Plate Characteristic Functions and Natural Frequencies of Vibration of Plates by Iterative Reduction of Partial Differential Equation

[+] Author and Article Information
R. B. Bhat, J. Singh, G. Mundkur

Department of Mechanical Engineering, Concordia University, Montreal, Quebec H3G 1M8

J. Vib. Acoust 115(2), 177-181 (Apr 01, 1993) (5 pages) doi:10.1115/1.2930328 History: Received September 01, 1991; Revised May 01, 1992; Online June 17, 2008


Natural frequency coefficients of rectangular plates and the corresponding plate characteristic functions are obtained by reduction of plate partial differential equation to an ordinary differential equation and solving it exactly. The reduction is carried out by assuming a deflection shape in one direction consistent with the boundary conditions and applying Galerkin’s averaging technique to eliminate the variable. The reduction method, commonly known as Kantorovich method, is applied sequentially on either directions of the plate and iterated until convergence is achieved for the natural frequency coefficients. The resulting plate characteristic functions are very good approximations to the normal modes of the plate. The results are tabulated for plates with combination of clamped, simply-supported, and free edge conditions.

Copyright © 1993 by The American Society of Mechanical Engineers
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