SUMMARY

Most 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 synthetic impedance circuit, allowing the effective stiffness of the system to be externally programmed in space and time. The first part of this research investigates spatial modulation via graded resonant piezoelectric metamaterials 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. Next, temporal modulation is explored via synthetic impedance circuits on the same piezoelectric metamaterial beam using resonant shunts for wave filtering. This is followed by spatiotemporal modulation of resonant shunts, which enables a directional bias, creating rich dynamics such as nonreciprocal wave propagation. Overall, synthetic impedance circuitry enables a truly programmable option for concepts from wave filtering to reciprocity breaking as compared to cumbersome analog circuit networks that appeared in the recent literature. Spatial, temporal, and spatiotemporal modulations on resonant synthetic shunts are explored with digital control to demonstrate design and performance flexibility. In all cases, experiments are compared against numerical simulations using analytical and finite element methods. Opportunities are sought in piezoelectric energy harvesting from the localized and defect modes.