hal-00838885
https://hal-ensta-paris.archives-ouvertes.fr/hal-00838885
https://hal-ensta-paris.archives-ouvertes.fr/hal-00838885/document
https://hal-ensta-paris.archives-ouvertes.fr/hal-00838885/file/2006-IJNLM_shellGeometryHardSoftB.pdf
doi:10.1016/j.ijnonlinmec.2005.12.004
[ENSTA] ENSTA Paris
[CNAM] Conservatoire National des Arts et Métiers
[ENSTA_UME] Unité de Mécanique
[LMSSC-CNAM] Laboratoire de mécanique des structures et des systèmes couplés
Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry
Touzé, Cyril
Thomas, Olivier
[PHYS.MECA.GEME] Physics [physics]/Mechanics [physics]/Mechanical engineering [physics.class-ph]
[SPI.MECA.GEME] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph]
ART
Shallow spherical shells
Hardening/softening behaviour
Non-linear normal modes
Internal resonance
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.
2006-06
2016-03-18
en
International Journal of Non-Linear Mechanics
Elsevier