应用数学和力学

1999 Vol. 20, No. 9

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A Generalization of Browder’s Fixed Point Theorem With Applications

Zhang Shisheng, Zhang Xian

1999, 20(9): 881-888.

Abstract(2499) PDF(1062)

Abstract:
The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms.As application,these results are utilized to study the existence problems of fixed points and nearest points.

Complex Equations of Flexible Circular Ring Shells Overall-Bending in a Meridian Plane and General Solution for the Slender Ring Shells

Zhu Weiping, Huang Qian, Guo Ping

1999, 20(9): 889-895.

Abstract(2445) PDF(704)

Abstract:
Complex equations of circular ring shells and slender ring shells overall-bending in a meridian plane are presented based on E.L.Axelrad's equations of flexible shells of revolution under asymmetrical loading.It turns out that the equations are analogous to Novozhilov's equations of symmetrical ring shells,where general solutions have been given by W.Z.Chien.Therefore,by analogy with Chien's solution,a general solution for equations of the slender ring shells is put forward,which can be used to solve bellows overall-bending problems.

Chaotic Motion of a Nonlinear Thermoelastic Elliptic Plate

Han Qiang, Zhang Nianmei, Yang Guitong

1999, 20(9): 896-901.

Abstract(2176) PDF(652)

Abstract:
In the paper the nonlinear dynamic equation of a harmonically forced elliptic plate is derived,with the effects of large deflection of plate and thermoelasticity taken into account.The Melnikov function method is used to give the critical condition for chaotic motion.A demonstrative example is discussed through the Poincaré mapping,phase portrait and time history.Finally the path to chaotic motion is also discussed.Through the theoretical analysis and numerical computation some beneficial conclusions are obtained.

On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅰ)

Liu Xianbin, Chen Dapeng, Chen Qiu

1999, 20(9): 902-912.

Abstract(2781) PDF(652)

Abstract:
For a real noise parametrically excited co-dimension two bifurcation system on a three-dimensional central manifold,a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system,namely,a zero-mean stationary Gaussian diffusion process that satisfies the detailed balance condition.On such basis,asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker-Planck operator.

Modal Part Analysis of Slosh of the Liquid in a Cylindrical Container in the Case of Small Bond Number

Gou Xingyu, Wang Benli, Ma Xingrui, Huang Huaide, Li Tieshou

1999, 20(9): 913-918.

Abstract(2082) PDF(614)

Abstract:
Reconstruction of liquid free slosh modes by curved quiet free surface was investigated in the case of small Bond number by means of modal part analysis method in this paper.It is shown that the curved liquid quiet free surface would couple the modes to form new eigen-modes while the orthogonality of the modes which participate the liquid slosh are given only by their Bessel modal parts and it would change their eigen-frequencies respectively while the orthogonality are given by their triangle function modal parts.By studying the laterally forced slosh of the liquid in a cylindrical container based on the new eigen-modes,a characteristic of modes-choosing was found.

The Matric Algorithm of Lyapunov Exponent for the Experimental Date Obtained in Dynamic Analysis

Ma Junhai, Chen Yushu, Liu Zengrong

1999, 20(9): 919-927.

Abstract(2464) PDF(774)

Abstract:
The Lyapunov exponent is important quantitative index for describing chaotic attractors.Since Wolf put up the trajectory algorithm to Lyapunov exponent in 1985,how to calculate the Lyapunov exponent with accuracy has become a very important question.Based on the theoretical algorithm of Zuo Binwu,the matric algorithm of Lyapunov exponent is given,and the results with the results of Wolf's algorithm are compared.The calculating results validate that the matric algorithm has sufficient accuracy,and the relationship between the character of attractor and the value of Lyapunov exponent is studied in this paper.The corresponding conclusions are given in this paper.

Existence and Uniqueness of Almost Periodic Solution to a Class of Nonautonomous System

Feng Chunhua, Huang Jianmin

1999, 20(9): 930-932.

Abstract(1929) PDF(717)

Abstract:
Almost periodic oscillations appearing in high-tension electricity network are considered in this paper.By utilization of Liapunov function,the foreboding conditions that result in almost periodic oscillations are obtained and thus the possibility of making precautions is presented.

Simulation and Application of Three Dimensional Migration Accumulation of Oil Resources

Yuan Yirang, Zhao Weidong, Cheng Aijie, Han Yuji

1999, 20(9): 933-942.

