Lahiri Anandaroop, Pratapa Phanisri Pradeep
Department of Civil Engineering, Indian Institute of Technology Madras , Chennai 600036, India.
Philos Trans A Math Phys Eng Sci. 2024 Oct 7;382(2283):20240012. doi: 10.1098/rsta.2024.0012.
The bar and hinge framework uses truss elements and rotational springs to efficiently model the structural behaviour of origami. The framework is especially useful to investigate origami metamaterials as they have repeating geometry, which makes conventional finite element simulations very expensive due to a large number of degrees of freedom. This work proposes improvements to the parameters of bar and hinge model within the context of structural dynamics, specifically modal analysis under small deformations, which has not been carried out previously in the literature. A range of low-frequency modes involving origami folding and panel bending deformations that can be accurately captured by the bar and hinge framework are identified. Within this range, bar and hinge parameters like the lumped masses and the rotational spring stiffness values are derived using conservation laws and finite element tests. The best among the proposed schemes is found to predict natural frequencies of the considered origami structures to within 10% maximum error, improving the accuracy by more than three times from existing schemes. In most cases, the errors in natural frequencies are less than 5%. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.
杆-铰链框架使用桁架单元和旋转弹簧来有效地模拟折纸的结构行为。该框架对于研究折纸超材料特别有用，因为它们具有重复的几何形状，这使得传统的有限元模拟由于大量的自由度而成本非常高。这项工作在结构动力学的背景下，特别是在小变形下的模态分析方面，提出了对杆-铰链模型参数的改进，这在以前的文献中尚未进行过。识别出了一系列可以由杆-铰链框架精确捕捉的涉及折纸折叠和面板弯曲变形的低频模态。在此范围内，利用守恒定律和有限元测试推导出了诸如集中质量和旋转弹簧刚度值等杆-铰链参数。结果发现，所提出的方案中最好的能够将所考虑的折纸结构的固有频率预测到最大误差在10%以内，比现有方案的精度提高了三倍多。在大多数情况下，固有频率的误差小于5%。本文是主题特刊“受折纸/剪纸启发的结构：从基础到应用”的一部分。
