理想传导弹性体中能量耗散的磁-热-弹性波

广义能量耗散弹性理论(TEWED,G-NⅢ理论)广泛应用于均匀磁场作用下的时谐平面波在无限大的理想导电弹性体中传播的研究.提出了更普遍的有复杂参数的色散方程,通过运用Ieguerre 方法解决复杂条件下耦合磁-热-弹性波的问题,表明耦合磁-热-弹性波问题相当于改进的膨胀波及通过有限热波速度、热弹性耦合、热扩散率及外加磁场修正的、有限速度热波的传播问题.在G-NⅢ模型(TEWED)中,耦合磁-热-弹性波传播时发生衰减和色散,扩散的热量由热传播方程中的阻尼项考虑,而在G-N Ⅱ模型没有发生衰减和耗散.最后给出了类铜材料的数值结果.     

不规则界面对扭转表面波在初应力各向异性多孔弹性层中传播的影响

研究了扭转表面波在一个半无限非均匀半空间中的传播,半空间上覆盖着具有初始应力的各向异性多孔弹性层,弹性层的刚度和密度线性地变化,造成了界面的不规则性．半空间中界面的不规则性,用一个矩形形式表示．可以发现,扭转表面波在这样假定的介质中传播,得到了没有不规则性时的扭转表面波的速度方程．还可以发现,对于均匀半空间覆盖的层状介质,扭转表面波的速度与Love波的速度相一致．     

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.     

多孔弹性层的刚性边界对扭转表面波传播的影响

根据介质的力学性能,正如Cowin及Nunziato一样,导出多孔弹性层覆盖在多孔弹性半空间上时,研究其刚性边界对扭转表面波传播的影响.导出了速度方程并对其结果进行了讨论.发现介质中可能存在两类扭转表面波阵面,而Dey等(Tamkang Journal of Science and Engineering,2003,6(4):241-249.)给出的没有刚性边界面时,存在3类扭转表面波阵面.研究还揭示,多孔弹性层中Love波也可能随同扭转表面波一起存在.值得注意的是,刚性边界面多孔弹性层中Love波的相速度,不同于自由边界面多孔弹性层中的相速度.实际观察到扭转波的色散性,以及速度随着振荡频率的增大而减小.     

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．     

考虑磁通流动效应的超导薄膜基底结构界面断裂行为研究北大核心CSCD

超导薄膜是一种采用化学涂层制备而成的多层薄膜结构,作为性能优越的导电功能结构材料,其载流能力与结构完整性直接相关.在超导薄膜制备过程中,超导层与金属基底之间的界面裂纹很难避免.因此,在载流运行过程中,由于外磁场的存在,这类界面裂纹的强度问题成为关键.为此,该文针对超导薄膜结构,以磁通量子穿透薄膜理论和线弹性断裂理论为基础,建立了研究超导层与基底界面裂纹强度问题的解析模型.深入分析了外加磁场作用下界面裂纹强度问题,得到了超导磁通流动对裂纹尖端应力场和能量释放率的影响.结果表明:磁通流动速度越大,界面裂纹尖端处应力越大且能量释放率越大,这将导致界面更容易发生裂纹破坏.该文所得结果有助于分析相关的界面裂纹问题.     

纤维复合材料中弹性波散射与动应力

基于弹性波动理论,对纤维增强复合材料结构中弹性波多重散射与动应力集中问题进行了分析研究,给出了介质各区域弹性波分析解的表达式.根据位移与应力在各区界面处的连续条件,确定了未知弹性波模式系数.采用Hankel函数的加法定理,将不同局部坐标系中散射波场的表达式变换到了同一个局部坐标系中,以给出弹性波模式系数和动应力集中因子的表达式.分析了多相纤维基体中两个散射体的间距、界层区材料性质以及界层区和纤维核区截面尺寸的变化,对各区界面动应力集中系数的影响.分析表明,两个散射体的间距、界层区材料性质和结构尺寸的变化对复合材料的力学特性具有显著影响.作为算例,给出了纤维增强复合材料结构中各区界面动应力集中系数的数值结果,并对其进行了分析讨论.     

n层角域点源电位似镜像性质与电位级数解

本文研究电动 角域点源电位的级数表示式，并导出了任意层介质电阻率与介质分界面夹解与地面实测电位的一个简单关系。     

轴向运动导电导磁梁的磁弹性振动方程

针对磁场环境中轴向运动导电导磁梁磁弹性耦合振动的理论建模问题进行研究.基于Timoshenko(铁木辛柯)梁理论并考虑几何非线性因素,给出轴向运动弹性梁在横向双向振动下的形变势能、动能计算式以及电磁力和机械力的虚功表达式.应用Hamilton(哈密顿)变分原理,推得磁场中轴向运动Timoshenko梁的非线性磁弹性耦合振动方程,并给出了简化形式的Euler-Bernoulli(欧拉 伯努利)梁磁弹性振动方程.根据电磁理论和相应的电磁本构关系,得到载流导电弹性梁所受电磁力的表达式,基于磁偶极子-电流环路模型给出铁磁弹性梁所受磁体力和磁体力偶的表述形式.通过算例,分析了轴向运动导电弹性梁的奇点分布及其稳定性问题.     

