Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field

The nonlinear combined resonance problem of a ferromagnetic circular plate in a transverse alternating magnetic field is investigated. On the basis of the deformation potential energy, the strain potential energy, and the kinetic energy of the circular plate, the Hamilton principle is used to induce the magnetoelastic coupling transverse vibration dynamical equation of the ferromagnetic circular plate. Based on the basic electromagnetic theory, the expressions of the magnet force and the Lorenz force of the circular plate are presented. A displacement function satisfying clamped-edge combined with the Galerkin method is used to derive the Duffing vibration differential equation of the circular plate. The amplitude-frequency response equations of the system under various combined resonance forms are obtained by means of the multi-scale method, and the stability of the steady-state solutions is analyzed according to the Lyapunov theory. Through examples, the amplitude-frequency characteristic curves with different parameters, the amplitude of resonance varying with magnetic field intensity and excitation force, and the time-course response diagram, phase diagram, Poincar′e diagram of the system vibration are plotted, respectively. The effects of different parameters on the amplitude and stability of the system are discussed. The results show that the electromagnetic parameters have a significant effect on the multi-valued attribute and stability of the resonance solutions, and the system may exhibit complex nonlinear dynamical behavior including multi-period and quasi-periodic motion.

A THEORETICAL MODEL OF MAGNETOELASTIC BUCKLING FOR SOFT FERROMAGNETIC THIN PLATES

As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.

First-principles calculations on elastic, magnetoelastic, and phonon properties of Ni_2FeGa magnetic shape memory alloys

The elastic, magnetoelastic, and phonon properties of Ni2FeGa were investigated through first-principles calculations. The obtained elastic and phonon dispersion curves for the austenite and martensite phases agree well with available the- oretical and experimental results. The isotropic elastic moduli are also predicted along with the polycrystalline aggregate properties including the bulk modulus, shear modulus, Young＇s modulus, and Poisson＇s ratio. The Pugh ratio indicates that Ni2FeGa shows ductility, especially the austenite phase, which is consistent with the experimental results. The Debye tem- peratures of the Ni2FeGa in the austenite and martensite phases are 344 K and 392 K, respectively. It is predicted that the magnetoelastic coefficient is -5.3 x 10^6 J/m3 and magnetostriction coefficient is between 135 and 55 ppm in the Ni2FeGa austenite phase.

Effect of negative permeability on elastic wave propagation in magnetoelastic multilayered composites

With the advent of left-handed magnetic materials, it is desirable to develop high-performance wave devices based on their novel properties of wave propagation. This letter reports the special properties of elastic wave propagation in magnetoelastic multilayered composites with negative permeability as compared to those in counterpart structures with positive permeability. These novel properties of elastic waves are discerned from the diversified dispersion curves, which represent the propagation and attenuation characteristics of elastic waves. To compute these dispersion curves, the method of reverberation-ray matrix is extended for the analysis of elastic waves in magnetoelastic multilayered composites. Although only the results of a single piezomagnetic and a binary magnetoelastic layers with mechanically free and magnetically short surfaces as well as perfect interface are illustrated in the numerical examples, the analysis is applicable to magnetoelastic multilayered structures with other kinds of boundaries/interfaces.

Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer

This paper studies the propagation of horizontally polarized shear waves in an internal magnetoelastic monoclinic stratum with irregularity in lower interface. The stratum is sandwiched between two magnetoelastic monoclinic semi-infinite media. Dispersion equation is obtained in a closed form. In the absence of magnetic field and irregularity of the medium, the dispersion equation agrees with the equation of classical case in three layered media. The effects of magnetic field and size of irregularity on the phase velocity are depicted by means of graphs.

MAGNETOELASTIC BENDING AND STABILITY OF CURRENT-CARRYING COIL STRUCTURES

As a results of magnetoelastic interaction, the mechanical behavior of current-carrying coil structures, such as deformation and instability, is a key problem in the design of strong held magnets. In this paper, a nonlinear mathematical model is presented to describe the deformation and buckling of D-type current-carrying coils, based on the Biot-Savart law and the bending theory of curved beams. The bending deformation, the critical value of current for the magnetoelastic buckling of the current-carrying coil, and the effects of the type and number of supports at middle part of the bending coil on the critical value are quantitatively investigated by a semi-analytical and semi-numerical method. The numerical results are shown to be in good agreement with the experimental data.

Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction

Based on the magnetoelastic generalized variational principle and Hamilton＇s principle, a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed in this paper. From the variational manipulation of magnetic scale potential and elastic displacement, all the fundamental equations for the magnetic field and mechanical deformation, as well as the magnetic body force and magnetic traction for describing magnetoelastic interaction are derived. The theoretical model is applied to a ferromagnetic rod vibrating in an applied magnetic field using a perturbation technique and the Galerkin method. The results show that the magnetic field will change the natural frequencies of the ferromagnetic rod by causing a decrease with the bending motion along the applied magnetic field where the magnetoelastic buckling will take place, and by causing an increase when the bending motion of the rod is perpendicular to the field. The prediction by the mode presented in this paper qualitatively agrees with the natural frequency changes of the ferromagnetic rod observed in the experiment.

Magnetoelastic performance of〈110〉aligned polycrystalline Tb_(0.3)Dy_(0.7)Fe_2

The magnetoelastic performance of 〈110〉 aligned polycrystalline Tb0.3Dy0.7Fe2 was investigated, It has been found that the strain-stress curve is nearly linear without magnetic field, reflecting the purely mechanical elastic properties of the Tb0.3Dy0.7Fe2 rod. The strain-stress curve exhibits a complex behavior in magnetic field and can be divided into three stages. The different stages are explained with magnetic domains in the Tb0.3Dy0.7Fe2 rod alloy and the higher the magnetic field, the larger the stress to switch domains. The Young＇s modulus is also obtained from measuring the strain-stress curve and the variability of Young＇s modulus as the strain is analyzed.

Magnetoelastic instability in the XXZ rings with next-nearest neighbour coupling

This paper numerically investigates the magnetoelastic instability in the S = 1/2 {XXZ} rings containing finite spins N with antiferromagnetic nearest-neighbour （{NN}） and next-nearest neighbour （{NNN}） coupling. It finds that, as the {NN} anisotropy Δ1 equals the {NNN} anisotropy ／varDelta2, there exists a critical {NNN} coupling strength J2c（≈0.5）, at which the systems always locate in dimerized phase for arbitrary large spring constant. As Δ1 ／ne Δ2, the values of J2^{／rm c} are dependent on N and the difference of （Δ1-／varDelta2）.

Magnetoelastic Instability in Ring-Shaped Molecule Magnets with Next-Nearest Neighbor Coupling

In considering next-nearest neighbor （NNN） coupling, we numerically investigate the magnetoelastic instability in ring-shaped mesoscopic antiferromagnetic Heisenberg spin 1/2 systems with spin-phonon interaction. The results indicate that, for antiferromagnetic NNN coupling J2, there may be a critical value J2^c, at which the ground state is dimerized for arbitrary lattice spring constant and beyond and below which the magnetoelastic instability behavior is different from each other. The values of J2^c are irrelevant to the system size. For ferromagnetic NNN coupling, only continuous transition is present from dimerized phase to uniform phase as lattice spring constant is increased.

A VARIATIONAL PRINCIPLE ON MAGNETOELASTIC INTERACTION OF FERROMAGNETIC THIN PLATES

The key to revealing the behaviors of magnetoelastic interaction is how to express the magnetic forces applying on a ferromagnetic elastic body. In this paper, a functional for a ferromagnetic thin plate in magnetic fields is proposed by taking the summation of the magnetic energy of the magnetic system and the strain energy of the elastic plates. We present a variational principle for the problem by choosing the variations of magnetic potential and deflection as independent variates each other. Based on the principle, not only are the simultaneous governing equations for magnetic fields and deformation of structures deduced, but also a general expression of magnetic force acting on the plates is gained, which makes it possible to commonly simulate the distinct two experiments of magnetoelastic interaction in a theoretical model. Thus, it can be used to theoretical prediction of the magnetoelastic interaction of ferromagnetic plates in a complex environment of applied magnetic fields.

