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.
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February 1976
This article was originally published in
Journal of Engineering for Industry
Research Papers
Bending and Vibration of Plates of Variable Thickness
S. S. H. Chen
S. S. H. Chen
Arizona State University, Tempe, Ariz.
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S. S. H. Chen
Arizona State University, Tempe, Ariz.
J. Eng. Ind. Feb 1976, 98(1): 166-170
Published Online: February 1, 1976
Article history
Received:
May 23, 1975
Online:
July 15, 2010
Citation
Chen, S. S. H. (February 1, 1976). "Bending and Vibration of Plates of Variable Thickness." ASME. J. Eng. Ind. February 1976; 98(1): 166–170. https://doi.org/10.1115/1.3438811
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