Analytical solution for a vibrating simply-supported cylinder subjected to 2-D concentric annular flow, considering friction

An analytical model of annular-flow-induced vibration of a pinned–pinned cylinder is proposed. The model is based on three main assumptions: (i) small perturbations in flow components, (ii) negligible radial flow to reduce the annular flow to two-dimensional flow, and axial flow only for reduction to a one-dimensional flow, and (iii) perturbation frictional loss depending on the variation of axial perturbation velocity in terms of space and time. In this study, it is concluded that (a) the difference in fluidelastic forces between two- and one-dimensional flow models mostly depends on cylinder radius, and on whether perturbation flow is mainly allowed in the axial or circumferential direction, (b) the one-dimensional flow model should be limited to 1-d.o.f. vibration analysis or the case of a cylinder having a large radius-to-length ratio, and (c) the perturbation assumption has little effect on the dynamics of annular-flow-induced vibrations; however, the critical flow velocity is diminished considerably. Finally, preliminary results suggest that fluid friction may significantly modify the predicted model dynamics.