Tunable wave coupling in periodically rotated Miura-ori tubes

Origami folding structures are vital in shaping programmable mechanical material properties. Of particular note, tunable dynamical properties of elastic wave propagation in origami structures have been reported. Despite the promising features of origami metamaterials, the influence of the kinematics of tessellated origami structures on elastic wave propagation remain unexplored. This study proposes elastic metamaterials using connected Miura-ori tubes, the kinematics of which are coupled by folding and unfolding motions in a tubular axis; achieved by periodically connecting non-rotated and rotated Miura-ori tubes. The kinematics generate wave modes with localized deformations within the unit cell of the metamaterials, affecting the global elastic deformation of Miura-ori tubes via the coupling of wave modes. Dispersion analysis, using the generalized Bloch wave framework based on bar-and-hinge models, verifies the influence of kinematics in the connected tubes on elastic wave propagation. Furthermore, folding the connected tubes changes the coupling strength of wave modes between the kinematics and global elastic deformation of the tubes by breaking the ideal kinematics. The coupling of wave modescontributes to the formation of the band gaps and their tunability. These findings enable adaptive and <i>in situ</i> tunability of band structures to prohibit elastic waves in the desired frequency ranges.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.