应用数学和力学

2003 Vol. 24, No. 11

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Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅳ)-Surface Couservation Laws

DAI Tian-min

2003, 24(11): 1101-1107.

Abstract(2706) PDF(738)

Abstract:
The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived. The existing related results are naturally derived as special cases from the results proposed in this paper. The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization.

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅴ)-Polar Thermomechanical Continua

DAI Tian-min

2003, 24(11): 1108-1113.

Abstract(2483) PDF(661)

Abstract:
The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity. The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle. The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case, respectively. Finally, the results of micropolar thermopiezoelectricity are directly given.

New Truncated Expansion Method and Soliton-Like Solution of Variable Coefficient KdV-MKdV Equation With Three Arbitrary Functions

ZHANG Jie-fang, LIU Yu-lu

2003, 24(11): 1114-1117.

Abstract(2374) PDF(675)

Abstract:
The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.

Computer Computation of the Method of Multiple Scales——Dirichlet Problem for a Class of System of Nonlinear Differential Equations

XIE La-bing, JIANG Fu-ru

2003, 24(11): 1118-1125.

Abstract(2522) PDF(605)

Abstract:
The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales.

Permanence and Asymptotic Properties of Nonlinear Delay Difference Equations

LI Wan-tong

2003, 24(11): 1126-1132.

Abstract(2242) PDF(680)

Abstract:
The asymptotic behavior of a class of nonlinear delay difference equation was studied. Some sufficient conditions are obtained for permanence and global attractivity. The results can be applied to a class of nonlinear delay difference equations and to the delay discrete Logistic model and some known results are included.

Formal Solutions and Projective Limit of P. D. E

SHI Wei-hui, SHEN Zhen

2003, 24(11): 1133-1140.

Abstract(2120) PDF(655)

Abstract:
The existence theorems of formal solutions of PDE are given. And the relationship between formal solutions and projective limit of Ehresmann chain is shown based on stratification theory.

Stability and Bifurcation of Unbalance Rotor/Labyrinth Seal System

LI Song-tao, XU Qing-yu, WAN Fang-yi, ZHANG Xiao-long

2003, 24(11): 1141-1150.

Abstract(2521) PDF(763)

Abstract:
The influence of labyrinth seal on the stability of unbalanced rotor system was presented. Under the periodic excitation of rotor unbalance, the whirling vibration of rotor is synchronous if the rotation speed is below stability threshold, whereas the vibration becomes severe and asynchronous which is defined as unstable if the rotation speed exceeds threshold. The Muszynska model of seal force and shooting method were used to investigate synchronous solution of the dynamic equation of rotor system. Then, based on Floquet theory the stability of synchronous solution and unstable dynamic characteristic of system were analyzed.

The Concentration Distribution of Fractional Anomalous Diffusion Caused by an Instantaneous Point Source

DUAN Jun-sheng, XU Ming-yu

2003, 24(11): 1151-1156.

Abstract(2272) PDF(752)

Abstract:
The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space(n=1, 2 or 3) are derived by means of the condition of mass conservation, the time-space similarity of the solution, Mellin transform and the properties of the Fox function. And the asymptotic behaviors for the solutions are also given.

Control Chaos in Transition System Using Sampled-Data Feedback

LU Jun-an, XIE Jin, LÜ Jin-hu, CHEN Shi-hua

2003, 24(11): 1157-1162.

Abstract(2381) PDF(581)

Abstract:
The method for controlling chaotic transition system was investigatede using sampled data. The output of chaotic transition system was sampled at a given sampling rate, then the sampled output was used by a feedbacks ubsystem to cosntruct a control signal for controlling chaotic transition system to the origin. Numerical simulations are presented to show the effectiveness and feasibility of the developed controller.

Study on Influence of Bending-Torsion Coupling in an Impacting-rub Rotor System

SUN Zheng-ce, XU Jian-xue, ZHOU Tong, TAN Ning

2003, 24(11): 1163-1169.

