Dynamic torsional buckling of multi-walled carbon nanotubes embedded in an elastic medium

In this paper the dynamic torsional buckling of multi-walled carbon nanotubes (MWNTs) embedded in an elastic medium is studied by using a continuum mechanics model. By introducing initial imperfections for MWNTs and applying the preferred mode analytical method, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for embedded double-walled carbon nanotubes (DWNTs). Numerical results show that, for both the DWNTs and embedded DWNTs, the buckling form shifts from the lower buckling mode to the higher buckling mode with increasing the buckling load, but the buckling mode is invariable for a certain domain of the buckling load. It is also indicated that, the surrounding elastic medium generally has effect on the lower buckling mode of DWNTs only when compared with the corresponding one for individual DWNTs