FoldingAngle Framework for Structural Modeling of Rigid Triangulated Miuraori Lattices

Abstract

Origami is rapidly gaining prominence in the research of metamaterials as it allows for tuning the properties of interest by change in the folded state. Origamibased lattices that allow lowfrequency wavepropagation can potentially find use as acoustic metamaterials. Rigidpanel origami tessellations have lattice modes which are exclusively due to the lowenergy folding deformations at creases and hence will be suitable for lowfrequency wavepropagation applications. Modeling frameworks like barandhinge that are typically used to study origami lattice mechanics allow for panel stretching behavior which is forbidden and redundant in rigidpanel origami lattices. This drives the necessity for an efficient analysis framework dealing exclusively with foldingangles for the study of origami lattices with rigid panels. As a first step in this direction, in this paper, we propose a foldinganglebased analytical framework for structural modeling of infinite lattices of triangulated Miuraori (an origami pattern studied widely for its metamaterial applications) with rigid panels. We assign rotational stiffness to the creases and analytically derive the stiffness matrix for the lattices based on a minimal number of foldingangle degrees of freedom. Finally, we study the influence of the equilibrium state of folding and the relative crease stiffness on the modal energies, to demonstrate the tunable and programmable nature of the structure. The framework proposed in our work could enable the study of wave dynamics in rigidpanel Miuraoribased lattices and our findings show significant promise for the future use of 1D origami with rigid panels as acoustic metamaterials.