应用数学和力学

2009 Vol. 30, No. 11

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Constraint Induced Restriction and Extension Operators With Applications

CHEN Bo, LI Xiao-wei, LIU Gao-lian

2009, 30(11): 1261-1267. doi: 10.3879/j.issn.1000-0887.2009.11.001

Abstract(1896) PDF(690)

Abstract:
The Stokes operator is a differential-integral operator induced by the Stokes equations. From the point of view of the Helm holtzminimum dissipation principle the Stokes operator was analyzed. It's shown that, th rough the Hodge orthogonal decomposition, a pair of bounded linear operators, namely, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence of the observation, it's utilized to calculate the eigenvalues of the Stokes operator.

Numerical Investigation of Variable Viscosity and Thermal Stratification Effects on MHD Mixed Convective Heat and Mass Transfer Past a Porous Wedge in the Presence of Chemical Reaction

I.Muhaimin, R.Kandasamy, Azme B. Khamis

2009, 30(11): 1268-1280. doi: 10.3879/j.issn.1000-0887.2009.11.002

Abstract(1682) PDF(671)

Abstract:
An analys is was presented to investigate the effects of variable viscosity and thermal stratification on MHD mixed convective heat and mass transfer of a viscous, incom pressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedgewas embedded in a uniform non-Darcian porousmedium in order to allow for possible fluid wall suction or in jection. The governing boundary layer equations were written into a dmiension less form by smiilarity transformations. The transformed coupled nonlinear ordinary differential equations were solved numerically by using finite difference methods. Numericalcal-culations up to third order level of truncation were carried out for different values of dmiensionless parameters. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly in fluenced by these parameters. The results are compared with those known from the literature and excellent agreement between the results is obtained.

Upwind Finite Difference Method for Miscible(Oil and Water) Displacement Problem With Moving Boundary Values

YUAN Yi-rang, LI Chang-feng, YANG Cheng-shun, HAN Yu-ji

2009, 30(11): 1281-1294. doi: 10.3879/j.issn.1000-0887.2009.11.003

Abstract(2075) PDF(685)

Abstract:
The research of the miscible (oil and water) displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the two-dimensional bounded region, the upwindfinite difference schemes were put forward. Some techniques, such as calculus of variations, change of variables, theory of a priori estimates and techniques were adopted. Optmial orderestmiates are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, for model numerical method and for software development.

Large Eddy Simulation of Hot and Cold Fluids Mixing in a T-Junction for Prediction of Thermal Fluctuations

ZHU Wei-yu, LU Tao, JIANG Pei-xue, GUO Zhi-jun, WANG Kui-sheng

2009, 30(11): 1295-1306. doi: 10.3879/j.issn.1000-0887.2009.11.004

Abstract(1832) PDF(839)

Abstract:
The temperature fluctuations in a mixing T-junction have been smiulated on the FLUENT platform using the large eddy simulation (LES) turbulent flow model with a sub-grid scale Smagorinsky-Lilly model. The normalized mean and root mean square temperatures, which are used to describe the time-averaged temperature and temperature fluctuation intensity, were obtained, as well as velocity. The power spectral densities of temperature fluctuations, which are key parameters for thermal fatigue analysis and life tmie evaluation, were analyzed. The simulation results were consistent with expermiental data published in the literature, which shows that the LES is reliable. Severalmixing processes under different conditions were smiulated in order to analyze the effects of varying Reynolds number (Re) and Richardson number (Ri) on the mixing course and thermal fluctuations.

Vibration Characteristics of FGM Circalar Cylindrical Shells Containing Fluid Using Wave Propagation Approach

Zafar Iqbal, Muhammad Nawaz Naeem, Nazra Sultana, Shahid Hussain Arshad, Abdulghafar Shah

2009, 30(11): 1307-1317. doi: 10.3879/j.issn.1000-0887.2009.11.005

Abstract(2118) PDF(711)

Abstract:
The vibration characteristics of functionally graded material circular cylindrical shell containing fluid are examined by employing the wave propagation approach. The shell was filled with a non-viscous and in compressible fluid. Axialmodal dependence was approxmiated by exponential functions. A theoretical study of shell vibration frequencies was analyzed for simply supported-simply supported, clamped-simply supported and clamped-clamped, boundary conditions with the fluid effect. Validity and accuracy of the present method was con firmed by comparing the present results with those available in the literature. A good agreement was observed between the two sets of the results.

Design Method of Multiple Time-Delay Controller for Active Structural Vibration Control

CHEN Long-xiang, CAI Guo-ping

2009, 30(11): 1318-1326. doi: 10.3879/j.issn.1000-0887.2009.11.006

Abstract(1689) PDF(737)

Abstract:
Optmial control method for seismically excited building structures with multiple tmie delays is investigated. Firstly the system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit tmie delay by a particular augmenting for state variables. Then a tmie-delay controller is designed based on this standard equation using the discrete optimal control method. Finally the effectiveness of the proposed controller is demonstrated by numerical smiulations. Smiulation results indicate that a very small tmie delaymay resultin in stability of the control system if it is not compensated in control design. Tmie delay may be compensated effectively by the proposed controller and good control effectiveness may be obtained simultaneously. Moreover, the proposed controller is available for both small and large tmie delay.

