Diffraction of a plane elastic wave by a wedge with a special form of boundary conditions

An exact solution of the antiplane problem of the diffraction of a plane elastic SH-wave with a step profile by a wedge is obtained. The stresses on the wedge sides are assumed to be proportional to a linear combination of the displacements, velocities and higher derivatives with respect to time of the displacements along the wedge axis. A solution of the problem is obtained using integral transformations with subsequent transformation using Cagniard's method. Solutions of the corresponding problems with boundary conditions of the Winkler and inertial types are considered. When a wave with a linear profile is incident on the wedge the stresses suffer a discontinuity of the second kind on the diffraction wave front; the same type of feature is observed in the problem with the inertial condition.