A continuum theory is developed for wave propagation normal to the layers of a laminated composite with elastic, periodic, microstructure. Construction is based upon an asymptotic scheme in which dominant signal wavelengths are assumed large compared to typical composite microdimensions. A hierarchy of models are defined by the order of truncation of the asymptotic sequence obtained. To estimate system accuracy, the phase velocity spectrum is investigated. Retention of all terms in the asymptotic sequence is found to yield the exact spectrum of Rytov. Based upon spectral collation of the lowest-order dispersive model, accuracy superior to several existing theories is observed. In addition, treatment of transient pulse cases show good correlation with exact data. Finally, the lowest-order dispersive theory is cast in a standard mixture form.

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