Elastic wave scattering in cracked cylinders

A brief review of the dispersion relations and Green's functions for cylinders is presented initially. Then a novel and computationally efficient numerical procedure is given for wave scattering by a circumferential crack in an isotropic as well as a laminated composite cylinder. By employing a wave function expansion in both the circumferential and axial directions, as well as symmetry and anti-symmetry decompositions, three dimensional wave scattering is reduced to two quasi-one-dimensional problems. This simplification greatly reduces the computational time. Illustrative numerical results are presented for the reflection and transmission coefficients of different incident wave modes in a steel cylinder and a laminated composite cylinder, each containing a crack having an arbitrary circumferential length and radial depth. They are shown to agree quite closely with available but limited experimental data.

The boundary element method is employed to analyze wave scattering by a crack that is oriented arbitrarily in an isotropic cylinder. However, computational data are presented for only two specific orientations that corresponding to an axial crack and a circumferential crack. A multidomain technique and 8-node quadrilateral elements handle the singularity introduced by the crack. Computed results show good agreement with limited available data.