An interesting field in the nano science studies, is based on modeling and simulation of vibrating carbon nanotubes (CNTs) in an elastic medium to predict the natural frequencies and associated mechanical properties. Meanwhile, in all of these models, the nanotube was assumed to be perfectly straight. However, photomicrographs of nanocomposites indicate that CNTs may exhibit significant waviness. This research prepares a model based on the continuum mechanics to determine vibrational property of circularly curved carbon nanotube. Analysis of free vibration of a curved single-walled carbon nanotube (SWCNT) is accorded to the Timoshenko theory under general boundary conditions. Winkler and Pasternak foundation models are employed to simulate the interaction of the SWCNT with the surrounding elastic medium and the differential equations of the model are solved using generalized differential quadrature rule. The present study shows that the curvature of a CNT has a strong effect on modal frequencies, especially when the stiffness of the foundation and aspect ratio of CNT are relatively small.

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