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.

Perturbed magnetic field of an infinite plate with a centered crack

Deforming a cracked magnetoelastic body in a magnetic field induces a perturbed magnetic field around the crack. The quantitative relationship between this perturbed field and the stress around the crack is crucial in developing a new generation of magnetism-based nondestructive testing technologies. In this paper, an analytical expression of the perturbed magnetic field induced by structural deforma- tion of an infinite ferromagnetic elastic plate containing a centered crack in a weak external magnetic field is obtained by using the linearized magnetoelastic theory and Fourier transform methods. The main finding is that the perturbed magnetic field intensity is proportional to the applied tensile stress, and is dominated by the displacement gradient on the boundary of the magnetoelastic solid. The tangential component of the perturbed magnetic-field intensity near the crack exhibits an antisymmetric distribution along the crack that reverses its direction sharply across its two faces, while the normal component shows a symmetric distribution along the crack with singular points at the crack tips.

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials, electric displacements, elastic deformations, and thermoelasticity, and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures （cylinder or sphere）, subjected to mechanical load and electric potential. The material properties, thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution. In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material, reinforced by elastic isotropic fibers, this material is considered as structurally anisotropic material. The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity, and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin＇s approximation method. Finally, numerical results are carried out and discussed.

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.

ANALYSIS ON DYNAMIC CHARACTERISTICS FOR FERROMAGNETIC CONDUCTING PLATES IN A TRANSVERSE UNIFORM MAGNETIC FIELD

In this paper, a set of basic equations for free vibration of ferromagnetic conducting plates in a transverse magnetic field are presented, in which the coupled effects of magnetization and eddy current on the mechanical behavior of the plate are included. Based on the quantitative analyses on the vibration frequency and the values of the critical magnetic field for several supporting conditions of the plate, the effects of the conductivity, the magnetic permeability, the thickness of the plate and supporting conditions on the vibration frequency of the plate and the critical magnetic field are discussed.

NONLINEAR STABILITY ANALYSIS OF A CLAMPED ROD CARRYING ELECTRIC CURRENT

This paper is devoted to the analysis of the nonlinear Stability of a clamped rodcarrying electric current in the magnetic field which is produced by the current frowingin a pair of inifinitely long parallel rigid wires. The natural State of the rod is in theplane of the wires and is equidistant from them.Firstly under the assumption of apatial deformation, the governing equations of the problem are derived, and the linearizedproblem and critical currents are discussed. Secondly, it ls proved that the buckledstates of the rod are always in planes. Finally. the global responses of the bifurcationproblem of the rod are compuled numerically and the distributions of the deflections.axial forces and bending monents are obtained. The results show that the buckledslates of the rod may be either supercritical or Subcritical. depending on the distancebetween the rod and the wires. Furthermore, it is found that -there exists a limit pointon the branch solution of the supercritical buckled State. This is distinctively differentfrom the buckled slate of the elastic compressive rods.

A Boundary Integral Formulation of the Plane Problem of Magneto-Elasticity for an Infinite Cylinder in a Transverse Magnetic Field

The objective of this work is to present a boundary integral formulation for the static, linear plane strain problem of uncoupled magneto-elasticity for an infinite magnetizable cylinder in a transverse magnetic field. This formulation allows to obtain analytical solutions in closed form for problems with relatively simple geometries, in addition to being particularly well-adapted to numerical approaches for more complicated cases. As an application, the first fundamental problem of Elasticity for the circular cylinder is investigated.

Milk Spoilage: Methods and Practices of Detecting Milk Quality

Milk spoilage is an indefinite term and difficult to measure with accuracy. This uncertainty can cause suffering for both milk manufacturers and consumers. Consumers who have been misled by ambiguous expiration dates on milk cartons waste resources by disposing of unspoiled milk or experience discomfort from drinking spoiled milk. Consumers are often unwilling to purchase products close to their inaccurate expiration dates. This consumer behavior has a negative financial impact on milk producers. Inaccurate milk spoilage detection methods also force milk producers to use overly conservative expiration dates in an effort to avoid the legal and economic consequences of consumers experiencing illness from drinking spoiled milk. Over the last decade, new methods have been researched with the purpose of developing more accurate and efficient means of detecting milk spoilage. These methods include indicators based on pH bacteria counts and gas-sensor arrays. This article explores various methods of spoilage detection designed to prevent such consequences. The respective level of effectiveness of each method is discussed, as well as several further approaches to contain freshness regardless of detection.

