Free access
Issue
ESAIM: M2AN
Volume 40, Number 4, July-August 2006
Page(s) 705 - 734
DOI http://dx.doi.org/10.1051/m2an:2006031
Published online 15 November 2006
  1. B. Brogliato, A.A. ten Dam, L. Paoli, F. Genot and M. Abadie, Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. ASME Appl. Mechanics Rev. 55 (2002) 107–149. [CrossRef]
  2. Y. Dumont, Vibrations of a beam between stops: Numerical simulations and comparison of several numerical schemes. Math. Comput. Simul. 60 (2002) 45–83. [CrossRef]
  3. Y. Dumont, Some remarks on a vibro-impact scheme. Numer. Algorithms 33 (2003) 227–240. [CrossRef] [MathSciNet]
  4. Y. Dumont and L. Paoli, Simulations of beam vibrations between stops: comparison of several numerical approaches, in Proceedings of the Fifth EUROMECH Nonlinear Dynamics Conference (ENOC-2005), CD Rom (2005).
  5. L. Fox, The numerical solution of two-point boudary values problems in ordinary differential equations, Oxford University Press, New York (1957).
  6. J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer-Verlag, New York, Berlin, Heidelberg (1983).
  7. T. Hughes, The finite element method. Linear static and dynamic finite element analysis. Prentice-Hall International, Englewood Cliffs (1987).
  8. K. Kuttler and M. Shillor, Vibrations of a beam between two stops. Dynamics of continuous, discrete and impulsive systems, Series B, Applications and Algorithms 8 (2001) 93–110.
  9. C.H. Lamarque and O. Janin, Comparison of several numerical methods for mechanical systems with impacts. Int. J. Num. Meth. Eng. 51 (2001) 1101–1132. [CrossRef]
  10. F.C. Moon and S.W. Shaw, Chaotic vibration of a beam with nonlinear boundary conditions. Int. J. Nonlinear Mech. 18 (1983) 465–477. [CrossRef]
  11. L. Paoli, Analyse numérique de vibrations avec contraintes unilatérales. Ph.D. thesis, University of Lyon 1, France (1993).
  12. L. Paoli, Time-discretization of vibro-impact. Phil. Trans. Royal Soc. London A. 359 (2001) 2405–2428. [CrossRef] [MathSciNet]
  13. L. Paoli, An existence result for non-smooth vibro-impact problems. Math. Mod. Meth. Appl. S. (M3AS) 15 (2005) 53–93. [CrossRef]
  14. L. Paoli and M. Schatzman, Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales : cas avec perte d'énergie. RAIRO Modél. Math. Anal. Numér. 27 (1993) 673–717. [MathSciNet]
  15. L. Paoli and M. Schatzman, Ill-posedness in vibro-impact and its numerical consequences, in Proceedings of European Congress on COmputational Methods in Applied Sciences and engineering (ECCOMAS), CD Rom (2000).
  16. L. Paoli and M. Schatzman, A numerical scheme for impact problems, I and II. SIAM Numer. Anal. 40 (2002) 702–733; 734–768. [CrossRef] [MathSciNet]
  17. P. Ravn, A continuous analysis method for planar multibody systems with joint clearance. Multibody Syst. Dynam. 2 (1998) 1–24. [CrossRef]
  18. R.T. Rockafellar, Convex analysis. Princeton University Press, Princeton (1970).
  19. M. Schatzman and M. Bercovier, Numerical approximation of a wave equation with unilateral constraints. Math. Comp. 53 (1989) 55–79. [CrossRef] [MathSciNet]
  20. S.W. Shaw and R.H. Rand, The transition to chaos in a simple mechanical system. Int. J. Nonlinear Mech. 24 (1989) 41–56. [CrossRef]
  21. J. Simon, Compact sets in the space Lp(0,T;B) Ann. Mat. Pur. Appl. 146 (1987) 65–96.
  22. D. Stoianovici and Y. Hurmuzlu, A critical study of applicability of rigid body collision theory. ASME J. Appl. Mech. 63 (1996) 307–316. [CrossRef]

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