基于精确数值积分的点声源反射声场模型研究

Study on the reflected sound field model based on the exact numerical integration

点声源辐射条件下的反射声场计算是一经典的Sommerfeld积分问题。在以往的研究中,含有表面波项的解由于其简便性和易计算性在室外声传播和大面积吸声材料的在体吸声测量中得到了较为广泛的应用,但对其在不同入射角度以及针对不同性质的材料(如局部响应或非局部响应材料)时带来的模型有效性问题较少提及。通过利用数值积分方法精确计算Sommerfeld积分,对两种不同性质的声学材料在不同入射角度下的辐射声场进行了研究,并和解析模型进行了对比,认为随着入射角度的降低和材料流阻的增加(即表现为局部响应性质),含有表面波项的解析解可以较好地表达辐射声场。

The sound field radiated by a point source can be represented by the classical Sommerfeld integration.During the past time,the analytical solution including the surface wave term is widely used in the outdoor sound propagation area as well as the in-situ measurement of sound absorption for large area material because of its simplicity and easier execution.However,the affectivity of this model is randomly evaluated when sound wave at different incidence angle impinged on the material surface with distinct characteristics（such as locally or nonlocally reacting）.In this paper,the exact numerical integration is performed on two different materials with largely different flow resistance at different incident angle.Through comparison with the traditional analytical solution,it is concluded that the analytical solution can well behave as the incident angle is decreasing and the flow resistance is increasing.