Diffractions of Horizontal Shear Waves by a Parabolic Cylinder and Dynamic Stress Concentrations

Diffractions of horizontally polarized shear waves by a parabolic cylinder are studied by using the expansion of solutions to the wave equation in terms of Weber’s functions. The parabolic cylinder is either empty or filled with rigid material. Also, the problems of a semi-infinite line crack and a semi-infinite rigid ribbon as two limiting cases are treated. Displacements and stresses are calculated near the base of the parabola. In the case of a line crack or a rigid ribbon, the singular behavior of stresses is shown to be of the order of (kr)−1/2, where k is the wave number and r the distance from the tip.