Diffraction of Vector Elastic Waves by a Finite Crack.

Communicated June 30, 1964 The problem of the diffraction of obliquely incident scalar waves by finite slits and strips with various boundary conditions has been considered previously.' Reference may be made to the work of other authors on the diffraction of scalar waves by finite slits.2 The problem of the diffraction of obliquely incident vector elastic waves by a clamped finite strip has also been treated.' In the present paper we consider the problem of the diffraction of an incident plane harmonic compressional wave by a finite crack. Let the crack be located at -1 < x < 1, y = 0 -o < z < o in an otherwise infinite homogeneous elastic medium. The normal components of the stresses at the crack vanish. Reference may be made at this point to a considerable published literature on the diffraction of elastic waves by semi-infinite cracks (or half planes) and allied problems for this geometry.4-8 Let the potential for the incident wave be