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On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction

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  • After previous works related to the equilibrium states, this paper goes deeper into the study of the effect of coupling between smooth and non-smooth non-linearities on the qualitative behavior of low dimensional dynamical systems. The non-smooth non-linearity is due to non-regularized unilateral contact and Coulomb friction while the smooth one is due to large strains of a simple mass spring system, which lead to a nonlinear restoring force. The main qualitative differences with the case of a linear restoring force are due to the shape of the set of equilibrium states.
    Mathematics Subject Classification: Primary: 70K42, 70K05; Secondary: 37M99.

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    A. Léger and E. Pratt, Qualitative analysis of a forced nonsmooth oscillator with contact and friction, Annals of Solid and Structural Mechanics, 2 (2011), 1-17.

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    A. Léger, E. Pratt and Q. J. Cao, A fully nonlinear oscillator with contact and friction, Nonlinear Dynamics, 70 (2012), 511-522.doi: 10.1007/s11071-012-0471-6.

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    J. J. Moreau, Unilateral contact and dry friction in finite freedom dynamics, in Nonsmooth Mechanics and Applications (eds. J. J. Moreau and P. D. Panagiotopoulos), CISM Courses and Lectures, 302, Springer-Verlag, Vienne-New York, 1988, 1-82.doi: 10.1007/978-3-7091-2624-0_1.

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