Flutter of cantilevered plates in axial flow

Abstract

Flow over an elastic plate is chosen to model the mechanics of the soft palate during oronasal snoring. The stability of the plate is investigated through an initial value problem. Theodorsen's classical solution is employed for the fluid loading. Viscosity is explicitly excluded, but its effect is embedded in the Kutta-Zhukovskii condition. Linear analysis is adopted because the interest lies mainly in the initial stage of instability. A predictor-corrector numerical method is developed to simulate the transient process, leading to the long-term periodic behaviour. The essential snoring mechanism is flutter. Energetics studies show that the part of fluid loading arising from the reaction of wake vortices always supplies the power while the pressure variation arising from the surface motion dissipates it. Wind tunnel experiments were carried out and found to agree with the theory both qualitatively and quantitatively. Our conclusion that the stability boundary can be extended by stiffening the plate has contributed to a new, simple and successful surgical procedure for curing snoring.