基于唯象相变理论的磁致伸缩材料耦合滞回动力学模拟

本文基于改进的Landau唯象相变理论,构造一个耦合的非线性常微分方程模型来模拟一维磁致伸缩材料的磁滞动态特性。模型的构造通过引入一个非凸的自由能函数来模拟磁致伸缩磁材料中不可逆的磁极化翻转与磁致应变,该自由能函数的每一个局部极小值都对应材料的一个磁化方向。通过热力学平衡条件建立能刻画磁致伸缩效应的非线性本构关系。所构造的模型成功地模拟出了磁场与弹性场之间的磁滞曲线和蝶形曲线,并采用实验结果对模型进行了验证。     

磁致伸缩作动器的电-磁-机耦合动力特性

基于磁致伸缩材料的本构关系模型,结合磁致伸缩作动器结构动力学模型建立了可描述磁致伸缩作动器的电-磁-机耦合动力特性的运动方程.方程中考虑了作动器工作时磁致伸缩材料的弹性模量随着应力和磁场的改变而发生的变化,磁致伸缩材料的这种特性使得作动器系统表现出具有时变刚度的参数振动特性.通过对此参数振动方程进行数值求解,得到磁致伸缩作动器的参数频响特性,并研究了激励电流幅值以及作动器负载质量对作动器频响特性的影响.     

层状柱壳磁电复合材料的非线性磁电效应研究

本文基于超磁致伸缩材料非线性本构,从基本的控制方程出发,对层状柱壳磁电复合材料的非线性磁电响应进行理论研究,讨论了不同边界下磁场频率以及压电材料厚度比对磁电系数的影响,并得到了不同预压力下磁场大小对于磁电系数的影响。数值计算结果显示,对于Tefernol-D/PZT-5层状磁电复合材料,随着预压力值增大,磁电系数最大值减小,取得最大值时对应的磁场值逐渐增大;不同边界条件、磁场频率和磁场大小下,材料厚度比对磁电系数的也有着不同的影响。特别地当外加磁场频率较大时,相应于压电层厚度比,磁电系数呈现多极值现象。     

稀土超磁致伸缩材料应力与电磁耦合特性的实验研究

讨论了稀土超磁致伸缩棒特性实验的若干应力与电磁耦合问题，利用自己设计制作的实验装置建立了应力电磁耦合系统的物理模型，应用阻抗分析方法得到了相应的等效电路。测定了在电磁场与应力场共同作用下ＴｂｘＤｙ１－ｘＦｅ２－ｚ三元稀土合金超磁致伸缩棒的磁致伸缩系数，机电耦合系数等。针对磁通泄漏问题，专门设计制作了圆柱型硅钢密闭磁路，本的实验结果为稀土眼磁致伸缩材料应用器提供了重要而准确的数据。     

超磁致伸缩换能器的磁滞非线性动力学仿真

在超磁致伸缩材料输出端位移假设的基础上,建立了以输出顶杆为研究对 象、考虑材料内部磁滞非线性及预压弹簧特性的超磁致伸缩换能器非线性动力学模 型; 并将Simulink仿真系统应用到超磁致伸缩换能器系统动力学仿真中. 仿真结果表 明: 换能器模型系统为稳定周期运动系统,并具有滞回非线性特性;弹簧非线性项中的平方 项是影响换能器模型系统的主要因素. 经验证,数值计算结果与文献给出的试验测试结果吻 合较好.     

超磁致伸缩换能器耦合磁弹性模型与振动特性分析

针对应用于非圆车削加工的超磁致伸缩换能器,建立了其耦合磁弹性动力学模型与复系数动力学微分方程,基于实验建立的激励电流磁致伸缩材料轴向位移-磁场强度三者之间的关系式,得到了换能器磁力-位移关系的磁动方程的解析解,分析了系统的频响特性及不同频率下,激励电流与换能器输出位移之间的滞回关系,对现有磁场-电流公式进行了修正,讨论...     

