力学学报

A study of linear long wave attenuation over a Maxwell mud bed

Yuezhang Xia, Keqin Zhu

In coastal area, the interactions between waves andmuddy seabed lead to energy dissipation. We use Maxwell model as theconstitutive equation of non-Newtonian mud and develope a new set ofBoussinesq-type equations to describe wave propagation under wave-mudinteraction. Based on these equations, the damping rate for one-dimensionallinear long waves is analytically obtained. The present result is consistentwith previous literatures when the model degenerates to Newtonian case. Whendimensionless relaxation time λ is large, extremums of the dampingrate appear quasi-periodically as the mud depth increases. These extremepoints correspond to the peaks of modal damping rates.

2010, 42(3): 343-349. doi: 10.6052/0459-1879-2010-3-2009-151

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Dynamic response research of underwater vehicle with consideration of hydroelascity

Haibo Lv, Xiaobo Quan, Yunyu Yin, Haipeng Wei, Xiongliang Yao

Cavitation occurs on the surface of the underwatervehicle in its high-speed motion. For reasons of cavity re-entry, cavitycollapse, flows and waves, the fluid excitations of the vehicle are verycomplicated to induce transient responses in structures. Such responses willchange the flow field around the structures thereby. Such an interactionrepresents the coupling phenomenon between fluid and structures in inertia,damping and elasticity. It is very hard to solve the fluid-solid couplingproblem like that.The key of hydroelasticity is to consider the interaction in inertia,damping and elasticity forces and to solve the hydrodynamic and structuraldynamic equations together. In recent years, many scholars have done a lotof work and solved many theoretical and engineering problems. In this paper,the added mass matrix, in which the interactions are taken into account inthe structural dynamic equations under the influence of hydroelasticity, isobtained based on three-dimensional potential theory and Boundary ElementMethod (BEM). Consequently, the exiting-water dynamic response of theunderwater vehicle with cavities is analyzed.The experimental and analytical results have shown that the cavity collapseproduces strong dynamic responses in structures. The wet frequency of thevehicle changes with the cavity length. The system constructed by the fluidand the structures is time-dependent. The influence of hydroelasticity onthe structural dynamic response can not be negligible. The structuralfrequency and the response amplitude in water have obvious differencescompared with those in air due to hydroelasticity. The present scheme tosolve the fluid-solid coupling problem has important significance inengineering applications.

2010, 42(3): 350-356. doi: 10.6052/0459-1879-2010-3-2008-241

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The study of vortex-induced vibrations by computation using coupling model of structure and wake oscillator

Fang Song, Liming Lin, Guocan Ling

A new model of coupling structure and wake oscillator invortex-induced vibration (VIV) is established. It is based on forcebalance between structure and near wake flow. The nonlinear near wakevortex dynamics is modeled by a nonlinear oscillator satisfied the Van derpol equation. According to the study of 2-DVIV, the coupling model describes the featuresof response versus reduced velocity qualitatively and quantitatively. These results prove that the peak amplitude of structure$A_{\max }^\ast $ decreases as the mass-damping $(m^\ast + C_A )\zeta $increases. An empirical formula on $A_{\max }^\ast $ versus $(m^\ast + C_A)\zeta $ is obtained based on these results. The present 3-D coupling modelis employed in the study of 3-D VIV of flexible slender cylinder. Dynamicresponse behavior of uniform flow presents a change from standing wave totraveling wave. Under non-uniform flow whose profile is sinusoidal, thestructure vibration is a combination of standing and traveling waves alongthe span. These results are similar with those from direct numericalsimulation (DNS), and some other previous results.

2010, 42(3): 357-365. doi: 10.6052/0459-1879-2010-3-2009-147

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System performance analysis of pulse detonation engines

Xudong Li, Aifeng Wang, Chun Wang, Zonglin Jiang

A simplified model of Pulse Deotonation Engines(PDEs) isadopted in present paper to estimate the system performance withthermodynamic cycle analysis method. The analytical expression of PDE'sthermodynamic cycle efficiency is derived in relation to the parameter oftotal pressure recovery coefficient. In addition, we attempt to investigatethe influence of the total pressure recovery coefficient of PDE inlets andinitial temperature of combustion chamber on the PDE thermodynamic cycleefficiency. The results demonstrates that, reducing total pressure loss ofthe inlets is beneficial to increase the thermodynamic cycle efficiency, andincreasing the initial temperature of combustion chamber can even apparentlyenhance thermal efficiency. Based on the current results, Multistage PulseRe-Detonation Engines(MPRDEs) configuration is presented in this paper forthe first time. We use the shockwave front of detonation waves decoupled atcorner to compress the working medium, which improves the thermodynamicalparameters of the working medium and PDE's system performance. Thethermodynamic cycle efficiency of this configuration is derived, whichdemonstrates the possibility of MPRDE configuration theoretically. Theresult shows that, MPRDE configuration can improve the thermal efficiencyeffectively via raising working medium's temperature in front of detonationwave. Finally, because some of the working medium is not perfectly expandedwhen rushing out of nozzle, a qualitative discussing is carried out on PDE'sthermal efficiency under different exit pressures. The moment of workingmedium will be promoted and thermal efficiency will be improved when theexit pressure is lowered.

