应用数学和力学

2000 Vol. 21, No. 2

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Existence of Solutions for Nonlinear Impulsive Hammerstein Integral Equations in Banach Spaces

Chen Fangqi, Chen Yushu

2000, 21(2): 111-118.

Abstract(2326) PDF(677)

Abstract:
The existence of solutions for nonlinear impulsive Hammerstein integral equations with infinite numbers of moments of impulse effect on the infinite interval R⁺ in Banach spaces is studied.By means of M^L nch fixed point theorem,an existence theorem of solutions is obtained.The result is demonstrated by means of an infinite system for impulsive integral equations.

Analysis of Thermal Post-Buckling of Heated Elastic Rods

Li Shirong, Cheng Changjun

2000, 21(2): 119-125.

Abstract(2450) PDF(856)

Abstract:
Based on the non-linear geometric theory of extensible rods,an exact mathematical model of thermal post-buckling behavior of uniformly heated elastic rods with axially immovable ends is developed,in which the arc length s(x)of axial line and the longitudinal displacement u(x)are taken as the basic unknown functions.This is a two point boundary value problem of first order ordinary differential equations with strong non-linearity.By using shooting method and analytical continuation, the nonlinear boundary value problems are numerically solved.The thermal post-buckled states of the rods with transversely simply supported and clamped ends are obtained respectively and the corresponding numerical data tables and characteristic curves are also given.

The Fractional Dimension Identification Method of Critical Bifurcated Parameters of Bearing-Rotor System

Zhao Yucheng, Yuan Shuqing, Xiao Zhonghui, Xu Qingyu

2000, 21(2): 126-130.

Abstract(2485) PDF(550)

Abstract:
The stable problem of rotor system,seen in many fields,has been cared for more. Nowadays the reasons of most losing stability are caused by nonlinear behaviors.This presents higher requirements to the designing of motor system:considering nonlinear elements,avoiding the unstable parameter points or regions where nonlinear phenomena will be presented.If a family of time series of the unbeknown nonlinear dynamical system can only be got(may be polluted by noise),how to identify the change of motive properties at different parameters?In this paper through the study of Jeffcott rot or system,the result that using the figures between the fractional dimension of time-serial and parameter can be gained,and the critical bifurcated parameters of bearing-rotor dynamical system can be identified.

Numerical Computation of the Flow Around Two Square Cylinders Arranged Side by Side

Chen Suqin, Gu Ming, Huang Ziping

2000, 21(2): 131-146.

Abstract(2046) PDF(745)

Abstract:
The numerical method is used to calculate the flow around two square cylinders arranged side by side and the mean and fluctuating aerodynamic forces,Strouhal numbers and power spectrum of lift force and drag force are obtained.An improved MAC method proposed by Chen Suqin et al., which uses three order upwind scheme to discretize the convection term and uses multigrid method to solve the Poisson equation for pressure is applied to simulate the flow around two square cylinders arranged side by side.Results show that the interference characteristic of two square cylinders arranged side by side is completely different with the different spacing ratio,when the spacing ratio is smaller than a certain critical value,the gap flow between two cylinders is biased to one side in a stable or unstable manner.

A Second-Order Dynamic Subgrid-Scale Stress Model

Gong Hongrui, Chen Shiyi, He Guowei, Cao Nianzhen

2000, 21(2): 147-153.

Abstract(2546) PDF(1254)

Abstract:
A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed.A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number(Taylor microscale Reynolds number R_λ=102~216)for homogeneous,isotropic forced flow,decaying flow,and homogeneous rotating flow.Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-oder dynamic models.

The Vector Fields Admitting One-Parameter Spatial Symmetry Group and Their Reduction

Huang Debin, Zhao Xiaohua

2000, 21(2): 154-160.

Abstract(2334) PDF(726)

Abstract:
For a n-dimensional vector fields preserving some n-form,the following conclusion is reached by the method of Lie group.That is,if it admits a one-parameter,n-form preserving symmetry group,a transformation independent of the vector field is constructed explicitly,which can reduce not only dimesion of the vector field by one,but also make the reduced vector field preserve the corresponding(n-1)-form.In particular,while n=3,an important result can be directly got which is given by Mezie and Wiggins in 1994.

Some Theorems in the X-M-PN Space

Zhu Chuanxi

2000, 21(2): 161-163.

