Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction

Abstract

This literature review focuses mainly on geometrically nonlinear (finite amplitude) free and forced vibrations of circular cylindrical shells and panels, with and without fluid-structure interaction. Work on shells and curved panels of different geometries is but briefly discussed. In addition, studies dealing with particular dynamical problems involving finite deformations, eg, dynamic buckling, stability, and flutter of shells coupled to flowing fluids, are also discussed. This review is structured as follows: after a short introduction on some of the fundamentals of geometrically nonlinear theory of shells, vibrations of shells and panels in vacuo are discussed. Free and forced vibrations under radial harmonic excitation (Section 2.2), parametric excitation (axial tension or compression and pressure-induced excitations) (Section 2.3), and response to radial transient loads (Section 2.4) are reviewed separately. Studies on shells and panels in contact with dense fluids (liquids) follow; some of these studies present very interesting results using methods also suitable for shells and panels in vacuo. Then, in Section 4, shells and panels in contact with light fluids (gases) are treated, including the problem of stability (divergence and flutter) of circular cylindrical panels and shells coupled to flowing fluid. For shells coupled to flowing fluid, only the case of axial flow is reviewed in this paper. Finally, papers dealing with experiments are reviewed in Section 5. There are 356 references cited in this article.

Non-linear vibrations of free-edge thin spherical shells: Experiments on a 1:1:2 internal resonance

“…In the abundant literature devoted to nonlinear vibrations of shells (see for example the reviews of Qatu [4], Amabili and Païdoussis [5] and Alhazza and Alhazza [6]), only a few studies propose experimental investigations, as compared to the number of theoretical works available. Moreover, the case of shallow spherical shells is generally reduced to axisymmetric vibrations, whereas asymmetric modes are of prime importance to understand the global dynamics exhibited: 1 they are numerous as compared to the axisymmetric ones, and since nonlinear couplings between any modes are possible [7], an axisymmetric excitation of the structure can lead to asymmetric vibrations.…”

Numerical analysis of non-linear vibrations of a fractionally damped cylindrical shell under the conditions of combinational internal resonance

“…Shell elements are in pipes and ducts, bodies of cars, space shuttles, aircraft fuselages, ship hulls, submarines and building structures. Recent investigations on dynamic response of cylindrical shells are based on nonlinear theories [1][2][3][4][5], and a comprehensive review could be found in [6,7].…”

Effects of in-plane inertia on natural frequency and stresses of long circular cylindrical shell

“…Readers interested by these works can turn to [1] and [2] or to the review paper presented recently by [3], and to a more recent review paper by [4], in which a set of papers are discussed and commented. It can be observed that although several works exist in literature on nonlinear vibrations of shells, only few papers are available which are concerned with the nonlinear free vibration of shells of infinite length.…”