Nonlinear Dynamics

, Volume 3, Issue 2, pp 145–162 | Cite as

On methods for continuous systems with quadratic and cubic nonlinearities

  • A. H. Nayfeh
  • J. F. Nayfeh
  • D. T. Mook


Methods for determining the response of continuous systems with quadratic and cubic nonlinearities are discussed. We show by means of a simple example that perturbation and computational methods based on first discretizing the systems may lead to erroncous results whereas perturbation methods that attack directly the nonlinear partial-differential equations and boundary conditions avoid the pitfalls associated with the analysis of the discretized systems. We describe a perturbation technique that applies either the method of multiple scales or the method of averaging to the Lagrangian of the system rather than the partial-differential equations and boundary conditions.

Key words

Averaged Lagrangian valve resonances Galerkin procedure 


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  1. 1.
    Nayfeh A. H., Perturbation Methods, Wiley-Interscience, New York, 1973.Google Scholar
  2. 2.
    Nayfeh A. H., Introduction to Perturbation Techniques, Wiley-Interscience, New York, 1981.Google Scholar
  3. 3.
    Nayfeh A. H. and Bouguerra H., ‘Non-linear response of a fluid valve’, International Journal of Non-Linear Mechanics 25, 1990, 433–449.Google Scholar
  4. 4.
    Nayfeh A. H. and Mook D. T., Nonlinear Oscillations, Wiley-Interscience, New York, 1979.Google Scholar
  5. 5.
    Nayfeh A. H. ‘The response of single-degree-of-freedom systems with quadratic and cubic nonlinearities to a subharmonic excitation’, Journal of Sound and Vibration 89, 1983, 457–470.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • A. H. Nayfeh
    • 1
  • J. F. Nayfeh
    • 2
  • D. T. Mook
    • 1
  1. 1.Department of Engineering Science and MechanicsVirginia Polytechnic Institute and State UniversityBlacksburgU.S.A.
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of Central FloridaOrlandoU.S.A.

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