Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing

Research output: Contribution to journalArticle

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Abstract

In this paper a linear oscillator undergoing impact with a secondary elastic support is studied experimentally and semi-analytically for near-grazing conditions. The experimentally observed bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. Smooth as well as nonsmooth bifurcations are observed, and the resulting atypical bifurcations are explained, often as an interplay between them. In order to understand the observed bifurcation scenarios, a global analysis is required, due to the influence of stable and unstable orbits which are born in distant bifurcations but become important at near-grazing conditions. The good degree of correspondence between experiment and theory fully justifies the modelling approach. (C) 2009 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)312-321
Number of pages10
JournalPhysica. D, Nonlinear Phenomena
Volume239
Issue number6
Early online date26 Nov 2009
DOIs
Publication statusPublished - 15 Mar 2010

Keywords

  • Piecewise linear oscillator
  • Grazing
  • Experimental study
  • Stability analysis
  • Border collision bifurcations
  • Piecewise-linear-oscillator
  • Sytems
  • Dynamics
  • Maps

Cite this

Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing. / Ing, James; Pavlovskaia, Ekaterina Evgenievna; Wiercigroch, Marian; Banerjee, Soumitro.

In: Physica. D, Nonlinear Phenomena, Vol. 239, No. 6, 15.03.2010, p. 312-321.

Research output: Contribution to journalArticle

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abstract = "In this paper a linear oscillator undergoing impact with a secondary elastic support is studied experimentally and semi-analytically for near-grazing conditions. The experimentally observed bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. Smooth as well as nonsmooth bifurcations are observed, and the resulting atypical bifurcations are explained, often as an interplay between them. In order to understand the observed bifurcation scenarios, a global analysis is required, due to the influence of stable and unstable orbits which are born in distant bifurcations but become important at near-grazing conditions. The good degree of correspondence between experiment and theory fully justifies the modelling approach. (C) 2009 Elsevier B.V. All rights reserved.",
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