Unstable Phenomena of a Thin Cylindrical Shell Subjected to Axial Leakage Flow

Abstract

The unstable phenomena of a thin cylindrical shell subjected to an axial leakage flow are investigated in this paper. The analytical model is composed of an elastic shell and a rigid one which are arranged co-axially. Considering the fluid structure interaction between a shell and a fluid flowing through a narrow passage, the coupled equation of motion between a shell and a flowing fluid is derived using the Donnell’s shell theory and the Navier-Stokes equation. Focusing on the vibrational characteristics of a thin cylindrical shell, that is, the axisymmetric (ring-like) vibration, the lateral (beam-like) vibration and the circumferential (ovaling) vibration, the unstable phenomena of a thin cylindrical shell are clarified by using the root locus (Argand diagram) based on the complex eigenvalue analysis. The critical fluid velocities for the divergence and flutter phenomena of a thin cylindrical shell subjected to an axial leakage flow are analyzed and defined. Moreover, comparing with the uncoupled vibration modes, namely dry modes, the coupled vibration modes between a shell and a flowing fluid, namely wet modes, are shown to be considerably changed between before and after the unstable phenomena. The numerical parameter studies on the shell with both simply-supported ends are performed taking the dimensions of a shell, the characteristics of a flowing fluid and the clearance of an annular gap between an elastic and a rigid shells as parameters. The influences of these parameters on the threshold of the instability of the coupled vibration between a shell and a flowing fluid are investigated and discussed.