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

Table 10

Nondimensional frequency parameter of stepped hemispherical 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	0.6956	0.6854	0.2263	0.1749	0.1388	0.0188
	2	0.9392	0.9327	0.9033	0.9041	0.9116	0.9036
	3	0.9699	0.9646	0.9581	0.9580	0.9620	0.9588
	4	0.9946	0.9938	0.9880	0.9880	0.9945	0.9916
	5	1.0250	1.0208	0.9968	0.9978	1.0176	1.0022
2	1	0.8180	0.8123	0.1475	0.1493	0.2365	0.0467
	2	0.9777	0.9777	0.8526	0.8444	0.8526	0.8471
	3	0.9899	0.9805	0.9775	0.9775	0.9776	0.9775
	4	1.0115	1.0115	0.9984	0.9970	1.0017	1.0036
	5	1.0522	1.0463	1.0110	1.0109	1.0129	1.0122
3	1	0.8572	0.8557	0.1388	0.1393	0.2365	0.0931
	2	0.9926	0.9921	0.8836	0.8832	0.8526	0.8856
	3	1.0054	0.9986	0.9928	0.9928	0.9776	0.9930
	4	1.0310	1.0310	1.0104	1.0103	1.0017	1.0266
	5	1.0796	1.0704	1.0309	1.0309	1.0129	1.0309