Absolutely unstable waves in inviscid hydroelastic systems
Résumé
The effect of inviscid plug flow on the stability of several hydroelastic systems is investigated by determining the absolute or convective nature of the instability from the linear dispersion relation. The fluid-structure systems consist of plates and membranes with bounded and unbounded flow. A method is proposed to derive systematically in parameter space the boundary between convective and absolute instability, based on the particular symmetries of the dispersion relation as originally noted by Crighton and Oswell. This method is then applied to the case of plates with superimposed tension, thick plates with rotary inertia and walls made of plates or membranes bounding channel flow, oscillating in a sinuous or varicose mode of deformation. A relation is drawn with solutions by previous authors for plates, for pipes and for the Kelvin-Helmholtz instability with surface tension. To illustrate these results some temporal evolutions are calculated by using an integration in the wavenumber space. Based on the large set of new cases solved in the paper some general trends are discussed as to the influence of flow velocity, confinement and structural stiffness on the existence of absolutely unstable waves in inviscid hydroelastic systems. © 2002 Published by Elsevier Science Ltd.