A short wave asymptotic analysis of the dispersion relation for a symmetric three-layered elastic plate

The dispersion relation for a symmetric 3-layered elastic plate is derived and analysed, both numerically and asymptotically. Each layer is assumed to be composed of a linear isotropic elastic material. Numerical solutions of the relation are first presented. After presentation of these numerical solutions, particular focus is applied to the short wave regime, within which appropriate asymptotic approximations are established. These are shown to provide excellent agreement with the numerical solution over a surprisingly larger than might be expected wave number regime. It is envisaged that these solutions might offer some potential for estimation of truncation error for wave number integrals and thereby enable the development of hybrid numerical-asymptotic methods to determine transient structural response to impact.