A Study on Leakage-Flow-Induced Vibrations of a Flexible Structure : A Stability Analysis of One Dimensional Flexible Plate and A Consideration of Self-Excited Oscillation Machanisms

Abstract

Leakage-flow-induced vibration was discussed for a one-dimensional, narrow, parallel passage in which a plate could vibrate in beam modes. A wave equation of plate displacement composed of first and second order wave equations, and a beam equation was derived. A method to estimate the linear stability of the plate was proposed, in which a spatial integration of the equations was done using the Runge-Kutta algorithm, and eigenvalues and eigenmodes were estimated to satisfy boundary conditions. The dispersion relation was investigated to clarify the basic characteristics of the waves. The mode was decomposed into six wave components, and the energy supplied to the wave components by the fluid force was estimated. It was suggested that there were at least two mechanisms. One was the phenomenon similar to interfacial instability of the thin liquid film flow. The other was the phenomenon that progressive wave on the plate was destabilized by the wave component expressed by a first order wave equation when the wave speed of the first order wave equation was faster than the wave speed on the plate.