应用数学和力学

2007 Vol. 28, No. 3

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Numerical Solutions of LQ Control for Time-Varying Systems Via Symplectic Conservative Perturbation

TAN Shu-jun, ZHONG Wan-xie

2007, 28(3): 253-262.

Abstract(3299) PDF(746)

Abstract:
Optimal control system of state space is a conservative system,whose approximate method should be symplectic conservation.Based on the precise integration method,an algorithm of symplectic conservative perturbation was presented.It gives a uniform way to solve the LQ control problems for linear time-varying systems accurately and efficiently,whose key points are solutions of differential Riccati equation and the state feedback equation with variable coefficient.The method is symplectic conservative and has a good numerical stability and high precision.Numerical examples demonstrate the effectiveness of the proposed method.

Theoretical Research on the Rotational Dispersion Coefficient of Fiber in the Turbulent Shear Flow of Fiber Suspension

GAO Zhen-yu, LIN Jian-zhong, LI Jun

2007, 28(3): 263-269.

Abstract(2479) PDF(643)

Abstract:
The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically.The function of correlation moment between the different fluctuating velocity gradient of the flow was built.Then the expression of rotational dispersion coefficient is derived.Which is dependent on the characteristic length,time,velocity and a dimensionless parameter related to the effect of wall.The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows.Furthermore it can be expanded to three-dimensional turbulent flows and serves as the theoretical basis for solving the turbulent flow of fiber suspension.

Effective Viscoelastic Behavior of Particulate Polymer Composites at Finite Concentration

LI Dan, HU Geng-kai

2007, 28(3): 270-280.

Abstract(2900) PDF(774)

Abstract:
Polymeric materials usually present some viscoelastic behavior.To improve the mechanical behavior of these materials,ceramics materials are often filled into the polymeric materials in form of fiber or particle.A micromechanical model was proposed to estimate the overall viscoelastic behavior for particulate polymer composites,especially for high volume concentration of filled particles.The method is based on Laplace transform technique and an elastic model including two-particle interaction.The effective creep compliance and the stress and strain relation at a constant loading rate were analyzed.The results show that the proposed method predicts a significantly stiffer response than those based on Mori-Tanaka's method at high volume concentration of particles.

Radiation Effect on Temperature Distribution in Three-Dimensional Couette Flow With Suction or Injection

Bhupendra Kumar Sharma, Mamta Agarwal, R. C. Chaudhary

2007, 28(3): 281-287.

Abstract(2623) PDF(553)

Abstract:
A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analyszed,when the injection of the fluid at the lower stationary plate is transverse sinusoidal one and its corresponding removal by constant suction through the upper porous plate in uniform motion.Due to this type of injection velocity the flow becomes three-dimensional. The effect of Prandtl number,radiation parameter and injection parameter on rate of heat transfer were examined with the help of graphs.The Prandtl number has a much greater effect on the temperature distribution than the injection or radiation parameters.

Analytical Investigation on the 3D Non-Boussinesq Mountain Wave Drag for Wind Profiles With Vertical Variations

TANG Jin-yun, TANG Jie, WANG Yuan

2007, 28(3): 288-296.

Abstract(2553) PDF(609)

Abstract:
A new analytical model was developed to predict the gravity wave drag(GWD)induced by an isolated 3-dimensional mountain,over which a stratified,non-rotating Non-Boussinesq sheared flow is impinged.The model is confined to small amplitude motion and assumes the ambient velocity varying slowly with height.The modified Taylor-Goldstein equation with variable coefficients was solved with a Wentzel-Kramers-Brillouin(WKB)approximation,formally valid at high Richardson numbers. With this WKB solution,generic formulae,of second order accuracy,for the GWD and surface pressure perturbation(both for hydrostatic and non-hydrostatic flow)were presented,enabling a rigorous treatment on the effects by vertical variations in wind profiles.In an ideal test to the circular bell- shaped mountain,it was found,when the wind is linearly sheared,that the GWD decreases as the Richardson number decreases.However,the GWD for a forward sheared wind(wind increases with height)decreases always faster than that for the backward sheared wind(wind decreases with height).This difference is evident whether the model is hydrostatic or not.

Simulation of Coupled Flowing-Reaction-Deformation With Mass Transfer in Heap Leaching Processes

WU Ai-xiang, LIU Jin-zhi, TANG Ling-yan

2007, 28(3): 297-304.

Abstract(2681) PDF(709)

Abstract:
Governing equations for a fully coupled Flowing-Reaction-Deformation behavior with Mass Transfer in heap leaching process were developed.These equations were solved using an explicit finite different method under the conditions of invarable application rate and constant hydraulic head.The distributions of the degree of the saturation as well as the distributions of the concentration of the reagent and the solute was given.A cubic relationship between the mineral recovery and the leaching duration is obtained based on the numerical results.The relationship can be used to predict the recovery percentage of the valuable metal.

Wave Propagation in a Liquid-Saturated Porous Solid With Micropolar Elastic Skeleton at Boundary Surface

Rajneesh Kumar, Mahabir Barak

2007, 28(3): 305-316.

