# Experimental Study on Streamwise Vortex-Induced Vibration of a Flexible, Slender Cylinder
## 1 Introduction  
Vortex-induced vibration (VIV) of a flexible, slender cylinder is a complicated fluid-structure interaction (FSI) phenomenon that may result in structural failure, due to fatigue damage accumulation. It is a problem of both industrial and academic interest, and has been studied for decades. Several key reviews and important milestones on this topic can be found in [PERSON] [1], [PERSON] [2], [PERSON] [3], [PERSON] and [PERSON] [4], [PERSON] and [PERSON] [5], [PERSON] et al. [6], [PERSON] and [PERSON] [7], and [PERSON] et al. [8]. The vast majority of previous work has focused on 2-degree-of-freedom (2-DOF) VIV of a cylinder in both transverse and streamwise directions [9; 10; 11], and on 1-degree-of-freedom (1-DOF) VIV in the transverse direction [12; 13; 14]. A generally accepted understanding is that the response amplitude and the fluctuating fluid force in the streamwise direction are one order of magnitude smaller than those in the transverse direction [15], and the streamwise vibrations are trivial and can be neglected in fatigue analysis. However, the recent experiments of [PERSON] et al. [16] on VIV of a flexible, slender cylinder showed that the streamwise responses might have a significant contribution to fatigue under tension-controlled conditions. This is because the streamwise vibrations take place at doublethe frequency and half the wavelength of those in the transverse direction. Given that the curvature is inversely proportional to the squared wavelength, fatigue caused by the streamwise vibrations dominates when the flow velocity is low. Due to its importance and less well-established dynamic behaviors, the streamwise VIV of an elastically supported, rigid, circular cylinder has been extensively studied. These investigations are ongoing. The pioneer work can be backtracked to [PERSON] (1977), in which the response regimes of streamwise VIV were characterized. [PERSON] and [PERSON] (2000) introduced a wake-oscillator model for predicting the VIV of a cylinder in the streamwise direction. [PERSON] and [PERSON] (1979) concluded from 2-DOF VIV experiments that there were three types of streamwise VIV. The first type originated from the symmetric vortex shedding in \(1.0<Vr<2.3\) (\(Vr=u/f_{1}D\), where \(Vr\) is the reduced velocity, \(u\) is the flow velocity, \(f_{1}\) is the natural frequency of the vibration system, and \(D\) is the cylinder diameter). The second type was caused by the alternate vortex shedding in \(2.3<Vr<3.8\). The third type occurred concurrently with the transverse vibrations in a higher region of \(Vr\). [PERSON] et al. (2010) performed laboratory tests on the streamwise VIV of a circular cylinder, either spring-mounted at both ends (two-dimensional (2D)), or cantilevered on one end (three-dimensional (3D)) in a water tunnel at subcritical Reynolds numbers. It was found that, in the 2D cases, the response amplitudes were sensitive to the reduced mass-damping parameter \(Cn\) (\(Cn=2m^{*}\zeta\), where \(m^{*}\) is the mass ratio, and \(\zeta\) is the structural damping ratio) in the first excitation region with symmetrically-shed vortices. While a \"lock-in\", similar to that in the transverse VIV, occurred in the second excitation region with alternately-shed vortices. [PERSON] et al. (2011) experimentally investigated the forced vibration of a circular cylinder in the streamwise direction. It was found that the added mass coefficient, which significantly affects the dynamic behaviors of low mass-ratio VIV, varied greatly in the two excitation regions, while the added damping coefficient could be negative. [PERSON] and [PERSON] (2012) investigated the near-wake modes of a 1-DOF cylinder undergoing streamwise VIV by using the particle-image velocimetry (PIV). Two modes--the S-I mode (in which two symmetric vortices are shed simultaneously per vibration cycle) and the A-II mode (similar to the well known von Karman vortex street)--were observed in the first excitation region.