力学学报

EXPERIMENTAL INVESTIGATION ON DYNAMIC STIFFENING PHENOMENON

The study on ``dynamic stiffening'' is currently a focusin the field of flexible multibody system dynamics. A lot of valuableresearches have been done to account for ``dynamic stiffening'' viamathematical model and numerical simulation. However, to one'ssurprise, never had experimental investigations on this problem beenreported. This paper presents experimental investigation on ``dynamicstiffening'' phenomenon. The experiment is based on the prototype of arotating cantilever beam that is often used to discuss the effects of``dynamic stiffening''. The experimental investigation is conducted on asingle-axis air-bearing testbed. A theory model incorporating theeffects of both viscous damping and air drag force is also developedfor the purpose of comparison with experimental results. The phenomenonof ``dynamic stiffening'' is verified by the results of experiment. Thevalidation of the proposed model is confirmed by the experiment, too.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2002-122

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In the conventional boundary element method, in order toobtain the last algebraic equation system a large number of integralsmust be calculated numerically on all boundary elements and internalcells so that a large amount of computing time is needed. If we canform similar boundary elements on the boundary and obtain the relationof the matrices on the similar boundary elements, it is not needed toobtain the matrices on all elements by numerical integrals, then agreat amount of numerical integrals will be decreased. In this paper,similar boundary element method (SBEM) for elastodynamic problems isdiscussed in detail. Similar boundary elements are classified and theirproperties are discussed. The interpolation method to obtain thematrices on the similar boundary elements is presented and the formulaeof the method are obtained. In similar boundary element method, theboundary is represented with some sub-domains on which the boundaryelements are similar. Then on a sub-domain of the boundary we only needto compute the matrices on a few boundary elements by numericalintegrals, and the ones on all other boundary elements can be obtainedby the interpolation method. Then superimposing the matrices on allboundary elements the coefficient matrix of the last algebraic equationsystem can be obtained. Comparing with the conventional boundaryelement method that the matrices on all boundary elements are obtainedindependently by numerical integrals, similar boundary element methodcan decrease the computing time to a great extent, and the solution isin total agreement with the one from the conventional boundary elementmethod. To obtain the singular stress at the tip of a dynamic crack,infinite similar boundary element method (ISBEM) is presented. In themethod the similar boundary element sub-domain at the tip of the crackcontains infinite similar boundary elements. From infinite similarboundary element method, the singular stress at the tip of a crack canbe obtained directly, but the singular boundary element is not neededand the degree of singular stress is not assumed. For some materialsthat we do not know the degree of singular stress at the tip of a crack,infinite similar boundary element method can be applied better than theconventional boundary element method does. In this method the numbersof boundary elements and nodes are infinite, so an infinite orderlinear algebraic equation system is formed, and then the numericalmethod for this infinite order system is discussed. For a problem withan irregular domain, we can use the curvilinear coordinate system onthe boundary of the domain, and then similar boundary element methodand infinite similar boundary element method presented in this papercan be applied too. Similar boundary element method can be applied toother problems which can be solved with the conventional boundaryelement method, and infinite similar boundary element method can beapplied to other crack problems.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2002-125

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PERTURBATIONAL FINITE VOLUME METHOD FOR CONVECTIVE DIFFUSION EQUATION AND DISCUSSION

A perturbational finite volume (PFV) method for the convectivediffusion equation is presented in this paper. PFV method uses first-orderupwind scheme as its starting point, the mass fluxes of the cell faces aremodified by a numerical-value perturbation technique i.e. the mass fluxesare expanded into power series of the grid spacing and the coefficients ofthe power series are determined withthe aid of the conservation equation itself. The resulting formulae of theabove perturbation operation are higher-order upwind and central PFVschemes. They include the second-, third-, and fourth-order upwind PFVschemes as well as the second- and fourth-order central PFV schemes.The properties of PFV schemes are discussed and proved.The second-, third- and fourth-order upwind PFV schemes satisfy theconvective boundedness criteria, they do not produce oscillatorysolutions, expecially their numerical diffusions are much smaller thanthose of the first-order upwind scheme. The central PFV schemes withsecond- and fourth-order accuracy are positive grid-centered FV ones forany values of the grid Peclet numbers and then are more better than thenormal second-order central FV scheme.Two numerical examples (including a lid-driven cavity flow and problem ofscalar quantity transport in the one-dimensional flow) are computed toillustrate excellent behaviors of PFV schemes. In addition, a conceptional comparison of PFV scheme is also given with the perturbational finite difference scheme, multinodes and compact schemes.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2002-219

