id	sid	tid	token	lemma	pos
aiti-4099	1	1	advances	advance	NOUN
aiti-4099	1	2	in	in	ADP
aiti-4099	1	3	technology	technology	NOUN
aiti-4099	1	4	innovation	innovation	NOUN
aiti-4099	1	5	,	,	PUNCT
aiti-4099	1	6	vol	vol	NOUN
aiti-4099	1	7	.	.	PROPN
aiti-4099	2	1	4	4	NUM
aiti-4099	2	2	,	,	PUNCT
aiti-4099	2	3	no	no	INTJ
aiti-4099	2	4	.	.	NOUN
aiti-4099	2	5	3	3	NUM
aiti-4099	2	6	,	,	PUNCT
aiti-4099	2	7	2019	2019	NUM
aiti-4099	2	8	,	,	PUNCT
aiti-4099	2	9	pp	pp	ADJ
aiti-4099	2	10	.	.	PUNCT
aiti-4099	3	1	152	152	NUM
aiti-4099	3	2	-	-	SYM
aiti-4099	3	3	164	164	NUM
aiti-4099	3	4	vibration	vibration	NOUN
aiti-4099	3	5	analysis	analysis	NOUN
aiti-4099	3	6	of	of	ADP
aiti-4099	3	7	two	two	NUM
aiti-4099	3	8	-	-	PUNCT
aiti-4099	3	9	directional	directional	NOUN
aiti-4099	3	10	functionally	functionally	ADV
aiti-4099	3	11	graded	grade	VERB
aiti-4099	3	12	sandwich	sandwich	NOUN
aiti-4099	3	13	beams	beam	NOUN
aiti-4099	3	14	using	use	VERB
aiti-4099	3	15	a	a	DET
aiti-4099	3	16	shear	shear	NOUN
aiti-4099	3	17	deformable	deformable	ADJ
aiti-4099	3	18	finite	finite	ADJ
aiti-4099	3	19	element	element	NOUN
aiti-4099	3	20	formulation	formulation	NOUN
aiti-4099	3	21	vu	vu	PROPN
aiti-4099	3	22	nam	nam	PROPN
aiti-4099	3	23	pham	pham	PROPN
aiti-4099	3	24	1	1	NUM
aiti-4099	3	25	,	,	PUNCT
aiti-4099	3	26	2	2	NUM
aiti-4099	3	27	,	,	PUNCT
aiti-4099	3	28	dinh	dinh	NOUN
aiti-4099	3	29	kien	kien	PROPN
aiti-4099	3	30	nguyen	nguyen	PROPN
aiti-4099	3	31	2	2	NUM
aiti-4099	3	32	,	,	PUNCT
aiti-4099	3	33	3	3	NUM
aiti-4099	3	34	,	,	PUNCT
aiti-4099	3	35	*	*	PUNCT
aiti-4099	3	36	,	,	PUNCT
aiti-4099	3	37	buntara	buntara	PROPN
aiti-4099	3	38	sthenly	sthenly	ADV
aiti-4099	3	39	gan	gin	VERB
aiti-4099	3	40	4	4	NUM
aiti-4099	3	41	1	1	NUM
aiti-4099	3	42	thuyloi	thuyloi	NOUN
aiti-4099	3	43	university	university	NOUN
aiti-4099	3	44	,	,	PUNCT
aiti-4099	3	45	175	175	NUM
aiti-4099	3	46	tay	tay	PROPN
aiti-4099	3	47	son	son	NOUN
aiti-4099	3	48	,	,	PUNCT
aiti-4099	3	49	dong	dong	PROPN
aiti-4099	3	50	da	da	PROPN
aiti-4099	3	51	,	,	PUNCT
aiti-4099	3	52	hanoi	hanoi	PROPN
aiti-4099	3	53	,	,	PUNCT
aiti-4099	3	54	vietnam	vietnam	PROPN
aiti-4099	3	55	2	2	NUM
aiti-4099	3	56	graduate	graduate	NOUN
aiti-4099	3	57	university	university	NOUN
aiti-4099	3	58	of	of	ADP
aiti-4099	3	59	science	science	NOUN
aiti-4099	3	60	and	and	CCONJ
aiti-4099	3	61	technology	technology	NOUN
aiti-4099	3	62	,	,	PUNCT
aiti-4099	3	63	vast	vast	ADJ
aiti-4099	3	64	,	,	PUNCT
aiti-4099	3	65	18	18	NUM
aiti-4099	3	66	hoang	hoang	PROPN
aiti-4099	3	67	quoc	quoc	PROPN
aiti-4099	3	68	viet	viet	PROPN
aiti-4099	3	69	,	,	PUNCT
aiti-4099	3	70	hanoi	hanoi	PROPN
aiti-4099	3	71	,	,	PUNCT
aiti-4099	3	72	vietnam	vietnam	PROPN
aiti-4099	3	73	3	3	NUM
aiti-4099	3	74	institute	institute	PROPN
aiti-4099	3	75	of	of	ADP
aiti-4099	3	76	mechanics	mechanic	NOUN
aiti-4099	3	77	,	,	PUNCT
aiti-4099	3	78	vast	vast	ADJ
aiti-4099	3	79	,	,	PUNCT
aiti-4099	3	80	18	18	NUM
aiti-4099	3	81	hoang	hoang	PROPN
aiti-4099	3	82	quoc	quoc	PROPN
aiti-4099	3	83	viet	viet	PROPN
aiti-4099	3	84	,	,	PUNCT
aiti-4099	3	85	hanoi	hanoi	PROPN
aiti-4099	3	86	,	,	PUNCT
aiti-4099	3	87	vietnam	vietnam	PROPN
aiti-4099	3	88	4	4	NUM
aiti-4099	3	89	department	department	NOUN
aiti-4099	3	90	of	of	ADP
aiti-4099	3	91	architecture	architecture	NOUN
aiti-4099	3	92	,	,	PUNCT
aiti-4099	3	93	college	college	NOUN
aiti-4099	3	94	of	of	ADP
aiti-4099	3	95	engineering	engineering	PROPN
aiti-4099	3	96	,	,	PUNCT
aiti-4099	3	97	nihon	nihon	PROPN
aiti-4099	3	98	university	university	PROPN
aiti-4099	3	99	,	,	PUNCT
aiti-4099	3	100	koriyama	koriyama	PROPN
aiti-4099	3	101	,	,	PUNCT
aiti-4099	3	102	japan	japan	PROPN
aiti-4099	3	103	received	receive	VERB
aiti-4099	3	104	17	17	NUM
aiti-4099	3	105	march	march	NOUN
aiti-4099	3	106	2019	2019	NUM
aiti-4099	3	107	;	;	PUNCT
aiti-4099	3	108	received	receive	VERB
aiti-4099	3	109	in	in	ADP
aiti-4099	3	110	revised	revise	VERB
aiti-4099	3	111	form	form	NOUN
aiti-4099	3	112	10	10	NUM
aiti-4099	3	113	april	april	PROPN
aiti-4099	3	114	2019	2019	NUM
aiti-4099	3	115	;	;	PUNCT
aiti-4099	3	116	accepted	accept	VERB
aiti-4099	3	117	10	10	NUM
aiti-4099	3	118	may	may	PROPN
aiti-4099	3	119	2019	2019	NUM
aiti-4099	3	120	abstract	abstract	ADV
aiti-4099	3	121	free	free	ADJ
aiti-4099	3	122	and	and	CCONJ
aiti-4099	3	123	forced	force	VERB
aiti-4099	3	124	vibration	vibration	NOUN
aiti-4099	3	125	analysis	analysis	NOUN
aiti-4099	3	126	of	of	ADP
aiti-4099	3	127	two	two	NUM
aiti-4099	3	128	-	-	PUNCT
aiti-4099	3	129	directional	directional	NOUN
aiti-4099	3	130	functionally	functionally	ADV
aiti-4099	3	131	graded	grade	VERB
aiti-4099	3	132	sandwich	sandwich	NOUN
aiti-4099	3	133	(	(	PUNCT
aiti-4099	3	134	2d	2d	NOUN
aiti-4099	3	135	-	-	PUNCT
aiti-4099	3	136	fgsw	fgsw	NOUN
aiti-4099	3	137	)	)	PUNCT
aiti-4099	3	138	beams	beam	NOUN
aiti-4099	3	139	using	use	VERB
aiti-4099	3	140	a	a	DET
aiti-4099	3	141	shear	shear	NOUN
aiti-4099	3	142	deformable	deformable	ADJ
aiti-4099	3	143	finite	finite	ADJ
aiti-4099	3	144	element	element	NOUN
aiti-4099	3	145	formulation	formulation	NOUN
aiti-4099	3	146	is	be	AUX
aiti-4099	3	147	presented	present	VERB
aiti-4099	3	148	.	.	PUNCT
aiti-4099	4	1	the	the	DET
aiti-4099	4	2	beams	beam	NOUN
aiti-4099	4	3	considered	consider	VERB
aiti-4099	4	4	in	in	ADP
aiti-4099	4	5	this	this	DET
aiti-4099	4	6	paper	paper	NOUN
aiti-4099	4	7	consists	consist	VERB
aiti-4099	4	8	of	of	ADP
aiti-4099	4	9	three	three	NUM
aiti-4099	4	10	layers	layer	NOUN
aiti-4099	4	11	,	,	PUNCT
aiti-4099	4	12	a	a	DET
aiti-4099	4	13	homogeneous	homogeneous	ADJ
aiti-4099	4	14	ceramic	ceramic	ADJ
aiti-4099	4	15	core	core	NOUN
aiti-4099	4	16	,	,	PUNCT
aiti-4099	4	17	and	and	CCONJ
aiti-4099	4	18	two	two	NUM
aiti-4099	4	19	functionally	functionally	ADV
aiti-4099	4	20	graded	grade	VERB
aiti-4099	4	21	skin	skin	NOUN
aiti-4099	4	22	layers	layer	NOUN
aiti-4099	4	23	.	.	PUNCT
aiti-4099	5	1	material	material	NOUN
aiti-4099	5	2	properties	property	NOUN
aiti-4099	5	3	of	of	ADP
aiti-4099	5	4	the	the	DET
aiti-4099	5	5	skin	skin	NOUN
aiti-4099	5	6	layers	layer	NOUN
aiti-4099	5	7	are	be	AUX
aiti-4099	5	8	supposed	suppose	VERB
aiti-4099	5	9	to	to	PART
aiti-4099	5	10	vary	vary	VERB
aiti-4099	5	11	in	in	ADP
aiti-4099	5	12	both	both	CCONJ
aiti-4099	5	13	the	the	DET
aiti-4099	5	14	thickness	thickness	NOUN
aiti-4099	5	15	and	and	CCONJ
aiti-4099	5	16	length	length	NOUN
aiti-4099	5	17	directions	direction	NOUN
aiti-4099	5	18	by	by	ADP
aiti-4099	5	19	power	power	NOUN
aiti-4099	5	20	gradation	gradation	NOUN
aiti-4099	5	21	laws	law	NOUN
aiti-4099	5	22	.	.	PUNCT
aiti-4099	6	1	based	base	VERB
aiti-4099	6	2	on	on	ADP
aiti-4099	6	3	a	a	DET
aiti-4099	6	4	refined	refined	ADJ
aiti-4099	6	5	shear	shear	NOUN
aiti-4099	6	6	deformation	deformation	NOUN
aiti-4099	6	7	beam	beam	NOUN
aiti-4099	6	8	theory	theory	NOUN
aiti-4099	6	9	,	,	PUNCT
aiti-4099	6	10	in	in	ADP
aiti-4099	6	11	which	which	PRON
aiti-4099	6	12	the	the	DET
aiti-4099	6	13	transverse	transverse	ADJ
aiti-4099	6	14	displacement	displacement	NOUN
aiti-4099	6	15	is	be	AUX
aiti-4099	6	16	split	split	VERB
aiti-4099	6	17	into	into	ADP
aiti-4099	6	18	bending	bend	VERB
aiti-4099	6	19	and	and	CCONJ
aiti-4099	6	20	shear	shear	NOUN
aiti-4099	6	21	parts	part	NOUN
aiti-4099	6	22	,	,	PUNCT
aiti-4099	6	23	a	a	DET
aiti-4099	6	24	novel	novel	ADJ
aiti-4099	6	25	finite	finite	NOUN
aiti-4099	6	26	element	element	NOUN
aiti-4099	6	27	formulation	formulation	NOUN
aiti-4099	6	28	is	be	AUX
aiti-4099	6	29	derived	derive	VERB
aiti-4099	6	30	and	and	CCONJ
aiti-4099	6	31	employed	employ	VERB
aiti-4099	6	32	in	in	ADP
aiti-4099	6	33	the	the	DET
aiti-4099	6	34	analysis	analysis	NOUN
aiti-4099	6	35	.	.	PUNCT
aiti-4099	7	1	natural	natural	ADJ
aiti-4099	7	2	frequencies	frequency	NOUN
aiti-4099	7	3	and	and	CCONJ
aiti-4099	7	4	dynamic	dynamic	ADJ
aiti-4099	7	5	response	response	NOUN
aiti-4099	7	6	to	to	ADP
aiti-4099	7	7	a	a	DET
aiti-4099	7	8	harmonic	harmonic	ADJ
aiti-4099	7	9	load	load	NOUN
aiti-4099	7	10	of	of	ADP
aiti-4099	7	11	the	the	DET
aiti-4099	7	12	beams	beam	NOUN
aiti-4099	7	13	with	with	ADP
aiti-4099	7	14	various	various	ADJ
aiti-4099	7	15	boundary	boundary	ADJ
aiti-4099	7	16	conditions	condition	NOUN
aiti-4099	7	17	are	be	AUX
aiti-4099	7	18	computed	compute	VERB
aiti-4099	7	19	,	,	PUNCT
aiti-4099	7	20	and	and	CCONJ
aiti-4099	7	21	the	the	DET
aiti-4099	7	22	influence	influence	NOUN
aiti-4099	7	23	of	of	ADP
aiti-4099	7	24	the	the	DET
aiti-4099	7	25	material	material	NOUN
aiti-4099	7	26	distribution	distribution	NOUN
aiti-4099	7	27	and	and	CCONJ
aiti-4099	7	28	the	the	DET
aiti-4099	7	29	layer	layer	NOUN
aiti-4099	7	30	thickness	thickness	NOUN
aiti-4099	7	31	ratio	ratio	NOUN
aiti-4099	7	32	on	on	ADP
aiti-4099	7	33	the	the	DET
aiti-4099	7	34	vibration	vibration	NOUN
aiti-4099	7	35	characteristics	characteristic	NOUN
aiti-4099	7	36	of	of	ADP
aiti-4099	7	37	the	the	DET
aiti-4099	7	38	beams	beam	NOUN
aiti-4099	7	39	is	be	AUX
aiti-4099	7	40	highlighted	highlight	VERB
aiti-4099	7	41	.	.	PUNCT
aiti-4099	8	1	numerical	numerical	ADJ
aiti-4099	8	2	results	result	NOUN
aiti-4099	8	3	reveal	reveal	VERB
aiti-4099	8	4	that	that	SCONJ
aiti-4099	8	5	the	the	DET
aiti-4099	8	6	variation	variation	NOUN
aiti-4099	8	7	of	of	ADP
aiti-4099	8	8	the	the	DET
aiti-4099	8	9	material	material	NOUN
aiti-4099	8	10	properties	property	NOUN
aiti-4099	8	11	in	in	ADP
aiti-4099	8	12	the	the	DET
aiti-4099	8	13	longitudinal	longitudinal	ADJ
aiti-4099	8	14	direction	direction	NOUN
aiti-4099	8	15	has	have	VERB
aiti-4099	8	16	a	a	DET
aiti-4099	8	17	significant	significant	ADJ
aiti-4099	8	18	influence	influence	NOUN
aiti-4099	8	19	on	on	ADP
aiti-4099	8	20	the	the	DET
aiti-4099	8	21	vibration	vibration	NOUN
aiti-4099	8	22	behavior	behavior	NOUN
aiti-4099	8	23	of	of	ADP
aiti-4099	8	24	the	the	DET
aiti-4099	8	25	beams	beam	NOUN
aiti-4099	8	26	,	,	PUNCT
aiti-4099	8	27	and	and	CCONJ
aiti-4099	8	28	fgsw	fgsw	NOUN
aiti-4099	8	29	beams	beam	NOUN
aiti-4099	8	30	can	can	AUX
aiti-4099	8	31	be	be	AUX
aiti-4099	8	32	designed	design	VERB
aiti-4099	8	33	to	to	PART
aiti-4099	8	34	achieve	achieve	VERB
aiti-4099	8	35	desired	desire	VERB
aiti-4099	8	36	vibration	vibration	NOUN
aiti-4099	8	37	characteristics	characteristic	NOUN
aiti-4099	8	38	by	by	ADP
aiti-4099	8	39	appropriate	appropriate	ADJ
aiti-4099	8	40	selection	selection	NOUN
aiti-4099	8	41	of	of	ADP
aiti-4099	8	42	material	material	NOUN
aiti-4099	8	43	grading	grade	VERB
aiti-4099	8	44	indexes	index	NOUN
aiti-4099	8	45	.	.	PUNCT
aiti-4099	9	1	keywords	keyword	NOUN
aiti-4099	9	2	:	:	PUNCT
aiti-4099	9	3	2d	2d	NUM
aiti-4099	9	4	-	-	PUNCT
aiti-4099	9	5	fgsw	fgsw	NOUN
aiti-4099	9	6	beam	beam	NOUN
aiti-4099	9	7	,	,	PUNCT
aiti-4099	9	8	refined	refine	VERB
aiti-4099	9	9	shear	shear	NOUN
aiti-4099	9	10	deformation	deformation	NOUN
aiti-4099	9	11	theory	theory	NOUN
aiti-4099	9	12	,	,	PUNCT
aiti-4099	9	13	vibration	vibration	NOUN
aiti-4099	9	14	analysis	analysis	NOUN
aiti-4099	9	15	,	,	PUNCT
aiti-4099	9	16	finite	finite	PROPN
aiti-4099	9	17	element	element	NOUN
aiti-4099	9	18	formulation	formulation	NOUN
aiti-4099	9	19	1	1	NUM
aiti-4099	9	20	.	.	PUNCT
aiti-4099	10	1	introduction	introduction	NOUN
aiti-4099	10	2	sandwich	sandwich	NOUN
aiti-4099	10	3	structures	structure	NOUN
aiti-4099	10	4	with	with	ADP
aiti-4099	10	5	high	high	ADJ
aiti-4099	10	6	strength	strength	NOUN
aiti-4099	10	7	-	-	PUNCT
aiti-4099	10	8	to	to	ADP
aiti-4099	10	9	-	-	PUNCT
aiti-4099	10	10	weight	weight	NOUN
aiti-4099	10	11	ratio	ratio	NOUN
aiti-4099	10	12	are	be	AUX
aiti-4099	10	13	widely	widely	ADV
aiti-4099	10	14	used	use	VERB
aiti-4099	10	15	to	to	PART
aiti-4099	10	16	fabricate	fabricate	VERB
aiti-4099	10	17	structural	structural	ADJ
aiti-4099	10	18	elements	element	NOUN
aiti-4099	10	19	in	in	ADP
aiti-4099	10	20	aerospace	aerospace	NOUN
aiti-4099	10	21	engineering	engineering	NOUN
aiti-4099	10	22	.	.	PUNCT
aiti-4099	11	1	in	in	ADP
aiti-4099	11	2	order	order	NOUN
aiti-4099	11	3	to	to	PART
aiti-4099	11	4	improve	improve	VERB
aiti-4099	11	5	the	the	DET
aiti-4099	11	6	mechanical	mechanical	ADJ
aiti-4099	11	7	performance	performance	NOUN
aiti-4099	11	8	of	of	ADP
aiti-4099	11	9	these	these	DET
aiti-4099	11	10	structures	structure	NOUN
aiti-4099	11	11	under	under	ADP
aiti-4099	11	12	complex	complex	ADJ
aiti-4099	11	13	loadings	loading	NOUN
aiti-4099	11	14	,	,	PUNCT
aiti-4099	11	15	functionally	functionally	ADV
aiti-4099	11	16	graded	grade	VERB
aiti-4099	11	17	materials	material	NOUN
aiti-4099	11	18	(	(	PUNCT
aiti-4099	11	19	fgms	fgms	PROPN
aiti-4099	11	20	)	)	PUNCT
aiti-4099	11	21	,	,	PUNCT
aiti-4099	11	22	a	a	DET
aiti-4099	11	23	new	new	ADJ
aiti-4099	11	24	type	type	NOUN
aiti-4099	11	25	of	of	ADP
aiti-4099	11	26	composite	composite	ADJ
aiti-4099	11	27	materials	material	NOUN
aiti-4099	11	28	initiated	initiate	VERB
aiti-4099	11	29	by	by	ADP
aiti-4099	11	30	japanese	japanese	ADJ
aiti-4099	11	31	researchers	researcher	NOUN
aiti-4099	11	32	in	in	ADP
aiti-4099	11	33	1984	1984	NUM
aiti-4099	11	34	[	[	X
aiti-4099	11	35	1	1	NUM
aiti-4099	11	36	]	]	PUNCT
aiti-4099	11	37	,	,	PUNCT
aiti-4099	11	38	have	have	AUX
aiti-4099	11	39	been	be	AUX
aiti-4099	11	40	incorporated	incorporate	VERB
aiti-4099	11	41	in	in	ADP
aiti-4099	11	42	the	the	DET
aiti-4099	11	43	sandwich	sandwich	NOUN
aiti-4099	11	44	construction	construction	NOUN
aiti-4099	11	45	in	in	ADP
aiti-4099	11	46	recent	recent	ADJ
aiti-4099	11	47	years	year	NOUN
aiti-4099	11	48	.	.	PUNCT
aiti-4099	12	1	understanding	understand	VERB
aiti-4099	12	2	the	the	DET
aiti-4099	12	3	mechanical	mechanical	ADJ
aiti-4099	12	4	behavior	behavior	NOUN
aiti-4099	12	5	of	of	ADP
aiti-4099	12	6	functionally	functionally	ADV
aiti-4099	12	7	graded	grade	VERB
aiti-4099	12	8	sandwich	sandwich	NOUN
aiti-4099	12	9	(	(	PUNCT
aiti-4099	12	10	fgsw	fgsw	NOUN
aiti-4099	12	11	)	)	PUNCT
aiti-4099	12	12	structures	structure	NOUN
aiti-4099	12	13	in	in	ADP
aiti-4099	12	14	general	general	ADJ
aiti-4099	12	15	,	,	PUNCT
aiti-4099	12	16	and	and	CCONJ
aiti-4099	12	17	vibration	vibration	NOUN
aiti-4099	12	18	of	of	ADP
aiti-4099	12	19	fgsw	fgsw	NOUN
aiti-4099	12	20	beams	beam	NOUN
aiti-4099	12	21	,	,	PUNCT
aiti-4099	12	22	in	in	ADP
aiti-4099	12	23	particular	particular	ADJ
aiti-4099	12	24	,	,	PUNCT
aiti-4099	12	25	is	be	AUX
aiti-4099	12	26	crucial	crucial	ADJ
aiti-4099	12	27	for	for	ADP
aiti-4099	12	28	using	use	VERB
aiti-4099	12	29	this	this	DET
aiti-4099	12	30	new	new	ADJ
aiti-4099	12	31	composite	composite	ADJ
aiti-4099	12	32	material	material	NOUN
aiti-4099	12	33	effectively	effectively	ADV
aiti-4099	12	34	.	.	PUNCT
aiti-4099	13	1	investigations	investigation	NOUN
aiti-4099	13	2	on	on	ADP
aiti-4099	13	3	the	the	DET
aiti-4099	13	4	vibration	vibration	NOUN
aiti-4099	13	5	of	of	ADP
aiti-4099	13	6	fgsw	fgsw	NOUN
aiti-4099	13	7	beams	beam	NOUN
aiti-4099	13	8	,	,	PUNCT
aiti-4099	13	9	the	the	DET
aiti-4099	13	10	topic	topic	NOUN
aiti-4099	13	11	discussed	discuss	VERB
aiti-4099	13	12	in	in	ADP
aiti-4099	13	13	this	this	DET
aiti-4099	13	14	paper	paper	NOUN
aiti-4099	13	15	,	,	PUNCT
aiti-4099	13	16	are	be	AUX
aiti-4099	13	17	briefly	briefly	ADV
aiti-4099	13	18	discussed	discuss	VERB
aiti-4099	13	19	below	below	ADV
aiti-4099	13	20	.	.	PUNCT
aiti-4099	14	1	pradhan	pradhan	PROPN
aiti-4099	14	2	and	and	CCONJ
aiti-4099	14	3	murmu	murmu	NOUN
aiti-4099	15	1	[	[	X
aiti-4099	15	2	2	2	X
aiti-4099	15	3	]	]	PUNCT
aiti-4099	15	4	used	use	VERB
aiti-4099	15	5	the	the	DET
aiti-4099	15	6	modified	modify	VERB
aiti-4099	15	7	differential	differential	NOUN
aiti-4099	15	8	quadrature	quadrature	NOUN
aiti-4099	15	9	method	method	NOUN
aiti-4099	15	10	to	to	PART
aiti-4099	15	11	compute	compute	VERB
aiti-4099	15	12	natural	natural	ADJ
aiti-4099	15	13	frequencies	frequency	NOUN
aiti-4099	15	14	of	of	ADP
aiti-4099	15	15	fgsw	fgsw	NOUN
aiti-4099	15	16	beams	beam	NOUN
aiti-4099	15	17	resting	rest	VERB
aiti-4099	15	18	on	on	ADP
aiti-4099	15	19	an	an	DET
aiti-4099	15	20	elastic	elastic	ADJ
aiti-4099	15	21	foundation	foundation	NOUN
aiti-4099	15	22	.	.	PUNCT
aiti-4099	16	1	the	the	DET
aiti-4099	16	2	dependence	dependence	NOUN
aiti-4099	16	3	of	of	ADP
aiti-4099	16	4	material	material	NOUN
aiti-4099	16	5	properties	property	NOUN
aiti-4099	16	6	upon	upon	SCONJ
aiti-4099	16	7	temperature	temperature	NOUN
aiti-4099	16	8	was	be	AUX
aiti-4099	16	9	considered	consider	VERB
aiti-4099	16	10	in	in	ADP
aiti-4099	16	11	the	the	DET
aiti-4099	16	12	work	work	NOUN
aiti-4099	16	13	.	.	PUNCT
aiti-4099	17	1	based	base	VERB
aiti-4099	17	2	on	on	ADP
aiti-4099	17	3	the	the	DET
aiti-4099	17	4	element	element	NOUN
aiti-4099	17	5	free	free	ADJ
aiti-4099	17	6	galerkin	galerkin	PROPN
aiti-4099	17	7	method	method	NOUN
aiti-4099	17	8	,	,	PUNCT
aiti-4099	17	9	amirani	amirani	PROPN
aiti-4099	17	10	et	et	PROPN
aiti-4099	17	11	al	al	AUX
aiti-4099	17	12	.	.	PUNCT
aiti-4099	18	1	[	[	X
aiti-4099	18	2	3	3	NUM
aiti-4099	18	3	]	]	PUNCT
aiti-4099	18	4	studied	study	VERB
aiti-4099	18	5	free	free	ADJ
aiti-4099	18	6	vibration	vibration	NOUN
aiti-4099	18	7	of	of	ADP
aiti-4099	18	8	an	an	DET
aiti-4099	18	9	fgsw	fgsw	NOUN
aiti-4099	18	10	beam	beam	NOUN
aiti-4099	18	11	with	with	ADP
aiti-4099	18	12	an	an	DET
aiti-4099	18	13	fgm	fgm	PROPN
aiti-4099	18	14	core	core	NOUN
aiti-4099	18	15	.	.	PUNCT
aiti-4099	19	1	the	the	DET
aiti-4099	19	2	authors	author	NOUN
aiti-4099	19	3	employed	employ	VERB
aiti-4099	19	4	two	two	NUM
aiti-4099	19	5	micromechanics	micromechanic	NOUN
aiti-4099	19	6	models	model	NOUN
aiti-4099	19	7	,	,	PUNCT
aiti-4099	19	8	voigt	voigt	PROPN
aiti-4099	19	9	and	and	CCONJ
aiti-4099	19	10	mori	mori	PROPN
aiti-4099	19	11	-	-	PUNCT
aiti-4099	19	12	tanaka	tanaka	PROPN
aiti-4099	19	13	models	model	NOUN
aiti-4099	19	14	,	,	PUNCT
aiti-4099	19	15	to	to	PART
aiti-4099	19	16	evaluate	evaluate	VERB
aiti-4099	19	17	the	the	DET
aiti-4099	19	18	effective	effective	ADJ
aiti-4099	19	19	material	material	NOUN
aiti-4099	19	20	properties	property	NOUN
aiti-4099	19	21	of	of	ADP
aiti-4099	19	22	the	the	DET
aiti-4099	19	23	beams	beam	NOUN
aiti-4099	19	24	,	,	PUNCT
aiti-4099	19	25	and	and	CCONJ
aiti-4099	19	26	they	they	PRON
aiti-4099	19	27	showed	show	VERB
aiti-4099	19	28	that	that	SCONJ
aiti-4099	19	29	the	the	DET
aiti-4099	19	30	natural	natural	ADJ
aiti-4099	19	31	frequencies	frequency	NOUN
aiti-4099	19	32	based	base	VERB
aiti-4099	19	33	on	on	ADP
aiti-4099	19	34	mori	mori	NOUN
aiti-4099	19	35	-	-	PUNCT
aiti-4099	19	36	tanaka	tanaka	PROPN
aiti-4099	19	37	scheme	scheme	NOUN
aiti-4099	19	38	are	be	AUX
aiti-4099	19	39	slightly	slightly	ADV
aiti-4099	19	40	lower	low	ADJ
aiti-4099	19	41	than	than	ADP
aiti-4099	19	42	that	that	PRON
aiti-4099	19	43	using	use	VERB
aiti-4099	19	44	voigt	voigt	PROPN
aiti-4099	19	45	model	model	NOUN
aiti-4099	19	46	.	.	PUNCT
aiti-4099	20	1	adopting	adopt	VERB
aiti-4099	20	2	a	a	DET
aiti-4099	20	3	hierarchical	hierarchical	ADJ
aiti-4099	20	4	displacement	displacement	ADJ
aiti-4099	20	5	field	field	NOUN
aiti-4099	20	6	,	,	PUNCT
aiti-4099	20	7	mashat	mashat	AUX
aiti-4099	20	8	et	et	PROPN
aiti-4099	20	9	al	al	PROPN
aiti-4099	20	10	.	.	PUNCT
aiti-4099	21	1	[	[	X
aiti-4099	21	2	4	4	X
aiti-4099	21	3	]	]	PUNCT
aiti-4099	21	4	derived	derive	VERB
aiti-4099	21	5	a	a	DET
aiti-4099	21	6	finite	finite	ADJ
aiti-4099	21	7	element	element	NOUN
aiti-4099	21	8	formulation	formulation	NOUN
aiti-4099	21	9	*	*	PUNCT
aiti-4099	21	10	corresponding	correspond	VERB
aiti-4099	21	11	author	author	NOUN
aiti-4099	21	12	.	.	PUNCT
aiti-4099	22	1	e	e	X
aiti-4099	22	2	-	-	NOUN
aiti-4099	22	3	mail	mail	NOUN
aiti-4099	22	4	address	address	NOUN
aiti-4099	22	5	:	:	PUNCT
aiti-4099	22	6	ndkien@imech.vast.vn	ndkien@imech.vast.vn	PROPN
aiti-4099	22	7	tel	tel	PROPN
aiti-4099	22	8	.	.	PUNCT
aiti-4099	22	9	:	:	PUNCT
aiti-4099	23	1	+84	+84	ADJ
aiti-4099	23	2	-	-	PUNCT
aiti-4099	23	3	24	24	NUM
aiti-4099	23	4	-	-	PUNCT
aiti-4099	23	5	37628006	37628006	NUM
aiti-4099	23	6	;	;	PUNCT
aiti-4099	23	7	fax	fax	NOUN
aiti-4099	23	8	:	:	PUNCT
aiti-4099	23	9	+84	+84	ADJ
aiti-4099	23	10	-	-	PUNCT
aiti-4099	23	11	24	24	NUM
aiti-4099	23	12	-	-	PUNCT
aiti-4099	23	13	37622039	37622039	NUM
aiti-4099	23	14	advances	advance	NOUN
aiti-4099	23	15	in	in	ADP
aiti-4099	23	16	technology	technology	NOUN
aiti-4099	23	17	innovation	innovation	NOUN
aiti-4099	23	18	,	,	PUNCT
aiti-4099	23	19	vol	vol	NOUN
aiti-4099	23	20	.	.	PROPN
aiti-4099	24	1	4	4	NUM
aiti-4099	24	2	,	,	PUNCT
aiti-4099	24	3	no	no	INTJ
aiti-4099	24	4	.	.	NOUN
aiti-4099	24	5	3	3	NUM
aiti-4099	24	6	,	,	PUNCT
aiti-4099	24	7	2019	2019	NUM
aiti-4099	24	8	,	,	PUNCT
aiti-4099	24	9	pp	pp	ADJ
aiti-4099	24	10	.	.	PUNCT
aiti-4099	25	1	152	152	NUM
aiti-4099	25	2	-	-	SYM
aiti-4099	25	3	164	164	NUM
aiti-4099	25	4	153	153	NUM
aiti-4099	25	5	for	for	ADP
aiti-4099	25	6	evaluating	evaluate	VERB
aiti-4099	25	7	natural	natural	ADJ
aiti-4099	25	8	frequencies	frequency	NOUN
aiti-4099	25	9	of	of	ADP
aiti-4099	25	10	laminated	laminated	ADJ
aiti-4099	25	11	and	and	CCONJ
aiti-4099	25	12	sandwich	sandwich	NOUN
aiti-4099	25	13	beams	beam	NOUN
aiti-4099	25	14	with	with	ADP
aiti-4099	25	15	material	material	NOUN
aiti-4099	25	16	properties	property	NOUN
aiti-4099	25	17	varying	vary	VERB
aiti-4099	25	18	by	by	ADP
aiti-4099	25	19	a	a	DET
aiti-4099	25	20	power	power	NOUN
aiti-4099	25	21	gradation	gradation	NOUN
aiti-4099	25	22	law	law	NOUN
aiti-4099	25	23	.	.	PUNCT
aiti-4099	26	1	free	free	ADJ
aiti-4099	26	2	vibration	vibration	NOUN
aiti-4099	26	3	and	and	CCONJ
aiti-4099	26	4	buckling	buckling	NOUN
aiti-4099	26	5	of	of	ADP
aiti-4099	26	6	fgsw	fgsw	NOUN
aiti-4099	26	7	beams	beam	NOUN
aiti-4099	26	8	were	be	AUX
aiti-4099	26	9	considered	consider	VERB
aiti-4099	26	10	by	by	ADP
aiti-4099	26	11	bennai	bennai	PROPN
aiti-4099	26	12	et	et	PROPN
aiti-4099	26	13	al	al	PROPN
aiti-4099	26	14	.	.	PUNCT
aiti-4099	27	1	[	[	X
aiti-4099	27	2	5	5	NUM
aiti-4099	27	3	]	]	PUNCT
aiti-4099	27	4	by	by	ADP
aiti-4099	27	5	using	use	VERB
aiti-4099	27	6	a	a	DET
aiti-4099	27	7	new	new	ADJ
aiti-4099	27	8	refined	refined	ADJ
aiti-4099	27	9	hyperbolic	hyperbolic	ADJ
aiti-4099	27	10	shear	shear	NOUN
aiti-4099	27	11	deformation	deformation	NOUN
aiti-4099	27	12	beam	beam	NOUN
aiti-4099	27	13	theory	theory	NOUN
aiti-4099	27	14	.	.	PUNCT
aiti-4099	28	1	in	in	ADP
aiti-4099	28	2	[	[	X
aiti-4099	28	3	6	6	NUM
aiti-4099	28	4	,	,	PUNCT
aiti-4099	28	5	7	7	NUM
aiti-4099	28	6	]	]	PUNCT
aiti-4099	28	7	,	,	PUNCT
aiti-4099	28	8	vo	vo	X
aiti-4099	28	9	et	et	PROPN
aiti-4099	28	10	al	al	PROPN
aiti-4099	28	11	.	.	PROPN
aiti-4099	28	12	presented	present	VERB
aiti-4099	28	13	a	a	DET
aiti-4099	28	14	refined	refined	ADJ
aiti-4099	28	15	shear	shear	NOUN
aiti-4099	28	16	deformation	deformation	NOUN
aiti-4099	28	17	theory	theory	NOUN
aiti-4099	28	18	and	and	CCONJ
aiti-4099	28	19	then	then	ADV
aiti-4099	28	20	improved	improve	VERB
aiti-4099	28	21	it	it	PRON
aiti-4099	28	22	to	to	PART
aiti-4099	28	23	form	form	VERB
aiti-4099	28	24	the	the	DET
aiti-4099	28	25	quasi-3d	quasi-3d	ADJ
aiti-4099	28	26	theory	theory	NOUN
aiti-4099	28	27	by	by	ADP
aiti-4099	28	28	taking	take	VERB
aiti-4099	28	29	thickness	thickness	NOUN
aiti-4099	28	30	stretching	stretch	VERB
aiti-4099	28	31	effect	effect	NOUN
aiti-4099	28	32	into	into	ADP
aiti-4099	28	33	account	account	NOUN
aiti-4099	28	34	for	for	ADP
aiti-4099	28	35	studying	study	VERB
aiti-4099	28	36	free	free	ADJ
aiti-4099	28	37	vibration	vibration	NOUN
aiti-4099	28	38	and	and	CCONJ
aiti-4099	28	39	buckling	buckling	NOUN
aiti-4099	28	40	of	of	ADP
aiti-4099	28	41	fgsw	fgsw	NOUN
aiti-4099	28	42	beams	beam	NOUN
aiti-4099	28	43	.	.	PUNCT
aiti-4099	29	1	recently	recently	ADV
aiti-4099	29	2	,	,	PUNCT
aiti-4099	29	3	su	su	PROPN
aiti-4099	29	4	et	et	PROPN
aiti-4099	29	5	al	al	PROPN
aiti-4099	29	6	.	.	PUNCT
aiti-4099	30	1	[	[	X
aiti-4099	30	2	8	8	NUM
aiti-4099	30	3	]	]	PUNCT
aiti-4099	30	4	employed	employ	VERB
aiti-4099	30	5	the	the	DET
aiti-4099	30	6	modified	modify	VERB
aiti-4099	30	7	fourier	fourier	NOUN
aiti-4099	30	8	series	series	NOUN
aiti-4099	30	9	to	to	PART
aiti-4099	30	10	compute	compute	VERB
aiti-4099	30	11	fundamental	fundamental	ADJ
aiti-4099	30	12	frequencies	frequency	NOUN
aiti-4099	30	13	of	of	ADP
aiti-4099	30	14	fgsw	fgsw	NOUN
aiti-4099	30	15	beams	beam	NOUN
aiti-4099	30	16	resting	rest	VERB
aiti-4099	30	17	on	on	ADP
aiti-4099	30	18	an	an	DET
aiti-4099	30	19	elastic	elastic	ADJ
aiti-4099	30	20	foundation	foundation	NOUN
aiti-4099	30	21	.	.	PUNCT
aiti-4099	31	1	in	in	ADP
aiti-4099	31	2	many	many	ADJ
aiti-4099	31	3	practical	practical	ADJ
aiti-4099	31	4	circumstances	circumstance	NOUN
aiti-4099	31	5	,	,	PUNCT
aiti-4099	31	6	the	the	DET
aiti-4099	31	7	unidirectional	unidirectional	ADJ
aiti-4099	31	8	fgm	fgm	PROPN
aiti-4099	31	9	in	in	ADP
aiti-4099	31	10	the	the	DET
aiti-4099	31	11	above	above	ADV
aiti-4099	31	12	-	-	PUNCT
aiti-4099	31	13	cited	cite	VERB
aiti-4099	31	14	papers	paper	NOUN
aiti-4099	31	15	may	may	AUX
aiti-4099	31	16	not	not	PART
aiti-4099	31	17	be	be	AUX
aiti-4099	31	18	so	so	ADV
aiti-4099	31	19	appropriate	appropriate	ADJ
aiti-4099	31	20	to	to	PART
aiti-4099	31	21	resist	resist	VERB
aiti-4099	31	22	multi	multi	ADJ
aiti-4099	31	23	-	-	ADJ
aiti-4099	31	24	directional	directional	ADJ
aiti-4099	31	25	variations	variation	NOUN
aiti-4099	31	26	of	of	ADP
aiti-4099	31	27	mechanical	mechanical	ADJ
aiti-4099	31	28	and	and	CCONJ
aiti-4099	31	29	thermal	thermal	ADJ
aiti-4099	31	30	loadings	loading	NOUN
aiti-4099	31	31	,	,	PUNCT
aiti-4099	31	32	and	and	CCONJ
aiti-4099	31	33	development	development	NOUN
aiti-4099	31	34	of	of	ADP
aiti-4099	31	35	fgm	fgm	PROPN
aiti-4099	31	36	with	with	ADP
aiti-4099	31	37	material	material	NOUN
aiti-4099	31	38	properties	property	NOUN
aiti-4099	31	39	varying	vary	VERB
aiti-4099	31	40	in	in	ADP
aiti-4099	31	41	two	two	NUM
aiti-4099	31	42	or	or	CCONJ
aiti-4099	31	43	three	three	NUM
aiti-4099	31	44	spatial	spatial	ADJ
aiti-4099	31	45	directions	direction	NOUN
aiti-4099	31	46	is	be	AUX
aiti-4099	31	47	necessary	necessary	ADJ
aiti-4099	31	48	.	.	PUNCT
aiti-4099	32	1	several	several	ADJ
aiti-4099	32	2	investigations	investigation	NOUN
aiti-4099	32	3	on	on	ADP
aiti-4099	32	4	vibration	vibration	NOUN
aiti-4099	32	5	analysis	analysis	NOUN
aiti-4099	32	6	of	of	ADP
aiti-4099	32	7	fgm	fgm	PROPN
aiti-4099	32	8	beams	beam	NOUN
aiti-4099	32	9	with	with	ADP
aiti-4099	32	10	material	material	ADJ
aiti-4099	32	11	gradation	gradation	NOUN
aiti-4099	32	12	in	in	ADP
aiti-4099	32	13	both	both	CCONJ
aiti-4099	32	14	the	the	DET
aiti-4099	32	15	thickness	thickness	NOUN
aiti-4099	32	16	and	and	CCONJ
aiti-4099	32	17	length	length	NOUN
aiti-4099	32	18	directions	direction	NOUN
aiti-4099	32	19	have	have	AUX
aiti-4099	32	20	been	be	AUX
aiti-4099	32	21	reported	report	VERB
aiti-4099	32	22	in	in	ADP
aiti-4099	32	23	recent	recent	ADJ
aiti-4099	32	24	years	year	NOUN
aiti-4099	33	1	[	[	X
aiti-4099	33	2	9	9	NUM
aiti-4099	33	3	-	-	SYM
aiti-4099	33	4	12	12	NUM
aiti-4099	33	5	]	]	PUNCT
aiti-4099	33	6	.	.	PUNCT
aiti-4099	34	1	investigation	investigation	NOUN
aiti-4099	34	2	on	on	ADP
aiti-4099	34	3	the	the	DET
aiti-4099	34	4	mechanical	mechanical	ADJ
aiti-4099	34	5	behavior	behavior	NOUN
aiti-4099	34	6	of	of	ADP
aiti-4099	34	7	2d	2d	NOUN
aiti-4099	34	8	-	-	PUNCT
aiti-4099	34	9	fgsw	fgsw	NOUN
aiti-4099	34	10	beams	beam	NOUN
aiti-4099	34	11	,	,	PUNCT
aiti-4099	34	12	however	however	ADV
aiti-4099	34	13	,	,	PUNCT
aiti-4099	34	14	is	be	AUX
aiti-4099	34	15	still	still	ADV
aiti-4099	34	16	very	very	ADV
aiti-4099	34	17	limited	limited	ADJ
aiti-4099	34	18	.	.	PUNCT
aiti-4099	35	1	to	to	ADP
aiti-4099	35	2	the	the	DET
aiti-4099	35	3	authors	author	NOUN
aiti-4099	35	4	’	’	PART
aiti-4099	35	5	best	good	ADJ
aiti-4099	35	6	knowledge	knowledge	NOUN
aiti-4099	35	7	,	,	PUNCT
aiti-4099	35	8	there	there	PRON
aiti-4099	35	9	is	be	VERB
aiti-4099	35	10	only	only	ADV
aiti-4099	35	11	a	a	DET
aiti-4099	35	12	study	study	NOUN
aiti-4099	35	13	by	by	ADP
aiti-4099	35	14	karamanli	karamanli	PROPN
aiti-4099	35	15	in	in	ADP
aiti-4099	35	16	[	[	X
aiti-4099	35	17	13	13	NUM
aiti-4099	35	18	]	]	PUNCT
aiti-4099	35	19	,	,	PUNCT
aiti-4099	35	20	where	where	SCONJ
aiti-4099	35	21	static	static	ADJ
aiti-4099	35	22	bending	bending	NOUN
aiti-4099	35	23	of	of	ADP
aiti-4099	35	24	fgsw	fgsw	NOUN
aiti-4099	35	25	beams	beam	NOUN
aiti-4099	35	26	with	with	ADP
aiti-4099	35	27	material	material	NOUN
aiti-4099	35	28	properties	property	NOUN
aiti-4099	35	29	varying	vary	VERB
aiti-4099	35	30	in	in	ADP
aiti-4099	35	31	both	both	CCONJ
aiti-4099	35	32	the	the	DET
aiti-4099	35	33	thickness	thickness	NOUN
aiti-4099	35	34	and	and	CCONJ
aiti-4099	35	35	length	length	NOUN
aiti-4099	35	36	directions	direction	NOUN
aiti-4099	35	37	by	by	ADP
aiti-4099	35	38	power	power	NOUN
aiti-4099	35	39	gradation	gradation	NOUN
aiti-4099	35	40	laws	law	NOUN
aiti-4099	35	41	under	under	ADP
aiti-4099	35	42	uniform	uniform	NOUN
aiti-4099	35	43	distributed	distribute	VERB
aiti-4099	35	44	load	load	NOUN
aiti-4099	35	45	was	be	AUX
aiti-4099	35	46	studied	study	VERB
aiti-4099	35	47	by	by	ADP
aiti-4099	35	48	the	the	DET
aiti-4099	35	49	symmetric	symmetric	ADJ
aiti-4099	35	50	smoothed	smooth	VERB
aiti-4099	35	51	particle	particle	NOUN
aiti-4099	35	52	hydrodynamics	hydrodynamic	NOUN
aiti-4099	35	53	method	method	NOUN
aiti-4099	35	54	.	.	PUNCT
aiti-4099	36	1	in	in	ADP
aiti-4099	36	2	order	order	NOUN
aiti-4099	36	3	to	to	PART
aiti-4099	36	4	explore	explore	VERB
aiti-4099	36	5	the	the	DET
aiti-4099	36	6	behavior	behavior	NOUN
aiti-4099	36	7	of	of	ADP
aiti-4099	36	8	this	this	DET
aiti-4099	36	9	new	new	ADJ
aiti-4099	36	10	type	type	NOUN
aiti-4099	36	11	of	of	ADP
aiti-4099	36	12	structure	structure	NOUN
aiti-4099	36	13	in	in	ADP
aiti-4099	36	14	some	some	DET
aiti-4099	36	15	further	far	ADV
aiti-4099	36	16	,	,	PUNCT
aiti-4099	36	17	a	a	DET
aiti-4099	36	18	finite	finite	ADJ
aiti-4099	36	19	beam	beam	NOUN
aiti-4099	36	20	element	element	NOUN
aiti-4099	36	21	is	be	AUX
aiti-4099	36	22	formulated	formulate	VERB
aiti-4099	36	23	in	in	ADP
aiti-4099	36	24	this	this	DET
aiti-4099	36	25	paper	paper	NOUN
aiti-4099	36	26	for	for	ADP
aiti-4099	36	27	studying	study	VERB
aiti-4099	36	28	free	free	ADJ
aiti-4099	36	29	and	and	CCONJ
aiti-4099	36	30	forced	force	VERB
aiti-4099	36	31	vibration	vibration	NOUN
aiti-4099	36	32	of	of	ADP
aiti-4099	36	33	two	two	NUM
aiti-4099	36	34	-	-	PUNCT
aiti-4099	36	35	directional	directional	NOUN
aiti-4099	36	36	functionally	functionally	ADV
aiti-4099	36	37	graded	grade	VERB
aiti-4099	36	38	sandwich	sandwich	NOUN
aiti-4099	36	39	(	(	PUNCT
aiti-4099	36	40	2d	2d	NOUN
aiti-4099	36	41	-	-	PUNCT
aiti-4099	36	42	fgsw	fgsw	NOUN
aiti-4099	36	43	)	)	PUNCT
aiti-4099	36	44	beams	beam	NOUN
aiti-4099	36	45	.	.	PUNCT
