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2009 Vol. 41, No. 5

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Effect of exit conditions on the self-preservation states of round jets
Baoping Feng, Jianchun Mi
Centerline velocity measurements are made in two round jet flows issuing with the same Reynolds number (86\,000) from a smooth contraction and a long straight pipe, respectively. The influence of exit flow conditions is investigated to induce the different self-preservation states in the far field of the two jets. The smooth contraction jet flow is found to approach more rapidly to self-preservation than the pipe jet. The study suggests that the observed self-preservation states may be related to the underlying turbulence structures in the near field of the two jets.
2009, 41(5): 609-617. doi: 10.6052/0459-1879-2009-5-2008-352
Comparisons of two types of immersed boundary methods in numerical simulations of a cylinder in uniform incompressible flows
Shengbai Xie, Peng Shan
The Immersed Boundary (IB) Methods have been proven to besuitable to handle complex geometrical boundaries, moving boundaries andfluid-structure interactions, etc, since only the fixed Cartesian grids arerequired. C. S. Peskin first introduced this method in the 1970s with a flatdevelopment period. In resent years, numerous modifications and refinementshave been proposed and variants of this approach now exist. In this study,two different types of IB methods are introduced, the Continuous ExplicitForcing Method (CEFM) and the Discrete Implicit Forcing Method (DIFM). InCEFM, the forcing terms are introduced into the controlling equations toreplace the boundary conditions on the surfaces and the controllingequations can be explicitly solved. In DIFM, the forcing effect isconsidered in the boundary conditions on the so-called ghost cells insidethe surfaces directly. To promote the computational accuracy near the solidsurface, this study firstly modifies the CEFM and then proposes a newtreatment called a predicted DIFM. They have been validated by numericalsimulations of the uniform incompressible flow past a cylinder. The resultssuggest that the present modification for CEFM leads to a higher accuracynear solid surfaces than the original one, which uses forcing terms in astaggered time-level comparing the time-level of velocities. Moreover, only1-order or even less of accuracy near surfaces can be obtained since thecontrolling equations are discretized by a 2-order scheme. Therefore, it maybe not useful for this type of methods to refine the meshes near thesurfaces to obtain a higher accuracy. Meanwhile, the DIFM can obtain muchmore accurate results especially and the assumption of pseudo-coincidentpoints is proven to be effective to promote the accuracy from 1-order to2-order with fine grids, even if the linear assumption of velocitydistribution near solid surfaces remains. Hence, the predicted DIFM isproven to lead less numerical errors and a faster convergence, even thoughit can't promote a higher order of accuracy. Moreover, the overallaccuracies are not affected obviously by the different methods and goodresults are obtained in simulations of the cylinder case. Further researchesare performed in the cases with moving boundaries, more complex geometricalboundaries and fluid-structure interactions.
2009, 41(5): 618-627. doi: 10.6052/0459-1879-2009-5-2008-282
Simulation of effects of blade rotation on tip clearacne flow in axial turbines}
Maosheng Niu, Shusheng Zang, Minghai Huang
Blade rotation is one of the most important factors thataffect tip clearance flow in turbine rotors. This paper presents a numericalinvestigation of flow structures within tip clearance of the LISA 1.5-stageaxial turbine. It shows that blade rotation obstructs tip clearance flow inaxial turbines. When blades are stationary, relative velocity at gapentrance becomes higher due to the disappearance of blocking effect, toinduce much more fluid into tip clearance. Furthermore, all the leakage flowrolls up to form tip clearance vortex. One more tip clearance vortex nearthe leading edge occurs beside the familiar one at the mid-chord,leading to greater flow losses. Moreover,over-under-turning induced by secondary flow increases with the decrease ofblade rotation speed. Also it can be found that in forward profiles thestatic pressure continues to increase from the entrance to the exit of thetip clearance, and it becomes more uniform in the profile near the trailingedge.
