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

Table 9

Results of annular spherical shell with different φ₀ (φ₁ = π/2, R = 1m, h = 0.06 m, and n = 2).

Boundary conditions	φ0	m
		1	2	3	4	5
F–C	π/8	0.3989	1.0838	1.3492	1.8882	2.0273
	π/6	0.3605	1.1020	1.4457	1.9971	2.2387
	π/5	0.3825	1.1269	1.5822	2.1260	2.5498
	π/4	0.4642	1.2032	1.9384	2.4367	2.9543
	π/3	0.7003	1.6772	3.0515	3.2570	3.7890
F–SS	π/8	0.3866	1.0528	1.2677	1.7819	2.0039
	π/6	0.3382	1.0643	1.3421	1.9560	2.1109
	π/5	0.3516	1.0790	1.4502	2.1219	2.3433
	π/4	0.4188	1.1248	1.7467	2.4282	2.9414
	π/3	0.6185	1.4280	3.0188	3.1409	3.4721
C–C	π/8	1.0663	1.2502	1.8101	2.4663	2.7955
	π/6	1.1451	1.3688	2.1017	2.8395	3.1365
	π/5	1.2226	1.5185	2.4320	3.0975	3.4107
	π/4	1.3782	1.8981	3.1363	3.4427	4.0992
	π/3	1.9276	3.4851	4.2397	6.1067	6.2292
C–SS	π/8	1.0554	1.1742	1.6726	2.3405	2.7515
	π/6	1.1290	1.2626	1.9256	2.7567	3.0247
	π/5	1.1987	1.3767	2.2190	3.0967	3.2830
	π/4	1.3275	1.6774	2.9001	3.3744	4.0740
	π/3	1.7085	3.0270	4.2397	5.5981	6.2292
C–SD	π/8	0.9343	1.1710	1.4259	1.6727	2.3894
	π/6	0.9540	1.2556	1.5831	1.9251	2.8368
	π/5	0.9749	1.3660	1.7503	2.2177	3.2817
	π/4	1.0298	1.6562	2.0976	2.9028	3.6387
	π/3	1.3407	2.8863	3.2496	4.5122	5.6032
E1–E1	π/8	0.9479	1.2473	1.3445	1.7968	2.5694
	π/6	0.9770	1.3532	1.4163	2.0912	2.7441
	π/5	1.0107	1.4143	1.5423	2.4289	2.7437
	π/4	1.0983	1.4399	1.9199	2.9001	3.2094
	π/3	1.3349	1.6564	3.5149	3.9016	6.0480
E2–E2	π/8	0.8894	1.2273	1.7592	2.1700	2.5066
	π/6	0.9195	1.3495	2.0245	2.3292	2.7795
	π/5	0.9510	1.5023	2.2801	2.5156	2.8662
	π/4	1.0284	1.8866	2.5227	2.9265	3.3212
	π/3	1.4026	2.6416	3.4850	4.0183	6.1066
E3–E3	π/8	0.6189	0.7555	1.2454	1.7337	2.1863
	π/6	0.6201	0.7010	1.3519	2.0211	2.2574
	π/5	0.6202	0.6865	1.4994	2.2344	2.4279
	π/4	0.5772	0.7677	1.8830	2.3026	3.1813
	π/3	0.4831	1.2823	2.3369	3.4941	4.5082