The European Physical Journal B

, Volume 70, Issue 3, pp 353–361 | Cite as

Nonlinear spring model for frictional stick-slip motion

  • G. Djuidjé KenmoéEmail author
  • A. Kenfack Jiotsa
  • T. C. Kofané
Solid State and Materials


Frictional stick-slip dynamics is discussed using a model of one oscillator pulled by a nonlinear spring force. We focus our attention on the nonlinear spring parameter k0. The dynamics of the model is carefully studied, both numerically and analytically. Our numerical investigation, which involves bifurcation diagrams, shows a rich spectrum of dynamical behavior including periodic, quasi-periodic and chaotic states. On the other hand, and for a good selection of parameters , the motion of the particle involves periodic stick-slip, erratic and intermittent motions, characterized by force fluctuations, and sliding. This study suggests that the transition between each of motion strongly depends on the nonlinear parameter k0. The system also displays resonance at fractional frequencies of the oscillator.


46.55.+d Tribology and mechanical contacts 68.35.Gy Mechanical properties; surface strains 81.40.Pq Friction, lubrication, and wear 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F.P. Bowden, D. Tabor, Friction and Lubrication (Oxford University Press, 1954)Google Scholar
  2. 2.
    Fundamentals of Friction: Macroscopic and Microscopic Processes, edited by I.L. Singer, H.M. Pollock (Kluwer Academic Publishers, Dordrecht, 1992)Google Scholar
  3. 3.
    B. Bhushan, J.N. Israelachvilli, U. Landman, Nature (London) 374, 607 (1995)CrossRefADSGoogle Scholar
  4. 4.
    B.N.J. Persson, Sliding Friction: Phisical Properties and Applications (Springer, Berlin, 1998)Google Scholar
  5. 5.
    H. Yoshizawa, P. McGuiggan, J. Israelachvili, Science 259, 1350 (1993)CrossRefGoogle Scholar
  6. 6.
    H. Yoshizawa, Y.L. Chen, J. Israelachvili, J. Phys. Chem. 97, 4128 (1993)CrossRefGoogle Scholar
  7. 7.
    A.D. Berman, W.A. Ducke, J.N. Israelachvili, Langmuir 12, 4559 (1996)CrossRefGoogle Scholar
  8. 8.
    J.M. Georges, A. Tonck, J.L. Loubet, J. Phys. II 6, 57 (1996)CrossRefGoogle Scholar
  9. 9.
    J. Crassous, E. Charlaix, J.L. Loubet, Phys. Rev. Lett. 78, 2425 (1997)CrossRefADSGoogle Scholar
  10. 10.
    L.I. Daikhin, M. Urbakh, Phys. Rev. E 59, 1921 (1999)CrossRefADSGoogle Scholar
  11. 11.
    V. Zaloj, M. Urbakh, J. Klafter, Phys. Rev. Lett. 82, 4823 (1999)CrossRefADSGoogle Scholar
  12. 12.
    G.D. Kenmoé, A.K. Jiotsa, T.C. Kofané, Physica D 191, 31 (2004)zbMATHCrossRefADSGoogle Scholar
  13. 13.
    G.D. Kenmoé, T.C. Kofané, Eur. Phys. J. B 55, 347 (2007)CrossRefADSGoogle Scholar
  14. 14.
    E.A. Brener, S.V. Malinin, V.I. Marchenko Eur. Phys. J. E 17, 101 (2005)CrossRefGoogle Scholar
  15. 15.
    J.S. Helman, W. Baltensperger, J.A. Holyst, Phys. Rev. B 49, 3831 (1994)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • G. Djuidjé Kenmoé
    • 1
    Email author
  • A. Kenfack Jiotsa
    • 1
  • T. C. Kofané
    • 1
  1. 1.Département de Physique, Laboratoire de Mécanique, Faculté des Sciences, Université de Yaoundé IYaoundéCameroun

Personalised recommendations