Axial leakage flow-induced vibration of a thin cylindrical shell with respect to axisymmetric vibration

In this paper, the stability of a thin cylindrical shell subjected to axial leakage flow is discussed. In this paper the first part of a study of the axial leakage flow-induced vibration of a thin cylindrical shell, we focus on axisymmetric vibration, that is, the ringlike 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 added mass, added damping and added stiffness matrices in the coupled equations are described by utilizing unsteady fluid,forces on a shell. The influence of the axial flow velocity on the unstable phenomena is clarified concerning axisymmetric vibration mode of shell. The numerical calculations ore performed taking the dimensions of shell and fluid as parameters.