Vibration Analysis of Non-homogenous Orthotropic Visco-elastic Rectangular Plate of Parabolically Varying Thickness with Thermal Effect

Abstract

The present work analyses the vibration behaviour of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness on the basis of classical plate theory when the all edges are clamped and are subjected to linearly thermal variation. For non-homogeneity of the plate material it is assumed that the density of the plate material varies parabolically along the x-direction. For visco-elastic materials, basic elastic and viscous elements are combined. The Kelvin model for visco-elasticity is considered here, which is a combination of elastic and viscous elements connected in parallel. Using the separation of variable method, the governing differential equation has been solved. The time period and deflection corresponding to the first two modes of vibrations of clamped plates have been calculated for different values of thermal gradients, non-homogeneity constants, taper constants, and aspect ratio, with the help of Rayleigh-Ritz techniques, and are shown by graphs.