Abhishek Thakur, Ashish Kumar Sharma, Umesh Bhardwaj
This study examines the free vibration behaviour of an orthotropic rectangular plate with variable thickness, temperature-dependent properties, and material non-homogeneity. The temperature distribution varies in circular and parabolic forms along the x- and y-directions, respectively, while the material non-homogeneity is assumed to vary linearly along the x -direction. The plate thickness is considered to vary from circular to parabolic profiles. The Rayleigh–Ritz method is employed to obtain approximate solutions of the governing differential equation and determine the natural frequencies corresponding to the first two vibration modes. Clamped boundary conditions are applied throughout the analysis. The influence of taper constants, thermal gradient, non-homogeneity parameter, and aspect ratio on the vibration characteristics is investigated. Numerical computations are performed using MATLAB, and the results are presented through tables and graphs to illustrate the effects of these parameters.