应用数学和力学

Study of Terahertz Wave Propagation in Carbon Nanotube Arrays Based on the Symplectic Formulation

ZHANG Yu, DENG Zi-chen, ZHAO Peng

2016, 37(9): 889-900. doi: 10.21656/1000-0887.370164

Abstract(1107) PDF(842)

Abstract:
With the effective medium model, the properties of terahertz wave propagation in the periodic arrays of carbon nanotubes were investigated. In view of the nonlocal quasistatic model, the relative permittivity was derived. The symplectic formulation was used to solve the eigenvalue problem of the electromagnetic wave propagation in the periodic arrays of carbon nanotubes and the dispersion relation was obtained. The properties of electromagnetic wave propagation in arrays of vertical and tilted carbon nanotubes were given through the numerical calculation. The numerical simulation shows that the effective medium model without nonlocal spatial dispersion gives results in good agreement with those from the electrodynamical model at the frequencies within the terahertz range, thus the spatial dispersion can be ignored. The research makes a theoretical reference for the design of the propagation devices for terahertz waves.

Grain-Size-Dependent Elastic Moduli and Strengths of Polycrystalline Graphene: Atomistic Simulations

LU Ying, QIAN Jin

2016, 37(9): 901-914. doi: 10.21656/1000-0887.370121

Abstract(1158) PDF(888)

Abstract:
For polycrystalline graphene, the existence of grain boundaries might strongly influence the mechanical properties. There had been increasing experimental and numerical studies on the stiffness and strength of polycrystalline graphene, where 2 methods of nanoindentation and uniaxial tension had been widely employed for tests. However, significant discrepancies in the elastic moduli and breaking strengths from the 2 methods had been reported. Herein atomistic simulations of both the nanoindentation and the uniaxial tension were performed to explore the effects of grain sizes on the mechanical properties of polycrystalline graphene. In the simulations, the failure of polycrystalline graphene always occurred at grain boundary junctions, showing that the poly-graphene samples were weakened by the combination of grain boundary junctions, holes and topological defects. The results indicate that, the Young’s moduli and breaking strengths, from both the nanoindentation test and the uniaxial tension test, are strongly influenced by the grain sizes of poly-graphene.

Mathematical Models for Deformation Between Steel Strand Wires and Induction Heating Effects

CHENG Ya-ping, LI Zhi-gang, ZHANG Qiang

2016, 37(9): 915-923. doi: 10.21656/1000-0887.370010

Abstract(1095) PDF(653)

Abstract:
The calculation model for deformation between wires was derived based on the Hertz contact theory and the structural characteristics of steel strands, and the contact area width between steel strand wires in the induction heating process was calculated with this model, which helped establish a precise finite element model for the induction heating of steel strands. Then the temperature fields in the steel strand under induction heating were simulated with the finite element method, where temperature data at different current densities and frequencies were given. Through the regression analysis of the temperature data, the average relative errors were used to evaluate the quality of several mathematical fitting models, so the optimal mathematical model for induction heating effects was found. The present work provides a theoretical basis for the control of the induction heating temperature in steel strands based on the classical control theory.

Multi-Objective Optimization of Composite Vibration Isolation Systems

HUANG Wei, XU Jian, ZHU Da-yong, HU Ming-yi, LU Jian-wei, LU Kun-lin

2016, 37(9): 924-935. doi: 10.21656/1000-0887.360238

Abstract(1088) PDF(1104)

Abstract:
The traditional vibration isolation methods were often aimed at the suppression of the power equipment vibration only, but the vibration participation of the simplified rigid foundation was usually ignored in practice. The ‘power equipment-isolator-thin plate’ combination was considered as a composite vibration isolation system where the equipment was 4-point installed, and the transmitted forces from the equipment to the plate foundation were derived according to the mechanical 4-pole connection properties. In turn, the multi-objective optimization was performed in which the minimum power flow transmitted to the plate and the uniform vibration of the power equipment were defined as the fitness functions, and the purpose of the latter one was to sustain normal work and service life of the equipment. The multi-objective particle swarm optimization (MOPSO) algorithm was selected as the optimization tool in view of the advantages of less parameter settings, fast convergence, strong optimization capability and unique global optimal solution based on the Pareto dominance. This study combined together the power equipment vibration isolation, the thin plate vibration, the power flow transmission and the intelligent multi-objective optimization; in addition, a latest vibration theory for clamped plates aptly supported this strategy. The application of the MOPSO promotes the traditional view of vibration isolation and control.

Conservation of Energy in the Barotropic Quasi-Geostrophic Model Under Orographic Effects

ZHANG Yong-li, YANG Lian-gui

2016, 37(9): 936-944. doi: 10.21656/1000-0887.370075

Abstract(900) PDF(588)

Abstract:
Based on the barotropic atmospheric model, the impact of the terrain on the atmospheric energy was studied. Firstly, the equations of the barotropic model were nondimensionalized for scale analysis. Next, an appropriate small parameter was selected and the small parameter expansion method was used to build successively the 0th- and 1st-level approximate equations for the nondimensionalized barotropic model. Under the orographic effects, the barotropic quasi-geostrophic potential vorticity equations were obtained from which the conservation of energy was deduced. Furthermore, the orographic effects on the westwind were analyzed and explained from the view of energy.

