Higher-order topological states and magnetic field control in elastic metamaterials

Recently, the concept of higher-order topological insulators has aroused widespread attention and research interest. However, current studies have predominantly focused on the domain of acoustic waves. Compared to acoustic waves, elastic waves are vector waves, making their study more complex and challenging. Therefore, achieving higher-order topological states in elastic waves holds significant research value. In this paper, we proposed the design of an intelligent topological metamaterial, which is composed of magneto-rheological thin layers and an elastic substrate. First, by adjusting the topological structure, we successfully excited first-order topological states of Lamb waves in numerical simulations. Subsequently, we constructed a two-dimensional topological structure to excite zero-order topological corner states. Given the unique advantages of magnetic fields in regulating material properties and behaviors, we investigated the effects of magnetic fields as an external control mechanism on Lamb waves in magneto-rheological materials. Our analysis focused on the regulation of Lamb wave topological edge states and corner states via magnetic fields. The results demonstrate that by varying the magnetic field strength, we can precisely control the characteristics of the topological states. Magnetic field modulation of the topological states in Lamb waves enables the realization of non-contact, controllable phononic devices, which is of great significance for the development of topological acoustics.

近年来，高阶拓扑绝缘体（higher-order topological insulators）的概念引发了广泛关注与研究热情。然而，当前的研究大多集中在声波领域。相较于声波，弹性波属于矢量波，其研究更为复杂且富有挑战。因此，在弹性波中实现高阶拓扑态具有重要的研究价值。本文提出了一种智能拓扑超材料的设计方案，该材料由磁流变（magneto-rheological）薄层与弹性基底构成。首先，通过调整拓扑结构，我们在数值模拟中成功激发了兰姆波（Lamb waves）的一阶拓扑态。随后，我们构建了二维拓扑结构以激发零阶拓扑角态。鉴于磁场在调控材料特性与行为方面的独特优势，我们研究了作为外部调控机制的磁场对磁流变材料中兰姆波的影响。本研究重点分析了通过磁场对兰姆波拓扑边缘态与角态的调控作用。研究结果表明，通过改变磁场强度，我们可以精准调控拓扑态的特性。对兰姆波拓扑态进行磁场调控，可实现非接触式、可调控的声子器件，这对于拓扑声学的发展具有重要意义。