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Nonsmooth Dynamics of a Double-Belt Friction Oscillator

  • P. Casini
  • F. Vestroni
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 122)

Abstract

The model of a double-belt friction oscillator is proposed, which exhibits multiple discontinuity boundaries in the phase space. The system consists of a visco-elastic oscillator dragged by two different rough supports moving with constant driving velocities. The evolution of steady-state attractors as the discontinuity parameters are varied is described. The presence of multiple discontinuity boundaries leads to nonsmooth responses which are studied here by means of analytical and numerical tools.

Key words

Stick-slip motions nonstandard bifurcations piecewise-smooth dynamical systems 

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References

  1. [1]
    A.F. Filippov, Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, 1988.Google Scholar
  2. [2]
    S.J. Hogan, “Heteroclinic bifurcations in damped rigid block motions,” Proc. Roy. Soc. London A, 439, pp. 155–162, 1992.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    K. Popp, N. Hinrichs, and M. Oestreich, “Analysis of a self-excited friction oscillator with external excitation,” in Dynamics with Friction, Guran A., Pfeiffer F., Popp K. (eds.), World Scientific, London, 1996.Google Scholar
  4. [4]
    J. Awrejcewicz and M.M. Holicke, “Melnikov’s method and stick-slip chaotic oscillations in very weakly forced mechanical systems,” International Journal of Bifurcations and Chaos, 9, pp. 505–518, 1999.CrossRefzbMATHGoogle Scholar
  5. [5]
    R.I. Leine, D.H. van Campen, A. De Kraker, and L. van Den Steen, “Stick-slip vibration induced by alternate friction models,” Nonlinear Dynamics, 16, pp. 41–54, 1998.CrossRefzbMATHGoogle Scholar
  6. [6]
    B. Brogliato, Nonsmooth Impact Mechanics. Springer-Verlag, London, 1999.Google Scholar
  7. [7]
    U. Galvanetto, S.R. Bishop, “Dynamics of a simple damped oscillator undergoing stick-slip vibrations,” Meccanica, 34, pp. 337–347, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    R.I. Leine, Bifurcations in Discontinuous Mechanical Systems of Filippov-type. PhD Thesis, Technische Universiteit Eindhoven, 2000.Google Scholar
  9. [9]
    M. Di Bernardo, C.J. Budd, and A.R. Champneys, “Unified framework for the analysis of grazing and border-collisions in piecewise-smooth systems,” Physical Review Letters, 86(12), pp. 2554–2556, 2001.Google Scholar
  10. [10]
    F. Pfeiffer and C. Glocker, “Contacts in multibody systems”, Journal of Applied Mathematics and Mechanics, 64, pp. 773–782, 2001.CrossRefGoogle Scholar
  11. [11]
    P. Casini and F. Vestroni, Bifurcations in hybrid mechanical systems with discontinuity boundaries,” Int. Journal of Bifurcation and Chaos, 2003, in press.Google Scholar
  12. [12]
    P. Casini and F. Vestroni, “Nonstandard bifurcations in oscillators with multiple discontinuity boundaries,” Nonlinear Dynamics, 2003, in press.Google Scholar
  13. [13]
    F. Peterka, “Behaviour of impact oscillator with soft and preloaded stop,” Chaos, Solitons & Fractals, 18, pp. 79–88, 2003.CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • P. Casini
    • 1
  • F. Vestroni
    • 1
  1. 1.Dipartimento di Ingegneria Strutturale e GeotecnicaUniversità di Roma “La Sapienza”RomaItalia

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