应用数学和力学

2003 Vol. 24, No. 8

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Stability Analysis in Spatial Mode for Channel Flow of Fiber Suspensions

LIN Jian-zhong, YOU Zhen-jiang

2003, 24(8): 771-778.

Abstract(2335) PDF(528)

Abstract:
Different from previous temporal evolution assumption,the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions.The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically.The results show that,the flow instability is governed by a parameter Hwhich represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid.Anincrease of Hleads to araise of the critical Reynolds number,adecrease of corresponding wave number,a slowdown of the decreasing of phase velocity,a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity.Although the unstable region is reduced on the whole,longwave disturbances are susceptible to fibers.

Bifurcation and Chaos of the Circular Plates on the Nonlinear Elastic Foundation

QIU Ping, WANG Xin-zhi, YEH Kai-yuan

2003, 24(8): 779-784.

Abstract(2267) PDF(675)

Abstract:
According to the large amplitude equation of the circular plate on nonlinear elastic foundation,elastic resisting force has linearitem,cubic nonlinearitem and resisting bend elasticitem.Anonlinear vibration equation is obtained with the method of Galerkin under the condition of fixed boundary.Floquet exponent at equilibrium point is obtained without external excitation.Its stability and condition of possible bifurcation is analysed.Possible chaotic vibration is analysed and studied with the method of Melnikov with external excitation.The critical curves of the chaotic region and phase figure under some foundation parameters are obtained with the method of digital artificial.

Aerodynamic Design Method of Cascade Profiles Based on Load and Blade Thickness Distribution

YAO Zheng, LIU Gao-lian

2003, 24(8): 785-790.

Abstract(2381) PDF(613)

Abstract:
Acascade profile design method was proposed using the aerodynamic load and blade thickness distribution as the design constraints,which were correspondent to the demands from the aerodynamic characteristics and the blade strength.These constraints,together with all the other boundary conditions,were involved in the stationary conditions of a variational principle,in which the anglefunction was employed as the unknown function.The angle-function(i.e.the circumferential angular coordinate) was defined in the image plane composed of the stream function coordinate(circumferential direction) and streamline coordinate.The solution domain,i.e.,the blade-to-blade passage,was transformed into a square in the image plane,while the blade contour was projected to a straight line;thus,the difficulty of the unknown blade geometry was avoided.The finite element method was employed to establish the calculation code.Applications show that this method can satisfy the design requests on the blade profile from both aerodynamic and strength respects.In addition,quite different from the most inverse-problem approaches that often encounter difficulties in the convergence of iteration,the present method shows a stable and fast convergence tendency.This will be significant for engineering applications.

On the Asymptotic Behaviour of Solutions of Certain Fifth-Order Ordinary Differential Equations

Cemil Tun

2003, 24(8): 791-798.

Abstract(2291) PDF(593)

Abstract:
The sufficient conditions are given for all solutions of certain non-autonomous differential equation to be uniformly bounded and convergence to zero as t→∞.The result given includes and improves that result obtained by Abou-El-Ela & Sadek.

Comparison of Two Methods in Satellite Formation Flying

GAO Yun-feng, BAOYIN He-xi, LI Jun-feng

2003, 24(8): 799-804.

Abstract(4252) PDF(977)

Abstract:
Recently,the research of dynamics and control of the satellite formation flying has been attracting a great deal of attentions of the researchers.The theory of the research was mainly based on Clohessy-Wiltshire's(C-W's) equations,which describe the relative motion between two satellites.But according to some special examples and qualitative analysis,neither the initial parameters nor the period of the solution of C-W's equations accord with the actual situation,and the conservation of energy is no longer held.Anew method developed from orbital element description of single satellite,named relative orbital element method(ROEM),was introduced.This new method,with clear physics conception and wide application range,overcomes the limitation of C-W's equation,and the periodic solution is a natural conclusion.The simplified equation of the relative motion is obtained when the eccentricity of the main satellite is small.Finally,the results of the two methods(C-W's equation and ROEM) are compared and the limitations of C-W's equations are pointed out and explained.

Absolute Stabilization Related to Circle Criterion: an LMI-Based Approach

YANG Ying, HUANG Lin

2003, 24(8): 805-811.

Abstract(2590) PDF(1315)

Abstract:
Amethod is proposed for synthesizing output feedback controllers for nonlinear Lur'e systems.The problem of designing an output dynamic controller for uncertain-free systems and systems subject to multiplicative norm-bounded perturbations in the linear part were proposed respectively.The procedure is based on the use of the absolute stability,through the circle criterion,and a linear matrix inequalities(LMI) formulation.The controller existence conditions are given in terms of existence of suitable solutions to a set of parameter-dependent LMIs.

Analysis on the Cohesive Stress at Half Infinite Crack Tip

WANG Li-min, XU Shi-lang

2003, 24(8): 812-820.

Abstract(2757) PDF(628)

Abstract:
The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip.Based on fracture character of quasi-brittle materials,a mechanical analysis model of half infinite crack with cohesive stress is presented.A pair of integral equations is established according to the superposition principle of crack opening displacement in solids,and the fictitious adhesive stress is unknown function.The properties of integral equations are analyzed,and the series function expression of cohesive stress is certified.By means of the data of actual crack opening displacement,two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation.They are the integral transformation method for continuous displacement of actual crack opening,and the least square method for the discrete data of crack opening displacement.The calculation examples of two approaches and associated discussions are given.

Flow Properties of a Dusty-Gas Point Source in a Supersonic Free Stream

WANG Bo-yi, Alexander N. Osiptsov, Misha A. Teverovshii

2003, 24(8): 821-826.

