Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos

Periodic shunted piezoelectric patches are employed for the design of a tunable, one-dimensional metamaterial. The configuration considered encompasses a beam undergoing longitudinal and transverse motion, and a periodic array of piezoelectric patches with electrodes connected to a resonant electric circuit. The resulting acousto-electrical system is characterized by an internal resonant behavior that occurs at the tuning frequency of the shunting circuits, and is analogous in its operation to other internally resonating systems previously proposed, with the addition of its simple tunability. The performance of the beam is characterized through the application of the transfer matrix approach, which evaluates the occurrence of bandgaps at the tuning frequencies and estimates wave attenuation within such bands. Moreover, a homogenization study is conducted to illustrate the internal resonant characteristics of the system within an analytical framework. Experiments performed on the considered beam structure validate the theoretical predictions and illustrate its internal resonant characteristics and the formation of the related bandgaps.