A nonlinear model for a free-clamped cylinder subjected to confined axial flow

In this paper a full nonlinear model1 is presented for the dynamics of a cantilevered cylinder, terminated by an ogival free end, and subjected to confined, inverted axial flow. This system is also known as “a free-clamped cylinder in axial flow”, since the flow is directed from the free end towards the clamped one. All the fluid-related forces and the gravity-related terms are derived separately to third-order accuracy; the inviscid forces are modelled using an extension of Lighthill's slender-body analysis to the same accuracy, and the viscous forces are obtained semi-empirically. The boundary conditions related to the free end are also derived separately, to first-order accuracy, and added to the model. The final equation of motion is obtained via Hamilton's principle, then discretized and solved numerically using AUTO and MATLAB software. The stability of the system is investigated by means of bifurcation diagrams, time histories, phase-plane and power-spectral-density plots, and the dynamical behaviour is compared to theoretical predictions and experimental observations, from the literature, for systems that have the same parameters. The theory is in good qualitative agreement with the experiments, and also good quantitative agreement in terms of the critical flow velocity of instability.