非线性磁电层合材料的对称等效电路理论及数值仿真分析

张小丽; 殷秋鹏; 李果; 姚曦; 丁礼磊

doi:10.7498/aps.73.20240934

摘要

本文研究了长度方向磁化、厚度方向极化的3层磁电复合材料的非线性特性. 首先, 基于Z-L模型, 根据磁化强度的数值解特征, 拟合了磁化强度函数, 进一步推导了超磁致伸缩材料的动态参数, 如动态压磁系数、动态弹性柔顺系数和动态磁导率, 并分析了偏置磁场和预应力对相应参数的影响; 其次, 基于非线性磁致伸缩本构方程, 建立了磁电层合材料的对称磁-弹-电等效电路模型, 并推导了磁电系数表达式, 分析了其随偏置磁场和预应力的变化曲线, 与已报道的结果具有很好的一致性; 最后, 为了与理论结果进行比较, 采用COMSOL软件设置相同的参数, 绘制相应的磁电系数频率曲线, 二者结果符合较好, 并提取了最大峰值模态振动形状, 可以方便地观察到磁电层合材料长度方向的振动情况. 结果表明, 这种对称磁-弹-电等效电路理论模型及使用COMSOL软件数值模拟的方法是可取的, 为进一步进行磁电层合材料的非线性分析奠定了基础, 使设计高精度磁电微型器件成为可能.

关键词:

Abstract

In order to further study the nonlinear characteristics of the resonance magnetoelectric coefficient and vibration mode at the resonance frequency, three-layer magnetoelectric composite with length direction magnetization and thickness direction polarization is investigated in the article. Firstly, based on the Z-L model and the numerical solution characteristics of magnetization intensity, the magnetization intensity function is fitted, and the dynamic parameters of the giant magnetostrictive material, including dynamic piezomagnetic coefficient, dynamic elastic compliance coefficient, and dynamic magnetic permeability, are further derived. The effects of bias magnetic field and prestress on the corresponding composite are analyzed. Secondly, based on the nonlinear magnetostrictive constitutive equation, a symmetric magneto-elastic-electric equivalent circuit model of magnetoelectric laminate composite is established, and the expression of magnetoelectric coefficient is derived. The variation curve with bias magnetic field and prestress is analyzed, which is consistent with the conclusions of existing literature [Zhou H M, Ou X W, Xiao Y, Qu S X, Wu H P 2013 Smart Mater. Struct. 22 035018; Zhou H M, Li C, Xuan L M, Wei J 2011 Smart Mater. Struct. 20 035001]. Finally, in order to compare with the theoretical results, the same parameters are set by using COMSOL software, and the corresponding magnetoelectric coefficient frequency curve is plotted. The two results are in good agreement with each other, and the maximum peak modal vibration shape is extracted, making it easy to observe the vibration of the magneto electric laminated composite in the length direction. The results indicate that the theoretical model of this symmetric magneto-elastic-electric equivalent circuit and the numerical simulation method using COMSOL software are feasible, thereby laying the foundation for further nonlinear analysis of magnetoelectric laminate composite and making it possible to design high-precision magnetoelectric micro devices.

Keywords:

作者及机构信息

1.
安康学院电子与信息工程学院, 安康　725000

2.
上海实问信息科技有限公司, 上海　201306

3.
西安邮电大学自动化学院, 西安　710121

4.
兰州交通大学数理学院, 兰州　730070

通信作者: 张小丽, zxlxlzhang@163.com

基金项目: 国家自然科学基金(批准号: 12174004, 12104369)、甘肃省自然科学基金(批准号: 23JRRA1805)和陕西省教育厅科学研究计划(批准号: 20JK0475)资助的课题.

Authors and contacts

1.
School of Electronic and Information Engineering, Ankang University, Ankang 725000, China

2.
Shanghai Shiwen Information Technology Limited Company, Shanghai 201306, China

3.
School of Automation, Xi’an University of Posts & Telecommunications, Xi’an 710121, China

4.
School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China

Corresponding author: Zhang Xiao-Li, zxlxlzhang@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12174004, 12104369), the Natural Science Foundation of Gansu Province, China (Grant No. 23JRRA1805), and the Scientific Research Program of Shaanxi Provincial Department of Education, China (Grant No. 20JK0475).

