THE VIBRATION OF A RECTANGULAR PLATE WITH EDGES ELASTICALLY RESTRAINED AGAINST ROTATION

Abstract

By means of the Rayleigh-Ritz method, an analysis is made of the vibration of a rectangular plate whose edges are elastically restrained against rotation. Plate deflexions are represented by a set of functions which define the normal modes of vibration of a beam whose ends are elastically restrained against rotation. Values of various integrals of these functions and their derivatives are established. Frequencies are obtained from a set of linear simultaneous equations which may be solved by a simple iterative process. An approximate frequency equation is also derived and numerical tables for use with this equation are presented.