Participation Factor and Vibration of Carbon Nanotube with Vacancies

Abstract

In this paper the finite element simulation is exploited to investigate dynamical behaviors of perfect and defected Single Walled Carbon Nanotube (SWCNT). The natural frequencies, mode shapes and modal participation factors those not be considered elsewhere, are consider through this analysis. Energy equivalent model is adopted to find a linkage between the energy stored in chemical atomic bonds and potential energy stored in mechanical beam structure. Nanotube software modeler is used to generate a geometry of SWCNT structure by defining its chiral angle, length of nanotube and bond distance between two carbon atoms. The whole tube of SWCNT is simulated as cage and bonds between each two atoms are represented by beam (A BEAM 188) with circular cross section, and carbon atoms as nodes. Numerical results are presented to show the fundamental frequencies and modal participation factors of SWCNTs. The effect of vacancies on activation and deactivation of vibration modes are illustrated. During manufacturing of SWCNTs, atoms may be not perfectly bonded with adjacent and some vacancies may be found, so this defect is considered in this study.