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Table of Content
23 March 2012, Volume 44 Issue 2
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Brief Report
TURBULENTLIKE QUANTITATIVE ANALYSIS ON THE SOUND ABSORBING CHARACTERISTICS OF METAL RUBBER
Hu Zhiping, Zhou Han, Wu Jiuhui
2012, 44(2): 197204. DOI:
10.6052/045918792012220120201
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Metal rubber has much penetrated pores from the surface to the core,and the quasiperiodic and irregularity features are very similar to those of turbulence. Because of the irregularity within the structure of metal rubber, even if the Reynolds number is very small, turbulence still occurs. Therefore, the concept of the Kolmogorov local isotropic turbulence is introduced and two assumptions on the local isotropic Kolmogorov turbulence are obtained. The physical model of turbulence is established, and the sound absorbing characteristics of metal rubber are quantitatively analyzed and the relationship of the expression between the energy dissipation rate of metal rubber material and its structural parameters is obtained. The results show that the introduction of turbulence statistical method provides not only a reliable theoretical basis for the optimal design of metal rubber instruments such as damper and muffler but an effective quantitative analysis method for engineering applications of ultralight metal porous materials.
NUMERICAL INVESTIGATION ON UNSTEADY SHOCK WAVE REFLECTIONS OVER THREE DIMENSIONAL INTERSECTING WEDGES
Yang Yang, Teng Honghui, Wang Chun, Jiang Zonglin
2012, 44(2): 205212. DOI:
10.6052/045918792012220120202
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An investigation into unsteady shock wave reflections over threedimensional intersecting wedges is described. The finite volume method with the MUSCLHancock interpretation is used on selfadaptive unstructured meshes. Numerical results demonstrate that threedimensional Mach reflection region predicted by the relations of twodimensional oblique shock wave reflection has limitations because of the threedimensional effect of shock reflections. An atypical threedimensional structure appears in this region, namely the second type of threedimensional Mach stem. Besides, for different combinations of shock wave Mach numbers and wedge angles, the threedimensional fourshock Mach reflections or threeshock regular reflections appear in the corner of the two intersecting wedges.
TOMOGRAPHIC TRPIV MEASUREMENT OF ANISOTROPIC EDDYVISCOSITY MODEL FOR COHERENT STRUCTURE REYNOLDS STRESS
Jiang Nan, Guan Xinlei, Yu Peining
2012, 44(2): 213221. DOI:
10.6052/045918792012220120203
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The time sequences dataset of 3D3C flow field of turbulent boundary layer in a water tunnel by tomographic TRPIV were employed to put forward the new concept of spatial locallyaveraged velocity structure function of turbulence that describes the spacial dilation, compression, shear deformation and rotation of the multiscale turbulent eddy structure. According to the physical characteristics of the multiscale vortex structures' stretch and compression in turbulent flow, a new conditional sampling method of coherent structure, based on the concept of multiscale spatial locally averaged velocity structure function along the longitudinal direction, was proposed to extract the spatial topology of physical quantities such as fluctuating velocity, mean velocity strain rate and Reynolds stress during the process of coherent structure burst in TRPIV dataset. In this paper, the relationship between mean velocity strain rate and Reynolds stress was studied. The validity of the anisotropic eddy viscosity model was confirmed for coherent structure Reynolds stress in wallbounded turbulence through investigating the spatial phase difference between Reynolds stress components and mean velocity strain rate components.
ESEC{ASSESSMENT OF THE COMPRESSIBLE TURBULENCE MODEL BY USING THE DNS DATA
Li Xinliang, Fu Dexun, Ma Yanwen
2012, 44(2): 222229. DOI:
10.6052/045918792012220120204
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Direct numerical simulation (DNS) of turbulent flatplate boundary layer flows with freestream Mach numbers of 2.25 and 6 are performed, and the data are validated by compared with theoretical, experimental and numerical results. Based on the DNS data, turbulence models (including
kε
varepsilon model, SA model and BL model) are assessed. For Mach 2.25 case, numerical results show that the realizable
kε
varepsilon model agrees the DNS data very well and the turbulent viscous coefficient of the classical
kε
varepsilon model is higher than that of the DNS data. SA model gives quite good turbulent viscous in the inner layer of the boundarylayer, but it gives higher turbulent viscous in the outer layer. For high Mach number case,
kε
varepsilon models and SA model overestimate turbulent viscous coefficient. In Mach 6 case, BL model cannot give good interface location between the inner and the outer layer. To improve the BL model, the authors modify the coefficients, and the new model's viscous coefficient agrees well with the DNS data.
