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 5

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

	Method	Mode number
		1	2	3	4	5	6	7	8	9
0.6	Ref [3]	80.10	110.93	158.60	195.20	259.10	273.52	321.39	360.77	396.83
	Ref [10]	80.15	111.03	158.61	195.49	259.31	273.52	321.38	361.16	397.06
	Present	80.14	110.95	158.62	195.57	259.18	273.62	321.42	361.38	397.12
1	Ref [3]	79.89	110.56	158.15	194.72	258.36	272.88	320.38	359.84	395.97
	Ref [10]	79.91	110.62	158.10	194.94	258.48	272.82	320.28	360.10	396.11
	Present	79.91	110.54	158.11	195.02	258.36	272.91	320.31	360.33	396.18
5	Ref [3]	78.92	108.45	156.07	192.86	254.58	270.76	315.52	356.30	393.68
	Ref [10]	78.86	108.39	155.87	192.87	254.45	270.51	315.12	356.20	393.55
	Present	78.86	108.31	155.88	192.95	254.33	270.60	315.16	356.42	393.62
20	Ref [3]	77.81	106.72	153.93	190.43	250.80	267.51	311.11	351.98	389.27
	Ref [10]	77.83	106.78	153.90	190.65	250.92	267.46	311.03	352.24	389.42
	Present	77.83	106.70	153.91	190.73	250.80	267.56	311.07	352.46	389.48
50	Ref [3]	76.57	105.58	151.56	187.03	247.32	262.39	306.75	345.73	381.29
	Ref [10]	76.63	105.69	151.60	187.34	247.57	262.43	306.81	346.17	381.56
	Present	76.63	105.62	151.61	187.43	247.45	262.53	306.85	346.39	381.63
0.6	Ref [3]	79.87	110.71	158.27	194.75	258.47	272.88	320.85	360.10	395.93
	Ref [10]	80.03	110.96	158.48	195.29	258.99	273.14	321.24	360.94	396.49
	Present	80.03	110.88	158.49	195.37	258.86	273.23	321.27	361.16	396.56
1	Ref [3]	79.54	110.22	157.64	194.02	257.39	271.89	319.56	358.81	394.58
	Ref [10]	79.73	110.51	157.90	194.63	257.99	272.21	320.05	359.76	395.23
	Present	79.73	110.43	157.91	194.71	257.86	272.31	320.08	359.98	395.30
5	Ref [3]	78.23	107.82	155.00	191.47	252.65	268.67	313.79	354.27	390.76
	Ref [10]	78.49	108.21	155.40	192.25	253.46	269.17	314.54	355.53	391.65
	Present	78.49	108.13	155.41	192.33	253.34	269.26	314.58	355.75	391.71
20	Ref [3]	77.49	106.44	153.43	189.81	249.93	266.54	310.31	351.07	387.92
	Ref [10]	77.67	106.70	153.67	190.37	250.47	266.83	310.75	351.94	388.52
	Present	77.66	106.63	153.68	190.45	250.35	266.92	310.78	352.16	388.59
50	Ref [3]	76.43	105.46	151.35	186.76	246.94	261.96	306.41	345.34	380.70
	Ref [10]	76.56	105.66	151.50	187.22	247.36	262.15	306.69	346.04	381.16
	Present	76.56	105.59	151.52	187.30	247.25	262.25	306.73	346.26	381.24