Static and dynamic analysis of functionally graded piezoelectric plates under mechanical and electrical loading

Analysis of the static bending, free vibration and dynamic response of functionally graded piezoelectric plates has been carried out by the finite element method under loadings. The FGPM (Functionally Graded Piezoelectric Material) plate is assumed to be graded through the thickness and simple power law distribution, in terms of the volume fractions of the constituents used for formulation. The electric potential is assumed linear through the thickness of the plate. The governing equations are obtained, using potential energy and Hamilton’s principle, based on the First order Shear Deformation Theory (FSDT), which can include thermo-piezoelectric effects. The finite element model is derived based on the constitutive equation of the piezoelectric material, accounting for coupling between the elasticity and electric effect, by four node 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 plates under different mechanical boundary conditions. Numerical results for a PZT-4/PZT-5H plate are given in both dimensionless tabular and graphical forms. Effects of material composition and boundary conditions on static bending, free vibration and dynamic response are also studied. The numerical results obtained by the present model are in good agreement with the solutions reported in the literature.