This study investigates the free transverse flow-induced vibration (FIV) of an elastically mounted low-mass-ratio square cylinder in a free stream, at three different incidence angles: ${{\alpha }}=0^\circ $ , $20^\circ $ and $45^\circ $ . This geometric setup presents a body with an angle of attack, sharp corners and some afterbody, and therefore is a generic body that can be used to investigate a wide range of FIV phenomena. A recent study by Nemes et al. (J. Fluid Mech., vol. 710, 2012, pp. 102–130) provided a broad overview of the flow regimes present as a function of both the angle of attack ${{\alpha }}$ and reduced flow velocity ${U^{*}}$ . Here, the focus is on the three aforementioned representative angles of attack: ${{\alpha }}=0^\circ $ , where the FIV is dominated by transverse galloping; ${{\alpha }}=45^\circ $ , where the FIV is dominated by vortex-induced vibration (VIV); and an intermediate value of ${{\alpha }}=20^\circ $ , where the underlying FIV phenomenon has previously been difficult to determine. For the ${{\alpha }}=0^\circ $ case, the amplitude of oscillation increases linearly with the flow speed except for a series of regimes that occur when the vortex shedding frequency is in the vicinity of an odd-integer multiple of the galloping oscillation frequency, and the vortex shedding synchronizes to this multiple of the oscillation frequency. It is shown that only odd-integer multiple synchronizations should occur. These synchronizations explain the ‘kinks’ in the galloping amplitude response for light bodies first observed by Bearman et al. (J. Fluids Struct., vol. 1, 1987, pp. 19–34). For the ${{\alpha }}=45^\circ $ case, the VIV response consists of a number of subtle, but distinctly different regimes, with five regimes of high-amplitude oscillations, compared to two found in the classic VIV studies of a circular cylinder. For the intermediate ${{\alpha }}=20^\circ $ case, a typical VIV ‘upper branch’ occurs followed by a ‘higher branch’ of very large-amplitude response. The higher branch is caused by a subharmonic synchronization between the vortex shedding and the body oscillation frequency, where two cycles of vortex shedding occur over one cycle of oscillation. It appears that this subharmonic synchronization is a direct result of the asymmetric body. Overall, the FIV of the square cylinder is shown to be very rich, with a number of distinct regimes, controlled by both ${{\alpha }}$ and ${U^{*}}$ . Importantly, ${{\alpha }}$ controls the underlying FIV phenomenon, as well as controlling the types of possible synchronization between the oscillation and vortex shedding.

This study examines the influence of angle of attack of a square section cylinder on the cylinder’s flow-induced vibration, where the direction of the vibration is transverse to the oncoming flow. Our experiments, which traversed the velocity–angle of attack parameter space in considerable breadth and depth, show that a low-mass ratio body can undergo combinations of both vortex-induced vibration and galloping. When the body has an angle of attack that makes it symmetric to the flow, such as when it assumes the square or diamond orientation, the two mechanisms remain independent. However, when symmetry is lost we find a mixed mode response with a new branch of vortex-induced oscillations that exceeds the amplitudes resulting from the two phenomena independently. The oscillations of this higher branch have amplitudes larger than the ‘upper branch’ of vortex-induced vibrations and at half the frequency. For velocities above this resonant region, the frequency splits into two diverging branches. Analysis of the amplitude response reveals that the transition between galloping and vortex-induced vibrations occurs over a narrow range of angle of incidence. Despite the rich set of states found in the parameter space the vortex shedding modes remain very similar to those found previously in vortex-induced vibration.

While it has been known that an afterbody (i.e. the structural part of a bluff body downstream of the flow separation points) plays an important role affecting the wake characteristics and even may change the nature of the flow-induced vibration (FIV) of a structure, the question of whether an afterbody is essential for the occurrence of one particular common form of FIV, namely vortex-induced vibration (VIV), still remains. This has motivated the present study to experimentally investigate the FIV of an elastically mounted forward- or backward-facing D-section (closed semicircular) cylinder over the reduced velocity range $2.3\leqslant U^{\ast }\leqslant 20$ , where $U^{\ast }=U/(f_{nw}D)$ . Here, $U$ is the free-stream velocity, $D$ the cylinder diameter and $f_{nw}$ the natural frequency of the system in quiescent fluid (water). The normal orientation with the body’s flat surface facing upstream is known to be subject to another common form of FIV, galloping, while the reverse D-section with the body’s curved surface facing upstream, due to the lack of an afterbody, has previously been reported to be immune to VIV. The fluid–structure system was modelled on a low-friction air-bearing system in conjunction with a recirculating water channel facility to achieve a low mass ratio (defined as the ratio of the total oscillating mass to that of the displaced fluid mass). Interestingly, through a careful overall examination of the dynamic responses, including the vibration amplitude and frequency, fluid forces and phases, our new findings showed that the D-section exhibits a VIV-dominated response for $U^{\ast }<10$ , galloping-dominated response for $U^{\ast }>12.5$ , and a transition regime with a VIV–galloping interaction in between. Also observed for the first time were interesting wake modes associated with these response regimes. However, in contrast to previous studies at high Reynolds number (defined by $Re=UD/\unicode[STIX]{x1D708}$ , with $\unicode[STIX]{x1D708}$ the kinematic viscosity), which have showed that the D-section was subject to ‘hard’ galloping that required a substantial initial amplitude to trigger, it was observed in the present study that the D-section can gallop softly from rest. Surprisingly, on the other hand, it was found that the reverse D-section exhibits pure VIV features. Remarkable similarities were observed in a direct comparison with a circular cylinder of the same mass ratio, in terms of the onset $U^{\ast }$ of significant vibration, the peak amplitude (only approximately 6 % less than that of the circular cylinder), and also the fluid forces and phases. Of most significance, this study shows that an afterbody is not essential for VIV at low mass and damping ratios.

While flow-induced vibration of bluff bodies has been extensively studied over the last half-century, only limited attention has been given to flow-induced vibration of elastically mounted rotating cylinders. Since recent low-Reynolds-number numerical work suggests that rotation can enhance or suppress the natural oscillatory response, the former could find applications in energy harvesting and the latter in vibration control. The present experimental investigation characterises the dynamic response and wake structure of a rotating circular cylinder undergoing vortex-induced vibration at a low mass ratio ( $m^{\ast }=5.78$ ) over the reduced velocity range leading to strong oscillations. The experiments were conducted in a free-surface water channel with the cylinder vertically mounted and attached to a motor that provided constant rotation. Springs and an air-bearing system allow the cylinder to undertake low-damped transverse oscillations. Under cylinder rotation, the normalised frequency response was found to be comparable to that of a freely vibrating non-rotating cylinder. At reduced velocities consistent with the upper branch of a non-rotating transversely oscillating cylinder, the maximum oscillation amplitude increased with non-dimensional rotation rate up to $\unicode[STIX]{x1D6FC}\approx 2$ . Beyond this, there was a sharp decrease in amplitude. Notably, this critical value corresponds approximately to the rotation rate at which vortex shedding ceases for a non-oscillating rotating cylinder. Remarkably, at $\unicode[STIX]{x1D6FC}=2$ there was approximately an 80 % increase in the peak amplitude response compared to that of a non-rotating cylinder. The observed amplitude response measured over the Reynolds-number range of ( $1100\lesssim Re\lesssim 6300$ ) is significantly different from numerical predictions and other experimental results recorded at significantly lower Reynolds numbers.