应用数学和力学

2000 Vol. 21, No. 10

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The Study of Quasi-Wavelets Based Numerical Method Applied to Burgers’ Equations

WAN De-cheng, WEI Guo-wei

2000, 21(10): 991-1001.

Abstract(2332) PDF(856)

Abstract:
A quasi-wavelet based numerical method was introduced for solving the evolution of the solutions of nonlinear partial differential Burgers' equations. The quasi wavelet based numerical method was used to discrete the spatial deriatives, while the fourth-order Runge-Kutta method was adopted to deal with the temporal discretization. The calculations were conducted at a variety of Reynolds numbers ranging from 10 to unlimited large. The comparisons of present results with analytical solutions show that the quasi wavelet based numerical method has distinctive local property, and is efficient and robust for numerically solving Burgers' equations.

The Research of Blow-up in 2D Weakly Damped Forced KdV Equation on Thin Domain

TIAN Li-xin, LIU Yu-rong, LIU Zeng-rong

2000, 21(10): 1002-1008.

Abstract(2247) PDF(732)

Abstract:
The time estimate of the blow-up of the weakly damped forced KdV equation in thin 2D domains is given.

Two Types of Traveling Wave Solutions to Burgers-KdV Equations

ZHANG Yu-feng, ZHANG Hong-qing

2000, 21(10): 1009-1012.

Abstract(2636) PDF(908)

Abstract:
Two Types of exact traveling wave solutions to Burgers-KdV equation by basis on work of XIONG Shu-lin are presented. Furthermore, some new results are replenished in work of FAN En-gui et al.

Numerical Analysis of Longtime Dynamic Behavior in Weakly Damped Forced KdV Equation

TIAN Li-xin, CHU Zhi-jun, LIU Zeng-rong, JIANG Yong

2000, 21(10): 1013-1020.

Abstract(2201) PDF(568)

Abstract:
The numerical analysis of the appro ximate inertial manifold in weakly damped fo rced KdV equation is given. The results of numerical analysis under five models is the same as that of nonline ar spectral analysis.

Local Attractors for the Weakly Damped Forced KdV Equation in Thin 2D Domains

TIAN Li-xin, LIU Yu-rong, LIU Zeng-rong

2000, 21(10): 1021-1027.

Abstract(2246) PDF(613)

Abstract:
The existence of local attractors in thin 2D domains for the weakly damped forced KdV equation, whose principal operator is a non-self adjoint and non-sectorial one is given.

Wavelet-Numerical Method in Crack Analysis

SHEN Yuan-tong, YI Xu-ming

2000, 21(10): 1028-1032.

Abstract(2434) PDF(568)

Abstract:
Properties of wavelet of good localization were used to approximate displacement fields near the crack tip. Wavelet-numerical algorithm and simulation singularity problem of the crack tip were established. As an example, stress intensity factors were obtained. The numerical results show that this algorithm has good precision.

Anomalous Diffusion in Fractal Porous Medium

WANG Zi-ting

2000, 21(10): 1033-1038.

Abstract(2961) PDF(902)

Abstract:
Fractal media has many characteristics different from those of homogeneous media, it has a correlated self-similar structure. The particle diffusion in pore fractal is different from Ficks diffusion, and its mean-squared displacement follows fractal scaling law. The model of particle diffusion in pore fractal by means of the statistics method of stochastic process is structured and some fractal characteristics and non-Markov property are proved.

The MLP Method for Subharmonic and Ultraharmonic Resonance Solutions of Strongly Nonlinear Systems

TANG Jia-shi

2000, 21(10): 1039-1045.

Abstract(2221) PDF(670)

Abstract:
A new parameter transformation α=α(ε,nω₀/m,ω₁) was defined for extending the applicable range of the modified Lindstedt-Poincar method. It is suitable for determining subharmonic and ultraharmonic resonance solutions of strongly nonlinear systems. The 1/3 subharmonic and 3 ultraharmonic resonance solutions of the Duffing equation and the 1/2 subharmonic resonance solution of the Vander Pol-Mathieu equation were studied. These examples show approximate solutions are in good agreement with numerical solutions.

Based on Wavelet Analysis to Optimal Control of Motion Planning of Space Manipulator

GE Xin-sheng, ZHANG Qi-zhi, LIU Yan-zhu

2000, 21(10): 1046-1052.

