Abstract
Propagation of elastic phononic waves in layered composite materials is analyzed by introducing nonsmooth periodic coordinates associated with structural specifics of the materials. Spatial scales of the original (smooth) coordinates are estimated by the wave lengths. In terms of the new coordinates, the homogenization procedure occurs naturally from the continuity conditions imposed on elastic displacements and forces at layer interfaces. As a result, higher-order asymptotic approximations describing spatiotemporal ‘macro’- and ‘micro’-effects of wave propagation are obtained in closed form. Such solutions provide visualizations for the wave shapes illustrating their structure induced local details. In particular, beat-wise mode shapes and effective anisotropy of acoustic wave propagation are revealed. The subharmonic beating in wave modes occur when wave lengths orthogonal to layers is about to ‘resonate’ with layer’ thickness. If the wave speed has a non-zero projection along the layers, then phase shifts between the beats are observed in different cross sections perpendicular to the layers.
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