THE INVESTIGATION OF EXPERIMENTAL TECHNIQUE FOR HIGH TEMPERATURE GAS JET FLOW TEST IN IMPULSE WIND TUNNEL
Chen Xuedong, Wang Famin, Tang Guiming
2012, 44(2): 230237. DOI:
10.6052/045918792012220120205
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This is the first report on the experimental results about the aerothermal environment of high temperature jet flow (HTJF) and its interaction flow. The significance of this experiment is to abstract the physical mode from the real flight of hypersonic aircraft in order to provide experimental evidence for the thermal protection requirements. This experiment used the compression corner as the research object to research the aerothermal environment influenced by the HTJF and the interaction flow by the HTJF in combine with the main flow filed. In this paper, the main flow came from the impulse wind tunnel; the HTJF came from the high enthalpy gas supply platform, which used the oxhydrogen burner to drive the Ludwieg tube. This paper used the pressure change of the driven section in the impulse wind tunnel to control the producing of the HTJF in order to assure the synchronous operation of the two parts of flow. This paper will present the research about: (1) To standardize the thermodynamic state of the HTJF; (2)The experimental research of the compress corner which include three experimental status: (i) the aerothermal environment in the main flow without the HTJF; (ii) the aerothermal environment in the high temperature jet flow without the main flow; (iii) the aerothermal environment in both the high temperature jet flow and the main flow. It is found from the experiment that the aerothermal environment of the part of the compress corner has great influenced by the high temperature gas flow. The high temperature gas jet flow can cause the heat flux peak an order of magnitude than the heat flux peak without it.
PRELIMINARY EXPERIMENTAL INVESTIGATION ON SUPERSONIC FLOW MAGNETOHYDRODYNAMIC(MHD) ACCELERATION
Li Yiwen, Li Yinghong, Zhang Bailing, Chen Feng, Zhu Tao
2012, 44(2): 238244. DOI:
10.6052/045918792012220120206
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Preliminary experimental investigation on Magnetohydrodynamic (MHD) acceleration using seeded supersonic flow as working fluid was presented in the paper. Helium and argon were used as driver and driven gas, respectively, in a shock tunnel. Equilibrium contact surface operating mode was used for obtaining high temperature gas. The conductivity was obtained by adding seed K
_{2}
CO
_{3}
powders into the driven section, and big capacitor was used for providing electric energy. Voltage and current characteristics, conductivity, load factor, electric efficiency and acceleration effect were measured or calculated on typical experimental condition when the nozzle entry total pressure is 0.7049MPa, theoretical equilibrium temperature of 8372.8K, nozzle outlet Mach number of 1.5, capacitance voltage of 400V, and magnetic field strength of 0.5T. The main results are as follows: the conductivity of supersonic flow is about 150S/m under the existence of magnetic field; the load factor of the MHD acceleration channel is about 4; electrical efficiency is about 28%, and average input power is 198kW; flow velocity was increased by 15.7% by means of electrical parameter measurement, and the conductivity of the supersonic flow has important influence on the electrical efficiency and acceleration effect.
A COORDINATE TRANSFORMATION METHOD FOR NUMERICAL SOLUTIONS OF TRAVELINGWAVE ELECTROOMTIC FLOWS IN MICROCHANNEL
Chen Bo, Wu Jiankang
2012, 44(2): 245251. DOI:
10.6052/045918792012220120207
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In this paper, a coordinate transformation method is employed to numerically solve the coupling PoissonNernstPlanck (PNP) equation and NavierStokes (NS) equations for studying the travelingwave electroosmotic flow in twodimensional microchannel. Numerical solutions indicate that the coordinate transformation effectively decreases the gradient of the solution in the electric double layer (EDL), and greatly improves the stability and convergence of the solution. The numerical solutions with and without the coordinate transformation are in good agreement. In a transformed coordinate system with a coarse grid, the numerical solutions can be as accurate as those in the original coordinate system with a refined grid. The approximate solutions of slip boundary are also presented for a comparison. It is found that the solutions of slip boundary agree with those of complete PNPNS equations in the cases of small ratio of EDL thickness and channel depth (
λ/H
). In cases of large
λ/H
, the solution of slip boundary overpredicts the electroosmotic flow velocity.
