任意阶次磁多极子场力线方程的解析表示

本文证明任意阶次磁多极子场力线方程总可以用有限形式解析地表示，并对偶极族和四极族磁多极子场力线的位形给予注记。

几种典型电力线的分析

利用力线方程，对几种典型的电力线方程进行求解，得出电力线图形。

基于Microcal Origin语言模拟典型静电场

利用Microcal Origin软件,对几种典型的电力线方程进行求解,得出电力线图形.

IMPROVEMENT OF MATRIX REPRESENTATION METHOD IN NORMAL FORM THEORY

In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.

振荡电偶极子电磁场的分布

本文由振荡电偶极子电磁场的力线方程出发讨论其场的分布。

A Precision-Positioning Method for a High-Acceleration Low-Load Mechanism Based on Optimal Spatial and Temporal Distribution of Inertial Energy

High-speed and precision positioning are fundamental requirements for high-acceleration low-load mechanisms in integrated circuit （IC） packaging equipment. In this paper, we derive the transient nonlinear dynamicresponse equations of high-acceleration mechanisms, which reveal that stiffness, frequency, damping, and driving frequency are the primary factors. Therefore, we propose a new structural optimization and velocity-planning method for the precision positioning of a high-acceleration mechanism based on optimal spatial and temporal distribution of inertial energy. For structural optimization, we first reviewed the commonly flexible multibody dynamic optimization using equivalent static loads method （ESLM）, and then we selected the modified ESLM for optimal spatial distribution of inertial energy; hence, not only the stiffness but also the inertia and frequency of the real modal shapes are considered. For velocity planning, we developed a new velocity-planning method based on nonlinear dynamic-response optimization with varying motion conditions. Our method was verified on a high-acceleration die bonder. The amplitude of residual vibration could be decreased by more than 20% via structural optimization and the positioning time could be reduced by more than 40% via asymmetric variable velocity planning. This method provides an effective theoretical support for the precision positioning of high-acceleration low-load mechanisms.

The First Integral Method to Study a Class of Reaction-Diffusion Equations

In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.

CALCULATION OF CONTACT STRESS OF PLASTIC GEARS

A calculation method of contact problem of plastic gears based on three parameter model of viscoelasticity material is presented. In this calculation method, the influence of temperature upon the property of plastics is considered and an iteration process of temperature-elasticity module-friction coefficient is proposed. From the rolling contact problem of two viscoelastic cylinders with parallel axis, a set of normal-tangential contact coupled integral equations is obtained. Through numerical treatment and normal-tangential iteration, the normal contact stress,tangential stress and contact width of plastic gears are acquired.

Using Symbolic Computation to Exactly Solve the Integrable Broer-Kaup Equations in （2＋1）-Dimensional Spaces

The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.

Forced oscillations with time-varying mesh stiffness and backlash in gear systems

A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error(DTE) were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.

Exact Solutions for a Higher-Order Nonlinear Schrodinger Equation in Atmospheric Dynamics

By giving prior assumptions on the form of the solutions, we succeed to find several exact solutions for a higher-order nonlinear Schroetinger equation derived from one important model in the study of atmospheric and ocean dynamical systems. Our analytical solutions include bright and dark solitary waves, and periodical solutions, which can be used to explain atmospheric phenomena.

Wave Interaction with Dual Circular Porous Plates

In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.

Nonlinear dynamics of flexible rotor system supported on fixed-tilting pad combination journal bearing

Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force of single-pad journal bearings is established. According to the structure of combination journal bearings, nonlinear oil film force of combination journal bearing is obtained by retrieval, interpolation and assembly techniques. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the nonlinear motions of the center of the rotor are calculated by the self-adaptive Runge-Kutta method and Poincar6 mapping with different rotational speeds. The numerical results show that the system performance is slightly better when the pivot ratio changes from 0.5 to 0.6, and reveals nonlinear phenomena of periodic, period-doubing, quasi-periodic motion, etc.

Dynamics of phase transformation of Cu-Ni-Si alloy with super-high strength and high conductivity during aging

The precipitation behaviors of the Cu-Ni-Si alloys during aging were studied by analyzing the variations of electric conductivity.The Avrami-equation of phase transformation kinetics and the Avrami-equation of electric conductivity during aging were established for Cu-Ni-Si alloys,on the basis of linear relationship between the electric conductivity and the volume fraction of precipitates,and the calculation results coincide well with the experiment ones.The transformation kinetics curves were established to characterize the aging process.The characteristics of precipitates in the supersaturated solid solution alloy aged at 723 K were established,and the results show that the precipitates areβ-Ni3Si andδ-Ni2Si phases.