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ON TANGENTIAL INTERACTION BETWEEN TWO RIGID SPHERES WITH INTERSTITIAL POWER-LAW FLUID

Discrete Element Modeling for wet particle assembly is based on the interactionsbetween two spheres with an interstitial fluid, when the fluid behaves as non-Newtonian, theanalysis for the tangential interaction becomes much more complicated. Up-to-date there is onlyGoldman's asymptotic solution for Newtonian fluid.In the authors' previous study, an approximate approach for the tangential interaction with aPower-law fluid was proceeded with an additional assumption for velocity, correspondingly anpressure equation was obtained and then solved numerically to get the viscous force and moment.However, its validity has not yet been estimated.In order to get the more accurate expressions, a new approach was carried out based onReynolds lubrication theory without the additional assumption. As a result a pressure equationwas derived and then simplified by using Fourier-series expansion, after the pressure equationwas solved, corresponding results for the viscous force and moment were obtained. Thenumerical results from the proposed equation were compared with those from the previousequation, showing that the additional assumption could be satisfied automatically for aNewtonian fluid, therefore the previous solutions can be applied to a Newtonian-like Power-lawfluid, otherwise the proposed pressure equation is necessary. For a Power-law fluid, the powerindex is a key factor affecting the accuracy. The more deviation of the index from 1, the moreerrors produced. Generally the differences of viscous force and moment between the previousand the proposed schemes are significant less than those of the pressure distribution.Especially when the power index approaches or exceeds 0.8, the previous results are ingood coincidence with the proposed ones, which suggest that the previous is valid with asatisfied accuracy, in this case, the additional assumption could be taken to simplify thederivation.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2002-232

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EXPERIMENTAL INVESTIGATION ON GASEOUS DETONATION PROPAGATION THROUGH A T-SHAPE BIFURCATED TUBE

The gaseous detonation of 2H$_{2}$/O$_{2}$/Ar mixturepropagation through a T-shape bifurcated tube with a square cross-section40\,mm$\times $40\,mm has been experimentally studied in this paper. Thepressure histories at the specific ports were recorded by pizeo-electrictransducers and cellular patterns around the T-shape were recorded by smokedfoils respectively. The average velocity of detonation and the cellevolution were obtained. Experimental results indicate that the detonationwave is strongly weakened by the geometry around the T-shape tube. Theinteractions of leading shock and transverse waves contribute to thetraveling characteristics of detonation. In the downstream region far awayfrom 3.5 to 6 times the tube cross-section size, a secondary steadydetonation wave is re-established accompanying the appearance of regularcellular structures with the same sizes as the previous one. The cellularpatterns also demonstrate the phenomena of diffraction, regular and Machreflections of gaseous detonation. In the pass-by tube, it is noted that thecellular structure disappears in the region just downstream the start of theT-shape due to the separation of leading shock and reaction zone. With thepropagation and reflection of the leading shock in the pass-by tube, there-initiation occurs in the separated region between the leading shock andreaction zone. The re-initiation can be demonstrated by the clusteredcellular structures on the smoked-foils, and it is critical inre-establishing of gaseous detonation here. As the initial pressuredecreases to 2.00\,kPa, the steady detonation can be re-established indownstream region, but detonation extinguishes in the bifurcated tube. Also,based on the smoked foil records, several characteristic lengths and angleswere measured and the initial pressure influences on them were analyzed.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2002-260

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MECHANISM OF DRAG REDUCTION BY SPANWISE WALL OSCILLATION IN TURBULENT CHANNEL FLOW

An investigation into a turbulent channel flow subjected to spanwisewall oscillation is carried out via direct numerical simulation. By walloscillation, turbulence is suppressed and friction drag is reduced. Thetransportation of Reynolds stresses under the influence of theoscillating wall is analyzed at the initial and statistically stationarystages to further disclose the mechanism of turbulence suppression anddrag reduction. It is found that the moving wall can cause the transientgrowth of spanwise velocity fluctuations only at the very beginning ofwall oscillation and thereafter the pressure-strain terms play animportant role. The attenuation of turbulence intensities and skinfriction at the statistically stationary stage is mainly due to thesustained reduction of the pressure-strain terms.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2002-368

