A perturbation approach for evaluating natural frequencies of moderately thick elliptic plates

Abstract

Natural frequencies for moderately thick elliptic plates are calculated by perturbing initial values corresponding to the Kirchhoff classical theory of plate bending. The proposed approach utilizes a universal algebraic equation for perturbed eigenvalues, previously derived by the authors. For elliptic plates of a small eccentricity, a dual procedure is developed to evaluate the sought for natural frequencies starting from those for a circular thin plate. A comparison with finite-element computations is presented. An importance of the perturbation techniques in question for interpreting of finite-element data is emphasized.