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.

SOME PROBLEMS IN ELECTROSTRICTIVE AND MAGNETOSTRICTIVE MATERIALS

Some of the previous theories in the electrostrictive and magnetostrictive materials and their differences are discussed in this paper. A variational principle in the general thermodynamic sense is given and the governing equations can be derived from this principle. Illustrational examples are given.

Novel mechanism for boring non-cylinder piston pinhole based on giant magnetostrictive materials

To bear more loads for heavy truck pistons, the shape of heavy truck piston pinhole is often designed as noncylinder form. Current methods cannot meet the needs for precision machining on non-cylinder piston pinhole （NCPPH）. A novel mechanism based on giant magnetostrictive materials （GMM） is presented. New models are established for the servo mechanism, GMM, and magnetizing force of the control solenoid to characterize the relationship between the control current of the solenoid and the displacement of the giant magnetostrictive actuator （GMA）. Experiments show that the novel mechanism can meet the needs to perform fine machining on NCPPH effectively.

Tailoring coercive field in rare earth giant magnetostrictive materials byα-Fe precipitation

Rare earth giant magnetostrictive materials(GMMs)Tb_(1-x)Dy_(x)Fe_(2±δ)(Tb-Dy-Fe)have been successfully employed in many microelectromechanical devices due to their excellent magnetostrictive properties at room temperature.However,Tb-Dy-Fe still shows a relatively large coercivity with high hysteresis,which inevitably limits its application range.Herein,micromagnetic simulations are performed to investigate the size effect of precipitated phase(α-Fe)on coercivity in Tb-Dy-Fe.Simulation results demonstrate that the coercivity is reduced from 31.46 to 12.48 mT with increasing the size ofα-Fe from 4 to 50 nm in Tb-Dy-Fe since the precipitated phase ofα-Fe can act as a magnetization reversal nucleus.This decreasing trend of coercivity can be well fitted with an inverse square relationship,which agrees well with the nucleation theory.Our study highlights that the coercivity of Tb-Dy-Fe can be tailored by tuning the size ofα-Fe precipitation.

A Nonlinear Magneto-Mechanical Coupled Constitutive Model for the Magnetostrictive Material Galfenol

In order to predict the performance of magnetostrictive smart material and pushits applications in engineering, it is necessary to build the constitutive relations for themagnetostrictive material Galfenol. For Galfenol rods under the action of the pre-stress andmagnetic field along the axial direction, the one-dimensional nonlinear magneto-mechanicalcoupling constitutive model is proposed based on the elastic Gibbs free energy, where theTaylor expansion of the elastic Gibbs free energy is made to obtain the polynomial forms. Andthen the constitutive relations are derived by replacing the polynomial forms with the propertranscendental functions based on the microscopic magneto-mechanical coupling mechanism.From the perspective of microscopic mechanism, the nonlinear strain related to magneticdomain rotation results in magnetostrictive strain changing with the pre-stress among theelastic strains induced by the pre-stress. By comparison, the predicted stress-strain,magnetostrictive strain, magnetic induction and magnetization curves agreed well withexperimental results under the different pre-stresses. The proposed model can describe notonly the influences of pre-stress on magnetostrictive strain and magnetization curves, butalso nonlinear magneto-mechanical coupling effect of magnetostrictive materialsystematically, such as the Young’s modulus varying with stress and magnetic field. In theproposed constitutive model, the key material constants are not chosen to obtain a good fitwith the experimental data, but aremeasured directly by experiments, such as the saturationmagnetization, saturation magnetostrictive coefficient, saturation Young’s modulus, linearmagnetic susceptibility and so on. In addition, the forms of the new constitutive relationsare simpler than the existing constitutive models. Therefore, this model could be appliedconveniently in the engineering applications.

Giant Magnetostrictive Material Loudspeaker System Acoustic Radiation Simulation

An infinite panel model of giant magnetostrictive material loudspeaker system （GMMLS） is proposed by making use of finite element method（FEM）. Bending wave eigenfunction is introduced to describe the acoustic radiation condition of the panel. Far-field response in different conditions is calculated by changing the mass surface density. Conclusion is obtained by analyzing the curves simulated, that panel which has larger mass surface density can hardly generate far-field acoustic radiation for lower frequency, while the panel has smaller mass surface density generates far-field acoustic radiation for lower frequency evenly and stronger.

Vibration suppression of magnetostrictive laminated beams resting on viscoelastic foundation

The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping.The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory(ECBT),Timoshenko’s first-order beam theory(TFBT),Reddy’s third-order shear deformation beam theory,and the simple sinusoidal shear deformation beam theory.Hamilton’s principle is utilized to give the equations of motion and then to describe the vibration of the current beam.Based on Navier’s approach,the solution of the dynamic system is obtained.The effects of the material properties,the modes,the thickness ratios,the lamination schemes,the magnitudes of the feedback coefficient,the position of magnetostrictive layers at the structure,and the foundation modules are extensively studied and discussed.

MEASUREMENTAL RESEARCH ON THE MAGNETOMECHANICAL COUPLING PROPERTIES OF RARERARTH GIANT MAGNETOSTRICTION MATERIALS

The physical modelanditsequivalentcircuitoftestapparatusissetup by meansofimpedanceanalysis method. The magnetostriction coefficient, magnetomechanicalcoupling coefficient,frequency and anti- frequency of TbxDy1 - xFe2 - z(0 27 ≤x ≤0 3 ,0 ≤z ≤0 1) rod are measured. Somecoupling problems with mechanicalstress and electromagnetic field such as flux leakage in magnetic path are discussed. The comparing calculated with tested resultsshowsthe accuracyof measurementand thesimplification of model.

