id	sid	tid	token	lemma	pos
aiti-7988	1	1	4___aiti#7988_in	4___aiti#7988_in	NUM
aiti-7988	1	2	press_20211213	press_20211213	NOUN
aiti-7988	1	3	advances	advance	NOUN
aiti-7988	1	4	in	in	ADP
aiti-7988	1	5	technology	technology	NOUN
aiti-7988	1	6	innovation	innovation	NOUN
aiti-7988	1	7	,	,	PUNCT
aiti-7988	1	8	vol	vol	NOUN
aiti-7988	1	9	.	.	PROPN
aiti-7988	1	10	7	7	NUM
aiti-7988	1	11	,	,	PUNCT
aiti-7988	1	12	no	no	INTJ
aiti-7988	1	13	.	.	NOUN
aiti-7988	1	14	1	1	NUM
aiti-7988	1	15	,	,	PUNCT
aiti-7988	1	16	2022	2022	NUM
aiti-7988	1	17	,	,	PUNCT
aiti-7988	1	18	pp	pp	ADJ
aiti-7988	1	19	.	.	PUNCT
aiti-7988	2	1	41	41	NUM
aiti-7988	2	2	-	-	SYM
aiti-7988	2	3	55	55	NUM
aiti-7988	2	4	determination	determination	NOUN
aiti-7988	2	5	of	of	ADP
aiti-7988	2	6	natural	natural	ADJ
aiti-7988	2	7	frequency	frequency	NOUN
aiti-7988	2	8	and	and	CCONJ
aiti-7988	2	9	critical	critical	ADJ
aiti-7988	2	10	velocity	velocity	NOUN
aiti-7988	2	11	of	of	ADP
aiti-7988	2	12	inclined	inclined	ADJ
aiti-7988	2	13	pipe	pipe	NOUN
aiti-7988	2	14	conveying	convey	VERB
aiti-7988	2	15	fluid	fluid	NOUN
aiti-7988	2	16	under	under	ADP
aiti-7988	2	17	thermal	thermal	ADJ
aiti-7988	2	18	effect	effect	NOUN
aiti-7988	2	19	by	by	ADP
aiti-7988	2	20	using	use	VERB
aiti-7988	2	21	integral	integral	ADJ
aiti-7988	2	22	transform	transform	NOUN
aiti-7988	2	23	technique	technique	NOUN
aiti-7988	2	24	jabbar	jabbar	ADJ
aiti-7988	2	25	hussein	hussein	PROPN
aiti-7988	2	26	mohmmed	mohmme	VERB
aiti-7988	2	27	*	*	PUNCT
aiti-7988	2	28	,	,	PUNCT
aiti-7988	2	29	mauwafak	mauwafak	PROPN
aiti-7988	2	30	ali	ali	PROPN
aiti-7988	2	31	tawfik	tawfik	PROPN
aiti-7988	2	32	,	,	PUNCT
aiti-7988	2	33	qasim	qasim	PROPN
aiti-7988	2	34	abbas	abbas	PROPN
aiti-7988	2	35	atiyah	atiyah	PROPN
aiti-7988	2	36	department	department	PROPN
aiti-7988	2	37	of	of	ADP
aiti-7988	2	38	mechanical	mechanical	ADJ
aiti-7988	2	39	engineering	engineering	NOUN
aiti-7988	2	40	,	,	PUNCT
aiti-7988	2	41	university	university	NOUN
aiti-7988	2	42	of	of	ADP
aiti-7988	2	43	technology	technology	NOUN
aiti-7988	2	44	,	,	PUNCT
aiti-7988	2	45	baghdad	baghdad	PROPN
aiti-7988	2	46	,	,	PUNCT
aiti-7988	2	47	iraq	iraq	PROPN
aiti-7988	2	48	received	receive	VERB
aiti-7988	2	49	28	28	NUM
aiti-7988	2	50	june	june	PROPN
aiti-7988	2	51	2021	2021	NUM
aiti-7988	2	52	;	;	PUNCT
aiti-7988	2	53	received	receive	VERB
aiti-7988	2	54	in	in	ADP
aiti-7988	2	55	revised	revise	VERB
aiti-7988	2	56	form	form	NOUN
aiti-7988	2	57	02	02	NUM
aiti-7988	2	58	september	september	PROPN
aiti-7988	2	59	2021	2021	NUM
aiti-7988	2	60	;	;	PUNCT
aiti-7988	2	61	accepted	accept	VERB
aiti-7988	2	62	03	03	NUM
aiti-7988	2	63	september	september	PROPN
aiti-7988	2	64	2021	2021	NUM
aiti-7988	2	65	doi	doi	NOUN
aiti-7988	2	66	:	:	PUNCT
aiti-7988	2	67	https://doi.org/10.46604/aiti.2021.7988	https://doi.org/10.46604/aiti.2021.7988	PROPN
aiti-7988	2	68	abstract	abstract	NOUN
aiti-7988	2	69	this	this	DET
aiti-7988	2	70	study	study	NOUN
aiti-7988	2	71	proposes	propose	VERB
aiti-7988	2	72	an	an	DET
aiti-7988	2	73	analytical	analytical	ADJ
aiti-7988	2	74	solution	solution	NOUN
aiti-7988	2	75	of	of	ADP
aiti-7988	2	76	natural	natural	ADJ
aiti-7988	2	77	frequencies	frequency	NOUN
aiti-7988	2	78	for	for	ADP
aiti-7988	2	79	an	an	DET
aiti-7988	2	80	inclined	inclined	ADJ
aiti-7988	2	81	fixed	fix	VERB
aiti-7988	2	82	supported	support	VERB
aiti-7988	2	83	euler	euler	NOUN
aiti-7988	2	84	-	-	PUNCT
aiti-7988	2	85	bernoulli	bernoulli	PROPN
aiti-7988	2	86	pipe	pipe	NOUN
aiti-7988	2	87	containing	contain	VERB
aiti-7988	2	88	the	the	DET
aiti-7988	2	89	flowing	flow	VERB
aiti-7988	2	90	fluid	fluid	NOUN
aiti-7988	2	91	subjected	subject	VERB
aiti-7988	2	92	to	to	ADP
aiti-7988	2	93	thermal	thermal	ADJ
aiti-7988	2	94	loads	load	NOUN
aiti-7988	2	95	.	.	PUNCT
aiti-7988	3	1	the	the	DET
aiti-7988	3	2	integral	integral	ADJ
aiti-7988	3	3	transform	transform	NOUN
aiti-7988	3	4	technique	technique	NOUN
aiti-7988	3	5	is	be	AUX
aiti-7988	3	6	employed	employ	VERB
aiti-7988	3	7	to	to	PART
aiti-7988	3	8	obtain	obtain	VERB
aiti-7988	3	9	the	the	DET
aiti-7988	3	10	spatial	spatial	ADJ
aiti-7988	3	11	displacement	displacement	ADJ
aiti-7988	3	12	-	-	PUNCT
aiti-7988	3	13	time	time	NOUN
aiti-7988	3	14	domain	domain	NOUN
aiti-7988	3	15	response	response	NOUN
aiti-7988	3	16	of	of	ADP
aiti-7988	3	17	the	the	DET
aiti-7988	3	18	pipe	pipe	NOUN
aiti-7988	3	19	-	-	PUNCT
aiti-7988	3	20	fluid	fluid	NOUN
aiti-7988	3	21	system	system	NOUN
aiti-7988	3	22	.	.	PUNCT
aiti-7988	4	1	then	then	ADV
aiti-7988	4	2	,	,	PUNCT
aiti-7988	4	3	a	a	DET
aiti-7988	4	4	closed	close	VERB
aiti-7988	4	5	-	-	PUNCT
aiti-7988	4	6	form	form	NOUN
aiti-7988	4	7	analytical	analytical	ADJ
aiti-7988	4	8	expression	expression	NOUN
aiti-7988	4	9	is	be	AUX
aiti-7988	4	10	presented	present	VERB
aiti-7988	4	11	.	.	PUNCT
aiti-7988	5	1	the	the	DET
aiti-7988	5	2	effects	effect	NOUN
aiti-7988	5	3	of	of	ADP
aiti-7988	5	4	various	various	ADJ
aiti-7988	5	5	geometric	geometric	ADJ
aiti-7988	5	6	and	and	CCONJ
aiti-7988	5	7	system	system	NOUN
aiti-7988	5	8	parameters	parameter	NOUN
aiti-7988	5	9	on	on	ADP
aiti-7988	5	10	the	the	DET
aiti-7988	5	11	vibration	vibration	NOUN
aiti-7988	5	12	characteristics	characteristic	NOUN
aiti-7988	5	13	of	of	ADP
aiti-7988	5	14	pipe	pipe	NOUN
aiti-7988	5	15	-	-	PUNCT
aiti-7988	5	16	fluid	fluid	NOUN
aiti-7988	5	17	system	system	NOUN
aiti-7988	5	18	with	with	ADP
aiti-7988	5	19	different	different	ADJ
aiti-7988	5	20	flow	flow	NOUN
aiti-7988	5	21	velocities	velocity	NOUN
aiti-7988	5	22	are	be	AUX
aiti-7988	5	23	discussed	discuss	VERB
aiti-7988	5	24	.	.	PUNCT
aiti-7988	6	1	the	the	DET
aiti-7988	6	2	results	result	NOUN
aiti-7988	6	3	illustrate	illustrate	VERB
aiti-7988	6	4	that	that	SCONJ
aiti-7988	6	5	the	the	DET
aiti-7988	6	6	proposed	propose	VERB
aiti-7988	6	7	analytical	analytical	ADJ
aiti-7988	6	8	solution	solution	NOUN
aiti-7988	6	9	agrees	agree	VERB
aiti-7988	6	10	with	with	ADP
aiti-7988	6	11	the	the	DET
aiti-7988	6	12	solutions	solution	NOUN
aiti-7988	6	13	achieved	achieve	VERB
aiti-7988	6	14	in	in	ADP
aiti-7988	6	15	previous	previous	ADJ
aiti-7988	6	16	works	work	NOUN
aiti-7988	6	17	.	.	PUNCT
aiti-7988	7	1	the	the	DET
aiti-7988	7	2	proposed	propose	VERB
aiti-7988	7	3	model	model	NOUN
aiti-7988	7	4	predicts	predict	VERB
aiti-7988	7	5	that	that	SCONJ
aiti-7988	7	6	the	the	DET
aiti-7988	7	7	pipe	pipe	NOUN
aiti-7988	7	8	loses	lose	VERB
aiti-7988	7	9	the	the	DET
aiti-7988	7	10	stability	stability	NOUN
aiti-7988	7	11	by	by	ADP
aiti-7988	7	12	divergence	divergence	NOUN
aiti-7988	7	13	with	with	ADP
aiti-7988	7	14	the	the	DET
aiti-7988	7	15	increasing	increase	VERB
aiti-7988	7	16	flow	flow	NOUN
aiti-7988	7	17	velocity	velocity	NOUN
aiti-7988	7	18	.	.	PUNCT
aiti-7988	8	1	it	it	PRON
aiti-7988	8	2	is	be	AUX
aiti-7988	8	3	evident	evident	ADJ
aiti-7988	8	4	that	that	SCONJ
aiti-7988	8	5	the	the	DET
aiti-7988	8	6	influences	influence	NOUN
aiti-7988	8	7	of	of	ADP
aiti-7988	8	8	inclination	inclination	NOUN
aiti-7988	8	9	angle	angle	NOUN
aiti-7988	8	10	and	and	CCONJ
aiti-7988	8	11	temperature	temperature	NOUN
aiti-7988	8	12	variation	variation	NOUN
aiti-7988	8	13	are	be	AUX
aiti-7988	8	14	dramatically	dramatically	ADV
aiti-7988	8	15	increased	increase	VERB
aiti-7988	8	16	at	at	ADP
aiti-7988	8	17	a	a	DET
aiti-7988	8	18	higher	high	ADJ
aiti-7988	8	19	aspect	aspect	NOUN
aiti-7988	8	20	ratio	ratio	NOUN
aiti-7988	8	21	.	.	PUNCT
aiti-7988	9	1	additionally	additionally	ADV
aiti-7988	9	2	,	,	PUNCT
aiti-7988	9	3	it	it	PRON
aiti-7988	9	4	is	be	AUX
aiti-7988	9	5	demonstrated	demonstrate	VERB
aiti-7988	9	6	that	that	SCONJ
aiti-7988	9	7	the	the	DET
aiti-7988	9	8	temperature	temperature	NOUN
aiti-7988	9	9	variation	variation	NOUN
aiti-7988	9	10	becomes	become	VERB
aiti-7988	9	11	a	a	DET
aiti-7988	9	12	more	more	ADV
aiti-7988	9	13	harmful	harmful	ADJ
aiti-7988	9	14	effect	effect	NOUN
aiti-7988	9	15	than	than	ADP
aiti-7988	9	16	the	the	DET
aiti-7988	9	17	internal	internal	ADJ
aiti-7988	9	18	fluid	fluid	ADJ
aiti-7988	9	19	velocity	velocity	NOUN
aiti-7988	9	20	on	on	ADP
aiti-7988	9	21	the	the	DET
aiti-7988	9	22	stability	stability	NOUN
aiti-7988	9	23	of	of	ADP
aiti-7988	9	24	the	the	DET
aiti-7988	9	25	pipe	pipe	NOUN
aiti-7988	9	26	at	at	ADP
aiti-7988	9	27	elevated	elevated	ADJ
aiti-7988	9	28	temperature	temperature	NOUN
aiti-7988	9	29	.	.	PUNCT
aiti-7988	10	1	keywords	keyword	NOUN
aiti-7988	10	2	:	:	PUNCT
aiti-7988	10	3	pipe	pipe	NOUN
aiti-7988	10	4	conveying	conveying	NOUN
aiti-7988	10	5	fluid	fluid	NOUN
aiti-7988	10	6	,	,	PUNCT
aiti-7988	10	7	natural	natural	ADJ
aiti-7988	10	8	frequency	frequency	NOUN
aiti-7988	10	9	,	,	PUNCT
aiti-7988	10	10	critical	critical	ADJ
aiti-7988	10	11	flow	flow	NOUN
aiti-7988	10	12	velocity	velocity	NOUN
aiti-7988	10	13	,	,	PUNCT
aiti-7988	10	14	finite	finite	PROPN
aiti-7988	10	15	fourier	fourier	PROPN
aiti-7988	10	16	sine	sine	NOUN
aiti-7988	10	17	transform	transform	NOUN
aiti-7988	10	18	,	,	PUNCT
aiti-7988	10	19	laplace	laplace	NOUN
aiti-7988	10	20	transform	transform	VERB
aiti-7988	10	21	1	1	NUM
aiti-7988	10	22	.	.	PUNCT
aiti-7988	11	1	introduction	introduction	NOUN
aiti-7988	11	2	fluid	fluid	NOUN
aiti-7988	11	3	-	-	PUNCT
aiti-7988	11	4	conveying	convey	VERB
aiti-7988	11	5	pipes	pipe	NOUN
aiti-7988	11	6	are	be	AUX
aiti-7988	11	7	very	very	ADV
aiti-7988	11	8	important	important	ADJ
aiti-7988	11	9	parts	part	NOUN
aiti-7988	11	10	in	in	ADP
aiti-7988	11	11	many	many	ADJ
aiti-7988	11	12	engineering	engineering	NOUN
aiti-7988	11	13	structures	structure	NOUN
aiti-7988	11	14	and	and	CCONJ
aiti-7988	11	15	have	have	VERB
aiti-7988	11	16	many	many	ADJ
aiti-7988	11	17	potential	potential	ADJ
aiti-7988	11	18	applications	application	NOUN
aiti-7988	11	19	in	in	ADP
aiti-7988	11	20	industry	industry	NOUN
aiti-7988	11	21	.	.	PUNCT
aiti-7988	12	1	practical	practical	ADJ
aiti-7988	12	2	applications	application	NOUN
aiti-7988	12	3	include	include	VERB
aiti-7988	12	4	chemical	chemical	NOUN
aiti-7988	12	5	plants	plant	NOUN
aiti-7988	12	6	,	,	PUNCT
aiti-7988	12	7	nuclear	nuclear	ADJ
aiti-7988	12	8	reactors	reactor	NOUN
aiti-7988	12	9	,	,	PUNCT
aiti-7988	12	10	oil	oil	NOUN
aiti-7988	12	11	and	and	CCONJ
aiti-7988	12	12	gas	gas	NOUN
aiti-7988	12	13	industries	industry	NOUN
aiti-7988	12	14	,	,	PUNCT
aiti-7988	12	15	heat	heat	NOUN
aiti-7988	12	16	exchangers	exchanger	NOUN
aiti-7988	12	17	,	,	PUNCT
aiti-7988	12	18	fuel	fuel	NOUN
aiti-7988	12	19	lines	line	NOUN
aiti-7988	12	20	of	of	ADP
aiti-7988	12	21	transportations	transportation	NOUN
aiti-7988	12	22	,	,	PUNCT
aiti-7988	12	23	monitoring	monitoring	NOUN
aiti-7988	12	24	and	and	CCONJ
aiti-7988	12	25	controlling	control	VERB
aiti-7988	12	26	tubes	tube	NOUN
aiti-7988	12	27	,	,	PUNCT
aiti-7988	12	28	marine	marine	ADJ
aiti-7988	12	29	risers	riser	NOUN
aiti-7988	12	30	,	,	PUNCT
aiti-7988	12	31	and	and	CCONJ
aiti-7988	12	32	so	so	ADV
aiti-7988	12	33	on	on	ADV
aiti-7988	12	34	.	.	PUNCT
aiti-7988	13	1	other	other	ADJ
aiti-7988	13	2	applications	application	NOUN
aiti-7988	13	3	in	in	ADP
aiti-7988	13	4	engineering	engineering	NOUN
aiti-7988	13	5	devices	device	NOUN
aiti-7988	13	6	involve	involve	VERB
aiti-7988	13	7	jet	jet	NOUN
aiti-7988	13	8	pumps	pump	NOUN
aiti-7988	13	9	,	,	PUNCT
aiti-7988	13	10	some	some	DET
aiti-7988	13	11	kinds	kind	NOUN
aiti-7988	13	12	of	of	ADP
aiti-7988	13	13	valves	valve	NOUN
aiti-7988	13	14	and	and	CCONJ
aiti-7988	13	15	parts	part	NOUN
aiti-7988	13	16	of	of	ADP
aiti-7988	13	17	hydraulic	hydraulic	ADJ
aiti-7988	13	18	machinery	machinery	NOUN
aiti-7988	13	19	,	,	PUNCT
aiti-7988	13	20	and	and	CCONJ
aiti-7988	13	21	submarine	submarine	NOUN
aiti-7988	13	22	systems	system	NOUN
aiti-7988	13	23	,	,	PUNCT
aiti-7988	13	24	etc	etc	X
aiti-7988	13	25	.	.	X
aiti-7988	13	26	hemodynamics	hemodynamic	NOUN
aiti-7988	13	27	and	and	CCONJ
aiti-7988	13	28	the	the	DET
aiti-7988	13	29	pulmonary	pulmonary	ADJ
aiti-7988	13	30	and	and	CCONJ
aiti-7988	13	31	urinary	urinary	ADJ
aiti-7988	13	32	systems	system	NOUN
aiti-7988	13	33	also	also	ADV
aiti-7988	13	34	may	may	AUX
aiti-7988	13	35	be	be	AUX
aiti-7988	13	36	including	include	VERB
aiti-7988	13	37	some	some	DET
aiti-7988	13	38	applications	application	NOUN
aiti-7988	13	39	of	of	ADP
aiti-7988	13	40	the	the	DET
aiti-7988	13	41	pipes	pipe	NOUN
aiti-7988	13	42	conveying	convey	VERB
aiti-7988	13	43	fluid	fluid	NOUN
aiti-7988	14	1	[	[	X
aiti-7988	14	2	1	1	NUM
aiti-7988	14	3	-	-	SYM
aiti-7988	14	4	2	2	NUM
aiti-7988	14	5	]	]	PUNCT
aiti-7988	14	6	.	.	PUNCT
aiti-7988	15	1	the	the	DET
aiti-7988	15	2	function	function	NOUN
aiti-7988	15	3	of	of	ADP
aiti-7988	15	4	these	these	DET
aiti-7988	15	5	pipes	pipe	NOUN
aiti-7988	15	6	is	be	AUX
aiti-7988	15	7	very	very	ADV
aiti-7988	15	8	important	important	ADJ
aiti-7988	15	9	and	and	CCONJ
aiti-7988	15	10	can	can	AUX
aiti-7988	15	11	be	be	AUX
aiti-7988	15	12	considered	consider	VERB
aiti-7988	15	13	the	the	DET
aiti-7988	15	14	blood	blood	NOUN
aiti-7988	15	15	circulation	circulation	NOUN
aiti-7988	15	16	of	of	ADP
aiti-7988	15	17	human	human	ADJ
aiti-7988	15	18	body	body	NOUN
aiti-7988	15	19	.	.	PUNCT
aiti-7988	16	1	the	the	DET
aiti-7988	16	2	fluid	fluid	NOUN
aiti-7988	16	3	flowing	flow	VERB
aiti-7988	16	4	inside	inside	ADP
aiti-7988	16	5	these	these	DET
aiti-7988	16	6	pipes	pipe	NOUN
aiti-7988	16	7	influences	influence	VERB
aiti-7988	16	8	the	the	DET
aiti-7988	16	9	dynamic	dynamic	ADJ
aiti-7988	16	10	behaviors	behavior	NOUN
aiti-7988	16	11	of	of	ADP
aiti-7988	16	12	the	the	DET
aiti-7988	16	13	piping	piping	NOUN
aiti-7988	16	14	systems	system	NOUN
aiti-7988	16	15	,	,	PUNCT
aiti-7988	16	16	which	which	PRON
aiti-7988	16	17	play	play	VERB
aiti-7988	16	18	a	a	DET
aiti-7988	16	19	significant	significant	ADJ
aiti-7988	16	20	role	role	NOUN
aiti-7988	16	21	in	in	ADP
aiti-7988	16	22	the	the	DET
aiti-7988	16	23	stability	stability	NOUN
aiti-7988	16	24	and	and	CCONJ
aiti-7988	16	25	the	the	DET
aiti-7988	16	26	performance	performance	NOUN
aiti-7988	16	27	of	of	ADP
aiti-7988	16	28	the	the	DET
aiti-7988	16	29	systems	system	NOUN
aiti-7988	16	30	.	.	PUNCT
aiti-7988	17	1	the	the	DET
aiti-7988	17	2	influences	influence	NOUN
aiti-7988	17	3	of	of	ADP
aiti-7988	17	4	the	the	DET
aiti-7988	17	5	fluid	fluid	ADJ
aiti-7988	17	6	and	and	CCONJ
aiti-7988	17	7	structure	structure	NOUN
aiti-7988	17	8	interaction	interaction	NOUN
aiti-7988	17	9	usually	usually	ADV
aiti-7988	17	10	lead	lead	VERB
aiti-7988	17	11	to	to	ADP
aiti-7988	17	12	the	the	DET
aiti-7988	17	13	vibration	vibration	NOUN
aiti-7988	17	14	of	of	ADP
aiti-7988	17	15	the	the	DET
aiti-7988	17	16	pipe	pipe	NOUN
aiti-7988	17	17	and	and	CCONJ
aiti-7988	17	18	even	even	ADV
aiti-7988	17	19	the	the	DET
aiti-7988	17	20	rupture	rupture	NOUN
aiti-7988	17	21	of	of	ADP
aiti-7988	17	22	the	the	DET
aiti-7988	17	23	pipe	pipe	NOUN
aiti-7988	17	24	.	.	PUNCT
aiti-7988	18	1	thus	thus	ADV
aiti-7988	18	2	,	,	PUNCT
aiti-7988	18	3	a	a	DET
aiti-7988	18	4	convenient	convenient	ADJ
aiti-7988	18	5	knowledge	knowledge	NOUN
aiti-7988	18	6	of	of	ADP
aiti-7988	18	7	the	the	DET
aiti-7988	18	8	dynamic	dynamic	ADJ
aiti-7988	18	9	behavior	behavior	NOUN
aiti-7988	18	10	of	of	ADP
aiti-7988	18	11	these	these	DET
aiti-7988	18	12	types	type	NOUN
aiti-7988	18	13	of	of	ADP
aiti-7988	18	14	systems	system	NOUN
aiti-7988	18	15	is	be	AUX
aiti-7988	18	16	essential	essential	ADJ
aiti-7988	18	17	and	and	CCONJ
aiti-7988	18	18	has	have	AUX
aiti-7988	18	19	motivated	motivate	VERB
aiti-7988	18	20	many	many	ADJ
aiti-7988	18	21	scholars	scholar	NOUN
aiti-7988	18	22	over	over	ADP
aiti-7988	18	23	the	the	DET
aiti-7988	18	24	last	last	ADJ
aiti-7988	18	25	six	six	NUM
aiti-7988	18	26	decades	decade	NOUN
aiti-7988	18	27	.	.	PUNCT
aiti-7988	19	1	extensive	extensive	ADJ
aiti-7988	19	2	investigations	investigation	NOUN
aiti-7988	19	3	have	have	AUX
aiti-7988	19	4	been	be	AUX
aiti-7988	19	5	executed	execute	VERB
aiti-7988	19	6	on	on	ADP
aiti-7988	19	7	the	the	DET
aiti-7988	19	8	vibration	vibration	NOUN
aiti-7988	19	9	analysis	analysis	NOUN
aiti-7988	19	10	of	of	ADP
aiti-7988	19	11	the	the	DET
aiti-7988	19	12	fluid	fluid	NOUN
aiti-7988	19	13	-	-	PUNCT
aiti-7988	19	14	conveying	convey	VERB
aiti-7988	19	15	pipes	pipe	NOUN
aiti-7988	19	16	subjected	subject	VERB
aiti-7988	19	17	to	to	ADP
aiti-7988	19	18	various	various	ADJ
aiti-7988	19	19	end	end	NOUN
aiti-7988	19	20	and	and	CCONJ
aiti-7988	19	21	loading	loading	NOUN
aiti-7988	19	22	conditions	condition	NOUN
aiti-7988	19	23	.	.	PUNCT
aiti-7988	20	1	the	the	DET
aiti-7988	20	2	first	first	ADJ
aiti-7988	20	3	correct	correct	ADJ
aiti-7988	20	4	motion	motion	NOUN
aiti-7988	20	5	equation	equation	NOUN
aiti-7988	20	6	of	of	ADP
aiti-7988	20	7	the	the	DET
aiti-7988	20	8	structure	structure	NOUN
aiti-7988	20	9	-	-	PUNCT
aiti-7988	20	10	fluid	fluid	NOUN
aiti-7988	20	11	coupling	coupling	NOUN
aiti-7988	20	12	vibration	vibration	NOUN
aiti-7988	20	13	for	for	ADP
aiti-7988	20	14	a	a	DET
aiti-7988	20	15	pipe	pipe	NOUN
aiti-7988	20	16	containing	contain	VERB
aiti-7988	20	17	flowing	flow	VERB
aiti-7988	20	18	fluid	fluid	NOUN
aiti-7988	20	19	was	be	AUX
aiti-7988	20	20	proposed	propose	VERB
aiti-7988	20	21	by	by	ADP
aiti-7988	20	22	housner	housner	NOUN
aiti-7988	20	23	[	[	X
aiti-7988	20	24	3	3	NUM
aiti-7988	20	25	]	]	PUNCT
aiti-7988	20	26	.	.	PUNCT
aiti-7988	21	1	thereafter	thereafter	ADV
aiti-7988	21	2	,	,	PUNCT
aiti-7988	21	3	the	the	DET
aiti-7988	21	4	vibration	vibration	NOUN
aiti-7988	21	5	characteristics	characteristic	NOUN
aiti-7988	21	6	of	of	ADP
aiti-7988	21	7	pipe	pipe	NOUN
aiti-7988	21	8	-	-	PUNCT
aiti-7988	21	9	fluid	fluid	NOUN
aiti-7988	21	10	system	system	NOUN
aiti-7988	21	11	have	have	AUX
aiti-7988	21	12	been	be	AUX
aiti-7988	21	13	increasingly	increasingly	ADV
aiti-7988	21	14	studied	study	VERB
aiti-7988	21	15	by	by	ADP
aiti-7988	21	16	several	several	ADJ
aiti-7988	21	17	other	other	ADJ
aiti-7988	21	18	scholars	scholar	NOUN
aiti-7988	21	19	.	.	PUNCT
aiti-7988	22	1	stein	stein	PROPN
aiti-7988	22	2	and	and	CCONJ
aiti-7988	22	3	tobriner	tobriner	NOUN
aiti-7988	23	1	[	[	X
aiti-7988	23	2	4	4	NUM
aiti-7988	23	3	]	]	PUNCT
aiti-7988	23	4	discovered	discover	VERB
aiti-7988	23	5	that	that	SCONJ
aiti-7988	23	6	the	the	DET
aiti-7988	23	7	internal	internal	ADJ
aiti-7988	23	8	pressure	pressure	NOUN
aiti-7988	23	9	of	of	ADP
aiti-7988	23	10	flowing	flow	VERB
aiti-7988	23	11	fluid	fluid	NOUN
aiti-7988	23	12	has	have	VERB
aiti-7988	23	13	inverse	inverse	ADJ
aiti-7988	23	14	effect	effect	NOUN
aiti-7988	23	15	on	on	ADP
aiti-7988	23	16	the	the	DET
aiti-7988	23	17	natural	natural	ADJ
aiti-7988	23	18	frequency	frequency	NOUN
aiti-7988	23	19	of	of	ADP
aiti-7988	23	20	the	the	DET
aiti-7988	23	21	system	system	NOUN
aiti-7988	23	22	.	.	PUNCT
aiti-7988	24	1	païdoussis	païdoussis	PRON
aiti-7988	25	1	[	[	X
aiti-7988	25	2	5	5	NUM
aiti-7988	25	3	]	]	PUNCT
aiti-7988	25	4	further	far	ADV
aiti-7988	25	5	investigated	investigate	VERB
aiti-7988	25	6	the	the	DET
aiti-7988	25	7	dynamic	dynamic	ADJ
aiti-7988	25	8	behavior	behavior	NOUN
aiti-7988	25	9	of	of	ADP
aiti-7988	25	10	conservative	conservative	ADJ
aiti-7988	25	11	system	system	NOUN
aiti-7988	25	12	,	,	PUNCT
aiti-7988	25	13	predicting	predict	VERB
aiti-7988	25	14	that	that	SCONJ
aiti-7988	25	15	the	the	DET
aiti-7988	25	16	system	system	NOUN
aiti-7988	25	17	may	may	AUX
aiti-7988	25	18	be	be	AUX
aiti-7988	25	19	undergoing	undergo	VERB
aiti-7988	25	20	the	the	DET
aiti-7988	25	21	flexural	flexural	ADJ
aiti-7988	25	22	oscillatory	oscillatory	ADJ
aiti-7988	25	23	instability	instability	NOUN
aiti-7988	25	24	by	by	ADP
aiti-7988	25	25	divergence	divergence	NOUN
aiti-7988	25	26	at	at	ADP
aiti-7988	25	27	a	a	DET
aiti-7988	25	28	certain	certain	ADJ
aiti-7988	25	29	high	high	ADJ
aiti-7988	25	30	flow	flow	NOUN
aiti-7988	25	31	speed	speed	NOUN
aiti-7988	25	32	,	,	PUNCT
aiti-7988	25	33	and	and	CCONJ
aiti-7988	25	34	that	that	SCONJ
aiti-7988	25	35	at	at	ADP
aiti-7988	25	36	higher	high	ADJ
aiti-7988	25	37	flow	flow	NOUN
aiti-7988	25	38	speed	speed	NOUN
aiti-7988	25	39	the	the	DET
aiti-7988	25	40	system	system	NOUN
aiti-7988	25	41	can	can	AUX
aiti-7988	25	42	be	be	AUX
aiti-7988	25	43	subjected	subject	VERB
aiti-7988	25	44	to	to	ADP
aiti-7988	25	45	coupled	couple	VERB
aiti-7988	25	46	-	-	PUNCT
aiti-7988	25	47	mode	mode	NOUN
aiti-7988	25	48	flutter	flutter	NOUN
aiti-7988	25	49	.	.	PUNCT
aiti-7988	26	1	plaut	plaut	PROPN
aiti-7988	26	2	and	and	CCONJ
aiti-7988	26	3	huseyin	huseyin	VERB
aiti-7988	27	1	[	[	X
aiti-7988	27	2	6	6	NUM
aiti-7988	27	3	]	]	PUNCT
aiti-7988	27	4	,	,	PUNCT
aiti-7988	27	5	hatfield	hatfield	PROPN
aiti-7988	27	6	et	et	PROPN
aiti-7988	27	7	al	al	PROPN
aiti-7988	27	8	.	.	PUNCT
aiti-7988	28	1	[	[	X
aiti-7988	28	2	7	7	NUM
aiti-7988	28	3	]	]	PUNCT
aiti-7988	28	4	,	,	PUNCT
aiti-7988	28	5	and	and	CCONJ
aiti-7988	28	6	lesmez	lesmez	NOUN
aiti-7988	28	7	et	et	PROPN
aiti-7988	28	8	al	al	PROPN
aiti-7988	28	9	.	.	PUNCT
aiti-7988	29	1	[	[	X
aiti-7988	29	2	8	8	NUM
aiti-7988	29	3	]	]	PUNCT
aiti-7988	29	4	further	far	ADV
aiti-7988	29	5	analyzed	analyze	VERB
aiti-7988	29	6	the	the	DET
aiti-7988	29	7	plain	plain	ADJ
aiti-7988	29	8	and	and	CCONJ
aiti-7988	29	9	u	u	NOUN
aiti-7988	29	10	-	-	ADJ
aiti-7988	29	11	bend	bend	ADJ
aiti-7988	29	12	piping	piping	NOUN
aiti-7988	29	13	systems	system	NOUN
aiti-7988	29	14	.	.	PUNCT
aiti-7988	30	1	*	*	PUNCT
aiti-7988	30	2	corresponding	correspond	VERB
aiti-7988	30	3	author	author	NOUN
aiti-7988	30	4	.	.	PUNCT
aiti-7988	31	1	e	e	X
aiti-7988	31	2	-	-	NOUN
aiti-7988	31	3	mail	mail	NOUN
aiti-7988	31	4	address:10493@uotechnology.edu.iq	address:10493@uotechnology.edu.iq	PROPN
aiti-7988	31	5	tel	tel	PROPN
aiti-7988	31	6	.	.	PUNCT
aiti-7988	31	7	:	:	PUNCT
aiti-7988	31	8	+9647805886894	+9647805886894	X
aiti-7988	31	9	advances	advance	VERB
aiti-7988	31	10	in	in	ADP
aiti-7988	31	11	technology	technology	NOUN
aiti-7988	31	12	innovation	innovation	NOUN
aiti-7988	31	13	,	,	PUNCT
aiti-7988	31	14	vol	vol	NOUN
aiti-7988	31	15	.	.	PROPN
aiti-7988	32	1	7	7	NUM
aiti-7988	32	2	,	,	PUNCT
aiti-7988	32	3	no	no	INTJ
aiti-7988	32	4	.	.	NOUN
aiti-7988	32	5	1	1	NUM
aiti-7988	32	6	,	,	PUNCT
aiti-7988	32	7	2022	2022	NUM
aiti-7988	32	8	,	,	PUNCT
aiti-7988	32	9	pp	pp	ADJ
aiti-7988	32	10	.	.	PUNCT
aiti-7988	33	1	41	41	NUM
aiti-7988	33	2	-	-	SYM
aiti-7988	33	3	55	55	NUM
aiti-7988	33	4	nowadays	nowadays	ADV
aiti-7988	33	5	,	,	PUNCT
aiti-7988	33	6	with	with	ADP
aiti-7988	33	7	the	the	DET
aiti-7988	33	8	existence	existence	NOUN
aiti-7988	33	9	of	of	ADP
aiti-7988	33	10	larger	large	ADJ
aiti-7988	33	11	pipeline	pipeline	NOUN
aiti-7988	33	12	systems	system	NOUN
aiti-7988	33	13	,	,	PUNCT
aiti-7988	33	14	the	the	DET
aiti-7988	33	15	demand	demand	NOUN
aiti-7988	33	16	for	for	ADP
aiti-7988	33	17	inclined	inclined	ADJ
aiti-7988	33	18	pipes	pipe	NOUN
aiti-7988	33	19	have	have	AUX
aiti-7988	33	20	been	be	AUX
aiti-7988	33	21	grown	grow	VERB
aiti-7988	33	22	due	due	ADP
aiti-7988	33	23	to	to	ADP
aiti-7988	33	24	their	their	PRON
aiti-7988	33	25	special	special	ADJ
aiti-7988	33	26	conditions	condition	NOUN
aiti-7988	33	27	,	,	PUNCT
aiti-7988	33	28	and	and	CCONJ
aiti-7988	33	29	it	it	PRON
aiti-7988	33	30	is	be	AUX
aiti-7988	33	31	therefore	therefore	ADV
aiti-7988	33	32	worthy	worthy	ADJ
aiti-7988	33	33	being	be	AUX
aiti-7988	33	34	concerned	concern	VERB
aiti-7988	33	35	about	about	ADP
aiti-7988	33	36	.	.	PUNCT
aiti-7988	34	1	moreover	moreover	ADV
aiti-7988	34	2	,	,	PUNCT
aiti-7988	34	3	these	these	DET
aiti-7988	34	4	pipes	pipe	NOUN
aiti-7988	34	5	can	can	AUX
aiti-7988	34	6	be	be	AUX
aiti-7988	34	7	possessed	possess	VERB
aiti-7988	34	8	various	various	ADJ
aiti-7988	34	9	aspect	aspect	NOUN
aiti-7988	34	10	ratios	ratio	NOUN
aiti-7988	34	11	of	of	ADP
aiti-7988	34	12	length	length	NOUN
aiti-7988	34	13	to	to	ADP
aiti-7988	34	14	external	external	ADJ
aiti-7988	34	15	diameter	diameter	NOUN
aiti-7988	34	16	.	.	PUNCT
aiti-7988	35	1	a	a	DET
aiti-7988	35	2	better	well	ADJ
aiti-7988	35	3	understanding	understanding	NOUN
aiti-7988	35	4	of	of	ADP
aiti-7988	35	5	the	the	DET
aiti-7988	35	6	influence	influence	NOUN
aiti-7988	35	7	of	of	ADP
aiti-7988	35	8	the	the	DET
aiti-7988	35	9	aspect	aspect	NOUN
aiti-7988	35	10	ratio	ratio	NOUN
aiti-7988	35	11	and	and	CCONJ
aiti-7988	35	12	inclination	inclination	NOUN
aiti-7988	35	13	angle	angle	NOUN
aiti-7988	35	14	on	on	ADP
aiti-7988	35	15	the	the	DET
aiti-7988	35	16	dynamic	dynamic	ADJ
aiti-7988	35	17	behavior	behavior	NOUN
aiti-7988	35	18	of	of	ADP
aiti-7988	35	19	a	a	DET
aiti-7988	35	20	pipe	pipe	NOUN
aiti-7988	35	21	is	be	AUX
aiti-7988	35	22	very	very	ADV
aiti-7988	35	23	essential	essential	ADJ
aiti-7988	35	24	to	to	PART
aiti-7988	35	25	design	design	VERB
aiti-7988	35	26	thin	thin	ADJ
aiti-7988	35	27	components	component	NOUN
aiti-7988	35	28	in	in	ADP
aiti-7988	35	29	different	different	ADJ
aiti-7988	35	30	industries	industry	NOUN
aiti-7988	35	31	.	.	PUNCT
aiti-7988	36	1	additionally	additionally	ADV
aiti-7988	36	2	,	,	PUNCT
aiti-7988	36	3	when	when	SCONJ
aiti-7988	36	4	the	the	DET
aiti-7988	36	5	pipes	pipe	NOUN
aiti-7988	36	6	are	be	AUX
aiti-7988	36	7	designed	design	VERB
aiti-7988	36	8	and	and	CCONJ
aiti-7988	36	9	analyzed	analyze	VERB
aiti-7988	36	10	,	,	PUNCT
aiti-7988	36	11	it	it	PRON
aiti-7988	36	12	is	be	AUX
aiti-7988	36	13	very	very	ADV
aiti-7988	36	14	important	important	ADJ
aiti-7988	36	15	to	to	PART
aiti-7988	36	16	take	take	VERB
aiti-7988	36	17	account	account	NOUN
aiti-7988	36	18	of	of	ADP
aiti-7988	36	19	the	the	DET
aiti-7988	36	20	working	working	NOUN
aiti-7988	36	21	conditions	condition	NOUN
aiti-7988	36	22	which	which	PRON
aiti-7988	36	23	can	can	AUX
aiti-7988	36	24	affect	affect	VERB
aiti-7988	36	25	the	the	DET
aiti-7988	36	26	dynamic	dynamic	ADJ
aiti-7988	36	27	behavior	behavior	NOUN
aiti-7988	36	28	and	and	CCONJ
aiti-7988	36	29	integrity	integrity	NOUN
aiti-7988	36	30	of	of	ADP
aiti-7988	36	31	such	such	ADJ
aiti-7988	36	32	components	component	NOUN
aiti-7988	36	33	.	.	PUNCT
aiti-7988	37	1	one	one	NUM
aiti-7988	37	2	of	of	ADP
aiti-7988	37	3	the	the	DET
aiti-7988	37	4	important	important	ADJ
aiti-7988	37	5	examples	example	NOUN
aiti-7988	37	6	of	of	ADP
aiti-7988	37	7	such	such	ADJ
aiti-7988	37	8	operating	operating	NOUN
aiti-7988	37	9	conditions	condition	NOUN
aiti-7988	37	10	is	be	AUX
aiti-7988	37	11	the	the	DET
aiti-7988	37	12	temperature	temperature	NOUN
aiti-7988	37	13	variation	variation	NOUN
aiti-7988	37	14	,	,	PUNCT
aiti-7988	37	15	which	which	PRON
aiti-7988	37	16	is	be	AUX
aiti-7988	37	17	undergone	undergo	VERB
aiti-7988	37	18	during	during	ADP
aiti-7988	37	19	the	the	DET
aiti-7988	37	20	conveyance	conveyance	NOUN
aiti-7988	37	21	of	of	ADP
aiti-7988	37	22	fluid	fluid	NOUN
aiti-7988	37	23	in	in	ADP
aiti-7988	37	24	pipes	pipe	NOUN
aiti-7988	37	25	.	.	PUNCT
aiti-7988	38	1	the	the	DET
aiti-7988	38	2	pipes	pipe	NOUN
aiti-7988	38	3	in	in	ADP
aiti-7988	38	4	such	such	ADJ
aiti-7988	38	5	cases	case	NOUN
aiti-7988	38	6	suffer	suffer	VERB
aiti-7988	38	7	the	the	DET
aiti-7988	38	8	compressive	compressive	ADJ
aiti-7988	38	9	stresses	stress	NOUN
aiti-7988	38	10	resulting	result	VERB
aiti-7988	38	11	from	from	ADP
aiti-7988	38	12	the	the	DET
aiti-7988	38	13	thermal	thermal	ADJ
aiti-7988	38	14	effect	effect	NOUN
aiti-7988	38	15	in	in	ADP
aiti-7988	38	16	addition	addition	NOUN
aiti-7988	38	17	to	to	ADP
aiti-7988	38	18	those	those	PRON
aiti-7988	38	19	generated	generate	VERB
aiti-7988	38	20	by	by	ADP
aiti-7988	38	21	the	the	DET
aiti-7988	38	22	fluid	fluid	NOUN
aiti-7988	38	23	flowing	flow	VERB
aiti-7988	38	24	through	through	ADP
aiti-7988	38	25	the	the	DET
aiti-7988	38	26	pipe	pipe	NOUN
aiti-7988	38	27	.	.	PUNCT
aiti-7988	39	1	such	such	ADJ
aiti-7988	39	2	pipes	pipe	NOUN
aiti-7988	39	3	can	can	AUX
aiti-7988	39	4	experience	experience	VERB
aiti-7988	39	5	buckling	buckling	NOUN
aiti-7988	39	6	and	and	CCONJ
aiti-7988	39	7	show	show	VERB
aiti-7988	39	8	the	the	DET
aiti-7988	39	9	complicated	complicated	ADJ
aiti-7988	39	10	dynamical	dynamical	ADJ
aiti-7988	39	11	behavior	behavior	NOUN
aiti-7988	39	12	related	relate	VERB
aiti-7988	39	13	to	to	ADP
aiti-7988	39	14	their	their	PRON
aiti-7988	39	15	divergence	divergence	NOUN
aiti-7988	39	16	even	even	ADV
aiti-7988	39	17	at	at	ADP
aiti-7988	39	18	a	a	DET
aiti-7988	39	19	very	very	ADV
aiti-7988	39	20	low	low	ADJ
aiti-7988	39	21	internal	internal	ADJ
aiti-7988	39	22	flow	flow	NOUN
aiti-7988	39	23	velocity	velocity	NOUN
aiti-7988	39	24	of	of	ADP
aiti-7988	39	25	fluid	fluid	NOUN
aiti-7988	39	26	[	[	X
aiti-7988	39	27	9	9	NUM
aiti-7988	39	28	]	]	PUNCT
aiti-7988	39	29	.	.	PUNCT
aiti-7988	40	1	consequently	consequently	ADV
aiti-7988	40	2	,	,	PUNCT
aiti-7988	40	3	temperature	temperature	NOUN
aiti-7988	40	4	is	be	AUX
aiti-7988	40	5	one	one	NUM
aiti-7988	40	6	of	of	ADP
aiti-7988	40	7	the	the	DET
aiti-7988	40	8	main	main	ADJ
aiti-7988	40	9	concerns	concern	NOUN
aiti-7988	40	10	among	among	ADP
aiti-7988	40	11	other	other	ADJ
aiti-7988	40	12	factors	factor	NOUN
aiti-7988	40	13	and	and	CCONJ
aiti-7988	40	14	operating	operating	NOUN
aiti-7988	40	15	conditions	condition	NOUN
aiti-7988	40	16	in	in	ADP
aiti-7988	40	17	designing	design	VERB
aiti-7988	40	18	slender	slender	ADJ
aiti-7988	40	19	structures	structure	NOUN
aiti-7988	40	20	like	like	ADP
aiti-7988	40	21	the	the	DET
aiti-7988	40	22	pipeline	pipeline	NOUN
aiti-7988	40	23	systems	system	NOUN
aiti-7988	40	24	containing	contain	VERB
aiti-7988	40	25	flowing	flow	VERB
aiti-7988	40	26	fluid	fluid	NOUN
aiti-7988	40	27	.	.	PUNCT
aiti-7988	41	1	recently	recently	ADV
aiti-7988	41	2	,	,	PUNCT
aiti-7988	41	3	qian	qian	PROPN
aiti-7988	41	4	et	et	PROPN
aiti-7988	41	5	al	al	PROPN
aiti-7988	41	6	.	.	PUNCT
aiti-7988	42	1	[	[	X
aiti-7988	42	2	9	9	NUM
aiti-7988	42	3	]	]	PUNCT
aiti-7988	42	4	studied	study	VERB
aiti-7988	42	5	the	the	DET
aiti-7988	42	6	effects	effect	NOUN
aiti-7988	42	7	of	of	ADP
aiti-7988	42	8	both	both	CCONJ
aiti-7988	42	9	linear	linear	ADJ
aiti-7988	42	10	and	and	CCONJ
aiti-7988	42	11	non	non	ADJ
aiti-7988	42	12	-	-	ADJ
aiti-7988	42	13	linear	linear	ADJ
aiti-7988	42	14	stress	stress	NOUN
aiti-7988	42	15	-	-	PUNCT
aiti-7988	42	16	temperature	temperature	NOUN
aiti-7988	42	17	cases	case	NOUN
aiti-7988	42	18	on	on	ADP
aiti-7988	42	19	the	the	DET
aiti-7988	42	20	stability	stability	NOUN
aiti-7988	42	21	of	of	ADP
aiti-7988	42	22	pipe	pipe	NOUN
aiti-7988	42	23	containing	contain	VERB
aiti-7988	42	24	flowing	flow	VERB
aiti-7988	42	25	fluid	fluid	NOUN
aiti-7988	42	26	.	.	PUNCT
aiti-7988	43	1	zhao	zhao	PROPN
aiti-7988	43	2	et	et	PROPN
aiti-7988	43	3	al	al	PROPN
aiti-7988	43	4	.	.	PUNCT
aiti-7988	44	1	[	[	X
aiti-7988	44	2	10	10	NUM
aiti-7988	44	3	]	]	PUNCT
aiti-7988	44	4	investigated	investigate	VERB
aiti-7988	44	5	the	the	DET
aiti-7988	44	6	stability	stability	NOUN
aiti-7988	44	7	of	of	ADP
aiti-7988	44	8	the	the	DET
aiti-7988	44	9	simply	simply	ADV
aiti-7988	44	10	supported	support	VERB
aiti-7988	44	11	pipes	pipe	NOUN
aiti-7988	44	12	induced	induce	VERB
aiti-7988	44	13	by	by	ADP
aiti-7988	44	14	pulsating	pulsate	VERB
aiti-7988	44	15	fluid	fluid	ADJ
aiti-7988	44	16	velocity	velocity	NOUN
aiti-7988	44	17	and	and	CCONJ
aiti-7988	44	18	thermal	thermal	ADJ
aiti-7988	44	19	loading	loading	NOUN
aiti-7988	44	20	.	.	PUNCT
aiti-7988	45	1	kukla	kukla	PROPN
aiti-7988	46	1	[	[	X
aiti-7988	46	2	11	11	NUM
aiti-7988	46	3	]	]	PUNCT
aiti-7988	46	4	studied	study	VERB
aiti-7988	46	5	the	the	DET
aiti-7988	46	6	temperature	temperature	NOUN
aiti-7988	46	7	distribution	distribution	NOUN
aiti-7988	46	8	and	and	CCONJ
aiti-7988	46	9	lateral	lateral	ADJ
aiti-7988	46	10	vibration	vibration	NOUN
aiti-7988	46	11	of	of	ADP
aiti-7988	46	12	beam	beam	NOUN
aiti-7988	46	13	induced	induce	VERB
aiti-7988	46	14	by	by	ADP
aiti-7988	46	15	external	external	ADJ
aiti-7988	46	16	heating	heating	NOUN
aiti-7988	46	17	source	source	NOUN
aiti-7988	46	18	.	.	PUNCT
aiti-7988	47	1	blandino	blandino	PROPN
aiti-7988	47	2	and	and	CCONJ
aiti-7988	47	3	thornton	thornton	PROPN
aiti-7988	48	1	[	[	X
aiti-7988	48	2	12	12	NUM
aiti-7988	48	3	]	]	PUNCT
aiti-7988	48	4	performed	perform	VERB
aiti-7988	48	5	a	a	DET
aiti-7988	48	6	study	study	NOUN
aiti-7988	48	7	about	about	ADP
aiti-7988	48	8	the	the	DET
aiti-7988	48	9	vibration	vibration	NOUN
aiti-7988	48	10	characteristic	characteristic	NOUN
aiti-7988	48	11	of	of	ADP
aiti-7988	48	12	an	an	DET
aiti-7988	48	13	internally	internally	ADV
aiti-7988	48	14	heated	heat	VERB
aiti-7988	48	15	beam	beam	NOUN
aiti-7988	48	16	.	.	PUNCT
aiti-7988	49	1	alfosail	alfosail	PROPN
aiti-7988	49	2	et	et	PROPN
aiti-7988	49	3	al	al	PROPN
aiti-7988	49	4	.	.	PUNCT
aiti-7988	50	1	[	[	X
aiti-7988	50	2	13	13	NUM
aiti-7988	50	3	]	]	PUNCT
aiti-7988	50	4	numerically	numerically	ADV
aiti-7988	50	5	evaluated	evaluate	VERB
aiti-7988	50	6	the	the	DET
aiti-7988	50	7	dynamic	dynamic	ADJ
aiti-7988	50	8	behavior	behavior	NOUN
aiti-7988	50	9	of	of	ADP
aiti-7988	50	10	inclined	inclined	ADJ
aiti-7988	50	11	risers	riser	NOUN
aiti-7988	50	12	.	.	PUNCT
aiti-7988	51	1	gan	gan	VERB
aiti-7988	51	2	et	et	PROPN
aiti-7988	51	3	al	al	PROPN
aiti-7988	51	4	.	.	PUNCT
aiti-7988	52	1	[	[	X
aiti-7988	52	2	14	14	NUM
aiti-7988	52	3	]	]	PUNCT
aiti-7988	52	4	investigated	investigate	VERB
aiti-7988	52	5	the	the	DET
aiti-7988	52	6	stability	stability	NOUN
aiti-7988	52	7	of	of	ADP
aiti-7988	52	8	an	an	DET
aiti-7988	52	9	inclined	inclined	ADJ
aiti-7988	52	10	cantilevered	cantilevered	ADJ
aiti-7988	52	11	pipe	pipe	NOUN
aiti-7988	52	12	containing	contain	VERB
aiti-7988	52	13	flowing	flow	VERB
aiti-7988	52	14	fluid	fluid	NOUN
aiti-7988	52	15	.	.	PUNCT
aiti-7988	53	1	yang	yang	PROPN
aiti-7988	53	2	and	and	CCONJ
aiti-7988	53	3	wang	wang	PROPN
aiti-7988	54	1	[	[	X
aiti-7988	54	2	15	15	NUM
aiti-7988	54	3	]	]	PUNCT
aiti-7988	54	4	analyzed	analyze	VERB
aiti-7988	54	5	the	the	DET
aiti-7988	54	6	dynamic	dynamic	ADJ
aiti-7988	54	7	behavior	behavior	NOUN
aiti-7988	54	8	of	of	ADP
aiti-7988	54	9	an	an	DET
aiti-7988	54	10	inclined	inclined	ADJ
aiti-7988	54	11	beam	beam	NOUN
aiti-7988	54	12	induced	induce	VERB
aiti-7988	54	13	by	by	ADP
aiti-7988	54	14	moving	move	VERB
aiti-7988	54	15	loads	load	NOUN
aiti-7988	54	16	.	.	PUNCT
aiti-7988	55	1	from	from	ADP
aiti-7988	55	2	the	the	DET
aiti-7988	55	3	literature	literature	NOUN
aiti-7988	55	4	review	review	NOUN
aiti-7988	55	5	,	,	PUNCT
aiti-7988	55	6	it	it	PRON
aiti-7988	55	7	is	be	AUX
aiti-7988	55	8	observed	observe	VERB
aiti-7988	55	9	that	that	SCONJ
aiti-7988	55	10	no	no	DET
aiti-7988	55	11	previous	previous	ADJ
aiti-7988	55	12	works	work	NOUN
aiti-7988	55	13	have	have	AUX
aiti-7988	55	14	been	be	AUX
aiti-7988	55	15	reported	report	VERB
aiti-7988	55	16	on	on	ADP
aiti-7988	55	17	the	the	DET
aiti-7988	55	18	response	response	NOUN
aiti-7988	55	19	of	of	ADP
aiti-7988	55	20	pipes	pipe	NOUN
aiti-7988	55	21	due	due	ADP
aiti-7988	55	22	to	to	ADP
aiti-7988	55	23	a	a	DET
aiti-7988	55	24	combination	combination	NOUN
aiti-7988	55	25	effect	effect	NOUN
aiti-7988	55	26	of	of	ADP
aiti-7988	55	27	internal	internal	ADJ
aiti-7988	55	28	fluid	fluid	NOUN
aiti-7988	55	29	,	,	PUNCT
aiti-7988	55	30	inclination	inclination	NOUN
aiti-7988	55	31	angle	angle	NOUN
aiti-7988	55	32	,	,	PUNCT
aiti-7988	55	33	aspect	aspect	NOUN
aiti-7988	55	34	ratio	ratio	NOUN
aiti-7988	55	35	,	,	PUNCT
aiti-7988	55	36	and	and	CCONJ
aiti-7988	55	37	thermal	thermal	ADJ
aiti-7988	55	38	loads	load	NOUN
aiti-7988	55	39	.	.	PUNCT
aiti-7988	56	1	furthermore	furthermore	ADV
aiti-7988	56	2	,	,	PUNCT
