Perturbation methods for moderately elliptical plates with a core

Fundamental frequencies of vibrating moderately elliptic plates with a concentric circular core have been determined analytically. A boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem. The method is then applied to moderately elliptic plates with clamped and simply supported outer boundary conditions. Clamped, simply supported, and free circular cores are considered. Approximate analytical formulations of the fundamental frequency for such plates with core are obtained.