Authors: Atanacković, Teodor
Oparnica, Ljubica
Zorica, Dušan 
Title: Bifurcation analysis of the rotating axially compressed nano-rod with imperfections
Journal: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume: 99
Issue: 7
Issue Date: 1-Jul-2019
Rank: M22
ISSN: 0044-2267
DOI: 10.1002/zamm.201800284
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: critical load parameters | Lyapunov-Schmidt reduction | rotating nano-rod | two-parameter universal unfolding
Publisher: Wiley
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Provincial Secretariat for Higher Education and Scientific Research, Grant 142-451-2384/2018

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