THREE DIMENSIONAL VIBRATION ANALYSIS OF FUNCTIONALLY GRADED SUPER-ELLIPTICAL PLATES

This paper describes a study of three-dimensional vibration characteristics of functionally graded super-elliptical plates with different boundary conditions. The analysis is based on the three-dimensional small-strain, linear and 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. The accuracy of these results is verified by appropriate convergence studies and checked with the available literature as well as the 3-D theory.