Dynamic Stability in Graded Waterbomb Origami Structures

Origami-inspired structures have recently emerged as a promising framework for the design of adaptive and lightweight systems with programmable stiffness and deployability. This work investigates the dynamic behavior and stability of graded Waterbomb origami tubes, emphasizing their geometric characteristics. The Waterbomb geometry, constructed from a tessellated pattern of mountain and valley folds, is modeled as a nonlinear lattice system with rigid panels, whose unit cells are modulated through geometric gradation along the axial direction. Both deterministic and stochastic gradation rules are implemented, giving rise to ordered and disordered configurations governed by a five-dimensional nonlinear iterated map. Numerical analyses reveal distinct dynamic regimes: wave-like folding modes with energy exchange between layers, and finite-size instabilities leading to localized deformation. The results demonstrate how stochastic gradation promotes energy dispersion and enhances dynamic stability. Complementary 3D models were developed and assembled in the laboratory to validate geometric predictions and to visualize the folding-induced wave-like patterns observed in simulations. This study provides insight into the design of architected origami-based structures for morphing systems and adaptive metamaterials.