Nonlinearity based wave redirection for acoustic metamaterials

Abstract

Advances in metamaterials have revealed novel opportunities for controlling wave propagation paths for various applications not realizable with conventional materials. Some prominent examples are schemes for electromagnetic and acoustic cloaking and focusing devices. In the classical approach to the formulations of these devices, one exploits a change of physical coordinates to achieve a desired wave behavior within a finite space. Such a change can be interpreted as a transformation of material properties when the field equations of interest are invariant to coordinate transformations. With regard to acoustics, this approach is constrained to fluid-like metamaterials amenable to the propagation of longitudinal waves only. Complications arise with solid materials because of their inherent ability to sustain both longitudinal and transverse waves, which refract differently in linear isotropic materials because of dissimilar propagation speeds. In this work, the authors explore wave redirection mechanisms that may take advantage of nonlinear wave propagation phenomena in a solid metamaterial. Starting from the classical nonlinear Murnaghan model, a hyper-elastic material is formulated to realize coupling between shear and compressional modes that could lead to a more suitable refractive behavior for acoustic wave redirection in a solid metamaterial. The formulated model is studied using analytical and numerical tools.