Homogenization and effective properties formulations for propagation in finely structured laminates - A multi-resolution approach

Multi-resolution approach is used to derive homogenized (large scale) formulation for propagation of waves in complex laminates. Basic entities such as boundary conditions, spatial and temporal spectrum (eigenvalues and resonances), Wronskian, modal expansions, and Green function representations associated with the homogenized formulation are discussed. The relations between them and their generic (all-scales, or complete) counterparts are studied. The dependence of these relations on parameters such as excitation frequency and heterogeneity length-scale are explored.