力学学报

2015, 47(1)

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A SURVEY OF GRANULAR DYNAMICS MODELING AND SIMULATION METHODS FOR RUBBLE-PILE ASTEROIDS

Zhang Yun, Li Junfeng

Asteroid exploration will be the spotlight of the research in aerospace science in upcoming decade. The present data indicates that most of the asteroids are loosely consolidated "rubble pile" structures, which have zero tensile strength and are easy to be disrupted by external force produced by exploration missions. Therefore, to guarantee the execution of the asteroid exploration mission, it is essential to build the dynamics model of the asteroid and explore the asteroid evolution's interaction effect. Based on the upcoming China's asteroid exploration mission, the research status and development of granular dynamics is reviewed and analyzed. Then, the dynamical modeling and numerical simulation methods of rubble-pile asteroids are recapitulated in detail, according to the state of art of international relating researches. Finally, the key technical problems of the modeling of rubble-pile asteroids in asteroid exploration mission are proposed.

2015, 47(1): 1-7. doi: 10.6052/0459-1879-14-329

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AERODYNAMIC CHARACTERISTICS MEASSUREMENT OF MARS VEHICLES DURING ENTRY FLIGHT

Yang Lei, Hou Yanze, Zuo Guang, Liu Yan, Guo Bin

Performing aerodynamic measurement can acquire a mounts of data during Mars entry exploration. This work benefits for aerodynamic characteristics confirmation and improves key flight performance, such as landing accuracy. In this study, an aerodynamic measurement system scheme is proposed based on trajectory reconstruction and flush air data system. Angle of attack and angle of side slip are measured by output error method with measured trajectory; dynamical pressure is measured via Flush air data system and least square optimal estimation. By simulation, it shows that the proposed measurement scheme has high measure accuracy, and dynamical pressure accuracy is 1%, and angle of attack and angle of side slip accuracy are improved more than one time. This study is helpful for aerodynamic measurement of deep-space exploration entry flight, such as Mars exploration entry flight.

2015, 47(1): 8-14. doi: 10.6052/0459-1879-14-331

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MARS GRAVITY CAPTURE DYNAMIC MODEL AND ERROR ANALYSIS

Fang Baodong, Wu Meiping, Zhang Wei

Mars orbit capture is a one and only opportunity for Mars probes and the key factor to determine whether the mission is successful. Starting with the constrained three-body problem, equations for calculating the Mars gravity sphere, influence sphere and Hill sphere are derived. Their property and applicability are discussed. Based on the definition and physical significance of influence sphere, an engineering definition of capture phase is proposed. The orbital dynamic model was built inside the influence sphere and the error sources that may affect the accuracy of capture orbit are presented. Finally, the influences on perigee and apogee of the capture orbit caused by the position and velocity navigation error, engine thrust error and timing errors are analyzed through Monte Carlo simulations. The limit exceed possibility caused by different error sources are also discussed and the dominating sources is pointed out. The result can be used as a reference for the orbit capture implementation of future Chinese Mars orbiters.

2015, 47(1): 15-23. doi: 10.6052/0459-1879-14-327

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MODEL AND ANALYSIS OF ΔDOR TRACKING BY CHINA DSN WITH TT&C MODE

Tang Geshi, Han Songtao, Cao Jianfeng, Chen Lüe, Ren Tianpeng, Wang Mei

Very long baseline interferometry (VLBI) can provide accurate plane of sky measurement of spacecraft. Based on the first implementation of interferometric tracking in CE'3 project by China DSN (Deep Space Network), this paper describes modeling interferometric tracking with TT&C mode. Earth based stations keeps pointing to the spacecraft while it is in view of antenna. So interruption of TT&C signal can be eliminated, which is unavoidable with traditional short-scan working mode. Compared with high accuracy orbit ephemeris, delay observable error is less than 1ns which corresponds to an angular accuracy of about 97nrad (37m uncertainty at the Earth-Moon distance). Accuracy of delay observable is in the same order with CVN baseline which has the similar configuration.

