The stability of twisted straight rods is described within the framework of the time dependent Kirchhoff equations for thin elastic filaments. A perturbation method is developed to study the linear stability of this problem and to find the dispersion relations. The general problem is to understand and describe the post bifurcation behavior of stationary structures. A nonlinear analysis results in a new 3-Dimensional amplitude equation, describing the deformation of the rod beyond the instability, which takes the form of a pair of nonlinear, second-order evolution equations coupling the local deformation amplitude to the twist density. Various solutions, such as solitary waves, are presented. In this we study the dynamical (i.e., time-dependent) stability of the full three-dimensional Kirchhoff equations for the twisted straight rod.
展开▼
