Studying the Vibrational Behavior of Single-Walled Carbon Nanotubes under Different Boundary Conditions using the Rayleigh-Ritz Technique

Year 2016, Volume: 8 Issue: 2, 51 - 67, 19.08.2016

R Ansari H Rouhi S Sahmani

https://doi.org/10.24107/ijeas.252145

Abstract

The vibrational response of single-walled carbon nanotubes (SWCNTs) is studied in this
paper. To take size effects into account, Eringen’s nonlocal elasticity equations are
incorporated into the Donnell shell theory. The Rayleigh-Ritz method is employed in
conjunction with the polynomial series as modal displacement functions to solve the problem.
Four commonly used boundary conditions namely as simply supported-simply supported,
clamped-clamped, clamped-simply supported, and clamped-free are considered. The
fundamental frequencies of SWCNTs with various values of aspect ratios and nonlocal
parameters are obtained. To propose the proper values of nonlocal parameter, the results of
nonlocal shell model are matched with those of molecular dynamics (MD) simulations for
armchair and zigzag SWCNTs through a nonlinear least square fitting procedure. The
appropriate values of nonlocal parameter corresponding to each type of chirality and
boundary condition are then derived. It is found that the results obtained via the presented
nonlocal shell model with its proposed proper values of nonlocal parameter are in excellent
agreement with those of MD simulations. 

Keywords

carbon nanotube, nonlocal elasticity, free vibration, donnell shell theory, molecular dynamics simulation