%0 Journal Article
%T Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry
%+ Dynamique des Fluides et Acoustique (DFA)
%+ Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC)
%A Touzé, Cyril
%A Thomas, Olivier
%< avec comité de lecture
%@ 0020-7462
%J International Journal of Non-Linear Mechanics
%I Elsevier
%V 41
%N 5
%P 678-692
%8 2006-06
%D 2006
%R 10.1016/j.ijnonlinmec.2005.12.004
%K Shallow spherical shells
%K Hardening/softening behaviour
%K Non-linear normal modes
%K Internal resonance
%Z Physics [physics]/Mechanics [physics]/Mechanical engineering [physics.class-ph]
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph]Journal articles
%X Non-linear vibrations of free-edge shallow spherical shells are investigated, in order to predict the trend of non-linearity (hardening/softening behaviour) for each mode of the shell, as a function of its geometry. The analog for thin shallow shells of von Kármán's theory for large deflection of plates is used. The main difficulty in predicting the trend of non-linearity relies in the truncation used for the analysis of the partial differential equations (PDEs) of motion. Here, non-linear normal modes through real normal form theory are used. This formalism allows deriving the analytical expression of the coefficient governing the trend of non-linearity. The variation of this coefficient with respect to the geometry of the shell (radius of curvature R, thickness h and outer diameter 2 a) is then numerically computed, for axisymmetric as well as asymmetric modes. Plates (obtained as R → ∞) are known to display a hardening behaviour, whereas shells generally behave in a softening way. The transition between these two types of non-linearity is clearly studied, and the specific role of 2:1 internal resonances in this process is clarified. © 2006 Elsevier Ltd. All rights reserved.
%G English
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-00838885/document
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-00838885/file/2006-IJNLM_shellGeometryHardSoftB.pdf
%L hal-00838885
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-00838885
%~ ENSTA
%~ CNAM
%~ ENSTA_UME
%~ LMSSC-CNAM