aiti-4099	37	1	the	the	DET
aiti-4099	37	2	beams	beam	NOUN
aiti-4099	37	3	are	be	AUX
aiti-4099	37	4	considered	consider	VERB
aiti-4099	37	5	to	to	PART
aiti-4099	37	6	be	be	AUX
aiti-4099	37	7	formed	form	VERB
aiti-4099	37	8	from	from	ADP
aiti-4099	37	9	three	three	NUM
aiti-4099	37	10	layers	layer	NOUN
aiti-4099	37	11	,	,	PUNCT
aiti-4099	37	12	a	a	DET
aiti-4099	37	13	homogeneous	homogeneous	ADJ
aiti-4099	37	14	isotropic	isotropic	NOUN
aiti-4099	37	15	ceramic	ceramic	ADJ
aiti-4099	37	16	core	core	NOUN
aiti-4099	37	17	and	and	CCONJ
aiti-4099	37	18	two	two	NUM
aiti-4099	37	19	fgm	fgm	PROPN
aiti-4099	37	20	skin	skin	NOUN
aiti-4099	37	21	layers	layer	NOUN
aiti-4099	37	22	with	with	ADP
aiti-4099	37	23	material	material	NOUN
aiti-4099	37	24	properties	property	NOUN
aiti-4099	37	25	varying	vary	VERB
aiti-4099	37	26	in	in	ADP
aiti-4099	37	27	both	both	CCONJ
aiti-4099	37	28	the	the	DET
aiti-4099	37	29	thickness	thickness	NOUN
aiti-4099	37	30	and	and	CCONJ
aiti-4099	37	31	length	length	NOUN
aiti-4099	37	32	directions	direction	NOUN
aiti-4099	37	33	by	by	ADP
aiti-4099	37	34	power	power	NOUN
aiti-4099	37	35	gradation	gradation	NOUN
aiti-4099	37	36	laws	law	NOUN
aiti-4099	37	37	.	.	PUNCT
aiti-4099	38	1	a	a	DET
aiti-4099	38	2	refined	refined	ADJ
aiti-4099	38	3	shear	shear	NOUN
aiti-4099	38	4	deformation	deformation	NOUN
aiti-4099	38	5	beam	beam	NOUN
aiti-4099	38	6	theory	theory	NOUN
aiti-4099	38	7	,	,	PUNCT
aiti-4099	38	8	in	in	ADP
aiti-4099	38	9	which	which	PRON
aiti-4099	38	10	the	the	DET
aiti-4099	38	11	transverse	transverse	ADJ
aiti-4099	38	12	displacement	displacement	NOUN
aiti-4099	38	13	is	be	AUX
aiti-4099	38	14	split	split	VERB
aiti-4099	38	15	into	into	ADP
aiti-4099	38	16	bending	bend	VERB
aiti-4099	38	17	and	and	CCONJ
aiti-4099	38	18	shear	shear	NOUN
aiti-4099	38	19	parts	part	NOUN
aiti-4099	38	20	,	,	PUNCT
aiti-4099	38	21	is	be	AUX
aiti-4099	38	22	adopted	adopt	VERB
aiti-4099	38	23	to	to	PART
aiti-4099	38	24	derive	derive	VERB
aiti-4099	38	25	the	the	DET
aiti-4099	38	26	element	element	ADJ
aiti-4099	38	27	stiffness	stiffness	NOUN
aiti-4099	38	28	and	and	CCONJ
aiti-4099	38	29	mass	mass	ADJ
aiti-4099	38	30	matrices	matrix	NOUN
aiti-4099	38	31	of	of	ADP
aiti-4099	38	32	the	the	DET
aiti-4099	38	33	beam	beam	NOUN
aiti-4099	38	34	element	element	NOUN
aiti-4099	38	35	.	.	PUNCT
aiti-4099	39	1	thus	thus	ADV
aiti-4099	39	2	,	,	PUNCT
aiti-4099	39	3	in	in	ADP
aiti-4099	39	4	addition	addition	NOUN
aiti-4099	39	5	to	to	ADP
aiti-4099	39	6	the	the	DET
aiti-4099	39	7	vibration	vibration	NOUN
aiti-4099	39	8	of	of	ADP
aiti-4099	39	9	the	the	DET
aiti-4099	39	10	2d	2d	NOUN
aiti-4099	39	11	-	-	PUNCT
aiti-4099	39	12	fgsw	fgsw	NOUN
aiti-4099	39	13	beams	beam	NOUN
aiti-4099	39	14	considered	consider	VERB
aiti-4099	39	15	herein	herein	NOUN
aiti-4099	39	16	for	for	ADP
aiti-4099	39	17	the	the	DET
aiti-4099	39	18	first	first	ADJ
aiti-4099	39	19	time	time	NOUN
aiti-4099	39	20	,	,	PUNCT
aiti-4099	39	21	the	the	DET
aiti-4099	39	22	refined	refined	ADJ
aiti-4099	39	23	theory	theory	NOUN
aiti-4099	39	24	which	which	PRON
aiti-4099	39	25	allows	allow	VERB
aiti-4099	39	26	to	to	PART
aiti-4099	39	27	include	include	VERB
aiti-4099	39	28	the	the	DET
aiti-4099	39	29	shear	shear	NOUN
aiti-4099	39	30	and	and	CCONJ
aiti-4099	39	31	rotary	rotary	NOUN
aiti-4099	39	32	inertia	inertia	NOUN
aiti-4099	39	33	effects	effect	NOUN
aiti-4099	39	34	by	by	ADP
aiti-4099	39	35	dividing	divide	VERB
aiti-4099	39	36	the	the	DET
aiti-4099	39	37	transverse	transverse	ADJ
aiti-4099	39	38	displacement	displacement	NOUN
aiti-4099	39	39	into	into	ADP
aiti-4099	39	40	bending	bend	VERB
aiti-4099	39	41	and	and	CCONJ
aiti-4099	39	42	shear	shear	NOUN
aiti-4099	39	43	parts	part	NOUN
aiti-4099	39	44	is	be	AUX
aiti-4099	39	45	also	also	ADV
aiti-4099	39	46	a	a	DET
aiti-4099	39	47	new	new	ADJ
aiti-4099	39	48	feature	feature	NOUN
aiti-4099	39	49	of	of	ADP
aiti-4099	39	50	this	this	DET
aiti-4099	39	51	paper	paper	NOUN
aiti-4099	39	52	.	.	PUNCT
aiti-4099	40	1	the	the	DET
aiti-4099	40	2	theory	theory	NOUN
aiti-4099	40	3	with	with	ADP
aiti-4099	40	4	the	the	DET
aiti-4099	40	5	parabolic	parabolic	ADJ
aiti-4099	40	6	distribution	distribution	NOUN
aiti-4099	40	7	of	of	ADP
aiti-4099	40	8	shear	shear	ADJ
aiti-4099	40	9	deformation	deformation	NOUN
aiti-4099	40	10	in	in	ADP
aiti-4099	40	11	the	the	DET
aiti-4099	40	12	beam	beam	NOUN
aiti-4099	40	13	thickness	thickness	NOUN
aiti-4099	40	14	does	do	AUX
aiti-4099	40	15	not	not	PART
aiti-4099	40	16	require	require	VERB
aiti-4099	40	17	a	a	DET
aiti-4099	40	18	shear	shear	NOUN
aiti-4099	40	19	correction	correction	NOUN
aiti-4099	40	20	factor	factor	NOUN
aiti-4099	40	21	,	,	PUNCT
aiti-4099	40	22	and	and	CCONJ
aiti-4099	40	23	with	with	ADP
aiti-4099	40	24	the	the	DET
aiti-4099	40	25	mentioned	mention	VERB
aiti-4099	40	26	advantages	advantage	NOUN
aiti-4099	40	27	,	,	PUNCT
aiti-4099	40	28	it	it	PRON
aiti-4099	40	29	has	have	AUX
aiti-4099	40	30	been	be	AUX
aiti-4099	40	31	widely	widely	ADV
aiti-4099	40	32	adopted	adopt	VERB
aiti-4099	40	33	in	in	ADP
aiti-4099	40	34	vibration	vibration	NOUN
aiti-4099	40	35	and	and	CCONJ
aiti-4099	40	36	buckling	buckle	VERB
aiti-4099	40	37	analysis	analysis	NOUN
aiti-4099	40	38	of	of	ADP
aiti-4099	40	39	fgsw	fgsw	NOUN
aiti-4099	40	40	plates	plate	NOUN
aiti-4099	40	41	[	[	X
aiti-4099	40	42	14	14	NUM
aiti-4099	40	43	-	-	SYM
aiti-4099	40	44	17	17	NUM
aiti-4099	40	45	]	]	PUNCT
aiti-4099	40	46	.	.	PUNCT
aiti-4099	41	1	using	use	VERB
aiti-4099	41	2	the	the	DET
aiti-4099	41	3	derived	derived	ADJ
aiti-4099	41	4	formulation	formulation	NOUN
aiti-4099	41	5	,	,	PUNCT
aiti-4099	41	6	natural	natural	ADJ
aiti-4099	41	7	frequencies	frequency	NOUN
aiti-4099	41	8	and	and	CCONJ
aiti-4099	41	9	dynamic	dynamic	ADJ
aiti-4099	41	10	response	response	NOUN
aiti-4099	41	11	of	of	ADP
aiti-4099	41	12	the	the	DET
aiti-4099	41	13	beams	beam	NOUN
aiti-4099	41	14	with	with	ADP
aiti-4099	41	15	various	various	ADJ
aiti-4099	41	16	boundary	boundary	ADJ
aiti-4099	41	17	conditions	condition	NOUN
aiti-4099	41	18	to	to	ADP
aiti-4099	41	19	a	a	DET
aiti-4099	41	20	harmonic	harmonic	ADJ
aiti-4099	41	21	load	load	NOUN
aiti-4099	41	22	are	be	AUX
aiti-4099	41	23	computed	compute	VERB
aiti-4099	41	24	,	,	PUNCT
aiti-4099	41	25	and	and	CCONJ
aiti-4099	41	26	the	the	DET
aiti-4099	41	27	effects	effect	NOUN
aiti-4099	41	28	of	of	ADP
aiti-4099	41	29	material	material	ADJ
aiti-4099	41	30	distribution	distribution	NOUN
aiti-4099	41	31	,	,	PUNCT
aiti-4099	41	32	the	the	DET
aiti-4099	41	33	layer	layer	NOUN
aiti-4099	41	34	thickness	thickness	NOUN
aiti-4099	41	35	ratio	ratio	NOUN
aiti-4099	41	36	and	and	CCONJ
aiti-4099	41	37	the	the	DET
aiti-4099	41	38	aspect	aspect	NOUN
aiti-4099	41	39	ratio	ratio	NOUN
aiti-4099	41	40	on	on	ADP
aiti-4099	41	41	the	the	DET
aiti-4099	41	42	vibration	vibration	NOUN
aiti-4099	41	43	behavior	behavior	NOUN
aiti-4099	41	44	of	of	ADP
aiti-4099	41	45	the	the	DET
aiti-4099	41	46	beams	beam	NOUN
aiti-4099	41	47	are	be	AUX
aiti-4099	41	48	examined	examine	VERB
aiti-4099	41	49	and	and	CCONJ
aiti-4099	41	50	highlighted	highlight	VERB
aiti-4099	41	51	.	.	PUNCT
aiti-4099	42	1	2	2	X
aiti-4099	42	2	.	.	X
aiti-4099	42	3	2d	2d	NOUN
aiti-4099	42	4	-	-	PUNCT
aiti-4099	42	5	fgsw	fgsw	NOUN
aiti-4099	42	6	beam	beam	NOUN
aiti-4099	42	7	model	model	NOUN
aiti-4099	42	8	a	a	DET
aiti-4099	42	9	2d	2d	NUM
aiti-4099	42	10	-	-	PUNCT
aiti-4099	42	11	fgsw	fgsw	NOUN
aiti-4099	42	12	beam	beam	NOUN
aiti-4099	42	13	with	with	ADP
aiti-4099	42	14	a	a	DET
aiti-4099	42	15	rectangular	rectangular	ADJ
aiti-4099	42	16	cross	cross	NOUN
aiti-4099	42	17	-	-	NOUN
aiti-4099	42	18	section	section	ADJ
aiti-4099	42	19	(	(	PUNCT
aiti-4099	42	20	bxh	bxh	NOUN
aiti-4099	42	21	)	)	PUNCT
aiti-4099	42	22	as	as	SCONJ
aiti-4099	42	23	depicted	depict	VERB
aiti-4099	42	24	in	in	ADP
aiti-4099	42	25	fig	fig	NOUN
aiti-4099	42	26	.	.	PUNCT
aiti-4099	43	1	1	1	NUM
aiti-4099	43	2	is	be	AUX
aiti-4099	43	3	considered	consider	VERB
aiti-4099	43	4	.	.	PUNCT
aiti-4099	44	1	the	the	DET
aiti-4099	44	2	beam	beam	NOUN
aiti-4099	44	3	is	be	AUX
aiti-4099	44	4	assumed	assume	VERB
aiti-4099	44	5	to	to	PART
aiti-4099	44	6	form	form	VERB
aiti-4099	44	7	from	from	ADP
aiti-4099	44	8	three	three	NUM
aiti-4099	44	9	layers	layer	NOUN
aiti-4099	44	10	,	,	PUNCT
aiti-4099	44	11	namely	namely	ADV
aiti-4099	44	12	a	a	DET
aiti-4099	44	13	core	core	NOUN
aiti-4099	44	14	of	of	ADP
aiti-4099	44	15	pure	pure	ADJ
aiti-4099	44	16	ceramic	ceramic	NOUN
aiti-4099	44	17	and	and	CCONJ
aiti-4099	44	18	two	two	NUM
aiti-4099	44	19	skin	skin	NOUN
aiti-4099	44	20	layers	layer	NOUN
aiti-4099	44	21	made	make	VERB
aiti-4099	44	22	of	of	ADP
aiti-4099	44	23	ceramic	ceramic	ADJ
aiti-4099	44	24	-	-	PUNCT
aiti-4099	44	25	metal	metal	NOUN
aiti-4099	44	26	fgm	fgm	PROPN
aiti-4099	44	27	.	.	PUNCT
aiti-4099	45	1	in	in	ADP
aiti-4099	45	2	the	the	DET
aiti-4099	45	3	figure	figure	NOUN
aiti-4099	45	4	,	,	PUNCT
aiti-4099	45	5	the	the	DET
aiti-4099	45	6	x	x	NOUN
aiti-4099	45	7	-	-	ADJ
aiti-4099	45	8	axis	axis	NOUN
aiti-4099	45	9	is	be	AUX
aiti-4099	45	10	chosen	choose	VERB
aiti-4099	45	11	on	on	ADP
aiti-4099	45	12	the	the	DET
aiti-4099	45	13	mid	mid	NOUN
aiti-4099	45	14	-	-	NOUN
aiti-4099	45	15	plane	plane	NOUN
aiti-4099	45	16	,	,	PUNCT
aiti-4099	45	17	and	and	CCONJ
aiti-4099	45	18	the	the	DET
aiti-4099	45	19	z	z	NOUN
aiti-4099	45	20	-	-	PUNCT
aiti-4099	45	21	axis	axis	NOUN
aiti-4099	45	22	is	be	AUX
aiti-4099	45	23	perpendicular	perpendicular	ADJ
aiti-4099	45	24	to	to	ADP
aiti-4099	45	25	the	the	DET
aiti-4099	45	26	mid	mid	NOUN
aiti-4099	45	27	-	-	NOUN
aiti-4099	45	28	plane	plane	NOUN
aiti-4099	45	29	and	and	CCONJ
aiti-4099	45	30	directs	direct	VERB
aiti-4099	45	31	upward	upward	ADV
aiti-4099	45	32	.	.	PUNCT
aiti-4099	46	1	denoting	denote	VERB
aiti-4099	46	2	z0	z0	PROPN
aiti-4099	46	3	,	,	PUNCT
aiti-4099	46	4	z1	z1	PROPN
aiti-4099	46	5	,	,	PUNCT
aiti-4099	46	6	z2	z2	NOUN
aiti-4099	46	7	,	,	PUNCT
aiti-4099	46	8	and	and	CCONJ
aiti-4099	46	9	z3	z3	PROPN
aiti-4099	46	10	as	as	ADP
aiti-4099	46	11	the	the	DET
aiti-4099	46	12	vertical	vertical	ADJ
aiti-4099	46	13	coordinates	coordinate	NOUN
aiti-4099	46	14	of	of	ADP
aiti-4099	46	15	the	the	DET
aiti-4099	46	16	bottom	bottom	ADJ
aiti-4099	46	17	layer	layer	NOUN
aiti-4099	46	18	,	,	PUNCT
aiti-4099	46	19	layer	layer	NOUN
aiti-4099	46	20	interfaces	interface	NOUN
aiti-4099	46	21	,	,	PUNCT
aiti-4099	46	22	and	and	CCONJ
aiti-4099	46	23	the	the	DET
aiti-4099	46	24	top	top	ADJ
aiti-4099	46	25	layer	layer	NOUN
aiti-4099	46	26	,	,	PUNCT
aiti-4099	46	27	respectively	respectively	ADV
aiti-4099	46	28	.	.	PUNCT
aiti-4099	47	1	layer	layer	NOUN
aiti-4099	47	2	1	1	NUM
aiti-4099	47	3	:	:	PUNCT
aiti-4099	47	4	2d	2d	NUM
aiti-4099	47	5	-	-	PUNCT
aiti-4099	47	6	fgm	fgm	PROPN
aiti-4099	47	7	layer	layer	NOUN
aiti-4099	47	8	3	3	NUM
aiti-4099	47	9	:	:	PUNCT
aiti-4099	47	10	2d	2d	NUM
aiti-4099	47	11	-	-	PUNCT
aiti-4099	47	12	fgm	fgm	PROPN
aiti-4099	47	13	layer	layer	NOUN
aiti-4099	47	14	2	2	NUM
aiti-4099	47	15	:	:	PUNCT
aiti-4099	47	16	ceramic	ceramic	PROPN
aiti-4099	47	17	b	b	NOUN
aiti-4099	47	18	0z	0z	ADJ
aiti-4099	47	19	=	=	NOUN
aiti-4099	47	20	-h/2	-h/2	PROPN
aiti-4099	47	21	3z	3z	NUM
aiti-4099	47	22	=	=	NOUN
aiti-4099	47	23	h/2	h/2	X
aiti-4099	47	24	y	y	PROPN
aiti-4099	47	25	z	z	NOUN
aiti-4099	47	26	h	h	NOUN
aiti-4099	48	1	x	x	X
aiti-4099	48	2	z	z	NOUN
aiti-4099	48	3	y	y	PROPN
aiti-4099	48	4	2z	2z	NUM
aiti-4099	48	5	1z	1z	NUM
aiti-4099	48	6	fig	fig	NOUN
aiti-4099	48	7	.	.	PUNCT
aiti-4099	49	1	1	1	NUM
aiti-4099	49	2	geometry	geometry	NOUN
aiti-4099	49	3	of	of	ADP
aiti-4099	49	4	2d	2d	NOUN
aiti-4099	49	5	-	-	PUNCT
aiti-4099	49	6	fgsw	fgsw	NOUN
aiti-4099	49	7	beam	beam	NOUN
aiti-4099	49	8	the	the	DET
aiti-4099	49	9	beam	beam	NOUN
aiti-4099	49	10	is	be	AUX
aiti-4099	49	11	considered	consider	VERB
aiti-4099	49	12	to	to	PART
aiti-4099	49	13	be	be	AUX
aiti-4099	49	14	made	make	VERB
aiti-4099	49	15	of	of	ADP
aiti-4099	49	16	ceramic	ceramic	ADJ
aiti-4099	49	17	and	and	CCONJ
aiti-4099	49	18	metal	metal	NOUN
aiti-4099	49	19	whose	whose	DET
aiti-4099	49	20	volume	volume	NOUN
aiti-4099	49	21	fraction	fraction	NOUN
aiti-4099	49	22	varies	vary	VERB
aiti-4099	49	23	in	in	ADP
aiti-4099	49	24	the	the	DET
aiti-4099	49	25	thickness	thickness	NOUN
aiti-4099	49	26	and	and	CCONJ
aiti-4099	49	27	length	length	NOUN
aiti-4099	49	28	directions	direction	NOUN
aiti-4099	49	29	by	by	ADP
aiti-4099	49	30	power	power	NOUN
aiti-4099	49	31	gradation	gradation	NOUN
aiti-4099	49	32	laws	law	NOUN
aiti-4099	49	33	as	as	ADP
aiti-4099	49	34	[	[	X
aiti-4099	49	35	13	13	NUM
aiti-4099	49	36	]	]	PUNCT
aiti-4099	49	37	advances	advance	NOUN
aiti-4099	49	38	in	in	ADP
aiti-4099	49	39	technology	technology	NOUN
aiti-4099	49	40	innovation	innovation	NOUN
aiti-4099	49	41	,	,	PUNCT
aiti-4099	49	42	vol	vol	NOUN
aiti-4099	49	43	.	.	PROPN
aiti-4099	49	44	4	4	NUM
aiti-4099	49	45	,	,	PUNCT
aiti-4099	49	46	no	no	INTJ
aiti-4099	49	47	.	.	NOUN
aiti-4099	49	48	3	3	NUM
aiti-4099	49	49	,	,	PUNCT
aiti-4099	49	50	2019	2019	NUM
aiti-4099	49	51	,	,	PUNCT
aiti-4099	49	52	pp	pp	ADJ
aiti-4099	49	53	.	.	PUNCT
aiti-4099	50	1	152	152	NUM
aiti-4099	50	2	-	-	SYM
aiti-4099	50	3	164	164	NUM
aiti-4099	50	4	154	154	NUM
aiti-4099	50	5			ADJ
aiti-4099	50	6			PUNCT
aiti-4099	50	7			ADJ
aiti-4099	50	8			PUNCT
aiti-4099	50	9			NOUN
aiti-4099	50	10			PROPN
aiti-4099	50	11	1	1	NUM
aiti-4099	50	12	0	0	NUM
aiti-4099	50	13	1	1	NUM
aiti-4099	50	14	0	0	NUM
aiti-4099	50	15	1	1	NUM
aiti-4099	50	16	1	1	NUM
aiti-4099	50	17	2	2	NUM
aiti-4099	50	18	2	2	NUM
aiti-4099	50	19	2	2	NUM
aiti-4099	50	20	3	3	NUM
aiti-4099	50	21	3	3	NUM
aiti-4099	50	22	2	2	NUM
aiti-4099	50	23	1	1	NUM
aiti-4099	50	24	for	for	ADP
aiti-4099	50	25	,	,	PUNCT
aiti-4099	50	26	2	2	NUM
aiti-4099	50	27	0	0	NUM
aiti-4099	50	28	for	for	ADP
aiti-4099	50	29	,	,	PUNCT
aiti-4099	50	30	1	1	NUM
aiti-4099	50	31	for	for	ADP
aiti-4099	50	32	,	,	PUNCT
aiti-4099	50	33	2	2	NUM
aiti-4099	50	34	and	and	CCONJ
aiti-4099	50	35	1z	1z	NUM
aiti-4099	50	36	x	x	SYM
aiti-4099	50	37	z	z	NOUN
aiti-4099	50	38	x	x	SYM
aiti-4099	50	39	n	n	CCONJ
aiti-4099	50	40	n	n	CCONJ
aiti-4099	50	41	m	m	VERB
aiti-4099	50	42	n	n	ADJ
aiti-4099	50	43	n	n	PROPN
aiti-4099	50	44	c	c	NOUN
aiti-4099	50	45	m	m	NOUN
aiti-4099	50	46	z	z	NOUN
aiti-4099	50	47	z	z	NOUN
aiti-4099	50	48	x	x	X
aiti-4099	50	49	z	z	NOUN
aiti-4099	50	50	z	z	NOUN
aiti-4099	50	51	z	z	NOUN
aiti-4099	50	52	z	z	NOUN
aiti-4099	50	53	z	z	NOUN
aiti-4099	50	54	l	l	NOUN
aiti-4099	50	55	v	v	NOUN
aiti-4099	50	56	z	z	NOUN
aiti-4099	50	57	z	z	NOUN
aiti-4099	50	58	z	z	NOUN
aiti-4099	50	59	z	z	NOUN
aiti-4099	50	60	z	z	NOUN
aiti-4099	50	61	x	x	PUNCT
aiti-4099	50	62	z	z	NOUN
aiti-4099	50	63	z	z	NOUN
aiti-4099	50	64	z	z	NOUN
aiti-4099	50	65	z	z	NOUN
aiti-4099	50	66	z	z	NOUN
aiti-4099	50	67	l	l	NOUN
aiti-4099	50	68	v	v	NOUN
aiti-4099	50	69	v	v	NOUN
aiti-4099	50	70			PUNCT
aiti-4099	50	71			ADJ
aiti-4099	50	72			NOUN
aiti-4099	50	73			PROPN
aiti-4099	50	74			NUM
aiti-4099	50	75			PROPN
aiti-4099	50	76			PROPN
aiti-4099	50	77			PROPN
aiti-4099	51	1			PROPN
aiti-4099	52	1			PROPN
aiti-4099	53	1			PROPN
aiti-4099	53	2			PROPN
aiti-4099	53	3			ADP
aiti-4099	53	4			NOUN
aiti-4099	53	5			NUM
aiti-4099	53	6			NUM
aiti-4099	53	7			PROPN
aiti-4099	53	8			NUM
aiti-4099	53	9			NOUN
aiti-4099	53	10			PROPN
aiti-4099	53	11			NOUN
aiti-4099	53	12			PROPN
aiti-4099	53	13			VERB
aiti-4099	53	14			PROPN
aiti-4099	53	15			PROPN
aiti-4099	53	16			PROPN
aiti-4099	53	17			PUNCT
aiti-4099	53	18			PROPN
aiti-4099	53	19			PROPN
aiti-4099	53	20			NOUN
aiti-4099	53	21			PROPN
aiti-4099	53	22			PROPN
aiti-4099	53	23	(	(	PUNCT
aiti-4099	53	24	1	1	NUM
aiti-4099	53	25	)	)	PUNCT
aiti-4099	53	26	where	where	SCONJ
aiti-4099	53	27	vc	vc	PROPN
aiti-4099	53	28	and	and	CCONJ
aiti-4099	53	29	vm	vm	PROPN
aiti-4099	53	30	are	be	AUX
aiti-4099	53	31	,	,	PUNCT
aiti-4099	53	32	respectively	respectively	ADV
aiti-4099	53	33	,	,	PUNCT
aiti-4099	53	34	the	the	DET
aiti-4099	53	35	volume	volume	NOUN
aiti-4099	53	36	fraction	fraction	NOUN
aiti-4099	53	37	of	of	ADP
aiti-4099	53	38	ceramic	ceramic	ADJ
aiti-4099	53	39	and	and	CCONJ
aiti-4099	53	40	metal	metal	NOUN
aiti-4099	53	41	;	;	PUNCT
aiti-4099	53	42	nx	nx	NOUN
aiti-4099	53	43	and	and	CCONJ
aiti-4099	53	44	nz	nz	PROPN
aiti-4099	53	45	are	be	AUX
aiti-4099	53	46	the	the	DET
aiti-4099	53	47	grading	grade	VERB
aiti-4099	53	48	indexes	index	NOUN
aiti-4099	53	49	,	,	PUNCT
aiti-4099	53	50	defining	define	VERB
aiti-4099	53	51	variations	variation	NOUN
aiti-4099	53	52	of	of	ADP
aiti-4099	53	53	the	the	DET
aiti-4099	53	54	constituent	constituent	NOUN
aiti-4099	53	55	materials	material	NOUN
aiti-4099	53	56	in	in	ADP
aiti-4099	53	57	the	the	DET
aiti-4099	53	58	xand	xand	NOUN
aiti-4099	53	59	z	z	NOUN
aiti-4099	53	60	-	-	PUNCT
aiti-4099	53	61	directions	direction	NOUN
aiti-4099	53	62	,	,	PUNCT
aiti-4099	53	63	respectively	respectively	ADV
aiti-4099	53	64	.	.	PUNCT
aiti-4099	54	1	noting	note	VERB
aiti-4099	54	2	that	that	SCONJ
aiti-4099	54	3	when	when	SCONJ
aiti-4099	54	4	nx=0	nx=0	PROPN
aiti-4099	54	5	the	the	DET
aiti-4099	54	6	beam	beam	NOUN
aiti-4099	54	7	deduces	deduce	VERB
aiti-4099	54	8	to	to	ADP
aiti-4099	54	9	the	the	DET
aiti-4099	54	10	conventional	conventional	ADJ
aiti-4099	54	11	1d	1d	NUM
aiti-4099	54	12	-	-	PUNCT
aiti-4099	54	13	fgsw	fgsw	NOUN
aiti-4099	54	14	beam	beam	NOUN
aiti-4099	54	15	with	with	ADP
aiti-4099	54	16	the	the	DET
aiti-4099	54	17	material	material	NOUN
aiti-4099	54	18	properties	property	NOUN
aiti-4099	54	19	vary	vary	VERB
aiti-4099	54	20	in	in	ADP
aiti-4099	54	21	the	the	DET
aiti-4099	54	22	thickness	thickness	NOUN
aiti-4099	54	23	direction	direction	NOUN
aiti-4099	54	24	only	only	ADV
aiti-4099	54	25	.	.	PUNCT
aiti-4099	55	1	the	the	DET
aiti-4099	55	2	effective	effective	ADJ
aiti-4099	55	3	property	property	NOUN
aiti-4099	55	4	such	such	ADJ
aiti-4099	55	5	as	as	ADP
aiti-4099	55	6	young	young	ADJ
aiti-4099	55	7	’s	’s	PART
aiti-4099	55	8	modulus	modulus	ADJ
aiti-4099	55	9	and	and	CCONJ
aiti-4099	55	10	mass	mass	ADJ
aiti-4099	55	11	density	density	NOUN
aiti-4099	55	12	,	,	PUNCT
aiti-4099	55	13	p(x	p(x	NOUN
aiti-4099	55	14	,	,	PUNCT
aiti-4099	55	15	z	z	NOUN
aiti-4099	55	16	)	)	PUNCT
aiti-4099	55	17	,	,	PUNCT
aiti-4099	55	18	evaluated	evaluate	VERB
aiti-4099	55	19	by	by	ADP
aiti-4099	55	20	the	the	DET
aiti-4099	55	21	voigt	voigt	PROPN
aiti-4099	55	22	model	model	NOUN
aiti-4099	55	23	is	be	AUX
aiti-4099	55	24	of	of	ADP
aiti-4099	55	25	the	the	DET
aiti-4099	55	26	forms	form	NOUN
aiti-4099	55	27			NOUN
aiti-4099	55	28			PROPN
aiti-4099	55	29			ADJ
aiti-4099	55	30			ADP
aiti-4099	55	31			ADJ
aiti-4099	55	32			PUNCT
aiti-4099	55	33			NOUN
aiti-4099	55	34			PROPN
aiti-4099	55	35	1	1	NUM
aiti-4099	55	36	0	0	NUM
aiti-4099	55	37	1	1	NUM
aiti-4099	55	38	0	0	NUM
aiti-4099	55	39	1	1	NUM
aiti-4099	55	40	1	1	NUM
aiti-4099	55	41	2	2	NUM
aiti-4099	55	42	2	2	NUM
aiti-4099	55	43	2	2	NUM
aiti-4099	55	44	3	3	NUM
aiti-4099	55	45	3	3	NUM
aiti-4099	55	46	2	2	NUM
aiti-4099	55	47	(	(	PUNCT
aiti-4099	55	48	)	)	PUNCT
aiti-4099	55	49	1	1	NUM
aiti-4099	56	1	if	if	SCONJ
aiti-4099	56	2	,	,	PUNCT
aiti-4099	56	3	2	2	NUM
aiti-4099	56	4	,	,	PUNCT
aiti-4099	56	5	if	if	SCONJ
aiti-4099	56	6	,	,	PUNCT
aiti-4099	56	7	(	(	PUNCT
aiti-4099	56	8	)	)	PUNCT
aiti-4099	56	9	1	1	NUM
aiti-4099	57	1	if	if	SCONJ
aiti-4099	57	2	,	,	PUNCT
aiti-4099	57	3	2	2	NUM
aiti-4099	57	4	z	z	NOUN
aiti-4099	57	5	x	x	X
aiti-4099	57	6	z	z	NOUN
aiti-4099	57	7	x	x	SYM
aiti-4099	57	8	p	p	X
aiti-4099	57	9	p	p	X
aiti-4099	57	10	m	m	NOUN
aiti-4099	57	11	c	c	NOUN
aiti-4099	57	12	c	c	NOUN
aiti-4099	57	13	c	c	NOUN
aiti-4099	57	14	p	p	X
aiti-4099	57	15	p	p	X
aiti-4099	57	16	m	m	NOUN
aiti-4099	57	17	c	c	NOUN
aiti-4099	57	18	c	c	NOUN
aiti-4099	57	19	z	z	NOUN
aiti-4099	57	20	z	z	NOUN
aiti-4099	57	21	x	x	PRON
aiti-4099	58	1	p	p	X
aiti-4099	58	2	p	p	X
aiti-4099	58	3	p	p	PROPN
aiti-4099	58	4	z	z	NOUN
aiti-4099	58	5	z	z	NOUN
aiti-4099	58	6	z	z	NOUN
aiti-4099	58	7	z	z	NOUN
aiti-4099	58	8	z	z	NOUN
aiti-4099	58	9	l	l	NOUN
aiti-4099	58	10	p	p	X
aiti-4099	58	11	x	x	X
aiti-4099	58	12	z	z	NOUN
aiti-4099	58	13	p	p	NOUN
aiti-4099	58	14	z	z	PROPN
aiti-4099	58	15	z	z	NOUN
aiti-4099	58	16	z	z	NOUN
aiti-4099	59	1	z	z	NOUN
aiti-4099	59	2	z	z	NOUN
aiti-4099	60	1	x	x	PRON
aiti-4099	61	1	p	p	X
aiti-4099	61	2	p	p	X
aiti-4099	61	3	p	p	PROPN
aiti-4099	61	4	z	z	NOUN
aiti-4099	61	5	z	z	NOUN
aiti-4099	61	6	z	z	NOUN
aiti-4099	61	7	z	z	NOUN
aiti-4099	61	8	z	z	NOUN
aiti-4099	61	9	l	l	NOUN
aiti-4099	61	10			X
aiti-4099	61	11			NOUN
aiti-4099	61	12			VERB
aiti-4099	61	13			NOUN
aiti-4099	61	14			PROPN
aiti-4099	61	15			NUM
aiti-4099	61	16			PROPN
aiti-4099	61	17			PROPN
aiti-4099	61	18			VERB
aiti-4099	61	19			PROPN
aiti-4099	61	20			PROPN
aiti-4099	62	1			PROPN
aiti-4099	62	2			PROPN
aiti-4099	62	3			PROPN
aiti-4099	62	4			PROPN
aiti-4099	62	5			ADJ
aiti-4099	62	6			PROPN
aiti-4099	62	7			NOUN
aiti-4099	62	8			NUM
aiti-4099	62	9			NUM
aiti-4099	62	10			PROPN
aiti-4099	62	11			NUM
aiti-4099	62	12			NOUN
aiti-4099	62	13			PROPN
aiti-4099	62	14			NOUN
aiti-4099	62	15			PROPN
aiti-4099	62	16			PROPN
aiti-4099	62	17			PROPN
aiti-4099	62	18			CCONJ
aiti-4099	62	19			PROPN
aiti-4099	62	20			PROPN
aiti-4099	63	1			PROPN
aiti-4099	63	2			PUNCT
aiti-4099	63	3			PROPN
aiti-4099	63	4			PROPN
aiti-4099	63	5			NOUN
aiti-4099	63	6			NOUN
aiti-4099	63	7	(	(	PUNCT
aiti-4099	63	8	2	2	NUM
aiti-4099	63	9	)	)	PUNCT
aiti-4099	63	10	where	where	SCONJ
aiti-4099	63	11	pm	pm	NOUN
aiti-4099	63	12	and	and	CCONJ
aiti-4099	63	13	pc	pc	NOUN
aiti-4099	63	14	are	be	AUX
aiti-4099	63	15	the	the	DET
aiti-4099	63	16	properties	property	NOUN
aiti-4099	63	17	of	of	ADP
aiti-4099	63	18	the	the	DET
aiti-4099	63	19	metal	metal	NOUN
aiti-4099	63	20	and	and	CCONJ
aiti-4099	63	21	ceramic	ceramic	NOUN
aiti-4099	63	22	,	,	PUNCT
aiti-4099	63	23	respectively	respectively	ADV
aiti-4099	63	24	.	.	PUNCT
aiti-4099	64	1	based	base	VERB
aiti-4099	64	2	on	on	ADP
aiti-4099	64	3	the	the	DET
aiti-4099	64	4	refined	refined	ADJ
aiti-4099	64	5	third	third	ADJ
aiti-4099	64	6	-	-	PUNCT
aiti-4099	64	7	order	order	NOUN
aiti-4099	64	8	shear	shear	NOUN
aiti-4099	64	9	deformation	deformation	NOUN
aiti-4099	64	10	beam	beam	NOUN
aiti-4099	64	11	theory	theory	NOUN
aiti-4099	64	12	[	[	X
aiti-4099	64	13	6	6	NUM
aiti-4099	64	14	]	]	PUNCT
aiti-4099	64	15	,	,	PUNCT
aiti-4099	64	16	the	the	DET
aiti-4099	64	17	displacements	displacement	NOUN
aiti-4099	64	18	in	in	ADP
aiti-4099	64	19	xand	xand	PROPN
aiti-4099	64	20	z	z	NOUN
aiti-4099	64	21	-	-	PUNCT
aiti-4099	64	22	directions	direction	NOUN
aiti-4099	64	23	,	,	PUNCT
aiti-4099	64	24	u1(x	u1(x	ADJ
aiti-4099	64	25	,	,	PUNCT
aiti-4099	64	26	z	z	PROPN
aiti-4099	64	27	,	,	PUNCT
aiti-4099	64	28	t	t	PROPN
aiti-4099	64	29	)	)	PUNCT
aiti-4099	64	30	and	and	CCONJ
aiti-4099	64	31	u3(x	u3(x	PROPN
aiti-4099	64	32	,	,	PUNCT
aiti-4099	64	33	z	z	PROPN
aiti-4099	64	34	,	,	PUNCT
aiti-4099	64	35	t	t	PROPN
aiti-4099	64	36	)	)	PUNCT
aiti-4099	64	37	,	,	PUNCT
aiti-4099	64	38	at	at	ADP
aiti-4099	64	39	any	any	DET
aiti-4099	64	40	point	point	NOUN
aiti-4099	64	41	of	of	ADP
aiti-4099	64	42	the	the	DET
aiti-4099	64	43	beam	beam	NOUN
aiti-4099	64	44	are	be	AUX
aiti-4099	64	45	respectively	respectively	ADV
aiti-4099	64	46	given	give	VERB
aiti-4099	64	47	by	by	ADP
aiti-4099	64	48			NOUN
aiti-4099	64	49			PROPN
aiti-4099	64	50			NOUN
aiti-4099	64	51			PROPN
aiti-4099	64	52	3	3	NUM
aiti-4099	64	53	1	1	NUM
aiti-4099	64	54	,	,	PUNCT
aiti-4099	64	55	,	,	PUNCT
aiti-4099	64	56	2	2	NUM
aiti-4099	64	57	3	3	NUM
aiti-4099	64	58	4	4	NUM
aiti-4099	64	59	,	,	PUNCT
aiti-4099	64	60	,	,	PUNCT
aiti-4099	64	61	(	(	PUNCT
aiti-4099	64	62	,	,	PUNCT
aiti-4099	64	63	)	)	PUNCT
aiti-4099	64	64	(	(	PUNCT
aiti-4099	64	65	,	,	PUNCT
aiti-4099	64	66	)	)	PUNCT
aiti-4099	64	67	(	(	PUNCT
aiti-4099	64	68	,	,	PUNCT
aiti-4099	64	69	)	)	PUNCT
aiti-4099	64	70	3	3	NUM
aiti-4099	64	71	,	,	PUNCT
aiti-4099	64	72	,	,	PUNCT
aiti-4099	64	73	(	(	PUNCT
aiti-4099	64	74	,	,	PUNCT
aiti-4099	64	75	)	)	PUNCT
aiti-4099	64	76	(	(	PUNCT
aiti-4099	64	77	,	,	PUNCT
aiti-4099	64	78	)	)	PUNCT
aiti-4099	64	79	b	b	X
aiti-4099	64	80	x	x	SYM
aiti-4099	64	81	s	s	NOUN
aiti-4099	64	82	x	x	X
aiti-4099	64	83	b	b	PROPN
aiti-4099	64	84	s	s	PROPN
aiti-4099	64	85	z	z	NOUN
aiti-4099	64	86	u	u	NOUN
aiti-4099	64	87	x	x	PROPN
aiti-4099	64	88	z	z	NOUN
aiti-4099	64	89	t	t	NOUN
aiti-4099	64	90	u	u	X
aiti-4099	64	91	x	x	X
aiti-4099	64	92	t	t	NOUN
aiti-4099	64	93	zw	zw	X
aiti-4099	64	94	x	x	SYM
aiti-4099	64	95	t	t	PROPN
aiti-4099	64	96	w	w	PROPN
aiti-4099	64	97	x	x	SYM
aiti-4099	64	98	t	t	NOUN
aiti-4099	64	99	h	h	NOUN
aiti-4099	64	100	u	u	NOUN
aiti-4099	64	101	x	x	X
aiti-4099	64	102	z	z	NOUN
aiti-4099	64	103	t	t	PROPN
aiti-4099	64	104	w	w	PROPN
aiti-4099	64	105	x	x	PROPN
aiti-4099	64	106	t	t	PROPN
aiti-4099	64	107	w	w	NOUN
aiti-4099	64	108	x	x	PROPN
aiti-4099	64	109	t	t	PROPN
aiti-4099	64	110			NUM
aiti-4099	64	111			PROPN
aiti-4099	64	112			PROPN
aiti-4099	64	113			PRON
aiti-4099	64	114			PUNCT
aiti-4099	64	115	(	(	PUNCT
aiti-4099	64	116	3	3	X
aiti-4099	64	117	)	)	PUNCT
aiti-4099	64	118	where	where	SCONJ
aiti-4099	64	119	u	u	NOUN
aiti-4099	64	120	,	,	PUNCT
aiti-4099	64	121	wb	wb	PROPN
aiti-4099	64	122	,	,	PUNCT
aiti-4099	64	123	ws	ws	PROPN
aiti-4099	64	124	are	be	AUX
aiti-4099	64	125	the	the	DET
aiti-4099	64	126	axial	axial	ADJ
aiti-4099	64	127	displacement	displacement	NOUN
aiti-4099	64	128	,	,	PUNCT
aiti-4099	64	129	transverse	transverse	NOUN
aiti-4099	64	130	bending	bending	NOUN
aiti-4099	64	131	and	and	CCONJ
aiti-4099	64	132	shear	shear	NOUN
aiti-4099	64	133	displacements	displacement	NOUN
aiti-4099	64	134	of	of	ADP
aiti-4099	64	135	a	a	DET
aiti-4099	64	136	point	point	NOUN
aiti-4099	64	137	on	on	ADP
aiti-4099	64	138	the	the	DET
aiti-4099	64	139	x	x	NOUN
aiti-4099	64	140	-	-	NOUN
aiti-4099	64	141	axis	axis	ADJ
aiti-4099	64	142	,	,	PUNCT
aiti-4099	64	143	respectively	respectively	ADV
aiti-4099	64	144	.	.	PUNCT
aiti-4099	65	1	in	in	ADP
aiti-4099	65	2	eq	eq	ADP
aiti-4099	65	3	.	.	PUNCT
aiti-4099	65	4	(	(	PUNCT
aiti-4099	65	5	3	3	NUM
aiti-4099	65	6	)	)	PUNCT
aiti-4099	65	7	and	and	CCONJ
aiti-4099	65	8	hereafter	hereafter	ADV
aiti-4099	65	9	,	,	PUNCT
aiti-4099	65	10	a	a	DET
aiti-4099	65	11	subscript	subscript	NOUN
aiti-4099	65	12	comma	comma	NOUN
aiti-4099	65	13	is	be	AUX
aiti-4099	65	14	used	use	VERB
aiti-4099	65	15	to	to	PART
aiti-4099	65	16	denote	denote	VERB
aiti-4099	65	17	the	the	DET
aiti-4099	65	18	derivative	derivative	NOUN
aiti-4099	65	19	with	with	ADP
aiti-4099	65	20	respect	respect	NOUN
aiti-4099	65	21	to	to	ADP
aiti-4099	65	22	the	the	DET
aiti-4099	65	23	followed	follow	VERB
aiti-4099	65	24	variable	variable	NOUN
aiti-4099	65	25	,	,	PUNCT
aiti-4099	65	26	e.g.	e.g.	ADV
aiti-4099	65	27	,	,	PUNCT
aiti-4099	65	28	/s	/s	PUNCT
aiti-4099	65	29	xw	xw	PROPN
aiti-4099	65	30	w	w	PROPN
aiti-4099	65	31	x	x	PROPN
aiti-4099	65	32			PROPN
aiti-4099	65	33			PROPN
aiti-4099	65	34	.	.	PUNCT
aiti-4099	66	1	the	the	DET
aiti-4099	66	2	strains	strain	NOUN
aiti-4099	66	3	resulted	result	VERB
aiti-4099	66	4	from	from	ADP
aiti-4099	66	5	eq	eq	ADP
aiti-4099	66	6	.	.	PUNCT
aiti-4099	67	1	(	(	PUNCT
aiti-4099	67	2	3	3	X
aiti-4099	67	3	)	)	PUNCT
aiti-4099	67	4	are	be	AUX
aiti-4099	67	5	of	of	ADP
aiti-4099	67	6	the	the	DET
aiti-4099	67	7	forms	form	NOUN
aiti-4099	67	8	3	3	NUM
aiti-4099	67	9	1	1	NUM
aiti-4099	67	10	,	,	PUNCT
aiti-4099	67	11	,	,	PUNCT
aiti-4099	67	12	,	,	PUNCT
aiti-4099	67	13	,	,	PUNCT
aiti-4099	67	14	2	2	NUM
aiti-4099	67	15	2	2	NUM
aiti-4099	67	16	1	1	NUM
aiti-4099	67	17	,	,	PUNCT
aiti-4099	67	18	3	3	NUM
aiti-4099	67	19	,	,	PUNCT
aiti-4099	67	20	,	,	PUNCT
aiti-4099	67	21	2	2	NUM
aiti-4099	67	22	4	4	NUM
aiti-4099	67	23	,	,	PUNCT
aiti-4099	67	24	3	3	NUM
aiti-4099	67	25	4	4	NUM
aiti-4099	67	26	1	1	NUM
aiti-4099	67	27	x	x	SYM
aiti-4099	67	28	x	x	PUNCT
aiti-4099	67	29	x	x	SYM
aiti-4099	67	30	b	b	X
aiti-4099	67	31	xx	xx	NUM
aiti-4099	67	32	s	s	NOUN
aiti-4099	67	33	xx	xx	NUM
aiti-4099	68	1	xz	xz	PROPN
aiti-4099	68	2	z	z	PROPN
aiti-4099	69	1	x	x	X
aiti-4099	69	2	s	s	X
aiti-4099	69	3	x	x	X
aiti-4099	69	4	z	z	PUNCT
aiti-4099	69	5	u	u	SYM
aiti-4099	69	6	u	u	NOUN
aiti-4099	69	7	zw	zw	PROPN
aiti-4099	69	8	w	w	PROPN
aiti-4099	69	9	h	h	PROPN
aiti-4099	69	10	z	z	PROPN
aiti-4099	69	11	u	u	NOUN
aiti-4099	69	12	u	u	PROPN
aiti-4099	69	13	w	w	PROPN
aiti-4099	69	14	h	h	PROPN
aiti-4099	69	15			PROPN
aiti-4099	69	16			NUM
aiti-4099	70	1			NUM
aiti-4099	70	2			PROPN
aiti-4099	70	3			PROPN
aiti-4099	70	4			PROPN
aiti-4099	70	5			NOUN
aiti-4099	70	6			PROPN
aiti-4099	70	7			PROPN
aiti-4099	70	8			ADV
aiti-4099	70	9			PRON
aiti-4099	70	10			PROPN
aiti-4099	70	11			CCONJ
aiti-4099	71	1			PROPN
aiti-4099	71	2			NOUN
aiti-4099	71	3	(	(	PUNCT
aiti-4099	71	4	4	4	NUM
aiti-4099	71	5	)	)	PUNCT
aiti-4099	71	6	assuming	assume	VERB
aiti-4099	71	7	linearly	linearly	ADV
aiti-4099	71	8	elastic	elastic	ADJ
aiti-4099	71	9	behavior	behavior	NOUN
aiti-4099	71	10	,	,	PUNCT
aiti-4099	71	11	the	the	DET
aiti-4099	71	12	constitutive	constitutive	ADJ
aiti-4099	71	13	equations	equation	NOUN
aiti-4099	71	14	for	for	ADP
aiti-4099	71	15	the	the	DET
aiti-4099	71	16	beam	beam	NOUN
aiti-4099	71	17	are	be	AUX
aiti-4099	71	18	of	of	ADP
aiti-4099	71	19	the	the	DET
aiti-4099	71	20	form	form	NOUN
aiti-4099	71	21	2	2	NUM
aiti-4099	71	22	,	,	PUNCT
aiti-4099	71	23	1	1	NUM
aiti-4099	71	24	2(1	2(1	NUM
aiti-4099	71	25	)	)	PUNCT
aiti-4099	71	26	x	x	X
aiti-4099	72	1	x	x	X
aiti-4099	72	2	xz	xz	PROPN
aiti-4099	72	3	xz	xz	PROPN
aiti-4099	72	4	e	e	PROPN
aiti-4099	72	5	e	e	PROPN
aiti-4099	72	6			PROPN
aiti-4099	72	7			PROPN
aiti-4099	72	8			NOUN
aiti-4099	72	9			NUM
aiti-4099	72	10			INTJ
aiti-4099	72	11			PUNCT
aiti-4099	73	1			NUM
aiti-4099	74	1			PROPN
aiti-4099	74	2			PROPN
aiti-4099	74	3			X
aiti-4099	74	4	(	(	PUNCT
aiti-4099	74	5	5	5	NUM
aiti-4099	74	6	)	)	PUNCT
aiti-4099	74	7	where	where	SCONJ
aiti-4099	74	8			NOUN
aiti-4099	74	9	is	be	AUX
aiti-4099	74	10	poisson	poisson	PROPN
aiti-4099	74	11	’s	’s	PART
aiti-4099	74	12	ratio	ratio	NOUN
aiti-4099	74	13	,	,	PUNCT
aiti-4099	74	14	assumed	assume	VERB
aiti-4099	74	15	to	to	PART
aiti-4099	74	16	be	be	AUX
aiti-4099	74	17	unchanged	unchanged	ADJ
aiti-4099	74	18	.	.	PUNCT
aiti-4099	75	1	the	the	DET
aiti-4099	75	2	strain	strain	ADJ
aiti-4099	75	3	energy	energy	NOUN
aiti-4099	75	4	(	(	PUNCT
aiti-4099	75	5	u	u	NOUN
aiti-4099	75	6	)	)	PUNCT
aiti-4099	75	7	resulted	result	VERB
aiti-4099	75	8	from	from	ADP
aiti-4099	75	9	eqs	eqs	PROPN
aiti-4099	75	10	.	.	PUNCT
aiti-4099	76	1	(	(	PUNCT
aiti-4099	76	2	4	4	NUM
aiti-4099	76	3	)	)	PUNCT
aiti-4099	76	4	and	and	CCONJ