超磁致伸缩材料多场耦合非线性力学行为的理论研究

超磁致伸缩材料由于具有位移大、响应快、驱动简单等性能优势,在智能系统中具有广阔的应用前景。对于其力学行为的研究,在理论上涉及的关键科学问题是多场耦合问题的理论建模与定量模拟,而其应用需求则涉及对超磁致伸缩器件性能的定量预测及优化。目前超磁致伸缩材料在工业上最广泛的应用是作为换能器的核心制动元件,其磁学、力学行为与工况密切相关。应力、外磁场、环境温度都会改变材料的磁化强度和应变状态,在交变磁场作用下磁致伸缩棒截面上产生涡电流,该损耗使材料的磁化和应变曲线出现洄滞。针对这些问题已有很多学者[1]-[4]进行了研究,这些工作揭示了外部条件对超磁致伸缩材料磁学、力学性质的单向联合作用,如图1中虚线所示。然而对于超磁致伸缩材料力学行为的准确刻画还需要考虑更深层次的多物理场耦合关系（图1中实线所示）：由于超磁致伸缩材料被外场磁化而产生磁致应变的同时,被磁化的介质也可以充当一种源而改变其周围的磁场,改变的程度依赖于介质的变形,因此需要考虑介质对周围磁场的反作用;棒截面上的涡电流除了会带来磁滞损耗外还会产生大量的热,改变周围温度,进而因为热膨胀、热磁效应等改变超磁致伸缩棒的磁学、力学输出,所以涡电流的热效应也不可忽略;此外,超磁致伸缩棒在交变磁场下的振动响应使其应力状态发生改变,在建模时不能只考虑所施加的预应力,材料的实时应力状态必须加以考虑。图1中虚线和实线所指向的过程共同构筑了超磁致伸缩材料的多物理场耦合框架,综合考虑这些因素才能准确描述超磁致伸缩材料多场耦合非线性力学行为。本文围绕上述内容逐步深入,针对这一在理论和应用上具有重要意义的问题,开展了理论建模和数值模拟研究。     

磁致伸缩主被动隔振装置中的磁机耦合效应研究

磁致伸缩材料和柔顺位移放大机构组成的主动驱动装置具有精度高、驱动力大等特点.将其与被动隔振装置并联,形成主被动隔振装置,可以弥补纯被动隔振在低频和微幅扰动工况下的不足.本文针对这类磁致伸缩主被动隔振装置进行磁机耦合效应研究.基于Jiles-Atherton模型,分析了磁致伸缩材料所受应力对有效磁场、磁化强度、磁致伸缩系数和材料杨氏模量的影响,表征了材料磁机耦合效应.在此基础上,建立了主被动隔振装置的动力学模型,分析了主动驱动装置与被动隔振装置间的耦合作用.在耦合作用影响下,若被动隔振装置刚度不同,即使输入磁场相同,驱动器产生的驱动位移和驱动力也不相同.磁致伸缩材料的变刚度效应使隔振装置整体等效刚度不再为定值,从而影响被动隔振效果.本文提出了通过柔顺机构参数设计减小前述两种耦合影响的方法.数值仿真结果表明,磁致伸缩主被动隔振装置在低于、接近和高于谐振频率三类扰动下,都能达到比被动隔振更好的振动抑制效果.此外,仿真结果验证了考虑磁机耦合效应的数值模型具有更高精度.      

磁致伸缩主被动隔振装置中的磁机耦合效应研究

磁致伸缩材料和柔顺位移放大机构组成的主动驱动装置具有精度高、驱动力大等特点.将其与被动隔振装置并联,形成主被动隔振装置,可以弥补纯被动隔振在低频和微幅扰动工况下的不足.本文针对这类磁致伸缩主被动隔振装置进行磁机耦合效应研究.基于Jiles-Atherton模型,分析了磁致伸缩材料所受应力对有效磁场、磁化强度、磁致伸缩系数和材料杨氏模量的影响,表征了材料磁机耦合效应.在此基础上,建立了主被动隔振装置的动力学模型,分析了主动驱动装置与被动隔振装置间的耦合作用.在耦合作用影响下,若被动隔振装置刚度不同,即使输入磁场相同,驱动器产生的驱动位移和驱动力也不相同.磁致伸缩材料的变刚度效应使隔振装置整体等效刚度不再为定值,从而影响被动隔振效果.本文提出了通过柔顺机构参数设计减小前述两种耦合影响的方法.数值仿真结果表明,磁致伸缩主被动隔振装置在低于、接近和高于谐振频率三类扰动下,都能达到比被动隔振更好的振动抑制效果.此外,仿真结果验证了考虑磁机耦合效应的数值模型具有更高精度.     

磁致伸缩薄膜力学行为的有限元仿真研究

建立了一种磁致伸缩薄膜力学行为的有限元计算方法.该方法将磁致伸缩薄膜在磁场中的形变行为等效为薄膜在热场中的各向异性热膨胀形变行为,基于该等效模型,利用有限元软件计算了磁致伸缩薄膜悬臂梁的力学行为与外加磁场的关系.结果表明,该方法可有效模拟磁致伸缩薄膜在外磁场下的力学行为.     

