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A Study of the Modal Interaction Amongst Three Nonlinear Normal Modes Using a Backbone Curve Approach

  • X. LiuEmail author
  • A. Cammarano
  • D. J. Wagg
  • S. A. Neild
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

In this paper, a three degree-of-freedom oscillator with cubic elastic nonlinearities is considered. For this system, the natural frequencies of its underlying linear modes are set to be approximately equal so that \(\omega _{n1}:\omega _{n2}:\omega _{n3} \approx 1:1:1\). As a result, the nonlinear normal modes in the system are able to potentially interact with each other. In this study, the underlying unforced and undamped system is considered. The second-order normal forms technique is used to estimate the backbone curves of the system, which give information on the frequency and modal response amplitudes and phases. Then, through choosing the activate modes and their specific phase differences, the single-, double- and triple-mode backbone curves are computed. The results show the effect of nonlinear multi-mode interactions on the dynamic response of nonlinear oscillators. These insights will be beneficial when considering how a structure will respond and for the system identification of nonlinear multi-degree-of-freedom systems.

Keywords

Backbone curve 3-DoF nonlinear oscillator Nonlinear modal interaction Cubic nonlinearity Second-order normal form method 

Notes

Acknowledgements

The authors would like to acknowledges the support of the Engineering and Physical Sciences Research Council. S.A.N is supported by EPSRC Fellowship EP/K005375/1. D.J.W is supported by EPSRC grant EP/K003836/1.

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Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  • X. Liu
    • 1
    Email author
  • A. Cammarano
    • 2
  • D. J. Wagg
    • 1
  • S. A. Neild
    • 3
  1. 1.Department of Mechanical EngineeringUniversity of SheffieldSheffieldUK
  2. 2.School of EngineeringUniversity of GlasgowGlasgowUK
  3. 3.Department of Mechanical EngineeringUniversity of BristolBristolUK

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