zbMATH — the first resource for mathematics

Radiation from a point source and scattering theory in a fluid-saturated porous solid. (English) Zbl 0579.73107
Starting with Biot’s theory of consolidation of poroelasticity, the time harmonic Green function for a point load in an unbounded fluid-saturated medium is derived, when the ideas of radiation and scattering are imposed. The imposition of their effects makes the mathematics more complicated in the problem which is based upon the already complicated mathematics. The solution contains two compressional waves and one transverse wave. At low frequency, the slow compressional wave is diffusive and only the fast compressional and transverse waves radiate energy. At high frequency, the slow wave radiates. The general problem of scattering is also considered. The method of transform calculus and delta function is used to obtain the solution. The paper is surely a good advancement in the area of the knowledge, specially from the physical and practical point of view.
Reviewer: G.Paria

74L10 Soil and rock mechanics
76S05 Flows in porous media; filtration; seepage
74J10 Bulk waves in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI