# Experimental Study on Streamwise Vortex-Induced Vibration of a Flexible, Slender Cylinder
## 2 Experimental Set-Up  
It is well known that there are three types of streamwise VIV, namely, the types falling in the first, second, and third instability region. The first excitation region originates from symmetric vortex shedding in the lower reduced velocity region of \(1.0<Vr<2.3\), and the second excitation region from alternate vortex shedding in the higher reduced velocity region of \(2.3<Vr<3.8\)[19]. The first and second instability regions constitute the pure streamwise regime, which is the main focus of our present research work. The third streamwise VIV region of slender marine structures occurs for reduced velocities where transverse oscillations have started. Our experiment was performed in the towing tank at the State Key Laboratory of Hydraulic Engineering Simulation and Safety of Tianjin University. The towing tank is 137.0 m long, 7.0 m wide and 3.3 m deep. A test apparatus, which had a supporting frame, two vertical supporting mechanisms, a cylinder model, and an axial tension system, was designed. The schematic model of the apparatus is shown in Figure 1.  
The supporting frame was composed of a number of vertical and horizontal steel beams. Each vertical supporting unit consisted of a vertical supporting rod, a supporting plate, and a guide plate. The vertical supporting rods were connected to the supporting plates at the bottom end and the supporting frame at the top end, respectively. The guide plate was installed on the inner side of the supporting plate by several long bolts to ensure that the flow around the towing cylinder model was two-dimensional. The cylinder model was pinned at one end using a universal joint and connected with a steel wire at the other end. The steel wire passed through two small hollow poles (one on the guide plate and the other on the supporting plate) and was connected to a spring at the end. The use of the spring allowed a gradual variation of axial tension on the cylinder model during the experiment. Four axial tensions of 0 N, 50 N, 100 N and 150 N were employed by adjusting the tensioner. A load cell was adopted to monitor the axial tension on the vibrating flexible cylinder. A pulley was used to change the direction of the steel wire. The flexible cylinder model was placed 1.0 m under the still water level, and the free-surface effect was negligible. As shown in Figure 2, the flexible cylinder model (with an outer diameter of 20 mm and a length of 3.91 m) was made of a coaxial composite tube. The inner tube was a steel pipe with an outer diameter of 19.8 mm and a wall thickness of 2.0 mm. The outer tube was a heat shrinkable PVC pipe with an outer diameter of 20.0 mm and a wall thickness of 0.1 mm. The use of the outer PVC pipe was due to the fact that it could provide a smooth external surface but also protect and insulate the instrumentation cables and strain gauges. The mass per unit length, \(m_{s}\), of the cylinder model, including the mass of  
Figure 1: Layout of the experiments. the measuring instruments and the trapped water inside the steel pipe, was 0.573 kg/m, resulting in a dimensionless mass ratio (\(m^{*}=4m_{s}/\rho\pi D^{2}\), where \(\rho\) is the density of water) of 1.39. The bending stiffness of the cylinder model, EI (see Table 1), was 324.94 N\(\cdot\)m\({}^{2}\). The structural damping ratio, \(\zeta\) (measured in a free-decaying test of the cylinder model in water), was 0.0598. The axial tension was directly employed on the inner steel pipe. Ten pairs of strain gauges were attached to the outer surface of the steel pipe and covered by the PVC pipe. Five of those were oriented in the \(x\)-direction (streamwise) while the others were in the \(y\)-direction (transverse). The measuring points were evenly distributed along the cylinder model, as illustrated in Figure 3. The aspect ratio (length to diameter) of the cylinder model was 195.5. The key parameters of the cylinder model are listed in Table 1.  
The cylinder model was towed horizontally in still water with a velocity from 0.05 m/s to 0.15 m/s with an increment of 0.05 m/s.