Arbitrary Shape Of The Plate Free Vibration Analysis

This paper uses Mindlin theory and presents a new method to solve the problem of free vibration of moderately thick plates with arbitrary shape. Firstly, the expressions of free vibration of moderately thick plates in polar coordinates are derived and the general solutions are obtained by the means of method of separation of variables. Then, a group of beelines are used to approximate the boundaries of the plates and the Fourier expansion method is applied to the boundary conditions along the plate boundaries. The frequency equation is given by truncating the orders of the expansion series. Finally, the roots of the frequency of the equation can be numerically worked out. Because the general solution exactly satisfies the differential equations of the moderately thick plate, the method can give the results with high precision. The calculating cost is little, the course of the analysis is rather simple and the programming is easy.The paper takes rectangular plates, circular plates, elliptical plates and triangular plates as examples, respectively. The numerical results demonstrate the convergence and accuracy of the present method.