Free Vibration Analysis of Isotropic SSS Non Homogenous Triangular Plate with Varying Bi Dimensional Thickness and Thermal Effect

Abstract

newline In first problem, the effect of non-homogeneity on vibration of visco-elastic triangular plate with bi-linear thickness variation has been studied. Thermal induced vibration of these plates has been assumed as bi-linear temperature circulation. For non-homogeneity of the plate material density is taken to be constant. The governing differential equation has been solved with the help of variables separation method. The approximated frequency equation is derived by using Rayleigh-Ritz method by two term deflection function. Frequency values for the first two modes of vibration have been calculated for a simply supported parallelogram plate for various values of thermal gradient, skew angle and taper constants. newlineIn second problem, free vibration of visco-elastic triangular plate under the effect of bi- parabolically thickness variation and linear temperature distribution in both directions has been studied. Density (due to non-homogeneity) of the plate is taken to be constant. The governing differential equation has been solved with the help of variables separation method. The approximated frequency equation is derived by using Rayleigh-Ritz method by two term deflection function. Frequency values for the first two modes of vibration have been calculated for a simply supported triangular plate for various values of thermal gradient, skew angle and taper constants with the help of MAPLE (latest computational software). newlineIn third problem, free vibration of visco-elastic triangular plate under the effect of bi- parabolic thickness variation and parabolic temperature distribution in both directions has been studied. Density (due to non-homogeneity) of the plate is taken to be constant. The governing differential equation has been solved with the help of variables separation method. The approximated frequency equation is derived by using Rayleigh-Ritz method by two term deflection function. Frequency values for the first two modes of vibration have been calculated for a simply supported triangular plate for various values of thermal gradient, skew angle and taper constants. newlineIn fourth problem, free vibration of visco-elastic triangular plate under the effect of bi- newlineii newlinelinear thickness and parabolic temperature distribution in both directions has been studied. Density (due to non-homogeneity) of the plate is taken to be constant. The governing differential equation has been solved with the help of variables separation method. The approximated frequency equation is derived by using Rayleigh-Ritz method by two term deflection function. Frequency values for the first two modes of vibration have been calculated for a simply supported triangular plate for various values of thermal gradient, skew angle and taper constants. newlineIn fifth problem, free vibration of a simply supported visco-elastic triangular plate under the effect of thickness linearly in one direction and parabolically in other direction and linear temperature variation along both directions has been studied. For non-homogeneity of material, density of the plate is taken to be constant. By use of separation of variables method, the governing differential equation has been solved for visco-elastic triangular plate. The approximated frequency equation is derived by using Rayleigh-Ritz method by two term deflection function. Latest computational software MAPLE has been used to calculate Frequency values for the first two modes of vibration at various values of plate s parameters (thermal gradient, taper constants and skew angle). Results are shown in form of tables and graphs.