aiti-7988	56	3	it	it	PRON
aiti-7988	56	4	is	be	AUX
aiti-7988	56	5	noted	note	VERB
aiti-7988	56	6	that	that	SCONJ
aiti-7988	56	7	most	most	ADJ
aiti-7988	56	8	of	of	ADP
aiti-7988	56	9	the	the	DET
aiti-7988	56	10	above	above	ADV
aiti-7988	56	11	-	-	PUNCT
aiti-7988	56	12	mentioned	mention	VERB
aiti-7988	56	13	analyses	analysis	NOUN
aiti-7988	56	14	have	have	AUX
aiti-7988	56	15	been	be	AUX
aiti-7988	56	16	based	base	VERB
aiti-7988	56	17	on	on	ADP
aiti-7988	56	18	numerical	numerical	ADJ
aiti-7988	56	19	or	or	CCONJ
aiti-7988	56	20	approximate	approximate	ADJ
aiti-7988	56	21	approaches	approach	NOUN
aiti-7988	56	22	in	in	ADP
aiti-7988	56	23	tackling	tackle	VERB
aiti-7988	56	24	linear	linear	ADJ
aiti-7988	56	25	and	and	CCONJ
aiti-7988	56	26	non	non	ADJ
aiti-7988	56	27	-	-	ADJ
aiti-7988	56	28	linear	linear	ADJ
aiti-7988	56	29	dynamics	dynamic	NOUN
aiti-7988	56	30	issues	issue	NOUN
aiti-7988	56	31	of	of	ADP
aiti-7988	56	32	these	these	DET
aiti-7988	56	33	slender	slender	ADJ
aiti-7988	56	34	structures	structure	NOUN
aiti-7988	56	35	.	.	PUNCT
aiti-7988	57	1	this	this	DET
aiti-7988	57	2	approximation	approximation	NOUN
aiti-7988	57	3	is	be	AUX
aiti-7988	57	4	valid	valid	ADJ
aiti-7988	57	5	only	only	ADV
aiti-7988	57	6	for	for	ADP
aiti-7988	57	7	small	small	ADJ
aiti-7988	57	8	values	value	NOUN
aiti-7988	57	9	of	of	ADP
aiti-7988	57	10	the	the	DET
aiti-7988	57	11	applied	apply	VERB
aiti-7988	57	12	loads	load	NOUN
aiti-7988	57	13	and	and	CCONJ
aiti-7988	57	14	self	self	NOUN
aiti-7988	57	15	-	-	PUNCT
aiti-7988	57	16	weight	weight	NOUN
aiti-7988	57	17	.	.	PUNCT
aiti-7988	58	1	it	it	PRON
aiti-7988	58	2	has	have	AUX
aiti-7988	58	3	been	be	AUX
aiti-7988	58	4	found	find	VERB
aiti-7988	58	5	that	that	SCONJ
aiti-7988	58	6	there	there	PRON
aiti-7988	58	7	are	be	VERB
aiti-7988	58	8	quite	quite	DET
aiti-7988	58	9	a	a	DET
aiti-7988	58	10	few	few	ADJ
aiti-7988	58	11	articles	article	NOUN
aiti-7988	58	12	that	that	PRON
aiti-7988	58	13	use	use	VERB
aiti-7988	58	14	analytical	analytical	ADJ
aiti-7988	58	15	approaches	approach	NOUN
aiti-7988	58	16	to	to	PART
aiti-7988	58	17	analyze	analyze	VERB
aiti-7988	58	18	the	the	DET
aiti-7988	58	19	dynamic	dynamic	ADJ
aiti-7988	58	20	problems	problem	NOUN
aiti-7988	58	21	of	of	ADP
aiti-7988	58	22	the	the	DET
aiti-7988	58	23	pipes	pipe	NOUN
aiti-7988	58	24	conveying	convey	VERB
aiti-7988	58	25	fluid	fluid	NOUN
aiti-7988	58	26	.	.	PUNCT
aiti-7988	59	1	an	an	DET
aiti-7988	59	2	analytical	analytical	ADJ
aiti-7988	59	3	solution	solution	NOUN
aiti-7988	59	4	is	be	AUX
aiti-7988	59	5	very	very	ADV
aiti-7988	59	6	important	important	ADJ
aiti-7988	59	7	for	for	ADP
aiti-7988	59	8	the	the	DET
aiti-7988	59	9	improvements	improvement	NOUN
aiti-7988	59	10	and	and	CCONJ
aiti-7988	59	11	verifications	verification	NOUN
aiti-7988	59	12	of	of	ADP
aiti-7988	59	13	effective	effective	ADJ
aiti-7988	59	14	applied	apply	VERB
aiti-7988	59	15	numerical	numerical	ADJ
aiti-7988	59	16	simulation	simulation	NOUN
aiti-7988	59	17	tools	tool	NOUN
aiti-7988	59	18	.	.	PUNCT
aiti-7988	60	1	to	to	PART
aiti-7988	60	2	address	address	VERB
aiti-7988	60	3	the	the	DET
aiti-7988	60	4	lack	lack	NOUN
aiti-7988	60	5	of	of	ADP
aiti-7988	60	6	research	research	NOUN
aiti-7988	60	7	in	in	ADP
aiti-7988	60	8	this	this	DET
aiti-7988	60	9	aspect	aspect	NOUN
aiti-7988	60	10	,	,	PUNCT
aiti-7988	60	11	the	the	DET
aiti-7988	60	12	analytic	analytic	ADJ
aiti-7988	60	13	solution	solution	NOUN
aiti-7988	60	14	based	base	VERB
aiti-7988	60	15	on	on	ADP
aiti-7988	60	16	integral	integral	ADJ
aiti-7988	60	17	transform	transform	NOUN
aiti-7988	60	18	technique	technique	NOUN
aiti-7988	60	19	(	(	PUNCT
aiti-7988	60	20	itt	itt	ADJ
aiti-7988	60	21	)	)	PUNCT
aiti-7988	60	22	approach	approach	NOUN
aiti-7988	60	23	(	(	PUNCT
aiti-7988	60	24	via	via	ADP
aiti-7988	60	25	the	the	DET
aiti-7988	60	26	combination	combination	NOUN
aiti-7988	60	27	of	of	ADP
aiti-7988	60	28	finite	finite	ADJ
aiti-7988	60	29	fourier	fourier	NOUN
aiti-7988	60	30	sine	sine	NOUN
aiti-7988	60	31	and	and	CCONJ
aiti-7988	60	32	laplace	laplace	NOUN
aiti-7988	60	33	transforms	transform	VERB
aiti-7988	60	34	)	)	PUNCT
aiti-7988	60	35	is	be	AUX
aiti-7988	60	36	adopted	adopt	VERB
aiti-7988	60	37	in	in	ADP
aiti-7988	60	38	this	this	DET
aiti-7988	60	39	work	work	NOUN
aiti-7988	60	40	to	to	PART
aiti-7988	60	41	analyze	analyze	VERB
aiti-7988	60	42	the	the	DET
aiti-7988	60	43	dynamic	dynamic	ADJ
aiti-7988	60	44	behavior	behavior	NOUN
aiti-7988	60	45	of	of	ADP
aiti-7988	60	46	an	an	DET
aiti-7988	60	47	inclined	inclined	ADJ
aiti-7988	60	48	and	and	CCONJ
aiti-7988	60	49	doubly	doubly	ADV
aiti-7988	60	50	fixed	fix	VERB
aiti-7988	60	51	supported	support	VERB
aiti-7988	60	52	pipe	pipe	NOUN
aiti-7988	60	53	subjected	subject	VERB
aiti-7988	60	54	to	to	ADP
aiti-7988	60	55	the	the	DET
aiti-7988	60	56	thermal	thermal	ADJ
aiti-7988	60	57	loads	load	NOUN
aiti-7988	60	58	.	.	PUNCT
aiti-7988	61	1	firstly	firstly	ADV
aiti-7988	61	2	,	,	PUNCT
aiti-7988	61	3	the	the	DET
aiti-7988	61	4	frequency	frequency	NOUN
aiti-7988	61	5	-	-	PUNCT
aiti-7988	61	6	domain	domain	NOUN
aiti-7988	61	7	response	response	NOUN
aiti-7988	61	8	of	of	ADP
aiti-7988	61	9	the	the	DET
aiti-7988	61	10	pipe	pipe	NOUN
aiti-7988	61	11	conveying	conveying	NOUN
aiti-7988	61	12	fluid	fluid	NOUN
aiti-7988	61	13	is	be	AUX
aiti-7988	61	14	obtained	obtain	VERB
aiti-7988	61	15	.	.	PUNCT
aiti-7988	62	1	then	then	ADV
aiti-7988	62	2	,	,	PUNCT
aiti-7988	62	3	the	the	DET
aiti-7988	62	4	corresponding	corresponding	ADJ
aiti-7988	62	5	inverse	inverse	NOUN
aiti-7988	62	6	transforms	transform	VERB
aiti-7988	62	7	on	on	ADP
aiti-7988	62	8	the	the	DET
aiti-7988	62	9	displacement	displacement	ADJ
aiti-7988	62	10	frequency	frequency	NOUN
aiti-7988	62	11	-	-	PUNCT
aiti-7988	62	12	domain	domain	NOUN
aiti-7988	62	13	responses	response	NOUN
aiti-7988	62	14	of	of	ADP
aiti-7988	62	15	the	the	DET
aiti-7988	62	16	pipe	pipe	NOUN
aiti-7988	62	17	are	be	AUX
aiti-7988	62	18	conducted	conduct	VERB
aiti-7988	62	19	to	to	PART
aiti-7988	62	20	obtain	obtain	VERB
aiti-7988	62	21	the	the	DET
aiti-7988	62	22	spatial	spatial	ADJ
aiti-7988	62	23	displacement	displacement	ADJ
aiti-7988	62	24	time	time	NOUN
aiti-7988	62	25	-	-	PUNCT
aiti-7988	62	26	domain	domain	NOUN
aiti-7988	62	27	responses	response	NOUN
aiti-7988	62	28	.	.	PUNCT
aiti-7988	63	1	moreover	moreover	ADV
aiti-7988	63	2	,	,	PUNCT
aiti-7988	63	3	the	the	DET
aiti-7988	63	4	effects	effect	NOUN
aiti-7988	63	5	of	of	ADP
aiti-7988	63	6	changing	change	VERB
aiti-7988	63	7	the	the	DET
aiti-7988	63	8	aspect	aspect	NOUN
aiti-7988	63	9	ratio	ratio	NOUN
aiti-7988	63	10	,	,	PUNCT
aiti-7988	63	11	inclination	inclination	NOUN
aiti-7988	63	12	angle	angle	NOUN
aiti-7988	63	13	,	,	PUNCT
aiti-7988	63	14	and	and	CCONJ
aiti-7988	63	15	temperature	temperature	NOUN
aiti-7988	63	16	variation	variation	NOUN
aiti-7988	63	17	on	on	ADP
aiti-7988	63	18	the	the	DET
aiti-7988	63	19	natural	natural	ADJ
aiti-7988	63	20	frequencies	frequency	NOUN
aiti-7988	63	21	,	,	PUNCT
aiti-7988	63	22	as	as	ADV
aiti-7988	63	23	well	well	ADV
aiti-7988	63	24	as	as	ADP
aiti-7988	63	25	the	the	DET
aiti-7988	63	26	critical	critical	ADJ
aiti-7988	63	27	velocities	velocity	NOUN
aiti-7988	63	28	of	of	ADP
aiti-7988	63	29	the	the	DET
aiti-7988	63	30	pipes	pipe	NOUN
aiti-7988	63	31	conveying	convey	VERB
aiti-7988	63	32	fluid	fluid	NOUN
aiti-7988	63	33	under	under	ADP
aiti-7988	63	34	different	different	ADJ
aiti-7988	63	35	fluid	fluid	ADJ
aiti-7988	63	36	speeds	speed	NOUN
aiti-7988	63	37	are	be	AUX
aiti-7988	63	38	evaluated	evaluate	VERB
aiti-7988	63	39	.	.	PUNCT
aiti-7988	64	1	this	this	DET
aiti-7988	64	2	work	work	NOUN
aiti-7988	64	3	is	be	AUX
aiti-7988	64	4	structured	structure	VERB
aiti-7988	64	5	as	as	SCONJ
aiti-7988	64	6	follows	follow	VERB
aiti-7988	64	7	.	.	PUNCT
aiti-7988	65	1	section	section	NOUN
aiti-7988	65	2	1	1	NUM
aiti-7988	65	3	introduces	introduce	NOUN
aiti-7988	65	4	the	the	DET
aiti-7988	65	5	problem	problem	NOUN
aiti-7988	65	6	under	under	ADP
aiti-7988	65	7	study	study	NOUN
aiti-7988	65	8	.	.	PUNCT
aiti-7988	66	1	section	section	NOUN
aiti-7988	66	2	2	2	NUM
aiti-7988	66	3	presents	present	VERB
aiti-7988	66	4	the	the	DET
aiti-7988	66	5	methods	method	NOUN
aiti-7988	66	6	used	use	VERB
aiti-7988	66	7	to	to	PART
aiti-7988	66	8	solve	solve	VERB
aiti-7988	66	9	motion	motion	NOUN
aiti-7988	66	10	equations	equation	NOUN
aiti-7988	66	11	.	.	PUNCT
aiti-7988	67	1	section	section	NOUN
aiti-7988	67	2	3	3	NUM
aiti-7988	67	3	provides	provide	VERB
aiti-7988	67	4	the	the	DET
aiti-7988	67	5	model	model	NOUN
aiti-7988	67	6	description	description	NOUN
aiti-7988	67	7	and	and	CCONJ
aiti-7988	67	8	solution	solution	NOUN
aiti-7988	67	9	procedure	procedure	NOUN
aiti-7988	67	10	of	of	ADP
aiti-7988	67	11	governing	govern	VERB
aiti-7988	67	12	equations	equation	NOUN
aiti-7988	67	13	.	.	PUNCT
aiti-7988	68	1	in	in	ADP
aiti-7988	68	2	section	section	NOUN
aiti-7988	68	3	4	4	NUM
aiti-7988	68	4	,	,	PUNCT
aiti-7988	68	5	results	result	NOUN
aiti-7988	68	6	are	be	AUX
aiti-7988	68	7	analyzed	analyze	VERB
aiti-7988	68	8	and	and	CCONJ
aiti-7988	68	9	discussed	discuss	VERB
aiti-7988	68	10	.	.	PUNCT
aiti-7988	69	1	finally	finally	ADV
aiti-7988	69	2	,	,	PUNCT
aiti-7988	69	3	the	the	DET
aiti-7988	69	4	paper	paper	NOUN
aiti-7988	69	5	ends	end	VERB
aiti-7988	69	6	in	in	ADP
aiti-7988	69	7	section	section	NOUN
aiti-7988	69	8	5	5	NUM
aiti-7988	69	9	with	with	ADP
aiti-7988	69	10	the	the	DET
aiti-7988	69	11	summary	summary	NOUN
aiti-7988	69	12	and	and	CCONJ
aiti-7988	69	13	conclusions	conclusion	NOUN
aiti-7988	69	14	of	of	ADP
aiti-7988	69	15	the	the	DET
aiti-7988	69	16	current	current	ADJ
aiti-7988	69	17	work	work	NOUN
aiti-7988	69	18	.	.	PUNCT
aiti-7988	70	1	2	2	X
aiti-7988	70	2	.	.	X
aiti-7988	70	3	methods	method	NOUN
aiti-7988	70	4	2.1	2.1	NUM
aiti-7988	70	5	.	.	PUNCT
aiti-7988	71	1	laplace	laplace	NOUN
aiti-7988	71	2	transform	transform	VERB
aiti-7988	71	3	laplace	laplace	NOUN
aiti-7988	71	4	transform	transform	NOUN
aiti-7988	71	5	is	be	AUX
aiti-7988	71	6	a	a	DET
aiti-7988	71	7	linear	linear	ADJ
aiti-7988	71	8	transform	transform	NOUN
aiti-7988	71	9	that	that	PRON
aiti-7988	71	10	is	be	AUX
aiti-7988	71	11	widely	widely	ADV
aiti-7988	71	12	applied	apply	VERB
aiti-7988	71	13	in	in	ADP
aiti-7988	71	14	the	the	DET
aiti-7988	71	15	dynamic	dynamic	ADJ
aiti-7988	71	16	problems	problem	NOUN
aiti-7988	71	17	of	of	ADP
aiti-7988	71	18	structure	structure	NOUN
aiti-7988	71	19	.	.	PUNCT
aiti-7988	72	1	it	it	PRON
aiti-7988	72	2	provides	provide	VERB
aiti-7988	72	3	easy	easy	ADJ
aiti-7988	72	4	and	and	CCONJ
aiti-7988	72	5	powerful	powerful	ADJ
aiti-7988	72	6	means	mean	VERB
aiti-7988	72	7	to	to	PART
aiti-7988	72	8	transform	transform	VERB
aiti-7988	72	9	partial	partial	ADJ
aiti-7988	72	10	differential	differential	ADJ
aiti-7988	72	11	equations	equation	NOUN
aiti-7988	72	12	into	into	ADP
aiti-7988	72	13	ordinary	ordinary	ADJ
aiti-7988	72	14	differential	differential	ADJ
aiti-7988	72	15	equations	equation	NOUN
aiti-7988	72	16	,	,	PUNCT
aiti-7988	72	17	or	or	CCONJ
aiti-7988	72	18	transform	transform	VERB
aiti-7988	72	19	ordinary	ordinary	ADJ
aiti-7988	72	20	differential	differential	ADJ
aiti-7988	72	21	equations	equation	NOUN
aiti-7988	72	22	into	into	ADP
aiti-7988	72	23	integral	integral	ADJ
aiti-7988	72	24	form	form	NOUN
aiti-7988	72	25	equations	equation	NOUN
aiti-7988	72	26	,	,	PUNCT
aiti-7988	72	27	which	which	PRON
aiti-7988	72	28	make	make	VERB
aiti-7988	72	29	them	they	PRON
aiti-7988	72	30	much	much	ADV
aiti-7988	72	31	easier	easy	ADJ
aiti-7988	72	32	to	to	PART
aiti-7988	72	33	be	be	AUX
aiti-7988	72	34	solved	solve	VERB
aiti-7988	72	35	.	.	PUNCT
aiti-7988	73	1	laplace	laplace	NOUN
aiti-7988	73	2	transform	transform	NOUN
aiti-7988	73	3	directly	directly	ADV
aiti-7988	73	4	obtains	obtain	VERB
aiti-7988	73	5	the	the	DET
aiti-7988	73	6	solution	solution	NOUN
aiti-7988	73	7	of	of	ADP
aiti-7988	73	8	differential	differential	ADJ
aiti-7988	73	9	equations	equation	NOUN
aiti-7988	73	10	with	with	ADP
aiti-7988	73	11	certain	certain	ADJ
aiti-7988	73	12	boundary	boundary	ADJ
aiti-7988	73	13	values	value	NOUN
aiti-7988	73	14	without	without	ADP
aiti-7988	73	15	determining	determine	VERB
aiti-7988	73	16	the	the	DET
aiti-7988	73	17	general	general	ADJ
aiti-7988	73	18	solution	solution	NOUN
aiti-7988	73	19	first	first	ADV
aiti-7988	73	20	42	42	NUM
aiti-7988	73	21	advances	advance	NOUN
aiti-7988	73	22	in	in	ADP
aiti-7988	73	23	technology	technology	NOUN
aiti-7988	73	24	innovation	innovation	NOUN
aiti-7988	73	25	,	,	PUNCT
aiti-7988	73	26	vol	vol	NOUN
aiti-7988	73	27	.	.	PROPN
aiti-7988	74	1	7	7	NUM
aiti-7988	74	2	,	,	PUNCT
aiti-7988	74	3	no	no	INTJ
aiti-7988	74	4	.	.	NOUN
aiti-7988	74	5	1	1	NUM
aiti-7988	74	6	,	,	PUNCT
aiti-7988	74	7	2022	2022	NUM
aiti-7988	74	8	,	,	PUNCT
aiti-7988	74	9	pp	pp	ADJ
aiti-7988	74	10	.	.	PUNCT
aiti-7988	75	1	41	41	NUM
aiti-7988	75	2	-	-	SYM
aiti-7988	75	3	55	55	NUM
aiti-7988	76	1	[	[	X
aiti-7988	76	2	16	16	NUM
aiti-7988	76	3	-	-	SYM
aiti-7988	76	4	17	17	NUM
aiti-7988	76	5	]	]	PUNCT
aiti-7988	76	6	.	.	PUNCT
aiti-7988	77	1	many	many	ADJ
aiti-7988	77	2	successful	successful	ADJ
aiti-7988	77	3	applications	application	NOUN
aiti-7988	77	4	of	of	ADP
aiti-7988	77	5	laplace	laplace	NOUN
aiti-7988	77	6	transform	transform	NOUN
aiti-7988	77	7	were	be	AUX
aiti-7988	77	8	done	do	VERB
aiti-7988	77	9	to	to	PART
aiti-7988	77	10	study	study	VERB
aiti-7988	77	11	the	the	DET
aiti-7988	77	12	dynamic	dynamic	ADJ
aiti-7988	77	13	behavior	behavior	NOUN
aiti-7988	77	14	of	of	ADP
aiti-7988	77	15	the	the	DET
aiti-7988	77	16	components	component	NOUN
aiti-7988	77	17	with	with	ADP
aiti-7988	77	18	and	and	CCONJ
aiti-7988	77	19	without	without	ADP
aiti-7988	77	20	external	external	ADJ
aiti-7988	77	21	forces	force	NOUN
aiti-7988	77	22	[	[	X
aiti-7988	77	23	18	18	NUM
aiti-7988	77	24	-	-	SYM
aiti-7988	77	25	19	19	NUM
aiti-7988	77	26	]	]	PUNCT
aiti-7988	77	27	.	.	PUNCT
aiti-7988	78	1	assume	assume	VERB
aiti-7988	78	2	that	that	SCONJ
aiti-7988	78	3	�	�	PROPN
aiti-7988	78	4	(	(	PUNCT
aiti-7988	78	5	�	�	PROPN
aiti-7988	78	6	)	)	PUNCT
aiti-7988	78	7	is	be	AUX
aiti-7988	78	8	a	a	DET
aiti-7988	78	9	real	real	ADJ
aiti-7988	78	10	function	function	NOUN
aiti-7988	78	11	of	of	ADP
aiti-7988	78	12	time	time	NOUN
aiti-7988	78	13	t	t	PROPN
aiti-7988	78	14	,	,	PUNCT
aiti-7988	78	15	which	which	PRON
aiti-7988	78	16	is	be	AUX
aiti-7988	78	17	defined	define	VERB
aiti-7988	78	18	in	in	ADP
aiti-7988	78	19	the	the	DET
aiti-7988	78	20	real	real	ADJ
aiti-7988	78	21	domain	domain	NOUN
aiti-7988	79	1	[	[	X
aiti-7988	79	2	0	0	NUM
aiti-7988	79	3	,	,	PUNCT
aiti-7988	79	4	+	+	NOUN
aiti-7988	79	5	∞	∞	NOUN
aiti-7988	79	6	)	)	PUNCT
aiti-7988	79	7	,	,	PUNCT
aiti-7988	79	8	the	the	DET
aiti-7988	79	9	laplace	laplace	NOUN
aiti-7988	79	10	transform	transform	NOUN
aiti-7988	79	11	and	and	CCONJ
aiti-7988	79	12	its	its	PRON
aiti-7988	79	13	inversion	inversion	NOUN
aiti-7988	79	14	are	be	AUX
aiti-7988	79	15	defined	define	VERB
aiti-7988	79	16	by	by	ADP
aiti-7988	79	17	:	:	PUNCT
aiti-7988	79	18	(	(	PUNCT
aiti-7988	79	19	)	)	PUNCT
aiti-7988	79	20	(	(	PUNCT
aiti-7988	79	21	)	)	PUNCT
aiti-7988	79	22	(	(	PUNCT
aiti-7988	79	23	)	)	PUNCT
aiti-7988	79	24	0	0	PUNCT
aiti-7988	80	1	[	[	PUNCT
aiti-7988	80	2	]	]	X
aiti-7988	80	3	st	st	PROPN
aiti-7988	80	4	s	s	PROPN
aiti-7988	80	5	t	t	PROPN
aiti-7988	80	6	tl	tl	PROPN
aiti-7988	80	7	f	f	PROPN
aiti-7988	80	8	f	f	PROPN
aiti-7988	80	9	e	e	PROPN
aiti-7988	80	10	dtψ	dtψ	PROPN
aiti-7988	80	11	∞	∞	PROPN
aiti-7988	80	12	−=	−=	PROPN
aiti-7988	80	13	=	=	SYM
aiti-7988	80	14	∫	∫	PROPN
aiti-7988	80	15	(	(	PUNCT
aiti-7988	80	16	1	1	NUM
aiti-7988	80	17	)	)	PUNCT
aiti-7988	80	18	1	1	NUM
aiti-7988	80	19	(	(	PUNCT
aiti-7988	80	20	)	)	PUNCT
aiti-7988	80	21	(	(	PUNCT
aiti-7988	80	22	)	)	PUNCT
aiti-7988	80	23	(	(	PUNCT
aiti-7988	80	24	)	)	PUNCT
aiti-7988	80	25	1	1	NUM
aiti-7988	81	1	[	[	PUNCT
aiti-7988	81	2	]	]	X
aiti-7988	81	3	2	2	NUM
aiti-7988	81	4	i	i	PRON
aiti-7988	81	5	st	st	PROPN
aiti-7988	82	1	t	t	PROPN
aiti-7988	82	2	s	s	X
aiti-7988	82	3	si	si	X
aiti-7988	82	4	f	f	PROPN
aiti-7988	82	5	l	l	NOUN
aiti-7988	82	6	e	e	NOUN
aiti-7988	82	7	ds	ds	INTJ
aiti-7988	82	8	i	i	PRON
aiti-7988	82	9	ε	ε	PROPN
aiti-7988	82	10	ε	ε	PROPN
aiti-7988	82	11	ψ	ψ	X
aiti-7988	82	12	ψ	ψ	X
aiti-7988	82	13	π	π	X
aiti-7988	82	14	+	+	CCONJ
aiti-7988	82	15	∞−	∞−	PROPN
aiti-7988	82	16	−	−	NOUN
aiti-7988	82	17	∞	∞	NUM
aiti-7988	82	18	=	=	PUNCT
aiti-7988	83	1	=	=	SYM
aiti-7988	83	2	∫	∫	PROPN
aiti-7988	83	3	(	(	PUNCT
aiti-7988	83	4	2	2	NUM
aiti-7988	83	5	)	)	PUNCT
aiti-7988	83	6	where	where	SCONJ
aiti-7988	83	7	l	l	NOUN
aiti-7988	83	8	is	be	AUX
aiti-7988	83	9	laplace	laplace	NOUN
aiti-7988	83	10	transform	transform	NOUN
aiti-7988	83	11	,	,	PUNCT
aiti-7988	83	12	l	l	NOUN
aiti-7988	83	13	−1	−1	NOUN
aiti-7988	83	14	is	be	AUX
aiti-7988	83	15	the	the	DET
aiti-7988	83	16	inverse	inverse	ADJ
aiti-7988	83	17	laplace	laplace	NOUN
aiti-7988	83	18	transform	transform	NOUN
aiti-7988	83	19	,	,	PUNCT
aiti-7988	83	20	s	s	VERB
aiti-7988	83	21	represents	represent	VERB
aiti-7988	83	22	a	a	DET
aiti-7988	83	23	complex	complex	ADJ
aiti-7988	83	24	number	number	NOUN
aiti-7988	83	25	in	in	ADP
aiti-7988	83	26	the	the	DET
aiti-7988	83	27	laplace	laplace	NOUN
aiti-7988	83	28	domain	domain	NOUN
aiti-7988	83	29	,	,	PUNCT
aiti-7988	83	30	and	and	CCONJ
aiti-7988	83	31	si	si	INTJ
aiti-7988	83	32	(	(	PUNCT
aiti-7988	83	33	i	i	NOUN
aiti-7988	83	34	=	=	NOUN
aiti-7988	83	35	1	1	NUM
aiti-7988	83	36	,	,	PUNCT
aiti-7988	83	37	2	2	NUM
aiti-7988	83	38	,	,	PUNCT
aiti-7988	83	39	3	3	NUM
aiti-7988	83	40	,	,	PUNCT
aiti-7988	83	41	…	…	PUNCT
aiti-7988	83	42	)	)	PUNCT
aiti-7988	83	43	are	be	AUX
aiti-7988	83	44	the	the	DET
aiti-7988	83	45	singularities	singularity	NOUN
aiti-7988	83	46	of	of	ADP
aiti-7988	83	47	�	�	PROPN
aiti-7988	83	48	(	(	PUNCT
aiti-7988	83	49	�	�	PROPN
aiti-7988	83	50	)	)	PUNCT
aiti-7988	83	51	.	.	PUNCT
aiti-7988	84	1	2.2	2.2	NUM
aiti-7988	84	2	.	.	PUNCT
aiti-7988	85	1	finite	finite	PROPN
aiti-7988	85	2	fourier	fourier	PROPN
aiti-7988	85	3	sine	sine	NOUN
aiti-7988	85	4	transform	transform	VERB
aiti-7988	85	5	the	the	DET
aiti-7988	85	6	fourier	fourier	NOUN
aiti-7988	85	7	transform	transform	NOUN
aiti-7988	85	8	method	method	NOUN
aiti-7988	85	9	was	be	AUX
aiti-7988	85	10	utilized	utilize	VERB
aiti-7988	85	11	into	into	ADP
aiti-7988	85	12	the	the	DET
aiti-7988	85	13	field	field	NOUN
aiti-7988	85	14	of	of	ADP
aiti-7988	85	15	structural	structural	ADJ
aiti-7988	85	16	dynamics	dynamic	NOUN
aiti-7988	85	17	by	by	ADP
aiti-7988	85	18	many	many	ADJ
aiti-7988	85	19	researchers	researcher	NOUN
aiti-7988	86	1	[	[	X
aiti-7988	86	2	20	20	NUM
aiti-7988	86	3	-	-	SYM
aiti-7988	86	4	21	21	NUM
aiti-7988	86	5	]	]	PUNCT
aiti-7988	86	6	.	.	PUNCT
aiti-7988	87	1	fourier	fourier	PROPN
aiti-7988	87	2	transform	transform	NOUN
aiti-7988	87	3	is	be	AUX
aiti-7988	87	4	helpful	helpful	ADJ
aiti-7988	87	5	in	in	ADP
aiti-7988	87	6	solving	solve	VERB
aiti-7988	87	7	the	the	DET
aiti-7988	87	8	differential	differential	ADJ
aiti-7988	87	9	and	and	CCONJ
aiti-7988	87	10	partial	partial	ADJ
aiti-7988	87	11	differential	differential	ADJ
aiti-7988	87	12	equations	equation	NOUN
aiti-7988	87	13	of	of	ADP
aiti-7988	87	14	non	non	ADJ
aiti-7988	87	15	-	-	ADJ
aiti-7988	87	16	periodic	periodic	ADJ
aiti-7988	87	17	functions	function	NOUN
aiti-7988	87	18	.	.	PUNCT
aiti-7988	88	1	it	it	PRON
aiti-7988	88	2	can	can	AUX
aiti-7988	88	3	be	be	AUX
aiti-7988	88	4	applied	apply	VERB
aiti-7988	88	5	to	to	PART
aiti-7988	88	6	solve	solve	VERB
aiti-7988	88	7	some	some	DET
aiti-7988	88	8	boundary	boundary	ADJ
aiti-7988	88	9	-	-	PUNCT
aiti-7988	88	10	value	value	NOUN
aiti-7988	88	11	and	and	CCONJ
aiti-7988	88	12	initial	initial	ADJ
aiti-7988	88	13	-	-	PUNCT
aiti-7988	88	14	value	value	NOUN
aiti-7988	88	15	problems	problem	NOUN
aiti-7988	88	16	for	for	ADP
aiti-7988	88	17	partial	partial	ADJ
aiti-7988	88	18	differential	differential	ADJ
aiti-7988	88	19	equations	equation	NOUN
aiti-7988	88	20	.	.	PUNCT
aiti-7988	89	1	fourier	fourier	PROPN
aiti-7988	89	2	transform	transform	NOUN
aiti-7988	89	3	is	be	AUX
aiti-7988	89	4	usually	usually	ADV
aiti-7988	89	5	used	use	VERB
aiti-7988	89	6	in	in	ADP
aiti-7988	89	7	order	order	NOUN
aiti-7988	89	8	to	to	PART
aiti-7988	89	9	reduce	reduce	VERB
aiti-7988	89	10	the	the	DET
aiti-7988	89	11	order	order	NOUN
aiti-7988	89	12	of	of	ADP
aiti-7988	89	13	differential	differential	ADJ
aiti-7988	89	14	equations	equation	NOUN
aiti-7988	89	15	.	.	PUNCT
aiti-7988	90	1	it	it	PRON
aiti-7988	90	2	can	can	AUX
aiti-7988	90	3	be	be	AUX
aiti-7988	90	4	employed	employ	VERB
aiti-7988	90	5	to	to	PART
aiti-7988	90	6	convert	convert	VERB
aiti-7988	90	7	the	the	DET
aiti-7988	90	8	infinite	infinite	ADJ
aiti-7988	90	9	degree	degree	NOUN
aiti-7988	90	10	of	of	ADP
aiti-7988	90	11	freedom	freedom	NOUN
aiti-7988	90	12	systems	system	NOUN
aiti-7988	90	13	into	into	ADP
aiti-7988	90	14	a	a	DET
aiti-7988	90	15	superimposed	superimpose	VERB
aiti-7988	90	16	double	double	ADJ
aiti-7988	90	17	or	or	CCONJ
aiti-7988	90	18	single	single	ADJ
aiti-7988	90	19	degree	degree	NOUN
aiti-7988	90	20	of	of	ADP
aiti-7988	90	21	freedom	freedom	NOUN
aiti-7988	90	22	system	system	NOUN
aiti-7988	90	23	.	.	PUNCT
aiti-7988	91	1	the	the	DET
aiti-7988	91	2	finite	finite	PROPN
aiti-7988	91	3	sine	sine	NOUN
aiti-7988	91	4	fourier	fourier	NOUN
aiti-7988	91	5	transform	transform	NOUN
aiti-7988	91	6	for	for	ADP
aiti-7988	91	7	a	a	DET
aiti-7988	91	8	function	function	NOUN
aiti-7988	91	9	of	of	ADP
aiti-7988	91	10	�	�	PROPN
aiti-7988	91	11	(	(	PUNCT
aiti-7988	91	12	�	�	PROPN
aiti-7988	91	13	)	)	PUNCT
aiti-7988	91	14	,	,	PUNCT
aiti-7988	91	15	which	which	PRON
aiti-7988	91	16	is	be	AUX
aiti-7988	91	17	a	a	DET
aiti-7988	91	18	real	real	ADJ
aiti-7988	91	19	function	function	NOUN
aiti-7988	91	20	of	of	ADP
aiti-7988	91	21	coordinate	coordinate	NOUN
aiti-7988	91	22	x	x	PUNCT
aiti-7988	91	23	in	in	ADP
aiti-7988	91	24	space	space	NOUN
aiti-7988	91	25	(	(	PUNCT
aiti-7988	91	26	0	0	NUM
aiti-7988	91	27	≤	≤	NUM
aiti-7988	91	28	x	x	SYM
aiti-7988	91	29	≤	≤	NUM
aiti-7988	91	30	l	l	NOUN
aiti-7988	91	31	)	)	PUNCT
aiti-7988	91	32	,	,	PUNCT
aiti-7988	91	33	can	can	AUX
aiti-7988	91	34	be	be	AUX
aiti-7988	91	35	represented	represent	VERB
aiti-7988	91	36	as	as	SCONJ
aiti-7988	91	37	follows	follow	VERB
aiti-7988	91	38	[	[	X
aiti-7988	91	39	22	22	NUM
aiti-7988	91	40	]	]	PUNCT
aiti-7988	91	41	.	.	PUNCT
aiti-7988	92	1	1	1	NUM
aiti-7988	92	2	(	(	PUNCT
aiti-7988	92	3	)	)	PUNCT
aiti-7988	92	4	(	(	PUNCT
aiti-7988	92	5	)	)	PUNCT
aiti-7988	92	6	(	(	PUNCT
aiti-7988	92	7	)	)	PUNCT
aiti-7988	92	8	0	0	PUNCT
aiti-7988	93	1	[	[	PUNCT
aiti-7988	93	2	]	]	X
aiti-7988	93	3	sins	sin	NOUN
aiti-7988	93	4	x	x	SYM
aiti-7988	93	5	x	x	SYM
aiti-7988	93	6	nf	nf	INTJ
aiti-7988	94	1	f	f	PROPN
aiti-7988	94	2	f	f	PROPN
aiti-7988	94	3	n	n	CCONJ
aiti-7988	94	4	xdx	xdx	PROPN
aiti-7988	94	5	fπ=	fπ=	PROPN
aiti-7988	94	6	=	=	PRON
aiti-7988	94	7	∫	∫	PROPN
aiti-7988	94	8	(	(	PUNCT
aiti-7988	94	9	3	3	NUM
aiti-7988	94	10	)	)	PUNCT
aiti-7988	94	11	(	(	PUNCT
aiti-7988	94	12	)	)	PUNCT
aiti-7988	94	13	(	(	PUNCT
aiti-7988	94	14	)	)	PUNCT
aiti-7988	94	15	1	1	NUM
aiti-7988	94	16	(	(	PUNCT
aiti-7988	94	17	)	)	PUNCT
aiti-7988	94	18	1	1	NUM
aiti-7988	94	19	[	[	PUNCT
aiti-7988	94	20	]	]	SYM
aiti-7988	94	21	2	2	NUM
aiti-7988	94	22	sin	sin	NOUN
aiti-7988	94	23	n	n	PROPN
aiti-7988	94	24	xs	xs	PROPN
aiti-7988	94	25	n	n	CCONJ
aiti-7988	94	26	n	n	PROPN
aiti-7988	95	1	f	f	NOUN
aiti-7988	95	2	f	f	PROPN
aiti-7988	95	3	f	f	PROPN
aiti-7988	95	4	n	n	PROPN
aiti-7988	95	5	x	x	PROPN
aiti-7988	95	6	fπ∞−	fπ∞−	NOUN
aiti-7988	95	7	=	=	X
aiti-7988	95	8	=	=	SYM
aiti-7988	95	9	=	=	NOUN
aiti-7988	95	10	∑	∑	PROPN
aiti-7988	95	11	(	(	PUNCT
aiti-7988	95	12	4	4	NUM
aiti-7988	95	13	)	)	PUNCT
aiti-7988	95	14	where	where	SCONJ
aiti-7988	95	15	�	�	PROPN
aiti-7988	95	16	�	�	PROPN
aiti-7988	95	17	is	be	AUX
aiti-7988	95	18	fourier	fourier	ADJ
aiti-7988	95	19	transform	transform	NOUN
aiti-7988	95	20	,	,	PUNCT
aiti-7988	95	21	�	�	PROPN
aiti-7988	95	22	�	�	PROPN
aiti-7988	95	23	is	be	AUX
aiti-7988	95	24	the	the	DET
aiti-7988	95	25	inverse	inverse	ADJ
aiti-7988	95	26	fourier	fourier	NOUN
aiti-7988	95	27	transform	transform	NOUN
aiti-7988	95	28	,	,	PUNCT
aiti-7988	95	29	and	and	CCONJ
aiti-7988	95	30	n	n	PRON
aiti-7988	95	31	is	be	AUX
aiti-7988	95	32	an	an	DET
aiti-7988	95	33	integer	integer	NOUN
aiti-7988	95	34	.	.	PUNCT
aiti-7988	96	1	3	3	X
aiti-7988	96	2	.	.	X
aiti-7988	96	3	model	model	NOUN
aiti-7988	96	4	description	description	NOUN
aiti-7988	96	5	3.1	3.1	NUM
aiti-7988	96	6	.	.	PUNCT
aiti-7988	97	1	governing	govern	VERB
aiti-7988	97	2	equation	equation	NOUN
aiti-7988	97	3	the	the	DET
aiti-7988	97	4	system	system	NOUN
aiti-7988	97	5	considered	consider	VERB
aiti-7988	97	6	in	in	ADP
aiti-7988	97	7	the	the	DET
aiti-7988	97	8	present	present	ADJ
aiti-7988	97	9	investigation	investigation	NOUN
aiti-7988	97	10	comprises	comprise	VERB
aiti-7988	97	11	a	a	DET
aiti-7988	97	12	linear	linear	ADJ
aiti-7988	97	13	elastic	elastic	ADJ
aiti-7988	97	14	,	,	PUNCT
aiti-7988	97	15	clamped	clamp	VERB
aiti-7988	97	16	ends	end	NOUN
aiti-7988	97	17	,	,	PUNCT
aiti-7988	97	18	and	and	CCONJ
aiti-7988	97	19	the	the	DET
aiti-7988	97	20	inclined	inclined	ADJ
aiti-7988	97	21	pipes	pipe	NOUN
aiti-7988	97	22	made	make	VERB
aiti-7988	97	23	of	of	ADP
aiti-7988	97	24	polypropylene	polypropylene	NOUN
aiti-7988	97	25	-	-	PUNCT
aiti-7988	97	26	random	random	ADJ
aiti-7988	97	27	(	(	PUNCT
aiti-7988	97	28	pp	pp	NOUN
aiti-7988	97	29	-	-	PUNCT
aiti-7988	97	30	r	r	NOUN
aiti-7988	97	31	)	)	PUNCT
aiti-7988	97	32	material	material	NOUN
aiti-7988	97	33	with	with	ADP
aiti-7988	97	34	total	total	ADJ
aiti-7988	97	35	length	length	NOUN
aiti-7988	97	36	(	(	PUNCT
aiti-7988	97	37	l	l	NOUN
aiti-7988	97	38	)	)	PUNCT
aiti-7988	97	39	,	,	PUNCT
aiti-7988	97	40	inner	inner	ADJ
aiti-7988	97	41	and	and	CCONJ
aiti-7988	97	42	outer	outer	ADJ
aiti-7988	97	43	diameter	diameter	NOUN
aiti-7988	97	44	(	(	PUNCT
aiti-7988	97	45	di	di	NOUN
aiti-7988	97	46	and	and	CCONJ
aiti-7988	97	47	do	do	VERB
aiti-7988	97	48	)	)	PUNCT
aiti-7988	97	49	,	,	PUNCT
aiti-7988	97	50	thickness	thickness	NOUN
aiti-7988	97	51	(	(	PUNCT
aiti-7988	97	52	t	t	PROPN
aiti-7988	97	53	)	)	PUNCT
aiti-7988	97	54	,	,	PUNCT
aiti-7988	97	55	cross	cross	ADJ
aiti-7988	97	56	-	-	ADJ
aiti-7988	97	57	sectional	sectional	ADJ
aiti-7988	97	58	area	area	NOUN
aiti-7988	97	59	(	(	PUNCT
aiti-7988	97	60	ap	ap	PROPN
aiti-7988	97	61	)	)	PUNCT
aiti-7988	97	62	,	,	PUNCT
aiti-7988	97	63	mass	mass	NOUN
aiti-7988	97	64	per	per	ADP
aiti-7988	97	65	unit	unit	NOUN
aiti-7988	97	66	length	length	NOUN
aiti-7988	97	67	(	(	PUNCT
aiti-7988	97	68	mp	mp	PROPN
aiti-7988	97	69	)	)	PUNCT
aiti-7988	97	70	,	,	PUNCT
aiti-7988	97	71	young	young	PROPN
aiti-7988	97	72	’s	’s	PART
aiti-7988	97	73	modulus	modulus	NOUN
aiti-7988	97	74	(	(	PUNCT
aiti-7988	97	75	e	e	NOUN
aiti-7988	97	76	)	)	PUNCT
aiti-7988	97	77	,	,	PUNCT
aiti-7988	97	78	and	and	CCONJ
aiti-7988	97	79	moment	moment	NOUN
aiti-7988	97	80	of	of	ADP
aiti-7988	97	81	inertia	inertia	NOUN
aiti-7988	97	82	(	(	PUNCT
aiti-7988	97	83	i	i	NOUN
aiti-7988	97	84	)	)	PUNCT
aiti-7988	97	85	.	.	PUNCT
aiti-7988	98	1	the	the	DET
aiti-7988	98	2	fluid	fluid	NOUN
aiti-7988	98	3	passing	pass	VERB
aiti-7988	98	4	through	through	ADP
aiti-7988	98	5	the	the	DET
aiti-7988	98	6	pipe	pipe	NOUN
aiti-7988	98	7	has	have	VERB
aiti-7988	98	8	a	a	DET
aiti-7988	98	9	mass	mass	NOUN
aiti-7988	98	10	per	per	ADP
aiti-7988	98	11	unit	unit	NOUN
aiti-7988	98	12	length	length	NOUN
aiti-7988	98	13	mf	mf	X
aiti-7988	98	14	with	with	ADP
aiti-7988	98	15	an	an	DET
aiti-7988	98	16	axial	axial	ADJ
aiti-7988	98	17	internal	internal	ADJ
aiti-7988	98	18	fluid	fluid	NOUN
aiti-7988	98	19	flowing	flow	VERB
aiti-7988	98	20	velocity	velocity	NOUN
aiti-7988	98	21	υ	υ	PROPN
aiti-7988	98	22	.	.	PUNCT
aiti-7988	99	1	a	a	PRON
aiti-7988	99	2	represents	represent	VERB
aiti-7988	99	3	the	the	DET
aiti-7988	99	4	cross	cross	ADJ
aiti-7988	99	5	-	-	ADJ
aiti-7988	99	6	sectional	sectional	ADJ
aiti-7988	99	7	area	area	NOUN
aiti-7988	99	8	of	of	ADP
aiti-7988	99	9	the	the	DET
aiti-7988	99	10	flow	flow	NOUN
aiti-7988	99	11	and	and	CCONJ
aiti-7988	99	12	is	be	AUX
aiti-7988	99	13	assumed	assume	VERB
aiti-7988	99	14	to	to	PART
aiti-7988	99	15	be	be	AUX
aiti-7988	99	16	a	a	DET
aiti-7988	99	17	constant	constant	ADJ
aiti-7988	99	18	.	.	PUNCT
aiti-7988	100	1	the	the	DET
aiti-7988	100	2	fluid	fluid	NOUN
aiti-7988	100	3	has	have	VERB
aiti-7988	100	4	no	no	DET
aiti-7988	100	5	compression	compression	NOUN
aiti-7988	100	6	properties	property	NOUN
aiti-7988	100	7	and	and	CCONJ
aiti-7988	100	8	has	have	VERB
aiti-7988	100	9	no	no	DET
aiti-7988	100	10	viscosity	viscosity	NOUN
aiti-7988	100	11	.	.	PUNCT
aiti-7988	101	1	unlike	unlike	ADP
aiti-7988	101	2	the	the	DET
aiti-7988	101	3	discrete	discrete	ADJ
aiti-7988	101	4	systems	system	NOUN
aiti-7988	101	5	(	(	PUNCT
aiti-7988	101	6	simple	simple	ADJ
aiti-7988	101	7	or	or	CCONJ
aiti-7988	101	8	torsional	torsional	ADJ
aiti-7988	101	9	)	)	PUNCT
aiti-7988	101	10	,	,	PUNCT
aiti-7988	101	11	the	the	DET
aiti-7988	101	12	continuous	continuous	ADJ
aiti-7988	101	13	systems	system	NOUN
aiti-7988	101	14	,	,	PUNCT
aiti-7988	101	15	like	like	ADP
aiti-7988	101	16	pipe	pipe	NOUN
aiti-7988	101	17	or	or	CCONJ
aiti-7988	101	18	beam	beam	NOUN
aiti-7988	101	19	,	,	PUNCT
aiti-7988	101	20	possess	possess	VERB
aiti-7988	101	21	an	an	DET
aiti-7988	101	22	infinite	infinite	ADJ
aiti-7988	101	23	number	number	NOUN
aiti-7988	101	24	of	of	ADP
aiti-7988	101	25	degrees	degree	NOUN
aiti-7988	101	26	of	of	ADP
aiti-7988	101	27	freedom	freedom	NOUN
aiti-7988	101	28	that	that	PRON
aiti-7988	101	29	make	make	VERB
aiti-7988	101	30	them	they	PRON
aiti-7988	101	31	more	more	ADV
aiti-7988	101	32	difficult	difficult	ADJ
aiti-7988	101	33	to	to	PART
aiti-7988	101	34	be	be	AUX
aiti-7988	101	35	treated	treat	VERB
aiti-7988	101	36	.	.	PUNCT
aiti-7988	102	1	hence	hence	ADV
aiti-7988	102	2	,	,	PUNCT
aiti-7988	102	3	many	many	ADJ
aiti-7988	102	4	assumptions	assumption	NOUN
aiti-7988	102	5	were	be	AUX
aiti-7988	102	6	made	make	VERB
aiti-7988	102	7	to	to	PART
aiti-7988	102	8	simplify	simplify	VERB
aiti-7988	102	9	the	the	DET
aiti-7988	102	10	working	work	VERB
aiti-7988	102	11	process	process	NOUN
aiti-7988	102	12	with	with	ADP
aiti-7988	102	13	these	these	DET
aiti-7988	102	14	systems	system	NOUN
aiti-7988	102	15	[	[	X
aiti-7988	102	16	23	23	NUM
aiti-7988	102	17	-	-	SYM
aiti-7988	102	18	24	24	NUM
aiti-7988	102	19	]	]	PUNCT
aiti-7988	102	20	.	.	PUNCT
aiti-7988	103	1	figs	fig	NOUN
aiti-7988	103	2	.	.	PUNCT
aiti-7988	104	1	1	1	NUM
aiti-7988	104	2	and	and	CCONJ
aiti-7988	104	3	2	2	NUM
aiti-7988	104	4	present	present	VERB
aiti-7988	104	5	the	the	DET
aiti-7988	104	6	geometry	geometry	NOUN
aiti-7988	104	7	and	and	CCONJ
aiti-7988	104	8	cartesian	cartesian	ADJ
aiti-7988	104	9	coordinate	coordinate	NOUN
aiti-7988	104	10	system	system	NOUN
aiti-7988	104	11	,	,	PUNCT
aiti-7988	104	12	assuming	assume	VERB
aiti-7988	104	13	that	that	SCONJ
aiti-7988	104	14	the	the	DET
aiti-7988	104	15	origin	origin	NOUN
aiti-7988	104	16	of	of	ADP
aiti-7988	104	17	the	the	DET
aiti-7988	104	18	(	(	PUNCT
aiti-7988	104	19	x	x	PROPN
aiti-7988	104	20	,	,	PUNCT
aiti-7988	104	21	y	y	PROPN
aiti-7988	104	22	,	,	PUNCT
aiti-7988	104	23	z	z	NOUN
aiti-7988	104	24	)	)	PUNCT
aiti-7988	104	25	framework	framework	NOUN
aiti-7988	104	26	is	be	AUX
aiti-7988	104	27	placed	place	VERB
aiti-7988	104	28	in	in	ADP
aiti-7988	104	29	the	the	DET
aiti-7988	104	30	space	space	NOUN
aiti-7988	104	31	at	at	ADP
aiti-7988	104	32	the	the	DET
aiti-7988	104	33	left	left	ADJ
aiti-7988	104	34	end	end	NOUN
aiti-7988	104	35	of	of	ADP
aiti-7988	104	36	the	the	DET
aiti-7988	104	37	pipe	pipe	NOUN
aiti-7988	104	38	.	.	PUNCT
aiti-7988	105	1	the	the	DET
aiti-7988	105	2	properties	property	NOUN
aiti-7988	105	3	of	of	ADP
aiti-7988	105	4	pipe	pipe	NOUN
aiti-7988	105	5	and	and	CCONJ
aiti-7988	105	6	fluid	fluid	NOUN
aiti-7988	105	7	and	and	CCONJ
aiti-7988	105	8	the	the	DET
aiti-7988	105	9	numeric	numeric	ADJ
aiti-7988	105	10	parameters	parameter	NOUN
aiti-7988	105	11	considered	consider	VERB
aiti-7988	105	12	in	in	ADP
aiti-7988	105	13	this	this	DET
aiti-7988	105	14	study	study	NOUN
aiti-7988	105	15	are	be	AUX
aiti-7988	105	16	presented	present	VERB
aiti-7988	105	17	in	in	ADP
aiti-7988	105	18	table	table	NOUN
aiti-7988	105	19	1	1	NUM
aiti-7988	105	20	.	.	PUNCT
aiti-7988	106	1	the	the	DET
aiti-7988	106	2	current	current	ADJ
aiti-7988	106	3	study	study	NOUN
aiti-7988	106	4	focuses	focus	VERB
aiti-7988	106	5	on	on	ADP
aiti-7988	106	6	finding	find	VERB
aiti-7988	106	7	the	the	DET
aiti-7988	106	8	natural	natural	ADJ
aiti-7988	106	9	frequencies	frequency	NOUN
aiti-7988	106	10	and	and	CCONJ
aiti-7988	106	11	critical	critical	ADJ
aiti-7988	106	12	velocities	velocity	NOUN
aiti-7988	106	13	of	of	ADP
aiti-7988	106	14	axial	axial	ADJ
aiti-7988	106	15	flow	flow	NOUN
aiti-7988	106	16	fluid	fluid	NOUN
aiti-7988	106	17	-	-	PUNCT
aiti-7988	106	18	carrying	carry	VERB
aiti-7988	106	19	pipes	pipe	NOUN
aiti-7988	106	20	under	under	ADP
aiti-7988	106	21	different	different	ADJ
aiti-7988	106	22	conditions	condition	NOUN
aiti-7988	106	23	.	.	PUNCT
aiti-7988	107	1	since	since	SCONJ
aiti-7988	107	2	the	the	DET
aiti-7988	107	3	non	non	ADJ
aiti-7988	107	4	-	-	ADJ
aiti-7988	107	5	planar	planar	ADJ
aiti-7988	107	6	motion	motion	NOUN
aiti-7988	107	7	(	(	PUNCT
aiti-7988	107	8	three	three	NUM
aiti-7988	107	9	-	-	PUNCT
aiti-7988	107	10	dimensional	dimensional	ADJ
aiti-7988	107	11	motion	motion	NOUN
aiti-7988	107	12	)	)	PUNCT
aiti-7988	107	13	does	do	AUX
aiti-7988	107	14	not	not	PART
aiti-7988	107	15	affect	affect	VERB
aiti-7988	107	16	the	the	DET
aiti-7988	107	17	values	value	NOUN
aiti-7988	107	18	of	of	ADP
aiti-7988	107	19	the	the	DET
aiti-7988	107	20	natural	natural	ADJ
aiti-7988	107	21	frequencies	frequency	NOUN
aiti-7988	107	22	or	or	CCONJ
aiti-7988	107	23	critical	critical	ADJ
aiti-7988	107	24	velocities	velocity	NOUN
aiti-7988	107	25	,	,	PUNCT
aiti-7988	107	26	it	it	PRON
aiti-7988	107	27	is	be	AUX
aiti-7988	107	28	neglected	neglect	VERB
aiti-7988	107	29	and	and	CCONJ
aiti-7988	107	30	the	the	DET
aiti-7988	107	31	planar	planar	ADJ
aiti-7988	107	32	motion	motion	NOUN
aiti-7988	107	33	(	(	PUNCT
aiti-7988	107	34	two	two	NUM
aiti-7988	107	35	-	-	PUNCT
aiti-7988	107	36	dimensional	dimensional	ADJ
aiti-7988	107	37	motion	motion	NOUN
aiti-7988	107	38	)	)	PUNCT
aiti-7988	107	39	of	of	ADP
aiti-7988	107	40	the	the	DET
aiti-7988	107	41	pipes	pipe	NOUN
aiti-7988	107	42	is	be	AUX
aiti-7988	107	43	adopted	adopt	VERB
aiti-7988	107	44	.	.	PUNCT
aiti-7988	108	1	fig	fig	NOUN
aiti-7988	108	2	.	.	PUNCT
aiti-7988	109	1	3	3	NUM
aiti-7988	109	2	illustrates	illustrate	VERB
aiti-7988	109	3	the	the	DET
aiti-7988	109	4	fluid	fluid	ADJ
aiti-7988	109	5	and	and	CCONJ
aiti-7988	109	6	pipe	pipe	NOUN
aiti-7988	109	7	elements	element	NOUN
aiti-7988	109	8	,	,	PUNCT
aiti-7988	109	9	and	and	CCONJ
aiti-7988	109	10	shows	show	VERB
aiti-7988	109	11	all	all	DET
aiti-7988	109	12	the	the	DET
aiti-7988	109	13	forces	force	NOUN
aiti-7988	109	14	acting	act	VERB
aiti-7988	109	15	on	on	ADP
aiti-7988	109	16	the	the	DET
aiti-7988	109	17	system	system	NOUN
aiti-7988	109	18	.	.	PUNCT
aiti-7988	110	1	43	43	NUM
aiti-7988	110	2	advances	advance	NOUN
