[考博复习资料]全国优秀博士学位论文中英文摘要精选(3)_考博_旭晨教育

以下是全国优秀博士学位论文中英文摘要精选系列连载，希望能为对备考的博友们和在读的博士生提供一份参考。

全国优秀博士学位论文中英文摘要

一维纳米结构的若干力学问题

作者姓名：王立峰

论文题目：一维纳米结构的若干力学问题

作者简介：王立峰，男，1977年12月出生，2002年4月师从于南京航空航天大学胡海岩教授，于2005年6月获博士学位。

中文摘要

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.用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.用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。

3.研究了碳纳米管的屈曲及后屈曲。先用基于 Tersoff-Brenner 势的分子动力学方法研究单壁碳纳米管在轴向载荷下的非线性后屈曲行为，结果表明：碳纳米管在后屈曲阶段近似为理想塑性弹簧，其屈曲过程是能量吸收的过程，碳纳米管可作为很好的吸能元件;连续介质力学可以较好地给出碳纳米管的屈曲点，但只能给出近似的后屈曲行为。该研究结果发表在Acta Mechanica Solida Sinica上。然后用分子动力学方法模拟了多壁碳纳米管在压缩、弯曲变形下力与变形的关系。通过与组成多壁碳纳米管的各单壁碳纳米管的比较分析，揭示了多壁碳纳米管层间Van der Waals力对碳纳米管力学性质的影响。采用6-12形式的 Lennard-Jones势描述碳纳米管壁间Van der Waals力。计算结果表明：多壁碳纳米管的比强度明显高于单壁碳纳米管;Van der Waals力对杨氏模量影响不大，但对碳纳米管屈曲行为的影响却相当显著。该研究结果发表在固体力学学报上。

4.用分子动力学方法模拟碳纳米管与刚性壁的正碰撞过程，并与弹性动力学方法的分析结果进行对比。在分子动力学模拟中，采用Tersoff-Brenner势描述碳纳米管的原子间相互作用，用6-12形式的Lennard-Jones势描述碳纳米管与刚性壁间相互作用。结果表明：两种方法所得到的应力波传播速度吻合较好，应力波的传播过程是原子的动能和原子间势能的转化过程;与弹性动力学分析结果不同的是，在发生屈曲以前，碳纳米管与刚性壁的接触时间不仅与碳纳米管的长度近似成线性关系，还与管径及碰撞初速度有关;碰撞过程中，碳纳米管端部应力并非定值，但其平均值与弹性动力学计算结果相差不大。该研究结果发表在固体力学学报上。

5.研究了尺寸效应对铜纳米线杨氏模量的影响，以及铜纳米线的动力屈曲问题。首先根据基于内嵌原子势的分子动力学模拟结果，利用铜纳米线的非均匀性解释了尺寸效应对铜纳米线的杆模型和梁模型的等效杨氏模量的影响。和分子动力学的结果相对比，新的杆模型与以前的杆模型都符合得很好，但新的非均匀梁模型比以前的梁模型符合得更好。从对铜纳米线纵向振动和横向振动的固有频率的分子动力学模拟中同样得到纳米铜金属线的尺寸效应。该研究结果发表在International Journal of computational method上。然后用分子动力学方法和弹性动力学方法研究了铜纳米线的动力屈曲，模拟了不同载荷下铜纳米线的动力屈曲型态。用弹性动力学理论分析铜纳米线的动力屈曲，并与分子动力学模拟的结果进行了比较。分子动力学模拟得到的屈曲临界载荷略高于弹性动力学所给出的临界载荷。根据弹性动力学预测，应力波会对铜纳米线的动力屈曲产生显著影响。该研究结果发表在 International Journal of Nonlinear Sciences and Numerical Simulation上。

6.此外，初步探索了纳米尺度和温度有关的一些问题。研究了多壁碳纳米管间的热传导、碳纳米管的热膨胀、温度对纳米振荡器中阻尼的影响、纳米振荡器的转动问题以及基于碳纳米管的纳米振荡器的热激振动问题，讨论了分子动力学模拟过程中温度的定义。在研究中，为了避免人为控制温度对纳米结构整体动力学运动的影响，采用热传导方法对纳米结构加热，而不是通过直接对结构进行控制来研究温度问题。

