Elastodynamics in Periodic Media – Approximation by Higher Order Homogenization and Metamaterials with Resonators

We consider elastodynamics in periodically heterogeneous solids described by 1D continua.The homogenization based on the higher order asymptotic expansions is applied to derive effective (macroscopic) models.Relevance of these models is extended beyond the assumption of the perfect scale separation to respect finite size of the heterogeneities.These models involve higher order gradients enabling to interpret models of the generalized continua introduced using phenomenological approaches.Particular examples of bi-and triple-layered periodic composites are explored in the context of the wave dispersion analysis.It appears that a variety of models which approximate the response up to the 2 nd order of accuracy with respect to the scale parameter can be used, leading to different dispersion properties.Due to the volume forces involved in the asymptotic analysis, structures with resonators can be represented to enhance band gap effects.