Design and identification methods of effective mechanical properties for carbon nanotubes

Atomic arrangement and configuration of carbon nanotubes (CNTs) imposes the necessity of the use of transversely isotropic or specially orthotropic material models in the description of their effective material properties instead of isotropic one. Therefore, in the present paper an identification technique based on the analysis of natural vibrations is introduced. Theoretical values of natural vibrations are derived with the use of theoretical relations valid for thin orthotropic cylindrical shells. They are compared with numerical ones calculated utilizing a three-dimensional finite element (FE) model for armchair and zigzag single-walled carbon nanotubes (SWCNTs). The numerical model development is consistent with molecular mechanics formulations and it is based on the assumption that carbon nanotubes, when subjected to free vibrations, behave like space-frame structures. In order to compare the numerical and theoretical values of eigenfrequencies two forms of the interatomic potentials are considered: the modified Morse potential and REBO potential. In order to avoid local modes of deformations the axisymmetric modes are investigated only. A detailed study of results demonstrates that CNTs should be considered as orthotropic structures.