基于上述研究发表的论文已被美国艺术与科学院、国家工程院院士T Belytschko教授(Meccanica 40: 455)、英国皇家学会院士 YW Mai教授(J. Appl. Phys. 103, 074309)、美国复合材料学会主席RF Gibson教授 (Compos. Sci. Technol. 67:1)，BI Yakobson教授 (J. Mech. Phys. Solids,2008 Available online)、HJ Gao教授 (Appl. Phys. Lett. 93, 013106)、TW Chou教授(Phys. Rev. B 73, 245407)等著名学者引用 60余次。其中，发表在Phys. Rev. B上关于弯曲波频散研究的论文被美国复合材料学会主席RF Gibson教授在长篇综述中作为“特别重要” 的研究举例(Compos. Sci. Technol. 67:1);被英国曼彻斯特大学的QM Li等在 P. Roy. Soc. A Math. Phys. (464:1941)上以近半页篇幅引述;被新加坡国立大学的CM Wang教授在多篇论文中列举为采用非弹性理论揭示纳尺度微结构效应的第一篇文献 (J. Phys. D: Appl. Phys. 39: 3904; Int. J. Struct. Stabil. Dynam. 7:555; Nanotechnology 18: 105401);被H Askes等作为应变梯度理论应用于纳尺度动力学的注解(Int. J. Numer. Meth. Engng, 72:111)。在 Acta Mechanica Solida Sinica 上发表的论文所预测的碳纳米管在循环载荷下的迟滞现象，被HW Yap等发表在 Nano Letters 7: 1149上的实验结果所证实。

关键词： 分子动力学，碳纳米管，屈曲，碰撞，Van der Waals力，纵波，弯曲波，频散，应变梯度，温度

On Some Mechanics Problems in One Dimensional Nanostructure

Wang Lifeng

ABSTR ACT

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 Young’s 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.

3. The buckling behavior of carbon nanotubes was revealed through the use of molecular dynamics simulation based on the Tersoff-Brenner potential. The dissertation presents the buckling and the postbuckling of single-walled carbon nanotubes subjected to a cyclic axial compressive load and gives the bifurcation behavior in buckling process simulated with very fine time steps. In the whole cycle of nonlinear deformation, the carbon nanotubes exhibit the profound hysteretic behavior and the energy absorption ability. The molecular dynamics simulation indicates that the carbon nanotube behaves approximately as an ideal plastic spring when the cyclic strain is applied within the same postbuckling mode. In comparison, the theory of continuum mechanics gives a good prediction for the critical buckling strength, but only provides a rough estimation for the post-buckling behaviors. The work has been published in Acta Mechanica Solida Sinica. It presents the molecular dynamics simulations for both single-walled and multi-walled carbon nanotubes subjected to different external loads to examine the influence of the van der Waals force on the property of multi-wall carbon nanotubes. In this part, the van der Waals force between the walls is approximated through the use of the ‘6-12’ Lennard-Jones potential. Although the van der Waals force has no remarkable effect on the Young’s modulus, its influence on the strength and buckling behavior of carbon nanotubes is significant. The work has been published in Acta Mechanica Solida Sinica (Chinses edition).

4. With help of molecular dynamics simulations the dissertation studied the impact of carbon nanotubes with a rigid wall, where the interatomic interactions are described by a Tersoff-Brenner potential and the interactions between the atoms of carbon nanotubes and the rigid wall are approximated by the ‘6-12’ Lennard-Jones potential. The simulations show that the velocity of stress waves predicted by molecular dynamics falls into the same range by the theory of elasticity. Different from an elastic rod, the impact duration of a nanotube is not only proportional to the length of nanotube, but also depends on the initial impact velocity and the diameter of nanotube. Furthermore, the stress at the end of nanotube is not a constant during impact. However, its mean value is close to the result given by theory of elasticity. The work has been published in Acta Mechanica Solida Sinica (Chinese Edition).

