应用数学和力学

2005 Vol. 26, No. 1

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Variation of Velocity Profile of Jet and Its Effect on Interfacial Stability

LI Xiao-jun, HU Guo-hui, ZHOU Zhe-wei

2005, 26(1): 1-6.

Abstract(2292) PDF(494)

Abstract:
Linear stability theory is used to study a double fluid model for a liquid jet surrounded by a coaxial gas steam.Under the different pressure gradients for liquid and gas flow,the variation of the velocity profile in the model and the thickness of the shear layer were investigated.The effects of such variation on the interfacial stability were discussed with the application of Chebyshev spectral collocation method.

Critical Damping of the Second-Order Pendulum-Like Systems

LI Xin-bin, HUANG Yong-nian, YANG Ying, HUANG Lin

2005, 26(1): 7-15.

Abstract(2717) PDF(593)

Abstract:
First,the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were dicussed.Then the case with a general form of nonlinearity is considered and its global properties were studied by using the qualitative theory of differential equations.As a result,sufficient conditions for estimating the critical damp are established,which improves the work by Leonov et al.

Scattering of Harmonic Anti-Plane Shear Waves by an Interface Crack in Magneto-Electro-Elastic Composites

ZHOU Zhen-gong, WANG Biao

2005, 26(1): 16-24.

Abstract(2292) PDF(612)

Abstract:
The dynamic behavior of an interface crack in magneto-electro-elastic composites under harmonic elastic anti-plane shear waves is investigated for the permeable electric boundary conditions.By using the Fourier transform,the problem can be solved with a pair of dual integral equations in which the unknown variable was the jump of the displacements across the crack surfaces.To solve the dual integral equations,the jump of the displacements across the crack surface was expanded in a series of Jacobi polynomials.Numerical examples were provided to show the effect of the length of the crack,the wave velocity and the circular frequency of the incident wave on the stress,the electric displacement and the magnetic flux intensity factors of the crack.From the results,it can be obtained that the singular stresses in piezoelectric/piezomagnetic materials carry the same forms as those in a general elastic material for anti-plane shear problem.

A Critical Pattern of Crossflow Around a Slender

LI Guo-hui, DENG Xue-ying

2005, 26(1): 25-31.

Abstract(2308) PDF(505)

Abstract:
Topological structure of a slender crossflow was discussed with topological analysis.It is pointed that the development of slender vortices leads to the change of topological structure about cross flow,and a critical flow pattern will appear.There is a high-order singular point in this critical flow pattern.And the index of the high-order singular is -3/2.The topological structure of this singular point is instable,so bifurcation will occur and the topological structure of flowfield will be changed by little disturbance.

Construction of Third-Order WNND Scheme and Its Application in Complex Flow

LIU Wei, ZHAO Hai-yang, XIE Yu-fei

2005, 26(1): 32-39.

Abstract(2929) PDF(699)

Abstract:
According to the Liu's weighted idea,a space third-order WNND scheme was constructed based on the stencils of second-order NND scheme.It was applied in solving linear-wave equation,1D Euler equations and 3D Navier-Stokes equations.The numerical results indicate that the WNND scheme which doesn't increase interpolated point(compared to NND scheme) has more advantages in simulating discontinues and convergence than NND scheme.Appling WNND scheme to simulating the hypersonic flow around lift-body shows:With the AoA(angle of attack) increasing from 0° to 50°,the structure of limiting streamline of leeward surface changes from unseparating,open-separating to separating,which occurs from the combined-point(which consists of saddle and node points).The separating area of upper wing surface is increasing with the AoA's increasing.The topological structures of hypersonic flowfield based on the sectional flow patterns perpendicular to the body axis agree well with ZHANG Han-xin's theory.Additionally,the unstable-structure phenomenon which is showed by two saddles connection along leeward symmetry line occurs at some sections when the AoA is bigger than 20°.