2010, 42(3): 366-372. doi: 10.6052/0459-1879-2010-3-2008-635

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Experimental study on perturbation mixing enhancement in supersonic mixing layers

Wubing Yang, Fenggan Zhuang, Qing Shen, Shihe Yi, Lin He, Yuxin Zhao

Perturbation mixing enhancement effects are evaluatedfor supersonic mixing layers by NPLS flow visualization technique. Someexperiments are carried out to optimize the parameters of the disturbances.The images reveal that the mixing layers are sensitive to the disturbanceswithin the splitter plate. 2D disturbances advance the unstable position ofthe mixing layer and thicken it to enhance mixing, while 3D disturbancespromote flow 3D characteristic to enhance mixing by inducing streamwisevortexes and spanwise convolution. The mixing-enhancement effect of 3Ddisturbances is better than that of 2D disturbances. Although the tape islocated in the sub-boundary layer, the shock wave is inevitable in thesupersonic flow. These Mach waves are the main reason for the loss of totalpressure in this mixing-enhancement method.

2010, 42(3): 373-382. doi: 10.6052/0459-1879-2010-3-2008-660

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New conception of aerothermal protection for hypersonic vehicles

Jing Pan, Chao Yan, Yunfei Geng, Jie Wu

High speed vehicles are designed to withstand severeaerodynamic heating conditions. Such vehicles include hypersonicprojectiles, reentry payload module and hypersonic aircraft. Maximum heatingand the consequent possibility for material erosion are typical problemsassociated in the nose region of the blunt body. The blunt nose shape alsoleads to very high aerodynamic drag accompanied by high structural pressureloadings, which exhibit significant effects in the final performance of thevehicle. So, there will be a trade-off study between thermal protectionsystem and high wave drag associated with shock wave formation on such highspeed vehicles.Waverider is favorable configuration for hypersonic aircrafts in terms ofthe high lift-to-drag ratio and integration design facility. However, theirsharp leading edge brings severe aero-heating problem, which seriouslyhinders them from practical applications. Current literatures aboutaerothermal protection for waveriders mainly focus on the leading edgeblunting. However, these researches are all motivated by aerothermalconsideration, and the requirements of high lift-to-drag ratio greatlylimits the bluntness of the leading edge, thus the effectiveness inaeroheating protection. In other words, the blunting of waverider's leadingedges seems a theoretically possible way to relieve aeroheating. Under thisbackground, the ``artificially blunted leading edge (ABLE)'' concept isfirst introduced into the waverider design in the present paper, expected topreserve a relatively sharp leading edge on the aerodynamic aspect, whileshowing virtual blunt leading edge on the aerothermal aspect, so as to finda new and effective way for waverider aerothermal protection.After a comprehensive formal parameter definition of the ABLE waverider, theinfluences of the parameters on the aerodynamic and aerothermalcharacteristics are investigated by means of the CFD numerical simulation.Basing on the flow analysis, with a circuitous process, feasibletwo-dimensional ABLE waverider configurations are finally obtained, and therules and disciplines of the aerothermal protection method for waveridersusing the ABLE concept are concluded. The results show that, if designedproperly, the maximum heat transfer rate can be reduced by 60{\%} or so,with a lift-to-drag ratio loss of no more than 19{\%}, compared to thecorresponding normal waverider configuration. Furthermore, the effectivenessis believed to be better with integral optimization of the ABLE formalparameters.

2010, 42(3): 383-388. doi: 10.6052/0459-1879-2010-3-2008-334

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Numerical research on the sudden change characteristic of the first bifurcation for natural convection of air enclosed in 2D rectangular cavity

Xiaohua Wang, Wenfang Zhu

Based on grid independence analysis, a second order Euler-Taylor-Galerkin finite element method of fractional steps was used to numerically investigate the first bifurcation of natural convection of air enclosed in a 2D rectangular cavity. The characteristics of the first bifurcation of natural convection in 2D cavities were numerically studied with different height-to-width ratios. The corresponding critical Rayleigh number for each case was estimated using the flow topologies varied with Ra and L/B, and the bisection method. It can be concluded that the first bifurcation depends on the values of Ra and L/B. Flow topologies and the first bifurcation experienced a sudden change as L/B varied between 2.5 (from 1 core to 2 cores) and 2.6 (from 2 cores to 3 cores). For each interval of L/B adjacent to the interval of sudden change, the critiacl Ra decreased with the increase in L/B. Furthermore, there is a step increase for Ra_{Cr} for the sudden change interval. It can then be concluded that natural convection of air enclosed in a rectangular cavity experiences local instability more easily with higher value of L/B. According to the given results, it can also be deduced that the variation of the characteristic of the first bifurcation should be more complex with higher L/B.

