应用数学和力学

2000 Vol. 21, No. 7

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Pseudo-Division Algorithm for Matrix Multivariable Polynomial and Its Application

Alatancang, Zhang Hongqing, Zhong Wanxie

2000, 21(7): 661-668.

Abstract(3541) PDF(918)

Abstract:
Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonian system andits concrete form are obtained. Then by combining this method with Wu's method, a new method of constructing general solution of a class of mechanical equationsis got, which several examples show very effective.

Research on Stability of Interface of Jet Containing Suspended Solid Particles

Zhou Zexuan, Tan Soon Keat, Lin Jianzhong

2000, 21(7): 669-674.

Abstract(2216) PDF(515)

Abstract:
The stability equation of interface of two-phase jet and the corresponding particle-gas disturbance velocity ratio equation are derived by means of the phase-coupled model.The stability curves of interface of two-phase jet for different particle properties and the corresponding particle-gas disturbance velocity ratio curves are given out through numerical computation.Further,several important conclusions in effect of particle property on growth and propagation of disturbance of interface of two-phase jet and particle disturbance property are presented on the basis of analyses of the obtained stability curves and particle-gas disturbance velocity ratio curves.These important conclusions can play a guiding role in studying development of two-phase jet and executing artificial controls over it in project practice.

Pansystems Methodology and Construction of Magic Squares

Li Yue, Li Lixi, Wu Xuemou

2000, 21(7): 675-678.

Abstract(2054) PDF(618)

Abstract:
Some patterns of refined epitomes of pansystems methodology were revealed roles and the related of them in problem-solving,modeling,algorithm-generating and theory-constructing were introduced.An important application of pansystems methodology is to give some methods of constructing the typical pansymmetries-magic squares:1.a method of recursively constructing magic squares of order n(n≥5);2.when magic squares of order m(m≥3)and magic squares of order n(n⑥≥3) are given.a formula of obtaining magic squares of order mn;3.when magic squares of order m(m≥3)are given,a method of obtaining magic squares of order 2m.

Dynamic Stress Analysis of the Interface in a Particle-Reinforced Composite

Chen Jiankang, Huang Zhuping, Bai Shulin

2000, 21(7): 679-685.

Abstract(2176) PDF(512)

Abstract:
The analysis of the dynamic stress on the particle-matrix interface in particle-reinforced composite for the reason that this stress may lead to the microvoids.nucleation due to the interfacial debonding were studied.For simplification,the representative volume element(RVE)was taken as an analysis model.The Laplace transformation was used to derive the basic equations,and the analytical solutions were obtained by means of Hankel transformation.Moreover,the influences of the inertia and viscosity on the debonding damage were also discussed.

Interaction of a Solitary Wave and a Front Step Simulated by Level Set Method

Xie Weisong, Tao Jianhua

2000, 21(7): 686-692.

Abstract(2416) PDF(669)

Abstract:
As a new method,the Level Set method had been developed to compute the interface of two-phase flow.The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated.Then,by using the Level Set method,the transformation of a solitary wave over a front step was simulated.The results are in good agreement with laboratory experiments.

Hopf Bifurcation for a Ecological Mathematical Model on Microbe Populations

Guo Ruihai, Yuan Xiaofeng

2000, 21(7): 693-700.

Abstract(2793) PDF(662)

Abstract:
The ecological Model of a class of the two microbe populations with second-order growth rate is studied.The methods of qualitative theory of ordinary differential equations are used in the four-dimension phase space.The qualitative property and stability of equilibrium points are analysed. The conditions under which the positive equilibrium point exists and becomes and O⁺ attractor are obtained.The problems on Hopf bifurcation are discussed in detail when small perturbation occurs.

Consider Saint-Venant’s Principle by Means of Chain Model

Wu Jianxun

2000, 21(7): 701-707.

Abstract(2462) PDF(619)

Abstract:
A precise background theory of computational mechanics is formed.Saint-Venant's principle is discussed in chain model by means of this precise theory.The classical continued fraction is developed into operator continued fraction to be the constrictive formulation of the chain model.The decay of effect of a self-equilibrated system of forces in chain model is decided by the convergence of operator continued fraction,so the reasonable part of Saint-Venant's principle is described as the convergence of operator continued fraction.In case of divergence the effect of a self-equilibrated system of forces may be non-zero at even infinite distant sections,so Saint-Venant's principle is not a common principle.

Vibrations of Stepped One-Way Thin Rectangular Plates Subjected to in-Plane Tensile/Compressive Force in y-Direction on Winkler’s Foundation

Zhang Yingshi

2000, 21(7): 708-714.

