应用数学和力学

2002 Vol. 23, No. 5

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Second Order Approximation Solution of Nonlinear Large Deflection Problem of Yongjiang Railway Bridge in Ningbo

CHIEN Wei-zang

2002, 23(5): 441-451.

Abstract(7586) PDF(4195)

Abstract:
The solution and computational aspects on nonlinear deflection of Yongjiang Railway Bridge in Ningbo were investigated.An approximate iteration algorithm on nonlinear governing equation was presented,and the obtained results show that,if altitude difference and span of the riverbanks are taken as 5 meters and 100 meters,respectively,the maximum gradient in the middle of the bridge exceeds 5%,much larger than maximum allowance gradient in railway design code.Therefor,a new solution scheme for decreasing gradient of the bridge is put forward,that is,the altitude difference between two riverbanks can be decreased to about 1/10 of the initial magnitude by building roadbeds with 0.5% gradient and 1 kilometer length at two riverbanks.As a direct result,the deflection gradient of the railway bridge is much reduced and the value is between 0.5%~0.6%.

2002, 23(5): 452-452.

Abstract(1800) PDF(639)

Abstract:

Dynamic Response of Plates Due to Moving Vehicles Using Finite Strip Method

CHENG Yuan-sheng, Y K CHEUNG, F T KAU

2002, 23(5): 453-458.

Abstract(2515) PDF(606)

Abstract:
Dynamic response of beam-like structures to moving vehicles has been extensively studied.However,the study on dynamic response of plates to moving vehicles has so far received but scant attention.A plate-vehicle strip for simulating the interaction between a rectangular plate and moving vehicles was described.For the portion of strips that are in direct contact with the moving vehicles,the plate-vehicle strips were empolyed.Conventional plate finite strips were used to model the portion of strips that are not directly under the action of moving vehicles.In the analysis,each moving vehicle is idealized as a one-foot dynamic system with the unsprung mass and sprund mass interconnected by a spring and a dashpot.The numerical results obtained from the proposed method agree well with available results.

The Three-Dimensional Fundamental Solution to Stokes Flow in the Oblato Spheroidal Coordinates With Applications to Multiple Spheroid Problems

ZHUANG Hong, YAN Zong-yi, WU Wang-yi

2002, 23(5): 459-476.

Abstract(3154) PDF(741)

Abstract:
A new three-dimensional fundamental solution to the Stokes flow was proposed by transforming the solid harmonic functions in Lamb.s solution into expressions in terms of the oblate spheroidal coordinates.These fundamental solutions are advantageous in treating flows past an arbitrary number of arbitrarily positioned and oriented oblate spheroids.The least squares technique was adopted herein so that the convergence difficulties often encountered in solving three-dimensional problems were completely avoided.The examples demonstrate that present approach is highly accurate,consistently stable and computationally effecient.The oblate spheroid may be used to model a variety of particle shapes between a circular disk and a sphere.For the first time,the effect of various geometric factors on the forces and torques exerted on two oblate spheroids were systematically studied by using the proposed fundamental solutions.The generality of this approach was illustrated by two problems of three spheroids.

Classification of Bifurcations for Nonlinear Dynamical Problems With Constraints

WU Zhi-qiang, CHEN Yu-shu

2002, 23(5): 477-482.

Abstract(2880) PDF(751)

Abstract:
Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind of constrained one in intrinsic quality because its amplitude is always non-negative.Classification of the bifurcations with the type of constraint was discussed.All its six types of transition sets are derived,in which three types are newly found and a method is proposed for analyzing the constrained bifurcation.

Research on the Effect of Cylinder Particles on the Turbulent Properties in Particulate Flows

LIN Jian-zhong, LIN Jiang, SHI Xing

2002, 23(5): 483-488.

Abstract(2479) PDF(635)

Abstract:
The fluid fluctuating velocity equations which include the term of cylinder particles were established.The turbulent intensity and Reynolds stress of fluid were obtained by averaging fluctuating velocity based on the solution of the fluctuating velocity equations.Above approach was used to solve the channel turbulent flows,and computational results were compared with the experimental ones for the case of single phase flow.The effects of volume fraction of particles,the ratio of particle length to diameter and the particle relaxation time on turbulent properties were illustrated by changing cylinder particle parameters.It is shown that particles play a restraining role to turbulent properties in the flows.The degree of restraint is directly proportional to the volume fraction of particle,the ratio of particle length to diameter and inversely proportional to particle relaxation time.

Localized Coherent Structures of the(2+1)-Dimensional Higher Order Broer-Kaup Equations

ZHANG Jie-fang, LIU Yu-lu

2002, 23(5): 489-496.

