应用数学和力学

2008 Vol. 29, No. 9

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Adaptive Explicit Magnus Numerical Method for Nonlinear Dynamical Systems

LI Wen-cheng, DENG Zi-chen

2008, 29(9): 1009-1016.

Abstract(3349) PDF(543)

Abstract:
Based on the new explicit Magnus expansion developed for nonlinear equation defined on matrix Lie group, an efficient numerical method was suggested for nonlinear dynamical system. To improve the computational efficiency, the integration step size can be controlled self adaptively. The validity and effectiveness of the method were proved by application to several nonlinear dynamical systems, including Duffing system, Van der Pol system with strong stiffness, and nonlinear Hamiltonian pendulum system.

Dynamic Stress Intensity Factor and Dynamic Crack Propagation Characteristics of Anisotropic Material

GAO Xin, WANG Han-gong, KANG Xing-wu

2008, 29(9): 1017-1027.

Abstract(3246) PDF(730)

Abstract:
Based on mechanics of anisotropic material, the dynamic propagation problem of mode Ⅲ crack in an infinite anisotropic body is investigated. The stresses and displacements around the crack tip were expressed as analytical complex function, which can be represented in power series. The constant coefficients of the series are determined by boundary conditions. The expression of dynamic stress intensity factors for mode Ⅲ crack was obtained, and the dynamic stress components, strain components and dynamic displacement components around the crack tip were derived. The crack propagation characteristics were represented with mechanical properties of anisotropic material, crack speeds M and parameters alpha. The faster the crack velocity, the greater the maximum of stress components and dynamic displacement components around crack tip. The parameters alpha particularly affect the stress components and dynamic displacement components around crack tip.

Adaptive Neural Network Control for Coordinated Motion of Dual-Arm Space Robot System With Uncertain Parameters

GUO Yi-shen, CHEN Li

2008, 29(9): 1028-1036.

Abstract(3299) PDF(554)

Abstract:
The control problem of coordinated motion between the base's attitude and the arms' joints of a free-floating dual-arm space robot with uncertain parameters was discussed. Combining the relationship of the system linear momentum conversation and the Lagrangian approach, the dynamic equation of a free-floating dual-arm space robot was established. Based on the above results, the free-floating dual-arm space robot system was modeled by the RBF neural network technique, the GL matrix and its product operator. With all uncertain inertial parameters of system, the adaptive RBF neural network control scheme was developed for coordinated motion between the base's attitude and the arms. joints of the free -floating dual-arm space robot. This proposed control scheme need neither linearly parameterize the dynamic equation of system and foreknow any actual inertial parameters accurately, nor train the neural network offline so that it could be prone to real-time and online application. A planar free-floating dual-arm space robot is simulated to verify the feasibility of the proposed control scheme.

Propagation of Plane Waves in Poroviscoelastic Anisotropic Media

A. K. Vashishth, M. D. Sharma

2008, 29(9): 1037-1047.

Abstract(3241) PDF(500)

Abstract:
The wave propagation in, perhaps, the most general model of a poroelastic medium is discussed. The medium is considered as a viscoelastic, anisotropic, porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid. The anisotropy, considered, is of general type and attenuating waves in the medium were treated as inhomogeneous waves. The complex slowness vector was resolved to define the phase velocity, homogeneous attenuation, inhomogeneous attenuation and angle of attenuation for each of the four attenuating waves in the medium. A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version. Numerical model of a North-Sea sandstone was used to analyze the effects of propagation direction, inhomogeneity parameter, frequency regime, anisotropy symmetry, anelasticity of frame and viscosity of pore-fluid on the propagation characteristics of waves in such a medium.

Boundary Slippage Used to Generate Hydrodynamic Load-Carrying Capacity

ZHANG Yong-bin

2008, 29(9): 1048-1056.

Abstract(2310) PDF(475)

Abstract:
Boundary slippage was used to generate the load-carrying capacity of the hydrodynamic contact between two parallel plane surfaces. In the fluid inlet zone the fluid-contact interfacial shear strength on the stationary surface is set as low to generate boundary slippage there, while in the fluid outlet zone the fluid-contact interfacial shear strength on the stationary surface is set as high enough to prevent the boundary slippage occurrence there. The fluid-contact interfacial shear strength on the whole moving surface is set as high enough to prevent boundary slippage on the moving surface. These hydrodynamic contact configurations are analyzed to generate the pronounced load-carrying capacity. The optimum ratio of the outlet zone width to the inlet zone width for the maximum loadcarrying capacity of the whole contact is analyzed to be 0.5.

Analytical Model of Sound Transmission Through Laminated Composite Cylindrical Shells Considering Transverse Shear Deformation

Kamran Daneshjou, Ali Nouri, Roohollah Talebitooti

2008, 29(9): 1057-1068.