MAGNETOELASTIC BENDING AND STABILITY OF SOFT FERROMAGNETIC RECTANGULAR PLATES

In this paper, the phenomenon of magnetoelastic bending is theoretically simulated for soft ferromagnetic rectangular thin plates in applied magnetic fields. A numerical program of 3d FEM is established to capture the nonlinear coupling interaction between magnetic fields and bending deflection. After the nonlinear characteristic of the bending deflection and the magnetic (field) force is quantitatively displayed, we discuss the critical magnetic field and the effect of the incident angle of obliquely applied magnetic field on the critical field to the phenomenon of magnetoelastic instability.

Effect of Point Source, Self-Reinforcement and Heterogeneity on the Propagation of Magnetoelastic Shear Wave

This paper investigates the propagation of horizontally polarised shear waves due to a point source in a magnetoelastic self-reinforced layer lying over a heterogeneous self-reinforced half-space. The heterogeneity is caused by consideration of quadratic variation in rigidity. The methodology employed combines an efficient derivation for Green’s functions based on algebraic transformations with the perturbation approach. Dispersion equation has been obtained in the closed form. The dispersion curves are compared for different values of magnetoelastic coupling parameters and inhomogeneity parameters. Also, the comparative study is being made through graphs to find the effect of reinforcement over the reinforced-free case on the phase velocity. It is observed that the dispersion equation is in assertion with the classical Love-type wave equation in the absence of reinforcement, magnetic field and heterogeneity. Moreover, some important peculiarities have been observed in graphs.

G-Type Seismic Wave in Magnetoelastic Monoclinic Layer

This paper deals with the study of propagation of G type waves along the plane surface at the interface of two different types of media. The upper medium is taken as monoclinic magnetoelastic layer whereas the lower half-space is inhomogeneous isotropic. Dispersion equation and condition for maximum energy flow near the surface are obtained in compact form. The dispersion equation is in assertion with the classical Love-type wave equation for the isotropic case. Effect of magnetic field and inhomogeneity on phase velocity and variation of group velocity with scaled wave number has been depicted by means of graphs. It is observed that inhomogenetity decreases phase velocity and the magnetic field has the favouring effect. A comparative study for the case of isotropic layer and monoclinic layer over the same isotropic inhomogeneous half space has been made through graphs.

Remotely activated, vibrational magnetoelastic array system for controlling cell adhesion

A new system was designed to selectively control cellular adhesion to medical implants. The system is based on magnetoelastic (ME) materials that can be remotely set to generate mechanical vibrations at submicron levels with predetermined amplitude and frequency. Previous studies have demonstrated the capacity of these vibrations to control cellular adhesion at a substrate surface. In this work, an ME film with two conjoined strips was developed to investigate the potential of this system to provide region specific control of cellular adhesion. In vitro cell culture experiments performed with L929 fibroblasts indicate that cellular adhesion can be increased or decreased at different regions of the film by changing the frequency of the magnetic field.

Spontaneous Magnetic Transitions and Corresponding Magnetoelastic Properties of Intermetallic Compounds RMn_2Ge_2(R=Gd, Tb and Dy)

The spontaneous magnetic transitions and corresponding magnetoelastic properties of intermetallic compounds RMn2Ge2（R=Gd, Tb and Dy） were investigated by using the X-ray diffraction method and magnetic measurement. The results showed that the compounds experience two magnetic transitions, namely the second-order paramagnetic to antiferromagnetic transition at temperature TN（TN=368, 423 and 443 K for Gd Mn2 Ge2, Tb Mn2 Ge2 and Dy Mn2 Ge2, respectively） and the first-order antiferromagnetic-ferrimagnetic transition at temperature Tt（Tt=96, 80 and 40 K for Gd Mn2 Ge2, Tb Mn2 Ge2 and Dy Mn2 Ge2, respectively） as the temperature decreases. The temperature dependence of the lattice constant a（T） displays a negative magnetoelastic anomaly at the second-order transition point TN and, at the first-order transition Tt, a increases abruptly for Gd Mn2 Ge2 and Tb Mn2 Ge2, Da/a about 10^（-3）. Nevertheless, the lattice constant c almost does not change at these transition points indicating that such magnetoelastic anomalies are mainly contributed by the Mn-sublattice. The transitions of the magnetoelastic properties are also evidenced on the temperature dependence of magnetic susceptibility χ. The first-order transition behavior at Tt is explained by the Kittel mode of exchange inversion.

