Tuning elastic wave propagation in multistable architected materials

In this paper, we analyze the propagation of elastic waves of small amplitudes in reconfigurable architected materials formed by a one-dimensional chain of bistable unit cells. Due to the bistability of the unit cells, these architected materials have multiple stable configurations. Using finite element models, we determine the dispersion relations and band gaps for the propagation of elastic waves in the undeformed and fully deformed stable configurations. Numerical results demonstrate that each of these two configurations has unique dispersion relations; in particular, low frequency band gaps emerge in the deformed configuration when the values of the design parameters are chosen to make the unit cell close to the limit between monostable and bistable behaviors. In order to obtain a deterministic sequence of multiple stable deformed configurations when an external stimulus is applied, multimaterial systems that consist of unit cells with different Young's modulus are considered. A reduced order model based on a one-dimensional lattice is developed to interpret and explain the emergence of low frequency band gaps in intermediate stable configurations in which some unit cells are undeformed while others are deformed. Simulations for systems of finite size demonstrate that applying a compressive deformation can be used to switch on and off the propagation of elastic waves in the frequency ranges that correspond to the band gaps, such that these materials might find applications as acoustic switches. (C) 2017 Elsevier Ltd. All rights reserved.