SHIFT OF SHOCK POSITION FOR A CLASS OF NONLINEAR SINGULARLY PERTURBED PROBLEMS

Thenonlinearsingularlyperturbedproblemisaveryattentiveobjectofstudyintheinternationalacademiccircles[1].Recently ,manyscholarsstudiedagreatdealofwork .Forexample,Boh啨[2 ],ButuzovandSmurov[3],O’Malley ,Jr.[4 ],Butuzov ,NefedovandSchneider[5 ]andKelley[6 ]andsoon .TheauthorconsideredaclassofsingularlyperturbednonlinearboundaryvalueproblemsfortheordinarydifferentialequationinRefs .[7～ 1 0 ] ,reactiondiffusionequationsinRefs.[1 1～ 1 3 ] ,singularlyperturbedproblemswithnonlocalboundarycond…     

CAVITY FORMATION AT THE CENTER OF A SPHERE COMPOSED OF TWO COMPRESSIBLE HYPER-ELASTIC MATERIALS

IntroductionHorgan[1] reviewedthecavitatedbifurcationproblemforhyper_elasticmaterials,includinginhomogeneousandanisotropicmaterialsaswellashomogeneousandisotropicmaterials .Forincompressiblematerials,HorganandPence[2 ,3 ] examinedtheeffectofmaterialinhomogeneityontheformationandgrowthofvoidandobtainedananalyticsolutionofthecavitatedbifurcationproblemforasolidspherecomposedoftwoneo_Hookeanmaterials.Thebifurcationmayoccurnotonlytotherightbutalsototheleftforthecomposedsphere .Thestabilitiesofth…     

ANALYTICAL SOLUTION OF A SIMPLY SUPPORTED PIEZOELECTRIC BEAM SUBJECTED TO A UNIFORMLY DISTRIBUTED LOADING

IntroductionIntelligentstructureisakindofnewstructuremodelsandhasbeenreceivedmuchattentioninrecentyears.Usedaspiezoelectricsensorsandactuators,thiskindofintelligentstructureshasmanyadvantagessuchasthepromptnessofresponseandtheconvenienceforthesignalcontrol.Soitisfollowedwithinterestbothinthetheoreticalstudyandintheengineeringapplications[1].Forexample ,theresearchoffundamentalsolution[2 ,3]andellipsoidalinclusion[4 ]forthree_dimensionalpiezoelectricmaterialbyuseofFouriertransformation ;thestu…     

POST-BUCKLING OF A CANTILEVER ROD WITH VARIABLE CROSS_SECTIONS UNDER COMBINED LOAD

IntroductionSinceEuler[1] ,Lagrange[2 ] ,Love[3 ] etal.investigatedtheslenderrod ,asoneofthebasicstructuralstabilityproblems ,manyattentionshavebeenpaidtothepost_bucklingofelasticrodsforalongtime .Today ,flexiblerodshavebeenwidelyusedasspring ,linkages ,robot’sarms,largeantennasandsoon .Hence ,thestudiesofpost_bucklingofelasticrodshavewideengineeringandapplyingbackgroundsinrecentdays .Basedontheassumptionthattheaxiallineoftherodisinextensible ,Timoshenkoetal.[4] examinedthepost_bucklingofco…     

MODEL OF CENTRIFUGAL EFFECT AND ATTITUDE MANEUVER STABILITY OF A COUPLED RIGID-FLEXIBLE SYSTEM

IntroductionThedynamicandcontrolofcoupledrigid_flexiblesystemisaleading_edgeresearchsubjectthathasdrawnextensiveattentionfromtheacademiccommunityintheworld[1].TheresearchconductedbyKaneetal.in 1 987[2 ]suggestedthat,thetraditionalmodelapplyingstructuraldynamicsassumptionaboutelasticdeformationindiscriminately[3,4 ],ineffect,hasneglectedtheso_called“dynamicstiffening”effectresultedfromcoupledrigid_flexiblesystem .Therefore ,itisofparticularimportancetoresearchtheactionofcoupledrigid_flexibles…     

BENDING OF A CIRCULAR CYLINDER CONTAINING A CRACK

The sludy of bending of cracked circular cylinders is of more significance.The bendingof cylinders containing radical crack or cracks was discussed by refs.[1]-[4]and that ofconcentrically craked circular cylinders was studied by[5].Continuing[6]and usingcomplex variable methods in elasticity,this paper deals with the bending problems of acircular cylinder,containing an internal linear crack at any position under an acting forceperopendicular to the crack.The general forms of displacements stresses,and stress-intensity factors,expressed in terms of series,are obtained and to this bending problemswith small Ah are presented good approximate formulas for the stress-intebsity factorswhose variations with the center of the crack are analysed.Finally,the twist angle per unitlength and the center of bending for the radically cracked circular cylinder,one of whosecrack-tips is located at the origin,have been computed and the results are almost the sameas that calculated in[1].     