复合多层介质在可变温度和集中荷载作用下的位移和应力

研究了多层介质中的热弹性位移和应力.多层介质具有不同厚度,各层又具有不同的弹性性质,最上层表面上作用热荷载和集中荷载.假设各层分别是均匀、各向同性弹性材料,各层相关的位移分量是轴对称的,对称轴为各层表面的垂线.因此,各层应力函数满足无体力的单一方程.利用积分变换法求解了该方程,对由任意多个层数构造的多层介质,给出了其相应层数基础热弹性位移和应力的解析表达式.并对3层介质和4层介质时的数值结果进行了比较.     

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 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.     

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.     

One-dimensional wave processes in a magneto-elastic medium

We construct different solutions of one-dimensional magnetoelastic problems. We analyze the process of propagation of disturbances in a magnetoelastic half-space with finite conductivity when a uniformly distributed force load and magnetic field intensity are prescribed on the surface. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 65–69.     

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.     

Some problems in nonlinear magnetoelasticity

In this paper we examine the influence of magnetic fields on the static response of magnetoelastic materials, such as magneto-sensitive elastomers, that are capable of large deformations. The analysis is based on a simple formulation of the mechanical equilibrium equations and constitutive law for such materials developed recently by the authors, coupled with the governing magnetic field equations. The equations are applied in the solution of some simple representative and illustrative problems, with the focus on incompressible materials. First, we consider the pure homogeneous deformation of a slab of material in the presence of a magnetic field normal to its faces. This is followed by a review of the problem of simple shear of the slab in the presence of the same magnetic field. Next we examine a problem involving non-homogeneous deformations, namely the extension and inflation of a circular cylindrical tube. In this problem the magnetic field is taken to be either axial (a uniform field) or circumferential. For each problem we give a general formulation for the case of an isotropic magnetoelastic constitutive law, and then, for illustration, specific results are derived for a prototype constitutive law. We emphasize that in general there are significant differences in the results for formulations in which the magnetic field or the magnetic induction is taken as the independent magnetic variable. This is demonstrated for one particular problem, in which restrictions are placed on the admissible class of constitutive laws if the magnetic induction is the independent variable but no restrictions if the magnetic field is the independent variable.Received: May 17, 2004     

Some problems in nonlinear magnetoelasticity

In this paper we examine the influence of magnetic fields on the static response of magnetoelastic materials, such as magneto-sensitive elastomers, that are capable of large deformations. The analysis is based on a simple formulation of the mechanical equilibrium equations and constitutive law for such materials developed recently by the authors, coupled with the governing magnetic field equations. The equations are applied in the solution of some simple representative and illustrative problems, with the focus on incompressible materials. First, we consider the pure homogeneous deformation of a slab of material in the presence of a magnetic field normal to its faces. This is followed by a review of the problem of simple shear of the slab in the presence of the same magnetic field. Next we examine a problem involving non-homogeneous deformations, namely the extension and inflation of a circular cylindrical tube. In this problem the magnetic field is taken to be either axial (a uniform field) or circumferential. For each problem we give a general formulation for the case of an isotropic magnetoelastic constitutive law, and then, for illustration, specific results are derived for a prototype constitutive law. We emphasize that in general there are significant differences in the results for formulations in which the magnetic field or the magnetic induction is taken as the independent magnetic variable. This is demonstrated for one particular problem, in which restrictions are placed on the admissible class of constitutive laws if the magnetic induction is the independent variable but no restrictions if the magnetic field is the independent variable.     

An analytical solution of a 3d problem of magnetoelasticity

A behavior of the soft ferromagnetic solid in a magnetic field is conventionally investigated with the framework of the developed by Brown, Pao and Yeh linear theory of magnetoelasticity. Beside of the general two-dimensional magnetoelastic problems have been successfully studied by Shindo and other researchers, the three-dimensional problems of magnetoelasticity have not been explored with some exceptions. For example the case of infinite solid with an ellipsoidal inclusion when its shape is essentially compressed in the direction of magnetic field propagation was considered using the series of simplifying assumptions. In the present paper a new approach to finding the solution for the solid with an inclusion of arbitrary ellipsoidal shape was offered. The problem was solved using a general method of constructions the exact analytical solutions of the static problem, which has been developed by Podil'chuk on the basis of Fourier method. This method implies the using of curvilinear coordinates and separating of variables in the governing equations. As a result magnetoelastic stresses was obtained in the closed form. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)