应用数学和力学

1999 Vol. 20, No. 4

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Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System

Lu Dongqiang, Dai Shiqiang, Zhang Baoshan

1999, 20(4): 331-336.

Abstract(2422) PDF(1080)

Abstract:
In this paper,it is dealt with that the Hamiltonian formulation of nonlinear water waves in a two-fluid system,which consists of two layers of constant-density incompressible inviscid fluid with a horizontal bottom,an interface and a free surface.The velocity potentials are expanded in power series of the vertical coordinate.By taking the kinetic thickness of lower fluid-layer and the reduced kinetic thickness of upper fluid-layer as the generalized displacements,choosing the velocity potentials at the interface and free surface as the generalized momenta and using Hamilton's principle,the Hamiltonian canonical equations for the system are derived with the Legendre transformation under the shallow water assumption.Hence the results for single-layer fluid are extended to the case of stratified fluid.

Bifurcation in a Parametrically Excited Two-Degree-of-Freedom Nonlinear Oscillating System with 1:2 Internal Resonance

Ji Jinchen, Chen Yushu

1999, 20(4): 337-345.

Abstract(2322) PDF(584)

Abstract:
The nonlinear response of a two-degree-of-freedom nonlinear oscillating system to parametric excitation is examined for the case of 1:2 internal resonance and,principal parametric resonance with respect to the lower mode.The method of multiple scales is used to derive four first-order autonomous ordinary differential equations for the modulation of the amplitudes and phases.The steady-state solutions of the modulated equations and their stability are investigated.The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions.The Melnikov method is used to study the global bifurcation behavior,the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.

The Double Mode Model of the Chaotic Motion for a Large Deflection Plate

Shu Xuefeng, Han Qiang, Yang Guitong

1999, 20(4): 346-350.

Abstract(1994) PDF(568)

Abstract:
The primary aim of this paper is to study the chaotic motion of a large deflection plate.Considered here is a buckled plate,which is simply supported and subjected to a lateral harmonic excitation.At first,the partial differential equation governing the transverse vibration of the plate is derived.Then,by means of the Galerkin approach,the partial differential equation is simplified into a set of two ordinary differential equations.It is proved that the double mode model is identical with the single mode model.The Melnikov method is used to give the approximate excitation thresholds for the occurrence of the chaotic vibration.Finally numerical computation is carried out.

Analysis of Sloping Elastic Pile Under Arbitrary Loads by Line-Loaded Integral Equation Method

Yun Tianquan

1999, 20(4): 351-357.

Abstract(2121) PDF(608)

Abstract:
For analysis of displacement and stress,an elastic sloping pile embedded in a homogeneous isotropic elastic half space under arbitrary loads at the top can be decomposed into two plane systems,i.e.,the inclined plane xOz and its normal plane yOz.Let Mindlin's forces be the fundamental loads with unknown intensity function X(t),Y(t),Z(t),parallel to x,y,z-axis respectively,be distributed along the t axis of the pile in and concentrated forces Q_x,Q_y,Z,couples M_y,M_x at top of the pile.Then,according to the boundary conditions of elastic pile,the problem is reduced to a set of Fredholm-Volterra type equations.Numerical solution is given and the accuracy of calculation can be checked by the reciprocal theorem of work.

Application of the Modified Method of Multiple Scales to the Bending Problems for Circular Thin Plate at Very Large Deflection and the Asymptotics of Solutions(Ⅱ)

Bissanga Cabriel, Jiang Furu

1999, 20(4): 358-362.

Abstract(2187) PDF(536)

Abstract:
This paper is a continuation of part(Ⅰ),on the asymptotics behaviors of the series solutions investigated in(Ⅰ).The remainder terms of the series solutions are estimated by the maximum norm.

A Uniformly Convergent Finite Difference Method for a Singularly Perturbed Initial Value Problem

G. M. Amiraliyev, Hakk Duru

1999, 20(4): 363-370.

Abstract(2620) PDF(589)

Abstract:
Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered.An exponentially fitted difference scheme with constant fitting factors is developed in a uniform mesh,which gives first-order uniform convergence in the sense of discrete maximum norm.Numerical results are also presented.

The Effective Properties of Piezoelectric Composite Materials with Transversely Isotropic Spherical Inclusions

Jiang Bing, Fang Daining

1999, 20(4): 371-380.

Abstract(2041) PDF(950)

Abstract:
The effective properties of piezoelectric composite materials are very important in engineering.In this paper,the closed-form solutions of the constraint-strain and the constraint-electric-field of a transversely isotropic spherical inclusion in an infinite non-piezoelectric matrix are obtained.The dilute solutions of piezoelectric composite materials with transversely isotropic spherical inclusions are also given.The solutions in the paper can be readily utilized in analysis and design of piezoelectric composite materials or smart materials and smart structures.

Mechanism in Pneumotransport of the Fibroid Substance

Xi Zhizhong

1999, 20(4): 381-385.

