Dynamics of helical strips

Alain Goriely, Patrick Shipman
2000 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
The dynamics of inertial elastic helical thin rods with non-circular cross sections and arbitrary intrinsic curvature, torsion, and twist is studied. The classical Kirchhoff equations are used together with a perturbation scheme at the level of the director basis and the dispersion relation for helical strips is derived and analyzed. It is shown that all naturally straight helical strips are unstable whereas freestanding helices are always stable. There exists a one-parameter family of
more » ... family of stationary helical solutions depending on the ratio curvature to torsion. A bifurcation analysis with respect to this parameter is performed and bifurcation curves in the space of elastic parameters are identified. The different modes of instabilities are analyzed.
doi:10.1103/physreve.61.4508 pmid:11088250 fatcat:wdlin2vxnnfa7ou767jjps2fhy