Shear waves in an elastic wedge

An elastic wedge of interior angle χπ is subjected to spatially uniform but time-dependent shear tractions, which are applied to one or both faces of the wedge, parallel to the line of intersection of the faces. The transient wave propagation problem is solved by taking advantage of the dynamic similarity which characterizes problems without a fundamental length in the geometry. The shear stress τ_θz is evaluated, and it is found that the singularity near the vertex of the wedge is of the form r^{( 1 χ)-1} (1 - χ). The results show that the stress is not singular for interior angles less than π. As a special case we obtain the dynamic shear stress generated by the sudden opening of a semi-infinite crack in a homogeneously sheared unbounded medium.