A numerical analysis of time-dependent two-dimensional magnetic fields

The nonlinear diffusion equation as applied to two-dimensional time-dependent magnetic fields is solved with a finite element algorithm. This algorithm permits the analysis of problems possessing complex geometries, induced eddy currents, permanent magnets, and nonperiodic excitation currents. The numerical procedure utilizes implicit time stepping with an iterative scheme to solve the resulting set of equations. Two examples of applications of this program are presented.     

Transverse electric and transverse magnetic pulsed-beam decomposition of time-dependent aperture fields

The present contribution is concerned with applying beam-type expansion to a planar aperture time-dependent (TD) electromagnetic field in which the propagating elements, the electromagnetic pulsed-beams, are a priori decomposed into transverse electric (TE) and transverse magnetic (TM) field polarizations. The propagating field is described as a discrete superposition of tilted, shifted, and delayed TE and TM electromagnetic pulsed-beam propagators over the frame spectral lattice. These waveobjects are evaluated by using TD plane-wave spectral representations. Explicit asymptotic expressions for electromagnetic isodiffracting pulsed-quadratic beam propagators are presented, as well as a numerical example.     

MHD flow in conducting circular expansions with strong transverse magnetic fields

This paper treats the steady, inertialess flow of an incompressible, electrically conducting fluid through perfectly conducting, variable-area ducts of circular cross section in the presence of strong transverse magnetic fields. The problem is of fundamental importance in the design of liquid-lithium cooling systems for fusion reactors, of liquid-metal MHD generators and of MHD machinery in metallurgy. First we find that, if a straight pipe of radius r is joined to an expansion or contraction, then the disturbance of the fully developed flow in the pipe dies out like exp ($\text{? 12.16¦x¦r}{}^{\mathrm{?1}}$), where x is distance from the join. Next we consider the flow in conical expansions with end effects neglected; and find that the flow becomes concentrated near the plane of symmetry as the divergence increases. Finally numerical schemes for determining the flow in more general expansions and contractions are outlined. Extension of the present analysis to non-circular sections is also discussed.     

多壁碳纳米管增强炭黑/聚丙烯导电复合材料导电行为

为了充分利用不同导电粒子的导电作用,在炭黑(CB)/聚丙烯(PP)导电复合体系中引入了多壁碳纳米管(CNTs)。研究发现：引入的CNTs分散在CB粒子间起到“桥梁”作用,使体系的导电性能得到明显改善,并且CB∶CNTs为19∶1时其协同导电效果最好,该复合体系出现逾渗现象,对应的导电填料体积分数明显降低。在导电填料总体积分数为4.76%时,少量CNTs的引入就可使复合体系的体积电阻率从109Ω·cm下降到105Ω·cm;同时少量的CNTs能明显抑制炭黑/聚丙烯导电复合材料的正温度效应(PTC),使PTC强度从6.10降低到1.48,PTC转变峰温度从166℃升高到174℃。少量的 CNTs可以使PP的结晶温度提高12℃,对PP结晶的成核作用比CB更加明显。复合体系力学性能随导电填料体积分数增加而明显降低,但因为体积电阻率一定时CB-CNTs/PP体系所需导电填料体积分数较CB/PP体系明显降低,因此少量CNTs的引入能够使复合体系的力学性能得到更大程度的保持。     

Time-frequency distributions of time-dependent hydrophysical processes and fields

Algorithms are analyzed and implemented for estimating the spectra of complex, multicomponent, time-dependent signals on the basis of time-frequency distributions (TFDs) of the pseudo-Wigner and Cohen types and distributions with a test function of the chirp type. The resolution and noise-immunity characteristics are estimated, along with the methodological errors of reconstruction of the instantaneous-frequency paths and amplitude nonstationarity of multicomponent signals for TFD algorithms.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 30–37, January, 1994.     

Applications of multiterminal representations to magnetic fields

A graph-theoretic approach to the formulation of discrete models of magnetic field problems with special emphasis on the application of multiterminal representations is presented. The discrete model is obtained directly from the physics of the field, thus obviating the need for the usual intermediate analytical formulation (partial differential equation, energy functional, etc.). Further, the discrete models of large sparsely connected subregions (elements) may be obtained from the discrete model in terms of multiterminal representations. These models are then used to solve the entire field while providing both conceptual and computational advantages.     

Dynamic response of a circular plate to a moving load

An analytical series solution for the dynamic response of a circular, thin, isotropic plate under a moving singular load is given. The mass of the agent applying the force is ignored. The response of the plate is computed in two example cases, to illustrate the solution, including the force moving on a straight line through the plate, and also for a load moving on a circular trajectory on the plate.     

采用导磁片改造磁控装置提高靶材利用率

通过对真空溅镀生产线靶材的刻蚀情况观测,发现所有产线均存在不同程度的靶面刻蚀不均现象,而3号线尤为突出,其端部刻蚀深度相对于其它部位刻蚀深度较深,导致靶材使用寿命短,利用率低.采用高磁导率材料电工纯铁DT4制作导磁片装入磁控装置,试验结果表明,降低了靶面刻蚀不均匀度,靶材利用率提高至少10％.     

Dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting infinite plate subjected to an arbitrary variation of magnetic field

Summary In the present paper, dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting infinite plate subjected to an arbitrary variation of the magnetic field are investigated. It is assumed that a magnetic field defined by an arbitrary function of time acts on both side surfaces of the infinite plate in the direction parallel to its surfaces. Fundamental equations of one-dimensional electromagnetic, temperature and elastic fields are formulated. Then, solutions of magnetic field, eddy current, temperature change and both dynamic solutions and quasi-static ones of stresses and deformations in the infinite plate are derived analytically. The solutions of stresses are determined to be sums of thermal stress caused by eddy current loss and magnetic stress caused by Lorentz force. For the case that the arbitrary function is given by the sine function, the dynamic and quasi-static behaviors of the stresses are examined by numerical calculations.     

Dynamical magnetothermoelastic problem in circular cylinders—II: Thermal,magnetic and elastic fields

On using the approximate small-parameter method, the linearized magnetothermoelastic equations[1] are solved. The analysis of the magnetic, thermal and elastic fields, and magnetothermoelastic waves, based on the solutions of above equations, is presented.     

Using an inverter to measure magnetic fields

A toroidal core may be used with an inverter circuit to measure magnetic fields in the .8 to 80,000 A/m (.01 to 1.0 KOe) range. The sensor core may be the inverter transformer itself or may be coupled to a nonsaturating inverter transformer. The sensor is most sensitive to fields parallel to the plane of the sensor and the sensitivity is greatest for a core biased to near saturation. An empirical expression for the demagnetization factor is used in calculating the ambient field required to saturate the sensor core, making it possible to calculate the range of fields for which a given core could be used as a sensor.     

Adaptive control of magnetic levitation system subject to external disturbances

In this paper, an adaptive controller is designed for a magnetic levitation system to cope with internal time-varying uncertainties and external disturbances. Since, in experimental studies, in experiments involving the traditional magnetic levitation design it is not easy to realize external disturbances to the system, a horizontal configuration is constructed in this paper. To facilitate the analysis and controller design, the equation of motion is derived in detail. Due to the asymmetric nature of the magnetic loop, there is a big challenge in the controller design process. In addition, since some of the uncertainties enter the system in a mismatched manner, few control strategies are feasible. A multiple-surface sliding control law is proposed with the function approximation technique to stabilize the closed loop system under various uncertainties and disturbances. A rigorous mathematical proof is given to verify the feasibility of the design. Experimental studies are conducted including comparisons with conventional PID design to clarify the performance of the proposed controller.     

Viscoplastic response of a circular plate to an underwater explosion shock

Summary Viscoplastic response of a fully-clamped circular plate to an underwater explosion shock is studied in this paper. Strain-rate effect is included in the response. A fluid-structure interaction model is introduced, which is characterized by two stages: In the early stage, only the shock wave in water is considered, and the motion of structure is neglected. In the second stage, the wave propagation in structure and fluid is disregarded, and only long-term fluid force (added mass) and long-term structural force (membrane stress) are considered. Based on this model, the equation of motion of a fully-clamped circular plate is established, the solutions of which are compared with two experiments. The calculated maximum plastic deformations from present model are close to the observed values. The dependence of maximum plastic deformation on charge weight, plate radius and material property is also discussed.     

Synthesis of magnetic fields

The paper deals with some problems of magnetic fields synthesis, depending on determination of the current density distribution, which generates the required magnetic field in the investigated region. Such problems can be reduced to the linear, or nonlinear Fredholm integral equations of the first kind, or to the set of these equations. Fredholm integral equation of the first kind belongs to the class of the ill-posed problems, and for its solving the method of regularisation has been used. In the paper there are given some useful results of synthesis of magnetic fields in few practical configurations.     

Nonlinear dynamics of composite laminated cantilever rectangular plate subject to third-order piston aerodynamics

This paper presents the analysis of the nonlinear dynamics for a composite laminated cantilever rectangular plate subjected to the supersonic gas flows and the in-plane excitations. The aerodynamic pressure is modeled by using the third-order piston theory. Based on Reddy’s third-order plate theory and the von Kármán-type equation for the geometric nonlinearity, the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate under combined aerodynamic pressure and in-plane excitation are derived by using Hamilton’s principle. The Galerkin’s approach is used to transform the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate to a two-degree-of-freedom nonlinear system under combined external and parametric excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation of the non-automatic nonlinear system. The case of 1:2 internal resonance and primary parametric resonance is taken into account. A numerical method is utilized to study the bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The frequency–response curves, bifurcation diagram, phase portrait and frequency spectra are obtained to analyze the nonlinear dynamic behavior of the composite laminated cantilever rectangular plate, which includes the periodic and chaotic motions.