Sound wave propagation in armchair single walled carbon nanotubes under thermal environment

Abstract

This paper develops a model that analyzes the wave propagation in armchair single-walled carbon nanotubes (SWCNTs) under thermal environment. The effect of a small length scale is incorporated in the formulations using nonlocal Levinson beam model. Unlike Timoshenko beam theory, Levinson beam theory satisfies zero traction boundary conditions on the upper and lower surface of the structures, so there is no need to use a shear correction factor. The equivalent Young’s modulus and shear modulus for armchair SWCNT are derived using an energy-equivalent model. Results indicate significant dependence of natural frequencies on the temperature change as well as the chirality of armchair carbon nanotube. These findings are important in mechanical design considerations of devices that use carbon nanotubes.