力学学报

Criteria on high-temperature gas effects around hypersonic vehicles

Based on the kinetic viewpoint, several quantitative criteria are suggested to measure at which flight conditions the molecular vibration, dissociation and ionization of high-temperature air around hypersonic vehicles become important.Key words hypersonic flight, high-temperature effects, molecular vibration, dissociation, ionization

2010, 42(4): 591-596. doi: 10.6052/0459-1879-2010-4-lxxb2010-088

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Numerical research on blunt body shock-induced oscillating combustion phenomena

Sun Ming-bo Liu Weidong

An improved uncoupled solver of non-equilibrium flow wasused to split the axisymmetric Euler equations for a reacting flow. Inviscidflux was calculated with fifth-order WENO scheme. Simplified implicitformulation was adopted to deal with the stiffness generated by the chemicalreacting source term of species equations. Time integration was performedwith two-order TVD Runge-Kutta scheme. At the flow Mach number M of 4.48 and4.79, shock-induced oscillating combustion phenomena around blunt body inH₂/Air mixture were calculated. It shows that the numerical results aremore sensitive to the grid refinement on normal direction than on flowdirection. To get accurate solution, there must be enough grid nodes in theheat release zone. At the flow Mach number of 4.48, sensitive analysis ofdifferent reaction mechanisms were studied. At the given experimentalconditions, the values of induction time calculated from J and B-Wmechanisms are close to each other and their calculated frequencies nearlyequal to the experimental results. Density-time distribution along thestagnation streamline from J and B-W mechanisms agree well with McVey-Toongtheory. Induction time calculated from JM mechanism is longer than others,and the calculated oscillating frequency is lower than experimental results.At flow Mach number of 4.79, calculated frequency of J mechanism agrees withexperimental result. B-W mechanism is sensitive to fluctuations offlowfield, and its release time is short. Fiercely oscillating combustionfront would easily lead to local detonations, which made the pressurehistory of stagnation point disordered. Due to using the fifth-order WENOscheme, relatively high-resolution of present calculation can be obtained.

2010, 42(4): 597-606. doi: 10.6052/0459-1879-2010-4-lxxb2010-086

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Kinetic modeling study of fuel-rich premixed toluene flame at low pressure

A kinetic model of toluene combustion, including 209 species and 1139 elementary reactions, was developed and validated on a fuel-rich premixed toluene flame at 30 Torr. According to the good accordance between simulation and experimental results, it is concluded that this model can satisfactorily predict the concentration profiles of major flame species and the key intermediates in the reaction sequences of decomposition and oxidation of toluene. Rates of production and sensitivity analyses of these key intermediates were performed to draw the major reaction pathways concerning the decomposition and oxidation of toluene. It is shown that toluene is mainly decomposed to benzyl radical, benzene and phenyl radical. These decomposition products can subsequently generate cyclopentadienyl radical and propargyl radical, which are then converted into carbon monoxide via further reactions of decomposition and oxidation. The successful simulation of the decomposition and oxidation processes of toluene will be an initial stage to develop the kinetic models of larger aromatic fuels in the near future, which is useful for the prediction of global combustion characteristics of aromatic components in practical fuels.[key word] Toluene combustion, kinetic model, decomposition pathways, oxidation pathways

2010, 42(4): 607-614. doi: 10.6052/0459-1879-2010-4-lxxb2010-087

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Suppression of vortex shedding from thin rectangular cylinders

A strip cross-sectional element was used to suppress vortex shedding fromthin rectangular cylinders with a width to thickness ratio range B/H of 2.0~5.0 at Reynolds number Re in the range of 3.75× 10³~1.05×10⁴, where B and H are the width andthickness of the cylinder's cross-section, respectively. The cylindersurface in width is parallel to the oncoming flow. The element and thecylinder have the same length and their axes are parallel. The element'swidth is 0.5, and its thickness is small. The element's position is varied,and its main surface is perpendicular to the oncoming flow. Measurements ofwake velocities, together with smoke wire visualization, show that, vortexshedding from both sides of the cylinder is suppressed if the element isplaced at points within an effective zone, while mono-side vortex sheddingis observed if the element is applied at points within a unilateraleffective zone. The effective zone is from upstream the leading edge todownstream the trailing edge of the cylinder, and it is enclosed by theunilateral zone. The areas of the two zones increase with the growth ofB/H and decrease with the growth of Reynolds number.

