## 1 Introduction
### Calculation of the Transfered Power Flow of the Coupling System
From the point of view of the average energy input value, improperly assigned \(g_{11}^{(5)}\) can also deteriorate the system's sound insulation in the high-frequency region. In this simulation, the significant effective sound insulation frequency range is about 1-400 Hz with proper assignment of \(g_{11}^{(5)}\). Combining Figure 6c-f, in the narrow region on the right side very close to \(g_{11}^{(5)}=0\), the first resonance peak is basically eliminated, which indicates that the sound insulation effect of the system is well. Outside this narrow region, the peak values are all significantly lower than at \(g_{11}^{(5)}=0\), indicating that the system also has some sound insulation effect. However, there is an elevated resonance peak in the local region on the left side very close to \(g_{11}^{(5)}=0\). This indicates that the \(g_{11}^{(5)}\) at this time exacerbates the resonance effect and deteriorates the system's sound insulation. In summary, the effective range of the feedback parameters for the relative velocity feedback control method is narrow. Within the effective range of values, it can improve the system's low- and medium-frequency sound insulation capability. However, outside the effective range, it does not play a role in the system's low- and medium-frequency sound insulation, and even plays a deteriorating role in the system's high-frequency sound insulation. On the whole, the sound insulation effect under the relative velocity feedback control method is worse than that of the absolute velocity feedback control method. As shown in Figure 7a,b, the overall \(P_{\rm tr}\) curve has a slight rightward shift as \(\left| \begin{matrix}g_{11}^{(6)}\\ \end{matrix} \right|\) increases. Small fluctuations precede the first resonance peak in the low- and medium-frequency domains under the action of \(g_{11}^{(6)}\). In the high-frequency region, \(g_{11}^{(6)}\) does not make the problem solved, where the system's higher-order modes are excited and trigger a large number of peaks, and even the \(P_{\rm tr}\) value increases slightly. From the point of view of resonant frequencies, improperly assigned \(g_{11}^{(6)}\) can slightly deteriorate the system's sound insulation in the low- and medium-frequency regions. From the point of view of the average energy input value, improperly assigned \(g_{11}^{(6)}\) can also deteriorate the system's sound insulation in the high-frequency region. In this simulation, the significant effective sound insulation frequency range is about 1-400 Hz with proper assignment of \(g_{11}^{(6)}\). Combining Figure 7c-f, in the narrow region on the right side very close to \(g_{11}^{(6)}=0\), the first resonance peak is basically eliminated, which indicates that the sound insulation effect of the system is well. Outside this narrow region, although the peak is reduced compared to that at \(g_{11}^{(6)}=0\), it is not very significant. In addition to the first resonance peak, the second and third resonance peaks are still present. Some values of \(g_{11}^{(6)}\) cause a fluctuation in the frequency domain before the first resonance peak of the system. This indicates that the system's sound insulation deteriorates at this time. In summary, the effective range of the feedback parameters for the relative acceleration feedback control method is narrow. Within the effective range of values, it can improve the system's low- and medium-frequency sound insulation capability. However, outside the effective range, it does not play a role in the system's low- and medium-frequency sound insulation, and even plays a deteriorating role in the system's low-, medium-, and high-frequency sound insulation. On the whole, the sound insulation effect under the relative acceleration feedback control method is worse than that of the absolute acceleration feedback control method.