Free vibration analysis of thin annular plates integrated with piezoelectric layers using differential quadrature method

In this article, using generalized differential quadrature (GDQ) methods, free vibration of a thin annular plate coupled with two open circuit piezoelectric layers, is numerically studied based on the classical plate theory. The governing differential equations with respective boundary conditions are derived and transformed into a set of algebraic equations by implementing the GDQ rule, then solved as an eigenvalue problem to obtain the natural frequencies and mode shapes of the plate. Convergence of the solutions obtained for the natural frequencies is studied. Also, the present numerical model validated by comparing its numerical results with those reported in literature. Finally, parametric studies are carried out and the effects of a number of important parameters on the natural frequencies are investigated.