Programmable Spatial and Spatiotemporal Modulation of Piezoelectric Metamaterials with Synthetic Impedance Circuits

We present numerical and experimental investigations on the dynamics of a piezoelectric metamaterial waveguide with unit cell shunt impedance that can be varied in both space and time in a fully programmable manner. A piezoelectric bimorph with 30 separately bonded pairs of piezoelectric patches (i.e. 30 unit cells) is connected to a fully programmable gate array (FPGA)-based synthetic impedance system with 32 individually addressable shunt circuits. Spatial impedance profiles are programmed and stored in memory on the FPGA, allowing the system to switch between impedances at very high frequencies, resulting in nearly smooth time-modulation at low modulation frequencies. The switching rate between the stored impedances is determined by a digital trigger and external pulse train, allowing the modulation frequency to be smoothly varied. Four separate triggers enable different modulation frequencies to be set across the waveguide, such that multifrequency modulation schemes can also be explored. In this way, the developed experimental platform is capable of smooth, multi-directional spatiotemporal modulation of circuit parameters. Experimental results are presented for various inductive spatiotemporal modulation schemes, investigating the effect of modulation amplitude and directional behavior of the waveguide (e.g. for non-reciprocal propagation). Scanning laser Doppler vibrometer (SLDV) measurements provide full-field characterization of the waveguide. Numerical and experimental results demonstrate non-reciprocal behavior in the modulated waveguide.