On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 2: Nonautonomous 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), 105-109 (Jan 01, 1999) (5 pages) doi:10.1115/1.2893935 History: Received April 01, 1998; Online February 26, 2008


This paper extends the bifurcation and stability analysis of the autonomous system considered in Part 1 to the case of a corresponding nonautonomous system. The effect of an external harmonic excitation on the Hopf bifurcation is studied via a modified Intrinsic Harmonic Balancing technique. It is observed that a shift in the critical value of the parameter occurs due to the external excitation. The analysis is carried out with the aid of MAPLE which is also instrumental in verifying the consistency of the approximations conveniently.

Copyright © 1999 by The American Society of Mechanical Engineers
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