## 3 Numerical Simulation Analysis
### Establishment and Validation of a Micro-Perforated Finite Element Model
From the perspective of the overall sound radiation power level, within the range of 1-1000 Hz, the structure's overall sound radiation power levels for inner shell perforation rates of 0.05%, 0.01%, 0.15%, 0.2%, 1%, and 2% are 135.69 dB, 135.59 dB, 135.51 dB, 135.45 dB, 134.90 dB, and 134.62 dB, respectively, with the structure's overall sound radiation power level decreasing as the perforation rate increases. Following the design of the previous experiment, finite element simulation models with micro-hole diameters of 0.02 mm, 0.06 mm, 0.1 mm, 0.14 mm, and 0.5 mm were constructed to investigate the influence of micro-pore diameter on the structural vibration and acoustic radiation performance. The radiation acoustic power level frequency spectra within the 1-1000 Hz frequency range were computed, as shown in Figure 14. It can be seen from the figure that, with a perforation rate of 0.1% and other parameters held constant within the indicated range, as the micro-hole diameter increases continuously, the peak value of the structural radiation acoustic power level curve significantly decreases. Moreover, there is a noticeable reduction in the peaks around 400 Hz and in the range of 600-700 Hz. From an analysis of overall radiation acoustic power levels within the 1-1000 Hz frequency range, it was found that the structural acoustic power levels for inner shell micro-hole diameters are as follows: 135.82 dB, 135.72 dB, 135.59 dB, 135.48 dB, and 134.18 dB. The overall structural radiation acoustic power level follows a downward trend as micro-hole diameter increases. Figure 13: Frequency spectra of structural radiated sound power levels at different perforation rates. Findings from the assessment of two variables imply that micro-perforated structures can effectively diminish structural radiated sound power levels at specific frequencies and, to a certain extent, decrease the overall radiated sound power levels from a structure. This is due to the fact that when sound waves pass through micro-perforated structures, a part of the sound energy is absorbed and transformed into heat instead of being reflected or transmitted, which consequently leads to a reduction in total sound power. However, the reduction in the overall radiated sound power level is not significantly notable due to the limited scope of its effect. Micro-perforated structures have inherent acoustic resonance frequencies, which are determined by the geometric dimensions of the small holes and material characteristics. When sound waves reach or match the inherent resonance frequencies, micro-perforated structures create a resonance effect. This phenomenon leads to a noteworthy sound absorption within the porous material, resulting in reduced radiation [27]. The Influence of Foam Laying on the Vibration and Acoustic Radiation Performance of Micro-Perforated Sandwich Cylindrical Shells  
Section 4 explored how the shell structure and micro-perforation parameters affect the vibrational acoustic radiation performance of micro-perforated laminated cylindrical shells. The study found that micro-perforations can decrease sound power levels near the shell's natural frequencies. However, it did not yield noteworthy outcomes in reducing overall structural acoustic radiation. In this chapter, the surface of the structural shell will be treated with sound-absorbing materials to decrease the outward radiation of acoustic energy. The study will explore how variables such as foam material type, thickness, and laying method affect the structure's vibration and acoustic radiation performance. This chapter examines a laminated shell structure with foam and micro-perforations, composed of upper and lower wooden cover plates, a micro-perforated inner shell, an outer shell, four ring ribs, and an outer shell surface sound-absorbing material layer, as illustrated in Figure 15a. Additionally, a corresponding finite element simulation model is established, as depicted in Figure 15b. The outer shell radius is \(R_{2}\) = 290 mm, while the diameter of the micro-holes measures 0.5 mm.