The nonlinear behaviour of a slender flexible cylinder pinned or clamped at both ends and subjected to axial flow

摘要

The nonlinear dynamics of a slender flexible cylinder subjected to axial flow is studied when both its ends are either pinned or clamped, particularly focusing on the post-critical behaviour. In both cases, the system is stable at low flow velocities until the critical flow for divergence, at which point the initial equilibrium position of the cylinder becomes unstable and a new stable buckled solution arises (together with its symmetric counterpart). The amplitude of the buckled solution increases with the flow velocity. At higher flow, the buckled stationary cylinder loses stability by a Hopf bifurcation, after which a periodic solution arises. The frequency of oscillation after this Hopf bifurcation, in the case of a pinned-pinned cylinder, is almost twice as high as that in the clamped-clamped case, due to the dynamic loss of stability in a higher mode in the former case. The periodic solution is followed by a period-doubling bifurcation, giving rise to period-2 oscillations. The system undergoes a torus bifurcation afterward, followed by quasiperiodic and chaotic oscillations at higher flow velocities. All the critical flow velocities for the pinned-pinned cylinder are smaller than those for the clamped-clamped one. In the case of a pinned-pinned cylinder, at still higher flow velocities, there exists a range of flow velocities in which chaotic and static solutions co-exist; this has not been observed in the clamped-clamped case.