Abstract(2090) PDF(665)

Abstract:
Numerical simulation of oil migration and accumulation is to describe the history of oil migration and accumulation in basin evolution.It is of great value in the exploration of oil resources and their rational evaluation.In this paper,from such actual conditions as the effects of mechanics of fluids in porous media and 3-dimensional geology characteristics,a kind of modified method of second order splitting up implicit interactive scheme is put forward.For the famous hydraulic experiment of secondary migration accumulation,the numerical simulation test has been done,and both the computational and experimental results are basically identical.For the actual problem of Dongying hollow of Shengli Petroleum Oil Field,the numerical simulation test and the actual conditions are basically coincident.Thus the well known problem has been solved.

About a Conditon for Blow up of Solutions of Cauchy Problem for a Wave Equation

Cao Zhenchao, Wang Bixiang

1999, 20(9): 943-946.

Abstract(2686) PDF(699)

Abstract:
For the nonlinear wave equation in R^N×R⁺(N≥2):∂²u(x,t)/∂t²-∂/∂x_i[a_ij(x)∂/∂x_ju=|u|^p-1·u,in 1980 Kato proved the solution of Cauchy problem may blow up in finite time if 1

Comprehensive Mathematical Model of Microcirculatory Dynamics(Ⅰ)——Basic Theory

Guo Zhongsan, Xiao Fan, Guo Siwen, Wu Yueqing, Gu Leye

1999, 20(9): 947-954.

Abstract(2193) PDF(659)

Abstract:
Under the basis of physiological data,a nonlinear and unsteady comprehensive mathematical model of microcirculatory dynamics with distributed parameters is developed.Hemodynamics,interstitium dynamics,lymph dynamics,dynamics of protein transport,oxygen dynamics,dynamics of heat transfer,and myogenic and metabolic regulation procedures are included.The interactions between these factors were comprehensively exhibited.The influences of arteriolar vasomotion and nonlinear viscoelasticity of blood in arteriole are considered.A simplified vessel network consisting of arteriole,open and reserved capillaries,venule,initial lymphatics and arteriole-venule anastomose is adopted as the geometrical model.This kind of comprehensive mathematical model is helpful in analyzing clinical data and developing a "numerical experiment method" in microcirculation research.

On Construction of High Order Exponentially Fitted Methods Based on Parameterized Rational Approximations to exp(q)

Yang Fengjian, Zhang Aiguo, Chen Xinming

1999, 20(9): 955-960.

Abstract(2279) PDF(694)

Abstract:
By the discussion of the formula and properties of(4,4) parametric form rational approximation to function exp(q),the fourth order derivative one-step exponentially fitted method and the third order derivative hybrid one-step exponentially fitted method are presented,their order p satisfying 6≤p≤8.The necessary and sufficient conditions for the two methods to be A-stable are given.Finally,for the fourth order derivative method,the error bound and the necessary and sufficient conditions for it to be median are discussed.

D’Alembert Principle in the Velocity Space

Song Kehui, Tang Jianguo

1999, 20(9): 961-968.

Abstract(2490) PDF(739)

Abstract:
According to Newton's dynamical equation of the system of particles,the force is considered to be the function of the coordinate r,velocity r> and time t,and the various formulae for D'Alembert principle of the velocity space in both the holonomic and nonholonomic systems are deduced by introducing the concept of kinetic energy in the velocity space(i.e.the accelerated energy).

Existence and Iterative Algorithms of Solutions for Generalized Mixed Quasi-Variational Inequalities

Luo Chunlin

1999, 20(9): 969-976.

Abstract(1941) PDF(845)

Abstract:
In this paper,by using the auxiliary technique of variational inequalities,the existence and iterative algorithms of solutions for a class of generalized mixed quasi-variational inequalities are studied.Our results answer the open problems mentioned by Noor,improve and generalize some recent known results.

The Double Determinant of Vandermonde’s Type Over Quaternion Field

Hou Renmin, Zhao Xuqiang, Wang Liangtao

1999, 20(9): 977-984.

Abstract(2923) PDF(703)

Abstract:
Based on the double determinant theory the problem about the determinant of Vandermonde's type over quaternion field is studied,and a necessary and sufficient condition that this double determinant is not equal to zero is got.

Continual Conditions Between Layers for Laminated Plates

Zhang Shenxue

1999, 20(9): 985-990.

Abstract(2273) PDF(724)

Abstract:
In this paper,various forms of functional on blending energy principles of composite laminated plates are given,which guarantee satisfied continual conditions of displacements and stress between layers,and then the reliability of the functional are proved by the computing example.