Vibration analysis of initially curved single walled carbon nanotube with vacancy defect for ultrahigh frequency nanoresonators

Single walled carbon nanotubes (SWCNTs) are ideal choices for resonators due to its ultrahigh natural frequency. Fundamental frequency of resonators significantly affects their functionality and performance; therefore, an accurate prediction of SWCNTs’ natural frequency is vital for designing and developing such devices. In reality, CNTs are not straight and perfect; indeed, they have some degree of vacancy defect and waviness, which occurs during growth and manipulation processes. This research investigates for the first time the combination effects of both initial curvature and vacancy defects on vibrational behaviour of SWCNTs in order to make the simulation closer to the “real world”. In this study, an efficient method based on the molecular dynamics model and the finite element method is used to simulate wavy SWCNTs with vacancy defects. Zigzag carbon nanotube with chirality indices (5, 0) is considered. Accuracy of our modelling method is verified by comparing our results with the results obtained from previous studies in simulating ideal SWCNT natural frequency. The effects of vacancy, vacancy location, curvature and aspect ratio on natural vibration of the defected wavy SWCNTs have been investigated, and a parameter of critical waviness ratio has been defined for the first time to emphasize the combination effect of vacancies and waviness on the natural frequency of SWCNTs. Our results show that critical waviness is sensitive to the aspect ratio and indicate that by increasing the length of SWCNTs, the critical waviness ratio increases.