力学学报

Three-dimensional numerical simulation on the thermocapillary convection in an annular pool of silicone oil heated from inner wall

Wanyuan Shi, Yourong Li, Imaishi Nobuyuki

In order to investigate the characteristics ofthermocapillary flow instability, thermocapillary convection is investigatedwith three-dimensional numerical simulation in a shallow annular pool (depthd =1mm) of silicone oil (0.65cSt, Pr= 6.7) with the heated inner walland the cooled outer wall. The numerical results show that, surface temperaturegradient in the pool heated from inner wall is 10% higher than thatheated from outer wall with a fixed temperature difference between the outerand inner walls. Meanwhile, the critical Marangoni number for the incipienceof hydrothermal wave (Ma_{c}=3.06\times 10^{5}) in the pool heated frominner wall is smaller than that (Ma_{c}=3.34\times 10^{5}) heated fromouter wall. Furthermore, numerical results indicate the oscillatorymulticellular wave in the pool heated from inner wall when Ma exceedsMa_{c}. The oscillatory multicellular wave is composed of two hydrothermalwaves propagating in opposite azimuthal directions, which are interferedeach other to be dot ripple.

2008, 40(4): 433-440. doi: 10.6052/0459-1879-2008-4-2007-151

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Numerical study on a simplified population balance approach for isothermal bubbly flows

Xiaodong Wang, Zibo Zhang, Jiyuan Tu

Population balance approach was presented for isothermalbubbly flows. An averaged bubble number density was introduced into thethree-dimensional two-fluid model to describe the evolution of the structureof the gas bubbles. Moreover, Yao and Morel theoretical models wereintroduced to account for the coalescence and breakage mechanisms ofbubbles. A numerical approach for five variables in bubbly flows ofdifferent locations in a tube: void fraction, Sauter mean diameter,interfacial area concentration, gas and liquid velocities, are carried out.The numerical results showed a good agreement with the experimental datafrom Hibiki et al.

2008, 40(4): 441-446. doi: 10.6052/0459-1879-2008-4-2007-320

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Focusing models for generating freak waves

Xizeng Zhao, Zhaochen Sun, Shuxiu Liang

A 2-D extreme wave focusing model is presented onthe basis of enhanced high-order spectral (HOS) numerical method,validated with the experimental and theoretical results, and applied toinvestgate the effect of wave-wave nonlinear interaction on the wavefocusing amplitude. Based on improved Longuet-Higgins wave model, four wavefocusing models for freak wave generation are proposed: 1.extreme wave modelwith random wave model; 2. extreme wave model with regular wave model; 3.wave focusing model from phase-interval modulation; 4. wave focusing modelfrom wave number modulation with the same phase. With the application ofdifferent energy distribution techniques in the four wave focusing models,freak wave with differentvalues of $H_{\max}/H_{s}$ are obtained in thefinite space and time domains.

2008, 40(4): 447-454. doi: 10.6052/0459-1879-2008-4-2007-270

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Numerical simulation of random wave-induced near-shore currents

Jun Tang, Yongming Shen, Lei Cui, Yonghong Zheng

Near-shore currents induced by the irregular water wavesand their breaking were numerically simulated based on the parabolic mildslope equation and near-shore current model. The unidirectional incidentirregular wave was first put into being discrete with the Jonswap wavespectrum and then simulated using the parabolic mild slope equation toobtain the wave radiation stresses with the effects of the wave irregularityand breaking. The breaking-wave-induced near-shore currents werenumerically simulated to further validate the numerical model. The numericalresults show that the model can be applied to study thebreaking-wave-induced currents.

2008, 40(4): 455-463. doi: 10.6052/0459-1879-2008-4-2007-090

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Two-dimensional simulation of the mixing induced by interface instabilities

Jinsong Bai, Ping Li, Liyong Zou, Tao Wang

The compressible multi-viscousity-fluid piecewiseparabolic method (MVPPM) is developed for Navier-Stokes equations based onthe Eulerian multi-fluid piecewise parabolic method (MFPPM), the secondorder space central difference method and two-stage Rung-Kutta time marchingmethod. Simultaneously, a common mathematical approach, operator splittingtechnique was applied to obtain the molecule dynamics viscosity and heatflux effects on flow field. With the application of MVPPM, a numerical caseof a two-dimensional shock wave tube experiment from Atomic WeaponsEstablishment (AWE) is investigated to show a good agreement with theexperimental results. Moreover, the interface instability and subsequentmixing model of implosion dynamics are simulated with MFPPM and MVPPM in thetwo-dimensional cylindrical symmetry case. The evolvement of the inner andouter interfaces, velocity history and the distribution of subsequent mixingin the central cavitations induced by Rayleigh-Taylor (RT) interfaceinstability are obtained. The effect of dynamics viscosity on the mixingdistribution in the interface was clearly observed in the numerical results.

