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

doi:10.1115/DETC2015-46366

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

Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférence › Article dans les actes d'une conférence/un colloque

Résumé

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.

langue originale	Anglais
titre	11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
Editeur	American Society of Mechanical Engineers (ASME)
Volume	6
ISBN (Electronique)	9780791857168
Les DOIs	https://doi.org/10.1115/DETC2015-46366
Etat de la publication	Publié - 2015
Modification externe	Oui
Evénement	ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015 - Boston, États-Unis Durée: 2 août 2015 → 5 août 2015

Une conférence

Une conférence	ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015
Pays/Territoire	États-Unis
La ville	Boston
période	2/08/15 → 5/08/15

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10.1115/DETC2015-46366

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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. Dans 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

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title = "Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator",

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.",

author = "Cirillo, {Giuseppe I.} and Alexandre Mauroy and Ludovic Renson and G{\"a}etan Kerschen and Rodolphe Sepulchre",

year = "2015",

doi = "10.1115/DETC2015-46366",

language = "English",

volume = "6",

booktitle = "11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control",

publisher = "American Society of Mechanical Engineers (ASME)",

note = "ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015 ; Conference date: 02-08-2015 Through 05-08-2015",

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

Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférence › Article dans les actes d'une conférence/un colloque

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AU - Cirillo, Giuseppe I.

AU - Mauroy, Alexandre

AU - Renson, Ludovic

AU - Kerschen, Gäetan

AU - Sepulchre, Rodolphe

PY - 2015

Y1 - 2015

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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DO - 10.1115/DETC2015-46366

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AN - SCOPUS:84982162252

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

PB - American Society of Mechanical Engineers (ASME)

T2 - ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015

Y2 - 2 August 2015 through 5 August 2015

ER -

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

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