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.