2010, 42(3): 389-399. doi: 10.6052/0459-1879-2010-3-2009-471

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Experiments on the interaction of internal waves with the semi-submersible platform in a stratified fluid

Yunxiaing You, Tianqun Hu, Hao Xu, Yongliu Fang, Zhong Yu, Zhongmin Shi, Yan Qu, Yue Xiao

In ocean engineering hydrodynamics, the fluid is mostlyassumed with constant density. However, the density does change in oceansowing to variations in salinity and temperature in the vertical directionthrough the water. Internal waves are abundant in stratified oceans. Suchwaves are known to produce significant effects on hydrodynamiccharacteristics of offshore structures. The aim of this paper is to presentthe experimental results on the interaction of internal waves in astratified fluid with a semi-submersible platform. The wavelength, thewaveheight as well as the wave period of the internal wave generated by therocker-flap wave maker are measured; the relations on both the wavelengthand the wave height with the wave period are obtained. Both the laser andthe clinometer are applied to measure the surge and pitch responses of thesemi-submersible platform due to the internal waves, and the relations onthe amplitudes of the surge and pitch motions for the platform with the waveperiods of internal waves are obtained. Results show that the influence ofinternal waves on the motion responses of the semi-submersible platforms cannot be neglected in their designs and applications. In particular, thesum-frequency effect of the motion response of the semi-submersible platformdue to internal waves is found over a wide range of wave periods.

2010, 42(3): 400-406. doi: 10.6052/0459-1879-2010-3-2008-793

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Pressure measurement of gas-solid two-phase flow driven by shock wave

Honghui Shi, Xiaona Zhang, Lite Zhang

An experimental study of compressible gas-solidtwo-phase flow has been carried out in a horizontal circular shock tube. Thegas parameters before and after shock waves interact with the particle grouphave been measured using a pressure measurement system which consists ofsensors, amplifiers, oscilloscope and computer. The pressures and velocitiesbehind the incident, reflected and transmitted shock waves have beenmeasured. The influences of particle material, loading ratio of particles,driven gas and incident-shock Mach number on the aerodynamic characteristicshave been examined. It is found that, during the interaction of shock waveswith a particle group, the reflection and transmission of shock waves dependon the parameters of driven gas, particle material, the loading ratio and soon. The attenuation rate of shock wave decreases with the increase of theloading ratio of particles and the incident-shock Mach number. It issuggested that at the initial stage of particles acceleration driven byshock waves, elastic collision among particles may play an important role.

2010, 42(3): 407-414. doi: 10.6052/0459-1879-2010-3-2008-655

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Numerical simulation of membranous labyrinth in vestibular system of human inner ear by fluid-structural interaction method

Shuang Shen Xiuzhen Sun Yingxi Liu

In this paper, a three-dimensional element model of the membranous labyrinth in the vestibular system of human inner ear was reconstructed according to complete histological slides from the right temporal bones of a healthy person. The endolymph was modeled as incompressible Newtonian fluid and the crista ampullaris was represented by a linearly elastic solid undergoing large deformation. The fluid-structural interaction problem was solved with different rotation velocity excitations to simulate body turning and back looking of human. Consequently, the fluid fields of endolymph and the displacement fields of crista ampullaris for different rotation velocities were obtained respectively. The research results will contribute to quantitatively analyze the mechanical characteristics of fluid-structural interaction in the membranous labyrinth of vestibular system when human being excited by rotation velocity from the view of biomechanics, and they have provided a basis for thoroughly understanding the relationship between the anatomical structure of membranous labyrinth and the ability of human equilibrium, and for clinical diagnosis and treatment of relevant diseases of vestibular system.

2010, 42(3): 415-421. doi: 10.6052/0459-1879-2010-3-2009-137

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A continuum theory and numerical procedure for chemo-mechanical coupling behavior

Qingsheng Yang, Lianhua Ma, Baosheng Liu

Many continuum media, often described asmultifunctional materials, exhibit multi-field coupling behavior and aresensitive to external environmental stimuli. Chemo-mechanical couplingbehavior for continuum media was investigated in this paper. From the pointview of the thermodynamics and chemical potential, we have obtained theconstitutive equations and governing equations of chemo-mechanical couplingproblem. Energy functional of chemo-mechanical coupling equations has beenestablished by variational principle, and then the equivalent integrationforms and finite element formulation of the coupled governing equations arederived. The chemo-mechanical coupling behaviors of continuum media areanalyzed by numerical examples. The numerical results show that themechanical and chemical fields interact with each other in a medium. Thedeformation of media is caused by the concentration variation. Similarly,the external mechanical force can also induce concentration redistribution.The basic theory and simulation method can be applied to analysis ofchemo-mechanical coupling behavior of continuum media. The chemo-mechanicalcoupling behavior of continuum media can be reflected clearly in the presentmodel.

