Table of Content

18 August 1999, Volume 20 Issue 8

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Articles

THE ENERGY CRITERION OF MINIMUM EQUIVALENT DIAMETER IN GAS ATOMIZATION

Ma Zheng;Zhou Zhewei

1999, 20(8):  825-829. 

Abstract ( 431 )   PDF (352KB) ( 281 )  

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Gas atomization has been studied by using energy method in this paper. It shows that the capillary potential energy of the atomization droplets is supplied by the impingement of the gas on the liquid. The energy criterion of the minimum equivalent diameter of the atomization droplets is obtained. The result is comparable to the empirical formulae.

THE STUDY ON THE CHAOTIC MOTION OF A NONLINEAR DYNAMIC SYSTEM

Han Qiang;Zhang Shanyuan;Yang Guitong

1999, 20(8):  830-836. 

Abstract ( 621 )   PDF (395KB) ( 234 )  

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In this paper, the system of the forced vibration T-λ₁T+λ₂T²+λ₃T³=ε(gcosωt-ε′T)is discussed, which contains square and cubic items. The critical condition that the system enters chaotic states is given by the Melnikov method. By Poincaré map, phase portrait and time_displacement history diagram, whether the chaos occurs is determined.

STABILITY OF BOREHOLES IN A GEOLOGIC MEDIUM INCLUDING THE EFFECTS OF ANISOTROPY

Dinesh Gupta;Musharraf Zaman

1999, 20(8):  837-856. 

Abstract ( 851 )   PDF (1698KB) ( 1335 )  

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An analytical formulation is developed to investigate the stability of a deep, inclined borehole drilled in a geologic medium and subjected to an internal pressure and a non_hydrostatic stress field. The formulation consists of a three_dimensional(3_D)analysis of stresses around a borehole, combined with internal pressurization of the borehole to obtain an approximate solution of the overall stress distribution. The orientation of the borehole, the in_situ stresses and bedding plane can all be arbitrarily related to each other to represent the actual field situations. Both tensile failure and shear failure potentials of a borehole are investigated. The failure criteria applied assume that when the least principal stress exceeds the strength of the formation in tension, a tensile failure occurs. Shear failure is represented using the modified Drucker_Prager failure criterion for anisotropic materials. A parametric study is carried out to assess the effect of material anisotropy, bedding plane inclination and in_situ stress conditions on borehole stability. Results of the parametric study indicate that wellbore stability is significantly influenced by a high borehole inclination, high degree of material anisotropy, in_situ stress conditions and high formation bedding plane inclination. The stability of a borehole in an elasto_plastic medium is also investigated. In order to evaluate the extent of the plastic zone around a borehole and the effect of anisotropy of the material on this plastic zone, a mathematical formulation is developed using theories of elasticity and plasticity. The borehole is assumed to be vertical, subjected to hydrostatic stresses, and drilled in a transversely isotropic geologic medium. A parametric study is carried out to investigate the effect of material anisotropy on the plastic behavior of the geologic medium. Results indicate that the stress distribution around a borehole, the extent of the plastic zone, and the failure pressure are influenced by the degree of material anisotropy and value of in_situ overburden stresses. It was observed that the borehole becomes less stable as the degree of anisotropy of the geologic medium increases.

THE ASYMPTOTIC SOLUTION OF A DYNAMIC BUCKLING PROBLEM IN ELASTIC COLUMNS

Han Qiang;Zhang Shanyuan;Yang Guitong

1999, 20(8):  867-872. 

Abstract ( 595 )   PDF (363KB) ( 248 )  

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For the dynamic buckling of an elastic column, which is subjected to a longitudinal impact by a rigid body, the form of the axial load is very complicated. The problem may be reduced to discuss the solution of nonlinear partial differential equations. So far, a theoretical solution may not be obtained. In this paper, this dynamic buckling problem of an ideal elastic column with finite length is discussed. By the perturbation method with a small parameter and the variational method, a solution of this problem is given. Finally, numerical computation is carried out, from this, some beneficial conclusions are obtained.

NUMERICAL METHOD FOR SOLVING LINEAR BOUNDARY VALUE PROBLEMS BY THE CHEBYSHEV τ_METHOD

Muhammed I. Syam;Hani I. Siyyam;Qassem Al-Moudalal

1999, 20(8):  873-879. 

Abstract ( 531 )   PDF (371KB) ( 356 )  

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A new τ_method is presented for the two dimensional linear boundary value problems. Theoretical and numerical analyses are presented. These results indicate that our method works nicely and efficiently.

DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION

Ke Honglu;Xie Hexi

1999, 20(8):  880-887. 

Abstract ( 571 )   PDF (387KB) ( 306 )  

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In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge.

ON THE STABILITY OF GENERAL NAVIER-STOKES TYPE EQUATION

Tang Yiming

1999, 20(8):  888-894. 

