Vibration in mode III of an elastic layer containing a crack perpendicular to the boundary edge

A mathematical formulation of the problem of stresses and displacements in an elastic layer which contains a crack perpendicular to the boundary and subjected to a vibrating stress, in mode III, is developed. The boundary conditions for the case of free loading at the edges of the strip are used to obtain a solution to this problem. The problem is reduced to the solution of a Fredholm integral equation. In Part II the problem describing the case of rigid constraint at the edges of an elastic strip containing a vibrating external crack in mode II is reduced to the Fredholm integral equation of the second kind. In Part III the solution of the problem describing the case of a strip containing a vibrational crack in mode III and laying on a rigid boundary is presented.