应用数学和力学

2008 Vol. 29, No. 11

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Exact Traveling Wave Solutions for the 2D-Generalized Benney-Luke Equation

LI Ji-bin

2008, 29(11): 1261-1267.

Abstract(2751) PDF(563)

Abstract:
By using the method of dynamical systems to the 2D-generalized Benney-Luke equation, the existence of kink wave solutions and uncountably infinite many smooth perio dic wave solutions is shown. Explicitexact parametric representations for the kink wave solutions, periodic wave solutions and unbo unded traveling wave solutionsare obtained.

Analytic Solutions of a Class of Nonlinear Partial Differential Equations

ZHANG Hong-qing, DING Qi

2008, 29(11): 1268-1278.

Abstract(2035) PDF(873)

Abstract:
Firstly, an approach is presented for computing the adjoint operator vector of a class of nonlinear (i. e. partial-nonlinear) operator matrix by generalizing the method presented by Zhang et al. and the conjugate operators. Secondly, a united theory is given for solving a class of nonlinear (i. e. partial-nonlinear and including all linear) and non-homogeneous differential equations by the mathe-matics-mechanization method. In other words, a transformation is constructed by homogenization and triangulation which can reduce the original system to the simpler one which is diagonal. Finally, some practical applications are given in elasticity equations.

Monte Carlo Simulation of Stage Separation Dynamic of a Multistage Launch Vehicle

J. Roshanian, M. Talebi

2008, 29(11): 1279-1292.

Abstract(2507) PDF(691)

Abstract:
The formulation used for studies of cold and hot separating stages of a multistage launch vehicle was provided. Monte Carlo simulation is employed to account for the off nominal design parameters of the bodies undergoing separation to evaluate the risk of failure for the separation event. All disturbances, effect of dynamic unbalance, residual thrust, separation disturbance which are caused by the separation mechanism and misalignment in cold and hot separation are analyzed to and out the nonoccurrence of collision between the separation bodies. The results indicate that the current design satisfies the separation requirements.

Stability Analysis of Delayed Cellular Neural Networks With and Without Noise Perturbation

ZHANG Xue-juan, WANG Guan-xiang, LIU Hua

2008, 29(11): 1293-1302.

Abstract(2654) PDF(732)

Abstract:
The stability of a class of delayed cellular neural networks (DCNN) either without or with noise perturbation are studied. After presenting a simple and easily checkable condition for global exponential stability of the deterministic system, the situations with noise perturbation were further investigated. When the DCNN is perturbed with an external noise, the system is globally stable. The important fact is that, when the system is perturbed with an internal noise, it's globally exponentially stable if only the total strength of the noise is within a certain bound. This fact is significant as stochastic resonance phenomena have been found exist in many nonlinear systems.

Streamline Upwind Finite Element Method Using 6-Node Triangular Element With Adaptive Remeshing Technique for Convective-Diffusion Problems

Niphon Wansophark, Pramote Dechaumphai

2008, 29(11): 1303-1313.

Abstract(3079) PDF(594)

Abstract:
A streamline upwind finite element method using the 6-node triangular element is presented. The method was applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples were used to evaluate the efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase the solution accuracy, and at the same time, to minimize the computational time and computer memory requirement.

Propagation of Rayleigh Waves at the Free Surface of Transversely Isotropic Generalized Thermoelastic Diffusion

Rajneesh Kumar, Tarun Kansal

2008, 29(11): 1314-1324.

Abstract(3436) PDF(636)

Abstract:
The propagation of Rayleigh waves in a homogeneous, transversely isotropic, thermoelastic diffusive half-space subjected to stress free, thermally insulated/isothermal and chemical potential boundary conditions, in the context of generalized theory of thermoelastic diffusion is studied. Green and Lindsay(GL) theory, in which, thermodiffusion and thermodiffusion-mechanical relaxations are governed by four different time constants, was selected for study. Secular equations for surface wave propagation in the considered media were derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient were presented graphically in order to illustrate and compare the analytically results. Some special cases of frequency equations were also deduced from the present investigation.

The Extended Intrinsic Mean Spin Tensor for Turbulence Modelling in a Non-Inertial Frame of Reference

HUANG Yu-ning, MA Hui-yang

2008, 29(11): 1325-1336.

Abstract(3489) PDF(717)

Abstract:
The role of the extended intrinsic mean spin tensor introduced for turbulence modelling in a non-inertial frame of reference which is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear Kepsilon model is investigated. To this end and for illustration of the effect of the extended intrinsic spin tensor on turbulence modelling, several recently developed nonlinear Kepsilon models were examined and their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with the LES data was compared. The results and analysis indicate that only if the deficiencies of these models and the like be well understood in detail and be properly corrected, may in the near future more sophisticated nonlinear Kepsilon models be developed to better predict the complex turbulent flows in a non-inertial frame of reference.

