Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional case

Non-local dispersive model for wave propagation in heterogeneous media is derived from the higherorder mathematical homogenization theory with multiple spatial and temporal scales. In addition to the usual space–time co-ordinates, a fast spatial scale and a slow temporal scale are introduced to account for rapid spatial uctuations of material properties as well as to capture the long-term behaviour of the homogenized solution. By combining various order homogenized equations of motion the slow time dependence is eliminated giving rise to the fourth-order di erential equation, also known as a ‘bad’ Boussinesq problem. Regularization procedures are then introduced to construct the so-called ‘good’ Boussinesq problem, where the need for C1 continuity is eliminated. Numerical examples are presented to validate the present formulation