Dark solitons, modulation instability and breathers in a chain of weakly non-linear oscillators with cyclic

Filipe Fontanela (1) , Aurélien Grolet (2) , Loic Salles (1) , Amin Chabchoub (3) , Norbert Hoffmann (1, 4)

1 Imperial College London
2 LISPEN - Laboratoire d’Ingénierie des Systèmes Physiques et Numériques
3 Aalto University
4 TUHH - Hamburg University of Technology

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.

Mots clés: vibration localisation; solitons; breathers; cyclic structures

Domaines: Sciences de l'ingénieur [physics]; Science non linéaire [physics]

Filipe Fontanela, Aurélien Grolet, Loic Salles, Amin Chabchoub, Norbert Hoffmann. Dark solitons, modulation instability and breathers in a chain of weakly non-linear oscillators with cyclic. Journal of Sound and Vibration, 2018, ⟨10.1016/j.jsv.2017.08.004⟩. ⟨hal-01492538v2⟩