The Vibrations of Carbon Nanotubes in Nonlocal Elasticity

In this paper, the transverse vibrations of Single and Double Walled Carbon Nanotubes are investigated by using the method of initial values within the framework of nonlocal elasticity. Carbon nanotubes are molecular-scale tubes which are envisioned as hollow cylindrical bars of graphitic carbon sheets at molecular scale with outstanding properties. They are one of the stiffest and strongest fibers known, have remarkable electronic properties and many other unique features as well. They are widely used in nanotechnological applications. The principal matrix required for the applicability of the method of initial values is presented. Explicit relations are presented for the transverse vibrations of Single and Double Walled Carbon Nanotubes. Advantages of nonlocal elasticity in representing the transverse vibrations of carbon nanotubes are discussed. The results indicate that nonlocal effects could be significant in transverse vibrations of carbon nanotubes.