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Global Parametrization of the Invariant Manifold Defining Nonlinear Normal Modes Using the Koopman Operator

[+] Author Affiliations
Giuseppe I. Cirillo, Alexandre Mauroy, Ludovic Renson, Gaëtan Kerschen

University of Liège, Liège, Belgium

Rodolphe Sepulchre

University of Cambridge, Cambridge, UK

Paper No. DETC2015-46366, pp. V006T10A049; 10 pages
  • 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
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5716-8
  • Copyright © 2015 by ASME


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 displacement-velocity coordinates.

Copyright © 2015 by ASME
Topics: Manifolds



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