# Experimental Study on Streamwise Vortex-Induced Vibration of a Flexible, Slender Cylinder
## 4 Results and Discussion
The second column graph presents the time history in a short time interval, from 28 s to 30 s, in order to clearly describe the characteristics of oscillation. The third column graph illustrates the  
Figure 7: \(x\)–\(y\) trajectories of the cylinder in the first excitation region with \(V_{r}\approx 2.3\). displacement response spectra, which was produced by fast Fourier transformation (FFT) analysis of the displacement data. Figure 8: \(x\)–\(y\) trajectories of the cylinder in the second excitation region, with \(V_{r}\approx 3.4\). Figure 9: Time histories and spectral plots of streamwise displacement with \(V_{r}\approx 1.05\). (**a**) Time-varying streamwise displacement for the last 30 s of a complete sampling period at five measuring positions along the cylinder model; (**b**) time history of streamwise displacement in a short time interval, from 28 s to 30 s; and (**c**) displacement response spectra. Figure 11: Time histories and spectral plots of streamwise displacement with \(V_{r}\approx 2.55\). (**a**) Time-varying streamwise displacement for the last 30 s of a complete sampling period at five measuring positions along the cylinder model; (**b**) time history of streamwise displacement in a short time interval, from 28 s to 30 s; and (**c**) displacement response spectra. Figure 10: Time histories and spectral plots of streamwise displacement with \(V_{r}\approx 2.29\). (**a**) Time-varying streamwise displacement for the last 30 s of a complete sampling period at five measuring positions along the cylinder model; (**b**) time history of streamwise displacement in a short time interval, from 28 s to 30 s; and (**c**) displacement response spectra. At the beginning of the first excitation region, the time history of the streamwise displacement, characterized by a small amplitude, was irregular and aperiodic, as shown in Figure 9. A similar  
Figure 5:0 Time histories and spectral plots of streamwise displacement with \(V_{r}\approx 3.44\). (**a**) Time-varying streamwise displacement for the last 30 s of a complete sampling period at five measuring positions along the cylinder model; (**b**) time history of streamwise displacement in a short time interval, from 28 s to 30 s; and (**c**) displacement response spectra. Figure 5:1 Time histories and spectral plots of streamwise displacement with \(V_{r}\approx 3.83\). (**a**) Time-varying streamwise displacement for the last 30 s of a complete sampling period at five measuring positions along the cylinder model; (**b**) time history of streamwise displacement in a short time interval, from 28 s to 30 s; and (**c**) displacement response spectra. phenomenon was also observed in the rigid cylinder experiments of [PERSON] and [PERSON] [22] and was attributed to the turbulent buffeting effects. The vibration amplitude of the flexible cylinder at the mid-span was generally larger than those near the pinned-ends due to the predominant first mode of vibration. The spectral plot showed a large peak at the frequency ratio of \(f_{x}/f_{1}\approx 1.0\) and numerous small spikes, indicating some unsteadiness in the vortex shedding. When the streamwise amplitude peaked in the first excitation region, the time history of the streamwise displacement showed a quasi-sinusoidal curve, except small irregularities observed at the measuring points near the pinned-ends of the cylinder model, as shown in Figure 5:2 In addition, it could be found that the dimensionless maximum displacement amplitude was roughly equal to 0.12, which was larger than the rigid cylinder results of [PERSON] and [PERSON] [22], where the dimensionless maximum displacement amplitude was between 0.06 and 0.09, with minor fluctuations in the middle of the first response branch. The spectral plot for the streamwise displacement was rather pure, with only one predominant peak observed at \(f_{x}/f_{1}\approx 1.0\).