Characteristics of a self-excited vibration of a plate supported by air pressure (Influence of chamber volume and slit width on occurrence conditions of the self-excited vibration)

Abstract

This paper presents experiments and an analysis of the self-excited vibration of a plate supported by air pressure. In the analysis, the unsteady fluid force acting on the plate is calculated based on the basic equation of a two-dimensional gap flow between the plate and a chamber surface. The basic equation considers the effect of air compressibility in the chamber. The characteristic equation of the system is derived from the plate motion coupled with the unsteady fluid force acting on the plate. The instability condition and vibration frequency are predicted through the root locus of the system with changing air flow rate supplied to the chamber. The experiment consists of a plate supported by the air pressure supplied from a slit on the upper surface of the chamber, where the vibration characteristics are examined. The influence of the slit width and chamber volume on the instability condition of the self-excited vibration is clarified comparing the analytical result with experiments. Moreover, the local work done by the unsteady fluid force acting on the plate (bottom surface) is shown in this paper, and the instability mechanism is discussed. Lastly, the influence of slit width on the unsteady fluid force is addressed by the block diagram showing the phase relationship of pressure fluctuation and plate displacement.