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 proceedingConference 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 languageEnglish
Title of host publicationASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Subtitle of host publicationVolume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers (ASME)
Volume6
ISBN (Print)9780791857168
DOIs
Publication statusPublished - 2015
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 Dive into the research topics of 'Global parametrization of the invariant manifold defining nonlinear normal modes using the koopman operator'. Together they form a unique fingerprint.

Cite this