An Iterative Method for the Interaction Between a Bounded Beam and an Interface Defect in Solids, Under Kirchhoff Approximation

The method of passive re-emission under Kirchhoff approximation is used in this paper in order to solve the problem of the interaction of a monochromatic ultrasonic bounded beam (emitted by a plane transducer) with a bi-dimensional structure fluid/solid/solid which includes a plane defect located at the plane interface separating the two solids (assumed to be isotropic). The ultrasonic beam is decomposed into plane waves, using Fourier transforms. The presence of both the interfaces and the defect produces successive reflections. In order to take into account all the corresponding fields, an iterative method has been implemented. At each iteration, the problem of the scattering by the defect is processed with the passive re- emission method, the data on the defect being calculated under Kirchhoff approximation (in good agreement with the Geometrical Theory of Diffraction for a defect located in a fluid medium); the transmission through the interfaces is performed for plane waves, the scattered field being expressed using Fourier integrals. This iterative method gives a more accurate solution than the global one, namely the passive re-emission principle under Kirchhoff approximation straightforwardly applied on the whole system of the structure. Numerical results are given (cartographies and cuts of the pressure field in the fluid), which show -i) the effect of the defect on the field which propagates in the structure, -ii) the convergence rate of the iterative process as a function of the incident angle, -iii) the changes in the field depending on the location of the defect.