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Grazing Bifurcation and Periodic Motion Switching in a Piecewise Linear, Impacting Oscillator Under a Periodical Excitation

[+] Author Affiliations
Albert C. J. Luo, Lidi Chen

Southern Illinois University at Edwardsville

Paper No. IMECE2005-80076, pp. 913-924; 12 pages
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Design Engineering, Parts A and B
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Design Engineering Division
  • ISBN: 0-7918-4215-0 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME


The grazing bifurcation and periodic motion switching of the harmonically forced, piecewise linear system with impacting are investigated. The generic mappings based on the discontinuous boundaries are introduced. Furthermore, the mapping structures are developed for the analytical prediction of periodic motions in such a system. The local stability and bifurcation conditions for specified periodic motions are obtained. The regular and grazing, periodic motions are illustrated. The grazing is the origin of the periodic motion switching for this system. Such a grazing bifurcation cannot be estimated through the local stability analysis. This model is applicable to prediction of periodic motions in nonlinear dynamics of gear transmission systems.

Copyright © 2005 by ASME
Topics: Motion , Bifurcation



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