Abstract(2305) PDF(739)

Abstract:
The optimal control problem of nonholonomic motion planning of space manipulator was discussed. Utilizing the method of wavelet analysis, the discrete orthogonal wavelets were introduced to solve the optimal control problem, the classical Fourier basic functions were replaced by the wavelet expansion approximation. A numerical algorithm of optimal control was proposed based on wavelet analysis. The numerical simulation shows, the method is effective for nonholonomic motion planning of space manipulator.

New Scalar-Type Equilibrium Equations of the General Space Force System

TANG Xin-yan

2000, 21(10): 1053-1059.

Abstract(2614) PDF(636)

Abstract:
Using the principle of analytical geometry, several properties of the space straight line are proved. Based on these properties, the equilibrium of general space force system is considered and its four new scalar-type equilibrium equations are derived which are equivalent to the vector-type necessary and sufficient conditions for equilibrium.

Analysis of Coupled-Mode Flutter of Pipes Conveying Fluid on the Elastic Foundation

WANG Zhong-min, FENG Zhen-yu, ZHAO Feng-qun, LIU Hong-zhao

2000, 21(10): 1060-1068.

Abstract(2878) PDF(942)

Abstract:
The governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by power series method. Compared with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio β, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.

The Double Resonances of Magnetism and Solid Coupling of Hydroelectric-Generator Stator System

LI Wen-lan, QIU Jia-jun, YANG Zhi-an

2000, 21(10): 1069-1076.

Abstract(2273) PDF(667)

Abstract:
A double-shell model of hydroelectric-generator stator system was established. Applying the theory of mechano-electric analytical dynamics theory, the nonlinear vibration equation of magnetism and solid coupling of hydroelectric-generator stator system, under steadily balanced threephases operating condition, was obtained. According to the method of multiple scales for nonlinear oscillations, the double resonances of magnetism and solid coupling of hydroelectric-generator stator system were investigated. It is pointed out that the system has abundant dynamics phenomenon including the attendant jumps and coexistence of multiple stable motions.

Forced Oscillation of Second Order Neutral Equations

WANG Pei-guang, GE Wei-gao

2000, 21(10): 1077-1080.

Abstract(1840) PDF(682)

Abstract:
A class of second order neutral equations with deviating arguments are studied, and sufficient conditions are derived for every solution to be oscillatory.

Linearized Inverse Scattering for Elastic Parameters in a Half-Space With Reflection Date

ZHU Wen-hao, DAI Hui, ZHONG Wei-fang

2000, 21(10): 1081-1086.

Abstract(2172) PDF(703)

Abstract:
The multi-parameter inversion of elastic wave equation in a half-space within the Born approximation is studied. A method of simultaneously reconstructing the configurations of the density and Lam parameters of the medium was presented by use of a wideband measuring schemes in which transmitters and receivers scan over the half-space surface. It is shown that the reflected waves generated by horizontal and vertical pulses on the surface can be decomposed into P→P、P→S、S→P and S→S types of scattering components. As is expected, these components contain enough information for desired restruction. From them the density and two Lam parameters are determined explicitly, and the results obtained have the form of filtered back-propagation as in the acoustic diffraction tomography.

A Family of High-Order Accuracy Explicit Difference Schemes With Branching Stability for Solving 3-D Parabolic Partial Differential Equation

MA Ming-shu, Wang Tong-ke

2000, 21(10): 1087-1092.

Abstract(2335) PDF(944)

Abstract:
A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r=Δt/Δx²=Δt/Δy²=Δt/Δz²<1/2, and the truncation error is O(Δt²+Δx⁴).

Coupled Fields of Two-Dimensional Anisotropic Magneto-Electro-Elastic Solids With an Elliptical Inclusion

JIANG Zhi-qing, LIU Jin-xi

2000, 21(10): 1093-1099.

Abstract(2093) PDF(724)

Abstract:
The two-dimensional elliptical inclusion problems in infinite anisotropic magneto-electroelastic solids are considered. Based on the extended Stroh formalism, the technique of conformal mapping and the concept of perturbation, the magneto-electro-elastic fields in both the matrix and the inclusion are obtained explicitly. The results are of very importance for studying the effective properties of piezoelectric-piezomagnetic composite materials.