应用数学和力学

2002 Vol. 23, No. 9

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Unsymmetrical Large Deformation Problem of Orthotropic Plates

WANG Xin-zhi, ZHAO Yong-gang, YEH Kai-yuan, HUANG Da-wen

2002, 23(9): 881-888.

Abstract(2427) PDF(802)

Abstract:
Based upon the theory of anisotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of non-linear differential equations. And the procedure to solve the problem using the iterative method is given.

Convergence of Ishikawa Type Iterative Sequence With Errors for Quasi-Contractive Mappings in Convex Metric Spaces

TIAN You-xan, ZHANG Shi-sheng

2002, 23(9): 889-895.

Abstract(2282) PDF(730)

Abstract:
Some convergence theorems of Ishikawa type iterative sequence with errors for nonline ar general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corre sponding results of L. B. Ciric, Q. H. Liu, H. E. Rho ades and H. K. Xu, at el but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces.

A New Model of Shape Memory Alloys

ZHU Yi-guo, LÜ He-xiang, YANG Da-zhi

2002, 23(9): 896-902.

Abstract(2383) PDF(662)

Abstract:
A new constitutive model of shape memory alloys (SMAs) based on Tanaka's martensite fraction exponential expression is produced. This new model can present recoverable shape memory strain during different phase transformation, and reflect the action of martensite reorientation. Also it can overcome the defect of Tanaka's Model when the SMAs. microstructure is fully martensite. The model is very simple and suitable for using, and the correct behavior of the model is proved by test.

The Drag Exerted by an Oblate Rotating Atmosphere on an Artificial Satellite

KH. I. Khalil

2002, 23(9): 903-914.

Abstract(2066) PDF(536)

Abstract:
A theory is formulated for the motion of an artificial satellite under the joint effects of Eearth oblateness and atmospheric drag. The Hamilton's equations of motion are derived including the zonal harmonics of the geopotential up to J₄ and the drag accelerations. The atmospheric model is an oblate rotating model in which the atmospheric rotation lags behind that of the earth as the increasing distance from the Earth. The drag free problem is first solved via two canonical transformations to eliminate in succession the short and long period terms. An operator D is then defined and used to formulate the drag acceleration in terms of the double primed variables expressing the solution of the drag-free problem.

Generalized Canonical Transformation and Symplectic Algorithm of the Autonomous Birkhoffian Systems

ZHANG Xing-wu, WU Ji-ke, ZHU Hai-ping, HUANG Ke-fu

2002, 23(9): 915-920.

Abstract(2495) PDF(560)

Abstract:
The Birkhoff systems are the generalization of the Hamiltonian systems. Generalized canonical transformations are studied. The symplectic algorithm of the Hamiltonian systems is extended into that of the Birkhoffian systems. Symplectic differential scheme of autonomous Birkhoffian systems was structured and discussed by introducing the Kailey Transformation.

Experimental Study of Measurement for Dissipation Rate Scaling Exponent in Heated Wall Turbulence

JIANG Nan, WANG Yu-chun, SHU Wei, WANG Zhen-dong

2002, 23(9): 921-928.

Abstract(2151) PDF(683)

Abstract:
Experimental investigations were devoted to the study of scaling exponent of coarse grained dissipation rate structure function for velocity and temperature fluctuation in a turbulent boundary layer at moderate Reynolds number. Longitudinal velocity and temperature were measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The effect of non-isotropy and inhomogeneity on scaling exponent of dissipation rate was studied because of the existence of organized coherent structure burst process in the near wall region. The scaling law of coarse-grained dissipation rate structure function is found to be independent of the mean velocity shear strain and the heating wall boundary condition. The scaling exponent of the dissipation rate structure function is verified to be in agreement with the hierarchical structure model which has been valid for isotropic and homogeneous turbulence.

Application of Mechanized Mathematics to Rotor Dynamics

HU Chao, WANG Yan, WANG Li-guo, HUANG Wen-hu

2002, 23(9): 929-935.