Multi-Objective Optimization Design for Lateral Buckling Control of Subsea Pipelines by Distributed Buoyancy Sections

ZHAN Li-chao, LI Gang

2016, 37(9): 945-952. doi: 10.21656/1000-0887.370153

Abstract(1046) PDF(550)

Abstract:
In order to meet different performance requirements, a multi-objective optimization strategy was presented for the lateral buckling control of large-scale subsea pipeline systems based on the analytical model. The multi-objective optimization was performed with the NSGA-II algorithm to improve the lateral buckling control effects on the subsea pipeline through optimization of the layout scheme and design parameters of the distributed buoyancy sections. The optimization results show that the amount of the distributed buoyancy sections does not have absolute influence on the lateral buckling performance, and the Pareto-optimal set obtained from the multi-optimization provides helpful reference for designers to consider multiple performance requirements and choose more rational schemes.

Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations

HAN Hong-yang, LUO Zhi-qiang

2016, 37(9): 953-968. doi: 10.21656/1000-0887.370118

Abstract(970) PDF(622)

Abstract:
A predictor-corrector finite difference method based on the linearized Navier-Stokes equations was developed to numerically simulate the single- and double-vortex motions in 2D rectangular water tanks. Numerical results obtained with the present method were compared with the linearized analytical solution and previously published numerical results, and the agreements were pretty good. It is found that the free surface wave oscillates with a decaying amplitude in the case of viscous fluid, and as the Reynolds number increases, the free surface wave elevation decays more slowly. Under the short-period pitching excitation, a clear single vortex cycle occurs at different Reynolds numbers. However, the single vortex will change to double ones in the case of a long-period pitching excitation, only when the Reynolds number is small to some extent.

Heat and Mass Transfer in the Casson Nanofluid Flow Over a Stretching Cylinder in Cylindrical Coordinates

XU Xiao-qin, CHEN Shu-mei

2016, 37(9): 969-980. doi: 10.21656/1000-0887.370091

Abstract(1034) PDF(455)

Abstract:
For the first time the cylindrical coordinates were employed to study the heat and mass transfer in the steady laminar Casson nanofluid flow over a stretching cylinder in view of velocity slip and convective surface boundary conditions. The governing partial differential equations (PDEs) were transformed into highly nonlinear coupled ordinary differential equations (ODEs) via appropriate similarity transformations and then solved numerically with the shooting method. The effects of different physical parameters on velocity profiles, temperature and concentration distributions were presented graphically and analyzed in detail. The results show that the velocity is strongly influenced by the slip parameter, while the temperature and the concentration are sensitive to the Biot number and the Lewis number respectively. An increase in the Casson parameter will decelerate the flow but elevate the temperature and the concentration. Increasing the Brownian motion parameter or the thermophoresis parameter will raise the temperature. A larger concentration will come with a lower Brownian motion parameter or a higher thermophoresis parameter. The back flow exists in the concentration profile for relatively large values of the thermophoresis parameter.

Numerical Solution of the 2D Compressible Euler Equations Based on the Unstructured Adaptive Grids

YANG Yu-wei, YU Jia-lei, ZHANG Ya-ping, LI Xing-gang, QIU Xiao-pu

2016, 37(9): 981-992. doi: 10.21656/1000-0887.370077

Abstract(1215) PDF(649)

Abstract:
A numerical method for the solution of the 2D Euler equations based on the unstructured adaptive grids was proposed. The finite-volume method was used to carry out the space discretization, and the flux was calculated with Jamson’s central scheme, which was suitable for the calculation of arbitrary polygons. In order to get the stationary solution, an explicit 4-step Runge-Kutta iterative method was adopted to do the time-domain integral. According to the gradients of the flow field parameters, the refining edges were determined. Under this refining criterion, the mesh distribution was reasonably improved. With the proposed method the 2D Euler equations were solved for the simulation of the NACA0012 airfoil. The numerical results show the correctness and validity of the present method.

Discussion on the Modified Reciprocal Theorem of Works

XU Xiao-ming, YANG Di-xiong

2016, 37(9): 993-998. doi: 10.21656/1000-0887.370021

Abstract(1038) PDF(821)

Abstract:
A comparative study was demonstrated between the BettiMaxwell reciprocal theorem of works and the modified reciprocal theorem of works in view of linearelastic beam systems. It is indicated that 2 different beam systems under the real equilibrium states can be equivalently transformed into an identical beam system subjected to 2 sets of different external forces. Moreover, it is revealed that the ‘2 different linear elastic bodies’ in the modified reciprocal theorem of works are the same structure with equivalent boundary conditions of displacements and forces. Consequently, the modified reciprocal theorem of works is actually an alternative representation of the BettiMaxwell reciprocal theorem of works.

2016 Vol. 37, No. 9