Nonlinear dynamics of filaments. IV Spontaneous looping of twisted elastic rods
Nonlinear dynamics of filaments. IV Spontaneous looping of twisted elastic rods
复制标题
细丝的非线性动力学。
DOI：
10.1098/rspa.1998.0297
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
M. Tabor
中科院分区：
文献类型：
--
作者：
A. Goriely;M. Tabor
日常经验表明，扭曲的弹力丝会自发形成环状。我们将这个循环过程的动力学模型化为描述弹性细丝演化的Kirchhoff方程解的一系列分支。控制参数取为直杆的初始扭转密度。当扭曲的直杆变形成螺旋时，第一个分叉发生。该螺旋线是Kirchhoff方程的精确解，其稳定性可以研究。当螺旋线本身变得不稳定时，达到二次分叉，并证明了这些解的后分叉模式的局部化。最后，当在杆的中间形成环时，发生三次分叉，并且环变得不可避免。通过对色散关系的研究和对不同构型的振幅方程的推导，着重分析了这种现象的动力学特征。
Everyday experience shows that twisted elastic filaments spontaneously form loops. We model the dynamics of this looping process as a sequence of bifurcations of the solutions to the Kirchhoff equation describing the evolution of thin elastic filaments. The control parameter is taken to be the initial twist density in a straight rod. The first bifurcation occurs when the twisted straight rod deforms into a helix. This helix is an exact solution of the Kirchhoff equations, whose stability can be studied. The secondary bifurcation is reached when the helix itself becomes unstable and the localization of the post–bifurcation modes is demonstrated for these solutions. Finally, the tertiary bifurcation takes place when a loop forms at the middle of the rod and the looping becomes ineluctable. Emphasis is put on the dynamical character of the phenomena by studying the dispersion relation and deriving amplitude equations for the different configurations.