## 3 Numerical Simulation Analysis
### Establishment and Validation of a Micro-Perforated Finite Element Model
Figure 10: Influence of micro-perforations on structural radiated sound power level. (**a**) Comparison of radiated sound power levels between a micro-perforated ribbed shell and a ribbed shell; (**b**) comparison of radiated sound power levels between a ribless shell and a ribless micro-perforated shell. Figure 12 shows a comparison of the radiated sound power levels with and without ribs in the structure. It can be seen that the structure with ribs has fewer structural resonance peaks. This is because the ribs enhance the stiffness of the structure, reducing structural vibrations. 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 rib-stiffened shell and the ribless perforated shell are 135.59 dB and 135.45 dB, respectively. The overall radiated sound power levels of the rib-stiffened shell and the ribless shell are 135.77 dB and 135.67 dB, respectively. The sound power radiated by the structure with ribs may be lower due to the fact that the energy is mainly transferred through the ribs, whereas without ribs, the medium between the shells becomes the primary path for radiated sound energy to pass through [26]. It is evident that making a rational design for ribs is essential in reducing the radiated sound energy of the shell when arranging ribs to enhance structural stiffness. In conclusion, micro-perforations can decrease the radiated sound power level at structural natural frequencies, reduce the amount of peaks in the radiated sound power level curve of the shell, and, to a certain extent, diminish the overall radiated sound power level of the structure. In the meantime, ribbed structures enhance the shell's stiffness, shifting the natural frequencies to higher frequencies, and decreasing the peak values in the radiated sound power level curve. Therefore, micro-perforated rib-stiffened cylindrical shells offer a distinct advantage in mitigating the radiation of vibrational sound from structural components. The Influence of Micro-Perforation on the Vibration and Acoustic Radiation Performance of Cylindrical Shells  
With a lower radiated sound power level than the non-micro-perforated rib-stiffened cylindrical shell in Section 4.1, the investigation in this section aims to unveil how micro-perforation parameters, such as perforation rate and micro-hole diameter, affect the vibration and sound radiation performance of the micro-perforated rib-stiffened structure. The basic geometric parameters and structural parameters maintain their consistency with the ones in Section 4.1. To examine the impact of micro-hole perforation rate on the vibration and sound radiation properties of the micro-perforated rib-stiffened cylindrical shell structure, finite  
Figure 12: Impact of ribs on structural radiated sound power levels. (**a**) Comparison of radiated sound power levels between a perforated ribbed shell and a perforated ribless shell; (**b**) comparison of radiated sound power levels between a ribbed shell and a ribless shell. element simulation models were created. The models featured perforation rates of 0.05%, 0.01%, 0.15%, 0.2%, 1%, and 2%, while the other geometric and material parameters of the structure remained unaltered. The vibration and sound radiation characteristics of the micro-perforated laminated cylindrical shell were analyzed in an unconfined state across a frequency range of 1-1000 Hz. Evaluation of the resulting sound power level spectrum is presented in Figure 13. As shown in the figure, with a micro-hole diameter of 0.1 mm and other parameters unchanged, within the specified range of variation, as the perforation rate increases, the peak of the structure's sound radiation power level curve significantly decreases. Additionally, the number of peaks in the 500-700 Hz range also decreases, corresponding to a reduction in the structural acoustic resonance peaks.