Flexural waves scattering at a through crack in an elastic plate

Abstract

The diffraction of a plane flexural wave by a through-the-thickness crack in an elastic plate is examined by application of Mindlin's theory of flexural motions of plates. In his theory, which takes into account the rotatory inertia and shear effects, an incident flexural wave passing through the crack is scattered into three types of flexural waves. By combining the incident and scattered waves, the complete stress distribution around the crack can be calculated. However, in the application of the theory of crack propagation, it is only necessary to determine the intensity of the moment distribution in a small region surrounding the crack tip. It is found that this intensity decreases as the circular frequency of the input wave is increased. In other words, the magnitude of the local bending stresses is always lower in the dynamic case than in the static case. Defined in the paper is a dynamic moment-intensity factor whose critical value may be used to determine the onset of crack extension in brittle materials. Moreover, the present investigation also covers the problem of a cracked plate vibrating at steady state.