Document Zbl 1254.74074

Magnetically-induced buckling of a whirling conducting rod with applications to electrodynamic space tethers. (English) Zbl 1254.74074

J. Nonlinear Sci. 20, No. 3, 309-339 (2010).

Summary: We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure, motivated by stability problems of electrodynamic space tethers. Both static (buckling) and dynamic (whirling) instability are considered and we also compute post-buckling configurations. The equations used are the geometrically exact Kirchhoff equations. Magnetic buckling of a welded rod is found to be described by a surprisingly degenerate bifurcation, which is unfolded when both transverse anisotropy of the rod and angular velocity are considered. By solving the linearised equations about the (quasi-) stationary solutions, we find various secondary instabilities. Our results are relevant for current designs of electrodynamic space tethers and potentially for future applications in nano- and molecular wires.

Cited in 3 Documents

MSC:

74K10	Rods (beams, columns, shafts, arches, rings, etc.)
74G60	Bifurcation and buckling
78A30	Electro- and magnetostatics
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

rod mechanics; Kirchhoff equations; magnetic buckling; degenerate pitchfork bifurcations; Hopf bifurcation; spinning electrodynamic tether

Software:

AUTO

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Full Text: DOI arXiv

References:

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