Skip to main content
Log in

Chaotic frictional vibrations excited by a quasiperiodic load

  • Published:
International Applied Mechanics Aims and scope

Abstract

A Duffing oscillator frictionally interacting with a moving belt under a quasiperiodic load is studied. The multiple-scales method is used to derive a system of two nonautonomous equations with small parameters, which describes the modulation of vibrations. It is shown that the system of modulation equations has a heteroclinic structure. Melnikov functions are used to analyze the domain of heteroclinic chaos

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. V. Avramov, “Bifurcation of almost periodically excited frictional vibrations,” Dop. NAN Ukrainy, 9, 40–43 (2004).

    MathSciNet  Google Scholar 

  2. K. V. Avramov, “Bifurcations at combination resonance and quasiperiodic vibrations of flexible beams,” Int. Appl. Mech., 39, No. 8, 976–982 (2003).

    Article  Google Scholar 

  3. A. A. Alifov and K. V. Frolov, Interaction of Nonlinear Vibrating Systems with Energy Sources [in Russian], Nauka, Moscow (1985).

    MATH  Google Scholar 

  4. A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Theory of Oscillators, Dover, New York (1987).

    Google Scholar 

  5. J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York (1983).

    MATH  Google Scholar 

  6. J. P. Den-Hartog, Mechanical Vibrations, McGraw-Hill, New York (1956).

    MATH  Google Scholar 

  7. V. H. Kauderer, Nichtlineare Mechanik, Springer-Verlag, Berlin (1958).

    MATH  Google Scholar 

  8. V. O. Kononenko, Vibrating Systems with a Limited Power Supply, Iliffe Books, London (1969).

    Google Scholar 

  9. I. V. Kragel’sknii and N. V. Gitis, Self-Excited Frictional Vibrations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  10. V. K. Mel’nikov, “On the stability of the center for time periodic perturbation,” Trans. Moscow Math. Soc., 12(1), 1–57 (1964).

    Google Scholar 

  11. A. H. Nayfeh, Perturbation Methods, Wiley, New York (1973).

    MATH  Google Scholar 

  12. K. V. Avramov, “Bifurcations of parametric oscillations of beams with three equilibriums,” Acta Mechanica, 164, 115–138 (2003).

    Article  MATH  Google Scholar 

  13. K. V. Avramov and Yu. V. Mikhlin, “Damping of free elastic vibrations in linear systems,” Int. Appl. Mech., 41, No. 2, 203–209 (2005).

    Article  Google Scholar 

  14. B. Feeny, A. Guran, N. Hinrichs, and K. Popp, “A historical review on friction in nonlinear dynamics,” Appl. Mech. Rev., 51, No. 5, 321–341 (1998).

    Article  Google Scholar 

  15. A. A. Martynyuk and N. V. Nikitina, “Complex oscillations revisited,” Int. Appl. Mech., 41, No. 2, 179–186 (2005).

    Article  Google Scholar 

  16. A. A. Martynyuk and N. V. Nikitina, “Complex behavior of a trajectory in single-and double-frequency systems,” Int. Appl. Mech., 41, No. 3, 315–323 (2005).

    Article  MathSciNet  Google Scholar 

  17. A. A. Martynyuk and N. V. Nikitina, “Nonlinear oscillations in a system with dry friction,” Int. Appl. Mech., 41, No. 4, 435–440 (2005).

    Article  MathSciNet  Google Scholar 

  18. Yu. V. Mikhlin and S. N. Reshetnikova, “Dynamic analysis of a two-mass system with essentially nonlinear vibration damping,” Int. Appl. Mech., 41, No. 1, 77–84 (2005).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 127–133, September 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avramov, K.V. Chaotic frictional vibrations excited by a quasiperiodic load. Int Appl Mech 42, 1071–1076 (2006). https://doi.org/10.1007/s10778-006-0178-9

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-006-0178-9

Keywords

Navigation