Free Vibration Characteristics of Moderately Thick Spherical Shell with General Boundary Conditions Based on Ritz Method

Table 4

Results of the annular spherical shell with classical boundary conditions (φ₀ = π/6, φ₁ = π/2, h = 0.06 m, and R = 1m).

n	m	Boundary conditions
		F–C	F–SS	F–SD	C–C	C–SS	C–SD	SD–SD	SD–SS	SS–SS
1	1	0.6817	0.6506	0.3576	1.2726	1.1611	0.7320	0.6097	1.0460	1.0823
	2	0.9894	0.9577	0.7359	1.2795	1.2727	1.1643	1.0542	1.1558	1.2720
	3	1.3427	1.2516	0.7955	2.0030	1.8598	1.5264	1.2667	1.7017	1.7203
	4	1.9047	1.8469	1.1163	2.3335	2.3046	1.8602	1.7053	2.1163	2.2841
	5	2.1354	2.1184	1.4217	2.8789	2.7077	2.5767	2.1325	2.3296	2.5383
2	1	0.3605	0.3382	0.2278	1.1451	1.1290	0.9540	0.9382	1.0524	1.1290
	2	1.1020	1.0643	0.9936	1.3688	1.2626	1.2556	1.1866	1.1893	1.1957
	3	1.4457	1.3421	1.1197	2.1017	1.9256	1.5831	1.3930	1.7653	1.7855
	4	1.9971	1.9560	1.3690	2.8395	2.7567	1.9251	1.7650	2.4661	2.5941
	5	2.2387	2.1109	2.0135	3.1365	3.0247	2.8368	2.6382	2.7026	2.9972
3	1	0.5538	0.5497	0.5485	1.1221	1.1032	1.0197	0.9967	1.0613	1.0987
	2	1.1934	1.1543	1.0763	1.4746	1.3692	1.3590	1.2831	1.3021	1.3158
	3	1.6014	1.4856	1.4830	2.1979	2.0213	1.9902	1.8637	1.8746	1.8970
	4	2.3367	2.1670	1.8228	3.0816	2.9144	2.0751	1.9907	2.7311	2.7447
	5	2.4780	2.4739	2.1649	3.3585	3.3122	2.9481	2.7569	3.0208	3.3013
4	1	0.8911	0.8884	0.8831	1.1667	1.1417	1.0872	1.0724	1.1201	1.1360
	2	1.2970	1.2470	1.1855	1.5956	1.4920	1.4687	1.4051	1.4324	1.4501
	3	1.7894	1.6701	1.6583	2.3293	2.1575	2.1439	2.0165	2.0296	2.0533
	4	2.5440	2.3725	2.3567	3.2899	3.0849	2.6580	2.6352	2.9121	2.9279
	5	3.1451	3.1322	2.5656	3.7065	3.7013	3.0904	2.9122	3.5558	3.6988