Solitons in cyclic and symmetric structures

Filipe Fontanela, Aurelien Grolet, Loic Salles, Norbert Hoffmann

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This research focuses on localised states arising from modulationally unstable plane waves in non-conservative cyclic and symmetric structures. The main application is on vibrations of bladed-disks of aircraft engines experiencing nonlinear effects, such as large displacements, friction dissipation, and/or complex fluid-structure interactions. The investigation is based on a minimal model composed of a chain of linearly damped Duffing oscillators under external travelling wave excitation. The computed results are based on two strategies: (1) a Non-Linear Schrödinger Equation (NLSE) approximation; and (2) the periodic and quasi-periodic Harmonic Balance Methods (HBM). In both cases, the results show that unstable plane waves may self-modulate, leading to stable and unstable single and multiple solitons configurations.

Original languageEnglish
Title of host publicationNonlinear Dynamics - Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018
EditorsGaetan Kerschen
PublisherSpringer Science and Business Media, LLC
Number of pages4
ISBN (Print)9783319742793
Publication statusPublished - 2019
Externally publishedYes
Event36th IMAC, A Conference and Exposition on Structural Dynamics, 2018 - Orlando, United States
Duration: 12 Feb 201815 Feb 2018

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652


Conference36th IMAC, A Conference and Exposition on Structural Dynamics, 2018
Country/TerritoryUnited States


  • Cyclic structures
  • Harmonic balance methods
  • Localised vibrations
  • Non-linear Schrödinger equation
  • Solitons


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