Bending and Vibration of Plates of Variable Thickness

[+] Author and Article Information
S. S. H. Chen

Arizona State University, Tempe, Ariz.

J. Eng. Ind 98(1), 166-170 (Feb 01, 1976) (5 pages) doi:10.1115/1.3438811 History: Received May 23, 1975; Online July 15, 2010


The problem of bending and vibration of plates of variable thickness and arbitrary shapes and with mixed boundary conditions was solved by a modified energy method of the Rayleigh-Ritz type. General trial functions of deflection were obtained, one in Cartesian coordinates for rectangular plates and the other in polar coordinates for other shapes. The forced boundary conditions were satisfied approximately by introducing fixity factors which depended upon the prescribed conditions. Central deflections for circular plates subjected to static bending were within 0.2 percent of published results while they were within 1 percent for rectangular plates. The differences of natural frequencies of various rectangular plates were from 0.05 percent for simple, 2.9 percent for clamp, and up to 4.3 percent for free-free plates based on the published values.

Copyright © 1976 by ASME
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