EFFECTS OF LAYER PLACEMENT IN ISOTROPIC LAYER PAIRS FOR PRODUCING EQUIVALENT MASS ANISOTROPY

摘要

Mass-anisotropy is an important ingredient for acoustic cloaking. In recent years, the idea of using two isotropic layer to effectively mimic an mass-anisotropic layer has created an intense interest. In this paper, this equivalency is studied, with a particular focus on how to place the two layers. It is found that the proper placement is to place the heavier layer of the pair closer to the center, and that a proper placement plays a significant role in the effectiveness of the resulting cloak. It is also noted that the equivalency does not provide sufficient conditions to completely determine the material properties of the two isotropic layers. This leaves the choices wide open as what other additional conditions can be imposed on the relation between the bulk modulus of the two layers. Three choices are examined in this paper: matching the modulus, the impedances, and the sound speeds, of the two layers. It is found that a proper layer placement is more important than these choices.