Two-degree-of-freedom vortex-induced vibration of a pivoted cylinder below critical mass ratio

In this study, we investigated two-degree-of-freedom (2d.f.) vortex-induced vibrations (VIVs) of a circular cylinder with a pinned attachment at its base; it had identical mass ratios and natural frequencies in both streamwise and transverse directions. The cylinder had a mass ratio, m(*) of 0.45, and a mass damping, (m(*) + C-A)zeta, equal to 0.0841. Laser-induced. uorescence flow visualization and digital particle image velocimetry experiments were conducted over a Reynolds number range, 820 <= Re <= 6050 (corresponding to the reduced velocity range, 1.1 <= U-* <= 8.3). Measurements and visualization studies were made in a fixed plane at the cylinder mid-height, providing a two-dimensional picture of a highly three-dimensional system. However, significant insights can be gained from these experiments and form the basis of this paper. A large transverse amplitude response, A(Y)(*) similar to 2 (or four diameters peak-to-peak), in the upper branch was observed. The streamwise amplitude response exhibits an even higher peak amplitude, A(X)(*) similar to 2.5, which is approximately 125% of peak A(Y)(*). Results show that there is no lower branch for this system and the transverse upper branch exhibits asymptotic behaviour, i.e. a wide regime of resonance. For Re > 3000, the Strouhal number for the vortex shedding was 0.16 (+/- 9%). Both the transverse cylinder oscillation and vortex-shedding frequencies, f(OS),(Y) and f(VS), respectively, were virtually identical throughout this range. While the streamwise oscillation frequency is typically twice the transverse oscillation frequency for a 2d.f. system, this is not the case at the lowest reduced velocities where oscillations first occur. Under these conditions the streamwise and transverse oscillation frequencies were identical. Finally, we observed that the cylinder wake exhibits both the PCS vortex-shedding mode and a desynchronized vortex pattern, which are uncommon for flow past a cylinder experiment. Very interestingly, the wide U-* range over which resonance occurs is dominated by a desynchronized vortex pattern. These results clearly demonstrate the differences that arise in 2d.f. VIV occurring below the critical mass ratio.