Spectro-spatial Analysis of Nonlinear Wave Propagation Behaviors in Damped Acoustic Metamaterial Systems

Background Acoustic metamaterials exhibit many novel wave propagation behaviors that can be designed to control and guide wave propagation in a variety of media. Due to the existence of damping, the attenuation effect of wave propagation significantly affects the elastic wave propagation in the nonlinear system. However, nonlinear wave propagation mechanisms in nonlinear damped acoustic metamaterial systems are largely unexplored. Purpose Therefore, it is extremely necessary to reveal unique nonlinear wave propagation behaviors in nonlinear acoustic metamaterials with damping. Methods In this paper, spectro-spatial analysis method is adopted to study propagation characteristics of nonlinear traveling wave packet in space- and time-domain. Results Numerical simulations demonstrate that influence of nonlinearity on dispersion relation will gradually disappear with time lapse for the nonlinear damped acoustic metamaterial systems, which indicates remarkable wave propagating decay in a nonlinear damped acoustic metamaterial system. The wave packets generated in nonlinear damped acoustic metamaterial systems have solitary waves caused by the interaction between dispersion, and nonlinearity exists in the nonlinear systems. Conclusions A possibility of tunable wave propagation characteristics is shown in the nonlinear damped acoustic metamaterial systems by selecting different value of damping coefficient. This study indicates that different wavelength region can affect existence of solitary waves on acoustic- and optical-mode wave packets in the damped acoustic metamaterial systems.