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

Table 10

Results of annular spherical shell with different φ₁ (φ₀ = π/8, R = 1m, h = 0.06 m, and n = 1).

Boundary conditions	Φ1	m
		1	2	3	4	5
F–C	π/6	3.6431	8.9681	12.6428	13.2118	22.9000
	π/5	1.6899	5.4835	5.8583	7.6132	12.5239
	π/4	1.1818	2.6133	3.8455	4.9257	5.9473
	π/3	0.9814	1.3664	2.4315	2.8442	3.3609
	π/2	0.6436	0.9719	1.2359	1.7010	1.9829
F–SS	π/6	1.3547	8.9681	11.6078	13.0808	22.8995
	π/5	1.1804	4.6180	5.6506	7.6055	11.5638
	π/4	1.0825	2.0957	3.8404	4.8865	5.2709
	π/3	0.9527	1.2149	2.2277	2.7311	3.3606
	π/2	0.6152	0.9440	1.1715	1.6221	1.9529
C–C	π/6	11.8237	15.0427	23.1127	25.1201	29.8383
	π/5	5.4266	8.5302	11.2836	14.0476	16.7648
	π/4	2.6824	5.2672	5.4583	8.4610	9.3175
	π/3	1.6279	2.4319	3.3373	4.3047	5.0647
	π/2	1.1348	1.1790	1.7292	2.1793	2.4499
C–SS	π/6	9.7987	15.0422	22.6127	25.1183	29.8370
	π/5	4.2515	8.5296	10.3896	14.0384	16.7648
	π/4	2.1955	4.7569	5.2871	8.4503	8.6874
	π/3	1.5333	2.0992	3.3372	3.8881	5.0582
	π/2	1.0521	1.1750	1.6077	2.1776	2.2916
C–SD	π/6	9.6128	12.3549	15.2373	22.6804	29.6584
	π/5	3.9637	6.7642	8.8407	10.4648	16.5420
	π/4	1.7120	3.9412	4.8167	5.7316	8.6811
	π/3	0.8811	2.0460	2.4136	3.7170	3.9839
	π/2	0.6681	1.0615	1.3325	1.6075	2.2854
E1–E1	π/6	2.5277	11.7245	14.9480	23.1578	25.3798
	π/5	2.1853	5.2760	8.4169	11.3354	14.3567
	π/4	1.6668	2.5613	5.1988	5.4749	8.8397
	π/3	0.9140	1.6802	2.4653	3.3383	4.2588
	π/2	0.6310	1.0695	1.2533	1.7324	2.1624
E2–E2	π/6	2.4058	11.8290	15.1668	23.1153	25.2815
	π/5	2.0827	5.4594	8.6829	11.2863	14.3044
	π/4	1.5810	2.8691	5.4120	5.4854	8.8295
	π/3	0.9655	2.0415	2.4579	3.4721	4.3036
	π/2	0.6508	1.1457	1.5671	1.9046	2.1187
E3–E3	π/6	0.6065	3.0523	11.7244	15.3288	23.1578
	π/5	0.4401	2.6234	5.2828	8.9518	11.3361
	π/4	0.3274	1.8676	2.6981	5.4573	5.8831
	π/3	0.2409	0.8808	1.9341	2.4549	4.0376
	π/2	0.1727	0.4252	1.1586	1.4577	1.7434