Axial leakage flow-induced vibration of the elastic rod as the axisymmetric continuous flexible beam

The evaluation methodologies for the flow-induced vibration instability of a long flexible rod due to axial leakage-flow are reported. In the previous papers, the axisymmetric rods are regarded as rigid bodies, not as continuous bodies. In this paper, we deal with the rod as a continuous flexible body. The equations for the fluid and the structure are coupled analytically and the added mass, added damping, and added stiffness are derived by considering unsteady pressure acting on the rod. The relation between the axial velocity and the unstable phenomena is clarified Concerning the critical flow velocity, the root locus (Argand diagram) is shown. We compared our results with the experimental results which one of the authors reported before.