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.