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From: "Effect of geometric imperfections on non-linear stability of circular cylindrical shells conveying fluid", by M. Amabili (1),
K. Karagiozis (2) and M.P. Paidoussis (1)
(1) Department of Mechanical Engineering, McGill University
(2) Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign
in International Journal of Non-Linear Mechanics, Vol. 44, pp. 276-28, 2009
ABSTRACT: Circular cylindrical shells conveying incompressible flow are addressed in this study; they lose stability by divergence when the flow velocity reaches a critical value. The divergence is strongly subcritical, becoming supercritical for larger amplitudes. Therefore the shell, if perturbed from the initial configu- ration, has severe deformations causing failure much before the critical velocity predicted by the linear threshold. Both Donnell's non-linear theory retaining in-plane displacements and the Sanders–Koiter non-linear theory are used for the shell. The fluid is modelled by potential flow theory but the effect of steady viscous forces is taken into account. Geometric imperfections are introduced and fully studied. Non-classical boundary conditions are used to simulate the conditions of experimental tests in a water tunnel. Comparison of numerical and experimental results is performed.
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