Dynamic Stability of Single Walled Carbon Nanotube Based on Nonlocal Strain Gradient Theory

Abstract

This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano- size structures such as single-walled carbon nanotubes. Influences of nonlocal effects, modulus parameter of elastic medium and aspect ratio of the SWCNT on the critical buckling loads and instability regions are analyzed. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanotubes.