Nonlocal material properties of single-walled carbon nanotubes

The results reported in this paper show that the nonlocal material properties of a model based on Eringen's nonlocal continuum mechanics and the Timoshenko beam theory for free vibration analysis of single-walled carbon nanotubes is natural frequency, length and diameter dependent. Moreover, and contrary to what was expected, the nonlocal material constant increases as the length or diameter increases. For short single-walled carbon nanotubes and certain values of the Young's modulus, the nonlocal material constant is zero, i.e. the nonlocal theory reduces to the local (classical) theory. Also, for higher natural frequencies we obtain nonlocal material constants with smaller values. The present results suggest that further studies are needed to fully comprehend the mechanical behavior of single-walled carbon nanotubes in the context of nonlocal theories.

http://dx.doi.org/10.1080/19475411.2011.649805