应用数学和力学

2004 Vol. 25, No. 5

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Chebyshev Approximation of the Second Kind of Modified Bessel Function of Order Zero

ZHANG Jing, ZHOU Zhe-wei

2004, 25(5): 441-445.

Abstract(2856) PDF(946)

Abstract:
The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J. P. Boyd's rational Chebyshev basis.

Observation and Modeling for Terrestrial Processes in Alpine Meadow

YAO De-liang, ZHANG Qiang, LI Jia-chun, XIE Zheng-tong, SHEN Zhen-xi

2004, 25(5): 446-454.

Abstract(2392) PDF(584)

Abstract:
The water-heat transfer process between land and atmosphere in Haibei alpine meadow area has been systematically observed. A multi-layer coupling model for land-atmosphere interaction was presented with special attention paid to the moisture transfer in leaf stomata under unsaturated condition. A profound investigation on the physical process of turbulent transfer inside the vegetation has been performed with a revised formula of water absorption for root system. The present model facilitates the study of vertically distributed physical variables in detail. Numerical simulation was conducted according to the transfer process of Kinesia humility meadow in the area of Haibei Alpine Meadow Ecosystem Station, CAS. The calculated results agree well with observation.

Effects of Time Delayed Velocity Feedbacks on Self-Sustained Oscillator With Excitation

XU Jian, CHEN Yu-shu

2004, 25(5): 455-466.

Abstract(2868) PDF(708)

Abstract:
Both the primary resonant solutions and their bifurcations due to time delayed velocity feedbacks used in a self-sustained oscillator with excitation were further investigated. A model was proposed by adding linear and nonlinear time delayed feedbacks to a representative non-autonomous system(with external forcing). The stablity condition of the linearized system at trivial equilibrium was discussed, which leads to a critical stability boundary where periodic solutions may occur. The main attention was focused on bifurcations from the primary resonant solutions. It is found that the stable primary resonant solution may appear periodically in the time delay. Meanwhile, the unstable regions for such solutions are also obtained, predicting the occurrence of quasi-periodic motions.

T-Stress in Piezoelectric Solid

MA Hao, WANG Biao

2004, 25(5): 467-471.

Abstract(2646) PDF(570)

Abstract:
The non-singular and bounded terms for stresses near the crack tip were investigated. The crack problem in a transversely isotropic piezoelectric solid for the plane problem was dealt with. The principle of superposition and the Plemelj formulation were introduced. The non-singular terms are given by solving Rieman-Hilbert problem. It is shown that the non-singular terms are influenced by the elastic and electric constants.

Nonlinear Analysis of Equatorial Eastern Pacific Air-Sea Coupling Oscillation and a Limit-Cycle Theory for ENSO Cycle

HUANG Si-xun, XIANG Jie, HAN Wei

2004, 25(5): 472-480.

Abstract(2521) PDF(607)

Abstract:
The troposphere and ocean mixed layer were considered as two components of a dynamic system operated by solar radiation as the constant source of energy, where upon an air-sea coupling self-exited coupling oscillation model was based with the aid of a locally averaged thermodynamic climate model, resulting mathematically in a closed self-governed dynamic system, a so-called El Nino-Southern Oscillation(ENSO) system. With the limit cycle solution of the system. It is shown that the essential physics of the coupled system can be described by the ENSO system. Compared with the observations, the theoretical limit cycle orbit mat ches the observed phase loop qualitatively. The ENSO system provides a useful theoretical framework for study of interannual variation of the tropical climate system.

Modulus Prediction and Discussion of Reinforced Syntactic Foams With Coated Hollow Spherical Inclusions

YUAN Ying-long, LU Zi-xing

2004, 25(5): 481-487.

Abstract(2256) PDF(628)

Abstract:
The elastic properties of syntactic foams with coated hollow spherical inclusions have been studied by means of Mori and Tanaka s concept of average stress in the matrix and Eshelby's equivalent inclusion theories. Some formulae to predict the effective modulus of this material have been derived theoretically. Based on these formulae, the influences of coating parameters such as the thickness and Poisson's ratio on the modulus of the syntactic foams have been discussed at the same time.

Difference Scheme for Two-phase Flow

LI Qiang, FENG Jian-hu, CAI Ti-min, HU Chun-bo

2004, 25(5): 488-496.

