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

Table 8

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

Boundary conditions	φ0	m
		1	2	3	4	5
F–C	π/8	0.6436	0.9719	1.2359	1.7010	1.9829
	π/6	0.6817	0.9894	1.3427	1.9047	2.1354
	π/5	0.7207	1.0168	1.4858	2.0655	2.1588
	π/4	0.7927	1.1003	1.8439	2.1205	2.4764
	π/3	0.9324	1.6052	2.3732	3.2253	3.7807
F–SS	π/8	0.6151	0.9440	1.1715	1.6221	1.9529
	π/6	0.6506	0.9577	1.2516	1.8469	2.1184
	π/5	0.6869	0.9768	1.3646	2.0592	2.1445
	π/4	0.7548	1.0298	1.6676	2.1047	2.4733
	π/3	0.8847	1.3469	2.3711	3.0294	3.5040
C–C	π/8	1.1348	1.1790	1.7292	2.1792	2.4499
	π/6	1.2726	1.2795	2.0030	2.3335	2.8789
	π/5	1.3572	1.4435	2.2659	2.5413	3.3283
	π/4	1.5028	1.8395	2.6605	3.2375	4.1434
	π/3	1.9826	3.4460	3.8057	6.0731	6.3115
C–SS	π/8	1.0521	1.1749	1.6077	2.1776	2.2916
	π/6	1.1611	1.2727	1.8598	2.3046	2.7077
	π/5	1.2836	1.3579	2.1425	2.4401	3.1824
	π/4	1.4597	1.6187	2.6498	2.9327	4.0995
	π/3	1.7692	2.9828	3.8054	5.5589	6.3115
C–SD	π/8	0.6681	1.0615	1.3325	1.6075	2.2854
	π/6	0.7320	1.1643	1.5264	1.8602	2.5767
	π/5	0.7894	1.2834	1.7247	2.1488	2.7264
	π/4	0.8963	1.5830	2.1195	2.7781	3.0742
	π/3	1.2719	2.8503	3.3175	3.9809	5.5639
E1–E1	π/8	0.6310	1.0695	1.2533	1.7324	2.1623
	π/6	0.6682	1.1437	1.3670	2.0209	2.1526
	π/5	0.6963	1.1792	1.5078	2.2043	2.3900
	π/4	0.7349	1.2160	1.8837	2.5220	3.1666
	π/3	0.7556	1.6250	3.4826	3.7092	6.0038
E2–E2	π/8	0.6508	1.1457	1.5671	1.9046	2.1186
	π/6	0.6744	1.2766	1.6952	2.1306	2.2726
	π/5	0.6929	1.4366	1.7664	2.3607	2.4996
	π/4	0.7327	1.7994	1.8725	2.7260	3.2327
	π/3	0.8902	2.1320	3.4461	3.8783	6.0731
E3–E3	π/8	0.1727	0.4252	1.1586	1.4577	1.7434
	π/6	0.1894	0.4576	1.2948	1.4920	2.0342
	π/5	0.2034	0.4968	1.4483	1.5153	2.3722
	π/4	0.2269	0.5911	1.5123	1.8613	3.0009
	π/3	0.2832	0.8905	1.7464	3.4707	4.0255