Abstract
Leakage-flow-induced vibrations were examined using linear stability analysis in the case of a one-dimensional narrow parallel passage in which a plate could vibrate in beam mode. It was found that unlike the case of the single-degree-of-freedom system, instability could occur for the parallel passage in a continuous system. Destabilizing mechanisms were considered by deriving a wave equation of plate displacement, and the characteristics of the waves were examined. The wave equation was expressed using first- and second-order wave equations, and a beam equation. The energy supplied to the wave components of the vibration mode and the dispersion relation was examined. It was found that the wave expressed by the first-order wave equation, which was derived from the dissipation term of the leakage flow, could act as a negative damping force to the wave on the plate propagating forward when the wave speed of the first-order wave equation was greater than that of the plate vibration. The mechanism was greatly different from that of the single-degree-of-freedom system where the delay due to fluid inertia could induce unstable vibration.
