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 6

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

	Method	Mode number
		1	2	3	4	5	6	7	8
0.6	Ref [1]	208.92	208.92	230.11	230.11	284.73	284.74	321.51	321.51
	Ref [29]	208.75	208.75	229.96	229.96	284.60	284.60	321.33	321.33
	Ref [11]	208.58	208.58	230.06	230.06	284.67	284.67	321.28	321.28
	Present	208.78	208.78	230.06	230.06	284.92	284.92	321.32	321.32
5	Ref [1]	204.81	204.81	223.84	223.84	275.52	275.53	316.64	316.64
	Ref [29]	204.25	204.25	223.36	223.36	275.02	275.02	315.94	315.94
	Ref [11]	203.36	203.36	223.72	223.72	275.26	275.26	315.48	315.48
	Present	204.28	204.28	223.46	223.46	275.35	275.35	315.93	315.93
20	Ref [1]	204.89	204.89	227.33	227.33	282.68	282.69	312.50	312.50
	Ref [29]	204.27	204.27	226.78	226.78	282.10	282.10	311.71	311.71
	Ref [11]	203.29	203.29	227.17	227.17	282.35	282.35	311.15	311.15
	Present	204.30	204.30	226.88	226.88	282.42	282.42	311.71	311.71
0.6	Ref [1]	208.49	208.49	229.65	229.65	284.17	284.17	321.18	321.18
	Ref [29]	208.54	208.54	229.70	229.70	284.25	284.25	321.30	321.30
	Ref [11]	208.74	208.74	229.61	229.61	284.21	284.21	321.33	321.33
	Present	208.57	208.57	229.80	229.80	284.58	284.58	321.30	321.30
5	Ref [1]	202.87	202.87	221.78	221.78	273.02	273.02	315.18	315.18
	Ref [29]	203.30	203.30	222.16	222.16	273.47	273.47	315.81	315.81
	Ref [11]	204.15	204.15	221.67	221.67	273.14	273.14	315.72	315.72
	Present	203.34	203.34	222.26	222.26	273.80	273.80	315.81	315.81
20	Ref [1]	202.60	202.60	224.87	224.87	279.65	279.66	310.83	310.83
	Ref [29]	203.09	203.09	225.30	225.30	280.17	280.17	311.53	311.53
	Ref [11]	203.98	203.98	224.73	224.73	279.80	279.80	311.39	311.39
	Present	203.12	203.12	225.40	225.40	280.49	280.49	311.53	311.53