The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Table 14

First six frequency parameters Ω of the functionally graded spherical shells with different boundary conditions.

Mode number	Boundary condition
	CC	CS	CF	SF	CE^1	SE^3	E^1E^1	E^2E^2	E^3E^3
1	12.293	11.727	1.7433	1.4432	6.5531	11.970	5.6226	10.036	12.242
2	12.293	11.727	1.7433	1.4432	6.5531	11.970	6.3197	10.838	12.242
3	12.552	11.918	2.7986	2.2795	7.2370	12.233	6.3199	10.838	12.488
4	12.552	11.918	2.7986	2.2795	8.2529	12.233	7.6911	12.060	12.488
5	13.316	12.855	3.0960	3.0509	8.2529	12.992	7.6912	12.060	13.286
6	13.316	12.855	3.0960	3.0510	10.393	12.992	8.6638	12.141	13.286
1	12.284	11.760	1.7406	1.4246	6.5481	12.002	5.6204	10.032	12.238
2	12.284	11.760	1.7406	1.4246	6.5481	12.002	6.3145	10.833	12.238
3	12.539	11.946	2.7974	2.2396	7.2331	12.251	6.3145	10.833	12.481
4	12.539	11.946	2.7974	2.2396	8.2452	12.251	7.6835	12.055	12.481
5	13.310	12.899	3.0896	3.0439	8.2452	13.032	7.6835	12.055	13.285
6	13.310	12.899	3.0896	3.0439	10.381	13.032	8.6633	12.132	13.285