Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain

Based upon a nonlocal shell model accounting for the small-scale effects, the vibration characteristics of single-walled carbon nanotubes (SWCNTs) with different boundary conditions subjected to initial strain are studied in this paper. The set of governing equations of motion is numerically solved by a method that emerged from incorporating the radial point interpolation approximation within the framework of the generalized differential quadrature method. The effectiveness of the present nonlocal shell model is assessed by the molecular dynamics simulations as a benchmark of good accuracy. Accordingly, nonlocal parameters for clamped and cantilever SWCNTs with thicknesses of 0.066 and 0.34 nm are proposed due to the uncertainty that exists in defining nanotube wall thickness. The simulation results show that the resonant frequencies of SWCNTs are very sensitive to the initial strain, although small.