应用数学和力学

2006 Vol. 27, No. 5

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Global Attractor for the Hasegawa-Mima Equation

ZHANG Rui-feng, GUO Bo-ling

2006, 27(5): 505-511.

Abstract(2803) PDF(723)

Abstract:
The long time behavior of solution of the Hasegawa-Mima equation with dissipation term is considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor are estimated.

Diffusion in the Micro-Channel Flow Driven by Electroosmosis

ZHANG Kai, LIN Jian-zhong, LI Zhi-hua

2006, 27(5): 512-518.

Abstract(5228) PDF(630)

Abstract:
Numerical simulation using the finite differential method was carried out to analyze the diffusion of an impulse sample in the micro-channel driven by electroosmosis. The results show that the electrical field strength applied externally and the concentration of buffer solution played a significant role in the diffusion of sample, however, hydraulic diameter and aspect ratio of height to width of channel played a small role in it. Weakening the electrical field strength applied externally and the concentration of buffer solution properly could prevent the sample band from broadening effectively, and promoted the efficiency of testing and separation as well as kept a faster speed of transport. The conclusions were helpful to the optimal design for micro-channel.

Dynamic Behavior of Two Parallel Symmetry Cracks in Magneto-Electro-Elastic Composites Under Harmonic Anti-Plane Waves

ZHOU Zhen-gong, WANG Biao

2006, 27(5): 519-526.

Abstract(2404) PDF(577)

Abstract:
The dynamic behavior of two parallel symmetry cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied by Schmidt method. By using the Fourier trans-form, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surface were expanded in a series of Jacobi polynomials. The relations among the electric filed, the magnetic flux and the stress field were obtained. From the results, it can be obtained that the singular stresses in piezoelectric/piezomagnetic materials carry the same forms as those in a general elastic material for the dynamic anti-plane shear fracture problem. The shielding effect of two parallel cracks was also discussed.

Approach for Layout Optimization of Truss Structures With Discrete Variables Under Dynamic Stress, Displacement and Stability Constraints

SHI Lian-shuan, WANG Yue-fang, SUN Huan-chun

2006, 27(5): 527-532.

Abstract(2442) PDF(554)

Abstract:
A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under the dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures included two parts, i.e. the topology optimization and the shape optimization. In each procedure, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

Numerical Simulation of Insect Flight

CHENG Mu-lin, MIAO Wen-bo, ZHONG Chang-sheng

2006, 27(5): 533-538.

Abstract(3027) PDF(966)

Abstract:
In the non-inertial coordinates attached to the model wing, the two-dimensional unsteady flow field triggered by the motion of the model wing, similar to the flapping of the insect wings, was numerically simulated. One of the advantages of our method is that it has avoided the difficulty related to the moving-boundary problem. Another advantage is that the model has three degrees of freedom and can be used to simulate arbitrary motions of a two-dimensional wing in plane only if the motion is known. Such flexibility allows us to study how insects control their flying. The results show that there are two parameters that are possibly utilized by insects to control their flight: the phase difference be tween the wing translation and rotation, and the lateral amplitude of flapping along the direction per pendicular to the average flapping plane.

Semi-Analytical and Semi-Numerical Method for Dynamic Analysis of Foundation

GONG Wen-hui, XIE Hong-yang, WANG Yuan-han

2006, 27(5): 539-546.

Abstract(2880) PDF(511)

Abstract:
A semi-analytical and semi-numerical method is proposed for the dynamic analysis of the foundations. The Lamb's solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of the foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of the foundation.

Effects of Viscous Dissipation on Thermally Developing Forced Convection in a Porous Saturated Circular Tube With an Isoflux Wall

K. Hooman, A. Pourshaghaghy, A. Ejlali

2006, 27(5): 547-554.

Abstract(2548) PDF(473)

Abstract:
The viscous dissipation effect on forced convection in a porous saturated circular tube with an isoflux wall is investigated on the basis of the Brinkman flow model. For the thermally developing region, a numerical study was reported while a perturbation analysis was presented to find expressions for the temperature profile and the Nusselt number for the fully developed region. The fully developed Nusselt number found by numerical solution for the developing region was compared with that of asymptotic analysis and a good degree of agreement is observed.

Probability Model and Solution on Earthquake Effects Combination in Along Wind Resistant Design of Tall-Flexible Buildings

HONG Xiao-jian, GU Ming

2006, 27(5): 555-563.

Abstract(2233) PDF(512)

Abstract:
A model on the earthquake effect combination in wind resistant design of high-rise flexible structures is proposed in accordance with the probability method. Based on the Turkstra criteria, the stochastic characters of wind velocity, earthquake ground acceleration and excitations occurrence probability were taken into account and then the combination of the earthquake effect in structure wind resistant design was analyzed with the convolution approach. The results indicate that as for the tall flexible buildings whose lateral force is governed by wind loading, the maximum lateral loads verification in terms of the wind resistant design combined with earthquake effect may be more unfavorable compared with that with respect to the earthquake resistant design involving wind effect.

Reduction Approaches for Vibration Control of Repetitive Structures

CHEN Wei-ming, SUN Dong-chang, WANG Da-jun, WEI Jian-ping, TONG Li-yong, WANG Quan

2006, 27(5): 564-570.