ANALYSIS OF VELOCITY ANNULAR EFFECT OF OSCILLATORY FLOW INSIDE PARALLEL PLATE CHANNEL
Tang Ke, Zhang Yu, Tang Wentao, Jin Tao, Zhang Xuejun
2012, 44(2): 252258. DOI:
10.6052/045918792012220120208
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This study focuses on the velocityannulareffect (VAE) of compressible oscillatory flow inside parallel plate channel. By analyzing the mechanism of VAE, we conclude that VAE, which inevitably occurs in viscous oscillatory pipe flow, is most visible at the phase when the centerline velocity reaches zero. In order to quantitatively evaluate the VAE, coefficient of velocity annular effect (CVAE) was proposed as an index parameter, based on the slope of velocity profile when the centerline velocity reaches zero. Numerical computations with the index parameter CVAE were conducted to analyze the impacts of dimensionless parameters, i.e., Valensi number
Va
and maximum Reynolds number
Re
_{max}
, on the VAE of oscillatory flow inside parallel plate channel.
THE PRACTICAL MFCAV RIEMANN SOLVER IS APPLIED TO A NEW CELLCENTERED LAGRANGIAN METHOD
Liu Yan, Tian Baolin, Shen Weidong, Mao Dekang
2012, 44(2): 259268. DOI:
10.6052/045918792012220120209
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Recently, Maire et al. developed a new cellcentered finitevolume Lagrangian method, which greatly eases the problem of spurious grid deformations that have long been troubling cellcentered Lagrangian methods. However, the new method uses only the WWAM approximate Riemann solver in the computation of numerical fluxes, which has much numerical dissipation; moreover, the design of the new method indicates that approximate Riemann solvers in forms other than that of WWAM are not able to be straightforwardly applied to the method. This work successfully applies the MFCAV approximate Riemann solver to Maire et al's method by viewing the MFCAV as a modification of the WWAM. Our numerical tests show that the new method using the MFCAV solver is effective. This study opens a door for applications of Riemann solvers in forms other than that of WWAM to Maire et al's new Lagrangian method.
A MODIFIED KUBOTA CAVITATION MODEL FOR COMPUTATIONS OF CRYOGENIC CAVITATING FLOWS
Shi Suguo, Wang Guoyu
2012, 44(2): 269277. DOI:
10.6052/045918792012220120210
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In order to predict the cavitating flow characteristics in cryogenic fluids more exactly, a revised cavitation model considering the thermal effect with modified the evaporation and condensation source terms is established, which is based on Kubota cavitation model. The computations for cavitating flows in liquid nitrogen are conducted around an axisymmetric ogive by employing Kubota cavitation model and the revised cavitation model, respectively. The computational results are compared with the experimental data to evaluate the revised cavitation model. It is found that for the results of the revised cavitation model due to considering the thermal effects, the evaporation becomes smaller and the condensation becomes larger, the cavity length is shorter and the cavity interface becomes more porous compared with the results of original Kubota model. The results of the revised cavitation model are more accordant with the experimental data, and it dictates that the revised cavitation model can describe the process of mass transport more accurately in the cavitation process in cryogenic fluids and it is applicable for computations of cavitating flows in cryogenic fluids flow.
KINETIC THEORY OF ROUGH SPHERES AND NUMERICAL SIMULATION OF DENSE GASPARTICLES FLOW
Wang Shuai, Hao Zhenhua, Xu Pengfei, Sun Liyan, Lu Huilin
2012, 44(2): 278286. DOI:
10.6052/045918792012220120211
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The collisional motion of rough particles is analyzed in consideration of translational and rotational motions of particles. The particle average fluctuation kinetic energy is introduced to measure the fluctuating translational and rotational energies of particles. Kinetic theory of rough spheres is proposed on the basis of the kinetic BoltzmannEnskog equation. The models for solids pressure and viscosity of particles are derived by the ChapmanEnskog method for gas kinetic theory. Flow behavior of particles is simulated using a gassolid twofluid model by taking into the effect of particle rotational motion on the interphase energy exchange and dissipations account. Simulated solids concentrations in a bubbling fluidized bed and axial velocity of particles in a riser are in agreement with experimental data published in literature. While the fluctuation kinetic energy increases, reaches maxima, and then decreases as the concentration of particles is increased. With the increase of tangential restitution coefficient, the particle fluctuation kinetic energy and energy dissipation is increased. These indicate that the frictions caused by the particle rotation alter fluctuating energy of particles, which influences the flow behavior of particles in bubbling fluidized beds.