文章全文 : translate this paragraph

参考文献

[1]	谢冰鸿, 徐国凯, 肖绍球, 喻忠军, 朱大立 2023 物理学报 72 117501 Google Scholar Xie B H, Xu G K, Xiao S Q, Yu Z J, Zhu D L 2023 Acta Phys. Sin. 72 117501 Google Scholar
[2]	Truong B D 2020 IEEE Sens. J. 20 2967808 Google Scholar
[3]	Han J, Zhang J J, Gao Y W 2018 J. Magn. Magn. Mater. 466 200 Google Scholar
[4]	杨娜娜, 陈轩, 汪尧进 2018 物理学报 67 157508 Google Scholar Yang N N, Chen X, Wang Y J 2018 Acta Phys. Sin. 67 157508 Google Scholar
[5]	Zhang X L, Zhou J P, Yao X, Yang Z P, Zhang G B 2020 J. Magn. Magn. Mater. 501 166411 Google Scholar
[6]	Zheng X J, Sun L 2006 J. Appl. Phys. 100 063906
[7]	Lin L Z, Wan Y P, Li F X 2012 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 7 1568
[8]	Zhou H M, Ou X W, Xiao Y, Qu S X, Wu H P 2013 Smart Mater. Struct. 22 035018 Google Scholar
[9]	Zhou H M, Li C, Xuan L M, Wei J 2011 Smart Mater. Struct. 20 035001 Google Scholar
[10]	Liang Y R, Zheng X J 2007 Acta Mech. Solida Sin. 20 283 Google Scholar
[11]	Moffett M B, Linberg J, Mclaughlin E A 1991 J. Acoust. Soc. Am. 89 1448 Google Scholar
[12]	Zheng X J, Liu X E 2005 J. Appl. Phys. 97 053901 Google Scholar
[13]	Zhou H M, Cui X L 2014 Smart Mater. Struct. 23 105104
[14]	Shi Y, 2018 Compos. Struct. 185 474 Google Scholar
[15]	Li J Z, Wen Y M, Li P, Yang J 2017 IEEE Trans. Power Electr. 53 2500406
[16]	Muchenik T I, Barbero E J 2015 Smart Mater. Struct. 24 025039 Google Scholar
[17]	Zhou J P, Yang Y, Zhang G B, Peng J H, Liu P 2016 Compos. Struct. 155 107 Google Scholar
[18]	Zhang X L, Zhou J P, Yao X, Yang Z P, Zhang G B 2019 AIP Adv. 9 105315 Google Scholar
[19]	卞雷祥, 文玉梅, 李平 2009 物理学报 58 4205 Google Scholar Bian L X, Wen Y M, Li P 2009 Acta Phys. Sin. 58 4205 Google Scholar
[20]	Zhou H M, Xuan L M, Li C, Wei J 2011 J. Magn. Magn. Mater. 323 2802
[21]	Boukazouha F, Poulin-Vittrant G, Tran-Huu-Hue L P, Bavencoffe M, Boubenider F 2015 Ultrasonics 60 41 Google Scholar
[22]	Malleron K, Talleb H, Gensbittel A, Ren Z 2017 IEEE Trans. Magn. 53 8102104
[23]	Fu X, Gou Y 2022 Appl. Acoust. 193 108752 Google Scholar
[24]	Zhang X L, Yin Q P, Li G, Yao X 2022 J. Magn. Magn. Mater. 564 170112

施引文献

图 1 磁电层状复合材料的结构示意图

Fig. 1. Structural schematic diagram of magnetoelectric laminated composite.

下载: 全尺寸图片幻灯片

图 2 磁化强度随偏置磁场和预应力的变化曲线

Fig. 2. Curves of magnetization intensity versus bias magnetic field and prestress.

下载: 全尺寸图片幻灯片

图 3 磁化强度拟合函数随偏置磁场和预应力的变化曲线

Fig. 3. Curves of magnetization intensity fitting function versus bias magnetic field and prestress.

下载: 全尺寸图片幻灯片

图 4 不同预应力下, 压磁系数随偏置磁场的变化曲线

Fig. 4. Curves of piezomagnetic coefficient versus bias magnetic field under different prestress.

下载: 全尺寸图片幻灯片

图 6 不同预应力下, 磁导率随偏置磁场的变化曲线

Fig. 6. Curves of piezomagnetic coefficient versus bias magnetic field under different prestress.

下载: 全尺寸图片幻灯片

图 5 不同偏置磁场下, 弹性柔顺系数随预应力的变化曲线

Fig. 5. Curves of elastic compliance coefficient versus prestress under different bias magnetic field.

下载: 全尺寸图片幻灯片

图 7 磁电层状复合材料　(a) 对称磁-弹-电等效电路; (b) 在自由边界条件下的对称等效电路

Fig. 7. (a) Symmetric magneto-elastic-electric equivalent circuit and (b) symmetric equivalent circuit under free boundary conditions of magnetoelectric laminated composite.

