Bifurcation analysis of rotating axially compressed imperfect nano-rod
Mathematical Physics
2019-07-23 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1811.12057,
title = {Bifurcation analysis of rotating axially compressed imperfect nano-rod},
author = {Teodor M. Atanacković and Ljubica Oparnica and Dušan Zorica},
journal= {arXiv preprint arXiv:1811.12057},
year = {2019}
}