Flow-induced vibration in a collapsible tube is relevant to many biomedical applications including human respiratory system. This paper presents a linear analysis of the coupling between a parallel, viscous, incompressible flow and a tensioned membrane of finite length using an eigen-value approach, followed by an energy conservation analysis similar to the acoustic energy flux analysis for sound propagation in a mean flow. Particular attention is paid to the relationship between the fluid-to- structure energy transfer with the various terms in the second order equation. It is shown that terms directly proportional to the fluid viscosity contribute most to the production of fluctuation energy, leading to a special type of dynamic instability which resembles both Tollmien Schlitchting instability in the sense that the fluid viscosity destabilizes, and traditional travelling wave flutter since the structural damping plays the role of stabilisation.
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