Free Vibration of Single-Walled Carbon Nanotubes Using Nonlocal Truncated Timoshenko-Ehrenfest Beam Theory

Carbon nanotubes with their outstanding mechanical, physical and electrical properties have stimulated a significant amount of scientific technological research due to uniqueness compared conventional materials. As result, an extensive study on mechanical has been conducted, the static dynamic behavior single- walled multi-walled carbon examined using Euler-Bernoulli Timoshenko beam models. The main objective this paper is free vibration behaviour single-walled (SWCNT) nonlocal truncated theory. According Hamilton principle, equation motion calculated taking into account theory; general corresponding boundary conditions are derived. Finally, some numerical examples performed evaluate effects coefficient length nanotube. obtained results validated by comparing them those found in literature, they show accuracy efficiency developed model. Particularly, demonstrate that present formulation highly efficient capable satisfactorily describing nanobeams.