二维正方晶格钨-硅橡胶声子晶体的带隙特性研究  

Characteristic of Bandgaps in Two-Dimensional Ternary Lattice Tungsten-Silicone Rubber Phononic Crystals

作　　者：郭翔鹰[1] 孙向洋 朱雨男 GUO Xiangying;SUN Xiangyang;ZHU Yunan(Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures,College of Mechanical Engineering,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学机械工程学院,机械结构非线性振动与强度北京市重点实验室,北京100124

出　　处：《人工晶体学报》2020年第9期1583-1589,共7页Journal of Synthetic Crystals

基　　金：国家自然科学基金(11772010,11572006,11602234)。

摘　　要：本文利用平面波展开法和有限元法计算了二维正方晶格钨-硅橡胶声子晶体的能带结构,分析了弹性波在嵌有周期性排列的相同孔径的圆柱形钨块声子晶体结构中的传播特性。对能带结构中出现的特殊现象,例如狄拉克点以及狄拉克点附近的简并态等进行了分析。给出了三维能带图以及不同模式下的主要变形情况,发现在基体与散射体结合的部位容易出现应力集中的现象。同时讨论了复合材料的不同参数对带隙的影响,发现随着密度比(散射体密度与基体密度的比值)的增大,第一完全带隙的起始频率逐渐增加,但是截止频率变化较小,带宽逐渐减小。相对于杨氏模量比,密度比对带隙的影响更大。本文的结果将对实际的工程应用提供一定的理论指导。The energy band characteristic of two-dimensional ternary lattice tungsten-silicone rubber phononic crystals was analyzed by both the plane wave expansion method and finite element method.The propagation characteristics of elastic wave in a silicone rubber plate were analyzed,which were embedded with periodically arranged cylindrical tungsten blocks of the same pore size.Moreover,the special phenomena in the band structure were also discussed,such as the Dirac point and the degeneracy near the Dirac point and so on.The three-dimensional energy band diagram and the main deformation under different modes were given.It is found that stress concentration easily occur in the combination part of the periodic composite material.Then the influence of different material parameters on the bandgap were studied and the initial frequency of the first complete bandgap gradually increases with the increase of the density ratio(the ratio of the scatterer density to the matrix density).However,the bandwidth decreases gradually since the cutoff frequency changes little.Compared with Young's modulus,density has more influence on the bandgap of the periodic composite material.The results of this paper could provide some theoretical guidance for practical engineering application.

关 键 词：声子晶体 平面波展开 简并态 能带结构 狄拉克点 

分 类 号：O734[理学—晶体学]