Tikhonov's regularization approach in mode shape curvature analysis applied to damage detection |
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| Institution: | 1. Institute of Materials and Structures, Riga Technical University, Kalku str. 1, Riga LV-1658, Latvia;2. Southern Federal University, Milchakova Street 8a, Rostov-on-Don 344090, Russia;1. School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK;2. Spencer Institute of Theoretical and Computational Mechanics, University of Nottingham, Nottingham NG7 2RD, UK;1. Division of Computational Mathematics and Engineering (CME), Institute for computational Science (INCOS), Ton Duc Thang University,700000, Vietnam;2. Faculty of Civil Engineering, Ton Duc Thang University, 700000, Vietnam;3. Ho Chi Minh City University of Techology, 700000, Vietnam;4. Faculty of Civil Engineering, Ho Chi Minh City University of Technology (HUTECH), 700000, Vietnam;1. Institute of Materials and Structures, Riga Technical University, Riga, Latvia;2. Department of Structural Mechanics, Faculty of Civil Engineering, Environment and Geodetic Sciences, Koszalin University of Technology, Poland |
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| Abstract: | In this paper an on-going research effort aimed at detecting and localizing damage in plate-like structures by using mode shape curvature based damage detection algorithm is described. The proposed damage index uses exclusively mode shape curvature data from the damaged structure. This method was originally developed for beam-like structures. In this paper, the method is generalized to plate-like structures which are characterized by two-dimensional mode shape curvature. To calculate mode shape curvatures from the measured mode shapes, three approaches are proposed: the first one is the well-known central difference approximation, the other two are classical approaches based on Tikhonov's regularization technique with smoothing functional. The applicability and effectiveness of the proposed damage detection algorithms are demonstrated experimentally on an aluminium plate containing mill-cut damage. The validity of the method is assessed by comparing the identification results of the experimental test case to the results obtained from the simulated test case. The modal frequencies and the corresponding mode shapes of the aluminium plate are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer (SLV) for the experimental study. |
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| Keywords: | Damage detection Modal analysis Plate Mode shape curvature Tikhonov's regularization |
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