应用数学和力学

2003 Vol. 24, No. 5

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Constrained Multiobjective Games in Locally Convex H-Spaces

DING Xie-ping

2003, 24(5): 441-449.

Abstract(2302) PDF(676)

Abstract:
A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.These theorems improve,unify and generalize the corresponding results of the multiobjective games in recent literatures.

Chaotic Belt Phenomena in Nonlinear Elastic Beam

ZHANG Nian-mei, YANG Gui-tong

2003, 24(5): 450-454.

Abstract(2075) PDF(839)

Abstract:
The chaotic motions of axial compressed nonlinear elastic beam subjected to transverse load were studied.The damping force in the system is nonlinear.Considering material and geometric nonlinearity,nonlinear governing equation of the system was derived.By use of nonlinear Galerkin method,differential dynamic system was set up.Melnikov method was used to analyze the characters of the system.The results showed that chaos may occur in the system when the load parameters P₀ and f satisfy some conditions.The zone of chaotic motion was belted.The route from subharmonic bifurcation to chaos was analyzed.The critical conditions that chaos occurs were determined.

Thermal Post-Buckling of an Elastic Beams Subjected to a Transversely Non-Uniform Temperature Rising

LI Shi-rong, CHENG Chang-jun, ZHOU You-he

2003, 24(5): 455-460.

Abstract(2185) PDF(741)

Abstract:
Based on the non-linear geometric theory of axially extensible beams and by using the shooting method,the thermal post-buckling responses of an elastic beams,with immovably simply supported ends and subjected to a transversely non-uniformly distributed temperature rising,were investigated.Especially,the influences of the transverse temperature change on the thermal post-buckling deformations were examined and the corresponding characteristic curves were plotted.The numerical results show that the equilibrium paths of the beam are similar to what of an initially deformed beam because of the thermal bending moment produced in the beam by the transverse temperature change.

Periodic Solutions in One-Dimensional Coupled Map Lattices

ZHENG Yong-ai, LIU Zeng-rong

2003, 24(5): 461-465.

Abstract(2042) PDF(635)

Abstract:
It is proven that the existence of no nlinear solutions with time period in one-dime nsional coupled map lattice with nearest neighbo rcoupling.This is a class of systmes whose behavior can be regarded as infinite array of coupled oscillators.A method for estimating the critical coupling strength below which these solutions with time period persist is given.For some particular nonlinear solutions with time period,ex ponential decay in space is proved.

The Nonlinear Nonlocal Singularly Perturbed Problems for Reaction Diffusion Equations

MO Jia-qi, ZHU Jiang

2003, 24(5): 466-470.

Abstract(2375) PDF(778)

Abstract:
A class of nonlinear nonlocal for singularly perturbed Robin initial bounday value problems for reaction diffusion equations is considered.Under suitable conditions,firstly,the outer solution of the original problem is obtained,secondly,using the stretched variable,the composing expansion method and the expanding theory of power series the initial layer is constructed,finally,using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.

The Steady/Pulsatile Flow and Macromolecular Transport in T-Bifurcation Blood Vessels

LI Ding, WEN Gong-bi

2003, 24(5): 471-483.

Abstract(2300) PDF(766)

Abstract:
A numerical analysis of the steady and pulsatile,macromolecular(such as low density lipopotein(LDL),Albumin)transport in T-bifurcation was proposed.The influence of Reynolds number and mass flow ratio etc parameters on the velocity field and mass transport were calculated.The computational results predict that the blood flow factors affect the macromolecular distribution and the transport across the wall,it shows that hemodynamic paly an important role in the process of atherosclerosis.The LDL and Albumin concentration on the wall varies most greatly in flow bifurcation area where the wall shear stress varies greatly at the branching vessel and the atherosclerosis of ten appears there.

On the Well Posedness of Initial Value Problem for Euler Equations of Incompressible Inviscid Fluid(Ⅰ)

SHEN Zhen

2003, 24(5): 484-492.

Abstract(2174) PDF(700)

Abstract:
The ill posed initial value problem of the Euler Equations and the formal solvability of ill posed problem based on stratification theory is discussed.For some ill posed initial value problems, the existence conditions of formal solutions and the methods of how to construct a formal solution are given.Finally,an example is given to discuss the ill posedness of the initial value problem on hyper plane{t=0}⊆R⁴ and explain that the problem has more than one solution.

On the Well Posedness of Initial Value Problem for Euler Equations of Incompressible Inviscid Fluid(Ⅱ)

SHEN Zhen

2003, 24(5): 493-504.