2009, 41(5): 628-634. doi: 10.6052/0459-1879-2009-5-2008-062
Simulation of Natural Convection Flow by the Thermal Lattice Boltzmann Method
Jianfei Xie, Chengwen Zhong, Yong Zhang, Dachuan Yin
In this paper, the thermal lattice Boltzmannscheme has been improved, which was proposed by J. G. M. Eggels and J. A.Somers, and a new equilibrium solution for temperature distribution functionhas been presented on the incompressible flow assumption. This newequilibrium solution can correct the compressibility effect on macroscopictemperature, and modify the statistical definition of macroscopictemperature. The half-way bounce-back boundary condition was used in themethod proposed by J. G. M. Eggels and J. A. Somers for velocity andtemperature. However, the boundary condition was not accurate for thetemperature in the physical view. Therefore, a non-equilibrium extrapolationscheme, which is a simple algorithm and very easy to implement, has beenadopted for velocity and temperature in the boundaries. Subsequently, theimproved TLBM has been used to simulate the natural convection in the cavityat $Ra=10^{6}$ and $Pr=0.71$ for air. The flow parameters obtained in thesimulation agreed very well with those of other numerical methods, toindicate that the improved TLBM can be used to simulate the non-isothermalflows efficiently and accurately.
2009, 41(5): 635-640. doi: 10.6052/0459-1879-2009-5-2008-193
Investigation of model reduction for aeroservoelasticity based on unsteady aerodynamics estimating
Zijian Zhang, Min Xu, Shilu Chen
Transonic unsteady aerodynamics model can be obtained by CFD/CSD couplingcomputation, but it is disadvantaged to analyze and integrate ASE problemsbecause of the high order of the model. The high order ASE model is dealtwith order reduction technique using system differentiate and analyses, andbalanced truncation in this paper, and to integrate with the low ordermodel. Outlines of this paper can be generalized as follow: (1) The unsteadyaerodynamics reduced-order model (ROM) is gained by applying Volterra seriestheory, and the aero-servo-elasticity (ASE) model is gained by couplingconfiguration dynamics and servo dynamics; (2) A lower ASE reduced-ordermodel is obtained using the balanced truncation method; (3) Based on ASEreduced-order model a mixed sensitivity $H_{\infty }$ controller is designedfor flutter suppression to reduce the order of the controller while keepingits robustness. At last, in a typical BACT system, simulations of modelreduction and active flutter suppression controller designing are given. Theresult shows that the ASE reduced-order model based on ROM can reflectflutter characteristic of practical system factually, and it has lower orderthan CFD/CSD coupling model, while the low-order robust controller designedbased on balanced truncated ASE model can apply to practical systemeffectually, and increased the flutter speed by 36%.
2009, 41(5): 641-650. doi: 10.6052/0459-1879-2009-5-2008-223
Numerical and experimental studies on unsteady shedding mechanisms of cloud cavitation
Bo Zhang, Guoyu Wang, Biao Huang, Zhiyi Yu
The unsteady characterics of cloud cavitating flow arounda hydrofoil are investigated by the experimental and numerical methods.Experiments on a hydrofoils are carried out in a rectangular test section ofa cavitation tunnel. A high-speed video camera is used to visualize theunsteady flow structures. The caculations are conducted on thetwo-dimensional hydrofoil section, based on a single-fluid model of thecavitation: the liquid/vapor mixture is considered as a homogeneous fluidwhose compsition is regulated by mass tranfer equation. The RNG$k$-$\varepsilon $ turbulence model with modified eddy viscosity coefficient isused in the computation, and the coefficient is related to the vapor andliquid densities in cavitated regions for simulating the cavitating flow.The experimental and numerical results show the unsteady features of theperidical cloud cavity departure; the increasing of a local pressure is amain factor to induce ruture of a cloud cavity; an interaction between there-entrant jet and the cavity interface in the closure region can lead tothe increasing of the local pressure; the adverse pressure gradient ismainly responsible for the generation of the re-entrant jet.
