PSI - Issue 83

Amal Lahrizi et al. / Procedia Structural Integrity 83 (2026) 162–170

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emphasis on non-destructive inspection methods, particularly vibration-based techniques, has grown in importance as an efficient and cost-effective means of monitoring structural change. By focusing on natural frequency variations, these methods offer valuable insights for crack detection and prediction, particularly in the context of beams, which are critical structural components. This paper presents the bee algorithm as an innovative solution to the complex challenge of crack detection in beams. Based on natural frequency changes, the bee algorithm shows promise in accurately predicting cracks. Consequently, this study represents a substantial contribution to advancing predictive maintenance practices and improving the durability of structures subjected to various stresses. It underlines the ongoing efforts to improve and innovate in the field of structural condition monitoring, with the ultimate aim of ensuring the safety and performance of industrial systems. [1] E.M. Elkhattabi, M. Boutahir, K. Termentzidis, K. Nakamura, A. Rahmani, eds., Advanced Materials for Sustainable Energy and Engineering, Springer Nature Switzerland, Cham, 2024. https://doi.org/10.1007/978-3-031-57022-3. [2] O. Outassafte, A. Adri, Y. El Khouddar, I. El Hantati, S. Rifai, R. Benamar, Crack identification in circular arches through natural frequency variations and the firefly hybrid algorithm, Mechanics of Advanced Materials and Structures (2023) 1–15. https://doi.org/10.1080/15376494.2023.2218857. [3] Y. El Khouddar, A. Adri, O. Outassafte, I. El Hantati, S. Rifai, R. Benamar, Influence of hygro-thermal effects on the geometrically nonlinear free and forced vibrations of piezoelectric functional gradient beams with arbitrary number of concentrated masses, Archive of Applied Mechanics 92 (2022) 2767–2784. https://doi.org/10.1007/s00419-022-02219-w. [4] O. Outassafte, A. Adri, Y. El Khouddar, I. El Hantati, R. Benamar, Linear and Geometrically Non-linear Free in-Plane Vibration of a Circular Arch with Damages, 2022. https://doi.org/10.14445/22315381/IJETT-V69I3P215. [5] A. Banerjee, B. Panigrahi, G. Pohit, Crack modelling and detection in Timoshenko FGM beam under transverse vibration using frequency contour and response surface model with GA, Nondestructive Testing and Evaluation 31 (2016) 142–164. https://doi.org/10.1080/10589759.2015.1071812. [6] A. Lahrizi, G. Ayad, A. Zaki, M. Moubaker, Predictive analysis toward the identification of cracks in functional gradient beam structures using an optimization algorithm based on the transit search technique, Mechanics of Advanced Materials and Structures (2022) 1–14. https://doi.org/10.1080/15376494.2022.2160035. [7] A. Lahrizi, A. Ghassane, A. Zaki, M. Moubaker, Exploration of Optimisation Algorithms for Predictive Crack Detection in Functional Gradient Beam Structures, in: 2024: pp. 113–121. https://doi.org/10.1007/978-3-031-57022-3_15. [8] I.E. Hantati, A. Adri, Y. El Khouddar, H. Fakhreddine, O. Outassafte, R. Benamar, Large amplitude forced vibrations of multi-stepped beams carrying concentric masses, Mech. Res. Commun. 132 (2023) 104163. https://doi.org/10.1016/j.mechrescom.2023.104163. [9] Y.E. El Khouddar, A. Adri, O. Outassafte, S. Rifai, R. Benamar, Non-linear forced vibration analysis of piezoelectric functionally graded beams in thermal environment, International Journal of Engineering, Transactions B: Applications 34 (2021). https://doi.org/10.5829/IJE.2021.34.11B.02. [10] N.T. Khiem, T.T. Hai, L.Q. Huong, Modal analysis of cracked FGM beam with piezoelectric layer, Mechanics Based Design of Structures and Machines 51 (2023) 5120–5140. https://doi.org/10.1080/15397734.2021.1992775. [11] S.A. Moezi, E. Zakeri, A. Zare, M. Nedaei, On the application of modified cuckoo optimization algorithm to the crack detection problem of cantilever Euler–Bernoulli beam, Comput. Struct. 157 (2015) 42–50. https://doi.org/10.1016/j.compstruc.2015.05.008. [12] R.Y. Liang, F.K. Choy, J. Hu, Detection of Cracks in Beam Structures Using Measurements of Natural Frequencies, 1991. https://doi.org/https://doi.org/10.1016/0016-0032(91)90023-V. [13] S. Casciati, Stiffness identification and damage localization via differential evolution algorithms, Struct. Control Health Monit. 15 (2008) 436– 449. https://doi.org/10.1002/stc.236. [14] J.W. Lee, J.Y. Lee, Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, Int. J. Mech. Sci. 122 (2017) 1–17. https://doi.org/10.1016/j.ijmecsci.2017.01.011. References