二维声子晶体的对称性对声学带隙的影响

Effect of Symmetry on Sonic Band-gap in Two-dimensional Phononic Crystals

用平面波展开方法计算了正三、四、六、八棱柱体及圆柱体按正方点阵排列的二维水-水银声子晶体的声学带隙结构．首先研究了非圆柱体的旋转对带隙的影响,发现在给定的柱体和(较低的)填充率下带隙宽度的最大值和最小值均出现在晶体结构对称性最高时．通过调节柱体的方位,找出各填充率下的最宽带隙,结果表明:在水／水银系统中,带隙宽度随柱体对称性的提高而增大;在水银／水系统中,除正四棱柱晶体带隙最宽以外,情况正好相反．

Using the plane-wave expansion method, we calculated the sonic band structures of two-dimensional water-mercury phononic crystals of regular triangle, quadrilateral, hexagon, octagon prisms and cylinders arrayed in square lattice respectively. Our study concerns the dependence of band gaps on rotation angle of the noncircular rods. And we found that, for each rod and （relatively small） filling fraction, both the maximum and minimum of band gap present in the case of the crystals＇ highest symmetry. By band gap for each filling fraction can be obtained adjusting the rods＇ orientation, the maximum of and, results show that for water/mercury system the width of band-gap increases with the heightening of rods＇ symmetry, while for mercury/water system the exact opposite is true except for the case of square rods, which produces the largest band-gaps.