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低频振动隔离和能量采集双功能超材料

赵龙 陆泽琦 丁虎 陈立群

赵龙, 陆泽琦, 丁虎, 陈立群. 低频振动隔离和能量采集双功能超材料. 力学学报, 2021, 53(11): 2972-2983 doi: 10.6052/0459-1879-21-471
引用本文: 赵龙, 陆泽琦, 丁虎, 陈立群. 低频振动隔离和能量采集双功能超材料. 力学学报, 2021, 53(11): 2972-2983 doi: 10.6052/0459-1879-21-471
Zhao Long, Lu Zeqi, Ding Hu, Chen Liqun. Low-frequency vibration isolation and energy harvesting simultaneously implemented by a metamaterial with local resonance. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 2972-2983 doi: 10.6052/0459-1879-21-471
Citation: Zhao Long, Lu Zeqi, Ding Hu, Chen Liqun. Low-frequency vibration isolation and energy harvesting simultaneously implemented by a metamaterial with local resonance. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 2972-2983 doi: 10.6052/0459-1879-21-471

低频振动隔离和能量采集双功能超材料

doi: 10.6052/0459-1879-21-471
基金项目: 国家自然科学基金资助项目(11872037)
详细信息
    作者简介:

    陆泽琦, 副研究员, 主要研究方向: 非线性振动隔离和能量采集. E-mail: luzeqi@shu.edu.cn

  • 中图分类号: O328

LOW-FREQUENCY VIBRATION ISOLATION AND ENERGY HARVESTING SIMULTANEOUSLY IMPLEMENTED BY A METAMATERIAL WITH LOCAL RESONANCE

  • 摘要: 振动隔离和能量采集一体化是一种能够将有害振动隔离并转化为电能收集利用的动力学机制. 本文从局域共振超材料存在低频带隙特性出发, 研究了振动隔离和能量采集双功能超材料的动力学行为. 通过在球型磁腔内放置固接了感应线圈的球摆构成具有能量采集功能的球摆型谐振器, 并将其周期性的放置在基体梁中, 可以将带隙频率范围内的振动聚集在谐振器内, 以实现振动隔离和能量采集双功能. 建立了横向激励下双功能超材料梁的动力学方程, 应用Bloch's定理得到超材料的能带结构, 通过有限元仿真验证了理论模型和研究方法. 研究了不同参数下超材料梁的带隙特性. 进一步将一维拓展到二维, 研究了二维双功能超材料板的振动隔离和能量采集性能. 最后, 设计并建造了振动隔离和能量采集一体化双功能超材料动力学实验平台, 解析、数值和实验结果表明, 在局域共振带隙的频率范围内, 超材料梁主体的振动明显被抑制, 与此同时, 振动被局限在谐振器中, 使采集到的电压达到了最大值. 通过对附加谐振器和没有附加谐振器的能带结构和幅频响应的对比, 发现球摆型谐振器的加入可以在低频范围内形成了一个局域共振带隙, 有效提高了超材料梁在低频处的振动隔离和能量采集性能.

     

  • 图  1  (a) 双功能超材料模型图; (b)带能量采集功能谐振器模型图

    Figure  1.  (a) View of the dual-functional metamaterial; (b) A spherical pendulum energy harvester

    图  2  超材料典型单胞的微元分析图

    Figure  2.  The infinitesimal analysis of Timoshenko beams

    图  3  球摆型谐振器模型

    Figure  3.  A spherical pendulum resonator

    图  4  附加谐振器单元有限元模型

    Figure  4.  Finite element model of unit cell

    图  5  附加谐振器超材料梁有限元模型

    Figure  5.  Finite element model of metamaterial beam

    6  超材料梁的能带结构与幅频响应对比

    6.  Band-gaps and amplitude-frequency response of metamaterial

    图  6  超材料梁的能带结构与幅频响应对比(续)

    Figure  6.  Band-gaps and amplitude-frequency response of metamaterial (continued)

    图  7  几何参数对带隙的影响

    Figure  7.  Effects of geometric parameters on band gap

    图  8  不同位置谐振器的输出电压曲线

    Figure  8.  Output voltage curve of resonator at different positions

    图  9  横向激励下超材料梁试验照片

    Figure  9.  photograph of the transverse excited metamaterial beam

    图  10  横向激励下超材料梁的扫频曲线

    Figure  10.  Sweep curve of metamaterial beam under transverse excitation

    图  11  不同频率的时域响应

    Figure  11.  Time domain response at different frequency

    图  12  5×5超材料板有限元模型示意图和超材料单胞简约Brillouin区间

    Figure  12.  Finite element model of metamaterial plate and Brillouin zone of metamaterial plate, (5×5)

    图  13  双功能超材料板特性和幅频响应

    Figure  13.  Band gap structure and amplitude frequency response

    图  14  激励点附近谐振器的输出电压曲线

    Figure  14.  Output voltage curve of resonator near excitation point

    表  1  双功能超材料物理参数

    Table  1.   Parameters of a dual-functional metamaterial

    ItemNotationValue
    length $ l/{\rm{m}} $ $ 0.1 $
    cross-sectional area $ A/{\rm{m}}^2$ $ 0.003\;6 $
    density of material $ \rho /\left( {{\rm{kg}} \cdot {{\rm{m}}^{ - {\rm{3}}}}} \right) $ $ 1810 $
    Young's modulus $E/{\rm{Pa}}$ $ 761\;761 $
    radius of spherical cavity $ R/{\rm{m}} $ $ 0.0{\text{2}} $
    radius of sliding-ball $r/{\rm{m}}$ $ 0.009 $
    density of sliding-ball $ {\rho _{\rm{b}}}/\left( {{\rm{kg}} \cdot {{\rm{m}}^{ - {\rm{3}}}}} \right) $ $ {\text{7780}} $
    magnetic flux $B/{\rm{T}} $ $ {\text{0}}{\text{.5}} $
    inductance $ {L_{{\rm{ind}}}}/{\rm{H}}$ $ {\text{0}}{\text{.5}} $
    coil length $ {L_{{\rm{coil}}}}/{\rm{m}} $ $ {\text{0}}{\text{.1}} $
    下载: 导出CSV

    表  2  试验仪器

    Table  2.   Experiment instruments

    InstrumentsVersionManufacturer
    shakerTV-51140TIRA
    accelerometer352C03PCB
    vibration controllerSCM2E02VSIEMENS
    下载: 导出CSV

    表  3  带隙内隔振效率

    Table  3.   Vibration isolation efficiency of band gap

    Band-gaps$ {\mu _{{\text{BGIE}}}} $/%
    local resonant band-gap59.54
    Bragg band-gap49.39
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-09-13
  • 录用日期:  2021-10-13
  • 网络出版日期:  2021-10-14
  • 刊出日期:  2021-11-18

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