aiti-7988	110	3	in	in	ADP
aiti-7988	110	4	technology	technology	NOUN
aiti-7988	110	5	innovation	innovation	NOUN
aiti-7988	110	6	,	,	PUNCT
aiti-7988	110	7	vol	vol	NOUN
aiti-7988	110	8	.	.	PROPN
aiti-7988	110	9	7	7	NUM
aiti-7988	110	10	,	,	PUNCT
aiti-7988	110	11	no	no	INTJ
aiti-7988	110	12	.	.	NOUN
aiti-7988	110	13	1	1	NUM
aiti-7988	110	14	,	,	PUNCT
aiti-7988	110	15	2022	2022	NUM
aiti-7988	110	16	,	,	PUNCT
aiti-7988	110	17	pp	pp	ADJ
aiti-7988	110	18	.	.	PUNCT
aiti-7988	111	1	41	41	NUM
aiti-7988	111	2	-	-	SYM
aiti-7988	111	3	55	55	NUM
aiti-7988	111	4	table	table	NOUN
aiti-7988	111	5	1	1	NUM
aiti-7988	111	6	numeric	numeric	ADJ
aiti-7988	111	7	values	value	NOUN
aiti-7988	111	8	of	of	ADP
aiti-7988	111	9	used	use	VERB
aiti-7988	111	10	parameters	parameter	NOUN
aiti-7988	111	11	specification	specification	NOUN
aiti-7988	111	12	value	value	NOUN
aiti-7988	111	13	material	material	NOUN
aiti-7988	111	14	pp	pp	ADP
aiti-7988	111	15	-	-	PUNCT
aiti-7988	111	16	r	r	NOUN
aiti-7988	111	17	fluid	fluid	NOUN
aiti-7988	111	18	water	water	NOUN
aiti-7988	111	19	outer	outer	ADJ
aiti-7988	111	20	diameter	diameter	NOUN
aiti-7988	111	21	do	do	VERB
aiti-7988	111	22	(	(	PUNCT
aiti-7988	111	23	m	m	NOUN
aiti-7988	111	24	)	)	PUNCT
aiti-7988	111	25	0.025	0.025	NUM
aiti-7988	111	26	inner	inner	ADJ
aiti-7988	111	27	diameter	diameter	NOUN
aiti-7988	111	28	di	di	X
aiti-7988	111	29	(	(	PUNCT
aiti-7988	111	30	m	m	NOUN
aiti-7988	111	31	)	)	PUNCT
aiti-7988	111	32	0.018	0.018	NUM
aiti-7988	111	33	thickness	thickness	NOUN
aiti-7988	111	34	t	t	PROPN
aiti-7988	111	35	(	(	PUNCT
aiti-7988	111	36	m	m	NOUN
aiti-7988	111	37	)	)	PUNCT
aiti-7988	111	38	0.0035	0.0035	NUM
aiti-7988	111	39	length	length	NOUN
aiti-7988	111	40	l	l	PROPN
aiti-7988	111	41	(	(	PUNCT
aiti-7988	111	42	m	m	NOUN
aiti-7988	111	43	)	)	PUNCT
aiti-7988	111	44	0.5	0.5	NUM
aiti-7988	111	45	-	-	SYM
aiti-7988	111	46	1.25	1.25	NUM
aiti-7988	111	47	aspect	aspect	NOUN
aiti-7988	111	48	ratio	ratio	NOUN
aiti-7988	111	49	(	(	PUNCT
aiti-7988	111	50	length	length	NOUN
aiti-7988	111	51	to	to	ADP
aiti-7988	111	52	outer	outer	ADJ
aiti-7988	111	53	diameter	diameter	NOUN
aiti-7988	111	54	)	)	PUNCT
aiti-7988	112	1	l	l	NOUN
aiti-7988	112	2	/	/	SYM
aiti-7988	112	3	do	do	AUX
aiti-7988	112	4	(	(	PUNCT
aiti-7988	112	5	20	20	NUM
aiti-7988	112	6	-	-	SYM
aiti-7988	112	7	50	50	NUM
aiti-7988	112	8	)	)	PUNCT
aiti-7988	112	9	do	do	VERB
aiti-7988	112	10	modulus	modulus	NOUN
aiti-7988	112	11	of	of	ADP
aiti-7988	112	12	elasticity	elasticity	NOUN
aiti-7988	112	13	e	e	X
aiti-7988	112	14	(	(	PUNCT
aiti-7988	112	15	gpa	gpa	PROPN
aiti-7988	112	16	)	)	PUNCT
aiti-7988	112	17	0.8	0.8	NUM
aiti-7988	112	18	at	at	ADP
aiti-7988	112	19	25	25	NUM
aiti-7988	112	20	°	°	NOUN
aiti-7988	112	21	c	c	NOUN
aiti-7988	112	22	0.38	0.38	NUM
aiti-7988	112	23	at	at	ADP
aiti-7988	112	24	50	50	NUM
aiti-7988	112	25	°	°	NOUN
aiti-7988	112	26	c	c	NOUN
aiti-7988	112	27	0.23	0.23	NUM
aiti-7988	112	28	at	at	ADP
aiti-7988	112	29	70	70	NUM
aiti-7988	112	30	°	°	NOUN
aiti-7988	112	31	c	c	NOUN
aiti-7988	112	32	density	density	NOUN
aiti-7988	112	33	of	of	ADP
aiti-7988	112	34	pipe	pipe	NOUN
aiti-7988	112	35	ρp	ρp	NOUN
aiti-7988	112	36	(	(	PUNCT
aiti-7988	112	37	kg	kg	PROPN
aiti-7988	112	38	/	/	SYM
aiti-7988	112	39	m	m	VERB
aiti-7988	112	40	3	3	NUM
aiti-7988	112	41	)	)	PUNCT
aiti-7988	112	42	909	909	NUM
aiti-7988	112	43	density	density	NOUN
aiti-7988	112	44	of	of	ADP
aiti-7988	112	45	fluid	fluid	NOUN
aiti-7988	112	46	ρf	ρf	X
aiti-7988	112	47	(	(	PUNCT
aiti-7988	112	48	kg	kg	PROPN
aiti-7988	112	49	/	/	SYM
aiti-7988	112	50	m	m	PROPN
aiti-7988	112	51	3	3	NUM
aiti-7988	112	52	)	)	PUNCT
aiti-7988	112	53	1000	1000	NUM
aiti-7988	112	54	coefficient	coefficient	NOUN
aiti-7988	112	55	of	of	ADP
aiti-7988	112	56	expansion	expansion	NOUN
aiti-7988	112	57	α	α	NOUN
aiti-7988	112	58	(	(	PUNCT
aiti-7988	112	59	1	1	NUM
aiti-7988	112	60	/	/	SYM
aiti-7988	112	61	k	k	NOUN
aiti-7988	112	62	)	)	PUNCT
aiti-7988	112	63	0.3	0.3	NUM
aiti-7988	112	64	×	×	NOUN
aiti-7988	112	65	10	10	NUM
aiti-7988	112	66	-4	-4	NOUN
aiti-7988	112	67	fig	fig	NOUN
aiti-7988	112	68	.	.	PUNCT
aiti-7988	113	1	1	1	NUM
aiti-7988	113	2	three	three	NUM
aiti-7988	113	3	-	-	PUNCT
aiti-7988	113	4	dimension	dimension	NOUN
aiti-7988	113	5	geometry	geometry	NOUN
aiti-7988	113	6	of	of	ADP
aiti-7988	113	7	the	the	DET
aiti-7988	113	8	clamped	clamp	VERB
aiti-7988	113	9	-	-	PUNCT
aiti-7988	113	10	end	end	NOUN
aiti-7988	113	11	pipeline	pipeline	NOUN
aiti-7988	113	12	fig	fig	NOUN
aiti-7988	113	13	.	.	PUNCT
aiti-7988	114	1	2	2	NUM
aiti-7988	114	2	schematic	schematic	ADJ
aiti-7988	114	3	of	of	ADP
aiti-7988	114	4	the	the	DET
aiti-7988	114	5	clamped	clamp	VERB
aiti-7988	114	6	-	-	PUNCT
aiti-7988	114	7	end	end	NOUN
aiti-7988	114	8	inclined	inclined	ADJ
aiti-7988	114	9	pipe	pipe	NOUN
aiti-7988	114	10	(	(	PUNCT
aiti-7988	114	11	a	a	PRON
aiti-7988	114	12	)	)	PUNCT
aiti-7988	114	13	fluid	fluid	ADJ
aiti-7988	114	14	element	element	NOUN
aiti-7988	114	15	(	(	PUNCT
aiti-7988	114	16	b	b	NOUN
aiti-7988	114	17	)	)	PUNCT
aiti-7988	114	18	pipe	pipe	NOUN
aiti-7988	114	19	element	element	NOUN
aiti-7988	114	20	fig	fig	NOUN
aiti-7988	114	21	.	.	PUNCT
aiti-7988	115	1	3	3	NUM
aiti-7988	115	2	free	free	ADJ
aiti-7988	115	3	-	-	PUNCT
aiti-7988	115	4	body	body	NOUN
aiti-7988	115	5	diagram	diagram	NOUN
aiti-7988	115	6	of	of	ADP
aiti-7988	115	7	the	the	DET
aiti-7988	115	8	fluid	fluid	ADJ
aiti-7988	115	9	and	and	CCONJ
aiti-7988	115	10	pipe	pipe	NOUN
aiti-7988	115	11	element	element	NOUN
aiti-7988	115	12	to	to	PART
aiti-7988	115	13	simplify	simplify	VERB
aiti-7988	115	14	the	the	DET
aiti-7988	115	15	derivation	derivation	NOUN
aiti-7988	115	16	process	process	NOUN
aiti-7988	115	17	,	,	PUNCT
aiti-7988	115	18	some	some	DET
aiti-7988	115	19	assumptions	assumption	NOUN
aiti-7988	115	20	are	be	AUX
aiti-7988	115	21	adopted	adopt	VERB
aiti-7988	115	22	:	:	PUNCT
aiti-7988	115	23	considering	consider	VERB
aiti-7988	115	24	the	the	DET
aiti-7988	115	25	vertical	vertical	ADJ
aiti-7988	115	26	motion	motion	NOUN
aiti-7988	115	27	(	(	PUNCT
aiti-7988	115	28	y	y	NOUN
aiti-7988	115	29	-	-	PUNCT
aiti-7988	115	30	axis	axis	NOUN
aiti-7988	115	31	)	)	PUNCT
aiti-7988	115	32	of	of	ADP
aiti-7988	115	33	the	the	DET
aiti-7988	115	34	pipe	pipe	NOUN
aiti-7988	115	35	;	;	PUNCT
aiti-7988	115	36	ignoring	ignore	VERB
aiti-7988	115	37	internal	internal	ADJ
aiti-7988	115	38	damping	damp	VERB
aiti-7988	115	39	(	(	PUNCT
aiti-7988	115	40	viscoelastic	viscoelastic	ADJ
aiti-7988	115	41	effect	effect	NOUN
aiti-7988	115	42	)	)	PUNCT
aiti-7988	115	43	,	,	PUNCT
aiti-7988	115	44	dissipation	dissipation	NOUN
aiti-7988	115	45	,	,	PUNCT
aiti-7988	115	46	external	external	ADJ
aiti-7988	115	47	tension	tension	NOUN
aiti-7988	115	48	,	,	PUNCT
aiti-7988	115	49	and	and	CCONJ
aiti-7988	115	50	internal	internal	ADJ
aiti-7988	115	51	pressurization	pressurization	NOUN
aiti-7988	115	52	;	;	PUNCT
aiti-7988	115	53	assuming	assume	VERB
aiti-7988	115	54	a	a	DET
aiti-7988	115	55	small	small	ADJ
aiti-7988	115	56	deformation	deformation	NOUN
aiti-7988	115	57	;	;	PUNCT
aiti-7988	115	58	treating	treat	VERB
aiti-7988	115	59	the	the	DET
aiti-7988	115	60	pipe	pipe	NOUN
aiti-7988	115	61	as	as	ADP
aiti-7988	115	62	an	an	DET
aiti-7988	115	63	euler	euler	VERB
aiti-7988	115	64	-	-	PUNCT
aiti-7988	115	65	bernoulli	bernoulli	PROPN
aiti-7988	115	66	beam	beam	PROPN
aiti-7988	115	67	model	model	PROPN
aiti-7988	115	68	.	.	PUNCT
aiti-7988	116	1	then	then	ADV
aiti-7988	116	2	,	,	PUNCT
aiti-7988	116	3	using	use	VERB
aiti-7988	116	4	the	the	DET
aiti-7988	116	5	newtonian	newtonian	ADJ
aiti-7988	116	6	method	method	NOUN
aiti-7988	116	7	by	by	ADP
aiti-7988	116	8	balancing	balance	VERB
aiti-7988	116	9	forces	force	NOUN
aiti-7988	116	10	on	on	ADP
aiti-7988	116	11	44	44	NUM
aiti-7988	116	12	advances	advance	NOUN
aiti-7988	116	13	in	in	ADP
aiti-7988	116	14	technology	technology	NOUN
aiti-7988	116	15	innovation	innovation	NOUN
aiti-7988	116	16	,	,	PUNCT
aiti-7988	116	17	vol	vol	NOUN
aiti-7988	116	18	.	.	PROPN
aiti-7988	116	19	7	7	NUM
aiti-7988	116	20	,	,	PUNCT
aiti-7988	116	21	no	no	INTJ
aiti-7988	116	22	.	.	NOUN
aiti-7988	116	23	1	1	NUM
aiti-7988	116	24	,	,	PUNCT
aiti-7988	116	25	2022	2022	NUM
aiti-7988	116	26	,	,	PUNCT
aiti-7988	116	27	pp	pp	ADJ
aiti-7988	116	28	.	.	PUNCT
aiti-7988	117	1	41	41	NUM
aiti-7988	117	2	-	-	SYM
aiti-7988	117	3	55	55	NUM
aiti-7988	117	4	the	the	DET
aiti-7988	117	5	fluid	fluid	ADJ
aiti-7988	117	6	and	and	CCONJ
aiti-7988	117	7	pipe	pipe	NOUN
aiti-7988	117	8	elements	element	NOUN
aiti-7988	117	9	in	in	ADP
aiti-7988	117	10	the	the	DET
aiti-7988	117	11	transverse	transverse	NOUN
aiti-7988	117	12	and	and	CCONJ
aiti-7988	117	13	longitudinal	longitudinal	ADJ
aiti-7988	117	14	directions	direction	NOUN
aiti-7988	117	15	,	,	PUNCT
aiti-7988	117	16	and	and	CCONJ
aiti-7988	117	17	after	after	ADP
aiti-7988	117	18	some	some	DET
aiti-7988	117	19	substitutions	substitution	NOUN
aiti-7988	117	20	processes	process	NOUN
aiti-7988	117	21	and	and	CCONJ
aiti-7988	117	22	mathematical	mathematical	ADJ
aiti-7988	117	23	calculations	calculation	NOUN
aiti-7988	117	24	,	,	PUNCT
aiti-7988	117	25	the	the	DET
aiti-7988	117	26	following	follow	VERB
aiti-7988	117	27	motion	motion	NOUN
aiti-7988	117	28	equation	equation	NOUN
aiti-7988	117	29	of	of	ADP
aiti-7988	117	30	the	the	DET
aiti-7988	117	31	heated	heated	ADJ
aiti-7988	117	32	and	and	CCONJ
aiti-7988	117	33	inclined	inclined	ADJ
aiti-7988	117	34	pipe	pipe	NOUN
aiti-7988	117	35	can	can	AUX
aiti-7988	117	36	be	be	AUX
aiti-7988	117	37	derived	derive	VERB
aiti-7988	117	38	(	(	PUNCT
aiti-7988	117	39	more	more	ADJ
aiti-7988	117	40	details	detail	NOUN
aiti-7988	117	41	about	about	ADP
aiti-7988	117	42	the	the	DET
aiti-7988	117	43	assumptions	assumption	NOUN
aiti-7988	117	44	and	and	CCONJ
aiti-7988	117	45	derivation	derivation	NOUN
aiti-7988	117	46	process	process	NOUN
aiti-7988	117	47	can	can	AUX
aiti-7988	117	48	be	be	AUX
aiti-7988	117	49	found	find	VERB
aiti-7988	117	50	in	in	ADP
aiti-7988	117	51	the	the	DET
aiti-7988	117	52	work	work	NOUN
aiti-7988	117	53	of	of	ADP
aiti-7988	117	54	mohmmed	mohmme	VERB
aiti-7988	117	55	et	et	PROPN
aiti-7988	117	56	al	al	PROPN
aiti-7988	117	57	.	.	PUNCT
aiti-7988	118	1	[	[	X
aiti-7988	118	2	25	25	NUM
aiti-7988	118	3	]	]	PUNCT
aiti-7988	118	4	)	)	PUNCT
aiti-7988	118	5	:	:	PUNCT
aiti-7988	118	6	(	(	PUNCT
aiti-7988	118	7	)	)	PUNCT
aiti-7988	118	8	(	(	PUNCT
aiti-7988	118	9	)	)	PUNCT
aiti-7988	118	10	(	(	PUNCT
aiti-7988	118	11	)	)	PUNCT
aiti-7988	118	12	(	(	PUNCT
aiti-7988	118	13	)	)	PUNCT
aiti-7988	118	14	(	(	PUNCT
aiti-7988	118	15	)	)	PUNCT
aiti-7988	118	16	4	4	NUM
aiti-7988	118	17	2	2	NUM
aiti-7988	118	18	2	2	NUM
aiti-7988	118	19	2	2	NUM
aiti-7988	118	20	2	2	NUM
aiti-7988	118	21	4	4	NUM
aiti-7988	118	22	2	2	NUM
aiti-7988	118	23	2	2	NUM
aiti-7988	118	24	2	2	NUM
aiti-7988	118	25	2	2	NUM
aiti-7988	118	26	2	2	NUM
aiti-7988	118	27	2	2	NUM
aiti-7988	118	28	sin	sin	NOUN
aiti-7988	118	29	sin	sin	NOUN
aiti-7988	118	30	cos	cos	ADP
aiti-7988	118	31	2	2	NUM
aiti-7988	118	32	0	0	NUM
aiti-7988	118	33	f	f	PROPN
aiti-7988	119	1	p	p	X
aiti-7988	119	2	f	f	PROPN
aiti-7988	120	1	f	f	PROPN
aiti-7988	121	1	p	p	X
aiti-7988	121	2	f	f	X
aiti-7988	122	1	p	p	X
aiti-7988	122	2	f	f	PROPN
aiti-7988	123	1	f	f	PROPN
aiti-7988	124	1	p	p	X
aiti-7988	124	2	y	y	PROPN
aiti-7988	124	3	y	y	PROPN
aiti-7988	124	4	y	y	PROPN
aiti-7988	124	5	y	y	PROPN
aiti-7988	124	6	y	y	PROPN
aiti-7988	124	7	ei	ei	INTJ
aiti-7988	124	8	m	m	VERB
aiti-7988	124	9	m	m	VERB
aiti-7988	124	10	l	l	NOUN
aiti-7988	124	11	x	x	X
aiti-7988	125	1	g	g	PROPN
aiti-7988	125	2	m	m	PROPN
aiti-7988	125	3	v	v	NOUN
aiti-7988	125	4	n	n	ADV
aiti-7988	125	5	m	m	NOUN
aiti-7988	125	6	m	m	VERB
aiti-7988	125	7	g	g	NOUN
aiti-7988	125	8	m	m	NOUN
aiti-7988	125	9	m	m	VERB
aiti-7988	125	10	g	g	NOUN
aiti-7988	125	11	x	x	X
aiti-7988	125	12	x	x	PUNCT
aiti-7988	125	13	x	x	PUNCT
aiti-7988	125	14	x	x	PUNCT
aiti-7988	125	15	x	x	SYM
aiti-7988	125	16	y	y	VERB
aiti-7988	125	17	y	y	PROPN
aiti-7988	125	18	m	m	VERB
aiti-7988	125	19	v	v	NOUN
aiti-7988	125	20	m	m	NOUN
aiti-7988	125	21	m	m	VERB
aiti-7988	125	22	x	x	X
aiti-7988	125	23	t	t	NOUN
aiti-7988	125	24	t	t	NOUN
aiti-7988	125	25	θ	θ	PROPN
aiti-7988	125	26	θ	θ	PROPN
aiti-7988	125	27	θ∂	θ∂	PROPN
aiti-7988	125	28	∂	∂	NOUN
aiti-7988	125	29	∂	∂	NUM
aiti-7988	125	30	∂	∂	NUM
aiti-7988	126	1	∂−	∂−	PROPN
aiti-7988	126	2	+	+	CCONJ
aiti-7988	126	3	−	−	PROPN
aiti-7988	127	1	+	+	CCONJ
aiti-7988	128	1	+	+	PUNCT
aiti-7988	129	1	+	+	PUNCT
aiti-7988	129	2	+	+	PUNCT
aiti-7988	129	3	+	+	NUM
aiti-7988	129	4	+	+	NUM
aiti-7988	129	5	∂	∂	NUM
aiti-7988	129	6	∂	∂	NUM
aiti-7988	129	7	∂	∂	NUM
aiti-7988	129	8	∂	∂	NUM
aiti-7988	129	9	∂	∂	NUM
aiti-7988	129	10	∂	∂	NOUN
aiti-7988	129	11	∂+	∂+	PROPN
aiti-7988	129	12	+	+	CCONJ
aiti-7988	129	13	+	+	CCONJ
aiti-7988	129	14	=	=	SYM
aiti-7988	129	15	∂	∂	NUM
aiti-7988	129	16	∂	∂	NUM
aiti-7988	129	17	∂	∂	NUM
aiti-7988	129	18	(	(	PUNCT
aiti-7988	129	19	5	5	NUM
aiti-7988	129	20	)	)	PUNCT
aiti-7988	129	21	where	where	SCONJ
aiti-7988	129	22	ei	ei	NOUN
aiti-7988	129	23	is	be	AUX
aiti-7988	129	24	the	the	DET
aiti-7988	129	25	flexural	flexural	ADJ
aiti-7988	129	26	rigidity	rigidity	NOUN
aiti-7988	129	27	of	of	ADP
aiti-7988	129	28	the	the	DET
aiti-7988	129	29	pipe	pipe	NOUN
aiti-7988	129	30	;	;	PUNCT
aiti-7988	129	31	g	g	PROPN
aiti-7988	129	32	is	be	AUX
aiti-7988	129	33	gravitational	gravitational	ADJ
aiti-7988	129	34	constant	constant	ADJ
aiti-7988	129	35	;	;	PUNCT
aiti-7988	129	36	θ	θ	PROPN
aiti-7988	129	37	is	be	AUX
aiti-7988	129	38	the	the	DET
aiti-7988	129	39	inclination	inclination	NOUN
aiti-7988	129	40	angle	angle	NOUN
aiti-7988	129	41	of	of	ADP
aiti-7988	129	42	the	the	DET
aiti-7988	129	43	pipe	pipe	NOUN
aiti-7988	129	44	with	with	ADP
aiti-7988	129	45	horizontal	horizontal	ADJ
aiti-7988	129	46	axis	axis	NOUN
aiti-7988	129	47	;	;	PUNCT
aiti-7988	129	48	qs	qs	PART
aiti-7988	129	49	represents	represent	VERB
aiti-7988	129	50	internal	internal	ADJ
aiti-7988	129	51	shear	shear	NOUN
aiti-7988	129	52	stress	stress	NOUN
aiti-7988	129	53	;	;	PUNCT
aiti-7988	129	54	p	p	PRON
aiti-7988	129	55	is	be	AUX
aiti-7988	129	56	internal	internal	ADJ
aiti-7988	129	57	fluid	fluid	ADJ
aiti-7988	129	58	pressure	pressure	NOUN
aiti-7988	129	59	;	;	PUNCT
aiti-7988	129	60	s	s	VERB
aiti-7988	129	61	is	be	AUX
aiti-7988	129	62	the	the	DET
aiti-7988	129	63	internal	internal	ADJ
aiti-7988	129	64	perimeter	perimeter	NOUN
aiti-7988	129	65	(	(	PUNCT
aiti-7988	129	66	internal	internal	ADJ
aiti-7988	129	67	section	section	NOUN
aiti-7988	129	68	circumference	circumference	NOUN
aiti-7988	129	69	)	)	PUNCT
aiti-7988	129	70	of	of	ADP
aiti-7988	129	71	the	the	DET
aiti-7988	129	72	pipe	pipe	NOUN
aiti-7988	129	73	;	;	PUNCT
aiti-7988	129	74	f	f	PROPN
aiti-7988	129	75	is	be	AUX
aiti-7988	129	76	the	the	DET
aiti-7988	129	77	transverse	transverse	NOUN
aiti-7988	129	78	force	force	NOUN
aiti-7988	129	79	between	between	ADP
aiti-7988	129	80	pipe	pipe	NOUN
aiti-7988	129	81	wall	wall	NOUN
aiti-7988	129	82	and	and	CCONJ
aiti-7988	129	83	fluid	fluid	NOUN
aiti-7988	129	84	(	(	PUNCT
aiti-7988	129	85	per	per	ADP
aiti-7988	129	86	unit	unit	NOUN
aiti-7988	129	87	length	length	NOUN
aiti-7988	129	88	)	)	PUNCT
aiti-7988	129	89	;	;	PUNCT
aiti-7988	129	90	t	t	PROPN
aiti-7988	129	91	represents	represent	VERB
aiti-7988	129	92	longitudinal	longitudinal	ADJ
aiti-7988	129	93	tension	tension	NOUN
aiti-7988	129	94	.	.	PUNCT
aiti-7988	130	1	m	m	PROPN
aiti-7988	130	2	is	be	AUX
aiti-7988	130	3	bending	bend	VERB
aiti-7988	130	4	moment	moment	NOUN
aiti-7988	130	5	;	;	PUNCT
aiti-7988	130	6	q	q	PUNCT
aiti-7988	130	7	represents	represent	VERB
aiti-7988	130	8	the	the	DET
aiti-7988	130	9	transverse	transverse	ADJ
aiti-7988	130	10	shear	shear	NOUN
aiti-7988	130	11	force	force	NOUN
aiti-7988	130	12	in	in	ADP
aiti-7988	130	13	the	the	DET
aiti-7988	130	14	pipe	pipe	NOUN
aiti-7988	130	15	;	;	PUNCT
aiti-7988	130	16	y(x	y(x	PROPN
aiti-7988	130	17	,	,	PUNCT
aiti-7988	130	18	t	t	PROPN
aiti-7988	130	19	)	)	PUNCT
aiti-7988	130	20	is	be	AUX
aiti-7988	130	21	the	the	DET
aiti-7988	130	22	lateral	lateral	ADJ
aiti-7988	130	23	displacement	displacement	NOUN
aiti-7988	130	24	of	of	ADP
aiti-7988	130	25	the	the	DET
aiti-7988	130	26	pipe	pipe	NOUN
aiti-7988	130	27	;	;	PUNCT
aiti-7988	130	28	x	x	SYM
aiti-7988	130	29	and	and	CCONJ
aiti-7988	130	30	t	t	PROPN
aiti-7988	130	31	are	be	AUX
aiti-7988	130	32	the	the	DET
aiti-7988	130	33	axial	axial	ADJ
aiti-7988	130	34	coordinate	coordinate	NOUN
aiti-7988	130	35	and	and	CCONJ
aiti-7988	130	36	time	time	NOUN
aiti-7988	130	37	,	,	PUNCT
aiti-7988	130	38	respectively	respectively	ADV
aiti-7988	130	39	.	.	PUNCT
aiti-7988	131	1	n	n	PUNCT
aiti-7988	131	2	represents	represent	VERB
aiti-7988	131	3	the	the	DET
aiti-7988	131	4	thermal	thermal	ADJ
aiti-7988	131	5	load	load	NOUN
aiti-7988	131	6	in	in	ADP
aiti-7988	131	7	the	the	DET
aiti-7988	131	8	pipe	pipe	NOUN
aiti-7988	131	9	due	due	ADP
aiti-7988	131	10	to	to	ADP
aiti-7988	131	11	temperature	temperature	NOUN
aiti-7988	131	12	variation	variation	NOUN
aiti-7988	131	13	and	and	CCONJ
aiti-7988	131	14	can	can	AUX
aiti-7988	131	15	be	be	AUX
aiti-7988	131	16	calculated	calculate	VERB
aiti-7988	131	17	as	as	ADP
aiti-7988	131	18	:	:	PUNCT
aiti-7988	131	19	n	n	NOUN
aiti-7988	131	20	=	=	SYM
aiti-7988	131	21	αeap∆t	αeap∆t	NOUN
aiti-7988	131	22	,	,	PUNCT
aiti-7988	131	23	where	where	SCONJ
aiti-7988	131	24	α	α	PROPN
aiti-7988	131	25	is	be	AUX
aiti-7988	131	26	thermal	thermal	ADJ
aiti-7988	131	27	expansion	expansion	NOUN
aiti-7988	131	28	coefficient	coefficient	NOUN
aiti-7988	131	29	(	(	PUNCT
aiti-7988	131	30	1/	1/	NUM
aiti-7988	131	31	°	°	NOUN
aiti-7988	131	32	c	c	NOUN
aiti-7988	131	33	)	)	PUNCT
aiti-7988	131	34	and	and	CCONJ
aiti-7988	131	35	l	l	NOUN
aiti-7988	131	36	is	be	AUX
aiti-7988	131	37	pipe	pipe	NOUN
aiti-7988	131	38	length	length	NOUN
aiti-7988	131	39	(	(	PUNCT
aiti-7988	131	40	m	m	NOUN
aiti-7988	131	41	)	)	PUNCT
aiti-7988	131	42	.	.	PUNCT
aiti-7988	132	1	∆t	∆t	PROPN
aiti-7988	132	2	=	=	SYM
aiti-7988	132	3	(	(	PUNCT
aiti-7988	132	4	tpt)x	tpt)x	NOUN
aiti-7988	132	5	−	−	NOUN
aiti-7988	132	6	ti	ti	NOUN
aiti-7988	132	7	is	be	AUX
aiti-7988	132	8	the	the	DET
aiti-7988	132	9	temperature	temperature	NOUN
aiti-7988	132	10	change	change	NOUN
aiti-7988	132	11	(	(	PUNCT
aiti-7988	132	12	°	°	ADP
aiti-7988	132	13	c	c	NOUN
aiti-7988	132	14	)	)	PUNCT
aiti-7988	132	15	.	.	PUNCT
aiti-7988	133	1	ti	ti	PROPN
aiti-7988	133	2	is	be	AUX
aiti-7988	133	3	the	the	DET
aiti-7988	133	4	initial	initial	ADJ
aiti-7988	133	5	temperature	temperature	NOUN
aiti-7988	133	6	of	of	ADP
aiti-7988	133	7	the	the	DET
aiti-7988	133	8	pipe	pipe	NOUN
aiti-7988	133	9	(	(	PUNCT
aiti-7988	133	10	°	°	ADP
aiti-7988	133	11	c	c	NOUN
aiti-7988	133	12	)	)	PUNCT
aiti-7988	133	13	.	.	PUNCT
aiti-7988	134	1	(	(	PUNCT
aiti-7988	134	2	tpt)x	tpt)x	PROPN
aiti-7988	134	3	is	be	AUX
aiti-7988	134	4	the	the	DET
aiti-7988	134	5	instantaneous	instantaneous	ADJ
aiti-7988	134	6	temperature	temperature	NOUN
aiti-7988	134	7	of	of	ADP
aiti-7988	134	8	the	the	DET
aiti-7988	134	9	pipe	pipe	NOUN
aiti-7988	134	10	after	after	ADP
aiti-7988	134	11	the	the	DET
aiti-7988	134	12	time	time	NOUN
aiti-7988	134	13	(	(	PUNCT
aiti-7988	134	14	°	°	ADP
aiti-7988	134	15	c	c	NOUN
aiti-7988	134	16	)	)	PUNCT
aiti-7988	134	17	.	.	PUNCT
aiti-7988	135	1	the	the	DET
aiti-7988	135	2	terms	term	NOUN
aiti-7988	135	3	of	of	ADP
aiti-7988	135	4	eq	eq	PROPN
aiti-7988	135	5	.	.	PUNCT
aiti-7988	136	1	(	(	PUNCT
aiti-7988	136	2	5	5	X
aiti-7988	136	3	)	)	PUNCT
aiti-7988	136	4	can	can	AUX
aiti-7988	136	5	be	be	AUX
aiti-7988	136	6	described	describe	VERB
aiti-7988	136	7	as	as	SCONJ
aiti-7988	136	8	follows	follow	VERB
aiti-7988	136	9	:	:	PUNCT
aiti-7988	136	10	the	the	DET
aiti-7988	136	11	first	first	ADJ
aiti-7988	136	12	component	component	NOUN
aiti-7988	136	13	represents	represent	VERB
aiti-7988	136	14	the	the	DET
aiti-7988	136	15	acceleration	acceleration	NOUN
aiti-7988	136	16	resulting	result	VERB
aiti-7988	136	17	from	from	ADP
aiti-7988	136	18	the	the	DET
aiti-7988	136	19	restoring	restore	VERB
aiti-7988	136	20	force	force	NOUN
aiti-7988	136	21	,	,	PUNCT
aiti-7988	136	22	and	and	CCONJ
aiti-7988	136	23	the	the	DET
aiti-7988	136	24	second	second	ADJ
aiti-7988	136	25	and	and	CCONJ
aiti-7988	136	26	third	third	ADJ
aiti-7988	136	27	components	component	NOUN
aiti-7988	136	28	represent	represent	VERB
aiti-7988	136	29	the	the	DET
aiti-7988	136	30	accelerations	acceleration	NOUN
aiti-7988	136	31	due	due	ADP
aiti-7988	136	32	to	to	ADP
aiti-7988	136	33	the	the	DET
aiti-7988	136	34	gravity	gravity	NOUN
aiti-7988	136	35	force	force	NOUN
aiti-7988	136	36	and	and	CCONJ
aiti-7988	136	37	the	the	DET
aiti-7988	136	38	centrifugal	centrifugal	ADJ
aiti-7988	136	39	force	force	NOUN
aiti-7988	136	40	respectively	respectively	ADV
aiti-7988	136	41	.	.	PUNCT
aiti-7988	137	1	after	after	ADP
aiti-7988	137	2	that	that	PRON
aiti-7988	137	3	,	,	PUNCT
aiti-7988	137	4	the	the	DET
aiti-7988	137	5	forth	forth	ADJ
aiti-7988	137	6	component	component	NOUN
aiti-7988	137	7	associates	associate	NOUN
aiti-7988	137	8	with	with	ADP
aiti-7988	137	9	the	the	DET
aiti-7988	137	10	acceleration	acceleration	NOUN
aiti-7988	137	11	due	due	ADP
aiti-7988	137	12	to	to	ADP
aiti-7988	137	13	the	the	DET
aiti-7988	137	14	thermal	thermal	ADJ
aiti-7988	137	15	force	force	NOUN
aiti-7988	137	16	caused	cause	VERB
aiti-7988	137	17	by	by	ADP
aiti-7988	137	18	the	the	DET
aiti-7988	137	19	temperatures	temperature	NOUN
aiti-7988	137	20	variation	variation	NOUN
aiti-7988	137	21	,	,	PUNCT
aiti-7988	137	22	then	then	ADV
aiti-7988	137	23	the	the	DET
aiti-7988	137	24	fifth	fifth	ADJ
aiti-7988	137	25	and	and	CCONJ
aiti-7988	137	26	sixth	sixth	ADJ
aiti-7988	137	27	components	component	NOUN
aiti-7988	137	28	illustrate	illustrate	VERB
aiti-7988	137	29	the	the	DET
aiti-7988	137	30	static	static	ADJ
aiti-7988	137	31	force	force	NOUN
aiti-7988	137	32	because	because	SCONJ
aiti-7988	137	33	of	of	ADP
aiti-7988	137	34	the	the	DET
aiti-7988	137	35	gravity	gravity	NOUN
aiti-7988	137	36	effect	effect	NOUN
aiti-7988	137	37	.	.	PUNCT
aiti-7988	138	1	the	the	DET
aiti-7988	138	2	seventh	seventh	ADJ
aiti-7988	138	3	component	component	NOUN
aiti-7988	138	4	stands	stand	VERB
aiti-7988	138	5	for	for	ADP
aiti-7988	138	6	the	the	DET
aiti-7988	138	7	acceleration	acceleration	NOUN
aiti-7988	138	8	due	due	ADP
aiti-7988	138	9	to	to	ADP
aiti-7988	138	10	the	the	DET
aiti-7988	138	11	coriolis	coriolis	PROPN
aiti-7988	138	12	forces	force	NOUN
aiti-7988	138	13	,	,	PUNCT
aiti-7988	138	14	following	follow	VERB
aiti-7988	138	15	the	the	DET
aiti-7988	138	16	acceleration	acceleration	NOUN
aiti-7988	138	17	because	because	SCONJ
aiti-7988	138	18	of	of	ADP
aiti-7988	138	19	the	the	DET
aiti-7988	138	20	system	system	NOUN
aiti-7988	138	21	’s	’s	PART
aiti-7988	138	22	inertia	inertia	NOUN
aiti-7988	138	23	force	force	NOUN
aiti-7988	138	24	.	.	PUNCT
aiti-7988	139	1	rearranging	rearrange	VERB
aiti-7988	139	2	eq	eq	ADP
aiti-7988	139	3	.	.	PUNCT
aiti-7988	140	1	(	(	PUNCT
aiti-7988	140	2	5	5	X
aiti-7988	140	3	)	)	PUNCT
aiti-7988	140	4	gives	give	VERB
aiti-7988	140	5	:	:	PUNCT
aiti-7988	140	6	(	(	PUNCT
aiti-7988	140	7	)	)	PUNCT
aiti-7988	140	8	(	(	PUNCT
aiti-7988	140	9	)	)	PUNCT
aiti-7988	140	10	(	(	PUNCT
aiti-7988	140	11	)	)	PUNCT
aiti-7988	140	12	(	(	PUNCT
aiti-7988	140	13	)	)	PUNCT
aiti-7988	140	14	(	(	PUNCT
aiti-7988	140	15	)	)	PUNCT
aiti-7988	140	16	4	4	NUM
aiti-7988	140	17	2	2	NUM
aiti-7988	140	18	2	2	NUM
aiti-7988	140	19	2	2	NUM
aiti-7988	140	20	4	4	NUM
aiti-7988	140	21	2	2	NUM
aiti-7988	140	22	2	2	NUM
aiti-7988	140	23	2	2	NUM
aiti-7988	140	24	sin	sin	NOUN
aiti-7988	140	25	sin	sin	NOUN
aiti-7988	140	26	cos	cos	ADP
aiti-7988	140	27	2	2	NUM
aiti-7988	140	28	0	0	NUM
aiti-7988	140	29	p	p	NOUN
aiti-7988	140	30	p	p	PROPN
aiti-7988	140	31	pf	pf	PROPN
aiti-7988	141	1	f	f	PROPN
aiti-7988	141	2	f	f	PROPN
aiti-7988	142	1	f	f	PROPN
aiti-7988	142	2	f	f	PROPN
aiti-7988	142	3	pf	pf	PROPN
aiti-7988	142	4	y	y	PROPN
aiti-7988	142	5	y	y	PROPN
aiti-7988	142	6	y	y	PROPN
aiti-7988	142	7	y	y	PROPN
aiti-7988	143	1	ei	ei	INTJ
aiti-7988	143	2	m	m	VERB
aiti-7988	143	3	m	m	VERB
aiti-7988	143	4	l	l	NOUN
aiti-7988	143	5	x	x	PUNCT
aiti-7988	143	6	g	g	PROPN
aiti-7988	143	7	n	n	INTJ
aiti-7988	143	8	m	m	NOUN
aiti-7988	143	9	v	v	NOUN
aiti-7988	143	10	m	m	NOUN
aiti-7988	143	11	m	m	NOUN
aiti-7988	143	12	g	g	NOUN
aiti-7988	143	13	m	m	NOUN
aiti-7988	143	14	m	m	VERB
aiti-7988	143	15	g	g	NOUN
aiti-7988	143	16	m	m	NOUN
aiti-7988	143	17	v	v	NOUN
aiti-7988	143	18	x	x	X
aiti-7988	143	19	x	x	X
aiti-7988	143	20	tx	tx	INTJ
aiti-7988	143	21	x	x	PUNCT
aiti-7988	143	22	y	y	VERB
aiti-7988	143	23	m	m	VERB
aiti-7988	143	24	m	m	VERB
aiti-7988	143	25	t	t	NOUN
aiti-7988	143	26	θ	θ	X
aiti-7988	143	27	θ	θ	NOUN
aiti-7988	143	28	θ	θ	AUX
aiti-7988	143	29			PROPN
aiti-7988	143	30			NUM
aiti-7988	143	31			NOUN
aiti-7988	143	32	∂	∂	NUM
aiti-7988	143	33	∂	∂	NUM
aiti-7988	143	34	∂	∂	NUM
aiti-7988	144	1	∂−	∂−	PROPN
aiti-7988	144	2	+	+	CCONJ
aiti-7988	144	3	−	−	PROPN
aiti-7988	144	4	−	−	NOUN
aiti-7988	144	5	−	−	PROPN
aiti-7988	145	1	+	+	CCONJ
aiti-7988	145	2	+	+	PUNCT
aiti-7988	146	1	+	+	PUNCT
aiti-7988	146	2	+	+	NUM
aiti-7988	146	3	+	+	NUM
aiti-7988	146	4	∂	∂	NUM
aiti-7988	146	5	∂	∂	NUM
aiti-7988	146	6	∂∂	∂∂	NOUN
aiti-7988	146	7	∂	∂	NUM
aiti-7988	146	8	∂+	∂+	PROPN
aiti-7988	146	9	+	+	CCONJ
aiti-7988	146	10	=	=	SYM
aiti-7988	146	11	∂	∂	NUM
aiti-7988	146	12	(	(	PUNCT
aiti-7988	146	13	6	6	NUM
aiti-7988	146	14	)	)	PUNCT
aiti-7988	146	15	eq	eq	NOUN
aiti-7988	146	16	.	.	PUNCT
aiti-7988	147	1	(	(	PUNCT
aiti-7988	147	2	6	6	NUM
aiti-7988	147	3	)	)	PUNCT
aiti-7988	147	4	can	can	AUX
aiti-7988	147	5	be	be	AUX
aiti-7988	147	6	rewritten	rewrite	VERB
aiti-7988	147	7	in	in	ADP
aiti-7988	147	8	non	non	ADJ
aiti-7988	147	9	-	-	ADJ
aiti-7988	147	10	dimensional	dimensional	ADJ
aiti-7988	147	11	form	form	NOUN
aiti-7988	147	12	as	as	SCONJ
aiti-7988	147	13	follows	follow	VERB
aiti-7988	147	14	:	:	PUNCT
aiti-7988	147	15	(	(	PUNCT
aiti-7988	147	16	)	)	PUNCT
aiti-7988	147	17	4	4	NUM
aiti-7988	147	18	2	2	NUM
aiti-7988	147	19	2	2	NUM
aiti-7988	147	20	2	2	NUM
aiti-7988	147	21	2	2	NUM
aiti-7988	147	22	1	1	NUM
aiti-7988	147	23	2	2	NUM
aiti-7988	147	24	4	4	NUM
aiti-7988	147	25	2	2	NUM
aiti-7988	147	26	2	2	NUM
aiti-7988	147	27	1	1	NUM
aiti-7988	147	28	sin	sin	NOUN
aiti-7988	147	29	sin	sin	NOUN
aiti-7988	147	30	cos	cos	ADP
aiti-7988	147	31	2	2	NUM
aiti-7988	147	32	0	0	NUM
aiti-7988	147	33	g	g	NOUN
aiti-7988	147	34	n	n	NUM
aiti-7988	147	35	u	u	NOUN
aiti-7988	147	36	g	g	NOUN
aiti-7988	147	37	g	g	PROPN
aiti-7988	147	38	u	u	PROPN
aiti-7988	147	39	t	t	PROPN
aiti-7988	147	40	t	t	PROPN
aiti-7988	147	41	φ	φ	PROPN
aiti-7988	147	42	φ	φ	PROPN
aiti-7988	147	43	φ	φ	PROPN
aiti-7988	147	44	φ	φ	PROPN
aiti-7988	147	45	φ	φ	PROPN
aiti-7988	147	46	ζ	ζ	PROPN
aiti-7988	147	47	θ	θ	NOUN
aiti-7988	147	48	θ	θ	PUNCT
aiti-7988	147	49	θ	θ	PUNCT
aiti-7988	147	50	β	β	X
aiti-7988	147	51	ζ	ζ	VERB
aiti-7988	147	52	ζ	ζ	NOUN
aiti-7988	147	53	ζ	ζ	NOUN
aiti-7988	147	54	ζ	ζ	NOUN
aiti-7988	147	55	∂	∂	NUM
aiti-7988	147	56	∂	∂	NUM
aiti-7988	147	57	∂	∂	NUM
aiti-7988	147	58	∂	∂	NUM
aiti-7988	147	59	∂	∂	NUM
aiti-7988	148	1	−	−	NOUN
aiti-7988	148	2	−	−	PROPN
aiti-7988	149	1	−	−	PROPN
aiti-7988	149	2	−	−	PROPN
aiti-7988	150	1	+	+	CCONJ
aiti-7988	150	2	+	+	PUNCT
aiti-7988	150	3	+	+	CCONJ
aiti-7988	150	4	+	+	CCONJ
aiti-7988	150	5	=	=	SYM
aiti-7988	150	6	∂	∂	NUM
aiti-7988	150	7	∂	∂	NUM
aiti-7988	150	8	∂	∂	NUM
aiti-7988	150	9	∂	∂	NUM
aiti-7988	150	10	∂	∂	NUM
aiti-7988	150	11	∂	∂	NOUN
aiti-7988	150	12			NOUN
aiti-7988	150	13			NOUN
aiti-7988	150	14			PROPN
aiti-7988	150	15	(	(	PUNCT
aiti-7988	150	16	7	7	NUM
aiti-7988	150	17	)	)	PUNCT
aiti-7988	150	18	where	where	SCONJ
aiti-7988	150	19	y	y	PROPN
aiti-7988	150	20	l	l	PROPN
aiti-7988	150	21	φ	φ	PROPN
aiti-7988	150	22	=	=	SYM
aiti-7988	150	23	(	(	PUNCT
aiti-7988	150	24	8)	8)	NUM
aiti-7988	150	25	x	x	SYM
aiti-7988	150	26	l	l	NOUN
aiti-7988	150	27	ζ	ζ	NOUN
aiti-7988	150	28	=	=	SYM
aiti-7988	150	29	(	(	PUNCT
aiti-7988	150	30	9	9	NUM
aiti-7988	150	31	)	)	PUNCT
aiti-7988	150	32	f	f	NOUN
aiti-7988	151	1	f	f	X
aiti-7988	151	2	p	p	X
aiti-7988	151	3	m	m	VERB
aiti-7988	151	4	m	m	VERB
aiti-7988	151	5	m	m	VERB
aiti-7988	151	6	β	β	X
aiti-7988	151	7	=	=	SYM
aiti-7988	152	1	+	+	CCONJ
aiti-7988	152	2	(	(	PUNCT
aiti-7988	152	3	10	10	NUM
aiti-7988	152	4	)	)	PUNCT
aiti-7988	152	5	(	(	PUNCT
aiti-7988	152	6	)	)	PUNCT
aiti-7988	152	7	3	3	NUM
aiti-7988	152	8	m	m	NOUN
aiti-7988	152	9	m	m	VERB
aiti-7988	152	10	gl	gl	NOUN
aiti-7988	152	11	g	g	NOUN
aiti-7988	152	12	ei	ei	X
aiti-7988	153	1	+	+	CCONJ
aiti-7988	153	2	=	=	SYM
aiti-7988	153	3	(	(	PUNCT
aiti-7988	153	4	11	11	NUM
aiti-7988	153	5	)	)	SYM
aiti-7988	153	6	1	1	NUM
aiti-7988	153	7	2	2	NUM
aiti-7988	153	8	f	f	NOUN
aiti-7988	153	9	m	m	VERB
aiti-7988	153	10	u	u	NOUN
aiti-7988	153	11	vl	vl	INTJ
aiti-7988	153	12	ei	ei	X
aiti-7988	153	13	=	=	SYM
aiti-7988	153	14			PROPN
aiti-7988	153	15			PROPN
aiti-7988	153	16			NOUN
aiti-7988	153	17			VERB
aiti-7988	153	18			PRON
aiti-7988	153	19			PUNCT
aiti-7988	154	1	(	(	PUNCT
aiti-7988	154	2	12	12	NUM
aiti-7988	154	3	)	)	PUNCT
aiti-7988	154	4	45	45	NUM
aiti-7988	154	5	advances	advance	NOUN
aiti-7988	154	6	in	in	ADP
aiti-7988	154	7	technology	technology	NOUN
aiti-7988	154	8	innovation	innovation	NOUN
aiti-7988	154	9	,	,	PUNCT
aiti-7988	154	10	vol	vol	NOUN
aiti-7988	154	11	.	.	PROPN
aiti-7988	155	1	7	7	NUM
aiti-7988	155	2	,	,	PUNCT
aiti-7988	155	3	no	no	INTJ
aiti-7988	155	4	.	.	NOUN
aiti-7988	155	5	1	1	NUM
aiti-7988	155	6	,	,	PUNCT
aiti-7988	155	7	2022	2022	NUM
aiti-7988	155	8	,	,	PUNCT
aiti-7988	155	9	pp	pp	ADJ
aiti-7988	155	10	.	.	PUNCT
aiti-7988	156	1	41	41	NUM
aiti-7988	156	2	-	-	SYM
aiti-7988	156	3	55	55	NUM
aiti-7988	156	4	1	1	NUM
aiti-7988	156	5	2	2	NUM
aiti-7988	156	6	2	2	NUM
aiti-7988	156	7	1	1	NUM
aiti-7988	156	8	f	f	NOUN
aiti-7988	156	9	p	p	X
aiti-7988	156	10	ei	ei	X
aiti-7988	156	11	t	t	PROPN
aiti-7988	156	12	l	l	NOUN
aiti-7988	156	13	m	m	VERB
aiti-7988	156	14	m	m	VERB
aiti-7988	156	15	=	=	ADJ
aiti-7988	157	1	+	+	NUM
aiti-7988	157	2			PROPN
aiti-7988	157	3			PROPN
aiti-7988	157	4			NOUN
aiti-7988	157	5			VERB
aiti-7988	157	6			PRON
aiti-7988	157	7			PUNCT
aiti-7988	157	8	(	(	PUNCT
aiti-7988	157	9	13	13	NUM
aiti-7988	157	10	)	)	SYM
aiti-7988	157	11	2	2	NUM
aiti-7988	157	12	nl	nl	NOUN
aiti-7988	157	13	n	n	X
aiti-7988	157	14	ei	ei	NOUN
aiti-7988	157	15	=	=	PUNCT
aiti-7988	157	16	(	(	PUNCT
aiti-7988	157	17	14	14	NUM
aiti-7988	157	18	)	)	PUNCT
aiti-7988	157	19	(	(	PUNCT
aiti-7988	157	20	)	)	PUNCT
aiti-7988	157	21	2	2	NUM
aiti-7988	157	22	1/	1/	NUM
aiti-7988	157	23	2	2	NUM
aiti-7988	157	24	1	1	NUM
aiti-7988	157	25	sin	sin	NOUN
aiti-7988	157	26	sin	sin	NOUN
aiti-7988	157	27	2	2	NUM
aiti-7988	157	28	cosg	cosg	NOUN
aiti-7988	157	29	n	n	ADP
aiti-7988	157	30	u	u	NOUN
aiti-7988	157	31	g	g	PROPN
aiti-7988	157	32	u	u	NOUN
aiti-7988	157	33	gφ	gφ	PROPN
aiti-7988	157	34	ζ	ζ	PROPN
aiti-7988	157	35	θ	θ	PROPN
aiti-7988	157	36	φ	φ	PROPN
aiti-7988	157	37	θφ	θφ	PROPN
aiti-7988	157	38	β	β	PROPN
aiti-7988	157	39	φ	φ	PROPN
aiti-7988	157	40	φ	φ	PROPN
aiti-7988	157	41	θ′′′′	θ′′′′	PROPN
aiti-7988	157	42	′′	′′	PROPN
aiti-7988	157	43	′	′	NOUN
aiti-7988	157	44	′−	′−	PROPN
aiti-7988	157	45	−	−	PROPN
aiti-7988	157	46	−	−	NOUN
aiti-7988	157	47	−	−	PROPN
aiti-7988	158	1	+	+	CCONJ
aiti-7988	158	2	+	+	PUNCT
aiti-7988	158	3	+	+	CCONJ
aiti-7988	158	4	=	=	NOUN
aiti-7988	158	5	−	−	NOUN
aiti-7988	158	6			NOUN
aiti-7988	158	7			PROPN
aiti-7988	158	8	ɺ	ɺ	NOUN
aiti-7988	158	9	ɺɺ	ɺɺ	NOUN
aiti-7988	158	10	(	(	PUNCT
aiti-7988	158	11	15	15	NUM
aiti-7988	158	12	)	)	PUNCT
aiti-7988	158	13	3.2	3.2	NUM
aiti-7988	158	14	.	.	PUNCT
aiti-7988	158	15	solution	solution	NOUN
aiti-7988	158	16	procedure	procedure	NOUN
aiti-7988	158	17	in	in	ADP
aiti-7988	158	18	order	order	NOUN
aiti-7988	158	19	to	to	PART
aiti-7988	158	20	discrete	discrete	VERB
aiti-7988	158	21	eq	eq	ADP
aiti-7988	158	22	.	.	PUNCT
aiti-7988	159	1	(	(	PUNCT
aiti-7988	159	2	15	15	NUM
aiti-7988	159	3	)	)	PUNCT
aiti-7988	160	1	and	and	CCONJ
aiti-7988	160	2	transform	transform	VERB
aiti-7988	160	3	it	it	PRON
aiti-7988	160	4	to	to	ADP
aiti-7988	160	5	an	an	DET
aiti-7988	160	6	ordinary	ordinary	ADJ
aiti-7988	160	7	differential	differential	ADJ
aiti-7988	160	8	equation	equation	NOUN
aiti-7988	160	9	,	,	PUNCT
aiti-7988	160	10	the	the	DET
aiti-7988	160	11	term	term	NOUN
aiti-7988	160	12	η(ζ	η(ζ	PROPN
aiti-7988	160	13	,	,	PUNCT
aiti-7988	160	14	τ	τ	X
aiti-7988	160	15	)	)	PUNCT
aiti-7988	160	16	is	be	AUX
aiti-7988	160	17	used	use	VERB
aiti-7988	160	18	to	to	PART
aiti-7988	160	19	decompose	decompose	VERB
aiti-7988	160	20	the	the	DET
aiti-7988	160	21	equation	equation	NOUN
aiti-7988	160	22	into	into	ADP
aiti-7988	160	23	space	space	NOUN
aiti-7988	160	24	and	and	CCONJ
aiti-7988	160	25	time	time	NOUN
aiti-7988	160	26	as	as	SCONJ
aiti-7988	160	27	follows	follow	VERB
aiti-7988	160	28	:	:	PUNCT
aiti-7988	160	29	(	(	PUNCT
aiti-7988	160	30	)	)	PUNCT
aiti-7988	161	1	(	(	PUNCT
aiti-7988	161	2	)	)	PUNCT
aiti-7988	161	3	(	(	PUNCT
aiti-7988	161	4	)	)	PUNCT
aiti-7988	161	5	,	,	PUNCT
aiti-7988	161	6	t	t	PROPN
aiti-7988	161	7	tφ	tφ	PROPN
aiti-7988	161	8	ζ	ζ	PROPN
aiti-7988	161	9	ζ=	ζ=	ADV
aiti-7988	161	10	γ	γ	X
aiti-7988	161	11	λ	λ	PROPN
aiti-7988	161	12	(	(	PUNCT
aiti-7988	161	13	16	16	NUM
aiti-7988	161	14	)	)	PUNCT
aiti-7988	161	15	where	where	SCONJ
aiti-7988	161	16	λ(	λ(	PROPN
aiti-7988	161	17	�	�	NOUN
aiti-7988	161	18	̅	̅	NOUN
aiti-7988	161	19	)	)	PUNCT
aiti-7988	161	20	the	the	DET
aiti-7988	161	21	generalized	generalized	ADJ
aiti-7988	161	22	coordinate	coordinate	NOUN
aiti-7988	161	23	of	of	ADP
aiti-7988	161	24	the	the	DET
aiti-7988	161	25	system	system	NOUN
aiti-7988	161	26	and	and	CCONJ
aiti-7988	161	27	γ(ζ	γ(ζ	NOUN
aiti-7988	161	28	)	)	PUNCT
aiti-7988	161	29	is	be	AUX
aiti-7988	161	30	a	a	DET
aiti-7988	161	31	trial	trial	NOUN
aiti-7988	161	32	/	/	SYM
aiti-7988	161	33	comparison	comparison	NOUN
aiti-7988	161	34	function	function	NOUN
aiti-7988	161	35	satisfying	satisfy	VERB
aiti-7988	161	36	both	both	CCONJ
aiti-7988	161	37	the	the	DET
aiti-7988	161	38	geometrical	geometrical	ADJ
aiti-7988	161	39	and	and	CCONJ
aiti-7988	161	40	natural	natural	ADJ
aiti-7988	161	41	boundary	boundary	ADJ
aiti-7988	161	42	conditions	condition	NOUN
aiti-7988	161	43	.	.	PUNCT
aiti-7988	162	1	the	the	DET
aiti-7988	162	2	pipe	pipe	NOUN
aiti-7988	162	3	end	end	VERB
aiti-7988	162	4	boundary	boundary	ADJ
aiti-7988	162	5	conditions	condition	NOUN
aiti-7988	162	6	considered	consider	VERB
aiti-7988	162	7	in	in	ADP
aiti-7988	162	8	the	the	DET
aiti-7988	162	9	current	current	ADJ
aiti-7988	162	10	study	study	NOUN
aiti-7988	162	11	is	be	AUX
aiti-7988	162	12	clamped	clamp	VERB
aiti-7988	162	13	-	-	PUNCT
aiti-7988	162	14	clamped	clamp	VERB
aiti-7988	162	15	support	support	NOUN
aiti-7988	162	16	,	,	PUNCT
aiti-7988	162	17	which	which	PRON
aiti-7988	162	18	can	can	AUX
aiti-7988	162	19	be	be	AUX
aiti-7988	162	20	symbolized	symbolize	VERB
aiti-7988	162	21	as	as	ADP
aiti-7988	162	22	c	c	NOUN
aiti-7988	162	23	-	-	PUNCT
aiti-7988	162	24	c.	c.	NOUN
aiti-7988	162	25	the	the	DET
aiti-7988	162	26	boundary	boundary	ADJ
aiti-7988	162	27	conditions	condition	NOUN
aiti-7988	162	28	at	at	ADP
aiti-7988	162	29	the	the	DET
aiti-7988	162	30	edges	edge	NOUN
aiti-7988	162	31	can	can	AUX
