We provide a theoretical framework to mold time-modulated mechanical metamaterials with frequency conversion and wave-steering capabilities. To illustrate the concept, we initially focus on 1D lattices, whereby a sufficiently slow time-modulation of the stiffness is employed to convert the frequency content of impinging waves. Based on the adiabatic theorem, we demonstrate that undesired reflections, which emerge in time-discontinuous materials, can be dramatically reduced by a careful choice of the modulation velocity. The concept is later explored in the context of 2D lattices, whereby a slow time modulation of the stiffness not only induces frequency conversion with minimal back-scattering, but also serves as a mechanism to steer waves. Our paper explores a new and exciting way to control wave propagation in elastodynamics with scattering-free guiding capabilities, and may open new avenues for the manipulation and transport of information through elastic waves.

Rainbow trapping is a phenomenon that enables vibration confinement due to the gradual variation of the wave velocity in space, which is typically achieved by means of locally resonant unit cells. In the context of electromechanical metastructures for energy harvesting, this strategy is employed to improve mechanical-to-electrical energy conversion and thereby to maximize the harvested power. In contrast to structures endowed with either mechanical or electromechanical resonators, we investigate a hybrid configuration that leverages the synergistic interplay between them. We compare numerical results for different grading laws in comparison to prior efforts on the topic, demonstrating enhanced energy harvesting and wideband vibration attenuation capabilities of the hybrid metastructure. We also discuss the formation of grading-induced localized modes and we shed light on the role of the motion of individual resonators on the overall power output increase.

No abstract