二维空心散射体声子晶体板的低频带隙特性及其形成机理  

Low-frequency band gap characteristics of two-dimensional hollow scatterer phonon crystal plate and its formation mechanism

作　　者：康太凤 孙小伟[1] 宋婷[1] 孙伟彬 廖涛 谭自豪 KANG Taifeng;SUN Xiaowei;SONG Ting;SUN Weibin;LIAO Tao;TAN Zilmo(Institute of Mathematical,Lanzhou Jiaotong University,Lanzhou 730070;Tonly Electronics Holdings Limited Company,Huizhou 516006)

机构地区：[1]兰州交通大学数理学院,兰州730070 [2]通力电子控股有限公司,惠州516006

出　　处：《声学学报》2020年第4期601-608,共8页Acta Acustica

基　　金：国家自然科学基金项目(51562021,11464027);甘肃省重点人才项目(2020RCXM100);兰州交通大学优秀科研团队(201803);兰州交通大学“百名青年优秀人才培养计划”项目资助。

摘　　要：利用有限元方法,对设计的涂有硅橡胶包裹层的空心铅柱体嵌入到4个环氧树脂短连接板中构成的声子晶体板的低频带隙特性进行了研究,分析了其能带结构、传输损失及位移场。与正方连接板粘连结构、嵌入结构和细连接短板粘连结构这3种传统声子晶体板的带隙特性作对比,说明具有包裹层、短连接板结构的声子晶体板更容易产生低频宽带;观察位移矢量场的振动模态,并结合弹簧质量模型,解释了带隙形成的机理;通过讨论连接板的宽度、散射体的内外半径及高度对第一完全带隙的影响,说明连接板宽度越窄,厚度越小,散射体内半径越小,外半径越大,高度越高,越有利于带隙的扩展。By using the finite element method,the characteristics of the low frequency band gap of the phononic crystal plate which is composed of hollow lead cylinder coated with silicone rubber and embedded in four epoxy resin short connecting plates are studied.The energy band structure,transmission loss and displacement field were analyzed.Compared with three kinds of traditional phononic crystal plates,which are square plate adhesion structure,embedded structure and thin plate adhesion structure,the model has more and wider band gaps in the low frequency range,indicating that the phononic crystal plates with cladding layers and short cladding plates are more likely to generate low frequency broadband.The vibration modes of the displacement vector field and the spring mass model are observed to explain the mechanism of bandgap formation.By discussing the influence of the width of the joint plate,the inner and outer radius and height of the scatterer on the first complete bandgap,it is found that the narrower the width of the connection plate,the smaller the thickness,the smaller the radius of the scatterer,the larger the outer radius and the higher the height,and the better the band gap expansion.

关 键 词：位移矢量场 连接板 声子晶体 散射体 传输损失 有限元方法 完全带隙 振动模态 

分 类 号：O735[理学—晶体学]