On the dynamics of elastic strips

A. Goriely, M. Nizette, Michael Tabor

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

The dynamics of elastic strips, i.e., long thin rods with noncircular cross section, is analyzed by studying the solutions of the appropriate Kirchhoff equations. First, it is shown that if a naturally straight strip is deformed into a helix, the only equilibrium helical configurations are those with no internal twist and whose principal bending direction is either along the normal or the binormal. Second, the linear stability of a straight twisted strip under tension is analyzed, showing the possibility of both pitchfork and Hopf bifurcations depending on the external and geometric constraints. Third, nonlinear amplitude equations are derived describing the dynamics close to the different bifurcation regimes. Finally, special analytical solutions to these equations are used to describe the buckling of strips. In particular, finite-length solutions with a variety of boundary conditions are considered.

Original languageEnglish (US)
Pages (from-to)3-45
Number of pages43
JournalJournal of Nonlinear Science
Volume11
Issue number1
DOIs
StatePublished - Jan 2001

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Strip
strip
Hopf bifurcation
Straight
Buckling
Boundary conditions
Binormal
Kirchhoff Equation
Pitchfork Bifurcation
Amplitude Equations
Geometric Constraints
Linear Stability
buckling
Helix
Twist
Hopf Bifurcation
helices
Analytical Solution
Nonlinear Equations
Cross section

Keywords

  • Amplitude equations
  • Elastic strips
  • Localized solutions

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

On the dynamics of elastic strips. / Goriely, A.; Nizette, M.; Tabor, Michael.

In: Journal of Nonlinear Science, Vol. 11, No. 1, 01.2001, p. 3-45.

Research output: Contribution to journalArticle

Goriely, A. ; Nizette, M. ; Tabor, Michael. / On the dynamics of elastic strips. In: Journal of Nonlinear Science. 2001 ; Vol. 11, No. 1. pp. 3-45.
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