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A model of a spring-mass-damper system with temperature-dependent friction†

Published online by Cambridge University Press:  10 September 2013

S. MIGORSKI ,
A. OCHAL ,
M. SHILLOR  and
M. SOFONEA
S. MIGORSKI
Affiliation:
Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, 30348 Krakow, Poland emails: migorski@ii.uj.edu.pl; ochal@ii.uj.edu.pl
A. OCHAL
Affiliation:
Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, 30348 Krakow, Poland emails: migorski@ii.uj.edu.pl; ochal@ii.uj.edu.pl
M. SHILLOR
Affiliation:
Department of Mathématics and Statistics, Oakland University, Rochester, MI 48309, USA email: shillor@oakland.edu
M. SOFONEA
Affiliation:
Laboratoire de Mathematicques et Physique, University of Perpignan Via Domitia, 66860 Perpignan, France email: sofonea@univ-perp.fr
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Abstract

This work models and analyses the dynamics of a general spring-mass-damper system that is in frictional contact with its support, taking into account frictional heat generation and a reactive obstacle. Friction, heat generation and contact are modelled with subdifferentials of, possibly non-convex, potential functions. The model consists of a non-linear system of first-order differential inclusions for the position, velocity and temperature of the mass. The existence of a global solution is established and additional assumptions yield its uniqueness. Nine examples of conditions arising in applications, for which the analysis results are valid, are presented.

Keywords

Spring-mass-damper systemContactTemperature-dependent frictionNormal complianceHeat generationDifferential inclusionClarke subdifferentialExistence and uniqueness
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 1 , February 2014 , pp. 45 - 64
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

†

Research supported by the Marie Curie IRSES Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118 and the National Science Center of Poland under Maestro Project no. DEC-2012/06/A/ST1/00262. The first two authors are also partially supported by the National Science Center of Poland under grant no. N N201 604640 and by the Ministry of Science and Higher Education of Republic of Poland under the International Cofinanced Project no. W111/7.PR/2012.

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