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ORTHOGONALITY CONDITIONS FOR ACTIVE PLATE

The adjoint structure of the active structure isdefined, the reciprocity theorem, which is derived from the basicequations of the discrete active structure, is extended from thediscrete active structures to the continuous active structures. Theactive plate with distributed sensor and actuator is studied. Thecontrol equation and the measurement equation are presented by usingthe functions locating actuation and measurement, respectively, and theorthogonality conditions are derived with the modal shapes of theactive plate and its adjoint active plate. As a numerical example arectangular plate is evaluated to give the notes about modes andorthogonality conditions of the active plate. The orthogonalityconditions can be used to decouple the motion differential equations ofthe active plate.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2002-392

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THE BIFURCATION ANALYSIS ON THE LAMINATED COMPOSITE PLATE WITH 1:1 PARAMETRICALLY RESONANCE

A simply supported rectangular symmetric cross-plylaminated composite plate with parametric excitation is considered. Thegoverning equations of motion for the laminated composite plate arederived by means of von K\'arm\'an equation. The material nonlinearity,geometric nonlinearity and nonlinear damping are included in thegoverning equations of motion. The Galerkin's approach is used toobtain a two-degree-of-freedom nonlinear system under parametricexcitation. The method of multiple scales is utilized to transform thesecond-order non-autonomous differential equations to first-orderaveraged equations. The averaged equations are numerically solved toobtain the bifurcation responses and to analyze the stability for thelaminated composite plate. Under certain conditions the laminatedcomposite plate may occur two non-steady-state bifurcation solutionsand jumping phenomena. The bifurcation and chaotic motion of therectangular symmetric cross-ply laminated composite plate is simulatednumerically. The effect of the Galerkin's truncation to nonlineardynamic analysis is presented. The way of the system going into chaosis also investigated and explained.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-024

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THE DECOMPOSED THEOREM OF THE TRANSVERSELY ISOTROPIC ELASTIC PLATE

In 1992, Gregory gave a rigorous proof about thedecomposed form when stress is anti-symmetrical about the mid-plane. Hisproof is dependent on his previous work, i.e., the Papkovich-Fadleeigenfunction expansion of bi-orthogonal functions. In this paper, wegeneralize isotropic elastic plate to transversely isotropic elastic plate.And give the decomposed theorem of the transversely isotropic elastic plate,ie. the general state of stress in the plate can be decomposed three parts:the interior state, the shear state and the transcendental state. Our proofis concise and direct and independent of the Papkovich-Fadle eigenfunctionexpansion of bi-orthogonal functions.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-034

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MIRROR POINT METHOD FOR STRESS ANALYSIS OF BONDED DISSIMILAR MATERIALS

To analyze the fundamental solution of bonded dissimilar material structures, this paperhas proposed an effective theoretical analysis method, based on the Dirichlet's uniquenesstheorem and the mirror point technology. This method can be used to solve the problems ofconcentrated forces acting at the inside or at the free surface of infinite bonded dissimilar materials,by regarding the interface and the free surface as the reflection planes to the loading point. Byintroducing the mirror points, it is found that the whole stress function can be given as thesummation of that defined under the local coordinate system fixed to each mirror point. From theinterfacial condition of continuity and the free boundary condition, by adopting the Dirichlet'suniqueness theorem, then all the stress functions can be determined from that for concentratedforces acting at the inside of a infinite homogeneous media or at the free surface of a semi-infinitespace. Therefore, the corresponding theoretical solution can be deduced in the closed series formof stress functions corresponding to each mirror point. If there are infinite mirror points, it is foundthat only the stress functions corresponding to the first several mirror points have effects on theaccuracy of the solution, by the comparison of numerical and theoretical results. Such a theoreticalsolution can be used as the Green function to deal with the problem of distributed force, and alsoas the fundamental solution for boundary element method, so that it has extensive applications inengineering. Though the proposed method has been illustrated by only two examples of planeproblem in this paper, it can also be used to deal with three dimensional problems. Moreover, thismethod can be applied not only for the case of single reflection plane, but also for the case ofmultiple reflection planes, which generally leads to infinite mirror points, due to the reflectionafter reflection.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-036

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THE EFFECT OF MOLECULAR PRANDTL NUMBERS ON TRANSPORTATION OF PASSIVE SCALAR IN FULLY DEVELOPED TURBULENCE

This paper studies the transportation of passive scalarin the turbulence with different molecular Prandtl numbers by directnumerical simulation. This paper provides sound evidence that theturbulence Prandtl number depends on molecular Prandtl number. In thelogarithm law region, the turbulence Prandtl number $Pr_{T}$ varieslinearly with the reciprocal of molecular Prandtl number in Reynoldsaverage. The relationship between subgrid-scale turbulence Prandtlnumber $Pr_{t}$ and molecular Prandtl number is more complicated, theminimum $Pr_{t}$ occurs at $Pr=1.0$