2010, 42(4): 615-622. doi: 10.6052/0459-1879-2010-4-lxxb2009-063

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Time-space analysis of vortex flow field in compressor at near-stall point

In order to study the time-space characteristics of vortexflow field in axial compressor, a time-critical CFD method was employed tonumerically simulate the flow field in a single rotor. After the mass flowanalysis at different axial positions in the rotor, it is found that thefluctuation value of inlet mass flow is 2% normalized by the maximum massflow. In addition, it is also found that the oscillation of vortex flowfield at suction side near the trailing edge was the main reason for theinlet mass flow fluctuation.

2010, 42(4): 623-628. doi: 10.6052/0459-1879-2010-4-lxxb2009-056

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Separation efficiency of microparticle in the divergent electrokinetic microchannel flow

This study reports a numerical simulation ofseparation efficiency of microparticles in the divergent microchannel flowusing the Eulerian and Lagrangian methods. The flow field, ion field andelectric field are simulated numerically with finite volume method first,then microparticles are injected from the inlet of the microchannel andtracked with the Langevin-equation-based model, in which dielectrophoreticforce is included. It has been found that the microchannel's pumpingcapability increases with the increase of divergent ratio (ER). In addition,the effective separation length between microparticles increases linearlywith the increase of ER. With and without consideration of Dielectrophoresis(DEP), the ration of ESL to ER is 5.9 and 4.79, respectively. Itmeans that thenegative DC-DEP always reduces the separation efficiency in the divergentmicrochannel. The aforementioned conclusion is helpful for the designoptimization of separation apparatus.

2010, 42(4): 629-636. doi: 10.6052/0459-1879-2010-4-lxxb2009-627

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Unsteady aerodynamic force modeling via proper orthogonal decomposition rom

A method for constructing reduced-order models (ROMs) of unsteady flows is presentedusing mode-based method. The mode vectors, developed from correlation matrix formed with thesnapshots in full-order system, are used for a Galerkin projection. Singular Values Decomposition(SVD) is then used for system proper realization. Results are obtained for reduction of three highorder systems: (1) an arbitrary state-space system with order (n = 406), allowing some insightsinto the performance of the method, (2) two-dimensional airfoilaeroelastic system with order (n =4800$), and (3) AGARD 445.6 wingaeroelastic system with order (n = 239400$). In the second case,basis procedure for Mode-based ROM is presented in detail. First, Linearized unsteady EULERmodels are derived to obtain snapshots either in time domain or frequency domain. Then modevectors are computed, allowing that reduced subspace project on full order system to derivemode-based ROM. The reduced order model obtained by the method captured the full ordersystem dynamics and is especially efficient in frequency domain. Finally, the method was appliedfor a practical wing system-AGARD 445.6. Flutter boundary of the wing was identified withROM, and the result agrees well with CFD/CSD direct coupling. All the results indicate thatmode-based ROM is efficient and accurate enough to provide a powerful tool for aeroelasticsystem analysis.

2010, 42(4): 637-644. doi: 10.6052/0459-1879-2010-4-lxxb2008-753

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Spatial composition and formation process of wave dissipative structure

Jia Chenxia

Since the theory of dissipative structures has beenproposed, many researches on them were performed. However, these studiesmostly focused on the thermodynamic theory, laws and stability ofdissipative structures, few studies were carried out on the basicstructure-cells and their interaction in the dissipative structures. Since1970's, different dissipative structures (patterns) have been found incrystal growth system, such as spoke patterns, rotating spoke patterns andwave patterns. In this paper a famous wave dissipative structure wasinvestigated, observed in the melt thermal convections in Czockralski (Cz)crystal growth system. The wave patterns with different wave numbers n areobtained numerically in a Cz oxide melt thermal convection system withcrucible radius r_{c}=100mm and crystal disc radius r_{s}=50\,mm. The oxidemelt is filled in a rest crucible, whose aspect ratio is r_{c}:h (radius:height). The motion of the oxide melt is induced by sidewall heating of thecrucible and a rotating disc. The disc has a common axis with the crucibleand just contacts with the free surface of the oxide melt. The rotating rateof the disc is \Omega_{s}. The governing equations of LiNbO_{3} meltflows were solved by a block- structured boundary-fitted-coordinate method. Toensure the correct coupling of pressure and velocity fields, the well-knownmomentum interpolation technique of Rhie and Chow was applied. For theconvective term, QUICK scheme was applied. A pressure - correction equationis derived according to SIMPLE algorithm. By changing r:h and\Omega_{s}, numericalsimulations are conducted to obtain stable n-folded wave patterns. Properorthogonal decomposition (POD) is applied to extract the basic modes of then-folded wave patterns (n=2,3,4 in the present paper). According to POD, thebasic modes are optimal structures to form the parental n-folded wavepatterns and consist of many small-scale vortexes in general. In the presentpaper some interesting findings are achieved: (1) n-folded wave dissipativestructure is made up of many small-scale basic modes; (2) basic modes appearin groups; (3) each group has n similar basic modes but of different phaseangle; (4) with the increase of group order, the number of the vortex in thebasic modes increases by twice. The contribution of the basic modes to formthe parental dissipative structure is different and time-dependent. Themacroscale wave dissipative structure is found to be formed by thealternative appearance and disappearance of the basic modes. These resultsenrich the knowledge of dissipative structure.

