• Structural Engineering and Mechanics
• /
• v.64 no.3
• /
• pp.329-337
• /
• 2017

This study concerns the vibrational behavior of multi-walled nested silicon-carbide and carbon nanotubes using the finite element method. The beam elements are used to model the carbon-carbon and silicon-carbon bonds. Besides, spring elements are employed to simulate the van der Waals interactions between walls. The effects of nanotube arrangement, number of walls, geometrical parameters and boundary conditions on the frequencies of nested silicon-carbide and carbon nanotubes are investigated. It is shown that the double-walled nanotubes have larger frequencies than triple-walled nanotubes. Besides, replacing silicon carbide layers with carbon layers leads to increasing the frequencies of nested silicon-carbide and carbon nanotubes. Comparing the first ten mode shapes of nested nanotubes, it is observed that the mode shapes of armchair and zigzag nanotubes are almost the same.

• Structural Engineering and Mechanics
• /
• v.84 no.1
• /
• pp.77-83
• /
• 2022

In the last ten years, many researchers have studied the vibrations of carbon nanotubes using different beam theories. The nano- and micro-scale systems have wavy shape and there is a demand for a powerful tool to mathematically model waviness of those systems. In accordance with the above mentioned lack for the modeling of the waviness of the curved tiny structure, a novel approach is employed by implementing the Timoshenko-beam model. Owing to the small size of the micro beam, these structures are very appropriate for designing small instruments. The vibrations of double walled carbon nanotubes (DWCNTs) are developed using the Timoshenko-beam model in conjunction with the wave propagation approach under support conditions to calculate the fundamental frequencies of DWCNTs. The frequency influence is observed with different parameters. Vibrations of the double walled carbon nanotubes are investigated in order to find their vibrational modes with frequencies. The aspect ratios and half axial wave mode with small length are investigated. It is calculated that these frequencies and ratios are dependent upon the length scale and aspect ratio.

• Advances in nano research
• /
• v.12 no.4
• /
• pp.345-352
• /
• 2022

In this paper, natural frequency curves are presented for three specific end supports considering distinct values of nonlocal parameter. The vibrational behavior of zigzag double walled carbon nanotubes is investigated using wave propagation with nonlocal effect. Frequency spectra of zigzag (12, 0) double walled carbon nanotubes have been analyzed with proposed model. Effects of nonlocal parameters have been fully investigated on the natural frequency against against variation of Poisson's ratio. A slow increase in frequencies against variation of Poisson's ratio also indicates insensitivity of it for suggested nonlocal model. Moreover, decrease in frequencies with increase in nonlocal parameter authenticates the applicability of nonlocal Love shell model. Also the frequency curves for C-F are lower throughout the computation than that of C-C curves.

• Advances in nano research
• /
• v.9 no.2
• /
• pp.69-82
• /
• 2020

In this paper, a new explicit analytical formula is derived for the critical buckling load of Double Walled Carbon Nanotubes (DWCNTs) embedded in Winkler elastic medium without taking into account the effects of the nonlocal parameter, which indicates the effects of the surrounding elastic matrix combined with the intertube Van der Waals (VdW) forces. Furthermore, we present a model which predicts that the critical axial buckling load embedded in Winkler, Pasternak or Kerr elastic medium under axial compression using the nonlocal Donnell shell theory, this model takes into account the effects of internal small length scale and the VdW interactions between the inner and outer nanotubes. The present model predicts that the critical axial buckling load of embedded DWCNTs is greater than that without medium under identical conditions and parameters. We can conclude that the embedded DWCNTs are less susceptible to axial buckling than those without medium.

