Homogenization Technique for Non-Linear Free Vibrations Analysis of FGM Rectangular Plates

Abstract

In the present study, the problem of geometrically nonlinear free vibrations of functionally graded rectangular plates (FGRP) is studied. A homogenization technique has been developed to reduce the FGRP problem under consideration to that of isotropic homogeneous rectangular plate. The material properties of the functionally graded composites examined herein are assumed to be graded in the thickness direction of the plate and estimated through the rule of mixture. The proposed theoretical model is based on the classical plate theory and the Von Karman relationships, and the amplitude equation is derived in the form of a set of non-linear algebraic equation using Hamilton’s principle and a multimode approach. The fundamental nonlinear frequency parameters and the bending stress are then calculated using the iterative and explicit methods of solution to show the effect of the vibration amplitudes and the material distributions. The results obtained in this study are found to be in a good agreement with the published ones dealing with the problem of large vibration of functionally graded plates.