M D Sharma
Articles written in Sadhana
Volume 34 Issue 6 December 2009 pp 1017-1032
Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identiﬁed as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reﬂection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous ﬂuid. At this ﬂuid-solid interface, an incident acoustic wave through the ﬂuid reﬂects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness deﬁne inhomogeneous refracted waves with a ﬁxed direction of attenuation, i.e. perpendicular to the interface.
Energy partition is calculated at the interface to ﬁnd energy shares of reﬂected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is veriﬁed in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reﬂected from isothermal interface is much signiﬁcant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any signiﬁcant effect on the reﬂected energy.