A Dispersive Model for Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales
Affiliation:
1. Department of Civil Engineering and Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY 12180
Abstract
A dispersive model is developed for wave propagation in periodic heterogeneous media. The model is based on the higher order mathematical homogenization theory with multiple spatial and temporal scales. A fast spatial scale and a slow temporal scale are introduced to account for the rapid spatial fluctuations 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 with oscillatory coefficients, is successfully resolved. A model initial boundary 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.
Publisher
ASME International
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference20 articles.
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