290 APM Proceedings Rayleigh waves in the isotropic and linear, reduced

We continue in this paper the work on the modeling of rocks and soils in terms of the linear, elastic, reduced Cosserat continuum. The reduced Cosserat continuum is a continuum where each point possesses rotational de-grees of freedom. Furthermore, the medium resists to rotation as well as to translation, while the couple stress is zero. The stress tensor is asymmet-ric. The objective of the model is to take into account the mictrostructure of rocks and soils which influences wave propagation. It was first suggested by Shwartz, Johnson, and Feng in 1984 to describe granular materials. Wave propagation in an unbounded 3D Cosserat continuum was investigated by Grekova and Herman in 2003–2005. In this work, we consider the Rayleigh wave for the isotropic case, using analytical and numerical methods. Instead of a straight line in the classical medium, we obtain two dispersion curves. The polarization differs both from the case of the classical medium and the case of a Cosserat continuum with couple stresses. For some frequency range, we observe a strong frequency dependence. There is a forbidden band of frequen-cies, lying below the analogous forbidden band for an unbounded medium. It indicates the possibility of localization phenomena. For the upper branch of the dispersion relation, there is also a forbidden domain of wave numbers: long waves may propagate only with one frequency. Far from the domain of frequencies where the microstructure influences the wave propagation, the medium behaves analogously to the classical one (as expected). We make a comparison with the classical medium and the Cosserat medium with couple stress for which the Rayleigh wave was investigated by Kulesh et al.