In this work we propose a strategy based on coordinate transformation to cloak Rayleigh waves. Rayleigh waves are in-plane elastic waves which propagate along the free surface of semi-infinite media. They are governed by Navier equations that retain their form for an in-plane arbitrary coordinate transformation $\mathbf{x}=\Xi \left(\mathbf{X}\right)$, upon choosing the specific kinematic relation $\mathbf{U}\left(\Xi \left(\mathbf{X}\right)\right)=\mathbf{u}\left(\mathbf{x}\right)$ between displacement fields in virtual, i.e. reference, ($\mathbf{U}$) and transformed, i.e. cloaked, ($\mathbf{u}$) domains. However, the elasticity tensor of the transformed domain is no longer fully symmetric, and thus, it is difficult to design with common materials. Motivated by this issue, we propose a symmetrization technique, based on the arithmetic mean, to obtain anisotropic, yet symmetric, elastic tensors for Rayleigh wave near-cloaking. In particular, by means of time-harmonic numerical simulations and dispersion analyses, we compare the efficiency of triangular and semi-circular cloaks designed with the original non-symmetric tensors and the related symmetrized versions. In addition, different coordinate transformations, e.g. linear, quadratic and cubic, are adopted for the semi-circular cloaks. Through the analyses, we show that a symmetrized semi-circular cloak, obtained upon the use of a quadratic transformation, performs better than the other investigated designs. Our study provides a step towards the design of feasible and efficient broadband elastic metamaterial cloaks for surface waves.

在这项工作中，我们提出了一种基于坐标变换的策略来隐藏瑞利波。瑞利波是沿半无限介质的自由表面传播的面内弹性波。它们由 Navier 方程控制，这些方程保留其平面内任意坐标变换的形式$\mathbf{X}=\infty \left(\mathbf{X}\right)$, 在选择特定的运动学关系时$\mathbf{ü}\left(\infty \left(\mathbf{X}\right)\right)=\mathbf{你}\left(\mathbf{X}\right)$在虚拟位移场之间，即参考，（$\mathbf{ü}$) 和转换，即隐形，($\mathbf{你}$) 域。然而，变换域的弹性张量不再完全对称，因此很难用普通材料进行设计。受此问题的启发，我们提出了对称化基于算术平均值的技术，以获得瑞利波近隐形的各向异性但对称的弹性张量。特别是，通过时谐数值模拟和色散分析，我们比较了用原始非对称张量和相关对称化版本设计的三角形和半圆形斗篷的效率。此外，半圆形斗篷还采用了不同的坐标变换，例如线性、二次和立方。通过分析，我们表明使用二次变换获得的对称半圆形斗篷比其他研究设计表现更好。我们的研究为设计可行且高效的表面波宽带弹性超材料斗篷提供了一步。