2008, 40(4): 464-472. doi: 10.6052/0459-1879-2008-4-2007-381

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Experimental study on the performance of the detonation-driven high-enthalpy shock expansion tube

Yunliang Gao, Wei Zhao, Zonglin Jiang

The performance of the detonation-driven high-enthalpyshock expansion tube (JF-16), manufractured recently in LHD of ChineseAcademy of Sciences, was experimentally investigated to obtain the velocityand the pressure of the incident shock speed. The velocity and otherthermodynamic parameters of the hypervelocity test flow was predicted withMirels' theory and the Gaseq software, respectively. The experimentalresults show that the test flow with a velocity of above 7\,000\,m/s, aneffective test duration between 50$\sim $100$\mu$s and the total enthalpyup to 30\,MJ/kg have been achieved with JF-16 shock expansion tube of16.35\,m length.

2008, 40(4): 473-478. doi: 10.6052/0459-1879-2008-4-2007-111

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The theoretical analysis of acoustic plate wave in piezoelectric plate with finite fluid loading

Mingyi Yang, Jichao chen

This article presents the attenuations and phase shiftsof the acoustic plate wave modes (APMs) with finite liquid loading inpiezoelectric plates. The partial wave theory is applied to analyze apiezoelectric plate loading with liquid. The first 20 APMs in128$^{{\circ}}$YX+90$^{{\circ} }$LiNbO$_{3}$ plate with DI water andglycerol loading are theoretically calculated. The variation of phasevelocity and attenuation of APMs with different thickness of glycerol alsopresented. The results shown in this paper are essential for using the APMsin the designs of liquid phase sensors.

2008, 40(4): 479-484. doi: 10.6052/0459-1879-2008-4-2007-301

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Experimental study on fracture behavior of linear functionally gradient materials

Wei Xu, Xuefeng Yao

Static and dynamic fracture behaviors of functionallygradient materials (FGMs) with linear variation of the shear modulus areexperimentally studied with caustics method and high speed photographytechnique, and numerically investigated through finite element method (FEM).Firstly the caustics equations relative to the caustics principles and theelastic solution at mode I crack in FGMs are deduced through an iterativenumerical method. Three kinds of specimens with different variation of shearmodulus are synthesized by a gravity-assisted vertical casting process. Thenthree-point-bending experiments are performed and the caustics patterns areshot through CCD and high speed photography equipment. The static anddynamic stress intensity factors of FGMs specimens are obtained throughcaustics method. Finally, The experimental results are validated with thenumerical results to investigate the influences of the stiffness variationon the static and dynamic fracture characteristics.

2008, 40(4): 485-495. doi: 10.6052/0459-1879-2008-4-2007-047

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Application of the base forces concept in geometrically nonlinear finite element method on complementary energy

Yijiang Peng, Yinghua Liu

In this paper, a new explicit expression of thegeometrically nonlinear finite element method was developed on thecomplementary energy principle for the large displacement and large rotationproblem on the basis of the concept of base forces as fundamental variables.The complementary energy of an element under large deformation case isdivided into the deformation part and rotation part. The formulations of thecontrol equations for the base forces finite element method are obtainedusing the Lagrange multiplier method, and an explicit displacementformulation of nodes is given. The numerical results are compared with thoseof the theoretical solution and the assumed displacement finite elementmethod based on potential energy principle. It has been demonstrated thatthe new finite element formulations proposed in this paper is effective,accurate, and capable of simulating the large rotation case under one largeload step.

