Nonreciprocal piezoelectric metamaterial framework and circuit strategies

Recent research has shown that a proper spatiotemporal modulation of material properties (i.e., mass density or stiffness) can break reciprocity for elastic waves; however, such concepts are challenging to implement experimentally in mechanical waveguides. Piezoelectric metamaterials offer the possibility of parameter modification via electrical circuitry, constituting a convenient platform for spatiotemporal modulation. We introduce a fully coupled electromechanical framework and circuit strategies to enable nonreciprocal piezoelectric metamaterials using various schemes that include capacitive and inductive shunts as well as smooth modulation and nonsmooth switching. The high-fidelity framework presented herein does not rely on the assumption of simplified effective material property representation, and can be used to explore and predict the complete dynamics of the modulated system, accounting for full-system stability, circuit limitations, and more complex modulation schemes. A set of results is presented based on nonreciprocal configurations that illustrate potential implementation schemes, and demonstrate the versatility of piezoelectric materials for the design of truly integrated acoustic/elastic wave devices featuring nonreciprocal transmission.