Sound and surface waves in poroelastic media
- Albers, Bettina
- Wilmanski, Krzysztof
2010 Mathematics Subject Classification
- 74J10 74J15 74F10
- Waves in porous media, monochromatic waves, surface waves
We consider two problems of propagation of weak discontinuity waves in porous materials. In the first part we present basic properties of bulk waves in fully saturated materials. These materials are modelled by a two-component immiscible mixture. We present general propagation conditions for such a model which yield three modes of propagation: P1-, S-, and P2-waves. Then we discuss the dispersion relation and we show that results are strongly dependent on the way in which waves are excited. In the second part we present some properties of surface waves. We begin with the classical Rayleigh and Love problems and then we extend them on heterogeneous materials important in practical applications. Subsequently we proceed to surface waves in two-component porous materials on the contact surface with vacuum (impermeable boundary) and with a liquid (permeable boundary). We show the existence of different modes of surface waves in the high frequency limit as well as the degeneration of the problem in the low frequency limit.
- Dynamic Response of Granular and Porous Materials under Large and Catastrophic Deformations, K. Hutter, N. Kirchner (eds.), Lecture Notes in Applied and Computational Mechanics, Vol. 11, Springer, Berlin, pp. 285--314, 2003