基于非线性特性的磁电效应分析模型研究

郑建校; 王楚友; 刘金颂; 周立明; 张卯

doi:10.21656/1000-0887.450238

基于非线性特性的磁电效应分析模型研究

doi: 10.21656/1000-0887.450238

1.
西安建筑科技大学机电工程学院，西安 710055
2.
吉林大学机械与航空航天工程学院，长春 130025

基金项目:

国家自然科学基金 52002309

陕西省自然科学基础研究计划 2023-JC-YB-313

陕西省自然科学基础研究计划 2023-JC-YB-294

详细信息

作者简介:
郑建校(1975—)，男，副教授，博士，硕士生导师(E-mail: zjx@xauat.edu.cn)

王楚友(2001—)，男，硕士生(E-mail: 1732230035@qq.com)

通讯作者:
刘金颂(1981—)，女，副教授，博士(通讯作者. E-mail: 592362106@qq.com)

中图分类号: TB331;TM201.3
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- 被引次数: 0
出版历程
- 收稿日期: 2024-08-29
- 修回日期: 2025-02-26
- 刊出日期: 2025-12-01

Analytical Modeling of Magneto-Electric Effects Based on Nonlinear Properties

1.
College of Mechanical and Electrical Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, P.R.China
2.
College of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, P.R.China

摘要

摘要: 针对磁致伸缩材料中复杂的非线性磁-力耦合关系以及磁电复合材料之间的界面耦合问题，提出了一种基于等效电路法的磁电效应分析模型. 根据磁致伸缩材料Tb_0.3Dy_0.7Fe_1.92(Terfenol-D)的非线性模型，通过理论推导得到磁致伸缩材料在复杂非线性磁-力耦合条件下的磁致伸缩系数、压磁系数以及相对磁导率的表达式，并将其等效在磁致伸缩材料线性本构方程中. 采用等效电路法分别对磁致伸缩材料Terfenol-D和压电材料Pb(Zr, Ti)O₃(PZT)进行建模，并引入界面耦合系数将两个等效电路进行耦合. 将压磁系数与磁电电压系数的理论预测值与试验数据对比，验证了等效参数表达式以及非线性理论模型的有效性. 研究表明，磁电电压系数与层合比、界面耦合系数以及外加磁场有着密切的关系. 研究结果为磁电复合材料磁电效应的优化提供了理论指导.
- 磁致伸缩材料 /
- 等效电路法 /
- 界面耦合系数 /
- 磁电电压系数 /
- 磁电复合
Abstract: A magnetoelectric effect analysis model based on the equivalent circuit method was proposed to address the complex nonlinear magneto-mechanical coupling in magnetostrictive materials and the interface coupling between magnetoelectric composites. With the nonlinear model for magnetostrictive material Tb_0.3Dy_0.7Fe_1.92 (Terfenol-D), theoretical derivations were carried out to obtain expressions for the magnetostrictive coefficient, the piezomagnetic coefficient, and the relative permeability of the magnetostrictive material under complex nonlinear magneto-mechanical coupling conditions, which were then incorporated into the linear constitutive equations of the magnetostrictive material. The equivalent circuit method was applied to model both magnetostrictive material Terfenol-D and piezoelectric material Pb(Zr, Ti)O₃ (PZT), with the introduction of an interface coupling coefficient to couple the 2 equivalent circuits. By comparison of the theoretical predictions of the piezomagnetic coefficient and the magnetoelectric voltage coefficient with experimental data, the effectiveness of the equivalent parameter expressions and the nonlinear theoretical model was validated. The study shows that, the magnetoelectric voltage coefficient is closely related to the laminate ratio, the interface coupling coefficient, and the applied magnetic field. The results provide a theoretical guidance for optimizing the magnetoelectric effects in magnetoelectric composites.
- magnetostrictive material /
- equivalent circuit method /
- interface coupling coefficient /
- magnetoelectric voltage coefficient /
- magnetoelectric composition

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图 1 L-T模式磁电层合材料示意图

Figure 1. Schematic of the L-T mode magneto-electric laminated material

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图 2 磁致伸缩层的等效电路

Figure 2. The equivalent circuit of the magnetostrictive layer

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图 3 自由振动时磁致伸缩层的等效电路

Figure 3. The equivalent circuit of the magnetostrictive layer during free vibration

