Modeling and Simulation of Vibrations of Non-Homogeneous Annular Plate of Quadratic Thickness Resting on Elastic Foundation

Abstract

Mathematical modeling is presented to analyze natural frequencies of vibrations of an isotropic annular plate of quadratic varying thickness resting on Winkler type elastic foundation where numerical simulation is carried out using quintic spline technique for three different combinations of edge conditions. Effect of elastic foundation, together with nonhomogeneity variation, on the natural frequencies of vibration is illustrated for variety of thickness variation for the first three modes. To compare parametric effect on a specific plate, transverse displacements are presented in normalized form. Accuracy of the results and validity of numerical method is demonstrated by comparing the existing results in the literature.