A Semianalytical Solution for In-Plane Vibration Analysis of Annular Panels with Arbitrary Distribution of Internal Point Constraints

Table 1

The first eight in-plane modal frequencies of annular panel with a single-point fixed constraint.

Methods	Modal frequencies (Hz)
	f1	f2	f3	f4	f5	f6	f7	f8
FEA	0.0001	573.73	952.49	1523.6	1604	2584.5	2827.8	2873.5
k = 0	0.0005	0.0014	0.2970	1249.0	1249.0	2514.2	2802.3	2802.3
k = 1e5	0.2042	0.4151	0.6036	1249.0	1249.0	2514.2	2802.3	2802.3
k = 1e8	0.2186	13.123	17.827	1249.0	1249.1	2514.2	2802.3	2802.4
k = 1e10	0.2186	128.94	176.65	1252.1	1260.0	2517.5	2803.2	2807.6
k = 1e11	0.2186	353.65	515.58	1281.4	1345.0	2540.2	2809.9	2842.3
k = 1e12	0.2186	579.11	946.21	1513.6	1613.4	2585.8	2827.4	2873.9
	—	0.94%	0.66%	0.66%	0.58%	0.05%	0.01%	0.01%