Vibration analysis of single-walled carbon nanocones using multiscale atomistic finite element method incorporating Tersoff–Brenner potential

Abstract

This research work addresses the free and forced vibration characteristics of single-walled carbon nanocones (SWCNCs) using multiscale atomistic finite element method (AFEM) incorporating Tersoff–Brenner (TB) potential. The multibody interatomic TB potential is used to represent the energy between two carbon atoms. Based on the TB potential, new set of force constant parameters is established for carbon nanocones, and the equivalent geometric and elastic properties of the space frame element to represent carbon–carbon bond are derived which are consistent with the material constitutive relations. The eigenvalues of clamped and cantilevered SWCNCs with different disclination angles are extracted using AFEM, and the effect of these angles on the resonant frequencies is investigated. A computational sine sweep test is carried out on the atomic structure of SWCNCs within the frequency range of 0–10 THz to investigate the steady-state forced vibration response under harmonic excitation. The frequency response of the SWCNCs to the cyclic and impulse load over an applied frequency range is calculated. Based on the forced vibration response spectra, the resonant frequency components of SWCNCs are identified. The results have been validated using molecular dynamics simulation.