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Determination by Iterative Method of Diffraction Field at the Interaction Longitudinal Shear Wave with the System of Thin Rigid Inclusions

  • Vsevolod PopovEmail author
Conference paper
Part of the Structural Integrity book series (STIN, volume 8)

Abstract

The problem of the diffraction field determination is arising as a result of the longitudinal shear wave interaction with the thin rigid inclusions system arbitrarily situated in an infinity body was solved. Inclusions are considered to be fully coupled to the elastic medium and are moving. Unknown amplitudes of inclusions are determined from the equations of motion. The solution method is based on the submission diffraction field displacement as sum of discontinuous solutions to the Helmholtz equation, the constructed for each inclusion. As result the original problem is reduced to the system of the singular integral equations for unknown jumps of stresses on the inclusions surface, The iterative method of this system solving, where the zero approximation are the solutions of the integral equations for the single inclusions, is proposed. This integral equation for single inclusions are numerical solved the mechanical quadrature method. The final result is the approximate formulas for calculating stress intensity factors and the amplitudes of the oscillations.

Keywords

Thin ridged inclusion Wave interaction Integral equations Iterative method 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National University “Odesa Maritime Academy”OdesaUkraine

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