aiti-4099	76	5	(	(	PUNCT
aiti-4099	76	6	5	5	X
aiti-4099	76	7	)	)	PUNCT
aiti-4099	76	8	is	be	AUX
aiti-4099	76	9			NOUN
aiti-4099	76	10			PROPN
aiti-4099	76	11	2	2	NUM
aiti-4099	76	12	2	2	NUM
aiti-4099	76	13	11	11	NUM
aiti-4099	76	14	,	,	PUNCT
aiti-4099	76	15	12	12	NUM
aiti-4099	76	16	,	,	PUNCT
aiti-4099	76	17	,	,	PUNCT
aiti-4099	76	18	22	22	NUM
aiti-4099	76	19	.	.	PUNCT
aiti-4099	76	20	23	23	NUM
aiti-4099	76	21	,	,	PUNCT
aiti-4099	76	22	,	,	PUNCT
aiti-4099	76	23	2	2	NUM
aiti-4099	76	24	0	0	NUM
aiti-4099	76	25	2	2	NUM
aiti-4099	76	26	2	2	NUM
aiti-4099	76	27	44	44	NUM
aiti-4099	76	28	,	,	PUNCT
aiti-4099	76	29	,	,	PUNCT
aiti-4099	76	30	66	66	NUM
aiti-4099	76	31	,	,	PUNCT
aiti-4099	76	32	11	11	NUM
aiti-4099	76	33	22	22	NUM
aiti-4099	76	34	44	44	NUM
aiti-4099	76	35	,	,	PUNCT
aiti-4099	76	36	2	2	NUM
aiti-4099	76	37	4	4	NUM
aiti-4099	76	38	2	2	NUM
aiti-4099	76	39	4	4	NUM
aiti-4099	76	40	1	1	NUM
aiti-4099	76	41	1	1	NUM
aiti-4099	76	42	8	8	NUM
aiti-4099	76	43	2	2	NUM
aiti-4099	76	44	2	2	NUM
aiti-4099	76	45	2	2	NUM
aiti-4099	76	46	3	3	NUM
aiti-4099	76	47	8	8	NUM
aiti-4099	76	48	16	16	NUM
aiti-4099	76	49	8	8	NUM
aiti-4099	76	50	16	16	NUM
aiti-4099	76	51	3	3	NUM
aiti-4099	76	52	9	9	NUM
aiti-4099	76	53	[	[	PUNCT
aiti-4099	76	54	]	]	X
aiti-4099	76	55	l	l	NOUN
aiti-4099	76	56	x	x	PUNCT
aiti-4099	76	57	x	x	SYM
aiti-4099	76	58	xz	xz	PROPN
aiti-4099	76	59	xz	xz	PROPN
aiti-4099	77	1	x	x	PROPN
aiti-4099	78	1	x	x	X
aiti-4099	78	2	b	b	X
aiti-4099	79	1	xx	xx	NUM
aiti-4099	79	2	b	b	NOUN
aiti-4099	79	3	xx	xx	NUM
aiti-4099	79	4	x	x	SYM
aiti-4099	79	5	s	s	VERB
aiti-4099	79	6	xx	xx	NUM
aiti-4099	79	7	v	v	NUM
aiti-4099	79	8	b	b	NOUN
aiti-4099	79	9	xx	xx	NUM
aiti-4099	79	10	s	s	NOUN
aiti-4099	79	11	xx	xx	NUM
aiti-4099	79	12	s	s	PART
aiti-4099	79	13	xx	xx	NUM
aiti-4099	79	14	s	s	PART
aiti-4099	79	15	x	x	SYM
aiti-4099	79	16	u	u	PROPN
aiti-4099	79	17	dv	dv	PROPN
aiti-4099	79	18	a	a	DET
aiti-4099	79	19	u	u	PROPN
aiti-4099	79	20	a	a	DET
aiti-4099	79	21	u	u	NOUN
aiti-4099	79	22	w	w	NOUN
aiti-4099	79	23	a	a	DET
aiti-4099	79	24	w	w	NOUN
aiti-4099	79	25	a	a	DET
aiti-4099	79	26	u	u	NOUN
aiti-4099	79	27	w	w	PROPN
aiti-4099	79	28	h	h	NOUN
aiti-4099	79	29	a	a	DET
aiti-4099	79	30	w	w	NOUN
aiti-4099	79	31	w	w	PROPN
aiti-4099	79	32	a	a	DET
aiti-4099	79	33	w	w	PROPN
aiti-4099	79	34	b	b	PROPN
aiti-4099	79	35	b	b	PROPN
aiti-4099	79	36	b	b	PROPN
aiti-4099	79	37	w	w	PROPN
aiti-4099	79	38	dx	dx	PROPN
aiti-4099	79	39	h	h	PROPN
aiti-4099	79	40	h	h	PROPN
aiti-4099	79	41	h	h	NOUN
aiti-4099	80	1	h	h	NOUN
aiti-4099	80	2			PROPN
aiti-4099	80	3			PROPN
aiti-4099	80	4			PROPN
aiti-4099	80	5			PROPN
aiti-4099	80	6			PROPN
aiti-4099	80	7			PROPN
aiti-4099	80	8			PROPN
aiti-4099	80	9			VERB
aiti-4099	80	10			PROPN
aiti-4099	80	11			NOUN
aiti-4099	80	12			PROPN
aiti-4099	80	13			ADV
aiti-4099	80	14			VERB
aiti-4099	80	15			PUNCT
aiti-4099	80	16			PROPN
aiti-4099	80	17			PROPN
aiti-4099	80	18			CCONJ
aiti-4099	80	19			PROPN
aiti-4099	80	20			NOUN
aiti-4099	80	21			PUNCT
aiti-4099	80	22			PUNCT
aiti-4099	80	23	(	(	PUNCT
aiti-4099	80	24	6	6	NUM
aiti-4099	80	25	)	)	PUNCT
aiti-4099	80	26	where	where	SCONJ
aiti-4099	80	27	a11	a11	PROPN
aiti-4099	80	28	,	,	PUNCT
aiti-4099	80	29	a12	a12	NOUN
aiti-4099	80	30	…	…	PUNCT
aiti-4099	80	31	,	,	PUNCT
aiti-4099	80	32	a66	a66	PROPN
aiti-4099	80	33	,	,	PUNCT
aiti-4099	80	34	b11	b11	PROPN
aiti-4099	80	35	,	,	PUNCT
aiti-4099	80	36	b22	b22	PROPN
aiti-4099	80	37	,	,	PUNCT
aiti-4099	80	38	b44	b44	PROPN
aiti-4099	80	39	are	be	AUX
aiti-4099	80	40	the	the	DET
aiti-4099	80	41	beam	beam	NOUN
aiti-4099	80	42	rigidities	rigidity	NOUN
aiti-4099	80	43	,	,	PUNCT
aiti-4099	80	44	defined	define	VERB
aiti-4099	80	45	as	as	ADP
aiti-4099	80	46	advances	advance	NOUN
aiti-4099	80	47	in	in	ADP
aiti-4099	80	48	technology	technology	NOUN
aiti-4099	80	49	innovation	innovation	NOUN
aiti-4099	80	50	,	,	PUNCT
aiti-4099	80	51	vol	vol	NOUN
aiti-4099	80	52	.	.	PROPN
aiti-4099	80	53	4	4	NUM
aiti-4099	80	54	,	,	PUNCT
aiti-4099	80	55	no	no	INTJ
aiti-4099	80	56	.	.	NOUN
aiti-4099	80	57	3	3	NUM
aiti-4099	80	58	,	,	PUNCT
aiti-4099	80	59	2019	2019	NUM
aiti-4099	80	60	,	,	PUNCT
aiti-4099	80	61	pp	pp	ADJ
aiti-4099	80	62	.	.	PUNCT
aiti-4099	81	1	152	152	NUM
aiti-4099	81	2	-	-	SYM
aiti-4099	81	3	164	164	NUM
aiti-4099	81	4	155	155	NUM
aiti-4099	81	5	1	1	NUM
aiti-4099	81	6	3	3	NUM
aiti-4099	81	7	2	2	NUM
aiti-4099	81	8	3	3	NUM
aiti-4099	81	9	4	4	NUM
aiti-4099	81	10	6	6	NUM
aiti-4099	81	11	2	2	NUM
aiti-4099	81	12	3	3	NUM
aiti-4099	81	13	4	4	NUM
aiti-4099	81	14	6	6	NUM
aiti-4099	81	15	11	11	NUM
aiti-4099	81	16	12	12	NUM
aiti-4099	81	17	22	22	NUM
aiti-4099	81	18	23	23	NUM
aiti-4099	81	19	44	44	NUM
aiti-4099	81	20	66	66	NUM
aiti-4099	81	21	2	2	NUM
aiti-4099	81	22	2	2	NUM
aiti-4099	81	23	1	1	NUM
aiti-4099	81	24	(	(	PUNCT
aiti-4099	81	25	,	,	PUNCT
aiti-4099	81	26	,	,	PUNCT
aiti-4099	81	27	,	,	PUNCT
aiti-4099	81	28	,	,	PUNCT
aiti-4099	81	29	,	,	PUNCT
aiti-4099	81	30	)	)	PUNCT
aiti-4099	81	31	(	(	PUNCT
aiti-4099	81	32	1	1	NUM
aiti-4099	81	33	,	,	PUNCT
aiti-4099	81	34	,	,	PUNCT
aiti-4099	81	35	,	,	PUNCT
aiti-4099	81	36	,	,	PUNCT
aiti-4099	81	37	,	,	PUNCT
aiti-4099	81	38	)	)	PUNCT
aiti-4099	81	39	(	(	PUNCT
aiti-4099	81	40	1	1	NUM
aiti-4099	81	41	,	,	PUNCT
aiti-4099	81	42	,	,	PUNCT
aiti-4099	81	43	,	,	PUNCT
aiti-4099	81	44	,	,	PUNCT
aiti-4099	81	45	,	,	PUNCT
aiti-4099	81	46	)	)	PUNCT
aiti-4099	81	47	1	1	NUM
aiti-4099	81	48	1	1	NUM
aiti-4099	81	49	i	i	PRON
aiti-4099	81	50	i	i	PROPN
aiti-4099	81	51	z	z	PROPN
aiti-4099	81	52	ia	ia	PROPN
aiti-4099	81	53	z	z	PROPN
aiti-4099	81	54	e	e	AUX
aiti-4099	81	55	be	be	AUX
aiti-4099	81	56	a	a	DET
aiti-4099	81	57	a	a	DET
aiti-4099	81	58	a	a	DET
aiti-4099	81	59	a	a	DET
aiti-4099	81	60	a	a	DET
aiti-4099	81	61	a	a	DET
aiti-4099	81	62	z	z	NOUN
aiti-4099	81	63	z	z	NOUN
aiti-4099	81	64	z	z	NOUN
aiti-4099	81	65	z	z	NOUN
aiti-4099	81	66	z	z	NOUN
aiti-4099	81	67	da	da	PROPN
aiti-4099	81	68	z	z	PROPN
aiti-4099	81	69	z	z	NOUN
aiti-4099	81	70	z	z	NOUN
aiti-4099	81	71	z	z	NOUN
aiti-4099	81	72	z	z	NOUN
aiti-4099	81	73	dz	dz	PROPN
aiti-4099	81	74			PROPN
aiti-4099	81	75			PROPN
aiti-4099	81	76			PROPN
aiti-4099	82	1			PROPN
aiti-4099	83	1			NUM
aiti-4099	83	2			PROPN
aiti-4099	83	3			PROPN
aiti-4099	83	4			NOUN
aiti-4099	83	5			NOUN
aiti-4099	83	6			PUNCT
aiti-4099	83	7	(	(	PUNCT
aiti-4099	83	8	7	7	NUM
aiti-4099	83	9	)	)	PUNCT
aiti-4099	83	10	and	and	CCONJ
aiti-4099	83	11	1	1	NUM
aiti-4099	83	12	3	3	NUM
aiti-4099	83	13	2	2	NUM
aiti-4099	83	14	4	4	NUM
aiti-4099	83	15	2	2	NUM
aiti-4099	83	16	4	4	NUM
aiti-4099	83	17	11	11	NUM
aiti-4099	83	18	22	22	NUM
aiti-4099	83	19	44	44	NUM
aiti-4099	83	20	1	1	NUM
aiti-4099	83	21	(	(	PUNCT
aiti-4099	83	22	,	,	PUNCT
aiti-4099	83	23	,	,	PUNCT
aiti-4099	83	24	)	)	PUNCT
aiti-4099	83	25	(	(	PUNCT
aiti-4099	83	26	,	,	PUNCT
aiti-4099	83	27	,	,	PUNCT
aiti-4099	83	28	)	)	PUNCT
aiti-4099	83	29	(	(	PUNCT
aiti-4099	83	30	1	1	NUM
aiti-4099	83	31	,	,	PUNCT
aiti-4099	83	32	,	,	PUNCT
aiti-4099	83	33	)	)	PUNCT
aiti-4099	83	34	2(1	2(1	NUM
aiti-4099	83	35	)	)	PUNCT
aiti-4099	83	36	2(1	2(1	NUM
aiti-4099	83	37	)	)	PUNCT
aiti-4099	84	1	i	i	PRON
aiti-4099	85	1	i	i	PRON
aiti-4099	85	2	z	z	PROPN
aiti-4099	85	3	ia	ia	PROPN
aiti-4099	85	4	z	z	PROPN
aiti-4099	85	5	e	e	NOUN
aiti-4099	85	6	be	be	AUX
aiti-4099	85	7	b	b	PROPN
aiti-4099	85	8	b	b	X
aiti-4099	85	9	b	b	PROPN
aiti-4099	85	10	z	z	PROPN
aiti-4099	85	11	z	z	NOUN
aiti-4099	85	12	z	z	NOUN
aiti-4099	85	13	da	da	PROPN
aiti-4099	85	14	z	z	PROPN
aiti-4099	85	15	z	z	NOUN
aiti-4099	85	16	dz	dz	PROPN
aiti-4099	85	17			PROPN
aiti-4099	85	18			PROPN
aiti-4099	85	19			PROPN
aiti-4099	85	20			PROPN
aiti-4099	86	1			PRON
aiti-4099	86	2			PROPN
aiti-4099	86	3			ADV
aiti-4099	86	4			PUNCT
aiti-4099	86	5			NOUN
aiti-4099	86	6			PUNCT
aiti-4099	86	7	(	(	PUNCT
aiti-4099	86	8	8)	8)	NUM
aiti-4099	86	9	in	in	ADP
aiti-4099	86	10	eqs	eqs	PROPN
aiti-4099	86	11	.	.	PUNCT
aiti-4099	87	1	(	(	PUNCT
aiti-4099	87	2	6	6	NUM
aiti-4099	87	3	-	-	SYM
aiti-4099	87	4	8)	8)	NUM
aiti-4099	87	5	,	,	PUNCT
aiti-4099	87	6	v	v	NOUN
aiti-4099	87	7	and	and	CCONJ
aiti-4099	87	8	a	a	DET
aiti-4099	87	9	denote	denote	NOUN
aiti-4099	87	10	the	the	DET
aiti-4099	87	11	volume	volume	NOUN
aiti-4099	87	12	and	and	CCONJ
aiti-4099	87	13	cross	cross	ADJ
aiti-4099	87	14	-	-	ADJ
aiti-4099	87	15	sectional	sectional	ADJ
aiti-4099	87	16	area	area	NOUN
aiti-4099	87	17	of	of	ADP
aiti-4099	87	18	the	the	DET
aiti-4099	87	19	beam	beam	NOUN
aiti-4099	87	20	,	,	PUNCT
aiti-4099	87	21	respectively	respectively	ADV
aiti-4099	87	22	.	.	PUNCT
aiti-4099	88	1	because	because	SCONJ
aiti-4099	88	2	the	the	DET
aiti-4099	88	3	effective	effective	ADJ
aiti-4099	88	4	young	young	ADJ
aiti-4099	88	5	modulus	modulus	NOUN
aiti-4099	88	6	e	e	NOUN
aiti-4099	88	7	varies	vary	VERB
aiti-4099	88	8	in	in	ADP
aiti-4099	88	9	both	both	CCONJ
aiti-4099	88	10	the	the	DET
aiti-4099	88	11	thickness	thickness	NOUN
aiti-4099	88	12	and	and	CCONJ
aiti-4099	88	13	length	length	NOUN
aiti-4099	88	14	directions	direction	NOUN
aiti-4099	88	15	,	,	PUNCT
aiti-4099	88	16	the	the	DET
aiti-4099	88	17	rigidities	rigidity	NOUN
aiti-4099	88	18	in	in	ADP
aiti-4099	88	19	eqs	eqs	PROPN
aiti-4099	88	20	.	.	PUNCT
aiti-4099	89	1	(	(	PUNCT
aiti-4099	89	2	7	7	NUM
aiti-4099	89	3	)	)	PUNCT
aiti-4099	89	4	and	and	CCONJ
aiti-4099	89	5	(	(	PUNCT
aiti-4099	89	6	8)	8)	NUM
aiti-4099	89	7	are	be	AUX
aiti-4099	89	8	functions	function	NOUN
aiti-4099	89	9	of	of	ADP
aiti-4099	89	10	x.	x.	NOUN
aiti-4099	89	11	the	the	DET
aiti-4099	89	12	kinetic	kinetic	ADJ
aiti-4099	89	13	energy	energy	NOUN
aiti-4099	89	14	(	(	PUNCT
aiti-4099	89	15	t	t	NOUN
aiti-4099	89	16	)	)	PUNCT
aiti-4099	89	17	of	of	ADP
aiti-4099	89	18	the	the	DET
aiti-4099	89	19	beam	beam	NOUN
aiti-4099	89	20	resulted	result	VERB
aiti-4099	89	21	from	from	ADP
aiti-4099	89	22	the	the	DET
aiti-4099	89	23	displacement	displacement	ADJ
aiti-4099	89	24	field	field	NOUN
aiti-4099	89	25	in	in	ADP
aiti-4099	89	26	eq	eq	ADP
aiti-4099	89	27	.	.	PUNCT
aiti-4099	90	1	(	(	PUNCT
aiti-4099	90	2	3	3	X
aiti-4099	90	3	)	)	PUNCT
aiti-4099	90	4	is	be	AUX
aiti-4099	90	5	as	as	SCONJ
aiti-4099	90	6	follows	follow	VERB
aiti-4099	90	7	2	2	NUM
aiti-4099	90	8	2	2	NUM
aiti-4099	90	9	2	2	NUM
aiti-4099	90	10	2	2	NUM
aiti-4099	90	11	234	234	NUM
aiti-4099	90	12	6644	6644	NUM
aiti-4099	90	13	11	11	NUM
aiti-4099	90	14	12	12	NUM
aiti-4099	90	15	,	,	PUNCT
aiti-4099	90	16	22	22	NUM
aiti-4099	90	17	,	,	PUNCT
aiti-4099	90	18	,	,	PUNCT
aiti-4099	90	19	,	,	PUNCT
aiti-4099	90	20	,	,	PUNCT
aiti-4099	90	21	,	,	PUNCT
aiti-4099	90	22	2	2	NUM
aiti-4099	90	23	2	2	NUM
aiti-4099	90	24	2	2	NUM
aiti-4099	90	25	0	0	NUM
aiti-4099	90	26	8	8	NUM
aiti-4099	90	27	168	168	NUM
aiti-4099	90	28	(	(	PUNCT
aiti-4099	90	29	2	2	NUM
aiti-4099	90	30	)	)	PUNCT
aiti-4099	90	31	2	2	NUM
aiti-4099	90	32	3	3	NUM
aiti-4099	90	33	3	3	NUM
aiti-4099	91	1	9	9	NUM
aiti-4099	91	2	l	l	NOUN
aiti-4099	91	3	b	b	PROPN
aiti-4099	91	4	s	s	PROPN
aiti-4099	91	5	b	b	X
aiti-4099	91	6	s	s	PROPN
aiti-4099	91	7	b	b	PROPN
aiti-4099	91	8	x	x	SYM
aiti-4099	91	9	b	b	PROPN
aiti-4099	91	10	x	x	SYM
aiti-4099	91	11	s	s	NOUN
aiti-4099	91	12	x	x	X
aiti-4099	91	13	b	b	PROPN
aiti-4099	91	14	x	x	SYM
aiti-4099	91	15	s	s	NOUN
aiti-4099	91	16	x	x	X
aiti-4099	91	17	s	s	NOUN
aiti-4099	91	18	x	x	X
aiti-4099	91	19	i	i	NOUN
aiti-4099	91	20	ii	ii	VERB
aiti-4099	91	21	t	t	NOUN
aiti-4099	91	22	i	i	PRON
aiti-4099	91	23	u	u	PROPN
aiti-4099	91	24	w	w	PROPN
aiti-4099	91	25	w	w	PROPN
aiti-4099	91	26	w	w	PROPN
aiti-4099	91	27	w	w	PROPN
aiti-4099	92	1	i	i	INTJ
aiti-4099	93	1	uw	uw	VERB
aiti-4099	94	1	i	i	PROPN
aiti-4099	94	2	w	w	PROPN
aiti-4099	94	3	uw	uw	PROPN
aiti-4099	94	4	w	w	PROPN
aiti-4099	94	5	w	w	PROPN
aiti-4099	94	6	w	w	PROPN
aiti-4099	94	7	dx	dx	PROPN
aiti-4099	95	1	h	h	NOUN
aiti-4099	95	2	h	h	PROPN
aiti-4099	95	3	h	h	NOUN
aiti-4099	96	1			PROPN
aiti-4099	96	2			PRON
aiti-4099	96	3			PROPN
aiti-4099	96	4			PROPN
aiti-4099	96	5			PUNCT
aiti-4099	96	6			PUNCT
aiti-4099	96	7			PROPN
aiti-4099	96	8			VERB
aiti-4099	96	9			PROPN
aiti-4099	96	10			VERB
aiti-4099	96	11			PROPN
aiti-4099	96	12			NOUN
aiti-4099	96	13			NOUN
aiti-4099	96	14			PROPN
aiti-4099	96	15			X
aiti-4099	96	16	(	(	PUNCT
aiti-4099	96	17	9	9	NUM
aiti-4099	96	18	)	)	PUNCT
aiti-4099	96	19	in	in	ADP
aiti-4099	96	20	which	which	PRON
aiti-4099	96	21	i11	i11	ADJ
aiti-4099	96	22	,	,	PUNCT
aiti-4099	96	23	i12	i12	NOUN
aiti-4099	96	24	,	,	PUNCT
aiti-4099	96	25	i22	i22	NOUN
aiti-4099	96	26	,	,	PUNCT
aiti-4099	96	27	i34	i34	NOUN
aiti-4099	96	28	,	,	PUNCT
aiti-4099	96	29	i44	i44	PROPN
aiti-4099	96	30	,	,	PUNCT
aiti-4099	96	31	and	and	CCONJ
aiti-4099	96	32	i66	i66	NOUN
aiti-4099	96	33	are	be	AUX
aiti-4099	96	34	the	the	DET
aiti-4099	96	35	mass	mass	NOUN
aiti-4099	96	36	moments	moment	NOUN
aiti-4099	96	37	,	,	PUNCT
aiti-4099	96	38	defined	define	VERB
aiti-4099	96	39	as	as	ADP
aiti-4099	96	40	1	1	NUM
aiti-4099	96	41	3	3	NUM
aiti-4099	96	42	2	2	NUM
aiti-4099	96	43	3	3	NUM
aiti-4099	96	44	4	4	NUM
aiti-4099	96	45	6	6	NUM
aiti-4099	96	46	2	2	NUM
aiti-4099	96	47	3	3	NUM
aiti-4099	96	48	4	4	NUM
aiti-4099	96	49	6	6	NUM
aiti-4099	96	50	11	11	NUM
aiti-4099	96	51	12	12	NUM
aiti-4099	96	52	22	22	NUM
aiti-4099	96	53	34	34	NUM
aiti-4099	96	54	44	44	NUM
aiti-4099	96	55	66	66	NUM
aiti-4099	96	56	1	1	NUM
aiti-4099	96	57	(	(	PUNCT
aiti-4099	96	58	,	,	PUNCT
aiti-4099	96	59	,	,	PUNCT
aiti-4099	96	60	,	,	PUNCT
aiti-4099	96	61	,	,	PUNCT
aiti-4099	96	62	,	,	PUNCT
aiti-4099	96	63	)	)	PUNCT
aiti-4099	96	64	(	(	PUNCT
aiti-4099	96	65	,	,	PUNCT
aiti-4099	96	66	)	)	PUNCT
aiti-4099	96	67	(	(	PUNCT
aiti-4099	96	68	1	1	NUM
aiti-4099	96	69	,	,	PUNCT
aiti-4099	96	70	,	,	PUNCT
aiti-4099	96	71	,	,	PUNCT
aiti-4099	96	72	,	,	PUNCT
aiti-4099	96	73	,	,	PUNCT
aiti-4099	96	74	z	z	NOUN
aiti-4099	96	75	)	)	PUNCT
aiti-4099	96	76	(	(	PUNCT
aiti-4099	96	77	,	,	PUNCT
aiti-4099	96	78	)	)	PUNCT
aiti-4099	96	79	(	(	PUNCT
aiti-4099	96	80	1	1	NUM
aiti-4099	96	81	,	,	PUNCT
aiti-4099	96	82	,	,	PUNCT
aiti-4099	96	83	,	,	PUNCT
aiti-4099	96	84	,	,	PUNCT
aiti-4099	96	85	,	,	PUNCT
aiti-4099	96	86	z	z	NOUN
aiti-4099	96	87	)	)	PUNCT
aiti-4099	97	1	i	i	PRON
aiti-4099	98	1	i	i	PRON
aiti-4099	98	2	z	z	PROPN
aiti-4099	98	3	ia	ia	PROPN
aiti-4099	99	1	z	z	VERB
aiti-4099	99	2	i	i	PRON
aiti-4099	100	1	i	i	PRON
aiti-4099	100	2	i	i	PRON
aiti-4099	101	1	i	i	PRON
aiti-4099	101	2	i	i	PRON
aiti-4099	102	1	i	i	VERB
aiti-4099	102	2	x	x	X
aiti-4099	103	1	z	z	NOUN
aiti-4099	103	2	z	z	NOUN
aiti-4099	103	3	z	z	NOUN
aiti-4099	103	4	z	z	NOUN
aiti-4099	103	5	z	z	NOUN
aiti-4099	103	6	da	da	PROPN
aiti-4099	103	7	b	b	PROPN
aiti-4099	103	8	x	x	PUNCT
aiti-4099	103	9	z	z	NOUN
aiti-4099	103	10	z	z	NOUN
aiti-4099	103	11	z	z	NOUN
aiti-4099	103	12	z	z	NOUN
aiti-4099	103	13	z	z	NOUN
aiti-4099	103	14	dz	dz	NOUN
aiti-4099	103	15			ADP
aiti-4099	103	16			VERB
aiti-4099	103	17			PROPN
aiti-4099	103	18			PROPN
aiti-4099	103	19			PUNCT
aiti-4099	103	20			X
aiti-4099	103	21	(	(	PUNCT
aiti-4099	103	22	10	10	NUM
aiti-4099	103	23	)	)	PUNCT
aiti-4099	103	24	the	the	DET
aiti-4099	103	25	above	above	ADJ
aiti-4099	103	26	mass	mass	NOUN
aiti-4099	103	27	moments	moment	NOUN
aiti-4099	103	28	,	,	PUNCT
aiti-4099	103	29	as	as	ADP
aiti-4099	103	30	the	the	DET
aiti-4099	103	31	beam	beam	NOUN
aiti-4099	103	32	rigidities	rigidity	NOUN
aiti-4099	103	33	,	,	PUNCT
aiti-4099	103	34	also	also	ADV
aiti-4099	103	35	are	be	AUX
aiti-4099	103	36	functions	function	NOUN
aiti-4099	103	37	of	of	ADP
aiti-4099	103	38	x.	x.	NOUN
aiti-4099	103	39	the	the	DET
aiti-4099	103	40	potential	potential	ADJ
aiti-4099	103	41	(	(	PUNCT
aiti-4099	103	42	v	v	NOUN
aiti-4099	103	43	)	)	PUNCT
aiti-4099	103	44	of	of	ADP
aiti-4099	103	45	a	a	DET
aiti-4099	103	46	harmonic	harmonic	ADJ
aiti-4099	103	47	load	load	NOUN
aiti-4099	103	48	,	,	PUNCT
aiti-4099	104	1	f	f	X
aiti-4099	104	2	=	=	NOUN
aiti-4099	104	3	f0cos(ωt	f0cos(ωt	NOUN
aiti-4099	104	4	)	)	PUNCT
aiti-4099	104	5	,	,	PUNCT
aiti-4099	104	6	considered	consider	VERB
aiti-4099	104	7	herein	herein	NOUN
aiti-4099	104	8	has	have	VERB
aiti-4099	104	9	a	a	DET
aiti-4099	104	10	simple	simple	ADJ
aiti-4099	104	11	form	form	NOUN
aiti-4099	104	12	0	0	NUM
aiti-4099	104	13	|cos	|co	NOUN
aiti-4099	104	14	(	(	PUNCT
aiti-4099	104	15	)	)	PUNCT
aiti-4099	104	16	(	(	PUNCT
aiti-4099	104	17	)	)	PUNCT
aiti-4099	104	18	fb	fb	INTJ
aiti-4099	104	19	s	s	VERB
aiti-4099	104	20	x	x	X
aiti-4099	104	21	xv	xv	PROPN
aiti-4099	104	22	f	f	PROPN
aiti-4099	104	23	t	t	PROPN
aiti-4099	104	24	w	w	PROPN
aiti-4099	104	25	w	w	PROPN
aiti-4099	104	26			NUM
aiti-4099	104	27			PROPN
aiti-4099	104	28			PROPN
aiti-4099	104	29			PUNCT
aiti-4099	104	30	(	(	PUNCT
aiti-4099	104	31	11	11	NUM
aiti-4099	104	32	)	)	PUNCT
aiti-4099	104	33	in	in	ADP
aiti-4099	104	34	the	the	DET
aiti-4099	104	35	above	above	ADJ
aiti-4099	104	36	equation	equation	NOUN
aiti-4099	104	37	,	,	PUNCT
aiti-4099	104	38	the	the	DET
aiti-4099	104	39	subscript	subscript	NOUN
aiti-4099	104	40	x	x	PRON
aiti-4099	104	41	=	=	NOUN
aiti-4099	104	42	xf	xf	PROPN
aiti-4099	104	43	means	mean	VERB
aiti-4099	104	44	that	that	SCONJ
aiti-4099	104	45	the	the	DET
aiti-4099	104	46	bending	bending	NOUN
aiti-4099	104	47	and	and	CCONJ
aiti-4099	104	48	shear	shear	NOUN
aiti-4099	104	49	transverse	transverse	NOUN
aiti-4099	104	50	displacements	displacement	NOUN
aiti-4099	104	51	are	be	AUX
aiti-4099	104	52	evaluated	evaluate	VERB
aiti-4099	104	53	at	at	ADP
aiti-4099	104	54	the	the	DET
aiti-4099	104	55	abscissa	abscissa	NOUN
aiti-4099	104	56	of	of	ADP
aiti-4099	104	57	the	the	DET
aiti-4099	104	58	load	load	NOUN
aiti-4099	104	59	f.	f.	PROPN
aiti-4099	104	60	equations	equation	NOUN
aiti-4099	104	61	of	of	ADP
aiti-4099	104	62	motion	motion	NOUN
aiti-4099	104	63	for	for	ADP
aiti-4099	104	64	the	the	DET
aiti-4099	104	65	beam	beam	NOUN
aiti-4099	104	66	can	can	AUX
aiti-4099	104	67	be	be	AUX
aiti-4099	104	68	obtained	obtain	VERB
aiti-4099	104	69	by	by	ADP
aiti-4099	104	70	applying	apply	VERB
aiti-4099	104	71	hamilton	hamilton	PROPN
aiti-4099	104	72	’s	’s	PART
aiti-4099	104	73	principle	principle	NOUN
aiti-4099	104	74	to	to	ADP
aiti-4099	104	75	eqs	eqs	PROPN
aiti-4099	104	76	.	.	PUNCT
aiti-4099	105	1	(	(	PUNCT
aiti-4099	105	2	6	6	NUM
aiti-4099	105	3	)	)	PUNCT
aiti-4099	105	4	,	,	PUNCT
aiti-4099	105	5	(	(	PUNCT
aiti-4099	105	6	9	9	NUM
aiti-4099	105	7	)	)	PUNCT
aiti-4099	105	8	and	and	CCONJ
aiti-4099	105	9	(	(	PUNCT
aiti-4099	105	10	11	11	NUM
aiti-4099	105	11	)	)	PUNCT
aiti-4099	105	12	.	.	PUNCT
aiti-4099	106	1	however	however	ADV
aiti-4099	106	2	,	,	PUNCT
aiti-4099	106	3	due	due	ADP
aiti-4099	106	4	to	to	ADP
aiti-4099	106	5	the	the	DET
aiti-4099	106	6	rigidities	rigidity	NOUN
aiti-4099	106	7	and	and	CCONJ
aiti-4099	106	8	mass	mass	ADJ
aiti-4099	106	9	moment	moment	NOUN
aiti-4099	106	10	are	be	AUX
aiti-4099	106	11	functions	function	NOUN
aiti-4099	106	12	of	of	ADP
aiti-4099	106	13	longitudinal	longitudinal	ADJ
aiti-4099	106	14	coordinate	coordinate	NOUN
aiti-4099	106	15	x	x	NOUN
aiti-4099	106	16	,	,	PUNCT
aiti-4099	106	17	the	the	DET
aiti-4099	106	18	coefficients	coefficient	NOUN
aiti-4099	106	19	of	of	ADP
aiti-4099	106	20	such	such	ADJ
aiti-4099	106	21	equation	equation	NOUN
aiti-4099	106	22	are	be	AUX
aiti-4099	106	23	dependent	dependent	ADJ
aiti-4099	106	24	on	on	ADP
aiti-4099	106	25	x	x	X
aiti-4099	106	26	,	,	PUNCT
aiti-4099	106	27	and	and	CCONJ
aiti-4099	106	28	thus	thus	ADV
aiti-4099	106	29	a	a	DET
aiti-4099	106	30	closed	closed	ADJ
aiti-4099	106	31	-	-	PUNCT
aiti-4099	106	32	form	form	NOUN
aiti-4099	106	33	solution	solution	NOUN
aiti-4099	106	34	is	be	AUX
aiti-4099	106	35	very	very	ADV
aiti-4099	106	36	difficult	difficult	ADJ
aiti-4099	106	37	to	to	PART
aiti-4099	106	38	obtain	obtain	VERB
aiti-4099	106	39	.	.	PUNCT
aiti-4099	107	1	a	a	DET
aiti-4099	107	2	finite	finite	ADJ
aiti-4099	107	3	element	element	NOUN
aiti-4099	107	4	formulation	formulation	NOUN
aiti-4099	107	5	is	be	AUX
aiti-4099	107	6	developed	develop	VERB
aiti-4099	107	7	below	below	ADV
aiti-4099	107	8	for	for	ADP
aiti-4099	107	9	computing	compute	VERB
aiti-4099	107	10	the	the	DET
aiti-4099	107	11	vibration	vibration	NOUN
aiti-4099	107	12	characteristics	characteristic	NOUN
aiti-4099	107	13	of	of	ADP
aiti-4099	107	14	the	the	DET
aiti-4099	107	15	beam	beam	NOUN
aiti-4099	107	16	.	.	PUNCT
aiti-4099	108	1	3	3	X
aiti-4099	108	2	.	.	X
aiti-4099	108	3	finite	finite	PROPN
aiti-4099	108	4	element	element	PROPN
aiti-4099	108	5	formulation	formulation	NOUN
aiti-4099	108	6	a	a	DET
aiti-4099	108	7	two	two	NUM
aiti-4099	108	8	-	-	PUNCT
aiti-4099	108	9	node	node	NOUN
aiti-4099	108	10	beam	beam	NOUN
aiti-4099	108	11	element	element	NOUN
aiti-4099	108	12	with	with	ADP
aiti-4099	108	13	length	length	NOUN
aiti-4099	108	14	l	l	NOUN
aiti-4099	108	15	is	be	AUX
aiti-4099	108	16	considered	consider	VERB
aiti-4099	108	17	in	in	ADP
aiti-4099	108	18	this	this	DET
aiti-4099	108	19	section	section	NOUN
aiti-4099	108	20	.	.	PUNCT
aiti-4099	109	1	the	the	DET
aiti-4099	109	2	element	element	NOUN
aiti-4099	109	3	contains	contain	VERB
aiti-4099	109	4	six	six	NUM
aiti-4099	109	5	degrees	degree	NOUN
aiti-4099	109	6	of	of	ADP
aiti-4099	109	7	freedom	freedom	NOUN
aiti-4099	109	8	per	per	ADP
aiti-4099	109	9	node	node	NOUN
aiti-4099	109	10	,	,	PUNCT
aiti-4099	109	11	and	and	CCONJ
aiti-4099	109	12	the	the	DET
aiti-4099	109	13	vector	vector	NOUN
aiti-4099	109	14	of	of	ADP
aiti-4099	109	15	nodal	nodal	NOUN
aiti-4099	109	16	displacements	displacement	NOUN
aiti-4099	109	17	is	be	AUX
aiti-4099	109	18	given	give	VERB
aiti-4099	109	19	by	by	ADP
aiti-4099	109	20	{	{	PUNCT
aiti-4099	109	21	}	}	PUNCT
aiti-4099	109	22	t	t	PROPN
aiti-4099	109	23	u	u	X
aiti-4099	109	24	wb	wb	PROPN
aiti-4099	109	25	wsd	wsd	PROPN
aiti-4099	109	26	d	d	PROPN
aiti-4099	109	27	d	d	X
aiti-4099	109	28	d	d	X
aiti-4099	109	29	(	(	PUNCT
aiti-4099	109	30	12	12	NUM
aiti-4099	109	31	)	)	PUNCT
aiti-4099	109	32	where	where	SCONJ
aiti-4099	109	33	1	1	NUM
aiti-4099	109	34	2	2	NUM
aiti-4099	109	35	1	1	NUM
aiti-4099	109	36	,	,	PUNCT
aiti-4099	109	37	1	1	NUM
aiti-4099	109	38	2	2	NUM
aiti-4099	109	39	,	,	PUNCT
aiti-4099	109	40	2	2	NUM
aiti-4099	109	41	1	1	NUM
aiti-4099	109	42	,	,	PUNCT
aiti-4099	109	43	1	1	NUM
aiti-4099	109	44	2	2	NUM
aiti-4099	109	45	,	,	PUNCT
aiti-4099	109	46	2	2	NUM
aiti-4099	109	47	{	{	PUNCT
aiti-4099	109	48	}	}	PUNCT
aiti-4099	109	49	,	,	PUNCT
aiti-4099	109	50	{	{	PUNCT
aiti-4099	109	51	}	}	PUNCT
aiti-4099	109	52	,	,	PUNCT
aiti-4099	109	53	{	{	PUNCT
aiti-4099	109	54	}	}	PUNCT
aiti-4099	109	55	u	u	PROPN
aiti-4099	109	56	wb	wb	PROPN
aiti-4099	109	57	b	b	PROPN
aiti-4099	109	58	b	b	PROPN
aiti-4099	109	59	x	x	SYM
aiti-4099	109	60	b	b	PROPN
aiti-4099	109	61	b	b	PROPN
aiti-4099	109	62	x	x	PROPN
aiti-4099	109	63	ws	ws	PROPN
aiti-4099	109	64	s	s	PROPN
aiti-4099	109	65	s	s	NOUN
aiti-4099	109	66	x	x	X
aiti-4099	109	67	s	s	X
aiti-4099	109	68	s	s	X
aiti-4099	109	69	xu	xu	PROPN
aiti-4099	109	70	u	u	PROPN
aiti-4099	109	71	w	w	PROPN
aiti-4099	109	72	w	w	PROPN
aiti-4099	109	73	w	w	PROPN
aiti-4099	109	74	w	w	PROPN
aiti-4099	109	75	w	w	PROPN
aiti-4099	109	76	w	w	PROPN
aiti-4099	109	77	w	w	PROPN
aiti-4099	109	78	w	w	NOUN
aiti-4099	109	79			PROPN
aiti-4099	109	80	d	d	ADP
aiti-4099	110	1	d	d	X
aiti-4099	110	2	d	d	PROPN
aiti-4099	110	3	(	(	PUNCT
aiti-4099	110	4	13	13	NUM
aiti-4099	110	5	)	)	PUNCT
aiti-4099	110	6	are	be	AUX
aiti-4099	110	7	,	,	PUNCT
aiti-4099	110	8	respectively	respectively	ADV
aiti-4099	110	9	,	,	PUNCT
aiti-4099	110	10	the	the	DET
aiti-4099	110	11	vectors	vector	NOUN
aiti-4099	110	12	of	of	ADP
aiti-4099	110	13	axial	axial	ADJ
aiti-4099	110	14	displacements	displacement	NOUN
aiti-4099	110	15	,	,	PUNCT
aiti-4099	110	16	bending	bend	VERB
aiti-4099	110	17	and	and	CCONJ
aiti-4099	110	18	shear	shear	NOUN
aiti-4099	110	19	transverse	transverse	NOUN
aiti-4099	110	20	displacements	displacement	NOUN
aiti-4099	110	21	at	at	ADP
aiti-4099	110	22	node	node	NOUN
aiti-4099	110	23	1	1	NUM
aiti-4099	110	24	and	and	CCONJ
aiti-4099	110	25	node	node	PROPN
aiti-4099	110	26	2	2	NUM
aiti-4099	110	27	.	.	PUNCT
aiti-4099	111	1	in	in	ADP
aiti-4099	111	2	eq	eq	ADP
aiti-4099	111	3	.	.	PUNCT
aiti-4099	112	1	(	(	PUNCT
aiti-4099	112	2	12	12	NUM
aiti-4099	112	3	)	)	PUNCT
aiti-4099	112	4	and	and	CCONJ
aiti-4099	112	5	hereafter	hereafter	ADV
aiti-4099	112	6	,	,	PUNCT
aiti-4099	112	7	a	a	DET
aiti-4099	112	8	superscript	superscript	PROPN
aiti-4099	112	9	“	"	PUNCT
aiti-4099	112	10	t	t	PROPN
aiti-4099	112	11	”	"	PUNCT
aiti-4099	112	12	is	be	AUX
aiti-4099	112	13	used	use	VERB
aiti-4099	112	14	to	to	PART
aiti-4099	112	15	denote	denote	VERB
aiti-4099	112	16	the	the	DET
aiti-4099	112	17	transpose	transpose	NOUN
aiti-4099	112	18	of	of	ADP
aiti-4099	112	19	a	a	DET
aiti-4099	112	20	vector	vector	NOUN
aiti-4099	112	21	or	or	CCONJ
aiti-4099	112	22	a	a	DET
aiti-4099	112	23	matrix	matrix	NOUN
aiti-4099	112	24	.	.	PUNCT
aiti-4099	113	1	it	it	PRON
aiti-4099	113	2	should	should	AUX
aiti-4099	113	3	be	be	AUX
aiti-4099	113	4	noted	note	VERB
aiti-4099	113	5	that	that	SCONJ
aiti-4099	113	6	the	the	DET
aiti-4099	113	7	order	order	NOUN
aiti-4099	113	8	of	of	ADP
aiti-4099	113	9	the	the	DET
aiti-4099	113	10	nodal	nodal	NOUN
aiti-4099	113	11	displacements	displacement	NOUN
aiti-4099	113	12	is	be	AUX
aiti-4099	113	13	not	not	PART
aiti-4099	113	14	necessary	necessary	ADJ
aiti-4099	113	15	as	as	ADP
aiti-4099	113	16	in	in	ADP
aiti-4099	113	17	eq	eq	NOUN
aiti-4099	113	18	.	.	PUNCT
aiti-4099	114	1	(	(	PUNCT
aiti-4099	114	2	12	12	NUM
aiti-4099	114	3	)	)	PUNCT
aiti-4099	114	4	,	,	PUNCT
aiti-4099	114	5	but	but	CCONJ
aiti-4099	114	6	it	it	PRON
aiti-4099	114	7	is	be	AUX
aiti-4099	114	8	convenient	convenient	ADJ
aiti-4099	114	9	to	to	PART
aiti-4099	114	10	split	split	VERB
aiti-4099	114	11	the	the	DET
aiti-4099	114	12	displacements	displacement	NOUN
aiti-4099	114	13	into	into	ADP
aiti-4099	114	14	axial	axial	ADJ
aiti-4099	114	15	,	,	PUNCT
aiti-4099	114	16	bending	bend	VERB
aiti-4099	114	17	and	and	CCONJ
aiti-4099	114	18	shear	shear	NOUN
aiti-4099	114	19	parts	part	NOUN
aiti-4099	114	20	.	.	PUNCT
aiti-4099	115	1	advances	advance	NOUN
aiti-4099	115	2	in	in	ADP
aiti-4099	115	3	technology	technology	NOUN
aiti-4099	115	4	innovation	innovation	NOUN
aiti-4099	115	5	,	,	PUNCT
aiti-4099	115	6	vol	vol	NOUN
aiti-4099	115	7	.	.	PROPN
aiti-4099	116	1	4	4	NUM
aiti-4099	116	2	,	,	PUNCT
aiti-4099	116	3	no	no	INTJ
aiti-4099	116	4	.	.	NOUN
aiti-4099	116	5	3	3	NUM
aiti-4099	116	6	,	,	PUNCT
aiti-4099	116	7	2019	2019	NUM
aiti-4099	116	8	,	,	PUNCT
aiti-4099	116	9	pp	pp	ADJ
aiti-4099	116	10	.	.	PUNCT
aiti-4099	117	1	152	152	NUM
aiti-4099	117	2	-	-	SYM
aiti-4099	117	3	164	164	NUM
aiti-4099	117	4	156	156	NUM
aiti-4099	117	5	the	the	DET
aiti-4099	117	6	displacements	displacement	NOUN
aiti-4099	117	7	inside	inside	ADP
aiti-4099	117	8	the	the	DET
aiti-4099	117	9	element	element	NOUN
aiti-4099	117	10	are	be	AUX
aiti-4099	117	11	interpolated	interpolate	VERB
aiti-4099	117	12	from	from	ADP
aiti-4099	117	13	their	their	PRON
aiti-4099	117	14	nodal	nodal	ADJ
aiti-4099	117	15	values	value	NOUN
aiti-4099	117	16	according	accord	VERB
aiti-4099	117	17	to	to	ADP
aiti-4099	117	18	0	0	NUM
aiti-4099	117	19	0	0	NUM
aiti-4099	117	20	0	0	NUM
aiti-4099	117	21	0	0	NUM
aiti-4099	117	22	0	0	NUM
aiti-4099	117	23	0	0	NUM
aiti-4099	118	1	uu	uu	PRON
aiti-4099	118	2	b	b	X
aiti-4099	118	3	wb	wb	NOUN
aiti-4099	118	4	wb	wb	PROPN
aiti-4099	118	5	wss	wss	PROPN
aiti-4099	118	6	ws	ws	PROPN
aiti-4099	118	7	u	u	PROPN
aiti-4099	119	1	w	w	PROPN
aiti-4099	119	2	w	w	NOUN
aiti-4099	120	1			NOUN
aiti-4099	120	2			NOUN
aiti-4099	120	3			ADP
aiti-4099	120	4			NOUN
aiti-4099	121	1			NOUN
aiti-4099	121	2			NUM
aiti-4099	121	3			NUM
aiti-4099	121	4			DET
aiti-4099	121	5			PROPN
aiti-4099	121	6			PROPN
aiti-4099	121	7			PROPN
aiti-4099	121	8			PROPN
aiti-4099	121	9			PROPN
aiti-4099	121	10			VERB
aiti-4099	121	11			NOUN
aiti-4099	121	12			NUM
aiti-4099	121	13			NUM
aiti-4099	121	14			NUM
aiti-4099	121	15			PROPN
aiti-4099	121	16			VERB
aiti-4099	121	17			NOUN
aiti-4099	122	1			PROPN
aiti-4099	123	1			NUM
aiti-4099	123	2			PROPN
aiti-4099	123	3	dn	dn	PROPN
aiti-4099	123	4	n	n	PROPN
aiti-4099	123	5	d	d	PROPN
aiti-4099	123	6	n	n	PROPN
aiti-4099	123	7	d	d	X
aiti-4099	123	8	(	(	PUNCT
aiti-4099	123	9	14	14	NUM
aiti-4099	123	10	)	)	PUNCT
aiti-4099	123	11	where	where	SCONJ
aiti-4099	123	12	nu	nu	PROPN
aiti-4099	123	13	,	,	PUNCT
aiti-4099	123	14	nwb	nwb	PROPN
aiti-4099	123	15	and	and	CCONJ
aiti-4099	123	16	nws	nws	PROPN
aiti-4099	123	17	are	be	AUX
aiti-4099	123	18	the	the	DET
aiti-4099	123	19	matrices	matrix	NOUN
aiti-4099	123	20	of	of	ADP
aiti-4099	123	21	shape	shape	NOUN
aiti-4099	123	22	functions	function	NOUN
aiti-4099	123	23	for	for	ADP
aiti-4099	123	24	u	u	NOUN
aiti-4099	123	25	,	,	PUNCT
aiti-4099	123	26	wb	wb	PROPN
aiti-4099	123	27	and	and	CCONJ
aiti-4099	123	28	ws	ws	NOUN
aiti-4099	123	29	,	,	PUNCT
aiti-4099	123	30	respectively	respectively	ADV
aiti-4099	123	31	.	.	PUNCT
aiti-4099	124	1	in	in	ADP
aiti-4099	124	2	the	the	DET
aiti-4099	124	3	present	present	ADJ
aiti-4099	124	4	work	work	NOUN
aiti-4099	124	5	,	,	PUNCT
aiti-4099	124	6	the	the	DET
aiti-4099	124	7	linear	linear	ADJ
aiti-4099	124	8	function	function	NOUN
aiti-4099	124	9	is	be	AUX
aiti-4099	124	10	used	use	VERB
aiti-4099	124	11	for	for	ADP
aiti-4099	124	12	the	the	DET
aiti-4099	124	13	axial	axial	ADJ
aiti-4099	124	14	displacement	displacement	NOUN
aiti-4099	124	15	,	,	PUNCT
aiti-4099	124	16	while	while	SCONJ
aiti-4099	124	17	the	the	DET
aiti-4099	124	18	hermite	hermite	ADJ
aiti-4099	124	19	cubic	cubic	ADJ
aiti-4099	124	20	polynomials	polynomial	NOUN
aiti-4099	124	21	are	be	AUX
aiti-4099	124	22	employed	employ	VERB
aiti-4099	124	23	for	for	ADP
aiti-4099	124	24	wb	wb	PROPN
aiti-4099	124	25	and	and	CCONJ
aiti-4099	124	26	ws	ws	NOUN
aiti-4099	124	27	.	.	PUNCT
aiti-4099	125	1	in	in	ADP
aiti-4099	125	2	this	this	DET
aiti-4099	125	3	regard	regard	NOUN
aiti-4099	125	4	,	,	PUNCT
aiti-4099	125	5	we	we	PRON
aiti-4099	125	6	can	can	AUX
aiti-4099	125	7	write	write	VERB
aiti-4099	125	8	1	1	NUM
aiti-4099	125	9	2	2	NUM
aiti-4099	125	10	{	{	PUNCT
aiti-4099	125	11	}	}	PUNCT
aiti-4099	125	12	u	u	NOUN
aiti-4099	125	13	u	u	NOUN
aiti-4099	125	14	u	u	NOUN
aiti-4099	125	15	l	l	NOUN
aiti-4099	125	16	x	x	X
aiti-4099	125	17	x	x	SYM
aiti-4099	125	18	n	n	CCONJ
aiti-4099	125	19	n	n	ADP
aiti-4099	125	20	l	l	NOUN
aiti-4099	125	21	l	l	NOUN
aiti-4099	125	22			NOUN
aiti-4099	126	1			PROPN
aiti-4099	126	2			NUM
aiti-4099	127	1			NOUN
aiti-4099	128	1			NOUN
aiti-4099	128	2			INTJ
aiti-4099	129	1			PROPN
aiti-4099	129	2			PROPN
aiti-4099	129	3	n	n	PROPN
aiti-4099	129	4	(	(	PUNCT
aiti-4099	129	5	15	15	NUM
aiti-4099	129	6	)	)	PUNCT
