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Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures

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Abstract
This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.
Keywords
FREE-VIBRATION ANALYSIS, NATURAL FREQUENCIES, CANTILEVER BEAM, TOPOLOGY OPTIMIZATION, TIMOSHENKO BEAMS, BENDING ANALYSIS, FINITE-ELEMENT, IDENTIFICATION, LOCATION, TRANSMISSIBILITY, crack detection, single variable shear deformation theory, transfer matrix formulations

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Citation

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MLA
Bozyigit, Baran, et al. “Transfer Matrix Formulations and Single Variable Shear Deformation Theory for Crack Detection in Beam-like Structures.” STRUCTURAL ENGINEERING AND MECHANICS, vol. 73, no. 2, 2020, pp. 109–21.
APA
Bozyigit, B., Yesilce, Y., & Abdel Wahab, M. (2020). Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures. STRUCTURAL ENGINEERING AND MECHANICS, 73(2), 109–121.
Chicago author-date
Bozyigit, Baran, Yusuf Yesilce, and Magd Abdel Wahab. 2020. “Transfer Matrix Formulations and Single Variable Shear Deformation Theory for Crack Detection in Beam-like Structures.” STRUCTURAL ENGINEERING AND MECHANICS 73 (2): 109–21.
Chicago author-date (all authors)
Bozyigit, Baran, Yusuf Yesilce, and Magd Abdel Wahab. 2020. “Transfer Matrix Formulations and Single Variable Shear Deformation Theory for Crack Detection in Beam-like Structures.” STRUCTURAL ENGINEERING AND MECHANICS 73 (2): 109–121.
Vancouver
1.
Bozyigit B, Yesilce Y, Abdel Wahab M. Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures. STRUCTURAL ENGINEERING AND MECHANICS. 2020;73(2):109–21.
IEEE
[1]
B. Bozyigit, Y. Yesilce, and M. Abdel Wahab, “Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures,” STRUCTURAL ENGINEERING AND MECHANICS, vol. 73, no. 2, pp. 109–121, 2020.
@article{8645549,
  abstract     = {This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.},
  author       = {Bozyigit, Baran and Yesilce, Yusuf and Abdel Wahab, Magd},
  issn         = {1225-4568},
  journal      = {STRUCTURAL ENGINEERING AND MECHANICS},
  keywords     = {FREE-VIBRATION ANALYSIS,NATURAL FREQUENCIES,CANTILEVER BEAM,TOPOLOGY OPTIMIZATION,TIMOSHENKO BEAMS,BENDING ANALYSIS,FINITE-ELEMENT,IDENTIFICATION,LOCATION,TRANSMISSIBILITY,crack detection,single variable shear deformation theory,transfer matrix formulations},
  language     = {eng},
  number       = {2},
  pages        = {109--121},
  title        = {Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures},
  url          = {http://dx.doi.org/10.12989/sem.2020.73.2.109},
  volume       = {73},
  year         = {2020},
}

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