The dynamics of a nonautonomous oscillator with friction memory

L. A. Igumnov1 , V. S. Metrikin2 , M. V. Zaytzev3

1, 2Research Institute for mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

3National Research Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

2Corresponding author

Vibroengineering PROCEDIA, Vol. 8, 2016, p. 356-360.
Received 22 May 2016; accepted 3 September 2016; published 7 October 2016

Copyright © 2016 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract.

In this article, an oscillator is considered in which one of its component moves periodically and for which static friction is taken to be time-dependent. The dynamics of the oscillator are analyzed using Poincare map to find shifts between periodic and chaotic motion with the change of the model parameters (amplitude and frequency of velocity of the periodic motion and the coefficient of static friction as a function of the time of stationary contact).

Keywords: mathematical model, Poincare map, bifurcation diagram, time-dependent static friction, chaos.

Acknowledgements

Development of mathematical model is financially supported by Russian Science Foundation, Project No. 16-19-10237. Investigation of numerical results was financed within the framework of the base part of State Task of the Ministry of Education and Science Project, No. 2014/134 2226.

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