Unexpected wave in a cylindrical rod placed in the elastic medium

Most problems of seismic prospecting deal with structures containing interfaces where different materials adhere to one another. It is usual practice to assume these interfaces to have welded contact across which both stresses and displacements are continuous. In engineering geology there exists the concept of a loosely bound interface at surfaces along which the rigid connection between adjacent parts of the medium is broken, which in some cases results in the arising of an emergency situation. In carrying out mining operations, the diagnostics and localization of surfaces with unwelded contacts by acoustic and seismic methods is an important practical task. Earlier it was shown that in a layer sandwiched between two elastic halfspaces and having an unwelded contact an unusual wave propagates. This wave has a number of interesting properties: the wave spectrum has resonance frequencies; wave group velocity is equal to an intermediate value between the shear (V_s) and longitudinal (V_p) velocities; attenuation of the wave increases when the frequency varies from the resonance frequencies. The important feature of this wave is the enrichment of its spectrum by the resonance frequencies during the wave propagation. Such behavior of the wave can be explained if we consider the problem of reflection and transmission of SV waves incident on the boundary of two media with sliding contact. For incidence of the SV wave at angle φ=arcsin(V_s/V_p) total reflection occurs. Here we show that an interference wave with such properties exists in a circular cylindrical body which has a sliding contact with the surrounding elastic medium