## 2 Fluid-Structure Interaction Vibration Analysis of Single Pipeline
### Experimental Verification  
Using a vibration table as the excitation equipment for the analyzed pipeline, complete the vibration experiment. The vibration table used in this study has a maximum excitation force of 10 KN, a maximum displacement of 51 mm, and a frequency range of 5-3000 Hz. The testing equipment used in the experiment is an IEPE piezoelectric acceleration sensor, model PCB356 A116, with a measurable frequency range of 0.5-5000 Hz and a range of \(\pm\)50 g. The data acquisition instrument is a DH5922 N dynamic signal tester, which uses a USB3.0 cable to connect with a computer for data transmission. The experimental operation process is as follows:  
1. Fill the interior of the pipeline with hydraulic oil and block both ends with screw plugs. The hydraulic pipeline used in the vibration experiment is fixed to the fixture with block clamps, and the installation diagram is shown in Figure 4. The material parameters of the pipeline and oil are shown in Table 1.
2. In the software section of the vibration test control system, create a new engineering file and select the sine sweep frequency method. Set the engineering units with displacement in mm, velocity in m/s, and acceleration in g.
3. The sensor type of the input channel is set as an acceleration sensor and is a charge sensor. The sensitivity is an inherent value of the sensor: 43.81 pc/G. Figure 3: Schematic diagram of local pipeline grid and pipe clamp grid. (**a**) Single pipeline grid local; (**b**) Pipe clamp grid. Figure 2: Actual pipeline and its geometric modeling. (**a**) Actual hydraulic pipeline; (**b**) Single pipe geometric modeling. 4. The setting of the sine target spectrum. The target spectrum of the sine sweep experiment adopts 5-19.92944 Hz as the positioning shift range, with a displacement peak to peak of 1.25 mm, and 19.9294-2000 Hz as the fixed acceleration range, with an acceleration value of 1 g.
5. Schedule settings. The schedule is used to arrange experiments to be automatically executed according to a predetermined sequence of events, with a frequency limit of 5 Hz for the lower limit and 2000 Hz for the upper limit. The starting frequency is 5 Hz, and the starting direction is upward. Choose logarithmic sweep as the sweep mode, with one sweep frequency. 6. Signal acquisition system settings. Create a new project management file and set the channel settings for the channels connected to the acquisition instrument. The sampling frequency is set to 20 KHz. Since the sensor used for signal collection is an acceleration sensor, the measurement quantity is chosen as acceleration, and the input method is IEPE. 7. After setting the relevant experimental parameters, return to the main operation interface of the controller and click \"Start\" to proceed with the experiment. This experiment mainly compares the natural frequencies of each order with the simulation results. The vibration parameters obtained through finite element simulation are in good agreement with the experimental results, and the specific data is shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Order**} & \multicolumn{2}{c}{**Experimental**} & \multicolumn{2}{c}{**Ansys Simulation**} & \multirow{2}{*}{**Error**} \\  & **Frequency (Hz)** & & **(Hz)** \\ \hline
1 & 210.20 & 218.11 & 3.8\% \\
2 & 309.29 & 322.59 & 4.3\% \\
3 & 483.39 & 496.23 & 2.7\% \\
4 & 577.39 & 592.66 & 2.6\% \\
5 & 601.81 & 606.25 & 0.7\% \\
6 & 714.11 & 721.65 & 1.1\% \\
7 & 901.24 & 913.27 & 1.3\% \\
8 & 955.81 & 931.62 & 2.5\% \\
9 & 989.99 & 979.6 & 1\% \\
10 & 1072.98 & 1055.7 & 1.6\% \\
11 & 1149.9 & 1156.3 & 0.6\% \\
12 & 1323.24 & 1379.1 & 4.2\% \\
13 & 1525.88 & 1498.4 & 1.8\% \\
14 & 1661.38 & 1682.1 & 1.2\% \\
15 & 1984.86 & 1993.9 & 0.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the first 15 natural frequencies of a single pipeline. Figure 4: Schematic diagram of pipe clamp and single pipe fixing.