The effect of finite primary deformations on harmonic waves in layered elastic media

The problem of extensional wave propagation in a pre-stressed, incompressible, 4-ply symmetric layered structure is considered. The high wave number behaviour of the harmonics is shown to fall into one of four distinct cases. Each of these are examined in detail and appropriate asymptotic expansions, giving phase speed as a function of wave number, are obtained. These are shown to provide excellent agreement with the numerical solution. A surface wave front arising from the combined in¯uence of all harmonics is observed numerically. Corresponding plots of the eigenfunctions con®rm that this is indeed a surface wave with the behaviour associated with each harmonic remarkably sensitive to changes in wave number. This paper concludes with a comparison of extensional and ¯exural waves.