DOI QR코드

DOI QR Code

Crack detection method for step-changed non-uniform beams using natural frequencies

  • Lee, Jong-Won (Department of Architectural Engineering, Namseoul University)
  • 투고 : 2021.08.09
  • 심사 : 2022.05.08
  • 발행 : 2022.08.25

초록

The current paper presents a technique to detect crack in non-uniform cantilever-type pipe beams, that have step changes in the properties of their cross sections, restrained by a translational and rotational spring with a tip mass at the free end. An equation for estimating the natural frequencies for the non-uniform beams is derived using the boundary and continuity conditions, and an equivalent bending stiffness for cracked beam is applied to calculate the natural frequencies of the cracked beam. An experimental study for a step-changed non-uniform cantilever-type pipe beam restrained by bolts with a tip mass is carried out to verify the proposed method. The translational and rotational spring constants are updated using the neural network technique to the results of the experiment for intact case in order to establish a baseline model for the subsequent crack detection. Then, several numerical simulations for the specimen are carried out using the derived equation for estimating the natural frequencies of the cracked beam to construct a set of training patterns of a neural network. The crack locations and sizes are identified using the trained neural network for the 5 damage cases. It is found that the crack locations and sizes are reasonably well estimated from a practical point of view. And it is considered that the usefulness of the proposed method for structural health monitoring of the step-changed non-uniform cantilever-type pipe beam-like structures elastically restrained in the ground and have a tip mass at the free end could be verified.

키워드

과제정보

This research was supported by Korea Electric Power Corporation. (Grant number: R20XO02-30)

참고문헌

  1. Cao, D. and Gao, Y. (2019), "Free vibration of non-uniform axially functionally graded beams using the asymptotic development method", Appl. Mathe. Mech., 40, 85-96. http://dx.doi.org/10.1007/s10483-019-2402-9
  2. Cao, D., Gao, Y., Wang, J., Yao, M. and Zhang, W. (2019), "Analytical analysis of free vibration of non-uniform and non-homogenous beams: Asymptotic perturbation approach", Appl. Mathe. Modell., 65, 526-534. http://dx.doi.org/10.1016/j.apm.2018.08.026
  3. Chen, D.W. and Wu, J.S. (2002), "The exact solutions for the natural frequencies and mode shapes of non-uniform beams with multiple spring-mass systems", J. Sound Vib., 255, 299-322. http://dx.doi.org/10.1006/jsvi.2001.4156
  4. Datta, N and Thekinen, J.D. (2016), "A Rayleigh-Ritz based approach to characterize the vertical vibration of non-uniform hull girder", Ocean Eng., 125, 113-123. http://dx.doi.org/10.1016/j.oceaneng.2016.07.046
  5. Ece, M.C., Aydogdu, M. and Taskin, V. (2007), "Vibration of a variable cross-section beam", Mech. Res. Commun., 34, 78-84. http://dx.doi.org/10.1016/j.mechrescom.2006.06.005
  6. Gorman, D.J. (1975), Free Vibration Analysis of Beams and Shafts, John Wiley & Sons, New York, NY, USA.
  7. Heshmati, M. and Daneshmand, F. (2019), "Vibration analysis of non-uniform porous beams with functionally graded porosity distribution", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 233, 1678-1697. https://doi.org/10.1177/1464420718780902
  8. Lee, J.W., Kim, S.R. and Huh, Y.C. (2014), "Pipe crack identification based on the energy method and committee of neural networks", Int. J. Steel Struct., 14, 345-354. http://dx.doi.org/10.1007/s13296-014-2014-0
  9. Ling, M., Chen, S., Li, Q. and Tian, G. (2018), "Dynamic stiffness matrix for free vibration analysis of flexure hinges based on non-uniform Timoshenko beam", J. Sound Vib., 437, 40-52. http://dx.doi.org/10.1016/j.jsv.2018.09.013
  10. Ma, Y., Du, X., Chen, G. and Yang, F. (2020), "Natural vibration of a non-uniform beam with multiple transverse cracks", J. Brazil. Soc. Mech. Sci. Eng., 42, 161. https://doi.org/10.1007/s40430-020-2246-1
  11. Matsuoka, K. (1992), "Noise injection into inputs in back-propagation", IEEE Transact. Syst. Man Cybernet., 22, 436-440. http://dx.doi.org/10.1109/21.155944
  12. Nikolic, A. and Salinic, S. (2020), "Free vibration analysis of 3D non-uniform beam: the rigid segment approach", Eng. Struct., 222, 110796. https://doi.org/10.1016/j.engstruct.2020.110796
  13. Rajasekaran, S. and Khaniki, H.B. (2019), "Size-dependent forced vibration of non-uniform bi-directional functionally graded beams embedded in variable elastic environment carrying a moving harmonic mass", Appl. Mathe. Modell., 72, 129-154. https://doi.org/10.1016/j.apm.2019.03.021
  14. Rosa, M.A.D., Lippiello, M., Maurizi, M.J. and Martin, H.D. (2010), "Free vibration of elastically restrained cantilever tapered beams with concentrated viscous damping and mass", Mech. Res. Commun., 37, 261-264. https://doi.org/10.1016/j.mechrescom.2009.11.006
  15. Swamidas, A.S.J., Yang, X.F. and Seshadri, R. (2004), "Identification of cracking in beam structures using Timoshenko and Euler formulations?, J. Eng. Mech., 130, 1297-1308. http://dx.doi.org/10.1061/(ASCE)0733-9399(2004)130:11(1297)
  16. Yang, X.F., Swamidas, A.S.J. and Seshadri, R. (2001), "Crack identification in vibrating beams using the energy method", J. Sound Vib., 244, 339-357. http://dx.doi.org/10.1006/jsvi.2000.3498
  17. Zhao, Y., Huang, Y. and Guo, M. (2017), "A novel approach for free vibration of axially functionally graded beams with non-uniform cross-section based on Chebyshev polynomials theory", Compos. Struct., 168, 277-284. http://dx.doi.org/10.1016/j.compstruct.2017.02.012