TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(φ)=(1+k)sinφ/ 1+kcosφ.     

THE TEMPERATURE ANALYSIS OF THE BILLET WITH PHASE CHANGE DURING CONTINUOUS CASTING

ＴＨＥＴＥＭＰＥＲＡＴＵＲＥＡＮＡＬＹＳＩＳＯＦＴＨＥＢＩＬＬＥＴＷＩＴＨＰＨＡＳＥＣＨＡＮＧＥＤＵＲＩＮＧＣＯＮＴＩＮＵＯＵＳＣＡＳＴＩＮＧＺｈａｏＸｉｎｇ－ｈｕａ（赵兴华），ＣｈｅｎｇＸｉａｏ－ｄｉ（陈小弟）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ...     

LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＳｏｌｉｔｏｎｉｓａｃｏｍｐｌｉｃａｔｅｄｍａｔｈｅｍａｔｉｃａｌｓｔｒｕｃｔｕｒｅｂａｓｅｄｏｎｔｈｅｎｏｎｌｉｎｅａｒｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎ[1].Ｔｈｏｕｇｈｓｏｌｉｔｏｎｓｔｒｕｃｔｕｒｅｓａｎｄｐｒｏｐｅｒｔｉｅｓｏｆｔｈｅ ( 1 + 1 )＿ｄｉｍｅｎｓｉｏｎａｌｎｏｎｌｉｎｅａｒｐｈｙｓｉｃａｌｍｏｄｅｌｓｈａｖｅｂｅｅｎｓｔｕｄｉｅｄｗｅｌｌａｎｄｕｎｄｅｒｓｔｏｏｄｆｕｒｔｈｅｒ,ｔｈｅｓｏｌｉｔｏｎｓｔｒｕｃｔｕｒｅｓｉｎｈｉｇｈｅｒｓｐａｔｉａｌｄｉ…     

THE LIE SYMMETRIES AND CONSERVED QUANTITIES OF VARIABLE-MASS NONHOLONOMIC SYSTEM OF NON-CHETAEV''''S TYPE IN PHASE SPACE

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｙｏｆｓｙｍｍｅｔｒｙａｎｄｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｉｓａｎｉｍｐｏｒｔａｎｔｔｏｐｉｃｉｎｍａｔｈｅｍａｔｉｃｓ,ｍｅｃｈａｎｉｃｓａｎｄｐｈｙｓｉｃｓ .ＴｈｅｍｏｄｅｒｎｔｈｅｏｒｉｅｓｏｆｓｙｍｍｅｔｒｙａｎｄｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｉｎｃｌｕｄｅＮｏｅｔｈｅｒｓｙｍｍｅｔｒｙｔｈｅｏｒｙａｎｄＬｉｅｓｙｍｍｅｔｒｙｔｈｅｏｒｙ .Ｉｎ 1979Ｍ .Ｌｕｔｚｋｙａｎｄｏ…     

ON THE STUDY OF THE INITIATION OF THE MICRO CRACK ON THE SMOOTH SURFACE OF POLYCRYSTALLINE

Crystallographic plasticity was applied to study the initiation of micro cracks on the smooth surface of polycrystalline under uniform applied stress. Even under the uniform external stress, due to the different crystallographic orientations of the grains in the polycrystalline, there is un-uniform stress distribution and the deformation is also not uniform. Under the fatigue loading, the roughness increases with the number of fatigue, and deformation will localize in some places, where micro cracks form.     

THE LINEARIZATION OF CERTAIN CLASS OF NONLINEAR SIMULTANEOUS EQUATION SET CONTAINING AMPLITUDE AND PHASE FREQUENCY CHARACTERISTICS AND APPLICATION

A class of complex function of rational fraction type G(jω)=[1 a_1jω a_2(jω)~2 … a_m(jω)~n]/[b_0 b_1jω b_2(jω)~2 … b_n(jω)~n ] is frequently used to describe the dyna-mical properties of systems.It is however quite difficult to es-tablish a mathematical model of this type on the basis of ampli-tude and phase frequency data collected from experiments conductedon the related physical system.Since the erection of mathematicalmodel G(jω)would involve the solution of a set of nonlinear si-multaneous equations|G(jω_i)|=g_i∠G (jω_i)=θ_i i=1, 2,…,r. with the unknown coefficients a_isand b_is(i=0,1,…,m,…,n)in G(jω).Up to now,these nonlinear equa-tions have been considered to be very difficult to solve directly.In spite of the fact there are special computer programmes in cer-tain software packages available to tackle this problem,it is byno means an easy task due to the complex procedures involved inpicking up a set of initial values that should be close enough tothe exact solutions.This paper     

THE EQUATIONS OF MOTION OF A SYSTEM UNDER THE ACTION OF THE IMPULSIVE CONSTRAINTS

In order to solve the problem of motion for the system withn degrees offreedom under the action of p impulsive constraints, we must solve the simultaneous equations consisting of n+p equations. In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for the cases of both the generalized coordinates and the quasi-coordinates. Thus there are only n-p equations of impact. Combining these equations with p impulsive constraint equations, we have simultaneous equations consisting of n equations. Therefore, only n equations are necessary to solve the problem of impact for the system subjected to impulsive constraints. The method proposed in this paper is simpler than ordinary methods.     

