Variational analysis of a plasma-arc armature inside a railgun solid-hydrogen-pellet accelerator for fueling fusion reactors

The physical properties of a plasma-arc armature inside a hydrogen-pellet injector composed of a two-stage electromagnetic railgun are calculated by solving appropriate governing equations under simplifying assumptions. A variational method is employed to solve the temperature equation with the constraints that the variational integral must be minimized for a given plasma arc current and that the global enthalpy must be conserved. The magnetic field and the propulsive force of the railgun are calculated by modeling each current path as a composite of straight lines. The resulting railgun force is compared with the data from a recent hydrogen-pellet acceleration experiment at the University of Illinois, with reasonable agreement.     

The motion of a railway wheelset

The rolling of a railway wheelset along rails without slipping is investigated taking the creep hypothesis into account. The wheelset is represented by two cones that have a common base, and the rails are represented by two circular cylinders with parallel axes. The kinematic characteristics of the unperturbed rolling motion of the wheelset, which occurs when the centre of mass moves along a straight line, and of the perturbed motion, which occurs when the centre of mass of the wheelset describes a sinusoidal trajectory, are determined. The constraint reactions are found for the motions investigated up to small second-order values of the perturbed variables. When the elastic properties of the material in the contact area are taken into account, the creep hypothesis is used, averaging over the fast variables is employed, and the value of the critical speed, above which the rectilinear rolling of the wheelset becomes unstable, is found using averaged equations. In the latter case a periodic mode with two time intervals when the wheel flanges come into contact with the rails is investigated. The reaction force, the work of the dry friction force, and the moment of the active forces needed to maintain the periodic mode are found at the flange/rail contact point within the dry friction model. The boundaries of the stability regions, the parameters of the periodic mode and the moment of the resistance forces as functions of the problem parameters are determined from the formulae obtained by analytical methods.     

Influence of electromagnetic stirrer position on fluid flow and solidification in continuous casting mold

A computational study of the effect of stirrer position on fluid flow and solidification in a continuous casting billet mold with in-mold electromagnetic stirring has been carried out. The numerical investigation uses a full coupling method in which alternating magnetic field equations are solved simultaneously with the governing equations of fluid flow and heat transfer. An enthalpy-porosity technique is used for the solidification analysis while the magnetohydrodynamics technique is used for studying the fluid flow behavior under the electromagnetic field. The streamline, liquid fraction, and solid shell thickness at the mold wall have been predicted with and without EMS application at different positions along the length of the mold. Recirculation loops are seen to be formed above and below the stirrer position when fluid flow and electromagnetic field equations were solved, without incorporating the solidification model. Application of the solidification model interestingly resulted in the reduction of the size of the recirculation loops formed. The tangential component of velocity of the fluid near the solidification front, stirring intensity and the effective length of stirring below the stirrer decrease as the stirrer position is moved downwards. Significant changes in characteristics of solid shell formation like delay in initiation of solidification at the mold wall and formation of a gap in the re-solidified shell have been observed with change in stirrer position.     

Bending of sinusoidal functionally graded piezoelectric plate under an in-plane magnetic field

This work investigates the bending of a simply supported functionally graded piezoelectric plate under an in-plane magnetic field. The extended sinusoidal plate theory for piezoelectric plate is adopted. The governing equations are derived by the principle of the virtual work considering the Lorentz magnetic force obtained from the Maxwell's relation. The effect of magnetic field, electric loading and gradient index on the displacement, electric potential, stress and electric displacement are numerically presented and discussed in detail. These conclusions will be of particular interest to the future analysis of piezoelectric plate in magnetic field.     

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．     

ALE-based 3D FE simulation of electromagnetic forming

Electromagnetic forming is a contact-free high-speed forming process. The deformation of the work piece is driven by the Lorentz force which results from the interaction of a pulsed magnetic field with eddy currents induced in the work piece by the field itself. The purpose of this work is to present a fully-coupled three-dimensional simulation of this process. For the mechanical structure, a thermoelastic, viscoplastic, electromagnetic material model is relevant, which is incorporated in a large-deformation dynamic formulation. The electromagnetic fields are governed by Maxwell's equations under quasistatic conditions. To consider their reduced regularity at material interfaces Nédélec elements are applied. Coupling takes the form of the Lorentz force, the electromotive intensity and the current geometry of the work piece. A staggered solution scheme based on a Lagrangian mesh for the work piece and an ALE formulation for the electromagnetic field is employed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electromagnetic force on the wall of cylindrical waveguide

When transverse electric (TE) wave or transverse magnetic (TM) wave propagates inside a cylindrical waveguide, the electromagnetic force on the wall is investigated. The characteristics of surface charge, current, electric force, magnetic force and electromagnetic force are studied. The results show that the electric force is tension and magnetic force is press. The surface density of electromagnetic force on the wall can be calculated by the difference between magnetic and electric energy density there. For TE wave, the electromagnetic force distribution on the walls may be either tension or pressure in general. However, the electromagnetic force is always pressure for TM wave.     