2010, 42(4): 645-651. doi: 10.6052/0459-1879-2010-4-lxxb2009-216

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Study on nonlinear dynamics of non-isothermal flow in broken rock

Miao Xiexing Zhanqing Chen Xianbiao Mao

The special physical environment with the high groundstress, high ground temperature, high karst hydraulic pressure, and intensemining disturbance`` in deep broken rocks, determines that their mechanicsystem is a complicated nonlinear dynamical one. Given a relative stablestress field, the flow in broken rock can be considered as a non-isothermalone, and the dynamical mechanism on the instability of non-isothermal flowin broken rock is analyzed by the theory of bifurcation and catastrophe ofnonlinear science.(1) According to the energy equations of the fluid and the solid, the energyconstitutive equation on non-isothermal flow in the broken rock isdeveloped, and combining with the continuity equation, kinetic equation andthe state equation of the flow, the one-dimensional nonlinear dynamicalequations of non-isothermal flow in broken rock are established.(2) Using these equations and boundary conditions, the dimensionless steadystates of the flow system are obtained by using Mathcad software. It isindicated that the obtaining of the steady states for the non-isothermalflow system is much more difficult than that for the isothermal flow systemand there are analytical solutions of steady states in isothermal flowsystem, while for the non-isothermal flow system, its analytical solutionsof steady states can not be obtained.(3) The branch figure of the steady states of flow velocity for thenon-isothermal flow system is drawn by the numerical analysis and comparedwith the isothermal flow, both the limited equilibrium point correspondingto the non-isothermal seepage field and the parameter value when thehysteresis appears all have an offset.(4) The stability of the steady states is analyzed by the iteration methodof successive lower relaxation, and the non-isothermal flow system has asaddle-node bifurcation and a fold catastrophe. But its catastrophe positionexist a rightward deviation, and the absolute value of the limited parameter$b$ decreases a magnitude, so the catastrophe is apt to take place in thenon-isothermal flow dynamical system , namely, even if the breakingphenomenon is not very serious, the fold catastrophe may take place possiblyin the non-isothermal flow system.

2010, 42(4): 652-659. doi: 10.6052/0459-1879-2010-4-lxxb2008-767

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Coupled thermo-hydro-mechanical-migratory model and fem analyses for dual-porosity medium

One kind of coupled thermo-hydro-mechanical-migratorymodel of dual-porosity medium for saturated-unsaturated ubiquitous-jointrockmass was established, in which the stress field and the temperaturefield are single, but the seepage field and the concentration field aredouble, and the influences of sets, spaces, angles, continuity ratios,stiffnesses on the constitutive relationship of the dual-porosity medium canbe considered, and also the corresponding two-dimensional program of finiteelement method was developed. Taking a hypothetical nuclear waste repositoryas a calculation example, the case in which the rockmass is unsaturateddual-porosity medium and radioactive nuclide leak was simulated numerically,and the temperatures, negative pore pressures, saturations, flow velocities,nuclide concentrations and principal stresses in the rockmass wereinvestigated. The results show that: (1) the negative pore pressures andnuclide concentrations in the porosity and fracture systems presentdifferent changes and distributions; (2) even though the saturation degreein porosity system is only about 1/10 of that in fracture system,the flow velocity of underground water in fracture system is about3 times of that in porosity system because the permeability coefficient offracture system is almost four orders higher than that of porosity system;(3) the value of nuclide concentration in fracture system is close to thatin porosity system in the medium.

