Complete Band Gaps in Nano-Piezoelectric Phononic Crystals

We study the band structure of elastic waves propagating in a nano-piezoelectric phononic crystal consisting of a polymeric matrix reinforced by BaTiO3 inclusions in square, rectangular, triangular, honeycomb and Kagome lattices. We also investigate the influence of inclusion cross section geometry circular, hollow circular, square and rotated square with a 45 degrees angle of rotation with respect to x and y axes. Plane wave expansion method is used to solve the governing equations of motion of a piezoelectric solid based on classical elasticity theory, ignoring nanoscopic size effects, considering two-dimensional periodicity and wave propagation in the xy plane. Complete band gaps between XY and Z modes are observed for all inclusions and the best performance is for circular inclusion in a triangular lattice. Piezoelectricity influences significantly the band gaps for hollow circular inclusion in lower frequencies. We suggest that nano-piezoelectric phononic crystals are feasible for elastic vibration management in GHz.