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 7

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

	Method	Mode number
		1	2	3	4	5	6	7	8	9
0.6	Ref [2]	71.12	94.44	147.32	173.88	237.31	315.92	407.09	412.60	442.60
	Ref [10]	71.01	94.37	147.25	173.87	237.25	315.55	406.65	412.62	441.76
	Present	71.09	94.36	147.37	174.05	237.21	315.66	406.80	412.48	441.77
1	Ref [2]	70.78	94.02	146.63	173.14	236.17	314.53	405.19	410.79	440.35
	Ref [10]	70.63	93.89	146.47	173.02	235.96	313.96	404.50	410.55	439.17
	Present	70.71	93.88	146.59	173.21	235.91	314.09	404.67	410.40	439.17
5	Ref [2]	71.68	96.03	148.75	177.58	237.24	321.15	409.51	420.41	435.62
	Ref [10]	71.54	95.89	148.59	177.46	237.03	320.58	408.82	420.09	434.56
	Present	71.62	95.88	148.69	177.67	237.00	320.69	408.99	420.00	434.54
20	Ref [2]	70.59	94.55	146.50	174.82	233.56	316.21	403.23	413.98	428.88
	Ref [10]	70.57	94.57	146.59	175.00	233.75	316.16	403.21	414.32	428.53
	Present	70.64	94.56	146.69	175.20	233.71	316.28	403.37	414.24	428.51
50	Ref [2]	69.54	92.95	144.28	171.59	230.57	310.83	397.57	406.64	425.16
	Ref [10]	69.57	93.01	144.45	171.87	230.90	310.98	397.80	407.27	425.06
	Present	69.64	92.98	144.56	172.07	230.86	311.10	397.96	407.60	425.06
0.6	Ref [2]	70.59	93.62	146.22	172.31	235.55	313.20	403.88	409.05	439.88
	Ref [10]	70.81	93.98	146.83	173.10	236.58	314.28	405.31	410.95	441.00
	Present	70.89	93.97	146.96	173.29	236.55	314.41	405.48	410.80	441.02
1	Ref [2]	70.12	92.99	145.26	171.15	233.94	311.11	401.15	406.32	436.81
	Ref [10]	70.39	93.41	145.95	172.05	235.11	312.37	402.82	408.46	438.20
	Present	70.48	93.40	146.08	172.21	235.08	312.48	402.97	408.30	438.21
5	Ref [2]	71.04	95.02	147.45	175.58	235.02	317.81	405.72	416.02	432.13
	Ref [10]	71.30	95.41	148.12	176.44	236.12	318.99	407.26	417.98	433.45
	Present	71.38	95.45	148.23	176.64	236.10	319.11	407.43	418.05	433.45
20	Ref [2]	70.33	94.13	145.98	174.00	232.64	314.84	401.67	412.16	427.43
	Ref [10]	70.47	94.36	146.40	174.57	233.35	315.49	402.55	413.44	428.05
	Present	70.55	94.37	146.50	174.77	233.33	315.61	402.71	413.34	428.03
50	Ref [2]	69.43	92.74	144.04	171.22	230.16	310.22	396.86	405.84	424.51
	Ref [10]	69.54	92.94	144.41	171.73	230.79	310.77	397.61	407.00	424.96
	Present	69.60	92.91	144.48	171.87	230.69	310.81	397.66	406.77	424.84