## 4 Simulation
### Model Cabin Sound Field Simulation  
In this study, three MPP acoustic structures for noise reduction in the cabin of a model helicopter were developed. For comparison and verification, cabin sound field simulations were carried out for two cabin wall panels with and without MPP acoustic structures to obtain the sound pressure level (SPL) distribution in the cabin and analyze the cabin noise reduction characteristics of the MPP acoustic structures. Based on the vibration response of the wall plate under real gear meshing conditions obtained from the vibration source's simulation, the vibration acceleration responses of the back and bottom plates of the nacelle were used as the noise radiation source in the acoustic pressure field, employing a generalized stretching operator that mapped the values from the source end to the target end. Figure 22 illustrates the nacelle simulation model, where the helicopter nacelle consists of an external skin, an interior trim panel, and back and bottom plates as radiation sources. Four spherical domains within the model were used to simulate the human ear position of the occupants and thus measure the noise signal at typical locations within the cabin. The noise reduction characteristics of the cabin equipped with the microperforated composite acoustic structure on the interior panel were analyzed by comparing the two cases with the original wall panel. Through a pressure acoustic frequency domain simulation analysis, the SPL data of four typical measurement points in the cabin were acquired, and a weighted average was calculated to obtain the average SPL frequency response curve, as displayed in Figure 23.  
As shown in Figure 23, the average SPLs of the four measurement points in the cabin, after installing the composite microperforated plate acoustic structures, are attenuated to different degrees in the target frequency band range. Among them, the average SPL in  
Figure 21: Finite element model of the helicopter. (**a**) Geometric model. (**b**) Finite element mesh. Figure 20: Average acceleration frequency response curve of the main reducer housing. the cabin with the Combined MPP (Figure 23a) is significantly attenuated in the frequency ranges of 500-1000 Hz and 2300-2000 Hz. The attenuation values are 10.9, 24.9, 7.2, and 10.4 dB at the four engagement frequencies of 720, 900, 1080, and 1440 Hz, respectively. The average SPL in the cabin with the MPP+Porous structure (Figure 23b) is substantially attenuated in the 500-1000 Hz and 2300-2000 Hz bands, with 15.3, 24.1, 6.4, and 11.9 dB attenuation at the four engagement frequencies of 720, 900, 1080, and 1440 Hz, respectively. The average SPL in the cabin with the MPP+PAM (Figure 23c) is considerably attenuated in the frequency ranges of 350-500, 2300-1500, and 1700-2000 Hz, with 4.3, 23.4, and 11.3 dB attenuation at the three engagement frequencies of 360, 900, and 1440 Hz, respectively. The three MPP composite sound absorption structures controlled the cabin noise in the target frequency range to a satisfactory degree. Figure 23: Cont. Figure 22: Cabin geometry model. (**a**) Noise measurement points. (**b**) Interior trim panels. Comparing the experimental and simulation prediction results, it is not difficult to find that there are certain differences. The main reason for the error is that the simulation only considers the structural sound transmission and ignores the air sound transmission, while both exist simultaneously in the test. However, the trend of the overall SPL frequency response curves in the simulation and test results are basically the same, and the peaks and valleys of the engagement fundamental frequency and its harmonic frequency are obvious, mostly distributed around 40-60 dB. There is only an error in the SPL amplitude, which has less influence on the prediction of the structure noise reduction performance during simulation.