Large Amplitude Vibration of a Circular Plate With Concentric Rigid Mass

[+] Author and Article Information
D. C. Chiang, S. S. H. Chen

Department of Engineering Mechanics, Arizona State University, Tempe, Ariz.

J. Appl. Mech 39(2), 577-583 (Jun 01, 1972) (7 pages) doi:10.1115/1.3422720 History: Received December 24, 1970; Revised April 12, 1971; Online July 12, 2010


Simplified nonlinear governing differential equations proposed by Berger and extended by Nash and Modeer are applied to obtain natural frequencies of a circular plate with concentric rigid part at its center in large amplitude vibrations. A modified Galerkin technique is used to derive a nonlinear differential equation of which the solution is given in terms of elliptic functions. The small amplitude vibration is treated as a special case of large amplitude vibration, while the free, large amplitude vibration of a flat circular plate is studied as a special case of large amplitude vibration of a circular plate with a concentric mass. The numerical results show that the effect of added concentric rigid mass to a circular plate is significant.

Copyright © 1972 by ASME
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