2009, 41(5): 651-659. doi: 10.6052/0459-1879-2009-5-2008-152
Wave run-up on a vertical wall protected by a submerged breakwater
Jingxin Zhang, Hua Liu
Submerged breakwaters have been constructed in coastal zones for shorelineor harbour protection or to prevent beach erosion. In the paper, the waverun-up on a vertical wall protected by a submerged breakwater is analyzed.The physical configurations include a rigid barrier and a semi-infinitelylong channel with finite depth. By means of numerical wave flume technique,the linear incident wave propagation and run-up on the vertical wall aresimulated. In the cases of different distances between the barrier and thewall with a fixed barrier height, the results of numerical simulations showthat the wave run-up depends on the ratio of the distance to the wavelength. There is no difference of the wave run-up on the vertical wall withor without the barrier, when the barrier is located at the anti-nodes of thestanding wave; while the wave run-up with the barrier is lower than thatwithout the barrier, when the barrier is located at the nodes of thestanding wave. Based on the linear wave theory, by matching the velocityalong the barrier and along the gap, the systems of linear equations aboutthe velocity potentials are obtained, i.e. the theoretical model.Furthermore, the wave run-up is further analyzed for more various settingsof barrier height and distance between the barrier and the wall with thetheoretical model. Not only the numerical wave flume simulations, but alsothe analytical results reveal that the wave run-up on the wall stronglydepends on the distance between the barrier and the vertical wall.
2009, 41(5): 660-665. doi: 10.6052/0459-1879-2009-5-2008-291
A new grid adaptive strategy combined characterized based split method
Yan Chen, Shuliang Cao, Kaihong Liang, Baoshan Zhu
A new self-adapting grid method is presented by adding the new point atthe centre of the grid cell. Compared with the traditional method addingthe new point at the median, the new refine method is more convenient toprogram and has better geometrical feature. At last, this paper combinesthe new refined method with characterized based split method to solveN-S equation. The convective acceleration term disappear along thecharacteristic. In order to avoid the restriction on the nature of theinterpolation function, the momentum equation is solved bynon-incremental split method, which satisfies the Babuska-Brezzi(BB)condition. The variable gradient is used as the adaptive parameter. Theresult shows the combined method has goodprecision and convergence.
2009, 41(5): 666-670. doi: 10.6052/0459-1879-2009-5-2008-446
A nonlinear viscoelastoplastic rheological model based on nishihara's model
Liangquan Li, Weiya Xu, Wei Wang
A new nonlinear viscoelastoplastic rheological model is proposed to perfectly describe the global creep behavior in this paper. The present model is based on Nishihara's model by adding two additional elements: one is the nonlinear viscoplastic element which is used to define the onset of the tertiary creep stage; the other is the plastic element describing the instantaneous plastic deformation. Firstly, a three-dimensional model is formulated on the basis of its one-dimensional form. Then, the identification of rheological parameters is investigated in detail. Moreover, the parameter sensibility analysis is performed. The experimental results of triaxial creep test are used to verify the validity of the model. It is shown that the proposed nonlinear viscoelastoplastic rheological model can be used to perfectly describe three creep stages at multiple deviatoric stress levels with a set of rheological parameters.
2009, 41(5): 671-680. doi: 10.6052/0459-1879-2009-5-2008-068
Analysis of doubly periodic in-plane cracks using the eigenfunction expansion-variational method
Peng YAN, Chiping Jiang
A variational functional for the unit cell for a doublyperiodic in-plane problem is presented, based on the variational principlein elasticity in conjunction with the double quasi-periodicity of thedisplacement field and the double periodicity of the stress and strainfields. Then by combining with the eigenfunction expansions of the complexstress functions satisfying the traction-free conditions on the cracksurfaces, an eigenfunction expansion-variational method for the unit cellmodel is developed. The general doubly periodic boundary conditions for aunit cell are considered, so the present method can be used to solve thegeneral doubly periodic crack problems. The convergency analysis of thenumerical results demonstrates the high efficiency and accuracy of thepresent method. Finally, for several general doubly periodic crack arrays,the influence of the stress intensity factors on the crack arrangement isexamined.
2009, 41(5): 681-687. doi: 10.6052/0459-1879-2009-5-2008-117
Research for the mechanics behavior of DD3 Ni-base Alloy with kinematic hardening effect
Junfeng Nie, Xiaochuan You, Zhuo Zhuang, Xudong Li
In the present paper, we describe the details of aplasticity constitutive model for nickel-based alloy crystal. Under the Arso(1983) crystal plasticity framework, the constitutive model involves thekinematic hardening rule, and also takes into account the temperature andstrain rate on the impact of crystal plastic deformation. In theconstitutive model, the yield criterion and flow rule are built onindividual slip system. We have derived the integral method of theconstitutive model, and implement the finite element integral algorithm ofthe constitutive model as a user material subroutine (UMAT) in ABAQUS.Moreover, we simulate the stress-strain response of DD3 Ni-base alloy underuniaxial tension and cyclic loadings on different crystal orientations.Compared with the corresponding experiment data, we find that this model isable to accurately describe the anisotropic deformation response of theNi-base single crystal, and could also capture the tension-compressionasymmetry of the cyclic plastic deformation of the Ni-base alloy singlecrystal.
