Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes - ENSTA Paris - École nationale supérieure de techniques avancées Paris Accéder directement au contenu
Article Dans Une Revue Journal of Sound and Vibration Année : 2004

Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes

Cyril Touzé
Olivier Thomas
Antoine Chaigne
  • Fonction : Auteur
  • PersonId : 883030

Résumé

The definition of a non-linear normal mode (NNM) as an invariant manifold in phase space is used. In conservative cases, it is shown that normal form theory allows one to compute all NNMs, as well as the attendant dynamics onto the manifolds, in a single operation. Then, a single-mode motion is studied. The aim of the present work is to show that too severe truncature using a single linear mode can lead to erroneous results. Using single-non-linear mode motion predicts the correct behaviour. Hence, the nonlinear change of co-ordinates allowing one to pass from the linear modal variables to the normal ones, linked to the NNMs, defines a framework to properly truncate non-linear vibration PDEs. Two examples are studied: a discrete system (a mass connected to two springs) and a continuous one (a linear Euler-Bernoulli beam resting on a non-linear elastic foundation). For the latter, a comparison is given between the developed method and previously published results.
Fichier principal
Vignette du fichier
CTOTAC_JSV2004.pdf (408.87 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00830693 , version 1 (05-10-2015)

Identifiants

Citer

Cyril Touzé, Olivier Thomas, Antoine Chaigne. Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes. Journal of Sound and Vibration, 2004, 273 (1-2), pp.77-101. ⟨10.1016/j.jsv.2003.04.005⟩. ⟨hal-00830693⟩

Collections

ENSTA ENSTA_UME
151 Consultations
1118 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More