The author describes a generalization of the theory of hysteresis to cover asymmetric or minor hysteresis loop excursions The original description of the model was found to be particularly useful because it enabled hysteresis loops of magnetic materials to be successfully modeled with a limited set of only five physically based parameters The extension of the model presented is completely self-consistent with the original formulation and requires no additional parameters to describe the minor loops Results of the model calculations are shown with the objective of demonstrating the morphology of the solutions These display the expected behavior and also include the phenomena of minor loop crossing the partial coincidence of minor loops under certain conditions >

A self consistent generalized model for the calculation of minor loop excursions in the theory of hysteresis

Weak magnetic nondestructive testing (e.g., metal magnetic memory method) concerns the magnetization variation of ferromagnetic materials due to its applied load and a weak magnetic surrounding them. One key issue on these nondestructive technologies is the magnetomechanical effect for quantitative evaluation of magnetization state from stress–strain condition. A representative phenomenological model has been proposed to explain the magnetomechanical effect by Jiles in 1995. However, the Jiles' model has some deficiencies in quantification, for instance, there is a visible difference between theoretical prediction and experimental measurements on stress–magnetization curve, especially in the compression case. Based on the thermodynamic relations and the approach law of irreversible magnetization, a nonlinear coupled model is proposed to improve the quantitative evaluation of the magnetomechanical effect. Excellent agreement has been achieved between the predictions from the present model and previous experimental results. In comparison with Jiles' model, the prediction accuracy is improved greatly by the present model, particularly for the compression case. A detailed study has also been performed to reveal the effects of initial magnetization status, cyclic loading, and demagnetization factor on the magnetomechanical effect. Our theoretical model reveals that the stable weak magnetic signals of nondestructive testing after multiple cyclic loads are attributed to the first few cycles eliminating most of the irreversible magnetization. Remarkably, the existence of demagnetization field can weaken magnetomechanical effect, therefore, significantly reduces the testing capability. This theoretical model can be adopted to quantitatively analyze magnetic memory signals, and then can be applied in weak magnetic nondestructive testing.

A general nonlinear magnetomechanical model for ferromagnetic materials under a constant weak magnetic field

Excessive vibrations in civil and mechanical systems can cause structural damage or detrimental noise. Structural vibrations can be mitigated either by attenuating energy from vibration sources or isolating external disturbance from target structures. Magnetostrictive materials coupling mechanical and magnetic energies have provided innovative solutions to vibration control challenges. Depending on the system’s tunability and power consumption, the existing vibration control strategies are categorized into active, passive, and semi-active types. This article first summarizes the unique properties of magnetostrictive materials that lead to compact and reliable vibration control strategies. Several magnetostrictive vibration control mechanisms together with their performance are then studied using lumped parameter models. Finally, this article reviews the current state of vibration control applications utilizing magnetostrictive materials, especially Terfenol-D and Galfenol.

https://iopscience.iop.org/article/10.1088/1361-665X/aadff5/pdf

Review of magnetostrictive materials for structural vibration control

Based on the equivalent circuit method, this paper adopts the nonlinear magnetostrictive constitutive relations to establish an analytical nonlinear magnetoelectric coefficient model for magnetostrictive/piezoelectric/magnetostrictive laminated magnetoelectric composites. When the pre-stress is set to zero in the model, the predicted results of the magnetoelectric coefficient coincide well with the available experimental results both qualitatively and quantitatively. Using the model, we can qualitatively predict the influence of the pre-stress, magnetic bias fields and the volume fraction of the magnetostrictive material on the magnetoelectric coefficient. The predicted results show that the influences of the pre-stress on the magnetoelectric coefficient, which varies with the magnetic bias field, before and after reaching the magnetoelectric coefficient maximum, are opposite. That is, the influence of the pre-stress on curves of the magnetoelectric coefficient reverses when the magnetoelectric coefficient reaches its maximum. Therefore, the correct setting of the pre-stress can lower the applied magnetic bias field and improve the magnetoelectric coefficient. The established nonlinear magnetoelectric effect model can provide a theoretical basis for regulating the magnetoelectric coefficient by the pre-stress and magnetic bias field and make it possible to design high-precision miniature magnetoelectric devices.

