Skip to main content
Log in

The response of nonlinear systems to modulated high-frequency input

  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.

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. Anderson, T. J., Balachandran, B., and Nayfeh, A. H., ‘Observations of nonlinear interactions in a flexible cantilever beam’, AIAA Paper No. 92-2332, Proceedings of the 33rd AIAA Structures, Structural Dynamics, and Materials Conference, Dallas, TX, 1992.

  2. Anderson, T. J., Nayfeh, A. H., and Balachandran, B., ‘Coupling between widely spaced modes and a low-frequency mode: Theory and experiment’, Nonlinear Dynamics, submitted, 1995.

  3. Evan-Iwanowski, R. M., Resonance Oscillations in Mechanical Systems, Elsevier, New York, 1976.

    Google Scholar 

  4. Ibrahim, R. A., Random Parametric Vibration, Wiley, New York, 1985.

    Google Scholar 

  5. Nayfeh, A. H., Introduction to Perturbation Techniques, Wiley-Interscience, New York, 1981.

    Google Scholar 

  6. Nayfeh, A. H., ‘The response of non-linear single-degree-of-freedom systems to multifrequency excitations’, Journal of Sound and Vibration 102, 1985, 403–414.

    Google Scholar 

  7. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley-Interscience, New York, 1979.

    Google Scholar 

  8. Nayfeh, S. A. and Nayfeh, A. H., ‘Energy transfer from high- to low-frequency modes in a flexible structure via modulation’, Journal of Vibration and Acoustics, to appear, 1993a.

  9. Nayfeh, S. A. and Nayfeh, A. H., ‘Nonlinear interactions between two widely spaced modes’, International Journal of Bifurcation and Chaos, to appear, 1993b.

  10. Schmidt, G. and Tondl, A., Non-Linear Vibrations, Akademie-Verlag, Berlin, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nayfeh, S.A., Nayfeh, A.H. The response of nonlinear systems to modulated high-frequency input. Nonlinear Dyn 7, 301–315 (1995). https://doi.org/10.1007/BF00046305

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00046305

Key words

Navigation