Abstract(2262) PDF(539)

Abstract:
A numerical method for two-phase flow with hydrodynamics behavior was considered. The nonconservative hyperbolic governing equations proposed by Saurel and Gallout were adopted. Dissipative effects were neglected but they could be included in the model without major difficulties. Based on the opinion proposed by Abgrall that "a two phase system, uniform in velocity and pressure at t=0 will be uniform on the same variable during its temporal evolution", a simple accurate and fully Eulerian numerical method was presented for the simulation of multiphase compressible flows in hydrodynamic regime. The numerical method relies on Godunov-type scheme, with HLLC and Lax-Friedrichs type approximate Riemann solvers for the resolution of conservation equations, and nonconservative equation. Speed relaxation and pressure relaxation processes were introduced to account for the interaction between the phases. Test problem was presented in one space dimension which illustrated that our scheme is accurate, stable and oscillation free.

Residual a Posteriori Error Estimate Two-Grid Methods for the Steady Navier-Stokes Equation With Stream Function Form

REN Chun-feng, MA Yi-chen

2004, 25(5): 497-510.

Abstract(3336) PDF(625)

Abstract:
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The a posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.

Parallel Arithmetic Numerical Simulation and Application of Secondary Migration-Accumulation of Oil Resources

YUAN Yi-rang, HAN Yu-ji

2004, 25(5): 511-522.

Abstract(2804) PDF(554)

Abstract:
From such actual conditions as the effects of characteristics of miltilayer petroleum geology and permeation fluid mechanics, a new numerical model is put forward and coupling splitting-up implicit interactive scheme is formed. For the actual situation of Dongying hollow (four-layer) and Tanhai region (three-layer) of Shengli Petroleum Field, the numerical simulation test results and the actual conditions are coincident.

Multiresolution Symplectic Scheme for Wave Propagation in Complex Media

MA Jian-wei, YANG Hui-zhu

2004, 25(5): 523-528.

Abstract(2627) PDF(562)

Abstract:
A fast adaptive symplectic algorithm named multiresolution symplectic scheme (MSS) was first presented to solve the problem of the wave propagation in complex media, using the symplectic scheme and Daubechies. compactly supported orthogonal wavelet transform to respectively discretise the time and space dimension of wave equation. The problem was solved in multiresolution symplectic geometry space under the conservative Hamiltonian system rather than the traditional Lagrange system. Due to the fascinating properties of the wavelets and symplectic scheme, MSS is a promising method because of little computational burden, robustness and reality of long-time simulation.

Homotopy Solution of the Inverse Generalized Eigenvalue Problems in Structural Dynamics

LI Shu, WANG Bo, HU Ji-zhong

2004, 25(5): 529-534.

Abstract(3307) PDF(719)

Abstract:
The structural dynamics problems, such as structural design, parameter identification and model correction, are considered as a kind of the inverse generalized eigenvalue problems mathematically. The inverse eigenvalue problems are nonlinear. In general, they could be transformed into nonlinear equations to solve. The structural dynamics inverse problems were treated as quasi multiplicative inverse eigenalue problems which were solved by homotopy method for nonlinear equations. This method had no requirements for initial value essentially because of the homotopy path to solution. Numerical examples were presented to illustrate the homotopy method.

Muhammet Yürüsoy

2004, 25(5): 535-541.

Abstract(2800) PDF(766)

Abstract:
Two dimensional equations of steade motion for third order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid. For the inviscid flow around an arbitrary object, the streamlines are the phi-coordinates and velocity potential lines are psi-coordinates which form an orthogonal curvilinear set of coordinates. The out come, boundary layer equations, is then shown to be independent of the body shape immersed into the flow. As a first approximation, assumption that second grade terms are negligible compared to viscous and third grade terms. Second grade terms spoil scaling transformation which is only transformation leading to similarity solutions for third grade fluid. By using Lie group methods, infinitesimal generators of boundary layer equations are calculated. The equations are transformed into an ordinary differential system. Numerical solutions of outcoming nonlinear differential equations are found by using combination of a Runge-Kutta algorithm and shooting technique.

Effective Stress and Strain in Finite Deformation

ZHOU Zhe, QIN Ling-li, HUANG Wen-bin, WANG Hong-wei

2004, 25(5): 542-550.

Abstract(3757) PDF(2895)

Abstract:
Whether the concept of effective stress and strain in elastic-plastic theory is still valid under the condition of finite deformation was mainly discussed. The uni-axial compression experiments in plane stress and plane strain states were chosen for study. In the two kinds of stress states, the stress-strain curve described by logarithm strain and rotated Kirchhoff stress matches the experiments data better than the curves defined by other stress-strain description.