Complex elastic wave band structures in three-dimensional periodic elastic media

Propagation of elastic waves can be completely inhibited, irrespective of propagation directions, if oscillation frequencies of elastic waves fall inside elastic wave band gaps—three-dimensional frequency stop bands of elastic waves generated in three-dimensional periodic elastic materials. The three-dimensional linear vector equation of motion is transformed into a matrix eigensystem and solved numerically by the plane wave expansion method. Existence of elastic wave band gaps is theoretically demonstrated for the face centered cubic lattice structure based on isotropie materials. The example structure is spherical tungsten scatterers embedded in a polyethylene matrix. Complex elastic wave band structures were also computed for tunneling evanescent waves at symmetric points at X and L points.