aiti-7988	162	32	be	be	AUX
aiti-7988	162	33	expressed	express	VERB
aiti-7988	162	34	as	as	ADP
aiti-7988	162	35	:	:	PUNCT
aiti-7988	162	36	clamped	clamp	VERB
aiti-7988	162	37	(	(	PUNCT
aiti-7988	162	38	ζ	ζ	NOUN
aiti-7988	162	39	=	=	SYM
aiti-7988	162	40	0	0	NUM
aiti-7988	162	41	)	)	PUNCT
aiti-7988	162	42	clamped	clamp	VERB
aiti-7988	162	43	(	(	PUNCT
aiti-7988	162	44	ζ	ζ	NOUN
aiti-7988	162	45	=	=	SYM
aiti-7988	162	46	1	1	NUM
aiti-7988	162	47	)	)	PUNCT
aiti-7988	162	48	,	,	PUNCT
aiti-7988	162	49	c	c	X
aiti-7988	162	50	-	-	PUNCT
aiti-7988	162	51	c	c	NOUN
aiti-7988	162	52	at	at	ADP
aiti-7988	162	53	ζ	ζ	NOUN
aiti-7988	162	54	=	=	SYM
aiti-7988	162	55	0	0	NUM
aiti-7988	162	56	,	,	PUNCT
aiti-7988	162	57	γ	γ	NOUN
aiti-7988	162	58	=	=	SYM
aiti-7988	162	59	0	0	NUM
aiti-7988	162	60	,	,	PUNCT
aiti-7988	162	61	and	and	CCONJ
aiti-7988	162	62	�	�	PROPN
aiti-7988	162	63	γ/	γ/	NOUN
aiti-7988	162	64	�	�	PROPN
aiti-7988	162	65	ζ	ζ	NOUN
aiti-7988	162	66	=	=	SYM
aiti-7988	162	67	0	0	NUM
aiti-7988	162	68	;	;	PUNCT
aiti-7988	162	69	at	at	ADP
aiti-7988	162	70	ζ	ζ	NOUN
aiti-7988	162	71	=	=	SYM
aiti-7988	162	72	1	1	NUM
aiti-7988	162	73	,	,	PUNCT
aiti-7988	162	74	γ	γ	NOUN
aiti-7988	162	75	=	=	SYM
aiti-7988	162	76	0	0	NUM
aiti-7988	162	77	,	,	PUNCT
aiti-7988	162	78	and	and	CCONJ
aiti-7988	162	79	�	�	PROPN
aiti-7988	162	80	γ/	γ/	NOUN
aiti-7988	162	81	�	�	PROPN
aiti-7988	162	82	ζ	ζ	NOUN
aiti-7988	162	83	=	=	SYM
aiti-7988	162	84	0	0	NUM
aiti-7988	162	85	.	.	PUNCT
aiti-7988	163	1	substituting	substitute	VERB
aiti-7988	163	2	eq	eq	PROPN
aiti-7988	163	3	.	.	PUNCT
aiti-7988	164	1	(	(	PUNCT
aiti-7988	164	2	16	16	NUM
aiti-7988	164	3	)	)	PUNCT
aiti-7988	164	4	into	into	ADP
aiti-7988	164	5	eq	eq	NOUN
aiti-7988	164	6	.	.	PUNCT
aiti-7988	165	1	(	(	PUNCT
aiti-7988	165	2	15	15	NUM
aiti-7988	165	3	)	)	PUNCT
aiti-7988	165	4	gives	give	VERB
aiti-7988	165	5	:	:	PUNCT
aiti-7988	165	6	(	(	PUNCT
aiti-7988	165	7	)	)	PUNCT
aiti-7988	165	8	(	(	PUNCT
aiti-7988	165	9	)	)	PUNCT
aiti-7988	165	10	(	(	PUNCT
aiti-7988	165	11	)	)	PUNCT
aiti-7988	165	12	(	(	PUNCT
aiti-7988	165	13	)	)	PUNCT
aiti-7988	165	14	(	(	PUNCT
aiti-7988	165	15	)	)	PUNCT
aiti-7988	165	16	(	(	PUNCT
aiti-7988	165	17	)	)	PUNCT
aiti-7988	165	18	(	(	PUNCT
aiti-7988	165	19	)	)	PUNCT
aiti-7988	165	20	(	(	PUNCT
aiti-7988	165	21	)	)	PUNCT
aiti-7988	165	22	(	(	PUNCT
aiti-7988	165	23	)	)	PUNCT
aiti-7988	165	24	(	(	PUNCT
aiti-7988	165	25	)	)	PUNCT
aiti-7988	165	26	(	(	PUNCT
aiti-7988	165	27	)	)	SYM
aiti-7988	165	28	2	2	NUM
aiti-7988	165	29	1	1	NUM
aiti-7988	165	30	21	21	NUM
aiti-7988	165	31	sin	sin	NOUN
aiti-7988	165	32	sin	sin	NOUN
aiti-7988	165	33	2	2	NUM
aiti-7988	165	34	cos	cos	ADP
aiti-7988	165	35	t	t	PROPN
aiti-7988	165	36	g	g	PROPN
aiti-7988	165	37	n	n	ADP
aiti-7988	165	38	u	u	NOUN
aiti-7988	165	39	t	t	NOUN
aiti-7988	165	40	g	g	NOUN
aiti-7988	165	41	t	t	PROPN
aiti-7988	165	42	u	u	NOUN
aiti-7988	165	43	t	t	PROPN
aiti-7988	165	44	t	t	NOUN
aiti-7988	165	45	g	g	PROPN
aiti-7988	165	46	ζ	ζ	PROPN
aiti-7988	165	47	ζ	ζ	NOUN
aiti-7988	165	48	θ	θ	NOUN
aiti-7988	165	49	ζ	ζ	NOUN
aiti-7988	165	50	θ	θ	X
aiti-7988	165	51	ζ	ζ	NOUN
aiti-7988	165	52	β	β	SYM
aiti-7988	165	53	ζ	ζ	NOUN
aiti-7988	165	54	ζ	ζ	PROPN
aiti-7988	165	55	θ	θ	PROPN
aiti-7988	165	56			NOUN
aiti-7988	165	57	′′′′	′′′′	PROPN
aiti-7988	165	58	′′	′′	PROPN
aiti-7988	165	59	′	′	NUM
aiti-7988	165	60	′γ	′γ	VERB
aiti-7988	165	61	λ	λ	NOUN
aiti-7988	165	62	−	−	NOUN
aiti-7988	165	63	−	−	PROPN
aiti-7988	166	1	−	−	PROPN
aiti-7988	166	2	−	−	PROPN
aiti-7988	166	3	γ	γ	X
aiti-7988	166	4	λ	λ	PROPN
aiti-7988	166	5	+	+	CCONJ
aiti-7988	166	6	γ	γ	X
aiti-7988	166	7	λ	λ	PROPN
aiti-7988	166	8	+	+	CCONJ
aiti-7988	166	9	γ	γ	X
aiti-7988	166	10	λ	λ	PROPN
aiti-7988	166	11	+	+	CCONJ
aiti-7988	166	12	γ	γ	PROPN
aiti-7988	166	13	λ	λ	PROPN
aiti-7988	166	14			PROPN
aiti-7988	166	15	=	=	SYM
aiti-7988	166	16	−	−	PROPN
aiti-7988	166	17	ɺ	ɺ	INTJ
aiti-7988	166	18	ɺɺ	ɺɺ	PROPN
aiti-7988	166	19	(	(	PUNCT
aiti-7988	166	20	17	17	NUM
aiti-7988	166	21	)	)	PUNCT
aiti-7988	166	22	to	to	PART
aiti-7988	166	23	solve	solve	VERB
aiti-7988	166	24	eq	eq	ADP
aiti-7988	166	25	.	.	PUNCT
aiti-7988	167	1	(	(	PUNCT
aiti-7988	167	2	17	17	NUM
aiti-7988	167	3	)	)	PUNCT
aiti-7988	167	4	,	,	PUNCT
aiti-7988	167	5	itts	itt	NOUN
aiti-7988	167	6	are	be	AUX
aiti-7988	167	7	used	use	VERB
aiti-7988	167	8	in	in	ADP
aiti-7988	167	9	this	this	DET
aiti-7988	167	10	work	work	NOUN
aiti-7988	167	11	.	.	PUNCT
aiti-7988	168	1	first	first	ADV
aiti-7988	168	2	,	,	PUNCT
aiti-7988	168	3	based	base	VERB
aiti-7988	168	4	on	on	ADP
aiti-7988	168	5	eq	eq	ADP
aiti-7988	168	6	.	.	PUNCT
aiti-7988	169	1	(	(	PUNCT
aiti-7988	169	2	1	1	NUM
aiti-7988	169	3	)	)	PUNCT
aiti-7988	169	4	,	,	PUNCT
aiti-7988	169	5	by	by	ADP
aiti-7988	169	6	assuming	assume	VERB
aiti-7988	169	7	zero	zero	NUM
aiti-7988	169	8	initial	initial	ADJ
aiti-7988	169	9	conditions	condition	NOUN
aiti-7988	169	10	case	case	NOUN
aiti-7988	169	11	,	,	PUNCT
aiti-7988	169	12	laplace	laplace	NOUN
aiti-7988	169	13	transform	transform	NOUN
aiti-7988	169	14	is	be	AUX
aiti-7988	169	15	introduced	introduce	VERB
aiti-7988	169	16	to	to	PART
aiti-7988	169	17	suppress	suppress	VERB
aiti-7988	169	18	the	the	DET
aiti-7988	169	19	time	time	NOUN
aiti-7988	169	20	dependency	dependency	NOUN
aiti-7988	169	21	.	.	PUNCT
aiti-7988	170	1	(	(	PUNCT
aiti-7988	170	2	)	)	PUNCT
aiti-7988	170	3	(	(	PUNCT
aiti-7988	170	4	)	)	PUNCT
aiti-7988	170	5	(	(	PUNCT
aiti-7988	170	6	)	)	PUNCT
aiti-7988	170	7	(	(	PUNCT
aiti-7988	170	8	)	)	PUNCT
aiti-7988	170	9	(	(	PUNCT
aiti-7988	170	10	)	)	PUNCT
aiti-7988	170	11	(	(	PUNCT
aiti-7988	170	12	)	)	PUNCT
aiti-7988	170	13	(	(	PUNCT
aiti-7988	170	14	)	)	PUNCT
aiti-7988	170	15	(	(	PUNCT
aiti-7988	170	16	)	)	PUNCT
aiti-7988	170	17	(	(	PUNCT
aiti-7988	170	18	)	)	PUNCT
aiti-7988	170	19	(	(	PUNCT
aiti-7988	170	20	)	)	SYM
aiti-7988	170	21	2	2	NUM
aiti-7988	170	22	1	1	NUM
aiti-7988	170	23	2	2	NUM
aiti-7988	170	24	2	2	NUM
aiti-7988	170	25	1	1	NUM
aiti-7988	170	26	sin	sin	NOUN
aiti-7988	170	27	sin	sin	NOUN
aiti-7988	170	28	2	2	NUM
aiti-7988	170	29	cos	cos	NOUN
aiti-7988	170	30	s	s	PROPN
aiti-7988	170	31	g	g	PROPN
aiti-7988	170	32	n	n	CCONJ
aiti-7988	170	33	u	u	NOUN
aiti-7988	170	34	s	s	PROPN
aiti-7988	170	35	g	g	NOUN
aiti-7988	170	36	us	we	PRON
aiti-7988	170	37	s	s	PART
aiti-7988	170	38	s	s	X
aiti-7988	170	39	s	s	X
aiti-7988	170	40	g	g	NOUN
aiti-7988	170	41	s	s	PART
aiti-7988	170	42	ζ	ζ	NOUN
aiti-7988	170	43	ζ	ζ	NOUN
aiti-7988	170	44	θ	θ	NOUN
aiti-7988	170	45	ζ	ζ	NOUN
aiti-7988	170	46	θ	θ	X
aiti-7988	170	47	ζ	ζ	NOUN
aiti-7988	170	48	β	β	X
aiti-7988	170	49	ζ	ζ	NOUN
aiti-7988	170	50	ζ	ζ	NOUN
aiti-7988	170	51	θ	θ	NOUN
aiti-7988	170	52	′′′′	′′′′	PROPN
aiti-7988	170	53	′′	′′	PROPN
aiti-7988	170	54	′	′	NUM
aiti-7988	170	55	′γ	′γ	VERB
aiti-7988	170	56	λ	λ	NOUN
aiti-7988	170	57	−	−	NOUN
aiti-7988	170	58	−	−	PROPN
aiti-7988	170	59	−	−	PROPN
aiti-7988	170	60	−	−	PROPN
aiti-7988	170	61	γ	γ	X
aiti-7988	170	62	λ	λ	PROPN
aiti-7988	170	63	+	+	CCONJ
aiti-7988	170	64	γ	γ	X
aiti-7988	170	65	+	+	X
aiti-7988	170	66	γ	γ	X
aiti-7988	170	67	λ	λ	PROPN
aiti-7988	170	68	+	+	CCONJ
aiti-7988	170	69	γ	γ	X
aiti-7988	170	70	λ	λ	PROPN
aiti-7988	170	71	=	=	SYM
aiti-7988	170	72	−	−	PROPN
aiti-7988	170	73			NOUN
aiti-7988	170	74			NOUN
aiti-7988	170	75			PROPN
aiti-7988	170	76	(	(	PUNCT
aiti-7988	170	77	18	18	NUM
aiti-7988	170	78	)	)	PUNCT
aiti-7988	170	79	next	next	ADV
aiti-7988	170	80	,	,	PUNCT
aiti-7988	170	81	for	for	ADP
aiti-7988	170	82	reducing	reduce	VERB
aiti-7988	170	83	the	the	DET
aiti-7988	170	84	difficulty	difficulty	NOUN
aiti-7988	170	85	of	of	ADP
aiti-7988	170	86	solving	solve	VERB
aiti-7988	170	87	eq	eq	NOUN
aiti-7988	170	88	.	.	PUNCT
aiti-7988	171	1	(	(	PUNCT
aiti-7988	171	2	18	18	NUM
aiti-7988	171	3	)	)	PUNCT
aiti-7988	171	4	,	,	PUNCT
aiti-7988	171	5	a	a	DET
aiti-7988	171	6	finite	finite	ADJ
aiti-7988	171	7	fourier	fourier	NOUN
aiti-7988	171	8	sine	sine	ADJ
aiti-7988	171	9	transform	transform	NOUN
aiti-7988	171	10	is	be	AUX
aiti-7988	171	11	introduced	introduce	VERB
aiti-7988	171	12	to	to	PART
aiti-7988	171	13	convert	convert	VERB
aiti-7988	171	14	the	the	DET
aiti-7988	171	15	infinite	infinite	ADJ
aiti-7988	171	16	degree	degree	NOUN
aiti-7988	171	17	of	of	ADP
aiti-7988	171	18	freedom	freedom	NOUN
aiti-7988	171	19	pipe	pipe	NOUN
aiti-7988	171	20	-	-	PUNCT
aiti-7988	171	21	fluid	fluid	NOUN
aiti-7988	171	22	system	system	NOUN
aiti-7988	171	23	into	into	ADP
aiti-7988	171	24	a	a	DET
aiti-7988	171	25	superimposed	superimpose	VERB
aiti-7988	171	26	double	double	ADJ
aiti-7988	171	27	degrees	degree	NOUN
aiti-7988	171	28	of	of	ADP
aiti-7988	171	29	freedom	freedom	NOUN
aiti-7988	171	30	system	system	NOUN
aiti-7988	171	31	.	.	PUNCT
aiti-7988	172	1	thus	thus	ADV
aiti-7988	172	2	,	,	PUNCT
aiti-7988	172	3	by	by	ADP
aiti-7988	172	4	using	use	VERB
aiti-7988	172	5	eq	eq	ADP
aiti-7988	172	6	.	.	PUNCT
aiti-7988	173	1	(	(	PUNCT
aiti-7988	173	2	3	3	NUM
aiti-7988	173	3	)	)	PUNCT
aiti-7988	173	4	,	,	PUNCT
aiti-7988	173	5	finite	finite	PROPN
aiti-7988	173	6	fourier	fourier	PROPN
aiti-7988	173	7	sine	sine	NOUN
aiti-7988	173	8	transform	transform	VERB
aiti-7988	173	9	with	with	ADP
aiti-7988	173	10	regard	regard	NOUN
aiti-7988	173	11	to	to	ADP
aiti-7988	173	12	spatial	spatial	ADJ
aiti-7988	173	13	(	(	PUNCT
aiti-7988	173	14	space	space	NOUN
aiti-7988	173	15	)	)	PUNCT
aiti-7988	173	16	coordinate	coordinate	NOUN
aiti-7988	173	17	γ	γ	X
aiti-7988	173	18	is	be	AUX
aiti-7988	173	19	conducted	conduct	VERB
aiti-7988	173	20	on	on	ADP
aiti-7988	173	21	eq	eq	ADP
aiti-7988	173	22	.	.	PUNCT
aiti-7988	174	1	(	(	PUNCT
aiti-7988	174	2	18	18	NUM
aiti-7988	174	3	)	)	PUNCT
aiti-7988	174	4	,	,	PUNCT
aiti-7988	174	5	and	and	CCONJ
aiti-7988	174	6	the	the	DET
aiti-7988	174	7	following	follow	VERB
aiti-7988	174	8	equation	equation	NOUN
aiti-7988	174	9	can	can	AUX
aiti-7988	174	10	be	be	AUX
aiti-7988	174	11	obtained	obtain	VERB
aiti-7988	174	12	:	:	PUNCT
aiti-7988	174	13	(	(	PUNCT
aiti-7988	174	14	)	)	PUNCT
aiti-7988	174	15	(	(	PUNCT
aiti-7988	174	16	)	)	PUNCT
aiti-7988	174	17	(	(	PUNCT
aiti-7988	174	18	)	)	PUNCT
aiti-7988	174	19	(	(	PUNCT
aiti-7988	174	20	)	)	PUNCT
aiti-7988	174	21	(	(	PUNCT
aiti-7988	174	22	)	)	PUNCT
aiti-7988	174	23	(	(	PUNCT
aiti-7988	174	24	)	)	PUNCT
aiti-7988	174	25	(	(	PUNCT
aiti-7988	174	26	)	)	PUNCT
aiti-7988	174	27	(	(	PUNCT
aiti-7988	174	28	)	)	PUNCT
aiti-7988	174	29	(	(	PUNCT
aiti-7988	174	30	)	)	PUNCT
aiti-7988	174	31	(	(	PUNCT
aiti-7988	174	32	)	)	PUNCT
aiti-7988	174	33	(	(	PUNCT
aiti-7988	174	34	)	)	PUNCT
aiti-7988	174	35	(	(	PUNCT
aiti-7988	174	36	)	)	PUNCT
aiti-7988	174	37	(	(	PUNCT
aiti-7988	174	38	)	)	PUNCT
aiti-7988	174	39	(	(	PUNCT
aiti-7988	174	40	)	)	PUNCT
aiti-7988	174	41	1	1	NUM
aiti-7988	174	42	1	1	NUM
aiti-7988	174	43	1	1	NUM
aiti-7988	174	44	2	2	NUM
aiti-7988	174	45	0	0	NUM
aiti-7988	174	46	0	0	NUM
aiti-7988	174	47	0	0	NUM
aiti-7988	174	48	1	1	NUM
aiti-7988	174	49	1	1	NUM
aiti-7988	174	50	1	1	NUM
aiti-7988	174	51	1	1	NUM
aiti-7988	174	52	2	2	NUM
aiti-7988	174	53	2	2	NUM
aiti-7988	174	54	0	0	NUM
aiti-7988	174	55	0	0	NUM
aiti-7988	174	56	0	0	NUM
aiti-7988	174	57	1	1	NUM
aiti-7988	174	58	0	0	NUM
aiti-7988	174	59	sin	sin	NOUN
aiti-7988	174	60	sin	sin	NOUN
aiti-7988	174	61	sin	sin	NOUN
aiti-7988	174	62	sin	sin	NOUN
aiti-7988	174	63	sin	sin	NOUN
aiti-7988	174	64	sin	sin	NOUN
aiti-7988	174	65	sin	sin	NOUN
aiti-7988	174	66	2	2	NUM
aiti-7988	174	67	sin	sin	NOUN
aiti-7988	174	68	sin	sin	NOUN
aiti-7988	174	69	cos	cos	ADP
aiti-7988	174	70	1	1	NUM
aiti-7988	174	71	sin	sin	NOUN
aiti-7988	174	72	s	s	NOUN
aiti-7988	174	73	n	n	NOUN
aiti-7988	174	74	d	d	NOUN
aiti-7988	174	75	g	g	PROPN
aiti-7988	174	76	n	n	CCONJ
aiti-7988	174	77	u	u	NOUN
aiti-7988	174	78	s	s	NOUN
aiti-7988	174	79	n	n	PROPN
aiti-7988	174	80	d	d	NOUN
aiti-7988	174	81	g	g	PROPN
aiti-7988	174	82	s	s	PROPN
aiti-7988	174	83	n	n	PROPN
aiti-7988	174	84	d	d	NOUN
aiti-7988	174	85	g	g	PROPN
aiti-7988	174	86	s	s	PART
aiti-7988	174	87	n	n	NOUN
aiti-7988	175	1	d	d	X
aiti-7988	175	2	us	us	PROPN
aiti-7988	175	3	s	s	PART
aiti-7988	176	1	n	n	PROPN
aiti-7988	176	2	d	d	PROPN
aiti-7988	176	3	s	s	PROPN
aiti-7988	176	4	s	s	NOUN
aiti-7988	176	5	n	n	NOUN
aiti-7988	176	6	d	d	NOUN
aiti-7988	176	7	g	g	PROPN
aiti-7988	177	1	n	n	PROPN
aiti-7988	177	2	d	d	NOUN
aiti-7988	177	3	s	s	PART
aiti-7988	177	4	ζ	ζ	NOUN
aiti-7988	177	5	πζ	πζ	INTJ
aiti-7988	177	6	ζ	ζ	NOUN
aiti-7988	177	7	θ	θ	NOUN
aiti-7988	177	8	ζ	ζ	NOUN
aiti-7988	177	9	πζ	πζ	PROPN
aiti-7988	177	10	ζ	ζ	NOUN
aiti-7988	177	11	θ	θ	NOUN
aiti-7988	177	12	ζ	ζ	NOUN
aiti-7988	177	13	ζ	ζ	NOUN
aiti-7988	177	14	πζ	πζ	PRON
aiti-7988	177	15	ζ	ζ	NOUN
aiti-7988	177	16	θ	θ	NOUN
aiti-7988	177	17	ζ	ζ	NOUN
aiti-7988	177	18	πζ	πζ	PRON
aiti-7988	177	19	ζ	ζ	NOUN
aiti-7988	177	20	β	β	X
aiti-7988	177	21	ζ	ζ	X
aiti-7988	178	1	πζ	πζ	INTJ
aiti-7988	178	2	ζ	ζ	NOUN
aiti-7988	178	3	ζ	ζ	NOUN
aiti-7988	178	4	πζ	πζ	PRON
aiti-7988	178	5	ζ	ζ	NOUN
aiti-7988	178	6	θ	θ	NOUN
aiti-7988	178	7	πζ	πζ	PRON
aiti-7988	178	8	ζ	ζ	PROPN
aiti-7988	178	9	′′′′	′′′′	PROPN
aiti-7988	178	10	′′	′′	PROPN
aiti-7988	178	11	′′λ	′′λ	VERB
aiti-7988	178	12	γ	γ	NOUN
aiti-7988	178	13	−	−	PROPN
aiti-7988	178	14	−	−	PROPN
aiti-7988	178	15	−	−	PROPN
aiti-7988	179	1	λ	λ	X
aiti-7988	179	2	γ	γ	X
aiti-7988	179	3	+	+	X
aiti-7988	179	4	λ	λ	PROPN
aiti-7988	179	5	⋅	⋅	PROPN
aiti-7988	179	6	γ	γ	X
aiti-7988	179	7	′	′	NOUN
aiti-7988	179	8	′+	′+	PUNCT
aiti-7988	180	1	λ	λ	X
aiti-7988	180	2	γ	γ	X
aiti-7988	180	3	+	+	X
aiti-7988	180	4	λ	λ	PROPN
aiti-7988	180	5	γ	γ	X
aiti-7988	180	6	+	+	X
aiti-7988	180	7	λ	λ	PROPN
aiti-7988	180	8	γ	γ	X
aiti-7988	180	9	=	=	PUNCT
aiti-7988	180	10	−	−	PROPN
aiti-7988	181	1	∫	∫	PROPN
aiti-7988	181	2	∫	∫	PROPN
aiti-7988	181	3	∫	∫	PROPN
aiti-7988	181	4	∫	∫	PROPN
aiti-7988	181	5	∫	∫	PROPN
aiti-7988	181	6	∫	∫	PROPN
aiti-7988	181	7	∫	∫	PROPN
aiti-7988	181	8	(	(	PUNCT
aiti-7988	181	9	19	19	NUM
aiti-7988	181	10	)	)	PUNCT
aiti-7988	181	11	γ(ζ	γ(ζ	NOUN
aiti-7988	181	12	)	)	PUNCT
aiti-7988	181	13	is	be	AUX
aiti-7988	181	14	beam	beam	ADJ
aiti-7988	181	15	eigen	eigen	PROPN
aiti-7988	181	16	function	function	PROPN
aiti-7988	181	17	and	and	CCONJ
aiti-7988	181	18	varies	vary	VERB
aiti-7988	181	19	according	accord	VERB
aiti-7988	181	20	to	to	ADP
aiti-7988	181	21	boundary	boundary	ADJ
aiti-7988	181	22	condition	condition	NOUN
aiti-7988	181	23	for	for	ADP
aiti-7988	181	24	the	the	DET
aiti-7988	181	25	clamped	clamp	VERB
aiti-7988	181	26	supported	support	VERB
aiti-7988	181	27	case	case	NOUN
aiti-7988	181	28	:	:	PUNCT
aiti-7988	181	29	(	(	PUNCT
aiti-7988	181	30	)	)	PUNCT
aiti-7988	181	31	(	(	PUNCT
aiti-7988	181	32	)	)	PUNCT
aiti-7988	181	33	(	(	PUNCT
aiti-7988	181	34	)	)	PUNCT
aiti-7988	181	35	(	(	PUNCT
aiti-7988	181	36	)	)	PUNCT
aiti-7988	181	37	(	(	PUNCT
aiti-7988	181	38	)	)	PUNCT
aiti-7988	181	39	(	(	PUNCT
aiti-7988	181	40	)	)	PUNCT
aiti-7988	181	41	(	(	PUNCT
aiti-7988	181	42	)	)	PUNCT
aiti-7988	181	43	(	(	PUNCT
aiti-7988	181	44	)	)	PUNCT
aiti-7988	181	45	(	(	PUNCT
aiti-7988	181	46	)	)	PUNCT
aiti-7988	181	47	cosh	cosh	PROPN
aiti-7988	181	48	l	l	PROPN
aiti-7988	181	49	cos	cos	PROPN
aiti-7988	181	50	l	l	PROPN
aiti-7988	181	51	cosh	cosh	PROPN
aiti-7988	181	52	cos	cos	PROPN
aiti-7988	181	53	[	[	PUNCT
aiti-7988	181	54	sinh	sinh	NOUN
aiti-7988	181	55	sin	sin	NOUN
aiti-7988	181	56	]	]	PUNCT
aiti-7988	181	57	sinh	sinh	NOUN
aiti-7988	181	58	l	l	PROPN
aiti-7988	181	59	sin	sin	NOUN
aiti-7988	182	1	l	l	NOUN
aiti-7988	182	2	r	r	NOUN
aiti-7988	182	3	r	r	NOUN
aiti-7988	182	4	r	r	NOUN
aiti-7988	182	5	r	r	NOUN
aiti-7988	182	6	r	r	NOUN
aiti-7988	182	7	r	r	NOUN
aiti-7988	182	8	r	r	NOUN
aiti-7988	182	9	r	r	NOUN
aiti-7988	182	10	λ	λ	X
aiti-7988	182	11	λ	λ	X
aiti-7988	182	12	ζ	ζ	NOUN
aiti-7988	182	13	λ	λ	X
aiti-7988	182	14	ζ	ζ	NOUN
aiti-7988	182	15	λ	λ	X
aiti-7988	182	16	ζ	ζ	NOUN
aiti-7988	182	17	λ	λ	X
aiti-7988	182	18	ζ	ζ	NOUN
aiti-7988	182	19	λ	λ	X
aiti-7988	182	20	ζ	ζ	NOUN
aiti-7988	182	21	λ	λ	X
aiti-7988	182	22	λ	λ	NOUN
aiti-7988	182	23	−	−	PROPN
aiti-7988	182	24	γ	γ	X
aiti-7988	182	25	=	=	SYM
aiti-7988	182	26	−	−	PROPN
aiti-7988	182	27	−	−	PROPN
aiti-7988	183	1	−	−	PROPN
aiti-7988	183	2	−	−	PROPN
aiti-7988	183	3			VERB
aiti-7988	183	4			PROPN
aiti-7988	183	5			ADJ
aiti-7988	183	6			PROPN
aiti-7988	183	7			X
aiti-7988	183	8			X
aiti-7988	183	9	(	(	PUNCT
aiti-7988	183	10	20	20	NUM
aiti-7988	183	11	)	)	PUNCT
aiti-7988	183	12	46	46	NUM
aiti-7988	183	13	advances	advance	NOUN
aiti-7988	183	14	in	in	ADP
aiti-7988	183	15	technology	technology	NOUN
aiti-7988	183	16	innovation	innovation	NOUN
aiti-7988	183	17	,	,	PUNCT
aiti-7988	183	18	vol	vol	NOUN
aiti-7988	183	19	.	.	PROPN
aiti-7988	184	1	7	7	NUM
aiti-7988	184	2	,	,	PUNCT
aiti-7988	184	3	no	no	INTJ
aiti-7988	184	4	.	.	NOUN
aiti-7988	184	5	1	1	NUM
aiti-7988	184	6	,	,	PUNCT
aiti-7988	184	7	2022	2022	NUM
aiti-7988	184	8	,	,	PUNCT
aiti-7988	184	9	pp	pp	ADJ
aiti-7988	184	10	.	.	PUNCT
aiti-7988	185	1	41	41	NUM
aiti-7988	185	2	-	-	SYM
aiti-7988	185	3	55	55	NUM
aiti-7988	185	4	(	(	PUNCT
aiti-7988	185	5	)	)	PUNCT
aiti-7988	185	6	(	(	PUNCT
aiti-7988	185	7	)	)	PUNCT
aiti-7988	185	8	(	(	PUNCT
aiti-7988	185	9	)	)	PUNCT
aiti-7988	185	10	(	(	PUNCT
aiti-7988	185	11	)	)	PUNCT
aiti-7988	185	12	(	(	PUNCT
aiti-7988	185	13	)	)	PUNCT
aiti-7988	185	14	(	(	PUNCT
aiti-7988	185	15	)	)	PUNCT
aiti-7988	185	16	(	(	PUNCT
aiti-7988	185	17	)	)	PUNCT
aiti-7988	185	18	(	(	PUNCT
aiti-7988	185	19	)	)	PUNCT
aiti-7988	185	20	(	(	PUNCT
aiti-7988	185	21	)	)	PUNCT
aiti-7988	185	22	sinh	sinh	NOUN
aiti-7988	185	23	l	l	PROPN
aiti-7988	185	24	sin	sin	NOUN
aiti-7988	185	25	l	l	PROPN
aiti-7988	185	26	cosh	cosh	PROPN
aiti-7988	185	27	cos	cos	PROPN
aiti-7988	185	28	[	[	PUNCT
aiti-7988	185	29	sinh	sinh	NOUN
aiti-7988	185	30	sin	sin	NOUN
aiti-7988	185	31	]	]	PUNCT
aiti-7988	185	32	cosh	cosh	PROPN
aiti-7988	185	33	l	l	PROPN
aiti-7988	185	34	cos	cos	PROPN
aiti-7988	185	35	l	l	NOUN
aiti-7988	185	36	r	r	NOUN
aiti-7988	185	37	r	r	NOUN
aiti-7988	185	38	r	r	NOUN
aiti-7988	185	39	r	r	NOUN
aiti-7988	185	40	r	r	NOUN
aiti-7988	185	41	r	r	NOUN
aiti-7988	185	42	r	r	NOUN
aiti-7988	185	43	r	r	NOUN
aiti-7988	185	44	λ	λ	X
aiti-7988	185	45	λ	λ	X
aiti-7988	185	46	ζ	ζ	NOUN
aiti-7988	185	47	λ	λ	X
aiti-7988	185	48	ζ	ζ	NOUN
aiti-7988	185	49	λ	λ	X
aiti-7988	185	50	ζ	ζ	NOUN
aiti-7988	185	51	λ	λ	X
aiti-7988	185	52	ζ	ζ	NOUN
aiti-7988	185	53	λ	λ	X
aiti-7988	185	54	ζ	ζ	NOUN
aiti-7988	185	55	λ	λ	X
aiti-7988	185	56	λ	λ	NOUN
aiti-7988	185	57	+	+	CCONJ
aiti-7988	185	58	γ	γ	X
aiti-7988	185	59	=	=	SYM
aiti-7988	185	60	−	−	PROPN
aiti-7988	185	61	−	−	PROPN
aiti-7988	185	62	−	−	PROPN
aiti-7988	185	63	−	−	PROPN
aiti-7988	185	64			VERB
aiti-7988	185	65			PROPN
aiti-7988	185	66			ADJ
aiti-7988	185	67			PROPN
aiti-7988	185	68			X
aiti-7988	185	69			X
aiti-7988	185	70	(	(	PUNCT
aiti-7988	185	71	21	21	NUM
aiti-7988	185	72	)	)	PUNCT
aiti-7988	185	73	where	where	SCONJ
aiti-7988	185	74	�	�	PROPN
aiti-7988	185	75	�	�	PROPN
aiti-7988	185	76	is	be	AUX
aiti-7988	185	77	the	the	DET
aiti-7988	185	78	root	root	NOUN
aiti-7988	185	79	of	of	ADP
aiti-7988	185	80	the	the	DET
aiti-7988	185	81	equation	equation	NOUN
aiti-7988	185	82	cosh(	cosh(	PROPN
aiti-7988	185	83	�	�	PROPN
aiti-7988	185	84	�	�	PROPN
aiti-7988	185	85	l	l	NOUN
aiti-7988	185	86	)	)	PUNCT
aiti-7988	185	87	cos(	cos(	PROPN
aiti-7988	185	88	�	�	PROPN
aiti-7988	185	89	�	�	PROPN
aiti-7988	185	90	l	l	NOUN
aiti-7988	185	91	)	)	PUNCT
aiti-7988	185	92	.	.	PUNCT
aiti-7988	186	1	the	the	DET
aiti-7988	186	2	using	using	NOUN
aiti-7988	186	3	of	of	ADP
aiti-7988	186	4	terms	term	NOUN
aiti-7988	186	5	included	include	VERB
aiti-7988	186	6	in	in	ADP
aiti-7988	186	7	eq	eq	PROPN
aiti-7988	186	8	.	.	PUNCT
aiti-7988	186	9	(	(	PUNCT
aiti-7988	186	10	20	20	NUM
aiti-7988	186	11	)	)	PUNCT
aiti-7988	186	12	or	or	CCONJ
aiti-7988	186	13	(	(	PUNCT
aiti-7988	186	14	21	21	NUM
aiti-7988	186	15	)	)	PUNCT
aiti-7988	186	16	for	for	ADP
aiti-7988	186	17	fixed	fix	VERB
aiti-7988	186	18	support	support	NOUN
aiti-7988	186	19	may	may	AUX
aiti-7988	186	20	contain	contain	VERB
aiti-7988	186	21	some	some	DET
aiti-7988	186	22	difficulty	difficulty	NOUN
aiti-7988	186	23	and	and	CCONJ
aiti-7988	186	24	complexity	complexity	NOUN
aiti-7988	186	25	in	in	ADP
aiti-7988	186	26	determining	determine	VERB
aiti-7988	186	27	the	the	DET
aiti-7988	186	28	integral	integral	ADJ
aiti-7988	186	29	transformation	transformation	NOUN
aiti-7988	186	30	for	for	ADP
aiti-7988	186	31	each	each	DET
aiti-7988	186	32	term	term	NOUN
aiti-7988	186	33	in	in	ADP
aiti-7988	186	34	eq	eq	ADP
aiti-7988	186	35	.	.	PUNCT
aiti-7988	187	1	(	(	PUNCT
aiti-7988	187	2	19	19	NUM
aiti-7988	187	3	)	)	PUNCT
aiti-7988	187	4	.	.	PUNCT
aiti-7988	188	1	thus	thus	ADV
aiti-7988	188	2	,	,	PUNCT
aiti-7988	188	3	for	for	ADP
aiti-7988	188	4	simplification	simplification	NOUN
aiti-7988	188	5	,	,	PUNCT
aiti-7988	188	6	a	a	DET
aiti-7988	188	7	polynomial	polynomial	ADJ
aiti-7988	188	8	function	function	NOUN
aiti-7988	188	9	can	can	AUX
aiti-7988	188	10	be	be	AUX
aiti-7988	188	11	applied	apply	VERB
aiti-7988	188	12	for	for	ADP
aiti-7988	188	13	this	this	DET
aiti-7988	188	14	type	type	NOUN
aiti-7988	188	15	of	of	ADP
aiti-7988	188	16	support	support	NOUN
aiti-7988	188	17	system	system	NOUN
aiti-7988	188	18	:	:	PUNCT
aiti-7988	188	19	(	(	PUNCT
aiti-7988	188	20	)	)	PUNCT
aiti-7988	188	21	2	2	NUM
aiti-7988	188	22	3	3	NUM
aiti-7988	188	23	4	4	NUM
aiti-7988	188	24	0	0	NUM
aiti-7988	188	25	1	1	NUM
aiti-7988	188	26	2	2	NUM
aiti-7988	188	27	3	3	NUM
aiti-7988	188	28	4	4	NUM
aiti-7988	188	29	a	a	DET
aiti-7988	188	30	a	a	DET
aiti-7988	188	31	a	a	DET
aiti-7988	188	32	a	a	DET
aiti-7988	188	33	aζ	aζ	NOUN
aiti-7988	188	34	ζ	ζ	NOUN
aiti-7988	188	35	ζ	ζ	NOUN
aiti-7988	188	36	ζ	ζ	NOUN
aiti-7988	188	37	ζγ	ζγ	NOUN
aiti-7988	188	38	=	=	PUNCT
aiti-7988	189	1	+	+	PUNCT
aiti-7988	190	1	+	+	PUNCT
aiti-7988	190	2	+	+	PUNCT
aiti-7988	190	3	+	+	CCONJ
aiti-7988	190	4	(	(	PUNCT
aiti-7988	190	5	22	22	NUM
aiti-7988	190	6	)	)	PUNCT
aiti-7988	190	7	applying	apply	VERB
aiti-7988	190	8	the	the	DET
aiti-7988	190	9	boundary	boundary	ADJ
aiti-7988	190	10	conditions	condition	NOUN
aiti-7988	190	11	of	of	ADP
aiti-7988	190	12	c	c	NOUN
aiti-7988	190	13	-	-	PUNCT
aiti-7988	190	14	c	c	NOUN
aiti-7988	190	15	gives	give	VERB
aiti-7988	190	16	:	:	PUNCT
aiti-7988	190	17	(	(	PUNCT
aiti-7988	190	18	)	)	PUNCT
aiti-7988	190	19	(	(	PUNCT
aiti-7988	190	20	)	)	SYM
aiti-7988	190	21	4	4	NUM
aiti-7988	190	22	3	3	NUM
aiti-7988	190	23	2	2	NUM
aiti-7988	190	24	4	4	NUM
aiti-7988	190	25	2	2	NUM
aiti-7988	190	26	aζ	aζ	NOUN
aiti-7988	190	27	ζ	ζ	NOUN
aiti-7988	190	28	ζ	ζ	NOUN
aiti-7988	190	29	ζγ	ζγ	NOUN
aiti-7988	190	30	=	=	SYM
aiti-7988	190	31	−	−	PROPN
aiti-7988	191	1	+	+	CCONJ
aiti-7988	191	2	(	(	PUNCT
aiti-7988	191	3	23	23	NUM
aiti-7988	191	4	)	)	PUNCT
aiti-7988	191	5	using	use	VERB
aiti-7988	191	6	orthogonal	orthogonal	ADJ
aiti-7988	191	7	functions	function	NOUN
aiti-7988	191	8	gives	give	VERB
aiti-7988	191	9	:	:	PUNCT
aiti-7988	191	10	(	(	PUNCT
aiti-7988	191	11	)	)	PUNCT
aiti-7988	191	12	4	4	NUM
aiti-7988	191	13	5	5	NUM
aiti-7988	191	14	4	4	NUM
aiti-7988	191	15	3	3	NUM
aiti-7988	191	16	2	2	NUM
aiti-7988	191	17	1	1	NUM
aiti-7988	191	18	3	3	NUM
aiti-7988	191	19	70	70	NUM
aiti-7988	191	20	70	70	NUM
aiti-7988	191	21	315	315	NUM
aiti-7988	191	22	540	540	NUM
aiti-7988	191	23	420	420	NUM
aiti-7988	191	24	126	126	NUM
aiti-7988	191	25	a	a	DET
aiti-7988	191	26	a	a	DET
aiti-7988	191	27	a	a	DET
aiti-7988	191	28	a	a	DET
aiti-7988	191	29	a	a	DET
aiti-7988	191	30	a−	a−	NOUN
aiti-7988	191	31	+	+	CCONJ
aiti-7988	191	32	−	−	PROPN
aiti-7988	192	1	+	+	CCONJ
aiti-7988	192	2	=	=	NOUN
aiti-7988	192	3			NOUN
aiti-7988	192	4			PROPN
aiti-7988	192	5			ADJ
aiti-7988	192	6			PROPN
aiti-7988	192	7			X
aiti-7988	192	8			X
aiti-7988	192	9	(	(	PUNCT
aiti-7988	192	10	24	24	NUM
aiti-7988	192	11	)	)	PUNCT
aiti-7988	192	12	by	by	ADP
aiti-7988	192	13	substituting	substitute	VERB
aiti-7988	192	14	�	�	PROPN
aiti-7988	192	15	=	=	SYM
aiti-7988	192	16	1	1	NUM
aiti-7988	192	17	in	in	ADP
aiti-7988	192	18	eq	eq	ADP
aiti-7988	192	19	.	.	PUNCT
aiti-7988	193	1	(	(	PUNCT
aiti-7988	193	2	21	21	NUM
aiti-7988	193	3	)	)	PUNCT
aiti-7988	193	4	,	,	PUNCT
aiti-7988	193	5	�	�	PROPN
aiti-7988	193	6	�	�	PROPN
aiti-7988	193	7	=	=	SYM
aiti-7988	193	8	25.20	25.20	NUM
aiti-7988	193	9	can	can	AUX
aiti-7988	193	10	be	be	AUX
aiti-7988	193	11	obtained	obtain	VERB
aiti-7988	193	12	for	for	ADP
aiti-7988	193	13	the	the	DET
aiti-7988	193	14	first	first	ADJ
aiti-7988	193	15	mode	mode	NOUN
aiti-7988	193	16	.	.	PUNCT
aiti-7988	194	1	by	by	ADP
aiti-7988	194	2	substituting	substitute	VERB
aiti-7988	194	3	eq	eq	PROPN
aiti-7988	194	4	.	.	PUNCT
aiti-7988	195	1	(	(	PUNCT
aiti-7988	195	2	23	23	NUM
aiti-7988	195	3	)	)	PUNCT
aiti-7988	195	4	in	in	ADP
aiti-7988	195	5	eq	eq	ADP
aiti-7988	195	6	.	.	PUNCT
aiti-7988	196	1	(	(	PUNCT
aiti-7988	196	2	19	19	NUM
aiti-7988	196	3	)	)	PUNCT
aiti-7988	196	4	,	,	PUNCT
aiti-7988	196	5	performing	perform	VERB
aiti-7988	196	6	the	the	DET
aiti-7988	196	7	integral	integral	ADJ
aiti-7988	196	8	transformation	transformation	NOUN
aiti-7988	196	9	,	,	PUNCT
aiti-7988	196	10	and	and	CCONJ
aiti-7988	196	11	reorganizing	reorganize	VERB
aiti-7988	196	12	and	and	CCONJ
aiti-7988	196	13	combining	combine	VERB
aiti-7988	196	14	similar	similar	ADJ
aiti-7988	196	15	terms	term	NOUN
aiti-7988	196	16	,	,	PUNCT
aiti-7988	196	17	the	the	DET
aiti-7988	196	18	following	follow	VERB
aiti-7988	196	19	equation	equation	NOUN
aiti-7988	196	20	is	be	AUX
aiti-7988	196	21	yielded	yield	VERB
aiti-7988	196	22	:	:	PUNCT
aiti-7988	196	23	(	(	PUNCT
aiti-7988	196	24	)	)	PUNCT
aiti-7988	196	25	(	(	PUNCT
aiti-7988	196	26	)	)	PUNCT
aiti-7988	196	27	(	(	PUNCT
aiti-7988	196	28	)	)	PUNCT
aiti-7988	196	29	{	{	PUNCT
aiti-7988	196	30	}	}	PUNCT
aiti-7988	196	31	{	{	PUNCT
aiti-7988	196	32	}	}	PUNCT
aiti-7988	196	33	(	(	PUNCT
aiti-7988	196	34	)	)	PUNCT
aiti-7988	196	35	(	(	PUNCT
aiti-7988	196	36	)	)	PUNCT
aiti-7988	196	37	(	(	PUNCT
aiti-7988	196	38	)	)	PUNCT
aiti-7988	196	39	(	(	PUNCT
aiti-7988	196	40	)	)	PUNCT
aiti-7988	196	41	(	(	PUNCT
aiti-7988	196	42	)	)	PUNCT
aiti-7988	196	43	(	(	PUNCT
aiti-7988	196	44	)	)	PUNCT
aiti-7988	196	45	(	(	PUNCT
aiti-7988	196	46	)	)	PUNCT
aiti-7988	196	47	(	(	PUNCT
aiti-7988	196	48	)	)	PUNCT
aiti-7988	196	49	(	(	PUNCT
aiti-7988	196	50	)	)	PUNCT
aiti-7988	196	51	1	1	NUM
aiti-7988	196	52	5	5	NUM
aiti-7988	196	53	5	5	NUM
aiti-7988	196	54	12	12	NUM
aiti-7988	196	55	1	1	NUM
aiti-7988	196	56	2	2	NUM
aiti-7988	196	57	2	2	NUM
aiti-7988	196	58	3	3	NUM
aiti-7988	196	59	3	3	NUM
aiti-7988	196	60	1	1	NUM
aiti-7988	196	61	3	3	NUM
aiti-7988	196	62	3	3	NUM
aiti-7988	196	63	1	1	NUM
aiti-7988	196	64	11	11	NUM
aiti-7988	196	65	3	3	NUM
aiti-7988	196	66	3	3	NUM
aiti-7988	196	67	3	3	NUM
aiti-7988	196	68	3	3	NUM
aiti-7988	196	69	1	1	NUM
aiti-7988	196	70	1	1	NUM
aiti-7988	196	71	3	3	NUM
aiti-7988	196	72	3	3	NUM
aiti-7988	196	73	3	3	NUM
aiti-7988	196	74	3	3	NUM
aiti-7988	196	75	24	24	NUM
aiti-7988	196	76	[	[	PUNCT
aiti-7988	196	77	1	1	NUM
aiti-7988	196	78	1	1	NUM
aiti-7988	196	79	]	]	SYM
aiti-7988	196	80	12	12	NUM
aiti-7988	196	81	24	24	NUM
aiti-7988	196	82	2	2	NUM
aiti-7988	197	1	[	[	X
aiti-7988	197	2	1	1	NUM
aiti-7988	197	3	1	1	NUM
aiti-7988	197	4	]	]	PUNCT
aiti-7988	198	1	[	[	X
aiti-7988	198	2	1	1	NUM
aiti-7988	198	3	1	1	NUM
aiti-7988	198	4	]	]	SYM
aiti-7988	198	5	1	1	NUM
aiti-7988	198	6	[	[	SYM
aiti-7988	198	7	1	1	NUM
aiti-7988	198	8	1	1	NUM
aiti-7988	198	9	]	]	SYM
aiti-7988	198	10	2	2	NUM
aiti-7988	198	11	24	24	NUM
aiti-7988	198	12	242	242	NUM
aiti-7988	198	13	[	[	X
aiti-7988	198	14	1	1	NUM
aiti-7988	198	15	1	1	NUM
aiti-7988	198	16	]	]	PUNCT
aiti-7988	199	1	[	[	X
aiti-7988	199	2	1	1	NUM
aiti-7988	199	3	1	1	NUM
aiti-7988	199	4	]	]	PUNCT
aiti-7988	199	5	[	[	X
aiti-7988	199	6	1	1	NUM
aiti-7988	199	7	1	1	NUM
aiti-7988	199	8	]	]	PUNCT
aiti-7988	199	9	sin	sin	NOUN
aiti-7988	199	10	24	24	NUM
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aiti-7988	217	5	1	1	NUM
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aiti-7988	235	14	(	(	PUNCT
aiti-7988	235	15	)	)	SYM
aiti-7988	235	16	1	1	NUM
aiti-7988	235	17	12	12	NUM
aiti-7988	235	18	1	1	NUM
aiti-7988	235	19	25	25	NUM
aiti-7988	235	20	5	5	NUM
aiti-7988	235	21	3	3	NUM
aiti-7988	235	22	3	3	NUM
aiti-7988	235	23	4	4	NUM
aiti-7988	235	24	24	24	NUM
aiti-7988	235	25	1	1	NUM
aiti-7988	235	26	1	1	NUM
aiti-7988	235	27	[	[	SYM
aiti-7988	235	28	1	1	NUM
aiti-7988	235	29	1	1	NUM
aiti-7988	235	30	]	]	PUNCT
aiti-7988	236	1	[	[	X
aiti-7988	236	2	1	1	NUM
aiti-7988	236	3	1	1	NUM
aiti-7988	236	4	]	]	PUNCT
aiti-7988	236	5	cos	cos	PROPN
aiti-7988	236	6	.1	.1	PROPN
aiti-7988	236	7	n	n	CCONJ
aiti-7988	236	8	n	n	PROPN
aiti-7988	237	1	f	f	NOUN
aiti-7988	237	2	f	f	PROPN
aiti-7988	237	3	g	g	PROPN
aiti-7988	237	4	s	s	PROPN
aiti-7988	237	5	z	z	PROPN
aiti-7988	237	6	s	s	PROPN
aiti-7988	237	7	z	z	NOUN
aiti-7988	237	8	s	s	NOUN
aiti-7988	237	9	f	f	PROPN
aiti-7988	237	10	n	n	PROPN
aiti-7988	237	11	n	n	PROPN
aiti-7988	237	12	a	a	DET
aiti-7988	237	13	s	s	NOUN
aiti-7988	237	14	θ	θ	NOUN
aiti-7988	237	15	π	π	NOUN
aiti-7988	237	16	π	π	X
aiti-7988	238	1	+	+	CCONJ
aiti-7988	238	2	+	+	ADJ
aiti-7988	238	3	∴	∴	NOUN
aiti-7988	238	4	+	+	CCONJ
aiti-7988	238	5	−	−	PROPN
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aiti-7988	239	1	+	+	CCONJ
aiti-7988	239	2	−	−	PROPN
aiti-7988	240	1	+	+	CCONJ
aiti-7988	240	2	+	+	NUM
aiti-7988	240	3	λ	λ	PROPN
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aiti-7988	240	5	−	−	PROPN
aiti-7988	240	6	(	(	PUNCT
aiti-7988	240	7	29	29	NUM
aiti-7988	240	8	)	)	PUNCT
aiti-7988	240	9	additionally	additionally	ADV
aiti-7988	240	10	,	,	PUNCT
aiti-7988	240	11	the	the	DET
aiti-7988	240	12	following	follow	VERB
aiti-7988	240	13	equations	equation	NOUN
aiti-7988	240	14	can	can	AUX
aiti-7988	240	15	be	be	AUX
aiti-7988	240	16	assumed	assume	VERB
aiti-7988	240	17	:	:	PUNCT
aiti-7988	240	18	(	(	PUNCT
aiti-7988	240	19	)	)	PUNCT
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aiti-7988	240	21	)	)	PUNCT
aiti-7988	241	1	1	1	NUM
aiti-7988	241	2	1	1	NUM
aiti-7988	241	3	1	1	NUM
aiti-7988	241	4	1	1	NUM
aiti-7988	241	5	5	5	NUM
aiti-7988	241	6	5	5	NUM
aiti-7988	241	7	3	3	NUM
aiti-7988	241	8	3	3	NUM
aiti-7988	241	9	24	24	NUM
aiti-7988	241	10	1	1	NUM
aiti-7988	241	11	[	[	X
aiti-7988	241	12	1	1	NUM
aiti-7988	241	13	1	1	NUM
aiti-7988	241	14	]	]	PUNCT
aiti-7988	241	15	[	[	X
aiti-7988	241	16	1	1	NUM
aiti-7988	241	17	1	1	NUM
aiti-7988	241	18	]	]	PUNCT
aiti-7988	241	19	f	f	PROPN
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aiti-7988	241	21	n	n	CCONJ
aiti-7988	241	22	n	n	PROPN
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aiti-7988	241	24	n	n	PROPN
aiti-7988	241	25	n	n	PRON
aiti-7988	241	26	ϕ	ϕ	NOUN
aiti-7988	241	27	π	π	X
aiti-7988	241	28	π	π	X
aiti-7988	242	1	+	+	CCONJ
aiti-7988	243	1	+	+	PUNCT
aiti-7988	243	2	=	=	SYM
aiti-7988	244	1	+	+	NUM
aiti-7988	244	2	−	−	PROPN
aiti-7988	245	1	−	−	PROPN
aiti-7988	246	1	+	+	CCONJ
aiti-7988	246	2	−	−	PROPN
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aiti-7988	246	4	30	30	NUM
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aiti-7988	246	7	)	)	PUNCT
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aiti-7988	246	9	)	)	PUNCT
aiti-7988	246	10	22	22	NUM
aiti-7988	246	11	1	1	NUM
aiti-7988	246	12	1	1	NUM
aiti-7988	246	13	5	5	NUM
aiti-7988	246	14	5	5	NUM
aiti-7988	246	15	3	3	NUM
aiti-7988	246	16	3	3	NUM
aiti-7988	246	17	24	24	NUM
aiti-7988	246	18	1	1	NUM
aiti-7988	246	19	[	[	X
aiti-7988	246	20	1	1	NUM
aiti-7988	246	21	1	1	NUM
aiti-7988	246	22	]	]	PUNCT
aiti-7988	247	1	[	[	X
aiti-7988	247	2	1	1	NUM
aiti-7988	247	3	1	1	NUM
aiti-7988	247	4	]	]	PUNCT
aiti-7988	247	5	f	f	PROPN
aiti-7988	247	6	f	f	PROPN
aiti-7988	247	7	n	n	CCONJ
aiti-7988	247	8	n	n	PROPN
aiti-7988	247	9	z	z	PROPN
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aiti-7988	247	12	ϕ	ϕ	NOUN
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aiti-7988	247	15	+	+	CCONJ
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aiti-7988	249	1	+	+	NUM
aiti-7988	249	2	−	−	PROPN
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aiti-7988	251	1	+	+	CCONJ
aiti-7988	251	2	−	−	PROPN
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aiti-7988	251	4	31	31	NUM
aiti-7988	251	5	)	)	PUNCT
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aiti-7988	251	7	)	)	PUNCT
aiti-7988	251	8	(	(	PUNCT
aiti-7988	251	9	)	)	PUNCT
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aiti-7988	251	11	)	)	PUNCT
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aiti-7988	251	13	)	)	PUNCT
aiti-7988	251	14	4	4	NUM
aiti-7988	251	15	1	1	NUM
aiti-7988	251	16	1	1	NUM
aiti-7988	251	17	5	5	NUM
aiti-7988	251	18	5	5	NUM
aiti-7988	251	19	3	3	NUM
aiti-7988	251	20	3	3	NUM
aiti-7988	251	21	2	2	NUM
aiti-7988	251	22	2	2	NUM
aiti-7988	251	23	1	1	NUM
aiti-7988	251	24	1	1	NUM
aiti-7988	251	25	cos	co	NOUN
aiti-7988	251	26	.1	.1	NUM
aiti-7988	251	27	24	24	NUM
aiti-7988	251	28	1	1	NUM
aiti-7988	251	29	[	[	X
aiti-7988	251	30	1	1	NUM
aiti-7988	251	31	1	1	NUM
aiti-7988	251	32	]	]	PUNCT
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aiti-7988	252	2	1	1	NUM
aiti-7988	252	3	1	1	NUM
aiti-7988	252	4	]	]	PUNCT
aiti-7988	252	5	n	n	CCONJ
aiti-7988	252	6	n	n	NOUN
aiti-7988	253	1	f	f	NOUN
aiti-7988	253	2	f	f	PROPN
aiti-7988	253	3	g	g	PROPN
aiti-7988	253	4	f	f	PROPN
aiti-7988	253	5	a	a	DET
aiti-7988	253	6	s	s	NOUN
aiti-7988	253	7	n	n	CCONJ
aiti-7988	253	8	n	n	NOUN
aiti-7988	253	9	s	s	NOUN
aiti-7988	253	10	s	s	NOUN
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aiti-7988	253	13	π	π	NOUN
aiti-7988	253	14	π	π	PROPN
aiti-7988	253	15	ϕ	ϕ	X
aiti-7988	253	16	ϕ	ϕ	PROPN
aiti-7988	253	17	+	+	PROPN
aiti-7988	254	1	+	+	CCONJ
aiti-7988	254	2	−	−	PROPN
aiti-7988	255	1	+	+	CCONJ
aiti-7988	255	2	−	−	PROPN
aiti-7988	255	3	−	−	PROPN
aiti-7988	256	1	+	+	CCONJ
aiti-7988	256	2	−	−	PROPN
aiti-7988	256	3	∴	∴	NOUN
aiti-7988	256	4	λ	λ	NOUN
aiti-7988	256	5	=	=	PUNCT
aiti-7988	257	1	+	+	CCONJ
aiti-7988	257	2	+	+	CCONJ
aiti-7988	257	3	(	(	PUNCT
aiti-7988	257	4	32	32	NUM
aiti-7988	257	5	)	)	PUNCT
aiti-7988	257	6	by	by	ADP
aiti-7988	257	7	applying	apply	VERB
aiti-7988	257	8	the	the	DET
aiti-7988	257	9	fourier	fourier	ADJ
aiti-7988	257	10	-	-	PUNCT
aiti-7988	257	11	laplace	laplace	NOUN
aiti-7988	257	12	inversion	inversion	NOUN
aiti-7988	257	13	,	,	PUNCT
aiti-7988	257	14	the	the	DET
aiti-7988	257	15	spatial	spatial	ADJ
aiti-7988	257	16	displacement	displacement	ADJ
aiti-7988	257	17	time	time	NOUN
aiti-7988	257	18	-	-	PUNCT
aiti-7988	257	19	domain	domain	NOUN
aiti-7988	257	20	response	response	NOUN
aiti-7988	257	21	(	(	PUNCT
aiti-7988	257	22	dynamic	dynamic	ADJ
aiti-7988	257	23	response	response	NOUN
aiti-7988	257	24	!	!	PUNCT
aiti-7988	257	25	)	)	PUNCT
aiti-7988	258	1	for	for	ADP
aiti-7988	258	2	the	the	DET
aiti-7988	258	3	inclined	incline	VERB
aiti-7988	258	4	fixed	fix	VERB
aiti-7988	258	5	supported	support	VERB
aiti-7988	258	6	pipe	pipe	NOUN
aiti-7988	258	7	conveying	conveying	NOUN
aiti-7988	258	8	fluid	fluid	NOUN
aiti-7988	258	9	can	can	AUX
aiti-7988	258	10	be	be	AUX
aiti-7988	258	11	given	give	VERB
aiti-7988	258	12	:	:	PUNCT
aiti-7988	258	13	(	(	PUNCT
aiti-7988	258	14	)	)	PUNCT
aiti-7988	258	15	(	(	PUNCT
aiti-7988	258	16	)	)	PUNCT
aiti-7988	258	17	(	(	PUNCT
aiti-7988	258	18	)	)	PUNCT
aiti-7988	258	19	4	4	NUM
aiti-7988	258	20	4	4	NUM
aiti-7988	258	21	4	4	NUM
aiti-7988	258	22	2	2	NUM
aiti-7988	258	23	2	2	NUM
aiti-7988	258	24	cos	cos	PROPN
