A Study of Dynamic Instability of Plates by an Extended Incremental Harmonic Balance Method

[+] Author and Article Information
C. Pierre, E. H. Dowell

School of Engineering, Duke University, Durham, N.C. 27706

J. Appl. Mech 52(3), 693-697 (Sep 01, 1985) (5 pages) doi:10.1115/1.3169123 History: Received March 01, 1984; Revised October 01, 1984; Online July 21, 2009


The dynamic instability of plates is investigated with geometric nonlinearities being included in the model, which allows one to determine the amplitude of the parametric vibrations. A modal analysis allowing one spatial mode is performed on the nonlinear equations of motion and the resulting nonlinear Mathieu equation is solved by the incremental harmonic balance method, which takes several temporal harmonics into account. When viscous damping is included, a new algorithm is proposed to solve the equation system obtained by the incremental method. For this purpose, a new characterization of the parametric vibration by its total amplitude—or Euclidian norm—is introduced. This algorithm is particularly simple and convenient for computer implementation. The instability regions are obtained with a high degree of accuracy.

Copyright © 1985 by ASME
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