Effective Elastic Moduli Evaluation of Single Walled Carbon Nanotubes Using Flexural Vibrations

Two new methods for effective elastic moduli evaluation of single walled carbon nanotubes (SWCNT) are presented. These methods rely on the Euler-Bernoulli and the Timoshenko beam theories, the modification of finite elements based on these theories, and an optimization technique. The proposed modification of the standard Euler-Bernoulli and Timoshenko finite elements assumes that the SWCNT diameter is much larger than its thickness. It is shown that the method based on the Timoshenko finite element presents better elastic moduli evaluations of short nanotubes than the ones based on the Euler-Bernoulli finite element.