Table of Content

01 May 2014, Volume 35 Issue 5

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Articles

Guided motion of short carbon nanotube driven by non-uniform electric field

XU Zhen;HU Guo-Hui;WANG Zhi-Liang;ZHOU Zhe-Wei

2014, 35(5):  535-540.  doi:10.1007/s10483-014-1810-x

Abstract ( 454 )   HTML   PDF (262KB) ( 425 )  

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The molecular dynamics simulations are performed to show that in aqueous environments, a short single-walled carbon nanotube (SWCNT) guided by a long SWCNT, either inside or outside the longer tube, is capable of moving along the nanotube axis unidirectionally in an electric field perpendicular to the carbon nanotube (CNT) axis with the linear gradient. The design suggests a new way of molecule transportation or mass delivery. To reveal the mechanism behind this phenomenon, the free energy profiles of the system are calculated by the method of the potential of mean force (PMF).

Short wave stability of homogeneous shear flows with variable topography

DOU Hua-Shu;V. GANESH

2014, 35(5):  541-548.  doi:10.1007/s10483-014-1811-7

Abstract ( 502 )   HTML   PDF (116KB) ( 319 )  

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For the stability problem of homogeneous shear flows in sea straits of arbitrary cross section, a sufficient condition for stability is derived under the condition of inviscid flow. It is shown that there is a critical wave number, and if the wave number of a normal mode is greater than this critical wave number, the mode is stable.

Study of shear-thinning/thickening effects on plane Couette-Poiseuille flow with uniform crossflow

LIU Yu-Quan;ZHU Ke-Qin

2014, 35(5):  549-566.  doi:10.1007/s10483-014-1812-6

Abstract ( 579 )   HTML   PDF (360KB) ( 319 )  

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The shear-thinning/thickening effects on the plane Couette-Poiseuille flow with a uniform crossflow are studied. The detailed solution procedures for both theoretical and numerical purposes are given. In order to clarify the difference between the Newtonian flow and the power-law flow, all cases of the plane Couette-Poiseuille flows with uniform crossflows for different power indexes are assigned to the phase diagram in the parameter plane corresponding to the Couette number and the crossflow Reynolds number. The effects of shear-thinning/thickening on the phase diagram are discussed. An important feature of the shear-thinning circumstance distinguished from the shearthickening circumstance is discovered.

Influence of atomic force microscope (AFM) probe shape on adhesion force measured in humidity environment

YANG Li;TU Yo-Song;TAN Hui-Li

2014, 35(5):  567-574.  doi:10.1007/s10483-014-1813-7

Abstract ( 529 )   HTML   PDF (247KB) ( 680 )  

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In micro-manipulation, the adhesion force has very important influence on behaviors of micro-objects. Here, a theoretical study on the effects of humidity on the adhesion force is presented between atomic force microscope (AFM) tips and substrate. The analysis shows that the precise tip geometry plays a critical role on humidity dependence of the adhesion force, which is the dominant factor in manipulating micro-objects in AFM experiments. For a blunt (paraboloid) tip, the adhesion force versus humidity curves tends to the apparent contrast (peak-to-valley corrugation) with a broad range. This paper demonstrates that the abrupt change of the adhesion force has high correlation with probe curvatures, which is mediated by coordinates of solid-liquid-vapor contact lines (triple point) on the probe profiles. The study provides insights for further understanding nanoscale adhesion forces and the way to choose probe shapes in manipulating micro-objects in AFM experiments.

Pulsatile blood flow in large arteries: comparative study of Burton’s and McDonald’s models

K. GAYATHRI;K. SHAILENDHRA

2014, 35(5):  575-590.  doi:10.1007/s10483-014-1814-7

Abstract ( 676 )   HTML   PDF (349KB) ( 397 )  

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To get a clear picture of the pulsatile nature of blood flow and its role in the pathogenesis of atherosclerosis, a comparative study of blood flow in large arteries is carried out using the two widely used models, McDonald’s and Burton’s models, for the pressure gradient. For both models, the blood velocity in the lumen is obtained analytically. Elaborate investigations on the wall shear stress (WSS) and oscillatory shear index (OSI) are carried out. The results are in good agreement with the available data in the literature. The superiority of McDonald’s model in capturing the pulsatile nat re of blood flow, especially the OSI, is highlighted. The present investigation supports the hypothesis that not only WSS but also OSI are the essential features determining the pathogenesis of atherosclerosis. Finally, by reviewing the limitations of the present investigation, the possibility of improvement is explored.

