FLEXURAL WAVE DISPERSION IN MULTI-WALLED CARBON NANOTUBES CONVEYING FLUIDS

Motivated by the great potential of carbon nanotubes for developing nanofluidic devices, this paper presents a nonlocal elastic, Timoshenko multi-beam model with the second order of strain gradient taken into consideration and derives the corresponding dispersion relation of flexural wave in multi-walled carbon nanotubes conveying fuids. The study shows that the moving flow reduces the phase velocity of flexural wave of the lowest branch in carbon nanotubes. The phase velocity of flexural wave of the lowest branch decreases with an increase of flow velocity. However, the effects of flow velocity on the other branches of the wave dispersion are not obvious. The effect of microstructure characterized by nonlocal elasticity on the dispersion of flexural wave becomes more and more remarkable with an increase in wave number.     

TRANSVERSE VIBRATION OF A HANGING NONUNIFORM NANOSCALE TUBE BASED ON NONLOCAL ELASTICITY THEORY WITH SURFACE EFFECTS

The aim of this paper is to study the free transverse vibration of a hanging nonuni- form nanoscale tube. The analysis procedure is based on nonlocal elasticity theory with surface effects. The nonlocal elasticity theory states that the stress at a point is a function of strains at all points in the continuum. This theory becomes significant for small-length scale objects such as micro- and nanostructures. The effects of nonlocality, surface energy and axial force on the natural frequencies of the nanotube are investigated. In this study, analytical solutions are formulated for a clamped-free Euler-Bernoulli beam to study the free vibration of nanoscale tubes.     

DYNAMIC BUCKLING BEHAVIOR OF MULTI-WALLED CARBON NANOTUBES SUBJECTED TO STEP AXIAL LOADING

This paper studies the dynamic buckling behavior of multi-walled carbon nanotubes (MWNTs) subjected to step axial loading.A buckling condition is derived,and numerical results are presented for MWNTs u...     

非局部—非对称拟连续统理论

本文基于原子点阵模型,应用广义函数论,建立了非局部一非对称拟连续统理论.并讨论了非对称应力的物理—力学模型,即微观—宏观相结合的模型理论.     

具有非局部体力矩的非局部弹性理论

本文基于非局部连续统场论的公理系统,建立了具有非局部体力矩作用的非局部弹性理论,我们证明了,在非局部弹性固体中存在着非局部体力矩,非局部体力矩引起了应力的非对称和非局部体力矩是由材料中的共价键产生的。     

基于无网格方法的碳纳米管自由振动分析1)

采用无网格方法分析了碳纳米管的自由振动问题。通过几个数值算例来证明本方法的收敛性。将不同长径比的碳纳米管的固有频率计算结果与公开文献的结果进行对比。对比结果表明：本文方法具有较高的计算精度,基于薄板样条径向基函数的无网格方法可以成功地分析碳纳米管的自由振动问题。     

TWISTING STATICS AND DYNAMICS FOR CIRCULAR ELASTIC NANOSOLIDS BY NONLOCAL ELASTICITY THEORY

The torsional static and dynamic behaviors of circular nanosolids such as nanoshafts, nanorods and nanotubes are established based on a new nonlocal elastic stress field theory. Based on a new expression for strain energy with a nonlocal nanoscale parameter, new higher-order governing equations and the corresponding boundary conditions are first derived here via the variational principle because the classical equilibrium conditions and/or equations of motion can- not be directly applied to nonlocal nanostructures even if the stress and moment quantities are replaced by the corresponding nonlocal quantities. The static twist and torsional vibration of circular, nonlocal nanosolids are solved and discussed in detail. A comparison of the conventional and new nonlocal models is also presented for a fully fixed nanosolid, where a lower-order governing equation and reduced stiffness are found in the conventional model while the new model reports opposite solutions. Analytical solutions and numerical examples based on the new nonlocal stress theory demonstrate that nonlocal stress enhances stiffness of nanosolids, i.e. the angular displacement decreases with the increasing nonlocal nanoscale while the natural frequency increases with the increasing nonlocal nanoscale.     

