应用数学和力学

Poincare-Lighthill-Kuo Method and Symbolic Computation

DAI Shi-qiang

2001, 22(3): 221-227.

Abstract(3141) PDF(786)

Abstract:
This paper elucidates the effectiveness of combining the Poincare-Lighthill-Kuo method(PLK method,for short) and symbolic computation.Firstly,the idea and hist ory of the PLK method are briefly introduced.Then,the difficulty of intermediate expression swell,often encountered in symbolic computation,is outlined.For overcoming the difficulty,a semi-inverse algorithm was proposed by the author,with which the lengthy parts of intermediate expressions are first frozen in the form of symbols till the final stage of seeking perturbation solutions.To discuss the applications of the above algorithm,the related work of the author and his research group on nonlinear oscillations and waves is concisely reviewed.The computer-extended perturbation solution of the Duffing equation shows that the asymptotic solution obtained with the PLK method possesses the convergence radius of 1 and thus the range of validity of the solution is considerably enlarged.The studies on internal solitary waves in stratified fluid and on the head-on collision between two solitary waves in a hyperelastic rod indicate that by means of the presented methods,very complicated manipulation,unconceivable in hand calculation,can be conducted and thus result in higher-order evolution equations and asymptotic solutions.The examples illustrate that the algorithm helps to realize the symbolic computation on micro-commputers.Finally,it is concluded that with the aid of symbolic computation,the vitality of the PLK method is greatly strengthened and at least for the solutions to conservative systems of oscillations and waves,it is a powerful tool.

Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments

SHEN Hui-shen

2001, 22(3): 228-238.

Abstract(2534) PDF(791)

Abstract:
The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model.The material properties of the composite are affected by the variation of temperature and moisture,and are based on a micromechanical model of a laminate.The governing equations are based on the classical laminated shell theory,and including hygrothermal effects.The nonlinear prebuckling deformations and initial geometric imperfections of the shell were both taken into account.A boundary layer theory of shell buckling was extended to the case of laminated cylindrical shells under hygrothermal environments,and a singular perturbation technique was employed to determine buckling loads and postbuckling equilibrium paths.The numerical illustrations concern the postbuckling behavior of perfect and imperfect,cross-ply laminated cylindrical shells under different sets of environmental conditions.The influences played by temperature rise,the degree of moisture concentration,fiber volume fraction,shell geometric parameter,total number of plies,stacking sequences and initial geometric imperfections are studied.

On the Asymptotic Solutions of Boundary Value Problems for a Class of Systems of Nonlinear Differential Equations(Ⅰ)

JIANG Fu-ru

2001, 22(3): 239-249.

Abstract(2389) PDF(640)

Abstract:
A new method is applied to study the asymptotic behavior of solutions of boundnary value problems for a class of systems of nonlinear differential equations u"=v,εv"+f(x,u,u')v'-g(x,u,u')v=0(0<ε≤1).The asymptotic expansions of solutions are constructed,the remainders are estimated.The former works are improved and generalized.

Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation

LI Gen-guo, ZHU Zheng-you, CHENG Chang-jun

2001, 22(3): 250-258.

Abstract(2456) PDF(714)

Abstract:
The dynamic stability of simple supported viscoelastic column,subjected to a periodic axial force,is investigated.The viscoelastic material was assumed to obey the fractional derivative constitutive relation.The governing equation of motion was derived as a weakly singular Volterra integro- partial-differential equation,and it was simplified into a weakly singular Volterra integro-ordinary-di-f ferential equation by the Galerkin method.In terms of the averaging method,the dynamical stability was analyzed.A new numerical method is proposed to avoid storing all history data.Numerical examples are presented and the numerical results agree with the analytical ones.

Research on Coherent Structures in a Mixing Layer of the FENE-P Polymer Solution

SHAO Xue-ming, LIN Jian-zhong, YU Zhao-sheng

2001, 22(3): 259-266.

Abstract(2262) PDF(502)

Abstract:
The evolution of the coherent structures in a two-dimensional time-developing mixing layer of the FENE-P fluids is examined numerically.By the means of an appropriate filtering for the polymer stress,some characteristics of the coherent structures at high b were obtained,which Azaiez and Homsy did not address.The results indicate that adding polymer to the Newtonian fluids wil cause stronger vorticity diffusion,accompanied with weaker fundamental and subharmonical perturbations and slower rotational motion of neighboring vortices during pairing.This effect decreases with the Weissenberg number,but increases with b.In addition,the time when the consecutive rollers are completely coalesced into one delays in the viscoelatic mixing layer compared with the Newtonian one of the same total viscosity.

Models for the Counter-Gradient-Transport Phenomena

JIANG Jian-bo, LU Zhi-ming, LIU Xiao-ming, LIU Yu-lu

2001, 22(3): 267-274.

