For the calculation of transducer generated three-dimensional, transient wave fields in layered media with curved interfaces a separation approach is proposed. The normal stress at the solid- to-solid interface with liquid coupling is sufficient for the calculation of the sound field in the adjacent medium. This gives the supposition for a decomposition of the problem - the layered test body with the coupled transducer - into layers and for a separate calculation in each layer. For this purpose, the transducer elements and the interfaces are discretized and are uniformly covered with point sources. The wave field results from the superposition of all elementary waves emitted by the point sources. At each interface, the normal stress is calculated in equal point-to-point distances. Each point is considered to be a new point source. Using the derived point source functions and the Green's functions of the half-space, the field radiated from a curved interface can be simulated. The approach is directed to calculate the forward wave propagation in thick layers. Multiple reflections are neglected in order to minimize the calculation time.

While finite element methods are mainly suitable for geometric dimensions in the region of the wavelength, the proposed method due to its shorter computation time has significant advantages for larger extensions of the sound fields. The decomposition method presented here, on the one hand gives an alternative to finite element modeling, on the other hand it seems to be reasonable to combine both approaches in a hybrid method. The method can be generalized to calculate the response in anisotropic materials.

The separation method was applied successfully to obtain calculation programs for transducer design. Calculation examples for typical situations in non-destructive testing with immersion techniques based on harmonic waves are demonstrated. For a curved foil transducer coupled to steel shaft by water for instance, it can be shown that by a variation of the water delay a precise positioning of the sensitivity zone is possible. In another example a focused transducer for the test of a longitudinal press-fit is optimized by a variation of the frequency, the curvature of lens and the water delay.

In the future the separations method will be extended to the calculation of transient wave fields. For this purpose, the harmonic excitation is replaced by impulse excitation. First results for sound fields of a finitely extended, rectangular transducer are presented and will be compared with the measured data.