Anomaly observed in the approximate analysis of vibrating rectangular plates with edges elastically restrained against rotation and translation

This paper deals with the solution of the title problem in the case of an orthotropic plate with three edges elastically restrained against rotation whilst transverse displacement is prevented. It is assumed that the fourth edge is elastically restrained against rotation and translation.The natural boundary conditions are satisfied approximately at the fourth edge.The Rayleigh-Ritz method is used to derive an approximate fundamental frequency equation and a rather curious anomaly is shown to exist in the frequency values for a certain range of values of the rotational and translational spring parameters which govern the motion of the fourth edge.