Generalized transformation acoustics for material design

Norris [“Acoustic cloaking theory,” Proc. R. Soc. London, Ser. A 464, 2411–2434 (2008)] presented a theory of transformation acoustics that enables the realization of pentamode acoustic materials having anisotropic density and finite mass. The design of acoustic materials for 3‐D objects composed of combinations of simple geometric shapes, e.g., a cylinder with spherical end‐caps, is considered. Certain classes of transformations which are well‐suited for the design of such shapes are described and conditions under which these transformations result in materials which minimize acoustic reflections are proposed. The concept is validated using 3‐D explicit transient finite element simulations, which closely emulate the physics of wave propagation in the proposed materials.