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 4

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

	Method	Mode number
		1	2	3	4	5	6	7	8
0	Ref [1]	152.93	152.93	220.06	220.06	253.78	253.78	383.55	383.56
	Ref [9]	152.89	152.89	219.97	219.97	253.79	253.79	383.44	383.44
	Present	152.89	152.89	220.12	220.12	253.77	253.77	383.95	383.95
0.6	Ref [1]	152.25	152.25	219.86	219.86	252.17	252.17	383.39	383.40
	Ref [27]	152.02	152.02	219.54	219.54	251.91	251.91	382.87	382.87
	Ref [9]	152.07	152.07	219.59	219.59	251.96	251.96	382.95	382.95
	Present	152.08	152.08	219.73	219.83	251.95	251.95	383.46	383.46
1	Ref [1]	151.77	151.77	219.56	219.56	251.14	251.14	382.97	382.97
	Ref [9]	151.52	151.52	219.19	219.19	250.81	250.81	382.35	382.35
	Present	151.53	151.53	219.33	219.33	250.80	250.80	382.85	382.85
5	Ref [1]	148.97	148.97	218.87	218.88	244.40	244.40	382.46	382.47
	Ref [27]	148.50	148.50	218.16	218.16	243.73	243.73	381.26	381.26
	Ref [9]	148.53	148.53	218.21	218.21	243.76	243.76	381.33	381.33
	Present	148.54	148.54	218.35	218.35	243.75	243.75	381.82	381.82
20	Ref [1]	146.46	146.46	215.90	215.90	239.84	239.84	377.34	377.34
	Ref [27]	146.21	146.21	215.50	215.50	239.54	239.54	376.69	376.69
	Ref [9]	146.24	146.24	215.55	215.55	239.57	239.57	376.76	376.76
	Present	146.25	146.25	215.69	215.69	239.56	239.56	377.23	377.23