ROSSBY WAVES WITH THE CHANGE OF β

In this paper, the change of the Rossby parameter β with latitude is considered and the parameter is introduced and the β-plane approximation is extended into which includes the parameter γ. Such approximation closes further to practice especially in the high latitude regions. We give emphasis to the research of the effect of the parameter γ on the Rossby waves. It is seen that the effect of the parameter γ is remarkable in the high latitude regions. It can produce the Rossby waves caused by the pure parameter γ. And the phase speed formula of Rossby waves with the change of β is generally given, which is degenerated into the well-known Rossby formula when γ_0=0. The researches also point out that when the change of β is regarded, even if the basic current a is a linear function of y the unstable modes can also take place. However, the parameter γ usually plays a stable part in the Rossby waves and it does affect the longitudinal scale and the structure of constant phase lines (trough-ridge li     

THE PROPAGATION OF SOLITARY WAVES IN A NONLINEAR ELASTIC ROD

In this paper, the inverse scattering method is used to analyse strain solitary waves in a nonlinear elastic rod[1]. Properties of solitary waves and their influence on solid structures are discussed in detail. Some quantitative results are given.     

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

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

THE POSITIVE SOLUTION OF CLASSICAL GELFAND MODEL WITH COEFFICIENT THAT CHANGE SIGN

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｎｏｎｌｉｎｅａｒｔｗｏ＿ｐｏｉｎｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ (ＢＶＰ)(Ｐ) ｗ″(ｔ) +λｈ(ｔ)ｅｗ(ｔ) =0 ,　　 0 ≤ｔ≤ 1 ,ｗ( 0 ) =ｗ( 1 ) =0(λ>0 )ｈａｓｂｅｅｎｐｒｏｐｏｓｅｄｂｙＧｅｌｆａｎｄ[1]ｗｉｔｈｈ(ｔ) ≡ 1 ,ｔｈｉｓｉｓｔｈｅｒｅａｓｏｎｗｈｙｗｅｓａｙｔｈｅｐｒｏｂｌｅｍ (Ｐ)ｉｓａＧｅｌｆａｎｄｍｏｄｅｌ.Ｓｅｍｉｌｉｎｅａｒｐｒｏｂｌｅｍｓｏｆｔｈｉｓｔｙｐｅａｒｉｓｅｉｎａｖａｒｉｅｔｙｏｆｉｎｔｅｒｅｓｔｉｎｇａｐｐｌｉｃａｔｉｏ…     

NONLINEAR MODULATION OF THE INTERFACIAL WAVES OF TWO SUPERPOSED FLUIDS

The slow modulation of the interfacial capillary—gravitywaves of two superposed fluids with uniform depths and solidwalls is investigated by using the method of multiple scales.Theevolution of a packet is described by the nonlinear Schr(?)dingerequation,and then the stabilitg of the so-called Stokes wavetrain is discussed.     

THE INTERACTION OF PLANE SH－WAVES AND CIRCULAR CAVITY SURFACED WITH LINING IN ANISOTBOPIC MEDIA

ＴＨＥＩＮＴＥＲＡＣＴＩＯＮＯＦＰＬＡＮＥＳＨ－ＷＡＶＥＳＡＮＤＣＩＲＣＵＬＡＲＣＡＶＩＴＹＳＵＲＦＡＣＥＤＷＩＴＨＬＩＮＩＮＧＩＮＡＮＩＳＯＴＢＯＰＩＣＭＥＤＩＡＨａｎＦｅｎｇ（韩峰）Ｗｅｉｙａｎｇ（韦扬）ＬｉｕＤｉａｎｋｕｉ（刘殿魁）（Ｒｅｃｅｉ...     

SOLITARY WAVES AT THE INTERFACE OF A TWO-LAYER FLUID

In this paper,we discuss the solitary waves at the interface of a two-layer incompressible inviscid fluid confined by two horizontal rigidwalls,taking the effect of surface tension into account.First of all,we establish the basic equations suitable for the model considered,and hence derive the Korteweg-de Vries(KdV)equation satisfied bythe first-order elevation of the interface with the aid of the reduc-tive perturbation method under the approximation of weak dispersion.Itis found that the KdV solitary waves may be convex upward or downward.It depends on whether the signs of the coefficients α and μof the KdVequation are the same or not.Then we examine in detail two criticalcases,in which the nonlinear effect and the dispersion effect cannotbalance under the original approximation.Applying other appropriateapproximations,we obtain the modified KdV equation for the criticalcase of first kind(α=0),and conclude that solitary waves cannot existin the case considered as μ>0,but may still occur as μ<0,be     

NUMERICAL CALCULATION FOR THE COEFFICIENTS OF STOKES HARMONIC WAVES OF HIGH ORDEB

This paper has reformulated the mathematical model and houndary comditions in the semi-physical plan (χ,Ψ) by using W.H.Hti's method and suggested. two new ways of numerical calculation for the coefficients of Stokes harmonic waves of high order. By transforming the perturbation parameter ε into a new one we rejind Cokelet's results (1977) of phase speed and semi-waveheight expressions.     

