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THE ALTERNATIVE KIRCHHOFF APPROXIMATION IN ELASTODYNAMICS WITH APPLICATIONS IN ULTRASONIC NONDESTRUCTIVE TESTING

Part of: Waves Special subfields of solid mechanics Dynamical problems

Published online by Cambridge University Press:  23 April 2020

L. J. FRADKIN Open the ORCID record for L. J. FRADKIN [Opens in a new window] ,
A. K. DJAKOU Open the ORCID record for A. K. DJAKOU [Opens in a new window] ,
C. PRIOR Open the ORCID record for C. PRIOR [Opens in a new window] ,
M. DARMON Open the ORCID record for M. DARMON [Opens in a new window] ,
S. CHATILLON Open the ORCID record for S. CHATILLON [Opens in a new window]  and
P.-F. CALMON Open the ORCID record for P.-F. CALMON [Opens in a new window]
L. J. FRADKIN*
Affiliation:
Sound Mathematics Ltd., CambridgeCB4 2AS, UK; e-mail: l.fradkin@soundmathematics.com
A. K. DJAKOU
Affiliation:
Sound Mathematics Ltd., Cambridge CB4 2AS, UK. Now at GEFCO, Courbevoie Cedex, France; e-mail: noelleaudrey@yahoo.fr
C. PRIOR
Affiliation:
Sound Mathematics Ltd., Cambridge CB4 2AS, UK. Now at Department of Mathematical Sciences, Durham University, Durham, UK; e-mail: christopher.prior@durham.ac.uk
M. DARMON
Affiliation:
CEA, LIST, Department of Imaging and Simulation for NDT, F-91191Gif-sur-Yvette, France; e-mail: Michel.DARMON@cea.fr, Sylvain.CHATILLON@cea.fr, Pierre.CALMON@cea.fr
S. CHATILLON
Affiliation:
CEA, LIST, Department of Imaging and Simulation for NDT, F-91191Gif-sur-Yvette, France; e-mail: Michel.DARMON@cea.fr, Sylvain.CHATILLON@cea.fr, Pierre.CALMON@cea.fr
P.-F. CALMON
Affiliation:
CEA, LIST, Department of Imaging and Simulation for NDT, F-91191Gif-sur-Yvette, France; e-mail: Michel.DARMON@cea.fr, Sylvain.CHATILLON@cea.fr, Pierre.CALMON@cea.fr
*
e-mail: l.fradkin@soundmathematics.com
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Abstract

The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing.

Keywords

nondestructive testingultrasoundhigh-frequency asymptoticsLamb’s Green’s tensorcritical Gaussian beam

MSC classification

Primary: 74H15: Numerical approximation of solutions
Secondary: 74H10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) 74J05: Linear waves 74J10: Bulk waves 74J15: Surface waves 74J20: Wave scattering 74L99: None of the above, but in this section
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 4 , October 2020 , pp. 406 - 422
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Copyright
© 2020 Australian Mathematical Society

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