Dynamics of helical strips
- 1 April 2000
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 61 (4), 4508-4517
- https://doi.org/10.1103/physreve.61.4508
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.Keywords
This publication has 20 references indexed in Scilit:
- The energy spectrum of a twisted flexible string under elastic relaxationJournal of Physics A: General Physics, 1995
- On the dynamics of flexure and stretch in the theory of elastic rodsArchive for Rational Mechanics and Analysis, 1995
- Supercoiling transitions of closed DNAPhysical Review E, 1994
- Fluid and solid fibers made of lipid molecular bilayersChemical Reviews, 1993
- Finite element analysis of DNA supercoilingThe Journal of Chemical Physics, 1993
- Elastic theory of helical fibersLangmuir, 1991
- Helical bilayer structures due to spontaneous torsion of the edgesThe Journal of Chemical Physics, 1986
- Calculation of the twist and the writhe for representative models of DNAJournal of Molecular Biology, 1986
- An elastic model of the large‐scale structure of duplex DNABiopolymers, 1979
- Helical Bacillus subtilis macrofibers: Morphogenesis of a bacterial multicellular macroorganismProceedings of the National Academy of Sciences, 1978