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-058

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QUANTITATIVE ANALYSIS OF APPARENT FATIGUE LIMITS OF NOTCHED SPECIMENS

In this work, the apparent fatigue limits of notched specimens were analyzed quantitatively from acomprehensive point. Three-point bending fatigue limits of smooth specimens and three kinds of notchedspecimens of quenched and then high temperature tempered 35CrMo steel are determined. The stress distributionsof notched specimens are calculated by finite element analysis software ANSYS. The experimental results areanalyzed with the ``micro-meso-process theory of fatigue sourcegeneration'': though the generation of fatiguesource appears in individual weak grains as a result of dislocation movements, it must satisfy certain deformationharmonization condition as well as probability condition, therefore a``meso-yielding region'' containing quite afew grains must be formed. According to above analyses, the apparent fatigue limit of specimens is the maximumstress (expressed as nominal stress) required to create a critical meso-yielding region on the dangerous section ofspecimen when it is bearing alternating loads. The analyses also show that when take the critical dimension of themeso-yielding region, $x_W$, as 11 grains, the compositive error between calculated apparent fatigue limits ofnotched specimens and their measured values reaches the least. Under this condition, the errors of calculated onesare all under 5\%, so $x_W$ can be considered as a characteristic parameter of material. The study above alsoelucidates the physical essence of concentration factor of fatiguestress $k_W$. In engineering practice, apparentfatigue limits of notched specimens can be predicted according tofatigue limits of material ($\sigma_W$), $x_W$ and thestress distributions on the notch section.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-068

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A REGULARIZATION ALGORITHM FOR THE NEARLY SINGULAR INTEGRALS IN 3-D BEM

The nearly singular integrals occur in the boundaryelement analysis for the thin-wall structures and calculating thequantities at interior points close to the boundary. In this paper, thetriangular boundary element with three nodes is considered in thethree-dimensional boundary element analysis, where the relativedistance from a source point to the element is introduced to measurethe singularities of the integrals. The smaller the relative distanceis, the more difficult the integrals are to be evaluated. The surfaceintegrals on the triangular element are expressed in a local polarcoordinate system $\rho \theta $. Then the integrals are analyticallyintegrated with respect to the polar variable $\rho $ by means of theintegral formulae of some elementary functions. Thus the nearlysingular surface integrals are transformed into a series of lineintegrals along the contour of the element. The resulting lineintegrals are computed efficiently by the Gauss numerical quadratureinstead of the original singular surface integrals. Moreover, theregularization algorithm can also be applied to higher order elementsby subdividing the elements into several triangular sub-elements. Here,the algorithm is employed successfully to analyze the thin-walledstructures of the three-dimensional elasticity problems.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-070

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OPTIMIZED GROUP VELOCITY CONTROL SCHEME

A new difference scheme called GVC8 is developed, and thescheme are used in the direct numerical simulation of decaying compressibleturbulence. In the DNS we have successfully improved the turbulent Machnumber up to 0.95. The statistical quantities thus obtained at lowerturbulent Mach number agree well with those from previous authors start withsame initial conditions, but they are limited to simulate at lower turbulentMach numbers due to so-called start-up problem. Energy spectrum ofcompressible turbulent flow is analyzed.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-072

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ANALYSIS ON 2D CRACKED STRUCTURE-ACOUSTIC COUPLING PROBLEMS

The effective control of noise and vibration in astructural acoustic system depends largely on the accurate evaluation of thesound-structure interaction which is characterized by the energytransferring back and forth between the acoustic field and the structure.When the fluid is heavy enough, both of the responses of the sound field andthe structure can be significantly affected by this sound-structureinteraction. Applications of interest include acoustic radiation andscattering from a submerged elastic structure, acoustic cavity analysis, anddynamics of fluid-filled elastic pipe systems.In this paper, the cracked 2D elastic structure sound interaction problemsare studied by employing fractal two level finite element method combinedwith boundary element method. The cracked elastic structure is discretizedby fractal two level finite element method, which is divided into two partsby an artificial boundary. The crack neighbouring domain is discretized bythe fractal finite element method, which can reduced the freedom degreesgreatly through transforming the nodal displacements to a set of generalizedcoordinates, the another domain is discretized by the conventional finiteelement method. The exterior acoustic field is calculated by boundaryelement method, which satisfies automatically Sommerfeld's radiationcondition.In the numerical simulation procedure, the radiation and scatteringacoustical pressure by an infinite long cracked aluminum cylinder immersedin fluid are calculated, the results show that the resonate frequencies ofthe structural-acoustic coupled system become lower with the depth of thecrack increase, and that the effect on the acoustical field by the crack isparticularly pronounced in vicinity of the crack tip.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-100

