A higher-order gradient theory for modeling of the vibration behavior of single-wall carbon nanocones

Abstract

A higher-order gradient theory is used to investigate the free vibration characteristics of single-wall carbon nanocones (SWCNCs). This atomistic–continuum model simulates SWCNCs at the atomistic level and links the deformation of the crystal lattice structure to that of the continuum field. The dependence of vibration frequencies of SWCNCs on apex angles, heights and top radii, as well as constraints, is studied under a developed mesh-free computational framework based on moving Kriging interpolation. It is found that the proposed model gives a good prediction of the MD simulation and Timoshenko beam model. Several kinds of SWCNCs were investigated and the results reveal that the apex angle markedly affects the vibration frequency. It is observed that the fundamental frequency increases as the top radius increases, until it reaches a critical value. The critical top radii are largely dependent on the constraints at the ends of the SWCNCs. It is also observed that for SWCNCs with different apex angles, the same fundamental frequency is obtained by an appropriate combination of height and top radius. As the top radius continues to increase, the change of fundamental frequency becomes smaller and smaller.