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

Table 6

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

Boundary conditions	h/R	m
		1	2	3	4	5
F–C	0.04	0.6692	0.9562	1.1605	1.5797	2.0162
	0.05	0.6756	0.9718	1.2491	1.7727	2.0984
	0.06	0.6817	0.9894	1.3427	1.9047	2.1354
	0.07	0.6877	1.0090	1.4362	1.9751	2.1365
	0.08	0.6934	1.0304	1.5255	2.0214	2.1366
F–SS	0.04	0.6462	0.9349	1.1077	1.4789	2.0101
	0.05	0.6484	0.9456	1.1760	1.6710	2.0767
	0.06	0.6506	0.9577	1.2516	1.8469	2.1184
	0.07	0.6528	0.9711	1.3316	1.9666	2.1361
	0.08	0.6549	0.9858	1.4133	2.0203	2.1365
C–C	0.04	1.1064	1.2307	1.6367	2.1884	2.3118
	0.05	1.1903	1.2545	1.8287	2.2869	2.5964
	0.06	1.2726	1.2795	2.0030	2.3335	2.8789
	0.07	1.2893	1.3702	2.1229	2.4235	3.0382
	0.08	1.3057	1.4598	2.1809	2.5630	3.1001
C–SS	0.04	1.0387	1.2263	1.5302	2.0551	2.2855
	0.05	1.0977	1.2542	1.6909	2.2863	2.4067
	0.06	1.1611	1.2727	1.8598	2.3046	2.7077
	0.07	1.2224	1.2931	2.0162	2.3314	2.9422
	0.08	1.2646	1.3327	2.1343	2.3903	3.0668
C–SD	0.04	0.7134	1.0543	1.3970	1.5920	2.0820
	0.05	0.7228	1.1071	1.4891	1.6985	2.4045
	0.06	0.7320	1.1643	1.5264	1.8602	2.5767
	0.07	0.7411	1.2221	1.5500	2.0314	2.6179
	0.08	0.7504	1.2770	1.5738	2.1938	2.6435
E1–E1	0.04	0.6581	1.0742	1.2416	1.6043	2.1274
	0.05	0.6625	1.1151	1.2956	1.8195	2.1364
	0.06	0.6682	1.1437	1.3670	2.0209	2.1526
	0.07	0.6747	1.1640	1.4497	2.1103	2.2708
	0.08	0.6817	1.1804	1.5370	2.1204	2.4550
E2–E2	0.04	0.6562	1.1071	1.4817	1.9230	2.1696
	0.05	0.6647	1.1891	1.6149	2.0143	2.2345
	0.06	0.6744	1.2766	1.6952	2.1306	2.2726
	0.07	0.6849	1.3656	1.7404	2.1930	2.3867
	0.08	0.6960	1.4532	1.7699	2.2105	2.5491
E3–E3	0.04	0.2181	0.4215	1.1221	1.4347	1.6467
	0.05	0.2007	0.4388	1.2062	1.4757	1.8292
	0.06	0.1894	0.4576	1.2948	1.4920	2.0342
	0.07	0.1820	0.4774	1.3808	1.5074	2.2341
	0.08	0.1775	0.4978	1.4480	1.5397	2.4198