THE GLOBAL BIFURCATION STRUCTURE OF A KIND OF DIGIT MAPPING

The global structure of the mapping T_n:x→[x~2]_n,is studied.The symmetricunconnected substructures of T_2 is coincident with[1]by computer,but for n=3 thesymmetry of these substructures vanishes.As n is increasing,the global bifurcationstructure of T_n is shown.Finally,similar results for the mapping T_n,μ:x→[μx~2 ]_n are alsoproved.     

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO SOLVING THE PROBLEM OF A THIN CLAMPED CIRCULAR PLATE OF A VERY LARGE DEFLECTION

In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.     

QUALITATIVE STUDY OF CAVITATED BIFURCATION FOR A CLASS OF INCOMPRESSIBLE GENERALIZED NEO-HOOKEAN SPHERES

IntroductionIn 1 958,GentandLindleyobservedthephenomenonofsuddenvoidnucleationinsolidsexperimentallyintensioningahomogenousclose_grainedvulcanizedrubbercylinderforthefirsttime.ButthemathematicalmodelonvoidnucleationandgrowthhasnotbeendescribedasabifurcationproblembasedonthetheoryofnonlinearelasticmechanicsbyBall[1]until1 982 .Inrecentyears,manyinvestigationshavebeenmadeonthisaspect.Theproblemofcavitatedbifurcationforincompressibleisotropichyperelasticmaterialswithpower_lawtypehasbeeninvestig…     

INTERNAL RESONANT INTERACTIONS OF THREE FREE SURFACE-WAVES IN A CIRCULAR CYLINDRICAL BASIN

IntroductionTheproblemofwavesofliquidinabasinhasbeenusedasaphysicalmodelinstudiesoftidalwaves ,seicheinlakes,oceanwaves,sloshingoffluidinacontainer (inindustry) .Itisstillanareaofcurrentlyvigorousresearchduetoitstheoreticalsignificance.McGoldrick[1]provedthattherewasthesecond_orderresonantinteractionsamongcapillarygravitysurface_waves.Hasselmann[2 ]studiedthenonlinearinteractionsofeveryfrequencyspectrumcomponentincontinuousspectrum ,andhederivedaformulathatdescribedtheenergytransformationsamo…     

Internal wave generation by a fountain in a stratified fluid

The purpose of the study is the direct numerical and theoretical modeling of fountain dynamics in a fluid with density stratification in the form of a pycnocline. The fountain is formed as a vertical jet penetrates through the pycnocline. In numerical simulation the jet flow is initiated by means of preassigning a boundary condition in the form of an upward-directed laminar flow of a neutral-buoyancy fluid with an axisymmetric Gaussian velocity profile. The calculations show that at a Froude number Fr greater than a certain critical value the flow becomes unstable and the fountain executes self-oscillations accompanied by internal wave generation in the pycnocline. Depending on Fr, two self-oscillation modes can be distinguished. At fairly low Fr the fountain executes circular motion in the horizontal plane, in the vicinity of the center of jet, its shape remaining almost invariant. In this case, internal waves in the form of unwinding spirals are radiated. At fairly high Fr another mode predominates, when the fountain top chaotically “strays” in the vicinity of the center of the jet and, periodically breaking down, generates wave packets propagating toward the periphery of the computation domain. In both cases, the main peak in the frequency spectrum of the internal waves coincides with the fountain top oscillation frequency which monotonically decreases with increase in Fr. In numerical simulation the Fr-dependence of the fountain top oscillation amplitude is in good agreement with that predicted by the theoretical model of the concurrence of the interacting modes in the soft self-excitation regime.     

Internal wave radiation by a turbulent fountain in a stratified fluid

Large eddy simulation is applied to model a fountain in a density-stratified fluid. The fountain is formed, as a vertical turbulent jet penetrates through a pycnocline. The jet flow is initiated by the formulation of a boundary condition in the form of an upward neutral-buoyancy fluid flow with the Gaussian axisymmetric mean-velocity profile and a given fluctuation level. It is shown that at a Froude number Fr higher than a certain critical value the fountain executes self-oscillations accompanied by internal wave generation within the pycnocline. The predominant self-oscillation mode is axisymmetric, when the fountain top periodically breaks down generating internal wave packets traveling toward the periphery of the computation domain. The characteristic frequency of the internal waves coincides with that of the fountain top oscillations and monotonically decreases with increase in Fr. The Fr-dependence of the fountain top oscillation amplitude obtained in the numerical solution is in good agreement with the predictions of the theoretical Landau model for the instability mode in the soft self-excitation regime.     

