A double coil method for simultaneously measuring the resistivity,permeability, and thickness of a moving metal sheet

A method to determine the resistivity, permeability and thickness of moving magnetic sheets is described. The parameters of a sample sheet inserted between two coils facing each other are determined by measuring the impedance of the two coils at two different frequencies. To compare the experimental data with theoretical values, the difference in the impedance of the coils between two cases is used: when the current passes through the coils in the same direction, and in opposite directions. The method was tested by measuring the resistivity, permeability and thickness of nickel and iron sheets, 1 mm thick, moving at velocities varying from 0 to 6 m/s. It was possible to accurately determine the resistivity, thickness, and permeability within 10%, 10%, and 20%, respectively, at frequencies of 400 and 800 Hz     

19英寸显示器110°矩形偏转线圈的设计

设计了用于 19英寸显示器、具有 110°偏转角的一种新型的矩形偏转线圈。这种矩形偏转线圈可节省偏转能量 ,提高偏转灵敏度。由于采用了一种简单新颖的设计方法 ,不仅避免了复杂的三维电磁场计算和优化 ,而且还可利用现有的旋转对称偏转线圈的计算结果 ,因此可节省大量的时间。文中给出了相应的设计结果。结果表明 ,采用该方法所设计的新型矩形偏转线圈具有很好的偏转性能 ,进一步证明了所用方法是一种行之有效的方法。该方法不仅可用于非旋转对称矩形线圈的设计 ,而且还可用于其它的电磁场问题。     

A moving crack in a rectangular magnetoelectroelastic body

The singular stress, electric fields and magnetic fields in a rectangular magnetoelectroelastic body containing a moving crack under longitudinal shear are obtained. Fourier transforms and Fourier sine series are used to reduce the mixed boundary value problems of the crack, which is assumed to be permeable or impermeable, to dual integral equations, and then expressed in terms of Fredholm integral equations of the second kind. Results show that the stress intensity factors are influenced by the material constants, the geometry size ratio and the velocity of the crack, and the propagation of the crack possibly brings about branching phenomena.     

Deflection of a floating sea ice sheet induced by a moving load

A large number of time-deflection curves was obtained from a field experiment carried out on the sea ice sheet at Lake Saroma, Hokkaido, Japan, using a Skidoo snowmobile as a moving load with the test speed changed from 0 to 14.2 m/s. The thickness of the ice sheet was 0.17–0.18 m, the ice temperature was ?2.5 to ?4°C at the surface, and the water depth was 6.8 m beneath the ice sheet. The experimental results indicated the existence of a critical speed u_c and its value was estimated to be 5.8 m/s. At speed above it two ice waves were generated, one ahead of and the other behind the vehicle. A variation of wavelength with vehicle speed was expressed by a modified dispersion relation for the flexural ice wave in a floating ice sheet. The ice deflection pattern was classified into five stages. At u_c the depression around the vehicle was maximal in depth and minimal in width. The center of the depression began to lag behind the vehicle even at fairly low speeds below u_c.     

Geometrically nonlinear rectangular simply supported plates subjected to a moving mass

The dynamic deformation of a geometrically nonlinear rectangular simply supported plate under a moving lumped mass is evaluated using mode expansion method. The governing differential equations of motion for a largely deformable rectangular plate are derived using Lagrange method based on appropriate in and out-of-plane spatial functions which satisfy the proposed boundary conditions. Although the proposed procedure is applicable for any arbitrary edge boundary conditions, only the simply supported plates are addressed in the present work. On the other hand, all inertial components of the moving mass are included in the derivation of the equations of motion. A numerical example is used to study the dynamic behavior of the plate, considering large deformations. The obtained results indicate that ignoring the geometric nonlinearity in determining the vertical deformations of plates under the effect of moving masses, especially those of considerable weight and velocity, results in excessively large linear amplitudes leading to an unfavorable conservative structural design.     

The solution of a rectangular orthotropic sheet with a central crack under anti-plane shear

Making use of the basic theorem of the Fourier transform and series, the solution of the stress intensity factor of a rectangular orthotropic plate containing a central crack under anti-plane shear, is obtained in this study. The result to the mixed boundary value problem is expressed in terms of a Fredholm integral equation of the second kind. It is easily proved that the problem of a strip with a central crack of mode III, are the special cases of the solution in this article.     

A stress concentration due to edge damage in a rectangular boron-epoxy sheet

The stress field in a square sheet of epoxy-boron composite with damaged fibers is determined for the case of applied uniform normal stress longitudinal to the fibers. The damage model assumes that damaged fibers are exactly as effective as the matrix and that the distribution of undamaged fibers can be given by polynomial. A Ritz solution for the displacements is obtained and used to investigate the stresses. A stress concentration is found and described. The energy release rate curve for a family of progressive damage configurations is exhibited.     