Free vibration of functionally graded beams based on both classical and first-order shear deformation beam theories

LI Shi-Rong;WAN Ze-Qing;ZHANG Jing-Hua

2014, 35(5):  591-606.  doi:10.1007/s10483-014-1815-6

Abstract ( 752 )   HTML   PDF (355KB) ( 618 )  

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The free vibration of functionally graded material (FGM) beams is studied based on both the classical and the first-order shear deformation beam theories. The equations of motion for the FGM beams are derived by considering the shear deformation and the axial, transversal, rotational, and axial-rotational coupling inertia forces on the assumption that the material properties vary arbitrarily in the thickness direction. By using the numerical shooting method to solve the eigenvalue problem of the coupled ordinary differential equations with different boundary conditions, the natural frequencies of the FGM Timoshenko beams are obtained numerically. In a special case of the classical beam theory, a proportional transformation between the natural frequencies of the FGM and the reference homogenous beams is obtained by using the mathematical similarity between the mathematical formulations. This formula provides a simple and useful approach to evaluate the natural frequencies of the FGM beams without dealing with the tension-bending coupling problem. Approximately, this analogous transition can also be extended to predict the frequencies of the FGM Timoshenko beams. The numerical results obtained by the shooting method and those obtained by the analogous transformation are presented to show the effects of the material gradient, the slenderness ratio, and the boundary conditions on the natural frequencies in detail.

Transverse vibrations of arbitrary non-uniform beams

GUO Shu-Qi;YANG Shao-Pu

2014, 35(5):  607-620.  doi:10.1007/s10483-014-1816-7

Abstract ( 618 )   HTML   PDF (162KB) ( 469 )  

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Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.

Unified proof to oscillation property of discrete beam

ZHENG Zi-Jun;CHEN Pu;WANG Da-Jun

2014, 35(5):  621-636.  doi:10.1007/s10483-014-1817-6

Abstract ( 736 )   HTML   PDF (308KB) ( 375 )  

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The oscillation property (OP) is a fundamental and important qualitative property for the vibrations of single span one-dimensional continuums such as strings, bars, torsion bars, and Euler beams. Any properly discretized continuum model should keep the OP. In literatures, the OP of discrete beam models is discussed essentially by means of matrix factorization. The discussion is model-specific and boundary-conditionspecific. Besides, matrix factorization is difficult in handling finite element (FE) models of beams. In this paper, according to a sufficient condition for the OP, a new approach to discuss the property is proposed. The local criteria on discrete displacements rather than global matrix factorizations are given to verify the OP. Based on the proposed approach, known results such as the OP for the 2-node FE beams via the Heilinger-Reissener principle (HR-FE beams) as well as the 5-point finite difference (FD) beams are verified. New results on the OP for the 2-node PE-FE beams and the FE Timoshenko beams with small slenderness are given. Through a simple manipulation, the qualitative property of discrete multibearing beams can also be discussed by the proposed approach.

Analysis of bonded anisotropic wedges with interface crack under anti-plane shear loading

M. GHADIRI;A. R. SHAHANI

2014, 35(5):  637-654.  doi:10.1007/s10483-014-1818-6

Abstract ( 698 )   HTML   PDF (473KB) ( 419 )  

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The antiplane stress analysis of two anisotropic finite wedges with arbitrary radii and apex angles that are bonded together along a common edge is investigated. The wedge radial boundaries can be subjected to displacement-displacement boundary conditions, and the circular boundary of the wedge is free from any traction. The new finite complex transforms are employed to solve the problem. These finite complex transforms have complex analogies to both kinds of standard finite Mellin transforms. The traction free condition on the crack faces is expressed as a singular integral equation by using the exact analytical method. The explicit terms for the strength of singularity are extracted, showing the dependence of the order of the stress singularity on the wedge angle, material constants, and boundary conditions. A numerical method is used for solving the resultant singular integral equations. The displacement boundary condition may be a general term of the Taylor series expansion for the displacement prescribed on the radial edge of the wedge. Thus, the analysis of every kind of displacement boundary conditions can be obtained by the achieved results from the foregoing general displacement boundary condition. The obtained stress intensity factors (SIFs) at the crack tips are plotted and compared with those obtained by the finite element analysis (FEA).

Contrast structure for singular singularly perturbed boundary value problem

WANG Ai-Feng;NI Ming-Kang

2014, 35(5):  655-666.  doi:10.1007/s10483-014-1819-7

Abstract ( 605 )   HTML   PDF (154KB) ( 330 )  

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The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the steptype solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.