HEORETICAL ANALYSIS OF THE VIBRATION AND SOUND RADIATION FROM AN INFINITE FLUIDSTRUCTURE COUPLED PLATE STIFFENED BY TWODIMENSIONAL PERIODIC STRUCTURES
Zhou Haian, Wang Xiaoming, Mei Yulin
2012, 44(2): 287296. DOI:
10.6052/045918792012220120212
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The vibration response of and sound radiation from an infinite fluidloaded plate, stiffened by two dimensional periodically spaced structures and excited by a timedependent plane harmonic pressure, are investigated in this paper. A semianalytical approach based on the finite element method (FEM) and space harmonic method to study the stiffened plate is also presented. To obtain the reaction forces of the periodic structures acting on the plate, the FEM is applied by discretizing each structure into a sufficient number of elements and nodal points, and the reaction forces are approximated by the equivalent nodal forces. Then using the vibration equations of the periodic structures combined with the displacement boundary conditions between them and the plate, the nodal forces are expressed in terms of the corresponding discrete point displacements of the plate. Based on the space harmonic method and Fourier transforms, the vibroacoustic equations of the stiffened plate are finally derived as functions of these point displacements of the plate, which are calculated numerically. In numerical examples, the validity of the present approach is demonstrated and the effects of the periodic structures on the vibroacoustic responses of the plate are also analyzed.
RESEARCH ON HEATSHIELDING PROPERTIES OF SUPERALLOY HONEYCOMB PANEL FOR NONLINEAR HIGH TEMPERATURE ENVIRONMENT
Wu Dafang, Zheng Liming, Pan Bing, Wang Yuewu, Sun Bing, Mu Meng
2012, 44(2): 297307. DOI:
10.6052/045918792012220120213
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The heatshielding characteristics of metallic honeycomb panel structure (MTPS) in high temperature environments are very important parameters for thermal protection design of highspeed aircrafts. Using the selfdeveloped transient aerodynamic heating simulation system designed for highspeed aircrafts, the heatshielding performance of MTPS in the nonlinear high temperature environment up to 800℃ was experimentally investigated. The heattransfer characteristics of MTPS at transient and steady states, and the heat insulation effects at various temperatures, were obtained. Also, by carefully considering the multiple heat exchange including the radiation among the inside honeycomb walls, the heat transfer of the metal structure and the heat transfer of the air within the honeycomb cavity, a three dimensional finite element model was established to simulate the heatshielding performance of the honeycomb panels. The numerical simulations agree well with the experimental results, verifying the correctness and effectiveness of the numerical simulation method. The good agreements also confirm the feasibility of substituting expensive air thermal simulation testing using numerical simulation. Some other key issues, such as heat shielding efficiency variation of the MTPS in complex nonlinear high temperature environment, the relationship among the heat shielding efficiency, the change speed of front surface temperature and selection of emissivity for the MTPS' surface, were also discussed in this work, which provide important references for the heatshielding of MTPS to be used in highspeed crafts.
CREEP BEHAVIOR OF VISCOELASTIC FUNCTIONALLY GRADED MATERIALS AND STRUCTURES IN THERMAL ENVIRONMENT
Peng Fan, Gu Yongjun, Ma Qingzhen
2012, 44(2): 308316. DOI:
10.6052/045918792012220120214
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Based on classical correspondence principle, MoriTanaka and other micromechanical approaches are extended to treat the case of linear viscoelasticity in the constant thermal environment. The relaxation modulus and coefficient of thermal expansion of linearly viscoelastic FGMs are given directly in Laplace phase space, and multidimensional viscoelastic constitutive relation coupling thermal strain is constructed through considering the weak timedependent feature of Poisson's ratio. Following the above work, the problem of axial symmetrical bending of viscoelastic functionally graded circular cylindrical thin shells is solved. The steady temperature field is determined taking into account of the temperature dependence of thermal and mechanical parameters. The analytic solution is derived in phase space and the creep deflection is obtained by means of Laplace numerical inversion. It is shown that the thermal effect is obvious at initial creep stage, but abates with the increase of time due to the relaxation of the thermal stresses, and the constraint effect for hinged ends is more prominent than that of clamped ends on the deflection near ends when circular cylindrical thin shell is subjected to axial compression. It is expected to give the general approach to analyze the creep deformation of viscoelastic functionally graded structures with arbitrary distribution of volume content under thermal and mechanical loading by solving above problem of axial symmetrical bending.
RESEARCH ON GENERALIZED THERMOELASTIC PROBLEMS OF A SOLID CYLINDER SUBJECTED TO THERMAL SHOCK
Wang Yingze, Zhang Xiaobing, Song Xinnan
2012, 44(2): 317325. DOI:
10.6052/045918792012220120215
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Based on the LS generalized thermoelasticity, one dimensional problem of a solid cylinder subjected thermal shock is studied. In accordance with the transient behaviors of thermal shock, the approximate shorttime analytical solutions of the temperature, displacement and stresses are obtained via the Laplace transform and inverse transform. Numerical simulation is conducted for an isotropic solid cylinder, and the distribution of each physical field including the temperature, radial displacement, radial stress, hoop stress and axial stress are obtained, and the influence of the delay and the coupling effects on these distributions are also obtained. The results show that the thermal disturbance propagates forwards with two different velocities when the effects of the delay and coupling are considered, and these effects have influences on the time of each physical field began to establish, the intervals of two jumps and the peak values of jumps.
