Diamagnetism of conductors moving in a magnetic field

Several theoretical [1–3] and experimental [4] studies have been made of the diamagnetic perturbations during expansion of a conducting material in a magnetic field. These studies have related either to superconducting media [1], or to a strong magnetic field which has a considerable effect on the motion of the medium [2], or to a weakly ionized media, in which the effects of field variation in the medium can be neglected [3]. In the following we examine the expansion of a substance with finite conductivity in a weak (having no effect on the motion of the medium) magnetic field with account for the effects of field attenuation within the expanding matter. This occurs in the diagnostics of the state of the matter of a spark at a laser focus on the basis of diamagnetic induction signals [4]. The relations obtained in the following appear to be applicable for estimating the diamagnetic properties of meteor trails.The method of solution of this problem may be of some interest; therefore, in the following the solution is obtained by several techniques for different basic geometries.     

动力刚化问题的实验研究

应用频散可控耗散格式对环形激波在圆柱形激波管内绕射、反射和聚焦 的问题进行了数值模拟研究. 研究结果表明环形激波形成强烈聚焦的关键因素是环形激波在 圆柱形管道中向对称轴运动时，绕射激波就不断加速而不作通常情况下的衰减；不同马赫数 的环形激波绕射也产生不同马赫数及形状的准柱形激波，导致聚焦效果和位置的差异；另外， 环形激波聚焦于一个点而圆柱形激波聚焦于一条线,两者有本质不同.     

锌黄铜-铝合金互配副干摩擦学特性的磁场干涉机制研究

采用改进的MPV-1500型摩擦磨损试验机,国内首次研究了直流磁场对抗磁性(锌黄铜)和顺磁性(铝合金)材料互配副干摩擦学特性的影响.结果表明:磁场的施加和增大,加剧了抗磁性锌黄铜的磨损,降低了顺磁性铝合金的磨损,互配副的摩擦系数均有增大趋势;在抗磁性锌黄铜背面添置铁磁性材料,即可克服磁场对锌黄铜干摩擦学特性的不利影响;销、环试样的化学性能以及装卡装置的磁性均可能影响试验研究结果.     

基于永磁体间的磁性负刚度的分析与优化

为了有效地降低磁性负刚度结构的非线性程度,从简单三磁体结构出发,引入新型负刚度结构模型——五磁体对称结构,运用MATLAB建立新型负刚度结构的磁力学模型并应用Ansoft Maxwell进行仿真验证。研究永磁体间的相对位置参数对五磁体对称结构的负刚度曲线走势的影响,在微幅振动下对基于磁引力的负刚度曲线拟合后使用谐波平衡法求解动力学方程。最终得出结论:在给定的条件下,五磁体负刚度结构的负刚度曲线的非线性相较于简单三磁体结构,一定程度上得到了改善,且其隔振性能相较于传统线性隔振系统有了大幅提高,为磁性负刚度结构的负刚度曲线非线性的优化和应用提供了理论上的参考。     

超导电磁悬浮力的数值模拟

利用超导体宏观电磁场的Kim模型对高温超导体－永磁铁悬浮系统中二才之间的电磁悬浮力进行了定量计算与模拟。通过与已有实验结果比较表明：对超导悬浮力的数值模拟能较好地反映悬浮力的主要特征。在此基础上，给出了超导体内屏蔽电流，铅直悬浮力和面内电磁力的分布情况，数值仿真结果显示了悬浮力的大小与永磁铁的表磁强度和尺寸有关。这些结果为提高超导悬浮力和改进超导宏观电磁场模型提供了理论依据。     

Revisited chaotic vibrations in dielectric elastomer systems with stiffening

Dielectric elastomer is a type of soft materials which can deform under applied voltage. Here, irregular vibrations in a circular dielectric elastomer membrane with stiffening under periodic forcing are studied. The stiffening phenomenon can induce fast increases in the potential energies near the limiting stretches, which induces challenges to the numerical simulations. By comparing different numerical strategies, the adaptive step size method with allowable very small step sizes is used to simulate the system. For the system with or without damping, the existence of chaos is then verified through the positive maximum Lyapunov exponent and the fractal structures in the phase plane simultaneously. The local dynamic analysis shows the strong contribution of regions near the limiting stretches to the occurrence of chaos, revealing the important role of the stiffening. For the system with damping, the rich dynamical behaviors accompanying chaos such as the period-doubling route to chaos and the long chaotic transients also provide further consistent supports for the existence of chaos. For the system without damping, chaos region in a parameter plane is located by using different initial conditions, revealing the transitional behaviors from periodic states to chaos. Besides, the chaos is more easily to occur in the system without damping. Thus, the study here is useful to avoid or further handle such complex irregular dynamics.

