## 5 Experimental Validation and Discussions
### Axial Vibration Velocity Experiment  
An experimental study on the FSI axial vibration velocity response of pipeline in different flow states was carried out. The pipeline is attached to the test bench system through hydraulic hoses, the pipeline ends are fixed on the bench by P-type clamp, the axial vibration response of different positions is measured by the acceleration sensor, as shown in Figure 9.  
The speed of piston pump is set to 1000 r/min and the system pressure is 12 MPa. By changing the displacement of the piston pump, the flow velocity is 2 m/s, 4 m/s, 6 m/s and 8 m/s respectively. The axial vibration response of the position 1 and position 2 is measured. The axial vibration velocity response of the pipeline is shown from Figures 12-15.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **1 st-Formant** & **2 nd-Formant** & **3 rd-Formant** & **4 th-Formant** \\ \hline Measuring point 1 & 206 Hz & 465 Hz & 737 Hz & 1190 Hz \\ Error compared with simulation & 1.4\% & 2.1\% & 1.9\% & 0.68\% \\ Measuring point 2 & 204 Hz & 463 Hz & 739 Hz & 1202 Hz \\ Error compared with simulation & 1.4\% & 1.9\% & 1.5\% & 1.6\% \\ \hline \end{tabular}
\end{table}
Table 4: The first four experimental modes of the two measuring points.  
Figure 11: Axial velocity response curve of pipeline.  
Figure 12: Axial velocity response curve when the flow rate is 2 m/s.  
Tables 5 and 6 show that there is little disparity between simulation and experiment, and the maximum error is less than 3.32%, it may be caused by several reasons.  
(1) There is residual stress in the pipeline because of the manufacturing error and installation error.  
(2) Despite the impact direction of exterior excitation is the radial direction of the pipeline, there will be other directions excitation. Hence, other directions vibration might be measured by acceleration sensor, this is why the experimental curves are not as smooth as the simulation curves.  
(3) Global error may cause by material parameters error, calculation error, etc.  
Though there are little tolerance between simulation and experiment, the results are consistent and acceptable. There are also several points worthy to be discussed.  
(1) The obvious valley value of axial vibration velocity is not obtained in the experiment. This is due to that the lower threshold of axial vibration velocity, which is the valley value of the axial vibration velocity of the FSI vibration of the pipeline, is set to 10\({}^{\circ}\)-12 m/s when using a computer for simulation. However, the three-axis acceleration sensor only used to measure the peak value, but not to valley value in the experiment.  
(2) The amplitude of axial vibration velocity response obtained by experiment is smaller than that obtained by numerical simulation at the same resonance frequency. This is because only the damping effect of fluid friction term is considered in numerical simulation, but there will be multiple damping and external signal interference of the system in the process of experiment.  
(3) The general trend of simulation curves come closer to the experimental curves in consideration of friction term, this indicates that considering friction term can improve the prediction accuracy of FSI dynamic characteristics of the hydraulic pipeline.