Effect of plate’s parameters on vibration of isotropic tapered rectangular plate with different boundary conditions

Abstract

A mathematical model is presented to analyse the vibration of a tapered isotropic rectangular plate under thermal condition. Tapering in the thickness of rectangular plate is considered bi-parabolic. Here, temperature variation is assumed bi-linearly, i.e. temperature varies linearly in the x-direction and linearly in the y-direction. First two modes of frequency of rectangular plate are calculated for five boundary conditions such as C-C-C-C, SS-SS-SS-SS, C-SS-SS-SS, C-SS-C-SS and C-C-C-SS, where C and SS stand for clamped boundary and simply supported boundary, respectively. The plate is considered homogeneous and made up of a visco-elastic isotropic material. Rayleigh Ritz technique is applied to get the first two modes of frequencies at different values of plate’s parameters. Numeric results are presented in tabulated and graphical forms.