Free Vibration Characteristics of Moderately Thick Spherical Shell with General Boundary Conditions Based on Ritz Method

Table 11

Results of annular spherical shell with different φ₁ (φ₀ = π/2, R = 1m, h = 0.06 m, and n = 2).

Boundary conditions	φ1	m
		1	2	3	4	5
F–C	π/6	3.8150	9.7744	12.7949	13.2675	23.3452
	π/5	1.7976	5.7957	6.5679	7.9042	12.6403
	π/4	1.0786	2.8407	4.3014	5.6835	6.0835
	π/3	0.6610	1.5900	2.6462	3.0491	4.1950
	π/2	0.3990	1.0838	1.3492	1.8882	2.0273
F–SS	π/6	1.7894	9.7735	11.8147	13.1186	23.3427
	π/5	1.2525	4.8691	6.4732	7.9034	11.7076
	π/4	0.8858	2.3609	4.3011	5.3930	5.6844
	π/3	0.5942	1.4280	2.4131	2.9757	4.1595
	π/2	0.3866	1.0528	1.2677	1.7819	2.0040
C–C	π/6	11.8721	15.5416	23.1968	25.0071	30.2760
	π/5	5.4699	9.2255	11.3802	13.9153	17.3881
	π/4	2.6771	5.5250	6.1150	8.3655	9.4051
	π/3	1.5265	2.5309	4.0903	4.4366	5.0917
	π/2	1.0663	1.2502	1.8101	2.4664	2.7956
C–SS	π/6	9.9024	15.5405	22.6995	25.0063	30.2709
	π/5	4.3291	9.2250	10.4991	13.9064	17.3881
	π/4	2.1852	4.8709	6.1028	8.3585	8.7829
	π/3	1.4057	2.2061	3.9147	4.2136	5.0848
	π/2	1.0555	1.1742	1.6726	2.3405	2.7516
C–SD	π/6	9.7048	12.0543	16.1126	22.7599	29.7101
	π/5	4.0875	6.4610	9.9060	10.5863	16.6106
	π/4	1.8688	3.7454	4.9063	6.8564	8.7765
	π/3	1.0948	2.1426	2.3305	3.9390	4.8355
	π/2	0.9344	1.1710	1.4259	1.6727	2.3895
E1–E1	π/6	3.4567	11.7824	15.1735	23.2436	25.6980
	π/5	2.9763	5.3506	8.8059	11.4264	14.7994
	π/4	2.2170	2.6997	5.5649	5.8007	9.2446
	π/3	1.2500	1.8752	2.5440	4.0978	4.3435
	π/2	0.9479	1.2473	1.3445	1.7968	2.5694
E2–E2	π/6	4.6941	11.8925	15.3560	23.2065	25.6246
	π/5	3.9936	5.6479	8.9445	11.3881	14.8358
	π/4	2.3491	3.8445	5.5347	5.7751	9.4039
	π/3	1.2645	2.4977	3.0776	3.7952	4.4128
	π/2	0.8894	1.2273	1.7592	2.1700	2.5066
E3–E3	π/6	0.7960	4.8777	11.7827	15.9717	23.2436
	π/5	0.8284	4.1400	5.4124	9.8944	11.4306
	π/4	0.8871	2.2813	3.6241	5.5559	7.0605
	π/3	0.8699	1.0742	2.4766	2.8647	4.2797
	π/2	0.6189	0.7555	1.2455	1.7337	2.1863