THE EFFECTS OF ROUGHNESS CHANGE ON THE SURFACE LAYER OF THE ATMOSPHERE (I)——THE VARIATIONS OF WIND SPEED AND SHEAR STRESS

A general four-layer structure linear theory for predicting the effects of arbitrarily distributed roughness change on the variations of wind speed and shear stress in the surface layer of 3D and 2D atmospheres was presented. The results derived by the theory were agreeable to the previous ones.     

THE EFFECTS OF ROUGHNESS CHANGE ON THE SURFACE LAYER OF THE ATMOSPHERE(Ⅰ)—THE VARIATIONS OF WIND SPEED AND SHEAR STRESS

A general four-layer structure linear theory for predicting the effects of arbitrarilydistributed roughness change on the variations of wind speed and shear stress in the surfacelayer of3D and2D atmospheres was presented.The results derived by the theory wereagreeable to the previous ones.     

THE NUMERICAL METHOD FOR ANALYSING THE TRANSIENT TEMPERATURE FIELD AND TRANSIENT PHASE TRANSFORMATION OF METAL MATERIALS IN HEAT TREATING

In this paper,the Kirchhoffs transformation is popularized to the nonlinear heat conduction problem which the heat conductivity can be expressd as a multinomial of temperature firstly,the boundary condition of heat conduction problem is determined by analytics.Secondly,the incubation peroid superposition and the linear combination law is employed to simulate the transient phasses transformation in the process of heat treatment of materials.That the begin time of phase transformation,the type of phase transformation and the amount of phase constitution is determined simply.Finally,the three-dimension Dual Reciprocity Boundary Element Method is usedto analysis the total process of various heat treatment of component,the results of numerical calculation of examples show that the method provided in this paper is effectivce.     

THE METHOD OF TRANSFORMATION OF THE BOUNDARIES FOR STRUCTURE THE ADMISSIBLE DISPLACEMENTS

In this paper the method of transformation of the boundaries for structure theadmissible displacements with various boundary conditions is presented What is called themethod of transformation of the boundaries is that. first we transform the actual systeminto the basic system and additional boundary forces and displacements on the basis of thesuperposition principle, then apply variational principles to the basic system,finally find thepermissible displacement of the actual system by means of the method of transformation ofthe series.In this paper, we also give mixed energy prinapies under Variation of boundaryconditions. The mixed energy principles as the potential and complementary energyprinciples under variation of boundary conditions are all the chief theoretical fundamentalof the method of transformation of the boundaries.Applying the method of transformation of the boundaries. we form the permissibledisplacements of rectangular plates of plane stress and bending problems with various edgeconditio     

THE RE－EXAMINATION OF DETERMINING THE COEFFICIENT OF THE AMPLITUDE EVOLUTION EQUATION IN THE NONLINEAR THEORY OF THE HYDRODYNAMIC STABILITY

ＴＨＥＲＥ－ＥＸＡＭＩＮＡＴＩＯＮＯＦＤＥＴＥＲＭＩＮＩＮＧＴＨＥＣＯＥＦＦＩＣＩＥＮＴＯＦＴＨＥＡＭＰＬＩＴＵＤＥＥＶＯＬＵＴＩＯＮＥＱＵＡＴＩＯＮＩＮＴＨＥＮＯＮＬＩＮＥＡＲＴＨＥＯＲＹＯＦＴＨＥＨＹＤＲＯＤＹＮＡＭＩＣＳＴＡＢＩＬＩＴＹＬｕｏＪ...     

THE VELOCITY OF THE COLLECTIVE MOTION OF SEDIMENTATION OF SAND AND CLAY

In this article.we shall discuss the velocity of the col-lective motion of sedimentation when the concentration ofclay particles is very high.we believe that the problemof the so-called velocity of the collective motion of sedi-mentation is not a real problem of sedimentation in physi-cal nature.but it is a problem of filtration in the porousmedium which is composed of colloidal clusters.That is tosay,those clusters consist of water and clay particles.Itis a problem of the water passing through the porous medium.Based upon this consideration.we put down the mathematicalexpression of the velocity of the collective motion of se-dimentation.In comparing with the theoretical curves withthe experimental data of the Institute of Hydraulic Research,of the Yellow River Conservancy Commission,we get congruousresults.     