Out-of-Plane Magnetic Anisotropy and Microwave Permeability of Magnetoelastic FeCoSiB Amorphous Thin Films

Theamorphous magnetoelastic Fe66Co17Si1B6 thin films have been deposited by dc magnetron sputtering. A lot of ＂nano-trenches＂ have been observed on the fdm surfaces by AFM. The permeability of amorphous Fe66COlTSilB6 thin films was measured within the frequency range of 0.6GHz-10.2 GHz. The ferromagnetic resonance frequency was found to be 1.2 GHz. MFM shows that the domain of thin film is a maze-type pattern, which indicates that an out-of-plane magnetic anisotropy exists. The out-of-plane anisotropy is believed due to the stress-induced magnetic anisotropy. It can be inferred that the internal stress is tensile stress and normal to the film plane. Index Terms

Bending of a Saturated Ferromagnetoelastic Plate Under a Local Mechanical Load

We study the bending of a magnetically saturated ferromagnetoelastic plate.The plate is rectangular and simply-supported along its edges.It is under a local distribution of normal mechanical load on its top surface,simulating a mechanical probe or manipulation of the magnetization field.The three-dimensional equations of saturated ferromagnetoelasticity for small fields superposed on finite biasing fields due to spontaneous magnetization are used.The plate is effectively piezomagnetic under the biasing fields.A trigonometric series solution is obtained.The perturbation of the magnetization field by the mechanical load is calculated and examined.It is found that the magnetization is sensitive to the mechanical load,particularly near the loading area.The perturbation of the magnetization is found to be associated with the transverse shear stresses in bending.

A generalized variational principle and theoretical model for magnetoelastic interaction of ferromagnetic bodies

The quantitative analysis shows that no theoretical model for 3-d magnetoelastic bodies, in literatures to date, can commonly simulate two kinds of distinct experimental phenomena on magnetoelastic interaction of ferromagnetic structures. This makes it difficult to effectively discribe the magnetoelastic mechanical behavior of structures with complex geometry, such as shells. Therefore, it is a key step for simulating magnetoelastic mechanical characteristics of structures with complex geometry to establish a 3-d model which also can commonly characterize the two distinct experimental phenomena. A theoretical model for three dimension magnetizable elastic bodies, which is commonly suitable for the two kinds of experimental phenomena on magnetoelastic interaction of ferromagnetic plates, is presented by the variational principle for the total energy functional of the coupling system of the 3-d ferromagnetic bodies. It is found that for the case of linear isotropic magnetic materials, the magnetic forces obtained by this model include not only the body magnetic force which is the same as that got from the magnetic dipole model, but also a distribution of the magnetic traction on the surface of the magnetizable body. And the value of the traction is equal to the jumping one of the Faraday electromagnetic stress on the two sides of the surface, which does not appear in any model, such as magnetic dipole model and axiomatic model.

Overview of magnetoelastic coupling in (Mn, Fe)2(P, Si)-type magnetocaloric materials

（MnFe）2（P, Si）-type compounds are, to date, one of the best candidates for magnetic refrigeration and energy conversion applications due to the combination of giant magnetocaloric effect （MCE）, tunable working temperature range and low material cost. The giant MCE in the （Mn, Fe）2（P, Si）-type compounds originates from strong mag- netoelastic coupling, where the lattice degrees of freedom and spin degrees of freedom are efficiently coupled. The tunability of the phase transition, in terms of the critical temperature and the character of the phase transition, is essentially attributed to the changes in the magnetoelastic coupling in the （Mn, Fe）2（P, Si）-type compounds. In this review, not only the fundamentals of the magnetoelastic coupling but also the related practical aspects such as magnetocaloric performance, hysteresis issue and mechanical stability are discussed for the （Mn, Fe）2（P, Si）- type compounds. Additionally, some future fundamental studies on the MCE as well as possible ways of solving the hysteresis and fracture issues are proposed.