## 6 Conclusions  
Through simulation analysis and experimental research, this paper investigates and analyses the fluid-structure interaction vibration stress response of liquid-filled pipelines under the superimposed effects of external random load and internal fluid pulsation. By analyzing the stress response of the liquid-filled pipeline at danger points, the influence mechanism and rule of different kurtoses, different working conditions and different pipe wall thicknesses on the fluid-structure interaction vibration stress response of the liquid-filled pipeline were investigated, and the following conclusions can be drawn:  
1. The danger point of the vibration response stress of the aircraft liquid-filled pipeline under the action of external random load is located above and below the contact between the support at both ends of the pipeline. The danger point of the vibration response stress under the action of internal fluid pulsation pressure is located at the inner corner of the pipe bend, so the damping device should be added in these two parts to reduce the vibration stress when designing the aircraft pipeline.
2. The vibration response stress of the aircraft liquid-filled pipe under external random load is mainly axial stress, while the vibration response stress under internal fluid pulsation pressure is mainly circumferential stress, and the radial stress generated by both loads can be ignored, which provides a basis for aircraft vibration response analysis.
3. Compared with the Gaussian random vibration load, the super-Gaussian random vibration load will have a larger response to the vibration of the aircraft liquid-filled pipe. Therefore, when carrying out the anti-fatigue design of the aircraft liquid-filled pipe, whether the external load has super-Gaussian characteristics should be fully considered.
4. Under the same external load, the vibration response of the aircraft pipe is more intense than that of the empty pipe after it is filled with liquid. In the anti-fatigue design and simulation test of the aircraft duct, in order to obtain real and reliable results, the relevant design and test should be carried out considering the presence of liquid.
5. The wall thickness of aircraft piping filled with liquid has a critical value. When the wall thickness is larger than this critical value, the stress decay of the vibration response gradually decreases with increasing wall thickness and tends to be stable under the same working conditions. Therefore, when designing aircraft piping, it is not the case that the thicker the wall thickness, the better. The appropriate wall  
Figure 28: Time domain curve of circumferential stress at danger points of Group D\({}_{1}\) and Group D\({}_{3}\) pipelines.  
thickness of the pipe should be selected by considering the economy, aircraft load capacity and vibration stress response of the pipe. At the same time, if the wall thickness of the pipe is below a certain value, plastic deformation will occur due to the pulsating pressure of the fluid, which should be taken into account when designing the aircraft pipe.  
These conclusions can provide guidance for aircraft piping design, vibration reduction design, simulation testing and fatigue life analysis. Next, based on the research in this paper, the method proposed in this paper can be used to simulate and verify the actual equipment according to the measured vibration load signal and fluid pulsating pressure signal on the aircraft engine pipeline.  
Conceptualization, C.C. and Y.J.; methodology, L.Z.; writing--original draft, C.C. and L.Z.; writing--review & editing, Y.J.; visualization, C.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.