Table of Content

18 February 2007, Volume 28 Issue 2

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Articles

Scale effect and geometric shapes of grains

GUO Hui;GUO Xing-ming

2007, 28(2):  141-149 .  doi:10.1007/s10483-007-0201-1

Abstract ( 1268 )   PDF (338KB) ( 587 )  

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The rule-of-mixture approach has become one of the widely spread ways to investigate the mechanical properties of nano-materials and nano-structures, and it is very important for the simulation results to exactly compute phase volume fractions. The nanocrystalline (NC) materials are treated as three-phase composites consisting of grain core phase, grain boundary (GB) phase and triple junction phase, and a two-dimensional three-phase mixture regular polygon model is established to investigate the scale effect of mechanical properties of NC materials due to the geometrical polyhedron characteristics of crystal grain. For different multi-sided geometrical shapes of grains, the corresponding regular polygon model is adopted to obtain more precise phase volume fractions and exactly predict the mechanical properties of NC materials.

Nonlinear dynamical behavior of shallow cylindrical reticulated shells

WANG Xin-zhi;LIANG Cong-xing;HAN Ming-jun;YEH Kai-yuan;WANG Gang

2007, 28(2):  151-156 .  doi:10.1007/s10483-007-0202-x

Abstract ( 1223 )   PDF (405KB) ( 610 )  

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By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the separating variable function, the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support. The tensile force is solved out from the compatible equations, a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin. The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function. The existence of the chaotic motion of thesingle-layer shallow cylindrical reticulated shell is approved by using the digital simulation method and Poincare mapping.

Generalized synchronization of continuous dynamical system

ZHANG Gang;LIU Zeng-rong;MA Zhong-jun

2007, 28(2):  157-162 .  doi:10.1007/s10483-007-0203-y

Abstract ( 1430 )   PDF (196KB) ( 589 )  

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Generalized synchronization between two continuous dynamical systems is discussed. By exploring the Liapunov stability theory and constructing appropriately unidirectional coupling term, a sufficient condition for determining the generalized synchronization between continuous systems is proved. Two examples are used to show the effectiveness of this result.

Renewal of basic laws and principles for polar continuum theories (XI)---consistency problems

DAI Tian-min

2007, 28(2):  163-172 .  doi:10.1007/s10483-007-0204-y

Abstract ( 1313 )   PDF (142KB) ( 523 )  

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Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum fieldn theories.

Analytical solutions of steady vibration of
free rectangular plate on semi-infinite elastic foundation

WANG Chun-ling;HUANG Yi;JIA Ji-hong

2007, 28(2):  173-182 .  doi:10.1007/s10483-007-0205-z

Abstract ( 1382 )   PDF (774KB) ( 752 )  

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The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load. And an integral representations for the displacements of the semi-infinite elastic foundation was presented. The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semi-infinite elastic foundation. Some computational results and the analysis on the influence of parameters were presented.

Effect of thermal diffusion and electrostatic force on evolution of wind-blown sand flow

YUE Gao-wei;ZHENG Xiao-jing

2007, 28(2):  183-192 .  doi:10.1007/s10483-007-0206-z

Abstract ( 1412 )   PDF (395KB) ( 855 )  

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A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow. An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow, saltating grains, and a kind of electrostatic force exerted on the grains are considered in this theoretical model. The numerical results show that the effect of the thermal diffusion on the evolution process of wind-blown grain flow is quite obvious and very similar to the effect of the electrostatic force on the evolution. Not only the time for the entire system to reach a steady state (called the duration time), the transport rate of grains, the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.

Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation

LIU Yan-hong;ZHANG Hui-ming

2007, 28(2):  193-200 .  doi:10.1007/s10483-007-0207-y

Abstract ( 1477 )   PDF (205KB) ( 811 )  

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Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve non-homogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.

Lunar landing trajectory design based on invariant manifold

GONG Sheng-ping;LI Jun-feng;BAOYIN He-xi;GAO Yun-feng

2007, 28(2):  201-207 .  doi:10.1007/s10483-007-0208-1

Abstract ( 1393 )   PDF (564KB) ( 671 )  

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The low-energy lunar landing trajectory design using the invariant manifolds of restricted three-body problem is studied. Considering angle between the ecliptic plane and lunar orbit plane, the four-body problem of sun-earth-moon-spacecraft is divided into two three-body problems, the sun-earth-spacecraft in the ecliptic plane and the earth-moon-spacecraft in the lunar orbit plane. Using the orbit maneuver at the place where the two planes and the invariant manifolds intersect, a genera method to design low energy lunar landing trajectory is given. It is found that this method can save the energy about 20% compared to the traditional Hohmann transfer trajectory. The mechanism that the method can save energy is investigated in the point of view of energy and the expression of the amount of energy saved is given. In addition, some rules of selecting parameters with respect to orbit design are provided. The method of energy analysis in the paper can be extended to energy analysis in deep space orbit design.

