On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction

Alain  Léger; Elaine  Pratt

doi:10.3934/dcdss.2016009

Article Contents

2016, Volume 9, Issue 2: 501-527. Doi: 10.3934/dcdss.2016009

This issue Previous Article On the space separated representation when addressing the solution of PDE in complex domains Next Article Kinematical structural stability

On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction

Alain Léger^1, and
Elaine Pratt^1,

1.
Laboratoire de Mécanique et d'Acoustique, LMA, CNRS, UPR 7051, Aix-Marseille Univ., Centrale Marseille, F-13402 Marseille Cedex 20

Received: November 30, 2014

Revised: September 30, 2015

Published: March 2016

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Abstract

After previous works related to the equilibrium states, this paper goes deeper into the study of the effect of coupling between smooth and non-smooth non-linearities on the qualitative behavior of low dimensional dynamical systems. The non-smooth non-linearity is due to non-regularized unilateral contact and Coulomb friction while the smooth one is due to large strains of a simple mass spring system, which lead to a nonlinear restoring force. The main qualitative differences with the case of a linear restoring force are due to the shape of the set of equilibrium states.

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Mathematics Subject Classification: Primary: 70K42, 70K05; Secondary: 37M99.

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References

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