aiti-4099	129	7	and	and	CCONJ
aiti-4099	129	8	1	1	NUM
aiti-4099	129	9	2	2	NUM
aiti-4099	129	10	3	3	NUM
aiti-4099	129	11	4	4	NUM
aiti-4099	129	12	{	{	PUNCT
aiti-4099	129	13	}	}	PUNCT
aiti-4099	129	14	w	w	PROPN
aiti-4099	129	15	w	w	PROPN
aiti-4099	129	16	w	w	PROPN
aiti-4099	129	17	w	w	PROPN
aiti-4099	129	18	wn	wn	PROPN
aiti-4099	129	19	n	n	PROPN
aiti-4099	129	20	n	n	PROPN
aiti-4099	129	21	nn	nn	NOUN
aiti-4099	129	22	(	(	PUNCT
aiti-4099	129	23	16	16	NUM
aiti-4099	129	24	)	)	PUNCT
aiti-4099	129	25	with	with	ADP
aiti-4099	129	26	2	2	NUM
aiti-4099	129	27	3	3	NUM
aiti-4099	129	28	2	2	NUM
aiti-4099	129	29	3	3	NUM
aiti-4099	129	30	2	2	NUM
aiti-4099	129	31	3	3	NUM
aiti-4099	129	32	2	2	NUM
aiti-4099	129	33	3	3	NUM
aiti-4099	129	34	1	1	NUM
aiti-4099	129	35	2	2	NUM
aiti-4099	129	36	3	3	NUM
aiti-4099	129	37	42	42	NUM
aiti-4099	129	38	3	3	NUM
aiti-4099	129	39	2	2	NUM
aiti-4099	129	40	2	2	NUM
aiti-4099	129	41	3	3	NUM
aiti-4099	129	42	2	2	NUM
aiti-4099	129	43	1	1	NUM
aiti-4099	129	44	3	3	NUM
aiti-4099	129	45	2	2	NUM
aiti-4099	129	46	,	,	PUNCT
aiti-4099	129	47	2	2	NUM
aiti-4099	129	48	,	,	PUNCT
aiti-4099	129	49	3	3	NUM
aiti-4099	129	50	2	2	NUM
aiti-4099	129	51	,	,	PUNCT
aiti-4099	129	52	w	w	PROPN
aiti-4099	129	53	w	w	PROPN
aiti-4099	129	54	w	w	PROPN
aiti-4099	129	55	w	w	PROPN
aiti-4099	129	56	x	x	PUNCT
aiti-4099	129	57	x	x	PUNCT
aiti-4099	129	58	x	x	PUNCT
aiti-4099	129	59	x	x	PUNCT
aiti-4099	129	60	x	x	PUNCT
aiti-4099	129	61	x	x	PUNCT
aiti-4099	129	62	x	x	SYM
aiti-4099	129	63	x	x	NOUN
aiti-4099	129	64	n	n	CCONJ
aiti-4099	129	65	n	n	NOUN
aiti-4099	129	66	x	x	SYM
aiti-4099	129	67	n	n	CCONJ
aiti-4099	129	68	n	n	CCONJ
aiti-4099	129	69	l	l	NOUN
aiti-4099	129	70	l	l	X
aiti-4099	129	71	l	l	X
aiti-4099	129	72	l	l	NOUN
aiti-4099	129	73	l	l	NOUN
aiti-4099	129	74	l	l	NOUN
aiti-4099	129	75	l	l	NOUN
aiti-4099	129	76	l	l	NOUN
aiti-4099	130	1			PROPN
aiti-4099	130	2			PROPN
aiti-4099	130	3			VERB
aiti-4099	130	4			PROPN
aiti-4099	130	5			PROPN
aiti-4099	130	6			VERB
aiti-4099	130	7			NUM
aiti-4099	130	8			PROPN
aiti-4099	130	9			PROPN
aiti-4099	130	10			PROPN
aiti-4099	130	11			X
aiti-4099	130	12	(	(	PUNCT
aiti-4099	130	13	17	17	NUM
aiti-4099	130	14	)	)	PUNCT
aiti-4099	130	15	using	use	VERB
aiti-4099	130	16	the	the	DET
aiti-4099	130	17	above	above	ADJ
aiti-4099	130	18	interpolation	interpolation	NOUN
aiti-4099	130	19	scheme	scheme	NOUN
aiti-4099	130	20	,	,	PUNCT
aiti-4099	130	21	one	one	PRON
aiti-4099	130	22	can	can	AUX
aiti-4099	130	23	write	write	VERB
aiti-4099	130	24	the	the	DET
aiti-4099	130	25	strain	strain	NOUN
aiti-4099	130	26	energy	energy	NOUN
aiti-4099	130	27	for	for	ADP
aiti-4099	130	28	the	the	DET
aiti-4099	130	29	beam	beam	NOUN
aiti-4099	130	30	in	in	ADP
aiti-4099	130	31	the	the	DET
aiti-4099	130	32	form	form	NOUN
aiti-4099	130	33			PROPN
aiti-4099	130	34			PROPN
aiti-4099	130	35			PROPN
aiti-4099	130	36			PROPN
aiti-4099	130	37			PROPN
aiti-4099	130	38			PROPN
aiti-4099	130	39	1	1	NUM
aiti-4099	130	40	1	1	NUM
aiti-4099	130	41	2	2	NUM
aiti-4099	130	42	ne	ne	NOUN
aiti-4099	130	43	t	t	NOUN
aiti-4099	131	1	i	i	PRON
aiti-4099	131	2	i	i	PRON
aiti-4099	132	1	i	i	PRON
aiti-4099	132	2	i	i	PRON
aiti-4099	132	3	u	u	VERB
aiti-4099	132	4			NOUN
aiti-4099	132	5			NUM
aiti-4099	132	6			X
aiti-4099	133	1	d	d	X
aiti-4099	133	2	k	k	PROPN
aiti-4099	133	3	d	d	X
aiti-4099	133	4	(	(	PUNCT
aiti-4099	133	5	18	18	NUM
aiti-4099	133	6	)	)	PUNCT
aiti-4099	133	7	where	where	SCONJ
aiti-4099	133	8	ne	ne	PROPN
aiti-4099	133	9	is	be	AUX
aiti-4099	133	10	the	the	DET
aiti-4099	133	11	total	total	ADJ
aiti-4099	133	12	number	number	NOUN
aiti-4099	133	13	of	of	ADP
aiti-4099	133	14	elements	element	NOUN
aiti-4099	133	15	,	,	PUNCT
aiti-4099	133	16	and	and	CCONJ
aiti-4099	133	17	k	k	PROPN
aiti-4099	133	18	is	be	AUX
aiti-4099	133	19	the	the	DET
aiti-4099	133	20	element	element	ADJ
aiti-4099	133	21	stiffness	stiffness	NOUN
aiti-4099	133	22	matrix	matrix	NOUN
aiti-4099	133	23	,	,	PUNCT
aiti-4099	133	24	which	which	PRON
aiti-4099	133	25	can	can	AUX
aiti-4099	133	26	be	be	AUX
aiti-4099	133	27	split	split	VERB
aiti-4099	133	28	into	into	ADP
aiti-4099	133	29	the	the	DET
aiti-4099	133	30	sub	sub	NOUN
aiti-4099	133	31	-	-	NOUN
aiti-4099	133	32	matrices	matrix	NOUN
aiti-4099	133	33	as	as	ADP
aiti-4099	133	34	(	(	PUNCT
aiti-4099	133	35	10x10	10x10	NUM
aiti-4099	133	36	)	)	PUNCT
aiti-4099	133	37	aa	aa	NOUN
aiti-4099	133	38	ab	ab	PROPN
aiti-4099	133	39	as	as	ADP
aiti-4099	133	40	t	t	PROPN
aiti-4099	133	41	ab	ab	PROPN
aiti-4099	134	1	bb	bb	INTJ
aiti-4099	134	2	bs	bs	PROPN
aiti-4099	134	3	t	t	PROPN
aiti-4099	134	4	t	t	PROPN
aiti-4099	134	5	as	as	ADP
aiti-4099	134	6	bs	bs	PROPN
aiti-4099	134	7	ss	ss	PROPN
aiti-4099	134	8			PROPN
aiti-4099	134	9			ADJ
aiti-4099	134	10			NOUN
aiti-4099	134	11			NOUN
aiti-4099	134	12			NUM
aiti-4099	134	13			NOUN
aiti-4099	134	14			NOUN
aiti-4099	134	15			NOUN
aiti-4099	135	1			PROPN
aiti-4099	135	2			PROPN
aiti-4099	135	3	k	k	PROPN
aiti-4099	135	4	k	k	PROPN
aiti-4099	135	5	k	k	PROPN
aiti-4099	135	6	k	k	PROPN
aiti-4099	135	7	k	k	PROPN
aiti-4099	135	8	k	k	PROPN
aiti-4099	135	9	k	k	PROPN
aiti-4099	135	10	k	k	PROPN
aiti-4099	135	11	k	k	PROPN
aiti-4099	135	12	k	k	X
aiti-4099	135	13	(	(	PUNCT
aiti-4099	135	14	19	19	NUM
aiti-4099	135	15	)	)	PUNCT
aiti-4099	135	16	in	in	ADP
aiti-4099	135	17	the	the	DET
aiti-4099	135	18	above	above	ADJ
aiti-4099	135	19	,	,	PUNCT
aiti-4099	135	20	aak	aak	NOUN
aiti-4099	135	21	,	,	PUNCT
aiti-4099	135	22	bbk	bbk	INTJ
aiti-4099	135	23	,	,	PUNCT
aiti-4099	135	24	ssk	ssk	PROPN
aiti-4099	135	25	,	,	PUNCT
aiti-4099	135	26	abk	abk	PROPN
aiti-4099	135	27	,	,	PUNCT
aiti-4099	135	28	ask	ask	VERB
aiti-4099	135	29	,	,	PUNCT
aiti-4099	135	30	bsk	bsk	PROPN
aiti-4099	135	31	are	be	AUX
aiti-4099	135	32	the	the	DET
aiti-4099	135	33	stiffness	stiffness	ADJ
aiti-4099	135	34	matrices	matrix	NOUN
aiti-4099	135	35	stemming	stem	VERB
aiti-4099	135	36	from	from	ADP
aiti-4099	135	37	axial	axial	ADJ
aiti-4099	135	38	stretching	stretching	NOUN
aiti-4099	135	39	,	,	PUNCT
aiti-4099	135	40	transverse	transverse	NOUN
aiti-4099	135	41	bending	bending	NOUN
aiti-4099	135	42	,	,	PUNCT
aiti-4099	135	43	transverse	transverse	ADJ
aiti-4099	135	44	shear	shear	NOUN
aiti-4099	135	45	and	and	CCONJ
aiti-4099	135	46	couplings	coupling	NOUN
aiti-4099	135	47	of	of	ADP
aiti-4099	135	48	these	these	DET
aiti-4099	135	49	terms	term	NOUN
aiti-4099	135	50	.	.	PUNCT
aiti-4099	136	1	these	these	DET
aiti-4099	136	2	sub	sub	NOUN
aiti-4099	136	3	-	-	NOUN
aiti-4099	136	4	matrices	matrix	NOUN
aiti-4099	136	5	can	can	AUX
aiti-4099	136	6	be	be	AUX
aiti-4099	136	7	obtained	obtain	VERB
aiti-4099	136	8	by	by	ADP
aiti-4099	136	9	twice	twice	ADJ
aiti-4099	136	10	differentiation	differentiation	NOUN
aiti-4099	136	11	of	of	ADP
aiti-4099	136	12	the	the	DET
aiti-4099	136	13	strain	strain	NOUN
aiti-4099	136	14	energy	energy	NOUN
aiti-4099	136	15	u	u	NOUN
aiti-4099	136	16	with	with	ADP
aiti-4099	136	17	respect	respect	NOUN
aiti-4099	136	18	the	the	DET
aiti-4099	136	19	nodal	nodal	NOUN
aiti-4099	136	20	displacements	displacement	NOUN
aiti-4099	136	21	,	,	PUNCT
aiti-4099	136	22	for	for	ADP
aiti-4099	136	23	example	example	NOUN
aiti-4099	136	24	2	2	NUM
aiti-4099	136	25	2	2	NUM
aiti-4099	136	26	2	2	NUM
aiti-4099	136	27	2	2	NUM
aiti-4099	136	28	2	2	NUM
aiti-4099	136	29	,	,	PUNCT
aiti-4099	136	30	,	,	PUNCT
aiti-4099	137	1	b	b	X
aiti-4099	137	2	b	b	X
aiti-4099	137	3	aa	aa	INTJ
aiti-4099	137	4	ab	ab	PROPN
aiti-4099	137	5	bb	bb	NUM
aiti-4099	137	6	u	u	PROPN
aiti-4099	137	7	u	u	PROPN
aiti-4099	137	8	w	w	PROPN
aiti-4099	137	9	w	w	PROPN
aiti-4099	137	10	u	u	PROPN
aiti-4099	137	11	u	u	NOUN
aiti-4099	137	12	u	u	PROPN
aiti-4099	137	13			ADJ
aiti-4099	137	14			PROPN
aiti-4099	137	15			PROPN
aiti-4099	137	16			NUM
aiti-4099	137	17			PROPN
aiti-4099	137	18			ADJ
aiti-4099	137	19			ADJ
aiti-4099	137	20			ADJ
aiti-4099	137	21			PROPN
aiti-4099	137	22	k	k	PROPN
aiti-4099	137	23	k	k	PROPN
aiti-4099	137	24	k	k	PROPN
aiti-4099	137	25	d	d	PROPN
aiti-4099	137	26	d	d	PROPN
aiti-4099	137	27	d	d	X
aiti-4099	137	28	d	d	X
aiti-4099	137	29	(	(	PUNCT
aiti-4099	137	30	20	20	NUM
aiti-4099	137	31	)	)	PUNCT
aiti-4099	137	32	eq	eq	NOUN
aiti-4099	137	33	.	.	PUNCT
aiti-4099	138	1	(	(	PUNCT
aiti-4099	138	2	20	20	NUM
aiti-4099	138	3	)	)	PUNCT
aiti-4099	138	4	gives	give	VERB
aiti-4099	138	5	the	the	DET
aiti-4099	138	6	sub	sub	NOUN
aiti-4099	138	7	-	-	NOUN
aiti-4099	138	8	matrices	matrix	NOUN
aiti-4099	138	9	in	in	ADP
aiti-4099	138	10	the	the	DET
aiti-4099	138	11	following	follow	VERB
aiti-4099	138	12	forms	form	NOUN
aiti-4099	138	13	,	,	PUNCT
aiti-4099	138	14	11	11	NUM
aiti-4099	138	15	,	,	PUNCT
aiti-4099	138	16	,	,	PUNCT
aiti-4099	138	17	12	12	NUM
aiti-4099	138	18	,	,	PUNCT
aiti-4099	138	19	,	,	PUNCT
aiti-4099	138	20	34	34	NUM
aiti-4099	138	21	,	,	PUNCT
aiti-4099	138	22	x2	x2	PROPN
aiti-4099	138	23	(	(	PUNCT
aiti-4099	138	24	2x2	2x2	NUM
aiti-4099	138	25	)	)	PUNCT
aiti-4099	138	26	(	(	PUNCT
aiti-4099	138	27	2x4	2x4	NUM
aiti-4099	138	28	)	)	PUNCT
aiti-4099	138	29	(	(	PUNCT
aiti-4099	138	30	2x4)0	2x4)0	NUM
aiti-4099	138	31	0	0	NUM
aiti-4099	138	32	0	0	NUM
aiti-4099	138	33	,	,	PUNCT
aiti-4099	138	34	x	x	PROPN
aiti-4099	138	35	22	22	NUM
aiti-4099	138	36	,	,	PUNCT
aiti-4099	138	37	x	x	NOUN
aiti-4099	138	38	,	,	PUNCT
aiti-4099	138	39	x	x	PROPN
aiti-4099	138	40	44	44	NUM
aiti-4099	138	41	,	,	PUNCT
aiti-4099	138	42	x2	x2	PROPN
aiti-4099	138	43	(	(	PUNCT
aiti-4099	138	44	4x4	4x4	NUM
aiti-4099	138	45	)	)	PUNCT
aiti-4099	138	46	(	(	PUNCT
aiti-4099	138	47	4x4)0	4x4)0	NUM
aiti-4099	138	48	0	0	NUM
aiti-4099	138	49	,	,	PUNCT
aiti-4099	138	50	x	x	PROPN
aiti-4099	138	51	66	66	NUM
aiti-4099	138	52	,	,	PUNCT
aiti-4099	138	53	x	x	NOUN
aiti-4099	138	54	,	,	PUNCT
aiti-4099	138	55	x	x	PROPN
aiti-4099	138	56	11	11	NUM
aiti-4099	138	57	224	224	NUM
aiti-4099	138	58	2	2	NUM
aiti-4099	138	59	(	(	PUNCT
aiti-4099	138	60	4x4	4x4	NUM
aiti-4099	138	61	)	)	PUNCT
aiti-4099	138	62	4	4	NUM
aiti-4099	138	63	,	,	PUNCT
aiti-4099	138	64	,	,	PUNCT
aiti-4099	138	65	,	,	PUNCT
aiti-4099	138	66	3	3	NUM
aiti-4099	138	67	4	4	NUM
aiti-4099	138	68	,	,	PUNCT
aiti-4099	138	69	,	,	PUNCT
aiti-4099	138	70	3	3	NUM
aiti-4099	138	71	16	16	NUM
aiti-4099	138	72	8	8	NUM
aiti-4099	138	73	16	16	NUM
aiti-4099	138	74	9	9	NUM
aiti-4099	138	75	l	l	NOUN
aiti-4099	138	76	l	l	NOUN
aiti-4099	138	77	l	l	NOUN
aiti-4099	138	78	t	t	NOUN
aiti-4099	138	79	t	t	X
aiti-4099	138	80	t	t	PROPN
aiti-4099	138	81	aa	aa	PROPN
aiti-4099	138	82	u	u	PROPN
aiti-4099	138	83	x	x	PROPN
aiti-4099	138	84	u	u	NOUN
aiti-4099	138	85	x	x	PROPN
aiti-4099	138	86	ab	ab	PROPN
aiti-4099	138	87	u	u	NOUN
aiti-4099	138	88	x	x	PROPN
aiti-4099	138	89	w	w	NOUN
aiti-4099	138	90	x	x	PUNCT
aiti-4099	138	91	as	as	ADP
aiti-4099	138	92	u	u	NOUN
aiti-4099	138	93	x	x	PROPN
aiti-4099	138	94	w	w	PROPN
aiti-4099	138	95	x	x	X
aiti-4099	138	96	l	l	NOUN
aiti-4099	138	97	l	l	NOUN
aiti-4099	138	98	t	t	NOUN
aiti-4099	138	99	t	t	X
aiti-4099	139	1	bb	bb	INTJ
aiti-4099	139	2	w	w	NOUN
aiti-4099	139	3	x	x	PROPN
aiti-4099	139	4	w	w	NOUN
aiti-4099	139	5	x	x	X
aiti-4099	139	6	bs	bs	NOUN
aiti-4099	139	7	w	w	NOUN
aiti-4099	139	8	x	x	PROPN
aiti-4099	139	9	w	w	PROPN
aiti-4099	139	10	x	x	SYM
aiti-4099	139	11	t	t	NOUN
aiti-4099	139	12	t	t	PROPN
aiti-4099	139	13	ss	ss	PROPN
aiti-4099	139	14	w	w	PROPN
aiti-4099	139	15	x	x	X
aiti-4099	139	16	w	w	PROPN
aiti-4099	139	17	x	x	PROPN
aiti-4099	139	18	w	w	PROPN
aiti-4099	139	19	a	a	DET
aiti-4099	139	20	dx	dx	PROPN
aiti-4099	139	21	a	a	DET
aiti-4099	139	22	dx	dx	PROPN
aiti-4099	139	23	a	a	DET
aiti-4099	139	24	dx	dx	PROPN
aiti-4099	139	25	h	h	PROPN
aiti-4099	139	26	a	a	DET
aiti-4099	139	27	dx	dx	PROPN
aiti-4099	139	28	a	a	DET
aiti-4099	139	29	dx	dx	PROPN
aiti-4099	139	30	h	h	PROPN
aiti-4099	139	31	a	a	DET
aiti-4099	139	32	dx	dx	PROPN
aiti-4099	139	33	b	b	PROPN
aiti-4099	139	34	b	b	PROPN
aiti-4099	139	35	h	h	NOUN
aiti-4099	139	36	h	h	NOUN
aiti-4099	139	37	h	h	NOUN
aiti-4099	140	1			PROPN
aiti-4099	140	2			PROPN
aiti-4099	140	3			PROPN
aiti-4099	140	4			PROPN
aiti-4099	140	5			PROPN
aiti-4099	140	6			NUM
aiti-4099	140	7			NUM
aiti-4099	140	8			PROPN
aiti-4099	140	9			ADV
aiti-4099	140	10			PROPN
aiti-4099	140	11			VERB
aiti-4099	140	12			PUNCT
aiti-4099	140	13			X
aiti-4099	140	14			X
aiti-4099	140	15			X
aiti-4099	140	16			PUNCT
aiti-4099	141	1	k	k	PROPN
aiti-4099	141	2	n	n	CCONJ
aiti-4099	141	3	n	n	CCONJ
aiti-4099	141	4	k	k	PROPN
aiti-4099	141	5	n	n	CCONJ
aiti-4099	141	6	n	n	CCONJ
aiti-4099	141	7	k	k	PROPN
aiti-4099	141	8	n	n	CCONJ
aiti-4099	141	9	n	n	CCONJ
aiti-4099	141	10	k	k	PROPN
aiti-4099	141	11	n	n	CCONJ
aiti-4099	141	12	n	n	CCONJ
aiti-4099	141	13	k	k	PROPN
aiti-4099	141	14	n	n	CCONJ
aiti-4099	141	15	n	n	CCONJ
aiti-4099	141	16	k	k	PROPN
aiti-4099	141	17	n	n	CCONJ
aiti-4099	141	18	n	n	CCONJ
aiti-4099	141	19	n	n	ADV
aiti-4099	141	20	44	44	NUM
aiti-4099	141	21	,	,	PUNCT
aiti-4099	141	22	x4	x4	PROPN
aiti-4099	141	23	0	0	NUM
aiti-4099	141	24	0	0	NUM
aiti-4099	141	25	l	l	NOUN
aiti-4099	141	26	l	l	NOUN
aiti-4099	141	27	wb	wb	PROPN
aiti-4099	141	28	dx	dx	PROPN
aiti-4099	141	29			NOUN
aiti-4099	141	30			PROPN
aiti-4099	141	31			PROPN
aiti-4099	141	32			PROPN
aiti-4099	142	1			ADJ
aiti-4099	142	2			NOUN
aiti-4099	142	3			PUNCT
aiti-4099	142	4			SYM
aiti-4099	142	5	n	n	CCONJ
aiti-4099	142	6	(	(	PUNCT
aiti-4099	142	7	21	21	NUM
aiti-4099	142	8	)	)	PUNCT
aiti-4099	142	9	similarly	similarly	ADV
aiti-4099	142	10	,	,	PUNCT
aiti-4099	142	11	the	the	DET
aiti-4099	142	12	kinetic	kinetic	ADJ
aiti-4099	142	13	energy	energy	NOUN
aiti-4099	142	14	of	of	ADP
aiti-4099	142	15	the	the	DET
aiti-4099	142	16	beam	beam	NOUN
aiti-4099	142	17	can	can	AUX
aiti-4099	142	18	also	also	ADV
aiti-4099	142	19	be	be	AUX
aiti-4099	142	20	written	write	VERB
aiti-4099	142	21	in	in	ADP
aiti-4099	142	22	the	the	DET
aiti-4099	142	23	form	form	NOUN
aiti-4099	142	24	advances	advance	VERB
aiti-4099	142	25	in	in	ADP
aiti-4099	142	26	technology	technology	NOUN
aiti-4099	142	27	innovation	innovation	NOUN
aiti-4099	142	28	,	,	PUNCT
aiti-4099	142	29	vol	vol	NOUN
aiti-4099	142	30	.	.	PROPN
aiti-4099	143	1	4	4	NUM
aiti-4099	143	2	,	,	PUNCT
aiti-4099	143	3	no	no	INTJ
aiti-4099	143	4	.	.	NOUN
aiti-4099	143	5	3	3	NUM
aiti-4099	143	6	,	,	PUNCT
aiti-4099	143	7	2019	2019	NUM
aiti-4099	143	8	,	,	PUNCT
aiti-4099	143	9	pp	pp	ADJ
aiti-4099	143	10	.	.	PUNCT
aiti-4099	144	1	152	152	NUM
aiti-4099	144	2	-	-	SYM
aiti-4099	144	3	164	164	NUM
aiti-4099	144	4	157	157	NUM
aiti-4099	144	5			PROPN
aiti-4099	144	6			PROPN
aiti-4099	144	7			PROPN
aiti-4099	144	8			PROPN
aiti-4099	144	9			PROPN
aiti-4099	144	10			PROPN
aiti-4099	145	1	1	1	NUM
aiti-4099	145	2	1	1	NUM
aiti-4099	145	3	2	2	NUM
aiti-4099	145	4	ne	ne	NOUN
aiti-4099	145	5	t	t	PROPN
aiti-4099	145	6	ii	ii	PROPN
aiti-4099	146	1	i	i	PRON
aiti-4099	146	2	i	i	PRON
aiti-4099	146	3	t	t	VERB
aiti-4099	146	4			NUM
aiti-4099	147	1			NUM
aiti-4099	147	2			X
aiti-4099	148	1	d	d	NOUN
aiti-4099	148	2	m	m	VERB
aiti-4099	148	3	d	d	X
aiti-4099	148	4	(	(	PUNCT
aiti-4099	148	5	22	22	NUM
aiti-4099	148	6	)	)	PUNCT
aiti-4099	148	7	where	where	SCONJ
aiti-4099	148	8	/	/	PUNCT
aiti-4099	148	9	t	t	PROPN
aiti-4099	148	10			PROPN
aiti-4099	148	11	d	d	VERB
aiti-4099	148	12	d	d	PROPN
aiti-4099	148	13	is	be	AUX
aiti-4099	148	14	the	the	DET
aiti-4099	148	15	element	element	NOUN
aiti-4099	148	16	nodal	nodal	NOUN
aiti-4099	148	17	velocity	velocity	NOUN
aiti-4099	148	18	,	,	PUNCT
aiti-4099	148	19	and	and	CCONJ
aiti-4099	148	20	m	m	PROPN
aiti-4099	148	21	is	be	AUX
aiti-4099	148	22	the	the	DET
aiti-4099	148	23	element	element	ADJ
aiti-4099	148	24	mass	mass	NOUN
aiti-4099	148	25	matrix	matrix	NOUN
aiti-4099	148	26	which	which	PRON
aiti-4099	148	27	can	can	AUX
aiti-4099	148	28	be	be	AUX
aiti-4099	148	29	written	write	VERB
aiti-4099	148	30	in	in	ADP
aiti-4099	148	31	sub	sub	NOUN
aiti-4099	148	32	-	-	NOUN
aiti-4099	148	33	matrices	matrix	NOUN
aiti-4099	148	34	as	as	ADP
aiti-4099	148	35	(	(	PUNCT
aiti-4099	148	36	10x10	10x10	NUM
aiti-4099	148	37	)	)	PUNCT
aiti-4099	148	38	b	b	PROPN
aiti-4099	148	39	s	s	PROPN
aiti-4099	148	40	b	b	PROPN
aiti-4099	148	41	b	b	PROPN
aiti-4099	148	42	b	b	PROPN
aiti-4099	148	43	b	b	PROPN
aiti-4099	148	44	s	s	X
aiti-4099	148	45	s	s	PROPN
aiti-4099	148	46	b	b	NOUN
aiti-4099	148	47	s	s	X
aiti-4099	148	48	s	s	X
aiti-4099	148	49	s	s	X
aiti-4099	148	50	uu	uu	PROPN
aiti-4099	148	51	uw	uw	PROPN
aiti-4099	148	52	uw	uw	PROPN
aiti-4099	148	53	t	t	PROPN
aiti-4099	148	54	uw	uw	PROPN
aiti-4099	148	55	w	w	PROPN
aiti-4099	148	56	w	w	PROPN
aiti-4099	148	57	w	w	PROPN
aiti-4099	148	58	w	w	PROPN
aiti-4099	148	59	t	t	PROPN
aiti-4099	148	60	t	t	PROPN
aiti-4099	148	61	uw	uw	PROPN
aiti-4099	148	62	w	w	PROPN
aiti-4099	148	63	w	w	PROPN
aiti-4099	148	64	w	w	PROPN
aiti-4099	148	65	w	w	PROPN
aiti-4099	148	66			PROPN
aiti-4099	148	67			NOUN
aiti-4099	148	68			NOUN
aiti-4099	149	1			PROPN
aiti-4099	149	2			ADJ
aiti-4099	149	3			ADJ
aiti-4099	149	4			NOUN
aiti-4099	149	5			NOUN
aiti-4099	149	6			NOUN
aiti-4099	149	7			PROPN
aiti-4099	149	8			PROPN
aiti-4099	149	9	m	m	VERB
aiti-4099	149	10	m	m	VERB
aiti-4099	149	11	m	m	VERB
aiti-4099	149	12	m	m	VERB
aiti-4099	149	13	m	m	VERB
aiti-4099	149	14	m	m	VERB
aiti-4099	149	15	m	m	VERB
aiti-4099	149	16	m	m	VERB
aiti-4099	149	17	m	m	VERB
aiti-4099	149	18	m	m	VERB
aiti-4099	149	19	(	(	PUNCT
aiti-4099	149	20	23	23	NUM
aiti-4099	149	21	)	)	PUNCT
aiti-4099	149	22	the	the	DET
aiti-4099	149	23	mass	mass	ADJ
aiti-4099	149	24	sub	sub	NOUN
aiti-4099	149	25	-	-	NOUN
aiti-4099	149	26	matrices	matrix	NOUN
aiti-4099	149	27	in	in	ADP
aiti-4099	149	28	the	the	DET
aiti-4099	149	29	above	above	ADJ
aiti-4099	149	30	equation	equation	NOUN
aiti-4099	149	31	are	be	AUX
aiti-4099	149	32	obtained	obtain	VERB
aiti-4099	149	33	by	by	ADP
aiti-4099	149	34	twice	twice	ADJ
aiti-4099	149	35	differentiation	differentiation	NOUN
aiti-4099	149	36	of	of	ADP
aiti-4099	149	37	the	the	DET
aiti-4099	149	38	kinetic	kinetic	ADJ
aiti-4099	149	39	energy	energy	NOUN
aiti-4099	149	40	with	with	ADP
aiti-4099	149	41	respect	respect	NOUN
aiti-4099	149	42	to	to	ADP
aiti-4099	149	43	the	the	DET
aiti-4099	149	44	associated	associated	ADJ
aiti-4099	149	45	nodal	nodal	NOUN
aiti-4099	149	46	velocities	velocity	NOUN
aiti-4099	149	47	and	and	CCONJ
aiti-4099	149	48	they	they	PRON
aiti-4099	149	49	have	have	VERB
aiti-4099	149	50	the	the	DET
aiti-4099	149	51	following	follow	VERB
aiti-4099	149	52	forms	form	NOUN
aiti-4099	149	53			NOUN
aiti-4099	150	1			PROPN
aiti-4099	150	2	11	11	NUM
aiti-4099	150	3	12	12	NUM
aiti-4099	150	4	,	,	PUNCT
aiti-4099	150	5	11	11	NUM
aiti-4099	150	6	,	,	PUNCT
aiti-4099	150	7	34	34	NUM
aiti-4099	150	8	,	,	PUNCT
aiti-4099	150	9	x2	x2	PROPN
aiti-4099	150	10	(	(	PUNCT
aiti-4099	150	11	2x2	2x2	NUM
aiti-4099	150	12	)	)	PUNCT
aiti-4099	150	13	(	(	PUNCT
aiti-4099	150	14	2x4	2x4	NUM
aiti-4099	150	15	)	)	PUNCT
aiti-4099	150	16	(	(	PUNCT
aiti-4099	150	17	2x4)0	2x4)0	NUM
aiti-4099	150	18	0	0	NUM
aiti-4099	150	19	0	0	NUM
aiti-4099	150	20	11	11	NUM
aiti-4099	150	21	,	,	PUNCT
aiti-4099	150	22	x	x	PROPN
aiti-4099	150	23	22	22	NUM
aiti-4099	150	24	,	,	PUNCT
aiti-4099	150	25	x	x	PROPN
aiti-4099	150	26	11	11	NUM
aiti-4099	150	27	,	,	PUNCT
aiti-4099	150	28	x	x	PROPN
aiti-4099	150	29	44	44	NUM
aiti-4099	150	30	,	,	PUNCT
aiti-4099	150	31	x2	x2	PROPN
aiti-4099	150	32	(	(	PUNCT
aiti-4099	150	33	4x4)(4x4	4x4)(4x4	NUM
aiti-4099	150	34	)	)	PUNCT
aiti-4099	150	35	0	0	NUM
aiti-4099	150	36	0	0	NUM
aiti-4099	150	37	11	11	NUM
aiti-4099	150	38	(	(	PUNCT
aiti-4099	150	39	4x4	4x4	NUM
aiti-4099	150	40	)	)	PUNCT
aiti-4099	150	41	4	4	NUM
aiti-4099	150	42	,	,	PUNCT
aiti-4099	150	43	,	,	PUNCT
aiti-4099	150	44	,	,	PUNCT
aiti-4099	150	45	3	3	NUM
aiti-4099	150	46	4	4	NUM
aiti-4099	150	47	,	,	PUNCT
aiti-4099	150	48	,	,	PUNCT
aiti-4099	150	49	3	3	NUM
aiti-4099	150	50	1	1	NUM
aiti-4099	150	51	b	b	PROPN
aiti-4099	150	52	s	s	PROPN
aiti-4099	150	53	b	b	PROPN
aiti-4099	150	54	b	b	PROPN
aiti-4099	150	55	l	l	NOUN
aiti-4099	150	56	l	l	X
aiti-4099	150	57	l	l	NOUN
aiti-4099	150	58	t	t	NOUN
aiti-4099	150	59	t	t	PROPN
aiti-4099	150	60	t	t	PROPN
aiti-4099	150	61	t	t	PROPN
aiti-4099	150	62	uu	uu	INTJ
aiti-4099	150	63	u	u	X
aiti-4099	150	64	u	u	PROPN
aiti-4099	150	65	uw	uw	PROPN
aiti-4099	150	66	u	u	PROPN
aiti-4099	150	67	w	w	PROPN
aiti-4099	150	68	x	x	PROPN
aiti-4099	150	69	uw	uw	PROPN
aiti-4099	150	70	w	w	PROPN
aiti-4099	150	71	w	w	PROPN
aiti-4099	150	72	u	u	PROPN
aiti-4099	150	73	x	x	PROPN
aiti-4099	150	74	w	w	PROPN
aiti-4099	150	75	l	l	PROPN
aiti-4099	150	76	l	l	NOUN
aiti-4099	151	1	t	t	NOUN
aiti-4099	151	2	t	t	PROPN
aiti-4099	151	3	t	t	PROPN
aiti-4099	151	4	t	t	PROPN
aiti-4099	151	5	m	m	VERB
aiti-4099	151	6	m	m	PROPN
aiti-4099	151	7	w	w	PROPN
aiti-4099	151	8	w	w	PROPN
aiti-4099	151	9	w	w	PROPN
aiti-4099	151	10	w	w	PROPN
aiti-4099	151	11	bs	bs	PROPN
aiti-4099	151	12	w	w	PROPN
aiti-4099	151	13	w	w	PROPN
aiti-4099	151	14	w	w	PROPN
aiti-4099	151	15	w	w	PROPN
aiti-4099	151	16	t	t	PROPN
aiti-4099	151	17	ss	ss	PROPN
aiti-4099	151	18	w	w	PROPN
aiti-4099	152	1	w	w	PROPN
aiti-4099	153	1	i	i	PRON
aiti-4099	153	2	dx	dx	PROPN
aiti-4099	154	1	i	i	PRON
aiti-4099	154	2	dx	dx	VERB
aiti-4099	155	1	i	i	PRON
aiti-4099	156	1	i	i	PRON
aiti-4099	156	2	dx	dx	VERB
aiti-4099	157	1	h	h	INTJ
aiti-4099	158	1	i	i	PRON
aiti-4099	159	1	i	i	PRON
aiti-4099	159	2	dx	dx	VERB
aiti-4099	160	1	i	i	PRON
aiti-4099	161	1	i	i	PRON
aiti-4099	161	2	dx	dx	VERB
aiti-4099	162	1	h	h	NOUN
aiti-4099	163	1	i	i	PRON
aiti-4099	163	2			VERB
aiti-4099	163	3			NOUN
aiti-4099	163	4			PROPN
aiti-4099	164	1			PROPN
aiti-4099	164	2			PROPN
aiti-4099	164	3			PROPN
aiti-4099	164	4			PROPN
aiti-4099	164	5			PROPN
aiti-4099	165	1			PROPN
aiti-4099	165	2			PROPN
aiti-4099	165	3			NOUN
aiti-4099	165	4			NOUN
aiti-4099	165	5			PROPN
aiti-4099	165	6			ADV
aiti-4099	165	7			NUM
aiti-4099	165	8			PROPN
aiti-4099	165	9			CCONJ
aiti-4099	165	10			PROPN
aiti-4099	165	11			NOUN
aiti-4099	165	12			NUM
aiti-4099	165	13			ADV
aiti-4099	165	14			X
aiti-4099	165	15			X
aiti-4099	165	16			X
aiti-4099	165	17			X
aiti-4099	165	18			PUNCT
aiti-4099	166	1	m	m	VERB
aiti-4099	166	2	n	n	VERB
aiti-4099	166	3	n	n	PRON
aiti-4099	166	4	m	m	VERB
aiti-4099	166	5	n	n	CCONJ
aiti-4099	166	6	n	n	PRON
aiti-4099	166	7	m	m	VERB
aiti-4099	166	8	n	n	ADP
aiti-4099	166	9	n	n	CCONJ
aiti-4099	166	10	n	n	CCONJ
aiti-4099	166	11	n	n	CCONJ
aiti-4099	166	12	m	m	VERB
aiti-4099	166	13	n	n	ADP
aiti-4099	166	14	n	n	CCONJ
aiti-4099	166	15	n	n	CCONJ
aiti-4099	166	16	n	n	CCONJ
aiti-4099	166	17	m	m	VERB
aiti-4099	166	18	n	n	ADP
aiti-4099	166	19	n	n	CCONJ
aiti-4099	166	20	n	n	CCONJ
aiti-4099	166	21	n	n	CCONJ
aiti-4099	166	22	m	m	VERB
aiti-4099	166	23	n	n	ADJ
aiti-4099	166	24	n	n	NOUN
aiti-4099	166	25	,	,	PUNCT
aiti-4099	166	26	x	x	PROPN
aiti-4099	166	27	66	66	NUM
aiti-4099	166	28	,	,	PUNCT
aiti-4099	166	29	4	4	NUM
aiti-4099	166	30	0	0	NUM
aiti-4099	166	31	6	6	NUM
aiti-4099	166	32	9	9	NUM
aiti-4099	166	33	l	l	NOUN
aiti-4099	166	34	t	t	PROPN
aiti-4099	166	35	w	w	PROPN
aiti-4099	166	36	w	w	PROPN
aiti-4099	166	37	xi	xi	PROPN
aiti-4099	166	38	dx	dx	PROPN
aiti-4099	167	1	h	h	PROPN
aiti-4099	167	2			PROPN
aiti-4099	167	3			PROPN
aiti-4099	167	4			PROPN
aiti-4099	167	5			PROPN
aiti-4099	168	1			ADJ
aiti-4099	168	2			NOUN
aiti-4099	168	3			PUNCT
aiti-4099	168	4	n	n	CCONJ
aiti-4099	168	5	n	n	CCONJ
aiti-4099	168	6	(	(	PUNCT
aiti-4099	168	7	24	24	NUM
aiti-4099	168	8	)	)	PUNCT
aiti-4099	168	9	due	due	ADP
aiti-4099	168	10	to	to	ADP
aiti-4099	168	11	the	the	DET
aiti-4099	168	12	rigidities	rigidity	NOUN
aiti-4099	168	13	and	and	CCONJ
aiti-4099	168	14	mass	mass	ADJ
aiti-4099	168	15	moments	moment	NOUN
aiti-4099	168	16	are	be	AUX
aiti-4099	168	17	functions	function	NOUN
aiti-4099	168	18	of	of	ADP
aiti-4099	168	19	x	x	PRON
aiti-4099	168	20	,	,	PUNCT
aiti-4099	168	21	the	the	DET
aiti-4099	168	22	integrals	integral	NOUN
aiti-4099	168	23	in	in	ADP
aiti-4099	168	24	eqs	eqs	PROPN
aiti-4099	168	25	.	.	PUNCT
aiti-4099	169	1	(	(	PUNCT
aiti-4099	169	2	21	21	NUM
aiti-4099	169	3	)	)	PUNCT
aiti-4099	169	4	and	and	CCONJ
aiti-4099	169	5	(	(	PUNCT
aiti-4099	169	6	24	24	NUM
aiti-4099	169	7	)	)	PUNCT
aiti-4099	169	8	are	be	AUX
aiti-4099	169	9	hardly	hardly	ADV
aiti-4099	169	10	computed	compute	VERB
aiti-4099	169	11	explicitly	explicitly	ADV
aiti-4099	169	12	.	.	PUNCT
aiti-4099	170	1	gauss	gauss	ADJ
aiti-4099	170	2	quadrature	quadrature	NOUN
aiti-4099	170	3	is	be	AUX
aiti-4099	170	4	employed	employ	VERB
aiti-4099	170	5	herein	herein	NOUN
aiti-4099	170	6	to	to	PART
aiti-4099	170	7	compute	compute	VERB
aiti-4099	170	8	the	the	DET
aiti-4099	170	9	stiffness	stiffness	NOUN
aiti-4099	170	10	and	and	CCONJ
aiti-4099	170	11	mass	mass	ADJ
aiti-4099	170	12	matrices	matrix	NOUN
aiti-4099	170	13	.	.	PUNCT
aiti-4099	171	1	with	with	ADP
aiti-4099	171	2	the	the	DET
aiti-4099	171	3	introduced	introduce	VERB
aiti-4099	171	4	interpolations	interpolation	NOUN
aiti-4099	171	5	,	,	PUNCT
aiti-4099	171	6	the	the	DET
aiti-4099	171	7	vector	vector	NOUN
aiti-4099	171	8	of	of	ADP
aiti-4099	171	9	nodal	nodal	ADJ
aiti-4099	171	10	external	external	ADJ
aiti-4099	171	11	load	load	NOUN
aiti-4099	171	12	given	give	VERB
aiti-4099	171	13	by	by	ADP
aiti-4099	171	14	eq	eq	PROPN
aiti-4099	171	15	.	.	PUNCT
aiti-4099	172	1	(	(	PUNCT
aiti-4099	172	2	11	11	NUM
aiti-4099	172	3	)	)	PUNCT
aiti-4099	172	4	can	can	AUX
aiti-4099	172	5	be	be	AUX
aiti-4099	172	6	written	write	VERB
aiti-4099	172	7	in	in	ADP
aiti-4099	172	8	the	the	DET
aiti-4099	172	9	form	form	NOUN
aiti-4099	172	10	0	0	NUM
aiti-4099	172	11	element	element	NOUN
aiti-4099	172	12	under	under	ADP
aiti-4099	172	13	loading	loading	NOUN
aiti-4099	172	14	cos	cos	PROPN
aiti-4099	172	15	(	(	PUNCT
aiti-4099	172	16	)	)	PUNCT
aiti-4099	172	17	0	0	NUM
aiti-4099	172	18	0	0	NUM
aiti-4099	172	19	0	0	NUM
aiti-4099	172	20	.....	.....	SYM
aiti-4099	172	21	0	0	NUM
aiti-4099	172	22	0	0	NUM
aiti-4099	172	23	0	0	NUM
aiti-4099	172	24	0	0	NUM
aiti-4099	172	25	...	...	SYM
aiti-4099	172	26	0	0	NUM
aiti-4099	172	27	0	0	NUM
aiti-4099	172	28	0	0	NUM
aiti-4099	173	1	t	t	NOUN
aiti-4099	173	2	ex	ex	NOUN
aiti-4099	173	3	w	w	PROPN
aiti-4099	173	4	wf	wf	PROPN
aiti-4099	173	5	t	t	PROPN
aiti-4099	173	6			ADV
aiti-4099	174	1			ADP
aiti-4099	174	2			NUM
aiti-4099	174	3			NUM
aiti-4099	174	4			PROPN
aiti-4099	174	5			PROPN
aiti-4099	174	6			PROPN
aiti-4099	174	7			NUM
aiti-4099	174	8			NOUN
aiti-4099	174	9			NUM
aiti-4099	174	10			NUM
aiti-4099	174	11			NUM
aiti-4099	174	12			PROPN
aiti-4099	174	13	f	f	PROPN
aiti-4099	174	14	n	n	CCONJ
aiti-4099	174	15	n	n	PROPN
aiti-4099	174	16	(	(	PUNCT
aiti-4099	174	17	25	25	NUM
aiti-4099	174	18	)	)	PUNCT
aiti-4099	174	19	the	the	DET
aiti-4099	174	20	matrix	matrix	NOUN
aiti-4099	174	21	of	of	ADP
aiti-4099	174	22	the	the	DET
aiti-4099	174	23	shape	shape	NOUN
aiti-4099	174	24	functions	function	NOUN
aiti-4099	174	25	in	in	ADP
aiti-4099	174	26	the	the	DET
aiti-4099	174	27	above	above	ADJ
aiti-4099	174	28	equation	equation	NOUN
aiti-4099	174	29	is	be	AUX
aiti-4099	174	30	evaluated	evaluate	VERB
aiti-4099	174	31	at	at	ADP
aiti-4099	174	32	x	x	X
aiti-4099	174	33	=	=	NOUN
aiti-4099	174	34	xf	xf	PROPN
aiti-4099	174	35	,	,	PUNCT
aiti-4099	174	36	the	the	DET
aiti-4099	174	37	abscissa	abscissa	NOUN
aiti-4099	174	38	measured	measure	VERB
aiti-4099	174	39	from	from	ADP
aiti-4099	174	40	the	the	DET
aiti-4099	174	41	load	load	NOUN
aiti-4099	174	42	to	to	ADP
aiti-4099	174	43	the	the	DET
aiti-4099	174	44	left	left	ADJ
aiti-4099	174	45	end	end	NOUN
aiti-4099	174	46	of	of	ADP
aiti-4099	174	47	the	the	DET
aiti-4099	174	48	element	element	NOUN
aiti-4099	174	49	.	.	PUNCT
aiti-4099	175	1	the	the	DET
aiti-4099	175	2	equations	equation	NOUN
aiti-4099	175	3	of	of	ADP
aiti-4099	175	4	motion	motion	NOUN
aiti-4099	175	5	for	for	ADP
aiti-4099	175	6	the	the	DET
aiti-4099	175	7	beam	beam	NOUN
aiti-4099	175	8	in	in	ADP
aiti-4099	175	9	term	term	NOUN
aiti-4099	175	10	of	of	ADP
aiti-4099	175	11	finite	finite	ADJ
aiti-4099	175	12	element	element	NOUN
aiti-4099	175	13	analysis	analysis	NOUN
aiti-4099	175	14	can	can	AUX
aiti-4099	175	15	be	be	AUX
aiti-4099	175	16	written	write	VERB
aiti-4099	175	17	in	in	ADP
aiti-4099	175	18	the	the	DET
aiti-4099	175	19	form	form	NOUN
aiti-4099	175	20	[	[	X
aiti-4099	175	21	18	18	NUM
aiti-4099	175	22	]	]	SYM
aiti-4099	175	23	ex	ex	PROPN
aiti-4099	175	24			PROPN
aiti-4099	175	25	md	md	PROPN
aiti-4099	175	26	cd	cd	PROPN
aiti-4099	175	27	kd	kd	PROPN
aiti-4099	175	28	f	f	PROPN
aiti-4099	175	29	(	(	PUNCT
aiti-4099	175	30	26	26	NUM
aiti-4099	175	31	)	)	PUNCT
aiti-4099	175	32	where	where	SCONJ
aiti-4099	175	33	d	d	NOUN
aiti-4099	175	34	,	,	PUNCT
aiti-4099	175	35	d	d	NOUN
aiti-4099	175	36	,	,	PUNCT
aiti-4099	175	37	d	d	X
aiti-4099	175	38	are	be	AUX
aiti-4099	175	39	,	,	PUNCT
aiti-4099	175	40	respectively	respectively	ADV
aiti-4099	175	41	,	,	PUNCT
aiti-4099	175	42	the	the	DET
aiti-4099	175	43	structural	structural	ADJ
aiti-4099	175	44	vectors	vector	NOUN
aiti-4099	175	45	of	of	ADP
aiti-4099	175	46	nodal	nodal	NOUN
aiti-4099	175	47	displacements	displacement	NOUN
aiti-4099	175	48	,	,	PUNCT
aiti-4099	175	49	velocities	velocity	NOUN
aiti-4099	175	50	and	and	CCONJ
aiti-4099	175	51	accelerations	acceleration	NOUN
aiti-4099	175	52	;	;	PUNCT
aiti-4099	175	53	k	k	X
aiti-4099	175	54	,	,	PUNCT
aiti-4099	175	55	m	m	PROPN
aiti-4099	175	56	,	,	PUNCT
aiti-4099	175	57	and	and	CCONJ
aiti-4099	175	58	c	c	PROPN
aiti-4099	175	59	are	be	AUX
aiti-4099	175	60	structural	structural	ADJ
aiti-4099	175	61	stiffness	stiffness	NOUN
aiti-4099	175	62	,	,	PUNCT
aiti-4099	175	63	mass	mass	NOUN
aiti-4099	175	64	and	and	CCONJ
aiti-4099	175	65	damping	damp	VERB
aiti-4099	175	66	matrices	matrix	NOUN
aiti-4099	175	67	,	,	PUNCT
aiti-4099	175	68	respectively	respectively	ADV
aiti-4099	175	69	.	.	PUNCT
aiti-4099	176	1	rayleigh	rayleigh	PROPN
aiti-4099	176	2	damping	damp	VERB
aiti-4099	176	3	,	,	PUNCT
aiti-4099	176	4	in	in	ADP
aiti-4099	176	5	which	which	PRON
aiti-4099	176	6	the	the	DET
aiti-4099	176	7	damping	damp	VERB
aiti-4099	176	8	matrix	matrix	NOUN
aiti-4099	176	9	c	c	NOUN
aiti-4099	176	10	is	be	AUX
aiti-4099	176	11	proportional	proportional	ADJ
aiti-4099	176	12	to	to	ADP
aiti-4099	176	13	a	a	DET
aiti-4099	176	14	linear	linear	ADJ
aiti-4099	176	15	combination	combination	NOUN
aiti-4099	176	16	of	of	ADP
aiti-4099	176	17	mass	mass	NOUN
aiti-4099	176	18	and	and	CCONJ
aiti-4099	176	19	stiffness	stiffness	NOUN
aiti-4099	176	20	,	,	PUNCT
aiti-4099	176	21	is	be	AUX
aiti-4099	176	22	employed	employ	VERB
aiti-4099	176	23	herein	herein	NOUN
aiti-4099	176	24			NOUN
aiti-4099	176	25			VERB
aiti-4099	176	26	c	c	PROPN
aiti-4099	176	27	k	k	PROPN
aiti-4099	177	1	m	m	PROPN