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aiti-7988	258	26	,	,	PUNCT
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aiti-7988	258	28	2	2	NUM
aiti-7988	258	29	f	f	NOUN
aiti-7988	258	30	g	g	PROPN
aiti-7988	258	31	t	t	PROPN
aiti-7988	258	32	t	t	PROPN
aiti-7988	258	33	a	a	DET
aiti-7988	258	34	n	n	CCONJ
aiti-7988	258	35	n	n	NUM
aiti-7988	258	36	θ	θ	NOUN
aiti-7988	258	37	φ	φ	NOUN
aiti-7988	259	1	ζ	ζ	NOUN
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aiti-7988	259	4	π	π	NOUN
aiti-7988	259	5	−	−	PUNCT
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aiti-7988	259	7	γ	γ	X
aiti-7988	259	8	−	−	VERB
aiti-7988	259	9			PROPN
aiti-7988	259	10			NOUN
aiti-7988	259	11			VERB
aiti-7988	259	12			PRON
aiti-7988	259	13			PUNCT
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aiti-7988	260	3	)	)	PUNCT
aiti-7988	260	4	(	(	PUNCT
aiti-7988	260	5	)	)	PUNCT
aiti-7988	260	6	(	(	PUNCT
aiti-7988	260	7	)	)	PUNCT
aiti-7988	260	8	(	(	PUNCT
aiti-7988	260	9	)	)	SYM
aiti-7988	260	10	2	2	NUM
aiti-7988	260	11	1	1	NUM
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aiti-7988	260	13	2	2	NUM
aiti-7988	260	14	1	1	NUM
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aiti-7988	260	17	2	2	NUM
aiti-7988	260	18	2	2	NUM
aiti-7988	260	19	1	1	NUM
aiti-7988	260	20	1	1	NUM
aiti-7988	260	21	1	1	NUM
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aiti-7988	260	23	f	f	PROPN
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aiti-7988	262	2	f	f	X
aiti-7988	263	1	f	f	X
aiti-7988	263	2	f	f	X
aiti-7988	264	1	f	f	PROPN
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aiti-7988	267	6	e	e	X
aiti-7988	267	7	α	α	X
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aiti-7988	267	9	α	α	NOUN
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aiti-7988	267	12	α	α	NOUN
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aiti-7988	267	15	α	α	NOUN
aiti-7988	267	16	−	−	NOUN
aiti-7988	267	17	−	−	PROPN
aiti-7988	268	1	=	=	SYM
aiti-7988	269	1	+	+	NUM
aiti-7988	270	1	−	−	PROPN
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aiti-7988	270	3			VERB
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aiti-7988	270	5			ADJ
aiti-7988	270	6			PROPN
aiti-7988	270	7			X
aiti-7988	270	8			X
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aiti-7988	270	11	)	)	SYM
aiti-7988	270	12	2	2	NUM
aiti-7988	270	13	1	1	NUM
aiti-7988	270	14	12	12	NUM
aiti-7988	270	15	1	1	NUM
aiti-7988	270	16	2	2	NUM
aiti-7988	270	17	4	4	NUM
aiti-7988	270	18	f	f	NOUN
aiti-7988	271	1	f	f	X
aiti-7988	272	1	f	f	PROPN
aiti-7988	273	1	f	f	X
aiti-7988	274	1	i	i	PRON
aiti-7988	274	2	ϕ	ϕ	X
aiti-7988	274	3	ϕ	ϕ	X
aiti-7988	274	4	α	α	NOUN
aiti-7988	274	5	ϕ=	ϕ=	PROPN
aiti-7988	275	1	+	+	CCONJ
aiti-7988	275	2	−	−	PROPN
aiti-7988	275	3	(	(	PUNCT
aiti-7988	275	4	35	35	NUM
aiti-7988	275	5	)	)	SYM
aiti-7988	275	6	2	2	NUM
aiti-7988	275	7	1	1	NUM
aiti-7988	275	8	12	12	NUM
aiti-7988	275	9	2	2	NUM
aiti-7988	275	10	2	2	NUM
aiti-7988	275	11	4	4	NUM
aiti-7988	276	1	f	f	NOUN
aiti-7988	276	2	f	f	X
aiti-7988	277	1	f	f	PROPN
aiti-7988	277	2	f	f	X
aiti-7988	278	1	i	i	PRON
aiti-7988	278	2	ϕ	ϕ	PROPN
aiti-7988	278	3	ϕ	ϕ	X
aiti-7988	278	4	α	α	NOUN
aiti-7988	278	5	ϕ=	ϕ=	NOUN
aiti-7988	278	6	−	−	PROPN
aiti-7988	279	1	−	−	PROPN
aiti-7988	280	1	(	(	PUNCT
aiti-7988	280	2	36	36	NUM
aiti-7988	280	3	)	)	PUNCT
aiti-7988	280	4	by	by	ADP
aiti-7988	280	5	isolating	isolate	VERB
aiti-7988	280	6	characteristic	characteristic	ADJ
aiti-7988	280	7	equations	equation	NOUN
aiti-7988	280	8	,	,	PUNCT
aiti-7988	280	9	the	the	DET
aiti-7988	280	10	dimensionless	dimensionless	ADJ
aiti-7988	280	11	fundamental	fundamental	ADJ
aiti-7988	280	12	natural	natural	ADJ
aiti-7988	280	13	frequency	frequency	NOUN
aiti-7988	280	14	(	(	PUNCT
aiti-7988	280	15	ωn	ωn	NUM
aiti-7988	280	16	)	)	PUNCT
aiti-7988	280	17	and	and	CCONJ
aiti-7988	280	18	its	its	PRON
aiti-7988	280	19	complimentary	complimentary	ADJ
aiti-7988	280	20	value	value	NOUN
aiti-7988	280	21	(	(	PUNCT
aiti-7988	280	22	ωm	ωm	X
aiti-7988	280	23	)	)	PUNCT
aiti-7988	280	24	are	be	AUX
aiti-7988	280	25	:	:	PUNCT
aiti-7988	280	26	2	2	NUM
aiti-7988	280	27	2	2	NUM
aiti-7988	280	28	2	2	NUM
aiti-7988	280	29	1	1	NUM
aiti-7988	280	30	1	1	NUM
aiti-7988	280	31	12	12	NUM
aiti-7988	280	32	2	2	NUM
aiti-7988	280	33	2	2	NUM
aiti-7988	280	34	2	2	NUM
aiti-7988	280	35	4	4	NUM
aiti-7988	280	36	4	4	NUM
aiti-7988	280	37	f	f	NOUN
aiti-7988	280	38	f	f	PROPN
aiti-7988	280	39	f	f	PROPN
aiti-7988	281	1	n	n	PROPN
aiti-7988	281	2	f	f	PROPN
aiti-7988	282	1	n	n	PROPN
aiti-7988	282	2	f	f	PROPN
aiti-7988	282	3	ϕ	ϕ	X
aiti-7988	282	4	ϕ	ϕ	PROPN
aiti-7988	282	5	ϕ	ϕ	PROPN
aiti-7988	282	6	ω	ω	PROPN
aiti-7988	282	7	ϕ	ϕ	PROPN
aiti-7988	282	8	ω	ω	PROPN
aiti-7988	282	9	ϕ=	ϕ=	NOUN
aiti-7988	282	10	−	−	NOUN
aiti-7988	282	11	⇒	⇒	NOUN
aiti-7988	282	12	=	=	PUNCT
aiti-7988	283	1	−	−	PROPN
aiti-7988	283	2			PROPN
aiti-7988	283	3			NOUN
aiti-7988	283	4			PROPN
aiti-7988	283	5			PROPN
aiti-7988	283	6			NOUN
aiti-7988	283	7			VERB
aiti-7988	283	8			NOUN
aiti-7988	283	9			PUNCT
aiti-7988	284	1			NOUN
aiti-7988	284	2			PUNCT
aiti-7988	285	1	∓	∓	NOUN
aiti-7988	285	2	(	(	PUNCT
aiti-7988	285	3	37	37	NUM
aiti-7988	285	4	)	)	SYM
aiti-7988	285	5	2	2	NUM
aiti-7988	285	6	m	m	NOUN
aiti-7988	285	7	f	f	NOUN
aiti-7988	285	8	ω	ω	NUM
aiti-7988	285	9	ϕ=	ϕ=	NOUN
aiti-7988	285	10	−	−	PROPN
aiti-7988	285	11	(	(	PUNCT
aiti-7988	285	12	38	38	NUM
aiti-7988	285	13	)	)	PUNCT
aiti-7988	285	14	the	the	DET
aiti-7988	285	15	fundamental	fundamental	ADJ
aiti-7988	285	16	natural	natural	ADJ
aiti-7988	285	17	frequency	frequency	NOUN
aiti-7988	285	18	ωn	ωn	VERB
aiti-7988	285	19	is	be	AUX
aiti-7988	285	20	adopted	adopt	VERB
aiti-7988	285	21	in	in	ADP
aiti-7988	285	22	this	this	DET
aiti-7988	285	23	work	work	NOUN
aiti-7988	285	24	.	.	PUNCT
aiti-7988	286	1	the	the	DET
aiti-7988	286	2	aforementioned	aforementioned	ADJ
aiti-7988	286	3	equations	equation	NOUN
aiti-7988	286	4	are	be	AUX
aiti-7988	286	5	solved	solve	VERB
aiti-7988	286	6	for	for	ADP
aiti-7988	286	7	each	each	DET
aiti-7988	286	8	value	value	NOUN
aiti-7988	286	9	of	of	ADP
aiti-7988	286	10	variables	variable	NOUN
aiti-7988	286	11	by	by	ADP
aiti-7988	286	12	using	use	VERB
aiti-7988	286	13	matlab	matlab	PROPN
aiti-7988	286	14	2019b	2019b	PROPN
aiti-7988	286	15	software	software	NOUN
aiti-7988	286	16	program	program	NOUN
aiti-7988	286	17	to	to	PART
aiti-7988	286	18	determine	determine	VERB
aiti-7988	286	19	the	the	DET
aiti-7988	286	20	fundamental	fundamental	ADJ
aiti-7988	286	21	natural	natural	ADJ
aiti-7988	286	22	frequency	frequency	NOUN
aiti-7988	286	23	of	of	ADP
aiti-7988	286	24	the	the	DET
aiti-7988	286	25	system	system	NOUN
aiti-7988	286	26	.	.	PUNCT
aiti-7988	287	1	the	the	DET
aiti-7988	287	2	simplified	simplified	ADJ
aiti-7988	287	3	flow	flow	NOUN
aiti-7988	287	4	chart	chart	NOUN
aiti-7988	287	5	is	be	AUX
aiti-7988	287	6	illustrated	illustrate	VERB
aiti-7988	287	7	in	in	ADP
aiti-7988	287	8	fig	fig	NOUN
aiti-7988	287	9	.	.	PUNCT
aiti-7988	288	1	4	4	NUM
aiti-7988	288	2	.	.	X
aiti-7988	288	3	48	48	NUM
aiti-7988	288	4	advances	advance	NOUN
aiti-7988	288	5	in	in	ADP
aiti-7988	288	6	technology	technology	NOUN
aiti-7988	288	7	innovation	innovation	NOUN
aiti-7988	288	8	,	,	PUNCT
aiti-7988	288	9	vol	vol	NOUN
aiti-7988	288	10	.	.	PROPN
aiti-7988	288	11	7	7	NUM
aiti-7988	288	12	,	,	PUNCT
aiti-7988	288	13	no	no	INTJ
aiti-7988	288	14	.	.	NOUN
aiti-7988	288	15	1	1	NUM
aiti-7988	288	16	,	,	PUNCT
aiti-7988	288	17	2022	2022	NUM
aiti-7988	288	18	,	,	PUNCT
aiti-7988	288	19	pp	pp	ADJ
aiti-7988	288	20	.	.	PUNCT
aiti-7988	289	1	41	41	NUM
aiti-7988	289	2	-	-	SYM
aiti-7988	289	3	55	55	NUM
aiti-7988	289	4	fig	fig	NOUN
aiti-7988	289	5	.	.	PUNCT
aiti-7988	290	1	4	4	NUM
aiti-7988	290	2	the	the	DET
aiti-7988	290	3	flowchart	flowchart	NOUN
aiti-7988	290	4	for	for	ADP
aiti-7988	290	5	matlab	matlab	PROPN
aiti-7988	290	6	code	code	PROPN
aiti-7988	290	7	4	4	NUM
aiti-7988	290	8	.	.	PUNCT
aiti-7988	290	9	results	result	NOUN
aiti-7988	290	10	and	and	CCONJ
aiti-7988	290	11	discussion	discussion	NOUN
aiti-7988	290	12	4.1	4.1	NUM
aiti-7988	290	13	.	.	PUNCT
aiti-7988	291	1	validation	validation	NOUN
aiti-7988	291	2	of	of	ADP
aiti-7988	291	3	analytical	analytical	ADJ
aiti-7988	291	4	model	model	NOUN
aiti-7988	291	5	to	to	PART
aiti-7988	291	6	validate	validate	VERB
aiti-7988	291	7	the	the	DET
aiti-7988	291	8	analytical	analytical	ADJ
aiti-7988	291	9	calculation	calculation	NOUN
aiti-7988	291	10	method	method	NOUN
aiti-7988	291	11	proposed	propose	VERB
aiti-7988	291	12	in	in	ADP
aiti-7988	291	13	this	this	DET
aiti-7988	291	14	work	work	NOUN
aiti-7988	291	15	,	,	PUNCT
aiti-7988	291	16	the	the	DET
aiti-7988	291	17	fundamental	fundamental	ADJ
aiti-7988	291	18	natural	natural	ADJ
aiti-7988	291	19	frequency	frequency	NOUN
aiti-7988	291	20	is	be	AUX
aiti-7988	291	21	calculated	calculate	VERB
aiti-7988	291	22	at	at	ADP
aiti-7988	291	23	stationary	stationary	ADJ
aiti-7988	291	24	fluid	fluid	NOUN
aiti-7988	291	25	case	case	NOUN
aiti-7988	291	26	(	(	PUNCT
aiti-7988	291	27	u	u	NOUN
aiti-7988	291	28	=	=	NOUN
aiti-7988	291	29	0	0	NUM
aiti-7988	291	30	)	)	PUNCT
aiti-7988	291	31	and	and	CCONJ
aiti-7988	291	32	at	at	ADP
aiti-7988	291	33	fluid	fluid	ADJ
aiti-7988	291	34	velocities	velocity	NOUN
aiti-7988	291	35	u	u	NOUN
aiti-7988	291	36	=	=	NOUN
aiti-7988	291	37	0.5	0.5	NUM
aiti-7988	291	38	,	,	PUNCT
aiti-7988	291	39	u	u	NOUN
aiti-7988	291	40	=	=	PROPN
aiti-7988	291	41	1	1	NUM
aiti-7988	291	42	,	,	PUNCT
aiti-7988	291	43	and	and	CCONJ
aiti-7988	291	44	u	u	X
aiti-7988	291	45	=	=	NOUN
aiti-7988	291	46	1.5	1.5	NUM
aiti-7988	291	47	,	,	PUNCT
aiti-7988	291	48	respectively	respectively	ADV
aiti-7988	291	49	,	,	PUNCT
aiti-7988	291	50	and	and	CCONJ
aiti-7988	291	51	compared	compare	VERB
aiti-7988	291	52	with	with	ADP
aiti-7988	291	53	those	those	PRON
aiti-7988	291	54	in	in	ADP
aiti-7988	291	55	the	the	DET
aiti-7988	291	56	work	work	NOUN
aiti-7988	291	57	of	of	ADP
aiti-7988	291	58	ni	ni	PROPN
aiti-7988	291	59	et	et	PROPN
aiti-7988	291	60	al	al	PROPN
aiti-7988	291	61	.	.	PUNCT
aiti-7988	292	1	[	[	X
aiti-7988	292	2	26	26	NUM
aiti-7988	292	3	]	]	PUNCT
aiti-7988	292	4	and	and	CCONJ
aiti-7988	292	5	liang	liang	PROPN
aiti-7988	292	6	et	et	PROPN
aiti-7988	292	7	al	al	PROPN
aiti-7988	292	8	.	.	PUNCT
aiti-7988	293	1	[	[	X
aiti-7988	293	2	27	27	NUM
aiti-7988	293	3	]	]	PUNCT
aiti-7988	293	4	.	.	PUNCT
aiti-7988	293	5	table	table	NOUN
aiti-7988	293	6	2	2	NUM
aiti-7988	293	7	presents	present	VERB
aiti-7988	293	8	the	the	DET
aiti-7988	293	9	geometry	geometry	NOUN
aiti-7988	293	10	and	and	CCONJ
aiti-7988	293	11	material	material	NOUN
aiti-7988	293	12	properties	property	NOUN
aiti-7988	293	13	used	use	VERB
aiti-7988	293	14	in	in	ADP
aiti-7988	293	15	this	this	DET
aiti-7988	293	16	comparison	comparison	NOUN
aiti-7988	293	17	,	,	PUNCT
aiti-7988	293	18	and	and	CCONJ
aiti-7988	293	19	lists	list	VERB
aiti-7988	293	20	the	the	DET
aiti-7988	293	21	obtained	obtain	VERB
aiti-7988	293	22	results	result	NOUN
aiti-7988	293	23	.	.	PUNCT
aiti-7988	294	1	it	it	PRON
aiti-7988	294	2	is	be	AUX
aiti-7988	294	3	clear	clear	ADJ
aiti-7988	294	4	from	from	ADP
aiti-7988	294	5	table	table	NOUN
aiti-7988	294	6	3	3	NUM
aiti-7988	294	7	that	that	SCONJ
aiti-7988	294	8	the	the	DET
aiti-7988	294	9	relative	relative	ADJ
aiti-7988	294	10	errors	error	NOUN
aiti-7988	294	11	between	between	ADP
aiti-7988	294	12	the	the	DET
aiti-7988	294	13	results	result	NOUN
aiti-7988	294	14	in	in	ADP
aiti-7988	294	15	current	current	ADJ
aiti-7988	294	16	study	study	NOUN
aiti-7988	294	17	and	and	CCONJ
aiti-7988	294	18	those	those	PRON
aiti-7988	294	19	in	in	ADP
aiti-7988	294	20	refs	ref	NOUN
aiti-7988	294	21	.	.	PUNCT
aiti-7988	295	1	[	[	X
aiti-7988	295	2	26	26	NUM
aiti-7988	295	3	-	-	SYM
aiti-7988	295	4	27	27	NUM
aiti-7988	295	5	]	]	PUNCT
aiti-7988	295	6	are	be	AUX
aiti-7988	295	7	less	less	ADJ
aiti-7988	295	8	than	than	ADP
aiti-7988	295	9	2.46	2.46	NUM
aiti-7988	295	10	%	%	NOUN
aiti-7988	295	11	.	.	PUNCT
aiti-7988	296	1	these	these	DET
aiti-7988	296	2	little	little	ADJ
aiti-7988	296	3	differences	difference	NOUN
aiti-7988	296	4	may	may	AUX
aiti-7988	296	5	be	be	AUX
aiti-7988	296	6	attributed	attribute	VERB
aiti-7988	296	7	to	to	ADP
aiti-7988	296	8	the	the	DET
aiti-7988	296	9	using	using	NOUN
aiti-7988	296	10	of	of	ADP
aiti-7988	296	11	different	different	ADJ
aiti-7988	296	12	models	model	NOUN
aiti-7988	296	13	in	in	ADP
aiti-7988	296	14	the	the	DET
aiti-7988	296	15	two	two	NUM
aiti-7988	296	16	references	reference	NOUN
aiti-7988	296	17	.	.	PUNCT
aiti-7988	297	1	in	in	ADP
aiti-7988	297	2	refs	ref	NOUN
aiti-7988	297	3	.	.	PUNCT
aiti-7988	298	1	[	[	X
aiti-7988	298	2	26	26	NUM
aiti-7988	298	3	-	-	SYM
aiti-7988	298	4	27	27	NUM
aiti-7988	298	5	]	]	PUNCT
aiti-7988	298	6	,	,	PUNCT
aiti-7988	298	7	the	the	DET
aiti-7988	298	8	pipe	pipe	NOUN
aiti-7988	298	9	is	be	AUX
aiti-7988	298	10	modeled	model	VERB
aiti-7988	298	11	according	accord	VERB
aiti-7988	298	12	to	to	ADP
aiti-7988	298	13	timoshenko	timoshenko	NOUN
aiti-7988	298	14	theory	theory	NOUN
aiti-7988	298	15	;	;	PUNCT
aiti-7988	298	16	in	in	ADP
aiti-7988	298	17	the	the	DET
aiti-7988	298	18	current	current	ADJ
aiti-7988	298	19	work	work	NOUN
aiti-7988	298	20	the	the	DET
aiti-7988	298	21	euler	euler	NOUN
aiti-7988	298	22	-	-	PUNCT
aiti-7988	298	23	bernoulli	bernoulli	PROPN
aiti-7988	298	24	beam	beam	NOUN
aiti-7988	298	25	is	be	AUX
aiti-7988	298	26	adopted	adopt	VERB
aiti-7988	298	27	.	.	PUNCT
aiti-7988	299	1	it	it	PRON
aiti-7988	299	2	can	can	AUX
aiti-7988	299	3	be	be	AUX
aiti-7988	299	4	concluded	conclude	VERB
aiti-7988	299	5	from	from	ADP
aiti-7988	299	6	this	this	DET
aiti-7988	299	7	comparison	comparison	NOUN
aiti-7988	299	8	that	that	SCONJ
aiti-7988	299	9	the	the	DET
aiti-7988	299	10	applied	apply	VERB
aiti-7988	299	11	integral	integral	ADJ
aiti-7988	299	12	transform	transform	NOUN
aiti-7988	299	13	method	method	NOUN
aiti-7988	299	14	(	(	PUNCT
aiti-7988	299	15	via	via	ADP
aiti-7988	299	16	the	the	DET
aiti-7988	299	17	combination	combination	NOUN
aiti-7988	299	18	of	of	ADP
aiti-7988	299	19	the	the	DET
aiti-7988	299	20	finite	finite	ADJ
aiti-7988	299	21	fourier	fourier	NOUN
aiti-7988	299	22	sine	sine	NOUN
aiti-7988	299	23	transform	transform	VERB
aiti-7988	299	24	and	and	CCONJ
aiti-7988	299	25	laplace	laplace	NOUN
aiti-7988	299	26	transform	transform	NOUN
aiti-7988	299	27	)	)	PUNCT
aiti-7988	299	28	gives	give	VERB
aiti-7988	299	29	quite	quite	ADV
aiti-7988	299	30	reliable	reliable	ADJ
aiti-7988	299	31	results	result	NOUN
aiti-7988	299	32	provided	provide	VERB
aiti-7988	299	33	that	that	SCONJ
aiti-7988	299	34	the	the	DET
aiti-7988	299	35	fluid	fluid	ADJ
aiti-7988	299	36	flow	flow	NOUN
aiti-7988	299	37	velocity	velocity	NOUN
aiti-7988	299	38	is	be	AUX
aiti-7988	299	39	moderate	moderate	ADJ
aiti-7988	299	40	.	.	PUNCT
aiti-7988	300	1	table	table	NOUN
aiti-7988	300	2	2	2	NUM
aiti-7988	300	3	parameters	parameter	NOUN
aiti-7988	300	4	of	of	ADP
aiti-7988	300	5	pipe	pipe	NOUN
aiti-7988	300	6	and	and	CCONJ
aiti-7988	300	7	fluid	fluid	ADJ
aiti-7988	300	8	young	young	ADJ
aiti-7988	300	9	’s	’s	PART
aiti-7988	300	10	modulus	modulus	ADJ
aiti-7988	300	11	pipe	pipe	NOUN
aiti-7988	300	12	size	size	NOUN
aiti-7988	300	13	pipe	pipe	NOUN
aiti-7988	300	14	length	length	NOUN
aiti-7988	300	15	pipe	pipe	NOUN
aiti-7988	300	16	density	density	NOUN
aiti-7988	300	17	fluid	fluid	NOUN
aiti-7988	300	18	density	density	NOUN
aiti-7988	300	19	210	210	NUM
aiti-7988	300	20	gpa	gpa	NOUN
aiti-7988	300	21	do	do	VERB
aiti-7988	300	22	=	=	NOUN
aiti-7988	300	23	324	324	NUM
aiti-7988	300	24	mm	mm	NUM
aiti-7988	300	25	32	32	NUM
aiti-7988	300	26	m	m	PROPN
aiti-7988	300	27	8200	8200	NUM
aiti-7988	300	28	kg	kg	NOUN
aiti-7988	300	29	/	/	SYM
aiti-7988	300	30	m	m	PROPN
aiti-7988	300	31	3	3	NUM
aiti-7988	300	32	908.2	908.2	NUM
aiti-7988	300	33	kg	kg	NOUN
aiti-7988	300	34	/	/	SYM
aiti-7988	300	35	m	m	PROPN
aiti-7988	300	36	3	3	NUM
aiti-7988	300	37	di	di	NOUN
aiti-7988	300	38	=	=	SYM
aiti-7988	300	39	292	292	NUM
aiti-7988	300	40	mm	mm	NOUN
aiti-7988	300	41	table	table	NOUN
aiti-7988	300	42	3	3	NUM
aiti-7988	300	43	comparison	comparison	NOUN
aiti-7988	300	44	of	of	ADP
aiti-7988	300	45	dimensionless	dimensionless	ADJ
aiti-7988	300	46	natural	natural	ADJ
aiti-7988	300	47	frequency	frequency	NOUN
aiti-7988	300	48	of	of	ADP
aiti-7988	300	49	the	the	DET
aiti-7988	300	50	fixed	fix	VERB
aiti-7988	300	51	supported	support	VERB
aiti-7988	300	52	pipe	pipe	NOUN
aiti-7988	300	53	with	with	ADP
aiti-7988	300	54	different	different	ADJ
aiti-7988	300	55	fluid	fluid	ADJ
aiti-7988	300	56	velocities	velocity	NOUN
aiti-7988	300	57	frequency	frequency	NOUN
aiti-7988	300	58	fluid	fluid	ADJ
aiti-7988	300	59	velocity	velocity	NOUN
aiti-7988	300	60	current	current	ADJ
aiti-7988	300	61	value	value	NOUN
aiti-7988	300	62	ref	ref	NOUN
aiti-7988	300	63	.	.	PUNCT
aiti-7988	301	1	[	[	X
aiti-7988	301	2	26	26	NUM
aiti-7988	301	3	]	]	PUNCT
aiti-7988	301	4	relative	relative	ADJ
aiti-7988	301	5	error	error	NOUN
aiti-7988	301	6	%	%	NOUN
aiti-7988	301	7	ref	ref	NOUN
aiti-7988	301	8	.	.	PUNCT
aiti-7988	302	1	[	[	X
aiti-7988	302	2	27	27	NUM
aiti-7988	302	3	]	]	PUNCT
aiti-7988	302	4	relative	relative	ADJ
aiti-7988	302	5	error	error	NOUN
aiti-7988	302	6	%	%	NOUN
aiti-7988	302	7	ωn	ωn	NOUN
aiti-7988	302	8	ωn	ωn	PROPN
aiti-7988	302	9	ωn	ωn	PROPN
aiti-7988	302	10	u	u	NOUN
aiti-7988	302	11	=	=	NOUN
aiti-7988	302	12	0	0	PROPN
aiti-7988	302	13	22.3087	22.3087	NUM
aiti-7988	302	14	22.2597	22.2597	NUM
aiti-7988	302	15	0.22	0.22	NUM
aiti-7988	302	16	22.42	22.42	NUM
aiti-7988	302	17	0.49	0.49	NUM
aiti-7988	302	18	u	u	NOUN
aiti-7988	302	19	=	=	NOUN
aiti-7988	302	20	0.5	0.5	NUM
aiti-7988	302	21	22.2534	22.2534	NUM
aiti-7988	302	22	22.0910	22.0910	NUM
aiti-7988	302	23	0.73	0.73	NUM
aiti-7988	302	24	22.27	22.27	NUM
aiti-7988	302	25	0.07	0.07	NUM
aiti-7988	302	26	u	u	NOUN
aiti-7988	302	27	=	=	NOUN
aiti-7988	302	28	1	1	NUM
aiti-7988	302	29	22.0864	22.0864	NUM
aiti-7988	302	30	21.9224	21.9224	NUM
aiti-7988	302	31	0.74	0.74	NUM
aiti-7988	302	32	22.11	22.11	NUM
aiti-7988	302	33	0.10	0.10	NUM
aiti-7988	302	34	u	u	NOUN
aiti-7988	302	35	=	=	PROPN
aiti-7988	302	36	1.5	1.5	NUM
aiti-7988	302	37	21.8053	21.8053	NUM
aiti-7988	302	38	21.4165	21.4165	NUM
aiti-7988	302	39	1.81	1.81	NUM
aiti-7988	302	40	21.28	21.28	NUM
aiti-7988	302	41	2.46	2.46	NUM
aiti-7988	302	42	4.2	4.2	NUM
aiti-7988	302	43	.	.	PUNCT
aiti-7988	302	44	natural	natural	ADJ
aiti-7988	302	45	frequency	frequency	NOUN
aiti-7988	302	46	in	in	ADP
aiti-7988	302	47	the	the	DET
aiti-7988	302	48	current	current	ADJ
aiti-7988	302	49	study	study	NOUN
aiti-7988	302	50	,	,	PUNCT
aiti-7988	302	51	the	the	DET
aiti-7988	302	52	natural	natural	ADJ
aiti-7988	302	53	frequency	frequency	NOUN
aiti-7988	302	54	and	and	CCONJ
aiti-7988	302	55	stability	stability	NOUN
aiti-7988	302	56	of	of	ADP
aiti-7988	302	57	an	an	DET
aiti-7988	302	58	elastic	elastic	ADJ
aiti-7988	302	59	,	,	PUNCT
aiti-7988	302	60	inclined	inclined	ADJ
aiti-7988	302	61	,	,	PUNCT
aiti-7988	302	62	and	and	CCONJ
aiti-7988	302	63	doubly	doubly	ADV
aiti-7988	302	64	fixed	fix	VERB
aiti-7988	302	65	supported	support	VERB
aiti-7988	302	66	pipe	pipe	NOUN
aiti-7988	302	67	conveying	convey	VERB
aiti-7988	302	68	a	a	DET
aiti-7988	302	69	newtonian	newtonian	ADJ
aiti-7988	302	70	and	and	CCONJ
aiti-7988	302	71	incompressible	incompressible	ADJ
aiti-7988	302	72	fluid	fluid	NOUN
aiti-7988	302	73	at	at	ADP
aiti-7988	302	74	different	different	ADJ
aiti-7988	302	75	temperature	temperature	NOUN
aiti-7988	302	76	are	be	AUX
aiti-7988	302	77	investigated	investigate	VERB
aiti-7988	302	78	.	.	PUNCT
aiti-7988	303	1	the	the	DET
aiti-7988	303	2	natural	natural	ADJ
aiti-7988	303	3	frequencies	frequency	NOUN
aiti-7988	303	4	of	of	ADP
aiti-7988	303	5	the	the	DET
aiti-7988	303	6	pipe	pipe	NOUN
aiti-7988	303	7	are	be	AUX
aiti-7988	303	8	analytically	analytically	ADV
aiti-7988	303	9	calculated	calculate	VERB
aiti-7988	303	10	based	base	VERB
aiti-7988	303	11	on	on	ADP
aiti-7988	303	12	eq	eq	ADP
aiti-7988	303	13	.	.	PUNCT
aiti-7988	304	1	(	(	PUNCT
aiti-7988	304	2	37	37	NUM
aiti-7988	304	3	)	)	PUNCT
aiti-7988	304	4	.	.	PUNCT
aiti-7988	305	1	the	the	DET
aiti-7988	305	2	values	value	NOUN
aiti-7988	305	3	of	of	ADP
aiti-7988	305	4	the	the	DET
aiti-7988	305	5	system	system	NOUN
aiti-7988	305	6	parameters	parameter	NOUN
aiti-7988	305	7	used	use	VERB
aiti-7988	305	8	to	to	PART
aiti-7988	305	9	obtain	obtain	VERB
aiti-7988	305	10	the	the	DET
aiti-7988	305	11	results	result	NOUN
aiti-7988	305	12	are	be	AUX
aiti-7988	305	13	listed	list	VERB
aiti-7988	305	14	in	in	ADP
aiti-7988	305	15	table	table	NOUN
aiti-7988	305	16	1	1	NUM
aiti-7988	305	17	.	.	PUNCT
aiti-7988	305	18	to	to	PART
aiti-7988	305	19	connect	connect	VERB
aiti-7988	305	20	the	the	DET
aiti-7988	305	21	subcritical	subcritical	ADJ
aiti-7988	305	22	,	,	PUNCT
aiti-7988	305	23	critical	critical	ADJ
aiti-7988	305	24	,	,	PUNCT
aiti-7988	305	25	and	and	CCONJ
aiti-7988	305	26	post	post	ADJ
aiti-7988	305	27	-	-	ADJ
aiti-7988	305	28	critical	critical	ADJ
aiti-7988	305	29	vibratory	vibratory	NOUN
aiti-7988	305	30	behaviors	behavior	NOUN
aiti-7988	305	31	,	,	PUNCT
aiti-7988	305	32	the	the	DET
aiti-7988	305	33	continuity	continuity	NOUN
aiti-7988	305	34	profile	profile	NOUN
aiti-7988	305	35	of	of	ADP
aiti-7988	305	36	the	the	DET
aiti-7988	305	37	real	real	ADJ
aiti-7988	305	38	and	and	CCONJ
aiti-7988	305	39	imaginary	imaginary	ADJ
aiti-7988	305	40	components	component	NOUN
aiti-7988	305	41	of	of	ADP
aiti-7988	305	42	pipe	pipe	NOUN
aiti-7988	305	43	-	-	PUNCT
aiti-7988	305	44	fluid	fluid	NOUN
aiti-7988	305	45	system	system	NOUN
aiti-7988	305	46	’s	’s	PART
aiti-7988	305	47	natural	natural	ADJ
aiti-7988	305	48	frequencies	frequency	NOUN
aiti-7988	305	49	(	(	PUNCT
aiti-7988	305	50	instead	instead	ADV
aiti-7988	305	51	of	of	ADP
aiti-7988	305	52	separated	separate	VERB
aiti-7988	305	53	profile	profile	NOUN
aiti-7988	305	54	as	as	SCONJ
aiti-7988	305	55	widely	widely	ADV
aiti-7988	305	56	observed	observe	VERB
aiti-7988	305	57	in	in	ADP
aiti-7988	305	58	the	the	DET
aiti-7988	305	59	literature	literature	NOUN
aiti-7988	305	60	)	)	PUNCT
aiti-7988	305	61	is	be	AUX
aiti-7988	305	62	adopted	adopt	VERB
aiti-7988	305	63	in	in	ADP
aiti-7988	305	64	this	this	DET
aiti-7988	305	65	study	study	NOUN
aiti-7988	305	66	by	by	ADP
aiti-7988	305	67	plotting	plot	VERB
aiti-7988	305	68	the	the	DET
aiti-7988	305	69	natural	natural	ADJ
aiti-7988	305	70	frequencies	frequency	NOUN
aiti-7988	305	71	in	in	ADP
aiti-7988	305	72	absolute	absolute	ADJ
aiti-7988	305	73	values	value	NOUN
aiti-7988	305	74	against	against	ADP
aiti-7988	305	75	the	the	DET
aiti-7988	305	76	internal	internal	ADJ
aiti-7988	305	77	flow	flow	NOUN
aiti-7988	305	78	velocity	velocity	NOUN
aiti-7988	305	79	.	.	PUNCT
aiti-7988	306	1	start	start	VERB
aiti-7988	306	2	input	input	NOUN
aiti-7988	306	3	constants	constant	NOUN
aiti-7988	306	4	g	g	NOUN
aiti-7988	306	5	,	,	PUNCT
aiti-7988	306	6	ρf	ρf	PROPN
aiti-7988	306	7	,	,	PUNCT
aiti-7988	306	8	ρp	ρp	NOUN
aiti-7988	306	9	,	,	PUNCT
aiti-7988	306	10	di	di	NOUN
aiti-7988	306	11	,	,	PUNCT
aiti-7988	306	12	do	do	AUX
aiti-7988	306	13	,	,	PUNCT
aiti-7988	306	14	ti	ti	NOUN
aiti-7988	306	15	,	,	PUNCT
aiti-7988	306	16	and	and	CCONJ
aiti-7988	306	17	α	α	PRON
aiti-7988	306	18	define	define	VERB
aiti-7988	306	19	variables	variable	NOUN
aiti-7988	306	20	v	v	NOUN
aiti-7988	306	21	,	,	PUNCT
aiti-7988	306	22	l	l	NOUN
aiti-7988	306	23	/	/	SYM
aiti-7988	306	24	do	do	AUX
aiti-7988	306	25	,	,	PUNCT
aiti-7988	306	26	θ	θ	PROPN
aiti-7988	306	27	,	,	PUNCT
aiti-7988	306	28	(	(	PUNCT
aiti-7988	306	29	tpt)x	tpt)x	PROPN
aiti-7988	306	30	,	,	PUNCT
aiti-7988	306	31	and	and	CCONJ
aiti-7988	306	32	t	t	PROPN
aiti-7988	306	33	calculate	calculate	VERB
aiti-7988	306	34	the	the	DET
aiti-7988	306	35	parameters	parameter	NOUN
aiti-7988	306	36	a	a	PRON
aiti-7988	306	37	,	,	PUNCT
aiti-7988	306	38	ap	ap	PROPN
aiti-7988	306	39	,	,	PUNCT
aiti-7988	306	40	mf	mf	PROPN
aiti-7988	306	41	,	,	PUNCT
aiti-7988	306	42	mp	mp	PROPN
aiti-7988	306	43	,	,	PUNCT
aiti-7988	306	44	and	and	CCONJ
aiti-7988	306	45	i	i	PRON
aiti-7988	306	46	define	define	VERB
aiti-7988	306	47	the	the	DET
aiti-7988	306	48	parameters	parameter	NOUN
aiti-7988	306	49	e	e	NOUN
aiti-7988	306	50	,	,	PUNCT
aiti-7988	306	51	n	n	CCONJ
aiti-7988	306	52	,	,	PUNCT
aiti-7988	306	53	a4	a4	NOUN
aiti-7988	306	54	,	,	PUNCT
aiti-7988	306	55	and	and	CCONJ
aiti-7988	306	56	n	n	PRON
aiti-7988	306	57	calculate	calculate	VERB
aiti-7988	306	58	the	the	DET
aiti-7988	306	59	dimensionless	dimensionless	NOUN
aiti-7988	306	60	parameters	parameter	NOUN
aiti-7988	306	61	β	β	X
aiti-7988	306	62	,	,	PUNCT
aiti-7988	306	63	g	g	PROPN
aiti-7988	306	64	,	,	PUNCT
aiti-7988	306	65	"	"	PUNCT
aiti-7988	306	66	#	#	NOUN
aiti-7988	306	67	,	,	PUNCT
aiti-7988	306	68	and	and	CCONJ
aiti-7988	306	69	�	�	NOUN
aiti-7988	306	70	̅	̅	NOUN
aiti-7988	306	71	set	set	VERB
aiti-7988	306	72	the	the	DET
aiti-7988	306	73	interval	interval	NOUN
aiti-7988	306	74	of	of	ADP
aiti-7988	306	75	ζ	ζ	NOUN
aiti-7988	306	76	find	find	VERB
aiti-7988	306	77	the	the	DET
aiti-7988	306	78	terms	term	NOUN
aiti-7988	306	79	$	$	SYM
aiti-7988	306	80	%	%	NOUN
aiti-7988	306	81	,	,	PUNCT
aiti-7988	306	82	$	$	SYM
aiti-7988	306	83	%	%	NOUN
aiti-7988	306	84	&	&	CCONJ
aiti-7988	306	85	,	,	PUNCT
aiti-7988	306	86	!	!	PUNCT
aiti-7988	307	1	%	%	INTJ
aiti-7988	307	2	,	,	PUNCT
aiti-7988	307	3	and	and	CCONJ
aiti-7988	307	4	!	!	PUNCT
aiti-7988	308	1	%	%	NOUN
aiti-7988	309	1	&	&	CCONJ
aiti-7988	309	2	find	find	VERB
aiti-7988	309	3	the	the	DET
aiti-7988	309	4	natural	natural	ADJ
aiti-7988	309	5	frequency	frequency	NOUN
aiti-7988	309	6	'	'	PUNCT
aiti-7988	309	7	(	(	PUNCT
aiti-7988	309	8	plot	plot	VERB
aiti-7988	309	9	the	the	DET
aiti-7988	309	10	results	result	NOUN
aiti-7988	309	11	print	print	VERB
aiti-7988	309	12	output	output	NOUN
aiti-7988	309	13	end	end	VERB
aiti-7988	309	14	49	49	NUM
aiti-7988	309	15	advances	advance	NOUN
aiti-7988	309	16	in	in	ADP
aiti-7988	309	17	technology	technology	NOUN
aiti-7988	309	18	innovation	innovation	NOUN
aiti-7988	309	19	,	,	PUNCT
aiti-7988	309	20	vol	vol	NOUN
aiti-7988	309	21	.	.	PROPN
aiti-7988	310	1	7	7	NUM
aiti-7988	310	2	,	,	PUNCT
aiti-7988	310	3	no	no	INTJ
aiti-7988	310	4	.	.	NOUN
aiti-7988	310	5	1	1	NUM
aiti-7988	310	6	,	,	PUNCT
aiti-7988	310	7	2022	2022	NUM
aiti-7988	310	8	,	,	PUNCT
aiti-7988	310	9	pp	pp	ADJ
aiti-7988	310	10	.	.	PUNCT
aiti-7988	311	1	41	41	NUM
aiti-7988	311	2	-	-	SYM
aiti-7988	311	3	55	55	NUM
aiti-7988	311	4	the	the	DET
aiti-7988	311	5	natural	natural	ADJ
aiti-7988	311	6	frequency	frequency	NOUN
aiti-7988	311	7	of	of	ADP
aiti-7988	311	8	the	the	DET
aiti-7988	311	9	pipe	pipe	NOUN
aiti-7988	311	10	-	-	PUNCT
aiti-7988	311	11	fluid	fluid	NOUN
aiti-7988	311	12	system	system	NOUN
aiti-7988	311	13	is	be	AUX
aiti-7988	311	14	demonstrated	demonstrate	VERB
aiti-7988	311	15	in	in	ADP
aiti-7988	311	16	figs	fig	NOUN
aiti-7988	311	17	.	.	PUNCT
aiti-7988	312	1	5	5	NUM
aiti-7988	312	2	-	-	SYM
aiti-7988	312	3	9	9	NUM
aiti-7988	312	4	.	.	PUNCT
aiti-7988	313	1	two	two	NUM
aiti-7988	313	2	zones	zone	NOUN
aiti-7988	313	3	are	be	AUX
aiti-7988	313	4	identified	identify	VERB
aiti-7988	313	5	by	by	ADP
aiti-7988	313	6	observing	observe	VERB
aiti-7988	313	7	the	the	DET
aiti-7988	313	8	profile	profile	NOUN
aiti-7988	313	9	of	of	ADP
aiti-7988	313	10	fundamental	fundamental	ADJ
aiti-7988	313	11	natural	natural	ADJ
aiti-7988	313	12	frequency	frequency	NOUN
aiti-7988	313	13	with	with	ADP
aiti-7988	313	14	respect	respect	NOUN
aiti-7988	313	15	to	to	ADP
aiti-7988	313	16	the	the	DET
aiti-7988	313	17	influence	influence	NOUN
aiti-7988	313	18	of	of	ADP
aiti-7988	313	19	flow	flow	NOUN
aiti-7988	313	20	speed	speed	NOUN
aiti-7988	313	21	in	in	ADP
aiti-7988	313	22	figs	fig	NOUN
aiti-7988	313	23	.	.	PUNCT
aiti-7988	314	1	5	5	NUM
aiti-7988	314	2	and	and	CCONJ
aiti-7988	314	3	8	8	NUM
aiti-7988	314	4	;	;	PUNCT
aiti-7988	314	5	where	where	SCONJ
aiti-7988	314	6	the	the	DET
aiti-7988	314	7	two	two	NUM
aiti-7988	314	8	zones	zone	NOUN
aiti-7988	314	9	illustrate	illustrate	VERB
aiti-7988	314	10	the	the	DET
aiti-7988	314	11	divergence	divergence	NOUN
aiti-7988	314	12	case	case	NOUN
aiti-7988	314	13	when	when	SCONJ
aiti-7988	314	14	the	the	DET
aiti-7988	314	15	flow	flow	NOUN
aiti-7988	314	16	is	be	AUX
aiti-7988	314	17	lower	low	ADJ
aiti-7988	314	18	and	and	CCONJ
aiti-7988	314	19	higher	high	ADJ
aiti-7988	314	20	than	than	ADP
aiti-7988	314	21	the	the	DET
aiti-7988	314	22	critical	critical	ADJ
aiti-7988	314	23	points	point	NOUN
aiti-7988	314	24	of	of	ADP
aiti-7988	314	25	flow	flow	NOUN
aiti-7988	314	26	.	.	PUNCT
aiti-7988	315	1	in	in	ADP
aiti-7988	315	2	general	general	ADJ
aiti-7988	315	3	,	,	PUNCT
aiti-7988	315	4	the	the	DET
aiti-7988	315	5	results	result	NOUN
aiti-7988	315	6	show	show	VERB
aiti-7988	315	7	that	that	SCONJ
aiti-7988	315	8	the	the	DET
aiti-7988	315	9	fundamental	fundamental	ADJ
aiti-7988	315	10	natural	natural	ADJ
aiti-7988	315	11	frequency	frequency	NOUN
aiti-7988	315	12	of	of	ADP
aiti-7988	315	13	the	the	DET
aiti-7988	315	14	system	system	NOUN
aiti-7988	315	15	is	be	AUX
aiti-7988	315	16	affected	affect	VERB
aiti-7988	315	17	by	by	ADP
aiti-7988	315	18	factors	factor	NOUN
aiti-7988	315	19	such	such	ADJ
aiti-7988	315	20	as	as	ADP
aiti-7988	315	21	fluid	fluid	ADJ
aiti-7988	315	22	velocity	velocity	NOUN
aiti-7988	315	23	,	,	PUNCT
aiti-7988	315	24	and	and	CCONJ
aiti-7988	315	25	tends	tend	VERB
aiti-7988	315	26	to	to	PART
aiti-7988	315	27	reduce	reduce	VERB
aiti-7988	315	28	as	as	ADP
aiti-7988	315	29	the	the	DET
aiti-7988	315	30	velocity	velocity	NOUN
aiti-7988	315	31	of	of	ADP
aiti-7988	315	32	fluid	fluid	NOUN
aiti-7988	315	33	flowing	flow	VERB
aiti-7988	315	34	within	within	ADP
aiti-7988	315	35	the	the	DET
aiti-7988	315	36	pipe	pipe	NOUN
aiti-7988	315	37	increases	increase	NOUN
aiti-7988	315	38	.	.	PUNCT
aiti-7988	316	1	with	with	ADP
aiti-7988	316	2	the	the	DET
aiti-7988	316	3	increasing	increase	VERB
aiti-7988	316	4	fluid	fluid	ADJ
aiti-7988	316	5	velocity	velocity	NOUN
aiti-7988	316	6	,	,	PUNCT
aiti-7988	316	7	the	the	DET
aiti-7988	316	8	fundamental	fundamental	ADJ
aiti-7988	316	9	natural	natural	ADJ
aiti-7988	316	10	frequency	frequency	NOUN
aiti-7988	316	11	of	of	ADP
aiti-7988	316	12	the	the	DET
aiti-7988	316	13	pipe	pipe	NOUN
aiti-7988	316	14	vanishes	vanish	VERB
aiti-7988	316	15	,	,	PUNCT
aiti-7988	316	16	and	and	CCONJ
aiti-7988	316	17	then	then	ADV
aiti-7988	316	18	the	the	DET
aiti-7988	316	19	divergence	divergence	NOUN
aiti-7988	316	20	instability	instability	NOUN
aiti-7988	316	21	happens	happen	VERB
aiti-7988	316	22	.	.	PUNCT
aiti-7988	317	1	the	the	DET
aiti-7988	317	2	corresponding	corresponding	ADJ
aiti-7988	317	3	fluid	fluid	ADJ
aiti-7988	317	4	velocity	velocity	NOUN
aiti-7988	317	5	,	,	PUNCT
aiti-7988	317	6	at	at	ADP
aiti-7988	317	7	which	which	PRON
aiti-7988	317	8	the	the	DET
aiti-7988	317	9	fundamental	fundamental	ADJ
aiti-7988	317	10	natural	natural	ADJ
aiti-7988	317	11	frequency	frequency	NOUN
aiti-7988	317	12	vanishes	vanish	VERB
aiti-7988	317	13	,	,	PUNCT
aiti-7988	317	14	is	be	AUX
aiti-7988	317	15	named	name	VERB
aiti-7988	317	16	critical	critical	ADJ
aiti-7988	317	17	velocity	velocity	NOUN
aiti-7988	317	18	.	.	PUNCT
aiti-7988	318	1	this	this	PRON
aiti-7988	318	2	is	be	AUX
aiti-7988	318	3	because	because	SCONJ
aiti-7988	318	4	the	the	DET
aiti-7988	318	5	increase	increase	NOUN
aiti-7988	318	6	of	of	ADP
aiti-7988	318	7	the	the	DET
aiti-7988	318	8	velocity	velocity	NOUN
aiti-7988	318	9	of	of	ADP
aiti-7988	318	10	fluid	fluid	NOUN
aiti-7988	318	11	flowing	flow	VERB
aiti-7988	318	12	inside	inside	ADP
aiti-7988	318	13	the	the	DET
aiti-7988	318	14	pipe	pipe	NOUN
aiti-7988	318	15	leads	lead	VERB
aiti-7988	318	16	to	to	ADP
aiti-7988	318	17	the	the	DET
aiti-7988	318	18	weakness	weakness	NOUN
aiti-7988	318	19	of	of	ADP
aiti-7988	318	20	the	the	DET
aiti-7988	318	21	pipe	pipe	NOUN
aiti-7988	318	22	stiffness	stiffness	NOUN
aiti-7988	318	23	.	.	PUNCT
aiti-7988	319	1	almost	almost	ADV
aiti-7988	319	2	similar	similar	ADJ
aiti-7988	319	3	conclusions	conclusion	NOUN
aiti-7988	319	4	in	in	ADP
aiti-7988	319	5	the	the	DET
aiti-7988	319	6	subcritical	subcritical	ADJ
aiti-7988	319	7	fluid	fluid	NOUN
aiti-7988	319	8	velocity	velocity	NOUN
aiti-7988	319	9	range	range	NOUN
aiti-7988	319	10	(	(	PUNCT
aiti-7988	319	11	1st	1st	ADJ
aiti-7988	319	12	zone	zone	NOUN
aiti-7988	319	13	)	)	PUNCT
aiti-7988	319	14	were	be	AUX
aiti-7988	319	15	observed	observe	VERB
aiti-7988	319	16	in	in	ADP
aiti-7988	319	17	the	the	DET
aiti-7988	319	18	work	work	NOUN
aiti-7988	319	19	of	of	ADP
aiti-7988	319	20	ni	ni	PROPN
aiti-7988	319	21	et	et	PROPN
aiti-7988	319	22	al	al	PROPN
aiti-7988	319	23	.	.	PUNCT
aiti-7988	320	1	[	[	X
aiti-7988	320	2	26	26	NUM
aiti-7988	320	3	]	]	PUNCT
aiti-7988	320	4	and	and	CCONJ
aiti-7988	320	5	in	in	ADP
aiti-7988	320	6	the	the	DET
aiti-7988	320	7	supercritical	supercritical	ADJ
aiti-7988	320	8	regime	regime	NOUN
aiti-7988	320	9	(	(	PUNCT
aiti-7988	320	10	2nd	2nd	ADJ
aiti-7988	320	11	zone	zone	NOUN
aiti-7988	320	12	)	)	PUNCT
aiti-7988	320	13	in	in	ADP
aiti-7988	320	14	the	the	DET
aiti-7988	320	15	work	work	NOUN
aiti-7988	320	16	of	of	ADP
aiti-7988	320	17	adelaja	adelaja	NOUN
aiti-7988	321	1	[	[	X
aiti-7988	321	2	28	28	NUM
aiti-7988	321	3	]	]	PUNCT
aiti-7988	321	4	and	and	CCONJ
aiti-7988	321	5	olunloyo	olunloyo	NOUN
aiti-7988	321	6	et	et	PROPN
aiti-7988	321	7	al	al	PROPN
aiti-7988	321	8	.	.	PUNCT
aiti-7988	322	1	[	[	X
aiti-7988	322	2	29	29	NUM
aiti-7988	322	3	]	]	PUNCT
aiti-7988	322	4	,	,	PUNCT
aiti-7988	322	5	while	while	SCONJ
aiti-7988	322	6	for	for	SCONJ
aiti-7988	322	7	the	the	DET
aiti-7988	322	8	whole	whole	ADJ
aiti-7988	322	9	spectrum	spectrum	NOUN
aiti-7988	322	10	results	result	VERB
aiti-7988	322	11	the	the	DET
aiti-7988	322	12	same	same	ADJ
aiti-7988	322	13	trend	trend	NOUN
aiti-7988	322	14	was	be	AUX
aiti-7988	322	15	found	find	VERB
aiti-7988	322	16	in	in	ADP
aiti-7988	322	17	the	the	DET
aiti-7988	322	18	work	work	NOUN
aiti-7988	322	19	of	of	ADP
aiti-7988	322	20	plaut	plaut	NOUN
aiti-7988	322	21	[	[	X
aiti-7988	322	22	30	30	NUM
aiti-7988	322	23	]	]	PUNCT
aiti-7988	322	24	.	.	PUNCT
aiti-7988	323	1	fig	fig	NOUN
aiti-7988	323	2	.	.	PUNCT
aiti-7988	324	1	5	5	NUM
aiti-7988	324	2	presents	present	VERB
aiti-7988	324	3	the	the	DET
aiti-7988	324	4	effect	effect	NOUN
aiti-7988	324	5	of	of	ADP
aiti-7988	324	6	different	different	ADJ
aiti-7988	324	7	aspect	aspect	NOUN
aiti-7988	324	8	ratio	ratio	NOUN
aiti-7988	324	9	(	(	PUNCT
aiti-7988	324	10	length	length	NOUN
aiti-7988	324	11	to	to	ADP
aiti-7988	324	12	diameter	diameter	NOUN
aiti-7988	324	13	ratio	ratio	NOUN
aiti-7988	324	14	)	)	PUNCT
aiti-7988	324	15	on	on	ADP
aiti-7988	324	16	the	the	DET
aiti-7988	324	17	natural	natural	ADJ
aiti-7988	324	18	frequency	frequency	NOUN
aiti-7988	324	19	.	.	PUNCT
aiti-7988	325	1	it	it	PRON
aiti-7988	325	2	is	be	AUX
aiti-7988	325	3	clear	clear	ADJ
aiti-7988	325	4	that	that	SCONJ
aiti-7988	325	5	the	the	DET
aiti-7988	325	6	natural	natural	ADJ
aiti-7988	325	7	frequencies	frequency	NOUN
aiti-7988	325	8	of	of	ADP
aiti-7988	325	9	the	the	DET
aiti-7988	325	10	fluid	fluid	NOUN
aiti-7988	325	11	-	-	PUNCT
aiti-7988	325	12	conveying	convey	VERB
aiti-7988	325	13	pipe	pipe	NOUN
aiti-7988	325	14	decrease	decrease	NOUN
aiti-7988	325	15	with	with	ADP
aiti-7988	325	16	the	the	DET
