Reflection, Transmission and Attenuation of Elastic Waves at a Loosely-Bonded Interface of Two Half Spaces

The problem of reflection and transmission of a longitudinal plane periodic wave incident on the interface between loosely-bonded half spaces is investigated by assuming that the interface behaves like a dislocation which preserves the continuity of traction while allowing a finite amount of slip. The wave equations are solved by imposing further the interface conditions that the normal displacement is continuous and that the shearing stress is proportional to velocity of slip. The results of numerical calculations are given in the form of graphs for different degrees of bonding, ranging from no bonding (zero shear stress) to full bonding (welded contact) between the half spaces. It is found that the elastic wave energy is attenuated at a loosely-bonded interface except at normal incidence, grazing incidence and at (approximately) critical incidence of the longitudinal wave at the interface.