Analytical Solution to Free Vibration of Sector Plates

Abstract

A solution is presented for the free out‐of‐plane vibration of thin, isotropic annular sector plates with different edge conditions. The classical method of separation of variables is employed. The basic functions in the tangential direction are chosen as the eigenfunctions for vibrating beams. These functions are employed in the finite‐strip method. However, the advantage of this method lies in the analytical, instead of numerical, representation of the funtctions in the radial direction. Satisfaction of the governing differential equation of the plate is achieved by the selection of general time‐dependent functions and the derivation of appropriate analytical radial functions in terms of Bessel functions. Sector plates of different radii and outer‐radius‐to‐thickness ratios, and with various end conditions along the straight and circular edges have been analyzed. Wherever possible, results are compared to previously published ones.