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 8

Comparisons of frequencies (Hz) of the functionally graded spherical shells with different power-law index p.

		FF			SS			CC
		Ref [9]	Ref [29]	Present	Ref [9]	Ref [29]	Present	Ref [9]	Ref [29]	Present
0.6	0	777.60	777.61	777.60	786.87	786.84	786.84	875.72	875.58	875.57
	1	771.92	771.92	771.91	827.85	827.82	827.82	910.70	910.57	910.56
	2	49.89	49.85	49.89	886.90	886.85	886.88	894.67	894.60	894.65
	3	133.68	133.53	133.68	881.65	881.61	881.64	889.45	889.41	889.43
	4	243.64	243.34	243.66	914.98	914.97	914.98	927.36	927.34	927.35
5	0	754.66	754.66	754.66	773.02	772.99	772.99	865.53	865.40	865.40
	1	748.83	748.82	748.83	812.64	812.61	812.62	899.65	899.53	899.54
	2	51.61	51.57	51.61	862.47	862.42	862.46	871.46	871.41	871.44
	3	137.94	137.80	137.95	858.21	858.18	858.20	868.66	868.63	868.65
	4	250.90	250.61	250.92	895.25	895.23	895.25	910.61	910.59	910.60
0.6	0	777.04	777.04	777.03	767.95	767.93	767.92	873.85	873.71	873.70
	1	771.53	771.53	771.52	815.18	815.16	815.15	908.81	908.68	908.67
	2	49.64	49.60	49.64	887.94	887.89	887.92	893.80	893.73	893.78
	3	133.03	132.88	133.03	885.56	885.52	885.55	888.32	888.28	888.30
	4	242.47	242.16	242.48	919.44	919.43	919.44	925.77	925.75	925.76
5	0	753.73	753.73	753.73	749.88	749.86	749.86	862.76	862.63	862.63
	1	748.18	748.17	748.17	796.86	796.84	796.85	896.89	896.77	896.77
	2	51.29	51.25	51.29	864.43	864.39	864.42	870.08	870.03	870.07
	3	137.10	136.95	137.10	863.25	863.22	863.24	866.87	866.84	866.84
	4	249.38	249.09	249.42	900.65	900.63	900.64	908.16	908.14	908.16