Vibration of Non-Homogeneous Plate Subject to Thermal Gradient

Abstract

A mathematical model is developed for the use of design engineers to analyze temperature-thickness coupling problem of a non-homogeneous isotropic visco elastic rectangular plate. Here, authors considered that temperature varies bi-parabolic i.e. parabolic in x– and parabolic in y– direction while thickness of plate varies linearly in one direction. The non-homogeneity of the plate's material is characterized by assuming an exponential variation of poisson's ratio of the plate's material. The first two modes of time period and deflection are reported here for various combinations of frequency parameters i.e. non-homogeneity constant, thermal gradient, taper constant and aspect ratio of the plate. Numerical results for time period and deflection for both the modes of vibration are shown in tabular form.