Viscoelastic wave propagation in the viscoelastic single walled carbon nanotubes based on nonlocal strain gradient theory

In this paper, the viscoelastic wave propagation in an embedded viscoelastic single-walled carbon nanotube (SWCNT) is studied based on the nonlocal strain gradient theory. The characteristic equation for the viscoelastic wave in SWCNTs is derived. The emphasis is placed on the influence of the tube diameter on the viscoelastic wave dispersion. A blocking diameter is observed, above which the wave could not propagate in SWCNTs. The results show that the blocking diameter is greatly dependent on the damping coefficient, the nonlocal and the strain gradient length scale parameters, as well as the Winkler modulus of the surrounding elastic medium. These findings may provide a prospective application of SWCNTs in nanodevices and nanocomposites.     

Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory

The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.     

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.     

Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method

In the present work, effect of von Kàrmàn geometric nonlinearity on the vibration behavior of a single-walled boron nitride nanotube (SWBNNT) is investigated based on nonlocal piezoelasticity theory. The SWBNNT is considered as a nanobeam within the framework of Timoshenko beam (TB). Loading is composed of a temperature change and an imposed axially electric potential throughout the SWBNNT. The interactions between the SWBNNT and its surrounding elastic medium are simulated by Winkler and Pasternak foundation models. The higher order governing equations of motion are derived using Hamilton's principle and the numerical solution of equations is obtained using Differential Quadrature (DQ) method. The effects of geometric nonlinearity, elastic foundation modulus, electric potential field, temperature change and nonlocal parameter on the frequency of the SWBNNT are studied in detail.     

Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory

Theoretical predictions are presented for wave propagation in nonlinear curved single-walled carbon nanotubes (SWCNTs). Based on the nonlocal theory of elasticity, the computational model is established, combined with the effects of geometrical nonlinearity and imperfection. In order to use the wave analysis method on this topic, a linearization method is employed. Thus, the analytical expresses of the shear frequency and flexural frequency are obtained. The effects of the geometrical nonlinearity, the initial geometrical imperfection, temperature change and magnetic field on the flexural and shear wave frequencies are investigated. Numerical results indicate that the contribution of the higher-order small scale effect on the shear deformation and the rotary inertia can lead to a reduction in the frequencies compared with results reported in the published literature. The theoretical model derived in this study should be useful for characterizing the mechanical properties of carbon nanotubes and applications of nano-devices.     

单壁碳纳米管单原子空位缺陷的紧束缚理论研究

文章在紧束缚势模型基础上系统地研究了非手性单壁碳纳米管上单原子空位缺陷结构和电子结构性质.计算表明,单原子空位缺陷会自发地形成5-1DB型缺陷, 且该缺陷的局域结构和形成能强烈地依赖于碳纳米管的尺寸、旋度和电学性质.同时作者发现这类缺陷在费米能级以上约0.2eV处产生局域的电子态.     

The nano scale vibration of protein microtubules based on modified strain gradient theory

This paper investigates the free vibration of protein microtubules (MTs) embedded in the cytoplasm by using linear and nonlinear Euler–Bernoulli beam model based on modified strain gradient theory. The protein microtubule is modeled as a simply support or clamped–clamped beam. Beside, the elastic medium surrounding of MTs is modeled with Pasternak foundation. Vibration equations are obtained by using Hamilton principle and these equations are solved according to boundary conditions. Finally the dependency of vibration frequencies on environmental conditions, MTs size, changes of temperature and material length scale parameters (size effects) is studied. By comparing the findings, it could be said that the MTs' frequency is greatly increased in the presence of cytoplasm and it is very dependent to material length scale parameters.     

Changes in the vibrational modes of carbon nanotubes induced by electron‐beam irradiation: resonance Raman spectroscopy

Influence of electron‐beam (e‐beam) irradiation on multi‐walled (MW) and single‐walled (SW) carbon nanotube films grown by microwave chemical vapor deposition technique is investigated. These films were subjected to an e‐beam energy of 50 keV from a scanning electron microscope for 2.5, 5.5, 8.0, and 15 h, and to 100 and 200 keV from a transmission electron microscope for a few minutes to ∼2 h continuously. Such conditions resemble an increased temperature and pressure regime enabling a degree of structural fluidity. To assess structural modifications, they were analyzed prior to and after irradiation using resonance Raman spectroscopy (RRS) in addition to in situ monitoring by electron microscopy. The experiments showed that with extended exposures, both types of nanotubes displayed various local structural instabilities including pinching, graphitization/amorphization, and formation of an intramolecular junction (IMJ) within the area of electron beam focus possibly through amorphous carbon aggregates. RRS revealed that irradiation generated defects in the lattice as quantified through (1) variation of the intensity of radial breathing mode (RBM), (2) intensity ratio of D to G band (I_D/I_G), and (3) positions of the D and G bands and their harmonics (D* and G*) and combination bands (D + G). The increase in the defect‐induced D band intensity, quenching of RBM intensity, and only a slight increase in G band intensity are some of the implications. The MW nanotubes tend to reach a state of saturation for prolonged exposures, while the SW ones transform from a semiconducting to a quasi‐metallic character. Softening of the q = 0 selection rule is suggested as a possible reason to explain these results. Furthermore, these studies provide a contrasting comparison between MW and SW nanotubes. Copyright © 2006 John Wiley & Sons, Ltd.