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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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)
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)
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)
Dubois, F.: LMGC 90, http://www.lmgc.univ-montp2.fr
Jean, M.: The Non Smooth Contact Dynamics method. Computer Methods Appl. Mech. Engn. 177, 235–257 (1999)
Klarbring, A.: Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction. Ing. Archives 60, 529–541 (1990)
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)
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)
Pratt, E., Léger, A., Jean, M.: Critical oscillations of mass-spring systems due to nonsmooth friction. Archive Appl. Mech. 78, 89–104 (2008)
Pratt, E., Léger, A., Jean, M.: About a stability conjecture concerning unilateral contact with friction. Journal of Nonlinear Dynamics 59, 73–94 (2010)
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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
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