Tunability of topological rainbow capture and waveguide in phononic crystals based on magnetorheological elastomers

In recent years, following the integration of topological insulators and the concept of rainbow trapping into acoustic/elastic wave systems, a highly unique form of edge state transport has been realized. This transport is immune to defects and perturbations, enabling the separation of acoustic/elastic waves with different frequency components at distinct interface positions. However, most existing studies have focused on structures with fixed operating frequencies and spatial positions for rainbow trapping, leaving the realization of a tunable topological rainbow trapping effect as an ongoing challenge. This work introduces magnetorheological elastomers into two-dimensional elastic topological phononic crystals. By optimizing design parameters using a genetic algorithm, the width of the topological bandgap is broadened. Applying a magnetic field allows active adaptation to different operating frequencies, achieving efficient edge state transport. Furthermore, by controlling the magnetic field strength in different regions, the proposed structure enables topological rainbow trapping functionality across different frequency ranges, spatial positions, and transmission paths. This study provides a promising approach and scheme for the active manipulation of elastic waves.