Elastic Guided Waves and the Floquet Concept in Periodically Layered Plates

This article describes the results of experiments and calculations on the interaction of ultrasound with aluminum/aramid-epoxy composites (ARALL™). the material is a planar laminate of alternating layers of aluminum and a uniaxial aramid-epoxy composite, where the outer layers are aluminum. Four plates, ranging from three to nine layers, have been investigated experimentally using fluid-coupled leaky wave techniques. the theoretical calculations for these plates, and related material combinations, have been made using both a partial wave analysis in conjunction with the transfer matrix method and also a stiffness-based numerical approach. Frequency zones of wave transmission and reflection, similar to those predicted for periodic media have been modeled and observed in the bilayered plates. The onset of this behavior has been simulated by calculating the reflection coefficient as a function of incremental lamina-property variations away from an average value. It is demonstrated that the transmission zones arise from a consolidation or clustering of the uniform-plate minima into frequency zones or bands, suggestive of Floquet wave behavior. Moreover, these bands, and the associated dispersion curves, are approximately constant in frequency, entirely unlike the behavior expected for a homogeneous plate. This phenomenon is explained on the basis of the large phase shifts induced in a layered medium composed of elastically contrasting media. This mechanism also leads to a correspondence between the number of reflection minima and layer unit cells. The effect of structural symmetry on the reflection function has also been studied. The theoretical predictions compare very well, in nearly every case, to the experimental results.