大弹性常数差二维声子晶体带隙计算中的集中质量法

Lumpedmass approach for the calculation of band structure of two-dimensional phononic crystals with high contrast of elastic constant

通过引入振动力学中的连续系统离散化的思想 ,将一维集中质量法延伸至二维 ,提出一种二维声子晶体带隙特性计算的集中质量法 .进而采用该算法对两种正方晶格的二维声子晶体的带结构进行了计算 ,计算结果与传统的平面波展开法相符合 .通过对计算结果以及两种算法收敛性的分析 ,发现集中质量法的收敛性对组成声子晶体的不同材料弹性参数差不敏感 ,这使得该算法在计算大弹性常数差二维声子晶体的带隙特性时较平面波展开法收敛速度更快 .此外 ,集中质量法对二维声子晶体单元形状没有特殊要求 ,这使得它更加适用于声子晶体带隙特性的计算 .

With each unit cell replaced by a system of finite freedoms of motion, two-dimensional phononic crystals can be simplified to an infinite discrete periodic system. Therefore, the elastic wave band structures of the two-dimensional phononic crystals can be calculated with a straightforward lumped-mass approach, whose computational cost is much lower than the well-known plane wave expansion(PWE) method. The numerical results of the two methods are in reasonable agreements. As the well-known Gibbs oscillations in the PWE can be eliminated with the lumped-mass method, this new approach is insensitive to the sharp variation of elastic constants on the interfaces inside the phononic crystals. Furthermore, the lumped-mass method can also be used to calculate the band structures of two-dimensional phononic crystals with arbitrary unit shapes easily.