Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions

Abstract

The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homogeneous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young's modulus and mass density is the main cause for the occurrence of non-homogeneity in plate's material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.