Bifurcation analysis of the rotating axially compressed nano‐rod with imperfections

Abstract

Static stability problem for axially compressed rotating nano‐rod clamped at one and free at the other end is analyzed by the use of bifurcation theory. It is obtained that the pitchfork bifurcation may be either super‐ or sub‐critical. Considering the imperfections in rod's shape and loading, it is proved that they constitute the two‐parameter universal unfolding of the problem. Numerical analysis also revealed that for non‐locality parameters having higher value than the critical one interaction curves have two branches, so that for a single critical value of angular velocity there exist two critical values of horizontal force.