Nonlinear vibrations of thin hyperelastic plates

Abstract : Static deflection as well as free and forced nonlinear vibration of thin square plates made of hyperelastic materials are investigated. Two types of materials, namely rubber and soft biological tissues, are considered. The involved physical nonlinearities are described through the Neo-Hookean, Mooney-Rivlin, and Ogden hyperelastic laws; geometrical nonlinearities are modeled by the Novozhilov nonlinear shell theory. Dynamic local models are first built in the vicinity of a static configuration of interest that has been previously calculated. This gives rise to the approximation of the plate's behavior in the form of a system of ordinary differential equations with quadratic and cubic nonlinear terms in displacement. Numerical results are compared and validated in the static case via a commercial finite element software package: they are found to be accurate for deflections reaching 100 times the thickness of the plate. The frequency shift between low- and large-amplitude vibrations weakens with an increased initial deflection.
Type de document :
Article dans une revue
Journal of Sound and Vibration, Elsevier, 2014, pp.1001002. <10.1016/j.jsv.2014.04.028>
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00983980
Contributeur : Mathias Legrand <>
Soumis le : lundi 28 avril 2014 - 15:12:26
Dernière modification le : mercredi 9 mars 2016 - 03:56:36
Document(s) archivé(s) le : lundi 28 juillet 2014 - 10:40:42

Fichiers

Licence


Distributed under a Creative Commons Paternité - Partage selon les Conditions Initiales 4.0 International License

Identifiants

Citation

Ivan Breslavsky, Marco Amabili, Mathias Legrand. Nonlinear vibrations of thin hyperelastic plates. Journal of Sound and Vibration, Elsevier, 2014, pp.1001002. <10.1016/j.jsv.2014.04.028>. <hal-00983980>

Partager

Métriques

Consultations de
la notice

243

Téléchargements du document

910