Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers

Abstract

In this paper, an analytical approach for free vibration analysis of moderately thick functionally graded rectangular plates coupled with piezoelectric layers is presented. The transverse distribution of electric potential satisfies the Maxwell equation as well as the electrical boundary conditions for both closed and open circuit piezoelectric layers. Based on the first order shear deformation plate theory and using both the Maxwell equation and Hamilton principle, the governing equations are obtained. These equations, which are six coupled partial differential equations, are decoupled through introducing four auxiliary functions. The decoupled equations are solved analytically for the Levy type of mechanical boundary condition, two opposite edges simply supported and arbitrary boundary conditions at the other edges. The numerical results for the plate natural frequency are established for various plate dimensions, power law indices and electrical and mechanical boundary conditions. Finally, the effect of piezoelectric layer thickness on the natural frequency is discussed for various plate parameters. It is found that the effect of the piezoelectric layer on the plate natural frequencies strongly depends on the mechanical and electrical boundary conditions.