** Abstract: **

###
Whittaker, R.J., Heil, M., Jensen, O.E., & Waters, S.L.
(2009) The onset of high-frequency self-excited
oscillations in elastic-walled tubes.
*Proceedings of the Royal Society A* (submitted)

We present a theoretical description of flow-induced self-excited
oscillations in the Starling resistor, a pre-stretched thin-walled
elastic tube that is mounted on two rigid tubes and enclosed in a
pressure chamber. Assuming that the flow through the elastic tube
is driven by imposing the flow rate at the downstream end, we study
the development of small-amplitude long-wavelength high-frequency
oscillations, combining the results of two previous studies in
which we analysed the fluid and solid mechanics of the problem in
isolation. We derive a one-dimensional eigenvalue problem for the
frequencies and mode shapes of the oscillations, and determine
the slow growth or decay of the normal modes by considering the
system's energy budget. We compare the theoretical predictions
for the mode shapes, frequencies and growth rates with the results
of direct numerical simulations, based on the solution of the
three-dimensional Navier-Stokes equations, coupled to the equations
of shell theory, and find good agreement between the results.
Our results provide the first asymptotic predictions for the
onset of self-excited oscillations in three-dimensional
collapsible tube flows.

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