## 5 Influences of Flow Velocity Pulsation and Mechanical Vibration
### Mechanical Vibration  
Because the fluid-conveying pipe is fixed at regular intervals with fixing devices to reduce pipe vibration in actual application, we added hoops to fix the pipe model to better simulate it. The inner diameter of the hoop was 68 mm. The hoop width was 6 mm, and the hoop thickness was 2 mm. Since steel has large rigidity and it is difficult to deform, it is suitable to use this material to support the pipeline structure. The hoop material was specified to be structural steel, of which the density was 7850 kg/m\({}^{3}\), Young's modulus was 200 GPa, and Poisson's ratio was 0.3. To study the influence of mechanical vibration, we applied a sinusoidal vibration (\(Y\) direction) to the inlet and outlet faces of the pipe, as shown in Figure 10a. First, the influence of the mechanical vibration frequency was studied. The vibration frequencies were set to 5, 10, 20, and 40 Hz, and the vibration amplitudes were all set to 0.1 mm. Simultaneously, the pulsation amplitudes of the flow velocity were set to 0.1 m/s, and the pulsation frequencies were set to 40 Hz. Figure 10b shows the sinusoidal vibration as the vibration frequency was 40 Hz and the vibration amplitude was 0.1 mm. Keeping other settings unchanged, we compared the circumferential stress and strain signals of the pipe wall and the fluid pressure signal with the voltage signal of PVDF piezoelectric thin film on the basis of simulation results. The correlation coefficients are listed in Tables 7 and 8. It is shown that the mechanical vibration frequency had little influence on the strong correlation between physical quantities (including circumferential stress and strain of the pipe wall and fluid pressure) and the signal of the PVDF piezoelectric film sensor when both ends of the pipe were fixed by hoops. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Pulsation Amplitude** **(m/s)**} & **Plane1 and PVDF1** & **Plane2 and PVDF2** & **Plane3 and PVDF3** \\ \cline{2-4}  & **Pressure and Voltage** & **Pressure and Voltage** & **Pressure and Voltage** \\ \hline
0 & 0.8651 & 0.9754 & 0.8598 \\
0.025 & 0.8756 & 0.9704 & 0.8689 \\
0.05 & 0.8085 & 0.9562 & 0.8897 \\
0.1 & 0.9164 & 0.9457 & 0.9098 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Correlation coefficient. Figure 10: Diagram of **(a)** mechanical vibration; **(b)** sinusoidal vibration. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Vibration Frequency** **(Hz)**} & \multicolumn{2}{c}{**Ponit1 and PVDF1**} & \multicolumn{2}{c}{**Point2 and PVDF2**} & \multicolumn{2}{c}{**Ponit3 and PVDF3**} \\ \cline{2-5}  & **Circumferential** & **Circumferential** & **Circumferential** & **Circumferential** & **Circumferential** \\
**Strain and** **Stress and** & **Stress and** & **Strain and** & **Stress and** & **Strain and** & **Stress and** \\
**PVDF Voltage** & **PVDF Voltage** & **PVDF Voltage** & **PVDF Voltage** & **PVDF Voltage** & **PVDF Voltage** \\ \hline
0 & 0.9544 & 0.9632 & 0.9641 & 0.9735 & 0.9533 & 0.9660 \\
5 & 0.9611 & 0.9692 & 0.9535 & 0.9656 & 0.9293 & 0.9468 \\
10 & 0.9752 & 0.9802 & 0.9564 & 0.9677 & 0.9387 & 0.9539 \\
20 & 0.9775 & 0.97 Then, the influence of the mechanical vibration amplitude was studied. The vibration amplitudes were set to 0.1, 0.2, 0.3, and 0.4 mm, and the vibration frequencies were all set to 40 Hz. Keeping all the other settings unchanged, we compared the circumferential stress and strain signals of the pipe wall and the fluid pressure signal with the voltage signal of PVDF piezoelectric thin film on the basis of simulation results. The correlation coefficients between physical quantities and PVDF signals are listed in Tables 9 and 10. Figure 11a-c displays the curves that compared the physical quantities and the measured signal of PVDF films as the vibration frequency was 40 Hz and the vibration amplitude was 0.1 mm. It can be concluded from Tables 9 and 10 and Figure 11 that the mechanical vibration amplitude had little influence on the measurement of the PVDF piezoelectric film sensor.