2015, 47(1): 24-30. doi: 10.6052/0459-1879-14-328

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RESEARCH PROGRESS OF JOINT EFFECTS MODEL IN MULTIBODY SYSTEM DYNAMICS

Wang Gengxiang, Liu Hongzhao

It is assumed that the kinematic joints are ideal or perfect in the dynamics research of general multi-body system. However, the realistic joints include not only the clearance and friction but also contact-impact, local deformation and wear between the joint element arising from the clearance. On the one hand, the presence of clearance effect in joints causes the impact dynamic load, noise and high frequency vibration. On the other hand, the system accuracy, reliability and the service life of mechanism system will be affected due to the joint clearance. The research background of joint effects in multi-body system dynamics over the past several decades is carried on the detailed analysis. The modeling processes of joint effects that contain the kinematics model of clearance, contact force model and wear model are summarized. The advanced in joint wear effect of multi-body system dynamics is focused on specially, and the comparative analysis of two common wear model of Reye's hypothesis and Archard's wear model are carried out to illustrate their differences. The evolution form and main wear parameters consisted in the contact pressure, sliding distance and contact area of the Archard's wear model are specific developed. The modeling method of key parameter for contact pressure is analyzed specially, and it is explained that the difficulty of contact pressure is formulated by Winkler elastic foundation theory. Moreover, the kinematic models of four different style joints with clearance are briefly introduced respectively. The general modeling method of multi-body system dynamics considering joint irregular wear clearance is discussed in a flow chart way, and the planar five-bar mechanisms is taken as an example to account for modeling process of multi-body system with irregular wear clearance. Lastly, the future development trend and application prospect of joint effect model in the multi-body system dynamics are discussed respectively.

2015, 47(1): 31-50. doi: 10.6052/0459-1879-14-091

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EFFECT OF CONSTANT PRESSURE SPECIFIC HEAT IN SHOCK WAVE CONTROL USING SURFACE DISCHARGE

Yan Hong, Wang Song

The flow control mechanism of discharge plasma is divided into two categories, namely, thermal effect and non-thermal effect, and the thermal effect of the discharge plasma has obvious control effect on the shock wave structure of the flow field. In the numerical simulation of the shock wave control using discharge plasma, the local temperature of the surface discharge region can reach above ten thousand degree centigrade or kelvin degree. If not considering the nonlinear change of the specific heat at constant pressure(C_p) with gas temperature in the process of numerical simulation, the result is lack of authenticity. In this article, a Mach 5 supersonic inlet is considered, and the process of shock wave control using surface discharge is numerically simulated. Both constant C_p and varied C_p are considered. Results show that: 1) for both cases, the electric excitation has a significant effect on shock wave control; 2) the temperature associated parameters (temperature, Mach number, total pressure recovery coefficient) are effected to great extent. Therefore, in order to obtain more realistic calculation results of surface plasma for shock wave control, the effect of variation of C_p with temperature should be considered.

2015, 47(1): 51-60. doi: 10.6052/0459-1879-14-031

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MODEL RESEARCH ON MECHANISM OF MODULATED FLOW PATTERNS FOR VERTICAL UPFLOW

Ma Xiaolin, Xu Jinliang, Xie Jian, Xing Feng, Cheng Yongpan

Due to the fact that micropores prevent gas while pump liquid according to their capillary force characteristics, the tube with mesh construction inside is proposed to modulate flow patterns and enhance heat transfer. Based on Lockhart-Martinelli's separated flow model and Zuber-Findlay's drift model, one-dimensional mathematic model is built to describe the flow dynamic behaviors in vertical flow pattern modulated tube. The experimental conditions are solved by mathematic model and the relative errors between model predicted and experimental results are no more than 20%. It is noted that liquid velocity plays a more important role on flow phenomena than gas velocity while gas velocity influences the degree of penetration through the mesh. Based on qualitative analysis, cubic interpolation and least squares B-spline fitting are used to obtain the quantitative function relationship between flow phenomena and superficial velocity. It comes to the conclusion that when Re_l < 6937, there must be the first kind of condition, and when Re_l > 6937 with Re_g < 67, there can be the second kind of condition which is more likely to present at lower gas velocity. The mathematic model and quantitative function can contribute to the optimal design of flow pattern modulated tube.