Abstract(2825) PDF(523)

Abstract:
Composite structures are often used in aerospace industries because of advantages offered by a high strength to weight ratio. Sound transmission through an infinite laminated composite cylindrical shell is studied in the context of the transmission of airborne sound into aircraft interior. The shell is immersed in external fluid medium and contains internal fluid, and airflow in external fluid medium is moving with a constant velocity. An exact solution was obtained by solving the first-order shear deformation theory(FSDT) of laminated composite shell and acoustic wave equations simultaneously. Transmission losses(TL) obtained from numerical solution were compared with those of other authors. The effects of structural properties and flight conditions on TL were studied for a range of values, especially, Mach number, stack sequences and angle of warp. Additionally, comparison of the transmission loss was made among classical thin shell theory(CST) and FSDT for laminated composite and isotropic cylindrical shells.

Effects of Chemical Reaction on MHD Micropolar Fluid Flow Past a Vertical Plate in Slip-Flow Regime

R. C. Chaudhary, Abhay Kumar Jha

2008, 29(9): 1069-1082.

Abstract(2886) PDF(622)

Abstract:
Heat and mass transfer effects on unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in slip-flow regime was studied, taking into account the homogeneous chemical reaction of first order. A uniform magnetic field acts perpendicular to the porous surface which absorbs the micropolar fluids with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using approximate method the expression for the velocity microrotation, temperature and concentration were obtained. Also the results of the skin friction coefficient, the couple stress coefficient, the rate of heat and mass transfer at the wall were presented with various values of fluid properties and flow conditions.

Limit Cycles and Homoclinic Orbits and Their Bifurcation of the Bogdanov-Takens System

HUANG Cheng-biao, LIU Jia

2008, 29(9): 1083-1088.

Abstract(3102) PDF(841)

Abstract:
The quantitative analysis of limit cycles and homoclinic orbits and the bifurcation curve for the Bogdanov-Takens system were discussed. The parameter incremental method for approximate analytical-expressions of these problems was given. These analytical-expressions of the limit cycle and homoclinic orbit were shown as the generalized harmonic function by employing a time transformation. Some curves for the parameters and the stability characteristic exponent of limit cycle versus amplitude were drawn. And some of the limit cycles and homoclinic orbits phase portraits were plotted. And the relationship curves of parameterand μ and λ with amplitude a and the bifurcation diagrams about the parameter were given too. The numerical accuracy of calculation results was good.

Anisotropic Rectangular Nonconforming Finite Element Analysis for Sobolev Equations

SHI Dong-yang, WANG Hai-hong, GUO Cheng

2008, 29(9): 1089-1100.

Abstract(3171) PDF(586)

Abstract:
The anisotropic rectangular nonconforming finite element method to Sobolev equations is discussed under semi-discrete and full discrete schemes, the corresponding optimal convergence error estimates and superclose property are derived, which are the same as the traditional conforming finite elements. Furthermore, the global superconvergence is obtained through post-processing technique. Finally, the numerical results illustrate the validity of our theoretical analysis.

Analytical Approximate Solutions and the Approximate Value of Skin Friction Coefficient for the Boundary Layer of Power Law Fluids

SU Xiao-hong, ZHENG Lian-cun, JIANG Feng

2008, 29(9): 1101-1106.

Abstract(2692) PDF(546)

Abstract:
A theoretical analysis for laminar boundary layer flow in power law non-Newtonian fluid was presented. The Adomian analytical decomposition technique was presented and an approximate analytical solution was obtained. The approximate analytical solution can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions. Moreover, the approximate solution can be successfully applied to provide the values of skin friction coefficient in the power law non-Newtonian fluid.

A New Alternating Group Explicit-Implicit Algorithm With Highly Accuracy for the Dispersive Equation

ZHANG Qing-jie, WANG Wen-qia

2008, 29(9): 1107-1116.

Abstract(3114) PDF(496)

Abstract:
A new alternating group explicit-implicit scheme (nAGEI) for the dispersive equation with a periodic boundary condition is derived. This new unconditionally stable scheme has the fourth-order truncation error in space and quicker ratio of convergence than some known alternating group methods (eg. ASEI and AGE). A comparison of the accuracy of this method with some prior ASEI and AGE methods is showed in the numerical experiment.

Convergence of Gradient Method for Elman Networks

WU Wei, XU Dong-po, LI Zheng-xue

2008, 29(9): 1117-1123.

Abstract(3119) PDF(814)

Abstract:
The gradient method for training Elman networks with finite training sample set is considered. The monotonicity of the error function in the iteration is shown. A weak and a strong convergence results are proved, indicating that the gradient of the error function goes to zero and the weight sequence goes to a fixed point, respectively. A numerical example is given to support the theoretical findings.

Dividend Function in the Jump-Diffusion Dual Model With Barrier Dividend Strategy

LI Bo, WU Rong

2008, 29(9): 1124-1134.

Abstract(2549) PDF(563)

Abstract:
A dual model of the perturbed classical compound Poisson risk model under a constant dividend barrier was considered. A new method is used in deriving the boundary condition of the equation satisfied by that expectation function, by using the local time of a related process. The expression for the expected discounted dividend function was obtained in terms of those in the corresponding perturbed compound Poisson risk model without barrier. The special cases where the gain size is phasetype distributed is illustrated in the last section. Also the existence of the optimal dividend level was considered.