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Theoretical Approaches for the Damage Identification in the Timoshenko Beam Based on Solving a Coefficient Inverse Problem

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Physics and Mechanics of New Materials and Their Applications (PHENMA 2023)

Part of the book series: Springer Proceedings in Materials ((SPM,volume 41))

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Abstract

The modal analysis problem for a beam performing bending vibrations is considered. The defect in the beam is modeled as a change in the cross-section area and the moment of inertia. The damage identification is based on the recovery of these coefficients by using additional information about resonant frequencies and eigenmodes. The solution of such a coefficient problem is conducted to minimize a special misfit functional. The paper presents the construction of this functional, considering the specificity of the modal analysis problem. The trust region method was used to solve the optimization problem. The gradient and the Hessian of the misfit functional were obtained on the sensitivity analysis of the forward problem.

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References

  1. Dahak, M., Touat, N., Kharoubi, M.: Damage detection in beam through change in measured frequency and undamaged curvature mode shape. Inverse Prob. Sci. Eng. 27(1), 89–114 (2019). https://doi.org/10.1080/17415977.2018.1442834

    Article  Google Scholar 

  2. Pastor, M., Binda, M., Harčarik, T.: Modal assurance criterion. Procedia Eng. 48, 543–548 (2012). https://doi.org/10.1016/j.proeng.2012.09.551

    Article  Google Scholar 

  3. Fan, W., Qiao, P.: Vibration-based damage identification methods: a review and comparative study. Struct. Health Monit. 10(1), 83–111 (2011). https://doi.org/10.1016/j.ymssp.2011.11.010

    Article  Google Scholar 

  4. Soloviev, A.N., Parinov, I.A., Cherpakov, A.V., Chaika, Y.A., Rozhkov, E.V.: Analysis of oscillation forms at defect identification in node of truss based on finite element modeling. Mater. Phys. Mech. 34(2), 192–197 (2018). https://doi.org/10.18720/MPM.3722018_12

  5. Gillich, N., et al.: Beam damage assessment using natural frequency shift and machine learning. Sensors 22, 1118 (2022). https://doi.org/10.3390/s22031118

    Article  PubMed  PubMed Central  Google Scholar 

  6. Lyapin, A., Shatilov, Y.: Vibration-based damage detection of the reinforced concrete column. Procedia Eng. 150, 1867–1871 (2016). https://doi.org/10.1016/j.proeng.2016.07.184

    Article  Google Scholar 

  7. Soloviev, A. N., Parinov, I. A., Cherpakov, A. V., Esipov, Yu. V.: Experimental vibration diagnostics of the floor plate set of building construction. In: Long, B.T., Kim, Y.-H., Ishizaki, K., Toan, N.D., Parinov, I.A., Vu, NPi. (eds.) MMMS 2020. LNME, pp. 255–260. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-69610-8_35

    Chapter  Google Scholar 

  8. Lebedev, I.M., Shifrin, E.I.: Solution of the inverse spectral problem for a rod weakened by transverse cracks by the Levenberg—Marquardt optimization algorithm. Mech. Solids 54, 857–872 (2019). https://doi.org/10.3103/S0025654419060025

    Article  Google Scholar 

  9. Vatul’yan, A.O., Osipov, A.V.: One approach to the determination of the parameters of a defect in a rod. Russ. J. Nondestruct. Test. 50, 649–658 (2014). https://doi.org/10.1134/S1061830914110084

    Article  Google Scholar 

  10. Burstedde, C., Ghattas, O.: Algorithmic strategies for full waveform inversion: 1D experiments. Geophysics 74(6), WCC37–WCC46 (2009). https://doi.org/10.1190/1.3237116

  11. Pratt, R.G., Shin, C., Hick, G.J.: Gauss-Newton and full Newton methods in frequency–space seismic waveform inversion. Geophys. J. Int. 133(2), 341–362 (1998). https://doi.org/10.1046/j.1365-246X.1998.00498.x

    Article  Google Scholar 

  12. More, J.J., Sorensen, D.C.: Computing a trust region step. SIAM J. Sci. Stat. Comput. 3, 553–572 (1983). https://doi.org/10.1137/0904038

    Article  Google Scholar 

  13. Cowper, G.: The shear coefficient in Timoshenko’s beam theory. J. Appl. Mech. 33(2), 335–340 (1996). https://doi.org/10.1115/1.3625046

    Article  Google Scholar 

  14. Kim, K.O.: A review of mass matrices for eigenproblems. Comput. Struct. 46(6), 1041–1048 (1993). https://doi.org/10.1016/0045-7949(93)90090-Z

    Article  Google Scholar 

  15. Tikhonov, A.N., Arsenin, V.A.: Solution of Ill-Posed Problems. Halsted Press, New York (1997)

    Google Scholar 

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Acknowledgements

The work was supported by the grant No. 22-29-01259 of the Russian Science Foundation in the Don State Technical University, https://rscf.ru/project/22-29-01259/.

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Authors and Affiliations

  1. I. I. Vorovich Mathematics, Mechanics and Computer Science Institute, Southern Federal University, 8a, Milchakov Street, Rostov-on-Don, Russia

    V. E. Yakovlev & A. V. Cherpakov

  2. Don State Technical University, 1, Gagarin Square, Rostov-on-Don, Russia

    A. V. Cherpakov

  3. Department of Microelectronics Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan (R.O.C.)

    S.-H. Chang

Authors
  1. V. E. Yakovlev
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  2. A. V. Cherpakov
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  3. S.-H. Chang
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Corresponding author

Correspondence to V. E. Yakovlev .

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Editors and Affiliations

  1. I. I. Vorovich Institute of Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don, Russia

    Ivan A. Parinov

  2. Department of Microelectronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan

    Shun-Hsyung Chang

  3. Institute for Research and Community Service, Universitas 17 Agustus 1945 Surabaya, Surabaya, Indonesia

    Erni Puspanantasari Putri

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Yakovlev, V.E., Cherpakov, A.V., Chang, SH. (2024). Theoretical Approaches for the Damage Identification in the Timoshenko Beam Based on Solving a Coefficient Inverse Problem. In: Parinov, I.A., Chang, SH., Putri, E.P. (eds) Physics and Mechanics of New Materials and Their Applications. PHENMA 2023. Springer Proceedings in Materials, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-031-52239-0_37

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