A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes

The free vibration analysis of Single-Walled Carbon NanoTubes (SWCNTs) is proposed in the present paper. A continuum approach (based on an exact elastic three-dimensional shell model) is used for natural frequency investigation of simply supported SWCNTs. In order to apply this continuum model, carbon nanotubes are defined as isotropic cylinders with an equivalent thickness and Young modulus. Preliminary remarks are proposed concerning the possible use of a continuum approach and the most convenient definitions of the equivalent thickness and Young modulus. Subsequently, the 3D shell method is compared with different beam analyses to show the limitations of 1D beam models. Finally, zigzag, armchair and general chirality SWCNTs (with various lengths and geometries) are analyzed via the 3D shell model to calculate their vibration modes.