aiti-4099	178	1	(	(	PUNCT
aiti-4099	178	2	27	27	NUM
aiti-4099	178	3	)	)	PUNCT
aiti-4099	178	4	where	where	SCONJ
aiti-4099	178	5	α	α	NOUN
aiti-4099	178	6	and	and	CCONJ
aiti-4099	178	7	β	β	X
aiti-4099	178	8	are	be	AUX
aiti-4099	178	9	,	,	PUNCT
aiti-4099	178	10	respectively	respectively	ADV
aiti-4099	178	11	,	,	PUNCT
aiti-4099	179	1	the	the	DET
aiti-4099	179	2	mass	mass	ADJ
aiti-4099	179	3	and	and	CCONJ
aiti-4099	179	4	stiffness	stiffness	ADJ
aiti-4099	179	5	proportional	proportional	ADJ
aiti-4099	179	6	rayleigh	rayleigh	NOUN
aiti-4099	179	7	damping	damp	VERB
aiti-4099	179	8	coefficient	coefficient	NOUN
aiti-4099	179	9	,	,	PUNCT
aiti-4099	179	10	which	which	PRON
aiti-4099	179	11	are	be	AUX
aiti-4099	179	12	calculated	calculate	VERB
aiti-4099	179	13	from	from	ADP
aiti-4099	179	14	the	the	DET
aiti-4099	179	15	critical	critical	ADJ
aiti-4099	179	16	damping	damp	VERB
aiti-4099	179	17	ratio	ratio	NOUN
aiti-4099	179	18	and	and	CCONJ
aiti-4099	179	19	the	the	DET
aiti-4099	179	20	natural	natural	ADJ
aiti-4099	179	21	frequencies	frequency	NOUN
aiti-4099	179	22	as	as	ADP
aiti-4099	179	23	1	1	NUM
aiti-4099	179	24	2	2	NUM
aiti-4099	179	25	1	1	NUM
aiti-4099	179	26	2	2	NUM
aiti-4099	179	27	1	1	NUM
aiti-4099	179	28	2	2	NUM
aiti-4099	179	29	2	2	NUM
aiti-4099	179	30	2	2	NUM
aiti-4099	179	31	,	,	PUNCT
aiti-4099	179	32			X
aiti-4099	179	33			X
aiti-4099	179	34			NOUN
aiti-4099	179	35			NOUN
aiti-4099	179	36			ADP
aiti-4099	179	37			NOUN
aiti-4099	179	38			X
aiti-4099	179	39			X
aiti-4099	179	40			X
aiti-4099	179	41			ADV
aiti-4099	179	42			PROPN
aiti-4099	179	43			PROPN
aiti-4099	179	44			X
aiti-4099	179	45	(	(	PUNCT
aiti-4099	179	46	28	28	NUM
aiti-4099	179	47	)	)	PUNCT
aiti-4099	179	48	in	in	ADP
aiti-4099	179	49	the	the	DET
aiti-4099	179	50	above	above	NOUN
aiti-4099	179	51	,	,	PUNCT
aiti-4099	179	52			PRON
aiti-4099	179	53	is	be	AUX
aiti-4099	179	54	the	the	DET
aiti-4099	179	55	damping	damp	VERB
aiti-4099	179	56	ratio	ratio	NOUN
aiti-4099	179	57	,	,	PUNCT
aiti-4099	179	58	taken	take	VERB
aiti-4099	179	59	by	by	ADP
aiti-4099	179	60	5	5	NUM
aiti-4099	179	61	%	%	NOUN
aiti-4099	179	62	for	for	ADP
aiti-4099	179	63	all	all	DET
aiti-4099	179	64	numerical	numerical	ADJ
aiti-4099	179	65	computation	computation	NOUN
aiti-4099	179	66	below	below	ADV
aiti-4099	179	67	.	.	PUNCT
aiti-4099	180	1	advances	advance	NOUN
aiti-4099	180	2	in	in	ADP
aiti-4099	180	3	technology	technology	NOUN
aiti-4099	180	4	innovation	innovation	NOUN
aiti-4099	180	5	,	,	PUNCT
aiti-4099	180	6	vol	vol	NOUN
aiti-4099	180	7	.	.	PROPN
aiti-4099	180	8	4	4	NUM
aiti-4099	180	9	,	,	PUNCT
aiti-4099	180	10	no	no	INTJ
aiti-4099	180	11	.	.	NOUN
aiti-4099	180	12	3	3	NUM
aiti-4099	180	13	,	,	PUNCT
aiti-4099	180	14	2019	2019	NUM
aiti-4099	180	15	,	,	PUNCT
aiti-4099	180	16	pp	pp	ADJ
aiti-4099	180	17	.	.	PUNCT
aiti-4099	181	1	152	152	NUM
aiti-4099	181	2	-	-	SYM
aiti-4099	181	3	164	164	NUM
aiti-4099	181	4	158	158	NUM
aiti-4099	181	5	4	4	NUM
aiti-4099	181	6	.	.	PUNCT
aiti-4099	181	7	results	result	NOUN
aiti-4099	181	8	and	and	CCONJ
aiti-4099	181	9	discussion	discussion	NOUN
aiti-4099	181	10	using	use	VERB
aiti-4099	181	11	the	the	DET
aiti-4099	181	12	derived	derive	VERB
aiti-4099	181	13	finite	finite	NOUN
aiti-4099	181	14	element	element	NOUN
aiti-4099	181	15	formulation	formulation	NOUN
aiti-4099	181	16	,	,	PUNCT
aiti-4099	181	17	natural	natural	ADJ
aiti-4099	181	18	frequencies	frequency	NOUN
aiti-4099	181	19	and	and	CCONJ
aiti-4099	181	20	dynamic	dynamic	ADJ
aiti-4099	181	21	response	response	NOUN
aiti-4099	181	22	of	of	ADP
aiti-4099	181	23	the	the	DET
aiti-4099	181	24	2d	2d	NOUN
aiti-4099	181	25	-	-	PUNCT
aiti-4099	181	26	fgsw	fgsw	NOUN
aiti-4099	181	27	beam	beam	NOUN
aiti-4099	181	28	are	be	AUX
aiti-4099	181	29	computed	compute	VERB
aiti-4099	181	30	,	,	PUNCT
aiti-4099	181	31	and	and	CCONJ
aiti-4099	181	32	numerical	numerical	ADJ
aiti-4099	181	33	results	result	NOUN
aiti-4099	181	34	are	be	AUX
aiti-4099	181	35	reported	report	VERB
aiti-4099	181	36	in	in	ADP
aiti-4099	181	37	this	this	DET
aiti-4099	181	38	section	section	NOUN
aiti-4099	181	39	.	.	PUNCT
aiti-4099	182	1	to	to	ADP
aiti-4099	182	2	this	this	DET
aiti-4099	182	3	end	end	NOUN
aiti-4099	182	4	,	,	PUNCT
aiti-4099	182	5	an	an	DET
aiti-4099	182	6	fgsw	fgsw	NOUN
aiti-4099	182	7	beam	beam	NOUN
aiti-4099	182	8	formed	form	VERB
aiti-4099	182	9	from	from	ADP
aiti-4099	182	10	alumina	alumina	NOUN
aiti-4099	182	11	(	(	PUNCT
aiti-4099	182	12	ceramic	ceramic	NOUN
aiti-4099	182	13	)	)	PUNCT
aiti-4099	182	14	and	and	CCONJ
aiti-4099	182	15	aluminum	aluminum	NOUN
aiti-4099	182	16	(	(	PUNCT
aiti-4099	182	17	metal	metal	NOUN
aiti-4099	182	18	)	)	PUNCT
aiti-4099	182	19	is	be	AUX
aiti-4099	182	20	considered	consider	VERB
aiti-4099	182	21	.	.	PUNCT
aiti-4099	183	1	the	the	DET
aiti-4099	183	2	material	material	NOUN
aiti-4099	183	3	properties	property	NOUN
aiti-4099	183	4	of	of	ADP
aiti-4099	183	5	the	the	DET
aiti-4099	183	6	constituents	constituent	NOUN
aiti-4099	183	7	are	be	AUX
aiti-4099	183	8	as	as	SCONJ
aiti-4099	183	9	follows	follow	VERB
aiti-4099	183	10	[	[	X
aiti-4099	183	11	7	7	NUM
aiti-4099	183	12	]	]	NUM
aiti-4099	183	13	:	:	PUNCT
aiti-4099	183	14	(	(	PUNCT
aiti-4099	183	15	1	1	X
aiti-4099	183	16	)	)	PUNCT
aiti-4099	183	17	ec=380	ec=380	PROPN
aiti-4099	183	18	mpa	mpa	PROPN
aiti-4099	183	19	,	,	PUNCT
aiti-4099	183	20	ρc=3800	ρc=3800	PROPN
aiti-4099	183	21	kg	kg	NOUN
aiti-4099	183	22	/	/	SYM
aiti-4099	183	23	m	m	PROPN
aiti-4099	183	24	3	3	NUM
aiti-4099	183	25	,	,	PUNCT
aiti-4099	183	26	0.3c	0.3c	NUM
aiti-4099	183	27			NOUN
aiti-4099	183	28	for	for	ADP
aiti-4099	183	29	alumina	alumina	NOUN
aiti-4099	183	30	(	(	PUNCT
aiti-4099	183	31	2	2	NUM
aiti-4099	183	32	)	)	PUNCT
aiti-4099	183	33	em=70	em=70	PROPN
aiti-4099	183	34	mpa	mpa	PROPN
aiti-4099	183	35	,	,	PUNCT
aiti-4099	183	36	ρm=2702	ρm=2702	PROPN
aiti-4099	183	37	kg	kg	PROPN
aiti-4099	183	38	/	/	SYM
aiti-4099	183	39	m	m	PROPN
aiti-4099	183	40	3	3	NUM
aiti-4099	183	41	,	,	PUNCT
aiti-4099	183	42	0.3m	0.3m	NOUN
aiti-4099	183	43			NOUN
aiti-4099	183	44	for	for	ADP
aiti-4099	183	45	aluminum	aluminum	NOUN
aiti-4099	183	46	for	for	ADP
aiti-4099	183	47	the	the	DET
aiti-4099	183	48	convenience	convenience	NOUN
aiti-4099	183	49	of	of	ADP
aiti-4099	183	50	discussion	discussion	NOUN
aiti-4099	183	51	,	,	PUNCT
aiti-4099	183	52	the	the	DET
aiti-4099	183	53	three	three	NUM
aiti-4099	183	54	numbers	number	NOUN
aiti-4099	183	55	as	as	SCONJ
aiti-4099	183	56	proposed	propose	VERB
aiti-4099	183	57	in	in	ADP
aiti-4099	183	58	[	[	X
aiti-4099	183	59	6	6	NUM
aiti-4099	183	60	]	]	PUNCT
aiti-4099	183	61	are	be	AUX
aiti-4099	183	62	used	use	VERB
aiti-4099	183	63	to	to	PART
aiti-4099	183	64	indicate	indicate	VERB
aiti-4099	183	65	the	the	DET
aiti-4099	183	66	layer	layer	NOUN
aiti-4099	183	67	thickness	thickness	NOUN
aiti-4099	183	68	ratio	ratio	NOUN
aiti-4099	183	69	,	,	PUNCT
aiti-4099	183	70	for	for	ADP
aiti-4099	183	71	example	example	NOUN
aiti-4099	183	72	(	(	PUNCT
aiti-4099	183	73	2	2	NUM
aiti-4099	183	74	-	-	SYM
aiti-4099	183	75	1	1	NUM
aiti-4099	183	76	-	-	PUNCT
aiti-4099	183	77	2	2	NUM
aiti-4099	183	78	)	)	PUNCT
aiti-4099	183	79	means	mean	VERB
aiti-4099	183	80	the	the	DET
aiti-4099	183	81	thickness	thickness	NOUN
aiti-4099	183	82	ratio	ratio	NOUN
aiti-4099	183	83	of	of	ADP
aiti-4099	183	84	the	the	DET
aiti-4099	183	85	bottom	bottom	NOUN
aiti-4099	183	86	,	,	PUNCT
aiti-4099	183	87	core	core	NOUN
aiti-4099	183	88	,	,	PUNCT
aiti-4099	183	89	and	and	CCONJ
aiti-4099	183	90	top	top	ADJ
aiti-4099	183	91	layers	layer	NOUN
aiti-4099	183	92	is	be	AUX
aiti-4099	183	93	2:1:2	2:1:2	NUM
aiti-4099	183	94	.	.	PUNCT
aiti-4099	184	1	fig	fig	NOUN
aiti-4099	184	2	.	.	PUNCT
aiti-4099	185	1	2	2	NUM
aiti-4099	185	2	shows	show	VERB
aiti-4099	185	3	the	the	DET
aiti-4099	185	4	variation	variation	NOUN
aiti-4099	185	5	of	of	ADP
aiti-4099	185	6	the	the	DET
aiti-4099	185	7	effective	effective	ADJ
aiti-4099	185	8	young	young	ADJ
aiti-4099	185	9	’s	’s	PART
aiti-4099	185	10	modulus	modulus	ADJ
aiti-4099	185	11	and	and	CCONJ
aiti-4099	185	12	mass	mass	ADJ
aiti-4099	185	13	density	density	NOUN
aiti-4099	185	14	in	in	ADP
aiti-4099	185	15	the	the	DET
aiti-4099	185	16	thickness	thickness	NOUN
aiti-4099	185	17	and	and	CCONJ
aiti-4099	185	18	length	length	NOUN
aiti-4099	185	19	directions	direction	NOUN
aiti-4099	185	20	for	for	ADP
aiti-4099	185	21	(	(	PUNCT
aiti-4099	185	22	1	1	NUM
aiti-4099	185	23	-	-	SYM
aiti-4099	185	24	1	1	NUM
aiti-4099	185	25	-	-	PUNCT
aiti-4099	185	26	1	1	NUM
aiti-4099	185	27	)	)	PUNCT
aiti-4099	185	28	beam	beam	NOUN
aiti-4099	185	29	made	make	VERB
aiti-4099	185	30	of	of	ADP
aiti-4099	185	31	alumina	alumina	NOUN
aiti-4099	185	32	and	and	CCONJ
aiti-4099	185	33	aluminum	aluminum	NOUN
aiti-4099	185	34	with	with	ADP
aiti-4099	185	35	nx	nx	NOUN
aiti-4099	185	36	=	=	NOUN
aiti-4099	185	37	nz=0.5	nz=0.5	NOUN
aiti-4099	185	38	according	accord	VERB
aiti-4099	185	39	to	to	ADP
aiti-4099	185	40	eq	eq	PROPN
aiti-4099	185	41	.	.	PUNCT
aiti-4099	186	1	(	(	PUNCT
aiti-4099	186	2	2	2	NUM
aiti-4099	186	3	)	)	PUNCT
aiti-4099	186	4	.	.	PUNCT
aiti-4099	187	1	it	it	PRON
aiti-4099	187	2	can	can	AUX
aiti-4099	187	3	be	be	AUX
aiti-4099	187	4	seen	see	VERB
aiti-4099	187	5	that	that	SCONJ
aiti-4099	187	6	young	young	PROPN
aiti-4099	187	7	’s	’s	PART
aiti-4099	187	8	modulus	modulus	ADJ
aiti-4099	187	9	and	and	CCONJ
aiti-4099	187	10	mass	mass	ADJ
aiti-4099	187	11	density	density	NOUN
aiti-4099	187	12	continuously	continuously	ADV
aiti-4099	187	13	vary	vary	VERB
aiti-4099	187	14	in	in	ADP
aiti-4099	187	15	both	both	CCONJ
aiti-4099	187	16	the	the	DET
aiti-4099	187	17	thickness	thickness	NOUN
aiti-4099	187	18	and	and	CCONJ
aiti-4099	187	19	length	length	NOUN
aiti-4099	187	20	directions	direction	NOUN
aiti-4099	187	21	of	of	ADP
aiti-4099	187	22	the	the	DET
aiti-4099	187	23	beam	beam	NOUN
aiti-4099	187	24	.	.	PUNCT
aiti-4099	188	1	(	(	PUNCT
aiti-4099	188	2	a	a	X
aiti-4099	188	3	)	)	PUNCT
aiti-4099	188	4	young	young	ADJ
aiti-4099	188	5	’s	’s	PART
aiti-4099	188	6	modulus	modulus	ADJ
aiti-4099	188	7	(	(	PUNCT
aiti-4099	188	8	b	b	NOUN
aiti-4099	188	9	)	)	PUNCT
aiti-4099	188	10	mass	mass	NOUN
aiti-4099	188	11	density	density	NOUN
aiti-4099	188	12	fig	fig	NOUN
aiti-4099	188	13	.	.	PUNCT
aiti-4099	189	1	2	2	NUM
aiti-4099	189	2	variation	variation	NOUN
aiti-4099	189	3	of	of	ADP
aiti-4099	189	4	young	young	ADJ
aiti-4099	189	5	’s	’s	PART
aiti-4099	189	6	modulus	modulus	ADJ
aiti-4099	189	7	and	and	CCONJ
aiti-4099	189	8	mass	mass	ADJ
aiti-4099	189	9	density	density	NOUN
aiti-4099	189	10	for	for	ADP
aiti-4099	189	11	(	(	PUNCT
aiti-4099	189	12	1	1	NUM
aiti-4099	189	13	-	-	SYM
aiti-4099	189	14	1	1	NUM
aiti-4099	189	15	-	-	PUNCT
aiti-4099	189	16	1	1	NUM
aiti-4099	189	17	)	)	PUNCT
aiti-4099	189	18	beam	beam	NOUN
aiti-4099	189	19	with	with	ADP
aiti-4099	189	20	nx	nx	PROPN
aiti-4099	189	21	=	=	NOUN
aiti-4099	189	22	nz=0.5	nz=0.5	ADJ
aiti-4099	189	23	4.1	4.1	NUM
aiti-4099	189	24	.	.	PUNCT
aiti-4099	190	1	formulation	formulation	NOUN
aiti-4099	190	2	verification	verification	NOUN
aiti-4099	190	3	before	before	ADP
aiti-4099	190	4	computing	compute	VERB
aiti-4099	190	5	vibration	vibration	NOUN
aiti-4099	190	6	characteristics	characteristic	NOUN
aiti-4099	190	7	of	of	ADP
aiti-4099	190	8	the	the	DET
aiti-4099	190	9	beam	beam	NOUN
aiti-4099	190	10	,	,	PUNCT
aiti-4099	190	11	the	the	DET
aiti-4099	190	12	derived	derived	ADJ
aiti-4099	190	13	formulation	formulation	NOUN
aiti-4099	190	14	is	be	AUX
aiti-4099	190	15	necessary	necessary	ADJ
aiti-4099	190	16	to	to	PART
aiti-4099	190	17	confirm	confirm	VERB
aiti-4099	190	18	.	.	PUNCT
aiti-4099	191	1	since	since	SCONJ
aiti-4099	191	2	there	there	PRON
aiti-4099	191	3	is	be	VERB
aiti-4099	191	4	no	no	DET
aiti-4099	191	5	data	datum	NOUN
aiti-4099	191	6	on	on	ADP
aiti-4099	191	7	the	the	DET
aiti-4099	191	8	vibration	vibration	NOUN
aiti-4099	191	9	of	of	ADP
aiti-4099	191	10	the	the	DET
aiti-4099	191	11	2d	2d	NOUN
aiti-4099	191	12	-	-	PUNCT
aiti-4099	191	13	fgsw	fgsw	NOUN
aiti-4099	191	14	beam	beam	NOUN
aiti-4099	191	15	considered	consider	VERB
aiti-4099	191	16	herein	herein	NOUN
aiti-4099	191	17	available	available	ADJ
aiti-4099	191	18	in	in	ADP
aiti-4099	191	19	the	the	DET
aiti-4099	191	20	literature	literature	NOUN
aiti-4099	191	21	,	,	PUNCT
aiti-4099	191	22	the	the	DET
aiti-4099	191	23	comparison	comparison	NOUN
aiti-4099	191	24	is	be	AUX
aiti-4099	191	25	carried	carry	VERB
aiti-4099	191	26	out	out	ADP
aiti-4099	191	27	for	for	ADP
aiti-4099	191	28	the	the	DET
aiti-4099	191	29	static	static	ADJ
aiti-4099	191	30	bending	bending	NOUN
aiti-4099	191	31	of	of	ADP
aiti-4099	191	32	the	the	DET
aiti-4099	191	33	beam	beam	NOUN
aiti-4099	191	34	as	as	SCONJ
aiti-4099	191	35	reported	report	VERB
aiti-4099	191	36	in	in	ADP
aiti-4099	191	37	[	[	X
aiti-4099	191	38	13	13	NUM
aiti-4099	191	39	]	]	PUNCT
aiti-4099	191	40	.	.	PUNCT
aiti-4099	192	1	table	table	NOUN
aiti-4099	192	2	1	1	NUM
aiti-4099	192	3	compares	compare	VERB
aiti-4099	192	4	the	the	DET
aiti-4099	192	5	maximum	maximum	ADJ
aiti-4099	192	6	dimensionless	dimensionless	NOUN
aiti-4099	192	7	deflection	deflection	NOUN
aiti-4099	192	8	of	of	ADP
aiti-4099	192	9	the	the	DET
aiti-4099	192	10	simply	simply	ADV
aiti-4099	192	11	supported	support	VERB
aiti-4099	192	12	beam	beam	NOUN
aiti-4099	192	13	(	(	PUNCT
aiti-4099	192	14	ss	ss	NOUN
aiti-4099	192	15	beam	beam	NOUN
aiti-4099	192	16	)	)	PUNCT
aiti-4099	192	17	under	under	ADP
aiti-4099	192	18	uniform	uniform	NOUN
aiti-4099	192	19	distributed	distribute	VERB
aiti-4099	192	20	load	load	NOUN
aiti-4099	192	21	q0	q0	PROPN
aiti-4099	192	22	obtained	obtain	VERB
aiti-4099	192	23	by	by	ADP
aiti-4099	192	24	the	the	DET
aiti-4099	192	25	present	present	ADJ
aiti-4099	192	26	finite	finite	PROPN
aiti-4099	192	27	element	element	NOUN
aiti-4099	192	28	formulation	formulation	NOUN
aiti-4099	192	29	with	with	ADP
aiti-4099	192	30	that	that	PRON
aiti-4099	192	31	of	of	ADP
aiti-4099	192	32	karamanli	karamanli	PROPN
aiti-4099	193	1	[	[	X
aiti-4099	193	2	13	13	NUM
aiti-4099	193	3	]	]	PUNCT
aiti-4099	193	4	using	use	VERB
aiti-4099	193	5	the	the	DET
aiti-4099	193	6	symmetric	symmetric	ADJ
aiti-4099	193	7	smoothed	smooth	VERB
aiti-4099	193	8	particle	particle	NOUN
aiti-4099	193	9	hydrodynamics	hydrodynamic	NOUN
aiti-4099	193	10	method	method	NOUN
aiti-4099	193	11	.	.	PUNCT
aiti-4099	194	1	regardless	regardless	ADV
aiti-4099	194	2	of	of	ADP
aiti-4099	194	3	the	the	DET
aiti-4099	194	4	grading	grade	VERB
aiti-4099	194	5	indexes	index	NOUN
aiti-4099	194	6	,	,	PUNCT
aiti-4099	194	7	the	the	DET
aiti-4099	194	8	layer	layer	NOUN
aiti-4099	194	9	thickness	thickness	NOUN
aiti-4099	194	10	ratio	ratio	NOUN
aiti-4099	194	11	and	and	CCONJ
aiti-4099	194	12	the	the	DET
aiti-4099	194	13	aspect	aspect	NOUN
aiti-4099	194	14	ratio	ratio	NOUN
aiti-4099	194	15	,	,	PUNCT
aiti-4099	194	16	the	the	DET
aiti-4099	194	17	maximum	maximum	ADJ
aiti-4099	194	18	deflection	deflection	NOUN
aiti-4099	194	19	of	of	ADP
aiti-4099	194	20	the	the	DET
aiti-4099	194	21	beam	beam	NOUN
aiti-4099	194	22	obtained	obtain	VERB
aiti-4099	194	23	in	in	ADP
aiti-4099	194	24	the	the	DET
aiti-4099	194	25	present	present	ADJ
aiti-4099	194	26	paper	paper	NOUN
aiti-4099	194	27	is	be	AUX
aiti-4099	194	28	in	in	ADP
aiti-4099	194	29	good	good	ADJ
aiti-4099	194	30	agreement	agreement	NOUN
aiti-4099	194	31	with	with	ADP
aiti-4099	194	32	that	that	PRON
aiti-4099	194	33	of	of	ADP
aiti-4099	194	34	ref	ref	NOUN
aiti-4099	194	35	.	.	PUNCT
aiti-4099	195	1	[	[	X
aiti-4099	195	2	13	13	NUM
aiti-4099	195	3	]	]	PUNCT
aiti-4099	195	4	.	.	PUNCT
aiti-4099	196	1	the	the	DET
aiti-4099	196	2	dimensionless	dimensionless	NOUN
aiti-4099	196	3	deflection	deflection	NOUN
aiti-4099	196	4	in	in	ADP
aiti-4099	196	5	table	table	NOUN
aiti-4099	196	6	1	1	NUM
aiti-4099	196	7	is	be	AUX
aiti-4099	196	8	defined	define	VERB
aiti-4099	196	9	as	as	SCONJ
aiti-4099	196	10	follows	follow	VERB
aiti-4099	196	11	[	[	X
aiti-4099	196	12	13	13	NUM
aiti-4099	196	13	]	]	X
aiti-4099	196	14			NOUN
aiti-4099	196	15			PROPN
aiti-4099	196	16	3	3	NUM
aiti-4099	196	17	*	*	SYM
aiti-4099	196	18	4	4	NUM
aiti-4099	196	19	0	0	NUM
aiti-4099	196	20	100	100	NUM
aiti-4099	196	21	max	max	NOUN
aiti-4099	196	22	(	(	PUNCT
aiti-4099	196	23	)	)	PUNCT
aiti-4099	196	24	me	i	PRON
aiti-4099	197	1	bh	bh	PROPN
aiti-4099	197	2	w	w	PROPN
aiti-4099	197	3	w	w	PROPN
aiti-4099	197	4	x	x	X
aiti-4099	197	5	q	q	X
aiti-4099	197	6	l	l	NOUN
aiti-4099	197	7			NUM
aiti-4099	197	8	(	(	PUNCT
aiti-4099	197	9	29	29	NUM
aiti-4099	197	10	)	)	PUNCT
aiti-4099	197	11	where	where	SCONJ
aiti-4099	197	12	em	em	PRON
aiti-4099	197	13	is	be	AUX
aiti-4099	197	14	young	young	ADJ
aiti-4099	197	15	’s	’s	PART
aiti-4099	197	16	modulus	modulus	NOUN
aiti-4099	197	17	of	of	ADP
aiti-4099	197	18	metal	metal	NOUN
aiti-4099	197	19	.	.	PUNCT
aiti-4099	198	1	advances	advance	NOUN
aiti-4099	198	2	in	in	ADP
aiti-4099	198	3	technology	technology	NOUN
aiti-4099	198	4	innovation	innovation	NOUN
aiti-4099	198	5	,	,	PUNCT
aiti-4099	198	6	vol	vol	NOUN
aiti-4099	198	7	.	.	PROPN
aiti-4099	199	1	4	4	NUM
aiti-4099	199	2	,	,	PUNCT
aiti-4099	199	3	no	no	INTJ
aiti-4099	199	4	.	.	NOUN
aiti-4099	199	5	3	3	NUM
aiti-4099	199	6	,	,	PUNCT
aiti-4099	199	7	2019	2019	NUM
aiti-4099	199	8	,	,	PUNCT
aiti-4099	199	9	pp	pp	ADJ
aiti-4099	199	10	.	.	PUNCT
aiti-4099	200	1	152	152	NUM
aiti-4099	200	2	-	-	SYM
aiti-4099	200	3	164	164	NUM
aiti-4099	200	4	159	159	NUM
aiti-4099	200	5	table	table	NOUN
aiti-4099	200	6	1	1	NUM
aiti-4099	200	7	comparison	comparison	NOUN
aiti-4099	200	8	of	of	ADP
aiti-4099	200	9	maximum	maximum	ADJ
aiti-4099	200	10	dimensionless	dimensionless	NOUN
aiti-4099	200	11	deflection	deflection	NOUN
aiti-4099	200	12	(	(	PUNCT
aiti-4099	200	13	*	*	NOUN
aiti-4099	200	14	w	w	NOUN
aiti-4099	200	15	)	)	PUNCT
aiti-4099	200	16	of	of	ADP
aiti-4099	200	17	ss	ss	PROPN
aiti-4099	200	18	beam	beam	NOUN
aiti-4099	200	19	under	under	ADP
aiti-4099	200	20	static	static	ADJ
aiti-4099	200	21	uniform	uniform	NOUN
aiti-4099	200	22	load	load	VERB
aiti-4099	200	23	nx	nx	PROPN
aiti-4099	200	24	nz	nz	PROPN
aiti-4099	200	25	source	source	PROPN
aiti-4099	200	26	l	l	PROPN
aiti-4099	200	27	/	/	SYM
aiti-4099	200	28	h	h	NOUN
aiti-4099	200	29	=	=	SYM
aiti-4099	200	30	5	5	NUM
aiti-4099	200	31	l	l	NOUN
aiti-4099	200	32	/	/	SYM
aiti-4099	200	33	h=20	h=20	NOUN
aiti-4099	200	34	1	1	NUM
aiti-4099	200	35	-	-	SYM
aiti-4099	200	36	1	1	NUM
aiti-4099	200	37	-	-	SYM
aiti-4099	200	38	1	1	NUM
aiti-4099	200	39	1	1	NUM
aiti-4099	200	40	-	-	SYM
aiti-4099	200	41	8	8	NUM
aiti-4099	200	42	-	-	SYM
aiti-4099	200	43	1	1	NUM
aiti-4099	200	44	2	2	NUM
aiti-4099	200	45	-	-	SYM
aiti-4099	200	46	2	2	NUM
aiti-4099	200	47	-	-	SYM
aiti-4099	200	48	1	1	NUM
aiti-4099	200	49	1	1	NUM
aiti-4099	200	50	-	-	SYM
aiti-4099	200	51	1	1	NUM
aiti-4099	200	52	-	-	SYM
aiti-4099	200	53	1	1	NUM
aiti-4099	200	54	1	1	NUM
aiti-4099	200	55	-	-	SYM
aiti-4099	200	56	8	8	NUM
aiti-4099	200	57	-	-	SYM
aiti-4099	200	58	1	1	NUM
aiti-4099	200	59	2	2	NUM
aiti-4099	200	60	-	-	SYM
aiti-4099	200	61	2	2	NUM
aiti-4099	200	62	-	-	SYM
aiti-4099	200	63	1	1	NUM
aiti-4099	200	64	0.1	0.1	NUM
aiti-4099	200	65	0.1	0.1	NUM
aiti-4099	200	66	ref	ref	NOUN
aiti-4099	200	67	.	.	PUNCT
aiti-4099	201	1	[	[	X
aiti-4099	201	2	13	13	NUM
aiti-4099	201	3	]	]	SYM
aiti-4099	201	4	10.7054	10.7054	NUM
aiti-4099	201	5	4.7401	4.7401	NUM
aiti-4099	201	6	10.9470	10.9470	NUM
aiti-4099	201	7	10.3994	10.3994	NUM
aiti-4099	201	8	4.4818	4.4818	NUM
aiti-4099	201	9	9.1047	9.1047	NUM
aiti-4099	201	10	present	present	ADJ
aiti-4099	201	11	10.8634	10.8634	NUM
aiti-4099	201	12	4.8064	4.8064	NUM
aiti-4099	201	13	9.4128	9.4128	NUM
aiti-4099	201	14	10.4116	10.4116	NUM
aiti-4099	201	15	4.4848	4.4848	NUM
aiti-4099	201	16	9.1096	9.1096	NUM
aiti-4099	201	17	0.5	0.5	NUM
aiti-4099	201	18	ref	ref	NOUN
aiti-4099	201	19	.	.	PUNCT
aiti-4099	202	1	[	[	X
aiti-4099	202	2	13	13	NUM
aiti-4099	202	3	]	]	SYM
aiti-4099	202	4	7.5039	7.5039	NUM
aiti-4099	202	5	4.2112	4.2112	NUM
aiti-4099	202	6	9.5412	9.5412	NUM
aiti-4099	202	7	7.2199	7.2199	NUM
aiti-4099	202	8	3.9561	3.9561	NUM
aiti-4099	202	9	6.5597	6.5597	NUM
aiti-4099	202	10	present	present	ADJ
aiti-4099	202	11	7.6124	7.6124	NUM
aiti-4099	202	12	4.2698	4.2698	NUM
aiti-4099	202	13	6.8473	6.8473	NUM
aiti-4099	202	14	7.2273	7.2273	NUM
aiti-4099	202	15	3.9586	3.9586	NUM
aiti-4099	202	16	6.5680	6.5680	NUM
aiti-4099	202	17	1	1	NUM
aiti-4099	202	18	ref	ref	NOUN
aiti-4099	202	19	.	.	PUNCT
aiti-4099	203	1	[	[	X
aiti-4099	203	2	13	13	NUM
aiti-4099	203	3	]	]	PUNCT
aiti-4099	203	4	6.0343	6.0343	NUM
aiti-4099	203	5	3.9030	3.9030	NUM
aiti-4099	203	6	6.9428	6.9428	NUM
aiti-4099	203	7	5.7613	5.7613	NUM
aiti-4099	203	8	3.6501	3.6501	NUM
aiti-4099	203	9	5.3608	5.3608	NUM
aiti-4099	203	10	present	present	VERB
aiti-4099	203	11	6.1185	6.1185	NUM
aiti-4099	203	12	3.9570	3.9570	NUM
aiti-4099	203	13	5.6327	5.6327	NUM
aiti-4099	203	14	5.7667	5.7667	NUM
aiti-4099	203	15	3.6525	3.6525	NUM
aiti-4099	203	16	5.3658	5.3658	NUM
aiti-4099	203	17	2	2	NUM
aiti-4099	203	18	ref	ref	NOUN
aiti-4099	203	19	.	.	PUNCT
aiti-4099	204	1	[	[	X
aiti-4099	204	2	13	13	NUM
aiti-4099	204	3	]	]	PUNCT
aiti-4099	204	4	4.8871	4.8871	NUM
aiti-4099	204	5	3.6275	3.6275	NUM
aiti-4099	204	6	4.6673	4.6673	NUM
aiti-4099	204	7	4.6274	4.6274	NUM
aiti-4099	204	8	3.3772	3.3772	NUM
aiti-4099	204	9	4.4070	4.4070	NUM
aiti-4099	204	10	present	present	ADJ
aiti-4099	204	11	4.9572	4.9572	NUM
aiti-4099	204	12	3.6775	3.6775	NUM
aiti-4099	204	13	4.7321	4.7321	NUM
aiti-4099	204	14	4.6313	4.6313	NUM
aiti-4099	204	15	3.3793	3.3793	NUM
aiti-4099	204	16	4.4101	4.4101	NUM
aiti-4099	204	17	0.5	0.5	NUM
aiti-4099	204	18	0.1	0.1	NUM
aiti-4099	204	19	ref	ref	NOUN
aiti-4099	204	20	.	.	PUNCT
aiti-4099	205	1	[	[	X
aiti-4099	205	2	13	13	NUM
aiti-4099	205	3	]	]	SYM
aiti-4099	205	4	8.4793	8.4793	NUM
aiti-4099	205	5	4.4862	4.4862	NUM
aiti-4099	205	6	5.7112	5.7112	NUM
aiti-4099	205	7	8.1706	8.1706	NUM
aiti-4099	205	8	4.4143	4.4143	NUM
aiti-4099	205	9	7.3680	7.3680	NUM
aiti-4099	205	10	present	present	VERB
aiti-4099	205	11	8.6148	8.6148	NUM
aiti-4099	205	12	4.5492	4.5492	NUM
aiti-4099	205	13	7.6764	7.6764	NUM
aiti-4099	205	14	8.1964	8.1964	NUM
aiti-4099	205	15	4.2298	4.2298	NUM
aiti-4099	205	16	7.3839	7.3839	NUM
aiti-4099	205	17	0.5	0.5	NUM
aiti-4099	205	18	ref	ref	NOUN
aiti-4099	205	19	.	.	PUNCT
aiti-4099	206	1	[	[	X
aiti-4099	206	2	13	13	NUM
aiti-4099	206	3	]	]	PUNCT
aiti-4099	206	4	6.5069	6.5069	NUM
aiti-4099	206	5	4.0580	4.0580	NUM
aiti-4099	206	6	7.7882	7.7882	NUM
aiti-4099	206	7	6.2253	6.2253	NUM
aiti-4099	206	8	4.2331	4.2331	NUM
aiti-4099	206	9	5.7569	5.7569	NUM
aiti-4099	206	10	present	present	ADJ
aiti-4099	206	11	6.6011	6.6011	NUM
aiti-4099	206	12	4.1143	4.1143	NUM
aiti-4099	206	13	6.0408	6.0408	NUM
aiti-4099	206	14	6.2338	6.2338	NUM
aiti-4099	206	15	3.8040	3.8040	NUM
aiti-4099	206	16	5.7660	5.7660	NUM
aiti-4099	206	17	1	1	NUM
aiti-4099	206	18	ref	ref	NOUN
aiti-4099	206	19	.	.	PUNCT
aiti-4099	207	1	[	[	X
aiti-4099	207	2	13	13	NUM
aiti-4099	207	3	]	]	SYM
aiti-4099	207	4	5.4735	5.4735	NUM
aiti-4099	207	5	3.8004	3.8004	NUM
aiti-4099	207	6	6.1257	6.1257	NUM
aiti-4099	207	7	5.2055	5.2055	NUM
aiti-4099	207	8	3.8068	3.8068	NUM
aiti-4099	207	9	4.9004	4.9004	NUM
aiti-4099	207	10	present	present	ADJ
aiti-4099	207	11	5.5523	5.5523	NUM
aiti-4099	207	12	3.8534	3.8534	NUM
aiti-4099	207	13	5.1692	5.1692	NUM
aiti-4099	207	14	5.2114	5.2114	NUM
aiti-4099	207	15	3.5490	3.5490	NUM
aiti-4099	207	16	4.9064	4.9064	NUM
aiti-4099	207	17	2	2	NUM
aiti-4099	207	18	ref	ref	NOUN
aiti-4099	207	19	.	.	PUNCT
aiti-4099	208	1	[	[	X
aiti-4099	208	2	13	13	NUM
aiti-4099	208	3	]	]	SYM
aiti-4099	208	4	4.6040	4.6040	NUM
aiti-4099	208	5	3.5666	3.5666	NUM
aiti-4099	208	6	4.4251	4.4251	NUM
aiti-4099	208	7	4.3451	4.3451	NUM
aiti-4099	208	8	3.3169	3.3169	NUM
aiti-4099	208	9	4.1669	4.1669	NUM
aiti-4099	208	10	present	present	ADJ
aiti-4099	208	11	4.6689	4.6689	NUM
aiti-4099	208	12	3.6155	3.6155	NUM
aiti-4099	208	13	4.4873	4.4873	NUM
aiti-4099	208	14	4.3491	4.3491	NUM
aiti-4099	208	15	3.3190	3.3190	NUM
aiti-4099	208	16	4.1706	4.1706	NUM
aiti-4099	208	17	1	1	NUM
aiti-4099	208	18	0.1	0.1	NUM
aiti-4099	208	19	ref	ref	NOUN
aiti-4099	208	20	.	.	PUNCT
aiti-4099	209	1	[	[	X
aiti-4099	209	2	13	13	NUM
aiti-4099	209	3	]	]	PUNCT
aiti-4099	209	4	6.9827	6.9827	NUM
aiti-4099	209	5	4.2462	4.2462	NUM
aiti-4099	209	6	6.4602	6.4602	NUM
aiti-4099	209	7	6.6753	6.6753	NUM
aiti-4099	209	8	3.5515	3.5515	NUM
aiti-4099	209	9	6.1562	6.1562	NUM
aiti-4099	209	10	present	present	ADJ
aiti-4099	209	11	7.0975	7.0975	NUM
aiti-4099	209	12	4.3050	4.3050	NUM
aiti-4099	209	13	6.5600	6.5600	NUM
aiti-4099	209	14	6.7054	6.7054	NUM
aiti-4099	209	15	3.9922	3.9922	NUM
aiti-4099	209	16	6.1781	6.1781	NUM
aiti-4099	209	17	0.5	0.5	NUM
aiti-4099	209	18	ref	ref	NOUN
aiti-4099	209	19	.	.	PUNCT
aiti-4099	210	1	[	[	X
aiti-4099	210	2	13	13	NUM
aiti-4099	210	3	]	]	PUNCT
aiti-4099	210	4	5.7178	5.7178	NUM
aiti-4099	210	5	3.9088	3.9088	NUM
aiti-4099	210	6	5.3861	5.3861	NUM
aiti-4099	210	7	5.4388	5.4388	NUM
aiti-4099	210	8	3.9943	3.9943	NUM
aiti-4099	210	9	5.1050	5.1050	NUM
aiti-4099	210	10	present	present	ADJ
aiti-4099	210	11	5.8019	5.8019	NUM
aiti-4099	210	12	3.9608	3.9608	NUM
aiti-4099	210	13	5.4616	5.4616	NUM
aiti-4099	210	14	5.4499	5.4499	NUM
aiti-4099	210	15	3.6551	3.6551	NUM
aiti-4099	210	16	5.1153	5.1153	NUM
aiti-4099	210	17	1	1	NUM
aiti-4099	210	18	ref	ref	NOUN
aiti-4099	210	19	.	.	PUNCT
aiti-4099	211	1	[	[	X
aiti-4099	211	2	13	13	NUM
aiti-4099	211	3	]	]	PUNCT
aiti-4099	211	4	4.9904	4.9904	NUM
aiti-4099	211	5	3.6976	3.6976	NUM
aiti-4099	211	6	4.7624	4.7624	NUM
aiti-4099	211	7	4.7252	4.7252	NUM
aiti-4099	211	8	3.6570	3.6570	NUM
aiti-4099	211	9	4.4948	4.4948	NUM
aiti-4099	211	10	present	present	ADJ
aiti-4099	211	11	5.0598	5.0598	NUM
aiti-4099	211	12	3.7487	3.7487	NUM
aiti-4099	211	13	4.8272	4.8272	NUM
aiti-4099	211	14	4.7288	4.7288	NUM
aiti-4099	211	15	3.4477	3.4477	NUM
aiti-4099	211	16	4.5000	4.5000	NUM
aiti-4099	211	17	2	2	NUM
aiti-4099	211	18	ref	ref	NOUN
aiti-4099	211	19	.	.	PUNCT
aiti-4099	212	1	[	[	X
aiti-4099	212	2	13	13	NUM
aiti-4099	212	3	]	]	SYM
aiti-4099	212	4	4.3387	4.3387	NUM
aiti-4099	213	1	3.5031	3.5031	NUM
aiti-4099	213	2	4.1978	4.1978	NUM
aiti-4099	213	3	4.0816	4.0816	NUM
aiti-4099	213	4	3.2549	3.2549	NUM
aiti-4099	213	5	3.9396	3.9396	NUM
aiti-4099	213	6	present	present	NOUN
aiti-4099	213	7	4.3982	4.3982	NUM
aiti-4099	213	8	3.5514	3.5514	NUM
aiti-4099	213	9	4.2549	4.2549	NUM
aiti-4099	213	10	4.0843	4.0843	NUM
aiti-4099	213	11	3.2566	3.2566	NUM
aiti-4099	213	12	3.9434	3.9434	NUM
aiti-4099	213	13	4.2	4.2	NUM
aiti-4099	213	14	.	.	PUNCT
aiti-4099	214	1	free	free	ADJ
aiti-4099	214	2	vibration	vibration	NOUN
aiti-4099	214	3	the	the	DET
aiti-4099	214	4	fundamental	fundamental	ADJ
aiti-4099	214	5	frequency	frequency	NOUN
aiti-4099	214	6	parameters	parameter	NOUN
aiti-4099	214	7	of	of	ADP
aiti-4099	214	8	the	the	DET
aiti-4099	214	9	ss	ss	PROPN
aiti-4099	214	10	beam	beam	NOUN
aiti-4099	214	11	are	be	AUX
aiti-4099	214	12	listed	list	VERB
aiti-4099	214	13	in	in	ADP
aiti-4099	214	14	tables	table	NOUN
aiti-4099	214	15	2	2	NUM
aiti-4099	214	16	and	and	CCONJ
aiti-4099	214	17	3	3	NUM
aiti-4099	214	18	for	for	ADP
aiti-4099	214	19	various	various	ADJ
aiti-4099	214	20	values	value	NOUN
aiti-4099	214	21	of	of	ADP
aiti-4099	214	22	the	the	DET
aiti-4099	214	23	grading	grade	VERB
aiti-4099	214	24	indexes	index	NOUN
aiti-4099	214	25	and	and	CCONJ
aiti-4099	214	26	the	the	DET
aiti-4099	214	27	layer	layer	NOUN
aiti-4099	214	28	thickness	thickness	NOUN
aiti-4099	214	29	ratio	ratio	NOUN
aiti-4099	214	30	and	and	CCONJ
aiti-4099	214	31	two	two	NUM
aiti-4099	214	32	value	value	NOUN
aiti-4099	214	33	of	of	ADP
aiti-4099	214	34	the	the	DET
aiti-4099	214	35	aspect	aspect	NOUN
aiti-4099	214	36	ratio	ratio	NOUN
aiti-4099	214	37	,	,	PUNCT
aiti-4099	214	38	l	l	NOUN
aiti-4099	214	39	/	/	SYM
aiti-4099	214	40	h=5	h=5	PROPN
aiti-4099	214	41	and	and	CCONJ
aiti-4099	214	42	l	l	NOUN
aiti-4099	214	43	/	/	SYM
aiti-4099	214	44	h=20	h=20	NOUN
aiti-4099	214	45	,	,	PUNCT
aiti-4099	214	46	respectively	respectively	ADV
aiti-4099	214	47	.	.	PUNCT
aiti-4099	215	1	the	the	DET
aiti-4099	215	2	frequency	frequency	NOUN
aiti-4099	215	3	parameters	parameter	NOUN
aiti-4099	215	4	in	in	ADP
aiti-4099	215	5	the	the	DET
aiti-4099	215	6	tables	table	NOUN
aiti-4099	215	7	(	(	PUNCT
aiti-4099	215	8	and	and	CCONJ
aiti-4099	215	9	below	below	ADV
aiti-4099	215	10	)	)	PUNCT
aiti-4099	215	11	are	be	AUX
aiti-4099	215	12	defined	define	VERB
aiti-4099	215	13	as	as	SCONJ
aiti-4099	215	14	follows	follow	VERB
aiti-4099	215	15	2	2	NUM
aiti-4099	216	1	i	i	PRON
aiti-4099	216	2	m	m	VERB
aiti-4099	216	3	i	i	NOUN
aiti-4099	216	4	m	m	VERB
aiti-4099	216	5	l	l	NOUN
aiti-4099	216	6	h	h	NOUN
aiti-4099	217	1	e	e	X
aiti-4099	217	2			X
aiti-4099	217	3			ADP
aiti-4099	217	4			NOUN
aiti-4099	217	5			NUM
aiti-4099	217	6	(	(	PUNCT
aiti-4099	217	7	30	30	NUM
aiti-4099	217	8	)	)	PUNCT
aiti-4099	217	9	where	where	SCONJ
aiti-4099	217	10	ωi	ωi	PROPN
aiti-4099	217	11	is	be	AUX
aiti-4099	217	12	the	the	DET
aiti-4099	217	13	i	i	NOUN
aiti-4099	217	14	th	th	X
aiti-4099	217	15	natural	natural	ADJ
aiti-4099	217	16	frequency	frequency	NOUN
aiti-4099	217	17	of	of	ADP
aiti-4099	217	18	the	the	DET
aiti-4099	217	19	beam	beam	NOUN
aiti-4099	217	20	.	.	PUNCT
aiti-4099	217	21	table	table	NOUN
aiti-4099	217	22	2	2	NUM
aiti-4099	217	23	fundamental	fundamental	ADJ
aiti-4099	217	24	frequency	frequency	NOUN
aiti-4099	217	25	parameter	parameter	NOUN
aiti-4099	217	26	(	(	PUNCT
aiti-4099	217	27	μ1	μ1	NOUN
aiti-4099	217	28	)	)	PUNCT
aiti-4099	217	29	of	of	ADP
aiti-4099	217	30	ss	ss	PROPN
aiti-4099	217	31	beam	beam	NOUN
aiti-4099	217	32	with	with	ADP
aiti-4099	217	33	l	l	PROPN
aiti-4099	217	34	/	/	SYM
aiti-4099	217	35	h	h	NOUN
aiti-4099	217	36	=	=	SYM
aiti-4099	217	37	5	5	NUM
aiti-4099	217	38	nx	nx	NUM
aiti-4099	217	39	nz	nz	PROPN
aiti-4099	217	40	1	1	NUM
aiti-4099	217	41	-	-	SYM
aiti-4099	217	42	0	0	NUM
aiti-4099	217	43	-	-	SYM
aiti-4099	217	44	1	1	NUM
aiti-4099	217	45	2	2	NUM
aiti-4099	217	46	-	-	SYM
aiti-4099	217	47	1	1	NUM
aiti-4099	217	48	-	-	SYM
aiti-4099	217	49	2	2	NUM
aiti-4099	217	50	1	1	NUM
aiti-4099	217	51	-	-	SYM
aiti-4099	217	52	1	1	NUM
aiti-4099	217	53	-	-	SYM
aiti-4099	217	54	1	1	NUM
aiti-4099	217	55	1	1	NUM
aiti-4099	217	56	-	-	SYM
aiti-4099	217	57	2	2	NUM
aiti-4099	217	58	-	-	SYM
aiti-4099	217	59	1	1	NUM
aiti-4099	217	60	1	1	NUM
aiti-4099	217	61	-	-	SYM
aiti-4099	217	62	8	8	NUM
aiti-4099	217	63	-	-	SYM
aiti-4099	217	64	1	1	NUM
aiti-4099	217	65	2	2	NUM
