Affiliation:
1. Department of General Systems Studies, Graduate School of Arts and Sciences, The University of Tokyo , Meguro-ku, Tokyo 153-8902, Japan
Abstract
Origami tessellations, whose crease pattern has translational symmetries, have attracted significant attention in designing the mechanical properties of objects. Previous origami-based engineering applications have been designed based on the “uniform-folding” of origami tessellations, where the folding of each unit cell is identical. Although “nonuniform-folding” allows for nonlinear phenomena that are impossible through uniform-folding, there is no universal model for nonuniform-folding, and the underlying mathematics for some observed phenomena remains unclear. Wavy folded states that can be achieved through nonuniform-folding of the tubular origami tessellation called a waterbomb tube are an example. Recently, the authors formulated the kinematic coupled motion of unit cells within a waterbomb tube as the discrete dynamical system and identified a correspondence between its quasiperiodic solutions and wavy folded states. Here, we show that the wavy folded state is a universal phenomenon that can occur in the family of rotationally symmetric tubular origami tessellations. We represent their dynamical system as the composition of the two 2D mappings: taking the intersection of three spheres and crease pattern transformation. We show the universality of the wavy folded state through numerical calculations of phase diagrams and a geometric proof of the system’s conservativeness. Additionally, we present a non-conservative tubular origami tessellation, whose crease pattern includes scaling. The result demonstrates the potential of the dynamical system model as a universal model for nonuniform-folding or a tool for designing metamaterials.
Funder
Japan Science and Technology Agency
Japan Society for the Promotion of Science
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Effective isometries of periodic shells;Journal of the Mechanics and Physics of Solids;2024-04
2. Frustration propagation in tubular foldable mechanisms;Frontiers in Physics;2023-12-13