Basins of attraction in nonsmooth models of gear rattle
Basins of attraction in nonsmooth models of gear rattle
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)
203-224
Mason, Joanna F.
93e4a752-4af3-4a12-9d05-40795c13f33f
Piiroinen, Petri T.
6b3ca19e-8be2-4613-bda8-95953c9fa248
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd
Homer, Martin E.
e71d28d1-c8df-4c08-a307-45e6efdd87ea
January 2008
Mason, Joanna F.
93e4a752-4af3-4a12-9d05-40795c13f33f
Piiroinen, Petri T.
6b3ca19e-8be2-4613-bda8-95953c9fa248
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd
Homer, Martin E.
e71d28d1-c8df-4c08-a307-45e6efdd87ea
Mason, Joanna F., Piiroinen, Petri T., Wilson, R. Eddie and Homer, Martin E.
(2008)
Basins of attraction in nonsmooth models of gear rattle.
International Journal of Bifurcation and Chaos, 19 (1), .
(doi:10.1142/S021812740902283X).
Abstract
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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Published date: January 2008
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Local EPrints ID: 184241
URI: http://eprints.soton.ac.uk/id/eprint/184241
ISSN: 0218-1274
PURE UUID: fcde7fc0-a28d-4e82-ae6e-8f8a42fdadc4
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Date deposited: 09 May 2011 07:39
Last modified: 14 Mar 2024 03:07
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Contributors
Author:
Joanna F. Mason
Author:
Petri T. Piiroinen
Author:
R. Eddie Wilson
Author:
Martin E. Homer
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