2009, 41(5): 688-695. doi: 10.6052/0459-1879-2009-5-2008-039
On thermodynamically consistent anisotropic unilateral damage model for concrete
Jianying Wu
The appropriate modeling of damage induced anisotropy and unilateral effectsdue to macrocracks evolution are rather crucial to predict the nonlinearresponses of concrete material and structures. With the introduction ofscalar, vector, second-order and fourth-order tensors, or even higher damageinternal variables, continuum damage mechanics (CDM) is capable ofmacroscopically describing the influences of microcracks evolution on thenonlinear behavior of concrete and therefore has been widely adopted in theliteratures. From the physically motivated viewpoint, the terminology``damage'' is directly characterized as the degradation of the stiffness orequivalently, the increase of the compliance. Therefore, the fourth-ordertensor and more specifically, the material stiffness (or the materialcompliance, or the change relative to the initial value), is perhaps themost rational candidate as the damage variable. Accordingly, the so-calledelastic degradation model which introduces the degradation strain rate waspreferred in the modeling of damage induced anisotropy. To describe theunilateral effects upon cyclic loadings, the decomposition of rank-twovariables (e.g. stress, strain, effective stress, etc.) into the positiveand negative components along with the corresponding fourth-order projectionoperators is generally adopted. Nevertheless, the expressions for theprojection operators are not unique, and all the existing CDM models formicrocracks induced anisotropy and unilateral effects imply athermodynamically consistent result, i.e. the non-zero energy generationsupon damage unloading when applied to describe the unilateral effects.In this paper based on the framework of irreversible thermodynamics and thetheory of internal variables, a thermodynamically consistent anisotropicdamage model for concrete is proposed. To model the unilateral effects, thestress tensor is decomposed into its positive and negative components. Theincrements of the intrinsic compliances under purely positive and purelynegative stress states are adopted as the internal damage variables todescribe the microcracks evolution on the macroscopic nonlinear behavior ofconcrete. The conditions for zero spurious energy dissipations are presentedand then new expressions for projection operators are introduced toguarantee the thermodynamical consistency. The damage evolution laws arepostulated by analogy to the flow rules in classical plasticity and theplastic-type rate constitutive relation is derived. The numericalimplementation of the proposed model including the back-Euler method basedstress updating algorithm and the algorithmic consistent tangent moduli arealso presented in details. Finally, the model is specialized to concretewith appropriate evolution laws and is applied to numerically simulate thestress-strain relations of several typical loading cases. The obtainednumerical predictions agree with the experimental data fairly well,demonstrating the validity of proposed model. It is worth to note that,neither the principle of strain equivalence nor the hypothesis of strainenergy equivalence is required in the developed model.
2009, 41(5): 696-707. doi: 10.6052/0459-1879-2009-5-2008-109
The study on the compressive behavior of ptfe/al energetic composite
Songlin Xu
The metal/fluoro-ploymer energetic composite is a new kindof advanced energetic material. The compressive behaviors and reactiveperformance of polytetrafluorethylene (PTFE)/Al reactive material based ondifferent Al contents are investigated experimentally by split Hopkinsonpressure bar (SHPB) and universal testing machine at different strain rates(ranged from 10^{-3}s^{-1} to 10^{3}s^{-1}) respectively atroom temperature. The experimental results showed that the compressivebehavior of PTFE/Al is sensitive to strain rates, that is, the dynamicmodulus and strength are higher at the high strain rate, while the strain islower. The failure behavior of PTFE/Al includes plastic deformation, crackand reaction. Along with the increasing of Al content in PTFE/Al, thecompressive strength is enhanced and then decreased, which achieves amaximal value of 102.6 MPa with static loading and 154 MPa with dynamicloading, respectively, at the content of 35 wt{\%} Al. Meanwhile, thedifficulty of reaction is increased and perfectibility of reaction isdecreased with the increase of strain rate, while the corresponding stressto initiate reaction of PTFE/Al is almost to be about 165 MPa.
