ON FREE VIBRATION OF THICK SUPERELLIPTICAL PLATES

This paper presents a free vibration study of moderately thick super-elliptical plates with various boundary constraints using the differential cubature method. The differential cubature method is a numerical procedure which expressing a linear operation of a continuous function or any orders of partial derivatives of multivariable function or combinations of them as a weighted linear sum of discrete function values within the overall domain of a problem. Through this new numerical procedure, the equilibrium governing equations and boundary conditions are transformed into a set of homogeneous linear algebraic equations about displacements at all discrete points. This is a typical eigenvalue problem, of which the eigenvalues can be calculated by the subspace iteration method. The applicability and the efficiency of this method are demonstrated through the convergence and comparison studies for the first five frequency parameters of super-elliptical plates with different boundary conditions.