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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.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 was fitted, and the dynamic parameters of the giant magnetostrictive material, including dynamic piezomagnetic coefficient, dynamic elastic compliance coefficient, and dynamic magnetic permeability, were further derived. The effects of bias magnetic field and prestress on the corresponding composite were analyzed; Secondly, based on the nonlinear magnetostrictive constitutive equation, a symmetric magneto-elastic-electric equivalent circuit model of magnetoelectric laminate composite was established, and the expression of magnetoelectric coefficient was derived. The variation curve with bias magnetic field and prestress was analyzed, which is consistent with the conclusions of existing literature [8] and [9]; Finally, in order to compare with the theoretical results, the same parameters were set using COMSOL software, and the corresponding magnetoelectric coefficient frequency curve was plotted. The two results were in good agreement, and the maximum peak modal vibration shape was extracted, which can conveniently observe the vibration of the magneto electric laminate 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, laying the foundation for further nonlinear analysis of magnetoelectric laminate composite and making it possible to design high-precision magnetoelectric micro devices.
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Keywords:
- nonlinear /
- magnetoelectric laminated composite /
- symmetric equivalent circuit theory /
- numerical simulation
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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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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