In Part 1 a general theory is presented to account for the small, free, lateral motions of a vertical, uniform, tubular cantilever conveying fluid, with the free end being either below the clamped one (‘hanging’ cantilever) or above it (‘standing’ cantilever). Gravity forces are not considered to be negligible. It is shown that, when the velocity of the fluid exceeds a certain value, the cantilever in all cases becomes subject to oscillatory instability. In the case of hanging cantilevers buckling instability does not occur. Standing cantilevers, on the other hand, may buckle under their own weight; it is shown that in some cases flow (within a certain range of flow velocities) may render stable a system which would buckle in the absence of flow. Extensive complex frequency calculations were conducted to illuminate the dynamical behaviour of the system with increasing flow. The conditions of stability have also been extensively calculated and stability maps constructed. It is shown that dissipative forces may have either a stabilizing or a destabilizing effect on the system, partly depending on the magnitude of these forces themselves. The experiments described in Part 2 were designed to illustrate the dynamical behaviour of vertical tubular cantilevers conveying fluid. The experiments were conducted with rubber tubes conveying either water or air. The tubes were either hanging down or standing upright. It was observed that for sufficiently high flow velocities both hanging and standing cantilevers become subject to oscillatory instability. It was also observed that standing cantilevers which would buckle under their own weight in the absence of flow, in some cases are rendered stable by flow within a certain range of flow velocities. Qualitative and quantitative agreement between theory and experiment was satisfactorily good.
Analytic Stability Maps of Unknown Exoplanet Companions for Imaging Prioritization
