Application of Three-dimensional Differential Transform Method to Dynamic Vibration Analysis of Rectangular Plate Resting on Elastic Foundation

Abstract

Research on vibration analysis of non-homogenous and varying thickness plate has gained a tremendous increment in recent year due to its vast application in many fields of engineering. This study investigate the dynamic behavior of rectangular plate with varying thickness resting on two-parameter foundation under simply supported free edge condition. The governing differential equation is analyzed using three-dimensional differential transform method. The accuracies of the established solutions are verified by comparing the solutions with earlier works. The analytical solutions obtained are used to investigate the effect of variation of density, thickness, foundation stiffness and natural frequency on maximum deflection. From the results, it is observed that increase in combined Pasternak and Winkler foundation stiffness results in decrease in maximum deflection, increase in taper constant results in increase in maximum deflection, increase in non-homogeneity leads to decrease maximum deflection and increase in natural frequency results in increase in maximum deflection. It is expected that findings from this research will contribute to studies of dynamic behavior of plates.