https://iopscience.iop.org/article/10.1088/0964-1726/22/3/035018/pdf

An analytical nonlinear magnetoelectric coupling model of laminated composites under combined pre-stress and magnetic bias loadings

This paper examines the vibration of fiber-steered laminated plates, such as those used in the skins of a sandwich panel, manufactured by automated fiber placement. We use third-order shear deformation theory, hybrid Fourier-Galerkin method, and numerical integration technique to predict their vibration responses, and to study the role of manufacturing defects, in particular gaps and overlpas, as well as the parameters representing the stiffness of the sandwich core. With the aim of improving both structural and vibration performance, we first adopt a passive approach to search for optimal fiber paths that can concurrently maximize the undamped dynamic out-of-plane and in-plane stiffness of laminates with gaps and overlaps. To further reduce vibration, we then follow an active approach that uses magnetostrictive layers to suppress the structural vibration of laminates with optimal vibration characteristics. The results of the vibration analysis show that for plates with gaps, as opposed to those with overlaps, the dynamic out-of-plane deflection has a higher amplitude and a lower frequency than that of a defect-free plate. In addition, the results show that magnetostrictive layers with a higher gain control can lead to a lower vibration frequency, and better attenuate the vibration response of the panel.

/pdf/vibration-responses-and-suppression-of-variable-stiffness-lhk1yxutak.pdf

Vibration responses and suppression of variable stiffness laminates with optimally steered fibers and magnetostrictive layers

This paper presents a simulation of vibration suppression of a laminated composite beam embedded with actuators of a giant magnetostrictive material subjected to control magnetic fields. It has been found that the strains generated in the material are not only significantly larger than ones created by many other smart materials but also exhibit some inherent nonlinearities. To utilize the full potential of these materials in active vibration control, these nonlinearities should be characterized in the control system as accurately as possible. In this simulation of nonlinear dynamic controls, the control law with negative velocity feedback and the analytical nonlinear constitutive model of the magnetostrictive layer are employed. The numerical results show that this proposed approach is efficient not only in a linear zone but also in nonlinear zones (dead zone and saturation zone) of magnetostrictive curves in vibration suppression. Compared with those from the control system based on the linear constitutive relations of the material, it is found that the simulation results based on the linear model are efficient only when the magnetostrictive relations are located in the linear zone. Once the system has some departure from the linear zone, however, the results from the linear model become unacceptable. Finally, the effect of material properties, lamination schemes and location of the magnetostrictive layers on vibration suppression of the practical system is evaluated.

Vibration suppression of laminated composite beams using actuators of giant magnetostrictive materials

This paper presents a general theoretical model of constitutive relationships for the soft ferromagnetic and/or the giant magnetostrictive rods under a prestress and a bias magnetic field on the basis of Gibbs’ free energy function. After Gibbs’ free energy function is expanded by Taylor’s series expansion with the stress and the magnetization in the materials as the independent variables, a transcendental function is appropriately selected to replace the first terms with higher order up to six on the basis of the meaning of mechanics and physical theory of magnetic domains, from which a set of closed and analytical expressions of the constitutive relationships for the soft ferromagnetic material rods are obtained, and the parameters appearing in the relationships are determined by those measurable experiments in mechanics and physics. It is found that the predictions from this model are in good accordance with the experimental data given by Kuruzar and Cullity [Int. J. Magn. 1, 323 (1971)] and Jiles and ...

