Static, Dynamic, and Free Vibration Analysis of Functionally Graded Piezoelectric Panels Using Finite Element Method

In this article, analysis of the static bending, free vibration, and dynamic response of functionally graded piezoelectric panels have been carried out by finite element method under different sets of mechanical, thermal, and electrical loadings. The temperature field is assumed to be of uniform distribution over the panel surface and through the thickness of panel. The governing equations are obtained using potential energy and Hamilton's principle based on the first-order shear deformation theory that includes thermo-piezoelectric effects. The finite element model is derived on the basis of constitutive equation of piezoelectric material accounting for coupling between 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. The temperature field is calculated by post-computation through constitutive equation. Results are presented for two constituent FGPM panels under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H panels 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 available solutions reported in the literature.