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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.

Reflection of transverse and microrotational waves from free surface in micropolar thermodiffusive elastic half-space

Kumar R., Kaushal S., Sharma K. D., Garg S. K.

International Journal of Applied Mechanics and Engineering

2012

Vol. 17, no. 1

143-159

The problem of reflection of plane waves in a micropolar thermodiffusive elastic has been investigated in the context of coupled theory. The amplitude ratios of various reflected waves are continuous function of the angle of incidence and material parameters of the medium. A graphical representation of amplitude ratios is presented and the impact of micropolarity and diffusive property of the medium is observed to be significant. Some special cases of interest are deduced.