A central crack of mode III in a rectangular sheet with fixed edges

This paper discusses the general solution, by use of the Fourier transform and Fourier series, of the stress intensity factor in a rectangular sheet containing a central crack of mode III, where its boundary is constrained, but its crack surface is subjected to an arbitrary anti-plane load. As examples of numerical computing, consider three circumstances: (1) the boundary parallel to a central crack is fixed; (2) the boundary perpendicular to a central crack is fixed; (3) all of the boundaries around a central crack are fixed but the crack surface is subjected to a constant load.En faisant appel à une transformation de Fourier et aux séries de Fourier, on discute dans cet article de la solution générale au facteur d'intensité de contraintes existant dans une tôle rectangulaire comportant une fissure centrale de mode III, lorsque les bords sont fixés mais que la surface de la fissure est soumise à une charge antiplanaire arbitraire. Comme exemple de calcul numérique, on envisage trois cas distincts:

The dynamical problem of a rectangular stamp moving on an elastic half plane

Summary In this work, the stresses under a rectangular rigid stamp moving on an elastic half plane are calculated. The boundary value problem has been formulated in the form of a singular integral equation whose unknown function is the stress distribution under the stamp. The solutions of the equation have been compared for the cases of absence or presence of friction and for the cases of motion or rest. The work is an extension of Muskhelishvili's results and differs numerically from these ones only when the speed of the stamp is comparable with the shear wave speed.     

Three-dimensional waves beneath an ice sheet due to a steadily moving pressure

Solutions of the nonlinear water wave equations under an ice sheet are computed using a boundary integral equation method. The ice sheet is modelled as a thin elastic plate and the fluid equations are nonlinear. Depending on the velocity of the moving disturbance generating the flow, different types of responses of the floating ice sheet are discussed.     

Integral analysis of a magnetic field for an arbitrary geometry coil with rectangular cross section

The integral method can effectively analyze magnetic fields, but the traditional integral method can analyze only coils with regular geometries. Therefore, a new integral method was developed to calculate the three-dimensional (3-D) magnetic field created by an arbitrary geometry coil with a rectangular cross section using the local coordinate method and a 3-D coordinate transformation. However, when the field points are on the surface of the coil or the basic segment is the right angle trapezoidal prism, singularities occur that make the numerical analysis of the magnetic field more difficult. Thus, we present here some mathematical methods to eliminate the singularities to allow accurate numerical analysis of the magnetic field. We validate the integral method by comparing it with the analytical solutions for regular geometry coils.     

Solution of a rectangular sheet containing a central crack propagating at constant velocity under antiplane shear

Making use of the Fourier transform and Fourier series, the dynamic stress intensity factor of a rectangular sheet with a central crack moving at a constant velocity under antiplane shear is obtained. It is also proved that the solutions of a strip with a central crack propagating at constant velocity for Mode III are the special cases of the solution in the present paper.     

平行导线间轴向运动导电梁主-内联合共振EI北大核心CSCD

研究轴向运动导电梁在平行导线产生的磁场环境中的主-内联合共振问题。基于电磁场基本理论和哈密顿原理,导出轴向运动梁在外激励和磁场共同作用下的非线性振动方程。针对一端夹支一端铰支的导电梁,采用多尺度法求解方程,得到非线性方程的近似解析解和幅频响应方程,并对稳态解的稳定性进行了分析。通过算例,得到系统前两阶幅值随频率调谐参数、外激励力、轴向速度、电流强度等参数的变化规律。结果表明:系统发生主-内联合共振时一阶和二阶响应都被激发,且存在不同的多解区域;一阶和二阶幅值的稳态解个数在几个多解区域同步变化,其个数取决于外激励力、运动速度和电流强度值。     

障板上矩形薄板在浅水环境中的振动及声辐射解析分析

通过推导得到浅水环境中矩形板声辐射阻抗矩阵的解析表达,进一步结合振动假设模态方法及辐射表面单元辐射器思想求解浅水环境中矩形板的振动响应,分析水深对矩形板模态附加质量的影响,给出矩形板模态附加质量随水深的变化情况,得到波导模态的激发对附加质量的影响,并通过对辐射抗矩阵的特征分析得到附加质量在板上分布的主要模式;进一步结合声辐射模态辐射效率,分析水深变化对矩形板振动响应峰值及远场声辐射的影响,分析结果表明:水深度变化对振动响应峰值及声辐射功率的影响与第1阶声辐射模态的辐射效率随深度的变化具有一致性。     

Electromagnetic field solution for a coil of arbitrary shape moving relative to a set of ferromagnetic layers

A general method is described for solving the electromagnetic field problem associated with a coil of arbitrary shape moving above a number of planar ferromagnetic layers. It is shown that power and the 3-axis forces may be determined using a Fourier transform technique, together with a transmission line analogue. If only power and the 3-axis forces are required, and not the actual field components, then the use of the inverse Fourier transforms can be obviated by utilising the Parseval identity. The method is illustrated with a simple example.     

