CUED Publications database

A spectral characterization of nonlinear normal modes

Cirillo, GI and Mauroy, A and Renson, L and Kerschen, G and Sepulchre, R (2016) A spectral characterization of nonlinear normal modes. Journal of Sound and Vibration, 377. pp. 284-301. ISSN 0022-460X

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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.

Item Type: Article
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:34
Last Modified: 19 Aug 2021 04:57
DOI: 10.1016/j.jsv.2016.05.016