Dissipative solitons in forced cyclic and symmetric structures

F. Fontanela*, A. Grolet, L. Salles, A. Chabchoub, A. R. Champneys, S. Patsias, N. Hoffmann

*Corresponding author for this work

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

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Abstract

The emergence of localised vibrations in cyclic and symmetric rotating structures, such as bladed disks of aircraft engines, has challenged engineers in the past few decades. In the linear regime, localised states may arise due to a lack of symmetry, as for example induced by inhomogeneities. However, when structures deviate from the linear behaviour, e.g. due to material nonlinearities, geometric nonlinearities like large deformations, or other nonlinear elements like joints or friction interfaces, localised states may arise even in perfectly symmetric structures. In this paper, a system consisting of coupled Duffing oscillators with linear viscous damping is subjected to external travelling wave forcing. The system may be considered a minimal model for bladed disks in turbomachinery operating in the nonlinear regime, where such excitation may arise due to imbalance or aerodynamic excitation. We demonstrate that near the resonance, in this non-conservative regime, localised vibration states bifurcate from the travelling waves. Complex bifurcation diagrams result, comprising stable and unstable dissipative solitons. The localised solutions can also be continued numerically to a conservative limit, where solitons bifurcate from the backbone curves of the travelling waves at finite amplitudes.

Original languageEnglish
Pages (from-to)280-292
Number of pages13
JournalMechanical Systems and Signal Processing
Volume117
Early online date13 Aug 2018
DOIs
Publication statusPublished - 15 Feb 2019

Keywords

  • Cyclic structures
  • Solitons
  • Travelling wave excitation
  • Vibration localisation

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