Acoustic Scattering Analysis of Underwater Elastic Spherical Shell under Point Sound Source Incidence
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摘要: 为了研究水下目标的声散射问题, 在经典Rayleigh简正级数解析解的基础上, 结合格林函数在球坐标系中的表达式, 计算了点声源球面波与平面波的折算因子; 基于平面波入射下弹性球壳的散射声场, 完成了点声源入射下的弹性球壳散射声场求解, 并进行了有限元验证。以此为基础, 计算并分析了典型球状目标的目标强度; 从目标强度的角度出发, 对点声源与球心的距离进行量化, 提出球面波可近似为平面波处理的条件。研究结果表明: 当点声源在球体表面附近时, 散射体的目标强度曲线峰值相对于平面波入射下会发生偏移; 此外在无因次频率 ka <50时, 球面波可近似为平面波入射, 点声源和球心的临界距离与球壳半径、球壳厚度有关。研究结果可为水下目标的探测、识别及水声测量实验提供理论参考。Abstract: In order to study the acoustic scattering of underwater targets, the conversion factor of plane wave and spherical wave of point sound source was calculated on the basis of the analytical solution of the classical Rayleigh normal series, combined with the expression of Green’s function in the spherical coordinate system. Based on the scattered sound field of the elastic spherical shell under the incidence of plane wave, the scattered sound field of the elastic spherical shell under the incidence of point sound source was solved, and finite element verification was carried out. On this basis, the target strength of typical spherical targets were calculated and analyzed. From the perspective of target strength, the distance from the center of the sphere and the point sound source was quantified, and the condition that the spherical wave was approximately equivalent to the plane wave was proposed. The results show that the peak value of the target strength curve of the sphere will shift relative to the incidence of plane wave when the point sound source is near the sphere. In addition, the spherical wave can be approximated to the plane wave incidence with the dimensionless frequency ka < 50, and the distance between the point sound source and the spherical center is related to the radius and thickness of the spherical shell. The results can provide a theoretical reference for the detection, identification, and underwater acoustic measurement experiments of underwater targets.
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图 4 不同截断数下ka<50时距离球心1 000 m处目标强度
Figure 4. Target strength at a distance of 1000 m from spherical center with ka<50 under different truncation numbers
图 6 有限元与理论解对比
Figure 6. Comparison of the finite element method and theoretical solution
图 8 平面波入射下点声源离球心不同距离时弹性球目标强度
Figure 8. Target strength of elastic sphere under different distances from point sound source to spherical center under plane wave incidence
图 11 平面波入射下不同ka及点声源距球心不同距离时弹性球回声强度
Figure 11. Echo strength of elastic sphere with different distances from point sound source to spherical center and different ka under plane wave incidence
图 12 平面波入射下不同ka及点声源距球心不同距离时弹性球壳回声强度
Figure 12. Echo strength of elastic spherical shell with different distances from point sound source to spherical center and different ka under plane wave incidence
表 1 壳厚比及球壳外径参数设置
Table 1. Parameter setting of shell thickness ratio and outer diameter of spherical shell
h a/m 0.01~0.39 0.2~4 0.41~0.81 
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