Transverse wave propagation in viscoelastic single-walled carbon nanotubes with small scale and surface effects

Abstract

The general governing equation of transverse wave motion in a viscoelastic single-walled carbon nanotube (SWCNT) adhered by surface material is formulated on the basis of the nonlocal elasticity theory and the Kelvin model. The properties of transverse wave propagation in the SWCNT are investigated. The explicit expressions are derived for the frequency and phase velocity of the wave motion. The small scale and surface effects and the influences of structural damping on the properties of wave propagation are elucidated. It is concluded that the frequency and phase velocity of transverse wave propagation in the viscoelastic SWCNT are related to the small scale, surface elasticity, residual surface tension, and structural damping. The small scale and surface effects and the impact of structural damping on the properties of transverse wave propagation are dependent upon the wave number and tube diameter.