Abstract ( 423 )   PDF (342KB) ( 367 )  

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In this paper, by proving that the equations discussed here are l_simple(l≥1)by stratification theory, the unstability of the equations is proved. And the un_uniqueness of the solution of forced dissipative non_linear system equations in atmospheric dynamics is used as an illustration for the result.

RESEARCH ON THE HYSTERESIS PROPERTIES OF UNSTEADY AERODYNAMICS ABOUT THE OSCILLATING WINGS

Gao Zhenghong

1999, 20(8):  895-907. 

Abstract ( 532 )   PDF (663KB) ( 378 )  

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In the work, it is shown the numerical investigations about the unsteady inviscid results obtained for the pitching oscillating wings at different angles of attack. The results are obtained by solving the unsteady Euler equations in a body_fitted coordinate system. It is based on the four_stage Runge_Kutta time stepping scheme. Meanwhile to increase the time step that is limited by Courant limit(CFL), the implicit residual smoothing with local variable parameters is used. As a result, the unsteady aerodynamics about a rectangular wing and a delta wing, which are oscillated in pitching with different frequencies, are shown in this paper. The properties of the unsteady aerodynamics in these cases are researched here.

ON THE EXISTENCE OF PERIODIC SOLUTIONS TO HIGHER DIMENSIONAL PERIODIC SYSTEM WITH DELAY

Huang Xiankai;Dong Qinxi

1999, 20(8):  908-911. 

Abstract ( 574 )   PDF (232KB) ( 446 )  

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In this paper, higher dimensional periodic systems with delay of the form
x′(t)=A(t,x(t))x(t)+f(t,x(t-τ)),
x′(t)= grad G(x(t))+f(t,x(t-τ))
are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive periodic solution for a logarithmic population model is proved.

STABILITY OF A CLASS OF NEURAL NETWORK MODELS WITH DELAY

Cao Jinde;Lin Yiping

1999, 20(8):  912-916. 

Abstract ( 597 )   PDF (369KB) ( 316 )  

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In this paper, by using Liapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type


WAVELET MODELING AND FORECASTING AND ITS APPLICATION IN THE CHINESE MONETARY MULTIPLIER

Liu Bin;Dong Qinxi

1999, 20(8):  917-923. 

Abstract ( 439 )   PDF (397KB) ( 279 )  

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In this paper, a time_varying AR model is constructed by using the vector_space algorithm of compactly_supported biorthonormal wavelet transform. It is developed for forecasting narrow monetary multipliers in China.

A SIGNIFICANT IMPROVEMENT ON NEWTON’S ITERATIVE METHOD

Wu Xinyuan

1999, 20(8):  924-927. 

Abstract ( 601 )   PDF (264KB) ( 364 )  

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For solving nonlinear and transcendental equation f(x)=0, a singnificant improvement on Newton’s method is proposed in this paper. New “Newton Like” methods are founded on the basis of Liapunov’s methods of dynamic system. These new methods preserve quadratic convergence and computational efficiency of Newton’s method, and remove the monotoneity condition imposed on f(x):f′(x)≠0.

A STUDY OF THE CATASTROPHE AND THE CAVITATION FOR A SPHERICAL CAVITY IN HOOKE’S MATERIAL WITH 1/2 POISSON’S RATIO

Jin Ming;Huang Kefu;Wu Jike

1999, 20(8):  928-935. 

Abstract ( 496 )   PDF (486KB) ( 465 )  

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In this paper, the catastrophe of a spherical cavity and the cavitation of a spherical cavity for Hooke’s material with 1/2 Poisson’s ratio are studied. A nonlinear problem, which is a moving boundary problem for the geometrically nonlinear elasticity in radial symmetric, is solved analytically. The governing equations are written on the deformed region or on the present configuration. And the conditions are described on moving boundary. A closed form solution is found. Furthermore, a bifurcation solution in closed form is given from the trivial homogeneous solution of a solid sphere. The results indicate that there is a tangent bifurcation on the displacement_load curve for a sphere with a cavity. On the tangent bifurcation point, the cavity grows up suddenly, which is a kind of catastrophe. And there is a pitchfork bifurcation on the displacement_load curve for a solid sphere. On the pitchfork bifurcation point, there is a cavitation in the solid sphere.

ARC-LENGTH METHOD FOR DIFFERENTIAL EQUATIONS

Wu Jike;W H Hui;Ding Hongli

1999, 20(8):  936-942. 

Abstract ( 602 )   PDF (353KB) ( 485 )  

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An arc_length method is presented to solve the ordinary differential equations(ODEs)with certain types of singularity such as stiff property or discontinuity on continuum problem. By introducing one or two arc_length parameters as variables, the differential equations with singularity are transformed into non_singularity equations, which can be solved by usual methods. The method is also applicable for partial differential equations(PDEs), because they may be changed into systems of ODEs by discretization. Two examples are given to show the accuracy, efficiency and application.