## 2 Methodology
### Design Parameters  
Based on the number of teeth and speed calculation, it was concluded that the internal gear meshing frequencies of this main reducer were 360 Hz and 900 Hz, and it produces harmonic frequencies at 720 Hz, 1080 Hz, 1440 Hz, and 1800 Hz. Considering the small space inside the nacelle and convenience of subsequent processing, the thickness of the MPP was selected as 1 mm, and the depth of the air-back cavity was set as 20 mm. Therefore, for the Combined MPP, one only needs to consider the perforation rate and aperture of the two MPPs. The design resonant frequencies corresponded to 900 Hz and 1440 Hz, and the design sound absorption bandwidth was 500-2000 Hz. The design parameters of the Combined MPP are listed in Table 2.  
The porous acoustic material was melamine acoustic sponge, and its basic acoustic parameters are described in Section 2. Here, we only need the MPP parameters for the design. The design resonant frequency was 900 Hz, and the design acoustic bandwidth was 500-2000 Hz. The design parameters of the MPP+Porous structure are listed in Table 3.  
In the MPP+PAM, the design of a single cell of a thin-plate acoustic metamaterial was first performed. As the boundary state of the thin-plate acoustic metamaterial affects the modal characteristics of the resonant system, a clamping device, consisting of two frames of the same size at the top and bottom, was used to fix it, as depicted in Figure 6.  
The main parameters of the MPP+PAM included the microperforated plate parameters, relevant parameters of the thin plate and mass block, and depth of the air-back cavity before and after the thin plate. The design resonance frequency was 360 Hz, and the design absorption bandwidth was 300-400 Hz. The design variables and ranges of the values for the MPP+PAM are listed in Table 4.  
Based on the three composite acoustic structure design parameters, the calculated absorption coefficient curves of the various composite acoustic structures in the frequency range of 0-2000 Hz were plotted, as shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Structure** & **Parameters** & **Numerical Value** & **Parameters** & **Numerical Value** \\ \hline MPP+PAM & Pore size \(d\) & 0.53 mm & Perforation rate \(p\) & 0.96\% \\  & Depth of cavity in front & Depth of cavity behind & & \\  & of thin plate \(D_{1}\) & 10 mm & thin plate \(D_{2}\) & 10 mm \\  & Thin plate thickness \(tp\) & 0.2 mm & Thin plate length \(B\) & 50 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MPP+PAM design parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Structure** & **Parameters** & **Numerical Value** & **Parameters** & **Numerical Value** \\ \hline Combined MPP & Pore size \(d_{1}\) & 0.40 mm & Perforation rate \(p_{1}\) & 2.88\% \\  & Pore size \(d_{2}\) & 0.57 mm & Perforation rate \(p_{2}\) & 0.94\% \\  & Plate thickness \(t\) & 1.00 mm & Dorsal cavity depth \(D\) & 20 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Combined MPP design parameters. Figure 6: Schematic of the PAM clamping device. As can be seen in Figure 7, the optimized structure exhibits good sound absorption at the designed resonant frequency and in the target frequency band. Under the condition of the positive incidence of sound waves, the peak absorption is close to 1, which is equivalent to the performance of \"perfect sound absorbers\". The combined MPP and MPP+Porous have absorption coefficients greater than 0.5 in the 700-1400 Hz range. In contrast, the MPP+PAM produces three absorption peaks through the mutual coupling of the microperforated plate and acoustic metamaterial owing to the introduction of new absorption peaks at low frequencies in the thin plate-mass block system. At the middle and high frequencies, the fourth-order modal resonance of the thin plate-mass block system coupled with the MPP forms a double absorption peak, but the absorption bandwidth becomes narrower.