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Numerical modelling of ultrasonic scattering

: Aulenbacher, U.; Bollig, G.; Fellinger, P.; Morbitzer, H.; Weinfurter, G.; Zanger, P.; Langenberg, K.-J.; Schmitz, V.

Mathematical Modelling in Non-Destructive Testing
Oxford: Clarendon Press, 1988
Mathematical Modelling in Non-Destructive Testing <1986, Cambridge>
Fraunhofer IZFP ()
Beugungstheorie; Elastodynamik; inverse Beugung; Modellierung; Numerik; Prüfkopf; Wellenausbreitung

Performance prediction of ultrasonic nondestructive testing experiments often requires the availability of system models, which combine mathematical modelling of the transducer with the propagation and scattering of elastic waves in complex environments; see Chapman (1986). For arbitrary applications a priori numerical methods, which appropriately discretize the underlying partial differential equations together with their boundary conditions, seem to be the only approach to model a specific experiment in full detail (Harumi, 1986; Bond et al in these proceedings; Ludwig, 1986). On the other hand, the physical understanding of the occurring wave phenomena can be considerably enhanced, investigating canonical ultrasonic testing situations of minor complexity, which can be tackled mostly by analytical or combined analytical - numerical techniques. Furthermore, these procedures may serve as a convenient tool to evaluate input data for inverse scattering algorithms in order to check their performance, for instance, if they were able to process mode converted field components even though developed for strictly scalar waves. Very often, an analytical technique to treat ultrasonic radiation or scattering may be explicitly exploited to approach the more important inverse problem; examples comprise the elastodynamic geometric theory diffraction and the time-of-flight crack sizing technique (Ogilvy and Temple, 1983), or, as outlined in the following the equivalent source integral representation as basis for various quantitative identification and imaging algorithms.