Thermal Effect on Frequencies of Non-homogeneous Trapezoidal Plate with Linearly Varying Thickness in One Direction and Linearly Varying Density in other Direction

Abstract

In this study thermal effect on vibrations of non homogeneous trapezoidal plate has been investigated whose thickness varies linearly in one direction and density varies linearly in other direction. Governing differential equation has been derived using classical plate theory. Rayleigh-Ritz method is applied to obtain the frequencies for the first two modes of vibration. Clamped-Simply supported-Clamped-Simply supported boundary condition is considered with two term deflection function. Effect of various plate parameters such as non-homogeneity, aspect ratios, thermal gradient and taper constant have been studied. Results are shown in tabular form. The obtained results have been compared with the published paper of the authors shows a very well agreement together. 

Keywords: Trapezoidal plate, taper constant, thermal gradient, non-homogeneity, linearly, aspect ratio.