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International Journal of Theoretical Physics

, Volume 36, Issue 8, pp 1921–1940 | Cite as

Parametric excitation of subharmonic oscillations

  • A. M. Elnaggar
  • A. A. Alhanadwah
Article

Abstract

Subharmonic oscillations of order one-half for a single-degree-of-freedom system with quadratic, cubic, and quartic nonlinearities under parametric excitation are investigated. Two approximate methods (multiple scales and generalized synchronization) are used for comparison. The modulation equations (reduced equations) of the amplitudes and the phases are obtained. Steady-state solutions (periodic solutions) and their stability are determined. Numerical solutions are carried out, and graphical representations of the results are presented and discussed. The results obtained by the two methods are in excellent agreement.

Keywords

Periodic Solution Multiple Scale Parametric Excitation Generalize Synchronization Jump Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • A. M. Elnaggar
    • 1
  • A. A. Alhanadwah
    • 1
  1. 1.Department of Mathematics, Faculty of Science, BenhaZagazig UniversityEgypt

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