Abstract
The evolution methodologies for the flow-induced vibration instability of a long flexible beam due to the axial leakage-flow are reported. In this paper we deal with the rod as a continuous flexible body. The relation between the axial velocity and the unstable phenomena are clarified. Concerning the critical flow velocity, the root locus (Argand diagram) is shown. And we considered coupled mode. As a result, we have our results of mode ratio trend (uncoupled mode). They are compared with the experimental results.