Size dependent torsional vibration of nanotubes

In this study, torsional vibration of nanotubes (NTs) is examined using a modified couple stress theory. Based on Hamilton’s principle, governing equation of torsional vibration is obtained. An explicit solution is derived for the natural oscillations of NTs considering length scale. It is found that the non-dimensional natural frequency of the vibration is size dependent. For the limiting case in which the NT characteristic length increases, the results tend to those obtained by classical models (length scale equal to zero). This study might be useful for the design of a wide range of MEMS and NEMS.