Influence of coulomb damping on wave propagation behaviors of nonlinear nonconservative phononic chains/lattices

Fascinating nonlinearity-induced behavior of phononic crystals (PCs) has recently become a hot research topic in the community. However, due to the limitations in the analytical modelling of damping in dynamic systems, the study of damped PCs has not received proper attention. In this paper, the influence of Coulomb damping on the wave propagation behavior of cubically nonlinear monoatomic phononic chains is investigated. To do so, the nonlinear dispersion relation is obtained analytically using the well-established multiple scales method and the band structure of the damped nonlinear chains is compared to the ones corresponding to the linear and nonlinear undamped chains. Due to the coupling between the amplitude and the frequency, stemmed from the nonlinear nature of the chain, Coulomb damping can lead to lower dispersion frequencies in the chain. The formulation and results are then expanded to 2D nonlinear lattices. The present manuscript is the first attempt to capture the effect of Coulomb damping on the wave propagation behavior of nonlinear lattices and the results put us one step closer to developing a comprehensive analytical model for the behavior of damped PCs which can in turn lead to invaluable design concepts for nonlinear nonconservative wave-manipulation devices.