Monte Carlo Simulation of Coupled Nonlinear Oscillators Under Random Excitations

[+] Author and Article Information
Wenlung Li, R. A. Ibrahim

Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202

J. Appl. Mech 57(4), 1097-1099 (Dec 01, 1990) (3 pages) doi:10.1115/1.2897638 History: Received June 05, 1989; Revised January 08, 1990; Online March 31, 2008


The main objectives of this note are to examine the random response of nonlinear three degree-of-freedom systems in the neighborhood of combination internal resonance by using Monte Carlo simulation and to compare the results with those obtained by first-order non-Gaussian closure. The numerical simulation is found to support the main features of the nonlinear interaction in the neighborhood of internal resonance conditions. For example, the nonlinear interaction takes place in the form of a randomly continuous energy exchange between the modes involved. In addition, the results verify the existence of energy absorbing effect as predicted by the non-Gaussian closure method. While the non-Gaussian closure exhibits regions of multiple solutions in the neighborhood of exact internal resonance, the numerical simulation gives only one solution depending on the assigned initial conditions. This observation requires further investigation to establish the domains of attraction in stochastic nonlinear dynamics.

Copyright © 1990 by The American Society of Mechanical Engineers
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