Hoffmann Falk-Martin, Fazi Filippo Maria, Williams Earl G, Fontana Simone
Institute of Sound and Vibration Research, University of Southampton, Southampton, Hampshire, SO17 1BJ, United Kingdom.
Naval Research Laboratory, Code 7106, Washington, D.C. 20375, USA.
J Acoust Soc Am. 2017 Sep;142(3):1249. doi: 10.1121/1.4998573.
In this work an expression for the solution of the Helmholtz equation for wedge spaces is derived. Such propagation spaces represent scenarios for many acoustical problems where a free field assumption is not eligible. The proposed sound field model is derived from the general solution of the wave equation in cylindrical coordinates, using sets of orthonormal basis functions. The latter are modified to satisfy several boundary conditions representing the reflective behaviour of wedge-shaped propagation spaces. This formulation is then used in the context of nearfield acoustical holography (NAH) and to obtain the expression of the Neumann Green function. The model and its suitability for NAH is demonstrated through both numerical simulations and measured data, where the latter was acquired for the specific case of a loudspeaker on a hemi-cylindrical rigid baffle.
在这项工作中，推导了楔形空间亥姆霍兹方程的解的表达式。这种传播空间代表了许多声学问题的场景，在这些场景中自由场假设并不适用。所提出的声场模型是从柱坐标下波动方程的通解出发，利用正交归一基函数集推导出来的。对后者进行了修改，以满足代表楔形传播空间反射特性的几个边界条件。然后将该公式用于近场声全息（NAH）的背景下，并得到诺伊曼格林函数的表达式。通过数值模拟和实测数据验证了该模型及其对NAH的适用性，其中实测数据是针对扬声器在半圆柱形刚性障板上的特定情况采集的。
