Vibrations of Dynamical Systems With Quadratic Nonlinearities

[+] Author and Article Information
P. R. Sethna

Department of Aeronautics and Engineering Mechanics, University of Minnesota, Minneapolis, Minn.

J. Appl. Mech 32(3), 576-582 (Sep 01, 1965) (7 pages) doi:10.1115/1.3627261 History: Received March 09, 1964; Revised December 03, 1964; Online September 15, 2011


General two-degree-of-freedom dynamical systems with weak quadratic nonlinearities are studied. With the aid of an asymptotic method of analysis a classification of these systems is made and the more interesting subclasses are studied in detail. The study includes an examination of the stability of the solutions. Depending on the values of the system parameters, several different physical phenomena are shown to occur. Among these is the phenomenon of amplitude-modulated motions with modulation periods that are much larger than the periods of the excitation forces.

Copyright © 1965 by ASME
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