The influence of phase-locking on internal resonance from a nonlinear normal mode perspective

Tom Hill, Simon Neild, Andrea Cammarano, DJ Wagg

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

7 Citations (Scopus)
367 Downloads (Pure)

Abstract

When a nonlinear system is expressed in terms of the modes of the equivalent linear system, the nonlinearity often leads to modal coupling terms between the linear modes. In this paper it is shown that, for a system to exhibit an internal resonance between modes, a particular type of nonlinear coupling term is required. Such terms impose a phase condition between linear modes, and hence are denoted phase-locking terms. The effect of additional modes that are not coupled via phase-locking terms is then investigated by considering the backbone curves of the system. Using the example of a two-mode model of a taut horizontal cable, the backbone curves are derived for both the case where phase-locked coupling terms exist, and where there are no phase-locked coupling terms. Following this, an analytical method for determining stability is used to show that phase-locking terms are required for internal resonance to occur. Finally, the effect of non-phase-locked modes is investigated and it is shown that they lead to a stiffening of the system. Using the cable example, a physical interpretation of this is provided.
Original languageEnglish
Pages (from-to)135-149
Number of pages15
JournalJournal of Sound and Vibration
Volume379
Early online date6 Jun 2016
DOIs
Publication statusPublished - 29 Sep 2016

Keywords

  • internal resonance
  • nonlinear normal modes
  • backbone curves
  • nonlinear dynamics
  • cable dynamics

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