Soft Ferromagnetic Plate Research Articles

The harmonic resonance and singularity analysis of bifurcation for the magnetized elastic plate with action of time-varying magnetic potential

This paper deals with the superharmonic resonance of a ferromagnetic thin rectangular plate in the air-gap magnetic field excited by armature magnetic potential. Electromagnetic forces applied on the plate by the air-gap magnetic field cause the plate to transversal vibrate, which affects the air-gap magnetic field in turn, resulting the vibration and magnetic field coupling. According to the basic electromagnetic field theory and considering the magnetoelastic coupling effect, the air-gap magnetic field intensity is obtained by solving the Laplace's equation satisfied the air-gap magnetic boundary conditions. The electromagnetic force model of soft ferromagnetic plates is determined based on theories of electromagnetic and elasticity. According to the large deflection theory of plates, basic energy relationships and variational equations of the elastic plate are given. Eventually, the nonlinear magnetoelastic vibration equation of ferromagnetic thin plates is derived using Hamilton's principle and Galerkin method. The multi-scale method is used to solve the superharmonic resonance to obtain the amplitude-frequency response equation and the stability discriminant of solutions. The topological analysis of amplitude-frequency equation is carried out using singularity theory, and the bifurcation characteristics of systems on physical parameter planes in different regions are obtained according to the transition set. The correctness of analytical solutions is verified by comparison with numerical solutions. Through numerical calculations, curves of the static deflection and equivalent magnetic force of plate with parameters are given, and the amplitude curves, dynamic phase plane trajectories and time history diagrams of system response with changes in electromagnetic and structural parameters are plotted. Results show that both the decrease of armature magnetic potential amplitude and the increases of plate thickness and initial air-gap thickness reduce the static deflection. The increase of armature magnetic potential amplitude increases the equivalent magnetic force. As the decrease of initial air-gap thickness and the increases of armature magnetic potential amplitude and excitation force amplitude, the amplitudes of the upper branch and lower branch curves representing stable solutions decrease and increase, respectively, and the single-value solution region increases.

Determination of the surface of defect location and restoration of its geometric parameters by the MFL method with one-sided access to the ferromagnetic plate

The paper presents a theoretical and experimental confirmation of the technique allowing the surface of defect location and its geometric parameters to be determined from measuring the values of the magnetic field components above one of the surfaces of a magnetically soft ferromagnetic plate. The technique allows one to take into account the nonlinearity of the response of a ferromagnet to an external magnetostatic field.

Increase of Levitation Force due to Soft Ferromagnetic Plate and Bar in Magnetic Levitation System Using <roman>GdBCO</roman> Bulk

We have studied a magnetic levitation system using a magnetic shielding effect of a high-temperature superconducting (HTS) bulk. The basic system is composed of a soft ferromagnetic bar, the HTS bulk, and a permanent magnet. To increase levitation force, we proposed two kinds of modified systems. One is that two basic systems are placed side by side. We name this the “2-set model.” The other is that two basic systems are commented with a common soft ferromagnetic bar. This system is called the “common bar model.” We experimentally obtained the levitation force of the modified systems. According to the experiments, the levitation force of the “2-set model” and the “common bar model” were 314 and 327%, respectively, of that of the basic model. We also numerically analyzed the magnetic flux distribution of the modified systems. From the analysis, the soft ferromagnetic bar and plate were effective to reduce magnetic resistance in a magnetic circuit of the systems, and hence, the levitation force became large.

Dynamic Analysis of Magnetoelasticity for Ferromagnetic Plates with Nonlinear Magnetization in Magnetic Fields

Based on a generalized variational principle of magnetoelasticity and Hamilton’s principle, a dynamic theoretical model is developed for magnetoelastic vibration of a soft ferromagnetic plate with nonlinear magnetization being in a stationary magnetic field. The fundamental equations of the magnetic field and the motion of the ferromagnetic plate are derived together with the expression of equivalent magnetic force acting on the ferromagnetic plate as a result of the reciprocity between the magnetizable ferromagnetic plate and the applied field. There involve twofold nonlinearities in which one is from the magnetoelastic coupling and the other arises from the nonlinear magnetization of the ferromagnetic medium. A numerical technique that combines the finite-element method for magnetic-field distribution with the finite-difference and Newmark methods for vibration of the ferromagnetic plate is proposed. Analyses of the dynamic behaviors and stability characteristics of a ferromagnetic cantilevered beam-plate vibrating in an applied stationary magnetic field are implemented numerically, which show that the frequency of magnetoelastic vibration of the ferromagnetic beam-plate increases with the intensity and the incident angle of the applied magnetic field, and that the magnetization nonlinearity obviously influences the magnetoelastic dynamics behavior. Especially for strong magnetic fields and certain geometrical parameters of the ferromagnetic plate, the magnetoelastic dynamic behavior of the ferromagnetic plate, taking into account nonlinear magnetization, exhibits distinctive magnetoelastic characteristics compared with that of the ferromagnetic plate with linear magnetization.

