Orbiting response in vortex-induced vibrations of a two-degree-of-freedom pivoted circular cylinder

Vortex-induced vibrations of a pivoted, rigid, circular cylinder were investigated experimentally. A cylinder with a mass ratio of 15.9 and a moment of inertia ratio of 66.8 was investigated at a constant Reynolds number of 2100 for a range of reduced velocities, 3.4≤U⁎≤11.3, and damping ratios, 0.4%≤ζ≤1.1%. A novel experimental set-up was designed to reproduce the orbiting response observed in some engineering applications involving vortex induced vibrations of cylindrical structures. The results show that, in the synchronization region, the frequencies of transverse and streamwise vibrations lock onto the natural frequency of the structure, and the cylinder traces elliptic trajectories. A mathematical model is introduced to investigate the mechanism responsible for the occurrence of the elliptic trajectories or the figure-8 type trajectories observed in previous laboratory studies. The results show that the occurrence of either elliptic or figure-8 type trajectory is governed primarily by structural coupling between vibrations in streamwise and transverse directions. Based on the experimental results, four distinct types of orbiting motion are identified in the synchronization region. Each of these four types corresponds to a specific range of phase angles between the streamwise and transverse vibrations defining the orientation of the trajectory and the direction of orbiting. The results indicate that the identified four types of elliptic trajectories are associated with four distinct ranges of a dimensionless parameter used to quantify structural coupling.