Thermally Induced Vibration of Non-homogeneous Trapezoidal Plate Whose Thickness Varies Linearly in One and Parabolically in Other Direction with Linearly Varying Density

Abstract

Based on classical plate theory, the natural frequencies of thermally induced vibration of non-homogeneous trapezoidal plate with varying thickness linearly in x-direction and parabolically in y-direction has been calculated by Rayleigh–Ritz method. Due to linear variation in density non-homogeneity arises in plate’s material. The frequency equation has been obtained by assuming the two-term deflection function with clamped-simply supported- clamped-simply supported boundary condition. For a symmetric, non-homogeneous trapezoidal plate the effect of non-homogeneity constant, aspect ratios, thermal gradient and taper constants on the frequencies has been studied for first two modes of vibration. All the numerical results which have been obtained presented in tabular and graphical form.