Asymptotic representations of the dispersion relation for a two-ply, pre-stressed incompressible elastic laminate

The dispersion relation associated with small amplitude waves propagating a long a common (in-plane) principal direction in a two layer perfectly bonde d elastic structure is derived. Each layer is composed of a pre-stressed in compressible elastic solid. An asymptotic analysis is carried out in the hi gh wave number region, giving phase speed as a function of harmonic number, pre-stress and wave number for each harmonic. These expansions concur very well with numerical results and indicate that the structure of the dispers ion relation may, for certain forms of pre-stress, differ significantly fro m that associated with the analogous classical problem within which pre-str ess is absent. The paper also includes a discussion of the stability of the structure, with the domain of linear stability being established.