## 5 Experimental Investigation on Aircraft Liquid-Filled Pipelines
### Experiment Result Analysis  
#### 5.3.1 Test Results Analysis of Group A  
The test conditions of Group A all involved being subjected to external random load, and three control tests were set up as A1, A2 and A3, respectively. The vibration signal \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multirow{2}{*}{**Oil-Filled**} & \multirow{2}{*}{**Kurtosis**} & \multirow{2}{*}{**Random**} & \multicolumn{2}{c}{**Pulsating**} & \multirow{2}{*}{**Pipe Wall**} \\  & & & **Load** & & **Pressure** & \\ \hline A\({}_{1}\) & No & 3 & Yes & No & 0.7 mm \\ A\({}_{2}\) & No & 5 & Yes & No & 0.7 mm \\ A\({}_{3}\) & No & 7 & Yes & No & 0.7 mm \\ B\({}_{1}\)(A\({}_{1}\)) & No & 3 & Yes & No & 0.7 mm \\ B\({}_{2}\) & Yes & 3 & Yes & 0 Mpa & 0.7 mm \\ B\({}_{3}\) & Yes & 3 & No & 0.5-5 Mpa & 0.7 mm \\ B\({}_{4}\) & Yes & 3 & Yes & 0.5-5 Mpa & 0.7 mm \\ C\({}_{1}\) & No & 3 & Yes & No & 0.5 mm \\ C\({}_{2}\)(A\({}_{1}\)) & No & 3 & Yes & No & 0.7 mm \\ C\({}_{3}\) & No & 3 & Yes & No & 1 mm \\ C\({}_{4}\) & No & 3 & Yes & No & 1.4 mm \\ D\({}_{1}\) & Yes & 3 & Yes & 0.5-5 Mpa & 0.5 mm \\ D\({}_{2}\)(B\({}_{4}\)) & Yes & 3 & Yes & 0.5-5 Mpa & 0.7 mm \\ D\({}_{3}\) & Yes & 3 & Yes & 0.5-5 Mpa & 1 mm \\ D\({}_{4}\) & Yes & 3 & Yes & 0.5-5 Mpa & 1.4 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pipeline vibration response test group. Figure 21: U-shaped pipe diagram. Figure 20: An aircraft engine pipeline layout diagram. kurtosis values of the three groups of random load were 3, 5 and 7, respectively. The purpose of setting up Group A was to explore the sensitivity of the pipeline vibration response to the kurtosis value of the non-Gaussian random vibration load. The axial and circumferential strain signals of the pipeline were collected by the strain gauge and converted to stress by calculation. MATLAB R2022a software was used to solve the kurtosis value of the axial and circumferential time domain stresses. As can be seen from Table 4, when the input signal is Gaussian random vibration, the stress response of the pipeline at the danger point is close to Gaussian distribution; that is, when the input excitation signal kurtosis is 3, the kurtosis of the stress response is attenuated to a certain extent, but it is still close to Gaussian distribution. When the excitation signal is super-Gaussian random vibration, that is, the kurtosis value is 5 or 7, the stress response of the pipeline at the danger point shows super-Gaussian characteristics. With the increase in kurtosis, the kurtosis attenuation degree of stress response is greater. Meanwhile, it was found that the kurtosis attenuation of axial stress was more severe than that of circumferential stress. Figure 22 shows the rainflow count diagram of axial stress and circumferential stress in group A\({}_{1}\), and Figure 23 shows the rainflow count diagram of axial stress in groups A\({}_{2}\) and A\({}_{3}\). It can be seen from the figure that the maximum axial stress value of group A\({}_{1}\) is 150 MPa, which is larger than the maximum circumferential stress value of 26 MPa. Therefore, it can be inferred that under the load of external random vibration only, the axial stress amplitude of the pipeline is much larger than the circumferential stress amplitude, the axial stress plays a decisive role in the vibration response stress of the pipeline. Therefore, the axial stress of the contact position between the pipe and the support is worth paying attention to under the condition of external random vibration. Comparing the axial stress of groups A\({}_{1}\), A\({}_{2}\) and A\({}_{3}\), it can be seen that when the applied load excitation is super-Gaussian random vibration, the stress amplitude of the pipeline at the danger point increases, so when the external load presents super-Gaussian characteristics, the vibration response of the pipeline will be increased.