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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
  • [1] Jiang LM, Yang Y, Chen RM, et al. Flexible piezoelectric ultrasonic energy harvester array for bio-implantable wireless generator. Nano Energy, 2019: 216-224
    [2] 刘婷, 赵程, 张刚华等. 应用于能量采集领域压电材料的研究进展. 机械工程材料, 2020, 44(6): 82-87+92 (Liu Ting, Zhao Cheng, Zhang Ganghua, et al. Research progress on piezoelectric materials in the field of energy harvesting. Materials for Mechanical Engineering, 2020, 44(6): 82-87+92 (in Chinese)
    [3] 魏胜, 胡泓. 基于压电振动的人体能量采集技术研究综述. 机械与电子, 2018, 36(10): 67-72 (Wei Sheng, Hu Hong. A review of human motion energy harvesting based on piezoelectric vibration. Machinery and electronics, 2018, 36(10): 67-72 (in Chinese) doi: 10.3969/j.issn.1001-2257.2018.10.015
    [4] 解锋. 基于压电换能器的心脏能量采集装置制备与实验研究. [博士论文]. 上海: 中国人民解放军海军军医大学, 2021

    Xie Feng. A research on preparation and application of the heart piezoelectric transducer in animal experiments. [PhD Thesis]. Shanghai: the PLA Naval Medical University, 2021 (in Chinese)
    [5] Gardonio P, Zilletti M. Vibration energy harvesting from an array of flexible stalks exposed to airflow: A theoretical study. Smart Materials and Structures, 2016, 25(3): 035014 doi: 10.1088/0964-1726/25/3/035014
    [6] Yang ZB, Zhou SX, Zu J, et al. High-performance piezoelectric energy harvesters and their applications. Joule, 2018, 2(4): 642-697 doi: 10.1016/j.joule.2018.03.011
    [7] Elvin NG, Elvin AA. An experimentally validated electromagnetic energy harvester. Journal of Sound and Vibration, 2011, 330(10): 2314-2324 doi: 10.1016/j.jsv.2010.11.024
    [8] Le CP, Halvorsen E, Sorasen O, et al. Microscale electrostatic energy harvester using internal impacts. Journal of Intelligent Material Systems and Structures, 2012, 23(13): 1409-1421 doi: 10.1177/1045389X12436739
    [9] 刘仲琳, 冷永刚, 刘进军等. 双稳悬臂梁电磁式振动能量采集研究. 振动与冲击, 2019, 38(23): 126-133+151 (Liu Zhonglin, Leng yonggang, Liu Jinjun, et al. Electromagnetic type vibration energy harvester based on bi-stable cantilever beam. Journal of Vibration and Shock, 2019, 38(23): 126-133+151 (in Chinese)
    [10] 王光庆, 崔素娟, 武海强等. 多稳态压电振动能量采集器的动力学模型及其特性分析. 振动工程学报, 2019, 32(2): 252-263 (Wang Guangqing, Cui Sujuan, Wu Haiqiang, et al. Dynamical model and characteristics of a multi-stable piezoelectric vibration energy harvester. Journal of Vibration Engineering, 2019, 32(2): 252-263 (in Chinese)
    [11] 李魁, 杨智春, 谷迎松等. 变势能阱双稳态气动弹性能量收集的性能增强研究. 航空学报, 2020, 41(9): 136-147 (Li Kui, Yang Zhichun, Gu Yingsong, et al. Performance enhancement of variable-potential-well bi-stable aeroelasticity energy harvesting. Acta Aeronautica et Astronautica Sinica, 2020, 41(9): 136-147 (in Chinese)
    [12] 张智娟, 杨瑞, 郑龙飞等. 悬臂梁双晶压电能量采集装置实验研究. 科学技术与工程, 2020, 20(35): 14518-14522 (Zhang Zhijuan, Yang Rui, Zheng Longfei, et al. Experimental exploration of double crystal piezoelectric energy collection device on cantilever beam. Science Technology and Engineering, 2020, 20(35): 14518-14522 (in Chinese) doi: 10.3969/j.issn.1671-1815.2020.35.025
    [13] Yuan TC, Yang J, Chen LQ. Nonlinear characteristic of a circular composite plate energy harvester: Experiments and simulations. Nonlinear Dynamics, 2017, 90(4): 1-12
    [14] Lu Q. Modeling of functionally graded circular energy harvesters due to flexoelectricity. Applied Mathematical Modelling, 2019: 587-590
    [15] Kim S, Clark WW, Wang QM. Piezoelectric energy harvesting with a clamped circular plate: Analysis. Journal of Intelligent Material Systems and Structures, 2005, 16(10): 847-854 doi: 10.1177/1045389X05054044
    [16] Kim S. Piezoelectric energy harvesting using a clamped circular plate: experimental study. Journal of Intelligent Material Systems and Structures, 2005, 16(10): 855-863 doi: 10.1177/1045389X05054043
