Tunable Frequency Band Structure of Origami-Based Mechanical Metamaterials

Abstract

In this study, we show the formation of frequency band structures in origami-based mechanical metamaterials composed of the Triangulated Cylindrical Origami (TCO). Interestingly, the folding behavior of this structure can exhibit both axial and rotational motions under external excitations. Therefore, these two motions can be strongly coupled with each other, which leads to unique dynamic behavior, particularly wave mixing effects. To analyze the folding behavior of the TCO cells, we model their triangular facets into a network of linear springs. We assemble a 1D chain of multiple TCO unit cells stacked vertically in various arrangements, e.g., changing their stacking sequences and/or orientation angles. We study frequency responses of this system to investigate wave mixing effects between axial and rotational motions under dynamic excitations. This dynamic analysis on the multi-cell structure demonstrates the formation of tunable frequency band structures, which can be manipulated by the arrangement of the unit cells and their initial configurations. By taking advantage of their unique dynamic mechanisms, the origami-based mechanical metamaterials have great potential to be used for controlling structural vibrations in an efficient manner.

Topological state transfer in Kresling origami

“…In this coupled 1D system, we can observe four branches: two lower and two upper branches (see the enlarged view in Fig. 2d; two lower branches are almost collapsing onto each other) 42 . Note that at k = π/h 0 there is a degeneracy between the two lower and the two upper branches.…”

“…In this study, we consider the 1D dimer lattice composed of the origami unit cells to explore the tunable wave dispersion relationship and the emerging topological edge states at finite frequency. The origami unit is based on the Kresling pattern with opposite chirality, which shows the axial-rotation coupling and nonlinear static responses 41,42 . Interestingly, due to this axial-rotation coupling in our system, alternating chirality along the length of the lattice itself leads to the opening of a lower band gap.…”

Topological state transfer in Kresling origami

“…Figure 2c shows the wave dispersion relationship with the unit cell geometrical parameters h 0 = 30 mm, In this coupled 1D system, we can observe four branches: two lower and two upper branches (see the enlarged view in Fig. 2d; two lower branches are almost collapsing onto each other) [41]. Note that at k = π/h 0 there is degeneracy between the two lower and the two upper branches.…”

“…In this study, we specifically consider the 1D dimer lattice composed of the origami unit cells to explore the tunable wave dispersion relationship and the emerging topological edge states. The origami unit is based on the Kresling pattern with opposite chirality, which shows the axial-rotation coupling and nonlinear static responses [40,41]. Interestingly, due to this axial-rotation coupling in our system, alternating chirality along the length of the lattice itself leads to the opening of a lower band gap.…”

Wave-packet spreading in disordered soft architected structures

“…The wave dynamics of disordered harmonic chains with two DoFs per site appear to be quite interesting, deserving further investigations. Such systems have been useful in modeling macroscopic mechanical devices including granular chains, highly deformable elastic assemblies and origami lattices [35,36,37,38,39,40]. This allows for easy tunability of the system's dispersion due to the geometrical characteristics and material properties, and makes these systems attractive for several applications.…”