aiti-4099	217	66	-	-	SYM
aiti-4099	217	67	2	2	NUM
aiti-4099	217	68	-	-	SYM
aiti-4099	217	69	1	1	NUM
aiti-4099	217	70	0	0	NUM
aiti-4099	217	71	0.5	0.5	NUM
aiti-4099	217	72	3.2500	3.2500	NUM
aiti-4099	217	73	3.3728	3.3728	NUM
aiti-4099	217	74	3.5186	3.5186	NUM
aiti-4099	217	75	3.7904	3.7904	NUM
aiti-4099	217	76	4.5227	4.5227	NUM
aiti-4099	217	77	3.7057	3.7057	NUM
aiti-4099	217	78	1	1	NUM
aiti-4099	217	79	3.5735	3.5735	NUM
aiti-4099	217	80	3.7297	3.7297	NUM
aiti-4099	217	81	3.8755	3.8755	NUM
aiti-4099	217	82	4.1105	4.1105	NUM
aiti-4099	217	83	4.6795	4.6795	NUM
aiti-4099	217	84	4.0189	4.0189	NUM
aiti-4099	217	85	5	5	NUM
aiti-4099	217	86	4.4615	4.4615	NUM
aiti-4099	217	87	4.5756	4.5756	NUM
aiti-4099	217	88	4.6582	4.6582	NUM
aiti-4099	217	89	4.7690	4.7690	NUM
aiti-4099	217	90	4.9899	4.9899	NUM
aiti-4099	217	91	4.7106	4.7106	NUM
aiti-4099	217	92	0.5	0.5	NUM
aiti-4099	217	93	0.5	0.5	NUM
aiti-4099	217	94	3.6300	3.6300	NUM
aiti-4099	217	95	3.7134	3.7134	NUM
aiti-4099	217	96	3.8194	3.8194	NUM
aiti-4099	217	97	4.0263	4.0263	NUM
aiti-4099	217	98	4.6176	4.6176	NUM
aiti-4099	218	1	3.9640	3.9640	NUM
aiti-4099	218	2	1	1	NUM
aiti-4099	218	3	3.8648	3.8648	NUM
aiti-4099	218	4	3.9816	3.9816	NUM
aiti-4099	218	5	4.0942	4.0942	NUM
aiti-4099	218	6	4.2804	4.2804	NUM
aiti-4099	218	7	4.7489	4.7489	NUM
aiti-4099	218	8	4.2086	4.2086	NUM
aiti-4099	218	9	5	5	NUM
aiti-4099	218	10	4.5673	4.5673	NUM
aiti-4099	218	11	4.6620	4.6620	NUM
aiti-4099	218	12	4.7311	4.7311	NUM
aiti-4099	218	13	4.8245	4.8245	NUM
aiti-4099	218	14	5.0125	5.0125	NUM
aiti-4099	218	15	4.7753	4.7753	NUM
aiti-4099	218	16	1	1	NUM
aiti-4099	218	17	0.5	0.5	NUM
aiti-4099	218	18	3.8922	3.8922	NUM
aiti-4099	218	19	3.9549	3.9549	NUM
aiti-4099	218	20	4.0378	4.0378	NUM
aiti-4099	218	21	4.2037	4.2037	NUM
aiti-4099	218	22	4.6942	4.6942	NUM
aiti-4099	218	23	4.1548	4.1548	NUM
aiti-4099	218	24	1	1	NUM
aiti-4099	218	25	4.0761	4.0761	NUM
aiti-4099	218	26	4.1687	4.1687	NUM
aiti-4099	218	27	4.2596	4.2596	NUM
aiti-4099	218	28	4.4123	4.4123	NUM
aiti-4099	218	29	4.8056	4.8056	NUM
aiti-4099	218	30	4.3538	4.3538	NUM
aiti-4099	218	31	5	5	NUM
aiti-4099	218	32	4.6520	4.6520	NUM
aiti-4099	218	33	4.7319	4.7319	NUM
aiti-4099	218	34	4.7906	4.7906	NUM
aiti-4099	218	35	4.8701	4.8701	NUM
aiti-4099	218	36	5.0315	5.0315	NUM
aiti-4099	218	37	4.8282	4.8282	NUM
aiti-4099	218	38	2	2	NUM
aiti-4099	218	39	0.5	0.5	NUM
aiti-4099	218	40	4.2427	4.2427	NUM
aiti-4099	218	41	4.2840	4.2840	NUM
aiti-4099	218	42	4.3402	4.3402	NUM
aiti-4099	218	43	4.4556	4.4556	NUM
aiti-4099	218	44	4.8093	4.8093	NUM
aiti-4099	218	45	4.4223	4.4223	NUM
aiti-4099	218	46	1	1	NUM
aiti-4099	218	47	4.3679	4.3679	NUM
aiti-4099	218	48	4.4318	4.4318	NUM
aiti-4099	218	49	4.4956	4.4956	NUM
aiti-4099	218	50	4.6043	4.6043	NUM
aiti-4099	218	51	4.8918	4.8918	NUM
aiti-4099	218	52	4.5629	4.5629	NUM
aiti-4099	218	53	5	5	NUM
aiti-4099	218	54	4.7785	4.7785	NUM
aiti-4099	218	55	4.8373	4.8373	NUM
aiti-4099	218	56	4.8807	4.8807	NUM
aiti-4099	218	57	4.9398	4.9398	NUM
aiti-4099	218	58	5.0609	5.0609	NUM
aiti-4099	218	59	4.9087	4.9087	NUM
aiti-4099	218	60	5	5	NUM
aiti-4099	218	61	0.5	0.5	NUM
aiti-4099	218	62	4.2427	4.2427	NUM
aiti-4099	218	63	4.2840	4.2840	NUM
aiti-4099	218	64	4.3402	4.3402	NUM
aiti-4099	218	65	4.4556	4.4556	NUM
aiti-4099	218	66	4.8093	4.8093	NUM
aiti-4099	218	67	4.4223	4.4223	NUM
aiti-4099	218	68	1	1	NUM
aiti-4099	218	69	4.3679	4.3679	NUM
aiti-4099	218	70	4.4318	4.4318	NUM
aiti-4099	218	71	4.4956	4.4956	NUM
aiti-4099	218	72	4.6043	4.6043	NUM
aiti-4099	218	73	4.8918	4.8918	NUM
aiti-4099	218	74	4.5629	4.5629	NUM
aiti-4099	218	75	5	5	NUM
aiti-4099	218	76	4.7785	4.7785	NUM
aiti-4099	218	77	4.8373	4.8373	NUM
aiti-4099	218	78	4.8807	4.8807	NUM
aiti-4099	218	79	4.9398	4.9398	NUM
aiti-4099	218	80	5.0609	5.0609	NUM
aiti-4099	218	81	4.9087	4.9087	NUM
aiti-4099	218	82	the	the	DET
aiti-4099	218	83	effects	effect	NOUN
aiti-4099	218	84	of	of	ADP
aiti-4099	218	85	the	the	DET
aiti-4099	218	86	grading	grade	VERB
aiti-4099	218	87	indexes	index	NOUN
aiti-4099	218	88	and	and	CCONJ
aiti-4099	218	89	the	the	DET
aiti-4099	218	90	layer	layer	NOUN
aiti-4099	218	91	thickness	thickness	NOUN
aiti-4099	218	92	ratio	ratio	NOUN
aiti-4099	218	93	on	on	ADP
aiti-4099	218	94	the	the	DET
aiti-4099	218	95	frequency	frequency	NOUN
aiti-4099	218	96	of	of	ADP
aiti-4099	218	97	the	the	DET
aiti-4099	218	98	beam	beam	NOUN
aiti-4099	218	99	are	be	AUX
aiti-4099	218	100	clearly	clearly	ADV
aiti-4099	218	101	seen	see	VERB
aiti-4099	218	102	from	from	ADP
aiti-4099	218	103	tables	table	NOUN
aiti-4099	218	104	2	2	NUM
aiti-4099	218	105	and	and	CCONJ
aiti-4099	218	106	3	3	NUM
aiti-4099	218	107	.	.	X
aiti-4099	218	108	for	for	ADP
aiti-4099	218	109	a	a	DET
aiti-4099	218	110	given	give	VERB
aiti-4099	218	111	value	value	NOUN
aiti-4099	218	112	of	of	ADP
aiti-4099	218	113	the	the	DET
aiti-4099	218	114	layer	layer	NOUN
aiti-4099	218	115	thickness	thickness	NOUN
aiti-4099	218	116	ratio	ratio	NOUN
aiti-4099	218	117	,	,	PUNCT
aiti-4099	218	118	the	the	DET
aiti-4099	218	119	frequency	frequency	NOUN
aiti-4099	218	120	parameter	parameter	NOUN
aiti-4099	218	121	of	of	ADP
aiti-4099	218	122	the	the	DET
aiti-4099	218	123	beam	beam	NOUN
aiti-4099	218	124	increases	increase	NOUN
aiti-4099	218	125	by	by	ADP
aiti-4099	218	126	the	the	DET
aiti-4099	218	127	increase	increase	NOUN
aiti-4099	218	128	of	of	ADP
aiti-4099	218	129	the	the	DET
aiti-4099	218	130	advances	advance	NOUN
aiti-4099	218	131	in	in	ADP
aiti-4099	218	132	technology	technology	NOUN
aiti-4099	218	133	innovation	innovation	NOUN
aiti-4099	218	134	,	,	PUNCT
aiti-4099	218	135	vol	vol	NOUN
aiti-4099	218	136	.	.	PROPN
aiti-4099	218	137	4	4	NUM
aiti-4099	218	138	,	,	PUNCT
aiti-4099	218	139	no	no	INTJ
aiti-4099	218	140	.	.	NOUN
aiti-4099	218	141	3	3	NUM
aiti-4099	218	142	,	,	PUNCT
aiti-4099	218	143	2019	2019	NUM
aiti-4099	218	144	,	,	PUNCT
aiti-4099	218	145	pp	pp	ADJ
aiti-4099	218	146	.	.	PUNCT
aiti-4099	219	1	152	152	NUM
aiti-4099	219	2	-	-	SYM
aiti-4099	219	3	164	164	NUM
aiti-4099	219	4	160	160	NUM
aiti-4099	219	5	material	material	NOUN
aiti-4099	219	6	grading	grade	VERB
aiti-4099	219	7	indexes	index	NOUN
aiti-4099	219	8	,	,	PUNCT
aiti-4099	219	9	regardless	regardless	ADV
aiti-4099	219	10	of	of	ADP
aiti-4099	219	11	the	the	DET
aiti-4099	219	12	aspect	aspect	NOUN
aiti-4099	219	13	ratio	ratio	NOUN
aiti-4099	219	14	.	.	PUNCT
aiti-4099	220	1	this	this	PRON
aiti-4099	220	2	can	can	AUX
aiti-4099	220	3	be	be	AUX
aiti-4099	220	4	explained	explain	VERB
aiti-4099	220	5	by	by	ADP
aiti-4099	220	6	the	the	DET
aiti-4099	220	7	fact	fact	NOUN
aiti-4099	220	8	that	that	SCONJ
aiti-4099	220	9	the	the	DET
aiti-4099	220	10	volume	volume	NOUN
aiti-4099	220	11	fraction	fraction	NOUN
aiti-4099	220	12	of	of	ADP
aiti-4099	220	13	the	the	DET
aiti-4099	220	14	metal	metal	NOUN
aiti-4099	220	15	,	,	PUNCT
aiti-4099	220	16	as	as	SCONJ
aiti-4099	220	17	seen	see	VERB
aiti-4099	220	18	from	from	ADP
aiti-4099	220	19	eq	eq	PROPN
aiti-4099	220	20	.	.	PUNCT
aiti-4099	221	1	(	(	PUNCT
aiti-4099	221	2	1	1	NUM
aiti-4099	221	3	)	)	PUNCT
aiti-4099	221	4	,	,	PUNCT
aiti-4099	221	5	is	be	AUX
aiti-4099	221	6	lower	low	ADJ
aiti-4099	221	7	,	,	PUNCT
aiti-4099	221	8	and	and	CCONJ
aiti-4099	221	9	thus	thus	ADV
aiti-4099	221	10	the	the	DET
aiti-4099	221	11	ceramic	ceramic	ADJ
aiti-4099	221	12	percentage	percentage	NOUN
aiti-4099	221	13	is	be	AUX
aiti-4099	221	14	larger	large	ADJ
aiti-4099	221	15	for	for	ADP
aiti-4099	221	16	the	the	DET
aiti-4099	221	17	beam	beam	NOUN
aiti-4099	221	18	associated	associate	VERB
aiti-4099	221	19	with	with	ADP
aiti-4099	221	20	higher	high	ADJ
aiti-4099	221	21	indexes	index	NOUN
aiti-4099	221	22	nx	nx	NOUN
aiti-4099	221	23	and	and	CCONJ
aiti-4099	221	24	nz	nz	PROPN
aiti-4099	221	25	.	.	PROPN
aiti-4099	222	1	since	since	SCONJ
aiti-4099	222	2	young	young	PROPN
aiti-4099	222	3	’s	’s	PART
aiti-4099	222	4	modulus	modulus	NOUN
aiti-4099	222	5	of	of	ADP
aiti-4099	222	6	the	the	DET
aiti-4099	222	7	ceramic	ceramic	NOUN
aiti-4099	222	8	is	be	AUX
aiti-4099	222	9	much	much	ADV
aiti-4099	222	10	higher	high	ADJ
aiti-4099	222	11	than	than	ADP
aiti-4099	222	12	that	that	PRON
aiti-4099	222	13	of	of	ADP
aiti-4099	222	14	the	the	DET
aiti-4099	222	15	metal	metal	NOUN
aiti-4099	222	16	,	,	PUNCT
aiti-4099	222	17	the	the	DET
aiti-4099	222	18	rigidities	rigidity	NOUN
aiti-4099	222	19	of	of	ADP
aiti-4099	222	20	the	the	DET
aiti-4099	222	21	beam	beam	NOUN
aiti-4099	222	22	with	with	ADP
aiti-4099	222	23	higher	high	ADJ
aiti-4099	222	24	ceramic	ceramic	ADJ
aiti-4099	222	25	content	content	NOUN
aiti-4099	222	26	are	be	AUX
aiti-4099	222	27	higher	high	ADJ
aiti-4099	222	28	.	.	PUNCT
aiti-4099	223	1	the	the	DET
aiti-4099	223	2	mass	mass	ADJ
aiti-4099	223	3	density	density	NOUN
aiti-4099	223	4	of	of	ADP
aiti-4099	223	5	the	the	DET
aiti-4099	223	6	beam	beam	NOUN
aiti-4099	223	7	with	with	ADP
aiti-4099	223	8	a	a	DET
aiti-4099	223	9	higher	high	ADJ
aiti-4099	223	10	ceramic	ceramic	ADJ
aiti-4099	223	11	content	content	NOUN
aiti-4099	223	12	also	also	ADV
aiti-4099	223	13	larger	large	ADJ
aiti-4099	223	14	,	,	PUNCT
aiti-4099	223	15	but	but	CCONJ
aiti-4099	223	16	for	for	ADP
aiti-4099	223	17	the	the	DET
aiti-4099	223	18	constituent	constituent	NOUN
aiti-4099	223	19	materials	material	NOUN
aiti-4099	223	20	considered	consider	VERB
aiti-4099	223	21	in	in	ADP
aiti-4099	223	22	this	this	DET
aiti-4099	223	23	paper	paper	NOUN
aiti-4099	223	24	,	,	PUNCT
aiti-4099	223	25	the	the	DET
aiti-4099	223	26	increase	increase	NOUN
aiti-4099	223	27	of	of	ADP
aiti-4099	223	28	the	the	DET
aiti-4099	223	29	rigidities	rigidity	NOUN
aiti-4099	223	30	by	by	ADP
aiti-4099	223	31	increasing	increase	VERB
aiti-4099	223	32	nx	nx	NOUN
aiti-4099	223	33	and	and	CCONJ
aiti-4099	223	34	nz	nz	PROPN
aiti-4099	223	35	is	be	AUX
aiti-4099	223	36	much	much	ADV
aiti-4099	223	37	faster	fast	ADJ
aiti-4099	223	38	than	than	ADP
aiti-4099	223	39	that	that	PRON
aiti-4099	223	40	of	of	ADP
aiti-4099	223	41	the	the	DET
aiti-4099	223	42	mass	mass	NOUN
aiti-4099	223	43	moments	moment	NOUN
aiti-4099	223	44	.	.	PUNCT
aiti-4099	224	1	this	this	PRON
aiti-4099	224	2	explains	explain	VERB
aiti-4099	224	3	the	the	DET
aiti-4099	224	4	increase	increase	NOUN
aiti-4099	224	5	of	of	ADP
aiti-4099	224	6	the	the	DET
aiti-4099	224	7	frequency	frequency	NOUN
aiti-4099	224	8	when	when	SCONJ
aiti-4099	224	9	increasing	increase	VERB
aiti-4099	224	10	the	the	DET
aiti-4099	224	11	grading	grade	VERB
aiti-4099	224	12	indexes	index	NOUN
aiti-4099	224	13	.	.	PUNCT
aiti-4099	225	1	the	the	DET
aiti-4099	225	2	layer	layer	NOUN
aiti-4099	225	3	thickness	thickness	NOUN
aiti-4099	225	4	ratio	ratio	NOUN
aiti-4099	225	5	,	,	PUNCT
aiti-4099	225	6	as	as	SCONJ
aiti-4099	225	7	seen	see	VERB
aiti-4099	225	8	from	from	ADP
aiti-4099	225	9	table	table	NOUN
aiti-4099	225	10	2	2	NUM
aiti-4099	225	11	and	and	CCONJ
aiti-4099	225	12	3	3	NUM
aiti-4099	225	13	,	,	PUNCT
aiti-4099	225	14	also	also	ADV
aiti-4099	225	15	influences	influence	VERB
aiti-4099	225	16	the	the	DET
aiti-4099	225	17	increase	increase	NOUN
aiti-4099	225	18	of	of	ADP
aiti-4099	225	19	the	the	DET
aiti-4099	225	20	frequency	frequency	NOUN
aiti-4099	225	21	.	.	PUNCT
aiti-4099	226	1	for	for	ADP
aiti-4099	226	2	example	example	NOUN
aiti-4099	226	3	,	,	PUNCT
aiti-4099	226	4	for	for	ADP
aiti-4099	226	5	the	the	DET
aiti-4099	226	6	ss	ss	PROPN
aiti-4099	226	7	beam	beam	NOUN
aiti-4099	226	8	with	with	ADP
aiti-4099	226	9	l	l	PROPN
aiti-4099	226	10	/	/	SYM
aiti-4099	226	11	h=20	h=20	NOUN
aiti-4099	226	12	and	and	CCONJ
aiti-4099	226	13	a	a	DET
aiti-4099	226	14	length	length	NOUN
aiti-4099	226	15	index	index	NOUN
aiti-4099	226	16	nx=0.5	nx=0.5	PROPN
aiti-4099	226	17	,	,	PUNCT
aiti-4099	226	18	the	the	DET
aiti-4099	226	19	frequency	frequency	NOUN
aiti-4099	226	20	parameter	parameter	NOUN
aiti-4099	226	21	μ1	μ1	PROPN
aiti-4099	226	22	of	of	ADP
aiti-4099	226	23	the	the	DET
aiti-4099	226	24	(	(	PUNCT
aiti-4099	226	25	1	1	NUM
aiti-4099	226	26	-	-	SYM
aiti-4099	226	27	0	0	NUM
aiti-4099	226	28	-	-	PUNCT
aiti-4099	226	29	1	1	NUM
aiti-4099	226	30	)	)	PUNCT
aiti-4099	226	31	beam	beam	NOUN
aiti-4099	226	32	increases	increase	NOUN
aiti-4099	226	33	21.02	21.02	NUM
aiti-4099	226	34	%	%	NOUN
aiti-4099	226	35	when	when	SCONJ
aiti-4099	226	36	increasing	increase	VERB
aiti-4099	226	37	nz	nz	NOUN
aiti-4099	226	38	from	from	ADP
aiti-4099	226	39	0.5	0.5	NUM
aiti-4099	226	40	to	to	ADP
aiti-4099	226	41	5	5	NUM
aiti-4099	226	42	,	,	PUNCT
aiti-4099	226	43	but	but	CCONJ
aiti-4099	226	44	the	the	DET
aiti-4099	226	45	corresponding	corresponding	ADJ
aiti-4099	226	46	value	value	NOUN
aiti-4099	226	47	is	be	AUX
aiti-4099	226	48	20.24	20.24	NUM
aiti-4099	226	49	%	%	NOUN
aiti-4099	226	50	,	,	PUNCT
aiti-4099	226	51	7.51	7.51	NUM
aiti-4099	226	52	%	%	NOUN
aiti-4099	226	53	,	,	PUNCT
aiti-4099	226	54	and	and	CCONJ
aiti-4099	226	55	8.44	8.44	NUM
aiti-4099	226	56	%	%	NOUN
aiti-4099	226	57	for	for	ADP
aiti-4099	226	58	the	the	DET
aiti-4099	226	59	(	(	PUNCT
aiti-4099	226	60	1	1	NUM
aiti-4099	226	61	-	-	SYM
aiti-4099	226	62	1	1	NUM
aiti-4099	226	63	-	-	SYM
aiti-4099	226	64	1	1	NUM
aiti-4099	226	65	)	)	PUNCT
aiti-4099	226	66	,	,	PUNCT
aiti-4099	226	67	(	(	PUNCT
aiti-4099	226	68	1	1	NUM
aiti-4099	226	69	-	-	SYM
aiti-4099	226	70	2	2	NUM
aiti-4099	226	71	-	-	PUNCT
aiti-4099	226	72	1	1	NUM
aiti-4099	226	73	)	)	PUNCT
aiti-4099	226	74	,	,	PUNCT
aiti-4099	226	75	and	and	CCONJ
aiti-4099	226	76	(	(	PUNCT
aiti-4099	226	77	1	1	NUM
aiti-4099	226	78	-	-	SYM
aiti-4099	226	79	8	8	NUM
aiti-4099	226	80	-	-	PUNCT
aiti-4099	226	81	1	1	NUM
aiti-4099	226	82	)	)	PUNCT
aiti-4099	226	83	beams	beam	NOUN
aiti-4099	226	84	,	,	PUNCT
aiti-4099	226	85	respectively	respectively	ADV
aiti-4099	226	86	.	.	PUNCT
aiti-4099	227	1	a	a	DET
aiti-4099	227	2	careful	careful	ADJ
aiti-4099	227	3	examination	examination	NOUN
aiti-4099	227	4	of	of	ADP
aiti-4099	227	5	table	table	NOUN
aiti-4099	227	6	2	2	NUM
aiti-4099	227	7	and	and	CCONJ
aiti-4099	227	8	3	3	NUM
aiti-4099	227	9	shows	show	VERB
aiti-4099	227	10	that	that	SCONJ
aiti-4099	227	11	the	the	DET
aiti-4099	227	12	increase	increase	NOUN
aiti-4099	227	13	of	of	ADP
aiti-4099	227	14	the	the	DET
aiti-4099	227	15	frequency	frequency	NOUN
aiti-4099	227	16	by	by	ADP
aiti-4099	227	17	increasing	increase	VERB
aiti-4099	227	18	nz	nz	PROPN
aiti-4099	227	19	depends	depend	VERB
aiti-4099	227	20	upon	upon	SCONJ
aiti-4099	227	21	the	the	DET
aiti-4099	227	22	value	value	NOUN
aiti-4099	227	23	of	of	ADP
aiti-4099	227	24	nx	nx	NOUN
aiti-4099	227	25	also	also	ADV
aiti-4099	227	26	.	.	PUNCT
aiti-4099	228	1	for	for	ADP
aiti-4099	228	2	example	example	NOUN
aiti-4099	228	3	,	,	PUNCT
aiti-4099	228	4	as	as	SCONJ
aiti-4099	228	5	seen	see	VERB
aiti-4099	228	6	from	from	ADP
aiti-4099	228	7	table	table	NOUN
aiti-4099	228	8	2	2	NUM
aiti-4099	228	9	,	,	PUNCT
aiti-4099	228	10	the	the	DET
aiti-4099	228	11	frequency	frequency	NOUN
aiti-4099	228	12	parameter	parameter	NOUN
aiti-4099	228	13	increases	increase	VERB
aiti-4099	228	14	20.35	20.35	NUM
aiti-4099	228	15	%	%	NOUN
aiti-4099	228	16	when	when	SCONJ
aiti-4099	228	17	increasing	increase	VERB
aiti-4099	228	18	nz	nz	NOUN
aiti-4099	228	19	from	from	ADP
aiti-4099	228	20	0.5	0.5	NUM
aiti-4099	228	21	to	to	ADP
aiti-4099	228	22	5	5	NUM
aiti-4099	228	23	for	for	ADP
aiti-4099	228	24	(	(	PUNCT
aiti-4099	228	25	1	1	NUM
aiti-4099	228	26	-	-	SYM
aiti-4099	228	27	1	1	NUM
aiti-4099	228	28	-	-	PUNCT
aiti-4099	228	29	1	1	NUM
aiti-4099	228	30	)	)	PUNCT
aiti-4099	228	31	beam	beam	NOUN
aiti-4099	228	32	with	with	ADP
aiti-4099	228	33	nx=0.5	nx=0.5	PROPN
aiti-4099	228	34	,	,	PUNCT
aiti-4099	228	35	but	but	CCONJ
aiti-4099	228	36	the	the	DET
aiti-4099	228	37	corresponding	corresponding	ADJ
aiti-4099	228	38	value	value	NOUN
aiti-4099	228	39	for	for	ADP
aiti-4099	228	40	the	the	DET
aiti-4099	228	41	(	(	PUNCT
aiti-4099	228	42	1	1	NUM
aiti-4099	228	43	-	-	SYM
aiti-4099	228	44	1	1	NUM
aiti-4099	228	45	-	-	PUNCT
aiti-4099	228	46	1	1	NUM
aiti-4099	228	47	)	)	PUNCT
aiti-4099	228	48	beam	beam	NOUN
aiti-4099	228	49	with	with	ADP
aiti-4099	228	50	nx=5	nx=5	PROPN
aiti-4099	228	51	is	be	AUX
aiti-4099	228	52	just	just	ADV
aiti-4099	228	53	11.44	11.44	NUM
aiti-4099	228	54	%	%	NOUN
aiti-4099	228	55	.	.	PUNCT
aiti-4099	229	1	in	in	ADP
aiti-4099	229	2	other	other	ADJ
aiti-4099	229	3	words	word	NOUN
aiti-4099	229	4	,	,	PUNCT
aiti-4099	229	5	the	the	DET
aiti-4099	229	6	increase	increase	NOUN
aiti-4099	229	7	of	of	ADP
aiti-4099	229	8	the	the	DET
aiti-4099	229	9	fundamental	fundamental	ADJ
aiti-4099	229	10	frequency	frequency	NOUN
aiti-4099	229	11	by	by	ADP
aiti-4099	229	12	increasing	increase	VERB
aiti-4099	229	13	the	the	DET
aiti-4099	229	14	thickness	thickness	NOUN
aiti-4099	229	15	index	index	NOUN
aiti-4099	229	16	is	be	AUX
aiti-4099	229	17	smaller	small	ADJ
aiti-4099	229	18	for	for	ADP
aiti-4099	229	19	the	the	DET
aiti-4099	229	20	beam	beam	NOUN
aiti-4099	229	21	associated	associate	VERB
aiti-4099	229	22	with	with	ADP
aiti-4099	229	23	a	a	DET
aiti-4099	229	24	higher	high	ADJ
aiti-4099	229	25	length	length	NOUN
aiti-4099	229	26	index	index	NOUN
aiti-4099	229	27	.	.	PUNCT
aiti-4099	230	1	table	table	NOUN
aiti-4099	230	2	3	3	NUM
aiti-4099	230	3	fundamental	fundamental	ADJ
aiti-4099	230	4	frequency	frequency	NOUN
aiti-4099	230	5	parameter	parameter	NOUN
aiti-4099	230	6	(	(	PUNCT
aiti-4099	230	7	μ1	μ1	NOUN
aiti-4099	230	8	)	)	PUNCT
aiti-4099	230	9	of	of	ADP
aiti-4099	230	10	ss	ss	PROPN
aiti-4099	230	11	beam	beam	NOUN
aiti-4099	230	12	with	with	ADP
aiti-4099	230	13	l	l	PROPN
aiti-4099	230	14	/	/	SYM
aiti-4099	230	15	h	h	NOUN
aiti-4099	230	16	=	=	SYM
aiti-4099	230	17	20	20	NUM
aiti-4099	230	18	nx	nx	NUM
aiti-4099	230	19	nz	nz	PROPN
aiti-4099	230	20	1	1	NUM
aiti-4099	230	21	-	-	SYM
aiti-4099	230	22	0	0	NUM
aiti-4099	230	23	-	-	SYM
aiti-4099	230	24	1	1	NUM
aiti-4099	230	25	2	2	NUM
aiti-4099	230	26	-	-	SYM
aiti-4099	230	27	1	1	NUM
aiti-4099	230	28	-	-	SYM
aiti-4099	230	29	2	2	NUM
aiti-4099	230	30	1	1	NUM
aiti-4099	230	31	-	-	SYM
aiti-4099	230	32	1	1	NUM
aiti-4099	230	33	-	-	SYM
aiti-4099	230	34	1	1	NUM
aiti-4099	230	35	1	1	NUM
aiti-4099	230	36	-	-	SYM
aiti-4099	230	37	2	2	NUM
aiti-4099	230	38	-	-	SYM
aiti-4099	230	39	1	1	NUM
aiti-4099	230	40	1	1	NUM
aiti-4099	230	41	-	-	SYM
aiti-4099	230	42	8	8	NUM
aiti-4099	230	43	-	-	SYM
aiti-4099	230	44	1	1	NUM
aiti-4099	230	45	2	2	NUM
aiti-4099	230	46	-	-	SYM
aiti-4099	230	47	2	2	NUM
aiti-4099	230	48	-	-	SYM
aiti-4099	230	49	1	1	NUM
aiti-4099	230	50	0	0	NUM
aiti-4099	230	51	0.5	0.5	NUM
aiti-4099	230	52	3.3781	3.3781	NUM
aiti-4099	230	53	3.4953	3.4953	NUM
aiti-4099	230	54	3.6472	3.6472	NUM
aiti-4099	230	55	3.9387	3.9387	NUM
aiti-4099	230	56	4.7473	4.7473	NUM
aiti-4099	230	57	3.8512	3.8512	NUM
aiti-4099	230	58	1	1	NUM
aiti-4099	231	1	3.7147	3.7147	NUM
aiti-4099	231	2	3.8768	3.8768	NUM
aiti-4099	231	3	4.0328	4.0328	NUM
aiti-4099	231	4	4.2889	4.2889	NUM
aiti-4099	231	5	4.9233	4.9233	NUM
aiti-4099	231	6	4.1906	4.1906	NUM
aiti-4099	231	7	5	5	NUM
aiti-4099	231	8	4.6783	4.6783	NUM
aiti-4099	231	9	4.8058	4.8058	NUM
aiti-4099	231	10	4.8987	4.8987	NUM
aiti-4099	231	11	5.0239	5.0239	NUM
aiti-4099	231	12	5.2748	5.2748	NUM
aiti-4099	231	13	4.9578	4.9578	NUM
aiti-4099	231	14	0.5	0.5	NUM
aiti-4099	231	15	0.5	0.5	NUM
aiti-4099	231	16	3.7880	3.7880	NUM
aiti-4099	231	17	3.8629	3.8629	NUM
aiti-4099	231	18	3.9727	3.9727	NUM
aiti-4099	231	19	4.1958	4.1958	NUM
aiti-4099	231	20	4.8533	4.8533	NUM
aiti-4099	231	21	4.1320	4.1320	NUM
aiti-4099	231	22	1	1	NUM
aiti-4099	231	23	4.0307	4.0307	NUM
aiti-4099	231	24	4.1510	4.1510	NUM
aiti-4099	231	25	4.2717	4.2717	NUM
aiti-4099	231	26	4.4760	4.4760	NUM
aiti-4099	231	27	5.0012	5.0012	NUM
aiti-4099	231	28	4.3988	4.3988	NUM
aiti-4099	231	29	5	5	NUM
aiti-4099	231	30	4.7962	4.7962	NUM
aiti-4099	231	31	4.9026	4.9026	NUM
aiti-4099	231	32	4.9806	4.9806	NUM
aiti-4099	231	33	5.0864	5.0864	NUM
aiti-4099	231	34	5.3005	5.3005	NUM
aiti-4099	231	35	5.0306	5.0306	NUM
aiti-4099	231	36	1	1	NUM
aiti-4099	231	37	0.5	0.5	NUM
aiti-4099	231	38	4.0732	4.0732	NUM
aiti-4099	231	39	4.1260	4.1260	NUM
aiti-4099	231	40	4.2112	4.2112	NUM
aiti-4099	231	41	4.3907	4.3907	NUM
aiti-4099	231	42	4.9391	4.9391	NUM
aiti-4099	231	43	4.3413	4.3413	NUM
aiti-4099	231	44	1	1	NUM
aiti-4099	231	45	4.2617	4.2617	NUM
aiti-4099	231	46	4.3563	4.3563	NUM
aiti-4099	231	47	4.4539	4.4539	NUM
aiti-4099	231	48	4.6222	4.6222	NUM
aiti-4099	231	49	5.0651	5.0651	NUM
aiti-4099	231	50	4.5594	4.5594	NUM
aiti-4099	231	51	5	5	NUM
aiti-4099	231	52	4.8911	4.8911	NUM
aiti-4099	231	53	4.9812	4.9812	NUM
aiti-4099	231	54	5.0476	5.0476	NUM
aiti-4099	231	55	5.1380	5.1380	NUM
aiti-4099	231	56	5.3220	5.3220	NUM
aiti-4099	231	57	5.0903	5.0903	NUM
aiti-4099	231	58	2	2	NUM
aiti-4099	231	59	0.5	0.5	NUM
aiti-4099	231	60	4.4581	4.4581	NUM
aiti-4099	231	61	4.4884	4.4884	NUM
aiti-4099	232	1	4.5450	4.5450	NUM
aiti-4099	232	2	4.6700	4.6700	NUM
aiti-4099	232	3	5.0686	5.0686	NUM
aiti-4099	232	4	4.6374	4.6374	NUM
aiti-4099	232	5	1	1	NUM
aiti-4099	232	6	4.5838	4.5838	NUM
aiti-4099	232	7	4.6477	4.6477	NUM
aiti-4099	232	8	4.7160	4.7160	NUM
aiti-4099	232	9	4.8365	4.8365	NUM
aiti-4099	232	10	5.1623	5.1623	NUM
aiti-4099	232	11	4.7923	4.7923	NUM
aiti-4099	232	12	5	5	NUM
aiti-4099	232	13	5.0334	5.0334	NUM
aiti-4099	232	14	5.1000	5.1000	NUM
aiti-4099	232	15	5.1494	5.1494	NUM
aiti-4099	232	16	5.2169	5.2169	NUM
aiti-4099	232	17	5.3554	5.3554	NUM
aiti-4099	232	18	5.1813	5.1813	NUM
aiti-4099	232	19	5	5	NUM
aiti-4099	232	20	0.5	0.5	NUM
aiti-4099	232	21	5.0070	5.0070	NUM
aiti-4099	232	22	5.0168	5.0168	NUM
aiti-4099	232	23	5.0398	5.0398	NUM
aiti-4099	232	24	5.0940	5.0940	NUM
aiti-4099	232	25	5.2756	5.2756	NUM
aiti-4099	232	26	5.0808	5.0808	NUM
aiti-4099	232	27	1	1	NUM
aiti-4099	232	28	5.0587	5.0587	NUM
aiti-4099	232	29	5.0853	5.0853	NUM
aiti-4099	232	30	5.1151	5.1151	NUM
aiti-4099	232	31	5.1690	5.1690	NUM
aiti-4099	232	32	5.3194	5.3194	NUM
aiti-4099	232	33	5.1496	5.1496	NUM
aiti-4099	232	34	5	5	NUM
aiti-4099	232	35	5.2595	5.2595	NUM
aiti-4099	232	36	5.2904	5.2904	NUM
aiti-4099	232	37	5.3134	5.3134	NUM
aiti-4099	232	38	5.3450	5.3450	NUM
aiti-4099	232	39	5.4104	5.4104	NUM
aiti-4099	232	40	5.3284	5.3284	NUM
aiti-4099	232	41	(	(	PUNCT
aiti-4099	232	42	a	a	X
aiti-4099	232	43	)	)	PUNCT
aiti-4099	232	44	the	the	DET
aiti-4099	232	45	first	first	ADJ
aiti-4099	232	46	parameter	parameter	NOUN
aiti-4099	232	47	μ1	μ1	PROPN
aiti-4099	232	48	(	(	PUNCT
aiti-4099	232	49	b	b	X
aiti-4099	232	50	)	)	PUNCT
aiti-4099	232	51	the	the	DET
aiti-4099	232	52	second	second	ADJ
aiti-4099	232	53	parameter	parameter	NOUN
aiti-4099	232	54	μ2	μ2	NOUN
aiti-4099	232	55	(	(	PUNCT
aiti-4099	232	56	c	c	X
aiti-4099	232	57	)	)	PUNCT
aiti-4099	232	58	the	the	DET
aiti-4099	232	59	third	third	ADJ
aiti-4099	232	60	parameter	parameter	NOUN
aiti-4099	232	61	μ3	μ3	NOUN
aiti-4099	232	62	(	(	PUNCT
aiti-4099	232	63	d	d	X
aiti-4099	232	64	)	)	PUNCT
aiti-4099	232	65	the	the	DET
aiti-4099	232	66	fourth	fourth	ADJ
aiti-4099	232	67	parameter	parameter	NOUN
aiti-4099	232	68	μ4	μ4	PROPN
aiti-4099	232	69	fig	fig	NOUN
aiti-4099	232	70	.	.	PUNCT
aiti-4099	232	71	3	3	NUM
aiti-4099	232	72	variation	variation	NOUN
aiti-4099	232	73	of	of	ADP
aiti-4099	232	74	the	the	DET
aiti-4099	232	75	first	first	ADJ
aiti-4099	232	76	four	four	NUM
aiti-4099	232	77	frequency	frequency	NOUN
aiti-4099	232	78	parameters	parameter	NOUN
aiti-4099	232	79	with	with	ADP
aiti-4099	232	80	grading	grade	VERB
aiti-4099	232	81	indexes	index	NOUN
aiti-4099	232	82	of	of	ADP
aiti-4099	232	83	(	(	PUNCT
aiti-4099	232	84	1	1	NUM
aiti-4099	232	85	-	-	SYM
aiti-4099	232	86	1	1	NUM
aiti-4099	232	87	-	-	SYM
aiti-4099	232	88	1	1	NUM
aiti-4099	232	89	)	)	PUNCT
aiti-4099	232	90	ss	ss	NOUN
aiti-4099	232	91	beam	beam	NOUN
aiti-4099	232	92	with	with	ADP
aiti-4099	232	93	l	l	PROPN
aiti-4099	232	94	/	/	SYM
aiti-4099	232	95	h	h	NOUN
aiti-4099	232	96	=	=	SYM
aiti-4099	232	97	20	20	NUM
aiti-4099	232	98	advances	advance	NOUN
aiti-4099	232	99	in	in	ADP
aiti-4099	232	100	technology	technology	NOUN
aiti-4099	232	101	innovation	innovation	NOUN
aiti-4099	232	102	,	,	PUNCT
aiti-4099	232	103	vol	vol	NOUN
aiti-4099	232	104	.	.	PROPN
aiti-4099	232	105	4	4	NUM
aiti-4099	232	106	,	,	PUNCT
aiti-4099	232	107	no	no	INTJ
aiti-4099	232	108	.	.	NOUN
aiti-4099	232	109	3	3	NUM
aiti-4099	232	110	,	,	PUNCT
aiti-4099	232	111	2019	2019	NUM
aiti-4099	232	112	,	,	PUNCT
aiti-4099	232	113	pp	pp	ADJ
aiti-4099	232	114	.	.	PUNCT
aiti-4099	233	1	152	152	NUM
aiti-4099	233	2	-	-	SYM
aiti-4099	233	3	164	164	NUM
aiti-4099	233	4	161	161	NUM
aiti-4099	233	5	the	the	DET
aiti-4099	233	6	aspect	aspect	NOUN
aiti-4099	233	7	ratio	ratio	NOUN
aiti-4099	233	8	l	l	PROPN
aiti-4099	233	9	/	/	SYM
aiti-4099	233	10	h	h	NOUN
aiti-4099	233	11	also	also	ADV
aiti-4099	233	12	slightly	slightly	ADV
aiti-4099	233	13	influences	influence	VERB
aiti-4099	233	14	the	the	DET
aiti-4099	233	15	change	change	NOUN
aiti-4099	233	16	of	of	ADP
aiti-4099	233	17	the	the	DET
aiti-4099	233	18	frequency	frequency	NOUN
aiti-4099	233	19	parameter	parameter	NOUN
aiti-4099	233	20	and	and	CCONJ
aiti-4099	233	21	the	the	DET
aiti-4099	233	22	change	change	NOUN
aiti-4099	233	23	in	in	ADP
aiti-4099	233	24	the	the	DET
aiti-4099	233	25	frequency	frequency	NOUN
aiti-4099	233	26	parameter	parameter	NOUN
aiti-4099	233	27	is	be	AUX
aiti-4099	233	28	not	not	PART
aiti-4099	233	29	significant	significant	ADJ
aiti-4099	233	30	for	for	ADP
aiti-4099	233	31	the	the	DET
aiti-4099	233	32	beam	beam	NOUN
aiti-4099	233	33	with	with	ADP
aiti-4099	233	34	a	a	DET
aiti-4099	233	35	lower	low	ADJ
aiti-4099	233	36	aspect	aspect	NOUN
aiti-4099	233	37	ratio	ratio	NOUN
aiti-4099	233	38	l	l	PROPN
aiti-4099	233	39	/	/	SYM
aiti-4099	233	40	h.	h.	NOUN
aiti-4099	233	41	for	for	ADP
aiti-4099	233	42	example	example	NOUN
aiti-4099	233	43	,	,	PUNCT
aiti-4099	233	44	the	the	DET
aiti-4099	233	45	fundamental	fundamental	ADJ
aiti-4099	233	46	frequency	frequency	NOUN
aiti-4099	233	47	parameter	parameter	NOUN
aiti-4099	233	48	increases	increase	VERB
aiti-4099	233	49	17.17	17.17	NUM
aiti-4099	233	50	%	%	NOUN
aiti-4099	233	51	for	for	ADP
aiti-4099	233	52	the	the	DET
aiti-4099	233	53	(	(	PUNCT
aiti-4099	233	54	2	2	NUM
aiti-4099	233	55	-	-	SYM
aiti-4099	233	56	1	1	NUM
aiti-4099	233	57	-	-	PUNCT
aiti-4099	233	58	2	2	NUM
aiti-4099	233	59	)	)	PUNCT
aiti-4099	233	60	beam	beam	NOUN
aiti-4099	233	61	with	with	ADP
aiti-4099	233	62	nx=1	nx=1	PROPN
aiti-4099	233	63	having	have	VERB
aiti-4099	233	64	l	l	NOUN
aiti-4099	233	65	/	/	SYM
aiti-4099	233	66	h=20	h=20	X
aiti-4099	233	67	when	when	SCONJ
aiti-4099	233	68	increasing	increase	VERB
aiti-4099	233	69	nz	nz	NOUN
aiti-4099	233	70	from	from	ADP
aiti-4099	233	71	0.5	0.5	NUM
aiti-4099	233	72	to	to	ADP
aiti-4099	233	73	5	5	NUM
aiti-4099	233	74	,	,	PUNCT
aiti-4099	233	75	but	but	CCONJ
aiti-4099	233	76	this	this	DET
aiti-4099	233	77	increase	increase	NOUN
aiti-4099	233	78	reduces	reduce	VERB
aiti-4099	233	79	to	to	ADP
aiti-4099	233	80	16.42	16.42	NUM
aiti-4099	233	81	%	%	NOUN
aiti-4099	233	82	for	for	ADP
aiti-4099	233	83	the	the	DET
aiti-4099	233	84	beam	beam	NOUN
aiti-4099	233	85	with	with	ADP
aiti-4099	233	86	l	l	PROPN
aiti-4099	233	87	/	/	SYM
aiti-4099	233	88	h=5	h=5	PROPN
aiti-4099	233	89	.	.	PUNCT
aiti-4099	234	1	thus	thus	ADV
aiti-4099	234	2	,	,	PUNCT
aiti-4099	234	3	the	the	DET
aiti-4099	234	4	material	material	NOUN
aiti-4099	234	5	gradation	gradation	NOUN
aiti-4099	234	6	,	,	PUNCT
aiti-4099	234	7	the	the	DET
aiti-4099	234	8	layer	layer	NOUN
aiti-4099	234	9	thickness	thickness	NOUN
aiti-4099	234	10	ratio	ratio	NOUN
aiti-4099	234	11	,	,	PUNCT
aiti-4099	234	12	and	and	CCONJ
aiti-4099	234	13	the	the	DET
aiti-4099	234	14	aspect	aspect	NOUN
aiti-4099	234	15	ratio	ratio	NOUN
aiti-4099	234	16	are	be	AUX
aiti-4099	234	17	all	all	PRON
aiti-4099	234	18	important	important	ADJ
aiti-4099	234	19	parameters	parameter	NOUN
aiti-4099	234	20	which	which	PRON
aiti-4099	234	21	should	should	AUX
aiti-4099	234	22	be	be	AUX
aiti-4099	234	23	considered	consider	VERB
aiti-4099	234	24	in	in	ADP
aiti-4099	234	25	designing	design	VERB
aiti-4099	234	26	the	the	DET
aiti-4099	234	27	2d	2d	NOUN
aiti-4099	234	28	-	-	PUNCT
aiti-4099	234	29	fgsw	fgsw	NOUN
aiti-4099	234	30	beam	beam	NOUN
aiti-4099	234	31	depends	depend	VERB
aiti-4099	234	32	in	in	ADP
aiti-4099	234	33	order	order	NOUN
aiti-4099	234	34	to	to	PART
aiti-4099	234	35	achieve	achieve	VERB
aiti-4099	234	36	a	a	DET
aiti-4099	234	37	beam	beam	NOUN
aiti-4099	234	38	with	with	ADP
aiti-4099	234	39	desired	desire	VERB
aiti-4099	234	40	natural	natural	ADJ
aiti-4099	234	41	frequencies	frequency	NOUN
aiti-4099	234	42	.	.	PUNCT
aiti-4099	235	1	the	the	DET
aiti-4099	235	2	effect	effect	NOUN
aiti-4099	235	3	of	of	ADP
aiti-4099	235	4	the	the	DET
aiti-4099	235	5	grading	grade	VERB
aiti-4099	235	6	indexes	index	NOUN
aiti-4099	235	7	on	on	ADP
aiti-4099	235	8	the	the	DET
aiti-4099	235	9	higher	high	ADJ
aiti-4099	235	10	frequency	frequency	NOUN
aiti-4099	235	11	parameters	parameter	NOUN
aiti-4099	235	12	is	be	AUX
aiti-4099	235	13	illustrated	illustrate	VERB
aiti-4099	235	14	in	in	ADP
aiti-4099	235	15	fig	fig	NOUN
aiti-4099	235	16	.	.	PUNCT
aiti-4099	236	1	3	3	NUM
aiti-4099	236	2	-	-	SYM
aiti-4099	236	3	5	5	NUM
aiti-4099	236	4	,	,	PUNCT
aiti-4099	236	5	where	where	SCONJ
aiti-4099	236	6	the	the	DET
aiti-4099	236	7	variation	variation	NOUN
aiti-4099	236	8	of	of	ADP
aiti-4099	236	9	the	the	DET
aiti-4099	236	10	first	first	ADJ
aiti-4099	236	11	four	four	NUM
aiti-4099	236	12	natural	natural	ADJ
aiti-4099	236	13	frequency	frequency	NOUN
aiti-4099	236	14	parameters	parameter	NOUN
aiti-4099	236	15	with	with	ADP
aiti-4099	236	16	the	the	DET
aiti-4099	236	17	grading	grade	VERB
aiti-4099	236	18	indexes	index	NOUN
aiti-4099	236	19	nx	nx	NOUN
aiti-4099	236	20	and	and	CCONJ
aiti-4099	236	21	nx	nx	PROPN
aiti-4099	236	22	is	be	AUX
aiti-4099	236	23	depicted	depict	VERB
aiti-4099	236	24	for	for	ADP
aiti-4099	236	25	the	the	DET
aiti-4099	236	26	ss	ss	PROPN
aiti-4099	236	27	,	,	PUNCT
aiti-4099	236	28	clamped	clamp	VERB
aiti-4099	236	29	(	(	PUNCT
aiti-4099	236	30	cc	cc	NOUN
aiti-4099	236	31	)	)	PUNCT
aiti-4099	236	32	and	and	CCONJ
aiti-4099	236	33	cantilever	cantilever	NOUN
aiti-4099	236	34	(	(	PUNCT
aiti-4099	236	35	cf	cf	NOUN
aiti-4099	236	36	)	)	PUNCT
aiti-4099	236	37	beams	beam	NOUN
aiti-4099	236	38	with	with	ADP
aiti-4099	236	39	a	a	DET
aiti-4099	236	40	layer	layer	NOUN
aiti-4099	236	41	thickness	thickness	NOUN
aiti-4099	236	42	ratio	ratio	NOUN
aiti-4099	236	43	of	of	ADP
aiti-4099	236	44	(	(	PUNCT
aiti-4099	236	45	1	1	NUM
aiti-4099	236	46	-	-	SYM
aiti-4099	236	47	1	1	NUM
aiti-4099	236	48	-	-	SYM
aiti-4099	236	49	1	1	NUM
