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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 .
By introducing the idea of continuous system discretization in vibration mechanics, a one-dimensional mass-centered method is extended to two-dimension, and a lumped mass method is proposed to calculate the bandgap characteristics of two-dimensional phononic crystals. Furthermore, Lattice two-dimensional phononic crystal band structure is calculated, the calculation results with the traditional plane wave expansion method is consistent with the calculation results and the convergence of the two algorithms analysis and found that the convergence of the mass-concentration method for the composition of phononic crystals The difference between the elastic parameters of different materials is insensitive, which makes the algorithm converge faster than the plane wave expansion method in calculating the bandgap characteristics of two-dimensional phononic crystals with large elastic constant difference. In addition, There are no special requirements, which makes it more suitable for the calculation of the bandgap characteristics of phononic crystals.