Laboratory of Applied Nonlinear Dynamics (LAND), Engineering Division, New York University, Abu Dhabi, UAE.
Phys Rev E. 2019 Dec;100(6-1):063001. doi: 10.1103/PhysRevE.100.063001.
Origami-inspired design has recently emerged as a major thrust area of research in the fields of science and engineering. One such design utilizes Kresling-pattern origami to construct nonlinear springs that can act as mechanical bit memory switches, wave guides, fluidic muscles, and vibration isolators. The main objective of this work is to characterize the static equilibria of such springs, their stability, and bifurcations as the geometric parameters of the Kresling pattern are varied. To this end, a mathematical model which assumes that the different panels can be represented by axially deformable truss elements is adopted. The adopted model demonstrates that the shape of the potential energy of the spring is very sensitive to changes in its geometric parameters. This causes the static configuration to undergo several bifurcations as one or more of the geometrical parameters are varied. In particular, it is shown that the geometric parameter space of the Kresling pattern can be divided into five regions, each of which results in a qualitatively different spring behavior. Results of the axial truss model are verified experimentally demonstrating that, for the most part, the model is capable of predicting the loci and bifurcations of the spring's equilibria. Nevertheless, it is also observed that, away from the equilibrium points, the quasistatic behavior of the spring is not well-approximated by the axial truss model. To overcome this issue, a modified model is developed which accounts for (i) the rotary stiffness of the creases, (ii) self avoidance due to panel contact at small angles between the panels, and (iii) buckling of the creases under compressive loads. It is shown that the modified model is capable of providing a better overall qualitative approximation of the quasistatic behavior.
折纸启发式设计最近已成为科学和工程领域的主要研究方向之一。这样的设计之一是利用 Kresling 模式折纸来构建非线性弹簧，这些弹簧可以作为机械位存储开关、波导、流体肌肉和隔振器。这项工作的主要目的是描述这些弹簧的静态平衡、稳定性和分叉，因为 Kresling 模式的几何参数发生变化。为此，采用了一种数学模型，该模型假设不同的面板可以用轴向可变形桁架元件来表示。所采用的模型表明，弹簧的势能形状对其几何参数的变化非常敏感。这导致静态配置会随着一个或多个几何参数的变化而经历几次分叉。特别是，表明 Kresling 模式的几何参数空间可以分为五个区域，每个区域都会导致弹簧行为发生定性变化。轴向桁架模型的结果通过实验得到验证，证明该模型在很大程度上能够预测弹簧平衡的轨迹和分叉。然而，也观察到，在平衡点之外，弹簧的准静态行为不能很好地被轴向桁架模型所逼近。为了克服这个问题，开发了一个改进的模型，该模型考虑了 (i) 折痕的旋转刚度，(ii) 面板之间小角度接触时的自回避，以及 (iii) 压缩载荷下折痕的屈曲。结果表明，改进的模型能够更好地整体定性逼近准静态行为。
