Abstract
The vibration analysis, based on the Donnell thin shell theory, of single-walled carbon nanotubes (SWCNTs) has been investigated. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in SWCNTs. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a carbon nanotube, have been used to compute the axial modal dependence. In our new investigations, the vibration frequency spectra are obtained and calculated for various physical parameters like length-to-diameter ratios for armchair and zigzag SWCNTs for different modes and in-plane rigidity and mass density per unit lateral area for armchair and zigzag SWCNTs on the vibration frequencies. The computer software MATLAB is used in order to compute these frequencies of the SWCNTs. The results obtained from wave propagation method are found to be in satisfactory agreement with that obtained through the previously known numerical molecular dynamics simulations.
Highlights
We present our numerical results for the predictions of fundamental frequency of single-walled carbon nanotubes (SWCNTs) for a wide range of material parameters (L/d, m, n) and varying higher in-plan rigidity (Eh) and mass density per unit lateral area
It is interesting that considerable accurate data have been obtained for the f (THz) of SWCNTs through newly developed cylindrical shell model (CSM) based on wave propagation approach (WPA) computations at nearly the same sets of data points, to show that the presented new numerical data of f (THz) are well matched with the earlier available theoretical and molecular dynamics (MD) simulation results
A newly developed CSM based on wave propagation approach has been employed for the SWCNTs and provide an alternative method to investigate the vibrational behaviors of CC and CF armchair and zigzag SWCNTs
Summary
Understanding of the vibrational properties of the carbon nanotubes (CNTs) and their uses have been involved in various areas such as electronics, optical, medicine, charge detectors, sensors, field emission devices, aerospace, defense, construction and even fashion. Investigation of their remarkable properties, a bulk of research work was performed for their high springiness and characteristic ratio, a very effective Young modulus and tensile potency, well-bonding strength and superconductivity between carbon atoms. Vibrations of CNTs have been studied extensively in the last fifteen years and various cost effective continuum models such as thin shell, beam and ring as well as other continuum models have been proposed to capture the new physical phenomena and quantify the mechanical properties, and identify the major factors that affect the mechanical behavior of CNTs, which are difficult to observed through experimental and at atomistic simulation methods. Understanding of the vibrational properties of the carbon nanotubes (CNTs) and their uses have been involved in various areas such as electronics, optical, medicine, charge detectors, sensors, field emission devices, aerospace, defense, construction and even fashion.. Understanding of the vibrational properties of the carbon nanotubes (CNTs) and their uses have been involved in various areas such as electronics, optical, medicine, charge detectors, sensors, field emission devices, aerospace, defense, construction and even fashion.1 Investigation of their remarkable properties, a bulk of research work was performed for their high springiness and characteristic ratio, a very effective Young modulus and tensile potency, well-bonding strength and superconductivity between carbon atoms.. Investigations of free vibration of CNTs have been examined with regard to their properties and material behavior. It needs more exploration to examine vibration characteristics of single-walled carbon nanotubes (SWCNTs). Vibration problems of SWCNTs can be investigated experimentally, theoretically and by simulation techniques
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