Free flexural vibrations of super elliptic plates

Abstract

This paper deals with a direct problem of the free flexural vibrations of a plate with rounded corners on the basis of the theory of thin plates. The plate of uniform thickness is made of linear elastic, isotropic materials, and its periphery is given by a super elliptic function with a power. The super elliptic power defines the shape of the plate ranging from an ellipse to a rectangle and indicates the degree of roundness. The method of solution is based on the method of separation of variables together with certain methods of weighted residuals (i.e., the method of moments, and the Galerkin and least squares methods). The shape functions are chosen in the form of double series polynomials, and they satisfy either a simply supported or a clamped boundary condition. Some numerical results are reported for the vibration frequencies in the case of both symmetric and antisymmetric mode shapes of the plate. The results are compared with the existing literature, and the convergence of solutions is discussed. [Work supported in part by TUBA.]