Stability of fluid flow in the presence of a compliant surface

This paper is concerned with the dynamic behaviour of a thin elastic plate in the presence of flow. The plate is excited by a time varying force applied on a line which is at right angles to the direction of flow. Causality is invoked to make the solution unique. It is found that the system responds differently for flow speeds above and below a critical value. Above this value, a temporal instability occurs and the amplitude of the motion grows with time at each point on the plate. Below this value there are travelling waves upstream of the driver, whilst downstream the behaviour is dominated by a disturbance which does not grow with time at any one position, but nevertheless grows as it is convected downstream. This type of instability is less severe than the temperal one and is of the type generally referred to as convective.