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Stability in Unilateral Contact Problems with Dry Friction

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Recent Advances in Contact Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 56))

Abstract

We discuss stability in the case of systems with unilateral contact and Coulomb friction. Classical stability results for dynamical systems concern perturbations of the initial data in a classical phase space. Here we establish results concerning the trajectories issued from a perturbation of the external forces. With such a notion of stability a conjecture is given that we back up in detail by analytical computations in the case of a simple model and that we begin to extend to more complex systems.

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References

  1. Alart, P., Curnier, A.: Contact discret avec frottement: unicité de la solution, convergence de l’algorithme. Publications du Laboratoire de Mécanique Appliquée, Ecole Polytechnique Fédérale de Lausanne (1986)

    Google Scholar 

  2. Ballard, P., Basseville, S.: Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem. Mathematical Modelling and Numerical Analysis 39(1), 57–77 (2005)

    Article  MathSciNet  Google Scholar 

  3. Basseville, S., Léger, A., Pratt, E.: Investigation of the equilibrium states and their stability for a simple model with unilateral contact and Coulomb friction. Archive Appl. Mech. 73, 409–420 (2003)

    Article  MATH  Google Scholar 

  4. Dubois, F.: LMGC 90, http://www.lmgc.univ-montp2.fr

  5. Jean, M.: The Non Smooth Contact Dynamics method. Computer Methods Appl. Mech. Engn. 177, 235–257 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  6. Klarbring, A.: Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction. Ing. Archives 60, 529–541 (1990)

    Google Scholar 

  7. Moreau, J.J.: Unilateral contact and dry friction in finite freedom dynamics. In: Moreau, J.J., Panagiotopoulos, P.D. (eds.) Nonsmooth Mechanics and Applications. CISM courses and lectures, vol. 302, Springer, Vienne-New York (1988)

    Google Scholar 

  8. Pinto da Costa, A.M.F.: Instabilidades e bifurcacoes em sistemas de comportamento no-suave. Phd Thesis, Universidade Técnica de Lisboa, Instituto Superior Técnico (2001)

    Google Scholar 

  9. Pratt, E., Léger, A., Jean, M.: Critical oscillations of mass-spring systems due to nonsmooth friction. Archive Appl. Mech. 78, 89–104 (2008)

    Article  MATH  Google Scholar 

  10. Pratt, E., Léger, A., Jean, M.: About a stability conjecture concerning unilateral contact with friction. Journal of Nonlinear Dynamics 59, 73–94 (2010)

    Article  MATH  Google Scholar 

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Correspondence to Elaine Pratt .

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Pratt, E., Léger, A., Jean, M. (2013). Stability in Unilateral Contact Problems with Dry Friction. In: Stavroulakis, G. (eds) Recent Advances in Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33968-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-33968-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33967-7

  • Online ISBN: 978-3-642-33968-4

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