Basins of Attraction in Nonsmooth Models of Gear Rattle

JF Mason, PT Piiroinen, RE Wilson, ME Homer

Research output: Contribution to journalArticle (Academic Journal)peer-review

40 Citations (Scopus)


This paper is concerned with the computation of the basins of attraction of a simple one degree-of-freedom backlash oscillator using cell-to-cell mapping techniques. This analysis is motivated by the modeling of order vibration in geared systems. We consider both a piecewise-linear stiffness model and a simpler infinite stiffness impacting limit. The basins reveal rich and delicate dynamics, and we analyze some of the transitions in the system's behavior in terms of smooth and discontinuity-induced bifurcations. The stretching and folding of phase space are illustrated via computations of the grazing curve, and its preimages, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit).
Translated title of the contributionBasins of Attraction in Nonsmooth Models of Gear Rattle
Original languageEnglish
Pages (from-to)203 - 224
JournalInternational Journal of Bifurcation and Chaos
Publication statusPublished - 2009

Structured keywords

  • Engineering Mathematics Research Group


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