Dynamic stability analysis of a plate supported by air pressure based on the theory of two-dimensional leakage-flow and experiments (Occurrence of a self-excited vibration when the number of supply slits is one and two)

Abstract

This paper presents a dynamic stability analysis of a plate supported by air pressure and experiments conducted using one and two supply slits. In the analysis, the steady-state such as flow distribution of the air supplied from the slits, 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 vibration characteristics and unstable condition of the self-excited vibration of the plate are calculated using the characteristic equation for the system. The experimental setup comprised a plate supported by the pressure of air supplied from one or two supply slits on the upper surface of the chamber, where the vibration characteristics are examined. The occurrence of the self-excited vibration is clarified by comparing the analysis and experiments. 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.