## 1 Introduction
### Calculation of the Transfered Power Flow of the Coupling System
Figure 4: The 2D view and 3D view of \(g_{11}^{(3)}\) — \(Fre\) — \(P_{\rm tr}\) under the absolute acceleration feedback control method (\(g_{11}^{(3)}\in(-10^{4},\,10^{4})\), the step size is set to 10): (**a**) comparison of \(P_{\rm tr}\) curves under \(g_{11}^{(3)}>0\); (**b**) comparison of \(P_{\rm tr}\) curves under \(g_{11}^{(3)}<0\); (**c**) the 3D view of \(P_{\rm tr}\) curve under continuous variation of \(g_{11}^{(3)}\); (**d**) X-Y plane view; (**e**) X-Z plane view; (**f**) Y-Z plane view. Figure 5: The 2D view and 3D view of \(g_{11}^{(4)}\) — \(Fre\) — \(P_{\rm tr}\) under the relative displacement feedback control method ( \(g_{11}^{(4)}\in\left(-10^{9},\,10^{9}\right)\), the step size is set to \(1\times 10^{6}\)): (**a**) comparison of \(P_{\rm tr}\) curves under \(g_{11}^{(4)}>0\); (**b**) comparison of \(P_{\rm tr}\) curves under \(g_{11}^{(4)}<0\); (**c**) the 3D view of \(P_{\rm tr}\) curve under continuous variation of \(g_{11}^{(4)}\);(**d**) X-Y plane view; (**e**) X-Z plane view; (**f**) Y-Z plane view. In Figures 2-7, both Figures (a) and (b) show the trends and comparisons of the curves of \(P_{\text{tr}}\) in the frequency domain from 0 to 1000 Hz for several different sets of feedback parameter values at \(g_{11}^{(k)}>0\) and \(g_{11}^{(k)}<0\), respectively. To more clearly and intuitively represent the distribution and variation of resonance peaks with smaller values, the scale value of the vertical coordinate is \(20\cdot\lg(P_{\text{tr}}/P_{\text{ref}})\), where \(P_{\text{ref}}\) is a reference power flow and takes the value of 1. The unit is also converted to dimensionless dB. Both Figures (c) show the distribution of the main resonance peak in the frequency domain for continuously varying \(g_{11}^{(k)}\). Figures (d), (e), and (f) show the planar views of Figures (c) in the X-Y, X-Z, and Y-Z directions, respectively. Here, there is no logarithmic treatment of the vertical coordinate \(P_{\text{tr}}\), and the order of magnitude of the \(P_{\text{tr}}\) values at the main resonance peaks in the low-frequency region is much larger than at other places. Therefore, except for these main resonance peaks, the \(P_{\text{tr}}\) values at other places are basically shown to converge to zero in these figures. In this simulation example, the area near the first order resonance peak is defined as the low-frequency region, which ranges from about 0 to 200 Hz; the area where the second- and third-order resonance peaks are located is defined as the medium-frequency region, which ranges from about 200 to 400 Hz; the area after the third-order resonance peak is defined as the high-frequency region, which ranges from about 400 Hz to more. The specific analysis of Figures 2-7 is as follows. As shown in Figure 2a,b, the overall \(P_{\text{tr}}\) curve shows a gradual sinking trend as \(\left|g_{11}^{(1)}\right|\) increases, but there is a local rising in the high-frequency region at \(g_{11}^{(1)}=1.0\times 10^{7}\). In the low- and medium-frequency region, the first resonance peak gradually shifts to the left with the increase of \(\left|g_{11}^{(1)}\right|\), and its peak is also reduced. In the high-frequency region, \(g_{11}^{(1)}\) does not make the problem solved, where the system's higher-order modes are excited and trigger a large number of peaks. This indicates that properly assigned \(g_{11}^{(1)}\) can optimize  
Figure 7: The 2D view and 3D view of \(g_{11}^{(6)}-Fre\to P_{\text{tr}}\) under the relative acceleration feedback control method ( \(g_{11}^{(6)}\in(-10^{3},\,10^{3})\), the step size is set to 1): (a) comparison of \(P_{\text{tr}}\) curves under \(g_{11}^{(6)}>0\); (b) comparison of \(P_{\text{tr}}\) curves under \(g_{11}^{(6)}<0\); (c) the 3D view of \(P_{\text{tr}}\) curve under continuous variation of \(g_{11}^{(6)}\); (d) X-Y plane view; (e) X-Z plane view; (f) Y-Z plane view. the system's sound insulation in the low- and medium-frequency region, but improperly assigned \(g_{11}^{(1)}\) may deteriorate it instead.