2015, 47(1): 61-70. doi: 10.6052/0459-1879-14-218

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EFFECT OF DISJOINING PRESSURE ON SPREADING OF LIQUID DROPLET CONTAINING SURFACTANT OVER CORRUGATED TOPOGRAPHY SURFACE

Li Chunxi, Yang Baocai, Ye Xuemin

For the spreading of an insoluble surfactant-laden droplet over corrugated topography, a disjoining pressure model induced by the concentration of the surfactant was established. The lubrication theory was applied to derive the evolution equations of droplet height and interfacial surfactant concentration and the droplet spreading characteristics under disjoining pressure were numerically simulated. Results indicate that under the effect of disjoining pressure, the evolution time of droplet is shortened significantly, and the spreading rate is accelerated. At the advancing front of the droplet, the number of wavelet tends to decrease obviously, which improves the stability of spreading. In addition, the effect of disjoining pressure on droplet spreading stability is closely related to surfactant concentration associativity. Reducing the attraction strength coefficient α₁ promotes the spreading of droplet. Conversely, decreasing repulsion strength coefficient α₂ exhibits the interfacial instability and enlarges the evolving disturbance energy resulting in spreading inhibited. Increasing height D or wave number k of corrugated topography slows down the spreading rate of the droplet.

2015, 47(1): 71-81. doi: 10.6052/0459-1879-14-161

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A NOVEL UNCOUPLED ALGORITHM FOR SOLVING CHEMICAL NONEQUILIBRIUM FLOWS

Liu Yu, Liu Jun, Tang Lingyan, Cui Xiaoqiang

The WENO5M scheme is modified to simulate the chemical reacting flow based on a novel uncoupled method for chemical nonequilibrium flow. For validating the new implementation, several benchmarks have been tested. The Oran's shock induced detonation experiment has been simulated first. The influences of different chemical reaction mechanisms and grid convergence have been considered and the results compare well with those from experiments. The second test case is the 2d H₂/O₂/Ar detonation, and the simulated cell structure compares well with the experiment results and other simulated results. Through these validations, we can conclude that the new implementation of WENO5M scheme for the simulation of chemical reacting flow based on the novel decoupled method is satisfied. Because the extension of original WENO5M scheme to calculate the chemical reacting flow based on the novel algorithm is straightforward and only minor modifications are needed, the advantages of this uncoupled algorithm is obvious.

2015, 47(1): 82-94. doi: 10.6052/0459-1879-14-089

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NANOINDENTATION EXPERIMENTS AND SIMULATIONS STUDIES ON MECHANICAL RESPONSES OF ENERGETIC CRYSTALS

Wang Xinjie, Wu Yanqing, Huang Fenglei

Nano-indentation experiments and numerical simulations using ABAQUS software are performed to investigate the mechanics responses of energetic crystals. Continuous stiffness method based nano-indentation tests was employed to obtain the elastic modulus and hardness of β-HMX crystal (010) face and α-RDX crystal (210) face. The modulus and hardness can be induced from the load-displacement curves. The hardness value of the energetic crystals shows size effect. Microstructure fracture behaviors were analyzed using atomic force microscope (AFM) observations. It has been found that cracks initiate and expand with the increase of load force. The direction of the crack is also the cleavage direction of the energetic crystal. The finite element code ABAQUS is applied to simulate the nano-indentation experiments. Some parameters measured by the experiment have been used in validating the damaged plasticity constitutive model parameters for finite element simulations. The consistency between the experimental and the numerical simulated results is strong evidence for verifying the damaged plasticity constitutive model. The results presented here may be crucial in predicting the ignition mechanism of energetic crystals.

