A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

Table 5

Frequency parameters Ω of the FG spherical shell with general boundary restraints.

Type	n	m	Boundary restraints
			F-C	F-SD	F-SS	F-E1	F-E2	F-E3
FGMI	1	1	0.54344	0.42713	0.52984	0.04785	0.27188	0.04321
		2	0.86399	0.59557	0.84739	0.68602	0.85997	0.31569
		3	1.00929	0.70402	0.98272	0.89117	1.00785	0.86468
		4	1.22272	0.78296	1.17760	1.02797	1.15260	1.01040
	3	1	0.91647	0.87653	0.91535	0.88783	0.87109	0.70835
		2	1.04516	0.99425	1.02219	1.02408	1.01579	0.98958
		3	1.25511	1.18707	1.19788	1.24297	1.23652	1.21332
		4	1.57540	1.48804	1.49167	1.56983	1.56403	1.53326
	5	1	1.03527	0.99251	1.02325	1.01610	1.01377	0.94606
		2	1.25095	1.18479	1.20594	1.23473	1.23299	1.19974
		3	1.57309	1.48549	1.49652	1.56201	1.56051	1.53629
		4	1.99882	1.89245	1.89858	1.99180	1.99023	1.97057
FGMII	1	1	0.53930	0.40319	0.51759	0.04746	0.26971	0.04288
		2	0.85652	0.54033	0.83533	0.68111	0.85236	0.31339
		3	0.99915	0.64814	0.96869	0.88341	0.99775	0.85687
		4	1.20899	0.70374	1.15712	1.01772	1.14534	1.00036
	3	1	0.91002	0.87183	0.90998	0.88174	0.86516	0.70315
		2	1.03665	0.98752	1.02261	1.01556	1.00731	0.98131
		3	1.24296	1.17683	1.19456	1.23077	1.22435	1.20139
		4	1.55819	1.47280	1.47928	1.55256	1.54679	1.51737
	5	1	1.02747	0.98777	1.02222	1.00845	1.00613	0.93868
		2	1.23970	1.17690	1.20853	1.22352	1.22178	1.18869
		3	1.55701	1.47264	1.49306	1.54594	1.54443	1.52033
		4	1.97685	1.87346	1.88570	1.96982	1.96824	1.94875