Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Table 5

Frequencies (Hz) of cylindrical shell with FFCF boundary constraints and varying gradient power-law exponent ( GPa,  GPa, ,  kg/m³,  kg/m³, , , , ).

	Method	Mode number
		1	2	3	4	5	6	7	8	9
0	Present	61.03	94.83	153.13	241.67	276.26	291.68	355.13	450.74	512.49
	[58]	61.02	94.82	153.13	241.39	275.83	291.45	355.14	450.76	511.92
	[26]	61.06	94.92	153.11	241.75	276.37	291.94	355.07	450.82	512.48
0.6	Present	59.11	92.94	148.16	234.52	266.87	287.37	342.44	442.01	495.33
	[58]	59.24	93.14	148.51	234.79	267.06	287.85	343.22	443.06	495.89
	[26]	59.13	93.03	148.14	234.60	266.97	287.63	342.38	442.09	495.31
1	Present	58.79	92.39	147.51	233.23	265.51	285.52	341.09	439.41	492.81
	[58]	58.96	92.65	147.94	233.64	265.86	286.16	342.08	440.72	493.67
	[26]	58.82	92.48	147.49	233.31	265.61	285.77	341.04	439.49	492.80
5	Present	59.93	91.45	151.59	236.35	272.08	278.81	353.89	435.11	504.54
	[58]	60.09	91.69	152.02	236.75	272.42	279.34	354.89	436.34	505.35
	[26]	59.96	91.54	151.57	236.42	272.19	279.06	353.83	435.18	504.56
20	Present	59.13	90.21	149.31	233.26	268.47	275.15	348.37	429.12	497.85
	[58]	59.19	90.29	149.49	233.27	268.37	275.23	348.80	429.63	497.87
	[26]	59.16	90.30	149.29	233.32	268.57	275.41	348.32	429.19	497.87
50	Present	58.18	89.52	146.47	229.93	263.84	274.07	340.84	425.59	489.36
	[58]	58.20	89.55	146.55	229.79	263.58	273.98	341.04	425.83	489.06
	[26]	58.21	89.60	146.45	230.00	263.95	274.32	340.79	425.66	489.36
100	Present	57.72	89.21	145.09	228.32	261.56	273.66	337.14	424.02	485.17
	[58]	57.73	89.21	145.14	228.12	261.23	273.51	337.25	424.15	484.75
	[26]	57.75	89.29	145.08	228.39	261.66	273.90	337.09	424.10	485.16
∞	Present	57.17	88.83	143.43	226.37	258.77	273.21	332.64	422.20	480.04
	[58]	57.16	88.81	143.43	226.11	258.36	273.00	332.65	422.21	479.49
	[26]	57.19	88.91	143.41	226.44	258.87	273.46	332.59	422.27	480.02