Abstract(2672) PDF(533)

Abstract:
By using Lagrangian method,the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained.It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves.In this region,formation of "multi-layer structure" inparticle distribution with alternating low-and high-density layers is revealed.Moreover,sharp accumulation of particles occurs near the envelopes of particle trajectories.

Optimal Selection for the Weighted Coefficients of the Constrained Variational Problems

WEI Ming, LIU Guo-qing, WANG Cheng-gang, GE Wen-zhong, XU Qin

2003, 24(8): 827-834.

Abstract(2224) PDF(719)

Abstract:
The aim is to putforward the optimal selecting of weights in variational problem in which the linear advection equation is used as constraint.The selection of the functional weight coefficients(FWC) is one of the key problems for the relevant research.It was arbitrary and subjective to some extent presently.To overcome this difficulty,the reasonable assumptions were given for the observation field and analyzed field,variational problems with "weak constraints" and "strong constraints" were considered separately.By solving Euler.sequation with the matrix theory and the finite difference method of partial differential equation,the objective weight coefficients were obtained in the minimumvariance of the difference between the analyzed field and idealfield.Deduction results show that theoretically the optimal selection indeed exists in the weighting factors of the cost function in the means of the minimal variance between the analysis and ideal field in terms of the matrix theory and partial differential(corresponding difference) equation,if the reasonable assumption from the actual problem is valid and the differnece equation is stable.It may realize the coordination among the weight factors,numerical models and the observational data.With its theoretical basis as well as its prospects of applications,this objective selecting method is probably a way towards the finding of the optimal weighting factors in the variational problem.

Generalization of Steiner Formula for the Homothetic Motions on the Planar Kinematics

N. Kuruoglu, M. Dldl, A. Tutar

2003, 24(8): 835-838.

Abstract(2070) PDF(609)

Abstract:
The Steiner formula and the mixture area formula given by Mller were expressed under the l-parameter closed planar homothetic motions in the complex sense.Also,using the generalization of Steiner formula,the result of Holditch theorem for homothetic motions is got.In the case of the homothetic scale h≡l the results given by Mller are obtained as aspecial case.

Level Set Methods Based on Distance Function

WANG De-jun, TANG Yun, YU Hong-chuan, TANG Ze-sheng

2003, 24(8): 839-848.

Abstract(3626) PDF(2160)

Abstract:
Some basic problems on the levelset methods were discussed,such as the method used to preserve the distance function,the existence and uniqueness of solution for the level set equations.The main contribution is to prove that in a neighborhood of the initial zero level set,the level set equations with the restriction of the distance function have a unique solution,which must be the signed distance function with respect to the evolving surface.Some skillful approaches were used: Noticing that any solution for the original equation was a distance function,the original level set equations were transformedinto a simpler alternative form.Moreover,since the new system was not a classical one,the system was transformed into an ordinary one,for which the implicit function method was adopted.

Paradox Solution on Elastic Wedge Dissimilar Materials

YAO Wei-an, ZHANG Bing-ru

2003, 24(8): 849-856.

Abstract(2447) PDF(558)

Abstract:
According to the Hellinger Reissner variational principle and introducing proper transformation of variables,the problem on elastic wedge dissimilar materials can be led to Hamiltonian system,so the solution of the problem can be got by employing the separation of variables method and symplectic eigenfunction expansion under symplectic space,which consists of original variables and their dual variables.The eigenvalue -1 is a special one of all symplectic eigenvalue for Hamiltonian system in polar coordinate.In general,the eigenvalue 1 is a single eigenvalue,and the classical solution ofan elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is got directly by solving the eigenfunction vector for eigenvalue 1.But the eigenvalue 1 becomes a double eigenvalue when the vertex angles and modulus of the materials satisfy certain definite relationships and the classical solution for the stress distribution becomes infinite at this moment,that is,the paradox should occur.Here the Jordan form eigenfunction vector for eigenvalue 1 exists,and solution of the paradox on elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is obtained directly by solving this special Jordan form eigenfunction.The result shows again that the solutions of the special paradox on elastic wedge in the classical theory of elasticity are just Jordan form solutions in symplectic space under Hamiltonian system.

Nonlinear Random Stability of Viscoelastic Cable With Small Curvature

LI Ying-hui, GAO Qing

2003, 24(8): 857-864.

Abstract(2218) PDF(465)

Abstract:
The non-linear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied.The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material.Amathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first.And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted.Finally,the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.

Interaction of a Screw Dislocation in the Interphase Layer With the Inclusion and Matrix

JIANG Chi-ping, LIU You-wen, XU Yao-ling

2003, 24(8): 865-873.

Abstract(2402) PDF(597)

Abstract:
The interaction of a screw dislocation in the interphase layer with the circular inhomogeneity and matrix was dealt with.An efficient method for multiply connected regions was developed by combining the sectionally subholomorphic function theory,Schwarz symmetric principle and Cauchy integral technique.The Hilbert problem of the complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer,resulting in an explicit series solution.By using the present solution the interaction energy and force acting dislocation were evaluated and discussed.

Chaos in Transiently Chaotic Neural Networks

RUAN Jiong, ZHAO Wei-rui, LIU Rong-song

2003, 24(8): 874-880.

Abstract(2201) PDF(647)

Abstract:
It was theoretically proved that one-dimensional transiently chaotic neural networks have chaotic structure in sense of Li-Yorke theorem with some given assumptions using that no division implies chaos.In particular,it is further derived sufficient conditions for the existence of chaos in sense of Li-Yorke theorem in chaotic neural network,which leads to the fact that Aihara has demonstrated by numerical method.Finally,an example and numerical simulation are shown to illustrate and reinforce the previous theory.