Rotational snap-through behavior of multi-stable beam-type metastructures
Yong Zhang, Marcel Tichem, Fred van Keulen
Abstract
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.