STUDY ON LOW CYCLE FATIGUE OF SINGLE CRYSTAL NIBASED SUPERALLOY UNDER MULTIAXIAL NONPROPORTIONAL LOADING
Ding Zhiping, Chen Jiping, Wang Tengfei, Zhao Ping
2012, 44(2): 326333. DOI:
10.6052/045918792012220120216
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Straincontrolled tension/torsion low cycle fatigue (LCF) tests of single crystal Nibased superalloy,DD3,were carried out under nonproportional loadings based on orthogonal design at elevated temperatures, using thinwalled tube specimens with [001] orientation. Experimental variable factors were chosen to be strain range, strain path angle, tension/torsion phase angle, strain ratio and temperature. Results show that strain path angle, tension/torsion phase angle and equivalent strain range, are the main affected factors on multiaxial LCF life. Dividing diamond strain loading path into proportional loading and nonproportional loading segments, the equivalent strain range parameter to characterize the effects of nonproportional loading was proposed, and a strain triaxiality factor for single crystal superalloy was introduced to reflect the tension/torsion strain path angle on multiaxial fatigue life. A formula of cyclic plastic strain energy, which is composed of the equivalent strain range taking account of the effects of nonproportional loading path and the strain triaxiality factor, is put forward as failure parameter. Multiple linear regression analysis show that a power law of the failure parameter has a good correlation with the failure cycle, and all test data fall into a scatter band of the factor of 2.0.
STUDY OF TWIP EFFECT ON STRAIN HARDENING BEHAVIOR IN V5Cr5Ti ALLOY
Yu Yong, Pan Xiaoxia, Xie Ruoze, Zhang Fangju, Hu Wenjun
2012, 44(2): 334341. DOI:
10.6052/045918792012220120217
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As an important potential structural material for fusion firstwall/blanket application, vanadium alloy (VCrTi) has been studied a great lot in recent years. In order to study the strain hardening behavior of V5Cr5Ti alloy under compressions with different strain rates, especially the twinning effect on the plastic deformation, the strain hardening model of this alloy has been constructed based on the evolutions of dislocation density and twin in this paper. The model considered that the slipping of dislocation in twins could contribute to the plastic strain. The simulation results indicated that strain hardening ratio of dynamic compression, which is smaller than that of quasistatic compression, is caused by dislocation density of the former smaller than that of the latter owing to twinning induced plasticity (TWIP). After the twins formed, the plastic strain rate induced by dislocation slipping increases with strain increasing, and approaches the loading strain rate, while the plastic strain rate induced by twinning decreases with strain increasing.
STRUCTURE DYNAMIC MODEL REDUCTION TECHNIQUE BASED ON LOCAL INTERPOLATION
Deng Jiadong, Cheng Gengdong
2012, 44(2): 342350. DOI:
10.6052/045918792012220120218
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Based on complex structural finite element model, a new reduction method of structural dynamic model using local interpolation is proposed in this paper. The displacement of a node in the finite element model is obtained through interpolation of the displacements of the condensation nodes it attaches to. Every entry of the dynamic condensation matrix is formed by interpolation functions. To improve accuracy of the reduction method, the shape function of the nonconforming element is adopted as the interpolation function to lower the reduced structural stiffness after condensation, and the eigenvalues and eigenvectors are ameliorated through inverse iteration on the finite element model. To enhance efficiency of the reduced method, regular grids which just encompass the structure are employed to generate the condensation points. Due to the regularity of the grids, we can easily determine the condensation points to which a node in the finite element model attaches. Finally, mode analyses of three machine tool components demonstrate the effectiveness and the feasibility of the reduction method proposed in this article.
IMPROVED SINGULAR BOUNDARY METHOD FOR THREE DIMENSIONAL POTENTIAL PROBLEMS
Gu Yan, Chen Wen
2012, 44(2): 351360. DOI:
10.6052/045918792012220120219
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The singular boundary method (SBM) is a relatively new meshless boundary collocation method for the numerical solution of certain boundary value problems. The key idea is to introduce the concept of the origin intensity factor to isolate the singularity of the fundamental solutions, so that the source points directly coincide with the collocation points on the realistic boundary. This overcomes a perplexing fictitious boundary outside physical domain in the recently popular method of fundamental solutions (MFS). However, the inverse interpolation technique requires the placement of a cluster of sample nodes inside or outside the physical domain for either interior or exterior problems. Our recent numerical experiments indicate that the overall accuracy of this SBM formulation is, to a certain degree, sensitive to the location of such sample nodes. To remedy the abovementioned drawbacks, this paper proposes an improved SBM formulation for threedimensional potential problems to circumvent sample nodes in the inverse interpolation technique with the traditional SBM. Numerical experiments demonstrate its significantly improved accuracy and stability in comparison with the traditional SBM formulation.
