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

Table 9

Nondimensional frequency parameter of uniform 30 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	1.0509	1.0509	0.3401	0.3023	0.3932	0.0573
	2	1.2192	1.1616	1.0094	1.0093	1.0797	1.0308
	3	1.6567	1.5103	1.1899	1.1898	1.3506	1.2739
	4	2.4021	2.1843	1.6437	1.6435	1.7893	1.8050
	5	3.4110	3.1362	2.3957	2.3964	2.4889	2.6276
2	1	1.1055	1.1004	0.1397	0.1399	0.5176	0.1421
	2	1.3866	1.2949	1.0628	1.0628	1.1624	1.1030
	3	1.9737	1.7928	1.3611	1.3611	1.5184	1.4768
	4	2.8563	2.6055	1.9615	1.9615	2.0803	2.1540
	5	3.9980	3.6856	2.8490	2.8490	2.8688	2.8690
3	1	1.1799	1.1560	0.1892	0.1893	0.6300	0.2519
	2	1.5988	1.4723	1.1532	1.1532	1.2734	1.2144
	3	2.3331	2.1221	1.5893	1.5893	1.7304	1.7333
	4	3.3468	3.0680	2.3315	2.3315	2.4289	2.5504
	5	4.6097	4.2700	3.3471	3.3471	3.4106	3.6318