Publisher DOI: 10.1016/j.jsv.2017.08.004
arXiv ID: 1704.00695v1
Title: Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry
Language: English
Authors: Fontanela, Filipe 
Grolet, Aurélien 
Salles, Loic 
Chabchoub, Amin 
Hoffmann, Norbert  
Keywords: Nonlinear Sciences - Pattern Formation and Solitons;Nonlinear Sciences - Pattern Formation and Solitons
Issue Date: 20-Jan-2018
Source: Journal of Sound and Vibration (413): 467-481 (2018-01-20)
Journal or Series Name: Journal of sound and vibration 
Abstract (english): 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.
ISSN: 0022-460X
Institute: Strukturdynamik M-14 
Type: (wissenschaftlicher) Artikel
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