In recent years, multi-stable origami structures have garnered increasing attention for their applications in dynamic scenarios such as robotic arm motions, impact energy absorption, and spectrum gap regulation. Understanding the intricate working mechanisms and exploring the rich dynamics of these structures necessitate the development of dynamic models. However, existing dynamic modeling methods for origami structures are often cumbersome, and the resulting dynamic models often lack interpretability. To overcome these limitations, we propose a novel data-driven dynamic modeling approach based on B-spline Galerkin method and subset selection strategy. This approach directly captures the dynamics of multi-stable origami structures using measured data, eliminating the need for reliance on empirical or prior knowledge. To validate the effectiveness of the proposed approach, we first evaluate it on the Duffing system, which has explicit expressions, successfully reconstructing the governing equation. Subsequently, we apply this method to the dynamic modeling of the origami ball structure with tri-stability and the multi-cell stacked Miura-origami (SMO) structure with high dimensionality through simulation, showing favorable results. Finally, using experimental data collected from a bi-stable SMO structure prototype, we employ the proposed method to obtain a global model that can accurately predict different dynamic behaviors over a broad range of excitation frequencies, including intra-well periodic vibrations, inter-well periodic vibrations, and inter-well chaotic vibrations. Overall, our method showcases outstanding efficacy in formulating interpretable, manageable, and comprehensive dynamic models. It plays a pivotal role in delving into the intricate dynamics of multi-stable origami structures.

中文翻译：

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多稳态折纸结构的数据驱动建模：提取全局控制方程并探索复杂动力学


近年来，多稳态折纸结构因其在机械臂运动、冲击能量吸收和谱隙调节等动态场景中的应用而受到越来越多的关注。了解复杂的工作机制并探索这些结构的丰富动态需要开发动态模型。然而，现有的折纸结构动态建模方法通常很麻烦，并且所得的动态模型通常缺乏可解释性。为了克服这些限制，我们提出了一种基于 B 样条伽辽金方法和子集选择策略的新型数据驱动动态建模方法。这种方法使用测量数据直接捕获多稳定折纸结构的动态，消除了对经验或先验知识的依赖。为了验证所提出方法的有效性，我们首先在具有显式表达式的 Duffing 系统上对其进行评估，成功地重建了控制方程。随后，我们将该方法应用到三稳态折纸球结构和高维多单元堆叠Miura-origami（SMO）结构的动态建模中，通过仿真得到了良好的结果。最后，利用从双稳态 SMO 结构原型收集的实验数据，我们采用所提出的方法获得了一个全局模型，该模型可以准确预测较宽的激励频率范围内的不同动态行为，包括井内周期性振动、井间振动等。周期性振动和井间混沌振动。总体而言，我们的方法在制定可解释、可管理和综合的动态模型方面展示了出色的功效。 它在深入研究多稳定折纸结构的复杂动力学方面发挥着关键作用。