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    28 December 2009, Volume 15 Issue 6
    Mathematics.Physics and Chemistry
    Recent Advances in Differential Quadrature Method with Applications to Mechanics
    CHENG Chang-jun,ZHU Zheng-you
    2009, 15(6):  551-559. 
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    In this article, we briefly introduce the principle of the differential quadrature method (DQM), its development,and factors that influence precision of the DQsolutions. The advantages over the finite difference method(FDM) and finite element method (FEM) are discussed. Emphasis is given to the recent advances of DQM, the applications to related fields in solid and fluid mechanics, and its prospects.

    Aerodynamic Characteristics of Fixed Wing for Miniature Air Vehicle with Synthetic Jet
    WENG Pei-fen,GE Tiao-lin,DING Jue
    2009, 15(6):  560-565. 
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    Synthetic jet actuator, which can be miniaturized, can improve aerodynamic performance of airfoils of miniature air vehicles (MAV) by suppressing separated flow. In this paper, synthetic jet actuator was placed into an NACA0012 airfoil to conduct wind tunnel tests. Conclusions are drawn as follows. (1) The synthetic jet significantly reduces the separation regions when the Reynolds number is 18 000and the angle of attack is less than 15°. (2)Different frequencies of actuatorare needed for various angles of attack. For example, when the angles of attack are 2.5°, 5°, and above 7.5°, the proper frequencies are 1 300 Hz, 400 Hz or 1 300 Hz, and 960 Hz respectively. (3) The synthetic jet can enhance the lift of airfoil by about 5% when the Reynolds number is 140 000 and the angle of attack is less than 15°.

    Dynamic Characteristics of Timoshenko Beam Partly Immersed in Water on Coupled Elastic Foundation
    YANG Xiao1,JIN Pan1,XU Xiao-hui2
    2009, 15(6):  566-575. 
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    Natural frequencies and the corresponding modes of an elastically supported cantilever Timoshenko beam carrying a tip mass partly immersed in water are investigated. Taking into account the effects of the cross-section rotation, shear distortion and compression axial force due to the tip mass, the mathematical model for free vibration of a cantilever beam is presented, in which constraints of the elastic horizontal displacement and elastic rotation are coupled. Due to the inertial force and inertial moment of the tip mass, boundary conditions of the mathematical model are frequency dependent. The frequency equation and the generalized orthogonal condition for the vibration modes are established. Influences of tip mass,moment of inertia, location of tip mass and coupled springstiffness coefficient, etc., on the natural frequencies are presented numerically and discussed. It is shown that, compared with the model of Euler-Bernoulli beam, due to the crosssection rotation and shear distortion of the beam, the natural frequencies of the Timoshenko beam decrease, especially for the higher order natural frequencies. The addition of coupled spring-stiffness coefficient will reduce the natural frequencies to different extent, and the axial force reduces the lower order natural frequencies while has a negligible influence on the higher order ones.

    Atomistic Simulations of Elastic Moduli in GaN Quantum Dots
    XU Kai-yu1,2,TANG Jun1,2
    2009, 15(6):  576-580. 
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    In this paper, molecular dynamic simulation is performed to predict elastic stiffness and bulk modulus for Gallium nitride (GaN) quantum dots with strain.Different strain configurations are first imposed on the zincblende and wurzite samples, respectively, and relations between bulk strain and system energy are obtained. All elastic moduli can be calculated from the system energy equations simulated with a molecular dynamic method. The calculated moduli without strain agree well with the previous theoretical studies and the available measured values.

    Boundary Point Method Based on Quadratic Moving Elements for Elasticity
    MA Hang,ZHOU Juan
    2009, 15(6):  581-585. 
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     The boundary point method (BPM) is a newly developed boundarytype meshless method with favorable features of both the method of fundamental solution (MFS) and the boundary element method (BEM). The present paper extends the BPM to the numerical analysis of linear elasticity. In order to improve accuracy of stresses near boundaries due to the near singularity in postprocessing and in the analysis of thinwall structures, quadratic moving elements are introduced into BPM in addition to the original constant moving elements. Numerical tests are carried out with benchmark examples in the two dimensional elasticity. Good agreement is observed between the numerical results and the rigorous solutions.

    Impulsive Consensus Problem in Complex Delayed Networked-Multi-agent Systems
    ZHOU Jin1,WU Quanjun1,LIU Zengrong2
    2009, 15(6):  586-593. 
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    This paper considers average consensus problems in directed delayed networked multi-agent systems having fixed topology as well as switching topology from the view of dynamics and control. Based on the impulsive control theory of delayed dynamical systems, two consensus protocols of the networks with communication delays are proposed. Some simple yet generic criteria for solving the average consensus problem are analytically derived. The distinctive features of this work indicate that the first consensus protocol is valid for any communication delays, and the second one is effective for all the nodes of the network achieving average global consensus exponentially. It is shown that the impulsive gain in the protocols plays a key role in seeking average consensus. Moreover, numerical simulations illustrate correctness of our theoretical results.

