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

Table 13

The first five frequency parameters of an open isotropic spherical shell with various boundary conditions and included angles (, ,  m, ,  GPa, and ).

	Mode	Boundary conditions
		FFFF	FFFC	CFFFF	FSFS	FCFC	SFSF	SSSS	SCSC	CFCF	CSCS	CCCC
	1	1.5434	0.5258	0.3956	1.1290	1.9941	0.2223	2.1807	2.4911	1.8990	2.2182	3.0667
	2	2.0638	0.8659	0.5747	1.6591	2.4592	1.0025	2.2182	2.7231	1.9102	2.4706	4.1467
	3	2.5408	1.0483	0.7678	2.2636	2.5999	1.2964	2.4712	4.1293	2.2036	3.9360	4.3251
	4	2.9590	1.8398	1.5304	2.4774	3.4859	1.9852	3.6766	4.1563	3.3344	4.3027	4.7985
	5	3.1493	2.2736	1.9231	3.2833	3.5635	2.5928	4.0103	4.5780	3.4008	4.3531	4.9817
	1	0.7468	0.1503	0.4323	0.2479	0.8889	0.2957	1.2670	1.3054	1.9184	2.1075	2.3646
	2	0.8246	0.2622	0.5281	0.4128	1.2374	1.0485	1.5707	1.7150	1.9212	2.2185	2.5819
	3	1.3824	0.5249	0.7754	1.1291	1.3836	1.1472	2.1811	2.3482	2.1685	2.4709	3.2073
	4	1.7188	0.6080	0.9511	1.2559	1.4004	1.3091	2.2185	2.4407	2.2848	3.1325	3.4764
	5	1.8750	1.0441	1.5353	1.6594	1.8157	1.9292	2.4717	3.0104	2.8882	3.2707	3.5592
	1	0.3418	0.0727	0.4725	0.0601	0.5198	0.3268	0.8917	0.9135	1.9210	2.0967	2.2406
	2	0.5192	0.1124	0.4959	0.0979	0.6987	0.8800	1.4624	1.5154	1.9236	2.1724	2.2484
	3	0.8172	0.2652	0.6403	0.5017	0.9143	1.0832	1.6389	1.6688	2.1366	2.2186	2.6379
	4	0.8719	0.3327	0.8189	0.8047	1.0622	1.1156	1.7514	1.8452	2.1756	2.4713	2.7068
	5	1.3417	0.6414	1.0216	1.0307	1.0907	1.5621	2.1816	2.3033	2.3414	2.7596	3.1727
	1	0.1888	0.0452	0.4689	0.2480	0.3235	0.3414	0.7145	0.7274	1.9243	2.1076	2.1555
	2	0.3385	0.0611	0.5233	0.4129	0.3853	0.6941	1.2672	1.2855	1.9255	2.1111	2.1944
	3	0.5085	0.1409	0.5676	0.6466	0.6937	1.0925	1.4292	1.4529	2.1144	2.2186	2.3711
	4	0.5841	0.2079	0.7232	0.9648	0.6970	1.1003	1.5709	1.6321	2.1613	2.2262	2.4572
	5	0.9281	0.4222	0.8582	1.0133	0.9779	1.2698	1.7908	1.8377	2.2045	2.4715	2.6920
	1	0.1177	0.0327	0.4867	0.0224	0.2086	0.3497	0.6155	0.6236	1.9278	2.0948	2.1323
	2	0.2184	0.0398	0.4900	0.0319	0.2259	0.5910	1.0399	1.0542	1.9282	2.1264	2.1506
	3	0.3231	0.0859	0.6039	0.1257	0.4760	1.0334	1.4150	1.4271	2.1169	2.1401	2.2870
	4	0.4395	0.1313	0.6105	0.2094	0.4815	1.0978	1.4948	1.5098	2.1215	2.2187	2.2974
	5	0.6178	0.2576	0.8022	0.3940	0.7802	1.1040	1.4989	1.5356	2.1970	2.2654	2.5086