## 6 Conclusions  
This study employs a finite element simulation analysis method and introduces micro-perforation acoustic parameters into the acoustic-vibration coupling model of laminated cylindrical shells. The accuracy of the finite element modeling method is verified through comparisons with experimental results from the literature. Based on this, the study investigates the influence of structural parameters, micro-perforation characteristics, foam materials, and foam installation methods on the vibration and acoustic radiation performance of laminated cylindrical shell structures within the 1-1000 Hz frequency range. The primary research work and findings of this paper are as follows:  
1. Under the simultaneous excitation of point force and point source, perforations in the inner shell effectively reduce the radiation acoustic power level at the characteristic frequency of the shell and reduce the number of acoustic structural resonance peaks, thereby lowering the structural radiation acoustic power level. Within the selected  
Figure 20: Frequency spectra of structural radiation sound power levels with varying placement positions for 20 mm foam. parameter range, as the micro-perforation rate and perforation diameter increase, the overall structural radiation acoustic power level decreases significantly, and the corresponding peaks decrease. However, due to its narrow operating range, the reduction in the overall structural radiation acoustic power level is not significant;
2. In the frequency range of 1-1000 Hz, the position of sound-absorbing foam has the most significant impact on the vibration and acoustic radiation performance of the structure within the 300-810 Hz frequency range. Various types of foam can lessen the acoustic power level caused by structural radiation, with polyurethane being the optimal choice for reducing it up to 11.14 dB. Nonetheless, the foam's placement has no effect on the natural vibration frequencies of the structure. When the foam thickness varies within the 80-810 Hz frequency range, the overall level of acoustic power radiated by the structure declines as the foam thickness increases. The performance reaches its maximum at a thickness of 40 mm, resulting in a decrease of up to 11.14 dB;
3. In the 300-810 Hz and 900-1000 Hz frequency ranges, as the sound-absorbing foam placement rate increases, the structural radiation acoustic power level gradually decreases, and the reduction values gradually diminish. Compared to the situation without the placement of sound-absorbing foam, the overall structural radiation acoustic power level is reduced by 0.4 dB, 0.77 dB, 0.94 dB, 1.16 dB, and 1.19 dB when 20%, 40%, 60%, 80%, and 100% foam is placed, respectively, indicating that the acoustic performance of the micro-perforated laminated cylindrical shell is optimal when fully equipped with foam;
4. In the frequency range of 1-1000 Hz and with no change in foam thickness, a 60% placement rate has a minimal effect on the level of structural radiation acoustic power, as the foam thickness is less than 6% of the cavity radius and only the placement location was modified. This finding indicates that to achieve better noise reduction results in practical applications, the relationship between foam thickness and acoustic wavelength must be considered. Conceptualization, B.L. ; methodology, Z.Z. ; validation, Z.Z. ; formal analysis, Z.Z. and N.W. ; resources, B.L. ; data curation, Z.Z. and N.W. ; writing--original draft preparation, N.W., Z.Z., W.K., L.W., Y.C., J.H. and S.C.; writing--review and editing, N.W. ; visualization, Z.Z. ; supervision, B.L. ; project administration, B.L. ; funding acquisition, B.L. All authors have read and agreed to the published version of the manuscript. The work is supported by the 2022 Knowledge Innovation Dawn Special Plan Project (2022010801020393), Research and Innovation Initiatives of WHPU (2022)04). This work was finished at Wuhan Polytechnic University, Wuhan, China. The data in this study are available in the article.