A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method

Table 7

Nondimensional frequency parameter of uniform 60 degrees spherical cap with different edge conditions.

n	m	Boundary conditions
		CE	SSE	Axial elastic support	Circumferential elastic support	Radial elastic support	Rotational elastic support
1	1	0.8668	0.8630	0.2822	0.2229	0.2215	0.0206
	2	0.9727	0.9651	0.9435	0.9437	0.9540	0.9442
	3	1.0305	1.0175	0.9906	0.9906	1.0120	0.9964
	4	1.1231	1.0974	1.0390	1.0390	1.0861	1.0554
	5	1.2777	1.2350	1.1297	1.1297	1.2057	1.1612
2	1	0.9745	0.9720	0.1614	0.1619	0.3248	0.0536
	2	1.0284	1.0280	0.9663	0.9663	0.9788	0.9686
	3	1.0927	1.0848	1.0098	1.0098	1.0390	1.0192
	4	1.2040	1.1700	1.0758	1.0758	1.1331	1.0980
	5	1.3895	1.3347	1.1957	1.1957	1.2773	1.2350
3	1	0.9978	0.9956	0.1513	0.1514	0.4081	0.0994
	2	1.0588	1.0587	0.9844	0.9844	0.9999	0.9885
	3	1.1444	1.1327	1.0352	1.0352	1.0721	1.0485
	4	1.2876	1.2465	1.1245	1.1245	1.1895	1.1529
	5	1.5093	1.4456	1.2772	1.2772	1.3602	1.3240