2010, 42(3): 422-431. doi: 10.6052/0459-1879-2010-3-2008-616

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Quasi-elastic release behavior in shock-loaded aluminum

Yuyin Yu hua Tan Danian Cheng Chengda Da Jianbo Hu Huanran Wang

Based on the intrinsic relations under uniaxial strain conditions, the effective shear modulus defined by Cochran and Guinan was correlated to the longitudinal and bulk sound velocities, and used to study the quasi-elastic behavior of LY12 Al. Unloading wave profile measurements using VISAR technique were performed on LY12 Al over the shock stress ranging from 20 to 100 GPa from which sound velocities and the effective shear modulus along the quasielastic release path were evaluated. Results show that the effective shear modulus decreases rapidly with the release stress and can be approximated by a linear function of release stress. The slopes of the linear function increase with the initial shock-loading stress which is implied that the quasi-elastic behaviors are depended on the shock-loading stress. By using the linear function of effective shear modulus, the performed numerical simulations well reproduce the release wave traces of the Al-alloys reported in the literature. The effective shear modulus in the present study is compared with that obtained from quasi-static experiments and the possible micromechanisms of quasi-elastic release behavior in shock-loaded materials are also discussed.

2010, 42(3): 432-438. doi: 10.6052/0459-1879-2010-3-2008-747

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Strain rate effects and material models of solders

Fei Qin, Tong An

Reliability of solder joints in electronic packages depends on themechanical properties of solder materials. Under drop impact loadings, thesolder joint undergoes high strain rate deformation. Therefore it isimportant to investigate the effect of strain rate on the mechanicalbehavior of the solder materials. In this paper, mechanical properties andstress-strain curves of one lead-containing solder, Sn37Pb, and twolead-free solders, Sn3.5Ag and Sn3.0Ag0.5Cu, were investigated at strainrates ranging from 600s^{-1} to 2200s^{-1} by the split Hopkinsonpressure and tensile bar techniques. Based on the experimental data of thequasi-static tensile tests and the split Hopkinson pressure bar tests,elastic-plastic material models independent of the strain rate andJohnson-Cook material models dependent of the strain rate of the threesolders were developed and employed to predict mechanical behaviors ofsolder joints in a board level electronic package under drop impactloadings. The results show that at high strain rates, the two lead-freesolders are more sensitive to the strain rate, and their tensile strengthsare about 1.5 times greater than that of the lead-containing solder, andtheir ductility is significantly greater than that of the lead-containingsolder. Under the drop impact, the solder joints experience a strain rate of1000s^{-1}, and the proposed material models in Johnson-Cook form areapplicable to predict more realistic stress and strain than theelastic-plastic models independent of strain rate.

2010, 42(3): 439-447. doi: 10.6052/0459-1879-2010-3-2008-680

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Stress singularity at axisymmetric interface wedge of bonded dissimilar materials considering dimension effects

Xiaogui Wang, Mei Wang

An eigenvalue method was proposed to study the stresssingularity behavior at the axisymmetric interface wedge of the bondeddissimilar isotropic materials. Based on the fundamental equations of thespacial axisymmetric problem and the assumption of first-orderapproximation, the discrete characteristic equation on the stresssingularity was derived by making use of the displacement functions in theform of separated variables and the technique of meshless method. Thephysical eigenvalue is associated with the order of the stress singularity,and the corresponding eigenvector is related to the displacement and stressangular variations. A dimensionless parameter δ, which was definedas the ratio between the distance from the singular point to theaxisymmetric axis and the dimension of the singularity-dominated region, wasused to characterize the dimension effects on the stress singularitybehavior. The characteristic equation of the fiber/matrix axisymmetricinterface wedge model was solved numerically, and the order of stresssingularity, the associated displacement and stress angular variations wereobtained. It was found that the parameter δ influenced both thestrength and the order of the stress singularity, and the analyticalsolutions derived by the quasi first-order approximation was just a specialcase while δ>>1.

