Transient, Two-Dimensional, Kirchhoff Diffraction of a Plane, Elastic, SH-Wave bya Generalized Linear-Slip Crack

摘要

We investigate the two-dimensional, transient, plane elastic SH-wave scatteringby a crack whose elastodynamic properties are described by a generalized linear-slip boundary condition. The crack is present in unbounded, homogeneous, isotropic, perfectly elastic solid. The scattering problem is solved in the (modified) Kirchhoff approximation, which amounts to replacing the actual values of the dynamic traction and the particle displacement on both faces of the crack by their values that would apply to the reflection and the transmission of the incident plane wave by a crack with the same elastodynamic properties, but of infinite width. The modified Cagniard method is used to obtain analytic, closed-form expressions for the particle displacement of the different constituents out of which the scattered wave motion is composed: viz., the geometrically reflected and transmitted plane waves, and the cylindrical diffracted waves originating at the two edges of the crack.