2010, 42(4): 660-669. doi: 10.6052/0459-1879-2010-4-lxxb2009-163

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Approximate theory and analytical solution for functionally graded piezoelectric rectangular plates

Qi Feng

Functionally graded piezoelectric material (FGPM) haselectric-mechanically coupled property. Furthermore, its material propertyparameters vary continuously in some direction so that the stressconcentration effect due to temperature change can be greatly decreased.Probably, some prospective properties can also be obtained by adjusting thevarying gradient of the material property. Thus, it has a good prospect inapplication.Recently, study of FGPM is focused on the analyses of thermal response,static and dynamic response of the material, buckling behavior, fracturebehavior of structures, optimal design and parameter identification ofstructures, etc. The theory and approaches for FGPM plates and shellsincludes simplified model method, laminated model method, asymptotic method,exact solution, finite element method, etc. But, the work for FGPM platesand shells based on approximate theory is rarely found. Although some exactsolutions and FEM solutions have been worked out, simplified approximatesolutions based on some assumptions with satisfactory precision are alsoattractive. In this work, several assumptions, such as Kirchhoff assumption,Reissner-Mindlin assumption and some other assumptions proposed by theauthors are introduced. The first order shearing theory for plates isemployed. Exponential gradient for material properties across the thicknessof the plates is prescribed. Using the governing equations of FGPM and thepertinent boundary conditions, the approximate theory for the FGPM plate isestablished. The solutions of deflection slopes and electric potential forsimply supported rectangular plate with its periphery grounded andelectric-mechanical transverse loading applied are obtained. The electricpotential solution is expressed in the form of double Fourier series. Thesolution is typically much simpler than the exact solutions, and itsnumerical computation is proved to be quite easy. The numerical results ofthis solution are given and compared with the 3D finite element solution byANSYS. It is shown that this solution is in good agreement with the 3Dfinite element solution. It is found that the present solution has highprecision even for thick plates. Finally, the limitation of this theory andthe analytical solution is discussed.

2010, 42(4): 670-681. doi: 10.6052/0459-1879-2010-4-lxxb2009-064

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Fracture toughness of eutectic ceramic composite

Xie-Quan LIU

This paper presents the fracture toughness of theeutectic ceramic composite which is mainly composed of eutectic ceramic rodswith random size and orientation. Firstly, on basis of the microstructure,considering the boundary slip of eutectic rods, the cracking stress of theeutectic ceramic composite is determined. When the applied tensile stressequals to the cracking stress, the crack will grow. Secondly, we imaginethat the load carried by the eutectic ceramic rods in the crack wake willproduce a crack-closing force. It will reduces the stress intensity in frontof the crack. The bridging toughening mechanism of eutectic rods isconstructed. Thirdly, the pull-out work is given by the integral of thefrictional force over the pull-out length. The pull-out toughening mechanismof eutectic rods is obtained. And lastly, based on the bridging tougheningmechanism and the pull-out toughening mechanism, the enhanced toughnessscales with the inherent matrix toughness, and the theoretical formula offracture toughness of the eutectic ceramics composite is determined. Theresult shows that the fracture toughness of the composite is dependent onthe aspect ratio of eutectic-rod.

2010, 42(4): 682-690. doi: 10.6052/0459-1879-2010-4-lxxb2009-228

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Growth of an array of cohesive crack points in brittle solids and the influence of crack spacing

In this paper, an analytical model is established forinvestigating the dynamic fragmentation process of a brittle material thatcontains an array of fictitious cohesive cracks. The material expands atuniform strain rate, and the crack points are equally-spaced. Using theelastodynamic equations for the undamaged material and a linear cohesivefracture model for the separation of the cracks, the governing equations forthe stress and velocity in the material are deduced, which turned to be aninitial-boundary value problem (IBVP). By using Laplace transform technique,the IBVP is solved to obtain an exact expression for the cohesive stresshistory at the crack point. The material's fracture process is then studiedto determine the critical time when full fracture occurs, and the criticalexpansion of a unit crack body at this time. The influences of the crackspacing and the applied strain rate on the fracture and fragmentationprocess are investigated. Furthermore, by assuming that the critical crackbody expansion has the minimum value during a natural fragmentation process,the fragment size is estimated for different applied strain rates in thepresent study.