2008, 40(4): 496-501. doi: 10.6052/0459-1879-2008-4-2007-340

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On Euclidean transformations of Space-Time Frames and Principle of Material Frame Indifference

Zhiwen Lan, Liangsen Chen, Mingfu Fu

The main purpose of the present paper is to obtain the relation between the abstract presentation of Euclidean objectivity and its component representation with respect to the general curvilinear coordinate systems with a relative rigid motion under a fixed frame of reference, so that the tensor representation of Euclidean objective quantity has its component form. This relation is based on the fact that an objective quantity under the frame of reference with respect to the fixed coordinate system of frame of reference has the same component with the objective quantity under the frame of reference relative to another coordinate system of with the same relative rigid motion as that of and to the fixed coordinate system of . On the other hand, it is exemplified in the present paper that the principle of material frame – indifference with the admissible equivalent dynamic processes of a body by Truesdell and Noll (1965) [14] is more convenient than the form-invariance of constitutive functionals by Svendsen and Bertram (1999) [13] and Liu (2004)[4], especially for the rate-form constitutive equations.

2008, 40(4): 502-510. doi: 10.6052/0459-1879-2008-4-2006-325

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Study on sub-cycling algorithm for a flexible multi-body system

Jiancheng Miao, Ping Zhu, Guanlong Chen, Dawei Zhu

Great developments have been made in the field offlexible multi-body system (FMS) with modeling, computational andexperimental studies for nearly 30 years. The subcycling algorithms, whichwere firstly presented by Belytschko T. et al. in 1979, havebeen successfully applied in the structural dynamic analysis of FMS. However,subcycling algorithms for the FMS are still not presented up to now. Thispaper introduces a central difference method based sub-cycling algorithm forthe FMS. First, common update formulae and sub-step update formulae forquickly changing variables and slowly changing variables of the FMS areestablished. Second, the nonlinear differential-algebraic equations arecontracted to the original differential equations. Third, algorithmstability is validated with an energy balance computation during theintegration procedure. Numerical results indicate that the sub-cyclingalgorithm is available to enhance the computational efficiency withappropriate computational accuracy. Furthermore, the algorithm stability canbe determined by means of modifying the integral step sizes with theperturbation method.

2008, 40(4): 511-519. doi: 10.6052/0459-1879-2008-4-2006-496

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Experimental study on active control of a rotating flexible beam with time delay

Longxiang Chen, Guoping Cai

In this paper, active control of a rotating flexible beamwith time delay is experimentally investigated. A servo motor is used todrive the beam in a rotating motion and a piezoelectric (PZT) actuatorsticked on the beam is used to control the beam in the elastic vibration.Three experimental cases were performed, that is, (1) only with the servomotor for active control and the time delay only for the motor; (2) with theservo motor and PZT actuator for active control and the time delay only forthe PZT actuator; (3) with the servo motor and PZT actuator for activecontrol and the time delay only two all. The experimental resultsdemonstrated the feasibility and effectiveness of time-delay feedbackcontroller.

2008, 40(4): 520-527. doi: 10.6052/0459-1879-2008-4-2008-010

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Study on signal recovery in bistable stochastic resonance

Ying Zhang, Taiyong Wang, Yonggang Leng, Hui Deng, Qian Ding

Aiming at the problem of the waveshape distortion in the output obtained by an SR system, this paper explains the signal recovery formula from the point of view of dynamics. Taking sinusoidal signal as the research object, the motion of the particle in the bistable system and the recovery system is investigated, and the recovery mechanism and rules with and without noise are explained. Moreover, a novel explanation about pulse distortion caused by the particle’s transition is put forward and a method to recover the output signal of subthreshold SR via cascaded-bistable system and the recovery system’s parameter choice is proposed. The numerical simulation has presented that this method, which applies to the output signal directly, can recover the waveform containing weak information submerged in noise effectively.

2008, 40(4): 528-534. doi: 10.6052/0459-1879-2008-4-2007-472

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Study on spalling response of materials under pre-stress

Shiwen Zhang, Cangli Liu, Qingzhong Li, Qiao Liu

The paper investigated the effect of pre-stress on thespalling of materials. Based on the deformation characteristic of sphericalspallation, pre-strain in the radial direction of LY12 plane sample was madeby heat assembly within excess conjugation. The spalling response of thesamples were tested by VISAR with one-dimensional gas-gun impact experimentsin different pre-strain states. The experimental results show that thepullback amplitudes of the free surface velocity and the spallation strengthof the samples obviously decrease in the pre-stress state under the sameimpact velocity. Moreover, numerical simulations were performed with thedamage constitutive model. The numerical results indicate that thespallation strength of materials have a strong relationship with theexternal stress fields, and indirect with the structures.

