Band Structure in Carbon Nanostructure Phononic Crystals

We investigate the band structure of elastic waves propagating in carbon nanostructure phononic crystals with square, rectangular, triangular, honeycomb and Kagomé lattices. We also study the influence of carbon nanostructure cross section geometry - circular, hollow circular, square and rotated square with a 45° angle of rotation with respect to the x and y axes. Plane wave expansion method is used to solve the governing equations of motion of a isotropic 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 types of carbon nanostructures. The best performance is for nanophononic crystal with circular carbon nanostructures in a triangular lattice with high band gap width in a broad range of filling fraction. We suggest that carbon nanostructure phononic crystals are feasible for elastic vibration management in GHz.本研究探究了搭载正方形、矩形、三角形、蜂窝形及Kagomé晶格的碳纳米结构声子晶体（phononic crystals）中弹性波的能带结构。同时研究了碳纳米结构截面几何形态的影响，包括圆形、空心圆形、正方形以及相对于x、y轴旋转45°的旋转正方形截面。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各向同性固体的运动控制方程，忽略纳米尺度尺寸效应，考虑二维周期性及xy平面内的波传播特性。所有类型的碳纳米结构均观测到XY模式与Z模式间的完整带隙。在三角形晶格中搭载圆形碳纳米结构的纳米声子晶体表现最优，其在较宽的填充率范围内均具备较高的带隙宽度。本研究表明，碳纳米结构声子晶体可应用于GHz频段的弹性振动调控。