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2011年 第32卷 第9期    刊出日期：2011-09-02

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Articles

Analytical solutions to edge effect of composite laminates based on symplectic dual system

姚伟岸 聂臆瞩 肖峰

2011, 32(9):  1091-1100.  doi:10.1007/s10483-011-1483-7

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In the symplectic space composed of the original variables, displacements, and their dual variables, stresses, the symplectic solution for the composite laminates based on the Pipes-Pagano model is established in this paper. In contrast to the traditional technique using only one kind of variables, the symplectic dual variables include displacement components as well as stress components. Therefore, the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously. After being introduced into the symplectic dual system, the uniform schemes, such as the separation of variables and symplectic eigenfunction expansion method, can be implemented conveniently to analyze composite laminate problems. An analytical solution for the free edge effect of composite laminates is obtained, showing the effectiveness of the symplectic dual method in analyzing composite laminates.

Orientations of special water dipoles that accelerate water molecules exiting from carbon nanotube

亓文鹏 涂育松 万荣正 方海平

2011, 32(9):  1101-1108.  doi:10.1007/s10483-011-1484-x

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One-dimensional ordered water molecules entering and exiting from a carbon nanotube with an appropriate radius are studied with molecular dynamics simulations. It can be found that a water molecule near the nanotube end is more likely to be expelled from the nanotube if its dipole is almost perpendicular to the nanotube axis. The key to this observation is that those water molecules are closer to the wall of the nanotube away from the equilibrium position of the Lennar-Jones (LJ) potential. Thus, the interaction energy for those water molecules is relatively high. There are two particular structures of the perpendicular water molecule depending on the dipole direction of the adjacent water molecule in the nanotube. Although the probabilities of these structures are quite small, their contributions to the net flux across the nanotube end are approximately equal to the predominant structures. The present findings further show the possibility of controlling the water flow by regulating the dipole directions of the water molecules inside the nanochannels.

Conservation form of Helbing’s fluid dynamic traffic flow model

李书峰 张鹏 S.C.WONG

2011, 32(9):  1109-1118.  doi:10.1007/s10483-011-1485-9

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A standard conservation form is derived in this paper. The hyperbolicity of Helbing’s fluid dynamic traffic flow model is proved, which is essential to the general analytical and numerical study of this model. On the basis of this conservation form, a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently. The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated. This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients, and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.

论文

Exact solution of electroosmotic flow in generalized Burgers fluid

T. HAYAT, S.AFZAL, A.HENDI

2011, 32(9):  1119-1126.  doi:10.1007/s10483-011-1486-6

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An exact solution is developed for the time periodic electroosmotic flow of a non-Newtonian fluid between the micro-parallel plates. The constitutive equations of a generalized Burgers fluid are used in the mathematical formulation. The resulting problem is solved by a Fourier transform technique. Graphs are plotted and discussed for various emerging parameters of interest.

Articles

Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

L. K. SAHA S. SIDDIQA M. A. HOSSAIN

2011, 32(9):  1127-1146.  doi:10.1007/s10483-011-1487-9

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The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF). The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method. Moreover, the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method, for the whole range of the local transpiration parameter ζ. Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough. However, in these particular regions, solutions are acquired with the aid of a regular perturbation method. The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (= 0.005, 0.01, 0.05).  Furthermore, the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.

Numerical simulation of particle sedimentation in 3D rectangular channel

刘马林

2011, 32(9):  1147-1158.  doi:10.1007/s10483-011-1488-7

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The 3D lattice Boltzmann method is used to simulate particle sedimentation in a rectangular channel. The results of single particle sedimentation indicate that the last position of the particle is along the center line of the channel regardless of the initial position, the particle diameter, and the particle Reynolds number. The wall effect on the terminal velocity is in good agreement with experimental results quantitatively. The drafting, kissing, and tumbling (DKT) process is reproduced and analyzed by simulating  two-particle cluster sedimentation. The effects of the diameter ratio, initial position, and wall on the DKT process are investigated. When the two particles have equal diameter sediment in the rectangular channel, a periodical DKT process and the spiraling trajectory are found. The last equilibrium configuration is obtained from the simulation results. The interesting regular sedimentation phenomena are found when 49 particles fall down under gravity.

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

戎海武 王向东 罗旗帜 徐伟 方同

2011, 32(9):  1159-1168.  doi:10.1007/s10483-011-1489-x

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The subharmonic response of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to the narrow-band random excitation is investigated. The analysis is based on a special Zhuravlev transformation, which reduces the system to the one without impacts or velocity jumps, and thereby permits the applications of asymptotic averaging over the period for slowly varying the inphase and quadrature responses. The averaged stochastic equations are exactly solved by the method of moments for the mean square response amplitude for the case of zero offset. A perturbation-based moment closure scheme is proposed for the case of nonzero offset. The effects of damping, detuning, and bandwidth and magnitudes of the random excitations are analyzed. The theoretical analyses are verified by the numerical results. The theoretical analyses and numerical simulations show that the peak amplitudes can be strongly reduced at the large detunings.

Bifurcation of elastic tank-liquid coupled sloshing system

钟顺 陈予恕

2011, 32(9):  1169-1176.  doi:10.1007/s10483-011-1490-x

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The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established. By means of the multi-scale method and the singularity theory, the bifurcation behaviors of the system are investigated and analyzed. The various nonlinear dynamical behaviors of the coupling system are obtained, which can further explain the relationship between the physical parameters and the bifurcation solutions. The results provide a theoretical basis to the realization of the parameter optimal control.

Hopf bifurcation in general Brusselator system with diffusion

郭改慧 吴建华 任小红

2011, 32(9):  1177-1186.  doi:10.1007/s10483-011-1491-6

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The general Brusselator system is considered under homogeneous Neumann boundary conditions. The existence results of the Hopf bifurcation to the ordinary differential equation (ODE) and partial differential equation (PDE) models are obtained. By the center manifold theory and the normal form method, the bifurcation direction and stability of periodic solutions are established. Moreover, some numerical simulations are shown to support the analytical results. At the same time, the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.

Uniformly ultimate boundedness for discontinuous systems with time-delay

慕小武 丁志帅 程桂芳

2011, 32(9):  1187-1196.  doi:10.1007/s10483-011-1492-9

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The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed. Based on the Lyapunov-Krasovskii functional, the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented. Furthermore, the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

Global exponential stability of switched systems

V. FILIPOVIC

2011, 32(9):  1197-1206.  doi:10.1007/s10483-011-1493-7

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This paper proposes a method for the stability analysis of deterministic switched systems. Two motivational examples are introduced (nonholonomic system and constrained pendulum). The finite collection of models consists of nonlinear models, and a switching sequence is arbitrary. It is supposed that there is no jump in the state at switching instants, and there is no Zeno behavior, i.e., there is a finite number of switches on every bounded interval. For the analysis of deterministic switched systems, the multiple Lyapunov functions are used, and the global exponential stability is proved. The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations.

Lyapunov-Kozlov method for singular cases

V. ˇCOVI′C D.DJURI′C M. VESKOVI′C A.OBRADOV

2011, 32(9):  1207-1220.  doi:10.1007/s10483-011-1494-6

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Lyapunov’s first method, extended by Kozlov to nonlinear mechanical systems, is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces. The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position. This fact renders the impossible application of Lyapunov’s approach
in the analysis of the stability because, in the equilibrium position, the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled. It is shown that Kozlov’s generalization of Lyapunov’s first method can also be applied in the mentioned cases on the conditions that, besides the known algebraic expression, more are fulfilled. Three theorems on the instability of the equilibrium position are formulated. The results are illustrated by an example.