Rotational snap-through behavior of multi-stable beam-type metastructures

• Published in: International journal of mechanical sciences Vol. 193; p. 106172
• Main Authors: Zhang, Yong, Tichem, Marcel, Keulen, Fred van
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2021
• Subjects: Metastructure; Multi-stability; Rotational state; Snapping beam; Multi-stability; Snapping beam; Metastructure; Rotational state
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2020.106172

•Arrangements of multiple bi-stable beams show rotational stability of the metastructure, next to the expected translational stability.•The geometric parameters (beam height h, thickness t and span L) for tuning the rotational responses are identified via parametric studies.•Using these parameters, and applying analytical modelling, stable and non-stable design domains for rotational behavior are defined as a function of t/L and h/L.•We demonstrate rotational stability and large deflections for 2D and 3D arrangements and stacks of bi-stable elements. [Display omitted] Metastructures consisting of planar arrangements of bi-stable snap-through beams are able to exhibit multiple stable configurations. Apart from the expected translational state transition, when all beam elements snap through, rotational states may exist as well. In this paper we explore the rotational properties of multi-stable metastructures on the basis of both experimental and theoretical investigations, and define the conditions for achieving rotational stable states. Results show that the metastructure is able to realize both translational and rotational states, while the rotational transitions require less energy as compared to their translational counterparts. The influence of geometric parameters on rotational stability is investigated via parametric studies. Furthermore, to determine the design criteria for rotational stability, a theoretical investigation based on mode superposition principle is performed to predict the nonlinear-deformation of a unit cell. The theoretical analysis predicts well the rotational snap-through transitions that are observed in finite element simulations. It is found that the rotational stability is determined by setting proper values for h/L and t/L (h, t, L represent apex height, thickness and span of the bi-stable beam structure, respectively). Finally, we experimentally demonstrate that the proposed metastructure with multiple layers is able to achieve large rotations and translations.