Elastic modelling of surface waves in single and multicomponent systems -- Lecture notes
- Wilmanski, Krzysztof
2010 Mathematics Subject Classification
- 74J10 74J15 74F10
- Surface waves, waves in porous media, monochromatic waves
The main aim of this article is to present a review of most important acoustic surface waves which are described by linear one- and two-component models. It has been written for the CISM-course: Surface waves in Geomechanics (Udine, September 6-10, 2004). Among the waves in one-component linear elastic media we present the classical Rayleigh waves on a plane boundary, Rayleigh waves on a cylindrical surface, Love waves, Stoneley waves (solid/solid and fluid/solid interface). In the second part of the article we discuss two two-component models of porous materials (Biot's model and a simple mixture model). We indicate basic differences of the models and demonstrate qualitative similarities. We introduce as well some fundamental notions yielding the description of surface waves in two-component systems (saturated porous materials) and review certain (porous materials with impermeable boundaries) asymptotic results for such waves. However, the full discussion of this subject including numerous results of computer calculations can be found in the article of B. Albers also included in this volume.
- Surface Waves in Geomechanics: Direct and Inverse Modelling for Soils and Rocks, C. Lai, K. Wilmanski, eds., CISM Courses and Lectures, Springer, Wien [u.a.], 2005, pp. 203--276.