Transient source current formulation for the analysis of arbitrarily shaped dielectric/conducting composite structures

In this paper, a novel time-domain integral equation (TDIE) approach is presented to analyze the transient electromagnetic response from three-dimensional dielectric/conducting composite structures. The composite bodies with different materials and conductor structures are considered as autonomous scattering objects. The scattered electromagnetic field is derived by superposition of the individual scatterers. The principal method is based on the application of electric and magnetic field boundary conditions on the surfaces of dielectric and conducting objects while considering the electric currents as unknowns. Triangular patches as well as quadrangular patches model the surfaces of the combined structure. The scattered electromagnetic fields inside and outside the combined structure depend only on the electric surface currents. This improves the post-processing time and complexity as compared with other methods using both equivalent electric and magnetic surface currents. To solve the resultant integral equations, the implicit method of moments is used. In our approach, the internal fields are independent of external currents and vice-versa, reducing the number of the matrix elements by considering them as zero.     

Current distribution in a parallel set of conducting strips

The current distribution in a parallel set of thin conducting sheets due to an external applied source is investigated. All sheets are placed in one plane. The source, and all excited fields, are time-harmonic. The frequency is low enough to allow for an electro quasi-static approximation (neglecting the displacement current). The conducting sheets are infinitely long and the current is uniform in the longitudinal direction of the sheets. The sheets have a thin rectangular cross-section, so thin that the current can be assumed uniform in the thickness-direction. Hence, the current distribution only depends on the transverse coordinate. Due to the mutual induction between the sheets, the current distribution over the width of the cross-section becomes non-uniform: it accumulates at the edges of the sheets. It is especially this so-called edge-effect, and its dependence on the applied frequency and the distances between the sheets, that is the aim of this investigation. From the Maxwell equations, a set of integral equations for the current distribution in the sheets is derived. These integral equations are solved, as far as possible by analytical means, by writing the current distribution in each sheet as a series of Legendre polynomials. The general method is worked out for N (N 1) sheets, but explicit results are presented for N=1 and 3. It turns out that the edge-effect becomes stronger for increasing frequencies. For this solution, only a very restricted number of Legendre polynomials are needed.     

The M-integral for calculating intensity factors of an impermeable crack in a piezoelectric material

In this study, a conservative integral is derived for calculating the intensity factors associated with piezoelectric material for an impermeable crack. This is an extension of the M-integral or interaction energy integral for mode separation in mechanical problems. In addition, the method of displacement extrapolation is extended for this application as a check on results obtained with the conservative integral. Poling is assumed parallel, perpendicular and at an arbitrary angle with respect to the crack plane, as well as parallel to the crack front. In the latter case, a three-dimensional treatment is required for the conservative integral which is beyond the scope of this investigation. The asymptotic fields are obtained; these include stress, electric, displacement and electric flux density fields which are used as auxiliary solutions for the M-integral.Several benchmark problems are examined to demonstrate the accuracy of the methods. Numerical difficulties encountered resulting from multiplication of large and small numbers were solved by normalizing the variables. Since an analytical solution exists, a finite length crack in an infinite body is also considered. Finally, a four point bend specimen subjected to both an applied load and an electric field is presented for a crack parallel, perpendicular and at an angle to the poling direction. It is seen that neglecting the piezoelectric effect in calculating stress intensity factors may lead to errors.     

Scattering from a cylindrical reflector: modified theory of physical optics solution

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.     

A three dimensional eddy current formulation using two potentials: The magnetic vector potential and total magnetic scalar potential

A formulation of the three dimensional eddy current problem is presented. The magnetic vector potential is used in regions with source currents and conducting material and the total magnetic scalar potential is employed elsewhere. The continuity of the normal component of flux density and tangential component of field intensity are used to couple the two potentials on the interface between regions. The formulation leads to a symmetric system amenable to traditional solution techniques. The formulation is also valid for static problems with modification that are easily implemented.     

Modeling and Analysis of a Long Thin Conducting Stripline

A long thin conducting stripline embedded in a dielectric and centered between two large conducting plates, i.e., the stripline environment, is considered. The stripline is modeled as infinitely long, infinitely thin, and perfectly conducting by first considering a stripline of finite length, thickness, and conductivity in a dielectric layer. Starting from Maxwell's equations and assuming that the current on the stripline is a propagating wave in length direction, asymptotic expressions for the fields inside and in the neighbourhood of the stripline are deduced. These expressions are used to model the stripline in the stripline environment, which leads to a boundary-value problem for the electric potential. This problem is solved by two different approaches, leading to integral equations for the current and for an auxiliary function describing the electric potential. A relation between the current and the auxiliary function is deduced, which is used to obtain asymptotic expressions for current and impedance. Results are compared with a numerical solution of the integral equation for the current and with results in literature.     

