Dynamics of Slender Tapered Beams With Internal or External Axial Flow—Part 1: Theory

This paper develops a general theory for the dynamics of slender, nonuniform axisymmetric beams subjected to either internal or external flow, or to both simultaneously. The effect of the boundary layer of the external flow is taken into account in the formulation. Typical solutions of the equations of motion are presented for cantilevered conical beams in external flow and for beams with a conical internal flow passage. Such systems lose stability at sufficiently high flow velocity, internal or external, either by flutter or by buckling. The effect of several parameters is investigated. For internal flow, the internal and external shape, whether uniform or conical, and the density of the surrounding fluid have sometimes unexpected effects on stability; e.g., tubular beams lose stability at lower internal flow when immersed in water than when in air. For external flow the effects of conicity, free end shape and boundary-layer thickness are investigated; the latter has a strong stabilizing influence, such that simple theory neglecting this effect results in serious error.