Dynamic Behavior Of Carbon Nanotubes And Wave Propagation In Carbon Nanotubes In Multi-physics Fields

With the advancement of the Nano-technology, Carbon nanotubes (CNTs) have beennow one of the most promising components in Nano-electromechanical systems (NEMS).Owing to their extraordinary mechanical, electronic, thermal and other physical attributions,they have been widely used in NEMS, for example in Nano-biological devices. In order toobtain a good understanding of CNTs and to design new Nano-devices, it is very important tobuild more accurate theoretical models and to analyse for their properties (e.g. frequencies).Although plenty of studies have been done to investigate the dynamic behaviour(including wave propagation) of CNTs, it is clear that further theoretical development isrequired to meet the need of NEMS, and there have been many trial and error attempts ofduring design of NEMS devices. There are two main reasons. One is that the design processof NEMS devices is a multidisciplinary task. NEMS devices can work in complex physicalenvironments, such as in magnetic field, temperature field and so on.Based on the aforementioned review, in this thesis, the dynamic response and wavepropagation of CNTs in multi-physics fields are investigated, the theoretical models of CNTshave been established, and the numerical simulations of CNTs have been carried out andanalysed. Meanwhile, the simulated numerical results validate the analytical models proposedin the present study and lead to conclusions that are potentially useful for the application ofCNTs as NEMS devices. In chapter1, a concise review of recent advances in CNTs has beenprovided. This main content of the dissertation is organized as follows:1. Based on the nonlocal theory of elasticity and the theory of elasticity, the CNTs aremodelled as Euler-Bernoulli and Timoshenko beams. The governing equations of motion arederived using Hamilton’s principle, and then the analysis are carried out using the Galerkinapproach, leading to a set of algebraic equations in a second-order dynamic system from thepartial differential equations of motion. The differential equations of second-order dynamicsystem are solved using Magnus expansion method, which can preserve qualitative geometricproperties of the exact solution. Numerical simulation is carried out to verify the analyticalmodel proposed in the present study and the effectiveness of the proposed method in thisdissertation. By comparing the different of the obtained results with Magnus expansionmethod and with Runge-Kutta method. It can be easily see that, the advantages of Magnusexpansion method not only are, the higher accuracy, but also the long-time stability. Thus, thenumerical method of Magnus expansion can be applied to study the nonlinear dynamicsystem in Chapter3. 2. Considering the effect of the stretching nonlinearity, and the nonlinearity of the initialgeometrical imperfection, due to their fabrication process using chemical vapour deposition,which can be seen from the images of CNTs taken by transmission electron microscopes, theforced nonlinear vibrations of CNTs are investigated in Chapter3. Firstly, the chaosbehaviour of double clamped single-walled carbon nanotubes (SWCNTs), on the basis ofMagnus expansion method, is studied. Secondly, based on the nonlocal theory of elasticity,CNTs are modelled as Euler-Bernoulli beam, and the vibration of embedded curved CNTssubjected to a moving harmonic load is analysed. Then, the effect of van der Waals force hasbeen taken into account. Via Euler-Bernoulli beam theory, the dynamic vibrations ofembedded double-walled carbon nanotubes (DWCNTs) subjected to a moving harmonic loadwith simply supported boundary conditions are investigated. The results show that the vander Waals force has an influence on the dynamic deflection. Compared with Euler-Bernoullibeam theory, it is more accurate to use Timoshenko beam theory to study the vibration ofSWCNTs, because the transverse shear deformation and rotary inertia are considered in aTimoshenko beam model. Based on nonlocal continuum mechanics and Timoshenko beammodel, the nonlinear vibration of embedded SWCNTs with a geometrical imperfection undera harmonic load is investigated, and the effects of the elastic medium constants, the wavinessratios, the material length, and other mechanical constants on the dynamic response areanalysed.3. Fluid-conveying CNTs have attracted intensive research and have been used inNEMS. In Chapter4, the free vibration of embedded Single-walled fluid-conveyingSWCNTs in magnetic and temperature fields is investigated. The SWCNTs are modelled as awavy Timoshenko beams based on the theory of nonlocal elasticity, where the Nano-scaleeffects are only included in bending moment and shear force through a nonlocal parameter.The wave analysis is carried out, leading to a set of algebraic equations from the partialdifferential equations of motion. Numerical examples are analysed to assess the differencebetween the present model and some models reported in the published literature and theeffects of the nonlocal parameter, the fluid velocity and flow density, the temperature andmagnetic field flux change, and the surrounding elastic medium are discussed.4. Wave propagation in SWCNTs in magnetic and temperature fields has been studied inChapter5. The CNTs are modelled as Timoshenko beams. Based on the nonlocal beamtheory, the governing equations of motion are derived using Hamilton’s principle. Waveanalysis is carried out to get the equations of the analytical solutions of wave propagation.The main aim is to improve the accuracy of theoretical models of SWCNTs and the main contributions are determination of the influence of the geometrical nonlinearity, small scaleeffect, temperature change on the frequency characteristic of SWCNTs. In order to discussterahertz wave characteristics of nonlinear structure CNTs, the governing equations ofSWCNTs are linearized and the dispersion characteristics of wave propagation are plotted.5. The problem of wave propagation in SWCNTs conveying fluids subjected to multi-physical included magnetic and temperature fields is addressed in Chapter6. Firstly, Basedon the nonlocal Timoshenko beam model, the influences of the nonlocal parameter, the fluidvelocity and flow density, the temperature and magnetic field flux change, and thesurrounding elastic medium on the wave behaviour of SWCNTs are analysed. Due to thermalstress, surface effect, mismatch between the material properties of CNTs or initially externalaxial load, and so on, CNTs acting as basic elements of Nano-structures are sometimessubjected to initial stress. A theoretical model for wave propagation in a fluid-conveyingSWCNTs, which is subjected to temperature and magnetic fields with an initial axial stress isestablished. Numerical results confirm the validity of present model by comparing the resultsin reduced cases with those reported in the published literature. The dispersion curves ofwave propagation show that the initial stress plays a very important role on the shear andflexural frequencies of fluid-conveying SWCNTs. Meanwhile, the influences of the nonlocalparameter, fluid velocity, flow density, temperature change and magnetic field on the criticalstress of fluid-conveying SWCNTs are discussed. This study may be useful for the design ofsmart Nano-devices for delivery of drugs to cells, carrying gases, and other applications ofNano-beam devices.