Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending

Table 1

First five natural frequencies and their relative errors of manifold calculation.

Element	First frequency		Second frequency		Third frequency		Fourth frequency		Fifth frequency
	𝑤^′11/Hz	𝜂	𝑤^′21/Hz	𝜂	𝑤^′31/Hz	𝜂	𝑤^′41/Hz	𝜂	𝑤^′51/Hz	𝜂
3×3	17.2564	0.084	22.5501	0.60	65.7306	111.79	70.9070	64.50
5×5	17.2427	0.0046	22.4204	0.026	31.2165	0.58	44.9846	4.36	63.9337	9.06
7×7	17.2413	0.0035	22.4141	0.0022	31.0619	0.085	43.3865	0.65	60.3066	2.87
9×9	17.2411	0.0046	22.4130	0.0071	31.0406	0.016	43.1758	0.16	59.0368	0.71
11×11	17.2412	0.0041	22.4126	0.0089	31.0348	0.0026	43.1275	0.052	58.7638	0.24
Theoretical solution	17.2419	0.00	22.4146	0.00	31.0356	0.00	43.1049	0.00	58.6227	0.00