Abstract
A diffusion approximation to the random evolution modeling of wave propagation in randomly imperfect periodic laminated composites is presented. It is shown that unless the material properties of the various layers satisfy some inequality (Eqn. (2)) all waves have exponentially decaying expected amplitudes.
Résumé
On utilise une diffusion comme approximation de l'évolution aléatoire modélisant la propagation des ondes dans un matériau composite laminaire avec imperfections aléatoires. On montre qu'à moins que les propriétés des matériaux formant les différentes couches satisfassent l'inéquation (2), toutes les ondes ont une amplitude qui décroit de façon exponentielle.
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References
G. A. Bécus,Wave Propagation in Imperfectly Periodic Structures: a Random Evolution Approach, Angew. Math. Phys.29, 252–261 (1978).
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G. A. Bécus,Homogenization and Random Evolutions: Applications to the Mechanics of Composite Materials, Rpt. No. ES 78-133, Dept. of Engineering Science, University of Cincinnati (1978).
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Bécus, G.A. Diffusion approximation to wave propagation in imperfectly periodic structures. Journal of Applied Mathematics and Physics (ZAMP) 30, 724–727 (1979). https://doi.org/10.1007/BF01590852
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DOI: https://doi.org/10.1007/BF01590852