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

Table 5

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

n	m	Boundary conditions
		E1–E1	E1–E2	E1–E3	E2–E2	E2–E3	E3–E3
1	1	0.6682	0.8025	0.4156	0.6744	0.4500	0.1894
	2	1.1437	1.2778	0.9634	1.2766	0.9529	0.4576
	3	1.3670	1.5104	1.3662	1.6952	1.3363	1.2948
	4	2.0209	2.0138	1.5122	2.1306	1.7902	1.4920
	5	2.1526	2.3845	2.0636	2.2725	2.1369	2.0342
2	1	0.9770	0.9395	0.6613	0.9195	0.6564	0.6201
	2	1.3532	1.3533	1.3517	1.3495	1.3495	0.7010
	3	1.4163	2.0186	1.3672	2.0245	1.4248	1.3519
	4	2.0912	2.1530	2.0360	2.3291	2.0251	2.0211
	5	2.7441	2.8315	2.3495	2.7795	2.4778	2.2574
3	1	1.0410	1.0240	0.8554	1.0209	0.8517	0.8132
	2	1.4542	1.4424	1.4052	1.4412	1.4061	1.2166
	3	1.9933	2.1648	1.8316	2.1619	1.8503	1.6942
	4	2.1833	2.6963	2.1766	2.7773	2.1761	2.1124
	5	3.1657	3.1378	3.1087	3.1375	3.1308	2.8808
4	1	1.1213	1.1154	1.0133	1.1150	1.0126	0.9892
	2	1.5674	1.5626	1.5162	1.5626	1.5167	1.4476
	3	2.3086	2.3037	2.2259	2.3033	2.2256	2.2244
	4	2.6444	3.2899	2.4510	3.2893	2.4567	2.3376
	5	3.3018	3.3037	3.2906	3.3361	3.2898	3.2623