Transverse Vibration and Waves in a Membrane: Frequency Domain Spectral Element Modeling and Analysis

Table 2

Comparison of the natural frequencies (Hz) of square membrane II obtained by exact theory, FEM, and SEM.

Modes	Exact	FEM				SEM
		= 90	= 870	= 9,900	= 25,440	= 18	= 98	= 258
(1, 1)	0.340	0.341	0.340	0.340	0.340	0.341	0.340	0.340
(2, 1)	0.549	0.553	0.549	0.549	0.549	0.549	0.549	0.549
(1, 2)	0.627	0.637	0.628	0.627	0.627	0.637	0.628	0.627
(2, 2)	0.761	0.771	0.762	0.761	0.761	0.769	0.761	0.761
(3, 1)	0.819	0.838	0.821	0.820	0.819	0.820	0.819	0.819
(1, 3)	0.926	0.959	0.929	0.926	0.926	0.959	0.927	0.926
(3, 2)	0.974	0.996	0.977	0.974	0.974	0.981	0.975	0.974
(2, 3)	1.021	1.053	1.024	1.021	1.021	1.051	1.022	1.021
(4, 1)	1.108	1.160	1.113	1.108	1.108	1.108	1.108	1.108
(3, 3)	1.188	1.227	1.193	1.189	1.188	1.215	1.189	1.188

Note: is the total number of active nodes used in the analysis.