The Onset of Chaos in a Two-Degree-of-Freedom Impacting System

[+] Author and Article Information
Jinsiang Shaw, Steven W. Shaw

Department of Mechanical Engineering, Michigan State University, East Lansing, Mich. 48824

J. Appl. Mech 56(1), 168-174 (Mar 01, 1989) (7 pages) doi:10.1115/1.3176040 History: Received March 09, 1988; Revised July 28, 1988; Online July 21, 2009


The dynamic response of a two-degree-of-freedom impacting system is considered. The system consists of an inverted pendulum with motion limiting stops attached to a sinusoidally excited mass-spring system. Two types of periodic response for this system are analyzed in detail; existence, stability, and bifurcations of these motions can be explicitly computed using a piecewise linear model. The appearance and loss of stability of very long period subharmonics is shown to coincide with a global bifurcation in which chaotic motions, in the form of Smale horseshoes, arise. Application of this device as an impact damper is also briefly discussed.

Copyright © 1989 by ASME
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