Supratransmission in a vibro-impact chain

•Supratransmission in boundary-driven vibro-impact chain has been revealed.•The supratransmission occurs through instability of the edge states, when frequency components enter the propagation zone.•This mechanism strongly differs from previously observed supratransmission scenarios, commonly related to a generation of the propagating breathers.•Analytic approach for analysis of the structure and stability of the edge states is developed. The paper addresses the supratransmission (ST), i.e., emergence of the propagating waves in a nonlinear chain forced in the attenuation zone of the linear substructure. In the considered model, the nonlinearity is realized through impacts of particles in a linear chain with on-site constraints. This special form of the nonlinearity allows deriving the exact solutions for edge states of the semi-infinite boundary-driven chain. Stability of these edge states is assessed through semi-analytic procedure for direct evaluation of the monodromy matrix. The ST appears when the instability of the localized edge states leads to solutions with frequency components belonging to the propagation zone of the linear substructure. This mechanism substantially differs from previously observed ST scenarios, related to a generation of the propagating breathers. Various bifurcation sequences eventually leading to the ST are revealed and discussed.