Resonant Excitation of a Spinning, Nutating Plate

[+] Author and Article Information
J. W. Klahs

Structural Dynamics Research Corporation, Cincinnati, Ohio

J. H. Ginsberg

School of Mechanical Engineering, Purdue University, West Lafayette, Ind. 47907

J. Appl. Mech 46(1), 132-138 (Mar 01, 1979) (7 pages) doi:10.1115/1.3424484 History: Received April 01, 1978; Online July 12, 2010


The equations of motion governing the three-dimensional finite-amplitude response of a plate in arbitrary space motion are derived and shown to lead to dynamic coupling between the transverse and in-plane displacement. A general method of solution for such problems is demonstrated in an example involving a simply supported rectangular plate spinning about an axis parallel to an edge and nutating through a small angle. The method involves an asymptotic expansion using the derivative expansion version of the method of multiple time scales, in conjunction with the Galerkin method. A critical spin rate leading to the loss of stability in divergence is determined. Then, a numerical example of resonant excitation of one principal coordinate demonstrates that the nonlinear response resembling the one obtained from linear theory may lose stability in favor of a second response in which several principal coordinates are mutually excited. Consideration of the interaction between in-plane and transverse displacements is shown to be crucial to the prediction of this “unusual” response.

Copyright © 1979 by ASME
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