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基于镜像T矩阵法的楔形波导中有限长圆柱声散射研究

The imaging T-matrix method for acoustic scattering of the finite cylinder in wedge-shaped waveguide

  • 摘要: 针对楔形波导中两端带球帽的有限长圆柱声散射问题, 提出了一种镜像T矩阵法进行求解。该方法是一种半解析方法, 能够根据镜像原理将楔形波导中点声源入射下有限长圆柱声散射等效为无界域中多点源入射下多目标声散射问题, 再结合球谐函数的平移加法定理和旋转加法定理获得楔形波导中有限长圆柱的转换矩阵(T矩阵), 即可计算出楔形波导中有限长圆柱声散射半解析解。通过数值计算研究了点声源相对位置、有限长圆柱的空间姿态、浸没深度和波导倾角对楔形波导中有限长圆柱背向散射以及散射声场空间分布的影响。该工作可推广至浅海波导中多目标声散射问题研究。

     

    Abstract: The imaging T-matrix method is proposed to semi-analytically solve the acoustic scattering from the finite cylinder with hemisphere endcaps in wedge-shaped waveguide. Based on the mirror imaging principle, the acoustic scattering from the finite cylinder under the point source incidence in wedge-shaped waveguide is equivalent to acoustic scattering from multiple cylinders under multiple point source incidence in free space. Then, the transition matrix (T-matrix) of finite cylinder in wedge-shaped waveguide can be obtained using the translation and the rotation addition theorems of spherical wave functions. Therefore, the solution to the acoustic scattering from this cylinder can be semi-analytically solved. Besides, the influences of some related parameters on the backscattering and the distributions of the scattering field are studied, such as source position, target attitude, immersion depth and the inclination angle. The method proposed in this work can be further extended for the analysis of the acoustic scattering from multiple targets in shallow water waveguide.

     

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