Abstract(2289) PDF(669)

Abstract:
By using the extended homogeneous balance method,the localized cohernet structures are studied.A nonlinear transformation was first established,and then the linearization form was obtained based on the extended homogeneous balance method for the higher order(2+1)-dimensional Broer-Kaup equations.Starting from this linearization form equation,a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed.The quite rich localized coherent structures were revealed.This method,which can be generalized to other(2+1)-dimensional nonlinear evolution equation,is simple and powerful.

The Concave or Convex Peaked and Smooth Soliton Solutions of Camassa-Holm Equation

TIAN Li-xin, XU Gang, LIU Zeng-rong

2002, 23(5): 497-506.

Abstract(2905) PDF(737)

Abstract:
The traveling wave soliton solutions and pair soliton solution to a class of new completely integralbe shallow water equation,Camassa-Holm equation are studied.The concept of concave or convex peaked soliton and smooth soliton were introduced.And the research shows that the traveling wave solution of that equation possesses concave and convex peaked soliton and smooth soliton solutions with the peakson.Simultaneously by applying Backlund transformation the new pair soliton solutions to this class of equation are given.

Set-Valued Extension of Operators via Steiner Selections(Ⅰ)-Theoretical Results

TERAN PEDRO, L PEZ-D1AZ MIGUEL

2002, 23(5): 507-517.

Abstract(2276) PDF(730)

Abstract:
A way to extend operators in spaces of continuo us functions to spaces of continuo us set-valued functions is proposed.This extension is developed through the Steiner selections of the set-valued functions.Their properties and chara cteristics of the convergence of sequences of operators of this class are studied.In Part ò of this series some applications to approximation theory will be shown.

Set-Valued Extension of Operators via Steiner Selections(Ⅱ)-Applications to Approximation

TERAN Pedro, L PEZ-DIAZ MIGUEL

2002, 23(5): 518-525.

Abstract(2029) PDF(565)

Abstract:
On the basis of Part(Ⅰ) of this series some applications to the approximation of set-valued functions are obtained: Korovkin type theorems,a method to extend classical approximation operators to the set-valued setting and a Jackson type estimate.

The Properties of a Kind of Random Symplectic Matricess

YAN Qing-you

2002, 23(5): 526-532.

Abstract(2420) PDF(683)

Abstract:
Several important properties of a kind of random symplectic matrix used by A.Bunse-Gerstner and V.Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by orthogonal similar transformation.2) Its condition unmber is a constant.3) The condition unmber of it is about 2.618.

Buckling Analysis of Woven Fabric Under Uniaxial Tension in Arbitrary Direction

ZHANG Yi-tong, XU Jia-fu

2002, 23(5): 533-540.

Abstract(2239) PDF(679)

Abstract:
The buckling of a fabric sheet subjected to a uniaxial tension in a direction making arbitrary angle,θ(0<θ<90°) say,with respect to that of warp is investigated.The equation to determine the buckling direction angle,B say,was obtained and,as illustration,the solution curves of the equation for θ=45° and θ=30° were plotted.It is shown that when the fabric sheet is subjected to tension in non-warp/ non-weft direction the out-of-plane buckling of fabric is possible,two buckling modes(flexural and extensional modes) and the both corresponding buckling conditions are obtained.The results given by Zhang and Fu(2001) are the special cases of this paper.

Proper Application of a Kind of Matrix Construction Method in Physical Parameter Identification of Dynamic Model

LI Shu, ZHANG Fang, WANG Bo, ZHANG Xiao-gu

2002, 23(5): 541-547.

Abstract(3177) PDF(642)

Abstract:
The expressions of matrix construction by using the singular value decomposition(SVD) are applied to the physics parameter identification of dynamic model.Then,based upon to the characteristics of a kind of matrix construction method,the orders of the parameter identification model can be reduced.After reducing,the mathematics and physics correspondence relations between the subsystem and the original system are distinct.the the condensation errors can be avoided.The numerical example shows the benefit of the presented methodology.

On the Isometric Isomorphism of Probabilistic Metric Spaces

LIU Ming-xue

2002, 23(5): 548-550.

Abstract(3421) PDF(931)

Abstract:
There are two kinds of isometric isomorpism in probabilistic meteric space theory.The first is that a PM space(E,F) is isometrically isomorphic to another PM space(E,F),and the second is that a PM space(E,F) is isometrically isomorphic to a generating space of quasi-metric family(E,d_r,r(0,1)).This paper establishes the connection between the two kinds of isometric isomorphism.