Dry friction is a main factor of self-sustained oscillations in dynamic systems. The mathematical modelling of dry friction forces result in strong nonlinear equations of motion. The bifurcation behaviour of a deterministic system has been investigated by the bifurcation theory. The stability of stationary solutions has been analyzed by the eigenvalues of the Jacobian. Period doublings and Hopf-bifurcations as well as turning points could be determined with the program package BIFPACK. Phase plane plots of periodic and chaotic motions have been shown for a better understanding of the bifurcation diagrams. Both, unstable branches and stable coexisting solutions have been calculated. Several jumping effects, which are typical for nonlinear systems, have been found.


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  1. [1]
    Feigenbaum, M.J.: Universal Behavior in Nonlinear Systems. In: Los Alamos Sci. 1(1980), S. 4–27MathSciNetGoogle Scholar
  2. [2]
    Hagedorn, P.: Nichtlineare Schwingungen. Wiesbaden: Akademische Verlagsgesellschaft, 1984Google Scholar
  3. [3]
    Iooss, G.; Joseph, P.: Elementary Stability and Bifurcation Theory. New York: Springer-Verlag, 1980zbMATHGoogle Scholar
  4. [4]
    Kreuzer, E.: Numerische Untersuchung nichtlinearer dynamischer Systeme. Berlin: Springer-Verlag, 1987zbMATHGoogle Scholar
  5. [5]
    Leven, R.W.; Koch, B.-P.; Pompe, B.: Chaos in dissipativen Systemem. Berlin: Akademie-Verlag, 1982.Google Scholar
  6. [6]
    Magnus, K.: Schwingungen. 3. Auflage, Stuttgart: Teubner, 1976zbMATHGoogle Scholar
  7. [7]
    Miyamoto, M.: Effect of Dry Friction in Link Suspension on Forced Vibration of Two-Axle Car. In: Quarterly Reports Vol. 14 No. 2 (1973), S. 99–103Google Scholar
  8. [8]
    Popp, K.; Stelter, P.: Nonlinear Oscillations of Structures Induced by Dry Friction. In: Proceedings of IUTAM Symposium on nonlinear dynamics in engineering systems. Stuttgart, (1989)Google Scholar
  9. [9]
    Seydel, R.: From Equilibrium to Chaos; Practical Bifurcation and Stability Analysis. Amsterdam: Elsevier, 1988zbMATHGoogle Scholar
  10. [10]
    Seydel, R.: BIFPACK—A Program Package for Continuation, Bifurcation and Stability Analysis. Mathematische Institute der Julius-Maximilians-Universitaet Wuerzburg, Version 2. 3 (1988)Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1991

Authors and Affiliations

  • Peter Stelter
    • 1
  • Walter Sextro
    • 1
  1. 1.Institute of MechanicsUniversity of HannoverGermany

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