半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场。在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场。在边界声阻抗已知和边界声阻抗未知两种条件下,对该方法进行了仿真验证和参数分析,并在全消声室内进行了实验验证。结果表明,所提方法能重构出半空间中典型声源即球形声源和平面声源的直接辐射声场;该方法在边界声阻抗已知时的重构精度与稳定性高于在边界声阻抗未知时的情形。 

Reconstruction of the direct radiation from a source using the expansion in half-space spherical wave functions

An acoustic field reconstruction method based on an expansion in half-space spherical wave functions is proposed to reconstruct the direct radiation generated by a source located in a half-space bounded by a surface with finite acoustic impedance.The half-space spherical wave basis functions are formulated firstly,based on the analytical solutions of the acoustic pressures generated by multipoles,where the boundary impedance is used as an independent variable.By solving the expansion coefficients of the half-space basis functions via an inverse calculation,the expansion coefficients of the basis functions in the free-space,corresponding to the directly radiated field,are obtained meanwhile.The direct radiation of the source is finally reconstructed by using the expansion coefficients.Numerical simulations are carried out to verify the proposed method,for the cases where the boundary impedance is known a priori and where it is not explicitly given.The impacts of various parameters on the performance of the method are analyzed.The proposed method is also verified by an experiment conducted in an anechoic chamber.The results show that,the direct radiation from both a spherical source and a planar source,which are the typical sources,can be reconstructed using the proposed method,and that the reconstruction accuracy and stableness of the method are better when the boundary impedance is known a priori than those when the boundary impedance is not explicitly given.