Applied Mathematics and Mechanics (English Edition)

UNSYMMETRICAL LARGE DEFORMATION PROBLEM OF ORTHOTROPIC PLATES

王新志;赵永刚;叶开沅;黄达文

2002, 23(9): 993-1000.

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Based upon the theory of ardsotropic 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 nonlinear 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

田有先;张石生

2002, 23(9): 1001-1008.

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Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., 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

朱祎国;吕和祥;杨大智

2002, 23(9): 1009-1015.

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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): 1016-1028.

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A theory is formulated for the motion of an artificial satellite under the joint effects of Earth 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

张兴武;武际可;朱海平;黄克服

2002, 23(9): 1029-1034.

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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

姜楠;王玉春;舒玮;王振东

2002, 23(9): 1035-1044.

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Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region. Longitudinal velocity and temperature have been 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 influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is 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 law of the dissipation rate structure function is verified to be in agreement with the hierarchical structure model that has been verified valid for isotropic and homogeneous turbulence.

APPLICATION OF MECHANIZED MATHEMATICS TO ROTOR DYNAMICS

胡超;王岩;王立国;黄文虎

2002, 23(9): 1045-1053.

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Based on the mechanized mathematics and WU Wen-tsun elimination method, using oil film forces of short-bearing 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 parameters of short-bearing model, which is usually solved by the numerical method, are analyzed. At the same time, stability of zero solution of Jeffcott rotor whirl equation and stability of self-excited vibration are studied. The conditions of stable motion are obtained by using theory of nonlinear vibration.

FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD

郭书祥;吕震宙;冯立富

2002, 23(9): 1054-1061.

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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 is 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

刘海峰;周炜星;王辅臣;龚欣;于遵宏

2002, 23(9): 1062-1070.

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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 this equation agrees well with the function.

ANALYSIS OF NONLINEAR DYNAMIC STABILITY OF LIQUID-CONVEYING PIPES

张立翔;黄文虎

2002, 23(9): 1071-1080.

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Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects 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 four 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

朱菊芬;初晓婷

2002, 23(9): 1081-1088.

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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 sheik 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

凌国平;方健雯

2002, 23(9): 1089-1096.

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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

沈新普;沈国晓

2002, 23(9): 1097-1104.

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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 geomateri-als. 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 friction-al sliding at both micro-scale and macro-scale is described.

LIE SYMMETRIES AND CONSERVED QUANTITIES OF SECOND-ORDER NONHOLONOMIC MECHANICAL SYSTEM

方建会

2002, 23(9): 1105-1110.

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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 THETA(t)-TYPE OSCILLATORY SINGULAR INTEGRALS

赵凯;王梅;王春杰

2002, 23(9): 1111-1114.

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The theta (t)-type oscillatory singular integral operators has been discussed.With the non-negative locally integrable weighted function, the weighted norm inequality of theta (t)-type oscillatory singular integral operators is proved, and the weighted function hasreplaced by action of Hardy-Littlewood maximal operators several times.

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