Abstract(2355) PDF(591)

Abstract:
Based on the mechanize d mathematics and WU Wen-tsun elimination method, using oil film forces of short be aring model and Muszynska's dynamic model, the dynamical behavior of rotor-bearing system and its stability of motion are investigated. As example, the concept of Wu characteristic set and Maple software, whirl par ameters of short-bearing model, which is usually solved by the numerical method, are analyzed. At tha same time, stability of zero solution of Jeffcott rotor whirl equation and stability of self-excited vibration are studied. The conditio ns of stable motion are obtained by using theory of nonlinear vibration.

Fuzzy Arithmetric and Solving of the Static Governing Equations of Fuzzy Finite Element Method

GUO Shu-xiang, LÜ Zheng-zhou, FENG Li-fu

2002, 23(9): 936-942.

Abstract(2325) PDF(627)

Abstract:
The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures in low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.

The Wavelet Transform of Periodic Function and Nonstationary Periodic Function

LIU Hai-feng, ZHOU Wei-xing, WANG Fu-chen, GONG Xin, YU Zun-hong

2002, 23(9): 943-950.

Abstract(2410) PDF(507)

Abstract:
Some properties of the wavelet transform of trigonometric function, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with the equation agress well with the function.

Analysis of Nonlinear Dynamic Stability of Liquid-Conveying Pipes

ZHANG Li-xiang, HUANG Wen-hu

2002, 23(9): 951-960.

Abstract(2734) PDF(744)

Abstract:
Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effect of Poisson, Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by 4 nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different.

An Improved Arc-Length Method and Application in the Post-Buckling Analysis for Composite Structures

ZHU Ju-fen, CHU Xiao-ting

2002, 23(9): 961-967.

Abstract(2866) PDF(1112)

Abstract:
Based on the conventional arc-length method, an improved arc-length method with high-efficiency is proposed. The weighted modifications with respect to the variation of structural stiffness and extra-interpolation modification by using the information of known equilibrium points are introduced to improve the incremental arc-length. An approximate expansion method for the accumulated and expected arc-length is used to ensure the convergence at given load levels in large range of applications. Numerical results show that the improved arc-length method has well adaptability and higher efficiency in the post-buckling analysis of plates and shells structures for tracing whole load-deflection path and obtaining the convergence values at any specified load levels.

Numerical Study on the Flow Around a Circular Cylinder With Surface Suction or Blowing Using Vorticity-Velocity Method

LING Guo-ping, FANG Jian-wen

2002, 23(9): 968-974.

Abstract(2404) PDF(567)

Abstract:
A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme (MILU-CG). The effects of surface suction or blowing's position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re=100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen, can reduce the drag force significantly, too.

A Fracture-Energy-Based Elasto-Softening-Plastic Constitutive Model for Joints of Geomaterials

SHEN Xin-pu, SHEN Guo-xiao

2002, 23(9): 975-981.

Abstract(2506) PDF(456)

Abstract:
On the basis of plasticity and fracture mechanics for quasi-brittle materials, this article presented a constitutive model for gradual softening behavior of joints of geomaterials. Corresponding numerical tests are carried out at the local level. Characteristics of the model proposed are:1) plastic softening and dilatancy behavior are directly related to the fracture process of joint, and much less material and model parameters are required compared with those proposed by references; 2) the process of decohesion coupled with frictional sliding at both micro-scale and macro-scale is described.

Lie Symmetries and Conserved Quantities of Second-Order Nonholonomic Mechanical System

FANG Jian-hui

2002, 23(9): 982-986.

Abstract(2635) PDF(745)

Abstract:
The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal transformations, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equation and the conservative quantities of the Lie symmetries are obtained. Secondly, the inverse problems of the Lie symmetries are studied. Finally, an example is given to illustrate the application of the result.

A Weighted Norm Inequality for Thela(t)-Type Oscillatory Singular Integrals

ZHAO Kai, WANG Mei, WANG Chun-jie

2002, 23(9): 987-990.

Abstract(2389) PDF(701)

Abstract:
The theta(t)-type oscillatory singular integral operators has been discussed. With the non-negative Locally integrable weighted funciton, the weighted norm inequalityof theta(t)-type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.