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

Table 6

Nondimensional frequency parameter of uniform 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	0.5678	0.5601	0.2366	0.1902	0.1312	0.0112
	2	0.8934	0.8852	0.8767	0.8779	0.8836	0.8764
	3	0.9655	0.9604	0.9531	0.9533	0.9599	0.9536
	4	1.0016	0.9959	0.9837	0.9838	0.9950	0.9865
	5	1.0435	1.0343	1.0114	1.0114	1.0322	1.0182
2	1	0.9012	0.9004	0.1734	0.1741	0.2397	0.0346
	2	0.9662	0.9661	0.9176	0.9175	0.9246	0.9177
	3	0.9975	0.9970	0.9682	0.9682	0.9762	0.9697
	4	1.0306	1.0254	0.9964	0.9964	1.0105	1.0006
	5	1.0791	1.0665	1.0293	1.0293	1.0539	1.0380
3	1	0.9476	0.9459	0.1608	0.1611	0.3283	0.0702
	2	0.9892	0.9878	0.9452	0.9452	0.9519	0.9460
	3	1.0239	1.0231	0.9819	0.9819	0.9913	0.9843
	4	1.0658	1.0654	1.0114	1.0114	1.0286	1.0171
	5	1.1226	1.1130	1.0517	1.0517	1.0806	1.0625