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

Abstract

AbstractNon‐local dispersive model for wave propagation in heterogeneous media is derived from the higher‐order 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 fluctuations 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 differential 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. Copyright © 2002 John Wiley & Sons, Ltd.