2009, 41(5): 708-712. doi: 10.6052/0459-1879-2009-5-2009-253
meshless local Petrov-Galerkin method for static shakedown analysis of elasto-plastic structures
Shenshen Chen, Yinghua Liu, Zhangzhi Cen
Shakedown analysis is an important branch of plasticityand can provide a theoretical basis for engineering designs and safetyassessments. Based on the static theorem of shakedown analysis, a novelnumerical method is developed to perform lower bound shakedown analysis bymeans of meshless local Petrov-Galerkin method (MLPG) with the Voronoi cellsand the reduced-basis technique. The natural neighbour interpolation isemployed instead of the moving least squares approximation to constructtrial functions. The natural neighbour interpolants are strictly linearbetween adjacent nodes on the boundary of the convex hull, which facilitatesimposition of essential boundary conditions with ease as it is in theconventional finite element method. By introducing the conception of loadvertex in the basic load domain, the numerical difficulties caused by thevariable of time parameter in lower bound shakedown analysis are overcome.Based on the reduced-basis technique, the lower bound shakedown analysisproblem is reduced to a series of non-linear programming sub-problems withrelatively few optimization variables. In each sub-problem of non-linearprogramming, the self-equilibrium stress field is simulated by linearcombination of several self-equilibrium stress basis vectors with parametersto be determined. These self-equilibrium stress basis vectors are generatedby performing an equilibrium iteration procedure during elasto-plasticincremental analysis. Several numerical examples are presented to verify theavailability of the developed method.
2009, 41(5): 713-721. doi: 10.6052/0459-1879-2009-5-2008-342
A new adaptive finite element method for multiscale dynamic simulation
Yun Xu, Jun Chen, Xijun Wei
A new adaptive finite element method coupling withmultiscale simulation for material computation is proposed in this paper.The early behaviors of the material damage are simulated by BSM thatcoupling microscale MD with macroscale FE, in which the macroscale finiteelement computation has been generalized to irregular triangular meshes.Once material fracture is formed, its further development is only describedby a macroscale model with the adaptive finite element method. A posteriorierror estimator was proposed with the variational multiscale theory.Meanwhile, the adaptive meshes were based on the residual distribution ofthe coarse scale and the Green's function in the fine scale. A given failurecriteria is used to determine the split of the mesh. Efficiency of theproposed method is validated by numerical experiments.
2009, 41(5): 722-729. doi: 10.6052/0459-1879-2009-5-2008-024
A new spherical indentation-based method to extract plastic material parameters
Peng Jiang, Taihua Zhang, Rong Yang, Naigang Liang
This paper presents a new spherical indentation-basedmethod to extract plastic properties of materials. With the specificevaluation on the response parameters in indentation tests, the energy ratio(the ratio of releasable work to total work) was chose and investigated inorder to avoid the estimation of contact radius. Based on expanding cavitymodels, finite element computations and dimensional analysis, therelationships between energy ratio and plastic parameters are established.With these relationships, the plastic properties of materials can beconsequently solved from instrumented spherical indentation test data.Furthermore, the stability of the method has been improved by reorganizationof parameters. Finally, the veracity and simplicity of this method ischecked by using two typical materials (Steel 45C and Al 6061), which haveknown true stress-true strain curves.
2009, 41(5): 730-738. doi: 10.6052/0459-1879-2009-5-2008-194
Modeling on mass abrasion of kinetic energy penetrator
Xiaowei Chen, Shiquan Yang, Liling He
An engineering model on mass abrasion of kinetic energy(KE) penetrator is presented to predict the nose shape and mass loss of theresidual projectile after high speed penetration into concrete. Theexperimental analysis indicates that the kinetic energy of penetrator (i.e.,mass and velocity of projectile) and the hardness of aggregate of concretenoticeably affect the mass abrasion of projectile. Generalized relationshipbetween mass loss and impact function I of projectile is constructed.Graphical analysis shows that the most mass loss occur on the nose ofprojectile and the eroding nose approach to an ogival shape with a smallvalue of caliber-radius-head (CRH). The mass loss from abrasion on KEpenetrator may be evaluated through the variation of nose shapes.
