M.Kumar, R.Saini. Reflection and Refraction of Attenuated Waves at the Boundary of an Elastic Solid With a Porous Solid Saturated With Two Immiscible Viscous Fluids[J]. Applied Mathematics and Mechanics, 2012, 33(6): 754-770. doi: 10.3879/j.issn.1000-0887.2012.06.009
Citation: M.Kumar, R.Saini. Reflection and Refraction of Attenuated Waves at the Boundary of an Elastic Solid With a Porous Solid Saturated With Two Immiscible Viscous Fluids[J]. Applied Mathematics and Mechanics, 2012, 33(6): 754-770. doi: 10.3879/j.issn.1000-0887.2012.06.009

Reflection and Refraction of Attenuated Waves at the Boundary of an Elastic Solid With a Porous Solid Saturated With Two Immiscible Viscous Fluids

doi: 10.3879/j.issn.1000-0887.2012.06.009
  • Received Date: 2011-04-20
  • Rev Recd Date: 2012-02-10
  • Publish Date: 2012-06-15
  • The propagation of elastic waves was studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves was represented through three scalar potential functions and a vector potential function represents the lone transverse wave. Displacements of particles in different phases of the aggregate were defined in terms of these potentials functions. It was shown that there could exist three longitudinal waves and one transverse wave. The phenomenon of reflection and refraction due to longitudinal and transverse wave at a plane interface between an elastic solid half-space and a porous solid halfspace saturated with two immiscible viscous fluids were investigated. For the presence of viscosity in porefluids, the waves refracted to porous medium attenuated in the direction normal to the interface. The ratios of amplitudes of reflected and refracted waves with that of the incident wave were calculated as a non-singular system of linear algebraic equations. These amplitudes ratios were used further to calculate the shares of different scattered waves in the energy of incident wave. Variations of modulus of amplitude and energy ratios with the angle of incidence were computed for particular numerical model. For postcritical incidence of SV wave, the reflected P wave became evanescent. The conservation of energy across the interface was verified. The effects of variations in non-wet saturation of pores and frequency on the energy partition were depicted graphically and discussed.
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