Free Vibration Analysis of Twisted Functionally Graded Material Plates

Abstract

The present paper will explore the free vibration behavior of thin twisted functionally graded material (FGM) plates. The vibration analysis is done using finite element method. An 8 noded shell element is used for finite element calculations. To model the FGM section, continuous variation in the material property along the thickness is approximated to a laminated composite section consisting of a number of layers and each layer is considered as isotropic. The material property in each layer is determined using power law. Material density, Young's modulus and Poisson's ratio change along the thickness based on power law. The first order shear deformation theory is used in the analysis of pretwisted FGM plate. Convergence of fundamental frequencies is observed, with an increase in mesh size and the number of layers in the thickness direction. To validate the finite element model, for different boundary conditions, the free vibration results are compared with analytical studies and experimental studies. Having fixed the mesh size and number of layers required to represent the material property variation along the depth, the changes in frequencies with variation in angle of twist and material property index is studied. The effect of geometric variables such as gradient index, aspect ratio, side to thickness ratio and angle of twist on the free vibration of cantilever twisted plates is studied. Temperature dependent material properties are considered as well as nonlinear material property variation along the thickness due to temperature. The influence of thermal gradient along the thickness direction on the free vibration of cantilever twisted plates is studied.