梯度超构表面对弹性波异常反射和折射的研究

Metasurface can be considered as a two-dimensional version of metamaterial. It is superior to three-dimensional metamaterial by occupying a smaller space, easy fabrication, and controlling wave propagation flexibly. Gradient metasurface has been a frontier and hot issue in metamaterial field since it is raised, as it can be used to control at will the reflection and refraction of waves. This project carries out research on how gradient metasurfaces reflect and refract elastic waves anomalously by finite element simulation, experimental verification, and effective theory. Through finite element simulation, we first present the phenomena of anomalous reflection and refraction of SH wave, P wave, SV wave and three-dimensional incident longitudinal and transverse waves. For SH wave, we design experiment to verify the phenomenon of anomalous refraction. Through establishments of spring-mass model and equivalent layer or equivalent boundary conditions，we derive scalar generalized Snell’s law composed of effective parameters. Then, we extend the scalar law to the vectorial one considering wave mode conversion for P wave and SV wave. By discussing the effective parameters in the laws, we give the conditions for the incident elastic waves when these special cases happen such as polarization transformation, surface wave conversion and focusing, etc. The work will provide certain theoretical guidance for designing metasurfaces for elastic waves. The study of this project will provide new ideas for defending against seismic waves or impact waves.

超构表面为超材料的二维存在形式，相比三维超材料具有体积小、易于制作和对波控制灵活的优点。而梯度超构表面因能实现对波的异常反射和折射的任意控制，自被提出以来，成为了超材料领域研究的一个前沿和热点。本项目从有限元模拟、实验验证和等效理论的应用三方面开展梯度超构表面对弹性波异常反射和折射的研究。通过有限元模拟直观呈现梯度超构表面对入射SH波、P波、SV波及三维纵波和横波的异常反射和折射；针对SH波，设计实验验证异常折射现象；通过弹簧质量模型和等效层或等效边界条件的构建，推导异常反射和折射现象满足的含等效参数的标量波广义斯涅尔定律，进一步针对P波和SV波，将其推广为考虑波型转换的矢量波广义斯涅尔定律；通过定律中等效参数的讨论获得弹性波入射后发生极化转换、表面波转换和聚焦等特殊情形需要的条件，为弹性波梯度超构表面的设计提供一定的理论指导。本项目的研究将为地震波或冲击波的防护提供新的思路。

超构表面作为超材料的二维存在形式，具有体积小、易于制作和对波控制灵活的优点，其有望成为近二三十年来实现声子晶体和超材料对波控制的所有功能。本项目将超构表面的概念拓展到弹性波领域，涉及SH波、瑞利表面波和弯曲波，从有限元模拟、透射系数和相位解析解的求解和实验验证三方面开展梯度超构表面对弹性波偏折的研究。主要内容包含：（a）基于双材料的超构表面对SH波的异常折射和泄露和基于电流变弹性体材料的梯度开槽结构对SH波的异常折射和聚焦的调节；（b）基于带梯度相位跳跃的超屋脊结构的表面波偏折；（c）含柱状梯度子胞和变厚度梯度子胞的板中弯曲波的高透射偏折和分波；（d）基于双层梯度超构表面的弯曲波非对称传播。受本项目资助共发表SCI收录论文15篇，EI收录会议论文5篇。本项目的研究有望在损伤检测、能量俘获、减振降噪、新型表面声波器件设计等方面提出基于超构表面的新方法。