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可控超结构复合带隙特性研究

杨子悦 刘欢 张红艳

杨子悦, 刘欢, 张红艳. 可控超结构复合带隙特性研究[J]. 复合材料学报, 2024, 42(0): 1-9.
引用本文: 杨子悦, 刘欢, 张红艳. 可控超结构复合带隙特性研究[J]. 复合材料学报, 2024, 42(0): 1-9.
YANG Ziyue, LIU Huan, ZHANG Hongyan. Study on the complex band gap characteristic of controllable metastructure[J]. Acta Materiae Compositae Sinica.
Citation: YANG Ziyue, LIU Huan, ZHANG Hongyan. Study on the complex band gap characteristic of controllable metastructure[J]. Acta Materiae Compositae Sinica.

可控超结构复合带隙特性研究

详细信息
    通讯作者:

    张红艳,博士,教授,硕士生导师,研究方向为结构非线性振动控制 E-mail: zhanghongyan@chd.edu.cn

  • 中图分类号: TB535

Study on the complex band gap characteristic of controllable metastructure

  • 摘要: 可控超结构可根据目标需求调节结构的带隙特性,实现对不同工况下结构减振的可控调节,在航空航天、轨道交通等工程领域具有广泛的应用前景。本文提出一种新型可控超结构构型,可同时产生局域共振和布拉格散射两种带隙,通过施加位移可实现对带隙的有效调控。应用COMSOL软件建立了该结构的有限元模型,研究了4种可控超结构构型的能带分布及其在外加位移激励作用下的带隙特性调控规律,开展了该结构的振动传输特性实验,并与数值结果进行对比验证。研究结果表明,四振子复合带隙可控超结构在0~800 Hz范围内共有3条完全带隙,第一阶带隙范围低至134.48~287.53 Hz,第二阶带隙范围为307.26~447.81 Hz,第三阶带隙范围为662.44~679.43 Hz。对比分析4种元胞构型带隙特性,在一定频率范围内,随着振子数量增加,带隙数量减少,带宽增加,带隙位置逐渐上移;施加结构位移可有效调控结构带隙,随着位移值增加,结构中低频局域共振带隙变化较小,布拉格带隙中心频率逐渐上移,并出现新带隙。本研究表明该结构在带隙范围内具有良好的减振特性。结果表明所设计的复合带隙可控超结构可实现对复合带隙的调控,为超结构减振设计研究提供有益的参考。

     

  • 图  1  不同构型复合带隙可控超结构元胞

    Figure  1.  Composite band gap controllable metastructure cells with different configurations

    图  2  不同轴向压缩下二振子构型超结构元胞及试件示意图

    Figure  2.  Schematic diagram of the metastructure cells and specimens of two-oscillator configurations under different axial compressions

    $ {Y_{P} } $ is the axial compression of the structure

    图  3  $ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $时二振子构型超结构元胞及其第一不可约布里渊区(蓝色区域)

    Figure  3.  Two-oscillator configuration metastructure cell and its first irreducible Brillouin zone (blue region) in $ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $

    图  4  不同元胞构型$ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $时能带结构对比图

    Figure  4.  Energy band structure comparison diagram of different cell configurations $ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $

    图  5  四振子复合带隙可控超结构$ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $时能带结构及振动模态

    Figure  5.  Band structure and vibration mode of the four-oscillator composite band gap controllable metastructure $ {Y_{{\mathrm{P}}} } = 0\;{{\mathrm{mm}}} $

    图  6  单振子元胞在不同轴向压缩值下的能带结构对比图

    Figure  6.  Energy band structure comparison diagram of single-oscillator cell under different axial compression values

    图  7  二振子元胞在不同轴向压缩值下的能带结构对比图

    Figure  7.  Energy band structure comparison diagram of two-oscillator cell under different axial compression values

    图  8  三振子元胞在不同轴向压缩值下的能带结构对比图

    Figure  8.  Energy band structure comparison diagram of three-oscillator cell under different axial compression values

    图  9  四振子元胞在不同轴向压缩值下的能带结构对比图

    Figure  9.  Energy band structure comparison diagram of four-oscillator cell under different axial compression values

    图  10  有限周期二振子超结构振动传输特性分析示意图

    Figure  10.  Analysis diagram of vibration transmission characteristics of finite period two-oscillator metastructure

    图  11  不同轴向压缩值下两种尺寸有限周期二振子超结构振动传输特性曲线对比图

    Figure  11.  Comparison of vibration transmission characteristics curves of finite-period two-oscillator metastructures with two different sizes under different axial compression values

    图  12  不同轴向压缩值二振子构型超结构的能带结构及振动传输特性曲线

    Figure  12.  Energy band structure and vibration transmission characteristic curves of two-oscillator configuration metastructures with different axial compression values

    图  13  实验试件

    Figure  13.  Experimental specimens

    图  14  实验设备图

    Figure  14.  Experimental equipment diagram

    图  15  实验流程图

    Figure  15.  Flow chart of experiment

    图  16  不同轴向压缩值下二振子构型超结构的实验、数值振动传输特性曲线对比图

    Figure  16.  Comparison of experimental and numerical vibration transmission characteristic curves of two-oscillator configuration metastructure under different axial compression values

    表  1  几何参数和材料参数

    Table  1.   Geometric parameters and material parameters

    Geometric parameters Value Material Material parameters Value
    R/mm 17.5 Silicon rubber E/MPa 0.870
    ρ/(kg·m−3) 1230
    D/mm 7.426 ν 0.499
    Lead E/MPa 40.8
    θ/(°) 45 ρ/(kg·m−3) 11340
    ν 0.37
    Notes:E is elastic modulus;ρ is density;ν is Poisson’s ratio.
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  • 收稿日期:  2024-03-18
  • 修回日期:  2024-04-16
  • 录用日期:  2024-04-26
  • 网络出版日期:  2024-06-14

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