## 6 Conclusions  
In this paper, based on the vibration control in the double-layer BHP to the hydraulic pump port, the BHP with a three-layer structure is made by adding the SWCNTs. The simulation analysis and experiments are carried out, and the results are compared with those for the double-layer BHPs with RTV as the elastic layer, thus the following conclusions are obtained: \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Length (mm)**} & **RTV** & **RTV-SWCNTs Composite Materials** & \\ \cline{3-4}  & & **The Standard Deviation for Radial Acceleration** & **Vibration Reduction (\%)** \\ \hline
1 & 130 & 0.179 & 0.174 & 2.8 \\
6 & 180 & 0.138 & 0.132 & 4.3 \\
7 & 230 & 0.1202 & 0.102 & 15.14 \\
8 & 280 & 0.108 & 0.0615 & 43.1 \\
9 & 330 & 0.0712 & 0.03697 & 48.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Suppression effect in the BHPs with different lengths of pipeline on pipe vibration. Figure 21: Effect of the length of the elastic layer on the radial acceleration at point P. (**a**) RTV as the elastic layer; (**b**) RTV-SWCNTs composite materials as the elastic layer. The RTV-SWCNTs composite is prepared by surface modification of the SWCNTs with noncovalent functionalization. And through the tensile test and SEM experiment, it is found that the CNTs are saturated in the composites when the content of the CNTs is 0.5 vol%-1 vol%, and the mechanical properties of the composites are better. When the content of the CNTs exceeds 1 vol%, the CNTs will agglomerate, which will reduce the mechanical properties of the composite. By comparing the experimental data, the mechanical properties of the RTV-SWCNTs composites are the best when the content of the CNTs is 0.5 vol%. 2. Based on the previously established BHP dynamic model, considering the influence of friction coupling, the dynamic model of BHP is modified. The response curve for the BHP in the frequency domain is obtained by solving the dynamic model with MATLAB software, and the modal test verified the correctness of the modified model. 3. The BHP with nanomaterials added is prepared, and the effect of the BHP on absorbing the flow pulsation and inhibiting pipeline vibration is verified through simulation analysis and experiments. Compared with the previous test data, the effect of the BHP with nanomaterials added on inhibiting pipeline system vibration is more obvious than that of the double-layer BHP with RTV as the elastic layer material. The effect increases with the increasing thickness of the elastic layer and increases with the growing length of the BHP. 4. This paper provides new theoretical and technical support for further design optimization of BHPs and the engineering application of vibration suppression. In the following research work, we will conduct further research on the BHP. In this paper, only THF is used as a dispersant to disperse SWCNTs in RTV. We will explore better dispersion methods and matrix materials to improve the material properties in the BHP's elastic layer. The thickness and length of the BHP's elastic layer will be further optimized to find the optimum thickness and length for absorbing pipeline vibration and flow pulsation in the pump outlet pipeline. Conceptualization, C.G. and L.Q. ; methodology, J.G. ; software, J.G. ; validation, J.G. and L.Q. ; formal analysis, C.G. ; investigation, J.G. ; resources, L.Q. ; data curation, J.Y. ; writing--original draft preparation, J.G. ; writing--review and editing, J.G. ; visualization, J.Y. ; supervision, C.G. and L.Q. ; project administration, C.G. and L.Q. ; funding acquisition, L.Q. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant numbers (51775477 and 51505410). Not applicable. The data presented in this study are available on request from the corresponding author.