On the dynamics of elastic strips

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