Elastodynamics of a wedge

The problem of wave propagation in an elastic wedge of arbitrary angle has defied standard mathematical approaches, and no analytical solution has been given, although respectable approximations are available. We give here a new approach to the problem of the response of an elastic wedge to dynamically-varying surface tractions, based on the Kontorovich-Lebedev transform and evaluation of joint distributions to give a singular integral equation. Algorithmic methods of solution of such equations are known, and thus the solution of the original problem is reduced to a series of numerical quadratures. However, the singular integral equation will be useful not only for such straightforward numerical methods, but as a convenient form for the development of ray theories.