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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 133

Nonlinear Stability of Shells Conveying Fluid Flow

M. Amabili1, K. Karagiozis2 and M.P. Païdoussis3

1Department of Industrial Engineering, University of Parma, Italy
2Mechanical Science and Engineering Department, University of Illinois at Urbana-Champaign, United States of America
3Department of Mechanical Engineering, McGill University, Montreal, Canada

Full Bibliographic Reference for this paper
M. Amabili, K. Karagiozis, M.P. Païdoussis, "Nonlinear Stability of Shells Conveying Fluid Flow", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 133, 2008. doi:10.4203/ccp.88.133
Keywords: nonlinear, cylindrical shells, experiments, comparison to theory, stability, flow, subcritical bifurcation, fluid viscosity.

Thin circular cylindrical shells supported at both ends and subjected to internal or external axial fluid flow may be found in many engineering and biomechanical systems. There are many applications of great interest in which shells are subjected to incompressible subsonic flows. For example, thin cylindrical shells are used as thermal shields in nuclear reactors and heat shields in aircraft engines; they may also be found in jet pumps and heat exchangers; they are used as storage tanks and thin-walled piping for aerospace vehicles. Furthermore, in biomechanics, veins, pulmonary passages and urinary systems may be modelled as shells conveying fluid.

In particular this paper presents experimental results for clamped aluminium shells and a recent nonlinear theoretical formulation that accounts for the effect of fluid viscosity. The shell system loses stability by divergence (which is a static pitchfork bifurcation of the equilibrium, exactly the same as buckling) when the flow speed reaches a critical value. According to the few available studies the divergence is strongly subcritical, becoming supercritical at larger amplitudes [1]. It is very interesting to observe that the shell system has two or more stable solutions concurrently, related to divergence in the first mode or a combination of the first and second longitudinal modes, much before the onset of the pitchfork bifurcation. This means that the shell, if perturbed from the initial configuration, may be subjected to severe deformations causing failure at flows much smaller than the critical velocity predicted by linear theory.

The novel features of the present study are:

the introduction of geometric imperfections, which give fundamental qualitative and quantitative differences in behaviour vis-à-vis a perfect shell;
the use of more refined nonlinear shell theories retaining in-plane displacements (without the introduction of a potential stress function), i.e. Donnell's theory with in-plane displacements and the Sanders-Koiter theory;
the introduction of non-classical boundary conditions that allows the exact simulation of the experimental conditions described in Karagiozis et al. [2,3]

M., Amabili, M.P. Païdoussis, "Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction", Applied Mechanics Reviews, 56, 349-381, 2003. doi:10.1115/1.1565084
K.N. Karagiozis, M.P. Païdoussis, A.K. Misra, E. Grinevich, "An experimental study of the nonlinear dynamics of cylindrical shells with clamped ends subjected to axial flow", Journal of Fluids and Structures, 20, 801-816, 2005. doi:10.1016/j.jfluidstructs.2005.03.007
K.N. Karagiozis, M.P. Païdoussis, M. Amabili, A.K. Misra, "Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments", Journal of Sound and Vibration, 309, 637-676, 2008. doi:10.1016/j.jsv.2007.07.061

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