应用数学和力学

2005 Vol. 26, No. 4

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A Mechanism for the Excitation of Coherent Structures in the Wall Region of a Turbulent Boundary Layer

ZHANG Dong-ming, LUO Ji-sheng, ZHOU Heng

2005, 26(4): 379-385.

Abstract(2207) PDF(698)

Abstract:
The problem of how the coherent structures in the wall region of a turbulent boundary layer could be excited by the disturbances from the outer region was investigated by using direct numerical simulation(DNS)method.The results show that velocity disturbances at the upper boundary of the wall region could excite coherent structures in the wall region,thus offering a more comprehensive model for individual coherent structures.

Unsymmetrical Nonlinear Bending Problem of Circular Thin Plate With Variable Thickness

WANG Xin-zhi, ZHAO Yong-gang, JU Xu, ZHAO Yan-ying, YE Kai-yuan

2005, 26(4): 386-393.

Abstract(3048) PDF(559)

Abstract:
Firstly,the cross large deflection equation of circular thin plate with variable thickness in rectangular coordinates system was transformed into unsymmetrical large deflection equation of circular thin plate with variable thickness in polar coordinates system.This cross equation in polar coordinates system is united with radical and tangential equations in polar coordinates system,and then three equilibrium equations were obtained.Physical equations and nonlinear deformation equations of strain at central plane are substituted into superior three equilibrium equations,and then three unsym-metrical nonlinear equations with three deformation displacements were obtained'solution with expression of Fourier series is substituted into fundamental equations;correspondingly fundamental equations with expression of Fourier series were obtained.The problem was solved by modified iteration method under the boundary conditions of clamped edges.As an example,the problem of circular thin plate with variable thickness subjected to loads with cosin form was studied.Characteristic curves of the load varying with the deflection were plotted.The curves vary with the variation of the parameter of variable thickness.Its solution is accordant with physical conception.

Transversely Isotropic Damage Around Conducting Crack-Tip in Four-Point Bending Piezoelectric Beam

YANG Xin-hua, DONG Liang, WANG Cheng, CHEN Chuan-yao, HU Yuan-tai

2005, 26(4): 394-402.

Abstract(2309) PDF(546)

Abstract:
A static damage constitutive model was proposed on basis of the electrical enthalpy density,and then some characteristics of transversely isotropic damage were discussed.Finally,the effects of both crack depth and applied loads on damage distributions were investigated through numerically analyzing transversely isotropic damage in a four-point bending PZT-PIC151 beam with a central conducting crack'some conclusions were given:1)Crack depth and mechanical loading have great influence on both mechanical and electrical damages.With their increment,the damages at crack-tip obviously increase and their region sizes also expand.2)Effects of electrical loading on the two kinds of damages are obviously different.Electrical loading monotonously changes magnitude but region size of mechanical damage,whose effect on electrical damage is very complex.

Oscillation Criteria for Second Order Nonlinear Differential Equation With Damping

LUO Hui, ZHUANG Rong-kun, GUO Xing-ming

2005, 26(4): 403-410.

Abstract(2340) PDF(637)

Abstract:
By the generalized Riccati transformation and the integral averaging technique'some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed'some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.

Analysis and Applied Study of Dynamic Characteristics of Chaotic Repeller in Complicated System

MA Jun-hai, REN Biao, CHEN Yu-shu

2005, 26(4): 411-417.

Abstract(2539) PDF(721)

Abstract:
Fractal characters and fractal dimension of time series created by repeller in one complicated system were studied and the time series were reconstructed by applying theory of phase space reconstruction for chaotic times series,for purpose of modeling and prediction of time series created by chaotic repellers.The influence of zero-mean treatment,Fourier filter on prediction for time series were studied.The choice of prediction sample affects the relative error and the prediction length which were also under good concern.Result shows the modeling and prediction model provided here is practical for time series created by chaotic repellers.Zero-mean treatment has changed prediction result quantitively for chaotic repeller sample data.But using Fourier filter may decrease the prediction precision.This is theoretical and practical for study on chaotic repeller of complicated system.

