Applied Mathematics and Mechanics (English Edition)

TWO SIMPLE PROOFS OF CAYLEY-HAMILTON THEOREM AND TWO REPRESENTATION THEOREMS

郑泉水;戴天民

1984, 5(1): 977-984.

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In this paper two simple proofs of Cayley-Hamilton theorem are given and by use of Cayley-Hamilton and l’Hopital’s two representation theorems concerning tensor functions of an arbitrary second-order tensor are given.

ON THE LAW OF ENERGY CONSERVATION IN THE CLASSICAL ELECTRODYNAMICS OF DEFORMABLE MEDIA——A GENERA-LIZATION OF THE POYNTING THEOREM

余燊

1984, 5(1): 985-994.

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This paper establishes the generalized Poynting theorem for the electrodynamics of deformable media with a view to shedding some light on the detailed mechanism of energy transfer between the electromagnetic field and the deformable media. Global field equations are chosen as the starting point and specialized forms of the theorem are derived based on the special postulates for the electromagnetic body force.

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅰ)

吴学谋

1984, 5(1): 995-1010.

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In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-trans formation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.

THE FINITE ELEMENT METHOD OF SINGULAR PERTURBATION PROBLEM

吴启光

1984, 5(1): 1011-1018.

摘要 ( 441 )

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In this paper we construct new finite element subspace using polynomials of different degrees and the new finite element scheme is established. The convergence of the scheme and the stability of the reduced difference equation are proved.

COMPARISON OF THE CALCULATIONS OF THREE-CONVOLUTION CIRCULAR ARC CORRUGATED DIAPHRAGMS BY TOROIDAL SHELL THEORY AND BY ORTHOGONAL ANISOTROPY PLATE THEORY

钱伟长;樊大钧;黄黔

1984, 5(1): 1019-1027.

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The calculation of elastic deformations of corrugated diaphragms was given by orthogonal anisotropy plate theory[1], and its result agrees with the experimental results. But it has never been discussed seriously how the number and form of convolutions affect the elastic deformations and stress distributions of anisotropy plate. As a result, adaptable limits of orthogonal anisotropy plate theory cannot be indicated when it is used to calculate diaphragms. It is said that the theory is fairly good for calculating elastic deformations of the diaphragms which have more convolutions. It is also said that the error in calculating stresses is rather large. This paper, by using the toroidal shell theory, presents the calculation of deformations and stresses of three-convolution circular arc corrugated diaphragms both. symmetrical and unsymmetrical, compares its result with that of the orthogonal anisotropy plate theory and gives definite adaptable limits of the latter theory.

EIGENVALUE PROBLEM FOR INTEGRO-DIFFERENTIAL EQUATION OF SUPERSONIC PANEL FLUTTER

董明德

1984, 5(1): 1029-1040.

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The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to the study of a new problem in mathematical physics: complex eigenvalue prob-lem for a non-self-adjoint fourth-order integro-differential equation of Volterra’s type.Exact solutions of the aeroelastic system is obtained. In contrast to various approximate analyses, our critical curve agrees satisfactorily with experimental data, being free from divergence in the low supe’rsonic region. Moreover, we observe some notable physical behaviors: (1) mutual separation of flutter and vacuum frequency spectrums, (2) degeneracy of critical Mach number. The present method may be generalized in solving the supersonic flutter for 3-dimensional airfoil model as well as blade cascade in turbo-generator.

EXTENSION OF WHITTAKER EQUATIONS TO NON-HOLONOMIC MECHANICAL SYSTEMS

梅凤翔

1984, 5(1): 1041-1045.

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In 1904, using the energy integral Whittaker studied the reduction of a dynamical problem to a problem with fewer degrees of freedom for the holonomic conservative systems and obtained the Whittaker equation^[1].In this article, Whittaker equations are extended to non-holonomic systems and the generalized Whittaker equations are obtained. And then these equations are transformed into Kiel-sen’s form.Finally an example is given.

THE NECESSARY AND SUFFICIENT CONDITION OF UNIFORMLY CONVERGENT DIFFERENCE SCHEMES FOR THE ELLIPTIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATION WITH A SMALL PARAMETER

林鹏程;刘发旺

1984, 5(1): 1047-1055.

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This paper studies the necessary and sufficient condition of uniformly convergent difference scheme for the elliptic-parabolic partial differential equation with a small parameter.

AN ANALYSIS ON ENTRANCE REGION EFFECT OF THE LAMINAR RADIAL FLOW BETWEEN TWO PARALLEL DISKS

刘震北;王致清

1984, 5(1): 1057-1070.

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In this paper, B. B. Golubef method^[1] is used for calculating the radial diffuse flow between two parallel disks for the first step. The momentum integral equation together with the energy integral equation is derived from the boundary layer momentum equation, and the expression of secondary approximation explicit function in which the channel length of entrance region varies with the boundary layer thickness can be obtained by using Picard iteration^[2] in the solution of the energy integral equation. Therefore, this has made it possible to analyze directly and analytically the coefficients of the entrance region effect. In particular, when the outer diameter of disk is smaller than the entrance region length, the advantage of this method can be prominently manifest.Only because the energy integral equation is employed, the terms in the pressure loss coefficient can be independently derived theoretically. The computable value of the pressure loss coefficient presented in this paper is nearer to the testing value than that in ref. ^[3] when the entrance correction Reynolds number Re<100. Therefore the results in this paper within Re<100 are both reliable and simple.

