## 5 Results and Discussion
### Dynamic Response Characteristics of Pipes  
The dynamic response of the pipe under four system work conditions (Table 2) is investigated in this subsection. Figures 11-14 shows the comparison of vibration velocity of measuring points A and B in the pipe by the DTTMM method and the experimental results.  
Figure 11: Vibration velocity of pipe (the first condition). (**a**) Axial vibration velocity of measuring point A; (**b**) Radial vibration velocity of measuring point A; (**c**) Axial vibration velocity of measuring point B; (**d**) Radial vibration velocity of measuring point B.  
Figure 12: Vibration velocity of pipe (the second condition). (**a**) Axial vibration velocity of measuring point A; (**b**) Radial vibration velocity of measuring point A; (**c**) Axial vibration velocity of measuring point B; (**d**) Radial vibration velocity of measuring point B.  
Figure 13: Vibration velocity of pipe (the third condition). (**a**) Axial vibration velocity of measuring point A; (**b**) Radial vibration velocity of measuring point A; (**c**) Axial vibration velocity of measuring point B; (**d**) Radial vibration velocity of measuring point B.  
From Figures 11-14, it is observed that the vibration response of the pipe under the flow pulsation excitation shows a forced vibration with periodic characteristics, and the vibration velocity response law of pipe is consistent with the variation law of fluid pulsation. The radial vibration response amplitude is generally higher than the axial vibration response amplitude, suggesting that the flow pulsation excitation will cause a large amplitude radial vibration of pipe.  
Comparing the velocity response of the pipe measuring points under different working conditions, it can be concluded that the vibration amplitude increases with the increasing flow velocity when the system pressure is constant. The waveform of vibration velocity response curves changes as well; it appears as the higher the flow velocity, the earlier the vibration velocity reaches the response peak. Moreover, when the flow velocity is constant, the vibration amplitude increases with the increasing system pressure, but the variation amplitude is relatively smaller, indicating that the fluid pressure has relatively less influence on the vibration velocity of the pipe.  
From Figures 11-14, we can see that the DTTMM results are in good agreement with the experimental results. However, compared with the theoretical predictions (DTTMM method), the waveform of the experimental curves has more small clutter and the vibration response amplitude is generally lower.  
The little disparity between theory and experiment may be caused by the following reasons:  
1. Calculation error of theoretical results from analytical approximations and numerical error, etc.
2. There are manufacturing error and installation deviation in the manufacturing and installation process of the test pipe.
3. The textile-reinforced rubber hoses and elastic clamps exist in the experimental system, which will increase the damping characteristics of the system, but the damping dissipation of the above components is neglected in numerical calculation.  
Figure 14: Vibration velocity of pipe (the fourth condition). (**a**) Axial vibration velocity of measuring point A; (**b**) Radial vibration velocity of measuring point A; (**c**) Axial vibration velocity of measuring point B; (**d**) Radial vibration velocity of measuring point B.  
There are measurement noises in the process of data acquisition, such as sensor noise, supply line noise and signal line noise, etc.