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

Breathers; Cyclic structures; Solitons; Vibration localisation; Localisation; Modulation instabilities; Non-linear phenomena; Nonlinear evolution equation; Nonlinear modulation; Undamped oscillators; Condensed Matter Physics; Mechanics of Materials; Acoustics and Ultrasonics; Mechanical Engineering; Nonlinear Sciences - Pattern Formation and Solitons

Abstract :

[en] 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.

Disciplines :

Mechanical engineering

Author, co-author :

Fontanela, F.; Department of Mechanical Engineering, Imperial College London, London, United Kingdom

Grolet, A.; Department of Mechanical Engineering, Arts et Métiers ParisTech, Lille, France

Salles, Loïc ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M) ; Department of Mechanical Engineering, Imperial College London, London, United Kingdom

Chabchoub, A.; Department of Mechanical Engineering, Aalto University, Aalto, Finland ; School of Civil Engineering, The University of Sydney, Sydney, Australia

Hoffmann, N.; Department of Mechanical Engineering, Imperial College London, London, United Kingdom ; Department of Mechanical Engineering, Hamburg University of Technology, Hamburg, Germany

Language :

English

Title :

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

Publication date :

20 January 2018

Journal title :

Journal of Sound and Vibration

ISSN :

0022-460X

eISSN :

1095-8568

Publisher :

Academic Press

Volume :

413

Pages :

467 - 481

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0022460X17306053?httpAccept=text/xml

Funders :

CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico

Funding text :

The first author thanks the financial support provided by the Brazilian agency CNPq (project number 01339/2015-3 ). Appendix A

Available on ORBi :

since 05 July 2025

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