Zheng Xiaojing

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.

Applications of wavelet galerkin fem to bending of beam and plate structures

In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavalet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.

Attenuation of an electromagnetic wave by charged dust particles in a sandstorm.

We calculate the light scattering properties of the partially charged dust particles with the Mie theory for electromagnetic waves with different frequencies, and the attenuation coefficients of an electromagnetic wave propagating in a sandstorm are also calculated. The results show that the electric charges distributed on the sand surface have a significant effect on the attenuation of the electromagnetic wave, especially for a frequency lower than 40 GHz, and attenuation coefficients increase with the magnitude of charges carried by the dust particles (expressed by the charge-to-mass ratio in this paper). For the higher frequency electromagnetic wave, such as visible light, the effect of charges carried by sand particles on its attenuation is very little, which can be ignored.

A theoretical model of magnetoelastic bucking for soft ferromagnetic thin plates

As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Paos model, or the couple model, is checked by quantitative results.

A seminumerical method for buckling of sector plates

A semianalytical-seminumerical method of solution is presented in this paper for the buckling problem of simply supported sector plates subjected to in-plane pressure along the straight edges. A set of analytical solutions of prebuckling in-plane stresses are first suggested here for the plane-stress problem of sector plates. Based on the analytical solutions, the critical load of the out-of-plane buckling is derived using a seminumerical method. The basic functions in the angular direction are chosen as the eigenfunctions for the simply supported beam. The resulting ordinary differential equation is solved by a one-dimensional finite difference technique. Comparison of results was possible for the specific case when the sector plate approaches a rectangular plate, and the results are in excellent agreement with existing ones.

An analytical formula of the exact solution to von Kármán's equations of a circular plate under a concentrated load

Abstract It is extremely difficult to obtain an exact solution of the non-linear coupled von Karmans equations in large deflection problems of a circular plate. So far only a few exact solutions have been investigated but no strict proof of convergence has been presented. In this paper, we first reduce von Karmans equations to be equivalent to integral equations which are non-linear, coupled and singular. The sequences of continuous functions with general form are then constructed using an iterative technique. Based on the sequences being uniformly convergent, an exact solution of von Karmans equations related to the large deflection problem of circular plates subjected to a concentrated load at the center is obtained.

Grain Size Effect on Electrical Conductivity and Giant Magnetoresistance of Bulk Magnetic Polycrystals

By solving the Boltzmann transport equation and considering the spin-dependent grain boundary scattering, the distribution of electrons in grains and the electrical transport properties in the applied magnetic field are studied. With regard to the dominant influence of grain boundary scattering which is taken as a boundary condition for the electrical transport, the grain size-dependent electrical conductivity is investigated. In addition, the reorientation of the relative magnetization between grains brings the change of the electron spin when the magnetonanocrystalline material is subjected to the magnetic field, resulting in the remarkable giant magnetoresistance effect.

Effect of thermal diffusion and electrostatic force on evolution of wind-blown sand flow

A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow. An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow, saltating grains, and a kind of electrostatic force exerted on the grains are considered in this theoretical model. The numerical results show that the effect of the thermal diffusion on the evolution process of wind-bown grain flow is quite obvious and very similar to the effect of the electrostatic force on the evolution. Not only the time for the entire system to reach a steady state (called the duration time), the transport rate of grains, the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow. An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow, saltating grains, and a kind of electrostatic force exerted on the grains are considered in this theoretical model. The numerical results show that the effect of the thermal diffusion on the evolution process of wind-bown grain flow is quite obvious and very similar to the effect of the electrostatic force on the evolution. Not only the time for the entire system to reach a steady state (called the duration time), the transport rate of grains, the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.

On some properties and calculation of the exact solution to von Kármán's equations of circular plates under a concentrated load

Abstract In this paper, we prove some properties of the exact solution obtained in our earlier paper for large deflection of a circular plate under a concentrated load. Using Newtons method, we also solve for the unknown constants Aij and Bij in the formula of an exact solution. Finally, we use the exact solution to check the accuracy of Chiens perturbation solution.

Magnetic charge model for 3D MMM signals

Stress concentration is a major cause of metal structure failures. Based on the metal magnetic memory (MMM) technique, detailed information of stress concentration or defects on ferromagnetic materials can be obtained from the changed magnetic signals. The magnetic charge model of MMM signal is described, and simulations based on this model are performed for a sample with stress-concentration zone or a long elliptical defect. Some basic characteristics produced by present model are coincident with existed experimental measurements. The agreements between simulations and experimental results confirm that the present magnetic charge model can be used as an MMM signal forward technique.