A finite rectangular sheet with a pair of edge cracks excited by a normal anti-plane shear wave

With the aid of the basic theorem of the Fourier cosine transform and Fourier sine series, the general solution of the dynamic stress intensity factor of a finite rectangular plate containing a pair of edge cracks excited by a normal anti-plane shear wave is found in the present paper. We can easily verify that the problems of a strip with a pair of edge cracks subjected to a normally incident anti-plane shear wave are the special cases of the general solution in this article. Especially, it is of interest to note that all of the solutions to the dynamic stress intensity factor of the subject are identical with those results in the paper by the author and Ma (Engng Fracture Mech. 30, 211–218, 1988).     

Forced convection over a continuous sheet with suction or injection moving in a flowing fluid

Summary The analysis of forced convection flow and heat transfer about a flat sheet with suction or injection continuously moving in a quiescent or flowing fluid has been carried out. This kind of problem finds applications in a variety of manufacturing processes such as hot rolling, extrusion of plastic sheets, continuous casting, and cooling of a metallic plate in a cooling bath. The governing differential equations are reduced to nonlinear ordinary differential equations by similarity transformations. These equations are solved numerically based on a finite difference algorithm. Representative velocity and temperature profiles within the boundary layer are presented at selected values of free stream velocity and injection parameter. The friction factor and Nusselt number are illustrated for a wide range of governing parameters. For the same injection parameter, Prandtl number, and normalized velocity difference |U _w–U |, higher values of the Nusselt number and friction factor result fromU _w>U than fromU _w<U . Also, an increase in the velocity ratioU /U _w results in an increase in the heat transfer rate, but a decrease in the friction factor. Furthermore, the heat transfer is enhanced due to increasing the values of the free stream velocity, the injection parameter, and Prandtl number; while it is reduced due to increasing the velocity difference.Nomenclature C _f friction factor, _w/(u_r ²/2) - F dimensionless stream function - F _w injection parameter - h local heat transfer coefficient - k thermal conductivity - Nu Nusselt number,hx/k - Pr Prandtl number, / - q _w wall heat flux - Re Reynolds number,u _rx/ - T temperature - T _w temperature at the fluid-sheet interface - T free stream temperature - U _w normalized velocity of the sheet,u _w/u_r - U normalized free stream velocity,u /u _r - u fluid velocity component inx-direction - u _r reference velocity, Eq. (8) - u _w velocity of the continuous sheet - u free stream velocity - v fluid velocity component iny-direction - v _w fluid velocity component iny-direction at the fluid-sheet interface - x streamwise coordinate - y cross-stream coordinate Greek symbols thermal diffusivity - boundary-layer thickness - dimensionless cross-stream coordinate - dimensionless temperature - kinematic viscosity - _w wall shear stress - stream function     

Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass

The governing differential equation of motion of a thin rectangular plate excited by a moving mass is considered. The moving mass is traversing on the plate’s surface at arbitrary trajectories. Eigenfunction expansion method is employed to solve the constitutive equation of motion for various boundary conditions. Approximate and exact expressions of the inertial effects are adopted for the problem formulation. In the approximate formulation, only the vertical acceleration component of the moving mass is considered while in the exact formulation all the convective acceleration components are included in the problem formulation as well. Parametric studies are carried out to investigate the effects of moving mass weight and velocity as well as its trajectory on the dynamic response of a simply supported plate. Rectilinear and orbiting paths are considered in the parametric studies as the two limiting cases for any possible moving mass trajectories. The obtained results demonstrate the importance of the moving mass inertia with respect to the moving load in most of the cases considered. In case of the rectilinear path, the approximate formulation underestimates the plate’s maximum response for mass velocities above certain limits. Furthermore, increasing the plate’s aspect ratio or the moving mass weight further reduces the range of velocities in which the approximate formulation can be used instead of the exact formulation. For the case of an orbiting path, the approximate formulation can capture the resonance excitation frequencies of the load reasonably well, even for large mass weight and radius of the orbiting mass. Considering small orbiting mass radii, the approximate formulation would provide an upper bound for the true response of the system for all orbiting frequencies as well as the mass weights. However, for larger radii, the maximum response values resulting from the approximate formulation are considerably lower than that of the exact one, especially for frequencies near to the resonance frequencies.