     

Analytic expression of magnetic field distribution of rectangular permanent magnets

From the molecular current viewpoint, an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart’s law. This expression is useful not only for the case of one rectangular permanent magnet bulk, but also for that of several rectangular permanent magnet bulks. By using this expression, the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top ( or bottom ) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets, in order to describe its distribution, two quantities, one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field, were defined. Furthermore, the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.     

A new Finite Element Method for magneto-dynamical problems: two-dimensional results

A mixed Lagrange finite element technique is used to solve the Maxwell equations in the magneto-hydrodynamic (MHD) limit in an hybrid domain composed of vacuum and conducting regions. The originality of the approach is that no artificial boundary condition is enforced at the interface between the conducting and the insulating regions and the non-conducting medium is not approximated by a weakly conducting medium as is frequently done in the literature. As a first evaluation of the performance of the method, we study two-dimensional (2D) configurations, where the flow streamlines of the conducting fluid are planar, i.e., invariant in one direction, and either the magnetic field (“magnetic scalar” case) or the electric field (“electric scalar” case) is parallel to the invariant direction. Induction heating, eddy current generation, and magnetic field stretching are investigated showing the usefulness of finite element methods to solve magneto-dynamical problems with complex insulating boundaries.     

Passive elasto-magnetic suspensions: nonlinear models and experimental outcomes

The paper presents a passive elasto-magnetic suspension based on rare-earth permanent magnets: the dynamical system is described with theoretical and numerical nonlinear models, whose results are validated through experimental comparison. The goal is to minimize the dependence on mass of the natural frequency of a single degree of freedom system. For a system with variable mass, static configuration and dynamical behaviour are compared for classic linear elastic systems, for purely magnetic suspensions and for a combination of the two. In particular the dynamics of the magneto-mechanic interaction is predicted by use of nonlinear and linearised models and experimentally observed through a suitable single degree of freedom test rig.     

Steady magnetic waves

Steady simple waves are investigated in an incompressible conducting ideal inhomogeneously and isotropically magnetizable fluid moving along the lines of force of a magnetic field. The integration of the system of equations describing such waves is reduced to the calculation of quadrature expressions in the case of an arbitrary magnetization law. It is shown that, depending on the magnetic properties of the medium, different types of steady waves are possible: magnetizing waves in a diamagnetic fluid and demagnetizing waves in a paramagnetic fluid. The results are given of calculations of demagnetizing waves in a conducting ferromagnetic fluid. An analysis is made of the various possible flow regimes of a conducting magnetizable fluid at the point of a perfectly conducting corner.     

线形?拱形组合梁式三稳态压电俘能器动力学特性研究

利用振动能量俘获技术将设备工况振动能转化为电能, 为实现煤矿井下无线监测节点自供电提供了新的思路. 通过引入非线性磁力设计了一种线形?拱形组合梁式三稳态压电俘能器, 分析了磁铁水平间距、垂直间距和激励加速度对动力学特性的影响规律. 利用磁偶极子法建立磁力模型, 通过实验测量线形?拱形组合梁的恢复力, 并采用多项式拟合得到恢复力模型, 基于欧拉?伯努利梁理论和拉格朗日方程建立系统的动力学模型, 从时域角度仿真分析了磁铁水平间距、垂直间距和激励加速度对系统动力学特性的影响规律. 研制线形?拱形组合梁式三稳态压电俘能器样机并搭建实验平台进行实验研究, 通过采集组合梁末端响应速度数据, 验证了理论分析的正确性. 研究表明: 引入非线性磁场能够使系统势能呈现单势阱、双势阱或三势阱, 激励一定时, 调整磁铁水平间距和垂直间距能够使系统实现单稳态、双稳态或三稳态运动, 且在三稳态运动时响应位移较大, 增大激励水平有利于系统越过势垒实现大幅响应. 研究为线形?拱形组合梁式三稳态压电俘能器的设计提供了理论指导.      

