Vibration and elastic buckling analyses of singlewalled carbon nanocones

This paper reports the result on elastic buckling and vibration behaviors of singlewalled carbon nanocones (SWCNCs) having the potential usage in atomic force microscope and scanning tunneling microscope tips. The modeling work employs the molecular mechanics based finite element approach in which Euler-Bernoulli beam element formulations are used with consistent mass matrix. Free-free, free-clamped and clamped-clamped boundary conditions are considered in vibration analysis of SWCNCs; on the other hand, axial compression and bending loading conditions are taken into account in elastic buckling behavior of SWCNCs. The effects of cone height and disclination or apex angles on the buckling force and natural frequencies of SWCNCs are investigated. Vibration analysis results indicate that the natural frequency decreases with increasing cone height in all types of SWCNCs, whereas it increases as the disclination angle increases. Buckling analysis results indicate that as the disclination angle increases, the critical buckling load increases in axial compression loading and decreases in bending loading. In addition, it is observed that bending loading is more critical than axial compression loading for buckling behavior of SWCNCs if the disclination angle increases.