Skip to main content
SpringerLink
Log in

Chaotic behaviour of forced oscillator containing a square nonlinear term on principal resonance curves

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

Abstract

In this paper based on [1] we go further into the study of chaotic behaviour of the forced oscillator containing a square nonlinear term by the methods of multiple scales and numerical simulation. Relation between the chaotic domain and principal resonance curve is discussed. By analyzing the stability of principal resonance curve we infer that chaotic motion would occur near the frequency at which the principal resonance curve has vertical tangent. Results of numerical simulation confirm this inference. Thus we offer an effective way to seek the chaotic motion of the systems which are hard to be investigated by Melnikov method.

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. Pei Qin-yuan and Li Li, Chaotic phenomenon of a nonlinear oscillator,Appl. Math. and Mech.,14, 5 (1993) 377–388.

    Article  MathSciNet  Google Scholar 

  2. Guckenheimer J. and P. J. Holmes,Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Revised and Corrected, Springer-Verlag (1986).

  3. Li Gi-bin and Liu Zheng-rong, Chaotic character of a class of 2nd order system exerted by periodic disturbance,Science Bulletin,7 (1985), 491–495.

    Google Scholar 

  4. Li Gi-bin and Liu Zheng-rong, Chaotic character of some nonlinear forced oscillators,Math. Phys.,5 (1986), 195–204 (in Chinese)

    Google Scholar 

  5. Lin Chang, An example of chaos caused by finite subharmonic bifurcation,Science Bulletin,14 (1985), 980–983.

    Google Scholar 

  6. Szemplinska-Stupnicka, W., Bifurcation of harmonic solution leading to chaotic motion in the softening type Duffing's oscillator,Int. J. Nonlinear Mechanics,23 (1988), 257–277.

    Article  MATH  MathSciNet  Google Scholar 

  7. Szemplinska-Stupnicka, W. and P. Niezgodzki, The approximate approach to chaos phenomena in oscillators having single equilibrium position,J. Sound and Vibration,14 (1990), 181–192.

    Article  MathSciNet  Google Scholar 

  8. Minorsky N., Introduction to Nonlinear Mechanics, J. W. Edwards,Ann. Arbor. Mich., (1947).

  9. Nayfeh A. H. and D. T. Mook,Nonlinear Oscillations, John Wiley, New York (1979).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Changsha Railway University, 410000, Changsha

    Pei Qin-yuan

  2. Beijing Polytechnic University, 100022, Beijing

    Li Li

Authors
  1. Pei Qin-yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the National Natural Science Foundation of China. First received Sept. 9, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qin-yuan, P., Li, L. Chaotic behaviour of forced oscillator containing a square nonlinear term on principal resonance curves. Appl Math Mech 16, 229–236 (1995). https://doi.org/10.1007/BF02450523

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02450523

Key words

Search

Navigation