THE BOUNDARY INTEGRAL-VARIATIONAL THEOREMS OF AN ARBITRARY ELEMENT IN THE SOLID—COMPUTE THE ENERGY RELEASE RATE OF AN ARBITRARY CRACK EXTENSION

牛庠均

1984, 5(1): 1071-1082.

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Based on the solid mechanics of the discrete form and its variational principles proposed by Niu^[1-2], this paper puts forward four kinds of boundary integral-variational theorems of an arbitrary element. In the course of the fracture analysis, they can be used to compute the energy release rate along the normal direction of the crack boundary. When there is a hole in the solid, and whether there are given surface forces on the hole boundary or not they can be used to compute the variation of the energy along the normal direction of the hole boundary. In the course of the discrete analysis, they can be used to establish the discrete equations, so that the values of the unknown functions are solved. At the same time, from this paper we know that the J -integral proposed by Rice^[3] represents an integral to be independent of a path imperfectly.

SUGGESTION OF A NEW DEFINITION OF ANGULAR STRAIN

严宗达

1984, 5(1): 1083-1090.

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A new definition of angular strain is put forward in this paper. Analogous to the definition of linear strain, angular strain is also defined as a rate of change (of angular displacement). It is verified that the new definition is equivalent to the original besides being more convenient for geometrical interpretations. Using this new definition we have deduced the transformation formulas for rotation of coordinate axes, established the strain tensor and proved the Hooke’s law for shearing.

A SPECTRAL RESOLVING METHOD FOR ANALYZING LINEAR RANDOM VIBRATIONS WITH VARIABLE PARAMETERS

金问鲁

1984, 5(1): 1091-1096.

摘要 ( 370 )

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This paper is a development of ref. [1]. Consider the following random equation: Z(t)+2βZ(t)+ω₀²Z(t)=(a⁰+a¹Z(t))I(t)+c in which excitation I(t) and response Z(y) are both random processes, and it is proposed that they are mutually independent. Suppose that a(t) is a known function of time and I(t) is a stationary random process. In this paper, the spectral resolving form of the random equation stated above, the numerical solving method and the solutions in some special cases are considered.

THE CORRELATIVE POTENTIAL FUNCTION AND A NEW METHOD FOR SOLVING MAXWELL EQUATIONS

李春宝;王百锁

1984, 5(1): 1097-1109.

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This paper is a continuation of Paper [1].1. A new potential ψ which is defined as the correlative potential is developed in this paper. The potential ψ is different from the classical scalar potential ψ and the vector potential A developed by Helmholtz. The new formulae of the solution of egs.▽xf=ω, ▽f=P are given in terms of ψ.2. In the time-varying electromagnetic field, two new retarded potentials, the electric type retarded correlative potential ψe and the magnetic-type retarded correlative potential ψ_m, which are distinct from the classical retarded potentials A and φ, are used to solve Maxwell equations. The new formulae of solution of Maxwell equation are given in terms of ψ and ψ_m.3. The methods for constructing a rotational field with given curl function (vorticity) is proposed.

QUALITATIVE INVESTIGATION OF DYNAMICAL EQUATION SYSTEM OF HEMOGLOBIN (OR ALLOSTERIC ENZYMES)

管克英

1984, 5(1): 1111-1119.

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For the dynamical equation system (a three-dimensional autonomous system) of hemoglobin given in ^[1], we make the following qualitative investigations: (1) point out that all meaningful solutions should be in a tetrahedroid, and that its four surfaces are without contact; (2) find all singular points, and prove that only two of them are respectively situated on a pair of them are respectively situated on a pair of separate edges, and that other singular points are outside the tetrahedroid and meaningless; (3) prove that, among seven physical parameters of this system, only the sign of a parameter determines the properties of these two singular points; (4) clear up the relation between this system and MWC model ^[3], The investigation shows that this system reflects the dynamical properties of hemoglobin satisfactorily.

LARGE DEFORMATION SOLUTION OF STIFFENED PLATES BY A MIXED FINITE ELEMENT METHOD

陈远汉

1984, 5(1): 1121-1135 .

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In the present paper, a finite element mixed variational functional and the iterative equations of the eccentric orthogonal stiffened plates are developed in accordance with nonlinear elasticity. By using an important technique the coupling coefficients of the two-dimensional coupling matrix are resolved into the known input data in the programming which is a three-dimensional coefficient matrix. The nonlinear equations are transformed into the instantaneous linear equations; and by using the conjugate gradient method the linear equations are solved. As a result, therefore, the calculation is enormously simplified, the precision manifested, and a satisfactory result obtained.

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