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.

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.

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.

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.

Manifestation of magnetoelastic interactions in Raman spectra of Ho_(x)Nd_(1-x)Fe_(3)(BO_(3))_(4) crystals

Raman spectra of Ho_(1-x)Nd_(x)Fe(BO_(3))4(x=1,0.75,0.5,0.25)have been studied in temperature range 10-400 K.Two compositions(x=1,x=0.75)demonstrate structural phase transition with soft mode restoration.The addition of Nd atoms increases interatomic spacing and decreases the temperature of structural phase transition.The solid solutions(x=0.75,0.5,0.25)demonstrate the emergence of the peaks corresponding to magnetoelastic interaction below Neel temperature.The order parameter of the magnetic phase transition has been determined.The equal concentrations of holmium and neodymium atoms prevent magnon soft modes condensation caused by exchange interactions in Fe-O-Fe chains are observed.Calculations confirm the data obtained in the experiment.