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 13

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

Mode number	Boundary condition
	CCCC	CSCS	CFCF	SFSF	CE^1CE^1	SE^3SE^3	E^1E^1E^1E^1	E^2E^2E^2E^2	E^3E^3E^3E^3
1	13.652	13.168	10.001	9.2907	12.374	12.924	5.215	11.613	13.567
2	14.297	14.090	10.057	9.3816	12.916	13.716	5.400	13.010	14.243
3	17.060	16.157	12.518	10.917	15.840	14.095	7.290	13.117	16.827
4	17.423	17.179	13.685	11.347	16.595	16.611	7.398	13.345	17.256
5	20.023	18.796	14.830	11.965	16.892	17.493	10.310	14.562	19.753
6	20.561	19.503	14.882	12.895	19.200	19.648	13.078	15.491	20.344
1	13.639	13.182	9.9925	9.4012	12.367	12.968	5.216	11.607	13.560
2	14.286	14.054	10.051	9.4953	12.902	13.764	5.401	13.001	14.234
3	17.037	16.214	12.508	10.878	15.817	14.029	7.282	13.110	16.801
4	17.401	17.167	13.668	11.330	16.599	16.660	7.399	14.553	17.243
5	19.993	18.755	14.805	11.985	16.867	17.486	10.295	15.478	19.726
6	20.531	19.495	14.860	12.923	19.170	19.644	13.073	15.824	20.314