Nonlocal vibration of carbon nanotubes with attached buckyballs at tip

Nonlocal longitudinal vibration of single-walled-carbon-nanotubes (SWCNTs) with attached buckyballs is considered. Attached buckyball at the tip of a SWCNT can significantly influence the resonance frequency of the vibrating system. Closed-form nonlocal transcendental equation for vibrating system with arbitrary mass ratio i.e. mass of buckyball to mass of SWCNT is derived. Nonlocal elasticity concept is employed to develop the frequency equations. Explicit analytical expressions of axial frequencies are proposed when mass of the attached buckyball is larger than the mass of SWCNT. Nonlocal longitudinal frequencies are validated with existing molecular dynamic simulation result. For arbitrary mass ratios, the frequency shifts in SWCNT due to (i) added buckyballs and (ii) nonlocal-effects are investigated. The present communication may be useful when designing tuneable resonator in NEMS applications.