Modelling carbon nano-tubes dynamical behaviour via nonlocal theory – free vibrations and dispersion relations

Abstract

Abstract In the present paper the influence of non-local gradient formulations on the dynamical behaviour (free vibrations and dispersion relations) of carbon nanotubes analysed with the use of 2D shell theory is discussed. At the beginning the compact, consistent approach to the nonlocal (the Mindlin-Tiersten theory) description of 2D carbon nanoshells is shown. The presented results demonstrate the equivalence of free vibration analysis to the normal displacement mode (RBM) of carbon nanoshells. The possible extension of the presented formulations are also discussed.