What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation

LUO Hai-ying, LI Ji-bin

2005, 26(4): 418-425.

Abstract(2777) PDF(898)

Abstract:
For a given system,by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle,the exact computation formula of the third separatrix values named by Leontovich for the multiple limit cycle bifurcation was given,which was one of the main criterions for the number of limit cycles bifurcated from a homoclinic orbit and the stability of the homoclinic loop,and a computation formula for higher separatrix values was conjectured.

Ergodic Theorem for Infinite Iterated Function Systems

O Hyong-chol, Ro Yong-hwa, Kil Won-gun

2005, 26(4): 426-430.

Abstract(2838) PDF(775)

Abstract:
A set of contraction maps of a metric space is called an iterated function systems.Iterated function systems with condensation can be considered infinite iterated function systems.Infinite iterated function systems on compact metric spaces were studied.Using the properties of Banach limit and uniform contractiveness it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces satisfy ergodicity.So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity,too.

Dependence of the Modulus of Elasticity and the Thermal Conductivity on the Reference Temperature in Generalized Thermoelasticity for an Infinite Material With a Spherical Cavity

Hamdy M. Youssef

2005, 26(4): 431-436.

Abstract(2637) PDF(527)

Abstract:
The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface.Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace tranforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.

Moving Inclined Load at Boundary Surface

Rajneesh Kumar, Praveen Ailawalia

2005, 26(4): 437-446.

Abstract(2697) PDF(558)

Abstract:
The analytic expressions for the displacement components and stresses at any point of an infinite micropolar orthotropic elastic medium with an overlying elastic half space as a result of moving inclined load of arbitrary orientation were obtained.The inclined load was assumed to be a linear combination of a normal load and a tangential load.The eigen value approach using Fourier transformas was employed and the transform was inverted by using a numerical technique.The numerical results were illustrated graphically for aluminium epoxy composite.

Equivalence of the Refined Theory and the Decomposed Theorem of an Elastic Plate

ZHAO Bao-sheng, WANG Min-zhong

2005, 26(4): 447-455.

Abstract(2532) PDF(837)

Abstract:
A connection between Cheng's refined theory and Gregory's decomposed theorem is analyzed.The equivalence of the refined theory and the decomposed theorem is given.Using operator matrix determinant of partial differential equation,Cheng gained one equation,and he substituted the sum of the general integrals of three differential equations for the equation's solution.But he didn't prove the rationality of substitute.There,a whole proof for the refined theory from Papkovich-Neuber solution was given.At first expressions were obtained for all the displacements and stress components in term of the mid-plane displacement and its derivatives.Using Lur'e method and the theorem of appendix,the refined theory was given.At last,using basic mathematic method,the equivalence between Cheng's refined theory and Gregory's decomposed theorem was proved,i.e.,Cheng's bi-harmonic equation,shear equation and transcendental equation are equivalent to Gregory's interior state,shear state and Papkovich-Fadle state,respectively.

Multi-Scale Coherent Structures in Turbulent Boundary Layer Detected by Locally Averaged Velocity Structure Functions

LIU Jian-hua, JIANG Nan, WANG Zhen-dong, SHU Wei

2005, 26(4): 456-464.

Abstract(2741) PDF(788)

Abstract:
Abstract:The time sequence of longitudinal velocity component at different vertical locations in turbulent boundary layer was finely measured in a wind tunnel.The concept of coarse-grained velocity structure functions,which describes the relative motions of straining and compressing for multi-scale eddy structures in turbulent flows,was put forward based on the theory of locally multi-scale average.Based on the consistency between coarse-grained velocity structure function and Harr wavelet transformation,detecting method was presented,by which the coherent structures and their intermittency was identified by multi-scale flatness factor calculated by locally average structure function. Phase-averaged evolution course for multi-scale coherent eddy structures in wall turbulence were extracted by this conditional sampling to educe scheme.The dynamics course of multi-scale coherent eddy structures and their effects on statistics of turbulent flows were studied.