2015, 47(1): 95-104. doi: 10.6052/0459-1879-14-160

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SIMULATION OF CRACK PROPAGATION OF ROCK BASED ON SPLITTING ELEMENTS

Wang Jie, Li Sihai, Zhang Qingbo

In conventional discrete element methods, fracture is judged by criterion of interface and cracks can only propagate along the boundary of elements. However, criterion of interface can only be used rationally on the condition that macro or micro fractures exist in physical problems. The path and direction of crack will be limited severely by the initial mesh when crack propagates along the boundary. Given these two limitations, a continuous-discontinuous element method is proposed and applied to simulate the progressing cracking problem of rocks. Specifically, criterion is applied on element and intra-element fracture will form. In continuous calculation, element is denoted by a discrete spring system which has specific physical meaning and its deformation and stress are calculated by the characteristic length and area of springs in local coordinate system. The continuous calculation results demonstrate a satisfactory agreement with the traditional finite element method. By updating spring information and local coordinate system, large displacement and rotation of elements can be calculated directly. In addition, Mohr-Coulomb criterion is implemented into the new model to specify the failure state and fracture direction, and intact element will be divided into two elements by means of cutting block. In this way, fracture may be inserted along the boundary of elements or within intact element. A cohesive zone model is employed to simulate the fracture and the elements on two sides of the crack are set to two different nodes at the same time, causing the displacement to be discontinuous. Finally, from numerical results of several intense examples with crack propagation, this method can satisfactorily simulate the progressing cracking problems under tensile, compressive and shear conditions, and its rationality is approved. The continuous-discontinuous element method has been shown to be insensitive to quality of mesh and thus has the potential to simulate crack initiation and propagation.

2015, 47(1): 105-118. doi: 10.6052/0459-1879-14-239

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MEASUREMENT OF LÜDERS BAND IN SMALL SIZE LOW CARBON STEEL SPECIMEN BY 3D DIGITAL IMAGE CORRELATION METHOD

Dai Yuntong, Chen Zhenning, Zhu Feipeng, He Xiaoyuan

Lüders band is phenomenon of stripped fold on material surface which is caused by the inhomogeneous deformation during the yield stage. It can reduce the quality of stamped parts' surface so that it is important to study the Lüders band in order to prevent it from appearing. To complete the observation and analysis of Lüders band in small size low carbon steel specimen, the 3D digital image correlation method under small view field (15mm×15mm) was used to realize the deformation measurement. The formation mechanism of Lüders band was studied and the change of strain and strain rate during the propagation of Lüders band was analyzed. Experimental study demonstrates that the 3D digital image correlation method is able to carry on the observation of meso-mechanical behavior like Lüders band and necking fracture. It provides an effective means for studying meso-mechanism of deformation.

2015, 47(1): 119-126. doi: 10.6052/0459-1879-14-175

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ANALYSIS OF THE MACROSCOPIC INTERFACIAL BEHAVIOUR OF THE FIBRE PULLOUT USING ELASTIC-PLASTIC COHESIVE MODEL

Zhao Yuping, Yuan Hong, Han Jun

A single fibre pullout behavior from polymer matrix was analytically investigated in this paper. The elastic-plastic cohesive zone model was employed to simulate the crack propagation and interfacial failure. The critical fibre embedded length is determined, which distinguishes two pull-out processes from different fibre embedded lengths. There are different interface states during the fibre pull-out process. When the fibre embedded length is shorter than the critical length, the debonding force for the interface is linear relationship to the fibre embedded length; while the debonding force is approximately constant if the fibre embedded length excesses the critical length. The influence of the interfacial parameters on the debonding force is studied. Increasing the interfacial shear strength and the interface fracture toughness, or decreasing the displacement of crack initiation, can raise the debonding force for the interface. Without the interfacial frictional shear stresses after interfacial debonding, the peak load in the pullout force-displacement curve equals the debonding force for the interface. Under the influence of interfacial frictional shear stress, longer fibre embedded length and larger interfacial frictional shear stress lead to the peak load exceeding the debonding force.

