The Ability Indexes if Shunt Piezoelectric Circuits for Manipulating Elastic Waves in Piezoelectric Metamaterials

The piezoelectric metamaterial based on the periodic array of piezoelectric sheets on both sides of the main structure controlled by the piezoelectric shunt circuit. In recent years, researches on piezoelectric metamaterials with a single specified shunt circuit have become very rich, but there is a lack of criteria to evaluate the performance of different types of circuits. In this paper, the transfer matrix method is used to study the influence of shunt piezoelectric circuits on the elastic wave propagation behavior in a piezoelectric metamaterial beam, and a set of indexes for measuring the ability of different circuits in tuning the elastic waves are proposed. The indexes are based on the phase diagram representing the bandgap tunability of the shunt circuit with the normalized bandgap position and normalized bandgap width as the coordinates. We believe that such indexes should be useful in the design of piezoelectric metamaterials.