## 5 Analysis of Vibro-Acoustic Coupling Characteristics  
### The Influence of ABHs and Damping Layer on Sound Pressure  
The damping material was attached to the four ABH regions, and the damping ABH plate-cavity vibro-acoustic model was established in the LMS Virtual.Lab(r). The parameters of the damping material are shown in Table 1, and the FEM model of ABH plate with the damping material is shown in Figure 6. The ABH rectangular plate and the damping layers were meshed using the second-order tetrahedral unit C3D10. The grid size of the uniform region of the ABH plate was 4 mm, and the grid size of the ABH region and the damping layers was 2 mm. The mesh in the small curved area of the ABH region and the damping layers was encrypted to ensure a smooth transition from small cells to large cells, and the minimum cell size was 0.2 mm during encryption. The inner surface of the damping ABH  
Figure 5: The influence of ABHs on coupling modes: (**a**) coupling mode of the ABH coupling system at 773 Hz; (**b**) coupling mode of the uniform plate-cavity coupling system at 805 Hz; (**c**) coupling mode of the ABH coupling system at 1035 Hz; (**d**) coupling mode of the uniform plate-cavity coupling system at 1051 Hz; (**e**) coupling mode of the ABH coupling system at 2075 Hz; (**f**) coupling mode of the uniform plate-cavity coupling system at 2085 Hz. plate model and the five inner surfaces of the shell model established in Section 4 are each fully coupled with the six surfaces of the corresponding acoustic mesh, through which the vibro-acoustic model of the damping ABH plate-cavity is obtained. The influence of ABHs and the damping layers is studied by comprehensively comparing the sound pressure in the acoustic cavity of the damping ABH coupling system, the undamping ABH plate-cavity coupling system, and the uniform thickness plate-cavity coupling system. Vibro-acoustic coupling calculations were performed on the damping ABH coupling system, the undamping ABH coupling system, and the uniform thickness plate-cavity coupling system to obtain the vibration response of the structure and the acoustic response of the acoustic fields. The acting position of the excitation force was the centre of the outer surface of the ABH plate (for the rectangular plate of uniform thickness, it was the centre of the outer surface of the uniform plate). The amplitude of the excitation force was 10 N, and the frequency started at 1 Hz and ended at 5000 Hz, with a step length of 1 Hz. The calculation frequency of the vibro-acoustic coupling response was 1-5 kHz, and the step length was 50 Hz. The results show that, compared with the uniform thickness plate-cavity coupling system, the damping ABH coupling system and the undamping ABH coupling system could not achieve significant sound suppression effects in the whole calculation frequency band, and only on some certain calculation frequencies, and the sound pressure in their cavities was greatly reduced. From the results of the 101 calculated frequencies, the sound pressure distributions at three frequencies where the ABHs and the damping layer had an obvious effect on the sound pressure suppression are selected, as seen in Figure 7. It can be seen from Figure 7 that at 751 Hz, 4201 Hz, and 4801 Hz, the undamping ABH coupling system had a significant reduction in the maximum sound pressure of the acoustic cavity compared to the uniform thickness plate-cavity coupling system, and the maximum sound pressure of the damping ABH coupling system was further reduced. At 751 Hz, the maximum sound pressure of the undamping ABH coupling system was nearly 10 dB lower than the maximum sound pressure of the uniform-thickness plate-cavity coupling system, while the maximum sound pressure of the damping ABH coupling system was 17 dB lower than that of the uniform-thickness plate-cavity coupling system.