R. Esquivel-Sirvent
G. H. Cocoletzi
Dept. of Phys., Ohio Univ., Athens, OH 45701
A simple matrix approach is presented to study the elastic properties of multilayered systems. Periodic superlattices are considered to calculate the dispersion relations of the collective normal modes, and finite and semi-infinite structures to obtain the reflectivity of longitudinal modes. The dispersion relations for a two layer period superlattice show band structure. For transverse waves, it is considered that the single layer may support surface modes and found that their interaction with those of the adjacent layers yield also a band structure. The reflectivity of normal incident longitudinal waves for the semi-infinite superlattices resembles the band and gap regions of the dispersion relations. The comparisons between theory and experiment of the reflectivity of sound waves for the three layer systems show good agreement.