Applied Mathematics and Mechanics (English Edition)

PSEUDO-DIVISION ALGORITHM FOR MATRIX MULTIVARIABLE POLYNOMIAL AND ITS APPLICATION

阿拉坦仓;张鸿庆;钟万勰

2000, 21(7): 733-740.

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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 Hamiltonianian system and its 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 equations is got, which several examples show very effective.

RESEARCH ON STABILITY OF INTERFACE OF JET CONTAINING SUSPENDED SOLID PARTICLES

周泽宣;Tan Soon Keat;林建忠

2000, 21(7): 741-746.

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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 on 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

李粤;李立希;吴学谋

2000, 21(7): 747-752.

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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(n≥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

陈建康;黄筑平;白树林

2000, 21(7): 753-760.

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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, a sphere containing a concentric rigid spherical particle was taken as the representative volume element (RVE). 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

谢伟松;陶建华

2000, 21(7): 761-766.

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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. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.

HOPF BIFURCATION FOR A ECOLOGICAL MATHEMATICAL MODEL ON MICROBE POPULATIONS

郭瑞海;袁晓凤

2000, 21(7): 767-774.

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The ecological model of a class of the two microbe populations with second-order growth rate was studied. The methods of qualitative theory of ordinary differential equations were used in the four-dimension phase space. The qualitative property and stability of equilibrium points were 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

武建勋

2000, 21(7): 775-782.

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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

张英世

2000, 21(7): 783-790.

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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 W operator. Influence functions for various cases deduced here may also be used to solve problems of static buckling or stability for beams and plates in relevant circumstances.

STRING STABILITY OF INFINITE INTERCONNECTED SYSTEMS

张继业;杨翊仁;曾京

2000, 21(7): 791-796.

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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 interconnected 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

何吉欢

2000, 21(7): 797-808.

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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 systematic 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 readily identified 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 INDIRECT CONTROL SYSTEMS

赵洪涌;滕志东

2000, 21(7): 809-818.

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

IMPROVED L-P METHOD FOR SOLVING STRONGLY NONLINEAR PROBLEMS

袁镒吾;刘又文

2000, 21(7): 819-824.

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Using the improved L-P method, the authors seek to solve a class of problems of square strongly nonlinear free oscillations and of strongly nonlinear nonoscillations. Their first-order approximate solutions which has high accuracy are obtained. The method of this paper is different from the known L-P methods.

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACETIME (Ⅰ)

张荣业

2000, 21(7): 825-835.

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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-R spacetime is established. Being divided it into some parts. This paper is one of them. The others are to be continued.

THE CONSERVATION LAW OF SECOND-ORDER NON-HOLONOMIC SYSTEM OF NON-CHETAEV’S TYPE

方建会

2000, 21(7): 836-840.

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The conservation law of second-order nonholonomic system of non-Chetaev’s type was studied by means of the Jourdain’s principle. 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

方锦暄;宋桂安

2000, 21(7): 841-848.

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The concept of (Ф, 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 corresponding results by M. Altman, A.C.Lee,W.J. Padgett et al.

LINEARIZED OSCILLATIONS FOR AUTONOMOUS DELAY DIFFERENTIAL EQUATIONS

李永昆

2000, 21(7): 849-854.

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The linearized oscillations of the nonlinear autonomous delay differential equation are

studied.

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