Abstract(2547) PDF(590)

Abstract:
Differential equations of free/forced vibrations of n-step one-way thin rectangular plates subjected to in-plane tensile/compressive force in y-direction on Winkler's foundation are established by using singular functions,their general solutions solved for,expression of vibration mode function and frequency equation on usual supports derived with Woperator.Influence functions for various cases deduced here may also be used to resolve problems of static buckling or stability for beams and plates in relevant circumstances.

String Stability of Infinite Interconnected Systems

Zhang Jiye, Yang Yiren, Zeng Jing

2000, 21(7): 715-720.

Abstract(2302) PDF(770)

Abstract:
The notion of string stability of a countably infinite interconnection of a class of nonlinear system was introduced.Intuitively,string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded.Vector V-function method used to judge the stability is generalized for infinite interconnected system and sufficient conditions which guarantee the asymptotic string stability of a class of inter-connected system are given.The stability regions obtained here are much larger than those in previous papers.The method given here overcomes some difficulties to deal with stability of infinite nonlinear interconnected system in previous papers.

Semi-Inverse Method and Generalized Variational Principles With Multi-Variables in Elasticity

He Jihuan

2000, 21(7): 721-731.

Abstract(2753) PDF(901)

Abstract:
Semi-inverse method,which is an integration and an extension of Hu's try-and-error method,Chien's veighted residual method and Liu's systematiic method,is proposed to establish generalized variational principles with multi-variables without any variational crisis phenomenon.The method is to construct an energy trial-functional with an unknown function F,which can be readilyi-dentified by making the trial-functional stationary and using known constraint equations.As a result generalized variational principles with two kinds of independent variables(such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle)and generalized variational principles with three kinds of independent variables(such as Chien's generalized variational principles)in elasticity have been deduced without using Lagrange multiplier method.By semi-inverse method,the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables,stress-strain relations are still its constraints.

On the Absolute Stability of a Class of Inditrect Control Systems

Zhao Hongyong, Teng Zhidong

2000, 21(7): 732-740.

Abstract(2351) PDF(733)

Abstract:
The absolute stability of a class of indirect control systems by applying the theory of Hermitian quadratic form and Jordan normal form was studied.The alge braic formal criteria for the absolute stability are established,and these results are new and useful.

Improved L-P Method for Solving Strongly Nonlinear Problems

Yuan Yiwu, Liu Youwen

2000, 21(7): 741-745.

Abstract(2235) PDF(714)

Abstract:
Using the improved L-P method,a class of problems of square strongly nonlinear free oscillations and of strongly nonlinear nonoscilations were solved.Their first order approximate solution which has high accuracy is obtained.The method of this paper is different from the known L-P methods.

Dynamics in Newtonian-Riemannian Spacetime(Ⅰ)

Zhang Rongye

2000, 21(7): 746-754.

Abstract(2180) PDF(644)

Abstract:
By the theory of Modern Geometry,the mechanical principle and advanced calculus,the dynamics in Newtonian-Galilean spacetime is generalized to Newtonian-Riemannian Spacetime,and the dynamics in N-Rspacetime is established.Beng divided into some parts,this paper is one of them.The other are to be continued.

The Conservation Law of Second-Order Nonholonomic System of Non-Chetaev’s Type

Fang Jianhui

2000, 21(7): 755-758.

Abstract(2558) PDF(773)

Abstract:
The conservation law of second-order nonholonomic system of non-chetaev's type by means of the Jourdain's principle was studied.The invariant condition of Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators.Then the conservation law of the system is obtained under certain conditions.Finally a calculating example is given.

A Note on Probabilistic Contractor Couple and Solutions for a System of Nonlinear Equations in N.A.Menger PN-Spaces

Fang Jinxuan, Song Guian

2000, 21(7): 759-765.

Abstract(2555) PDF(700)

Abstract:
The concept of(Φ,Δ)-type probabilistic contractor couple was introduced which simplifies and weakens the definition of probabilistic contractor couple given by Zhang Shisheng.The existence and uniqueness of the solutions for a system of nonlinear operator equations with this kind of propabilistic contractor couple in N.A.Menger PN-spaces were studied.The works improve and extend the corrosponding results by M.Altman,A.C.Lee,W.J.Padgett et al.

Linearized Oscillations for Autonomous Delay Differential Equations

Li Yongkun

2000, 21(7): 766-770.

Abstract(2262) PDF(744)

Abstract:
The linearized oscillations of the nonlinear autonomous delay differential equation are studied.