铁磁介质结构若干磁弹性问题的理论与实验研究
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摘要
铁磁材料广泛应用于国民经济的各个部门,其力学响应行为涉及变形场和磁场的相互耦合问题,直接关系到各类现代高新装置设备的性能指标和可靠运行。本论文针对铁磁介质结构的磁弹性行为进行了理论和实验研究。
基于连续介质理论针对一个在电磁场中运动的可变形连续固体进行了描述,将铁磁颗粒增强聚合物整体看作为一个可磁化的高弹性体,研究了材料的磁弹性行为,并给出材料应力与外磁场的依赖关系。同时根据材料细观组分的单独力学行为以及它们的相互作用对该磁弹性特征予以验证。在此基础上加入了聚合物粘弹性行为的影响建立了一个铁磁颗粒增强聚合物的磁弹性本构模型。模型在静态、动态加载下的预测结果与实验测量数据均十分吻合。相对于已有模型,本文模型可以在同一组参数下描述不同磁场下的力-位移以及应力-应变回线,并可较为准确地刻画聚合物的力-磁耦合行为。定量分析了在不同磁场区域内材料本构关系的非线性程度以及剪切模量的磁场敏感性；讨论了动态加载下应力-应变回线的洄滞特性；揭示了应力-应变回线及剪切模量随外磁场与加载频率的变化规律。
在上文连续介质力学、电磁学方程的基础上展开了对于变形场和磁场耦合问题处理方法的讨论,分析了不同解耦方法对于铁磁介质结构内部及附近磁场分布的影响,针对铁磁板在横向磁场下的磁弹性变形问题讨论了有限元数值迭代以及摄动技术在描述磁场分布方面的区别,以及这些差异对铁磁结构受力分析的影响。研究表明摄动方法只能分析铁磁弹性介质由于变形而引起的磁场分布变化,不能考虑介质磁化对附近磁场的改变;即使采用相同的磁力模型,有限元方法和摄动方法计算出的磁场分布不同也会进一步导致磁力分布不一样。揭示了两种方法在预测铁磁悬臂板磁弹性屈曲这一经典磁弹性耦合问题上存在差异的原因。给出的有限元模型可以退化到铁磁刚性结构情况,并选取磁屏蔽这一实际问题验证了模型的有效性,为屏蔽装置的设计提供了选型依据。
在经典磁弹性振动问题研究的基础上,分析讨论了铁磁悬臂板正负磁刚度现象的临界角度范围,采用上文连续介质理论建立了与磁场相关的铁磁板共振频率的解析模型,并通过与实验结果的对比验证了模型的有效性,证明铁磁介质的非线性磁化行为是使铁磁板共振频率随着磁场的增大呈现饱和趋势的原因。模型可以很好的刻画出不同角度磁场下共振频率的变化规律,预测的临界角度与实验测量的角度范围吻合,揭示了临界角度与铁磁板长厚比之间的关系。
针对铁磁圆柱壳的磁弹性变形行为展开了实验研究,测量了圆柱壳在横向磁场下的环向应变,发现随着外磁场增大,环向应变与外磁场的“B2关系”失效,表明薄壳的磁弹性变形行为在高场与低场下具有不同的变化规律。对软铁磁圆柱薄壳进行了较为全面的磁弹性变形实验研究,揭示了不同大小、方向的磁场,试件的厚径比以及不同的约束条件对铁磁薄壳磁弹性变形规律的影响。研究表明,外磁场的大小仅改变壳体的环向应变大小,而对应变的分布状态并没有明显影响；而磁场的倾斜角度以及试件的厚径比对圆柱薄壳环向应变的大小以及分布均有影响；端部的约束条件对整个壳体的环向变形有显著的影响,完全固定的边界条件不仅会使环向应变减小,而且会抑制应变随磁场增大的饱和趋势。
综上,通过本文的研究工作,加深了对于铁磁介质结构中的磁场分布、铁磁薄壳的磁弹性变形规律以及铁磁薄板磁弹性共振现象的认识,完善了铁磁结构磁弹性力学行为的理论和实验的研究,分析了新型铁磁材料——铁磁颗粒增强聚合物的力-磁耦合行为,对已有实验结果做出了较为合理的解释。研究结果为铁磁材料及结构在实际工程中的应用提供了必要的理论依据。
Ferromagnetic materials and structures are widely used in national economic construction. The mechanical behavior of ferromagnetic materials is usually influenced by the coupling effect between mechanical field and magnetic field. It is directly related to the performance of high-tech devices and the reliability of operation. In this dissertation, we investigated the magnetoelastic interactions by theoretical and experimental methods.
Firstly, a deformable continuous solid moving in the electromagnetic field has been described based on the continuum theory, the ferromagnetic particles reinforced composite has been seen as a magnetizable elastomer, then the dependency of the stress and the magnetic field is discussed. The magnetoelastic characteristics of such ferromagnetic composites obtained from continuum theory are similar to the ones based on the mesoscopic model. Furthermore, a constitutive model which can describe the viscoelastic and the magnetoelastic behaviors of ferromagnetic composites is proposed, the predictions show good correlation with experimental data. Comparing this model with other existing models, the quantitative results can reflect the mechanics-magneto interaction without changing parameters in the model. The nonlinear characteristics of the constitutive relations in different regions of magnetic field and the magnetic field sensitivity of the shear modulus for such ferromagnetic composites are also discussed. It is also shown that the shear modulus change with the external magnetic field and loading frequency under dynamic loading.