• Carbon letters
• /
• v.15 no.2
• /
• pp.77-88
• /
• 2014

Double walled carbon nanotubes (DWCNTs) are considered an ideal model for studying the coupling interactions between different concentric shells in multi-walled CNTs. Due to their intrinsic coaxial structures they are mechanically, thermally, and structurally more stable than single walled CNTs. Geometrically, owing to the buffer-like function of the outer tubes in DWCNTs, the inner tubes exhibit exciting transport and optical properties that lend them promise in the fabrication of field-effect transistors, stable field emitters, and lithium ion batteries. In addition, by utilizing the outer tube chemistry, DWCNTs can be useful for anchoring semiconducting quantum dots and also as effective multifunctional fillers in producing tough, conductive transparent polymer films. The inner tubes meanwhile preserve their excitonic transitions. This article reviews the synthesis of DWCNTs, their electronic structure, transport, and mechanical properties, and their potential uses.

• Steel and Composite Structures
• /
• v.42 no.3
• /
• pp.353-361
• /
• 2022

In this study, an estimation regarding nonlocal shell model based on wave propagation approach has been considered for vibrational behavior of the double walled carbon nanotubes with distinct nonlocal parameters. Vibrations of double walled carbon nanotubes for chiral indices (8, 3) have been analyzed. The significance of small scale is being perceived by developing nonlocal Love shell model. The influence of changing mechanical parameter Poisson's ratio has been investigated in detail. The dominance of boundary conditions via nonlocal parameter is shown graphically. It is found that on increasing the Poisson's ratio, the frequencies increases. It is noted that the frequencies of clamped-clamped frequencies are higher than that of simply-supported and clamped-free edge conditions. The outcomes of frequencies are tested with earlier computations.

• Computers and Concrete
• /
• v.32 no.2
• /
• pp.165-172
• /
• 2023

The vibration analysis of armchair, zigzag and chiral double-walled carbon nanotubes has been developed by inserting the nonlocal theory of elasticity into thin shell theory. First Donnell shell theory is employed while exercising wave propagation approach. Scale effects are realized by using different values of nonlocal parameters under certain boundary conditions. The natural frequencies have been investigated and displayed for various non-local parameters. It is noticed that on increasing nonlocal parameter, the frequency curve tends to decrease. The frequency estimates of clamped-free boundary condition are less than those of clamped-clamped and simply supported computations. The frequency comparisons are presented for armchair, zigzag and chiral nanotubes. The software MATLAB is used to extract the frequencies of double walled carbon nanotubes.

• Advances in nano research
• /
• v.1 no.1
• /
• pp.1-11
• /
• 2013

The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.

• Advances in nano research
• /
• v.5 no.2
• /
• pp.179-192
• /
• 2017

The transverse vibration of double walled carbon nanotube (DWCNT) embedded in elastic medium with an initial imperfection is considered. In this paper, Timoshenko beam theory is employed. However the nonlocal theory is used for modeling the nano scale of nanotube. In addition, the governing Equations of motion are obtained utilizing the Hamilton's principle and simply-simply boundary conditions are assumed. Furthermore, the Navier method is used for determining the natural frequencies of DWCNT. Hence, some parameters such as nonlocality, curvature amplitude, Winkler and Pasternak elastic foundations and length of the curved DWCNT are analyzed and discussed. The results show that, the curvature amplitude causes to increase natural frequency. However, nonlocal coefficient and elastic foundations have important role in vibration behavior of DWCNT with imperfection.

• Computers and Concrete
• /
• v.31 no.1
• /
• pp.1-7
• /
• 2023

In this paper, Timoshenko-beam model is developed for the vibration of double carbon nanotubes. The resulting frequencies are gained for axial wave mode and length-to-diameter ratios. The natural frequency becomes more prominent for lower length-to-diameter ratios and diminished for higher ratios. The converse behavior is observed for axial wave mode with clamped-clamped and clamped-free boundary conditions. The frequencies of clamped-free are lower than that of clamped-clamped boundary condition. The eigen solution is obtained to extract the frequencies of double walled carbon nanotubes using Galerkin's method through axial deformation function. Computer softer MATLAB is used for formation of frequency values. The frequency data is compared with available literature and found to be in agreement.