Abstract(2519) PDF(563)

Abstract:
The reflection and transmission of plane waves at an interface between homogenous inviscid liquid half space and a micropolar liquid-saturated porous solid half space are studied.The reflection and transmission coefficients of various reflected and transmitted waves with the angle of incident were obtained.Numerical calculation were performed for amplitude ratios of variously reflected and transmitted waves.Micropolarity and porosity effects on the reflection and transmission coefficients were depicted graphically.Some particular cases were deduced from the present formulation.

Dynamic Response of a Liquid-Filled Rectangular Tank With Elastic Appendages Under Pitching Excitation

LÜ Jing, LI Jun-feng, WANG Tian-shu

2007, 28(3): 317-327.

Abstract(2824) PDF(678)

Abstract:
Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of the ideal fluid,the coupling dynamics equations of rigid tank,elastic appendages and liquid fuel were derived using H-O principle.In the case of pitch excitation,the modified potential function and wave height function were introduced to describe the moving boundary of fluid. Then Galerkin's method was used to discrete the dynamic equations into ordinary differential equations.The natural frequencies of the coupling system were formulated in liquid depth,the length of the tank,and etc.The formulae are confirmed by numerical simulation,which also show the effect of liquid and elastic appendages on the attitude angular of rigid.

Global Asymptotic Stability for Hopfield-Type Neural Networks With Diffusion Effects

YAN Xiang-ping, LI Wan-tong

2007, 28(3): 328-334.

Abstract(3081) PDF(830)

Abstract:
The existence,uniqueness and global asymptotic stability of the equilibrium for Hopfield-type neural networks with diffusion were discussed.The sufficient conditions of the existence and uniqueness of the equilibrium of the system were obtained by applying the topological degree theory when the activation functions are monotonous non-decreasing and differential,and the interconnected matrix is related to the Lianupov diagonal stable matrix.By constructing the average Liapunov functions,the global asymptotic stability of the equilibrium of the system was obtained.

Axisymmetric Free Vibrations of an Infinite Micropolar Thermoelastic Plate

Rajneesh Kumar, Geeta Partap

2007, 28(3): 335-348.

Abstract(2707) PDF(593)

Abstract:
The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated.The secular equations for homogeneous isotropic micropolar thermoe-lastic plate without energy dissipation in closed form for symmetric and skewsymmetric wave modes of propagation were derived.The different regions of secular equations were obtained.At short wave-length limits,the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation.The results for thermoelastic,micropolar elastic and elastic materials were obtained as particular cases from the derived secular equations.The amplitudes of displacement components,microrotation and temperature distribution were also computed during the symmetric and skew symmetric motion of the plate.The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components,microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes were presented graphically.The analytical and numerical results are found to be in close agreement.

Analytical Solution of the Basic Equations Set of Atmospheric Motion

SHI Wei-hui, SHEN Chun, WANG Yue-peng

2007, 28(3): 349-358.

Abstract(2895) PDF(888)

Abstract:
In the smooth function classes,the basic equations set of atmospheric motion possesses the best stability,under this condition,its structure of solution space for local analytical solution was discussed,by which the third-class initial value problem with typicality and application was also analyzed.And in the analytic function classes,the calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third kind were given.In the meaning of local solution,near a appointed point,the relevant theoretical and computational problems about analytical solution of initial value problem were solved completely.Meanwhile,it is pointed out here that,with other types of problems for determining solution,the computational method and process of their stable analytical solution can be obtained in a similar way if needed.

Petrov-Galerkin Least Squares Mixed Element Method for the Stationary Incompressible Magnetohydrodynamics

LUO Zhen-dong, MAO Yun-kui, ZHU Jiang

2007, 28(3): 359-368.

Abstract(2664) PDF(706)

Abstract:
A Galerkin-Petrov least squares mixed finite element method for the stationary magnetohy-drodynamics problems was introduced and the existence and error estimates of the Galerkin-Petrov least squares mixed finite element solution were derived.The combination among mixed finite element spaces of this method dose not demand the discrete Babuska-Brezzi stability conditions so that the mixed finite element spaces could be arbitrarily chosen and the error estimates with optimal order could be obtained.

Risk-Sensitive Reinforcement Learning Algorithms With Generalized Average Criterion

YIN Chang-ming, WHANG Han-xing, ZHAO Fei

2007, 28(3): 369-378.

Abstract(2280) PDF(850)

Abstract:
A new algorithm which immolates optimality of control policies potentially to obtain the robusticity of solutions is proposed.The robusticity of solutions may become a very important property for a learning system due to when there exists nonOmatching between theory models and practical physical system,or the practical system is not static,or availability of a control action will change along with variety of time.The main contribution is that a set of approximation algorithms and its convergence results will be given.Applying generalized average operator instead of the general optimal operator max(or min)a class of important learning algorithm,dynamic programming algorithm were studied,and their convergence from theoretic point of view was discussed.The purpose is to improve robusticity of reinforcement learning algorithms theoretically.