Transverse vibration characteristics of axially moving viscoelastic plate

ZHOU Yin-feng;WANG Zhong-min

2007, 28(2):  209-218 .  doi:10.1007/s10483-007-0209-1

Abstract ( 1321 )   PDF (304KB) ( 733 )  

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The dynamic characteristics and stability of axially moving viscoelastic rectangular thin plate are investigated. Based on the two dimensional viscoelasti differential constitutive relation, the differential equations of motion of the axially moving viscoelastic plate are established. Dimensionless complex frequencies of an axially moving viscoelastic plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The effects of the aspect ratio, moving speed and dimensionless delay time of the material on the transverse vibration and stability of the axially moving viscoelastic plate are analyzed.

Analytical solution of fractionally damped beam by Adomian decomposition method

LIANG Zu-feng;TANG Xiao-yan

2007, 28(2):  219-228 .  doi:10.1007/s10483-007-0210-z

Abstract ( 1391 )   PDF (395KB) ( 519 )  

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The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the Adomian decomposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to how the displacement of the beam under different sets of parameters ncluding different orders of the fractional derivatives.

Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry

CUI Deng-lan;LI Yang-cheng

2007, 28(2):  229-235 .  doi:10.1007/s10483-007-0211-x

Abstract ( 1421 )   PDF (158KB) ( 720 )  

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Based on the contact equivalent elation of smooth map-germs in singularity theory, the stability of quivariant bifurcation problems with two types of state variables nd their unfoldings in the presence of parameter symmetry is iscussed. Some basic results are obtained. Transversality condition s used to characterize the stability of equavariant bifurcation roblems.

Hausdorff dimension of set generated by exceptional oscillations of a class of N-parameter Gaussian processes

LIN Zheng-yan;CHENG Zong-mao

2007, 28(2):  237-245 .  doi:10.1007/s10483-007-0212-z

Abstract ( 1261 )   PDF (184KB) ( 591 )  

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A class of N-parameter Gaussian rocesses are introduced, which are more general than the -parameter Wiener process. The definition of the set generated by xceptional oscillations of a class of these processes is given, and hen the Hausdorff dimension of this set is defined. The Hausdorff imensions of these processes are studied and an exact epresentative for them is given, which is similar to that for the wo-parameter Wiener process by Zacharie (2001). Moreover, the time et considered is a hyperrectangle which is more general than a yper-square used by Zacharie (2001). For this more general case, a ernique-type inequality is established and then using this nequality and the Slepian lemma, a Lévy's continuity modulus theorem is shown. Independence of increments is required for showing he representative of the Hausdorff dimension by Zacharie (2001). his property is absent for the processes introduced here, so we ave to find a different way.

A class of two-dimensional dual integral equations and its application

FAN Tian-you;SUN Zhu-feng

2007, 28(2):  247-252 .  doi:10.1007/s10483-007-0213-y

Abstract ( 1377 )   PDF (188KB) ( 682 )  

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Because exact analytic solution is not vailable, we use double expansion and boundary collocation to onstruct an approximate solution for a class of two-dimensional ual integral equations in mathematical physics. The integral quations by this procedure are reduced to infinite algebraic quations. The accuracy of the solution lies in the boundary ollocation technique. The application of which for some complicated nitial-boundary value problems in solid mechanics indicates the ethod is powerful.

State-vector equation with damping and vibration analysis of laminates

QING Guang-hui;XU Jian-xin;QIU Jia-jun

2007, 28(2):  253-259 .  doi:10.1007/s10483-007-0214-1

Abstract ( 1374 )   PDF (217KB) ( 654 )  

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Based on the modified mixed Hellinger-Reissner(H-R) variational principle for elastic bodies with damping, the state-vector equation with parameters is directionally derived from the principle. A new solution for the harmonic vibration of simply supported rectangular laminates with damping is proposed by using the precise integration method and Muller method. The general solutions for the free vibration of underdamping, critical damp and overdamping of composite laminates are given simply in terms of the linear damping vibration theory. The effect of viscous damping force on the vibration of composite laminates is investigated through numerical examples. The state-vector equation theory and its application areas are extended.

Stability for basic system of equations of atmospheric motion

SHI Wei-hui;XU Ming;WANG Yue-peng

2007, 28(2):  261-268 .  doi:10.1007/s10483-007-0215-y

Abstract ( 1476 )   PDF (159KB) ( 440 )  

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The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about "speculating future from past'' in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.

Inequalities relating to L_p-version of Petty's conjectured projection inequality

WANG Wei-dong;LENG Gang-song

2007, 28(2):  269-276 .  doi:10.1007/s10483-007-0216-x

Abstract ( 1121 )   PDF (157KB) ( 495 )  

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Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to L_p-version of the Petty's conjectured projection inequality is developed by using the notions of the L_p-mixed volume and the L_p-dual mixed volume, the relation of the L_p-projection body and the geometric body T_-pK, the Bourgain-Milman inequality and the L_p-Busemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body T_-pK, the reverses of L_p-version of the Petty's conjectured projection inequality and the L_p-Petty projection inequality are given, respectively.