2015, 47(1): 127-134. doi: 10.6052/0459-1879-14-165

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THE ORTHOGONALITY AND ENERGY TRANSMITION CHARACTERISTICS OF EULER-BERNOULLI BEAM DYNAMIC MOTION FIELD

Zhou Jun, Rao Zhushiy, Ta Na

Based on analytical solution of undamped Euler-Bernoulli beam's equation of motion, the temporal & spatial average of mechanical energy and power flow's calculation formula are derived. The formula is related to spectral coefficients and based on finite length beam. From the view of functional analysis, the bending motion field, which can be decomposed into evanescent vibration and travelling wave mode, is investigated and the discussion focuses on orthogonality. The result shows that, the evanescent vibration mode is mutual independent of travelling wave mode with regard to energy and power flow functional. In another word, there is no interference between these two modes and the energy superposition principle is satisfied. The important difference between evanescent vibration and wave energy transfer is that the superposition principle is unsatisfied in the evanescent vibration energy transmit mode. That means the interference of two local vibration mode is the reason why the whole vibration field having the capability of energy conduction. The simulation result of a beam with damping at right end and harmonic exciting at middle length is given. The result exhibits that evanescent vibration energy transmit mode shouldn't be neglected in low-frequency range and it is existed that energy exchange between the two modes. But with the increase of frequency, evanescent vibration transmission mode decreases and the total efficiency of energy conducting also falls down.

2015, 47(1): 135-146. doi: 10.6052/0459-1879-14-116

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SECOND-ORDER PARAMETER PERTURBATION METHOD FOR DYNAMIC STRUCTURES WITH INTERVAL PARAMETERS

Li Qi, Qiu Zhiping, Zhang Xudong

When considering the problem of the dynamic responses of structures with interval parameters, previous interval analysis methods are mostly restricted to its first-order. But if the uncertainties of the parameters are fairly large, the response region obtained using the first-order interval analysis method would fail to contain the real region of the dynamic response of uncertain structures. Therefore, the second-order analysis method should be considered. However, the second-order analysis method relating to operations of interval may result in an exorbitantly overestimated dynamic response region, which makes the result useless for practical engineering problems. To circumvent this drawback, firstly the general function of the dynamic response of structures in terms of structural parameters is obtained based on the second-order parameter perturbation method. Then via solving the maximum and minimum of the function, the problem of determining the bounds of the dynamic response of uncertain structures is changed into a series of low dimensional box constrained quadratic problems, and these box constrained quadratic programming problems can be solved using the DC algorithm (difference of convex functions algorithm) effectively. The proposed method can avoid the exorbitant overestimate of the dynamic response region of uncertain structures, while does not introduce much more computational expense. A numerical example is used to illustrate the accuracy and the efficiency of the proposed method when comparing with other methods.

2015, 47(1): 147-153. doi: 10.6052/0459-1879-14-088

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AN IMPROVED MODEL OF ORBITAL DYNAMICS

Yang Mengjie, Yuan Jianping

The radius vector of spacecraft can be decomposed into the product of the mold and the unit vector. Using this property, the traditional orbital dynamics equation can be transformed into two equations which describe the mold's and direction's motions separately. The mold's equation can be converted to a linear equation without singularity by introducing the inverse of the mold; and using the variation of constants method, the linear equation can be reduced to one-order. As for the direction's equation, the quaternion description is suitable. This equation can be completely solved. Through the above handling methods, we obtain a new orbital dynamic model which contains seven equations. In the sense of the virtual time, the angular velocity of the spacecraft depends only on the normal force. This new orbital model is applicable to any form of thrust or perturbation. At the same time, we get seven new stable variables which completely equivalent to the kepler elements. And the transforming relationship has been established. In the end of this article, we verify the accuracy and applicability of the new model in the cases of constant and variable thrusts.

2015, 47(1): 154-162. doi: 10.6052/0459-1879-14-298

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STUDY ON THE NUMERICAL ERROR INTRODUCED BY DISSATISFYING THE CONSERVATION CONSTRAINT IN UGKS AND ITS EFFECTS

Jiang Dingwu, Mao Meiliang, Li Jin, Deng Xiaogang

The Unified Gas Kinetic Scheme (UGKS) was developed by Xu Kun especially for simulating rarefied flows. In UGKS, the conservation constraint can not be satisfied with conventional Discrete Ordinate Method (DOM) and numerical error would be introduced. We found theoretically and numerical experimentally that the error was proportional to the freestream Mach number and inversely proportional to the freestream Knudsen number. Conservative discrete ordinate method (CDOM) was introduced with which the conservation constraint was satisfied at discrete level. The supersonic and hypersonic flows around a cylinder at different Knudsen numbers were simulated and results showed that whether the conservative constraint was satisfied would have a big effect on the variable distributions and the drag coefficients when the Mach number was high or the Knudsen number was low. With CDOM, the grid-free solution could be obtained with a relative coarse velocity grid, resulting in a maximum cost reduction of 2/3.

