Elastodynamic response of a wedge to surface pressures

An elastic wedge of interior angle κπ, where 1 < κ ≤ 2, is subjected to the impact of spatially uniform pressures on its faces. The application of the pressures produces a system of longitudinal waves, transverse waves and head waves. In this paper the elastodynamic stress singularity in the circumferential stress at the vertex of the wedge is analyzed. The analysis is based on self-similarity of first-order time derivatives of the displacement potentials. By means of appropriate transformations the statement of the problem is reduced to two Laplace's equations, whose solutions in half-planes are coupled along the real axes. The solutions to this system are obtained by using elements of analytic function theory, together with summations over Chebychev polynomials along the real axes.