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

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

3 Citations (Scopus)

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 language	English
Title of host publication	ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Subtitle of host publication	Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
Publisher	American Society of Mechanical Engineers (ASME)
Volume	6
ISBN (Print)	9780791857168
DOIs	https://doi.org/10.1115/DETC2015-46366
Publication status	Published - 2015
Event	ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015 - Boston, United States Duration: 2 Aug 2015 → 5 Aug 2015

Conference

Conference	ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015
Country/Territory	United States
City	Boston
Period	2/08/15 → 5/08/15

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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. In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 6: 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 et al. / Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator. ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2015.

@inproceedings{a0807bfc93e64c6bace20110e74c496c,

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",

isbn = "9780791857168",

volume = "6",

booktitle = "ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference",

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

address = "United States",

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",

}

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 ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 6: 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 et al.
ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2015.

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

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

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.

UR - https://www.scopus.com/pages/publications/84982162252

U2 - 10.1115/DETC2015-46366

DO - 10.1115/DETC2015-46366

M3 - Conference Contribution (Conference Proceeding)

AN - SCOPUS:84982162252

SN - 9780791857168

VL - 6

BT - ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

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 -

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 ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6. American Society of Mechanical Engineers (ASME). 2015 doi: 10.1115/DETC2015-46366

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

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