Shape reconstruction of parallelogram flaw

Abstract

To reconstruct the shape of the scatterer in elastic media, the authors deduce the Born approximation solution of the two-dimensional scattering problem, which includes the shape factor that embodies all information about the shape of the scatterer. Accordingly, the change in the shape of the scatterer only necessitates the number of the corresponding new shape factors. For a parallelogram void in a long Al rod, its shape factor can be obtained. In view of the definition of a characteristic function, the shape factor has a corresponding integral representation. Obviously, the shape factor can be considered as a Fourier transform of the characteristic function, which is reconstructed from the inverse Fourier transform. The integral equation is considered as the basic equation to reconstruct the shape of the scatterer. The identification of the geometrical character of a flaw is then given by the two dimensional inverse Born approximation in a low-frequency range. For the parallelogram void, a theoretical calculating identification is performed. At the same time, the numerical results are obtained by the finite element method.

References

1. Achenbach J D WavePropagation in Elastic SolidsNorth Holland,Amsterdam 1973
2. Gubernatis J E DomanyE, Krumhansl J A. Formal aspects of the theory of the scattering ofultrasound by flaws in elastic materials. Journal of Applied Physics 1977 (7)28042811
3. Zhu Jin Researchon Born approximation and the inverse of elastic waveHarbinSchool of Aerospace, HarbinInstitute of Technology 1987 (inChinese)
4. J H Richardson T M Time domain born approximationJournal of Nondestructive Evaluation 1982 (3)4553
5. Hsu D K Rose J H Thompson D O Reconstruction of inclusions in solids using ultrasonicBorn inversionJournal of Applied Physics 1984 (1)162168
6. Darmon M Calmon P Bele B An integrated model to simulate the scattering of ultrasoundsby inclusions in steelsUltrasonics 2004 (42)237241
7. Jain D L Kanwal R P The Born approximation forthe scattering theory of elastic waves by two dimensional flawsJournal of Applied Physics 1982 (6)42064217
8. Kitahara M Kazuyuki N Hirose S Elastodynamic inversion for shape reconstruction and typeclassification of flawsWave Motion 2002 (36)443455
9. Nakahata K Kitahara M Shape reconstruction methodswith incomplete dataReview of QuantitativeNondestructive Evaluation 2000 (1)919926