FREE VIBRATION ANALYSIS OF CARBON NANOTUBES BASED ON THE MESHLESS METHOD1)

采用无网格方法分析了碳纳米管的自由振动问题。通过几个数值算例来证明本方法的收敛性。将不同长径比的碳纳米管的固有频率计算结果与公开文献的结果进行对比。对比结果表明：本文方法具有较高的计算精度,基于薄板样条径向基函数的无网格方法可以成功地分析碳纳米管的自由振动问题。     

脆性断裂的非局部力学理论

本文提出一种脆性材料断裂的非局部力学理论,内容包括:Ⅰ、Ⅱ、Ⅲ型Griffith裂纹的非局部弹性应力场,裂纹尖端邻域非局部弹性应力场的渐近形式,脆性开裂的最大拉应力准则。文中给出了这种理论应用于三种基本型裂纹和Ⅰ-Ⅱ、Ⅰ-Ⅲ复合型裂纹临界开裂条件的计算结果,并把它们与一些试验资料和最小应变能密度因子理论进行了对比。     

非对称的非局部塑性理论

从非局部连续场论出发，假定形变与局部转动均属微小，当存在体力矩出现非对称应力场时，设对称应力的能量函数和非对称应力的能量函数可以独立计算。基于热力学原理和屈服面的概念，建立了一种新的非对称－非局部弹塑性力学理论。     

FREE VIBRATION ANALYSIS OF FLUID-CONVEYING CARBON NANOTUBE VIA WAVE METHOD

The wave method is introduced to vibration analysis of the fluid-conveying carbon nanotube. The constitutive relation of carbon nanotube on micro-scale is founded using the non- local elastic theory. The governing equation on micro-scale is obtained. And the first five orders of the natural frequency of the carbon nanotube conveying fluid with various speeds are calculated through the wave method. Besides, the critical flow velocity when the carbon nanotube loses stability is obtained. Meanwhile, a contrast is made between the result obtained through tile wave method and that in previous researches.     

碳纳米管的力学

在发现碳纳米管后不久,对于这些有趣结构的力学性质--包括高强度、高硬度、低密度和结构的完美性的理论预测,使人们认识到它们可能具有理想的科技应用价值.对这些预测的实验验证或个别验伪以及大量基于不同模型的计算机模拟方法,使得逾10年来对碳纳米管力学的理解日趋深入但远未达到尽头.本文回顾了理论预测,并对这种微小结构的观察和操作中经常用到的富有挑战性的实验技术进行了讨论.略述了采用的计算方法包括从头算法量子力学模拟、经典分子动力学和连续介质模型.多尺度和多物理模型的发展和模拟工具自然而然作为连接基础科学问题和工程应用的结果而出现,而这个主题仍然正在抓紧研究中.这里介绍了研究此主题的一些方法.注意力主要集中于研究力学性质的揭示方面,如杨氏模量、弯曲刚度、屈曲准则、拉伸和压缩强度.最后,讨论了利用这些性质的几个令人兴奋的应用例子,包括纳米绳束、填充的纳米管、纳米机电系统、纳米传感器和纳米管增强复合材料,引用了349篇参考文献. 图41参349     

基于非局部效应和表面效应的输流碳纳米管稳定性分析

应用非局部黏弹性夹层梁模型分析双参数弹性介质中输送脉动流碳纳米管的稳定性. 新模型中同时考虑了由管道内、外壁上的薄表面层引起的表面弹性效应和表面残余应力,经典的欧拉梁模型因此通过引入非局部参数和表面参数得到了改进. 用平均法对其控制方程进行求解,得到了管道稳定性区域. 数值算例揭示了纳米材料的非局部效应、表面效应及两个弹性介质参数对管道固有频率、临界流速和动态稳定性的复杂影响,结论可为纳米流体机械的结构设计和振动分析提供理论基础.     

基于非局部效应和表面效应的输流碳纳米管稳定性分析简

应用非局部黏弹性夹层梁模型分析双参数弹性介质中输送脉动流碳纳米管的稳定性. 新模型中同时考虑了由管道内、外壁上的薄表面层引起的表面弹性效应和表面残余应力，经典的欧拉梁模型因此通过引入非局部参数和表面参数得到了改进. 用平均法对其控制方程进行求解，得到了管道稳定性区域. 数值算例揭示了纳米材料的非局部效应、表面效应及两个弹性介质参数对管道固有频率、临界流速和动态稳定性的复杂影响，结论可为纳米流体机械的结构设计和振动分析提供理论基础.     

