Dynamics of helical strips

Alain Goriely and Patrick Shipman
Phys. Rev. E 61, 4508 – Published 1 April 2000
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Abstract

The dynamics of inertial elastic helical thin rods with noncircular 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 free-standing helices are always stable. There exists a one-parameter family of stationary helical solutions depending on the ratio of 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.

  • Received 4 October 1999

DOI:https://doi.org/10.1103/PhysRevE.61.4508

©2000 American Physical Society

Authors & Affiliations

Alain Goriely1,2,* and Patrick Shipman2

  • 1Program in Applied Mathematics, Building No. 89, University of Arizona, Tucson, Arizona 85721
  • 2Department of Mathematics, Building No. 89, University of Arizona, Tucson, Arizona 85721

  • *Electronic address: goriely@math.arizona.edu

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Vol. 61, Iss. 4 — April 2000

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