积分方程法与求解谐振频率的声散射

Solving sound scattering at resonance frequencies by using integral equation method

表面Ｈｅｌｍｈｏｌｔｚ积分公式可以有效地求解物体的辐射声场和散射声场，但并不是在任何频率下都能得到满意的结果。当波数等于或接近目标内部问题的特征值时，将产生非唯一解，严重影响求解的准确性。本文根据混合Ｈｅｌｍｈｏｌｔｚ积分公式，用最小平方正交法有效地求解谐振频率的声散射。文中以圆柱和椭圆柱的声散射为例进行了计算，并讨论了目标内附加计算点的选取问题。

The surface Helmholtz integral equation may effectively works out sound radiation and scattering field of an object. However it can not get satisfactory results at all frequencies. When the wave numberk is close the eigenvalue (resonance frequency ) of the interior problem of the target, it is shown that there isno unique solution and it affects seriously the accuracy of solutions. In this paper, according to CombinedSurface Helmholtz Integral Formulation (CHIEF ), the least-squares orthonomalizing procedure is usedeffectively to get the exact solution of the sound scattering by a target at resonance frequencies. The soundscattering by circular and elliptical cylinders were calculated as an example and how to make the interiorpoints for additional calculating were presented.