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arXiv · 1201.6351

Helical buckling of a whirling conducting rod in a uniform magnetic field

J. Valverde·G. H. M. van der Heijden
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Abstract

We study the effect of a magnetic field on the behaviour of a conducting elastic rod subject to a novel set of boundary conditions that, in the case of a transversely isotropic rod, give rise to exact helical post-buckling solutions. The equations used are the geometrically exact Kirchhoff equations and both static (buckling) and dynamic (whirling) instability are considered. Critical loads are obtained explicitly and are given by a surprisingly simple formula. By solving the linearised equations about the (quasi-)stationary solutions we also find secondary instabilities described by (Hamiltonian-)Hopf bifurcations, the usual signature of incipient `breathing' modes. The boundary conditions can also be used to generate and study helical solutions through traditional non-magnetic buckling due to compression, twist or whirl.

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J. Valverde, G. H. M. van der Heijden. 2012-01-30. Helical buckling of a whirling conducting rod in a uniform magnetic field. https://doi.org/10.1016/j.ijnonlinmec.2011.12.005

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