A spectral characterization of nonlinear normal modes
| Autor: | Gaëtan Kerschen, Rodolphe Sepulchre, Giuseppe Ilario Cirillo, Ludovic Renson, Alexandre Mauroy |
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| Přispěvatelé: | Université de Liège, Department of Engineering Mathematics, University of Bristol [Bristol], Space Structures and Systems Lab, Department of Aerospace and Mechanical Engineering, Université de Liège-Université de Liège, Control Group, Department of Engineering, University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Cirillo, GI [0000-0002-1162-3225], Apollo - University of Cambridge Repository |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
invariant manifolds
Acoustics and Ultrasonics Invariant manifold Dynamical Systems (math.DS) 01 natural sciences 010305 fluids & plasmas [SPI]Engineering Sciences [physics] Normal mode 0103 physical sciences FOS: Mathematics characterization Mathematics - Dynamical Systems Invariant (mathematics) [MATH]Mathematics [math] Nonlinear normal modes Koopman operator 010301 acoustics Mathematics Spectral Parametrization Mechanical Engineering Operator (physics) Mathematical analysis nonlinear normal modes parametrization Eigenfunction Condensed Matter Physics Nonlinear system Invariant manifolds Mechanics of Materials Phase space spectral |
| Zdroj: | Journal of Sound and Vibration Journal of Sound and Vibration, Elsevier, 2016, 377, pp.284-301. ⟨10.1016/j.jsv.2016.05.016⟩ Cirillo, G I, Mauroy, A, Renson, L, Kerschen, G & Sepulchre, R 2016, ' A spectral characterization of nonlinear normal modes ', Journal of Sound and Vibration, vol. 377, pp. 284-301 . https://doi.org/10.1016/j.jsv.2016.05.016 |
| ISSN: | 0022-460X 1095-8568 |
| DOI: | 10.17863/cam.208 |
| Popis: | 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. Belgian Network DYSCO (Dynamical Systems, Control, and Optimization) funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jsv.2016.05.016 |
| Databáze: | OpenAIRE |
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