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Wave scattering by an elastic obstacle with interior cuts
Author(s) -
Castro Luís P.,
Natroshvili David,
Stratis Ioannis G.
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510531
Subject(s) - mathematics , gravitational singularity , obstacle , scattering , obstacle problem , mathematical analysis , traction (geology) , displacement (psychology) , enhanced data rates for gsm evolution , displacement field , surface (topology) , field (mathematics) , geometry , pure mathematics , physics , finite element method , optics , psychology , telecommunications , boundary (topology) , geomorphology , political science , law , computer science , psychotherapist , thermodynamics , geology
We consider the direct interaction problem describing the scattering of acoustic waves by an elastic obstacle with interior cracks. By the potential method we reduce the problem to an equivalent system of integral (pseudodifferential) equations and study its solvability. In particular, we formulate necessary and sufficient conditions for the solvability in terms of the so‐called Jones modes. We show that the direct scattering problem is solvable for arbitrary values of the frequency parameter and for arbitrary incident wave functions if the crack surface is traction free. We also investigate the regularity of the displacement field, and analyze the stress singularities at the crack edge. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)