A MDBEM BASED ON ROW ELIMINATIONBACKSUBSTITUTION METHOD
Gao Xiaowei, Hu Jinxiu, Cui Miao
2012, 44(2): 361368. DOI:
10.6052/045918792012220120220
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A novel multidomain boundary element method (MDBEM) analysis technique is presented to solve largescale engineering problems. Firstly, the basic integral equations of each domain formulated in terms of internal, boundary and interface nodal variables are reduced to the algebraic equations in terms of interface nodal variables only by the threestep variable condensing technique. Then, a sparse system of equations formulated in terms of interface nodal quantities is assembled using the equilibrium equation and consistence condition at interface nodes. To solve the system of equations efficiently, this paper, for the first time, introduces a robust linear equation solution method, called the row eliminationbacksubstitution method (REBSM), to solve the nonsymmetric sparse system of equations. REBSM performs both the elimination and backsubstitution procedures when each row of the system is formed. When the last row is finished for assembling, the solutions of the system are obtained at the same time, without the need of the last backsubstitution procedure. Since some repeated terms are incorporated, REBSM needs less storage than the Gaussian elimination method, has an improvement in computational speed by orders of magnitude, and provide BEM a robust equation solver for solving large engineering problems.
IMPOSING DISPLACEMENT BOUNDARY CONDITIONS WITH NITSCHE'S METHOD IN ISOGEOMETRIC ANALYSIS
Chen Tao, Mo Rong, Wan Neng, Gong Zhongwei
2012, 44(2): 371381. DOI:
10.6052/045918792012220120221
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Isogeometric analysis uses the exact geometric representations for the modeling and numerical simulations by NURBS basis functions. It eliminates the geometric approximation errors during the mesh discretization, and the highorder conforming NURBS elements can be conveniently constructed. In the structural analysis, smooth stress fields can be directly computed without the stress recovery procedure as in the finite element method. Due to the lack of the interpolation properties for the NURBS basis functions, it is difficult to enforce the displacement boundary conditions in isogeometric analysis. The imposition of prescribed values is not as straightforward as the conventional approaches. In order to solve this issue, a weak imposition method was proposed basing on the Nitsche's variational principle. It has some attractive advantages: (i) the consistent and stabilized weak form, (ii) the degreeoffreedoms are not increased, (iii) the resulting system is symmetric and positive, (iv) the matrix condition number is not very large in order to ensure convergence. Meantime, the stability conditions were derived for the structural analysis. The stability parameters were evaluated by solving a generalized eigenvalue problem. Through several numerical examples, the optimal rates of convergence were observed under the
h
refinement of the NURBS meshes. Contrasting with directly imposing into the control points, the better results were obtained by the proposed method.
SCALED BOUNDARY ISOGEOMETRIC ANALYSIS AND ITS APPLICATION I:EIGENVALUE PROBLEM OF WAVEGUIDE
Zhang Yong, Lin Gao, Hu Zhiqiang
2012, 44(2): 382392. DOI:
10.6052/045918792012220120222
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Scaled boundary isogeometric analysis (SBIGA) is approved and applied for waveguide eigenvalue problem. Based on scaled boundary isogeometric transformation, the governing partial differential equations (PDEs) for waveguide eigenvalue problem are semiweakened to a set of 2nd order ordinary differential equations (ODEs) by weighted residual methods, and transformed to a set of 1st order ODEs about the dynamic stiffness matrix in wavenumber domain. Approximating the dynamic stiffness matrix in the continued fraction expression and introducing auxiliary variables, the ODEs are finally exported to algebraic general eigenvalue equations, and thus the cutoff wavenumber of waveguide is obtained. The main property of SBIGA is that the governing PDEs are isogeometricly discretized on domain boundary, which reduces the spatial dimension by one and analytical feature in the radial direction like traditional SBFEM, additionally, boundary is exactly discretized as its geometry design. The numerical examples, including rectangular and Lshaped waveguides, are presented and compared with analytic solution and other numerical methods. The results show that SBIGA yields high precision results with fewer amounts of DOFs than other methods do.