aiti-7988	325	17	increase	increase	NOUN
aiti-7988	325	18	of	of	ADP
aiti-7988	325	19	length	length	NOUN
aiti-7988	325	20	to	to	ADP
aiti-7988	325	21	diameter	diameter	NOUN
aiti-7988	325	22	ratio	ratio	NOUN
aiti-7988	325	23	.	.	PUNCT
aiti-7988	326	1	similarly	similarly	ADV
aiti-7988	326	2	,	,	PUNCT
aiti-7988	326	3	the	the	DET
aiti-7988	326	4	critical	critical	ADJ
aiti-7988	326	5	fluid	fluid	NOUN
aiti-7988	326	6	velocity	velocity	NOUN
aiti-7988	326	7	decreases	decrease	VERB
aiti-7988	326	8	with	with	ADP
aiti-7988	326	9	the	the	DET
aiti-7988	326	10	increase	increase	NOUN
aiti-7988	326	11	of	of	ADP
aiti-7988	326	12	the	the	DET
aiti-7988	326	13	aspect	aspect	NOUN
aiti-7988	326	14	ratio	ratio	NOUN
aiti-7988	326	15	.	.	PUNCT
aiti-7988	327	1	this	this	PRON
aiti-7988	327	2	suggests	suggest	VERB
aiti-7988	327	3	that	that	SCONJ
aiti-7988	327	4	the	the	DET
aiti-7988	327	5	pipe	pipe	NOUN
aiti-7988	327	6	-	-	PUNCT
aiti-7988	327	7	fluid	fluid	NOUN
aiti-7988	327	8	system	system	NOUN
aiti-7988	327	9	will	will	AUX
aiti-7988	327	10	hastily	hastily	ADV
aiti-7988	327	11	reach	reach	VERB
aiti-7988	327	12	divergence	divergence	NOUN
aiti-7988	327	13	instability	instability	NOUN
aiti-7988	327	14	situation	situation	NOUN
aiti-7988	327	15	with	with	ADP
aiti-7988	327	16	higher	high	ADJ
aiti-7988	327	17	aspect	aspect	NOUN
aiti-7988	327	18	ratio	ratio	NOUN
aiti-7988	327	19	.	.	PUNCT
aiti-7988	328	1	the	the	DET
aiti-7988	328	2	reason	reason	NOUN
aiti-7988	328	3	is	be	AUX
aiti-7988	328	4	that	that	SCONJ
aiti-7988	328	5	the	the	DET
aiti-7988	328	6	higher	high	ADJ
aiti-7988	328	7	length	length	NOUN
aiti-7988	328	8	to	to	ADP
aiti-7988	328	9	diameter	diameter	NOUN
aiti-7988	328	10	ratio	ratio	NOUN
aiti-7988	328	11	leads	lead	VERB
aiti-7988	328	12	to	to	ADP
aiti-7988	328	13	the	the	DET
aiti-7988	328	14	increase	increase	NOUN
aiti-7988	328	15	of	of	ADP
aiti-7988	328	16	the	the	DET
aiti-7988	328	17	pipe	pipe	NOUN
aiti-7988	328	18	weight	weight	NOUN
aiti-7988	328	19	resulting	result	VERB
aiti-7988	328	20	in	in	ADP
aiti-7988	328	21	the	the	DET
aiti-7988	328	22	weakness	weakness	NOUN
aiti-7988	328	23	of	of	ADP
aiti-7988	328	24	its	its	PRON
aiti-7988	328	25	stuffiness	stuffiness	NOUN
aiti-7988	328	26	.	.	PUNCT
aiti-7988	329	1	the	the	DET
aiti-7988	329	2	same	same	ADJ
aiti-7988	329	3	trend	trend	NOUN
aiti-7988	329	4	was	be	AUX
aiti-7988	329	5	observed	observe	VERB
aiti-7988	329	6	in	in	ADP
aiti-7988	329	7	the	the	DET
aiti-7988	329	8	work	work	NOUN
aiti-7988	329	9	of	of	ADP
aiti-7988	329	10	liang	liang	PROPN
aiti-7988	330	1	[	[	X
aiti-7988	330	2	27	27	NUM
aiti-7988	330	3	]	]	PUNCT
aiti-7988	330	4	and	and	CCONJ
aiti-7988	330	5	olunloyo	olunloyo	NOUN
aiti-7988	330	6	et	et	PROPN
aiti-7988	330	7	al	al	PROPN
aiti-7988	330	8	.	.	PUNCT
aiti-7988	331	1	[	[	X
aiti-7988	331	2	31	31	NUM
aiti-7988	331	3	]	]	PUNCT
aiti-7988	331	4	with	with	ADP
aiti-7988	331	5	the	the	DET
aiti-7988	331	6	increase	increase	NOUN
aiti-7988	331	7	of	of	ADP
aiti-7988	331	8	the	the	DET
aiti-7988	331	9	pipe	pipe	NOUN
aiti-7988	331	10	length	length	NOUN
aiti-7988	331	11	.	.	PUNCT
aiti-7988	332	1	meanwhile	meanwhile	ADV
aiti-7988	332	2	,	,	PUNCT
aiti-7988	332	3	by	by	ADP
aiti-7988	332	4	observing	observe	VERB
aiti-7988	332	5	fig	fig	NOUN
aiti-7988	332	6	.	.	PUNCT
aiti-7988	333	1	5	5	NUM
aiti-7988	333	2	,	,	PUNCT
aiti-7988	333	3	it	it	PRON
aiti-7988	333	4	is	be	AUX
aiti-7988	333	5	evident	evident	ADJ
aiti-7988	333	6	that	that	SCONJ
aiti-7988	333	7	the	the	DET
aiti-7988	333	8	level	level	NOUN
aiti-7988	333	9	of	of	ADP
aiti-7988	333	10	reduction	reduction	NOUN
aiti-7988	333	11	in	in	ADP
aiti-7988	333	12	the	the	DET
aiti-7988	333	13	magnitude	magnitude	NOUN
aiti-7988	333	14	of	of	ADP
aiti-7988	333	15	natural	natural	ADJ
aiti-7988	333	16	frequencies	frequency	NOUN
aiti-7988	333	17	and	and	CCONJ
aiti-7988	333	18	critical	critical	ADJ
aiti-7988	333	19	velocity	velocity	NOUN
aiti-7988	333	20	for	for	ADP
aiti-7988	333	21	the	the	DET
aiti-7988	333	22	same	same	ADJ
aiti-7988	333	23	aspect	aspect	NOUN
aiti-7988	333	24	ratio	ratio	NOUN
aiti-7988	333	25	reduces	reduce	VERB
aiti-7988	333	26	with	with	ADP
aiti-7988	333	27	the	the	DET
aiti-7988	333	28	increase	increase	NOUN
aiti-7988	333	29	of	of	ADP
aiti-7988	333	30	the	the	DET
aiti-7988	333	31	support	support	NOUN
aiti-7988	333	32	angle	angle	NOUN
aiti-7988	333	33	.	.	PUNCT
aiti-7988	334	1	at	at	ADP
aiti-7988	334	2	the	the	DET
aiti-7988	334	3	same	same	ADJ
aiti-7988	334	4	time	time	NOUN
aiti-7988	334	5	,	,	PUNCT
aiti-7988	334	6	by	by	ADP
aiti-7988	334	7	observing	observe	VERB
aiti-7988	334	8	fig	fig	NOUN
aiti-7988	334	9	.	.	PUNCT
aiti-7988	335	1	5	5	NUM
aiti-7988	335	2	,	,	PUNCT
aiti-7988	335	3	it	it	PRON
aiti-7988	335	4	is	be	AUX
aiti-7988	335	5	clear	clear	ADJ
aiti-7988	335	6	that	that	SCONJ
aiti-7988	335	7	the	the	DET
aiti-7988	335	8	level	level	NOUN
aiti-7988	335	9	of	of	ADP
aiti-7988	335	10	reduction	reduction	NOUN
aiti-7988	335	11	in	in	ADP
aiti-7988	335	12	the	the	DET
aiti-7988	335	13	value	value	NOUN
aiti-7988	335	14	of	of	ADP
aiti-7988	335	15	the	the	DET
aiti-7988	335	16	natural	natural	ADJ
aiti-7988	335	17	frequency	frequency	NOUN
aiti-7988	335	18	and	and	CCONJ
aiti-7988	335	19	critical	critical	ADJ
aiti-7988	335	20	velocity	velocity	NOUN
aiti-7988	335	21	decreases	decrease	VERB
aiti-7988	335	22	for	for	ADP
aiti-7988	335	23	the	the	DET
aiti-7988	335	24	same	same	ADJ
aiti-7988	335	25	aspect	aspect	NOUN
aiti-7988	335	26	ratio	ratio	NOUN
aiti-7988	335	27	with	with	ADP
aiti-7988	335	28	the	the	DET
aiti-7988	335	29	increase	increase	NOUN
aiti-7988	335	30	of	of	ADP
aiti-7988	335	31	the	the	DET
aiti-7988	335	32	inclination	inclination	NOUN
aiti-7988	335	33	angle	angle	NOUN
aiti-7988	335	34	.	.	PUNCT
aiti-7988	336	1	(	(	PUNCT
aiti-7988	336	2	a	a	X
aiti-7988	336	3	)	)	PUNCT
aiti-7988	336	4	)	)	PUNCT
aiti-7988	337	1	=	=	PUNCT
aiti-7988	337	2	0	0	NUM
aiti-7988	337	3	°	°	NUM
aiti-7988	337	4	(	(	PUNCT
aiti-7988	337	5	b	b	NOUN
aiti-7988	337	6	)	)	PUNCT
aiti-7988	337	7	)	)	PUNCT
aiti-7988	338	1	=	=	PUNCT
aiti-7988	339	1	15	15	NUM
aiti-7988	339	2	°	°	NOUN
aiti-7988	339	3	(	(	PUNCT
aiti-7988	339	4	c	c	NOUN
aiti-7988	339	5	)	)	PUNCT
aiti-7988	339	6	)	)	PUNCT
aiti-7988	339	7	=	=	PUNCT
aiti-7988	340	1	30	30	NUM
aiti-7988	340	2	°	°	NUM
aiti-7988	340	3	fig	fig	NOUN
aiti-7988	340	4	.	.	PUNCT
aiti-7988	341	1	5	5	NUM
aiti-7988	341	2	the	the	DET
aiti-7988	341	3	natural	natural	ADJ
aiti-7988	341	4	frequency	frequency	NOUN
aiti-7988	341	5	value	value	NOUN
aiti-7988	341	6	versus	versus	ADP
aiti-7988	341	7	fluid	fluid	ADJ
aiti-7988	341	8	velocity	velocity	NOUN
aiti-7988	341	9	with	with	ADP
aiti-7988	341	10	different	different	ADJ
aiti-7988	341	11	aspect	aspect	NOUN
aiti-7988	341	12	ratios	ratio	NOUN
aiti-7988	341	13	for	for	ADP
aiti-7988	341	14	the	the	DET
aiti-7988	341	15	case	case	NOUN
aiti-7988	341	16	of	of	ADP
aiti-7988	341	17	t	t	NOUN
aiti-7988	341	18	=	=	SYM
aiti-7988	341	19	25	25	NUM
aiti-7988	341	20	°	°	NUM
aiti-7988	341	21	c	c	NOUN
aiti-7988	341	22	and	and	CCONJ
aiti-7988	341	23	n	n	CCONJ
aiti-7988	341	24	=	=	SYM
aiti-7988	341	25	1	1	NUM
aiti-7988	341	26	50	50	NUM
aiti-7988	341	27	advances	advance	NOUN
aiti-7988	341	28	in	in	ADP
aiti-7988	341	29	technology	technology	NOUN
aiti-7988	341	30	innovation	innovation	NOUN
aiti-7988	341	31	,	,	PUNCT
aiti-7988	341	32	vol	vol	NOUN
aiti-7988	341	33	.	.	PROPN
aiti-7988	342	1	7	7	NUM
aiti-7988	342	2	,	,	PUNCT
aiti-7988	342	3	no	no	INTJ
aiti-7988	342	4	.	.	NOUN
aiti-7988	342	5	1	1	NUM
aiti-7988	342	6	,	,	PUNCT
aiti-7988	342	7	2022	2022	NUM
aiti-7988	342	8	,	,	PUNCT
aiti-7988	342	9	pp	pp	ADJ
aiti-7988	342	10	.	.	PUNCT
aiti-7988	343	1	41	41	NUM
aiti-7988	343	2	-	-	SYM
aiti-7988	343	3	55	55	NUM
aiti-7988	343	4	the	the	DET
aiti-7988	343	5	effect	effect	NOUN
aiti-7988	343	6	of	of	ADP
aiti-7988	343	7	the	the	DET
aiti-7988	343	8	pipe	pipe	NOUN
aiti-7988	343	9	’s	’s	PART
aiti-7988	343	10	inclination	inclination	NOUN
aiti-7988	343	11	angle	angle	NOUN
aiti-7988	343	12	and	and	CCONJ
aiti-7988	343	13	aspect	aspect	VERB
aiti-7988	343	14	ratio	ratio	NOUN
aiti-7988	343	15	on	on	ADP
aiti-7988	343	16	the	the	DET
aiti-7988	343	17	fundamental	fundamental	ADJ
aiti-7988	343	18	natural	natural	ADJ
aiti-7988	343	19	frequency	frequency	NOUN
aiti-7988	343	20	of	of	ADP
aiti-7988	343	21	the	the	DET
aiti-7988	343	22	structure	structure	NOUN
aiti-7988	343	23	is	be	AUX
aiti-7988	343	24	studied	study	VERB
aiti-7988	343	25	further	far	ADV
aiti-7988	343	26	in	in	ADP
aiti-7988	343	27	figs	fig	NOUN
aiti-7988	343	28	.	.	PUNCT
aiti-7988	344	1	6	6	NUM
aiti-7988	344	2	and	and	CCONJ
aiti-7988	344	3	7	7	NUM
aiti-7988	344	4	respectively	respectively	ADV
aiti-7988	344	5	.	.	PUNCT
aiti-7988	345	1	in	in	ADP
aiti-7988	345	2	general	general	ADJ
aiti-7988	345	3	,	,	PUNCT
aiti-7988	345	4	the	the	DET
aiti-7988	345	5	results	result	NOUN
aiti-7988	345	6	indicate	indicate	VERB
aiti-7988	345	7	the	the	DET
aiti-7988	345	8	increase	increase	NOUN
aiti-7988	345	9	of	of	ADP
aiti-7988	345	10	natural	natural	ADJ
aiti-7988	345	11	frequencies	frequency	NOUN
aiti-7988	345	12	with	with	ADP
aiti-7988	345	13	the	the	DET
aiti-7988	345	14	increase	increase	NOUN
aiti-7988	345	15	of	of	ADP
aiti-7988	345	16	the	the	DET
aiti-7988	345	17	inclination	inclination	NOUN
aiti-7988	345	18	angle	angle	NOUN
aiti-7988	345	19	.	.	PUNCT
aiti-7988	346	1	in	in	ADP
aiti-7988	346	2	addition	addition	NOUN
aiti-7988	346	3	,	,	PUNCT
aiti-7988	346	4	it	it	PRON
aiti-7988	346	5	can	can	AUX
aiti-7988	346	6	be	be	AUX
aiti-7988	346	7	observed	observe	VERB
aiti-7988	346	8	that	that	SCONJ
aiti-7988	346	9	the	the	DET
aiti-7988	346	10	enhancement	enhancement	NOUN
aiti-7988	346	11	in	in	ADP
aiti-7988	346	12	the	the	DET
aiti-7988	346	13	natural	natural	ADJ
aiti-7988	346	14	frequency	frequency	NOUN
aiti-7988	346	15	values	value	NOUN
aiti-7988	346	16	is	be	AUX
aiti-7988	346	17	larger	large	ADJ
aiti-7988	346	18	at	at	ADP
aiti-7988	346	19	higher	high	ADJ
aiti-7988	346	20	aspect	aspect	NOUN
aiti-7988	346	21	ratio	ratio	NOUN
aiti-7988	346	22	.	.	PUNCT
aiti-7988	347	1	for	for	ADP
aiti-7988	347	2	example	example	NOUN
aiti-7988	347	3	,	,	PUNCT
aiti-7988	347	4	the	the	DET
aiti-7988	347	5	natural	natural	ADJ
aiti-7988	347	6	frequency	frequency	NOUN
aiti-7988	347	7	value	value	NOUN
aiti-7988	347	8	increases	increase	VERB
aiti-7988	347	9	approximately	approximately	ADV
aiti-7988	347	10	by	by	ADP
aiti-7988	347	11	0.18	0.18	NUM
aiti-7988	347	12	%	%	NOUN
aiti-7988	347	13	(	(	PUNCT
aiti-7988	347	14	from	from	ADP
aiti-7988	347	15	23.104	23.104	NUM
aiti-7988	347	16	for	for	ADP
aiti-7988	347	17	θ	θ	PROPN
aiti-7988	347	18	=	=	PUNCT
aiti-7988	347	19	0	0	NUM
aiti-7988	347	20	°	°	NUM
aiti-7988	347	21	to	to	ADP
aiti-7988	347	22	23.146	23.146	NUM
aiti-7988	347	23	for	for	ADP
aiti-7988	347	24	θ	θ	PROPN
aiti-7988	347	25	=	=	SYM
aiti-7988	347	26	60	60	NUM
aiti-7988	347	27	°	°	NUM
aiti-7988	347	28	)	)	PUNCT
aiti-7988	347	29	at	at	ADP
aiti-7988	347	30	aspect	aspect	NOUN
aiti-7988	347	31	ratio	ratio	NOUN
aiti-7988	347	32	=	=	NOUN
aiti-7988	347	33	20	20	NUM
aiti-7988	347	34	while	while	SCONJ
aiti-7988	347	35	its	its	PRON
aiti-7988	347	36	value	value	NOUN
aiti-7988	347	37	increases	increase	VERB
aiti-7988	347	38	by	by	ADP
aiti-7988	347	39	5.2	5.2	NUM
aiti-7988	347	40	%	%	NOUN
aiti-7988	347	41	(	(	PUNCT
aiti-7988	347	42	from	from	ADP
aiti-7988	347	43	22.223	22.223	NUM
aiti-7988	347	44	for	for	ADP
aiti-7988	347	45	θ	θ	PROPN
aiti-7988	347	46	=	=	PUNCT
aiti-7988	347	47	0	0	NUM
aiti-7988	347	48	°	°	NUM
aiti-7988	347	49	to	to	ADP
aiti-7988	347	50	23.380	23.380	NUM
aiti-7988	347	51	for	for	ADP
aiti-7988	347	52	θ	θ	PROPN
aiti-7988	347	53	=	=	SYM
aiti-7988	347	54	60	60	NUM
aiti-7988	347	55	°	°	NUM
aiti-7988	347	56	)	)	PUNCT
aiti-7988	347	57	at	at	ADP
aiti-7988	347	58	aspect	aspect	NOUN
aiti-7988	347	59	ratio	ratio	NOUN
aiti-7988	347	60	=	=	SYM
aiti-7988	347	61	50	50	NUM
aiti-7988	347	62	.	.	PUNCT
aiti-7988	348	1	additionally	additionally	ADV
aiti-7988	348	2	,	,	PUNCT
aiti-7988	348	3	the	the	DET
aiti-7988	348	4	results	result	NOUN
aiti-7988	348	5	in	in	ADP
aiti-7988	348	6	fig	fig	NOUN
aiti-7988	348	7	.	.	PUNCT
aiti-7988	349	1	7	7	NUM
aiti-7988	349	2	show	show	VERB
aiti-7988	349	3	an	an	DET
aiti-7988	349	4	interesting	interesting	ADJ
aiti-7988	349	5	phenomenon	phenomenon	NOUN
aiti-7988	349	6	.	.	PUNCT
aiti-7988	350	1	when	when	SCONJ
aiti-7988	350	2	the	the	DET
aiti-7988	350	3	aspect	aspect	NOUN
aiti-7988	350	4	ratio	ratio	NOUN
aiti-7988	350	5	equals	equal	VERB
aiti-7988	350	6	50	50	NUM
aiti-7988	350	7	and	and	CCONJ
aiti-7988	350	8	the	the	DET
aiti-7988	350	9	inclination	inclination	NOUN
aiti-7988	350	10	angle	angle	NOUN
aiti-7988	350	11	is	be	AUX
aiti-7988	350	12	in	in	ADP
aiti-7988	350	13	the	the	DET
aiti-7988	350	14	range	range	NOUN
aiti-7988	350	15	of	of	ADP
aiti-7988	350	16	40	40	NUM
aiti-7988	350	17	-	-	SYM
aiti-7988	350	18	90	90	NUM
aiti-7988	350	19	,	,	PUNCT
aiti-7988	350	20	the	the	DET
aiti-7988	350	21	influence	influence	NOUN
aiti-7988	350	22	of	of	ADP
aiti-7988	350	23	the	the	DET
aiti-7988	350	24	inclination	inclination	NOUN
aiti-7988	350	25	angle	angle	NOUN
aiti-7988	350	26	on	on	ADP
aiti-7988	350	27	the	the	DET
aiti-7988	350	28	fundamental	fundamental	ADJ
aiti-7988	350	29	natural	natural	ADJ
aiti-7988	350	30	frequencies	frequency	NOUN
aiti-7988	350	31	becomes	become	VERB
aiti-7988	350	32	higher	high	ADJ
aiti-7988	350	33	than	than	ADP
aiti-7988	350	34	the	the	DET
aiti-7988	350	35	influence	influence	NOUN
aiti-7988	350	36	of	of	ADP
aiti-7988	350	37	the	the	DET
aiti-7988	350	38	aspect	aspect	NOUN
aiti-7988	350	39	ratio	ratio	NOUN
aiti-7988	350	40	on	on	ADP
aiti-7988	350	41	the	the	DET
aiti-7988	350	42	fundamental	fundamental	ADJ
aiti-7988	350	43	natural	natural	ADJ
aiti-7988	350	44	frequencies	frequency	NOUN
aiti-7988	350	45	,	,	PUNCT
aiti-7988	350	46	i.e.	i.e.	X
aiti-7988	350	47	,	,	PUNCT
aiti-7988	350	48	the	the	DET
aiti-7988	350	49	increase	increase	NOUN
aiti-7988	350	50	of	of	ADP
aiti-7988	350	51	inclination	inclination	NOUN
aiti-7988	350	52	angle	angle	NOUN
aiti-7988	350	53	compensates	compensate	VERB
aiti-7988	350	54	the	the	DET
aiti-7988	350	55	loss	loss	NOUN
aiti-7988	350	56	in	in	ADP
aiti-7988	350	57	natural	natural	ADJ
aiti-7988	350	58	frequency	frequency	NOUN
aiti-7988	350	59	value	value	NOUN
aiti-7988	350	60	due	due	ADP
aiti-7988	350	61	to	to	ADP
aiti-7988	350	62	the	the	DET
aiti-7988	350	63	increase	increase	NOUN
aiti-7988	350	64	of	of	ADP
aiti-7988	350	65	aspect	aspect	NOUN
aiti-7988	350	66	ratio	ratio	NOUN
aiti-7988	350	67	.	.	PUNCT
aiti-7988	351	1	also	also	ADV
aiti-7988	351	2	,	,	PUNCT
aiti-7988	351	3	it	it	PRON
aiti-7988	351	4	can	can	AUX
aiti-7988	351	5	be	be	AUX
aiti-7988	351	6	observed	observe	VERB
aiti-7988	351	7	from	from	ADP
aiti-7988	351	8	fig	fig	NOUN
aiti-7988	351	9	.	.	PUNCT
aiti-7988	352	1	7	7	NUM
aiti-7988	352	2	that	that	SCONJ
aiti-7988	352	3	the	the	DET
aiti-7988	352	4	natural	natural	ADJ
aiti-7988	352	5	frequency	frequency	NOUN
aiti-7988	352	6	of	of	ADP
aiti-7988	352	7	the	the	DET
aiti-7988	352	8	pipe	pipe	NOUN
aiti-7988	352	9	has	have	VERB
aiti-7988	352	10	an	an	DET
aiti-7988	352	11	increasing	increase	VERB
aiti-7988	352	12	trend	trend	NOUN
aiti-7988	352	13	up	up	ADP
aiti-7988	352	14	to	to	ADP
aiti-7988	352	15	the	the	DET
aiti-7988	352	16	inclination	inclination	NOUN
aiti-7988	352	17	angle	angle	NOUN
aiti-7988	352	18	of	of	ADP
aiti-7988	352	19	θ	θ	PROPN
aiti-7988	352	20	=	=	PUNCT
aiti-7988	353	1	90	90	NUM
aiti-7988	353	2	°	°	NUM
aiti-7988	353	3	and	and	CCONJ
aiti-7988	353	4	a	a	DET
aiti-7988	353	5	reverse	reverse	ADJ
aiti-7988	353	6	trend	trend	NOUN
aiti-7988	353	7	afterward	afterward	ADV
aiti-7988	353	8	,	,	PUNCT
aiti-7988	353	9	i.e.	i.e.	X
aiti-7988	353	10	,	,	PUNCT
aiti-7988	353	11	beyond	beyond	ADP
aiti-7988	353	12	the	the	DET
aiti-7988	353	13	angle	angle	NOUN
aiti-7988	353	14	90	90	NUM
aiti-7988	353	15	°	°	NOUN
aiti-7988	354	1	the	the	DET
aiti-7988	354	2	behavior	behavior	NOUN
aiti-7988	354	3	is	be	AUX
aiti-7988	354	4	reflected	reflect	VERB
aiti-7988	354	5	.	.	PUNCT
aiti-7988	355	1	this	this	PRON
aiti-7988	355	2	can	can	AUX
aiti-7988	355	3	be	be	AUX
aiti-7988	355	4	explained	explain	VERB
aiti-7988	355	5	as	as	SCONJ
aiti-7988	355	6	follows	follow	VERB
aiti-7988	355	7	:	:	PUNCT
aiti-7988	355	8	for	for	ADP
aiti-7988	355	9	an	an	DET
aiti-7988	355	10	inclined	inclined	ADJ
aiti-7988	355	11	pipe	pipe	NOUN
aiti-7988	355	12	,	,	PUNCT
aiti-7988	355	13	the	the	DET
aiti-7988	355	14	gravitational	gravitational	ADJ
aiti-7988	355	15	force	force	NOUN
aiti-7988	355	16	generated	generate	VERB
aiti-7988	355	17	by	by	ADP
aiti-7988	355	18	the	the	DET
aiti-7988	355	19	weight	weight	NOUN
aiti-7988	355	20	of	of	ADP
aiti-7988	355	21	the	the	DET
aiti-7988	355	22	pipe	pipe	NOUN
aiti-7988	355	23	and	and	CCONJ
aiti-7988	355	24	the	the	DET
aiti-7988	355	25	fluid	fluid	NOUN
aiti-7988	355	26	is	be	AUX
aiti-7988	355	27	divided	divide	VERB
aiti-7988	355	28	into	into	ADP
aiti-7988	355	29	two	two	NUM
aiti-7988	355	30	components	component	NOUN
aiti-7988	355	31	,	,	PUNCT
aiti-7988	355	32	the	the	DET
aiti-7988	355	33	lateral	lateral	ADJ
aiti-7988	355	34	component	component	NOUN
aiti-7988	355	35	and	and	CCONJ
aiti-7988	355	36	the	the	DET
aiti-7988	355	37	axial	axial	ADJ
aiti-7988	355	38	component	component	NOUN
aiti-7988	355	39	relative	relative	ADJ
aiti-7988	355	40	to	to	ADP
aiti-7988	355	41	the	the	DET
aiti-7988	355	42	pipe	pipe	NOUN
aiti-7988	355	43	axes	axis	NOUN
aiti-7988	355	44	.	.	PUNCT
aiti-7988	356	1	when	when	SCONJ
aiti-7988	356	2	the	the	DET
aiti-7988	356	3	angle	angle	NOUN
aiti-7988	356	4	of	of	ADP
aiti-7988	356	5	inclination	inclination	NOUN
aiti-7988	356	6	of	of	ADP
aiti-7988	356	7	the	the	DET
aiti-7988	356	8	pipe	pipe	NOUN
aiti-7988	356	9	is	be	AUX
aiti-7988	356	10	*	*	ADJ
aiti-7988	356	11	90	90	NUM
aiti-7988	356	12	,	,	PUNCT
aiti-7988	356	13	,	,	PUNCT
aiti-7988	356	14	the	the	DET
aiti-7988	356	15	axial	axial	ADJ
aiti-7988	356	16	component	component	NOUN
aiti-7988	356	17	exerts	exert	VERB
aiti-7988	356	18	a	a	DET
aiti-7988	356	19	tensile	tensile	NOUN
aiti-7988	356	20	force	force	NOUN
aiti-7988	356	21	on	on	ADP
aiti-7988	356	22	the	the	DET
aiti-7988	356	23	pipe	pipe	NOUN
aiti-7988	356	24	,	,	PUNCT
aiti-7988	356	25	which	which	PRON
aiti-7988	356	26	increases	increase	VERB
aiti-7988	356	27	with	with	ADP
aiti-7988	356	28	the	the	DET
aiti-7988	356	29	increase	increase	NOUN
aiti-7988	356	30	of	of	ADP
aiti-7988	356	31	the	the	DET
aiti-7988	356	32	inclination	inclination	NOUN
aiti-7988	356	33	angle	angle	NOUN
aiti-7988	356	34	of	of	ADP
aiti-7988	356	35	the	the	DET
aiti-7988	356	36	pipe	pipe	NOUN
aiti-7988	356	37	and	and	CCONJ
aiti-7988	356	38	the	the	DET
aiti-7988	356	39	aspect	aspect	NOUN
aiti-7988	356	40	ratio	ratio	NOUN
aiti-7988	356	41	.	.	PUNCT
aiti-7988	357	1	this	this	PRON
aiti-7988	357	2	in	in	ADP
aiti-7988	357	3	turn	turn	NOUN
aiti-7988	357	4	reduces	reduce	VERB
aiti-7988	357	5	the	the	DET
aiti-7988	357	6	impact	impact	NOUN
aiti-7988	357	7	of	of	ADP
aiti-7988	357	8	the	the	DET
aiti-7988	357	9	lateral	lateral	ADJ
aiti-7988	357	10	component	component	NOUN
aiti-7988	357	11	,	,	PUNCT
aiti-7988	357	12	responsible	responsible	ADJ
aiti-7988	357	13	for	for	ADP
aiti-7988	357	14	the	the	DET
aiti-7988	357	15	occurrence	occurrence	NOUN
aiti-7988	357	16	of	of	ADP
aiti-7988	357	17	the	the	DET
aiti-7988	357	18	lateral	lateral	ADJ
aiti-7988	357	19	displacement	displacement	NOUN
aiti-7988	357	20	of	of	ADP
aiti-7988	357	21	the	the	DET
aiti-7988	357	22	pipe	pipe	NOUN
aiti-7988	357	23	,	,	PUNCT
aiti-7988	357	24	and	and	CCONJ
aiti-7988	357	25	thus	thus	ADV
aiti-7988	357	26	increases	increase	VERB
aiti-7988	357	27	natural	natural	ADJ
aiti-7988	357	28	frequencies	frequency	NOUN
aiti-7988	357	29	of	of	ADP
aiti-7988	357	30	the	the	DET
aiti-7988	357	31	inclined	inclined	ADJ
aiti-7988	357	32	pipe	pipe	NOUN
aiti-7988	357	33	.	.	PUNCT
aiti-7988	358	1	on	on	ADP
aiti-7988	358	2	the	the	DET
aiti-7988	358	3	contrary	contrary	NOUN
aiti-7988	358	4	,	,	PUNCT
aiti-7988	358	5	as	as	SCONJ
aiti-7988	358	6	the	the	DET
aiti-7988	358	7	pipe	pipe	NOUN
aiti-7988	358	8	’s	’s	PART
aiti-7988	358	9	inclination	inclination	NOUN
aiti-7988	358	10	angle	angle	NOUN
aiti-7988	358	11	)	)	PUNCT
aiti-7988	358	12	90	90	NUM
aiti-7988	358	13	,	,	PUNCT
aiti-7988	358	14	,	,	PUNCT
aiti-7988	358	15	the	the	DET
aiti-7988	358	16	axial	axial	ADJ
aiti-7988	358	17	component	component	NOUN
aiti-7988	358	18	gradually	gradually	ADV
aiti-7988	358	19	decreases	decrease	VERB
aiti-7988	358	20	and	and	CCONJ
aiti-7988	358	21	the	the	DET
aiti-7988	358	22	lateral	lateral	ADJ
aiti-7988	358	23	component	component	NOUN
aiti-7988	358	24	becomes	become	VERB
aiti-7988	358	25	larger	large	ADJ
aiti-7988	358	26	with	with	ADP
aiti-7988	358	27	the	the	DET
aiti-7988	358	28	increase	increase	NOUN
aiti-7988	358	29	of	of	ADP
aiti-7988	358	30	the	the	DET
aiti-7988	358	31	inclination	inclination	NOUN
aiti-7988	358	32	angle	angle	NOUN
aiti-7988	358	33	which	which	PRON
aiti-7988	358	34	causes	cause	VERB
aiti-7988	358	35	the	the	DET
aiti-7988	358	36	natural	natural	ADJ
aiti-7988	358	37	frequency	frequency	NOUN
aiti-7988	358	38	become	become	VERB
aiti-7988	358	39	lower	low	ADJ
aiti-7988	358	40	and	and	CCONJ
aiti-7988	358	41	eventually	eventually	ADV
aiti-7988	358	42	same	same	ADJ
aiti-7988	358	43	as	as	ADP
aiti-7988	358	44	the	the	DET
aiti-7988	358	45	horizontal	horizontal	ADJ
aiti-7988	358	46	case	case	NOUN
aiti-7988	358	47	.	.	PUNCT
aiti-7988	359	1	(	(	PUNCT
aiti-7988	359	2	a	a	X
aiti-7988	359	3	)	)	PUNCT
aiti-7988	359	4	l	l	NOUN
aiti-7988	359	5	/	/	SYM
aiti-7988	359	6	d	d	NOUN
aiti-7988	359	7	=	=	SYM
aiti-7988	359	8	20	20	NUM
aiti-7988	359	9	(	(	PUNCT
aiti-7988	359	10	b	b	NOUN
aiti-7988	359	11	)	)	PUNCT
aiti-7988	359	12	l	l	NOUN
aiti-7988	359	13	/	/	SYM
aiti-7988	359	14	d	d	NOUN
aiti-7988	359	15	=	=	SYM
aiti-7988	359	16	30	30	NUM
aiti-7988	359	17	(	(	PUNCT
aiti-7988	359	18	c	c	NOUN
aiti-7988	359	19	)	)	PUNCT
aiti-7988	359	20	l	l	NOUN
aiti-7988	359	21	/	/	SYM
aiti-7988	359	22	d	d	NOUN
aiti-7988	359	23	=	=	SYM
aiti-7988	359	24	50	50	NUM
aiti-7988	359	25	fig	fig	NOUN
aiti-7988	359	26	.	.	PUNCT
aiti-7988	360	1	6	6	NUM
aiti-7988	360	2	the	the	DET
aiti-7988	360	3	natural	natural	ADJ
aiti-7988	360	4	frequency	frequency	NOUN
aiti-7988	360	5	value	value	NOUN
aiti-7988	360	6	versus	versus	ADP
aiti-7988	360	7	internal	internal	ADJ
aiti-7988	360	8	fluid	fluid	ADJ
aiti-7988	360	9	velocity	velocity	NOUN
aiti-7988	360	10	with	with	ADP
aiti-7988	360	11	different	different	ADJ
aiti-7988	360	12	inclination	inclination	NOUN
aiti-7988	360	13	angles	angle	NOUN
aiti-7988	360	14	and	and	CCONJ
aiti-7988	360	15	aspect	aspect	VERB
aiti-7988	360	16	ratios	ratio	NOUN
aiti-7988	360	17	for	for	ADP
aiti-7988	360	18	the	the	DET
aiti-7988	360	19	case	case	NOUN
aiti-7988	360	20	of	of	ADP
aiti-7988	360	21	t	t	NOUN
aiti-7988	360	22	=	=	SYM
aiti-7988	360	23	25	25	NUM
aiti-7988	360	24	°	°	NUM
aiti-7988	360	25	c	c	NOUN
aiti-7988	360	26	and	and	CCONJ
aiti-7988	360	27	n	n	CCONJ
aiti-7988	360	28	=	=	SYM
aiti-7988	360	29	1	1	NUM
aiti-7988	360	30	51	51	NUM
aiti-7988	360	31	advances	advance	NOUN
aiti-7988	360	32	in	in	ADP
aiti-7988	360	33	technology	technology	NOUN
aiti-7988	360	34	innovation	innovation	NOUN
aiti-7988	360	35	,	,	PUNCT
aiti-7988	360	36	vol	vol	NOUN
aiti-7988	360	37	.	.	PROPN
aiti-7988	361	1	7	7	NUM
aiti-7988	361	2	,	,	PUNCT
aiti-7988	361	3	no	no	INTJ
aiti-7988	361	4	.	.	NOUN
aiti-7988	361	5	1	1	NUM
aiti-7988	361	6	,	,	PUNCT
aiti-7988	361	7	2022	2022	NUM
aiti-7988	361	8	,	,	PUNCT
aiti-7988	361	9	pp	pp	ADJ
aiti-7988	361	10	.	.	PUNCT
aiti-7988	362	1	41	41	NUM
aiti-7988	362	2	-	-	SYM
aiti-7988	362	3	55	55	NUM
aiti-7988	362	4	fig	fig	NOUN
aiti-7988	362	5	.	.	PUNCT
aiti-7988	363	1	7	7	NUM
aiti-7988	363	2	the	the	DET
aiti-7988	363	3	natural	natural	ADJ
aiti-7988	363	4	frequency	frequency	NOUN
aiti-7988	363	5	value	value	NOUN
aiti-7988	363	6	versus	versus	ADP
aiti-7988	363	7	inclination	inclination	NOUN
aiti-7988	363	8	angle	angle	NOUN
aiti-7988	363	9	with	with	ADP
aiti-7988	363	10	different	different	ADJ
aiti-7988	363	11	aspect	aspect	NOUN
aiti-7988	363	12	ratios	ratio	NOUN
aiti-7988	363	13	for	for	ADP
aiti-7988	363	14	the	the	DET
aiti-7988	363	15	case	case	NOUN
aiti-7988	363	16	of	of	ADP
aiti-7988	363	17	t	t	NOUN
aiti-7988	363	18	=	=	SYM
aiti-7988	363	19	25	25	NUM
aiti-7988	363	20	°	°	NOUN
aiti-7988	363	21	c	c	NOUN
aiti-7988	363	22	,	,	PUNCT
aiti-7988	363	23	u	u	NOUN
aiti-7988	363	24	=	=	NOUN
aiti-7988	363	25	1	1	NUM
aiti-7988	363	26	,	,	PUNCT
aiti-7988	363	27	and	and	CCONJ
aiti-7988	363	28	n	n	CCONJ
aiti-7988	363	29	=	=	SYM
aiti-7988	363	30	1	1	NUM
aiti-7988	363	31	fig	fig	NOUN
aiti-7988	363	32	.	.	PUNCT
aiti-7988	364	1	8	8	NUM
aiti-7988	364	2	describes	describe	VERB
aiti-7988	364	3	the	the	DET
aiti-7988	364	4	effect	effect	NOUN
aiti-7988	364	5	of	of	ADP
aiti-7988	364	6	the	the	DET
aiti-7988	364	7	temperature	temperature	NOUN
aiti-7988	364	8	variation	variation	NOUN
aiti-7988	364	9	on	on	ADP
aiti-7988	364	10	the	the	DET
aiti-7988	364	11	fundamental	fundamental	ADJ
aiti-7988	364	12	natural	natural	ADJ
aiti-7988	364	13	frequency	frequency	NOUN
aiti-7988	364	14	and	and	CCONJ
aiti-7988	364	15	the	the	DET
aiti-7988	364	16	critical	critical	ADJ
aiti-7988	364	17	velocity	velocity	NOUN
aiti-7988	364	18	of	of	ADP
aiti-7988	364	19	the	the	DET
aiti-7988	364	20	pipe	pipe	NOUN
aiti-7988	364	21	conveying	convey	VERB
aiti-7988	364	22	fluid	fluid	NOUN
aiti-7988	364	23	for	for	ADP
aiti-7988	364	24	different	different	ADJ
aiti-7988	364	25	aspect	aspect	NOUN
aiti-7988	364	26	ratios	ratio	NOUN
aiti-7988	364	27	.	.	PUNCT
aiti-7988	365	1	the	the	DET
aiti-7988	365	2	results	result	NOUN
aiti-7988	365	3	reveal	reveal	VERB
aiti-7988	365	4	that	that	SCONJ
aiti-7988	365	5	the	the	DET
aiti-7988	365	6	temperature	temperature	NOUN
aiti-7988	365	7	variation	variation	NOUN
aiti-7988	365	8	has	have	VERB
aiti-7988	365	9	a	a	DET
aiti-7988	365	10	great	great	ADJ
aiti-7988	365	11	influence	influence	NOUN
aiti-7988	365	12	on	on	ADP
aiti-7988	365	13	the	the	DET
aiti-7988	365	14	fundamental	fundamental	ADJ
aiti-7988	365	15	natural	natural	ADJ
aiti-7988	365	16	frequencies	frequency	NOUN
aiti-7988	365	17	and	and	CCONJ
aiti-7988	365	18	the	the	DET
aiti-7988	365	19	critical	critical	ADJ
aiti-7988	365	20	velocity	velocity	NOUN
aiti-7988	365	21	.	.	PUNCT
aiti-7988	366	1	here	here	ADV
aiti-7988	366	2	,	,	PUNCT
aiti-7988	366	3	as	as	ADP
aiti-7988	366	4	temperature	temperature	NOUN
aiti-7988	366	5	increases	increase	NOUN
aiti-7988	366	6	,	,	PUNCT
aiti-7988	366	7	a	a	DET
aiti-7988	366	8	significant	significant	ADJ
aiti-7988	366	9	reduction	reduction	NOUN
aiti-7988	366	10	in	in	ADP
aiti-7988	366	11	fundamental	fundamental	ADJ
aiti-7988	366	12	natural	natural	ADJ
aiti-7988	366	13	frequency	frequency	NOUN
aiti-7988	366	14	and	and	CCONJ
aiti-7988	366	15	critical	critical	ADJ
aiti-7988	366	16	velocity	velocity	NOUN
aiti-7988	366	17	is	be	AUX
aiti-7988	366	18	observed	observe	VERB
aiti-7988	366	19	.	.	PUNCT
aiti-7988	367	1	thus	thus	ADV
aiti-7988	367	2	,	,	PUNCT
aiti-7988	367	3	the	the	DET
aiti-7988	367	4	temperature	temperature	NOUN
aiti-7988	367	5	variations	variation	NOUN
aiti-7988	367	6	have	have	VERB
aiti-7988	367	7	a	a	DET
aiti-7988	367	8	softening	soften	VERB
aiti-7988	367	9	effect	effect	NOUN
aiti-7988	367	10	on	on	ADP
aiti-7988	367	11	the	the	DET
aiti-7988	367	12	pipe	pipe	NOUN
aiti-7988	367	13	stiffness	stiffness	NOUN
aiti-7988	367	14	,	,	PUNCT
aiti-7988	367	15	which	which	PRON
aiti-7988	367	16	is	be	AUX
aiti-7988	367	17	consistent	consistent	ADJ
aiti-7988	367	18	with	with	ADP
aiti-7988	367	19	the	the	DET
aiti-7988	367	20	work	work	NOUN
aiti-7988	367	21	of	of	ADP
aiti-7988	367	22	ashley	ashley	PROPN
aiti-7988	367	23	et	et	PROPN
aiti-7988	367	24	al	al	PROPN
aiti-7988	367	25	.	.	PUNCT
aiti-7988	368	1	[	[	X
aiti-7988	368	2	32	32	NUM
aiti-7988	368	3	]	]	PUNCT
aiti-7988	368	4	where	where	SCONJ
aiti-7988	368	5	the	the	DET
aiti-7988	368	6	natural	natural	ADJ
aiti-7988	368	7	frequency	frequency	NOUN
aiti-7988	368	8	was	be	AUX
aiti-7988	368	9	found	find	VERB
aiti-7988	368	10	to	to	PART
aiti-7988	368	11	be	be	AUX
aiti-7988	368	12	inversely	inversely	ADV
aiti-7988	368	13	proportional	proportional	ADJ
aiti-7988	368	14	to	to	ADP
aiti-7988	368	15	the	the	DET
aiti-7988	368	16	temperature	temperature	NOUN
aiti-7988	368	17	and	and	CCONJ
aiti-7988	368	18	with	with	ADP
aiti-7988	368	19	the	the	DET
aiti-7988	368	20	work	work	NOUN
aiti-7988	368	21	of	of	ADP
aiti-7988	368	22	orolu	orolu	PROPN
aiti-7988	368	23	et	et	PROPN
aiti-7988	368	24	al	al	PROPN
aiti-7988	368	25	.	.	PUNCT
aiti-7988	369	1	[	[	X
aiti-7988	369	2	33	33	NUM
aiti-7988	369	3	]	]	PUNCT
aiti-7988	369	4	where	where	SCONJ
aiti-7988	369	5	the	the	DET
aiti-7988	369	6	critical	critical	ADJ
aiti-7988	369	7	velocity	velocity	NOUN
aiti-7988	369	8	reduces	reduce	VERB
aiti-7988	369	9	with	with	ADP
aiti-7988	369	10	the	the	DET
aiti-7988	369	11	increase	increase	NOUN
aiti-7988	369	12	of	of	ADP
aiti-7988	369	13	temperature	temperature	NOUN
aiti-7988	369	14	.	.	PUNCT
aiti-7988	370	1	also	also	ADV
aiti-7988	370	2	,	,	PUNCT
aiti-7988	370	3	it	it	PRON
aiti-7988	370	4	is	be	AUX
aiti-7988	370	5	noted	note	VERB
aiti-7988	370	6	that	that	SCONJ
aiti-7988	370	7	the	the	DET
aiti-7988	370	8	temperature	temperature	NOUN
aiti-7988	370	9	effect	effect	NOUN
aiti-7988	370	10	on	on	ADP
aiti-7988	370	11	the	the	DET
aiti-7988	370	12	fundamental	fundamental	ADJ
aiti-7988	370	13	natural	natural	ADJ
aiti-7988	370	14	frequency	frequency	NOUN
aiti-7988	370	15	and	and	CCONJ
aiti-7988	370	16	the	the	DET
aiti-7988	370	17	critical	critical	ADJ
aiti-7988	370	18	velocity	velocity	NOUN
aiti-7988	370	19	of	of	ADP
aiti-7988	370	20	the	the	DET
aiti-7988	370	21	pipe	pipe	NOUN
aiti-7988	370	22	conveying	conveying	NOUN
aiti-7988	370	23	fluid	fluid	NOUN
aiti-7988	370	24	is	be	AUX
aiti-7988	370	25	considerably	considerably	ADV
aiti-7988	370	26	growing	grow	VERB
aiti-7988	370	27	at	at	ADP
aiti-7988	370	28	higher	high	ADJ
aiti-7988	370	29	aspect	aspect	NOUN
aiti-7988	370	30	ratio	ratio	NOUN
aiti-7988	370	31	.	.	PUNCT
aiti-7988	371	1	for	for	ADP
aiti-7988	371	2	example	example	NOUN
aiti-7988	371	3	,	,	PUNCT
aiti-7988	371	4	the	the	DET
aiti-7988	371	5	natural	natural	ADJ
aiti-7988	371	6	frequency	frequency	NOUN
aiti-7988	371	7	and	and	CCONJ
aiti-7988	371	8	critical	critical	ADJ
aiti-7988	371	9	velocity	velocity	NOUN
aiti-7988	371	10	reduce	reduce	VERB
aiti-7988	371	11	from	from	ADP
aiti-7988	371	12	“	"	PUNCT
aiti-7988	371	13	23.23	23.23	NUM
aiti-7988	371	14	and	and	CCONJ
aiti-7988	371	15	7.46	7.46	NUM
aiti-7988	371	16	”	"	PUNCT
aiti-7988	371	17	to	to	ADP
aiti-7988	371	18	“	"	PUNCT
aiti-7988	371	19	22.89	22.89	NUM
aiti-7988	371	20	and	and	CCONJ
aiti-7988	371	21	7.35	7.35	NUM
aiti-7988	371	22	”	"	PUNCT
aiti-7988	371	23	respectively	respectively	ADV
aiti-7988	371	24	at	at	ADP
aiti-7988	371	25	l	l	PROPN
aiti-7988	371	26	/	/	SYM
aiti-7988	371	27	d	d	NOUN
aiti-7988	371	28	=	=	SYM
aiti-7988	371	29	20	20	NUM
aiti-7988	371	30	,	,	PUNCT
aiti-7988	371	31	while	while	SCONJ
aiti-7988	371	32	the	the	DET
aiti-7988	371	33	lowering	lowering	NOUN
aiti-7988	371	34	is	be	AUX
aiti-7988	371	35	from	from	ADP
aiti-7988	371	36	“	"	PUNCT
aiti-7988	371	37	23.2	23.2	NUM
aiti-7988	371	38	and	and	CCONJ
aiti-7988	371	39	7.38	7.38	NUM
aiti-7988	371	40	”	"	PUNCT
aiti-7988	371	41	to	to	ADP
aiti-7988	371	42	“	"	PUNCT
aiti-7988	371	43	4.55	4.55	NUM
aiti-7988	371	44	and	and	CCONJ
aiti-7988	371	45	0.09	0.09	NUM
aiti-7988	371	46	”	"	PUNCT
aiti-7988	371	47	respectively	respectively	ADV
aiti-7988	371	48	at	at	ADP
aiti-7988	371	49	l	l	PROPN
aiti-7988	371	50	/	/	SYM
aiti-7988	371	51	d	d	NOUN
aiti-7988	371	52	=	=	SYM
aiti-7988	371	53	50	50	NUM
aiti-7988	371	54	.	.	PUNCT
aiti-7988	372	1	it	it	PRON
aiti-7988	372	2	can	can	AUX
aiti-7988	372	3	be	be	AUX
aiti-7988	372	4	inferred	infer	VERB
aiti-7988	372	5	from	from	ADP
aiti-7988	372	6	these	these	DET
aiti-7988	372	7	results	result	NOUN
aiti-7988	372	8	that	that	SCONJ
aiti-7988	372	9	the	the	DET
aiti-7988	372	10	pipe	pipe	NOUN
aiti-7988	372	11	may	may	AUX
aiti-7988	372	12	be	be	AUX
aiti-7988	372	13	losing	lose	VERB
aiti-7988	372	14	their	their	PRON
aiti-7988	372	15	stability	stability	NOUN
aiti-7988	372	16	even	even	ADV
aiti-7988	372	17	with	with	ADP
aiti-7988	372	18	zero	zero	NUM
aiti-7988	372	19	fluid	fluid	ADJ
aiti-7988	372	20	velocity	velocity	NOUN
aiti-7988	372	21	with	with	ADP
aiti-7988	372	22	the	the	DET
aiti-7988	372	23	increasing	increase	VERB
aiti-7988	372	24	temperature	temperature	NOUN
aiti-7988	372	25	.	.	PUNCT
aiti-7988	373	1	this	this	PRON
aiti-7988	373	2	suggests	suggest	VERB
aiti-7988	373	3	that	that	SCONJ
aiti-7988	373	4	the	the	DET
aiti-7988	373	5	temperature	temperature	NOUN
aiti-7988	373	6	effect	effect	NOUN
aiti-7988	373	7	becomes	become	VERB
aiti-7988	373	8	more	more	ADV
aiti-7988	373	9	essential	essential	ADJ
aiti-7988	373	10	parameter	parameter	NOUN
aiti-7988	373	11	,	,	PUNCT
aiti-7988	373	12	for	for	ADP
aiti-7988	373	13	engineers	engineer	NOUN
aiti-7988	373	14	and	and	CCONJ
aiti-7988	373	15	designers	designer	NOUN
aiti-7988	373	16	,	,	PUNCT
aiti-7988	373	17	than	than	ADP
aiti-7988	373	18	the	the	DET
aiti-7988	373	19	velocity	velocity	NOUN
aiti-7988	373	20	of	of	ADP
aiti-7988	373	21	fluid	fluid	NOUN
aiti-7988	373	22	flowing	flow	VERB
aiti-7988	373	23	inside	inside	ADP
aiti-7988	373	24	the	the	DET
aiti-7988	373	25	pipe	pipe	NOUN
aiti-7988	373	26	at	at	ADP
aiti-7988	373	27	higher	high	ADJ
aiti-7988	373	28	aspect	aspect	NOUN
aiti-7988	373	29	ratio	ratio	NOUN
aiti-7988	373	30	as	as	ADP
aiti-7988	373	31	designing	design	VERB
aiti-7988	373	32	the	the	DET
aiti-7988	373	33	pipelines	pipeline	NOUN
aiti-7988	373	34	systems	system	NOUN
aiti-7988	373	35	.	.	PUNCT
aiti-7988	374	1	the	the	DET
aiti-7988	374	2	temperature	temperature	NOUN
aiti-7988	374	3	effect	effect	NOUN
aiti-7988	374	4	on	on	ADP
aiti-7988	374	5	natural	natural	ADJ
aiti-7988	374	6	frequencies	frequency	NOUN
aiti-7988	374	7	is	be	AUX
aiti-7988	374	8	further	far	ADV
aiti-7988	374	9	examined	examine	VERB
aiti-7988	374	10	by	by	ADP
aiti-7988	374	11	plotting	plot	VERB
aiti-7988	374	12	in	in	ADP
aiti-7988	374	13	fig	fig	NOUN
aiti-7988	374	14	.	.	PUNCT
aiti-7988	375	1	9	9	NUM
aiti-7988	375	2	the	the	DET
aiti-7988	375	3	variation	variation	NOUN
aiti-7988	375	4	of	of	ADP
aiti-7988	375	5	the	the	DET
aiti-7988	375	6	fundamental	fundamental	ADJ
aiti-7988	375	7	natural	natural	ADJ
aiti-7988	375	8	frequencies	frequency	NOUN
aiti-7988	375	9	with	with	ADP
aiti-7988	375	10	the	the	DET
aiti-7988	375	11	pipe	pipe	NOUN
aiti-7988	375	12	’s	’s	PART
aiti-7988	375	13	inclination	inclination	NOUN
aiti-7988	375	14	angle	angle	NOUN
aiti-7988	375	15	for	for	ADP
aiti-7988	375	16	different	different	ADJ
aiti-7988	375	17	temperatures	temperature	NOUN
aiti-7988	375	18	.	.	PUNCT
aiti-7988	376	1	the	the	DET
aiti-7988	376	2	curves	curve	NOUN
aiti-7988	376	3	in	in	ADP
aiti-7988	376	4	fig	fig	NOUN
aiti-7988	376	5	.	.	PUNCT
aiti-7988	377	1	9	9	NUM
aiti-7988	377	2	manifest	manifest	NOUN
aiti-7988	377	3	that	that	SCONJ
aiti-7988	377	4	when	when	SCONJ
aiti-7988	377	5	the	the	DET
aiti-7988	377	6	variation	variation	NOUN
aiti-7988	377	7	in	in	ADP
aiti-7988	377	8	the	the	DET
aiti-7988	377	9	pipe	pipe	NOUN