Geometric mechanics of many-body systems

Geometric mechanics for many-body systems is first reviewed, and then applied to jointed cylinders with twist-free condition in order to obtain equations of motion under vanishing total angular momentum condition. The resultant equations are integrated numerically to set the system to turn a somersault.     

Reissner板中的夹杂和缺陷问题研究

基于保角变换技术和Faber级数展开,研究了含任意形状夹杂或缺陷的无限大Reissner板弯曲问题．将变换域中单位圆内、外解析函数分别展开成Faber级数,并将波动函数展开成第一类和第二类修正的n阶Bessel函数;利用边界位移、剪力和弯矩连续性条件得到问题的高阶线性方程组．以含椭圆形夹杂和缺陷的无限大Reissner板柱面弯曲为例,进一步给出了数值算例和理论分析．结果表明,对于软夹杂,板内力矩随夹杂与板厚尺寸比a/h变化非常敏感;在含硬夹杂条件下,板内力矩随夹杂尺寸变化相对不敏感．     

Non-linearity of multibody dynamic equations with respect to Lagrange multipliers: application to railway dynamics

In this paper, the dynamics of multibody systems with closed kinematical chains of bodies is considered. The main focus is set on non-linearity of the multibody equations with respect to the Lagrange multipliers. When closed chains are considered, loop cutting procedure is a solution to express the constraint equations associated with the loops. Dynamic equations of the multibody tree-like structure are thus completed with the constraint forces via the Lagrange multipliers. In the considered case of railway vehicles, constraints arise from the contact between the rigid wheels and the rails. Corresponding contact forces applied to the wheels appears via the Lagrange multipliers λ and the tangent creep forces as well. Resulting differential-algebraic equations can be transformed into an ODE system and then time-integrated using the coordinate partitioning method [3], when the system is linear with respect to λ. This paper presents an algorithm allowing us to solve this system in case of nonlinearities with respect to λ, which is typical of wheel/rail contact force models. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Investigation of the Effective Space–Time of the Vacuum Nonlinear Electrodynamics in a Magnetic Dipole Field

The metric tensor of the effective pseudo-Riemannian space–time for an electromagnetic wave propagating in the magnetic dipole field and the gravitational field of a neutron star is obtained within a parameterized post-Maxwellian vacuum electrodynamics. The angles of the nonlinear electrodynamic and gravitational ray bending for electromagnetic waves propagating in the magnetic equatorial plane of the star are calculated based on an analysis of isotropic geodesics of this space. We show that for all nonlinear theories whose post-Maxwellian parameters do not coincide, the velocity of the electromagnetic signal propagation in external fields and the rays along which these signals propagate depend on the polarization of the electromagnetic waves. The difference of the source-to-detector propagation time of these signals for two principal polarization states is calculated.     

线载和弹性支承作用面内运动薄板磁固耦合双重共振

针对磁场环境中具有线载荷和弹性支承作用的面内运动薄板,给出了系统的势能、动能及电磁力表达式,应用Hamilton变分原理,推得面内运动条形板的磁固耦合非线性振动方程.考虑边界为夹支-铰支的约束条件,利用变量分离法和Galerkin积分法,得到了含简谐线载力和电磁阻尼力项的两自由度非线性振动微分方程组.应用多尺度法对主-...     

CFRP修复缺陷钢板应力解析模型

在使用碳纤维复合材料(carbon fiber reinforced polymer, CFRP)修复钢结构腐蚀缺陷的修复方式中,CFRP应力及胶层应力是确定碳纤维修复结构承载能力的关键。基于平截面假设,得到弯矩作用下应力与应变分布;基于胶层剪切模型,得到胶层剪应力与CFRP和钢板位移间的关系;基于力的平衡,得到CFRP和钢板的应力关系。结合得到的各种材料之间关系,推导出轴力和弯矩联合作用状态下CFRP双面修复钢板的CFRP与胶层应力分布解析解。采用数值分析对CFRP双侧粘贴修复缺陷钢板进行分析,分析结果与解析结果具有一致性,同时获得了CFRP双侧粘贴修复缺陷钢板的应力分布特点,以及构件可能发生破坏的位置,为计算构件极限承载力提供了基础。     

On magnetoelastic problems of a plane with an arbitrarily shaped hole under stress and displacement boundary conditions

