Free vibration analysis of single-walled carbon nanotubes using a higher-order gradient theory

Free vibration characteristics of single-walled carbon nanotubes (SWCNTs) with various constraints, tube chiralities, lengths and diameters are examined using a higher-order gradient theory. The theory describes deformations of C–C bond vectors at the atomic level and links to the continuum level. The capture of curved effects of C–C bond vectors makes the established constitutive model accords extremely well with physical behaviors. Numerical simulations have been conducted using the mesh-free computational framework based on the moving Kriging interpolation. It reveals that the present method gives a good prediction of atomistic simulation results, especially in the treatment of a larger system. SWCNTs of various types of chirality are investigated and computational results reveal that the fundamental frequency increases as the tube diameter increases, until it reaches a critical diameter beyond which it decreases. As the diameter continues to increase, the change of fundamental frequency becomes smaller and smaller and converges to that of counterpart graphite sheet. The critical diameter is largely dependent on tube lengths and constraints but independent of chiralities. It is found that the increase of tube length gives rise to an increase of critical diameter. As far as constraints are concerned, the critical diameter of fixed–free style is much larger than that of the fixed–fixed style.

► A higher-order gradient theory is applied to study free vibration of SWCNTs.
► We model two states of SWCNTs to study edge effect on the vibration behavior.
► Frequency increases as CNT's diameter increases until it reaches a critical diameter.
► Increasing the CNT's length increases the critical diameter.