2010, 42(3): 448-455. doi: 10.6052/0459-1879-2010-3-2008-615

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3D crack propagation mechanism on co-seismic slip under P- and S- waves by wave time-domain hypersingular integral method

Bojing Zhu, Yaolin Shi, Taiyan Qin

This work presents a wave time-domain hypersingularintegral equation (WTD-HIE) method proposed by the authors for modeling 3Dcrack propagation problem on co-seismic slip under fully coupledelectromagnetothermoelastic P- and S- wave fields through theoretical analysisand numerical simulations. First, the general extended incrementaldisplacement wave solutions are obtained by wave time-domain Green'sfunction method. Then, based on the nonlinear boundary element method, theproblem is reduced to solving a set of WTD-HIEs coupled with nonlinearboundary integral equations, in which the unknown functions are the generalextended displacement discontinuity waves. The behavior of the generalextended singular stress indices around the crack front terminating at theslip surface is analyzed by the time-domain main-part analysis method. Thegeneral extended incremental singular stress waves and the extended stressintensity factors are obtained by closed-form solutions. In addition, anumerical method for the problem is put forward with the extendedincremental displacement discontinuity waves approximated by the product oftime-domain basic density functions and polynomials. Finally, extendedstress intensity factors radiation distribution for P- and S- waves at the cracksurface are calculated, and the results are presented to demonstrate theapplicability of the proposed method.

2010, 42(3): 456-474. doi: 10.6052/0459-1879-2010-3-2008-328

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Study on creep properties of rocks and long-time stability of shaft in high ground stress zone

Meihua Zhang, Qian Gao, Shuhua Zhai

According to actual demand of Jinchuan No.3 minefield, aset of bend creep experiments was performed to study the creep behavior oftypical four ore-rocks under step increment load by the developedgravitation-style rock creep test machine. The creep properties of theore-rocks were experimentally obtained. A new viscoelastic-plastic model ofhomogenous mixed rock, named improved Burger's creep model, was thenestablished by combining the Burger's creep model and experimental data withMohr-Coulomb criterion, whose parameters values were achieved by using amixed technique of pattern search and non-linear least -square regression.The theoretic curves of the improved Burger's creep model are in goodgreement with those of the creep tests for homogenous mixed rock, to showthat the improved Burger's creep mode can be applied to describe the creepcharacteristic of homogenous mixed rock. Furthermore, based on creepparameters values, the three -dimensional creep numerical simulation ofrepaired main shaft and its horsehead engineering was conducted by adoptingthe improved Burger's creep model. Reasonable suggestion and evaluation forthe long-term stability and safety of repaired main shaft were put forwardon the basis of the simulaton results.

2010, 42(3): 474-481. doi: 10.6052/0459-1879-2010-3-2009-506

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Theoretical analysis of T-stress effects on photoelastic fringe patterns in cracks

Zhenkun Lei, Hai Yun

Based on the multi-parameter mathematic model of theelastic stress field near a crack-tip, the influences of the stressintensity factors K_{\rm I}, K_{\rm II}, and T-stress on thephotoelastic isochromaticand isoclinic fringe patterns are presented for the mode I, mode II andmixed mode I/II crack, respectively. It is confirmed that T-stressinfluences the radius and rotate direction of the isochromatic fringe loops.The rotated angle of the loop only relates to the T-stress for the mode I orII crack, while to the intensity factors K_{\rm I}, K_{\rm II}, and T-stress for themixed mode I/II crack. There are two isotropic points along ±π/3directions in the mode I crack under positive T-stress, while none ofisotropic point under the negative T-stress. For the mode II crack only oneisotropic point appears behind the crack-tip under T-stress. For the mixedI/II crack, three isotropic points with different radius appear at thecorresponding positions under the positive T-stress, however, one pointexists behind the crack-tip for the negative T-stress. Thses isotropic pointsfor the mixed I/II crack comply with rules in the mode I and mode II,respectively.

2010, 42(3): 482-490. doi: 10.6052/0459-1879-2010-3-2008-565

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Phase extraction from a single speckle fringe pattern guided by frequencies

Kai Li, Qingchuan Zhang

A method for automatic phase extraction from a singlespeckle fringe pattern based on the guidance of frequencies is presented.The method uses a windowed Fourier operation to calculate frequencies of afringe pattern, and to demodulate the wrapped phase values of the fringepattern in the guidance of the frequencies. The validity of the proposedmethod is demonstrated by use of some simulated and experimental fringepatterns.

2010, 42(3): 491-498. doi: 10.6052/0459-1879-2010-3-2008-604

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A simulation study on migration technique for damage imaging based on mindlin plate theory

Gang Yan, Li Zhou

Currently, structural health monitoring (SHM) is one ofthe most promising directions in the research field of smart materials andstructures. However, up to now, most of the developed methods can onlydetect and localize the damage, quantitatively identify the extent of thedamage, especially for multiple damages, remain a challenge task. This paperproposed a migration approach for identification of multiple damages inplate-like structure in real time using scattered Lamb waves. Based onMindlin plate theory, the fast frequency-wavenumber domain migrationtechnique for dispersive flexural wave was deduced for the first time.According to the Huygens' Principle, damages were imaged by applying atime-coincidence imaging condition after extrapolating the excited andscattered wave fields. Numerical simulation study employed a Mindlin platetheory-based finite difference method to generate synthetic scattered wavefields with damages of different shapes and sizes in the structure. Imagingresults for the synthetic wave fields have demonstrated that the proposedmethod has the capability of not only localizing multiple damages but alsoidentifying their extent; its advantage of fast calculation meets therequirement of real-time damage identification for an on-line structuralhealth monitoring system.

