Free Vibration of Clamped Polygonal Plates

Abstract

This paper presents an analytical method to study free vibration of polygonal plates clamped at the edges. A polygonal plate is formed by setting some rigid line supports on a simply supported rectangular plate. Regarding the reaction force and moment acting on all edges of the polygonal plate as unknown harmonic exciting loads, the stationary response of the plate to these loads is obtained. The force and moment distributed along the edges are expanded into a Fourier sine series with unknown coefficients, and homogeneous linear equations are derived with use of restraint conditions at the edges. The natural frequencies and the mode shapes of the polygonal plate are determined by calculating the eigenvalues and eigenvectors of the equations. From the numerical calculation carried out on an equilateral triangular through a regular octagonal plate, it was clarified that the mode shapes of clamped polygonal plates can be classified into several groups of various types.