2009, 41(5): 739-747. doi: 10.6052/0459-1879-2009-5-2008-295
Constrained Substructure Model Updating Method Based on Local Mode
Jilin Hou, Jinping Ou
Modal updating is a crucial problem in Structure HealthMonitoring (SHM) and has strongly attracted researchers' attentions.Recently the structures have been becoming much huger and more complex, soit's getting harder to update the global structural model precisely usingthe classical model updating methods. In general, only some localsubstructure model is important and it is not necessary to update the wholestructure. Therefore the substructure technologies are important for thatthey require only few sensors and the local dynamic information toaccurately update the interested substructure model.Usually the updating of the element stiffness is enough to reflect thedamage and the structural dynamic performance. This paper proposes a conceptof the Isolated Substructure. It aims at updating local substructure elementstiffness only by the relative mode at the substructure location. Thepresent Isolated Substructure refers to a new structure formed by isolatingthe substructure from the global structure. Then the substructure can beupdated indirectly through updating the Isolated Substructure, such that theoptimizing variables become much less and the convergent speed is fastened.The key process of this method is to construct the flexibility matrix of theIsolated Substructure by measured data. First the lower order frequenciesand shape modes of the substructure are identified from the measured impulseresponse by utilizing Eigensystem Realization Algorithm (ERA), and therelative modal masses are estimated by Least Square Method (LSM); Second,according to its independence and convergence properties, the flexibilitymatrix corresponding to the substructure can be approximately constructed bythe identified lower order modes and be improved by the calculated higherorder modes from the theoretical model; and then utilizing the concept ofthe flexibility matrix, the substructure is isolated from the globalstructure through applying numerical supporting on the substructureboundary; synchronously the flexibility matrix of the Isolated Substructureis constructed from the advanced obtained flexibility matrix of the globalstructure, and is used to update the Isolated Substructure, that is, toequally update the substructure.The optimization method based on sensitivity idea is adopted, and therelative formulas are deduced. It makes the iteration and convergencefaster.A numerical example of a plane truss separately with 5% or 10% rmsGaussian measurement error validates that the substructure can be updatedeffectively by the Isolated Substructure model updating method.
2009, 41(5): 748-756. doi: 10.6052/0459-1879-2009-5-2008-319
Mechanistic principles of sensory analysis on object softness by touch means
Jiyong Hu, Xin Ding, Rubin Wang, Wei Lin
It is a fascinating field for elucidating and quantifyingthe tactual performance of object softness in sensory engineering. In termof the macroscopically contacting interaction between fingerpad and objectsurfaces as well as the touching means, an equivalent biomechanical model isdeveloped to simulate the process of cutaneous low-thresholdmechanoreceptors sensing object softness. And then, two indexes whichcharacterize the ability of human tactual system in detecting anddiscriminating object softness, namely mechanical sensitivity and perceptualsensitivity are established on the basis of the developed biomechanicalmodel. By the established indexes, it is discussed parametrically that thegeneral mechanistic principle that human tactual system processes theproperty of object against compression. With the former discussion intheory, it is concluded that the mechanical resistance of object againstcompression is the tentative potential physical property on which humantactual system discriminate the softness of objects. Furthermore, thedecetability and discriminability of human tactual system in object softnessdepends on the ratio of the mechanical resistance against compression ofobjects to that of soft tissues within fingertip, and on the touching forceexerted by fingertip. Meanwhile, in terms of the deformable medium of softtissues within human fingertip communicating mechanical resistance of thedetected objects against compression, the working principle of human tactualsystem is different from that of the man-made testing machine with adesigned sensitivity, and human can not discriminate from all of compliantobjects with significant instrumental differences by compression testers.All of conclusions will help to understand the variation of estimation onfabric softness by touch means, and to improve the performance of predictionmodel and virtual rendering of object softness.
