	339	7	.	.	PROPN
american_scientific_journal-7479	339	8	34	34	NUM
american_scientific_journal-7479	339	9	,	,	PUNCT
american_scientific_journal-7479	339	10	p.	p.	NOUN
american_scientific_journal-7479	339	11	635	635	NUM
american_scientific_journal-7479	339	12	,	,	PUNCT
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american_scientific_journal-7479	339	14	.	.	PUNCT
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american_scientific_journal-7479	340	2	22	22	NUM
american_scientific_journal-7479	340	3	]	]	PUNCT
american_scientific_journal-7479	340	4	m.	m.	NOUN
american_scientific_journal-7479	340	5	m.	m.	PROPN
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american_scientific_journal-7479	340	8	h.	h.	PROPN
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american_scientific_journal-7479	340	10	,	,	PUNCT
american_scientific_journal-7479	340	11	“	"	PUNCT
american_scientific_journal-7479	340	12	on	on	ADP
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american_scientific_journal-7479	340	17	decomposition	decomposition	NOUN
american_scientific_journal-7479	340	18	method	method	NOUN
american_scientific_journal-7479	340	19	,	,	PUNCT
american_scientific_journal-7479	340	20	”	"	PUNCT
american_scientific_journal-7479	340	21	appl	appl	NOUN
american_scientific_journal-7479	340	22	.	.	PROPN
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american_scientific_journal-7479	340	24	.	.	PUNCT
american_scientific_journal-7479	341	1	comput	comput	NOUN
american_scientific_journal-7479	341	2	.	.	PUNCT
american_scientific_journal-7479	341	3	,	,	PUNCT
american_scientific_journal-7479	341	4	vol	vol	NOUN
american_scientific_journal-7479	341	5	.	.	PROPN
american_scientific_journal-7479	341	6	182	182	NUM
american_scientific_journal-7479	341	7	,	,	PUNCT
american_scientific_journal-7479	341	8	no	no	INTJ
american_scientific_journal-7479	341	9	.	.	NOUN
american_scientific_journal-7479	341	10	1	1	NUM
american_scientific_journal-7479	341	11	,	,	PUNCT
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american_scientific_journal-7479	341	13	.	.	PUNCT
american_scientific_journal-7479	342	1	536–543	536–543	NUM
american_scientific_journal-7479	342	2	,	,	PUNCT
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american_scientific_journal-7479	342	4	.	.	PUNCT
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american_scientific_journal-7479	343	4	m.	m.	NOUN
american_scientific_journal-7479	343	5	m.	m.	PROPN
american_scientific_journal-7479	343	6	hosseini	hosseini	PROPN
american_scientific_journal-7479	343	7	and	and	CCONJ
american_scientific_journal-7479	343	8	h.	h.	PROPN
american_scientific_journal-7479	343	9	nasabzadeh	nasabzadeh	PROPN
american_scientific_journal-7479	343	10	,	,	PUNCT
american_scientific_journal-7479	343	11	“	"	PUNCT
american_scientific_journal-7479	343	12	on	on	ADP
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american_scientific_journal-7479	343	19	,	,	PUNCT
american_scientific_journal-7479	343	20	”	"	PUNCT
american_scientific_journal-7479	343	21	appl	appl	NOUN
american_scientific_journal-7479	343	22	.	.	PROPN
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american_scientific_journal-7479	343	24	.	.	PUNCT
american_scientific_journal-7479	344	1	comput	comput	NOUN
american_scientific_journal-7479	344	2	.	.	PUNCT
american_scientific_journal-7479	344	3	,	,	PUNCT
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american_scientific_journal-7479	344	5	.	.	PROPN
american_scientific_journal-7479	344	6	182	182	NUM
american_scientific_journal-7479	344	7	,	,	PUNCT
american_scientific_journal-7479	344	8	no	no	INTJ
american_scientific_journal-7479	344	9	.	.	NOUN
american_scientific_journal-7479	344	10	1	1	NUM
american_scientific_journal-7479	344	11	,	,	PUNCT
american_scientific_journal-7479	344	12	pp	pp	ADJ
american_scientific_journal-7479	344	13	.	.	PUNCT
american_scientific_journal-7479	345	1	536–543	536–543	NUM
american_scientific_journal-7479	345	2	,	,	PUNCT
american_scientific_journal-7479	345	3	2006	2006	NUM
american_scientific_journal-7479	345	4	.	.	PUNCT