On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 1: Autonomous System

[+] Author and Article Information
M. Moh’d

Civil Engineering Department, Eastern Mediterranean University, Gazi Magusa, K. Kibris, Mersin 10, Turkey

K. Huseyin

Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

J. Vib. Acoust 121(1), 101-104 (Jan 01, 1999) (4 pages) doi:10.1115/1.2893934 History: Received April 01, 1998; Online February 26, 2008


The static and dynamic bifurcations of an autonomous system associated with a twofold zero eigenvalue (of index one) are studied. Attention is focused on Hopf bifurcation solutions in the neighborhood of such a singularity. The family of limit cycles are analyzed fully by applying the formula type results of the Intrinsic Harmonic Balancing method. Thus, parameter-amplitude and amplitude-frequency relationships as well as an ordered form of approximations for the periodic motions are obtained explicitly. A verification technique, with the aid of MAPLE, is used to show the consistency of ordered approximations.

Copyright © 1999 by The American Society of Mechanical Engineers
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