Axial Leakage Flow-induced Vibration of a Thin Cylindrical Sheel with Respect to Lateral Vibration by Donnell Shell Theory

In this paper, the stability of a thin cylindrical sheel subjected to an axial leakage flow is discussed. Here, we focus on a lateral vibration of a cylindrical shell, that is the beam-like vibration of a shell. The coupled equations between a shell and a fluid are obtained by using the Donnell's shell theory and the Navier Stokes equation. The influence of the axial velocity on the unstable vibration phenomena is clarified concerning the beam-like vibration mode of a shell. The applicable range of Donnel shell theorry is confirmed for axial leakage flow-induced vibration of a thin cylindrical shell. The numerical results on the shell theory are compared with those on beam theory which have been already reported by the authors. And, the numerical parameter studies are done for several dimensions of shell and fluid.