Mode exchange and unstable modes in the dynamics of conical pipes conveying fluid

Abstract

When the velocity of fluid flow in a slender pipe, fixed at the upstream end and free at the other, is increased beyond a certain critical value, the system may become unstable by flutter. This paper is concerned with exploring the unstable modes and mode exchange in the dynamics of a conical pipe conveying fluid. Compared with uniform pipes conveying fluid, the equation of motion of conical pipes conveying fluid has several terms as functions of the axial coordinate, thus yielding more complexity. It is shown that, when the taper angle of the conical pipe is varied in an actual range, the system becomes subject to flutter instability at certain flow velocities. For mass ratio equal to 0.433, flutter does not always first occur in the third mode of the system. With successively increasing values of the taper angle, the transference of flutter instability from one mode to another has been detected. Thus, flutter instability may also first occur in the second or first mode, strongly depending on the value of the taper angle.