Patterns of Bifurcation Suppressing Escape at Internal Resonance

  • G.H.M. van der Heijden
  • J.M.T. Thompson
Conference paper

DOI: 10.1007/1-4020-3268-4_7

Part of the Solid Mechanics and its Applications book series (SMIA, volume 122)
Cite this paper as:
van der Heijden G., Thompson J. (2005) Patterns of Bifurcation Suppressing Escape at Internal Resonance. In: Rega G., Vestroni F. (eds) IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics. Solid Mechanics and its Applications, vol 122. Springer, Dordrecht

Abstract

For an archetypal two-degree-of-freedom forced oscillator, relevant to a large class of mechanical problems, we examine the patterns of bifurcation that govem the internal 1:2 resonance of the system. A knowledge of these bifurcations allows the counter-intuitive suppression and control of escape by internal modal interactions. The bifurcations examined include symmetry-breaking pitchforks, Neimark bifurcations (secondary Hopf bifurcations) to a toroidal attractor, and chaotic crises which trigger dangerous large-amplitude excursions. We particularly focus on the effect that a symmetry-breaking imperfection has on the suppression of escape.

Key words

Suppression of escape 2 DOF forced oscillator symmetry breaking 1:2 resonance Neimark bifurcation unfolding 

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Copyright information

© Springer 2005

Authors and Affiliations

  • G.H.M. van der Heijden
    • 1
  • J.M.T. Thompson
    • 1
  1. 1.Centrefor Nonlinear DynamicsUniversity College LondonLondonUK

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