Tunable topological edge states and rainbow trapping in two dimensional magnetoelastic phononic crystal plates based on an external magnetostatic field

• Magnetically tunable pseudospin-Hall edge states. ○ The reconfigurable interface propagation routes of edge modes achieved by controlling external magnetostatic field. ○ Frequency tunability of edge states induced by altering interfacial magnetostatic field intensity. ○ A topological rainbow of tunable operating frequency in elastic systems attained by adjusting graded interfacial magnetic field. The elastic analogs of topological insulators (TIs) have attracted substantial research interest owing to their potential prospects in wave manipulation and low-loss transmission. However, most work in solid phononic crystal (PC) systems suffering from fixed-structure restrictions lack the active tunability of topological edge states, hindering their practical applications in dynamic situations. Here, we present a new design of tunable elastic TIs made up of smart magnetostrictive materials and perforated silicon plates. The topological phase transition is induced by altering the spatial intensity distribution of external magnetostatic field. Placing two topologically distinct magnetoelastic PC plates adjacent to each other, the pseudospin-Hall edge modes for plate-mode waves are obtained at the interface between them. Moreover, the reconfigurable propagation route and topological robustness of edge states are demonstrated by numerical simulations. Finally, the frequency and group velocity of edge modes can be continuously adjusted by an interfacial magnetic field. Utilizing such a contactless tunability, a reconfigurable topological rainbow is attained by reconstructing the gradient-descent interfacial magnetic field along the topological interface. The proposed system with magnetically tunable edge states can become a stepping-stone platform towards the designs of elastic wave devices with more applicability for dynamic conditions, such as waveguides, energy harvesters and buffers.