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On the dynamics of elastic strips

机译:关于弹性条动力学

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摘要

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. [References: 42]
机译:通过研究适当的Kirchhoff方程的溶液,通过研究适当的Kirchhoff方程的解决方案来分析弹性条的动态,即具有非圆形横截面的长薄杆。 首先,示出,如果天然直条带变形成螺旋,则唯一的平衡螺旋配置是没有内部扭曲的,并且其主弯曲方向沿正常或二英寸。 其次,分析了在张力下的直捻条带的线性稳定性,显示出根据外部和几何约束的虎嘴和跳槽分叉的可能性。 第三,导出非线性幅度方程,其描述接近不同分叉制度的动态。 最后,使用对这些方程的特殊分析解决方案来描述条带的屈曲。 特别地,考虑具有各种边界条件的有限溶液。 [参考:42]

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