Identifying the significance of nonlinear normal modes

Tom Hill, Andrea Cammarano, Simon Neild, David Barton

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)
256 Downloads (Pure)


Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system - highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared to simulated forced responses to verify these findings.
Original languageEnglish
Article number20160789
Number of pages25
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Early online date1 Mar 2017
Publication statusPublished - Mar 2017


  • structural dynamics
  • nonlinear normal modes
  • backbone curves
  • energy transfer
  • resonance
  • second-order normal form technique

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