Free Vibration Analysis of Thick Superelliptical Plates

Abstract

This paper investigates the free vibration of thick plates with rounded corners subject to different boundary conditions. The periphery of this class of plates is defined by a superelliptical function, and the degree of roundedness can be adjusted by a superelliptical power to acquire the level of stress distribution desired. The Ritz method is employed to derive the governing eigenvalue equation, where the Ritz function consists of polynomials that include a basic function to impose the various boundary constraints. A higher-order shear deformation plate theory is used to account for the effects of transverse shear deformation. The numerical accuracy is ascertained by studying the convergence characteristics of the plate vibration frequencies and, where possible, by comparing the solutions with existing literature. In this paper, the results presented include sensitivities of free vibration frequencies to variations in geometry, boundary constraints and thickness, and also their interactions.