Scattering of the Lowest Lamb Wave Modes by a Corrosion Pit

Scattering of time-harmonic Lamb wave modes by a partial spherical corrosion pit in a plate is investigated. By using superposition, the total field consists of the incident and scattered fields, where the latter is generated by tractions on the surface of the cavity. In the approximation advanced in this article these tractions are represented by time-harmonic body forces on a trace of the cavity in the interior of the plate. The acoustic radiation from the resultants of these body forces applied to the surface of the plate approximates the scattered field. The resultant forces are decomposed in symmetric and anti-symmetric systems, which generate symmetric and anti-symmetric radiating modes. The time-harmonic elastodynamic form of the reciprocity theorem is employed to obtain an analytical solution to the scattered field amplitudes. We obtain the ratio of scattered to incident Lamb mode amplitudes, which in a closed generalized form include material properties, geometry of the pit and layer, and angular frequency of the incident wave. Results of this study yield graphical representations for the amplitude ratios with respect to pit geometry and has the potential to lead to a unique solution of the inverse problem under some conditions.