Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis

Table 1

Comparison of the natural frequencies (Hz) of the simply supported square plate (Example ) obtained by the exact theory, FEM [27], and SEM.

Modes	Exact	FEM			SEM
		= 50 × 50; = 7399	100 × 100; 29799	120 × 120; 42959	= 1; = 72	1; 152	1; 392
(1, 1)	4.857	4.857	4.857	4.866	4.866	4.857	4.857
(1, 2)	12.14	12.14	12.14	12.16	12.16	12.14	12.14
(2, 2)	19.43	19.42	19.43	19.46	19.46	19.43	19.43
(1, 3)	24.28	24.26	24.28	24.28	24.28	4.857	24.28
(2, 3)	31.57	31.54	31.57	31.60	31.60	31.58	31.57
(4, 1)	41.28	41.20	41.26	41.30	41.30	41.29	41.28
(3, 3)	43.71	43.68	43.71	43.75	43.75	43.73	43.71
(4, 2)	48.57	48.49	48.52	48.53	48.53	48.60	48.57
(4, 3)	60.71	60.59	60.64	60.72	60.72	60.73	60.71
(4, 4)	77.71	77.51	77.60	77.66	77.66	77.73	77.71

Note. : total number of finite elements; : total number of degrees of freedom.