Free Vibration Analysis of Single-Walled Carbon Nanotubes Based on the Nonlocal Higher-Order Cylindrical Beam Model

In this paper, the free vibration behavior of single-walled carbon nanotubes (SWCNTs) is presented via a higher-order theory of nonlocal elastic cylindrical beams by taking the rotary inertia, shear deformation and small scale effect into account simultaneously. In our model, the shear-free surface condition is identically satisfied and does not need to introduce the shear correction factor. The characteristic equations of natural frequencies and the expressions of vibration mode shapes are derived in closed form for different boundary conditions. Compared our numerical results with those obtained by the molecular dynamics simulation, the effectiveness and validity of the present model are examined. The effects of the length-to-diameter ratio, the scale coefficient, the Poisson's ratio, chirality and boundary conditions on the free vibration of SWCNTs are investigated.