Origami, a centuries old Japanese art of paper folding, enables the transformation of flat sheets into complex 3D shapes, inspiring innovations across the spectrum of science and technology. The recent popularity of origami in engineering stems from its roots in geometric mechanics that render it largely independent of base material and scale, particularly useful for the development of deployable structures, robotics, and metamaterials.
Metamaterials are engineered materials with periodically repeating units designed to exhibit properties not found naturally in conventional materials. Their precise geometry gives them unique “smart” properties which can manipulate electromagnetic, acoustic, or seismic waves, thus making them useful for a variety of applications such as antennae, absorbers, super-lens, cloaking devices, and radars to name a few. Metamaterials fashioned from origami are already known to exhibit interesting properties such as auxetic behaviour, extreme Poisson’s ratios, tunable thermal expansion, programmable stiffness, multi-stability, and exotic wave dynamics.
The compliant nature of origami structures due to folding about the crease lines allows for large nonlinear global deformations. This motivated past researchers to focus primarily on nonlinear static and dynamic behaviour of origami involving large folding deformations. Because of this, a careful study on structural dynamics, specifically modal analysis of origami, within the linear regime of small deformations had been left untouched in literature.
Modelling and simulation play an important role in the study of origami structures as conducting experiments is highly complicated. Finite element (FE) simulations commonly adopted for structural modelling and analysis are found to be prohibitively expensive for metamaterials with repeating geometries. The structural behaviour of origami structures is commonly modelled through a combination of truss elements and rotational springs, called the bar and hinge framework (BHF). Previous studies of origami using bar and hinge framework have either ignored accurate modelling of inertial effects or have restricted to nonlinear dynamics and mechanics. The authors investigate the accuracy of the BHF models through mode-by-mode comparison of natural frequencies with reference to FE simulations.
The Miura-ori tessellation, investigated by the authors, is a popularly researched origami pattern with parallelogram-shaped panels that employs rigid folding to support applications ranging from solar arrays in space to surgical stents and collapsible furniture units.
In this study, the authors Dr. Anandaroop Lahiri and Prof. Phanisri Pradeep Pratapa from the Department of Civil Engineering, Indian Institute of Technology (IIT) Madras, Chennai, India, have, for the first time presented an extensive mode-by-mode analysis of the low-frequency dynamic modes of origami. In BHF models, the panel mass is replicated typically by lumping it to a few point masses, and flexural stiffness of panels is reflected through rotational springs assigned to creases provided along the bending axes.
This research proposes a combination of mass lumping schemes as well as techniques to estimate panel bending stiffness, which reduces the maximum error by 60 to 80 percent for a wide variety of both one- and two-dimensional structures of different sizes and aspect ratios for a wide range of folded states.
Prof. Diego Misseroni, Professor of Aerospace Structures at the University of Trento and recipient of the 2024 Thomas J. R. Hughes (ASME) Young Investigator Award, was kind enough to give his comments as follows: “This paper introduces a groundbreaking framework for understanding and predicting the dynamic behavior of origami-based deployable structures, bridging scientific research and practical technological applications. With origami systems rapidly transforming fields like wave control, seismic shielding, cloaking, vibration suppression, and energy harvesting, the need for accurate dynamic modeling is essential. The authors present innovative mass lumping strategies rooted in conservation laws, alongside a novel method for estimating panel bending stiffness based on edge restraints. By focusing on low-frequency dynamic modes dominated by crease-folding and panel-bending, this work achieves unprecedented accuracy, paving the way for advancements in both theory and application.”
Article by Akshay Anantharaman
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