Field-stiffening effect of magneto-rheological elastomers

Magneto-rheological elastomers (MREs) are a class of soft active materials known for their tunable stiffness. Dispersed with magnetic particles, these polymer-based composites tend to be stiffer under a magnetic field. Such a stiffening effect is often attributed to the magnetic interaction among filler particles, but the well-acknowledged dipole-interaction model fails to explain the stiffening effect in tension/compression, which was observed in experiments. Other mechanisms, such as the effect of non-affine deformation, have been proposed, but there is no conclusive evidence on the dominating mechanism for the field-stiffening effect. This paper investigates various filler-chain structures, and seeks to identify the ultimate origin of the field-stiffening effect in MREs. Two different methods are used for cross verification: a dipole-interaction model and a finite-element simulation based on continuum field theories. This paper studies both the shear and axial deformation of the material, with a magnetic field applied in the particle-chain direction. It is found that while the magnetic interaction between particles is indeed the major cause of the stiffening effect, the wavy chain structure is the key to the modulus increase. Besides, chain–chain interaction and non-affine deformation are shown to be insignificant. In addition, the dependence of the stiffening effect on filler concentration is calculated, and the results qualitatively agree with experimental observations. The models also predict some interesting results that could be easily verified by future experiments.     

Dynamic characteristic and stability analysis of a beam mounted on a moving rigid body

The phenomenon of dynamic stiffening has drawn general interest in flexible multi-body systems. In fact, approximately analytical, numerical and experimental research have proved that both dynamic stiffening and dynamic softening can occur in flexible multi-body systems. In this paper, the nonlinear dynamic model of a beam mounted on both the exterior and the interior of a rigid ring is established by adopting the general Hamiltons variational principle. The dynamic characteristics of the system are studied using a theoretical method when the rigid ring translates with constant acceleration or rotates steadily. The research proves theoretically that both dynamic stiffening and dynamic softening can occur in both the translation as well as the rotation state of multi-body systems. Furthermore, the approximate vibration frequency, critical value and post-buckling equilibria of the translational beam with constant acceleration are obtained by employing the assumed modes method, which validates the theoretical results. The L² norm stability of the trivial equilibrium of the system with the external beam and the L norm stability of the bending of the external beam are proved by employing the energy–momentum method.This research was supported by the National Natural Science Foundation of China (10272002) and the Doctoral Program from the Ministry of Education of China (20020001032).     

Nonlinear behaviour of piezoceramics under weak electric fields. Part-II: Numerical results and validation with experiments

When excited near resonance in the presence of weak electric fields, piezoceramic materials exhibit typical nonlinearities similar to a Duffing oscillator such as jump phenomena and presence of superharmonics in the response spectra. In an accompanying paper, a generalized nonlinear 3D finite element formulation has been developed incorporating quadratic and cubic terms in the electric enthalpy density function and the virtual work done by damping forces. In this paper, the formulation has been validated by conducting experiments on test pieces of various geometries and of three different materials (in all, four case studies). Both proportional damping and nonlinear damping formulations have been used to predict the frequency response of these systems. Newmark-β method has been used to obtain the dynamic response of the systems using FE analysis. It is demonstrated that the nonlinear finite element model is able to predict the responses of the various test cases studied and the results match very well with those of experimental observations.     

Identification of the elastic and damping characteristics of carbon fiber-reinforced plastic based on a study of damping flexural vibrations of test specimens

A theoretical and experimental method for determining the elastic and damping characteristics of materials is proposed based on analysis of vibrograms of damping flexural vibrations of test specimens with different structures. It is shown that during tension–compression and shear of a carbon fiber-reinforced plastic made of Porcher 3692 carbon fabric and EDT-69NM polymer binder, its dynamic elastic modulus decreases considerably with increasing frequency of deformation in the range of 0–120 Hz. The amplitude dependences of the logarithmic vibration decrements of the carbon fiber-reinforced plastic are determined by minimizing the discrepancy between the experimental and calculated internal-damping parameters of the test specimens in tension–compression and shear.     