Abstract(2196) PDF(735)

Abstract:
The counter gradient transport phenomena on momentum,energy and passive scalar in turbulent flows were studied by use of the single response function for TSDIA.As a result,models that can describe qualitatively the phenomena are obtained.Then the results are simplifled by use of the inertial range theory,and the results for lower degrees agree with results of predecessor.Finally the counter gradient-transport phenomena in channel flow and circular wake flow are analyzed.

Estimation of Attraction Domain and Exponential Convergence Rate of Continuous Feedback Associative Memory

ZHOU Dong-ming, CAO Jin-de, LI Ji-bin

2001, 22(3): 275-280.

Abstract(2003) PDF(735)

Abstract:
The attraction domain of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated again by using of some analysis techniques and Liapunov method,some new results are obtained,and these results can be used for evaluation of fault-tolerance capability and the synthesis procedures for continuous feedback associative memory neural networks.

A Simple Fast Method in Finding Particular Solutions of Some Nonlinear PDE

LIU Shi-kuo, FU Zun-tao, LIU Shi-da, ZHAO Qiang

2001, 22(3): 281-286.

Abstract(2580) PDF(1195)

Abstract:
The "trial function method"(TFM for short) and a routine way in finding traveling wave solutions to some nonlinear partial differential equations(PDE for short) wer explained.Two types of evolution equations are studied,one is a generalized Burgers or KdV equation,the other is the Fisher equation with special nonlinear forms of its reaction rate term.One can see that this method is simple,fast and allowing further extension.

Blow-up Estimates for a Non-Newtonian Filtration System

YANG Zuo-dong, LU Qi-shao

2001, 22(3): 287-294.

Abstract(2526) PDF(763)

Abstract:
The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first.Hence,the result of nonexistence for differential equation system of radially nonincreasing positive solutions was implied.By using this nonexistence result,blow-up estimates for a class quasilinear reaction-diffusion systems(non-Newtonian filtration systems) are established,which extencds the result of semilinear reaction-diffusion(Fujita type) systems.

On the Homoclinic Orbits in a Class of Two-Degree of Freedom Systems Under the Resonance Conditions

WANG Mao-nan, XU Zhen-yuan

2001, 22(3): 295-306.

Abstract(2203) PDF(505)

Abstract:
A class of two-degree-of-freedom systems in resonance with an external,parametric excitation is investigated,the existence of the periodic solutions locked to 8 is proved by the use of the method of multiple scales.This systems can be transformed into the systems of Wiggins,under some conditions.A calculating formula which determines the exsitence of homoclinic orbits of the systems is given.

One Dimensional Consolidation of Layered and Visco-Elastic Solids Under Arbitrary Loading

CAI Yuan-qiang, XU Chang-jie, YUAN Hai-ming

2001, 22(3): 307-313.

Abstract(2628) PDF(696)

Abstract:
Based on the layered visco-elastic soil model,according to the Terzaghi s one dimensional consolidation theory,by the method of Laplace transform and matrix transfer technique,the problems about the consolidation of layered and saturated visco-elastic soils under arbitrary loading were solved.Through deductions,the general solution,in the terms of layer thickness,the modulus and the coefficients of permeability and Laplacian transform's parameters was obtained.The strain and deformation of the layered and saturated visco-elastic soils under arbitrary loading can be calculated by Laplace inversion.According to the results of several numerical examples,the consolidation of visco-elastic soils lags behind that of elastic soils.The development of effective stress and the displacement is vibrant process under cyclic loading.Finally,an engineering case is studied and the results prove that the methods are very effective.

A Universal Matrix Perturbation Technique for Complex Modes

LIU Ji-ke, XU Wei-hua, CAI Cheng-wu

2001, 22(3): 314-320.

Abstract(2726) PDF(788)

Abstract:
A universal matrix perturbation technique for complex modes is presented.This technique is applicable to all the three cases of complex eigenvalues:distinct,repeated and closely spaced eigenvalues.The lower order perturbation formulas are obtained by performing two complex eigensubspace condensations,and the higher order perturbation formulas are derived by successive approximation process.Three illustrative examples are given to verify the proposed method and satisfactory results are observed.

An Analytical Solution for an Exponential- Type Dispersion Process

WANG Zi-ting

2001, 22(3): 321-324.

Abstract(2377) PDF(578)

Abstract:
The dispersion process in heterogeneous porous media is distance-dependent,which results from multi-scaling property of heterogeneous structure.An analytical model describing the dispersion with an exponential dispersion function is build,which is transformed into ODE problem with variable coefficients,and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique.Acoording to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed.

A Class of Singularly Perturbed Generalized Boundary Value Problems for Quasilinear Elliptic Equation of Higher Order

MO Jia-qi, OUYANG Cheng

2001, 22(3): 325-330.

Abstract(2388) PDF(595)

Abstract:
The singularly perturbed generalized boundary value problems for the quasilinear elliptic equation of higher order are considered.Under suitable conditions,the existence,uniqueness and asymptotic behavior of the generalized solution for the Dirichlet problems are studied.

2001 Vol. 22, No. 3