Giant Magnetostrictive Material Exciter for Panel Loudspeaker

The exciter component in a panel loudspeaker has a profound effect on the overall performance of the system. The equivalent circuit analysis of the combination of giant magnetostrictive material exciter and distributed mode panel is introduced and how exciter parameters influence panel lo＇udspeaker＇ s performance is discussed. Numerical predictions are given in order to show how these influences are manifested.

Prospect of TbDyFe Magnetostrictive Material

1. Global Market: Increasing Demand for TbDyFe Mater There is steady demand for TbDyFe materials international market, especially in USA, Europe and Jap Following table shows global status of such materials si their emergence in 1984. Development course of American Etrema Company reflects the prospect of such materials. At present, besi domestic market, Etrema Company has sales

Preparation of Giant Mangetostrictive Sintered Compacts by Powder Metallurgy

Powder metallurgy technique was applied to prepare rare earth giant magnetostrictive materials. This preparation process consists of casted Tb0.30Dy0.70 Fe1.80 alloy, in magnetic atmosphere. which is pulverized by ball mill, aligned field, compacted and sintered in inertial The experimental results indicate that when the magnetic field is 240 kA ·m^-1, the sample with particle size less than 0. 147 mm being compacted in magnetic field exhibits 1613 × 10^-3 magnetostriction under a compressive pre-stress 8.0 MPa after being sintered at 1200 ℃ for 2 h and annealed at 950 ℃ for 24 h.

FEM COUPLING FIELD ITERATION AND ITS CONVERGENCE FOR A GMM ACTURATOR

The coupling iteration (CI) of the finite element method(FEM) is used to simulate the magnetic and mechanical characteristics for a GMM actuator. The convergent ability under different prestress and different load types is investigated. Then the calculated deformations are compared with the experimental values. The results convince that the CI of FEM is suitable for the simulation of energy coupling and transformation mechanism of the GMM. At last, the output deformation properties are studied under different input currents, showing that there is a good compromise between good linearity and large strain under the prestress 6 MPa.

Magnetic Properties and Phase Transformation of Tb_(1-x)Pr_xFe_(1.96)(x=0 to 0.7) Compounds

The magnetic properties and the phase Transformation of Tb1-xPrx Fe1.96（x = 0 to 0.7） compounds were studied by means of vibrating sample magnetometer（VSM）, X-ray diffraction（XRD） and SEM back-scattered electron （BSE）. The result indicates that the saturation magnetization σs of compounds along an easy axis decreases with the addition of Pr contents, which reduces from 77.24 Am^2·kg^-1（x =0） to 11.84 Am^2·kg^-1（x =0.5） and then returns to 37.14 Am2·kg^-1 （ x = 0.7）. The non-cubic phases appear when x exceeds 0.2, and the matrix of Tb1-xPrxFe1.96 compounds changes from （Tb, Pr）Fe2 phase with x = 0 to （Tb, Pr）Fe3 phase with x = 0.4, and at last to （Tb, Pr）2Fe17 phase in Tb0.3Pr0.7Fe1.96. Moreover, the structure, of the compounds may become more complex with the increase of Pr content.

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 ofa Terfenol-D （Tbo.3Dyo.rFei.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 giant 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 re- sponse 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.

湿热环境下嵌入黏弹性基础中的黏弹性磁致伸缩板的振动

本文研究了湿热荷载作用下自适应夹芯板在黏弹性介质中的振动.简单支撑的夹芯板包含三种类型的层:纤维增强层、两个磁致伸缩致动器和黏弹性面.结构的顶部和底部建模为Kelvin-Voigt黏弹性模型.基于板理论,主要振动模式应用汉密尔顿原理.数值算例研究了各种参数对湿热振动特性的影响,如厚度比、长径比、黏弹性与磁致伸缩层厚度比、模态、黏弹性基体刚度和阻尼系数、层压方案、反馈系数大小、磁致伸缩层位置、黏弹性结构阻尼、温升和水分浓度的程度.研究结果表明温度和湿度浓度是影响振动的主要因素.对于在湿热荷载作用下板的设计,上述研究结果有助于智能结构的开发与应用并控制其在这种环境条件下的振动.

Modeling and experiments on Galfenol energy harvester

Vibration energy harvesting can solve the energy supplying problem of systems like wireless sensors networks.The Galfenol cantilever beam energy harvester is suitable for this application.According to the electromechanical conversion principle,the constitutive relation of Galfenol is built.A magnetization model is also established,based on the hysteresis model of Galfenol.Combining the magneto-mechanical coupling model,the constitutive relation of Galfenol and the electromagnetic induction law,the mathematical model of Galfenol vibration energy harvester is established.A hyperbolic curve-shaped cantilever beam is designed and its performance is compared to three types of cantilever beams:rectangle,trapezoidal,and triangle.The stress distribution,modal analysis and frequency response of these four shapes of beams are compared.The hyperbolic beam is more suitable for low frequency vibration harvesting.The strain on the beams,output voltage and power output response to these energy harvesters,under different natural vibration frequencies,are determined by simulation.Finally,the simulation results are compared to experimental electric outputs of all four types of prototype beams.The comparative study showed consistency between the experimental and the simulation results,and also that the peak-to-peak induction voltage value of the hyperbolic beam is larger than other shapes of energy harvesters,whose average value is at 269.8 mV.The maximum power output of the hyperbolic beam is 403.8μW when connected with a 50Ω resistance.