W. Chen et J. Fish, A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales, J APPL MECH, 68(2), 2001, pp. 153-161
Citations number
20
Categorie Soggetti
Mechanical Engineering
Journal title
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
A dispersive model is developed for wave propagation in periodic heterogene
ous media. The model is based on the higher order mathematical homogenizati
on theory with multiple spatial and temporal scales. A fast spatial scale a
nd a slow temporal scale ai e introduced to account for the rapid spatial f
luctuations as well as to capture the long-term behavior of the homogenized
solution. By this approach the problem of secularity, which arises in the
conventional multiple-scale higher order homogenization of wave equations w
ith oscillatory coefficients, is successfully resolved. A model initial bou
ndary value problem is analytically solved and the results have been found
to be in good agreement with a numerical solution of the source problem in
a heterogeneous medium.