## 3 Results And Discussion
### Coupling Calculation and Structural Radiation Noise Analysis  
To fully characterize the radiated noise of underwater vehicle, the relevant structure-radiated noise calculations were also carried out. In structure-radiated noise calculations, the structure is considered as an elastomer, which deforms and vibrates under the pulsating pressure at the vehicle wall and acts as a radiated noise source. Therefore, the structural mesh is imported, and the pulsating pressure is applied to the solid surface for coupled calculations. When the deformation of the surface of structure is small, the changes in flow field caused by the deformation of structure are negligible. Therefore, only the action of the fluid on the solid can be considered to simplify the calculation process, while ensuring the accuracy and precision of the calculation. In this section, the results of flow field calculations are used as input boundary conditions for subsequent related calculations, and the computational domain is still taken as a spherical region of the same size. To simulate the shell vibration of a realistic underwater vehicle, the interior of underwater vehicle shown in Figure 1a was selectively hollowed out with a shell thickness of 20 mm. The material is set to Aluminum alloy with a Young's modulus of \(8.2\times 10^{10}\) N/m\({}^{2}\), Poisson's ratio of 0.33, and density of 2820 kg/m\({}^{3}\), and its intersection was set to the coupling surface. Figure 8: Spectral characteristics of sound pressure at different monitoring points along the flow direction considering Lighthill volume excition. (**a**) Receiver 1–3 (**b**) Receiver 4–6 (**c**) Receiver 6–7 (**d**) Receiver 8–11 (**e**) Receiver 12–14. Figure 9: Comparison results of spectral characteristics. (**a**) Receiver 1 (**b**) Receiver 13. Using the vehicle wall pressure pulsation data as a boundary condition, coupled calculations were carried out to obtain the vibration displacement of underwater vehicle, as shown in Figure 10. The results show that under the effect of wall pulsation pressure, the vibration displacements throughout the solid domain are similar to the wall pressure pulsation distribution, both showing a trend towards larger values in the low-frequency part and smaller values in the high-frequency part. At 50 Hz, the underwater vehicle's stern section reached a maximum vibration displacement of the order of \(10^{-5}\) m, while the high-frequency section is much less than this. For example, the maximum vibration displacement of a 750 Hz torpedo is only in the order of \(10^{-9}\) m. It is precise because the low-frequency part of vibration is more intense, and the large eddies can be considered to play a crucial role while generating the vibration. The mean square vibration speed characteristics of underwater vehicle were obtained, as shown in Figure 11. In general, the mean square speed decreases as the frequency increases, i.e., the mean square speed is generally higher in the low-frequency part than in the high-frequency band. The results of other researchers show that the location of peak frequency point is only related to the structural model itself and is not related to the strength of flow excitation vibration at different flow velocities. Therefore, it can be assumed that the larger peak vibration velocity points for this structural underwater vehicle are located roughly at the frequency points of 300 Hz, 850 Hz, 1400 Hz, and 1850 Hz. The frequency domain distribution curve of the structure's radiated noise shows distinctly different characteristics from the flow field radiated noise, showing a more pronounced vibration profile.