Analytical extension of Finite Element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack |
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| Institution: | 1. School of Mechanical & Mining Engineering, University of Queensland, Brisbane, QLD 4072, Australia;2. University of Bordeaux, CNRS, Arts et Metiers ParisTech, I2M, UMR 5295, F-33400 Talence, France;3. Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854-8058, USA;1. Imperial College London, Department of Mechanical Engineering, Exhibition Road, London SW7 2AZ, UK;2. E.ON Technologies (Ratcliffe) Ltd., Technology Centre, Nottingham NG11 0EE, UK;1. Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH 45221, USA;2. Rolls-Royce Corporation, Indianapolis, IN 46225, USA;1. Chear of Production Technology, Faculty of Engineering Technology, University of Twente, 7500AE Enschede, The Netherlands;2. Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States;1. Acoustics Research Group, Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA;2. Detonation Science and Technology Group (Q-6), MS C925, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;3. Geophysics Group (EES-17), MS D446, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA;1. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China;2. State Key Laboratory for Manufacturing System Engineering, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China;3. Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China |
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| Abstract: | Nonlinear scattering of ultrasonic waves by closed cracks subject to contact acoustic nonlinearity (CAN) is determined using a 2D Finite Element (FE) coupled with an analytical approach. The FE model, which includes unilateral contact with Coulomb friction to account for contact between crack faces, provides the near-field solution for the interaction between in-plane elastic waves and a crack of different orientations. The numerical solution is then analytically extended in the far-field based on a frequency domain near-to-far field transformation technique, yielding directivity patterns for all linear and nonlinear components of the scattered waves. The proposed method is demonstrated by application to two nonlinear acoustic problems in the case of tone-burst excitations: first, the scattering of higher harmonics resulting from the interaction with a closed crack of various orientations, and second, the scattering of the longitudinal wave resulting from the nonlinear interaction between two shear waves and a closed crack. The analysis of the directivity patterns enables us to identify the characteristics of the nonlinear scattering from a closed crack, which provides essential understanding in order to optimize and apply nonlinear acoustic NDT methods. |
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| Keywords: | Nonlinear acoustics Scattering Contact acoustic nonlinearity Closed crack Finite Element Analytical propagation |
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