Non-linear vibrations of free-edge thin spherical shells: Modal interaction rules and 1:1:2 internal resonance

Abstract : This paper is devoted to the derivation and the analysis of vibrations of shallow spherical shell subjected to large amplitude transverse displacement. The analog for thin shallow shells of von Kármán's theory for large deflection of plates is used. The validity range of the approximations is assessed by comparing the analytical modal analysis with a numerical solution. The specific case of a free edge is considered. The governing partial differential equations are expanded onto the natural modes of vibration of the shell. The problem is replaced by an infinite set of coupled second-order differential equations with quadratic and cubic non-linear terms. Analytical expressions of the non-linear coefficients are derived and a number of them are found to vanish, as a consequence of the symmetry of revolution of the structure. Then, for all the possible internal resonances, a number of rules are deduced, thus predicting the activation of the energy exchanges between the involved modes. Finally, a specific mode coupling due to a 1:1:2 internal resonance between two companion modes and an axisymmetric mode is studied. © 2004 Elsevier Ltd. All rights reserved.
Liste complète des métadonnées

Littérature citée [59 références]  Voir  Masquer  Télécharger

https://hal-ensta.archives-ouvertes.fr/hal-00830689
Contributeur : Aurélien Arnoux <>
Soumis le : vendredi 18 mars 2016 - 17:31:12
Dernière modification le : jeudi 13 septembre 2018 - 15:24:05
Document(s) archivé(s) le : dimanche 19 juin 2016 - 23:07:13

Fichier

2005-IJSS_res112BC.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

O. Thomas, Cyril Touzé, Antoine Chaigne. Non-linear vibrations of free-edge thin spherical shells: Modal interaction rules and 1:1:2 internal resonance. International Journal of Solids and Structures, Elsevier, 2005, 42 (11-12), pp.3339-3373. 〈10.1016/j.ijsolstr.2004.10.028〉. 〈hal-00830689〉

Partager

Métriques

Consultations de la notice

237

Téléchargements de fichiers

166