应用数学和力学

1989 Vol. 10, No. 11

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Hopf Bifurcation in a Three-Dimensional System

Li De-ming, Huang Ke-lei

1989, 10(11): 816-968.

Abstract(1810) PDF(422)

Abstract:
In this paper,Liapunor-Schmidl reduction and singularity theory are employed to discuss Hopf and degenerate Hopf bifureations in global parametric region in a three-dimensional system , The conditions on existence and stability are given.

Analytical Solutions for Equations of Unsteady Flow of Non-Newtonian Fluids in Tube

Liu Ci-qun, Huang Jun-qi

1989, 10(11): 939-946.

Abstract(2075) PDF(649)

Abstract:
This paper presents analytieal solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of nun-Newtonian v...

A Rectangular Element of Thin Plates Based upon the Generalized Variational Principles

Chien Wei-zhang, Wang Gang

1989, 10(11): 947-953.

Abstract(2005) PDF(492)

Abstract:
Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generaliz...

Numerical Solution of Quasilinear Singularly Perturbed Ordinary Differential Equation without Turning Points

Lin Ping, Su Yu-cheng

1989, 10(11): 955-959.

Abstract(1872) PDF(656)

Abstract:
In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter ε, Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary ε>0.

Shakedown Analysis of Shell Structures of Kinematic Hardening Materials

Jin Yong-jie, Zhao Xiao-jin

1989, 10(11): 969-976.

Abstract(2017) PDF(555)

Abstract:
It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.In this paper, same further understanding of the shakedown theorem for kinematic hardening materials has been made, and it is applied to analy...

The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅰ)

Zhang Jing-zhong, Yang Lu, Zhang Lei

1989, 10(11): 977-985.

Abstract(1871) PDF(542)

Abstract:
In recent years, there is a wide interest in Sarkovskii's theorem ami the related study. According to Sarkovskii's theoren if the continuous self-mapf of the closed interval has a 3-pcriodic orbit, then fmust has an n-pcriodic orbit for any positive integer n. But f can not has all n-periodic orbits...

Stability of Stationary State Solution for a Reaction Density-Dependent Diffusion Equation

Zhang Guo-chu

1989, 10(11): 987-996.

Abstract(1984) PDF(569)

Abstract:
In this paper we are interested in the large time behavior of the nonlinear diffusion equation u₁=(φ(u))_xx+φ(u), (x∈R, f∈R+=(0,+∞)) We consider functions φ(u) and φ(u) which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some compariso...

Elastic Media with Randomly Distributed Defects

Wang Biao, Wang Dian-fu, Wang Duo

1989, 10(11): 997-1008.

Abstract(1644) PDF(414)

Abstract:
In this paper, the clastic field in a solid with randomly distributed defects is derived. These defects are composed of cavities and microcracks, whose locations, orientation and size are random variables. The Random Point field Model is proposed to describe the random defects, and the basic equatio...

An Analytic Solution on Hypersonic Flow over an Arbitrary Slender Body with Near Power-Law Profile (Ⅰ)

Chen Yao-song, Chen Yong-ze

1989, 10(11): 1009-1024.

Abstract(1770) PDF(608)

Abstract:
On the basis of a self-similar solution as well as of the assumption of the "Transserse Motion",a general linear theory on hypersonic flow over a general slender body is set up in this paper By means of this theory, the problem concerned can he put into a universal system of O.D Eqs.which can be int...

Chaos and Bifurcation of Phase Locking Loops under Periodic Perturbation

Guo Rui-hai, Yuan Xiao-feng

1989, 10(11): 1026-1032.

Abstract(1809) PDF(452)

Abstract:
This paper discusses the chaos and bifurcation for equation . By use of the Melnikov method the conditions to have the chaotic behavior and to have subharmonic oscillations are given.