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带附加质量块的压电圆板能量采集器振动分析

孟莹 丁虎 陈立群

孟莹, 丁虎, 陈立群. 带附加质量块的压电圆板能量采集器振动分析. 力学学报, 2021, 53(11): 2950-2960 doi: 10.6052/0459-1879-21-441
引用本文: 孟莹, 丁虎, 陈立群. 带附加质量块的压电圆板能量采集器振动分析. 力学学报, 2021, 53(11): 2950-2960 doi: 10.6052/0459-1879-21-441
Meng Ying, Ding Hu, Chen Liqun. Vibration analysis of a piezoelectric circular plate energy harvester considering a proof mass. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 2950-2960 doi: 10.6052/0459-1879-21-441
Citation: Meng Ying, Ding Hu, Chen Liqun. Vibration analysis of a piezoelectric circular plate energy harvester considering a proof mass. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 2950-2960 doi: 10.6052/0459-1879-21-441

带附加质量块的压电圆板能量采集器振动分析

doi: 10.6052/0459-1879-21-441
基金项目: 国家自然科学基金资助项目(12025204)
详细信息
    作者简介:

    陈立群, 教授, 主要研究方向: 振动理论和应用, 非线性动力学和控制. E-mail: lqchen@shu.edu.cn

  • 中图分类号: O321

VIBRATION ANALYSIS OF A PIEZOELECTRIC CIRCULAR PLATE ENERGY HARVESTER CONSIDERING A PROOF MASS

  • 摘要: 基于圆板的压电能量采集技术在取代化学电池为低功耗电子器件提供能源方面具有巨大的潜能. 本文通过理论建模和数值仿真研究了考虑附加质量接触面积的压电圆板能量采集器的采集性能. 首先, 基于基尔霍夫薄板理论, 用广义哈密顿原理推导了带附加质量块的压电圆板能量采集器的机电耦合方程, 并用伽辽金法对方程近似离散, 通过离散方程得到电压、功率输出和最优负载阻抗的闭合解. 用有限元仿真对所提出的理论模型进行了验证, 结果表明该理论模型可以成功地预测压电圆板能量采集器输出电压和功率. 最后, 基于闭合解探讨了负载阻抗、附加质量块、压电圆板的内外半径等相关参数对压电圆板能量采集器固有频率、输出电压和功率的影响. 结果表明, 当质量块与复合板的接触半径足够小(本文中接触半径小于板半径的1/14)时, 质量块与复合圆板的接触面积可以忽略; 相较于无孔的压电片, 内径位于2.5 ~ 4 mm范围内的压电片可以提高能量采集器的采集性能; 附加质量、压电片外径和负载阻抗的合理选择既可以降低压电圆板的固有频率, 还可以提高其采集性能.

     

  • 图  1  附加质量块的圆板能量采集器的剖面图

    Figure  1.  The cutaway view of the circular energy harvester considering proof mass

    图  2  不同模态数下输出电压随基础激励频率变化

    Figure  2.  The variation of the voltage output with base excitation frequency for different number of modes

    图  3  压电圆板能量采集器的有限元模型

    Figure  3.  Finite element model of the piezoelectric circular plate energy harvester

    图  4  负载阻抗对输出电压和功率的影响

    Figure  4.  The effect of the load resistance on the output voltage and power

    图  5  附加质量对能量采集器采集性能的影响

    Figure  5.  The influence of the mass on the harvesting performance of the energy harvester

    图  6  压电片外径对能量采集器的固有频率、最大输出电压和功率的影响

    Figure  6.  The effect of the outer radius of the piezoelectric plate on the natural frequency, maximum output voltage and power of the energy harvester

    图  7  压电片内半径对能量采集器采集性能的影响

    Figure  7.  The effect of the inner radius of the piezoelectric plate on the harvesting performance of energy harvester

    A1  能量采集器3个截面受力分析

    A1.  The force analysis of the three sections of the energy harvester

    表  1  圆板能量采集器的参数

    Table  1.   The parameters of the circular energy harvester

    ParameterUnitValue
    Eb GPa 90
    $ S_{11}^E $ m2/N 1.65 × 10−11
    ρb kg/m3 8500
    ρp kg/m3 7500
    vb 0.33
    vp 0.2897
    d31 m/V −2.74 × 10−10
    $\varepsilon _{33}^T$ F/m 3.021 × 10−8
    hb mm 0.2
    hp mm 0.2
    rb mm 28
    μ s−1 57.7715
    γ s 7.7022 × 10−6
    下载: 导出CSV

    表  2  m0 = 0时压电圆板能量采集器的固有频率理论值与仿真值比较

    Table  2.   Comparison of natural frequency of circular energy harvester with m0 = 0 from theory and simulation

    rpi/mmRL = 0 ΩRL = 10 kΩRL→∞
    FEA/Hzmodel/Hz error/%FEA/Hzmodel/Hz error/%FEA/Hzmodel/Hz error/%
    0 581.73 580.72 −0.174 656.66 654.05 −0.397 663.88 662.87 −0.152
    3 572.56 571.56 −0.175 640.32 638.01 −0.361 647.41 646.75 −0.102
    4 566.81 565.82 −0.175 629.94 627.88 −0.328 636.95 636.46 −0.077
    5 560.64 559.64 −0.178 618.72 616.81 −0.309 625.64 625.48 −0.026
    下载: 导出CSV

    表  3  m0 = 74.3 g时压电圆板能量采集器的固有频率理论值与仿真比较

    Table  3.   Comparison of natural frequency of circular energy harvester with m0 = 74.3 g from theory and simulation

    rpi/mmRL = 0 ΩRL→∞
    model/HzFEA (χ = 1/28)/Hzerror/%FEA (χ = 1/14)/Hzerror/%model/HzFEA (χ = 1/28)/Hzerror/%FEA (χ = 1/14)/Hzerror/%
    0 109.81 110.23 −0.383 113.6 −3.33 125.61 126.88 −1.003 130.89 −4.04
    3 97.89 97.73 0.164 102.02 −4.05 108.72 108.27 0.411 113.96 −4.60
    4 92.85 92.03 0.893 96.81 −4.09 101.54 100.42 1.116 106.55 −4.70
    5 87.57 86.58 1.141 91.66 −4.46 94.04 93.26 0.835 99.56 −5.87
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-09-01
  • 录用日期:  2021-09-23
  • 网络出版日期:  2021-09-24
  • 刊出日期:  2021-11-18

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