梯度型非局部高阶梁理论与非局部弯曲新解法

针对文献中关于纳米结构刚度受非局部效应影响趋势的不一致预测,基于梯度型的非局部微分本构模型,利用迭代法及泰勒展开法求得了非局部高阶应力的无穷级数表达,非局部应力相当于经典弯曲应力与非局部挠度的逐阶梯度之和. 然后推导了梯度型非局部高阶梁弯曲的挠曲轴微分方程,并结合正则摄动思想,求解了非局部挠度的表达式. 最后给出数值算例,具体量化挠度受非局部尺度因子的影响大小. 研究表明:相比于其经典值,纳米结构的非局部弯曲挠度可呈现出或增大或减小或不变的趋势,考虑梯度型非局部高阶应力降低或提高或不影响纳米结构的刚度,具体结果依赖于外载和边界约束的类型. 算例显示外载形式和边界约束条件均各自独立地影响着纳米结构的非局部弯曲挠度,同时首次观察到非局部最大弯曲挠度的位置可能受非局部尺度因子的影响. 研究结论解决了非局部弹性力学应用于纳米结构的若干疑点,并为理论的发展和优化提供支持.      

CARBON NANOTUBES VIA METHANE DECOMPOSITION ON AN ALUMINA SUPPORTED COBALT AEROGEL CATALYST

An alumina-supported cobalt aerogel catalyst prepared from a sol-gel and a supercritical drying method was used in the catalytic decomposition of methane.The physical-chemical properties of the catalyst were characterized and its activity for methane decomposition was investigated.The effects of calcination and reaction temperatures on the activity of the catalyst and the morphology of the carbon nanotubes produced were discussed.A COAl2O4 spinel structure formed in the calcined catalyst.The quantity of the nanotubes produced in the reaction increases with the amount of cobalt in the reduced catalyst.A higher reaction temperature leads to a higher reaction rate,though faster deactivation of the catalyst occurs with the change.The carbon nanotubes grown on the catalyst have smooth walls and uniform diameter distribution.     

EXPLICIT SOLUTION FOR G-BAND MODE FREQUENCY OF SINGLE-WALLED CARBON NANOTUBES

G-band mode is one of the most important Raman modes of single-walled carbon nanotubes （SWCNTs）. The vibrational frequency of the mode can be used to characterize SWC- NTs. However, analytical expression that can link the frequency to the geometrical parameters of a SWCNT is to date not reported. Based on a molecular mechanics model, the analytical solution is obtained for G-band mode frequency of SWCNTs. The result calculated from the present solutions is in good agreement with the existing experimental and numerical data.     

INTERACTION-MEDIATED GROWTH OF CARBON NANOTUBES ON ACICULAR SILICA-COATED a-Fe CATALYST BY CHEMICAL VAPOR DEPOSITION BY CHEMICAL VAPOR DEPOSITION

1. Introduction Carbon nanotubes (CNTs), a kind of the most advanced nanomaterials with novel properties and promising for many applications, have aroused great interest of the world in a number of research fields (Iijima, 1991; Baughman et al., 2002; Iijima & Ichihashi, 1993; Rao & Govindaraj, 2002; Rueckes et al., 2000; Adrian et al., 2001; Javey et al., 2003). Catalytic chemical vapor deposition (CCVD) is re-garded as the most suitable method for the preparation of microstructured CN…     

INTERACTION-MEDIATED GROWTH OF CARBON NANOTUBES ON ACICULAR SILICA-COATED α-Fe CATALYST BY CHEMICAL VAPOR DEPOSITION

Multi-walled carbon nanotubes (MWNTs) with 20 nm outer diameter were prepared by chemical vapor deposition of ethylene using ultrafine surface-modified acicular α-Fe catalyst particles.The growth mechanism of MWNTs on the larger catalyst particles are attributed to the interaction between the Fe nanoparticles with the surface-modified silica layer.This interaction-mediated growth mechanism is illustrated by studying the electronic,atomic and crystal properties of surface-modified catalysts and MWNTs products by characterization with X-ray diffraction (XRD),transmission electron microscopy (TEM),high resolution transmission electron microscopy (HRTEM),thermal gravimetric analysis (TGA) and Raman spectra.     

INVESTIGATIONS ON THE MECHANICAL CHARACTERISTICS OF NANOBEAMS BASED ON THE NONLOCAL STRAIN GRADIENT THEORY1)

基于非局部应变梯度理论,建立了一种具有尺度效应的高阶剪切变形纳米梁的力学模型. 其中,考虑了应变场和一阶应变梯度场下的非局部效应. 采用哈密顿原理推导了纳米梁的控制方程和边界条件,并给出了简支边界条件下静弯曲、自由振动和线性屈曲问题的纳维级数解. 数值结果表明,非局部效应对梁的刚度产生软化作用,应变梯度效应对纳米梁的刚度产生硬化作用,梁的刚度整体呈现软化还是硬化效应依赖于非局部参数与材料特征尺度的比值. 梁的厚度与材料特征尺度越接近,非局部应变梯度理论与经典弹性理论所预测结果之间的差异越显著.