应用数学和力学

1995 Vol. 16, No. 4

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The Hamiltonian Structures of 3D ODE with Time-Independent Invariants

Guo Zhong-heng, Chen Yu-ming

1995, 16(4): 283-288.

Abstract(2351) PDF(458)

Abstract:
We have proved that any 3-dimensional dynamical system of ordinary differential equations(in short, 3D ODE)With time-independent invariants can be rewritten as Haniltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants. As an example,we discuss the Kermack-Mckendrick modelfor epidemics in detail. The results we obtained are generalization of those obtained by Y. Nutku.

Interaction Between Crack and Elastic Inclusion

Zhang Ming-huan, Tang Ren-ji

1995, 16(4): 289-300.

Abstract(1941) PDF(549)

Abstract:
By using the basic displacements and stresses caused by a single elastic inclusion and a single crack on infinite plane,the interaction problem between a crack and anelastic inclusion is reduced io solve a set of Cauchy-type singular integral equation.Based on this result,the singular behaviour of the solution for the inclusion-branching crack is analysed theoretically and the oscillating singular interface stress field isobtained. For the separating inclusion-crack problem,the stress intensity factors at thetips and the interface stress of the inclusion are calculated and the results of which are satisfactory.

On the Mechanism of Turbulent Coherent Structure(Ⅰ)——The Physical Model of the Coherent Structure for the Smooth Boundary Layer

Tsai Shu-tang, Liu Yu-lu

1995, 16(4): 301-305.

Abstract(2411) PDF(563)

Abstract:
In this paper, based on the discussion of properties of the turbulent coherent structure for smooth boumdary layer a physical model has been established. The widthof slowly-moving streak line and bursting time of coherent structure expressed bymomentum thickness Reynolds mumber of boundary layer layer have been obtained,which are in agreement with The experimental data^[3.4.5.7].

Topologically Finite Intersection Property and Minimax Theorems

Zhang Shi-sheng, Zhang Xian

1995, 16(4): 307-314.

Abstract(2407) PDF(705)

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A more general lopologically finite intersection property is obtained. As an application,we utilize this result to obtain some more general minimax theorems. The results presented in this paper unify and extend the main results of [5, 6, 9].

The Mechanical Method of Constructing the Displacement Functions in Elasticity

Zhang Hong-qing, Feng Hong

1995, 16(4): 315-322.

Abstract(2205) PDF(528)

Abstract:
In this paper we have proven the general solution to the equations of linear operators Au=f as u=Cv+e. where v satisfies the equation Dv=g and D is adiagonal matrix. Basing on the consstructive proof of Hilbert Nullstellensatz. we hare given the mechanical method of constucting C. D and e, and some of the mechanical algorithm displacement functions in elasticity are given by this method also.

Unsteady Rotative Flow of Non-Newtonian Fluid In an Annular Pipe

Huang Jun-qi, Liu Ci-qun

1995, 16(4): 323-328.

Abstract(2603) PDF(451)

Abstract:
This paper studies power law non-Newtonian fluid rotative flow in an annular pipe. The governing equation is nonlinear one, we linearized the governing equationby assuming that partial factor is at state. With Laplace transform we obtain ananalytical solution of the problem In the paper several groups of curves are given.these curves reflect the temporal change law and spatial distribution of fluid velocity.In addition we study the effection of power law index on the flow field the result indicates that when the power law index n<1. the flow velocity is highly sensitive tothe index and this fact is importanl in related engineering decisions.

An Iterative Method for the Discrete Problems of a Class of Elliptical Variational Inequalities

Zheng Tie-sheng, Li Li, Xu Qing-yu

1995, 16(4): 329-335.

Abstract(2162) PDF(641)

Abstract:
Based on the nonlinear characiers of the discrete problems of some elliptical variational inequalities, this paper presents a numerical iterative method, the schemes of which are pithy and converge rapidly The new method possesses a high efficiency insolving such applied engineering problems as obstacle problems and.free boundary problems arising in fluid lubrications.

The Eccentric Effect of a Coaxial Viscometer

Guo Zhi-rong, Yan Zong-yi

1995, 16(4): 337-344.

Abstract(1821) PDF(451)

Abstract:
This paper studies the effect of the eccentricity between the inner bob and theouter cup in a coaxial viscometer on the measurements of the viscosity by using aperturbation scheme, Our numerical examples demonstrate that the error incurred bythe eccentricity would become larger as the characteristic Reynolds number decreasesor as the gap width between the bob and the cup gets narrower. However, such errorsmay not be signifcant if the eccentric distance is not larger than 1/10 of the gapwidth for the usual working range of a coaxial viscometer.

Variational Principle and Generalized Variational Principle in Hydrodynamics of a Class of Non-Newtonian Fluid

Shen Min, Sun Qi-ren

1995, 16(4): 345-351.

Abstract(2684) PDF(538)

Abstract:
In this paper. the principle of maximum power losses for the incompressible viscous fluid proposed by professor Chien Wei-zang is extended to the hydrodynamic problems of a special class of non-Newtonian fluid——generalized Newtonian fluid.The constraint condition of variation are eliminated by the method of idetified Lagrangian multipliers and a generalized variational principle is established.

An Application of Schauder’s Fxed Point Theorem to the Existence of Solutions of Impulsively Differential Equations

Dong Yu-jun, Zou Er-xin

1995, 16(4): 353-357.

Abstract(2168) PDF(480)

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In this paper the existence of solutions of a boundary value problem for impulsively differential equations that is difficult to solve by the upper and lower solution method will be proved by means of Schauder's fixed point theorem,which improves some existing results.

Secondary Instability of Large Scale Structure in Free Turbulent Shear Layer

Zhao Geng-fu

1995, 16(4): 359-365.

Abstract(1824) PDF(530)

Abstract:
The secondary instability theory is used to study the behavior of spatially growing disturbance in free turbulent shear layer.The numerical results indicate that secondary instability of subharmonic mode shows a strong choice of spanwise wavenumber andthe maximum growth two dimensional case.In contrast to that secondary instabilities of the fundamental mode occur in a wide scope of spanwise wavenumber.We have found so called translative at β=0 and bifurcation phenomenon for an amplitude of the KH wave larger than 0.06.

Reciprocal Theorem Method for Solving the Problems of Bending of Thick Rectangular Plates

Fu Bao-lian, Tan Wen-feng

1995, 16(4): 367-379.

Abstract(2450) PDF(801)

Abstract:
In this paper,reciprocal theorem method(RTM) is generalized to solve theof bending of thick rectangular plates based on Reissner's theory.First,the paper gives the basic solution of the bending of thick rectangular platesand then the exact analytical solution of the bending of thick rectangular plate with three clamped edges and one free edge under umiformly distributed load is found by RTM, finally, we analyze numerical results of the solution.

1995, 16(4): 380-381.

Abstract(1635) PDF(529)

Abstract: