Vibrations of a Rectangular Cantilever Plate

Abstract

A Fourier sine-series method is used to solve the differential equation, together with the boundary conditions, for the transverse vibrations of a thin rectangular cantilever plate. Frequencies of vibration and the corresponding nodal lines are calculated and plotted as functions of the ratio of sides for five symmetric and four antisymmetric modes. Because of the large number of calculations made, some interesting phenomena appear which have not previously been reported in the literature.