Fundamental Resonance and Bifurcation of Large Generator End Winding When Its Clamping Plates Are Loose

HU Yu-da, QIU Jia-jun, TA Na

2005, 26(4): 465-473.

Abstract(2816) PDF(658)

Abstract:
Vibration problems of a segment of winding between two clamping plates are studied when the clamping plates,which are used to fix stator end winding,are loose.First,magnetic induction expressions of the winding when the generator was running were given by using separation of variables method.Also,the expressions of the winding electromagnetic force and dry friction force between loosing clamping plates were gotten.Secondly,a mechanical model,which was used to study nonlinear vibration problem of the winding,was set up.Fundamental resonance was analyzed by using multiple scales method,and a resonance equation of amplitude and frequency in steady state was given. Then stability,bifurcation and singularity of the steady solution were studied.Criterions of stability and transition set of the bifurcation equation were obtained.At last,through numerical calculations, resonance curves were obtained.The results are helpful for analysis and protection of generator accidents.

Stratified Model for Estimating Fatigue Crack Growth Rate of Metallic Materials

YANG Yong-yu, LIU Xin-wei, YANG Fan

2005, 26(4): 474-480.

Abstract(2440) PDF(483)

Abstract:
The curve of relationship between fatigue crack growth rate and the stress strength factor amplitude represented an important fatigue property in designing of damage tolerance limits and predicting life of metallic component parts.In order to have a more reasonable use of testing data,samples from population were stratified suggested by stratified random sample model(SRAM).The data in each stratum corresponded to the same experiment conditions.A suitable weight was assigned to each stratified sample according to the actual working states of the pressure vessel,so that the estimation of fatigue crack growth rate equation was more accurate for practice.An empirical study shows that the SRAM estimation by using fatigue crack growth rate data from different stoves is obviously better than the estimation from simple random sample model.

Taylor Expansion Method for the Nonlinear Evolution Equations

HE Yin-nian

2005, 26(4): 481-488.

Abstract(3128) PDF(1172)

Abstract:
A new numerical method of integrating the nonlinear evolution equations,namely the Taylor expansion method,was presented.The standard Galerkin method can be viewed as the 0-th order Taylor expansion method;while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method.Moreover,the existence of the numerical solution and its convergence rate were proven.Finally,a concrete example,namely the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided.The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.

Unfolding of Multiparameter Equivariant Bifurcation Problems With Two Groups of State Variables Under Left-Right Equivalent Group

GUO Rui-zhi, LI Yang-cheng

2005, 26(4): 489-496.

Abstract(2324) PDF(713)

Abstract:
Based on the left-right equivalent relation of smooth map-germs in singularity theory,the unfoldings of multiparameter equivariant bifurcation problems with respect to left-right equivalence are discussed.The state variables of such an equivariant bifurcation problem were divided into two groups,in which the first can vary independently,while the others depend on the first in the varying process.By applying related methods and techniques in the unfolding theory of smooth map-germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.

Difference Schemes Basing on Coefficient Approximation

MOU Zong-ze, LONG Yong-xing, QU Wen-xiao

2005, 26(4): 497-504.

Abstract(2703) PDF(549)

Abstract:
In respect of variable coefficient differential equations,the equations of coefficient function approximation were more accurate than the coefficient to be frozen as a constant in every discrete subinterval.Usually,the difference schemes constructed based on Taylor expansion approximation of the solution don't suit the solution with sharp function.Introducing into local bases to be combined with coefficient function approximation,the difference can well depict more complex physical phenomena,for example,boundary layer as well as high oscillatory,with sharp behavior.The numerical test shows the method is more effective than the traditional one.