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Diffraction of antiplane shear waves by a finite crack in a piezoelectric material
Author(s) -
Singh B.M.,
Rokne J.,
Dhaliwal R.S.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201000160
Subject(s) - antiplane shear , electric displacement field , integral equation , fredholm integral equation , diffraction , mathematical analysis , stress intensity factor , fourier transform , boundary value problem , integral transform , mathematics , piezoelectricity , physics , optics , fracture mechanics , acoustics , thermodynamics
The problem of diffraction of antiplane shear waves by a crack of finite length under the permeable electric boundary conditions is investigated analytically. Using Fourier transforms the mixed boundary value problem is reduced to two pairs of dual integral equations. These dual integral equations are further reduced to a pair of Fredholm integral equations of the second kind. The iterative solutions of the Fredholm integral equations have been obtained for small values of the wave number. And analytical expressions for the dynamic stress intensity factor and electric displacement intensity factor are obtained. Finally the numerical results for dynamic stress intensity factor are displayed graphically.