Tailored Topological Edge Waves via Chiral Hierarchical Metamaterials

Abstract: Precise manipulation of the direction and re-direction of vibrational wave energy is a key demand in wave physics and engineering. We consider the paradigm of a finite frame-like structure and the requirement to channel energy away from critical regions, leaving them vibration-free, and redirect energy along edges towards energy concentrators for damping or energy harvesting. We design an exemplar frame metamaterial, combining two distinct areas of wave physics. Firstly, topological edge states taking an unconventional tetrachiral lattice. We control these highly localised protected edge states leveraging a hierarchy of scales through the addition of micro-resonators that impose tuneable symmetry breaking and reconfigurable mass. This allows us to achieve precise positional control in the macro-scale frame lattice, thereby opening opportunities for robust signal transport and vibration control. Experiments, theory, simulation are all utilised to provide a comprehensive analysis and interpretation of the physics.