Abstract(2321) PDF(742)

Abstract:
A new concept of the X-M-PN space is introduced,and the acute angle principle in the X-M-PN space is proved.Meanwhile,some new results are obtained.

The Virtual Work Principle and Linear Complementary Method for Coupling Analysis of Elasto-Plastic Damage Structure

Ma Jinghuai

2000, 21(2): 164-170.

Abstract(2682) PDF(607)

Abstract:
The virtual displacement principle of elasto-plastic damage mechanics is presented.A linear complementary method for elasto-plastic damage problem is proposed by using FEM technique. This method is applicable to solving the damage structure analysis of hardened and softened nonlinear material.

Multi-Solitary Wave Solutions for Variant Boussinesq Equations and Kupershmidt Equations

Zhang Jiefang

2000, 21(2): 171-175.

Abstract(2455) PDF(853)

Abstract:
Using the homogeneous balance method introduced by Wang Mingliang,the multi-solitary wave solutions are obtained for the variant Boussinesq equation and Kupershmidt equation.The Wang's result is a special case of above results for the variant Boussinesq equation.

The Solving Problem and the Difference Solving Process for the Shear of a Bonded Elastic Bodies

Zhang Luming, Chang Qianshun

2000, 21(2): 176-184.

Abstract(2473) PDF(614)

Abstract:
A long elastomer with rectangular section bonded between two parallel rigid surfaces will come about deformation because of the role of two opposite shear forces in both the top and bottom plate.The mathematic model of the deformation is deduced and a new difference solving process is proposed.For boundary condition with singularity,a detailed analysis and deduction is given and a new rational and effective discrete boundary condition is proposed.Simulate computation demonstrates that the result is identical with qualitative analysis.Therefore,a new and functional numerical method and quantitative analysis method are provided.

Analysis and Calculation of the Nonlinear Stability of the Rotational Composite Shell

Huang Jinsong, Zeng Guangwu

2000, 21(2): 185-191.

Abstract(2514) PDF(571)

Abstract:
By adopting the energy method,a new method to calculate the stability of the composite shell of revolution is presented.This method takes the influence of nonlinear prebuckling deformations and stresses on the buckling of the shell into account.The relationships between the prebuckling deformations and strains are calculated by nonlinear Kûrmûn equations.The numerical method is used to calculate the energy of the total system.The nonlinear equations are solved by combining gradient method and amendatory Newton iterative method.The computer program is also developed.An example is given to demonstrate the accuracy of the method presented.

Nonlinear Vibration of Circular Sandwich Plate Under the Uniformed Load

Du Guojun, Li Huijian

2000, 21(2): 192-200.

Abstract(2402) PDF(587)

Abstract:
The differential equations of the axisymmetric large amplitude free vibration for circular sandwich plates under static load are derived,and a set of nonlinearly coupled algebraic and differential eigenvalue equations of the problem are formulated following an assumed time mode approach suggested.The analytic solutions are presented and a relation for amplitude frequency-load of the plates with edge clamped is derived by modified iteration method.The effects of static load on vibrations of plates are investigated.

Singular Perturbation of Second Order Nonlinear System With Boundary Perturbation

Chen Yusen

2000, 21(2): 201-208.

Abstract(2314) PDF(647)

Abstract:
The singular perturbation of boundary value problem of second order nonlinear system of differential equations with integral operators and boundary perturbation is discussed.Under the suitable assumed conditions,by the technique of diagonalization,the existence of the solutions is proved and its remainder term is estimated.

Convergence and Stability of Recursive Damped Least Square Algorithm

Chen Zengqiang, Lin Maoqiong, Yuan Zhuzhi

2000, 21(2): 209-214.

Abstract(3268) PDF(1384)

Abstract:
The recursive least square is widely used in parameter identification.But it is easy to bring about the phenomena of parameters burst-off.A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed.This is done by normalizing the measurement vector entering into the identification algorithm.It is shown that the parametric distance converges to a zero mean random variable.It is also shown that under persistent excitation condition,the condition number of the adaptation gain matrix is bounded,and the variance of the parametric distance is bounded

Existence of Boundary Value Problems for TFD Equation in Quantum Mechanics

Wang Guocan, Ding Peizhu, Zheng Chengde

2000, 21(2): 215-220.

Abstract(2460) PDF(621)

Abstract:
TFD equation in quantum mechancis is established.The existence theorems of the solutions are obtained by singular boundary value problem theory of ordinary differential equation and upper and lower solution method.