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.

Experimental study of a technique for load measurement of powered supports

Despite the increasing popularity of mechanized coal mining, there are no convenient and accurate means available to measure the loads of powered supports. The measurement of such loads is important for monitoring mine pressure and ensuring production safety. The load-carrying features of a powered support were used to develop a method for load measurement using the mag-netoelastic principle. A cross bridge-type magnetoelastic stress sensor was designed for the support structures to measure the different parts of the supports. Tests on single-body hydraulic cylinders and simulated linkages showed that an approximately linear relationship between the values of the sensor output signal and the loads borne by the hydraulic cylinders or linkages. The results were used to analyze the load-carrying measurements of powered supports with the cross bridge-type magnetoelastic stress sensor.

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.

Magneto-elastic waves in the orthoferrite plates induced by solitary domain wall

Dynamics of domain walls(DWs) was studied in transparent thin orthoferrite samples with weak ferromagnetic ordering at subsonic and supersonic speeds.Direct measurements were made of flexural vibration amplitude in the samples studied,which were induced by a solitary DW with periodic actions of a driving magnetic field.The values of the amplitude reached 7 nm at a resonance.The formation of magnetoelastic solitons was observed and their dynamics was studied at a resonance between an elastic and a spin subsystems.Solitons lag behind the DW at the moment when the DW surpasses the sound barrier and are ahead of it at the subsonic motion.

Magnetic properties of L1_0 FePt thin film influenced by recoverable strains stemmed from the polarization of Pb(Mg_(1/3)Nb_(2/3))O_3–PbTiO_3 substrate

The magnetic properties and magnetization reversible processes of Llo FePt （3 nm）/Pb（Mg1/3Nb2/3）O3-PbTiO3 （PMN-PT） heterostructure were investigated by using the phase field model. The simulation results show that the magnetic coercivities and magnetic domains evolution in the Llo FePt thin film are significantly influenced by the compressive strains stemming from the polarization of single crystal PMN-PT substrate under an applied electric field. It is found that the magnetic coercivities increase with increasing of the compressive strain. A large compressive strain is beneficial to aligning the magnetic moments along the out-of-plane direction and to the enhancement of perpendicular magnetic anisotropy. The variations of magnetic energy densities show that when compressive strains are different at the magnetization reversible processes, the magnetic anisotropy energies and the magnetic exchange energies firstly increase and then decrease, the negative demagnetization energy peaks appear at coercivities fields, and the magnetoelastic energies are invariable at large external magnetic field with the energy maximum appearing at coercivities fields. The variations of the magnetoelastic energies bring about the perpendicular magnetic anisotropy so that the magnetoelastic energy is lower at the large external magnetic fields, whereas the appearance of magnetoelastic energy peaks is due to the magnetization-altered direction from the normal direction of the plane of the Llo FePt thin film at coercivities fields.

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.

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.

Influences of P doping on magnetic phase transition and structure in MnCoSi ribbon

The structure and magnetic properties of MnCoSil_xPx （x = 0.054）.50） are systematically investigated. With P content increasing, the lattice parameter a increases monotonically while both b and c decrease. At the same time, the temperature of metamagnetic transition from a low-temperature non-collinear ferromagnetic state to a high-temperature ferromagnetic state decreases and a new magnetic transition from a higher-magnetization ferromagnetic state to a lower- magnetization ferromagnetic state is observed in each of these compounds for the first time. This is explained by the changes of crystal structure and distance between Mn and Si atoms with the increase of temperature according to the high- temperature XRD result. The metamagnetic transition is found to be a second-order magnetic transition accompanied by a low inversed magnetocaloric effect （1.0 J·kg-1 ·K- 1 at 5 T） with a large temperature span （190 K at 5 T） compared with the scenario of MnCoSi. The changes in the order of metamagnetic transition and structure make P-doped MoCoSi compounds good candidates for the study of magnetoelastic coupling and the modulation of magnetic phase transition.

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.