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

Table 7

Results of annular spherical shell with different h/R ratios (φ₀ = π/6, φ₁ = π/2, R = 1m, and n = 2).

Boundary conditions	h/R	m
		1	2	3	4	5
F–C	0.04	0.3173	1.0318	1.2223	1.6683	2.0346
	0.05	0.3388	1.0646	1.3318	1.8857	2.0902
	0.06	0.3605	1.1020	1.4457	1.9971	2.2387
	0.07	0.3822	1.1431	1.5581	2.0342	2.4495
	0.08	0.4039	1.1867	1.6631	2.0619	2.6536
F–SS	0.04	0.3000	1.0164	1.1589	1.5550	2.0328
	0.05	0.3191	1.0385	1.2469	1.7688	2.0668
	0.06	0.3382	1.0643	1.3421	1.9560	2.1109
	0.07	0.3571	1.0932	1.4406	2.0338	2.2578
	0.08	0.3756	1.1249	1.5391	2.0558	2.4519
C–C	0.04	1.1066	1.1798	1.6578	2.2737	2.9366
	0.05	1.1257	1.2714	1.8821	2.6280	2.9990
	0.06	1.1451	1.3688	2.1017	2.8395	3.1365
	0.07	1.1657	1.4681	2.3079	2.9045	3.2323
	0.08	1.1874	1.5664	2.4943	2.9362	3.2494
C–SS	0.04	1.1007	1.1217	1.5389	2.1120	2.9141
	0.05	1.1163	1.1881	1.7305	2.4621	2.9791
	0.06	1.1290	1.2626	1.9256	2.7567	3.0247
	0.07	1.1414	1.3413	2.1162	2.8988	3.1550
	0.08	1.1543	1.4217	2.2976	2.9341	3.2243
C–SD	0.04	0.9349	1.1176	1.4644	1.6288	2.1378
	0.05	0.9437	1.1841	1.5576	1.7428	2.4991
	0.06	0.9540	1.2556	1.5831	1.9251	2.8368
	0.07	0.9657	1.3281	1.5982	2.1151	3.1190
	0.08	0.9785	1.3965	1.6159	2.2991	3.2221
E1–E1	0.04	0.9466	1.1784	1.3930	1.6351	2.3054
	0.05	0.9606	1.2694	1.3990	1.8645	2.6915
	0.06	0.9770	1.3532	1.4163	2.0912	2.7441
	0.07	0.9953	1.3832	1.4898	2.3070	2.7448
	0.08	1.0152	1.3891	1.5870	2.5076	2.7457
E2–E2	0.04	0.8823	1.1596	1.5964	2.2714	2.3228
	0.05	0.9000	1.2514	1.8179	2.3222	2.6258
	0.06	0.9195	1.3495	2.0245	2.3292	2.7795
	0.07	0.9405	1.4497	2.1927	2.3539	2.8304
	0.08	0.9628	1.5490	2.2714	2.4375	2.8825
E3–E3	0.04	0.5684	0.6661	1.1828	1.5763	2.2037
	0.05	0.5944	0.6853	1.2625	1.8042	2.2456
	0.06	0.6201	0.7010	1.3519	2.0211	2.2574
	0.07	0.6455	0.7142	1.4462	2.1883	2.3034
	0.08	0.6694	0.7268	1.5414	2.2310	2.4565