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Journal of Porous Media
REFLECTION OF PLANE WAVES FROM SURFACE OF A THERMOELASTIC SATURATED POROUS SOLID HALF-SPACE WITH IMPEDANCE BOUNDARY CONDITIONS
Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh-160 011, India
In the present paper, a problem on reflection of plane waves from a plane thermally insulated as well as isothermal surfaces of a half-space is studied in the context of Lord-Shulman (LS) and Green-Naghdi (GN) theories of generalized thermoelasticity of a saturated porous medium. The mechanical boundary conditions at the surface of the half-space are considered as impedance boundary conditions, where the normal and shear force tractions are assumed to vary linearly with the normal and tangential displacement components multiplied by the frequency, respectively. The impedance corresponds to the constants of proportionality. The governing equations are specialized in the x-z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermoelastic saturated porous medium. For an incident plane wave (longitudinal or shear), four reflected waves will propagate in the medium. The appropriate potentials for incident and reflected waves in a half-space are formulated, which satisfy the required boundary conditions with the help of Snell's law. Finally, a nonhomogeneous system of four equations is obtained in the amplitude ratios, where the ratios depend on the material parameters, impedance parameter, angle of incidence, thermal relaxation, and speeds of plane waves. For relevant material parameters, the amplitude ratios are computed numerically for certain ranges of impedance parameters and the angle of incidence. For the purpose of validation, the numerical results are compared with those without thermal and porous parameters.
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