Free vibration analysis of FGM plates by using layer wise displacement model

Abstract

In this paper, the free vibration analysis of simply supported functionally graded material (FGM) plate is analyzed. The displacement model based on Generalized Laminate Plate Theory (GLPT) assumes layer wise (LW) linear variation of in–plane displacements, constant transverse displacement, linear strain–displacement relations and linear material properties. The effective material properties of FGMs are assumed to be given by the Voigt’s rule of mixture (ROM). The Power law distribution of volume fraction is assumed through the plate thickness. The mathematical model includes the quadratic variation of transverse shear stresses within each mathematical layer of the plate. The principle of virtual displacements (PVD) is used to derive Euler–Lagrange differential equations of motions for free vibration problem. The Closed form solution is derived following the Navier’s technique and solving the eigenvalue problem. An original MATLAB computer program is coded for the numerical solution. The results reveal that the effects of side–to–thickness ratio, power–low index and material properties have significant effect on free vibration frequencies of FGM plates.