A spectral characterization of nonlinear normal modes

Characterization; Invariant manifolds; Koopman operator; Nonlinear normal modes; Parametrization; Spectral; Degrees of freedom (mechanics); Eigenvalues and eigenfunctions; Phase space methods; Parametrizations; Spectrum analyzers

Abstract :

[en] This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity. © 2016 Elsevier Ltd

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Cirillo, G. I.; Control Group, Department of Engineering, University of Cambridge, Cambridge, United Kingdom

Mauroy, A.; Systems and Modeling Research Group, Department of Electrical Engineering and Computer Science, University of Liège, Liège, Belgium

Renson, Ludovic

Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Language :

English

Title :

A spectral characterization of nonlinear normal modes

Publication date :

2016

Journal title :

Journal of Sound and Vibration

ISSN :

0022-460X

eISSN :

1095-8568

Publisher :

Academic Press

Volume :

377

Pages :

284-301

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 11 November 2017

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Bibliography

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