Landau level and active manipulation of elastic waves in topological robotic metamaterials

An artificial pseudomagnetic structure generates Landau levels in the dispersion relation, which leads to magnetic-like behaviors of elastic waves in mechanical metamaterials. This work reports three kinds of pseudomagnetic structures composed of parallel platforms and active connecting springs, i.e., zigzag-edged ribbons, armchair-edged ribbons, and triaxial configurations. On the basis of the effective asymptotic model, the momentum shift of Dirac cone is investigated for periodic unit cells with the inhomogeneous stiffness distribution. When different gauges are applied to the vector potential provided by the momentum shift, pseudomagnetic structures are generated by the uniaxial or triaxial stiffness modulation. With the emergence of Landau levels, multiple propagation modes can be selectively excited, e.g., topological edge state, snake state transmission, wave beam bending, and ring waveguide. Moreover, different kinds of pseudomagnetic structures can be switched by changing the stiffness layout of robotic metamaterials. With the active programmable stiffness, robotic metamaterials have the potential to achieve elastic wave propagation along special paths by attitude transformation, e.g., beam splitter, obstacle avoidance, and channel switching.