## 4 Simulation Analysis of Aircraft Liquid-Filled Pipelines
### Finite Element Modeling
#### 4.2.3 Load Generation  
The type of load on a pipeline filled with liquid can be divided into two categories: an external random load and a pulsating pressure load inside the pipeline.  
Random Load Extraction  
Transient dynamics analysis requires time domain loads as input signals, and these time domain load data need to have different load parameters to control the relevant variables. In this paper, the random vibration signal measured directly from the vibration table is used as the external random load excitation of the pipeline. A 5-ton electromagnetic vibration test bench was selected, a non-Gaussian vibration controller developed by the laboratory (which can control the kurtosis of the signals, so as to obtain the Gaussian and non-Gaussian vibration signals) was adopted and the vibration signal test system of the B&K company was used to measure the acceleration of the vibration table, so as to obtain the time domain load data. Modal simulation was carried out under the two working conditions (empty pipeline and liquid-filled pipeline). The modal module in Ansys Workbench 2022 R1 software was used. The diameter of the U-shaped pipeline is 60 mm and the thickness of the pipe wall is 2 mm. The grid division method of the pipeline is the Sweep Method and the grid division method of the fluid is Tetrahedron. The number of grid nodes is 142,078 and the number of cells is 84,430. The modal simulation shows that the first two natural frequencies of the pipeline in the empty pipe state are 529.54 Hz and 532.27 Hz, respectively, and the first two natural frequencies of the pipeline when it is filled with liquid are about 430 Hz. In order to excite the first two modes of the pipeline to generate a sufficient vibration response, the frequency band of the extracted random vibration load is 400-800 Hz. The spectral type is a flat spectrum, the root mean square acceleration value is 15 g, the kurtosis value is 3 (considering the Gaussian distribution load first), the sampling frequency is 2560 Hz, the analytical spectral line is 200 and a random time domain signal with 1 frame of 0.2 s and 512 data points is extracted. Figure 5a shows the power spectral density function of the acceleration load, and Figure 5b shows the time domain signal of the acceleration load.  
Generation of Fluid Pulsation Pressure in Pipe  
The fluid pressure pulsation in the pipe is due to changes in equipment working conditions, such as the sudden opening and closing of the valve, which will form a water  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Group** & **Simulation Condition** \\ \hline A & only stimulated by external random excitation \\ B & only stimulated by the pulsating fluid pressure in the pipe \\ C & combined action \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation group of fluid–structure interaction vibration response of liquid-filled pipelines.  
Figure 5: Generation of random loads. (**a**) The power spectral density function of the acceleration load. (**b**) The time domain signal of the acceleration load.  
hammer effect in an instant. The water hammer will cause a continuous oscillation of the pressure in the pipe, forming a periodic high and low pressure. For example, the reciprocating movement of the plunger pump in the aircraft engine will cause the oil pressure in the pipe to change periodically. Generally speaking, the pressure change curve over time is a square wave, and the high pressure duration of the square wave is basically the same as the low pressure duration. At the same time, the period of the liquid pulsating pressure in the plunger pump is not very high, generally not more than 20 Hz. Therefore, the pulsating pressure square wave is used to simulate the pulsating pressure of the fluid in the simulation. Figure 6 shows the time domain load of the pulsating pressure signal. The pressure amplitude is 5 MPa, the pressure pulsation frequency is 20 Hz and the pulsation waveform is a square wave.