Tailored Topological Edge Waves via Chiral Hierarchical Metamaterials

Precise manipulation of the direction and redirection of vibrational wave energy is a key demand in wave physics and engineering. We consider the paradigm of a finite framelike structure and the require-ment to channel energy away from critical regions, leaving them vibration free, and redirect energy along edges toward energy concentrators for damping or energy harvesting. We design an exemplar frame meta -material, combining two distinct areas of wave physics. First, we consider topological edge states, taking an unconventional tetrachiral lattice. We control these highly localized protected edge states leveraging a hierarchy of scales through the addition of microresonators that impose tunable symmetry breaking and reconfigurable mass. This allows us to achieve precise positional control in the macroscale frame lattice, thereby opening up opportunities for robust signal transport and vibration control. Experiments, theory, and simulation are all utilized to provide a comprehensive analysis and interpretation of the physics.