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多稳态俘能系统的准确磁力建模方法

张颖 王伟 曹军义

张颖, 王伟, 曹军义. 多稳态俘能系统的准确磁力建模方法. 力学学报, 2021, 53(11): 2984-2995 doi: 10.6052/0459-1879-21-446
引用本文: 张颖, 王伟, 曹军义. 多稳态俘能系统的准确磁力建模方法. 力学学报, 2021, 53(11): 2984-2995 doi: 10.6052/0459-1879-21-446
Zhang Ying, Wang Wei, Cao Junyi. An accurate modelling method of magnetic force in multi-stable energy harvesting system. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 2984-2995 doi: 10.6052/0459-1879-21-446
Citation: Zhang Ying, Wang Wei, Cao Junyi. An accurate modelling method of magnetic force in multi-stable energy harvesting system. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(11): 2984-2995 doi: 10.6052/0459-1879-21-446

多稳态俘能系统的准确磁力建模方法

doi: 10.6052/0459-1879-21-446
基金项目: 国家自然科学基金资助项目(51975453)
详细信息
    作者简介:

    曹军义, 教授, 主要研究方向: 智能结构与振动能量俘获. E-mail: caojy@mail.xjtu.edu.cn

  • 中图分类号: TH39

AN ACCURATE MODELLING METHOD OF MAGNETIC FORCE IN MULTI-STABLE ENERGY HARVESTING SYSTEM

  • 摘要: 混沌和分岔使得多稳态俘能系统的非线性动力学响应对系统结构参数非常敏感, 导致了系统的非线性特性正向设计比较困难. 为了定量地表征非线性恢复力与结构参数的关系, 提出了一种多稳态俘能系统的准确磁力建模方法. 推导了多稳态俘能系统端部磁铁和外部磁铁的相对距离和转角位置, 并采用磁荷理论建立了多稳态系统的非线性磁力模型. 通过搭建实验平台测量了不同结构参数条件下多稳态系统的非线性磁力, 并对比了本方法与传统方法和实验测量的结果. 结果表明: 本方法的磁力计算结果与实验测量值吻合较好, 双稳态系统和三稳态系统的磁力峰值误差分别仅为4.3%和6.49%, 验证了本方法计算多稳态系统非线性磁力的有效性. 此外, 基于本方法探究了多稳态系统结构参数对系统势阱的影响机理, 获取了多稳态系统的稳态临界位置, 研究了双稳态和三稳态系统在不同结构参数下的响应电压规律. 参数优化结果表明, 双稳态系统在竖直距离为34 mm时, 均方电压最大为10.22 V; 三稳态系统在竖直距离为28 mm且水平距离为8 mm时, 均方电压最大为12.7 V. 该研究提出的模型以期为多稳态系统的输出性能优化设计提供借鉴.

     

  • 图  1  压电双稳态俘能结构

    Figure  1.  Piezoelectric bi-stable energy harvester

    图  2  双稳态系统磁铁空间位置

    Figure  2.  Spatial position of magnets for bi-stable system

    图  3  非线性磁力测量实验

    Figure  3.  Experimental setup of nonlinear magnetic force

    图  4  双稳态系统非线性磁力

    Figure  4.  Nonlinear magnetic force in bi-stable system

    图  5  三稳态系统非线性磁力

    Figure  5.  Nonlinear magnetic force in tri-stable system

    图  6  竖直距离h对双稳态系统势阱的影响

    Figure  6.  Influence of vertical distance h on bi-stable potential well

    图  7  竖直距离h对双稳态系统响应电压的影响

    Figure  7.  Influence of vertical distance h on bi-stable voltage response

    图  8  竖直距离h对双稳态系统频带影响

    Figure  8.  Influence of vertical distance h on bandwidth of bi-stable system

    图  9  不同竖直距离h的双稳态系统相轨迹图

    Figure  9.  Phase trajectory of bi-stable system under different vertical distance h

    图  10  双稳态系统最优竖直距离h

    Figure  10.  The optimal vertical distance h for bi-stable system

    图  11  竖直距离h对三稳态系统势阱的影响

    Figure  11.  Influence of vertical distance h on tri-stable potential well

    图  12  竖直距离h对三稳态系统响应电压的影响

    Figure  12.  Influence of vertical distance h on tri-stable voltage response

    图  13  竖直距离h对三稳态系统频带影响

    Figure  13.  Influence of vertical distance h on bandwidth of tri-stable system

    图  14  不同竖直距离h的三稳态系统相轨迹图

    Figure  14.  Phase trajectory of tri-stable system under different vertical distance h

    图  15  水平距离d对三稳态系统势阱的影响

    Figure  15.  Influence of horizontal distance d on tri-stable potential well

    图  16  水平距离d对三稳态系统响应电压的影响

    Figure  16.  Influence of horizontal distance d on tri-stable voltage response

    图  17  水平距离d对三稳态系统频带影响

    Figure  17.  Influence of horizontal distance d on bandwidth of tri-stable system

    图  18  不同水平距离d的三稳态系统相轨迹图

    Figure  18.  Phase trajectory of tri-stable system under different horizontal distance d

    图  19  三稳态系统参数优化

    Figure  19.  Parameters optimization of tri-stable system

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出版历程
  • 收稿日期:  2021-09-13
  • 录用日期:  2021-10-16
  • 网络出版日期:  2021-10-17
  • 刊出日期:  2021-11-18

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