Experimental studies of carbon nanotube mechanical properties demonstrated discrepancies with regard to analytical predictions. Since the atomic structure of carbon nano-tubes exhibited clearly anisotropic mechanical properties, an analytical molecular structural mechanics model was introduced in order to derive the longitudinal and circumferential moduli of nanotubes. The identification was based upon eigen-frequency analysis of the proposed computational model. It was combined with finite element analysis and interatomic potentials (Tersoff-Brenner, Morse). For simply supported cylindrical shells made of a specially orthotropic material, the eigen-frequencies could be easily derived in the analytical manner, using the Rayleigh-Ritz method, as the roots of third-order algebraic equations.

Vibration Control of Defects in Carbon Nanotubes. A.Muc, M.Chwał: Solid Mechanics and its Applications, 2011, 30, 239-46