Analysis on the magneto-elastic-plastic buckling/snapping of cantilever rectangular ferromagnetic plates

An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented. Based on the expression of magnetic force from the variational principle of ferromagnetic plates, the buckling and bending theory of thin plates, the Mises yield criterion and the increment theory for plastic deformation, we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method. Along with the phenomena of buckling/snapping and bending, or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed, the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads, the plastic regions expanding with the magnitude of applied magnetic field, as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.

A strain gage method for determination of magnetic-moment intensity factors in through-cracked soft ferromagnetic plates

This paper presents the results of a study on the effect of magnetic fields on the moment intensity factors in the through-cracked soft ferromagnetic plates with fixed ends. The experiments were conducted on a ferritic stainless steel with the through-cracked plate specimen geometries in a uniform, static transverse magnetic field. Strain gages were used to evaluate the magnetic-moment intensity factors. The experimental results were given for a single-internal crack, a single-edge crack, and two symmetric-edge cracks. The magnetic-moment intensity factor estimated from the measured strains was in good agreement with the theoretical calculations based on the authors’ previous work.

Manipulation of Self-Assembled Structures of Magnetic Beads for Microfluidic Mixing and Assaying

We present an original concept of manipulation of magnetic microbeads in a microchannel. It is based on the dynamic motion of a self-assembled structure of ferrimagnetic beads that are retained within a microfluidic flow using a local alternating magnetic field. The latter induces a rotational motion of the magnetic particles, thereby strongly enhancing the fluid perfusion through the magnetic structure that behaves as a dynamic random porous medium. The result is a very strong particle-liquid interaction that can be controlled by adjusting the magnetic field frequency and amplitude, as well as the liquid flow rate, and is at the basis of very efficient liquid mixing. The principle is demonstrated using a microfluidic chip made of poly(methyl methacrylate) with integrated soft ferromagnetic plate structures. The latter are part of an electromagnetic circuit and serve to locally apply a magnetic field over the section of the microchannel. Starting from a laminar flow pattern of parallel fluorescein dye and nonfluorescent liquid streams, we demonstrate a 95% mixing efficiency using a mixing length of only 400 microm and at liquid flows of the order of 0.5 cm/s. We anticipate that the intense interaction between the fluid and magnetic particles with functionalized surfaces holds large potential for the development of future bead-based assays.

Magneto-thermo-elastic instability of ferromagnetic plates in thermal and magnetic fields

Based on a generalized variational principle for magneto-thermo-elasticity, a theoretical model is proposed to describe the coupled magneto-thermo-elastic interaction of soft ferromagnetic plates. Using the linearized theory of magneto-elasticity and perturbation technique, we analyze the magneto-elastic and magneto-thermo-elastic instability of simply supported ferromagnetic plates subjected to thermal and magnetic loadings. A coupled nonlinear finite element procedure is developed next to simulate the magneto-thermo-elastic behavior of a ferromagnetic plate. The effects of thermal and magnetic fields on the magneto-thermo-elastic bending and buckling is investigated in some detail.

Experimental and theoretical results for bending of a soft ferromagnetic plate in a transverse magnetic field

The results of an experimental and theoretical investigation of the bending behavior of a soft ferromagnetic cantilever beam-plate in a transverse magnetic field are presented. The theoretical model based on a beam-plate theory for magneto-elastic interactions in a soft ferromagnetic material predicts the deflection and strain for several values of the magnetic field and the geometrical parameter. The experiments were conducted on ferritic stainless steel SUS430 in the bore of a superconducting magnet at room temperature. The experiments show the predicted increase in the deflection and strain with increasing magnetic field. The theoretical results agree very well with the experimental data.

Scattering of flexural waves by a cracked Mindlin plate of soft ferromagnetic material in a uniform magnetic field

Consider the impingement of time harmonic flexural waves on a through crack in a soft ferromagnetic plate the surface of which is subjected to a uniform magnetic field at normal incidence. Mindlin's plate theory is used to account for the magneto-elastic interaction. For an incident wave that gives rise to moments symmetric about the crack plane, Fourier transforms are applied reducing the mixed boundary value problem to a Fredholm integral equation that can be solved numerically. The dynamic moment intensity factor versus frequency is computed to exhibit the influence of the magnetic field.