Third-Order Modified Coefficient Scheme Based on the Essentially Non-Oscillatory Scheme

LI Ming-jun, YANG Yu-yue, SHU Shi

2008, 29(11): 1337-1346.

Abstract(2816) PDF(793)

Abstract:
A third-order numerical scheme was presented for approximating solutions of multi dimensional hyperbolic conservation laws only using the modified coefficients of essentially non-oscillatory (MCENO) scheme without increasing the base points during the construction of the scheme. The construction process of scheme shows that the modified coefficient approach preserves the favourable properties inherent in the original essentially non-oscillatory (ENO) scheme for its essentially non-oscillation, total variation bounded (TVB) etc. The new scheme improves the accuracy by one order compared to the original one. Furthermore, the MCENO scheme was applied to simulate two-dimensional Rayleigh-Taylor (RT) instability with densities 1:3 and 1:100 and solve the Lax shock-wave tube numerically. It is also noted that the ratio of CPU times used implementing the MCENO, the third-order ENO and fifth-order weighed ENO (WENO) schemes is 0.62:1:2.19. These indicate that the MCENO scheme improves the accuracy in smooth regions and has higher accuracy and better efficiency compared with the original ENO scheme.

Numerical Investigation on the Evolution of the Cylindrical Cellular Detonation

WANG Chun, JIANG Zong-lin, HU Zong-min, HAN Gui-lai

2008, 29(11): 1347-1354.

Abstract(3120) PDF(644)

Abstract:
Cylindrical cellular detonation was numerically investigated by solving the two-dimensional reactive Euler equations with finite volume method on a two-dimensional self-adaptive unstructured mesh. The one-step reversible chemical reaction model was used to simplify the control parameters of chemical reaction. Numerical results demonstrate the evolution of cellular cell splitting of cylindrical cellular detonation which has been explored by experimental results. The splitting of cellular structures shows different features in the near and far field from the initiation zone. The variation of the local curvature is a key factor for behaviors of cell splitting of cylindrical cellular detonation in propagation. Numerical results also show that the splitting of cellular structures is dominated by from the selforganization of transverse waves which correspond to the development of small disturbances along the detonation front related to detonation instability.

Wavelet Finite-Difference Method for the Numerical Simulation of Wave Propagation in Fluid-Saturated Porous Media

HE Ying, HAN Bo

2008, 29(11): 1355-1346.

Abstract(2923) PDF(776)

Abstract:
The numerical simulation of wave propagation in fluid-saturated porous media is considered. A wavelet finite-difference method was proposed for solving the 2-D elastic wave equation. This algorithm combines the flexibility and computational efficiency of wavelet multiresolution method with the easy implementation of finite-difference method. And the orthogonal wavelet basis provides a natural framework, which adapts spatial grids to local wavefield properties. Numerical results illustrate the value of the approach as an accurate and stable tool for the simulation of wave propagation in fluid-saturated porous media.

Evolution of Global Enstrophy in Cylinder Wake Controlled by Lorentz Force

ZHANG Hui, FAN Bao-chun, CHEN Zhi-hua

2008, 29(11): 1365-1375.

Abstract(2223) PDF(1145)

Abstract:
The Okubo-Weiss function is correlated with the fluid particle compression, deformation and vorticity, which provides a simple way to characterize the different regions of flowfield. It had been proved mathematically that the global integration of Okubo-Weiss function is always equal to zero for a two dimensional incompressible flow with no-slip boundaries. Moreover, as an example to validate above conclusion, the flow past a circular cylinder controlled by electromagnetic force was calculated numerically. The distributions of global enstrophy, total squared strain and Okubo-Weiss function in controlled flowfield were discussed, and the influences of Lorentz force on them were also analyzed.

Dynamic Stress Intensity Factor Analysis of Adhesively Bonded Material Interface With Damage Under Shear Loading

CAI Yan-hong, CHEN Hao-ran, TANG Li-qiang, YAN Cheng, JIANG Wan

2008, 29(11): 1376-1386.

Abstract(3312) PDF(803)

Abstract:
The dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading is investigated. The material damage was considered. By introducing dislocation density function and using integral transform, the problem was reduced to algebraic equations and could be solved with collocation dots method in the Laplace domain. Finally, the time response of DSIF was calculated with the inverse Laplace integral transform. The conclusions show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, but decreases with swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is 0.5 and independent of the material parameters and damage conditions of materials and time. The oscillatory index is controlled by viscoelastic material parameters.