Role of cross-flow vibrations in the flow-induced rotations of an elastically mounted cylinder-plate system

Vibration and rotation represent two common fluid-structure-interaction phenomena, which can occur independently or concurrently. While extensive research has been conducted on individual vibration/rotation cases, there is relatively limited literature on coupled cases. However, it is crucial to recognize that coupled responses, such as those observed in falling leaves, are more prevalent in both natural occurrences and engineering scenarios. Hence, this study aims to investigate the influence of cross-flow vibrations on the flow-induced rotations of an elastically mounted cylinder-plate system. A broad range of rotational reduced velocities, spanning U _θ = 2-18, is examined across four distinct vibrational reduced velocities, namely U _y = 5, 8, 12, and 18. Numerical results indicated that a bifurcation phenomenon, wherein the cylinder-plate deflects to a non-zero equilibrium position, occurs at relatively high values of U _θ and U _y. Four distinct response modes have been identified: vibration-dominated, rotation-dominated, augmentation (VIV-like), and augmentation (galloping-like) mode. These response modes exert significant influence on phase angles between rotary angle and displacement as well as vortex shedding modes. In the rotation-dominated region, VIV-like region, and galloping-like region, phase angles exhibit a continuous decreasing trend, a consistent level of 180° and 90°, respectively. Transitions between vibration and rotation responses result in sharp increases in phase angles. The wake flow in the rotation-dominated mode and VIV-like mode demonstrates a 2S mode (two single vortices), while the vibration-dominated mode is characterized by a predominant 2T mode (two triplets of vortices). In the galloping-like region, large amplitudes lead to the increase in numbers of vortices, presenting 2S, 2S ^*, and 2P (two pairs of vortices) mode at U _y = 8, and 2P, P + S (one pair and one single vortices) and 2P+S (two pairs and one single vortices) mode at U _y = 12, where the 2S ^* mode consists of two single vortices, each exhibiting a tendency to split into two smaller vortices as they migrate downward. The mechanism behind the notable amplification of rotation/vibration responses is elucidated. Apart from the pressure difference induced by vortex shedding, the additional driving force resulting from relative motion in the transverse direction contributes to the total torsional force, thereby leading to significant rotary responses. Furthermore, the streamlined profile accounts for the escalation in vibration amplitudes.