## 5 Analysis of Vibro-Acoustic Coupling Characteristics
### The Influence of ABHs and Damping Layer on Sound Pressure
At 4201 Hz, the maximum sound pressure of the undamping ABH coupling system was nearly 9 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 19 dB lower than that of the uniform-thickness plate-cavity coupling system. At 4801 Hz, these two values were 4 dB and 10 dB. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Density (kg/m\({}^{3}\))** & **Young’s Modulus (Pa)** & **Poisson’s Ratio** & **Loss Factor** \\ \hline Viscoelastic material & 1812 & \(9\times 10^{6}\) & 0.45 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Damping material properties. Figure 6: FEM model of the damping ABH plate. To investigate the sound pressure at key positions in the acoustic cavity in the full frequency range of 1 Hz to 5 kHz, six monitoring points were established at the same positions in every acoustic cavity of the three coupling systems, as shown in Figure 8. The origin of the coordinates in Figure 8 is the centre of the outer surface of the bottom rectangular plate. The coordinates of the six monitoring points are as follows: left below (\(-\)155, 0, 85), middle below (0, 0, 85), right below (155, 0, 85), left up (\(-\)155, 0, 315), middle up (0, 0, 315), and right below (155, 0, 315). The acoustic response of these six monitoring points in 1-5 kHz was obtained through vibro-acoustic coupling calculation so as to study the influence of the ABHs and damping layer on the sound pressure in the acoustic cavity of the coupling systems. Figure 7: The sound pressure distribution of damping ABH, undamping ABH, uniform thickness plate-cavity coupling system: (**a**) damping ABH coupling system at 751 Hz; (**b**) undamping ABH coupling system at 751 Hz; (**c**) uniform thickness ABH coupling system at 751 Hz; (**d**) damping ABH coupling system at 4201 Hz; (**e**) undamping ABH coupling system at 4201 Hz; (**f**) uniform thickness coupling system at 4201 Hz; (**g**) damping ABH coupling system at 4801 Hz; (**h**) undamping ABH coupling system at 4801 Hz; and (**i**) uniform thickness ABH coupling system at 4801 Hz. Figure 9 is the spectrum diagram of the sound pressure response of the six monitoring points in the acoustic cavity of the damping ABH coupling system, the undamping ABH coupling system, and the uniform thickness plate-cavity coupling system. It can be seen from Figure 9 that compared with the uniform thickness plate-cavity coupling system, neither the damping ABH coupling system nor the undamping ABH coupling system could reduce the sound pressure in the full frequency range from 1-5 kHz. However, for a certain frequency range and specific frequencies, the damping ABH coupling system and the undamping ABH coupling system could significantly suppress the sound pressure in the acoustic cavity, and in most cases, the suppression effect of the damping ABH coupling system was greater. For the left below and left up monitoring points, the sound pressure of the uniform thickness plate-cavity coupling system was the lowest in 0-700 Hz, and at most frequencies in the range of 1000-3600 Hz, the peak values of the sound pressure of the undamping ABH coupling system was significantly higher than that of the other two coupling systems and the sound pressure of the damping ABH coupling system was not significantly reduced. At most frequencies in the range of 3600-5000 Hz, the damping ABH coupling system could significantly suppress the sound pressure and greatly reduce the peak values. For the left below point, the sound pressure of the damping ABH coupling system at 3701 Hz, 4201 Hz, and 4751 Hz was reduced by 24.2 dB, 15 dB, and 14.2 dB, respectively, compared to that of the uniform thickness plate-cavity coupling system. However, the sound pressure of the left below point of the damping ABH coupling system at 4501 Hz was 4.9 dB higher than that of the uniform thickness plate-cavity coupling system.