• français
    • English
    français
  • Login
Help
View Item 
  •   Home
  • Laboratoire d’Ingénierie des Systèmes Physiques Et Numériques (LISPEN)
  • View Item
  • Home
  • Laboratoire d’Ingénierie des Systèmes Physiques Et Numériques (LISPEN)
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Article dans une revue avec comité de lecture
Author
ccTOUZÉ, Cyril
563936 Institut Polytechnique de Paris [IP Paris]
300065 École Nationale Supérieure de Techniques Avancées [ENSTA Paris]
421305 Institut des Sciences de la mécanique et Applications industrielles [IMSIA - UMR 9219]
VIZZACCARO, Alessandra
220393 University of Bristol [Bristol]
THOMAS, Olivier
543315 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [LISPEN]

URI
http://hdl.handle.net/10985/22642
DOI
10.1007/s11071-021-06693-9
Date
2021-07
Journal
Nonlinear Dynamics

Abstract

This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear-based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations. They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then, the specific case of structures discretised with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.

Files in this item

Name:
LISPEN_ND_2021_THOMAS.pdf
Size:
2.075Mb
Format:
PDF
View/Open

Collections

  • Laboratoire d’Ingénierie des Systèmes Physiques Et Numériques (LISPEN)

Related items

Showing items related by title, author, creator and subject.

  • Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements 
    Article dans une revue avec comité de lecture
    VIZZACCARO, Alessandra; GIVOIS, Arthur; LONGOBARDI, Pierluigi; ccSHEN, Yichang; DEÜ, Jean-François; SALLES, Loïc; ccTOUZÉ, Cyril; THOMAS, Olivier (Springer Verlag, 2020)
    Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on ...
  • Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures 
    Article dans une revue avec comité de lecture
    ccSHEN, Yichang; VIZZACCARO, Alessandra; KESMIA, Nassim; SALLES, Loïc; THOMAS, Olivier; ccTOUZÉ, Cyril (MDPI AG, 2021-03)
    The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods ...
  • Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect 
    Article dans une revue avec comité de lecture
    SHAMI, Zein Alabidin; ccSHEN, Yichang; GIRAUD-AUDINE, Christophe; ccTOUZÉ, Cyril; THOMAS, Olivier (Springer Science and Business Media LLC, 2022-08)
    This article considers the nonlinear dynamics of coupled oscillators featuring strong coupling in 1:2 internal resonance. In forced oscillations, this particular interaction is the source of energy exchange, leading to a ...
  • Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances 
    Article dans une revue avec comité de lecture
    MONTEIL, Mélodie; ccTOUZÉ, Cyril; THOMAS, Olivier; BENACCHIO, Simon (Springer Verlag, 2014)
    This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second order internal resonances resulting from a harmonic tuning of their natural ...
  • Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification 
    Article dans une revue avec comité de lecture
    GIVOIS, Arthur; TAN, Jin-Jack; ccTOUZÉ, Cyril; THOMAS, Olivier (Springer Science and Business Media LLC, 2020-02)
    A system composed of two cubic nonlinear oscillators with close natural frequencies, and thus displaying a 1:1 internal resonance, is studied both theoretically and experimentally, with a special emphasis on the free ...

Browse

All SAMCommunities & CollectionsAuthorsIssue DateCenter / InstitutionThis CollectionAuthorsIssue DateCenter / Institution

Newsletter

Latest newsletterPrevious newsletters

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales