Use of equivalent body forces for acoustic emission from a crack in a plate |
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| Institution: | 1. Acoustics Institute, Chinese Academy of Sciences, Beijing, China;2. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, United States;1. Faculty of Mathematics, Al. I. Cuza University of Iaşi, 700506 Iaşi, Romania;2. Octav Mayer Mathematics Institute, Romanian Academy, 700505 Iaşi, Romania;3. Università della Calabria, Via Pietro Bucci, 87036 Arcavacata di Rende (CS), Italy;1. Department of Mathematics, Modelling and Scientific Computing (MOX) – Politecnico di Milano, Via Bonardi 9, I-20133 Milan, Italy;2. Fondazione CEN, Piazza Leonardo da Vinci, 32, I-20133 Milan, Italy;3. Department of Mathematical Sciences (DISMA) “G.L. Lagrange” – Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy;1. Department of Mathematics and Computer Science, University of Messina, Viale F. Stagno d’Alcontres 31, Messina 98166, Italy;2. Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell’Ateneo Lucano 10, Potenza 85100, Italy |
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| Abstract: | A method to determine acoustic emission of surface waves from a crack near the free edge of a plate, is presented, in terms of the function f(t), which defines the time dependence of the crack opening process, the crack opening volume per unit thickness of the plate, and the elastic constants of the plate. The determination of the time-varying displacement is based on the use of equivalent body forces, which are shown to be two double forces. The acoustic emission of the crack, or the equivalent radiation from the double forces, has been obtained by a novel use of the elastodynamic reciprocity theorem. It is of interest that the normal surface-wave displacement at a position x0 of the free edge comes out as depending on df/dt evaluated at x0 for t > x0/cR, where cR is the velocity of surface waves on the free edge. |
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| Keywords: | Crack Acoustic emission Surface waves Equivalent body forces |
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