A survey of the literature reveals that the title problem has not been treated in the open literature [1]. Clamped and simply supported outer edges are considered in the present study which makes use of an approach previously developed by the senior author and coworkers [2, 3]. In the case of a clamped edge the boundary conditions at the outer edge are identically satisfied while for the situation where it is simply supported only the essential outer edge condition is considered. The natural boundary conditions at the hole edge are not taken into account. This is permissible since use is made of the classical Rayleigh-Ritz method using the polynomial co-ordinate functions applicable in the case of solid plates. In the case of simply connected clamped and simply supported elliptical and circular plates the fundamental eigenvalues determined using the present approach are in excellent agreement with the results available in the literature [1, 2].
展开▼
