WIAS Preprint No. 1190, (2006)

New results on the stability of quasi-static paths of a single particle system with Coulomb friction and persistent contact



Authors

  • Schmid, Florian
  • Martins, João A. C.
  • Rebrova, Natalia

2010 Mathematics Subject Classification

  • 74H55 74M10 74B05 34D20

Keywords

  • Coulomb friction, quasistatic, persistent contact, stability

Abstract

In this paper we announce some new mathematical results on the stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle.A quasi-static path is said to be stable at some value of the load parameter if, for some finite interval of the load parameter thereafter, the dynamic solutions behave continuously with respect to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces, $varepsilon$ (as in singular perturbation problems). In this paper we prove sufficient conditions for stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle. The present system has the additional difficulty of its non-smoothness: the friction law is a multivalued operator and the dynamic evolutions of this system may have discontinuous accelerations.

Appeared in

  • Topics on Mathematics for Smart Systems, B. Miara, G. Stavroulakis, V. Valente, eds., World Scientific Publishing Co. Pte. Ltd., 2007, pp. 208--217

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