Nonlinear dynamics of filaments. III. Instabilities of helical rods
Nonlinear dynamics of filaments. III. Instabilities of helical rods
复制标题
细丝的非线性动力学。
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
M. Tabor
中科院分区：
文献类型：
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作者：
A. Goriely;M. Tabor
利用弹性细杆的含时Kirchhoff方程，研究了具有固有曲率和扭转的扭转螺旋杆的线性稳定性。利用新发展的微扰格式，我们导出了控制各种螺旋构型稳定性的一般色散关系。我们证明了没有终端力的螺旋线总是动态稳定的。我们还计算了在扭转扰动下最稳定的螺旋形状，表明不同的不稳定模可以在参数空间的不同区域被激发，并且有时可以共存。计算了线性不稳定模式，并给出了显式形式。
The time‐dependent Kirchhoff equations for thin elastic rods are used to study the linear stability of twisted helical rods with intrinsic curvature and twist. Using a newly developed perturbation scheme, we derive the general dispersion relations governing the stability of various helical configurations. We show that helices with no terminal forces are always dynamically stable. We also compute the most stable helical shape against twist perturbations and show that different unstable modes can be excited in different regions of the parameter space and can sometimes coexist. The linearly unstable modes are computed and explicit forms are given.