Mono- and multi-frequency vortex-induced vibrations of a long tensioned beam in shear flow

The mono-frequency as well as multi-frequency vortex-induced vibrations of a tensioned beam of aspect ratio 200, immersed in a linear shear flow at Reynolds number 330 and free to move in both the in-line and cross-flow directions, are studied by means of direct numerical simulation. The structural responses are composed of mixed standing-traveling wave patterns. We observe a switch between mono- and multi-frequency vibrations when the mass ratio changes from a value of 3 to 6, while keeping constant the non-dimensional cable and beam phase velocities. This switch is attributed to the accompanying change in the time-averaged in-line curvature of the beam, which alters the oncoming flow velocity component normal to the structure configuration. It is shown, in general, that the mono- or multi-frequency nature of the response is controlled by the form of the profile of the normal component of the oncoming flow. Mono- and multi-frequency vibrations may occur in both the in-line and cross-flow directions, with a frequency ratio close to 2. Each excited frequency is associated with a single structural wavenumber. The local synchronization between the vortex shedding and the cross-flow oscillation, i.e. the lock-in condition, occurs in the high velocity zone and covers a similar spanwise extent in both the mono- and multi-frequency cases. Counter-clockwise figure-eight trajectories are very likely to occur within the lock-in region. In both the mono- and multi-frequency types of response, the flow excites the structural vibrations within the lock-in region and damps the structural motions in the non-lock-in region. The multi-frequency character of the response impacts both the lock-in phenomenon and the fluid-structure energy transfer.