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Bifurcation Control for a S.D.O.F. Nonlinear System to a Principal Parametric Resonance With Time Delay

[+] Author Affiliations
Changzhao Qian

Changsha University of Science and Technology, Changsha, Hunan, China

Changping Chen

Xiamen University of Technology, Xiamen, Fujian, China

Liming Dai

University of Regina, Regina, SK, Canada

Paper No. IMECE2010-38122, pp. 307-312; 6 pages
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 8: Dynamic Systems and Control, Parts A and B
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4445-8
  • Copyright © 2010 by ASME


The bifurcation and response of one-degree-of-freedom system with quadratic and cubic non-linearities to a principal parametric is investigated. Using time delay damp, the bifurcation is controlled. The method of multiple scales is used to determine the equations that describe to second order the modulation of the amplitude and phase with time about one of foci. These equations are used to determine the fixed points and their stability. Because there are some items which are time delay’s function in the bifurcation equations, changing the time delay parameters may change the bifurcation form or bifurcation point. Using numerical method, saddle-node bifurcation and transcritical bifurcation control are investigated. The result indicates that time delay controller can effectively control to this kind system.

Copyright © 2010 by ASME



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