Non-linear constitutive relations for magnetostrictive materials

In this paper, non-linear deformation behavior of magnetostrictive materials is studied and three magnetoelastic coupling constitutive models are developed. The standard square (SS) constitutive model is developed by means of truncating the polynomial expansion of the Gibbs free energy. The hyperbolic tangent (HT) constitutive equations, which involve a hyperbolic tangent magnetic-field dependence, are proposed to model the magnetic-field-induced strain saturation of magnetostrictive materials in the region of intense magnetic fields. A new model based on density of domain switching (DDS) is established in terms of the basic truth that magnetic domain switching underlies magnetostrictive deformation. In this model, it is assumed that the relation between density of domain switching, defined by the quantity of magnetic domains switched by per unit magnetic field and magnetic field can be described by a density function with normal distribution. The moduli in these constitutive models can be determined by a material function that is proposed to describe the dependence of the peak piezomagnetic coefficient on the compressive pre-stress for one-dimensional cases based on the experimental results published. The accuracy of the non-linear constitutive relations is evaluated by comparing the theoretical values with experimental results of a Terfenol-D rod operated under both compressive pre-stress and bias magnetic field. Results indicate that the SS constitutive equations can accurately predict the experimental results under a low or moderate magnetic field while the HT model can, to some extent, reflect the trend of saturation of magnetostrictive strain under a high magnetic field. The model based on DDS, which is more effective in simulating the experimental curves, can capture the main characteristics of the mechanism of magnetoelastic coupling deformation of a Terfenol-D rod, such as the notable dependence of magnetoelastic response on external stress and the saturation of magnetostrictive strain under intense magnetic fields. In addition, the SS constitutive relation for a general three-dimensional problem is discussed and an approach to characterize the modulus tensors is proposed.     

A nonlinear constitutive model for magnetostrictive materials

A general nonlinear constitutive model is proposed for magnetostrictive materials, based on the important physical fact that a nonlinear part of the elastic strain produced by a pre-stress is related to the magnetic domain rotation or movement and is responsible for the change of the maximum magnetostrictive strain with the pre-stress. To avoid the complicity of determining the tensor function describing the nonlinear elastic strain part, this paper proposes a simplified model by means of linearizing the nonlinear function. For the convenience of engineering applications, the expressions of the 3-D (bulk), 2-D (film) and 1-D (rod) models are, respectively, given for an isotropic material and their applicable ranges are also discussed. By comparison with the experimental data of a Terfenol-D rod, it is found that the proposed model can accurately predict the magnetostrictive strain curves in low, moderate and high magnetic field regions for various compressive pre-stress levels. The numerical simulation further illustrates that, for either magnetostrictive rods or thin films, the proposed model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves, while none of the known models can capture all of them. Therefore, the proposed model enjoys higher precision and wider applicability than the previous models, especially in the region of the high field.The project supported by the National Natural Science Foundation of China (10132010 and 90405005)     

Surface effect on band structure of magneto-elastic phononic crystal nanoplates subject to magnetic and stress loadings

This paper presents a theoretical model for the size-dependent band structure of magneto-elastic phononic crystal(PC) nanoplates according to the Kirchhoff plate theory and Gurtin-Murdoch theory, in which the surface effect and magneto-elastic coupling are considered. By introducing the nonlinear coupling constitutive relation of magnetostrictive materials, Terfenol-D/epoxy PC nanoplates are carried out as an example to investigate the dependence of the band structure on the surface effect, magn...     

Experimental and theoretical study of the nonlinear response of agiant magnetostrictive rod

In this paper, a magnetomechanical coupling constitutive relation of the giant magnetostrictive material was investigated experimentally and theoretically. A grain-oriented magnetostrictive rod of iron and rare earth was tested under a combined magnetomechanical loading. Two types of experimental curves were obtained, i.e., the magnetostrictive curve of the extensional strain vs the magnetic field, and the curve of the magnetic polarization intensity vs the pre-stress. A new theoretical constitutive model, based on the density of domain switching, is developed. Comparison of the theoretical predictions with the experimental results indicates that this model can capture the main characteristics of the magnetoelastic coupling deformation of a giant magnetostrictive rod. The project supported by the National Natural Science Foundation of China (10025209, 10132010, 10102007)     

EXPERIMENTAL RESEARCHES ON MAGNETO-THERMO-MECHANICAL CHARACTERIZATION OF TERFENOL-D

The coupling effects of axial pre-stress,temperature and magnetic field on magne- tostrictive strain and magnetization as well as Young's modulus of a Terfenol-D (Tb_(0.3)Dy_(0.7)Fe_(1.93)) rod are tested to give a good understanding of magneto-thermal-mecha-nical characteristics of giant magnetostrictive materials.Results show that magneto-thermo-mechanical coupling of gi- ant magnetostrictive materials is very strong;and the influences of pre-stress and temperature on magnetostrictive strain and Young's modulus vary with the intensity of magnetic field.     

