# Vibration Control of an Aero Pipeline System with Active Constraint Layer Damping Treatment
## 3 Results and Discussion
### Results of the FEM-Based Control Parameters Analysis  
When the first-order bending vibration occurs in the pipeline with fixed support at both ends, the stress on both ends of the pipeline is large, and failure will occur after a long period of time. Therefore, it is considered that the ACLD patches are adhered to the place where the stress at the root of the pipe reaches the maximum and its damping effect is evaluated. Different control voltages are applied on the piezoelectric constraint layer to compare the damping performance of the ACLD patches. A constant acceleration excitation of 0.2 g is applied on the pipeline, the acceleration response near the middle node of the pipeline is extracted, and the results are shown in Figure 16.  
As can be seen from the above figure, when different control voltages are applied, the damping effect of the ACLD patches will change. With the increase of the control voltage, the damping effect becomes more obvious, as is shown in Table 5.  
The above results show that with the increase of the control voltage, the acceleration response decreases gradually. When the control voltage reaches 50 V, the acceleration response value decreases by 56.93%; However, as the voltage increases, the acceleration response that can be reduced per unit voltage becomes smaller. That is, under certain conditions, the effect of ACLD patches on vibration reduction is limited.  
Figure 16: Vibration response in the (**a**) time domain and (**b**) frequency domain under different control voltages.  
Figure 15: Influence of thickness of viscoelastic layer on the (**a**) modal frequency and (**b**) loss factor.  
The vibration control responses of the pipeline under different excitations shows that as the amplitude of the excitation increases, the peak value of the resonance response of the pipeline gradually increases. When the same control voltage is applied to the surface of the ACLD patches, the vibration control effect is gradually reduced. When the excitation is 0.1 g, the resonance peak of the pipeline can be decreased by 58.14%. When the base excitation is 0.3 g, the resonance peak of the pipeline can be decreased by 33.19%. Therefore, it is necessary to realize that the damping effect of the ACLD patches is limited under certain conditions due to the limitation of the hardware and control strategy.  
To investigate the influence of the piezoelectric material on the vibration control effect, a control voltage is applied to different numbers of piezoelectric ceramics. The excitation amplitude is 0.3 g and the amplitude of voltage is 50 V. The vibration control response curve shown in Figure 20 is obtained.  
Figure 20 shows that under the different number of ACLD patches, the performance of vibration control is different. With the increase of the number of ACLD patches, the amplitude of vibration acceleration response decreases gradually.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Amplitude of** **Excitations (g)**} & **Amplitude of** **Acceleration Before** **Vibration Control (g)** & **Acceleration Before** **Amplitude After** **Vibration Control (g)** & **DDoop Rate** \\ \hline
0.1 & 6.581 & 2.755 & 58.14\% \\
0.2 & 13.26 & 7.514 & 37.18\% \\
0.3 & 18.38 & 12.28 & 33.19\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Amplitude of the acceleration response under different excitations.  
Figure 19: Vibration response in the (**a**) time domain and (**b**) frequency domain under excitation of 0.3 g.  
Figure 20: Vibration response in the (**a**) time domain and (**b**) frequency domain with a different number of ACLD patches.