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(2486) 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 w...

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(2428) 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(2858) 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(2331) 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(2404) 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(2614) 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 al...

Anomalous Diffusion in Fractal Porous Medium

WANG Zi-ting

2000, 21(10): 1033-1038.

Abstract(3117) 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 po...

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

TANG Jia-shi

2000, 21(10): 1039-1045.

Abstract(2388) 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 so...

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(2491) 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 expansio...

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

TANG Xin-yan

2000, 21(10): 1053-1059.

Abstract(2837) 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 necessar...

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(3045) 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 ...

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(2469) PDF(668)

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 ...

Forced Oscillation of Second Order Neutral Equations

WANG Pei-guang, GE Wei-gao

2000, 21(10): 1077-1080.

Abstract(1979) 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(2363) 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...

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(2514) 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(2239) 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 a...