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Dynamics of an impact oscillator near a degenerate graze

Dynamics of an impact oscillator near a degenerate graze
Dynamics of an impact oscillator near a degenerate graze
We give a complete analysis of low-velocity dynamics close to grazing
for a generic one degree of freedom impact oscillator.
This includes nondegenerate (quadratic) grazing and minimally
degenerate (cubic) grazing, corresponding respectively to nondegenerate
and degenerate chatter. We also describe the dynamics associated
with generic one-parameter bifurcation at a more degenerate (quartic)
graze, showing in particular how this gives rise to the often-observed
highly convoluted structure in the stable manifolds of chattering orbits.
The approach adopted is geometric, using methods from singularity theory.
impact oscillator, vibro-impact dynamics, chatter, non-smooth dynamical system
0951-7715
2723-2748
Chillingworth, D.R.J.
39d011b7-db33-4d7d-8dc7-c5a4e0a61231
Chillingworth, D.R.J.
39d011b7-db33-4d7d-8dc7-c5a4e0a61231

Chillingworth, D.R.J. (2010) Dynamics of an impact oscillator near a degenerate graze. Nonlinearity, 23, 2723-2748. (doi:10.1088/0951-7715/23/11/001).

Record type: Article

Abstract

We give a complete analysis of low-velocity dynamics close to grazing
for a generic one degree of freedom impact oscillator.
This includes nondegenerate (quadratic) grazing and minimally
degenerate (cubic) grazing, corresponding respectively to nondegenerate
and degenerate chatter. We also describe the dynamics associated
with generic one-parameter bifurcation at a more degenerate (quartic)
graze, showing in particular how this gives rise to the often-observed
highly convoluted structure in the stable manifolds of chattering orbits.
The approach adopted is geometric, using methods from singularity theory.

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More information

Submitted date: 5 January 2010
Accepted/In Press date: 16 August 2010
Published date: 3 September 2010
Keywords: impact oscillator, vibro-impact dynamics, chatter, non-smooth dynamical system

Identifiers

Local EPrints ID: 71868
URI: http://eprints.soton.ac.uk/id/eprint/71868
ISSN: 0951-7715
PURE UUID: b62e3579-844f-4f42-bb90-f9cb4703d966

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Date deposited: 08 Jan 2010
Last modified: 13 Mar 2024 20:48

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