Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses.
Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses.
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DOI：
10.1103/physreve.101.053002
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Ousmane Kodio;A. Goriely;D. Vella
中科院分区：
文献类型：
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作者：
Ousmane Kodio;A. Goriely;D. Vella
细长的弹性物体，如柱子，在荷载作用下往往会屈曲。虽然静态屈曲被理解为一个分叉问题，但在动态屈曲过程中形状的演变要难得多。常压弹性环已成为研究受控载荷作用下动力屈曲的一种理论和实验范式。在实验中，在肥皂膜中放置一个弹性环。当环外的薄膜被移除时，表面张力将环向内拉，模拟外部加压。在这里，我们通过对受压弹性环进行后分叉分析，对这一过程进行了理论分析。这一分析使我们能够了解惯性、材料特性和载荷如何影响观察到的形状。特别地，我们将直接数值解与分叉后的渐近分析相结合，表明惯性驱动系统朝着静态屈曲中不能选择的高阶振型发展。我们的理论结果解释了标准线性稳定性分析无法捕捉到的实验观察结果。
Slender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal pressure have emerged as a theoretical and experimental paradigm for the study of dynamic buckling with controlled loads. Experimentally, an elastic ring is placed within a soap film. When the film outside the ring is removed, surface tension pulls the ring inward, mimicking an external pressurization. Here we present a theoretical analysis of this process by performing a postbifurcation analysis of an elastic ring under pressure. This analysis allows us to understand how inertia, material properties, and loading affect the observed shape. In particular, we combine direct numerical solutions with a postbifurcation asymptotic analysis to show that inertia drives the system towards higher modes that cannot be selected in static buckling. Our theoretical results explain experimental observations that cannot be captured by a standard linear stability analysis.