Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

Table 8

Comparison between the normalized fundamental frequency β, elastic foundation parameter, and different boundary conditions for the square plate (, , and  = 50).

		Nonlinear treatment methods	SSSS	SCSC	SSSC	SSSF
0	0	Perturbation	19.7349	28.9157	23.6398	11.6883
		Iterative quadrature	19.7349	28.9157	23.6398	11.6883
	100	Perturbation	48.6329	54.6505	51.3365	37.1656
		Iterative quadrature	48.6329	54.6505	51.3365	37.1656
	1000	Perturbation	141.9431	146.7559	144.2712	111.7952
		Execution time (sec)	1.24152	1.2158	1.22158	1.187421
		Iterative quadrature	141.9425	146.7553	144.2706	111.7947
		Execution time (sec)	0.784509	0.70355	0.76487	0.69457
100	0	Perturbation	22.1402	30.6741	25.6818	15.3870
		Iterative quadrature	22.1402	30.6741	25.6818	15.3870
	100	Perturbation	49.6324	55.5689	52.2925	38.4718
		Iterative quadrature	49.6324	55.5689	52.2925	38.4718
	1000	Perturbation	142.2904	147.1665	144.7015	112.3010
		Execution time (sec)	1.24115	1.1187	1.24005	1.12571
		Iterative quadrature	142.3024	147.1790	144.7098	112.3075
		Execution time (sec)	0.77785	0.70254	0.75714	0.70478
1000	0	Perturbation	37.2791	42.8293	39.4889	33.7090
		Iterative quadrature	37.2791	42.8293	39.4889	33.7090
	100	Perturbation	57.9569	63.1485	60.8547	48.6837
		Iterative quadrature	57.9569	63.1485	60.8547	48.6837
	1000	Perturbation	145.3461	150.1200	147.6716	116.1315
		Execution time (sec)	1.14287	1.11276	1.01451	0.99475
		Iterative quadrature	145.4915	150.2702	147.6863	116.2471
		Execution time (sec)	0.75415	0.70125	0.74583	0.69573