Filled To The Study Of The Dynamics Of Multi-walled Carbon Nanotubes

Recent years have witnessed an increasing interest in the mechanics of nano-structures with rapid development of nano-technology. One most important new feature of micro/ nanomechanics, in contrast to macro mechanics, is the significance of some "weak" forces, such as van der Waals (vdw) forces, which are negligible in macro scale but become dominant at micro/nanoscale.Nanomechanics arised from Carbon nanotubes (CNTs), have become a topic of interest in recent years. The studies showed that CNTs exhibit superior mechanical, electronic and chemical properties, and almost all the potential applications of CNTs require thorough understanding of mechanical behavior of CNTs. CNTs possess exceptionally high strength, stiffness and elastic modulus. CNTs are about 6 times lighter and 100 times stronger than steel. It is the highest of all known materials, no mater strength or stiffness higher than any known fiber. CNTs are used as composite material reinforcement to present excellent strength, flexibility and resistance to fatigue. At the same time, CNTs have the high chemical resistance to acid/alkaline and oxidation under 973K. It would be expected that CNTs hold substantial promise as reinforced composite materials, nanocontainers for fluid storage, and nanopipes for conveying fluid (such as gas or water).There exist three methods to study mechanical behaviors of CNTs in which molecular dynamics simulation (MDS) is the main tool used. MDS is, however, complex and time consuming, especially for a large-sized atomic system, so it has limited application due to the current computing capacity. Considering the difficulties of conducting an experiment on a micro-or nanoscale, theoretical and numerical simulations seem to be a better way to investigate the dynamic properties of CNTs. The continuum theory is verified to be effective in the prediction of the mechanical characteristics of not only single-walled carbon nanotubes (SWCNTs) but also multiwalled carbon nanotubes (MWCNTs). As we know, though the continuum models have some limitations in rigorously simulating physical phenomena on a molecular level, they gives simple general formulas in many important cases, and have the potential to identify the key parameters affecting the basic mechanical behavior of CNTs. In addition, the continuum models allow researchers to develop new and more accurate models for more complex physical phenomena of CNTs, which have the potential to explain or predict new physical phenomena, and stimulate and guide further experiments and molecular dynamics simulations. However, there is strong evidence that the vdW forces between adjacent nanotubes have a crucial effect on mechanical behavior of carbon nanotube ropes and MWCNTs. On the other hand, the existing continuum models are directed to single-layer models or solid fibers and thus inapplicable to CNTs in the presence of the vdW forces which represents a major challenge to traditional continuum models. Hence, a significant research topic is to develop continuum models for MWCNTs in the presence of the intertube vdW forces.The objective of this dissertation is to study the dynamical behaviors of MWCNTs based on the modified continuum mechanics. Three vibrational problems about vdw forces are considered:Dynamical characteristics and the bifurcating behaviors of MWCNTs-fluid system; Twice dynamical mode transitions of double-walled carbon nanotubes (DWCNTs) because of the existence of vdw forces; The free vibration of MWCNTs with the nonlocal elasticity theory. The dissertation is generally outlined into 7 chapters. The main contributions are stated as following.(1) Based on an elastic beam model (Donnell's shell model) and potential flow theory, and by adopting N-mode Galerkin discretization technique, the dynamical stability behaviors of fluid-conveyed MWCNTs are studied. On the whole, a great deal of literature has been published on topics such as nanomechanics properties, but less literature on nanofluid, even much less on fluid structure interaction and instability of the CNTs-fluid system. Recently, the influences of the internal flow on free vibration and instability of SWCNTs have been studied by modeling CNTs with the Euler-Bernoulli beam model. It is known to us that a continuum model for the dynamical stability of fluid-conveying MWCNTs with the vdW interaction has not been reported in literature so far. So, for the first time, we discuss the influences of the flow inside the innermost tube and vdW interaction between any two walls on the instabilities of the CNTs-fluid system on the numerical simulations in detail. The governing equations for the vibration and structural instability of a MWCNT conveying fluid are derived by using the Hamilton's principle. Then, the flow-induced instability and bifurcations of TWCNTs are investigated in detail. In particular, the effects of the innermost tube radius, the length and the layer quantity of MWCNTs on the critical velocities of the destabilized system are intensively analyzed and compared. The results show that the critical velocities increase sharply as the radius becomes larger, the layer quantity increases, and the length decreases. The bifurcations happen in divergence and Hopf types. Fluid flow has very little influence on the dynamic characteristics of the outer tube. At the same time, it is observed that the vdW interaction plays an important role in the natural frequencies of outer tube. In addition, a comparison of Donnell's shell model with the Eulerian beam model shows that Donnell's shell model predicts more accurate results than does the Eulerian beam model for CNTs that are shorter because the shear effects can be taken into account in the model.(2) The nonlinear vibration behaviors of DWCNTs are investigated based on Donnell's cylindrical shell model with vdW forces between the inner and outer tubes. At present, most of the studies are limited to linearity, less of nonlinearity is investigated. When large deformations of the tubes need to be considered, the nonlinearity in vibration is significantly effective in the numerical performance. In this dissertation, harmonic balance method is used to analyze the relation between the amplitudes and the frequencies of nonlinear vibrations of the tubes. Theory analyses are carried out to understand the effects of vdW forces and nonlinearity on the CNTs. The results show that the vibration is close to coaxial at low frequency, and difference can be discriminated at higher frequencies, at last, the amplitude-frequency curves trend to the case that of without vdW forces as the frequency increasing. The reason may be ascribed to that the influence of vdW force and nonlinearity on the CNTs. When one layer vibrates, the existence of the vdW interaction will generate force to resist the relative movement between each layer and keep the space of them unchanged. With the frequency increasing, nonlinear terms gradually play important role in the vibrating behaviors and the influence of vdW forces on vibrating modes gets smaller, which causes the amplitude-frequency curves of DWCNTs gradually approximate to that of without vdW forces. It can also be seen that the vdW forces makes the vibrating pattern more complex, twice mode transitions corresponding to the noncoaxial vibrations occur, which play a critical role in electronic and transport properties of CNTs. In particular, the topologies of the amplitude-frequency curves are unchangeable to the different aspect ratios and the axial and circumferential wave number combinations.(3) Based on the nonlocal elasticity theory which allows for the small scale effect, Euler-Bernoulli beam model (Timoshenko beam model) and the more refined vdW interaction formulas, the equations of motion are first derived and then solved analytically. On a nanoscale, the physical and chemical properties of many materials change rapidly as the materials get smaller gradually. Nanoscale devices would exhibit nonlocal effects and the nonlocal continuum mechanics could potentially play a useful role in analyses related to nanotechnology applications. To the knowledge of the authors, however, the function of the vdW interaction to the small scale effect has not been seen in publications so far. Hence, for the first time, we compare the small scale effect with different layer quantity and to show the small effect on the choice of the MWCNTs models. The results reveal that the small scale effect is significant for small aspect ratios of MWCNTs and high vibrational modes, whereas insensitive to the different total layer quantity of MWCNTs under aforementioned two conditions and weakly dependent on the wall thickness of MWCNTs.