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图 4 压电层的等效电路

Figure 4. The equivalent circuit of the piezoelectric layer

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图 5 自由振动时压电层的等效电路

Figure 5. The equivalent circuit of the piezoelectric layer during free vibration

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图 6 磁电层合等效电路

Figure 6. The magnetoelectric lamination equivalent circuit

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图 7 压磁系数的理论预测结果与试验结果对比

Figure 7. Comparison of predicted and experimental results of piezomagnetic coefficients

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图 8 磁电电压系数的理论预测结果与文献结果对比

Figure 8. Theoretical prediction of magnetoelectric voltage coefficients compared to experimental results

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图 9 不同界面耦合系数下磁电电压系数与层合比的关系

Figure 9. Magnetoelectric voltage coefficients vs. layer ratios for different interfacial coupling coefficients

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图 10 最佳磁电电压系数、最佳层合比与界面耦合系数之间的关系

注为了解释图中的颜色，读者可以参考本文的电子网页版本.

Figure 10. Relationships between the optimal magnetoelectric voltage coefficient, the optimal lamination ratio and the interfacial coupling coefficient

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图 11 最佳磁电电压系数和相应的外加磁场与界面耦合系数之间的关系

注为了解释图中的颜色，读者可以参考本文的电子网页版本.

Figure 11. Relationships between the optimal magnetoelectric voltage coefficient, the corresponding applied magnetic field and the interface coupling coefficient

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表 1 压电层材料参数

Table 1. Piezo layer material parameters

material s₁₁^E/(10^-12 m²/N) d_31p/(10^-12 C/N) k₃₁

PMN-PT 141.3 -2 645 0.95

PZT 16.5 -270 0.38

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参考文献(24)

