The model for predicting the field radiated into solids by ultrasonic transducer developed at CEA (Champ-Sons) has been extended to the case of heterogeneous media. It allows the calculation of reflected or refracted components at the various interfaces (inside the piece or at piece boundaries). Arbitrary geometry of interfaces (possibly defined by CAD) may be considered. The extension uses a pencil model for the propagation from an elementary source point to the calculation point. The pencil evolution is described by a matrix formulation. The overall matrix for the whole propagation process of a given pencil results from the product of elementary matrices, corresponding either to the crossing of an interface or to the propagation into a homogeneous medium. From this matrix is extracted an amplitude factor allowing the prediction of the elementary contribution of the source point to the overall impulse-response at the calculation point. Then, the field radiated by an arbitrary transducer is simply obtained by the further numerical integration over the radiating surface of the transducer. Since an impulse-response is computed for the field at a given calculation point, arbitrary excitation pulse may be considered. Examples have been given illustrating the new capabilities of the model. Other examples of application to the case of phased-array transducers may be found in Ref.
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