aiti-7988	377	10	temperature	temperature	NOUN
aiti-7988	377	11	is	be	AUX
aiti-7988	377	12	slight	slight	ADJ
aiti-7988	377	13	,	,	PUNCT
aiti-7988	377	14	the	the	DET
aiti-7988	377	15	change	change	NOUN
aiti-7988	377	16	of	of	ADP
aiti-7988	377	17	the	the	DET
aiti-7988	377	18	inclination	inclination	NOUN
aiti-7988	377	19	angle	angle	NOUN
aiti-7988	377	20	has	have	VERB
aiti-7988	377	21	very	very	ADV
aiti-7988	377	22	little	little	ADJ
aiti-7988	377	23	effect	effect	NOUN
aiti-7988	377	24	on	on	ADP
aiti-7988	377	25	the	the	DET
aiti-7988	377	26	fundamental	fundamental	ADJ
aiti-7988	377	27	natural	natural	ADJ
aiti-7988	377	28	frequency	frequency	NOUN
aiti-7988	377	29	.	.	PUNCT
aiti-7988	378	1	however	however	ADV
aiti-7988	378	2	,	,	PUNCT
aiti-7988	378	3	as	as	ADP
aiti-7988	378	4	the	the	DET
aiti-7988	378	5	pipe	pipe	NOUN
aiti-7988	378	6	temperature	temperature	NOUN
aiti-7988	378	7	increases	increase	NOUN
aiti-7988	378	8	,	,	PUNCT
aiti-7988	378	9	the	the	DET
aiti-7988	378	10	influence	influence	NOUN
aiti-7988	378	11	of	of	ADP
aiti-7988	378	12	inclination	inclination	NOUN
aiti-7988	378	13	angle	angle	NOUN
aiti-7988	378	14	becomes	become	VERB
aiti-7988	378	15	more	more	ADV
aiti-7988	378	16	noticeable	noticeable	ADJ
aiti-7988	378	17	.	.	PUNCT
aiti-7988	379	1	(	(	PUNCT
aiti-7988	379	2	a	a	X
aiti-7988	379	3	)	)	PUNCT
aiti-7988	379	4	l	l	NOUN
aiti-7988	379	5	/	/	SYM
aiti-7988	379	6	d	d	NOUN
aiti-7988	379	7	=	=	SYM
aiti-7988	379	8	20	20	NUM
aiti-7988	379	9	fig	fig	NOUN
aiti-7988	379	10	.	.	PUNCT
aiti-7988	380	1	8	8	NUM
aiti-7988	380	2	the	the	DET
aiti-7988	380	3	natural	natural	ADJ
aiti-7988	380	4	frequency	frequency	NOUN
aiti-7988	380	5	value	value	NOUN
aiti-7988	380	6	versus	versus	ADP
aiti-7988	380	7	fluid	fluid	ADJ
aiti-7988	380	8	velocity	velocity	NOUN
aiti-7988	380	9	with	with	ADP
aiti-7988	380	10	different	different	ADJ
aiti-7988	380	11	temperatures	temperature	NOUN
aiti-7988	380	12	and	and	CCONJ
aiti-7988	380	13	aspect	aspect	VERB
aiti-7988	380	14	ratios	ratio	NOUN
aiti-7988	380	15	for	for	ADP
aiti-7988	380	16	the	the	DET
aiti-7988	380	17	case	case	NOUN
aiti-7988	380	18	of	of	ADP
aiti-7988	380	19	θ	θ	PROPN
aiti-7988	380	20	=	=	PUNCT
aiti-7988	380	21	0	0	NUM
aiti-7988	380	22	°	°	NUM
aiti-7988	380	23	and	and	CCONJ
aiti-7988	380	24	n	n	CCONJ
aiti-7988	380	25	=	=	SYM
aiti-7988	380	26	1	1	NUM
aiti-7988	380	27	52	52	NUM
aiti-7988	380	28	advances	advance	NOUN
aiti-7988	380	29	in	in	ADP
aiti-7988	380	30	technology	technology	NOUN
aiti-7988	380	31	innovation	innovation	NOUN
aiti-7988	380	32	,	,	PUNCT
aiti-7988	380	33	vol	vol	NOUN
aiti-7988	380	34	.	.	PROPN
aiti-7988	381	1	7	7	NUM
aiti-7988	381	2	,	,	PUNCT
aiti-7988	381	3	no	no	INTJ
aiti-7988	381	4	.	.	NOUN
aiti-7988	381	5	1	1	NUM
aiti-7988	381	6	,	,	PUNCT
aiti-7988	381	7	2022	2022	NUM
aiti-7988	381	8	,	,	PUNCT
aiti-7988	381	9	pp	pp	ADJ
aiti-7988	381	10	.	.	PUNCT
aiti-7988	382	1	41	41	NUM
aiti-7988	382	2	-	-	SYM
aiti-7988	382	3	55	55	NUM
aiti-7988	382	4	(	(	PUNCT
aiti-7988	382	5	b	b	NOUN
aiti-7988	382	6	)	)	PUNCT
aiti-7988	382	7	l	l	NOUN
aiti-7988	382	8	/	/	SYM
aiti-7988	382	9	d	d	NOUN
aiti-7988	382	10	=	=	SYM
aiti-7988	382	11	30	30	NUM
aiti-7988	382	12	(	(	PUNCT
aiti-7988	382	13	c	c	NOUN
aiti-7988	382	14	)	)	PUNCT
aiti-7988	382	15	l	l	NOUN
aiti-7988	382	16	/	/	SYM
aiti-7988	382	17	d	d	NOUN
aiti-7988	382	18	=	=	SYM
aiti-7988	382	19	50	50	NUM
aiti-7988	382	20	fig	fig	NOUN
aiti-7988	382	21	.	.	PUNCT
aiti-7988	383	1	8	8	NUM
aiti-7988	383	2	the	the	DET
aiti-7988	383	3	natural	natural	ADJ
aiti-7988	383	4	frequency	frequency	NOUN
aiti-7988	383	5	value	value	NOUN
aiti-7988	383	6	versus	versus	ADP
aiti-7988	383	7	fluid	fluid	ADJ
aiti-7988	383	8	velocity	velocity	NOUN
aiti-7988	383	9	with	with	ADP
aiti-7988	383	10	different	different	ADJ
aiti-7988	383	11	temperatures	temperature	NOUN
aiti-7988	383	12	and	and	CCONJ
aiti-7988	383	13	aspect	aspect	VERB
aiti-7988	383	14	ratios	ratio	NOUN
aiti-7988	383	15	for	for	ADP
aiti-7988	383	16	the	the	DET
aiti-7988	383	17	case	case	NOUN
aiti-7988	383	18	of	of	ADP
aiti-7988	383	19	θ	θ	PROPN
aiti-7988	383	20	=	=	PUNCT
aiti-7988	383	21	0	0	NUM
aiti-7988	383	22	°	°	NUM
aiti-7988	383	23	and	and	CCONJ
aiti-7988	383	24	n	n	CCONJ
aiti-7988	383	25	=	=	SYM
aiti-7988	383	26	1	1	NUM
aiti-7988	383	27	(	(	PUNCT
aiti-7988	383	28	continued	continued	ADJ
aiti-7988	383	29	)	)	PUNCT
aiti-7988	383	30	fig	fig	NOUN
aiti-7988	383	31	.	.	PUNCT
aiti-7988	384	1	9	9	NUM
aiti-7988	384	2	the	the	DET
aiti-7988	384	3	natural	natural	ADJ
aiti-7988	384	4	frequency	frequency	NOUN
aiti-7988	384	5	value	value	NOUN
aiti-7988	384	6	versus	versus	ADP
aiti-7988	384	7	pipe	pipe	NOUN
aiti-7988	384	8	’s	’s	PART
aiti-7988	384	9	inclination	inclination	NOUN
aiti-7988	384	10	angle	angle	NOUN
aiti-7988	384	11	with	with	ADP
aiti-7988	384	12	different	different	ADJ
aiti-7988	384	13	temperatures	temperature	NOUN
aiti-7988	384	14	for	for	ADP
aiti-7988	384	15	the	the	DET
aiti-7988	384	16	case	case	NOUN
aiti-7988	384	17	of	of	ADP
aiti-7988	384	18	u	u	NOUN
aiti-7988	384	19	=	=	PROPN
aiti-7988	384	20	1	1	NUM
aiti-7988	384	21	,	,	PUNCT
aiti-7988	384	22	n	n	NOUN
aiti-7988	384	23	=	=	SYM
aiti-7988	384	24	1	1	NUM
aiti-7988	384	25	,	,	PUNCT
aiti-7988	384	26	and	and	CCONJ
aiti-7988	384	27	l	l	NOUN
aiti-7988	384	28	/	/	SYM
aiti-7988	384	29	d	d	NOUN
aiti-7988	384	30	=	=	SYM
aiti-7988	384	31	50	50	NUM
aiti-7988	384	32	5	5	NUM
aiti-7988	384	33	.	.	PUNCT
aiti-7988	385	1	summary	summary	NOUN
aiti-7988	385	2	and	and	CCONJ
aiti-7988	385	3	conclusions	conclusion	NOUN
aiti-7988	385	4	the	the	DET
aiti-7988	385	5	itt	itt	NOUN
aiti-7988	385	6	for	for	ADP
aiti-7988	385	7	natural	natural	ADJ
aiti-7988	385	8	frequency	frequency	NOUN
aiti-7988	385	9	and	and	CCONJ
aiti-7988	385	10	dynamic	dynamic	ADJ
aiti-7988	385	11	response	response	NOUN
aiti-7988	385	12	computation	computation	NOUN
aiti-7988	385	13	of	of	ADP
aiti-7988	385	14	pp	pp	ADJ
aiti-7988	385	15	-	-	PUNCT
aiti-7988	385	16	r	r	NOUN
aiti-7988	385	17	pipe	pipe	NOUN
aiti-7988	385	18	containing	contain	VERB
aiti-7988	385	19	incompressible	incompressible	ADJ
aiti-7988	385	20	flowing	flow	VERB
aiti-7988	385	21	fluid	fluid	NOUN
aiti-7988	385	22	is	be	AUX
aiti-7988	385	23	proposed	propose	VERB
aiti-7988	385	24	in	in	ADP
aiti-7988	385	25	this	this	DET
aiti-7988	385	26	article	article	NOUN
aiti-7988	385	27	.	.	PUNCT
aiti-7988	386	1	the	the	DET
aiti-7988	386	2	euler	euler	PROPN
aiti-7988	386	3	-	-	PUNCT
aiti-7988	386	4	bernoulli	bernoulli	PROPN
aiti-7988	386	5	beam	beam	NOUN
aiti-7988	386	6	model	model	NOUN
aiti-7988	386	7	is	be	AUX
aiti-7988	386	8	applied	apply	VERB
aiti-7988	386	9	to	to	PART
aiti-7988	386	10	obtain	obtain	VERB
aiti-7988	386	11	the	the	DET
aiti-7988	386	12	transverse	transverse	ADJ
aiti-7988	386	13	vibration	vibration	NOUN
aiti-7988	386	14	of	of	ADP
aiti-7988	386	15	the	the	DET
aiti-7988	386	16	pipe	pipe	NOUN
aiti-7988	386	17	containing	contain	VERB
aiti-7988	386	18	flowing	flow	VERB
aiti-7988	386	19	fluid	fluid	NOUN
aiti-7988	386	20	.	.	PUNCT
aiti-7988	387	1	the	the	DET
aiti-7988	387	2	closed	close	VERB
aiti-7988	387	3	-	-	PUNCT
aiti-7988	387	4	form	form	NOUN
aiti-7988	387	5	analytical	analytical	ADJ
aiti-7988	387	6	expression	expression	NOUN
aiti-7988	387	7	used	use	VERB
aiti-7988	387	8	to	to	PART
aiti-7988	387	9	calculate	calculate	VERB
aiti-7988	387	10	both	both	DET
aiti-7988	387	11	natural	natural	ADJ
aiti-7988	387	12	frequency	frequency	NOUN
aiti-7988	387	13	and	and	CCONJ
aiti-7988	387	14	overall	overall	ADJ
aiti-7988	387	15	dynamic	dynamic	NOUN
aiti-7988	387	16	of	of	ADP
aiti-7988	387	17	the	the	DET
aiti-7988	387	18	fixed	fix	VERB
aiti-7988	387	19	supported	support	VERB
aiti-7988	387	20	pipe	pipe	NOUN
aiti-7988	387	21	containing	contain	VERB
aiti-7988	387	22	flowing	flow	VERB
aiti-7988	387	23	fluid	fluid	NOUN
aiti-7988	387	24	is	be	AUX
aiti-7988	387	25	derived	derive	VERB
aiti-7988	387	26	based	base	VERB
aiti-7988	387	27	on	on	ADP
aiti-7988	387	28	the	the	DET
aiti-7988	387	29	combination	combination	NOUN
aiti-7988	387	30	of	of	ADP
aiti-7988	387	31	finite	finite	ADJ
aiti-7988	387	32	fourier	fourier	NOUN
aiti-7988	387	33	sine	sine	NOUN
aiti-7988	387	34	and	and	CCONJ
aiti-7988	387	35	laplace	laplace	NOUN
aiti-7988	387	36	transforms	transform	VERB
aiti-7988	387	37	and	and	CCONJ
aiti-7988	387	38	their	their	PRON
aiti-7988	387	39	inverse	inverse	NOUN
aiti-7988	387	40	transform	transform	NOUN
aiti-7988	387	41	.	.	PUNCT
aiti-7988	388	1	the	the	DET
aiti-7988	388	2	effect	effect	NOUN
aiti-7988	388	3	of	of	ADP
aiti-7988	388	4	various	various	ADJ
aiti-7988	388	5	parameters	parameter	NOUN
aiti-7988	388	6	(	(	PUNCT
aiti-7988	388	7	internal	internal	ADJ
aiti-7988	388	8	flow	flow	NOUN
aiti-7988	388	9	velocity	velocity	NOUN
aiti-7988	388	10	,	,	PUNCT
aiti-7988	388	11	aspect	aspect	NOUN
aiti-7988	388	12	ratio	ratio	NOUN
aiti-7988	388	13	,	,	PUNCT
aiti-7988	388	14	inclination	inclination	NOUN
aiti-7988	388	15	angle	angle	NOUN
aiti-7988	388	16	,	,	PUNCT
aiti-7988	388	17	and	and	CCONJ
aiti-7988	388	18	temperature	temperature	NOUN
aiti-7988	388	19	variation	variation	NOUN
aiti-7988	388	20	)	)	PUNCT
aiti-7988	388	21	on	on	ADP
aiti-7988	388	22	the	the	DET
aiti-7988	388	23	vibration	vibration	NOUN
aiti-7988	388	24	characteristic	characteristic	NOUN
aiti-7988	388	25	of	of	ADP
aiti-7988	388	26	the	the	DET
aiti-7988	388	27	pipe	pipe	NOUN
aiti-7988	388	28	conveying	conveying	NOUN
aiti-7988	388	29	fluid	fluid	NOUN
aiti-7988	388	30	is	be	AUX
aiti-7988	388	31	presented	present	VERB
aiti-7988	388	32	.	.	PUNCT
aiti-7988	389	1	the	the	DET
aiti-7988	389	2	comparison	comparison	NOUN
aiti-7988	389	3	of	of	ADP
aiti-7988	389	4	the	the	DET
aiti-7988	389	5	numerical	numerical	ADJ
aiti-7988	389	6	results	result	NOUN
aiti-7988	389	7	of	of	ADP
aiti-7988	389	8	natural	natural	ADJ
aiti-7988	389	9	frequency	frequency	NOUN
aiti-7988	389	10	at	at	ADP
aiti-7988	389	11	different	different	ADJ
aiti-7988	389	12	internal	internal	ADJ
aiti-7988	389	13	fluid	fluid	ADJ
aiti-7988	389	14	velocity	velocity	NOUN
aiti-7988	389	15	with	with	ADP
aiti-7988	389	16	the	the	DET
aiti-7988	389	17	results	result	NOUN
aiti-7988	389	18	in	in	ADP
aiti-7988	389	19	published	publish	VERB
aiti-7988	389	20	references	reference	NOUN
aiti-7988	389	21	is	be	AUX
aiti-7988	389	22	conducted	conduct	VERB
aiti-7988	389	23	and	and	CCONJ
aiti-7988	389	24	shows	show	VERB
aiti-7988	389	25	a	a	DET
aiti-7988	389	26	good	good	ADJ
aiti-7988	389	27	agreement	agreement	NOUN
aiti-7988	389	28	.	.	PUNCT
aiti-7988	390	1	the	the	DET
aiti-7988	390	2	results	result	NOUN
aiti-7988	390	3	reveal	reveal	VERB
aiti-7988	390	4	that	that	SCONJ
aiti-7988	390	5	the	the	DET
aiti-7988	390	6	fundamental	fundamental	ADJ
aiti-7988	390	7	natural	natural	ADJ
aiti-7988	390	8	frequency	frequency	NOUN
aiti-7988	390	9	of	of	ADP
aiti-7988	390	10	the	the	DET
aiti-7988	390	11	pipe	pipe	NOUN
aiti-7988	390	12	containing	contain	VERB
aiti-7988	390	13	flowing	flow	VERB
aiti-7988	390	14	fluid	fluid	ADJ
aiti-7988	390	15	reduces	reduce	NOUN
aiti-7988	390	16	as	as	ADP
aiti-7988	390	17	the	the	DET
aiti-7988	390	18	internal	internal	ADJ
aiti-7988	390	19	flow	flow	NOUN
aiti-7988	390	20	velocity	velocity	NOUN
aiti-7988	390	21	increases	increase	NOUN
aiti-7988	390	22	.	.	PUNCT
aiti-7988	391	1	once	once	ADV
aiti-7988	391	2	the	the	DET
aiti-7988	391	3	fundamental	fundamental	ADJ
aiti-7988	391	4	natural	natural	ADJ
aiti-7988	391	5	frequency	frequency	NOUN
aiti-7988	391	6	reduces	reduce	VERB
aiti-7988	391	7	to	to	ADP
aiti-7988	391	8	zero	zero	NUM
aiti-7988	391	9	,	,	PUNCT
aiti-7988	391	10	the	the	DET
aiti-7988	391	11	divergence	divergence	NOUN
aiti-7988	391	12	instability	instability	NOUN
aiti-7988	391	13	happens	happen	VERB
aiti-7988	391	14	.	.	PUNCT
aiti-7988	392	1	the	the	DET
aiti-7988	392	2	findings	finding	NOUN
aiti-7988	392	3	of	of	ADP
aiti-7988	392	4	the	the	DET
aiti-7988	392	5	current	current	ADJ
aiti-7988	392	6	study	study	NOUN
aiti-7988	392	7	can	can	AUX
aiti-7988	392	8	be	be	AUX
aiti-7988	392	9	summarized	summarize	VERB
aiti-7988	392	10	as	as	SCONJ
aiti-7988	392	11	follows	follow	VERB
aiti-7988	392	12	:	:	PUNCT
aiti-7988	392	13	(	(	PUNCT
aiti-7988	392	14	1	1	X
aiti-7988	392	15	)	)	PUNCT
aiti-7988	392	16	the	the	DET
aiti-7988	392	17	proposed	propose	VERB
aiti-7988	392	18	analytical	analytical	ADJ
aiti-7988	392	19	method	method	NOUN
aiti-7988	392	20	has	have	VERB
aiti-7988	392	21	a	a	DET
aiti-7988	392	22	clear	clear	ADJ
aiti-7988	392	23	concept	concept	NOUN
aiti-7988	392	24	,	,	PUNCT
aiti-7988	392	25	suitable	suitable	ADJ
aiti-7988	392	26	for	for	ADP
aiti-7988	392	27	hand	hand	NOUN
aiti-7988	392	28	computation	computation	NOUN
aiti-7988	392	29	,	,	PUNCT
aiti-7988	392	30	and	and	CCONJ
aiti-7988	392	31	gives	give	VERB
aiti-7988	392	32	a	a	DET
aiti-7988	392	33	theoretical	theoretical	ADJ
aiti-7988	392	34	basis	basis	NOUN
aiti-7988	392	35	for	for	ADP
aiti-7988	392	36	more	more	ADJ
aiti-7988	392	37	engineering	engineering	NOUN
aiti-7988	392	38	applications	application	NOUN
aiti-7988	392	39	of	of	ADP
aiti-7988	392	40	the	the	DET
aiti-7988	392	41	inclined	incline	VERB
aiti-7988	392	42	fixed	fix	VERB
aiti-7988	392	43	supported	support	VERB
aiti-7988	392	44	pipe	pipe	NOUN
aiti-7988	392	45	conveying	conveying	NOUN
aiti-7988	392	46	fluid	fluid	NOUN
aiti-7988	392	47	under	under	ADP
aiti-7988	392	48	thermal	thermal	ADJ
aiti-7988	392	49	loads	load	NOUN
aiti-7988	392	50	.	.	PUNCT
aiti-7988	393	1	(	(	PUNCT
aiti-7988	393	2	2	2	X
aiti-7988	393	3	)	)	PUNCT
aiti-7988	393	4	the	the	DET
aiti-7988	393	5	aspect	aspect	NOUN
aiti-7988	393	6	ratio	ratio	NOUN
aiti-7988	393	7	,	,	PUNCT
aiti-7988	393	8	temperature	temperature	NOUN
aiti-7988	393	9	variation	variation	NOUN
aiti-7988	393	10	,	,	PUNCT
aiti-7988	393	11	and	and	CCONJ
aiti-7988	393	12	inclination	inclination	NOUN
aiti-7988	393	13	angle	angle	NOUN
aiti-7988	393	14	strongly	strongly	ADV
aiti-7988	393	15	affect	affect	VERB
aiti-7988	393	16	both	both	CCONJ
aiti-7988	393	17	the	the	DET
aiti-7988	393	18	natural	natural	ADJ
aiti-7988	393	19	frequency	frequency	NOUN
aiti-7988	393	20	and	and	CCONJ
aiti-7988	393	21	critical	critical	ADJ
aiti-7988	393	22	velocity	velocity	NOUN
aiti-7988	393	23	of	of	ADP
aiti-7988	393	24	the	the	DET
aiti-7988	393	25	system	system	NOUN
aiti-7988	393	26	.	.	PUNCT
aiti-7988	394	1	53	53	NUM
aiti-7988	394	2	advances	advance	NOUN
aiti-7988	394	3	in	in	ADP
aiti-7988	394	4	technology	technology	NOUN
aiti-7988	394	5	innovation	innovation	NOUN
aiti-7988	394	6	,	,	PUNCT
aiti-7988	394	7	vol	vol	NOUN
aiti-7988	394	8	.	.	PROPN
aiti-7988	394	9	7	7	NUM
aiti-7988	394	10	,	,	PUNCT
aiti-7988	394	11	no	no	INTJ
aiti-7988	394	12	.	.	NOUN
aiti-7988	394	13	1	1	NUM
aiti-7988	394	14	,	,	PUNCT
aiti-7988	394	15	2022	2022	NUM
aiti-7988	394	16	,	,	PUNCT
aiti-7988	394	17	pp	pp	ADJ
aiti-7988	394	18	.	.	PUNCT
aiti-7988	395	1	41	41	NUM
aiti-7988	395	2	-	-	SYM
aiti-7988	395	3	55	55	NUM
aiti-7988	395	4	(	(	PUNCT
aiti-7988	395	5	3	3	NUM
aiti-7988	395	6	)	)	PUNCT
aiti-7988	395	7	there	there	PRON
aiti-7988	395	8	is	be	VERB
aiti-7988	395	9	a	a	DET
aiti-7988	395	10	strong	strong	ADJ
aiti-7988	395	11	coupling	coupling	NOUN
aiti-7988	395	12	between	between	ADP
aiti-7988	395	13	the	the	DET
aiti-7988	395	14	aspect	aspect	NOUN
aiti-7988	395	15	ratio	ratio	NOUN
aiti-7988	395	16	of	of	ADP
aiti-7988	395	17	pipe	pipe	NOUN
aiti-7988	395	18	length	length	NOUN
aiti-7988	395	19	to	to	ADP
aiti-7988	395	20	its	its	PRON
aiti-7988	395	21	outside	outside	ADJ
aiti-7988	395	22	diameter	diameter	NOUN
aiti-7988	395	23	with	with	ADP
aiti-7988	395	24	temperature	temperature	NOUN
aiti-7988	395	25	variation	variation	NOUN
aiti-7988	395	26	and	and	CCONJ
aiti-7988	395	27	inclination	inclination	NOUN
aiti-7988	395	28	angle	angle	NOUN
aiti-7988	395	29	.	.	PUNCT
aiti-7988	396	1	(	(	PUNCT
aiti-7988	396	2	4	4	X
aiti-7988	396	3	)	)	PUNCT
aiti-7988	396	4	the	the	DET
aiti-7988	396	5	temperature	temperature	NOUN
aiti-7988	396	6	variation	variation	NOUN
aiti-7988	396	7	is	be	AUX
aiti-7988	396	8	a	a	DET
aiti-7988	396	9	major	major	ADJ
aiti-7988	396	10	concern	concern	NOUN
aiti-7988	396	11	rather	rather	ADV
aiti-7988	396	12	than	than	ADP
aiti-7988	396	13	the	the	DET
aiti-7988	396	14	internal	internal	ADJ
aiti-7988	396	15	fluid	fluid	ADJ
aiti-7988	396	16	velocity	velocity	NOUN
aiti-7988	396	17	in	in	ADP
aiti-7988	396	18	the	the	DET
aiti-7988	396	19	design	design	NOUN
aiti-7988	396	20	of	of	ADP
aiti-7988	396	21	the	the	DET
aiti-7988	396	22	pipe	pipe	NOUN
aiti-7988	396	23	containing	contain	VERB
aiti-7988	396	24	flowing	flow	VERB
aiti-7988	396	25	fluid	fluid	NOUN
aiti-7988	396	26	at	at	ADP
aiti-7988	396	27	higher	high	ADJ
aiti-7988	396	28	aspect	aspect	NOUN
aiti-7988	396	29	ratio	ratio	NOUN
aiti-7988	396	30	.	.	PUNCT
aiti-7988	397	1	(	(	PUNCT
aiti-7988	397	2	5	5	X
aiti-7988	397	3	)	)	PUNCT
aiti-7988	397	4	the	the	DET
aiti-7988	397	5	inclination	inclination	NOUN
aiti-7988	397	6	angle	angle	NOUN
aiti-7988	397	7	has	have	VERB
aiti-7988	397	8	larger	large	ADJ
aiti-7988	397	9	impact	impact	NOUN
aiti-7988	397	10	on	on	ADP
aiti-7988	397	11	vibration	vibration	NOUN
aiti-7988	397	12	characteristics	characteristic	NOUN
aiti-7988	397	13	at	at	ADP
aiti-7988	397	14	higher	high	ADJ
aiti-7988	397	15	aspect	aspect	NOUN
aiti-7988	397	16	ratio	ratio	NOUN
aiti-7988	397	17	,	,	PUNCT
aiti-7988	397	18	which	which	PRON
aiti-7988	397	19	should	should	AUX
aiti-7988	397	20	be	be	AUX
aiti-7988	397	21	paid	pay	VERB
aiti-7988	397	22	attention	attention	NOUN
aiti-7988	397	23	in	in	ADP
aiti-7988	397	24	engineering	engineering	NOUN
aiti-7988	397	25	.	.	PUNCT
aiti-7988	398	1	(	(	PUNCT
aiti-7988	398	2	6	6	NUM
aiti-7988	398	3	)	)	PUNCT
aiti-7988	398	4	the	the	DET
aiti-7988	398	5	natural	natural	ADJ
aiti-7988	398	6	frequency	frequency	NOUN
aiti-7988	398	7	and	and	CCONJ
aiti-7988	398	8	critical	critical	ADJ
aiti-7988	398	9	velocity	velocity	NOUN
aiti-7988	398	10	of	of	ADP
aiti-7988	398	11	the	the	DET
aiti-7988	398	12	pipe	pipe	NOUN
aiti-7988	398	13	-	-	PUNCT
aiti-7988	398	14	fluid	fluid	NOUN
aiti-7988	398	15	system	system	NOUN
aiti-7988	398	16	decrease	decrease	NOUN
aiti-7988	398	17	while	while	SCONJ
aiti-7988	398	18	its	its	PRON
aiti-7988	398	19	dynamic	dynamic	ADJ
aiti-7988	398	20	deflection	deflection	NOUN
aiti-7988	398	21	increases	increase	VERB
aiti-7988	398	22	with	with	ADP
aiti-7988	398	23	the	the	DET
aiti-7988	398	24	increase	increase	NOUN
aiti-7988	398	25	of	of	ADP
aiti-7988	398	26	temperature	temperature	NOUN
aiti-7988	398	27	.	.	PUNCT
aiti-7988	399	1	the	the	DET
aiti-7988	399	2	divergence	divergence	NOUN
aiti-7988	399	3	can	can	AUX
aiti-7988	399	4	occur	occur	VERB
aiti-7988	399	5	even	even	ADV
aiti-7988	399	6	when	when	SCONJ
aiti-7988	399	7	the	the	DET
aiti-7988	399	8	fluid	fluid	ADJ
aiti-7988	399	9	velocity	velocity	NOUN
aiti-7988	399	10	equals	equal	VERB
aiti-7988	399	11	zero	zero	NUM
aiti-7988	399	12	with	with	ADP
aiti-7988	399	13	the	the	DET
aiti-7988	399	14	increasing	increase	VERB
aiti-7988	399	15	temperature	temperature	NOUN
aiti-7988	399	16	of	of	ADP
aiti-7988	399	17	the	the	DET
aiti-7988	399	18	pipe	pipe	NOUN
aiti-7988	399	19	.	.	PUNCT
aiti-7988	400	1	(	(	PUNCT
aiti-7988	400	2	7	7	X
aiti-7988	400	3	)	)	PUNCT
aiti-7988	400	4	the	the	DET
aiti-7988	400	5	natural	natural	ADJ
aiti-7988	400	6	frequency	frequency	NOUN
aiti-7988	400	7	and	and	CCONJ
aiti-7988	400	8	critical	critical	ADJ
aiti-7988	400	9	velocity	velocity	NOUN
aiti-7988	400	10	of	of	ADP
aiti-7988	400	11	the	the	DET
aiti-7988	400	12	pipe	pipe	NOUN
aiti-7988	400	13	conveying	convey	VERB
aiti-7988	400	14	fluid	fluid	ADJ
aiti-7988	400	15	decrease	decrease	NOUN
aiti-7988	400	16	while	while	SCONJ
aiti-7988	400	17	its	its	PRON
aiti-7988	400	18	dynamic	dynamic	ADJ
aiti-7988	400	19	deflection	deflection	NOUN
aiti-7988	400	20	increases	increase	VERB
aiti-7988	400	21	with	with	ADP
aiti-7988	400	22	the	the	DET
aiti-7988	400	23	increase	increase	NOUN
aiti-7988	400	24	of	of	ADP
aiti-7988	400	25	aspect	aspect	NOUN
aiti-7988	400	26	ratio	ratio	NOUN
aiti-7988	400	27	.	.	PUNCT
aiti-7988	401	1	conflicts	conflict	NOUN
aiti-7988	401	2	of	of	ADP
aiti-7988	401	3	interest	interest	NOUN
aiti-7988	401	4	the	the	DET
aiti-7988	401	5	authors	author	NOUN
aiti-7988	401	6	declare	declare	VERB
aiti-7988	401	7	no	no	DET
aiti-7988	401	8	conflict	conflict	NOUN
aiti-7988	401	9	of	of	ADP
aiti-7988	401	10	interest	interest	NOUN
aiti-7988	401	11	.	.	PUNCT
aiti-7988	402	1	references	reference	NOUN
aiti-7988	402	2	[	[	X
aiti-7988	402	3	1	1	NUM
aiti-7988	402	4	]	]	PUNCT
aiti-7988	402	5	m.	m.	NOUN
aiti-7988	402	6	p.	p.	NOUN
aiti-7988	402	7	païdoussis	païdoussis	NOUN
aiti-7988	402	8	,	,	PUNCT
aiti-7988	402	9	fluid	fluid	ADJ
aiti-7988	402	10	-	-	PUNCT
aiti-7988	402	11	structure	structure	NOUN
aiti-7988	402	12	interactions	interaction	NOUN
aiti-7988	402	13	:	:	PUNCT
aiti-7988	402	14	slender	slender	ADJ
aiti-7988	402	15	structures	structure	NOUN
aiti-7988	402	16	and	and	CCONJ
aiti-7988	402	17	axial	axial	ADJ
aiti-7988	402	18	flow	flow	NOUN
aiti-7988	402	19	,	,	PUNCT
aiti-7988	402	20	2nd	2nd	ADJ
aiti-7988	402	21	ed	ed	NOUN
aiti-7988	402	22	.	.	PROPN
aiti-7988	402	23	,	,	PUNCT
aiti-7988	402	24	london	london	PROPN
aiti-7988	402	25	:	:	PUNCT
aiti-7988	402	26	academic	academic	ADJ
aiti-7988	402	27	press	press	NOUN
aiti-7988	402	28	,	,	PUNCT
aiti-7988	402	29	2014	2014	NUM
aiti-7988	402	30	.	.	PUNCT
aiti-7988	403	1	[	[	X
aiti-7988	403	2	2	2	X
aiti-7988	403	3	]	]	PUNCT
aiti-7988	403	4	v.	v.	CCONJ
aiti-7988	403	5	olunloyo	olunloyo	PROPN
aiti-7988	403	6	,	,	PUNCT
aiti-7988	403	7	c.	c.	PROPN
aiti-7988	403	8	osheku	osheku	PROPN
aiti-7988	403	9	,	,	PUNCT
aiti-7988	403	10	and	and	CCONJ
aiti-7988	403	11	p.	p.	PROPN
aiti-7988	403	12	olayiwola	olayiwola	NOUN
aiti-7988	403	13	,	,	PUNCT
aiti-7988	403	14	“	"	PUNCT
aiti-7988	403	15	concerning	concern	VERB
aiti-7988	403	16	the	the	DET
aiti-7988	403	17	effect	effect	NOUN
aiti-7988	403	18	of	of	ADP
aiti-7988	403	19	a	a	DET
aiti-7988	403	20	viscoelastic	viscoelastic	ADJ
aiti-7988	403	21	foundation	foundation	NOUN
aiti-7988	403	22	on	on	ADP
aiti-7988	403	23	the	the	DET
aiti-7988	403	24	dynamic	dynamic	ADJ
aiti-7988	403	25	stability	stability	NOUN
aiti-7988	403	26	of	of	ADP
aiti-7988	403	27	a	a	DET
aiti-7988	403	28	pipeline	pipeline	NOUN
aiti-7988	403	29	system	system	NOUN
aiti-7988	403	30	conveying	convey	VERB
aiti-7988	403	31	an	an	DET
aiti-7988	403	32	incompressible	incompressible	ADJ
aiti-7988	403	33	fluid	fluid	NOUN
aiti-7988	403	34	,	,	PUNCT
aiti-7988	403	35	”	"	PUNCT
aiti-7988	403	36	journal	journal	NOUN
aiti-7988	403	37	of	of	ADP
aiti-7988	403	38	applied	applied	ADJ
aiti-7988	403	39	and	and	CCONJ
aiti-7988	403	40	computational	computational	ADJ
aiti-7988	403	41	mechanics	mechanic	NOUN
aiti-7988	403	42	,	,	PUNCT
aiti-7988	403	43	vol	vol	NOUN
aiti-7988	403	44	.	.	PROPN
aiti-7988	403	45	2	2	NUM
aiti-7988	403	46	,	,	PUNCT
aiti-7988	403	47	no	no	INTJ
aiti-7988	403	48	.	.	NOUN
aiti-7988	403	49	2	2	NUM
aiti-7988	403	50	,	,	PUNCT
aiti-7988	403	51	pp	pp	ADJ
aiti-7988	403	52	.	.	PUNCT
aiti-7988	404	1	96	96	NUM
aiti-7988	404	2	-	-	SYM
aiti-7988	404	3	117	117	NUM
aiti-7988	404	4	,	,	PUNCT
aiti-7988	404	5	2016	2016	NUM
aiti-7988	404	6	.	.	PUNCT
aiti-7988	405	1	[	[	X
aiti-7988	405	2	3	3	X
aiti-7988	405	3	]	]	X
aiti-7988	405	4	g.	g.	PROPN
aiti-7988	405	5	w.	w.	PROPN
aiti-7988	405	6	housner	housner	PROPN
aiti-7988	405	7	,	,	PUNCT
aiti-7988	405	8	“	"	PUNCT
aiti-7988	405	9	bending	bend	VERB
aiti-7988	405	10	vibration	vibration	NOUN
aiti-7988	405	11	of	of	ADP
aiti-7988	405	12	a	a	DET
aiti-7988	405	13	pipe	pipe	NOUN
aiti-7988	405	14	line	line	NOUN
aiti-7988	405	15	containing	contain	VERB
aiti-7988	405	16	flowing	flow	VERB
aiti-7988	405	17	fluid	fluid	NOUN
aiti-7988	405	18	,	,	PUNCT
aiti-7988	405	19	”	"	PUNCT
aiti-7988	405	20	journal	journal	NOUN
aiti-7988	405	21	of	of	ADP
aiti-7988	405	22	applied	apply	VERB
aiti-7988	405	23	mechanics	mechanic	NOUN
aiti-7988	405	24	,	,	PUNCT
aiti-7988	405	25	vol	vol	NOUN
aiti-7988	405	26	.	.	PROPN
aiti-7988	405	27	19	19	NUM
aiti-7988	405	28	,	,	PUNCT
aiti-7988	405	29	no	no	INTJ
aiti-7988	405	30	.	.	NOUN
aiti-7988	405	31	2	2	NUM
aiti-7988	405	32	,	,	PUNCT
aiti-7988	405	33	pp	pp	ADJ
aiti-7988	405	34	.	.	PUNCT
aiti-7988	406	1	205	205	NUM
aiti-7988	406	2	-	-	SYM
aiti-7988	406	3	208	208	NUM
aiti-7988	406	4	,	,	PUNCT
aiti-7988	406	5	june	june	PROPN
aiti-7988	406	6	1952	1952	NUM
aiti-7988	406	7	.	.	PUNCT
aiti-7988	407	1	[	[	X
aiti-7988	407	2	4	4	X
aiti-7988	407	3	]	]	PUNCT
aiti-7988	407	4	r.	r.	PROPN
aiti-7988	407	5	a.	a.	PROPN
aiti-7988	407	6	stein	stein	PROPN
aiti-7988	407	7	and	and	CCONJ
aiti-7988	407	8	m.	m.	PROPN
aiti-7988	407	9	w.	w.	PROPN
aiti-7988	407	10	tobriner	tobriner	PROPN
aiti-7988	407	11	,	,	PUNCT
aiti-7988	407	12	“	"	PUNCT
aiti-7988	407	13	vibration	vibration	NOUN
aiti-7988	407	14	of	of	ADP
aiti-7988	407	15	pipes	pipe	NOUN
aiti-7988	407	16	containing	contain	VERB
aiti-7988	407	17	flowing	flow	VERB
aiti-7988	407	18	fluids	fluid	NOUN
aiti-7988	407	19	,	,	PUNCT
aiti-7988	407	20	”	"	PUNCT
aiti-7988	407	21	journal	journal	NOUN
aiti-7988	407	22	of	of	ADP
aiti-7988	407	23	applied	apply	VERB
aiti-7988	407	24	mechanics	mechanic	NOUN
aiti-7988	407	25	,	,	PUNCT
aiti-7988	407	26	vol	vol	NOUN
aiti-7988	407	27	.	.	PROPN
aiti-7988	408	1	37	37	NUM
aiti-7988	408	2	,	,	PUNCT
aiti-7988	408	3	no	no	INTJ
aiti-7988	408	4	.	.	NOUN
aiti-7988	408	5	4	4	NUM
aiti-7988	408	6	,	,	PUNCT
aiti-7988	408	7	pp	pp	ADJ
aiti-7988	408	8	.	.	PUNCT
aiti-7988	409	1	906	906	NUM
aiti-7988	409	2	-	-	SYM
aiti-7988	409	3	916	916	NUM
aiti-7988	409	4	,	,	PUNCT
aiti-7988	409	5	december	december	PROPN
aiti-7988	409	6	1970	1970	NUM
aiti-7988	409	7	.	.	PUNCT
aiti-7988	410	1	[	[	X
aiti-7988	410	2	5	5	NUM
aiti-7988	410	3	]	]	PUNCT
aiti-7988	410	4	m.	m.	NOUN
aiti-7988	410	5	p.	p.	NOUN
aiti-7988	410	6	païdoussis	païdoussis	NOUN
aiti-7988	410	7	,	,	PUNCT
aiti-7988	410	8	“	"	PUNCT
aiti-7988	410	9	flutter	flutter	NOUN
aiti-7988	410	10	of	of	ADP
aiti-7988	410	11	conservative	conservative	ADJ
aiti-7988	410	12	systems	system	NOUN
aiti-7988	410	13	of	of	ADP
aiti-7988	410	14	pipes	pipe	NOUN
aiti-7988	410	15	conveying	convey	VERB
aiti-7988	410	16	incompressible	incompressible	ADJ
aiti-7988	410	17	fluid	fluid	NOUN
aiti-7988	410	18	,	,	PUNCT
aiti-7988	410	19	”	"	PUNCT
aiti-7988	410	20	journal	journal	NOUN
aiti-7988	410	21	of	of	ADP
aiti-7988	410	22	mechanical	mechanical	ADJ
aiti-7988	410	23	engineering	engineering	NOUN
aiti-7988	410	24	science	science	NOUN
aiti-7988	410	25	,	,	PUNCT
aiti-7988	410	26	vol	vol	NOUN
aiti-7988	410	27	.	.	PROPN
aiti-7988	410	28	17	17	NUM
aiti-7988	410	29	,	,	PUNCT
aiti-7988	410	30	no	no	INTJ
aiti-7988	410	31	.	.	NOUN
aiti-7988	410	32	1	1	NUM
aiti-7988	410	33	,	,	PUNCT
aiti-7988	410	34	pp	pp	ADJ
aiti-7988	410	35	.	.	PUNCT
aiti-7988	411	1	19	19	NUM
aiti-7988	411	2	-	-	SYM
aiti-7988	411	3	25	25	NUM
aiti-7988	411	4	,	,	PUNCT
aiti-7988	411	5	february	february	PROPN
aiti-7988	411	6	1975	1975	NUM
aiti-7988	411	7	.	.	PUNCT
aiti-7988	412	1	[	[	X
aiti-7988	412	2	6	6	NUM
aiti-7988	412	3	]	]	PUNCT
aiti-7988	412	4	r.	r.	PROPN
aiti-7988	412	5	h.	h.	PROPN
aiti-7988	412	6	plaut	plaut	PROPN
aiti-7988	412	7	and	and	CCONJ
aiti-7988	412	8	k.	k.	PROPN
aiti-7988	412	9	huseyin	huseyin	PROPN
aiti-7988	412	10	,	,	PUNCT
aiti-7988	412	11	“	"	PUNCT
aiti-7988	412	12	instability	instability	NOUN
aiti-7988	412	13	of	of	ADP
aiti-7988	412	14	fluid	fluid	NOUN
aiti-7988	412	15	-	-	PUNCT
aiti-7988	412	16	conveying	convey	VERB
aiti-7988	412	17	pipes	pipe	NOUN
aiti-7988	412	18	under	under	ADP
aiti-7988	412	19	axial	axial	ADJ
aiti-7988	412	20	load	load	NOUN
aiti-7988	412	21	,	,	PUNCT
aiti-7988	412	22	”	"	PUNCT
aiti-7988	412	23	journal	journal	NOUN
aiti-7988	412	24	of	of	ADP
aiti-7988	412	25	applied	apply	VERB
aiti-7988	412	26	mechanics	mechanic	NOUN
aiti-7988	412	27	,	,	PUNCT
aiti-7988	412	28	vol	vol	NOUN
aiti-7988	412	29	.	.	PROPN
aiti-7988	412	30	42	42	NUM
aiti-7988	412	31	,	,	PUNCT
aiti-7988	412	32	no	no	INTJ
aiti-7988	412	33	.	.	NOUN
aiti-7988	412	34	4	4	NUM
aiti-7988	412	35	,	,	PUNCT
aiti-7988	412	36	pp	pp	ADJ
aiti-7988	412	37	.	.	PUNCT
aiti-7988	412	38	889	889	NUM
aiti-7988	412	39	-	-	SYM
aiti-7988	412	40	890	890	NUM
aiti-7988	412	41	,	,	PUNCT
aiti-7988	412	42	december	december	PROPN
aiti-7988	412	43	1975	1975	NUM
aiti-7988	412	44	.	.	PUNCT
aiti-7988	413	1	[	[	X
aiti-7988	413	2	7	7	X
aiti-7988	413	3	]	]	X
aiti-7988	413	4	f.	f.	PROPN
aiti-7988	413	5	j.	j.	PROPN
aiti-7988	413	6	hatfield	hatfield	PROPN
aiti-7988	413	7	,	,	PUNCT
aiti-7988	413	8	d.	d.	PROPN
aiti-7988	413	9	c.	c.	PROPN
aiti-7988	413	10	wiggert	wiggert	PROPN
aiti-7988	413	11	,	,	PUNCT
aiti-7988	413	12	and	and	CCONJ
aiti-7988	413	13	r.	r.	PROPN
aiti-7988	413	14	s.	s.	PROPN
aiti-7988	413	15	otwell	otwell	PROPN
aiti-7988	413	16	,	,	PUNCT
aiti-7988	413	17	“	"	PUNCT
aiti-7988	413	18	fluid	fluid	ADJ
aiti-7988	413	19	structure	structure	NOUN
aiti-7988	413	20	interaction	interaction	NOUN
aiti-7988	413	21	in	in	ADP
aiti-7988	413	22	piping	piping	NOUN
aiti-7988	413	23	by	by	ADP
aiti-7988	413	24	component	component	NOUN
aiti-7988	413	25	synthesis	synthesis	NOUN
aiti-7988	413	26	,	,	PUNCT
aiti-7988	413	27	”	"	PUNCT
aiti-7988	413	28	journal	journal	NOUN
aiti-7988	413	29	of	of	ADP
aiti-7988	413	30	applied	apply	VERB
aiti-7988	413	31	mechanics	mechanic	NOUN
aiti-7988	413	32	,	,	PUNCT
aiti-7988	413	33	vol	vol	NOUN
aiti-7988	413	34	.	.	PROPN
aiti-7988	413	35	104	104	NUM
aiti-7988	413	36	,	,	PUNCT
aiti-7988	413	37	no	no	INTJ
aiti-7988	413	38	.	.	NOUN
aiti-7988	413	39	3	3	NUM
aiti-7988	413	40	,	,	PUNCT
aiti-7988	413	41	pp	pp	ADJ
aiti-7988	413	42	.	.	PUNCT
aiti-7988	414	1	318	318	NUM
aiti-7988	414	2	-	-	SYM
aiti-7988	414	3	325	325	NUM
aiti-7988	414	4	,	,	PUNCT
aiti-7988	414	5	september	september	PROPN
aiti-7988	414	6	1982	1982	NUM
aiti-7988	414	7	.	.	PUNCT
aiti-7988	415	1	[	[	X
aiti-7988	415	2	8	8	NUM
aiti-7988	415	3	]	]	PUNCT
aiti-7988	415	4	m.	m.	NOUN
aiti-7988	415	5	w.	w.	PROPN
aiti-7988	415	6	lesmez	lesmez	PROPN
aiti-7988	415	7	,	,	PUNCT
aiti-7988	415	8	d.	d.	PROPN
aiti-7988	415	9	c.	c.	PROPN
aiti-7988	415	10	wiggert	wiggert	PROPN
aiti-7988	415	11	,	,	PUNCT
aiti-7988	415	12	and	and	CCONJ
aiti-7988	415	13	f.	f.	PROPN
aiti-7988	415	14	j.	j.	PROPN
aiti-7988	415	15	hatfield	hatfield	PROPN
aiti-7988	415	16	,	,	PUNCT
aiti-7988	415	17	“	"	PUNCT
aiti-7988	415	18	modal	modal	ADJ
aiti-7988	415	19	analysis	analysis	NOUN
aiti-7988	415	20	of	of	ADP
aiti-7988	415	21	vibrations	vibration	NOUN
aiti-7988	415	22	in	in	ADP
aiti-7988	415	23	liquid	liquid	NOUN
aiti-7988	415	24	-	-	PUNCT
aiti-7988	415	25	filled	fill	VERB
aiti-7988	415	26	piping	piping	NOUN
aiti-7988	415	27	systems	system	NOUN
aiti-7988	415	28	,	,	PUNCT
aiti-7988	415	29	”	"	PUNCT
aiti-7988	415	30	journal	journal	NOUN
aiti-7988	415	31	of	of	ADP
aiti-7988	415	32	fluids	fluid	NOUN
aiti-7988	415	33	engineering	engineering	NOUN
aiti-7988	415	34	,	,	PUNCT
aiti-7988	415	35	vol	vol	NOUN
aiti-7988	415	36	.	.	PROPN
aiti-7988	415	37	112	112	NUM
aiti-7988	415	38	,	,	PUNCT
aiti-7988	415	39	no	no	INTJ
aiti-7988	415	40	.	.	NOUN
aiti-7988	415	41	3	3	NUM
aiti-7988	415	42	,	,	PUNCT
aiti-7988	415	43	pp	pp	ADJ
aiti-7988	415	44	.	.	PUNCT
aiti-7988	416	1	311	311	NUM
aiti-7988	416	2	-	-	SYM
aiti-7988	416	3	318	318	NUM
aiti-7988	416	4	,	,	PUNCT
aiti-7988	416	5	september	september	PROPN
aiti-7988	416	6	1990	1990	NUM
aiti-7988	416	7	.	.	PUNCT
aiti-7988	417	1	[	[	X
aiti-7988	417	2	9	9	NUM
aiti-7988	417	3	]	]	PUNCT
aiti-7988	417	4	q.	q.	PROPN
aiti-7988	417	5	qian	qian	PROPN
aiti-7988	417	6	,	,	PUNCT
aiti-7988	417	7	l.	l.	PROPN
aiti-7988	417	8	wang	wang	PROPN
aiti-7988	417	9	,	,	PUNCT
aiti-7988	417	10	and	and	CCONJ
aiti-7988	417	11	q.	q.	PROPN
aiti-7988	417	12	ni	ni	PROPN
aiti-7988	417	13	,	,	PUNCT
aiti-7988	417	14	“	"	PUNCT
aiti-7988	417	15	instability	instability	NOUN
aiti-7988	417	16	of	of	ADP
aiti-7988	417	17	simply	simply	ADV
aiti-7988	417	18	supported	support	VERB
aiti-7988	417	19	pipes	pipe	NOUN
aiti-7988	417	20	conveying	convey	VERB
aiti-7988	417	21	fluid	fluid	NOUN
aiti-7988	417	22	under	under	ADP
aiti-7988	417	23	thermal	thermal	ADJ
aiti-7988	417	24	loads	load	NOUN
aiti-7988	417	25	,	,	PUNCT
aiti-7988	417	26	”	"	PUNCT
aiti-7988	417	27	mechanics	mechanic	NOUN
aiti-7988	417	28	research	research	NOUN
aiti-7988	417	29	communications	communication	NOUN
aiti-7988	417	30	,	,	PUNCT
aiti-7988	417	31	vol	vol	NOUN
aiti-7988	417	32	.	.	PROPN
aiti-7988	417	33	36	36	NUM
aiti-7988	417	34	,	,	PUNCT
aiti-7988	417	35	no	no	INTJ
aiti-7988	417	36	.	.	NOUN
aiti-7988	417	37	3	3	NUM
aiti-7988	417	38	,	,	PUNCT
aiti-7988	417	39	pp	pp	ADJ
aiti-7988	417	40	.	.	PUNCT
aiti-7988	418	1	413	413	NUM
aiti-7988	418	2	-	-	SYM
aiti-7988	418	3	417	417	NUM
aiti-7988	418	4	,	,	PUNCT
aiti-7988	418	5	april	april	PROPN
aiti-7988	418	6	2009	2009	NUM
aiti-7988	418	7	.	.	PUNCT
aiti-7988	419	1	[	[	X
aiti-7988	419	2	10	10	NUM
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aiti-7988	419	4	d.	d.	PROPN
aiti-7988	419	5	zhao	zhao	PROPN
aiti-7988	419	6	,	,	PUNCT
aiti-7988	419	7	j.	j.	PROPN
aiti-7988	419	8	liu	liu	PROPN
aiti-7988	419	9	,	,	PUNCT
aiti-7988	419	10	and	and	CCONJ
aiti-7988	419	11	c.	c.	PROPN
aiti-7988	419	12	q.	q.	PROPN
aiti-7988	419	13	wu	wu	PROPN
aiti-7988	419	14	,	,	PUNCT
aiti-7988	419	15	“	"	PUNCT
aiti-7988	419	16	stability	stability	NOUN
aiti-7988	419	17	and	and	CCONJ
aiti-7988	419	18	local	local	ADJ
aiti-7988	419	19	bifurcation	bifurcation	NOUN
aiti-7988	419	20	of	of	ADP
aiti-7988	419	21	parameter	parameter	NOUN
aiti-7988	419	22	-	-	PUNCT
aiti-7988	419	23	excited	excited	ADJ
aiti-7988	419	24	vibration	vibration	NOUN
aiti-7988	419	25	of	of	ADP
aiti-7988	419	26	pipes	pipe	NOUN
aiti-7988	419	27	conveying	convey	VERB
aiti-7988	419	28	pulsating	pulsate	VERB
aiti-7988	419	29	fluid	fluid	NOUN
aiti-7988	419	30	under	under	ADP
aiti-7988	419	31	thermal	thermal	ADJ
aiti-7988	419	32	loading	loading	NOUN
aiti-7988	419	33	,	,	PUNCT
aiti-7988	419	34	”	"	PUNCT
aiti-7988	419	35	applied	apply	VERB
aiti-7988	419	36	mathematics	mathematic	NOUN
aiti-7988	419	37	and	and	CCONJ
aiti-7988	419	38	mechanics	mechanic	NOUN
aiti-7988	419	39	,	,	PUNCT
aiti-7988	419	40	vol	vol	NOUN
aiti-7988	419	41	.	.	PROPN
aiti-7988	419	42	36	36	NUM
aiti-7988	419	43	,	,	PUNCT
aiti-7988	419	44	no	no	INTJ
aiti-7988	419	45	.	.	NOUN
aiti-7988	419	46	8	8	NUM
aiti-7988	419	47	,	,	PUNCT
aiti-7988	419	48	pp	pp	ADJ
aiti-7988	419	49	.	.	PUNCT
aiti-7988	420	1	1017	1017	NUM
aiti-7988	420	2	-	-	SYM
aiti-7988	420	3	1032	1032	NUM
aiti-7988	420	4	,	,	PUNCT
aiti-7988	420	5	august	august	PROPN
aiti-7988	420	6	2015	2015	NUM
aiti-7988	420	7	.	.	PUNCT
aiti-7988	421	1	[	[	X
aiti-7988	421	2	11	11	NUM
aiti-7988	421	3	]	]	PUNCT
aiti-7988	421	4	j.	j.	PROPN
aiti-7988	421	5	k.	k.	PROPN
aiti-7988	421	6	kukla	kukla	PROPN
aiti-7988	421	7	,	,	PUNCT
aiti-7988	421	8	“	"	PUNCT
aiti-7988	421	9	application	application	NOUN
aiti-7988	421	10	of	of	ADP
aiti-7988	421	11	the	the	DET
aiti-7988	421	12	green	green	ADJ
aiti-7988	421	13	functions	function	NOUN
aiti-7988	421	14	to	to	ADP
aiti-7988	421	15	the	the	DET
aiti-7988	421	16	problem	problem	NOUN
aiti-7988	421	17	of	of	ADP
aiti-7988	421	18	the	the	DET
aiti-7988	421	19	thermally	thermally	ADV
aiti-7988	421	20	induced	induced	ADJ
aiti-7988	421	21	vibration	vibration	NOUN
aiti-7988	421	22	of	of	ADP
aiti-7988	421	23	a	a	DET
aiti-7988	421	24	beam	beam	NOUN
aiti-7988	421	25	,	,	PUNCT
