Skip to main content
Log in

Asymptotic analysis of strongly nonlinear oscillators

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, an asymptotic method is presented for the analysis of a class of strongly nonlinear autonomous oscillators. The equations governing the amplitude and phase factor are obtained, and the amplitude and stability of the corresponding limit cycles are determined.

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. Chien Wei-zang (ed.),Singular Perturbation Theory and Its Applications in Mechanics, Science Press, Beijing (1981). (in Chinese).

    Google Scholar 

  2. Kevorkian, J. and J. D. Cole,Perturbation Methods in Applied Mathematics, Springer-Verlag, New York (1981).

    Google Scholar 

  3. Kuzmak, G. E., Asymptotic solutions of nonlinear second order diffential equations with variable cofficients,PMM (USSR),23 (1959), 515–526 (in Russian)

    Google Scholar 

  4. Luke, J. C., A perturbation method for nonlinear dispersive wave problems,Proc. Roy. Soc. Ser. A292 (1966), 403–412.

    Google Scholar 

  5. Whitham, G. B.,Linear and Nonlinear Waves, John Wiley & Sons, Inc., New York (1974).

    Google Scholar 

  6. Burton, T. D., Non-linear oscillator limit cycle analysis using a time transformation approach,Int. J. Non-Linear Mech.,17 (1982), 7–19.

    Google Scholar 

  7. Bogoliubov, N. N. and Y. A. Mitropolsky,Asymptotic Methods in the Theory of Nonlinear Oscillations, 4th Ed., “Nauka” Press, Moscow (1974). (in Russian).

    Google Scholar 

  8. Byrd, P. F. and M. D. Friedman,Handbook of Elliptic Integrals for Engineers and Scientists, 2nd Ed., Springer-Verlag, New York (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shi-qiang, D. Asymptotic analysis of strongly nonlinear oscillators. Appl Math Mech 6, 409–415 (1985). https://doi.org/10.1007/BF01895378

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01895378

Keywords

Navigation