Dynamic analysis of piezoelectric delaminated composite plates resting on viscoelastic foundation via differential quadrature techniques

This article demonstrated the effectiveness of four differential quadrature shape functions (i.e., Lagrange interpolation polynomial, Cardinal Sine function, Delta Lagrange, and regularized Shannon kernel [RSK]) in solving the nonlinear vibration of multilayered piezoelectric composite plates that include delaminations, and rest on nonlinear Winkler and Visco-Pasternak elastic foundations. The governing equations are derived based on three-dimensional (3D) elasticity theory and piezoelectricity theory, and are subsequently solved using the differential quadrature method (DQM). The perturbation method is utilized in overcoming the nonlinearity of the obtained eigenvalue problem. MATLAB schemes are designed for each shape function, and are verified by comparing obtained results with the published exact solutions. In addition, a parametric study is presented to study the effect of various geometrical parameters, Winkler and Pasternak foundation parameters, and viscoelastic materials properties on the natural frequencies and shapes of the modes. It may be concluded that the obtained results from the proposed methods may be applied in structural health monitoring.