COMPUTER SIMULATION OF THE MOTION OF THE BULLET BELT OF AIRPLANE GUN

ＣＯＭＰＵＴＥＲＳＩＭＵＬＡＴＩＯＮＯＦＴＨＥＭＯＴＩＯＮＯＦＴＨＥＢＵＬＬＥＴＢＥＬＴＯＦＡＩＲＰＬＡＮＥＧＵＮＺｈａｎｇＤｉｎｇｇｕｏ（章定国）（ＲｅｃｅｉｖｅｄＭａｒｃｈ１７，１９９５；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＷｕＲｕｉｆｅｎｇ）Ａｂｓｔｒ...     

PREDICTION OF THE VISCOELASTIC PROPERTIES OF THE EQUIVALENT PARTICLE FOR THE INTERCALATED MULTI-LAYER STACK OF NANOPLASTICS

The aim of this paper is to apply the asymptotic homogenization method to deter- mining analytically and numerically the transversely isotropic viscoelastic relaxation moduli of the equivalent particle for the intercalated multi-layer stack of intercalated type nanoplastics.A two-phase multilayered material containing n layers is considered.The matrix is assumed to be an isotropic viscoelastic standard linear body and the reinforcement is assumed to be an isotropic elastic body.Final explicit analytical formulae for the effective elastic moduli of the multilay- ered material are derived first;and then the correspondence principle is employed to obtain the homogenized relaxation moduli of the equivalent intercalated particle.A numerical example is given.Final explicit analytical formulae in the time domain derived here make it convenient to estimate the influence of all the particle parameters of micro-structural details on the effective properties of the equivalent intercalated particle.The results of this paper can also be applied to multi-layer composites.     

THE IMPROVEMENT OF THE GENERAL EXPRESSION FOR THE STRESS FUNCTION φ OF THE TWO-DIMENSIONAL PROBLEM

In this paper,it is pointed that the general expression for the stress functionφ_0 of theplane problem in polar coordinates is incomplete.The problems of the curved bar with anarbitrary distributive load at the boundries can’t be solved by this stress function.For thisreason,we suggest two new stress functions and put them into the general expression.Then,the problems of the curved bar applied with an arbitrary distributive load at r=a,bboundaries can be solved.This is a new stress function including geometric boundaryconstants.     

THE DESCRIPTION OF THE CHARACTERISTICS OF THE STRUCTURE AND THE QUANTITY IN FIXED PANSYSTEMS THEOREMS

Pansymmetry is the abstract of symetry, stability and other concepts in physics and so on. Fixed pansystems theorems portray a typical pansymmetry of systemic structure. The present paper complements and extends the Work in concerned in fixed pansystems theorems. It gives in finite case the structural character of fixed subsets; the criterion of existence of the least fixed subset, and the numbering formula of fixed subsets and minimal fixed subsets.     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE Ⅰ CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅱ)—THE ANALYSES OF THE STRESS STRUCTURE

Based on[1],the stress structures of the smooth region and shear lip of thespecimens have been investigated in the paper.The characteristics of the stress structure inthe smooth region have been found that the variable z can separated out;the stressesin the midsection can be obtained by the plane strain FEM results or HRR structuremodified by the stress triaxiality.The effects of load level and thickness on the stressstructure can be reflected by the distribution of CTOD along the thickness direction.The obtained expressions of the stresses are very simple and visualized.The analysesof the stress structure in the shear lip show that the stresses can be obtained bydifferent methods of interpolation to a certain precise degree.A new degree parameter of the plane strain state has been put forward andstudied.The parameter can reflect relatively well the variation of the kind andthickness of the specimen as well as the load level.The fracture parameter has alsobeen investigated to be sure that it can be obta     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(II)—THE ANALYSES OF THE STRESS STRUCTURE

Based on [1], the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper. The characteristics of the stress structure in the smooth region have been found that the variable z can separated out; the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality. The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction. The obtained expressions of the stresses are very simple and visualized. The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree. A new degree parameter of the plane strain state has been put forward and studied. The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level. The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.     

SOME THEOREMS FOR DETERMINING THE DEFINITENESS AND CHANGEABILITY OF SIGN OF FUNCTIONS AND THE APPLICATION TO THE CONDITIONAL STABILITY OF THE MOTION OF THE AXIS OF A SLEEPING TOP

This paper gives some theorems for determiningthe definiteness and changeabilitg of sign of func-tions as well as the application to the axis of asleeping top.The necessarg and sufficient condi-tion of the conditional stabilitg of the rotion isobtained.Which coincides With that.of the stabilitgof nutation angle and also with that of the stabili-ty of total variables in the equations of cotion.