Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Table 2

Convergence of frequency parameters for clamped annular sector plate and circular sector plate (, = 120°, = 0.2, and ).

	Mode number
	1	2	3	4	8	10	12	16
Annular sector plate: Type 1-1 (2-2-1)
4 × 4	93.796	103.03	120.55	187.65	245.38	294.84	351.42	379.08
5 × 5	93.758	102.74	119.84	146.16	238.17	267.17	332.81	376.02
6 × 6	93.680	102.66	119.30	144.14	238.15	266.69	295.52	373.65
7 × 7	93.674	102.60	119.23	143.62	229.48	244.89	294.36	351.15
8 × 8	93.656	102.58	119.10	143.44	229.47	244.72	266.02	351.11
9 × 9	93.655	102.56	119.08	143.29	229.43	244.68	265.83	326.85
10 × 10	93.649	102.55	119.04	143.25	229.42	244.61	265.81	326.66
12 × 12	93.646	102.54	119.00	143.17	229.40	244.56	265.73	326.36
14 × 14	93.645	102.53	118.99	143.14	229.40	244.53	265.69	326.25
16 × 16	93.644	102.53	118.99	143.13	229.39	244.52	265.67	326.19
18 × 18	93.644	102.53	118.99	143.13	229.39	244.51	265.66	326.16
Circular sector plate: Type 1-1 (2-2-1)
4 × 4	41.679	68.054	91.458	100.58	184.45	221.56	243.92	302.38
5 × 5	41.617	67.665	91.386	99.181	171.33	201.68	221.52	257.70
6 × 6	41.585	67.575	91.114	98.546	169.74	184.82	214.70	249.33
7 × 7	41.574	67.496	91.101	98.424	168.53	184.81	212.39	243.85
8 × 8	41.565	67.477	91.040	98.282	167.86	184.81	208.42	243.85
9 × 9	41.562	67.452	91.037	98.255	167.61	184.81	207.67	243.85
10 × 10	41.559	67.447	91.017	98.208	167.40	184.80	207.22	243.85
12 × 12	41.557	67.435	91.007	98.179	167.24	184.80	206.88	243.84
14 × 14	41.556	67.430	91.003	98.167	167.18	184.80	206.75	243.84
16 × 16	41.555	67.427	91.001	98.160	167.15	184.80	206.69	243.84
18 × 18	41.555	67.426	91.001	98.159	167.15	184.80	206.66	243.84