Scattering of two‐dimensional elastodynamic waves by a rigid plane strip or a plane crack of finite width: The transition matrix

The diffraction of time‐harmonic, vertically polarized, elastic waves by a two‐dimensional plane obstacle is investigated theoretically. The plane rigid strip and the plane crack of finite width are considered in detail. For these particular obstacles the transition matrix has been obtained using a boundary‐integral‐equation technique. It is shown that some symmetry considerations lead to a separation of the even and odd parts of the fields. Taking complete sequences of Chebyshev polynomials, an expansion of the fundamental unknown quantities at the obstacle has been obtained in such a way that each member of the expansion satisfies the elastodynamic conditions at the edges of the obstacle. This choice of the expansion functions then leads to a rather simple form of the transition matrix. In the derivation of the transition matrix we avoid the evaluation of singular integrals for the so‐called Q‐matrix elements.