## 4 Effect of Viscoelastic Damping on Underwater Acoustic Radiation
### Location of Damping  
Taking the 10 mm thick damping as an example, the damping is laid on the panel, web and ribbed slab respectively, as shown in Figure 11.  
Figure 10: Acoustic radiation field corresponding to different damping thickness (1000 Hz): (**a**) 5 mm; (**b**) 10 mm; (**c**) 20 mm.  
Figure 9: Acoustic radiation field corresponding to different damping thickness (50 Hz): (**b**) 5 mm; (**c**) 20 mm.  
Figure 12 shows the sound power level corresponding to different damping locations. As shown in Figure 12, the sound power increases at a low frequency after applying damping, while the sound power starts to decrease as the frequency continues to increase. However, the sound power of the undamped structure keeps increasing. By comparing, it is found that applying damping on the structural bases can effectively reduce the sound power level at a high frequency. Moreover, if the damping is laid on the web, the decrease in the sound power level is the greatest and the best vibration damping effect is achieved. If the damping is laid on the ribbed slab, the sound power of the structure would first increase and then decrease, and the peak appears at 800 Hz. If the damping is laid on the plate, the sound power has the same tendency as that of undamped structures, and the overall amplitude is relatively low.  
Figures 13 and 14 present the acoustic radiation field corresponding to the four damping application methods of damping in the yoz plane. As shown, although the damping application method is different, the distributions of sound pressure level are much similar at a low frequency. As the frequency increases, the effect of the damping position on the acoustic radiation field can be observed. Since the interval of natural frequencies is larger at low frequencies, the structures corresponding to the four damping application methods are in the same mode at 50 Hz. The intervals of natural frequencies become small as the frequency increases. When the frequency reaches 1500 Hz, the structure is in different modes, so the acoustic radiation field shows notable difference.  
Figure 11: Location of the damping on the base.  
Figure 12: Sound power level corresponding to different damping positions.  
In addition, when the excitation frequency is 50 Hz, although the shapes of the acoustic radiation field are similar, the values of sound pressure are different. The sound pressure level with the damping on the plate is the lowest. Compared with the undamped condition, the maximum value of sound pressure is reduced by 17 dB, while the minimum value decreases by around 9 dB. The changes in sound pressure level with the damping on the web and ribbed slab are almost same. Moreover, it can be seen from Figure 13 that when the damping is laid on the ribbed slab, the sound pressure level in the far-field reaches a minimum. In other words, the radiation range is minimal. It is found that the different locations of damping have different influences on the acoustic radiation field at different excitation frequencies, which has a significant relationship with the vibration modes of structure at the corresponding frequency.  
Figure 13: Acoustic radiation field in the yoz plane (50 Hz): (**a**) no damping; (**b**) damping on the plate; (**c**) damping on the web; (**d**) damping on the ribbed slab.