2010, 42(3): 499-505. doi: 10.6052/0459-1879-2010-3-2008-210

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Calculation for optimized movement trajectories of human multi-joint arm

Pengwei Sun, Shimin Wang, Qi Wang, Jie Wang

The calculation for optimized trajectories ofunrestricted multi-joint human arm in point-to-point reaching movement wasinvestigated. The planar motion equations of multi-joint arm were introducedat first, then the optimal criterion was constructed according to minimaleffort criterion, and the human arm point-to-point reaching movement wastreated as a two-point boundary value problem, finally an iterativealgorithm was presented to find the optimized arm trajectories and velocityprofile. The simulation results show that the equilibrium point or jointtorque varies smoothly，which avoids the large fluctuation of arm speed andreduces energy consumption when arm moves; the movement trajectory of handis roughly a straight line, and the corresponding velocity profile issingle-peaked and bell-shaped, which is in good agreement with the kinematicdata from the arm movement. Therefore the minimal effort criterion is alsoeffective for calculating the optimal movement trajectories of multi-jointarm.

2010, 42(3): 506-511. doi: 10.6052/0459-1879-2010-3-2009-054

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Time-domain method for dynamic reliability of structural systems subjected to non-stationary random excitations

Cheng Su, Rui Xu

Structural dynamic equations are first transformed intothe form of state equations, which are solved by the precise time integralmethod, and then explicit expressions of structural random responses undernon-stationary excitations are deduced in the time domain. The computationaleffort for such explicit formulation is only equivalent to that for twodeterministic time-history analyses of the structure. Based on the aboveexplicit expressions and combined with the first-excursion failurecriterion, a numerical simulation method is proposed for solving dynamicreliability of structural system under non-stationary random excitations. Ascompared with the power spectrum method, the proposed method does notrequire a large amount of numerical integrals in both frequency and timedomains. Furthermore, the assumptions are no longer required in the presentapproach with respect to the probability distribution of the excursionnumber and the correlation between different failure modes. With numericalexamples, the calculation accuracy and efficiency of the proposed method arecompared with those of the conventional Monte Carlo simulation method, thePoisson process method and the Markov process method. Numerical resultsindicate that the proposed method has perfect accuracy and reasonably highefficiency.

2010, 42(3): 512-520. doi: 10.6052/0459-1879-2010-3-2009-042

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The maximal lyapunov exponent for a three-dimensional stochastic system

Jianhua Liu, Xianbi Liu

The investigation of the maximal Lyapunov exponent for a random dynamicalsystem is the primary research focus in the field of stochastic bifurcation.This is mainly attributed to the fact that for a random dynamical system,Lyapunov exponent is analogous to the real part of the eigenvalue, whichcharacterizes the exponential rate of change of the response. Therefore, thealmost-sure stability of the stationary solution of a random dynamicalsystem depends on the sign of its maximal Lyapunov exponent.The system considered in this paper is a typical co-dimension twobifurcation system that is on a three-dimensional center manifold. Based onthe perturbation method of Arnold and the singularity theory forthe one-dimensional diffusion process, the maximal Lyapunovexponents for the co-dimensional two bifurcation system subjected toparametric excitation by a white noise of small intensity are evaluated. Itis well known that the expression of the maximal Lyapunov exponent dependson the form of coefficient matrix B that is included in the noiseexcitation term, and the singularities of the diffusion behaviors of thephase diffusion process take place as a consequence of a general form ofmatrix B. As an extension of the work of Liu and Liew[10], thepresent study attempts to investigate in detail the general conditions thatlead to the coexistence of the two kinds of singular boundaries of theone-dimensional phase diffusion process and then the conditions of theexistence of the stationary solutions to the relevant FPK equation. And thenthe analytical expressions of the invariant measure are given. Via theanalysis on one special kind of matrix B, the comparisons betweenthe analytical solutions of the invariant measure and the relevant MonteCarlo simulations are given, and then the P-bifurcation point for theone-dimensional phase diffusion process is determined. Finally, for themaximal Lyapunov exponent, the explicit asymptotic expression is obtainedfor the case of one special kind of matrix B, andfor the case of a general matrix B. In addition, the numericalresults are given.

