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2018年 第39卷 第8期    刊出日期：2018-08-01

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论文

Controllable wave propagation in a weakly nonlinear monoatomic lattice chain with nonlocal interaction and active control

Jiao WANG, Weijian ZHOU, Yang HUANG, Chaofeng LYU, Weiqiu CHEN, Weiqiu ZHU

2018, 39(8):  1059-1070.  doi:10.1007/s10483-018-2360-6

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The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincaré perturbation method. The dispersion relation is derived with the consideration of both the nonlocal and the active control effects. The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve. When the nonlocal effect is strong enough, zero and negative group velocities will be evoked at different points along the dispersion curve, which will provide different ways of transporting energy including the forward-propagation, localization, and backwardpropagation of wavepackets related to the phase velocity. Both the nonlinear effect and the active control can enhance the frequency, but neither of them is able to produce zero or negative group velocities. Specifically, the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero, and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range. With a combinational adjustment of all these effects, the wave propagation behaviors can be comprehensively controlled, and energy transferring can be readily manipulated in various ways.



Two-dimensional equations for thin-films of ionic conductors

Shuting LU, Chunli ZHANG, Weiqiu CHEN, Jiashi YANG

2018, 39(8):  1071-1088.  doi:10.1007/s10483-018-2354-6

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A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck (PNP) theory, the two-dimensional (2D) equations for thin ionic conductor films are obtained from the three-dimensional (3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.

Frequency equations of nonlocal elastic micro/nanobeams with the consideration of the surface effects

H. S. ZHAO, Y. ZHANG, S. T. LIE

2018, 39(8):  1089-1102.  doi:10.1007/s10483-018-2358-6

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A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia, in which the nonlocal and surface effects are considered. Three types of boundary conditions, i.e., hinged-hinged, clamped-clamped, and clamped-hinged ends, are examined. For a hinged-hinged beam, an exact and explicit natural frequency equation is derived based on the established mathematical model. The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams. In sum, the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity, the surface elasticity, the residual surface stress, and the rotatory inertia, providing a more convenient means in comparison with numerical computations.

An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks

M. HAJIMOHAMADI, R. GHAJAR

2018, 39(8):  1103-1118.  doi:10.1007/s10483-018-2356-6

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The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors (SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole (a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.

Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties

F. E. ÁLVAREZ-BORGES, J. BRAVO-CASTILLERO, M. E. CRUZ, R. GUINOVART-DÍAZ, L. D. PÉREZ-FERNÁNDEZ, R. RODRÍGUEZ-RAMOS, F. J. SABINA

2018, 39(8):  1119-1146.  doi:10.1007/s10483-018-2352-6

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A family of one-dimensional (1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method (RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.

Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field

Hongxia GUO, Ping LIN, Lin LI

2018, 39(8):  1147-1164.  doi:10.1007/s10483-018-2355-6

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The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.

Dripping retardation with corrugated ceiling

Dong LUO, Jianjun TAO

2018, 39(8):  1165-1172.  doi:10.1007/s10483-018-2357-6

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The instabilities of a pendent viscous thin film underneath two corrugated ceilings are studied numerically and theoretically in comparison with the case of a flat wall. With the same initial interface perturbations, it is shown numerically that both the supercritical instability and the subcritical instability can be retarded by the in-phase corrugated ceilings. The lubrication approximation is used to explain the retardation effect of the corrugated ceiling on the supercritical instability of the pendant film, where the linear growth rate is revealed to be power three of the initial film thickness.

Jeffrey fluid flow due to curved stretching surface with Cattaneo-Christov heat flux

T. HAYAT, S. QAYYUM, M. IMTIAZ, A. ALSAEDI

2018, 39(8):  1173-1186.  doi:10.1007/s10483-018-2361-6

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The two-dimensional (2D) motion of the Jeffrey fluid by the curved stretching sheet coiled in a circle is investigated. The non-Fourier heat flux model is used for the heat transfer analysis. Feasible similarity variables are used to transform the highly nonlinear ordinary equations to partial differential equations (PDEs). The homotopy technique is used for the convergence of the velocity and temperature equations. The effects of the involved parameters on the physical properties of the fluid are described graphically. The results show that the curvature parameter is an increasing function of velocity and temperature, and the temperature is a decreasing function of the thermal relaxation time. Besides, the Deborah number has a reverse effect on the pressure and surface drag force.

Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution

K. JAVAHERDEH, A. NAJJARNEZAMI

2018, 39(8):  1187-1200.  doi:10.1007/s10483-018-2353-6

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The lattice Boltzmann method (LBM) is used to simulate the effect of magnetic field on the natural convection in a porous cavity. The sidewalls of the cavity are heated sinusoidally with a phase derivation, whereas the top and bottom walls are thermally insulated. Numerical simulation is performed, and the effects of the pertinent parameters, e.g., the Hartmann number, the porosity, the Darcy number, and the phase deviation, on the fluid flow and heat transfer are investigated. The results show that the heat transfer is affected by the temperature distribution on the sidewalls clearly. When the Hartmann number is 0, the maximum average Nusselt number is obtained at the phase deviation 90°. Moreover, the heat transfer enhances when the Darcy number and porosity increase, while decreases when the Hartman number increases.

TiO₂-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

A. A. SIDDIQUI, M. SHEIKHOLESLAMI

2018, 39(8):  1201-1216.  doi:10.1007/s10483-018-2359-6

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The TiO₂-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem (BVP). The BVP is analytically solved with the homotopy analysis method (HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO₂ nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO₂ nanoparticles increases. This confirms the fact that the occurrence of the TiO₂ nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased. An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water, while the Nusselt number of the nanofluid is larger than that of pure water. However, both the parameters increase if the magnetic field intensity increases.

Corrigendum: incompatible deformation field and Riemann curvature tensor

Bohua SUN

2018, 39(8):  1217-1218. 

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