## 4 Analysis Example and Methods
### Results from the BHP Vibration Experiment  
.3.1 Pulsation Absorption Experiment Results for the BHP with Different Thicknesses of Elastic Layer  
The outlet flow pulsation curves for the different BHPs are shown in Figure 17.  
The amplitude of the flow pulsation at the outlet of the double-layer BHP with RTV as the elastic layer and the three-layer BHP with RTV-SWCNTs composite materials as the elastic layer decreases with the increase in the thickness of the elastic layer. This shows that the elastic materials (RTV and RTV-SWCNTs composite materials) have an absorption effect on the flow pulsation at the outlet of the hydraulic pump. And with the increase in the thickness of the pipeline, the absorption effect of the flow pulsation increases.  
The comparison curves for the flow pulsation at the outlet of the double-layer BHP with RTV as the elastic layer and the three-layer BHP with RTV-SWCNTs composite materials as the elastic layer under the same thickness of the elastic layer are shown in Figure 18.  
Figure 18 shows that the amplitude of the flow pulsation in the three-layer BHP with RTV-SWCNTs composite materials as the elastic layer is significantly lower than that of the double-layer BHP with RTV as the elastic layer.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Length (mm)**} & **RTV** & **RTV-SWCNTs Composite Materials** & \\ \cline{2-3}  & **The Standard Deviation for the Vibration Acceleration** & **Vibration Reduction (\%)** \\ \hline
100 & \(1.956\times 10^{-6}\) & \(1.675\times 10^{-6}\) & 14.4 \\
150 & \(1.736\times 10^{-6}\) & \(1.435\times 10^{-6}\) & 17.3 \\
250 & \(1.542\times 10^{-6}\) & \(1.237\times 10^{-6}\) & 19.8 \\
300 & \(1.373\times 10^{-6}\) & \(1.176\times 10^{-6}\) & 14.3 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The suppressive effect of the different lengths in the BHP on the vibration of the pipeline wall.  
Figure 17: Effect of thickness of the elastic layer on flow pulsation. (**a**) BHP with RTV as the elastic layer; (**b**) BHP with RTV-SWCNTs composite materials as the elastic layer.  
The absorption effect of the flow pulsation in the BHPs with different thicknesses of the elastic layer is shown in Table 8. The pulsation reduction is 'the standard deviation of flow pulsation at the outlet of BHP with RTV as the elastic layer subtracts the standard deviation of flow pulsation at the outlet of BHP with RTV-SWCNTs as the composite elastic layer'. The pulsation reduction reflects the flow pulsation absorption effect for the BHP with the same pipeline thickness and different elastic layer materials.  
The standard deviation for the flow pulsation in the three-layer BHP with SWCNTs added is significantly lower than that of the double-layer BHP with RTV as the elastic layer. With the increase in the thickness of the pipeline, the standard deviation for the flow pulsation at the outlet of the pipeline decreases, and the effect of the pulsation absorption increases. When the thickness of the elastic layer is 15 mm, the percentage of pulsation reduction is the largest and the absorption effect of the flow pulsation is the best, which lays the experimental foundation for further optimization of BHPs.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Thickness (mm)**} & **RTV** & **RTV-SWCNTs Composite Materials** & \multirow{2}{*}{**Pulsation Reduction (\%)**} \\ \cline{3-3}  & & **The Standard Deviation for the Flow Pulsation** & \\ \hline
1 & 5 & 0.319 & 0.248 & 22.3 \\
2 & 10 & 0.291 & 0.215 & 26.1 \\
3 & 15 & 0.253 & 0.177 & 30.04 \\
4 & 20 & 0.1802 & 0.128 & 28.97 \\
5 & 25 & 0.1197 & 0.0872 & 27.15 \\ \hline \end{tabular}
\end{table}
Table 8: The absorption effect of the flow pulsation for the BHP with different thicknesses of the elastic layer.  
Figure 18: Effect of different elastic layer materials with the same thickness on flow pulsation. The thickness of the elastic layer is: (**a**) 5 mm; (**b**) 10 mm; (**c**) 15 mm; (**d**) 20 mm; (**e**) 25 mm.