Dynamics of a bistable Miura-origami structure

Abstract

Origami-inspired structures and materials have shown extraordinary properties and performances originating from the intricate geometries of folding. However, current state of the art studies have mostly focused on static and quasistatic characteristics. This research performs a comprehensive experimental and analytical study on the dynamics of origami folding through investigating a stacked Miura-Ori (SMO) structure with intrinsic bistability. We fabricate and experimentally investigated a bistable SMO prototype with rigid facets and flexible crease lines. Under harmonic base excitation, the SMO exhibits both intrawell and interwell oscillations. Spectrum analyses reveal that the dominant nonlinearities of SMO are quadratic and cubic, which generate rich dynamics including subharmonic and chaotic oscillations. The identified nonlinearities indicate that a third-order polynomial can be employed to approximate the measured force-displacement relationship. Such an approximation is validated via numerical study by qualitatively reproducing the phenomena observed in the experiments. The dynamic characteristics of the bistable SMO resemble those of a Helmholtz-Duffing oscillator (HDO); this suggests the possibility of applying the established tools and insights of HDO to predict origami dynamics. We also show that the bistability of SMO can be programmed within a large design space via tailoring the crease stiffness and initial stress-free configurations. The results of this research offer a wealth of fundamental insights into the dynamics of origami folding, and provide a solid foundation for developing foldable and deployable structures and materials with embedded dynamic functionalities.

Dual constant-flux energy cascades to both large scales and small scales

“…Large-scale anisotropy has been attributed to truncation errors [196] at low wavenumbers, and is sensitive to the form of the energy input, or rather to the ratio of the scale at which energy is fed into the system to the overall size of the container. Given the computational cost to increase such a ratio, it is further suggested in [196] that a damping be introduced at large scales, a point that will require further study. An inadequate simulation of the isotropy of the large scales can also lead to spurious energy decay, as clearly shown in two dimensions [59].…”

Transformation Dynamics in Origami

“…Existing models of origami dynamics are built on the assumption that a fold pattern is equivalent to a set of rigid linkages connected by rotary joints and, like other linkage systems, has a limited number of degrees of freedom (d.o.f.) [19]. However, preliminary results indicate that compliance in the facets and hinges leads to additional degrees of freedom, including in nominally 0-d.o.f.…”

Mutual transformations of fractional-order and integer-order optical vortices

“…Past recent years of singular optic's [6] development have been marked by the surge of interest to optical vortices with fractional topological charges [7][8][9][10][11][12][13][14][15][16][17][18]. The first announcement of the fractional-order vortex instability in principle was reported by Soskin et al [7,8] for the vortices produced by a computergenerated hologram while the vortices propagate in free space.…”

“…Difference between these approaches lies in different contribution of the individual integer-order vortices in the complex field when the fractional-order beam evolves through the optical medium. Some typical features of such dynamical transformations were considered experimentally in the recent paper [18].…”

“…Half-order   2 1 /2 n  vortex-beams occupy a special place among variety of the fractional-charged optical fields because they can be easily and reliably generated at the initial plane by q-plates [23], photonic crystals [24] and arrays of microchip lasers [25]. Special types of singular beams with the fractional topological charges and fractional orbital angular momentum (OAM) in the closed form (e.g, erf-G beams and others) have been recently considered in number of papers [17,18,21,26].…”