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Reflection of plane waves from surface of a generalized thermo-viscoelastic porous solid half-space with impedance boundary conditions

Singh B.

Mechanics and Mechanical Engineering

2018

Vol. 22, nr 4

1483--1496

A phenomenon of reflction of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in 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 thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions at free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of impedance parameter and the angle of incidence.

Wave propagation in couple stress thermoelastic half space underlying an inviscid liquid layer

Kumar R., Kumar K., Nautiyal R. C.

International Journal of Applied Mechanics and Engineering

2012

Vol. 17, no. 1

161-177

The present paper is concerned with the propagation of waves in a couple stress elastic half space lying under an inviscid liquid layer in the context of Lord and Shulman (L-S) and Green and Lindsay (G-L) theories of thermoelasticity. It is observed that shear waves get decoupled from the rest of the motion. After developing the formal solution, the secular equations for surface wave propagation are derived. The dispersion curve giving the phase velocity and attenuation coefficient related to wave number are plotted graphically to depict the effect of thermal relaxation times. The amplitude ratios of displacement components and temperature distribution are also computed numerically and shown graphically to depict the effect of thermal relaxation times. Some special cases are also deduced from the present investigation.