Digitally tunable non-reciprocal wave propagation using piezoelectric metamaterials with synthetic impedance circuits

Abstract

One common approach to enable non-reciprocal wave propagation in elastic media relies on introducing a directional bias by parameter modulation (e.g., stiffness modulation) in space and time. Researchers have successfully demonstrated non-reciprocal wave propagation by coupling elastic waveguides with magnetic electrical coil elements, piezoelectric elements shunted to capacitive analog circuits, or rotating mechanical resonators. The existing efforts are often limited by narrow operation frequency ranges and cumbersome implementations that lack smooth modulation (e.g., with analog circuit elements and switches). In this work, we demonstrate precise and smooth non-reciprocal wave propagation in a piezoelectric metamaterial by connecting each unit cell to a digitally controlled synthetic impedance circuit. The effective impedance of each unit cell can be externally controlled according to a desired space-time modulation scheme over a wide frequency range. We present numerical and experimental investigations on the dynamics of a piezoelectric metamaterial beam with 30 bimorph unit cells whose impedances can be varied smoothly. Specifically, we employ the spatiotemporal modulation on synthetic inductance circuits rather than capacitive. Experimental results are presented for various space-time modulation profiles, investigating the effects of the inductance value (target frequency), as well as the modulation frequency and amplitude on digitally tunable non-reciprocal wave propagation.