下载: 全尺寸图片幻灯片

图 8 频率1 kHz处不同预应力时磁电系数随偏置磁场的变化曲线

Fig. 8. The variation curve of magnetoelectric coefficient with bias magnetic field under different prestress at frequency of 1 kHz.

下载: 全尺寸图片幻灯片

图 9 共振频率处不同预应力时磁电系数随偏置磁场的变化曲线

Fig. 9. The variation curve of magnetoelectric coefficient with bias magnetic field under different prestress at resonance frequency.

下载: 全尺寸图片幻灯片

图 10 磁电层合材料的(a)仿真模型和(b)网格划分

Fig. 10. (a) Simulation model and (b) grid division of magnetoelectric laminated composite.

下载: 全尺寸图片幻灯片

图 11 偏置磁场750 Oe预应力0 MPa处磁电系数的频率曲线

Fig. 11. Frequency curve of magnetoelectric coefficient at bias magnetic field of 750 Oe and prestress of 0 MPa.

下载: 全尺寸图片幻灯片

图 12 磁电层合材料共振频率处的振动模态

Fig. 12. Vibration mode at the resonance frequency of magnetoelectric laminated composite.

下载: 全尺寸图片幻灯片

[1]	谢冰鸿, 徐国凯, 肖绍球, 喻忠军, 朱大立 2023 物理学报 72 117501 Google Scholar Xie B H, Xu G K, Xiao S Q, Yu Z J, Zhu D L 2023 Acta Phys. Sin. 72 117501 Google Scholar
[2]	Truong B D 2020 IEEE Sens. J. 20 2967808 Google Scholar
[3]	Han J, Zhang J J, Gao Y W 2018 J. Magn. Magn. Mater. 466 200 Google Scholar
[4]	杨娜娜, 陈轩, 汪尧进 2018 物理学报 67 157508 Google Scholar Yang N N, Chen X, Wang Y J 2018 Acta Phys. Sin. 67 157508 Google Scholar
[5]	Zhang X L, Zhou J P, Yao X, Yang Z P, Zhang G B 2020 J. Magn. Magn. Mater. 501 166411 Google Scholar
[6]	Zheng X J, Sun L 2006 J. Appl. Phys. 100 063906
[7]	Lin L Z, Wan Y P, Li F X 2012 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 7 1568
[8]	Zhou H M, Ou X W, Xiao Y, Qu S X, Wu H P 2013 Smart Mater. Struct. 22 035018 Google Scholar
[9]	Zhou H M, Li C, Xuan L M, Wei J 2011 Smart Mater. Struct. 20 035001 Google Scholar
[10]	Liang Y R, Zheng X J 2007 Acta Mech. Solida Sin. 20 283 Google Scholar
[11]	Moffett M B, Linberg J, Mclaughlin E A 1991 J. Acoust. Soc. Am. 89 1448 Google Scholar
[12]	Zheng X J, Liu X E 2005 J. Appl. Phys. 97 053901 Google Scholar
[13]	Zhou H M, Cui X L 2014 Smart Mater. Struct. 23 105104
[14]	Shi Y, 2018 Compos. Struct. 185 474 Google Scholar
[15]	Li J Z, Wen Y M, Li P, Yang J 2017 IEEE Trans. Power Electr. 53 2500406
[16]	Muchenik T I, Barbero E J 2015 Smart Mater. Struct. 24 025039 Google Scholar
[17]	Zhou J P, Yang Y, Zhang G B, Peng J H, Liu P 2016 Compos. Struct. 155 107 Google Scholar
[18]	Zhang X L, Zhou J P, Yao X, Yang Z P, Zhang G B 2019 AIP Adv. 9 105315 Google Scholar
[19]	卞雷祥, 文玉梅, 李平 2009 物理学报 58 4205 Google Scholar Bian L X, Wen Y M, Li P 2009 Acta Phys. Sin. 58 4205 Google Scholar
[20]	Zhou H M, Xuan L M, Li C, Wei J 2011 J. Magn. Magn. Mater. 323 2802
[21]	Boukazouha F, Poulin-Vittrant G, Tran-Huu-Hue L P, Bavencoffe M, Boubenider F 2015 Ultrasonics 60 41 Google Scholar
[22]	Malleron K, Talleb H, Gensbittel A, Ren Z 2017 IEEE Trans. Magn. 53 8102104
[23]	Fu X, Gou Y 2022 Appl. Acoust. 193 108752 Google Scholar
[24]	Zhang X L, Yin Q P, Li G, Yao X 2022 J. Magn. Magn. Mater. 564 170112

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非线性磁电层合材料的对称等效电路理论及数值仿真分析