An analytical approach to reconstruction of axisymmetric defects in pipelines using T (0, 1) guided waves
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2661-9
An analytical approach to reconstruction of axisymmetric defects in pipelines using T(0, 1) guided waves∗ Yihui DA1 , Bin WANG1 , D. Z. LIU2,† , Zhenghua QIAN1,† 1. State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2. School of Engineering, University of East Anglia, Norwich NR4 7TJ, U. K. (Received Feb. 25, 2020 / Revised Jul. 11, 2020) Abstract Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission. Especially, the torsional mode T (0, 1), which is the first order of torsional guided waves, plays the irreplaceable position and role, mainly because of its non-dispersion characteristic property. However, one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy. Taking into account this situation, a quantitative reconstruction method using the torsional guided wave T (0, 1) is proposed in this paper. The methodology for defect reconstruction consists of three steps. First, the reflection coefficients of the guided wave T (0, 1) scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method (HFEM). Then, applying the boundary integral equation (BIE) and Born approximation, the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T (0, 1) and the fundamental solution of the intact pipeline in the frequency domain. Finally, reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain. Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes. Meanwhile, the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated. It is noted that the reconstructive error is less than 10%, providing that the defect depth is no more than one half of the pipe thickness. Key words torsional guided wave, hybrid finite element method (HFEM), boundary integral equation (BIE), quantitative reconstruction Chinese Library Classification O343 2010 Mathematics Subject Classification
74J05, 74J20, 74J25
∗ Citation: DA, Y. H., WANG, B., LIU, D. Z., and QIAN, Z. H. An analytical approach to reconstruction of axisymmetric defects in pipelines using T (0, 1) guided waves. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2661-9 † Corresponding authors, E-mail: [email protected], [email protected] Project supported by the National Natural Science Foundation of China (Nos. 11502108 and 1611530686), the State Key Laboratory of Mechanics and Control of M
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