Based on the equations from the continuum mechanics and electromagnetism discussed above, we further analyze the decoupled approaches for the problems of magneto-mechanical coupling. The differences of magnetic field distributions inner and near the ferromagnetic structures are due to the differences of the decoupled approaches, so we discuss the differences between the numerical iterative of finite element method and the perturbation technique in the descriptions of the magnetic field distributions, furthermore, the changes of distributions of the magnetic force in the ferromagnetic media. The predictions show that the perturbation method can only deal with the changes of magnetic field distributions since the deformation of the ferromagnetic elastic media, it can't consider the effect that the changes of the magnetic field nearby the structures due to the magnetization of the ferromagnetic media. The differences of magnetic field distributions simulated by these two methods will led to the differences of the distributions of the magnetic force even though adopting the same magnetic force model. The finite element model presented above can degraded to the situation of the ferromagnetic rigid media, then it is applied to the problem of magnetic shielding to verify the validity of the model.
The theoretical as well as experimental investigations on the natural frequency of a ferromagnetic plate in an inclined magnetic field are presented. A novel analytical model with the nonlinear law of magnetization is proposed for the field-dependent natural frequency of a ferromagnetic plate. Model predictions show good correlation with the experimental data at different inclined angles. Both the theoretical and experimental investigations show that there exists a critical angle of the inclined field, below which the natural frequency of the ferromagnetic plate will increase with the magnetic field, and above which the frequency will decrease with increasing the field. The predictions show that the critical angle is sensitive to the length-to-thick ratio of the plate.
Experimental studies on the magnetoelastic deformation of ferromagnetic cylindrical shell are carried on. The circumferential strains of the shell in the transverse magnetic field are measured. It is noted that the circumferential strain do not show a B2dependence at high field, which means the magnetoelastic behavior of shell at low field is different from the one at high field. Moreover, it is shown that the intensity of the magnetic field only affects the values of the circumferential strain, not the strain distribution, while the directions of the applied magnetic field and the ratio of thickness-to-radius of shell show a dramatical influence on both the values and the distributions of strain. The supported conditions at shell ends also have effects on the magnetoelastic deformation.
In summary, these essential and important investigations will be of significant benefit to both the theoretical researches and applications of the ferromagnetic materials in intelligent structures and systems.
基于连续介质理论针对一个在电磁场中运动的可变形连续固体进行了描述,将铁磁颗粒增强聚合物整体看作为一个可磁化的高弹性体,研究了材料的磁弹性行为,并给出材料应力与外磁场的依赖关系。同时根据材料细观组分的单独力学行为以及它们的相互作用对该磁弹性特征予以验证。在此基础上加入了聚合物粘弹性行为的影响建立了一个铁磁颗粒增强聚合物的磁弹性本构模型。模型在静态、动态加载下的预测结果与实验测量数据均十分吻合。相对于已有模型,本文模型可以在同一组参数下描述不同磁场下的力-位移以及应力-应变回线,并可较为准确地刻画聚合物的力-磁耦合行为。定量分析了在不同磁场区域内材料本构关系的非线性程度以及剪切模量的磁场敏感性；讨论了动态加载下应力-应变回线的洄滞特性；揭示了应力-应变回线及剪切模量随外磁场与加载频率的变化规律。
在上文连续介质力学、电磁学方程的基础上展开了对于变形场和磁场耦合问题处理方法的讨论,分析了不同解耦方法对于铁磁介质结构内部及附近磁场分布的影响,针对铁磁板在横向磁场下的磁弹性变形问题讨论了有限元数值迭代以及摄动技术在描述磁场分布方面的区别,以及这些差异对铁磁结构受力分析的影响。研究表明摄动方法只能分析铁磁弹性介质由于变形而引起的磁场分布变化,不能考虑介质磁化对附近磁场的改变;即使采用相同的磁力模型,有限元方法和摄动方法计算出的磁场分布不同也会进一步导致磁力分布不一样。揭示了两种方法在预测铁磁悬臂板磁弹性屈曲这一经典磁弹性耦合问题上存在差异的原因。给出的有限元模型可以退化到铁磁刚性结构情况,并选取磁屏蔽这一实际问题验证了模型的有效性,为屏蔽装置的设计提供了选型依据。
在经典磁弹性振动问题研究的基础上,分析讨论了铁磁悬臂板正负磁刚度现象的临界角度范围,采用上文连续介质理论建立了与磁场相关的铁磁板共振频率的解析模型,并通过与实验结果的对比验证了模型的有效性,证明铁磁介质的非线性磁化行为是使铁磁板共振频率随着磁场的增大呈现饱和趋势的原因。模型可以很好的刻画出不同角度磁场下共振频率的变化规律,预测的临界角度与实验测量的角度范围吻合,揭示了临界角度与铁磁板长厚比之间的关系。
针对铁磁圆柱壳的磁弹性变形行为展开了实验研究,测量了圆柱壳在横向磁场下的环向应变,发现随着外磁场增大,环向应变与外磁场的“B2关系”失效,表明薄壳的磁弹性变形行为在高场与低场下具有不同的变化规律。对软铁磁圆柱薄壳进行了较为全面的磁弹性变形实验研究,揭示了不同大小、方向的磁场,试件的厚径比以及不同的约束条件对铁磁薄壳磁弹性变形规律的影响。研究表明,外磁场的大小仅改变壳体的环向应变大小,而对应变的分布状态并没有明显影响；而磁场的倾斜角度以及试件的厚径比对圆柱薄壳环向应变的大小以及分布均有影响；端部的约束条件对整个壳体的环向变形有显著的影响,完全固定的边界条件不仅会使环向应变减小,而且会抑制应变随磁场增大的饱和趋势。
综上,通过本文的研究工作,加深了对于铁磁介质结构中的磁场分布、铁磁薄壳的磁弹性变形规律以及铁磁薄板磁弹性共振现象的认识,完善了铁磁结构磁弹性力学行为的理论和实验的研究,分析了新型铁磁材料——铁磁颗粒增强聚合物的力-磁耦合行为,对已有实验结果做出了较为合理的解释。研究结果为铁磁材料及结构在实际工程中的应用提供了必要的理论依据。