An analytical method for the static plane problem of magnetoelasticityis developed for an infinite plane containing a hole of arbitraryshape under stress and displacement boundary conditions in aprimary uniform magnetic field. The magnetic field influencesthe elastic field by introducing a body force called the Lorentzponderomotive force in the equilibrium equations. The body forcecan be further described in a form relating with the electromagneticstress tensor. The complex variable method in conjunction withthe rational mapping function technique is used in the analysisfor both magnetic field and mechanical field. Governing equationsand boundary conditions are expressed in terms of complex functions.Complex magnetic potential and stress functions are obtainedusing Cauchy integrals for the paramagnetic and soft ferromagneticmaterials, respectively. The distributions of magnetic fieldand the stress components are shown for certain directions ofprimary magnetic fields in an infinite plane with a square hole,as an example. It is found that the stress distributions forthe two types of materials are identical despite the differenceof magnetic fields. The extreme cases of a free and a fixedhole reduced to a crack and a rigid fibre, respectively, arealso investigated. The stress intensity factors at the tipsof crack and rigid fibre are computed, and their variation forcertain directions of primary magnetic field is shown.     

The velocity-current formulation of magnetohydrodynamics

The traditional formulation of the MHD equations employs the magnetic field as the primary electromagnetic variable. Unless the flow region is electromagnetically shielded from the surrounding space, boundary conditions are needed for the magnetic field; these can rarely be derived from physical principles. Using the current density as the primary electromagnetic variable, it is possible to avoid artificial boundary conditions and fully account for the electromagnetic interaction between flow region and surrounding space. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electromagnetic fields induced by electric current in an infinite plate with an elliptical hole

Analytical solutions to the electromagnetic field in a thinconductive plate with an elliptical hole are derived by meansof complex potentials and conformal mapping techniques. Thesteady-state current field in a thin conductive plate is twodimensional (2D) and is explored by a standard complex variabletechnique. The current is disturbed around the elliptical hole,and produces a three dimensional magnetic field. In this case,using the complex variable method to solve the real magneticfield can be challenging. The magnetic boundary conditions takedifferent forms for the soft ferromagnetic and the para- ordiamagnetic materials under consideration. A simplified analysistaking account of the magnitude of the magnetic permeabilityof the magnetic material and air surrounding the material isproposed to reduce the magnetic field in a thin plate to 2Dcalculations. The magnetic field distributions are derived foreach material and the equations of the magnetic components atthe tip of elliptical hole are presented.     

A general method for constructing Timoshenko-type theories

The equations of the plane theory of for the elasticity bending of a long strip are reduced by the method of simple iterations to the solution of a system of two equations for the displacement of the axis of the strip and the shear stress. If the transverse load varies slowly along the strip, the resolvent equations reduce to a single equation that is identical to the classical equation for the bend of a beam. When a local load is applied, the resolvent equation acquires an additional singular term that is the solution of the equation for the shear stresses under the assumption that the displacement (deflection) is a function of small variability. The convergence of the solution in an asymptotic sense is demonstrated. The application of the method of simple iterations to the dynamic equations for the bending of a strip also leads to a system of two resolvent equations in the displacement of the axis of the strip and the shear stress. These equations reduce to a single equation that is identical with the well-known Timoshenko equation. Hence, the procedure for using the method of simple iterations that has been developed can be classified as a general method for obtaining Timoshenko-type theories. An equation is derived for the bending of a strip on an elastic base with an isolated functional singular part with two bed coefficients, corresponding to the transverse and longitudinal springiness of the base.     

轴对称金属模具电磁热裂纹止裂中热应力场的分析

为求解金属模具脉冲放电止裂瞬间裂纹尖端附近的热应力场,选择具有半埋藏环形裂纹的金属凹模为研究对象,采用复变函数方法求解了凹模内外环面均匀通入强脉冲电流放电止裂时的热应力场．理论分析结果证实:由于放电瞬间脉冲电流的绕流集中效应,使金属凹模内部环形裂纹尖端附近金属迅速升温,金属熔化形成堆焊,并由于瞬间温升产生热压应力场．研究结果表明:应用电磁热效应止裂技术可以减小裂纹尖端的应力集中,形成的热压应力场有效地阻止金属模具中干线裂纹源的开裂趋势,达到了裂纹止裂目的．     

Generalized Electrodynamics With Ternary Internal Structure

In Refs. [2]–[7] we suggested generalized dynamic equations of motion of relativistic charged particles inside electromagnetic fields. The dynamic equations had been formulated in terms of external as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, had been derived from evolution equations for internal momenta. In this paper, along with relativistic dynamics we generalize electromagnetic fields within the scope of ternary algebras. The full theory is constructed in 4D euclidean space. This space possesses an advantage to build ternary mappings from three vectors onto one. The dynamics is given by non-linear evolution equations with cubic characteristic polynomial. In polar representation the internal momenta obey the Jacobi equations whereas external momenta obey the Weierstrass equations for elliptic functions. The generalized electromagnetic fields are defined by the triple fields where the first one has properties of the electric field and the other two have properties of the magnetic field. The field equations for the triple fields analogous to the Maxwell equations are suggested.