Free Vibration Analysis of Single-Walled Carbon Nanotubes Using Semi-Analytical Finite Element

Abstract

Presented in this paper are the vibration characteristics of single-walled carbon nanotubes (SWCNTs) with different boundary conditions. A nonlocal shell model accounting for the size effect is adopted. The set of governing equations of motion are numerically solved using a semi-analytical finite element method. The effectiveness of the present nonlocal shell model is assessed by molecular dynamics simulations as a benchmark of good accuracy. The significance of the small size effects on the resonant frequencies is indicated to be dependent on the sizes, boundary conditions of nanotubes, and the tube wall thickness varying within 0.066 nm to 0.34 nm.

Keywords:

• Nonlocal continuum
• Natural frequency
• Semi-analytical method
• Single-walled carbon nanotube
• Molecular dynamics simulations