Axial vibration of single-walled carbon nanotubes with fractional damping using doublet mechanics

This paper investigates the axial vibration of single-walled carbon nanotubes (SWCNTs) with fractional damping based on doublet mechanics. The Kelvin-Vigot model is used to incorporate damping effect for CNTs. By solving the equation of motion, the relation between natural frequency with scale parameter and fractional order is derived in the axial mode of vibration. It is shown that fractional order and scale parameter play significant roles in the axial vibration behavior of SWCNTs. Such effects decrease the natural frequency compared to the predictions of the classical continuum mechanics models and also ignores the damping effects. These effects on the natural frequency are more apparent in higher mode numbers and lower tube lengths and radii. Results for complex roots of characteristic equation obtained for a SWCNT without viscoelastic foundation, where imaginary parts represent damped frequencies, were compared with the results found from molecular mechanics simulations and a good agreement was achieved.