## 3 Numerical Simulation Analysis
### Establishment and Validation of a Micro-Perforated Finite Element Model
(**a**) Finite element model of a micro-perforated plate; (**b**) comparative graph of literature results and simulation results. As shown in Figure 9b, the ring-stiffened sandwich cylindrical shell includes upper and lower aluminum thin cover plates, an inner shell, an outer shell, and four ring stiffeners. The inner shell of this structure does not contain micro-perforations, while the remaining geometric parameters and material parameters remain consistent with the micro-perforated ring-stiffened sandwich cylindrical shell. As shown in Figure 9c, the ribless sandwich cylindrical shell includes only upper and lower aluminum thin cover plates, an inner shell, and an outer shell. In Figure 9d, on the basis of the ribless sandwich structure, micro-perforations are introduced into the inner shell of the ribless structure, with a micro-perforation hole diameter of 0.1 mm and a perforation ratio of 0.1%. The simulation load comprises a point force excitation with a 10 N magnitude, applied at the inner shell center, radially outwards. Additionally, a sound point source, located at the center of the inner cavity and with a radiated power of 1 W, is included. The boundary conditions entail free ends on both sides of the shell. The simulation considers a frequency range of 1-1000 Hz. Figure 10 illustrates a contrast of the radiated sound power level with and without micro-perforated structures. In the presence of the rib (Figure 10a), micro-perforations have an effect solely on the peak of the structural radiated sound power level within the frequency range of 1-500 Hz, with negligible impact on other frequencies. Within this frequency range, the structure's resonance is primarily caused by the upper and lower thin cover plates. As demonstrated in Figure 11a, the shell vibration's lowest natural frequency is 554.44 Hz. Since the cover plates lack micro-perforated structures, the effect of the micro-perforations is weaker. Within the range of 500-1000 Hz, the micro-perforated structure can effectively reduce the radiated sound power level at the characteristic frequency of the shell while reducing the acoustic field-structure resonance peaks (e.g., 600-700 Hz), thereby lowering the structural radiated sound power level. Similarly, for the case without ribs (Figure 10b), within the frequency range of 1-300 Hz, the structure with micro-perforations has an impact only at the peak of the structural radiated sound power level, with minimal influence at other frequencies. Within the 300-1000 Hz frequency range, the micro-perforated structure can effectively reduce the radiated sound power level at the characteristic frequency of the shell while reducing the acoustic field-structure resonance peaks (e.g., 600-800 Hz), thus lowering the structural radiated sound power level. From the perspective of overall radiated sound power level, within the 1-1000 Hz frequency range, the overall radiated sound power levels of the micro-perforated ring-stiffened sandwich shell and the ring-stiffened sandwich shell are 135.59 dB and 135.77 dB, respectively. For the ribless sandwich shell and the ribless micro-perforated sandwich shell, the overall radiated sound power levels are 135.67 dB and 135.45 dB, respectively. Therefore, micro-perforations can reduce the overall radiated sound power level of the structure to some extent. Figure 9: _Cont._  
Figure 9: Schematic diagrams of different sandwich structures. (**a**) Micro-perforated ribbed sandwich cylinder shell structure; (**b**) ribbed sandwich cylinder shell structure; (**c**) ribless sandwich cylinder shell structure; (**d**) ribless perforated sandwich cylinder shell structure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Density (kg/m3)** & **Elastic Modulus (GPa)** & **Poisson’s Ratio** \\ \hline Aluminum & 2700 & 70 & 0.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of aluminum. Figure 11: Structural mode shapes. (**a**) vibration mode shapes of a ribbed cylindrical shell; (**b**) vibration mode shapes of a ribless cylindrical shell.