Vibration Analysis of Annular Sector Plates under Different Boundary Conditions

Table 4

Frequency parameters, Ω=𝜔𝑏²(𝜌ℎ/𝐷)^1/2, for fully clamped annular sector plates (𝜇=0.3).

𝜙	𝑎/𝑏	Source	Mode number
			1	2	3	4	5	6
𝜋/6	0.2	Present	188.21	300.11	417.61	429.57	577.84	599.88
	0.4	Present	188.37	305.06	417.47	461.14	600.03	671.78
		FEM	188.41	305.11	417.76	461.26	600.35	672.18
		Reference [13]	188.36	305.04	417.39	461.00	596.16	672.01
	0.6	Present	216.12	422.67	454.32	662.94	728.63	820.91
𝜋/2	0.2	Present	50.283	87.826	113.99	136.90	165.36	195.50
	0.4	Present	69.822	95.706	138.96	179.79	195.38	207.76
		FEM	69.839	95.709	138.98	179.85	195.49	207.84
		Reference [13]	60.835	95.701	138.96	179.79	195.51	207.82
	0.6	Present	144.27	159.26	187.24	228.34	285.34	351.81
2𝜋/3	0.2	Present	41.835	63.382	93.964	104.76	129.64	133.58
	0.4	Present	65.700	78.393	101.37	133.72	174.32	175.71
	0.6	Present	142.05	149.60	163.44	184.16	212.92	249.07
𝜋	0.2	Present	37.061	45.338	59.618	78.667	98.872	100.43
		FEM	37.043	45.334	59.767	78.671	98.962	100.81
	0.4	Present	63.331	68.008	76.617	89.647	107.22	128.75
		FEM	63.329	68.006	76.606	89.639	107.14	128.75
	0.6	Present	140.80	143.64	149.03	156.59	167.53	181.84
		FEM	140.64	143.68	149.98	156.85	167.62	181.55
7𝜋/6	0.2	Present	36.241	41.835	52.102	66.284	83.552	98.083
		FEM	36.244	41.844	52.088	66.314	83.364	98.114
	0.4	Present	62.904	66.110	72.109	80.996	93.532	108.83
		FEM	62.900	66.142	72.044	81.035	93.320	108.84
	0.6	Present	140.34	142.53	146.35	151.85	159.58	170.05
		FEM	140.36	142.53	146.28	151.78	159.25	168.88
3𝜋/2	0.2	Present	35.495	38.369	44.053	52.411	63.089	75.717
	0.4	Present	62.412	64.212	67.419	72.312	79.187	87.876
	0.6	Present	140.00	140.83	143.54	146.75	150.99	155.98
16𝜋/9	0.2	Present	35.192	37.153	40.797	46.446	54.017	63.212
	0.4	Present	62.298	63.555	65.696	69.042	73.579	79.273
	0.6	Present	139.94	141.66	142.46	144.56	147.48	151.01
2𝜋	0.2	Present	35.061	36.520	39.252	43.464	49.307	56.495
		FEM	35.056	36.502	39.208	43.417	49.199	56.438
	0.4	Present	62.188	63.167	64.820	67.263	70.707	75.100
		FEM	62.192	65.153	64.821	67.294	70.663	75.033
	0.6	Present	139.72	140.68	141.75	143.44	145.58	148.37
		FEM	139.88	140.57	141.74	143.41	145.61	148.38