2010, 42(4): 691-701. doi: 10.6052/0459-1879-2010-4-lxxb2009-075

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Dynamic flexure buckling of elastic cylindrical shells under axial impact

Lim C.W.

In this paper, the dynamic buckling of elasticcylindrical shells, which are impacted by axial load on one end, is studied.By introducing Hamiltonian system to the problem, critical loads andbuckling modes are reduced to the problems of eigenvalues andeigensolutions, respectively. In the system, symplectic eigensolutions aregrouped into two classes: the local compressive buckling and global flexurebuckling. Especially, when the impacted boundary is free, buckling modeshave special forms. Numerical results show some rules about the curves ofcritical load and corresponding buckling modes.

2010, 42(4): 702-709. doi: 10.6052/0459-1879-2010-4-lxxb2008-685

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Infuence of the boundary film shear elastic modulus on the performance of a micro contact

A contact model is developed to theoretically analyze the influence of shear elastic modulus of the boundary film on the performance of a micro contact. The contact is one-dimensional and formed by two sliding parallel planes. The upper contact surface is rough with rectangular micro projections, while the lower contact surface is smooth. Both of the contact surfaces are treated as rigid. The micro contact is filled with fluid. It consists of two sub-zones. In the outlet zone, the micro contact is distributed with boundary film because of the nanometer-scale contact separation, while in the inlet zone, the micro contact is distributed with fluid film because of the relatively high contact separation. The performance of the micro contact is determined by the behaviors of the boundary film and the fluid film. When the film thickness is relatively high, the boundary film here can be considered as the nanometer-scale thin film. Because of the limited shear stress capacity at the upper contact surface, the boundary film can slip at the upper contact surface. It is assumed that the shear stress capacity at the lower contact surface is high enough so that the boundary film can not slip at the lower contact surface. Because of the interaction between the boundary film and the contact surface, the viscosity, density and shear elastic modulus of the boundary film are all varied across the film thickness; their equivalent values, which are dependent on the boundary film thickness, are used in theoretical analysis. The analytical approach proposed by the author and his colleagues is used for analyzing the boundary film behavior. The fluid film is assumed not to slip at both of the contact surfaces. The effect of the shear elastic modulus of the fluid film is neglected in the analysis. The conventional approach is used for analyzing the fluid film behavior. The present paper gives the theoretical analysis and some of the computational results for different operating conditions.

2010, 42(4): 710-718. doi: 10.6052/0459-1879-2010-4-lxxb2008-724

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The biothermomechanical behaviour of skin tissue under electromagnetic heating

Electromagnetic heating is widely used in medicaltreatments, such as microwave, radiofrequency, laser, etc. Recent advancesin these technologies resulted in remarkable developments of thermaltreatments for a multitude of diseases and injuries involving skin tissue.The comprehension of heat transfer and related thermomechanics in skintissue during these treatments is thus of great importance, and cancontribute to the further developments of these medical applications.Biothermomechanics of skin is highly interdisciplinary, involving bioheattransfer, burn damage, biomechanics and physiology. The aim of this study isto develop a computational approach to examine the heat transfer process,heat-induced mechanical response as well as the associated pain level, sothat the differences among the clinically applied heating modalities can bequantified. In this paper, numerical simulations with the finite differencemethod (FDM) was used to analyze the temperature, burn damage and thermalstress distributions in the skin tissue subjected to various thermaltreatments. The results showed that the thermo-mechanical behavior of skintissue is very complex: blood perfusion has little effect on thermal damagebut large influence on skin temperature distribution, which, in turn,influences significantly the resulting thermal stress field; for laserheating, the peak temperature is higher for laser with shorter wavelength,but the peak is closer to the skin surface; the thermal stress due to laserand microwave heating is mainly limited to the top epidermis layer due tothe exponential decrease of heat generation along skin depth; the thin (andcommonly overlooked) stratum corneum layer dominates the thermomechanicalresponse of skin tissue.

2010, 42(4): 719-732. doi: 10.6052/0459-1879-2010-4-lxxb2008-623

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A numerical simulation of cells adhesion based on the natural growth

Cao Jinfeng Long Quan

Cells adhere to each other through the binding of cell adhesion molecules atthe cell surface. This process is fundamental in many areas of biology,including early embryo development, tissue homeostasis and tumor growth.Considering the free motion of cells, the adhesion-force between cells andthe natural growth of cells, the paper developed series of mathematicalmodels. Through numerical simulation with the case of 2 Groups in 2D, we can simulate the wholeprocess of cells adhesion and the ultimate form of cells adhesion, usingdifferent parameters, can be divided into four categories, including mixing,engulfment, partial engulfment and separation. The result is close to theexperimental result, so it shows that the model can forecast the phenomenonof cells adhesion well.