Abstract(2078) PDF(737)

Abstract:
A mathematical model of an impacting-rub rotor system with bending-torsion coupling was established. It was compared with the model without bending-torsion coupling through the modern nonlinear dynamic theory. It is observed that periodical, chaotic, period adding phenomena in them and the two models have a similar bifurcation process in their bifurcation figures. But the influence of bending-torsion on the dynmaic characteristics of the system is not neglected. The results have considerable meanings to analyze and improve the characteristics of an impacting-rub rotor system.

Existence and Algorithm of Solutions for General Multivalued Mixed Implicit Quasi-Variational Inequalities

ZENG Liu-chuan

2003, 24(11): 1170-1178.

Abstract(2157) PDF(754)

Abstract:
A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case, introduced and studied by Ding Xie-ping. The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex, lower semicontinuous, binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality. Secondly, this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities. Here, the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the existence of solutions and convergence of approximate solutions for general multivalued mixed implicit quasi-variational nequalities are proved. Moreover, the new convergerce criteria for the algorithm were provided. Therefore, the results give an affirmative answer to the open question raised by M. A. Noor, and extend and improve the earlier and recent results for various variational inequalities and complementarity problems including the corresponding results for mixed variational inequalities, mixed quasi-variatoinal inequalities and quasi-complementarity problems involving the single-valued and set-valued mappings in the recent literature.

Analysis and Application of Ellipticity of Stability Equations on Fluid Mechanics

LI Ming-jun, GAO Zhi

2003, 24(11): 1179-1185.

Abstract(2569) PDF(946)

Abstract:
By using characteristic analysis of the linear and nonlinear parabolic stability equations(PSE), PSE of primitive disturbance variables are prored to be parabolic in total. By using sub-characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic, for velocity U, in subsonic and supersonic:respectively U+u in subsonic and supersonic, respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.

Periodical Interfacial Cracks in Anisotropic Elastoplastic Media

XIAO Wan-shen, ZHOU Jian-ping, TANG Guo-jin

2003, 24(11): 1186-1190.

Abstract(2489) PDF(652)

Abstract:
By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy-anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement(COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks. In addition, COD also relates it with moduli of the materials.

Dynamic Responses of Viscoelatic Axially Moving Belt

LI Ying-hui, GAO Qing, JIAN Kai-lin, YIN Xue-gang

2003, 24(11): 1191-1196.

Abstract(2365) PDF(697)

Abstract:
Based on the Kelvin viscoelastic differential constitutive law and the motion equation of the axially moving belt, the nonlinear dynamic model of the viscoelastic axial moving belt was established. And then it was reduced to be a linear differential system which the analytical solutions with a constant transport velocity and with a harmonically varying transport velocity were obtained by applying Lie group transformations. According to the nonlinear dynamic model, the effects of material parameters and the steady-state velocity and the perturbed axial velocity of the belt on the dynaic responses of the belts were investigated by the research of digital simulation. The result shows:1) The nonlinear vibration frequency of the belt will become small when the velocity of the belt increases. 2) Increasing the value of viscosity or decreasing the value of elasticity leads to a deceasing in vibration frequencies. 3) The most effects of the transverse amplitudes come from the frequency of the perturbed velocity when the belt moves with harmonic velocity.

Approximate Sampling Theorem for Bivariate Continuous Function

YANG Shou-zhi, CHENG Zheng-xing, TANG Yuan-yan

2003, 24(11): 1197-1203.

Abstract(3551) PDF(762)

Abstract:
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one's requirement, so that one may controll the decay speed of the approximate sampling function.

The Blowup Properties for a Class of Nonlinear Degenerate Diffusion Equation With Nonlocal Source

DENG Wei-bing, LIU Qi-lin, XIE Chun-hong

2003, 24(11): 1204-1210.

Abstract(2633) PDF(617)

Abstract:
A nonlinear degenerate parabolic equation with nonlocal source was considered. It is shown that under certain assumptions the solution of the equation blows up in finite time and the set of blow-up points is the whole region. The integral method is used to investigate the blowup properties of the solution.