2010, 42(3): 521-528. doi: 10.6052/0459-1879-2010-3-2008-745

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Parametric stability of a translational rigid-liquid coupled system subject to vertical excitations

Qing Li, Tianshu Wang, Xingrui Ma

Parametric stability of liquid sloshing under verticalexcitations is widely concerned in spacecraft dynamics. However, theinfluence of the coupling between the liquid sloshing and the spacecraftmotion on the parametric stability has not been investigated in the previousstudies. In this paper, the Mathieu's equation of a translationalrigid-liquid coupled system subject to vertical excitations is presentedwith the equivalent pendulum model of liquid sloshing. The one-halfsubharmonic and harmonic stability boundaries of the coupled system areanalyzed using the perturbation method. It is illustrated that, the lateralcoupling between the liquid sloshing and the rigid body motion enlarges theparametric unstable regions and enhances the resonance frequencies. Theeffects decline with the decrease of equivalent sloshing mass. Due to thelinear slosh damping, the reduction of the one-half subharmonic unstableregion is much less than that of the harmonic unstable region. The one-halfsubharmonic responses associated with the first sloshing mode of thecoupled system show that, when the parameters of vertical excitations dropin the unstable region, the rigid body may experience a vertical-lateralcoupling vibration.

2010, 42(3): 529-534. doi: 10.6052/0459-1879-2010-3-2008-795

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Spectral components and their distributions of the response for parametric vibration system

Jianjun Wang, Qinkai Han, Qihan Li

Utilizing Sylvester's theorem and Fourier seriesapproximations, commonly used in the matrix decomposition, the spectralcomponents for both the free and forced responses of linear parametricallyexcited system are obtained theoretically, and the effects of parametricstability and damping on the spectral amplitudes are discussed in detail.Consequently, the outer excitation resonant condition for parametric systemis found. It is concluded from the theoretical results as follows:parametric excitation leads to multi-frequency response; these spectra areclosely related to the natural frequency, parametric frequency and the outerexcitation frequency (only for the forced response) of the system; thedistribution for these spectra in frequency domain follow certain laws;there are multi-resonances caused by outer excitation in parametricvibration system.

2010, 42(3): 534-540. doi: 10.6052/0459-1879-2010-3-2008-707

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The effect of spring stiffness on the stability of passive dynamic walking

Xiuhua Ni, Weishan Chen, Junkao Liu, Shengjun Shi

Compared with traditional biped robots, passive dynamicwalker has simpler structure and higher energy efficiency. However, it hasvery weak tolerance for disturbances. Inspired by the biomechanics of humanwalking, we added a torsional spring at the hip of the passive dynamicwalker to improve its stability. We studied the effect of spring stiffnesson the stability of passive dynamic walking by simulations and experiments.In the simulations, the basin of attraction used as a measure for stability,was obtained with the cell mapping method. The effect of spring stiffness onthe basin of attraction was then studied. The size of the basin ofattraction increases with the increasing spring stiffness. In theexperiments, we quantified the stability of each walker by observing passivewalking trials down a gentle slope of finite length for 100 times andrecording the fraction of trials which successfully walked to the end. Theexperimental results show that spring stiffness with a moderate value caninduce maximal stability for passive dynamic walker. The hip momentcontributed to the spring is quite similar to that of human in a walkingcycle. This might indicate that the spring improves the stability. Thespring torque in a whole walking cycle has positive effect on stability,which can be used to explain the simulation results. The discrepancy betweensimulations and experiments might be explained by the fact that the steplength decreases with increasing spring stiffness, to induce the increasingchance of foot scuffing at mid-stance in experiments, which was ignored insimulations.

2010, 42(3): 541-547. doi: 10.6052/0459-1879-2010-3-2009-270

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Coupling dynamic model and dynamic analysis for whole aero-engine

Guo Chen

In this paper, a rotor-ball baring-stator couplingdynamic model for whole aero-engine vibration is established. The maincharacteristics of the new model are as follows: 1) the coupling effectbetween rotor, ball bearing and stator is considered fully; 2) the flexiblesupport and the squeeze film damper (SFD) are considered; 3) the rotor isconsidered as Equisection Euler Free Beam model, and its vibration isanalyzed through cutting limited modes; 4) nonlinear factors of ball bearingare modeled, such as the clearance of bearing, nonlinear Hertzian contractforce, and the varying compliance; 5) rubbing fault between rotor and statoris considered. In this paper, the numerical integral method is employed toobtain system's responses, and the whole aero-engine vibrationcharacteristics are studied. Research topics are investigated, such as ballbearing VC vibration analysis, effect of elastic support stiffness on thesystem critical speeds, effect of cutting modes number on system responses,sudden-adding imbalance transient response simulation, and rotor-statorrubbing fault characteristics analysis.

