The Dynamics of a Harmonically Excited System Having Rigid Amplitude Constraints, Part 1: Subharmonic Motions and Local Bifurcations

[+] Author and Article Information
S. W. Shaw

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

J. Appl. Mech 52(2), 453-458 (Jun 01, 1985) (6 pages) doi:10.1115/1.3169068 History: Received March 01, 1984; Revised June 01, 1984; Online July 21, 2009


A simple model for the response of mechanical systems having two-sided amplitude constraints is considered. The model consists of a piecewise-linear single degree-of-freedom oscillator subjected to harmonic excitation. Encounters with the constraints are modeled using a simple impact rule employing a coefficient of restitution, and excursions between the constraints are assumed to be governed by a linear equation of motion. Symmetric double-impact motions, both harmonic and subharmonic, are studied by means of a mapping that relates conditions at subsequent impacts. Stability and bifurcation analyses are carried out for these motions and regions are found in which no stable symmetric motions exist. The possible motions that can occur in such regions are discussed in the following paper, Part 2.

Copyright © 1985 by ASME
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