Antisymmetric modes of vibration of a circular plate elastically restrained against rotation and subjected to a hydrostatic state of in‐plane stress

Abstract

The analysis of flexural vibrations of plates with edges elastically restrained against rotation is of interest to the design engineer since ideal supports or clamps are difficult to obtain in practice. A survey of the literature reveals that several investigations have been performed in the past on (a) vibrating circular edges (without in‐plane loading) and (b) vibrating simply supported and clamped circular plates subjected to hydrostatic in‐plane loading. The present paper deals with the determination of very simple, approximate frequency equations which allow prediction of natural frequencies in the case of a vibrating circular plate which executes antisymmetric modes. It is shown that use of simple polynomial expression and a variational approach leads, in some cases, to numerical values which are more accurate than those available in the technical literature. The approach followed in the present investigation can be extended in a straightforward fashion to the case where the edge has translational flexibility.