2009, 41(5): 757-764. doi: 10.6052/0459-1879-2009-5-2008-301
The dynamical behavior of a piecewise-linear electric circuit with periodical excitation
xiaofang zhang, zhangyao chen, Ying Ji, Qinsheng Bi
Since the chaotic phenomenon in Chua's circuit was reported, the complicateddynamics in nonlinear circuits has been one of the key topics to attract alot of researchers. Based on Chua's circuits, many modified models have beenestablished, which exhibit rich nonlinear behaviors, such as intermittencyand chaos crisis. Because of the piecewise-linear function between thecurrent and the voltage introduced, non-smooth bifurcation may occur at thesingular positions. Up to now, most of the obtained results focus on thedynamics of autonomous vector fields. However, many real electric circuitsare non-autonomous, in which the time-dependent terms may come from thealternating current or the controllers. Therefore, it is very important toexplore the evolution of the dynamics of such types of systems.Based on the bifurcation prosperities of a fourth-order autonomouspiecewise-linear electric circuit, complicated dynamics of the oscillatorwith periodic excitation for two different excitation amplitudes has beeninvestigated in details. Two coexisted bifurcation forms for weak excitationare presented. Different chaotic attractors can be observed via sequences ofassociated bifurcations, which may interact with each other to form anenlarged chaotic attractor. While for the relatively strong excitation, theperiodic orbit circling around the original two equilibrium points does notsplit into two parts, resulting in the disappearance of the coexistedphenomenon. Because of the different scale between the natural frequency andthe excitation frequency, fast-slow effect was obviously found on thebehaviors of both the weak and strong excitation, such as periodicsolutions, quasi-periodic movements, and even for chaotic oscillation.Furthermore, the mechanism of fast-slow effect has been discussed from theview point of bifurcation.
2009, 41(5): 765-774. doi: 10.6052/0459-1879-2009-5-2008-075
The relationship between stochastic resonance and the average phase-synchronization time
Xiaojuan Dong
The phenomenon of stochastic resonance (SR) andphase-synchronization between the input signal and the output signal in abistable system were investigated. At first, we obtained the expressions ofthe output signal-to-noise ratio (SNR) and the averagephase-synchronization time between the input signal and the output signal,and then the relationship between SR and the averagephase-synchronization time was studied. The results show that: (1) SRappears, and the average phase-synchronization time is sensitive tonoise. For the simultaneous existence of the multiplicative noise andadditive noise, there is a restraint, and then a peak in the curve of theoutput SNR and the average phase-synchronization time with theincrease of additive noise intensity. Moreover, the decrease of the ratio ofmultiplicative noise intensity and additive noise intensity can increase theoutput SNR and the average phase-synchronization time. (2) SR andthe maximum of the average phase-synchronization time appear atdifferent times, but the average phase-synchronization time issensitive to the output SNR. These results may be helpful in signalprocessing where the working environment can be tuned according to theprinciple of SR.
2009, 41(5): 775-782. doi: 10.6052/0459-1879-2009-5-2008-549
Analyzing and interpreting the quoted theses in the chinese journal of theoretical and applied mechanics by literature metrology
Huixiang Wang, Caijun Tao
Based on the database of Chinese TechnologicalJournal(cited) created by Vip information Lid., the paper is analyzed andstudied the quoted passages in Chinese Journal of Theoretical andApplied Mechanics over the last19 years(1990-2008.6). It aims at impartially shedding light on how to refer anduse the quoted theses in Chinese Journal of Theoretical andApplied Mechanics scholars as well as thisjournal's whole level and role in Chinese academia.Key words Journal research , Acta Mechanica Sinica, the quoted theses , Core authors,analyzing and interpreting
2009, 41(5): 783-788. doi: 10.6052/0459-1879-2009-5-2008-563
The lyapunov exponent of vortex dynamics
Hao Zhu, Keming Cheng
Three-vortex system in an ideal fluid in the plane satisfies Hamiltonian form and the motion equations are integrable. However, the behavior of vertices are still complex so that it is difficult to study the passive particle in three point vertices system. Our focus is on the stability of passive particle with respect to an initial small perturbation, and Lyapunov exponent is introduced by employing Oseledec theory to describe the stability of passive particle quantitatively. In order to avoid fussy calculation, the simple expression of Lyapunov exponent is obtained by the conservation of volume in Hamiltonian system. Moreover, this definition leads to the partition of the instantaneous flow field in the point vortex system to show that the chaos motion of the passive particle only occurs in some especial regions.
