Effect of imperfections and damping on the type of nonlinearity of circular plates and shallow spherical shells
type: Item
instance of: scholarly article
title: Effect of imperfections and damping on the type of nonlinearity of circular plates and shallow spherical shells
zbMATH Open document ID: 1163.74035
DOI: 10.1155/2008/678307
author: Cyril Touzé
author: Cédric Camier
author: Gaël Favraud
author: Olivier Thomas
published in: Mathematical Problems in Engineering
publication date: 2009-06-11T00:00:00Z
full work available at URL: https://eudml.org/doc/55553
review text: Summary: We investigate the effect of geometric imperfections and viscous damping on the type of nonlinearity (i.e., the hardening or softening behaviour) of circular plates and shallow spherical shells with free edges. The von Kármán large-deflection theory is used to derive the continuous models. Then, nonlinear normal modes are used for predicting with accuracy the coefficient, the sign of which determines the hardening or softening behaviour of the structure. The effect of geometric imperfections, unavoidable in real systems, is studied by adding a static initial component in the deflection of a circular plate. Axisymmetric as well as asymmetric imperfections are investigated, and their effect on the type of nonlinearity of the modes of an imperfect plate is documented. Transitions from hardening to softening behaviour are predicted quantitatively for imperfections having the shapes of eigenmodes of a perfect plate. The role of 2:1 internal resonance in this process is underlined. When damping is included in the calculation, it is found that the softening behaviour is generally favoured, but its effect remains limited.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74K25
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 5564168
zbMATH Keywords: von Kármán large-deflection theory
zbMATH Keywords: nonlinear normal modes
zbMATH Keywords: 2:1 internal resonance
MaRDI profile type: Publication
OpenAlex ID: W2041880237
Wikidata QID: Q58646237
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description: scientific article; zbMATH DE number 5564168