Bifurcations in Dynamical Systems With Internal Resonance

[+] Author and Article Information
P. R. Sethna, A. K. Bajaj

Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minn. 55455

J. Appl. Mech 45(4), 895-902 (Dec 01, 1978) (8 pages) doi:10.1115/1.3424438 History: Received January 01, 1978; Revised May 01, 1978; Online July 12, 2010


Dynamical systems with quadratic nonlinearities and exhibiting internal resonance under periodic excitations are studied. Two types of transition from stable to unstable motions are shown to occur. One kind are shown to be associated with jump phenomena while the other kind are shown to be associated with Hopf bifurcations of the averaged system of equations. In the case of the latter, the motions are shown to be amplitude modulated motions at the excitation frequency with the amplitude of modulation determined by the motion of a point on a torus.

Copyright © 1978 by ASME
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