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

Table 9

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+0.5𝑥²)(1+0.5𝑦²)).

Boundary condition	𝑎/𝑏	ℎ0/𝑎	Model sequence
			1	2	3	4	5	6
S-S-S-S	1	0.1	23.462	54.999	55.573	82.950	100.900	101.187
			(23.741^a)	(55.114)	(55.983)	(83.146)	(101.004)	(101.347)
		0.2	18.606	42.725	42.971	60.040	71.167	71.761
			(18.936^a)	(43.014)	(43.148)	(60.247)	(71.642)	(71.993)
	3/2	0.1	53.055	65.251	85.404	106.700	114.880	143.531
			(53.467^a)	(65.472)	(85.984)	(107.211)	(115.687)	(144.007)
		0.2	17.439	21.531	32.170	44.987	59.438	64.179
			(17.874^a)	(21.748)	(32.651)	(45.264)	(60.188)	(64.879)
C-F-F-F	1	0.1	3.658	9.317	24.135	32.816	35.433	59.179
			(3.749^a)	(9.547)	(24.034)	(33.627)	(36.308)	(60.142)
		0.2	3.520	7.986	19.591	26.959	27.491	43.882
			(3.611^a)	(8.176)	(20.075)	(27.125)	(27.625)	(43.984)
	3/2	0.1	3.901	9.963	28.984	69.187	73.686	89.360
			(3.930^a)	(10.095)	(29.381)	(69.578)	(73.994)	(90.242)
		0.2	3.292	4.439	13.385	23.947	40.850	44.758
			(3.386^a)	(4.498)	(14.012)	(24.068)	(41.221)	(45.142)
S-S-F-F	1	0.1	3.557	21.268	22.762	43.524	60.253	62.429
			(3.649^a)	(21.441)	(22.796)	(43.916)	(60.622)	(62.630)
		0.2	3.171	17.822	19.512	33.616	45.042	46.833
			(3.489^a)	(18.006)	(20.430)	(33.815)	(45.247)	(49.004)
	3/2	0.1	6.738	31.658	52.071	75.625	86.604	94.903
			(6.957^a)	(31.882)	(52.518)	(75.823)	(86.939)	(95.610)
		0.2	3.653	12.930	20.955	26.517	44.097	48.058
			(6.807^a)	(13.160)	(21.312)	(26.864)	(44.422)	(48.873)
C-C-C-C	1	0.1	41.020	75.196	75.614	104.142	119.683	120.949
			(41.405^a)	(75.452)	(75.882)	(104.711)	(119.637)	(121.137)
		0.2	31.237	51.686	51.868	68.411	76.868	77.864
			(32.010^a)	(52.960)	(52.145)	(69.335)	(77.481)	(78.099)
	3/2	0.1	95.823	128.727	163.657	173.751	190.890	223.595
			(95.364^a)	(128.932)	(163.588)	(172.350)	(190.350)	(222.948)
		0.2	53.306	71.372	89.384	102.404	104.660	120.908
			(53.587^a)	(71.759)	(90.103)	(102.503)	(105.174)	(121.275)
S-C-S-C	1	0.1	33.715	60.298	71.446	94.187	103.802	117.928
			(34.148^a)	(60.786)	(71.828)	(94.515)	(104.263)	(119.326)
		0.2	26.143	45.499	49.458	64.253	72.941	76.191
			(26.789^a)	(46.622)	(50.680)	(64.329)	(73.474)	(76.843)
	3/2	0.1	73.228	115.845	137.445	148.166	168.342	182.542
			(73.761^a)	(116.121)	(137.788)	(148.530)	(168.698)	(182.921)
		0.2	41.302	53.648	65.630	72.202	81.632	88.105
			(41.304^a)	(53.757)	(65.842)	(72.794)	(82.033)	(88.474)

aResults in parentheses are taken from FEM.