2010, 42(4): 733-739. doi: 10.6052/0459-1879-2010-4-lxxb2009-185

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On hysteresis and retardation

Hysteresis and retardation are two kinds of popularphenomena in natural sciences, engineering sciences and social sciences.However, they are often confused in both academic and technical circles.This paper, starting from the definition and the nature of two kinds ofphenomena, presents their general and individual characteristics, as well astheir relations. The illustrative examples in the paper show that thehysteresis implies the phase delay of two processes varying periodicallywith a physical parameter, while the retardation reflects the time delay oftwo dynamic processes varying arbitrarily in the time domain. In the case ofboth linear hysteresis and harmonically time-varying input, they lookidentical. The nonlinear hysteresis, however, will reduce their relevanceeven the harmonically time-varying input remains unchanged. In general, theyare two kinds of quite different phenomena by nature. In the aspect ofmemory, for example, the hysteresis and retardation characterize localmemory and global memory, respectively. As for their transfer property, ahysteretic system corresponds to the rational fractional and a delayedsystem corresponds to that with one or more exponential functions.Even though there is a closed hysteretic loop for the linear hystereticsystem, the output of a nonlinear system under harmonic input may not behaveperiodically. The nature of hysteresis comes from the multiple branches of ahysteretic loop, instead of the closed loop.The nature of a delayed system defines a continuous mapping between twocontinuous functions in their corresponding closed intervals. Such a delayedsystem, hence, is infinitely dimensional, no matter how short the time delayis and how many degrees of freedom the system has. As a matter of fact, alinear dynamic system involving any time delays has to be modeled as a delaydifferential equation, which has infinite dimensions and infinite number ofeigenvalues. Furthermore, nonlinear dynamic systems with time delays exhibiteven more complicated dynamics. Time delays are usually very short inmechanical systems. However, the neglect of time delays in the dynamicanalysis of a delayed system may result in essential mistakes.

2010, 42(4): 740-746. doi: 10.6052/0459-1879-2010-4-lxxb2009-414

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Effects of delay on effective band drift in nonlinear saturation control system

ZHAO Yanying YAN Zhigang

For active control systems, all operations in thecontrol process are not instantaneous. It implies that various delays existinevitably in the real-time control systems. In fact, time delay in controlsystem is derived from measurement of system states, caused by physicalprosperities of the equipment used for control and transport delay, byperforming on-line computation, filtering and processing data and bycalculating and executing the control forces as required. Thus, effects ofthe delays in the designed controller should be considered since they cannotbe eliminated even with the present technology. It should be noted that dueto the complexity of the nonlinear dynamical system, most scholars studiedthe effect of delay on the control performance in the linear dynamicalsystem. However, the effect of both nonlinearity and delay on dynamicalbehaviors of the system is very complex. The authors investigate theeffective band drift due to internal resonance frequency deviation existedin the nonlinear saturation control system. The effects of delays incontrol, feedback and self-feedback signals on effective band drift andbandwidth are studied. Then, the effective band drift may be controlled bychoosing appropriate delays. From the examples illustrated, in the originalsystem without considering delays, the effective band may drift to theprimary resonance point upward or downward when the internal resonancefrequency deviation exists. Moreover, the greater the absolute values ofinternal resonance frequency deviation is, the greater the effective bandwill drift. The effective band drift can lead to the performance degradationof vibration suppression about the primary resonance point. However, theeffective band drift can be eliminated by choosing appropriate delays ofcontrol, feedback and self-feedback signals according to the changes ofinternal resonance frequency deviation. Meantime, the effective bandwidth isbroadened. Both analytical and numerical results show that the greater theabsolute values of internal resonance frequency deviation is, the moreeffects of the delays on the effective band drift and bandwidth will be.

