Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields

This paper presents an analysis on electromagneto-thermo-mechanical behaviors of conductive plates, an analytical solution is given for a conductive circular plate in a time-dependent magnetic field by using a T-method of the eddy current which is widely used in the eddy current analysis of conductive and superconductive structures. The solution is expressed in an analytical series form and it is suitable for a circular plate under any arbitrary axisymmetric magnetic fields changing in time. Some interesting results including the eddy current, the increment of temperature, and the electromagneto-thermal stresses are investigated, respectively, in this paper. Some characteristics such as the distribution of temperatures, the in-plane electromagnetic stresses and the dynamic response of the conductive plate are first studied and displayed. This study not only reveals some characteristics on the eddy current, the temperature of the plate, the in-plane electromagnetic thermal stresses and the dynamic responses of the conductive plate which is in a time-dependent magnetic field, but presents a new possible way to simplify the analysis of the electromagnetic coupling problem for conductive structures.     

A differential quadrature analysis of dynamic and quasi-static magneto-thermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field

A rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical simulation of dynamic and quasi-static magneto-thermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field. Fundamental equations of plane electromagnetic, temperature and elastic fields are formulated. To the best of the authors’ knowledge, this is the first attempt to apply the DQM to magneto-thermo-elasticity and the first attempt to analyze a finite two-dimensional magneto-thermo-elastic problem. The fundamental equations and the inhomogeneous time-dependent boundary conditions are discretized in spatial and temporal domain by differential quadrature (DQ) rules. The unknowns satisfying the governing equations, the boundary and initial conditions simultaneously are computed in the entire domain by means of DQM with high efficiency and accuracy using dramatically less grid points in both spatial and time domain. Solutions of magnetic field, eddy current, temperature change and dynamic solutions of stresses and deformations are illustrated graphically.     

Magneto-thermo-elastic problem of a conducting rectangular cylinder subjected to sinusoidal change in time of magnetic field

This study is concerned with a magneto-thermo-elastic problem of a conducting rectangular cylinder in an external magnetic field which varies sinusoidally in time. Analytical solutions of eddy currents induced in the cylinder are derived on the basis of a theory of the quasi-stationary current. Two-dimensional transient temperature change produced by the eddy current loss is derived by means of the Green’s function method. The stresses in the infinitely long cylinder in a plane state are derived by making use of the Airy’s stress function. The effect of a frequency in a sinusoidal change in time of the external magnetic field on behaviors of eddy current loss, temperature change and stresses in the cylinder is examined by numerical calculation. The skin effect with an increase in a frequency of the external magnetic field on the transient response of temperature change and stresses in the cylinder is discussed.     

Thermoelastic State of a Conducting Plate under the Action of an Electromagnetic Field in the Form of Damped Sinusoid

We determine the temperature fields and stresses formed in an infinite nonferromagnetic conducting plate of constant thickness under the action of a pulsed electromagnetic field specified by the values of the tangential component of magnetic vector on the surfaces. In the case of electromagnetic action obeying the law of damped sinusoid, we perform the comparative numerical analysis of ponderomotive forces, temperature, and components of the dynamic stress tensor for plates made of stainless steel and copper. It is shown that the influence of electric and thermal conductivity, thermal diffusivity, the coefficient of linear thermal expansion, and Young's modulus on the quantitative and qualitative behavior of the analyzed parameters as functions of time is significant.     

Numerical Solution of a Problem of Thermal Stresses of a Magnetothermoelastic Cylinder with Rotation by Finite-Difference Method

The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation, open or closed circuit, thermal and mechanical boundary conditions. The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions. A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method. The fundamental equations’ system is solved by utilizing an implicit finite-difference method. This current method is a second-order accurate in time and space; it is also unconditionally stable. To illustrate the present model’s efficiency, we consider a suitable material and acquire the numerical solution of temperature, displacement components, and the components of stresses with time t and through the radial of an infinite cylinder. The results indicate that the effect of coupled thermoelasticity, magnetic field, and rotation on the temperature, stresses, and displacement is quite pronounced. In order to illustrate and verify the analytical developments, the numerical solution of partial differential equations, stress components, displacement components and temperature is carried out and computer simulated results are presented graphically. This study is helpful in the development of piezoelectric devices.     

