任意形状无奇异二维声学隐身衣的设计
Design Arbitrary Shaped 2D Acoustic Cloak without Singularity
摘要：
提出了一种无奇异性的任意形状二维各向同性惯性声隐身衣的设计方法。该方法基于变换方法的变形观点，将变换张量A确定为变形梯度张量，变换后的材料参数可以用变形主系统中的主拉伸来表示。一个理想的2D斗篷的无限材料参数是由一个方向上的无限主拉伸，而其他两个保持有限的内边界在转换过程中。为了克服这个困难，对于二维斗篷，我们可以选择垂直于斗篷平面的主拉伸也是无限的，但在变换过程中与斗篷平面中的无限主拉伸的顺序相同，因此变换后的材料参数可以保持有限。为了说明这一思想，给出了圆柱形声隐身衣的非奇异材料参数的解析表达式。对于不规则形状的声隐身衣，提出了一种计算其主伸缩量进而计算非奇异材料参数的数值方法。通过数值仿真验证了所设计的二维隐身衣的有效性。
英文摘要：
A method is proposed to design arbitrary shaped two dimensional (2D) isotropic-inertia acoustic cloaks without singularity. The method is based on the deformation view of the transformation method, where the transformation tensor A is identified as the deformation gradient tensor and the transformed material parameters can be expressed by the principal stretches in the principal system of the deformation. The infinite material parameters of a perfect 2D cloak is induced by an infinite principal stretch in one direction while the other two remains finite at the inner boundary during the transformation. To circumvent this difficulty, for a 2D cloak we can choose the principal stretch perpendicular to the cloak plane to be also infinite but in the same order as the infinite principal stretch in the cloak plane during the transformation, so the transformed material parameters may keep finite. To illustrate this idea, the analytical expressions of nonsingular material parameters for a cylindrical acoustic cloak are given. For the acoustic cloaks with irregular shapes, the numerical method is proposed to evaluate the principal stretches and in turn the nonsingular material parameters. The designed 2D cloaks are validated by numerical simulation.
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