A general theoretical model of magnetostrictive constitutive relationships for soft ferromagnetic material rods

This paper presents some simulation results of nonlinear dynamic responses for a laminated composite beam embedded by actuators of the giant magnetostrictive material (Terfenol-D) subjected to external magnetic fields, where the giant magnetostrictive materials utilizing the realignment of magnetic moments in response to applied magnetic fields generate nonlinear strains and forces significantly larger than those generated by other smart materials. To utilize the full potential application of the materials in the function and safety designs, e.g., active control of vibrations, the analysis of dynamic responses is requested in the designs as accurately as possible on the basis of those inherent nonlineary constitutive relations among stain, force and applied magnetic field existed in the materials. Here, a numerical code for the nonlinear vibration of laminated beams is proposed on the basis of a nonlinearly coupling constitutive model which fully behaves for the characteristics what are measured in experiments. It is found from this code that the natural frequency of the laminated beams changes with both the bias magnetic field and the pre-stresses, and the dynamic responses excited by an alternating magnetic field of simple harmonic form display strong nonlinear characteristics, for example, the frequency multiplication and the ultraharmonic resonance phenomena. Keyword: Laminated beams, actuator layers of giant magnetostrictive material, analytical model of nonlinear constitutive model, nonlinear code of 1 Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, P. R. China. 2 College of Information Engineering, China Jiliang University, Hangzhou, 310018, P. R. China. 3 Corresponding author. Tel: 086-0931-8910340; Fax: 0860931-8625576; Email: zhouyh@lzu.edu.cn. vibration analysis, frequency multiplication phenomenon, ultraharmonic resonance phenomenon

http://or.nsfc.gov.cn/bitstream/00001903-5/1506/1/1000000859510.pdf

Numerical Simulation of Nonlinear Dynamic Responses of Beams Laminated with Giant Magnetostrictive Actuators

From the viewpoint of energy, a general magnetoelastic coupling theory including magnetic forces and magnetostriction effects is proposed for deformable magnetized medium. Firstly, a Taylor series expansion of independent variables of stress and magnetization in the elastic Gibbs free energy function is applied to obtain a polynomial expression; and then based on the magnetoelastic coupling mechanism, appropriate transcendental functions are substituted for some terms in a polynomial constitutive relationship derived by way of substituting the polynomial Gibbs free energy function in thermodynamic equations to achieve a more compact magnetostrictive constitutive relationship. The numerical simulation exhibits that the predicted magnetostrictive strain and magnetization curves under various pre-stresses are in good agreement with the experimental data given by Kuruzar et al (1971) and Jiles et al (1984). Secondly, based on the above magnetization constitutive relationship, a general magnetic forces expression is presented according to the variational principle for the total energy functional of the coupling system of the 3-d deformable magnetized materials. It is found that for the case of linear isotropic ferromagnetic materials, the magnetic forces expression can be degenerated into the Zhou-Zheng Model (1999). Combining the above nonlinear magnetostrictive constitutive relationship and magnetic forces expression, a general nonlinear magnetoelastic coupling theory is presented in this paper for deformable magnetized medium.

A General Magnetoelastic Coupling Theory of Deformable Magnetized Medium Including Magnetic Forces and Magnetostriction Effects

This paper presents a numerical simulation of active vibration control of the Terfenol-D rod of a giant magnetostrictive transducer with nonlinear constitutive relations. In this control system, the goal is to suppress vibration of the displacement at the free end of the rod that is usually connected with a platform. Due to the inherent nonlinear relation among the applied magnetic field, pre-stress, and strain, the extension of the rod is also nonlinear relative to the external applications. Having an analytical nonlinear constitutive model of the Terfenol-D rod proposed by the last author of this paper and the finite element method employed in the deformation analysis, we propose a numerical code to simulate the dynamic behavior of the control system when the negative displacement and velocity control law is utilized to feed back the signals to the actuator. The simulation results display that this control is more effective that other existing control algorithms bas ed on linear constitutive models.

/pdf/active-vibration-control-of-terfenol-d-rod-of-giant-3s999k04qn.pdf

Hao-Miao Zhou

Papers

Vibration suppression of laminated composite beams using actuators of giant magnetostrictive materials

A general theoretical model of magnetostrictive constitutive relationships for soft ferromagnetic material rods

Numerical Simulation of Nonlinear Dynamic Responses of Beams Laminated with Giant Magnetostrictive Actuators

A General Magnetoelastic Coupling Theory of Deformable Magnetized Medium Including Magnetic Forces and Magnetostriction Effects

Active vibration control of Terfenol-D rod of giant magnetostrictive actuator with nonlinear constitutive relations