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Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

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Abstract

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.

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Authors and Affiliations

  1. Department of Mathematics, Kurukshetra University, Haryana, 136119, India

    M. Kumar & R. Saini

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  1. M. Kumar
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  2. R. Saini
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Correspondence to M. Kumar.

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Project supported by the Council of Scientific and Industrial Research (CSIR) of New Delhi (Nos. 09/105(0169)/2008-EMR-I and 09/105(0185)/2009-EMR-I)

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Kumar, M., Saini, R. Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids. Appl. Math. Mech.-Engl. Ed. 33, 797–816 (2012). https://doi.org/10.1007/s10483-012-1587-6

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  • DOI: https://doi.org/10.1007/s10483-012-1587-6

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