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含有末端质量的竖直梁压电俘能器参数共振及其特性研究

邹政 谢进 马戈 汪灿

邹政,谢进,马戈, 等. 含有末端质量的竖直梁压电俘能器参数共振及其特性研究[J]. 机械科学与技术,2021,40(4):508-517 doi: 10.13433/j.cnki.1003-8728.20200096
引用本文: 邹政,谢进,马戈, 等. 含有末端质量的竖直梁压电俘能器参数共振及其特性研究[J]. 机械科学与技术,2021,40(4):508-517 doi: 10.13433/j.cnki.1003-8728.20200096
ZOU Zheng, XIE Jin, MA Ge, WANG Can. Study on Parametric Resonance of Vertical Cantilevered Piezoelectric Energy Harvester with End Mass and Its Characteristics[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(4): 508-517. doi: 10.13433/j.cnki.1003-8728.20200096
Citation: ZOU Zheng, XIE Jin, MA Ge, WANG Can. Study on Parametric Resonance of Vertical Cantilevered Piezoelectric Energy Harvester with End Mass and Its Characteristics[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(4): 508-517. doi: 10.13433/j.cnki.1003-8728.20200096

含有末端质量的竖直梁压电俘能器参数共振及其特性研究

doi: 10.13433/j.cnki.1003-8728.20200096
基金项目: 国家自然科学基金项目(51575457)
详细信息
    作者简介:

    邹政(1993−),硕士研究生,研究方向为压电俘能器及非线性动力学的研究,861134395@qq.com

    通讯作者:

    谢进,教授,博士生导师,xj_6302@263.net

  • 中图分类号: TH113.1

Study on Parametric Resonance of Vertical Cantilevered Piezoelectric Energy Harvester with End Mass and Its Characteristics

  • 摘要: 为了改善参数共振压电俘能器的俘能特性,提出在竖直梁的自由端固结一个质量块。利用拉格朗日方程和高斯定律建立了系统的机电耦合方程,并进行了数值仿真。仿真结果表明,梁从竖直的单稳态系统转变为屈曲的双稳态系统的临界末端质量Mc为0.0509 kg。当梁的阻尼比为0.05,末端质量从0增加到Mc时,参数共振激励阈值从47.5 m/s2减小到趋向于0;当M大于Mc时,对于任何阻尼比的梁,激励阈值都为零,并且当外激励的幅值和频率使得梁处于两稳态势阱间的大幅周期运动时,俘能器才可以产生出较高的输出功率。
  • 图  1  参数激励俘能器结构示意图

    图  2  确定位置矢量的末端质量运动图

    图  3  系统的平衡点和固有频率

    图  4  末端质量对激励阈值的全局影响

    图  5  M < Mc时的激励阈值

    图  6  激励幅值小于激励阈值的时域图与相图

    图  7  激励达到激励阈值的时域图和相图

    图  8  M > Mc时的激励阈值

    图  9  系统关于激励幅值和激励频率的分岔图

    图  10  系统在不同激励幅值时的时域图和相图

    图  11  系统在不同激励频率的时域图和相图(激励幅值A = 0.3 m/s2

    表  1  俘能器仿真参数

    参数压电片
    长度$(L,{L_{{p}}})/{\rm{mm}}$20030
    宽度$({w_{{b}}},{w_{{p}}})/{\rm{mm}}$1616
    厚度$({t_{{b}}},{t_{{p}}})/{\rm{mm}}$0.40.3
    密度$\rho /{\rm{(kg}} \cdot {{\rm{m}}^{{\rm{ - 3}}}}{\rm{)}}$7165
    杨氏模量$(E,{E_{{p}}})/{\rm{GPa}}$10066
    压电常数${d_{31}}/({\rm{pC}} \cdot {{\rm{N}}^{{\rm{ - 1}}}})$−190
    介电常数${\varepsilon _{33}}/{\rm{(nF}} \cdot {{\rm{m}}^{{\rm{ - 1}}}}{\rm{)}}$13.28
    负载电阻$R/{\rm{M\Omega }}$5
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-08-14
  • 网络出版日期:  2021-04-16
  • 刊出日期:  2021-04-16

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