The dynamics of cantilevered structures subject to axial flow

The dynamics of slender cantilevered cylinders subjected to internal or external axial flow has been studied extensively from the 1960s onwards. In the early studies, the flow was directed from the clamped end towards the free end of the cantilever. The same is true for cantilevered plates (or "flags") in axial flow. More recently, however, the dynamics in reverse axial flow, i.e., flow directed from the free towards the clamped end, has received attention, partly as curiosity-driven research, but also because of engineering applications. For example, cantilevered pipes aspirating fluid are used in ocean mining, cantilevered cylinders in reverse axial flow may be found as control rods in nuclear reactors, and cantilevered plates in reverse axial flow are a candidate system for energy harvesting. The present paper provides a summary of the dynamics of these systems in conventional and reverse axial flow and compares their dynamical behaviour. For example, cantilevered cylinders in conventional axial flow are subject to a weak static divergence (buckling) at sufficiently high flow velocities, and to vigorous flutter at higher flow velocities. Cylinders in reverse axial flow, on the other hand, are subject to weak flutter at low flow velocities and to a large amplitude static divergence at higher flows. In the first case the dynamics is sensitive to the shape of the free end, and in the second hardly at all. The differences in the dynamical behaviour in reverse flow vis-à-vis conventional flow for pipes and plates, not so neatly reversed as for cylinders, are also discussed, and some general conclusions drawn for all three systems, regarding similarities and differences in the dynamics and sensitivity to free-end shape arising from the direction of fluid flow.