期刊
JOURNAL OF NONLINEAR SCIENCE
卷 20, 期 3, 页码 309-339出版社
SPRINGER
DOI: 10.1007/s00332-010-9059-9
关键词
Rod mechanics; Kirchhoff equations; Magnetic buckling; Degenerate pitchfork bifurcations; Hopf bifurcation; Spinning electrodynamic tether
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.
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