Cutting-off effect at reflection–transmission of acoustic waves in anisotropic media with sliding-contact interfaces

The specific feature of the interface, which maintains sliding contact between elastic media, is that it can be impervious to the wave field existing in one of the adjoined materials. As a result, reflection–transmission of plane acoustic waves at the sliding-contact interface may enjoy the cutting-off effect, which implies that neither bulk, nor inhomogeneous modes are being transmitted at particular angles of incidence. The necessary and sufficient criteria for this phenomenon are obtained for a binary structure, constituted by two elastic half-spaces in sliding contact, and for a sandwich structure with sliding-contact interfaces between the enclosed layer and the substrates. In the generic case of unrestricted anisotropy (triclinic materials), the criterion for cutting-off in a binary structure involves acoustic parameters of solely that of the half-spaces, which contains the incident mode, and proves to be independent of an adjacent medium. The frequency-dispersive criterion for the absence of transmission through a triclinic layer in the sliding-contact sandwich structure is independent of substrates. By appeal to the Stroh formalism, the cutting-off conditions in a binary and a sandwich structure are further elaborated under the assumption that one of the half-spaces, or a layer, is orthorhombic, and its two symmetry planes are parallel, respectively, to the plane of incidence and to the sliding-contact interface with arbitrary adjacent media. It is shown that the transmission cut-off in a binary structure is necessarily accompanied by the absence of mode conversion at reflection, but the reverse is not true. The angles of incidence which give rise to these effects are determined in terms of elastic coefficients. Transmission cut-off through an orthorhombic layer comes about at an arbitrary angle of incidence, related to guided-modes range in the layer, for the corresponding aperiodic infinite set of the frequency values. Relations for the coefficients of reflection and transmission at the sliding-contact interface between two orthorhombic half-spaces are obtained in concise form, expressed solely via normal components of the partial Stroh-normalized traction amplitudes. Provided that the adjoined orthorhombic half-spaces in sliding contact are identical, the same value of wave-vector tangential projection, which stipulates transmission cut-off at the incidence of, say, the fast mode, entails total transmission at the incidence of the slow mode.