Dynamic Stability of a Plate Supported by Air Pressure(Influence of shape and placement of air supplying parts on occurrence condition of a self-excited vibration)

Abstract

This paper presents a dynamic stability analysis and experiments of a plate supported by air pressure. In the analysis, the steady-state such as flow distribution of the air supplied from slits or holes, a floating gap of the plate, pressure and air density in the gap under the plate are calculated by a floating analysis (steady-state analysis) based on the theory of two-dimensional leakage-flow. Then, unstable condition of a self-excited vibration of the plate is calculated by the dynamic stability analysis (unsteady-state analysis) when the plate vibrates around the steady-state. The basic equation of leakage-flow considers the effect of air compressibility. The equation of continuous air flow in the chamber includes the effect of air compressibility. The experimental setup comprised a plate supported by the pressure of air supplied from slits or holes on the upper surface of the chamber, where the vibration characteristics are examined. Finally, the local work done by the unsteady fluid force acting on the plate (bottom surface) is presented, and the instability mechanism of the self-excited vibration is discussed.