Long wave motion in layered elastic media

Long wave motion in a geometrically symmetric 3-layer laminated elastic structure is investigated. The associated dispersion relation is established for three different boundary value problems. For all three cases, numerical solutions are presented and a long wave asymptotic analysis carried out, in each case the cut-off frequencies being shown to satisfy transcendental equations. Long wave approximations are employed to determine the asymptotic orders of the displacement components in the various long wave regimes. The asymptotic structures in a single layer plate associated with bending, extension, thickness stretch resonance and thickness shear resonance are well-known. It is shown that these structures are preserved within the multi-layer problem. This work provides the theoretical framework to generalise the above mentioned theories.