Internal scales and dispersive properties of microstructured materials

The Mindlin–Engelbrecht–Pastrone model is used for describing 1D longitudinal waves in microstructured solids. The effect of the underlying microstructure is best seen in the emergence of the optical dispersion branch. Dispersive properties of the Mindlin–Engelbrecht–Pastrone model are analyzed. It is shown by making use of the solutions to the boundary value problem that the influence of the optical dispersion branch has a significant effect on wave motion as shown in numerical experiments.