应用数学和力学

1986 Vol. 7, No. 2

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Road to Chaos for a Soft Spring System under Weak Periodic Disturbance

Liu Zeng-rong, Yao Wei-guo, Zhu Zhao-xuan

1986, 7(2): 103-108.

Abstract(1852) PDF(669)

Abstract:
The Mel'nikov-Holmes method is used to discuss the road to chaos for an elastic system with soft spring constant and under weak periodic disturbance. It is found that according to how the disturbance is applied, forced vibration or parametric excitation, the response may pass to chaos through different sequences of subharmonic bifurcations, and that the orders in the sequences may be different for different disturbance frequencies.

The Response Analysis of Several Nonlinear Isolation Systems Subjected to Random Excitation

Zhuang Biao-zhong, Chen Nai-li, Fu Bo, Gao Zhan

1986, 7(2): 109-1114.

Abstract(1969) PDF(533)

Abstract:
The nonlinear isolation system is popular in modern isolation mounting. By using Fokker-Planck equation and the statistical linearization met hod and under the condition of random excitation are discussed in this article the best damping selection of the dashpots of the stiffening nonlinear stiffness, the response characteristics of the single-degree-of-freedom isolation system ofnon-antisymmetrical and nonlinear stiffness, and the response analysis of two-degree-of-freedom nonlinear isolation systems. The selection of some parameters of the nonlinear isolation system is also dealt with by virtue of calculation examples.

On the Problem of Axisymmetrically Loaded Shells of Revolution with Small Elastic Strains and Arbitrarily Large Axial Deflections

Huang Qian

1986, 7(2): 115-125.

Abstract(2162) PDF(705)

Abstract:
For the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections, this paper suggests a group of state variables: radial displacement u, axial displacement w, angular deflection of tangent in the meridian X. radial stress resultant H and meridional bending moment M_φ. and derives a System of First-order Nonlinear Differential Equations under global coordinate system with these variables. The Principle of Minimum Potential Energy for the problem is obtained by means of weighted residual method, and its Generalized Variational Principle by means of identified Lagrange multiplier method.This paper also presents a Method of Variable-characteristic Nondimensionization with a scale of load parameter, which may efficiently raise the probability of success for nonlinearity calculation. The obtained Nondimensional System of Differential Equations and Nondimensional Principle of Minimum Potential Energy could be taken as the theoretical basis for the numerical computation of axisymmetrical shells with arbitrarily large deflections.

Pansystems Research on a Type of Fixed Subsets

Li Gui-hua

1986, 7(2): 127-132.

Abstract(2114) PDF(500)

Abstract:
The present paper continues the pansystems research, on fixed suhsi is. Unier ihe pansystems framework it gives the existence criterion of I-type fixed subsets, and the theorems about the relations between the classes of reflexive and equivalent relations and fixed subsets; introduces the concept of fixpoints of binary relations existence theorems about fixpoints for a kind of panveeighted network.

Fixed Point Theorems for Fuzzy Mapping(Ⅱ)

Zhang Shi-sheng

1986, 7(2): 133-138.

Abstract(1987) PDF(495)

Abstract:
This paper presents some new fixed point theorems for fuzzy mappings. The results given in this paper improve and extend some recent results of [1, 4, 5].

The Periodic Cracks of an Infinite Anisotropic Media for Plane Skew-Symmetric Loadings

Cai Hai-tao

1986, 7(2): 139-144.

Abstract(1853) PDF(503)

Abstract:
This paper attempts to solve the periodic crack problems of infinitive anisotropic media for plane skew-symmetric loadings by means of the method of complex function. The problems are now reduced to the determination of two complex functions that must satisfy certain boundary conditions. In this paper, the stresses, the displacements and the boundary conditions are assumed to be periodic, md further, the stresses are assumed to be bounded at infinity. The solutions are expressed in closed forms.

A Difference Method for Singular Perturbation Problem of Hyperbolic-Parabolic Partial Differential Equation

Sheng Jin-reng

1986, 7(2): 145-153.

Abstract(1744) PDF(612)

Abstract:
In this paper we constructed an exponentially fitted difference scheme for singular perturbation problem of hyperbolic-parabolic partial differential equation. Not only do we take a fitting factor in the equation, but also we put one in the approximation of second initial condition. By means of the asymptotic solution of singular perturbation problem we proved the uniform convergence of this scheme with respect to the small parameter.

Representing General Solution of Equations in Theory of Elasticity by Harmonic Functions

Nie Yi-yong

1986, 7(2): 155-160.

Abstract(1988) PDF(506)

Abstract:
The general solution of the equations in the theory of elasticity is represented by seven harmonic functions, where there are only three harmonic functions independent of each other and every one of them has certain mechanics meaning. The examples applying the general solution to solve several simple inverse problems in elastostatics are presented.

Application of Subregion Function Method in the Method of Weighted Residuals

Qian Guo-zhen

1986, 7(2): 161-167.

Abstract(1650) PDF(505)

Abstract:
In this paper, a new concept of subregion function method is suggested. According to the boundary shape and the stiffness and loading conditions of the structure, the original zone of the structure is divided into some subregions, in each of which different trial functions may be adopted. Conditions of compatibilities between subregioni are considered. Finally residual equations consisted of interior residuals, boundary residuals and co-boundary residuals between subregions are given.A numerical example to illustrate the theory of this method is given.

The Theorem of the Stability of Linear Nonautonomous ystems under the Frequently-Acting Perturbation

Zhang Shu-shun

1986, 7(2): 169-171.

Abstract(1573) PDF(551)

Abstract:
In the paper a theorem on the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of Malkin's Theorem.

Function of Region

Ho Chong

1986, 7(2): 173-179.

Abstract(1948) PDF(465)

Abstract:
The purpose of this paper is to extend points function and interval functions theoretics to an arbitrary region. For this, the new theory, the contraction of a region, and the retraction of a region; the extension of a region, and the kernel-preserving extension of a region are established by the author. Starting from these concepts, the new definitions of a region function is given. And a kernel(i.e. fixed point) of a region function is connected with a stable centre of defining region of such a region function. Thereby, the region theoretics and algorithms are established.In applications, to find a stable centre of a region, the author has utilized the measure theoretics of matrice defined by Hartfiel[7] and other authors. The measure problems of coefficient matrice of system of equations of linear algebra associated with some region are discussed.

The Finite Element Technique for Predicting the Natural Frequencies, Mode Shapes and Damping Values of Filamentary Composite Plates

Lin Dun-xiang, Ni Rong-gen

1986, 7(2): 181-196.

Abstract(1743) PDF(830)

Abstract:
This article presents the numerical method for predicting the natural frequencies, mode shapes and damping values of filamentary composite plates. This method is based on finite element technique, using damped element and allowing transverse shear deformation. For the example of this technique, the theoretical results comparing.with experimental values of carbon fibre and glass fibre reinforced plastics plates(mid-plane symmetric) are provided. The dynamic properties of these laminates are discussed. Finally, a simple graphic technique to estimate the natural frequencies and damping values is suggested.