Interaction between a cantilevered-free flexible plate and ideal flow

We develop a new computational model of the linear fluid–structure interaction of a cantilevered flexible plate with an ideal flow in a channel. The system equation is solved via numerical simulations that capture transients and allow the spatial variation of the flow–structure interaction on the plate to be studied in detail. Alternatively, but neglecting wake effects, we are able to extract directly the system eigenvalues to make global predictions of the system behaviour in the infinite-time limit. We use these complementary approaches to conduct a detailed study of the fluid–structure system. When the channel walls are effectively absent, predictions of the critical velocity show good agreement with those of other published work. We elucidate the single-mode flutter mechanism that dominates the response of short plates and show that the principal region of irreversible energy transfer from fluid to structure occurs over the middle portion of the plate. A different mechanism, modal-coalescence flutter, is shown to cause the destabilisation of long plates with its energy transfer occurring closer to the trailing edge of the plate. This mechanism is shown to allow a continuous change to higher-order modes of instability as the plate length is increased. We then show how the system response is modified by the inclusion of channel walls placed symmetrically above and below the flexible plate, the effect of unsteady vorticity shed at the trailing edge of the plate, and the effect of a rigid surface placed upstream of the flexible plate. Finally, we apply the modelling techniques in a brief study of upper-airway dynamics wherein soft-palate flutter is considered to be the source of snoring noises. In doing so, we show how a time-varying mean flow influences the type of instability observed as flow speed is increased and demonstrate how localised stiffening can be used to control instability of the flexible plate.