Abstract(2384) PDF(643)

Abstract:
The solvability of the Euler equations about imcompressible inviscid flow based on the stratification theory is discussed.And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed initial value problems.Two examples are given as the evidence that the initial problems at the hyper surface does not exist any unique solution.

Plane Infinite Analytical Element and Hamiltonian System

SUN Yan, ZHOU Gang, LIU Zheng-xing

2003, 24(5): 505-511.

Abstract(2071) PDF(559)

Abstract:
It is not convenient to solve those engineering problems defined in an infinite field by using FEM.An infinite area can be divided into a regular infinite external area and a finite internal area.The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate.All governing equations were transformed into the Hamiltonian system.The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element,like a super finite element,can be combined with commonly used finite elements.The proposed method was verified by numerical case studies.The results show that the preparation work is very simple,the infinite analytical element has a high precision,and it can be used conveniently.The method can also be easily extended to a three-dimensional problem.

Gurtin-Type Region-Wise Variational Principles for Thermopiezoelectric Elastodynamics

HUANG Bo

2003, 24(5): 512-518.

Abstract(1999) PDF(656)

Abstract:
The variation of new Gurtin-type region-wise variational principles results in continuous conditions,boundary conditions,all equations and relations in linear thermo piezoelectric elastodynamics.Gurtin-type region-wise variational principles comprise very important parts of linear thermo piezoelectric elastodynamics,and can fully characterize the initial-boundary-value problem in linear thermopiezoelectric elastodynamics.

A Study on the Unsteady Flow in a Helical Pipe

ZHANG Ben-zhao, MA Zhai-pu, SU Xiao-yan, ZHANG Jin-suo

2003, 24(5): 519-528.

Abstract(2199) PDF(717)

Abstract:
A study on the unsteady low-frequency oscillatory flow in a helical circular pipe is carried out based upon the blood flow in vessels,using the method of bi-parameter perturbation.The second order perturbation results were obtained and the characteristics were analyzed at different time of the axial velocity,of the secondary flow,and of the wall shearing stress.Also done the analysis of above-mentioned variables that varied along with time and Womersley number.The results indicate that for a helical pipe,the torsion exerts the main influence on the distribution of secondary flow velocity,especially when the absolute value of axial press gradient is rather small.The severe variation of stream function takes place within a very short period,during which time the stream function develops from positive value to negative value and vice versa,while in most cases in a cycle,the variation is smooth.The wall shearing stress changes severely with theta too.

Nonlinear Dynamic Response and Active Vibration Control of the Viscoelastic Cable With Small Sag

LI Ying-hui, GAO Qing, YIN Xue-gang

2003, 24(5): 529-536.

Abstract(2109) PDF(604)

Abstract:
The problem considered is an initially stressed viscoelastic cable with small sag.The cable material is assumed to be constituted by the hereditary differential type.The partial differential equations of motion is derived first.Then by applying Galerkin.s method,the governing equations are reduced to a set of third order non-linear ordinary differential equations which are solved by Runge-Kutta numerical integration procedures.Only after the transverse vibration of the plane is considered and the nonlinear terms are neglected,can the non-linear ordinary differential equations be expressed as a continuous state equation in the state space.The matrix of state transition is approximated stepwise by the matrix exponential;in addition,the state equation is discretized to a difference equation to improve the computing efficiency.Furthermore,an optimal control of procedure system based on the minimization of a quadratic performance index for state vector and control forces is developed.Finally,the effect of dynamic response of the cable,which is produced by viscoelastic parameters,is testified by the research of digital simulation.

The 3-Layered Explicit Difference Scheme for 2-D Heat Equation

LIU Ji-jun

2003, 24(5): 537-544.

Abstract(2767) PDF(1575)

Abstract:
A 3-layered explicit difference scheme for the numerical solution of 2-D heart equation is proposed.Firstly,a general symmetric difference scheme is constructed and its optimal error is obtained.Then two kinds of condition for choosing the parameters for optimal error and stable difference scheme are given.Finally some numerical results are presented to show the advantage of the schemes.

Analytical Solutions for Some Nonlinear Evolution Equations

HU Jian-lan, ZHANG Han-lin

2003, 24(5): 545-550.

Abstract(2316) PDF(927)

Abstract:
The following partial differential equations are studied:generalized fifth-order KdV equation,water wave equation,kupershmidt equation,couples KdV equation.The analytical solutions to these problems via using various ansatzes by introducing a second-order ordinary differential equation are found out.