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Non-linear vibrations of shells: A literature review from 2003 to 2013

Abstract : The present literature review focuses on geometrically non linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non linear vibrations of shells subjected to normal and in plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non linear vibrations of shells and panels, including (i) fluid structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non linear normal modes and meshless methods are reviewed in depth.
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Contributor : Mathias Legrand <>
Submitted on : Friday, April 8, 2016 - 4:53:16 AM
Last modification on : Thursday, February 7, 2019 - 5:23:25 PM
Document(s) archivé(s) le : Monday, November 14, 2016 - 10:45:54 PM


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Farbod Alijani, Marco Amabili. Non-linear vibrations of shells: A literature review from 2003 to 2013. International Journal of Non-Linear Mechanics, Elsevier, 2014, ⟨10.1016/j.ijnonlinmec.2013.09.012⟩. ⟨hal-01299631⟩



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