Leakage-flow-induced vibration of an elastic plate with steady deformation

Abstract

In fluid equipment, self-excited vibration may occur in components exposed to gap flow. Furthermore, in the case of a thin plate component for switching the flow path, steady deformation may also occur and change the gap height. The present paper analyzes a leakage-flow-induced vibration on such an elastic plate with steady deformation. The upper surface of the plate is exposed to the inlet pressure, and the lower surface partially faces a gap connecting the inlet and outlet fields. First, an experiment for this thin plate is conducted to observe the change in the gap height and the occurrence of vibration with respect to the inlet pressure. The initial gap height is varied to investigate its effect on the occurrence of vibration. Second, with a view to understanding the mechanism of the vibration occurrence, a theoretical analysis method is presented. The plate deformation is expanded in eigenmodes, and the gap is discretized in the cross direction to apply the theory for one-dimensional gaps. The solution for steady deformation is then subjected to a dynamic stability analysis. In the experiment, the vibration occurs when the inlet pressure is increased and the gap height becomes small, and the vibration disappears before the plate contacts the opposing body and the gap closes. The plate escapes the vibration in cases in which the initial gap height is small. The unsteady pressure obtained by the theory indicates that, as the inlet pressure increases, the phase of the unsteady pressure once experiences the excitation side and reverses to the damping side before the gap closes. In a small initial gap height, the amplitude of the unsteady pressure remains small until the phase reverses, allowing the plate to escape the vibration.