Skip to main content
SpringerLink
Log in

Impact Oscillator with Hertz's Model of Contact

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

Dynamic properties of simple mechanical 1 DOF system containing soft stop is described and analyzed. The proposed general dynamical impact model respects the nonlinearity of the restoring contact force between solid bodies as function of deformation and velocity. It describes the real behavior of impacting system more exact than the piecewise linear model or the Kelvin–Voigt model and even model based on application of constant coefficient of restitution. Free and forced vibrations of system with Hertz's contact are investigated and domains of various types of impact motion, response curves and phase-plane trajectories are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kobrinskij, A.E., Mechanisms with Elastic Constraints, (in Russia), Izd. Nauka, Moscow, 1964, see also translation: Dynamics of Mechanisms with Elastic Connections and Impact Systems, Iliffe Books Ltd., London, 1969.

    Google Scholar 

  2. Peterka, F., Introduction to Vibration of Mechanical System with Internal Impacts, (in Czech), Academia, Prague, 1981.

    Google Scholar 

  3. Pfeiffer, F., ‘On unsteady dynamics in machines with plays’, in: Bautista, E., Garcia, J. and Navarro, A. (eds), Proc. 7th World Congress on TMM, Vol. I, Pergamon Press, 1987, pp. 471-423.

  4. de Pater, A.D., ‘The vibrations of nonlinear mechanical systems with rigid stops’, in: Proc. International Symposium on Nonlinear Oscillations, Vol. III, AS USSR, Kiew, 1963, pp. 326-345.

    Google Scholar 

  5. Maezawa, S., ‘On the stability of forced vibration in piecewise-linear system’, in: Proc. 4th Conference on Nonlinear Oscillations, Academia, Prague, 1967, pp. 361-371.

    Google Scholar 

  6. Shaw, S.W. and Holmes, P.J., ‘A periodically forced piecewise linear oscillator’, J. Sound Vib. 90(1) (1983) 129-155.

    Google Scholar 

  7. Aoki, S. and Watanabe, T., ‘Stationary random vibration of nonlinear system with hysteresis loop characteristics’, in: Proc. 2nd European Nonlinear Oscillations Conference, Vol. I, Publishing House of CTU, Prague, 1996, pp. 61-64.

    Google Scholar 

  8. Lok, H.-P. and Wiercigroch, M., ‘Modelling discontinuities in mechanical systems by smooth functions’, in: Proc. 2nd European Nonlinear Oscillations Conference, Vol. II, Publishing House of CTU, Prague, 1996, pp. 121-124.

    Google Scholar 

  9. Sin, V.W.T. and Wiercigroch, M., ‘Experimental study of a symmetrical piecewise linear oscillator’, in: Proc. 2nd European Nonlinear Oscillations Conference, Vol. II, Publishing House of CTU, Prague, 1996, pp. 227-230.

    Google Scholar 

  10. Peterka, F., Kocanda, L. and Quasmi, M., ‘Sub-harmonic and chaotic motions of oscillator with soft impacts’, in: Proc. Dynamics of Machines 2000, IT AS CR, Prague, 2000, pp. 171-178.

    Google Scholar 

  11. Peterka, F. and Tondl, A., ‘Dynamics of oscillator with piecewise linear model of impact interaction’, in: Colloquium Dynamics of Machines 2001, Institute of Thermomechanics, Prague, February 6–7, 2001.

    Google Scholar 

  12. Hayashi, T., Crossley, F.R.E. and Larionescu, D., ‘Analog simulation of repetitive impacts’, in: Proc. 4th World Congress on TMM, Vol. 4, Publication Sales, Univ. Newcastle Upon Tyne, 1975, pp. 1073-1077.

  13. Hunt, K.H. and Crossley, F.R.E., ‘Coefficient of restitution interpreted as damping in vibro-impact’, J. Appl. Mech. Trans. ASME Vol. 42, (June 1975), 440-445.

  14. Půst, L., ‘Equivalent coefficient of restitution’, Eng. Mech. 5(5) (1998) 303-318.

    Google Scholar 

  15. Půst, L., ‘Impact of bodies with nonlinear damping’, in: Proc. Dynamics of Machines '99, IT AS CR, 1999, pp. 209-216.

  16. Půst, L., ‘Models of weak stops — application to 2DOF system’, in: Proc. X World Congress on TMM, Vol 4, Oulu Univ. Press, 1999, pp. 1607-1612.

  17. Půst, L., Selected Problems of Nonlinear Oscillations, Chapters 8 and 9, Report No. Z-1293/00, IT AS CR, 2000, pp. 50-67.

  18. Půst, L., ‘Impact system with Hertz's contact’, in: Colloquium Dynamics of Machines 2001, Institute of Thermomechanics, Prague, 2001, pp. 167-174.

    Google Scholar 

  19. Peterka, F. and Formánek, P., ‘Simulation of motion with strong nonlinearities’, in: Proc. CISS, ETH Zürich, 1994, pp. 137-141.

  20. Peterka, F. and Szöllös, O., ‘Influence of the stop stiffness on the impact oscillator dynamics’, in: Proc. IUTAM Symposium on Unilateral Multibody Contacts, Kluwer Academic Publishers, 1999, pp. 127-135.

  21. Wagg, D.J., Karpodinis, G. and Bishop, S.R., ‘An experimental study of the impulse response of a vibro-impacting cantilever beam’, J. Sound Vib. 228 (1999) 243-264.

    Google Scholar 

  22. Wiercigroch, M. and Sin, V.T.W., ‘Experimental study of base excited symmetrically piecewise linear oscillator’, Trans. ASME, J. Appl. Mech. 65(3) (1998) 657-663.

    Google Scholar 

  23. Wiercigroch, M., ‘Modelling of dynamical systems with motion dependent discontinuities’, Chaos Solitons and Fractals 11(15) (2000) 2429-2442.

    Google Scholar 

  24. Pavlovskaia, E.E., Wiercigroch, M. and Grebogi, C., ‘Modelling of an impact system with a drift’, Phys. Rev. E 64 (2001) 056224.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Thermomechanics AS CR, Dolejškova 5, 18200, Prague 8, Czech Republic

    Ladislav Půst & František Peterka

Authors
  1. Ladislav Půst
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. František Peterka
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Půst, L., Peterka, F. Impact Oscillator with Hertz's Model of Contact. Meccanica 38, 99–116 (2003). https://doi.org/10.1023/A:1022075519038

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022075519038

Search

Navigation