    Extended Finite Volume WENO Scheme for Solving Hyperbolic -Conservation Laws with Discontinuous Fluxes
    ZHANG Peng,QIAO Dian-liang,LI Shu-feng
    2009, 15(6):  594-599. 
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     This paper combines δ-mapping algorithm with the classical fifthorder finite volume weighted essentially non-oscillatory (WENO) scheme for numerical solution of hyperbolic conservation laws with discontinuous fluxes. Numerical examples show that the hybrid scheme is efficient when applied to nonlinear elasticity in heterogeneous media and a multi-class Lighthill-Whitham-Richards (LWR) traffic model. 

    Large Eddy Simulation of Particle Motion in Shear Turbulent -Flow Due to Thermal Buoyancy
    DONG Yu-hong,CHEN Lin-feng,TANG Yi-min
    2009, 15(6):  600-606. 
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    The behavior of dilute dispersion of particles in a stratified channel flow is investigated with large eddy simulation. The threedimensional NavierStokes and energy equations under the Boussinesq approximation are numerically solved using a fractionalstep method based on highorder accurate temporal schemes. The Lagrangian tracking approach is used to describe the dynamics of particles. The objectives of this study are to deal with the effect of the thermal buoyancy on the behavior of particles in the thermally stratified turbulent channel flow and examine particle concentrations under the stratified turbulent environment. In the present study, some typical cases are computed. To depict the effect of the thermal stratification on the particles transport, the mean value and fluctuation of resolved velocities of particles, as well as some typical instantaneous velocity fluctuation patterns are analyzed. Numerical results provide the characteristics of particle concentrations under different Stokes numbers. 

    Third-Order Theory for Surface Capillary-Gravity Short Crested Waves
    HUANG Hu
    2009, 15(6):  607-610. 
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    Considering the rich capillary effects on surface waves, a system for surface capillary-gravity shortcrested waves is developed. The unique solution condition is given, and the thirdorder solution obtained, leading to expressions for a series of kinematic and dynamic variables closely related to coastal and ocean engineering. These expressions deal with surface elevation, velocity potential, angular frequency, wave steepness, phase velocity, wave-particle velocities and accelerations, and wave pressure. It is found that locations of zeros and poles of the thirdorder angular frequency directly correspond to the harmonic resonances.

    Measurement and Analysis of Noise in Multi-layer Urban Rail Transit
    ZHU Huai-liang1,YUAN Er-na2,LI Peng1,WANG Meng-jue1
    2009, 15(6):  611-614. 
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    This study takes the multi-layer mass transit of Gonghexin Road, Shanghai, as an example, which has a subway line with a doubledecker elevated track. Vibration and environmental noise caused by the urban mass transit was investigated. Noise measurement was done in the subway, on the ground and on the double-decker elevated track. Based on the date and their spectral decomposition, curves of one third octave characteristics and equivalent sound pressure levels were obtained. Further analyses were carried out on the rules of normal noise for different mass transits. The results are useful for the urban development, environmental evaluation and noise control.

    Cyclic Test of Architectural PVC Membrane Materials under -Biaxial Orthogonality Tensile Loads
    LUO Ren-an1,2,HUA Ling2,NI Jing3,TONG Kai4
    2009, 15(6):  615-620. 
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    Through biaxial cyclic tensile tests of PVC membrane materials at seven different ratios between warp and weft stress, which are 0∶1, 1∶5, 1∶2, 1∶1, 2∶1, 5∶1 and 1∶0 respectively, tensile performances of the samples under biaxial tensile loads are analyzed. The tests indicate that after three cyclic loading, the experimental properties of membrane materials agree well with actual properties of membrane materials used in structures. The test results show that the behavior of membrane material is highly nonlinear and orthotropic under biaxial tensile loads. During the cyclic loading test, the residual strain is obvious at the end of first unloading. With the increase of loading cycles (usually after three cycles), the total residual strain is nearly unchangeable and the hysteresis curve becomes stable. The generalized Poisson’s ratio is measured using the results of biaxial tensile tests of PVCmembrane materials, which verifies the nonlinear characteristics of generalized Poisson’s ratio. It is illustrated in the test that the strain in warp direction is positive when C≥1, while for C≤0.5, the generalized Poisson’s ratio turns to negative. When the stress ratio is 1∶0 or 0∶1, the biaxial test turns to uniaxial test, and the determination of the generalized Poisson’s ratio becomes routine Poisson’s ratio test. Both the theory and test results indicate that under the condition of C=1, both warp and weft directions have the biggest elastic moduli.

