Band gap transmission in periodic bistable mechanical systems

Abstract

We theoretically and numerically investigate the supratransmission phenomenon in discrete, nonlinear systems containing bistable elements. While linear waves cannot propagate within the band gaps of periodic structures, supratransmission allows large-amplitude waves to transmit energy through the band gap. For systems lacking bistability, the threshold amplitude for such energy transmission at a given frequency in the linear band gap is fixed. We show that the topological transitions due to bistability provide an avenue for switching the threshold amplitude between two well-separated values. Moreover, this versatility is achieved while leaving the linear dispersion properties of the system essentially unchanged. Interestingly, the behavior changes when an elastic chain is coupled to bistable resonators (in an extension of the well-studied linear locally resonant metamaterials). Here, we show that a fraction of the injected energy is confined near the boundary due to the resonators, providing a means of regulating the otherwise unrestrained energy flow due to supratransmission. Together, the results illustrate new means of controlling nonlinear wave propagation and energy transport in systems having multi-stable elements.