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 3

Comparison of the first nine frequencies (Hz) of functionally graded cylindrical panels with different power-law index .

	Method	Mode numbers
		1	2	3	4	5	6	7	8	9
0	Ref [52]	61.02	94.82	153.13	241.39	275.83	291.45	355.14	450.76	511.92
	Ref [8]	61.06	94.92	153.11	241.75	276.37	291.94	355.07	450.82	512.48
	Present	61.02	94.82	153.12	241.60	276.22	291.64	355.09	450.72	512.31
0.6	Ref [52]	59.24	93.14	148.51	234.79	267.06	287.85	343.22	443.06	495.89
	Ref [8]	59.13	93.03	148.14	234.60	266.97	287.63	342.38	442.09	495.31
	Present	59.09	92.93	148.15	234.45	266.83	287.34	342.39	441.99	495.15
1	Ref [52]	58.96	92.65	147.94	233.64	265.86	286.16	342.08	440.72	493.67
	Ref [8]	58.82	92.48	147.49	233.31	265.61	285.77	341.04	439.49	492.80
	Present	58.78	92.38	147.50	233.16	265.47	285.48	341.05	439.39	492.63
5	Ref [52]	60.09	91.69	152.02	236.75	272.42	279.34	354.89	436.34	505.35
	Ref [8]	59.96	91.54	151.57	236.42	272.19	279.06	353.83	435.18	504.56
	Present	59.92	91.44	151.59	236.29	272.04	278.78	353.84	435.09	504.37
20	Ref [52]	59.19	90.29	149.49	233.27	268.37	275.23	348.80	429.63	497.87
	Ref [8]	59.16	90.30	149.29	233.32	268.57	275.41	348.32	429.19	497.87
	Present	59.12	90.20	149.30	233.20	268.43	275.13	348.33	429.10	497.69
50	Ref [52]	58.20	89.55	146.55	229.79	263.58	273.98	341.04	425.83	489.06
	Ref [8]	58.21	89.60	146.45	230.00	263.95	274.32	340.79	425.66	489.36
	Present	58.17	89.51	146.46	229.87	263.81	274.04	340.80	425.57	489.19