On modelling dispersion in microstructured solids

The Mindlin-type model is used for describing the longitudinal deformation waves in microstructured solids. A simplified hierarchical model is derived in one-dimensional setting which is a two-wave equation. In addition, the evolution equations (one-wave equations) are derived for both the full and simplified models. It is shown that the simplified model as well as evolution equations grasp main effects of dispersion in a wide range of physical parameters.