包裹层结构对轻质声子晶体低频振动带隙的影响  

Effect of Cladding Structure on Low-frequency Vibration Band Gap of Lightweight Phononic Crystals

作　　者：刘威 何泽银[1,2] 陶平安 孙世政 王承登[1] Wei Liu;Zeyin He;Ping'an Tao;Shizheng Sun;Chengdeng Wang(School of Mechatronics and Vehicle Engineering,Chongqing Jiaotong University,Chongqing,400074;Chongqing Construction Automotive Systems Co.,Ltd.,Chongqing,400052)

机构地区：[1]重庆交通大学机电与车辆工程学院,重庆400074 [2]重庆建设汽车系统股份有限公司,重庆400052

出　　处：《固体力学学报》2022年第5期658-668,共11页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(52005066);重庆市自然科学基金项目(cstc2019jcyj-msxmX0799);重庆市九龙坡科技计划项目(2020-02-001-Z)资助。

摘　　要：基于局域共振机理提出新型轻质声子晶体包裹层结构设计方法.借助有限元法,计算新型声子晶体能带结构、本征模态,分析包裹层总缺口度数一定时不同包裹层缺口数量及布置位置对第一完全带隙截止频率的影响;设计包裹层与散射体连接形式为线连接与点连接两种新型声子晶体模型,分别得到起始频率为37.4 Hz及19.0 Hz的第一完全带隙,分析第一完全带隙起始频率处散射体本征模态,揭示新型声子晶体极低第一完全带隙起始频率产生机理;进而,与传统面连接型声子晶体通过增加散射体质量降低第一完全带隙起始频率的方法对比.研究结果表明,包裹层总缺口度数一定时,采用缺口数量更多且缺口位置距离连接短板更大的包裹层布置形式能得到更宽的第一完全带隙;提出的包裹层与散射体线连接与点连接型声子晶体在获得极低第一完全带隙起始频率的同时,显著降低了声子晶体质量,突破了传统声子晶体通过增加散射体质量降低第一完全带隙起始频率的限制,为轻质声子晶体获得极低局域共振带隙起始频率的研究设计提供了参考.A new design method for lightweight phononic crystal cladding structure is proposed based on the local resonance mechanism. The effect of cladding structure on the low-frequency vibration band gap of lightweight phononic crystals is studied. With the help of the finite element method, the energy band structure and eigenmodes of a new type of phononic crystal are calculated. When the total notch degree of the cladding is fixed, the influences of the numbers and locations of different cladding notches on the cut-off frequency of the first complete band gap are analyzed. Two new phononic crystal models, i.e., line connection and point connection, are designed to connect the cladding and the scatterer. The first complete band gaps with an initial frequency of 37.4 Hz and 19.0 Hz are obtained, respectively. The eigenmodes of scatterers at the initial frequency of the first complete band gap are analyzed, and the generation mechanism of the very low initial frequency of the first complete band gap of the new phononic crystals is revealed. Furthermore, it is compared with the traditional method in reducing the initial frequency of the first complete band gap by increasing the mass of the scatterer. The results show that when the total notch degree of the cladding is fixed, a wider first complete band gap can be obtained by using the cladding arrangement with more notches and being farther away from the connecting short plate. The proposed design method for phononic crystals with the cladding and scatterer being line-connected and point-connected can not only obtain a very low initial frequency of the first complete band gap, but also significantly reduce the weight phononic crystals. This weak connection between the cladding and the scatterer breaks through the limitation of traditional phononic crystals in reducing the initial frequency of the first complete band gap by increasing the mass of the scatterer. It provides a reference for the research and design of lightweight phononic crystals in obtaining a very low init

关 键 词：包裹层 声子晶体 局域共振 连接形式 低频带隙 

分 类 号：O735[理学—晶体学]