Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based on expansion in half-space spherical wave functions is proposed. First, the series of half-space spherical wave functions is derived based on the analytical solution of the sound field due to a multipole source located near an impedance plane. Then the sound field in the half-space is approximated by the superposition of a finite number of half-space expansion terms. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching this assumed solution to the total acoustic pressures in the half-space. The free-space radiation can finally be reconstructed via multiplying the free-space spherical wave functions by the corresponding coefficients. Numerical simulation examples of a vibrating sphere and a vibrating baffled plate are demonstrated. The effects of specific acoustic impedance of the boundary and the locations of the measurement points on the accuracy of reconstruction are examined.

中文翻译：

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有限声阻抗无源曲面半空间振动结构声辐射重构

振动结构通常安装在或位于具有有限声阻抗的无源平面表面上，因此在以表面为界的半空间中测量的声压包括来自结构的直接辐射和来自边界表面的反射。为了可视化从源直接辐射到自由空间，提出了一种基于半空间球面波函数展开的重建方法。首先，基于位于阻抗平面附近的多极源声场的解析解，导出了一系列半空间球面波函数。然后半空间中的声场通过有限数量的半空间展开项的叠加来近似。通过求解一个超定线性方程组来确定膨胀系数，该方程组通过将该假定解与半空间中的总声压相匹配而获得。自由空间辐射最终可以通过将自由空间球面波函数乘以相应的系数来重建。演示了振动球和振动挡板的数值模拟示例。研究了边界的比声阻抗和测量点的位置对重建精度的影响。演示了振动球和振动挡板的数值模拟示例。研究了边界的比声阻抗和测量点的位置对重建精度的影响。演示了振动球和振动挡板的数值模拟示例。研究了边界的比声阻抗和测量点的位置对重建精度的影响。