The role of boundary conditions in the instability of one-dimensional systems

Abstract : We investigate the instability properties of one-dimensional systems of finite length that can be described by a local wave equation and a set of boundary conditions. A method to quantify the respective contributions of the local instability and of wave reflections in the global instability is proposed. This allows to differentiate instabilities that emanate from wave propagation from instabilities due to wave reflections. This is illustrated on three different systems, that exhibit three different behaviors. The first one is a model system in fluid mechanics (Ginzburg-Landau equation), the second one is the fluid-conveying pipe (Bourrières equation), the third one is the fluid-conveying pipe resting on an elastic foundation (Roth equation). © 2006 Elsevier SAS. All rights reserved.
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Submitted on : Monday, July 22, 2013 - 11:25:56 AM
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Olivier Doaré, Emmanuel de Langre. The role of boundary conditions in the instability of one-dimensional systems. European Journal of Mechanics - B/Fluids, Elsevier, 2006, 25 (6), pp.948-959. ⟨10.1016/j.euromechflu.2006.01.001⟩. ⟨hal-00838884⟩

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