## 5 Experimental Investigation on Aircraft Liquid-Filled Pipelines
### Experiment Result Analysis
#### 5.3.2 Test Results Analysis of Group B  
Group B was set up to compare the vibration response analysis of four different working conditions of the pipeline. First, the results of groups B\({}_{1}\) and B\({}_{2}\) were analyzed; that is, an empty pipeline subjected to external random load and a liquid-filled pipeline subjected to external random load (hydraulic pressure is 0 MPa), respectively. Figure 24 shows the results of the rainflow counting of the axial stress at the danger points of groups B\({}_{1}\) and B\({}_{2}\).  
As can be seen from Figure 24, the maximum value of the axial stress of the danger point in Group B\({}_{1}\) is 150 MPa and the maximum value of the axial stress of the danger point in Group B\({}_{2}\) is 250 MPa. The maximum value of the axial stress rainflow number of the danger point in Group B\({}_{2}\) is larger than that in Group B\({}_{1}\). The results show that the vibration response of the pipeline filled with liquid is more intense than that of the empty pipeline under random vibration load.  
Figure 25 shows the time domain response curves of axial and circumferential stress at the danger points of group B\({}_{3}\). The stress of the group B\({}_{3}\) liquid-filled pipeline presents a periodic change, and there is a pulse pressure at the position of high and low pressure change. At the same time, it can be observed that the circumferential stress at the danger point of the liquid-filled pipeline is significantly greater than the axial stress. The axial stress is about 0.3 times the circumferential stress and the Poisson's ratio of stainless steel is also 0.3. According to the definition of Poisson's ratio, when the linear elastic material is stretched and deformed in one direction, the strain is \(\varepsilon\). The strain perpendicular to the direction is \(\varepsilon_{1}\). The negative value of the ratio of \(\varepsilon_{1}\) and \(\varepsilon\)  
Figure 23: Group A\({}_{2}\) and A\({}_{3}\) danger point axial stress rainflow count.  
Figure 24: Group B\({}_{1}\) and B\({}_{2}\) danger point axial stress rainflow count.  
It can be inferred that the pulsating pressure of the fluid on the pipe will generate only circumferential stress, while the axial stress will be generated by the Poisson's ratio effect of the materials. When investigating the response of the pulsating pressure of the fluid to the vibrational stress of the pipe, only the circumferential stress of the pipe should be considered.  
Figure 26 shows the time domain response curves of axial stress and circumferential stress of the Group B4 liquid-filled pipeline at the danger point under the combined action. From the previous analysis, it can be seen that the axial stress of the liquid-filled pipeline is more sensitive to random vibration, and the circumferential stress is more sensitive to the fluctuating pressure of the fluid, which is confirmed by Figures 22 and 25.  
The rainflow count of the axial stress of Group B4 can be compared with the rainflow count of the axial stress of the liquid-filled pipeline in Group B2, which only has a random vibration effect, as shown in Figure 27. As can be seen from the figure, the maximum axial stress amplitude of Group B4 is 300 MPa, while that of Group B2 is 250 MPa. At the same time, due to the presence of fluid pressure, the average axial stress of Group B4 is greater than that of Group B2. Therefore, it can be seen that the vibration response of the pipeline  
Figure 26: The time domain response curves of axial stress and circumferential stress of group B4.  
Figure 25: Time domain response curves of axial and circumferential stress of group B3 pipeline danger points.  
under the combined action is more intense than that under the external random vibration action alone (fluid pressure is 0 MPa).