Vibration response of the exponential functionally graded material plate with variable thickness resting on the orthotropic Pasternak foundation

Abstract

The manuscript aims to perform the free and forced vibration analysis considering the porosity and orthotropic foundation effect. For the first time, the study is conducted on a variable thickness FGM plate resting on an orthotropic foundation. This study uses the first-order shear deformation plate theory (FSDT) model to present an exact solution for free and forced vibration analysis of the functionally graded material (FGM) plate with variable thickness. The FGM plate, having exponentially varied material properties in the thickness direction, was restrained on simply supported (S-S-S-S) and clamped-clamped (C-C-C-C) boundary conditions. Three different types of microstructural defects (porosity) are taken into consideration during the establishment of the mathematical modeling. In addition, the effect of the orthotropic Pasternak foundation has been incorporated during the formulation. The governing differential equation for thick to thin plates is derived using a variational approach, and further, the Galerkin method is applied to solve the equation of motion. The results have been compared and validated with the existing literature available for a rectangular plate on an elastic foundation. The parametric studies have been done to explore the detailed understanding of the E-FGM (Exponentially graded material) plate including microstructural defects. Even the benchmark results have been investigated for free and forced vibration analysis of the E-FGM plate on the orthotropic elastic foundation.