Dynamic Modeling and Transient Analysis of a Deployable Miura-Origami Tube

Abstract

Origami provides a rich library and unique benefits for developing deployable structures. Comparing with the vast amount of progress in pattern design, static configuration analysis, and folding kinematics, research on the dynamics of origami deployable structures remains at the early stage. This paper presents our effects in developing an effective and addressable dynamic model for studying the transient dynamics of a Miura-origami tube consisting of stacked Miura-ori (SMO) cells. The Miura-ori tube, in an ideal scenario, is rigid-foldable and flat-foldable, and its folding can be described via a single-degree-of-freedom (DOF) mechanism. However, practically, these features cannot be fully satisfied in a real prototype. In this research, five assumptions are proposed for dynamic modeling purposes, which, on one hand, retain the key characteristics of folding, and on the other hand, significantly simplify the problem. With the five assumptions and based on the Lagrange Equation for the general case, the governing equation of the Miura-ori tube can be derived. Taking a six-cell Miura-ori tube under free deployment as an example, numerical analyses reveal that in addition to the decayed vibrations in the deploying direction, the tube would also exhibit significant transverse vibrations. The transient dynamics in both the deploying and the transverse directions can be quantified by the overshoot values and the settling times. Moreover, by increasing the additionally-introduced crease torsional stiffness, which is used to constrain the deviation between the folding of adjacent half SMO cells, the multiple-DOF dynamic model would degenerate into the single-DOF dynamic model. In such a scenario, only vibrations in the deploying direction are possible. The constructed model and the preliminary understanding of the transient dynamics could provide useful guidelines for designing and optimizing origami-based tubular deployable structures.