Propagation of sound and surface waves in porous materials
- Wilmański, Krzysztof
2010 Mathematics Subject Classification
- 35C20 35L50 74J15
- asymptotic expansions, waves in porous media
We review main properties of acoustic waves which are described by continuous models of saturated porous materials. Bulk waves are only mentioned in the introduction, and we concentrate on the propagation of surface waves. We demonstrate differences between a one-component approach to the problem typical for seismology, and a two-component approach. In the latter case we rely on a model proposed by K. Wilmanski in the recent ten years, and we indicate similarities, and differences of results obtained within this model and that of the classical Biot's model of porous materials. The main conclusion is that both models predict the same modes of propagation, and differences are only quantitative in spite of flaws of the Biot's model which contains contributions violating the second law of thermodynamics, and the principle of material objectivity.