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.

本研究针对由钛酸钡（BaTiO3）夹杂物增强的聚合物基体构成的纳米压电声子晶体（nano-piezoelectric phononic crystal）展开研究，分析其在正方形、矩形、三角形、蜂窝状及Kagomé晶格中传播的弹性波能带结构。本研究同时探究夹杂物截面几何形状对能带结构的影响，所考察的截面类型包括圆形、空心圆形、正方形，以及相对于x、y轴旋转45°的旋转正方形。本研究采用平面波展开法（Plane Wave Expansion Method），基于经典弹性理论求解压电固体的运动控制方程，忽略纳米尺度尺寸效应，考虑二维周期性以及波在xy平面内的传播。研究结果显示，所有夹杂物构型均观测到XY模式与Z模式之间的完全带隙，其中三角形晶格内嵌圆形夹杂物的结构性能最优。对于空心圆形夹杂物，压电效应在低频段对带隙具有显著影响。本研究表明，纳米压电声子晶体可应用于GHz频段的弹性振动管理。