    [17] Mehdipour I, Honarvar F. Finding the optimum polarization boundary line for enhancing the performance of clamped piezoelectric circular plates. Applied Mathematical Modelling, 2021: 1141-1153
    [18] Yuan JB, Xie T, Chen WS, et al. Performance of a drum transducer for scavenging vibration energy. Journal of Intelligent Material Systems and Structures, 2009, 20(14): 1771-1777 doi: 10.1177/1045389X09343477
    [19] Kan JW, Qiu JH, Tang KH, et al. Modeling and simulation of piezoelectric composite diaphragms for energy harvesting. International Journal of Applied Electromagnetics and Mechanics, 2009, 30(1-2): 95-106 doi: 10.3233/JAE-2009-1039
    [20] Shahri MB, Moeenfard H. Energy harvesting from unimorph piezoelectric circular plates under random acoustic and base acceleration excitations. Mechanical Systems and Signal Processing, 2019, 130: 502-523
    [21] Chen XR, Yang TQ, Wang W, et al. Vibration energy harvesting with a clamped piezoelectric circular diaphragm. Ceramics International, 2012, 38(1): S271-S274 doi: 10.1016/j.ceramint.2011.07.001
    [22] Palosaari J, Leinonen M, Juuti J, et al. Piezoelectric circular diaphragm with mechanically induced pre-stress for energy harvesting. Smart Materials and Structures, 2014, 23(8): 085025 doi: 10.1088/0964-1726/23/8/085025
    [23] Liu YZ, Yang TQ, Shu FM. Optimization of energy harvesting based on the uniform deformation of piezoelectric ceramic. Functional Materials Letters, 2016, 9(5): 1650069 doi: 10.1142/S1793604716500697
    [24] Shu FM, Yang TQ, Liu YZ. Enhancement of power output by a new stress-applied mode on circular piezoelectric energy harvester. AIP Advances, 2018, 8(4): 045102 doi: 10.1063/1.5016200
    [25] Han Y, Li YB, Yang YYW, et al. Improvement of uneven charge distribution on piezoelectric circular diaphragm with notched-substrate. AIP Advances, 2020, 10(4): 045330 doi: 10.1063/1.5141890
    [26] Solovyev AN, Duong LV. Optimization for the harvesting structure of the piezoelectric bimorph energy harvesters circular plate by reduced order finite element analysis. International Journal of Applied Mechanics, 2016, 8(3): 1650029
    [27] Jiang SN, Hu YT. Analysis of a piezoelectric bimorph plate with a central-attached mass as an energy harvester. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2007, 54(7): 1463-1469 doi: 10.1109/TUFFC.2007.407
    [28] Yang YYW, Wang S, Stein P, et al. Vibration-based energy harvesting with a clamped piezoelectric circular diaphragm: analysis and identification of optimal structural parameters. Smart Materials and Structures, 2017, 26(4): 045011 doi: 10.1088/1361-665X/aa5fda
    [29] Yang YYW, Li YB, Guo YQ, et al. Improved vibration-based energy harvesting by annular mass configuration of piezoelectric circular diaphragms. Smart materials and structures, 2018, 27(3): 3680-3684
    [30] Xu CQ, Li YB, Yang TQ. Optimization of non-uniform deformation on piezoelectric circular diaphragm energy harvester with a ring-shaped ceramic disk. Micromachines, 2020, 11(11): 963 doi: 10.3390/mi11110963
    [31] Erturk A, Inman DJ. Piezoelectric Energy Harvesting. New York: Wiley, 2011
    [32] Nayfeh AH, Pai PF. Linear and Nonlinear Structural Mechanics. New York: Wiley, 2004
    [33] 刘延柱, 陈立群, 陈文良. 振动力学. 第3版. 北京: 高等教育出版社, 2019

    Liu Yanzhu, Chen Liqun, Chen Wenliang. Mechanics of Vibration. (3rd Edn.) Beijing: Higher Education Press, 2019 (in Chinese)
    [34] 曹志远. 板壳振动理论. 北京: 中国铁道出版社, 1989

    Cao Zhiyuan. Theory of Vibration of Plates and Shells. Beijing: China Railway Press, 1989 (in Chinese)
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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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