Scattering of cylindrical waves by an elastic inclusion in an electrically conducting compressible medium

We study the problems of diffraction of cylindrical waves at an elastic homogeneous weakly conducting cylinder in a liquid weakly conducting medium and at a magnetohydrodynamic liquid cylinder in a magnetoelastic medium.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 127–131.     

The equations of the thermodynamic model of magnetoelasticity of dielectric ferromagnetic bodies

We develop a thermodynamic approach to the mathematical modeling of magnetoelastic processes in dielectric ferromagnetic bodies that are subject to the action of force loading, heating, and an external electromagnetic field. The basis for the construction of the physical relations is the principle of local thermodynamic state. In the computations of the momentum balance equation of the magnetization process account is taken of its tensor character.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 30–34.     

Some Models of Coupled Magnetoelastic Fields and Their Application to the Investigation of Propagation and Diffraction of Waves

We present models of mechanics of continua which generalize the known classical models to the case of the motion of inhomogeneous magnetohydrodynamic and magnetoelastic media and to the case of an active magnetizable elastic medium and magnetoelastic body with voids. We give certain examples illustrating new effects.     

The influence of an external magnetic field on the dynamic stress of an elastic conducting one-sided layer with a longitudinal shear crack

We study the interaction of a magnetoelastic shear wave with a curvilinear tunnel crack in an ideally conducting diamagnetic (resp. paramagnetic) one-sided (resp. two-sided) layer in the presence of an external static magnetic field. The bases of the one-sided layer are free of mechanical load, and the rim of the face is clamped or free. The corresponding linearized boundary-value problem of magnetoelasticity is reduced to a singular integrodifferential equation with subsequent implementation on a computer. We give numerical results that characterize the influence of the size of the preliminary magnetic field, the frequencies of the load, the curvature, and the orientation of the crack on the stress intensity factor. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 96–102.     

Diffraction of a magnetoelastic wave on stress concentrators in conducting bodies (antiplanar deformation)

We consider a two-dimensional boundary-value problem of magnetoelasticity for a half-space weakened by tunnel stress concentrators (cracks, holes) in the presence of a static magnetic field. The mechanical stimulus is taken as a magnetoelastic shear wave incident from infinity or a shear load that varies harmonically in time and is prescribed on the edges of the crack or hole. The problem reduces to a singular integral equation that can be solved numerically by the method of mechanical quadratures. We give the results of computation of the coefficient of stress intensity K₁₁₁ for a slit and the stress concentration on the edge of a hole. We conclude that it is necessary to take account of electromagnetic effects in estimating the strength of diamagnetic or paramagnetic bodies. Four figures. Bibliography: 6 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 103–110 1991.     

On an initial boundary value problem in nonlinear 3D-magnetoelasticity

We prove existence and uniqueness of a weak solution to an initial boundary value problem, related to the Maxwell and Lamé systems nonlinearly coupled through the so-called magnetoelastic effect. Uniqueness is proved under additional assumptions on the smoothness of the solution.     

Properties of transfer matrices for magnetoelastic waves in nonferromagnetic regularly stratified media

The characteristic equation of the transfer matrix (or the monodromy matrix) is analyzed for magnetoelastic plane-polarized waves in regularly stratified nonferromagnetic ideally conducting media. The analysis has made it possible to derive the propagation conditions of magnetoelastic volume waves.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 78–83, 1985.     

On a hyperbolic-parabolic system arising in magnetoelasticity

The evolution of a magnetoelastic material is described by a nonlinear hyperbolic-parabolic system. We introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem.     

2D-1D Dimensional reduction in a toy model for magnetoelastic interactions

The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.     

磁弹性耦合效应引起的铁磁直杆磁场中振动频率的改变

基于磁弹性广义变分原理和Hamilton原理,对处于外加磁场中的软铁磁体,建立了磁弹性动力学理论模型．分别通过关于铁磁杆磁标势和弹性位移的变分运算,获得了包含磁场和弹性变形的所有基本方程,并给出描述磁弹性耦合作用的磁体力和磁面力．采用摄动技术和Galerkin方法,将所建立的磁弹性理论模型用于外加磁场中铁磁直杆的振动分析．结果表明,由于磁弹性耦合效应,外加磁场将对铁磁杆的振动频率产生影响:当铁磁杆的振动位移沿着磁场方向时,其频率减小并出现磁弹性屈曲失稳;当铁磁杆的振动位移垂直于磁场方向时,其频率将会增大．理论模型能够很好地解释已有实验观测的振动频率改变现象．     

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.     

