Effect of uniform and nonuniform porosity on free vibration of functionally graded circular plate

Abstract

The purpose of this study is to determine the natural frequencies of functionally graded (FG) porous circular plates while taking into account the uniform and nonuniform porosity distribution in the thickness direction. The material properties of FG plates are assumed to be varying continuously in the thickness direction. The material properties are calculated based on Voigt’s micro-mechanical model taking power law distribution method with arbitrary power index. The mathematical model of the FG circular porous plate is based on the first-order shear deformation theory (FSDT). The motion of equations is derived using Hamilton’s energy principle and the Differential Quadrature Method (DQM) is applied to solve this equation. Convergence studies with respect to the number of nodes are used to validate the established solution methodology for nondimensional frequencies of FG circular plates. The nondimensional frequency for the FG circular plate is calculated and compared to the existing literature results. The effects of the thickness to radius ratio, material parameters, porosity distribution, and boundary conditions on the fundamental frequency for FG porous circular plates are also discussed in detail.