Padé approximations for low-frequency motion in a pre-stressed compressible elastic layer

In this paper, we derive an asymptotic approximation of the low-frequency motion in a pre-stressed compressible elastic layer, valid in both long- and short-wave regimes. For this purpose, we shall use Padé approximations. Comparisons with numerical solutions are provided and show good agreement for all wavelength. Results appropriate to the classical linear isotropic case are also briefly provided.