Abstract(2001) PDF(636)

Abstract:
In this paper,the mechanism of pneumotransport of the fibroid material is discussed.It is thought that the motion of air relative to the material is the filtration of the air passing through the porous medium which is composed of the cluster of fibroid material.It is found that the deviations of the experimental data with the theoretical results are within experimental error.

Numerical Simulation Analysis for Migration Accumulation of Oil and Water

Yuan Yirang, Zhao Weidong, Cheng Aijie, Han Yuji

1999, 20(4): 386-392.

Abstract(2163) PDF(603)

Abstract:
Numerical simulation of oil migration and accumulation is to describe the history of oil migration and accumulation in basin evolution.It is of great value in the exploration oil resources and their rational evaluation.This paper,puts forward the mathematical model and the modified method of alternating direction implicit interactive scheme.For the famous hydraulic experiment of secondary migration-accumulation(cut plane and plane problem),it has been done the numerical simulation test,and both the computational and experimental results are identical.

Thermal Stresses Analysis of Ceramic/Metal Functionally Gradient Material Cylinder

Lü Yunbing, Zhang Kaiyin, Xiao Jinsheng, Wen Dongsheng

1999, 20(4): 393-397.

Abstract(2285) PDF(640)

Abstract:
In this paper,the composite cylinder system is made of three layers:metal,functionally gradient material(FGM) and ceramics is studied.The formulas of the steady-state temperature distribution and the associate thermal stress distribution in the cylinder are obtained.For ZrO₂/Ti6Al4V system,the distribution of steady_state temperature and thermal stress are calculated and discussed.

The Motion of Organization Center of Scroll Waves in Excitable Media with Single Diffusion

Liu Shenquan, Lu Qishao, Huang Kelei

1999, 20(4): 398-404.

Abstract(2283) PDF(588)

Abstract:
The motion of organization center of three-dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper.The relation of curvature and the linear law are derived for untwisted organization center.These results have explicit physical meaning and are in good agreement with experiments.

Torsional Buckling of Spherical Shells Under Circumferential Shear Loads

Zhang Yinyi

1999, 20(4): 405-410.

Abstract(2326) PDF(624)

Abstract:
By the aid of differential geometry analysis on the initial buckling of shell element,a set of new and exact buckling bifurcation equations of the spherical shells is derived.Making use of Galerkin variational method,the general stability of the hinged spherical shells with the circumferential shear loads is studied.Constructing the buckling mode close to the bifurcation point deformations,the critical eigenvalues,critical load intensities and critical stresses of torsional buckling ranging from the shallow shells to the hemispherical shell are obtained for the first time.

A Symmetrical Nonsingular Boundary Element Method

Yao Zhiyuan

1999, 20(4): 411-417.

Abstract(2310) PDF(545)

Abstract:
In this paper,on the basis of the theory of functional analysis,by the use of the complete orthogonal eigenfunction system,a fundamental solution of the control equation is constructed.By this method,a symmetrical nonsingular boundary element method is derived.

A Discussion of Non-Linear Mechanism on Subtropical Anticyclone’s Extending/Shrinking Over East-Asia in Summer

Zhang Ren, Shi Hanshen, Sha Wenyu

1999, 20(4): 418-426.

Abstract(2039) PDF(591)

Abstract:
Based on the actual circulation structure as well as weather characters over East-Asia subtropical region in summer,by using three-dimension non-linear forced/dissipated dynamic model,the activities of subtropical anticyclone over East-Asia have been studied and discussed.The potential enstrophy criteria of system stability have been derived and also been analysed.The criterion can provide useful reference for analysing and predicting subtropical anticyclone's extending/shrinking as well as corresponding weather over East-Asia in summer.

An Approximate Method for Determing the Veloctiy Profile in a Laminar Boundary-Layer on Flat Plate

Yuan Yiwu, Liu Youwen

1999, 20(4): 427-431.

Abstract(2267) PDF(961)

Abstract:
In this paper,using the integration method,it is sought to solve the problem for the laminar boundary-layer on a flat plate.At first,a trial function of the velocity profile which satisfies the basical boundary conditions is selected.The coefficients in the trial function awaiting decision are decided by using some numerical results of the boundary-layer differential equations.It is similar to the method proposed by Peng Yichuan,but the former is simpler.According to the method proposed by Peng,when the awaiting decision coefficients of the trial function are decided,it is sought to solve a third power algebraic equation.On the other hand,in this paper,there is only need for solving a linear algebraic equation.Moreover,the accuracy of the results of this paper is higher than that of Peng.

Persistence of Two-Species Ayala Competitive Model with Different Diffusions

Yuan Cunde, Pei Yongzhen

1999, 20(4): 432-440.

Abstract(2206) PDF(598)

Abstract:
In this paper,the stabilities of boundary equilibrium and positive equilibrium of two-species Ayala competitive systems with two different diffusions are discussed,and dynamic behaviors of species are obtained.At the same time,the dynamic behaviors between systems with diffusion and those without diffusion are compared.This shows the influence of diffusions on the persistence of species.