A nonlinear iterated map for a graded Waterbomb origami tube
Résumé
The classic Waterbomb tube is a periodic three-dimensional origami, with a complex geometry capable of exhibiting wave-like behavior along its longitudinal axis, which originates from a tessellation of degree 6 vertex. It is an attractive pattern with potential applications in several fields such as metamaterials, energy harvesting and medical implants. Due to its rich mathematical structure, a recent approach has explained its wave property as a quasi-periodic solution of a discrete two-dimensional dynamical system associated with the origami geometry. Such dynamics is defined by a nonlinear recurrence relation (iterated map) involving distances between the vertices in different rings of the origami tube. Building on this idea, the present study investigated gradation of the unit cells along the tessellation lines, giving rise to a graded origami structure with similar unit cells along horizontal rings but with different rings along the longitudinal direction of the tube. This dynamical system is non-autonomous and is accessed for different grading patterns, following deterministic and stochastic rules, which generate ordered and disordered origami tubes, respectively. The systems are studied and the respective properties reported in this presentation.