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Dynamic response of an elastic medium containing crack |
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| Affiliation: | 1. Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma “La Sapienza”, 00184 Roma, Italy;2. Institute of Mechanics and Printing, Warsaw University of Technology, 85 Narbutta, Warsaw 02-524, Poland;3. Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA;4. International Research Center for the Mathematics and Mechanics of Complex Systems – MeMoCS, Università dell’Aquila, Italy;1. Laboratory for Multiscale Mechanics (LM2), École Polytechnique de Montréal, Department of Mechanical Engineering, P.O. Box 6079, Station Centre-Ville, H3C 3A7 Montréal, Québec, Canada;2. Department of Mechanical Engineering, École de technologie supérieure, 1100, Rue Notre-Dame Ouest, H3C 1K3 Montréal, Québec, Canada |
| Abstract: | A fundamental solution for an infinite elastic medium containing a penny-shaped crack subjected to dynamic torsional surface tractions is attempted. A double Laplace–Hankel integral transform with respect to time and space is applied both to motion equation and boundary conditions yielding dual integral equations. The solution of the derived dual integral equations is based on an analytic procedure using theorems of Bessel functions and ordinary differential equations. The dynamic displacements’ field is obtained by inversion of the corresponding Laplace–Hankel transformed variable. Results of a representative example for a crack subjected to pulse surface tractions are obtained and discussed. |
| Keywords: | Hankel transform Laplace transform Pulse Torsion Crack |
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