Ferromagnetic materials and structures are widely used in national economic construction. The mechanical behavior of ferromagnetic materials is usually influenced by the coupling effect between mechanical field and magnetic field. It is directly related to the performance of high-tech devices and the reliability of operation. In this dissertation, we investigated the magnetoelastic interactions by theoretical and experimental methods.
Firstly, a deformable continuous solid moving in the electromagnetic field has been described based on the continuum theory, the ferromagnetic particles reinforced composite has been seen as a magnetizable elastomer, then the dependency of the stress and the magnetic field is discussed. The magnetoelastic characteristics of such ferromagnetic composites obtained from continuum theory are similar to the ones based on the mesoscopic model. Furthermore, a constitutive model which can describe the viscoelastic and the magnetoelastic behaviors of ferromagnetic composites is proposed, the predictions show good correlation with experimental data. Comparing this model with other existing models, the quantitative results can reflect the mechanics-magneto interaction without changing parameters in the model. The nonlinear characteristics of the constitutive relations in different regions of magnetic field and the magnetic field sensitivity of the shear modulus for such ferromagnetic composites are also discussed. It is also shown that the shear modulus change with the external magnetic field and loading frequency under dynamic loading.
Based on the equations from the continuum mechanics and electromagnetism discussed above, we further analyze the decoupled approaches for the problems of magneto-mechanical coupling. The differences of magnetic field distributions inner and near the ferromagnetic structures are due to the differences of the decoupled approaches, so we discuss the differences between the numerical iterative of finite element method and the perturbation technique in the descriptions of the magnetic field distributions, furthermore, the changes of distributions of the magnetic force in the ferromagnetic media. The predictions show that the perturbation method can only deal with the changes of magnetic field distributions since the deformation of the ferromagnetic elastic media, it can't consider the effect that the changes of the magnetic field nearby the structures due to the magnetization of the ferromagnetic media. The differences of magnetic field distributions simulated by these two methods will led to the differences of the distributions of the magnetic force even though adopting the same magnetic force model. The finite element model presented above can degraded to the situation of the ferromagnetic rigid media, then it is applied to the problem of magnetic shielding to verify the validity of the model.
The theoretical as well as experimental investigations on the natural frequency of a ferromagnetic plate in an inclined magnetic field are presented. A novel analytical model with the nonlinear law of magnetization is proposed for the field-dependent natural frequency of a ferromagnetic plate. Model predictions show good correlation with the experimental data at different inclined angles. Both the theoretical and experimental investigations show that there exists a critical angle of the inclined field, below which the natural frequency of the ferromagnetic plate will increase with the magnetic field, and above which the frequency will decrease with increasing the field. The predictions show that the critical angle is sensitive to the length-to-thick ratio of the plate.
Experimental studies on the magnetoelastic deformation of ferromagnetic cylindrical shell are carried on. The circumferential strains of the shell in the transverse magnetic field are measured. It is noted that the circumferential strain do not show a B2dependence at high field, which means the magnetoelastic behavior of shell at low field is different from the one at high field. Moreover, it is shown that the intensity of the magnetic field only affects the values of the circumferential strain, not the strain distribution, while the directions of the applied magnetic field and the ratio of thickness-to-radius of shell show a dramatical influence on both the values and the distributions of strain. The supported conditions at shell ends also have effects on the magnetoelastic deformation.
In summary, these essential and important investigations will be of significant benefit to both the theoretical researches and applications of the ferromagnetic materials in intelligent structures and systems.
引文
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