Effect of Exponential Temperature Variation on Vibration of Orthotropic Rectangular Plate whose Thickness varies Parabolically in Both Directions

Abstract

A simple model presented here is to study the exponentially thermal effect on vibration of orthotropic rectangular plate having bi-direction parabolically varying thickness having clamped boundary conditions on all the four edges. Rayleigh Ritz method is used to evaluate the frequency parameter. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Yet the method used for the solution of present problem provides an approximate solution but it is quite convenient and authentic one. A two-term deflection function is used and frequency corresponding to first two modes of vibration is calculated for different values of temperature gradient and two taper constants.