aiti-7988	421	26	”	"	PUNCT
aiti-7988	421	27	journal	journal	NOUN
aiti-7988	421	28	of	of	ADP
aiti-7988	421	29	sound	sound	NOUN
aiti-7988	421	30	and	and	CCONJ
aiti-7988	421	31	vibration	vibration	NOUN
aiti-7988	421	32	,	,	PUNCT
aiti-7988	421	33	vol	vol	NOUN
aiti-7988	421	34	.	.	PROPN
aiti-7988	421	35	262	262	NUM
aiti-7988	421	36	,	,	PUNCT
aiti-7988	421	37	no	no	INTJ
aiti-7988	421	38	.	.	NOUN
aiti-7988	421	39	4	4	NUM
aiti-7988	421	40	,	,	PUNCT
aiti-7988	421	41	pp	pp	ADJ
aiti-7988	421	42	.	.	PUNCT
aiti-7988	422	1	865	865	NUM
aiti-7988	422	2	-	-	SYM
aiti-7988	422	3	876	876	NUM
aiti-7988	422	4	,	,	PUNCT
aiti-7988	422	5	may	may	PROPN
aiti-7988	422	6	2003	2003	NUM
aiti-7988	422	7	.	.	PUNCT
aiti-7988	423	1	[	[	X
aiti-7988	423	2	12	12	NUM
aiti-7988	423	3	]	]	PUNCT
aiti-7988	423	4	j.	j.	PROPN
aiti-7988	423	5	r.	r.	PROPN
aiti-7988	423	6	blandino	blandino	PROPN
aiti-7988	423	7	and	and	CCONJ
aiti-7988	423	8	e.	e.	PROPN
aiti-7988	423	9	a.	a.	PROPN
aiti-7988	423	10	thornton	thornton	PROPN
aiti-7988	423	11	,	,	PUNCT
aiti-7988	423	12	“	"	PUNCT
aiti-7988	423	13	thermally	thermally	ADV
aiti-7988	423	14	induced	induce	VERB
aiti-7988	423	15	vibration	vibration	NOUN
aiti-7988	423	16	of	of	ADP
aiti-7988	423	17	an	an	DET
aiti-7988	423	18	internally	internally	ADV
aiti-7988	423	19	heated	heated	ADJ
aiti-7988	423	20	beam	beam	NOUN
aiti-7988	423	21	,	,	PUNCT
aiti-7988	423	22	”	"	PUNCT
aiti-7988	423	23	journal	journal	NOUN
aiti-7988	423	24	of	of	ADP
aiti-7988	423	25	vibration	vibration	NOUN
aiti-7988	423	26	and	and	CCONJ
aiti-7988	423	27	acoustics	acoustic	NOUN
aiti-7988	423	28	,	,	PUNCT
aiti-7988	423	29	vol	vol	NOUN
aiti-7988	423	30	.	.	NOUN
aiti-7988	424	1	123	123	NUM
aiti-7988	424	2	,	,	PUNCT
aiti-7988	424	3	no	no	INTJ
aiti-7988	424	4	.	.	NOUN
aiti-7988	424	5	1	1	NUM
aiti-7988	424	6	,	,	PUNCT
aiti-7988	424	7	pp	pp	ADJ
aiti-7988	424	8	.	.	PUNCT
aiti-7988	425	1	67	67	NUM
aiti-7988	425	2	-	-	SYM
aiti-7988	425	3	75	75	NUM
aiti-7988	425	4	,	,	PUNCT
aiti-7988	425	5	january	january	PROPN
aiti-7988	425	6	2001	2001	NUM
aiti-7988	425	7	.	.	PUNCT
aiti-7988	426	1	[	[	X
aiti-7988	426	2	13	13	NUM
aiti-7988	426	3	]	]	PUNCT
aiti-7988	426	4	f.	f.	PROPN
aiti-7988	426	5	k.	k.	PROPN
aiti-7988	426	6	alfosail	alfosail	PROPN
aiti-7988	426	7	,	,	PUNCT
aiti-7988	426	8	a.	a.	PROPN
aiti-7988	426	9	h.	h.	PROPN
aiti-7988	426	10	nayfeh	nayfeh	PROPN
aiti-7988	426	11	,	,	PUNCT
aiti-7988	426	12	and	and	CCONJ
aiti-7988	426	13	m.	m.	PROPN
aiti-7988	426	14	i.	i.	PROPN
aiti-7988	426	15	younis	younis	PROPN
aiti-7988	426	16	,	,	PUNCT
aiti-7988	426	17	“	"	PUNCT
aiti-7988	426	18	natural	natural	ADJ
aiti-7988	426	19	frequencies	frequency	NOUN
aiti-7988	426	20	and	and	CCONJ
aiti-7988	426	21	mode	mode	NOUN
aiti-7988	426	22	shapes	shape	NOUN
aiti-7988	426	23	of	of	ADP
aiti-7988	426	24	statically	statically	ADV
aiti-7988	426	25	deformed	deform	VERB
aiti-7988	426	26	inclined	inclined	ADJ
aiti-7988	426	27	risers	riser	NOUN
aiti-7988	426	28	,	,	PUNCT
aiti-7988	426	29	”	"	PUNCT
aiti-7988	426	30	international	international	ADJ
aiti-7988	426	31	journal	journal	NOUN
aiti-7988	426	32	of	of	ADP
aiti-7988	426	33	non	non	ADJ
aiti-7988	426	34	-	-	ADJ
aiti-7988	426	35	linear	linear	ADJ
aiti-7988	426	36	mechanics	mechanic	NOUN
aiti-7988	426	37	,	,	PUNCT
aiti-7988	426	38	vol	vol	NOUN
aiti-7988	426	39	.	.	PROPN
aiti-7988	426	40	94	94	NUM
aiti-7988	426	41	,	,	PUNCT
aiti-7988	426	42	pp	pp	ADJ
aiti-7988	426	43	.	.	PUNCT
aiti-7988	427	1	12	12	NUM
aiti-7988	427	2	-	-	SYM
aiti-7988	427	3	19	19	NUM
aiti-7988	427	4	,	,	PUNCT
aiti-7988	427	5	september	september	PROPN
aiti-7988	427	6	2017	2017	NUM
aiti-7988	427	7	.	.	PUNCT
aiti-7988	428	1	[	[	X
aiti-7988	428	2	14	14	NUM
aiti-7988	428	3	]	]	X
aiti-7988	428	4	c.	c.	PROPN
aiti-7988	428	5	gan	gan	PROPN
aiti-7988	428	6	,	,	PUNCT
aiti-7988	428	7	s.	s.	PROPN
aiti-7988	428	8	jing	jing	PROPN
aiti-7988	428	9	,	,	PUNCT
aiti-7988	428	10	s.	s.	PROPN
aiti-7988	428	11	yang	yang	PROPN
aiti-7988	428	12	,	,	PUNCT
aiti-7988	428	13	and	and	CCONJ
aiti-7988	428	14	h.	h.	PROPN
aiti-7988	428	15	lei	lei	PROPN
aiti-7988	428	16	,	,	PUNCT
aiti-7988	428	17	“	"	PUNCT
aiti-7988	428	18	effects	effect	NOUN
aiti-7988	428	19	of	of	ADP
aiti-7988	428	20	supported	support	VERB
aiti-7988	428	21	angle	angle	NOUN
aiti-7988	428	22	on	on	ADP
aiti-7988	428	23	stability	stability	NOUN
aiti-7988	428	24	and	and	CCONJ
aiti-7988	428	25	dynamical	dynamical	ADJ
aiti-7988	428	26	bifurcations	bifurcation	NOUN
aiti-7988	428	27	of	of	ADP
aiti-7988	428	28	cantilevered	cantilevered	ADJ
aiti-7988	428	29	pipe	pipe	NOUN
aiti-7988	428	30	conveying	convey	VERB
aiti-7988	428	31	fluid	fluid	NOUN
aiti-7988	428	32	,	,	PUNCT
aiti-7988	428	33	”	"	PUNCT
aiti-7988	428	34	applied	apply	VERB
aiti-7988	428	35	mathematics	mathematic	NOUN
aiti-7988	428	36	and	and	CCONJ
aiti-7988	428	37	mechanics	mechanic	NOUN
aiti-7988	428	38	,	,	PUNCT
aiti-7988	428	39	vol	vol	NOUN
aiti-7988	428	40	.	.	PROPN
aiti-7988	428	41	36	36	NUM
aiti-7988	428	42	,	,	PUNCT
aiti-7988	428	43	no	no	INTJ
aiti-7988	428	44	.	.	NOUN
aiti-7988	428	45	6	6	NUM
aiti-7988	428	46	,	,	PUNCT
aiti-7988	428	47	pp	pp	ADJ
aiti-7988	428	48	.	.	PUNCT
aiti-7988	429	1	729	729	NUM
aiti-7988	429	2	-	-	SYM
aiti-7988	429	3	746	746	NUM
aiti-7988	429	4	,	,	PUNCT
aiti-7988	429	5	may	may	PROPN
aiti-7988	429	6	2015	2015	NUM
aiti-7988	429	7	.	.	PUNCT
aiti-7988	430	1	[	[	X
aiti-7988	430	2	15	15	NUM
aiti-7988	430	3	]	]	X
aiti-7988	430	4	d.	d.	PROPN
aiti-7988	430	5	s.	s.	PROPN
aiti-7988	430	6	yang	yang	PROPN
aiti-7988	430	7	and	and	CCONJ
aiti-7988	430	8	c.	c.	PROPN
aiti-7988	430	9	m.	m.	PROPN
aiti-7988	430	10	wang	wang	PROPN
aiti-7988	430	11	,	,	PUNCT
aiti-7988	430	12	“	"	PUNCT
aiti-7988	430	13	dynamic	dynamic	ADJ
aiti-7988	430	14	response	response	NOUN
aiti-7988	430	15	and	and	CCONJ
aiti-7988	430	16	stability	stability	NOUN
aiti-7988	430	17	of	of	ADP
aiti-7988	430	18	an	an	DET
aiti-7988	430	19	inclined	inclined	ADJ
aiti-7988	430	20	euler	euler	NOUN
aiti-7988	430	21	beam	beam	NOUN
aiti-7988	430	22	under	under	ADP
aiti-7988	430	23	a	a	DET
aiti-7988	430	24	moving	move	VERB
aiti-7988	430	25	vertical	vertical	ADJ
aiti-7988	430	26	concentrated	concentrated	ADJ
aiti-7988	430	27	load	load	NOUN
aiti-7988	430	28	,	,	PUNCT
aiti-7988	430	29	”	"	PUNCT
aiti-7988	430	30	engineering	engineering	NOUN
aiti-7988	430	31	structures	structure	NOUN
aiti-7988	430	32	,	,	PUNCT
aiti-7988	430	33	vol	vol	NOUN
aiti-7988	430	34	.	.	PROPN
aiti-7988	430	35	186	186	NUM
aiti-7988	430	36	,	,	PUNCT
aiti-7988	430	37	pp	pp	ADJ
aiti-7988	430	38	.	.	PUNCT
aiti-7988	431	1	243	243	NUM
aiti-7988	431	2	-	-	SYM
aiti-7988	431	3	254	254	NUM
aiti-7988	431	4	,	,	PUNCT
aiti-7988	431	5	may	may	AUX
aiti-7988	431	6	2019	2019	NUM
aiti-7988	431	7	.	.	PUNCT
aiti-7988	432	1	54	54	NUM
aiti-7988	432	2	advances	advance	NOUN
aiti-7988	432	3	in	in	ADP
aiti-7988	432	4	technology	technology	NOUN
aiti-7988	432	5	innovation	innovation	NOUN
aiti-7988	432	6	,	,	PUNCT
aiti-7988	432	7	vol	vol	NOUN
aiti-7988	432	8	.	.	PROPN
aiti-7988	432	9	7	7	NUM
aiti-7988	432	10	,	,	PUNCT
aiti-7988	432	11	no	no	INTJ
aiti-7988	432	12	.	.	NOUN
aiti-7988	432	13	1	1	NUM
aiti-7988	432	14	,	,	PUNCT
aiti-7988	432	15	2022	2022	NUM
aiti-7988	432	16	,	,	PUNCT
aiti-7988	432	17	pp	pp	ADJ
aiti-7988	432	18	.	.	PUNCT
aiti-7988	433	1	41	41	NUM
aiti-7988	433	2	-	-	SYM
aiti-7988	433	3	55	55	NUM
aiti-7988	433	4	[	[	X
aiti-7988	433	5	16	16	NUM
aiti-7988	433	6	]	]	X
aiti-7988	433	7	b.	b.	PROPN
aiti-7988	433	8	ram	ram	PROPN
aiti-7988	433	9	,	,	PUNCT
aiti-7988	433	10	engineering	engineering	NOUN
aiti-7988	433	11	mathematics	mathematic	NOUN
aiti-7988	433	12	,	,	PUNCT
aiti-7988	433	13	india	india	PROPN
aiti-7988	433	14	:	:	PUNCT
aiti-7988	433	15	pearson	pearson	PROPN
aiti-7988	433	16	education	education	PROPN
aiti-7988	433	17	,	,	PUNCT
aiti-7988	433	18	2009	2009	NUM
aiti-7988	433	19	.	.	PUNCT
aiti-7988	434	1	[	[	X
aiti-7988	434	2	17	17	NUM
aiti-7988	434	3	]	]	PUNCT
aiti-7988	434	4	x.	x.	PROPN
aiti-7988	434	5	liang	liang	PROPN
aiti-7988	434	6	,	,	PUNCT
aiti-7988	434	7	z.	z.	PROPN
aiti-7988	434	8	wu	wu	PROPN
aiti-7988	434	9	,	,	PUNCT
aiti-7988	434	10	l.	l.	PROPN
aiti-7988	434	11	wang	wang	PROPN
aiti-7988	434	12	,	,	PUNCT
aiti-7988	434	13	g.	g.	PROPN
aiti-7988	434	14	liu	liu	PROPN
aiti-7988	434	15	,	,	PUNCT
aiti-7988	434	16	z.	z.	PROPN
aiti-7988	434	17	wang	wang	PROPN
aiti-7988	434	18	,	,	PUNCT
aiti-7988	434	19	and	and	CCONJ
aiti-7988	434	20	w.	w.	PROPN
aiti-7988	434	21	zhang	zhang	PROPN
aiti-7988	434	22	,	,	PUNCT
aiti-7988	434	23	“	"	PUNCT
aiti-7988	434	24	semianalytical	semianalytical	ADJ
aiti-7988	434	25	three	three	NUM
aiti-7988	434	26	-	-	PUNCT
aiti-7988	434	27	dimensional	dimensional	ADJ
aiti-7988	434	28	solutions	solution	NOUN
aiti-7988	434	29	for	for	ADP
aiti-7988	434	30	the	the	DET
aiti-7988	434	31	transient	transient	ADJ
aiti-7988	434	32	response	response	NOUN
aiti-7988	434	33	of	of	ADP
aiti-7988	434	34	functionally	functionally	ADV
aiti-7988	434	35	graded	grade	VERB
aiti-7988	434	36	material	material	ADJ
aiti-7988	434	37	rectangular	rectangular	ADJ
aiti-7988	434	38	plates	plate	NOUN
aiti-7988	434	39	,	,	PUNCT
aiti-7988	434	40	”	"	PUNCT
aiti-7988	434	41	journal	journal	NOUN
aiti-7988	434	42	of	of	ADP
aiti-7988	434	43	engineering	engineering	NOUN
aiti-7988	434	44	mechanics	mechanic	NOUN
aiti-7988	434	45	,	,	PUNCT
aiti-7988	434	46	vol	vol	NOUN
aiti-7988	434	47	.	.	PROPN
aiti-7988	434	48	141	141	NUM
aiti-7988	434	49	,	,	PUNCT
aiti-7988	434	50	no	no	INTJ
aiti-7988	434	51	.	.	NOUN
aiti-7988	434	52	9	9	NUM
aiti-7988	434	53	,	,	PUNCT
aiti-7988	434	54	pp	pp	ADJ
aiti-7988	434	55	.	.	PUNCT
aiti-7988	435	1	1	1	NUM
aiti-7988	435	2	-	-	SYM
aiti-7988	435	3	17	17	NUM
aiti-7988	435	4	,	,	PUNCT
aiti-7988	435	5	september	september	PROPN
aiti-7988	435	6	2015	2015	NUM
aiti-7988	435	7	.	.	PUNCT
aiti-7988	436	1	[	[	X
aiti-7988	436	2	18	18	NUM
aiti-7988	436	3	]	]	X
aiti-7988	436	4	y.	y.	PROPN
aiti-7988	436	5	d.	d.	PROPN
aiti-7988	436	6	li	li	PROPN
aiti-7988	436	7	and	and	CCONJ
aiti-7988	436	8	y.	y.	PROPN
aiti-7988	436	9	r.	r.	PROPN
aiti-7988	436	10	yang	yang	PROPN
aiti-7988	436	11	,	,	PUNCT
aiti-7988	436	12	“	"	PUNCT
aiti-7988	436	13	forced	force	VERB
aiti-7988	436	14	vibration	vibration	NOUN
aiti-7988	436	15	of	of	ADP
aiti-7988	436	16	pipe	pipe	NOUN
aiti-7988	436	17	conveying	conveying	NOUN
aiti-7988	436	18	fluid	fluid	NOUN
aiti-7988	436	19	by	by	ADP
aiti-7988	436	20	the	the	DET
aiti-7988	436	21	green	green	ADJ
aiti-7988	436	22	function	function	NOUN
aiti-7988	436	23	method	method	NOUN
aiti-7988	436	24	,	,	PUNCT
aiti-7988	436	25	”	"	PUNCT
aiti-7988	436	26	archive	archive	NOUN
aiti-7988	436	27	of	of	ADP
aiti-7988	436	28	applied	apply	VERB
aiti-7988	436	29	mechanics	mechanic	NOUN
aiti-7988	436	30	,	,	PUNCT
aiti-7988	436	31	vol	vol	NOUN
aiti-7988	436	32	.	.	PROPN
aiti-7988	436	33	84	84	NUM
aiti-7988	436	34	,	,	PUNCT
aiti-7988	436	35	no	no	INTJ
aiti-7988	436	36	.	.	NOUN
aiti-7988	436	37	12	12	NUM
aiti-7988	436	38	,	,	PUNCT
aiti-7988	436	39	pp	pp	ADJ
aiti-7988	436	40	.	.	PUNCT
aiti-7988	436	41	1811	1811	NUM
aiti-7988	436	42	-	-	SYM
aiti-7988	436	43	1823	1823	NUM
aiti-7988	436	44	,	,	PUNCT
aiti-7988	436	45	july	july	PROPN
aiti-7988	436	46	2014	2014	NUM
aiti-7988	436	47	.	.	PUNCT
aiti-7988	437	1	[	[	X
aiti-7988	437	2	19	19	NUM
aiti-7988	437	3	]	]	PUNCT
aiti-7988	437	4	h.	h.	PROPN
aiti-7988	437	5	b.	b.	PROPN
aiti-7988	437	6	wen	wen	PROPN
aiti-7988	437	7	,	,	PUNCT
aiti-7988	437	8	y.	y.	PROPN
aiti-7988	437	9	r.	r.	PROPN
aiti-7988	437	10	yang	yang	PROPN
aiti-7988	437	11	,	,	PUNCT
aiti-7988	437	12	p.	p.	PROPN
aiti-7988	437	13	li	li	PROPN
aiti-7988	437	14	,	,	PUNCT
aiti-7988	437	15	y.	y.	PROPN
aiti-7988	437	16	d.	d.	PROPN
aiti-7988	437	17	li	li	PROPN
aiti-7988	437	18	,	,	PUNCT
aiti-7988	437	19	and	and	CCONJ
aiti-7988	437	20	y.	y.	PROPN
aiti-7988	437	21	huang	huang	PROPN
aiti-7988	437	22	,	,	PUNCT
aiti-7988	437	23	“	"	PUNCT
aiti-7988	437	24	a	a	DET
aiti-7988	437	25	new	new	ADJ
aiti-7988	437	26	method	method	NOUN
aiti-7988	437	27	based	base	VERB
aiti-7988	437	28	on	on	ADP
aiti-7988	437	29	laplace	laplace	NOUN
aiti-7988	437	30	transform	transform	NOUN
aiti-7988	437	31	and	and	CCONJ
aiti-7988	437	32	its	its	PRON
aiti-7988	437	33	application	application	NOUN
aiti-7988	437	34	to	to	ADP
aiti-7988	437	35	stability	stability	NOUN
aiti-7988	437	36	of	of	ADP
aiti-7988	437	37	pipe	pipe	NOUN
aiti-7988	437	38	conveying	conveying	NOUN
aiti-7988	437	39	fluid	fluid	NOUN
aiti-7988	437	40	,	,	PUNCT
aiti-7988	437	41	”	"	PUNCT
aiti-7988	437	42	shock	shock	NOUN
aiti-7988	437	43	and	and	CCONJ
aiti-7988	437	44	vibration	vibration	NOUN
aiti-7988	437	45	,	,	PUNCT
aiti-7988	437	46	vol	vol	NOUN
aiti-7988	437	47	.	.	PROPN
aiti-7988	437	48	2017	2017	NUM
aiti-7988	437	49	,	,	PUNCT
aiti-7988	437	50	1472601	1472601	NUM
aiti-7988	437	51	,	,	PUNCT
aiti-7988	437	52	2017	2017	NUM
aiti-7988	437	53	.	.	PUNCT
aiti-7988	438	1	[	[	X
aiti-7988	438	2	20	20	NUM
aiti-7988	438	3	]	]	PUNCT
aiti-7988	438	4	z.	z.	PROPN
aiti-7988	438	5	lai	lai	PROPN
aiti-7988	438	6	,	,	PUNCT
aiti-7988	438	7	l.	l.	PROPN
aiti-7988	438	8	jiang	jiang	PROPN
aiti-7988	438	9	,	,	PUNCT
aiti-7988	438	10	and	and	CCONJ
aiti-7988	438	11	w.	w.	PROPN
aiti-7988	438	12	zhou	zhou	PROPN
aiti-7988	438	13	,	,	PUNCT
aiti-7988	438	14	“	"	PUNCT
aiti-7988	438	15	an	an	DET
aiti-7988	438	16	analytical	analytical	ADJ
aiti-7988	438	17	study	study	NOUN
aiti-7988	438	18	on	on	ADP
aiti-7988	438	19	dynamic	dynamic	ADJ
aiti-7988	438	20	response	response	NOUN
aiti-7988	438	21	of	of	ADP
aiti-7988	438	22	multiple	multiple	ADJ
aiti-7988	438	23	simply	simply	ADV
aiti-7988	438	24	supported	support	VERB
aiti-7988	438	25	beam	beam	NOUN
aiti-7988	438	26	system	system	NOUN
aiti-7988	438	27	subjected	subject	VERB
aiti-7988	438	28	to	to	ADP
aiti-7988	438	29	moving	move	VERB
aiti-7988	438	30	loads	load	NOUN
aiti-7988	438	31	,	,	PUNCT
aiti-7988	438	32	”	"	PUNCT
aiti-7988	438	33	shock	shock	NOUN
aiti-7988	438	34	and	and	CCONJ
aiti-7988	438	35	vibration	vibration	NOUN
aiti-7988	438	36	,	,	PUNCT
aiti-7988	438	37	vol	vol	NOUN
aiti-7988	438	38	.	.	NOUN
aiti-7988	438	39	2018	2018	NUM
aiti-7988	438	40	,	,	PUNCT
aiti-7988	438	41	2149251	2149251	NUM
aiti-7988	438	42	,	,	PUNCT
aiti-7988	438	43	2018	2018	NUM
aiti-7988	438	44	.	.	PUNCT
aiti-7988	439	1	[	[	X
aiti-7988	439	2	21	21	NUM
aiti-7988	439	3	]	]	PUNCT
aiti-7988	439	4	x.	x.	PROPN
aiti-7988	439	5	tan	tan	PROPN
aiti-7988	439	6	,	,	PUNCT
aiti-7988	439	7	h.	h.	PROPN
aiti-7988	439	8	ding	ding	PROPN
aiti-7988	439	9	,	,	PUNCT
aiti-7988	439	10	and	and	CCONJ
aiti-7988	439	11	l.	l.	PROPN
aiti-7988	439	12	q.	q.	PROPN
aiti-7988	439	13	chen	chen	PROPN
aiti-7988	439	14	,	,	PUNCT
aiti-7988	439	15	“	"	PUNCT
aiti-7988	439	16	nonlinear	nonlinear	ADJ
aiti-7988	439	17	frequencies	frequency	NOUN
aiti-7988	439	18	and	and	CCONJ
aiti-7988	439	19	forced	force	VERB
aiti-7988	439	20	responses	response	NOUN
aiti-7988	439	21	of	of	ADP
aiti-7988	439	22	pipes	pipe	NOUN
aiti-7988	439	23	conveying	convey	VERB
aiti-7988	439	24	fluid	fluid	NOUN
aiti-7988	439	25	via	via	ADP
aiti-7988	439	26	a	a	DET
aiti-7988	439	27	coupled	couple	VERB
aiti-7988	439	28	timoshenko	timoshenko	NOUN
aiti-7988	439	29	model	model	NOUN
aiti-7988	439	30	,	,	PUNCT
aiti-7988	439	31	”	"	PUNCT
aiti-7988	439	32	journal	journal	NOUN
aiti-7988	439	33	of	of	ADP
aiti-7988	439	34	sound	sound	NOUN
aiti-7988	439	35	and	and	CCONJ
aiti-7988	439	36	vibration	vibration	NOUN
aiti-7988	439	37	,	,	PUNCT
aiti-7988	439	38	vol	vol	NOUN
aiti-7988	439	39	.	.	PROPN
aiti-7988	439	40	455	455	NUM
aiti-7988	439	41	,	,	PUNCT
aiti-7988	439	42	pp	pp	ADJ
aiti-7988	439	43	.	.	PUNCT
aiti-7988	440	1	241	241	NUM
aiti-7988	440	2	-	-	SYM
aiti-7988	440	3	255	255	NUM
aiti-7988	440	4	,	,	PUNCT
aiti-7988	440	5	september	september	PROPN
aiti-7988	440	6	2019	2019	NUM
aiti-7988	440	7	.	.	PUNCT
aiti-7988	441	1	[	[	X
aiti-7988	441	2	22	22	NUM
aiti-7988	441	3	]	]	PUNCT
aiti-7988	441	4	l.	l.	PROPN
aiti-7988	441	5	jiang	jiang	PROPN
aiti-7988	441	6	,	,	PUNCT
aiti-7988	441	7	y.	y.	PROPN
aiti-7988	441	8	zhang	zhang	PROPN
aiti-7988	441	9	,	,	PUNCT
aiti-7988	441	10	y.	y.	PROPN
aiti-7988	441	11	feng	feng	PROPN
aiti-7988	441	12	,	,	PUNCT
aiti-7988	441	13	w.	w.	PROPN
aiti-7988	441	14	zhou	zhou	PROPN
aiti-7988	441	15	,	,	PUNCT
aiti-7988	441	16	and	and	CCONJ
aiti-7988	441	17	z.	z.	PROPN
aiti-7988	441	18	tan	tan	PROPN
aiti-7988	441	19	,	,	PUNCT
aiti-7988	441	20	“	"	PUNCT
aiti-7988	441	21	dynamic	dynamic	ADJ
aiti-7988	441	22	response	response	NOUN
aiti-7988	441	23	analysis	analysis	NOUN
aiti-7988	441	24	of	of	ADP
aiti-7988	441	25	a	a	DET
aiti-7988	441	26	simply	simply	ADV
aiti-7988	441	27	supported	support	VERB
aiti-7988	441	28	double	double	ADJ
aiti-7988	441	29	-	-	PUNCT
aiti-7988	441	30	beam	beam	NOUN
aiti-7988	441	31	system	system	NOUN
aiti-7988	441	32	under	under	ADP
aiti-7988	441	33	successive	successive	ADJ
aiti-7988	441	34	moving	move	VERB
aiti-7988	441	35	loads	load	NOUN
aiti-7988	441	36	,	,	PUNCT
aiti-7988	441	37	”	"	PUNCT
aiti-7988	441	38	applied	apply	VERB
aiti-7988	441	39	sciences	science	NOUN
aiti-7988	441	40	,	,	PUNCT
aiti-7988	441	41	vol	vol	NOUN
aiti-7988	441	42	.	.	NOUN
aiti-7988	441	43	9	9	NUM
aiti-7988	441	44	,	,	PUNCT
aiti-7988	441	45	no	no	INTJ
aiti-7988	441	46	.	.	NOUN
aiti-7988	441	47	10	10	NUM
aiti-7988	441	48	,	,	PUNCT
aiti-7988	441	49	2162	2162	NUM
aiti-7988	441	50	,	,	PUNCT
aiti-7988	441	51	may	may	AUX
aiti-7988	441	52	2019	2019	NUM
aiti-7988	441	53	.	.	PUNCT
aiti-7988	442	1	[	[	X
aiti-7988	442	2	23	23	NUM
aiti-7988	442	3	]	]	X
aiti-7988	442	4	w.	w.	PROPN
aiti-7988	442	5	t.	t.	PROPN
aiti-7988	442	6	thomson	thomson	PROPN
aiti-7988	442	7	,	,	PUNCT
aiti-7988	442	8	theory	theory	NOUN
aiti-7988	442	9	of	of	ADP
aiti-7988	442	10	vibration	vibration	NOUN
aiti-7988	442	11	with	with	ADP
aiti-7988	442	12	applications	application	NOUN
aiti-7988	442	13	,	,	PUNCT
aiti-7988	442	14	london	london	PROPN
aiti-7988	442	15	:	:	PUNCT
aiti-7988	442	16	unwin	unwin	PROPN
aiti-7988	442	17	hyman	hyman	PROPN
aiti-7988	442	18	,	,	PUNCT
aiti-7988	442	19	1988	1988	NUM
aiti-7988	442	20	.	.	PUNCT
aiti-7988	443	1	[	[	X
aiti-7988	443	2	24	24	NUM
aiti-7988	443	3	]	]	PUNCT
aiti-7988	443	4	m.	m.	PROPN
aiti-7988	443	5	ali	ali	PROPN
aiti-7988	443	6	,	,	PUNCT
aiti-7988	443	7	i.	i.	PROPN
aiti-7988	443	8	alshalal	alshalal	PROPN
aiti-7988	443	9	,	,	PUNCT
aiti-7988	443	10	and	and	CCONJ
aiti-7988	443	11	j.	j.	PROPN
aiti-7988	443	12	h.	h.	PROPN
aiti-7988	443	13	mohmmed	mohmme	VERB
aiti-7988	443	14	,	,	PUNCT
aiti-7988	443	15	“	"	PUNCT
aiti-7988	443	16	effect	effect	NOUN
aiti-7988	443	17	of	of	ADP
aiti-7988	443	18	the	the	DET
aiti-7988	443	19	torsional	torsional	ADJ
aiti-7988	443	20	vibration	vibration	NOUN
aiti-7988	443	21	depending	depend	VERB
aiti-7988	443	22	on	on	ADP
aiti-7988	443	23	the	the	DET
aiti-7988	443	24	number	number	NOUN
aiti-7988	443	25	of	of	ADP
aiti-7988	443	26	cylinders	cylinder	NOUN
aiti-7988	443	27	in	in	ADP
aiti-7988	443	28	reciprocating	reciprocate	VERB
aiti-7988	443	29	engines	engine	NOUN
aiti-7988	443	30	,	,	PUNCT
aiti-7988	443	31	”	"	PUNCT
aiti-7988	443	32	international	international	ADJ
aiti-7988	443	33	journal	journal	NOUN
aiti-7988	443	34	of	of	ADP
aiti-7988	443	35	dynamics	dynamic	NOUN
aiti-7988	443	36	and	and	CCONJ
aiti-7988	443	37	control	control	NOUN
aiti-7988	443	38	,	,	PUNCT
aiti-7988	443	39	vol	vol	NOUN
aiti-7988	443	40	.	.	PROPN
aiti-7988	444	1	9	9	NUM
aiti-7988	444	2	,	,	PUNCT
aiti-7988	444	3	pp	pp	ADJ
aiti-7988	444	4	.	.	PUNCT
aiti-7988	445	1	901	901	NUM
aiti-7988	445	2	-	-	SYM
aiti-7988	445	3	909	909	NUM
aiti-7988	445	4	,	,	PUNCT
aiti-7988	445	5	january	january	NOUN
aiti-7988	445	6	2021	2021	NUM
aiti-7988	445	7	.	.	PUNCT
aiti-7988	446	1	[	[	X
aiti-7988	446	2	25	25	NUM
aiti-7988	446	3	]	]	PUNCT
aiti-7988	446	4	j.	j.	PROPN
aiti-7988	446	5	h.	h.	PROPN
aiti-7988	446	6	mohmmed	mohmme	VERB
aiti-7988	446	7	,	,	PUNCT
aiti-7988	446	8	m.	m.	NOUN
aiti-7988	446	9	a.	a.	NOUN
aiti-7988	446	10	tawfik	tawfik	PROPN
aiti-7988	446	11	,	,	PUNCT
aiti-7988	446	12	and	and	CCONJ
aiti-7988	446	13	q.	q.	PROPN
aiti-7988	446	14	a.	a.	PROPN
aiti-7988	446	15	atiyah	atiyah	PROPN
aiti-7988	446	16	,	,	PUNCT
aiti-7988	446	17	“	"	PUNCT
aiti-7988	446	18	natural	natural	ADJ
aiti-7988	446	19	frequency	frequency	NOUN
aiti-7988	446	20	and	and	CCONJ
aiti-7988	446	21	critical	critical	ADJ
aiti-7988	446	22	velocities	velocity	NOUN
aiti-7988	446	23	of	of	ADP
aiti-7988	446	24	heated	heated	ADJ
aiti-7988	446	25	inclined	incline	VERB
aiti-7988	446	26	pinned	pin	VERB
aiti-7988	446	27	pp	pp	ADJ
aiti-7988	446	28	-	-	PUNCT
aiti-7988	446	29	r	r	NOUN
aiti-7988	446	30	pipe	pipe	NOUN
aiti-7988	446	31	conveying	convey	VERB
aiti-7988	446	32	fluid	fluid	NOUN
aiti-7988	446	33	,	,	PUNCT
aiti-7988	446	34	”	"	PUNCT
aiti-7988	446	35	journal	journal	NOUN
aiti-7988	446	36	of	of	ADP
aiti-7988	446	37	achievements	achievement	NOUN
aiti-7988	446	38	in	in	ADP
aiti-7988	446	39	materials	material	NOUN
aiti-7988	446	40	and	and	CCONJ
aiti-7988	446	41	manufacturing	manufacturing	NOUN
aiti-7988	446	42	engineering	engineering	NOUN
aiti-7988	446	43	,	,	PUNCT
aiti-7988	446	44	vol	vol	NOUN
aiti-7988	446	45	.	.	PUNCT
aiti-7988	447	1	107	107	NUM
aiti-7988	447	2	,	,	PUNCT
aiti-7988	447	3	no	no	INTJ
aiti-7988	447	4	.	.	NOUN
aiti-7988	447	5	1	1	NUM
aiti-7988	447	6	,	,	PUNCT
aiti-7988	447	7	pp	pp	ADJ
aiti-7988	447	8	.	.	PUNCT
aiti-7988	448	1	15	15	NUM
aiti-7988	448	2	-	-	SYM
aiti-7988	448	3	27	27	NUM
aiti-7988	448	4	,	,	PUNCT
aiti-7988	448	5	2021	2021	NUM
aiti-7988	448	6	.	.	PUNCT
aiti-7988	449	1	[	[	X
aiti-7988	449	2	26	26	NUM
aiti-7988	449	3	]	]	X
aiti-7988	449	4	q.	q.	PROPN
aiti-7988	449	5	ni	ni	PROPN
aiti-7988	449	6	,	,	PUNCT
aiti-7988	449	7	z.	z.	PROPN
aiti-7988	449	8	l.	l.	PROPN
aiti-7988	449	9	zhang	zhang	PROPN
aiti-7988	449	10	,	,	PUNCT
aiti-7988	449	11	and	and	CCONJ
aiti-7988	449	12	l.	l.	PROPN
aiti-7988	449	13	wang	wang	PROPN
aiti-7988	449	14	,	,	PUNCT
aiti-7988	449	15	“	"	PUNCT
aiti-7988	449	16	application	application	NOUN
aiti-7988	449	17	of	of	ADP
aiti-7988	449	18	the	the	DET
aiti-7988	449	19	differential	differential	ADJ
aiti-7988	449	20	transformation	transformation	NOUN
aiti-7988	449	21	method	method	NOUN
aiti-7988	449	22	to	to	PART
aiti-7988	449	23	vibration	vibration	VERB
aiti-7988	449	24	analysis	analysis	NOUN
aiti-7988	449	25	of	of	ADP
aiti-7988	449	26	pipes	pipe	NOUN
aiti-7988	449	27	conveying	convey	VERB
aiti-7988	449	28	fluid	fluid	NOUN
aiti-7988	449	29	,	,	PUNCT
aiti-7988	449	30	”	"	PUNCT
aiti-7988	449	31	applied	apply	VERB
aiti-7988	449	32	mathematics	mathematic	NOUN
aiti-7988	449	33	and	and	CCONJ
aiti-7988	449	34	computation	computation	NOUN
aiti-7988	449	35	,	,	PUNCT
aiti-7988	449	36	vol	vol	NOUN
aiti-7988	449	37	.	.	PROPN
aiti-7988	449	38	217	217	NUM
aiti-7988	449	39	,	,	PUNCT
aiti-7988	449	40	no	no	INTJ
aiti-7988	449	41	.	.	NOUN
aiti-7988	449	42	16	16	NUM
aiti-7988	449	43	,	,	PUNCT
aiti-7988	449	44	pp	pp	ADJ
aiti-7988	449	45	.	.	PUNCT
aiti-7988	450	1	7028	7028	NUM
aiti-7988	450	2	-	-	SYM
aiti-7988	450	3	7038	7038	NUM
aiti-7988	450	4	,	,	PUNCT
aiti-7988	450	5	april	april	PROPN
aiti-7988	450	6	2011	2011	NUM
aiti-7988	450	7	.	.	PUNCT
aiti-7988	451	1	[	[	X
aiti-7988	451	2	27	27	NUM
aiti-7988	451	3	]	]	PUNCT
aiti-7988	451	4	x.	x.	PROPN
aiti-7988	451	5	liang	liang	PROPN
aiti-7988	451	6	,	,	PUNCT
aiti-7988	451	7	x.	x.	PROPN
aiti-7988	451	8	zha	zha	PROPN
aiti-7988	451	9	,	,	PUNCT
aiti-7988	451	10	x.	x.	PROPN
aiti-7988	451	11	jiang	jiang	PROPN
aiti-7988	451	12	,	,	PUNCT
aiti-7988	451	13	l.	l.	PROPN
aiti-7988	451	14	wang	wang	PROPN
aiti-7988	451	15	,	,	PUNCT
aiti-7988	451	16	j.	j.	PROPN
aiti-7988	451	17	leng	leng	PROPN
aiti-7988	451	18	,	,	PUNCT
aiti-7988	451	19	and	and	CCONJ
aiti-7988	451	20	z.	z.	PROPN
aiti-7988	451	21	cao	cao	PROPN
aiti-7988	451	22	,	,	PUNCT
aiti-7988	451	23	“	"	PUNCT
aiti-7988	451	24	semi	semi	ADJ
aiti-7988	451	25	-	-	ADJ
aiti-7988	451	26	analytical	analytical	ADJ
aiti-7988	451	27	solution	solution	NOUN
aiti-7988	451	28	for	for	ADP
aiti-7988	451	29	dynamic	dynamic	ADJ
aiti-7988	451	30	behavior	behavior	NOUN
aiti-7988	451	31	of	of	ADP
aiti-7988	451	32	a	a	DET
aiti-7988	451	33	fluid	fluid	NOUN
aiti-7988	451	34	-	-	PUNCT
aiti-7988	451	35	conveying	convey	VERB
aiti-7988	451	36	pipe	pipe	NOUN
aiti-7988	451	37	with	with	ADP
aiti-7988	451	38	different	different	ADJ
aiti-7988	451	39	boundary	boundary	ADJ
aiti-7988	451	40	conditions	condition	NOUN
aiti-7988	451	41	,	,	PUNCT
aiti-7988	451	42	”	"	PUNCT
aiti-7988	451	43	ocean	ocean	NOUN
aiti-7988	451	44	engineering	engineering	NOUN
aiti-7988	451	45	,	,	PUNCT
aiti-7988	451	46	vol	vol	NOUN
aiti-7988	451	47	.	.	PROPN
aiti-7988	451	48	163	163	NUM
aiti-7988	451	49	,	,	PUNCT
aiti-7988	451	50	pp	pp	ADJ
aiti-7988	451	51	.	.	PUNCT
aiti-7988	452	1	183	183	NUM
aiti-7988	452	2	-	-	SYM
aiti-7988	452	3	190	190	NUM
aiti-7988	452	4	,	,	PUNCT
aiti-7988	452	5	september	september	PROPN
aiti-7988	452	6	2018	2018	NUM
aiti-7988	452	7	.	.	PUNCT
aiti-7988	453	1	[	[	X
aiti-7988	453	2	28	28	NUM
aiti-7988	453	3	]	]	X
aiti-7988	453	4	a.	a.	NOUN
aiti-7988	453	5	o.	o.	PROPN
aiti-7988	453	6	adelaja	adelaja	PROPN
aiti-7988	453	7	,	,	PUNCT
aiti-7988	453	8	“	"	PUNCT
aiti-7988	453	9	natural	natural	ADJ
aiti-7988	453	10	frequencies	frequency	NOUN
aiti-7988	453	11	of	of	ADP
aiti-7988	453	12	pressurized	pressurized	ADJ
aiti-7988	453	13	hot	hot	ADJ
aiti-7988	453	14	fluid	fluid	NOUN
aiti-7988	453	15	conveying	conveying	NOUN
aiti-7988	453	16	pipes	pipe	NOUN
aiti-7988	453	17	,	,	PUNCT
aiti-7988	453	18	”	"	PUNCT
aiti-7988	453	19	fuoye	fuoye	NOUN
aiti-7988	453	20	journal	journal	NOUN
aiti-7988	453	21	of	of	ADP
aiti-7988	453	22	engineering	engineering	NOUN
aiti-7988	453	23	and	and	CCONJ
aiti-7988	453	24	technology	technology	NOUN
aiti-7988	453	25	,	,	PUNCT
aiti-7988	453	26	vol	vol	NOUN
aiti-7988	453	27	.	.	PROPN
aiti-7988	454	1	3	3	NUM
aiti-7988	454	2	,	,	PUNCT
aiti-7988	454	3	no	no	INTJ
aiti-7988	454	4	.	.	NOUN
aiti-7988	454	5	2	2	NUM
aiti-7988	454	6	,	,	PUNCT
aiti-7988	454	7	pp	pp	ADJ
aiti-7988	454	8	.	.	PUNCT
aiti-7988	455	1	131	131	NUM
aiti-7988	455	2	-	-	SYM
aiti-7988	455	3	135	135	NUM
aiti-7988	455	4	,	,	PUNCT
aiti-7988	455	5	september	september	PROPN
aiti-7988	455	6	2018	2018	NUM
aiti-7988	455	7	.	.	PUNCT
aiti-7988	456	1	[	[	X
aiti-7988	456	2	29	29	NUM
aiti-7988	456	3	]	]	X
aiti-7988	456	4	v.	v.	CCONJ
aiti-7988	456	5	o.	o.	PROPN
aiti-7988	456	6	olunloyo	olunloyo	PROPN
aiti-7988	456	7	,	,	PUNCT
aiti-7988	456	8	c.	c.	PROPN
aiti-7988	456	9	a.	a.	PROPN
aiti-7988	456	10	osheku	osheku	PROPN
aiti-7988	456	11	,	,	PUNCT
aiti-7988	456	12	and	and	CCONJ
aiti-7988	456	13	p.	p.	PROPN
aiti-7988	456	14	s.	s.	PROPN
aiti-7988	456	15	olayiwola	olayiwola	PROPN
aiti-7988	456	16	,	,	PUNCT
aiti-7988	456	17	“	"	PUNCT
aiti-7988	456	18	a	a	DET
aiti-7988	456	19	note	note	NOUN
aiti-7988	456	20	on	on	ADP
aiti-7988	456	21	an	an	DET
aiti-7988	456	22	analytic	analytic	ADJ
aiti-7988	456	23	solution	solution	NOUN
aiti-7988	456	24	for	for	ADP
aiti-7988	456	25	an	an	DET
aiti-7988	456	26	incompressible	incompressible	ADJ
aiti-7988	456	27	fluid	fluid	NOUN
aiti-7988	456	28	-	-	PUNCT
aiti-7988	456	29	conveying	convey	VERB
aiti-7988	456	30	pipeline	pipeline	NOUN
aiti-7988	456	31	system	system	NOUN
aiti-7988	456	32	,	,	PUNCT
aiti-7988	456	33	”	"	PUNCT
aiti-7988	456	34	advances	advance	NOUN
aiti-7988	456	35	in	in	ADP
aiti-7988	456	36	acoustics	acoustic	NOUN
aiti-7988	456	37	and	and	CCONJ
aiti-7988	456	38	vibration	vibration	NOUN
aiti-7988	456	39	,	,	PUNCT
aiti-7988	456	40	vol	vol	NOUN
aiti-7988	456	41	.	.	PROPN
aiti-7988	456	42	2017	2017	NUM
aiti-7988	456	43	,	,	PUNCT
aiti-7988	456	44	8141523	8141523	NUM
aiti-7988	456	45	,	,	PUNCT
aiti-7988	456	46	2017	2017	NUM
aiti-7988	456	47	.	.	PUNCT
aiti-7988	457	1	[	[	X
aiti-7988	457	2	30	30	NUM
aiti-7988	457	3	]	]	X
aiti-7988	457	4	r.	r.	PROPN
aiti-7988	457	5	h.	h.	PROPN
aiti-7988	457	6	plaut	plaut	PROPN
aiti-7988	457	7	,	,	PUNCT
aiti-7988	457	8	“	"	PUNCT
aiti-7988	457	9	postbuckling	postbuckle	VERB
aiti-7988	457	10	and	and	CCONJ
aiti-7988	457	11	vibration	vibration	NOUN
aiti-7988	457	12	of	of	ADP
aiti-7988	457	13	end	end	NOUN
aiti-7988	457	14	-	-	PUNCT
aiti-7988	457	15	supported	support	VERB
aiti-7988	457	16	elastic	elastic	ADJ
aiti-7988	457	17	pipes	pipe	NOUN
aiti-7988	457	18	conveying	convey	VERB
aiti-7988	457	19	fluid	fluid	NOUN
aiti-7988	457	20	and	and	CCONJ
aiti-7988	457	21	columns	column	NOUN
aiti-7988	457	22	under	under	ADP
aiti-7988	457	23	follower	follower	NOUN
aiti-7988	457	24	loads	load	NOUN
aiti-7988	457	25	,	,	PUNCT
aiti-7988	457	26	”	"	PUNCT
aiti-7988	457	27	journal	journal	NOUN
aiti-7988	457	28	of	of	ADP
aiti-7988	457	29	sound	sound	NOUN
aiti-7988	457	30	and	and	CCONJ
aiti-7988	457	31	vibration	vibration	NOUN
aiti-7988	457	32	,	,	PUNCT
aiti-7988	457	33	vol	vol	NOUN
aiti-7988	457	34	.	.	PROPN
aiti-7988	458	1	289	289	NUM
aiti-7988	458	2	,	,	PUNCT
aiti-7988	458	3	no	no	INTJ
aiti-7988	458	4	.	.	NOUN
aiti-7988	458	5	1	1	NUM
aiti-7988	458	6	-	-	SYM
aiti-7988	458	7	2	2	NUM
aiti-7988	458	8	,	,	PUNCT
aiti-7988	458	9	pp	pp	ADJ
aiti-7988	458	10	.	.	PUNCT
aiti-7988	459	1	264	264	NUM
aiti-7988	459	2	-	-	SYM
aiti-7988	459	3	277	277	NUM
aiti-7988	459	4	,	,	PUNCT
aiti-7988	459	5	january	january	PROPN
aiti-7988	459	6	2006	2006	NUM
aiti-7988	459	7	.	.	PUNCT
aiti-7988	460	1	[	[	X
aiti-7988	460	2	31	31	NUM
aiti-7988	460	3	]	]	PUNCT
aiti-7988	460	4	v.	v.	CCONJ
aiti-7988	460	5	o.	o.	PROPN
aiti-7988	460	6	olunloyo	olunloyo	PROPN
aiti-7988	460	7	,	,	PUNCT
aiti-7988	460	8	c.	c.	PROPN
aiti-7988	460	9	a.	a.	PROPN
aiti-7988	460	10	osheku	osheku	PROPN
aiti-7988	460	11	,	,	PUNCT
aiti-7988	460	12	and	and	CCONJ
aiti-7988	460	13	s.	s.	PROPN
aiti-7988	460	14	i.	i.	PROPN
aiti-7988	460	15	kuye	kuye	PROPN
aiti-7988	460	16	,	,	PUNCT
aiti-7988	460	17	“	"	PUNCT
aiti-7988	460	18	vibration	vibration	NOUN
aiti-7988	460	19	and	and	CCONJ
aiti-7988	460	20	stability	stability	NOUN
aiti-7988	460	21	behaviour	behaviour	NOUN
aiti-7988	460	22	of	of	ADP
aiti-7988	460	23	sandwiched	sandwich	VERB
aiti-7988	460	24	viscoelastic	viscoelastic	ADJ
aiti-7988	460	25	pipes	pipe	NOUN
aiti-7988	460	26	conveying	convey	VERB
aiti-7988	460	27	a	a	DET
aiti-7988	460	28	non	non	ADJ
aiti-7988	460	29	-	-	ADJ
aiti-7988	460	30	newtonian	newtonian	ADJ
aiti-7988	460	31	fluid	fluid	NOUN
aiti-7988	460	32	,	,	PUNCT
aiti-7988	460	33	”	"	PUNCT
aiti-7988	460	34	29th	29th	ADJ
aiti-7988	460	35	international	international	ADJ
aiti-7988	460	36	conference	conference	NOUN
aiti-7988	460	37	on	on	ADP
aiti-7988	460	38	ocean	ocean	NOUN
aiti-7988	460	39	,	,	PUNCT
aiti-7988	460	40	offshore	offshore	ADV
aiti-7988	460	41	,	,	PUNCT
aiti-7988	460	42	and	and	CCONJ
aiti-7988	460	43	arctic	arctic	PROPN
aiti-7988	460	44	engineering	engineering	NOUN
aiti-7988	460	45	,	,	PUNCT
aiti-7988	460	46	pp	pp	ADJ
aiti-7988	460	47	.	.	PUNCT
aiti-7988	461	1	99	99	NUM
aiti-7988	461	2	-	-	SYM
aiti-7988	461	3	111	111	NUM
aiti-7988	461	4	,	,	PUNCT
aiti-7988	461	5	june	june	PROPN
aiti-7988	461	6	2010	2010	NUM
aiti-7988	461	7	.	.	PUNCT
aiti-7988	462	1	[	[	X
aiti-7988	462	2	32	32	NUM
aiti-7988	462	3	]	]	PUNCT
aiti-7988	462	4	h.	h.	PROPN
aiti-7988	462	5	ashley	ashley	PROPN
aiti-7988	462	6	and	and	CCONJ
aiti-7988	462	7	g.	g.	PROPN
aiti-7988	462	8	haviland	haviland	PROPN
aiti-7988	462	9	,	,	PUNCT
aiti-7988	462	10	“	"	PUNCT
aiti-7988	462	11	bending	bend	VERB
aiti-7988	462	12	vibrations	vibration	NOUN
aiti-7988	462	13	of	of	ADP
aiti-7988	462	14	a	a	DET
aiti-7988	462	15	pipe	pipe	NOUN
aiti-7988	462	16	line	line	NOUN
aiti-7988	462	17	containing	contain	VERB
aiti-7988	462	18	flowing	flow	VERB
aiti-7988	462	19	fluid	fluid	NOUN
aiti-7988	462	20	,	,	PUNCT
aiti-7988	462	21	”	"	PUNCT
aiti-7988	462	22	journal	journal	NOUN
aiti-7988	462	23	of	of	ADP
aiti-7988	462	24	applied	apply	VERB
aiti-7988	462	25	mechanics	mechanic	NOUN
aiti-7988	462	26	,	,	PUNCT
aiti-7988	462	27	vol	vol	NOUN
aiti-7988	462	28	.	.	PROPN
aiti-7988	462	29	17	17	NUM
aiti-7988	462	30	,	,	PUNCT
aiti-7988	462	31	no	no	INTJ
aiti-7988	462	32	.	.	NOUN
aiti-7988	462	33	3	3	NUM
aiti-7988	462	34	,	,	PUNCT
aiti-7988	462	35	pp	pp	ADJ
aiti-7988	462	36	.	.	PUNCT
aiti-7988	462	37	229	229	NUM
aiti-7988	462	38	-	-	SYM
aiti-7988	462	39	232	232	NUM
aiti-7988	462	40	,	,	PUNCT
aiti-7988	462	41	september	september	PROPN
aiti-7988	462	42	1950	1950	NUM
aiti-7988	462	43	.	.	PUNCT
aiti-7988	463	1	[	[	X
aiti-7988	463	2	33	33	NUM
aiti-7988	463	3	]	]	PUNCT
aiti-7988	463	4	k.	k.	PROPN
aiti-7988	464	1	o.	o.	PROPN
aiti-7988	464	2	orolu	orolu	PROPN
aiti-7988	464	3	,	,	PUNCT
aiti-7988	464	4	t.	t.	PROPN
aiti-7988	464	5	a.	a.	NOUN
aiti-7988	464	6	fashanu	fashanu	PROPN
aiti-7988	464	7	,	,	PUNCT
aiti-7988	464	8	and	and	CCONJ
aiti-7988	464	9	a.	a.	NOUN
aiti-7988	464	10	a.	a.	NOUN
aiti-7988	464	11	oyediran	oyediran	PROPN
aiti-7988	464	12	,	,	PUNCT
aiti-7988	464	13	“	"	PUNCT
aiti-7988	464	14	cusp	cusp	NOUN
aiti-7988	464	15	bifurcation	bifurcation	NOUN
aiti-7988	464	16	of	of	ADP
aiti-7988	464	17	slightly	slightly	ADV
aiti-7988	464	18	curved	curved	ADJ
aiti-7988	464	19	tensioned	tensione	VERB
aiti-7988	464	20	pipe	pipe	NOUN
aiti-7988	464	21	conveying	convey	VERB
aiti-7988	464	22	hot	hot	ADJ
aiti-7988	464	23	pressurized	pressurized	ADJ
aiti-7988	464	24	fluid	fluid	NOUN
aiti-7988	464	25	,	,	PUNCT
aiti-7988	464	26	”	"	PUNCT
aiti-7988	464	27	journal	journal	NOUN
aiti-7988	464	28	of	of	ADP
aiti-7988	464	29	vibration	vibration	NOUN
aiti-7988	464	30	and	and	CCONJ
aiti-7988	464	31	control	control	NOUN
aiti-7988	464	32	,	,	PUNCT
aiti-7988	464	33	vol	vol	NOUN
aiti-7988	464	34	.	.	PROPN
aiti-7988	464	35	25	25	NUM
aiti-7988	464	36	,	,	PUNCT
aiti-7988	464	37	no	no	INTJ
aiti-7988	464	38	.	.	NOUN
aiti-7988	464	39	5	5	NUM
aiti-7988	464	40	,	,	PUNCT
aiti-7988	464	41	pp	pp	ADJ
aiti-7988	464	42	.	.	PUNCT
aiti-7988	465	1	1109	1109	NUM
aiti-7988	465	2	-	-	SYM
aiti-7988	465	3	1121	1121	NUM
aiti-7988	465	4	,	,	PUNCT
aiti-7988	465	5	march	march	PROPN
aiti-7988	465	6	2019	2019	NUM
aiti-7988	465	7	.	.	PUNCT
aiti-7988	466	1	copyright	copyright	NOUN
aiti-7988	466	2	©	©	PROPN
aiti-7988	466	3	by	by	ADP
aiti-7988	466	4	the	the	DET
aiti-7988	466	5	authors	author	NOUN
aiti-7988	466	6	.	.	PUNCT
aiti-7988	467	1	licensee	licensee	PROPN
aiti-7988	467	2	taeti	taeti	PROPN
aiti-7988	467	3	,	,	PUNCT
aiti-7988	467	4	taiwan	taiwan	PROPN
aiti-7988	467	5	.	.	PUNCT
aiti-7988	468	1	this	this	DET
aiti-7988	468	2	article	article	NOUN
aiti-7988	468	3	is	be	AUX
aiti-7988	468	4	an	an	DET
aiti-7988	468	5	open	open	ADJ
aiti-7988	468	6	access	access	NOUN
aiti-7988	468	7	article	article	NOUN
aiti-7988	468	8	distributed	distribute	VERB
aiti-7988	468	9	under	under	ADP
aiti-7988	468	10	the	the	DET
aiti-7988	468	11	terms	term	NOUN
aiti-7988	468	12	and	and	CCONJ
aiti-7988	468	13	conditions	condition	NOUN
aiti-7988	468	14	of	of	ADP
aiti-7988	468	15	the	the	DET
aiti-7988	468	16	creative	creative	ADJ
aiti-7988	468	17	commons	common	NOUN
aiti-7988	468	18	attribution	attribution	NOUN
aiti-7988	468	19	(	(	PUNCT
aiti-7988	468	20	cc	cc	NOUN
aiti-7988	468	21	by	by	ADP
aiti-7988	468	22	-	-	PUNCT
aiti-7988	468	23	nc	nc	NOUN
aiti-7988	468	24	)	)	PUNCT
aiti-7988	468	25	license	license	NOUN
aiti-7988	468	26	(	(	PUNCT
aiti-7988	468	27	https://creativecommons.org/licenses/by-nc/4.0/	https://creativecommons.org/licenses/by-nc/4.0/	NOUN
aiti-7988	468	28	)	)	PUNCT
aiti-7988	468	29	.	.	PUNCT
aiti-7988	469	1	55	55	NUM