Effect of Elastic Foundation on Nonlocal Vibration of CNTs With Attached Buckyballs at Tip

چکیده مقاله

Effect of elastic foundation on nonlocal longitudinal vibration of single-walled-carbon-nanotubes (SWCNTs) with attached buckyballs is investigated. Attached buckyball at the tip of a SWCNT can significantly influence the resonance frequency of the vibrating system. The SWCNT is assumed to be nonlocal rod while the buckyballs are assumed to be as nonlocal point mass. 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. 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. It is obtained that, the axial vibration frequencies of the embedded SWCNTs are highly over estimated by the classical continuum rod model which ignores the effect of small length scale. Axial resonant frequency of the vibrating system is sensitive to the attached mass. With increase of the mass of buckyballs in vibrating system, the shift in the frequencies increases. Also the shift in the nonlocal frequencies increases with the increasing nonlocal parameter; and is more pronounced for lighter buckyballs.