3-D vibration analysis of generalized super elliptical plates using Chebyshev-Ritz method

Abstract

The three-dimensional free vibration of generalized super elliptical plates is analysed, based on the exact, small-strain and linear elasticity theory. The Ritz method is applied to derive the frequency equation. The triplicate Chebyshev polynomial series form the backbones of the admissible functions, as modified by a characteristic boundary function to ensure the satisfaction of geometric boundary conditions of the plate. Utilizing the symmetry of the plate under consideration, eight distinct vibration modes can be classified and individually solved while maintaining the same level of accuracy. The accuracy of the present method has been examined by the convergence and comparison studies. The effect of geometric parameters on vibration behaviour of the generalized super elliptical plates with free and fixed perimeters have been studied for different powers, thickness ratios and aspect ratios. © 2004 Published by Elsevier Ltd.