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Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Article dans une revue avec comité de lecture
Auteur
PAPANGELO, Antonio
484412 Hamburg University of Technology [TUHH]
FONTANELA, Filipe
69530 Imperial College London
GROLET, Aurélien
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]
CIAVARELLA, Michele
484412 Hamburg University of Technology [TUHH]
HOFFMANN, Norbert
69530 Imperial College London
484412 Hamburg University of Technology [TUHH]

URI
http://hdl.handle.net/10985/16779
DOI
10.1016/j.jsv.2018.10.028
Date
2019
Journal
Journal of Sound and Vibration

Résumé

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.

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