Design and Analysis of Piezoelectric Metamaterial Beams with Synthetic Impedance Shunt Circuits

We present an electromechanical modeling framework and a detailed numerical investigation for the design and analysis of piezoelectric metamaterial beams whose unit cells with segmented electrode pairs are shunted to synthetic impedance circuits. This framework aims to extend the well-studied locally resonant piezoelectric metamaterials and resulting finite metastructures with specified boundary conditions to novel concepts beyond bandgaps associated with simple inductive shunts. Overcoming the bandgap limitations of the locally resonant design requires more advanced considerations in the electrical domain. To this end, we bridge piezoelectric metamaterials and synthetic impedance shunts, and present a general design and analysis framework along with numerical case studies. A general procedure is implemented based on the root locus method for choosing the shunt circuit impedance, with an emphasis on vibration attenuation and practical design considerations. Case studies are presented for systems with locally resonant bandgaps with or without negative capacitance, as well as systems with multiple distinct bandgaps, and the necessary shunt admittance is derived for each case. Simulations are performed for a typical finite meta material beam with synthetic impedance shunts, accounting for the finite sampling rate and circuit dynamics. Time-domain simulations using these synthetic impedance circuits are compared to the ideal frequency-domain results with very good agreement.