Li Shao-Zhe, Zhuang Tao, Zhong Jia-Xin, Lu Jing
Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing 210093, China.
Graduate Program in Acoustics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
J Acoust Soc Am. 2024 Oct 1;156(4):2189-2199. doi: 10.1121/10.0030403.
Parametric array loudspeakers have been widely used in audio applications for generating directional audio beams. However, accurately calculating audio sound with a low computational load remains challenging, even for basic axisymmetric source profiles. This work addresses this challenge by extending the King integral in linear acoustics to incorporate both cumulative and local nonlinear effects, under the framework of the quasilinear solution without the paraxial approximation. The proposed method exploits the azimuthal symmetry in cylindrical coordinates to simplify modeling. To further improve computational efficacy, fast Hankel and Fourier transforms are employed for the radial and beam radiation directions, respectively. Numerical results with both uniform and focusing profiles demonstrate the advantages of the proposed approach over the traditional spherical wave expansion and direct integration methods, especially for larger aperture sizes. Specifically, for typical configurations with source aperture size of 0.2 m, we observe at least a 24-fold improvement in computational speed and a 227-fold reduction in memory requirements. These advancements allow us, for the first time, to present the sound field radiated by parametric array loudspeakers with a large aperture size of up to 0.5 m, without paraxial approximations. The implementation codes are available on https://github.com/ShaoZhe-LI/PAL_King.
参量阵扬声器已广泛应用于音频应用中，用于生成定向音频波束。然而，即使对于基本的轴对称源轮廓，以低计算量精确计算音频声音仍然具有挑战性。这项工作通过在无傍轴近似的准线性解框架下，扩展线性声学中的金积分以纳入累积和局部非线性效应，来应对这一挑战。所提出的方法利用柱坐标系中的方位对称性来简化建模。为了进一步提高计算效率，分别对径向和波束辐射方向采用快速汉克尔变换和快速傅里叶变换。具有均匀和聚焦轮廓的数值结果证明了所提出方法相对于传统球面波展开和直接积分方法的优势，特别是对于较大孔径尺寸。具体而言，对于源孔径尺寸为0.2 m的典型配置，我们观察到计算速度至少提高了24倍，内存需求减少了227倍。这些进展首次使我们能够在无傍轴近似的情况下，呈现孔径尺寸高达0.5 m的参量阵扬声器辐射的声场。实现代码可在https://github.com/ShaoZhe-LI/PAL_King上获取。