5. The molecular dynamics simulation on the basis of embedded atom potential show the inhomogeneous property of the nanowires, and then establishes the continuum model of either a rod or a beam to predict the size dependence of the effective Young’s modulus. The comparison with molecular dynamics simulation shows that the rod model here enables one to predict the effective Young’s modulus as accurately as current models for the nanowires of different sizes of cross sections under axial load. Furthermore, the beam model gives better prediction than the current model for the nanowires subject to pure bending. The size effect on the elastic property can also be observed from the longitudinal and transverse natural vibration of the nanowires. In this case, the effective Young’s modulus is nearly the same as that obtained through axial deformation and pure bending, respectively. The work has been published in International Journal of Computational Method. The dynamic buckling of a copper nanowire, including the effects of stress wave was studied, with help of molecular dynamics simulation and dynamic buckling theory in continuum mechanics. The dynamic buckling of the copper nanowire under an axial step load is simulated. As a comparison, the nanowire is modeled as an elastic rod subject to the axial step load, and is analyzed on the basis of buckling theory. The molecular dynamics simulation gives a slightly higher critical load than the buckling theory. Furthermore, the buckling theory predicts that the stress wave has a remarkable effect on the dynamic buckling of copper nanowires. The work has been published in International Journal of Nonlinear Sciences and Numerical Simulation.

6. As an exploration, the dissertation presents a preliminary study on the temperature in nano-scale problems. To avoid the effect of temperature control on the dynamic behavior of nano-structures in molecular dynamics simulations, the conduction method is used to control the temperature of multi-walled carbon nanotubes of concern. The dissertation gives the heat conduction and the corresponding expansion of carbon nanotubes with an increase of temperature, the effect of damping in nano-oscillators made of multi-walled carbon nanotubes，the rotation and the intrinsic thermal vibration of nano-oscillators as well. The dissertation terminates with a discussion about the definitions of temperature in the molecular dynamics simulations for nano-oscillators.

The publications of the above studies have been cited over 60 times by many leading scientists including Prof. T Belytschko (American for Academy of Arts and Science, U. S. National Academy of Engineering) (Meccanica 40: 455), Prof. YW Mai (Follow of Royal Society) (J. Appl. Phys. 103, 074309), Prof. RF Gibson (President of American Society for Composites) (Compos. Sci. Technol. 67:1)，Prof. BI Yakobson (J. Mech. Phys. Solids, 2008 Available online), Prof. HJ Gao (Appl. Phys. Lett. 93, 013106), Prof. TW Chou (Phys. Rev. B 73, 245407). For example, Prof. RF Gibson et.al cited the work published in Phys. Rev. B as an example of “particularly important” research in their review in Compos. Sci. Technol. 67:1. Prof. QM Li et. al. cited the work as a long paragraph of over 400 words in P. Roy. Soc. A Math. Phys. 464: 1941. Prof. CM Wang from National University of Singapore cited the work as the first reference of studing carbon nanotubes by using non-local elastic models in his three papers, such as J. Phys. D: Appl. Phys. 39: 3904, Int. J. Struct. Stabil. Dynam. 7:555 and Nanotechnology 18: 105401. H Askes et. al. cited the work as a remark that the strain gradient theory be used to nano-scale dynamics in Int. J. Numer. Meth. Engng, 72:111. Furthermore, HW Yap reported t in Nano Letters 7:1149 that the experimental results coincide with the large hysteresis between the loading and unloading curves predicted in Acta Mechanica Solida Sinica.

Key words: Molecular dynamics，Carbon nanotube，Buckling，Impact，Van der waals force，Longitudinal wave，Flexural wave, Wave dispersion，Strain gradient，Temperature

以上就是全国优秀博士学位论文中英文摘要精选连载。此外， 考博英语 复习参考【 考博词汇书 】更多资料请持续关注本站。选择【 在线考博课程 】，讲练结合，实用高效。有关考博初试成绩、复试安排、考博问答以及后程指导请参考最新专题【 2014考博成绩查询 】，希望对大家考试有实质性的帮助。真题发布请持续关注【 点击查看2014考博真题 】。祝考生们顺利通过考试！更多资讯请关注 旭晨教育考博频道 。