Journal
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
Volume 68, Issue 2, Pages 153-161Publisher
ASME-AMER SOC MECHANICAL ENG
DOI: 10.1115/1.1357165
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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 ai e 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.
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