DYNAMIC IMPEDANCE OF FOUNDATION ON SATURATED POROELASTIC SOIL
Chen Shaolin, Zhen Cheng
2012, 44(2): 393400. DOI:
10.6052/045918792012220120223
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Based on the method of lumpedmass explicit finite element and local transmitting artificial boundary, a time domain method is presented for the computation of dynamic stiffness of rigid foundations resting on or embedded in saturated poroelastic soil. The twophase behavior of porous medium is represented according to Biot's theory. The technique is applied to the computation of dynamic stiffness of rigid plate on a saturated poroelastic halfspace. Compliance component are computed and compared with existing results. The effects of properties of porous medium and the embedded depth on the dynamic stiffness are examined. The method presented in this paper is able to represent more general properties and geometries of soil and foundation than the existing approaches do.
ANALYTICAL LAYERELEMENT OF PLANE STRAIN BIOT'S CONSOLIDATION
Ai Zhiyong, Cao Guojun, Cheng Yichong
2012, 44(2): 401407. DOI:
10.6052/045918792012220120224
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An efficient algorithm is presented to solve plane strain Biot's consolidation of a single soil layer with an arbitrary depth. Starting from the governing equations of Biot's consolidation, an exactly symmetric stiffness matrix, i.e. the analytical layerelement, is deduced in LaplaceFourier transformed domain by using the eigenvalue approach. According to the relationship between generalized displacements and stresses of a single layer in the transformed domain described by the matrix, and the boundary conditions of the soil layer, the solutions of any point can be obtained. The actual solutions in the physical domain can further be acquired by inverting the LaplaceFourier transform. Finally, numerical examples are presented to verify the theory and study the influence of the soil properties and time history on the consolidation behavior.
DEPLOYMENT AND ATTITUDE CONTROL OF A TETHERED SUBSATELLITE WITH CONTROLLABLE ARM
Wen Hao, Chen Hui, Jin Dongping, Hu Haiyan
2012, 44(2): 408414. DOI:
10.6052/045918792012220120225
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The paper presents an investigation on the position and attitude control problem concerning the inplane motions of a tethered subsatellite, the attitude of which is controlled by using a controllable arm instead of momentumwheel actuation in the phase of tether deployment. There are two main steps in the design of the controller. Firstly, a study accounting for the statecontrol constraints is presented on the nonlinear optimal control problems of the position and attitude of the subsatellite, the openloop solution of which is determined by using the Legendre pseudospectral algorithm in the secondorder form. Secondly, a feedback control law is derived to track the reference trajectory prescribed by the openloop control law, and the gains of online feedback control are determined by interpolating a sequence of gain data precomputed via the algorithm of openloop optimal control. The case studies in the paper well demonstrate the performance of the proposed strategy.
ATTITUDE REORIENTATION CONTROL FOR LIQUIDFILLED SPACECRAFT WITH ONE KIND OF APPENDAGE
Yang Dandan, Yue Baozeng
2012, 44(2): 415424. DOI:
10.6052/045918792012220120226
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Attitude reorientation control by momentum transfer via Lyapunov stability theory for liquidfilled spacecraft with lightweight cantilever appendage is studied. The sloshing liquid is substituted by a viscous pendulum ball, and the cantilever appendage is substituted by several concentrated particals. Dynamics equations of the major rigid body, the pendulum ball, and the concentrated particles are derived through the theorem of moment of momentum and Lagrange equation. The feedback control law used a weighting coefficient related nearly with the angular acceleration of the wheel, which can be determined by the initial and final states of the system and the steady state time of attitude maneuver. A criterion guarantying to achieve attitude reorientation is attained by Lyapunov stability theorem. Numerical simulations indicate the validity of the control law. Sensitivity of residual nutation angle of the spacecraft is analyzed to the rotation angle of the appendage to the plane of the major rigid body, the relative height of the appendage to the center of mass of the system, the length of the appendage, the rigidity of the appendage, the mass of the appendage, the vibration damping of the appendage and the steady state time of the attitude maneuver.
PARAMETRIC INDENTIFICATION FOR HIGHDIMENSIONAL NONLINEAR VIBRATION SYSTEM
Su Luanming, Ye Min
2012, 44(2): 425436. DOI:
10.6052/045918792012220120227
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The incremental harmonic balance nonlinear identification (IHBNID) is extended to highdimensional nonlinear vibration system. The identification equation of multidegreeoffreedom nonlinear dynamic system is derived. Numerical simulation on a twodegreesoffreedom nonlinear system example, based on the IHBNID, was carried out on the period1, the perioddoubling and the chaotic motions. The effect of noise on the identification parameters is analyzed. The effectiveness of the IHBNID is verified for multidegreeoffreedom nonlinear dynamic system. The simulating results show that the proposed method has high accuracy and efficiency, and can improve the antinoise ability.
