Out-of-Plane Vibration and Stability of Curved Tubes Conveying Fluid

Abstract

A general theory is presented to account for the out-of-plane motion of uniformly curved tubes containing flowing fluid. The systems are grouped as conservative and nonconservative according to the support conditions. A general solution for the natural frequency is obtained and numerical results are presented. The effects of the flow velocity and Coriolis force on the natural frequency are discussed. It is shown that when the flow velocity exceeds a certain value, the tube becomes subject to the buckling-type instability for conservative cases and the fluttering-type instability for nonconservative cases. In the subcritical range of flow velocity, the conservative system performs free oscillations, while the nonconservative system performs damped oscillations.