应用数学和力学

1999 Vol. 20, No. 8

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The Energy Criterion of Minimum Equivalent Diameter in Gas Atomization

Ma Zheng, Zhou Zhewei

1999, 20(8): 771-775.

Abstract(2362) PDF(655)

Abstract:
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): 776-782.

Abstract(2531) PDF(703)

Abstract:
In this paper the system of the forced vibration -λ₁T+λ₂T²+λ₃T³=ε(gcosωt-ε'T) is discussed, which contains square and cubic items. The critical condition that the systementers chaotic states is given by the Melnikov method. By Poincarmap, phase portrait and time-displacement history diagram, whether the chaos occurs is determined.

Dinesh Gupta, Musharraf Zaman

1999, 20(8): 783-802.

Abstract(2462) PDF(568)

Abstract:

The Asymptotic Solution of a Dynamic Buckling Problem in Elastic Columns

Han Qiang, Zhang Shanyuan, Yang Guitong

1999, 20(8): 809-814.

Abstract(2576) PDF(616)

Abstract:
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.

Numerical Method for Solving Linear Boundary Value Problems by the Chebyshev Tau Method

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

1999, 20(8): 815-821.

Abstract(2028) PDF(643)

Abstract:
A new Tau-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): 822-828.

Abstract(2882) PDF(1170)

Abstract:
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): 829-834.

Abstract(2290) PDF(711)

Abstract:
In this paper, by proving that the equations discussed here are l-simple(l≥1) by strati-fication theory, the unstabilit y 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): 835-846.

Abstract(2618) PDF(762)

Abstract:
In the work, I t is shown the numerical investigations about the unsteady inviscid results obtained for the pitching oscillating wings at different angles of at tack. The results are obtained by solving the unsteady Euler equations in a body-fit ted 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): 847-850.

Abstract(2203) PDF(1000)

Abstract:
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)=gradG(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 populat ion model is proved.

Stability of a Class of Neural Network Models with Delay

Cao Jinde, Lin Yiping

1999, 20(8): 851-855.

Abstract(2167) PDF(810)

Abstract:
In this paper, by using L yapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type τ_j≥0,i=1,2,…,n.

Wavelet Modeling and Forecasting and Its Application in the Chinese Monetary Multiplier

Liu Bin, Dong Qinxi

1999, 20(8): 856-862.

Abstract(2264) PDF(585)

Abstract:
In this paper, a time-varying AR model is constructed by using the vector-space algorithm of compactly-supported biorthonormal wavelets transform, and a time-varying AR model for forecasting narrow monetary multipliers in China is developed.

A Significant Improvement on Newton’s Iterative Method

Wu Xinyuan

1999, 20(8): 863-866.

Abstract(2771) PDF(1285)

Abstract:
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 Liapunovs methods of dynamic system. These new methods preserve qudratic convergence and computation efficiency of Newtons method, but 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): 867-874.

Abstract(2472) PDF(612)

Abstract:
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, was solved analytically. The governing equations were written on the deformed region or on the present configuration. And the conditions were described on moving boundary. A closed form solution was found. Furthermore, a bifurcation solution in closed form was 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 pit chfork 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): 875-880.

Abstract(2695) PDF(928)

Abstract:
A kind arc-length method is presented to solve the ordinary differential equations(ODEs) with certain types of singularit y 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.