The Behavior of Vibration in a Non-Homogeneous Orthotropic Rectangular Plate with a Linearly Varying Temperature and Circularly Varying Thickness in Two Dimensions

In present paper analysis, we try to figure out first two mode of vibration of a non-homogeneous orthotropic rectangular plate with linearly varying temperature and circularly varying thickness in two dimensions. For non-homogeneity of the plate material the density vary linearly in x-direction. Rayleigh–Ritz method is used to solve the general differential equation of the orthotropic rectangular plate which is circular in two dimensions. The governing equations provide the frequencies for the first two vibration modes. Under clamped boundary condition several parameters including taper constants, thermal gradient, non-homogeneity, and aspect ratio, are analyzed. All calculations are calculated with the help of MATLAB, and the results are presented through graphs and tables for first two modes of vibration.