Effective non-reflective boundary for Lamb waves: Theory,finite element implementation,and applications |
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| Institution: | 1. Department of Aerospace Engineering, University of Michigan, Ann Arbor, USA;2. Department of Mechanical Engineering, University of South Carolina, Columbia, USA;1. Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA, USA;2. Department of Mechanical Engineering, California State University, Northridge, CA, USA;1. Department of Civil Engineering, Indian Institute of Technology Guwahati, Assam 781039, India;2. Department of Physics and Technology, UiT The Arctic University of Norway, Norway;3. Department of Civil & Architectural Engineering & Mechanics, University of Arizona, Tucson, USA;1. Rolls-Royce Nuclear, PO BOX 2000, Derby DE21 7XX, UK;2. UK Research Centre for NDE, Imperial College London, Exhibition Road, London SW7 2AZ, UK |
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| Abstract: | This article presents a new approach to designing non-reflective boundary (NRB) for inhibiting Lamb wave reflections at structural boundaries. Our NRB approach can be effectively and conveniently implemented in commercial finite element (FE) codes. The paper starts with a review of the state of the art: (a) the absorbing layers by increasing damping (ALID) approach; and (b) the Lysmer–Kuhlemeyer absorbing boundary conditions (LK ABC) approach is briefly presented and its inadequacy for Lamb wave applications is explained. Hence, we propose a modified Lysmer–Kuhlemeyer approach to be used in the NRB design for Lamb wave problems; we call our approach MLK NRB. The implementation of this MLK NRB was realized using the spring–damper elements which are available in most commercial FE codes. Optimized implementation parameters are developed in order to achieve the best performance for Lamb wave absorption. Our MLK NRB approach is compared with the state of the art ALID and LK ABC methods. Our MLK NRB shows better performance than ALID and LK ABC for all Lamb modes in the thin-plate structures considered in our examples. Our MLK NRB approach is also advantageous at low frequencies and at cut-off frequencies, where extremely long wavelengths exist. A comprehensive study with various design parameters and plate thicknesses which illustrates the advantages and limitations of our MLK NRB approach is presented. MLK NRB applications for both transient analysis in time domain and harmonic analysis in frequency domain are illustrated. The article finishes with conclusions and suggestions for future work. |
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| Keywords: | Lamb waves Non-reflective boundary Absorbing boundary Finite element simulation Local finite element model Structural health monitoring |
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