Analyses on Structural Damage Identification Based on Combined Parameters

TANG He-sheng, XUE Song-tao, CHEN Rong, WANG Yuan-gong

2005, 26(1): 40-46.

Abstract(2108) PDF(514)

Abstract:
The relative sensitivities of structural dynamical parameters were analyzed using a directive derivation method.The neural network is able to approximate arbitrary non-linear mapping relationship,so it is a powerful damage identification tool for undnown systems.A neural network-based approach was presented for the structural damage detection.The combined parameters were presented as the input vector of the neural network,which computed with the change rates of the several former natural frequencies(C),the change ratios of the frequencies(R),and the assurance criterions of flexibilities(A).Some numerical simulation examples,such as,cantilever and truss with different damage extends and different damage locations were analyzed.The results indicate that the combined parameters are more suitable for the input patterns of neural networks than the other parameters alone.

Stable and Unstable Stationary Trajectories

J. M. Soriano

2005, 26(1): 47-52.

Abstract(2647) PDF(548)

Abstract:
The stability of stationary trajectories of a particular autonomous system is studied.The proof of the result is based upon continuation methods.

Shift of Shock Position for a Class of Nonlinear Singularly Perturbed Problems

MO Jia-qi, WANG Hui

2005, 26(1): 53-57.

Abstract(2591) PDF(644)

Abstract:
The shift of shock position for a class of nonlinear singularly perturbed problems is considered using a special and simple method.The location of the shock wave will be larger move,even from interior layer to the boundary layer when the boundary conditions change smaller.

Computational Technique for Flow in Blood Vessels With Porous Effects

Anil Kumar, C. L. Varshney, G. C. Sharma

2005, 26(1): 58-66.

Abstract(2739) PDF(482)

Abstract:
A finite element solution for the Navier-Stokes equations for steady flow under the porosity effects through a double branched two dimensional section of a three dimensional model of a canine aorta was obtained.The numerical solution involves transforming a physical coordinates to a curvilinear boundary fitted coordinate system.The steady flow,branch flow and shear stress under the porous effects were discussed in detail.The shear stress at the wall was calculated for Reynold's number of 1000 with branch to main aortic flow rate ratio as a parameter.The results are compared with earlier works involving experimental data and it has observed that our results are very close to the exact solutions.This work in fact is an improvement of the work of Sharma et al.(2001) in the sense that computations technique is economic and Reynolds number is large.

Explicit Square Conserving Schemes of Landau-Lifshitz Equation With Gilbert Component

SUN Jian-qiang, MA Zhong-qi, QIN Meng-zhao

2005, 26(1): 67-71.

Abstract(2573) PDF(715)

Abstract:
A kind of explicit square-conserving scheme is proposed for the Landau-Lifshitz equation with Gilbert component.The basic idea was to semidiscrete the Landau-Lifshitz equation into the ordinary differential equations is skewsymmtery matrix.Then the Lie group method and the Runge-Kutta (RK) method were applied to the ordinary differential equations.The square conserving property and the accuracy of the two methods were compared.Numerical experiment results show the Lie group method has the good accuracy and the square conserving property than the RK method.

On the Nonlinear Riemann Problems for General First Elliptic Systems in the Plane

LI Ming-zhong, SONG Jie

2005, 26(1): 72-76.

Abstract(2447) PDF(602)

Abstract:
The nonlinear Riemann problem for general systems of two first order linear and quasi-linear equations in the plane are considered.It translates them to singular integral equations and proves the existence of the solution by means of contract principle or general contract principle.The known results are generalized.

Analysis of Simple Shear Endochronic Equations for Finite Plastic Deformation

JIANG Wu-gui, HUANG Ming-hui

2005, 26(1): 77-82.

