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2011年 第32卷 第1期    刊出日期：2011-01-10

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Articles

Analysis method of chaos and sub-harmonic resonance of nonlinear system without small parameters

刘延彬 陈予恕 曹庆杰

2011, 32(1):  1-10.  doi:10.1007/s10483-011-1388-x

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The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations. Unfortunately, the traditional Melnikov methods strongly depend on small parameters, which do not exist in most practical systems. Those methods are limited in dealing with the systems with strong nonlinearities. This paper presents a procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practical systems by employing a homotopy method that is used to extend the Melnikov functions to the strongly nonlinear systems. Applied to a given example, the procedure shows the effectiveness via the comparison of the theoretical results and the numerical simulation.

Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise

郑言 黄建华

2011, 32(1):  11-22.  doi:10.1007/s10483-011-1389-7

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The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.

Unsteady generalized Couette flow in composite microchannel

M.L.KAURANGIN B.K.JHA

2011, 32(1):  23-32.  doi:10.1007/s10483-011-1390-6

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A numerical study is reported on the fully developed unsteady laminar fluid flow in microchannel parallel-plates partially filled with a uniform porous medium and partially filled with a clear fluid. The flow is induced by the movement of one of the plates and the pressure gradient. The Brinkman-extended Darcy model is utilized to model the flow in the porous region, while the Stokes equation is used in the clear fluid region. A theoretical analysis is also presented for the fully developed steady flow to find closedform expressions for the interfacial velocity and the velocity and skin frictions at the bounding plates. Numerical computations shows excellent agreement between the closedform solutions for fully developed steady flow and the numerical solution to unsteady flow at large values of time.

Numerical simulation of vortex evolution based on adaptive wavelet method

赵勇 宗智 邹文楠

2011, 32(1):  33-44.  doi:10.1007/s10483-011-1391-6

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The application of the wavelet method to vortex motion prediction is investigated. First, the wavelet method is used to solve two initial boundary problems so as to verify its abilities of controlling numerical errors and capturing local structures. Then, the adaptive wavelet method is used to simulate the vortex emerging process. The results show that the wavelet method can control numerical errors easily, can capture local structures adaptively, and can predict the vortex fluctuation evolution. Therefore, the application of the wavelet method to turbulence is suggested.

论文

MHD stagnation point flow of a micropolar fluid towards a heated surface

M.ASHRAF M.M.ASHRAF

2011, 32(1):  45-54.  doi:10.1007/s10483-011-1392-7

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The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations are then solved numerically by an algorithm based on the finite difference discretization. The results are further refined by Richardson’s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields are predicted in tabular and graphical forms to show the important features of the solution. The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.

Articles

Inverse estimation for unknown fouling geometry on inner wall of forced-convection pipe

陈文立 杨俞青 李浩榕

2011, 32(1):  55-68.  doi:10.1007/s10483-011-1393-9

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A conjugate gradient method (CGM) based on the inverse algorithm is used to estimate the unknown fouling-layer profile on the inner wall of a pipe system using simulated temperature measurements taken within the pipe wall. It is assumed that no prior information is available about the functional form of the unknown profile. Therefore, the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined using the simulated exact and inexact temperature measurements. The results show that the excellent estimation of the fouling-layer profile can be obtained for the test case considered in this study. The technique presented in this study can be used in a warning system to call for pipe maintenance when the thickness of fouling exceeds a predefined criterion.

Analytical solution for laminar flow through leaky tube

M.GORJI M.ALIPANAH M.SHATERI E.FARNAD

2011, 32(1):  69-74.  doi:10.1007/s10483-011-1394-6

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The laminar flow through a leaky tube is investigated, and the momentum and conservation of energy equations are solved analytically. By using the Hagen-Poiseuille velocity profile and defining unknown functions for the axial and radial velocity components, the pressure and mass transfer equations are obtained, and their profiles are plotted according to different parameters. The results indicate that the axial velocity, the radial velocity, the mass transfer parameter, and the pressure in the tube decrease as the fluid moves along the tube.

Anti-plane analysis of semi-infinite crack in piezoelectric strip

郭俊宏 刘萍 卢子兴 秦太验

2011, 32(1):  75-82.  doi:10.1007/s10483-011-1395-9

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Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.

Orthogonal basic deformation mode method for zero-energy mode suppression of hybrid stress elements

张灿辉 王东东 李同姗

2011, 32(1):  83-96.  doi:10.1007/s10483-011-1396-6

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A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The resulting orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. Moreover, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.

Powell’s optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

张剑 叶见曙 周储伟

2011, 32(1):  97-106.  doi:10.1007/s10483-011-1397-x

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A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell’s optimization theory is used to perform the stochastic identification of material constants  of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell’s identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element (FCSE) method. Some classical examples show that Powell’s identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell’s theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses are simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.

Finite-dimensional approximation to global minimizers in functional spaces with R-convergence

陈熙 姚奕荣 郑权

2011, 32(1):  107-118.  doi:10.1007/s10483-011-1398-8

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A new concept of convergence (R-convergence) of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.

Numerical simulations of Richtmyer-Meshkov instabilities using conservative front-tracking method

M.A.ULLAH 高文斌 茅德康

2011, 32(1):  119-132.  doi:10.1007/s10483-011-1399-x

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This paper presents the numerical simulations of two Richtmyer-Meshkov (RM) instability experiments using the conservative front-tracking method developed in (Mao, D. Towards front-tracking based on conservation in two space dimensions II, tracking discontinuities in capturing fashion. J. Comput. Phys., 226, 1550–1588 (2007)). The numerical results are compared with those obtained in (Holmes, R. L., Grove, J. W., and Sharp, D. H. Numerical investigation of Richtmyer-Meshkov instability using front-tracking. J. Fluid Mech., 301, 51–64 (1995)). The present simulations are generally in good agreement with those obtained by Holmes et al., and also capture the nonlinear and compessive phenomenon, i.e., the self-interactions of the transmitted and reflected wave edges, which was pointed out by Holmes et al. as the cause of the deceleration of the interfaces. However, the perturbation amplitudes and the amplitude growth rates of the interfaces obtained with the present conservative front-tracking method are a bit larger than those obtained by Holmes et al.