Peer-Reviewed Journal Details
Mandatory Fields
Mason, JF,Piiroinen, PT,Wilson, RE,Homer, ME
2009
January
International Journal Of Bifurcation And Chaos
BASINS OF ATTRACTION IN NONSMOOTH MODELS OF GEAR RATTLE
Published
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Optional Fields
Gear rattle basins of attraction dynamical systems nonlinear dynamics mathematical modeling nonsmooth IMPACT OSCILLATORS DYNAMICAL-SYSTEMS BIFURCATIONS BACKLASH
19
203
224
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).
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