2010, 42(4): 747-757. doi: 10.6052/0459-1879-2010-4-lxxb2009-178

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Study on the vibration silicon cantilevers under laser excitation

Microcantilevers were used widely in physical, chemical,biological and mechanical system as sensors to detect the tiny change ofenvironment. The resonance frequency and Q-factor were usual outputquantities during detection. So the study of vibration characteristics ofcantilever under different excitation was very important for its uses.In this paper the vibration of silicon cantilever, subjected to a uniformlaser excitation on one surface, was investigated experimentally andtheoretically. The spectrum analyzer was used to obtain the spectrumresponse curve of cantilevers. The result showed that the resonancefrequency obtained from experimental measurement agreed very well with thatobtained from theoretical calculation. To measure the cantilever deflection,an optical experimental apparatus called thermoelastic microscopy, which wasbased on the principle of heterodyne interferometer, was used to obtain theamplitude and phase of the cantilever deflection under different frequenciesof excitation laser. Theoretically, the thermal wave model, along withplasma wave model, was adopted to simulate the vibration of siliconcantilever under optical excitation. The thermal wave model was widely usedto describe the change of sample temperature in the physical process duringlaser operation, while the plasma wave was the specific characterization ofsemiconducting samples under strong laser excitation, and the plasma wavemodel was used to describe the change of excess carrier density in sample.These two models were used together here to study the cantilever vibration.The expressions of excess carrier density and temperature of cantilever wereobtained. Also the curves of amplitude and the phase of silicon cantileverdeflection versus modulation frequency were calculated. The good agreementbetween measurements and simulations was observed from the results. Fromlinear fitting analysis we obtained a linear relationship between thevibration phase and the square root of modulation frequency. This conclusionwas the same as the result from other authors.

2010, 42(4): 758-764. doi: 10.6052/0459-1879-2010-4-lxxb2009-005

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Bursting phenomena as well as the bifurcation mechanism in periodically excited hartley model

zhang xiaofang bi qinsheng

By introducing periodically alternated current source aswell as suitable values for the parameters to ensure that there exists ordergap between the natural frequency and the exited frequency, nonlinearelectric circuit with fast-slow effect has been established. Based on theconception of generalized autonomous system and the analysis of theproperties of equilibrium points, all possible bifurcation forms have beendiscussed. Different types of bursting phenomena, such as fold/fold burster,fold/subHopf/supHopf burster, in which the fold or Hopf bifurcations mayconnect the quiescent states and the spiking states, have been presented.The mechanism of the bursters is explored via bifurcation analysis, whichhas been illustrated by transformed phase portraits of the generalizedautonomous system.

2010, 42(4): 765-773. doi: 10.6052/0459-1879-2010-4-lxxb2009-614

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Vibration control of multi-mode flexible structure based on hybrid extra-insensitive shaper

The modal experiment of flexible structures is so complexthat it is difficult and unrealistic to get the accurate frequency anddamping of the structures in engineering. The parameters will change becauseof the variations of the external environment and disturbance even if theparameters can be measured. Therefore, it is necessary to design a shaperthat is robust to system parameters. In this paper, a new hybridExtra-Insensitive(EI) input shaping method based on zero-placement technique(ZPT) is presented. Based on the deviation value points, the ZV shaper basedon ZPT is changed into EI or ZVD shaper easily, but the quantity of impulsesand delay time do not increase. From the principle of deviation valuepoints, the higher hybrid EI shaper and Multi-EI shaper are designed and theincreasing amplitude of the robustness is much larger than the increasingamplitude of delay time. At last, the vibration of multi-mode flexiblestructure is suppressed using the EI shaper through the periodicity ofshaper. This method make the quantity of impulse reduce largely, while makethe delay time change little. The simulations validate the present shaper.

2010, 42(4): 774-781. doi: 10.6052/0459-1879-2010-4-lxxb2009-133

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Physics and numerical simulations of mhd acceletrated supersonic boundary layer

Su Weiyi Chen Lihong

The mechanism of magnetohydrodynamics (MHD) controlling onsupersonic flat-plate turbulent boundary layer was explored in theory andnumerical simulation. The collision frequencies between theelectron-molecules and ion-molecules at the boundary layer were obtained bylow frequency approximation in the plasma, and the force balances forelectrons and ions were set up to solve the plasma velocities, polarizationelectric field and the boundary layer velocities. HLLE schemes and LU-SGSmethod were used to numerically solve the sst-k$\omega$ turbulent model.The results show that, (1) the relative error between numerical results andtheoretic results are in the range of 7%; (2) in the absence of electricfield, the Lorentz force can decrease the skin friction. With an externalelectric field applied, the low velocity fluid in the boundary layer can beaccelerated; (3) in the outer layer of boundary layer, the interactionparameter decreases with the distance to the wall, but in the inner layer asthe viscous force dominates the flow, the interaction parameter increaseswith the distance to the wall.

