Zhong Jiaxin, Kirby Ray, Karimi Mahmoud, Zou Haishan
Centre for Audio, Acoustics and Vibration, University of Technology, Sydney, New South Wales 2007, Australia.
Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing 210093, China.
J Acoust Soc Am. 2021 Nov;150(5):3797. doi: 10.1121/10.0007280.
In this work, a cylindrical expansion for the audio sound generated by a steerable baffled parametric array loudspeaker (PAL) based on the phased array technique is derived from the Westervelt equation. The expansion is a series of twofold summations with uncoupled angular and radial components in the cylindrical coordinate system. The angular component is determined by the trigonometric functions, and the radial component is an integral containing the Bessel functions and an arbitrary excitation velocity profile. The numerical results for a typical steerable PAL are presented and compared to those obtained using the convolution model. It is found that the prediction of the audio sound using the proposed cylindrical expansion improves the agreement with the experimental results when compared to the existing models. This is because no further approximations are required in the cylindrical expansion of the quasilinear solution of the Westervelt equation, whereas the complex near field nonlinear interactions between the ultrasonic waves cannot be correctly captured in a convolution model. The proposed cylindrical expansion does, therefore, provide an alternative approach to modeling a phased array PAL and high accuracy with a relatively low computational cost.
在这项工作中，基于相控阵技术的可控障板参量阵扬声器（PAL）产生的音频声音的柱面展开式是从韦斯特维尔特方程推导出来的。该展开式是柱面坐标系中具有非耦合角向和径向分量的双重求和系列。角向分量由三角函数确定，径向分量是一个包含贝塞尔函数和任意激励速度分布的积分。给出了典型可控PAL的数值结果，并与使用卷积模型获得的结果进行了比较。结果发现，与现有模型相比，使用所提出的柱面展开式预测音频声音能更好地与实验结果吻合。这是因为在韦斯特维尔特方程的准线性解的柱面展开中不需要进一步近似，而卷积模型无法正确捕捉超声波之间复杂的近场非线性相互作用。因此，所提出的柱面展开式确实为相控阵PAL建模提供了一种替代方法，并且能以相对较低的计算成本实现高精度。
