Anisotropy of homogenized phononic crystals with anisotropic material

The anisotropy of elastic waves propagating in two-dimension phononic crystals with cubic crystal material was theoretically investigated in the long wavelength limit. The anisotropy can be tuned efficiently by either rotating the crystalline orientation of the material or changing the filling fraction. It can even disappear at a given orientation and filling fraction. The pure vibration mode direction and the pure propagation mode direction can be efficiently tuned to a desired direction deviating from the symmetric plane of the phononic crystal lattice. These results will be useful in manipulating the anisotropy of a homogenized composite and dealing with a PC with anisotropic material.