Quasi-Static and Dynamic Electric Currents and Magnetic Fields in a Coil-Extended Ferromagnetic Rod System

The results of an experimental investigation of the change in the electric currents and the magnetic fields in a coil – extended electrically conducting ferromagnetic rod system in the 0–50 kHz frequency band are presented.     

3D source simulation method for static fields in inhomogeneous media

In this paper, an integral approach based on the source simulation method (SSM) for the solution of three dimensional (3D) static electric fields is presented. This is an extension of the well‐known charge simulation method to the electric and current static fields. The formulation allows the solution of 3D electrostatic or static current field problems, where several perfectly conducting bodies (electrodes) are placed in inhomogeneous media. Only electrode surfaces and dielectric interfaces need to be discretized by triangular elements. Matrix coefficients are accurately evaluated by using closed integral forms of 1/r and of grad(1/r). Dirichlet and Neumann conditions can be imposed on the different conducting bodies; in particular, floating potential problem can also be solved. The method of images allows ground plane to be taken into account. The procedure has been applied to several practical cases and it represents an efficient tool for the evaluation of lumped circuit parameters such as capacitances of 3D conducting bodies and ground resistances of grounding systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Losses in Coated Conductors Under Nonsinusoidal Currents and?Magnetic Fields

The study of AC losses in superconducting wires and tapes is usually restricted by consideration of applied sinusoidal currents and/or magnetic fields. However, currents in electric power systems contain a wide variety of harmonics. The currents become strongly nonsinusoidal in the operation of converters and nonlinear reactors, and during transient and overload conditions. Recently it has been shown that the contribution of higher harmonics to AC losses in superconducting bulk and thin film samples can be tens times larger than in normal-metal samples of the same form, and the 5% harmonic can increase the losses by up to 20%. Here we report the results of an analysis of the influence of higher harmonics of the current and magnetic field on AC losses in coated conductors. Analytical expressions are obtained in the framework of the critical state model, neglecting the response of the normal-metal substrate and stabilization layers. Losses in the superconducting and normal-metal parts of a coated conductor are compared for various designs of the conductor. It is also shown that the 5% third current harmonic can increase the losses in the normal-metal parts by up to 60%. This increase is caused by a nonlinear response of the superconducting layers and should be taken into account in the determination of the optimal operation regimes of superconducting devices.     

Nanometer-scale loop currents and induced magnetic dipoles in carbon nanotubes with defects

In metallic carbon nanotubes with defects, the electric current flow is expected to have characteristic spatial patterns depending on the nature of the defects. Here, we show, using first-principles transport calculations, that locally rotating loop currents in nanometer scale can be generated near defects in carbon nanotubes by quantum interference of conducting and quasi-bound states of electrons. The loop currents appear at energies near transmission dips, having opposite directions at lower- and higher-energy sides of the transmission dips and disappearing exactly at the centers of the dips. Temporal modulations of gate voltage around a transmission dip can produce oscillating magnetic dipoles, inducing magnetic fields that reflect characteristics of defects. This generation of loop currents and magnetic dipoles by quantum interference can generally occur in any nanostructure and it is potentially useful for novel electronic and magnetic nanodevices.     

Analysis of diffracted fields with the extended theory of the boundary diffraction wave for impedance surfaces

Uniform diffracted fields from impedance surfaces are investigated by the extended theory of boundary diffraction wave (ETBDW). The new vector potential of the ETBDW is constructed by considering the pseudoimpedance boundary condition. The method is applied to the diffraction problem from an impedance half-plane. It is shown that the total fields from an impedance half-plane reduce to the case of a perfectly electric or magnetic conducting and opaque half-plane for special values of surface impedance. The total and diffracted fields are compared numerically with the exact solution for the impedance half-plane and modified theory of physical optics (MTPO) solution for an impedance wedge. The numerical results show that the field expressions are in very good agreement with the exact and MTPO solutions.     

Dugdale plastic zone of a penny-shaped crack in a piezoelectric material under axisymmetric loading

The Dugdale plastic zone ahead of a penny-shaped crack in a piezoelectric material, subjected to electric and axisymmetric mechanical loadings, is evaluated analytically. Hankel transform is employed to reduce the mixed boundary-value problem of the penny-shaped crack to dual integral equations, which are solved exactly under the assumption of electrically permeable crack face conditions. A closed-form solution to the mixed boundary-value problem is obtained to predict the relationship between the length of the plastic zone and the applied loading. The stress distribution in and outside of the yield zone has been derived analytically, and the crack opening displacement has been investigated. The electric displacement has a constant value in the strip yield zone. The current Dugdale crack model leads to non-singular stress and electric fields near the crack front, and it is observed that the material properties affect the crack opening displacement.     

