Nonlocal Torsional Vibration of Nanorods

Abstract

The present work deals with the torsional vibration of nanorods based on nonlocal elasticity theory. The nonlocal elasticity theory is incorporated into classical rod model to capture unique features of the nanorods under the continuum mechanics theory. The strong effect of the nonlocal scale has been obtained which leads to substantially different behaviors of nanorods from those of macroscopic rods. Nonlocal rod model is developed for torsional vibration of nanorods. It is found that the torsional vibration frequencies are highly over estimated by the classical rod model because of ignoring the effect of small length scale. It has also been shown that the axial vibration frequencies of nanorods are always higher than that of the torsional vibration. The effects of the nonlocal scale, modenumber and the length of the nanorod on torsional frequencies are highlighted in the present manuscript. The results provided in this article are useful guidance for the study and design of the next generation of nanodevices that make use of the torsional vibration properties of carbon nanotubes. The present analysis includes nonlocal effects with acceptable accuracy in the solution and thus may be useful when designing nanodevices in nano-electro-mechanical-systems applications. In summary, this nonlocal study may be employed for the design of a resonator with proper selection of nonlocal scale coefficient.

Keywords: Nanorod, Nonlocal continuum mechanics, Torsional vibration, Modenumber, Small scale coefficient