Vibration of a rectangular plate supported at an arbitrary number of points

Abstract

A method is described for establishing the natural frequencies of a rectangular plate supported at points. The number and the location of these points may be completely arbitrary. The method is based on some extensions to the intermediate problem technique of Aronszjan and Weinstein [1–4] through the use of finite sets of constraints, which has been developed recently [5–8]. The method is called the modal constraint method. The merits of this method lie in the fact that the eigenvalues and eigenfunctions of a completely free vibrating rectangular plate are used as the reference structure. The modifications associated with the point supports are taken into account by Lagrangian generalized forces of constraint acting on the reference structure. The method has been verified with many known solutions. Furthermore the convergence is very fast with any desirable accuracy to exact known natural frequencies.