2008, 40(4): 535-542. doi: 10.6052/0459-1879-2008-4-2006-619

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Vibration sensor placement method based on principal subset selection

Qingguo Fei, Aiqun Li, Changqing Miao, Lingmi Zhang

Dynamic testing is one of the major approaches tounderstand the dynamic properties of structures. Consequently, sensorplacement has great effects on the collection of sufficient information inthe testing, even to be the decisive factor for the experimental resolutionin dynamic modal analysis. In the paper, a new sensor placement method isdeveloped on the basis of mode independence and principal subset selection.The present method is uniterative and efficient for that the sensorpositions are determined all at once. Moreover, four evaluation criteriawere proposed and numerical simulations were performed with an antenna modelto validate the feasibility of the developed method.

2008, 40(4): 543-549. doi: 10.6052/0459-1879-2008-4-2007-244

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A powder compaction mechanical model for diffusion coupled with stress field

Yanqing Wu, Fenglei Huang

An analytical model was developed to investigate thecoupled effects of stress field and surface diffusion bonding during powdercompaction taking elastic contact stress distribution as theinitial condition. The stress function including the term of surface energyis introduced for describing the surface diffusion evolution and itsinfluence on stress distributions. Simultaneously, stress-induced chemicalpotential gradients may promote (or impede) diffusion bonding. Effects ofexternal load amplitude, temperature and stress distribution along the bondinterface are obtained using the present model. The results showed theeffect of initial bonded width and stress distributions in the cases ofadhesional and un-adhesional contact, respectively. Furthermore, the powderdensification process was analyzed under the initial condition of stressdistribution derived from elastic contact with adhesion.

2008, 40(4): 550-556. doi: 10.6052/0459-1879-2008-4-2006-489

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Symplectic solution for the bending of annular sector plate in circumferential direction

Weian Yao, Zhen Sun

The bending of annular sector plates is investigated withthe symplectic solution in this paper. On the analogy between planeelasticity and plate bending theory, moment functions of plate bending inpolar coordinates are introduced as original variables to establish asymplectic space in circumferential direction for the bending of annularsector plate with an appropriate definition of symplectic innerproduct. With the application of the Pro-Hellinger-Reissner variationalprinciple, dual equations in the symplectic space are yielded to present ananalytical method for the bending of annular sector plates. Moreover, twocases of the symplectic eigenvalue problems are presented: one is for theplate simply supported on the two arc sides, the other for the arccantilever plate.. The transcendental equations of the eigenvalues and theireigenvectors are obtained. The comparison between the theoretical results inthe paper and in other literatures shows a good convergence and accuracy ofthe symplectic solution.

2008, 40(4): 557-563. doi: 10.6052/0459-1879-2008-4-2007-417

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A new method for free vibration analysis of piezoelectric-elastic laminated beams

Yang Li, Zhifei Shi

Free vibration of the piezoelectric-elastic laminatedbeams is studied by combining the state-space method and differentialquadrature method. The state equations are dispersed at every sample pointby using the differential quadrature technique to obtain the solutions. Theconvergence of the present method is also studied by choosing differentnumber of sample points. The obtained results are validated to show that thedeveloped method is convenient for vibration analysis ofpiezoelectric-elastic laminated beams.

2008, 40(4): 564-571. doi: 10.6052/0459-1879-2008-4-2007-433

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Phase synchronization of two coupled Rossler oscillators with internal resonance

Yong Liu, Zuo-lei Wang, Bi Qin-Sheng

Phase synchronization between linearly and nonlinearlycoupled systems with internal resonance was investigated in this paper. Theconception of phase for a chaotic motion was introduced to demonstrate theeffect of the detuning parameter $\sigma $ between the two naturalfrequencies $\omega _1 $ and $\omega _2 $ on the phase dynamics. The resultsshowed that phase synchronization between two subsystems was enhanced withthe increase of the linear coupling strength and decayed with the increaseof nonlinear coupling strength. Further investigation reveals that thetransition of phase states between the two oscillators are related to thecritical changes of the Lyapunov exponents.

2008, 40(4): 572-576. doi: 10.6052/0459-1879-2008-4-2007-499

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2008 Vol. 40, No. 4

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