Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator

Giuseppe I. Cirillo, Alexandre Mauroy, Ludovic Renson, Gäetan Kerschen, Rodolphe Sepulchre

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

Abstract

Nonlinear normal modes of vibration have been the focus of many studies during the past years and different characterizations of them have been proposed. The present work focuses on damped systems, and considers nonlinear normal mode motions as trajectories lying on an invariant manifold, following the geometric approach of Shaw and Pierre. We provide a novel characterization of the invariant manifold, that rests on the spectral theory of the Koopman operator. A main advantage of the proposed approach is a global parametrization of the manifold, which avoids folding issues arising with the use of displacementvelocity coordinates.

Original languageEnglish
Title of host publication11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers (ASME)
Volume6
ISBN (Electronic)9780791857168
DOIs
Publication statusPublished - 2015
Externally publishedYes
EventASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015 - Boston, United States
Duration: 2 Aug 20155 Aug 2015

Conference

ConferenceASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015
CountryUnited States
CityBoston
Period2/08/155/08/15

Fingerprint

Normal Modes
Invariant Manifolds
Parametrization
Geometric Approach
Spectral Theory
Operator
Folding
Damped
Vibration
Trajectories
Trajectory
Motion

Cite this

Cirillo, G. I., Mauroy, A., Renson, L., Kerschen, G., & Sepulchre, R. (2015). Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator. In 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2015-46366
Cirillo, Giuseppe I. ; Mauroy, Alexandre ; Renson, Ludovic ; Kerschen, Gäetan ; Sepulchre, Rodolphe. / Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator. 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2015.
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Cirillo, GI, Mauroy, A, Renson, L, Kerschen, G & Sepulchre, R 2015, Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator. in 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. vol. 6, American Society of Mechanical Engineers (ASME), ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015, Boston, United States, 2/08/15. https://doi.org/10.1115/DETC2015-46366

Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator. / Cirillo, Giuseppe I.; Mauroy, Alexandre; Renson, Ludovic; Kerschen, Gäetan; Sepulchre, Rodolphe.

11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2015.

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

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T1 - Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator

AU - Cirillo, Giuseppe I.

AU - Mauroy, Alexandre

AU - Renson, Ludovic

AU - Kerschen, Gäetan

AU - Sepulchre, Rodolphe

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N2 - Nonlinear normal modes of vibration have been the focus of many studies during the past years and different characterizations of them have been proposed. The present work focuses on damped systems, and considers nonlinear normal mode motions as trajectories lying on an invariant manifold, following the geometric approach of Shaw and Pierre. We provide a novel characterization of the invariant manifold, that rests on the spectral theory of the Koopman operator. A main advantage of the proposed approach is a global parametrization of the manifold, which avoids folding issues arising with the use of displacementvelocity coordinates.

AB - Nonlinear normal modes of vibration have been the focus of many studies during the past years and different characterizations of them have been proposed. The present work focuses on damped systems, and considers nonlinear normal mode motions as trajectories lying on an invariant manifold, following the geometric approach of Shaw and Pierre. We provide a novel characterization of the invariant manifold, that rests on the spectral theory of the Koopman operator. A main advantage of the proposed approach is a global parametrization of the manifold, which avoids folding issues arising with the use of displacementvelocity coordinates.

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M3 - Conference contribution

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BT - 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

PB - American Society of Mechanical Engineers (ASME)

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Cirillo GI, Mauroy A, Renson L, Kerschen G, Sepulchre R. Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator. In 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6. American Society of Mechanical Engineers (ASME). 2015 https://doi.org/10.1115/DETC2015-46366