Metamaterial piezoelectric beam with synthetic impedance shunts

Abstract

We present a metamaterial beam based on a piezoelectric bimorph with segmented electrodes. Previously, we found the theoretical response of the beam using the assumed-modes method, and derived the effect of the shunt circuit impedance applied to each pair of electrodes. The structural response is governed by a frequency- dependent stiffness term, which depends on a material/geometry-based electromechanical coupling parameter and the impedance of the shunt circuits. A simple way to interpret the response of the system with frequency- dependent stiffness is the root locus method, which immediately yields the poles of each mode of the system using simple geometric rules. Case studies are shown for creating locally resonant bandgap with or without negative capacitance. To justify the use of these admittances that often require power input to the system, the concept of synthetic impedance is extended to symmetric voltages, as are encountered in series-connected piezoelectric bimorphs. Synthetic impedance or admittance is a method for obtaining an arbitrary impedance across a load by measuring the voltage and applying the corresponding current using digital signal processing and an analog circuit. Time domain simulations using these synthetic impedance circuits are compared to the ideal frequency domain results with good agreement. Surprisingly, the necessary digital sampling rate for stability is significantly higher than the Nyquist frequency.