FIRSTPASSAGE OF COUPLED DUFFINGVAN DER POL SYSTEM IN THE CASE OF EXTERNAL RESONANCE
Zhang Lei, Wu Yongjun
2012, 44(2): 437446. DOI:
10.6052/045918792012220120228
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Firstpassage failure of twoDOF Duffingvan der Pol system with strong nonlinearity under combined harmonic and wideband stochastic excitations was studied. In the case of external resonance, the equations of motion of the system are reduced to a set of averaged It\^{o} stochastic differential equations after stochastic averaging. Then, the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean firstpassage time are established. Under specified boundary and initial conditions, the method of finite difference is used to solve the highdimensional backward Kolmogorov equation and Pontryagin equation to yield the conditional reliability function, the mean firstpassage time and the conditional probability density function of the mean firstpassage time. Different parameters are chosen to show the influence on the reliability and mean firstpassage time of the original system. All theoretical results are verified by Monte Carlo simulation.
GRANULAR SOLID HYDRODYNAMICS AND ANALYSES ON TRIAXIAL COMPRESSIONS
Sun Qicheng, Song Shixiong, Jiang Yimin, Jin Feng, Zhang Chuhan
2012, 44(2): 447450. DOI:
10.6052/045918792012220120229
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Hydrodynamics theory was originally developed Newtonian fluids. The theory combines mass, energy, moment, entropy flow and dissipation flows in Onsager relations. As an extension to granular materials, granular solid hydrodynamics(GSH) constructs a thermodynamics function and a series of transport coefficients for irreversible processes in granular matter. In this paper, GSH is used to analyze mechanical properties of dry sands under triaxial compressions. The stressstrain relations and volumetric strainaxial strain relations are obtained, which are of great engineering concerns. The evolution of granular temperature is studied as well.
THE ANALYTICAL SOLUTION OF THE ANNULAR AXISYMMETRIC STAGNATION FLOW WITH SLIP
Zhu Jing, Zheng Liancun, Zhang Zhigang
2012, 44(2): 451455. DOI:
10.6052/045918792012220120230
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This paper presents a theoretical analysis for the annular axisymmetric stagnation slip flow on a moving cylinder. The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. By using the homotopy analysis method, a convergent series solution is obtained. The solutions indicate that the flow and shear stress depend heavily on the velocity slip parameter. Also, effect of increasing values of
λ
is to decrease the surface shear stress. Besides, both drag and moment experienced by the inner cylinder are increased by the increased Reynolds number and the decreased ratio of axial velocity to injection velocity.
THE NONSTATIONARY DIFFERENTIAL CONSTITUTIVE MODELS OF VISCOELASTICITY
Kang Yonggang, Zhang Xiu'e
2012, 44(2): 456459. DOI:
10.6052/045918792012220120231
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Based on nonstationary viscous components, the nonstationary Maxwell model, the nonstationary Kelvin model and the nonstationary Zener model were developed. Their relaxation moduli, creep compliances and unloading functions were obtained by resolving the nonstationary constitutive relation. The results show that many empirical functions, such as power law relaxation, stretched exponential relaxation, logarithmic creep, can be seen as nonstationary model. The corresponding relaxation modulus and unloading functions of empirical creep functions, the corresponding creep compliance and unloading functions of empirical relaxation function were obtained by resolving the nonstationary constitutive relation.
A SMOOTHED FINITE ELEMENTPERFECTLY MATCHED LAYER METHOD FOR TWODIMENSIONAL STEADYSTATE RADIATION ACOUSTIC FIELD PROBLEMS
Xia Baizhan, Yu Dejie, Yao Lingyun
2012, 44(2): 460464. DOI:
10.6052/045918792012220120232
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Aiming at the problem of low accuracy of finite element method (FEM) for exterior acoustics analysis, the smoothed finite element method perfectly matched layer (SFEMPML) method is proposed for the analysis of twodimensional steadystate acoustic radiation problem. In SFEMPML, the computational region, truncated by perfectly matched layer(PML), is discreted into fournode isoparametric elements. The mapping relation between the PML's parameter coordinates and Cartesian coordinates is implemented by using the exponential absorbing function. In order to recast the domain integrals involving shape function gradients to the boundary integrals involving only shape functions，the radiant acoustic stiffness matrix is calculated by using the smoothed acoustic pressure gradient matrix. Numerical example of a twodimensional radiation field of acoustic cavity of automobile is presented，which shows that SFEMPML achieves better absorbing effect in PML, and higher accuracy in the computational region as compared with FEMPML. Hence the SFEMPML can be well applied in solving two dimensional acoustic radiation problems, and has a wide application foreground.