Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

Abstract

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton’s principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.