Effects of inter-cell connections on the multi-stable dynamics of dual-cell stacked Miura-origami structures

Abstract

Origami has become an important source for the development of mechanical metamaterials because folding can often lead to enhanced or unconventional mechanical properties. Metamaterials are always made of repeating cells by stacking and tessellating. The inter-cell connection thus plays a key role in determining the overall mechanics and dynamics of the metamaterial, but current studies mainly focus on the effects of inter-cell connection on statics. To overcome the shortcomings and advance the state of the art, this research employs the dual-cell stacked Miura-origami (SMO) structure as a platform to comprehensively dissect the effects of inter-cell connection forms on the dynamics. The two constituent SMO cells, by design, can be bi-stable such that the dual-cell structure possesses four stable states that are fundamentally different in configuration. Two inter-cell connection forms, a rod connection and a crease connection, are examined both theoretically and experimentally in this research. Assuming rigid-foldability of the constituent SMO structures and by equivalently quantifying the inter-cell connection constraint via additional elastic potential energy, a refined and processible dynamic model of the multi-stable dual-cell SMO structure is developed. Comprehensive numerical calculations reveal, on the one hand, the rich and complex dynamics of the dual-cell structure and, on the other hand, uncover the significant differences caused by the inter-cell connection forms. With relatively weak inter-cell constraint (e.g., the rod connection), dynamic configuration switches would occur at low excitation amplitudes, and the dynamic response types of the two cells can be fundamentally different; however, with relatively strong inter-cell constraint (e.g., the crease connection), more energy input is required to switch the configuration, and the dynamic response types of the two cells remain consistent. Such findings are qualitatively verified via dynamic experiments on the dual-cell SMO structures. We also extend our research to global dynamics by analyzing the basins of attraction and basin stability, which demonstrates from a probabilistic viewpoint that stronger inter-cell constraint would converge the dynamics to synchronous response types. The results of this research would offer a solid foundation for regulating the multi-stable dynamics of multi-cell origami structures/metamaterials and advancing their dynamic applications.