Abstract— Carbon nanotubes are widely used in the design of nanosensors and actuators. Any defect in the manufactured nanotube plays an important role in the natural frequencies of these structures. In this paper, the effect of vacancy defects on the vibration of carbon nanotubes is investigated by using an atomistic modeling technique, called the molecular structural mechanics method. Vibration analysis is performed for armchair and zigzag nanotubes with cantilever boundary condition. The shift of the principal frequency of the nanotube with vacancy defect at different locations on the length is plotted. The results indicate that the frequency of the defective nanotube can be larger or smaller or equal to the frequency of perfect one. The results also show that with the reduction in the tube length, the variations of principal frequency are enhanced. However, the frequency variation is insensitive to the nanotube diameter. As the number of vacancy defects increases, shift in the natural frequency also increases as expected. INTRODUCTION Carbon nanotubes (CNTs) were first reported by Iijima [1] in 1991. Since then, they hold immense promise as new materials for nanotechnology. This is due to their excellent properties. The mechanical properties of CNTs provide great potential for a variety of applications such as oscillators, resonators and sensors [2]. The carbon nanotubes act as basic elements of these nanostructures; therefore vibrations of CNTs get considerable importance. Gao et al. studied the vibrations of CNTs with aspect ratios of approximately L/D out =100. They found the fundamental flexural resonance frequency of cantilevered single-walled carbon nanotubes (SWCNTs) in the MHz range [3]. Although there are some experimental studies on the vibrations of CNTs, however because of the very small size of CNTs and some difficulties in nanoscale experiments, the theoretical approaches are good options. Using molecular dynamics simulations, Zhou and Shi showed that applying tensile load to a SWCNT excite the radial vibration of the SWCNT with the frequency of 4700 GHz [4]. Snow et al. considered the vibration responses of single-walled carbon nanotubes (SWCNTs) as atomic force microscope probes [5]. They assumed the nanotube as a continuum shell with Young’s modulus of 1.0 TPa. Li and Chou applied an atomistic modeling, the molecular structural mechanics, to find the fundamental frequencies of SWCNTs [6]. Their results indicate that these frequencies can achieve the level of 15-300 GHz. All these researches have focused on the simulation and estimation of the mechanical properties of perfect CNTs and have ignored the effect of initial defects. Whereas experimental observations have reported the presence of topological defects, such as the Stone– Wales (SW) defect and vacancy defects in CNTs [7]. In recent years, the study of defects in carbon nanostructures has become considerably important. Tserpes and Papanikos studied the effect of SW defect on the tensile behavior and fracture of armchair, zigzag and chiral SWCNTs [8]. In contrast to zigzag SWCNTs, their results show a significant reduction in the failure stress and the failure strain for armchair ones, ranging from 18% to 25% and from 30% to 41%, respectively. The results of chiral SWCNTs were reported between the results of zigzag and armchair ones. Mielke et al. used quantum mechanical calculations to explore the role of vacancy defects on the fracture of CNTs under axial tension [9]. Their results expose a reduction in the failure stress about 26%. Chandra et al. studied the SW defect in CNTs [10]. They have reported reduction of the stiffness at the defected area by 30–50%. Effect of defects on vibration analysis of CNTs is not yet known. In this paper, the variation of fundamental frequency of single-walled carbon nanotubes with vacancy defects is studied. The monovacancy and the divacancy in SWCNTs are addressed by using an atomistic modeling technique, the molecular structural mechanics method. To create this model, nodes are placed at the location of carbon atoms and the covalent bonds between them are modeled using elastic beam elements. To calculate the beam element properties, a linkage between molecular and continuum mechanics is applied. ATOMIC STRUCTURE OF CNTs A single-walled carbon nanotube may be regarded as a graphene sheet rolled into a cylindrical shell. The tube chirality, which is defined by the chiral vector h C  and the chiral angle  , Effect of Vacancy Defects on the Fundamental Frequency of Carbon Nanotubes Mostafa Pirmoradian 1 , Mohammad Taghi Ahmadian 1 , Ahmad Asempour 1 , Seyyed Ahmad Tajalli 1 1Center of Excellence in Design, Robotics and Automation, School of Mechanical Engineering, Sharif University of Technology, Iran. 1000 978-1-4244-1908-1/08/$25.00 ©2008 IEEE. Proceedings of the 3rd IEEE Int. Conf. on Nano/Micro Engineered and Molecular Systems January 6-9, 2008, Sanya, China