|Publication date||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: 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)
- gear rattle, basins of attraction, nonsmooth