Publisher DOI: 10.1016/j.jsv.2018.10.028
arXiv ID: 1810.07441v1
Title: Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators
Language: English
Authors: Papangelo, Antonio 
Fontanela, Filipe 
Grolet, Aurélien 
Ciavarella, Michele 
Hoffmann, Norbert  
Keywords: Nonlinear Sciences - Pattern Formation and Solitons; Nonlinear Sciences - Pattern Formation and Solitons
Issue Date: 3-Feb-2019
Source: Journal of Sound and Vibration (440): 202-211 (2019-02-03)
Abstract (english): 
Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems.
ISSN: 0022-460X
Journal: Journal of sound and vibration 
Institute: Strukturdynamik M-14 
Document Type: Article
Project: Reibflächendynamik in Schraubenverbindungen 
Untersuchung und Anwendung komplexer, nichtlinearer, dynamischer Zustände in reiberregten mechanischen Systemen 
More Funding information: Deutsche Forschungsgemeinschaft (DFG)
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