Influence of magnetic fields on turbo-molecular pumps

Recently, turbo-molecular pumps (TMPs) have been widely used in nuclear fusion devices and sometimes used in particle accelerators. In order to use them in the quasi-static magnetic field often employed in these devices, the influence of these fields on TMPs was investigated in detail.First of all, the influence of two special magnetic fields was examined, a magnetic field orthogonal to the TMP, and one which was parallel. The parallel magnetic field had no influence on the operation of the TMP. On the other hand, the driving power and the rotor temperature were greatly affected by the vertical magnetic field. The eddy current loss in the vertical field increased rapidly with the field strength, proportionally to the square of the field strength. The eddy current loss also increased with the rotation frequency; however, it was roughly proportional to the square root of the frequency at higher frequencies. These dependences are well explained by the skin depth, which indicates the region beneath the surface of the rotor where a localized magnetic field and current flow exist.Then, we successfully calculated the influence of a magnetic field in an arbitrary direction by adding the contributions from the above two magnetic components. Furthermore, experiment revealed that a magnetic field with symmetry around the rotor axis does not affect the operation of the TMP.     

An elastic strip with periodic surface cracks under thermal shock

The problem of two periodic edge cracks in an elastic infinite strip located symmetrically along the free boundaries under thermal shock is investigated. It is assumed that the infinite strip is initially at constant temperature. Suddenly the surfaces containing the edge cracks are quenched by a ramp function temperature change. Very high tensile transient thermal stresses arise near the cooled surface resulting in severe damage. The degree of the severity for a subcritical crack growth mode is measured by determining the stresses intensity factors. The thermoelastic problem is treated as uncoupled quasi-static. The superposition technique is used to solve the problem. The thermal stresses obtained from the uncracked strip with opposite sign are utilized as the only external loads to formulate the perturbation problem. By expressing the displacement components in terms of finite and infinite Fourier transforms, a hypersingular integral equation is derived with the crack surface displacement as the unknown function. Numerical results for stress intensity factors are carried out and presented as a function of time, cooling rate, crack length, and periodic crack spacing.     

Braking forces and damping coefficients of eddy current brakes consisting of cylindrical magnets and plate conductors of arbitrary shape

A method for analyzing a magnetic damper (eddy current brake) consisting of a cylindrical magnet and a plate conductor of arbitrary shape is considered. Since the magnetic flux is a function of the position, the analytical solution to obtain the eddy current, braking force, and damping coefficient is obtained by dividing the magnetic flux into the narrow circular bands, and the unit step function is applied to solve the differential equation of the electromagnetic fields. The boundary condition of the plate conductor of arbitrary shape is satisfied directly by making use of the Fourier expansion collocation method. Numerical calculations have been carried out for the conductor of rectangular plates, circular plates with eccentric fluxes. The theoretical results are in very good agreement with the experimental ones.     

Fundamental thermo-elasticity equations for thermally induced flexural vibration problems for inhomogeneous plates and thermo-elastic dynamical responses to a sinusoidally varying surface temperature

Equations of motion governing thermally induced vibration of plates with inhomogeneous material properties through the thickness direction are presented. Equations of motion for thermally induced flexural vibration for inhomogeneous rectangular plates in which the material properties are given in the form of a power of the thickness coordinate are derived from the above-mentioned fundamental equations. An exact solution of the one-dimensional temperature change is presented for an inhomogeneous plate in which one surface is exposed to a sinusoidally varying temperature, and the other is kept at zero temperature change. The associated quasi-static and dynamic solutions pertinent to deflection and thermal stresses in the inhomogeneous rectangular plate are derived under the condition of simply supported edges. Numerical calculations are performed, and the effects of material inhomogeneity such as Young’s modulus, coefficient of linear thermal expansion, and mass density, angular frequency in cyclic heating, and aspect ratio on the thermo-elastic response of the rectangular plate are shown in graphical form. Comparing the dynamic solutions with quasi-static ones, the effect of inertia on the thermo-elastic response of the inhomogeneous rectangular plate is evaluated.     