Abstract(2717) PDF(675)

Abstract:
Jaumann rate,generalized Jaumann rate,Fu rate and Wu rate were incorporated into endochronic equations for finite plastic deformation to analyze simple shear finite deformation.The results show that an oscillatory shear stress and normal stress response to a monotonically increasing shear strain occurs when Jaumann rate objective model is adopted for hypoelastic or endochronic materials.The oscillatory response is dependent on objective rate adopted,independent on elastoplastic models.Normal stress is unequal to zero during simple shear finite deformation.

Numerical Study on the Stability and Mixing of Vertical Round Buoyant Jet in Shallow Water

ZENG Yu-hong, HUAI Wen-xin

2005, 26(1): 83-91.

Abstract(2483) PDF(536)

Abstract:
The k-epsilon model was applied to establish the mathematical model of vertical round buoyant jet discharging into confined depth,and it was solved using the Hybrid Finite Analytic Method (HFAM).The numerical predictions demonstrate two generic flow patterns for different jet discharge and environmental parameters:( ) a stable buoyant flow discharge with the mixed warm fluid leaving the near-field warm in a surface warm water layer;( ) an unstable buoyant flow discharge with recirculation and re-entrainment of warm water in the near field.Furthermore,the mixing characters of vertical round buoyant jet were numerically predicted.Both the stability criterion and numerical predictions of bulk dilutions are in excellent agreement with Lee and Jirkas experiments and theory.

Explicit Solutions to the Coupled KdV Equations with Variable Coefficients

XU Gui-qiong, LI Zhi-bin

2005, 26(1): 92-98.

Abstract(2776) PDF(601)

Abstract:
By means of sn-function expansion method and cn-function expansion method,several kinds of explicit solutions to the coupled KdV equations with variable coefficients are obtained,which include three sets of periodic wave-like solutions.These solutions degenerate to solitary wave-like solutions at a certain limit.Some new solutions are presented.

Averaging Principle for Quasi-Geostrophic Motion Under Rapidly Oscillating Forcing

GAO Hong-jun, DUAN Jin-qiao

2005, 26(1): 99-110.

Abstract(2392) PDF(602)

Abstract:
A class of large scale geophysical fluid fows are modelled by the quasi-geostrophic equation.An averaging principle for quasi-geostrophic motion under rapidly oscil-lating(non-autonomous) forcing was obtained,both on finite but large time intervals and on the entire time axis.This includes comparison estimate,stability estimate,and convergence result between quasi-geostrophic motions and its averaged motions.Furthermore,the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.

On Plastic Anisotropy of Constitutive Model for Rate-Dependent Single Crystal

ZHANG Guang, ZHANG Ke-shi, FENG Lu

2005, 26(1): 111-119.

Abstract(2585) PDF(805)

Abstract:
An algorithm for single crystals was developed and implemented to simulate plastic anisotropy using a rate-dependent slip model.The proposed procedure was a slightly modified form of single crystal constitutive model of Sarma and Zacharia.Modified Euler method,together with New ton-Raphson method was used to integrate this equation which was stable and efficient.The model together with the developed algorithm was used to study three problems.First,plastic anisotropy was examined by simulating the crystal deformation in tension and plane strain compression respectively.Secondly,the orientation effect of some material parameters in the model and applied strain rate on plastic anisotropy for single crystal also is investigated.Thirdly,the influence of loading direction on the active slip system was discussed.

Cublic Spline Solutions of Axisymmetrical Nonlinear Bending and Buckling of Circular Sandwich Plates

HOU Chao-sheng, ZHANG Shou-kai, LIN Feng

2005, 26(1): 120-126.

Abstract(2700) PDF(629)

Abstract:
Cubic B-spline taken as trial function,the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation.The support could be elastic.A sandwich plate was assumed to be Reissner Model.The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads,uniformly distributed moments,radial pressure or radial prestress along the edge and their combination.Buckling load was calculated for the first time by nonlinear theory.Under action of uniformly distributed loads,results were compared with that obtained by the power series method.Excellences of the program written by the spline collocation method are wide convergent range,high precision and universal.