Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

Research output: Contribution to journalArticleScientificpeer-review

Researchers

  • F. Fontanela
  • A. Grolet
  • L. Salles
  • A. Chabchoub
  • N. Hoffmann

Research units

  • Imperial College London
  • Arts et Métiers ParisTech
  • Hamburg University of Technology

Abstract

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

Details

Original languageEnglish
Pages (from-to)467-481
JournalJournal of Sound and Vibration
Volume413
Early online date2017
Publication statusPublished - 20 Jan 2018
MoE publication typeA1 Journal article-refereed

    Research areas

  • Breathers, Cyclic structures, Solitons, Vibration localisation

ID: 15924317