Detailed mechanism of self-excited vibration of a plate supported by air pressure

Abstract

This study presents a dynamic stability analysis of the self-excited vibration of a plate supported by air pressure. In the analysis, the unsteady fluid force acting on the plate surface is calculated based on the theory of two-dimensional leakage flow. The model built in the dynamic stability analysis applies iterative calculation using a numerical solution to determine the floating displacement of the plate, its steady state, and the pressure and rate of air that flow through the bottom of the plate. This model demonstrates the dynamic stability of the plate when it vibrates close to the steady state. In addition, the local work done by the unsteady fluid force acting on the plate (bottom surface) is calculated, and the region on which the excitation fluid force acts is examined. Furthermore, the fluid force acting on the plate is separated into factors such as compressibility and viscosity. This is necessary for analyzing the effect of the work done by the fluid force derived from these factors on the dynamic stability of the system. The results reveal a critical factor for the occurrence of self-excited vibration; additionally, the detailed instability mechanism of the self-excited vibration is discussed.

Keywords

• self-excited vibration
• plate
• dynamic stability analysis
• instability mechanism
• unsteady fluid force