2015, 47(1): 163-168. doi: 10.6052/0459-1879-14-083

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VERTICAL COUPLING VIBRATION OF BEAM-PILE-SOIL SYSTEM

Lü Shuhui, Wang Kuihua, Zhang Peng

The vertical coupling vibration of beam-pile-soil system is investigated. First, the piles are assumed to be viscoelastic rods, and the plane strain model is employed to simulate the dynamic interactions between piles and surrounding soil layers. The dynamic beam-pile interactions are simplified as vertical point loads. On this basis, the matrix equation for solving the governing equations of motions for beam and piles is constructed in the frequency domain. The quasi-analytical solution in the time domain is then obtained by the discrete inverse Fourier transform. A comparison with numerical simulation is conducted to verify the rationality of the present solution. Finally, the effects of the geometric parameters of beam and pile defect on the dynamic response of beam-pile-soil system are discussed.

2015, 47(1): 169-173. doi: 10.6052/0459-1879-14-082

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MOLECULAR DYNAMICS SIMULATIONS OF HIGH VELOCITY SHOCK COMPRESSED TNT

Liu Hai, Li Qikaiy, He Yuanhang

We simulate the shock compression behavior of TNT with ReaxFF-MD. When shock compression is complete, all of the TNT molecules are decomposed, and when volume compression is up to the 40% of original volume, pressure of the system reaches a peak. Close behind is rarefaction wave reverse stretching the compressed energetic materials and leading to a large number of atoms or molecules group splash to the downstream, pressure begin to unload at the same time. Density and particle wave velocity profile show a greater density in the compressed region, and the particles in a stationary state, but sharp velocity gradient in the region of compression wave. In the earlier chemical characteristics, TNT molecules shed the H, O atoms under the effect of shock compression, and then the residues aggregate to the larger clusters, and this phase associated with translational-vibrational relaxation processes. The rotational mode is subsequently transferred into vibrational modes with a time scale of 0.5 ps. Fragment analysis shows that a large number of C—H, O＝N bonds rupture to form the OH, H₂, H₂O, N₂ groups and parts of H, O atoms are free in the system. The molar mass of the carbon-containing clusters under the joint actions of compressional wave ahead and rear compression is accumulating gradually from the analysis. Atomic ratio in the carbon-containing clusters tends to balance (O/C=0.680, H/C=0.410, N/C=0.284), but less than the ratio in the initial structure.

2015, 47(1): 174-179. doi: 10.6052/0459-1879-14-141

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SPACECRAFT'S TRANSFER ORBIT DESIGN BASED ON THE VIRTUAL CENTRAL GRAVITY FIELD METHOD

Yuan Jianping, Sun Chong, Fang Qun

The space maneuver technology is the basis of space mission operation. In this paper, a novel method named virtual central gravitational field method for continuous thrust maneuver trajectory design for the spacecraft is proposed, which can decrease the number of trajectories' parameters. Because there is no assumption in this approach, it can be used in general case. This approach applies in orbit transfer in both 2-D and 3-D spaces, and the results show that in the same condition, the required thrust acceleration and energy cost are smaller than that of shape-based methods.

2015, 47(1): 180-184. doi: 10.6052/0459-1879-14-112

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REVIEW OF THE EIGHTH NATIONAL SYMPOSIUM ON DYNAMICS AND CONTROL FOR YOUNG SCHOLARS

Ma Shaojuan, Wang Lifengy, Zhan Shigey, Xu Jian

The paper brief introduced the eighth national symposium on dynamics and control for young scholars. Reports of the symposium were recrived, and some constructive suggestions were put forward.

2015, 47(1): 185-190. doi: 10.6052/0459-1879-14-395

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2015, 47(1): 191-196.

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