aiti-4099	236	50	)	)	PUNCT
aiti-4099	236	51	and	and	CCONJ
aiti-4099	236	52	an	an	DET
aiti-4099	236	53	aspect	aspect	NOUN
aiti-4099	236	54	ratio	ratio	NOUN
aiti-4099	236	55	l	l	PROPN
aiti-4099	236	56	/	/	SYM
aiti-4099	236	57	h=20	h=20	NOUN
aiti-4099	236	58	,	,	PUNCT
aiti-4099	236	59	respectively	respectively	ADV
aiti-4099	236	60	.	.	PUNCT
aiti-4099	237	1	similar	similar	ADJ
aiti-4099	237	2	to	to	ADP
aiti-4099	237	3	the	the	DET
aiti-4099	237	4	fundamental	fundamental	ADJ
aiti-4099	237	5	frequency	frequency	NOUN
aiti-4099	237	6	,	,	PUNCT
aiti-4099	237	7	the	the	DET
aiti-4099	237	8	higher	high	ADJ
aiti-4099	237	9	frequencies	frequency	NOUN
aiti-4099	237	10	also	also	ADV
aiti-4099	237	11	increase	increase	VERB
aiti-4099	237	12	by	by	ADP
aiti-4099	237	13	increasing	increase	VERB
aiti-4099	237	14	the	the	DET
aiti-4099	237	15	grading	grade	VERB
aiti-4099	237	16	indexes	index	NOUN
aiti-4099	237	17	nx	nx	NOUN
aiti-4099	237	18	and	and	CCONJ
aiti-4099	237	19	nz	nz	PROPN
aiti-4099	237	20	,	,	PUNCT
aiti-4099	237	21	regardless	regardless	ADV
aiti-4099	237	22	of	of	ADP
aiti-4099	237	23	the	the	DET
aiti-4099	237	24	boundary	boundary	ADJ
aiti-4099	237	25	conditions	condition	NOUN
aiti-4099	237	26	.	.	PUNCT
aiti-4099	238	1	the	the	DET
aiti-4099	238	2	boundary	boundary	ADJ
aiti-4099	238	3	conditions	condition	NOUN
aiti-4099	238	4	may	may	AUX
aiti-4099	238	5	affect	affect	VERB
aiti-4099	238	6	the	the	DET
aiti-4099	238	7	amplitude	amplitude	NOUN
aiti-4099	238	8	of	of	ADP
aiti-4099	238	9	the	the	DET
aiti-4099	238	10	natural	natural	ADJ
aiti-4099	238	11	frequencies	frequency	NOUN
aiti-4099	238	12	,	,	PUNCT
aiti-4099	238	13	but	but	CCONJ
aiti-4099	238	14	it	it	PRON
aiti-4099	238	15	hardly	hardly	ADV
aiti-4099	238	16	influences	influence	VERB
aiti-4099	238	17	the	the	DET
aiti-4099	238	18	dependence	dependence	NOUN
aiti-4099	238	19	of	of	ADP
aiti-4099	238	20	the	the	DET
aiti-4099	238	21	frequency	frequency	NOUN
aiti-4099	238	22	parameters	parameter	NOUN
aiti-4099	238	23	upon	upon	SCONJ
aiti-4099	238	24	the	the	DET
aiti-4099	238	25	material	material	NOUN
aiti-4099	238	26	grading	grade	VERB
aiti-4099	238	27	indexes	index	NOUN
aiti-4099	238	28	.	.	PUNCT
aiti-4099	239	1	(	(	PUNCT
aiti-4099	239	2	a	a	X
aiti-4099	239	3	)	)	PUNCT
aiti-4099	239	4	the	the	DET
aiti-4099	239	5	first	first	ADJ
aiti-4099	239	6	parameter	parameter	NOUN
aiti-4099	239	7	μ1	μ1	PROPN
aiti-4099	239	8	(	(	PUNCT
aiti-4099	239	9	b	b	X
aiti-4099	239	10	)	)	PUNCT
aiti-4099	239	11	the	the	DET
aiti-4099	239	12	second	second	ADJ
aiti-4099	239	13	parameter	parameter	NOUN
aiti-4099	239	14	μ2	μ2	NOUN
aiti-4099	239	15	(	(	PUNCT
aiti-4099	239	16	c	c	X
aiti-4099	239	17	)	)	PUNCT
aiti-4099	239	18	the	the	DET
aiti-4099	239	19	third	third	ADJ
aiti-4099	239	20	parameter	parameter	NOUN
aiti-4099	239	21	μ3	μ3	NOUN
aiti-4099	239	22	(	(	PUNCT
aiti-4099	239	23	d	d	X
aiti-4099	239	24	)	)	PUNCT
aiti-4099	239	25	the	the	DET
aiti-4099	239	26	fourth	fourth	ADJ
aiti-4099	239	27	parameter	parameter	NOUN
aiti-4099	239	28	μ4	μ4	PROPN
aiti-4099	239	29	fig	fig	NOUN
aiti-4099	239	30	.	.	PUNCT
aiti-4099	240	1	4	4	NUM
aiti-4099	240	2	variation	variation	NOUN
aiti-4099	240	3	of	of	ADP
aiti-4099	240	4	the	the	DET
aiti-4099	240	5	first	first	ADJ
aiti-4099	240	6	four	four	NUM
aiti-4099	240	7	frequency	frequency	NOUN
aiti-4099	240	8	parameters	parameter	NOUN
aiti-4099	240	9	with	with	ADP
aiti-4099	240	10	grading	grade	VERB
aiti-4099	240	11	indexes	index	NOUN
aiti-4099	240	12	of	of	ADP
aiti-4099	240	13	(	(	PUNCT
aiti-4099	240	14	1	1	NUM
aiti-4099	240	15	-	-	SYM
aiti-4099	240	16	1	1	NUM
aiti-4099	240	17	-	-	SYM
aiti-4099	240	18	1	1	NUM
aiti-4099	240	19	)	)	PUNCT
aiti-4099	240	20	cc	cc	VERB
aiti-4099	240	21	beam	beam	NOUN
aiti-4099	240	22	with	with	ADP
aiti-4099	240	23	l	l	PROPN
aiti-4099	240	24	/	/	SYM
aiti-4099	240	25	h	h	NOUN
aiti-4099	240	26	=	=	SYM
aiti-4099	240	27	20	20	NUM
aiti-4099	240	28	(	(	PUNCT
aiti-4099	240	29	a	a	NOUN
aiti-4099	240	30	)	)	PUNCT
aiti-4099	240	31	the	the	DET
aiti-4099	240	32	first	first	ADJ
aiti-4099	240	33	parameter	parameter	NOUN
aiti-4099	240	34	μ1	μ1	PROPN
aiti-4099	240	35	(	(	PUNCT
aiti-4099	240	36	b	b	X
aiti-4099	240	37	)	)	PUNCT
aiti-4099	240	38	the	the	DET
aiti-4099	240	39	second	second	ADJ
aiti-4099	240	40	parameter	parameter	NOUN
aiti-4099	240	41	μ2	μ2	NOUN
aiti-4099	240	42	(	(	PUNCT
aiti-4099	240	43	c	c	X
aiti-4099	240	44	)	)	PUNCT
aiti-4099	240	45	the	the	DET
aiti-4099	240	46	third	third	ADJ
aiti-4099	240	47	parameter	parameter	NOUN
aiti-4099	241	1	μ3	μ3	NOUN
aiti-4099	241	2	(	(	PUNCT
aiti-4099	241	3	d	d	X
aiti-4099	241	4	)	)	PUNCT
aiti-4099	241	5	the	the	DET
aiti-4099	241	6	fourth	fourth	ADJ
aiti-4099	241	7	parameter	parameter	NOUN
aiti-4099	241	8	μ4	μ4	PROPN
aiti-4099	241	9	fig	fig	NOUN
aiti-4099	241	10	.	.	PUNCT
aiti-4099	242	1	5	5	NUM
aiti-4099	242	2	variation	variation	NOUN
aiti-4099	242	3	of	of	ADP
aiti-4099	242	4	the	the	DET
aiti-4099	242	5	first	first	ADJ
aiti-4099	242	6	four	four	NUM
aiti-4099	242	7	frequency	frequency	NOUN
aiti-4099	242	8	parameters	parameter	NOUN
aiti-4099	242	9	with	with	ADP
aiti-4099	242	10	grading	grade	VERB
aiti-4099	242	11	indexes	index	NOUN
aiti-4099	242	12	of	of	ADP
aiti-4099	242	13	(	(	PUNCT
aiti-4099	242	14	1	1	NUM
aiti-4099	242	15	-	-	SYM
aiti-4099	242	16	1	1	NUM
aiti-4099	242	17	-	-	SYM
aiti-4099	242	18	1	1	NUM
aiti-4099	242	19	)	)	PUNCT
aiti-4099	242	20	cf	cf	NOUN
aiti-4099	242	21	beam	beam	NOUN
aiti-4099	242	22	with	with	ADP
aiti-4099	242	23	l	l	PROPN
aiti-4099	242	24	/	/	SYM
aiti-4099	242	25	h	h	NOUN
aiti-4099	242	26	=	=	SYM
aiti-4099	242	27	20	20	NUM
aiti-4099	242	28	advances	advance	NOUN
aiti-4099	242	29	in	in	ADP
aiti-4099	242	30	technology	technology	NOUN
aiti-4099	242	31	innovation	innovation	NOUN
aiti-4099	242	32	,	,	PUNCT
aiti-4099	242	33	vol	vol	NOUN
aiti-4099	242	34	.	.	PROPN
aiti-4099	242	35	4	4	NUM
aiti-4099	242	36	,	,	PUNCT
aiti-4099	242	37	no	no	INTJ
aiti-4099	242	38	.	.	NOUN
aiti-4099	242	39	3	3	NUM
aiti-4099	242	40	,	,	PUNCT
aiti-4099	242	41	2019	2019	NUM
aiti-4099	242	42	,	,	PUNCT
aiti-4099	242	43	pp	pp	ADJ
aiti-4099	242	44	.	.	PUNCT
aiti-4099	243	1	152	152	NUM
aiti-4099	243	2	-	-	SYM
aiti-4099	243	3	164	164	NUM
aiti-4099	243	4	162	162	NUM
aiti-4099	243	5	4.3	4.3	NUM
aiti-4099	243	6	.	.	PUNCT
aiti-4099	244	1	dynamic	dynamic	ADJ
aiti-4099	244	2	response	response	NOUN
aiti-4099	244	3	the	the	DET
aiti-4099	244	4	dynamic	dynamic	ADJ
aiti-4099	244	5	response	response	NOUN
aiti-4099	244	6	of	of	ADP
aiti-4099	244	7	the	the	DET
aiti-4099	244	8	2d	2d	NOUN
aiti-4099	244	9	-	-	PUNCT
aiti-4099	244	10	fgsw	fgsw	NOUN
aiti-4099	244	11	beam	beam	NOUN
aiti-4099	244	12	to	to	ADP
aiti-4099	244	13	a	a	DET
aiti-4099	244	14	harmonic	harmonic	ADJ
aiti-4099	244	15	load	load	NOUN
aiti-4099	244	16	p	p	X
aiti-4099	244	17	=	=	NOUN
aiti-4099	244	18	p0cos(ωt	p0cos(ωt	NOUN
aiti-4099	244	19	)	)	PUNCT
aiti-4099	244	20	is	be	AUX
aiti-4099	244	21	investigated	investigate	VERB
aiti-4099	244	22	in	in	ADP
aiti-4099	244	23	this	this	DET
aiti-4099	244	24	sub	sub	NOUN
aiti-4099	244	25	-	-	NOUN
aiti-4099	244	26	section	section	NOUN
aiti-4099	244	27	.	.	PUNCT
aiti-4099	245	1	in	in	ADP
aiti-4099	245	2	order	order	NOUN
aiti-4099	245	3	to	to	PART
aiti-4099	245	4	calculate	calculate	VERB
aiti-4099	245	5	the	the	DET
aiti-4099	245	6	response	response	NOUN
aiti-4099	245	7	of	of	ADP
aiti-4099	245	8	the	the	DET
aiti-4099	245	9	beam	beam	NOUN
aiti-4099	245	10	,	,	PUNCT
aiti-4099	245	11	the	the	DET
aiti-4099	245	12	average	average	ADJ
aiti-4099	245	13	acceleration	acceleration	NOUN
aiti-4099	245	14	newmark	newmark	NOUN
aiti-4099	245	15	method	method	NOUN
aiti-4099	245	16	is	be	AUX
aiti-4099	245	17	employed	employ	VERB
aiti-4099	245	18	to	to	PART
aiti-4099	245	19	solve	solve	VERB
aiti-4099	245	20	eq	eq	ADP
aiti-4099	245	21	.	.	PUNCT
aiti-4099	246	1	(	(	PUNCT
aiti-4099	246	2	26	26	NUM
aiti-4099	246	3	)	)	PUNCT
aiti-4099	246	4	.	.	PUNCT
aiti-4099	247	1	the	the	DET
aiti-4099	247	2	beam	beam	NOUN
aiti-4099	247	3	with	with	ADP
aiti-4099	247	4	two	two	NUM
aiti-4099	247	5	types	type	NOUN
aiti-4099	247	6	of	of	ADP
aiti-4099	247	7	boundary	boundary	ADJ
aiti-4099	247	8	conditions	condition	NOUN
aiti-4099	247	9	,	,	PUNCT
aiti-4099	247	10	namely	namely	ADV
aiti-4099	247	11	ss	ss	NOUN
aiti-4099	247	12	and	and	CCONJ
aiti-4099	247	13	cf	cf	NOUN
aiti-4099	247	14	beams	beam	NOUN
aiti-4099	247	15	,	,	PUNCT
aiti-4099	247	16	with	with	ADP
aiti-4099	247	17	a	a	DET
aiti-4099	247	18	harmonic	harmonic	ADJ
aiti-4099	247	19	load	load	NOUN
aiti-4099	247	20	acting	act	VERB
aiti-4099	247	21	at	at	ADP
aiti-4099	247	22	the	the	DET
aiti-4099	247	23	mid	mid	NOUN
aiti-4099	247	24	-	-	NOUN
aiti-4099	247	25	span	span	NOUN
aiti-4099	247	26	and	and	CCONJ
aiti-4099	247	27	free	free	ADJ
aiti-4099	247	28	and	and	CCONJ
aiti-4099	247	29	,	,	PUNCT
aiti-4099	247	30	respectively	respectively	ADV
aiti-4099	247	31	are	be	AUX
aiti-4099	247	32	considered	consider	VERB
aiti-4099	247	33	herein	herein	NOUN
aiti-4099	247	34	.	.	PUNCT
aiti-4099	248	1	the	the	DET
aiti-4099	248	2	variation	variation	NOUN
aiti-4099	248	3	of	of	ADP
aiti-4099	248	4	the	the	DET
aiti-4099	248	5	dimensionless	dimensionless	NOUN
aiti-4099	248	6	deflections	deflection	NOUN
aiti-4099	248	7	with	with	ADP
aiti-4099	248	8	the	the	DET
aiti-4099	248	9	time	time	NOUN
aiti-4099	248	10	at	at	ADP
aiti-4099	248	11	the	the	DET
aiti-4099	248	12	loaded	load	VERB
aiti-4099	248	13	points	point	NOUN
aiti-4099	248	14	of	of	ADP
aiti-4099	248	15	the	the	DET
aiti-4099	248	16	ss	ss	NOUN
aiti-4099	248	17	and	and	CCONJ
aiti-4099	248	18	cf	cf	NOUN
aiti-4099	248	19	beams	beam	NOUN
aiti-4099	248	20	with	with	ADP
aiti-4099	248	21	an	an	DET
aiti-4099	248	22	aspect	aspect	NOUN
aiti-4099	248	23	ratio	ratio	NOUN
aiti-4099	248	24	l	l	PROPN
aiti-4099	248	25	/	/	SYM
aiti-4099	248	26	h=20	h=20	NOUN
aiti-4099	248	27	and	and	CCONJ
aiti-4099	248	28	a	a	DET
aiti-4099	248	29	layer	layer	NOUN
aiti-4099	248	30	thickness	thickness	NOUN
aiti-4099	248	31	ratio	ratio	NOUN
aiti-4099	248	32	of	of	ADP
aiti-4099	248	33	(	(	PUNCT
aiti-4099	248	34	2	2	NUM
aiti-4099	248	35	-	-	SYM
aiti-4099	248	36	1	1	NUM
aiti-4099	248	37	-	-	SYM
aiti-4099	248	38	2	2	NUM
aiti-4099	248	39	)	)	PUNCT
aiti-4099	248	40	is	be	AUX
aiti-4099	248	41	illustrated	illustrate	VERB
aiti-4099	248	42	in	in	ADP
aiti-4099	248	43	fig	fig	NOUN
aiti-4099	248	44	.	.	PUNCT
aiti-4099	249	1	6	6	NUM
aiti-4099	249	2	and	and	CCONJ
aiti-4099	249	3	7	7	NUM
aiti-4099	249	4	for	for	ADP
aiti-4099	249	5	an	an	DET
aiti-4099	249	6	excitation	excitation	NOUN
aiti-4099	249	7	frequency	frequency	NOUN
aiti-4099	249	8	ω=10	ω=10	PUNCT
aiti-4099	249	9	rad	rad	PROPN
aiti-4099	249	10	/	/	SYM
aiti-4099	249	11	s	s	PROPN
aiti-4099	249	12	,	,	PUNCT
aiti-4099	249	13	respectively	respectively	ADV
aiti-4099	249	14	.	.	PUNCT
aiti-4099	250	1	the	the	DET
aiti-4099	250	2	deflections	deflection	NOUN
aiti-4099	250	3	w	w	PROPN
aiti-4099	250	4	*	*	VERB
aiti-4099	250	5	in	in	ADP
aiti-4099	250	6	the	the	DET
aiti-4099	250	7	figures	figure	NOUN
aiti-4099	250	8	are	be	AUX
aiti-4099	250	9	normalized	normalize	VERB
aiti-4099	250	10	by	by	ADP
aiti-4099	250	11	the	the	DET
aiti-4099	250	12	static	static	ADJ
aiti-4099	250	13	bending	bend	VERB
aiti-4099	250	14	transverse	transverse	NOUN
aiti-4099	250	15	displacements	displacement	NOUN
aiti-4099	250	16	of	of	ADP
aiti-4099	250	17	the	the	DET
aiti-4099	250	18	ceramic	ceramic	ADJ
aiti-4099	250	19	beam	beam	NOUN
aiti-4099	250	20	,	,	PUNCT
aiti-4099	250	21	that	that	PRON
aiti-4099	250	22	are	be	AUX
aiti-4099	250	23	3	3	NUM
aiti-4099	250	24	48	48	NUM
aiti-4099	250	25	*	*	PUNCT
aiti-4099	251	1	(	(	PUNCT
aiti-4099	251	2	/	/	SYM
aiti-4099	251	3	2	2	NUM
aiti-4099	251	4	)	)	PUNCT
aiti-4099	251	5	for	for	ADP
aiti-4099	251	6	ss	ss	PROPN
aiti-4099	251	7	beamc	beamc	PROPN
aiti-4099	251	8	b	b	PROPN
aiti-4099	252	1	e	e	X
aiti-4099	252	2	i	i	PRON
aiti-4099	252	3	w	w	PROPN
aiti-4099	252	4	w	w	PROPN
aiti-4099	252	5	l	l	NOUN
aiti-4099	252	6	pl	pl	X
aiti-4099	252	7			NUM
aiti-4099	252	8	(	(	PUNCT
aiti-4099	252	9	31	31	NUM
aiti-4099	252	10	)	)	PUNCT
aiti-4099	252	11	3	3	NUM
aiti-4099	252	12	3	3	NUM
aiti-4099	252	13	*	*	PUNCT
aiti-4099	252	14	(	(	PUNCT
aiti-4099	252	15	)	)	PUNCT
aiti-4099	252	16	for	for	ADP
aiti-4099	252	17	cf	cf	NOUN
aiti-4099	252	18	beamc	beamc	PROPN
aiti-4099	252	19	b	b	PROPN
aiti-4099	252	20	e	e	X
aiti-4099	253	1	i	i	PRON
aiti-4099	253	2	w	w	PROPN
aiti-4099	253	3	w	w	PROPN
aiti-4099	253	4	l	l	NOUN
aiti-4099	253	5	pl	pl	X
aiti-4099	253	6			NUM
aiti-4099	253	7	(	(	PUNCT
aiti-4099	253	8	32	32	NUM
aiti-4099	253	9	)	)	PUNCT
aiti-4099	253	10	(	(	PUNCT
aiti-4099	253	11	a	a	X
aiti-4099	253	12	)	)	PUNCT
aiti-4099	253	13	nx=1	nx=1	PROPN
aiti-4099	253	14	,	,	PUNCT
aiti-4099	253	15	nz	nz	PROPN
aiti-4099	253	16	is	be	AUX
aiti-4099	253	17	variable	variable	ADJ
aiti-4099	253	18	(	(	PUNCT
aiti-4099	253	19	b	b	NOUN
aiti-4099	253	20	)	)	PUNCT
aiti-4099	253	21	nz=1	nz=1	PROPN
aiti-4099	253	22	,	,	PUNCT
aiti-4099	253	23	nx	nx	PROPN
aiti-4099	253	24	is	be	AUX
aiti-4099	253	25	variable	variable	ADJ
aiti-4099	253	26	fig	fig	NOUN
aiti-4099	253	27	.	.	PUNCT
aiti-4099	254	1	6	6	NUM
aiti-4099	254	2	variation	variation	NOUN
aiti-4099	254	3	of	of	ADP
aiti-4099	254	4	mid	mid	ADJ
aiti-4099	254	5	-	-	ADJ
aiti-4099	254	6	span	span	NOUN
aiti-4099	254	7	dimensionless	dimensionless	NOUN
aiti-4099	254	8	deflection	deflection	NOUN
aiti-4099	254	9	with	with	ADP
aiti-4099	254	10	the	the	DET
aiti-4099	254	11	time	time	NOUN
aiti-4099	254	12	of	of	ADP
aiti-4099	254	13	ss	ss	NOUN
aiti-4099	254	14	(	(	PUNCT
aiti-4099	254	15	2	2	NUM
aiti-4099	254	16	-	-	SYM
aiti-4099	254	17	1	1	NUM
aiti-4099	254	18	-	-	PUNCT
aiti-4099	254	19	2	2	NUM
aiti-4099	254	20	)	)	PUNCT
aiti-4099	254	21	beam	beam	NOUN
aiti-4099	254	22	under	under	ADP
aiti-4099	254	23	harmonic	harmonic	ADJ
aiti-4099	254	24	load	load	NOUN
aiti-4099	254	25	with	with	ADP
aiti-4099	254	26	ω=10	ω=10	NOUN
aiti-4099	254	27	rad	rad	PROPN
aiti-4099	254	28	/	/	SYM
aiti-4099	254	29	s	s	AUX
aiti-4099	254	30	acting	act	VERB
aiti-4099	254	31	at	at	ADP
aiti-4099	254	32	mid	mid	NOUN
aiti-4099	254	33	-	-	NOUN
aiti-4099	254	34	span	span	NOUN
aiti-4099	254	35	(	(	PUNCT
aiti-4099	254	36	a	a	NOUN
aiti-4099	254	37	)	)	PUNCT
aiti-4099	254	38	nx=1	nx=1	PROPN
aiti-4099	254	39	,	,	PUNCT
aiti-4099	254	40	nz	nz	PROPN
aiti-4099	254	41	is	be	AUX
aiti-4099	254	42	variable	variable	ADJ
aiti-4099	254	43	(	(	PUNCT
aiti-4099	254	44	b	b	NOUN
aiti-4099	254	45	)	)	PUNCT
aiti-4099	254	46	nz=1	nz=1	PROPN
aiti-4099	254	47	,	,	PUNCT
aiti-4099	254	48	nx	nx	PROPN
aiti-4099	254	49	is	be	AUX
aiti-4099	254	50	variable	variable	ADJ
aiti-4099	254	51	fig	fig	NOUN
aiti-4099	254	52	.	.	PUNCT
aiti-4099	255	1	7	7	NUM
aiti-4099	255	2	variation	variation	NOUN
aiti-4099	255	3	of	of	ADP
aiti-4099	255	4	dimensionless	dimensionless	NOUN
aiti-4099	255	5	deflection	deflection	NOUN
aiti-4099	255	6	at	at	ADP
aiti-4099	255	7	the	the	DET
aiti-4099	255	8	free	free	ADJ
aiti-4099	255	9	end	end	NOUN
aiti-4099	255	10	with	with	ADP
aiti-4099	255	11	a	a	DET
aiti-4099	255	12	time	time	NOUN
aiti-4099	255	13	of	of	ADP
aiti-4099	255	14	cf	cf	NOUN
aiti-4099	255	15	(	(	PUNCT
aiti-4099	255	16	2	2	NUM
aiti-4099	255	17	-	-	SYM
aiti-4099	255	18	1	1	NUM
aiti-4099	255	19	-	-	PUNCT
aiti-4099	255	20	2	2	NUM
aiti-4099	255	21	)	)	PUNCT
aiti-4099	255	22	beam	beam	NOUN
aiti-4099	255	23	under	under	ADP
aiti-4099	255	24	harmonic	harmonic	ADJ
aiti-4099	255	25	load	load	NOUN
aiti-4099	255	26	with	with	ADP
aiti-4099	255	27	ω=10	ω=10	NOUN
aiti-4099	255	28	rad	rad	PROPN
aiti-4099	255	29	/	/	SYM
aiti-4099	255	30	s	s	AUX
aiti-4099	255	31	acting	act	VERB
aiti-4099	255	32	at	at	ADP
aiti-4099	255	33	the	the	DET
aiti-4099	255	34	free	free	ADJ
aiti-4099	255	35	end	end	NOUN
aiti-4099	255	36	the	the	DET
aiti-4099	255	37	effect	effect	NOUN
aiti-4099	255	38	of	of	ADP
aiti-4099	255	39	the	the	DET
aiti-4099	255	40	grading	grade	VERB
aiti-4099	255	41	indexes	index	NOUN
aiti-4099	255	42	on	on	ADP
aiti-4099	255	43	the	the	DET
aiti-4099	255	44	harmonic	harmonic	ADJ
aiti-4099	255	45	response	response	NOUN
aiti-4099	255	46	of	of	ADP
aiti-4099	255	47	the	the	DET
aiti-4099	255	48	beams	beam	NOUN
aiti-4099	255	49	can	can	AUX
aiti-4099	255	50	be	be	AUX
aiti-4099	255	51	seen	see	VERB
aiti-4099	255	52	from	from	ADP
aiti-4099	255	53	the	the	DET
aiti-4099	255	54	figures	figure	NOUN
aiti-4099	255	55	,	,	PUNCT
aiti-4099	255	56	where	where	SCONJ
aiti-4099	255	57	the	the	DET
aiti-4099	255	58	dynamic	dynamic	ADJ
aiti-4099	255	59	deflections	deflection	NOUN
aiti-4099	255	60	are	be	AUX
aiti-4099	255	61	clearly	clearly	ADV
aiti-4099	255	62	decreased	decrease	VERB
aiti-4099	255	63	by	by	ADP
aiti-4099	255	64	increasing	increase	VERB
aiti-4099	255	65	the	the	DET
aiti-4099	255	66	material	material	NOUN
aiti-4099	255	67	grading	grade	VERB
aiti-4099	255	68	indexes	index	NOUN
aiti-4099	255	69	nx	nx	NOUN
aiti-4099	255	70	and	and	CCONJ
aiti-4099	255	71	nz	nz	PROPN
aiti-4099	255	72	,	,	PUNCT
aiti-4099	255	73	regardless	regardless	ADV
aiti-4099	255	74	of	of	ADP
aiti-4099	255	75	the	the	DET
aiti-4099	255	76	boundary	boundary	ADJ
aiti-4099	255	77	conditions	condition	NOUN
aiti-4099	255	78	.	.	PUNCT
aiti-4099	256	1	advances	advance	NOUN
aiti-4099	256	2	in	in	ADP
aiti-4099	256	3	technology	technology	NOUN
aiti-4099	256	4	innovation	innovation	NOUN
aiti-4099	256	5	,	,	PUNCT
aiti-4099	256	6	vol	vol	NOUN
aiti-4099	256	7	.	.	PROPN
aiti-4099	257	1	4	4	NUM
aiti-4099	257	2	,	,	PUNCT
aiti-4099	257	3	no	no	INTJ
aiti-4099	257	4	.	.	NOUN
aiti-4099	257	5	3	3	NUM
aiti-4099	257	6	,	,	PUNCT
aiti-4099	257	7	2019	2019	NUM
aiti-4099	257	8	,	,	PUNCT
aiti-4099	257	9	pp	pp	ADJ
aiti-4099	257	10	.	.	PUNCT
aiti-4099	258	1	152	152	NUM
aiti-4099	258	2	-	-	SYM
aiti-4099	258	3	164	164	NUM
aiti-4099	258	4	163	163	NUM
aiti-4099	258	5	this	this	DET
aiti-4099	258	6	effect	effect	NOUN
aiti-4099	258	7	can	can	AUX
aiti-4099	258	8	also	also	ADV
aiti-4099	258	9	be	be	AUX
aiti-4099	258	10	explained	explain	VERB
aiti-4099	258	11	by	by	ADP
aiti-4099	258	12	the	the	DET
aiti-4099	258	13	increase	increase	NOUN
aiti-4099	258	14	of	of	ADP
aiti-4099	258	15	ceramic	ceramic	ADJ
aiti-4099	258	16	content	content	NOUN
aiti-4099	258	17	for	for	ADP
aiti-4099	258	18	the	the	DET
aiti-4099	258	19	beam	beam	NOUN
aiti-4099	258	20	associated	associate	VERB
aiti-4099	258	21	with	with	ADP
aiti-4099	258	22	the	the	DET
aiti-4099	258	23	higher	high	ADJ
aiti-4099	258	24	indexes	index	NOUN
aiti-4099	258	25	,	,	PUNCT
aiti-4099	258	26	and	and	CCONJ
aiti-4099	258	27	this	this	PRON
aiti-4099	258	28	leads	lead	VERB
aiti-4099	258	29	to	to	ADP
aiti-4099	258	30	higher	high	ADJ
aiti-4099	258	31	rigidities	rigidity	NOUN
aiti-4099	258	32	for	for	ADP
aiti-4099	258	33	the	the	DET
aiti-4099	258	34	beam	beam	NOUN
aiti-4099	258	35	associated	associate	VERB
aiti-4099	258	36	with	with	ADP
aiti-4099	258	37	higher	high	ADJ
aiti-4099	258	38	grading	grading	NOUN
aiti-4099	258	39	indexes	index	NOUN
aiti-4099	258	40	,	,	PUNCT
aiti-4099	258	41	as	as	SCONJ
aiti-4099	258	42	explained	explain	VERB
aiti-4099	258	43	above	above	ADV
aiti-4099	258	44	.	.	PUNCT
aiti-4099	259	1	as	as	ADP
aiti-4099	259	2	a	a	DET
aiti-4099	259	3	result	result	NOUN
aiti-4099	259	4	,	,	PUNCT
aiti-4099	259	5	the	the	DET
aiti-4099	259	6	dynamic	dynamic	ADJ
aiti-4099	259	7	deflection	deflection	NOUN
aiti-4099	259	8	of	of	ADP
aiti-4099	259	9	the	the	DET
aiti-4099	259	10	beam	beam	NOUN
aiti-4099	259	11	is	be	AUX
aiti-4099	259	12	decreased	decrease	VERB
aiti-4099	259	13	by	by	ADP
aiti-4099	259	14	increasing	increase	VERB
aiti-4099	259	15	the	the	DET
aiti-4099	259	16	material	material	NOUN
aiti-4099	259	17	grading	grade	VERB
aiti-4099	259	18	indexes	index	NOUN
aiti-4099	259	19	.	.	PUNCT
aiti-4099	260	1	5	5	X
aiti-4099	260	2	.	.	X
aiti-4099	260	3	conclusions	conclusion	NOUN
aiti-4099	260	4	in	in	ADP
aiti-4099	260	5	this	this	DET
aiti-4099	260	6	paper	paper	NOUN
aiti-4099	260	7	,	,	PUNCT
aiti-4099	260	8	a	a	DET
aiti-4099	260	9	finite	finite	ADJ
aiti-4099	260	10	element	element	NOUN
aiti-4099	260	11	formulation	formulation	NOUN
aiti-4099	260	12	was	be	AUX
aiti-4099	260	13	developed	develop	VERB
aiti-4099	260	14	for	for	ADP
aiti-4099	260	15	analyzing	analyze	VERB
aiti-4099	260	16	the	the	DET
aiti-4099	260	17	free	free	ADJ
aiti-4099	260	18	and	and	CCONJ
aiti-4099	260	19	forced	force	VERB
aiti-4099	260	20	vibration	vibration	NOUN
aiti-4099	260	21	of	of	ADP
aiti-4099	260	22	2d	2d	NOUN
aiti-4099	260	23	-	-	PUNCT
aiti-4099	260	24	fgsw	fgsw	NOUN
aiti-4099	260	25	beams	beam	NOUN
aiti-4099	260	26	.	.	PUNCT
aiti-4099	261	1	the	the	DET
aiti-4099	261	2	beams	beam	NOUN
aiti-4099	261	3	were	be	AUX
aiti-4099	261	4	considered	consider	VERB
aiti-4099	261	5	to	to	PART
aiti-4099	261	6	be	be	AUX
aiti-4099	261	7	formed	form	VERB
aiti-4099	261	8	from	from	ADP
aiti-4099	261	9	three	three	NUM
aiti-4099	261	10	layers	layer	NOUN
aiti-4099	261	11	,	,	PUNCT
aiti-4099	261	12	a	a	DET
aiti-4099	261	13	homogeneous	homogeneous	ADJ
aiti-4099	261	14	ceramic	ceramic	ADJ
aiti-4099	261	15	core	core	NOUN
aiti-4099	261	16	and	and	CCONJ
aiti-4099	261	17	two	two	NUM
aiti-4099	261	18	functionally	functionally	ADV
aiti-4099	261	19	graded	grade	VERB
aiti-4099	261	20	skin	skin	NOUN
aiti-4099	261	21	layers	layer	NOUN
aiti-4099	261	22	with	with	ADP
aiti-4099	261	23	material	material	NOUN
aiti-4099	261	24	properties	property	NOUN
aiti-4099	261	25	varying	vary	VERB
aiti-4099	261	26	in	in	ADP
aiti-4099	261	27	both	both	CCONJ
aiti-4099	261	28	the	the	DET
aiti-4099	261	29	thickness	thickness	NOUN
aiti-4099	261	30	and	and	CCONJ
aiti-4099	261	31	length	length	NOUN
aiti-4099	261	32	directions	direction	NOUN
aiti-4099	261	33	by	by	ADP
aiti-4099	261	34	power	power	NOUN
aiti-4099	261	35	gradation	gradation	NOUN
aiti-4099	261	36	laws	law	NOUN
aiti-4099	261	37	.	.	PUNCT
aiti-4099	262	1	based	base	VERB
aiti-4099	262	2	on	on	ADP
aiti-4099	262	3	the	the	DET
aiti-4099	262	4	refined	refined	ADJ
aiti-4099	262	5	third	third	ADJ
aiti-4099	262	6	-	-	PUNCT
aiti-4099	262	7	order	order	NOUN
aiti-4099	262	8	shear	shear	NOUN
aiti-4099	262	9	deformation	deformation	NOUN
aiti-4099	262	10	theory	theory	NOUN
aiti-4099	262	11	,	,	PUNCT
aiti-4099	262	12	in	in	ADP
aiti-4099	262	13	which	which	PRON
aiti-4099	262	14	the	the	DET
aiti-4099	262	15	transverse	transverse	ADJ
aiti-4099	262	16	displacement	displacement	NOUN
aiti-4099	262	17	is	be	AUX
aiti-4099	262	18	split	split	VERB
aiti-4099	262	19	into	into	ADP
aiti-4099	262	20	bending	bend	VERB
aiti-4099	262	21	and	and	CCONJ
aiti-4099	262	22	shear	shear	NOUN
aiti-4099	262	23	parts	part	NOUN
aiti-4099	262	24	,	,	PUNCT
aiti-4099	262	25	expressions	expression	NOUN
aiti-4099	262	26	for	for	ADP
aiti-4099	262	27	stiffness	stiffness	NOUN
aiti-4099	262	28	and	and	CCONJ
aiti-4099	262	29	mass	mass	ADJ
aiti-4099	262	30	matrices	matrix	NOUN
aiti-4099	262	31	of	of	ADP
aiti-4099	262	32	a	a	DET
aiti-4099	262	33	two	two	NUM
aiti-4099	262	34	-	-	PUNCT
aiti-4099	262	35	node	node	NOUN
aiti-4099	262	36	beam	beam	NOUN
aiti-4099	262	37	element	element	NOUN
aiti-4099	262	38	were	be	AUX
aiti-4099	262	39	derived	derive	VERB
aiti-4099	262	40	and	and	CCONJ
aiti-4099	262	41	employed	employ	VERB
aiti-4099	262	42	in	in	ADP
aiti-4099	262	43	computing	compute	VERB
aiti-4099	262	44	natural	natural	ADJ
aiti-4099	262	45	frequencies	frequency	NOUN
aiti-4099	262	46	and	and	CCONJ
aiti-4099	262	47	dynamic	dynamic	ADJ
aiti-4099	262	48	response	response	NOUN
aiti-4099	262	49	of	of	ADP
aiti-4099	262	50	the	the	DET
aiti-4099	262	51	beams	beam	NOUN
aiti-4099	262	52	.	.	PUNCT
aiti-4099	263	1	numerical	numerical	ADJ
aiti-4099	263	2	results	result	NOUN
aiti-4099	263	3	obtained	obtain	VERB
aiti-4099	263	4	by	by	ADP
aiti-4099	263	5	using	use	VERB
aiti-4099	263	6	the	the	DET
aiti-4099	263	7	formulation	formulation	NOUN
aiti-4099	263	8	was	be	AUX
aiti-4099	263	9	compared	compare	VERB
aiti-4099	263	10	with	with	ADP
aiti-4099	263	11	the	the	DET
aiti-4099	263	12	published	publish	VERB
aiti-4099	263	13	data	datum	NOUN
aiti-4099	263	14	to	to	PART
aiti-4099	263	15	confirm	confirm	VERB
aiti-4099	263	16	the	the	DET
aiti-4099	263	17	accuracy	accuracy	NOUN
aiti-4099	263	18	of	of	ADP
aiti-4099	263	19	the	the	DET
aiti-4099	263	20	proposed	propose	VERB
aiti-4099	263	21	formulation	formulation	NOUN
aiti-4099	263	22	.	.	PUNCT
aiti-4099	264	1	a	a	DET
aiti-4099	264	2	parametric	parametric	ADJ
aiti-4099	264	3	study	study	NOUN
aiti-4099	264	4	has	have	AUX
aiti-4099	264	5	been	be	AUX
aiti-4099	264	6	carried	carry	VERB
aiti-4099	264	7	to	to	PART
aiti-4099	264	8	highlight	highlight	VERB
aiti-4099	264	9	the	the	DET
aiti-4099	264	10	effects	effect	NOUN
aiti-4099	264	11	of	of	ADP
aiti-4099	264	12	the	the	DET
aiti-4099	264	13	material	material	NOUN
aiti-4099	264	14	distribution	distribution	NOUN
aiti-4099	264	15	,	,	PUNCT
aiti-4099	264	16	the	the	DET
aiti-4099	264	17	layer	layer	NOUN
aiti-4099	264	18	thickness	thickness	NOUN
aiti-4099	264	19	ratio	ratio	NOUN
aiti-4099	264	20	and	and	CCONJ
aiti-4099	264	21	the	the	DET
aiti-4099	264	22	aspect	aspect	NOUN
aiti-4099	264	23	ratio	ratio	NOUN
aiti-4099	264	24	on	on	ADP
aiti-4099	264	25	the	the	DET
aiti-4099	264	26	vibration	vibration	NOUN
aiti-4099	264	27	characteristics	characteristic	NOUN
aiti-4099	264	28	of	of	ADP
aiti-4099	264	29	the	the	DET
aiti-4099	264	30	beams	beam	NOUN
aiti-4099	264	31	.	.	PUNCT
aiti-4099	265	1	the	the	DET
aiti-4099	265	2	obtained	obtain	VERB
aiti-4099	265	3	results	result	NOUN
aiti-4099	265	4	reveal	reveal	VERB
aiti-4099	265	5	that	that	SCONJ
aiti-4099	265	6	the	the	DET
aiti-4099	265	7	material	material	NOUN
aiti-4099	265	8	distribution	distribution	NOUN
aiti-4099	265	9	and	and	CCONJ
aiti-4099	265	10	the	the	DET
aiti-4099	265	11	layer	layer	NOUN
aiti-4099	265	12	thickness	thickness	NOUN
aiti-4099	265	13	ratio	ratio	NOUN
aiti-4099	265	14	of	of	ADP
aiti-4099	265	15	the	the	DET
aiti-4099	265	16	beams	beam	NOUN
aiti-4099	265	17	play	play	VERB
aiti-4099	265	18	an	an	DET
aiti-4099	265	19	important	important	ADJ
aiti-4099	265	20	role	role	NOUN
aiti-4099	265	21	on	on	ADP
aiti-4099	265	22	the	the	DET
aiti-4099	265	23	vibration	vibration	NOUN
aiti-4099	265	24	response	response	NOUN
aiti-4099	265	25	of	of	ADP
aiti-4099	265	26	the	the	DET
aiti-4099	265	27	2d	2d	NOUN
aiti-4099	265	28	-	-	PUNCT
aiti-4099	265	29	fgsw	fgsw	NOUN
aiti-4099	265	30	beams	beam	NOUN
aiti-4099	265	31	.	.	PUNCT
aiti-4099	266	1	the	the	DET
aiti-4099	266	2	numerical	numerical	ADJ
aiti-4099	266	3	results	result	NOUN
aiti-4099	266	4	of	of	ADP
aiti-4099	266	5	the	the	DET
aiti-4099	266	6	present	present	ADJ
aiti-4099	266	7	paper	paper	NOUN
aiti-4099	266	8	guide	guide	NOUN
aiti-4099	266	9	to	to	PART
aiti-4099	266	10	design	design	VERB
aiti-4099	266	11	2d	2d	NOUN
aiti-4099	266	12	-	-	PUNCT
aiti-4099	266	13	fdsw	fdsw	NOUN
aiti-4099	266	14	beams	beam	NOUN
aiti-4099	266	15	to	to	PART
aiti-4099	266	16	achieve	achieve	VERB
aiti-4099	266	17	desired	desire	VERB
aiti-4099	266	18	vibration	vibration	NOUN
aiti-4099	266	19	characteristics	characteristic	NOUN
aiti-4099	266	20	.	.	PUNCT
aiti-4099	267	1	though	though	SCONJ
aiti-4099	267	2	the	the	DET
aiti-4099	267	3	paper	paper	NOUN
aiti-4099	267	4	examined	examine	VERB
aiti-4099	267	5	only	only	ADV
aiti-4099	267	6	harmonic	harmonic	ADJ
aiti-4099	267	7	response	response	NOUN
aiti-4099	267	8	of	of	ADP
aiti-4099	267	9	the	the	DET
aiti-4099	267	10	beam	beam	NOUN
aiti-4099	267	11	,	,	PUNCT
aiti-4099	267	12	the	the	DET
aiti-4099	267	13	finite	finite	PROPN
aiti-4099	267	14	element	element	NOUN
aiti-4099	267	15	formulation	formulation	NOUN
aiti-4099	267	16	developed	develop	VERB
aiti-4099	267	17	herein	herein	NOUN
aiti-4099	267	18	can	can	AUX
aiti-4099	267	19	be	be	AUX
aiti-4099	267	20	employed	employ	VERB
aiti-4099	267	21	to	to	PART
aiti-4099	267	22	compute	compute	VERB
aiti-4099	267	23	dynamic	dynamic	ADJ
aiti-4099	267	24	response	response	NOUN
aiti-4099	267	25	of	of	ADP
aiti-4099	267	26	2d	2d	NOUN
aiti-4099	267	27	-	-	PUNCT
aiti-4099	267	28	fgsw	fgsw	NOUN
aiti-4099	267	29	beams	beam	NOUN
aiti-4099	267	30	subjected	subject	VERB
aiti-4099	267	31	to	to	ADP
aiti-4099	267	32	other	other	ADJ
aiti-4099	267	33	types	type	NOUN
aiti-4099	267	34	of	of	ADP
aiti-4099	267	35	dynamic	dynamic	ADJ
aiti-4099	267	36	loads	load	NOUN
aiti-4099	267	37	as	as	ADV
aiti-4099	267	38	well	well	ADV
aiti-4099	267	39	.	.	PUNCT
aiti-4099	268	1	conflicts	conflict	NOUN
aiti-4099	268	2	of	of	ADP
aiti-4099	268	3	interest	interest	NOUN
aiti-4099	268	4	the	the	DET
aiti-4099	268	5	authors	author	NOUN
aiti-4099	268	6	declare	declare	VERB
aiti-4099	268	7	no	no	DET
aiti-4099	268	8	conflict	conflict	NOUN
aiti-4099	268	9	of	of	ADP
aiti-4099	268	10	interest	interest	NOUN
aiti-4099	268	11	.	.	PUNCT
aiti-4099	269	1	acknowledgement	acknowledgement	NOUN
aiti-4099	269	2	this	this	DET
aiti-4099	269	3	work	work	NOUN
aiti-4099	269	4	was	be	AUX
aiti-4099	269	5	supported	support	VERB
aiti-4099	269	6	by	by	ADP
aiti-4099	269	7	vietnam	vietnam	PROPN
aiti-4099	269	8	national	national	PROPN
aiti-4099	269	9	foundation	foundation	PROPN
aiti-4099	269	10	for	for	ADP
aiti-4099	269	11	science	science	NOUN
aiti-4099	269	12	and	and	CCONJ
aiti-4099	269	13	technology	technology	NOUN
aiti-4099	269	14	development	development	NOUN
aiti-4099	269	15	(	(	PUNCT
aiti-4099	269	16	nafosted	nafoste	VERB
aiti-4099	269	17	)	)	PUNCT
aiti-4099	269	18	under	under	ADP
aiti-4099	269	19	grant	grant	NOUN
aiti-4099	269	20	no	no	NOUN
aiti-4099	269	21	.	.	PUNCT
aiti-4099	270	1	107.02	107.02	NUM
aiti-4099	270	2	-	-	SYM
aiti-4099	270	3	2018.23	2018.23	NUM
aiti-4099	270	4	.	.	PUNCT
aiti-4099	271	1	references	reference	NOUN
aiti-4099	271	2	[	[	X
aiti-4099	271	3	1	1	NUM
aiti-4099	271	4	]	]	PUNCT
aiti-4099	271	5	m.	m.	NOUN
aiti-4099	271	6	koizumin	koizumin	PROPN
aiti-4099	271	7	,	,	PUNCT
aiti-4099	271	8	“	"	PUNCT
aiti-4099	271	9	fgm	fgm	PROPN
aiti-4099	271	10	activities	activity	NOUN
aiti-4099	271	11	in	in	ADP
aiti-4099	271	12	japan	japan	PROPN
aiti-4099	271	13	,	,	PUNCT
aiti-4099	271	14	”	"	PUNCT
aiti-4099	271	15	composites	composite	NOUN
aiti-4099	271	16	:	:	PUNCT
aiti-4099	271	17	part	part	NOUN
aiti-4099	271	18	b	b	PROPN
aiti-4099	271	19	,	,	PUNCT
aiti-4099	271	20	vol	vol	NOUN
aiti-4099	271	21	.	.	PROPN
aiti-4099	271	22	28	28	NUM
aiti-4099	271	23	,	,	PUNCT
aiti-4099	271	24	pp	pp	ADJ
aiti-4099	271	25	.	.	PUNCT
aiti-4099	272	1	1	1	NUM
aiti-4099	272	2	-	-	SYM
aiti-4099	272	3	4	4	NUM
aiti-4099	272	4	,	,	PUNCT
aiti-4099	272	5	1997	1997	NUM
aiti-4099	272	6	.	.	PUNCT
aiti-4099	273	1	[	[	X
aiti-4099	273	2	2	2	X
aiti-4099	273	3	]	]	PUNCT
aiti-4099	273	4	s.	s.	PROPN