两层流体中水波在垂直薄板上的反射与透射

研究在两层流体中表面波模态和内波模态的波浪与半潜式刚性垂直薄板 相互作用的问题. 基于特征函数展开理论，建立了两种模态入射波作用下，半潜式刚性垂直 薄板的反射与透射能量的计算方法，证明了对每一种模态的入射波，另一种模态波浪的反射 与透射能量是相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量，以及作用在其上的 水平波浪力进行了数值计算分析，表明在某个频率范围内，流体的分层效应对这些水动力 量的影响是不可忽视的. 特别地，当薄板的一端位于两层流体的内界面上时，两种模态波浪 的能量转化是最大的.     

旋涡与行进表面水波相互作用的实验研究

采用振动板式造波器在二维水槽中生成近似单色的行进表面水波，采用夹板式涡发生器生成稳定上浮的涡对，在Ｆｒｏｕｄｅ数约为０．５的条件下，得到了水下涡对与不同波长和振幅的行进表面水波相互作用时的干扰图象，以实验方法验证了理论分析和数值计算的结果，并为进一步研究旋涡与行进表面水波的相互作用提供了一种实验研究方法     

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave, also known as surface acoustic wave(SAW), solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.     

流体动力干扰对单排圆柱桩列波浪力的影响

多物体之间的流体动力干扰特性对超大型海洋结构物的设计和研究十分重要用波动源在截面周线上分布的方法，就垂直桩柱间三维流体动力干扰对波浪力的影响进行了系统的研究，桩柱的数目可达１００余根得到了柱间流体动力干扰力学机理的若干新的特性尤应指出的是，当桩柱根数超过某一数量后，桩柱上的受力表现出有规律的连续依赖性当柱数很大时，无论柱数是奇数还是偶数，中间大部分的桩柱都将表现出均匀的受力特征这些特性的发现对其他形式多体结构物流体动力干扰的研究也有重要的借鉴和指导意义     

A meshless numerical wave tank for simulation of nonlinear irregular waves in shallow water

Time domain simulation of the interaction between offshore structures and irregular waves in shallow water becomes a focus due to significant increase of liquefied natural gas (LNG) terminals. To obtain the time series of irregular waves in shallow water, a numerical wave tank is developed by using the meshless method for simulation of 2D nonlinear irregular waves propagating from deep water to shallow water. Using the fundamental solution of Laplace equation as the radial basis function (RBF) and locating the source points outside the computational domain, the problem of water wave propagation is solved by collocation of boundary points. In order to improve the computation stability, both the incident wave elevation and velocity potential are applied to the wave generation. A sponge damping layer combined with the Sommerfeld radiation condition is used on the radiation boundary. The present model is applied to simulate the propagation of regular and irregular waves. The numerical results are validated by analytical solutions and experimental data and good agreements are observed. Copyright © 2008 John Wiley & Sons, Ltd.     

波作用量守恒原理在波流相互作用中的应用

波和流相遇后，经过相互作用产生稳定的波流场．基于波作用量守恒原理，本文提出了解决Ｓｔｏｋｅｓ波与指数剖面流同向或反向相遇过程中波传播特性改变问题的五阶理论，给出了这种相互作用前后波参数间的关系和相应流场的变化，并与线性结果进行了比较．结果表明，当波流同向时，波变平缓；当波流反向时，波明显变陡．随着波流强度的增加，非线性的影响变得越来越明显，尤其当波同反向流相遇时，波幅显著增大，这时必须用非线性理论来考虑波流相互作用的影响     

A holographic interferometric study of shock wave focusing in a circular reflector

A holographic interferometric study was made of the focusing of reflected shock waves from a circular reflector. A diaphragmless shock tube was used for incident shock Mach numbers ranging from 1.03 to 1.74. Hence, the process of reflected shock wave focusing was quantitatively observed. It is found that a converging shock wave along the curved wall undergoes an unsteady evolution of mach reflection and its focusing is, therefore, subject to the evolution of the process of shock wave reflections. The collision of triple points terminates the focusing process at the geometrical focus. In order to interprete quantitatively these interferograms, a numerical simulation using an Eulerian solver combined with adaptive unstructured grids was carried out. It is found numerically that the highest density appears immediately after the triple point collision. This implies that the final stage of focusing is mainly determined by the interaction between shock waves and vortices. The interaction of finite strength shock waves, hence, prevents a curved shock wave from creating the infinite increase of density or pressure at a focal point which is otherwise predicted by the linear acoustic theory.     

Drag increment of internal waves generated by horizontally moving spheroid in supercritical regime

A theory on the drag increment of internal waves with a spheroid moving horizontally at a high velocity （or for large internal Froude number） in uniformly vertically stratified fluid （or ocean） is presented in the present paper. A surface source distribution is employed to model a hydrodynamic interaction between the spheroid and the stratified fluid. From theoretical results, it is shown that there exists an asymptote of zero-drag increment in supercritical regimes, where internal Froude numbers are larger than the critical internal Froude numbers. When the spheroid reduces to a sphere, the results in this paper is in good agreement with the previous theoretical and experimental results of the sphere.