[1]	SHI S H, LI P, JIN F. The mechanical analysis of thermo-magneto-electric laminated composites in nanoscale with the consideration of surface and flexoelectric effects[J]. Smart Materials and Structures, 2018, 27(1): 015018. doi: 10.1088/1361-665X/aa995c
[2]	ZHOU J P, YANG Y, ZHANG G B, et al. Symmetric relationships between direct and converse magnetoelectric effects in laminate composites[J]. Composite Structures, 2016, 155: 107-117. doi: 10.1016/j.compstruct.2016.08.009
[3]	黄颖妆, 齐岩, 杜安, 等. 复合多铁链的磁电耦合行为与外场调控[J]. 物理学报, 2018, 67(24): 225-233. HUANG Yingzhuang, QI Yan, DU An, et al. Magnetoelectric coupling and external field modulation of a composite multiferroic chain[J]. Acta Physica Sinica, 2018, 67(24): 225-233. (in Chinese)
[4]	BURDIN D A, CHASHIN D V, EKONOMOV N A, et al. Nonlinear magnetoelectric effects in a composite ferromagnetic-piezoelectric structure under harmonic and noise magnetic pumping[J]. Journal of Magnetism and Magnetic Materials, 2018, 449: 505-509. doi: 10.1016/j.jmmm.2017.10.096
[5]	TALLEB H, GENSBITTEL A, REN Z. Multiphysics modeling of a magnetoelectric composite Rosen-type device[J]. Composite Structures, 2016, 137: 1-8. doi: 10.1016/j.compstruct.2015.11.001
[6]	HARSHE G, DOUGHERTY J P, NEWNHAM R. Theoretical modelling of multilayer magnetoelectric composites[J]. International Journal of Applied Electromagnetics in Materials, 1993, 4(2): 145-145.
[7]	HARSHE G, DOUGHERTY J P, NEWNHAM R E. Magnetoelectric effect in composite materials[J]. Mathematics in Smart Structures, 1993, 1919: 224.
[8]	AVELLANEDA M, HARSHE G. Magnetoelectric effect in piezoelectric/magnetostrictive multilayer (2-2) composites[J]. Journal of Intelligent Material Systems and Structures, 1994, 5(4): 501-513. doi: 10.1177/1045389X9400500406
[9]	BICHURIN M I, PETROV V M, SRINIVASAN G. Theory of low-frequency magnetoelectric effects in ferromagnetic-ferroelectric layered composites[J]. Journal of Applied Physics, 2002, 92(12): 7681-7683. doi: 10.1063/1.1522834
[10]	BICHURIN M I, FILIPPOV D A, PETROV V M, et al. Resonance magnetoelectric effects in layered magnetostrictive-piezoelectric composites[J]. Physical Review B, 2003, 68(13): 132408. doi: 10.1103/PhysRevB.68.132408
[11]	NAN C W. Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases[J]. Physical Review B, 1994, 50(9): 6082-6088. doi: 10.1103/PhysRevB.50.6082
[12]	NAN C W, LI M, HUANG J H. Calculations of giant magnetoelectric effects in ferroic composites of rare-eart-iron alloys and ferroelectric polymers[J]. Physical Review B, 2001, 63(14): 144415. doi: 10.1103/PhysRevB.63.144415
[13]	NAN C W, LI M, FENG X Q, et al. Possible giant magnetoelectric effect of ferromagnetic rare-earth-iron-alloys-filled ferroelectric polymers[J]. Appl Phys Lett, 2001, 78(17): 2527-2529. doi: 10.1063/1.1367293
[14]	DONG S X, ZHAI J Y. Equivalent circuit method for static and dynamic analysis of magnetoelectric laminated composites[J]. Chinese Science Bulletin, 2008, 53(14): 2113-2123. doi: 10.1007/s11434-008-0304-7
[15]	DONG S X, LI J F, VIEHLAND D. Longitudinal and transverse magnetoelectric voltage coefficients of magnetostrictive/piezoelectric laminate composite: experiments[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2004, 51(7): 794-799. doi: 10.1109/TUFFC.2004.1320738
[16]	LIU X E, ZHENG X J. A nonlinear constitutive model for magnetostrictive materials[J]. Acta Mechanica Sinica, 2005, 21(3): 278-285. doi: 10.1007/s10409-005-0028-8
[17]	ZHENG X J, LIU X E. A nonlinear constitutive model for Terfenol-D rods[J]. Journal of Applied Physics, 2005, 97(5): 053901. doi: 10.1063/1.1850618
[18]	郁国良. 基于磁致伸缩/压电层状复合材料的磁电效应研究[D]. 成都: 电子科技大学, 2018. YU Guoliang. Study on magnetoelectric effect based on magnetostrictive/piezoelectric layered composites[D]. Chengdu: University of Electronic Science and Technology of China, 2018. (in Chinese)
[19]	RYU J, CARAZO A V, UCHINO K, et al. Magnetoelectric properties in piezoelectric and magnetostrictive laminate composites[J]. Japanese Journal of Applied Physics, 2001, 40(8): 4948.
[20]	RYU J, PRIYA S, CARAZO A V, et al. Effect of the magnetostrictive layer on magnetoelectric properties in lead zirconate titanate/Terfenol-D laminate composites[J]. Journal of the American Ceramic Society, 2001, 84(12): 2905-2908. doi: 10.1111/j.1151-2916.2001.tb01113.x
[21]	楼国峰, 于歆杰, 卢诗华. 引入界面耦合系数的长片型磁电层状复合材料的等效电路模型[J]. 物理学报, 2018, 67(2): 027501. LOU Guofeng, YU Xinjie, LU Shihua. Equivalent circuit model of long-slice magnetoelectric layered composites with interface coupling coefficients[J]. Acta Physica Sinica, 2018, 67(2): 027501. (in Chinese)
[22]	FANG F, ZHOU Y Y, XU Y T, et al. Magnetoelectric coupling of multiferroic composites under combined magnetic and mechanical loadings[J]. Smart Material Structures, 2013, 22(7): 075009. doi: 10.1088/0964-1726/22/7/075009
[23]	WANG Y, OR S W, CHAN H L W, et al. Enhanced magnetoelectric effect in longitudinal-transverse mode Terfenol-D/Pb(Mg1/3Nb2/3)O3-PbTiO3 laminate composites with optimal crystal cut[J]. Journal of Applied Physics, 2008, 103(12): 124511. doi: 10.1063/1.2943267
[24]	YANG C H, WEN Y M, LI P, et al. Influence of bias magnetic field on magnetoelectric effect of magnetostrictive/elastic/piezoelectric laminated composite[J]. Acta Physica Sinica, 2008, 57(11): 7292. doi: 10.7498/aps.57.7292