A dispersive effective equation for wave propagation through spatio-temporal laminates

We consider the problem of wave propagation through one-dimensional spatio-temporal or dynamic laminates when the wavelength of the disturbance is large relative to the scale of the microstructure. Dynamic materials are heterogeneous formations assembled from materials which are distributed on a microscale in space and in time. Using the techniques of Floquet analysis and asymptotic expansions, we reveal the dispersive nature of the effective medium. The effects are supported by direct numerical simulation of the heterogeneous problem. These results are compared with the exact solution of the effective equation. (C) 2003 Elsevier Science B.V. All rights reserved.