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Abstract Origami has great potential for creating deployable structures, however, most studies have focused on their static or kinematic features, while the complex and yet important dynamic behaviors of the origami deployment process have remained largely unexplored. In this research, we construct a dynamic model of a Miura origami sheet that captures the combined panel inertial and flexibility effects, which are otherwise ignored in rigid folding kinematic models but are critical in describing the dynamics of origami deployment. Results show that by considering these effects, the dynamic deployment behavior would substantially deviate from a nominal kinematic unfolding path. Additionally, the pattern geometries influence the effective structural stiffness, and it is shown that subtle changes can result in qualitatively different dynamic deployment behaviors. These differences are due to the multistability of the Miura origami sheet, where the structure may snap between its stable equilibria during the transient deployment process. Lastly, we show that varying the deployment rate can affect the dynamic deployment configuration. These observations are original and these phenomena have not and cannot be derived using traditional approaches. The tools and outcomes developed from this research enable a deeper understanding of the physics behind origami deployment that will pave the way for better designs of origami-based deployable structures, as well as extend our fundamental knowledge and expand our comfort zone beyond current practice. 

Origami has emerged as a promising tool for the design of mechanical structures that can be folded into small volume and expanded to large structures, which enables the desirable features of compact storage and effective deployment. Most attention to date on origami deployment has been on its geometry, kinematics, and quasi-static mechanics, while the dynamics of deployment has not been systematically studied. On the other hand, deployment dynamics could be important in many applications, especially in high speed operation and low damping conditions. This research investigates the dynamic characteristics of the deploying process of origami structures through investigating a Miura-Ori sheet (Fig. 1(b, c)). In this study, we have utilized the stored energy in pre-deformed spring elements to actuate the deployment. We theoretically model and numerically analyze the deploying process of the origami sheet. Specifically, the sheet is modeled by bar-and-hinge blocks, in which the facet and crease stiffnesses are modeled to be related to the bar axial deformation and torsional motion at the creases. On the other hand, the structural inertia is modelled as mass points assigned at hinges. Numerical simulations show that, apart from axial contraction and expansion, the origami structure can exhibit transverse motion during the deploying process. Further investigation reveals that the transverse motion has close relationship with the controlled deploying rate. This research will pave the way for further analysis and applications of the dynamics of origami-based structures. 

Origami-inspired mechanical metamaterials could exhibit extraordinary properties that originate almost exclusively from the intrinsic geometry of the constituent folds. While most of current state of the art efforts have focused on the origami’s static and quasi-static scenarios, this research explores the dynamic characteristics of degree-4 vertex (4-vertex) origami folding. Here we characterize the mechanics and dynamics of two 4-vertex origami structures, one is a stacked Miura-ori (SMO) structure with structural bistability, and the other is a stacked single-collinear origami (SSCO) structure with lockinginduced stiffness jump; they are the constituent units of the corresponding origami metamaterials. In this research, we theoretically model and numerically analyze their dynamic responses under harmonic base excitations. For the SMO structure, we use a third-order polynomial to approximate the bistable stiffness profile, and numerical simulations reveal rich phenomena including small-amplitude intrawell, largeamplitude interwell, and chaotic oscillations. Spectrum analyses reveal that the quadratic and cubic nonlinearities dominate the intrawell oscillations and interwell oscillations, respectively. For the SSCO structure, we use a piecewise constant function to describe the stiffness jump, which gives rise to a frequencyamplitude response with hardening nonlinearity characteristics. Mainly two types of oscillations are observed, one with small amplitude that coincides with the linear scenario because locking is not triggered, and the other with large amplitude and significant nonlinear characteristics. The method of averaging is adopted to analytically predict the piecewise stiffness dynamics. Overall, this research bridges the gap between the origami quasi-static mechanics and origami folding dynamics, and paves the way for further dynamic applications of origami-based structures and metamaterials.