Magneto-elastic analysis of a soft ferromagnetic plate with a through crack under bending

Following a classical plate bending theory of magneto-elasticity, we consider the crack problem of a soft ferromagnetic plate under a uniform magnetic field. By the use of Fourier transforms we reduce the problem to solving a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral of the second kind. The bending moment intensity factor is computed and the influence of the magnetic field on the normalized values is displayed graphically.

A general expression of magnetic force for soft ferromagnetic plates in complex magnetic fields

The experiments of ferromagnetic plates in different magnetic environments exhibit two distinct phenomena, i.e. the magnetoelastic instability of a ferromagnetic plate in transverse magnetic fields, and the increase of natural frequency of a ferromagnetic plate with low susceptibility in an inplane magnetic field. Although these two typical phenomena can be predicted separately by two kinds of theoretical models in which the magnetic forces are formulated by totally different expressions, no theoretical model has been found to commonly describe them. This makes it difficult to predict theoretically magnetoelastic interaction of a ferromagnetic structure in complex magnetic environment. A variational principle, here, is proposed to establish the governing equations of magnetoelastic interaction for soft ferromagnetic thin plate structures under complex magnetic fields. The functional is chosen as the summation of the magnetic energy and the strain energy as well as the external work from applied magnetic fields. From manipulations of the variational principle, the governing equations of the magnetic field and mechanical deformation together with an expression of equivalent magnetic force exerted on the ferromagnetic plates are obtained. It is shown that this theoretical model can commonly characterize the experimental phenomena of the magnetoelastic interaction aforementioned.

Flux distributions near boundaries of magnetizable shells

The singular behavior of magnetic fields near the boundary curves of thin-walled structural members such as soft ferromagnetic plates or open shells is explored. Employing the concept of magnetic surface flux and results from potential theory, together with some reasonable assumptions concerning modeling and nonlinear magnetizability, explicit expressions and field plots are obtained. The paper includes a discussion on "forces of magnetic origin" in the present context.

A theoretical model of magnetoelastic bucking 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.

Magnetoelastic bending and snapping of ferromagnetic plates in oblique magnetic fields

Ferritic stainless steel has been considered for structural components such as first walls and blankets of fusion power reactors because the material shows low rates of irradiation swelling. Since it is magnetizable, the magnetoelastic interaction between magnetic field and deformation of the structures in a fusion reactor is so strong that their safety is of concern due to the magnetoelastic bending, buckling and magnetic damping, etc. Basic research of the magnetoelastic characteristics of ferromagnetic plate has been paid special attention by researchers. In this paper, the magnetoelastic bending and snapping are studied for a ferromagnetic plate in an oblique magnetic field. The theoretical model is based on the variational principle where the functional is employed as real total energy in the system including external work. The obtained expression of magnetic force on the plate is the same as that derived from the dipole model when the total magnetic field in the ferromagnetic medium is considered. In order to effectively solve the nonlinearly coupled interaction problem between magnetic field and mechanical deformation, a numerical program combining the finite element method for analyzing the magnetic field with the finite difference technique for finding out the bending deformation of the plate is employed to obtain the solution of magnetoelastic bending of a soft ferromagnetic plate. The numerical calculations are carried out for the typical example of a ferromagnetic cantilevered beam-plate in an oblique magnetic field. From the bending curves, that is the tip deflection versus applied magnetic fields, the critical magnetic field for the magnetoelastic snapping is predicted by the Southwell plot. The theoretical predictions show that the critical magnetic field decreases with the increase in incident angle of the oblique magnetic field. By the effect of incident angle on the magnetic buckling, the discrepancy between theoretical and experimental data can be explained well.

Dynamic bending of cracked soft ferromagnetic plate in uniform magnetic field

The scattering of time harmonic flexural waves by a through crack in a soft ferromagnetic thin plate under a uniform magnetic field is considered. Fourier transform is employed reducing the magneto-elastodynamic problem to the solution of a Fredholm integral equation of the second kind. Numerical results are obtained for the dynamic moment intensity factor that tends to increase with increasing magnetic induction and effect becomes more and more pronounced as the frequency of the flexural waves is decreased.

Magnetoelastic interaction of a soft ferromagnetic plate with a through crack under bending.

A magneto-elastic analysis is presented for the bending problem of a soft ferromagnetic thin plate of finite width with a through crack under a uniform magnetic field. Fourier transform method is used to solve the magneto-elastic problem and the result is expressed in terms of an integro-differential equation for the deflection. The integro-differential equation is solved by the standard iteration method and the mixed boundary value problem is reduced to the solution of a Fredholm integral equation of the second kind. The moment intensity factor is computed and the influence of the magnetic field on the normalized values is displayed graphically.