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Different numerical schemes are introduced to formulate and solve nonlinear vibration analysis of elastically supported multilayer composite plate problems. The type of elastic foundation is Winkler - Pasternak foundation model. The governing equations are formulated according to a first order transverse shear theory. Examined schemes are based on polynomial, sinc, discrete singular convolution differential quadrature (DSCDQ) methods. These schemes are appointed to reduce the problem to nonlinear Eigen-value problem. The reduced system is solved iteratively. Numerical analysis is performed to explore influence of different computational characteristics on convergence and efficiency of the obtained results. Comprehensive numerical results validate the solutions by comparison with those obtained by the exact and numerical ones. Moreover, a parametric study is introduced to investigate the influence of supporting conditions, foundation parameters, elastic and geometric characteristics of the vibrated plate, on natural frequencies and mode shapes. The obtained results exhibit that the (DSCDQM) is an accurate efficient method in the dynamic analysis of discontinuity plates resting on nonlinear elastic foundation.

Nonlinear vibration analysis of elastically supported multi-layer composite plates using efficient quadrature techniques