Homogeneous solutions in elastic wave propagation

Busemann’s method of conical flows is formulated for two-dimensional elastic wave propagation. The equations of motion are reduced to either Laplace’s equation in two dimensions or the wave equation in one dimension, and solutions then are obtained with the aid of complex variable or characteristics theory, respectively. Special attention is paid to that class of problems in which the hyperbolic domains (of the two-dimensional wave equation) are simple wave zones, in consequence of which the solutions may be continued into the elliptic domain (of Laplace’s equation) without explicitly posing the boundary conditions on the boundary separating the two domains. The method is applied to the diffraction of $P$- and $SV$-pulses by a perfectly weak half-plane.