Free vibration analysis of heated shear flexible functionally graded plates using finite element method

Abstract

In this paper, free vibration analysis of through thickness functionally graded plates is studied by using versatile Finite Element Method (FEM) based on Reissner - Mindlin shear deformable plate theory. The properties of the plate are considered to vary according to a power law distribution across the thickness. The Euler-Lagrange equations of the first order theory are derived using the dynamic version of the principle of virtual displacements. Two classical boundary conditions, namely clamped and simply supported at all edges, are considered. Numerical results are provided to demonstrate the effect of material variations, boundary conditions, plate aspect ratios and plate length to thickness ratios on the free vibration. The effect of transverse shear on fundamental frequency is demonstrated. Free vibration analysis is carried out with temperature independent and dependent material properties. The importance of considering temperature dependent material properties for free vibration analysis of FGM plate operating in thermal environment is clearly established for the first time.