陶瓷圆球的抗热震参数

在陶瓷材料临界应力断裂理论的基础上，通过求解陶瓷圆球体第三类边界条件的瞬态温度场和瞬态热应力场，研究了陶瓷圆球的热冲击行为，建立了一个引起陶瓷圆球表面临界应力的临界温差表达式，并以此作为陶瓷圆球的抗热震参数。计算结果表明，陶瓷圆球体的临界温差大于相同Biot模数的无限大陶瓷平板的临界温差，但其表面达到临界热应力的无量纲时间远远小于无限大平板的数值。     

Stress intensity factor for center-cracked plate with crack surface interference

This paper presents a simple and physically acceptable analysis of stress intensity factor (SIF) for the center-cracked infinite and finite-width plates. The analysis includes the effect of crack surface interference (i.e., the upper and lower crack surfaces are not allowed to overlap) that influences both the SIF at the tension-side crack tip and the crack opening displacement (COD) profile. For an infinite plate, exact solutions are obtained by superimposing the classical (overlapping) solutions. For a finite-width plate, where the SIF solutions cannot be found in closed form, the solutions are carried out numerically. The overlapping SIF solutions from the weight function method are used. An example is given for the case of a finite-width plate under bending. It was found that the overlapping solutions underestimate the stress intensity factor at the tension-side crack tip up to 15%. The analysis results are also compared with the finite element solutions for verification purpose.     

SGBEM analysis of crack-particle(s) interactions due to elastic constants mismatch

The effects of elastic constants mismatch on the interaction between a propagating crack and single or multiple inclusions in brittle matrix materials are investigated using numerical simulations. The simulations employ a quasi-static crack-growth prediction tool based upon the symmetric-Galerkin boundary element method (SGBEM) for multiregions, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating stress intensity factors (SIFs), and the maximum principal stress criterion for crack-growth direction. It is shown that, even with this simple method for calculating SIF, the crack-growth prediction tool is both highly accurate and computationally effective. This is evidenced by results for the case of a single inclusion in an infinite plate, where the SGBEM results for the SIFs show excellent agreement with known analytical solutions. The simulation results for crack growth and stress intensity behaviors in particulate media are very stable. The crack-tip shielding and amplification behaviors, as seen in similar studies using other numerical approaches, can be clearly observed.     

A New Approach for Finite-Element Modeling of Hysteresis and Dynamic Effects

Macroscopic behavior of ferromagnetic materials can be considered as the resultant of three phenomena: hysteresis, eddy current, and excess loss. Hysteresis is the behavior of the material under quasi-static variation of magnetic field. Eddy-current and excess losses are dependent on the rate of field variation and are evident in the fast variation of the magnetic field, so they are called dynamic effects. This paper presents a simple and practical technique in field analysis of electromagnetic systems having hysteresis and dynamic effects. Based on the Preisach model for hysteresis and existing formulations for eddy currents and excess loss, an equivalent expression for field intensity has been introduced. A new technique has been presented in order to include this expression in the finite-element code. A typical system has been modeled by this code. Effects of relaxation and time step were examined on the stability and the convergence rate of the method. The validity of the proposed model has been checked by comparing its results with experimental measurements     

Thermal shock analysis and thermo-elastic stress waves in functionally graded thick hollow cylinders using analytical method

Transient stress field and thermo-elastic stress wave propagation are studied in functionally graded thick hollow cylinder under arbitrary thermo-mechanical shock loading, in this article. Thermo-mechanical properties of functionally graded (FG) cylinder are assumed to be temperature independent and vary continuously and smoothly in the radial direction. The governing dynamic equations are analytically solved in temperature and elastic fields. To solve the problem, Laplace transform is used respect to time in all constitutive equations and boundary conditions. At first, temperature field equation analytically solved using Laplace transform and series method. The dynamic behaviors of thermo-elastic stresses are illustrated and discussed for various grading patterns of thermo-mechanical properties in several points across the thickness of FG cylinder. Time history of temperature field and thermal stresses are obtained using the residual theorem and the fast Laplace inverse transform method (FLIT), respectively. Also, the effects of the cylinder thickness and convection heat transfer coefficient on dynamic response of FG cylinder are revealed and discussed. The presented analytical method provides a ground to study the time histories of radial and hoop stresses in FG cylinders with different thickness and various volume fraction exponents. The advantage of this method is its mathematical ability to support simple and complicated mathematical function for the thermo-mechanical boundary conditions. A reasonable agreement can be seen in comparison of obtained results based on the presented analytical method with published data.     

