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FROM:
M. Amabili, A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach, Journal of Sound and Vibration 264 (2003) 1091–1125.
Also see:
Farbod Alijani and Marco Amabili, “Non-linear vibrations of shells: A literature review from 2003 – 2013”, International Journal of Non-Linear Mechanics 01/2014; 58:233–257. DOI:10.1016/j.ijnonlinmec.2013.09.012
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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