2010, 42(4): 782-788. doi: 10.6052/0459-1879-2010-4-lxxb2008-785

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Measured data analysis of urban expressway and research on traffic flow models

Traffic flow models are important to describe various complex trafficprocedures on highway or road network and to establish intelligence trafficsystems (ITS). Lots of improvement has been made in traditional traffic flowmodels, and many new traffic flow theories have been developed.Generally the formation of a traffic flow model requires massive observationas well as in-depth analysis of real road traffic. Empirical data areindispensable to identifying parameters when the corresponding model isutilized. One of the basic demands of collecting such data is repeatability,that is, a large amount of measuring must be conducted under nearlyidentical circumstances to provide the data and model parameters.It is drawn in this paper that over 26000 ``car velocity-headway distance''data pairs are obtained from the long time video recordings of a section inYanan Expressway of Shanghai with three traffic circumstances: peak hour;low traffic hour; snow day. This way to collect traffic data is differentfrom some traditional methods in which sensors are fixed along the road orburied underground to measure the ``car velocity-traffic flow'' datapairs. The obtained ``velocity-headway distance'' data pairshave better synchronized characteristics and are easy to transform into``velocity-density'' or ``flow-density'' data pairs for further research.After comparison study of manifold well-known traffic flow velocity-densitymodels based on above measuring data, the superiorities of one-dimensionalpipe-flow model are found in calculating thetraffic flow parameters of expressway in our country.Since the key parameter in 1-D pipe-flow model, named traffic behaviorparameter m, can be adjusted, a basic method is proposed to draw thenon-linear characteristics of traffic flow by 1-D pipe-flow model withchanging parameters.

2010, 42(4): 789-803. doi: 10.6052/0459-1879-2010-4-lxxb2009-091

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A study of boundary integral method for a type of nonlinear problem based on generalized quasilinearlization theory

The nonlinear Poisson problems are very common in heatconduction and diffusion with simultaneous reaction in a porous catalystparticle, so the generalized quasilinearization theory is exploited and anew numerical iterative method is proposed for this type nonlinear Poissonproblem. In this method, the nonlinear equation is replaced by a set ofiterative linear equation. An advantage of this method is that a theorybackground is substantial for the choice of the initial value of theiteration, and with a wide range of initial value the result of thisiteration is monotonously converged to the exact value. This new iterativemethod is combined with boundary element method and dual reciprocity hybridboundary node method for solving nonlinear Poisson problems, and theaccuracy, the convergence rate and stability with different initial valuesof these two methods are compared with each other. It is shown that, themethod based on dual reciprocity hybrid boundary node method and generalizedquasilinearization theory, has the high stability and efficiency, and theiterative rate is quadratic.

2010, 42(4): 798-803. doi: 10.6052/0459-1879-2010-4-lxxb2009-470

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A new computational model of metal plasticity based on von mises criterion correction and tangent modulus correction

The simulation precision of metal plasticity is closelyrelated to yield criteria and constitutive law which are used incomputational model. In order to improve this precision under complex stressstate, tensile tests with five kinds of samples, such as smoothround bar, round bar with small notch, round bar with large notch, thinplate with central hole and thick plate with central hole, were conducted.Parallel finite element models were built for each test and solved inABAQUS. In these simulations, von Mises yield criterion, Tresca criterion,Twin-Shear criterion were separately used based on equivalent stress-straincurve as the constitutive law. The results showed that none of them had asatisfying precision for all these different tests. So Von Mises criterionwith stress triaxiality dependence was used as yield function. Tangentmodulus with principal stresses correction based on equivalent stress-straincurve was used as elasto-plastic constitutive law. With this theory, theabove tests were recomputed. The results further showed that, comparing withother criterions, von Mises criterion with stress triaxiality correction hasa better precision than other yield functions. The tangent modulus withprincipal stresses correction which is first postulated in this paper has abetter estimation of 2A12-T4 Aluminum Alloy's Elasto-plastic behavior thanthe assumption with unique equivalent stress-strain curve.

2010, 42(4): 804-810. doi: 10.6052/0459-1879-2010-4-lxxb2009-081

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2010 Vol. 42, No. 4

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