## 3 Results And Discussion
### Coupling Calculation and Structural Radiation Noise Analysis
Several representative monitoring points were selected to show the frequency domain curves of sound pressure levels at their locations, as shown in Figure 12. It can be observed that whether the monitoring point is located at the leading, middle, or trailing edge of underwater vehicle, the structure-radiated noise has several corresponding peaks, all corresponding to the same frequency and peak frequency corresponding to the mean square vibration speed characteristic of torpedo. It can be inferred that this characteristic is related to the structure of underwater vehicle, and it is an inherent characteristic. From the sound pressure level curves of each monitoring point, it can be observed that the structure  
Figure 10: (**a–d**) Vibration displacement distribution. radiated noise is not very much related to distribution along the flow direction. Most of the monitoring points have the same trend and amplitude. In the low-frequency part, most of them are located around 125 dB, and the main peak points are located around 130 dB. Compared to the central part of underwater vehicle (receivers 4-7), the sound pressure levels at the leading edge of underwater vehicle (receivers 1-3) are in contrast larger than those at the trailing edge, which is an important feature that clearly differs from the fluid-radiated noise. In the high-frequency part, the sound pressure levels are also around 100 dB. In addition, monitoring point 13 has consistently higher sound pressure levels in fluid-radiated noise and lower values in structure-radiated noise, indicating that structure-radiated noise is very different from fluid-radiated noise in terms of propagation direction. Figure 11: Mean square vibration characteristics. Figure 12: Spectral characteristics of sound pressure at different monitoring points along the flow direction considering vibration excitation. (**a**) Receiver 1–3 (**b**) Receiver 4–6 (**c**) Receiver 6–7 (**d**) Receiver 8–11 (**e**) Receiver 12–14. For Monitoring Points 1, 2, and 3, the sound pressure level frequency domain distribution curves are shown in Figure 12a. Apart from the obvious peak in the curve, the sound pressure levels at monitoring point 2 are substantially different from the other two monitoring points. After the peak sound pressure level point at 1400 Hz, the sound pressure level in the high-frequency part of monitoring point 2 decreased below 90 dB, while the sound pressure level of the other two monitoring points remained at around 100 dB. After comparing the curves of monitoring points in the trailing edge section (shown in Figure 12e), it is demonstrated that the structure radiates less noise in the direction of axis of the underwater vehicle, which is particularly noticeable at high frequencies. To facilitate further analysis of radiation characteristics of sound field, a cloud of sound pressure levels for structure-radiated noise generated by structural vibration due to pulsating pressure at the vehicle wall is given in Figure 13. It can be observed that the pulsating sound pressure cloud at 100 Hz is a left-right symmetrical pattern, which is due to the axisymmetrical shape of underwater vehicle, i.e., the low-frequency band has a stronger acoustic directivity at the head and tail, but the blade section radiates more widely, indicating that the tail is more directive than the head of underwater vehicle. Above 100 Hz, the sound field gradually becomes more \"flap-like\", and the flap-like features become more pronounced as the frequency increases. When the frequency reaches 2000 Hz, the \"flap-like\" distribution is already very dense. As the frequency increases further, the \"flap-like\" features gradually develop to the left and right, and this flap-like feature, which characterizes the fluctuation and oscillation of sound pressure, often leads to a lower sound pressure level region in the direction of underwater vehicle axis.