Dynamics of a bistable Miura-origami structure

Origami-inspired structures and materials have shown extraordinary properties and performances originating from the intricate geometries of folding. However, current state of the art studies have mostly focused on static and quasistatic characteristics. This research performs a comprehensive experimental and analytical study on the dynamics of origami folding through investigating a stacked Miura-Ori (SMO) structure with intrinsic bistability. We fabricate and experimentally investigated a bistable SMO prototype with rigid facets and flexible crease lines. Under harmonic base excitation, the SMO exhibits both intrawell and interwell oscillations. Spectrum analyses reveal that the dominant nonlinearities of SMO are quadratic and cubic, which generate rich dynamics including subharmonic and chaotic oscillations. The identified nonlinearities indicate that a third-order polynomial can be employed to approximate the measured force-displacement relationship. Such an approximation is validated via numerical study by qualitatively reproducing the phenomena observed in the experiments. The dynamic characteristics of the bistable SMO resemble those of a Helmholtz-Duffing oscillator (HDO); this suggests the possibility of applying the established tools and insights of HDO to predict origami dynamics. We also show that the bistability of SMO can be programmed within a large design space via tailoring the crease stiffness and initial stress-free configurations. The results of this research offer a wealth of fundamental insights into the dynamics of origami folding, and provide a solid foundation for developing foldable and deployable structures and materials with embedded dynamic functionalities.

受折纸启发的结构和材料由于折叠的复杂几何形状而展现出非凡的特性和性能。然而，目前最先进的研究大多集中在静态和准静态特性上。本研究通过对具有固有双稳态的堆叠式三浦折（SMO）结构进行研究，对折纸折叠的动力学进行了全面的实验和分析研究。我们制作并通过实验研究了一个具有刚性面和柔性折痕线的双稳态SMO原型。在谐波基底激励下，SMO表现出阱内和阱间振荡。频谱分析表明，SMO的主要非线性是二次和三次的，这产生了丰富的动力学现象，包括次谐波和混沌振荡。所确定的非线性表明，可以采用三阶多项式来近似测量得到的力 - 位移关系。通过数值研究定性地重现实验中观察到的现象，验证了这种近似。双稳态SMO的动态特性类似于亥姆霍兹 - 达芬振子（HDO）；这表明有可能应用已有的HDO工具和见解来预测折纸动力学。我们还表明，可以通过调整折痕刚度和初始无应力配置，在较大的设计空间内对SMO的双稳态进行编程。这项研究的结果为折纸折叠动力学提供了大量的基本见解，并为开发具有嵌入式动态功能的可折叠和可展开结构及材料奠定了坚实的基础。