A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales

Authors
Citation
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
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanical Engineering
Journal title
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
ISSN journal
0021-8936 → ACNP
Volume
68
Issue
2
Year of publication
2001
Pages
153 - 161
Database
ISI
SICI code
0021-8936(200103)68:2<153:ADMFWP>2.0.ZU;2-O
Abstract
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.