A study of the modal interaction amongst three nonlinear normal modes using a backbone curve approach

X Liu, Andrea Cammarano, D.J. Wagg, Simon Neild

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

1 Citation (Scopus)


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 ωn1 : ωn2 : ωn3 ≈ 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.
Original languageEnglish
Title of host publicationNonlinear Dynamics, Volume 1
Subtitle of host publicationProceedings of the 34th IMAC, A Conference and Exposition on Structural Dynamics 2016
PublisherSpringer, Cham
Number of pages9
ISBN (Electronic)9783319297392
ISBN (Print)9783319297385
Publication statusPublished - 2016

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644


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


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