A “quasi-elastic” affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

The derivation of the overall behaviour of nonlinear viscoelastic (or rate-dependent elastoplastic) heterogeneous materials requires a linearisation of the constitutive equations around uniform per phase stress (or strain) histories. The resulting Linear Comparison Material (LCM) has to be linear thermoviscoelastic to fully retain the viscoelastic nature of phase interactions. Instead of the exact treatment of this LCM (i.e., correspondence principle and inverse Laplace transforms) as proposed by the “classical” affine formulation, an approximate treatment is proposed here. First considering Maxwellian behaviour, comparisons for a single phase as well as for two-phase materials (with “parallel” and disordered morphologies) show that the “direct inversion method” of Laplace transforms, initially proposed by Schapery (1962), has to be adapted to fit correctly exact responses to creep loading while a more general method is proposed for other loading paths. When applied to nonlinear viscoelastic heterogeneous materials, this approximate inversion method gives rise to a new formulation which is consistent with the classical affine one for the steady-state regimes. In the transient regime, it leads to a significantly more efficient numerical resolution, the LCM associated to the step by step procedure being no more thermoviscoelastic but thermoelastic. Various comparisons for nonlinear viscoelastic polycrystals responses to creep as well as relaxation loadings show that this “quasi-elastic” formulation yields results very close to classical affine ones, even for high contrasts.     

铁磁介质捕捉顺磁颗粒的动力学模型

通过对磁场状态、流体速度分布等因素的综合考虑，提出了在磁分离技术中捕捉顺磁颗粒机理的动力学模型，得到了捕捉机理的物理解释；通过考察用高梯度磁选对精煤进行的脱硫降灰试验结果，发现由于介质被磁化，磁化场与背景磁场相叠加，磁场分布不具有轴对称性，对顺磁颗粒的捕捉半径的概念很大程度上是不准确的．根据J．E．Nesset和J．A．Finch静态聚集模型，提出了捕捉范围的概念，其捕捉区和排斥区的分界线为一简单双曲线，并因此得到捕捉横断面积的新计算公式．     

铁磁介质捕捉顺磁颗粒的动力学模型

 通过对磁场状态、流体速度分布等因素的综合考虑，提出了在磁分离技术中捕捉顺磁颗粒 机理的动力学模型，得到了捕捉机理的物理解释；通过考察用高梯度磁选对精煤 进行的脱硫降灰试验结果,发现由于介质被磁化, 磁化场与背景磁场相叠加, 磁场 分布不具有轴对称性, 对顺磁颗粒的捕捉半径的概念很大程度上是不准确的. 根 据J.E.Nesset 和J.A. Finch静态聚集模型,提出了捕捉范围的概念,其捕捉区和排 斥区的分界线为一简单双曲线, 并因此得到捕捉横断面积的新计算公式.     

Unstable waves at the interface of a diamagnetic liquid column contained in a magnetic fluid

A magnetically held pipeless fluid transporting system is a potentially useful noncontact technique in science and technology. Keeping a stable interface between the diamagnetic liquid column and the surrounding magnetic fluid is essential. The present study gives an experimental study on the unstable interfacial wave leading to discontinuity of a liquid column maintained in a magnetic fluid by a non-uniform magnetic field. The experiments were carried out by setting two magnetic north poles in opposite position to produce the magnetic field, using water to form the diamagnetic liquid column, and a diluted kerosene-base magnetic fluid as the surrounding fluid. Unstable interfacial waves were measured. It was found that the magnetic pressure acting on the interface can stabilise the interface. The experimental results agree well with the theoretical stability condition derived from a two-fluids model.     

Modeling of non-ideal hard permanent magnets with an affine-linear model,illustrated for a bar and a horseshoe magnet

This study is dedicated to continuum-scale material modeling of isotropic permanent magnets. An affine-linear extension to the commonly used ideal hard model for permanent magnets is proposed, motivated, and detailed. In order to demonstrate the differences between these models, bar and horseshoe magnets are considered. The structure of the boundary value problem for the magnetic field and related solution techniques are discussed. For the ideal model, closed-form analytical solutions were obtained for both geometries. Magnetic fields of the boundary value problems for both models and differently shaped magnets were computed numerically by using the boundary element method. The results show that the character of the magnetic field is strongly influenced by the model that is used. Furthermore, it can be observed that the shape of an affine-linear magnet influences the near-field significantly. Qualitative comparisons with experiments suggest that both the ideal and the affine-linear models are relevant in practice, depending on the magnetic material employed. Mathematically speaking, the ideal magnetic model is a special case of the affine-linear one. Therefore, in applications where knowledge of the near-field is important, the affine-linear model can yield more accurate results—depending on the magnetic material.