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1、On Some Mechanics Problems in One Dimensional Nanostructure Carbon nanotubes and copper nanowires are so promising nano-components that their mechanical properties have received more and more attention over the past decade. In studying the nano-components, molecular dynamics simulations can only pre
2、dict the dynamics results case by case and can hardly reveal the relation between multiple physical variables. On the other hand, it is still an open problem whether the continuum mechanics is valid to those discrete nano-components by nature. If not, is it possible to get any modified approach to d
3、eal with nano-components? The objective of this dissertation is to check the validity of the continuum mechanics, especially the continuum dynamics, for the nano-structures of one dimension, such as the carbon nanotubes and copper nanowires, with help of molecular dynamics simulations. The studies p
4、resented in the dissertation include the dispersion of both flexural and longitudinal waves in carbon nanotubes, the buckling of both single- walled and multi-walled carbon nanotubes, the impact of carbon nanotubes with a rigid wall, the size effect on the effective Youngs modulus of copper nanowire
5、s, the dynamic buckling of copper nanowires and the effect of temperature in nano-scale problems. The results and the main contributions of the dissertation are as following. 1. The flexural wave propagation in single-walled carbon nanotubes was studied through the use of the continuum mechanics and
6、 the molecular dynamics simulation based on the Terroff-Brenner potential. The study focuses on the wave dispersion caused not only by the rotary inertia and the shear deformation in the model of a traditional Timoshenko beam, but also by the non-local elasticity characterizing the microstructure of
7、 a carbon nanotube in a wide frequency range up to THz. For this purpose, the study starts with the dynamic equation of a generalized Timoshenko beam made of the non-local elastic material, and then gives the dispersion relations of the flexural wave in the non-local elastic Timoshenko beam, the tra
8、ditional Timoshenko beam and the Euler beam, respectively. Afterwards, it presents the molecular dynamics simulations for the flexural wave propagation in an armchair (5,5) and an armchair (10,10) single-walled carbon nanotubes for a wide range of wave numbers. The simulation results show that the E
9、uler beam holds for describing the dispersion of flexural waves in these two single-walled carbon nanotubes only when the wave number is small. The Timoshenko beam provides a better prediction for the dispersion of flexural waves in the two single-walled carbon nanotubes when the wave number becomes
10、 a little bit large. Only the non-local elastic Timoshenko beam is able to predict the decrease of phase velocity when the wave number is so large that the microstructure of carbon nanotubes has a significant influence on the flexural wave dispersion. The work has been published in Physical Review B
11、. The referee wrote: “This is an extremely interesting paper which would, most likely, make a significant contribution and impact to the study of dynamic behavior of CNTs”. 2. The study on the longitudinal wave propagation and dispersion in single-walled carbon nanotubes was presented through the us
12、e of the continuum mechanics and the molecular dynamics simulation based on the Terroff-Brenner potential. The study focuses on the effects of non-local elasticity characterizing the microstructure on the wave dispersion of single-walled carbon nanotubes. The study begins with the numerical simulati
13、on of molecular dynamics for the longitudinal wave of single-walled carbon nanotubes. Then, it presents the wave dispersion relations based on the models of rods or shells, made of either the elastic materials or the non-local elastic materials so as to characterize the micro-structure, for the carb
14、on nanotubes. Among them, only the model of non-local elastic shell is able to get a good agreement with the molecular dynamics in a wide frequency range up to THz. The study shows that both the micro-structure and the coupling of longitudinal wave and radial motion play an important role in the wav
15、e dispersion of carbon nanotubes. The work has been published in Nanotechnology. 题目：一维纳米结构的若干力学问题 碳纳米管、铜纳米线是构成未来纳米器件的重要元素，如何了解和描述其 力学特性成为人们近几十年非常关注的科学问题。采用分子动力学方法研究这 类纳尺度结构，只能得到个案结果，难以获得多个物理量之间的一般关系。连 续介质力学方法能否适用于这类本质离散的纳尺度结构呢？若不适用，是否可 以改造之？ 本文以碳纳米管及铜纳米线等一维纳米结构为研究对象，采用连续介质力学分 析与分子动力学计算相结合的方法，探索连续介质力
16、学的有效性及失效时的改 进，对碳纳米管中纵波与弯曲波的传播、单壁及多壁碳纳米管的屈曲、碳纳米 管与刚性壁的碰撞、铜纳米线的表面效应引起的尺寸效应、铜纳米线的动力屈 曲和纳尺度的温度等问题进行了研究，其主要创新及学术贡献如下： 1.通过连续介质力学方法及基于 Tersoff-Brenner 势的分子动力学方法对 比研究了碳纳米管中弯曲波的传播及频散问题，主要考虑了转动惯量、剪切变 形及非局部弹性所描述的微结构对碳纳米管中弯曲波频散的影响。建立了考虑 转动惯量及剪切变形的非局部弹性梁动力学方程。基于考虑转动惯量及剪切变 形的非局部弹性梁模型，Timoshenko 梁模型及 Euler 梁模型，给出了单壁碳纳 米管中弯曲波传播的频散关系。然后用分子动力学方法模拟了不同周期的弯曲 波在碳纳米管中的传播。结果表明：Euler 梁模型只在很小的波数范围内适用， Timoshenko 梁模型能更好地给出单壁碳纳米管中弯曲波的频散关系；当波数非 常大时，碳纳米管的微结构对波的传播将产生非常重要的影响，此
