Modeling and analysis of dynamic characteristics of multi-stable waterbomb origami base
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ORIGINAL PAPER
Modeling and analysis of dynamic characteristics of multistable waterbomb origami base Hesheng Han . Lihua Tang
. Dengqing Cao . Lun Liu
Received: 10 May 2020 / Accepted: 7 November 2020 Ó Springer Nature B.V. 2020
Abstract Origami has recently received wide attention, and the study on its dynamic characteristics remains a nascent field. The waterbomb origami is a common subtype of origami, and its base structure is treated as a bi-stable configuration in the literature. The systematical framework for modeling, simulation and dynamic analysis of the vibration for the waterbomb origami base is established in this paper. In the presented model, the motion of the waterbomb origami base is divided into two working patterns according to its geometric characteristic. The nonlinear governing equation of motion of the waterbomb origami base is formulated based on the Lagrange’s equation. The base’s free and forced responses can be calculated by using the fourth-order Runge–Kutta method. The developed model is validated by the results predicted by the simulation in ADAMS. With the developed theoretical framework, the base’s
vertical effective stiffness and natural frequency of its linearized system are discussed to reveal their programmability with respect to the base’s structure and design parameters. Remarkably, the bifurcations of its equilibria, including the pitchfork, transcritical and (special) saddle-node bifurcations, are analyzed. Unlike the bi-stable configuration reported in the literature, the mono- and tri-stable configurations can also be realized by the base due to gravity. Furthermore, the complex nonlinear dynamic behaviors, including chaos, are revealed. Keywords Waterbomb origami base Multistability Nonlinearity Dynamic characteristics Bifurcation
1 Introduction H. Han D. Cao (&) School of Astronautics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China e-mail: [email protected] H. Han L. Tang (&) Department of Mechanical Engineering, The University of Auckland, Auckland 1010, New Zealand e-mail: [email protected] L. Liu Institute of Dynamics and Control Science, Shandong Normal University, Jinan 250014, People’s Republic of China
Origami is an ancient art of paper folding, which can produce complicated geometrical objects by folding a flat sheet of paper with seemingly straightforward operations [1]. It has now been used beyond purely aesthetic pursuits for the design of the structures in various fields, such as energy harvesting [2], material science [3], biological engineering [4] and space engineering [5]. Since the mechanical property of a structure is significant for its engineering application, the study on the mechanical and dynamic
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characteristics for origami becomes an active area in recent years [6–8]. Many researches were focused on the folding kinematics, static and quasi-static characteristics of origami [9–12]. The intricate geometries of origami caused by foldin
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