Liquidus and phase equilibria in CaO-SiO2-5%MgO-20%Al2O3-TiO2 system

The single hot thermocouple technique （SHTT） and high temperature equilibrium technique were combined to investigate the phase diagram of the CaO-SiO2-5%MgO-20%AlzO3-TiO2 system. The 1300 ℃ to 1500 ℃ liquidus lines are calculated according to the thermodynamic equations based on the pseudo-melting temperatures measured by the single hot thermocouple technique. The phase equilibria relationships are experimentally determined at 1400 ℃ using the high temperature equilibria technique followed by X-ray fluorescence （XRF）, X-ray diffraction（XRD）, scanning electron microscopy （SEM） and energy dispersive X-ray spectroscopy （EDX） analysis. The liquid phase（L）, melilite solid solution phase （（C2MSz,C2AS）ss）, diopside phase（CMS2） and perovskite phase （CaO·TiO2） are found. Coupled with the liquidus lines and equilibria results, the phase diagram is constructed for the specified region of the CaO-SiO2-5%MgO-20%Al2O3-TiO2 system.

Three-Dimensional Numerical Investigation of the Separation Process in a Vortex Tube at Different Operating Conditions

Air separators provide safe, clean, and appropriate air flow to engines and are widely used in vehicles with large engines such as ships and submarines. In this operational study, the separation process in a Ranque-Hilsch vortex tube cleaning （cooling） system is investigated to analyze the impact of the operating gas type on the vortex tube performance; the operating gases used are air, nitrogen, oxygen, carbon dioxide and nitrogen dioxide. The computational fluid dynamic model used is equipped with a three-dimensional structure, and the steady-state condition is applied during computations. The standard k-c turbulence model is employed to resolve nonlinear flow equations, and various key parameters, such as hot and cold exhaust thermal drops, and power separation rates, are described numerically. The results show that nitrogen dioxide creates the greatest separation power out of all gases tested, and the numerical results are validated by good agreement with available experimental data. In addition, a comparison is made between the use of two different boundary conditions, the pressure-far-field and the pressure-outlet, when analyzing complex turbulent flows in the air separators. Results present a comprehensive and practical solution for use in future numerical studies.

Multi-domain modeling and simulation of proportional solenoid valve

A multi-domain nonlinear dynamic model of a proportional solenoid valve was presented.The electro-magnetic,mechanical and fluid subsystems of the valve were investigated,including their interactions.Governing equations of the valve were derived in the form of nonlinear state equations.By comparing the simulated and measured data,the simulation model is validated with a deviation less than 15%,which can be used for the structural design and control algorithm optimization of proportional solenoid valves.

Dynamic Analysis of Kineto-Elastic Beam System with Second-order Effect

Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in non-linear structural analysis,three-node beam elements are used to deduce shape functions and stiffness matrices in dynamic equations of flexible elements. Static condensation method was used to obtain the finial dynamic equations of three-node beam elements. According to geometrical relations of nodal displacements in concomitant and global coordinate system,dynamic equations of elements can be transformed to global coordinate system by concomitant coordinate method in order to build the global dynamic equations. Analyzed amplitude condition of flexible arm support of a port crane,the results show that second-order effect should be considered in kinetic-elastic analysis for heavy load machinery of big flexibility.

Some Notes of p-Moment Boundedness of Nonlinear Differential Equation with Pandom Impulses

A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.

Comparison of SCS-CN Determination Methodologies in a Heterogeneous Catchment

The aim of this study was to assess the runoff amount from a catchment characterized by diverse land uses by using the Soil Conservation Service Curve Number(SCS-CN) method based on Curve Number(CN) defined for dominant homogeneous elementary sub-regions.The calculations employed the SCS-CN method,involving the division of the catchment in two homogeneous parts and determining the runoff amount.The obtained results were compared with the results provided by three other CN determination methods,i.e.the Hawkins function,the kinetics equation,and a complementary error function peak.The catchment is located in a mountain dominated by forest land cover.Empirical CN-Precipitation(CN_(emp)-P) data pairs were analyzed using the mentioned methods,and the highest quality score was achieved from model 1.The results suggest that dividing a catchment into two homogeneous areas and determining their separate CN parameters,used later on to calculate the runoff by means of the presented approach,could be an alternative to the standard methods.The described method is relatively easy,and as it does not require an adoption of numerous parameters,and it can be employed for designing hydraulic facilities.