Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry

Bistability; Localised vibration; Nonlinear dynamics; Self-excitation; Snaking bifurcation; Subcritical Hopf bifurcation; Bi-stability; Cyclic symmetry; Localised; Localized vibration; Mechanical oscillators; Oscillator chains; Self excitation; Self-excited oscillators; Numerical Analysis; Modeling and Simulation; Applied Mathematics

Abstract :

[en] Snaking bifurcations in a chain of mechanical oscillators are studied. The individual oscillators are weakly nonlinear and subject to self-excitation and subcritical Hopf-bifurcations with some parameter ranges yielding bistability. When the oscillators are coupled to their neighbours, snaking bifurcations result, corresponding to localised vibration states. The snaking patterns do seem to be more complex than in previously studied continuous systems, comprising a plethora of isolated branches and also a large number of similar but not identical states, originating from the weak coupling of the phases of the individual oscillators.

Disciplines :

Mechanical engineering

Author, co-author :

Papangelo, A. ; Polytechnic of Bari, Italy ; Imperial College London, United Kingdom

Grolet, A.; Imperial College London, United Kingdom

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

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

Ciavarella, M.; Polytechnic of Bari, Italy

Language :

English

Title :

Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry

Publication date :

March 2017

Journal title :

Communications in Nonlinear Science and Numerical Simulation

ISSN :

1007-5704

Publisher :

Elsevier

Volume :

Pages :

108 - 119

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S1007570416302738?httpAccept=text/plain

Funders :

MIUR - Ministero dell'Istruzione, dell'Università e della Ricerca
DFG - Deutsche Forschungsgemeinschaft

Funding text :

A.P. is grateful to the Italian Ministry of Education, Universities and Research, which funded his PhD research. Part of the work has been supported by Deutsche Forschungsgemeinschaft in project HO 3852/11-1 .

Available on ORBi :

since 05 July 2025

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