    Mechanical Analysis of Micromachined Accelerometer with Piezoelectric Thin Films Read-out
    SUN Bohua,HAN Li-feng
    2009, 15(6):  621-627. 
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    A micromachined accelerometer with piezoelectric thin film based on the piezoelectric effect is studied. By static analysis of accelerometer with twolayer piezoelectric thin film (PZT), a sensitivity formula is derived, and numerical calculation is then performed. It is found that sensitivity first increases with the increase of PZT thickness, and reversed when the thickness reaches a certain level. Dynamics analysis is discussed. Noise, the quality factor and the minimum detectable signal are obtained. Curves of the dynamic response can be obtained with ANSYS in the harmonic analysis.

    A Numerical Method for Imposing Slip Boundary Conditions in Dissipative Particle Dynamics
    LI Zhen,HU Guo-hui,ZHOU Zhe-wei
    2009, 15(6):  628-633. 
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    Velocity slippage on a solid wall is usually neglected in macroscopic flow. However, the effect of slippage on the fluid dynamics can be significant in a microscopic scale. Therefore, slip condition at solid boundary should be considered in microscopic or mesoscopic hydrodynamics. Dissipative particle dynamics (DPD) is a promising approach to the study of mesoscale hydrodynamic behaviors. Noslip boundary conditions are widely used in previous DPD simulations. A numerical method for imposing slip boundary conditions was proposed in the DPD simulation. To show validity of the approach, velocity profiles obtained by DPD are found to be consistent with the analytic solutions based on Navier condition for the Poiseuille flow.

    Correspondence Principle for Nonhomogeneous Hygro-thermo-viscoelastic  Quasi-static Problems
    ZHANG Neng-hui1,2,QIN Xiao-jun1
    2009, 15(6):  634-636. 
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    The Christensen’s isotropic thermoviscoelastic constitutive relation is adopted to consider influence of moisture and thermal changes on the reduced time for simple thermorheological materials. The Laplace transform method is used to show that the correspondence principle for isotropic and nonhomogeneous hygro-thermo-viscoelastic quasi-static problems still holds when relaxation functions have separable forms in space and time, and the given temperature and moisture fields are only related to time variable.

    Experimental Investigation of Cliff-Structure Properties of Active and Passive Scalars in Turbulent Rayleigh-énard Convection
    ZHOU Quan
    2009, 15(6):  637-643. 
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    Statistical properties of cliff structures of active and passive scalar fields in a waterfilled turbulent RayleighBénard convection cell are investigated experimentally at Ra=1.2×1010 and Pr=5.3. An arithmetic with a parameter β used to describe “intensity” of cliffs is applied to extract cliff structures from time series of the local concentration (passive scalar) of fluorescence dye and the local temperature (active scalar). Both scalars are measured near the sidewall of a rectangular cell. Histograms of the cliffs’ width, amplitude and size are studied quantitatively. It is found that, for both scalars, shapes of the histograms for cliffs’ width are invariant with respective to the β value, while the cliffs’ most probable amplitude shifts to higher values with increasing β. The obtained results show that the sizes of cliff structures of both scalars are log-normal distributed and the passive scalar mixing in turbulent thermal convection is determined by thermal plumes. 

    Mechanical Behavior and Failure Strength of Fiber Braided High Pressure Rubber Hoses
    REN Jiu-sheng1,2,ZHOU Jin-wen1,2,YUAN Xue-gang3
    2009, 15(6):  644-648. 
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    A three-layer heterogeneous tube is modeled for the fiber braided hoses based on the finite deformation theory of continuum mechanics and the hyper-elastic theory. Relationship between the stresses and the deformation with internal pressure is obtained. Mechanical behaviors such as deformation, stress distribution and failure strength are analyzed. The effect of materials and geometric factors of the hoses such as modulus of the fibers and axial extension of the hose on its deformation and strength is discussed.

    Coupled Forced Response of Nonlinear Axially Moving Viscoelastic Beam
    DING Hu1,CHEN Li-qun1,2
    2009, 15(6):  649-652. 
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    Forced vibration is numerically investigated for planar vibration of axially moving viscoelastic beams with simple supports. The material time derivative is used in the viscoelastic constitutive relation for the governing equation.It is assumed that excitation is spatially uniform and temporally harmonic. A finite difference scheme is developed to calculate steady-state response numerically. Numerical results demonstrate that there are steady-state periodic responses in transverse vibration, and resonance occurs if the external load frequency approaches the linear natural frequencies.Numerical results also indicate that amplitudes of stable steady-state responses decrease with the viscosity coefficient and the nonlinear coefficient, and increase with the amplitude of excitation.

     

    Sedov-Type Solution to Two-Dimensional Isotropic Turbulence and Its Applications
    RAN Zheng,WAN Shu-xiao
    2009, 15(6):  653-658. 
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    This work provides analytical results of the two-dimensional Karman-Howarth equation. A self-similar decay of two-dimensional turbulence energy spectrum has also been determined. These expressions are a counterpart of three-dimensional turbulence. The behavior of the inverse energy cascade in a two-dimensional isotropic homogeneous turbulence can be understood from the view point of present statistical solution. 