REFLECTION AND REFRACTION OF ANTIPLANE SHEAR-WAVES AT A PLANE BOUNDARY BETWEEN VISCOELASTIC ANISOTROPIC MEDIA

We consider two monoclinic viscoelastic media in contact, with the inc idence and refraction planes coincident with the respective planes of symmetry. Then, an incident homogeneous antiplane shear wave generates pure reflected and refracted antiplane waves, whose slowness and Umov -Poynting vectors lie in the planes of symmetry. The simplicity of the problem permits a detailed investigation of the phenomena caused by t he combined anisotropic-anelastic properties of the media and waves. A general approach and the analysis of a numerical example provide a co mplete picture of the physics. In general, the reflected and refracted waves are inhomogeneous, i.e. equiphase planes do not coincide with e quiamplitude planes. The reflected wave is homogeneous only when the i ncidence medium is transversely isotropic, i.e. its symmetry axis is p erpendicular to the interface. If the refraction medium is elastic, th e refracted wave is inhomogeneous of the elastic type, i.e. the attenu ation vector is perpendicular to the Umov-Poynting vector (energy dire ction). The angle between the attenuation and the real slowness vector s may exceed 90 degrees, but the angle between the attenuation and the Umov-Poynting vector is always less than 90 degrees. If the incidence medium is elastic, the attenuation of the refracted wave is perpendic ular to the interface. As in the anisotropic elastic case, energy flow parallel to the interface is the criterion for obtaining a critical a ngle. As in the isotropic viscoelastic case, critical angles exist onl y in rare instances. Indeed, they do not exist if one of the media is elastic. The existence of Brewster angles (related to a zero reflectio n coefficient) is also severely restricted by anelasticity. To balance the energy flux at the boundary, it is necessary to consider the inte rference flux between the incident and reflected waves (this flux vani shes in the elastic case). For the particular example, the refracted f lux is always greater than zero and there is transmission for all the incident angles. This phenomenon is related to the absence of critical angles. For a transversely isotropic incidence medium, attenuations, quality factors and phase and energy velocities of the incident and re flected waves coincide for all the incidence angles. It is important t o point out that the relevant physical phenomena are related to the en ergy flow direction (Umov-Poynting vector) rather than to the propagat ion direction (real slowness vector). For instance, the characteristic s of the elastic type inhomogeneous waves, the existence of critical a ngles, and the fact that the amplitudes of the reflected and refracted waves decay in the direction of energy flow despite the fact that the y grow in the direction of phase propagation.