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

Table 1

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

Modes	Exact	FEM				SEM
		= 81	= 2,401	= 9,801	= 17,956	= 9	= 29	= 69
(1, 1)	0.430	0.432	0.430	0.430	0.430	0.431	0.430	0.430
(1, 2)	0.680	0.690	0.681	0.680	0.680	0.681	0.681	0.680
(2, 2)	0.861	0.875	0.861	0.861	0.861	0.868	0.862	0.861
(1, 3)	0.962	0.995	0.964	0.963	0.962	0.963	0.962	0.962
(2, 3)	1.097	1.131	1.099	1.098	1.097	1.102	1.098	1.097
(1, 4)	1.255	1.333	1.258	1.255	1.255	1.256	1.255	1.255
(3, 3)	1.291	1.438	1.293	1.292	1.291	1.315	1.294	1.291
(2, 4)	1.361	1.607	1.364	1.362	1.361	1.365	1.361	1.361
(3, 4)	1.522	1.705	1.525	1.522	1.522	1.542	1.524	1.522
(1, 5)	1.552	1.788	1.558	1.553	1.552	1.642	1.552	1.552

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