Experience and Simulation in Dynamic Systems with Discontinuities

  • Hans Weber
  • Sandor Divenyi
  • Marcelo Savi
  • Luiz Franca
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 1)


Non-smooth nonlinearity is abundant in nature being usually related to either the friction phenomenon or the discontinuous characteristics as intermittent contacts of some system components. Non-smooth systems appear in many kinds of engineering systems and also in everyday life. Examples may be mentioned by the stick-slip oscillations of a violin string or grating brakes [1]. Some related phenomena as chatter and squeal causes serious problems in many industrial applications [2].


Impact Mass Support Characteristic Support Inertia Internal Impact Chaotic Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Hinrichs N., Oestreich M., Popp K. (1998) “On the Modelling of Friction Oscillators”, Journal of Sound and Vibration, v.216(3), pp.435–459.CrossRefGoogle Scholar
  2. 2.
    Andreaus U., Casini P. (2001) “Dynamics of Friction Oscillators Excited by a Moving Base and/or Driving Force”, Journal of Sound and Vibration, v.245, n.4, pp.685–699.CrossRefGoogle Scholar
  3. 3.
    Wiercigroch M. (2000) “Modelling of Dynamical Systems with Motion Dependent Discontinuities”, Chaos, Solitons and Fractals, v.11, pp.2429–2442.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Leine R.I. (2000) “Bifurcations in Discontinuous Mechanical Systems of Filippov-Type”, Ph.D. Thesis, Technische Universiteit Eindhoven.Google Scholar
  5. 5.
    Leine R.I., van Campen D.H., van de Vrande B.L. (2000) “Bifurcations in Nonlinear Discontinuous Systems”, Nonlinear Dynamics, v.23, pp.105–164.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Divenyi S., Savi M.A., Franca L.F.P., Weber, H.I. (2006) “Nonlinear Dynamics and Chaos in Systems with Discontinuous Support”, Shock and Vibration, to appear.Google Scholar
  7. 7.
    Wiercigroch M., Sin V. W. T., Li K. (1998) “Measurement of Chaotic Vibration in a Symmetrically Piecewise Linear Oscillator”, Chaos, Solitons and Fractals, v.9, n.1/2, pp.209–220.CrossRefGoogle Scholar
  8. 8.
    Wiercigroch M., Sin V.W.T. (1998) “Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator”, Journal of Applied Mechanics-ASME, v.65, pp.657–663.Google Scholar
  9. 9.
    Todd M.D., Virgin L.N. (1997) “An Experimental Impact Oscillator”, Chaos, Solitons & Fractals, v.8, n.4, pp. 699–714.MATHCrossRefGoogle Scholar
  10. 10.
    Begley C.J., Virgin L.N. (1998) “Impact Response and the Influence of Fiction”, Journal of Sound and Vibration, v.211, n.5, pp.801–818.CrossRefGoogle Scholar
  11. 11.
    Slade K.N, Virgin L.N., Bayly P.V. (1997) “Extracting Information from Interimpact Intervals in a Mechanical Oscillator”, Physical Review E, v.56, n.3, pp.3705–3708.CrossRefGoogle Scholar
  12. 12.
    Savi M.A., Divenyi S., Franca L.F.P., Weber H.I. (2006) “Numerical and Experimental Investigations of the Nonlinear Dynamics and Chaos in Non-Smooth Systems”, submitted to the Journal of Sound and Vibration.Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Hans Weber
    • 1
  • Sandor Divenyi
    • 2
  • Marcelo Savi
    • 2
  • Luiz Franca
    • 3
  1. 1.Department of Mechanical EngineeringPUC/RioBrazil
  2. 2.Department of Mechanical EngineeringUFRJ/COPPEBrazil
  3. 3.CSIRO Petroleum — Drilling MechanicsAustralia

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