Radisson Basile, Kanso Eva
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089-1191, USA.
Phys Rev E. 2023 Jun;107(6-2):065001. doi: 10.1103/PhysRevE.107.065001.
Elastic strips provide a general motif for studying shape transitions. When actuated through rotation of its boundaries, a buckled strip exhibits, depending on the direction of rotation, three types of shape transitions: buckling, algebraic snap-through, or exponential snap-through. The transition dynamics is linked to the character of the bifurcation, which, in turn, is disclosed by the normal form of the system, but deriving normal forms is challenging. Recent work has used asymptotic methods to obtain this form for algebraic snap-through, but, to date, there is no methodology for extending this analysis to other transitions. Here we introduce a method to analyze the dynamic characteristics of an elastic strip near a transition and extend, in a straightforward manner, the previously proposed asymptotic analysis to exponential snap-through and buckling transitions. Importantly, we show that these normal forms dictate all the dynamic characteristics of the elastic strip near a shape transition. Our analysis provides reliable tools to diagnose and anticipate elastic shape transitions.
弹性条带为研究形状转变提供了一个通用模型。当通过其边界的旋转来驱动时，一个弯曲的条带根据旋转方向会呈现出三种类型的形状转变：屈曲、代数型快速翻转或指数型快速翻转。转变动力学与分岔的特征相关联，而分岔特征又由系统的范式揭示，但推导范式具有挑战性。最近的工作已使用渐近方法来获得代数型快速翻转的这种形式，但迄今为止，尚无将此分析扩展到其他转变的方法。在此，我们介绍一种分析弹性条带在转变附近的动态特性的方法，并以直接的方式将先前提出的渐近分析扩展到指数型快速翻转和屈曲转变。重要的是，我们表明这些范式决定了弹性条带在形状转变附近的所有动态特性。我们的分析提供了可靠的工具来诊断和预测弹性形状转变。
