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Basins of attraction in nonsmooth models of gear rattle

Research output: Working paperWorking paper and Preprints

Original languageEnglish
StatePublished - 14 Mar 2008


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 modelling 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 analyse some of the transitions in the system's behaviour 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 pre-images, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit).

Additional information

Additional information: A revised version of an earlier preprint paper Sponsorship: JM gratefully acknowledges the support of a CASE award from BOC Edwards Ltd. and the Engineering and Physical Sciences Research Council. PP gratefully acknowledges the support from the European Union (FP5 Project SICONOS, grant no. IST-201-37172)

    Research areas

  • gear rattle, basins of attraction, nonsmooth

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  • Preprint

    Submitted manuscript, 17 MB, PDF-document


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