2010, 42(3): 548-559. doi: 10.6052/0459-1879-2010-3-2008-706

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Study on the extreme value estimating method of non-gaussian wind pressure

Yong Quan, Ming Gu, Bin Chen, Tamura Yokio Tamura

Based on the classical extreme-value theory, an estimatingmethod for expected extreme-value of wind pressure with non-Gaussianprobability distribution is proposed with a sample whose length is just onestandard observation interval. At first, the wind tunnel test and test dataprocess of this study are introduced in detail. A method to calculateexpected extreme values of time series with a long time interval is thenproposed with its sub-sections based on the classical Gumbel theory forextreme values and the independence of observed extreme values. At last, theextreme values of the wind pressure coefficients of the present wind tunneltest are calculated with the proposed method and methods used widely atpresent, such as peak factor method, improved peak factor method andSadek-Simiu method. The results indicate that the probatilistic parametersof extreme values of sub-sections of a non-Gaussian wind pressure timeseries can be used to estimate accurately expected extreme value of theirparent section with the proposed method. The length of the sub-section canbe determined with auto-correlation analysis on the parent section.Comparison shows that the proposed method can estimate extreme values ofnon-Gaussian wind pressure more accurately than other methods used widely atpresent.

2010, 42(3): 560-566. doi: 10.6052/0459-1879-2010-3-2009-062

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Experimental study on electrospray modes and steady spray characteristics with multiple metal capillaries

LIU Ming-Ming, CHEN Xiao-Peng, XU Xiao-Jian

Electrospray is an atomization process, in which the liquid is broken byelectrical forces. It's applied widely in nano-material preparation,mass-spectrometer, et al. Coupled with MEMS fabrications, multi-emitterelectrospray attracts great attention for its high output, integration andminiaturization.In this study, both single and multiple emitter electrospray apparatus areset up based on traditional metal capillaries to study the spray modes andsteady spray characteristics. Two of the crucial behaviors are comparedbetween the two setups, the onset voltage ($V_C$) of ``cone-jet'' spray modeand the relationship between electrical current (I) and flow rate (Q).Though the capillary configuration influences the spray states on differentneedles, $V_C$ and $I$ for both setups are proportional to$ \sqrt{ \cos \theta }$ ($\theta$ is the cone degree) and $Q^{1/2}$,respectively. It implies that the resulted jet is affected mainly by ratherthe local electrical distribution around the cone-jet transition region,than the external global conditions. The further electrospray withmicro-fabricated multi-emitter arrays can be supported by these results.

2010, 42(3): 567-571. doi: 10.6052/0459-1879-2010-3-2009-126

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Simulation of shock induced combustion based on a novel uncoupled method

Jun Liu, Yu LiuS, ongbai Zhou

This paper improved a novel uncoupled method of simulating chemical non-equilibrium flow whichwas introduced in Ref.1. The flow operator can be numerical solved by Runge-Kutta method; the reaction operatorcan be solved by trapezoidal rule, quasi steady state approximation and VODE.The oscillating shock-inducedcombustion experiments conducted by Lehr had been studied, and the numerical scheme and stiff ode solver wereevaluated. The effects of computing grid and chemical reaction mechanism also were studied.Key words chemical non-equilibrium flow, uncoupled method, numerical method刘

2010, 42(3): 572-578. doi: 10.6052/0459-1879-2010-3-2008-775

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The research on the axisymmetric plane strain problem of compressed hollow cylinder composed of elastomeric foam

Shijun Li, Guowen Lin, Dawei Ma

This paper adopts Euler-Lagrange variational principle toresearch the compression behavior of hollow cylinder composed of elastomericfoam, and establishes nonlinear differential equations about itsaxisymmetric plane strain problem based on Blatz-Ko material model. Aparametric analytical solution is obtained through the parametertransformation. Finally by utilizing the corresponding numerical case, thevariation rules of radial stress and tangential stress along the radial ofcylinder, and the influences of magnitude of interference aresummarized.

2010, 42(3): 579-582. doi: 10.6052/0459-1879-2010-3-2009-509

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Vibration control for launcher of multiple launch rocket system based on transfer matrix method of multibody system

Zhihuan Zhan, Xiaoting Rui, Guoping Wang, Fufeng Yang, Junyi He

High fire accuracy is one of performance goals of MultipleLaunch Rocket System (MLRS). One of effective methods to improve the fireaccuracy with low cost is the vibration control of launcher in MLRS. In thispaper, transfer matrix method of multibody system (MSTMM) is used to developdynamical model of MLRS. Active vibration control law is designed for pulsethruster using quadratic performance index as cost function. In the law, thepulse thruster is taken as an actuator for launcher vibration control.Vibration control system of MLRS launcher is established under the impact ofgas jet from rocket motor. A numerical simulation example on vibrationcontrolling of MLRS launcher is given to obtain optimum amplitude of pulsecontrol force and working times of pulse thruster. Numerical results ofcontrolled and uncontrolled vibration response of launcher show that controllaw in this paper is efficient to reduce launcher vibration. Furthermore,the present method in this paper is easy to realize in practicalengineering, and it is important to be used to control launcher vibration soas to improve fire accuracy of MLRS.

2010, 42(3): 583-590. doi: 10.6052/0459-1879-2010-3-2009-431

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