水下低频球面声波近场散射声压的渐近解研究

Asymptotic solution of near-field scattering acoustic pressure of underwater low-frequency spherical sound

为研究水下低频声波的近场散射机理,导出了近场散射声压的渐近解。首先,给出了刚性边界、软边界、阻抗边界条件下,低频球面声波遇到球形障碍物散射声压的无穷级数解;然后,结合低频和近场的假设条件,合理选取无穷级数解中Bessel函数、Hankel函数的近似形式,导出了散射声压的渐近解,并进行了仿真计算。研究表明:低频近场散射声压可以表示为位于散射体中心的单极子声源和散射体中心与(0,0,a^2/b)之间分布的偶极子源的叠加;对于低频近场散射问题,采用平面波近似球面波有较大误差。

For investigating the scattering mechanism of the underwater low-frequency sound wave,the asymptotic solution of near-field scattering acoustic pressure is derived.Firstly,the exact solution of a spherical sound wave on a sphere is given by an infinite series involving the products under the condition of rigid boundary,soft boundary and impedance boundary.Secondly,based on the assumptions of low-frequency and near-field,the approximate forms of the Bessel functions and Hankel functions are employed to derive the asymptotic solution.The results show that the low-frequency scatte-ring acoustic pressure could be expressed as a sum of fields due to a monopole source in the center of the scatter and dipoles distributed along the segment between the centre and the point(0,0,a^2/b).For the low frequency scattering problem,the plane wave approximation could not be used in place of the spherical wave.