This talk will investigate the inverse design of the dispersion curves of a class of non-local piezoelectric metamaterials. The use of non-local circuit connections between unit cells introduces both frequency and wavenumber-dependence to the dispersion curves, greatly expanding the possibilities for wave manipulation in non-local metamaterials. Furthermore, the use of non-local interaction enables symmetry-breaking, such that non-reciprocal behavior can be obtained without nonlinearity or time-varying material properties. To explore the full design space of non-local piezoelectric metamaterials, we present a general analytical model and inverse design methods to calculate the required shunt circuitry for a given set of non-reciprocal dispersion curves. Numerical case studies are given for non-local resistive, inductive, and capacitive shunt circuits, which provide insight into the uses of each of these circuits in non-local metamaterial systems. We then experimentally demonstrate this approach using a piezoelectric bimorph beam with local and non-local circuit interactions, highlighting non-reciprocity and the tunability of the dispersion relation of the system.
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