VIBRATION SUPPRESSION OF CANTILEVER LAMINATED COMPOSITE PLATE WITH NONLINEAR GIANT MAGNETOSTRICTIVE MATERIAL LAYERS

In this paper, a nonlinear and coupled constitutive model for giant magnetostrictive materials(GMM) is employed to predict the active vibration suppression process of cantilever laminated composite plate with GMM layers. The nonlinear and coupled constitutive model has great advantages in demonstrating the inherent and complicated nonlinearities of GMM in response to applied magnetic field under variable bias conditions(pre-stress and bias magnetic field).The Hamilton principle is used to derive the nonlinear and coupled governing differential equation for a cantilever laminated composite plate with GMM layers. The derived equation is handled by the finite element method(FEM) in space domain, and solved with Newmark method and an iteration process in time domain. The numerical simulation results indicate that the proposed active control system by embedding GMM layers in cantilever laminated composite plate can efficiently suppress vibrations under variable bias conditions. The effects of embedded placement of GMM layers and control gain on vibration suppression are discussed respectively in detail.     

A constitutive model for magnetostrictive and piezoelectric materials

This paper is concerned with a macroscopic nonlinear constitutive law for magnetostrictive alloys and ferroelectric ceramics. It accounts for the hysteresis effects which occur in the considered class of materials. The uniaxial model is thermodynamically motivated and based on the definition of a specific free energy function and a switching criterion. Furthermore, an additive split of the strains and the magnetic or electric field strength into a reversible and an irreversible part is suggested. Analog to plasticity, the irreversible quantities serve as internal variables. A one-to-one-relation between the two internal variables provides conservation of volume for the irreversible strains. The material model is able to approximate the ferromagnetic or ferroelectric hysteresis curves and the related butterfly hysteresis curves. Furthermore, an extended approach for ferrimagnetic behavior which occurs in magnetostrictive materials is presented. A main aspect of the constitutive model is its numerical treatment. The finite element method is employed to solve the coupled field problem. Here the usage of the irreversible field strength permits the application of algorithms of computational inelasticity. The algorithmic consistent tangent moduli are developed in closed form. Hence, quadratic convergence in the iterative solution scheme of governing balance equations is obtained.     

Numerical simulation on coupling behavior of Terfenol-D rods

Terfenol-D rods, as a kind of giant magnetostrictive materials, are often used as active elements of device for anti-vibration application due to its superior material properties. Their magneto-mechanical responses exhibited in many experiments are nonlinear and coupled. In order to have a good understanding on their coupling characters for accurate control, the numerical simulation on dynamic behavior of a Terfenol-D rod is conducted based on a nonlinear and coupling constitutive model proposed in this paper. The results show that the constitutive model can effectively describe some intrinsic coupling phenomena observed by experiments involving the maximum magnetostrictive strain of a Terfenol-D rod changing with pre-stresses and the corresponding dynamic responses show that the frequency and the amplification of the Terfenol-D rod change with magnetic bias field and pre-stresses, which are also consistent with experimental data and cannot be captured by previous constitutive model.     

A small-scale magnetic-yielding model for an infinite magnetostrictive plane with a crack-like flaw

The effect of an external magnetic field on the fracture toughness of magnetostrictive materials has been investigated by determining the local stress fields around the tip of a very slender elliptical flaw embedded in an infinite magnetostrictive plane subjected to magnetic loading, based on the assumption of linear magnetization. In this paper, the above-mentioned analytical approach is extended to develop a small-scale magnetic-yielding model. The magnetic saturation zone is constructed and the distributions of magnetic field and magnetization are obtained around the tip of a slender elliptical crack. Based on the complex potential theory, the stress field is obtained in the vicinity of the tip of the slender elliptical crack by implementing the continuity conditions of displacement and resultant force at the interface between the magnetic saturation and magnetoelastic zones. The stress fields near the tip of the slender elliptical crack are obtained for two kinds of soft ferromagnetic materials each with a small induction magnetostrictive modulus. The theoretical results obtained show that the stresses in the neighborhood of a crack-tip are finite even when the elliptical crack reduces to a sharp crack, and are much smaller than the yield stress or the nominal fracture stress of the material. This suggests that, generally, the magnetic field has no obvious effects on the apparent fracture toughness of soft ferromagnetic materials, which is in agreement with the existing experimental results published in the existing literature. In addition, the theoretical analysis illustrates that no crack is magnetically impermeable, and the corresponding boundary conditions are inappropriate for fracture analysis of soft ferromagnetic materials.