Analysis of the Flow of Magnetoelastic Materials

We consider evolutionary models for magnetoelastic materials. The PDEs modeling the flow of the material were derived from variational principles in a continuum mechanical setting. In this article, we discuss the existence of weak solutions for two models, one with gradient flow type dynamics on the magnetic variable and in the other the dynamics of the magnetization is described by the Landau-Lifshitz-Gilbert equation. We highlight the main differences of the proofs in the two cases. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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. Project supported by the National Natural Science Foundation of China( Grant No. 19572031), the National Science Fundation for Outstanding Young Scientiests in China, and a united foundation of the State Education Committee of China and National Natural Science Foundation Committee.     

Structure and magnetic properties of nanocrystalline ferromagnets (II)

The role of magnetoelastic coupling effects in nanocrystalline ferromagnets is investigated by means of high-field magnetization and Doppler-broadening spectrum measurements. For the nanocrystalline Fe_{73 5}Cu₁Nb₃Si_13.5B₉ alloy, the results show that the pinning effects resulting from the quasidislocation dipole intensely influence the movement of domain wall; by coupling with the magnetostriction the defects-induced stress fields determine the magnetic properties at the early stage of crystallization. In view of the effective anisotropy and magnetoelastic coupling energy the optimal annealing conditions of alloys are discussed.     

Surface stability of nonlinear magnetoelastic solids

The present paper proposes to identify surface stability when a magnetoelastic half-space is subjected to a pure homogeneous pre-deformation and to a magnetic field normal to its (plane) boundary. Clearly, the aim is to find the critical stretch ratio beyond which surface instabilities may develop, or in other words, to establish a bifurcation criterion based on the incremental static solution of the boundary value problem. We want to analyse how the presence of a coupling between magnetism and nonlinear elasticity modify the conditions of stability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Revisiting the stabilization of a three-dimensional hybrid magnetoelastic structure

In this article, we are concerned with the stabilization of a three-dimensional–two-dimensional hybrid magnetoelastic structure for a reference configuration of rectangular type. We use energy methods to establish the polynomial stability of the energy associated with the interactive system of partial differential equations that govern the motions of the structure. The coupled nature of the model presents some intricacies in the construction of a Lyapunov functional.     

On Love-type waves in a finitely deformed magnetoelastic layered half-space

In this paper, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space of an incompressible non-conducting magnetoelastic material in the presence of an initial uniform magnetic field is analyzed. The equations and boundary conditions governing linearized incremental motions superimposed on an underlying deformation and magnetic field for a magnetoelastic material are summarized and then specialized to a form appropriate for the study of Love-type waves in a layered half-space. The wave propagation problem is then analyzed for different directions of the initial magnetic field for two different magnetoelastic energy functions, which are generalizations of the standard neo-Hookean and Mooney?CRivlin elasticity models. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein?CGulyaev waves in piezoelectric materials. Such waves are discussed briefly at the end of the paper.     

矩形铁磁板的磁弹性弯曲与稳定性

本文对于在外加磁场中的矩形软铁磁弹性板的磁弹性弯曲现象进行了定量模拟;建立了能反映磁弹性相互耦合作用的数值计算程序;揭示了铁磁板弯曲变形与磁(场)力的非线性特征关系,并据此讨论了磁弹性失稳临界磁场随倾斜角变化的规律.     

不规则单斜地层中磁弹性剪切波的色散方程

在内夹磁弹性单斜地层中,下界面不规则变化时,研究水平偏振剪切波的传播,该地层夹在两个半无限磁弹性单斜介质之间,得到了闭式的色散方程.不计磁场及介质界面的不规则性,该色散方程与三层介质中经典方程相一致.图示了磁场和界面不规则深度对相速度的影响.