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Nonlinear Dynamics

, Volume 25, Issue 1–3, pp 183–205 | Cite as

Nonlinear Modal Analysis of Structural Systems Using Multi-Mode Invariant Manifolds

  • Eric Pesheck
  • Nicolas Boivin
  • Christophe Pierre
  • Steven W. Shaw
Article

Abstract

In this paper, an invariant manifold approach is introduced for the generationof reduced-order models for nonlinear vibrations of multi-degrees-of-freedomsystems. In particular, the invariant manifold approach for defining andconstructing nonlinear normal modes of vibration is extended to the case ofmulti-mode manifolds. The dynamic models obtained from this technique capture the essential coupling between modes of interest, while avoiding coupling fromother modes. Such an approach is useful for modeling complex systemresponses, and is essential when internal resonances exist between modes.The basic theory and a general, constructive methodology for the method arepresented. It is then applied to two example problems, one analytical andthe other finite-element based. Numerical simulation results are obtainedfor the full model and various types of reduced-order models, including theusual projection onto a set of linear modes, and the invariant manifoldapproach developed herein. The results show that the method is capable ofaccurately representing the nonlinear system dynamics with relatively fewdegrees of freedom over a range of vibration amplitudes.

normal modes modal analysis nonlinear vibration invariant manifolds 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Eric Pesheck
    • 1
  • Nicolas Boivin
    • 1
  • Christophe Pierre
    • 1
  • Steven W. Shaw
    • 2
  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of MichiganAnn ArborU.S.A
  2. 2.Department of Mechanical EngineeringMichigan State UniversityEast LansingU.S.A

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