Scatter of toroidal elastic waves from a plane

Fradkin, Larissa Ju.; Borovikov, V. A.
May 2000
AIP Conference Proceedings;2000, Vol. 509 Issue 1, p81
Academic Journal
Experiments indicate that the radiating near zone of a compressional circular transducer directly coupled to a homogeneous and isotropic solid has the following structures: there are geometrical zones where one can distinguish a plane compressional wave and toroidal waves, both compressional and shear, radiated by the transducer rim. As we have shown previously, the modern diffraction theory allows to describe these explicitly. It also gives explicit asymptotic description of waves present in the transition zones. A lot of work has been done by other authors in calculating the fields obtained as the result of a plane wave incident on a plane crack. Here, we present calculations which have been carried out in the framework of Geometrical Elastodynamics and pertain to scattering of toroidal waves by an infinite plane crack. We demonstrate that when the incident wave is toroidal shear there are gaps in the portion of the crack which at a given moment in time contribute to the scattered compressional waves. Using the uniform Keller’s GTD our results may be extended to modeling diffraction of the toroidal waves by elliptic cracks and included in the code for high-frequency simulation of ultrasonic scattering in such cracks situated in the vicinity of a compressional circular transducer, currently under development at our Center. © 2000 American Institute of Physics.


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