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NUMERICAL INVESTIGATION OF AN UNSTEADY TYPE IV SHOCK-SHOCK INTERACTION

Self-sustained unsteady turbulent flow resulting from a IV typed shock-shock interactionis simulated numerically. Full N-S equations implemented with thealgebraic Baldwin-Lomax model are solved by using finite volume method,second-order Harten-TVD spatial scheme and second-order Runge-Kutta method.Regular oscillatoins and a periodic structure of dual eddies areobserved, which do not exist in steady cases. The peak pressure alsooscillates regularly in its value and position, but theirvariation are very small. Time-averaged wall pressure coefficient and Stanton numberdistributions appear in good agreement with steady experimental results.From variationsof three representative lines in the flow field, the inherent unsteady mechanism and influencefactors are then analyzed by studying disturbances propagating in one cycle, and the phases ofthe structure variation. The disturbances propagate through subsonic areas, shocks and shear layers.Because of different structures having different phases, thedisturbances finally result a regular periodicflow field. It shows that the phase difference between two shear layers near the wall, and thelength difference between shear layers abuting against the supersonicjet are two facts that influence the flow field significantly.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-155

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COUPLING SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION OF THERMO-STRUCTURAL TRANSIENT RESPONSES

The numerical methods of sensitivity analysis and designoptimization for structures with transient thermal deformation and thermalstresses as design criterions are studied in this paper. In the sensitivityanalysis of thermal stress and deformation, two kinds of algorithms of thedirect method and the adjoint method have been proposed and the couplingeffect of temperature field is considered. To deal with the coupling effectof temperature field, the derivatives of temperature field with respect tovariables are required in sensitivity calculation for thermal loads andthermal stresses in the direct method, while the derivatives of thermal loadwith respect to the temperature field are required in the adjoint method. Anumerical example is given to demonstrate the effectiveness of shape designoptimization reducing the thermal stress, evaluate the accuracy ofsensitivity analysis methods, and show the effect of temperature fieldderivatives in the coupling sensitivity analysis. The implementation of theadjoint method in application software provides efficient sensitivityanalysis for large-scale problems of structural design optimization.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-165

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NUMERICAL STUDIES ABOUT A SYMMETRIC VORTEX FLOW AROUND A SLENDER BODY AT HIGH INCIDENCE

Numerical simulations of low-speed turbulent flowsaround a slender body are conducted to explore the effect of a minutenose geometrical disturbance on the formation and development of flowasymmetry. The result shows that the asymmetric flows observed inexperiment are simulated successfully by the introduction of a smallbump placed near the body apex. The asymmetric vortex structure growsgradually along the symmetry axis of the slender body, and thedistribution of sectional side force takes the sinusoid character ofvariation. Disturbance energy presents exponential spatial growth fromthe tip until it reaches the saturation. Disturbance scale influencesthe size and the distribution of flow asymmetry. The flow asymmetryshows a single periodicity when the circumferential position of thesingle disturbance changes. Numerical results show that the asymmetricvortex flow originates from the spatial instability of the forebodywake induced by a small disturbance.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-180

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NUMERICAL INVESTIGATION OF DIFFRACTION, FOCUSING AND REFLECTION OF TOROIDAL SHOCK WAVES

An investigation of toroidal shock wave motion in acylindrical shock tube is described in this paper. Numerical simulationswere carried out by using dispersion controlled dissipation scheme (DCDscheme) and validated with experimental data. From the numerical results,the toroidal shock wave diffraction, focusing and reflection were discussedin detail. It was found out that the key factor of cylindrical shockfocusing is the shock acceleration when diffracting shock waves propagatetoward the axis of symmetry. Mach numbers of incident toroidal shock wavesplay an important role in shock wave diffraction and focusing. The toroidalshock waves focus at certain point on the axis of symmetry while usualcylindrical shock waves focus on the entire the axis of symmetry, therefore,the focusing effect resulting from the two cases of focusing points aredifferent essentially.

2004, 36(1) doi: 10.6052/0459-1879-2004-1-2003-341

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