Madine K H, Colquitt D J
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
Department of Materials Engineering, National Tsing Hua University, Hsinchu City, Taiwan.
Philos Trans A Math Phys Eng Sci. 2022 Nov 28;380(2237):20210379. doi: 10.1098/rsta.2021.0379. Epub 2022 Oct 10.
We consider the propagation of flexural and torsional waves in a square lattice of Euler-Bernoulli beams. The refraction and reflection of waves across interfaces between two dissimilar lattices is investigated. By carefully controlling the inertial and elastic properties of the lattice elements, we demonstrate that it is possible to induce negative refraction and other associated phenomena. These effects are shown to be broadband and are facilitated by the unprecedented control over wave propagation afforded by the interaction between torsional and flexural waves and the additional freedom associated with the applied forcing. Closed-form analytical findings are accompanied by numerical simulations, which demonstrate negative refraction, unidirectional reflection and mode trapping. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.
我们研究了欧拉 - 伯努利梁方形晶格中弯曲波和扭转波的传播。研究了波在两个不同晶格界面处的折射和反射。通过仔细控制晶格单元的惯性和弹性特性，我们证明了可以诱导负折射和其他相关现象。这些效应被证明是宽带的，并且通过扭转波和弯曲波之间的相互作用以及与外加激励相关的额外自由度所提供的对波传播的前所未有的控制而得以实现。封闭形式的分析结果伴随着数值模拟，这些模拟展示了负折射、单向反射和模式捕获。本文是主题为“多尺度复杂介质和结构化超材料中的波产生与传输（第2部分）”的一部分。