Abstract(2026) PDF(639)

Abstract:
The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the location of sensors and actuators, and the relation between system inputs and control forces were assumed to be set in a symmetric way so that the control system possess the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputed, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.

Behavior of Obstructed Square Buoyant Vertical Jets in Static Ambient(Ⅰ)——Verification of Mathematical Model and Numerical Method

HUAI Wen-xin, FANG Shen-guang, DAI Hui-chao

2006, 27(5): 571-578.

Abstract(2452) PDF(561)

Abstract:
Some experiments were made for the buoyant jet from a square orifice with a square disc placed on it in static ambient and concentration along the axis in self-similar area behind disc was measured. And at the same time a three-dimensional mathematical model was established to simulate the whole flowing under different conditions. All the results predicted by the numerical calculation are substantiated by the experiments. The results were compared with experiential formula for obstructed round buoyant vertical jets in static ambient and it was found that the two concentration distributions had good accordance. Star shape of temperature isolines on cross sections in the near areas from the disc was found and it was a very special figure for obstructed square buoyant vertical jets with a square disc. The shape will transform to concentric circles gradually alike to the round buoyant vertical jet in self-similar area with increasing of the distance from the disc.

Behavior of Obstructed Square Buoyant Vertical Jets in Static Ambient(Ⅱ)——Analysis on the Behavior of Flow Field

HUAI Wen-xin, FANG Shen-guang, DAI Hui-chao

2006, 27(5): 579-585.

Abstract(2174) PDF(482)

Abstract:
Based on a series of numerical calculations, the behavior of flow field in obstructed square buoyant vertical jet is summarized and analyzed. Based on the axial line velocity distribution, the flow after the disc can be divided into three regions: i.e. recirculation region, transitional region and selfsimilar region. The characteristic of self-similarity of upright velocity was validated. The three regions can also be distinguished based on the axial velocity. The axial velocity in self-similar region was found to obey the same law and the formula was presented by introducing the velocity expression used by Chen and Rodi. The isolines of pressure on cross sections of different heights were displayed and the production, expansion, breaking and disappearing of negative pressure regions were found.

Nonlinear Dynamical Bifurcation and Chaotic Motion of a Shallow Conical Lattice Shell

WANG Xin-zhi, HAN Ming-jun, ZHAO Yan-ying, ZHAO Yong-gang

2006, 27(5): 586-590.

Abstract(2249) PDF(624)

Abstract:
The nonlinear dynamical equations of axle symmetry were established by using the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations were given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items was derived under the boundary conditions of fixed and clamped edges by using the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation to a kind of nonlinear dynamics system were solved. Then an exact solution to nonlinear free oscillation of the single-layer shallow conic lattice shell was found as well. The critical conditions of chaotic motion were obtained by solving Melnikov functions, some phase planes were drawn by using digital simulation and proved the existence of chaotic motion.

Qualitative Analysis of an SEIS Epidemic Model With Nonlinear Incidence Rate

WANG La-di, LI Jian-quan

2006, 27(5): 591-596.

Abstract(2868) PDF(999)

Abstract:
By means of limit theory and Fonda's theorem, an SEIS epidemic model with constant recruitment and the disease-related rate is considered. The incidence term is of the nonlinear form, and the basic reproduction number was found. If the basic reproduction number is less than one, there exists only the disease-free equilibrium which is globally asymptotically stable, and the disease dies out eventually. If the basic reproduction number is greater than one, besides the unstable disease-free equilibrium, there exists also a unique endemic equilibrium, which is locally asymptotically stable, and the disease is uniformly persistent.

Meshless Analysis for Three-Dimensional Elasticity With Singular Hybrid Boundary Node Method

MIAO Yu, WANG Yuan-han

2006, 27(5): 597-604.

Abstract(2492) PDF(498)

Abstract:
The singular hybrid boundary node method (SHBNM) is proposed for solving threedimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ‘boundary layer effect', which is the main drawback of the original hybrid BNM, was overcomed by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3-D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.

Numerical Method for the Three-Dimensional Nonlinear Convection-Dominated Problem of Dynamics of Fluids in Porous Media

YUAN Yi-rang, DU Ning, WANG Wen-qia, CHENG Ai-jie, HAN Yu-ji

2006, 27(5): 605-614.

Abstract(2378) PDF(468)

Abstract:
For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic were put forward. Fractional steps techniques were needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates were adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.

Dynamic Analysis of Flexible-Link and Flexible-Joint Robots

ZHANG Ding-guo, ZHOU Sheng-feng

2006, 27(5): 615-623.

Abstract(2634) PDF(835)

Abstract:
The dynamic modeling and simulation of an N-flexible-link and N-flexible-joint robot was reported. Each flexible joint is modeled as a linearly elastic torsional spring and the approach of assumed modes was adopted to describe the deformation of the flexible-link. The complete governing equations of motion of the flexible-link-joint robots were derived via Kane's method. An illustrative example is given to validate the algorithm presented and to show the effects of flexibility on the dynamics of robots.

Existence of Solutions for Higher Order Multi-Point Boundary Value Problems at Resonance

LIN Xiao-jie, DU Zeng-ji, GE Wei-gao

2006, 27(5): 624-630.

Abstract(2072) PDF(619)

Abstract:
Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differerntial equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates.