Resonant Layers in Nonlinear Dynamics

[+] Author and Article Information
R. P. S. Han

Department of Mechanical Engineering, University of lowa, 2136 Seamans Center, lowa City, IA 52242-1527

A. C. J. Luo

Department of Mechanical Engineering, University of Southern Illinois at Edwardsville, Edwardsville, IL 62026

J. Appl. Mech 65(3), 727-736 (Sep 01, 1998) (10 pages) doi:10.1115/1.2789117 History: Received January 23, 1997; Revised December 10, 1997; Online October 25, 2007


A new method based on an incremental energy approach and the standard mapping technique is proposed for the study of resonant layers in nonlinear dynamics. To demonstrate the procedure, the method is applied to four types of Duffing oscillators. The appearance, disappearance and accumulated disappearance strengths of the resonant layers for each type of oscillator are derived. A quantitative check of the appearance strength is performed by computing its value using three independent methods: Chirikov overlap criterion, renormalization group technique, and numerical simulations. It is also observed that for the case of the twin-well Duffing oscillator, its perturbed left and right wells are asymmetric.

Copyright © 1998 by The American Society of Mechanical Engineers
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