Mode Shape Variation for a Low-Mode Number Flexible Cylinder Subject to Vortex-Induced Vibrations

The excitation of two low-mode number, flexible cylinders in uniform-flow is investigated to determine effects of structural mode shape on vortex-induced vibrations. Experiments are performed in a re-circulating flow channel and in a small flow visualization tank using object tracking and digital particle image velocimetry (DPIV) to measure the excitation of the cylinder, to estimate forces acting on the structure, and to observe the wake of the structure under the observed body motions. Previous research has focused on understanding the effect of in-line to cross-flow natural frequency ratio on the excitation of the structure in an attempt to model the excitation of multiple structural modes on long, flexible bodies. The current research investigates the impact of structural mode shape on this relationship by holding the in-line to cross-flow natural frequency constant and attempting to excite a specific structural mode shape. It is found that the combination of an odd mode shape excited in the cross-flow direction with an even mode shape in the in-line direction results in an incompatible synchronization condition, where the dominant forcing frequency in-line may experience a frequency equal to the cross-flow forcing frequency, a condition only observed in rigid cylinder experiments when the natural frequency ratio is less than one. This is consistent with the first mode being excited in both in-line and cross-flow directions, however this leads to an asymmetric wake. The wake is observed using DPIV on a rigid cylinder with forced motions equivalent to the flexible body. A case of mode switching is also observed where the even in-line mode exhibits an excitation at twice the cross-flow frequency; however the spatial mode shape in-line appears similar to the first structural mode shape. It is hypothesized that this situation is possible due to variation in the effective added mass along the length of the cylinder.