A series of Timoshenko beams connected through elastic layers are used to model the vibrations of a multi-walled carbon nanotube. The elastic layers model the interatomic Van der Waals forces. The model is used to predict the natural frequencies of coaxial and non coaxial modes for double-walled and triple-walled nanotubes. Differences in the natural frequencies and mode shapes between the Timoshenko beam model and the simpler Euler-Bernoulli beam model are identified and explained. The theory is used to develop a modal analysis procedure to study the forced vibrations of multi-walled nanotubes.
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