Instability of a whirling conducting rod in the presence of a magnetic field

G.H.M. van der Heijden & J. Valverde

We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure subject to end forces. Both statical (buckling) and dynamical (whirling) instability are considered and we also compute post-buckling configurations. The theory used is the geometrically exact Cosserat rod theory. We consider two types of boundary conditions: the traditional welded boundary conditions and a novel set of boundary conditions that give rise to exact helical post-buckling solutions. Our results are relevant for current designs of electrodynamic space tethers and potentially for future applications in nano- and molecular wires.

keywords: conducting rod, magnetic field, Cosserat theory, bifurcation, helical solutions, space tether

Proc. of the 5th EUROMECH Nonlinear Dynamics Conference (ENOC 2005), 7-12 August 2005, Eindhoven, The Netherlands, D.H. van Campen, M.D. Lazurko, W.P.J.M. van den Oever (eds), pp. 2624-2633, ISBN 90-386-2667-3 (2005)