Wave engineering in programmable piezoelectric metamaterials with digital shunts

This talk will review our recent and ongoing efforts on programmable piezoelectric metamaterials that exploit synthetic impedance circuits, eliminating not only the need for mechanical (manual) reconfiguration but also bulky analog circuit components used in prior efforts. The examples of piezoelectric metamaterials we will discuss span from digital programming of directional bandgap formation to tunable wave mode conversion. In all cases, the piezoelectric unit cells are shunted to separate synthetic impedance circuits that act as voltage-controlled current sources employing a digital filter. Following a generalized electromechanical framework of piezoelectric metamaterials for arbitrary shunt admittance, we will first review locally resonant bandgap formation and its tuning over a broad frequency range. Then, we will discuss spatial modulation of circuit impedance especially for gradient concepts such as the rainbow phenomenon and the acoustic/elastic black hole. These concepts also employ resonant unit cells, and we will explore various spatial profiles of synthetic shunt inductance distribution for wave localization and compression, along with multifunctional implementations such as concurrent energy harvesting from the trapped/localized modes. Spatial modulation will be followed by spatiotemporal modulation, with some of the first locally resonant piezoelectric metamaterial case studies with reciprocity breaking. Unlike the existing counterparts with analog switching circuits on capacitive shunts, we use smooth parameter variation and inductive shunts, providing additional (resonant) tunability to create directional bandgaps. Topologically protected counterparts will also be shown, as well as Rayleigh-to-shear wave mode conversion and double-negative refractive index scenarios enabled by resonant shunts. We will then discuss further programmable examples including exceptional points (via degeneracy introduced electrically) using a waveguide with piezoelectric elements having a balanced gain and loss. Nonlinear synthetic impedance implementations will also be demonstrated for Duffing-type (hardening or softening) shunts, specifically for solitary wave generation as part of our ongoing work with waveguides obeying the nonlinear Schrödinger equation form.