Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

Table 15

The first five frequencies (Hz) of an open orthotropic spherical shell with various boundary conditions and thickness-radius ratios (, ,  m, and ).

	Mode	Boundary conditions
		FFFF	FFFC	CFFFF	FSFS	FCFC	SFSF	SSSS	SCSC	CFCF	CSCS	CCCC
0.1	1	19.896	4.7150	145.92	26.597	43.825	92.211	204.15	206.87	637.75	640.79	687.84
	2	38.600	7.1240	151.20	59.003	64.965	199.05	364.74	367.14	681.48	686.93	808.17
	3	55.399	15.160	153.30	71.455	97.762	340.84	417.88	420.49	799.24	804.31	947.86
	4	79.201	30.990	171.24	130.15	139.07	344.15	430.75	437.31	932.69	937.60	1020.7
	5	106.85	49.233	187.33	145.77	167.10	371.91	434.46	442.39	1001.0	1008.7	1047.7
0.2	1	33.414	7.9209	214.98	45.180	72.592	96.974	207.03	210.15	633.78	636.74	684.33
	2	69.721	12.651	216.11	93.424	80.087	200.08	371.20	375.03	677.97	683.38	807.60
	3	93.999	25.374	226.26	121.23	146.55	370.53	517.60	521.02	798.38	803.76	963.56
	4	132.28	47.581	230.62	219.47	176.25	457.82	528.68	536.52	946.63	953.19	1072.6
	5	177.78	80.265	263.47	233.78	233.90	460.49	533.26	539.54	1041.4	1057.8	1113.8
0.3	1	47.187	11.234	241.04	63.466	84.092	97.431	205.91	209.10	626.26	629.50	676.95
	2	94.608	16.780	244.82	109.78	97.592	198.64	368.42	372.44	669.88	676.00	800.45
	3	129.46	35.164	254.48	166.60	176.89	367.72	540.50	543.66	789.91	796.76	961.81
	4	157.36	55.245	254.74	250.56	185.67	495.01	557.49	561.94	941.27	952.43	1092.2
	5	237.51	106.95	277.95	270.09	254.20	499.55	572.32	582.43	1040.1	1079.2	1132.3
	1^A	47.232	11.217	242.75	63.374	84.068	97.543	206.35	209.48	627.38	631.29	678.57
	2^A	95.033	16.795	246.89	110.14	97.313	198.87	369.20	373.16	670.22	677.73	801.91
	3^A	129.90	35.127	255.38	167.11	176.99	368.44	542.07	545.12	790.89	798.61	963.97
	4^A	157.94	55.319	256.78	251.11	185.96	499.94	563.57	567.98	943.59	955.28	1097.9
	5^A	238.72	106.97	279.74	271.36	254.70	504.74	578.49	588.35	1046.1	1084.8	1140.1
0.4	1	60.205	14.431	251.07	80.237	85.760	96.770	203.49	206.68	615.23	618.93	665.74
	2	113.00	19.698	253.75	116.83	117.06	196.17	363.47	367.52	657.54	664.82	787.70
	3	160.03	43.922	259.74	204.51	187.57	362.74	533.94	536.72	775.23	784.31	949.69
	4	164.11	58.904	270.40	257.72	191.75	507.17	578.32	583.76	924.19	941.97	1098.0
	5	264.31	126.28	299.87	281.51	261.86	515.22	597.45	609.14	1021.8	1088.6	1129.6
0.5	1	72.074	17.420	250.27	94.752	86.482	95.525	200.21	203.37	600.93	605.18	650.82
	2	125.55	21.692	255.44	119.83	131.16	192.94	356.93	360.93	641.35	649.95	769.50
	3	162.84	51.465	266.92	233.65	186.52	356.18	523.57	526.18	755.11	766.45	927.68
	4	185.83	60.700	279.17	262.21	200.00	506.90	591.05	597.40	898.66	921.41	1086.3
	5	265.90	132.30	316.99	285.08	265.40	519.90	605.18	625.92	997.61	1079.3	1112.8

1^A to 5^A: results obtained by ANSYS.