新型竖向电涡流-磁力混合阻尼装置试验研究

针对大跨轻质结构的减振需要,研制了一种新型竖向电涡流-磁力混合阻尼器样机.介绍混合阻尼器的减振原理及振动方程;接着介绍了3种不同的磁路设计和制作过程;随后对样机进行试验,测量其动力参数和减振性能.结果 表明:在铜板后方和底板上方安装磁铁均能改变阻尼器的附加刚度;特定磁路设计减少电涡流阻尼系数,增大等效磁力阻尼系数和负刚...     

Stress distribution,crack shape and energy for a penny-shaped crack in a plate of finite thickness

The shape of a penny-shaped crack located at the center of an elastic plate of finite thickness is related to the arbitrary axisymmetrical internal pressures applied to the crack surfaces in the form of a Fredholm integral equation, without using the methods of dual-integral equations. General expressions for the stresses in the plane containing the crack are written as the sums of the associated infinite solid stresses and the integrals accounting for the effect of plate thickness. The crack shape due to uniform crack pressures and the fracture criterion for brittle plates subjected to uniform stresses are obtained for various plate thicknesses.     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Transient hygrothermoelastic analysis of layered plates with one-dimensional temperature and moisture variations through the thickness

Transient heat and moisture diffusion and the resulting hygrothermal stress field are analysed in a layered plate subjected to hygrothermal loadings at the external surfaces. The one-dimensional transient diffusion is formulated as a one-way coupled problem wherein moisture-induced effects on heat diffusion are neglected, but the exact continuity in moisture flux at layer interfaces holds unlike existing analytical studies. An analytical solution to the diffusion problem is obtained by extending a previously derived solution for double-layered plates. Hygrothermal stresses are evaluated by superposition of stresses due to the applied temperature and moisture fields. First, numerical calculations are performed for a double-layered plate to investigate the influence of moisture-flux continuity at the layer interface on hygrothermal stress distribution. Second, the obtained solutions are applied to the hygrothermoelastic problem of a functionally graded material-like (FGM-like) non-homogeneous plate whose physical properties vary along the thickness direction. Numerical results show that the use of inappropriately simplified continuity conditions for moisture flux may cause a significant error in evaluating the transient hygrothermal stresses in a layered body. Moreover, it is demonstrated that a gradual change in the material composition of FGM-like non-homogeneous plates induces considerable hygrothermal stress relaxation.     

Fundamental solutions for the generalised plane strain theory

This paper presents some fundamental solutions of the three-dimensional stress distribution pertaining to a point force and an edge dislocation in an infinite plate of arbitrary thickness. These solutions are obtained using the generalised plane strain theory, which assumes that the through-the-thickness extensional strain is uniform in the thickness direction. These solutions recover, as special cases, the plane-strain solutions of the classical theory of elasticity close to the source and the plane-stress solution at large distance away from the source. Using these new solutions, the problem of a through-crack in an infinite plate of arbitrary thickness has been solved analytically.     

Dynamic stresses around two cracks placed symmetrically to a large crack

Dynamic stresses around three cracks in an infinite elastic plate have been solved. Two cracks, which are small and equal, are situated ahead of a large crack so as to allow for geometrical symmetry. Time-harmonic normal traction acts on each surface of these cracks. To solve the problem, two solutions are combined. One of them is a solution for a crack in an infinite plate and another is that for two collinear cracks in an infinite plate. The Schmidt method is used to satisfy the boundary conditions on the cracks' surfaces with use of the combined solutions. Stress intensity factors are calculated numerically for some of these crack configurations.