Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction

Table 4

Comparison of the natural frequency for FG spherical shell (m = 1).

Type	p	n	F–F			SS–SS			C–C
			Present	Ref [21]	Ref [18]	Present	Ref [21]	Ref [18]	Present	Ref [21]	Ref [18]
FGMI(a=1/b=0/c/p)	0.6	0	777.61	777.54	777.60	786.84	786.25	786.87	875.58	875.24	875.72
		1	771.92	771.87	771.92	827.82	827.30	827.85	910.57	910.27	910.70
		2	49.85	49.96	49.89	886.85	886.29	886.90	894.60	894.14	894.67
		3	133.53	133.81	133.68	881.61	881.14	881.65	889.41	888.99	889.45
		4	243.34	243.85	243.64	914.97	914.57	914.98	927.34	927.02	927.36
	5	0	754.66	754.38	754.66	772.99	772.77	773.02	865.40	865.49	865.53
		1	748.82	748.63	748.83	812.61	812.47	812.64	899.53	899.65	899.65
		2	51.57	51.70	51.61	862.42	862.25	862.47	871.41	871.34	871.46
		3	137.80	138.15	137.94	858.18	858.10	858.21	868.63	868.62	868.66
		4	250.61	250.26	250.90	895.23	895.26	895.25	910.59	910.71	910.61
FGMII(a=1/b=0/c/p)	0.6	0	777.04	777.57	777.04	767.93	768.03	767.95	873.71	873.61	873.85
		1	771.53	771.34	771.53	815.16	815.18	815.18	908.68	908.54	908.81
		2	49.60	49.47	49.64	887.89	887.83	887.94	893.73	893.63	893.80
		3	132.88	132.53	133.03	885.52	885.47	885.56	888.28	888.22	888.32
		4	242.16	242.53	242.47	919.43	919.33	919.44	925.75	925.64	925.77
	5	0	753.73	753.15	753.73	749.86	749.67	749.88	862.63	862.18	862.76
		1	748.17	748.56	748.18	796.84	796.56	796.86	896.77	896.27	896.89
		2	51.25	51.09	51.29	864.39	864.03	864.43	870.03	869.63	870.08
		3	136.95	136.53	137.10	863.22	862.89	863.25	866.84	866.50	866.87
		4	249.09	249.35	249.38	900.63	900.25	900.65	908.14	907.74	908.16