应用数学和力学

1984 Vol. 5, No. 1

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Two Simple Proofs of Cayley-Hamilton Theorem and Two Representation Theoremsx

Zheng Quan-shui, Tai Tian-min

1984, 5(1): 1-8.

Abstract(3096) PDF(717)

Abstract:
In this paper two simple proofs of Caplep-Hamilton theorem are given and by making use of Cayley-Hamilton theorem and I'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 Generalization of the Poynting Theorem

Yu Xin

1984, 5(1): 9-18.

Abstract(2419) PDF(439)

Abstract:
This paper establishes the generalized pointing theorem for the electro dynamics 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 theorem are derived based on the special vostulates for the electromagnetic body force.

Investigation and Applications of Pansystems Recognition Theory and Pansystems-Operations Research of Large-Scale Systems( I )

Wu Xue-mou

1984, 5(1): 19-32.

Abstract(1523) PDF(560)

Abstract:
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 inter-disciplines from the viewpoint of generalized sgstem-transformation-symmetry in things mechanism, and they are connected closely with mathematical physics systems sciences, thinking science, bioecological medical sciences and the methodological investigation of mechanical foundation. This saner offers 100 oansvstems theorems.

Qualitative Investigation of Dynamical Equation System of Hemoglobin(or Allosteric Enzymes)

Guan Ke-ying

1984, 5(1): 31-138.

Abstract(1668) PDF(412)

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

The Finite Element Method of Singular Perturbation Problem

Wu Qi-Guang

1984, 5(1): 33-40.

Abstract(1762) PDF(459)

Abstract:
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

Chien Wei-zhang, Fan Da-jun, Hwang Qien

1984, 5(1): 41-48.

Abstract(1665) PDF(624)

Abstract:
The calculation of elastic deformations of corrugated diaphragms has been given by orthogonal anisotropy plate theory^[1],and its result agrees with the experimental results.But it has never beer 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 applied 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 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-Differentiai Equation of Supersonic Panel Flutter

Dong Ming-de

1984, 5(1): 49-59.

Abstract(1796) PDF(424)

Abstract:
The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to study a new problem in mathematical physis:complex eigenvalue problem for a non-self-adjoint integro-differential equation(4-th order) of Yolterra's type.Exact solution for the aeroelastic system is obtained In contrast to various approximate analysis,our resulting critical curve agrees satisfactorily with experimental data, free from divergence in low supersonic region.Moreover, we observe some notable physical behaviors;(1)mutual separation between flutter and vacuum frequency spectrum,(2) degeneracy of critical Mach number.The present method may be generalized in solving the supersonic flutter problems for 3-din ensiunal airfoil models as well as blade cascade in turbo-generator.

Extension of the Whittaker Equations to Non Holonomic Mechanical Systems

Mei Feng-xiang

1984, 5(1): 61-66.

Abstract(1604) PDF(651)

Abstract:
In 1904,using the energy integral Whittaker studied the redaction of a dynamical problem to a problem with fewer degrees of freedom for the holonomic conservative systems and obtained the Whittaker equations^[1].In this articfe, the Whittaker equations are extended to non-holonomic systems and the generalized Whittaker equations are obtained And then these equations are transformed to Nielsen's form. Finally an example a given.

The Necessary and Sufficient Condition of Uniformly Convergent Difference Schemes for the Elliptic——Parabolic Partial Differential Equation with a Small Parameter

Lin Peng-cheng, Liu Fa-wang

1984, 5(1): 67-75.

Abstract(1593) PDF(511)

Abstract:
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

Liu Zhen-bei, Wang Zhi-qing

1984, 5(1): 77-89.

Abstract(1809) PDF(493)

Abstract:
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,then the expression of secondary approximation explicit function which is the entrance region duct length accompanied by the boundary layer thickness can be obtained by using Picard iteration^[2] in the solution of the energy integral equatio,.Therefore, this has made it possible to analyze directly and analytically the coefficients of entrance region effect, Especially when the outer diameter of the disk is less than the entrance region length, the advantage of this method can be prominently shown.Because energy integral equation was employed, the terms in the pressure loss coefficient can only be independently derived theoretically.The computable value of the pressure loss coefficient presented in this paper is nearer to the testing value than 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 Intergral-Variational Theorems of an Arbitrary Element in the Solid——To Compute the Energy Release Rate of an Arbitrary Crack Extension

Niu Xiang-jun

1984, 5(1): 91-102.

Abstract(1465) PDF(473)

Abstract:
Based on the solid mechanics of the discrete form and its variational principles pro-posed by Niu^[1,2], this paper puts forward four kinds of the boundary integral-variational theorems of an aroitrary 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 the hole in the solid, and there are the given surface forces on the hole boundary or there are not any given surface forces on the hole boundary, 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

Yan Zong-da

1984, 5(1): 103-109.

Abstract(1807) PDF(717)

Abstract:
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, but it is more convenient for geometrical interpretations. Using this new definition we deduce the transformation formulas for the rotation of coordinate axes, erect the strain tensor and verify the Hooke's law for shearing.

A Spectral Resolving Method for Analyzing Linear Random Vibrations with Variable Parameters

Jin Wen-lu

1984, 5(1): 111-116.

Abstract(1576) PDF(439)

Abstract:
This paper is a development of Ref.[1].Consider the following random equation:(t)+2?(t)+₀²Z(t)=(a₀+a_lZ(t)).I(t)+c,in which excitation I⁰(t)and response Z(t)are both random processes, and it is proposed that they are mutually independent.Suppose that I(t)=a(t)I⁰(t),a(t)is a known function of time and I^O(t)is a stationary random process.In this paper, the spectral resolving form of the random equation stated above, the numenca solving method and the solutions in some special cases are considered.

The Correlative Potential Function and a New Method for Solving Maxwell Equations

Li Chun-bao, Wang Bai-suo

1984, 5(1): 117-129.

Abstract(2075) PDF(520)

Abstract:
This paper is a continuation of paper[1].1.A new potential φ which is defined as the correlative potential has been developed in this paper. The potential φ is different from the classical scalar potential φ and vector potential developed by Helmholtz. The new formulae of the solution of eqs.∇×=,∇·=P are given in terms of φ.2. In time varying electromagnetic field, two new retarded potentials,the electric-type retarded correlative potential ire and the magnetic-type retarded correlative potentia: φ_m, which are distinct from the classical retarded potentials and φ have been used to solve Maxwell equations, The new formulae of solution of Maxwell equation are given in terms of rye and φ_e and φ_m.

Large Deformation Solution of Stiffened Plates by a Mixed Finite Element Method

Chen Yuan-han

1984, 5(1): 139-151.

Abstract(1671) PDF(634)

Abstract:
In the present paper, a finite element mined 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. The linear equations are solved by using the conjugate gradient method, As a result therefore, the calculation is simplified enormously, the precision is improved. and a satisfactory result is obtained.