Neurodynamics Analysis of Transmission of Brain Information

WANG Ru-bin, ZHANG Zhi-kang, Chi K. Tse

2009, 30(11): 1327-1340. doi: 10.3879/j.issn.1000-0887.2009.11.007

Abstract(1881) PDF(853)

Abstract:
A model of neural networks consisting of populations of perceptive neurons, interneurons and motor neurons according to the theory of stochastic phase resetting dynamics, was proposed. According to this model, dynamical characteristics of neural networks were studied under three coup ling cases, nam ely, series and parallel coup ling, series coup ling and un ilateral coupling. The results allow the structure of neural networks to be identified, and enable the basic characteristics of neural in formation processing to be described in terms of action of both the optional motor and the reflected motor. The excitation of local neural networks is caused by action of the optional motor. In particular, the excitation of neural population caused by action of the optional motor in the motor cortexis larger than that caused by action of there flected motor. It is reflected that there are more neurons participating in neural information processing and excited synchronization motion under the action of the optional motor.

First Fundamental Problems of Anisotropic Elastic Plane Weakened by Periodic Collinear Cracks

CAI Hai-tao, LU Jian-ke

2009, 30(11): 1341-1348. doi: 10.3879/j.issn.1000-0887.2009.11.008

Abstract(1448) PDF(601)

Abstract:
The first fundamental problems of anisotropic in finite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cracks were discussed by means of the method of complex function. This problem was considered by Cai[Eng Fracture Mech, 1993, 46:127-131], however, his method of solution is imperfect and so his results are incorrect. His method was revised and the correct solution was obtained here.

Plane Strain Consolidation of Soil Layer With Anisotropic Permeability

AI Zhi-yong, WU Chao

2009, 30(11): 1349-1356. doi: 10.3879/j.issn.1000-0887.2009.11.009

Abstract(2023) PDF(730)

Abstract:
An alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability was presented. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer was established at between the ground surface (z=0) and the depth z in the LaplaceFourier transformed domain. Combined with the boundary conditions, an exact solution was derived for plane strain Biot's consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform were adopted to obtain the actual solution in the physical doma in. Numerical results of plane strain Biot's conso lidation for a single soil layer shows that the an isotropy of perm eability has great in fluence on the consolidation behavior of the soils.

Propagation of Plane Waves at the Imperfect Boundary of an Elastic and Electro-Microstretch Generalized Thermoelastic Solid

Rajneesh Kumar, Rupender

2009, 30(11): 1355-1368. doi: 10.3879/j.issn.1000-0887.2009.11.010

Abstract(1434) PDF(564)

Abstract:
The problem of reflection and transm ission of plane waves incident on the contact surface of an elastic solid (medium M) and electro-micro stretch generalized thermoe lastic solid (medium M), was discussed. It is found that there exist five reflected waves (longitudinal displacement (LD) wave, thermal (T) wave, longitudinalm icrostretch (LM) wave and two coupled transverse displacement and microrotational (CD(Ⅰ) and CD (Ⅱ) waves)) in medium Mand two transmitted waves (longitudinal (P) and tran sverse (SV) waves) in medium M. The amplitude ratios of different reflected and transmitted waves were obtained for an miperfect boundary, and deduced fo r no rm al fo rce stiffness, tran sverse force stiffness and perfect bond ing. The variations of am plitude ratios with angle of incidence were depicted graphically for LD-wave, and CD(Ⅰ)-wave. It is noticed that the am plitude ratios of reflected and transmitted waves are affected by stiffness, electric field, stretch and thermal properties of the media. Some particular cases of interest were deduced from the present investigation.

On a Class of Singular Perturbation Solution for Semilinear Equtions of Fourth Order

MO Jia-qi

2009, 30(11): 1369-1373. doi: 10.3879/j.issn.1000-0887.2009.11.011

Abstract(1837) PDF(781)

Abstract:
A class of singularly perturbed boundary value problem for semilinear equation of fourth order with two parameters is considered. Under suitable conditions, using lower and upper solutions method, the existence and asymptotic behavior of solution for boundary value problem were studied. It is pointed out that the solution for original singularly perturbed problem with two parameters has only one boundary layer.

Existence and Nonexistence of Positive Solutions of Semilinear Elliptic Equation With Inhomogeneous Strong Allee Effect

LIU Guan-qi, WANG Yu-wen, SHI Jun-ping

2009, 30(11): 1374-1380. doi: 10.3879/j.issn.1000-0887.2009.11.012

Abstract(1625) PDF(685)

Abstract:
A semilinear elliptic equation defined on a bounded smooth domain is studied. This type of problem arises from the studies of spatial ecology model, and the growth function in the equation was of strong Allee effect and inhom ogeneous. It was proved by variational methods that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. Some nonexistence results were also proved.

Stability of Schr^Ldinger-Poisson Type Equations

HUANG Juan, ZHANG Jian, CHEN Guan-gan

2009, 30(11): 1381-1386. doi: 10.3879/j.issn.1000-0887.2009.11.013

Abstract(1368) PDF(882)

Abstract:
Variationalm ethods were used to study the nonlinear Schr^Ldinger-Poisson type equations which model the electromagnetic wave propagates in the plasma in physics. Through analyzing the Hamiltonian property to construct a constrained variational problem, the existence of the ground state of the system was obtained. Furthermore, the ground state being orbitally stable was proved.