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 Kagomé lattices. We also investigate the influence of inclusion cross section geometry - circular, hollow circular, square and rotated square with a 45º 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.