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Diffraction of Antiplane Shear Waves by a Finite Crack in the Presence of the Magnetic Field
Author(s) -
Shjndo Y.
Publication year - 1976
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.19760560106
Subject(s) - physics , stress intensity factor , diffraction , magnetic field , isotropy , scattering , mathematical analysis , integral equation , optics , fracture mechanics , mathematics , quantum mechanics , thermodynamics
Under the assumption that the motion of the body cases only weak perturbations in the electromagnetic field, the scattering of horizontally polarized shear waves by a finite crack in a uniform magnetostatic field is considered for two cases of the magnetic field being parallel to the crack surfaces and perpendicular to the crack surfaces. It is assumed that the elastic medium under consideration is a homogeneous, isotropic and infinitely conducting one. Using an integral transform technique, the problem is reduced to that of solving a Fredholm integral equation of the second kind having the kernel of a finite integration which can be solved numerically by the use of Gaussian quadrature formulas. By obtaining the singular stress distributions near the crack tip and dynamic stress‐intensity factors, the effects on the stress‐intensity factors due to the presence of the magnetic field are shown graphically. For the low frequencies, the stress‐intensity factors are expressed in series of ascending powers of the normalized frequency. The approximate solutions are compared with exact solutions.