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On the space separated representation when addressing the solution of PDE in complex domains
On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction
1. | Laboratoire de Mécanique et d'Acoustique, LMA, CNRS, UPR 7051, Aix-Marseille Univ., Centrale Marseille, F-13402 Marseille Cedex 20, France, France |
References:
[1] |
S. Basseville, A. Léger and E. Pratt, Investigation of the equilibrium states and their stability for a simple model with unilateral contact and Coulomb friction, Arch. Appl. Mech., 73 (2003), 409-420.
doi: 10.1007/s00419-003-0300-y. |
[2] |
Q. J. Cao, M. Wiercigroch, E. Pavvlovskaia, C. Grebogi, J. Thompson, An archetypal oscillator for smooth and discontinuous dynamics, Phys. Review, 74 (2006), 046218, 5pp.
doi: 10.1103/PhysRevE.74.046218. |
[3] |
Q. J. Cao, A. Léger and Z. X. Li, The equilibrium stability of a smooth to discontinous oscillator with dry friction, J. of Computational and Nonlinear Dynamics, (2013). |
[4] |
A. Charles and P. Ballard, Existence and uniqueness of solution to dynamical unilateral contact problems with Coulomb friction: the case of a collection of points, Mathematical Modelling and Numerical Analysis, 48 (2014), 1-25.
doi: 10.1051/m2an/2013092. |
[5] |
A. Cimetière and A. Léger, Some problems about elastic-plastic post-buckling, Int. J. Solids Structures, 32 (1996), 1519-1533. |
[6] |
M. Jean, The nonsmooth contact dynamics method, Computer Methods Appl. Mech. Engn, 177 (1999), 235-257.
doi: 10.1016/S0045-7825(98)00383-1. |
[7] |
A. Klarbring, Examples of nonuniqueness and nonexistence of solutions to quasistatic contact problems with friction, Ing. Arch., 60 (1990), 529-541. |
[8] |
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. |
[9] |
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. |
[10] |
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. |
show all references
References:
[1] |
S. Basseville, A. Léger and E. Pratt, Investigation of the equilibrium states and their stability for a simple model with unilateral contact and Coulomb friction, Arch. Appl. Mech., 73 (2003), 409-420.
doi: 10.1007/s00419-003-0300-y. |
[2] |
Q. J. Cao, M. Wiercigroch, E. Pavvlovskaia, C. Grebogi, J. Thompson, An archetypal oscillator for smooth and discontinuous dynamics, Phys. Review, 74 (2006), 046218, 5pp.
doi: 10.1103/PhysRevE.74.046218. |
[3] |
Q. J. Cao, A. Léger and Z. X. Li, The equilibrium stability of a smooth to discontinous oscillator with dry friction, J. of Computational and Nonlinear Dynamics, (2013). |
[4] |
A. Charles and P. Ballard, Existence and uniqueness of solution to dynamical unilateral contact problems with Coulomb friction: the case of a collection of points, Mathematical Modelling and Numerical Analysis, 48 (2014), 1-25.
doi: 10.1051/m2an/2013092. |
[5] |
A. Cimetière and A. Léger, Some problems about elastic-plastic post-buckling, Int. J. Solids Structures, 32 (1996), 1519-1533. |
[6] |
M. Jean, The nonsmooth contact dynamics method, Computer Methods Appl. Mech. Engn, 177 (1999), 235-257.
doi: 10.1016/S0045-7825(98)00383-1. |
[7] |
A. Klarbring, Examples of nonuniqueness and nonexistence of solutions to quasistatic contact problems with friction, Ing. Arch., 60 (1990), 529-541. |
[8] |
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. |
[9] |
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. |
[10] |
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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