Wave propagation in one-dimensional infinite acoustic metamaterials with long-range interactions

In this paper, the effect of long-range interactions on the wave propagation in one-dimensional acoustic metamaterials is investigated. The wave dispersion relations of these materials are expressed in closed-form solutions. In addition, a nonlocal continuum model is developed to approximate the behavior of the metamaterials with general long-range interactions. The influences of various parameters including the mass and stiffness ratios are also examined. The numerical results show that the long-range interactions affect the shape of the dispersion curves, while the range of the band-gap slightly changes. Furthermore, the results indicate that the proposed nonlocal model with appropriate nonlocal parameters can predict the dispersion behavior of the one-dimensional mass-in-mass system with long-range interactions very well, especially for the acoustic mode.