Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions

Table 5

Frequency parameter Ω=𝜔𝑎²(𝜌ℎ₀/𝐷₀)^1/2 for moderately thick plates with linearly varying thickness in different boundary conditions (ℎ(𝑥,𝑦)=ℎ₀(1+0.5𝑥)(1+0.5𝑦)).

Boundary; condition	𝑎/𝑏	ℎ0/𝑎	Model sequence
			1	2	3	4	5	6
S-S-S-S	1	0.1	27.261	62.397	62.926	92.423	111.537	111.732
			(27.263^a)	(62.410)	(63.842)	(92.445)	(111.867)	(111.921)
		0.2	23.103	47.010	47.191	65.018	75.831	75.865
			(23.489^a)	(47.209)	(47.349)	(65.057)	(76.605)	(76.473)
	3/2	0.1	59.338	99.101	138.798	151.102	166.710	204.855
			(59.874^a)	(99.249)	(138.177)	(151.362)	(166.644)	(205.381)
		0.2	41.175	63.765	63.765	73.598	83.956	89.084
			(41.586^a)	(63.313)	(63.669)	(73.661)	(83.918)	(89.547)
C-F-F-F	1	0.1	4.173	10.331	27.407	37.826	38.809	64.095
			(4.856^a)	(10.680)	(27.513)	(37.203)	(39.135)	(64.858)
		0.2	3.983	8.702	21.403	29.443	30.286	46.705
			(4.118^a)	(9.306)	(21.990)	(29.670)	(30.602)	(47.156)
	3/2	0.1	4.868	15.488	35.620	63.523	89.969	100.089
			(4.887^a)	(15.320)	(35.175)	(63.353)	(89.159)	(100.783)
		0.2	4.469	9.763	22.338	42.188)	50.104	56.331
			(4.944^a)	(9.636)	(22.087)	(42.177)	(50.580)	(56.559)
S-S-F-F	1	0.1	4.117	24.795	26.216	48.567)	68.195	69.667
			(4.789^a)	(24.149)	(26.751)	(49.324)	(68.842)	(70.575)
		0.2	3.820	20.516	21.924	37.523	48.980	50.327
			(4.103^a)	(20.041)	(22.125)	(37.221)	(48.894)	(50.622)
	3/2	0.1	7.935	39.454	65.063	92.877	92.877	136.176
			(7.856^a)	(40.145)	(65.162)	(92.462)	(93.022)	(136.336)
		0.2	6.389	26.149	35.627	49.539	56.844	65.170
			(6.406^a)	(26.536)	(35.626)	(49.831)	(57.144)	(65.981)
C-C-C-C	1	0.1	44.471	80.299	80.681	109.422	126.871	128.207
			(45.102^a)	(80.271)	(80.656)	(110.015)	(126.328)	(128.888)
		0.2	32.162	52.781	52.933	69.410	78.474	79.482
			(32.240^a)	(52.629)	(53.166)	(70.063)	(79.059)	(80.266)
	3/2	0.1	82.975	115.587	151.992	161.579	176.601	212.330
			(83.139^a)	(115.838)	(152.200)	(162.193)	(177.058)	(212.849)
		0.2	48.577	66.022	83.468	90.830	97.474	98.157
			(49.187^a)	(66.259)	(84.065)	(91.749)	(97.827)	(98.777)
S-C-S-C	1	0.1	36.847	66.664	76.965	101.045	113.594	125.551
			(37.901^a)	(68.568)	(78.356)	(101.200)	(113.978)	(125.651)
		0.2	27.673	48.469	51.220	67.027	76.358	78.241
			(27.897^a)	(48.685)	(51.491)	(67.447)	(77.530)	(79.573)
	3/2	0.1	77.378	106.848	150.079	154.569	173.120	208.391
			(78.003^a)	(107.058)	(150.991)	(155.171)	(173.099)	(208.402)
		0.2	45.895	64.732	73.393	83.282	90.325	97.089
			(45.803^a)	(64.131)	73.656	83.801	90.518	97.015

aResults in parentheses are taken from FEM.