共形Mikaelian声透镜设计*

该文研究了利用共形变换设计声学器件的一般方法,在此基础上根据普通Mikaelian透镜的折射率分布规律,利用指数映射设计出了弧形的Mikaelian透镜,分析并讨论了弧形透镜的密度、模量和折射率分布规律。对160 k Hz的声波进行了仿真实验,仿真结果表明,在弧形透镜的理论预测焦点处出现能量汇聚的现象,即实现了弧形聚焦的效果。同时,声波在经过该透镜后传播方向产生了一定角度的偏转。该工作为实现弧形声学器件提供了理论方法,在水下声探测及水下声通讯等方面有着潜在的应用。

The design of a bending Mikaelian acoustic lens by conformal transformation

In this paper, we show the way to design an isotropic acoustic device by conformal transformation. Based on the conformal transformation theory, a bending Mikaelian lens is designed by exponential mapping. The refraction index, density and modulus are obtained by the transformation. The focus effect was verified by finite element method. In the simulation, the incident acoustic wave is Gassian beam with central frequency at 160 kHz. The simulation results demonstrate that the acoustic energy converges at the theoretical predicted focal point. This means the bending lens has a good performance as. It is shown that the focus effect of the bending Mikaelian lens is the same to that of the ordinary one. This work has potential application in under water acoustics.