2009, 41(5): 789-793. doi: 10.6052/0459-1879-2009-5-2008-469
Numerical simulation of inhibitory effects of endostatin on tumor angiogenesis
Jie Wu, Shixiong Xu
The inhibitory effects of anti-angiogenic drug Endostatinon tumor angiogenesis are simulated by adopting 2D and 3D discretemathematical models, which are used to describe the formation of capillarynetworks inside and outside the tumor. In the discrete mathematical models,five factors were mainly taken into account the influence of the migrationof endothelial cells: (i) proliferation and (ii) random motility of theendothelial cells; (iii) chemotaxis in response to tumor angiogenic factor(TAF) released by the tumor; (iv) haptotaxis in response to fibronectingradients in the extracellular matrix, especially the inhibitory action ofanti-angiogenic drug Endostatin, and (v) inhibitory effects of Endostatin.Meanwhile, spatiotemporal evolution of 2D and 3D tumor microvascularnetworks is performed. The simulation results indicate that anti-angiogenicdrug Endostatin obviously has the inhibitory effects on the rate of bloodvessels growth, the bifurcation amount and the development of themicrovascular network inside and outside the tumor. Furthermore, themicrovascular networks generated by the present mathematical models haverelatively realistic structure and morphology inside and outside the tumor.These results may provide beneficial information for anti-angiogenesistreatment of tumor and further clinical research.
2009, 41(5): 794-800. doi: 10.6052/0459-1879-2009-5-2008-122
Plane strain consolidation of a multi-layered soil with anisotrpic permeability and compressible constituents
Zhiyong Ai, Chao Wu
This paper study the plane strain consolidation of a multi-layered soil, and the anisotropy of permeability and the compressibility of pore fluid are considered. Starting from the governing equations of plane strain Biot’s consolidation, taking the Laplace transform and the Fourier transform with respect to t, z and x, the transfer matrix relationship of basic variables in the transform domain between z = 0 and an arbitrary depth is obtained. The solutions of plane strain consolidation for the multi-layered soil with anisotropic permeability and compressible constituents can be acquired by using the transfer matrix method, continuity conditions and boundary conditions of the multi-layered soil and the inversion of the Laplace-Fourier transform. Numerical analysis is carried out by using corresponding program to investigate the influences of the anisotropy of permeability, the compressibility of pore fluid and the layered characteristic of soil on the consolidation behavior of soil.
2009, 41(5): 801-807. doi: 10.6052/0459-1879-2009-5-2008-477
An exponential matrix function and its application
Minghui Fu, Jinghua Lin
A new exponential matrix function is introduced to obtainthe special solutions, based on Duhamel convolution integration for thenon-homogenous polynomial terms of the first order constant coefficientordinary equation, exponential functions or their products., Based on thenew exponential matrix, an efficient recursive algorithm is proposed in thispaper with a precise integration method (PTM) applied to the specialsolution. The processes of PTM for general solution and the proposed methodfor special solution are closely integrated. This combination is confirmedto have a high computational efficiency.. The proposed method is alsovalidated to have more convenient and more applied range. A general formulais given to greatly save computation time. Numerical examples are alsodemonstrated the validity and efficiency of the method.
2009, 41(5): 808-814. doi: 10.6052/0459-1879-2009-5-2008-052
Research on the reliability of damping valve with annular slice
Yijie Chen, Zhanhua Yang, Qiangshun Lei, Yajun Wang, Dan Ning
Water hammer pressure of throttle valve is presentedbased on the invalidation of throttle slice in hydro-pneumatic spring duringthe field tests. The physical model of throttle valve with annular slice isbuilt. The water hammer calculation of damping valve is performed by usingthe water hammer theory and the solving method of latent line for thepartial differential equations. The invalidation reasons of throttle sliceare analyzed through numerical simulation. The influences of throttleorifice structure on water hammer and damping force of throttle valve arealso researched. The method of valve reliability is evaluated from yield andfatigue and the calculation example is carried out. The obtained results canprovide reference for the throttle valve reliability in order to avoid thebreak of the throttle slice.
2009, 41(5): 815-820. doi: 10.6052/0459-1879-2009-5-2008-546