Considering the role of the phononic dispersion relations in understanding the performance of phononic pseudocrystals and similar structures

Dispersion calculations have been an essential tool for investigating and predicting the performance of conventional phononic crystals because they offer the opportunity to accurately characterize the behavior of a structure based on the smallest characteristic piece of that structure. For phononic pseudocrystals—in which translational symmetry is replaced by cyclic symmetry and radial self similarity—the scaled dispersion relations of the unit pseudocell provide useful information; however, the behavior of a completed article comprised of multiple pseudocells is less completely articulated than for conventional phononic crystals. This paper will explore the uses of dispersion-type calculations applied to characteristic wedges of phononic pseudocrystals in an effort to evaluate what additional information they can potentially provide. [SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.]