Abstract
This paper presents a stability analysis and exciting mechanism of coupled vibration of translation and rotation of a plate supported by air pressure. In stability analysis, the basic equation of fluid flow and the equation of motion of the plate are separated into the steady-state equation and the unsteady-state equation by the perturbation method. The unsteady-state equations are then Laplace transformed, and the steady-state terms obtained by solving the steady-state equations are substituted. The Laplace transformed equations are rearranged to obtain the characteristic equations for the vibration of the plate. The vibration characteristics and unstable condition of the self-excited vibration of the plate are calculated using the characteristic equations. The stability of the plate is affected by the air flow rate, the mass of the plate, the volume of chamber supplying air. we clarified those influences on the instability conditions of the self-excited vibration. 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 exciting mechanism of translational and rotational vibration is discussed.
