Effect of Parabolically Varying Non-Homogeneity on Thermally Induced Vibration of Orthotropic Trapezoidal Plate with Thickness Varies Linearly in One Direction and Parabolically in Other Direction

The present paper deals with the effect of parabolically varying non-homogeneity on thermally induced vibration of orthotropic trapezoidal plate with thickness varies linearly in one direction and parabolically in other direction. The two term deflection function corresponding to clamped-simply supported clamped-simply supported (C-S-C-S) boundary condition is defined by the product of the equation of the prescribed continuous piecewise boundary shape. The non-homogeneity of the plate varies parabolically. Rayleigh-Ritz method is used to solve the governing differential equation for maximum strain energy and maximum kinetic energy for orthotropic trapezoidal plate. The effect of frequencies for first and second mode investegated with the variations in structural parameters such as taper constant, non-homogeneity constant, aspect ratio and thermal gradient respectively. Results are calculated with great accuracy and compare the present model with the other in literature with the help of tables and graphs. All the results presented here are new and are not found elsewhere.