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Wave Motion 33 (2001) 723 On transient oscillations of plates in moving fluids
 

Summary: Wave Motion 33 (2001) 723
On transient oscillations of plates in moving fluids
I. David Abrahamsa,, Gerry R. Wickhamb
a Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
b Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, UK
Received 20 February 1999; accepted 14 January 2000
Abstract
In recent years, various groups of researchers have looked at the two-dimensional motions of an undamped infinite thin
elastic plate lying under a uniformly moving incompressible inviscid fluid. The plate is driven, usually by a single frequency
time-harmonic line-source switched on at a finite time. The system's behaviour is interesting as it can be shown to be absolutely
unstable for flow velocities above a critical value, and below this the long-time solution is convectively unstable (downstream
of the source) for a sufficiently low forcing frequency. These results do not appear particularly plausible from a physical
point of view, and there is some question regarding the realisation of long-time steady behaviour, and so this article attempts
to examine ways in which the model problem can be improved. In particular, the effects of introducing plate thickness and
fluid compressibility to the model are studied. This is carried out by comparing the morphology of the original and modified
solutions in the complex wavenumber space. It is found that, in the limit of small fluid-to-plate density ratio, the two problems
exhibit qualitatively identical behaviour. However, the addition of structural damping is shown herein to lead to a very different
solution the initial boundary value problem is absolutely unstable at all flow velocities. Various other modifications to the
original model, including finiteness of the plate, three-dimensional effects and nonlinearity, are discussed and their impact on
the long-time response of the system is assessed. 2001 Elsevier Science B.V. All rights reserved.

  

Source: Abrahams, I. David - Department of Mathematics, University of Manchester

 

Collections: Mathematics