aiti-4099	273	5	c.	c.	PROPN
aiti-4099	273	6	pradhan	pradhan	PROPN
aiti-4099	273	7	and	and	CCONJ
aiti-4099	273	8	t.	t.	PROPN
aiti-4099	273	9	murmu	murmu	NOUN
aiti-4099	273	10	,	,	PUNCT
aiti-4099	273	11	“	"	PUNCT
aiti-4099	273	12	thermo	thermo	NOUN
aiti-4099	273	13	-	-	PUNCT
aiti-4099	273	14	mechanical	mechanical	ADJ
aiti-4099	273	15	vibration	vibration	NOUN
aiti-4099	273	16	of	of	ADP
aiti-4099	273	17	fgm	fgm	PROPN
aiti-4099	273	18	sandwich	sandwich	NOUN
aiti-4099	273	19	beam	beam	NOUN
aiti-4099	273	20	under	under	ADP
aiti-4099	273	21	variable	variable	ADJ
aiti-4099	273	22	elastic	elastic	ADJ
aiti-4099	273	23	foundations	foundation	NOUN
aiti-4099	273	24	using	use	VERB
aiti-4099	273	25	differential	differential	ADJ
aiti-4099	273	26	quadrature	quadrature	NOUN
aiti-4099	273	27	method	method	NOUN
aiti-4099	273	28	,	,	PUNCT
aiti-4099	273	29	”	"	PUNCT
aiti-4099	273	30	journal	journal	NOUN
aiti-4099	273	31	of	of	ADP
aiti-4099	273	32	sound	sound	NOUN
aiti-4099	273	33	and	and	CCONJ
aiti-4099	273	34	vibration	vibration	NOUN
aiti-4099	273	35	,	,	PUNCT
aiti-4099	273	36	vol	vol	NOUN
aiti-4099	273	37	.	.	PROPN
aiti-4099	273	38	321	321	NUM
aiti-4099	273	39	,	,	PUNCT
aiti-4099	273	40	pp	pp	ADJ
aiti-4099	273	41	.	.	PUNCT
aiti-4099	273	42	342	342	NUM
aiti-4099	273	43	-	-	SYM
aiti-4099	273	44	362	362	NUM
aiti-4099	273	45	,	,	PUNCT
aiti-4099	273	46	march	march	PROPN
aiti-4099	273	47	2009	2009	NUM
aiti-4099	273	48	.	.	PUNCT
aiti-4099	274	1	[	[	X
aiti-4099	274	2	3	3	NUM
aiti-4099	274	3	]	]	PUNCT
aiti-4099	274	4	m.	m.	NOUN
aiti-4099	274	5	c.	c.	PROPN
aiti-4099	274	6	amirani	amirani	PROPN
aiti-4099	274	7	,	,	PUNCT
aiti-4099	274	8	s.	s.	PROPN
aiti-4099	274	9	m.	m.	PROPN
aiti-4099	274	10	r.	r.	PROPN
aiti-4099	274	11	khalili	khalili	PROPN
aiti-4099	274	12	,	,	PUNCT
aiti-4099	274	13	and	and	CCONJ
aiti-4099	274	14	n.	n.	PROPN
aiti-4099	274	15	nemati	nemati	PROPN
aiti-4099	274	16	.	.	PUNCT
aiti-4099	275	1	“	"	PUNCT
aiti-4099	275	2	free	free	ADJ
aiti-4099	275	3	vibration	vibration	NOUN
aiti-4099	275	4	analysis	analysis	NOUN
aiti-4099	275	5	of	of	ADP
aiti-4099	275	6	sandwich	sandwich	NOUN
aiti-4099	275	7	beam	beam	NOUN
aiti-4099	275	8	with	with	ADP
aiti-4099	275	9	fg	fg	PROPN
aiti-4099	275	10	core	core	PROPN
aiti-4099	275	11	using	use	VERB
aiti-4099	275	12	the	the	DET
aiti-4099	275	13	element	element	NOUN
aiti-4099	275	14	free	free	ADJ
aiti-4099	275	15	galerkin	galerkin	PROPN
aiti-4099	275	16	method	method	NOUN
aiti-4099	275	17	,	,	PUNCT
aiti-4099	275	18	”	"	PUNCT
aiti-4099	275	19	composite	composite	ADJ
aiti-4099	275	20	structures	structure	NOUN
aiti-4099	275	21	,	,	PUNCT
aiti-4099	275	22	vol	vol	NOUN
aiti-4099	275	23	.	.	PROPN
aiti-4099	276	1	90	90	NUM
aiti-4099	276	2	,	,	PUNCT
aiti-4099	276	3	pp	pp	ADJ
aiti-4099	276	4	.	.	PUNCT
aiti-4099	277	1	373	373	NUM
aiti-4099	277	2	-	-	SYM
aiti-4099	277	3	379	379	NUM
aiti-4099	277	4	,	,	PUNCT
aiti-4099	277	5	october	october	PROPN
aiti-4099	277	6	2009	2009	NUM
aiti-4099	277	7	.	.	PUNCT
aiti-4099	278	1	[	[	X
aiti-4099	278	2	4	4	X
aiti-4099	278	3	]	]	X
aiti-4099	278	4	d.	d.	PROPN
aiti-4099	278	5	s.	s.	PROPN
aiti-4099	278	6	mashat	mashat	PROPN
aiti-4099	278	7	,	,	PUNCT
aiti-4099	278	8	e.	e.	PROPN
aiti-4099	278	9	carrera	carrera	PROPN
aiti-4099	278	10	,	,	PUNCT
aiti-4099	278	11	a.	a.	PROPN
aiti-4099	278	12	m.	m.	NOUN
aiti-4099	278	13	zenkour	zenkour	PROPN
aiti-4099	278	14	,	,	PUNCT
aiti-4099	278	15	s.	s.	PROPN
aiti-4099	278	16	a.	a.	PROPN
aiti-4099	278	17	al	al	PROPN
aiti-4099	278	18	khateeb	khateeb	PROPN
aiti-4099	278	19	,	,	PUNCT
aiti-4099	278	20	and	and	CCONJ
aiti-4099	278	21	m.	m.	PROPN
aiti-4099	278	22	filippi	filippi	PROPN
aiti-4099	278	23	,	,	PUNCT
aiti-4099	278	24	“	"	PUNCT
aiti-4099	278	25	free	free	ADJ
aiti-4099	278	26	vibration	vibration	NOUN
aiti-4099	278	27	of	of	ADP
aiti-4099	278	28	fgm	fgm	PROPN
aiti-4099	278	29	layered	layered	ADJ
aiti-4099	278	30	beams	beam	NOUN
aiti-4099	278	31	by	by	ADP
aiti-4099	278	32	various	various	ADJ
aiti-4099	278	33	theories	theory	NOUN
aiti-4099	278	34	and	and	CCONJ
aiti-4099	278	35	finite	finite	ADJ
aiti-4099	278	36	elements	element	NOUN
aiti-4099	278	37	,	,	PUNCT
aiti-4099	278	38	”	"	PUNCT
aiti-4099	278	39	composites	composite	NOUN
aiti-4099	278	40	:	:	PUNCT
aiti-4099	278	41	part	part	NOUN
aiti-4099	278	42	b	b	PROPN
aiti-4099	278	43	,	,	PUNCT
aiti-4099	278	44	vol	vol	NOUN
aiti-4099	278	45	.	.	PROPN
aiti-4099	278	46	59	59	NUM
aiti-4099	278	47	,	,	PUNCT
aiti-4099	278	48	pp	pp	ADJ
aiti-4099	278	49	.	.	PUNCT
aiti-4099	279	1	269	269	NUM
aiti-4099	279	2	-	-	SYM
aiti-4099	279	3	278	278	NUM
aiti-4099	279	4	,	,	PUNCT
aiti-4099	279	5	march	march	PROPN
aiti-4099	279	6	2014	2014	NUM
aiti-4099	279	7	.	.	PUNCT
aiti-4099	280	1	[	[	X
aiti-4099	280	2	5	5	NUM
aiti-4099	280	3	]	]	X
aiti-4099	280	4	r.	r.	PROPN
aiti-4099	280	5	bennai	bennai	PROPN
aiti-4099	280	6	,	,	PUNCT
aiti-4099	280	7	h.	h.	PROPN
aiti-4099	280	8	a.	a.	PROPN
aiti-4099	280	9	atmane	atmane	PROPN
aiti-4099	280	10	,	,	PUNCT
aiti-4099	280	11	and	and	CCONJ
aiti-4099	280	12	a.	a.	NOUN
aiti-4099	280	13	tounsi	tounsi	NOUN
aiti-4099	280	14	,	,	PUNCT
aiti-4099	280	15	“	"	PUNCT
aiti-4099	280	16	a	a	DET
aiti-4099	280	17	new	new	ADJ
aiti-4099	280	18	higher	high	ADJ
aiti-4099	280	19	-	-	PUNCT
aiti-4099	280	20	order	order	NOUN
aiti-4099	280	21	shear	shear	NOUN
aiti-4099	280	22	and	and	CCONJ
aiti-4099	280	23	normal	normal	ADJ
aiti-4099	280	24	deformation	deformation	NOUN
aiti-4099	280	25	theory	theory	NOUN
aiti-4099	280	26	for	for	ADP
aiti-4099	280	27	functionally	functionally	ADV
aiti-4099	280	28	graded	grade	VERB
aiti-4099	280	29	sandwich	sandwich	NOUN
aiti-4099	280	30	beams	beam	NOUN
aiti-4099	280	31	,	,	PUNCT
aiti-4099	280	32	”	"	PUNCT
aiti-4099	280	33	steel	steel	NOUN
aiti-4099	280	34	and	and	CCONJ
aiti-4099	280	35	composite	composite	ADJ
aiti-4099	280	36	structures	structure	NOUN
aiti-4099	280	37	,	,	PUNCT
aiti-4099	280	38	vol	vol	NOUN
aiti-4099	280	39	.	.	PROPN
aiti-4099	280	40	19	19	NUM
aiti-4099	280	41	,	,	PUNCT
aiti-4099	280	42	pp	pp	ADJ
aiti-4099	280	43	.	.	PUNCT
aiti-4099	281	1	521	521	NUM
aiti-4099	281	2	-	-	SYM
aiti-4099	281	3	546	546	NUM
aiti-4099	281	4	,	,	PUNCT
aiti-4099	281	5	september	september	PROPN
aiti-4099	281	6	2015	2015	NUM
aiti-4099	281	7	.	.	PUNCT
aiti-4099	282	1	[	[	X
aiti-4099	282	2	6	6	NUM
aiti-4099	282	3	]	]	PUNCT
aiti-4099	282	4	t.	t.	PROPN
aiti-4099	282	5	p.	p.	PROPN
aiti-4099	282	6	vo	vo	NOUN
aiti-4099	282	7	,	,	PUNCT
aiti-4099	282	8	h.-t	h.-t	NOUN
aiti-4099	282	9	.	.	PUNCT
aiti-4099	283	1	thai	thai	PROPN
aiti-4099	283	2	,	,	PUNCT
aiti-4099	283	3	t.-k	t.-k	PROPN
aiti-4099	283	4	.	.	PUNCT
aiti-4099	284	1	nguyen	nguyen	PROPN
aiti-4099	284	2	,	,	PUNCT
aiti-4099	284	3	a.	a.	NOUN
aiti-4099	284	4	maheri	maheri	PROPN
aiti-4099	284	5	,	,	PUNCT
aiti-4099	284	6	and	and	CCONJ
aiti-4099	284	7	j.	j.	PROPN
aiti-4099	284	8	lee	lee	PROPN
aiti-4099	284	9	,	,	PUNCT
aiti-4099	284	10	“	"	PUNCT
aiti-4099	284	11	finite	finite	PROPN
aiti-4099	284	12	element	element	NOUN
aiti-4099	284	13	model	model	NOUN
aiti-4099	284	14	for	for	ADP
aiti-4099	284	15	vibration	vibration	NOUN
aiti-4099	284	16	and	and	CCONJ
aiti-4099	284	17	buckling	buckling	NOUN
aiti-4099	284	18	of	of	ADP
aiti-4099	284	19	functionally	functionally	ADV
aiti-4099	284	20	graded	grade	VERB
aiti-4099	284	21	sandwich	sandwich	NOUN
aiti-4099	284	22	beams	beam	NOUN
aiti-4099	284	23	based	base	VERB
aiti-4099	284	24	on	on	ADP
aiti-4099	284	25	a	a	DET
aiti-4099	284	26	refined	refined	ADJ
aiti-4099	284	27	shear	shear	NOUN
aiti-4099	284	28	deformation	deformation	NOUN
aiti-4099	284	29	theory	theory	NOUN
aiti-4099	284	30	,	,	PUNCT
aiti-4099	284	31	”	"	PUNCT
aiti-4099	284	32	engineering	engineering	NOUN
aiti-4099	284	33	structures	structure	NOUN
aiti-4099	284	34	,	,	PUNCT
aiti-4099	284	35	vol	vol	NOUN
aiti-4099	284	36	.	.	PROPN
aiti-4099	285	1	64	64	NUM
aiti-4099	285	2	,	,	PUNCT
aiti-4099	285	3	pp	pp	ADJ
aiti-4099	285	4	.	.	PUNCT
aiti-4099	286	1	12	12	NUM
aiti-4099	286	2	-	-	SYM
aiti-4099	286	3	22	22	NUM
aiti-4099	286	4	,	,	PUNCT
aiti-4099	286	5	april	april	PROPN
aiti-4099	286	6	2014	2014	NUM
aiti-4099	286	7	.	.	PUNCT
aiti-4099	287	1	[	[	X
aiti-4099	287	2	7	7	X
aiti-4099	287	3	]	]	PUNCT
aiti-4099	287	4	t.	t.	PROPN
aiti-4099	287	5	p.	p.	PROPN
aiti-4099	287	6	vo	vo	PROPN
aiti-4099	287	7	,	,	PUNCT
aiti-4099	287	8	h.	h.	PROPN
aiti-4099	287	9	-t	-t	PROPN
aiti-4099	287	10	.	.	PUNCT
aiti-4099	288	1	thai	thai	PROPN
aiti-4099	288	2	,	,	PUNCT
aiti-4099	288	3	t	t	PROPN
aiti-4099	288	4	.	.	PUNCT
aiti-4099	289	1	-k	-k	PUNCT
aiti-4099	289	2	.	.	PUNCT
aiti-4099	289	3	nguyen	nguyen	PROPN
aiti-4099	289	4	,	,	PUNCT
aiti-4099	289	5	f.	f.	PROPN
aiti-4099	289	6	inam	inam	PROPN
aiti-4099	289	7	,	,	PUNCT
aiti-4099	289	8	and	and	CCONJ
aiti-4099	289	9	j.	j.	PROPN
aiti-4099	289	10	lee	lee	PROPN
aiti-4099	289	11	,	,	PUNCT
aiti-4099	289	12	“	"	PUNCT
aiti-4099	289	13	a	a	DET
aiti-4099	289	14	quasi-3d	quasi-3d	ADJ
aiti-4099	289	15	theory	theory	NOUN
aiti-4099	289	16	for	for	ADP
aiti-4099	289	17	vibration	vibration	NOUN
aiti-4099	289	18	and	and	CCONJ
aiti-4099	289	19	buckling	buckling	NOUN
aiti-4099	289	20	of	of	ADP
aiti-4099	289	21	functionally	functionally	ADV
aiti-4099	289	22	graded	grade	VERB
aiti-4099	289	23	sandwich	sandwich	NOUN
aiti-4099	289	24	beams	beam	NOUN
aiti-4099	289	25	,	,	PUNCT
aiti-4099	289	26	”	"	PUNCT
aiti-4099	289	27	composite	composite	ADJ
aiti-4099	289	28	structures	structure	NOUN
aiti-4099	289	29	,	,	PUNCT
aiti-4099	289	30	vol	vol	NOUN
aiti-4099	289	31	.	.	PROPN
aiti-4099	290	1	119	119	NUM
aiti-4099	290	2	,	,	PUNCT
aiti-4099	290	3	pp	pp	ADJ
aiti-4099	290	4	.	.	PUNCT
aiti-4099	291	1	1	1	NUM
aiti-4099	291	2	-	-	SYM
aiti-4099	291	3	12	12	NUM
aiti-4099	291	4	,	,	PUNCT
aiti-4099	291	5	january	january	PROPN
aiti-4099	291	6	2015	2015	NUM
aiti-4099	291	7	.	.	PUNCT
aiti-4099	292	1	[	[	X
aiti-4099	292	2	8	8	NUM
aiti-4099	292	3	]	]	PUNCT
aiti-4099	292	4	z.	z.	PROPN
aiti-4099	292	5	su	su	PROPN
aiti-4099	292	6	,	,	PUNCT
aiti-4099	292	7	g.	g.	PROPN
aiti-4099	292	8	jin	jin	PROPN
aiti-4099	292	9	,	,	PUNCT
aiti-4099	292	10	y.	y.	PROPN
aiti-4099	292	11	wang	wang	PROPN
aiti-4099	292	12	,	,	PUNCT
aiti-4099	292	13	and	and	CCONJ
aiti-4099	292	14	x.	x.	NOUN
aiti-4099	292	15	ye	ye	PROPN
aiti-4099	292	16	,	,	PUNCT
aiti-4099	292	17	“	"	PUNCT
aiti-4099	292	18	a	a	DET
aiti-4099	292	19	general	general	ADJ
aiti-4099	292	20	fourier	fourier	NOUN
aiti-4099	292	21	formulation	formulation	NOUN
aiti-4099	292	22	for	for	ADP
aiti-4099	292	23	vibration	vibration	NOUN
aiti-4099	292	24	analysis	analysis	NOUN
aiti-4099	292	25	of	of	ADP
aiti-4099	292	26	functionally	functionally	ADV
aiti-4099	292	27	graded	grade	VERB
aiti-4099	292	28	sandwich	sandwich	NOUN
aiti-4099	292	29	beams	beam	NOUN
aiti-4099	292	30	with	with	ADP
aiti-4099	292	31	arbitrary	arbitrary	ADJ
aiti-4099	292	32	boundary	boundary	ADJ
aiti-4099	292	33	condition	condition	NOUN
aiti-4099	292	34	and	and	CCONJ
aiti-4099	292	35	resting	rest	VERB
aiti-4099	292	36	on	on	ADP
aiti-4099	292	37	elastic	elastic	ADJ
aiti-4099	292	38	foundations	foundation	NOUN
aiti-4099	292	39	,	,	PUNCT
aiti-4099	292	40	”	"	PUNCT
aiti-4099	292	41	acta	acta	PROPN
aiti-4099	292	42	mechanica	mechanica	PROPN
aiti-4099	292	43	,	,	PUNCT
aiti-4099	292	44	vol	vol	NOUN
aiti-4099	292	45	.	.	PROPN
aiti-4099	293	1	227	227	NUM
aiti-4099	293	2	,	,	PUNCT
aiti-4099	293	3	pp	pp	ADJ
aiti-4099	293	4	.	.	PUNCT
aiti-4099	294	1	1493	1493	NUM
aiti-4099	294	2	-	-	SYM
aiti-4099	294	3	1514	1514	NUM
aiti-4099	294	4	,	,	PUNCT
aiti-4099	294	5	may	may	AUX
aiti-4099	294	6	2016	2016	NUM
aiti-4099	294	7	.	.	PUNCT
aiti-4099	295	1	[	[	X
aiti-4099	295	2	9	9	NUM
aiti-4099	295	3	]	]	PUNCT
aiti-4099	295	4	m.	m.	NOUN
aiti-4099	295	5	şimşek	şimşek	NOUN
aiti-4099	295	6	,	,	PUNCT
aiti-4099	295	7	“	"	PUNCT
aiti-4099	295	8	bi	bi	ADJ
aiti-4099	295	9	-	-	ADJ
aiti-4099	295	10	directional	directional	ADJ
aiti-4099	295	11	functionally	functionally	ADV
aiti-4099	295	12	graded	grade	VERB
aiti-4099	295	13	materials	material	NOUN
aiti-4099	295	14	(	(	PUNCT
aiti-4099	295	15	bdfgms	bdfgms	PROPN
aiti-4099	295	16	)	)	PUNCT
aiti-4099	295	17	for	for	ADP
aiti-4099	295	18	free	free	ADJ
aiti-4099	295	19	and	and	CCONJ
aiti-4099	295	20	forced	force	VERB
aiti-4099	295	21	vibration	vibration	NOUN
aiti-4099	295	22	of	of	ADP
aiti-4099	295	23	timoshenko	timoshenko	ADJ
aiti-4099	295	24	beams	beam	NOUN
aiti-4099	295	25	with	with	ADP
aiti-4099	295	26	various	various	ADJ
aiti-4099	295	27	boundary	boundary	ADJ
aiti-4099	295	28	conditions	condition	NOUN
aiti-4099	295	29	,	,	PUNCT
aiti-4099	295	30	”	"	PUNCT
aiti-4099	295	31	composite	composite	ADJ
aiti-4099	295	32	structures	structure	NOUN
aiti-4099	295	33	,	,	PUNCT
aiti-4099	295	34	vol	vol	NOUN
aiti-4099	295	35	.	.	PROPN
aiti-4099	295	36	133	133	NUM
aiti-4099	295	37	,	,	PUNCT
aiti-4099	295	38	pp.968	pp.968	PROPN
aiti-4099	295	39	-	-	SYM
aiti-4099	295	40	978	978	NUM
aiti-4099	295	41	,	,	PUNCT
aiti-4099	295	42	december	december	PROPN
aiti-4099	295	43	2015	2015	NUM
aiti-4099	295	44	.	.	PUNCT
aiti-4099	296	1	advances	advance	NOUN
aiti-4099	296	2	in	in	ADP
aiti-4099	296	3	technology	technology	NOUN
aiti-4099	296	4	innovation	innovation	NOUN
aiti-4099	296	5	,	,	PUNCT
aiti-4099	296	6	vol	vol	NOUN
aiti-4099	296	7	.	.	PROPN
aiti-4099	297	1	4	4	NUM
aiti-4099	297	2	,	,	PUNCT
aiti-4099	297	3	no	no	INTJ
aiti-4099	297	4	.	.	NOUN
aiti-4099	297	5	3	3	NUM
aiti-4099	297	6	,	,	PUNCT
aiti-4099	297	7	2019	2019	NUM
aiti-4099	297	8	,	,	PUNCT
aiti-4099	297	9	pp	pp	ADJ
aiti-4099	297	10	.	.	PUNCT
aiti-4099	298	1	152	152	NUM
aiti-4099	298	2	-	-	SYM
aiti-4099	298	3	164	164	NUM
aiti-4099	298	4	164	164	NUM
aiti-4099	298	5	[	[	X
aiti-4099	298	6	10	10	NUM
aiti-4099	298	7	]	]	PUNCT
aiti-4099	298	8	z.	z.	PROPN
aiti-4099	298	9	wang	wang	PROPN
aiti-4099	298	10	,	,	PUNCT
aiti-4099	298	11	x.	x.	PROPN
aiti-4099	298	12	wang	wang	PROPN
aiti-4099	298	13	,	,	PUNCT
aiti-4099	298	14	g.	g.	PROPN
aiti-4099	298	15	xu	xu	PROPN
aiti-4099	298	16	,	,	PUNCT
aiti-4099	298	17	s.	s.	PROPN
aiti-4099	298	18	cheng	cheng	PROPN
aiti-4099	298	19	,	,	PUNCT
aiti-4099	298	20	and	and	CCONJ
aiti-4099	298	21	t.	t.	PROPN
aiti-4099	298	22	zeng	zeng	PROPN
aiti-4099	298	23	,	,	PUNCT
aiti-4099	298	24	“	"	PUNCT
aiti-4099	298	25	free	free	ADJ
aiti-4099	298	26	vibration	vibration	NOUN
aiti-4099	298	27	of	of	ADP
aiti-4099	298	28	two	two	NUM
aiti-4099	298	29	-	-	PUNCT
aiti-4099	298	30	directional	directional	NOUN
aiti-4099	298	31	functionally	functionally	ADV
aiti-4099	298	32	graded	grade	VERB
aiti-4099	298	33	beams	beam	NOUN
aiti-4099	298	34	,	,	PUNCT
aiti-4099	298	35	”	"	PUNCT
aiti-4099	298	36	composite	composite	ADJ
aiti-4099	298	37	structures	structure	NOUN
aiti-4099	298	38	,	,	PUNCT
aiti-4099	298	39	vol	vol	NOUN
aiti-4099	298	40	.	.	PROPN
aiti-4099	298	41	135	135	NUM
aiti-4099	298	42	,	,	PUNCT
aiti-4099	298	43	pp.191	pp.191	NOUN
aiti-4099	298	44	-	-	SYM
aiti-4099	298	45	198	198	NUM
aiti-4099	298	46	,	,	PUNCT
aiti-4099	298	47	january	january	PROPN
aiti-4099	298	48	2016	2016	NUM
aiti-4099	298	49	.	.	PUNCT
aiti-4099	299	1	[	[	X
aiti-4099	299	2	11	11	NUM
aiti-4099	299	3	]	]	PUNCT
aiti-4099	299	4	d.	d.	PROPN
aiti-4099	299	5	k.	k.	PROPN
aiti-4099	299	6	nguyen	nguyen	PROPN
aiti-4099	299	7	,	,	PUNCT
aiti-4099	299	8	q.	q.	PROPN
aiti-4099	299	9	h.	h.	PROPN
aiti-4099	299	10	nguyen	nguyen	PROPN
aiti-4099	299	11	,	,	PUNCT
aiti-4099	299	12	t.	t.	PROPN
aiti-4099	299	13	t.	t.	PROPN
aiti-4099	299	14	tran	tran	PROPN
aiti-4099	299	15	,	,	PUNCT
aiti-4099	299	16	and	and	CCONJ
aiti-4099	299	17	v.	v.	ADP
aiti-4099	299	18	t.	t.	NOUN
aiti-4099	299	19	bui	bui	PROPN
aiti-4099	299	20	,	,	PUNCT
aiti-4099	299	21	“	"	PUNCT
aiti-4099	299	22	vibration	vibration	NOUN
aiti-4099	299	23	of	of	ADP
aiti-4099	299	24	bi	bi	ADJ
aiti-4099	299	25	-	-	ADJ
aiti-4099	299	26	dimensional	dimensional	ADJ
aiti-4099	299	27	functionally	functionally	ADV
aiti-4099	299	28	graded	grade	VERB
aiti-4099	299	29	timoshenko	timoshenko	NOUN
aiti-4099	299	30	beams	beam	NOUN
aiti-4099	299	31	excited	excite	VERB
aiti-4099	299	32	by	by	ADP
aiti-4099	299	33	a	a	DET
aiti-4099	299	34	moving	move	VERB
aiti-4099	299	35	load	load	NOUN
aiti-4099	299	36	,	,	PUNCT
aiti-4099	299	37	”	"	PUNCT
aiti-4099	299	38	acta	acta	PROPN
aiti-4099	299	39	mechanica	mechanica	PROPN
aiti-4099	299	40	,	,	PUNCT
aiti-4099	299	41	vol	vol	NOUN
aiti-4099	299	42	.	.	PROPN
aiti-4099	300	1	228	228	NUM
aiti-4099	300	2	,	,	PUNCT
aiti-4099	300	3	pp.141	pp.141	NOUN
aiti-4099	300	4	-	-	PUNCT
aiti-4099	300	5	155	155	NUM
aiti-4099	300	6	,	,	PUNCT
aiti-4099	300	7	january	january	PROPN
aiti-4099	300	8	2017	2017	NUM
aiti-4099	300	9	.	.	PUNCT
aiti-4099	301	1	[	[	X
aiti-4099	301	2	12	12	NUM
aiti-4099	301	3	]	]	X
aiti-4099	301	4	d.	d.	PROPN
aiti-4099	301	5	k.	k.	PROPN
aiti-4099	301	6	nguyen	nguyen	PROPN
aiti-4099	301	7	and	and	CCONJ
aiti-4099	301	8	t.	t.	PROPN
aiti-4099	301	9	t.	t.	PROPN
aiti-4099	301	10	tran	tran	PROPN
aiti-4099	301	11	,	,	PUNCT
aiti-4099	301	12	“	"	PUNCT
aiti-4099	301	13	free	free	ADJ
aiti-4099	301	14	vibration	vibration	NOUN
aiti-4099	301	15	of	of	ADP
aiti-4099	301	16	tapered	tapered	ADJ
aiti-4099	301	17	bfgm	bfgm	PROPN
aiti-4099	301	18	beams	beam	NOUN
aiti-4099	301	19	using	use	VERB
aiti-4099	301	20	an	an	DET
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aiti-4099	301	22	shear	shear	NOUN
aiti-4099	301	23	deformable	deformable	ADJ
aiti-4099	301	24	finite	finite	ADJ
aiti-4099	301	25	element	element	NOUN
aiti-4099	301	26	model	model	NOUN
aiti-4099	301	27	,	,	PUNCT
aiti-4099	301	28	”	"	PUNCT
aiti-4099	301	29	steel	steel	NOUN
aiti-4099	301	30	and	and	CCONJ
aiti-4099	301	31	composite	composite	ADJ
aiti-4099	301	32	structures	structure	NOUN
aiti-4099	301	33	,	,	PUNCT
aiti-4099	301	34	vol	vol	NOUN
aiti-4099	301	35	.	.	PROPN
aiti-4099	301	36	29	29	NUM
aiti-4099	301	37	,	,	PUNCT
aiti-4099	301	38	pp	pp	ADJ
aiti-4099	301	39	.	.	PUNCT
aiti-4099	302	1	363	363	NUM
aiti-4099	302	2	-	-	SYM
aiti-4099	302	3	377	377	NUM
aiti-4099	302	4	,	,	PUNCT
aiti-4099	302	5	november	november	PROPN
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aiti-4099	302	7	.	.	PUNCT
aiti-4099	303	1	[	[	X
aiti-4099	303	2	13	13	NUM
aiti-4099	303	3	]	]	PUNCT
aiti-4099	303	4	a.	a.	NOUN
aiti-4099	303	5	karamanli	karamanli	PROPN
aiti-4099	303	6	,	,	PUNCT
aiti-4099	303	7	“	"	PUNCT
aiti-4099	303	8	bending	bend	VERB
aiti-4099	303	9	behaviour	behaviour	NOUN
aiti-4099	303	10	of	of	ADP
aiti-4099	303	11	two	two	NUM
aiti-4099	303	12	directional	directional	ADJ
aiti-4099	303	13	functionally	functionally	ADV
aiti-4099	303	14	graded	grade	VERB
aiti-4099	303	15	sandwich	sandwich	NOUN
aiti-4099	303	16	beams	beam	NOUN
aiti-4099	303	17	by	by	ADP
aiti-4099	303	18	using	use	VERB
aiti-4099	303	19	a	a	DET
aiti-4099	303	20	quasi-3d	quasi-3d	ADJ
aiti-4099	303	21	shear	shear	NOUN
aiti-4099	303	22	deformation	deformation	NOUN
aiti-4099	303	23	theory	theory	NOUN
aiti-4099	303	24	,	,	PUNCT
aiti-4099	303	25	”	"	PUNCT
aiti-4099	303	26	composite	composite	ADJ
aiti-4099	303	27	structures	structure	NOUN
aiti-4099	303	28	,	,	PUNCT
aiti-4099	303	29	vol	vol	NOUN
aiti-4099	303	30	.	.	PROPN
aiti-4099	303	31	174	174	NUM
aiti-4099	303	32	,	,	PUNCT
aiti-4099	303	33	pp	pp	ADJ
aiti-4099	303	34	.	.	PUNCT
aiti-4099	304	1	70	70	NUM
aiti-4099	304	2	-	-	SYM
aiti-4099	304	3	86	86	NUM
aiti-4099	304	4	,	,	PUNCT
aiti-4099	304	5	august	august	PROPN
aiti-4099	304	6	2017	2017	NUM
aiti-4099	304	7	.	.	PUNCT
aiti-4099	305	1	[	[	X
aiti-4099	305	2	14	14	NUM
aiti-4099	305	3	]	]	X
aiti-4099	305	4	m.	m.	NOUN
aiti-4099	305	5	a.	a.	PROPN
aiti-4099	305	6	a.	a.	PROPN
aiti-4099	305	7	meziane	meziane	PROPN
aiti-4099	305	8	,	,	PUNCT
aiti-4099	305	9	h.	h.	PROPN
aiti-4099	305	10	h.	h.	PROPN
aiti-4099	305	11	abdelaziz	abdelaziz	PROPN
aiti-4099	305	12	,	,	PUNCT
aiti-4099	305	13	a.	a.	NOUN
aiti-4099	305	14	tounsi	tounsi	NOUN
aiti-4099	305	15	,	,	PUNCT
aiti-4099	305	16	“	"	PUNCT
aiti-4099	305	17	an	an	DET
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aiti-4099	305	19	and	and	CCONJ
aiti-4099	305	20	simple	simple	ADJ
aiti-4099	305	21	refined	refined	ADJ
aiti-4099	305	22	theory	theory	NOUN
aiti-4099	305	23	for	for	ADP
aiti-4099	305	24	buckling	buckle	VERB
aiti-4099	305	25	and	and	CCONJ
aiti-4099	305	26	free	free	ADJ
aiti-4099	305	27	vibration	vibration	NOUN
aiti-4099	305	28	of	of	ADP
aiti-4099	305	29	exponentially	exponentially	ADV
aiti-4099	305	30	graded	grade	VERB
aiti-4099	305	31	sandwich	sandwich	NOUN
aiti-4099	305	32	plates	plate	NOUN
aiti-4099	305	33	under	under	ADP
aiti-4099	305	34	various	various	ADJ
aiti-4099	305	35	boundary	boundary	ADJ
aiti-4099	305	36	conditions	condition	NOUN
aiti-4099	305	37	”	"	PUNCT
aiti-4099	305	38	,	,	PUNCT
aiti-4099	305	39	journal	journal	NOUN
aiti-4099	305	40	of	of	ADP
aiti-4099	305	41	sandwich	sandwich	NOUN
aiti-4099	305	42	structures	structure	NOUN
aiti-4099	305	43	and	and	CCONJ
aiti-4099	305	44	materials	material	NOUN
aiti-4099	305	45	,	,	PUNCT
aiti-4099	305	46	vol	vol	NOUN
aiti-4099	305	47	.	.	PROPN
aiti-4099	305	48	16	16	NUM
aiti-4099	305	49	,	,	PUNCT
aiti-4099	305	50	pp	pp	ADJ
aiti-4099	305	51	.	.	PUNCT
aiti-4099	306	1	293	293	NUM
aiti-4099	306	2	-	-	SYM
aiti-4099	306	3	318	318	NUM
aiti-4099	306	4	,	,	PUNCT
aiti-4099	306	5	march	march	PROPN
aiti-4099	306	6	2014	2014	NUM
aiti-4099	306	7	.	.	PUNCT
aiti-4099	307	1	[	[	X
aiti-4099	307	2	15	15	NUM
aiti-4099	307	3	]	]	X
aiti-4099	307	4	m.	m.	NOUN
aiti-4099	307	5	bennoun	bennoun	PROPN
aiti-4099	307	6	,	,	PUNCT
aiti-4099	307	7	m.	m.	NOUN
aiti-4099	307	8	s.	s.	PROPN
aiti-4099	307	9	a.	a.	PROPN
aiti-4099	307	10	houari	houari	PROPN
aiti-4099	307	11	,	,	PUNCT
aiti-4099	307	12	and	and	CCONJ
aiti-4099	307	13	a.	a.	NOUN
aiti-4099	307	14	tounsi	tounsi	NOUN
aiti-4099	307	15	,	,	PUNCT
aiti-4099	307	16	“	"	PUNCT
aiti-4099	307	17	a	a	DET
aiti-4099	307	18	novel	novel	ADJ
aiti-4099	307	19	five	five	NUM
aiti-4099	307	20	variable	variable	ADJ
aiti-4099	307	21	refined	refined	ADJ
aiti-4099	307	22	plate	plate	NOUN
aiti-4099	307	23	theory	theory	NOUN
aiti-4099	307	24	for	for	ADP
aiti-4099	307	25	vibration	vibration	NOUN
aiti-4099	307	26	analysis	analysis	NOUN
aiti-4099	307	27	of	of	ADP
aiti-4099	307	28	functionally	functionally	ADV
aiti-4099	307	29	graded	grade	VERB
aiti-4099	307	30	sandwich	sandwich	NOUN
aiti-4099	307	31	plates	plate	NOUN
aiti-4099	307	32	”	"	PUNCT
aiti-4099	307	33	,	,	PUNCT
aiti-4099	307	34	mechanics	mechanic	NOUN
aiti-4099	307	35	of	of	ADP
aiti-4099	307	36	advanced	advanced	ADJ
aiti-4099	307	37	materials	material	NOUN
aiti-4099	307	38	and	and	CCONJ
aiti-4099	307	39	structures	structure	NOUN
aiti-4099	307	40	,	,	PUNCT
aiti-4099	307	41	vol	vol	NOUN
aiti-4099	307	42	.	.	PROPN
aiti-4099	307	43	23	23	NUM
aiti-4099	307	44	,	,	PUNCT
aiti-4099	307	45	pp	pp	ADJ
aiti-4099	307	46	.	.	PUNCT
aiti-4099	307	47	423	423	NUM
aiti-4099	307	48	-	-	SYM
aiti-4099	307	49	431	431	NUM
aiti-4099	307	50	,	,	PUNCT
aiti-4099	307	51	january	january	PROPN
aiti-4099	307	52	2016	2016	NUM
aiti-4099	307	53	.	.	PUNCT
aiti-4099	308	1	[	[	X
aiti-4099	308	2	16	16	NUM
aiti-4099	308	3	]	]	PUNCT
aiti-4099	308	4	h.	h.	PROPN
aiti-4099	308	5	h.	h.	PROPN
aiti-4099	308	6	abdelaziz	abdelaziz	PROPN
aiti-4099	308	7	,	,	PUNCT
aiti-4099	308	8	m.	m.	NOUN
aiti-4099	308	9	a.	a.	NOUN
aiti-4099	308	10	a.	a.	PROPN
aiti-4099	308	11	meziane	meziane	PROPN
aiti-4099	308	12	,	,	PUNCT
aiti-4099	308	13	a.	a.	NOUN
aiti-4099	308	14	a.	a.	NOUN
aiti-4099	308	15	bousahla	bousahla	PROPN
aiti-4099	308	16	,	,	PUNCT
aiti-4099	308	17	a.	a.	NOUN
aiti-4099	308	18	tounsi	tounsi	PROPN
aiti-4099	308	19	,	,	PUNCT
aiti-4099	308	20	s.	s.	PROPN
aiti-4099	308	21	r.	r.	PROPN
aiti-4099	308	22	mahmoud	mahmoud	PROPN
aiti-4099	308	23	,	,	PUNCT
aiti-4099	308	24	and	and	CCONJ
aiti-4099	308	25	a.	a.	PROPN
aiti-4099	308	26	s.	s.	PROPN
aiti-4099	308	27	alwabli	alwabli	PROPN
aiti-4099	308	28	,	,	PUNCT
aiti-4099	308	29	“	"	PUNCT
aiti-4099	308	30	an	an	DET
aiti-4099	308	31	efficient	efficient	ADJ
aiti-4099	308	32	hyperbolic	hyperbolic	ADJ
aiti-4099	308	33	shear	shear	NOUN
aiti-4099	308	34	deformation	deformation	NOUN
aiti-4099	308	35	theory	theory	NOUN
aiti-4099	308	36	for	for	ADP
aiti-4099	308	37	bending	bend	VERB
aiti-4099	308	38	,	,	PUNCT
aiti-4099	308	39	buckling	buckle	VERB
aiti-4099	308	40	and	and	CCONJ
aiti-4099	308	41	free	free	ADJ
aiti-4099	308	42	vibration	vibration	NOUN
aiti-4099	308	43	of	of	ADP
aiti-4099	308	44	fgm	fgm	PROPN
aiti-4099	308	45	sandwich	sandwich	NOUN
aiti-4099	308	46	plates	plate	NOUN
aiti-4099	308	47	with	with	ADP
aiti-4099	308	48	various	various	ADJ
aiti-4099	308	49	boundary	boundary	ADJ
aiti-4099	308	50	conditions	condition	NOUN
aiti-4099	308	51	,	,	PUNCT
aiti-4099	308	52	”	"	PUNCT
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aiti-4099	308	55	,	,	PUNCT
aiti-4099	308	56	vol	vol	NOUN
aiti-4099	308	57	.	.	PROPN
aiti-4099	308	58	25	25	NUM
aiti-4099	308	59	,	,	PUNCT
aiti-4099	308	60	pp	pp	ADJ
aiti-4099	308	61	.	.	PUNCT
aiti-4099	309	1	693	693	NUM
aiti-4099	309	2	-	-	SYM
aiti-4099	309	3	704	704	NUM
aiti-4099	309	4	,	,	PUNCT
aiti-4099	309	5	december	december	PROPN
aiti-4099	309	6	2017	2017	NUM
aiti-4099	309	7	.	.	PUNCT
aiti-4099	310	1	[	[	X
aiti-4099	310	2	17	17	NUM
aiti-4099	310	3	]	]	X
aiti-4099	310	4	f.	f.	PROPN
aiti-4099	310	5	bourada	bourada	PROPN
aiti-4099	310	6	,	,	PUNCT
aiti-4099	310	7	k.	k.	PROPN
aiti-4099	310	8	amara	amara	PROPN
aiti-4099	310	9	,	,	PUNCT
aiti-4099	310	10	a.	a.	NOUN
aiti-4099	310	11	a.	a.	NOUN
aiti-4099	310	12	bousahla	bousahla	PROPN
aiti-4099	310	13	,	,	PUNCT
aiti-4099	310	14	a.	a.	NOUN
aiti-4099	310	15	tounsi	tounsi	NOUN
aiti-4099	310	16	,	,	PUNCT
aiti-4099	310	17	and	and	CCONJ
aiti-4099	310	18	s.r	s.r	PROPN
aiti-4099	310	19	.	.	PROPN
aiti-4099	310	20	mahmoud	mahmoud	PROPN
aiti-4099	310	21	,	,	PUNCT
aiti-4099	310	22	“	"	PUNCT
aiti-4099	310	23	a	a	DET
aiti-4099	310	24	novel	novel	ADJ
aiti-4099	310	25	refined	refined	ADJ
aiti-4099	310	26	plate	plate	NOUN
aiti-4099	310	27	theory	theory	NOUN
aiti-4099	310	28	for	for	ADP
aiti-4099	310	29	stability	stability	NOUN
aiti-4099	310	30	analysis	analysis	NOUN
aiti-4099	310	31	of	of	ADP
aiti-4099	310	32	hybrid	hybrid	NOUN
aiti-4099	310	33	and	and	CCONJ
aiti-4099	310	34	symmetric	symmetric	ADJ
aiti-4099	310	35	s	s	NOUN
aiti-4099	310	36	-	-	PUNCT
aiti-4099	310	37	fgm	fgm	PROPN
aiti-4099	310	38	plates	plate	NOUN
aiti-4099	310	39	”	"	PUNCT
aiti-4099	310	40	,	,	PUNCT
aiti-4099	310	41	structural	structural	ADJ
aiti-4099	310	42	engineering	engineering	NOUN
aiti-4099	310	43	and	and	CCONJ
aiti-4099	310	44	mechanics	mechanic	NOUN
aiti-4099	310	45	,	,	PUNCT
aiti-4099	310	46	vol	vol	NOUN
aiti-4099	310	47	.	.	PROPN
aiti-4099	311	1	68	68	NUM
aiti-4099	311	2	,	,	PUNCT
aiti-4099	311	3	pp	pp	ADJ
aiti-4099	311	4	.	.	PUNCT
aiti-4099	312	1	661	661	NUM
aiti-4099	312	2	-	-	SYM
aiti-4099	312	3	675	675	NUM
aiti-4099	312	4	,	,	PUNCT
aiti-4099	312	5	december	december	PROPN
aiti-4099	312	6	2018	2018	NUM
aiti-4099	312	7	.	.	PUNCT
aiti-4099	313	1	[	[	X
aiti-4099	313	2	18	18	NUM
aiti-4099	313	3	]	]	PUNCT
aiti-4099	313	4	m.	m.	NOUN
aiti-4099	313	5	géradin	géradin	PROPN
aiti-4099	313	6	and	and	CCONJ
aiti-4099	313	7	r.	r.	PROPN
aiti-4099	313	8	rixen	rixen	PROPN
aiti-4099	313	9	,	,	PUNCT
aiti-4099	313	10	mechanical	mechanical	ADJ
aiti-4099	313	11	vibrations	vibration	NOUN
aiti-4099	313	12	,	,	PUNCT
aiti-4099	313	13	theory	theory	NOUN
aiti-4099	313	14	and	and	CCONJ
aiti-4099	313	15	application	application	NOUN
aiti-4099	313	16	to	to	ADP
aiti-4099	313	17	structural	structural	ADJ
aiti-4099	313	18	dynamics	dynamic	NOUN
aiti-4099	313	19	,	,	PUNCT
aiti-4099	313	20	2nd	2nd	PROPN
aiti-4099	313	21	edition	edition	PROPN
aiti-4099	313	22	.	.	PUNCT
aiti-4099	314	1	england	england	PROPN
aiti-4099	314	2	;	;	PUNCT
aiti-4099	314	3	chichester	chichester	PROPN
aiti-4099	314	4	,	,	PUNCT
aiti-4099	314	5	john	john	PROPN
aiti-4099	314	6	wiley	wiley	PROPN
aiti-4099	314	7	and	and	CCONJ
aiti-4099	314	8	sons	son	NOUN
aiti-4099	314	9	,	,	PUNCT
aiti-4099	314	10	1997	1997	NUM
aiti-4099	314	11	.	.	PUNCT
aiti-4099	315	1	copyright	copyright	NOUN
aiti-4099	315	2	©	©	PROPN
aiti-4099	315	3	by	by	ADP
aiti-4099	315	4	the	the	DET
aiti-4099	315	5	authors	author	NOUN
aiti-4099	315	6	.	.	PUNCT
aiti-4099	316	1	licensee	licensee	PROPN
aiti-4099	316	2	taeti	taeti	PROPN
aiti-4099	316	3	,	,	PUNCT
aiti-4099	316	4	taiwan	taiwan	PROPN
aiti-4099	316	5	.	.	PUNCT
aiti-4099	317	1	this	this	DET
aiti-4099	317	2	article	article	NOUN
aiti-4099	317	3	is	be	AUX
aiti-4099	317	4	an	an	DET
aiti-4099	317	5	open	open	ADJ
aiti-4099	317	6	access	access	NOUN
aiti-4099	317	7	article	article	NOUN
aiti-4099	317	8	distributed	distribute	VERB
aiti-4099	317	9	under	under	ADP
aiti-4099	317	10	the	the	DET
aiti-4099	317	11	terms	term	NOUN
aiti-4099	317	12	and	and	CCONJ
aiti-4099	317	13	conditions	condition	NOUN
aiti-4099	317	14	of	of	ADP
aiti-4099	317	15	the	the	DET
aiti-4099	317	16	creative	creative	ADJ
aiti-4099	317	17	commons	common	NOUN
aiti-4099	317	18	attribution	attribution	NOUN
aiti-4099	317	19	(	(	PUNCT
aiti-4099	317	20	cc	cc	NOUN
aiti-4099	317	21	by	by	ADP
aiti-4099	317	22	-	-	PUNCT
aiti-4099	317	23	nc	nc	NOUN
aiti-4099	317	24	)	)	PUNCT
aiti-4099	317	25	license	license	NOUN
aiti-4099	317	26	(	(	PUNCT
aiti-4099	317	27	https://creativecommons.org/licenses/by-nc/4.0/	https://creativecommons.org/licenses/by-nc/4.0/	NOUN
aiti-4099	317	28	)	)	PUNCT
aiti-4099	317	29	.	.	PUNCT
aiti-4099	318	1	https://journals.sagepub.com/doi/abs/10.1177/1099636214526852?journalcode=jsma	https://journals.sagepub.com/doi/abs/10.1177/1099636214526852?journalcode=jsma	PROPN
aiti-4099	318	2	https://journals.sagepub.com/doi/abs/10.1177/1099636214526852?journalcode=jsma	https://journals.sagepub.com/doi/abs/10.1177/1099636214526852?journalcode=jsma	PROPN
aiti-4099	318	3	https://journals.sagepub.com/doi/abs/10.1177/1099636214526852?journalcode=jsma	https://journals.sagepub.com/doi/abs/10.1177/1099636214526852?journalcode=jsma	PROPN
aiti-4099	318	4	callto:16(3),%20293	callto:16(3),%20293	PROPN
aiti-4099	318	5	-	-	PUNCT
aiti-4099	318	6	318	318	NUM
aiti-4099	318	7	https://www.tandfonline.com/author/bennoun%2c+mohammed	https://www.tandfonline.com/author/bennoun%2c+mohammed	ADJ
aiti-4099	318	8	https://www.tandfonline.com/author/houari%2c+mohammed+sid+ahmed	https://www.tandfonline.com/author/houari%2c+mohammed+sid+ahmed	PROPN
aiti-4099	318	9	https://www.tandfonline.com/author/tounsi%2c+abdelouahed	https://www.tandfonline.com/author/tounsi%2c+abdelouahe	VERB
aiti-4099	318	10	https://www.researchgate.net/journal/1225-4568_structural_engineering_mechanics	https://www.researchgate.net/journal/1225-4568_structural_engineering_mechanic	NOUN