SUMMARY

Metamaterials are engineered structures whose large‐scale effective properties depend on their small-scale repeated architecture. These structures exhibit effective properties that cannot otherwise be found in nature, such as negative dynamic mass or stiffness, that dramatically alter their wave propagation properties. Still, purely mechanical metamaterials are limited by having only a fixed set of effective properties; by contrast, a metamaterial with integrated smart materials has effective properties that can be controlled through external stimuli. Specifically, piezoelectric metamaterials have effective stiffness that depends on the shunt circuitry connected to each unit cell, offering greatly increased design freedom over their purely mechanical counterparts. In this work, each unit cell of the piezoelectric metamaterial domain is connected to a digitally controlled shunt circuit, allowing the effective stiffness of the system to be externally programmed in space and time. The first part of this research investigates graded piezoelectric metamaterials (e.g. the rainbow concept) both computationally and experimentally. The effect of different spatial profiles of resistive-inductive shunt circuits is explored to alter the group velocity variation in space with a focus on enhancing the vibration attenuation bandwidth and creating mode localization along the waveguide. Opportunities are sought also in piezoelectric energy harvesting from the localized modes. Furthermore, in addition to spatial modulation, by varying the shunt circuit behavior in time (via spatiotemporal modulation), a directional bias can be introduced into the stiffness of the metamaterial, creating rich dynamics such as nonreciprocal wave propagation. Synthetic impedance circuitry enables a truly programmable option for reciprocity breaking as compared to cumbersome analog circuit networks that appeared in the recent literature. In this context, spatiotemporal modulation on resonant synthetic shunts is explored to demonstrate digitally tunable nonreciprocity. Further metamaterial concepts that explore spatial and temporal programming via digital signal processing are shown, and experiments are compared against numerical simulations using analytical and finite-element methods.