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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 predict 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 deal 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 presented 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 nanowires, 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 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 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 traditional 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 Euler 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 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. 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 use 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 simulation 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 carbon 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 wave 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,此时随着波数的增加相速度将会降低;考虑了转动惯量、剪切变形及非局部弹性的梁模型可以较好预测这时的频散关系。该研究结果发表在Physical Review B上,被评价为“这是一篇非常有趣的论文,很有可能对碳纳米管动力学行为的研究产生重要的贡献和影响”。 2.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纵波的传播及频散问题,主要考虑了微结构对碳纳米管中纵波频散的影响。首先用分子动力学模拟了不同周期的纵波在碳纳米管中的传播。然后基于各种弹性杆模型、弹性壳模型、非局部弹性杆模型及非局部弹性壳模型得出了频散关系。结果表明:只有考虑非局部弹性的壳模型能很好地预测两支频散关系,微结构以及纵波与管壁径向运动的耦合会影响碳纳米管中高频纵波的频散。该研究结果发表在Nanotechnology上。Summary:(skills&examples& the differences between English and Chinese)1. 分译(division)英语长句中,有不少从句、短语或单词与主句间关系并不十分密切。翻译时,要按汉语中多用短句的习惯,把这些从句、短语或单词翻译为句子,与其他分句一起,表达出原句意思。Example:文中第一句,“Carbon nanotubes and copper nanowires are so promising nano-components that their mechanical properties have received more and more attention over the past decade.”用到了“sothat/太以至于”句式,但直译为中文有所不妥。所以可将关系不十分密切的从句拆开,译为“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”。中英差异:“汉语重意合hypotaxis,英语重形合parataxis”。汉语句法特征是“意合”,注意语意功能。一个句子可以由好几个短语组成,它们之间强调逻辑关联与意义关联,句子内部很少有关联词语前后照应。而英语句法的特征是“形合”,注意语法形式和功能,句子要按照语法规则来组织。句子的主语和谓语要在数、语态、时态等上保持一致主句与从句间要用连接词来衔接起来。由此可见,英汉语言的区别还显示于:英语结构紧凑,汉语结构松散。英语多长句,汉语多短句。英语多从句,汉语多分句。2. 增补这是在译文中增添一些原文中有其义而无其行的词,使译文的语法结构、表达方式、修辞、语气以及文化思想和思维方式既有英语特色,又符合汉语表达习惯。Example:原文第二句,“molecular dynamics simulations can only predict the dynamics results case by case”此处应进行语义性增补,补充“采用”,翻译为“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”。中英差异:“汉语重动词,英语重名词”汉语句子特点之一是可连用动词,而英语中,主语和谓语使句子的主干,其他句子成分都围绕主谓展开,因此名词介词使用较多。3. 省略(Omission)1)英译汉时,在英语中把某些仅仅为了语法需要而存在的词语适当删减,译文更加严谨、简明、合乎汉语习惯。Examples:原文在翻译时多次用到形式主语it的省略翻译的技巧,如:“On the other hand, it is still an open problem whether the continuum mechanics is valid to those discrete nano-components by nature.”此句中“it”为形式主语,翻译时可将其省略,“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?”。此类例子十分普遍,如文中“Afterwards, it presents the molecular dynamics simulations for”和“Then, it presents the wave dispersion relations based on the models of rods or shells”,翻译时都可将其省略。再如,“If not, is it possible to get any modified approach to deal with nano-components?”只需翻译为“若不适用,是否可以改造之?”即可。中英差异:“英语重结构,汉语重语义”此差异类似“形合”与“意合”的差异,在此便不再过多赘述。2)省略主语Example: 译文中多为无主句,而原文中均有明确主语。例子很多,此处不一一列举。中英差异:“汉语无主句多,英语主语突出”汉语句子中主语隐含不显或无主语的情况时常可见。一是实际环境不需要把主语说出来;二是主语见于上下文,不必重复;三是主语泛指,也就不必说出。而英语句法特点是主语突出。除省略句外,英语句子都要有主语。4. 调整语序1)英汉两种语言在表达上语序有所不同,为使译文符合汉语规范,英译汉时,有必要对原文语序进行一定的调整。同时,英语中有许多被动结构,英译汉时,可翻译为主动结构,这时,语序也需做相应调整。Example: 本文1及2两个部分的首句都用
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