Free vibration analysis of functionally graded porous circular and annular plates using differential quadrature method

Abstract

The research aims to find the fundamental frequencies of functionally graded (FG) porous circular and annular plates while accounting for three alternative porosity distributions in the thickness direction: uniform, O-shape, and X-shape. In the thickness direction, the material characteristics of FG plates are considered to vary constantly. The material characteristics are determined using Voigt's micromechanical model, which uses the power-law distribution approach with an arbitrary power index. The first-order shear deformation theory (FSDT) is used to derive the mathematical formulation of functionally graded plates. The equilibrium equation is determined using Hamilton's energy principle, and the problem is solved using the differential quadrature method (DQM). The established solution approach for non-dimensional frequencies of FG circular/annular plates is validated using convergence studies concerning the number of nodes. The FG circular/annular plate's non-dimensional frequency is determined and compared to current literature results. The natural frequency of FG porous circular/annular plates is studied in-depth in terms of thickness to radius ratio, material properties, porosity distribution, and boundary conditions.