应用数学和力学

2011 Vol. 32, No. 9

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Analytical Solutions to Edge Effect of Composite Laminates Based on Symplectic Dual System

YAO Wei-an, NIE Yi-zhu, XIAO Feng

2011, 32(9): 1021-1029. doi: 10.3879/j.issn.1000-0887.2011.09.001

Abstract(1642) PDF(874)

Abstract:
In symplectic space composed of the original variables-displacements and their dual variables-stresses,the symplectic solution for the composite laminated based on the Pipes-Pagano model was established.In contrast to traditional technique,the symplectic dual variables include displacement components as well as stress components,so the compatibility conditions of displacement and stress at interfaces can be formulated simultaneously.After introducing into the symplectic dual system,the uniform scheme,such as the separation of variables and symplectic eigenfunction expansion method,can be implemented conveniently to analyze problem of composite laminates.An analytical solution for free edge effect of composite laminates was gained,and it shows that the symplectic dual method is efficient for the analysis of composite laminates.

Water Molecules Exiting a Carbon Nanotube Driven by Special Water Dipole Orientations

QI Wen-peng, TU Yu-song, WAN Rong-zheng, FANG Hai-ping

2011, 32(9): 1030-1036. doi: 10.3879/j.issn.1000-0887.2011.09.002

Abstract(1592) PDF(1127)

Abstract:
One-dimensional ordered water molecules entering and exiting a carbon nanotube with appropriate radius were studied by molecular dynamics simulations.It was found that a water molecule near the nanotube end was more likely to be expelled from the nanotube if its dipole was almost aligned perpendicular to the nanotube axis.The key to this observation is that those water molecules are closer to the wall of nanotube away from the equilibrium position of Lennar-Jones potential,so that the interaction energy for those water molecules is relatively high.There are two particular structures of the perpendicular water 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 findings show the possibility of controlling the water flow by regulating the dipole directions of water molecules inside the nanochannels.

Conservation Form of Helbing’s Fluid Dynamic Traffic Flow Model

LI Shu-feng, ZHANG Peng, Wong S C

2011, 32(9): 1037-1045. doi: 10.3879/j.issn.1000-0887.2011.09.003

Abstract(1809) PDF(894)

Abstract:
A standard conservation form was derived,the hyperbolicity of Helbing's fluid dynamic traffic flow model was proved,which was essential for 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 model efficiently.The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave was simulated.This simulation also verifies that the model has been truly improved through the introduction of modified diffusion coefficients,thereby helping to protect vehicles from collisions and avoiding the appearance of extremely large density.

Exact Solution of Electroosmotic Flow in a Generalized Burgers’ Fluid

Tasawar Hayat, Saira Afzal, Awatif Hendi

2011, 32(9): 1046-1053. doi: 10.3879/j.issn.1000-0887.2011.09.004

Abstract(1346) PDF(678)

Abstract:
An exact solution for time periodic electroosmotic flow of a non-Newtonian fluid between the micro-parallel plates was developed.Constitutive equations of a generalized Burgers' fluid were utilized in the mathematical formulation.The resulting problem was solved by a Fourier transform technique.Finally,the graphs were plotted and discussed for various emerging parameters of interest.

Effect of Hall Current on the MHD Natural Convection Flow From a Vertical Permeable Flat Plate With Uniform Surface Heat Flux

L. K. Saha, S. Siddiqa, M. A. Hossain

2011, 32(9): 1054-1070. doi: 10.3879/j.issn.1000-0887.2011.09.005

Abstract(2010) PDF(750)

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

Numerical Simulation of Particle Sedimentation in a 3D Rectangular Channel

LIU Ma-lin

2011, 32(9): 1071-1083. doi: 10.3879/j.issn.1000-0887.2011.09.006

Abstract(1661) PDF(1082)

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

Subharmonic Response of a Single-Degree-of-Freedom Linear Vibroimpact System to a Narrow-Band Random Excitation

RONG Hai-wu, WANG Xiang-dong, LUO Qi-zhi, XU Wei, FANG Tong

2011, 32(9): 1084-1091. doi: 10.3879/j.issn.1000-0887.2011.09.007

Abstract(1847) PDF(741)

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

Bifurcation of a Class of Elastic Tank-Liquid Coupled Sloshing System

ZHONG Shun, CHEN Yu-shu

2011, 32(9): 1092-1099. doi: 10.3879/j.issn.1000-0887.2011.09.008

Abstract(1736) PDF(671)

Abstract:
The nonlinear equations of an elastic tank-liquid coupling system which was subjected to external excitation were established.By means of multi-scale method and singularity theory,the bifurcation behaviors of the system were investigated and analyzed,so that abundant nonlinear dynamical behaviors of the coupling system were obtained,which could make a further explanation of the relationship between physical parameters and bifurcation solutions.In order to realize the parameters' optimal control,the results provide its theoretical basis.

Hopf Bifurcation in the General Brusselator System With Diffusion

GUO Gai-hui, WU Jian-hua, REN Xiao-hong, YU Peng

2011, 32(9): 1100-1109. doi: 10.3879/j.issn.1000-0887.2011.09.009

Abstract(2028) PDF(798)

Abstract:
The general Brusselator system was considered under homogeneous Neumann boundary conditions.The existence results of Hopf bifurcation to the ODE and PDE models were obtained.By the center manifold theory and the normal form method,the bifurcation direction and stability of periodic solutions were also established.Moreover,some numerical simulations were shown to support the analytical results.At the same time,the figures of positive steady-state solutions and spatially inhomogeneous periodic solutions were drawn,which supplement the analytical results.

Uniformly Ultimate Boundedness for a Class of Discontinuous Systems With Time-Delays

MU Xiao-wu, DING Zhi-shuai, CHENG Gui-fang

2011, 32(9): 1110-1117. doi: 10.3879/j.issn.1000-0887.2011.09.010

Abstract(1764) PDF(841)

Abstract:
Uniformly ultimate boundedness of discontinuous systems with time-delays in the sense of Filippov solutions were mainly discussed.Based on Lyapunov-Krasovskii functional,Lyapunov theorem for globally strongly uniformly ultimate boundedness of retarded discontinuous systems was shown.Furthermore,the result is applied to a class of mechanical systems with retarded discontinuous friction item.

Global Exponential Stability of Switched Systems

V. Filipovic

2011, 32(9): 1118-1126. doi: 10.3879/j.issn.1000-0887.2011.09.011

Abstract(1991) PDF(781)

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

Liapunov-Kozlov Method for Singular Cases

V. Čović, D. Djurić, M. Vesković, A. Obradović

2011, 32(9): 1127-1138. doi: 10.3879/j.issn.1000-0887.2011.09.012

Abstract(1380) PDF(677)

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