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 abeam 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. It was suggested that the leakage-flow-induced vibration of continuous system be similar to the Oil whip of the journal bearing.