ON THE NEW FORMS OF THE DIFFERENTIAL EQUATIONS OF THE SYSTEMS WITH HIGHER-ORDER NONHOLONOMIC CONSTRAINTS

In this paper,the new forms of the differential equations of motion of the systems withhigher-order nonholonomic constraints are obtained at first,and then the equivalencebetween these equations and the known equations is demonstrated.Finally an example isgiven to illustrate the application of our new equations.     

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 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 INTERACTION OF PLANE SH－WAVES AND NON－CIRCULAR CAVITY SURFACED WITH LINING IN ANISOTROPIC MEDIA

ＴＨＥＩＮＴＥＲＡＣＴＩＯＮＯＦＰＬＡＮＥＳＨ－ＷＡＶＥＳＡＮＤＮＯＮ－ＣＩＲＣＵＬＡＲＣＡＶＩＴＹＳＵＲＦＡＣＥＤＷＩＴＨＬＩＮＩＮＧＩＮＡＮＩＳＯＴＲＯＰＩＣＭＥＤＩＡＳｈｉＳｈｏｕｘｉａ（史守峡）；ＨａｎＦｅｎｇ（韩峰）；ＷａｎｇＺｈｅｎｑｉｎ...     

THE EXAMINATION OF TURBULENCE MODELING WITH LES DATABASE

ＴＨＥＥＸＡＭＩＮＡＴＩＯＮＯＦＴＵＲＢＵＬＥＮＣＥＭＯＤＥＬＩＮＧＷＩＴＨＬＥＳＤＡＴＡＢＡＳＥＳｕＭｉｎｇ－ｄｅ（苏铭德）（ＱｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ）Ｒ．Ｆｒｉｅｄｒｉｃｈ（ＬｅｈｒｓｉｒｈｌｆｕｒＦｌｕｉｄｓｍｅｃｈａ...     

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     

EFFECTS OF BOTTOM TOPOGRAPHY ON THE STANDING WAVES IN CIRCULAR BASINS

Standing waves in the cylinder basins with inhomogeneous bottom are considered inthis paper.We assume that the inviscid,incompressible fluid is in irrotational undulatorymotion.For convemence sake.cylindrical coordinates are chosen.The velocity potentials,the wave profiles and the modified frequencies are determined(to the third order)us powerseries in terms of the amplitude divided by the wavelength.Axisymmetrical analyticalsolutions are worked out.Whenω_1=0,the second order frequency are gained.As an example,we assume that cylinder bottom is an axisymmetrical paraboloid.Wefind out that the uneven bottom has influences on standing waves.In the end.we go intodetail on geometric factors.     

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.     

CHAOTIC BEHAVIOR OF THE MEASURE-PRESERVING MAPPINGS WITH ODD DIMENSION

In this paper,we consider the measure-preserving mapping C with dimension 3 which isalso the expansion of Henon mapping.Then we study the character of its fixed points andchaotic behavior.Next we offer a possibility that using the chaotic behavior of the lowerdimensional mappings brings about the higher.     

ON THE TORSION OF A CYLINDER WITH SEVERAL CRACKS

In this paper, based on paper, the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained. The probtem is reduced to solve a system of singular integral equations for the unknown dislocation density functions. Using the numerical method of the singular integral equations, the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders. Next, the cr(?)kcutting method is firstly extended to lve the torsion problem for a rectangular prism. The numerical results show that the method presented here is successful.     

THE ANALYSIS OF THE TRANSLATION-TORSION COUPLING EARTHQUAKE RESPONSES OF SINGLE-STORY ECCENTRIC FACTORY BUILDINGS WITH CONSIDERATION OF ROOF WHOLE-SPACE-WORK

In this paper, the translation-torsion coupling earthquake responses, of single-story ecoentric factory buildings with consideration of whole-space-work of the roof in 3-dimension non-inertia system are analysed and studied, and its calculation model has been established. And what is more, corresponding motion equations of earthquake responses have been derived, analysed and discussed. And it points out that under the action of the earthquake including rotational component, the principle of superposition of independent action for each earthquake component and mode-superposition method of dynamic responses analysis are already not applicable. In this paper, the translation-torsion coupling earthquake responses of sorne singlestory eccentric factory building are calculated and analysed by comparison methods without consideration of the earthquake torsional component. The conclusion is that when whole-space-work of the roof is considered, the results of calculation are more conformable to the actual earthq     

SOLVING THE VELOCITY PARAMETER OF THE 2-D WAVE INVERSE PROBLEMS WITH THE INTEGRATION-CHARACTERISTIC METHOD

For the 2-D wave inverse problems introduced from geophysical exploration,in thispaper,the author presents integration-characteristic method to solve the velocityparameter,and then applies it to common shotpoint model data,in noise-free case.Theaccuracy is quite good.