Influence of Electric Current on Kirkendall Diffusion of Zn/Cu Couples

The influence of electric current on Kirkendall diffusion in Zn/Cu couples was investigated. Under the action of different electric currents, the Zn/Cu diffusion couples were annealed at 785℃ for different holding time. The experimental results show that the displacement of the Kirkendall plane increases with increasing holding time. However, the displacement of the Kirkendall plane with electric current is larger than that without electric current. The relationship between the displacement of the Kirkendall plane and the holding time is changed under the action of electric current. The likely reason for the electric current enhancing effect is the energy transfer from electron to jumping atom, increasing the integrated diffusion coefficient, which leads to the increase in the velocity of Kirkendall plane.     

电磁材料中广义螺型位错与圆形界面刚性线夹杂的干涉效应

研究了广义螺型位错和圆形界面刚性导体线夹杂的磁电弹耦合干涉效应.采用Riemann-Schwarz对称原理并结合复势函数奇性主部分析,得到该问题的一般解答.当界面只含一条刚性线时,获得了封闭形式解.运用扰动技术,求解了位错点的扰动应力、电位移和磁感应强度场.由推广的Peach-Koehler公式求出了作用在位错上的位错力,讨论了圆弧形刚性线几何条件和材料失配对位错力的影响规律.解答不但可作为格林函数获得任意分布位错的相应解答,而且可以用于研究无穷远纵向剪切和面内电磁场作用下界面刚性线夹杂和任意形状裂纹的磁电弹耦合干涉效应问题.     

Problem in electromagneto thermoelasticity for an infinitely long solid conducting circular cylinder with thermal relaxation

The problem of an infinitely long solid conducting circular cylinder whose lateral surface is traction free and subjected to known surrounding temperatures in the presence of a uniform magnetic field in the direction of the axis is considered. The problem is in the context of generalized magneto-thermo-elasticity theory with one relaxation time. The solution is obtained by a direct approach without the customary use of potential functions. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions.Numerical computations for the temperature, the displacement and stress distributions as well as for the induced magnetic and electric fields are carried out and represented graphically. Comparison is made with the results obtained when using the coupled equation of heat conduction.     

Influence of the impedance to the surface currents induced on a spherical cap by a ring source

Explicit expressions for the high-frequency surface currents induced on a spherical cap having impedance property are obtained. It is shown that the induced electric current is always accompanied by a magnetic current as long as the impedance is different from zero. The results permit us to extend the application of the Physical Theory of Diffraction (PTD) to the cases of imperfectly conducting scatterers.     

Three-dimensional nonlinear thermo-elastic analysis of functionally graded cylindrical shells with piezoelectric layers by differential quadrature method

Three-dimensional nonlinear thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. The strain–displacement relations are based on the nonlinear Lagrangian strain–displacement relations; that is, nonlinear terms containing derivatives of the displacement in the radial direction are included. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson’s ratio is assumed to be constant. Cylindrical shells are assumed to be under the effect of pressure loading in cosine form, ring pressure loads, electric and temperature fields. Numerical results of stress, displacement, electric and thermal fields are obtained by using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. The convergence of the solution is studied, and results of the axisymmetric loadings are verified with reported results for a cylindrical shell with material properties obeying a power law. Effects of the grading index of material properties, the temperature difference, the ratio of the mean radius to the thickness of the shell, boundary conditions, the thickness of piezoelectric layers and electric excitation on stress, displacement, electric and temperature fields are presented.     

Effects of modified Ohm’s and Fourier’s laws on generalized magneto-viscoelastic thermoelasticity with relaxation volume properties

A model of the equations of the linear theory of generalized thermo-viscoelasticity for an electrically conducting isotropic media permeated by a primary uniform magnetic field, taking into account the rheological properties of the volume, is established. The modified Ohm’s law, including the temperature gradient and charge density effects, and the generalized Fourier’s law, including the current density effect, to the equations are considered. A normal mode analysis is applied to obtain the exact formulas of temperature, displacement, stresses, electric field, magnetic field and current density. Application is employed to our problem to get the solution in the complete form. The considered variables are presented graphically and discussions are made.     

Generalized electromagneto-thermoviscoelastic in case of 2-D thermal shock problem in a finite conducting medium with one relaxation time

Summary. This paper studies the problem of two-dimensional electromagneto-thermovisco-elasticity based on Lord-Shulman theory for a thermally and electrically conducting half-space solid whose surface is subjected to a thermal shock. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deforms because of thermal shock and due to the application of the magnetic field, it results in induced magnetic and electric fields in the medium. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the temperature, displacement, stress, induced magnetic and electric fields are represented graphically. Comparisons are made with the results predicted by both the coupled theory and with the theory of generalized thermo-viscoelasticity with one relaxation time.